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RES EARCH
R E S E A R C H A R T I C L E
◥
SLEEP
Brain activity of diving seals reveals
short sleep cycles at depth
Jessica M. Kendall-Bar1,2*, Terrie M. Williams2, Ritika Mukherji3, Daniel A. Lozano2, Julie K. Pitman4,
Rachel R. Holser5, Theresa Keates6, Roxanne S. Beltran2, Patrick W. Robinson2, Daniel E. Crocker7,
Taiki Adachi2, Oleg I. Lyamin8,9, Alexei L. Vyssotski10, Daniel P. Costa2,5
Sleep is a crucial part of the daily activity patterns of mammals. However, in marine species that spend
months or entire lifetimes at sea, the location, timing, and duration of sleep may be constrained. To
understand how marine mammals satisfy their daily sleep requirements while at sea, we monitored
electroencephalographic activity in wild northern elephant seals (Mirounga angustirostris) diving in Monterey
Bay, California. Brain-wave patterns showed that seals took short (less than 20 minutes) naps while
diving (maximum depth 377 meters; 104 sleeping dives). Linking these patterns to accelerometry and the
time-depth profiles of 334 free-ranging seals (514,406 sleeping dives) revealed a North Pacific sleepscape in
which seals averaged only 2 hours of sleep per day for 7 months, rivaling the record for the least sleep
among all mammals, which is currently held by the African elephant (about 2 hours per day).
A cross the animal kingdom, sleep is crit-
ical for energy conservation, immune
function, memory, and learning (1). Dis-
ruptions to sleep, including obstructive
sleep apnea and shift work, negatively
affect human health (2, 3). By comparison,
diverse sleeping habits among wild animals
reflect adaptations to resolve conflicts between
sleeping or feeding while avoiding predation
and exhaustion (4–6). In response to these
trade-offs, cows sleep-chew, horses sleep-
stand, ostriches sleep-stare, and frigate birds
sleep-fly (7–10).
Marine mammals face unique challenges in
obtaining adequate daily sleep (11). Most of
them feed underwater and breathe at the ocean
surface, where predators typically attack (12).
Activity budgets of mammals at sea reflect the
balance between these survival needs, which
often push the animals toward physiological
extremes such as large body size, prolonged
activity, and enhanced oxygen stores (13). For
example, northern elephant seals (Mirounga
angustirostris) travel >10,000 km during
7-month-long foraging trips. Seals minimize
time at the surface (~2 min between 10- to
30-min dives) to reduce predation risk by killer
1Scripps Institution of Oceanography, University of California
San Diego, San Diego, CA, USA. 2Ecology and Evolutionary
Biology, University of California Santa Cruz, Santa Cruz, CA,
USA. 3Department of Neuroscience, University of Oxford,
Oxford, UK. 4Sleep Health MD, Santa Cruz, CA, USA.
5Institute of Marine Sciences, University of California Santa
Cruz, Santa Cruz, CA, USA. 6Ocean Sciences Department,
University of California Santa Cruz, Santa Cruz, CA, USA.
7Department of Biology, Sonoma State University, Rohnert
Park, CA, USA. 8Semel Institute for Neuroscience and
Human Behavior, University of California Los Angeles, Los
Angeles, CA, USA. 9A.N. Severtsov Institute of Ecology and
Evolution, Moscow, Russia. 10Institute of Neuroinformatics,
University of Zurich and Swiss Federal Institute of
Technology (ETH), Zurich, Switzerland.
*Corresponding author. Email: jkb@ucsc.edu
whales and white sharks while maximizing
foraging time (12, 14–16). They also feed around
the clock on small prey to satisfy the energy
requirements associated with their large body
size (17). Given these ecophysiological demands,
a long-standing question has been when, where,
and how do seals sleep at sea?
A new tool to detect sleep at sea
We developed a new submersible system to
record brain activity (electroencephalogram,
EEG) and heart rate (electrocardiogram, ECG)
concurrently with dive depth and motion of
elephant seals at sea [Fig. 1E; (18)]. These sen-
sors identified sleep states [rapid eye move-
ment (REM) sleep and slow-wave sleep (SWS);
figs. S1 to S3 and table S2], swimming effort
(stroke rate), and three-dimensional (3D)
diving behavior in freely moving female ju-
venile seals (n = 13 seals) (18). We recorded
sleep in a controlled laboratory environment
(n = 5 seals) and in the wild (n = 8 seals) at
four locations, including on the beach, in shal-
low water, offshore along the continental shelf
(depth <250 m), and in the open ocean (depth
>250 m; table S1). EEG recordings allowed
us to pair sleep states with diving behavior
recorded in time-depth profiles for juveniles
over multiple days at sea (104 sleeping dives).
We used these sleep signatures to estimate
sleep patterns across >3 million dives by 334
free-ranging adult females over prolonged
trips at sea (514,406 sleeping dives across
53,581 recording days).
On a typical sleeping dive, seals transitioned
from an awake glide into SWS. Although
asleep, they could maintain their upright
posture for several minutes (Fig. 1 and movie
S1). These results underscore the importance
of EEG in assessing sleep state (18). As seals
shifted from SWS to REM sleep, sleep paraly-
sis resulted in a loss of postural control. Seals
turned upside down and drifted downwards
in a “sleep spiral.” Sleep spirals tightened from
a median diameter of 7.5 ± 7.9 m [median ±
interquartile range (IQR)] at 71 ± 97 s (median ±
IQR) in SWS to 3.3 ± 3.5 m loops at 40 ± 29 s
in REM (Fig. 1). Sleep spirals consisted of two
to 13 consecutive 360-degree loops at 82 to
377 m depth. On the continental shelf, seals
slept motionless on the ocean floor at 64 to
249 m depth.
The predation risk of sleep at sea
Among marine mammals, unihemispheric
sleep (SWS in only one hemisphere) allows
captive cetaceans and otariids (fur seals and
sea lions) to swim and keep one eye open during
sleep (11, 19). This suggests that cetaceans and
otariids can sleep while monitoring predators
(20, 21). Unihemispheric sleep has not been
detected in captive true seals (family Phocidae)
such as elephant seals (22). Similarly, our study
did not reveal sleep asymmetry between hemi-
spheres (<2-fold difference). This suggests that
true seals use an alternative solution to mit-
igate predation risk. This study experimen-
tally confirms the hypothesis (22, 23) that in
the absence of unihemispheric sleep, elephant
seals’ extreme diving abilities allow sleep deep
below the ocean surface, out of view of visual
predators.
The sleep paralysis that co-occurs with REM
sleep would make seals especially vulnerable
to predation (1). REM is often minimized for
aquatic mammals because the accompanying
paralysis can also prevent access to air (22). In
captive fur seals confined to water, REM is
virtually eliminated (24). Elephant seals at sea
reduce REM sleep, as is seen in captive fur seals
and true seals in water (24–27), but unexpec-
tedly exhibit a large proportion of REM [26.5 ±
5.0% (mean ± SD) in total sleep time over-
all and 29.1 ± 4.3% of at-sea total sleep time;
table S3]. This compares to 11%, 6%, 5%, and
1% in aquatic sleep for captive Caspian seals,
harp seals, walruses, and fur seals, respectively
[(22, 24–27); see the materials and methods).
Our at-sea deployments occurred during late
spring, when juvenile seal aggregations at-
tract predators (14). While transiting over the
continental shelf, juvenile seals alter their
swimming behavior to avoid predation (28).
Unexpectedly, we found that seals slept pro-
portionally more on the continental shelf than
in the open ocean (Figs. 2 and 3A). One seal
performed up to 36 consecutive sleeping dives
on the continental shelf but fewer than five at
sea. This suggests that seals can safely sleep at
depth despite elevated coastal predation risk.
Finding time to sleep at sea
Without unihemispheric sleep allowing con-
tinuous vigilance, seals are vulnerable and
Kendall-Bar et al., Science 380, 260–265 (2023)
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Fig. 1. 3D drift dive sleep patterns. (A) A 23-min sleeping dive showing
stroke rate [strokes per minute (spm)], heart rate [beats per minute (bpm)],
left (L) EEG (mV), right (R) EEG (mV), L EEG spectrogram [power (dB)
for frequency (Hz) over time], pitch (radians), roll (absolute value; radians)
and heading (radians), and time (minutes of dive). (B to D) Raw EEG and
ECG signals during the transition to light SWS (B), deep SWS (C), and
REM (D). During SWS, high-voltage, low-frequency slow waves are present.
During REM, low-voltage, high-frequency EEG activity co-occurs with heart
rate variability. (E) EEG logger configuration demonstrating headcap and
logger placement. (F) Schematic demonstrating placement of electrodes for
electrooculogram (EOG), EEG, ECG, and electromyogram (EMG). (G) 3D
dive profile color-coded by sleep state: Active waking is shown in dark
blue, quiet waking in light blue, light SWS in light green, deep SWS in teal,
and REM in yellow. (H) Top view of sleep spiral. (I) Depth over time
showing nested durations of gliding, electrophysiological sleep, constant
drift rate, and spiraling.
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Fig. 2. Sleep patterns from land to sea. (A) Daily sleep quotas for seals in the
laboratory (on land and in the pool) and in the wild (on land, in shallow water,
on the continental shelf, and in the open ocean), including active waking (dark blue),
calm (lighter blue), drowsiness (purple), REM sleep (yellow), and SWS (light blue).
REM sleep totals include certain and putative REM (see “REM scoring” section in the
supplementary materials). (B) Schematic showing the resting postures of seals in
each habitat, including seals resting on the ocean floor on the continental shelf and
drifting in the open ocean. (C) 2D map with bathymetry showing georeferenced
dead-reckoned tracks for three animals recorded at sea. (D) 3D map demonstrating
sleeping dive sequence, including the sleeping dive from Fig. 1.
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. Sleep identification model performance. Time-depth records for two
juvenile seals (A and B) are colored to indicate surface intervals (light blue),
dives (dark blue), glides (blue), SWS (green), and REM sleep (yellow). In panels
(A1) and (B1), the identified sleep segments are denoted below the dive
profile, where outlined dots at the beginning and end of sleep segments are
colored from yellow to dark blue according to overlap with sleep (“percent nap
overlap”). Light shaded regions above the dive profile in panels (A1) and (B1)
demonstrate sleep identification accuracy (false positives in blue, false negatives
in yellow, and true positives in green). Panels (A2) and (B2) display EEG
spectrograms and heart rate for two adjacent sleeping dives. Panels (A3) and
(B3) quantify daily activity budgets (or provide estimates) in hours per day
of diving, sleep estimates (upper bound – unfiltered sleep ID; best estimate/
lower bound includes only sleep ID segments that meet filter criteria), gliding
(long glides >200 s), sleeping (both SWS and REM), and REM sleep.
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Fig. 4. Estimating daily sleep for 334 adult females. (A) Map showing estimated
sleep (hours per day) for two of 15 seals instrumented with stroke rate loggers
(basemap matches bathymetry legend in Fig. 2). Each circle represents 1 day,
with circle size and color reflecting daily sleep (hours per day). (B1 and B2) Time-
depth records for two 24-hour days far from shore (B1) and close to Vancouver
Island (B2), demonstrating the difference in sleep during pelagic versus coastal
foraging. Yellow dots and green shaded regions above dive profiles indicate identified
sleep segments that 100% overlap with a long glide segment (yellow and blue
shading represent false negatives and false positives, respectively). (C) Map with
spatially averaged daily sleep estimates clipped to the extent of tracking data
(1 point per seal day) across 342 good-quality tracks from 267 adult females. Note
the higher sleep time along the coast and foraging grounds. (D) Daily activity
budgets for long postmolt foraging trips (n = 164 seals) including surface intervals,
diving, long glides, long drifts, sleep estimates (filtered long drifts), and long
surface intervals. Sleep estimates demonstrate low sleep time throughout the trip.
(E) Comparative figure showing total sleep time in terrestrial mammalian
carnivores, omnivores, and herbivores [reprinted with permission (1)]. Extremes
of sleep time on land and at sea from EEG recordings in juveniles (Fig. 2) are
plotted for comparison. Sleep durations for other mammals are based on behavior
and/or EEG in the laboratory and/or wild. Differences in recording location
(laboratory versus wild) and sleep identification technique (EEG versus behavior)
complicate sleep quantification and direct comparison.
unable to actively transit during sleep to max-
imize foraging efficiency. Between heightened
predation risk and lost foraging opportunities,
we expected sleep to be strongly restricted at
sea. Supporting this hypothesis, we discovered
that seals’ daily sleep time was >5 times higher
on land than at sea (Fig. 2). Seals slept up to
14 hours/day on land [10.8 ± 3.0 hours/day
(mean ± SD)] but as little as 0 hours/day at
sea (1.7 ± 0.7 hours/day; tables S3 and S4).
After returning from 2 to 3 days at sea, seals
remained on land for 18 to 43 hours, sleeping
up to 53.3% of each hour before returning to
shallow water (fig. S4). This moderate sleep
rebound was comparable to the daily patterns
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of other seals at the colony (fig. S4), suggesting
that this relatively short multiday trip did not
incur a notable sleep debt.
Substantial fluctuations in sleep duration
allow birds to prioritize migration and breed-
ing for several days (5, 10). As mammals, ele-
phant seals similarly partition strategies over
long time scales, sacrificing sleep at sea to sup-
port the energy requirements associated with
their large size and deferring sleep until they
leave the water and are on land with no preda-
tors. Seals in laboratory settings show modest
differences between total sleep time on land and
water (24, 25). Here, we demonstrate greater ex-
tremes in total sleep time for wild seals that
are necessary to balance sleep with the need to
replenish the energy stores of a large, highly
mobile predator at sea.
Mapping range-wide sleep patterns at the
population level
Using the paired electrophysiological and
time-depth signatures of SWS and REM sleep
from instrumented seals (Figs. 1 and 2), we
developed a high-accuracy sleep identifica-
tion algorithm that identified segments of
inactivity characterized by low vertical speed
and acceleration from time-depth data (93%
accuracy; Fig. 3 and figs. S5 to S7). This algo-
rithm allowed us to estimate sleep quotas for
334 adult seals from their diving data recorded
over several months at sea [n = 170 short trips
(74.6 ± 9.5 days) and n = 164 long trips (217.7 ±
24.7 days)] (Fig. 4). These analyses indicated
that daily sleep quotas were likely to be uni-
versally low (1.1 ± 1.1 hours/day for short 70-day
trips and 2.2 ± 1.6 hours/day for >200-day trips)
(Fig. 4).
Expanding this analysis to the population
level, we can map range-wide sleep patterns
to identify critical habitats for protecting wild
seals while they sleep at sea. These “sleep-
scapes,” which are based on 342 foraging trips
by seals across the North Pacific (Fig. 4C), re-
veal the same unexpected sleep patterns as in
juvenile EEG records. That is, seals slept more
while closer to the coastline despite greater
predation risk (Fig. 4B1) (14). Because coastal
foragers consume fewer, larger prey (17), our
findings suggest that these seals must either
expend more energy hunting for larger prey or
require more time to rest and process such
prey. Although the coastal water column may
harbor more predators, the continental shelf
may also facilitate sleep by providing shelter
from predators and relative proximity to the
surface. These findings and the resulting sleep-
scape aid in identifying critical habitats that
may guide coastal conservation efforts for wild
animals.
By connecting locomotion with different
forms of sleep (SWS versus REM) in northern
elephant seals, the present study provides
conclusive evidence of sleep during drift dives
(23, 29, 30). Furthermore, these unique record-
ings of brain activity for a wild, free-ranging
marine mammal at sea show that sleeping at
depth allows seals to drift safely in and out of
sleep paralysis. However, these respites are
short, because the large body size [456 to 687 kg
(min-max adult female arrival breeding mass);
(31)] of this elite diver that forages and sleeps in
the dark must be sustained by near-constant
foraging at sea. Sleep patterns interpreted
from the dive records of hundreds of seals re-
vealed only 2 hours/day of sleep for months,
rivaling the record for the least sleep among
mammals [the African elephant at 2 hours
per day; (32)]. Both this method (applying
sleep signatures from a small sample to reveal
population-level patterns) and these find-
ings (a detailed understanding of sleep for a
highly mobile, large mammal) provide oppor-
tunities for understanding sleep’s function,
evolution, and pathology across mammals,
including in humans.
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AC KNOWLED GME NTS
We acknowledge the students, volunteers, and researchers
contributing to the long-term Año Nuevo elephant seal research
program, especially C. Kuhn, J. Hassrick, S. Simmons, M. Fowler,
S. Peterson, A. Favilla, S. Kienle, and L. Hückstädt for their
assistance in collecting female tracking data. We also thank
volunteers C. Lopez and J. Nichols for their help with data collection
and analysis; Año Nuevo State Park and the Año Nuevo UC
Natural Reserve for their ongoing support, TMMC veterinarians
C. Field and S. Johnson for assistance with pilot studies; and Long
Marine Lab staff and volunteers for facilitating lab-based studies.
Engineers and technicians P. Guerrero, E. Slattery, J. Bielke,
and colleagues at Ocean Innovations, Scripps Institution of
Oceanography, and the Shorter laboratory at the University of
Michigan assisted with the development of the tag housing. Funding:
This work was supported by the National Ocean Partnership
Program (grant N00014-02-1-1012 to D.P.C.); the National
Science Foundation (grant N1656282 to D.P.C.); the Strategic
Environmental Research and Development Program (SERDP
grant RC20-C2-1284 to D.P.C.); the Office of Naval Research
(grants N00014-18-1-2822, N00014-00-1-0880, N00014-03-1-0651,
and N00014-08-1-1195 to D.P.C. and grant N00014-20-1-2762
to T.M.W.); the Office of Naval Research Defense University
Research Instrumentation Program (grant N00014-19-1-2178 to
T.M.W. and J.M.K.-B.); the E&P Sound and Marine Life Joint
Industry Project (JIP) of the International Association of Oil and
Gas Producers (IOGP grant JIP2207-23 to D.P.C.); a National
Geographic Early Career Grant (J.M.K.-B.); a Steve & Rebecca
Sooy Graduate Research Fellowship (J.M.K.-B.); Achievement
Rewards for College Scientists (J.M.K.-B.); the National Science
Foundation Graduate Research Fellowship Program (J.M.K.-B.);
and a Special Research Grant from the Committee on Research at
UC Santa Cruz (D.P.C. and J.M.K.-B.). Author contributions:
Conceptualization: J.M.K.-B., T.M.W., D.P.C.; Funding acquisition:
J.M.K.-B., T.M.W., D.P.C.; Investigation: J.M.K.-B., R.M., D.A.L.,
J.K.P., R.R.H., T.K., R.S.B., P.W.R., D.E.C., T.A.; Methodology:
J.M.K.-B., A.L.V.; Supervision: T.M.W., D.P.C.; Visualization: J.M.K.-B.;
Writing – original draft: J.M.K.-B., T.M.W., D.P.C.; Writing –
review and editing: J.M.K.-B., T.M.W., R.M., D.A.L., J.K.P.,
R.R.H., T.K., R.S.B., P.W.R., D.E.C., T.A., O.I.L., A.L.V., D.P.C.
Competing interests: The authors declare no competing interests.
Data and materials availability: Statistical data are presented
primarily in the main text and online supplementary materials,
with electronic versions of original sleep data and analysis scripts
directly available online through Dryad (33) and Zenodo (34),
respectively. License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf0566
Materials and Methods
Figs. S1 to S7
Tables S1 to S5
References (35–60)
Movie S1
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
27. O. I. Lyamin, P. O. Kosenko, J. L. Lapierre, L. M. Mukhametov,
J. M. Siegel, J. Neurosci. 28, 12614–12621 (2008).
Submitted 30 September 2022; accepted 14 March 2023
10.1126/science.adf0566
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RES EARCH
SEMICONDUCTORS
Room-temperature wavelike exciton transport in
a van der Waals superatomic semiconductor
Jakhangirkhodja A. Tulyagankhodjaev, Petra Shih†, Jessica Yu†, Jake C. Russell, Daniel G. Chica,
Michelle E. Reynoso, Haowen Su, Athena C. Stenor, Xavier Roy, Timothy C. Berkelbach, Milan Delor*
The transport of energy and information in semiconductors is limited by scattering between electronic
carriers and lattice phonons, resulting in diffusive and lossy transport that curtails all semiconductor
technologies. Using Re6Se8Cl2, a van der Waals (vdW) superatomic semiconductor, we demonstrate
the formation of acoustic exciton-polarons, an electronic quasiparticle shielded from phonon scattering.
We directly imaged polaron transport in Re6Se8Cl2 at room temperature, revealing quasi-ballistic,
wavelike propagation sustained for a nanosecond and several micrometers. Shielded polaron transport
leads to electronic energy propagation lengths orders of magnitude greater than in other vdW
semiconductors, exceeding even silicon over a nanosecond. We propose that, counterintuitively, quasi-
flat electronic bands and strong exciton–acoustic phonon coupling are together responsible for the
transport properties of Re6Se8Cl2, establishing a path to ballistic room-temperature semiconductors.
S emiconductor technologies rely on trans-
porting energy and information carriers,
often in the form of electrons or excitons
(bound electron-hole pairs), from source
to target. At room temperature, these
carriers rapidly scatter with lattice vibrations
(phonons) on nanometer and femtosecond
scales. Scattering leads to electronic energy
dissipation, joule heating, and loss of phase co-
herence and directionality, imposing strict speed
and efficiency limits on all semiconductor tech-
nologies. Breaking through these limits requires
semiconductors that sustain ballistic (scatter-
free), wavelike flow of energy over macroscopic
distances at room temperature, a long-sought
goal that would enable ballistic transistors (1),
low-loss energy harvesting, and wave-based
information technologies (2).
Here, we demonstrate macroscopic, wavelike
exciton flow at room temperature in the van der
Waals (vdW) superatomic material Re6Se8Cl2
(Fig. 1A). Re6Se8Cl2 is a semiconductor with
an indirect bandgap of 1.6 eV and an exciton
binding energy of ~100 meV (3). Its superatom
building blocks consist of Re6 octahedra en-
closed in Se8 cubes. Each Re6Se8 unit is co-
valently bonded to four neighbors to form a
two-dimensional (2D) pseudosquare lattice
capped by Cl atoms at the apical positions.
The Re6Se8Cl2 layers stack out of plane to create
a bulk vdW crystal with weak interlayer electron-
ic coupling (4). The crystal can be exfoliated to
the monolayer limit, which is advantageous
for integration in gated devices (3, 5, 6).
Re6Se8Cl2 exhibits relatively weak intercluster
electronic coupling, as evidenced by the elec-
tronic band structure (Fig. 1B) (3, 7). Strong
coupling of electrons to intercluster optical
Department of Chemistry, Columbia University, New York, NY
10027, USA.
*Corresponding author. Email: milan.delor@columbia.edu
†These authors contributed equally to this work.
phonons (8) leads to further band flattening
at room temperature (7) and has been impli-
cated in the emergence of superconductivity
in this material and related classes (6, 9). In
this work, we demonstrate that these quasi-flat
electronic bands, in combination with strong
coupling to acoustic phonons, lead to the for-
mation of acoustic exciton-polarons (Fig. 1C),
quasiparticles of excitons bound to an acoustic
lattice deformation. Through direct imaging
of polaron propagation, we reveal that they are
shielded from lattice scattering, leading to quasi-
ballistic transport over several micrometers
at room temperature, currently limited only
by crystal size. Our observations challenge the
common notion that strong electronic cou-
pling is required for long-range transport.
Exciton transport in Re6Se8Cl2 is quasi-ballistic
We directly imaged exciton transport in single-
crystal Re6Se8Cl2 using ultrafast stroboscopic
scattering microscopy (stroboSCAT) (10–12)
(Fig. 1D and figs. S1 to S3). An above-gap,
diffraction-limited visible pump generates
excitons, and then a backscattering widefield
probe (1.55 eV) slightly below the electronic
bandgap spatially resolves how the excitons
modify the local polarizability of the material.
By varying the pump-probe time delay, we
spatiotemporally tracked the evolution of photo-
excitations in an all-optical, noninvasive, and
contact-free measurement. Figure 1E and movie
S1 display representative stroboSCAT data
obtained in a 60-nm-thick Re6Se8Cl2 flake pre-
pared by mechanical exfoliation (13). Two key
features emerge from these data: First, the
initial negative (dark) stroboSCAT contrast
turns to positive (bright) contrast on picosecond
timescales, which, as discussed below (Fig. 2),
represents a transition from a bare exciton to
an exciton-polaron. Second, the exciton-polaron
propagates several micrometers to the edge of
the flake in less than a nanosecond. This very
fast and long-range transport differs starkly
from exciton transport in other molecular or 2D
semiconductors (table S1). For comparison, Fig.
1F displays stroboSCAT data of exciton trans-
port in the archetypal vdW semiconductor WSe2
(bilayer flake on glass; see fig. S4 for monolayer
and bulk data), exhibiting much slower and
shorter-range transport. These results are coun-
terintuitive, given that the effective mass of ex-
citons in WSe2 is much smaller than in Re6Se8Cl2
(table S1).
To quantify and rationalize the exceptional
transport properties of Re6Se8Cl2, we plotted
the mean squared displacement (MSD) of the
photoexcited population profile observed in
stroboSCAT as MSD = s2(t) − s2(0), where s
is the Gaussian width of the population den-
sity profile at time delay t (13). Figure 1G
compares the MSD for exciton-polarons in
Re6Se8Cl2 against the MSD for excitons in
bilayer WSe2 and charge carriers in intrinsic
monocrystalline Si (14), which exhibit some
of the best transport among 2D and 3D semi-
conductors, respectively. We find that the MSD
at 1.1 ns in Re6Se8Cl2 is 23 times that in bulk
WSe2, 65 times that in bilayer WSe2, 120 times
that in monolayer WSe2, and almost twice that
of electrons in intrinsic Si and the recently
reported cubic boron arsenide (15, 16) (table
S1). On the basis of the 11-ns polaron lifetime
(fig. S5), we estimate that the polaron propa-
gation length in Re6Se8Cl2 would exceed 25 mm
in the absence of crystal boundaries.
The superlinear behavior of the MSD for
Re6Se8Cl2 differs from the linear behavior in
Si and WSe2. We fit the MSD to a power law,
MSD º ta (11, 12, 17). In the limit of diffusive
transport, where scattering lengths are much
shorter than the propagation length, a ¼ 1. This
regime, exemplified by the linear MSD for Si
and WSe2 in Fig. 1F, is observed in virtually all
semiconductors beyond the first few femto-
seconds after photoexcitation (18). In the limit
of coherent, ballistic transport (no scattering),
a = 2, meaning that distance is proportional to
time with a slope that defines the velocity. In
Re6Se8Cl2, we observe quasi-ballistic transport
(a = 1.67 ± 0.13) (Fig. 1G) sustained for nano-
seconds, until the flake edge is reached. Plot-
ting the same data as distance versus time
provides an effective propagation velocity of
2.3 km/s (fig. S6). Monte Carlo simulations re-
producing the observed MSD yield an exciton–
lattice scattering time of 215 ps, indicating an
extraordinary mean free path between scattering
events exceeding 1 mm for exciton-polarons
in Re6Se8Cl2 (Fig. 1H; see figs. S7 and S8 for
simulation details and alternative models). These
findings reveal that the mechanism for fast
and long-range transport in Re6Se8Cl2 is effi-
cient shielding from scattering, amply compen-
sating for the large effective mass (and thus low
intrinsic velocity) of the polaron. These results
are reproducible in multiple flakes of different
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Fig. 1. Imaging exciton transport in Re6Se8Cl2. (A) Crystal structure of
Re6Se8Cl2. (B) Band structure of Re6Se8Cl2 calculated using density functional
theory with the Perdew-Burke-Ernzerhof (PBE) exchange correlation functional
(13). (C) Formation of acoustic polarons through a deformation potential interaction.
(D) Schematic for optical far-field imaging of polaron transport (details in the text
and figs. S1 to S3). (E) Picosecond stroboSCAT time series displaying exciton
(dark contrast) and exciton-polaron (bright contrast) propagation in a 60-nm-thick
Re6Se8Cl2 flake on glass. DI/I refers to the pump-induced change in backscattered
light intensity. (F) Exciton propagation in bilayer WSe2 on glass. (G) Mean squared
displacement (MSD) of exciton-polarons in Re6Se8Cl2 (red), excitons in WSe2
(blue), and charge carriers in Si (gray and black). Error bars are 1 SD. Only
Re6Se8Cl2 displays superlinear behavior, indicating superdiffusive transport
characterized by the exponent a. The box plot shows the spread of a values
across 11 different datasets, indicating mean and median values of 1.67 and 1.7,
respectively. (H) Monte Carlo simulation of a for different particle velocities (v)
and scattering times (t) for our experimental configuration. The circle corresponds
to simulation parameters of v = 5.5 km/s and t = 215 ps that reproduce the
experimental MSD. The black contour traces a = 1.67. (I) Illustration of quasi-ballistic
motion of polarons in Re6Se8Cl2 compared with diffusive motion for excitons in
WSe2 and other semiconductors. Data acquired at 295 K.
thicknesses (Figs. 1 and 3), for both above-gap
and band-edge pump excitation (fig. S9), for
pump temporal pulse widths spanning 60 fs to
60 ps (fig. S10), and across a range of fluences
explored in detail below (Fig. 3), indicating
that neither hot carrier transport (19), phonon
winds (20, 21), nonlinear recombination (22),
thermal gradients (23), nor strain waves (24–27)
are responsible for the observed behavior (figs.
S9 to S12 and table S2).
Excitons in Re6Se8Cl2 form exciton-polarons
To confirm that polaron formation is respon-
sible for the observed transport behavior, we
tracked the energetic evolution of excitons after
photoexcitation and correlated these dynamics
to optical transport measurements. Figure 2A
displays transient reflectance spectra in the re-
gion of the semiconductor band edge, exhibiting
a bleach around 1.57 eV and a photoinduced
absorption ~90 meV higher in energy. The
primary dynamic evolution observed is a spec-
tral redshift on a 1.5-ps timescale that convolves
all peaks. Identical dynamics are observed for
near-band-edge excitation (fig. S9), ruling out
the possibility that electronic thermalization
is responsible for the redshift. Tracking the zero-
crossing of the transient reflectance profile
(dashed line in Fig. 2A) provides a handle on
redshift kinetics, plotted in Fig. 2B. We observe
an overall 48 meV redshift with an evolution re-
sembling a strongly damped oscillator (red line
in Fig. 2B). These dynamics echo those previous-
ly observed for (large) polaron formation (28–31),
wherein energetic stabilization occurs over a sin-
gle vibrational period of the associated lattice de-
formation. This spectral evolution is responsible
for the switch from dark to bright contrast in
stroboSCAT in Fig. 1E: The probe at 1.55 eV is
initially pre-resonant with the exciton transition
(dark contrast) but switches to resonant with
the induced polaron absorption after the red-
shift, generating a bright contrast (additional
stroboSCAT datasets at different probe wave-
lengths are displayed in fig. S13). Below, we
discuss measurements of correlated spatio-
energetic dynamics, fluence-dependent red-
shift dynamics, and population saturation that
cement our assignment of these redshift dy-
namics to polaron formation.
Polarons should exhibit correlated spatial and
spectral dynamics, given that energetic stabi-
lization associated with polaron formation
results in a modification of transport proper-
ties. To directly image these correlated dynamics
and further support the correspondence be-
tween the redshift timescale and the polaron
formation timescale, we developed an approach
capable of simultaneously resolving spectral
and spatial evolution by merging stroboSCAT
with transient reflectance microscopy (fig. S2).
Figure 2C displays spatially resolved transient
spectra at different pump-probe time delays
(see also movies S2 and S3). At early times, the
transient reflectance signal associated with ex-
citons is concentrated around the pump exci-
tation location at 0 mm. Between 4 and 50 ps, a
V-shaped pattern emerges (highlighted with
arrows in Fig. 2C), indicating that the spectral
redshift associated with polaron formation is
correlated to transport away from the excitation
location. By 1 ns, only the redshifted polaron spec-
tral signature remains, showing propagation
over several micrometers. The correlated spatio-
energetic dynamics are a clear indication that
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Fig. 2. Spatio-energetic
tracking of polaron
formation in Re6Se8Cl2.
(A) Transient reflectance
spectra near the band
edge after 2.41 eV
pump excitation at an
initial exciton density
of 5 × 1017/cm3. DR/R
refers to the pump-
induced change in
reflected light intensity.
(B) Trace of the redshift
highlighted with a dashed
line in (A). The red line
is a fit using a damped
oscillator model with
a frequency of 0.31 THz
and damping time of
0.37 ps, combined with a
3-ps exponential decay. (C) Spacetime-transient reflection spectra after 2.41 eV pump excitation at an initial
exciton density of 8 × 1018/cm3 for three time delays. The correlated redshift and transport dynamics are
emphasized with arrows in the middle panel. Movies S2 and S3 display these coupled spatio-energetic
dynamics for different excitation fluences. Data acquired at 295 K.
excitons in Re6Se8Cl2 become substantially mo-
bile only after they have formed exciton-polarons;
bare excitons are effectively immobile, whereas
polarons propagate over micrometers. The ob-
served transport dynamics also rule out traditional
exciton self-trapping (small polarons), which
would reduce the exciton mobility upon polaron
formation (32). These results illustrate the power
of our correlative approach for understanding
how polaron formation affects transport.
Finally, we confirmed the formation of pola-
rons in Re6Se8Cl2 and experimentally inferred
their size by determining the density at which
they begin to interact. At high densities, lattice
deformations compete to displace the same
atoms, resulting in a diminished ability to form
polarons (Fig. 3A) (32). stroboSCAT data dis-
played in Fig. 3B shows that as the photo-
excitation density increases, the bare exciton
signal (dark contrast) begins to dominate over
the polaron signal (bright contrast), indicating
that polaron formation is suppressed in re-
gions of high excitation density. Figure 3C
compares the polaron population (red trace)
and bare exciton population (black trace) as
a function of excitation fluence (analysis in
fig. S14). We observed clear saturation of the
polaron population at exciton densities between
0.45 × 1018/cm3 and 1.8 × 1018/cm3 (highlighted
with a blue rectangle). This behavior signals
that polarons are overlapping in space, analo-
gous to a Mott transition that prevents further
polaron formation (33). The onset of polaron
saturation is also reflected in a transition from
superdiffusive to almost diffusive transport (Fig.
3D), which we attribute to polaron–polaron scat-
tering above the saturation density. The sup-
pression of exciton-to-polaron conversion above
saturation is most evident in the spectral dy-
namics (Fig. 3E and fig. S15), where the redshift
time associated with exciton stabilization in-
creases from ~1.5 ps to hundreds of picoseconds.
We reproduced these spectral dynamics (right
panels of Fig. 3E) with a saturation model ac-
counting for a kinetic blockade and polaron
transport away from the excitation area (figs. S15
and S16). According to the Mott criterion (34),
the polaron interaction radius associated with
the observed critical density range of 0.45 × 1018/
cm3 to 1.8 × 1018/cm3 is 2.1 to 3.4 nm, corre-
sponding to three- to five-unit cells in Re6Se8Cl2.
Acoustic polarons are responsible for
wavelike transport
Large polarons, known to form in materials
such as lead halide perovskite semiconductors,
have been suggested to partially shield carrier-
lattice scattering (35). Nevertheless, experiments
consistently demonstrate a diffusive transport
regime (10, 18, 19, 36), with sub-100-fs scat-
tering times that indicate insufficient shielding
to switch into the much-desired macroscopic
ballistic transport regime. In contrast, the
sustained quasi-ballistic behavior observed in
Re6Se8Cl2 is reminiscent of acoustic polarons,
which can form in low-dimensional materials
and were theoretically invoked to rationalize
the transport properties of polydiacetylene in
one dimension (37, 38).
The formation of acoustic polarons is rare,
as is our observation of micrometer-scale exci-
ton mean free paths at room temperature. To
rationalize this notable behavior in Re6Se8Cl2,
we use an approximate strong-coupling theory
that describes an exciton of mass m coupled to
acoustic phonons with a strength quantified by
the deformation potential D in two dimensions.
The acoustic phonons derive from superatoms
of mass M with intercluster vibrational fre-
quency W. In two dimensions, the energy to form
a circular polaron with radius a and area pa2 is
E ¼
ħ2
2ma2
þ
1
2
MW2D2pa2 (cid:2) DD
ð1Þ
where D is the dimensionless lattice displace-
ment and ħ is the reduced Planck constant (39).
In this simple picture, the polaron is only bound
if the electron–phonon interaction outweighs
the energetic penalties associated with exciton
localization and lattice deformation. Minimizing
Eq. 1 with respect to the lattice displacement D
gives the existence criterion
l > lc; l ¼
mD2
2ħ2MW2
=
2 ≈ 1:6
¼
D2
4JMs2
;
ð2Þ
lc ¼ p
where l is a dimensionless measure of the
exciton–acoustic phonon coupling strength,
and in the second equality we have intro-
duced the exciton transfer integral J and the
speed of sound s = Wa. Applying density
functional theory to Re6Se8Cl2, we calculate
D = 4.4 eV (13). Taking into account the ex-
perimentally inferred electronic band flat-
tening due to intercluster optical phonons,
which increases the exciton effective mass
from 1.9me at 0 K to 60me at 300 K (7), we
calculate a very small J of 1.5 meV at 300 K
(13). When combined with the other material
parameters (table S3), we find that l = 7 > lc,
predicting a strongly bound polaron. Figure 4A
plots the coupling strength l for Re6Se8Cl2,
monolayer WSe2, crystalline pentacene, and 2D
organic-inorganic halide perovskites. Re6Se8Cl2
has a coupling strength l that is 10 to 1000
times greater than that of the other materials
and is thus the only material considered in
Fig. 4 that is predicted to exhibit bound acous-
tic polarons according to the criterion in Eq. 2.
Within this theory, the key parameters setting
Re6Se8Cl2 apart from other 2D and 3D semi-
conductors is the combination of a quasi-flat
electronic band structure at room temperature
(small J) and strong exciton–acoustic phonon
interactions (large D), yielding a large coupling
strength l and associated strongly bound
acoustic polarons. The polaron binding energy
is reduced with decreasing temperature owing
to the increase in the transfer integral J (7, 13).
The estimate in Eq. 2 predicts that the polaron is
not bound below ~175 K. Temperature-dependent
stroboSCAT experiments (fig. S17) display a
drastic reduction in MSD below ~150 K, lend-
ing support to our central hypothesis and
theory of acoustic polarons. We emphasize
that Eq. 2 only provides a qualitative criterion
for polaron formation and a detailed under-
standing of the polaron stability and lifetime
at finite temperature requires a more com-
plete theoretical treatment (13).
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Fig. 3. Determining polaron size in Re6Se8Cl2. (A) Depiction of polaron
blockade at high densities. (B) Femtosecond stroboSCAT images at pump/probe
energies of 2.41 eV/1.55 eV at initial exciton densities ranging from 1 × 1018/cm3 to
20 × 1018/cm3 in a 350-nm-thick Re6Se8Cl2 flake on glass. Bare excitons are
associated with dark contrast, whereas polarons are associated with bright contrast.
The rings observed at high exciton densities are diffraction rings. All scale bars
are 3 mm. (C) Relative populations of polarons and bare excitons at a pump-probe
time delay of 5 ps as a function of initial exciton density, indicating saturation
of the polaron population. The blue shaded region for exciton densities between
0.45 × 1018/cm3 and 1.8 × 1018/cm3 indicates the range of critical polaron overlap
density. (D) MSD exponent, a, as a function of initial exciton density. Error bars
are 1 SD. (E) Experimental (left) and simulated (right) transient reflectance
spectra taken at the center of the focused pump excitation (B) for different initial
exciton densities. Simulations are based on a saturation model accounting for
exciton-to-polaron conversion and polaron transport away from the excitation
spot (13). Data acquired at 295 K.
Fig. 4. Energy of an
acoustic polaron.
(A) The coupling strength
l for different systems,
presented as a function
of their exciton transfer
integral J. The boxed
regions represent the
upper and lower bounds
for a range of deformation
potentials and exciton
transfer integrals within 30% of reported data (material properties collected in table S3). The critical value of
lc = 1.6 is plotted as a dashed line. (B) Calculated polaron dispersion for Re6Se8Cl2 (13). The band effective
mass is estimated by a parabolic fit at the minimum (dashed blue line). The solid red line emphasizes
the linearity of the dispersion for higher values of momentum.
Rationalizing the quasi-ballistic dynamics
of acoustic polarons requires a more sophis-
ticated quantum mechanical treatment. We
generalize the stationary polaron description
above and propose a variational wave function
for the moving polaron defined by its average
crystal momentum (13). Energy minimization
produces the polaron dispersion shown in Fig.
4B. Near the band bottom, we extract a large
effective polaron mass m* ≈ 200me, a substantial
increase from the bare exciton mass of 60me at
300 K. More importantly, at higher momenta,
the polaron inherits the linear dispersion of
acoustic phonons—a renormalization evocative
of light–matter hybridization to form polari-
tons (40). The linear dispersion of acoustic
polarons with a slope below that of other acous-
tic phonons implies weak scattering because
there are no dissipation channels that conserve
both energy and momentum (38). The polaron
is thus predicted to move quasi-ballistically
at a speed proportional to the speed of sound
of the lattice, consistent with our experimen-
tal observations.
Discussion and outlook
We have observed a transport regime medi-
ated by acoustic exciton-polarons in the vdW
superatomic semiconductor Re6Se8Cl2. Polaron
formation shields excitons from scattering with
lattice phonons, resulting in quasi-ballistic elec-
tronic energy flow over several micrometers
within a nanosecond at room temperature.
We reveal a very long exciton mean free path of
~1 mm, suggesting the possibility of ballistic
excitonic transistors. Our discovery of this
regime in a material with weak electronic
dispersion provides an alternative to the cur-
rent paradigm of increasing electronic conju-
gation to improve transport. Indeed, our model
for 2D acoustic polarons suggests that quasi-flat
electronic bands and strong electron–phonon
interactions can counterintuitively result in
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exceptional electronic transport. Beyond 2D
superatomic materials such as Re6Se8Cl2 and the
recently reported graphullerene (41), moiré su-
perlattices of 2D semiconductors may provide an
interesting testing ground for acoustic polarons.
Their superlattice potentials enable tuning elec-
tronic bands (42, 43) to achieve values of J down
to ~0. Combined with their strong deformation
potentials (44), these flat bands could yield
acoustic polarons with tunable transport prop-
erties across a large temperature range. Gen-
eralizing wavelike, ultralong-range electronic
energy flow in 2D materials could herald an
era of essentially lossless nanoelectronics.
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ACKN OWLED GMEN TS
We are grateful to P. Batail for bringing this family of materials to
our attention and for ensuing productive discussions. We also
thank L. E. Brus, X. Zhu, C. Nuckolls, and D. R. Reichman for
helpful discussions and D. Xu and J. Baxter for technical help with
measurements and analysis. Funding: This material is primarily
based on work supported by the National Science Foundation
(NSF) through the Columbia MRSEC on Precision-Assembled
Quantum Materials (PAQM) (DMR-2011738) (M.D., X.R., and
T.C.B.) and by the Air Force Office of Scientific Research (AFOSR)
under grant number FA9550-22-1-0389 (M.D. and X.R.).
stroboSCAT instrument development was supported by the NSF
under grant number DMR-2115625 (M.D.). M.D. acknowledges
support from the Arnold and Mabel Beckman Foundation through a
Beckman Young Investigator award. X.R. and J.Y. acknowledge
support from NSF CAREER Award DMR-1751949. J.A.T. was
supported by an NSF Graduate Research Fellowship. J.C.R. was
supported by a Department of Defense National Defense Science
and Engineering Graduate Fellowship. Author contributions:
J.A.T. and M.D. conceived of and designed the experiments. J.A.T.
performed, analyzed, and simulated stroboSCAT and spacetime
transient reflection experiments with assistance from A.C.S. J.Y.,
J.C.R., D.G.C., and X.R. synthesized and characterized Re6Se8Cl2
single crystals. J.Y. performed and analyzed heat capacity
measurements. J.A.T., M.E.R., J.Y., and H.S. prepared exfoliated
samples. P.S. and T.C.B. developed the theory and performed
density functional theory calculations and polaron dispersion
calculations. M.D. supervised the project. J.A.T., P.S., J.Y., X.R.,
T.C.B., and M.D. wrote the manuscript, with input from all authors.
Competing interests: The authors declare that they have no
competing interests. Data and materials availability: All data and
code necessary to reproduce the figures in the main text and
supplementary materials are available on Zenodo (45). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf2698
Materials and Methods
Supplementary Text
Figs. S1 to S17
Tables S1 to S3
References (46–71)
Movies S1 to S3
Submitted 11 October 2022; accepted 21 September 2023
10.1126/science.adf2698
Tulyagankhodjaev et al., Science 382, 438–442 (2023)
27 October 2023
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RES EARCH
2D MATERIALS
A quantum ruler for orbital magnetism in
moiré quantum matter
M. R. Slot1,2†, Y. Maximenko1,3†, P. M. Haney1, S. Kim1,4, D. T. Walkup1, E. Strelcov1,3, Son T. Le1,
E. M. Shih1,3, D. Yildiz1,4, S. R. Blankenship1, K. Watanabe5, T. Taniguchi6, Y. Barlas7, N. B. Zhitenev1,
F. Ghahari8*, J. A. Stroscio1*
For almost a century, magnetic oscillations have been a powerful “quantum ruler” for measuring
Fermi surface topology. In this study, we used Landau-level spectroscopy to unravel the energy-resolved
valley-contrasting orbital magnetism and large orbital magnetic susceptibility that contribute to the
energies of Landau levels of twisted double-bilayer graphene. These orbital magnetism effects led to
substantial deviations from the standard Onsager relation, which manifested as a breakdown in scaling
of Landau-level orbits. These substantial magnetic responses emerged from the nontrivial quantum
geometry of the electronic structure and the large length scale of the moiré lattice potential. Going beyond
traditional measurements, Landau-level spectroscopy performed with a scanning tunneling microscope
offers a complete quantum ruler that resolves the full energy dependence of orbital magnetic
properties in moiré quantum matter.
M oiré quantum matter (MQM) systems
(1) consist of stacked and twisted layers
of van der Waals materials and have
emerged as versatile condensed-matter
quantum simulators (2). The twist
angle, choice of material, number of layers, and
the application of electric and magnetic fields
provide a vast arena for realizing quantum
phases that result from the interplay between
electron correlations and topology. The dis-
covery of flat electronic bands that host super-
conductivity and correlated insulating states in
magic-angle twisted bilayer graphene (MATBG)
inspired rapid exploration of the parameter
space (3–5). The most recent endeavors have
focused on heterostructures of three, four, and
five layers of alternating twisted graphene
monolayers (6–11).
The moiré systems of MATBG and related
heterostructures support topological bands with
nonzero Chern number (4, 12), which is de-
rived from the Berry curvature of the Bloch
wave functions (13). Berry curvature is intimately
related to orbital magnetization, and indeed,
previous work on MATBG and related systems
has observed orbital magnetic order, valley Hall,
1Physical Measurement Laboratory, National Institute of
Standards and Technology, Gaithersburg, MD 20899, USA.
2Department of Physics, Georgetown University, Washington,
DC 20007, USA. 3Department of Chemistry and Biochemistry,
University of Maryland, College Park, MD 20742, USA.
4Joint Quantum Institute, Department of Physics,
University of Maryland, College Park, MD 20742, USA.
5Research Center for Functional Materials, National
Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki
305-0044, Japan. 6International Center for Materials
Nanoarchitectonics, National Institute for Materials Science,
1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan. 7Department
of Physics, University of Nevada, Reno, NV 89557, USA.
8Department of Physics and Astronomy, George Mason
University, Fairfax, VA 22030, USA.
*Corresponding author. Email: fghahari@gmu.edu (F.G.);
joseph.stroscio@nist.gov (J.A.S.)
†These authors contributed equally to this work.
and quantum anomalous Hall effects (14–16).
Berry curvature and the related quantum met-
ric also provide significant contributions to the
orbital magnetic susceptibility (17, 18). The
valley-contrasting orbital magnetism and or-
bital magnetic susceptibility play a central role
in the material response to applied magnetic
fields. Landau-level (LL) spectroscopy is a well-
established tool to experimentally deduce the
zero-field properties of the band structure,
and in this work, we expand its application
to extracting higher-order magnetic response
functions.
Semiclassically, LLs are described by the
Onsager relation, relating the extremal cross-
sectional area of the Fermi surface to the pe-
riod of oscillations in the de Haas–van Alphen
effect (19). The orbital magnetism and orbital
magnetic susceptibility give rise to energy-
dependent first- and second-order corrections
with magnetic field in the Onsager relation
(20), which was recently formulated as a
general expansion in higher-order response
functions (21). To determine these effects and
their full energy dependence, high-resolution
measurements of the LLs in the electronic
bands are required: a “quantum ruler” prob-
ing the evolution of LLs at all energies as a
function of displacement field and magnetic
field.
In this work, we used LL measurements as a
quantum ruler for twisted double-bilayer graph-
ene (TDBG) to quantitatively determine the
tunable electronic structure, energy-dependent
valley-contrasting orbital magnetism, and or-
bital magnetic susceptibility. TDBG is MQM
with highly reconfigurable bands; the Bernal
bilayer constituents have an electrostatically
tunable band structure in themselves (22–31).
Flat bands exist over a wide range of small
twist angles (q), from about 0.8° to 1.5°. Pre-
vious transport and scanning tunneling micros-
copy (STM) measurements have focused on
correlated states, which form at various partial
fillings (22–30), or density wave states at larger
twist angles of q ≈ 2.4° (31). Our intermediate
twist angle of 1.74° gives rise to moiré mini-
bands that are narrow but not extremely flat.
This slightly wider bandwidth allows LLs to be
resolved over the entire band structure, which
has not been observed in previous local probe
measurements (29).
Tuning the electronic structure of TDBG
Figure 1A shows the simulated band structure
of TDBG at q = 1.75° with the Bistritzer–
MacDonald (BM) continuum model (3). The
moiré periodic potential leads to narrow
moiré minibands, composed of two low-energy
bands—the valence V1 and conduction C1
bands—and higher remote energy bands—V2
and C2. The narrow bands V1 and C1 have a
bandwidth of about 50 meV and are isolated
from other bands (Fig. 1B). The TDBG system
displays a large tunability in its electronic
structure (12, 32–39). A perpendicular electric
field induces a potential difference between
the layers of TDBG, drastically altering the V1
band structure. The V1 band is relatively flat at
zero displacement field (D) (Fig. 1B) and de-
velops pronounced electron and hole pockets
at D ≠ 0 (Fig. 1C and fig. S8). In the next
section, we first describe the measurement
of this band structure evolution under a dis-
placement field.
Measurements were performed in a custom-
built dilution refrigerator–based scanning probe
system operating at 10 mK (40, 41). Figure 1D
shows the STM topograph of the TDBG sam-
ple used in this study (fig. S1). The measured
moiré periodicity of l = (8.1 ± 0.1) nm cor-
responds to a twist angle of q = (1.74° ± 0.02°),
and the local heterostrain was found to be
<0.1%, as determined from atomically resolved
spatial measurements (42). Scanning tunnel-
ing spectroscopy (STS) measures the differen-
tial tunneling conductance (dI/dV) signal, which
is proportional to the local density of states
(LDOS) (43). For TDBG, the measured dI/dV
reflects the LDOS of the topmost layer of the
four-layer system. The finite tip potential
leads to a fixed top gate VT, determined by the
contact-potential difference between probe
and sample. Varying the back-gate voltage VG
simultaneously tunes the displacement field
D and the carrier density n following D º
CGVG − CTVT and n º CGVG + CTVT, where
CG and VG are the back-gate capacitance and
voltage, and CT and VT are tip capacitance
and potential, respectively (42). We mapped
the differential tunneling conductance as a
function of sample bias VB, the displacement
field D, carrier density n, and magnetic field
B. Figure 1E shows the experimental LDOS
map at B = 0 T. The low-energy bands V1 and
C1 and remote bands V2 and C2 and their
Slot et al., Science 382, 81–87 (2023)
6 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
D
18.8
U = 0 meV
U = 0 meV
U = 80 meV
C2
C1
V1
V2
B
)
V
e
m
(
E
150
100
50
0
-50
-100
-150
C
)
V
e
m
(
E
150
100
50
0
-50
-100
-150
C2
C1
EF
V1
V2
hole pocket
C2
C1
EF
electron pocket
V1
V2
saddle point
g
k'
m
k
g
g
k'
m
k
g
Z (pm)
108.8
E
Experimental
dI/dV (nS)
2
4
B = 0 T
0
F
B = 0 T
0
1
Theory
LDOS (arb. units)
2
3
4
5
6
0.4
-
)
1
m
n
V
(
D
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
V1
C1
C2
0.2
saddle point
V2
V1
C1
0
n
/
n
0
-0.2
-0.4
-0.6
-
)
1
m
n
V
(
D
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
0.4
V1
C1
C2
0.2
saddle point
V2
V1
C1
0
n
/
n
0
-0.2
-0.4
-0.6
1 nm
10 nm
-100
-50
0
(mV)
V
B
50
100
-100
-50
0
E (meV)
50
100
Fig. 1. Tuning the narrow electronic bands in TDBG with displacement
field at q = 1.75°. (A) Energy-band structure of TDBG showing the four
low-energy bands computed by using a continuum model with interlayer
potential U = 0 meV and q = 1.75°. Line cuts from the energy bands in (A) along
Bloch wave vector kx = 0 for (B) U = 0 meV and (C) U = 80 meV. A dashed
horizontal line indicates the position of the Fermi level (EF), which moves through
the bands as the displacement field and carrier density are varied. The x-axis
labels (g, k′, m, and k) denote high-symmetry points in the mini-Brillouin
zone. (D) STM topographic image of the TDBG moiré pattern, with moiré
wavelength l = (8.1 ± 0.1) nm. (Inset) A magnified portion of the image
showing the atomic lattice of graphene. A twist angle of q = (1.74° ± 0.02°) was
determined from the atomically resolved moiré lattice (42). The red dot indicates
the ABBC symmetry position where the spectral maps with applied magnetic
field were acquired. Tunneling setpoint I = 20 pA; VB = 100 mV; temperature T =
0.01 K. (E) Tunneling spectral maps in the D versus VB plane for B = 0 T. n0 (–n0)
indicates the electron density at full filling of the C1 (V1) band. Setpoints:
I = 20 pA, VB = 120 mV, T = 0.01 K. (F) Corresponding theory map for B = 0 T
(continuum-model calculation). arb. units, arbitrary units.
evolution with displacement field are clearly
visible. The experimental data qualitatively
agree with the modeled LDOS of the top layer
of the four-layer graphene system obtained
with continuum-model calculations [Fig. 1F
(42)]. The calculations in this work are pre-
sented for qualitative comparison and are
not meant for quantitative comparison with
the experiment.
The trends in the dI/dV map can be quali-
tatively understood by considering how the
theoretically predicted bands in Fig. 1, B and C,
fill with n as the Fermi level is raised from
negative to positive energies while the bands
are modified by the displacement field D. At
negative displacement field approaching D = 0,
the Fermi level is initially pinned to the flat
portions of V1 with its associated high LDOS
(Fig. 1B). This appears in the spectral maps
(Fig. 1, E and F) with the high LDOS of the V1
band located near the Fermi level, correspond-
ing to zero sample bias. Above a displacement
field of 0.2 V/nm, the relatively flat C1 band
becomes pinned at the Fermi level, and the V1
band develops a larger dispersion while its
highest LDOS at its saddle point moves to
lower energies away from C1 with increasing
positive displacement field (Fig. 1C). This re-
sults in a bright spectral line associated with
the saddle point in the V1 band with a negative
slope in the top portion of the spectral maps in
Fig. 1, E and F.
Mapping Landau levels
Application of a magnetic field creates sharp
LLs in the dI/dV spectrum of all four bands, as
shown in the dI/dV maps at B = 4 T and 8 T in
Fig. 2, B and D, respectively (see figs. S11 to S13
for additional data sets). All dI/dV maps with
magnetic field are acquired on an ABBC site
(Fig. 1D, red dot). The experimental maps can
be compared with the theoretical maps in Fig. 2,
C and E, obtained from magnetic field–dependent
quantum mechanical calculations (42), follow-
ing the methods in (44). A series of LL spectra
at different displacement fields are extracted
from the experimental map at B = 4 T (Fig. 2A).
The LLs in the V1 band are clearly pronounced
and show that the LL energies are irregularly
spaced, showing neither the equal spacing char-
acteristic for a parabolic band nor the square
root dependence on orbital index as observed
in graphene. In the next section, we use the
evolution of the V1 LL spacing to experimentally
demonstrate the characteristics of the tunable
band.
The electron-like versus hole-like character
of a band is manifested in the energy variation
with LL index and magnetic field B. LLs orig-
inating from electron-like Fermi pockets in-
crease in energy with LL index and B, whereas
the opposite trend applies for hole-like LLs. The
saddle-point energy separates electron-like
from hole-like pockets. With this in mind, we
examined the experimental spectra of Fig. 2A.
At negative displacement field, a set of well-
resolved V1 LLs is clearly visible in the dI/dV
map at B = 4 T (Fig. 2B) and the corresponding
extracted spectra (Fig. 2A). We identified the
zeroth LL at the bottom of the V1 band, which
was at VB ≈ –45 mV for zero displacement
field. For a given displacement field in Fig. 2A,
the LL energy spacing in the V1 band is ob-
served to gradually decrease with increasing
bias voltage, followed by a gradual increase,
Slot et al., Science 382, 81–87 (2023)
6 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
V2
B = 4 T
V1
hole pocket
C1
B
B = 4 T
0
dI/dV (nS)
2
1
3
)
s
t
i
n
u
.
b
r
a
(
V
d
/
I
d
2.5
2
1.5
1
0.5
0
electron pocket
D = -0.05 V nm-1
D = -0.10 V nm-1
hole pocket
electron pocket
saddle point
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
)
1
-
m
n
V
(
D
C
)
n
/
n
0
1
-
m
n
V
(
D
B = 4 T
0
-0.2
LDOS (arb. units)
0.2
0.6
0.4
0.8
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0
(mV)
V
B
dI/dV (nS)
2
1
D = -0.15 V nm-1
-100
-50
D = -0.20 V nm-1
D = -0.25 V nm-1
electron pocket
hole pocket
B = 8 T
0
D
0.5
)
1
-
m
n
V
(
D
0.4
0.3
0.2
0.1
0
-0.1
-0.2
50
100
-100
-50
0
E (meV)
50
E
)
n
/
n
0
1
-
m
n
V
(
D
3
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
B = 8 T
0
-0.2
LDOS (arb. units)
0.2
0.6
0.4
0.8
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
0.4
0.2
0
-0.2
n
/
n
0
-0.4
-0.6
-0.8
100
0.4
0.2
0
-0.2
n
/
n
0
-0.4
-0.6
-0.8
100
-100
-50
0
50
-100
-50
V
B
(mV)
0
(mV)
V
B
50
100
-100
-50
0
E (meV)
50
Fig. 2. Tuning LLs in TDBG with displacement and magnetic fields.
(A) Tunneling spectra versus VB of TDBG at selected displacement fields
taken from the map in (B). Tunneling spectral map in the D versus VB plane
at (B) B = 4 T. (C) Corresponding theory map for B = 4 T (quantum
calculation). (D) Tunneling spectral map in the D versus VB plane at B = 8 T.
(E) Corresponding theory map for B = 8 T (quantum calculation) (42).
The maps in (B) and (D) were acquired on the maxima positions in the
moiré structure indicated by the red dot in Fig. 1D. Setpoints: I = 20 pA,
VB = 120 mV for (B) and (D), T = 0.01 K. See figs. S11 to S13 for additional
spectral map data.
pointing to a transition from an electron-like
to a hole-like pocket through a saddle point.
The LL spacing is inversely proportional to
the LDOS, which peaks at the Van Hove sin-
gularity at the saddle point. The saddle point
is pinned at the Fermi level for negative carrier
densities and visible as the high LDOS cross-
ing through the V1 band at positive densities
(Fig. 2, B and D).
We used the B-field dependence of the LLs
to confirm the nature of the tunable band struc-
ture. Figure 3, A to C, displays dI/dV maps in
the B versus VB planes at a fixed displacement
field, showing the dispersion of the LLs with
B in the V1 band. At negative displacement
fields (Fig. 3, B and C), the LLs below the
saddle point at the Fermi level disperse with
positive slope, and those above the saddle
point disperse with negative slope. This con-
firms the electron versus hole-pocket nature
of the V1 band. The transition from electron
to hole pocket in the V1 band is similar at
positive displacement fields, where increasing
displacement fields tunes the V1 saddle point
to lower energies (Fig. 3A). At D = 0.35 V nm–1
(Fig. 3A), the saddle point is tuned to the mid-
dle of the band with an equal number of posi-
tive and negative dispersing LLs on either side,
which demonstrates the well-determined tun-
ability of electron and hole pockets with dis-
placement field.
Deviations from the Onsager relation
We now zoom in on the detailed features in
the V1 band, leveraging LL spectroscopy to
extract quantitative information about the
zero-field material properties involving valley-
contrasting orbital magnetism and orbital mag-
netic susceptibility. Figure 3D shows extracted,
well-resolved spectra at selected B fields. In
Fig. 3E, we show the corresponding peak po-
sitions of the LLs in the V1 band versus B for
n = 0 to 7, which shows how the LLs disperse
with magnetic field. LLs are semiclassically
described by Onsager’s quantization condition,
which requires that the total phase accumula-
tion over a cyclotron orbit be an integer mul-
tiple of 2p (19). This yields
S Enð
Þf
0
=2p ¼ 2pBn n þ 1=2
ð
Þ
ð1Þ
relating the k-space area S(En) of the zero-field
iso-energy contour of the nth LL En to the
magnetic field Bn, where f0 = h/e is the mag-
netic flux quantum, h is Planck’s constant,
½
and e is the elementary charge. With the equal-
energy k-space area scaling as Bn(n + 1/2)
for all LLs at energy En, a plot of Sº Bn n þð
1=2Þ(cid:2)
n¼0;1;2… versus LL energy for all LLs would
collapse onto a single curve. From Fig. 3E, we
plot Sº½Bnðn þ 1=2Þ(cid:2)
n¼0…7 in Fig. 3F. The fact
that experimental data points fail to collapse
onto a single curve demonstrates the in-
adequacy of the Onsager relation and the need
for higher-order corrections.
Recently, a systematic expansion of the semi-
classical Onsager relation described in Eq. 1 was
derived by adding corrections in terms of
powers of B (21):
Bn n þ 1=2
ð
m′ Enð
Þ=f0 ¼ S Enð
ÞB2
n
Þ=4p2 þ
=2 þ …
ÞBn þ c′ Enð
ð2Þ
The coefficients of the first- and second-order
correction, m′(E) and c′(E), are the derivatives
with respect to energy of the total orbital mag-
netic moment and orbital magnetic susceptibil-
ity, respectively. Eq. 2 is thus a powerful tool to
either infer the zero-field material properties
S(E), m′(E), and c′(E) from a given LL spec-
trum, or to predict the detailed LL spectrum
given the knowledge of the zero-field material
properties. In the next section, we extract these
properties for TDBG from the LL spectrum
Slot et al., Science 382, 81–87 (2023)
6 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
electron pocket
saddle point
hole pocket
D = 0.35 V nm-1
A
)
T
(
B
8
6
4
D
-60
-40
-20
V
B
20
0
(mV)
40
60
saddle point
electron pocket
hole pocket
D = -0.05 V nm-1
B
)
T
(
B
8
6
4
-60
-40
-20
V
B
20
0
(mV)
40
60
saddle point
hole pocket
D = -0.10 V nm-1
electron pocket
C
)
T
(
B
8
6
4
-60
-40
-20
V
B
20
0
(mV)
40
60
D
)
s
t
i
n
u
.
b
r
a
(
V
d
/
I
d
2
1
0
-100
LL0
LL0
V1 band
LL0
D = -0.05 V nm-1
B = 8 T
B = 6 T
B = 4 T
-50
0
B (mV)
V
50
100
D = -0.05 V nm-1
E
)
T
(
B
12
10
8
6
4
LL0
2
-50
LL1 LL2 LL3
-40
-30
V
-20
B (mV)
-10
0
n=0
n=1
n=2
n=3
n=4
n=5
n=6
n=7
D = -0.05 V nm-1
0.4
F
0.35
)
2
-
m
n
(
S
0.3
0.25
0.2
0.15
0.1
0.05
low
dI/dV (arb. units)
high
0
-50
-40
S(E) to 0th Order
-30
-20
E (meV)
-10
0
Fig. 3. Breakdown of the standard Onsager relation in TDBG. Spectral maps in the B versus VB
plane for displacement fields of (A) D = 0.35 V nm–1, (B) D = –0.05 V nm–1, and (C) D = –0.1 V nm–1
showing the dispersion of the electron and hole-pocket LLs with magnetic field, and the shift of
the V1 saddle point to lower energies with increasing displacement field. (D) Tunneling spectra
versus VB of TDBG as a function of magnetic field at fixed D = –0.05 V nm–1. (E) LL peak positions
versus B for D = –0.05 V nm–1. Data from LLs n = 0 to n = 8 are shown. Symbols, experimental
peak positions; solid lines, cubic-spline interpolation of experimental peak positions. (F) S(E)
computed from the solid lines in (E) with Eq. 1. The lack of data collapse indicates that second-order
contributions to the LL energies are substantial.
and show a large contribution of c′(E ) for
moiré systems that scale with an increase in
moiré lattice constant.
Extracting zero-field properties
The first-order correction m′(E) includes con-
tributions from the total Berry curvature en-
closed by an equal energy contour (Fig. 4, A
and B), which yields the well-known Berry
phase correction, and the average orbital mag-
netic moment per carrier at energy E (21, 45).
The calculated Berry curvature W for the V1 band
is represented by a hue in the mini-Brillouin
zone for each valley K and K′ in the Brillouin
zone in Fig. 4, A and B, respectively. The
valleys have equal and opposite Berry curva-
ture and orbital moment. By symmetry, the
total intravalley orbital magnetic moment is
finite only at nonzero displacement field. This
tunability of the valley-contrasting orbital mag-
netism enables the disentangling of the orbital
susceptibility from the orbital magnetic moment,
which we use in the analysis of the LLs below.
The strength of these contributions in Eq. 2
can be evaluated by using the continuum model.
Figure 4C shows the terms on the right side of
Eq. 2 for LL0, calculated with the zero-field
continuum model and multiplied by f0/B to
obtain the phase contribution in the extended
Onsager relation in Eq. 2 (see fig. S5 for all
phase contributions). We note that these phase
terms are energy dependent and are large in
TDBG; for comparison, a value of 0.5 would be
equivalent to the p Berry phase in single-layer
graphene. The sign of the orbital moment and
its derivative m′(E) is opposite for the K and K′
valleys, as expected from the valley-contrasting
Berry curvature shown in Fig. 4, A and B.
Figure 4D shows how the phase contribu-
tions displayed in Fig. 4C drastically alter the
semiclassical LL spectrum. The semiclassical,
zeroth-order LL spectrum (Eq. 1) is displayed
in blue for the lowest LLs in the V1 band by
using S(E) obtained from the zero-field contin-
uum model. The first-order correction m′(E )
leads to a valley splitting of the LLs indicated
by the dashed red and black lines. The calcu-
lated valley splitting at the bottom of the V1
band is substantial but within the LL spacing,
where the LL index can be assigned unambig-
uously. This makes LL0 ideally suitable to de-
termine the experimental valley splitting from
our high-resolution measurements.
High-resolution dI/dV spectra of LL0 at
increasing magnetic fields 9 to 13 T at D =
–0.25 V/nm are shown in Fig. 4E. We observed
a clear experimental splitting, with the red lines
indicating the fitted peak positions. At 13 T, the
LL0 peak is very broad owing to many levels
forming from the Hofstadter spectrum at high
magnetic fields. We present a comparison to
the spectrum computed quantum mechanically
in Fig. 4F (gray peaks) to show the onset of
Hofstadter minibands at higher fields. The
values of splitting obtained with semiclassical
calculations are similar (Fig. 4D). Using an
energy broadening comparable to the experi-
ment, shown as the black curve, we obtained
qualitative agreement with the experiment.
Figure 4G shows a direct comparison of the
experimental LL0 splitting in Fig. 4E (blue
data points) with the quantum mechanical
calculations in Fig. 4F (open orange circles) as
a function of B field. We found semiquanti-
tative agreement between the calculated and
measured valley-splitting values, demonstrat-
ing the tunable valley-contrasting orbital mag-
netism present in TDBG. Most notably, the
splitting was much larger than the standard
Zeeman effect with Landé g factor of 2 (solid
black line) and did not increase linearly with
B field as one would expect for a Zeeman-
type splitting mechanism. The latter indicates
that the splitting is not only given by m′(B),
but rather, a considerable nonzero second-
order correction c′ leads to nonlinearity in the
splitting with B. We obtained an estimate of
m′ in the middle of the V1 band of ≈ 3.5 × 1013
Slot et al., Science 382, 81–87 (2023)
6 October 2023
4 of 7
RES EARCH | R E S E A R C H A R T I C L E
A
K Valley U = -40 meV
k’
k
m
orb
B
K’ Valley U = -40 meV
k’
m
orb
k
Quantum K
Quantum K'
0th order
1st order K
1st order K'
1st+2nd order K
1st+2nd order K'
D
12
10
)
T
(
B
8
6
4
2
E
)
s
t
i
n
u
.
b
r
a
(
V
d
/
I
d
13 T
12 T
11 T
10 T
9 T
-20
-10
(mV)
V
B
0
F
)
s
t
i
n
u
.
b
r
a
(
S
O
D
L
13 T
12 T
11 T
10 T
9 T
G
)
V
e
m
(
g
n
i
t
t
i
l
p
s
0
L
L
5.5
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
C
n
o
i
t
u
b
i
r
t
n
o
C
e
s
a
h
P
0.2
0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.25
-0.3
-45
-40
-35
-30
-25
-20
E (meV)
quantum U = -40 meV
experiment D = -0.25 V nm-1
Zeeman g = 2.0
Zeeman g = 6.5
-40
-35
E (meV)
-30
-40
-30
E (meV)
-20
0
0
5
10
15
B (T)
Fig. 4. LL splitting originating from valley-contrasting orbital magnetism
and Berry curvature in TDBG. Calculated three-dimensional plot of the V1
band with Berry curvature shading at U = –40 meV for (A) K and (B) K′ valleys. K
and K′ valleys have equal and opposite nonzero Berry curvature and equal and
opposite orbital magnetic moment (orbital moments depicted schematically). Eb is
the D-dependent energy of the bottom of the V1 band. (C) A comparison of the
calculated first- (m′) and second-order (c′) correction magnitude with the extended
Onsager relation for the V1 TDBG band (U = –40 meV). See fig. S5 and S6 for
additional phase contribution results (42). (D) Calculation of the first few LLs (n = 0,
1, and 2) versus B, comparing quantum mechanical to semiclassical methods with
zeroth-, first-, and second-order corrections. The first-order correction is grossly
deficient in matching the quantum results, particularly in the n = 0 level, whereas
including both first- and second-order corrections provides a good agreement
with the quantum results (U = –40 meV). (E) Tunneling spectra of the LL0 peak as a
function of B for D = –0.25 V nm–1 that show a splitting of the LLs in high magnetic
fields. The red lines indicate peak positions determined from nonlinear least-square
fitting of a double Lorentzian function to LL0. (F) Quantum calculation of LL0 as a
function of magnetic field for an interlayer potential U = –40 meV, corresponding to
a displacement field of D = –0.25 V nm–1. The LL shows a valley splitting upon
application of a displacement field. The solid black lines have a Gaussian energy
broadening of s = 1 meV to match experiment; gray lines, s = 0.05 meV. (G) The
energy difference of the split n = 0 LL from (E) compared with quantum calculations
in (F). For the quantum calculation in higher fields, we plot the splitting as the
difference in energy between lowest levels in the Hofstadter bands of the K and K′
valleys. The uncertainty in the experimental points is derived from twice the
standard deviation obtained from the nonlinear least-square fits of the peaks in (E).
For comparison, the solid lines show the calculated Zeeman splitting with
Landé g factor of (black) g = 2 and (red) 6.5.
C/(J s), comparable to a calculated estimate
of ≈ 4.4 × 1013 C/(J s), using the values for the
splitting, S′(E) and c′(E), extracted from the ex-
periment (42).
The first-order correction m′ does not ex-
plain the lack of collapse of the LLs onto a
single curve. This is the result of a strong,
experimentally observable second-order cor-
rection, given by the energy-dependent orbital
magnetic susceptibility c′(E). This contribu-
tion originates from several mechanisms, as elu-
cidated in recent theoretical works (18, 46, 47),
including the geometrical origin, namely the
Berry curvature and quantum metric (48). The
calculated c′(E) of TDBG has the same sign for
both the K and K′ valley, as shown for LL0 in
Fig. 4C. This results in a shift of the valley-split
LLs, quadratically increasing with B field,
as shown by the black and red solid lines in
the continuum-model calculation in Fig. 4D.
This fully expanded semiclassical approxi-
mation with first- and second-order correction
(Eq. 2) agrees well with the quantum me-
chanical spectrum obtained for the same
system (red and black open circles), again
emphasizing the importance of the second-
order correction to adequately describe the
system. For a large region of energies and mag-
netic fields, the second-order correction is
larger than the first one (Fig. 4, C and D, and
fig. S6). This means that the energy-dependence
of the magnetic field–induced orbital moment
exceeds the displacement field–induced orbi-
tal moment.
To extract the second-order correction to
the LL energy, we note that the first-order split-
ting is typically not visually evident for most
electron-like LLs in the V1 band at smaller
displacement fields owing to smaller valley
splitting from orbital magnetism, and pre-
sumably, to broadening. The energy value of
a single LL peak is then approximately the
average of the valley-split values. The valley-
averaged energy at a fixed displacement field
is obtained from Eq. 2 by letting m′(E ) = 0,
keeping only the second-order correction. For
equal energy LLs n and m with associated
fields Bn and Bm, Eq. 2 yields the following
for S and c′:
S Eð Þ ¼
2pe
h
BnBm
ð
"
Bm n þ 1=2
B2
m
(cid:1)
Þ (cid:3) Bn m þ 1=2
ð
Þ
(cid:3)
(cid:3) B2
n
#
c′ Eð Þ ¼
e
ph
ð
"
Þ (cid:3) Bm m þ 1=2
Bn n þ 1=2
ð
(cid:3)
(cid:1)
B2
n
(cid:3) B2
m
ð3Þ
#
Þ
ð4Þ
Figure 5A shows the average values of S(E)
obtained by evaluating Eq. 3 for all pairs of LLs
in Fig. 3E at each energy value. By contrast
to Fig. 3F, S(E ) collapses onto a single curve
(blue data points) in Fig. 5A, confirming the
Slot et al., Science 382, 81–87 (2023)
6 October 2023
5 of 7
RES EARCH | R E S E A R C H A R T I C L E
experiment
D = -0.05 V nm-2
theory U = -8 meV
S(E) to 2nd Order
A
0.4
)
2
-
m
n
(
S
0.35
0.3
0.25
0.2
0.15
0.1
0.05
B
10
5
0
-5
-10
-15
experiment
D = -0.05 V nm-2
theory U = -8 meV
0
-50
-40
-30
-20
E (meV)
-10
0
10
-20
-40
-30
-20
-10
0
10
E (meV)
Fig. 5. Extraction of enhanced energy-dependent orbital magnetic susceptibility in moiré quantum
matter from the extended Onsager relation. (A) The symbols represent S(E) computed from the solid
lines in Fig. 3E with Eq. 3, demonstrating data collapse onto one continuous curve. The solid line
represents S(E) computed for the V1 band from continuum-model calculations. (B) The symbols represent
c′(E) computed from the solid lines in Fig. 3E with Eq. 4. The solid line represents c′(E) computed from
continuum-model calculations. See (42) for a discussion of the error analysis.
applicability of the second-order correction.
The result has a similar trend to that of the
zero-field continuum-model calculation of S(E)
(orange solid line).
Similarly, we obtained the average value of
c′(E) by evaluating Eq. 4 (blue data points in
Fig. 5B). The experimentally extracted values
are in qualitative agreement with the zero-
field orbital magnetic susceptibility (orange
line), computed with the continuum model
according to the formalism of (49). The un-
certainty in the extracted c′(E ) and the de-
viation in overlap of segments from different
pairs of LLs are attributed to two factors. First,
corrections to Landau quantization energies
have a smaller impact on the high-index LLs
located at higher energies (50). Extracting the
relatively smaller corrections at these energies
therefore leads to larger uncertainty. Second,
variations of the chemical potential with mag-
netic field shift the LL energy positions, espe-
cially at high magnetic fields (42). We do not
believe interactions make a qualitative impact
on our analysis. The LL scaling obtained with
the extended Onsager relation is highly con-
strained, and we find it is well satisfied over
a wide range of electron filling. Presumably,
interactions would renormalize LL energies in
a distinct manner, which would depend strongly
on filling factor.
Discussion and outlook
There are several distinct microscopic mecha-
nisms that underlie the orbital magnetic suscep-
tibility, including recently identified geometric
contributions (18, 46). In fig. S9, we show the
contributions to c′(E) from these mechanisms
[see (42) for the full breakdown]. The contri-
butions from the Pauli paramagnetism and
the quantum geometry involve the orbital mag-
netic moment, Berry curvature, and quantum
metric. These mechanisms make the domi-
nant contribution to c′(E ) near the top of V1
and bottom of C1 bands, where the Berry cur-
vature is peaked (Fig. 4, A and B). The con-
tributions from the van Vleck paramagnetism
and k-space energy polarization are dominant
in the middle of the V1 band, whereas the well-
known Landau-Peierls susceptibility is sub-
stantial at the band edges.
We attribute the large value of c′(E) to the
large lattice constant a of the moiré potential.
This can be roughly understood with dimen-
sional analysis: for a single band model, the
total orbital magnetic susceptibility c general-
ly scales as Wa2, where W is the bandwidth,
so that the derivative of c with respect to
energy then scales as a2, which can be large for
moiré quantum systems. For a more in-depth
analysis, see fig. S10, A and B, which shows
that the maximum value of c′ increases dra-
matically with increasing moiré wavelength,
indicating that future measurements of orbi-
tal magnetism should be even more observable
at larger wavelengths.
MQM holds great opportunities for efficient
magnetization control, topological transport
phenomena, the quantum anomalous Hall
effect, and technological applications in mag-
netoelectric, magneto-optics, and topological
spintronics. Understanding the underlying band
topology and magnetic response functions
are the key metrological capability required
to practically harness all these opportunities.
Our measurements and analysis point a way
forward to this goal.
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RES EARCH | R E S E A R C H A R T I C L E
ACKN OW LEDG MEN TS
We thank F. J. Giessibl for providing the qPlus AFM sensors and
general advice on AFM measurements. Funding: University of
Maryland and the National Institute of Standards and Technology
(NIST) PREP program grant no. 70NANB18H165 (Y.M., E.M.S., and
E.S.); Georgetown University and NIST PREP program grant no.
70NANB18H161 (M.R.S.); University of Maryland and NIST Joint
Quantum Institute grant no. 70NANB21H126 (S.K. and D.Y.); Office
of Naval Research grant no. N00014-20-1-2352 (S.K. and D.Y.);
Japan Society for the Promotion of Science KAKENHI grant
nos. 19H05790, 20H00354, and 21H05233 (T.T. and K.W.);
Dutch Research Council (NWO) through Rubicon grant no.
019.193EN.026 (M.R.S.); University of Reno start-up grant no.
PG19012 (Y.B.). Author contributions: Conceptualization: F.G.,
P.M.H., J.A.S., and N.B.Z.; Methodology: P.M.H. and Y.B.;
Investigation: M.R.S., Y.M., S.K., D.T.W., E.S., S.T.L., E.M.S., D.Y.,
S.R.B., and F.G.; Visualization: Y.M., M.R.S., P.M.H., and J.A.S.;
Project administration: J.A.S.; Supervision: J.A.S. and N.B.Z.;
Resources: K.W. and T.T.; Software: P.M.H., Y.B., M.R.S., Y.M., S.K.,
D.T.W., and J.A.S.; Writing – original draft: M.R.S., Y.M., P.M.H.,
N.B.Z., F.G., and J.A.S.; Writing – review and editing: M.R.S., Y.M.,
P.M.H., S.K., D.T.W., E.S., S.T.L., E.M.S., D.Y., S.R.B., K.W., T.T.,
T.B., N.B.Z., F.G., and J.A.S. Competing interests: The authors
declare that they have no competing interests. Data and
materials availability: The data from this study and the code used
to generate theoretical results in this study are available at
the George Mason University Dataverse (51). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf2040
Materials and Methods
Supplementary Text
Figs. S1 to S13
References (52–56)
Submitted 5 October 2022; resubmitted 1 March 2023
Accepted 30 August 2023
10.1126/science.adf2040
Slot et al., Science 382, 81–87 (2023)
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RES EARCH
3D PRINTING
A silicone-based support material eliminates interfacial
instabilities in 3D silicone printing
Senthilkumar Duraivel1, Dimitri Laurent2, Didier A. Rajon2, Georg M. Scheutz3, Abhishek M. Shetty4,
Brent S. Sumerlin3, Scott A. Banks5, Frank J. Bova2, Thomas E. Angelini1,5,6*
Among the diverse areas of 3D printing, high-quality silicone printing is one of the least available
and most restrictive. However, silicone-based components are integral to numerous advanced
technologies and everyday consumer products. We developed a silicone 3D printing technique that
produces precise, accurate, strong, and functional structures made from several commercially available
silicone formulations. To achieve this level of performance, we developed a support material made from a
silicone oil emulsion. This material exhibits negligible interfacial tension against silicone-based inks, eliminating
the disruptive forces that often drive printed silicone features to deform and break apart. The versatility
of this approach enables the use of established silicone formulations in fabricating complex structures
and features as small as 8 micrometers in diameter.
S ilicone elastomer’s resistance to heat,
chemical agents, weathering, ozone,
moisture, and ultraviolet (UV) irradia-
tion makes it critical for manufacturing
countless products, including electronic
devices, automobiles, aircraft, and medical de-
vices (1). Silicone elastomers have been used in
medical devices for many years (2), and their
applications include embedded sensors (3),
flexible electronics (4), soft robotics (5), and
additive manufacturing (6). Silicone structures
can be fabricated by using conventional tech-
niques such as molding, or advanced techniques
such as soft lithography and 3D printing (7–9).
However, 3D printing with silicone generally
results in low-quality products because of chal-
lenges created by the interfacial behaviors of
silicone pre-elastomer in its liquid state. These
challenges can be partially addressed by using
an embedding support material that flows
around the translating printing nozzles while
trapping deposited inks in space, providing
stability to printed structures (10–14). How-
ever, even under such stabilizing conditions,
the interfacial tension between printed inks
and their support media drives the deforma-
tion and breakup of printed structures before
they solidify (Fig. 1, A and B) (9, 15). Modifying
silicone inks with additives can stabilize 3D
printed structures (16, 17), yet a versatile ap-
proach to additive manufacturing with un-
modified silicone inks remains elusive. One
1Department of Materials Science and Engineering, University
of Florida, Gainesville, FL 32603, USA. 2Department of
Neurosurgery, University of Florida College of Medicine,
Gainesville, FL 32608, USA. 3George and Josephine Butler
Polymer Research Laboratory, Center for Macromolecular
Science and Engineering, Department of Chemistry,
University of Florida, Gainesville, FL 32611, USA. 4Advanced
Technical Center, Anton Paar USA, Ashland, VA 23005, USA.
5Department of Mechanical and Aerospace Engineering,
University of Florida, Gainesville, FL 32611, USA. 6J. Crayton
Pruitt Family Department of Biomedical Engineering,
University of Florida, Gainesville, FL 32611, USA.
*Corresponding author. Email: t.e.angelini@ufl.edu
route to achieving high-quality 3D silicone
printing without ink modification is to elim-
inate the disruptive role of interfacial tension
by using support materials that are chemically
similar to the printed inks they stabilize (Fig.
1C). Thus, there is a critical need to develop
support materials that are chemically similar
to poly(dimethylsiloxane) (PDMS) inks.
We describe a method for 3D printing pre-
cise, intricately detailed structures made from
PDMS that makes use of a support material ex-
hibiting negligible interfacial tension when in
contact with silicone inks. We call this method
additive manufacturing at ultralow interfacial
tension (AMULIT). The AMULIT support mate-
rial is a packed inverse emulsion composed of
aqueous droplets in a continuum of silicone
oil. The ultralow interfacial tension between
the AMULIT support material and PDMS inks
enabled us to print features with diameters as
small as 8 mm. We achieved high-performance
printing by tuning the elasticity and flow
properties of this support material, which
allowed us to fabricate complicated shapes
such as brain aneurysm models and func-
tional trileaflet heart valves. We demonstrated
that the AMULIT technique does not require
specialized inks by using several different com-
mercially available PDMS formulations to print
various structures. With mechanical testing,
we found that 3D printed structures produced
by using AMULIT were more extensible than
their molded counterparts and equally robust.
We also found that these structures have a
smooth surface finish at the macroscale and
microscale roughness, which is facilitated by
the low interfacial tension between PDMS inks
and the AMULIT support medium. Our results
show that the AMULIT 3D printing technique
could be used to fabricate intricate silicone
structures for biomaterial design and surgical
simulators, and they introduce the possibility
of expanding the method for printing with
other materials.
Results
Formulation and testing of AMULIT
support material
To formulate an AMULIT support medium
for 3D printing with PDMS inks, we prepared
inverse emulsions in which silicone oil was the
continuous phase and varied the aqueous drop-
let packing fraction, f, and the average drop-
let radius, a, between samples; f and a can be
tuned independently to determine an emul-
sion’s rheological properties and its corre-
sponding performance as a printing support
medium (18). We expected a to strongly influ-
ence the printed feature roughness because
the material interfaces will not spontaneously
flatten under conditions of ultralow interfacial
tension. Thus, we formulated small emulsion
droplets and chose f on the basis of the emul-
sions’ rheological properties (fig. S1). The elastic
shear modulus, G′, and yield stress, sy, of each
formulation, were measured with rheological
tests (materials and methods and fig. S2). For
AMULIT printing, we chose an emulsion having
sy = 9 Pa and G′ = 320 Pa; the emulsion with
these properties is weak enough to flow around
a translating printing needle yet strong enough
to support complex 3D printed structures
(9, 10). For this formulation, we estimated the
Reynolds number near the translating nozzle
during a typical print to be 10−6 to 10−2, which
indicates that irregular flow patterns should
be suppressed (supplementary text). For all
formulations, we found that emulsions made
from pure water droplets in silicone oil were
extremely cloudy and inhibited visualizing the
printing process. To make optically clear emul-
sions, we matched the refractive indices of the
two phases by adding glycerol to the droplets,
which allowed the 3D printing process to be
imaged at the macroscale with photography
and at the microscale with confocal fluores-
cence microscopy (CFM) (Fig. 1, D to G, and
fig S3).
To test the role of interfacial tension in em-
bedded 3D printing, we compared the perform-
ance of the AMULIT support medium with
an all-aqueous support medium made from
packed hydrogel microparticles swollen in
water. In both cases, we 3D printed features
made from a fluorescent PDMS liquid and
imaged the ink-support interfaces using CFM
(materials and methods). We formulated the
packed microgels to have sy = 10 Pa and G′ =
550 Pa, values comparable to those of the
AMULIT material. Examining the 3D fluores-
cence images, we found that printed silicone
features broke up and formed spherical drop-
lets within the aqueous support. When a liquid
ink is printed into a packed granular support
medium, the smallest stable feature has a
diameter given by dmin ≈ 2g/sy, where g is
the interfacial tension between the ink and
the support medium (15). For the aqueous
medium, g = 25 mN/m, so dmin was ≈5 mm,
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Fig. 1. Interfacial tension drives feature breakup in embedded 3D printing.
(A) High interfacial tension between aqueous support materials and silicone inks
destabilizes 3D printed features, driving them to break into spherical droplets.
(B) Intermediate interfacial tension between organic support materials and
silicone inks provides some stability but limits minimum stable feature size.
(C) Ultralow interfacial tension between silicone oil–based support materials and
silicone inks eliminates interfacial instabilities, removing the limits on minimum
stable feature size. (D) CFM image showing silicone-based inks (green) that
break into droplets when printed into support materials made from aqueous
microgels (red). (E) A droplet digitally isolated from the support and examined
from different angles. The droplet appears nearly spherical and exhibits a smooth
surface. (F) By contrast, the silicone-based ink (green) remains continuous
and retains its shape indefinitely after printing into a silicone-based support material
(red). (G) When viewed from different angles, the printed features exhibit roughness
with a characteristic length scale of the microparticles composing the support
material, facilitated by ultralow interfacial tension.
50 times the 100-mm diameter of the printed
feature (Fig. 1, D and E). Thus, the breakup of
the feature into droplets was expected. By con-
trast, the 100-mm diameter silicone feature
printed into the AMULIT support material re-
mained intact, indicating that g < 0.5 mN/m.
To better estimate g between a PDMS ink and
the AMULIT support medium, we performed
a series of test prints in which dmin was mea-
sured for multiple values of sy, finding that
g ≈ 0.08 mN/m (fig. S4). We also observed
that the characteristic roughness length scale
at the feature surface was about one order
of magnitude smaller than the feature di-
ameter, from which we would estimate g ≈
0.05 mN/m. These results indicate that the
AMULIT approach can potentially achieve
features 300 to 500 times smaller than those
achievable when printing PDMS into an aque-
ous support medium having the same material
properties.
Complex device fabrication using the
AMULIT technique
The improvement in complexity, quality, and
functionality of PDMS vessel models traced
in the published literature parallels a decrease
in interfacial tension of silicone inks against
their embedding materials. For example, hy-
drocarbon support materials (9) improved on
aqueous support materials (19). As a first test of
the AMULIT method’s capabilities, we printed
a model brain aneurysm; models with accu-
rate vasculature are needed for improved
patient simulators to train neurosurgeons in
cerebrovascular procedures. Current simulated
tissues provide unrealistic tactile feedback,
lack small-diameter intracranial angioarchi-
tecture, and often exclude the aortic arch and
extracranial vascular anatomy that determine
which catheters and instruments are used in
each procedure (20, 21).
To create a model, we collected a 3D an-
giogram of a patient’s brain aneurysm using
x-ray computed tomography (XRCT). The 3D
scan was segmented and processed to create
a series of 3D printing trajectories (Fig. 2A
and materials and methods). We used Gelest
ExSil 100 silicone pre-elastomer, which can be
formulated to have material properties that
mimic a wide range of tissues. A snapshot
from a video of the printing process demon-
strates how the translating needle flows easily
through the jammed emulsion, which traps
the deposited silicone in place (Fig. 2B and
movie S1). The printed structure was cured
at 60°C for 24 hours and then imaged with
XRCT (Fig. 2C). Horizontal and vertical slices
through the 3D scan revealed that the highly
branched, complex printed network of vessels
is hollow, with an average wall thickness of
≈400 mm (Fig. 2D and movie S2). The CT
scan of the printed structure was used to
create a 3D model for quantitative comparison
with the original angiogram. The registration
between the patient-derived model and the
printed model is excellent; 68% of the printed-
surface locations lie within 500 mm of their
programmed locations, and 95% lie within
1 mm (Fig. 2, E and F).
Our ability to accurately model brain vascu-
lature raises the question of whether such fine
structures can be manufactured to be both
highly compliant and physically robust. The
artificial aortic heart valve belongs to a class
of devices with such requirements. Native
aortic heart valves are subject to dynamic
mechanical loads during the cardiac cycle (22).
Prosthetic replacement is widely used to treat
aortic valve failure, yet the predominantly
used mechanical valves and allogeneic- or
xenogeneic-tissue valve replacements often
result in mechanical failure, hemolysis, blood
coagulation, or structural degradation due to
calcification. A potential alternative is an arti-
ficial silicone valve prosthesis; silicone is es-
tablished in vascular applications because of
its hemocompatibility and durability (22–27).
The AMULIT 3D printing method can be used
to replicate the intricate semilunar shape of
the thin aortic leaflets in manufactured sili-
cone valves. We designed a model heart valve
based on physiologically representative dimen-
sions of the different valve components (Fig. 2,
G and H, and fig. S5) (28). We used a UV-
curable silicone formulation, Silopren UV
Electro-225-1 (Momentive), as the ink and
printed it into the AMULIT material (Fig. 2I).
To create highly flexible leaflets, we printed
the structure by translating the needle tip at
a speed of 2 mm/s and depositing material at a
rate of 125 mL/hour, producing features ≈150 mm
in diameter. Correspondingly, we chose a layer
spacing of 100 mm for good layer adhesion.
The printed model was then UV cured, re-
moved from the AMULIT material, washed
with detergent, and rinsed in deionized water
(materials and methods). The cured part had a
final wall thickness of ≈250 mm. Despite having
very thin, flexible walls, the model valves were
physically robust enough to connect to pipe
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Fig. 2. AMULIT printing of brain aneurysm and aortic heart valve models.
(A) Brain aneurysm models for surgical simulations comprise complex, intercon-
nected, hollow tubes with intricate details. (B) Photograph of the aneurysm model
being printed into the AMULIT material. (C) CT imaging of the 3D printed model
within the printing container shows the complexity of the printed aneurysm.
(D) Slices through the CT scan show that the printed structure exhibits the hollow
channels of the patients’ neurovasculature. (E and F) The printed structure overlays
well with the patient’s neurovasculature, and quantitative error analysis demon-
strates agreement between the two (±1 mm error range corresponds to 95% of all
points). (G and H) A model tricuspid aortic heart valve designed by using the
geometric measurements of the native heart valve. (I) A silicone heart valve model
printed in a single seamless trajectory with a wall thickness of 250 mm within
the AMULIT support medium and cured under a UV lamp. (J and K) Once cured
and washed, the valve model is robust enough to be coupled with a water supply,
simulating transvalvular flow of the cardiac cycle. The thin leaflets of the valve are
observed to open and close during the systolic and diastolic flow of the simulation.
explore how well d can be predicted with the
AMULIT technique, we printed a series of
linear features using the Smooth-On Mold
Max 10 PDMS formulation at different com-
binations of n and Q and then measured d
(Fig. 3A and materials and methods).We pre-
dicted the relationship between d, Q, and n,
given by p (d/2)2 = Q/n, according to basic
fluid continuity. Performing many experi-
ments at different combinations of Q and n,
we found that this prediction matched the
measured feature diameter very well with no
adjustable parameters (Fig. 3B). These printed
features were stable over time; the change in
measured feature size over the course of
120 min postprinting was found to be neg-
ligible (fig. S6). We were able to fabricate
stable silicone features as small as 8 mm in di-
ameter using the AMULIT printing technique;
the smallest stable feature diameter we have
seen previously demonstrated with unmodified
silicone was 40 mm, although smaller unstable
features were also reported (9). A feature di-
ameter of 10 mm was previously achieved by
modifying silicone ink with emulsion droplets
(16, 29). To print these very fine features, we
formulated an AMULIT support material with
an increased yield stress using droplets 1 mm
in diameter (fig. S1); the high-magnification
images in Fig. 1F indicate that larger droplets
would impose interfacial roughness compara-
ble to these small feature diameters.
We have shown that highly controlled 3D
printing with PDMS is possible with the AMULIT
Fig. 3. Control of AMULIT printed feature size. (A) (Left) Intensity-inverted images. These images are
averaged along the x axis, yielding an intensity profile across each feature. (Right) A Gaussian function is
fit to the intensity profile to determine the diameter of the printed line. We measured printed feature
diameter with brightfield microscopy, varying the translation speed, n, of the printing nozzle and the ink
deposition rate, Q. (B) Feature diameter of the printed silicone is controllable and can be predicted from a
fluid continuity equation with no fitting parameters.
fittings and simulate transvalvular blood flow
through cyclic pumping of water (movie S3).
During the negative flow of the pulse rep-
resenting the diastolic cycle, the valves re-
mained closed with very little deflection on
the thin leaflets (Fig. 2J), and during the posi-
tive pulse corresponding to the systolic cycle,
the leaflets deflected, opening the valve and
letting the water flow (Fig. 2K).
AMULIT performance: Feature size and
print quality
The wall thicknesses of the brain vasculature
and heart valve models were set by using a
combination of feature diameter and layer
spacing. The feature diameter, d, for different
prints, can be chosen by selecting a combi-
nation of nozzle translation speed, n, and ma-
terial deposition rate, Q. To systematically
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Fig. 4. Material and surface properties of the AMULIT printed silicone
structures. (A and B) Silicone tensile specimens are subject to unidirectional tensile
stress and are stretched to failure. (C) Tensile stress-strain curves of the specimens
printed with their features oriented parallel and perpendicular to the tensile force
show linear stress-strain relationships at low strains and exhibit an elastic modulus
of 28 kPa. (D and E) Surface profiles of the printed silicone heart valves exhibit
microroughness with an RMS value of 5.5 mm, likely determined by the emulsion droplet
radius and the ultralow interfacial tension with the AMULIT support material.
technique, and the functionality of the heart
valve model suggests that such structures may
be sufficiently compliant and durable for use in
applications. To test the mechanical perform-
ance of printed silicone structures, we fabri-
cated tensile specimens using PlatSil-71 RTV
(room-temperature vulcanizing) (Polytek) sili-
cone formulation following ASTM standard
D412 Type C specifications. To test the role of
layer-to-layer adhesion in the mechanical in-
tegrity of the samples, we printed them with
their extruded features oriented in both the
longitudinal and lateral directions with respect
to the long axis of the specimen geometry.
The printed structures were cured at 60°C for
4 hours and then tested by using an Instron
5943 at a loading rate of 500 mm/min (Fig. 4,
A and B). The tensile stress-strain data showed
that both the lateral and longitudinal print
specimens differed negligibly from one anoth-
er and had the same elastic modulus of 28 kPa
(Fig. 4C). All printed specimens exhibited
linear stress-strain relationships at low strain
levels and repeatable stress-strain curves at
higher strains, failing at strains greater than
1000%. Comparing these results with the per-
formance of molded specimens, we found that
all the stress-strain curves had the same shape
but that printed structures failed at higher
strains than molded structures, whereas molded
structures exhibited elastic moduli approxi-
mately twice those of printed structures. This
softening effect could arise from systematic
heterogeneities in the printed structures in-
herent to the 3D printing process. Addition-
ally, we conducted fatigue tests, imposing 105
cycles of ±10% strain, alternately stretching
and buckling the samples. Subsequent tensile
tests showed that the printed structures ex-
hibited less fatigue than did their molded
counterparts; the elastic modulus dropped
by 18% for the cast samples and 14% for the
printed structures (fig. S7).
As a final assessment of the quality of struc-
tures fabricated with the AMULIT printing
technique, we investigated the surface finish
of fabricated parts. The ultralow interfacial
tension between the silicone and the AMULIT
support material was expected to produce micro-
rough surfaces on the printed shapes. Using
CFM, we imaged a segment of the heart valve
model immersed in a rhodamine solution, vis-
ualizing and quantifying the surface roughness
in 3D. We found the root mean square (RMS)
roughness to be 6.54 ± 0.95 mm (mean and
standard error, respectively) which is compa-
rable to the average diameter of emulsion
droplets used in these tests, ≈4 mm. Thus, we
expect a smaller roughness with smaller emul-
sion droplets such as those used to print very
fine features (Fig. 3B). This value is also com-
parable to the roughness of PDMS structures
printed into support materials that exhibit a
high interfacial tension against silicone inks
(9), so it may be limited by other factors. In
either case, our results demonstrate that elimi-
nating disruptive interfacial driving forces with
the AMULIT technique enables precise silicone
printing without reducing surface quality or
mechanical performance of fabricated struc-
tures. The added role of emulsion droplet size
in surface roughness may enable a printed
structure’s optical properties to be tuned while
independently controlling its mechanical per-
formance through ink composition or feature
diameter.
can be used to make precise, smooth, strong,
and functional devices from commercially
available PDMS formulations. The versatility
of the AMULIT technique eliminates the need
to formulate specialized PDMS inks for 3D
applications and broadens the toolbox for re-
searchers and industrial manufacturers seek-
ing to 3D print PDMS-based devices, while
improving on previous silicone printing meth-
ods. The AMULIT strategy hinges on formu-
lating support materials that are chemically
similar to the inks they support—in this case,
PDMS inks printed into a continuum of PDMS
oil—although the same principle could be used
with aqueous polymers. Despite the chemical
similarity between the ink and the support
medium, we never observed intermixing be-
tween the two materials that interfered with
printing quality. The very low Reynolds num-
ber exhibited during embedded 3D printing
with materials such as those we used should
facilitate the formation of ink–support inter-
faces (30), potentially stabilized by an effective
interfacial tension (31) or a form of liquid–
liquid phase separation (32), likely influenced
by the jammed emulsion phase. Additionally,
weak attractive interactions between the emul-
sion droplets may help to retain them on their
side of the interfaces (33–35). In the near term,
we envision the AMULIT method to be useful
in 3D printing for a wide range of applications
beyond silicone-based devices, given the diver-
sity and availability of polymer systems and
the simplicity of formulating AMULIT support
materials.
Conclusions
The AMULIT 3D printing method eliminates
the disruptive effects of interfacial tension be-
tween printed inks and their support mate-
rials. Our results show that AMULIT printing
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ACKN OWLED GMEN TS
The authors thank Anton Paar for use of their MCR 702 rheometer
through the Anton Paar VIP research program. Funding: No
funding was received. Author contributions: Conceptualization:
S.D. and T.E.A. Methodology: S.D., D.L., D.A.R., G.M.S., A.M.S.,
B.S.S., S.A.B., F.J.B., and T.E.A. Investigation: S.D., D.L., D.A.R.,
A.M.S., and T.E.A. Visualization: S.D., D.L., D.A.R., A.M.S., B.S.S.,
S.A.B., F.J.B., and T.E.A. Funding acquisition: B.S.S., S.A.B., F.J.B.,
and T.E.A. Project administration: T.E.A. Supervision: B.S.S.,
F.J.B., and T.E.A. Writing – original draft: S.D. and T.E.A. Writing –
review and editing: S.D., D.L., D.A.R., G.M.S., A.M.S., B.S.S., S.A.B.,
F.J.B., and T.E.A. Competing interests: S.D., B.S.S., and T.E.A
are inventors on a US patent application (PCT/US2021/037346).
All other authors declare that they have no competing interests.
Data and materials availability: All data are available in the
manuscript and the supplementary material; code for the design
and generation of print trajectories for the heart valve model is
freely accessible at Zenodo (36). License information: Copyright
© 2023 the authors, some rights reserved; exclusive licensee
American Association for the Advancement of Science. No claim to
original US government works. https://www.science.org/about/
science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.ade4441
Materials and Methods
Supplementary Text
Figs. S1 to S7
Movies S1 to S3
Submitted 17 August 2022; accepted 17 February 2023
10.1126/science.ade4441
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RES EARCH
R E S E A R C H A R T I C L E S U M M A R Y
◥
CELL BIOLOGY
Protein import into peroxisomes occurs through a
nuclear pore–like phase
Yuan Gao†, Michael L. Skowyra†, Peiqiang Feng, Tom A. Rapoport*
INTRODUCTION: Peroxisomes are organelles
that are enclosed by a single membrane and
exist in nearly all eukaryotic cells. They per-
form important functions related to lipid
metabolism and redox homeostasis, among
others. Peroxisomes are also vital for human
health; inborn defects in peroxisome biogene-
sis cause devastating and often life-threatening
disorders such as the Zellweger spectrum. Per-
oxisomal enzymes are made in the cytosol,
where they are recognized by PEX5 and re-
lated mobile receptors and are shuttled by
the receptors into the organelle. How the re-
ceptors move proteins across the peroxi-
somal membrane has been a long-standing
question, particularly because peroxisomes
can mysteriously import folded or even oligo-
meric proteins. This property fundamentally
differs from the way in which proteins are
imported into the endoplasmic reticulum or
mitochondria.
RATIONALE: Protein translocation into perox-
isomes requires a number of components
embedded in the peroxisomal membrane—
notably PEX13. We recognized that PEX13
contains an extensive unstructured region
that is enriched in the amino acids tyrosine (Y)
and glycine (G). This tyrosine- and glycine-rich
YG domain resembles the phenylalanine (F)–
and glycine-rich FG domains of nucleoporins
that reside in nuclear pores. FG domains form
a meshwork inside nuclear pores that restricts
passage of soluble molecules yet allows nu-
clear transport receptors to diffuse through
and bring cargo along. By analogy to FG do-
mains, we hypothesized that the YG domain of
PEX13 might form a similarly selective phase
on peroxisomes, through which import recep-
tors could move folded proteins across the
peroxisomal membrane.
RESULTS: We show that the YG domain is
found in PEX13 proteins from all classes of
eukaryotic organisms. Our analysis reveals that
this domain is distinguished by the presence
of repeated aromatic amino acids, predomi-
nantly tyrosines, which are separated from
one another by short flexible linkers composed
mostly of glycines and serines. The tyrosine
residues are essential for peroxisomal protein
import in the yeast Saccharomyces cerevisiae.
YG domains from different organisms vary
extensively in their amino acid sequence and
in the number of tyrosines, yet despite this
diversity, the domains are functionally inter-
changeable in yeast. The YG domain is followed
by a long amphipathic helix that we show is
PEX5
Cargo
PEX13
NTR
Cargo
Nuclear
pore
Peroxisome
Nucleus
Peroxisomal protein import resembles nuclear transport. A dense meshwork is formed in the
peroxisome’s membrane by the YG domain of multiple copies of the peroxisomal protein PEX13. This
meshwork functions as a conduit through which the import receptor PEX5 can selectively diffuse and deliver
bound cargo into the peroxisome. The process is similar to how a nuclear transport receptor (NTR) moves
through the FG meshwork inside a nuclear pore.
also conserved across eukaryotic organisms
and required for peroxisomal import.
Using disulfide-mediated cross-linking, we
demonstrate that YG domains from multiple
PEX13 molecules associate with one another
in the membrane of yeast peroxisomes. This
interaction leads to the formation of a dense
meshwork, which excludes large soluble mate-
rial such as proteases and bulky molecules but
remains permeable to small molecules that
are less than 2 kD in size. The formation of the
meshwork and its barrier properties depend
on the aromatic residues within the YG do-
main. Using protease-protection and cysteine-
modification experiments, we further show
that PEX13 resides in the peroxisomal mem-
brane in two opposite orientations, an unusual
feature among membrane proteins. PEX13
molecules of both orientations associate with
one another, an interaction that involves the
proteins’ YG domains.
Crucially, we find that the purified YG do-
main forms a hydrogel that is held together
by the domain’s tyrosine residues. The import
receptor PEX5 fused to green fluorescent pro-
tein (GFP) can selectively partition into the
hydrogel, whereas GFP alone is excluded. The
entry of PEX5 into the hydrogel requires con-
served aromatic WXXXF/Y motifs (where W is
tryptophan and X denotes any residue) in the
receptor’s flexible N-terminal region. Further-
more, PEX5 can also bring cargo proteins into
the YG hydrogel. Delivery of cargo into the gel
requires the presence of WXXXF/Y motifs in
the receptor.
CONCLUSION: Our results with intact yeast mem-
branes and synthetic hydrogels reveal that per-
oxisomal import resembles transport through
the nuclear pore. A dense meshwork—a selec-
tive phase—is suspended within the peroxi-
somal membrane by multiple PEX13 molecules
of opposite orientations. This meshwork pro-
vides an aqueous conduit across the membrane
into the peroxisomal lumen. The walls of the
proposed conduit might be assembled from the
protein’s conserved amphipathic helix. Peroxi-
somal import receptors such as PEX5 can dif-
fuse through the meshwork and bring cargo
along, using their WXXXF/Y motifs to locally
dissolve the cohesive interactions holding
the meshwork together. This mechanism ex-
plains how folded and oligomeric proteins
are imported into peroxisomes and represents
a previously unidentified principle by which
proteins cross membranes.▪
The list of author affiliations is available in the full article online.
*Corresponding author. Email: tom_rapoport@hms.harvard.edu
†These authors contributed equally to this work.
Cite this article as Y. Gao et al., Science 378, eadf3971
(2022). DOI: 10.1126/science.adf3971
READ THE FULL ARTICLE AT
https://doi.org/10.1126/science.adf3971
Gao et al., Science 378, 1187 (2022)
16 December 2022
1 of 1
RES EARCH
R E S E A R C H A R T I C L E
◥
CELL BIOLOGY
Protein import into peroxisomes occurs through a
nuclear pore–like phase
Yuan Gao1,2†, Michael L. Skowyra1,2†, Peiqiang Feng1,2, Tom A. Rapoport1,2*
Peroxisomes are ubiquitous organelles whose dysfunction causes fatal human diseases. Most
peroxisomal proteins are imported from the cytosol in a folded state by the soluble receptor PEX5. How
folded cargo crosses the membrane is unknown. Here, we show that peroxisomal import is similar to
nuclear transport. The peroxisomal membrane protein PEX13 contains a conserved tyrosine (Y)– and
glycine (G)–rich YG domain, which forms a selective phase resembling that formed by phenylalanine-
glycine (FG) repeats within nuclear pores. PEX13 resides in the membrane in two orientations that
oligomerize and suspend the YG meshwork within the lipid bilayer. Purified YG domains form hydrogels
into which PEX5 selectively partitions, by using conserved aromatic amino acid motifs, bringing cargo
along. The YG meshwork thus forms an aqueous conduit through which PEX5 delivers folded proteins
into peroxisomes.
P eroxisomes are organelles enclosed by
a single membrane and are found in
most eukaryotic cells (1). They provide
vital functions, including fatty acid oxi-
dation (2) and detoxification of reactive
oxygen species (3). Peroxisomes are essential
for human health: Various debilitating and
often fatal disorders, notably the Zellweger
spectrum, arise from the defective import of
enzymes into the peroxisomal lumen, other-
wise known as the matrix (4).
Matrix proteins are made in the cytosol and
then imported into peroxisomes. Most contain
a type 1 peroxisome targeting signal (PTS1) at
their C terminus, which comprises the amino
acid sequence Ser-Lys-Leu (SKL) or variants of
it (5). The PTS1 is recognized in the cytosol by
the soluble receptor PEX5 through the recep-
tor’s tetratricopeptide repeat (TPR) domain
(6). PEX5 also contains a flexible N-terminal
region that includes several aromatic motifs
conforming to the amino acid sequence
WXXXF/Y (where W is Trp, X denotes any
residue, F is Phe, and Y is Tyr) (7). Some matrix
proteins contain an alternative N-terminal
signal called PTS2, whose recognition requires
the adapter PEX7 (8). In humans, PEX7 binds
a short motif in PEX5, whereas in many fungi,
PEX7 associates with PEX5 paralogs that lack
a TPR domain but retain the unstructured
N-terminal region with its characteristic
WXXXF/Y motifs (9).
PEX5 is recruited to peroxisomes by the
membrane proteins PEX13 and PEX14 (and
PEX17 in yeast) (7). Recruitment requires the
1Department of Cell Biology, Harvard Medical School, Boston,
MA 02115, USA. 2Howard Hughes Medical Institute, Harvard
Medical School, Boston, MA 02115, USA.
*Corresponding author. Email: tom_rapoport@hms.harvard.edu
†These authors contributed equally to this work.
receptor’s WXXXF/Y motifs (10) and is fol-
lowed by translocation of the cargo-bound
receptor completely into the matrix (10–12). To
return to the cytosol, PEX5 is ubiquitinated by
the PEX2-PEX10-PEX12 ubiquitin ligase com-
plex (13) and pulled out through a pore in the
ligase complex (14) by a hexameric adenosine
triphosphatase (ATPase) consisting of alternat-
ing copies of PEX1 and PEX6 (15). Deubiquiti-
nation in the cytosol resets PEX5 for a new
import cycle (16, 17).
How PEX5 crosses the peroxisomal mem-
brane to deliver cargo into the lumen has been
a long-standing question. Particularly myste-
rious is the receptor’s ability to import folded
or oligomeric proteins (18), or even gold beads
(19). Thus, translocation into peroxisomes fun-
damentally differs from that into the endoplas-
mic reticulum (ER) or mitochondria, which
can only import proteins in an unfolded con-
formation (20, 21). It is also puzzling that trans-
location across the peroxisomal membrane
does not require nucleotide hydrolysis (22),
even though import occurs against a concen-
tration gradient of the cargo (23).
Translocation into peroxisomes is thought
to be mediated by PEX13 or PEX14. Although
PEX14 has historically been favored (24), the
protein lacks obvious features that could form
an aqueous conduit for moving hydrophilic
proteins across the membrane (25). In addi-
tion, PEX14 may be dispensable for import in
some organisms (26, 27). PEX13, by contrast, is
essential for import in all organisms that have
been tested (28, 29). Curiously, PEX13 contains
an unstructured N-terminal region of unknown
function that is required for import (30) and is
enriched in the amino acids tyrosine and glycine
(31). We noted that this tyrosine- and glycine-
rich YG domain resembles the phenylalanine-
and glycine-rich FG domains of nucleoporins,
which reside within the nuclear pore and form
a meshwork that restricts the entry of large
molecules into the nucleus (32). This mesh-
work is locally broken by nuclear transport
receptors (NTRs), allowing them to rapidly dif-
fuse through nuclear pores along with bound
cargo (33).
Here, we show that the YG domain of PEX13
forms a similarly selective phase on peroxi-
somes. Our results lead to a model whereby
the YG phase is locally disrupted by aromatic
residues in the receptor’s WXXXF/Y motifs,
allowing PEX5 to diffuse across the membrane
into the matrix and carry cargo along. This
mechanism explains how folded and oligomeric
proteins are imported into peroxisomes.
The YG domain of PEX13 is conserved and
essential for peroxisomal import
The YG domain is found in PEX13 homologs
from species representative of all eukaryotic
clades (Fig. 1A). The domain is characterized
by a preponderance of aromatic amino acids,
predominantly tyrosine, but phenylalanines
also occur in some organisms (Fig. 1A and
fig. S1A). The number and position of the
aromatic residues vary (Fig. 1A). The aro-
matic residues are separated by short linkers
of about four amino acids (fig. S1B), which
are enriched in small residues, notably glycine
and serine, and lack charged residues (Fig. 1A
and fig. S1A). These properties are generally
similar to those of cohesive nucleoporin FG-
repeat domains (fig. S1C), except that the linkers
between FG repeats are longer (fig. S1D).
The YG domain is followed by a long am-
phipathic helix (AH) (Fig. 1A and fig. S2), which
has clearly defined hydrophobic and hydrophilic
surfaces (fig. S3). Whether the AH consists of a
straight helical segment or has a kink in the
middle is unclear (fig. S3). Downstream of the
AH, most PEX13 homologs contain a canoni-
cal transmembrane segment (TM) and an SH3
domain that binds PEX5 (28) (Fig. 1A and fig.
S2), although these are absent in some plants
(34) (fig. S2). Thus, only the YG domain and
the AH are strictly conserved.
The YG domain is necessary for peroxi-
somal import, which we measured in the
yeast Saccharomyces cerevisiae using an
engineered pathway that generates a pigment
when import is impaired (35). When all 14
tyrosines in the YG domain were mutated
to serines, import was abolished (Fig. 1B),
whereas converting all of the tyrosines into
phenylalanines caused only a modest defect
(Fig. 1B). Thus, the residues’ aromaticity is
critical. A minimum of 11 tyrosines seems to be
required in yeast (fig. S4A), but their position
can be varied. The YG domain could also be
replaced by the analogous domain from other
organisms (Fig. 1C), albeit with variable ef-
ficiency, indicating that the domain’s function
is conserved despite its sequence diversity.
Gao et al., Science 378, eadf3971 (2022)
16 December 2022
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RES EARCH | R E S E A R C H A R T I C L E
A
unstructured
PEX13
N
YG
AH
TM
SH3
S. cerevisiae (yeast)
71
141
214
263 285
303
374
yeast
Torula.
Pichia
amoeba
algae
plant
fruit fly
human
B
YG
AH
TM
SH3
* * * *
* *
pex13
WT
Y S
Y F
AH mut
AH mut
SH3
N
Import activity (%)
50
100
0
C
Import activity (%)
50
100
0
pex13
yeast
human
fruit fly
Torula.
plant
algae
Pichia
amoeba
YG
Fig. 1. The YG domain of PEX13 is required for peroxisomal protein import.
(A) The domain organization of PEX13 from S. cerevisiae (yeast) is shown at the
top. Numbers denote amino acid coordinates. Sequences of the YG domain in
PEX13 homologs from organisms representing the indicated eukaryotic clades
(Torula., Torulaspora) are shown at the bottom. (B) Peroxisomal protein
import activity (mean ± SE of three experiments) in yeast cells expressing the
indicated PEX13 mutants compared with wild-type (WT) cells and a PEX13
knockout strain (pex13D). Y→S and Y→F denote conversion of all tyrosines
(positions indicated by vertical bars) in the YG domain into serines or
phenylalanines, respectively. AH mut z and ϕ denote conversion of four
hydrophilic residues in the AH into alanine or two hydrophobic residues into
glutamate, respectively. (C) Import activity in yeast cells expressing PEX13
chimeras with YG domains from the indicated organisms. Single-letter
abbreviations for the amino acid residues are as follows: A, Ala; C, Cys; D, Asp;
E, Glu; F, Phe; G, Gly; H, His; I, Ile; K, Lys; L, Leu; M, Met; N, Asn; P, Pro; Q, Gln; R,
Arg; S, Ser; T, Thr; V, Val; W, Trp; and Y, Tyr.
Taken together, these data demonstrate that
the YG domain is a universal and essential
feature of PEX13.
Import was also abolished by point muta-
tions in either the hydrophilic face (mut z) or
the hydrophobic face (mut ϕ) of the AH (Fig.
1B), revealing that the AH is likewise essential.
Whereas loss of the SH3 domain (DSH3) re-
duced import (Fig. 1B) as reported previously
(36), deleting the flexible region that precedes
the YG domain (DN) had no effect (Fig. 1B),
indicating that this region is dispensable. We
confirmed that all mutants were similarly
expressed (fig. S4, A to C).
YG domains of multiple PEX13 molecules
interact on peroxisomes
To determine whether YG domains form a
nuclear pore–like phase on peroxisomes, we
first tested whether these domains associate
with one another in the peroxisomal mem-
brane. Individual cysteines were introduced
at either of two positions (residue 104 or 131)
in the YG domain of FLAG-tagged yeast PEX13
(which lacks natural cysteines) (Fig. 2A), without
affecting import activity (fig. S5A). Formation
of disulfide-linked dimers was then assessed
using an oxidizing agent (Fig. 2A). Both
positions indeed yielded efficient dimerization
(>70%) (Fig. 2B, top). Dimers were disulfide-
linked because the corresponding bands dis-
appeared upon reduction with dithiothreitol
(DTT) (Fig. 2B, bottom). Dimerization was also
sensitive to detergent (Fig. 2B, lanes 4 and 8),
suggesting that the interaction requires an
intact membrane. These results thus show that
the YG domains of individual PEX13 molecules
interact in the peroxisomal membrane.
The interaction between YG domains is
indeed multivalent and does not involve just
two molecules. When two cysteines were intro-
duced into the YG domain (at positions 104 and
131), a ladder of disulfide-linked bands was
observed (Fig. 2C, right). Some cross-linking
occurred even without oxidant (lane 4), sug-
gesting that the interaction is highly favored.
The largest cross-linked species reveal that
more than eight PEX13 molecules interact
through their YG domains. Cross-linking was
greatly reduced after converting all tyrosines in
the YG domain into serines (Fig. 2D, compare
lanes 3 and 6 and corresponding quantifica-
tion). Cross-linking was unaffected by the ab-
sence of other import components, including
PEX2, PEX5, PEX14, or PEX17 (fig. S4D), sug-
gesting that PEX13 forms oligomers by itself.
This conclusion agrees with previous studies
showing that PEX13 forms oligomers inde-
pendently of other import components (37, 38).
Our analysis demonstrates that multiple PEX13
molecules associate with one another on peroxi-
somes through their YG domains, analogously
to how nucleoporin FG domains interact within
the nuclear pore.
The YG domain is inaccessible to
large molecules
We next asked whether the interaction between
YG domains restricts access to soluble material,
similar to the FG meshwork inside nuclear pores
that excludes large proteins and other mole-
cules. A 3C protease–cleavage site was inserted
at different positions in the YG domain of
FLAG-tagged PEX13 or outside this domain
near the N terminus (Fig. 3A, scheme). The
resulting constructs replaced endogenous PEX13
in yeast and were fully active (fig. S5B). When
membranes isolated from the corresponding
Gao et al., Science 378, eadf3971 (2022)
16 December 2022
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RES EARCH | R E S E A R C H A R T I C L E
A
B
104 131
FLAG
YG
AH
TM
SH3
oxidant quench
IP
FLAG
blot
FLAG
C
cysteine
104 + 131
+ DTT
– DTT
cysteine
104
131
oxidant
det
det
oxidant
90
– DTT
50
90
+ DTT
50
2×
1×
1×
260
160
90
50
D
1
WT
Y S
fraction
crosslinked
0
1
2
3
4
5
6
cysteine
104 + 131
WT
Y S
oxidant
260
160
90
50
50
8×>
5-8×
4×
3×
2×
1×
– DTT
+ DTT
1
2
3
4
5
FLAG
6
7
8
1
2
3
4
FLAG
5
6
1
2
4
3
FLAG
5
6
Fig. 2. The YG domain of PEX13 forms oligomers in the peroxisomal mem-
brane. (A) Scheme for the experiments shown in (B) to (D). To test whether YG
domains associate with one another, cysteines were introduced at the indicated
positions in the YG domain of FLAG-tagged yeast PEX13 (which lacks native
cysteines), and the resulting constructs were expressed in yeast. Intact
membranes from the corresponding strains were treated with Aldrithiol-4
(oxidant), unreacted cysteines were then quenched with NEM, and the proteins
were immunoprecipitated (IP) and analyzed by immunoblotting (blot). (B) As
described in (A), using PEX13 proteins containing individual cysteines at the
indicated positions. Reactions were performed in the presence of 0, 50, or 200 mM
oxidant with or without detergent (det) and resolved by nonreducing (–DTT) or
reducing (+DTT) SDS–polyacrylamide gel electrophoresis (SDS-PAGE) before
immunoblotting. Monomers (1×) and disulfide-linked dimers (2×) are indicated on
the right. Numbers along the left side specify relative molecular weights (in kD).
(C) Same as in (B), but with PEX13 containing two cysteines. The number of
disulfide-linked molecules is indicated on the right (1× to 8×). (D) Same as in (C),
but comparing PEX13 with tyrosines (WT) or serines (Y→S) in the YG domain.
Cross-linking efficiency is plotted at the top (mean ± SE of three experiments).
strains were treated with the protease, the
constructs with N-terminal cleavage sites were
readily digested (Fig. 3A, lanes 2 and 6),
consistent with the reported cytosolic accessi-
bility of the N terminus (39). By contrast, sites
in the YG domain were much more resistant
to cleavage (lanes 10 and 14) unless detergent
was added (lanes 11 and 15). No cleavage oc-
curred at any site when the protease was
preinactivated by N-ethylmaleimide (NEM;
lanes marked by skull and crossbones). These
data thus show that the YG domain is not
easily accessed by the 30-kD 3C protease.
To confirm this result, we probed the
accessibility of the YG domain to cysteine-
reactive polyethylene glycol (PEGmal). Indi-
vidual cysteines were introduced throughout
FLAG-tagged PEX13 in yeast (Fig. 3B, scheme),
and membranes from the corresponding strains
were treated with different sizes of PEGmal.
Cysteines near the N terminus were readily
modified by all sizes of PEGmal (Fig. 3B, upper
two blots) as expected. By contrast, cysteines
in the YG domain were barely modified by
the two largest PEGmal reagents (5 and 10 kD)
unless detergent was included (lanes 1 to 6
in the two middle blots). This resistance to
modification depended on size, because the
two smallest forms of PEGmal (0.8 and 2 kD)
efficiently modified either cysteine (lanes 7
to 12 in the two middle blots). As a control,
we tested the accessibility of a cysteine in the
TM, which was not modified by PEGmal of
any size (bottom blot).
Converting all tyrosines in the YG domain
to serines (Y→S) increased accessibility to
10-kD PEGmal (Fig. 3C), consistent with this
mutant’s reduced self-association (Fig. 2D).
Converting all tyrosines to phenylalanines
(Y→F) instead improved the resistance to
modification (Fig. 3C), again highlighting the
importance of the aromatic residues in cement-
ing the interaction between PEX13 molecules.
The absence of PEX5 (pex5D) had no effect on
accessibility (Fig. 3C), suggesting that active
import may not be necessary for the YG
domain’s exclusion properties. Taken together,
our results reveal that multiple YG domains
form a meshwork in the peroxisomal mem-
brane, which excludes large molecules but not
small ones, similarly to the FG meshwork in
nuclear pores.
To confirm this conclusion, we introduced
single cysteines on either side of the trans-
membrane segment of the peroxisomal mem-
brane protein PEX14 (which also lacks native
cysteines) and examined their accessibility to
different sizes of PEGmal as above (fig. S6A).
The C terminus of PEX14 faces the cytosol
(10, 39), and accordingly, a cysteine located
near the C terminus (position 242) was readily
modified by all sizes of PEGmal in the absence
of detergent (fig. S6B, upper blot). By contrast,
a cysteine located near the N terminus (posi-
tion 65), which is oriented toward the lumen
(10, 39), was modified only by the smallest
PEGmal tested (fig. S6B, lower blot). In the
presence of detergent, both cysteines were
indiscriminately modified by all sizes of the
reagent. These results thus confirm that the
peroxisomal membrane is permeable to small
molecules, as suggested before (35, 40), and are
Gao et al., Science 378, eadf3971 (2022)
16 December 2022
3 of 14
RES EARCH | R E S E A R C H A R T I C L E
A
protease
site
protease
55
36
34 67
96 133
YG
AH
TM
SH3
FLAG
protease quench
IP
FLAG
blot
FLAG
B
39 68 104 131
FLAG
YG
AH
270
TM
SH3
detergent
(kD) PEGmal
+
10 10 –
+
5
5
+
2
+
– 0.8 0.8
2
34
det
+
+
+
67
det
+
+
+
96
det
+
+
+
133
det
+
+
+
un-
cleaved
1
2
3
4
5
6
7
9
8
FLAG
10 11 12
13
14 15 16
C
cysteine at position 104
WT
Y S
Y F
pex5
+
WT
detergent
(10-kD) PEGmal
+
+
+
+
+
+
+
+
+
+
+
+
70
55
1
2
3
4
5
7
6
FLAG
8
9
10 11 12
1
0
fraction
modified
Y S
T
W
Y F
pex5
70
55
70
55
70
55
70
55
70
55
39
68
104
cysteine
position
131
270
1
2
3
4
5
7
6
FLAG
8
9
10 11 12
Fig. 3. The YG domain is poorly accessible to large molecules. (A) To test
accessibility of the YG domain to proteins, a 3C protease–cleavage site was
introduced into FLAG-tagged yeast PEX13 at the indicated positions, and the
resulting constructs were expressed in yeast. Intact membranes from each
strain were first treated with the protease with or without detergent (det) and
then quenched with NEM to inactivate the protease. Where indicated (skull
and crossbones), NEM was added before the protease. Scissors designate the
cleaved forms. (B) Same as in (A), except that accessibility of the YG domain
to differently sized molecules was assessed by introducing individual
cysteines into FLAG-tagged PEX13 at the positions shown. Membranes from
the corresponding strains were treated with different sizes (in kD) of
cysteine-reactive PEGmal and then quenched with excess cysteine. Covalent
modification of the proteins was visualized by immunoblotting. Modified
and unmodified forms of the protein are designated by yellow and white
triangles, respectively, in the top blot. (C) Same as in (B), but with PEX13
containing a cysteine at position 104 and tyrosines in the YG domain (WT),
or tyrosines mutated to serines (Y→S) or phenylalanines (Y→F). Where
indicated, membranes were isolated from a strain lacking PEX5 (pex5D).
Modification was performed with 10-kD PEGmal. Modification efficiency is
plotted on the right (mean ± SE of four experiments).
consistent with a dense meshwork of limited
porosity residing in the membrane.
PEX13 adopts two orientations in the
peroxisomal membrane
The YG meshwork must be suspended within
the peroxisomal membrane to form a conduit
for cargo. To determine how the YG meshwork
is formed, we examined the membrane topology
of PEX13. The N terminus of the protein was
fused to a 3C protease–cleavage site preceded
by a streptavidin-binding peptide (SBP) tag, and
the C terminus was fused to a tobacco etch virus
(TEV) protease–cleavage site followed by a FLAG
tag (Fig. 4A, upper scheme). The construct was
expressed from the endogenous locus in yeast and
supported peroxisomal protein import (fig. S5B).
We first ascertained the orientation of the
C terminus. Membranes were treated with TEV
protease, and PEX13 was then immunopreci-
pitated by the N-terminal SBP tag (Fig. 4A).
Interestingly, only half of the PEX13 popula-
tion was cleaved (lane 2; quantification in fig.
S7A). The resistant pool was protected by the
membrane, because it could be cleaved in the
presence of detergent (Fig. 4A, lane 3). No
cleavage occurred when the protease was
preinactivated by NEM (lane 4). These data
thus suggest that PEX13 resides in the mem-
brane in two orientations: one whose C terminus
faces the cytosol and another whose C terminus
faces the lumen (Fig. 4A, bottom scheme). The
interaction between YG domains in the mem-
brane might thus be mediated by PEX13 mole-
cules of both orientations (see below).
To infer the orientation of the N terminus,
membranes were treated with 3C protease,
and PEX13 was then immunoprecipitated by
the C-terminal FLAG tag (Fig. 4A). In contrast
to the C terminus, more than 50% of the
molecules had their N termini accessible to
the protease (lane 6), and the exact propor-
tion varied between experiments (fig. S7A).
The remaining pool was again cleaved in
detergent (Fig. 4A, lane 7). The N terminus
might thus not be fixed in one specific orien-
tation but may instead be free to move between
the cytosol and the lumen (Fig. 4A, bottom
scheme). Notably, these results agree with the
cytosolic accessibility of the N terminus that
was reported above (Fig. 3, A and B).
Controls were performed with PEX14 (Fig.
4B) and PEX17 (fig. S7B), which are conven-
tional single-pass membrane proteins whose
N termini face the lumen and C termini face
the cytosol (10, 25, 39). Using analogously
tagged constructs that supported peroxisomal
import (fig. S5B), we found that the C termini
of both proteins were fully cleaved in the ab-
sence of detergent, whereas their N termini
Gao et al., Science 378, eadf3971 (2022)
16 December 2022
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RES EARCH | R E S E A R C H A R T I C L E
A
3C
N
(SBP)
PEX13
TEV
B
3C
PEX14
YG
AH
TM
SH3
C
(FLAG)
N
(SBP)
PBD
TM
CC
TEV
C
(FLAG)
protease quench
IP
FLAG / SBP
blot
FLAG / SBP
IP : SBP
IP : FLAG
det
det
IP : SBP
IP : FLAG
det
det
N
C
cytosol
N
M
T
or
T
M
lumen
N
FLAG
SBP
55
55
cytosol
FLAG
lumen
SBP
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
PEX13
TEV 3C
C
N
D
PEX13
229
246
295
55
55
C
FLAG
YG
AH
TM
SH3
FLAG
YG
AH
TM
SH3
det
det
det
cysteine
detergent
(5-kD) PEGmal
229
+
+
+
246
+
+ +
295
+
+ +
246
+
229
+
+ +
246
+
295
+
+ +
55
36
full-length
fragment (3C)
fragment (TEV)
70
50
C
M
T
N
+2
+1
1
2
3
4
5
FLAG
6
7
8
1
2
3 4
5
6
7
8
10 11 12 13 14 15
9
FLAG
Fig. 4. PEX13 adopts two transmembrane orientations. (A) Membrane
topology determined by protease protection. The indicated protease-cleavage
sites (scissors) and epitope tags were introduced into yeast PEX13. Membranes
containing this protein were treated with protease with or without detergent
(det), the reactions were quenched with NEM, and PEX13 was immunoprecipi-
tated (IP); cleavage was visualized by immunoblotting (see scheme). Where
indicated (skull and crossbones), NEM was added before the proteases.
The position of the C terminus is deduced from cleavage with TEV protease and
immunoprecipitation by the N-terminal SBP tag, and the position of the N
terminus is deduced from cleavage with 3C protease and immunoprecipitation
by the C-terminal FLAG tag. The two inferred orientations of PEX13 are depicted
on the right; the N terminus can face either side, whereas the C terminus is
fixed in one of two orientations. (B) Same as in (A), but for PEX14. PBD, PEX5-
binding domain; TM, transmembrane segment; CC, coiled-coil oligomerization
domain. (C) Same as in (A), but with protease sites flanking the TM and a FLAG
tag as shown. (D) TM orientation determined by modification of flanking
cysteines with membrane-impermeable PEGmal. One or two cysteines were
introduced into FLAG-tagged PEX13, as indicated. Membranes were treated
with 5-kD PEGmal and then quenched with excess cysteine; single (+1) or double
(+2) modification was visualized by immunoblotting.
were completely protected unless detergent
was included (Fig. 4B and fig. S7B). The topol-
ogies of PEX14 and PEX17 thus agree with
previous reports.
The dual topology of PEX13 is supported by
two observed orientations of the protein’s TM.
We incorporated 3C protease– and TEV protease–
cleavage sites on either side of the TM and
added a FLAG tag to the N terminus for im-
munodetection (Fig. 4C, scheme). The resulting
construct allowed peroxisomal import (fig. S5B).
Again, half of the molecules were accessible to
either protease in the absence of detergent (Fig.
4C, lanes 2 and 4), whereas the entire population
was cleaved when detergent was included (lanes
3 and 5). Notably, addition of both proteases
produced both cleavage products (lanes 6 to 8),
consistent with two orientations of the protein
in the membrane.
We confirmed the dual topology of PEX13
by PEGmal accessibility. Single cysteines were
introduced on either side of the TM (Fig. 4D,
scheme) without affecting import (fig. S5A),
and membranes from the corresponding strains
were treated with 5-kD PEGmal. Regardless of
whether the cysteine resided upstream (position
229 or 246) or downstream (position 295) of the
TM, about half of the molecules showed the
increase in molecular weight that was expected
from cysteine modification (Fig. 4D, left blot).
All molecules were modified in detergent. With
two cysteines on the same side of the TM
(positions 229 and 246), half of the PEX13
molecules were modified on both cysteines,
whereas the other half were not modified at
all (Fig. 4D, right blot), as expected. By con-
trast, with two cysteines on opposite sides (po-
sitions 246 and 295), essentially all PEX13
molecules were modified but only on one or the
other cysteine. These results confirm that the
TM of PEX13 spans the membrane in two pos-
sible orientations.
Gao et al., Science 378, eadf3971 (2022)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 5. The two orientations of PEX13
are bridged by the YG domain. (A) To
test whether the two orientations of
PEX13 associate with each other, a single
cysteine and a 3C protease–cleavage site
were incorporated into FLAG-tagged
yeast PEX13 as shown. An SBP tag was
included at the C terminus to enhance
the size shift after proteolytic cleavage.
The resulting construct was integrated
into yeast. Intact membranes from the
corresponding strain were treated with
the protease to reveal the protein’s two
orientations, oxidized with Aldrithiol-4 to
induce disulfide-bridge formation, and
quenched to inactivate the protease and
oxidant. (B) Disulfide-linked dimers were
visualized by reducing (+DTT) or non-
reducing (–DTT) SDS-PAGE and immu-
noblotting for the FLAG tag. Where
indicated, detergent (det) was included
during protease cleavage. Cleaved
(scissors) and uncleaved (∅) species are
marked on the right. The topologies of
the three observed dimers (numbered)
are depicted below.
A
FLAG
104
YG
PEX13
3C
AH
TM
SH3
SBP
protease oxidize quench
IP
FLAG
B
cysteine 104
+
oxidant
+ DTT
– DTT
det
det
+
+
+
1
2
3
1
2
3
4
5
6
1
2
3
FLAG
100
55
cytosol
lumen
The dual topology does not require forma-
tion of the YG meshwork, because both orien-
tations were retained after mutating all tyrosines
in the YG domain into serines (fig. S8A). Both
orientations were also retained in the absence
of PEX2, PEX5, PEX8, PEX14, or PEX17 (fig.
S8B), indicating that other import components
are dispensable. By contrast, in the absence of
PEX3, all PEX13 molecules became accessible
to the proteases and the abundance of PEX13
was also reduced (fig. S8C). This observation
agrees with previous reports of PEX13 being
destabilized in the absence of PEX3 (41, 42)
and with the proposed role of PEX3 in peroxi-
somal membrane protein insertion (43).
The YG domain bridges both orientations
of PEX13
We next asked whether the two orientations
of PEX13 associate with each other, allowing
the YG domains of these molecules to interact
within the membrane. We introduced a single
cysteine into the YG domain and tested
whether disulfide-linked dimers would form
between the two orientations. To discern both
orientations, the C terminus was fused to a 3C
protease–cleavage site followed by an SBP tag
(to enhance the size shift), and an N-terminal
FLAG tag was added for immunodetection
(Fig. 5A). Cleavage by the protease produced
two bands of equal intensity in a reducing gel
(Fig. 5B, left blot), corresponding to the two
orientations of the C terminus. Under oxidizing
conditions, however, three disulfide-linked bands
were seen after cleavage (right blot), corres-
ponding to PEX13 dimers in which the two
molecules have the same or opposite topologies
(Fig. 5B, scheme). These results establish that
both orientations of PEX13 directly interact
with each other through their YG domains
and thereby explain how the YG meshwork is
localized to the plane of the membrane.
YG domains form hydrogels
Given that the nucleoporin FG meshwork can
be reconstituted as a hydrogel (44) whose per-
meation properties mimic transport through
the nuclear pore (45), we wondered whether
the YG domain of PEX13 might behave sim-
ilarly. After screening expression of YG domains
from different organisms, we found that the
entire unstructured N-terminal region (includ-
ing the YG domain) from Arabidopsis thaliana
PEX13 (Fig. 6A) expressed well in bacteria and
could be purified under denaturing conditions
using a His tag. Notably, the YG domain from
this species could complement the yeast YG
domain in peroxisomal import (Fig. 1C). After
proteolytic removal of the tag (fig. S9) and con-
centration to 40 mg/ml (2 mM) in the pres-
ence of denaturant, the fragment indeed
formed a rigid, translucent gel after several
hours (Fig. 6B, left photograph). Higher con-
centrations could not be reached because the
fragment gelled spontaneously, even when
denaturant was included to retard gelation.
A more dilute solution at 4 mg/ml (0.2 mM)
also formed a hydrogel but after several days.
The YG domain is necessary and sufficient
for gelation. When all tyrosines in the YG do-
main were mutated to serines (Y→S; Fig. 6A),
a solution of the corresponding purified frag-
ment never formed a gel and remained fluid
(Fig. 6B, middle photograph). Furthermore,
the isolated YG domain (without the upstream
flexible segment; Fig. 6A) gelled as readily as
the full-length fragment (Fig. 6B, right photo-
graph). Interestingly, the gels liquified after
heating to >50°C and resolidified after cooling
to room temperature; this cycle could be re-
peated many times. The purified protein thus
behaves like gelatin, even though the amino
acid compositions of the two proteins are very
different. This reversible thermosensitivity dif-
fers from that of the FG domain of the nu-
cleoporin NUP98, whose phase separation is
more favorable at higher temperatures (46).
The difference might be due to hydrogen bonds
between tyrosine hydroxyl groups contribut-
ing to the cohesion of the YG hydrogel.
PEX5 partitions into YG hydrogels
We next examined the permeation properties of
the YG hydrogels. Small drops of the N-terminal
fragment were gelled at 40 mg/ml in a glass-
bottomed dish, and the influx of fluorescently
labeled PEX5 or other proteins was imaged on
a microscope (Fig. 7A). When buffer contain-
ing full-length PEX5 fused to green fluores-
cent protein (PEX5-GFP; Fig. 7B) was added,
the fusion protein rapidly accumulated at the
gel edge and then moved inward (Fig. 7C) at a
rate of ~16 nm/s (fig. S10). PEX5-GFP was de-
pleted from the buffer just outside the gel,
indicating that the rate of entry into the gel is
limited only by diffusion. Fluorescence behind
the front was essentially constant in the gel,
indicating that PEX5-binding sites in this
region became saturated. After 30 min of per-
meation, the concentration of PEX5-GFP inside
the gel was ~20-fold greater than the protein’s
concentration in the buffer (Fig. 7D). Although
GFP alone could also enter the gel, it showed
no enrichment (Fig. 7, C and D). Thus, PEX5
efficiently and specifically partitions into the
YG hydrogel, analogously to how NTRs par-
tition into hydrogels formed from nucleoporin
FG domains.
Admission of PEX5 into YG hydrogels re-
quires the receptor’s unstructured N terminus.
When just the N-terminal region of PEX5
(including all WXXXF/Y motifs) was fused
to GFP (Fig. 7B), the resulting fusion protein
permeated the gel as rapidly as the full-length
version (Fig. 7C) and became similarly enriched
(Fig. 7D). By contrast, a fusion between the
cargo-binding TPR domain and GFP (Fig. 7B)
accumulated to a much lower extent (Fig. 7,
C and D). Entry into the gel was driven by the
receptor’s WXXXF/Y motifs, because ablating
Gao et al., Science 378, eadf3971 (2022)
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RES EARCH | R E S E A R C H A R T I C L E
A
B
unstructured
full-length
YG
AH
TM
SH3
N + YG
N + YG (Y > S)
YG alone
used for gelation
N + YG
(Y > S)
N + YG
YG alone
Fig. 6. The YG domain of PEX13 forms hydrogels. (A) Scheme depicts the domain organization of A. thaliana PEX13, which lacks a TM and an SH3 domain
(enclosed by dashed lines). The fragments indicated below were expressed in Escherichia coli and purified. Y→S denotes conversion of all tyrosines in the YG domain
into serines. (B) Concentrated solutions (40 mg/ml) of the three purified fragments were pipetted into silicone tubing and allowed to gel and then squeezed out
of the tubing onto a colored surface and photographed. If gelation had occurred, the solution retained the shape of the tubing; otherwise, the solution remained fluid.
Note that the YG domain is necessary and sufficient for gelation.
all of the motifs (Fig. 7B) abolished the ac-
cumulation of the N-terminal fusion protein
inside the gel (Fig. 7, C and D).
PEX5 could also drag cargo into the YG
hydrogels. GFP fused to a PTS1 import signal
(GFP-SKL) showed no enrichment inside the
gel on its own but accumulated ~10-fold in the
presence of full-length PEX5 (Fig. 7, E to G).
The lower partitioning coefficient likely reflects
the modest affinity between the import signal
and the receptor’s TPR domain (47). The per-
meation rate was comparable to that of the
linear PEX5-GFP fusion (fig. S10). Partitioning
of cargo required the receptor’s WXXXF/Y
motifs, because full-length PEX5 that lacked
all of the motifs (Fig. 7E) was unable to drag
GFP-SKL into the gel (Fig. 7, F and G). Al-
though the TPR domain is necessary for the
interaction with the import signal, the domain
is dispensable for the actual partitioning. Indeed,
GFP that lacked the import signal was completely
inert in the presence of full-length PEX5 but
could be efficiently brought into the gel by a
construct consisting of the receptor’s N-terminal
region fused to a GFP nanobody (PEX5-GNB;
Fig. 7, E and F). In this case, GFP was enriched
~30-fold inside the gel (Fig. 7G), consistent with
the higher affinity of the nanobody for the
fluorescent protein (48). These results dem-
onstrate that the YG domain of PEX13 forms
hydrogels which selectively admit PEX5 and
PEX5•cargo complexes.
Discussion
Our results with intact yeast membranes and
synthetic hydrogels reveal the existence of a
nuclear pore–like conduit on peroxisomes
(Fig. 8A). This conduit consists of a dense
meshwork—a selective phase—assembled from
the YG domains of multiple PEX13 molecules
that sit in the membrane in opposite orienta-
tions. Similarly to the meshwork formed by
cohesive nucleoporin FG domains inside nu-
clear pores, the YG phase restricts passage of
large soluble molecules. The YG phase can be
selectively traversed by the import receptor
PEX5, allowing bound cargo to move across
the peroxisomal membrane. This mechanism
thus allows folded and oligomeric proteins to
be imported into peroxisomes, analogously to
how folded cargo is moved into and out of the
nucleus.
The use of tyrosines to form a selective
phase is not unprecedented. For example,
the protein FUS relies on tyrosine repeats to
form hydrogels in vitro and to phase-separate
into stress granules in vivo (49). Nucleoporin
FG domains with tyrosines in place of phenyl-
alanines also retain their ability to form hy-
drogels (44). Although these gels no longer
accommodate NTRs, they do allow the entry
of proteins engineered to bind the modified
phase (50).
The permeation rate of PEX5 into the per-
oxisomal YG hydrogels (~16 nm/s) implies that
cargo would traverse the 4-nm peroxisomal
membrane in less than a second, which seems
physiologically reasonable, although trans-
location rates in vivo are not known. PEX5
presumably enters the YG phase by locally
dissolving the meshwork, relying predominantly
on the WXXXF/Y motifs in its flexible N-
terminal region (Fig. 8B). Entry of PEX5 into
the YG phase might be regulated by cargo
binding, because the association of the recep-
tor with peroxisomes has been reported to rely
on the presence of cargo (51). The interaction
between PEX5 and the YG phase must be
weak and transient, allowing the receptor to
rapidly bind and dissociate to diffuse through
the meshwork. The receptor’s TPR domain
also has some affinity for the YG phase and
would therefore enhance diffusion, which might
be relevant for translocation of larger cargo.
However, only the WXXXF/Y motifs are strictly
conserved among peroxisomal import recep-
tors (1), suggesting that they are sufficient to
drive import both of PTS1 and PTS2 proteins.
The proposed mechanism implies that
peroxisomal import receptors can diffuse
through the YG phase in either direction,
similarly to how NTRs move bidirectionally
through the nuclear pore. Whereas the direc-
tionality of nuclear transport is enforced by
the Ran•GTP/GDP gradient (GTP, guanosine
triphosphate; GDP, guanosine diphosphate),
peroxisomal import may be driven instead by
the highly favorable interaction between the
receptors’ WXXXF/Y motifs and the lumenal
domain of the membrane protein PEX14 (52).
This interaction might help pull PEX5 out of
the YG phase on the lumenal side and would
also prevent retrograde diffusion of the receptor
back into the cytosol (Fig. 8A). The interaction
is likely potentiated by avidity, because import
receptors frequently have several WXXXF/Y
motifs (53), and PEX14 is known to form oligo-
mers that associate with PEX13 (25, 54, 55).
Sustained import would thus require unliganded
PEX14, which could only be generated by con-
tinual retrieval of PEX5 from the lumen by ATP-
dependent recycling (Fig. 8A). This model
explains why import, per se, is independent
of nucleotide hydrolysis and yet occurs against
Gao et al., Science 378, eadf3971 (2022)
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RES EARCH | R E S E A R C H A R T I C L E
A
buffer
PEX5
influx
gel
microscope
objective
-150
150
0
distance
( m)
C
PEX5
(full-length)
GFP
GFP
PEX5
(N)
GFP
B
full-length
N
TPR
PEX5
GFP
TPR
N
N + WF
TPR
GFP
GFP
WxxxF/Y
N
AxxxA
N
PEX5
(TPR)
GFP
GFP
GFP
GFP
PEX5
(N + WF)
GFP
buffer
side
gel
side
buffer
side
gel
side
buffer
side
gel
side
buffer
side
gel
side
buffer
side
gel
side
1 min
10 min
30 min
40
enrich-
ment
1
-150
0
distance ( m)
150
-150
0
distance ( m)
150
-150
0
distance ( m)
150
-150
0
distance ( m)
150
-150
0
distance ( m)
150
D
F
full-length
GFP
N
TPR
N + WF
0.9
4.3
0.9
E
24.4
29.3
PEX5
WF
0
10
20
30
GNB
enrichment
PEX5
TPR
TPR
GNB
N
AxxxA
N
N
N
G
PEX5
+ GFP-SKL
PEX5 + GFP-SKL
+ GFP-SKL
+ GFP-SKL
+ GFP-SKL
PEX5 ( WF)
PEX5
PEX5-GNB
11.6
0.7
0.4
0.0
33.2
0
10
20
30
enrichment
PEX5
+
GFP-SKL
buffer
side
gel
side
GFP-SKL
buffer
side
gel
side
PEX5 ( WF)
+
GFP-SKL
buffer
side
gel
side
PEX5
+
GFP
PEX5-GNB
+
GFP
buffer
side
gel
side
buffer
side
gel
side
1 min
10 min
30 min
40
enrich-
ment
1
-150
0
distance ( m)
150
-150
0
distance ( m)
150
-150
0
distance ( m)
150
-150
0
distance ( m)
150
-150
0
distance ( m)
150
Fig. 7. The import receptor PEX5 selectively enters YG hydrogels and
brings cargo along. (A) YG-hydrogel droplets (40 mg/ml) were prepared in
glass-bottomed dishes; permeation of the gels by fluorescently labeled PEX5
or other proteins was imaged by point-scanning confocal microscopy.
(B) Scheme depicting the PEX5 fragments that were fused to GFP. PEX5’s
N-terminal region contains several WXXXF/Y motifs (magenta arrows), which
were mutated to AXXXA in the N + DWF mutant. (C) YG-hydrogel droplets
were bathed in buffer containing the indicated GFP-fusion proteins (or GFP
alone), and the interface between the buffer and gel was imaged over time.
Shown are three selected time points; the fold enrichment of each protein,
relative to buffer, across the imaged field is plotted below (mean ± the
range of three experiments). (D) Mean enrichment (± the range of three
experiments) of the indicated proteins inside the gel compared to buffer after
30 min of imaging as in (C). (E) Nonfluorescent PEX5 variants used for
experiments with fluorescent cargo. GNB, anti-GFP nanobody. (F) Same as in
(C) except with the indicated PEX5 variants, and GFP with or without the
PEX5-binding SKL signal. (G) Mean enrichment (± the range of three
experiments) of GFP or GFP-SKL after 30 min of imaging as in (F).
Gao et al., Science 378, eadf3971 (2022)
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RES EARCH | R E S E A R C H A R T I C L E
A
PEX5
cargo
PEX13
cytosol
PEX14
B
Ub
PEX1
PEX6
PEX5
lumen
PEX2-10-12
import
cargo
cargo
nuclear pore
C
cytosol
nucleus
D
export
NTR
import
Fig. 8. Model of peroxisomal matrix protein import. (A) PEX13 molecules form a conduit (blue) in the
peroxisomal membrane filled with a meshwork (orange) of their YG domains. PEX5 crosses this barrier with
bound cargo, using WXXXF/Y motifs (magenta) in its flexible N-terminal region. The interaction between the
WXXXF/Y motifs and the lumenal domain of PEX14 retains the receptor inside the organelle. To return to
the cytosol, PEX5 is monoubiquitinated (Ub) by the PEX2-10-12 ubiquitin ligase complex and pulled out by
the PEX1-PEX6 ATPase. Unfolding of PEX5 during export enables cargo to be released in the lumen. After refolding
in the cytosol, and having Ub removed by deubiquitinases, PEX5 can begin another import cycle. (B) PEX5
partitions into the YG meshwork as an extended polypeptide, whose WXXXF/Y motifs locally disrupt the cohesive
tyrosine interactions that hold the meshwork together. (C) Diagram illustrating the scaffold (yellow) of
the nuclear pore complex, filled with a meshwork of nucleoporin FG domains (orange). Note how the nuclear pore
is suspended outside the bilayer instead of being embedded in it like the peroxisomal pore. (D) NTRs use
hydrophobic pockets and patches in folded domains to partition into the FG meshwork and diffuse through the
nuclear pore.
the concentration gradient of the cargo: The
energy derives from PEX5 export, because new
receptor molecules can only enter the lumen
once the previously imported ones have been
retrieved. Notably, the proposed model does
not contradict a possible role of PEX14 in re-
cruiting cargo to peroxisomes (39).
The YG meshwork is suspended in the per-
oxisomal membrane by PEX13 molecules of
opposite orientations. Such dual topology is
unusual (56) and may be generated by random
insertion of PEX13 directly into the peroxisomal
membrane, likely with the involvement of PEX3.
The dual topology facilitates assembly of the
meshwork by allowing the YG domains to
meet and associate within the plane of the
membrane. The location of the YG meshwork
directly in the lipid bilayer contrasts with the
nucleoporin FG meshwork, which forms out-
side the nuclear membrane in the aqueous
central channel of the nuclear pore complex
(compare Fig. 8, A and C). Our hydrogel ex-
periments demonstrate that the N-terminal
region preceding the YG domain can be ac-
commodated in the YG meshwork. This obser-
vation explains why the N terminus of PEX13
can cross the membrane and become acces-
sible to proteases and modification reagents
while the C terminus remains fixed in the
membrane in one of the two orientations.
Notably, the two orientations reconcile previ-
ously conflicting observations regarding the
topology of the C terminus (39). The popula-
tion of PEX13 with its PEX5-binding SH3
domain exposed to the cytosol could help
recruit PEX5 to the organelle.
We suspect that the membrane-spanning
walls that encircle the YG meshwork are
formed by the long AH of PEX13. The AH is
the only feature of PEX13, besides the YG
domain, that is strictly conserved. Our data
show that the AH is also essential for import.
Given its length (>60 residues) and dual
topology, we surmise that alternating orienta-
tions of the AH assemble in a tilted manner
into a pore-like structure in the peroxisomal
membrane (fig. S11A), with their hydrophilic
face oriented toward the aqueous YG phase
in the middle and their hydrophobic face
toward the lipids on the outside (fig. S11B).
The diameter of this structure must be at least
9 nm (the size of the largest cargo reported to
enter yeast peroxisomes) (19) but considerably
smaller than the nuclear pore (~40 nm in
yeast) (57). Indeed, PEX13 has been observed
to form nanometer-sized clusters in the per-
oxisomal membrane by super-resolution micro-
scopy (58), which are potentially consistent
with such a conduit. By analogy to the nuclear
pore, the concentration of YG domains inside
the conduit must be very high (≥200 mg/ml).
Our inability to reach such high concentra-
tions in vitro likely explains why our YG hydro-
gels incompletely exclude inert material.
The similarity between peroxisomal import
and nuclear transport raises the question of
how proteins are targeted to the correct com-
partment. A possible answer is that NTRs have
evolved to bind the phenylalanine-rich motifs
of FG nucleoporins and exhibit low affinity for
tyrosine (44). The peroxisomal meshwork might
also be denser than the nuclear pore phase,
given the shorter distance between aromatic
residues in YG domains compared with nucleo-
porin FG domains. Whereas peroxisomal
import receptors bind the YG phase using
unstructured segments (Fig. 8B), NTRs bind
nucleoporin FG domains using large folded
domains (59) (Fig. 8D). NTRs could thus be
sterically impeded from penetrating the denser
peroxisomal meshwork and would also have a
lower affinity for the YG phase. PEX5 might not
be impeded from traversing the nuclear pore,
however, because it does leak into nuclei and
maintains its steady-state nuclear exclusion
only through continuous CRM1-mediated export
(60). A similar export pathway does not exist
in peroxisomes, which might therefore require
a denser permeability barrier to exclude foreign
proteins. Nevertheless, the barrier is likely not so
tight as to exclude small molecules (35, 40). The
limited permeability of the peroxisomal mem-
brane might explain why a nuclear pore–like
import mechanism, by which a folded protein
crosses the membrane, can be accommodated.
By contrast, other organelles (such as the ER and
mitochondria) need a mechanism that main-
tains a tighter seal during protein translocation
Gao et al., Science 378, eadf3971 (2022)
16 December 2022
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RES EARCH | R E S E A R C H A R T I C L E
and thus require imported proteins to be
unfolded.
Materials and methods
All reagents were obtained from Millipore-
Sigma unless specified otherwise. Buffers were
prepared in ultrapure water. RT denotes room
temperature.
Plasmid construction
The coding sequence of each recombinant
protein was codon-optimized for Escherichia
coli and inserted into plasmid pET-28b(+) by
Gibson Assembly (from New England BioLabs).
PEX5 proteins and cargo were produced as
fusions containing N-terminal glutathione-
S-transferase (GST). A 3C protease–cleavage
site was introduced between the GST and the
recombinant protein, preceded by the amino
acid sequence GSD. The sequence coding for
full-length, wild-type PEX5 corresponds to iso-
form X3 of the Xenopus laevis PEX5.S gene
(GenBank accession no. XP_018082765.1). The
fragment corresponding to the N-terminal
region spans amino acids 1 to 268, whereas the
fragment corresponding to the cargo-binding
TPR domain spans amino acids 260 to 579.
WXXXF/Y motifs in the N-terminal region
were converted to AXXXA by mutagenesis.
GFP fusions to PEX5 or to the fragments re-
ported in the text were generated by inserting
the sequence encoding monomeric enhanced
GFP (mEGFP) downstream of each protein,
separated by either a GGSGGS linker (for full-
length PEX5 or the TPR domain) or a GS linker
(for the N-terminal region). GFP-SKL was as-
sembled by fusing a modified peroxisomal
targeting signal from Photinus pyralis (firefly)
luciferase (i.e., the amino acid sequence
YKGLKSKL) (47) to the C terminus of mEGFP,
preceded by a glycine. GFP alone corresponds
to mEGFP without the targeting signal. The
plasmid encoding the N-terminal region of
PEX5 fused to an anti-GFP nanobody was
described previously (10).
Fragments encoding the YG domain of PEX13
were produced as fusions to an N-terminal 14×
polyhistidine (14×His) tag corresponding to the
amino acid sequence SKHHHHSGHHHTGHH-
HHSGSHHHTGS. A TEV protease–cleavage
site was introduced between the 14×His tag
and the recombinant protein. The fragment
encompassing the entire unstructured N ter-
minus of PEX13 corresponds to amino acids
1 to 193 of PEX13 from A. thaliana (GenBank
accession no. NP_187412.1); the YG domain
alone corresponds to amino acids 76 to 193.
Tyrosines within the YG domain were mu-
tated to serines by mutagenesis. All con-
structs additionally included a single engineered
cysteine at the C terminus for covalent
derivatization.
Constructs designed for gene deletion and
gene expression cassette integration in S. cerevi-
siae (yeast) were assembled by restriction-enzyme
cloning or Gibson Assembly. The coding se-
quence of yeast PEX13 (UniProt accession no.
P80667) represents the wild type. Conventional
sequences for FLAG and SBP epitope tags, as
well as cleavage sites for 3C and TEV proteases,
were incorporated into PEX13 at the positions
indicated in the text. Constructs containing a
C-terminal TEV protease-cleavage site addi-
tionally included a diserine linker between
the cleavage site and the PEX13 coding se-
quence. All cysteine point mutations reported
in the text were made by mutagenesis, as well
as mutations in the hydrophilic face (mut z:
Q150A, E153A, Q164A, and E167A) or the hy-
drophobic face (mut ϕ: L155E and L166E) of
the AH in PEX13. Conversion of tyrosines in
the YG domain of PEX13 (amino acids 71, 81,
86, 90, 95, 101, 108, 110, 114, 115, 119, 123, 127,
and 133) into either serines or phenylalanines
was performed by de novo gene synthesis (by
Integrated DNA Technologies).
To replace the YG domain (amino acids 70
to 134) of yeast PEX13, the sequences of YG
domains from the following organisms were
used: Homo sapiens (human; amino acids 67
to 121, UniProt accession no. Q92968); Dro-
sophila melanogaster (fruit fly; amino acids
70 to 133, UniProt accession no. Q7JRD4); A.
thaliana (plant; amino acids 79 to 187, UniProt
accession no. Q9SRR0); Pichia pastoris (amino
acids 25 to 114, UniProt accession no. C4R2I6);
Torulaspora delbrueckii (amino acids 59 to 135,
UniProt accession no. G8ZRC9); Dictyostelium
discoideum (amoeba; amino acids 99 to 214,
UniProt accession no. Q54CL3); and Chlamy-
domonas reinhardtii (algae; amino acids 70 to
194, UniProt accession no. A0A2K3CZW8).
All constructs were verified by sequencing.
Yeast strains and culture conditions
All yeast strains reported in this study were
derived from the S. cerevisiae parental strain
UTL7A (MATa, ura3-52, trp1, leu2-3/112). Strains
were maintained on yeast extract–peptone-
dextrose (YPD) medium (1% w/v yeast extract,
2% w/v peptone, 2% w/v dextrose) with or
without the antibiotics hygromycin (250 mg/ml;
from Fisher, no. 10687010), geneticin (200 mg/
ml; from Fisher, no. 10131035), or nourseo-
thricin (100 mg/ml; from Jena Bioscience, no.
AB-101), as appropriate. Genomic deletions and
insertions were performed by homologous re-
combination using lithium acetate–based trans-
formation (61).
The UTL7A strain was first derivatized by
integrating the expression cassette for the
violacein biosynthetic pathway (see below) at
the leu2 locus. Briefly, the plasmid pWCD1401
(35) was linearized by the restriction enzyme
NotI, and the excised 11.5-kb fragment was
purified by agarose gel electrophoresis and
used to transform exponentially growing
UTL7A cells. Clones were selected on synthetic
defined (SD) medium containing 2% w/v glucose
and 6.7 g/liter yeast nitrogen base without
amino acids (from BD Difco) and supplemented
with an amino acid mixture lacking leucine
(from Sunrise Science). Correct integration of
the cassette was confirmed by polymerase chain
reaction (PCR), and the resulting violacein-
positive (Vio+) strain was used to generate all
subsequent strains and corresponds to the
wild type.
All gene deletions used the natMX nour-
seothricin-resistance cassette as the selective
marker. The cassette was amplified from plas-
mid pFA6A-natMX (from Addgene, no. 19343)
by PCR, using primers that introduced 60–base
pair (bp) overhangs corresponding to the 5′ and
3′ untranslated regions immediately upstream
and downstream of each gene’s open reading
frame, respectively. Clones were selected on YPD
medium containing nourseothricin (100 mg/ml),
and replacement of each reading frame by the
natMX cassette was confirmed by PCR.
To generate strains expressing mutant or
epitope-tagged versions of the peroxisomal pro-
teins described in the text, the natMX marker
in the corresponding knockout strain was re-
placed with each mutant’s coding sequence,
using either the hygMX hygromycin-resistance
or the kanMX geneticin-resistance cassette
as the selective marker. Briefly, the relevant
coding sequence was PCR-amplified either
from plasmid pFA6A-hygMX (from Addgene,
no. 19342) or pFA6A-kanMX (from Addgene,
no. 39296), together with the corresponding
antibiotic resistance marker, using primers that
introduced 60-bp overhangs as above. Clones
were selected on YPD medium containing hy-
gromycin (250 mg/ml) or geneticin (200 mg/ml),
as appropriate, and correct insertion of the mu-
tant reading frame was validated by PCR.
Peroxisomal matrix protein import assay
A modified violacein biosynthetic pathway (35)
was used to quantitatively measure peroxisomal
matrix protein import activity in S. cerevisiae
cells. Briefly, an expression cassette encoding
three enzymes (VioA, VioB, and VioE), which
together produce a green pigment, was integrated
into the genome along with a leucine auxotro-
phic marker as described above. The first two
enzymes (VioA and VioB) reside in the cytosol,
whereas the third enzyme (VioE) contains a
peroxisome targeting signal and is sequestered
inside peroxisomes when import is functional.
Only when import is compromised does VioE
accumulate in the cytosol and the green pig-
ment is made. Pigment production is inverse-
ly proportional to import efficiency (35).
To measure pigment production, strains
were cultured overnight in YPD medium at
30°C with shaking. The next morning, cul-
tures were diluted 150-fold in 3 ml of freshly
prepared synthetic defined (SD) medium lack-
ing leucine and cultured at 30°C for a further
Gao et al., Science 378, eadf3971 (2022)
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48 hours. Cells were collected by centrifugation
and resuspended in 300 ml of glacial acetic acid
(from Fisher). The cell suspension was transfer-
red to 1.5-ml microfuge tubes and incubated for
10 min at 95°C and then mixed by inversion
and incubated for a further 10 min. Debris were
sedimented by centrifugation at 8000g for
5 min at RT, and the resulting supernatants
were transferred to a 96-well, round-bottom
black-walled plate (from Corning, no. 3792).
Fluorescence of each solution was measured
with a Bio-Tek Synergy Neo2 microplate reader,
using excitation and emission bands of 535 ± 5
and 585 ± 5 nm, respectively. To calculate rel-
ative import activity, the fluorescence reading
from each strain was normalized to the average
reading from wild-type cells (set to 100%) and
pex13D cells (set to 0%) by linear interpolation.
Disulfide-mediated cross-linking
Yeast cells expressing FLAG-tagged PEX13 with
introduced cysteines were cultured overnight
in YPD medium at 30°C. Cells were collected
by centrifugation, washed once with water,
and resuspended in cold lysis buffer (20 mM
HEPES•KOH pH 6.8 at RT, 150 mM potassium
acetate, 5 mM magnesium acetate, 250 mM
sorbitol, and 1 mM EDTA) supplemented with
1 mM phenylmethylsulfonyl fluoride (PMSF)
and a protease inhibitor cocktail (from Bimake,
no. B14001) according to the manufacturer’s
instructions. The cell suspension was transferred
to 2-ml screw-capped tubes (from Sarstedt, no.
726994005) on ice and mixed with 0.5-mm
prechilled glass beads, and the cells were lysed
by bead-beating on a Biospec Products Mini-
Beadbeater-16 (no. 607) for four 30-s cycles
with 2-min cooling on ice in between. The cell
lysate was clarified by low-speed centrifuga-
tion at 2000g for 5 min at 4°C to remove intact
cells and cellular debris, and the resulting
supernatant was recentrifuged at 20,000g for
10 min at 4°C to sediment heavy membranes,
including peroxisomes. The final pellet was
gently resuspended in assay buffer (20 mM
HEPES•NaOH pH 7.2, 50 mM NaCl, 250 mM
sucrose, and 1 mM EDTA) by pipeting followed
by mixing on a rotator at 4°C for 15 min.
The homogeneous membrane suspension
was treated with or without the oxidizing
agent 4,4′-dithiodipyridine (Aldrithiol-4; from
Millipore-Sigma, no. 143057), at the concentra-
tions indicated in the text, for 30 min at 30°C
with gentle agitation. Where indicated, 0.5%
w/v of n-dodecyl-b-D-maltoside (DDM; from
Anatrace, no. D310) was added before the oxi-
dant to solubilize the membranes. Unreacted
cysteines were quenched with 10 mM NEM at
30°C for 5 min. Membranes were then solubi-
lized by shaking for 1 hour at 4°C with 0.5% w/v
DDM, and the solubilisate was clarified by
centrifugation at 20,000g for 10 min at 4°C.
PEX13 was immunoprecipitated from the re-
sulting supernatant using anti-FLAG M2 aga-
rose beads (no. A2220) and eluted by heating
in Laemmli buffer as described below.
Protease protection
Homogeneous membrane suspensions from
yeast cells expressing PEX13 with protease-
cleavage sites (and FLAG or SBP epitope tags)
were prepared as described above. Suspen-
sions were mixed with 2 mM homemade 3C
protease, 2 mM homemade TEV protease, or
both proteases together, as indicated in the
text, and incubated for 16 hours at 4°C. Where
specified, 10 mM NEM was included in the
reactions to preinactivate the proteases. All
reactions were ultimately quenched with 10 mM
NEM, and the membranes were solubilized with
0.5% w/v DDM for 1 hour at 4°C with shaking.
The solubilisate was clarified by centrifugation
at 20,000g for 10 min at 4°C, and PEX13 was
then immunoprecipitated from the resulting
supernatant using either anti-FLAG M2 agarose
or streptavidin agarose beads (from Thermo-
Fisher, no. 20353), as indicated in the text.
Precipitated material was eluted with 0.4 mg/
ml 3×FLAG peptide (from Bimake, no. B23112)
or 4 mM biotin, as appropriate, in assay buffer
containing 0.05% w/v DDM, before being
prepared for SDS-PAGE.
For the experiment shown in Fig. 5B, the
membrane suspension was first digested with
3C protease as described above and then
treated with 200 mM Aldrithiol-4 for 30 min at
30°C to promote disulfide-bond formation.
Reactions were quenched with NEM and pro-
cessed for SDS-PAGE.
PEGmal modification
Homogeneous membrane suspensions from
yeast cells expressing FLAG-tagged PEX13 with
introduced cysteines were prepared as de-
scribed above. Suspensions were incubated
for 90 min at 4°C and gentle agitation with
2 mM methoxypolyethylene glycol maleimide
(PEGmal) of the following sizes (all from
Millipore-Sigma), as specified in the text:
10-kD (no. 712469), 5-kD (no. 63187), 2-kD
(no. JKA3124), and 0.8-kD (no. 712558). Where
indicated, 0.5% w/v DDM was added before
PEGmal to solubilize the membranes. Unre-
acted PEGmal was quenched with 10 mM
cysteine, and PEX13 was immunoprecipitated
with anti-FLAG M2 agarose and prepared for
SDS-PAGE as described above.
Electrophoresis and immunoblotting
Unless specified otherwise, samples were heated
in Laemmli buffer (from Bio-Rad, no. 1610747)
for 5 min at 95°C, with or without 50 mM DTT
(from GoldBio), and electrophoretically resolved
under denaturing conditions on 4-20% TGX
precast polyacrylamide gels (from Bio-Rad).
For Coomassie-blue staining, gels were first
fixed in 50% v/v methanol and 10% v/v acetic
acid for 30 min at RT, then incubated for a
further 30 min in 50% v/v methanol, 10% v/v
acetic acid, and 0.001% w/v Coomassie Brilliant
Blue R-250 (from Bio-Rad), and finally destained
overnight in 10% v/v acetic acid before being
washed into water. For immunoblotting, proteins
were transferred overnight onto nitrocellulose
membranes (from Bio-Rad, no. 1620112). Mem-
branes were blotted in TBST buffer (20 mM
Tris•NaOH pH 7.5, 150 mM NaCl, and 0.1% v/v
Tween 20) containing 3% w/v non-fat milk
solids (from Apex, no. 20241) using antibodies
against the FLAG epitope (no. F7425) or the
SBP tag (no. MAB10764), and fluorescently
labeled secondary antibodies IRDye 800CW
or IRDye 680CW (from LI-COR Biosciences),
as appropriate. Blots were imaged on a LI-COR
Odyssey M imaging system.
Determination of expression levels
To validate expression of FLAG-tagged PEX13
constructs reported in this study, membranes
from the relevant strains were first solubilized
in 0.5% w/v DDM as described above, followed
by immunoprecipitation using anti-FLAG M2
beads before processing for SDS-PAGE.
Bioinformatic analysis
The amino acid composition of the YG domain
of PEX13 versus nucleoporin FG domains was
calculated by the ProtParam tool on the ExPASy
server (62), using the sequences of PEX13,
NUP62, and NUP98 homologs from the orga-
nisms shown in table S1. The number of amino
acids between consecutive aromatic residues
(i.e., the spacer length) in YG domains versus
nucleoporin FG domains was calculated using
a custom script and the sequences of PEX13,
NUP62, and NUP98 homologs from the orga-
nisms listed in table S1. Because FG repeats
consist not only of individual FG motifs but
also of FXFG motifs (where “X” denotes any
amino acid), such tandem motifs were considered
as single aromatic clusters for calculating the
spacer length.
Protein purification
Recombinant proteins were produced in E. coli
BL21 Rosetta 2(DE3) cells (from Novagen) by
induction with isopropyl b-D-1-thiogalactopyra-
noside (IPTG; from GoldBio, no. I2481C50). All
PEX5 proteins and cargo were expressed and
purified by glutathione-affinity and size-exclusion
chromatographies as described previously (10).
Briefly, the proteins were eluted from the
glutathione resin by proteolytic removal of their
GST tag, gel-filtered into 40 mM HEPES•KOH
pH 7.8 at RT, 100 mM KCl, 250 mM sucrose,
1 mM MgCl2, and 1 mM DTT, and concentrated
to 100 mM before snap-freezing in single-use
aliquots.
PEX13 fragments containing the YG domain
were purified under denaturing conditions.
Bacteria transformed with the desired plas-
mid were cultured in baffled flasks on an orbital
Gao et al., Science 378, eadf3971 (2022)
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RES EARCH | R E S E A R C H A R T I C L E
shaker at 37°C in 2×YT medium (from Fisher)
containing 50 mg/ml kanamycin and 34 mg/ml
chloramphenicol. On reaching an optical den-
sity (OD) of 0.6, the cultures were cooled at RT
for 30 min and then supplemented with 1 mM
IPTG and incubated with shaking at 30°C for
an additional 6 hours. Cells were collected by
centrifugation at 4000g, rinsed in phosphate-
buffered saline, and frozen. Cell pellets were
resuspended in freshly prepared lysis buffer
(8 M urea, 100 mM sodium phosphate, 10 mM
HEPES•NaOH, 10 mM imidazole, 5 mM DTT,
and pH adjusted to 8.0 at RT just before use),
incubated for 30 min at RT, and then homo-
genized by sonication. The cell lysate was clari-
fied by centrifugation at 15,000g for 30 min at
20°C, and the resulting supernatant incubated
with nickel-charged nitriloacetic acid (Ni-NTA;
from ThermoFisher) resin for 1 hour at RT with
agitation. Beads were washed with an excess
of lysis buffer and then with an excess of
gelation buffer (2 M urea, 50 mM HEPES•
NaOH, and 1 mM EDTA, pH adjusted to 8.0
at RT just before use) supplemented with
1 mM tris(2-carboxyethyl)phosphine (TCEP;
from GoldBio). Bound protein was eluted with
500 mM imidazole in gelation buffer, supple-
mented with homemade 6×His-tagged TEV
protease, and dialyzed overnight at RT against
gelation buffer containing TCEP. The dialyzed
solution was clarified by centrifugation and
passed over additional nickel resin to remove
the released 14×His tag and TEV protease. The
final flow-through served as the starting point
for gelation.
Preparation and photography of YG hydrogels
To initiate gelation, each recombinant fragment
(dissolved in 2 M urea, 50 mM HEPES•NaOH
pH 8.0 at RT, 1 mM TCEP, and 1 mM EDTA),
was concentrated to 2 mM on a centrifugal filter
device (from Amicon) at 40°C. The resulting
solutions were promptly injected into short
pieces of Tygon S3 silicone tubing (from Saint-
Gobain) that had been plugged at one end
with hot-melt adhesive and incubated at RT
for several days to complete gelation. The con-
tents of each piece of tubing were then squeezed
out onto a colored grid and photographed using
a Canon EF 75-300 mm f/4-5.6 III zoom lens
and a Canon EOS 20D digital single-lens reflex
(DSLR) camera configured to maximize spa-
tial resolution and minimize digital noise.
YG-hydrogel permeation assay
A solution of the unstructured N-terminal region
(including the YG domain) from A. thaliana
PEX13 was concentrated to 2 mM in gelation
buffer as described above. Two-microliter drops
were promptly spotted on the bottom of multiple
wells of a 96-well glass-bottom plate (from
Cellvis, no. P96-1.5H-N) and allowed to set for
several hours at RT. The resulting gel droplets
were equilibrated overnight in excess assay
buffer (25 mM HEPES•KOH pH 7.8 at RT,
130 mM KCl), and imaged on a Leica SP8 X
point-scanning confocal system, using a DMI6000
inverted microscope and a 20× 0.70 NA HC Plan
Apochromat CS air objective. The objective was
centered on the boundary between the buffer
and gel, and focus was maintained 5 mm above
the glass surface by the Leica Adaptive Focus
Control (AFC) system. Six initial frames were
acquired at a rate of two frames per minute,
and then a solution of fluorescently labeled
protein (as indicated in the text) in assay buffer
was added and the acquisition continued for a
further 30 min. All proteins were used at a final
concentration of 500 nM. Images were acquired
in Leica LAS X software using a pixel size of
1.14 mm2, scan speed of 100 Hz, and pinhole
dilated to 1 Airy unit. Fluorescence was excited
using a 490-nm bandlet selected from a white-
light laser by an acousto-optic tunable filter
(AOTF), and a 500- to 700-nm emission band
was collected by a hybrid pixel detector (HyD)
operating in standard mode without gating
and gain set to 100. Imaging parameters were
configured to maximize the signal-to-noise
ratio while avoiding saturation. All samples
intended to be compared were imaged under
identical acquisition settings.
Image analysis
All analysis was performed in ImageJ (63) on
the original, unmodified image data using
routine functions. For images of immunoblots,
band intensities were measured by densitom-
etry. Fluorescence images of YG hydrogels were
first background-subtracted and corrected for
experimental variations in fluorophore con-
centration. To estimate the background, six
successive images of the buffer-gel interface
were acquired before addition of fluorescently
labeled protein and then averaged. The result-
ing matrix was subtracted, pixel by pixel, from
all frames of the time course acquired after ad-
dition of fluorescently labeled protein. Background-
subtracted time courses were then normalized
by mean fluorescence intensity in the buffer.
To measure the protein concentration across
the buffer-gel interface over time, a rectangu-
lar selection 60 mm by 300 mm was centered on
the gel edge, and the mean fluorescence in-
tensity across this field was measured at all
time points using the plot profile function in
ImageJ. The intensities were then normalized
to the maximum value for each experimental
cohort. To calculate the fold enrichment of
each protein inside the gel, the mean intensity
was measured inside a 15-mm arc that followed
the inner contour of the gel edge at the 30-min
time point. This value was then divided by the
mean intensity in the buffer 150 mm away from
the edge. To calculate permeation rates, the
total area inside the gel occupied by the relevant
permeating species at each time point was
identified by intensity-based thresholding.
The resulting displacement values were plot-
ted as a function of time and fitted to straight
lines whose slope corresponded to the perme-
ation rate.
Data plotting and statistical analysis
All experiments were independently per-
formed at least three times. Data were plotted
in GraphPad Prism (v. 9.3.1), and, where indi-
cated, statistical significance was calcula-
ted using Student’s two-tailed unpaired t test.
Fits to mathematical models were performed
by nonlinear least squares regression in Prism.
Image processing for publication and
figure assembly
All images intended to be compared were
processed identically. Fluorescence micrographs
were first background-subtracted and corrected
as described above and then linearly contrast-
stretched in ImageJ to the same bit range.
Digitized images of immunoblots and stained
gels were contrast-stretched to reveal rele-
vant bands but avoid clipping of the back-
ground. Digital photographs of YG hydrogels
were processed using the Camera Raw plugin
(v. 14.5.0.1177) in Adobe Photoshop (v. 23.5.1).
Helical wheel diagrams were prepared using
HeliQuest (64). Secondary structure predic-
tions were performed with AlphaFold (65).
Figures were assembled for publication in
Adobe Illustrator (v. 25.4.1).
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tskn79gd9p.1.
AC KNOWLED GME NTS
We thank R. Erdmann (Ruhr-University Bochum) for the
S. cerevisiae wild-type strain UTL7A, B. Gardner (University of
California, Santa Barbara) for plasmid pWCD1401 encoding the
violacein biosynthetic pathway, and J. Jia for the thermosensitivity
analysis. We are also grateful to D. Görlich (Max Planck Institute,
Göttingen), S. Shao (Harvard Medical School), and members of the
Rapoport lab for insightful discussions and helpful comments on
the manuscript. Imaging was performed with the help of M. Lowe
Ocaña at the Neurobiology Imaging Facility at Harvard Medical
School. Funding: This work was funded by National Institutes of
Gao et al., Science 378, eadf3971 (2022)
16 December 2022
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RES EARCH | R E S E A R C H A R T I C L E
Health grant R01GMO52586 (T.A.R.), the Howard Hughes Medical
Institute (HHMI) (T.A.R.), HHMI-sponsored Helen Hay Whitney
Foundation fellowship award F-1255 (M.L.S.), and HHMI-sponsored
Damon Runyon Cancer Research Foundation fellowship award
2354-19 (Y.G.). Author contributions: Y.G. performed the
experiments in yeast and with peroxisomal membranes. M.L.S.
performed the experiments with hydrogels in vitro. M.L.S. noted
the similarity of PEX13’s YG domain with the FG-repeat domain of
nucleoporins. P.F. assisted with the experiments. All authors
were involved in the experimental design. M.L.S. and T.A.R. wrote
a draft of the manuscript with edits from all authors. T.A.R.
supervised the project. Competing interests: The authors declare
that they have no competing interests. Data and materials
availability: All data are available in the main text or the
supplementary materials; the original unmodified image data are
available from Mendeley Data (66). Reagents generated by this
study are available from the corresponding author with a
completed materials transfer agreement. License information:
Copyright © 2022 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse. This article is subject
to HHMI’s Open Access to Publications policy. HHMI lab heads
have previously granted a nonexclusive CC BY 4.0 license to the
public and a sublicensable license to HHMI in their research articles.
Pursuant to those licenses, the author-accepted manuscript of this
article can be made freely available under a CC BY 4.0 license
immediately upon publication.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf3971
Figs. S1 to S11
Table S1
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
Submitted 18 October 2022; accepted 15 November 2022
10.1126/science.adf3971
Gao et al., Science 378, eadf3971 (2022)
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RES EARCH
QUANTUM INFORMATION
On-demand entanglement of molecules in
a reconfigurable optical tweezer array
Connor M. Holland1†, Yukai Lu1,2†, Lawrence W. Cheuk1*
Entanglement is crucial to many quantum applications, including quantum information processing, quantum
simulation, and quantum-enhanced sensing. Because of their rich internal structure and interactions, molecules
have been proposed as a promising platform for quantum science. Deterministic entanglement of individually
controlled molecules has nevertheless been a long-standing experimental challenge. We demonstrate on-
demand entanglement of individually prepared molecules. Using the electric dipolar interaction between pairs
of molecules prepared by using a reconfigurable optical tweezer array, we deterministically created Bell pairs
of molecules. Our results demonstrate the key building blocks needed for quantum applications and may
advance quantum-enhanced fundamental physics tests that use trapped molecules.
E ntanglement lies at the heart of quantum
mechanics. It is central to the practical
advantage provided by quantum devices
(1–3) and relevant to understanding the
behavior of many-body quantum systems
(4). The ability to create entanglement control-
lably has been a long-standing experimental
challenge. Molecules have been proposed as a
promising platform for quantum simulation
and quantum information processing because
of their rich internal structure and long-lived
interacting states (5–8). In the past two dec-
ades, much progress has been made in pro-
ducing and controlling molecules at ultracold
temperatures, both through coherent assem-
bly of ultracold alkali atoms (9) and direct
laser-cooling (10). Rapid advances have been
made in recent years, including the creation
of degenerate molecular gases (11, 12), the
creation of molecular magneto-optical traps
(10, 13–15), high-fidelity detection of single
molecules (16–18), and laser-cooling of com-
plex polyatomic molecules (19, 20). In addi-
tion, coherent dipolar interactions have been
observed in bialkali molecules trapped in op-
tical lattices (18, 21).
A major outstanding challenge to fully real-
izing the potential of molecules has been
achieving deterministic entanglement with
microscopic control. In this work, we real-
ized on-demand entanglement between indi-
vidual laser-cooled molecules trapped in a
reconfigurable optical tweezer array (Fig. 1A).
The approach of molecular tweezer arrays
(16, 17, 22, 23) combines the microscopic
controllability offered by reconfigurable opti-
cal tweezer traps (24–28) with the ability to
generate entanglement through the electric
dipolar interaction between molecules. We
specifically made use of effective spin-exchange
1Department of Physics, Princeton University, Princeton, NJ
08544, USA. 2Department of Electrical and Computer
Engineering, Princeton University, Princeton, NJ 08544, USA.
*Corresponding author. Email: lcheuk@princeton.edu
†These authors contributed equally to this work.
interactions that arise between rotational states
to entangle pairs of molecules into Bell states
(Fig. 1B) (29), which are prototypical maximally
entangled states of two particles. Our entangle-
ment protocol implements an iSWAP gate (8)
that, along with site-resolved single-qubit rota-
tions achievable in our platform through the
optical addressing of individual molecules, ful-
fills the requirement for universal quantum
computation.
Preparing and initializing arrays of
laser-cooled molecules
Our work starts with single laser-cooled cal-
cium monofluoride (CaF) molecules trapped
in a dynamically reconfigurable array of opti-
cal tweezer traps (17, 23). Through a series of
steps involving laser-cooling, optical trapping,
and transport, single molecules are transfer-
red from a magneto-optical trap into a one-
dimensional (1D) array of 37 identical optical
tweezer traps with a uniform spacing of
4.20(6) mm (numbers in parentheses are the
standard deviation). Because our laser-cooling
scheme relies on a closed optical cycle present
only for the X2S(v = 0, N = 1) manifold in CaF
(30)—where v and N denote the molecular
vibrational and rotational state, respectively—
the molecules loaded into the tweezers occupy
a single rovibrational manifold.
To remove the randomness in tweezer oc-
cupation, we used a rearrangement approach
pioneered in neutral atom experiments (24, 25).
We nondestructively detected the tweezer oc-
cupations using a variant of L-imaging (31). The
empty tweezers were identified then switched
off, and the remaining occupied tweezers were
then rearranged into the desired 1D pattern. We
characterized the rearrangement procedure by
measuring the probability of successfully creat-
ing uniform arrays and found a single-particle
rearrangement fidelity of 97.4(1)%. As shown
in Fig. 2A, we were able to create uniform ar-
rays up to a size of 16, with a probability >0.6.
The rearrangement fidelity was limited by the
nondestructive detection fidelity, with mini-
mal loss [0.2(10)%] caused by movement of
the tweezer traps.
ð
After rearrangement, we initialized the in-
ternal state of the molecules, which were dis-
tributed among the 12 hyperfine states in the
X2S(v = 0, N = 1) rovibrational manifold. To
prepare molecules into a single hyperfine state,
we optically pumped molecules into Dj i ¼
X 2S v ¼ 0; N ¼ 1; J ¼ 3=2; F ¼
2; mF ¼ 2Þ,
where J denotes the total angular momentum
excluding nuclear spin, F denotes the total
angular momentum, and mF denotes its proj-
ection onto the quantization axis. Subsequent
microwave sweeps along with an optical clean-
out pulse transferred the molecules into the
target final state ↑j i ¼ X 2S v ¼ 0; N ¼ 1; J ¼
1=2; F ¼ 0; mF ¼ 0Þ (Fig. 2C). The overall
fidelity of preparing molecules in ↑j i was
82.4(11)%. Our preparation sequence ensures
that the dominant preparation error is in the
form of unoccupied tweezers, with a small
contribution coming from molecules prepared
ð
i ¼ X 2S v ¼ 0;
in the incorrect internal state þj
N ¼ 0; J ¼ 1=2; F ¼ 1; mF ¼ 1Þ. The state ini-
tialization errors come from imperfect micro-
wave transfer, polarization impurity of the
optical pumping light, and loss caused by heat-
ing in the tweezer traps. After state prepara-
tion, we measured a molecular temperature
of T = 151(10) mK.
ð
Probing rotational coherence
of single molecules
To produce entanglement through the dipo-
lar interactions between molecules, we re-
quired long coherence times compared with
the typical interaction timescales of ~10 ms
at our tweezer separations. Achieving long
coherence times for optically trapped mole-
cules has been an ongoing experimental chal-
lenge, with steady advances being made. For
molecules, different internal states can expe-
rience different trapping potentials that, in
combination with motion caused by finite
temperature, can lead to decoherence. For
1S bialkali molecules, long coherence times
of different nuclear spin states have been
reported (32). Work using “magic” trapping
conditions has also demonstrated extended
coherence times between rotational states in
both 1S and 2S molecules (18, 33–36).
ð
Because the effective spin-exchange inter-
actions couple different rotational states, we
wanted long rotational coherence times be-
tween the two interacting states ↑j i and ↓j i ¼
X 2S v ¼ 0; N ¼ 0; J ¼ 1=2; F ¼
1; mF ¼ 0Þ.
Building on previous work in CaF (36), we iden-
tified a pseudo-magic trapping condition in
which both spin states experience approxi-
mately identical trapping potentials. Our pseudo-
magic condition takes into account vector
and tensor shifts and is achieved by applying
a magnetic field orthogonal to the tweezer
light polarization at a reduced tweezer depth
Holland et al., Science 382, 1143–1147 (2023)
8 December 2023
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RES EARCH | R E S E A R C H A R T I C L E
compared with that used for initial loading
and imaging.
To measure the resulting coherence time,
we prepared pairs of tweezer traps in which
one trap is empty and the other is occupied by
a molecule initialized in ↑j i. We next applied a
Ramsey pulse sequence consisting of two p/2
microwave pulses (first pulse along ^x , second
A
B
1
2
1
2
...
C
(1) Load
(2) Rearrange
(3) Initialize
(4) Interact
(5) Detect
Fig. 1. Laser-cooled molecules in a reconfigurable optical tweezer array. (A) Single CaF molecules
trapped in an optical tweezer array are prepared into closely separated tweezer pairs. Molecules in each pair
held by separate tweezer traps interact through the long-range electric dipolar interaction
electric dipolar interaction leads to dipolar spin-exchange of rotational excitations. (C) Molecules are loaded
stochastically, detected nondestructively, and rearranged into the desired 1D configuration. The molecules
are then initialized into a single internal state, and the pair separations are reduced to switch on interactions.
After specific interaction times, the pairs are separated and detected state-selectively.
^HSE. (B) The
pulse along ^n ¼ cos q^x þ sin q^y) separated by
a variable free evolution time (Fig. 3A). The
remaining fraction of ↑j i molecules, P↑, oscil-
lates as a function of q, with the oscillation
amplitude directly measuring the coherence.
Fitting to an exponential decay curve yields
a bare coherence time T (cid:2)
2 of 2.5(3) ms. Add-
ing a spin-echo improves the coherence time
to T2 = 29(2) ms. Following previous work
that explored dipolar interactions of KRb
molecules in an optical lattice (21, 37), we
implemented the XY8 dynamical decoupling
sequence depicted in Fig. 3B and found that
the 1/e coherence time was further extended
to 215(30) ms (Fig. 3C). This is consistent with
our understanding that the bare coherence
times are primarily limited by slow (millisec-
ond timescale) fluctuations of ambient mag-
netic fields.
Observing coherent intermolecular
interactions
Having achieved sufficiently long rotational
coherence times, we next set out to observe
coherent spin-exchange interactions. The long-
range electric dipolar interaction between the
molecules gives rise to resonant exchange of
rotational excitations between ↑j i and ↓j i. The
resulting spin-exchange interaction is described
by the Hamiltonian
(cid:1)
(cid:3)
J
HSE ¼
(cid:1)
2
¼ J ^S
þ
(cid:3)
^S
1
x
^S
þ ^S
y
^S
2
x
þ ^S
(cid:3)
1
^S
þ
^S
2
(cid:3)
y
1
2
1
2
(cid:3)
þ
where ^S
i , ^S
molecule i and
i , ^S
x
i , ^S
y
i are spin-1/2 operators for
(cid:4)
(cid:5)
D
J ¼
1
r3 1 (cid:3) 3 cos2q′
d2
4pe0
E
↑jd^j↓
with d ¼
being the transition dipole
moment, r ¼ r→(cid:6)
(cid:6)
(cid:6) being the intermolecular sepa-
(cid:6)
ration, q′ being the angle between r→
and the
quantization axis, and e0 being the free space
permittivity. Starting with two molecules in a
product state, time evolution under ^H SE can
lead to entanglement. For example, two mole-
cules initially prepared in the product state
↑j i (cid:4) ↓j i become maximally entangled after
interacting for a time t = pħ/(2J), where ħ is
Planck’s constant h divided by 2p. In our sys-
tem, the quantization axis is orthogonal to the
intermolecular separation—that is, q′ = 90°.
Fig. 2. Tweezer rearrangement and internal state initialization. (A) Probability of creating defect-
free molecular arrays through rearrangement. A fit to pn, where n is the array size, gives a single-particle
rearrangement fidelity of p = 0.974(1). (B) Example images of defect-free arrays. (C) Optical pumping
(orange arrow) prepares molecules in Dj i. Microwave sweeps (dashed green arrows) transfer Dj i
molecules to ↑j i.
To observe the effect of spin-exchange inter-
actions, we first created pairs of ↑j i molecules
at an initial separation of 4.20(6) mm, over
which interactions were negligible. We next
reduced the pair separation to 1.93(3) mm over
3 ms, at which the interaction strength J (J =
h × 43 Hz) becomes appreciable on the co-
herence timescale. Subsequently, we applied
the Ramsey pulse sequence used above with
q = 0. To retain long coherence times, the XY8
decoupling pulses were kept on during the free
Holland et al., Science 382, 1143–1147 (2023)
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Fig. 3. Single-particle coherence and spin-exchange oscillations. (A) Ramsey
pulse sequence used to measure rotational coherence. (Bottom) Bloch sphere
diagrams show the action of the various pulses for a molecule initialized in ↓j i.
(B) The XY8 dynamical decoupling sequence. (C) Ramsey contrast of
noninteracting molecules versus free evolution time t. Green triangles, red
squares, and blue circles indicate the cases for which no spin-echo, one spin-
echo, and the XY8 sequence is applied, respectively. Exponential fits give
coherence times (1/e) of 2.5(3) ms, 29(2) ms, and 215(30) ms, respectively.
(Insets) Ramsey fringes with corresponding sinusoidal fits indicated with
the dashed lines. (D) Spin-exchange oscillations at a tweezer separation of
1.93(3) mm. Shown are the ↑↑j
i populations measured after the Ramsey pulse
sequence, P↑↑, as a function of interaction time t, for molecular pairs initialized in
i. The solid curve is a fit to a phenomenological model. (Insets) Fluorescence
↑↑j
images at the indicated times. (E) Spin-exchange oscillations at separations of
1.26(2) mm (red pentagons), 1.43(2) mm (orange hexagons), 1.60(2) mm
(yellow diamonds), 1.68(2) mm (green squares), 1.93(3) mm (blue circles), and
2.35(3) mm (purple triangles). Curves are offset vertically by 0.3 for clarity.
(F) The extracted spin-exchange strength J versus pair separation r. The light red
band indicates the theoretical prediction taking into account the finite temperature
of the molecules and the uncertainty in the electric dipole moment of CaF. The
dashed blue curve indicates the prediction without taking into account finite
temperature. (Inset) The single-particle loss rate gD versus pair separation r.
evolution time. Because the p-pulses in the XY8
sequence leave ^H SE unchanged, spin-exchange
interactions are preserved (38).
i, the re-
sulting state after the Ramsey sequence is given by
(cid:10)
yj i ¼ ie(cid:3)i Jt
For a molecular pair initialized in ↑↑j
(cid:7) (cid:8)
Jt
4ℏ
(cid:7) (cid:8)
Jt
4ℏ
i þ i cos
4ℏ sin
↓↓j
↑↑j
(cid:9)
i
ð1Þ
and P↑↑ oscillates at an angular frequency of J/(2ħ).
As shown in Fig. 3D, we observed oscillations of
P↑↑, directly revealing the presence of coherent
spin-exchange interactions. By varying the pair
separation between 1.26(2) and 2.35(3) mm, we
verified that the interaction strength J, as ex-
tracted from the oscillation frequency, approx-
imately scales as 1/r3, as expected for dipolar
interactions (Fig. 3F). Experiments with bulk sam-
ples of bialkali molecules in optical lattices have
observed coherent spin-exchange both through
macroscopic measurements (21, 37) and with
single-molecule resolution (18), whereas in this
work, we observed coherent interactions between
individually prepared, laser-cooled molecules.
Examining the P↑↑ oscillations in detail, we
found that they damp more quickly when the
molecules are closer. This could arise from
increased molecular loss and reduced single-
particle coherence times at close separations.
Additionally, the thermal motion of molecules
gives rise to disorder in the spin-exchange cou-
pling constant J through variations in the in-
termolecular separations, leading to damping.
At a fixed molecular temperature, this ef-
fect increases at closer separations. To deter-
mine which damping mechanism is dominant,
we first measured single-particle loss rates and
found that they increase at close separations
(Fig. 3F, inset). We believe that the loss is caused
by parametric heating specific to our scheme
of generating tweezer traps using an acousto-
optical deflector (AOD) and can be circumvented
with other tweezer-generation techniques. Mo-
lecular loss, however, does not account for all of
the observed damping, especially at close sepa-
rations. Independently measured single-particle
decoherence rates are also insufficient to ex-
plain the damping. This leaves finite molecular
temperature as the dominant cause of damp-
ing at close distances. Simulations that used
experimentally measured temperatures revealed
damping rates comparable with the observa-
tions (supplementary text and fig. S2) (39).
Creating and verifying entanglement
of molecules
Having established the presence of coherent
spin-exchange interactions, we next used them
to entangle molecules. Specifically, as proposed
in (8), time evolution by ^H SE for a specific time
of T = pħ/J implements an iSWAP gate, which
is maximally entangling. By applying two
additional p/2 pulses along the x axis before
and after the iSWAP gate, one can convert a
molecular pair prepared in ↑↑j
i into the Bell
Þ, which is max-
ð
i þ i ↓↓j
state yB
imally entangled. As a compromise between
maximizing J and minimizing heating loss,
we chose a pair separation of 1.93(3) mm for
creating yB
i ¼ 1ffiffi
p
2
↑↑j
i.
i
j
j
To demonstrate entanglement of molecules,
we measured the Bell state creation fidelity
F ¼ yB rj jyB
i, where r is the experimentally
h
obtained density matrix. As pointed out in
(40), F acts as an entanglement witness, with
F > 1=2 indicating two-particle entanglement.
To extract F experimentally, we made use of
the relation (41)
(cid:4)
P↑↑ þ P↓↓ þ C
(cid:5)
F ¼
1
2
ð2Þ
i and ↓↓j
where P↑↑ and P↓↓ are the probabilities of mea-
i, respectively, and C is the
suring ↑↑j
i and ↓↓j
amplitude of the coherence between ↑↑j
i.
To measure P↑↑, we separated the two mo-
i and subsequently
j
lecules after preparing yB
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Fig. 4. Creating and probing Bell pairs. (A) (Top left) The two-tweezer detection
probabilities Pij for the Bell pairs. (Top right) Corresponding probabilities when
an additional p pulse is applied before measurement. (Bottom) The full probabilities
extracted from top left and top right. The SPAM-corrected populations for
the ↑j i– ↓j i subsystem are indicated with the green triangles. (B) Probing Bell
state coherence through parity oscillations. The coherence C between ↑↑j
i
and ↓↓j
i is obtained from the amplitude of the oscillations in P as a function
of q. (Insets) Example images at the maxima and minima of P. (C) SPAM-
corrected Bell state fidelity F SPAM versus hold time t at the initial pair creation
distance of 1.93(3) mm are indicated with blue circles. Red squares indicate
the corresponding data for pairs separated to a larger distance of 4.20(6) mm
after creation. (Inset) The contrast CSPAM versus hold time t for the two separations.
The extracted 1/e lifetimes are (F SPAM, CSPAM) = [85(5) ms, 61(3) ms] at the Bell
creation distance, and [70(16) ms, 57(8) ms] at the larger separation.
measured the probability that both tweezers
in a pair appear bright. Because our imaging
scheme detects only ↑j i molecules, to measure
P↓↓ we applied an additional p-pulse before
detection (Fig. 4A) to convert molecules from
↓j i to ↑j i. To obtain the coherence envelope C,
we measured parity oscillations as follows. We
applied a p/2 pulse about a variable axis ^n ¼
cos q^x þ sin q^y after preparing yB
i. From the
two-tweezer probabilities Pij, we constructed
the parity signal P = P11 + P00 – P10 – P01,
where 1 and 0 denote a bright or dark tweezer
site, respectively.
j
i and ↓↓j
For a general density matrix that includes
the possibility of empty tweezers ( ej i) caused
by imperfect state preparation, P can display
modulation periodic in 2q and q. The 2q mod-
ulation is directly related to the coherence be-
tween ↑↑j
i, whereas the q modulation
is related to single-molecule coherences, such
as that between e↑j
i and e↓j
i. The amplitude of
the 2q modulation directly gives C. As shown in
Fig. 4B, we found that P displays modulation
periodic in 2q. The lack of oscillations periodic
in q is consistent with the pulse sequence
used. Single molecules prepared in e↑j
i
i or ↓ej
effectively experienced a p-pulse, and no single
particle coherence was created.
From the population and parity oscillation
measurements, we obtained a raw Bell state
fidelity of F RAW ¼ 0:524ð6Þ. Correcting for
detection errors, we obtained a Bell state fidel-
ity F ¼ 0:540 7ð Þ. The raw and measurement-
corrected fidelities were above 1/2, showing
that entanglement was indeed present and
created on demand.
Correcting additionally for state preparation
errors, we obtained a state-preparation and
measurement (SPAM)–corrected fidelity of
F SPAM ¼ 0:80ð2Þ. In the context of quantum
information processing, the SPAM-corrected
Bell state fidelity provides an indication of the
quality of the iSWAP gate implemented through
spin exchange. Nevertheless, full characteriza-
tion of our iSWAP gate and a measurement of
its fidelity will require full quantum process
tomography. With relevance to quantum simu-
lation, our measurements of spin-exchange
interactions demonstrate the fundamental
building block for simulating XY spin models.
In particular, the phase of the 2q oscillation
in parity measures the relative phase between
↑↑j
i in the Bell state, which is sen-
sitive to the sign of J. The observed phase of
the oscillation shows that J > 0, indicating anti-
ferromagnetic spin-exchange interactions. In
addition to quantum information processing
and quantum simulation, the ability to create
entanglement in our system also paves the way
toward quantum-enhanced metrology with
trapped molecules (42).
i and ↓↓j
Having demonstrated deterministic creation
of Bell pairs, we next probed their lifetime. We
measured the Bell state fidelity F SPAM as a
function of hold time and found a lifetime of
85(5) ms, which is largely consistent with but
somewhat shorter than that expected from
uncorrelated single-particle decoherence. We
also examined whether the Bell pairs survive
when separated to larger distances after their
creation. Specifically, we separated the Bell
pairs to a distance of 4.20(6) mm over 3 ms
after their creation and measured F SPAM as a
function of hold time. Within experimental
uncertainty, we found a lifetime identical to
the case without separation (Fig. 4C). This abil-
ity to preserve entanglement while separating
molecules could allow one to bypass the lim-
ited range of dipolar interactions through
movement of molecules and obtain arbitrary
connectivity useful for quantum simulation
and information processing. Similar abilities
to preserve entanglement have recently been
demonstrated in atomic tweezer arrays (43).
Last, we examined how Bell state fidelities
can be improved. The measurement-corrected
fidelities were affected substantially by state
preparation infidelity, which is caused by a
variety of technical imperfections such as in-
complete microwave transfers. A detailed ac-
counting of errors shows that state preparation
fidelities exceeding 0.95 can be achieved (39).
Separately, the SPAM-corrected Bell state fi-
delity, which reflects the quality of the iSWAP
gate, is substantially affected by the finite mo-
lecular temperature. To reveal the importance
of state preparation fidelity and molecular
temperature, we implemented an alternate
state preparation procedure (39) that both
provides a higher state preparation fidelity
[0.85(1)] and a lower molecular temperature
[T = 107(5) mK]. The resulting fidelities without
state preparation correction were improved to
F RAW ¼ 0:608ð14Þ and F ¼ 0:629ð14Þ , re-
vealing the importance of state preparation
(two-tweezer probabilities and parity oscilla-
tion data are provided in fig. S4) (39). In addition,
F SPAM improves to 0.863(25) (39), suggest-
ing that molecular temperature is a key factor
in achieving high-fidelity entanglement.
Discussion and Outlook
The observed dependence of SPAM-corrected
Bell state fidelities on temperature agrees
well with numerical simulations, which in-
dicate that lowering the molecular temper-
atures further by a factor of ~10 could allow
fidelities to reach the 0.99 level (39). Such fur-
ther cooling could be achieved with methods
such as Raman sideband cooling for molecules
Holland et al., Science 382, 1143–1147 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
(44, 45). Further improvements are also pos-
sible through optimized entanglement schemes.
Recent theoretical work that used quantum
optimal control has proposed a robust two-qubit
entangling gate for CaF molecules in tweezer
traps that provides entanglement fidelities ex-
ceeding 0.999, under the assumption that they
are cooled near their motional ground state (46).
We have demonstrated on-demand entan-
glement of molecules in a reconfigurable opti-
cal tweezer array. Our work was enabled by
several advances we have made in controlling
laser-cooled molecules, including initialization
of defect-free molecular arrays, achievement
of long rotational coherence times in tightly
focused tweezer traps, and observation of
coherent dipolar interactions between indi-
vidual laser-cooled molecules. The ability to
entangle molecules on demand is a key build-
ing block toward simulating quantum spin
models, processing quantum information, and
performing quantum-enhanced measurements
in the emerging platform of molecular tweezer
arrays. Specifically for quantum simulation and
information processing, the interactions be-
tween long-lived molecular states could offer
long evolution times and deep circuit depths.
With further advances in lowering molecular
temperatures, molecular tweezer arrays could
potentially provide performance similar to that
of established platforms such as Rydberg atom
arrays, trapped ions, and superconducting
qubits. Our work on entangling molecules
on demand, combined with the recent rapid
progress in extending laser-cooling to molec-
ular species of increasing complexity (19, 20),
opens research avenues such as quantum-
enhanced precision measurement by using
trapped molecules (47) and explorations of
molecular collisions (48) and chemical reac-
tions with entangled matter.
After the initial submission of this work, we
became aware of related work reporting dipo-
lar spin-exchange and entanglement between
molecules in an optical tweezer array (49).
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AC KNOWLED GME NTS
We thank S. J. Li, W. Bakr’s group, S. Gopalakrishnan, and
J. Thompson for fruitful discussions. We also thank W. Bakr,
J. Thompson, S. J. Li, and C. Chiu for careful readings of the
manuscript. Funding: This work was supported by National
Science Foundation grant 2207518, the Alfred P. Sloan
Foundation, and Princeton University. Author contributions:
Conceptualization: L.W.C. Methodology: C.M.H., Y.L., and L.W.C.
Investigation: C.M.H., Y.L., and L.W.C. Visualization: C.M.H., Y.L.,
and L.W.C. Funding acquisition: L.W.C. Supervision: L.W.C.
Writing – original draft: C.M.H., Y.L., and L.W.C. Writing – review
and editing: C.M.H., Y.L., and L.W.C. Competing interests: The
authors declare that they have no competing interests. Data and
materials availability: Data and code are available at Dryad
(50) and Zenodo (51). License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf4272
Materials and Methods
Supplementary Text
Figs. S1 to S5
Table S1
References (52–56)
Submitted 20 October 2022; resubmitted 30 November 2022
Accepted 28 September 2023
10.1126/science.adf4272
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RES EARCH
POLLUTION
Mortality risk from United States coal
electricity generation
Lucas Henneman1,2*, Christine Choirat3, Irene Dedoussi4, Francesca Dominici2,
Jessica Roberts5, Corwin Zigler2,6
Policy-makers seeking to limit the impact of coal electricity-generating units (EGUs, also known as power
plants) on air quality and climate justify regulations by quantifying the health burden attributable to
exposure from these sources. We defined “coal PM2.5” as fine particulate matter associated with coal EGU
sulfur dioxide emissions and estimated annual exposure to coal PM2.5 from 480 EGUs in the US. We estimated
the number of deaths attributable to coal PM2.5 from 1999 to 2020 using individual-level Medicare death
records representing 650 million person-years. Exposure to coal PM2.5 was associated with 2.1 times greater
mortality risk than exposure to PM2.5 from all sources. A total of 460,000 deaths were attributable to coal
PM2.5, representing 25% of all PM2.5-related Medicare deaths before 2009 and 7% after 2012. Here, we
quantify and visualize the contribution of individual EGUs to mortality.
A ir pollution exposure is associated with
adverse health effects and increased risk
of death (1–4). Coal electricity-generating
units (EGUs), or power plants, are a major
contributor to poor air quality (5–7). Coal,
historically a relatively inexpensive fuel, is
burned to provide electricity worldwide even
as the US and other nations continue to de-
bate whether it should remain a part of the
energy portfolio amid public health and cli-
mate concerns. Global coal use for electricity
generation is projected to increase (8), and
ongoing instability has pushed European na-
tions to increase coal use (9, 10). Although coal
EGU air pollution emissions have declined in
the US in recent decades (11), defining the
health burden posed by coal EGUs and the
benefits of actions that have reduced EGU emis-
sions remains paramount to informing public
health, climate, and energy policies in the US
(12) and worldwide.
Previous studies that quantified the mor-
tality burden from coal EGUs in the US (13–18)
relied on estimated concentration response
functions (CRFs), which assume that fine par-
ticulate matter (PM2.5) from coal emissions has
the same toxicity as PM2.5 from all sources. How-
ever, evidence indicates (19–25) that exposure to
sulfur, sulfates, or PM2.5 from coal emissions
may be associated with higher relative morbid-
ity or mortality risk than that to other PM2.5 con-
stituents or PM2.5 from other sources per unit
concentration, although uncertainty remains
(26, 27). The limited regional (19–22) and tem-
poral (23–25) scope of previous studies, along
with the lack of availability of coal-specific ex-
posure estimates, has hindered the adoption
of coal-specific PM2.5 CRFs in mortality burden
calculations, likely leading to underestimates
of the mortality burden associated with coal
EGUs. In addition, previous studies lack tar-
geted evidence regarding which coal EGUs are
most responsible for increased mortality risk,
and this information is needed to inform policies.
To estimate the number of deaths associa-
ted with exposure to coal PM2.5 from EGUs, we
conducted a national-scale study of individual-
level health records covering >650 million
person-years in the US Medicare population
(≥65 years of age) from 1999 to 2016 (unless
otherwise noted, populations throughout this
study refer specifically to the Medicare popu-
lation) (28). We defined “coal PM2.5” as PM2.5
from coal EGU SO2 emissions. We estimated
coal PM2.5 using the HYSPLIT with Average
Dispersion (HyADS) model, which accounts
for date-specific atmospheric transport of PM2.5
to characterize exposure to PM2.5 from individ-
ual EGUs (29–32). We used HyADS, a reduced
complexity model, to estimate 22 years of ex-
posure to coal PM2.5 (from 1999 to 2020) from
each of 480 US EGUs. These calculations would
have required multiple orders of magnitude
more computation time using a typical full-
scale chemical transport model.
Our study offers the following contribu-
tions. First, we estimated and compared mor-
tality risk associated with exposure to coal
PM2.5 versus total PM2.5 from all sources,
showing that previous analyses underestimated
the mortality burden from coal EGUs in the US.
Second, we calculated the number of deaths
linked to each of the 480 coal EGUs, ranking
each with respect to its contribution to the
mortality burden and tracking its contribu-
tion to the overall mortality burden over time
amid implementation of emissions controls
1Department of Civil, Environmental, and Infrastructure
Engineering, George Mason University Volgenau School of
Engineering, Fairfax, VA, USA. 2Department of Biostatistics,
Harvard T.H. Chan School of Public Health, Harvard Data Science
Initiative, Harvard University, Boston, MA, USA. 3Institute of
Global Health, Faculty of Medicine, University of Geneva, Geneva,
Switzerland. 4Section Aircraft Noise and Climate Effects,
Faculty of Aerospace Engineering, Delft University of Technology,
Delft, Netherlands. 5School of Interactive Computing, Georgia
Institute of Technology, Atlanta, GA, USA. 6Department of
Statistics and Data Sciences, University of Texas, Austin, TX, USA.
*Corresponding author. Email: lhennem@gmu.edu
Fig. 1. ZIP code–level coal PM2.5 over time. Box plots (median, first, and third quartiles are shown as horizonal lines and outliers as dots) summarize the distribution
of ZIP code levels of coal PM2.5. Map areas shown in white do not have ZIP codes. Plots were produced in R using ggplot2; spatial information comes from the
USAboundaries package.
Henneman et al., Science 382, 941–946 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
and retirements. Third, we documented the
spatial distribution of the mortality burden
across the US.
Results
Changes in exposure to coal PM2.5 over time
By averaging ZIP (postal) code levels of coal
PM2.5 across the conterminous US, we found
that the annual average coal PM2.5 declined
from 2.34 mg m−3 (range, 0.01 to 8.80) in 1999
to 0.07 mg m−3 (range, 0.00 to 0.39) in 2020
(Fig. 1). Coal PM2.5 was elevated in the eastern
US relative to the western US, with annual
average concentrations exceeding 4 mg m−3
in multiple ZIP codes in all years from 1999 to
2008. Coal PM2.5 exposure is a combination
of emissions from nearby and distant EGUs
(figs. S1 and S2).
Coal PM2.5 CRF
The Medicare dataset contains records of
32.5 million deaths from 1999 to 2016 (table S1),
with the annual number of deaths increasing and
death rates decreasing across the study period
(fig. S3). We found that a 1 mg m−3 increase in
annual average coal PM2.5 was associated with
a 1.12% increase in all-cause mortality [relative
risk (RR): 1.0125; 95% confidence interval (CI):
1.0113 to 1.0137]). This risk is ~2.1 times greater
than the RR associated with exposure to PM2.5
from any source (1.0060 per mg m−3; 95% CI:
1.0053 to 1.0067), which was estimated by
Wu et al. in 2020 in the same Medicare cohort
using an analogous statistical model (4).
Number of excess deaths attributable to
coal PM2.5
For each year from 1999 to 2020, we estimated
the excess number of deaths attributable to coal
PM2.5 relative to what would have occurred
assuming zero SO2 emissions from coal EGUs
(i.e., coal PM2.5 = 0). Summing over the study
period, we estimated that 460,000 (95% CI:
420,000 to 500,000) deaths would have been
avoided if all coal EGU SO2 emissions were
eliminated (Fig. 2 and table S2). Annual ex-
cess deaths attributable to coal PM2.5 were
highest between 1999 and 2007, averaging
more than 43,000 deaths per year for a total
of 390,000 (95% CI: 360,000 to 430,000). After
2007, annual excess deaths declined substan-
tially, reaching 1600 (95% CI: 1400 to 1700) in
2020. The total number of deaths in the Medi-
care population for the period 1999 to 2020
was 38.6 million (we projected annual deaths
in each ZIP code for the period 2017 to 2020 as
the average from 2014 to 2016; fig. S3). There-
fore, Medicare deaths associated with coal
PM2.5 exposure represent 1.2% (95% CI: 1.1 to
1.3%) of all Medicare deaths. Changes in base-
line mortality rates had a much smaller influence
than changes in coal PM2.5 on the variability in
annual deaths associated with coal PM2.5 since
1999 (figs. S4 and S5).
Fig. 2. Annual number of excess deaths attributable to coal PM2.5, estimated using the RR for coal
PM2.5 from this study and RRs for total PM2.5 from the literature. All excess deaths are estimated
relative to zero coal PM2.5. The area filled by horizontal hashing indicates deaths estimated using RRs derived
from this study (bounds represent 95% CI). Areas filled by vertical and diagonal hashing correspond to
deaths estimated using RRs for total ambient PM2.5 exposure from the literature (4, 33). The gray shaded
region from 2017 to 2020 represents years for which ZIP code–specific baseline death rates were assumed
from the 2014 to 2016 average. This figure was produced in R using ggplot2.
The estimated RR for coal PM2.5 from the
statistical model was higher than the previous-
ly estimated RRs for total PM2.5 exposure that
are often used for risk assessments, implying
that the number of excess deaths attributa-
ble to coal EGUs was underestimated in prior
studies (13–18). For example, by combining
coal PM2.5 exposure with two RRs for total
PM2.5 previously used in risk assessments,
1.0060 per 1 mg m−3 (95% CI: 1.0053 to 1.0067)
estimated for the Medicare population (4) and
1.6% per 10 mg m−3 (95% CI: 1.4 to 1.8) esti-
mated for the general population (33), we esti-
mated 240,000 (95% CI: 220,000 to 260,000)
and 200,000 (95% CI: 130,000 to 280,000)
excess deaths from coal EGUs, respectively
(Fig. 2).
We compared mortality from coal PM2.5 es-
timated in the main analysis with an aggre-
gate health burden associated with total PM2.5
from all sources. Using the RR reported by
Wu et al. (4) for the Medicare population and the
same annual PM2.5 exposure used in that analy-
sis, we calculated 2,000,000 excess deaths due
to ambient PM2.5 from 2000 to 2016 relative to
a PM2.5 concentration of 0 (a portion of these
excess deaths is attributable to natural emis-
sions sources). Thus, our estimates imply that
exposure to coal PM2.5 was associated with
25% of all PM2.5-related Medicare deaths from
2000 to 2008 and with 7% of all PM2.5 deaths
from 2013 to 2016 (fig. S6).
Individual EGU contributions to mortality burden
We identified 138 of the 480 coal EGUs that
were associated with >1000 excess deaths across
the study period and 10 EGUs that were asso-
ciated with >5000 deaths (Fig. 3). Although
EGUs east of the Mississippi River were asso-
ciated with the greatest numbers of deaths
because of their high emissions and proxim-
ity to population centers, each geographical
region contained at least one EGU associated
with >400 deaths. The distribution of EGU-
specific deaths was heavily skewed; 91% of the
total deaths were associated with EGUs that
accounted for 50% of nationwide coal EGU
SO2 emissions during the study period. Nor-
malizing excess deaths by energy produced
may rank EGUs differently.
Figure 4 shows the temporal trend in the
number of deaths associated with each EGU,
highlighting the two most harmful coal EGUs
within each region. Large declines in the num-
ber of deaths corresponded with SO2 emission
control installations and facility retirements.
For example, for the Keystone facility in
Pennsylvania, the average annual number of
attributable deaths was 640 (95% CI: 580 to
700) before 2008, but declined to 80 (95% CI:
70 to 90) after scrubber installations in 2009
to 2010. We developed an interactive tool to
examine individual EGUs and their contri-
butions to state-specific Medicare deaths in
relation to SO2 emissions control installations
and unit retirements (34).
Sensitivity of results to unmeasured
confounding
The stratified Poisson regression for estimat-
ing the CRF was chosen based on its use in
previous health impact studies of exposure to
total PM2.5 in the Medicare population. The
log-linear CRF implied by the model was chosen
to facilitate the source-specific attribution of
health impacts, but it may not reflect the true
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Fig. 3. Excess deaths associated with individual coal EGUs from 1999 to 2020. EGUs (N = 480) are organized by region to improve interpretability, and the facilities
associated with the most deaths are labeled. Inset: total SO2 emissions by location from 1999 to 2020 (hexagonal grids may include multiple EGUs) and
regional boundaries. Plots were produced in R using ggplot2; spatial information comes from the USAboundaries package.
relationship between coal PM2.5 and mortality
risk across all exposure levels during the study
period. Although the stratified Poisson model
adjusts for many confounders and has been
shown in the context of total PM2.5 exposure
to be robust to a variety of strategies for con-
founding adjustment, we cannot rule out the
possibility that unmeasured factors related to
mortality risk vary systematically with coal
PM2.5 in a manner not captured by observed
characteristics in the model. Using the E-value
(34, 35), we found that a potential confounder
would need to have an association with both
mortality rate and coal PM2.5 of 1.125 (lower
confidence interval: 1.118) on the RR scale to
explain away the association between mortal-
ity and coal PM2.5.
To explore the potential confounding by air
pollution sources other than coal PM2.5, we
performed several additional sensitivity analy-
ses. We present coal PM2.5 RRs from models
that adjust for total PM2.5, residual PM2.5 (total
PM2.5 minus coal PM2.5) as a marker for all
other sources, NO2 as a marker for primary
traffic-related air pollution, and both NO2 and
residual PM2.5 (table S3). Adjusting for total
PM2.5 attenuated the risk of coal PM2.5 sub-
stantially, which is consistent with coal PM2.5
being captured by the total PM2.5 metric. When
including residual PM2.5 and/or NO2, we found
a slight attenuation in RR from the main mod-
el, and the RR for coal PM2.5 remained higher
than the RR for total PM2.5 found by Wu et al.
(4). Including markers for other PM2.5 sources
as confounders introduced important limita-
tions, as explained in the supplementary text.
Furthermore, we implemented a “first-differences”
analysis of within–ZIP code changes over time
to adjust for observed and unobserved differ-
ences across ZIP codes (fig. S7). This analysis
addresses possible threats to validity caused
by confounding differences across different
locations, providing strong evidence that areas
experiencing larger decreases in coal PM2.5
also experienced larger decreases in mortality
rates. Results from this analysis support the
validity of the primary analysis to quantify the
mortality burden with a relative risk adjusted
for individual- and ZIP code–level confounders
measured throughout the entire study period.
Sensitivity of results to HyADS characterization
of coal PM2.5
HyADS rescales air parcel location counts ex-
tracted from HYSPLIT to coal PM2.5 using a
single year’s chemical transport model output,
which may introduce errors. Our comparisons
(30) of coal PM2.5 with coal PM2.5 source im-
pacts from year 2006 Hybrid CMAQ-DDM, a
full form model (FFM) bias corrected against
observations, confirmed that the spatial pat-
tern is well captured and that error and bias
are within the typical range of FFMs (although
the bias-corrected CMAQ-DDM itself has un-
certainty). Because we expected potential errors
in coal PM2.5 to be smaller in years surrounding
the year when the scaling was performed, we
retrained the Poisson regression model three
times using data only from subsets of the total
years available (1999 to 2003, 2004 to 2007,
and 2008 to 2016). The estimated RRs from
coal PM2.5 were comparable but slightly larger
than in the main analysis from the 1999 to 2003
and 2004 to 2007 models, with a more pro-
nounced difference in RR from the 2008 to 2016
model (table S3). The change in RR across
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Fig. 4. Total annual excess deaths associated with each of the coal EGUs in each region, with the two most harmful facilities highlighted. Scrubber
installations designate the earliest year that a scrubber was installed at one or more of each EGU’s units [facility information from (46)]. Plots were produced
in R using ggplot2.
different periods may be consistent with either
genuine changes in risk or deterioration of
HyADS’ performance in years further from the
year on which the scaling was based (2005).
To explore sensitivity to the process for scal-
ing HyADS to coal PM2.5, we estimated the RR
and corresponding excess deaths from coal
EGUs using unscaled air parcel counts for each
ZIP code output by HyADS and found similar
estimates of attributable deaths (650,000; 95%
CI: 590,000 to 710,000). Comparing coal PM2.5
estimates against observed sulfate PM2.5 at
rural monitors indicated that HyADS may have
underestimated exposure and exaggerated ex-
posure declines during the study period (a por-
tion of this decline in coal PM2.5 is attributable
to decreasing EGU contributions to total US
SO2 emissions). A sensitivity analysis using a
sulfate-adjusted coal PM2.5 metric (fig. S8) es-
timates a mortality RR of 1.0147 (95% CI: 1.0135–
1.0158) and 790,000 (95% CI: 720,000–850,000)
excess deaths. These findings indicate that, to
the extent that HyADS might underestimate
coal-derived PM2.5 and exaggerate exposure
declines, it provides a conservative estimate of
the mortality burden associated with exposure
to SO2 emissions from coal EGUs. Future studies
may use newly developed approaches for esti-
mating CRFs that account for uncertainty in
air pollution exposure (36).
We used SO2 emissions from coal to derive
coal PM2.5 because of evidence that secondary
PM2.5 from SO2 emissions constitutes most of
the ambient PM2.5 from coal EGUs during the
study period (13, 17, 37). Because SO2 emissions
and related atmospheric physical-chemical
processes that increase ambient PM2.5 are cor-
related with complementary processes of other
species, e.g., primary PM2.5 and NOx, coal PM2.5
captures the influence of these other species.
Although primary PM2.5 emissions are not mea-
sured at each EGU, estimated nationwide an-
nual primary PM2.5 EGU emissions are correlated
(R2 = 0.97) with measured nationwide annual
SO2 emissions (38). Sensitivity analyses using
observed sulfate and comparisons with alter-
native modeling strategies revealed broad con-
sistency with the primary analysis, particularly
in EGU relative rankings by excess deaths, in-
dicating bounds on uncertainties associated
with the diversity of technologies and assump-
tions available for assessing exposure to EGU
SO2 emissions.
Comparison with deaths estimated using a
chemistry-transport air quality model
Although it is impossible to directly validate
the estimated number of excess deaths attrib-
utable to coal PM2.5, we compared our results
with analogous coal EGU health burdens de-
rived using atmospheric sensitivities from an
FFM. Using GEOS-Chem adjoint PM2.5 sensi-
tivities (13) and the coal PM2.5 RR from the
main analysis, we estimated 20,000 (95% CI:
19,000 to 22,000) and 13,000 (95% CI: 12,000
to 14,000) excess deaths in 2006 and 2011, re-
spectively (these years were chosen to span
emissions reductions after 2006 and to align
with previously published GEOS-Chem adjoint
results). These values are comparable, although
smaller (especially in 2006) than the excess
deaths estimated from coal PM2.5 exposure in
this study of 35,000 (95% CI: 32,000 to 38,000)
and 15,000 (95% CI: 13,000 to 16,000) in 2006
and 2011, respectively. Correlations between the
number of deaths assigned to each coal EGU
by HyADS and GEOS-Chem adjoint were high
(R2 ≥ 0.85) for all EGUs and for EGUs in most
regions (fig. S9 and table S4), and the two
models rank ordered EGUs similarly by their
associated deaths (fig. S10). Mean differences
in nationwide HyADS EGU-specific death esti-
mates relative to the chemical transport model
were higher in 2006 (71% for all EGUs) than in
2011 (15%). Although GEOS-Chem adjoint re-
sults from the 2 years available are difficult
to project to all 22 years of this study, and be-
cause chemical transport models, including
GEOS-Chem, have uncertainties due to potential
bias in emissions inputs, model parameter-
izations, and meteorology, agreement between
the models at levels consistent with previous
studies (39) increases confidence in the results
reported here.
Implications
We conducted the longest-term national study
to date estimating the excess number of deaths
associated with exposure to SO2 emissions from
US coal EGUs. A key innovation in this study is
the combined use of coal EGU-specific expo-
sure estimates and individual-level health data
on the same population during the same time
period to estimate the mortality burden. This
approach has been hampered until now by the
limited availability of large-scale health data-
bases and source-specific exposure estimates.
Our approach illustrates the utility of deriving
air pollution exposure with a combination of
dispersion-based and chemical transport models
in epidemiological and risk assessment for well-
characterized sources.
We found that, over the past two decades in
the US, coal PM2.5 was associated with 460,000
extra deaths, constituting >22% of total excess
deaths attributable to PM2.5. We also found
that the mortality burden of coal PM2.5 has
been underestimated using traditional impact
assessments that rely on CRFs for total PM2.5
mass (13, 16–18, 39–41). The elevated mortality
RR associated with annual exposure to coal
PM2.5 aligns with previous evidence of in-
creased relative health risks associated with coal-
related PM2.5 or sulfur or sulfate exposure per
unit concentration (19–25), although other studies
have found little evidence of increased risk
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related to secondary sulfate PM2.5 or PM2.5
associated with coal (26, 27). Large decreases
in annual deaths across the study period high-
light the success of emissions reductions brought
about by regulations under the 1990 Clean Air
Act Amendments. Although coal use in the US
has remained low, global use is expected to
increase and plateau by 2025 (8), suggesting
the potential for high mortality costs from coal
for years to come.
We used SO2 emissions from coal to derive
coal PM2.5; however, we cannot conclude that
the portion of ambient PM2.5 associated with
SO2 emissions emitted from coal power plants
is more or less harmful than ambient PM2.5
from other species emitted from coal power
plants. Disentangling the mortality risks of
the various PM2.5 species emitted from coal
EGU emissions is not possible within our mod-
eling framework because of the high correla-
tion between species emitted from coal EGUs
such as NOx and primary PM2.5. Given how we
estimate exposure to “coal PM2.5,” our find-
ing of a higher mortality risk of exposure to
coal PM2.5 relative to other PM2.5 suggests the
potential for population health benefits of re-
ducing SO2 emissions from coal power plants,
for example, by installing emissions control
devices or shutting coal facilities completely.
Full separation of the health impacts of var-
ious emitted species from coal EGUs is of ad-
ditional interest to policy-makers because of
the varying technologies available to reduce
EGU emissions of specific pollutants, and it
should be considered in future studies.
HyADS benefits from well-characterized source
locations and emissions, along with the rela-
tively slow atmospheric transformation of
emitted SO2 to particulate sulfate. Expanded
incorporation of information from observa-
tion and chemical transport model–based source
apportionment techniques in reduced com-
plexity models may enable linkages between
emitted species beyond SO2, atmospheric pro-
cesses, exposure, and health outcomes. Although
source-specific PM2.5 cannot be directly mea-
sured, observation-based receptor methods for
PM2.5 source apportionment (42) could pro-
vide an approximate ground truth (albeit with
their own uncertainties) for evaluating mod-
eled source-specific exposure. Advanced sensi-
tivity approaches incorporated within chemical
transport models, such as GEOS-Chem Adjoint
used here, and sensitivity methods such as the
direct decoupled method (DDM) (43) or the
integrated source apportionment method (ISAM)
(44) offer model-based approaches that more
explicitly incorporate atmospheric chemistry
and physics. Expanding computational capac-
ity will make comparisons with these types of
models in applications with many sources in-
creasingly feasible.
These results advance the growing body of
evidence showing varying toxicity of PM2.5 orig-
inating from different sources. Although the US
and other countries continue to regulate total
ambient PM2.5 concentrations, entities such as
the EPA Clean Air Scientific Advisory Commit-
tee have specifically cited a need for research to
assess health effects associated with changes in
PM2.5 composition and sources over time as an
important consideration for future PM2.5 policy
assessments (45). Our findings have implica-
tions for current air pollution risk assessments,
which incorrectly assume equal toxicity for am-
bient PM2.5 from all sources and for all loca-
tions. The research platform that we used to
quantify exposure associated with individual
coal EGUs, which accounts for pollution trans-
port and location relative to population centers,
can support more efficient regulatory efforts
by producing targeted evidence of how indi-
vidual EGU sources contribute to the existing
health burden.
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AC KNOWLED GME NTS
We thank S. Jin of the Georgia Institute of Technology for work
on the interactive data visualization development. Funding: This
work was supported by the National Institutes of Health
(grant NIHR01ES026217 to C.Z. and grants R01MD012769,
R01ES028033, 1R01ES030616, 1R01AG066793, 1R01MD016054-01A1,
1R01ES 034373-01, 1RF1AG080948, and 1R01ES029950 to F.D.);
the US Environmental Protection Agency (EPA) (grant 835872 to
C.Z., F.D., and L.H.); EmPOWER Air Data Challenge (L.H., C.Z.,
and J.R.); the Alfred P. Sloan Foundation (grant G-2020-13946
to F.D.); and The Health Effects Institute (HEI) (grant R-82811201
to L.H. and grant 4953 to C.Z.). The manuscript contents
are solely the responsibility of the grantee and do not necessarily
represent the official views of the EPA. Further, the EPA does not
endorse the purchase of any commercial products or services
mentioned in the publication. Research described in this article
was conducted under contract to the HEI, an organization jointly
funded by the EPA and certain motor vehicle and engine
manufacturers. The contents of this article do not necessarily reflect
the views of HEI, or its sponsors, nor do they necessarily reflect
the views and policies of the EPA or motor vehicle and engine
manufacturers. Author contributions: Conceptualization: L.H.,
C.Z.; Funding acquisition: C.Z.; Investigation: L.H., I.D.;
Methodology: L.H., C.C., I.D., C.Z., F.D.; Project administration:
F.D., C.Z.; Supervision: C.Z.; Visualization: L.H., J.R., C.Z.;
Writing – original draft: L.H., C.Z.; Writing – review and editing:
L.H., C.C., I.D., J.R., F.D., C.Z. Competing interests: The
authors declare no competing interests. Data and materials
availability: The online data exploration tool is available online (47).
Code to support analyses in this work is documented on GitHub
(48). Coal PM2.5 source impacts and coal EGU information are
available for download from the Open Science Framework (49). CMS
Henneman et al., Science 382, 941–946 (2023)
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Medicare datasets, in accordance with the data use agreement,
must be acquired from the Centers for Medicare & Medicaid Services
(28). Instructions for acquiring CMS data and code for processing
this data are available on GitHub (50). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse. In the interest of rapid
dissemination of results with immediate public health relevance, the
author will make the Author Accepted Manuscript (AAM) version
available under a CC BY public copyright license.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf4915
Materials and Methods
Supplementary Text
Figs. S1 to S10
Tables S1 and S2
References (51–64)
MDAR Reproducibility Checklist
Submitted 28 October 2022; accepted 2 October 2023
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Henneman et al., Science 382, 941–946 (2023)
24 November 2023
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RES EARCH
STRUCTURAL BIOLOGY
Reorientation of INO80 on hexasomes reveals basis
for mechanistic versatility
Hao Wu1†, Elise N. Muñoz1,2†, Laura J. Hsieh1, Un Seng Chio1, Muryam A. Gourdet1,2*,
Geeta J. Narlikar1*, Yifan Cheng1,3*
Unlike other chromatin remodelers, INO80 preferentially mobilizes hexasomes, which can form during
transcription. Why INO80 prefers hexasomes over nucleosomes remains unclear. Here, we report structures of
Saccharomyces cerevisiae INO80 bound to a hexasome or a nucleosome. INO80 binds the two substrates
in substantially different orientations. On a hexasome, INO80 places its ATPase subunit, Ino80, at superhelical
location –2 (SHL –2), in contrast to SHL –6 and SHL –7, as previously seen on nucleosomes. Our results
suggest that INO80 action on hexasomes resembles action by other remodelers on nucleosomes such that
Ino80 is maximally active near SHL –2. The SHL –2 position also plays a critical role for nucleosome remodeling
by INO80. Overall, the mechanistic adaptations used by INO80 for preferential hexasome sliding imply that
subnucleosomal particles play considerable regulatory roles.
I n eukaryotes, central nuclear processes
such as gene expression, DNA replication,
and DNA repair are coordinated with dy-
namic changes in chromatin states (1–3).
ATP-dependent chromatin-remodeling en-
zymes play essential roles in catalyzing such
changes. These enzymes are broadly catego-
rized into four major families: SWI/SNF, ISWI,
CHD, and INO80 (4, 5). Each of these enzymes
contains a core remodeling ATPase subunit
and several auxiliary subunits that regulate the
core ATPase. It has typically been presumed
that the preferred substrate of these enzymes
is a nucleosome, the smallest unit of chromatin
containing ~147 base pairs (bp) of DNA wrapped
around an octamer of histone proteins (6). Con-
sistent with this assumption, between them,
these four classes slide the histone octamer,
exchange histone variants, and transfer en-
tire octamers (5, 7).
The INO80 complex has been shown to play
roles in regulating transcription, DNA repli-
cation, and DNA repair (8–11). However, how
INO80’s biochemical activities relate to its
diverse biological roles is not well understood.
Unlike remodelers from other families, in
which the core ATPase subunits bind the nu-
cleosome near superhelical location 2 (SHL +2
or SHL −2), Ino80, the core ATPase subunit of
the INO80 complex, binds nucleosomes near
SHL –6 or SHL −7 (fig. S1A) (12–14). It has been
speculated that this key difference in nucleo-
some engagement reflects a fundamentally dif-
ferent remodeling mechanism (15, 16). Indeed,
we showed that the preferred substrate of the
1Department of Biochemistry and Biophysics, University
of California San Francisco, San Francisco, CA 94158,
USA. 2Tetrad Graduate Program, University of California
San Francisco, San Francisco, CA 94158, USA. 3Howard Hughes
Medical Institute, University of California San Francisco,
San Francisco, CA 94158, USA.
*Corresponding author. Email: muryam.gourdet.mg@gmail.com
(M.A.G.); geeta.narlikar@ucsf.edu (G.J.N.); yifan.cheng@ucsf.edu (Y.C.)
†These authors contributed equally to this work.
Wu et al., Science 381, 319–324 (2023)
21 July 2023
Saccharomyces cerevisiae INO80 complex is
not a nucleosome but a hexasome, which is a
subnucleosomal particle that lacks a histone
H2A-H2B dimer (17). Hexasomes are gener-
ated during transcription and may also be
formed during DNA replication and repair
(18–21). Further, INO80’s activity on nucleo-
somes is more dependent on flanking DNA
length than on hexasomes (17, 22). These re-
sults suggested that INO80 has the versatility
to act on hexasomes or nucleosomes based on
the density of nucleosomes and hexasomes at
a given locus. However, fundamental mecha-
nistic questions remain. It is not clear how
INO80 can act on both nucleosomes and hex-
asomes, which differ substantially in their
structures. It is also unclear why INO80 has
different flanking DNA length dependencies
on hexasomes versus nucleosomes.
Here, we report cryo–electron microscopy
(cryo-EM) structures of endogenously purified
S. cerevisiae INO80 bound to a hexasome and
a nucleosome. We found that INO80 binds
hexasomes and nucleosomes in opposite ori-
entations, with Ino80 binding near SHL –2 on
hexasomes and near SHL –6 or SHL −7 on
nucleosomes. The location of the Arp8 module
suggests how flanking DNA length differen-
tially regulates nucleosome and hexasome slid-
ing. DNA gaps near SHL –2 inhibit sliding of
both substrates by INO80. Our findings pro-
vide mechanistic insights into how INO80
slides both hexasomes and nucleosomes.
Structures of the INO80-hexasome and
INO80-nucleosome complexes
To visualize how INO80 binds to a hexasome
or a nucleosome, we prepared hexasomes and
nucleosomes on the same DNA templates
containing the 147-bp, 601-nucleosome posi-
tioning sequence with 80 bp of additional
DNA as described previously (+80H and
+80N; with definition explained in Fig. 1A;
fig. S1, A and B; and the supplementary text)
(17, 23, 24). Complexes were formed by mix-
ing hexasomes or nucleosomes with endoge-
nously purified S. cerevisiae INO80 without
adding nucleotide (fig. S1, C to H).
We determined cryo-EM structures of the
INO80-hexasome complex in three different
conformational snapshots (Fig. 1, B and C,
and figs. S2 to S6). The overall shape of
INO80 is similar within these structures and
also to previously published structures of the
nucleosome in complex with human (12) and
Chaetomium thermophilum (14) INO80. Using
prior convention, we grouped subunits of the
INO80 complex into four modules: the Rvb mod-
ule (Rvb1/Rvb2), the Arp8 module (Arp8/Arp4/
Actin/Ies4 and Taf14), the Ino80 module (Ino80/
Ies2), and the Arp5 module (Arp5/Ies6). The Ino80
protein consists of three major regions: the N-
terminal domain, the HSA region (Ino80HSA),
and the ATPase domain (Ino80ATPase). Detailed
descriptions of these modules in our structures
are provided in the supplementary text.
Although the INO80 architecture appears
similar to that in the INO80-nucleosome struc-
tures, a major difference is that it is rotated
~180° on a hexasome compared with a nu-
cleosome (Fig. 1, B to E). We identified two
primary interactions between INO80 and the
hexasome: Ino80ATPase binds the hexasome
near SHL –3 (class 1), SHL –2.5 (class 2), or
SHL –2 (class 3), and the Arp5/Ies6 module
binds near SHL +1, SHL +1.5, or SHL +2 (fig.
S6, A and B), respectively. Class 3 is the predom-
inant INO80-hexasome class. All Ino80ATPase
locations on hexasomes are different than
those on nucleosomes, which are near SHL –6
or SHL –7 (12–14). However, the Ino80 orien-
tation on hexasomes is consistent with struc-
tures of other major chromatin remodelers
on nucleosomes such as S. cerevisiae ISW1
(25–27), Chd1 (28–30), RSC (31–33), Snf2 (34),
and in particular the SWR1 complex (35),
which is from the same subfamily as the INO80
complex. In these structures, the ATPase do-
mains interact with nucleosomes near either
SHL +2 or SHL –2 (Fig. 1E).
Loss of an H2A-H2B dimer in a hexasome
causes an additional ~35 bp of DNA to un-
wrap from the histone core (free DNA) (Fig.
1A and fig. S1B). Comparison of our hexa-
some structures with an unbound hexasome
(PDB: 6ZHY) (36) reveals different levels of
further DNA unwrapping. In class 1, the hex-
asome is almost identical to the unbound
hexasome, without detectable additional DNA
unwrapping. The level of DNA unwrapping
increases as the Ino80ATPase-binding position
changes from SHL –3 (class 1) to SHL –2
(class 3) (Fig. 2 and fig. S6C).
For comparison, we also determined structures
of S. cerevisiae INO80 bound to a nucleosome
and captured two conformational snapshots
(class 1 and 2) from the same dataset (figs. S7
to S9 and supplementary text). Ino80ATPase
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Fig. 1. Structure of the INO80-hexasome complex reveals large rotation.
(A) Cartoon illustration of a +X nucleosome and a +X hexasome. H2A-H2B dimer
proximal to the flanking DNA (entry side dimer) is shown in cyan; H3-H4, light
gray; 601 DNA, dark gray; flanking DNA, orange; additional free (unwrapped)
DNA is also shown in cyan; SHLs are shown as yellow dots; DNA from the bottom
gyre is shown as a dotted line. (B) Two different views of cryo-EM density map
of the INO80-hexasome complex (class 3). (C) Atomic model of the INO80-
hexasome complex (class 3) viewed in the same orientation as the map is viewed
in (B). (D) Cryo-EM density map of the C. thermophilum INO80-nucleosome
complex [EMDB: 4277 (14)] displayed with its nucleosome dyad and H3-H4
tetramer aligned with that of the hexasome in the right panel of (B). Note that
INO80 on a hexasome rotates ~180° from where it sits on a nucleosome
when keeping the nucleosome-hexasome dyad and H3-H4 aligned. (E) Structural
comparisons of INO80-nucleosome complex (left), the SWR-nucleosome
complex (middle), and the INO80-hexasome complex (right), with the dyad and
H3-H4 of nucleosome and hexasome aligned.
Wu et al., Science 381, 319–324 (2023)
21 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Conformational snapshots of INO80-hexasome complexes. Comparison of DNA from each INO80-hexasome class (blue) with DNA from an unbound
hexasome (PDB: 6ZHY, gray), showing the degree of DNA unwrapping (top row) and binding locations of Ino80ATPase and Arp5 (bottom row).
in class 1 is located near SHL –7, similar to its
location in the human INO80-nucleosome
structure (12), whereas in class 2, it binds near
SHL –6, similar to the C. thermophilum struc-
ture (14) (fig. S9, A and C). The Arp5/Ies6
module interacts with the nucleosome near
SHL –3 and SHL –2 (fig. S9D), respectively.
These observations are also consistent with
previous findings showing that nucleosomal
DNA between SHL –5 and SHL –7 is protected
by INO80 (13).
The SHL –2 position plays a critical role in
nucleosome and hexasome sliding
We observed that Ino80ATPase engages the hex-
asome predominantly near SHL –2. These
results raise the possibility that Ino80ATPase
acts near SHL –2 when sliding hexasomes.
By contrast, consistent with prior findings
(12, 14), we observed that Ino80ATPase engages
the nucleosome near two positions, SHL –7
and SHL –6. Also as previously proposed, our
findings are consistent with the possibility that
Ino80ATPase acts near SHL –6 when sliding
nucleosomes (13). A commonly used assay to
identify the DNA location from which the
ATPase domain of a remodeler acts to trans-
Wu et al., Science 381, 319–324 (2023)
21 July 2023
locate DNA is to place a single nucleotide gap
at the proposed site of action and test whether
the gap inhibits DNA translocation (37–39).
Therefore, to directly test the importance of
the SHL –6 and SHL –2 locations, we as-
sembled nucleosomes and hexasomes with
single base gaps near SHL –2 or SHL –6 and
measured INO80 activity using a gel-based
sliding assay (Fig. 3A).
We found that a gap at SHL –6 inhibited
INO80’s sliding activity on nucleosomes by
~200-fold, but so did a gap at SHL –2 (Fig. 3,
B to G). By contrast, a gap at SHL –6 did not
inhibit INO80’s sliding activity on hexasomes,
but a gap at SHL –2 slowed hexasomes slid-
ing by ~2000-fold (Fig. 3, B to G). These
results are consistent with Ino80ATPase acting
near SHL –2 when sliding hexasomes and
raise new questions about why both the SHL –2
and SHL –6 locations are critical for nucleo-
some sliding by INO80. We describe possible
explanations in the Discussion.
Role of the Arp8 module in flanking DNA
length dependence
S. cerevisiae INO80 slides +40 nucleosomes
~100-fold more slowly than +80 nucleosomes
(17, 22). However, sliding hexasomes is less
flanking DNA dependent. Our structures sug-
gest that the Arp8 module requires ~40 bp
of DNA for appropriate engagement. In class
1 of the INO80-hexasome structure, Arp8 en-
gages with the ~35 bp of DNA unwrapped
from removal of the H2A-H2B dimer and an
additional ~5 bp of flanking DNA. In class 3
of the INO80-hexasome structure, the Arp8
module engages entirely with ~40 bp of un-
wrapped DNA that now includes additional
DNA unwrapped relative to the unbound hex-
asome (Fig. 4). Conversely, in class 2 of the
INO80-nucleosome structure, the Arp8 mod-
ule engages entirely with flanking DNA, which
is consistent with previous findings (40) (Fig.
4). Our structural data with hexasomes, along
with the previous data with nucleosomes,
suggest that 40 bp may be the minimum
amount of DNA needed for the Arp8 module
to bind and that proper Arp8 module engage-
ment is essential for maximal remodeling
activity (40).
Altered interactions by the Arp5 module
To understand why Ino80 may not bind a nu-
cleosome directly near SHL –2, we compared
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Fig. 3. Inhibition of DNA translocation at specific SHL sites influences
nucleosome and hexasome sliding by INO80. (A) Cartoon illustration of a
+80 nucleosome (left) and a +80 hexasome (right) with approximate locations
of site-specific single base gaps indicated. Colors are the same as in Fig. 1A.
(B and C) Example gels and time courses of native gel–based remodeling assays
of WT INO80 on +80 nucleosomes with no gap, a gap near SHL –2, and a gap
near SHL –6. (D and E) Example gels and time courses of native gel–based
remodeling assays of wild-type INO80 on +80 hexasomes with no gap, a gap
near SHL –2, and a gap near SHL –6. (F and G) Average observed rate constants
of INO80 sliding activity. kobs (min−1): +80N: 1.551 ± 0.1846; +80N Gap @ SHL –2:
0.005995 ± 0.001054; +80N Gap @ SHL –6: 0.006497 ± 0.0007117; +80H:
1.01 ± 0.1668; +80H Gap @ SHL –2: 0.000379 ± 0.0002849; +80H Gap @ SHL –6:
1.213 ± 0.2209. Data represent the mean ± SEM for three technical replicates
performed under single-turnover conditions with saturating enzyme and ATP.
interactions made by Arp5/Ies6 in hexasomes
versus nucleosomes (see the supplementary
text). When INO80 binds to a hexasome, the
Arp5/Ies6 regions used in the context of a nu-
cleosome are repurposed for different interac-
tions. Modeling the missing H2A-H2B dimer
into our INO80-hexasome structure reveals
steric clashes of the Arp5 module with the en-
try side proximal H2A-H2B dimer and with
part of the DNA that wraps around the H2A-
H2B dimer (fig. S11). These clashes could
be avoided if the H2A-H2B dimer is suffi-
ciently dislodged. To test for this possibility,
we inhibited dimer dislodgement by intro-
ducing a site-specific disulfide cross-link be-
tween the two H2A molecules (N38C) (41) or
promoted dimer dislodgement by using an
H2A mutant (R81A) that destabilizes the H2A-
H2B/H3-H4 interface (42) (fig. S12, A, B, and
H). The disulfide cross-link did not inhibit nu-
cleosome sliding, and the H2A mutant did not
promote nucleosome sliding (fig. S12, C to G),
indicating that complete dimer dislodgement
is not necessary for INO80-mediated nucleo-
some sliding. In the absence of dimer dislodge-
ment, another way to avoid these clashes could
be by substantial rearrangement of the Arp5
module together with subtle rearrangements
of the H2A-H2B dimer (fig. S9E).
Discussion
Implications of the INO80-hexasome structure
for nucleosome sliding by INO80
The major conformation of the INO80-hexasome
complex (class 3) has Ino80ATPase near SHL
–2 and ~15 bp of unwrapped DNA from the
entry site in addition to the ~35 bp of DNA
that is unwrapped from removal of an H2A-
H2B dimer. The placement of Ino80ATPase near
SHL –2 is consistent with how the ATPase
subunits of other remodelers bind the nu-
cleosome. Together with our prior finding that
hexasomes are remodeled faster than nucleo-
somes, these results suggest that the class 3
structure represents the sliding-competent
conformation of INO80 on hexasomes (Fig. 5A
and fig. S13A). By contrast, the states of INO80
bound to a nucleosome have Ino80ATPase bound
near either SHL –6 or SHL –7, also consistent
with previous findings. These differences raise
the question of whether the INO80-nucleosome
structures represent sliding-competent confor-
mations or if a rearrangement of Ino80ATPase to
SHL –2 is necessary to achieve efficient nucleo-
some sliding.
Previous cross-linking studies have shown
that detachment of nucleosomal DNA from
Wu et al., Science 381, 319–324 (2023)
21 July 2023
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Fig. 4. The Arp8 module engages different regions of DNA in nucleosomes versus hexasomes. Overlay
of atomic models of the hexasome (class 1 and class 3) and the nucleosome (class 2) with the Arp8 module
(PDB: 8A5O), aligned by the H3-H4 tetramer.
Fig. 5. Model of INO80-induced hexasome and nucleosome sliding. (A) Hexasome sliding. The
Ino80ATPase samples different positions between SHL –3 and SHL –2 but binds predominantly near SHL –2.
The INO80 complex becomes sliding competent when Ino80ATPase engages near SHL –2. (B) Nucleosome
sliding. INO80 initially binds with Ino80ATPase at SHL –7 or SHL –6. Upon ATP hydrolysis, Ino80ATPase moves
toward SHL –2, where INO80 becomes sliding competent.
H2A-H2B close to the entry site occurs during
INO80 remodeling (13). Our data show that
progressively more DNA is unwrapped as
Ino80ATPase binds closer to SHL –2 on hex-
asomes (Fig. 2 and fig. S6C). Together, these
results suggest that DNA unwrapping is
coupled to Ino80ATPase accessing its most
sliding-competent state. Footprinting studies
have shown that whereas binding of INO80
to nucleosomes mainly protects nucleosomal
DNA from SHL –5 to SHL –7 and near SHL –3,
there is modest but detectable protection
near SHL –2 (13). Nicks and gaps between SHL
–7 and SHL –2 have been shown to inhibit
nucleosome sliding to different extents (13, 43).
Here, we show that site-specific gaps near
SHL –2 or SHL –6 substantially inhibit INO80’s
sliding of nucleosomes (by ~200 fold). DNA
gaps are commonly used to identify the site of
action of the ATPase domain of remodelers
(37–39). We therefore speculate that INO80
initially binds the nucleosome with Ino80ATPase
near SHL –6 or SHL –7, and that this is fol-
lowed by an ATP-dependent rotation around
the nucleosome to position Ino80ATPase near
SHL –2, from which Ino80ATPase then trans-
locates nucleosomal DNA (Fig. 5B and fig.
S14A). A gap near SHL –6 would then inhibit
ATP-dependent movement of Ino80ATPase on
the nucleosome, whereas the gap near SHL –2
would inhibit translocation of nucleosomal
DNA by INO80 relative to the histone octa-
mer (fig. S14). Single-molecule fluorescence
resonance energy transfer studies have iden-
tified an ATP-dependent pause phase be-
fore ATP-dependent nucleosome sliding (22).
The pause could represent the reorientation
of Ino80ATPase from SHL –6 or SHL –7 toward
SHL –2 and add a step that slows remodeling
of nucleosomes compared with hexasomes.
Simply placing the INO80 complex as is on
nucleosomes with the Ino80ATPase near SHL
–2 results in steric clashes of the Arp5 module
with the nucleosome (fig. S11). Although partial
H2A-H2B dimer dislodgment, as previously
proposed (17), could avoid such clashes, our
biochemical data here indicate that dimer dis-
lodgement is not essential for nucleosome
sliding by INO80 (fig. S12). More structural
studies are needed to understand how INO80
might rotate around a nucleosome.
Alternatively, a gap near SHL –2 may affect
the action of the Arp5 module. For such a
scenario, we speculate that Ino80ATPase trans-
locates DNA near SHL –6, and effective trans-
location also requires action of the Arp5
module near SHL –2, as previously proposed
(12, 14). A gap near SHL –6 would then in-
hibit translocation of nucleosomal DNA by
Ino80ATPase, and a gap near SHL –2 would
inhibit productive engagement of the Arp5
module (fig. S15).
Clearly distinguishing between these two mod-
els will require substantial additional structural
Wu et al., Science 381, 319–324 (2023)
21 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
analysis of INO80-remodeling intermediates on
nucleosomes.
Implications for hexasome sliding by INO80
Our structures provide a view into how INO80
engages a hexasome. In the predominant
INO80-hexasome structure, Ino80ATPase binds
near SHL –2. A site-specific gap near SHL –2
substantially inhibits INO80’s sliding of hex-
asomes (~2000 fold), whereas a gap near
SHL –6 does not have a major effect. We
therefore hypothesize that Ino80ATPase bound
at SHL –2 on a hexasome represents the active
structure. Compared with the subtle changes
at SHL –2 observed when other remodelers
bind nucleosomes (16), the additional 15 bp of
unwrapped DNA (up to SHL –2.5) in class 3
substantially loosens histone DNA interactions
and thus may allow more ready translocation
from SHL –2. We further propose that the new
contacts made by the Arp5/Ies6 module with
the exposed H3-H4 surface provide an anchor
that allows the Ino80 motor to efficiently
pump DNA through the hexasome. These
findings also explain the differential effects
of the Arp5/Ies6 module on hexasome versus
nucleosome sliding (17). The location of the
Arp8 module is also different on hexasomes
than on nucleosomes. On nucleosomes the
Arp8 module binds ~40 bp entirely on the
flanking DNA (Fig. 4). In the most prevalent
INO80-hexasome state (class 3), the Arp8
module is bound entirely to the unwrapped
DNA, substantially reducing the need to bind
flanking DNA (Fig. 4). These different binding
modes of the Arp8 module could explain why
hexasome sliding by INO80 is less dependent
on flanking DNA length compared with nu-
cleosome sliding.
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41. T. D. Frouws, P. D. Barth, T. J. Richmond, J. Mol. Biol. 430,
45–57 (2018).
AC KNOWLED GME NTS
We thank L. Zheng for advice on model building, Z. Yu for providing
GO grids, J. Tretyakova for expressing and purifying histones,
U. Kaur for providing INO80 WT enzyme, members of the Narlikar
and Cheng laboratories for helpful discussions, C. Wu and
A. Ranjan for sharing unpublished data showing inhibition of INO80
activity on nucleosomes containing a gap near SHL –2, and
S. Diendl and A. Sabantsev for detailed advice on generating DNAs
with site-specific base gaps. The cryo-EM facility at UCSF is
managed by D. Bulkley and G. Gilbert; computation at the Cheng
laboratory is supported by M. Harrington and J. Li. Funding: This
work was supported by the National Institutes of Health (NIH
grant R35GM140847 to Y.C., grant R35GM127020 to G.J.N.,
grant F31GM136187 to M.A.G., grant F31GM142271 to E.N.M., and grant
F32GM137463 to U.S.C.) and by the American Cancer Society
(Roaring Fork Valley Research Fund Postdoctoral Fellowship PF-18-155-
01-DMC to L.J.H.). Equipment at the UCSF cryo-EM facility was partially
supported by the NIH (grants S10OD020054, S10OD021741, and
S10OD025881). Y.C. is an investigator at the Howard Hughes Medical
Institute. Author contributions: H.W., M.A.G., L.J.H., and E.N.M. purified
INO80; M.A.G., L.J.H., and E.N.M. assembled and purified hexasomes and
nucleosomes; H.W. performed cryo-EM; E.N.M. performed and
quantified all biochemical experiments; U.S.C. generated the H2A
R81A mutant; M.A.G., G.J.N., and Y.C. conceived and oversaw
the project; and all authors participated in interpretation and
discussion of the results and writing of the manuscript. Competing
interests: Y.C. is scientific advisory board member of ShuiMu
BioSciences Ltd. Data and materials availability: For the core INO80
of the INO80-Hexasome complex (class 1, class 2, and class 3)
and the core INO80 of the INO80-Nucleosome complex (class 1 and
class 2), the coordinates are deposited in the Protein Data Bank
with the accession codes 8ETS, 8ETU, 8ETW, 8EU9, and 8EUF; the
cryo-EM density maps are deposited in the Electron Microscopy Data
Bank (EMDB) with the accession codes EMD-28597, EMD-28599,
EMD-28601, EMD-28609, and EMD-28613. For the hexasome of the
INO80-Hexasome complex (class 1, class 2, and class 3) and the
nucleosome of the INO80-Nucleosome complex (class 1 and class 2),
the coordinates are deposited in the Protein Data Bank with the
accession codes 8ETT, 8ETV, 8EU2, 8EUE, and 8EUJ; the cryo-EM
density maps are deposited in the Electron Microscopy Data Bank
(EMDB) with the accession codes EMD-28598, EMD-28600,
EMD-28602, EMD-28612, and EMD-28614. License information:
This article is subject to HHMI’s Open Access to Publications
policy. HHMI lab heads have previously granted a nonexclusive CC
BY 4.0 license to the public and a sublicensable license to HHMI in
their research articles. Pursuant to those licenses, the author-
accepted manuscript (AAM) of this article can be made freely
available under a CC BY 4.0 license immediately upon publication.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf4197
Materials and Methods
Supplementary Text
Figs. S1 to S15
Tables S1 and S2
References (44–71)
MDAR Reproducibility Checklist
42. K. Lehmann et al., Sci. Rep. 7, 13303 (2017).
43. F. Mueller-Planitz, H. Klinker, P. B. Becker, Nat. Struct.
Mol. Biol. 20, 1026–1032 (2013).
Submitted 21 October 2022; accepted 17 June 2023
Published online 29 June 2023
10.1126/science.adf4197
Wu et al., Science 381, 319–324 (2023)
21 July 2023
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RES EARCH
MECHANOCHEMISTRY
Acceleration of Diels-Alder reactions
by mechanical distortion
Yerzhan S. Zholdassov1,2,3, Li Yuan4, Sergio Romero Garcia5, Ryan W. Kwok2,3,
Alejandro Boscoboinik4, Daniel J. Valles1,2,3, Mateusz Marianski2,3, Ashlie Martini5,
Robert W. Carpick4, Adam B. Braunschweig1,2,3*
Challenges in quantifying how force affects bond formation have hindered the widespread adoption
of mechanochemistry. We used parallel tip-based methods to determine reaction rates, activation
energies, and activation volumes of force-accelerated [4+2] Diels-Alder cycloadditions between
surface-immobilized anthracene and four dienophiles that differ in electronic and steric demand.
The rate dependences on pressure were unexpectedly strong, and substantial differences were
observed between the dienophiles. Multiscale modeling demonstrated that in proximity to a surface,
mechanochemical trajectories ensued that were distinct from those observed solvothermally or
under hydrostatic pressure. These results provide a framework for anticipating how experimental
geometry, molecular confinement, and directed force contribute to mechanochemical kinetics.
T he great majority of organic reactions
carried out in industry and research
laboratories rely on strictly solvothermal
activation, in which solvent and heat act
in concert to drive reactions along a
trajectory toward products (1). The organic
solvents used in these reactions account for
>60% of all chemical manufacturing waste
(2) and are often toxic (3), while as a result of
the energy demand of solvothermal syntheses,
the chemical industry consumes 37% of the total
energy used in manufacturing (4). As such,
there is a critical need to supplement and
ideally replace solvothermal chemistry with
less wasteful activation approaches. Mechani-
cally activated organic chemistry (5)—in which
force, rather than heat and solvent or hydro-
static pressure, drives the making and break-
ing of covalent bonds—can help to ameliorate
the waste and energy challenges of organic
synthesis because the reactions are run neat or
with minimal solvent (6), and energy can be
provided more efficiently through mechanical
rather than thermal means (7). Even when
solvents are added to mechanochemical reac-
tions, in a process called liquid-assisted grind-
ing, they are added in comparatively small
amounts (8). Another benefit is that mecha-
nochemically activated conditions often pro-
duce stereoisomers and regioisomers that are
not favored, or cannot be produced at all, under
solvothermal conditions (9), although why such
mechanically favored products arise is often
not well understood.
1The Advanced Science Research Center, Graduate Center of
the City University of New York, New York, NY 10031, USA.
2Department of Chemistry, Hunter College, New York, NY
10065, USA. 3Ph.D. Program in Chemistry, Graduate Center
of the City University of New York, New York, NY 10016,
USA. 4Department of Mechanical Engineering and Applied
Mechanics, University of Pennsylvania, Philadelphia, PA
19104, USA. 5Department of Mechanical Engineering,
University of California, Merced, CA 95343, USA.
*Corresponding author. Email: abraunschweig@gc.cuny.edu
Despite its many potential advantages, organ-
ic mechanochemistry has not been widely
adopted in chemical synthesis and manu-
facturing. This can be attributed in part to
substantial remaining gaps in the understand-
ing of reaction kinetics under mechanochemical
activation. Until physical models are devel-
oped that reliably account for experimental
observations, the products of mechanochemical
reactions cannot be predicted, and the reac-
tions cannot be easily translated to large
scales. Mechanochemical reactions are typi-
cally carried out in ball mill (10) or planetary
mill reactors (11) or in twin-screw extruders
(12), for which it is difficult to determine even
the most basic reaction parameters, such as
the magnitude of the applied force (F), the
reaction time under force (t), or conversion at
different time points. Polymer mechano-
chemistry (13–15) entails the use of mechan-
ical energy to activate mechanophores (16–18)
embedded within long polymer chains: Soni-
cation (19, 20), atomic force microscopy (AFM)
(21, 22), and/or laser pulses (23) apply me-
chanical energy that ruptures the mechani-
cally susceptible bonds in the mechanophores.
However, these methods are used to initiate
bond rupture, and as a consequence, such
studies do not explain bond-formation events
in mills and extruders. This difficulty in acquir-
ing quantitative experimental data on bond
formation under stress complicates the develop-
ment and validation of generalizable kinetic
models of mechanochemical bond-forming
reactions. Furthermore, because mechano-
chemical reactions are carried out on powders,
rather than well-solvated molecules, the kine-
tics of grinding to expose molecular reactants
adds another layer of complexity to kinetic
models. For example, the rate of pericyclic
[4+2] Diels-Alder cycloadditions in ball (10)
and planetary (24) mills are dependent on
particle size (25), shaking frequency (10), ball
mass (25), and vessel loading (26) in addition
to the molecular-scale factors that are known
to affect rates, such as reactant structure and
temperature (T) (27).
Given all these macroscopic factors, it has
been challenging to explain how mechanical
energy acts on the reaction potential energy
surface. One such explanation is the “hotspot”
model (28), which postulates that localized
heating occurs when milling balls collide with
surfaces and with each other, causing the re-
lease of kinetic energy. Rate increases in
mechanochemical reactions are thus posited
to arise because of conventional thermal acti-
vation at the collision sites. Although some
local heating is observed upon milling, these
temperature increases are small and are not
commensurate with observed reaction rate
increases (29). The other dominant kinetic
theory of mechanochemistry argues that
grinding increases the surface area of powders,
increasing the collision probability of reac-
tants, which explains the dependence of rates
on powder size (25). Ultimately, current kinetic
models of organic mechanochemistry—the
molecular-scale hotspot theory and the macro-
scopic model that considers increases in area
during grinding—are incomplete because they
fail to account for all experimental observations.
In particular, they fail to account for the forma-
tion of different isomers under mechano-
chemical activation versus strictly solvothermal
activation, which indicates that F can move
reactants along a different reaction trajectory
than that from heat. As such, any accurate
molecular-scale kinetic model of mechano-
chemical reactions must consider how F
distinctly alters reaction trajectories and
explain quantitatively how F affects reaction
barriers and, in turn, reaction rates. With the
physical understanding inherent to an accu-
rate molecular-scale model of mechanical
reactivity, the reactions that are susceptible
to mechanical activation could be anticipated
and their rates and products predicted accu-
rately, leading to the wider adoption of sustain-
able mechanochemical methods in organic
synthesis and chemical manufacturing.
We experimentally and computationally
investigated the reaction kinetics of mecha-
nically activated [4+2] Diels-Alder cycloaddition
reactions between dienophiles and surface-
confined diene monolayers to measure how
force affects reaction rates. Pericyclic reactions
were chosen because they proceed in con-
certed fashion without intermediates (30),
which minimizes challenges in analyzing their
kinetics. The reactions were carried out on
monolayers so that the complexities associ-
ated with grinding powders during milling
and reactant availability were not factors in
the kinetic analysis, and the effects of F on the
free energy of activation (DG‡) and reaction
trajectories would be isolated. The experiment
Zholdassov et al., Science 380, 1053–1058 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
(Fig. 1) used elastomeric arrays (figs. S7 and
S23) that contained 900 pyramidal tips with
heights of 21.9 mm and base edge lengths of
31 mm (31, 32) to bring fluorescently labeled
dienophiles into contact with monolayers of
the tethered diene, anthracene, that was immo-
bilized covalently onto the surface of a silica
(SiO2) wafer (33, 34). The tip arrays were
mounted onto piezoactuators so that they
could be pushed into the monolayer with pre-
cise control over F and t (32, 35, 36), resulting
in a nanoreactor where the anthracene and
dienophile react under mechanical activation.
The tips themselves were coated with an ink
mixture that consisted of a large excess of the
fluorescent dienophiles embedded within a
polymer matrix that solubilized the dienophiles
and ensured that they were accessible to react
with the immobilized anthracene (37). We
used fluorescence microscopy to track the
Fig. 1. Force-activated Diels-Alder reactions on
anthracene monolayers. (A) Diels-Alder cyclo-
addition reaction between anthracenes immobilized
onto SiO2 surfaces and dienophiles under applied
force. (B) Structures of dienophiles Alk, Mal, MAcr,
and Acr. (C) (i) Elastomeric tip arrays transfer an
ink mixture (red coating), consisting of a dienophile
and PEG, onto an anthracene-modified surface. The tip
arrays are tilted so that different forces are applied by
the tips at different locations across the surface.
Thick arrows indicate areas of the tip array that exert
high force, and thin arrows indicate areas that exert
low force. (ii) Upon contact with the surface, the
tips form nanoreactors, (iii) where forces are applied
that accelerate the Diels-Alder cycloaddition reactions.
(iv) After washing the surface, only covalently
bound molecules remain on the surface.
Diels-Alder adduct formation as a function
of F and t. We studied the reaction rates of
the anthracene monolayer with four different
dienophiles—an alkene (Alk), a maleimide
(Mal), a methacrylate (MAcr), and an acryl-
ate (Acr)—because they differ in the electron
demand (38) and the steric environment (39)
around the reactive alkene, factors that af-
fect the reaction rates of Diels-Alder reactions
(27, 30) under strictly solvothermal conditions,
which allowed us to examine how mechano-
chemical reactivity trends differ from strictly
solvothermal trends. We determined the pres-
sure (p) of the reaction using a scale below the
tips and finite element analysis modeling
(FEM). The fluorescence data were fit to a
first-order kinetic model to determine acti-
vation parameters, including the activation
energy (Ea), which is the energy difference
between the transition state and the initial
state in the absence of stress; DG‡; and the
activation volume (DV‡), which is a measure of
the sensitivity of a reaction to mechanical
activation (40, 41). These data reveal that
rate constant (k) increases of a factor of >10×
occur at only a few atmospheres of p, and the
sensitivity of this experimental approach is
such that the effects of subtle differences in
dienophile structure on rates could be deter-
mined, revealing that mechanochemical re-
activity trends are distinct from solvothermal
trends. Molecular dynamics (MD) and density
functional theory (DFT) modeling of the sur-
face and reaction revealed how molecular
distortions account for changes in DG‡, providing
a generalizable model for mechanochemical
reactivity that suggests that the scope of me-
chanically susceptible reactions may be substan-
tially broader than previously anticipated.
Experimental setup
For the printing experiment, we modified an
approach we have developed for studying
mechanochemical surface reactions quanti-
tatively (31, 32), in which the reactions occur
under a ~1-cm2 elastomeric polymer tip array
(42, 43). The inked 900-tip arrays were mounted
onto the z-piezoactuator of an atomic force
microscope equipped with a specialized mount
for the tip arrays and an x,y–tilting stage. Upon
moving the arrays in and out of contact with
the surface, each tip in the array prints a two-
by-five array of 10 features, in which each
feature in a two-by-five array is printed with a
different tip-surface contact time t that varies
from 1 to 600 s. The substrate is intentionally
tilted with respect to the tip-array so that the
F applied by individual tips varies systemati-
cally across one axis of the surface (36). In this
experiment, the effect of 30 different values
of F, ranging from 1.91 to 89.4 mN (table S1),
and 10 different values of t on reaction con-
version could all be assessed from a single
printed surface. In addition, each two-by-five
pattern generated at a given F is repeated 30
times by the tip arrays, resulting in denser
data sets that enable higher-fidelity fitting. After
printing, the surface was sonicated in ethyl
alcohol (EtOH) for 5 min to remove any phy-
sisorbed dienophile and polyethylene glycol
(PEG) from the substrate, and F, k, Ea, DV‡,
and DG‡ values for the reaction between a
fluorescent diene and surface-bound anthra-
cene could be determined from the normalized
fluorescence intensity I (fluorescence of feature/
fluorescence of background) from images
taken from a single printed surface.
Characterization of patterned surfaces
We relied on several complementary analytic-
al techniques to confirm the formation of the
anthracene monolayer and, subsequently, the
formation of the Diels-Alder adduct. Fluores-
cence intensity data derived from fluorescence
microscopy images (Fig. 2A) confirmed that
the immobilization of the fluorophores occurs
only where the tips contact the surface, and
that I is dependent on both F and t (Fig. 2B).
Time-of-flight secondary ion mass spectro-
metry (ToF-SIMS) data (Fig. 2C) show that
fluorescent features of the two-by-three patterns
are chemically distinct from unprinted areas,
with the spectra of the former containing fea-
tures consistent with the presence of the
dienophile, whereas the latter are consistent
with an unreacted anthracene monolayer. X-ray
photoelectron spectroscopy (fig. S3), contact
angle measurements (fig. S6), and AFM imag-
ing (fig. S13) were carried out, and all data are
consistent with the proposed modified sur-
faces. Control experiments (fig. S12), including
patterning of the fluorophores onto a bare
SiO2 surface or the patterning of dyes that lack
the reactive alkene onto anthracene surfaces,
failed to produce fluorescence patterns, fur-
ther confirming that the fluorescent patterns
are the result of the covalent bond formation
that occurs during the Diels-Alder cycloaddition.
Although no single surface technique is capa-
ble of directly confirming the formation of
new covalent bonds in monolayers, the totality
of the data makes any explanation of the
fluorescent patterns for a reason other than
covalent bond formation through a [4+2]
Diels-Alder reaction unlikely.
Determination of activation parameters
To analyze the fluorescence data and ex-
tract kinetic parameters, we assumed that the
Diels-Alder reaction in this system follows a
first-order kinetic rate law (eq. S10) and that
fluorescence images can be used to quantify
conversion as a function of F and t. We adopted
the pseudo–first order assumption because
at the interface, the dienophile concentration
is substantially greater than the anthracene
concentration. We have previously applied
this same model to the kinetic data of other
Zholdassov et al., Science 380, 1053–1058 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Experimental data for Diels-Alder reactions on anthracene mono-
layers with varying force and times. (A) Fluorescence image (lex = 530 to
550 nm and lem = 575 to 750 nm, where lex is the excitation wavelength and
lem is the emission wavelength), observed after washing and sonication, of surfaces
after patterning with fluorescently labeled dienophile Alk onto the anthracene-
modified SiO2 surface. The imaged areas vary from high (top) to low (bottom)
F applied to the substrate during the cycloaddition reaction by the tilted tip arrays.
Scale bar, 90 mm. (B) Normalized fluorescence intensity (I is fluorescence of
feature/fluorescence of background) of the printed features of Alk as a function
of F and t. Arrows above the bars indicate the data taken from the fluorescent
images in (A); the wide arrows indicate high F, and narrow arrows indicate
low F. (C) Time-of-flight secondary-ion mass spectrometry (ToF-SIMS) map
(positive ion mode) of a surface patterned with Alk after sonication and washing.
(Middle left) Fluorescent image. (Middle right) Corresponding ToF-SIMS map.
Scale bar, 100 mm. Mass spectrometer data were taken from unreacted (top)
and reacted (bottom) areas of the surface. The peak at mass/charge ratio
+ fragment corresponding to anthracene,
(m/z) = 178.08 is identified as a C14H10
and the peak at m/z = 73.01 is identified as a C4H11N+ fragment corresponding
to the secondary dialkyl amine of the rhodamine dye. (D) QCM measurement
tracking the formation of the Diels-Alder adduct from the reaction of Mal with
anthracene-functionalized QCM crystal in PhMe solution. The abrupt drop in
the frequency corresponds to the introduction of new solutions into the QCM.
The spike in the frequency and inset correspond to the introduction of a solution
of EtOH to wash physisorbed molecules from the surface. (E and F) Plots of
surface density of the adduct (Gadd) versus t for the reaction of Alk with the
anthracene surface. (G and H) Plots of Gadd versus F for the reaction of Alk with
the anthracene surface. Error bars are 1 SD from the mean of three independent
measurements. Fits were weighted to the error bars.
pericyclic reactions on monolayers under
applied F and found good agreement between
the model and the experimental data (32).
To determine the rate constant k, it was nec-
essary to track conversion of anthracenes on
the surface to adduct by measuring the grafting
density of the anthracene (Ganth) and of the ad-
duct (Gadd) in the fluorescent features. A quartz
crystal microbalance (QCM) measurement on a
SiO2 crystal that was subjected to the anthra-
cene monolayer formation protocols provided
Ganth,max, the concentration of anthracene in the
unreacted monolayer, of 1.12 ± 0.33 mol·nm−2
(fig. S18), which is in good agreement with
the value obtained from MD simulations of
Ganth,max = 1.20 ± 0.08 mol·nm−2 (figs. S36 and
S37). The maximum grafting density of the
adduct (Gadd,max) was determined by moni-
toring the reaction between an anthracene-
modified QCM crystal and a solution of Mal
within the fluid cell of the QCM (Fig. 2D).
This reaction was selected because it occurs
rapidly, even in the absence of F, so that the
reaction would proceed to completion in the
QCM. The QCM data were consistent with
the formation of the adduct with Gadd,max =
0.94 ± 0.14 mol·nm−2, suggesting that only 75
to 84% of the anthracene can react with Mal,
at which point the surface is saturated with
adduct. For the ensuing calculations, we assumed
that the adducts that formed with the differ-
ent dienophiles had similar volumes and, in
turn, similar Gadd,max. An accurate measure of
F at each feature was needed to understand
the relationship between reaction rate and
F. We determined F using a balance below the
printed surface and measuring the recorded
weight and feature edge length (fig. S22 and
table S1) (35), and these calculations deter-
mined that the F across the substrate ranged
from 1.91 to 89.4 mN. We conducted FEM of
individual pyramidal tips to validate the force
measurements, and the relationship between
feature length and z-displacement matched
the experiments and was nearly indepen-
dent of the assumed elastic constants for poly-
dimethylsiloxane (PDMS). Furthermore, the
values of the simulated F as a function of
z-piezo extension could be readily fit to the
experimental data by using values of the PDMS
elastic constants well within typical measured
values (figs. S23 and S24). Last, we considered
whether surface roughness could create local-
ized asperities of high force and found that
average surface roughness (0.41 nm) (fig. S25)
was too low to cause any noteworthy effect.
With these data in hand, the surface density
of the adduct (Gt,F) could be determined from
the fluorescence intensity of the features printed
at different F and t from It,F using Eq. 1
(cid:4)
(cid:1)
(cid:3)
(cid:5)
Gt;F ¼ 1 (cid:2)
Imax (cid:2) It;F
Imax
where Imax is the fluorescence intensity of a
feature that has reached saturation with the
adduct. This equation assumes Gt,F and It,F
(cid:3) Gadd;max
ð1Þ
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RES EARCH | R E S E A R C H A R T I C L E
are linearly related, an assumption that can
be used in organic monolayers when the fluo-
rophores do not couple (44). The relationship
between Gt,F, F, and t for each feature was
plotted for all anthracene-dienophile pairs
(Fig. 2, E to H, and figs. S27 to S30). In all
cases, we observed that Gt,F increased with
increasing t and F. Mal is the only dieno-
phile that formed adduct in the absence of F,
and the rate quickly reached a maximum upon
the application of minimal F. This is consistent
with known trends for Diels-Alder reactions
with normal electron demand, in which the
presence of electron withdrawing groups on
the dienophile lowers the Ea (27, 30). The plots
of Gt,F versus t (Fig. 2, E and F) and Gt,F versus
F (Fig. 2, G and H) fit well to a first-order
rate model, further validating the pseudo–
first order assumption. All fits of kinetic data
were weighted to the error bars, and c2 analysis
showed that the fits were statistically signifi-
cant at a 95% level of confidence.
A mathematical framework was needed to
derive the activation parameters k, Ea, DV‡,
and DG‡ from the experimental data. We
adapted the model, developed from examining
chemical reactions under hydrostatic pressure
(45, 46) and based on the work of Evans and
Polanyi (47) and Eyring (48), that considers how
p affects k. Under hydrostatic pressure, cyclo-
addition reactions have finite and negative DV‡,
meaning that p will increase k according to
Eq. 2
ln kð Þ ¼ ln Að Þ (cid:2)
Ea
kBT
(cid:2)
pDV ‡
kBT
ð2Þ
where A is the preexponential factor, T is the
temperature, and kB is Boltzmann’s constant.
This model, which considers the effects of
thermal and mechanical activation on the
rate, has DG‡ = Ea + pDV‡. We follow the
convention, used broadly in the study of
the effects of p on chemical kinetics, in which
a negative DV‡ acts to reduce DG‡. To apply
this model, the mean p in the nanoreactor
contacts was determined as a function of F
by dividing by the feature area. Our use of
mean pressure is consistent with current pub-
lished work on probe-based mechanochemistry
(32, 49, 50). There was a spatial distribution
of that pressure, as seen in our finite element
simulations (fig. S23D), but this does not alter
the observed trends nor our primary conclu-
sion that nonhydrostatic compression increases
reaction rates as a result of molecular distor-
tion, lowering the reaction energy.
With these experimental data, we deter-
mined all the activation parameters of interest
for each dienophile-anthracene pair. Isothermal
first-order Arrhenius plots of lnGanth versus t
were fitted, and k at each pressure was deter-
mined from the best-fit linear correlation (Fig.
3A and fig. S31) that was weighted to the error
bars; errors are reported as the standard error
of the fit. For Alk, k increased from 3.8 ±
0.25 × 10−3 s−1 at p = 0.16 MPa to 1.55 ± 0.19 ×
10−2 s−1 at p = 0.32 MPa, and this trend of in-
creasing k with increasing p is consistent
throughout all the data. The greatest change
in k was observed for MAcr (from 4.07 ±
0.58 × 10−3 to 1.77 ± 0.77 × 10−1 s−1) and the
smallest for Mal (from 4.0 ± 0.050 × 10−2 to
1.57 ± 0.77 × 10−1 s−1). The Ea and DV‡ were
determined from the extrapolated y-intercept
and slope, respectively, of the linear fit of the
plot of lnk versus p (Fig. 3B). The Ea follow the
trend MAcr > Acr > Alk > Mal. The mag-
nitudes of Ea in the anthracene monolayers,
84.5 to 96.4 kJ·mol−1, are similar in magni-
tude to values for Diels-Alder reactions with
anthracene reported in the literature of 63.6 to
83.7 kJ·mol−1 (51, 52), and these small differences
in magnitude in the Ea between reactions in
solution and monolayers can be attributed to
differences in molecular structures, reaction
geometry, lack of solvent, and the influence of
the SiO2 surface. All DV‡ are negative, and the
differences in DV‡ between the dienophile-
anthracene pairs reflect the relative sus-
ceptibilities of their rates to mechanically
induced pressure. The DV‡ range from –60.7 ×
103 cm3·mol−1 for MAcr to –21.8 × 103 cm3·mol−1
for Mal and follow the identical trend of
MAcr > Acr > Alk > Mal, meaning that the
reactions with larger Ea are more sensitive to
mechanochemical activation. Also, these DV‡
values are substantially greater than the DV‡
of –20 to –45 cm3·mol−1 for Diels-Alder re-
actions observed (46) under hydrostatic p in
solution, where interfaces do not have a role in
the reaction. Last, we calculated the change
in free energy of activation DDG‡ = pDV‡ at
every p for each dienophile-anthracene pair
(Fig. 3C) and found that DDG‡ range from
–3.53 to –19.46 kJ·mol−1, with an average value
of –8.21 kJ·mol−1, which would cause a ~14-fold
rate increase in rate. The relative sensitivity to
p shown in Fig. 3B was validated by adding
the rhodamine-labeled Mal (Fig. 3B, red) and
a MAcr that was labeled with fluorescein (Fig.
3B, green) to the same tip array (fig. S33) and
then printing them simultaneously (fig. S34),
which led to the fluorescence intensity of the
red dye remaining constant as force was in-
creased, whereas the intensity of the green dye
increased with increasing force (fig. S35).
Modeling mechanical distortion
We used DFT calculations to generate a
theoretical model for the energetics of the
reactants and the transition states (TSs) and to
understand mechanistically how F acts on the
system to lower the reaction energy (DE). Al-
though experiments determined DG‡, our
calculations and the ensuing theoretical treat-
ment involve DE, which is the reaction energy
that does not take into account vibrational
and entropic effects that are not included in
the DFT calculations. Anthracene was simu-
lated as attached to a Si4O9H3 cluster to mimic
the effect of the surface. DFT calculations
predicted the Ea, which is the activation en-
ergy for the strictly solvothermal reactions,
as defined by Eq. 2, for the Diels-Alder reac-
tion to be between 77.1 (Mal) and 90.0 (Alk)
kJ·mol−1 (Fig. 4A and fig. S44). These values
are within range of the experimental values.
The overestimation of the Ea of Alk is likely
caused by limiting the reaction system to the
anthracene, SiO2 cluster, and dienophile. In
doing so, we neglected the destabilizing ef-
fects caused by the interactions between the
surrounding SiO2 surface and the rhodamine
fluorophore. This omission led to interactions
Fig. 3. Activation parameters for the Diels-Alder reactions on anthracene monolayers. (A) Isothermal Arrhenius plots of ln(Ganthracene) versus t at different F for the
reaction between Alk and the anthracene monolayers. Fits are based on eq. S12. The slope of these lines provide k. (B) Plot of lnk versus p for all four dienophiles, the slope of
which provides DV‡, whereas y-intercept provides Ea. Fits were weighted to the error bars, and coefficients of determination (R2) are 0.97 to 0.99. (C) DDG‡ as a function of p.
Zholdassov et al., Science 380, 1053–1058 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
in the calculations that stabilized the Alk-
anthracene reactant complex, resulting in a
higher reaction barrier than was measured
experimentally. MD simulations showed that
the anthracene responds to tip-induced com-
pression by bending toward the surface, that
the fraction of molecules with distorted CCH
angles increases with increasing pressure (fig.
S42), and that compression causes deforma-
tion of the molecules themselves (figs. S40 to
S42). To model the effect of the mechanical
distortion caused by uniaxial stress acting on
the reactant from the top, we used DFT to
distort the anthracene along three angles—
OSiC, SiCC, or CCH (Fig. 4A)—and the geo-
metry of the reactant and TS were fully
relaxed, while keeping those angles fixed.
In this model, we envision that F increases
the energy of the reactants by distorting the
anthracene in a way that increases its re-
activity. The acceleration of the reaction can
be then achieved when the distortion energy
of the reactants (DEd
R) is larger than the dis-
tortion energy of the TS (DEd
TS) (53). The
change in the reaction energy (DDE) that oc-
Fig. 4. Mechanical distortion under uniaxial
stress. (A) The activation energy Ea and the
geometry of the relaxed transition state involving
Acr. Blue lines indicate OSiC, SiCC, and CCH angles,
distortion of which by the applied F is explored in
(B) and (C). All calculations have been performed at
M06-2X/6-311+G(d,p) level of theory (31, 32, 57, 58).
(B) The relative change (DDE) to the reaction energy
(DE) as a function of the CCH angle. The gray box
indicates the fully relaxed TS geometry. The bending
of the CCH angle leads to the decrease of the DE for
MAcr, Acr, and Alk. (C) The effect of distorting the
CCH coordinate on the geometry of the TS. Pushing
the H atom toward the dienophile creates an
asynchronous TS, which lowers the reaction energy.
curs during the distortion of the anthracene
reactant and TS are shown in Fig. 4B and fig.
S45. We observed that distorting the anthra-
cene along OSiC and SiCC angles increases DE.
However, bending the top H (CCH) toward the
dienophile, from the relaxed geometry of be-
tween 180° and 190° to 200°, decreases the
DE of Alk, Acr, and MAcr by 2.6, 4.4, and
5.6 kJ·mol−1, respectively, which is consis-
tent with the experimentally determined DDG‡
and follows the identical trend MAcr > Acr >
Alk > Mal. Only in the case of Mal did bend-
ing of the CCH angle increase the DE, most
likely because of repulsive electrostatic inter-
actions between the bulky dienophile and the
SiO2 cluster, although this is still consistent
with the smallest DDG‡ observed experimen-
tally for Mal. Subsequently, we explored the
effect of bending of other angles or bending
multiple angles simultaneously (fig. S46 and
table S14), and these calculations did not re-
sult in substantially different values of DE.
This particular bending motion is productive
because it increases asynchronicity—the dif-
ference in length (DrC–C) between newly formed
C–C bonds—of the TS (Fig. 4C). This deforma-
tion from the relaxed, nearly synchronous TS
of the Acr (DrAcr
C(cid:2)C ¼ 0:07 Å) to the distorted,
asynchronous TS (DrAcr(cid:2)200
¼ 0:18 Å) reduces
C(cid:2)C
the destabilizing activation strain and unfav-
orable Pauli repulsion between the reactants,
which results in a lower DE (53, 54). Fur-
thermore, the predicted degree of the asyn-
chronicity of the distorted TSs (table S13) is
consistent with the increasing acceleration of
the reaction, MAcr > Acr > Alk > Mal.
Mechanical force, which acts as uniaxial
compression, modifies the potential energy
surface of the Diels-Alder reaction differently
than does hydrostatic pressure. Under strictly
solvothermal conditions (Fig. 5A), DE is equal
to the strictly solvothermal activation energy
Ea. Hydrostatic pressure (Fig. 5B) acts along
the reaction coordinate by reducing the ener-
TS), and DDE =
gy of the transition state (DEH
TS = pDV‡. DV‡ of Diels-Alder reactions
DEH
under hydrostatic pressure are modest (−20
to −45 cm3·mol−1) (46) because hydrostatic
pressure squeezes equally along three axes
and does not cause molecular distortion. As
such, a p of ~150 MPa is needed for a DDE of
−4.4 kJ·mol−1, which is an arbitrarily chosen
value of DDE that is in the range of those DDG‡
measured here experimentally. Uniaxial com-
pression (Fig. 5C) distorts the reactants, rais-
ing their energy by DEd
R, and also distorts the
transition state to raise its energy by DEd
TS. So,
under mechanochemical conditions, in which
uniaxial compression can cause distortions to
R = pDV ‡. Because
TS − DEd
occur, DDE = DEd
the magnitudes for the DV‡ we observed for
mechanically distorted Diels-Alder reactions
are large (>104 cm3·mol−1), the same DDE of
−4.4 kJ·mol−1 can be achieved at p < 1 MPa.
We also found that similarities exist (fig.
S47) in how force modifies the potential ener-
gy surfaces of mechanochemical bond forma-
tion (pushing, which causes uniaxial stress)
and mechanochemical bond rupture reactions
(pulling, which involves uniaxial stress in the
opposite direction). In 2007, Hickenboth et al.
studied bond rupture in another pericyclic
reaction, the ring opening of a benzocyclobutene
mechanophore, while using sonication to
drive the ring-opening reaction (20). Since then,
other pericyclic reactions, including the retro
Diels-Alder reaction driven by pulling, have
also been examined (17, 22). The Diels-Alder
reaction (bond forming) and benzocyclobutene
ring-opening–retro Diels-Alder reactions (bond
rupture) are all pericyclic reactions, meaning
that their regioselectivities and stereoselectiv-
ities are governed by the Woodward-Hoffmann
rules. The studies by Hickenboth et al. first
revealed that a distorted state also precedes
the TS and bond rupture in ring opening,
and the result of this distorted state is a
decrease in DE, where the relationship DDE =
DEd
R, the same relationship that we
observed for mechanochemical bond formation,
also applies. Thus, the key to understanding re-
gioselectivity and stereoselectivity in mecha-
nochemical pericyclic reactions—and bringing
mechanochemically driven pericyclic reactions
within the Woodward-Hoffmann manifold—
necessitates understanding the distortion that
uniaxial mechanical stress induces in the re-
actants and the TSs. There is, however, an im-
portant difference between how pushing and
pulling modify the reaction potential energy
surface: a Diels-Alder reaction driven by com-
pression will follow a distinct trajectory along the
potential energy surface than the retro Diels-Alder
reaction of its products. As such, the geometries
and energies of the TSs and the distorted states
of the Diels-Alder reaction and the retro Diels-
Alder reaction will be very different.
TS − DEd
We have used elastomeric tip arrays to con-
trol precisely the t and F applied between
dienes and dienophiles on a surface to deter-
mine k, Ea, DV‡, DG‡, and DDG‡ for the Diels-Alder
reaction between immobilized anthracene
and four dienophiles that differ in steric
and electronic demand. We found that DV‡ is
~1000-fold greater on surfaces under uniaxial
compression than under hydrostatic pressure,
indicating that the reactions follow different
trajectories. The value of tip-based approaches
for measuring the kinetic parameters of mech-
anochemical bond-breaking reactions is well
known, and in this work we show that the
techniques are equally valuable for studying
bond-forming mechanochemical reactions. These
results have important implications for the
study, understanding, and wider application
and adoption of mechanochemistry. These
results also explain that the large DV‡ for
mechanochemical reactions occur as a result
Zholdassov et al., Science 380, 1053–1058 (2023)
9 June 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 5. Comparison of reaction trajectories under strictly solvothermal
activation, hydrostatic pressure, and uniaxial stress. (A) Reaction potential
energy diagram of the Diels-Alder reaction under strictly solvothermal activation.
(B) Reaction potential energy diagram of the Diels-Alder reaction under
hydrostatic pressure. The arrows indicate the hydrostatic forces that accelerate
the reaction. DEH
the change in the DE in the hydrostatic mechanism at a p of 150 MPa.
(C) Reaction potential energy diagram of the Diels-Alder reaction under uniaxial
TS was calculated by using DV‡ of −30 cm3·mol−1 to predict
R) and TS deformation energy (DEd
mechanochemical activation. The arrows indicate the deformation of the CCH
angle on the diene from the solvothermal TS value of 187° to the arbitrarily
chosen distorted TS value of 200° and associated reactant deformation energy
(DEd
TS). All calculations have been performed
at M06-2X/6-311+G(d,p) level of theory. The equations for calculating the
reaction energy (DE) in each of the three reaction conditions—solvothermal
activation, hydrostatic pressure, and mechanical distortion—are provided below
the potential energy diagrams.
of the proximity to surfaces and uniaxial stress
that cause molecular distortion. This distor-
tion lowers the reaction energy and drives the
reaction through a distinct reaction trajectory,
which explains why different isomers are often
obtained under F than in solvent (9, 55). This
phenomenon—the distortion of molecules near
surfaces that occurs under F to lower DG‡—
will be relatively independent of molecular
structure and suggests that mechanochemical
reactivity is more widespread than previously
anticipated. As a consequence, these results
should encourage the adoption of mechano-
chemical methods for sustainable chemical
synthesis and for accelerating reactions that
are otherwise impractically slow.
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AC KNOWLED GME NTS
We thank P. Nautiyal for assistance with acquiring AFM images. We
also thank T.-D. Li for assistance with acquiring ToF-SIMS data.
Funding: A.B.B., R.W.C., and A.M. are grateful to the National
Science Foundation Center for the Mechanical Control of
Chemistry (CCI CHE-2023644) for generous support. A.B.B. also
acknowledges award DBI-2032176 from the National Science
Foundation. This work was carried out in part at the Singh Center
for Nanotechnology, which is supported by the NSF National
Nanotechnology Coordinated Infrastructure Program under
grant NNCI-2025608. Author contributions: Y.S.Z., A.M., R.W.C.,
M.M., and A.B.B. conceived the research. Y.S.Z., L.Y., S.R.G.,
A.B., R.W.K., and D.J.V. carried out the experiments. All authors
contributed to the writing of the manuscript. Competing interests:
The authors declare no competing financial interests. Data and
materials availability: All data are available in the supplementary
materials. Tables S1 to S14 have been uploaded in more reusable
tabular format to the Dryad repository (56). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf5273
Materials and Methods
Figs. S1 to S47
Tables S1 to S14
References (59–78)
Submitted 27 October 2022; resubmitted 14 February 2023
Accepted 13 April 2023
10.1126/science.adf5273
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RES EARCH
GEOPHYSICS
Ultralow frictional healing explains recurring
slow slip events
Srisharan Shreedharan1,2*, Demian Saffer1,3*, Laura M. Wallace1,4, Charles Williams4
Plate motion on shallow subduction megathrusts is accommodated by a spectrum of tectonic slip
modes. However, the frictional properties and conditions that sustain these diverse slip behaviors remain
enigmatic. Frictional healing is one such property, which describes the degree of fault restrengthening
between earthquakes. We show that the frictional healing rate of materials entrained along the
megathrust at the northern Hikurangi margin, which hosts well-characterized recurring shallow slow slip
events (SSEs), is nearly zero (<0.0001 per decade). These low healing rates provide a mechanism for the
low stress drops (<50 kilopascals) and short recurrence times (1 to 2 years) characteristic of shallow
SSEs at Hikurangi and other subduction margins. We suggest that near-zero frictional healing rates,
associated with weak phyllosilicates that are common in subduction zones, may promote frequent,
small-stress-drop, slow ruptures near the trench.
O ver the past 2.5 decades, a rapidly grow-
ing body of observations has revealed a
continuum of slip behavior on tectonic
plate boundary faults globally, spanning
time scales from seconds to years (1).
These modes of slip include fast elastodynamic
earthquakes, tectonic tremors, low-frequency
earthquakes (LFEs), very-low-frequency earth-
quakes (VLFEs), slow slip events (SSEs), and
aseismic creep. The recognition of these diverse
slip modes has sparked a rethinking of the
underlying mechanics of earthquakes and
fault slip and raised fundamental questions
about in situ conditions, rheology, and processes
along the subduction interface that govern this
spectrum of behavior (1, 2).
SSEs, in particular, have emerged as a poten-
tially important mode of slip on the shallow
subduction zone megathrust. During SSEs, the
fault slips slowly over a period of days, weeks,
or even months (1), rather than in seconds as in
typical elastodynamic earthquakes. In some
cases, SSEs may be accompanied by tremors,
LFEs, and VLFEs, which radiate seismic energy
(1, 3) and are detected seismologically.
Numerous hypotheses have been proposed
to explain this spectrum of fault slip modes,
including highly elevated pore-fluid pressures
(4, 5), dilatant strengthening (6), transitional
frictional properties (7–10), low-rigidity fault
rocks (11), and lithological and geometric hetero-
geneities within the fault zone (12). These hy-
potheses center around material properties
that control the nucleation of an instability on
a fault and its ability (or inability) to grow into
a dynamic rupture. A relatively unexplored yet
1Institute for Geophysics, Jackson School of Geosciences,
University of Texas at Austin, Austin, TX, USA. 2Department
of Geosciences, Utah State University, Logan, UT, USA.
3Department of Geological Sciences, Jackson School of
Geosciences, University of Texas at Austin, Austin, TX, USA.
4GNS Science, Lower Hutt, New Zealand.
*Corresponding author. Email: srisharan.shreedharan@usu.edu
(S.S.); demian@ig.utexas.edu (D.S.)
equally fundamental control on earthquake
occurrence is frictional healing, which describes
the ability of a fault to restrengthen and store
elastic strain energy between events (2, 10). In
the absence of a mechanism for restrengthen-
ing, a fault will fail only by aseismic creep.
Frictional healing of an earthquake source
region is particularly important because it
plays a primary role in controlling rupture
properties, including stress drop, recurrence
interval, and potentially slip mode and amount
(2, 10).
Measuring the frictional properties of rocks
in the fault zones hosting these complex slip
behaviors has proved challenging because the
SSE source depths are often inaccessible to
direct sampling or drilling (13). One notable
exception is the Hikurangi subduction zone
offshore New Zealand, where regularly recur-
ring shallow (<15 km) SSEs are well documented.
We report on laboratory measurements of fric-
tional healing conducted on samples of rock
types involved in slow slip, obtained by drill-
ing at the offshore Hikurangi margin. We then
integrate these measurements with models
of interevent tectonic loading and observa-
tions of SSE stress drop. We show that the
very low healing rates of fault zone materials
along the megathrust, which are typical of
clay-rich faults in both subduction zones and
other geological settings, are a key ingredi-
ent for the occurrence of recurring, frequent,
small-stress-drop, slow slip transients.
Tectonic setting of the northern
Hikurangi margin
Westward subduction of the Pacific plate
beneath the Australian plate occurs along
the northern Hikurangi Trough at 50 to
60 mm/year (14) (Fig. 1, A and B). The sub-
ducting plate is primarily composed of the
Hikurangi Plateau, a Cretaceous large igneous
province, and is overlain by ~1 km of volcani-
clastic, pelagic, and siliciclastic sediments (12).
The northern Hikurangi margin represents an
ideal natural laboratory to investigate the
origin of slow earthquake phenomena, owing to
the shallow source depth of regularly recurring
SSEs, which has enabled a host of high-resolution
near-source geophysical investigations, as well as
acquisition of host rock samples by drilling (15).
The shallow SSEs here originate at depths of 2 to
15 km (12, 13), in a structurally complex region of
seamount subduction (Fig. 1C) and intervening
areas of high-amplitude seismic reflectivity
and low seismic velocity (5, 16), with the latter
usually inferred to represent elevated pore-
fluid pressure (16). These SSEs propagate to
within a few kilometers of, and possibly to, the
trench (13); recur every 1 to 2 years; and last
for a few weeks (Fig. 1, D and E), during which
the plate interface experiences slip rates of
~1 cm/day (15, 17). The SSEs are character-
ized by small stress drops (<10 kPa) and a
range of energy release equivalent to that for
moment magnitude (Mw)~6 to 7 earthquakes
(18). Microseismicity and tremor have been
documented along and above the plate inter-
face during and after the shallow SSEs (15).
The megathrust in this region has also hosted
two tsunami earthquakes (long-duration elasto-
dynamic earthquakes with slow rupture veloc-
ities of ~1 km/s) in 1947 (19). Thus, the shallow
megathrust here is home to a rich variety of slip
modes that appear to interact in complex ways
in space and time.
International Ocean Discovery Program (IODP)
Expedition 375 sampled Cretaceous volcani-
clastic conglomerates overlying the subduct-
ing Hikurangi Plateau at Site U1520, located
~10 km east of the trench (Fig. 1, A to C). Seismic
imaging indicates that these materials are
entrained along and eventually form the shal-
low megathrust here (12, 20). The margin is
characterized by low heat flow, with tempera-
tures on the megathrust expected to remain
<150°C at a distance of ≳70 to 100 km from the
trench (21). Thus, the frictional and rheologi-
cal properties of the volcaniclastic material
recovered at Site U1520 are likely represen-
tative of those along the shallow megathrust
(to ~10- to 12-km depth), well into the source
region of regularly recurring SSEs.
Frictional healing, fault failure, recurrence,
and stress drop
Frictional healing describes the ability of a
material to restrengthen frictionally over time
and is a prerequisite for repeating stick-slip
(seismic) failure of faults because it allows
interseismic coupling and elastic strain accu-
mulation (22). Healing is thought to reflect a
time-dependent increase in asperity contact
area at the micro- to nanoscopic scales (22).
In the laboratory, frictional healing is commonly
measured via slide-hold-slide (SHS) tests (23)
and typically increases log-linearly with time
(22). Healing (b) is usually reported as the
Shreedharan et al., Science 379, 712–717 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
B
D
40
30
20
10
)
s
y
a
d
(
n
o
i
t
a
r
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d
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a
P
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(
p
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s
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t
S
2004
2008
2012
Year
C
Fig. 1. Tectonic setting of the Gisborne area shallow slow slip events. (A) Bathymetric map of the
northern Hikurangi margin showing the trench (bold black curve), depth to the plate interface (dashed
contours), slip contours of the 2014 SSE in millimeters (black, as labeled), location of the 05CM-04 seismic
line (black line), and locations of IODP expedition 375 drill sites (red circles) [modified from (12)]. Hypocenter
of the 1947 tsunami earthquake (blue star), tremor activity (small yellow circles), and microseismicity
(white stars) are also shown. (B) Regional tectonic map showing the Pacific plate subducting beneath the
Australian plate, forming the northern Hikurangi margin. (C) Interpretation of the 05CM-04 seismic line
[modified from (12)] showing the plate interface (bold black line), active upper-plate splay faults (red lines),
and location and depth extent of IODP drill site U1520. The blue star at a depth of ~6 km represents the
hypocenter of the 1947 tsunami earthquake. (D) Slip duration and (E) Spatiotemporally averaged stress drop
of the quasiperiodic SSEs rupturing the Gisborne patch from 2002 to 2016 (table S2).
rate of increase in fault strength (or friction)
per logarithmic (10-fold) increase in time.
We analyze the SHS experiments conducted
by (10) on Cretaceous volcaniclastic sediments
from Site U1520 (Fig. 2A). Modal compositions
of these samples (table S1) (24) determined
from x-ray diffraction indicate that they contain
>55 wt % clay minerals and that the clay is
dominantly smectite. These experiments were
performed on water-saturated gouges under an
effective normal stress of 25 MPa, pore pres-
sures of 5 to 10 MPa, and for driving velocities
of 1 to 30 mm/s. These experimental boundary
conditions were selected to best represent
appropriate conditions of stress and sliding
velocity at shallow SSE source depths along
the subduction megathrust. The healing
rates inferred for these materials (b < 10−4, Fig.
2B) represent some of the lowest values of
fault healing reported for fault rocks and are
more than 10 to 100 times below those com-
monly reported for carbonates and tectosili-
cates (25). Our observations are consistent
with near-zero healing rates documented in
phyllosilicate-rich synthetic and natural fault
gouges, including smectite and serpentinite
(25, 26) (Fig. 2B).
We compare these frictional healing rates to
average stress drops reported for repeating
shallow SSEs that ruptured the Gisborne patch
(18) (table S2) (Figs. 1 and 2). Seismic evidence
indicates that the materials participating in
shallow SSEs here may be compositionally
similar to the input materials that were fric-
tionally tested (12, 20). Although we have
incomplete knowledge of the exact in situ
effective stress (seff) along the shallow SSE
source fault (2, 12, 15), indirect observations
strongly suggest significant overpressure along
the plate interface (2, 5). To honor these obser-
vations and also allow for reasonable uncer-
tainty in seff, we convert the friction drop from
SHS experiments to a stress drop (Fig. 2C) by
considering a range of pore-fluid overpressure
values along the plate interface of l = 0.8 to
0.95 (where l = Pf/Pl, and Pf and Pl are the
fluid and lithostatic pressures, respectively)
(23) (fig. S1).
The laboratory data for the frictionally weak
volcaniclastic conglomerates are in excellent
agreement with the geodetically defined stress
drops for the Gisborne shallow SSEs (Fig. 2C).
Together, these analyses suggest near-zero fric-
tional restrengthening rates. In comparison,
repeating earthquakes along the Calaveras fault
exhibit substantially higher stress drops (1 to
10 MPa) that are strongly correlated with repeat-
ing earthquake recurrence intervals (Fig. 2C),
increasing by nearly 2 MPa per 10-fold in-
crease in time (27). SHS experiments on the
predominantly quartzofelspathic material
recovered from the Calaveras fault indicate
correspondingly high frictional healing rates
of ~0.007 (28), at least two orders of mag-
nitude higher than the healing rates we re-
port for the Hikurangi megathrust materials
(Fig. 2B). Along the San Andreas Fault, ex-
perimentally estimated frictional healing
rates on materials recovered from drilling
are also in agreement with both the recur-
rence and stress drop of small repeating earth-
quakes along bounding faults and with the
creeping behavior of the central deforming
zone (25, 26, 28).
Competition between loading and healing on
the shallow subduction megathrust
To further explore the role of the experimen-
tally observed near-zero healing rates in govern-
ing event recurrence and strain accumulation
and release, we consider the balance between
tectonic loading and healing rates. We com-
pute loading rates along the plate interface
using a two-dimensional (2D) numerical
model of the margin that incorporates heter-
ogeneous elastic properties, which are well
constrained by geophysical surveys (29) (Fig. 3,
A and B) (23). We then compare these loading
rates to the event-averaged stress drop and
recurrence intervals of the ~10-year sequence
of observed Gisborne slip events (Fig. 3C). The
latter assumes that all of the strain energy
accumulated during an interevent period is
released during slip.
The numerical model predicts tectonic stress-
ing rates ranging from 30 kPa/year at 95 km
from the trench (near the downdip edge of the
SSE region) to 0.3 kPa/year at 30 km (the updip
end of the likely SSE source region), with an
average loading rate of ~4.5 kPa/year over the
outer ~65 km of the megathrust (Fig. 3B). Event-
based estimates of stress accumulation rates
using observed stress drops and recurrence
intervals for each SSE range between 1 to
30 kPa/year, with an average of ~9 kPa/year
across the seven events (Fig. 3, B to C). The two
estimates of tectonic loading rates are in excel-
lent agreement and suggest that on average,
the loading rate along the shallow megathrust
is ~4 to 10 kPa/year. The slip distributions for
most offshore Gisborne SSEs are poorly con-
strained, with the exception of the most recent
Shreedharan et al., Science 379, 712–717 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
slide
hold
A
reslide
μss
μpeak
p5391
U1520 28R5
μss
μpeak
μss
μss
μ
2
0
.
0
µ
i
,
t
n
e
c
fi
f
e
o
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n
o
i
t
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r
F
p5392
U1520 38R5
200
Loadpoint displacement (μm)
300
100
400
Laboratory
experiments
SSEs and
repeaters
λ = 0.80
λ = 0.90
λ = 0.95
7)
2
(
ult
fa
s
era
v
ala
C
e
d
a
c
e
a/d
P
M
1-2
Gisborne SSEs
102
104
Hold time or recurrence interval (s)
106
108
C
8
6
4
2
0
)
a
P
M
(
Δ
,
p
o
r
d
s
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e
r
t
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100
0
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8
6
4
2
0
-2
100
3
-
0
1
x
µ
Δ
,
g
n
i
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e
h
l
a
n
o
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t
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Δμ peak , p5391
Δμ peak , p5392
SAFOD CDZ and cuttings (26, 28)
Δμss (10)
(25)
fault
7x10-3
Calaveras
=
β
β=10-3
0-2
1
=
β
β = 10-4
101
102
Hold time (s)
103
104
Fig. 2. Frictional healing constrained from laboratory experiments. (A) Overlay of multiple SHS
protocols with different durations (3 to 3000 s) for two phyllosilicate-rich sediment samples from Site U1520.
mss represents the pre- and posthold steady-state values of the friction coefficient, and mpeak represents the
location of the (near-zero) peak friction upon reshear after a hold. (B) The change in friction (healing)
between mpeak and mss shows little or no correlation with hold time. Error bars quantify electrical noise in
the load cell and represent the limit of resolution of the friction drops. Fiducial lines show three different
healing rates representing a range of values reported in prior studies (25), as well as values encompassed by
the experiments reported here. Gray line represents the friction drops from SHS experiments conducted on
samples from the Calaveras fault (25), where seismic repeaters have been observed. Pink area shows the
range of values reported from SHS experiments conducted on smectite-rich San Andreas Fault Observatory
at Depth (SAFOD) Central Deforming Zone (CDZ) cuttings (26, 28). Light blue region represents changes in
steady-state friction coefficient from pre- to posthold reported by (10). (C) Changes in stress drop versus
recurrence interval for the Gisborne SSEs and versus hold time for the experimental data. Stress drops for
experimental data are calculated as the product of friction drop and effective stress for three different
degrees of overpressure. Gray triangles represent stress drops estimated from the seismic source for
Calaveras repeaters (27).
events, for which seafloor geodetic data were
available (13). This makes a precise compari-
son of the stress drops in the events with the
predicted loading rates for an identical fault
region difficult. Nonetheless, our results are
consistent with similarly small loading rates in
the outer forearc at the Nankai margin (30).
Frictional restrengthening increases logarith-
mically with time (as b × seff), whereas the shear
stress borne by the fault increases, to first order,
linearly with time as a function of tectonic
loading, which in turn is a function of rock
and fault elastic properties, geometry, and
plate convergence rate (Figs. 2 and 3). At a
given location, and in the absence of addi-
tional loading—for example, associated with
slip of adjacent fault patches—the fault reaches
a threshold for failure when the accumulated
stress exceeds the fault strength (or when the
interevent loading exceeds the amount of fric-
tional restrengthening; Fig. 4, A to C). In this
simplified framework, the time to failure repre-
sents the recurrence interval and the stress at
failure is the average stress drop of a quasiperi-
odic event. Here, we combine our numerically
determined loading rates (Fig. 3) with a re-
strengthening model to understand the size
and recurrence of time- and slip-predictable
events both through time at specific locations
(Fig. 4, A to C) and as a function of position
along the megathrust (Fig. 4, D to F).
Both tectonic loading and fault healing
increase with depth along the plate inter-
face (Figs. 2 and 3). As noted above, without
strong constraints on seff, we consider a
range of likely pore-fluid pressure ratios based
on geological and geophysical inferences (2, 5)
(Fig. 4 and fig. S2). We evaluate the competi-
tion between the loading rate and healing—
and thus the expected recurrence and stress
drops of repeating fault failure events—as a
function of distance from the trench by con-
sidering the spatial distribution of excess
strength at different times. We do so for a
range of likely pore-fluid pressures (and by
proxy seff), as well as for a range of b that are
consistent with our data. Because our exper-
imental data provide only an upper bound
on b, we explore values in the range of b = 3 ×
10−5 to 3 × 10−6, representing up to 1.5 orders
of magnitude lower than this upper bound.
We illustrate the competition between load-
ing and restrengthening at three representa-
tive locations along the plate interface, i.e., 25,
50, and 75 km from the trench (Fig. 4, A to C)
for an effective stress profile corresponding to
l = 0.9. At 75 km from the trench, well within
the SSE source region, the plate interface
experiences tectonic loading of ~3.5 kPa/year
(Fig. 3B). For our upper bound of b (3 × 10−5),
we predict a recurrence interval of 2.3 years,
with events having average stress drops of
~8 kPa; the lowest value of b (3 × 10−6) that
we consider yields events with recurrence in-
tervals of 3 to 4 months and <1 kPa stress drops
(Fig. 4A). Closer to the trench, at a distance of
25 km, the loading rate on the plate interface
is much lower (0.3 kPa/year). As a result, for
our upper bound on b, we predict considerably
longer times to failure (15 years) and stress
drops of 4 kPa (Fig. 4C). Our lower bound
on b yields recurrence intervals of ~1.3 years
and stress drops of ~0.4 kPa.
Low b (<10−4), coupled with the slow loading
rates on the shallow plate interface, suggest
that the fault is likely to fail in repeating, fre-
quent (1- to 3-year) events, with small maxi-
mum total slip (on the order of a few to ~10 cm),
on the basis of the slip deficit accrued during the
interevent time and on low stress drops (on the
order of a few to ~10 kPa). Although b and seff
are not perfectly constrained, other combina-
tions of these parameters (fig. S2) yield similar
outcomes. The observed recurrence and stress
drops in the Gisborne SSEs are most consistent
with scenarios presenting modest-to-high fluid
overpressure (l > 0.8), although near-lithostatic
pressures are not required (fig. S2). Also, Be-
cause the rate of fault restrengthening (b × seff)
scales with effective normal stress, this frame-
work provides a mechanism, in addition to
conditional frictional stability (2, 7), that links
Shreedharan et al., Science 379, 712–717 (2023)
17 February 2023
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RES EARCH | R E S E A R C H A R T I C L E
)
m
k
(
t
h
p
e
D
0
2
4
6
8
10
12
)
r
y
/
a
P
k
(
e
t
a
r
i
g
n
d
a
o
L
102
101
100
10-1
102
101
100
10-1
Slow slip rupture region
Subducted
seamount
1947 tsunami
earthquake
Gisborne events
GS04
GS11
GS10
GS14
GS07
GS13
GS06
SSE source region
90
80
70
60
50
30
Distance from trench (km)
40
A
B
C
Numericalmodel
Model average
in SSE source
20
10
0
Fig. 3. Inter-SSE loading rates in the northern Hikurangi margin. (A) An illustration of the 05CM-04
line showing upper-plate splay faults (red curves), the hypocenter of the 1947 tsunami earthquake (red star),
a subducting seamount, and the likely shallow SSE rupture region (thick yellow bars). (B) Annual tectonic
loading rates (for convergence at 50 mm/year) along the 05CM-04 seismic transect, computed from 2D
finite-element numerical model in Pylith (29). Loading rates increase from ~0.15 kPa/year near the trench to
~30 kPa/year at a depth of 15 km. (C) Tectonic loading rates constrained from the Gisborne SSEs as the
ratio of average stress drops and interevent times. The black (~4.5 kPa/year) dashed line shows average
loading rates from models.
elevated pore pressure with frequent small-
stress-drop events, as is commonly postulated
or inferred for SSEs (5).
We evaluate the spatial variation of this
competition in more detail by considering the
strength excess along the plate interface,
defined as the difference between strength
(or amount of restrengthening) and accumu-
lated tectonic stress at different times (Fig. 4,
D to F), i.e., after 1, 2, and 3 years, for an
effective stress profile corresponding to l = 0.9
(fig. S1). A positive strength excess represents a
fault that has healed more than it has been
loaded tectonically, indicating that it is still far
from failure. Conversely, a negative strength
excess indicates a fault that has already failed
because it has experienced more tectonic stress-
ing than restrengthening. For the case where b <
3 × 10−5, the strength excess is nearly zero to a
depth of ~8.5 km (corresponding to distances
~0 to 50 km from the trench), indicating that
the ultralow healing rates of the SSE source at
such shallow depths may allow it to fail fre-
quently (i.e., on a time scale of months or
shorter) and with very small (sub-kilopascal)
stress drops (Fig. 4, D and E). Further landward
from the trench and deeper, the strength excess
reaches zero after 1 to 3 years, which is in good
agreement with the recurrence intervals of the
shallow SSEs here.
An additional complexity in extrapolating
healing rates to natural faults arises because
some studies indicate that healing (b) may
vary with effective stress, temperature, and
lithology (10, 31, 32). This variation is cap-
tured across the suite of cases that we ex-
plore for values of b ranging from 3 × 10−6 to
3 × 10−5 (Fig. 4, A to F). Some studies in-
dicate that experimental healing rates could
increase with larger hold times (>3000 s) via
pressure solution or other mechanisms, par-
ticularly in strong quartzofeldspathic minerals
(32, 33), whereas others indicate that healing
rates may reduce over long time scales, par-
ticularly for clay-rich materials as the quality
and quantity of contact area becomes saturated
(28). Here, in accordance with (25, 28), we
consider a constant healing rate in mapping
from the experimental to natural SSE time
scales. In the constant b model (Fig. 4G, left),
stress drops are relatively constant at ~6 to
10 kPa regardless of the downdip location of
the SSE source, but there is considerable
variability in predicted recurrence intervals.
If b increases with depth (Fig. 4G, right), we
predict frequent (<9- to 14-months recur-
rence) SSEs with stress drops of <1 kPa near
the trench, and larger, less-frequent SSEs
further downdip (~10 kPa, 1- to 3-year re-
currence) at 10- to 15-km depth. The latter
are detectable by traditional onshore geo-
detic instruments (15), whereas the former
may be detectable only by offshore borehole
observatories near the trench (34). These
small, frequent, slow transients, if real, raise
the possibility of a spectrum of slip spanning
from quasiperiodic creep or undulating slip
on the shallowest reaches of the megathrust.
These transients originate near the trench
because, although loading is small, healing is
negligible. This would result in a continuum
from recurring larger SSEs farther from the
trench transitioning to more frequent, smaller
events near the trench. Moreover, depending
on the timescale and nature of observations,
these small, slow, and frequently repeating
transients could present themselves as aseismic
creep, particularly in the absence of continuous,
near-field, and high-precision offshore moni-
toring; in the limit as healing approaches zero,
slip will occur via stable creep. In other words,
when healing and loading are equivalently
small, such as near the trench, aseismic creep
and SSEs may be indistinguishable from one
another.
The small stress drops and small total slip
predicted by low healing rates are also phys-
ically consistent with fault failure via slow
earthquakes or SSEs as opposed to rapid slip
(35). Small stress drops and slip limit the
stored elastic energy available for the accel-
eration of slip, therefore favoring slip in slow
motion and over a long duration (35, 36).
Additionally, SSEs are thought to involve
substantial ductile deformation that extends
beyond a narrow slip zone (37), which would
dissipate a substantial amount of energy off-
fault, further reducing the energy available
for propagating a dynamic rupture on-fault
(38), and in turn, keeping any instability
slow. Taken together, the recurring small stress
drop events of <10 kPa (18) and velocity-neutral
frictional stability of the volcaniclastic materials
(10) indicate an inability of the SSE source
region to heal between SSEs and an inability
to nucleate large, dynamic earthquakes char-
acterized by large fault slip and rapid slip
velocities.
Shreedharan et al., Science 379, 712–717 (2023)
17 February 2023
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RES EARCH | R E S E A R C H A R T I C L E
t
RI
10
A
8
6
4
2
x = 75 km
B
x = 50 km
C
x = 25 km
g
β = 3 x 10-5
Δ
β = 10-5
β = 3 x 10-6
g
g
g
g
)
a
P
k
(
g
n
i
l
a
e
h
r
o
g
n
d
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l
i
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2
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4
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e
c
x
e
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t
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n
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r
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10
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-10
-20
β = 3 x 10-6
D
Gisborne
SSE source
Not
failed
E
a
1yr
2
3
1yr
2
3
Failed
2
4
Time (years)
6
β = 10-5
b
Not
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Failed
0
4
8
12
16
β = 3 x 10-5
F
1yr
2
3
Not
failed
c
Failed
a
P
k
0
1
s
s
e
r
t
s
r
a
e
h
S
Distance landward from trench (km)
G
Constant healing with depth, β = 3x10-5
Increasing healing with depth
x = 75 km
x = 75 km, β = 3x10-5
x = 50 km
x = 50 km, β = 10-5
x = 25 km
x = 25 km, β = 3x10-6
Time
5 years
Fig. 4. A framework to quantify competition between tectonic loading and frictional healing. Tectonic
loading as shown in Fig. 3 (black lines) and fault restrengthening (colored curves) as a function of time, for
three different assumed healing rates (3 × 10−6, purple; 1 × 10−5, orange; and 3 × 10−5, green) at (A) 75 km,
(B) 50 km, and (C) 25 km from the trench. Strength excess as a function of distance from the trench,
after 1 year (dotted curve), 2 years (dashed curve), and 3 years (solid curve) for healing rates of (D) 3 × 10−6,
(E) 1 × 10−5, and (F) 3 × 10−5 [same color scheme as in panels (A) to (C)]. (G) Simplified models of recurrence
and stress drop for two scenarios of depth-varying healing, showing shear-stress variations over time.
Constant healing with depth (left, light to dark blue) results in small-stress-drop events with large recurrence
intervals near the trench; increasing healing rate with depth (right, gray to black) results in very-small-stress-drop
events (~1 kPa) every few weeks or months. Effective stress corresponds to l = 0.90 for all panels.
The prediction that a near-zero strength
excess is attained simultaneously over a broad
region of the plate interface (e.g., Fig. 4, D and
E) also implies that the shallow megathrust
reaches failure over a broad region. This is
consistent with observations of shallow SSEs
having a large slip patch with small total slip
(35), because the low loading rates combined
with low healing rates never allow for a large
accumulation of slip deficit. In contrast, or-
dinary earthquakes with similar amounts of
slip (a few centimeters) commonly nucleate
over much smaller areas (35).
In addition to hosting SSEs, the northern
Hikurangi margin (12, 13) and other shallow
plate boundaries (2, 34, 39, 40) also host
tsunami earthquakes, microseismicity, LFEs,
VLFEs, and tremor. Carbonates, which are
characterized by substantially larger b (10)
(compare to Fig. 2) and capable of nucleating
instabilities even at modestly elevated temper-
atures (41, 42), are also present in the North
Hikurangi SSE source region, though with less
abundance than the volcaniclastics (10, 12, 41).
This heterogeneity of lithology may provide
one explanation for the diverse slip behaviors
observed along the margin. For example, it
raises the possibility that infrequent tsunami
earthquakes could nucleate locally where
strong and unstable materials such as carbon-
ates are embedded and/or abundant within
the broader SSE region (12). In this scenario,
such ruptures could then propagate through
the weak, phyllosilicate-rich volcanoclastic-rich
portions of the megathrust (43), producing
tsunami earthquakes (19). Alternatively, small
carbonate- or quartz-filled fractures along the
décollement may be loaded during an SSE.
This increased loading, coupled with the ele-
vated healing rates of these materials, could
result in tremorgenic failure that is spatiotem-
porally colocated with SSE slip (34, 44).
We integrate experimental measurements of
healing and healing rates on relevant mega-
thrust materials, a numerical model of fault
loading, and observed shallow SSE source
properties. Taken together, they indicate that
low healing rates on weak faults are a key
ingredient in the generation of frequent, low-
stress-drop, recurring slip events with small
amounts of total slip, such as those observed
at the northern Hikurangi margin and many
plate boundaries globally. Because the low
rates of healing limit the stored strain and
stress (and strain energy) available in the
system, materials with low healing rates are
likely to host SSEs, creep, and other slow earth-
quake phenomena. Furthermore, because re-
strengthening is controlled by the product
of frictional healing and effective normal
stress, our results highlight an additional path-
way by which high pore pressure (or low ef-
fective stress) may directly influence the size,
frequency, and nature of failure, and ultimate-
ly modulate the mode of failure in a host of
tectonic and geologic settings, particularly at
shallow depths (1). Weak phyllosilicate min-
erals, which typically exhibit low healing rates,
are common along shallow subduction mega-
thrusts (2), raising the possibility that shallow
SSEs and near-trench creep may be the norm
at subduction zones and that the compara-
tively limited observations of shallow SSEs
at subduction zones globally may simply be a
consequence of our inability to detect them
with land-based geodetic networks.
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ACKN OWLED GMEN TS
D.M.S. acknowledges funding from a US Science Support Program
post-expedition award and the Scott Petty Jr. Director’s Chair
endowment. L.W. acknowledges funding from the New Zealand MBIE
Endeavor Research Fund (contract C05X1605) and the Marsden Fund
(grant 20-GNS-001). Author contributions: Conceptualization: S.S.,
D.M.S. Methodology: S.S., D.M.S., L.W., and C.W. Investigation: S.S.,
D.M.S., L.W., and C.W. Visualization: S.S., D.M.S. Funding acquisition:
S.S., D.M.S., and L.W. Writing – original draft: S.S. Writing – review
and editing: S.S., D.M.S., L.W., and C.W. Competing interests:
The authors declare that they have no competing interests. Data and
materials availability: All data are available in the main text,
supplementary materials, or from Zenodo (45). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf4930
Materials and Methods
Supplementary Text
Figs. S1 to S3
Tables S1 and S2
References (46–53)
We thank L. Lavier and D. C. Bolton for insightful discussions. Funding:
S.S. was funded by the UTIG Palisades Postdoctoral Fellowship.
Submitted 25 October 2022; accepted 25 January 2023
10.1126/science.adf4930
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Climate-driven changes in soil conditions
alter hibernation
We used long-term climate records of air and
soil temperature from two field sites, Toolik
(68°38′ N, 149°38′ W; elevation 719 m) and
Atigun (68°27′ N, 149°21′ W; elevation 812 m),
in the Alaskan Arctic to document recent envi-
ronmental change. The dataset durations were
as follows: air temperatures at Toolik were
measured from fall 1993 to spring 2020, Toolik
soil temperatures from fall 1993 to spring 2019,
and Atigun soil temperatures from fall 2002 to
spring 2019. These measures were paired with
hibernation records collected using biologgers
(Toolik, fall 1996 to spring 2019; Atigun, fall 1999
to spring 2021) (15) to evaluate the physiological
impact of recent climate change on arctic ground
squirrels (see the supplementary materials). The
use of biologgers that measured abdominal
and/or skin temperature allowed us to record
detailed information about physiological and
phenological events during hibernation (Fig. 1,
fig. S1, and table S1) from 199 free-living arctic
ground squirrel individuals over 25 years.
Average annual air temperatures increased
from 1994 to 2020 (b = 0.070, t = 2.552, P =
0.02; Fig. 2A). This was driven by increases in
winter temperatures, because seasonal analyses
revealed increases in winter temperatures (b =
0.119, t = 2.375, P = 0.025; fig. S2), but no
annual trends for spring, summer, or fall (see
the supplementary materials and fig. S2). Dates
of soil freeze, measured at 1-m depth adjacent
to hibernacula, shifted to be ~4 days/decade
later in the fall (n = 446, b = 0.409, t = 2.851,
df = 383, P = 0.0045; Fig. 2B), and minimum
soil temperatures in winter increased by al-
most 2°C/decade (n = 366, b = 0.185, t = 6.922,
P < 0.001; Fig. 2C). Further, dates of soil thaw
in summer advanced by ~0.3 days/decade
RES EARCH
HIBERNATION
Climate change is altering the physiology and
phenology of an arctic hibernator
Helen E. Chmura1,2*, Cassandra Duncan3, Grace Burrell3, Brian M. Barnes1,
C. Loren Buck4, Cory T. Williams5*
Climate warming is rapid in the Arctic, yet impacts to biological systems are unclear because few
long-term studies linking biophysiological processes with environmental conditions exist for this
data-poor region. In our study spanning 25 years in the Alaskan Arctic, we demonstrate that
climate change is affecting the timing of freeze-thaw cycles in the active layer of permafrost soils and
altering the physiology of arctic ground squirrels (Urocitellus parryii). Soil freeze has been delayed
and, in response, arctic ground squirrels have delayed when they up-regulate heat production during
torpor to prevent freezing. Further, the termination of hibernation in spring has advanced 4 days
per decade in females but not males. Continued warming and phenological shifts will alter hibernation
energetics, change the seasonal availability of this important prey species, and potentially disrupt
intraspecific interactions.
C limate change is particularly rapid in the
Arctic (1), where systematic warming is
reducing sea ice extent, altering hydro-
logical cycles, thawing permafrost, increas-
ing shrubs, and changing the timing of
key seasonal events (phenological shifts) (2).
Despite the rapid pace of climate change in the
Arctic, it is a relatively data-poor region (3),
and few long-term records combining physical
records of climate change and physiological
responses of organisms exist [but see (4, 5)].
Further, although changes in the spring and
summer have received considerable attention,
recent work has called for more research into
the consequences of warmer and wetter win-
ters (6). Winter conditions shape life histories,
because many animal species have evolved strat-
egies such as seasonal migration or dormancy
to cope with prolonged periods of low food
availability (7). In resident species that hiber-
nate, climate change could lead to changes
in energy expenditure and overwinter sur-
vival. Energy requirements increase markedly
when hibernacula temperatures drop below
an animal’s thermal set point [near freezing
for ground squirrels (8)], because animals
must produce heat to prevent tissue damage
and death (9). Winter temperatures may also
contribute to the regulation of spring life his-
tory events (10, 11), and phenological shifts
can have important ecological repercussions
if they result in mismatches such that histor-
ically synchronous interactions within or among
species are no longer temporally aligned (12, 13).
1Institute of Arctic Biology, University of Alaska Fairbanks,
Fairbanks, AK 99775, USA. 2Rocky Mountain Research
Station, United States Forest Service, Missoula, MT 59801,
USA. 3Department of Biology and Wildlife, University of
Alaska Fairbanks, Fairbanks, AK 99775, USA. 4Department of
Biological Sciences, Northern Arizona University, Flagstaff,
AZ 86011, USA. 5Department of Biology, Colorado State
University, Fort Collins, CO 80523, USA.
*Corresponding author. Email: cory.williams@colostate.edu (C.T.W.);
helen.chmura@usda.gov (H.E.C.)
As part of a 25-year field study of arctic ground
squirrels (Urocitellus parryii) in the Alaskan
Arctic, we evaluated the impacts of climate
change on this high-latitude mammalian hi-
bernator, focusing on changes in hibernation
physiology and emergence phenology. Unlike
hibernators in most temperate or montane re-
gions, which sequester themselves in hibernacula
that remain above freezing, arctic ground squir-
rels overwintering in frozen soils must defend
themselves against large thermal gradients (or
differences between ambient and body tem-
peratures) while torpid using nonshivering
thermogenesis (thermogenic torpor) (9, 14)
(Fig. 1). We demonstrate that significant warm-
ing in ambient air and soil (hibernacula) tem-
peratures is altering hibernation phenology
and the duration of thermogenic torpor in
this arctic species.
Fig. 1. Seasonal changes
in arctic ground squirrel
body temperature and soil
temperature of the hiber-
naculum. Abdominal body
temperature of a hibernating
arctic ground squirrel (blue
line) and temperature of the
surrounding hibernaculum
(soil temperature at 1-m
depth adjacent to the burrow
entrance, dashed brown line)
from a site near Toolik Field
Station. Squirrels expend
energy to maintain their body
temperature above that of the
hibernaculum (“thermogenic
torpor”) such that their brain
temperatures never drop
below 0°C (9).
Chmura et al., Science 380, 846–849 (2023)
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Fig. 2. Long-term changes in temperature and hibernation physiology. Over the past 25 years at Toolik
Field Station in the Alaskan Arctic, mean annual air temperatures increased (A), soil freeze date occurred
later (sampling at 1-m depth, adjacent to hibernacula) (B), and minimum overwinter soil temperatures
increased (C). Concurrently, the onset of thermogenic torpor occurred later in the fall [(D); shown for females
only]. Although the date at which female ground squirrels initiated hibernation in the fall did not change
over time (E), the date that they ended hibernation in the spring became earlier (F). Lines represent mean
results of linear mixed effects models, and shaded regions represent 95% confidence intervals of the
mean. Points represent raw data, and colors represent study sites (Atigun or Toolik). For all animal data, data
points are plotted against the year in which an individual initiated hibernation.
(n = 262, b = –0.36, 95% credible interval, –0.57
to –0.15). In combination, this resulted in an
~10-day reduction in the annual duration that
soil was frozen at 1-m depth over the study
period.
In arctic ground squirrels, the date on which
core body temperatures first decreased below
0°C each hibernation season, i.e., the date when
squirrels first became thermogenic during
torpor (9), was delayed by ~15 days per decade
over the 25-year course of our study (n = 256,
b = 1.484, t = 4.800, df = 91, P < 0.001; Fig. 2D),
with no difference seen between sexes (b =
3.039, t = 1.041, df = 161, P = 0.299). However,
other phenological events did not show the
same pattern. Neither adult males (n = 122, b =
–0.354, t = –1.454, df = 32, P = 0.156) nor adult
females (n = 182, b = –0.163, t = –0.819, df = 71,
P = 0.416; Fig. 2E) changed the date at which
hibernation began in fall. Adult females, how-
ever, ended hibernation earlier in spring (n = 166,
b = –0.389, t = –3.592, df = 60, P < 0.001; Fig. 2F)
at a rate of ~4 days/decade. As females ended
hibernation earlier over the 25-year period, ani-
mal mass measured during the first 2 weeks
after emergence increased (n = 91, b = 3.472,
95% credible interval 0.196 to 6.781; see the sup-
plementary materials and fig. S3). Males did
not shift spring phenology (n = 120, b = –0.192,
t = –1.103, df = 30, P = 0.279). No directional
changes were observed in parturition timing
(n = 91, b = –0.003, t = –1.343, df = 28, P = 0.190).
Discussion
Winter plays a fundamental role in determin-
ing species’ range limits and local popula-
tion dynamics (6, 16). We show that warming
in the AlaskanArctic has altered seasonal freeze-
thaw dynamics of the soil active layer and
thus the thermoregulatory patterns of arctic
ground squirrels during hibernation. Delayed
freeze of the soil active layer near hibernacula
is delaying the onset of thermogenic torpor
and presumably reducing energy expenditure
and overwinter weight loss. Further, we found
sex differences in phenological responses to
climate change, with females advancing their
spring active season by 10 days over 25 years
and males showing no change.
Warmer winter conditions and the short-
ening of the hibernation season in females
have the potential to affect the survival prob-
ability of free-living arctic ground squirrels.
There are several general mechanisms through
which this could occur, including changes in
energetics and predation exposure. First, de-
laying thermogenic torpor will decrease the
total amount of time that arctic ground squir-
rels spend defending body temperature dur-
ing hibernation, which will reduce overwinter
energy expenditures (9, 17) and increase spring
mass in females, as we have demonstrated in
this study. Additionally, changes in winter tem-
peratures will alter the energetic costs of torpor
bouts and episodic interbout arousals (8) that
characterize hibernation in small mammals.
Arctic ground squirrels spend most of the
hibernation season generating heat to avoid
freezing, unlike most hibernators in more mod-
erate climates, which can safely thermoconform
because the surrounding soil temperatures
remain above freezing during torpor (18). Re-
duced intensity and/or duration of thermo-
genesis caused by warmer conditions would
Chmura et al., Science 380, 846–849 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
allow arctic ground squirrels to conserve en-
ergy and potentially increase winter survival,
particularly among vulnerable, energy-limited
age classes such as juveniles (19, 20). Alter-
natively, warmer conditions associated with
climate change could shorten the hibernation
season and increase the number of days that
arctic ground squirrels are active above ground,
increasing mortality rates because of increased
exposure to predators (21). Thus, the conse-
quences of climate change for hibernators
will likely be heterogeneous (22). Although
our study focused on a system in which warmer
air temperatures lead to warmer hibernacula
temperatures and likely reduced energy expen-
diture, in other systems, climate change may
reduce snow depth, which can decrease burrow
temperatures and decrease energetic savings
through hibernation (20).
We found sex differences in phenological
flexibility, with female arctic ground squirrels,
but not males, terminating hibernation earlier.
Other studies suggest that female ground
squirrels are less sensitive to the direct effects
of temperature (23, 24) and instead are respon-
sive to temperature-driven changes in spring
snow cover conditions (25). Thus, female flex-
ibility appears to allow them to match ener-
getic demands with the environment, and we
expect that earlier snowmelt will also corre-
spond with earlier vegetation green-up (26).
As winters continue to warm, sex differences
in phenological shifts may lead to disrupted
intersexual interactions. For example, dur-
ing one extremely warm spring in eastern
Canada, female Richardson’s ground squir-
rels (Urocitellus richardsonii) became sexually
receptive before most males were physiologi-
cally prepared to mate, resulting in a pheno-
logical mismatch between the sexes (27). In
the short term, mismatches such as these could
affect population reproductive rates, and over
longer time scales, continued warming in the
Arctic may be a strong selective force resulting
in evolutionary changes in male phenology.
The consequences of climate change may
be direct, such as the changes in hibernation
physiology and phenology that we report here,
as well as indirect. If the population size and
temporal availability of arctic ground squirrels
above ground are altered by climate change,
then this could have cascading indirect effects
on diverse tundra predators. Understanding the
impact of climate change on species such as the
arctic ground squirrel will aid assessments of
how arctic food webs will function in a rapidly
warming world, and research linking physiol-
ogy and phenology to demographic responses
is an important component of understanding
community responses to climate change.
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AC KNOWLED GME NTS
We thank J. T. Moore, F. Kohl, M. Richter, and many additional
students and technicians who worked countless hours in the field
to support this work. We are also grateful for 30 years of
outstanding support from staff and facilities at the Toolik Field
Station, which made this research possible. Funding: This work
was supported by the National Science Foundation (grant
IOS-1558056 to C.T.W. and C.L.B.); the National Science
Foundation (grant IOS-1558160 to B.M.B.); a University of Alaska
Centennial Postdoctoral Fellowship (H.E.C.); the National Institute of
General Medical Sciences of the National Institutes of Health
[Institutional Development Award (IDeA) grant P20GM103395 to
B.M.B. and C.D.]; and a University of Alaska Fairbanks URSA
undergraduate research award (G.B.). Author contributions:
Conceptualization: H.E.C., C.T.W.; Data curation: H.E.C., C.D., G.B.;
Formal analysis: H.E.C., C.D., G.B.; Funding acquisition: B.M.B.,
C.L.B., C.T.W.; Investigation: H.E.C., C.D., G.B., C.L.B., C.T.W.;
Methodology: H.E.C., B.M.B., C.L.B., C.T.W.; Project administration:
C.T.W.; Resources: B.M.B., C.L.B., C.T.W.; Supervision: C.T.W.;
Visualization: H.E.C.; Writing – original draft: H.E.C., C.T.W.; Writing –
review and editing: H.E.C., B.M.B., C.L.B., C.T.W. Competing
interests: The authors declare no competing interests. Data and
materials availability: The datasets and code generated during
the study are available in the Dryad repository (28). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement
of Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf5341
Materials and Methods
Supplementary Text
Figs. S1 to S3
Table S1
References (29–39)
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
Submitted 31 October 2022; accepted 25 April 2023
10.1126/science.adf5341
Chmura et al., Science 380, 846–849 (2023)
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RES EARCH
POPULATION DYNAMICS
Boom-bust cycles in gray whales associated with
dynamic and changing Arctic conditions
Joshua D. Stewart1*, Trevor W. Joyce2,3, John W. Durban3,4, John Calambokidis5, Deborah Fauquier6,
Holly Fearnbach4, Jacqueline M. Grebmeier7, Morgan Lynn3, Manfredi Manizza8, Wayne L. Perryman3,
M. Tim Tinker9,10, David W. Weller3
Climate change is affecting a wide range of global systems, with polar ecosystems experiencing the
most rapid change. Although climate impacts affect lower-trophic-level and short-lived species most
directly, it is less clear how long-lived and mobile species will respond to rapid polar warming because
they may have the short-term ability to accommodate ecological disruptions while adapting to new
conditions. We found that the population dynamics of an iconic and highly mobile polar-associated species
are tightly coupled to Arctic prey availability and access to feeding areas. When low prey biomass
coincided with high ice cover, gray whales experienced major mortality events, each reducing the
population by 15 to 25%. This suggests that even mobile, long-lived species are sensitive to dynamic and
changing conditions as the Arctic warms.
T he Bering and Chukchi seas in the Pacific
Arctic are extremely productive shallow
basins (1–3) that support seasonal for-
aging opportunities for a wide variety of
migratory and Arctic-associated taxa (4).
The Pacific Arctic food web is characterized
by ice-associated algal growth during spring
and early summer, which is transported to the
benthos through decay and sinking of particu-
late organic carbon (3). This tight pelagic-
benthic coupling historically resulted in some
of the most productive nearshore benthic sys-
tems in the world (3), attracting migrants from
throughout the Pacific and supporting large
populations of marine species (4, 5).
As the Arctic has rapidly warmed, sea ice
retreat has occurred progressively earlier in the
spring, and the Bering and Chukchi seas have
remained ice free for longer in the autumn (6).
This has resulted in increased water-column
productivity (7, 8) but has reduced the amount
of particulate organic carbon that reaches the
sea floor through pelagic-benthic coupling that
is dependent on sinking ice-associated algae
(5). In addition, decreased sea ice cover allows
stronger current-driven flow over the shallow
basins of the Pacific Arctic, reducing the quan-
tity of finer-sediment grain size within the
1Ocean Ecology Lab, Marine Mammal Institute, Department
of Fisheries, Wildlife and Conservation Sciences, Oregon
State University, Newport, OR, USA. 2Ocean Associates,
Arlington, VA, USA. 3Marine Mammal and Turtle Division,
National Oceanic and Atmospheric Administration (NOAA)
Southwest Fisheries Science Center, La Jolla, CA, USA.
4Sealife Response, Rehabilitation and Research (SR3), Des
Moines, WA, USA. 5Cascadia Research Collective, Olympia, WA,
USA. 6Office of Protected Resources, National Marine Fisheries
Service, Silver Spring, MD, USA. 7Chesapeake Biological
Laboratory, University of Maryland Center for Environmental
Science, Solomons, MD, USA. 8Geosciences Research Division,
Scripps Institution of Oceanography, University of California
San Diego, La Jolla, CA, USA. 9Nhydra Consulting, Halifax, NS,
Canada. 10Ecology and Evolutionary Biology, University of
California, Santa Cruz, Santa Cruz, CA, USA.
*Corresponding author. Email: joshua.stewart@oregonstate.edu
benthos that support habitat for tube-building
amphipods, which have some of the highest
lipid content of benthic crustaceans (9, 10).
Collectively, these impacts have driven changes
to the structure of Arctic benthic communities,
which may translate into impacts on higher-
trophic-level species that migrate seasonally to
access these foraging hotspots (5, 9, 10).
Eastern North Pacific gray whales (Eschrichtius
robustus) undertake one of the longest mam-
malian migrations between wintering areas in
Baja California, Mexico, and summer feeding
areas in the Bering and Chukchi seas to take
advantage of these highly concentrated ben-
thic prey resources (11). Gray whales have spe-
cialized baleen plates adapted to suction feeding
in soft sediments and are the only baleen
whale to feed primarily on benthic prey (11). Al-
though they are capable of feeding on pelagic
zooplankton, the diet of gray whales feeding in
the Arctic is dominated by benthic crustaceans—
in particular, ampeliscid amphipods—that are
found in abundance in shallow Arctic basins (12).
Estimates of pre-whaling population sizes
range from 15,000 to 30,000 individuals for
the eastern North Pacific gray whale popula-
tion, based on population models fitted to esti-
mates from abundance surveys combined with
commercial and aboriginal harvest data (13).
Genetic estimates of prehistoric abundance
are much higher, ranging from ~75,000 to
120,000 individuals (14), although this likely
included the now endangered western North
Pacific population and may reflect a larger
carrying capacity supported by increased ben-
thic habitat availability during the Last Glacial
Minimum (15). Commercial whaling in the
lagoons of Baja California and throughout
the North Pacific depleted the eastern North
Pacific gray whale population to fewer than
5000 individuals by the early 1900s (13). A
rapid and sustained post-whaling increase in
abundance led to the delisting of the popula-
tion from the Endangered Species Act in 1994
and is widely viewed as an iconic example of
successful conservation and species recovery (16).
The status and stability of eastern North
Pacific gray whales has come into question
as the population experienced two major docu-
mented mortality events in 1999–2000 and
2019–2022 (17, 18). In response to the first
mortality event in 1999, there was speculation
that the population may have reached its
carrying capacity and was suffering from
density-dependent effects on survival (19). In
light of fluctuations in reproductive output and
a second major mortality event two decades
later, many studies have proposed that variable
and changing Arctic conditions may be drivers
of eastern North Pacific gray whale population
dynamics (12, 20–22).
Arctic sea ice extent has been proposed as a
contributor to gray whale vital rates—especially
reproduction—by physically restricting access
to summer feeding areas (20, 22, 23). However,
in recent years previously identified relation-
ships between gray whale reproduction and
Arctic sea ice extent have begun to decouple
(22, 23), and variability in sea ice has been
insufficient to explain mortality rates (20).
Eastern North Pacific gray whales have the
most complete long-term abundance and demo-
graphic data available for any large whale
species, and we leveraged these extensive data-
sets to examine environmental drivers of pop-
ulation dynamics not possible in other species.
We combined time series of gray whale abun-
dance, reproduction, nutritive condition, and
strandings spanning more than half a century
into a population dynamics model to esti-
mate annual carrying capacity for the pop-
ulation. We show that this annual carrying
capacity is well explained by ice-mediated
access to the population’s primary foraging
grounds in the Arctic and biomass of benthic
crustaceans. The observed boom-bust cycles in
gray whale abundance and vital rates suggest
that as large whales recover from post-whaling
depletion, their populations may become in-
creasingly governed by environmental con-
straints and climate variability.
Results and discussion
We combined 31 estimates of eastern North
Pacific gray whale abundance over 54 years
(1968 to 2022) (24), 30 estimates of calf pro-
duction over 42 years (1980 to 2022) (22, 25),
1391 records of stranded gray whales on the
United States coastline over 48 years (1974 to
2022), and 1334 body condition measure-
ments over 32 years (1987 to 2019) (26) into an
integrated population dynamics model that
estimates annual abundance, birth rates, and
mortality rates. The model uses evidence of
human interactions in stranded gray whales
to estimate proportional hazards of anthropo-
genic and natural contributions to mortality.
Stewart et al., Science 382, 207–211 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Population dynamics of
eastern North Pacific gray
whales. (A) Gray whales have
experienced major fluctuations in
abundance after an initial post-
whaling recovery, including three
major declines beginning in 1987,
1999, and 2019. (B to E) These
declines and subsequent recoveries
in the 1990s and 2000s were
associated with synchronous
changes in (B) births and
(C) mortality, as well as changes
in nutritive condition in
(D) southbound and (E) northbound
migrating whales. Black points in
(A) and (B) indicate the median
estimated abundance and calf pro-
duction from visual surveys, with
standard errors of model estimates
(vertical bars). Black points in (D)
and (E) indicate the mean values
of body condition measurements
from each survey year and the
standard deviation of observations
(vertical bars). In (A) to (E), the
black lines indicate the median of
the posterior distribution of model-
estimated values, and the shaded
regions indicate the 95% posterior
credible intervals.
In addition, the model estimates both the long-
term carrying capacity (K), as well as an annually
varying carrying capacity (Kt) that reflects
year-to-year variation in the strength of negative
density dependence as determined by environ-
mental covariates and stochastic effects. We
considered three Arctic time series as candi-
date covariates for annual gray whale carrying
capacity: (i) access to feeding grounds, defined
as the number of days with <50% sea ice cover
on the historic gray whale foraging grounds
in the Chirikov basin and southern Chukchi
Sea (1979 to 2021) (23, 27); (ii) benthic infaunal
crustacean biomass, averaged over the same
foraging hotspots as sea ice access (1971 to
2019) (28); and (iii) zooplankton density es-
timated by using a global ocean ecosystem
model that includes the entire Arctic Ocean
ecosystem, averaged over gray whale foraging
hotspots (1992 to 2020) (29). The data and
population model are described in detail in the
Data sources and Integrated population model
sections of the supplementary materials.
The eastern North Pacific gray whale pop-
ulation has experienced three major mortality
events, each resulting in reductions of 15 to
25% of total abundance within the half-century
of nearly continuous monitoring, representing
extraordinarily high periodic mortality rates for
a long-lived vertebrate (Fig. 1). These mortality
events were associated with peaks in reported
strandings during the 1999–2000 and 2019–2022
periods. The 1987–1989 abundance decline is
the largest in magnitude but was not asso-
ciated with an increase in strandings, likely
because reporting structures and survey effort
to detect strandings were expanded and im-
proved substantially beginning in 1990. How-
ever, this major impact to the population is also
reflected in the poorest recorded body condi-
tion of the survey history in 1988, falling rapidly
from very good condition in 1987 (Fig. 1D). The
population dynamics model estimated low an-
nual carrying capacities (Kt) of approximately
10,000 individuals during each of these die-
offs (Fig. 2A), indicating that Arctic foraging
grounds periodically experience major disrup-
tions, limiting the number of whales that
they can support. These fluctuations in annual
carrying capacity were represented in mortality
rates, body condition, and most strongly in
birth rates, which had the greatest propor-
tional change with varying carrying capacity
(fig. S5). On the basis of anthropogenic injury
rates in stranded whales, model-estimated an-
thropogenic mortality rates remained low and
stable, whereas natural mortality rates varied
substantially and peaked during major die-
offs, suggesting direct human impacts such
as vessel strikes and entanglements in fishing
gear are not the primary drivers of mortality in
this population.
The maximum birth rate estimated by the
model was 0.111 (95% credible intervals 0.108
to 0.114). The realized annual birth rate ranged
from a low of 0.0046 in 1998 (0.0024 to
0.0076) to a high of 0.085 in 1975 (0.062 to
0.102). Within the span of calf production ob-
servations (1994–2022), the minimum birth
rate was 0.007 in 2000 (0.004 to 0.01), and the
maximum was 0.082 in 2004 (0.069 to 0.09).
The minimum estimated mortality rate was
0.011 (0.009 to 0.014). The realized annual
mortality rate ranged from a low of 0.019 in
1975 (0.014 to 0.027) to a high of 0.13 in 1988
(0.099 to 0.162). During the three major mortal-
ity events, median estimated mortality rates
were 0.13 and 0.079 (in 1988 and 1989); 0.065
and 0.099 (in 1999 and 2000); and 0.092, 0.089,
0.061, and 0.067 (from 2019 to 2022).
Model-estimated mean body condition was
lowest in 1988 [median 0.162, 95% confidence
interval (CI) 0.158 to 0.166], 2000 (0.165, 0.163
to 0.168), and 2020 (0.167, 0.163 to 0.170). The
highest estimated body condition was in 1975
(0.184, 0.181 to 0.187), although there were no
photogrammetric measurements before 1987.
The 3 years with highest estimated body con-
dition and corresponding condition measure-
ments were 2013 (0.181, 0.180 to 0.183), 2012
(0.181, 0.179 to 0.183), and 1997 (0.181, 0.179
to 0.182). The estimated northbound body
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Drivers of eastern
North Pacific gray whale
carrying capacity. (A) Esti-
mated annual carrying
capacity (Kt) from the
population dynamics model,
with reference lines at
25,000 (dashed line) and
10,000 (dotted line).
(B) Estimated ice access
anomaly, which is the
Z-scored number of days
with 50% or lower ice cover
on gray whale feeding
grounds. (C) Estimated
crustacean biomass anom-
aly, which is the Z-scored
mean grams of carbon of
benthic crustaceans on key
gray whale feeding grounds.
(D) Decline in benthic crus-
tacean per capita biomass
from 1970 to 2019, showing
the relationship each
sampling year between ben-
thic crustacean abundance
and biomass in grams of
carbon (gC). In (A) to (C),
the black lines indicate the
median of the posterior
distribution of estimates,
and the shaded regions indicate the 95% posterior credible intervals.
condition scaling factor was 0.922 (0.913 to
0.930), indicating an ~8% decline in body con-
dition between southbound and northbound
measurements.
The estimated long-term average K was
22,062 (18,967 to 24,725). This long-term average
is lower than the median of annual Kt values
(24,500, 95% CI 21,771 to 27,797), which is to be
expected given that it is the arithmetic mean
outcome of a stochastic process and thus re-
flects the effects of environmental variability
on expected abundance (30).
We found a significant positive relationship
between benthic crustacean biomass and carry-
ing capacity (99.9% probability slope > 0), no
relationship with zooplankton density (39.2% > 0),
and a high probability of a positive relation-
ship with sea ice access (93.5% > 0). With the
zooplankton density covariate eliminated from
the model, both crustacean biomass (100% > 0)
and sea ice access (96.2% > 0) had significant
positive relationships with carrying capacity.
This suggests that the ability of the eastern
North Pacific gray whale population to physi-
cally access key feeding areas, in combination
with in situ prey availability, explains fluctua-
tions in body condition, reproduction, and
mortality. The three major mortality events
occurred during periods of simultaneous low
crustacean biomass and restricted access to
feeding areas (Fig. 2). In 2010, a rapid decrease
in crustacean biomass but a period of average
ice access led to a depression in birth rates and
a modest decrease in abundance but not a
major mortality event. The onset of the 2019
mortality event appears to have been driven
initially by low crustacean biomass and exacer-
bated by a steep reduction in access to feeding
areas over the following 2 years.
The decision to model gray whale popula-
tion dynamics by applying annual covariate
effects to carrying capacity (K), rather than
the population’s intrinsic growth rate (r), is
uncommon. Although in theory either model
formulation could be used to explain fluctua-
tions in abundance and vital rates, we believe
that applying covariate effects to carrying ca-
pacity better reflects biological reality. The
Bering and Chukchi seas are the primary feed-
ing area for virtually all eastern North Pacific
gray whales, suggesting that the quality and
quantity of prey in these areas will have a
greater impact on vital rates when there is high
intraspecific competition at higher levels of
gray whale abundance. This is supported empiri-
cally by our estimates of population growth rate
relative to abundance. Mean population growth
rates were significantly higher at low than at
high abundance levels, and major busts (annual
declines of >9 to 10%) only occurred when the
gray whale population was at high abundance
(fig. S9), which supports the existence of density-
dependent controls on vital rates. By applying
covariate effects to carrying capacity, we simul-
taneously account for environmental conditions
and the effects of negative density depen-
dence (31). In addition, this avoids a scenario in
which, in a model that applies covariate effects
to r instead of K, the population exceeds a sta-
tionary carrying capacity but continues to grow
because of positive covariate effects on growth
rate. Instead, our estimated annual carrying
capacity (Kt) captures short-term fluctuations
in the strength of density dependence and can
be interpreted as an abstract parameter corres-
ponding to the expected equilibrium abundance
if environmental conditions remained fixed at
the values recorded during that year (32).
Over the past 50 years, the per capita bio-
mass of benthic infaunal crustaceans has de-
clined precipitously (Fig. 2D and fig. S3), and
the three major gray whale mortality events
coincided with periods of low per capita bio-
mass, which translated into low total crusta-
cean biomass. This decline in per capita biomass
is most likely associated with species distri-
bution shifts of benthic amphipods and other
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RES EARCH | R E S E A R C H A R T I C L E
crustaceans. As ice cover decreases in response
to rapid Arctic warming, current speed in the
Chirikov basin has increased, leading to larger
sediment grain size and reduced particulate
organic carbon reaching the seafloor (5). These
conditions favor smaller amphipods with lower
lipid content over the lipid-rich, tube-building
ampeliscid amphipods that historically domi-
nated the shallow basins of the Bering and
Chukchi seas (10). This regime shift has likely
contributed to declining per capita biomass of
gray whale prey, which despite steady or in-
creasing prey abundance has resulted in lower
overall available biomass (fig. S3).
The combined effect of sea ice cover and
benthic productivity on gray whale population
dynamics has driven major boom-bust cycles,
including two modern booms in abundance
that may have exceeded preexploitation levels
(13). High benthic biomass and prey quality in
the late 1970s and early 1980s supported al-
most 25,000 gray whales, contributing to their
delisting from the US Endangered Species Act.
More recently, rapid Arctic warming in re-
sponse to climate change increased access to
feeding areas (Fig. 2B), supporting a sustained
increase in gray whale abundance over the
past decade (Fig. 1A). Although recent Arctic
warming may have provided sufficient benefit
to the population to counteract decreasing
benthic biomass over the short term, the
outlook for benthic prey quality is not favorable.
Rising water column and bottom water tem-
peratures and projected decoupling of pelagic
and benthic productivity caused by retreating
sea ice will likely lead to continued declines in
Arctic benthic crustacean biomass (5). Access
to feeding areas reached a peak of 266 days
in 2019, which is presumably approaching a
point of diminishing returns given that the spe-
cies migrates to Mexico each winter. Poleward
shifts in gray whale feeding locations have
already been documented, which likely reflect
the declining quality and shifting distribution
of their preferred prey (12). Future declines in
benthic biomass will likely drive decreases
in gray whale carrying capacity that cannot be
offset by continued increases in ice access.
Reports of gray whales shifting their Arctic
feeding distribution and targeting pelagic prey
(12) suggest that they may have the ability to
compensate for these changing conditions to
some extent, but our results suggest that any
ongoing behavioral adaptations have thus far
been insufficient to prevent major mortality
events.
Eastern North Pacific gray whales are the
most closely monitored large whale species, with
records of abundance, reproduction, mortality,
and condition spanning more than half a cen-
tury. The abundance of most large whale species
remains far below pre-whaling levels (33, 34),
which limits our understanding of the dyna-
mics and behavior of whale populations as
they approach carrying capacity and become
increasingly governed by density-dependent
processes. By contrast, gray whales have re-
covered rapidly from post-whaling lows to num-
bers that may approach or exceed pre-whaling
levels and have low rates of direct human
mortality, providing a rare window into the
possible natural fluctuations of large whale
populations. The periodic mortality events and
major population swings that we report are
surprising for a long-lived vertebrate that must
by definition have high average survival rates
to facilitate longevity. However, whales achieve
their immense body sizes by feeding on large
quantities of low-trophic-level prey (35), which
may make them sensitive to oceanographic
and environmental fluctuations. The feeding-
fasting cycles associated with migratory baleen
whales may also increase their susceptibility
to environmental perturbations. Gray whales
migrate more than 15,000 km each year and
rely on a 4- to 5-month feeding season to sup-
port a majority of their energetic requirements
for the year. This strategy may place them at a
physiological threshold at which disruptions
to their food supply translate into major im-
pacts to vital rates—a pattern that may be
widespread across migratory whales and may
become more pronounced as species and pop-
ulations recover to their pre-whaling abun-
dances. Climate-driven ocean warming is
expected to have profound impacts on ocean
circulation, upwelling strength, and primary
production (36, 37), which may in turn have
major implications for large whale population
dynamics and viability through predator-prey
interactions (34).
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AC KNOWLED GME NTS
We thank past and present members of the Working Group
for Marine Mammal Unusual Mortality Events; the Gray Whale
Unusual Mortality Event Investigative Teams; as well as the
US, Canadian, and Mexico marine mammal stranding network
responders. We thank the NOAA Office of Marine and Aviation
Operations and D. LeRoi for their support of drone flights to
measure whale body condition. We thank J. Baker for feedback
on analyses and interpretation. The scientific results and
conclusions and any views or opinions expressed herein are
those of the authors and do not necessarily reflect the views or
policies of the US government, its agencies, or any of the
included organizations. Funding: J.D.S. was supported by a
National Academies NRC Research Associateship and the
Oregon State University Marine Mammal Institute Research
Endowment. Abundance, calf production, and aerial
photogrammetry surveys were supported by NOAA, US
Department of Commerce. Drone photogrammetry surveys at
Piedras Blancas, California, from 2015 to 2019 were supported
by SeaLife Response, Rehabilitation, and Research (SR3)
and NOAA, with facility and property use provided by the Bureau
of Land Management, US Department of the Interior. J.M.G.
was supported for benthic time series sampling for crustaceans
and associated fauna through multiple awards, most recently
the US National Science Foundation Office of Polar Programs
Stewart et al., Science 382, 207–211 (2023)
13 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
(OPP 1917469) and the National Oceanic and Atmospheric
Administration Arctic Research Program (CINAR 25984.02).
Author contributions: Conceptualization: J.D.S. and J.W.D.
Funding acquisition: W.L.P., J.W.D., D.W.W., and H.F.
Investigation: All authors. Methodology: J.D.S., J.W.D., W.L.P.,
D.W.W., and M.T.T.; Data curation: T.W.J., J.W.D., J.C., D.F.,
H.F., J.M.G., M.L., M.M., W.L.P., and D.W.W. Formal analysis:
J.D.S. and M.T.T. Visualization: J.D.S. Writing – original draft:
J.D.S. Writing – review and editing: All authors. Competing
interests: The authors declare no competing interests. Data
and materials availability: All data and code required to
reproduce the analyses presented in the main text and online
supplementary materials are available online through Zenodo
(38). License information: Copyright © 2023 the authors,
some rights reserved; exclusive licensee American Association
for the Advancement of Science. No claim to original US
government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi1847
Materials and Methods
Figs. S1 to S9
References (39–55)
MDAR Reproducibility Checklist
Submitted 8 April 2023; accepted 16 August 2023
10.1126/science.adi1847
Stewart et al., Science 382, 207–211 (2023)
13 October 2023
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10.1126_science.ade3332
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RES EARCH
R E S E A R C H A R T I C L E
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RESPIRATORY COMPLEXES
Structural basis of mammalian respiratory complex I
inhibition by medicinal biguanides
Hannah R. Bridges1*, James N. Blaza1,2, Zhan Yin1, Injae Chung1, Michael N. Pollak3, Judy Hirst1*
The molecular mode of action of biguanides, including the drug metformin, which is widely used in
the treatment of diabetes, is incompletely characterized. Here, we define the inhibitory drug-target
interaction(s) of a model biguanide with mammalian respiratory complex I by combining cryo–electron
microscopy and enzyme kinetics. We interpret these data to explain the selectivity of biguanide binding to
different enzyme states. The primary inhibitory site is in an amphipathic region of the quinone-binding
channel, and an additional binding site is in a pocket on the intermembrane-space side of the enzyme. An
independent local chaotropic interaction, not previously described for any drug, displaces a portion
of a key helix in the membrane domain. Our data provide a structural basis for biguanide action and
enable the rational design of medicinal biguanides.
T he biguanide metformin is central to the
treatment of millions of patients with
type 2 diabetes worldwide (1) and has
been studied intensely in recent years for
treatment of other conditions, including
ischemia-reperfusion injury (2, 3), fibrosis (4),
viral infections (5), and cancer (6). Optimiza-
tion of biguanides for distinctive indications
has been hindered by incomplete understanding
of their molecular pharmacology, and although
preclinical evidence for the antineoplastic action
of metformin was sufficient to justify dozens
of clinical trials (7), the results have been dis-
appointing (8, 9). Biguanides have been reported
to target many cellular proteins, including
mitochondrial glycerophosphate dehydrogenase
(mGPD) (10), presenilin enhancer 2 (11), F1FO
adenosine 5′-triphosphate (ATP) synthase (12),
cytochrome c oxidase (13), and the chloride
intracellular channel 1 (14). Several studies have
described biguanide inhibition of mitochon-
drial respiratory complex I (proton-translocating
NADH:ubiquinone oxidoreductase, where NADH
is the reduced form of NAD+) (12, 15–18), sup-
porting a mode of biguanide action in which
decreased production of ATP from oxidative
phosphorylation triggers the activation of
adenosine 5′-monophosphate kinase and inhi-
bition of adenylate cyclase, leading to bene-
ficial downstream effects on gluconeogenic
enzymes (in diabetes) and mTOR (in cancer
and antiviral treatments) (1, 6, 18, 19).
Complex I is a 1-MDa multiprotein assembly
that is central to mitochondrial and cellular
1MRC Mitochondrial Biology Unit, University of Cambridge,
The Keith Peters Building, Cambridge Biomedical Campus,
Cambridge CB2 0XY, UK. 2Structural Biology Laboratory and
York Biomedical Research Institute, Department of Chemistry,
The University of York, York YO10 5DD, UK. 3Lady Davis
Institute of the Jewish General Hospital and Department of
Oncology, McGill University, Montreal, QC H3T 1E2, Canada.
*Corresponding author. Email: hrb@mrc-mbu.cam.ac.uk (H.R.B.);
jh@mrc-mbu.cam.ac.uk (J.H.)
metabolism. It oxidizes the NADH produced
by oxidation of carbohydrates and lipids to
maintain the redox state of the mitochondrial
nicotinamide adenine dinucleotide (NAD+) pool,
reduces ubiquinone-10 to drive the respiratory
chain and oxygen consumption, and pumps
protons out of the mitochondrial matrix. This
proton pumping contributes to the proton-
motive force (PMF) that drives ATP synthesis
through oxidative phosphorylation (20). Cryo–
electron microscopy (cryo-EM) studies of com-
plex I have revolutionized our understanding
of its structure, mechanism, and regulation,
informing on redox catalysis in the hydro-
philic domain, proton translocation across
the membrane, and possible mechanisms of
coupling between ubiquinone-10 reduction and
proton translocation (21, 22). Furthermore,
cryo-EM has discriminated different resting
states of the enzyme (22–25) on the basis of
domain-level reorientations linked to altered
conformational states of the quinone-binding
channel (Q-channel): the “active” state with a
structurally ordered, turnover-ready Q-channel
and the pronounced “deactive” state with a
locally disordered Q-channel that requires
restructuring and reactivation for catalysis.
Biguanides bind with an unusual preference to
the deactive state of the enzyme (16), but their
binding site(s) and modes of interaction are
unknown: They are expected to bind in a site
downstream of the Fe-S clusters (12) but do not
inhibit in a simple competitive manner. Their
interaction site is expected to be amphipathic
on the basis of the biguanide positive charge
and strong correlations between inhibitory po-
tency, cytotoxicity, and hydrophobicity (12, 26).
We use cryo-EM to reveal the molecular in-
teractions of biguanides with mammalian res-
piratory complex I, defining how they inhibit
catalysis. We identify distinctive binding modes
and rationalize biguanide protein-state se-
lectivity to enable future implementation of
structure-based drug design in the develop-
ment of biguanide-based therapies for diverse
applications.
IM1761092 as a model biguanide for
structural studies
The antidiabetic biguanides metformin and
phenformin are relatively weak inhibitors of
complex I, with simple molecular shapes. We
sought to avoid technical risks in cryo-EM
(excessive adventitious binding and reduced
image contrast) from using these compounds
in high millimolar concentrations by identify-
ing a stronger-binding derivative, which would
also exhibit a more distinctive cryo-EM den-
sity. For structural investigation of the com-
plex I binding site(s) of biguanides, we therefore
assessed IM1761092 (hereafter IM1092) (27), a
more hydrophobic (logP 2.37) derivative of the
metformin-related antidiabetic biguanide phen-
formin (logP 0.34) that contains a 3-chloro-4-
iodo-phenyl ring (Fig. 1A and fig. S1). IM1092
inhibits cellular oxygen consumption (fig. S1D)
and exhibits a stronger inhibition of complex I
catalysis in bovine heart mitochondrial mem-
branes than phenformin and metformin [half-
maximal inhibitory concentration (IC50) in the
membrane is more than 10 and 2000 times lower,
respectively, depending on the conditions; Fig.
1, B and C]. Its behavior is thus consistent with
the reported correlation between biguanide
inhibitory potency (IC50) and hydrophobicity
(logP) (28).
Mammalian mitochondrial membranes “as-
prepared” contain a mixture of active and
deactive complex I. In the deactive state, an
important structural feature of the Q-channel,
the loop between TMH1 and -2 in subunit
ND3 (ND3 TMH1-2 loop) that carries Cys39 is
disordered (24, 25), but in the active state, it
is ordered and Cys39 is buried (23, 25, 29, 30).
The two states can be discriminated biochem-
ically by their sensitivity to N-ethyl maleimide
(NEM), which derivatizes ND3-Cys39 in the de-
active state, preventing catalysis, but leaves the
active state unaffected. We found biguanide
inhibition depends on the amount of the de-
active state present in membranes (Fig. 1B).
As-prepared membranes incubated with both
200 mM IM1092 (10 × IC50) and NEM at 4°C
exhibited essentially the same deactive con-
tent as biguanide-free controls (fig. S2A), in-
dicating that biguanides do not shift the
deactive:active population equilibrium in this
condition. Furthermore, biguanide inhibition
is stronger at higher pH (Fig. 1C). As biguanides
[pKa ~11 (where Ka is the acid dissociation
constant) (31)] remain singly protonated at all
pH levels tested, the pH dependence likely arises
from changes in the protein, such as in local
charges on residue side chains or phospholipid
headgroups, or conformational changes. Hav-
ing established that IM1092 inhibits cellular
Bridges et al., Science 379, 351–357 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
oxygen consumption and shares the same se-
lectivity for inhibiting catalysis by binding to
the deactive state of complex I that is observed
for antidiabetic biguanides, as well as the same
pH-dependent mode of action, we proceeded
with this tighter-binding synthetic biguanide
as a representative model compound for struc-
tural studies for the technical reasons outlined
previously.
To investigate the selectivity of biguanides
for different states, IM1092 was added to the
mixed population of states in the purified rest-
ing enzyme, without purposeful deactivation,
for cryo-EM. No substrates were added be-
cause inhibition is weaker when biguanides
are added during catalysis, rather than before
(12). IM1092 has an IC50 value of 86 mM for
catalysis of detergent-solubilized, purified bo-
vine complex I (fig. S2B), and cryo-EM grid
conditions with 350 mM IM1092 were chosen
to maximize binding within the limits of pH-
and biguanide-induced protein aggregation at
high concentrations (fig. S2). When purified
complex I (fig. S3) was incubated in the same
conditions as for cryo-EM grid preparation and
then diluted into inhibitor-free assay buffer, 98%
of the control catalytic rate was recovered (fig.
S2F), demonstrating full reversibility of inhi-
bition under this condition.
Overview of cryo-EM particle populations
A total of 17,203 micrographs collected from a
single cryo-EM grid yielded 598,287 good par-
ticles, which refined to an estimated global res-
olution of 2.1 Å (fig. S4), but with such a high
degree of heterogeneity that it was not possible
to model parts of the map. Subsequent global
classification yielded three major classes resem-
bling the active and deactive states mentioned
A
H2N
N
N
NH2 NH2
Metformin
H2N
N
H
N
NH2 NH2
Phenformin
H2N
N
H
N
NH2 NH2
IM1092
Metformin
99 mM
52 mM
33 mM
B
120
100
)
M
m
(
0
5
C
I
80
60
40
20
5
4
3
2
1
Phenformin
3.8 mM
539 µM
131 µM
I
Cl
0
0
50
100
Deactive content (%)
0
50
0
Deactive content (%)
100
C
)
M
m
(
0
5
C
I
300
250
200
150
100
50
0
Metformin
M
m
8
3
M
m
8
7
1
M
m
1
2
1
M
m
5
1
M
m
8
M
m
9
6
7
8
pH
9
9D 9D(i)
6
5
4
3
2
1
0
Phenformin
M
m
3
.
5
M
m
4
.
1
M
µ
0
3
4
M
µ
1
9
1
M
µ
3
4
M
µ
0
5
6
7
8
9
9D 9D(i)
Hp
)
M
µ
(
0
5
C
I
50
40
30
20
10
0
M
µ
3
4
M
µ
7
2
M
µ
4
M
µ
1
2
M
n
6
4
8
M
n
6
1
8
6
7
8
Hp
9
9D 9D(i)
50
40
30
20
10
)
M
µ
(
0
5
C
I
IM1092
32 µM
20 µM
4 µM
0
0
50
100
Deactive content (%)
IM1092
Fig. 1. Characterization of biguanide effects on
catalysis and regions of structural interest.
(A) Chemical structures of metformin, phenformin,
and IM1092 in monoprotonated form. (B) Correlation
between membrane deactive complex I content
and IC50 for metformin (gray), phenformin (teal), and
IM1092 (orchid). Error bars represent SEM for
deactive content and 95% confidence intervals for
IC50. Data are fit to an exponential regression for
visualization. (C) Effect of pH on IC50 in bovine
heart membranes for metformin (gray), phenformin
(teal), and IM1092 (orchid). 9D, pH 9 deactivated
membranes; 9D(i), pH 9 deactivated membranes
measured in the presence of antimycin A to inhibit
complex III and the alternative oxidase to oxidize quinol
by a different route, confirming inhibition is on complex I.
Error bars represent 95% confidence intervals.
Table 1. Key characteristics of classes presented in this work. Unclear, unclear binding position, but confident identity; unidentified, the presence of
density of unknown nonprotein origin.
Model
Classification scheme
PDB ID
Features
Q-channel
(C-Cmask)
ND5 and NDUFB4 interface
ND2, NDUFB5, and NDUFA11
(C-Cmask)
Active inhibitor-free
............................................................................................................................................................................................................................................................................................................................................
Active-1092-i
............................................................................................................................................................................................................................................................................................................................................
Active-1092-ii
............................................................................................................................................................................................................................................................................................................................................
Active-1092-iii
............................................................................................................................................................................................................................................................................................................................................
Active-1092-iv
............................................................................................................................................................................................................................................................................................................................................
Deactive-1092-i
............................................................................................................................................................................................................................................................................................................................................
Deactive-1092-ii
............................................................................................................................................................................................................................................................................................................................................
Deactive-1092-iii
............................................................................................................................................................................................................................................................................................................................................
Deactive-1092-iv
............................................................................................................................................................................................................................................................................................................................................
Deactive-1092-v
............................................................................................................................................................................................................................................................................................................................................
Deactive-1092-vi
............................................................................................................................................................................................................................................................................................................................................
Slack-1092-i
............................................................................................................................................................................................................................................................................................................................................
Slack-1092-ii
............................................................................................................................................................................................................................................................................................................................................
Inhibitor-free (fig. S5)
Q-channel (fig. S7)
Lateral helix (fig. S8)
Lateral helix (fig. S8)
Lateral helix (fig. S8)
Q-channel (fig. S7)
Q-channel (fig. S7)
Q-channel (fig. S7)
Lateral helix (fig. S8)
Lateral helix (fig. S8)
Lateral helix (fig. S8)
Q-channel (fig. S7)
Q-channel (fig. S7)
NDUFC2 N terminus
IM1092-bound (0.49)
IM1092-bound (0.52)
Unidentified
IM1092-bound (0.63)
IM1092-bound (0.60)
Unidentified
IM1092-bound (0.68)
IM1092-bound (0.65)
IM1092-bound (0.64)
IM1092-bound (0.67)
IM1092-bound (0.65)
IM1092-bound (0.64)
No density
Unidentified
Unidentified
Unidentified
Unidentified
IM1092-bound (0.66)
IM1092-bound (0.72)
IM1092-bound (0.68)
IM1092-bound (0.66)
IM1092-bound (0.71)
IM1092 unclear
IM1092 unclear
IM1092-bound (0.64)
Intact
Mixed
Intact
Displaced
Disordered
Mixed
Mixed
Mixed
Intact
Displaced
Disordered
Mixed
Mixed
7QSD
7R41
7R42
7R43
7R44
7R45
7R46
7R47
7R48
7R4C
7R4D
7R4F
7R4G
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above and a state called slack (supplementary
text), which is of unknown functional relevance
but has been described previously in cryo-EM
studies of bovine complex I (22, 24, 25). Inhibitor-
free reference maps of bovine complex I from
separate inhibitor-free preparations in deter-
gent [figs. S5 and S6 and EMD-3731 (24)] were
used for comparison to identify and evaluate
features found in the maps with IM1092 present.
Three regions of interest are (i) densities occupy-
ing the Q-channel; (ii) unusually poor density in
a portion of the C-terminal lateral helix in sub-
unit ND5 and the adjacent subunit NDUFB4;
and (iii) altered density at the expected po-
sition of the NDUFC2 subunit N terminus.
Different classification strategies were tested
to disentangle the different states and IM1092
interactions, leading to implementation of
a “local-first” classification regime (supplemen-
tary text) used in two separate schemes to
describe 12 distinct classes (Table 1 and figs.
S7 to S9).
Biguanide-binding site 1:
Ubiquinone-binding channel
Density was observed in the Q-channel, close to
its entrance from the membrane, in all three
major classes. Using local-first classification
(fig. S7), we separated the particles into one
active class (Active-1092-i; fig. S10), three de-
active classes (Deactive-1092-i, -ii, and -iii; figs.
S11 to S13), and two slack classes (Slack-1092-i
and -ii; Table 1 and figs. S14 and S15). The ma-
jor classes were assigned by global comparisons
to reference maps and key local features (table
S1 and supplementary text). Densities for IM1092
in the Q-channel are clear in the Deactive-1092-i,
-ii, and -iii and Slack-1092-ii maps (Fig. 2, C to
E and H, and figs. S16 and S17), and the cross-
correlation fits (C-Cmask) (32) for the fit of the
IM1092 molecule into its density were high (0.66
to 0.72) (Table 1). In Slack-1092-i, although the
density is consistent for the chloro-iodo-phenyl
moiety, the biguanide moiety of the putative
IM1092 molecule was insufficiently resolved
to confidently model its orientation (Fig. 2G).
The density in the Active-1092-i map occupies
a position similar to that of the densities ob-
served in the other classes (Fig. 2F), but a smaller
additional density feature is also observed fur-
ther into the Q-channel so that, together, they
resemble density observed in the Q-channel of
the active-apo (inhibitor-free) class of bovine
complex I in nanodiscs (EMD-14133) (22).
With an IM1092 molecule refined in different
orientations into the density in the Active-
1092-i map near the Q-channel entrance, C-
Cmask values are low (<0.5), and the shape of
the density was visibly a poor fit; the second
density was too small and featureless to as-
certain its origin, and the identity of these two
densities remain unconfirmed. Overall, ~45
to ~60% of the total population and ~56 to
~75% of the (deactive and slack) population
presents clear evidence of IM1092 occupying
the Q-channel.
In the deactive and slack states, IM1092 binds
in an amphipathic site straddling two zones of
the Q-channel: the hydrophobic region next to
the exit (Fig. 2A) and the charged central re-
gion of the channel (33). The chloro-iodo-phenyl
group of IM1092 points toward the channel
exit (Fig. 2A), forming weak halogen bonds
from the Cl to the ND1-Pro48 carbonyl and
from the I to the S of ND1-Met225, as well as
van der Waals interactions with ND1-Phe224,
ND1-Phe220, ND1-Leu55, and NDUFS7-Trp46.
The halogen bonds are specific to IM1092, rel-
ative to phenformin, likely contributing to its
higher binding affinity; and metformin, which
lacks the phenyl ring, is not stabilized by the
above interactions or by p-stacking to ND1-
Phe224, consistent with its much lower binding
affinity. The biguanide moiety faces into the
channel, toward the charged region, and adopts
a range of different orientations (Fig. 2, C to
E and H). In the Deactive-1092-i and Slack-
1092-ii states, it forms a cation-p interaction
with NDUFS7-Trp46 and, in the Deactive-1092-i
state, a weak ionic interaction with the ND1-
Glu24 carboxyl also. In the Deactive-1092-ii
and -iii states, its orientation brings it closer
A
90°
B
Deactive
ND1
Glu-24
Slack
Thr-21
Arg-77
Tyr-228
Arg-77
Phe-224
IM1092
Phe-224
Active
Trp-46
IM1092
NDUFS7
ND1
Pro-48
cluster N2
NDUFS7
IM1092
ND1
Met-225
NDUFS7
C
4.4 Å
4.4 Å
Deactive-1092-i
F
D
G
3.1 Å
2.5 Å
4.5 Å
E
3.3 Å
2.8 Å
3.5 Å
4.8 Å
Deactive-1092-ii
Deactive-1092-iii
H
4.6 Å
4.9 Å
Active-1092-i
Slack-1092-i
Slack-1092-ii
Fig. 2. Binding of IM1092 in the Q-channel. (A) Overview showing the location of the biguanide-binding
site and inset showing a closer view and bonding interactions of the chloro-iodo-phenyl group for
Deactive-1092-i. Orange arrow shows the route for exit from the Q-channel into the lipid bilayer. (B) Overlay
of models for the Active-1092-i; Deactive-1092-i, -ii, and -iii; and Slack-1092-i and -ii states, aligned to
subunit ND1, showing the location and variability of biguanide-binding orientations and relative position of
NDUFS7-Arg77. NDUFS7-Arg77 and ND1-Phe224 are white in the active models, mint or orchid in the
slack models, and black in the deactive models. (C to H) Cryo-EM difference map densities (composite
versus models) for biguanides bound to Deactive-1092-I (C), Deactive-1092-ii (D), Deactive-1092-iii (E),
Active-1092-i (F), Slack-1092-i (G), and Slack-1092-ii (H). The insets show the difference map density for
the biguanide for each model shown. Biguanides are not modeled in (F) and (G), owing to uncertainties in the
ligand identity or orientation. Side-chain and ligand density for (C) to (H) are shown in fig. S16.
Bridges et al., Science 379, 351–357 (2023)
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to ND1-Glu24, and it forms a hydrogen bond
with the ND1-Tyr228 hydroxyl. In each state with
modeled biguanide, the experimental IM1092
map density at higher thresholds is consistent
with a mixture of inhibitor binding poses.
Notably, the conformation of the biguanide-
binding region of the Q-channel differs between
the three major states (21–23), regardless of
whether an inhibitor is bound (Fig. 2B). No-
tably, NDUFS7-Arg77 swings in an arc from its
position in the active state, with its side chain
pointing toward the Q-channel exit, to point
approximately toward cluster N2 in the de-
active state, adopting an intermediate position
in the slack state (Fig. 2B). The NDUFS7-Arg77
guanidinium is ~7 Å (slack) and 10 to 14 Å (de-
active) away from the bound biguanide (N-N
distance), but only ~4 Å away when IM1092 is
refined into the density in the Active-1092-i
map in the same orientation, indicating that
repulsion between their positive charges may
disfavor biguanide binding in the active state.
Available Protein Data Bank (PDB) models
for mammalian, fungal, bacterial, and plant
complexes I were compared to assess the con-
servation of key residues interacting with the
biguanide moiety; NDUFS7-Trp46, ND1-Glu24,
ND1-Tyr228, and NDUFS7-Arg77 are conserved
in all species surveyed. The only high-quality
reported human mutation in these residues in
the ClinVar database (34) is the ND1-E24K
(Glu24→Lys) mutation associated with Leber
hereditary optic neuropathy–mitochondrial en-
cephalopathy, lactic acidosis, and stroke-like
episodes (LHON-MELAS) overlap syndrome
(35). Human mutations of the residues involved
in the biguanide-binding site are therefore rare,
consistent with their important role in enzyme
function. Because they are mitochondrially en-
coded and/or essential for function, these re-
sidues cannot easily be artificially mutated in
a mammalian system. Methods for mutating
mitochondrial DNA are advancing, but site spe-
cificity and the efficiency of reaching homoplas-
mic edits remain challenging (36).
Biguanide interaction site 2: ND5 lateral helix
and NDUFB4 interface
Transmembrane subunit ND5 contains an un-
usual long helix that runs laterally alongside
ND4 and ND2, which has been proposed to
either stabilize the proton-pumping modules
or act as a transmissive element in proton
pumping (37). Substantial evidence of disorder
at the ND5 lateral helix–subunit NDUFB4 in-
terface was observed in preliminary maps, so
the dataset was subject to a separate local-first
classification that focused on this region (figs.
S8 and S18). The strategy yielded three major
classes: one with a typical well-ordered ND5
lateral helix and NDUFB4 and two with dis-
tortion or disordering of ND5 residues 547 to
564 and nearby NDUFB4 residues 77 to 92.
The classes were further separated into Active-
A
NDUFB8
Pro-77
Lys-564
Tyr-288
ND4
Lys-218
Tyr-148
3.0 Å
His-213
2.6 Å
3.1 Å
2.6 Å
75°
Asp-554
Glu-559
ND5
Lys-547
45°
Phe-92
NDUFB4
ND5
Trp-557
2.7 Å
NDUFA11
NDUFB4
Thr-85
NDUFA11
B
Intact: Active-1092-ii
C
Displaced: Active-1092-iii
D
Disordered: Active-1092-iv
Fig. 3. Biguanide-induced distortion and disordering of the ND5 lateral helix and NDUFB4 loop.
(A) Location of the structure disturbance and two views of the model of Deactive-1092-iv with hydrogen-
bonding interactions indicated with black dotted lines and distances indicated. Orchid, NDUFB4; teal, ND5;
orange, NDUFA11; dark gray, NDUFB8. Side-chain density for this region of Deactive-1092-iv is shown in
fig. S18. (B to D) Models and composite cryo-EM maps for Active-1092-ii (B), Active-1092-iii (C), and Active-1092-iv
(D) showing progressive disordering within the series. Details of p-bulge stabilizing interactions and equivalent
disordering for the deactive states (Deactive-1092-iv, -v, and -vi) are shown in fig. S18.
1092-ii, -iii, and -iv (figs. S19 to S21); Deactive-
1092-iv, -v, and -vi (Table 1 and figs. S22 to S24);
and three slack classes, which all displayed poor
density for the downstream ND5 lateral helix
and were not further investigated. Overall, ~65%
of the protein population was perturbed in this
region, with similar proportions observed for
active, deactive, and slack (~52, ~66, and ~58%,
respectively). Deactive classes with a disrupted
helix exhibit a small “opening” of the angles be-
tween the membrane and hydrophilic domains
and distal and proximal membrane domains
compared with their better-ordered equivalents
(fig. S25 and supplementary text).
This interesting region of the usually well-
ordered ND5 lateral helix does not form a
perfect a helix even in inhibitor-free active or
deactive mammalian enzyme structures (21–25).
The Active-1092-ii and Deactive-1092-iv mod-
els match the well-ordered inhibitor-free active
model in this region. Two p-bulges (fig. S18) are
stabilized by interactions between the lateral
helix and nearby waters and by ionic and hy-
drogen bonding to ND4 (Fig. 3A, right).
In Active-1092-iii and Deactive-1092-v (re-
ferred to as displaced), a short portion of the
ND5 lateral helix is altered: Lys547 to Ser550 are
disordered, and an interruption of the helical
structure at Leu562 to Pro563 allows a short
stretch of helix (residues 550 to 559) to move
outwards, away from the complex, and later-
ally, along the membrane plane (Fig. 3 and fig.
S18). A loop in NDUFB4 at residues 78 to 83,
which usually wraps around the lateral helix,
becomes disordered from Pro77 to Leu91. In
Active-1092-iv and Deactive-1092-vi (referred
to as disordered), the whole ND5 region from
Lys547 to Lys564 appears disordered, along with
the NDUFB4 loop described previously (Fig.
3D and fig. S18). Although not observed in the
detergent-solubilized protein, the bovine enzyme
in nanodiscs (22) contains two phospholipids
near to the distorted region. No nearby density
features can be interpreted as a tightly bound
biguanide. Considering the positive charge on
IM1092, it may interact with ND5-Asp554 and/or
Glu559, thereby disrupting hydrogen bonding
from the lateral helix to subunit ND4, or interact
with nearby stabilizing phospholipids. Gen-
erally, p-bulges are energetically unfavorable
elements (38) that require stabilization by hy-
drogen bonding to polar side chains or water
molecules (39). The strained nature of this region
may make it particularly prone to destabilization
by guanidium-like biguanides. No mutations
of Asp554 or Glu559 are observed in the ClinVar
database (34), and acidic residues in these posi-
tions are conserved in current mammalian and
plant structures, which suggests their important
role in stabilizing the membrane domain.
Biguanide-binding site 3: ND2, NDUFB5,
and NDUFA11
Density that matches IM1092 was observed in
a pocket formed by subunits ND2, NDUFB5,
and NDUFA11 on the intermembrane-space
Bridges et al., Science 379, 351–357 (2023)
27 January 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
C
5BFUDN
IM1092
ND2
B
D
NDUFC2
ND2
Glu-347
Asn-197
Trp-122
IM1092
Phe-123
Val-140-C
NDUFB5
NDUFA11
5BFUDN
ND2
Fig. 4. Location of the biguanide binding at the ND2-NDUFB5-NDUFA11 interface. (A) Overall location of
the binding site. Purple, NDUFC2; teal, ND2; orange, NDUFB5. (B) Overlay of all models aligned to ND2. White,
NDUFA11; Val-140-C, C terminus of NDUFA11. (C) Surface representation (Active-1092-ii model) showing subunit
NDUFC2 in cartoon, with atoms shown for IM1092. (D) Same view from the active inhibitor-free model showing
the atoms from residues 1 to 7 of NDUFC2. Local interactions and density for the individual maps and models are
shown in figs. S26 and S27.
side of the enzyme (Fig. 4 and figs. S26 and S27).
The pocket is occupied by the N-terminal seven
residues of NDUFC2 in the inhibitor-free en-
zyme, both in n-dodecyl-B-D-maltoside (DDM)
and in all states of the bovine enzyme in nano-
discs (22). The NDUFC2 N terminus is displaced
by the biguanide, with inhibitor densities ob-
served in most classes in this study (figs. S26
and S27). The biguanide moiety is stabilized by
an ionic interaction with ND2-Glu347 and by
hydrogen bonds with the ND2-Tyr196 back-
bone carbonyl, ND2-Thr199 hydroxyl, ND2-Asn197
side chain, and NDUFA11-Val140 C-terminal car-
boxyl, as well as nearby water molecules re-
solved in some maps (figs. S26 and S27). The
IM1092 bound in this site does not interfere
with any known catalytically relevant struc-
tural elements in the complex and so is likely
to represent a noninhibitory interaction.
Independence of interaction sites
The two local classification schemes used (figs.
S7 and S8) each yielded six models, and a
summary of their key features is shown in
Table 1. All six classes from Q-channel clas-
sification (fig. S7) had poor density for the
ND5-NDUFB4 interface, consistent with a
mixture of the three lateral helix states being
represented there. Overall, ~65% of the im-
aged protein population is disrupted in this
region (fig. S8), and disorder is observed in
all three major classes, as well as in states with
(e.g., Deactive-1092-i) or without clear binding
of IM1092 at the Q-channel (Active-1092-i). Fur-
thermore, in the classes from the lateral helix
classification (fig. S8), density for IM1092 was
observed in the Q-channel of deactive classes
with both ordered and displaced lateral helix.
Taken together, biguanide binding in the Q-
channel and the state of the lateral helix are
not correlated. IM1092 is observed in the ND2,
NDUFB5, and NDUFA11 pocket regardless of
the occupancy of the Q-channel or the status of
the lateral helix (Table 1). Therefore, the three
interaction sites are independent of one other.
Discussion
Biguanide access to complex I binding sites
Substantial inhibition of complex I in vivo re-
quires the biguanide positive charge, an in-
herent feature of the two cojoined guanidinium
moieties at physiological pH (31), to drive
biguanide accumulation in the mitochondrial
matrix (40) by up to 1000-fold relative to the
cytosol in response to the mitochondrial PMF.
This mitochondrial concentrating effect makes
the intramitochondrial biguanide concentra-
tion sufficient for the inhibition of targets with
only relatively weak biguanide affinity, such as
complex I, making them as potentially rele-
vant as targets outside of the mitochondrial
matrix that exhibit greater intrinsic affinities,
such as rat mGPD (10). Recent work has ques-
tioned mGPD itself as a therapeutic target be-
cause metformin was found to be noninhibitory
against the human enzyme (41). All three inter-
action or binding sites described in complex I
contain acidic residues close to the membrane-
aqueous interface, suggesting that IM1092 ac-
cesses them from the membrane, likely with
the chloro-iodo-phenyl group acting as an an-
chor into the hydrophobic membrane core
and the hydrophilic biguanide moiety inter-
acting with the negatively charged phosphate
headgroups, as proposed previously (42, 43).
The most likely route of access for hydrophobic
biguanides to the Q-channel is therefore via the
matrix-facing phospholipid leaflet. Although
the Q-channel is reproducibly well ordered in
the active state, deactive (or slack) states have
mobile regions of the Q-channel loops that
face the mitochondrial matrix (21–24, 44), so
it is also possible that the Q-channel may be-
come exposed to the matrix in these states,
providing an alternative route for hydrophilic
biguanides with poor membrane solubility,
such as metformin, to enter the Q-channel.
Major inhibitory site and selectivity for the
deactive state
Biguanides, including IM1092 and the anti-
diabetic compounds metformin and phenformin,
all share a preference to bind to the deactive
state of complex I. This behavior is not observed
for any other class of complex I inhibitor, and
we expect all three biguanides to share the
same inhibitory binding site and mode of ac-
tion. In comparison with canonical hydropho-
bic complex I inhibitors such as rotenone,
biguanides are relatively hydrophilic, water-
soluble molecules that are unlikely to bind in
highly hydrophobic or membrane-intrinsic
sites. We suggested previously that metformin
might interact at the junction of the hydro-
philic and hydrophobic domains where a set of
mobile elements (in subunits NDUFS7, NDUFS2,
ND3, and ND1) change their conformation be-
tween the active and deactive states by bind-
ing to a resting state and preventing a return
to catalysis (12). Our structures now demon-
strate that the biguanide-binding site is inside
the Q-channel, in a region that likely becomes
exposed to the matrix in the deactive state,
and adjacent to the mobile element in NDUFS7
that carries Arg77 and that switches its confor-
mation between the active and deactive states.
In the Q-channel, IM1092 binds in an am-
phipathic region with the biguanide moiety
stabilized by hydrogen bonding, cation-p inter-
actions, and ionic bonding, and the hydropho-
bic chloro-iodo-phenyl group is stabilized by
weak halogen bonding and van der Waals in-
teractions. These additional stabilizing inter-
actions between the hydrophobic portion of the
Q-binding site and hydrophobic biguanides
explain the relationship observed previously
between biguanide hydrophobicity and inhib-
itory potency (12). Other neutral and highly
hydrophobic ligands (DDM, cholate, rotenone,
and IACS-2858) have also been observed binding
Bridges et al., Science 379, 351–357 (2023)
27 January 2023
5 of 7
RES EARCH | R E S E A R C H A R T I C L E
in overlapping sites in various protein states
(fig. S28) (21, 22, 45). Yet biguanides remain
distinctive inhibitors in their state selectivity,
shown here and previously (16). Of the other
inhibitors, only rotenone has been demon-
strated to bind to a deactive-like open state,
but the binding was not state specific (21) and
the protein interactions and in vivo effects of
biguanides and rotenone are different (46, 47).
Despite the locations of the biguanide- and
ubiquinone-binding sites overlapping, met-
formin does not display classical competitive
behavior (12). This is likely because neutral,
hydrophobic inhibitors such as piericidin A,
IACS-2858, and acetogenin (45, 48, 49) com-
pete for (active-like) enzyme states capable of
forming the Michaelis complex, but biguanide
binding occurs most readily in deactive-like
states that are not preorganized, owing to dis-
ordering of the Q-channel loops in NDUFS2,
ND3, and ND1 (24). The deactive state of com-
plex I is stabilized by high pH (50), and we see
a strong correlation between pH and inhibi-
tory potency. Weak biguanide inhibition of
active complex I could originate either from
binding to the Q-channel or from an inhib-
itory nature to the ND5 lateral helix interac-
tion. The conformation of the NDUFS7 b1–b2
loop that contains Arg77 differs between the
active, deactive, and slack states. Biguanides
bind 7 to 14 Å from Arg77 in deactive and slack
states, but the arginine guanidinium position
is shifted relative to the positions in the DDM-
and cholate-bound bovine nanodisc deactive
and slack states (PDB IDs 7QSM and 7QSO)
(fig. S28) (22). In all active models, Arg77 is much
closer to the putative biguanide-binding site
(Fig. 2B), presenting a source of steric hin-
drance and charge repulsion that acts against
strong inhibitory binding and explains the
preference of biguanide inhibitors to bind to
NEM-sensitive (deactive) complex I [manifest-
ing as a lower IC50 for deactivated complex I
(Fig. 1B) (16)]. Biguanides are less powerful
inhibitors when added during catalysis rather
than before (12), and metformin has been pro-
posed to act by slowing down activation (51)
rather than by classical inhibition. Our data
support an inhibitory mode that primarily acts
by preventing reactivation of the resting de-
active state, and we conclude that the major
inhibitory interaction site of biguanides is the
Q-channel.
Local chaotropic drug-protein interactions
A key feature of biguanide interactions with
complex I is the displacement and disordering
of a portion of the ND5 lateral helix. This type
of localized disruption has not been observed
previously but may be facilitated by nonspe-
cific interactions with phospholipids (42).
Considering the similarity of biguanides to the
well-known chaotrope and protein denaturant
guanidinium, the biguanide may be attracted
to the negatively charged ND5-Asp554 and
ND5-Glu559 and specifically destabilize the
hydrogen-bonding networks between the lat-
eral helix and subunit ND4. In particular,
biguanide binding could weaken the inter-
actions of the lateral helix p-bulge segment,
allowing secondary structure shifts to form
an a helix and a disordered loop. After this
process, the unraveled segment of the helix
would no longer provide lateral support to
keep the strained junction between ND2 and
ND4 (52) tightly together, explaining the slight
“opening” of the proximal and distal mem-
brane domain interface (fig. S25). Protein sta-
bility assays (fig. S2) suggest that complex I is
stabilized close to the IM1092 IC50 ranges but
is destabilized at higher concentrations, and
we interpret this behavior to indicate that bind-
ing to the Q-channel (and/or ND2-NDUFB5 in-
terface) stabilizes the protein and that chaotropic
action occurs at higher concentrations. Our
structures in this study are in a detergent micelle
with tightly bound lipids present, and the chao-
tropic interaction site we observe is within the
phospholipid headgroup plane. Notably, any
inhibitory consequences of structural distur-
bance in this study are fully reversible, which
is demonstrated by full recovery of activity
after inhibitor dilution (fig. S2F). We propose
that biguanides such as metformin, phenformin,
and related drug leads could exert similar local
chaotropic actions on any number of cellular
proteins, especially membrane proteins, to in-
hibit or stimulate their usual functions, present-
ing a novel mode of enzyme-drug interaction
and a potential explanation for the breadth of
biguanide targets identified thus far.
Implications for in vivo mechanism of action
Although other complex I inhibitor classes have
been proposed as possible therapeutic com-
pounds (53–56), biguanides appear to offer a
lower toxicity profile than neutral species such
as rotenone, with reduced risk of Parkinsonism
(47). The key factor may lie in self-limitation of
action in the form of negative feedback at the
organelle level, meaning that their mechanism
of action lowers the risk of complete inhibi-
tion of the respiratory chain. The membrane
potential leads to increased concentration of
biguanides at the complex I site of action,
but as complex I is inhibited, the membrane
potential falls (57), creating an equilibrium
that limits the concentration and therefore the
degree of inhibition. Toxicity may also be in-
fluenced by the ready reversibility of biguanide
inhibition seen here and previously (12), com-
pared with the irreversibility of very hydropho-
bic, neutral compounds. In vivo, the active-like
state that binds canonical inhibitors is expected
to be prevalent in normal tissues (44), where
the opportunities for biguanides to inhibit may
be restricted to the weak binding observed in
this study against active-like states, or to the
binding of putative catalytic intermediates
where NDUFS7-Arg77 has moved away from
the inhibitory binding site. The deactive state
of complex I forms during oxygen starvation
(51), such as during ischemia (2) and in solid
tumor microenvironments (58). Discrimina-
tion of biguanides for this state means that,
unlike canonical inhibitors, hypoxic tissues
can be selectively targeted with less risk of
also compromising mitochondrial respira-
tion in tissues with normally functioning (active)
complex I. In such low-oxygen environments,
only complex I in the active state may work
in the reverse direction, using the PMF and
ubiquinol to drive NAD+ reduction and reac-
tive oxygen species production (51). By targeting
the deactive state formed in these environ-
ments, preventing reactivation, biguanides may
diminish reactive oxygen species production
by reverse electron transfer, as has been ob-
served previously for metformin (59).
Metformin has proven to be a safe and ef-
fective biguanide for diabetes treatment, and
our data now provide a structure-based ratio-
nale for its mode of action on complex I. This
work also offers a basis for future structure-based
biguanide drug design for the state-specific
inhibition of complex I for other potential ther-
apeutic applications (such as cancer treatment)
in which metformin has been less successful,
as well as improved prediction of additional
protein target binding sites for biguanide
drugs.
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We thank D. Chirgadze (Cambridge), J. Radecke, and Z. Yang
(eBIC) for their assistance with grid screening and data collection;
Diamond for access and support of the cryo-EM facilities at the UK
national electron Bio-Imaging Centre (eBIC), proposals BI22238-10
and EM17057-23, funded by the Wellcome Trust, MRC, and BBSRC;
members of the Hirst laboratory, especially N. Agip, for their
participation in bovine mitochondrial preparations; S. McLaughlin
(LMB, Cambridge) for access to the nano-DSF; T. Terwilliger (Los
Alamos, NM) for guidance with map sharpening and composite
map generation; S. Ding (MBU) for recording mass spectrometry
data; H. Prag (MBU) for recording liquid chromatography data;
P. Gierth (Cambridge) for recording nuclear magnetic resonance
data; J. Bosak (MBU) for culturing and authenticating cells; and
M. Iadanza (Leeds) and P. Afanasyev (ETH, Zurich) for their
scripts deposited on Github. Funding: This work was supported
by the Medical Research Council (MC_U105663141 and
MC_UU_00015/2 to J.H.) and by ImmunoMet Therapeutics Inc.
Author contributions: Conceptualization: H.R.B., M.N.P., and
J.H. Methodology: H.R.B. and J.N.B. Validation: H.R.B. Formal analysis:
H.R.B. Investigation: H.R.B., J.N.B., Z.Y., and I.C. Data curation:
H.R.B. Writing – original draft: H.R.B. Writing – review and editing:
H.R.B., J.N.B., Z.Y., I.C., M.N.P., and J.H. Visualization: H.R.B.
Supervision: J.H. Project administration: H.R.B. and J.H. Funding
acquisition: J.H. Competing interests: ImmunoMet Therapeutics
Inc. are the inventors on patent US2017/007331 for the biguanide
compound IM1761092 used in this study. M.N.P. is on the scientific
advisory board of ImmunoMet Therapeutics and holds shares
in the company. The authors declare that they have no further
competing interests. Data and materials availability: The
structure data accession codes are EMD-14251, EMD-14252, EMD-
14253, EMD-15254, EMD-15355, and PDB-7R41 (Active-1092-i);
EMD-4256, EMD-14257, EMD-14258, EMD-14259, EMD-14260, and
PDB-7R42 (Active-1092-ii); EMD-14261, EMD-14262, EMD-14263,
EMD-14264, EMD-14265, and PDB-7R43 (Active-1092-iii); EMD-
14266, EMD14267, EMD-14268, EMD-14269, EMD-14270, and
PDB-7R44 (Active-1092-iv); EMD-4272, EMD-14273, EMD-14274,
EMD14275, EMD14276, and PDB-7R45 (Deactive-1092-i); EMD-
14277, EMD-14278, EMD14279, EMD-14280, EMD-14281, and PDB-
7R46 (Deactive-1092-ii); EMD-14282, EMD-14283, EMD-14284,
EMD-14285, EMD-14286, and PDB-7R47 (Deactive-1092-iii); EMD-
14287, EMD-14288, EMD-14289, EMD-14290, EMD-14291, and PDB-
7R48 (Deactive-1092-iv); EMDB-14292, EMD-14293, EMD-14294,
EMD-14295, EMD-14296, and PDB-7R4C (Deactive-1092-v); EMDB-
14297, EMD-14298, EMD-14299, EMD-14300, EMD-14301, and PDB-
7R4D (Deactive-1092-vi); EMDB-14302, EMD-14304, EMD-14305,
EMD-14306, and PDB-7R4F (Slack-1092-i); EMD-14307, EMD-
14308, EMD-14309, EMD-14310, EMD-14311, and PDB-7R4G
(Slack-1092-ii); EMBD-14127, EMD-14128, EMD-14129, EMD14130,
EMD-14131, and PDB-7QSD (Inhibitor-free active); and EMDB-14126
(Inhibitor-free slack). Raw micrograph images are available at
EMPIAR with accession codes EMPIAR-10991 (in presence of
IM1761092) and EMPIAR-10984 (inhibitor-free). Otherwise, all data
needed to evaluate the conclusions in the paper are present in
the paper and/or the supplementary materials. IM1092 was supplied
by ImmunoMet Therapeutics Inc. by collaboration agreement.
ImmunoMet Therapeutics Inc. accepts proposals to supply IM1092
and ~1000 other biguanide compounds from their biguanide
library for research purposes. Such proposals should be directed
to dwelsch@immunomet.com. License information: Copyright ©
2023 the authors, some rights reserved; exclusive licensee
American Association for the Advancement of Science. No claim to
original US government works. https://www.science.org/about/
science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.ade3332
Materials and Methods
Supplementary Text
Figs. S1 to S28
Tables S1 to S15
References (60–78)
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
Submitted 10 August 2022; accepted 23 December 2022
10.1126/science.ade3332
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RES EARCH
R E S E A R C H A R T I C L E S U M M A R Y
◥
RENEWABLE ENERGY
Declining cost of renewables and climate change
curb the need for African hydropower expansion
Angelo Carlino, Matthias Wildemeersch, Celray James Chawanda, Matteo Giuliani,
Sebastian Sterl, Wim Thiery, Ann van Griensven, Andrea Castelletti*
INTRODUCTION: Driven by population growth
and the goal of improving living standards,
especially in the least-developed regions, many
African countries plan to expand their power
generation capacities to meet future energy
demand. Indeed, total electricity demand is
expected to grow by 5 to 6% per year until
2050, mainly in sub-Saharan Africa. Yet the
future of African energy systems will not only
be driven by the additional energy demand
but also by the need to mitigate and adapt to
anthropogenic climate change. Hydropower
is an important component of African power
systems, especially in sub-Saharan countries.
It provides around 20% of total electricity gen-
eration, but its full potential has not been ex-
ploited yet. Traditionally considered a cheap
source of low-carbon electricity, more than
300 hydropower plants, corresponding to an
additional 100-GW power capacity, are under
consideration across the continent.
RATIONALE: Although an apparently effective
strategy, the long-term planning of hydropower
systems is complex. First, as the cost of renew-
ables continues to decline, solar and wind power
are becoming more competitive and potentially
cheaper alternatives. Second, in recent years,
hydroclimatic variability has negatively affected
hydropower generation in major river basins.
Climate change will alter the spatiotemporal
distribution of water availability, exacerbating
the impacts of extreme events and reducing
the predictability of future power generation.
Finally, future energy demands and climate
policies depend on evolving socioeconomic
conditions that are fundamentally uncertain.
In this work, we investigated the power capa-
city expansion across the African continent
over the next 30 years and elucidated the
cost-optimal sequencing of hydropower projects.
We built an integrated modeling framework
that captures individual power project charac-
teristics within an energy system model that
simulates three socioeconomic scenarios that
harmonize land-use change, climate impacts
on water availability, final energy demands,
and climate policy options. Our model relies
on a combination of the Shared Socioeconomic
Pathways (SSPs) and Representative Concen-
Niger
Nile
Continent
10
0
)
W
G
(
y
t
i
c
a
p
a
C
)
W
G
(
y
t
i
c
a
p
a
C
20
0
20
0
MED
DRY
MED
DRY
Congo
Zambezi
10
0
MED
DRY
MED
DRY
100
)
W
G
(
y
t
i
c
a
p
a
C
50
0
MED
DRY
River basins
Proposed hydropower projects
Sustainability
Inequality
Fossil-fuel development
Cost-optimal hydropower expansion. Proposed (dashed line) and cost-optimal (bars) capacity expansion for
continental Africa and its major river basins under the scenarios considered. In total, 32 to 60% of the proposed
capacity is not cost-optimal. More than half of the capacity proposed for the Nile, Congo, and Niger basins is
always cost-optimal, whereas the expansion in the Zambezi River basin depends on the considered scenario. The
colors of the shaded areas in the map correspond to the river basins represented by each graph.
tration Pathways, namely SSP1-2.6, SSP4-6.0,
and SSP5-8.5. SSP1-2.6 describes a sustain-
able development scenario that aims to main-
tain the global mean temperature below 2°C,
whereas the other two scenarios result in higher
levels of warming and are characterized by
rising inequalities and fossil-fueled develop-
ment, respectively. We considered median
(MED) and very dry (DRY) water availability
scenarios to capture hydroclimatic variability
reflecting a risk-neutral and risk-averse plan-
ning perspective.
RESULTS: Our results show that between 32
and 60% of the proposed hydropower capacity
is not cost-optimal. Moreover, our analysis
suggests that hardly any new hydropower will
be built after 2030, meaning that its role in
terms of installed capacity and generation will
gradually decrease in favor of solar and wind
power. Across the scenarios, hydropower expan-
sion is robust in the Nile, Congo, and Niger river
basins, whereas it remains uncertain in the
Zambezi and smaller river basins. These find-
ings emphasize the importance of connecting
hydropower planning with capacity expansion
models, because cost-optimality cannot be deter-
mined solely based on each project’s technical
characteristics. Finally, we discover that an in-
crease in annual capital investment between
1 and 4% at the continental level can ensure
the reliability of the power system against hydro-
climatic variability. Yet the required increase
in capital investments and the observed reduc-
tions in vulnerability do not necessarily overlap
at the country level. As local interests conflict
and diverge from system-wide ones, we under-
line the importance of electricity exchanges
between countries and cooperation for power
system reliability.
CONCLUSION: Traditional planning of hydro-
power facilities is challenged by the dynamics
of technological innovation, climate impacts on
water availability, and uncertainty in long-term
socioeconomic projections that affect energy
demands and climate policies. Using a multi-
sectoral modeling framework, we designed capa-
city expansion plans that avoid commitments to
cost-inefficient hydropower infrastructures that
are often associated with substantial impacts on
the local communities and environment. Yet, in
the short term, especially in the transition to a
net-zero emissions energy system, hydropower
represents a cheap alternative to displace fossil
fuels, especially coal.▪
The list of author affiliations is available in the full article online.
*Corresponding author. Email: andrea.castelletti@polimi.it
Cite this article as A. Carlino et al., Science 381, eadf5848
(2023). DOI: 10.1126/science.adf5848
READ THE FULL ARTICLE AT
https://doi.org/10.1126/science.adf5848
Carlino et al., Science 381, 645 (2023)
11 August 2023
1 of 1
RES EARCH
R E S E A R C H A R T I C L E
◥
RENEWABLE ENERGY
Declining cost of renewables and climate change
curb the need for African hydropower expansion
Angelo Carlino1,2†, Matthias Wildemeersch2‡, Celray James Chawanda3, Matteo Giuliani1,
Sebastian Sterl3,4, Wim Thiery3, Ann van Griensven3, Andrea Castelletti1*
Across continental Africa, more than 300 new hydropower projects are under consideration to meet
the future energy demand that is expected based on the growing population and increasing energy
access. Yet large uncertainties associated with hydroclimatic and socioeconomic changes challenge
hydropower planning. In this work, we show that only 40 to 68% of the candidate hydropower capacity in
Africa is economically attractive. By analyzing the African energy systems’ development from 2020 to
2050 for different scenarios of energy demand, land-use change, and climate impacts on water
availability, we find that wind and solar outcompete hydropower by 2030. An additional 1.8 to 4%
increase in annual continental investment ensures reliability against future hydroclimatic variability.
However, cooperation between countries is needed to overcome the divergent spatial distribution of
investment costs and potential energy deficits.
O ver the next few decades, African energy
systems are expected to undergo pro-
found changes. The total electricity de-
mand is predicted to increase by 5 to 6%
per year over the next 10 years until 2050
(1–3), an increase that is driven by sustained
population growth, mainly in sub-Saharan
Africa (4), and the continuous infrastructural
investments aimed at improving energy access
and living standards, especially in the least-
developed areas (5, 6). This increasing demand,
together with the need to mitigate and adapt
to anthropogenic climate change (7), will shape
the future development of African energy sys-
tems. The use of low-carbon energy sources
(3, 8, 9) will gradually lessen the historical
dependency on fossil fuels, which are abun-
dant across the continent (10). In the short
term, annual investments of US$190 billion
are required to ensure such a successful energy
transition, with more than two-thirds of this
financial investment allocated to clean-energy
sources (3). Among these, hydropower has
historically been favored as a low-cost source
of baseload power (11), and policies that are in
place now imply a substantial infrastructural
expansion (12). Moreover, hydropower is an
attractive component of the future African
power system owing to its ability to balance
1Department of Electronics, Information, and Bioengineering,
Politecnico di Milano, Milano, Italy. 2International Institute
for Applied Systems Analysis, Laxenburg, Vienna, Austria.
3Department of Hydrology and Hydraulic Engineering,
Vrije Universiteit Brussel, Brussels, Belgium. 4World
Resources Institute, Regional Hub for Africa, Addis Ababa,
Ethiopia.
*Corresponding author. Email: andrea.castelletti@polimi.it
†Present address: Department of Global Ecology, Carnegie
Institution for Science, Stanford, CA, USA.
‡Present address: Environmental Change Institute, Oxford University,
Oxford, UK.
grid load in support of intermittent renewable
electricity sources (13–15) and because the
remaining untapped potential across the con-
tinent is relatively large (11). According to
plans of national and regional agencies, more
than 300 new hydropower projects are, at
present, committed, planned, or under consid-
eration across the African continent (16). These
projects amount to a total of around 100 GW of
additional hydropower capacity, with 168 large
(≥100-MW) projects accounting for almost 90
GW (16).
Nevertheless, climate change makes future
hydropower generation uncertain (17) and in-
creases the risk of cascading power system
failures across countries and power pools (18),
likely jeopardizing its potential to foster resil-
ience (19). Moreover, capacity expansion pro-
jections are linked to future energy demand,
technology costs, and climate policy, which are
fundamentally uncertain factors (20, 21). The
excessive reliance on hydropower in many sub-
Saharan countries is presently a source of con-
cern and a reason for caution in additional
hydropower investment (22). Further doubts
are cast on hydropower capacity expansion
(23) when socioeconomic and environmental
impacts of hydropower are analyzed, such as
population displacement (24), reduced sediment
connectivity (25), loss of biodiversity (26), and
competition with other water uses, most impor-
tantly with agriculture (21).
Given the scale of future infrastructure devel-
opment, the socioeconomic and environmental
impacts of hydropower expansion, and the
need to bridge continental as well as regional
power system development, it is crucial to
identify the hydropower projects that should
be prioritized and the ones that should be
discarded based on the cost-optimal power
system capacity expansion. Indeed, the selection
and sequencing of the required hydropower
infrastructure, given energy, socioeconomic,
and technological development, is a critical
first step. Further research should evaluate
the ensuing social, climatic, and environmental
impacts on the alternatives of interest to sup-
port final planning decisions. To what extent
do the planned hydropower expansion and its
spatial distribution over the main river basins
change depending on socioeconomic, land-use,
and climatic uncertainties? What are the costs
of climate-proofing the energy system, and how
are these costs spatially distributed compared
with power deficits driven by hydroclimatic
variability?
In this work, we build an integrated model-
ing framework to examine the role of hydro-
power in a sustainable energy transition that
is cognizant of hydroclimatic and land-use
change, socioeconomic projections, and climate
policy options. Although previous studies on
strategic dam planning (27–30) rarely included
the power system and rarely went beyond the
basin scale (31, 32), our analysis examines the
full energy portfolio at the continental scale.
Specifically, we consider cross-basin interac-
tions across the power grid (33), hydropower
projects proposed at the river basin and national
scales, and socioeconomic and land-use projec-
tions. By doing so, we limit undesirable out-
comes that result from the integration of national,
regional, and continental policies across multi-
ple sectors and scales (34).
Our results show that hydropower will have
lost its dominant role in Africa’s renewable
electricity mix by 2050, with solar and wind
power representing at least 29 to 38% and 8 to
12% of generation, respectively, and hydro-
power’s share shrinking to 7 to 14% under all
considered scenarios. Between 40 and 68% of
the proposed new hydropower capacity or, in
other words, between 120 and 251 of the 367
proposed projects could potentially be cost-
optimal, and nearly no new hydropower plants
are recommended to be built after 2030. Al-
though the viability of hydropower expansion
in the Zambezi River basin is dependent on
the scenario that is considered, many of the
proposed projects for the Nile, Congo, and
Niger remain economically viable under all
considered scenarios. Finally, guaranteeing
the reliability of the energy system against
hydroclimatic risks only requires reallocat-
ing some of the investments in hydropower
toward other sources, especially solar power
and firming technologies, with a small in-
crease in annual capital investments. Yet the
need for additional investment and the risk
of shortages are often located in different
regions. As a consequence, we highlight the
importance of transnational governance mea-
sures to guarantee climate-resilient energy
systems.
Carlino et al., Science 381, eadf5848 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Sequencing hydropower projects within power
capacity expansion
To obtain plans for hydropower project se-
quencing and associated power capacity ex-
pansion, we set up a multiscale, multisector
modeling approach (fig. S1). We combined
input data from three main datasets. First,
we used the Shared Socioeconomic Pathways
(SSPs) database (35) to obtain projected energy
demands. Second, we relied on the African
Hydropower Atlas (16) to characterize each
hydropower project in the OSeMOSYS-TEMBA
model (36). Third, to coherently account for
the coevolution of the climatic and the socio-
economic system, we used the Inter-Sectoral
Impact Model Intercomparison Project (ISI-
MIP2b) scenarios (37) to represent the future
hydrological regime that will result from changes
in the climate system and the land-use sector.
Natural climate variability was considered using
a median and a very dry hydrological scenario.
These correspond to the 50th and 5th percen-
tiles of the distribution of simulated annual
average generation, which is obtained by simu-
lating a distributed hydrological model under
an ensemble of climate projections from 2020
to 2050 (see materials and methods).
We used this model to study the expansion
trajectory of the African energy systems over
the period from 2020 to 2050 at the continen-
tal scale assuming centralized decision-making.
We considered three socioeconomic scenarios
that aggregate socioeconomic, land-use, and
climatic assumptions: (i) a sustainable develop-
ment scenario, using a carbon emission con-
straint compatible with a 2°C long-term warming,
according to SSP1-2.6; (ii) a scenario designed
to focus on heterogeneous economic develop-
ment among regions not associated with climate
policy efforts, according to SSP4-6.0; and (iii) a
fossil-fueled economic growth scenario asso-
ciated with high greenhouse gas emissions,
according to SSP5-8.5. For each socioeconomic
scenario, we consider the median (MED) and
very dry (DRY) hydrological scenarios. We use
the first to represent traditional hydropower
planning and the second to stress-test the
power system under worst-case hydroclimatic
conditions. Indeed, these two scenarios can be
seen as describing different risk-preparedness
targets (risk–neutral and risk-averse, respectively)
with respect to the uncertainty associated with
hydroclimatic variability. For each considered
scenario, we optimized the power capacity ex-
pansion for each energy source and the sequenc-
ing of the proposed (i.e., planned, committed,
and candidate) hydropower projects collected
in the African Hydropower Atlas. Moreover, we
examined the cost-reliability trade-off at differ-
ent spatial scales, which would otherwise remain
hidden behind the large-scale formulation of
the least-cost capacity expansion problem.
Cost-effectiveness of solar energy avoids the
need for long-term hydropower expansion
Our model results show that at least one-third
of the new hydropower capacity proposed at
the regional and country levels is not cost-
optimal across continental Africa, and this result
holds under all considered scenarios (Fig. 1).
Under ensemble median hydrologic change (i.e.,
under the MED scenarios), new hydropower
installed capacity ranges from 52 GW under
SSP4-6.0 to 66 GW under SSP1-2.6, whereas
these values drop to between 39 GW (SSP4-6.0)
47 GW (SSP1-2.6) when considering dry
hydrology conditions under the risk-averse
approach (i.e., under the DRY scenarios),
meaning that more than half of the proposed
capacity is not economically viable at the
continental scale. In all these plans, two large
projects are responsible for more than 17 GW
of viable capacity: the soon to be completed
6.4-GW Grand Ethiopian Renaissance Dam and
the 11.0-GW Inga 3 candidate project in the
Democratic Republic of the Congo. In general,
the SSP1-2.6 scenario consistent with a warming
of 2°C at the global level requires more hydro-
power than other scenarios owing to the reduced
reliance on fossil fuels. To isolate the impact
of climate change on hydropower expansion,
we examined capacity expansion strategies by
considering hydropower generation based on
observations from 1986 to 2005. We see that
climate change is particularly affecting the
scenarios with the largest hydropower expan-
sion and is responsible for a reduction of 9 GW
(SSP1-2.6) and 8 GW (SSP5-8.5) (fig. S2). As we
consider the salvage value of infrastructure at
the end of the planning horizon that corresponds
with the remaining operational life, our results
remain consistent when we extend the horizon
until 2070 (fig. S3).
Under all socioeconomic and hydrological
scenarios, at least half of the additional hydro-
power capacity is installed in the period from
2020 to 2030 (Fig. 1, A to C), with the window
in which hydropower can still compete econo-
mically with solar photovoltaics (PV) rapidly
closing. Beyond 2030, the share of new invest-
ments in solar power increases substantially,
and further development of hydropower in
Africa is unlikely to be cost-effective (Fig. 2).
Although hydropower could still be competitive
with solar PV until the end of this decade, the
often-witnessed build time and cost overruns
for hydropower projects (38) may even pre-
clude large-scale hydropower expansion before
that time, paving the way for further solar PV
deployment. In addition, all capacity invest-
ments are expected to grow rapidly in the
decades after 2030, thus further diminishing
the role of hydropower in the future energy
portfolio (39). Similarly, given the large expan-
sion of the power system in the next few
decades, the decline of hydropower is also
substantial in the total capacity share (fig. S4).
The gap is even more pronounced for the
DRY scenarios in which more than half of the
Fig. 1. Decadal and total hydropower capacity expansion under the considered scenarios. The dashed line indicates the capacity of proposed projects reported
in the African Hydropower Atlas. The colors of the bars are associated with the considered SSP scenarios, which coherently capture socioeconomic, land-use,
and hydroclimatic change. For each decade and for the total, the bars on the left report the capacity expansion plan designed under ensemble median hydrology
(MED), and the bars on the right correspond to the capacity expansion plan designed under dry hydrology (DRY). The arrows indicate the fraction of proposed
capacity, which is not cost-optimal under the two different risk-preparedness targets.
Carlino et al., Science 381, eadf5848 (2023)
11 August 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Power capacity expansion at the continental level. The share of new installed capacity for each power source (left y axis) and the new installed capacity
(right y axis) are reported against the three decades examined. The top row reports the share of each power source in new capacity under median hydrology (MED
scenarios), and the bottom row reports the capacity expansion plans designed under dry hydrology (DRY scenarios). Each column represents the different SSP
scenarios. Each power source is described in the legend, the order of which, from top to bottom, follows the order of the stacked bars from top to bottom. CCS,
carbon capture and storage; CSP, concentrating solar power.
proposed capacity is not economically optimal,
resulting in higher investments in solar pow-
er (bottom row in Fig. 2). Solar power becomes
a option, displacing hydropower projects whose
generation changes the most from median to
very dry hydrology. In SSP1-2.6, an important
role is played by nuclear power by mid-century,
which is used to further reduce investment in
fossil fuel power sources and represents an
important share of energy generation in 2050
(fig. S5). Contrary to SSP1-2.6, where coal be-
comes almost absent, under SSP4-6.0 and
SSP5-8.5, it still contributes around 40% of
the energy generation mix by mid-century,
with more than 2000 terawatt-hours under
SSP5-8.5 (fig. S5). With respect to the flexibility
required in the power system to balance the
reduced output of solar plants at night, hydro-
power comes after biomass and fossil fuels,
and wind has a complementary diurnal profile
to solar as well (fig. S6). Consequently, our
results do not suggest that hydropower will
still be a major provider of firm generation
and flexibility by mid-century.
Location and drivers of hydropower expansion
Most of the planned African hydropower pro-
jects concentrate in four major river basins—
Nile, Congo, Zambezi, and Niger—which account
for around 66% of the total proposed additio-
nal hydropower capacity (16). Across the socio-
economic and risk-preparedness scenarios,
the cost-optimal dam portfolio varies substan-
tially, even though some projects are consistently
selected (fig. S7). A robust finding over the
considered scenarios and river basins is that
less hydropower is installed in the DRY capa-
city expansion scenarios and under SSP4-6.0
and SSP5-8.5 (Fig. 3). The Congo River basin is
consistently cost-optimal for around half of its
potential through the Inga 3 Dam, accounting
for 11 GW in the Democratic Republic of the
Congo and built in all the scenarios. Half of the
proposed potential for the Nile River basin is
always cost-optimal, mainly in Ethiopia and
Uganda, up to 80% in SSP5-8.5 with MED
capacity expansion. The hydropower expan-
sion in the Zambezi River basin is instead very
uncertain and strongly dependent upon the
considered scenario, ranging from 30% (SSP5-
8.5) to 70% (SSP1-2.6) of the proposed capacity
in the MED scenarios and between 13% (SSP4-
6.0 and SSP5-8.5) and 39% (SSP1-2.6) in the
DRY scenarios. Finally, the cost-optimal hydro-
power potential in the Niger River basin is
between 86% (SSP4-6.0) and 91% (SSP1-2.6)
of the proposed capacity for the MED scenarios,
and it is reduced to between 53% (SSP4-6.0) and
83% (SSP5-8.5) in the DRY scenarios. These
projects are located mainly in Nigeria, a po-
tential hotspot of hydropower development.
For what concerns the remaining smaller basins,
the development of projects varies considerably
from 38% (SSP4-6.0) to 71% (SSP1-2.6) of their
total capacity in the MED capacity expansion
scenarios and between 24% (SSP4-6.0) and
32% (SSP1-2.6) for the DRY capacity expan-
sion scenarios.
Given these results, we can partially trace
the cost-optimal power expansion decisions
back to the characteristics of the proposed hydro-
power projects. High average capacity factors
and high capacity are usually good indicators
of cost-optimality (Fig. 4). Indeed, the higher
the capacity, the lower the capital cost of new
hydropower (40), even though the probabilities
of delays and cost overruns increase as well (41).
Furthermore, the higher the average capacity
factor, the higher the annual generation of a
power plant. The construction of new hydro-
power projects is not sensitive to the interannual
variability in the capacity factor. Then again,
spatial and temporal energy system constraints,
such as transmission line capacity and prox-
imity to more economically favorable hydro-
power projects, enable a full understanding
of the cost-optimal power system development.
This is, for example, the case for projects in the
Zambezi basin in Zambia, a region well con-
nected to the Democratic Republic of the Congo.
The development of the Inga 3 Dam in the
latter allows for substantial cheap electricity
exports to neighboring countries, reducing the
viability of domestic hydropower expansion
in Zambia.
The regional distribution of costs and deficits
requires cooperation
It is presently unclear how the magnitude of
drought-induced power deficits compares with
the size of additional investment costs that are
required to climate-proof the energy system
Carlino et al., Science 381, eadf5848 (2023)
11 August 2023
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RES EARCH | R E S E A R C H A R T I C L E
SSP1-2.6
SSP4-6.0
SSP5-8.5
UG
ET
15.3
23.1
22.0
Full
Potential
11.5
31.0
10.0
2
2.1
CM
AO
9.1
NG
MED
1
2.2
CD
DRY
1
3.0
CD
7.7
Z
M
ET
14.0
23.1
31.0
10.0
Full
Potential
22.0
11.5
5
.
4
Z
M
UG
ET
13.7
23.1
1
2.1
CD
22.0
Full
Potential
31.0
10.0
11.5
1
.
5
M
Z
8.6
NG
ET
18.5
23.1
UG
31.0
10.0
22.0
Full
Potential
11.5
1
6
.
0
ET
8.9
NG
3
.
2
1
1
2.1
CD
3
.
3
ET
14.6
23.1
ET
13.1
23.1
22.0
31.0
10.0
Full
Potential
11.5
4
.
0
1
1
1.7
CD
5.4
NG
5
.
1
7.5
1
1.7
CD
22.0
5.3
NG
5
.
1
31.0
10.0
Full
Potential
11.5
8.0
8.3
NG
Fig. 3. Basin- and country-level hydropower capacity expansion. The full capacity of proposed projects is
reported by river basin in the inner ring. The cost-optimal capacity in each river basin is reported in the
middle ring and is assigned to the corresponding countries in the outer ring. All values are reported in GW
units. The columns correspond to the SSP scenarios examined. The top and bottom rows report results from
the MED and DRY capacity expansion scenarios, respectively. For each scenario, only countries that are
building more than 2.5 GW of new hydropower are labeled, namely Angola (AO), Democratic Republic of the
Congo (CD), Cameroon (CM), Ethiopia (ET), Mozambique (MZ), Nigeria (NG), Uganda (UG), and Zambia (ZM).
(i.e., to guarantee demand satisfaction under
dry hydrological conditions). For this reason,
we stress-test the MED capacity expansion plans,
obtained under median hydrology, by simulat-
ing it under dry hydrology to estimate the po-
tential deficit that can occur. The observed
generation deficits should be understood as
the result of planning the power capacity expan-
sions for each source, not only for hydropower,
without explicitly accounting for hydroclimatic
variability. The reported deficits present a worst-
case scenario because safety mechanisms such
as reserve margins are supposed to be in place
to reduce the probability of occurrence and the
magnitude of these events. The DRY capacity
expansion plans can remove this risk with a
capital cost increase between 1.8% (SSP5-8.5)
and 4% (SSP1-2.6) in annual capital investments
at the continental level under all the socio-
economic scenarios. Yet at the country level,
the cost increase and potential deficit are un-
evenly distributed and vary widely across the
scenarios (Fig. 5).
Generally, reduced hydropower generation
requires backing up with existing, mainly fossil
fuel–based technologies or with additional capa-
city. This additional capacity is typically solar
PV under cost-optimal expansion scenarios,
especially under SSP1-2.6, in which the reliance
on fossil fuels for power generation is con-
strained. Consequently, spatial planning of
the deployment of renewable power plants will
be affected as well.
For many regions that are not dependent on
hydropower, there is no difference between the
two plans because they are not affected by
power deficits or additional costs induced by
hydrological variability (Northern Africa and
South Africa). Nonetheless, power pools strongly
dependent on hydropower, such as the Southern
African, Eastern Africa, and West African Power
Pools, are more subject to cost increase and
power deficit. Under SSP1-2.6, West Africa is
affected by generation deficit events that
require substantial capital investments to en-
sure reliability (e.g., Senegal, Guinea-Bissau,
Ghana, and Togo). Conversely, the power de-
ficits in Nigeria and Burkina Faso require a
modest increase in annual capital cost. In the
other scenarios, the power deficit affects most-
ly Mali, Niger, and Benin, but the costs to achieve
reliability remain low in all the power pool.
With respect to the Eastern Africa Power Pool,
Ethiopia, Tanzania, Uganda, Rwanda, and South
Sudan are most at risk of power outages induced
by hydroclimatic variability. All of these coun-
tries require substantial investments to reduce
this risk, and additional economic efforts will
be required from Egypt, Sudan, and Kenya,
especially in the case of SSP1-2.6. With respect to
the Southern African Power Pool and scenario
SSP1-2.6, Zambia, Namibia, and Mozambique
remain most vulnerable to droughts. Zambia
is particularly at risk because the power deficit
would be around 13%, which could be miti-
gated with an 11% increase in annual capital in-
vestment. In addition to the above-mentioned
countries, in the Central African Power Pool,
Angola, Zimbabwe, and the neighboring Demo-
cratic Republic of the Congo are also required to
increase their investments to climate-proof their
energy systems to a substantial extent. Under
the other scenarios, Zambia always remains ex-
posed to drought-related power outage risk,
together with Namibia, whose cost to ensure
reliability remains lower. In all scenarios, a
generation deficit is observed if power trade is
not allowed between countries, underscoring
the importance of cooperation and political
stability in the region (fig. S8).
Discussion
As African power demand grows, especially in
sub-Saharan Africa, the remaining untapped
hydropower potential represents a cheap, clean
energy source, which explains the large number
of infrastructural projects that are presently
under consideration. However, as costs associ-
ated with solar and wind power generation
continue to decline, the historical reliance on
hydropower of many sub-Saharan African coun-
tries might come to an end. Solar and wind
power are expected to become the primary
power sources in 2050, representing 50% of the
electricity mix of the continent in the sustaina-
ble development scenario compatible with a
2°C long-term warming (SSP1-2.6) and always
representing at least 50% of new installed
capacity in the next three decades under all
scenarios considered. Even under the SSP1-2.6
scenario, which pushes for extensive renewable
capacity expansion, no more than 67% of pro-
posed hydropower capacity is cost-optimal,
and this percentage shrinks to 48% under the
assumption of aversion to hydroclimatic risk.
Project delays and cost overruns might further
favor solar and wind projects, making hydro-
power development even less competitive from
an economic perspective (42). Yet in the short
term, especially in the transition to a final net-
zero configuration, hydropower represents a
cheap alternative to avoid the high costs of
installing solar and wind at the present level of
technological maturity and to displace fossil
fuels, mainly coal. The Nile, Congo, and Niger
River basins provide reliable hydropower gener-
ation. Yet the development of projects in these
regions needs to be accompanied by investment
in grid capacity in order to reap all the benefits
of large hydropower. Climate-proofing the
energy system against hydroclimatic variability
requires reducing investment in hydropower
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Fig. 4. Main characteristics
of projects and their role in
least-cost capacity expan-
sion. Capacity, average capacity
factor under very dry hydrology,
and maximum interannual
capacity factor variability under
very dry hydrology of the
examined hydropower projects
are reported on the x axis, the
y axis, and with different colors,
respectively. The diamond
marker indicates a project that
is always cost-optimal. The
circles correspond to projects
that are cost-optimal at least
once, whereas the crosses
correspond to the projects that
are never built. The always–
cost-optimal projects correlate
with the average capacity
factor (point biserial correlation
coefficient = 0.37; p = 2 × 10−19)
and capacity (point biserial
correlation coefficient = 0.18; p =
3 × 10−5). Their correlation with
capacity factor's variability is
weaker (point biserial correlation
coefficient = 0.09; p = 0.03).
Fig. 5. Country-level cost-deficit trade-offs. Maximum annual power deficit as a percentage of demand over the period from 2020 to 2050 obtained from
simulation of the MED capacity expansion plan under dry hydrology. The additional cost of eliminating the power deficits is derived as the percentage increase
obtained from the annualized capital costs of the MED and the DRY capacity expansion plans. Their joint value is reported for each country in the maps by the
bidimensional color scale that is visible in the legend, and each map corresponds to a different SSP scenario.
and investing in additional solar, wind, and firm-
ing capacity, particularly in the scenarios where
emissions are constrained. These additional
costs are not necessarily distributed uniformly
or fairly across the countries, highlighting the
need for coordination and incentive mecha-
nisms to support capacity expansion plans,
which are robust to climate change impacts.
Through the reduction in economically
viable hydropower capacity associated with
the declining cost of wind and solar, techno-
logical innovation helps reduce pressure on
riverine ecosystems and small communities in
the proximity of proposed impoundments and
further downstream as far as the impacts of
these changes propagate (43). Indeed, previous
research on hydropower’s social and environ-
mental trade-offs (25, 27, 30) and the effects
of environmental risks on the financial per-
formance of this infrastructure (44) has sug-
gested caution in construction of new projects.
Introducing these factors into our modeling
framework is likely to further reduce the space
for hydropower in future energy systems. Analy-
ses at the river-basin level remain complemen-
tary to our study and might be better tailored
to address such concerns. However, additional
research and development of new methods are
needed to connect local, regional, and continen-
tal scales for a robust planning of water and
energy systems (34). Similarly, greenhouse gas
emissions from reservoirs (30, 45–47) are a de-
terrent for hydropower capacity expansion,
particularly in tropical areas where life-cycle
emissions associated with new dams might
be comparable to those of fossil fuel power
sources (48, 49). Accounting for this factor will
likely further promote the expansion of wind,
solar, and other carbon-neutral technologies.
Additionally, we are not able to fully capture
the contribution of hydropower projects to
ancillary services such as frequency regulation
and improved renewable integration associ-
ated with the rapid ramp-up of power output.
Although these services are rarely considered
Carlino et al., Science 381, eadf5848 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
in hydropower planning, their importance
will rise as more wind power and solar power
are added to the grid, potentially affecting our
results. Moreover, electricity generation is not
always the main purpose for which water res-
ervoirs are built. If some of the reservoir hydro-
power projects were to be associated with other
needs (e.g., agriculture, flood control, drinking
water supply), cross-sectoral interactions could
improve their economic performance and make
them attractive investments. In this case, reser-
voir greenhouse gas emissions should not be at-
tributed to electricity generation only, but the
exact attribution of greenhouse gas emissions
to the different sectors remains a complex issue.
Governance and political stability are key to
ensuring sustainable exploitation of the eco-
nomically viable hydropower potential, parti-
cularly in transboundary river basins (50). The
Nile and the Niger River basins, identified as
hotspots of hydropower development, are high-
risk areas because of their transboundary nature
in regions of political instability and presence
of armed conflict (51). Implementation of coop-
eration schemes is crucial to reduce tensions
and provide water and energy security in these
areas (13, 15, 52–54).
In a broader sense, cooperation and govern-
ance are fundamental to allow all African
countries to switch their focus from energy
independence to energy security (55). In this
regard, establishing power pools and the Africa
Clean Energy Corridor has been crucial for en-
ergy governance. These mechanisms and in-
vestments paved the way for increased energy
security across the continent (56). To prepare
for the impacts of dry years, investment in
alternative power sources is required, even in
locations that might not be directly affected
by generation deficits. Understanding the con-
sequences of interconnected power systems
can therefore promote the design of agree-
ments and policy interventions that foster
energy security and resilience in the face of
hydroclimatic change. Growing evidence moti-
vates concerns about the increased risk of
conflict and instability associated with the
growing impacts of climate change (57). Govern-
ments and power pools must prepare for
stressful contexts where local strategies do
not match large-scale cost-optimal develop-
ment. To confront the friction between coor-
dinated and decentralized decision-making
levels, mechanisms building on incentive
schemes and side payments need to be designed.
In this conundrum, our results can inform future
research to ensure multiscale coordination for
energy security and sustainable hydropower
development within the African continent.
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ACKN OWLED GMEN TS
Part of the research was developed while A.Car. was participating
in the Young Scientists Summer Program at the International
Institute for Applied Systems Analysis, Laxenburg. Funding:
European Union’s Horizon 2020 grant 101003722 (GoNEXUS)
(M.G., A.Cas.) Author contributions: Conceptualization: All
authors contributed to the conceptualization; Methodology: A.Car.,
M.W., and M.G. A.Cas. designed the integrated modeling framework
and the computational experiments. A.Car. performed data processing
and ran the energy system model optimizations. C.J.C., S.S., W.T.,
and A.v.G. designed and performed computational experiments
needed for this specific version of the African Hydropower Atlas;
Visualization: A.Car.; Writing – original draft: A.Car., M.W., M.G., and
A.Cas.; Writing – review and editing: All the authors reviewed and
edited the manuscript. Competing interests: The authors declare
that they have no competing interests. Data and materials
availability: The code and the instructions for replication of the
computational experiments and to produce the figures supporting the
results discussed in this paper are available at Zenodo (58). In
particular, the repository contains the final energy demands, the
updated version of the African Hydropower Atlas, the scripts for data
processing and input preparation for the energy system model, the
energy system model with instructions to run the optimizations, and
the scripts to produce the figures. License information: Copyright ©
2023 the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original US
government works. https://www.science.org/about/science-licenses-
journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf5848
Materials and Methods
Supplementary Text
Figs. S1 to S8
Table S1
References (59–82)
Submitted 2 November 2022; accepted 1 July 2023
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RES EARCH
NEUROSCIENCE
GluD1 binds GABA and controls inhibitory plasticity
Laura Piot1, Christina Heroven2†‡, Simon Bossi1†, Joseph Zamith1, Tomas Malinauskas3,
Chris Johnson2, Doris Wennagel1, David Stroebel1, Cécile Charrier1, A. Radu Aricescu2*,
Laetitia Mony1*, Pierre Paoletti1*
Fast synaptic neurotransmission in the vertebrate central nervous system relies primarily on ionotropic
glutamate receptors (iGluRs), which drive neuronal excitation, and type A g-aminobutyric acid receptors
(GABAARs), which are responsible for neuronal inhibition. However, the GluD1 receptor, an iGluR family
member, is present at both excitatory and inhibitory synapses. Whether and how GluD1 activation may
affect inhibitory neurotransmission is unknown. In this work, by using a combination of biochemical,
structural, and functional analyses, we demonstrate that GluD1 binds GABA, a previously unknown
feature of iGluRs. GluD1 activation produces long-lasting enhancement of GABAergic synaptic currents in
the adult mouse hippocampus through a non-ionotropic mechanism that is dependent on trans-synaptic
anchoring. The identification of GluD1 as a GABA receptor that controls inhibitory synaptic plasticity
challenges the classical dichotomy between glutamatergic and GABAergic receptors.
M ost excitatory neurotransmission in the
central nervous system is mediated
by the ionotropic glutamate receptor
(iGluR) family members, which are
classified as AMPA (GluA1 to 4), N-
methyl-D-aspartate (NMDA) (GluN1, GluN2A
to D, and GluN3A and B), kainate (GluK1 to 5),
and delta (GluD1 and D2) receptors (1). At a
typical excitatory synapse, glutamate released
in the synaptic cleft binds postsynaptic iGluRs
and drives opening of their cation-conductive
ion channel, which results in membrane de-
polarization. Although structurally related (2),
GluD1 and GluD2 receptors depart from other
iGluRs by their insensitivity to glutamate and
inability to gate the ion channel pore upon
ligand binding (3, 4). Instead, GluD receptors
are thought to exert their physiological func-
tion by binding D-serine (or glycine) (5–7) and
through metabotropic (i.e., non-ionotropic)
signaling (4, 8) [although ionotropic GluD sig-
naling that is dependent on G protein–coupled
receptors has also been suggested (9)]. This
mechanism is best characterized for GluD2
receptors. Postsynaptic GluD2 binds cerebellin-1,
a “molecular bridge” attached to presynaptic
membrane proteins from the neurexin family,
to form tripartite complexes that span the syn-
aptic cleft and are involved in synapse forma-
tion, maintenance, and plasticity (4, 10–13).
Although GluD1 can also form triads with
cerebellins and neurexins (8, 14), relatively
little is known about GluD1 signaling and its
functional roles. Expressed throughout the
1Institut de Biologie de l’ENS (IBENS), Ecole Normale
Supérieure, Université PSL, CNRS, INSERM, F-75005 Paris,
France. 2MRC Laboratory of Molecular Biology, Cambridge
CB2 0QH, UK. 3Division of Structural Biology, Wellcome
Centre for Human Genetics, University of Oxford, Oxford
OX3 7BN, UK.
*Corresponding author. Email: radu@mrc-lmb.cam.ac.uk (A.R.A.);
laetitia.mony@ens.psl.eu (L.M.); pierre.paoletti@ens.psl.eu (P.P.)
†These authors contributed equally to this work.
‡Present address: CAMS Oxford Institute, University of Oxford, Oxford
OX3 7BN, UK.
forebrain (15–17), GluD1 receptors participate
in excitatory synaptogenesis (18, 19) and reg-
ulate the balance between AMPA and NMDA
receptors (20). GluD1 also specifies the forma-
tion of inhibitory synapses in the neocortex
(21–24).
Results
GluD1 receptors bind GABA
Intrigued by the presence of GluD1 receptors
at inhibitory postsynaptic sites (23, 24), which
is unparalleled among iGluRs, we investigated
the ligand-binding profile and activation of
GluD1 receptors. Because agonist binding does
not elicit currents in delta receptors, we first
introduced in GluD1 the “Lurcher” A654T
(Ala654→Thr) mutation, which renders GluD2
receptors constitutively active (25, 26). After
the expression of GluD1-A654T mutant recep-
tors into Xenopus oocytes, small but reliable
constitutive inward currents were observed
(fig. S1, A and B). Application of D-serine or
glycine potentiated these currents (fig. S1, B
and C), which contrasts with the current in-
hibition observed on GluD2-Lurcher receptors
(fig. S2, A to C) (5, 27). Because GluD1-A654T
constitutive currents were small, we inserted
an additional mutation, C645I (Cys645→Ile), to
match the equivalent GluD2 M3 pore segment
(fig. S1D). This double mutant GluD1-A654T-
C645I, named GluD1-Lurcher hereafter, yielded
larger constitutive currents (fig. S1E) that were
also potentiated by D-serine and glycine (Fig. 1,
A to C) while displaying almost no sensitivity to
glutamate (Fig. 1C and fig. S3, A to C). Agonist
dose-response curves on GluD1-Lurcher revealed
D-serine potency in the high micromolar range
[median effective concentration (EC50) of 320 ±
10 mM (n = 13 to 17 cells); Fig. 1C and table S1],
similar to that measured on GluD2-Lurcher
receptors [median inhibitory concentration
(IC50) of 260 ± 10 mM (n = 5 or 6 cells); fig. S2,
A to C, and (5, 27, 28)]. Glycine sensitivity
appeared rightward shifted, in the low milli-
molar range [EC50 of 3.4 ± 0.2 mM (n = 9
cells); Fig. 1C and table S1], reminiscent of
the glycine sensitivity of GluD2-Lurcher recep-
tors [IC50 = 0.75 ± 0.05 mM (n = 10 cells); fig.
S2C]. We then tested the ability of GluD1 re-
ceptors to sense g-aminobutyric acid (GABA).
GABA robustly potentiated GluD1-Lurcher cur-
rents with an apparent affinity in the low milli-
molar range [EC50 = 3.0 ± 0.2 mM (n = 15 to 17
cells)], lower than that of D-serine but sim-
ilar to that of glycine, and with equal efficacy
(Fig. 1, B and C; see also fig. S1, B and C, and
table S1). This GABA effect was displaced by
D-serine (fig. S3, D to F). By contrast, GABA was
essentially ineffective on GluD2-Lurcher recep-
tors, producing modest current inhibition and
limited D-serine displacement only at high con-
centrations (fig. S2, D to F). Mutating conserved
iGluR agonist-binding residues (1) in the GluD1
ligand-binding domain (LBD) fully abolished
responses to GABA (figs. S2, G to I, and S3, G
to I), revealing the primary role of the GluD1
LBD in GABA sensing. Application of GABA
(10 mM) onto NMDA (fig. S4, A to D) and AMPA
(fig. S4, E to H) receptors triggered negligible
effects, which is consistent with insensitivity
to GABA.
We next aimed to confirm these observations
in GluD1 receptors devoid of the Lurcher muta-
tions. We used voltage clamp fluorometry (VCF),
a technique that enables detection of ligand (or
voltage)–induced conformational changes in
membrane proteins (29). We designed a series
of GluD1 receptors with cysteines engineered
at various positions in the LBDs for attachment
of the environment-sensitive fluorescent probe
Alexa488 and screened for potential VCF fluo-
rescence changes (DFs) upon ligand addition
(Fig. 1D). Several positions yielded robust DFs
upon D-serine (or glycine) application. Posi-
tion E525 (E, Glu) in the structurally sensitive
D1-D1 dimer interface (27) produced particu-
larly strong signals (table S2). We verified that
the E525C (Glu525→Cys) mutation and the flu-
orescent probe attachment had minimal ef-
fects on the properties of the receptor (fig.
S5). Application of GABA on labeled GluD1-
E525C receptors also triggered marked DFs,
which revealed the ability of GABA to bind and
elicit conformational changes at (non-Lurcher)
GluD1 receptors (Fig. 1, D to F, and fig. S6, A to
C). Glutamate application had hardly any effect
(Fig. 1, E and F). No fluorescent signals were
detected upon D-serine, glycine, or GABA ad-
dition onto binding-deficient GluD1 receptors
(Fig. 1, E and F, and fig. S6, D to F), which
demonstrates that ligand binding at the GluD1
LBD is the critical initial molecular event.
VCF-based dose-response curves showed agonist
apparent affinities in the sub- to low-millimolar
range, with GABA sensitivity similar to that of
glycine but lower than that of D-serine (fig. S6, B
and C), which thus corroborates results ob-
tained on GluD1 Lurcher receptors. Thermal
Piot et al., Science 382, 1389–1394 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. GABA binds and triggers conformational changes at GluD1 recep-
tors. (A) Schematic of the two-electrode voltage clamp technique performed on
Xenopus oocytes that express GluD1-Lurcher receptors. TMD, transmembrane
domain. (B) D-serine and GABA potentiate GluD1-Lurcher constitutive currents.
The pore blocker pentamidine (Penta, 100 mM) was used to estimate the amount
of constitutive current. Dashed lines represent the constitutive Lurcher currents.
(C) Dose-response curves for GABA, D-serine, glycine, and glutamate on GluD1-
Lurcher receptors. Values and sample numbers are provided in table S1. Error
bars indicate SD. (D) Schematic of VCF performed on Xenopus oocytes that
express GluD1*-E525C labeled with Alexa488-maleimide. GluD1* is the receptor
containing the C721S mutation (Cys721→Ser). (E) VCF signals of GluD1*-E525C
and GluD1*-E525C-R526K-D742A receptors upon application of D-serine, glycine,
GABA, and glutamate (10 mM each). R526K, Arg526→Lys; D742A, Asp742→Ala.
(F) DF amplitudes triggered by 10-mM ligand application on oocytes that express
either GluD1*-E525C or GluD1*-E525C-R526K-D742A receptors and on non-
injected oocytes. The center line represents the median, box limits are upper and
lower quartiles, and whiskers are minimum and maximum values. Values and
sample numbers are listed in table S5. ***P < 0.001, and n.s. is not significant
(Dunn’s post hoc test). Detailed replicate numbers and the full statistical analysis
are provided in table S6.
shift assay and isothermal titration calorimetry
(ITC) experiments on isolated LBDs confirmed
direct binding of GABA (and D-serine, but not
glutamate) to the GluD1 LBD with a binding
affinity of 2 mM (Fig. 2, A and B; fig. S7, A and
B; and table S3), which is consistent with our
results on full-length GluD1 receptors. Con-
versely, GluD2 LBDs bound D-serine but not
GABA (fig. S7, C to F). Therefore, GABA ap-
pears to be an active ligand at GluD1, but not
GluD2, receptors.
Structure of the GABA binding site
To understand how GluD1 interacts with GABA,
we determined the crystal structure of the GluD1
LBD–GABA complex using x-ray crystallography
(Fig. 2, C and D; fig. S8, A and B; and table S4).
The GluD1 LBD–GABA complex formed well-
ordered crystals that diffracted to 1.9-Å reso-
lution, which allowed for the unambiguous
identification of GABA electron density (Fig.
2D). GABA binds the central LBD interlobe
cleft and, typical of iGluR agonists (1, 30), forms
multiple interactions with both the upper and
lower lobes (Fig. 2, D and E). In particular, the
guanidinium group of GluD1-R526 (R, Arg)
engages in a bidentate salt bridge with the
carboxyl group of GABA, whereas the g-amino
group forms a dual electrostatic interaction
with the carboxylates of GluD1-E446 (upper
lobe) and GluD1-D742 (lower lobe) (D, Asp).
Disrupting these interactions prevented GABA
action on GluD1 receptors (fig. S3, G to I). Thus,
charged interactions that include the strictly
conserved bond between the arginine side chain
of LBD helix D and the ligand a-carboxylate
(1, 30) are major anchors for GABA binding
on GluD1. In addition, three aromatic tyrosine
(Y) residues line the GABA binding pocket,
including GluD1-Y492, which acts as a lid on
top of the GABA molecule (Fig. 2, D and E).
For comparison, we also solved the structure
of the GluD1 LBD in the apo state and in the
presence of D-serine (Fig. 2C; fig. S8, C to H;
and table S4). The apo GluD1 LBD crystal form
contained three dimers in the asymmetric
unit and displayed open cleft conformations
(Fig. 2C and fig. S9, A to C), which is reminis-
cent of other apo iGluR LBD structures (1, 30).
By contrast, the GABA-bound GluD1 LBD
crystallized as an asymmetric dimer, in which
LBDs adopt closed-cleft conformations, albeit
the closure angles differed between the two
protomers (17.3° and 10.5°, respectively, rel-
ative to chain E of the apo state; Fig. 2C and
fig. S8, A to C). The GluD1 LBD–D-serine com-
plex crystal diffracted to 1.63-Å resolution
and contained one homodimer per asymmetric
unit (table S4). Only one monomer had D-serine
bound, and it adopted a closed-cleft confor-
mation identical to that observed with GABA
(closure of 17.3° relative to chain E of the apo
state; fig. S8, D to F). The D-serine interactions
with GluD1 LBD lobes again involve both ionic
and hydrogen bonding (Fig. 2F and fig. S8F).
Overall, the ligand-binding pose is notably sim-
ilar to that described for D-serine bound to the
GluD2 receptor LBD (5, 31) (fig. S8).
Molecular determinants of GABA selectivity
To examine the molecular basis of GluD1 GABA
binding and selectivity, we performed structure-
based mutagenesis experiments. Substituting
the LBD upper lobe residue E446 to Ser (S),
Gln (Q), or Asp (N) abolished GABA effects on
GluD1-Lurcher currents, but D-serine remained
active (Fig. 3, A to C, and fig. S10). The more
conservative E446D (Glu446→Asp) mutant was
not as discriminating and retained sensitivity
to both ligands, although with reduced affinity
(Fig. 3C, fig. S10, and table S1). These results
are consistent with E446 making ionic inter-
actions with GABA but not D-serine, which thus
identifies E446 as pivotal for GABA recognition
Piot et al., Science 382, 1389–1394 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
GluD1LBD vs D-serine
B
GluD1LBD vs GABA
C
r
e
w
o
p
l
a
i
t
n
e
r
e
f
f
i
d
s
s
e
c
x
E
t
a
e
h
s
s
e
c
x
E
6.2
6.0
5.8
5.6
5.4
)
s
/
l
a
c
µ
(
)
t
n
a
t
c
e
n
j
i
l
o
m
/
l
a
c
k
(
0.0
-0.2
-0.4
-0.6
D
R526
6.2
6.1
6.0
5.9
5.8
5.7
0
10 20 30 40 50 60
Time (min)
0 10 20 30 40 50 60
Time (min)
KD = 248 µM
0.10
0.00
-0.01
-0.02
-0.03
-0.04
-0.05
KD = 2 mM
0
10
20
30
40
50
Molar ratio N
0
100
50
Molar ratio N
150
Upper lobe
Y492
E446
17.3°
17.3°
GluD1LBD
+ GABA
GluD1LBD
+ D-Serine
GABA
17.3°
GluD1LBD apo
D-Serine
17.3°
E
Asp 742
CA
F
Trp 741
Trp 741
Ala 686
Val 687
Asp 742
CA
2.9
3.0
2.9
2.7
3.0
2.9
GABA
2.8
T521
Lower lobe
D742
Glu 446
CA
CA
Ala 519
Tyr 492
GABA
CA
Ala 686
Tyr 539
D-Ser
Thr 521
CA
Ala 519
CA
Ile 520
Ile 520
Arg 526
CA
Thr 521
Tyr 492
CA
CA
Arg 526
Fig. 2. Structures of the GABA-GluD1 and D-serine–GluD1 LBD complexes. (A and B) ITC analysis of D-serine (A) and GABA (B) binding to the isolated GluD1 LBD;
values are listed in table S3. KD, dissociation constant. (C) X-ray crystal structures of the GluD1 LBD in complex with GABA (left, blue) and D-serine (right, cyan)
superimposed with the apo GluD1 LBD structure (tan). The extent of GluD1 LBD clamshell closure upon ligand binding is indicated. (D) Close-up view of the GABA
binding site, which shows the 2mFo-DFc electron density map contoured at 1.0s. Distances (in Å) between interacting atoms are indicated. (E and F) LigPlot diagrams
of the GluD1-GABA (E) and GluD1–D-serine (F) complexes. CA, a-carbon atom.
Fig. 3. Molecular deter-
minants of GABA recog-
nition by GluD1
receptors. (A) Schematic
of a GluD1-Lurcher recep-
tor that harbors the
E446Q (Glu446→Gln)
mutation. (B) The E446Q
mutation eliminates the
sensitivity of GluD1-
Lurcher to GABA but not
to D-serine. Dashed lines
represent the constitutive
Lurcher currents.
(C) GABA dose-response
curves of various GluD1-
Lurcher-E446 mutants.
Error bars indicate SD.
(D) A schematic of the
GluN1-Q405E-Q536Y/
GluN2A NMDA receptor
mutant is shown at the
top. An alignment of the
GluD1 and GluN1 LBD
sequences is shown at the
bottom. Q405E, Gln405→Glu; Q536Y, Gln536→Tyr. (E) Mutations Q405E and Q536Y in the GluN1 LBD confer GABA sensitivity to GluN1/GluN2A NMDA receptors.
Current traces elicited by successive applications of glutamate plus glycine, GABA alone, and glutamate plus GABA are shown. (F) GABA and glycine (coagonist) dose-
response curves (in 1 mM glutamate) of GluN1-Q405E-Q536Y/GluN2A and wild-type (WT) GluN1/GluN2A receptors. The latter receptors are insensitive to GABA (10 mM). Error
bars indicate SD. Values and sample numbers are provided in table S1.
Piot et al., Science 382, 1389–1394 (2023)
22 December 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
IUE E15.5
-
+
Acute
slice
Adult mice
Control
ShGluD1
CA1
slm
CA2
CA3
D
Recording
B
Stimulation
N
H
P
G
1
D
u
G
l
e
g
r
e
M
Control
GluD1#
E
5
9
-
D
S
P
1
D
u
G
l
e
g
r
e
M
i
n
o
i
t
a
c
o
s
s
a
f
o
e
g
a
t
n
e
c
r
e
P
80
60
40
20
0
***
GPHN
PSD-95
Post HFS
Baseline
100pA
25ms
*
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
150
125
100
75
50
100 pA
25 ms
HFS
50 pA
25 ms
n.s
Control
ShGluD1 + GluD1#
0
5
15
10
Time (min)
20
25
Control
GluD1#-V617R
50 pA
HFS
25 ms
100 pA
25 ms
n.s.
Control
ShGluD1 + GluD1#-V617R
0
5
10
15
Time (min)
20
25
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
150
125
100
75
50
H
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
150
125
100
75
50
Control
GluD1#-R526K
50 pA
25 ms
HFS
50 pA
25 ms
**
Control
ShGluD1 + GluD1#-R526K
0
5
10
15
Time (min)
20
25
Control
GluD1#-E446S
GABA
D-serine
or glycine
100 pA
25 ms
HFS
100 pA
25 ms
****
Control
ShGluD1 + GluD1#-E446S
0
5
10
15
Time (min)
20
25
Control
ShGluD1
5
10
15
Time (min)
20
F
Control
GluD1#-R341A-W343A
G
50 pA
25 ms
HFS
50 pA
25 ms
*
Control
ShGluD1 + GluD1#-R341A-W343A
0
5
10
15
Time (min)
20
25
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
150
125
100
75
50
*
n.s.
**
*
n.s.
****
J
l
o
r
t
n
o
C
l
1
D
u
G
h
S
l
o
r
t
n
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C
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#
1
D
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G
+
1
D
u
G
h
S
l
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t
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C
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1
D
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G
h
S
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K
6
2
5
R
-
#
1
D
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+
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#
1
D
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G
+
1
D
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G
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S
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7
1
6
V
-
#
1
D
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G
+
l
l
1
D
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G
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S
A
3
4
3
W
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1
4
3
R
-
-
S
6
4
4
E
-
1
D
u
G
+
l
#
l
1
D
u
G
h
S
GABA
D-serine
or glycine
SR KO
50 pA
25 ms
HFS
Serine Racemase KO
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
150
100
50
0
0
10
20
Time (min)
30
SR KO
150
125
100
75
50
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
100pA
25ms
150
125
HFS
C
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
100
75
50
0
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
150
125
100
75
50
I
)
%
(
e
d
u
t
i
l
p
m
a
C
S
P
I
e
v
i
t
a
e
R
l
200
150
100
50
0
Fig. 4. GluD1 receptors mediate GABAergic synaptic plasticity. (A) A schematic
of in utero electroporation (IUE) for cell-specific labeling and manipulation of GluD1
expression in the mouse hippocampus performed at embryonic day 15.5 (E15.5)
is shown on the left. A confocal image of the hippocampus of a P21 mouse
electroporated with tdTomato that shows selective targeting of CA1 pyramidal
neurons is shown on the right. Imaging and whole-cell patch-clamp recordings were
performed at CA1 synapses in the SLM, a region enriched in GluD1 receptors
(15–17). Scale bar, 0.5 mm. (B) GluD1 preferentially associates with inhibitory SLM
synapses. Colocalization images are shown on the left. The white arrowheads
highlight the association between GluD1 and the indicated synaptic markers. A
quantification is shown on the right. The center line represents the median, box
limits are upper and lower quartiles, and whiskers are minimum and maximum
values. For gephyrin (GPHN), n = 20 dendrites, and for postsynaptic density protein
95 (PSD-95), n = 18 dendrites; ***P < 0.001 (two-sided unpaired Student’s t test).
Scale bars, 2 mm. (C) HFS potentiates IPSCs in control neurons but not in neurons
that express short hairpin RNA downregulating GluD1 expression (ShGluD1). For
each condition, n = 8 cells. Representative IPSC traces before (black) and after
(green) HFS are shown at the top. (D) Molecular replacement experiments.
Reexpression of WT GluD1 rescues HFS-induced plasticity. n = 7 cells for control, and
n = 8 cells for ShGluD1 plus GluD1# (the # indicates the shRNA-resistant GluD1
construct). (E to H) Ligand binding–deficient (E) (n = 9 cells versus n = 10 cells for
control) and cerebellin binding–deficient (F) (n = 8 cells versus n = 10 cells for control)
GluD1 receptors do not rescue HFS-induced inhibitory plasticity in neurons in
which GluD1 is knocked down, but ion channel flux–deficient (G) (n = 9 cells versus
n = 8 cells for control) GluD1 receptors do. GluD1-E446S (H), which allows
binding of glycine and D-serine but not of GABA, does not rescue HFS plasticity
(n = 9 cells versus n = 8 cells for control). R341A, Arg341→Ala; V617R, Val617→Arg;
W343A, Trp343→Ala. (I) Pooled data of molecular replacement experimental
Piot et al., Science 382, 1389–1394 (2023)
22 December 2023
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RES EARCH | R E S E A R C H A R T I C L E
results on HFS-induced IPSC amplitude. The control group is nonelectroporated
neurons from the same electroporated mouse. (J) HFS-induced inhibitory
plasticity is present in serine racemase knockout (SR KO) mice (n = 8 cells)
(left). A quantification of HFS-induced plasticity in SR KO mice is shown on
the right. Error bars indicate SEM. Detailed replicate numbers and the full
statistical analysis are provided in in table S6. For (C) to (I), *P < 0.05, **P <
0.01, ***P < 0.0001, and n.s. is not significant (two-sided Mann-Whitney test);
error bars indicate SEM.
by GluD1. The importance of this residue as a key
GABA anchor was reinforced by gain-of-function
experiments performed on (GABA-insensitive)
NMDA receptors. In the glycine-binding GluN1
subunit, the equivalent residue of GluD1-E446
is a glutamine (Q405) (Fig. 3D and fig. S11).
Introduction of the single-point mutation Q405E
(Gln405→Glu) into the GluN1 LBD allowed direct
activation of GluN1/GluN2A NMDA receptors
by coapplication of glutamate and GABA (in
replacement of glycine; fig. S12, A to C). The
gating efficacy of GABA at NMDA receptors
was further enhanced by introducing a second
mutation in GluN1 [mutant GluN1-Q405E-
Q536Y (Gln536→Tyr)] to better mimic the GluD1
GABA binding environment (Fig. 3, D and E,
and fig. S12C). On GluN1-Q405E-Q536Y/GluN2A
receptors, the efficacy of GABA as a coagonist
reached >50% of that of glycine (Fig. 3F), which
points to E446 and Y539 as critical determi-
nants of GABA recognition in GluD1 receptors.
E446 and Y539 are conserved in GluD2 recep-
tors (fig. S11), which suggests that other GluD1
determinants contribute to GABA selectivity
among delta receptors.
GABA binding to GluD1 controls inhibitory
synaptic strength
We then assessed the impact of GluD1 activation
on synaptic transmission at mature GABAergic
synapses. We focused on the stratum lacunosum-
moleculare (SLM) of the mouse hippocampus,
a region highly enriched in GluD1 receptors
(15–17) (Fig. 4A). Confocal microscopy imaging
revealed that GluD1 preferentially accumu-
lates at inhibitory synapses rather than at
excitatory synapses (Fig. 4B), as previously ob-
served in distal dendrites of cortical pyramidal
neurons (23, 24). We recorded GABAergic in-
hibitory postsynaptic currents (IPSCs) from CA1
pyramidal cells while performing electrical stim-
ulations in the SLM (fig. S13A). Application of
the GluD1 agonist D-serine potentiated the IPSC
amplitudes [EC50 of 180 ± 0.05 mM (n = 5 to
16 cells); fig. S13, B to D]. The continuous inclu-
sion of D-aminophosphovalerate (D-APV) in these
experiments ruled out a direct activation of NMDA
receptors by D-serine as an underlying mech-
anism. Application of 5,7-dichlorokynurenic
acid (DCKA), a ligand that, like D-serine, binds
iGluR glycine sites (7) and potentiates GluD1-
Lurcher receptors (fig. S14), also produced
robust enhancement of IPSC amplitude (fig.
S13E). Short hairpin RNA (shRNA)–based
down-regulation of GluD1 expression following
hippocampus-targeted in utero electropora-
tion eliminated the D-serine– and DCKA-induced
potentiation (fig. S13, B and E). It furthermore
decreased the density of SLM inhibitory syn-
apses (fig. S13F), as previously shown in the
cortex (23). This indicates both developmen-
tal and acute effects of GluD1 signaling on
GABAergic transmission at SLM CA1 syn-
apses. We next induced short bursts of high-
frequency stimulation (HFS) to promote the
release of endogenous GABA from presynaptic
inhibitory terminals (32). After HFS, IPSC am-
plitude increased by ~30% in control neurons
but not in neurons in which GluD1 was knocked
down, an effect that persisted throughout the
recording (15 min; Fig. 4C) and likely involved
a postsynaptic mechanism (fig. S13G). A mo-
lecular replacement strategy with mutant GluD1
receptors deficient in distinct signaling modali-
ties (23) revealed that ligand binding and inter-
action with the extracellular scaffolding protein
cerebellin, but not ion flux through GluD1 chan-
nels, are required for GluD1 to mediate enhance-
ment of inhibitory neurotransmission (Fig.
4, D to I, and fig. S13H). Preventing binding of
GABA, but not of D-serine or glycine, with the
GluD1-E446S (Glu446→Ser) mutant abolished
HFS-induced plasticity (Fig. 4, H and I), whereas
inhibitory plasticity was conserved in mice de-
ficient in D-serine signaling (33) (Fig. 4J). Thus,
activation of GluD1 receptors at SLM CA1 hippo-
campal GABAergic synapses induces prolonged
potentiation of inhibitory synaptic strength
through a non-ionotropic GABA-induced mech-
anism that relies on trans-synaptic anchoring.
Discussion
Our study unveils that, in the SLM of the mouse
hippocampus, GluD1 receptors operate at GABAergic
synapses as receptors that bind GABA and
control inhibitory synaptic plasticity. We pro-
pose that synaptically released GABA, together
with cerebellin, binds to and triggers conforma-
tional changes of postsynaptic GluD1 receptors,
which activates intracellular signaling path-
ways, leading to an increase in the number and/
or activity of type A GABA receptors (GABAARs).
This GluD1-driven mechanism of inhibitory
plasticity, which is embedded in the inhibitory
synapse itself, departs from previously des-
cribed mechanisms of inhibitory plasticity that
commonly rely on cross-talk with neighboring
excitatory (glutamatergic) synapses (34). By
contrast, the non-ionotropic, trans-synaptic, and
ligand-induced mechanism echoes the GluD2-
induced plasticity at glutamatergic parallel
fiber–Purkinje cell synapses in the cerebellum,
where GluD2 activation by extracellular D-serine
regulates AMPA receptor content (4, 6, 35, 36).
The high (10 mM) concentrations of neuro-
transmitter reached at fast chemical synapses
after vesicular release (37–39) indicate substan-
tial activation of GluD1 receptors by GABA
despite their relatively low affinity for this
agonist. The detailed mechanisms that couple
GluD1 activation to the modulation of GABAAR
activity, however, remain to be deciphered. The
question of whether this previously unknown
form of GABAergic synaptic plasticity interacts
with other forms of inhibitory plasticity (34)
also remains open. Because GluD1 receptors
are broadly expressed in the forebrain (15–17),
including at inhibitory synapses in the neo-
cortex (23), GABA signaling through GluD1
receptors likely represents a general mechanism
that extends the computational rules of inhib-
itory plasticity with consequences on neuronal
circuit function.
In humans, GluD1 mutations are associated
with susceptibility to autism and schizophrenia
(4, 40) as well as major depressive disorders
(41). With their dual ability to reside at excitatory
and inhibitory synapses, GluD1 receptors are not
only specially equipped to act as powerful reg-
ulators of synaptic circuits but are also vulnerable
nodes of excitation-inhibition imbalance during
neuropsychiatric disorders. In that context, our
finding that GluD1 receptors are molecular
machines with hybrid features—functionally
GABAergic but structurally glutamatergic—
opens fresh perspectives on GluD1-targeted
neuropharmacology.
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ACKN OW LEDG MEN TS
We thank L. Tricoire [Institute of Biology Paris Seine (IBPS),
Sorbonne Université, Paris, France] for the gift of the GluD1 and
GluD2 plasmids, D. B. Arnold (University of Southern California,
USA) for plasmids available through Addgene, D. Bellini and
F. Gorrec [MRC Laboratory of Molecular Biology (MRC-LMB), UK]
for access to the crystallization facility and x-ray data collection,
and J. Grimmett and T. Darling (MRC-LMB, UK) for support with
scientific computing. We thank P.-J. Corringer (Institut Pasteur,
Paris, France), S. Pless (University of Copenhagen, Denmark), and
members of their teams for helpful discussions and advice on VCF,
as well as the Institut de Biologie de l’École Normale Supérieure
(IBENS) FabLab for help with 3D printing of the VCF perfusion
chamber. We also thank N. Rebola [Institut du Cerveau (ICM),
Paris] for the serine racemase knockout mice. Funding: This work
was supported by the French government (Investissements
d’Avenir ANR-10-LABX-54 MEMOLIFE and ANR-11-IDEX-0001-02
PSL* Research University), Sorbonne University (fellowships to
L.P.), the Fondation pour la Recherche Médicale (FRM) (fellowship
no. FDT202012010605 to L.P.), the European Research Council
(ERC Advanced Grant no. 693021 to P.P. and ERC Starting Grant
no. 803704 to C.C.), and the UK Medical Research Council (grants
MR/L009609/1 and MC UP 1201/15 to A.R.A.). Author
contributions: Experiments on Xenopus oocytes (two-electrode
voltage clamp and VCF): L.P.; VCF set-up building and operation:
L.M. and L.P.; Crystallography experiments analysis and design:
C.H., T.M., and A.R.A.; Biochemical experiments (ITC) analysis and
design: C.J. and C.H.; In utero electroporation experiments and
design, confocal imaging, and analysis: J.Z. and C.C.; Western blot
experiments: D.W.; Brain slice electrophysiological experiments:
S.B.; Study design and data analysis: L.M., D.S., P.P.; Writing –
original draft, review, and editing: L.P., C.C., A.R.A., L.M., P.P.
Competing interests: A.R.A. is an employee of BioNTech UK Ltd.
and has equity interests in BioNTech SE. All other authors declare
that they have no competing interests. Data and materials
availability: All data are available in the main text or the supplementary
materials. Structure factors and coordinates of apo, D-serine–bound,
and GABA-bound GluD1 LBDs were deposited in the Protein Data Bank
(PDB) under IDs 8BLJ, 8BN2, and 8BN5, respectively. License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf3406
Materials and Methods
Figs. S1 to S14
Tables S1 to S6
References (42–69)
MDAR Reproducibility Checklist
Submitted 20 November 2022; accepted 25 October 2023
Published online 7 December 2023
10.1126/science.adf3406
Piot et al., Science 382, 1389–1394 (2023)
22 December 2023
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transfer interactions during C–H activation by
metal complexes. Using time-resolved x-ray
absorption spectroscopy (XAS) at the metal
L-edge (11, 25–30), we probe the short-lived
reaction intermediates from the vantage point
of the reactive metal site to interrogate the
decisive charge-transfer interactions that deter-
mine the overall reaction. In two ultraviolet
(UV)–pump and x-ray–probe experiments at
the Swiss Free Electron Laser facility (SwissFEL)
and the Swiss Light Source synchrotron radi-
ation facility (SLS), we track s-complex forma-
tion and oxidative addition using CpRh(CO)2
(where Cp is cyclopentadienyl) (10, 18–20) in
octane solution. The time-resolved Rh L-edge
absorption spectra were recorded by collecting
the x-ray fluorescence as a function of incident
x-ray photon energy around the Rh L3 absorption
edge (Fig. 1C; see supplementary materials for
experimental details). As is the case for other
4d transition metal complexes (27, 31, 32), the
Rh L3-edge transitions can be assigned to ex-
citations of Rh 2p core electrons to unoccupied
molecular orbitals (see Fig. 1D). Changes in
transition energies reflect changes in orbital
energies, whereas oscillator strengths vary
with the degree to which Rh 4d and ligand
orbitals hybridize. In combination with our
calculations, the data provide direct access to
back-and-forth charge-transfer interactions
along the C–H activation reaction trajectory
at the level of individual orbitals.
Time-resolved XAS of C–H activation
The steady-state Rh L3-edge absorption spec-
trum of CpRh(CO)2 shown in Fig. 1D exhibits a
peak at a photon energy of ~3006 eV that
results from excitation of Rh 2p core elec-
trons into the lowest unoccupied molecular
orbital (LUMO), the empty 4d-derived orbital
of the Rh(I) d8 ground state configuration.
The second peak at ~3007.5 eV is assigned to
transitions of Rh 2p electrons into unoccupied
orbitals of mainly CO and/or Cp ligand char-
acter. Through metal-ligand back-donation,
these ligand-derived orbitals acquire Rh 4d
character and become accessible by the Rh
2p→d dipole transitions in L3-edge XAS (33).
Upon laser excitation, as seen in the dif-
ference spectrum recorded at a pump-probe
time delay of 250 fs, a pre-edge peak appears at
~3002.5 eV together with substantial bleaching
RES EARCH
ULTRAFAST DYNAMICS
Tracking C–H activation with orbital resolution
Raphael M. Jay1*†, Ambar Banerjee1*†, Torsten Leitner1‡, Ru-Pan Wang2, Jessica Harich2,
Robert Stefanuik1, Hampus Wikmark1§, Michael R. Coates3, Emma V. Beale4, Victoria Kabanova4¶,
Abdullah Kahraman4#**, Anna Wach4,5, Dmitry Ozerov4, Christopher Arrell4, Philip J. M. Johnson4,
Camelia N. Borca4, Claudio Cirelli4, Camila Bacellar4, Christopher Milne6, Nils Huse2,
Grigory Smolentsev4, Thomas Huthwelker4, Michael Odelius3, Philippe Wernet1*
Transition metal reactivity toward carbon–hydrogen (C–H) bonds hinges on the interplay of electron
donation and withdrawal at the metal center. Manipulating this reactivity in a controlled way is
difficult because the hypothesized metal-alkane charge-transfer interactions are challenging to access
experimentally. Using time-resolved x-ray spectroscopy, we track the charge-transfer interactions
during C–H activation of octane by a cyclopentadienyl rhodium carbonyl complex. Changes in
oxidation state as well as valence-orbital energies and character emerge in the data on a femtosecond
to nanosecond timescale. The x-ray spectroscopic signatures reflect how alkane-to-metal donation
determines metal-alkane complex stability and how metal-to-alkane back-donation facilitates C–H
bond cleavage by oxidative addition. The ability to dissect charge-transfer interactions on an orbital
level provides opportunities for manipulating C–H reactivity at transition metals.
density from the occupied C–H s-orbital into
unoccupied metal d-orbitals concomitant with
back-donation from occupied metal d-orbitals
into the unoccupied antibonding C–H s*-orbital
(21–24) (similar to, albeit substantially weaker
than, metal-carbonyl bonds, as illustrated in
Fig. 1B). Both types of interactions simulta-
neously enhance metal-alkane bonding and
weaken the alkane C–H bond. Because it is
the balance of back-and-forth charge-transfer
via different orbitals that determines whether
a s-complex ultimately proceeds to C–H bond
cleavage, dissecting individual charge-transfer
interactions could provide orbital-based design
principles as a guide for catalyst development.
Experimentally, time-resolved infrared (IR)
spectroscopy has been instrumental in iden-
tifying reaction intermediates in C–H activa-
tion (17) by probing shifts in infrared marker
modes of spectator ligands. Such shifts are the
result of changes in spectator-ligand bond
strengths induced by changes in the integrated
charge-transfer interactions in the complex. Sepa-
rately accessing donation and back-donation
to and from the metal in a s-complex, however,
would be a way to experimentally correlate
individual orbital interactions with reactivity
toward C–H bond cleavage (7).
In this work, we demonstrate a distinct way
to experimentally evaluate metal-ligand charge-
T he transformation of saturated hydro-
carbons under mild conditions into more
valuable products constitutes a long-
standing challenge in chemistry (1–4).
Photoinitiated reactions of transition
metal carbonyl complexes with alkanes have
long served as fruitful model systems (5, 6),
providing detailed insights into the cleavage
mechanism of strong C–H bonds at a metal
center (1, 2, 4, 7). In these systems, photo-
induced ligand loss is known to create a highly
reactive species with an undercoordinated
and electron-deficient metal center (Fig. 1A).
The metal then rapidly binds an alkane from
solution to form a s-complex, in which the
metal coordinates to one or more C–H s-bonds.
Ultimately, metal insertion between C and
H atoms breaks the C–H bond to form a metal
alkyl hydride product. The s-complex inter-
mediates have been extensively studied over the
past several decades to probe their molecu-
lar structure and mechanistic role (8–20).
Quantum chemical calculations, in par-
ticular, suggest that the metal-alkane bond in
s-complexes is formed by donation of electron
1Department of Physics and Astronomy, Uppsala University, 751
20 Uppsala, Sweden. 2Center for Free-Electron Laser Science,
Department of Physics, University of Hamburg, 22761 Hamburg,
Germany. 3Department of Physics, Stockholm University, 106 91
Stockholm, Sweden. 4Paul-Scherrer Institute, CH-5232 Villigen
PSI, Switzerland. 5Institute of Nuclear Physics, Polish Academy
of Sciences, PL-31342 Krakow, Poland. 6European XFEL GmbH,
22869 Schenefeld, Germany.
*Corresponding author. Email: raphael.jay@physics.uu.se (R.M.J.);
ambar.banerjee@physics.uu.se (A.B.);
philippe.wernet@physics.uu.se (P.W.)
†These authors contributed equally to this work.
‡Present address: MCA Engineering GmbH, 80807 Munich, Germany.
§Present address: Proximion AB, 164 40 Kista, Sweden.
¶Present address: Department of Physics and Astronomy, Uppsala
University, 751 20 Uppsala, Sweden.
#Present address: Stanford PULSE Institute, SLAC National Accelerator
Laboratory, Stanford University, Menlo Park, CA 94025, USA.
**Present address: Physical Sciences Division, Pacific Northwest
National Laboratory, Richland, WA 99352, USA.
Jay et al., Science 380, 955–960 (2023)
2 May 2023
Table 1. Mulliken charge and orbital properties of the CpRh(CO)-octane and Rh(acac)(CO)-
octane s-complexes (B3LYP level of theory).
s-complex
Rh Mulliken charge
LUMO character
Rh 4d (%) Cp or acac (%) CO (%) Octane (%)
CpRh(CO)-octane
.....................................................................................................................................................................................................................
Rh(acac)(CO)-octane
.....................................................................................................................................................................................................................
0.37
0.46
28.8
15.2
39.3
52.2
4.2
1.5
6.2
9.2
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RES EARCH | R E S E A R C H A R T I C L E
of main-edge features (Fig. 1D). The temporal
evolution of the pre-edge peak intensity, shown
as a time trace in Fig. 1E, is well described by a
biexponential decay to a metastable species
(reduced c2 = 1.11; see supplementary mate-
rials for a kinetic model). The two time con-
stants are assigned to CO dissociation from
excited states of CpRh(CO)2 within 370 ± 50 fs
followed by octane association within 2.0 ±
0.1 ps. These assignments agree with the time-
scales for ligand substitution in other metal
carbonyls from previous femtosecond mea-
surements (28, 34). Our experiment establishes
the timescale of formation of the CpRh(CO)-
octane s-complex, and the spectrum at 10 ps
in Fig. 1D constitutes a direct fingerprint of
how metal-ligand charge-transfer interactions
change upon substituting a CO with an alkane
ligand. On nanosecond timescales, the disap-
pearance of the s-complex pre-edge peak (time
trace at 3004.4 eV in Fig. 1F) and the simul-
taneous emergence of a positive absorption
feature (time trace at 3006.6 eV in Fig. 1F
and transient spectrum at nanosecond delay
times in Fig. 1D) reflect how the metal-ligand
charge-transfer interactions further change
upon C–H activation by oxidative addition.
Fig. 1. Mechanistic model and time-resolved XAS of C–H activation
by CpRh(CO)2 in octane solution. (A) Schematic of C–H activation by
CpRh(CO)2 via photoextrusion of CO followed by alkane complexation and
oxidative addition. hn, UV photon. (B) Orbital-specific metal-ligand charge-
transfer interactions for metal-alkane and metal-carbonyl bonds. (C) Schematic of the
experiment with UV–laser pump pulses triggering the reaction and x-ray pulses
probing orbital evolution as a function of time delay between pump and probe pulses.
Reaction intermediates and products [as well as ground-state CpRh(CO)2] are
characterized by detecting the Rh fluorescence as a measure of the Rh-specific
x-ray absorption (see supplementary materials). (D) Steady-state and transient
Rh L3-edge absorption spectra at indicated pump-probe time delays as well as a
schematic depiction of the L-edge absorption process [difference spectra are
plotted relative to the edge-jump of the steady-state spectrum (intensity at
3015 eV), which is normalized to 1; steady-state and difference spectrum at
delays >190 ns are scaled for illustration]. Rel. abs., relative absorption.
(E and F) Time traces (intensities versus time delay) measured at indicated
x-ray photon energies with (E) femtosecond and (F) picosecond time resolution.
In (E), the gray, orange, and purple shaded regions represent the relative
populations of the CpRh(CO)2 excited state, the CpRh(CO) fragment, and the
CpRh(CO)-octane s-complex, respectively.
Jay et al., Science 380, 955–960 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Both time traces are modeled with a single
exponential (reduced c2 = 1.01), yielding a
time constant of 14 ± 2 ns, which is in ex-
cellent agreement with the ~14 ns for C–H
activation of octane with CpRh(CO)2 from
time-resolved IR measurements (18).
Comparison with theory
This assignment of the transient x-ray absorp-
tion spectra is further validated and detailed
by the calculated spectra in Fig. 2A. Because
shapes and intensities of the measured spectra
are well reproduced, we can robustly assign
x-ray transitions to underlying charge-transfer
interactions (see supplementary materials for
computational details and discussion of devia-
tions between experiment and theory). We use
the experiment-theory comparison to extract
the orbital correlation diagram shown in Fig. 2B.
Fig. 2. X-ray absorption signatures
of s-formation and C–H activation
by oxidative addition. (A) Experi-
mental spectra at time t = 10 ps and
>190 ns (top) compared with
calculated spectra of CpRh(CO)-
octane and CpRh(CO)-H-R [middle,
calculated on the B3LYP level of
theory (43)]. L3-edge transitions and
spectra calculated for intermediate
structures (bottom) illustrate the
interconversion of spectral features
from reactant to product along
the C–H activation reaction coordinate
(39). Calculated difference spectra
are scaled such that the CpRh(CO)-
octane difference spectrum matches
the pre-edge intensity of the experi-
mental spectrum at 10 ps. Vertical
lines indicate positions of spectral
fingerprints a, b, and c. (B) Correla-
tion diagram between the valence
orbitals of CpRh(CO)2, CpRh(CO)-
octane, and CpRh(CO)-H-R detailing
the interconversion of orbital
energies and character upon ligand
substitution and C–H activation.
The calculated orbital plots represent
the antibonding counterpart of the
bonding interactions that are sche-
matically shown in Fig. 1B. For
illustration, calculated orbitals are
displayed with varying isovalues
(see supplementary materials).
(C) Calculated free energies (top),
Rh 4d character of LUMO+1 and
LUMO+3 orbitals (middle), and
oscillator strengths of transitions into
LUMO+1 and LUMO+3 orbitals
(bottom) as a function of reaction
coordinate of oxidative addition.
arb. u., arbitrary units.
Jay et al., Science 380, 955–960 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Importantly, this correlation diagram, which
is based on robust experimental observations,
relates orbital interactions from ligand substi-
tution and s-complex formation to C–H bond
breaking and oxidative addition.
Two major effects in metal-ligand bonding
of the CpRh(CO)-octane s-complex compared
with CpRh(CO)2 are reflected in the 10-ps
transient spectrum. First, substituting the
strong-field CO ligand with the weakly inter-
acting octane stabilizes (decreases the ener-
gy of) the Rh 4d-derived LUMO orbital (Fig.
2B). This is directly reflected in a decrease of
2p→LUMO transition energies: The pre-edge
peak that is due to 2p→LUMO transitions
is shifted to lower energy in the s-complex
(3004.2 eV) compared with CpRh(CO)2 (3006 eV;
Fig. 2A). Second, an overall reduced degree
of back-donation in the s-complex compared
with CpRh(CO)2 lowers the hybridization of
ligand orbitals with Rh 4d orbitals. This dimi-
nishes intensities of the Rh 2p transitions to
ligand-derived orbitals in the s-complex and
causes the depletion in the main-edge region
of 3006 to 3009 eV (Fig. 2A).
For the subsequent C–H bond breaking and
oxidative addition step from the s-complex
to the metal alkyl hydride, calculations of
the free-energy landscape shown in the top
panel of Fig. 2C suggest a barrier of ~7 kcal/mol
and an exothermic reaction. The underlying
reaction coordinate is constructed from a
Nudged-Elastic-Band (NEB)/TPPSh/Def2-TZVP
computation (35–37). Using the geometries of
this reaction path scan, the free-energy land-
scape was computed at the DLPNO-CCSD(T)/
Def2-TZVP level of theory (38). Although we
do not experimentally observe the intermediate
structures along the reaction coordinate, the
L3-edge x-ray absorption spectra computed for
these structures relate the spectral changes
from the s-complex reactant to the metal alkyl
hydride product, which we observe. The key
spectral fingerprint regions (denoted as a, b,
and c in Fig. 2A) can be assigned to excitations
of Rh 2p electrons predominantly into the LUMO,
LUMO+1, LUMO+2, and LUMO+3 orbitals
(LUMO+4, +5, … are not discussed because
they contribute to a negligible degree only).
Changes of the features a to c hence report
on the combined transformations of the four
lowest unoccupied orbitals upon C–H bond
breaking and oxidative addition. As detailed
in the following paragraphs, feature a re-
flects changes in metal-alkane orbital over-
lap as metal-alkane bond distances change,
feature b reports on the oxidation of the metal,
and feature c reflects changes in metal-ligand
back-donation.
In line with previous work (39), our cal-
culated reaction coordinate describes the C–H
bond moving toward the Rh center and, at the
same time, the C–H bond elongating and
breaking until the individual Rh–C and Rh–H
Jay et al., Science 380, 955–960 (2023)
2 May 2023
Fig. 3. X-ray orbital view of reactivity modulations in C–H activation by varying the ligand environ-
ments in s-complexes. (A) Schematic of the LUMO orbitals of CpRh(CO)-octane and Rh(acac)(CO)-octane
with variations in metal-ligand bonding (charge-transfer indicated by arrows) and their effect on the
affinity for oxidative addition (calculated free energies). Me, methyl. (B) Calculated difference spectra of
CpRh(CO)-octane and Rh(acac)(CO)-octane compared with transient difference L3-edge absorption spectra
measured at SwissFEL at a pump-probe delay time of 10 ps. For comparison, the experimental Rh(acac)(CO)-
octane spectrum is scaled to match the depletion of the CpRh(CO)-octane. This scaling is validated by
the excellent agreement with the calculated spectra, which are shown with the same scaling as in Fig. 2A
(see supplementary materials).
bonds are established (see schematic of the
reaction coordinate in Fig. 2A, bottom). As a
consequence of these atomic rearrangements
along the reaction coordinate, the Rh 4d-derived
LUMO orbital shifts to higher energies be-
cause of increasing orbital overlap with the
approaching C–H group with minor changes in
hybridization (Fig. 2B and fig. S7). The cor-
responding increase of 2p→LUMO transition
energies is directly observed experimentally
by the disappearance of the pre-edge feature
a in the spectrum upon transformation of the
s-complex to the alkyl hydride product: The
2p→LUMO transitions shift to higher energy
and merge with the main edge of the spec-
trum, thereby contributing to the generation
of feature b in the spectrum of the CpRh(CO)–
H–R alkyl hydride product.
LUMO+1 in the s-complex is the energeti-
cally lowest ligand-derived orbital with domi-
nant CO p* character and with some Rh 4d
admixture due to Rh-CO back-donation (see
orbital plots in Fig. 2B). Upon oxidative ad-
dition, LUMO+1 shifts to slightly lower energy
and, importantly, gains considerable Rh 4d
character (see calculated Rh 4d character in
Fig. 2C). The increase is so substantial that
the Rh 4d character becomes the dominating
contribution. This can be interpreted as an
effective transformation of the former ligand-
derived orbital into a second unoccupied Rh
4d-derived orbital (in addition to the LUMO;
see orbital plots in Fig. 2B). The increase of
Rh 4d character directly scales with an increase
of oscillator strength of the Rh 2p→LUMO+1
transitions (Fig. 2C). Feature b hence emerges
as a strong peak, drawing intensity from both
the LUMO+1 transforming into a second un-
occupied Rh 4d-derived orbital and the LUMO
shifting to higher energy and merging with the
main edge (Fig. 2A). The emergence of feature
b thus reflects the combined electronic-structure
effects of C–H bond cleavage (LUMO destabi-
lization) and oxidative addition (LUMO+1
transformation). In particular, the oxidation of
the metal center from a Rh(I) (d8) to a Rh(III)
(d6) configuration is evidenced by the emer-
gence of two unoccupied Rh 4d orbitals.
The increase of the Rh oxidation state sub-
stantially destabilizes LUMO+2 (Fig. 2B) and
slightly reduces its Rh 4d character (see fig.
S7). As the second CO p* orbital, its destab-
ilization thus directly reflects a decrease in
back-donation from the oxidized metal onto
CO p*. This effect has also been associated
with the shift of CO marker modes to higher
energy upon C–H activation (17), consistent
with our results. Finally, LUMO+3 in the
s-complex constitutes the octane C–H s* orbi-
tal, which exhibits weak Rh 4d admixture be-
cause of low back-donation from Rh to C–H
(orbital plot in Fig. 2B). Back-donation, how-
ever, increases as the C–H bond is broken and
the covalent Rh–C and Rh–H bonds are formed,
as evidenced by the substantial increase in Rh
4d character in LUMO+3 (see Rh 4d character
in Fig. 2C and orbital plots in Fig. 2B). Ac-
cordingly, the oscillator strengths of Rh
2p→LUMO+3 transitions also strongly increase
upon oxidative addition (Fig. 2C). Together
with the transitions into LUMO+2 shifting
toward higher energies, this causes the for-
mation of the strong peak c in the alkyl hydride
spectrum, which exhibits an intensity similar
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RES EARCH | R E S E A R C H A R T I C L E
to the steady-state spectrum of CpRh(CO)2
and one considerably stronger than that in the
s-complex (Fig. 2A). Experimentally, this is
reflected in negligible intensities in the alkyl
hydride difference spectrum at the energies of
feature c compared with the strong bleaching
in the transient s-complex spectrum.
A more stable s-complex
By experimentally observing individual charge-
transfer interactions, we verify the validity of
orbital correlation diagrams along C–H activation
reactions that were previously derived from
quantum chemical calculations alone (40).
Our approach allows us, in particular, to ex-
pand upon established notions of charge-
transfer interactions between the metal and
the C–H group by experimentally assessing
the critical role of additional orbital interac-
tions between the metal and the spectator
ligands. We further demonstrate this here by
evaluating how different s-complexes exhibit
different reactivities toward C–H activation
owing to specific differences in orbital inter-
actions as a result of their different ligand
environments. It has previously been shown
that replacing the Cp moiety with an acetyl-
acetonate (acac) group leads to a stable
s-complex, which, however, does not proceed
to oxidative addition of the C–H bond (41).
Our calculations shown in Fig. 3A suggest a
4.2 kcal/mol stabilization of the Rh(acac)
(CO)-octane with respect to the CpRhCO-
octane s-complex. Together with the endo-
thermic free-energy profile we calculated,
this renders the C–H activated product un-
favorable. We find the extra stabilization of
Rh(acac)(CO)-octane to be predominantly due
to a higher donation from the octane onto the
Rh center. This stronger donation is favored by
the higher charge deficiency at the Rh in the
case of the more ionic bond between Rh and
the acac group compared with the bond
between Rh and Cp (see the Mulliken charges
in Table 1).
Our calculations predict this variation in
ionicity and the related variation in reactivity for
C–H activation to manifest in the x-ray absorp-
tion difference spectra of the two s-complexes as
shown in Fig. 3B. Our experiment directly
confirms this prediction. In quantitative agree-
ment with theory, the measured spectrum
of Rh(acac)(CO)-octane shows a higher pre-edge
intensity than CpRh(CO)-octane (Fig. 3B). We
find this difference to be due to a higher Rh 4d
character in the LUMO (at the expense of a
lower hybridization with the acac group; see
Table 1), which causes the more intense
2p→LUMO pre-edge transitions in Rh(acac)
(CO)-octane. This higher Rh 4d character,
which directly correlates with higher Rh
ionicity, renders the reaction step to the
Rh(acac)(CO)-H-R species endothermic. A
more charge-deficient Rh(I) center—in the
Jay et al., Science 380, 955–960 (2023)
2 May 2023
case of acac, having a lower propensity to be
further oxidized to Rh(III)—is consistent with
and extends established trends in alkane oxi-
dative addition (7). We thus establish a direct
measure of how the lower hybridization of Rh
4d with spectator-ligand orbitals in the more
ionic bond to the acac ligands modulates
reactivity for C–H activation by unfavorably
changing the balance of charge-transfer inter-
actions that bind (alkane-to-metal s-donation)
versus those that break the C–H bond (pro-
pensity for oxidation via metal-to-alkane
back-donation).
Our results demonstrate the value of time-
resolved, metal-specific, L-edge x-ray absorp-
tion spectroscopy for understanding, on an
orbital level, which factors determine reactivity
for C–H activation at a metal complex. We
anticipate that our approach will be used in
the future to systematically screen s-complexes
and alkyl hydride reaction products to provide
a distribution of valence orbital energies and
character as measures of metal-alkane bond
stability and propensity toward C–H activation
with oxidative addition and, potentially, other
mechanisms (40). With C–H activation ranging
from nucleophilic to electrophilic, depending
on the relative weight of charge donation and
back-donation, the here established experi-
mental observables can be used to ascertain
where in the range of mechanisms a probed
system lies. Such insight can then be used to
pin the results from computational studies that
correlate valence electronic structure with
reactivity. We envision this approach to extend
established trends for reactivity (7) by pro-
viding experimentally verified correlations
between metal-ligand charge-transfer inter-
actions and reactivity for orbital-level control
of C–H activation.
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AC KNOWLED GME NTS
We acknowledge the Paul Scherrer Institut, Villigen, Switzerland,
for provision of beamtime at the Alvra beamline of SwissFEL as
well as at the PHOENIX beamline of the Swiss Light Source (SLS).
We thank R. Wetter and C. Frieh for their excellent technical
support. The computations were partly enabled by resources
provided by the Swedish National Infrastructure for Computing
(SNIC) at UPPMAX, which is partially funded by the Swedish
Research Council through grant agreement nos. 2021-22968 and
2022-22975. The computations were also partly enabled by
resources provided by the National Academic Infrastructure
for Supercomputing in Sweden (NAISS) and the SNIC at the
National Supercomputer Centre in Sweden (NSC) and the PDC
(Parallelldatorcentrum) Center for High Performance Computing,
which are partially funded by the Swedish Research Council
through grant agreement nos. 2022-06725 and 2018-05973.
Funding: A.B. and P.W. acknowledge funding from the Carl
Tryggers Foundation (contract CTS 19: 399). P.W. acknowledges
funding from the Swedish Research Council (grant agreement no.
2019-04796). J.H. and N.H. acknowledge funding from the Cluster of
Excellence “CUI: Advanced Imaging of Matter” of the Deutsche
Forschungsgemeinschaft (DFG), EXC 2056, project ID 390715994.
R.-P.W. acknowledges funding from the German Ministry of Education
and Research (BMBF), project ID 05K19GU2. V.K., A.K., and
C.B. acknowledge support from the Swiss National Science
Foundation (SNSF) through the NCCR:MUST. A.W. acknowledges
the National Science Centre, Poland (NCN), for partial support
through grant no. 2019/03/X/ST3/00035. Author contributions:
R.M.J., A.B., and P.W. originated the project concept. R.M.J., P.J.M.J.,
C.C., C.B., C.M., N.H., G.S., T.H., and P.W. planned and conceived
the experiments. R.M.J., T.L., R.S., R.-P.W., J.H., E.V.B., V.K., A.K.,
A.W., D.O., C.A., P.J.M.J., C.N.B., C.C., C.B., G.S., T.H., and P.W.
executed the experiments. R.M.J., T.L., H.W., C.C., and P.W. analyzed
the experimental data. R.M.J., A.B., M.R.C., and M.O. performed
the theoretical calculations. R.M.J., A.B., and P.W. wrote the paper
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RES EARCH | R E S E A R C H A R T I C L E
with input from all the authors. Competing interests: The authors
declare that they have no competing interests. Data and materials
availability: All data presented in the main text and the
supplementary materials are freely available through Zenodo (42).
License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for
the Advancement of Science. No claim to original US
government works. https://www.science.org/about/science-licenses-
journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf8042
Materials and Methods
Supplementary Text
Figs. S1 to S11
Table S1
References (44–65)
Movies S1 to S4
Submitted 20 January 2023; accepted 2 May 2023
10.1126/science.adf8042
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a coherent superposition of two or more states
with well-separated phase-space distributions.
Experimental setup
Our device, which we call a ℏBAR, as in pre-
vious works (19), consists of a high-overtone
bulk acoustic-wave resonator (HBAR) coupled
to a superconducting transmon qubit. The
transmon qubit allows us to create, control,
and read out phonon states in the HBAR.
Qubit and HBAR are fabricated on separate
sapphire chips, which are subsequently flip
chip bonded into the final device (Fig. 1A). A
dome of piezoelectric aluminum nitride on the
HBAR chip coherently couples the electric
field of the qubit with the strain field of the
resonator modes. The device is placed inside a
three-dimensional Al cavity, which allows us
to control the qubit with the standard circuit
quantum electrodynamics toolbox (20). The
acoustic free spectral range is ∼12 MHz, and
frequency tuning the qubit via a microwave
drive–induced Stark shift allows us to address
several longitudinal phononic modes. The
acoustic lattice oscillations are localized within
a Gaussian mode with waist w0 ¼ 27 mm and
length L ¼ 435 mm, giving a mode volume of
0L ≈ 0:001 mm3 [see supplementary text
pw2
(21) section B for details]. More details about
this circuit quantum acoustodynamics (cQAD)
system (19, 22) and the device (23) can be
found in previous works.
In the classical picture, one can imagine a
coherent state jai in the phonon mode as a
coherent displacement of the atomic lattice
with an amplitude proportional to a. In the
quantum picture, an example of a cat state is
a quantum superposition of two coherent
states with opposite displacement amplitudes,
leading to the physical interpretation of such
a state as the superposition of two oscillations
RES EARCH
QUANTUM MECHANICS
Schrödinger cat states of a 16-microgram
mechanical oscillator
Marius Bild1,2†, Matteo Fadel1,2†*, Yu Yang1,2†, Uwe von Lüpke1,2, Phillip Martin1,2,
Alessandro Bruno1,2, Yiwen Chu1,2*
According to quantum mechanics, a physical system can be in any linear superposition of its possible
states. Although the validity of this principle is routinely validated for microscopic systems, it is still
unclear why we do not observe macroscopic objects to be in superpositions of states that can be
distinguished by some classical property. Here we demonstrate the preparation of a mechanical
resonator in Schrödinger cat states of motion, where the ~1017 constituent atoms are in a superposition
of two opposite-phase oscillations. We control the size and phase of the superpositions and investigate
their decoherence dynamics. Our results offer the possibility of exploring the boundary between the
quantum and classical worlds and may find applications in continuous-variable quantum information
processing and metrology with mechanical resonators.
Q uantum mechanics is one of the most
successful scientific theories ever for-
mulated. However, from the early days
of quantum mechanics until now, it has
been unclear why quantum phenomena,
such as state superpositions, are never ob-
served in the macroscopic world. In his 1935
work (1), Erwin Schrödinger imagined a de-
vice able to poison a cat as a consequence of a
radioactive decay, concluding that the super-
position of an atom being “decayed” and “not
decayed” could be mapped onto a superposi-
tion of the cat being simultaneously “dead”
and “alive.” There are two aspects of this hy-
pothetical scenario that make it seem absurd
and counterintuitive: First, a cat is a macro-
scopic, everyday object; and second, “dead” and
“alive” are states that are mutually exclusive
within our classical experience.
Many explanations have been proposed as
to why we may never encounter a cat in such
an unfortunate situation. Macroscopic objects
may simply be too complex and subject to too
many sources of decoherence to sustain a super-
position of classically distinct states. Other
theories introduce additional effects beyond
standard quantum mechanics, such as wave
function collapse due to intrinsic stochastic
noise or gravitational decoherence (2). These
effects are typically expected to scale with the
mass of the system and the distinctness of the
states that are superposed. Therefore, observ-
ing state superpositions in massive objects is
of key importance for exploring the validity
range of quantum mechanics as we know it.
Beyond its fundamental interest, preparing and
detecting Schrödinger’s cat states is essential
1Department of Physics, ETH Zürich, 8093 Zürich,
Switzerland. 2Quantum Center, ETH Zürich, 8093 Zürich,
Switzerland.
*Corresponding author. Email: fadelm@phys.ethz.ch (M.F.);
yiwen.chu@phys.ethz.ch (Y.C.)
†These authors contributed equally to this work.
for applications in quantum technologies. Main
examples include Heisenberg-limited parame-
ter estimation protocols (3, 4) and error-protected
quantum information processing (5, 6).
There have been many experimental dem-
onstrations of Schrödinger cat states (which
we will call “cat states” from here on). These
include superpositions of internal and mo-
tional degrees of freedom in trapped ions (7, 8),
phase-space superpositions of electromagnetic
waves in both the optical (9, 10) and microwave
domains (11–13), Greenberger–Horne–Zeilinger
states (14, 15), current superpositions in super-
conducting quantum interference devices (16),
and spatial superpositions of atomic clouds
(17) and large molecules (18). We experimen-
tally demonstrate the preparation of cat states
in the motional degree of freedom of a solid-
state mechanical resonator. Given the variety
of definitions found in previous works, we
define a cat state of a harmonic oscillator as
Fig. 1. Illustration of the h– BAR device and
system evolution. (A) Schematics of the ħBAR
device. The HBAR chip (top) has a layer of piezo-
electric aluminum nitride (orange) and supports
standing acoustic waves (pink). The transmon qubit on
the lower chip has a circular antenna to couple
with the HBAR. The inset shows the superposition
of two opposite-phase oscillations of atoms in the
crystal lattice. (B) Simulated evolution without
decoherence of the qubit jei state population Pjei and
purity g under the JC interaction when the qubit is
initialized in j(cid:2)Zi and the phonon in a coherent
state. (C) Illustration of the evolution of an initial
phonon coherent state (red circle on the left) in phase
space. The blue (yellow) crescent shapes indicate
the state jFþi (jF(cid:2)i), which is the phonon state when
the qubit is initialized in j þXi (j(cid:2)Xi). Interference
fringes appear around time tC when the qubit is
prepared in a superposition of jþXi and j(cid:2)Xi.
Around the revival time tR, the two phonon states
again overlap (purple).
Bild et al., Science 380, 274–278 (2023)
21 April 2023
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RES EARCH | R E S E A R C H A R T I C L E
of the atomic lattice with the same frequency
wp and relative phase p. Considering a snap-
shot in time where both oscillations are at
their displacement maximum, Schrödinger’s
cat being in a superposition of dead and alive
is analogous to a superposition of atoms in
the HBAR being in two distinct positions in
space, as illustrated in the inset of Fig. 1A.
Here, we define the positions as distinct when
their separation is larger than the fluctua-
tions due to quantum, thermal, or other sources
of noise.
Generating cat states
To realize a cat state in our system, we use the
Jaynes-Cummings (JC) interaction with the
qubit and phonon on resonance (11, 24). The in-
teraction Hamiltonian is
(cid:1)
H=ℏ ¼ g0 sþa þ s(cid:2)a†
(cid:3)
ð1Þ
(cid:1)
p
ffiffiffi
n
where g0 is the coupling strength between
qubit and phonon mode, sþ is the raising op-
erator for the qubit, and a† is the raising op-
erator for the phonon mode. This results in
Rabi oscillations between the states je; n (cid:2) 1i
p
ffiffiffi
, where jgi (jei) is the
and jg; ni at a rate g0
n
qubit ground (excited) state andjni is the Fock
state of n phonons. As a consequence of this
p
scaling, if the phonon mode is prepared in
a coherent state with large enough amplitude
and the qubit is prepared in jgi or jei, their
coherent interaction rapidly dephases. Hence,
the oscillations of the qubit population “col-
lapse” (Fig. 1B) with a decaying amplitude
(cid:3)
ð
proportional to (25, 26) exp (cid:2) t=tcollapse
,
where tcollapse ¼
=g0 is the collapse time in
the limit of a ≫ 1. At this time, the qubit and
phonon states are entangled. This can be seen
in Fig. 1B as a minimum in the qubit state pu-
rity g tð Þ ¼ Tr rq
around tcollapse, where
rq tð Þ is the reduced density matrix of the
qubit. Notably, owing to the quantized phonon
energy and the consequent discrete oscilla-
tion frequency spectrum, the oscillations revive
in finite time (24). For a ≫ 1, this revival occurs
at tR ¼ 2pa=g0 (27). Between the collapse and
revival, at time tR=2, the qubit and phonon
disentangle from each other. The state being
separable at tR=2 coincides with the occur-
rence of a superposition of two distinct states
in phase space, realizing a cat state in the pho-
non mode (11, 21, 24, 28).
ðtÞ2
ffiffiffi
2
Þ2
(cid:3)
(cid:1)
A more intuitive explanation for the origin
of the cat state comes from the time evolution
of the reduced phonon state in phase space.
As illustrated in Fig. 1C and shown in sup-
plementary text section A, if the qubit is ini-
tialized in the state TXj
and
in the limit of large a, the evolution leads to a
rotation in phase space with an angular veloc-
ity ∓ g0=2a
j and a distortion of the coherent
j
states. We call the resulting statesjFT tð Þi, whose
full expressions are given in the supplemen-
i ≡ ej i T gj i
ffiffiffi
2
Þ=
p
ð
Fig. 2. Collapse and revival
dynamics. (A) Experimental
sequence for observing collapse
and revivals dynamics and for
preparing cat states (details in the
main text). (B) Measured qubit
population and state purity. The solid
and dashed black lines are the
simulation results of the qubit
population and purity, respectively.
Three time points of particular
interest are highlighted (dashed
lines): initial state time, cat
state time (tC), and revival state
time (tR). (C) Measured Wigner
function of the phonon state at the
three time points. Axes are the
real and imaginary parts of the
complex displacement amplitude b
used during Wigner tomography
(23). The black crosses indicate the
positions of the two coherent states
composing the fitted CSS state
Eq. 2) (D) Corresponding simulated
Wigner functions.
ð
p
j(cid:2)X i
tary text (eq. S15). If the the qubit is initialized
ffiffiffi
in the state jTZi ≡ þX i T
Þ=
j
2
, the
phonon state will evolve into Fþ tð Þi T
jF(cid:2) tð Þi
j
as shown in Fig. 1C. At time tR=2, the two state
components jFTi have covered a rotation angle
of ∓p=2 around a circle of radius a, maximiz-
ing their separation in phase space and form-
ing a cat state (24). Finally, at the revival time
tR , the two phonon state components jFTi
have both rotated by a phase of p and approx-
imately recombine in phase space.
Experimental results
We experimentally confirm both the predicted
collapse and revival of Rabi oscillations and
the creation of mechanical cat states in the
phonon mode. The basic sequence used in the
experimental demonstration of the JC dynam-
ics described above can be seen in Fig. 2A. We
displace the phonon mode with a resonant
drive of amplitude A to a coherent state with
amplitude a. To mitigate any effect of the drive
on the qubit state, we then cool the qubit with
an ancillary phonon mode (22, 23). The qubit
is subsequently prepared in its initial state by
applying a drive pulse with variable phase and
amplitude. To induce the resonant interaction,
we tune the qubit to the phonon mode frequency
for a variable interaction time t. Depending
on which of the subsystems we want to char-
acterize, we choose a measurement sequence
that implements the appropriate measure-
ment operator. First, we simply measure the
qubit excited state population. The resulting
data are shown in Fig. 2B for A ¼ 0:35. Here
the value for A is a scaling factor for the am-
plitude of a microwave drive, which we cali-
brate to find a corresponding initial coherent
state size of a ¼ 1:75 (supplementary text sec-
tion E). As expected, we observe oscillations
that collapse after a time tcollapse ≈ 0:9 ms
and revive at tR ≈ 6:7 ms. This revival indicates
the coherent exchange of energy quanta between
the qubit and phonon mode during the resonant
interaction. By performing full qubit tomog-
raphy after the resonant interaction, we can
also reconstruct the reduced density matrix
of the qubit subsystem rq and calculate the
purity of the qubit state g tð Þ . We confirm a
local minimum of g tð Þ around the predicted
collapse time tcollapse, followed by a local max-
imum around tR=2 (Fig. 2B).
We now focus on the time evolution of the
phonon subsystem by performing full Wigner
tomography of the phonon state after the
resonant interaction times t = 0, 2.9 and 7.0 ms.
To this end, we use the parity measurement
technique established in a previous work (23).
To compensate for the effect of qubit dephasing
during the parity measurement, we normalize
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. Cat state amplitude
and phase control. (A) Cat
states prepared with different
displacement pulse amplitudes A.
Top row: Measured Wigner
functions; bottom row: analytical
state r tCð Þ that best fits the
data. The fitted CSS states, with
coherent state positions indicated
by black crosses, have D = 1.09
(1.43) for A = 0.25 (0.30). (B) Cat
state sizes as a function of the
displacement amplitude A, obtained
from fitting the data in (A) to
analytical states r tCð
states jCi. Numbers are the fidelity
with respect to the fitted state.
Error bars show cat state sizes
resulting in 1 % deviation in the
fidelity (supplementary text section
G) (C) Cat states resulting from
the initial qubit states indicated by
the respective labels. (D) Cross-
cuts of interference fringes from (C)
for four initial qubit states, obtained
by averaging the data between
(cid:2)0:11 < Im bð Þ < 0:16.
Þ and CSS
pected, Fig. 2D shows the results of a master
equation simulation of the full experimental
protocol with independently measured sys-
tem parameters, showing good agreement
with the measurements in Fig. 2C.
The state we obtained resembles the two-
component coherent state superpositions (CSS)
jCi ¼ N a1
(cid:1)
j
i þ eiϑ a2j
i
(cid:3)
ð2Þ
(cid:1)
(cid:3)
; jCi Ch j
a type of cat state that is often invoked in
quantum information (5, 6) and parameter
estimation protocols (3, 4). Here ja1;2i are two
coherent states and N is the appropriate nor-
malization constant. We can fit our recon-
structed state to Eq. 2 by optimizing a1 , a2,
and ϑ for maximum fidelity F rp
. Be-
cause our state is not centered around the origin
in phase space, we use half the phase space dis-
tance between the coherent state components
D ¼ a1 (cid:2) a2
j=2 as a measure of the cat state
j
size. This choice is motivated by considering a
coherent state superposition centered around
the origin in phase space, such that a1 ¼ (cid:2)a2.
ffiffiffi
, where (cid:1)n is the average
(cid:1)n
Then D ¼ a1;2
phonon population of the state created. For the
state in Fig. 2C, we obtain a state size D ¼ 1:61,
corresponding to (cid:1)n ¼ D2 ¼ 2:60, with a fidel-
ity of F ≈66%. The smaller state size D com-
pared to the initial coherent displacement is
a combination of decoherence and the choice
of interaction time tC < tR=2, resulting in the
two counter-rotating state components not
reaching their maximum separation in phase
space. The fidelity is lower compared to the
fitted analytical state r tCð
Þ itself
has a finite infidelity to the CSS state jCi.
Þ, because r tCð
(cid:5)
(cid:5) ¼
p
(cid:5)
(cid:5)
all measured parity values to that of the Fock
j0i phonon state (supplementary text section
D). The measured Wigner functions are shown
in Fig. 2C, where axes in phase space are nor-
malized by measuring the distribution of pop-
ulations in the phonon Fock states for coherent
states created with different drive amplitudes
(22) (supplementary text section E).
From the measured data, we confirm the
evolution of the initial coherent state (Fig. 2C,
left) into a cat state at tC ¼ 2:9 ms (Fig. 2C, cen-
ter), showing two state components clearly
distinct in phase space and interference fringes
located between them. We choose this value
of tC because it corresponds to the measured
maximum in the qubit state purity. It de-
viates somewhat from the value predicted by
using the large a limit, which is tR=2 ≈ 3:3 ms.
For the evolution time t ¼ 7:0 ms, the predicted
refocusing into a crescent-shaped overlap be-
tween the counter-rotating state components
can be observed (Fig. 2C, right).
To benchmark the cat state and obtain an
estimate of its size, we implement a maximum-
likelihood reconstruction (29) of the phonon
staterp from the measured state with A ¼ 0:35
and tC ¼ 2:9 ms. We then fit the reconstructed
state to an analytical expression of the expected
phonon state r tCð
Þ in the absence of decoher-
ence and after tracing out the qubit (supple-
mentary text section A). Fixing the interaction
time to tC from the experiment, the fit max-
Þ by
imizes the fidelity between rp and r tCð
varying the initial coherent state size afit of
r tCð
Þ. The result yields a fidelity of F ≈ 76%
to an analytical state with initial coherent
state size afit ¼ 1:62, which is smaller than
the initial displacement a ¼ 1:75 because the
expression for r tCð
Þ does not include phonon
losses. We attribute the infidelity to a com-
bination of decoherence and measurement
imperfections that lead to additional artifacts
in the Wigner function (23). To further con-
firm that the phonon state behaves as ex-
We can now translate the parameters of the
measured cat state into physical properties of
the phonon mode, such as the spatial separa-
tion between atoms. A state size of D ¼ 1:61
corresponds to a maximal delocalization of
7:0 (cid:3) xZPF, where xZPF is the zero point motion
of an equivalent one-dimensional (1D) quan-
tum harmonic oscillator (supplementary text
section B). Because we are not considering a
center-of-mass mode, there is some freedom in
choosing xZPF , which is then associated with
an effective oscillating mass of the mode. If we
choose the root-mean-square (RMS) value of
the atomic displacements, we find an effec-
¼ 16:2 mg, corresponding
tive mass of M RMS
to ∼1017 atoms, delocalized over a distance of
2.1 × 10−18 m (supplementary text section B).
In applications such as bosonic encodings of
a qubit state, full control over the phase and
amplitude of the created cat state is required
(5, 6, 30). In the following, we demonstrate this
level of control in our experiment. By varying
the amplitude A of the phonon displacement
drive, we can control the amplitude of the initial
coherent state and the size of the resulting cat
state. For displacement amplitudes A ¼ 0:25
and 0:30, we create cat states with D ¼ 1:09
eff
Bild et al., Science 380, 274–278 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 4. Decoherence of cat
states. (A) Measured 1D cuts
through the interference fringes
of the D ¼ 1:43 cat state for
a range of wait times between
state creation and measure-
ment. (B) Extracted negativities
(squares) from each cut versus
wait times for three cat state
sizes, together with fitted expo-
nential decays (solid lines).
Both data and fitted curves are
normalized to the fitted value
at t ¼ 0. (C) Characteristic
decay times tcat extracted from the fits in (B) for all three cat state sizes. Error bars are uncertainties extracted from the fit.
and 1:43, respectively (Fig. 3A). The fidelities
of reconstructions of the measured states to
Þ are given in Fig.
both a CSS state and r tCð
3B. The best fit r tCð
Þ is plotted in the lower
row of Fig. 3A, showing good qualitative agree-
ment with the data. As before, the finite fidel-
ities and lower-contrast fringes of the measured
Þ arise
states as compared to the best-fit r tCð
mainly from decoherence of the state during
measurement.
In the two-component cat state encoding of
a qubit, the six cardinal points of the Bloch
sphere are given by two coherent states ja1i
and ja2i, along with their four superpositions
with p=2 difference in the phase ϑ (Eq. 2). We
can prepare similar states by initializing the
transmon qubit state in all six cardinal points
jTY i; jTZi of its Bloch sphere before per-
TX i;
j
forming the cat state generation protocol. The
preparation of jTX i and jTY i is calibrated
using collapse and revival measurements as a
function of the qubit drive phase (supplemen-
tary text section A). The results for A ¼ 0:35
and tC ¼ 2:10 ms are shown in Fig. 3C. We ob-
serve a distorted coherent state located on the
upper (lower) half of phase space for the qubit
initially in jTX i. This separation in phase space
is expected from the opposite rotation directions
between the phonon states when the qubit is
prepared in jTX i (Fig. 1C). The TY i;
jTZi states
then give rise to four cat states that differ in
phase by p=2, as can be observed in the phases
of the interference fringes in Fig. 3 D. The ini-
tial energy of the qubit, and thus of the total
system, is not the same for all six scenarios,
resulting in slightly different sizes for the cat
states. In the limit of large cat state size, this
difference becomes negligible, and the pho-
non subspace maps onto that of the cat state
encoding.
j
Superposition states are nonclassical states
that are notoriously prone to decoherence. We
now investigate the quantum-to-classical tran-
sition of different-sized cat states by letting
them evolve freely for a varying wait time t
before performing Wigner tomography. Dur-
ing this evolution, the qubit is far detuned
from the phonon mode. In particular, we fo-
cus on a slice through the Wigner function’s
interference fringes at Im(b) = 0, which high-
lights the nonclassical features of the super-
position. Figure 4A shows the time evolution
of this slice for the D ¼ 1:43 cat state. We ob-
serve that the negative features disappear on a
time scale much faster than T ph
≈ 84 ms, the
1
energy relaxation time of the phonon mode.
ð
Þ
ð
Þ
ð
j(cid:2)W b; t
As a measure for the nonclassicality of the
state, we extract the-time dependent negativity
(31), defined as d tð Þ ≡ ∫ W b; t
Þdb.
ð
j
Here,W b; t
Þ is the measured Wigner function
of the cat state at time t, and the integration is
over the 1D slice in phase space parameter-
ized by the complex displacement amplitude
b. Figure 4B shows the resulting d tð Þ for the
three different cat state sizes of Fig. 3B. We
fit each dataset to an exponential decay plus
a constant offset. The offset in the measured
Wigner values arises from the fact that our
Wigner tomography is not performed in the
ideal dispersive limit (23). The extracted decay
time scales tcat are plotted in Fig. 4C. We show
in section H of the supplementary text that, in
j, d tð Þ decays exponentially
the limit of large aj
(cid:3)
(cid:1)
with a time constant tcat ¼ T ph
= 2 aj
. How-
1
j, tcat deviates from this ex-
ever, for small aj
pression and is in fact dependent on properties
of the exact state, such as the phase of the super-
position. The data in Fig. 4C show the ex-
pected qualitative behavior of faster-decaying
negativity for larger-sized cat states, and we
present a more detailed quantitative analysis
in the supplementary text (21).
j2
Concluding remarks
Our results show the generation of cat states
in a microgram-mass solid-state mechanical
mode using the tools of cQAD and pave the
way toward using such systems for tests of wave
function collapse models (32). These tests would
benefit from larger-sized cat states, resonators
with higher masses (33), and longer phonon
lifetimes. To facilitate comparison with other
mechanical resonators and theoretical models
that often consider center-of-mass motion, we
note that the HBAR mode is a standing wave
in which a half-wavelength section approxi-
mates a center-of-mass mode where all atoms
oscillate in the same direction. Such a section
has a mass on the order of 30 ng, obtained by
dividing the total effective mass of 16 mg by
the longitudinal mode number of ∼500.
The maximum size of the cat state that we
can prepare is currently limited by our device
parameters, including both the qubit and pho-
non decoherence rates. The latter is especially
important given that, in general, the decoher-
ence rate of the cat state is proportional to the
square of the cat state size D . Furthermore,
additional improvements to the properties of
qubit and phonon resonator would enable al-
ternative cat state generation protocols that
can in principle lead to states with a higher
fidelity to, for example, a CSS state (12, 13). We
point out, however, that although CSS states
represent a useful benchmark (because they
have been extensively studied for applications
such as quantum information and quantum
metrology), many of their salient features
are present already in the states that we have
demonstrated. These include the phase-space
separation of state components, which is im-
portant for error protection of encoded qubits
(30, 34, 35), and the presence of interference
fringes with high Fisher information, which is
useful for quantum-enhanced sensing (4, 36, 37).
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ACKN OWLED GMEN TS
We thank O. Romero-Isart, A. Grimm, and I. C. Rodrigues for useful
discussions, and A. Brooks for help with figure making. Fabrication
of devices was performed at the FIRST cleanroom of ETH Zürich
and the BRNC cleanroom of IBM Zürich. Funding: M.B. was
supported by the QuantERA II Program that has received funding
from the European Union’s Horizon 2020 research and innovation
program under grant agreement no 101017733, and with the Swiss
National Science Foundation. M.F. was supported by The Branco
Weiss Fellowship–Society in Science, administered by the ETH
Zürich. P.M. was supported by the ThinkSwiss fellowship. Author
contributions: U.v. L. fabricated the device. M.B., M.F., Y.Y., and
U.v. L. performed the experiments and analyzed the data. All
authors performed theoretical calculations and simulations. Y.C.
conceived of the project and supervised the work. M.B., M.F.,
Y.Y., U.v. L., and Y.C. wrote the manuscript. Competing interests:
The authors declare no competing interests. Data and materials
availability: All data and software are available in the manuscript or
the supplementary material or are deposited at Zenodo (38).
License information: Copyright © 2023 the authors, some rights
reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.sciencemag.org/about/science-licenses-
journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf7553
Supplementary Text
Figs. S1 to S8
Tables S1 and S2
References (39–46)
Submitted 10 November 2022; accepted 20 March 2023
10.1126/science.adf7553
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RES EARCH
MESOSCOPIC PHYSICS
Universal chiral Luttinger liquid behavior in a
graphene fractional quantum Hall point contact
Liam A. Cohen1†, Noah L. Samuelson1†, Taige Wang2,3, Takashi Taniguchi4, Kenji Watanabe5,
Michael P. Zaletel2,3, Andrea F. Young1*
One-dimensional conductors are described by Luttinger liquid theory, which predicts a power-law
suppression of the single-electron tunneling density of states at low voltages. The scaling exponent is
predicted to be quantized when tunneling into a single isolated chiral edge state of the fractional
quantum Hall effect. We report conductance measurements across a point contact linking integer and
fractional quantum Hall edge states (at fillings 1 and 1
the predicted universal quadratic scaling with temperature and voltage. At strong coupling, we
demonstrate perfect Andreev reflection of fractionalized quasiparticles at the point contact. We use the
strong coupling physics to realize a nearly dissipationless direct current voltage step-up transformer,
whose gain arises directly from topological fractionalization of electrical charge.
3, respectively). At weak coupling, we observe
T he Landau theory of Fermi liquids pro-
vides a near-ubiquitous description of
interacting fermion systems. One excep-
tion is provided when electrons are con-
fined to one dimension, where arbitrarily
weak interactions favor a distinct phase known
as the Tomonaga-Luttinger liquid (1–4). In this
phase, the low-energy collective excitations are
orthogonal to the single-electron operators
from which they are microscopically constructed.
This “orthogonality catastrophe” manifests
experimentally as a power-law suppression
of the electron tunneling density of states,
(cid:3)
(cid:1)
(cid:2)1
N Eð ÞºðE (cid:2) EFÞ
, at the Fermi energy EF,
even though the system remains conductive.
The power law is characterized by an ex-
ponent g known as the Luttinger parameter,
which depends continuously on the nature
and strength of the interparticle interactions
(5). Experimentally, Luttinger liquid behavior
can manifest through a non-Ohmic current-
voltage relation I Vð
ÞºV
g , as observed, for
example, in ropes of single-walled carbon
nanotubes (6, 7).
1
g
1
Chiral Luttinger liquids
An alternative means of creating a one-
dimensional (1D) wire can be found at the
boundary of a topologically ordered phase,
as occurs in the fractional quantum Hall (FQH)
effect (8). Here, the right- and left- moving
modes are physically separated to opposite
edges of the 2D sample, resulting in a chiral
Luttinger liquid in which backscattering is
suppressed entirely and the Luttinger param-
1Department of Physics, University of California at Santa
Barbara, Santa Barbara, CA 93106, USA. 2Department of
Physics, University of California, Berkeley, CA 94720, USA.
3Material Science Division, Lawrence Berkeley National
Laboratory, Berkeley, CA 94720, USA. 4International Center
for Materials Nanoarchitectonics, National Institute for
Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.
5Research Center for Functional Materials, National Institute
for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.
*Corresponding author. Email: andrea@physics.ucsb.edu
†These authors contributed equally to this work.
eter g becomes quantized (9). In this setting, g
becomes a fingerprint of the topological order
of the enclosed bulk; for example g ¼ 1
3 for the
Laughlin state at Landau level filling n ¼ 1
3
(9, 10). In such a scenario, tunneling of whole
electrons into the fractionalized edge of the
n ¼ 1
3 state is predicted to exhibit a quadratic
scaling of the tunneling conductance G ≡ dI
dV
with both the temperature T and bias voltage
V: G º T2, V2. The quadratic scaling is a direct
result of the quantized value of g ¼ 1
3, and a
central prediction of the theory is that this
behavior is universal and independent of mi-
croscopic details at sufficiently low tempera-
tures and bias voltages (9).
Experimentally, one of the most successful
tests of the chiral Luttinger liquid theory was
obtained by studying tunneling between the
edge of a 2D-electron gas (2DEG) hosting a
FQH state at n ¼ 1
3 and a 3D electrode grown
on the cleaved edge of the semiconductor
wafer (3, 11). Although striking power-law
behavior was observed over a wide range of
bias voltages and temperatures (11), the ex-
∼2:7 was found to vary across sam-
ponent 1
g
3 plateau (12, 13)—in
ples and within the n ¼ 1
disagreement with the predicted quantized
¼ 3. This sparked a thorough dis-
exponent 1
g
cussion about the nature of bulk-boundary
correspondence and whether g is indeed a
distinct imprint of the topological order of the
bulk (14–16). However, the possibility of edge
reconstruction was soon identified as a con-
founding factor that could reconcile the range
of observed exponents with the chiral Luttinger
liquid theory (17–19).
In principle, a quantum point contact be-
tween integer and fractional quantum Hall
edge states (5, 9, 10, 20, 21–23) provides a richer
test bed for chiral Luttinger liquid physics. In
this geometry, the collective modes of the
3 and n = 1 edges may be modeled as
n ¼ 1
chiral bosonic fields fa and fb, respectively,
coupled by a single point scatterer of strength
G. The low energy physics are described by
the Lagrangian
L ¼
1
4p
X
@xf
i
ð
@t (cid:2) @x
Þf
i
þ
i¼a;b
(cid:1)
(cid:3)
b
b
a
a
½
p
y
ð1Þ
(cid:3) ¼ 1
¼ ei
Gd xð Þ y†
a
½
2 whereas y
þ y†
y
b
ffiffi
¼ eifb
fa and y
where the operators y
3
3 and n = 1 edges,
remove an electron on the n ¼ 1
respectively. In Eq. 1, the first term describes
the gapless bosonic edge modes on either side
of the junction, whereas the second term de-
scribes inter-edge tunneling of electrons at the
point contact. In the language of the renor-
malization group, the scaling dimensions of
(cid:3) ¼ 3
the electron operator y
b
2
is three times larger, reflecting the topological
order of the n ¼ 1
3 fractional quantum Hall
bulk. For the corresponding 2D Euclidean ac-
(cid:3)(cid:2)
tion to remain dimensionless, G½
(cid:3) ¼ (cid:2)1, meaning that edge-to-edge tunnel-
½
y
ing is irrelevant and becomes increasingly less
important at low energies. This leads to the
conclusion that no matter how “open” the junc-
tion is made—in other words, no matter how
large the bare value of G is— the conductance
will vanish at a sufficiently low temperature
and voltage bias (24). Near this decoupled fixed
point, the conductance can be computed with-
in perturbation theory (3), giving
(cid:3) ¼ 1 (cid:2) y
½
a
a
b
Þ
(cid:5)
ð
G V ; T
e2
2h
¼
2pT
T0
(cid:6)
"
2 1
3
þ
(cid:5)
eV
2pkbT
(cid:6)
2
#
þ …
ð2Þ
for small temperatures T and voltage bias V.
Here, the bare tunneling strength is repre-
sented by T0, where for weakly coupled edges
T0º 1
G. In this limit, the power law exponent
(cid:8)
(cid:3)
(cid:7)(cid:1)
¼ 2 describing the T and V depen-
(cid:2) 1
1
g
dence provides a direct probe of the bulk topo-
logical order.
Quantum point contact experiments in semi-
conductor quantum wells have indicated power-
law behavior near the decoupled fixed point
(close to full pinch-off) over a limited temper-
ature range (25, 26); however, the presence of
disorder at the tunnel junction often compli-
cates the physical interpretation (25–31). In a
more recent experiment (32) focused on the
weak quasiparticle backscattering limit, the
conductance showed clear characteristics of a
Luttinger liquid but remained quantitatively
inconsistent with the predictions of chiral
Luttinger liquid theory: The measured value of
the Luttinger parameter g did not align with
predictions for any candidate incompressible
ground states at the filling factors studied in
(31). It appears that for both quantum point
contact and cleaved-edge overgrowth experi-
ments, nonuniversal effects arising from the de-
tailed structure of experimentally realized edges
Cohen et al., Science 382, 542–547 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Universal conductance scaling at weak coupling. (A) Optical micrograph
of the device with schematic depiction of chiral edge states. (B) Device schematic
showing the patterned top graphite layer, graphene monolayer, and global
bottom graphite gate. The tunneling conductance across the junction is
determined from the transmitted current I and diagonal voltage VD as G (cid:4) I
VD
(C) G measured as function of V at Tprobe = 56 mK, with VNS = −2.465 V
and B = 10 T. (Inset) parabolic fit to the low-V regime, giving T0 = 9.02 ±
0.007 K as defined in Eq. 2. The main panel shows G − Gmin, where
.
(cid:2)4 e2
h is the minimum conductance. Fitting a power law gives an
Gmin ¼ 7:5 (cid:5) 10
exponent of 2.00 ± 0.06 (44), where the error represents the standard
deviation in the fit parameter. (D) G measured at V = 0 as a function of
temperature at the same gate voltages as (C). The dashed line is a plot of the
conductance given by the first term of Eq. 2, using T0 = 9.02 K. (E) Nonlinear
differential conductance for Tprobe = 202, 245, 290, 344, 450, 549, 618,
and 666 mK at VNS = −2.456 V. (F) The same data as in (E) after scaling G
and V as described in the text. The black dashed line is G˜ as predicted by Eq. 2.
(22, 33, 34, 35) push the universal scaling regime
to energy scales beyond experimental reach.
Conductance scaling in graphene quantum
point contact heterojunction
Recently, graphene has emerged as a useful
platform for precision tests of chiral Luttinger
liquid physics. Notably, the low disorder avail-
able in field effect–controlled devices make a
wide range of fractional quantum Hall states
accessible (36, 37). However, prior studies of
quantum point contacts have been limited to
regimes dominated by resonant tunneling effects,
owing at least in part to disorder introduced
during the fabrication of local split gates (38–41).
We use anodic oxidation lithography to pattern
nanoscale features in graphite gates, which are
then incorporated into a van der Waals hetero-
structure to produce a clean quantum point
contact (42). A micrograph and schematic of
our device is shown in Fig. 1, A and B. 44-nm-
thick hexagonal boron nitride (hBN) dielectric
layers are used as spacers between the mono-
layer graphene layer and the top and bottom
A
)
h
/
2
e
(
G
B
V
r
V
i
C
i
V
/
r
V
1.0
0.5
0.0
-0.5
0.5
1/2
1/3
0.0
-3.4
VNS (V)
-3.0
-e*
1/3
1
2e*
e
0
-1/2
-3.4
VNS (V)
-3.0
3 on the east and west
Fig. 2. Andreev-like quasiparticle
scattering. (A) G versus VNS taken at
B = 9 T with a finite DC voltage bias of
145 µV. Here, VBG = 2.0 V, VE = −1.460 V,
and VW = −1.775 V to maintain n = 1
and n ¼ 1
sides of the junction, respectively.
(B) Schematic representation of the
Andreev scattering process for fraction-
ally charged quasiparticles in the strong
coupling limit (23) of a n ¼ 1
3 to n =
1 point heterojunction. (C) Ratio of
the reflected voltage Vr to the source
voltage Vi versus VNS; all other gate
voltages are the same as in (A).
Cohen et al., Science 382, 542–547 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. Crossover from weak to strong coupling. (A) Schematic of renormalization
group flow in the G−U plane, where U represents additional perturbations to Eq. 1.
(B) G as a function of the voltage on the north and south gates, VNS, and the DC
voltage bias V at Tprobe = 56 mK and B = 10 T. (C) Line cuts of the data in (B) at
the values of VNS indicated by the colored points. Black dashed lines are plotted using
the value of G predicted by Eq. 3 where the parameter T0 is extracted from the
low-bias conductance. (D) The zero-bias conductance also scales with temperature
in agreement with Eq. 3 for low energies. Although the data deviate from
the model at high energies, G nevertheless exceeds G ¼ e2
3h for T >> T0,
indicating strong coupling at high T. (E) The data from (D), after scaling
T by T0. The curves collapse onto the universal scaling formula Eq. 3, shown
in black.
gates. The device architecture features a four-
quadrant split gate geometry (42) where
independent voltages may be applied to the
north, south, east, and west top gates (VN, VS,
VE, and VW, respectively) as well as a global
bottom gate (VBG). With VBG held constant, VE
and VW fix the filling factors of the east and
west regions to 1 and 1
3, respectively, whereas
VNS = VN = VS is used to create a constriction by
tuning the filling of the north and south re-
gions to n ≤ 0.
The choice of VBG controls the “sharpness” of
the potential profile at the constriction, pa-
rameterized by the energy scale EV ≡ e @V
‘b.
@x
Here V, which is defined as the applied po-
tential, is purely a function of the applied
gate voltages and does not take into account
the finite compressibility of the 2DEG at a
high magnetic field. EV plays a key role in the
physics of fractional quantum Hall edges:
When the confinement energy EV is smaller
than the Coulomb energy, the edge may re-
construct (33, 43), introducing additional edge
modes which may push the universal tunneling
behavior to experimentally inaccessible energy
scales. As described in (42) and (44), the control
available in our geometry allows us to access
the universal regime of EC < EV while main-
taining independent control of the bulk filling
factor and quantum point contact transparency.
We begin by investigating the “weak coupl-
ing” regime where G ≪ e2
h . This corresponds to
the limit of eV ≪ 2pkbT0 and T ≪ T0
2p where Eq. 2
holds. We measure G ≡ I
(see Fig. 1B), which is
VD
a four-terminal measurement of the tunneling
conductance (42, 44). We tune T0 through
VNS. Figure 1C shows G measured as a func-
tion of the direct current (DC) voltage bias V at
a fixed Tprobe = 56 mK and VNS = −2.465 V. As
seen in the inset, the V dependence is well fit
by a parabola, with a curvature corresponding
to T0 = 9.02 K in Eq. 2. To assess the quality of
the power law fit, we subtract the minimum
conductance Gmin and plot G − Gmin on a
logarithmic scale (Fig. 1C). We find a simple V2
power law over one order of magnitude in V,
corresponding to two orders of magnitude in
G − Gmin. Specifically, we find an exponent of
2.00 ± 0.06. Although we have not studied the
filling factor dependence in detail, fig. S7 shows
a second measurement taken at a different
magnetic field and different value of the bulk
filling factor within the n ¼ 1
3 plateau, which
yields the same exponent (44).
We next compare experiment with the pre-
dicted zero-bias temperature dependence, G
(V = 0, T, T0) of Eq. 2. The result for T0 = 9.02 K
is shown in Fig. 1D. In contrast to the volt-
age dependence, a T2 power law is observed
only for a limited range of T, between 200 and
700 mK. We attribute deviations at lower tem-
peratures to a decoupling of the electronic tem-
perature from Tprobe. At high temperatures,
deviations are expected as corrections to Eq. 2
become important, with significant deviations
4p ≈ 750mK (44). Although
onsetting for T > T0
the power law behavior in T occurs over a lim-
ited range, the observed power law in T is con-
sistent with the more robust power law in V,
Cohen et al., Science 382, 542–547 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
which is a manifestation of a general scal-
(cid:1)
(cid:3)2⋅ h
ing relation. Defining ~G ¼ 2G⋅ T0
e2 and
(cid:1) (cid:3)
2pT
Þ, it follows that ~G ¼ 1
x ¼ eV
þ x2 þ ⋯
ð
2pkBT
provides a universal low-energy collapse.
3
Figure 1E shows G as a function of V for sev-
eral different temperatures at VNS = −2.456 V.
The same data, plotted as G̃ (x), are shown in
Fig. 1F. In these datasets, T0 = 6.87 K is de-
termined by fitting the lowest temperature
curve in Fig. 1E to Eq. 2. For low values of V
where universality is expected (44), the curves
collapse onto the universal parabolic curve
expected from chiral Luttinger liquid theory.
From weak to strong coupling
As seen in Fig. 1E, G approaches e2
2h at high bias.
One might expect that full transmission of the
incoming fractional edge mode would cause
the conductance to saturate at G ¼ e2
3h. In fact,
the observed G≈ e2
2h can be understood from the
peculiar properties of the point contact at
strong coupling, defined as eV ≫kbT0 or T ≫T0.
The strong coupling regime is accessed most
readily by lowering T0 (i.e., increasing VNS) at
fixed V and T, leading to a plateau in the dif-
ferential G≈ e2
2h (Fig. 2A).
Microscopically, the excess conductance can
be understood by analogy to Andreev scattering
at a metal-superconductor interface (22, 23, 45).
In this picture, conduction occurs when a pair
of incident quasiparticles, each with charge
e(cid:6) ¼ (cid:2) e
3, is transmuted into a single electron on
the n = 1 side through the simultaneous retro-
reflection of a charge e
3 quasi-hole into the
downstream chiral edge state (see Fig. 2B). This
process leads to the observed nearly quantized
increase in G. Moreover, when the Andreev pro-
cess is the dominant form of charge transfer
across the junction, the downstreamn ¼ 1
3 edge
hosting the retroreflected hole is expected to
develop a negative chemical potential with mag-
nitude one-half of the voltage of the incoming
edge (23, 46). Figure 2C shows the measured
reflected voltage Vr under the same conditions
as the G data in Fig. 2A. The near-quantization
of both G and Vr
over the same broad range of
Vi
junction transparency implies that the described
Andreev process completely dominates charge
transfer. This contrasts with previous experi-
ments in semiconductor wells (30), where a
much smaller effect was observed, likely me-
diated by resonant scattering.
In our discussion, we have considered only
single-electron tunneling between edges, pa-
rameterized by G; however, additional pro-
cesses such as electron co-tunneling may also
contribute, which would be represented by
additional operators not included in Eq. 1. Re-
normalization group analyses have shown (10)
that as G → 0 these terms are more irrelevant
than G. This guarantees that regardless of mi-
croscopic details Eq. 1 becomes a good approx-
imation to the physical system at sufficiently
low energies. This is characteristic of a stable
Fig. 4. Zero frequency
voltage step-up trans-
former. (A) The differen-
tial gain dVo
and resulting
dVi
integrated DC gain b ¼ dVo
,
dVi
measured in the config-
uration shown in the inset,
with B = 9 T, Tprobe =
48 mK, VE = −1.460 V,
VW = −1.775 V, VNS =
−3.225 V, VBG = 2.0 V. The
FQH Andreev scattering
process yields an
enhancement of the
output voltage on the FQH
side (46), with the DC
gain predicted to reach a
value of 1.5 in the dis-
sipationless limit. Experi-
mentally, we find a gain
b ¼ 1:46, despite the
nonlinearity at low bias
arising from the sup-
pression of the Andreev scattering at low energies. (B) The DC power dissipation ratio, calculated from b
through Pout=Pin ¼ ð2b
þ 1, is plotted versus V, and reaches a maximum value of 97.6% (49).
(cid:9) (cid:10)
Þ2 (cid:2) 2b
3
3
fixed point of the renormalization group and
accounts for the universal scaling behavior
demonstrated in Fig. 1.
A different result is obtained at strong cou-
pling, formally G → ∞, which represents an
unstable fixed point (23, 47). At this fixed point
the dominant process that transfers charge
across the junction is Andreev scattering. How-
ever, while other processes vanish when G = ∞,
giving G ¼ e2
2h, for any finite value of G, G is
expected to vanish at low energies as the sys-
tem flows toward the stable G = 0 fixed point.
This is shown schematically in Fig. 3A, which
depicts a renormalization group flow diagram
indicating the trajectory of the conductance as
the energy is lowered. In this plot, the y-axis, G,
represents the coefficient of the operator which
transfers an electron between the two edge modes,
whereas the x-axis represents the coefficient “U”
of any operator not explicitly captured in Eq. 1.
As is seen in the diagram, finite U, expected for
realistic heterojunctions, would seem incom-
patible with approaching the strong coupling
fixed point. For this reason, the strong coupling
limit was previously thought to be practically in-
accessible except through highly tuned resonant
scattering (46, 48). Although fine-tuned, this
limit would arise if the QPC forms an adiabatic
constriction in which approximate momentum
conservation along the QPC prevents backscat-
tering between the N and S edge (49).
The fact that we observe near-perfect Andreev
reflection when the junction is highly transmis-
sive suggests that the microscopics of the system
approach the strong coupling fixed point with
negligible contributions from the additional
operators represented by U. When U = 0, Eq.
1 can be mapped to an integrable “quantum
impurity model” with an exact solution for
all values of G (24, 47). The solution provides
an expression for G at arbitrary V, T, and T0,
ð
G V ; T
Þ ¼
∫∞
(cid:2)∞
e2
2h
ð
Þ2
(cid:2) 2E þ eV
Þ2 þ kbT0
ð
ð
2E þ eV
Þ2 f ′ Eð ÞdE
ð3Þ
where f(E) is the Fermi-Dirac function (47).
Equation 3 provides a universal crossover
function which describes the transition be-
tween weak and strong coupling, depicted as
a single line along the y-axis (U = 0) of Fig.
3A (22, 23, 47). The integral reduces to Eq.
2 for T0 → ∞, corresponding to the weak
coupling fixed point, and gives e2
2h for T0 = 0
corresponding to strong coupling.
Figure 3B shows G as a function of V and
VNS at a probe temperature Tprobe = 56 mK.
Throughout the plotted range, the high-V
conductance saturates to approximately e2
2h as
expected for the strong coupling fixed point.
Meanwhile, a zero-bias dip remains visible
for all VNS, indicative of the instability of the
point contact to edge decoupling at low ener-
gies. To quantify how closely the quantum im-
purity model describes our system, we compare
Eq. 3 with our experimental data as a function
of V and T, and T0. In Fig. 3C, we plot four
curves extracted for different values of VNS.
For each curve, T0 is determined from a fit to
the low bias behavior with an appropriate low-
energy expansion of Eq. 3 (44). For the largest fit
values of T0, the residual value of G when V = 0
Cohen et al., Science 382, 542–547 (2023)
3 November 2023
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RES EARCH | R E S E A R C H A R T I C L E
can then be used as a primary thermometer—in
effect allowing us to correct for a possible lack of
equilibration between the electron temper-
ature and the probe thermometer. Using this
method, we find Telectron = 91 mK for the T0 =
9.02 K trace, in contrast to the measured probe
temperature of 56 mK. Taking 91 mK as the
electron temperature for the remaining data sets
in Fig. 3C, Eq. 3 may then be used to generate V-
dependent curves interpolating between weak
and strong coupling. These curves are overlaid
in black on the experimental data in Fig. 3C.
Figure 3D shows G (V = 0, T) plotted as a
function of the probe temperature for the same
values of VNS as in Fig. 3C, along with the
results of Eq. 3 for the corresponding values of
T0. Although Eq. 3 does not provide a simple
scaling between temperature and voltage as is
available at the weak coupling fixed point, for
V = 0 the conductance can be written as a
function of the scaled temperature, T
. Figure
T0
3E shows the V = 0 conductance plotted as a
function of T
. The four data sets shown in
T0
unscaled form in Fig. 3E collapse onto different
parts of the universal crossover function be-
tween weak and strong coupling. Note that for
Fig. 3, D and E, the temperature is measured
on the probe and no corrections are made for
disequilibrium between Telectron and Tprobe,
leading to systematic deviations between
experiment and theory at the lowest tempera-
tures. The collapse of the experimental data
onto a single universal curve over nearly two
orders of magnitude in T0 strongly supports
the conclusion that our quantum point contact
realizes the exactly solvable Lagrangian of Eq.
1 to a high degree of accuracy, and in particular,
that tunneling predominantly occurs through a
single point at the QPC rather than by multiple
disorder-induced scattering centers.
Near-dissipationless step-up transformer
At the strong coupling fixed point the quantum
point contact acts as a nearly dissipationless
splitter, partitioning current injected on the n =
1 edge equally between the downstream n ¼ 1
3
and the upstream n = 1 edge states (23). For G =
∞, the partitioning happens with unit proba-
bility. In this limit, no entropy is generated and
dissipation does not occur, leading to unity
power efficiency (46). This contrasts with the
more conventional case of partial transmission
of edge modes at a quantum point contact,
where fluctuations arising from partition noise
lead to dissipation. The dissipationless current
splitting property of the strong coupling fixed
point allows us to operate our device as a
voltage step-up transformer (23, 46). Figure 4
shows the differential gain, dVo
, where Vi is the
dVi
input voltage applied to the upstream n = 1 edge
state and Vo is the output voltage measured on
the downstream n ¼ 1
3 edge state with all other
contacts grounded. The differential gain is very
close to the theoretically expected value of 3
2
(46). Because it is built on a purely zero fre-
quency effect, the transformer gain remains al-
most the same even in the “direct current” (DC)
limit, as can be seen in the behavior of the
integrated gain, Vo
, in comparison to its differ-
Vi
ential counterpart. The exceptionally high power
efficiency, which peaks at 97.6%, is a testament
to how closely the experiment realizes the
strong-coupling fixed point and contrasts fa-
vorably with zero frequency voltage amplifi-
cation based on superconductors (50, 51) and
bilayer quantum Hall systems (49, 51).
Discussion and outlook
Our observation of universal chiral Luttinger
liquid physics at both weak and strong coupl-
ing directly paves the way for experiments on
two dimensional systems where mesoscopic
electrostatic control plays a key role in address-
ing unanswered questions about strong cor-
relations, topological order, and quantum
statistics. Examples include even denominator
fractional quantum Hall states observed in
mono- (52, 53) and bilayer (38, 54, 55) gra-
phene, where taming edge reconstruction in a
quantum point contact may allow for un-
ambiguous experimental constraints on the
ground state topological order (45, 56–59).
In addition, the flexibility inherent in anodic
oxidation prepatterning will allow independent
tuning of quasiparticle number, edge sharp-
ness, and quantum point contact transparency
in interferometer geometries where direct
access to quantum statistics is possible (60, 61).
Finally, gate-defined point contacts may allow
for precision measurements of order parame-
ters in the recently discovered crystalline
graphene superconductors (62–64).
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AC KNOWLED GME NTS
The authors acknowledge discussions with B. L. Halperin, C. Nayak,
and C. Kane, and A. Assouline and A. M. Potts for helpful comments
on the manuscript. Funding: Work at UCSB was primarily
supported by the Air Force Office of Scientific Research under
award FA9560-20-1-0208 and by the Gordon and Betty Moore
Foundation EPIQS program under award GBMF9471. L.C. and N.S.
received additional support from the Army Research Office under
award W911NF20-1-0082. T.W. and M.Z. were supported by the
Director, Office of Science, Office of Basic Energy Sciences,
Cohen et al., Science 382, 542–547 (2023)
3 November 2023
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RES EARCH | R E S E A R C H A R T I C L E
Materials Sciences and Engineering Division of the US Department
of Energy under contract no. DE-AC02-05-CH11231 (van der Waals
heterostructures program, KCWF16). M.Z. received additional
support from the Army Research Office through the MURI program
(grant number W911NF-17-1-0323) K.W. and T.T. acknowledge
support from JSPS KAKENHI (Grant Numbers 19H05790,
20H00354 and 21H05233). Author contributions: L.A.C. and
N.L.S. fabricated the device and performed the measurements.
L.A.C., N.L.S., M.P.Z., T.W., and A.F.Y. analyzed the data and
wrote the paper. T.T. and K.W. synthesized the hBN crystals.
Competing interests: A.F.Y. is a board member of sp2 quantum.
L.A.C. and A.F.Y. are inventors on the patent application PCT/
US23/14059, which is related to this work. Data and materials
availability: All of the experimental data presented and code for
generating the figures from the datasets are available in a public
Zenodo repository (65). License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.sciencemag.org/about/
science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf9728
Materials and Methods
Supplementary Text
Figs. S1 to S10
Reference (66)
Submitted 29 November 2022; resubmitted 17 December 2022
Accepted 29 September 2023
10.1126/science.adf9728
Cohen et al., Science 382, 542–547 (2023)
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RES EARCH
CHROMATIN BIOPHYSICS
Stochastic motion and transcriptional dynamics of
pairs of distal DNA loci on a compacted chromosome
David B. Brückner1†, Hongtao Chen2,3†, Lev Barinov3,4, Benjamin Zoller5,6, Thomas Gregor3,5,6*
Chromosomes in the eukaryotic nucleus are highly compacted. However, for many functional
processes, including transcription initiation, the pairwise motion of distal chromosomal elements
such as enhancers and promoters is essential and necessitates dynamic fluidity. Here, we used
a live-imaging assay to simultaneously measure the positions of pairs of enhancers and promoters and
their transcriptional output while systematically varying the genomic separation between these two
DNA loci. Our analysis reveals the coexistence of a compact globular organization and fast subdiffusive
dynamics. These combined features cause an anomalous scaling of polymer relaxation times with
genomic separation leading to long-ranged correlations. Thus, encounter times of DNA loci are much
less dependent on genomic distance than predicted by existing polymer models, with potential
consequences for eukaryotic gene expression.
L iving systems are built based on informa-
tion encoded in chromosomes confined
in each cell’s nucleus. These meter-long
DNA polymers must be highly compacted
to fit into the micrometer-sized structure
(1, 2). At the same time, for cells to function,
chromosome organization must allow the in-
formation content to be accessed and read out
through transcription (3, 4). Often, transcrip-
tion can only occur through the spatial inter-
action of DNA loci such as enhancers and
promoters, which find each other dynamically
and remain in physical proximity (5–8). Al-
though the distances over which many en-
hancers function in higher eukaryotes can
be up to mega–base pairs in genomic separa-
tion (9–12), it is unknown how these elements
come into proximity, what their typical dis-
tance is in three-dimensional (3D) space, and
how they explore this space dynamically in the
process. Specifically, it remains unclear how
the real-time physical motion of such coupled
pairs of DNA loci determines transcriptional
encounters and how this depends on their
genomic separation.
Over the past decade, the advent of chromo-
some capture and imaging methods (13) has
given key insights into the 3D spatial orga-
nization of chromosomes, with the discovery
of structural features such as topologically
associating domains (TADs) (14–17), phase-
separated nuclear condensates (18–20), and
larger-scale compartments (21, 22). These or-
1Institute of Science and Technology, Am Campus 1,
Klosterneuburg, Austria. 2School of Life Science and
Technology, ShanghaiTech University, Shanghai, China.
3Lewis-Sigler Institute for Integrative Genomics, Princeton
University, Princeton, NJ, USA. 4Memorial Sloan Kettering
Cancer Center, New York, NY, USA. 5Joseph Henry
Laboratories of Physics, Princeton University, Princeton, NJ,
USA. 6Department of Developmental and Stem Cell Biology,
CNRS UMR3738 Paris Cité, Institut Pasteur, Paris, France.
*Corresponding author. Email: tg2@princeton.edu
†These authors contributed equally to this work.
ganizing structures have key implications for
transcriptional regulation (23), but they are
not static. Rather, they have been revealed to
be heterogeneous across cells (24, 25) and dy-
namic and short lived in time (26, 27). The role
of the real-time dynamics of pairs of loci is
only beginning to be understood and remains
elusive for focal contacts that are key to es-
tablishing enhancer–promoter interactions in
many systems (28).
Similarly, from a polymer physics perspec-
tive, there is a gap in our understanding of the
static and dynamic properties of chromosomes.
At large scales, across tens to hundreds of
TADs, chromosome organization has been
shown to be highly compacted in a space-filling
configuration (22, 29, 30). A useful null model
for this configuration is the crumpled chain
(also referred to as fractal globule) with fractal
dimension three (22, 31–33). However, the
real-time dynamics of DNA loci revealed by
live-imaging experiments exhibit subdiffu-
sion with exponents in the range of 0.5 to 0.6
(26, 27, 34–36), close to the predictions of the
simple Rouse polymer model, which predicts a
loosely packed ideal chain polymer configura-
tion with fractal dimension two that is in
contrast to the compacted architecture of the
crumpled chain model. A promising technique
to address this gap are scaling approaches that
combine fractal organization and subdiffusive
dynamics (37–39), but these have never been
tested experimentally.
Thus far, experimental datasets have given
insight into static organization (14–17, 22, 30, 40),
dynamic properties of chromosomes (26, 27,
34, 35, 41), or transcription (8, 36, 42–44), but
rarely all at the same time. For instance, pre-
vious live measurements of locus pairs occurred
at fixed genomic separation in transcription-
ally silent loci (26, 27). To investigate how 3D
spatial organization and dynamic locus mo-
tion control the encounter times of functional
DNA loci and thus transcriptional activation,
we require an approach to simultaneously
monitor the movement of DNA locus pairs
and transcription across a series of genomic
separations in vivo.
Here, we addressed this problem by live im-
aging the joint dynamics of two cis-regulatory
DNA elements, an enhancer and a promoter,
while monitoring the transcriptional output
resulting from their functional dynamic en-
counters in developing fly embryos. We sys-
tematically varied the genomic separation
between these loci spanning many TADs.
Stochastic real-time trajectories of the 3D
motion of the two loci showed a dynamic
search process, with physical proximity re-
quired for successful transcription and a
power-law scaling of transcription probability
with genomic separation. Although typical 3D
distances between the locus pair follow a com-
pact packing consistent with the crumpled
chain model, the dynamic properties exhibit
fast diffusion, albeit with a diffusion coeffi-
cient that increases with genomic separation.
These features give rise to an anomalous
scaling of polymer relaxation times and long-
range correlations in the relative motion of the
two loci. This suggests that the enhancer-
promoter search process is much less depen-
dent on genomic separation than expected
based on existing polymer models.
Results
Live imaging of chromosome dynamics
and transcription
To simultaneously monitor the coupled mo-
tion of enhancer-promoter pairs and trans-
cription across multiple genomic separations,
we generated fly lines in which a reporter gene
was introduced at various genomic locations
from the well-studied Drosophila even-skipped
(eve) locus (8). The locations of both the endo-
genous eve enhancers and the promoter of the
reporter gene, as well as the transcriptional
activity of the reporter gene, were measured
together using a three-color imaging system
(see the materials and methods, section 1.2,
and Fig. 1A) (8). To facilitate transcription, the
reporter cassette contained the insulator ele-
ment homie, which allowed stable loop forma-
tion with the endogenous homie element in
the eve locus (Fig. 1B).
We built seven such reporter constructs,
with genomic separations s varying over close
to two orders of magnitude from 58 kb to
3.3 Mb, comparable to the distances over
which many enhancers function in higher
eukaryotes (see the materials and methods,
section 1.1) (9–12). These genomic length
scales span across multiple TADs in the Dro-
sophila genome, with typical median TAD
sizes of ~90 kb (45) (here, 18 kb for the eve
locus).
Imaging took place for ~30 min during
the second half of nuclear cycle 14 (NC14) of
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Fig. 1. Simultaneous tracking of DNA loci and transcriptional activity in
living embryos. (A) Typical surface view of a representative fly embryo
displaying fluorescent foci for MS2, parS, and PP7 in the corresponding blue
(top), green (center), and red (bottom) channels. Top inset shows schematic
with image location in the embryo; bottom inset shows a close-up. (B) Top:
schematic of the gene cassettes used for three-color imaging. The endogenous
eve locus (left) is tagged with MS2 stem loops that are labeled with blue
fluorescence. A reporter with an eve promoter driving PP7 transcription (labeled
with red fluorescence) is integrated at a genomic separation s from the eve
locus on the second chromosome in the Drosophila genome. It includes a homie
insulator sequence allowing loop formation through homie-homie pairing and
a parS sequence that is permanently labeled with green fluorescence. Seven such
constructs were generated with varying genomic separation s (triangles).
Bottom: sample interlocus distance trajectories R(t) for six genomic separations,
with standardized y-axis limits (0, 2 mm) and x-axis limits (0, 30 min) obtained
after nucleus and locus segmentation, tracking, chromatic aberration, and
motion correction (see the materials and methods, section 1). The sampling time
interval is 28 s. (C) Trajectories of interlocus distance R and transcriptional
activity, with inferred topological states shown by the colored top bar (blue,
Ooff; cyan, Poff; red, Pon; see the materials and methods, section 2). Inset:
schematic of the three topological states. (D) 200 examples of state trajectories
sampled from a total set of N = 579 trajectories acquired in n = 30 embryos
(genomic separation s = 149 kb). Colors are as in (C). Gray trajectory parts
correspond to untrackable time points.
embryo development (Fig. 1C), well after the
completion of DNA replication. Sister chro-
matids are tightly coupled together at inter-
vals <10 kb (46). Therefore, our two tagged
DNA loci are connected by a single chromatin
polymer composed of two coupled chromatids
that were not resolved by our microscopy.
Accordingly, our measurements are associ-
ated with increased localization uncertainty
and reflect both intra- and interchromosomal
interactions, which may not be fully represen-
tative of pure intrachromosomal interactions.
Interlocus distance scaling suggests a
space-filling organization
In previous work using a single fixed genomic
distance (s = 149 kb) (8), this system was
shown to exhibit three topological states (Fig.
1C): an open configuration, Ooff, in which the
homie elements are not bound to each other,
and two paired configurations, Poff and Pon,
in which a loop is formed with either inac-
tive or active transcription, respectively. As-
suming that these configurations apply to all
genomic distances, we determined the in-
stantaneous topological and transcriptional
states of the system. To this end, we used an
inference approach with a hidden Markov
model that is based on the time series of inter-
locus distances and transcriptional activity
(see the materials and methods, section 2).
We assigned one of these states to each mea-
sured configuration, including the hidden Poff
state (Fig. 1D).
A key question is how the interlocus dis-
tances R in the open configuration Ooff vary
with the linear genomic separation s. These
distances exhibit broad distributions, which
shift systematically with larger separation
(Fig. 2A). From a polymer physics perspec-
tive, the mean distance hRi is expected to
scale as s1/d, where d is the fractal dimension.
Whereas an ideal chain polymer, as predicted
by the simple Rouse model, has fractal dimen-
sion d = 2, the compact crumpled chain or-
ganization has dimension d = 3 (33, 47). Our
experiments show a scaling exponent of 1/d =
0.31 ± 0.07 for genomic separations up to s =
190 kb, consistent with the crumpled chain
model (Fig. 2B). The smaller-than-expected
average distances observed for the largest sep-
arations (s = 595 kb, 3.3 Mb) are most likely
affected by the average folding of the chromo-
some (48).
The distances of the paired configurations
were independent of genomic separation, as
anticipated, and exhibited typical distances of
350 to 400 nm (Fig. 2B), consistent with pre-
vious measurements of distances within the
eve locus (8, 49). Together, these results re-
veal a compact crumpled chain architecture
of chromosome configurations in a range of
genomic separations consistent with Hi-C ex-
periments in Drosophila (17).
Transcriptional activity scales with
genomic separation
From the latent state trajectories revealed by
our inference approach, we estimated the sur-
vival curves of the transcriptionally active
state (see the materials and methods, section
2.4, and Fig. 2C). We found a median tran-
scriptional lifetime independent of genomic
separation of 10 ± 5 min (SD across separa-
tions; Fig. 2D). This corresponds to about three
to five independent rounds of transcription on
average, given the typical promoter switch-
ing correlation time of the system (50). Sim-
ilarly, the relative proportion of transcriptionally
active states within the paired subpopulation
is insensitive to genomic separation (Fig. 2E).
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Fig. 2. Scaling of interlocus distances and transcriptional activity across
genomic separations. (A) Probability distributions of the interlocus distances
R. Distributions are separated by state, with paired states pooled across genomic
separations, and individual distributions are shown for the open state.
(B) Average interlocus distances hRi for each of the three transcriptional states.
Blue dashed line indicates a linear best fit to the Ooff data for the range of
genomic separations 58 to 190 kb, with exponent 1/d = 0.31 ± 0.07. Dashed cyan
and red lines are average values of the interlocus distances of the Poff and
Pon states, respectively, with shaded areas indicating SEM. Solid dark green and
red lines indicate predictions for ideal and crumpled polymers, respectively.
(C) Survival curves S(t) of the transcriptionally active state Pon, giving the
probability that transcription remains active after time t. Orange curve: data
for no-homie constructs (s = 58 kb). Curves were estimated using the
Kaplan-Meier estimator, which accounts for censoring that occurs if the
trajectory begins or ends in the transcriptionally active state (81). Shaded
areas show 95% confidence intervals (see the materials and methods,
section 2.4). (D) Median lifetime of the transcriptionally active state Pon as a
function of genomic separation using the Kaplan-Meier estimator (dots) and a
maximum-likelihood estimator assuming exponential decay of the survival
curves (triangles) (see the materials and methods, section 2.4). (E) Probability
of the paired on and off states conditioned on the system being in one of
these two paired configurations. (F) Overall probability of the paired
configurations Poff and Pon as a function of genomic separation. Gray line is
the best fit with exponent 0.9 ± 0.2. Green and dark red lines indicate predicted
exponents for the contact probabilities of the ideal and crumpled chain
polymer models, respectively.
By contrast, the overall probability of observ-
ing either of the paired configurations decreases
with genomic separation and exhibits a power-
law scaling P(s) ~ s–f, with f = 0.9 ± 0.2 (Fig.
2F). Because transcriptional lifetimes are in-
dependent of distance, the scaling of P(s) is
likely dominated by the search of the two loci
to come into contact. Different polymer mod-
els make distinct predictions of the scaling
of contact probabilities (22, 33, 51). For ideal
chains, f = 3/2, whereas crumpled chains ex-
hibit f ≈ 1.15 (52), which is close to the scaling
that we observed.
To determine how these results depend on
the nature of the homie insulator–mediated
focal contacts in our system, we used a re-
porter construct in which the homie sequence
was replaced by a l DNA sequence of the same
length. At a 58-kb separation, transcriptional
encounters still occur, albeit with a shorter
median lifetime of 4.9 ± 1.2 min (Fig. 2C and
fig. S13). Furthermore, the probability of observ-
ing a transcriptional state was reduced from
(30 ± 5)% for the homie version to (8.5 ± 0.8)%
in the no-homie version. By contrast, very few
such encounters were found for a 149-kb no-
homie separation (8), where contact probabil-
ity decreases from (6 ± 1)% to >1% when the
homie sequence was replaced by a l DNA.
Together, these results demonstrate quanti-
tatively how both genomic sequence and geno-
mic separation control the rate of transcriptional
encounters. The scaling of transcription prob-
abilities with separation suggests that the
transition from the open to the paired config-
uration is a key limiting step in transcriptional
activation of distal DNA loci, which is limited
by the time taken to diffuse into proximity.
Characterizing the subdiffusive locus
search process
To understand these diffusive timescales, we
considered the real-time dynamics of the blue-
and green-labeled DNA loci. We found that
the majority of single-cell trajectories sampled
the whole range of physical distances in each
topological state, because they showed a simi-
lar spread as the ensemble-averaged distri-
bution (Fig. 3, A to C, and fig. S8). Thus, rather
than existing in constrained configurations
as observed in other genomic contexts (41),
this observation supports the picture of a dy-
namic search process exploring a broad range
of distances.
Þ (cid:2) ri t0ð ÞÞ2it0
We quantified how this search process is
reflected in the motion of individual DNA loci
by computing the single-locus MSD M1 tð Þ ¼
hðri t0 þ t
¼ Gtb , where ri(t) is
ð
the 3D position of the locus, G is diffusivity,
and b is the dynamic exponent. This expo-
nent quantifies how locus diffusion scales with
time and can be related theoretically to the
packing of the chromosome through the frac-
tal dimension d: b = 2/(2 + d) (37, 39, 53).
Although the ideal chain model predicts b =
1/2 (54), we expected b = 2/5 for a crumpled
polymer (37). Our system showed a scaling
exponent of b = 0.52 ± 0.04 across genomic
separations (error bar: SD calculated from
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total variance across separations) for both the
endogenous eve locus (blue) and the ectopic
reporter (green), which is close to the predic-
tion of the ideal chain model and consistent
with previous works (26, 27, 35) (see the mate-
rials and methods, section 3, and Fig. 3, D and
E). Our data further indicate that the single-
locus dynamics are not affected by transcrip-
tional activity, unlike previous accounts (43),
because they were consistent across the three
topological states (Fig. 3F).
ð
To further understand how the locus dynamics
are determined by the interplay of chromosome
organization and single-locus dynamics, we an-
alyzed the joint dynamics of the two coupled
chromosomal loci. From the statistics of the 3D
distance vector R(t), we computed the two-
Þ (cid:2) R t0ð ÞÞ2it0
locus MSD M2 tð Þ ¼ hðR t0 þ t
(26), which quantifies the crossover between
two intuitive regimes. Whereas at small time
lags, the MSD is determined by the indepen-
dent diffusion of the two loci [M2(t) = 2Gtb],
it exhibits a crossover to a plateau at large
times, given by the average squared interlo-
cus distance [M2(t) = 2hR2i] (see the ma-
terials and methods, section 5, and Fig. 4, A
and B). Consistent with the observed single-
locus dynamics, we found that the subdiffu-
sive regime of the experimental two-locus
MSD exhibited an exponent close to 1/2 for
those datasets in which this regime was sam-
pled (Fig. 4A and fig. S16). Similarly, for large
time lags, the two-locus autocorrelation re-
vealed agreement with the ideal chain scal-
ing (Fig. 4, C and D). Thus, the full time
dependence of the MSD is well described by
the ideal chain predictions, both for single
and coupled loci.
Interlocus relaxation times exhibit an anomalous
scaling with genomic separation
Having established the static and dynamic
properties of the system, we next investigated
the consequences of these features for the time-
scales of the two-locus search process. This
process is determined by the interplay of chro-
mosome dynamics and organization and can
be characterized by a relaxation time t, which
corresponds to the timescale of the crossover
of the two regimes of the two-locus MSD (Fig.
2A). Specifically, t is the time taken by the two
loci to diffuse (dynamics) over their typical dis-
tance of separation (organization): Gtb ~ s2/d.
This relationship predicts a scaling of relax-
ation times with genomic separation t ~ sg.
For ideal chains with fractal dimension d = 2
and a diffusion exponent b = 1/2, this yields
the classical result g = 2. By contrast, for crum-
pled chains, b = 2/5 and d = 3, yielding g = 5/3
(see the materials and methods, section 5,
and table S7).
To infer the relaxation time in our data as a
function of genomic separation, we performed
a Bayesian fitting of the two-locus MSD with
Fig. 3. Dynamics of DNA locus search and single-locus fluctuations. (A) Single-cell interlocus
distance trajectories for the three topological states (s = 149 kb). For each state, 80 trajectories are
shown, with one sample trajectory highlighted in bold. (B) Distance distributions (bar histogram) of
the highlighted trajectory in (C) compared with the ensemble distribution obtained by averaging over all
cells (line). (C) Single-cell interlocus distance distributions (thin lines) of all trajectories for the three
states compared with ensemble distributions in bold (s = 149 kb). Distributions are smoothed using
Gaussian kernel density estimation with a width of 100 nm. Only trajectories with at least 10 time points
are included to ensure sufficient statistics for comparison. (D) Single-locus MSDs for all genomic
separations (color code corresponds to Fig. 2A). Single-locus MSDs were calculated by estimating 3D
MSDs from motion-corrected trajectories in the x-y plane of the system (see the materials and methods,
section 3). Open data points correspond to a shorter imaging time interval Dt = 5.4 s (s = 149 kb).
(E) Single-locus MSDs comparing enhancer (blue) and promoter (green) fluctuations (s = 149 kb).
(F) Single-locus MSDs comparing fluctuations in the three states (s = 149 kb).
the ideal chain expression (26) (see the mate-
rials and methods, section 4.1). We found that
the fitted two-locus diffusion coefficient in-
creased with genomic separation up to 595 kb,
with an approximate scaling G(s) ~ s0.27 ± 0.03
(Fig. 4E). This scaling appeared to plateau for
the largest genomic separation (3.3 Mb) at a
value close to the single-locus diffusion, which
remained approximately constant across separa-
tions (Fig. 4E). The absolute value of the diffu-
sivity at the plateau was almost 20-fold larger
than previous measurements in mammalian
stem cells with similar genomic separation (26),
suggesting comparatively fast chromosome dy-
namics (fig. S23).
The relaxation time was determined by com-
bining our estimate of the two-locus diffusivity
with the average interlocus distances. The com-
bination of static and dynamic exponents in
our system, as well as the scale-dependent dif-
fusivity, results in an anomalous scaling of
relaxation times with genomic separation with
an exponent g = 0.7 ± 0.2 (Fig. 4F). This ex-
ponent corresponds to a much shallower scal-
ing with separation than predicted by either
the ideal or crumpled chain theory. This result
was further confirmed by a data collapse of the
two-locus autocorrelation functions (Fig. 4D
and fig. S20). Although these results are de-
rived from the trajectories in the Ooff state,
they are insensitive to the details of the state
inference (fig. S11). In sum, the key result here
is that the relaxation time, which sets the time-
scale of two-locus encounters, is much less de-
pendent on genomic separation than predicted
by existing polymer models.
Anomalous relaxation time scaling induces
long-ranged velocity correlations
ð
Þit0
t0 þ t
tð Þ ¼ hv dð Þ
The anomalous relaxation time scaling makes
a key prediction for the correlations of the ab-
solute motion of DNA loci, quantified by the
velocity cross-correlation C dð Þ
t0ð Þ(cid:3)
vv
v dð Þ
. These correlations are deter-
j
mined by the relaxation time through the
dimensionless ratio d/t, where d is the exper-
imental observation timescale (Fig. 4G) (55).
Having determined the relaxation times t,
one can therefore make a parameter-free
prediction of the correlations, which decay
i
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ð
Þi
t0
Fig. 4. Joint dynamics of DNA locus pairs. (A) Ideal
chain Rouse prediction of the two-locus MSD M2(t) =
2Gt1/2(1 – e–t/pt) + 2J erfc[(t/pt)1/2] (26) (gray line) using
best-fit values G, J, b = 1/2, and t = (J/G)2, compared
with experiment (s = 595 kb). Green and red lines
give expected scaling tb for t ≪ t for the generalized
Rouse model for ideal and crumpled chains, respectively
(see the materials and methods, section 5). (B) All
experimental two-locus MSDs with relaxation times
(dashed lines) and expected asymptotes 2hR2i
(solid lines; color code corresponds to Fig. 2A).
(C) Scaling of the diffusion coefficients G from two-locus
MSD fits (black dots) compared with single-locus
diffusion coefficients obtained from single-locus MSDs
(Fig. 3, F to H). Dashed line is the best fit to two-locus
diffusivity with exponent 0.27 ± 0.03 (s = 58 to
595 kb); solid lines are the average value of single-
locus diffusivities; shaded area shows SE calculated from
total variance across separations. (D) Two-locus auto-
correlation function (ACF) C2 tð Þ ¼ hR t0ð Þ(cid:3) R t0 þ t
¼
hR2i (cid:2) M2 tð Þ=2 (gray) compared with data (s = 149 kb).
Green and red curves indicate the power-law exponent
l = 2(1 – d)/(2 + d) of the correlation function C2(t) ~ tl
for ideal and crumpled chains for t ≫ t, respectively
(39). (E) Collapsed correlations C2 ~ C2(ts–g)/hR2i with
g = 0.7. Inset: raw correlations C2(t) for varying
genomic separation. Open data points correspond to
data obtained with a higher sampling rate. (F) Scaling
of inferred relaxation times compared with predicted
ideal and crumpled chain exponents. Gray line is
the best fit with exponent g = 0.7 ± 0.2. (G) Predicted
velocity cross-correlation functions C dð Þ
hv dð Þ
Þi
t0
dimensionless ratio d/t (55). Velocities are calculated
on a time interval d as v(d)(t) = [x(t + d) – x(t)]/d.
(H) Scaling of the zero-time velocity cross-correlation
intercept normalized by the zero-time autocorrelation,
vv 0ð Þ=C dð Þ
C dð Þ
v 0ð Þ, for the Ooff (blue) and Pon (red) states;
d = 300 s. Green line is the prediction based on ideal
chain Rouse scaling of the relaxation times (g = 2) with an
intercept determined based on the 58-kb data point; gray
line is the parameter-free prediction using the inferred anomalous relaxation time scaling (g ≈ 0.7) (see the materials and methods, section 4.3); dashed red line is the
average correlation in the Pon state.
vv
for increasing values of the
t0ð Þ (cid:3) v dð Þ
ð
t0 þ t
tð Þ ¼
i
j
substantially more slowly than for the ideal
Rouse model (see the materials and methods,
section 4.3, and Fig. 4H, green and gray lines).
We found that the experimental correlations
were quantitatively captured by this parameter-
free prediction (Fig. 4H), including the full
time dependence of the correlations (fig. S22).
This demonstrates that the anomalous relaxa-
tion time scaling indeed leads to long-range
velocity cross-correlations of chromosomal
loci, pointing toward potential long-range
interactions.
Discussion
We developed an experimental approach to
perform in vivo imaging of the joint dynam-
ics of enhancer-promoter pairs with varying
genomic separation and simultaneous moni-
toring of their transcriptional output. Observ-
ing the dynamics of pairs of DNA loci has only
become possible recently and has been done
for tagged DNA loci at a single fixed genomic
separation (8, 26, 27, 36). Here, we show how
imaging across genomic separations gives
insight into the relative motion, dynamic
encounters, and transcriptional activation
of such loci.
Many features of the two-locus dynamics,
including the subdiffusive exponent close to
0.5, are very well conserved with measure-
ments of CTCF sites at TAD boundaries in
mammalian systems (26, 27), despite CTCF
not being essential for Drosophila embryo-
genesis (56). In absolute numbers, however,
our measurements revealed large diffusion
coefficients of DNA loci that are ~20-fold
larger than in mammalian cells (26) (fig. S23).
Early fly development follows a tight sched-
ule, suggesting that the chromosome dynam-
ics may have evolved to operate on much
faster timescales than mammalian systems.
By contrast, the median lifetime of focal con-
tacts in our system of 12 ± 5 min is well within
the range of typical CTCF loop lifetimes of
10 to 30 min in mammalian cells (26, 27). These
timescales facilitate transcriptional lifetimes
of 10 ± 5 min in our system, which in the ab-
sence of the homie insulator are reduced to
4.9 ± 1.2 min (Fig. 2C and fig. S13), highlighting
the importance of focal elements for contact
formation in Drosophila.
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To initiate such transcriptional encoun-
ters, the two loci perform a search process to
reach physical proximity. The timescale of this
search process is given by the lifetimes of the
unpaired Ooff state, which depends on multi-
ple factors. These factors typically include the
landscape of the search process (57, 58), the
biochemical binding properties of the focal
elements when proximity has been reached
(59), and the correlation time of the system
(i.e., the relaxation time). Indeed, we found
that lifetimes increased with the relaxation
times and were ~10 times larger on average
(fig. S19).
We have demonstrated how key features of
our system, tight crumpled chain packing, sub-
diffusion with exponent 0.5, and a separation-
dependent two-locus diffusivity, lead to relaxation
times that are much less dependent on genomic
separation than predicted by existing polymer
models. Indeed, for an ideal Rouse polymer,
the relaxation time for our largest genomic
separation (3.3 Mb) would be ~3000 times
longer than for the shortest 58-kb separation.
Our measurements, however, revealed that it
only takes ~20 times longer, corresponding
to a >100-fold reduction. This reduced depen-
dence on distance implies that transcriptional
encounters are possible across large genomic
distances, allowing enhancers dispersed across
the chromosome to find their target promoter
efficiently. This might be one of the reasons
that evolution can act on distal sequences
from a given target promoter. Overall, our find-
ings have crucial implications for the spatio-
temporal organization of the cell nucleus,
including the dynamics of long-range focal con-
tacts (28) and mammalian enhancer-promoter
interactions (9–12, 44).
From a polymer physics perspective, our
measured exponents suggest that the rela-
tionship between static and dynamic prop-
erties in the generalized Rouse framework,
which relies on the assumption of local fric-
tion, does not apply to chromosomes. This
implies that long-range interactions such as
hydrodynamics or active motor-mediated
interactions (60, 61) could play a role. Indeed,
the simplest polymer model that relaxes the
Rouse assumption and includes long-range
hydrodynamic interactions, the Zimm mod-
el (54), predicts a scaling relationship of re-
laxation times with genomic separations with
an exponent of g = 1 (table S7), which is close
to our measured value of g ≈ 0.7. Furthermore,
the observed separation-dependent diffusivity
points to additional interactions or heteroge-
neities along the polymer. Such heterogeneities
could be caused by a number of processes,
such as cross-linking (41), out-of-equilibrium
activity (61), entanglements (62), or the pres-
ence of condensates (18–20). Together, these
processes may orchestrate the anomalous
scaling of relaxation times with genomic sep-
aration. In future work, the mechanistic un-
derpinnings of our findings should be tested
using polymer simulations (40, 41, 51, 63–69) to
generate hypotheses for new sets of experiments.
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AC KNOWLED GME NTS
We thank R. Evearers, L. Giorgetti, A. Grosberg, S. Grosse-Holz,
M. Levo, L. Mirny, A. Rosa, V. Scolari, A. Spakowitz, and G. Tkacik
for helpful comments and discussion; K. Bystricky for introducing
us to the ParB/parS system; and F. Payre and P. Valenti for
sharing the ParB-eGFP plasmid and the parS sequence. Funding:
This work was supported in part by the U.S. National Science
Foundation, the Center for the Physics of Biological Function (grant
PHY-1734030), and the National Institutes of Health (grants
R01GM097275, U01DA047730, and U01DK127429). D.B.B. was
supported by the NOMIS Foundation as a fellow and by an EMBO
postdoctoral fellowship (ALTF 343-2022). H.C. was supported
by a Charles H. Revson Biomedical Science Fellowship. Author
contributions: H.C. and T.G. designed the experiments. H.C. and
L.B. performed the experiments and analyzed the images. D.B.B.
and B.Z. analyzed the data. D.B.B. and T.G. interpreted the
data. D.B.B., B.Z., and T.G. wrote the manuscript. Competing
interests: The authors declare no competing interests. Data
and materials availability: The code and software used in this
study (70) and the raw trajectory data (71) are freely available
through Zenodo. License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf5568
Materials and Methods
Figs. S1 to S23
Tables S1 to S8
References (72–86)
Movies S1 to S7
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
dependent spatial organization of a gene locus. arXiv:2012.
15819 [q-bio.MN] (2020).
Submitted 29 October 2022; accepted 31 May 2023
10.1126/science.adf5568
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RES EARCH
SENSATION
PIEZO2 and perineal mechanosensation are essential
for sexual function
Ruby M. Lam1,2, Lars J. von Buchholtz3, Melanie Falgairolle1, Jennifer Osborne1, Eleni Frangos1,
M. Rocio Servin-Vences4, Maximilian Nagel1, Minh Q. Nguyen3, Monessha Jayabalan1, Dimah Saade5,
Ardem Patapoutian4, Carsten G. Bönnemann5, Nicholas J. P. Ryba3, Alexander T. Chesler1,5*
Despite the potential importance of genital mechanosensation for sexual reproduction, little is known
about how perineal touch influences mating. We explored how mechanosensation affords exquisite
awareness of the genitals and controls reproduction in mice and humans. Using genetic strategies and in
vivo functional imaging, we demonstrated that the mechanosensitive ion channel PIEZO2 (piezo-type
mechanosensitive ion channel component 2) is necessary for behavioral sensitivity to perineal touch.
PIEZO2 function is needed for triggering a touch-evoked erection reflex and successful mating in both
male and female mice. Humans with complete loss of PIEZO2 function have genital hyposensitivity and
experience no direct pleasure from gentle touch or vibration. Together, our results help explain how
perineal mechanoreceptors detect the gentlest of stimuli and trigger physiologically important sexual
responses, thus providing a platform for exploring the sensory basis of sexual pleasure and its
relationship to affective touch.
S exual reproduction is a fundamental
driver for animal behavior, and adap-
tations required for courtship, including
sexual ornamentation and ritual dis-
plays, are cornerstones of evolutionary
theory (1–3). Visual, auditory, and olfactory
cues promote mating in various mammalian
species (4–8); however, the act of copulation
itself can be considered a specialized form of
touch endowed with its own cortical field (9).
Although the discovery of the mechanically
gated ion-channel PIEZO2 (piezo-type mecha-
nosensitive ion channel component 2) (10) has
spurred remarkable progress in our under-
standing of discriminative touch (11, 12), far
less is known about mechanosensation in
the genitals (13, 14), including how it triggers
physiological responses and elicits pleasure.
We hypothesized that sexual touch might
exhibit unusual response specialization to con-
trol mating and provide affective and mo-
tivational feedback. We also expected that
there would be sexual dimorphism both in
sensation and in responses triggered by genital-
innervating mechanosensors. To test these
hypotheses, we developed a series of behav-
ioral and functional imaging assays to probe
the role of PIEZO2 in genital mechanosen-
sation and sexual function. In addition, by
exploring the impact of PIEZO2 loss of func-
tion caused by a rare inherited syndrome, we
1National Center for Complementary and Integrative Health
(NCCIH), Bethesda, MD 20892, USA. 2Brown-National Institutes
of Health Graduate Partnerships Program, Brown University,
Providence, RI 02912, USA. 3National Institute of Dental
and Craniofacial Research, Bethesda, MD 20892, USA. 4Howard
Hughes Medical Institute, Department of Neuroscience, Dorris
Neuroscience Center, The Scripps Research Institute, La Jolla,
CA 92037, USA. 5National Institute of Neurological Disorders and
Stroke, Bethesda, MD 20892, USA.
*Corresponding author. Email: alexander.chesler@nih.gov
determined how these findings relate to hu-
man sexual experience.
Unusual sensitivity and PIEZO2 dependence
of perineal touch
A standard touch sensitivity test uses cal-
ibrated von Frey filaments to measure detec-
tion threshold. In mice, von Frey sensitivity of
the glabrous hind-paw and hairy skin of the
face have similar withdrawal thresholds (15–17)
despite very different patterns of innervation
(18). We adapted this assay to compare stim-
ulation of the perineum (the region extend-
ing from the anus to the genitals in male and
female mice) with that of the plantar surface
of the paw. In the hind-paw assay, mice res-
pond by withdrawing the paw with no indi-
cation of pain or distress. Our data (Fig. 1A)
match literature reports, with filaments ≥0.4 g
eliciting responses in the majority of trials, but
filaments ≤0.16 g rarely provoking reaction
(15, 17). By contrast, stimulation of the peri-
neum evoked a highly stereotyped startle and
investigative response (movie S1) both in male
and female mice. Even the finest filament avail-
able (0.008 g) elicited this reaction from every
animal (Fig. 1B), demonstrating exquisite sensi-
tivity of the perineum to forces below those that
reliably trigger responses from other sites, even
in mice with profound allodynia (15, 17); female
mice were marginally but consistently more
sensitive than males (Fig. 1B).
The mechanically activated ion channel
PIEZO2 is essential for discriminative touch
in mice and humans (11, 12). We anticipated
that this mechanoreceptor would also be re-
sponsible for the sensitivity of the perineum.
Piezo2-null mice die as neonates (19); therefore,
we generated conditional genetic deletions using
a Hoxb8-Cre line (Piezo2Hoxb8) to target cells
below the mid-thoracic region (17). We used
this strategy to assess the role of PIEZO2 in
perigenital sensation and observed profound
loss of behavioral response to von Frey fila-
ments (Fig. 1C), with the highest force tested
(1.4 g) eliciting responses in only ~40% of trials
(movie S1). Local inhibition of the perineum
with lidocaine attenuated von Frey responses
of controls (fig. S1), and Piezo2Hoxb8 responses to
noxious mechanical pinprick were indistinguish-
able from those of controls (Fig. 1C and movie
S1). Therefore, the Piezo2Hoxb8 deficit is likely
to be sensory rather than related to a move-
ment disorder (20). These experiments dem-
onstrated that PIEZO2 is crucial for triggering
behavioral responses to the gentlest of peri-
genital touch in mice; without this touch re-
ceptor, von Frey stimulation of the genital
region rarely elicited responses even at inten-
sities considered noxious.
We previously studied a rare cohort of peo-
ple with biallelic loss-of-function variants of
PIEZO2 who have sensory deficits fully con-
sistent with those described in animal models
(11, 21). In our clinical interviews, five adult hu-
man subjects with PIEZO2-deficiency syndrome
(three male and two female) reported severe
hyposensitivity in genital sensation (table S1);
however, comprehensive quantitative testing
has not been possible. One individual adult
male consented to quantitative sensory testing
of his genitalia during clinical evaluation. His
penile von Frey detection threshold (3.1 ± 1.5 g)
was far higher than values reported in the litera-
ture: 0.3 to 0.6 g in a similar location (22). He
had difficulty detecting pressure below 1 kg/cm2
at the midshaft and was insensitive to strong
vibration at 50 and 100 Hz, which is consistent
with our findings in mice. By contrast, litera-
ture values for penile fine-touch pressure
thresholds in a range of healthy men are far
lower (23), and vibration is normally readily
detected (23).
Anatomy of perineal neurons
Somatosensory neurons in the lower body have
soma in lumbar (L1 to L6) and sacral (S1 to S4)
dorsal root ganglia (DRG) (24). However, few
details about the types or sensitivity of neurons
that target the genitals are known. Multicolor
cholera toxin subunit-b (CTB) tracing from both
hind-paw and genitals robustly labeled neurons
in S1 and S2 DRG (fig. S2A) and distinguished
neurons that target perigenital subregions
(Fig. 1, D and E). Injections to the perineum,
prepuce, and glans (male mice) or vaginal open-
ing (female mice) resulted in largely nonover-
lapping labeling of neurons with a range of
cell diameters (Fig. 1D and fig. S2B). In both
sexes, dense projections targeted the (L6 to
S2) spinal cord, with perineal neurons (Fig. 1,
D and E, cyan) synapsing in the touch recip-
ient zone (25) of the lateral dorsal horn (Fig. 1E
and fig. S2C). Neurons innervating male pre-
puce (Fig. 1, D and E, yellow) projected to a
Lam et al., Science 381, 906–910 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
medial portion of the touch zone (Fig. 1E),
whereas glans axons (Fig. 1, D and E, magenta)
terminated proximal to the central canal (Fig.
1E). In females, axons from the vaginal opening
targeted the medial dorsal horn, whereas those
from the prepuce, which includes the clitoris,
closely resembled those from the glans in males.
To visualize the peripheral anatomy of touch
neurons in the perineum, we generated mice
in which Piezo2-expressing neurons were se-
lectively labeled by crossing a Piezo2-Cre allele
(26) into a neural-specific Snap25-LSL-GFP re-
porter line (27). Green fluorescent protein
(GFP) staining of cleared skin demonstrated
that the perineum was densely innervated
with lanceolate and circumferential endings
surrounding hair follicles (Fig. 1F), which is
consistent with innervation by a broad range
of low-threshold mechanosensory neurons
(LTMRs) and the PIEZO2-dependent behav-
ioral sensitivity of mice to perineal touch.
Perineal sensory neurons exhibit high
sensitivity to punctate stimulation
We developed a sacral ganglia imaging prep-
aration to compare neural responses to a range
of gentle and intense mechanical stimuli (28)
applied to the hind-paw and perineum (fig. S3
and movie S2). Neurons innervating paw gla-
brous skin divided into LTMRs and high-
threshold mechanosensory neurons (HTMRs)
on the basis of their response selectivity (Fig.
2A; fig. S3; and supplementary materials, mate-
rials and methods). HTMRs that innervate the
paw outnumbered LTMRs by a factor of 2. In
particular, LTMRs exhibited graded von Frey
sensitivity (Fig. 2A and fig. S3D) and could be
activated by forces as low as 0.008 g, whereas
HTMRs were essentially silent at forces below
0.4 g, matching behavioral withdrawal thresh-
old and implicating HTMRs in this response.
By contrast, perineal sensation was dominated
by LTMRs, with ~60% of mechanosensory neu-
rons responding to gentle stimuli (Fig. 2B and
figs. S3 and S4) and broad similarity between
male and female mice (fig. S4). Almost all per-
ineal mechanosensors could be activated by
von Frey stimulation (Fig. 2B, figs. S3, S4), and
their calcium (GCaMP) signals were markedly
stronger than for paw-innervating neurons
(fig. S3D). Few HTMRs responded to the fine
filaments that reliably evoked behavioral re-
sponses (Fig. 1B and movie S1). Therefore, both
male and female mice are attuned to perineal
LTMR input, and the stereotyped reaction to
genital touch is not a sign of pain.
A broad role for PIEZO2 in perineal sensation
To measure the contribution of PIEZO2 to
perigenital touch and to dissect the mecha-
nism underlying the extreme sensitivity to
von Frey stimulation, we next used the sacral
imaging platform to selectively image cells
that lack this stretch-gated ion channel (fig. S4D).
Fig. 1. Behavioral sensitivity of mice to perineal touch and underlying anatomy. (A to C) Reaction of
mice to punctate touch (A) wild-type hind-paw, (B) wild-type perineum, and (C) Piezo2Hoxb8 perineum. (Left)
Example responses for individual mice (points and thin lines; four males and four females) and mean
(solid lines) to a series of calibrated von Frey filaments (grams, each tested 10 times per mouse). (Middle)
Quantitation of von Frey threshold (≥5/10; n = 12 males and 12 females). Thresholds are different between all
three groups [one-way analysis of variance (ANOVA) on ranks P < 0.001]. Wild-type females exhibited a lower
perineal touch threshold than that of males (Mann-Whitney t test; P < 0.0001); there were no significant
differences in other responses (supplementary materials, statistical reporting). (D and E) Triple-color
retrograde CTB tracing from the perineum (cyan), prepuce (yellow), and glans (magenta) showing (D) cell
bodies of lumbar-sacral sensory neurons in the DRG and (E) termini in the dorsal spinal cord. The dotted
line indicates approximate extent of dorsal horn. In (E) and (F), n = 4 mice. Scale bars, 100 mm. (F) Anatomy
of sensory ending of Piezo2-expressing sensory neurons in the perineum. (Inset) A magnified view of a
single hair (boxed) highlighting prominent lanceolate and circumferential endings (n = 2 males and 1 female).
Scale bar, 50 mm.
As expected, deletion of Piezo2 (Piezo2cKO) dra-
matically affected the mechanosensitivity of
genital-innervating neurons. The great major-
ity of responses to air puff, vibration, and brush
were eliminated. Thus, mechanosensory neu-
rons were only stimulated by pinch and were
almost exclusively HTMRs (fig. S4E). The overall
number of HTMRs was similar between wild-
type and Piezo2cKO mice (fig. S4F), which is
consistent with earlier studies (17, 20, 21).
Piezo2cKO mice responses to von Frey stim-
ulation were substantially reduced and reca-
pitulated those of control perineal HTMRs
(Fig. 2, C to E). These results likely explain the
absence of behavioral reactions to von Frey
stimulation in Piezo2Hoxb8 mice (Fig. 1C), sup-
port the hypothesis that perineal LTMRs drive
this characteristic withdrawal in wild-type mice
(movie S1), and are consistent with human re-
ports and sensory testing (table S1).
A subset of touch neurons is required for
mechanically induced erection responses
Perineal investigation and touch precedes
mating in many species, including mice (29).
These behaviors are linked to motivational
drive in both partners and trigger physiological
reflexes. For example, gentle retraction of the
prepuce induces penile cupping (erection) and
flipping (ejaculation) in spinalized rodents (30).
We reasoned that mechanosensory input drives
the erection reflex and developed an assay to
monitor this in restrained awake mice. A soft,
transparent tube was used to gently retract
the prepuce, allowing the physiological erec-
tion reflex (extension of the penis into the tube)
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A
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Air puff Brush Vibration Pinch
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Fig. 2. Functional characterization of perineal mechanoreceptors and role of PIEZO2. (A to C) Heatmaps
representing calcium (GCaMP6f) responses to (left) repetitive application of naturalistic stimuli and
(right) graded von Frey stimulation. LTMRs and HTMRs are separated, and relative fluorescence changes
(DF/F) are colored as indicated. Scale bar, 10 s. (A) Wild-type hind-paw, n = 4 mice. (B) Wild-type perineum,
n = 4 mice. (C) Piezo2cKO perineum, n = 6 mice. Additional analysis is provided in figs. S3 and S4. (D) Spatial
activity maps of control and Piezo2cKO neurons to von Frey filaments. Scale indicates response intensity.
Scale bar, 100 mm. (E) Quantitation of von Frey responsive neurons in control mice (gray), Piezo2cKO mice
(red), and response profile of control HTMRs (black) (mean ± SEM, n = 8 control mice, n = 6 Piezo2cKO
mice). Piezo2cKO mice had fewer von Frey responsive neurons at all filament strengths (Mann Whitney U test;
P < 0.0087).
to be scored. Wild-type controls responded in
almost every single trial (Fig. 3A); isoflurane
anesthesia completely eliminated responses,
and local numbing of the perineum with lido-
caine greatly dampened the reflex (fig. S5).
As we anticipated, Piezo2Hoxb8 mice only very
rarely exhibited penile extension in response
to prepuce retraction (Fig. 3A).
Piezo2Hoxb8 mice exhibit broad loss of touch
but also have proprioceptive (and potentially
other mechanosensory) deficits (17, 28). There-
fore, we examined mice with more selective
Piezo2 deletions. Piezo2Pvalb mice (in which
Piezo2 is inactivated by using parvalbumin-
driven Cre) lack proprioceptive input but still
respond to gentle touch (20). These mice had
perfectly normal responses to prepuce retrac-
tion (Fig. 3A) despite severe ataxia. We also
generated Piezo2 deletions using an Scn10a-
Cre line, which is commonly used to target a
broad range of nociceptors, including HTMRs
(31). Perineal HTMR responses are PIEZO2
independent (Fig. 2 and fig. S4); therefore,
these mice (Piezo2Scn10a) were predicted to have
normal proprioception, touch, and consequently
erection reflexes. Piezo2Scn10a mice walked with
normal gait, and recombination of Scn10a-Cre
in sacral ganglia neurons was faithful (Fig. 3, B
and C, and fig. S6A), with only a few large-
diameter Scn10a-negative LTMRs labeled (fig.
S6A). Nonetheless, Piezo2Scn10a mice displayed
severe deficits in their erection reflex, closely
recapitulating the phenotype of Piezo2Hoxb8
animals (Fig. 3A) and the effects of lidocaine
(fig. S5A). Single-cell sequencing data from
lumbar DRG (32) and trigeminal neurons (33)
validate Scn10a as a robust marker for noci-
ceptors but reveal expression in c-fiber LTMRs
(cLTMRs). We used in situ hybridization (ISH)
to confirm coexpression of Scn10a, the cLTMR
marker Tyrosine hydroxylase (Th) (24), and
Piezo2 in sacral ganglia (Fig. 3C), with only
very limited recombination in other potential
LTMRs (fig. S6A). Because cLTMR responses
to gentle mechanical stimulation depend on
Piezo2 expression (34), these data strongly sug-
gest a causal role for perineal cLTMR input in
triggering the erection reflex. Consistent with
this hypothesis, tdTomato–positive lanceolate
endings (typical of cLTMRs) surround perineal
hair follicles in Scn10a-Cre, Ai9 mice (Fig. 3D).
Moreover, functional imaging of perineal touch
responses in Scn10a-Cre, Ai95 mice revealed
that neurons responding to gentle mechanical
stimuli (fig. S6, B and C) had uniform small
diameters, as would be expected for cLTMRs
(24, 34).
Severely impaired sexual function in mice
lacking PIEZO2
Loss of a touch-induced erection response in
Piezo2Hoxb8 males should impair mating. In-
deed, 10 pairs of mating-age Piezo2Hoxb8 males
and females housed together for 6 months
never produced pups, whereas wild-type (C57Bl/6)
controls delivered 61 litters in this time (range,
five to seven litters per pair). To assess copula-
tory success more directly, we also examined
the frequency of vaginal plug formation after
introducing virgin females in estrus to single
housed males; to eliminate bias from prior ex-
perience, all mice were naïve. For C57Bl/6 mice,
7 from 10 homozygous pairings had plugs after
4 hours (Fig. 3E). By contrast, plugs were never
seen for Piezo2Hoxb8 male mice when paired
either with Piezo2Hoxb8 or wild-type females (Fig.
3E). As predicted from their normal erection re-
flexes, Piezo2Pvalb males successfully mated with
C57Bl/6 females despite severe ataxia (Fig. 3E).
However, Piezo2Scn10a males failed to plug re-
ceptive C57Bl/6 females, substantiating the
importance of PIEZO2-dependent mechano-
sensory input for male mating behavior (Fig.
3E). Although loss of erection reflexes may
explain why Piezo2Hoxb8 mice fail to breed,
mechanosensation probably has additional
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roles in mating. For example, female mice have
similar PIEZO2-dependent perineal mechano-
sensitivity to males (fig. S4) and are even more
sensitive to perigenital touch (Fig. 1); Piezo2Hoxb8
females exhibited strong mating deficits when
paired with wild-type males: 9 from 10 remained
unplugged after 4 hours (Fig. 3E).
Ethogram analysis of female intruder assays
(Fig. 3F) assess motivation by quantifying
stereotyped male behaviors, including partner-
grooming, anogenital chemosensory investi-
gation, and mounting attempts (35, 36). We
analyzed behavior for 1 hour after introduction
of receptive females (supplementary materials,
materials and methods). Control animals ex-
hibited considerable variation in mating be-
havior (Fig. 3F) but in every case (n = 10 pairs
of mice) engaged in chemosensory investiga-
tion and mounting attempts shortly after in-
troduction of the female. Similarly, pairs of
Piezo2Hoxb8 males and females (n = 10 pairs)
(Fig. 3F) as well as male or female Piezo2Hoxb8
mice paired with C57Bl/6 partners (n = 10 pairs
in each case) (fig. S5B) exhibited strong sexually
motivated behavior, not very different from
controls. However, Piezo2Hoxb8 males never
achieved intromission, which was regularly
observed in wild-type controls. Similarly,
Piezo2Scn10a males paired with receptive C57Bl/6
females showed normal sexual motivation
(n = 10 males and 10 females) (fig. S5B) but
without copulatory success (Fig. 3E). Moreover,
Piezo2Hoxb8 females paired with C57Bl/6 males
also engaged in premating behavior, including
male mounting attempts (fig. S5B), but Piezo2Hoxb8
females adopted a sit-rejection posture, pre-
venting intromission (37). These data show
that mechanosensation plays a substantial
role in productive mating and exposes dimor-
phic need for PIEZO2 and gentle touch in
sexual function.
Impact of PIEZO2 in human sexual experience
The genital sensation of a man with complete
loss of PIEZO2 function and comprehensive
touch- and proprioception-related studies of
individuals with PIEZO2-deficiency syndrome
(11, 21) demonstrate strongly conserved roles
for PIEZO2 in mammalian mechanosensation.
For humans, sexual experience is not simply
related to reproduction but is central to large
parts of many people’s social lives and behav-
ior. Information from human clinical evalua-
tions (n = 5; three men and two women) (table
S1) provided several consistent themes about
the role of gentle touch in sex. First, these in-
dividuals with biallelic loss of function (table
S1A) had diagnostic clinical presentation, with
loss of proprioception, absent vibration sensing,
highly elevated touch threshold, and scoliosis
but no cognitive difficulties, and all underwent
puberty without clinically relevant problems.
Second, all five people with PIEZO2 deficiency
reported being sexually active and able to be
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Fig. 3. A role for PIEZO2-dependent perineal mechanosensation in mating. (A) Physiological responses
of male mice to perineal stimulation with transparent soft tubing. Penile protrusion was scored for two sets of
10 trials. Bars indicate mean ± SEM, and points indicate individual responses. Control versus Piezo2Hoxb8
mice and Piezo2Pvalb versus Piezo2Scn10a mice were different (Mann-Whitney U test; P < 0.0001; n = 18
control mice; n = 10 Piezo2-deleted mice). (B) Representative whole-mount ISH of sacral ganglion showing
faithful recombination [tdTomato (TdT); magenta] of Scn10a-Cre mouse in Scn10a (green) neurons; >90%
(670 of 738) TdT cells expressed Scn10a (n = 3 ganglia). Scale bar, 50 mm. (C) Example ISH of sacral
ganglion section probed for Th (magenta), Scn10a (green), and Piezo2 (cyan), illustrating expression of
Scn10a and Piezo2 in cLTMRs identified with Th (n = 6 ganglia). Scale bar, 50 mm. (D) Anatomy of sensory
ending of Scn10a-expressing sensory neurons in the perineum (maximum projection, full-stack). (Right)
Magnified and focal views of single hairs (boxed at left), highlighting lanceolate endings of Scn10a-Cre–
labeled neurons (n = 2 male mice). (E) Successful mating scored by vaginal plugs (n = 10 mice). Differences
are significant for C57Bl/6 versus Piezo2Hoxb8 mice (P = 0.0031) and Piezo2Pvalb versus Piezo2Scn10a mice
(P = 0.0325) (Fisher’s exact test, two-tailed). (Right) Mating success for female and male Piezo2Hoxb8
mice with C57Bl/6 partners. (F) Representative ethogram plots showing sexual motivation of three isogenic
pairings of C57Bl/6 and 3 Piezo2Hoxb8 mice: social interaction (gray), anogenital investigation (pale blue),
and mounting attempts (red).
aroused by physical genital stimulation, erotic
thoughts, or videos, reflecting motivation seen
in Piezo2Hoxb8 mice (Fig. 3F). Third, individuals
with PIEZO2 deficiency reported delayed, at-
tenuated, or absent physiological responses to
gentle genital stimulation. This included clinical
diagnosis of hypo-orgasmia for the male and
anorgasmia for the female participants, which
again is consistent with the animal model. How-
ever, the five people had strategies to compen-
sate for deficits in genital sensation (table S1B).
Discussion
Erogenous touch conveys different meanings
according to circumstance; however, many key
details remain unknown. We explored how de-
ficits in PIEZO2-dependent mechanosensation
interfere with perigenital sensation, physiolog-
ical response, copulation, and reproduction. Our
results demonstrate that PIEZO2-dependent
touch is required for all of these in mice.
Anatomical studies have identified specialized
corpuscles composed of myelinated afferents
likely involved in genital sensation (38, 39). Our
data strongly implicate an additional type of
touch neuron, the perineal cLTMRs, as crucial
drivers of sexual function. Previous studies in
mice and humans suggest specialized roles for
cLTMRs in conveying affective and pleasur-
able touch (40, 41). Thus, it is of note that five
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individuals without PIEZO2 function described
sexual activity as satisfying and rewarding
despite marked mechanosensory deficits and
clinical evaluations of hypo-orgasmia (men)
and anorgasmia (women). We have previously
shown that for humans, other types of sensory
input can compensate for deficits caused by
loss of PIEZO2 function (11). For example,
these individuals use vision to overcome pro-
prioceptive deficits and mechanonociception
or thermosensation to mitigate deficits in touch
(11). This is also true for human sexual touch
(table S1). Nonetheless, the crucial role of
PIEZO2 for perineal touch in mice and hu-
mans may have therapeutic potential: Topical
PIEZO2 inhibitors could provide targeted re-
lief of genital hypersensitivity and pain, whereas
agonists of PIEZO2 are candidates for alleviat-
ing genital hyposensitivity.
There are a number of limitations to this work.
For example, PIEZO2 deficiency is extremely
rare, and we were unable to carry out detailed
quantitative sensory testing in a larger group
of human subjects. Additionally, functional
imaging experiments were carried out in anes-
thetized mice, precluding evaluation of re-
sponses during mating. Moreover, although
we showed the necessity of gentle touch input
for mating, we have not yet demonstrated the
sufficiency of this sensory pathway for sexual
function in awake behaving animals. We also
anticipate that there are likely to be additional
specialized roles for mechanosensory neurons
in mating that were not revealed in this study.
Even the very gentlest of perineal touches
elicits a highly stereotyped startle reaction from
mice that is easy to anthropomorphize (movie
S1). This PIEZO2-dependent response is quite
different from touch to other parts of the body,
which typically evokes more modest reactions
and does so only at much greater forces. PIEZO2-
dependent perineal touch is also a crucial driver
of successful mating both for male and female
mice. Future studies should help define addi-
tional subtypes of sensory neurons needed for
sexually dimorphic reactions and how peri-
genital sensation is organized in the spinal cord
and brain to prioritize salience. Ultimately, how-
ever, the profound impact of PIEZO2 deficiency
that we describe provides a sensory basis at the
molecular and cellular level for an aspect of life
that throughout history has engaged in human
imagination (42) and thought (1).
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AC KNOWLED GME NTS
We thank T. Delong, M. Singh, and M. Bradson for distributing
questionnaires to human subjects and collating clinical notes;
members of the clinical staff at NCCIH and Bönnemann groups for
support in arranging human studies; and M. Szczot, N. Ghitani,
D. Macdonald, and R. Hardy for input and expertise with animal
experiments. Hormone analysis was carried out by the University
of Virginia Center for Research in Reproduction Ligand Assay
and Analysis Core. Funding: This work was supported by the
National Institutes of Health, NCCIH Z01-ZIAAT000028 (to A.T.C.);
National Institutes of Health, NIDCR Z01-ZIADE000561 (to
N.J.P.R.); National Institutes of Health, NINDS Z01-ZIANS003129
(to C.G.B.); and the Howard Hughes Medical Institute (to A.P.)
Author contributions: Conceptualization: R.M.L., N.J.P.R., and
A.T.C. Methodology: R.M.L., M.F., L.J.v.B., E.F., C.G.B., N.J.P.R., and
A.T.C. Investigation: R.M.L., M.F., J.O., E.F., M.R.S.-V., M.N., M.Q.N.,
M.J., and D.S. Funding acquisition: A.P., C.G.B., N.J.P.R., and
A.T.C. Supervision: A.P., C.G.B., N.J.P.R., and A.T.C. Writing – original
draft: R.M.L., L.J.v.B., N.J.P.R., and A.T.C. Writing – review and
editing: R.M.L., M.F., L.J.v.B., E.F., A.P., C.G.B., N.J.P.R., and A.T.C.
Competing interests: The authors declare that they have no
competing interests. Data and materials availability: All data
generated and/or analyzed during the current study are provided in
the supplementary materials and/or have been deposited in
Dryad. License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government works.
https://www.science.org/about/science-licenses-journal-article-
reuse. This article is subject to HHMI’s Open Access to Publications
policy. HHMI lab heads have previously granted a nonexclusive
CC BY 4.0 license to the public and a sublicensable license to HHMI
in their research articles. Pursuant to those licenses, the author-
accepted manuscript (AAM) of this article can be made freely
available under a CC BY 4.0 license immediately upon publication.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg0144
Materials and Methods
Figs. S1 to S7
Table S1
References (43–46)
Movies S1 and S2
Submitted 27 November 2022; accepted 13 July 2023
10.1126/science.adg0144
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leaf microbiota ecology
Martin Schäfer†, Alan R. Pacheco†, Rahel Künzler, Miriam Bortfeld-Miller, Christopher M. Field,
Evangelia Vayena, Vassily Hatzimanikatis, Julia A. Vorholt*
INTRODUCTION: Microbiome composition is
tied to host health and ecosystem function.
However, the processes that determine spe-
cies abundances in an environmental context
remain poorly understood. Given that micro-
biomes are bounded by resource availability,
insights into the metabolic capacities of their
constituent organisms present a key avenue
for predicting interspecies interactions and
broader microbiome assembly rules.
Plants constitute the largest biomass on
Earth and are colonized by a variety of micro-
organisms that affect their health and growth.
The composition of plant microbiomes has
been found to be largely deterministic, sug-
gesting the presence of defined drivers of
community assembly. However, the metabolic
mechanisms of the interactions underlying
these patterns remain poorly understood.
RATIONALE: To assess the degree to which pat-
terns of resource allocation contribute to micro-
bial interactions, we first profiled the carbon
source–utilization capabilities of 224 represen-
tative bacterial strains isolated from leaves of
wild Arabidopsis thaliana plants. To do this,
we cultivated each isolate on 45 different carbon
sources and developed a computational tool
to score the growth of each strain in an auto-
mated way. This screen allowed us to calculate
the degree of metabolic niche overlap between
the strains, which informed predictions of re-
source competition on the plant host. We further
leveraged this experimental data to generate
a collection of 224 genome-scale metabolic mod-
els, which encompass the metabolic networks of
each organism. We used these models to predict
the outcomes of interspecies interactions on
the plant host and to obtain mechanistic in-
sight into specific patterns of resource use and
exchange between these bacteria.
RESULTS: We found that the carbon source–
utilization profiles of the strains exhibited a
strong phylogenetic signature, on the basis of
both the experimental screen and the path-
ways represented in the genome-scale models.
We validated the performance of the models
and of predictions based on niche overlap by
conducting competition experiments with two
sets of strains on the Arabidopsis host. These
experiments revealed a dominance of negative
interaction outcomes (i.e., a strain reached a
lower overall population level upon cocoloni-
zation compared with monoassociation), which
was in agreement with predictions of high
interstrain niche overlap. The genome-scale
models provided an additional degree of
insight into these interactions, also correctly
predicting instances of positive outcomes
observed in planta and further underscoring
the importance of carbon metabolism to com-
munity assembly. After this experimental
validation, we modeled interaction outcomes
for more than 17,500 pairs of strains. We
predicted that in 94% of pairings, at least one
strain would experience a reduction in abun-
dance compared with monoassociation. We
then analyzed the metabolic fluxes underlying
these predicted outcomes, which revealed a
high prevalence of competition for sugars.
This competition could be offset by increased
uptake of amino and organic acids in our
simulations, which points to the metabolic
mechanisms underpinning the positive inter-
action outcomes that we observed in planta.
CONCLUSION: Our results indicate a major role
for carbon source availability and metabolic
interactions in community assembly in the
plant host, which, together with the trait con-
servation observed here, likely contribute to
the overall deterministic outcomes of plant
microbiome assembly. In addition to recapi-
tulating interspecies interactions in situ, our
modeling framework represents a powerful
tool for determining the metabolic mecha-
nisms that lead to the emergence of specific
ecological patterns. This knowledge will ulti-
mately enable targeted microbiome design,
which is pivotal to microbiome applications
in health, agriculture, and the environment.▪
The list of author affiliations is available in the full article online.
*Corresponding author. Email: jvorholt@ethz.ch
†These authors contributed equally to this work.
Cite this article as M. Schäfer et al., Science 381, eadf5121
(2023). DOI: 10.1126/science.adf5121
READ THE FULL ARTICLE AT
https://doi.org/10.1126/science.adf5121
Carbon utilization profiles of leaf
bacterial strains
45 carbon sources
224 strains
Metabolic niche overlap
and genome-scale models
Predicted pairwise and community
interaction outcomes
Experimental
validation in planta
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Interaction types
23%
46%
2%
3%
1%
25%
Growth
No growth
with strain or community B
Negative
Positive
Competitive
Parasitic
Amensal
Commensal
Mutualistic
Neutral
Modeling of metabolic interactions predicts ecological outcomes for leaf microbiota members in situ. We mapped the resource-use capabilities of 224
representative bacterial strains of the A. thaliana leaf microbiome by testing their ability to grow on 45 different carbon sources. These data allowed us to predict
interaction outcomes between these strains using genome-scale models and metrics of niche overlap. Experimental validation in planta underscored the importance
of resource competition and suggested metabolic mechanisms underlying specific interaction outcomes.
Schäfer et al., Science 381, 42 (2023)
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◥
MICROBIAL ECOLOGY
Metabolic interaction models recapitulate
leaf microbiota ecology
Martin Schäfer1†, Alan R. Pacheco1†, Rahel Künzler1, Miriam Bortfeld-Miller1, Christopher M. Field1,
Evangelia Vayena2, Vassily Hatzimanikatis2, Julia A. Vorholt1*
Resource allocation affects the structure of microbiomes, including those associated with living
hosts. Understanding the degree to which this dependency determines interspecies interactions may
advance efforts to control host-microbiome relationships. We combined synthetic community
experiments with computational models to predict interaction outcomes between plant-associated
bacteria. We mapped the metabolic capabilities of 224 leaf isolates from Arabidopsis thaliana by
assessing the growth of each strain on 45 environmentally relevant carbon sources in vitro. We used
these data to build curated genome-scale metabolic models for all strains, which we combined
to simulate >17,500 interactions. The models recapitulated outcomes observed in planta with >89%
accuracy, highlighting the role of carbon utilization and the contributions of niche partitioning and
cross-feeding in the assembly of leaf microbiomes.
V arious hosts, including animals (1, 2), hu-
mans (3, 4), and plants (5), support mi-
crobial communities with hundreds to
thousands of different species. Recent
studies have revealed that a determi-
nistic relationship exists between environmental
composition and community structure, even for
complex microbiomes (6–10). Thus, a thorough
understanding of the resources available to a
community could enable prediction of its spe-
cies and functional composition. Not only would
the ability to make such predictions help us bet-
ter understand the relationship between envi-
ronment and phenotype, but it would also
provide an accessible way to rationally design
synthetic communities with defined functions.
Despite this potential, we still lack a com-
prehensive understanding of the information
necessary to predict whether a specific orga-
nism will survive or be outcompeted in a parti-
cular environmental context. Resolving this
question remains an active area of research,
with studies that use interaction outcomes
between pairs of organisms to predict overall
community behavior representing a particu-
larly attractive approach (11–13). Nonetheless,
conducting the necessary mapping of pos-
sible interactions between all organisms re-
mains experimentally challenging even for
relatively simple communities and largely out
of reach for complex host-associated micro-
biomes in situ.
Given these limitations, one may ask which
ecological concepts can be used to predict the
1Institute of Microbiology, ETH Zurich, Zurich, Switzerland.
2Laboratory of Computational Systems Biotechnology, École
Polytechnique Fédérale de Lausanne, EPFL, Lausanne,
Switzerland.
*Corresponding author. Email: jvorholt@ethz.ch
†These authors contributed equally to this work.
role of individual organisms within a commu-
nity context. Microbial populations are fun-
damentally bounded by resource availability,
where limiting amounts of micronutrients
such as carbon, nitrogen, and phosphorus act
to constrain community size and lead to the
emergence of competition between organisms
(14–16). Although the prevalence of these com-
petitive interactions has begun to be quanti-
fied in a variety of ecosystems (12, 17–20),
the general rules by which they influence
community-wide assembly patterns remain
unresolved. As such, a commonly used ap-
proach is to infer the competitive potential
between organisms from the degree of metab-
olic niche overlap between them, which relies
solely on knowing their individual resource-
utilization capabilities (21, 22). Although a
resource-by-resource understanding of the
metabolic profiles of complex microbiomes
can be challenging to obtain, it represents a
more accessible approach for inferring inter-
species interactions and has proven success-
ful at predicting high-level patterns of species
diversity in communities (10, 23–26).
Despite its benefits, the predictive power of
niche overlap is limited in that it cannot
account for the emergence of positive ecolo-
gical interactions between organisms either
through resource partitioning, cross-feeding,
orthogonal resource-acquisition strategies, or
evolved cooperation (27–30). As a complementary
approach, genome-scale metabolic models pres-
ent a tractable way to integrate the effects of
these additional mechanisms into predictions
of community structure (31, 32). Genome-scale
models are mathematical representations of
the metabolic capabilities of individual organ-
isms. They incorporate genes, reactions, and
metabolites associated with a given organism’s
metabolic network and are applied to quanti-
tatively assess how organisms can use available
resources for growth (32). In addition to gener-
ating predictions of resource allocation for
individual organisms, combinations of genome-
scale models of different organisms have been
increasingly used to mechanistically describe
pairwise and community-wide dynamics (33–35).
Combining genome-scale models with pre-
dictions of niche overlap therefore presents a
powerful way to predict interspecies interac-
tions within microbiomes.
In this study, we generated metrics of metab-
olic niche overlap and a collection of genome-
scale models to predict interaction outcomes
between 224 bacterial members of the Arabidopsis
thaliana leaf microbiome. This environment,
known as the phyllosphere, is an oligotrophic
habitat where competitive interactions between
its resident microbes are prevalent (19, 36, 37).
Because it contains a variety of different car-
bon sources (38, 39), it is an ecosystem that is
well suited for studying the effects of resource
allocation on interspecies interactions and
community structure. In particular, the exposed
nature of the phyllosphere makes it a relatively
accessible setting for study in controlled con-
ditions. The microbiota of the phyllosphere
has been shown to confer beneficial functions
to the plant host (40–42), which, together with
the scale of colonizable surfaces presented by
leaves (37, 43, 44) and the economic impor-
tance of crops (45, 46), underscores the value
of studying the processes underlying its assem-
bly (47, 48).
Results
Profiling the carbon source–utilization
capabilities of phyllosphere bacteria
Comprehensive collections of environmental
strains are valuable resources for studying
relevant host-microbe and microbe-microbe
interactions (42, 49–52). To examine interaction
outcomes among members of the Arabidopsis
phyllosphere (Fig. 1), we used the At-LSPHERE:
a collection of 224 strains isolated from leaves
of wild A. thaliana plants that represent a cross
section of the taxonomic and functional diver-
sity of the phyllosphere microbiota (53). We
first assessed the ability of each strain to grow
on solidified minimal medium supplemented
with individual carbon sources from a set of 45
(table S1). These carbon sources, comprising
a range of sugars, organic acids, sugar alco-
hols, one-carbon compounds, aromatic com-
pounds, and amino acids, were selected on the
basis of the high prevalence of resources such
as glucose, sucrose, and some amino acids that
are known to account for a substantial frac-
tion of carbon available to leaf epiphytes
(36, 38, 39, 54). These carbon sources were
also selected in part on the basis of the known
ability of certain leaf strains to metabolize
aromatic compounds, cleave glycosidic bonds,
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Data acquisition
Model generation
Prediction
Validation
Annotated genomes
Genome-scale models
Evaluate model performance
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Carbon source utilization patterns
Niche overlap
negative interaction
positive interaction
Fig. 1. Overview of experimentally and computationally guided prediction and testing of metabolic interactions among bacterial members of the
Arabidopsis phyllosphere microbiota.
and/or utilize one-carbon compounds (37, 55).
In addition to these carbon sources, we sup-
plemented the media with vitamins to en-
able the growth of auxotrophs (the set of
carbon sources included amino acids, so we
did not supply additional amino acids to the
media). We used a plate assay to evaluate the
growth of a given strain on a particular carbon
source, which was compared with a carbon-
free control, using both manual inspection
and automated image processing (Materials
and methods).
Our in vitro metabolic screen revealed phy-
logenetically contingent patterns of carbon-
utilization capabilities across the At-LSPHERE
collection (Fig. 2 and fig. S1). We found that
strains belonging to the same genus displayed
similar—or even identical—carbon source–
utilization profiles, suggesting trait conserva-
tion between closely related species (Fig. 2A).
We also identified genus-specific signatures of
resource utilization, as well as cases in which
strains could not grow on any of the tested
carbon sources (e.g., Chryseobacterium and
Exiguobacterium). These latter strains most
likely have nutritional requirements that are
not met by the minimal medium we provided
(e.g., amino acid auxotrophies), because they
were able to produce visible colonies on a
complex medium (R-2A+M, Materials and
methods). By contrast, strains belonging to
the genera Arthrobacter, Pseudomonas, and
Rhizobium grew on a large number of carbon
sources [27.5 ± 6.9, 27.1 ± 3.7, and 25.8 ± 3.6,
respectively (mean ± SD)]. To quantify these
differences, we assigned a metric of substrate
versatility, V , to each strain, defined as the
percentage of all 44 growth-yielding carbon
sources that each organism was able to use
for growth (for this analysis, methylamine
was excluded because it did not support the
growth of any strain). The most versatile
strain was Arthrobacter sp. Leaf145 (V ¼ 77%),
followed by Pseudomonas spp. Leaf15 and
Leaf98, and Rhizobium sp. Leaf202 (V ¼ 73,
70, and 68%, respectively). When comparing
the phylogenetic distribution of strain-specific
substrate versatilities, we observed that Beta-
and Gammaproteobacteria had above-average
versatilities (Fig. 2B), whereas Actinobacte-
ria (with the exception of Arthrobacter) and
Bacteroidetes had below-average versatili-
ties. Furthermore, our screen revealed the
presence of a canonical niche occupied by
methylotrophs that was distinct from and
smaller than that of many other strains (Fig.
2A and fig. S2). Indeed, the lower average
versatility of Alpha- and Betaproteobacteria—
which include Methylobacterium and Methyl-
ophilus spp., respectively—relative to Gam-
maproteobacteria reflects the low versatility
of methylotrophs.
Our screen also revealed the varying degrees
to which each resource promotes growth (Fig.
2C). To quantify these patterns, we assigned a
measure of substrate fertility, F, to each tested
carbon source, defined as the percentage of
strains that was able to grow on that particular
carbon source. The most fertile or commonly
used carbon source was glucose (F ¼ 81% of
strains), followed by succinic acid (F ¼ 80%)
and glutamate (F ¼ 78%) (Fig. 2C and table S2).
Among the most rarely used carbon sources
were aromatic compounds, including trypto-
phan (F ¼ 9%) and coniferyl alcohol (F ¼ 8%),
a common component of lignin.
Given the largely orthogonal metabolic
niche occupied by methylotrophs relative to
all other strains, we repeated our calculations
of substrate fertility without methylotrophs to
more clearly detect patterns of fertility among
the other substrates. This analysis revealed that
mono- and disaccharides build a core set of
carbon sources commonly used by the large
majority (F ≥ 75%) of tested strains and that
the most fertile substrate, glucose, was con-
sumed by 95% of the strains. The next most
common group of carbon sources (≥ 50%)
included organic acids and amino acids that
feed into the tricarboxylic acid (TCA) cycle
(fig. S3).
These experimentally determined carbon
source–utilization capabilities allowed us to
calculate the degree of niche overlap among
our strains. We defined a niche overlap index
(NOI) for each focal strain, A, with respect to
any other strain, B, as the set of usable carbon
sources shared by the focal strain and the
competitor divided by the total number of car-
bon sources used by the focal strain (23, 56):
NOIA;B ¼
NC Sources; A ∩ B
NC Sources; A
We calculated NOI values for all pairs of
strains, setting a threshold of 75% as likely
prone to competitive exclusion (57) (Fig. 2D).
In accordance with the similar carbon source–
utilization profiles, we found high niche over-
lap within most genera, suggesting frequent
intragenus competitive interactions. Addition-
ally, we found that methylotrophic strains
form two interconnected interaction spaces:
one comprising Methylobacterium and the other
comprising Methylophilus strains, underscoring
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A
Monosaccharide
Disaccharide
Sugar alcohol
Organic acid
C1 compound
Alcohol
Aromatic
Amino acid
Alphaproteobacteria
Betaproteobacteria Gammaproteobacteria
Bacteroidetes
Deinococcus−Thermus
Actinobacteria
Firmicutes
At-LSPHERE strain
paired with strain B
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50
Substrate versatility [%]
75
100
B
Alphaproteobacteria
Betaproteobacteria
Gammaproteobacteria
Actinobacteria
Bacteroidetes
Firmicutes
Deinococcus−Thermus
0
C
Monosaccharide
Disaccharide
Organic acid
Amino acid
C1 compound
Alcohol
Aromatic compound
0
25
50
Substrate fertility [%]
75
100
Rhizobium
Arthrobacter
Methylobacterium
Methylophilus
Microbacteriaceae
NOI
0 0.25 0.5 0.75 1
Fig. 2. Carbon source–utilization screen reveals hotspots of high
nutritional niche overlap. (A) Carbon source–utilization map of 224 At-
LSPHERE strains. Fill color of the boxes indicates growth (black) or no growth
(gray) for each strain on the x axis on a given carbon source on the y axis.
Top-level clustering for strains reflects phylogeny based on full-length 16S
ribosomal RNA gene sequences. Colored bars indicate phylum or Proteobacterium
class and correspond to the order in the legend. Carbon sources are sorted by
compound groups. (B and C) Density plots showing (B) strain-specific substrate
versatility grouped by phylum or Proteobacterium class (corresponding to the order
in the legend) and (C) substrate fertility grouped by compound group. Black dots
indicate individual values, and the red vertical line shows the median for
each group. Substrates in classes C1 and aromatic compounds that also fall into
another substrate group are only shown once and omitted from the other group.
(D) Heatmap of niche overlap indices (NOI) for all binary combinations of
215 At-LSPHERE strains. The color of the tile indicates high (>0.75, blue shades)
or low (<0.75, gray shades) degree of niche overlap for the strain on the
y axis in combination with the strain on the x axis. Strains are sorted by
phylogeny, and the colored bars indicate the phylum or Proteobacterium class.
NOI was only calculated for strains that grew on ≥1 carbon source
in vitro.
Schäfer et al., Science 381, eadf5121 (2023)
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their degree of metabolic specialization com-
pared with all other strains. Moreover, we
found that members of the Microbacteriaceae
had high niche overlap with a high number of
other taxa, largely owing to their low substrate
versatilities. We also observed the opposite
case: Rhizobium strains had a low NOI with
other taxa, whereas essentially all strains (ex-
cept Methylobacteria) had a high NOI with
Rhizobium strains.
An in silico representation of phyllosphere
bacterial communities
Having screened the carbon source–utilization
capabilities of the At-LSPHERE collection, we
sought to model how these bacteria would
interact metabolically in a leaf environment.
To do this, we adopted a stoichiometric metab-
olic modeling approach because it allowed us
to explicitly simulate strain- and substrate-
specific patterns of resource utilization, con-
version, and exchange in a multitude of
defined environmental conditions. We thus
began by creating draft genome-scale metab-
olic reconstructions (58) for each member of
the At-LSPHERE. This process yielded a
separate metabolic network for each of the
224 At-LSPHERE strains, containing all the
metabolic reactions predicted to be contained
by each organism on the basis of its genome
annotation. After generating these draft metab-
olic reconstructions, we used flux balance
analysis (31) to simulate the growth of each
strain individually within a complete medium
containing all 45 carbon sources used in our
in vitro screen. We found that whereas some
of our reconstructions were predicted to pro-
duce biomass when using this complete me-
dium, the majority could not do so when only
individual carbon sources were provided (Fig.
3A). Although this inability to grow was at
odds with our experimental results, it was not
unexpected because models generated solely
from genomic information are often missing
key metabolic pathways and thus have limited
predictive power without additional experi-
mental curation (33, 59–61). We therefore used
the results of our carbon source screen to fill
the apparent gaps in each metabolic reconstruc-
tion by using the tool NICEgame (62), which
suggests biologically relevant alternative path-
ways to account for missing reactions by lever-
aging information on reaction thermodynamics.
We followed this step with additional manual
curation (Materials and methods, table S3,
and fig. S4) and then compared each of the
resulting 224 models with their correspond-
ing strains on the basis of their ability (or in-
ability) to use the 45 carbon sources selected
for our in vitro screen (fig. S5). This process
resulted in each genome-scale model having
a final balanced accuracy of 0.98 ± 0.07 (Fig.
3A) (mean precision 1, mean recall 0.96), with
214 models (96%) having a balanced accuracy
of at least 0.85, and 189 models (84%) being
100% accurate.
Our curation process yielded a collection
of 224 genome-scale models that revealed
further metabolic capabilities and physiologi-
cal characteristics of the At-LSPHERE collec-
tion (Fig. 3). The models contained between
1568 (Flavobacterium sp. Leaf359) and 3004
(Pseudomonas sp. Leaf15) reactions (Fig. 3B),
which moderately correlated with the genome
size of their corresponding strain [coefficient
of determination (R2) = 0.54, fig. S6A]. Reac-
tions involved in the biosynthesis of glycero-
phospholipids, key components of the cell
membranes of Gram-negative bacteria, were
enriched in members of the Proteobacteria
within our collection (Fig. 3C). We also found
Firmicutes and Actinobacteria to contain
more reactions related to degradation of plant
polysaccharides (e.g., melibiose, raffinose, and
sucrose) relative to other taxonomic classes
and identified an enrichment for benzoate
degradation capabilities as previously reported
in Betaproteobacteria (63, 64). The high degree
of similarity to our strains’ known carbon
source–utilization capabilities was supported
by a clustering analysis of the reactions con-
tained in each model (Fig. 3D). In this analysis,
Methylobacteriaceae spp. and Methylophilaceae
spp. formed clusters distinct from most other
models, and Acidovorax strains clustered to-
gether with the majority of Pseudomonas and
Rhizobium organisms. These clusters largely
mirrored those generated from our in vitro
data alone (Fig. 3E), which underscored the
phylogenetic contingency of resource-utilization
patterns and may underlie the deterministic
assembly of microbiomes in general. With this
in silico representation of the At-LSPHERE col-
lection, we proceeded to use our genome-scale
models to simulate the ecological outcomes of
mixed-culture experiments.
Computational models recapitulate ecological
patterns in planta
We assessed the predictive power of the
genome-scale models and the NOI against
experimental data in two in planta experi-
ments (Fig. 4, A and B). In a first experiment,
we inoculated A. thaliana seedlings with pair-
wise combinations of seven bacterial strains,
or with a community consisting of all seven
strains (referred to as SynCom7), and com-
pared the colonization level of each strain in
combination with the colonization density
achieved in monoassociation (Fig. 4B). To
represent a range of metabolic capabilities,
we selected strains across a gradient of sub-
strate versatility values and hence a gradient
of NOI. For the first experiment, we selected
representative strains from the highly versatile
Arthrobacter spp., Pseudomonas spp., and
Rhizobium spp. (Leaf145, V ¼ 77%; Leaf15,
V ¼ 73%; and Leaf202, V ¼ 68%; respec-
tively), along with four additional strains with
intermediate-to-low versatility values: Rhodo-
coccus sp. Leaf233, Sphingomonas spp. Leaf34
and Leaf257, and Microbacterium sp. Leaf179
(V ¼ 55, 36, 45, and 41%, respectively). On
the basis of NOI, we expected the strains
with lower versatilities to more frequently de-
crease in abundance upon cocolonization with
other strains, either in pairwise combinations
or in a community context (Fig. 4C). How-
ever, all other strain pairings had low NOI
values (<75%), limiting the degree to which
we could infer interaction outcomes for these
combinations.
We used the genome-scale models corres-
ponding to these seven strains to simulate
their growth within an environment reflecting
the carbon source availability of the Arabidopsis
phyllosphere (Materials and methods). To
obtain an indicator of the ecological outcomes
of these pairings, we compared the predicted
growth of each strain on its own with that in
coassociation with another: A strain was
deemed to have experienced a negative inter-
action outcome if its biomass production rate
in coassociation was lower than that on its
own, and a positive outcome if its biomass
production rate was higher in coassociation.
These simulations predicted an approximately
even distribution of positive and negative
outcomes for all seven organisms (Fig. 4C).
However, when we considered the magnitude
of the changes in growth experienced by each
strain, we found that predictions skewed more
strongly negative than positive. This observa-
tion is consistent with previous descriptions of
the prevalence of competitive interactions in
the phyllosphere (18, 19), which suggests the
commonality of exclusion of one strain by
another. Indeed, when we compared the growth
of each strain on its own with that in the
presence of all six other strains, we predicted
almost exclusively negative outcomes. Despite
this overall distribution, we found that the
number of positive or negative outcomes dif-
fered depending on the strain in question, with
Microbacterium sp. Leaf179 and Sphingomonas
sp. Leaf257 almost always experiencing a re-
duction in growth when paired with another
strain. By contrast, Rhizobium sp. Leaf202,
Pseudomonas sp. Leaf15, and Arthrobacter
sp. Leaf145 were most often predicted to
benefit from coinoculation with another of
our selected strains. These predicted positive
outcomes corresponded to instances of low
NOI values (Fig. 4C), suggesting that these
strains could metabolically evade competition
by a partner strain and may additionally bene-
fit from changes in the ecosystem (e.g., cross-
feeding) induced by the partner strain.
The interaction outcomes of these seven
strains in planta were largely congruent with
those predicted by NOI and metabolic model-
ing. Of the outcomes that showed a fold change
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Plant polysaccharide degradation
Oxidative phosphorylation
Methane metabolism
Selenoamino acid metabolism
Biotin metabolism
tRNA charging
Nitrogen metabolism
Beta-alanine metabolism
Ascorbate and aldarate metabolism
Benzoate degradation
Glutathione metabolism
Sulfur metabolism
Nucleotide salvage pathway
ROS detoxification
Cholesterol metabolism
Inositol phosphate metabolism
Peptide metabolism
Vitamin B12 metabolism
Galactose metabolism
Propanoate metabolism
Terpenoid backbone biosynthesis
Heme synthesis
Urea cycle
Aminosugar metabolism
Thiamine metabolism
Tyrosine metabolism
Ubiquinone and other terpenoid-quinone biosynthesis
Alanine and aspartate metabolism
Fructose and mannose metabolism
CoA synthesis
Pentose and glucuronate interconversions
Vitamin B6 metabolism
Starch and sucrose metabolism
Purine catabolism
Histidine metabolism
Purine synthesis
Phenylalanine metabolism
Butanoate metabolism
Energy metabolism
Glyoxylate and dicarboxylate metabolism
Tryptophan metabolism
Cell wall biosynthesis
Glutamate metabolism
Lysine metabolism
Vitamin B2 metabolism
NAD metabolism
Pyrimidine synthesis
Citric acid cycle
Fatty acid oxidation
Arginine and proline metabolism
Pyruvate metabolism
Pentose phosphate pathway
Methionine and cysteine metabolism
Folate metabolism
Pyrimidine catabolism
Glycine, serine, alanine, and threonine metabolism
Fatty acid synthesis
Glycolysis/gluconeogenesis
Valine, leucine, and isoleucine metabolism
Glycerophospholipid metabolism
2
2
63
83
83
4
02
01
7
3
5
73
73
4
2
3
0
2
4
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76
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220
274
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400
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416
459
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408
98
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59
434
48
129
127
58
83
130
51
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404
394
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180
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1084663999212211912190123456118361344401396202167681
86
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89
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465
94
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326
72
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196
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13
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233
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285
307
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350
289
245
272
291
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395
334
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145
137
141
69
337
261
6
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7
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4
Alphaproteobacteria
Betaproteobacteria
Gammaproteobacteria
Bacteroidetes
Actinobacteria
Firmicutes
Deinococcus-Thermus
No. of reactions
1500, 2500
Alphaproteobacteria
Gammaproteobacteria
Actinobacteria
Betaproteobacteria
Firmicutes
Bacteroidetes
Deinococcus-Thermus
0.5
1
2.9
7.9
0
0.73
Balanced accuracy
Genome size (Mb)
Model versatility
D
1200
800
400
0
)
.
r
a
v
.
l
p
x
e
%
9
.
3
1
(
2
o
C
P
-400
E
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)
.
r
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v
.
l
p
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e
%
5
.
5
3
(
2
o
C
P
Acidovorax
Methylobacterium
Methylophilus
Xanthomonas
Sphingomonas
Pseudomonas
Rhizobium
Microbacterium
All others
-1000
-500
0
500
1000
-20
-10
0
10
20
PCo1 (22.8% expl. var.)
PCo1 (46.3% expl. var.)
Fig. 3. Overview of collection of metabolic models for 224 bacterial
members of the A. thaliana leaf microbiota. (A) Distributions of balanced
accuracy as tested on 45 carbon sources for models generated solely from
genomic information (top) and after curation (bottom). (B) Attributes of models
as clustered by taxonomic phylum and class. Numbers bordering phylogenetic
tree denote strain identity (e.g., 220 corresponds to Xylophilus sp. Leaf220). The
innermost ring represents the balanced accuracy of each model, the second
ring indicates the size of the genome used to generate each model (53), and the
third ring represents the versatility, V, of each model. The
outermost bars represent the number of reactions contained in each model
(minimum = 1568, maximum = 3004). (C) Clustered heatmap of 60 most
highly represented reaction types, scaled by the number of models
corresponding to each phylum and class. (D and E) Principal coordinates
analysis (PCo) of strains as determined by (D) reactions in genome-scale
models and (E) in vitro carbon source screen, with select genera
highlighted.
greater than 2 or less than 0.5, we found that
a majority were negative, confirming the dom-
inance of competition between these strains
(Fig. 4D). In the SynCom7 condition, a sig-
nificant abundance reduction was observed
for all strains except for Rhizobium sp. Leaf202,
matching our predictions and supporting the
presence of increased competitive pressure in a
community context. Our experimental data
also highlighted the predictive power of NOI
data alone for predicting interaction outcome
directionality, with 93% of instances of nega-
tive outcomes corresponding to an NOI >0.75.
Predictions generated by the genome-scale
models yielded an increased degree of gra-
nularity, recapitulating the significant inter-
action directionalities that we observed in
planta with a balanced accuracy of 89% (tables
S4 and S5). These predictions additionally
captured the weaker directionalities of border
cases that did not meet our experimental
Schäfer et al., Science 381, eadf5121 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
B
n
o
i
t
i
a
c
o
s
s
a
o
n
o
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n
o
x
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B
i
s
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c
U
F
C
Δt
i
t
i
a
n
b
m
o
c
n
i
mono association
in combination
mono association
in combination
C
Leaf34
Leaf179
Leaf257
Leaf233
Leaf202
Leaf15
Leaf145
E
Leaf8
Leaf154
Leaf164
Leaf304
Leaf202
Leaf145
4
3
f
a
e
L
9
7
1
f
a
e
L
7
5
2
f
a
e
L
3
3
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L
2
0
2
f
a
e
L
5
1
f
a
e
L
5
4
1
f
a
e
L
7
m
o
C
n
y
S
NOI
GSM
NOI
GSM
0 0.25 0.5 0.75 1
−5.0 −2.5 0.0 2.5 5.0
D
Leaf34
Leaf179
Leaf257
Leaf233
Leaf202
Leaf15
Leaf145
F
Leaf8
Leaf154
Leaf164
Leaf304
Leaf202
Leaf145
4
3
f
a
e
L
9
7
1
f
a
e
L
7
5
2
f
a
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L
3
3
2
f
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L
2
0
2
f
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5
1
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5
4
1
f
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L
7
m
o
C
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y
S
|log2FC| < 1
padj ≤ 0.05
log2 FC
−4 −2
0
2
4
f
8
a
e
L
4
5
1
a
e
L
f
4
6
1
f
a
e
L
4
0
3
a
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L
f
2
0
2
f
a
e
L
5
4
1
f
a
e
L
3
m
o
C
n
y
S
f
8
a
e
L
4
5
1
a
e
L
f
4
6
1
f
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4
0
3
a
e
L
f
2
0
2
f
a
e
L
5
4
1
f
a
e
L
3
m
o
C
n
y
S
Fig. 4. Model predictions and in planta validation of interactions. (A and B) Schematic overview of
(A) interaction simulations using genome-scale models and (B) phyllosphere inoculation and interaction
mapping procedure. Interactions are inferred by comparing a strain’s growth in combination with another
strain with that in monoculture. This is computed as the log2 ratio of biomass fluxes for the genome-scale
models or as the log2-fold change in CFUs per gram plant fresh weight for the in planta experiments.
(C and E) Predicted interaction outcome for the strain indicated on the y axis in combination with the
strain or SynCom indicated on the x axis, based on niche overlap index (NOI, top left) and genome
scale models (GSM, bottom right). The fill color indicates high (>0.75, blue shades) or low (<0.75, gray
shades) degree of niche overlap and predicted positive (red shades) or negative (blue shades) interactions
based on genome-scale metabolic models. (D and F) Interaction outcomes observed in planta. Heatmap
showing the log2-fold changes (log2FCs) (pairwise or SynCom inoculation versus monoassociation) for the
strain on the y axis in combination with the strain or SynCom indicated on the x axis, based on absolute
abundances obtained by CFU enumeration (n ¼ 11 to 12). The color of the boxes reflects the observed log2FC,
and the black frames around the boxes indicate a significant difference compared with the monoassociation
condition (two-sided Wilcoxon rank sum test, Holm-adjusted P ≤ 0.05). |Log2FC| < 1 are overlaid with a
crosshatched pattern. Confusion matrices comparing modeling predictions and in planta outcomes are
provided in table S4, and colony counts for the in planta experiments are provided in table S5.
cutoff, as seen in the positive interaction out-
come for Sphingomonas sp. Leaf34 paired with
Microbacterium sp. Leaf179, of Arthrobacter sp.
Leaf145 paired with Rhizobium sp. Leaf202,
and of Rhizobium sp. Leaf202 in the SynCom7
condition. These weakly positive effects occurred
despite high predicted NOI, suggesting the in-
fluence of additional metabolic mechanisms
not encompassed by competition.
We sought to further validate our predic-
tions with a second experiment spanning
more extreme degrees of niche overlap. We
generated pairings including the two highly
versatile strains Rhizobium sp. Leaf202 and
Arthrobacter sp. Leaf145 (V ¼ 68% and 77%,
respectively) as well as the low-versatility
strains Frigoribacterium sp. Leaf8, Curtobac-
terium sp. Leaf154, Rathayibacter sp. Leaf164,
and Frondihabitans sp. Leaf304 (V ¼ 27% for
all four strains). All pairings resulted in a high
degree of niche overlap for the low-versatility
strains, whereas the NOI for either Leaf202
or Leaf145 with any other strain was low. Cor-
respondingly, the genome-scale models pre-
dicted almost exclusively negative interaction
outcomes for all low-versatility strains, with
weakly positive outcomes for Leaf202 in com-
bination with all strains except Leaf145, as
well as stronger positive outcomes for Leaf145
in combination with most other strains (Fig.
4E). We additionally predicted interaction out-
comes for each of the three low-versatility
strains paired with a combination of Leaf202
and Leaf145 (referred to as SynCom3), which
resulted in strongly negative interaction out-
comes for each strain. These predictions were
tested with in planta experiments for these
pairings: As predicted, all significant instances
of log2-fold changes greater than 1 were nega-
tive, including those for each low-versatility
strain in the SynCom3 condition (Fig. 4F).
Additionally, Leaf202 and Leaf145 each exper-
ienced two instances of weakly positive out-
comes when paired with other low-versatility
strains, which were captured by our genome-
scale modeling predictions. Our experiments
confirmed the validity of the computational
predictions (tables S4 and S5) and highlighted
the strong contribution of resource competition
to strain-specific interaction outcomes in situ.
To test the specificity of our predictions to a
leaf environment, we carried out a series of
in vitro cultivations in which we cultured the
same strain pairs and communities in shake
flasks (Materials and methods). These culti-
vations resulted in exclusively negative inter-
action outcomes for all strains in the SynCom7
and SynCom3 conditions (fig. S7), similarly to
our in planta experiments. These outcomes,
which are consistent with an additional set of
community simulations that used randomly
selected strains (fig. S8), highlight the increased
degrees of competition that organisms may be
subject to in multispecies settings. However,
Schäfer et al., Science 381, eadf5121 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
Leaf145 + Leaf8
Leaf145 + Leaf233
C
-4
-2
0
-4
-2
0
log2FC biomass flux
Leaf145
Leaf8
Leaf233
B
Sugars
Amino
acids
Organic
acids
-4
-2
0
-4
-2
0
log2FC uptake flux (mmol/gDW/hr)
Leaf145
Leaf8
Leaf233
Strongly
negative
Strongly
positive
E
23%
23%
2% 1%
3%
2
25%
D
y
c
n
e
u
q
e
r
f
e
m
o
c
t
u
O
4000
2000
0
Outcome
Positive
Neutral
Negative
No growth
i
A
n
a
r
t
s
f
o
e
m
o
c
t
u
o
n
o
i
t
c
a
r
e
t
n
I
-8
-4
0
4
log2FC biomass flux
46%
Competitive (-,-)
Parasitic (-,+)
Amensal (-,0)
Commensal (+,0)
Mutualistic (+,+)
Neutral (0,0)
in combination with strain B
Alphaproteobacteria
Betaproteobacteria
Gammaproteobacteria
Bacteroidetes
Deinococcus-Thermus
Actinobacteria
Firmicutes
F
6000
88.6%
50.8%
7.6%
37.0%
y
c
n
e
u
q
e
r
F
0
0
Negative outcome
Positive outcome
6000
90.7%
27.5%
8.5%
70.1%
Negative outcome
Positive outcome
6000
78.4%
38.3%
14.3%
49.9%
Negative outcome
Positive outcome
2
4
6
Ratio of total sugar uptake flux
0
0
8
2
4
6
Ratio of total amino acid uptake flux
0
0
8
2
4
6
8
Ratio of total organic acid uptake flux
Fig. 5. Model-predicted interaction outcomes and mechanisms. (A and
B) Log2FCs of (A) biomass and (B) resource uptake fluxes for two representative
interactions validated in planta. Dots indicate absolute log2FCs of less than
0.05 mmol gDW–1 hour–1. (C) Predicted pairwise interaction outcomes between
all 188 nonmethylotrophic strains in the At-LSPHERE (n ¼ 35,156 outcomes
for 17,578 pairs). Hierarchical clustering was performed on interaction outcomes,
with strain-specific phylogeny highlighted. White cells denote instances of no
predicted growth in both mono- and coculture. (D) Distribution of pairwise
interaction outcomes (n ¼ 35,156). Dashed lines separate outcomes in which a
strain’s predicted biomass flux in coculture was either less than 90% of that
in monoculture (strongly negative), within 10% of that in monoculture (neutral),
or more than 110% of that in monoculture (strongly positive). (E) Classification
of pairwise ecological outcomes (n ¼ 17,578). (F) Distributions of flux ratios
between resource uptake in coculture and monoculture, according to corresponding
interaction outcome. Only simulations in which a strain achieved growth in both
monoculture and coculture are considered (n ¼ 28,316 outcomes). Differences
between uptake rates of resource types provided in the simulated medium are
highlighted for sugars (left), amino acids (center), and organic acids (right).
Distributions of uptake fluxes are statistically significant for all three resource types
(p << 1 (cid:2) 10
horizontal axes are truncated and show 98.8% of outcomes for sugars, 98.7%
for amino acids, and 94.7% for organic acids. The dashed line at ratio of 1 separates
instances of lower or higher uptake flux between coculture and monoculture, with
percentages highlighting the number of instances less than or greater than 1.
(cid:3)10) as determined by one-tailed Mann-Whitney U tests. For clarity,
our in vitro experiments also resulted in sub-
stantially fewer positive outcomes of pairwise
interactions when compared with our in planta
results, suggesting competitive pressures in-
herent to batch cultures that are not captured
by our use of NOI and genome-scale models.
In particular, the lack of spatial structure may
favor strains that experience fast growth when
substrate availability is high and thus out-
compete slower-growing strains within the
timescale of a batch experiment. Moreover,
this rapid depletion of nutrients contrasts with
the resource dynamics of leaf surfaces, which
exhibit a steady resupply of resources that can
be accessed by epiphytic microbes (38). Al-
though we do not explicitly consider spatial
structure in our use of NOI and genome-scale
models, these tools generate predictions based
on a broader consideration of the various re-
sources that can be used by the organisms at
steady state. This assumption may therefore
better reflect a broader and more continuously
supplied pool of resources, which can be used
by microbes on a population level in spatially
structured settings.
Compensatory metabolic mechanisms offset
resource competition
In addition to predicting interaction outcome
directionalities, we used genome-scale model-
ing to explore the metabolic mechanisms that
could be underlying the observed ecological
patterns. We first examined experimentally
validated interactions to determine changes
in resource uptake rates that emerged as a
result of pairing two strains together. As rep-
resentative examples, we looked specifically
at two interactions involving Arthrobacter sp.
Leaf145, a highly versatile strain that experi-
enced a weakly positive effect when paired
with Frigoribacterium sp. Leaf8 and a negative
effect when paired with Rhodococcus sp. Leaf233
(Fig. 4, C to F, and Fig. 5A). Our flux balance
simulations had predicted that in both cocul-
tures, Leaf145 would have a lower net uptake
flux of sugars compared with those experi-
enced in monoculture (Fig. 5B). This was also
the case for Leaf8, which was additionally pre-
dicted to experience a reduction in amino acid
uptake flux when paired with Leaf145. Whereas
a similar reduction in amino and organic acid
uptake occurred for Leaf233, Leaf145 was able
to take up amino acids at rates similar to those
noted in monoculture. The contribution of this
reallocation of resources to the dominance
of Leaf145 can be seen in its interaction with
Leaf8, in which Leaf145 was able to shift its
Schäfer et al., Science 381, eadf5121 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
metabolism to take up a slightly greater quan-
tity of amino acids, as occurred in monoculture.
The increased availability of these resources,
in part a product of the low metabolic activity
of Leaf8, suggests metabolic cross-feeding as
a contributing factor in the positive effect ex-
perienced by Leaf145 in coculture.
The emergence of distinct resource-allocation
patterns between these strain pairs prompted
us to ask how widespread they could be across
a wider ecosystem. We thus used the genome-
scale models to generate predictions of pairwise
interaction outcomes for all nonmethylotrophic
strains in the At-LSPHERE, carrying out a total
of 17,578 pairwise simulations (Fig. 5C). These
simulations revealed the high prevalence of
competitive effects, with 63.2% of outcomes
predicted to be negative (Fig. 5D). Of these,
the large majority (representing 58.2% of all
outcomes) were predicted to be strongly nega-
tive, which we defined as a strain’s biomass
production rate in coculture being less than
90% of that in monoculture. Conversely, 25.5%
of all outcomes were predicted to be strongly
positive (biomass production in coculture more
than 110% of that in monoculture), further un-
derscoring the strength of competitive pres-
sures within leaf bacterial communities. We
combined these strain-specific effects to de-
fine interaction outcomes between pairs, which
revealed that in 94% of interactions, at least
one participant experienced a negative out-
come (Fig. 5E). As such, cooperative inter-
actions were predicted to be relatively rare,
with 3% of all pairwise interactions resulting
in commensalism and only 1% resulting in
mutualism.
An analysis of metabolic fluxes across our
simulations revealed key differences in rates of
resource uptake between positive and nega-
tive interaction outcomes (Fig. 5F). As expected,
the models predicted significantly lower re-
source uptake rates for organisms that de-
creased in abundance relative to monoculture
than for organisms that increased in abun-
dance. However, whereas nearly all flux ratios
associated with negative outcomes were below
1 (occurring for sugars, amino acids, and or-
ganic acids in 88.6, 90.7, and 78.4% of nega-
tive outcomes, respectively), many positive
interaction outcomes displayed increases in
amino acid and organic acid uptake flux (in
70.1 and 49.9% of positive outcomes, respec-
tively). These patterns thus suggest a stron-
ger degree of competition for sugars among
phyllosphere bacteria, which is more likely
to be offset by increased uptake of amino and
organic acids.
These predicted compensatory mechanisms
suggested that strains with higher substrate
versatilities would be more likely to increase
in abundance when in the presence of another
strain. Indeed, strains with very high versatil-
ities (e.g., Acidovorax spp. and Pseudomonas
spp.) were predicted to have higher than aver-
age rates of experiencing positive outcomes
(fig. S9). However, strain-specific substrate
versatility itself was a poor predictor of posi-
tive outcome frequency ( R2 ¼ 0.10) because
strains with very low versatilities (e.g., Chrys-
eobacterium spp., which did not grow on any of
the supplied carbon sources individually, or
Bosea sp. Leaf344) were also predicted to ex-
perience strongly positive outcomes in rare
cases. These effects suggest a role of cross-fed
amino or organic acids as valuable sources of
metabolic complementation (65), which in ad-
dition to enabling highly versatile strains to
outcompete a partner strain, can also facil-
itate the survival of specialized organisms.
Discussion
Understanding the factors that contribute to
the assembly of microbiomes remains a chal-
lenge for the study of natural ecosystems. In
this study, we have shown how predictions
based on the resource-utilization capabilities
of individual bacteria enable recapitulation of
interaction outcomes observed in the phyllo-
sphere. These predictions underscored the
prevalence of competitive interactions between
leaf strains. Additionally, the high accuracy
(Fig. 4) of these predictions suggested that
competition for resources is responsible for
many outcomes observed in situ, as also re-
cently observed in community contexts (19).
In particular, our experiments showed how
high degrees of niche overlap were reliably
predictive of negative interaction outcomes
in planta. This relationship demonstrates the
role that highly versatile organisms play in
communities, as well as the implications for
the design of microbial consortia based on co-
operative interactions, where pairings of highly
competitive organisms can be avoided with
greater certainty. Our work highlights how a
resource-by-resource understanding of an orga-
nism’s catabolic potential in monoculture is
sufficient for making high-level predictions of
competition in an ecologically relevant setting.
In addition to mapping the metabolic ca-
pabilities of a large strain collection at high
resolution, our in vitro carbon source screen
informed the curation of genome-scale meta-
bolic models for each of the 224 strains. Our
experimentally curated collection of genome-
scale models allowed us to go beyond the po-
tential of niche overlap by predicting positive
interaction outcomes and suggesting their
molecular mechanisms. Our curation process
provided a quantitative basis for the need to
incorporate experimental data into model
generation, given the low accuracy of the ini-
tial draft models, which were based on ge-
nome annotations alone. Although improved
annotation resources, as well as organism-
specific biomass compositions, may serve to
reduce this source of uncertainty (60, 61), we
expect experimental curation to remain es-
sential for selecting the optimal combination
of gap-filled reactions to recapitulate an orga-
nism’s exact resource-utilization profile.
Our metabolic modeling predicted interac-
tion outcomes on the basis of carbon source–
utilization capabilities. Further curation that
integrates additional properties such as vita-
min auxotrophies and storage (66), as well as
metabolic shifts occurring from gene regula-
tion (67, 68), is likely to improve the quantitative
predictive power of this framework (33, 69).
Moreover, although our predictions based
on metabolic mechanisms are informative of
key aspects underlying the assembly of plant-
associated microbiomes, they do not consider
additional factors that are known to shape
leaf communities, such as signaling mole-
cules, antagonistic interactions, or host immu-
nity (5, 70–73). A potential consequence of this
limitation may be seen in the example of
Pseudomonas sp. Leaf15, which experienced
a strong negative interaction in planta when
paired with Rhizobium sp. Leaf202 (Fig. 4, C
and D). Even though this outcome was qual-
itatively predicted by our simulations, the pres-
ence of a type VI secretion system in Leaf202,
previously described to be active against a
Pseudomonas strain (42), may also be produc-
ing an additional inhibitory effect not captured
in our modeling framework. Furthermore, al-
though our experimental approach that quan-
tified community composition on the basis
of bulk sampling aligns with our use of flux
balance analysis, it abstracts away the influ-
ence of spatial structure on interaction out-
comes. Leaf surfaces are known to exhibit
considerable nutrient heterogeneity, which,
together with the aggregation of microbes
around stomata or in microdroplets, is likely
to affect interaction directions at the micro-
scale (36, 74, 75). Capturing varying degrees
of uncertainty in our modeling predictions
can partially represent this heterogeneity
(fig. S10), but an improved understanding of
the nutrient compositions at specific locations
on the leaf may enable future parametrization
of existing metabolic modeling tools that can
explicitly consider spatial structure (76–79).
Our present results underscore the strengths
of an integrated approach for generating eco-
logical predictions in a mechanistic yet scal-
able way, while establishing a computational
resource for further exploration of the molec-
ular mechanisms that underlie the assembly
of complex microbiomes.
Materials and methods
Cultivation of bacteria
At-LSPHERE strains were grown on R-2A agar
(Sigma-Aldrich) supplemented with 0.5% (v/v)
methanol (R-2A+M) at 22°C. Strains were rou-
tinely streaked out from a cryo stock stored
at −80°C, grown for 4 days, streaked on fresh
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R-2A+M plates, and grown for 3 more days
before the start of experiments. If necessary,
streptomycin (20 mg ml−1) was added to the
medium for selection.
Carbon source screen
The minimal medium agar plates were pre-
pared with a common minimal medium com-
position (80). One liter of the final medium
contained 2.4 g K2HPO4, 1.08 g NaH2PO4 · 2H2O,
1.62 g NH4Cl and 0.2 g MgSO4 · 7H2O, and 15 g
noble agar (Becton, Dickinson and Company).
The medium was supplemented with the fol-
lowing trace elements: 15 mg Na2EDTA · 2H2O,
3 mg FeSO4 · 7H2O, 4.5 mg ZnSO4 · 7H2O, 3 mg
CoCl2 · 6H2O, 0.64 mg MnCl2, 1 mg H3BO3,
0.4 mg Na2MoO4 · 2H2O, 0.3 mg CuSO4 · 5H2O,
and 3 mg CaCl2 · 2H2O, and vitamins: 500 mg
D-pantothenic acid hemi calcium salt, 100 mg
biotin, 400 mg riboflavin, 400 mg thiamine
HCl, 200 mg pyridoxal HCl, 150 mg p-amino
benzoic acid, 200 mg cobalamin, 50 mg lipoic
acid, 150 mg nicotinic acid, and 100 mg folic
acid. All media components were prepared
with Milli-Q quality water (Millipore). Each
carbon source was added as a 10× stock
solution to the premixed medium, except for
coniferyl alcohol and tyrosine, which were
added to the medium directly as powder. The
concentration of each carbon source was nor-
malized to 30 mM carbon (e.g., 5 mM glucose
and 30 mM methanol). A list of all 45 carbon
sources and final concentrations can be found
in table S1.
At-LSPHERE isolates grown on R-2A+M
medium were suspended (1 ml loopful) in 1 ml
10 mM magnesium chloride solution, which
corresponds to an optical density at 600 nm
(OD600) of approximately 0.1 to 0.3. The cell
suspensions were transferred to 96-well plates
before spotting on agar plates, leaving every
other well empty in a checkerboard manner to
reduce the risk of contamination and allow
more space on the agar plate for each strain.
Increasing the distance between spots also
strongly reduces the risk of strain interactions
based on secondary metabolite production
(e.g., antibiotics) that could lead to false-negative
results (42). Cell suspensions (2 ml) were spotted
on top of each minimal medium plate con-
taining individual carbon sources, as well as
on a minimal medium plate without carbon
source and a R-2A+M plate. Spotting was
carried out using a Rainin Liquidator Man-
ual Pipetting System (Mettler Toledo). Plates
were dried under laminar flow. Bacteria were
incubated at 22°C and photographs were taken
at 5, 7, and 10 days after spotting. In sum, the
screen comprised three total rounds includ-
ing 96 strains each, and the last round also
comprised 56 randomly selected strains that
were screened a second time for validation
purposes (table S7). Plate images are availa-
ble through Zenodo (81).
Analysis of bacterial growth in carbon
source screen
Colony growth was scored for all strains after
7 days (0 = no growth, 1 = growth) by compar-
ing growth on each carbon source with the
control plate without a carbon source. We used
a dual approach incorporating automated
growth scoring based on pixel intensities,
using a common threshold for all strains and
manual scoring through visual inspection.
For the automated analysis, we developed
the software tool platescan (github.com/
MicrobiologyETHZ/platescan), which enables
unbiased scoring of all strains over different
conditions with a firm growth cutoff. Briefly,
platescan uses cross-correlation techniques to
crop the plate image, locate the colony grid
layout, and then determine the best-fitting
colony size and location on the basis of the
assumption that they are approximately cir-
cular. The pixel intensities are rescaled between
1 and 99% of the intensity distribution to en-
sure that the images have approximately the
same contrast. The program then reports fore-
ground and background pixel intensities in red,
green, blue, and grayscale, which are then used
to threshold growth versus no growth. An
example can be found on the program’s GitHub
repository.
We used platescan to assign growth values to
each strain with the following parameters: -r:20,
-p: 10,–min_r: 15,–max_r: 40,–edge: 200 40 200
40. In addition, two parameters were set indi-
vidually for each screening round because of
variation in picture zoom level. Screen1: -x 105
-y 108, screen2: -x 110 -y 109, screen3: -x 114 -y 113.
We used the pixel intensities reported in the
red channel with a defined minimum thresh-
old to consider a strain as having grown. Pixel
intensities were obtained by subtracting back-
ground values from foreground values for
each colony and subsequently subtracting the
no-carbon control value. For the few cases in
which strains spread into the area used for
background intensity calculation, the back-
ground value of the neighboring colony was
subtracted.
For a fraction of strains, we also observed
substantial growth without the addition of a
carbon source to the medium, suggesting that
these strains could either grow on a compo-
nent or impurity within the agar or were able
to grow on volatile compounds present in the
surrounding environment. Therefore, we also
manually scored growth for all strains rela-
tive to the control plate containing no carbon.
Because the magnitude of colony formation
differed between carbon sources, assigning a
binary growth (1) or no growth (0) value was
challenging for strains that exhibited residual
growth on the no-carbon control or were gen-
erally slow growing. We therefore introduced
a third category of nonsignificant (NS) growth
for the initial screen analysis but considered
them as no growth for subsequent analyses to
keep the number of false positives low (fig. S11A).
The results of the computational analysis with
platescan and the manual analysis showed a
very high overlap between the two methods. The
highest overlap (with 94.6% of matches com-
pared with the manually scored data) was ob-
tained with a cutoff of 20 arbitrary units (a.u.).
The comparison of the manually and com-
putationally scored data showed that the
computational method scored growth more
often than the manual analysis (n ¼ 485), but
most of these were scored as NS initially (n ¼
332) (fig. S12). To achieve the best accuracy
possible, we applied a rigorous curation pro-
cess to the screening data. First, we reinspected
all cases that did not agree between the manual
and computational analysis (20 a.u. cutoff) and
all cases that were scored as NS manually. This
revealed few false-positive and false-negative
scores for both the manual and computational
analysis. In the case of the computational
analysis, these mistakes were due to either a
slight misalignment of the grid or reflections
on the plate. To account for slow-growing strains
and strains that exhibited high background
growth on the no-carbon control condition, we
also reinspected all instances that were close to
the chosen pixel cutoff (10 to 40 a.u.). For these,
we also inspected the growth after 10 days and
scored growth on the basis of whether there was
an increase in colony density over time. This
latter step reduced the number of NS values
observed in the initial analysis and mainly
improved scoring of the previously mentioned
slow-growing Actinobacteria (fig. S11B). The
curation procedure reduced the false-positive
rate compared with the original analysis from
3.3 to 2.3%, whereas the false-negative rate
increased from 5.8 to 6.5%, with most uncer-
tainty remaining for Methylobacterium spp.
and some members of the Actinobacteria.
Plant cultivation
Plants were cultivated as described previously
(19). In brief, A. thaliana Columbia (Col-0) seeds
were surface sterilized (82) and stratified for
4 days at 4°C. Arabidopsis were cultivated in six-
well tissue culture plates (TechnoPlasticProducts)
filled with 5 ml washed and heat-sterilized
calcined clay mixed with 2.5 ml half-strength
Murashige & Skoog medium pH 5.8 includ-
ing vitamins (½ MS, Duchefa). Seeds were
placed in the center of each well. If a seedling
did not germinate, a different seedling was
transplanted from a separate plate after 7 days.
Starting at day 7, each well was supplemented
twice per week with 200 ml ½ MS, respectively.
Plates were incubated in a growth chamber
(Percival, CU41-L4) set to 22°C and 54% relative
humidity with an 11-hour photoperiod, fitted
with full-spectrum lights (Philips Master TL-D
18 W/950 Graphica) and lights emitting a
higher fraction of UVA and UVB (Sylvania
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Reptistar F18W/6500 K). The combined light
intensity was set to 200 to 210 mmol m−2 s−1 for
wavelength 400 to 700 nm and 4 to 5 mmol m−2
s−1 for wavelength 280 to 400 nm.
on minimal medium containing isoleucine.
Mock treated plants (n ¼ 12) were included in
each plant experiment to detect any system-
atic contamination with external bacteria.
Phyllosphere inoculation
Bacteria grown on R-2A+M agar plates were
suspended in 10 mM MgCl2 solution, and the
OD600 was adjusted to 0.2 for each strain. The
final inoculation suspension had an OD600 of
0.02 for all treatments. For single-strain inocu-
lations, 150 ml of OD-adjusted strain suspension
was added to 1.35 ml 10 mM MgCl2 solution.
For two- and three-strain combinations, 75 or
50 ml of each strain were added, respectively.
For the seven-strain community, 100 ml of each
OD-adjusted strain suspension was mixed,
and then a 10-fold dilution was prepared for
the final inoculum. The final suspension was
mixed well, and then 10-day-old Arabidopsis
seedlings were inoculated by slowly pipetting
50 ml over the whole seedling. A 10-fold dilu-
tion series was prepared of each inoculum and
spotted on R-2A+M agar plates to enumerate
total bacterial load. For strain mixes, appro-
priate dilutions were plated on R-2A+M agar
plates to verify presence of all strains on the
basis of colony morphology.
Phyllosphere harvest and bacterial colony
forming unit (CFU) enumeration
Bacterial colonization in the phyllosphere was
enumerated when plants were 28 or 29 days
old. The whole phyllosphere was harvested
with sterile tweezers and a scalpel and was
placed in a 2-ml tube containing 200 ml 100 mM
phosphate buffer pH 7 and a sterile 5-mm metal
ball. The weight of the tube was recorded with
and without the plant for plant fresh-weight
calculation. The harvested phyllosphere was
subsequently crushed for 45 s at 30 Hz with a
TissueLyser II (Qiagen). Phosphate buffer (600 ml)
was added to the crushed plant material and
was mixed thoroughly; 100 ml of this suspension
were transferred to a 96-well plate to prepare a
10-fold dilution series in 100 mM phosphate
buffer. The dilution series was spotted on R-2A+M
agar plates. In addition, 50 ml of each 10−3- and
10−4-fold dilutions were plated on 9-cm round
R-2A+M agar plates. If selective plates contain-
ing streptomycin were used (for Sphingomonas
selection), 50 ml of dilutions 10−1 and 10−2 were
plated in addition. Plates were incubated at
room temperature and CFUs were counted
after 1 to 3 days on dilution series and after 4 to
7 days on round plates. If a strain was not found
on the lowest-available dilution, its value was
set to 0.9 CFUs for this sample for further anal-
ysis. Rhodococcus sp. Leaf233 was selectively
grown on minimal medium supplemented
with maltose (5 mM) when combined with
Pseudomonas sp. Leaf15. Colonies of Leaf233
in mixtures with Microbacterium sp. Leaf179
were differentiated by re-streaking colonies
Shake flask cultivations
At-LSPHERE isolates grown on R-2A+M me-
dium were suspended in 4 ml 10 mM magne-
sium chloride solution at an approximate OD600
of 3. Each strain was inoculated at an OD600 of
0.025 into 100-ml baffled Erlenmeyer flasks
containing 10 ml of a liquid minimal medium
with the same base composition (ions and
vitamins) as in the carbon source screen. This
medium contained all 44 growth yielding car-
bon sources used in the in vitro screen (table
S1) at a total concentration of 10 mM C, with
each carbon source at a relative concentration
corresponding to the medium composition
used in the modeling. Strains were inoculated
in four biological replicates in monocultures
and in the pairwise and community combina-
tions used in the plant experiments. Cultures
were grown at 22°C with shaking at 200 rpm
for 60 hours to allow strains to reach stationary
phase. Cell numbers in each culture were enu-
merated through a 10-fold dilution series
spotted on R-2A+M agar plates.
Data analysis
Carbon source–utilization data, plant colo-
nization experiments, and shake flask experi-
ments were analyzed with R 4.04 in RStudio.
For the carbon source screen, false-positive
and false-negative rates were calculated on the
basis of 56 isolates that were screened twice
(table S7). The strain phylogeny was based on
full-length 16S ribosomal RNA gene sequences
extracted from the genome sequence of each
strain as described previously (18). Strains that
did not grow on any carbon source were ex-
cluded from all further analyses. The Manhattan
distances of all strains based on carbon source
utilization were calculated with the vegdist
function of the vegan 2.5 package (83). Hier-
archical clustering was conducted with the
hclust function with Ward method (ward.D2).
Principal coordinate analysis was performed
with the cmdscale function in MATLAB R2021a.
Bacterial colonization data was log10 trans-
formed to calculate the median colonization
and statistical significance on the basis of the
Wilcoxon rank sum test. P-values were corrected
for multiple testing with the Holm method.
Effect sizes for the shake flask experiments
were calculated with the cohens_d function
(var.equal = FALSE, hedges.correction = TRUE)
in the rstatix package (84). Log2-fold changes
(combination/monoassociation) were calculated
on the basis of the median absolute abundance.
Data was visualized in R with the package
ggplot2 (85) and was further annotated with
Adobe Illustrator. For data analysis and visu-
alization, the following R packages were used:
tidyverse (86), ape 5.4-1 (87), ggridges 0.5.3 (88),
shades1.4 (89), phylloR (18), and dendextend
1.14 (90).
Generation and curation of genome-scale models
The tool CarveMe (58) was first used to generate
draft metabolic models based on the assembled
genomes of each strain in the At-LSPHERE
collection [(53), BioProjects PRJNA297956 and
PRJEB47672]. The quality of these genomes was
assessed using the tool CheckM (91) (table S8),
which reported a mean completeness of 0.993 ±
0.007 and a mean contamination of 0.005 ±
0.007 (mean ± SD, [0,1]). We compared the pre-
dicted growth capabilities of each draft model
against data from our in vitro carbon source
screen and performed the following steps on each
draft model: First, we used the tool NICEgame
[(62), github.com/EPFL-LCSB/NICEgame] to
generate sets of new biosynthetic and transport
reactions [drawn from the BiGG database (92)]
that would allow the model to produce biomass
from each growth-supporting carbon source
identified in our in vitro screen. We used this
process, which relies on known reaction thermo-
dynamic constraints (93, 94), to produce at most
10 alternative sets of reactions for each growth-
supporting carbon source. We separately integ-
rated each set of reactions into the draft model
and tested whether it could produce biomass
on a simulated minimal medium (table S6) sup-
plemented with each of the 45 carbon sources
used in the in vitro screen. We also tested the
growth of the model when combinations of re-
action sets from up to three carbon sources were
integrated, selecting the most accurate model
(i.e., the most representative with the fewest
false positives) as measured by Matthews cor-
½
Þ=
ð
relation coefficient TP (cid:2) TN (cid:3) FP (cid:2) FN
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
p
(cid:4)
Þ
ð
Þ TN þ FN
ð
Þ TN þ FP
ð
Þ TP þ FN
ð
TP þ FP
for further curation. Most models reached this
stage having had sets of reactions from only
one (111 models) or two (82 models) growth-
supporting carbon sources integrated, as add-
ing reactions that enable growth on one
resource can resolve additional gaps that
enable growth on other resources. The carbon
sources most often used for gap-filling were
maltose, succinate, gluconate, and xylose (being
used to gap-fill 40, 26, 23, and 21 models, re-
spectively). To correct for remaining false nega-
tives (i.e., the model did not grow on a carbon
source that supported growth in vitro), we
further added reactions from a different model
in our collection that did recapitulate growth
on the relevant carbon source. A maximum
false-positive rate of either 10 carbon sources or
half of all true positives for the model, which-
ever was smaller, was set to avoid integrating
an excessive number of new reactions. False
positives for a given carbon source were cor-
rected by removing internal reactions rele-
vant to its metabolism or by restricting the
relevant transport reaction when this was not
Schäfer et al., Science 381, eadf5121 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
successful. Model- and carbon source–specific
accuracies are summarized in fig. S5, and re-
actions added to the models as part of the
curation are enumerated in fig. S4 and table S3.
We identified no relationship between model
accuracy and either the size (fig. S6B) or the
completeness of the underlying genome (fig.
S13). A final quality control was performed on
each model (59), consisting of testing for mass
and charge balance; performing a leak test to
ensure no metabolites could be produced from
nothing; standardizing the metabolite name-
space; adding reaction subsystems; and adding
additional gene, metabolite, and reaction iden-
tifiers when available. A final report was gen-
erated for each model with the validation tool
MEMOTE [total score = 0.84 ± 0.02 (mean ±
SD, n ¼ 224)] (95), and balanced accuracies for
individual models and pairwise interaction pre-
Þ=2,
dictions were calculated as TPR þ TNR
where TPR and TNR represent the true-positive
rate and false-positive rates, respectively. All
scripts for model generation and simulation, as
well as the models and quality reports, are avail-
able at github.com/VorholtLab/i-At-LSPHERE.
ð
Computing mono- and coculture growth
All growth simulations were performed using
the COBRA Toolbox v2.24.3 (96) with the
CPLEX solver v12.10 (IBM) in MATLAB R2021a
(MathWorks). Nonlimiting amounts ( vmax ¼
1000 mmol gDW–1 hour–1) of a minimal me-
dium composition containing ions, water, and
sources of nitrogen, sulfur, and phosphorus
were provided to the models, along with vita-
mins at vmax ¼ 0.15 mmol gDW–1 hour–1 (table
S6). Limiting amounts of the 45 carbon sources
tested in our in vitro screen were provided at
abundances intended to broadly estimate the
relative availabilities of resource types on leaf
surfaces (36, 38, 39, 54) (vmax ¼ 0.15 mmol
gDW –1 hour–1 for sugars and organic acids,
0.075 mmol gDW–1 hour–1 for amino acids,
and 1.5 mmol gDW–1 hour–1 for methanol).
Model growth was simulated with biomass
as the objective function and a minimal ATP
maintenance flux of 0.5 mmol gDW–1 hour–1.
Optimizations were also set to minimize all
reaction fluxes to more closely simulate efficient
proteome utilization and minimize metabolite
cycling (97). For each pair or community, the
growth of each strain was first simulated in-
dividually, and the resulting biomass flux val-
ues and resource uptake fluxes were recorded.
Models were then merged by integrating them
into a common extracellular compartment
(98, 99). Coupling constraints were introduced
to avoid infeasible solutions in which one or-
ganism produced metabolic flux for the other
without producing biomass itself (34, 100).
Additionally, metabolite uptake directional-
ities were fixed to those observed in monocul-
ture to minimize inconsistencies in resource
preferences between mono- and coculture.
The sum of biomass reactions was set as the
objective to be optimized, and exchange reac-
tion vmax values were set as equal to those of
the models in monoculture, thus simulating
an equal abundance of resources between the
mono- and coculture conditions. The resulting
biomass flux values were recorded and used to
calculate interaction scores, which were de-
fined as the log2 ratio of biomass flux in co-
culture to that in monoculture. Interaction
scores were limited to between –5 and 5, with
extreme log2-fold changes falling outside this
range being set to –5 or 5.
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AC KNOWLED GME NTS
We thank S. Hegi and M. Berger for experimental support;
A. Şahin, O. Oftadeh, and D. Machado for helpful discussions on
the metabolic modeling; and C. Pestalozzi for contributing to
the visualization shown in Fig. 3B. Funding: This study was
supported by Swiss National Science Foundation grant NRP72
(J.A.V.), a European Research Council Advanced Grant (PhyMo, no.
668991) (J.A.V.), Swiss National Science Foundation grant
200021_188623 (V.H.), NCCR Microbiomes, Swiss National
Science Foundation (51NF40_180575) (V.H. and J.A.V.), and a
James S. McDonnell Postdoctoral Fellowship (2020-1332) (A.R.P.).
Author contributions: Conceptualization: M.S., A.R.P., and
J.A.V. Methodology: M.S., A.R.P., C.M.F., E.V., and V.H.
Investigation: M.S., A.R.P., R.K., and M.B.-M. Visualization: M.S. and
A.R.P. Funding acquisition: A.R.P., V.H., and J.A.V. Project
administration: J.A.V. Supervision: V.H. and J.A.V. Writing – original
draft: M.S., A.R.P., and J.A.V. Writing – review and editing: M.S.,
A.R.P., R.K., M.B.-M., E.V., C.M.F., V.H., and J.A.V. Competing
interests: The authors declare that they have no competing
Schäfer et al., Science 381, eadf5121 (2023)
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interests. Data and materials availability: Materials and
methods are available as supplementary materials. The collection
of genome-scale models, as well as scripts for generating the
models and conducting simulations are available through
Zenodo (101). The platescan software (102) and plate images used
for the carbon source screen (81) are available through Zenodo.
License information: Copyright © 2023 the authors, some rights
reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-
article-reuse
Tables S1 to S8
MDAR Reproducibility Checklist
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf5121
Figs. S1 to S13
View/request a protocol for this paper from Bio-protocol.
Submitted 27 October 2022; resubmitted 23 March 2023
Accepted 18 May 2023
10.1126/science.adf5121
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RES EARCH
MICROBIOTA
Emergent coexistence in multispecies
microbial communities
Chang-Yu Chang1,2,3*, Djordje Bajić1,2,4*, Jean C. C. Vila1,2, Sylvie Estrela1,2†, Alvaro Sanchez1,2,5*
Understanding the mechanisms that maintain microbial biodiversity is a critical aspiration in ecology. Past
work on microbial coexistence has largely focused on species pairs, but it is unclear whether pairwise
coexistence in isolation is required for coexistence in a multispecies community. To address this question,
we conducted hundreds of pairwise competition experiments among the stably coexisting members of
12 different enrichment communities in vitro. To determine the outcomes of these experiments, we
developed an automated image analysis pipeline to quantify species abundances. We found that
competitive exclusion was the most common outcome, and it was strongly hierarchical and transitive.
Because many species that coexist within a stable multispecies community fail to coexist in pairwise
co-culture under identical conditions, we concluded that multispecies coexistence is an emergent
phenomenon. This work highlights the importance of community context for understanding the origins of
coexistence in complex ecosystems.
E xplaining species coexistence and the be-
wildering diversity of ecological com-
munities is a major goal of ecology (1).
Historically, this problem has been in-
vestigated through the lens of species
interactions and population dynamics. This
work has played a central role in theoretical
ecology (2, 3), establishing, for example, the
importance of competitive interactions for
community stability (4, 5) and the criteria re-
quired for stable coexistence in species pairs
and pairwise networks (6, 7). An important
caveat is that the ability of any model to fully
capture the population dynamics of empirical
populations is limited, and interactions be-
tween species are often modulated by envi-
ronmental context (8, 9) and by the presence
of additional species (10, 11). As a result, in
recent years, research has started to shift to
directly study coexistence networks (12–14).
A central question is whether the known out-
come of competition between pairs of species,
i.e., their coexistence or competitive exclusion,
can be leveraged to predict the composition of
complex communities and the paths leading
to their assembly (12, 13, 15). If this approach
were fruitful, then it would circumvent the
need to know the full mathematical structure
of population dynamics models to predict com-
munity assembly (14).
There are two opposing views on species
coexistence (Fig. 1A). A reductionist perspec-
tive is that multispecies coexistence is an ad-
1Department of Ecology & Evolutionary Biology, Yale
University, New Haven, CT, USA. 2Microbial Sciences
Institute, Yale University, New Haven, CT, USA. 3Department
of Biology, University of Pennsylvania, Philadelphia, PA, USA.
4Department of Biotechnology, Delft University of
Technology, Delft, Netherlands. 5Department of Microbial
Biotechnology. Centro Nacional de Biotecnología - CSIC,
Campus de Cantoblanco, Madrid, Spain.
*Corresponding author. Email: alvaro.sanchez@cnb.csic.es (A.S.);
d.bajic@tudelft.nl (D.B.); cychang2@sas.upenn.edu (C.-Y.C.)
†Present address: Department of Bioengineering, Stanford University,
Stanford, CA, USA.
ditive affair, and all of the coexisting members
of a community must also coexist as pairs
when isolated from the community context
(14). An alternative view is that coexistence
in a multispecies community is a more com-
plex, or emergent, property of the community,
which is not exhibited by its most elementary
units of coexistence, pairs of species in isola-
tion (16). Which of these two views best reflects
the reality of empirical communities (Fig. 1A)?
Determining which view is more accurate re-
quires deconstructing a community into spe-
cies pairs to determine whether all possible
combinations can coexist. If most can, then
the reductionist view is supported. If few can,
then coexistence is an emergent property of
the community, as is seen in nontransitive
competition [i.e., as in the rock, paper, scissors
game (17–24)], which may allow multiple spe-
cies to coexist even when none of them do as a
pair in isolation (17–24).
Resolving this question is essential in mi-
crobial ecology given the enormous and still
largely unexplained diversity of microbial eco-
systems (13, 25). Directly testing the two
hypothesized scenarios described above is
generally not feasible in natural microbial
communities because of their diversity. Even if
we managed to isolate most community mem-
bers from a given habitat, the number of rep-
licate environments that we would need to
recreate to culture every single pair would
scale quadratically with the community rich-
ness. Recent studies have taken a synthetic
approach by reconstituting species pairs from
natural communities in well-controlled lab-
oratory environments (14, 26, 27). Although
these studies found support for the reduc-
tionist hypothesis, their limitation lies in the
small fraction of coexisting species that could
be isolated and the differences between the
laboratory environment and the original com-
munity habitat.
Here, we sought to directly test the two
hypotheses in an empirical system that is well
suited for this purpose. Our starting point was
a collection of bacterial enrichment commu-
nities that we have recently assembled in well-
controlled synthetic environments containing
glucose as the single externally supplied limit-
ing nutrient (Fig. 1B) (9, 28–31). These com-
munities formed in a manner that is similar to
the “random zoo” model in theoretical ecology
(32). In brief, 12 soil and plant microbiomes
were resuspended in separate test tubes con-
taining M9 minimal medium (9) (Fig. 1B). This
provided us with a diverse pool of bacterial
species containing between 110 and 1290 exact
sequence variants (ESVs) (fig. S1) (9). These
12 initial microbiota solutions were then in-
oculated by a 125-fold dilution into separate
bioreactors containing M9-glucose growth
medium (see the materials and methods), in-
cubated for 48 hours under static conditions
at 30°C, and then serially passaged 12 times
each (~84 bacterial generations under our
conditions) (Fig. 1B) (9). Community composi-
tion at various time points was determined by
16S ribosomal RNA (rRNA) amplicon sequenc-
ing. All communities contained multiple (N <
25) coexisting ESVs belonging primarily to the
families Enterobacteriaceae and Pseudomona-
daceae (Fig. 1B) (9, 28, 30, 33). It was thus pos-
sible in this system to deconstruct multiple
stable communities and reconstitute and com-
pete most pairs of species under the same
starting conditions. This experimental system
allowed us to evaluate whether all pairs of
organisms that coexist as a part of a multispe-
cies community also coexist in isolation (29),
thus directly testing whether coexistence is a
pairwise or an emergent phenomenon.
RESULTS
Coexistence is stable in our
enrichment communities
To establish whether coexistence in these mul-
tispecies enrichment communities is stable,
we set out to analyze the published commu-
nity assembly dynamics data from previous
studies (9, 34, 35) in which the frequencies
(xi) of all ESVs were quantified at the end of
each transfer (i) for 26 representative com-
munities (fig. S2). We determined the inva-
sion fitness [F = log(xi/xi–1)] of every ESV in
these communities over their full assembly
dynamics (i = 2,3, …, 12; see the materials
and methods) and found that a large majority
of the ESVs found at the end of the experiment
exhibited hallmarks of negative frequency–
dependent selection. For 95/99 of these ESVs,
the dependence between fitness and frequen-
cy was best fit by a negative regression slope
(fig. S3), and the equilibrium frequency (x*)
predicted from this linear regression model
[the frequency for which F(x*) = 0] agreed very
well with the empirically observed equilibrium
Chang et al., Science 381, 343–348 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
Is species coexistence an emergent property of communities?
Community
(system)
Species pairs
(elementary units)
No, species coexistence is
predictable from pairs
Yes, species coexistence
is an emergent property
Coexistence
Exclusion
?
Both the community
and all its pairs coexist
The community coexists
but not all the pairs do
ESV equilibrium frequency
four representative
communities
in current study
other 22 communities
C
y
c
n
e
u
q
e
r
f
m
o
r
f
d
e
t
c
d
e
r
i
P
)
*
x
(
n
o
i
t
c
e
e
s
l
t
n
e
d
n
e
p
e
d
1.00
0.75
0.50
0.25
0.00
B
(I) Community assembly dynamics
1.00
Colonization
Isolation
Dilution
x12
Growth
Stable
community
Replicate identical
abiotic environment
Pairs
reconstitution
Dilution
x8
Growth
0.00 0.25 0.50 0.75 1.00
Average frequency over
the last four transfers
D
Pseudomonas.10
x*=0.173
Klebsiella
x*=0.762
y
c
n
e
u
q
e
r
F
0.75
0.50
0.25
2
0
2
0
s
s
e
n
t
i
f
i
n
o
s
a
v
n
I
0.00
inoculum
1 2 3 4 5 6 7 8 9 10 11 12
Transfer
0.00 0.25 0.50 0.75 1.00
Frequency
(II) Isolated abundant species
y
c
n
e
u
q
e
r
F
1.00
0.75
0.50
0.25
0.00
1 2 3 4 5 6 7 8 9 10 11 12
Community
Enterobacteriaceae
Citrobacter
Enterobacteriaceae
Klebsiella
Raoultella
Raoultella.1
Salmonella
Salmonella.1
Yersinia
Pseudomonadaceae
Pseudomonas
Pseudomonas.1
Pseudomonas.10
Pseudomonas.13
Pseudomonas.2
Pseudomonas.3
Pseudomonas.4
Pseudomonas.9
Comamonadaceae
Comamonadaceae
Comamonadaceae.1
Comamonas.1
Delftia
Delftia.1
Aeromonadaceae
Aeromonas
Moraxellaceae
Acinetobacter.2
Acinetobacter.3
Alcaligenaceae
Bordetella.1
Other
Not isolated
Fig. 1. Enrichment microbial communities allowed us to test the complexity
of species coexistence. (A) The two hypotheses about species coexistence
tested in our study. (B) To discriminate between the two hypotheses, we used an
empirical system constructed from previously assembled enrichment in vitro
bacterial communities under serial growth and dilution cycles (9). In inset I,
we present the full assembly dynamics for a representative community,
showing the frequency of each ESV at the end of every growth period
(transfers). We only show ESVs >2% in frequency, each in a different color.
We chose 12 representative communities with richness ranging between
N = 5 and N = 13 ESVs at transfer 12 (inset II) and isolated most community
members (colored bars) covering an average of 89.4% of the abundance.
Gray bars represent ESVs that we were not able to isolate (see the materials
and methods). Raw data were obtained from previous studies (9, 34, 35).
(C) Frequency-dependent dynamics predicted the empirically observed
equilibrium frequencies. Empirical equilibrium frequencies (horizontal axis)
were quantified as the average frequency of an ESV in the last four transfers
of the community assembly process (transfers nine to 12). To determine the
predicted equilibrium frequency x* (x axis), we first quantified the invasion
fitness Fi = log (xi/xi–1) for each ESV at each transfer and then regressed this
Fi against ESV frequency. This regression yielded a negative slope for 95/99
ESVs found near the equilibrium in their respective community (fig. S3),
indicating that these ESVs are subject to negative frequency–dependent
selection. In these cases, we estimated the equilibrium frequency x* as
the x-intercept of the regression line (figs. S3 and S4). (D) Two examples of
invasion fitness analysis from the community in inset I showing negative
frequency–dependent selection. The yellow line represents the linear fit
as determined by least-squares regression (N = 11, R2 = 0.92 and N = 11, R2 =
0.70 for the top and bottom panels, respectively). The x-intercept was used
to estimate the equilibrium frequency x*, which is shown as a vertical
dashed line.
frequencies, which we determined as the av-
erage frequency of the ESV over the last four
transfers (Fig. 1C, fig. S3, and materials and
methods). By contrast, ESVs that were only tran-
siently present during community assembly but
were not part of the final stable community
generally exhibited either negative average
fitness values or equilibrium frequencies close
to 0 (figs. S4 and S5). Overall, our quantitative
analyses indicated that the ESVs that were pres-
ent in the final transfer of our multispecies
enrichment communities could invade from
low frequency, fulfilling the mutual invisibility
criterion of stable coexistence (36).
Quantification of pairwise competition assays
To empirically test whether stable multispe-
cies coexistence was a pairwise phenomenon
in our enrichment communities, we chose 12
representative communities containing between
five and 13 ESVs in stable equilibrium, plated
them on their final transfer, and then selected
at least three morphologically distinct isolates
from each community (fig. S6 and materials
and methods). Using Sanger sequencing, we
obtained the full-length sequence of the 16S
rRNA gene of these isolates, aligned it with the
ESVs that were found in their communities of
origin, and retained all isolates with at least
200–base pair consensus sequence and four
or fewer mismatches. This resulted in a total
of 62 isolates, 40 with fully matching align-
ments and 22 with one to four mismatches
Chang et al., Science 381, 343–348 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
Pairwise competition experiment
Initial frequencies
One stable
community
Isolation
95% 5%
50% 50%
5% 95%
Dilution
x8
Growth
Start
End
B
n
o
i
t
c
a
r
F
1.0
0.8
0.6
0.4
0.2
0.0
6
3
2
9
3
333
7
3
33
6 12 5
4
4
4
6666
666
666
9
5
888
9 13 11
7
8
5
9 10
7
5
9999 101010 2121212121
3030303030 4040404040
n. of ESVs
n. of isolates
n. of tested pairs
competitive exclusion
on the path to
competitive exclusion
stable coexistence
(mutual invasibility)
coexistence without
evidence of
mutual invasibility
inconclusive
9 10 11 12
1
2
3
4
6
7
5
8
Community
C
y
c
n
e
u
q
e
r
F
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
Competitive exclusion
On the path to
competitive exclusion
Stable coexistence
(mutual invasibility)
Coexistence without
evidence of
mutual invasibility
Inconclusive
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
y
c
n
e
u
q
e
r
F
0
8
0
8
y
c
n
e
u
q
e
r
F
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
y
c
n
e
u
q
e
r
F
0
8
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
y
c
n
e
u
q
e
r
F
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
8
0
8
0
8
8
0
Transfer
0
8
0
8
0
8
0
8
0
8
8
0
Transfer
0
8
0
8
0
8
0
8
8
0
Transfer
8
0
Transfer
0
8
Transfer
Initial frequencies
95%
50%
5%
Fig. 2. Multispecies coexistence is an emergent property of the community.
(A) To determine whether isolated species pairs coexist or outcompete one
another, we cultured each pair at three different initial frequencies. Pairs were
propagated in the same culture conditions as their community of origin for
eight consecutive passages. The pairwise competition outcomes of all 12
enrichment communities are shown in (B), and communities are ordered
by the number of strains in each community from the smallest (three taxa) to
the largest (10 taxa). The numbers above in each bar show the number of ESVs,
the number of isolated strains, and the number of tested pairs, respectively.
Note that some communities have missing pairs because these pairs either
did not have any colonies in co-culture or had low classification model accuracy.
(C) Competition outcomes of 144 pairwise co-cultures. Mean frequencies and
95% confidence intervals were determined by Poisson sampling (N = 1000;
see the materials and methods). For clarity, we plotted in all cases the frequency
of the isolate ending with a lower average frequency in time point 8 (T8). In
coexisting pairs, the mean equilibrium frequency on the final transfer is
represented by a horizontal dashed line, and the 95% confidence interval
(computed from Poisson sampling, N = 1000) as a shaded area around it. Each
of the inset grids indicates the change in frequency from the initial time point
(T0) to the final one (T8). The background color represents the competition
outcomes, and the line color indicates the three initial frequencies. To establish
significant changes in frequency between T0 and T8 in each experiment, we
used Wilcoxon–Mann-Whitney tests with N = 2000 and a significance threshold
of P < 0.05 (see the materials and methods).
(fig. S7 and materials and methods), covering
on average 89.4% of the ESV composition of
the original communities (Fig. 1B).
We then performed every possible pairwise
competition experiment among the isolates of
each community by mixing inocula of pairs of
isolates and passaging each mixture for eight
growth-dilution cycles in the same glucose
minimal medium at the same temperature
(30°C) used in the original community enrich-
ment experiments (Fig. 2A). All pairwise com-
petition experiments were performed three
times, each at a different starting count pro-
portion of ~5:95, ~50:50, and ~95:5 (Fig. 2A
and materials and methods). During each
growth cycle, the cells were incubated for
48 hours, after which the resulting culture
was diluted 125-fold into fresh medium, as
was done in the original community assembly
experiment (9). At the end of the last dilution
cycle, we measured the composition of our
pairwise co-cultures by plating them on Petri
dishes and counting the colonies belonging to
each isolate.
To avoid human bias in colony morphology
identification, we adopted an automated image-
processing pipeline (fig. S8) combined with a
machine-learning approach for classification
using 159 × 3 = 477 co-culture images on the
basis of 40 colony morphology features (figs.
S9 and S10, table S1, and supplementary mate-
rials). The pipeline started by extracting color
channels and correcting for uneven backgrounds,
followed by segmenting colony objects and ex-
tracting the morphological features from these.
These colony features were analyzed using ran-
dom forest classification to determine whether
each colony present in the co-culture image
belonged to one morphotype or another (fig.
S10). This approach allowed us to quantify the
number of colony-forming units of each of
the two competitors in pairwise co-culture. Of
Chang et al., Science 381, 343–348 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
Community
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
7
8
9
R
a
n
k
competitive exclusion
on the path to
competitive exclusion
stable coexistence
(mutual invasibility)
coexistence without
evidence of mutual invasibility
B
t
n
u
o
C
900
600
300
0
0
Number of expected nontransitivity
10
20
30
Fig. 3. Competitive hierarchy prevails among species pairs in stably coexist-
ing communities. (A) All isolates in our 12 communities were rank-ordered from top
to bottom on the basis of the number of other isolates that they excluded in pairwise
competition, using data from the experiments shown in Fig. 2. The gray nodes in
the network represent each individual isolate. Red arrows point from the winning
isolate of a pairwise competition to the losing one. Blue lines connect isolates that
coexist. (B) Binomial distribution with N = 77, P = 0.25 showing the expected number
of pairs that exhibit transitivity if we randomly swapped the coexistence and exclusion
links in (A). The red open circle marks the experimentally determined number of
trios that broke transitivity (in our case, zero).
the 159 competing pairs, six did not yield a
measurable optical density in either of the
three competition assays regardless of their
inoculation frequencies, and no colonies were
detected. Because we could assign neither co-
existence nor competitive exclusion to these
pairs, which were also formed by pairs of
isolates that were not present at the final
transfer in monoculture, we excluded them
from further analysis. We removed nine ad-
ditional pairs for which the trained model
performed poorly on the validation datasets
(accuracy score <0.9; fig. S11 and materials
and methods). We therefore used N = 144
pairs in our analysis. The automated pipe-
line approach agreed well with visual colony
identification, yielding comparable results for
both the total colony count on a plate [R2 =
0.85; root-mean-square deviation (RMSD) =
17.67; N = 381] and the relative frequency
of different colony morphotypes (R2 = 0.87;
RMSD = 0.17; N = 381) (fig. S12) for the 127
pairs with an accuracy score > 0.9 that could
be discriminated by eye.
Multispecies coexistence is an
emergent property
In 26.4% of the pairs (38/144), one of the two
competitors had become competitively excluded
by the end of the last dilution cycle in all three
competition experiments (i.e., no colonies
were detected on the plates) regardless of its
starting inoculation proportion (Fig. 2, B and
C, dark red). We marked these outcomes as
competitive exclusion. For 45.1% of the pairs
(65/144), the frequency of the losing species
declined (DF < 0) in all three competition
experiments regardless of its initial propor-
tion (Fig. 2, B and C, light red box, and
materials and methods). This indicates that
its trajectory was on the path to competitive
exclusion. Adding these outcomes to the com-
petitive exclusion category, we found that
71.6% of the pairs (103/144) failed to coexist
in the absence of the other community mem-
bers. These results were not driven by the poor
competitive ability of the least-abundant ESVs,
because eliminating from the analysis those
isolates with ESVs with <0.05 frequency in the
stable multispecies communities still produced
a majority of competitive exclusion outcomes
(61/84 = 72.6%) (fig. S13).
All 12 communities contained at least one
pair, but generally more, that could not coexist
in isolation (Fig. 2B). The fraction of pairs ex-
hibiting competitive exclusion was similar
across communities regardless of their rich-
ness (Fig. 2B). These results are not consistent
with the additive assembly rule proposed pre-
viously (14), which would have predicted less-
diverse communities composed only of those
taxa that can coexist in isolated pairs. There-
fore, complex multispecies coexistence could
not be reduced to pairwise relationships in our
communities, and it is thus likely an emergent
property of the whole community.
A substantial fraction of pairwise competi-
tions (28.5% of the pairs, 41/144) did not result
in competitive exclusion, indicating that pair-
wise coexistence may still be common among
members of a stable multispecies community.
Among these 41 pairs, 29 were still coexisting
in all three competition experiments after eight
transfers (Fig. 2, B and C, blue). To identify
those pairs that coexist stably, we apply the
mutual invasibility criterion, which requires
that both species must be able to invade each
other from low frequency (36) (Fig. 2, B and C,
dark blue). Methodologically, this requires that
sign(Dx) = sign[x* – x(T0)] for both species in
all three pairwise competition experiments
(see the materials and methods). Here, Dx de-
notes the change in a species frequency be-
tween the final and initial transfers, x* is the
equilibrium frequency for that species (which
we determined by averaging the final transfer
frequencies of the three experiments; see the
materials and methods), and x(T0) is the spe-
cies’ inoculation frequency on the first day of
the experiment. This condition was met in 21
of the 29 coexisting pairs. The criteria for mu-
tual invasibility were not met in the remaining
eight coexisting pairs, so we classified these as
Chang et al., Science 381, 343–348 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
coexisting without evidence of mutual invasi-
bility (Fig. 2, B and C, light blue). The remain-
ing fraction of our pairs (12/144, 8.3%) did not
offer conclusive results because the outcome
of the competition was not consistent in the
three experiments. We left these as inconclu-
sive (Fig. 2, B and C, gray).
Competitive exclusion is hierarchical and transitive
In an effort to better explore the structure of
our pairwise competition network, we used
the competition outcomes shown in Fig. 2 to
rank all isolates in each community by the
number of competitors that each of them ex-
cluded (see the materials and methods). We
found that competitive exclusion was almost
fully hierarchical: In all but one of the 103 pairs
in which one of the two isolates was excluded,
the lower-rank species was the one that was
excluded (Fig. 3A). The ranks in the competi-
tive hierarchy were positively correlated with
the frequency rank of the corresponding ESV
in the parent community (Spearman’s r = 0.42,
P < 0.001, N = 62; fig. S14), but this pattern was
mostly driven by less-diverse communities (fig.
S14), which recapitulates previous findings from
plant communities (37). We also found that
competitive hierarchy was positively correlated
with the strain’s growth rate in glucose medium
(Pearson’s r = –0.314, P = 0.0129, N = 62; fig. S15).
Regarding the type of metabolism, respiro-
fermenters had a higher average competitive
rank (mean = 2.54) than obligate respirers
(mean = 4.72) (Wilcoxon–Mann-Whitney test
P < 0.001, N = 62; fig. S16), a pattern consistent
with our previous work (9, 28).
An extreme case of emergent coexistence
may occur when coexistence networks are non-
transitive (17, 24). However, we found that
nontransitive cycles were unlikely to stabilize
coexistence in our communities. Of 77 triplets
of species that could be connected by compet-
itive exclusion links in our 12 communities, we
did not find a single violation of transitivity
(Fig. 3B). Because the expected fraction of
nontransitive triplets in a random network is
P = 1/4, the probability of observing this out-
come by chance is given by P(0) = (1/4)77 =
4.4 × 10−47 (Fig. 3B).
Discussion
The aim of this study was to empirically test
whether coexistence in microbial communi-
ties is a pairwise phenomenon or if it is an
emergent property of the community. To ad-
dress this question, we isolated most mem-
bers of 12 stable enrichment communities
and determined whether each possible pair
could coexist in the absence of the other mem-
bers of their communities under the same cul-
ture conditions as in the enrichment. Although
a substantial fraction of pairs did coexist
(29/144, 20.1%), a majority (103/144, 71.5%)
of them ended up in competitive exclusion,
with one of the two members becoming ex-
cluded or on the path to it. This indicates that
coexistence could not be reduced to a pairwise
phenomenon in our enrichment communities
and that the community context is generally
required for species pairs to coexist. Our find-
ing contrasts with the outcome of a recent
empirical study supporting the reductionist
hypothesis, which concluded that the coex-
istence of multiple species in bottom-up as-
sembled communities requires every pair to
coexist in isolation (14).
Given that both hypotheses can be correct
in different communities (14, 16), our results
prompt the question of under which condi-
tions each is most likely to occur. We have not
yet determined whether the complex nature
of multispecies coexistence in our enrichment
communities derives from higher-order inter-
actions, or if it can be explained by a complex
network of pairwise interactions. Another pos-
sible factor that may stabilize coexistence, but
which our study has not addressed, is the rapid
emergence of intra-strain diversity through evo-
lutionary processes. Evolution of new species
interactions, such as the appearance of a new
mutualism, may mediate the emergent coex-
istence of pairs of strains that would other-
wise end in competitive exclusion (16). As for
broader evolutionary patterns, we did not find
a correlation between pairwise coexistence
and sequence similarity (fig. S17), although our
analysis was limited to the 16S marker gene.
Finally, spatial structure is also known to af-
fect microbial coexistence [e.g., (38)], but the
number and nature of spatial niches could not
be identified in a straightforward manner in
our experiments.
Theoretical studies have suggested that
nontransitivity can stabilize the coexistence
of multiple competing species in the presence
of spatial heterogeneity (18) or when com-
petitors have differential competitive abil-
ities on multiple limiting resources (17, 21).
Although the idea of nontransitivity is well
established in theory, empirical studies on
its prevalence are sparse. Our mutual inva-
sion experiments with 144 species pairs from
each of the 12 communities did not find a
single nontransitive trio, suggesting strongly
hierarchical competition among our species.
This discrepancy between theory and our
findings may be caused by the underlying eco-
logical interactions among competing spe-
cies. In our communities, exploitation of the
single externally supplied limiting nutrient
and cross-feeding appeared to be the domi-
nant ecological interactions determining the
community structure (9, 28), whereas non-
transitivity may emerge through interference
competition (39) or through changes in spe-
cies’ competitiveness across resources (40).
Our experiments suggest that pairwise co-
existence is not necessarily required for the
stable assembly of multispecies communities.
However, more complex assembly rules might
still be found to predict and explain multispe-
cies coexistence. Future empirical work with
communities assembled under growing envi-
ronmental complexity will be necessary to es-
tablish how factors such as spatial structure,
the number of supplied resources, the existence
of higher-order interactions, and fluctuating
conditions may influence the complexity of
coexistence in multispecies communities.
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record/8015230.
ACKN OW LEDG MEN TS
We thank the members of the Sanchez laboratory for helpful
discussions. Funding: This work was partially funded by Young
Investigator Award RGY0077/2016 from the Human Frontier
Science Program to A.S. C.-Y.C. was supported by a Graduate
Student Fellowship for Studying Abroad from the Ministry of
Education, Taiwan. A.S. was partially supported by grant PID2021-
125478NA-100 funded by MCIN/AEI/10.13039/501100011033
and by “ERDF: A way of making Europe.” Author contributions:
C.-Y.C., D.B., and A.S. conceived the idea and designed the study.
C.-Y.C. performed the experiments. C.-Y.C. and D.B. analyzed
the data. C.-Y.C., D.B., J.C.C.V., and S.E. provided reagents and
data. C.-Y.C., D.B., J.C.C.V, S.E., and A.S. discussed the results and
drafted the paper. C.-Y.C., D.B., and A.S. wrote the final version
of the paper. Competing interests: The authors declare no
competing interests. Data and materials availability: Processed
and raw data can be accessed at Dryad (41). Code used to perform
analyses can be accessed on Zenodo (42). Detailed methods for
assembling the original communities used in this study are
described in (9). License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg0727
Materials and Methods
Figs. S1 to S17
Tables S1 to S3
References (43–53)
MDAR Reproducibility Checklist
Submitted 2 December 2022; accepted 15 June 2023
10.1126/science.adg0727
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RES EARCH
ANTHROPOLOGY
Cooperation across social borders in bonobos
Liran Samuni1,2,3* and Martin Surbeck2,4*
Cooperation beyond familial and group boundaries is core to the functioning of human societies, yet its
evolution remains unclear. To address this, we examined grooming, coalition, and food-sharing
patterns in bonobos (Pan paniscus), one of our closest living relatives whose rare out-group
tolerance facilitates interaction opportunities between groups. We show that, as in humans, positive
assortment supports bonobo cooperation across borders. Bonobo cooperative attitudes toward in-
group members informed their cooperative relationships with out-groups, in particular, forming
connections with out-group individuals who also exhibited high cooperation tendencies. Our findings
show that cooperation between unrelated individuals across groups without immediate payoff is not exclusive
to humans and suggest that such cooperation can emerge in the absence of social norms or strong
cultural dispositions.
M ore than any other species, humans
cooperate across vast contexts, numbers,
and social scales. We live in complex
multilevel societies that promote the
formation of strong cooperative rela-
tionships not only with kin, allies, and friends
but also with distant acquaintances and even
strangers. The extent of human nonkin coop-
eration is unmatched, with trade and sharing
of commodities, knowledge, and skills (1–3)
taking place not only within human residen-
tial units (hereafter “groups”) but also across
these units.
Kin relations and repeated interaction op-
portunities are important foundations of within-
group cooperation across taxa (4, 5). However,
these appear insufficient in explaining human
large-scale cooperation (6). In humans, theoret-
ical and empirical models consistently identify
population structures, individual attributes, and
cultural processes as critical components that
promote cooperation (2, 7–13). These models
predict that cooperation, such as the sharing
of food resources, can emerge if the population
structure permits clustering of similar individ-
uals, for example, when cooperators co-reside
or interact preferentially with one another
(10, 11, 13).
Tolerance and cooperation across groups
are apparent in various animal taxa, including
insects, birds, and mammals (14–17). However,
the ability to cooperate with unrelated out-
group partners with no immediate return is
considered to be an exclusively human feature
(18, 19). Human cooperation across residential
groups facilitates resource and information
transfer and the accumulation of knowledge,
both of which support our long life spans and
1Cooperative Evolution Lab, German Primate Center,
Göttingen, Germany. 2Department of Human Evolutionary
Biology, Harvard University, Cambridge, MA, USA. 3School of
Psychology and Neuroscience, University of St Andrews,
St Andrews, UK. 4Department of Human Behavior, Ecology and
Culture, Max Planck Institute for Evolutionary Anthropology,
Leipzig, Germany.
*Corresponding author. Email: lsamuni@dpz.eu (L.S.);
msurbeck@fas.harvard.edu (M.S.)
prolonged development and allow our species
to thrive across the globe (2, 20, 21). But how
distinctive is this human capacity? And what
are the evolutionary foundations of human
broad cooperation?
Observations of the between-group rela-
tions of bonobos (Pan paniscus), our closest
living relatives together with chimpanzees, chal-
lenge the notion that cooperation with no
immediate return between distantly related
individuals across groups is exclusive to humans.
Within certain bonobo populations, individuals
from distinct groups engage in a diverse range
of interactions that span from aggression to
cooperation, including grooming, forming
alliances, and sharing high-value food resources
(22–31). Despite prolonged and tolerant inter-
actions between different groups, bonobos still
maintain a clear in-group–out-group distinction
(32). However, our understanding of bonobo
cooperation across groups largely relies on des-
criptive information, which lacks empirical ex-
amination of the frequency, social structures,
and underlying mechanisms that are involved.
In this study, we characterized bonobo coop-
eration across groups by observing within- and
between-group interactions of 31 adults living in
two social groups (Ekalakala: three adult males
and eight adult females; and Kokoalongo:
seven adult males and 13 adult females) in
the Kokolopori Bonobo Reserve, Democratic
Republic of the Congo (DRC). During a 2-year
observation period, we documented 95 en-
counters between the two groups, which lasted
for around 20% of the total observation time.
The durations of bonobo between-group en-
counters varied substantially, from less than
1 hour to 14 consecutive days [12.5 ± 17.2 hours
(mean ± SD)], which emphasizes that bonobo
groups can associate in a nontransient manner,
thereby facilitating opportunities for consistent
cross-group exchange.
Results
Bonobo within- and between-group interac-
tions consisted of a variety of cooperative acts,
including 3744 grooming interactions, 592 coa-
litions, 2920 cases of noncoalitionary aggressions,
and 650 cases of food transfers (see supple-
mentary materials for definitions). Between-
group interactions represented 10% (N = 383,
between 115 dyads) of all cases of grooming,
15% (N = 87, between 43 dyads) of all co-
alitions, 14% (N = 402, between 126 dyads) of
all noncoalitionary aggressions, and 6% (N = 41,
between 28 dyads, including 16 donors and
15 recipients) of all food transfers observed.
Although kin selection is a powerful driver
of cooperation and between-group connections,
interactions in this bonobo population are
unlikely to be driven solely by genetic related-
ness. Bonobos are a male philopatric species,
and the only mother-offspring pairs in the two
groups are four mothers and their sons who
reside in the same group. Whereas female
migration can produce close familial connec-
tions across groups, permanent female immi-
gration between the two groups has not been
observed since the establishment of the research
site in 2016, despite numerous (N = 22) immi-
grant females arriving to or leaving from the two
groups. Finally, analysis of 15-loci autosomal
microsatellite genotypes revealed that only 6%
of both within- and between-group dyads are
second-degree relatives or higher (see supple-
mentary materials).
The bonobo cooperative acts vary in their
susceptibility to cheating and delay of potential
payoff. Grooming in bonobos is a frequent be-
havior that necessitates little initial investment
by actors and allows immediate return; it there-
fore involves opportunities to both test partners’
willingness to cooperate and to receive imme-
diate reward. Bonobo coalition formation re-
quires joint action against a common opponent,
which may provide benefits to all partners.
Finally, food transfer (hereafter “sharing”) is an
act that can incur an initial cost to actors (re-
duced energetic or nutrient intake) and offers
little guarantee of a future return, which re-
sults in an uncertain payoff to actors. Increased
defection opportunities in between-group food
sharing relative to grooming are visible in our
dataset. Across the 2 years of observation, food
sharing was reciprocated only among 4 of the
28 between-group dyads that shared food. In
comparison, grooming investment was highly
reciprocated within and between groups (fig.
S1), and >70% of between-group grooming in-
teractions involved immediate return (within
the same interaction). The variability of the
risk that benefits will be reciprocated among
these cooperative interactions provides a plat-
form through which to explore the underlying
structures of cooperation across borders in a
nonhuman species.
In human networks, population structures
that allow for the positive assortment of coop-
erators support the proliferation of coopera-
tion by pooling the benefits among those who
Samuni et al., Science 382, 805–809 (2023)
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cooperate (9–11, 13). Cooperation assortment
refers to the proclivity of individuals to selec-
tively interact with others who have similar
cooperative tendencies or traits and requires
interaction strategies to be nonrandom. To
investigate whether nonrandom assortment
underlies bonobo cooperation across social
borders, we first established that bonobos
interacted nonrandomly and exhibited a pref-
erence for specific partners both within and
between groups. Specifically, using data per-
mutations (see supplementary materials), we
calculated the expected variance of bonobo
within- and between-group grooming, coalition,
and food-sharing interactions if interactions
were randomly distributed among available
partners and compared this variance against
the “true” interaction variance (observed vari-
ance). In accordance with assortativity predic-
tions, the observed variance of all interaction
types significantly exceeded what is expected
by chance, both within and between groups
(all P < 0.001; fig. S2).
Partner selectivity in our bonobo population
provides a basis upon which cooperation
assortment can emerge. If bonobos selectively
interact with partners who are more likely to
cooperate, they can increase their chances for
a positive net gain. To examine cooperation
assortment, we operationalized bonobo coop-
erative tendencies using interindividual var-
iation in grooming, coalition formation, and
food-sharing acts expressed within groups
(fig. S3). We constructed a social network for
each of the bonobo interactions and exam-
ined whether individuals categorized as high
cooperators within their groups are more
likely to connect groups in the different net-
works (Fig. 1).
The social network analyses illustrate that
bonobos who groom, form coalitions, or donate
more food to in-group members are more likely
to form the same kinds of connections with
out-group members (Fig. 1 and fig. S4). By
contrast, within-group cooperative tendencies
within one form of cooperation do not appear
to predict connections between groups in another
form of cooperation (figs. S5 to S7). These pat-
terns may emerge if bonobos have consistent
cooperative tendencies within, rather than across,
the different cooperation forms—whether inter-
acting with in-group or out-group. It is unlikely
that kin relations explain the observed coop-
erative patterns between groups because none
of the between-group dyads were parent-
offspring and only 5, 12, and 11% of the dyads
that groomed, formed a coalition, and shared
food between the groups, respectively, were
identified as at least second-degree relatives
(see supplementary materials).
Overall, the social networks suggest that
bonobos who more frequently cooperate within
their groups are (i) more likely to engage in
the same behavior with out-group individuals
relative to less-frequent within-group cooper-
ators and (ii) engage with out-group members
who are also frequent within-group coopera-
tors (assortment of cooperators). To test these
two characteristics of the bonobo networks,
we used Bayesian Poisson regression models.
First, we tested how individual within-group
cooperative tendencies affected cooperative
relationships with out-group members. Account-
ing for interaction opportunities, we found that
bonobos who showed higher within-group
food-sharing or coalitionary tendencies were
also more likely to form the same kind of
connections with out-group individuals [food
sharing: estimate = 0.74, 95% credible in-
terval (CI95%) = 0.38 to 1.14, odds ratio 2.1
per 1–standard deviation (SD) increase, table S1;
coalition: estimate = 1.11, CI95% = 0.78 to 1.47,
odds ratio 3 per 1-SD increase, table S2]. We did
not find the same pattern when using grooming
as the cooperative behavior (table S3). Identical
analyses conducted to examine the impact of
the within-group cooperative tendencies on
between-group interactions across behaviors
supported the idea of consistent cooperative
tendencies within, but not across, currencies
Grooming
Coalition
Food sharing
High within-group cooperator
Medium within-group cooperator
Low within-group cooperator
Within-group
Between-group
Female
Male
Unrelated
Kin
Fig. 1. Cooperation assortment in bonobo social networks. Social networks
indicate that high within-group cooperators tend to be located more centrally and
form the same types of connections across groups. Within-group cooperative
tendencies were operationalized for each cooperative interaction: (i) grooming
network, by dividing the amount of time a bonobo groomed an in-group member
(average individual grooming time: Ekalakala, 2268 ± 881 min; Kokoalongo,
704 ± 439 min) by the average grooming duration within their group; (ii) coalition
network, by dividing the number of times a bonobo formed a coalition with
an in-group member (average individual coalition: Ekalakala, 36 ± 27; Kokoalongo,
63 ± 53) by the average coalition times within their group; and (iii) food-sharing
network, by dividing the number of times a bonobo donated food to an in-group
member (average individual sharing: Ekalakala, 27 ± 18; Kokoalongo, 16 ± 15) by the
average food-sharing times within their group. Node colors indicate high (66th
percentile; red), medium (between the 33rd and 66th percentile; blue),
and low (below the 33rd percentile; white) within-group cooperators. Node shape
indicates males (square) or females (circles), and node size indicates the number
of both incoming and outgoing connections possessed by an individual, with
larger nodes signifying a greater number of connections. Edges represent
connections with values equal to or greater than the population mean, with their
colors indicating whether partners reside in the same (yellow) or different (gray)
groups or whether partners are related (dashed line) or not (solid line). Only
individuals that appeared in the data during both observation years (N = 27 out
of the 31 individuals in the data) are depicted in the social network illustrations.
The individuals that are not connected to the main network are three males from
the Kokoalongo group (food-sharing network) and one male from Kokoalongo
and three nulliparous females from Ekalakala (coalition network).
Samuni et al., Science 382, 805–809 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
(tables S1 to S3). Finally, we also found that
bonobos who had higher sharing tendencies,
but not higher grooming or coalition tenden-
cies, within groups were less likely to engage in
aggression with out-group members (estimate =
−0.36, CI95% = −0.53 to −0.20; fig. S5 and table
S4). Competition and aggression may jeopardize
cooperative relationships, particularly with a
delay between action and reward, as with food
sharing. As such, the reduced likelihood of
between-group aggressions in those with high
food-sharing tendencies may offer a pathway
to foster the maintenance of food-sharing rela-
tionships across groups.
Cooperation assortment can emerge if indi-
viduals interact with those who are more able
and willing to confer benefits (33). Accordingly,
we would expect individuals who are higher
cooperators within their groups to be more likely
to cooperate with out-group members who are
themselves higher cooperators. Therefore, in a
second step, we tested whether the combined
within-group cooperation tendencies of dyads
(examining each cooperation form separately)
predicted interactions between groups. Consis-
tent with this prediction, cooperation patterns
between groups were best explained by the
sum of the within-group cooperative tendencies
of partners (i.e., “cooperation score”). A 1-SD
increase in the food sharing, coalition, or
grooming cooperation scores increased between-
group food sharing, coalition, or grooming odds
by factors of 1.77, 2.63, and 1.35, respectively
(Fig. 2, fig. S8, and table S5). Further, part-
ners who groomed more frequently also had
a higher relative sharing probability (esti-
A
Grooming
B
Food sharing
Cooperation score
Food sharing
Coalition
Female-Male
Male-Male
Cooperation score
Grooming
Coalition
Female-Male
Male-Male
-4 -3 -2 -1 0 1
-4 -3 -2 -1 0 1
1.00
0.75
0.50
0.25
0.00
C
e
e
r
g
e
d
-
n
i
i
g
n
m
o
o
r
G
E
e
e
r
g
e
d
-
n
i
i
g
n
m
o
o
r
G
1.00
0.75
0.50
0.25
0.00
Within-groups
0.75
0.50
0.25
Grooming out-degree
1.00
Between-groups
0.00
0.75
0.50
0.25
Grooming out-degree
1.00
D
e
e
r
g
e
d
-
n
i
g
n
i
r
a
h
S
F
e
e
r
g
e
d
-
n
i
g
n
i
r
a
h
S
1.00
0.75
0.50
0.25
0.00
1.00
0.75
0.50
0.25
0.00
Within-groups
0.00
0.50
0.25
0.75
Sharing out-degree
1.00
Between-groups
0.0
0.1
0.2
0.3
Sharing out-degree
Fig. 2. Positive assortment underlies bonobo cooperation across borders. (A and B) Estimates based
on models that test whether the joint within-group cooperative tendencies of individuals (i.e., cooperation
score) or interactions in other currencies explain their likelihood to groom (A) or share food (B) across
groups. The cooperation score is calculated as the sum of the cooperative tendencies of a dyad based on
either within-group grooming (A) or food donations (B). Shown are the model estimates (black diamonds)
with 50% (yellow rectangles) and 95% (black lines) credible intervals derived from a Bayesian Poisson
regression. (C to F) Generous bonobos are more attractive as interaction partners. The relationships between
grooming [(C) and (E)] and food-sharing [(D) and (F)] in- and out-degree within [(C) and (D)] and between
[(E) and (F)] groups are shown. The in-degree represents the number of partners from whom an individual
received grooming or food, whereas the out-degree represents the number of partners that an individual
groomed or donated food to. The in- and out-degrees are proportional to the potential number of partners
that one can interact with within and between groups. Shown are the data points (N = 31 individuals; females
are represented by circles and males by squares), model estimates (yellow, within-group; blue, between-
group), and the 95% credible intervals (gray) derived from a Bayesian regression.
mate = 0.33, CI95% = 0.05 to 0.61, odds ratio
1.39 per 1-SD increase), and vice versa (esti-
mate = 0.35, CI95% = 0.25 to 0.46, odds ratio
1.42 per 1-SD increase). The sex combination of
the partners had no obvious consistent impact
on their cooperation patterns (Fig. 2, fig. S8,
and table S5).
The between-group connections of coopera-
tors in the different networks confirm the pres-
ence of cooperation assortment in bonobos
and that reciprocity might be at play in sup-
porting bonobo cooperative acts. Nonetheless,
strong connections of high cooperators be-
tween groups may also arise as a result of ran-
dom processes. For example, in a population
with random partner selection and varying
interindividual sharing tendencies, food sharing
is expected to accumulate between those indi-
viduals who share more. The same is true for the
other cooperative interactions. Such a process
can generate stronger cross-group connections
between high within-group cooperators by
chance, without the need for preferential inter-
actions. However, given that partner selection
in Kokolopori bonobos is not random (see
permutation procedure), the observed assort-
ment of cooperators in the different networks
is unlikely to be a mere artifact of random
processes. Further, in the context of food shar-
ing, that only four (14%) between-group dyads
reciprocated food sharing further strengthens
the idea that cooperation assortment is not a
product of chance.
Finally, cooperation can evolve when more-
generous individuals are also more likely to
obtain benefits, whether through reciprocity
or because of their attractiveness as interac-
tion partners. Subsequently, it is predicted
that those who are more able or willing to
benefit others will be more readily chosen by
others as interaction partners. We therefore
examined whether bonobos who groomed or
donated food to more partners (“high out-
degree”) also received grooming or food from
more partners (“high in-degree”) by dividing
the number of partners each individual groomed
or donated food to or received food from by the
total number of potential partners with whom
one could have interacted. Following this pro-
cedure, we generated values between 0 and 1,
with 1 indicating that an individual interacted
with all potential partners. We could not eval-
uate the same question for coalition formation
because there is no clear actor or receiver in
this type of interaction. We found a strong
relationship (Fig. 2) between the grooming
and food sharing in- and out-degrees of bonobos
both within groups [grooming: regression co-
efficient (R) = 0.99; food sharing: R = 0.81]
and between groups (grooming: R = 0.94; food
sharing: R = 0.41). Overall, individuals that were
more generous, by grooming more partners
or donating food to more individuals, were
also more likely to receive benefits from more
Samuni et al., Science 382, 805–809 (2023)
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individuals. The in- and out-degree grooming
patterns were similarly strong within and be-
tween groups, likely because of high grooming
return in bonobos (fig. S1). In comparison, the
relationship between food-sharing in- and
out-degree was especially evident within groups,
where repeated interaction opportunities, and
hence reciprocity or knowledge about part-
ners, are more certain (53% of within-group
dyads shared food reciprocally versus 14% of
between-group dyads).
Discussion
Bonobos, our closest living relative together
with chimpanzees, maintain stable but variable
cooperative relationships that transcend group
boundaries. The bonobo population structure
permits repeated interactions and partner se-
lectivity, which are fundamental components
for the emergence of cooperative relationships.
Bonobo nonkin cooperation across groups in-
cluded food sharing, a prosocial act with
uncertain returns and a high defection proba-
bility that is considered to be a key aspect of
the human collaborative foraging niche. Food
sharing in humans promotes cooperative rela-
tionships that support our expensive life his-
tories by offsetting the risk of food shortfalls
(34). Although the relevance of nonkin food
sharing to the survival and reproduction of
bonobos is unknown, we find that, like humans,
bonobo sharing networks rely on the positive
assortment of cooperators. Nonetheless, the pro-
cesses that support cooperation assortment in
humans and bonobos likely differ.
Our results suggest that various mechanisms,
including reciprocal altruism (i.e., cooperative
investments based on past return) and partner
choice, may explain cooperation assortment
between bonobo groups. Whereas reciprocal
altruism requires repeated interactions be-
tween the same partners and some form of
bookkeeping, partner choice assumes stable
interindividual differences in cooperative char-
acteristics and that individuals have knowledge
of the characteristics of potential partners to
make effective choices (35). Both repeated
interactions and knowledge about partners are
nontrivial when interactions occur between
members of different social groups. As such,
the high group-membership fluidity, transient
interactions, and large social network in human
societies at present may limit the efficiency
and explanatory power of these mechanisms.
Instead, cultural processes and norm psychology
are suggested to stabilize assortment and large-
scale cooperation in humans (2, 13, 19, 20). In
bonobos, the small social network relative to
that of humans and the frequent associations
between individuals from different groups
(32) facilitate interactions and the accumu-
lation of social knowledge beyond one’s own
group (e.g., which out-group individuals are
more able and willing to confer benefits than
others). Such a social structure provides a
basis upon which partner familiarity can enforce
reciprocity beyond group boundaries and co-
operation between groups can be sustained.
Although social norms and culture are consid-
ered the main cooperation mechanisms that
sustain human large-scale cooperation, it is
reasonable to assume that reciprocity may
have played a more crucial role in our evolu-
tionary past when living in smaller societies.
Bonobo society offers a rare opportunity to
study a social system in which individuals from
different groups engage in resource and com-
modity exchange. Our research builds upon
previous experiments in captivity that show
that bonobo food sharing with unrelated and
unfamiliar individuals is not solely motivated
by selfish interests or immediate rewards
(30, 31). The convergence of evidence from
both wild and captive studies suggests that the
xenophilic tendencies of bonobos may be in-
trinsic to the species as a whole.
The tolerant and cooperative between-group
relations of bonobos (22–26, 28, 32) stand in
contrast to the ubiquitously hostile between-
group relations and the strong in-group favoritism
observed in their sister species, chimpanzees
[Pan troglodytes (36–38)]. A leading hypothe-
sis in Pan speciation posits that bonobos have
experienced a selection against aggression [the
self-domestication hypothesis (39, 40)], which
has led to a reduction of in-group favoritism
and an overall increase in prosocial tendencies
toward others, whether in-group or out-group
(41). Therefore, it is often assumed that bonobos
are inclined to interact prosocially with every-
one, both strangers and familiar individuals,
and that it is their nondiscriminatory pro-
social tendencies that permit out-group rela-
tionships and cooperation. Although the marked
prosocial tendencies that the Kokolopori bonobos
exhibit toward out-groups support the self-
domestication hypothesis, our findings addi-
tionally suggest that bonobo prosocial tendencies
are discriminatory. Instead of generally high
prosocial tendencies, we propose that it is the
strategic social ties that bonobos form with those
who are more able and likely to confer benefits
to others that stabilizes bonobo cooperation
across borders.
Bonobos are not the only nonhuman species
that exhibit cooperative relationships between
nonkin across groups (14–17). For example, in
bottlenose dolphins, males form “third-order
alliances” with unrelated out-group males that
allow them to successfully compete over fe-
males (16). Third-order social alliances in dol-
phins are akin to the bonobo coalitions that
are formed between males and females of
different groups. In both species, these inter-
actions confer improved access to contested
resources to all allies and/or increased social
status, which is therefore better categorized
as mutualism. However, bonobo cooperation
across borders also includes a behavior that
cannot be explained by mutualism, thereby
incorporating cooperation aspects that are
considered exclusive to humans, such as the
ability to act prosocially toward unrelated
out-group members with no guarantee of a
return.
Owing to habituation status and data col-
lection constraints, our study only included two
out of at least four bonobo groups that are ob-
served to regularly interact within the Kokolopori
population (32), resulting in an investigation
of a relatively small social network (31 indi-
viduals). Although these bonobos maintain a
wider social network than that represented
here, the overall size of this bonobo social
network is limited and residential mobility is
considerably reduced compared with humans
(32), making it challenging to examine coopera-
tion mechanisms of bonobos and humans on
an equal footing. Further, unlike bonobos,
cooperation across groups in humans extends
beyond pair-wise interactions to also include
large-scale cooperation (1–3). Nevertheless, our
bonobo results suggest that the higher-order
social connections and cooperative pair-wise
relationships that humans form across groups
may have a different evolutionary history than
is often assumed.
Theories in human evolution posit that pair
bonding, exogamy, and the ability to recognize
maternal and paternal kin and affines (i.e.,
relatives by marriage) are necessary compo-
nents of between-group bonds and cooperation
(19, 42). Here, bonobos offer an alternative
scenario, in which cooperative ties between
groups are formed in the absence of exogamy
or strong bilateral kin recognition. It is there-
fore plausible that an ancestral state of human
between-group, pair-wise cooperation is that
of a bonobo-like social system, in which toler-
ance toward out-groups facilitates the emergence
of cooperation in the absence of high degrees
of genetic relatedness. Consequently, bonobos
offer a key comparative model to human social
systems and a rare opportunity to reconstruct
the ancestral conditions of human large-scale
cooperation.
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ACKN OWLED GMEN TS
We thank the Institut Congolais pour la Conservations de la Nature
(ICCN) and the Ministry of Scientific Research and Technology
in the DRC for their support and permission to work in the Kokolopori
Bonobo Reserve, DRC. We also thank the Bonobo Conservation
Initiative and Vie Sauvage, especially S. Coxe, A. Lotana Lokasola,
A. Menante, and staff members of the Kokolopori Bonobo Research
Project for supporting our work. We thank L. Vigilant and V. Städele
for conducting the genetic analysis and J. Henrich, C. Curtin, and
E. Wessling for helpful discussions and comments. Funding: This
work was funded by Harvard University (M.S.), the Max Planck
Society (M.S., L.S.), the British Academy (L.S.), and Deutsche
Forschungsgemeinschaft (L.S.). Author contributions: Conceptualization:
L.S., M.S.; Methodology: L.S., M.S.; Investigation: L.S.; Funding
acquisition: L.S., M.S.; Project administration: M.S.; Writing – original
draft: L.S.; Writing – review and editing: L.S., M.S. Competing
interests: The authors declare that they have no competing interests.
Data and materials availability: All processed data and code used in
the analyses are available on Zenodo (43). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg0844
Materials and Methods
Figs. S1 to S9
Tables S1 to S5
References (44–55)
MDAR Reproducibility Checklist
Submitted 2 December 2022; accepted 29 September 2023
10.1126/science.adg0844
Samuni et al., Science 382, 805–809 (2023)
17 November 2023
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10.1126_science.adg3812
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150-mm-thick lithium niobate optical reso-
nator placed inside a superconducting alu-
minum microwave cavity at a temperature of
7 mK, described in detail in (24). The micro-
wave mode âe is electro-optically coupled to
the colocalized optical whispering gallery
modes at wo/2p ≈ 193.46 THz through the
Pockels effect (Fig. 1A). The microwave reso-
nance frequency we/2p is tuned to the optical
free spectral range (FSR) of 8.799 GHz to re-
alize a triply resonant system with interaction
Hamiltonian:
^H int ¼ ħg0^ap^ae
†^ao
† þ h:c:
ð1Þ
p
^a†
e
(cid:3)
ffiffiffiffiffi
(cid:2)np
† þ ^ae^ao
^ao
where g0 is the vacuum electro-optical coupling
rate and âp (âo) is the annihilation operator of
the optical pump (Stokes) mode (25–28). Herein,
we have ignored the interaction with the sup-
pressed optical anti-Stokes mode ât (Fig. 1B) (29).
In this sideband suppressed situation, two-
mode squeezing interaction was achieved with
a strong resonant optical pump tone, yield-
ing the simple effective Hamiltonian, ^H eff ¼
(cid:4)
†^api is
, where (cid:2)np ¼ h^ap
ħg0
the mean intracavity photon number of the op-
tical pump mode. Entanglement between the
out-propagating microwave and the optical field
was generated through spontaneous parame-
tric down-conversion (SPDC) below the para-
metric instability threshold (C < 1). Here, C ¼
4(cid:2)npg2
Þ is the cooperativity with the vac-
0
uum coupling rate g0/2p ≈ 37 Hz and the total
loss rates of the microwave and optical Stokes
modes ke/2p ≈ 11 MHz and ko/2p ≈ 28 MHz.
The required ultralow-noise operation for en-
tanglement generation was achieved in the
pulsed regime because of the slow heating of
this millimeter-sized device despite the required
high-power optical pump (24).
ð
= keko
Establishing nonclassical correlations
We characterized the microwave and optical
output fields using continuous variables, i.e.,
RES EARCH
QUANTUM OPTICS
Entangling microwaves with light
R. Sahu1*†, L. Qiu1*†, W. Hease1‡, G. Arnold1, Y. Minoguchi2, P. Rabl2,3,4,5, J. M. Fink1*
Quantum entanglement is a key resource in currently developed quantum technologies. Sharing
this fragile property between superconducting microwave circuits and optical or atomic systems
would enable new functionalities, but this has been hindered by an energy scale mismatch of
>104 and the resulting mutually imposed loss and noise. In this work, we created and verified
entanglement between microwave and optical fields in a millikelvin environment. Using an optically
pulsed superconducting electro-optical device, we show entanglement between propagating
microwave and optical fields in the continuous variable domain. This achievement not only paves
the way for entanglement between superconducting circuits and telecom wavelength light, but
also has wide-ranging implications for hybrid quantum networks in the context of modularization,
scaling, sensing, and cross-platform verification.
T he ability to manipulate and measure
quantum mechanical properties such as
quantum superpositions and entangle-
ment in a variety of physical systems
serves as the basis for the development
of quantum technologies, for which the dem-
onstration of quantum advantage with tens
of superconducting qubits (1), an ultracoher-
ent quantum memory with nuclear spins (2),
and distributed quantum entanglement over
tens of kilometers using optical photons (3)
represents just a few of the highlights that
have already been achieved. Combining these
techniques (4–6) will enable the realization of
general-purpose quantum networks in which
remote quantum nodes capable of storing and
processing quantum information seamlessly
communicate with each other by distribut-
ing entanglement over optical channels (7).
Aspects of this approach have already been
adopted to connect and entangle various quan-
tum platforms remotely. These involve single
atoms, ions, atomic ensembles, quantum dots,
rare-earth ions, and nitrogen-vacancy centers
(8). However, such long-distance quantum
connectivity is considerably more difficult to
achieve with microwave-based platforms such
as semiconductor spin qubits (9) or local cryo-
genic networks of superconducting circuits
(10, 11), for which no natural interface to prop-
agating optical photons is available.
To overcome this limitation, efforts are cur-
rently focused on the development of coher-
ent quantum transducers between microwave
and optical photons (12–17). Direct noiseless
1Institute of Science and Technology Austria, am Campus 1,
3400 Klosterneuburg, Austria. 2Vienna Center for Quantum
Science and Technology, Atominstitut, TU Wien, 1040
Vienna, Austria. 3Walther-Meißner-Institut, Bayerische
Akademie der Wissenschaften, 85748 Garching, Germany.
4Technische Universität München, TUM School of Natural
Sciences, 85748 Garching, Germany. 5Munich Center
for Quantum Science and Technology (MCQST), 80799
Munich, Germany.
*Corresponding author. Email: rsahu@ist.ac.at (R.S.); liu.qiu@
ist.ac.at (L.Q.); jfink@ist.ac.at (J.M.F.)
†These authors contributed equally to this work.
‡Present address: Quandela SAS, 91120 Palaiseau, France.
conversion of a quantum state typically relies
on a beam-splitter process in which a strong
driving field mediates the conversion be-
tween weak microwave and optical signals.
However, a deterministic channel based on
direct transduction has exceptionally strin-
gent requirements on conversion efficiency
and added classical noise that are still out of
reach. Alternatively, quantum states can be
teleported over long distances (18–20) by
first establishing an entangled state between
microwave and optical photons. Because they
are assisted by an error-free classical signal
(21, 22), such teleportation-based commu-
nication channels are more tolerant to noise
and losses, and their channel capacity is never
zero as long as a finite amount of entangle-
ment can be shared between the communi-
cating nodes (22).
Theoretical outline and experimental setup
We generated and verified entanglement be-
tween microwave and optical fields in the
continuous-variable domain (23) using an
ultralow-noise cavity electro-optical device
(21). Our device consists of a 5-mm-diameter,
Fig. 1. Physical and conceptual mode
configuration. (A) Simulated microwave (left)
and optical (right) mode distribution with
azimuthal number me = 1 and mo = 17 (for
illustration, experimentally mo ≈ 20,000).
Phase matching is fulfilled from the condition
mo = mp – me, and entanglement is generated
and verified between the out-propagating
microwave field âe,out and the optical Stokes
field âo,out. (B) Sketch of the density of states
of the relevant modes. Under the condition
wp – wo = we, the strong pump tone in âp
produces entangled pairs of microwave and
optical photons in âe and âo through spontaneous
parametric down-conversion. Frequency up-
conversion is suppressed through hybridization of
the anti-Stokes mode ât with an auxiliary mode.
Sahu et al., Science 380, 718–721 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Measurement sequence and noise powers. (A) Schematic pulse
sequence of a single measurement. The optical pulse 1 is applied at wp and amplifies
the vacuum (and any thermal noise) in the two modes âe and âo, thus generating
the SPDC signals. One micro-second later, a second optical pump with ~10 times
lower power is applied, together with a coherent microwave pulse at we. The
microwave photons stimulate the optical pump to down-convert, which generates
a coherent pulse in the âo mode that is used to extract slow local oscillator phase
drifts. (B and C) Measured output power from the âe and âo modes in units of
photons per second in a 1-Hz bandwidth and averaged over a million experiments.
The SPDC signals are shown in the insets, with the dashed gray lines indicating the
calibrated detection noise floor Nj,add + 0.5. (D) Corresponding microwave output
power spectral density versus Dwe = w – we centered on resonance right before
the entanglement pulse, during the pulse, and right after the pulse, as indicated in (A).
Yellow and green dashed lines are fits to a Lorentzian function that yields the
microwave bath occupancies before and after the entangling pulse. Error bars
represent the 2s statistical SE, and the shaded regions represent the 95% confidence
interval of the fit. (E) Corresponding optical output power spectral density versus
Dwo = wo – w during and after the entanglement pulse, both normalized to the
measured noise floor before the pulse. The in-pulse noise spectra in (D) and (E) are fit
jointly with theory, which yields C = 0.18 ± 0.01 and (cid:2)ne;int ¼ 0:07 T 0:03.
ð
the dimensionless quadrature pairs Xj and Pj
(where j = e,o for microwave and optics),
which satisfy the canonical commutation rela-
tions [Xj, Pj] = i. A pair of Einstein-Podolsky-
Rosen–type operators, Xþ ¼ 1ffiffi
Þ and
p Xe þ Xo
ð
2
P(cid:2) ¼ 1ffiffi
Þ, were then constructed (30).
p Pe (cid:2) Po
2
The microwave and optical output fields are
entangled if the variance of the joint op-
erators is reduced below the vacuum level,
i.e., D(cid:2)
(cid:2)i < 1. This is common-
ly referred to as the Duan-Simon criterion
(31, 32). Here, the entanglement was estab-
lished deterministically between the quad-
ratures of two propagating bosonic modes
and verified through the measured quad-
rature variances based on all collected data
(33). This is in contrast to probabilistic en-
tanglement in the single photon basis, which
is established with finite probability only after
þ þ P2
¼ hX 2
EPR
successful heralding from an auxiliary mea-
surement (34).
For entanglement generation, we used a
250-ns-long optical pump pulse (≈154 mW,
C ≈ 0.18, (cid:2)np ≈ 1:0 (cid:3) 1010 ) at a 2-Hz repeti-
tion rate (pulse 1 in Fig. 2A). The output
optical signal was filtered through a Fabry-
Perot cavity to reject the strong pump. The
microwave output field was amplified by a
high-electron-mobility transistor amplifier.
Both outputs were down-converted to an in-
termediate frequency of 40 MHz with two
local oscillators, and the four quadratures
were extracted from heterodyne detection.
Long-term phase stability between the two
local oscillators was achieved by extraction
of the relative phase drift by means of a sec-
ond phase-alignment pump pulse that was
applied 1 ms after each entanglement pulse,
together with a coherent resonant microwave
pulse (Fig. 2A). This generated a high signal-
to-noise coherent optical signal through stim-
ulated parametric down-conversion and
allowed for phase alignment in each indi-
vidual measurement (29).
Figure 2, B and C, shows the time-domain
power over 1 million averages for the on-
resonance microwave and optics signal with
a 40-MHz measurement bandwidth. The two
insets show the microwave (optical) signal
from spontaneous parametric down-conversion
(SPDC) from pulse 1 (compare Fig. 2A) with
an emission bandwidth of ≈10 MHz. The
larger signals during the second pump pulse
are the reflected microwave pulse and the
generated optical tone, and these were used
for phase alignment. The off-resonance raw
power measurements were rescaled to the
Sahu et al., Science 380, 718–721 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. Characterization of the two-mode squeezed state. (A) Measured
covariance matrix Vij in its standard form plotted for Dwj = 0 based on 925,000
measurements. (B) Corresponding Wigner function marginals of different
output quadrature pairs compared with vacuum. The contours in blue (gray)
represent the 1/e fall-off from the maximum for the measured state (vacuum).
The middle two plots show two-mode squeezing below the vacuum level in the
diagonal and off-diagonal directions. (C) Top, measured average microwave
output noise
Þ=2 (purple), average optical output noise
(cid:2)V11 ¼ V11 þ V22
ð
(cid:2)V13 ¼ V13 (cid:2) V24
ð
Þ=2 (green), and average correlations
(cid:2)V33 ¼ V33 þ V44
ð
(yellow) as a function of measurement detunings. Solid lines represent the joint
theory fit, and dashed lines are individual Lorentzian fits to serve as a guide to
the eye. Middle bottom, two-mode squeezing in red (antisqueezing in blue)
(cid:2)V13. The darker-colored
calculated from the top panels as DT
error bars represent the 2s statistical error, and the outer (faint) 2s error bars
also include the systematic error in calibrating the added noise of the
measurement setup.
¼ (cid:2)V11 þ (cid:2)V33 T 2
Þ=2
EPR
detection noise floor Nj,add + 0.5, with the
added noise Ne,add = 13.1 ± 0.4 (2s errors
throughout) due to loss and amplifier noise
and No,add = 5.5 ± 0.2 due to optical losses,
which were carefully determined using noise
thermometry of a temperature-controlled 50 W
load and four-port calibration, respectively (29).
Because the emission bandwidth was smaller
than the measurement bandwidth, the time
domain measurement does not reveal the full
SPDC amplitude.
We continued the analysis in the frequency
domain by calculating the Fourier transform
of each measurement for three separate time
intervals: before (2 ms), during (200 ns), and
immediately after (500 ns) the entangling pump
pulse. Figure 2D shows the resulting average
microwave noise spectra for all three time in-
tervals with corresponding fit curves (dashed
lines) and theory (solid line). The spectra were
in situ calibrated using the before-pulse off-
resonance (waveguide noise) noise floor (29).
Using independent measurements, we deter-
mined this noise floor (cid:2)ne;wg ¼ 0:001 T 0:002
at the low average pump power of ≈0.12 mW used
in this experiment (29). Before and after the
pump pulse, the intrinsic microwave bath occu-
pancies were fitted to be (cid:2)ne;int ¼ 0:03 T 0:01
and 0.09 ± 0.03, respectively, above the vacuum
level. Similarly, Fig. 2E shows the obtained av-
erage optical noise spectra during and after
the pump pulse, calibrated through the shot
noise level in the heterodyne measurement
before the pulse. As expected, the optical noise
level after the pulse returned back to the shot
noise level.
During the pump pulse, approximately
Lorentzian-shaped microwave and optical power
spectra were generated through the SPDC
process. A joint fit of the microwave and op-
tical power spectral density during the pulse
was performed using a five-mode theoretical
model that includes the effects of measure-
ment bandwidth. In this model, the in-pulse
microwave bath occupancy (cid:2)ne;int ¼ 0:07 T 0:03
and the cooperativity C = 0.18 ± 0.01 are the
only free fit parameters (29). The narrowed
microwave linewidth ke,eff/2p = 9.8 ± 1.8 MHz
(taken from a Lorentzian fit) agrees with co-
herent electro-optical back-action (28). From
the extracted numbers, we conclude that dur-
ing the entanglement pulse, the quantum noise
dominates the intrinsic microwave thermal
noise, a prerequisite for microwave-optics en-
tanglement generation.
The quadratures Xj and Pj were extracted as
a function of frequency, i.e., at Dwj = ±(w – wj)
around the resonances due to energy conser-
vation in the SPDC process (29, 35) during
the pump pulse. At each frequency, the bi-
partite Gaussian state of the propagating out-
put fields was fully characterized by the 4 × 4
covariance matrix (CM) Vij = hduiduj + dujduii/2,
where dui = ui – huii and u ∈ {Xe, Pe, Xo, Po}
(29). The CM corresponds to the quantum
state of the propagating fields in the coaxial
line and the coupling prism at the device out-
put, i.e., before setup losses or amplification
incur. The diagonal elements in V correspond
to the individual output field quadrature var-
iances in dimensionless units, which can be
obtained by subtracting the added detection
Sahu et al., Science 380, 718–721 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
noise offsets from the measured variances, i.e.,
Vii(Dw) = Vii,meas(Dw) – Ni,add.
The obtained CM from the data in Fig. 2 at
Dw = 0 is shown in Fig. 3A in its standard form
(31, 32). The nonzero off-diagonal elements
indicate strong correlations between micro-
wave and optical quadratures. To verify the
quantum correlation, the two-mode squeezed
quadratures are more intuitively visualized in
terms of the quasiprobability Wigner function:
(cid:5)
exp (cid:2) 1
p
2
p2
uV (cid:2)1uT
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
det Vð Þ
W uð Þ ¼
ð2Þ
(cid:6)
where u = (Xe, Pe, Xo, Po). Different marginals
of this Wigner function are shown in Fig. 3B.
The marginals from the same quadratures
(Xe, Pe) and (Xo, Po) show uncorrelated ther-
mal noise above the vacuum noise (gray circle)
from SPDC. The cross-quadrature marginals
(Xe, Xo) and (Pe, Po) show two-mode squeezing
in the diagonal and off-diagonal directions be-
low the vacuum level. The amount of squeez-
ing was slightly different between the two
because of the statistical uncertainty in the
measured CM.
ð
ð
Figure 3C shows the amount of two-mode
squeezing between microwave and optical out-
put fields. The averaged microwave quadra-
ture variance (purple dots) (cid:2)V 11 ¼ V11 þ V22
Þ=2
and the averaged optics quadrature variance
(green dots) (cid:2)V 33 ¼ V33 þ V44
Þ=2 are shown
in the top panel, along with the prediction
from the five-mode theory (solid line) and a
simple fit to a Lorentzian function (dashed
line), which show perfect agreement. Measured
microwave-optical correlations (yellow dots)
(cid:2)V 13 ¼ V13 (cid:2) V24
Þ=2 and the Lorentzian fit
ð
(dashed line) lie slightly below the theoret-
ical prediction (solid line), which we attrib-
ute to remaining imperfections in the phase
stability (29).
EPR
EPR
The bottom two panels of Fig. 3C show the
squeezed and antisqueezed joint quadra-
¼ (cid:2)V 11 þ (cid:2)V 33 ∓ 2 (cid:2)V 13 (red
ture variances D∓
and blue, respectively). We observed two-
mode squeezing below the vacuum level, i.e.,
D(cid:2)
< 1, with a bandwidth close to the ef-
fective microwave linewidth. The maximal
two-mode squeezing of 0:72þ0:31
(cid:2)0:25 dB is ob-
served on resonance where D(cid:2)
¼ 0:85þ0:05
(cid:2)0:06
EPR
(2s, 95% confidence) obtained from ~1 mil-
lion pulses with (cid:2)V 11 ¼ 0:93, (cid:2)V 33 ¼ 0:84, and
(cid:2)V 13 ¼ 0:46. The reported 2s error on D(cid:2)
EPR
takes both statistical and systematic errors
into account. Thus, the value of D(cid:2)
EPR beats the
classical limit ( D(cid:2)
¼ 1 ) by >5s (29). The
measured two-mode squeezing signifies an
itinerant microwave-optical entangled state
with a logarithmic negativity of EN = 0.17. The
supplementary materials contain additional
data for longer pulses and varying optical pump
power, which corroborate the presented re-
sults and findings (29).
EPR
Conclusions
The demonstration of deterministic quantum
entanglement between propagating microwave
and optical photons establishes a nonclassical
communication channel between circuit quan-
tum electrodynamics and quantum photonics.
The achieved entanglement generation rate of
≈0.11 ebits/200-ns-long pulse (29) is in prac-
tice limited by the slow pulse repetition rate.
We expect orders-of-magnitude higher rates
with improved thermalization, higher micro-
wave and optical quality factors, and electro-
optic coupling enhancements that reduce
the required pump power and the associated
thermal load. Coupling efficiency improve-
ments will allow for higher levels of two-mode
squeezing (29) and facilitate deterministic
entanglement distribution schemes to qubits
(29, 36), teleportation-based state transfer
(21, 22, 29), and quantum-enhanced remote
detection (37). This device and state prepa-
ration scheme can also be used directly for
probabilistic heralding assisted protocols
(7, 38, 39) when the cooperativity is some-
what reduced. This is the most promising way
forward to mitigating optical setup losses
and extending the entanglement to room-
temperature fiber optics. Being fully com-
patible with superconducting qubits in a
millikelvin environment, such a device will
facilitate the integration of remote supercon-
ducting quantum processors into a single co-
herent optical quantum network. This is
relevant not only for modularization and
scaling (40, 41) but also for efficient cross-
platform verification of classically intractable
quantum processor results (42).
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AC KNOWLED GME NTS
L.Q. thanks J. Li and D. Vitali for fruitful discussions. Funding: This
work was supported by the European Research Council (grant
no. 758053, ERC StG QUNNECT) and the European Union’s
Horizon 2020 Research and Innovation Program (grant no.
899354, FETopen SuperQuLAN). L.Q. acknowledges generous
support from the ISTFELLOW program. W.H. is the recipient of an
ISTplus postdoctoral fellowship with funding from the European
Union’s Horizon 2020 Research and Innovation Program (Marie
Sklodowska-Curie grant no. 754411). G.A. is the recipient of a DOC
fellowship of the Austrian Academy of Sciences at IST Austria.
J.M.F. acknowledges support from the Austrian Science Fund (FWF)
through BeyondC (grant no. F7105) and the European Union’s
Horizon 2020 Research and Innovation Program (grant no.
862644, FETopen QUARTET). Author contributions: R.S., W.H.,
L.Q., and G.A. worked on the experimental setup. R.S. and
L.Q. performed the measurements. L.Q. and R.S. analyzed the
data. L.Q. developed the theory with contributions from R.S., Y.M.,
and P.R. R.S. and L.Q. wrote the manuscript with contributions
from all authors. J.M.F. supervised the project. Competing
interests: The authors declare no competing interests. Data
and materials availability: All data are available in the manuscript
or the supplementary materials or have been deposited on
Zenodo (43). License information: Copyright © 2023 the authors,
some rights reserved; exclusive licensee American Association
for the Advancement of Science. No claim to original US
government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg3812
Supplementary Text
Figs. S1 to S15
Tables S1 and S2
References (44–54)
18. S. Takeda, T. Mizuta, M. Fuwa, P. van Loock, A. Furusawa,
Nature 500, 315–318 (2013).
Submitted 20 December 2022; accepted 19 April 2023
10.1126/science.adg3812
Sahu et al., Science 380, 718–721 (2023)
19 May 2023
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RES EARCH
CONSERVATION
Widespread diversity deficits of coral reef sharks
and rays
Colin A. Simpfendorfer1,2*, Michael R. Heithaus3, Michelle R. Heupel2,4, M. Aaron MacNeil5, Mark Meekan6,
Euan Harvey7, C. Samantha Sherman1,8, Leanne M. Currey-Randall4, Jordan S. Goetze9,10, Jeremy J. Kiszka3,
Matthew J. Rees6,11, Conrad W. Speed6, Vinay Udyawer12, Mark E. Bond3, Kathryn I. Flowers3,13,
Gina M. Clementi3, Jasmine Valentin-Albanese14, M. Shiham Adam15, Khadeeja Ali3,16, Jacob Asher17,
Eva Aylagas17, Océane Beaufort18, Cecilie Benjamin19, Anthony T. F. Bernard20,21, Michael L. Berumen22,
Stacy Bierwagen4, Chico Birrell23, Erika Bonnema3, Rosalind M. K. Bown24, Edward J. Brooks25,
J. Jed Brown26, Dayne Buddo27, Patrick J. Burke28,29, Camila Cáceres3, Marta Cambra30,31,
Diego Cardeñosa3, Jeffrey C. Carrier32, Sara Casareto3, Jennifer E. Caselle33, Venkatesh Charloo34,
Joshua E. Cinner35, Thomas Claverie36, Eric E. G. Clua37,38, Jesse E. M. Cochran22, Neil Cook39,40,
Jessica E. Cramp41,42, Brooke M. D’Alberto1,43, Martin de Graaf44, Mareike C. Dornhege45,
Mario Espinoza30,31, Andy Estep46, Lanya Fanovich40, Naomi F. Farabaugh3, Daniel Fernando24,
Carlos E. L. Ferreira47, Candace Y. A. Fields3,25, Anna L. Flam48, Camilla Floros49,50,
Virginia Fourqurean51,52, Laura Gajdzik22,53, Laura García Barcia3, Ricardo Garla54,55, Kirk Gastrich3,
Lachlan George2, Tommaso Giarrizzo56,57, Rory Graham5, Tristan L. Guttridge59,60, Valerie Hagan13,
Royale S. Hardenstine16,22, Stephen M. Heck13, Aaron C. Henderson61, Patricia Heithaus3,
Heidi Hertler61, Mauricio Hoyos Padilla62,63, Robert E. Hueter64,65, Rima W. Jabado1,66,
Jean-Christophe Joyeux67, Vanessa Jaiteh68,69, Mohini Johnson70, Stacy D. Jupiter71,
Muslimin Kaimuddin72,70, Devanshi Kasana3, Megan Kelley3, Steven T. Kessel73, Benedict Kiilu74,
Taratau Kirata75†, Baraka Kuguru76, Fabian Kyne77, Tim Langlois78,79, Frida Lara80,81, Jaedon Lawe82,
Elodie J. I. Lédée1, Steve Lindfield83, Andrea Luna-Acosta84, Jade Q. Maggs85,
B. Mabel Manjaji-Matsumoto86, Andrea Marshall87, Lucy Martin88, Daniel Mateos-Molina89,90,
Philip Matich60, Erin McCombs91, Ashlie McIvor22,92, Dianne McLean6,93, Llewelyn Meggs82,
Stephen Moore1, Sushmita Mukherji1,2, Ryan Murray94, Stephen J. Newman95, Josep Nogués88,
Clay Obota96,97, Domingo Ochavillo98, Owen O'Shea99,100, Kennedy E. Osuka96,101,
Yannis P. Papastamatiou3, Nishan Perera23, Bradley Peterson14, Caio R. Pimentel67,102,
Fabián Pina-Amargós103,104, Hudson T. Pinheiro105, Alessandro Ponzo106, Andhika Prasetyo107,
L. M. Sjamsul Quamar108, Jessica R. Quinlan3, José Amorim Reis-Filho109, Hector Ruiz110,
Alexei Ruiz-Abierno104, Enric Sala111, Pelayo Salinas-de-León112,113, Melita A. Samoilys96,114,
William R. Sample3, Michelle Schärer-Umpierre110, Audrey M. Schlaff1, Kurt Schmid55,115,
Sara N. Schoen3, Nikola Simpson116, Adam N. H. Smith117, Julia L. Y. Spaet118,
Lauren Sparks119, Twan Stoffers120, Akshay Tanna24, Rubén Torres121, Michael J. Travers95,
Maurits van Zinnicq Bergmann3,58, Laurent Vigliola122, Juney Ward123, Joseph D. Warren14,
Alexandra M. Watts47,124, Colin K. Wen125, Elizabeth R. Whitman3, Aaron J. Wirsing126, Aljoscha Wothke40,
Esteban Zarza-González127,128, Demian D. Chapman3,60
A global survey of coral reefs reveals that overfishing is driving resident shark species toward
extinction, causing diversity deficits in reef elasmobranch (shark and ray) assemblages. Our species-
level analysis revealed global declines of 60 to 73% for five common resident reef shark species
and that individual shark species were not detected at 34 to 47% of surveyed reefs. As reefs
become more shark-depleted, rays begin to dominate assemblages. Shark-dominated assemblages
persist in wealthy nations with strong governance and in highly protected areas, whereas
poverty, weak governance, and a lack of shark management are associated with depauperate
assemblages mainly composed of rays. Without action to address these diversity deficits, loss of
ecological function and ecosystem services will increasingly affect human communities.
C oral reef ecosystems are under increas-
ing pressure from human activities—
including intense fishing, degraded water
quality, and climate change (1, 2)—that
threaten species supporting a wide range
of ecosystem functions (3). Sharks and rays
(hereafter “elasmobranchs”) have diverse roles
Affiliations are listed at the end of this paper.
*Corresponding author. Email: colin.simpfendorfer@jcu.edu.au
†Deceased.
on coral reefs as predators and prey across
multiple trophic levels and in the cycling and
movement of nutrients (3–5). Recent evidence
indicates that overfishing has driven sharks
toward functional extinction on many reefs. In
a global survey, sharks were not observed on
nearly 20% of reefs surveyed (6). Yet until re-
cently, reef shark species were listed in lower
risk extinction categories by the International
Union for the Conservation of Nature (IUCN).
With ~37% of all elasmobranch species threat-
ened with extinction (7), a key question for
coral reef ecosystems lies in understanding
the global extent of species loss in elasmo-
branch assemblages. We characterized elas-
mobranch assemblage structure on coral reefs
across a gradient of human pressures to esti-
mate the local depletion and global extinction
risk of the most common reef species, reveal-
ing the human and environmental factors that
influence assemblage structure and that lead
to a deficit in predator diversity that could
affect reef ecological functioning.
To understand the extent of the reef elasmo-
branch diversity deficit, we surveyed 391 coral reefs
in 67 nations and territories using 22,756 baited
remote underwater video stations (BRUVS).
We examined reef-level species richness, spe-
cies composition of elasmobranch assem-
blages, and species relative abundance (MaxN;
the maximum number of each species ob-
served in a single frame of each 60-min de-
ployment then averaged across all deployments
on one reef) (8). We examined how elasmo-
branch species assemblages changed in re-
sponse to human pressures, using unweighted
pair group with arithmetic mean (UPGMA)
clustering to identify reefs with the most simi-
lar assemblages (8). We then compared these
clusters with estimated depletion of key resi-
dent elasmobranch species at the reef level and
examined whether socioeconomic, management,
or environmental factors could predict cluster
membership, using linear discriminant analy-
sis. Reef-level depletion was estimated by divid-
ing the observed mean MaxN of a species at
individual reefs by a model-estimated baseline
abundance (without human pressures) for each
sampling site (a small group of closely asso-
ciated reefs) and subtracting this value from 1.
Baseline abundance (also expressed as MaxN)
was estimated from a general linear model
relating observed MaxN to sampling site, hu-
man pressure [represented by total market
gravity, the size and travel time to human mar-
kets (2)], and marine protected area (MPA)
status [closed to all fishing, open to fishing,
or restricted (some fishing but with restric-
tions)]. The baseline was estimated by setting
all parameters to those expected at a site with
no human pressure (gravity to the minimum
for an ocean basin and protection status to
closed) (8).
Sampling identified 104 distinct elasmobranch
species or species complexes (table S1), repre-
senting more than 77% of elasmobranch spe-
cies known to occur on coral reefs at some
point during their lives (9). More than half
(n = 53) of the species were rarely observed,
with 10 or fewer sightings. We estimated reef-
level depletion for the nine most commonly
occurring species of shark [n = 5; Caribbean
reef sharks (Carcharhinus perezi) and nurse
sharks (Ginglymostoma cirratum) in the Atlantic;
grey reef sharks (Carcharhinus amblyrhynchos),
Simpfendorfer et al., Science 380, 1155–1160 (2023)
16 June 2023
1 of 6
A
30N
15N
e
d
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0
15S
30S
B
4
RES EARCH | R E S E A R C H A R T I C L E
blacktip reef sharks (Carcharhinus melanopterus),
and whitetip reef sharks (Triaenodon obesus)
in the Indo-Pacific] and rays [n = 4; yellow
stingrays (Urobatis jamaicensis) and southern
stingrays (Hypanus americanus) in the Atlan-
tic; blue spotted mask rays (Neotrygon spp.)
and blue spotted ribbontail rays (Taeniura
lymma and Taeniura lessoni) in the Indo-
Pacific]. The Galapagos shark was excluded
from estimates of global depletion because
sampling only covered a relatively small pro-
portion of its range, but the results for this
species were broadly similar. The nine key
resident species represented 77.7% of all elas-
mobranchs observed in the study and are
those that serve important ecological roles
(10) and contribute the most to, and under-
pin, livelihoods through fishing (11) and dive
tourism (12).
We found that mean depletion of five key
resident reef sharks on individual reefs ranged
from 100% depletion (none observed) to 0%
(no depletion), averaging 62.8% (Fig. 1A). Mean
depletion of key resident reef sharks followed
the overall decline in elasmobranch abun-
dance as measured with MaxN (Fig. 1B), de-
creased as the fraction of the elasmobranch
assemblage comprised of sharks decreased
(Fig. 1C), and showed little change across a
range of elasmobranch species richness (Fig.
1D); these patterns were generally consistent
between ocean basins. Across the range of
depletion, five main clusters of reefs were iden-
tified in the Atlantic, and eight were identified
in the Indo-Pacific (Figs. 2 and 3), including at
least one cluster in each ocean basin (cluster
1 in the Atlantic and cluster 2 in the Indo-
Pacific) having shark populations in a rela-
tively intact state, with low levels of depletion
of the five main resident reef shark species
(Caribbean reef and nurse sharks in the At-
lantic; grey reef, blacktip reef, and whitetip
reef sharks in the Indo-Pacific) (8). Remain-
ing clusters represented assemblages with
increasing depletion of resident shark spe-
cies and greater proportions of the overall elas-
mobranch assemblage represented by rays
(Figs. 2C and 3B). Both ocean basins show a
similar transition through these assemblages
as key resident shark species became depleted.
The four key ray species (yellow and south-
ern stingrays in the Atlantic; blue spotted
mask and blue spotted ribbontail rays in the
Indo-Pacific) increased only with depletion of
one or more resident reef shark species, with
rays dominating in the most shark-depleted
areas. These predictable changes in assem-
blage provide the ability to infer the status of
reef shark populations, and the level of hu-
man pressure they are experiencing, in future
surveys.
Elasmobranch species assemblage clusters
on reefs in both basins were significantly relat-
ed to certain socioeconomic and manage-
Depletion
1.00
0.75
0.50
0.25
0.00
30E
60E
90E
120E
150E
180E
Longitude
150W
120W
90W
60W
30W
Atlantic
Indo−Pacific
3
) Basin
p
o
r
d
r
e
p
N
x
a
M
h
c
n
a
r
b
o
m
s
a
e
(
2
l
e
c
n
a
d
n
u
b
A
1
0
C
k
r
a
h
s
d
e
s
i
r
p
m
o
c
N
x
a
M
h
c
n
a
r
b
o
m
s
a
e
l
.
p
o
r
P
1.00
0.75
0.50
0.25
0.00
D
25
20
s
s
e
n
h
c
i
r
i
s
e
c
e
p
S
15
10
5
0
1.00
0.75
0.25
0.50
Shark depletion
0.00
1.00
0.50
0.75
0.25
Shark depletion
0.00
1.00
0.75
0.50
0.25
Shark depletion
0.00
Fig. 1. The global decline of coral reef elasmobranchs. (A) Reef-scale estimates of depletion of
resident coral reef shark species. Depletion is proportion of unfished population lost, represented as
the measured MaxN as a proportion of MaxN in an unfished state (gravity, lowest in basin; MPA status,
closed) (8). Open circles indicate no sharks or rays were observed; gray circles indicate none of the
resident shark species used to calculate mean depletion were present. (B) Relationship between
depletion of resident shark species and MaxN by ocean basin. (C) Relationship between depletion of
resident shark species and the proportion of elasmobranch MaxN that comprised shark, demonstrating
the transition from shark- to ray-dominated assemblages. (D) Relationship between depletion of
resident shark species and species richness.
ment factors, with linear discriminant analysis
(LDA) accounting for ~85% of variance be-
tween clusters (tables S2 and S3). Important
socioeconomic factors included the Human
Development Index (an index of a nation’s
level of education, life expectancy and stan-
dard of living) and Voice and Accountability
Index (an index of the extent to which people
in each nation can participate in governance,
free expression, free media, and free associ-
ation). Important management factors were
whether the reef occurred in a marine pro-
tected area (MPA) or whether a reef was within
a nation where all targeted shark fishing and
trade is prohibited, known as a “shark sanc-
tuary.” Given that shark sanctuaries have
largely been implemented in nations in which
fishing for sharks was limited for economic
or cultural reasons (6), their effectiveness as
tools for recovering reef shark populations
remains an open question. Total market grav-
ity was more important in the Indo-Pacific
than the Atlantic, possibly because remote reefs
(>4 hours travel time from human settlements)
Simpfendorfer et al., Science 380, 1155–1160 (2023)
16 June 2023
2 of 6
RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Structure of shark and ray assemblages
on Atlantic coral reefs. (A and B) Clusters of
reefs with similar species composition from
UPGMA clustering of 106 reefs in the Atlantic
basin based on a global set of 31 coral reef–
associated species. Five main clusters,
representing 87.0% of reefs, were identified.
Their locations are indicated with colored triangles.
Reefs with minor clusters are indicated with gray
dots (n = 7). Reefs where no elasmobranchs were
observed are indicated with black dots (n = 5).
(C) Regime plot showing all species assemblage
clusters as a function of the mean depletion of the
resident reef shark species (Caribbean reef and
nurse sharks) and the proportion of all observed
elasmobranchs that were sharks. Size of points
(and numbers) indicate the number of reefs in
each cluster, and colors indicate cluster identity as
per (A). (D) Population level relative to original levels
of four resident reef species in each of the five main
clusters. Proportion of original level = 1 – depletion.
Horizontal lines indicate mean, boxes indicates
25 to 75 percentile, and whiskers indicate 95%
confidence interval.
A
30N
e
d
u
t
i
t
a
L
20N
10N
C
k
r
a
h
s
f
o
n
o
i
t
r
o
p
o
r
P
1.00
0.75
0.50
0.25
0.00
90W
80W
70W
60W
B
45W
30W
Cluster
1
2
6
10
3
Brazil
0
30N
10S
20N
20S
10N
0
10S
20S
90W
80W
Longitude
70W
1.00
0.75
0.50
0.25
0.00
60W
D
45W
Longitude
30W
Caribbean reef shark
1
12
25
2
14
6
6
2
1.00
0.75
0.50
Shark depletion
0.25
1
1.00
0.75
0.50
0.25
0.00
0.00
1.0
0.5
0.0
1.0
0.5
0.0
4
2
0
4
2
0
l
i
a
n
g
i
r
o
n
o
i
t
r
o
p
o
r
P
1
3
Nurse shark
2
6
10
1
3
2
6
10
Southern stingray
1
3
2
6
10
Yellow stingray
1
3
2
6
10
are relatively rare in the Atlantic compared
with the Indo-Pacific (fig. S1) (13). Environ-
mental factors (coral cover and relief) had lit-
tle influence in predicting cluster membership.
Elasmobranch assemblage structure on coral
reefs in both the Atlantic and Indo-Pacific are
therefore mainly driven by management and
socioeconomic factors, with shark-dominated
assemblages more likely to occur in wealthy,
well-governed nations and in highly protected
areas or shark sanctuaries, whereas poverty,
limited governance, and a lack of shark pro-
tection are associated with assemblages mainly
composed of rays.
To further characterize the diversity deficits
that underpin these assemblage differences, we
compared species observations in our BRUVS
with their historical ranges drawn from pub-
lished literature, including historical accounts,
and found that sharks were not detected at
13.6% of reefs (19 Atlantic and 34 Indo-Pacific),
whereas rays were not detected at 21.5% of
reefs (10 Atlantic and 74 Indo-Pacific); both
groups were not detected at 6.6% of reefs sur-
veyed (5 Atlantic and 19 Indo-Pacific). At the
species level, absences were severe. On the
basis of their known historic distribution, def-
icits were 46.9% of reefs (112 of 246) for black-
tip reef sharks, 41.3% (31 of 75) for Caribbean
reef sharks, 40.8% (102 of 250) for grey reef
sharks, 36.2% (89 of 246) for whitetip reef
sharks, and 34.7% (n = 26 of 75) for nurse sharks
(fig. S2). Among rays, deficits were even more
stark: 78.9% (75 of 95) for yellow stingray,
62.8% (81 of 129) for blue spotted ribbontail
rays, and 55.6% (79 of 142) for blue spotted
maskrays. An exception was the southern sting-
ray, which was not detected at only 19.8% (n =
20 of 101) of expected reefs in the Atlantic. A
failure to detect rays may not always indicate
absence because they are often cryptic and
therefore missed on BRUVS, especially when
sharks are present (14). Collectively, these di-
versity deficits show that elasmobranch loss
on coral reefs is more extensive than previ-
ously demonstrated, with widespread losses
of key species across many of the world’s coral
reefs, especially in Asia, eastern Africa, conti-
nental South America, and the central-eastern
Caribbean.
Previous estimates of the status of reef shark
and ray species have been geographically
limited, varying among surveyed reefs from
very high abundances (15) to local extinction
(16). This disparity has made it difficult to
assess the global status of individual species.
Therefore, we used our estimates of reef-level
depletion to estimate the global depletion
and extinction risk of the most common res-
ident reef sharks (five species) and rays (four
species). Mean and standard error reef-level
depletion was calculated within jurisdic-
tions (nations or remote territories) and used
to produce confidence intervals for jurisdic-
tional depletion levels. To estimate an overall
global depletion level by species, we weighted
the jurisdictional depletion by the percent-
age of the world’s coral reefs in their waters
and produced a weighted global mean de-
pletion (8). Extinction risk was estimated
by comparing proportional global depletion
to the criteria for the IUCN Red List A2 (pop-
ulation decline) category (17), assuming that
the decline had occurred in the past three
generations (29 to 90 years). In IUCN assess-
ments before the availability of this global
survey, all reef-resident shark species were
considered at lower risk of extinction (Near
Threatened) (18). Grey reef shark had the
highest level of global decline [69.8% ± 1 stan-
dard error (SE) 62.6 to 77.1], followed by
nurse shark (68.6% ± 49.7 to 87.4), Caribbean
reef shark (64.8% ± 42.0 to 87.5), blacktip
reef shark (64.5% ± 58.7 to 70.4), and white-
tip reef shark (60.4% ± 51.2 to 70.2) (Fig. 4).
The estimated declines of resident species of
reef sharks met the IUCN Red List criteria for
Endangered. Population changes of rays were
more variable, with increasing populations
in some nations and declines in others (fig.
S3), reflecting the compositional changes seen
across our gradient of human pressures. When
examined at the global level, no ray species ex-
amined met criteria for elevated extinction risk,
which is consistent with current nonthreatened
status of these species on the Red List.
Simpfendorfer et al., Science 380, 1155–1160 (2023)
16 June 2023
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RES EARCH | R E S E A R C H A R T I C L E
30E
60E
90E
120E
150E
180E
150W
120W
90W
A
30N
15N
e
d
u
t
i
t
a
L
0
15S
30S
B
1.00
30E
60E
90E
120E
1.00
0.75
0.50
0.25
0.00
1.00
7
2
85
1
57
6
27
0.75
1
3
k
r
a
h
s
0.50
f
o
n
o
i
t
r
o
p
o
r
P
0.25
0.00
2
4
12
3
22
1
1
6
1.00
0.50
0.75
Shark depletion
0.25
0.75
0.50
0.25
0.00
0.00
30N
15N
0
15S
30S
Cluster
1
2
5
7
10
13
14
18
150W
120W
90W
180E
150E
Longitude
C
Grey reef shark
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0
2
0
3
2
1
0
l
i
a
n
g
i
r
o
n
o
i
t
r
o
p
o
r
P
2
5
1
10
13
14
18
7
Blacktip reef shark
2
5
1
10
13
14
18
7
Whitetip reef shark
2
5
1
10
13
14
18
7
Blue spotted maskray
2
5
1
10
13
14
18
7
Blue spotted ribbontail ray
2
5
1
10
13
14
18
7
Fig. 3. Structure of shark and ray assemblages on Indo-Pacific coral reefs.
(A) Clusters of reefs with similar species composition from UPGMA clustering
of 285 reefs in the Indo-Pacific basin based on a global set of 31 coral reef-
associated species. Eight main clusters, representing 82.1% of reefs, were
identified. Their locations are indicated with colored triangles. Reefs with minor
clusters are indicated with gray dots (n = 30). Reefs where no elasmobranchs
were observed are indicated with black dots (n = 21). (B) Regime plot showing
all species assemblage clusters as a function of the mean depletion of the
resident species of reef shark (grey reef, blacktip reef, whitetip reef, and
Galapagos sharks) and the proportion of all observed elasmobranchs that were
sharks. Size of points (and numbers) indicate the number of reefs in each cluster,
and colors indicate cluster identity as per (A); minor clusters are indicated
in gray. (C) Population level relative to original levels of five core shark and
ray species in each of the eight main species assemblage clusters. Proportion
of original level = 1 – depletion. Horizontal lines indicate mean, boxes indicate
25 to 75 percentile, and whiskers indicate 95% confidence interval.
Our study of nations hosting ~90% of global
reefs reveals that resident reef shark species
are at much higher risk of extinction than
previously thought. Local declines, shaped
by human pressures that vary across ocean
basins, have led to consistent changes in the
structure of coral reef elasmobranch assem-
blages that may have profound effects on
the broader ecosystem. The direct and indi-
rect effects of fishing have driven shifts in
species composition from shark-dominated
to ray-dominated assemblages and ultimate-
ly the complete loss of sharks and rays at a
small proportion (~ 7%) of reefs surveyed. In
addition to changes in the structure of as-
semblages, all major resident shark species
have declined to such levels that they qualify
as Endangered by the IUCN Red List Criteria.
These changes wrought on coral reef elasmo-
branch assemblages demonstrate the per-
vasiveness of fishing on coral reefs (19) and
the substantial risks to reef-dependent hu-
man communities of continued overfishing.
Elasmobranch species vary widely in their eco-
nomic value, with some fished for subsistence,
others fished for local or export markets, and
others valued alive as tourism resources (12, 20).
Thus, understanding threats and conservation
options for rebuilding populations at a species
level will assist in developing effective man-
agement of coral reef elasmobranchs as part
of a sustainable social-ecological system.
Although reef sharks are at considerable
risk over broad spatial scales, our results show
that declines at one reef will have little effect
on reefs tens to hundreds of kilometers dis-
tant. Thus, despite populations being func-
tionally extinct at the reef level, the potential
to rebuild abundances remains relatively high
if there are protected areas or strong fisheries
management within a region (6). These source
populations are present among many small
oceanic islands where low human populations
and the high cultural value of sharks has re-
sulted in fishing levels that are below those
seen elsewhere (21). MPAs also provide the
opportunity to act as source populations; how-
ever, their designation alone is insufficient to
deliver benefits. As others have observed (22),
high compliance is required. We show that
there are reefs in regions with widespread
depletion of reef shark species that had metrics
indicating that they are in a relatively healthy
state compared with those around them. These
Simpfendorfer et al., Science 380, 1155–1160 (2023)
16 June 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
n
o
i
t
a
N
Sri Lanka
Kenya
Qatar
Japan
Indonesia
Tanzania
Taiwan
Saudi Arabia (Red Sea)
Philippines
Vanuatu
USA−Pacific
Madagascar
South Africa
Mayotte
Mozambique
Christmas Island
American Samoa
Malaysia
Guam
Samoa
Species
Blacktip reef
Grey reef
Whitetip reef
Papua New Guinea
Seychelles
Cook Islands
Maldives
French Polynesia
Australia−Indian Ocean
Fiji
Kiribati
Fed. States of Micronesia
Niue
Cocos−Keeling
Palau
Solomon Islands
Australia−Pacific
New Caledonia
Tonga
Jarvis Island
Species
Caribbean reef
Nurse
B
Martinique
Jamaica
Montserrat
Dominican Republic
Barbados
Colombia
USA−Western Atlantic
Trinidad and Tobago
Brazil
Cuba
Belize
Pedro Bank
The Bahamas
Turks and Caicos
Colombia (Offshore Islands)
Dutch Caribbean South
Antigua and Barbuda
1.00
0.75
0.50
Depletion level
0.25
0.00
1.00
0.75
0.50
Depletion level
0.25
0.00
Fig. 4. Depletion of core coral reef shark species in the Indo-Pacific and Atlantic basins at national or near-national scale. (A) Indo-Pacific basin.
(B) Atlantic basin. Depletion was calculated by comparing reef-level species MaxN values to unfished, estimated by using a linear model in which market
gravity (a measure of the human pressure from population and access to reefs) was set to the ocean basin minimum and reef protected status was
“closed” (no take MPA) (8). Reef-level depletion scores were modeled by nation and used to estimate a global level of depletion (vertical dashed
lines) ± 1 standard error (shaded area) calculated by weighting national-level depletion by coral reef area (as a percent of global total coral reef area that
occurs within the range of each shark species).
included Tubbataha (Philippines), Sipidan
(Island Malaysia), Glover’s Reef and Light-
house Reef (Belize), and Misool (Indonesia);
in all of these locations, there are programs to
actively manage and enforce MPA regulations
that are likely to account for these successes
(23–25).
Multiple nations have strong management
measures (such as spatial protections and/or
fishing restrictions) in place that benefit
reef species. This study builds the case that
species-specific reef shark management pro-
vides the best way forward for conservation
and rebuilding of reef sharks in places where
they have declined, among nations with the
desire and capacity to do so (7, 8). Recent
studies show that populations of reef sharks
can rebound in under a decade if appropri-
ate management strategies that reduce fish-
ing pressure are in place (26). Although direct
management is critical, local and national
socioeconomic factors that affect the ability of
nations to develop, implement, and enforce
regulations, and the likelihood that fishers
comply with regulations, will be critical to
maintaining or rebuilding populations and
diverse elasmobranch assemblages. If not ad-
dressed, pressures causing the shark and ray
diversity deficits we outline will continue to
result in a loss of species, ecological func-
tions, and ecosystem services that support
sustainable livelihoods for millions of people
worldwide.
Simpfendorfer et al., Science 380, 1155–1160 (2023)
16 June 2023
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RES EARCH | R E S E A R C H A R T I C L E
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ACKN OW LEDG MEN TS
We thank our individual funders for country-specific deployments,
whose contributions greatly enhanced the sampling coverage of
the projects; all of the government permitting agencies that
allowed us to work in their waters; and the Global FinPrint
volunteers from Stony Brook University, Florida International
University, James Cook University, the Aquarium of the Pacific,
and Shedd Aquarium who watched the BRUVS footage.
Funding: Core funding for Global FinPrint was provided by the
Paul G. Allen Family Foundation (to D.D.C. and M.R.Hei.). Author
contributions: Conceptualization: D.D.C., M.R.Hei., C.A.S., M.R.Heu.,
M.A.M., M.M., and E.H. Methodology: D.D.C., M.R.Hei., C.A.S., M.R.Heu.,
M.A.M., M.M., and E.H. Investigation: All authors. Visualization:
C.A.S. Funding acquisition: D.D.C. and M.R.Hei. Project administration:
D.D.C., M.R.Hei., C.A.S., M.R.Heu., M.A.M., M.M., and E.H. Writing –
original draft: C.A.S., D.D.C., M.R.Hei., M.R.Heu., M.A.M., M.M., E.H.,
and C.S.S. Writing – review and editing: All authors. Competing
interests: The authors declare that they have no competing interests
Data and materials availability: Data files have been deposited in
Dryad (27), and R script has been deposited in Zenodo (28). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
1College of Science and Engineering, James Cook University,
Townsville, QLD, Australia. 2Institute for Marine and Antarctic
Studies, University of Tasmania, Hobart, TAS, Australia. 3Institute of
Environment, Department of Biological Sciences, Florida International
University, North Miami, FL, USA. 4Australian Institute of Marine
Science, Townsville, QLD, Australia. 5Ocean Frontier Institute,
Department of Biology, Dalhousie University, Halifax, NS, Canada.
6Australian Institute of Marine Science, Perth, WA, Australia.
7School of Molecular and Life Sciences, Curtin University, Bentley, WA,
Australia. 8Earth to Ocean Group, Biological Sciences, Simon Fraser
University, Burnaby, BC, Canada. 9School of Molecular and Life
Sciences, Curtin University, Perth, WA, Australia. 10Marine Science
Program, Biodiversity and Conservation Science, Department
of Biodiversity, Conservation and Attractions, Perth, WA, Australia.
11Centre for Sustainable Ecosystems Solutions, School of Earth,
Atmospheric and Life Sciences, University of Wollongong,
Wollongong, NSW, Australia. 12Australian Institute of Marine Science,
Darwin, NT, Australia. 13Sharks and Rays Conservation Program, Mote
Marine Laboratory, Sarasota, FL, USA. 14School of Marine and
Atmospheric Sciences, Stony Brook University, Stony Brook, NY, USA.
15International Pole and Line Foundation–Maldives, Malé, Republic of
Maldives. 16Maldives Marine Research Institute, Ministry of Fisheries,
Marine Resources and Agriculture, Malé, Republic of Maldives.
17Red Sea Global, Department of Environmental Protection and
Regeneration, AlRaidah Digital City, Riyadh, Saudi Arabia. 18Kap Natirel
NGO, Fort l’Olive, Guadeloupe, France. 19Mahonia Na Dari Research and
Conservation Centre, Kimbe, Papua New Guinea. 20South African
Institute for Aquatic Biodiversity, National Research Foundation,
Makhanda, South Africa. 21Department of Zoology and Entomology,
Rhodes University, Makhanda, South Africa. 22Red Sea Research
Center, King Abdullah University of Science and Technology, Thuwal,
Saudi Arabia. 23Marine Conservation, Madagascar Program, Wildlife
Conservation Society, Antananarivo, Madagascar. 24Blue Resources
Trust, Colombo, Sri Lanka. 25Cape Eleuthera Institute, Cape Eleuthera,
Eleuthera, The Bahamas. 26Center for Sustainable Development,
College of Arts and Sciences, Qatar University, Doha, Qatar. 27Georgia
Aquarium–IUCN Center for Species Survival, Atlanta, GA, USA.
28School of Natural Sciences, Macquarie University, Sydney, NSW,
Australia. 29Bimini Biological Field Station, Bimini, Bahama. 30Centro de
Investigación en Ciencias del Mar y Limnología, Universidad de Costa
Rica, San José, Costa Rica. 31MigraMar, Olema, CA, USA.
32Department of Biology, Albion College, Albion, MI, USA. 33Marine
Science Institute, University of California Santa Barbara, Santa Barbara,
CA, USA. 34Coastal Impact, Goa, India. 35College of Arts, Society, and
Education, James Cook University, Townsville, QLD, Australia. 36Centre
Universitaire de Formation et de Recherche de Mayotte, Dembeni,
France. 37Paris Sciences Lettres, Centre de Recherche Insulaire et
Observatoire de l’Environnement, Opunohu Bay, Papetoai, French
Polynesia. 38Laboratoires d’Excellence Corail, Ecole Pratique des
Hautes Etudes, Perpignan, France. 39School of Biosciences, Cardiff
University, Cardiff, UK. 40Environmental Research Institute Charlotte-
ville, Charlotteville, Trinidad and Tobago. 41Australian Research Council
Centre of Excellence for Coral Reef Studies, James Cook University,
Townsville, QLD, Australia. 42Sharks Pacific, Rarotonga, Cook Islands.
43Oceans and Atmosphere, Commonwealth Scientific and Industrial
Research Organization, Hobart, TAS, Australia. 44Wageningen
Marine Research, Wageningen University & Research, IJmuiden,
Netherlands. 45Graduate School for Global Environmental Studies,
Sophia University, Tokyo, Japan. 46Waitt Institute, La Jolla, CA, USA.
47Reef Systems Ecology and Conservation Lab, Departamento
de Biologia Marinha, Universidade Federal Fluminense, Rio de Janeiro,
Brazil. 48Marine Megafauna Foundation, Palm Beach, FL, USA.
49Oceanographic Research Institute, Durban, South Africa. 50TRAFFIC
International, Cambridge, UK. 51College of Arts, Science, and Education,
Florida International University, North Miami, FL, USA. 52Science
Department, Georgia Jones-Ayers Middle School, Miami, FL, USA.
53Division of Aquatic Resources, Department of Land and Natural
Resources, Honolulu, HI, USA. 54Centro de Biociências, Departmento de
Botânica e Zoologia, Universidade Federal do Rio Grande do Norte,
Brazil. 55Beacon Development Company, King Abdullah University of
Science and Technology, Thuwal, Saudi Arabia. 56Instituto de Ciencias
do Mar, Universidade Federal do Ceará, Fortaleza, Brazil. 57Grupo de
Ecologia Aquática, Espaço Inovação do Parque de Ciência e Tecnologia
Guamá, Guamá, Pará, Brazil. 58Independent consultant, Hull, UK.
59Bimini Biological Field Station Foundation, South Bimini, The
Bahamas. 60Saving the Blue, Cooper City, FL, USA. 61The School for
Field Studies, Center for Marine Resource Studies, South Caicos, Turks
and Caicos Islands. 62Pelagios Kakunjá, La Paz, Mexico. 63Fins
Attached, Colorado Springs, CO, USA. 64Center for Shark Research,
Mote Marine Laboratory, Sarasota, FL, USA. 65OCEARCH, Park City, UT,
USA. 66Elasmo Project, Dubai, United Arab Emirates. 67Departamento
de Oceanografia e Ecologia, Universidade Federal do Espírito Santo,
Vitória, Espírito Santo, Brazil. 68Murdoch University, Murdoch, WA,
Australia. 69Centre for Development and Environment, University of
Bern, Bern, Switzerland. 70Operation Wallacea, Spilsby, Lincolnshire,
UK. 71Melanesia Program, Wildlife Conservation Society, Suva, Fiji.
72Wasage Divers, Wakatobi & Buton, Southeast Sulawesi, Indonesia.
73Daniel P. Haerther Center for Conservation and Research,
John G. Shedd Aquarium, Chicago, IL, USA. 74Kenya Fisheries Service,
Mombasa, Kenya. 75Ministry of Fisheries and Marine Resources,
Kiritimati, Kiribati. 76Tanzania Fisheries Research Institute, Dar Es
Salaam, Tanzania. 77University of the West Indies, Kingston, Jamaica.
78School of Biological Sciences, University of Western Australia, Perth,
WA, Australia. 79The UWA Oceans Institute, University of Western
Australia, Perth, WA, Australia. 80Departamento de Pesquerias, Centro
Interdisciplinario de Ciencias Marinas del IPN, La Paz, Baja California
Sur, Mexico. 81Pelagios Kakunjá, La Paz, Baja California Sur, Mexico.
82Yardie Environmental Conservationists Limited, Kingston, Jamaica.
83Coral Reef Research Foundation, Koror, Palau. 84Departamento de
Ecología y Territorio, Facultad de Estudios Ambientales y Rurales,
Pontificia Universidad Javeriana, Bogotá, Colombia. 85National Institute
of Water and Atmospheric Research, Auckland, New Zealand. 86Borneo
Marine Research Institute, Universiti Malaysia Sabah, Kota Kinabalu,
Sabah, Malaysia. 87Marine Megafauna Foundation, West Palm, FL, USA.
88Island Conservation Society Seychelles, Victoria, Mahé, Seychelles.
89Emirates Nature - World Wide Fund for Nature, Dubai, United Arab
Emirates. 90College of Marine Sciences and Aquatic Biology, University
of Khorfakkan, Sharjah, UAE. 91Aquarium of the Pacific, Long Beach,
CA, USA. 92Marine and Environmental Sciences Centre/ Aquatic
Research Network, Regional Agency for the Development of Research,
Technology and Innovation, Funchal, Madeira, Portugal. 93Oceans
Institute, University of Western Australia, Perth, WA, Australia. 94Inland
Fisheries Ireland, Dublin, Ireland. 95Western Australian Fisheries and
Marine Research Laboratories, Department of Primary Industries and
Regional Development, Government of Western Australia, Hillarys, WA,
Australia. 96CORDIO East Africa, Mombasa, Kenya. 97Blue Ventures,
Mombasa, Kenya. 98American Samoa Department of Marine and
Wildlife Resources, Pago Pago, American Samoa. 99The Centre for
Ocean Research and Education, Gregory Town, Eleuthera, The
Bahamas. 100Department of Ocean Science, Memorial University, NL,
Canada. 101Department of Environment and Geography, University of
York, York, UK. 102Departamento de Ciências Agrárias e Biológicas,
Universidade Federal do Espírito Santo, São Mateus, Espírito Santo,
Brazil. 103Blue Sanctuary-Avalon, Jardines de la Reina, Cuba. 104Centro
de Investigaciones Marinas, Universidad de La Habana, Habana, Cuba.
105Center for Marine Biology, University of São Paulo, São Sebastião,
São Paulo, Brazil. 106Large Marine Vertebrates Research Institute
Philippines, Puerto Princesa City, Palawan, Philippines. 107Center for
Fisheries Research, Ministry for Marine Affairs and Fisheries, Jakarta
Utara, Indonesia. 108Fisheries Department, Universitas Dayanu
Ikhsanuddin, Bau Bau, Southeast Sulawesi, Indonesia. 109Programa de
Pós Graduação em Ecologia: Teoria, Aplicação e Valores, Instituto de
Biologia, Universidade Federal da Bahia, Salvador, BA, Brazil.
110HJR Reefscaping, Boquerón, Puerto Rico. 111Pristine Seas, National
Geographic Society, Washington, DC, USA. 112Charles Darwin Research
Station, Charles Darwin Foundation, Puerto Ayora, Galapagos Islands,
Ecuador. 113Save Our Seas Foundation Shark Research Center and
Guy Harvey Research Institute, Nova Southeastern University, Dania
Beach, FL, USA. 114School of Pure and Applied Sciences, Pwani
University, Kilifi, Kenya. 115Thurgau Hunting and Fishing Administration,
Frauenfeld, Switzerland. 116SalvageBlue, Kingstown, Saint Vincent and
the Grenadines. 117School of Mathematical and Computational
Sciences, Massey University, Auckland, New Zealand. 118Evolutionary
Ecology Group, Department of Zoology, University of Cambridge,
Cambridge, UK. 119Indo Ocean Project, Jln Toyapakeh DESA Toyapakeh,
Nusa Penida, Bali, Indonesia. 120Aquaculture and Fisheries Group,
Wageningen University & Research, Wageningen, Netherlands. 121Reef
Check Dominican Republic, Santo Domingo, Dominican Republic.
122Institut de Recherche pour le Développement, UMR Entropie (IRD-
UR-UNC-CNRS-IFREMER), Nouméa, New Caledonia, France.
123Secretariat of the Pacific Regional Environment Programme, Apia,
Samoa. 124Department of Natural Sciences, Faculty of Science
Engineering, Manchester Metropolitan University, Manchester, UK.
125Department of Life Science, Tunghai University, Taichung, Taiwan.
126School of Environmental and Forest Sciences, University of
Washington, Seattle, WA, USA. 127GIBEAM Research Group, Universi-
dad del Sinú, Cartagena, Colombia. 128Corales del Rosario and San
Bernardo National Natural Park, Colombia.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.ade4884
Materials and Methods
Figs. S1 to S8
Tables S1 to S9
References (29–37)
MDAR Reproducibility Checklist
Submitted 31 August 2022; accepted 27 April 2023
10.1126/science.ade4884
Simpfendorfer et al., Science 380, 1155–1160 (2023)
16 June 2023
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RES EARCH
CHEMICAL PHYSICS
Femtosecond symmetry breaking and coherent
relaxation of methane cations via x-ray spectroscopy
Enrico Ridente1,2†, Diptarka Hait1,2†‡, Eric A. Haugen1,2, Andrew D. Ross1,2§, Daniel M. Neumark1,2,
Martin Head-Gordon1,2, Stephen R. Leone1,2,3*
Understanding the relaxation pathways of photoexcited molecules is essential to gain atomistic-level
insight into photochemistry. We performed a time-resolved study of ultrafast molecular symmetry
breaking through geometric relaxation (Jahn-Teller distortion) on the methane cation. Attosecond
transient absorption spectroscopy with soft x-rays at the carbon K-edge revealed that the distortion
occurred within 10 ± 2 femtoseconds after few-femtosecond strong-field ionization of methane. The
distortion activated coherent oscillations in the asymmetric scissoring vibrational mode of the
symmetry-broken cation, which were detected in the x-ray signal. These oscillations were damped within
58 ± 13 femtoseconds because vibrational coherence was lost with the energy redistributing into
lower-frequency vibrational modes. This study completely reconstructs the molecular relaxation
dynamics of this prototypical example and opens avenues for exploring complex systems.
C hemical reactions arise from the motion
of atomic nuclei. Atomic displacements
can be described in terms of either fluc-
tuations about a local minimum of energy
or relaxation toward such a minimum
from a nonequilibrium configuration. The latter
often results from interaction with light because
photon absorption can lead to excited electronic
states with minimum energy geometries quite
distinct from the initial starting point. The
nonequilibrium configurations arising from
light-matter interaction thus can have sub-
stantial surplus potential energy, which can
drive chemical transformations. Therefore,
intramolecular relaxation dynamics of photo-
excited molecules are of fundamental photo-
chemical interest.
Jahn-Teller (JT) distortion (1, 2) is a special
type of relaxation mechanism that spontane-
ously reduces the spatial symmetry of non-
linear molecules in degenerate electronic
states. Molecular geometries where multiple
electronic states are isoenergetic are not sta-
ble for any of the associated states (1) and
represent a fundamental breakdown of the
Born-Oppenheimer approximation (3). It there-
fore becomes energetically favorable to under-
go distortions that lift the degeneracy by
breaking spatial symmetry. JT distortions are
ubiquitous in solids (4) and gas-phase mol-
ecules (5). In this work, we used attosecond
x-ray transient absorption spectroscopy (XTAS)
to study symmetry breaking of the methane
+) generated through vertical
cation (CH4
1Department of Chemistry, University of California, Berkeley,
CA 94720, USA. 2Chemical Sciences Division, Lawrence
Berkeley National Laboratory, Berkeley, CA 94720, USA.
3Department of Physics, University of California, Berkeley,
CA 94720, USA.
*Corresponding author. Email: srl@berkeley.edu
†These authors contributed equally to this work.
‡Present address: Department of Chemistry and PULSE Institute,
Stanford University, Stanford, CA 94305, USA.
§Present address: TOPTICA Photonics Inc., Pittsford, NY 14534, USA.
strong-field ionization (SFI). This work un-
equivocally revealed the role and timescale of
JT-induced dynamics experimentally and pro-
vided an understanding of relaxation mecha-
nisms in molecular systems.
21t2
21t2
CH4
22a1
22a1
+ is a classic system in which JT dis-
tortions occur (6–9). The process starts with
CH4, which is the smallest stable molecule
with tetrahedral (Td) geometry. The equilibrium
C-H bond distances are 1.087 Å (10), and all of
the H-C-H bond angles are ≈109.5° because of
Td symmetry. The ground-state molecular
orbitals (MOs) are shown in Fig. 1A, and the
electronic configuration of neutral CH4 is
6 (1A1). The electronic ground-state
1a1
+ at the Td geometry is
configuration of CH4
5, which is triply degenerate (2T2)
1a1
because each of the three 1t2 orbitals is equally
+
likely to be singly occupied. Therefore, CH4
undergoes JT distortion away from the Td
geometry to a lower symmetry C2v form (7, 11–14).
This JT distortion involves t2 and e symmetry
+ the
vibrational modes of CH4, making CH4
simplest T2 (cid:1) (t2 + e) JT problem (15). The
resulting C2v equilibrium structure was com-
puted to have two long (1.187 Å) and two
short (1.083 Å) C-H bonds (Fig. 1A), which
indicates antisymmetric stretching (t2 symmetry)
relative to neutral CH4. The angle formed by
the long C-H bonds is 55.0°, and the short
bonds form an angle of 125.7°, representing
considerable deviations from the initial Td
geometry through bending motions (of t2 and
e symmetry in CH4). These distortions lower
the energy of the doubly occupied 3a1 and 1b1
MOs (Fig. 1A) but also destabilize the 1b2 singly
occupied MO (SOMO). The electronic ground
+ therefore is 2B2 (12).
state of CH4
+ in
Molecular JT-distorted forms, and CH4
particular, have been extensively studied both
theoretically (15–18) and experimentally (6, 19).
Experimentally, time resolving the JT distor-
+ remained an open challenge
tion in CH4
(7, 13) because of the ultrafast nature of the
process. JT-distorted species have been charac-
terized in photoelectron spectroscopy experi-
ments (6, 20), but such measurements lack
the temporal resolution to obtain the femto-
second timescale dynamics of symmetry break-
ing. Baker et al. (21) used attosecond-resolution
high-harmonic emission spectroscopy to report
+ and
on the onset of the JT distortions in CH4
+ up to the first 1.6 fs. The nu-
deuterated CD4
clear motion in those experiments, however,
cannot be reconstructed at longer times, which
precludes a complete analysis of the JT rela-
xation process and subsequent coherent mo-
tion. Coulomb explosion experiments by
Li et al. (22) probed the dynamics of CH4
+
by recording the photofragments after inter-
action with two time-delayed strong-field
800-nm pulses, but temporal resolution was
limited by the 25-fs pulses used as pump and
probe. Furthermore, their use of a multicycle
pump pulse led to several additional photo-
products from higher-energy fragmentation
pathways that compete with JT distortions.
It has been shown that the use of shorter, few-
cycle 800-nm pulses increased the relative
+ by suppressing additional pro-
amount of CH4
duct channels (23).
XTAS, based on attosecond- and few-
femtosecond-duration soft x-ray pulses gener-
ated through high-harmonic generation (24),
has been successfully used to study ultrafast
molecular relaxation processes with high
structural and temporal resolution (25, 26).
XTAS at the carbon K-edge is therefore an
ideal platform to observe few-femtosecond
timescale dynamics such as those associated
+ (27, 28). The x-ray
with the JT distortion of CH4
probe excites C 1s electrons to unoccupied
levels, such as the SOMO, or completely un-
occupied antibonding or Rydberg levels. In
particular, the dipole-allowed 1s → SOMO
+ is expected to be energetically
signal in CH4
well resolved from other features. Geometric
changes as a result of JT distortion will
strongly affect the SOMO energy, which can be
traced by XTAS with few-femtosecond time
resolution.
In this work, we report a joint experimental
and theoretical study of the symmetry-breaking
+. The cations were pro-
JT dynamics of CH4
duced from neutral methane through abrupt,
few-femtosecond SFI of CH4 with an 800-nm,
few-cycle pump pulse generated by a table-top
Ti:sapphire laser. The induced dynamics were
then probed with XTAS using high-harmonic–
generated soft x-ray pulses at the C K-edge
obtained with a 1300-nm source (24). The non-
perturbative nature of SFI leads to an ionization
window that is temporally much narrower
than the 5-fs width of the pump pulse (29). We
observed a substantial energy shift in the XTAS
signal immediately upon ionization because of
JT distortion. The C2v minimum geometry was
Ridente et al., Science 380, 713–717 (2023)
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Fig. 1. XTAS measurements of CH4
probe process. Pump-induced SFI produces Td symmetry CH4
JT distortion toward a C2v minimum. MOs for both structures are also shown
(energies not to scale). The 1a1 orbital is the C 1s core-level, and the remainder
are sC-H bonding orbitals. The dynamics are mapped by the 1s → SOMO probe
+ dynamics. (A) Schematic of the pump-
+, which undergoes
transition induced by a time-delayed (Dt) soft x-ray probe. (B) Ground-state
carbon K-edge x-ray absorption spectrum for CH4. (C) Transient x-ray
absorption at Dt < 35 fs. Negative time indicates probe preceding pump. The
low-energy signal (278 to 282 eV) corresponds to the 1s → SOMO probe
transition, which indicates that the C2v minimum is reached by ≈10 fs.
attained within ≈10 fs, which was followed by
two coherent oscillations in the signal that
revealed large-amplitude scissoring motion.
These coherent oscillations were damped out
by ≈60 fs, indicating vibrational dephasing and
eventual decoherence. The behavior of fully
+) was also
deuterated methane cations (CD4
investigated to understand the effect of sub-
stituent masses on the JT dynamics.
General features of XTAS signal
CH4 has a simple ground-state x-ray absorp-
tion spectrum (Fig. 1B). There is only one pro-
minent peak (288 eV), which arises from the
1s → 3p Rydberg excitation (30). No other
noteworthy pre-edge features were observed,
and 1s ionization occurred at ≈290.8 eV (31).
Figure 1C shows the experimental carbon
+ up to 35 fs
K-edge XTAS spectrum for CH4
after the pump pulse abruptly ionizes the
molecule at time t = 0. The intensity of the
pump beam was 3 × 1014 W/cm2, which gener-
+ without substantial photo-
ated sufficient CH4
dissociation, as discussed in the supplementary
materials. Previous investigations have con-
firmed that the major photoproduct for an
800-nm pump pulse of similar intensity and
+ (32). The negative (blue)
pulse duration is CH4
transient signal (feature IV) corresponds to the
depletion of neutral CH4 and can be more
clearly observed at higher values of the pump
power (see the supplementary materials). At
t = 0, other prominent features were the po-
sitive (red) signals at 278 to 282 eV (I), 284 eV
(II), 287 eV (III), and 290 to 292 eV (V). The
broad features II, III, and V had substantial
temporal overlap with the pump pulse and
could be attributed to the Stark effect of the
pump pulse on core-excitation energies of
CH4 (supplementary materials). Their tem-
poral width is longer than the pump pulse
because the Stark shift in XTAS measurements
is proportional to the cross-correlation and
timing jitter between pump and probe. After
t = 0, a positive feature at ≈287.5 eV could be
observed. This feature arose because of Raman
activation of the symmetric stretch vibrational
mode of CH4 by the pump pulse (supplemen-
tary materials), like the behavior that has been
observed in other molecules (33, 34).
Feature I was assigned to CH4
+ on the basis
of orbital-optimized density functional theory
(OO-DFT) calculations (35) that revealed that
this feature corresponded to the 1s → SOMO
+. OO-DFT
excitation of nonequilibrium Td CH4
indicated that other core-level excitations of
+ (such as 1s → s* or the Rydberg levels)
CH4
were above 288 eV in energy (supplementary
materials). Feature VI in Fig. 1C corresponds
to such excitations and could be observed at
long times. However, feature VI did not show
discernible time evolution. Conversely, feature I
was well separated from all the other features
and was particularly sensitive to changes in mo-
lecular geometry as the SOMO is of sC-H char-
acter. The time evolution of this signal was the
+, and
clearest reporter of the dynamics of CH4
the analysis below therefore focuses on it.
+
Relaxation dynamics of CH4
The long-time experimental XTAS of the JT
feature corresponding to the 1s → SOMO tran-
sition is given in Fig. 2A. The energetic average
(henceforth abbreviated as CM1, for the first
central moment) of the differential absorption
[change in milli–optical density (DmOD)] signal
(solid black line) showed three main charac-
teristics. A rapid blue shift in energy from 278 eV
(at t ≈ 0) to ≈282 eV (at t ≈ 18 fs) was followed
by damped oscillations until t ≈ 60 fs and
subsequently an almost time-independent sig-
nal between 281 and 281.5 eV. The width of the
spectral feature increased considerably starting
around t ≈ 10 fs, leading to a very broad signal
at longer times.
We interpreted the behavior of this signal
using quasiclassical ab initio molecular dyna-
mics (AIMD) (36) trajectories on CH4
+. Figure
2B shows the XTAS signal computed using
OO-DFT from 255 AIMD trajectory geometries
at different time points, revealing good agree-
ment with the experimental results. This
comparison indicates that the trajectories under-
lying the spectrum are a good reporter of the
molecular dynamics under the experimental
conditions. It is worth noting that all of the
AIMD calculations were performed on the elec-
+ (i.e., were adia-
tronic ground state of CH4
batic). Nonadiabatic effects from higher-energy
+ could potentially
electronic states of CH4
contribute to the small differences between
experiment and theory, but the experimental
evidence suggests that the system is always in
Ridente et al., Science 380, 713–717 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
the ground electronic state under experimen-
tal conditions (supplementary materials). In
general, no explicit signature of nonadiaba-
ticity was observed in the experimental spec-
trum, as made evident by the good agreement
between Fig. 2, A and B. The potential role of
nonadiabatic effects on other aspects related
to the JT distortion of CH4 has been considered
elsewhere (9, 15–18).
The timescale for the JT process can be di-
rectly estimated by the time taken by the CM1
to attain the 281.5-eV value that we associate
+. This value was
with the C2v form of CH4
chosen because it corresponds to the asymp-
totic long-time limit of the experimental signal
CM1, and this value was also estimated by
OO-DFT to be the upper bound for the 1s →
+ at the C2v equilibrium
SOMO excitation of CH4
geometry (supplementary materials). This value
was measured at 10 ± 2 fs from experiment
by fitting an error function to the first 20 fs of
the 1s → SOMO feature (supplementary mate-
rials). OO-DFT calculations find this time to
be 9.4 ± 0.3 fs, confirming that JT relaxation
occurs on a timescale associated with high-
frequency vibrational motion.
In general, the time evolution of the signal
corresponds to atomic motions associated with
the relaxation process, with the oscillatory
patterns suggesting involvement of vibrational
+. This evolution could be anal-
modes of CH4
yzed further using a Fourier transform (FT) of
the CM1 position from both theory and experi-
ment (Fig. 2C). Even though the FT features
were broad owing to the rapid decay in the os-
cillation amplitude, it was possible to identify
critical frequencies. The most intense peak in
the FT was at ≈1200 cm−1, a frequency that
corresponded to a computed normal mode
of the C2v minimum associated with scissoring
about the H-C-H bond angles. This mode is an
asymmetric scissoring mode (supplementary
materials), where the scissoring motion about
the smallest bond angle (i.e., the angle be-
tween the two long C-H bonds) is opposite in
direction to the scissoring motion about the
largest bond angle (i.e., the angle between the
two short C-H bonds). However, caution must
be taken in interpreting the FT features in
terms of the fundamental frequencies of the C2v
+ ground-state surface has
minimum; the CH4
12 distinct C2v minima (37) and multiple seams
corresponding to electronic state degeneracies,
resulting in a highly anharmonic potential
energy surface (PES). The FT is nonetheless an
indication of several molecular motions that
affect the signal and the associated timescales.
The damping rate for the 1200 cm−1 frequency
could also be estimated by fitting to the time
domain experimental CM1 (Fig. 2D), revealing
a lifetime of 58 ± 13 fs for the oscillations.
We used the AIMD trajectories to uncover
the origins of the signal oscillations in the x-ray
spectra. The trajectories indicated that the C-H
Fig. 2. Time evolution of the 1s → SOMO transition of CH4
+, with the first central moment (CM1) shown with the solid black line. The dotted black lines
transition of CH4
indicate the asymptotic long-time signal CM1 (281.5 eV), which corresponds to the vibrationally hot C2v cation
generated by the experiment, and at what time this energy is first reached (10 fs, JT timescale). (B) Theoretical
XTAS for the same excitation. (C) FT of the CM1 from experiment (solid line) and theory (dashed line). The
theoretical intensities have been uniformly scaled to match experiment for peak absorbance. (D) Experimental CM1 fit
with −e−t/t × cos(wt), with w = 1200 cm−1, indicating a damping lifetime of t = 58 ± 13 fs for the vibrational dephasing.
+. (A) Experimental XTAS for the 1s → SOMO
Fig. 3. Role of the smallest H-C-H angle on XTAS signal. (A) Time evolution of the smallest bond angle
over the trajectories. (B) Correlation between the computed 1s → SOMO excitation energies versus the smallest
bond angle of the corresponding structures. (C) Evolution of the SOMO with change in the smallest bond angle.
Ridente et al., Science 380, 713–717 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
+ and CH4
+. (A) Experimental
Fig. 4. Comparison between CD4
XTAS of the 1s → SOMO transition of CD4
+, with the CM1 as the solid
black line. The dotted lines indicate when the JT equilibrium energy
is reached for the first time. (B) Theoretical XTAS for the same
+ from
excitation. (C) Comparison of the CM1 for CH4
experiment (solid lines) and theory (dashed lines). The JT distortion
is slower for CD4
lines indicate when the experimental signal CM1 first attained the value of
281.5 eV (corresponding to the C2v geometry) for CH4
+ by a factor of ≈1.4. The vertical dotted
+.
+ and CD4
+ than CH4
+ and CD4
bond lengths oscillate on a timescale roughly
twice as fast as the principal oscillation in the
CM1 (supplementary materials). The angular
oscillations were slower than the stretches,
with Fig. 3A showing that the mean of the
smallest molecular bond angle over all trajec-
tories underwent a damped oscillatory motion
on the same timescale as the predicted and
observed XTAS signal CM1 (Fig. 2, A and B).
The computed bond angle distribution also
broadened rapidly over time after t ≈ 10 fs,
similar to the XTAS signal. A direct correla-
tion between the observed signal and the
smallest bond angle is revealed in Fig. 3B,
which plots the smallest bond angle of the
trajectory geometries used for Fig. 2B against
the computed 1s → SOMO excitation energies
for those geometries. It is evident that a simple
linear model could capture much of the rela-
tionship between the two quantities. The ex-
citation energy had weaker correlation with
other bond angles and bond lengths (supple-
mentary materials). Theory therefore indi-
cated that the most important contribution
to the observed time evolution of the XTAS ab-
sorption energy was from the dynamics of the
smallest bond angle, to the extent that the
signal could be interpreted in terms of a single
parameter.
This connection can be understood using a
simple orbital model (Fig. 3C). The SOMO at
+
the C2v symmetry minimum geometry of CH4
is the bonding orbital arising from mixing be-
tween a C 2p orbital and a symmetry-adapted
linear combination (SALC) of the 1s orbitals
corresponding to H atoms in the long bonds.
This SALC has antibonding character because
the two H 1s orbitals have opposite phases. For
small bond angles, the H 1s SALC has poorer
overlap with the C 2p level as it gets closer to
the nodal plane of the latter. This behavior
leads to a weaker interaction and therefore
lowers the mixing between the C and H centered
orbitals. Furthermore, smaller angles lead to
decreased H-H distance, elevating the energy
of the H 1s SALC because of the local anti-
bonding character. The resulting sC-H bonding
orbital therefore has greater nonbonding (pure
C 2p) character as the angle decreases, made
evident visually by the 30° angle case in Fig. 3C.
Conversely, larger bond angles lead to a more
stabilized SOMO with greater contribution from
H orbitals. This picture is consistent with the
observed increase in the 1s → SOMO x-ray probe
excitation energy with decreasing bond angle
shown in Fig. 3B. The x-ray oscillator strength
also increased with a decrease in bond angle
(supplementary materials). This behavior of the
oscillator strength highlighted the increase in
C 2p character of the SOMO because transitions
from the C 1s level to other possible valence
atomic orbitals that may contribute to the SOMO,
such as C 2s or H 1s, have negligible oscillator
strength. Therefore, the XTAS signal revealed
the extent to which the SOMO lost C-H bonding
character during the relaxation process.
It is thus apparent that the Td → C2v JT
distortion activates scissoring motion about
the smallest bond angle in the C2v minimum,
which was the most evident feature in the
x-ray spectra. Furthermore, the frequencies
indicated in Fig. 1C suggest that the asym-
metric scissoring mode is activated to a greater
extent than the symmetric scissoring mode.
The greater activation of the asymmetric scis-
soring mode is further supported by the short
time (<10 fs) evolution of the molecular bond
angles (supplementary materials), which revealed
that the smallest H-C-H bond angle decreases
over time, whereas the largest H-C-H bond angle
increases in value. For a perfectly harmonic PES,
the excess energy accumulated in this asym-
metric scissoring mode would remain undissi-
pated therein, leading to undamped oscillation
of the XTAS signal and geometric parameters
about the minimum before radiative relaxation
to the vibrational ground state. However, the
+ is highly anharmonic (see discus-
PES of CH4
sion above), and the surplus energy spreads out
to all other modes. This redistribution was ob-
served through damping in the oscillations for
both the experimental XTAS signal CM1 and
the mean geometric parameters from the AIMD
trajectories (Figs. 2 and 3). In addition, consid-
erable broadening of the XTAS signal was ob-
served after the initial 10 fs, which was mirrored
by an increase in the width of the probability
distributions for the geometric parameters.
Figure 2D indicates that the experimental XTAS
CM1 oscillations had a damping lifetime of 58 fs,
and oscillations in parameters computed from
AIMD trajectories were mostly damped out
within 60 fs (supplementary materials). It
therefore appears that a large proportion of
energy was transferred out of the JT-activated
asymmetric scissoring mode to other internal
degrees of freedom within this timescale, con-
stituting an ultrafast example of intramolecular
vibrational energy redistribution. This process
can also be described in terms of dephasing of
the asymmetric scissoring mode (i.e., relaxation
Ridente et al., Science 380, 713–717 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
toward thermal equilibrium), which was ulti-
mately reflected in the decoherence of the
XTAS signal.
+ and CD4
Comparison between experiment and theory
revealed that the XTAS signal was reporting
the nuclear motion over the duration of the re-
laxation process. It is important to consider
that SFI experiments could potentially exhibit
electronic relaxation dynamics without consid-
erable nuclear motion, involving highly excited
Rydberg or cationic states (38, 39). To prove
that the observed XTAS signal dynamics solely
arose from nuclear (rather than electronic)
relaxation, we performed experiments and
computations for the dynamics after SFI of CD4.
Figure 4A presents the time evolution of the
resulting experimental XTAS signal, and Fig.
4B shows the computed XTAS spectrum from
+.
OO-DFT on 255 AIMD trajectories of CD4
The good agreement between experiment and
theory further validated the ability of the com-
puted trajectories to successfully simulate the
experimental molecular dynamics. The greater
mass of the deuterium isotope should slow the
scissoring motion, leading to slower time evo-
+.
+ relative to CH4
lution of the signal for CD4
Figure 4C confirms this to be the case by com-
paring the time evolution of the CM1 for both
+ from experiment and theory.
CH4
The time taken by the CM1 to reach the 281.5-eV
value associated with the C2v cation geometry
+, and the effect
+ than for CH4
was longer for CD4
of deuteration could be gauged by the ratio
+) of these times. This ratio was
(CD4
measured to be 1.4 ± 0.3 from experiment and
calculated to be 1.44 ± 0.06 from theory (sup-
plementary materials). The value thus calculated
was close to the ratio between the asymmetric
scissoring frequencies for the smallest bond
+ (computed to be 1.34).
angle in CH4
However, it is important to note that all the
+ have similar fre-
normal modes of C2v CH4
quency ratios upon isotopic substitution (sup-
plementary materials). Nonetheless, the slower
+ unambiguously
dynamics observed for CD4
reveal that the signal was reporting on nuclear
dynamics. We also note that Fig. 4C shows
that the relaxation dynamics after JT distor-
+ continue to be slower up to 45 fs,
tion for CD4
from both experiment and theory. Longer time
+ XTAS signal is
behavior for the computed CD4
+ in the supplementary
compared with CH4
materials (up to 85 fs), revealing slower coherent
+. We also
oscillations in the signal CM1 for CD4
note that Baker et al. (21) have reported that
dynamics within the first 1.6 fs of ionization
+ versus
were a factor of 2 to 3 slower for CD4
+. This behavior at very short times resulted
CH4
from the decay of the autocorrelation of the
nuclear wave function (9, 21), which is distinct
from the longer time dynamics reported here
involving substantial atomic displacements,
therefore representing almost nonoverlapping
nuclear wave functions.
+ and CD4
+/CH4
Conclusions
+ was prepared from SFI of CH4 and
CH4
probed with XTAS near the carbon K-edge
with few-femtosecond time resolution. Evo-
lution of the excitation from the C 1s level to
the valence hole revealed the dynamics of JT
symmetry breaking away from the parent Td
geometry, as well as subsequent coherent
motion and dissipation of released energy out
of active modes. All three of these aspects of
intramolecular relaxation have been success-
fully observed and analyzed. The combina-
tion of experiment and theory revealed that
the molecule first reached the JT-distorted form
within 10 ± 2 fs after ionization. This distortion
involved reduction of a H-C-H bond angle from
109.5° toward 55°, which was directly reported
by a blue shift in the x-ray absorption signal.
The JT dynamics were found to be 1.4× slower
in deuterated methane on account of the larger
substituent mass, proving that the observed dy-
namics arose from nuclear motions. The energy
released by the JT distortion drove a few
coherent oscillations in the activated modes
before being distributed over other molecular
internal degrees of freedom, leading to damping
of the oscillations within 60 fs of ionization.
+
We note that the observed behavior for CH4
is distinct from that observed in previous XTAS
studies (26, 28) on the dynamics of CF4
+ and
+ because those species are highly unstable
CCl4
+ has not been
against bond dissociation. CF4
experimentally detected to date (26); meta-
+ has been previously observed (28),
stable CCl4
but signals from the intramolecular relaxation
pathways were unable to be disentangled from
bond breaking. The subsequent coherence and
dissipation of energy from the JT activated
asymmetric scissoring mode to other internal
+.
degrees of freedom was only observed in CH4
This work thus opens the door to studies on
how ultrafast vibrational coherence influences
the redistribution of excess energy in more
complex systems.
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AC KNOWLED GME NTS
Funding: This work is funded by the US Department of Energy
(DOE) Office of Science, Basic Energy Sciences (BES) Program,
Chemical Sciences, Geosciences, and Biosciences Division, under
contract no. DE-AC02-05CH11231, through the Gas Phase
Chemical Physics program (E.R., E.A.H., A.D.R., D.M.N., and S.R.L.)
and the Atomic, Molecular, and Optical Sciences program
(D.H. and M.H.-G.). The instrument was built with funds from the
National Science Foundation through NSF MRI 1624322 and
matching funds from the Lawrence Berkeley National Laboratory,
the College of Chemistry, the Department of Physics, and the
Vice Chancellor for Research at UC Berkeley. This research used
resources of the National Energy Research Scientific Computing
Center, a DOE Office of Science User Facility supported by the
Office of Science of the US DOE under contract no. DE-AC02-
05CH11231 using NERSC award BES-ERCAP0020263. A.D.R.
was additionally funded by the US DOE, Office of Science,
Office of Basic Energy Sciences, Materials Sciences and
Engineering Division, under contract no. DE-AC02-05-CH11231,
within the Physical Chemistry of Inorganic Nanostructures
Program (KC3103); by the W. M. Keck Foundation, grant no.
042982; and by the US Army Research Office under grant no.
W911NF-20-1-0127. Author contributions: Experimental
investigation: E.R., E.A.H., and A.D.R. Theoretical investigation: D.H.
Experiment supervision: S.R.L. and D.M.N. Theory supervision:
M.H.-G. Writing – original draft: E.R., D.H., and E.A.H. Writing –
review & editing: E.R., D.H., E.A.H., A.D.R., M.H.-G., D.M.N., and
S.R.L. Competing interests: The electronic structure calculations
were performed in Q-Chem, which is partially owned by M.H.-G.
The other authors declare no competing interests. Data and
materials availability: All data needed to evaluate the conclusions
in the paper are present in the paper or the supplementary
materials. The experimental and theoretical data can be accessed
on Zenodo (40). License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg4421
Materials and Methods
Figs. S1 to S25
Tables S1 to S3
References (41–64)
Submitted 23 December 2022; accepted 19 April 2023
10.1126/science.adg4421
Ridente et al., Science 380, 713–717 (2023)
19 May 2023
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RES EARCH
BIOGEOGRAPHY
Paleoenvironments shaped the exchange of
terrestrial vertebrates across Wallace’s Line
A. Skeels1,2,3*, L. M. Boschman4, I. R. McFadden1,2,5, E. M. Joyce6, O. Hagen7, O. Jiménez Robles3,8,
W. Bach1,2, V. Boussange1,2, T. Keggin1,2, W. Jetz9,10, L. Pellissier1,2
Faunal turnover in Indo-Australia across Wallace’s Line is one of the most recognizable patterns in
biogeography and has catalyzed debate about the role of evolutionary and geoclimatic history in biotic
interchanges. Here, analysis of more than 20,000 vertebrate species with a model of geoclimate and
biological diversification shows that broad precipitation tolerance and dispersal ability were key for
exchange across the deep-time precipitation gradient spanning the region. Sundanian (Southeast
Asian) lineages evolved in a climate similar to the humid “stepping stones” of Wallacea, facilitating
colonization of the Sahulian (Australian) continental shelf. By contrast, Sahulian lineages predominantly
evolved in drier conditions, hampering establishment in Sunda and shaping faunal distinctiveness. We
demonstrate how the history of adaptation to past environmental conditions shapes asymmetrical
colonization and global biogeographic structure.
of environmental gradients between regions
(9, 13). To date, our ability to distinguish be-
tween hypotheses regarding the processes
that shape the unevenness of different biotic
interchanges has been limited by the avail-
able process-based methodologies and paleo-
environmental reconstructions.
Distributional patterns of terrestrial verte-
brates in the Indo-Australian archipelago have
fascinated naturalist for centuries (14) and
have provided a model system for understand-
ing biotic interchange. As the Australian con-
tinental plate approached the Eurasian plate,
subduction at the northern boundary led to
the formation of a geologically complex archi-
pelago, today composed of thousands of islands
and known biogeographically as Wallacea (5)
(Fig. 1). The oceanic boundary separating the
Sunda continental shelf (including Myanmar,
Cambodia, Vietnam, Laos, Thailand, Malaysia,
and Indonesia west of Lombok on the Eurasian
plate) from Wallacea and the Sahul continental
shelf (including Australia and New Guinea on
the Australian plate) is named Wallace’s Line
after Alfred Russell Wallace (14) (Fig. 1), who
noted a clear disjunction in the distribution of
some taxa across it (14, 15). Today, Wallace’s
Line marks the boundary of the Indomalayan
and Australasian zoogeographic realms (2, 16)
(Fig. 1), but there are many lines in the region
that mark turnover between a predominantly
Sundanian or Sahulian fauna (15), such as the
Heilprin-Lydekker Line (Fig. 1). The persistent
presence of oceanic barriers has led to the
dominant idea that dispersal limitation is the
primary process shaping interchange (12). For
example, the mammalian faunas of Sunda
and Sahul are largely endemic, and only vagile
rodents (17) and bats (18) have been successfully
exchanged between continents. However, envi-
ronmental niche traits may also have played a
role (19, 20) as the distinctly drier Australian
continent (20, 21) shaped the evolution of
T he world’s major biotic interchanges have
had a disproportionate impact on the dis-
tribution of the world’s terrestrial fauna
(1–3). Well-known systems include the
American interchange, which followed
the formation of the Panamanian isthmus be-
tween North and South America (4), and the
Indo-Australian interchange, which followed
the convergence of the Australian and Eur-
asian tectonic plates and was shaped by com-
plex dynamics of island formation (5). Far
from an even diffusion of species between re-
gions, interchanges have displayed an asym-
metry in the direction of exchange (6–8) and
have been dominated by particular functional
traits (9, 10). This unevenness may reflect a
predisposition for dispersion in particular
groups of organisms, because successful colo-
nization is dependent on the ability both to
disperse to a new region and to establish
within new environmental conditions and
ecological communities (11). Dispersal ability
may act as a primary filter on colonization
success (12), but lineages with broad environ-
mental tolerances, or those with the ability
to adapt to new environments, might contrib-
ute more to an interchange in the presence
1Department of Environmental Systems Science, Ecosystems
and Landscape Evolution, Institute of Terrestrial Ecosystems,
ETH Zurich, 8092 Zurich, Switzerland. 2Swiss Federal
Institute for Forest, Snow and Landscape Research WSL,
8903 Birmensdorf, Switzerland. 3Research School of Biology,
Australian National University, Canberra 0200, Australia.
4Department of Earth Sciences, Utrecht University, 3584 CB
Utrecht, Netherlands. 5Institute for Biodiversity and
Ecosystem Dynamics, University of Amsterdam, 1090 GE
Amsterdam, Netherlands. 6Systematics, Biodiversity and
Evolution of Plants, Ludwig Maximilian University of Munich,
80331 Munich, Germany. 7German Centre for Integrative
Biodiversity Research (iDiv) Halle-Jena-Leipzig, 04103
Leipzig, Germany. 8Institute of Biology, École Normale
Supérieure, 75005 Paris, France. 9Department of Ecology
and Evolutionary Biology, Yale University, New Haven,
CT 06520, USA. 10Center for Biodiversity and Global Change,
Yale University, New Haven, CT 06520, USA.
*Corresponding author. Email: alexander.skeels@gmail.com
Skeels et al., Science 381, 86–92 (2023)
7 July 2023
Wallace’s Line
Heilprin-Lydekker Line
Arid and temperate
Tropical rainforest
Tropical savanna
Sunda
Wallacea
New Guinea
Indomalayan
Realm
Australasian
Realm
Sahul
Australia
120°E
140°E
0°
10°S
20°S
Fig. 1. Climate and geography of the Indo-Australian archipelago at present. The Sunda continental
shelf is part of the Indomalayan zoogeographic realm and is separated from the Australasian zoogeographical
realm by Wallace’s Line. Wallacea is the island archipelago between the Sunda and Sahul continental shelves.
The Sahul continental shelf, which includes the Australian mainland and New Guinea, is separated from
Wallacea by the Heilprin-Lydekker Line. Sunda, Wallacea, and New Guinea are dominated by the tropical
rainforest Köppen-Geiger climate belt, except for eastern Java, Bali, South Sulawesi, the Lesser Sunda
isles, and southern New Guinea, which are dominated by the drier tropical savanna climate belt. The
Australian mainland is dominated by tropical savanna, arid, and temperate climate belts. The climate maps
are adapted from (48).
1 of 6
RES EARCH | R E S E A R C H A R T I C L E
an arid-adapted fauna (22). The interchange
has been highly asymmetrical, with rates of
exchange estimated to be at least twice as
high from Sunda to Sahul than in the oppo-
site direction (23). This could be shaped by the
uneven sizes of the species pools, as stable
areas of tropical rainforest in Sunda, connected
to the Eurasian continent, supported a bio-
diverse fauna throughout the Cenozoic (24).
Conversely, increasing aridity and a less connected
continental area bound by oceans may have
led to a reduced species pool in Sahul. Our
current understanding of interchanges is pat-
tern oriented, with historical biogeographic
analyses determining where, when, and in
which direction exchanges occur (2, 12, 15, 23, 25).
A process-oriented understanding, however,
requires the synthesis of paleogeographic
and paleoclimatic information with biological
traits and diversification histories across a
range of taxa.
Paleoenvironmental and biological informa-
tion united under a mechanistic modeling
approach makes it possible to compare empir-
ical observations with theoretical expectations
and provides a framework with which to ex-
plore the mechanisms behind one of the
world’s major biotic interchanges. We hypoth-
esize that, beyond a simple dispersal filter
across oceanic barriers, paleoenvironmental
niche dynamics also influence patterns of ex-
change. In addition to each clade’s dispersal
ability (12) and the size of the species pool,
exchange patterns should be related to either
the variability in the environmental conditions
in which species occur (25) (mean realized
niche breadth) or the rate at which environ-
mental niche traits change over time (13)
(rates of niche evolution). Further, the spa-
tial distribution of climate, and how it has
changed through time, should also explain
asymmetry and the spatial distribution of
lineages with either Sundanian or Sahulian
ancestry (19). Here, we combined paleoenvi-
ronmental reconstructions of temperature,
precipitation, and plate tectonics over the past
30 million years (Ma) (26–28) with a mecha-
nistic model of biodiversity (29) to explore
how dispersal and niche traits interact with
the environment to shape regional diversifi-
cation and patterns of exchange through time
(30). The selected time period captures the on-
set of the convergence of the Australian and
Eurasian plates (5) and the origin of most ter-
restrial vertebrate families in the region (fig. S1).
We used published, well-sampled phylogenetic
and spatial information on 20,433 species be-
longing to all 227 families of terrestrial vertebrates
present in the Indo-Australian archipelago
to estimate phylogenetic and taxonomic b di-
versity across Wallace’s Line as measures of
compositional dissimilarity between the two
regions, as well as the number and direction
of colonization events (31).
Trait-based drivers of faunal exchange
We estimated a minimum of 381 independent
colonization events across Wallace’s Line based
on a conservative phylogenetic hypothesis for
each family [figs. S2 to S5 (30)], explaining the
widespread distribution across Sunda and
Sahul of 87 out of 227 terrestrial vertebrate
families (Fig. 2 and Fig. 3A). Older colonization
events were associated with greater species
diversity (Spearman r = 0.68; Fig. 2A), most
likely because these older lineages had a longer
time to diversify. Precipitation niche breadth
was the most consistent predictor of exchange in
the Indo-Australian archipelago, indicating that
colonization is more common in lineages that
can tolerate wider variation in precipitation.
Using phylogenetic multiple regression (table
S1), we found that families with broader pre-
cipitation niche breadths were more likely
to be exchanged between regions, to have a
larger number of exchange events, and to have
lower taxonomic b diversity and phyloge-
netic b diversity (Fig. 3B and table S1) across
Wallace’s Line. Temperature niche breadth
was negatively associated with exchange dy-
namics (Fig. 3B and table S1), because tem-
perature and precipitation niche breadths
are inversely related in vertebrates (32). The
20
Region of origin
a
M
/
Sunda
Sahul
A
B
i
)
y
t
i
s
r
e
v
d
s
e
c
e
p
s
(
n
i
l
10
0
20
10
a
M
/
s
t
n
e
v
e
n
o
i
t
i
a
z
n
o
o
C
l
C
Line
Heilprin-Lydekker
Wallace
d
e
s
s
o
r
c
s
e
i
l
i
m
a
f
.
N
100
50
0
Sunda
Sahul
Origin
Oligocene
30
Miocene
Pliocene
Pleistocene
0
10
0
20
Age (Ma)
ClimPC1
10 N
150
0
100
10 S
50
20 S
30.0 Ma
22.5 Ma
15.0 Ma
7.5 Ma
0.0 Ma
90 E
100 E
110 E
120 E
130 E
140 E
150 E 90 E
100 E
110 E
120 E
130 E
140 E
150 E
90 E
100 E
110 E
120 E
130 E
140 E
150 E 90 E
100 E
110 E
120 E
130 E
140 E
150 E 90 E
100 E
110 E
120 E
130 E
140 E
150 E
Fig. 2. Colonization dynamics of terrestrial vertebrates and geoclimatic
changes in Indo-Australia. (A) Bars show the log-transformed number of
species derived from independent colonization events across Wallace’s Line from
Sunda to Wallacea (blue) or in the opposite direction (yellow). Dashed lines
show the number of colonization events through time. (B) Paleogeography
(28) and paleoclimate (26, 27) of the Indo-Australian archipelago over the past
30 Ma (26, 28). (C) Numbers of families crossing between regions across
two different biogeographic boundaries. Principle component analysis was
performed on paleotemperature and paleoprecipitation to decompose a single
climate axis (ClimPC1), explaining 88% of the variation in climate, where similar
colors represent similar climates. Warm, wet conditions are shown in red; cold,
dry conditions are shown in blue.
Skeels et al., Science 381, 86–92 (2023)
7 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
mechanistic model enabled the disentangle-
ment of these factors and validated the role
of broader precipitation niche breadths in
the rate of exchange (table S2). Niche breadth
may affect colonization dynamics through two
pathways: (i) Clades more tolerant of a broad
range of conditions may be less prone to ex-
tinction and therefore have a larger number
of potential dispersing lineages (8), or (ii) they
may be more able to establish in a diverse
range of environmental conditions with greater
establishment success. Our mechanistic model
supports the second pathway, because higher
rates of colonization were not associated with
lower rates of extinction (fig. S6), but instead
associated with certain dispersal and niche
characteristics of the modeled lineages. Al-
though the simulation results cannot exclude
the role of differential extinction on coloni-
zation dynamics [e.g., (8)], they do suggest that
differences in the rate of lineage diversifica-
tion are not required to explain asymmetrical
exchange. These results support the hypoth-
esis that the precipitation gradient between
Sunda and Sahul is a sharp barrier to the estab-
lishment of range-expanding lineages (10, 33),
and that lineages able to persist in a diversity
of conditions can overcome this barrier.
Supplementing the effect of climatic niche
breadth, our empirical and in silico model
results support the importance of dispersal
ability and the species pool in exchange pat-
terns. More diverse biotas might facilitate in-
terchange by having a greater number and
variation of potential colonist species, increas-
ing the number of potential colonization at-
tempts (34), and this pathway is considered
the null expectation in invasion biology (35).
We found that the size of the source species
pool was positively associated with exchange
success and the number of colonization events
in terrestrial vertebrates (Fig. 3B and table S1),
as well as with all exchange metrics in the
mechanistic model (table S2). As a key dis-
persal trait, flight was negatively associated
with phylogenetic b diversity (Fig. 3B), and
most exchanged taxa were highly volant, with
64% of families being either birds or bats,
A
Prec. breadth (mm/yr)
1000
500
Origin
48
Sahul
Sunda
Equivocal
Exchanged?
Yes
No
47
46
45
44
43
42
41
40
39
38
37
36
35
34
33
32
31
30
3
2
4
5
1
6
7
8
9
10
11
12
B
Succesful exchange
13
14
15
16
17
18
19
20
-1
Number of colonizations
-2
Taxonomic ß−diversity
0
0
1
2
350
Time (Ma)
250
150
50
-0.05
0.00
0.05
Phylogenetic ß−diversity
29
8
2
7
2
6
2
5
2
4
2
3
2
2
2
21
-0.10
-0.05
0.00
Coefficient estimate
0.05
Temperature rate
Temperature breadth
Precipitation rate
Precipitation breadth
Species pool
Dispersal ability
Temperature rate
Temperature breadth
Precipitation rate
Precipitation breadth
Species pool
Dispersal ability
Temperature rate
Temperature breadth
Precipitation rate
Precipitation breadth
Species pool
Dispersal ability
Temperature rate
Temperature breadth
Precipitation rate
Precipitation breadth
Species pool
Dispersal ability
0.10
Fig. 3. Exchange dynamics and precipitation niche breadth of terrestrial
vertebrates on a family-level phylogenetic tree and effect size of the
predictors of exchange. (A) The circle in the center displays each family’s
reconstructed origin as Sunda, Sahul, or uncertain (equivocal support) based on
biogeographic estimation models. The middle colored ring shows whether the
family is present in both Sunda and Sahul and was reconstructed to have
been exchanged across Wallace’s Line. In the outer colored ring, the color and
height of the bars represent the mean precipitation niche breadth of the
family. Niche breadth was measured as the SD of mean annual rainfall across
each species distribution (in millimeters per year). The numbered lines at the
perimeter indicate the number of taxonomic orders, with representative taxa
highlighted as silhouettes (images are from PhyloPic: http://phylopic.org/).
1, Carnivora; 2, Pholidota; 3, Cetartiodactyla; 4, Perrissodactyla; 5, Chiroptera;
6, Eulipotyphla; 7, Primates; 8, Scandentia; 9, Dermoptera; 10, Rodentia;
11, Lagomorpha; 12, Probosoidea; 13, Diprotodontia; 14, Dasyuromorphia; 15,
Peramelemorphia; 16, Notoryctemorphia; 17, Monotremata; 18, Anura; 19,
Caudata; 20, Gymnophiona; 21, Passeriformes; 22, Psittaciformes; 23,
Falconiformes; 24, Piciformes; 25, Coraciiformes; 26, Bucerotiformes;
27, Trogoniformes; 28, Strigiformes; 29, Accipitriformes; 30, Charadriiformes; 31,
Apodiformes; 32, Caprimulgiformes; 33, Eurypygiformes; 34, Suliformes; 35,
Pelecaniformes; 36, Ciconiiformes; 37, Procellariiformes; 38, Sphenisciformes;
39, Gruiformes; 40, Cuculiformes; 41, Otidiformes; 42, Phaethontiformes;
43, Podicipediformes; 44, Columbiformes; 45, Galliformes; 46, Anseriformes; 47,
Casuariiformes; 48, Squamata. (B) Coefficients of phylogenetic linear models
of four exchange metrics with mean temperature and precipitation niche
breadths, rates of temperature and precipitation niche evolution, dispersal ability,
and species pool size. Predictors that were statistically significant based on
phylogenetic linear models are in bold, and nonsignificant predictors are gray.
Skeels et al., Science 381, 86–92 (2023)
7 July 2023
3 of 6
RES EARCH | R E S E A R C H A R T I C L E
A
)
C
°
(
e
r
u
t
a
r
e
p
m
e
T
B
)
C
°
(
e
r
u
t
a
r
e
p
m
e
T
C
)
C
°
(
e
r
u
t
a
r
e
p
m
e
T
25
20
15
10
5
0
25
20
15
10
5
0
25
20
15
10
5
0
Sunda
Niche centroids
exchanged
non-exchanged
Wallacea
Age (Ma)
30
20
10
0
5
10
15
Prepicitation (mm/day)
Sahul
Wallacea
Age (Ma)
30
20
10
0
5
10
15
Prepicitation (mm/day)
Wallacea
Proportion
Sahulian
1.00
0.75
0.50
0.25
0.00
0
5
10
15
Prepicitation (mm/day)
Fig. 4. Age of paleoclimatic space in the Indo-
Australian archipelago and distribution of
climatic niche centroids of terrestrial vertebrates.
(A and B) Gridded representation of climate space
defined by temperature and precipitation. Each tile in
the grid represents a unique combination of these two
variables. The tiles are colored by the age of that
climate’s first appearance in Sunda (A) and Sahul (B).
Climate spaces that have been present longer are in
darker colors. The climatic space occupied by the
“stepping stone” region of Wallacea during the past
30 Ma is highlighted with an orange dashed line. This
space has been present longer in Sunda than in Sahul.
Symbols indicate the median climate niche centroid
of species from Sahul (yellow) or Sunda (blue) that
belong to families that have been exchanged (circle) or
have not been exchanged (star). (C) Proportion of
species of Sahulian origin in climate space. Species
niche positions in climate space show that the area
occupied by Wallacea is more densely filled with
species from Sundanian families than with species
from Sahulian families, and that species from both
exchanged and nonexchanged Sundanian families
are more commonly found in the climate space
occupied by Wallacea.
Skeels et al., Science 381, 86–92 (2023)
7 July 2023
accounting for 93% of the colonization events
of Sunda. All exchange metrics were strongly
positively associated with dispersal ability in
the mechanistic model (table S2). We found
that exchange of bird families across the Indo-
Australian archipelago was proportionally
higher than during other major biotic inter-
changes (36), reflecting the greater propensity
of volant taxa to disperse over the deep-sea
oceanic barriers such as Wallace’s Line, which
uniquely define the Indo-Australian interchange.
Contrary to our prediction, rates of niche
evolution were not commonly associated with
exchange dynamics (Fig. 3B and tables S1 and
S2), possibly reflecting the widespread pheno-
menon of niche conservatism, the tendency
for lineages to retain their ancestral environ-
mental niche through time (37), during trans-
oceanic colonization (38). For instance, many
families that we reconstructed as having a
Sundanian origin, such as Colubrid snakes and
Pteropodid bats, are typically restricted to
similar biomes in Sahul. Instead of the ability
to rapidly adapt to new environmental condi-
tions, we show that broader precipitation niche
breadths and higher dispersal ability were
the primary biological traits that allowed line-
ages to expand their geographic ranges in the
face of oceanic barriers and a steep precip-
itation gradient.
Paleoclimate and exchange asymmetry
We demonstrate that asymmetrical rates of
exchange have been shaped by the distinctly
different paleoclimatic histories of Sunda and
Sahul. At least 46 families originating in Sunda
(43% of all Sundanian families) crossed the
Heilprin-Lydekker Line (Fig. 1 and table S3)
to Sahul, whereas only 19 families originating
in Sahul (24% of all Sahulian families) crossed
Wallace’s Line to Sunda. A necessary step to
colonization involves crossing Wallacea (Fig. 1).
Our paleoenvironmental reconstruction, which
combines paleotopography (28), reconstructed
Köppen belts (27), and a global circulation
model (26), show that the humid climate space
occupied by Wallacea emerged in Sunda at
least 20 and 30 Ma (Fig. 4A and fig. S7) in a
period associated with the spread of tropical
rainforests (21, 24). Conversely, in Sahul, areas
with similarly humid conditions were present
during the mid-Miocene (fig. S8) (39) and only
became widespread in their contemporary lo-
cation on Sahul at least 10 and 5 Ma (Fig. 4B),
after the northward movement of Sahul and
the uplift of New Guinea (20, 24). An almost
uninterrupted humid climate throughout the
Indo-Australian archipelago, from Sunda to
New Guinea, facilitated the establishment of
Sundanian lineages in Sahul, and this can
also explain the observation that Wallacean
and New Guinean flora are compositionally
more similar to the flora of Sunda than to
that of the Australian mainland (33). Support-
ing this finding, we show that the climate
space currently present in Wallacea and New
Guinea is more densely occupied by vertebrate
lineages from Sunda than by lineages from
Sahul (Fig. 4C). By contrast, species from Sahul
in families that did not colonize Sunda occupy
an older and drier component of the Sahulian
climate than species in families that colonized
Sunda (Fig. 4C and fig. S9). A higher density of
species in older climate space suggests that
niche evolution has been truncated through
time by the available climate on each continent,
highlighting that niche conservatism limits
exchange between Sunda and Sahul.
Greater connectivity of a humid climate at
the interface of the exchange explains the ob-
served patterns of asymmetrical interchange
in terrestrial vertebrates, and this was sup-
ported by the mechanistic model. In the mod-
el, evolution of climatic niches was directed by
the environmental conditions where species
evolved (fig. S7). Therefore, Sundanian line-
ages evolved in niches closer to the condi-
tions of Wallacea and colonized emergent
Wallacean islands earlier (mean colonization =
15.27 Ma; fig. S10). In the opposite direction,
Sahul lineages were generally unable to suc-
cessfully colonize proto-Wallacea. Coloniza-
tion events by Sahulian species across Wallace’s
Line generally occurred after the uplift of
New Guinea’s highlands (mean colonization
time = 5.4 Ma; fig. S10), supporting the role
of New Guinea as an ecological “stepping
stone” between Wallacea and the Australian
mainland (40).
We evaluated how climate connectivity ex-
plains exchange asymmetry by performing
an in-silico counter-factual simulation experi-
ment. Here, we either removed the precipi-
tation or temperature constraints on species
distributions or removed the tectonic history
by holding the landscape constant with sea
levels at the time period with maximum con-
nectivity between the regions (Last Glacial
Maximum, ~20,000 years ago). This effectively
allowed dispersal within each continental re-
gion to be unconstrained by oceanic barriers
and provided equivalent geographic isolation
of each continental region from Wallacea. We
found that the proportion of Sahulian species
in Wallacea and New Guinea increased only
when both the precipitation constraint and
tectonic history were modified together, be-
cause this promoted more opportunities for
dispersal and a higher likelihood of establish-
ment (Fig. 5 and figs. S11 and S12). The propor-
tion of simulations with colonization events
between Sahul and Sunda was 16.6% in the
full model, which was similar to the observed
proportion in terrestrial vertebrates (24%).
The proportion increased to 48.6% in the
counterfactual model (fig. S11), which is more
similar to the observed proportion of line-
ages moving in the opposite direction, from
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RES EARCH | R E S E A R C H A R T I C L E
A Terrestrial vertebrates
B Birds
20 N
10 N
0
10 S
20 S
30 S
40 S
Prop. of species from
Sahulian families
1.00
0.75
0.50
0.25
0.00
M5
M6
C Amphibians
M3
M1L
M1
M4
M2
M1H
D Mammals
E Reptiles
80 E
90 E
100 E
110 E
120 E
130 E
140 E
150 E
Fig. 5. Spatial distribution of the proportion of terrestrial vertebrate
species of Sahul origin and biogeographic turnover predictions from the
biodiversity simulation model. Proportion of total species richness in each
grid cell that belongs to families of Sahul origin, based on biogeographic
estimation, over the count of all species in the grid cell, for all terrestrial
vertebrates (A), birds (B), amphibians (C), mammals (D), and reptiles
(E). Dashed lines in (A) show the location of the sharpest spatial turnover
of proportional Sahulian richness under six different simulations models
(M1 to M6), as well as under high (M1H) and low (M1L) values of precipitation
niche breadth and dispersal ability parameters of the full model (M1). The
precipitation constraint on species distributions is removed in M2, the
temperature constraint is removed in M3, tectonic history is removed in M4,
both the precipitation constraint and tectonic history are removed in M5,
and both the temperature constraint and tectonic history are removed in M6.
The dashed lines illustrate how removing certain constraints that limit
colonization changes the distribution of species from families with either
Sahulian or Sundanian ancestry. Grid cell size is 110 × 110 km for all panels
(Behrmann projection).
Sunda to Sahul (43%). Therefore, more sym-
metrical exchange could only be observed in
the absence of climatic and dispersal bar-
riers. A similar climate-mediated scenario has
been suggested to explain exchange asym-
metry during the American interchange (9, 41)
and between India and Eurasia (7, 42). Our
study clarifies how distinct climatic histories
of continental regions can generate a near-
ubiquitous pattern of asymmetrical terres-
trial biotic interchanges.
Dispersal and environmental niche shape
spatial patterns of faunal exchange
Patterns of turnover among taxa have long
been a source of contention for designating bio-
geographic boundaries in the Indo-Australian
archipelago (15) because there is a high dis-
cordance in the distributional extent of differ-
ent taxa across the Indo-Australian archipelago.
Across the four classes of terrestrial vertebrates,
gradients of turnover from a predominantly
Sundanian to a predominantly Sahulian fauna
differed, with a high proportion of sites in
Sahul having high richness of Sundanian rep-
tile species (100% of sites; Fig. 5E) and mam-
mal species (68.8%; Fig. 5D) (which is driven
by the exceptional diversity of Sundanian
squamates, rodents, and bats), but not for
amphibian species (11%; Fig. 5C) or bird spe-
cies (1.4%; Fig. 5B). In the mechanistic model,
a combination of dispersal and niche traits
shaped gradients in biotic turnover, which
could explain the emergence of these differ-
ent patterns in vertebrates. When simulations
were run with increased species’ precipitation
niche breadth and dispersal ability parame-
ters, we found that lines demarcating turn-
over from a Sundanian to Sahulian biota (Fig.
5A) were located southward into regions of
increased aridity, varying from a pattern corre-
sponding with amphibians (Spearman’s r =
0.85 to 0.87; Fig. 5C) to a pattern correspond-
ing with mammals (r = 0.71 to 0.74; Fig. 5D),
respectively. For birds, New Guinea is predom-
inantly Sahulian, and this pattern was only
reproduced by completely lifting the dispersal
and precipitation constraints from the model
Skeels et al., Science 381, 86–92 (2023)
7 July 2023
5 of 6
RES EARCH | R E S E A R C H A R T I C L E
(r = 0.96; Fig. 5B and fig. S11). This could be
because birds have the broadest precipitation
tolerances and the highest volancy of any class
of vertebrate, and therefore have fewer con-
straints on colonization (fig. S13). Because the
simulation model is agnostic to the taxa in-
vestigated, we expect a similar mechanism to
operate across a range of taxa not explored
here, and there is some evidence that niche
and dispersal traits are important drivers of
interchange and patterns of turnover in plants
(10, 43).
Conclusion
The longstanding view of biotic interchange
is that it is primarily governed by plate tec-
tonics and dispersal ability, with rates of colo-
nization in terrestrial organisms being directly
proportional to the source pool size (1), the
geographic distance between regions, and the
emergence of land bridges (9). A more com-
plete picture emerges when the deep-time
legacy of climate connectivity and niche con-
servatism on species distributions are also
considered. Advances in deep-time climate re-
constructions make it possible to test this
directly, and support for a key role of climate
connectivity is emerging in the Indo-Australian
archipelago (33) and more broadly in other
systems such as Indo-Eurasia (7, 42) and the
American interchange (41). The factors that
shape colonization success are relevant in
both a historical and a contemporary context,
because biotic exchange is exacerbated by
human intervention, and understanding these
factors is therefore relevant for predicting
the success of new biological colonizations
and invasions (35). This is particularly true
in the Indo-Australian archipelago, where bio-
logical ivasions are contributing to some of the
highest rates of native species extinction on
the planet (45). An emerging view of global
biodiversity patterns is that they are largely
the outcome of historical changes in plate
tectonics shuffling lineages around the planet,
in concert with major fluctuations in precip-
itation and temperature shaping dispersal,
speciation, and extinction dynamics through
environmental niches (46, 47). A mechanistic
modeling approach enables us to move be-
yond “lines” in biogeography and instead con-
sider the processes that shape global variation
in biodiversity patterns.
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AC KNOWLED GME NTS
We thank the Ecosystems and Landscape Evolution Group at WSL
and ETH Zurich for feedback, B. Flück for technical support, and
M. Dawes for editing the manuscript for English. Funding: This
work was supported by the Swiss National Science Foundation
(grant 310030_188550 to L.P. and supporting A.S. and W.B.); ETH
Zürich (internal grant ETH-34 18-1 to L.P.) and postdoctoral
fellowship 18-2 FEL-52 to L.M.B.); the German Research
Foundation (grant DFG-FZT 118, 202548816 to O.H.); the Swiss
National Science Foundation (Postdoc Mobility Fellowship 206844
to I.M.); the European Union’s Horizon 2020 Research and
Innovation Programme (Marie Skłodowska-Curie grant 896323 to
O.J.R.); and the Prinzessin Therese von Bayern Foundation
(E.M.J.). Author contributions: Conceptualization: A.S., L.M.B., I.M.,
E.M.J., O.H., O.J.R., W.B., V.B., T.K., W.J., L.P.; Funding acquisition:
L.P.; Methodology: A.S., L.M.B., I.M., O.H., V.B., T.K.; Investigation:
A.S., L.M.B.; Project administration: A.S.; Supervision: L.P.; Visualization:
A.S.; Writing – original draft: A.S.; Writing – review & editing: A.S., L.M.B.,
I.M., E.M.J., O.H., O.J.R., W.B., V.B., T.K., W.J., L.P. Competing
interests: The authors declare no competing interests. Data and
materials availability: All data generated and analyzed during this
study and the code required to replicate the analyses are available in
the manuscript or have been deposited at Dryad (49). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf7122
Materials and Methods
Figs. S1 to S13
Tables S1 to S3
References (50–143)
33. E. M. Joyce, K. R. Thiele, J. W. F. Slik, D. M. Crayn, Biol. J. Linn.
Soc. Lond. 132, 374–387 (2021).
Submitted 9 November 2022; accepted 1 June 2023
10.1126/science.adf7122
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RES EARCH
R E S E A R C H A R T I C L E
◥
PHYSICS
An improved bound on the electron’s electric
dipole moment
Tanya S. Roussy1,2†, Luke Caldwell1,2†, Trevor Wright1,2, William B. Cairncross1,2‡,
Yuval Shagam1,2§, Kia Boon Ng1,2, Noah Schlossberger1,2, Sun Yool Park1,2, Anzhou Wang1,2,
Jun Ye1,2, Eric A. Cornell1,2*
The imbalance of matter and antimatter in our Universe provides compelling motivation to search
for undiscovered particles that violate charge-parity symmetry. Interactions with vacuum
fluctuations of the fields associated with these new particles will induce an electric dipole moment of
the electron (eEDM). We present the most precise measurement yet of the eEDM using electrons
confined inside molecular ions, subjected to a huge intramolecular electric field, and evolving
coherently for up to 3 seconds. Our result is consistent with zero and improves on the previous best
upper bound by a factor of ~2.4. Our results provide constraints on broad classes of new physics
above 1013 electron volts, beyond the direct reach of the current particle colliders or those likely
to be available in the coming decades.
E lectric dipole moments of fundamental
particles, such as the electron, are sig-
natures of time-reversal symmetry viola-
tion, equivalent to violation of combined
charge and parity (CP) symmetry (1). CP
symmetry is broken in the standard model but
only in the quark sector (2), so the coupling to
leptons is weak and the predicted electron’s
electric dipole moment (eEDM) several orders
of magnitude below current experimental sen-
sitivity (3, 4). Explaining the imbalance of mat-
ter and antimatter in the Universe requires
additional CP violation, beyond that present
in the Standard Model (5–7). Many proposed
extensions predict new particles at energies
higher than any so far discovered, with CP-
violating interactions. These new particles
can induce a much larger eEDM, often within
reach of near-term experiments (8–10). A non-
zero measurement at current experimental
sensitivities would unambiguously signal new
physics, whereas a more precise measurement
consistent with zero imposes challenging
constraints on possible explanations of the
matter-antimatter imbalance. Our measure-
ment uses quantum projection–noise-limited
spectroscopy on samples of hundreds of mo-
lecular ions with interrogation times of up to
→
→
e (cid:4) E
3 s. Our result, de ¼ (cid:2)1:3 T 2:0stat T 0:6syst
Þ(cid:3)
ð
10(cid:2)30 e cm, is consistent with zero and gives
j < 4:1 (cid:3) 10(cid:2)30 e cm at
an upper bound of dej
90% confidence.
→
An eEDM d
e ¼ de^s—with ^s a unit vector
along the spin of the electron—subject to an
→
→
electric field, E
, has an energy of (cid:2)d
. The
essence of an eEDM search is to measure the
energy shift when ^s is aligned with E
com-
pared with when it is antialigned. The size
of the observable shift scales with the size
→
, and thus many existing (11–13) and pro-
of E
posed (14–17) eEDM experiments use elec-
trons embedded inside polar molecules, where
intramolecular electric fields can be ∼105
times larger than what can be directly ap-
plied in the lab. These internal electric fields
can be aligned in the lab frame by orienting
the molecules with modest external electric
fields.
Our measurement uses HfFþ molecular ions.
In an applied electric field of ∼58 V cm(cid:2)1, the
3D1 v ¼ 0; J ¼ 1
Þ “science” state of the mo-
lecule is split into a series of doublets (Fig. 1A).
In two of these doublets, highlighted in col-
or, the molecule is oriented (18); the upper
doublet (orange) has the intramolecular axis
parallel to the applied field, whereas the lower
doublet (blue) is antiparallel. This intramolec-
ular axis defines the direction of an effective
ð
1JILA, NIST and University of Colorado, Boulder, CO 80309,
USA. 2Department of Physics, University of Colorado,
Boulder, CO 80309, USA.
†These authors contributed equally to this work.
‡Present address: Atom Computing, Berkeley, CA 94710, USA.
§Present address: Schulich Faculty of Chemistry, Technion–Israel
Institute of Technology, Haifa 3200003, Israel.
*Corresponding author. Email: cornell@jila.colorado.edu
Fig. 1. Experiment outline. (A) Level structure of the eEDM-sensitive 3D 1 v ¼ 0; J ¼ 1
Þ state. The horizontal axis indicates mF, the projection of the total angular
momentum onto the externally applied electric field. The vertical axis indicates the energy of the states. The direction of the electron spin and effective electric field,
Eeff, is indicated for each of the states used in the experiment. (B) Schematic of ion trap, composed of eight radial electrodes and a pair of endcap electrodes. (Inset)
Fields applied during experimental sequence: the rotating electric bias field, E
→0.
rot, and the quadrupole magnetic field, B
ð
→
Roussy et al., Science 381, 46–50 (2023)
7 July 2023
1 of 5
(cid:3)
(cid:3)
(cid:1)
(cid:1)
(cid:1)
(cid:1)
i and ↓l
We prepare an incoherent mixture of one
of the spin states from each doublet, either
or ↓uj
↑uj
i and ↑l
(Fig. 1A), and
p
2 pulse to create a coherent
then apply a
superposition of the two states in each dou-
blet. We allow the superpositions to evolve
for a variable amount of time, then apply a
p
2 pulse to map the accumulated rela-
second
tive phase between the states in a doublet
onto a population difference between those
states. We clean out the population in one of
(cid:1)
(cid:1)
(cid:3)
(cid:3)
the spin states in each doublet, either ↑u=l
or
(cid:1)
(cid:1)
↓u=l
, then count the number of ions in the
remaining stretched states by state-selectively
photodissociating the molecules and detect-
ing the resultant Hf+ ions (25). We use the op-
posing orientations of the two doublets in
the trap to send the Hf+ ions originating from
molecules in each doublet to opposite sides of
our imaging microchannel plate (MCP) and
phosphor screen assembly (26, 27). We then
repeat the procedure with the opposite initial
Table 1. Summary of systematic shifts and their uncertainties. Data are as presented in (23). All
values are in microhertz.
Effect
Correction
Uncertainty
Magnetic
.....................................................................................................................................................................................................................
.....................................................................................................................................................................................................................
0.1
→
Nonreversing B
0
Stray B fields + distortion of Erot
.....................................................................................................................................................................................................................
Berry’s phase
.....................................................................................................................................................................................................................
.....................................................................................................................................................................................................................
Rotation-odd axial secular motion
Axial fields at harmonics of Erot
.....................................................................................................................................................................................................................
Simultaneous doublet spectroscopy
.....................................................................................................................................................................................................................
3.4
3.4
.....................................................................................................................................................................................................................
Imperfect spatial overlap
Imperfect imaging contrast
.....................................................................................................................................................................................................................
Other
.....................................................................................................................................................................................................................
Rotation-induced mF-level mixing
.....................................................................................................................................................................................................................
Total
.....................................................................................................................................................................................................................
0.1
< 0:1
3.2
3.5
1.4
0.4
6.9
RES EARCH | R E S E A R C H A R T I C L E
electric field, Eeff ≈ 23 GV cm−1 (19–22), acting
on the spin of one of the valence electrons. In
the presence of a small magnetic field, the two
states in a doublet correspond to the spin of
this valence electron being aligned or anti-
aligned with Eeff. We prepare a coherent super-
position of the two spin states and measure
the energy difference using Ramsey spec-
troscopy. The eEDM will give a contribution
to this energy, T2deEeff, with opposite sign in
the two doublets. We perform the measure-
ment simultaneously on spatially overlapping
clouds of ions prepared in each of the dou-
blets. The difference between the measured
energies is our science signal.
Experimental overview
Our experimental apparatus is shown sche-
matically in Fig. 1B. An overview of the ex-
perimental sequence is given here; more details,
including an account of improvements made
since our earlier result (12), are presented in
(23, 24). The sequence begins with produc-
tion and radiofrequency trapping of roughly
20; 000 HfFþ ions. To orient the molecules
while maintaining confinement, we rotate
→
the orienting field, E
rot, at angular frequency
wrot ¼ 2p (cid:3) 375 kHz and perform our spec-
troscopy in this rotating frame. We also apply
→
0 , to
a quadrupole magnetic field gradient, B
create a time-averaged effective bias magnetic
field, Brot (24).
A
B
C
Fig. 2. Example Ramsey data. (A) Detection of Hfþ ions; ions are assigned to the upper or lower doublet based on their position (upper doublet shown in orange, lower
doublet in blue). Counts from a thin central swatch where the assignment is ambiguous (shown in gray) are removed. Images shown are averaged over 60 shots of
the experiment. (B) Asymmetries for the upper and lower doublet. (C) Fitted sum and difference asymmetries, AS and AD, used to extract mean and difference frequencies,
fm and fd. Middle-time data, where the two doublets are out of phase, were collected in this example dataset for illustrative purposes only. Such data contribute very
little to the frequency determination and were not collected during the final precision dataset.
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spin state. Example data are shown in Fig. 2A.
We count the ions on each side of the screen,
in each configuration—typically ∼120 ions from
each doublet after a 3-s hold time—and from
these two measurements construct the two
asymmetries, Au and Al, where
Au=l ¼
N u=l
In
N u=l
In
(cid:2) N u=l
Anti
þ N u=l
Anti
ð1Þ
Here, N u=l
In and N u=l
Anti are the number of ions
counted, u/l indicates the upper or lower dou-
blet, and the subscripts indicate whether we
read out the same state that we prepare (In) or
the opposite (Anti). We repeat our measurement
at different free-evolution times, generating a
pair of Ramsey fringes as shown in Fig. 2B. The
frequencies of these two fringes are proportional
to the energy splitting in the two doublets. The
primary contribution to this energy splitting is
the Zeeman splitting, 3gF mBBrot, where gF ¼
(cid:2)0:0031 1ð Þ is the g factor of the science state
(28). For our typical experimental parameters,
this produces fringe frequencies of ∼100Hz.
Other effects, including the eEDM, make small
modifications to this frequency.
Instability of the intensity of the pulsed
lasers used for creation and photodissociation
of the ions (24) creates considerable noise in
the number of ions measured in each shot of
the experiment, typically approximately three
times as large as the quantum projection–
A
B
Fig. 3. Systematic shifts in
the measurement. (A) Shift in
fDB caused by nonreversing
magnetic quadrupole field,
which can be corrected by
using the shift in the fB
channel, which is ~460 times
as large as the fDBshift. (B)
Shift in the fB channel caused
by deliberately applied second-
harmonic electric field E2h with
transverse magnetic field, B.
Data show variation in shift as
angle q2h between E2h and x axis
is varied. E2h is ∼250 times
as large as that present in the
experiment; B is ∼ 14 mG. (Inset)
Lissajous figure traced out by
total electric field for greatly
exaggerated ratio of E2h=Erot;
blue and orange show one-half
cycle each. The field points in
the (cid:2)x direction for more time
than in the þx direction.
noise limit on the side of the fringe at 3 s.
However, these sources of noise, and many
others, are common mode between the two
doublets—the exact same laser pulses address
both clouds of ions—and so the noise in Au and
Al is highly correlated. To take advantage of
this, we form the sum and difference asymme-
tries AS ¼ Au þ Al and AD ¼ Au (cid:2) Al (Fig.
2C). If we take data when the two doublets are
close to being in phase, the noise in AD is
drastically reduced (27). The two doublets
oscillate at slightly different frequencies, fu
and fl, owing to a ∼1=230 fractional difference
in their magnetic moments, and so during
the eEDM dataset we deliberately take our
data at a beat. We take two sets of points: the
early-time data, when the two doublets are in
phase, and the late-time data ∼230 oscillations
later, when they come back into phase again.
We can control the time of the second beat
by varying the strength of the magnetic bias
field, Brot. We fit to AS and AD to extract the
fm ¼
mean of the two fringe frequencies,
Þ.
ð
2 fu (cid:2) fl
Þ, and their difference, fd ¼ 1
ð
2 fu þ fl
1
We collect Ramsey fringes in 23 ¼ 8 exper-
imental states, corresponding to each possi-
ble combination of three binary experimental
(cid:5)
¼ T1. ~B is the direction of
switches, ~B; ~R; ~I
→
rot , ~R the
the magnetic bias field relative to E
→
rot, and ~I the direction of
rotation direction of E
→
E
rot relative to the imaging MCP at the instant
of photodissociation, determining which side
(cid:4)
of the phosphor screen each of the doublets is
imaged onto. A set of Ramsey fringes in each of
the 8 switch states forms a block. To minimize
the effects of experimental drifts, within a block
we interleave data collection for the switch
states; the first Ramsey time is recorded for all
switch states before moving onto the second
Ramsey time for each switch state, and so on.
We take the 16 fitted frequencies from each
block and form 16 linear combinations to give
the components of the measured frequencies,
which are even or odd under each of the experi-
mental switches. Following (29), we label the
components with superscripts that denote
the switches under which the quantity is odd.
For example, our science signal is f DB , the
component of the difference frequency that is
odd under ~B but even under ~R and ~I (30). The
other channels allow us to diagnose system-
atics and monitor experimental performance.
Over the course of the dataset, we varied a
number of other experimental parameters on
timescales slower than a block. These include
the state we read out at the end of the Ramsey
sequence, denoted ~P ¼ T1 and alternated each
block; the order in which the switch states
are recorded at each Ramsey time, alternated
every other block; three different magnitudes
of the magnetic bias field, corresponding to
mean fringe frequencies of f 0∼77 , 105, and
151 Hz; and reversal of the waveplates that
set the lab-frame handedness of the light used
for state preparation and readout. During data
collection and analysis, we “blinded” our mea-
surement of f DB by adding an unknown offset
to this channel. The offset was not removed
until our systematics search and analysis (23)
were complete.
Accuracy evaluation
To evaluate the accuracy of our measurement,
we searched extensively for systematic shifts
before data collection; a summary is given in
Table 1. In general, we tuned a variety of ex-
perimental parameters over ranges that were
large compared with those present during
data collection, exaggerating any accompany-
ing systematic effects, and observed the re-
sponse in our data channels. The only shift we
could observe directly in the eEDM channel
stems from a nonreversing quadrupole mag-
netic field and the difference in magnetic
moments between the two doublets, caused
primarily by the applied electric field mixing
the states of the two doublets with higher
rotational levels of the molecule. The f B chan-
nel provides a direct measurement of the non-
reversing magnetic field and allows us to apply
¼
a correction to our science channel, df DB
corr
f B dgF
, where dgF is half the difference between
gF
the g factors for the upper and lower doublets
(Fig. 3A). Before applying any corrections to
the science channel, we suppress this system-
atic by actively shimming the currents through
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Fig. 4. Summary of our
dataset. Cuts have been
applied and the uncer-
tainty on each block
p
ffiffiffiffiffi
c2
scaled by
to account
for overscatter. (A) Histo-
gram of data. Error bars
show standard deviation of
bin counts expected from
Poisson distribution. The
blue line shows normal
distribution. (B) Normal
probability plot of fDB,
showing that the data are
consistent with a normal
distribution. The gray
line shows expected
probability for a normal
distribution. (C) Variation
of central value under
different experimental
parameters compared with
the overall average value
of fDB. Here, N is the
average number of trapped HfF+ ions per experimental trial during a block. Other panels in (C) are described
in the final paragraph of the Experimental Overview section.
¼ 90 nHz.
the coils that apply the magnetic bias field
to minimize f B. This shimming was so ef-
fective that the mean correction that we ap-
plied was well below our statistical sensitivity,
df DB
corr
The shimming and correction procedure
leaves us susceptible to other possible effects
that cause shifts in f B and f DB with a ratio
different from dgF
. An important example of
gF
such a shift is the combination of a transverse
magnetic field with an electric field oscillating
at 2wrot, which was present in our experiment
owing to harmonic distortion in the amplifiers
driving the trap electrodes. The harmonic dis-
tortion causes the electric field, and thus the
magnetic moment of the molecule, to spend
more time pointing in one spatial direction
than the other, giving a nonzero time-averaged
Zeeman interaction with a background mag-
netic field. This causes shifts in f B but no cor-
responding shifts in f DB, where the effect is
canceled by the coincident change in the size
of the differential magnetic moment owing
to the distortion. Figure 3B shows the shift
in f B when we deliberately apply a second-
harmonic electric field and vary its angle. We
shim out the second harmonic on each elec-
trode by feeding forward a second-harmonic
signal with the opposite phase, suppressing
the amplitude by ∼80 dB. We used magnetic
shim coils to null the ambient magnetic field
at the trap center to <10 mG. The measured
sizes of the residual effects were used to com-
pute the maximum size of the systematic
during our dataset.
A full account of all systematic shifts con-
sidered is presented in (23).
Measuring the eEDM
We collected 1370 blocks over about 2 months,
corresponding to ∼620 hours of data and ∼108
ion detection events. Each block results in one
value of f DB and thus a single measurement of
de . The uncertainty on f DB for each block is
calculated with only the standard errors on the
asymmetries for that block. We applied cuts to
the blinded data on the basis of non-eEDM
channels that indicated signal quality. Blocks
with late-time contrast <0.2 were cut because
of a low signal-to-noise ratio, as were blocks
containing fitted fringe frequencies that were
>3.5s different from the mean fringe frequen-
cy for that switch state. After applying cuts, we
were left with 1329 blocks with c2 ¼ 1:07 4ð Þ
for f DB. Figure 4, A and B, show the distrib-
ution of measured f DB values over the 1329
blocks after relaxing the uncertainty for each
¼ 1:035. The
of the blocks by a factor of
data are consistent with a normal distribution.
Our final statistical uncertainty of 22.8 mHz
is obtained with these relaxed uncertainties.
Based on the number of ions detected in
each shot, this uncertainty is ∼30% above the
quantum projection–noise limit. More details
on how we determine uncertainties are given
in (24).
ffiffiffiffiffi
c2
p
Figure 4C shows how the measured value
of f DB depends on experimental parameters
varied during the dataset; we find no con-
cerning dependencies.
We removed our blind on 1 November 2022,
and obtained a final value for the eEDM-
sensitive frequency channel
f DB ¼ (cid:2)14:6 T 22:8stat T 6:9syst mHz
ð2Þ
Þ
Dividing by (cid:2)2Eeff
≃ 1:11 (cid:3) 1031 mHz
e−1 cm−1 (21, 31), we obtain a value for the eEDM
Þ (cid:3) 10(cid:2)30 e cm ð3Þ
de ¼ (cid:2)1:3 T 2:0stat T 0:6syst
ð
sgn gFð
h
which is consistent with zero within one stan-
dard error. The combined statistical and sys-
¼ 2:1 (cid:3) 10(cid:2)30 e cm,
tematic uncertainty, sde
improves on our previous work (12) by a factor
of ∼37, and on the previous state-of-the-art
from the ACME collaboration (13) by a factor
of ∼2 . This result and that of the ACME
collaboration—two measurements using very
different experimental platforms with con-
trasting sources of systematic shifts—are con-
sistent at slightly above one standard error.
Discussion
We use our result to obtain an upper bound
using a folded Gaussian distribution
dej
j < 4:1 (cid:3) 10(cid:2)30 e cm 90% confidence
Þ
ð4Þ
ð
This limit constrains extensions to the
Standard Model that predict new sources of
CP-symmetry violation to explain the matter-
antimatter asymmetry of the Universe (32).
Many extensions, including supersymmetry,
the two-Higgs model, and left-right symmetric
models, generate an eEDM at the one-loop
level (33), with magnitude (9)
de ∼
ea0a
2
g2
2p
sinf
CP
m2
e
M 2
ð5Þ
Here, M is the characteristic mass of new par-
ticles with effective coupling strength, g, to the
electron; f
CP is the phase that describes how
strongly the interaction violates CP symmetry;
me and e are the mass and charge of the elec-
tron respectively; and a is the fine-structure
constant. Because deºM (cid:2)2 , and because our
limit in Eq. 4 is a factor of ∼2:4 smaller than
the limit reported in (13), we are sensitive to new
¼ 1:5 times
particles with mass that is
as large.
ffiffiffiffiffiffiffi
2:4
p
To estimate the mass reach of our exper-
iment, we need to make assumptions for the
size of g2 and sinfCP. For the strong force,
quantum electrodynamics, and the weak force,
g2 ≈ 1; 1=137; and 10(cid:2)6, respectively. For exten-
sions to the Standard Model seeking to explain
the matter-antimatter asymmetry, the naive ex-
∼ 1. With this assump-
pectation is that sinf
CP
tion, we can interpret our new limit on de as
(cid:8)
(cid:7)
M ≳ g=a1
40 TeV. For new particles with g2
of order a ∼ 1=137, this bound is an order of
magnitude greater than the largest-mass
particles that can be directly detected at the
Large Hadron Collider (34).
2
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So far, we have assumed that CP violation
arises purely from de. Diatomic molecules are
also sensitive to pseudoscalar-scalar electron-
nucleon coupling, CS (35, 36), and we can
interpret our measurement as a linear combi-
nation, hf DB (cid:3) sgn gFð
Þ ¼ (cid:2)2Eeff de þ 2WSCS ,
¼ (cid:2)51 kHz (31) is a molecule-specific
where WS
h
structure constant. Assuming that de is zero, we
can instead attribute our measurement to CS,
and we find
CS ¼ (cid:2)1:4 T 2:2stat T 0:7syst
ð
Þ (cid:3) 10(cid:2)10
ð6Þ
Determining rigorous limits on de and CS
requires combining the results of two or more
measurements using molecules with different
ratios of Eeff to WS. Figure S1 shows a combined
fit to the results of this work and (13), giving
j < 2:1 (cid:3) 10(cid:2)29 e cm and
upper bounds of dej
j < 1:9 (cid:3) 10(cid:2)9 with 90% confidence. Our
CSj
measurement improves these bounds by fac-
tors of 16 and 12, respectively (37).
RE FE RENCES AND N OT ES
1.
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Strangeness: Electric Dipole Moments of Particles,
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10. Y. Nakai, M. Reece, J. High Energy Phys. 2017, 31 (2017).
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21. L. V. Skripnikov, J. Chem. Phys. 147, 021101 (2017).
22. T. Fleig, Phys. Rev. A 96, 040502 (2017).
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experiment. arXiv:2212.11837 [physics.atom-ph] (2022).
24. Materials and methods are available as supplementary
materials.
25. K. K. Ni et al., J. Mol. Spectrosc. 300, 12–15 (2014).
26. Y. Shagam et al., J. Mol. Spectrosc. 368, 111257 (2020).
27. Y. Zhou et al., Phys. Rev. Lett. 124, 053201 (2020).
28. H. Loh, “Search for an electron electric dipole moment with
trapped molecular ions,” thesis, University of Colorado Boulder
and JILA (2013).
29. J. Baron et al., Science 343, 269–272 (2014).
30. We define the mean frequency to be always positive. If we had
instead allowed the fringe frequency to change sign when the
sign of the magnetic bias field changes, our science signal
would have been fD.
31. T. Fleig, M. Jung, J. High Energy Phys. 2018, 12 (2018).
32. L. Canetti, M. Drewes, M. Shaposhnikov, New J. Phys. 14,
Rev. Mod. Phys. 91, 015001 (2019).
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Study, Seattle, WA, 17 to 26 July 2022.
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035502 (2015).
36. M. Denis et al., New J. Phys. 17, 043005 (2015).
37. Improvements are given with respect to equivalent bounds
calculated from combined fit to results of (13) and (12).
38. T. S. Roussy et al., Data presented in “An improved bound
on the electron’s electric dipole moment,” Zenodo (2023);
https://doi.org/10.5281/zenodo.7837398.
AC KNOWLED GME NTS
We thank the staff at JILA for making this experiment possible.
Funding: This work was supported by the Cydney and Tom
Marsico Family Foundation, the Sloan Foundation, the Gordon and
Betty Moore Foundation, NIST, and the NSF (award PHY-1125844).
T.W. acknowledges funding support from NSF GRFP. Author
contributions: All authors contributed, in varying degrees, to the
conception of experimental approach, molecular survey
spectroscopy, apparatus design and construction, apparatus
debugging and commissioning, apparatus maintenance, data
collection and analysis, analysis of systematic errors, and
preparation of publications. We are all responsible for the accuracy
of the bottom-line result and of the written account we have
submitted to Science. Competing interests: The authors declare
that they have no competing interests. Data and materials
availability: Data and code used for analysis are available at
Zenodo (38). License information: Copyright © 2023 the authors,
some rights reserved; exclusive licensee American Association
for the Advancement of Science. No claim to original US
government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg4084
Materials and Methods
Figs. S1 and S2
References (39–42)
Submitted 22 December 2022; accepted 18 May 2023
10.1126/science.adg4084
(1967).
095012 (2012).
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◥
FRACTURE MECHANICS
Tensile cracks can shatter classical speed limits
Meng Wang, Songlin Shi, Jay Fineberg*
Brittle materials fail by means of rapid cracks. Classical fracture mechanics describes the motion
of tensile cracks that dissipate released elastic energy within a point-like zone at their tips. Within
this framework, a “classical” tensile crack cannot exceed the Rayleigh wave speed, cR. Using brittle neo-
hookean materials, we experimentally demonstrate the existence of “supershear” tensile cracks that
exceed shear wave speeds, cR. Supershear cracks smoothly accelerate beyond cR, to speeds that
could approach dilatation wave speeds. Supershear dynamics are governed by different principles than
those guiding “classical” cracks; this fracture mode is excited at critical (material dependent) applied
strains. This nonclassical mode of tensile fracture represents a fundamental shift in our understanding
of the fracture process.
H ow do materials break? How fast can a
crack propagate? These related and fun-
damental questions are of essential in-
terest to a broad range of scientific and
engineering communities. In tensile
fracture, the maximal velocity of a moving
crack is classically considered to be (1) the
Rayleigh wave speed, cR , although there have
been suggestions that cracks could surpass
this speed (2, 3). In the vicinity of a crack’s
tip, remotely applied stresses are amplified
to an approximate singularity. Crack motion
is guided by the principle of energy balance.
This principle states that fracture takes place
when the flux of stored potential energy flow-
ing from large (system-size) scales to the crack’s
tip balances the material’s fracture energy, G.G,
the energy dissipated at the tip, is defined as
the energy per unit crack advance required to
separate the material. Provided that dissipa-
tion is confined to this point-like zone and
crack instabilities are suppressed, fracture
mechanics provide the fundamental theoret-
ical framework to describe crack dynamics
(1, 4, 5). Crack velocities, v, smoothly accelerate
to cR while maintaining energy balance (6).
Beyond cR, fracture mechanics predict that the
energy flux into a crack’s tip will become
negative, rendering v > cR to be unphysical.
An exception to this speed limit could oc-
cur in the case of cracks driven by shear load-
ing (mode II) (7, 8). Analytical solutions of
mode II cracks having a finite-sized dissipa-
tive zone (9) predict positive energy flux into
“supershear” cracks moving with speeds be-
tween the shear wave speed, cs , and the di-
latational wave speed, cp . Such rapid shear
cracks are observed in interfacial and fric-
tional failure (10, 11), as well as in earthquakes
(12, 13). When sufficient elastic energy exists,
shear cracks approaching cR may transition
to supershear by giving birth to a daughter
crack that moves faster than cs (14–16), thereby
Racah Institute of Physics, Hebrew University of Jerusalem,
Jerusalem 91904, Israel.
*Corresponding author. Email: jay@mail.huji.ac.il
ð
Fig. 1. Experimental setup and examples of
subsonic and supershear cracks. (A) Cracks
propagating along unweakened (left) and weakened
(middle) materials driven through applied uniaxial
stretch, l ¼ h þ Dh
Þ=h (Dh is the imposed constant
displacement in y). Deformation fields are measured
via distortions of 80-mm grids, imprinted on one xy
surface at z ¼ 0. (Right) Grooves along y ¼ 0 form
straight weak layers by reducing material thicknesses
from W0 to W. (B) Photographs of cracks propagating
at v ¼ 0:68cR along unweakened (left, l ¼ 1:10)
W ¼ W0 and weakened (right, l ¼ 1:07) W=W0 ¼ 0:5
materials demonstrate parabolic CTODs at the
millimeter scale (dashed lines). Black regions along
weak layers are caustics (diverging light paths)
caused by the highly curved boundaries of weak
layers. (C) Measured energy flux, G vð Þ, for
W=W0 ¼ 0:5 (red) and W=W0 ¼ 1 [blue; data
taken from (6, 28)]. G vð Þ was measured via
either the CTOD (open circles) or the J-integral
calculated with measured deformation fields
(filled circles). G vð Þ scales linearly with W=W0.
(D) Supershear cracks in samples without
(left, l ¼ 1:36) and with (middle, l ¼ 1:34) a
weak layer. (Right) Magnified views of areas
denoted by dashed rectangles highlight
discontinuous deformation fronts formed
by shock waves emanating from crack tips
in supershear (v > cs) propagation.
Wang et al., Science 381, 415–419 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
extending the dissipative region from a point
to a finite region in space. The motion of such
supershear cracks can be approximately de-
scribed through the principle of energy bal-
ance (17).
Cracks driven by the tensile loading (mode I)
are commonly believed to be limited by cR (18).
This limit, as well as the corresponding equa-
tion of motion predicted by linear elastic frac-
ture mechanics (LEFM), has been confirmed
experimentally (6, 19, 20). Extensions of clas-
sical fracture to hyperelastic materials predict
that tensile cracks could surpass cR (21). A qual-
itatively different mode of supershear tensile
fracture not incorporated in classical fracture
mechanics has been predicted by lattice models
to occur at high applied stretch (22–24). This
theory predicts cracks that are able to exceed
cs and even cp, regardless of material stiffening
or softening (25). Moreover, these states are
not expected to be governed by the principle of
energy balance, the cornerstone of the classi-
cal theory of fracture. In rubber, experiments
have observed marginal supershear propaga-
tion under extreme stretches (2, 3); however,
both unequivocal experimental evidence and
fundamental understanding of supershear ten-
sile fracture are still lacking.
Experimental system
Our experiments were performed in thin, strip-
like sheets of polyacrylamide hydrogels having
varied heights, h, where x; y; z are the propa-
gation, loading, and sheet thickness directions
(Fig. 1A). Polyacrylamide gels are brittle neo-
hookean materials: linearly elastic at small
stretches, l≈1, and nonlinearly elastic as l
is increased. LEFM describes the motion of
straight single cracks in these materials (6) for
crack speeds v < cR. The elastic nonlinearity
Fig. 2. Typical experiments with and without a weak layer. (A) Crack speed v, as a function of crack
lengths l in x, for cracks propagating along weak layers under different applied stretches. Sample height h =
20 mm and W=W0 ¼ 0.5. The values of cR and cs are shown by the gray dashed and solid line, respectively.
Colored dashed lines denote va. (B) Photographs of supershear cracks (top) and the strain energy
density (SED) fields (in J/m3) around the crack tip in the reference frame (bottom) at different values
of va corresponding to the four supershear cases shown in (A). (C) Mach cones angles, a, measured from
the SED fields in the reference frame, as a function of va=cs, with cs measured from the shear modulus. a
of the four cases shown in (A) and (B) are denoted by the colors in (A). (D) Examples of dynamics of
supershear oscillatory cracks. Orange markers show, as an example, the crack speed component in x, vx
for l = 1.26, attaining an asymptotic value highlighted by the orange dashed line. (E) Three snapshots
of supershear oscillatory cracks, whose speeds are noted by the full markers in (D), at l = 1.50.
in the near-tip region (26, 27) causes oscilla-
tory crack motion when v→~0.9cs. In Fig. 1A,
we experimentally show that crack oscillations
and microbranching instabilities (4) can be
suppressed by guiding cracks through a straight
weak layer (at y ¼ 0 ) that constrains crack
motion to straight paths (materials and meth-
ods). The deformation fields of the material
surrounding crack tips, for both straight (weak
layer) and oscillatory (no weak layer) cracks,
were measured by imprinting an initially square
grid mesh on one (z ¼ 0) of the sample’s xy
faces. During crack propagation, we recorded
the grid’s instantaneous deformation with a
high-resolution fast camera (Fig. 1B).
For subsonic crack propagation at small
stretches, G vð Þ, the instantaneous energy flux
from the effectively two-dimensional medium
into the crack tip (the “energy release rate”)
was measured by using both the grid defor-
mation and the crack tip’s opening displace-
ment (6, 28). When a weak layer is used, the
strain in the loading direction within the weak
layer is larger than within the outside region
by a factor of W0=W, where W =W0 is the
thickness ratio of the fractured region (fig. S1
and supplementary text section 1). The strain
energy driving fracture is, however, mainly
supplied by the outer region. As a result, in
samples with weak layers, G vð Þ is propor-
tional to W =W0 (Fig. 1C); the effective energy
dissipation of cracks within weak layers is
~G vð Þ ¼ G vð ÞW =W0, where G vð Þ is the fracture
energy of the material. No additional effects
of the weak layer on crack dynamics or struc-
ture were observed. For low l, straight crack
dynamics are well-described by LEFM (6), ac-
celerating smoothly until cR; increasing l sim-
ply increases acceleration toward cR.
Observation of supershear cracks for
large stretches
At higher l (beyond ∼1.2), crack dynamics
change substantially; supershear cracks appear.
Figure 1D presents typical examples of both
supershear oscillatory cracks and straight super-
shear cracks that are guided by weak layers
(movies S1 to S3). Deformation fields sur-
rounding supershear cracks radically differ
from sub-Rayleigh (v < cR) cracks. Supershear
cracks have wedge-like opening displacements
(23, 29) and shock waves emanating from
their tips. At a shock wave, deformation fields
discontinuously jump. Behind these shocks,
deformation fields are highly distorted, and
the kinetic energy density (fig. S2) increases
precipitously relative to the strain energy den-
sity with v. Ahead of the shock, variations of
the deformations, as well as the kinetic and
strain energy densities, are much smaller.
Supershear crack speeds, v, versus crack
lengths,l, for variousl are presented in Fig. 2A,
for propagation along a weak layer. Cracks
initiate at subsonic speeds and accelerate
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Fig. 3. Strain field dependence of supershear cracks. (A and B) Measurement of
the Dxx strain component of supershear cracks propagating at (A) va ¼ 1:04cs
(l ¼ 1:22) and (B) va ¼ 1:28cs (l ¼ 1:56). Dashed lines denote angular locations
of the strain measurements. r and q represent the distance to the crack tip and the
angle relative to x, respectively. (C) Radial dependences of the strain fields for
va ¼ 1:04cs ahead, Dp
xx (right, inset) the Mach cone.
xx (left, inset) and behind Ds
ð
xx (left) and Ds
xx (right) when normalized by the far-field values
Measurements were performed at the values of q denoted by the colors in (A).
Main panels: Dp
Dxx r ¼ 5mm; q
(D) Radial dependences of Dp
xx qð Þ (left, inset) and Ds
xx
Main panels demonstrate the collapse of these functions, when normalized as in
(C). Colors are the same as for the dashed lines in (B).
Þ for each q. The black dashed line (right) depicts a 1=r dependence.
qð Þ (right, inset) at va ¼ 1:28cs.
smoothly until reaching l-dependent asymp-
totic speeds, va (movie S1). This continuous
transition is very different from the transition
to supershear of shear cracks, which both
nucleate at finite distances ahead of sub-
Rayleigh cracks, and the range cR < v < cs is
forbidden (7–9). Figure 2B shows the grid de-
formations and corresponding strain energy
densities surrounding crack tips for 1:04cs ≤
v ≤ 1:31cs. In the reference (material) frame,
the shock waves generated form Mach cones
angles, a, relative to x, where sin að Þ ¼ cs=va
(Fig. 2C). Shear wave speeds derived from the
Mach cones, cs = 5.75 T 0.22 m/s, agree well
with both values calculated from the shear
modulus,m, and directly measured values (mate-
rials and methods). The speed of waves prop-
agating in a stretched medium was determined
to be accurately described by the neo-hookean
constitutive law of the material in our experi-
ments, with a constant value of cs (fig. S3 and
supplementary text section 2). Without weak
layers, supershear oscillatory cracks appear
at the same l levels (Fig. 2D) as the straight
supershear examples presented in Fig. 2A.
Here, whereas the global speed, v, oscillates
with increasing amplitudes, the velocity com-
ponent in x, vx, reaches a constant (asymptotic)
speed, va = vx, before the oscillation develops
(fig. S4 and supplementary text section 3).
Oscillatory supershear cracks generate shock
waves that, in contrast to Mach cones of straight
cracks, have irregular shapes that vary in time
(Fig. 2E) as they reflect the spatially oscillating
crack tips.
ð
xx r; qð
For supershear cracks, Dxx is the strain
component with the largest variations near
the crack tip. In Fig. 3, A and B, we present
measurements of Dxx for va = 1.04cs and 1.28cs.
We first consider the (P-wave governed) fields
ahead of the Mach cones, which we denote as
Dp
xx. For both velocities, Fig. 3, C and D (left),
show that Dp
Þ have very different radial
dependences for each q. When, however, nor-
Þ col-
malized by Dp
lapse onto well-defined radial (v-dependent)
Þ. This collapse suggests that
functions, fr r; vð
Þ
xx r; qð
xx are separable functions of the form Dp
Dp
≈fr r; vð
Þ. This separable nature is also
true for Dp
xy . Although neither of the
functions fr r; vð
Þ possesses a pure power-law
Þ in-
form, near the transition, fr r; v ¼ 1:04cs
creases sharply as r approaches the shock
front, whereas at the larger velocity, fr r; v ¼
1:28csÞ is significantly “less” singular.
xx r ¼ 5mm; q
yy and Dp
Þ (cid:2) fq q; vð
Þ, all Dp
xx r; qð
We now consider the (shear wave–dominated)
strain fieldsDs
xx behind the Mach cone (Fig. 3, C
and D, right panels). The same normalization for
ð
ð
va = 1.04cs produces an approximate collapse to
a ∼1=r form for large r, but does not collapse
the strain fields for r < 2 mm. At the higher
Þ do approximately collapse to
velocity, Ds
the form Ds
Þ (Fig. 3D,
Þ (cid:2) gq q; vð
Þ≈gr r; vð
right), with a nearly linear nonsingular decay
of gr that is much weaker than the decay of
Ds
xx for va = 1.04cs. This qualitative behavior is
echoed by the Ds
xx r; qð
xx r; qð
xy components.
yy and Ds
The transition to supershear cracks and their
dynamics are governed by l
The energy released by supershear cracks, Ga,
is measured at va in the strip geometry. At
vx ¼ va, translational invariance in x exists,
so for both straight and oscillatory supershear
cracks, the strain energy density, we lð Þ (we is
defined in supplementary text section 5), is
constant far ahead of the crack tip. Hence, the
energy released per unit crack advance is
Ga ¼ we lð Þ (cid:2) h. For v < cR, Ga ¼ G vð Þ ¼ ~G vð Þ
(1). For v < cR, the values of G vð Þ measured
via the J-integral, crack tip opening displace-
ment (CTOD), and strip methods are identical
(supplementary text section 5).
In Fig. 4A, we triggered supershear cracks
for various values of Ga by varying h and l.
Although va varies with Ga for a given h, va is
not a universal function of Ga; variation of h
Wang et al., Science 381, 415–419 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
produces different va for the same values of
Ga. Thus, in contrast to sub-Rayleigh fracture,
Fig. 4A demonstrates that the “classical” en-
ergy balance [Ga ¼ ~G vð Þ] is not the governing
principle for supershear dynamics.
What drives cracks to be supershear? Figure
4B indicates that the supershear transition
takes place at a critical value of l ¼ lt ¼
1:19 T 0:01, for the gel composition used. In
particular, the dependence of va on l remains
Fig. 4. Dynamics of supershear cracks. (A) Asymptotic crack speeds va as a function of Ga for three different
system heights, h, of 20, 40, and 80 mm with W=W0 ¼ 0:5 while varying l. Each data point corresponds
to a single experiment. cR and cs are denoted by the gray dashed and solid line, respectively. When h is varied, each
va corresponds to different values of Ga. This breakdown of the collapse of crack dynamics with G (that is an
inherent property of LEFM) already takes place within the transition region (cR < v < cs) to supershear.
(B) Asymptotic crack speeds va as a function of l. Symbols with the colors in (A) represent the same experiments.
Purple and black symbols correspond to straight supershear cracks with different values of W=W0 for h ¼ 20 mm.
All va collapse to a unique function of l (including va within the transition region), regardless the value
of W=W0. Supershear oscillatory cracks (red) collapse onto the same curve. Representative error bars (SD) for
oscillatory cracks are shown. Orange dashed line denotes the value of l ¼ 1:19 T 0:01 at the supershear transition.
Fig. 5. Dependence of supershear cracks on
the chemical composition of gels. (A) Asymp-
totic crack speeds, va, as a function of l for gels
with different concentrations. Gray dashed and
solid lines correspond to cR and cs, respectively. Orange
symbols are the data shown in Fig. 4B. Supershear
cracks appear at increased values of lt when
either the crosslinker concentration is decreased
(green and purple) or the amount of monomer is
increased (blue). When crosslinker and monomer
concentrations are proportionally varied, va versus l
is invariant (red, orange). (B) Strain at the supershear
transition, lt (cid:3) 1, for gels of different monomer-to-
crosslinker molar ratios, M. (lt values were determined by a spline interpolation at va=cs = 1). Symbol colors
correspond to the respective gels in (A). A representative error bar (SD) is presented. The black dashed line, with
a slope of 0.5, is a guide to the eye. (Inset) A linear fit of lt (cid:3) 1 with
(red dashed line) produces a slope of
0.021 with no intercept. (C) Collapse of va versus l curves for gels of different chemical compositions when l is
normalized by lt. A transition in the va versus l relation appears at va ecR.
ffiffiffiffi
M
p
invariant even when ~G vð Þ is changed by vary-
ing W =W0 . Even without a weak layer, the
same critical value of lt ¼ 1:19T0:01 governs
the transition from subshear to supershear
oscillatory cracks. Moreover, Fig. 4B demon-
strates that va depends solely on l; for a given
gel, all supershear velocities, both for straight
and oscillatory cracks, collapse to a single,
well-defined function of l. No effects of the
geometry and weak layer height on the dynam-
ics of supershear cracks were observed (fig. S5
and supplementary text section 4). Supershear
dynamics are governed by the stretch level,
l, not by Ga.
G must still be greater than G csð Þ for super-
shear fracture to take place. Even if l > lt, sub-
shear propagation will occur when h is so
small that G 0ð Þ < Ga < G csð Þ (supplementary
text section 5 and figs. S6 and S7). As Ga >
G csð Þ is necessary, a critical strip height hc ¼
G csð Þ=we ltð
Þ, is required to support super-
shear. For the gels used in Fig. 4, hc≈ 12.8 mm
for W ¼ W0. hc decreases proportionally with
W =W0.
What controls the value of lt? To address
this question, we performed experiments
on samples composed of varying monomer
and crosslinker concentrations (Fig. 5). M, the
monomer-to-crosslinker molar ratio, deter-
mines the number of polymer segments be-
tween crosslinks (supplementary text section
6). Figure 5A shows that both lt and the
overall dependence of va on l are unaffected
when monomer and crosslinker concentra-
tions are increased proportionally (thus fix-
ing M while appreciably varying both the
elastic moduli and G; table S1). When, how-
ever, M is changed by separately varying the
monomer or crosslinker concentrations, the
relation between va and l systematically var-
ies. In particular, Fig. 5B shows that the strain
at the transition, lt (cid:3) 1, scales approximately
with a proportionality factor,
linearly with
a∼0:021. Figure 5C demonstrates that nor-
malizing l by lt collapses all of the va − l
relations for different gels to a single curve
with a sharp transition from subsonic cracks
to the supershear branch at l=lt ¼ 1. The
slight divergence for gels with high mono-
mer concentrations may be due to extensive
polymer entanglement, which also produces
high G (30).
ffiffiffiffiffi
M
p
Discussion
Figure 5B demonstrates that lt , the macro-
scopic critical stretch at the supershear tran-
sition, depends critically on a microscopic
quantity, M, that characterizes the gels’ in-
ternal structure. Fracture mechanics enables
us to relate the applied stretch to a micro-
scopic scale, the cohesive zone size, dt . We
will now show that this connection provides
ffiffiffiffiffi
us with a way to understand the lt (cid:3) 1º
M
scaling presented in Fig. 5B.
p
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RES EARCH | R E S E A R C H A R T I C L E
We consider the simplest cohesive zone
model, the Dugdale model (1)
dt ¼
G csð Þ
sc
¼
Þhc
we ltð
sc
ð1aÞ
where sc is the maximal stress that the mate-
rial can sustain. Replacing we ltð
Þ in Eq. 1a by
its leading order term, 3m=2ðlt (cid:3) 1Þ2, and sub-
stituting the scaling result suggested by Fig. 5B,
lt (cid:3) 1 ≈ a
, yields
ffiffiffiffiffi
M
p
p
ffiffiffiffiffi
M
ð1bÞ
dt ≈
3ma2hcM
2sc
Equation 1b predicts that dt is proportional
to d ¼ Mb=2, the unfolded (stretched) polymer
length between two crosslinks. The propor-
tionality factor is 3ma2hc= scbð
Þ, where b is the
length of a monomer unit. The fact that dt and
d scale in the same way with M and 3ma2hc=
scbð
Þ ∼ O 1ð Þ (table S1 and supplementary ma-
terial section 6) suggests that these two os-
tensibly independent quantities are related.
p
ffiffiffiffiffi
M
Hence, the scaling of lt (cid:3) 1 with
sug-
gests a transition of the polymer structure
within the cohesive zone, from coiled polymer
chains (whose lengths scale as
) to stretched
chains whose strength, sc , is determined by
the internal forces within the polymer chains
(31). This transition may both explain the heu-
ristic scaling presented in Fig. 5B and could
provide a clue toward a physical picture of the
transition from classical fracture to supershear.
Fracture mechanical solutions for supershear
tensile cracks do exist in the literature (1), al-
though they are considered to be nonphysical
on energy grounds. These solutions exhibit
qualitative behavior that is very different from
what we experimentally observe here. Both
ahead and behind the Mach cone, the theo-
retical solutions are singular (∼1=rq), with the
same singularity, q vð Þ. Moreover, these solu-
tions predict q vð Þ to be q ∼ 0 at the transition
to supershear with an increase to a maximal
value of q ¼ 1=2 at v ¼
cs. By contrast, our
experiments clearly show that the observed
supershear cracks have very different radial
dependences on both sides of their Mach
cones. In addition, although the measured
fields are not truly singular, they have their
strongest r dependence when propagating at
speeds close to cs. Beyond cs, the fields’ radial
dependence then weakens with increasing v.
There also exist numerical solutions for
supershear cracks in hyperelastic materials in
which the local wave speed within the highly
stretched region at the crack tip is higher than
the wave speeds in the surrounding bulk mate-
rial (21). In such cases, cracks are “locally” sub-
sonic, whereas crack velocities appear to be
beyond cs to material far from the crack tip.
Such effects have been recently observed in
shear fracture (32). The supershear branch
described in our experiments does not ap-
ffiffiffi
2
p
pear to correspond to these types of cracks
because, at the strains applied in our experi-
ments, the gels used are well-described by neo-
hookean constitutive relations—even within
the weak layers up to l≈ 1.8 (fig. S1). In neo-
hookean materials, it is known that cs is in-
variant with stretch (23, 28), and we have
verified this with direct measurements (sup-
plementary text section 2 and fig. S3).
Our results therefore suggest that, as Marder
(23) predicted, an entirely different branch of
solutions for propagating cracks exists. More-
over, these results suggest that the supershear
solution branch is both entirely general and
independent of the microscopic material struc-
ture; the elastic gels in the experiments and the
brittle lattices in the numerics possess wholly
different microscopic properties. Even if the
experimentally observed supershear states cor-
respond to the branch of solutions observed in
these lattice models (22–25), many important
fundamental questions arise that challenge
our fundamental understanding of fracture.
For example, our results imply that the tran-
sition mechanism to supershear takes place
within the small scales surrounding the crack
tip. The polymer-stretching transition sug-
gested here is, however, certainly not realized
in lattice models. As such, it is unclear what
general mechanisms within the dissipative re-
gion surrounding the crack tip give rise to the
supershear transition.
There are also puzzles at large (system-size)
scales. In contrast to supersonic cracks driven
by extreme (explosive) loading rates (33), the
supershear cracks described here are driven
by the release of elastic energy that is stored
within the macroscopic scales that are roughly
defined by hc. hc is both insensitive to local
stretch along the crack path and is a scale that
is much larger than both the crack tip region
and/or the weak layer scale. An important
question is, therefore, by what mechanism does
the material supporting these rapidly propagat-
ing states self-organize, to transport the strain
energy within h≤hc to the dissipative region at
supershear crack tips? This mechanism must
be wholly different from that described by clas-
sical fracture mechanics; a “classical” crack is
unable to transport energy to its tip for v≥cR.
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AC KNOWLED GME NTS
We thank M. Adda-Bedia (ENS Lyon) and D. Kammer (ETH Zurich)
for helpful discussions. Funding: This work was supported by
Israel Science Foundation (grant no. 840/19). M.W. acknowledge
the support of the Lady Davis Fellowship Trust. Author
contributions: M.W. and J.F. conceived of the project. M.W.
designed and performed research. J.F. assisted with experimental
design. M.W., S.S., and J.F. analyzed the results. M.W. and
J.F. wrote the manuscript. J.F. supervised the research. All authors
discussed the result and commented on the manuscript.
Competing interests: The authors declare no competing interests.
Data and materials availability: All data are available in the
manuscript or the supplementary materials and are available at
the Dryad repository (34). License information: Copyright ©
2023 the authors, some rights reserved; exclusive licensee
American Association for the Advancement of Science. No claim to
original US government works. https://www.sciencemag.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg7693
Materials and Methods
Supplementary Text
Figs. S1 to S7
Table S1
References (35–41)
Movies S1 to S3
Submitted 19 January 2023; accepted 2 June 2023
10.1126/science.adg7693
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RES EARCH
R E S E A R C H A R T I C L E
◥
PHYSICS
Quantum control of trapped polyatomic molecules
for eEDM searches
Loïc Anderegg1,2*, Nathaniel B. Vilas1,2, Christian Hallas1,2, Paige Robichaud1,2, Arian Jadbabaie3,
John M. Doyle1,2, Nicholas R. Hutzler3*
Ultracold polyatomic molecules are promising candidates for experiments in quantum science and precision
searches for physics beyond the Standard Model. A key requirement is the ability to achieve full quantum
control over the internal structure of the molecules. In this work, we established coherent control of individual
quantum states in calcium monohydroxide (CaOH) and demonstrated a method for searching for the
electron electric dipole moment (eEDM). Optically trapped, ultracold CaOH molecules were prepared in a single
quantum state, polarized in an electric field, and coherently transferred into an eEDM-sensitive state where
an electron spin precession measurement was performed. To extend the coherence time, we used eEDM-
sensitive states with tunable, near-zero magnetic field sensitivity. Our results establish a path for eEDM
searches with trapped polyatomic molecules.
T he rich structure of polyatomic molecules
makes them an appealing platform for
experiments in quantum science (1–4),
ultracold chemistry (5), and precision mea-
surements (6–10). Key to this structure is
the presence of near-degenerate states of oppo-
site parity, which allow the molecules to be
easily polarized in the laboratory frame with
the application of a small electric field. Such
states are generic among polyatomic mole-
cules, but rare in diatomics, and may be useful
for applications such as analog simulation of
quantum magnetism models (1, 2) or for real-
izing switchable interactions and long-lived
qubit states for quantum computing (4). Addi-
tionally, the parity-doublet states in trapped
polyatomic molecules are expected to be an
invaluable tool for systematic error rejection
in precision measurements of physics beyond
the Standard Model (BSM) (6). To date, several
species of polyatomic molecules have been
laser cooled and/or trapped at ultracold tem-
peratures (11–17).
One powerful avenue for tabletop BSM
searches is probing for the electron electric
dipole moment (eEDM) (18–22), de, which
violates time-reversal (T) symmetry and is
predicted by many BSM theories to be orders-
of-magnitude larger than the Standard Model
prediction (19, 20). Present state-of-the-art
eEDM experiments are broadly sensitive to
T-violating physics at energies much greater
than 1 TeV (23–28). All such experiments use
Ramsey spectroscopy to measure an energy
shift caused by the interaction of the electron
1Department of Physics, Harvard University, Cambridge, MA
02138, USA. 2Harvard-MIT Center for Ultracold Atoms,
Cambridge, MA 02138, USA. 3Division of Physics,
Mathematics, and Astronomy, California Institute of
Technology, Pasadena, CA 91125, USA.
*Corresponding author. Email: anderegg@g.harvard.edu (L.A.);
hutzler@caltech.edu (N.R.H.)
with the large electric field that is present in-
side a polarized molecule (24–26, 27, 29). Mo-
lecular beam experiments have achieved high
statistical sensitivity by measuring a large num-
ber of molecules over a ≈1-ms coherence time
(24, 25), whereas molecular ion–based exper-
iments have used long Ramsey interrogation
times (≈1 s), though with lower numbers
(26, 27, 29). Measurements with trapped neu-
tral polyatomic molecules can potentially com-
bine the best features of each approach to
achieve orders-of-magnitude improved statis-
tical sensitivity (6).
Experimental approach for polyatomic
molecule control
In this work, we demonstrate full quantum
control over the internal states of a trapped
polyatomic molecule in a vibrational bending
mode with high polarizability in small electric
fields. The protocol starts with preparing
ultracold, optically trapped molecules in a
single hyperfine level, after which a static elec-
tric field is applied to polarize the molecules.
The strength of the polarizing electric field is
tuned to obtain near-zero g-factor spin states,
which have strongly suppressed sensitivity to
magnetic field noise while retaining eEDM
sensitivity. Microwave pulses are applied to
create a coherent superposition of these zero
g-factor spin states, which precesses under the
influence of an external magnetic field. The
precession phase is then read out by a combi-
nation of microwave pulses and optical cycling.
We observed spin precession over a range of
electric and magnetic fields and characterized
the present limitations to the coherence time
of the measurement. With readily attainable
experimental parameters, coherence times on
the order of the state lifetime (>100 ms) could
be realistically achieved. We therefore realized
the key components of an eEDM measure-
ment in this system. Note that eEDM sensitiv-
ity arises from the relativistic motion of the
electron, which is enhanced by higher-mass
nuclei. Although the light mass of CaOH pre-
cludes a competitive eEDM measurement (30),
the protocol demonstrated here is directly
transferable to heavier laser-cooled alkaline
earth monohydroxides with identical inter-
nal level structures, such as SrOH, YbOH, and
RaOH, which have substantially enhanced sen-
sitivity to the eEDM (6, 11, 12, 30, 31).
In eEDM measurements with polarized mol-
→
precesses under the
ecules, the electron spin S
influence of an external magnetic field BZ and
the internal electric field of the molecule Eeff,
which can be large owing to relativistic effects.
Time evolution is described by the Hamiltonian
H ¼ gSm
→
BBZ S
(cid:2) ^Z (cid:3) deEeff S
→
(cid:2) ^n
¼ gSmBBZ MS (cid:3) deEeff S
ð1Þ
→
→
(cid:2) ^Z and S ¼ S
Here, gS ≈ 2 is the electron spin g-factor, mB is the
Bohr magneton, BZ points along the lab ^Z axis,
and the internal field Eeff points along the mol-
ecule’s internuclear axis ^n . We define the
(cid:2) ^n to de-
quantities MS ¼ S
scribe the electron’s magnetic sensitivity and
EDM sensitivity, respectively. The effect of the
eEDM can be isolated by switching the orien-
tation of the applied magnetic field or, alter-
natively, by switching internal states to change
the sign of MS or S. Performing both switches
is a powerful technique for suppressing sys-
tematic errors (25, 26).
Present EDM bounds rely on specific states
in diatomic molecules that have an unusually
small g-factor, which reduces sensitivity to stray
magnetic fields (24, 26). However, CaOH, like
other laser-coolable molecules with structure
amenable to eEDM searches (6, 31–33), has a
single valence electron, which results in large
magnetic g-factors. In this work, we engineered
reduced magnetic sensitivity by using an ap-
plied electric field EZ to tune MS to a zero-
crossing while maintaining substantial eEDM
sensitivity S. This technique is generic to poly-
atomic molecules with parity doublets. Details
of a specific M = ±1 pair of zero g-factor states
are shown in Fig. 1, A and B, with further in-
formation provided in (34). We emphasize that
near the zero g-factor crossing, the eEDM sen-
sitivity is nearly maximal because of the large
projection of the electron spin onto the inter-
nal electric field of the molecule. Sensitivity to
transverse magnetic fields is also suppressed
in these zero g-factor states (34).
Experimental overview and
single-state preparation
The experiment begins with laser-cooled CaOH
molecules loaded from a magneto-optical trap
(14) into an optical dipole trap (ODT) formed
by a 1064-nm laser beam with a 25-mm waist
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Fig. 1. Overview of the experiment. (A) A geometric picture of the bending
→
molecule at the zero g-factor crossing, showing that the electron spin (S
) has a finite
→
projection on the molecule axis (^n), giving eEDM sensitivity. However, the electron spin (S
)
→
), which results in suppressed magnetic field
is orthogonal to the magnetic field (B
sensitivity. (B) The magnetic sensitivity (top) and eEDM sensitivity (bottom)
for a pair of zero g-factor states (N = 1, J = 1/2+, F = 1, MF = ±1) are shown as
a function of the applied electric field. (C) Experimental sequence to prepare the
eEDM-sensitive state. First, the molecules are pumped into a single quantum state
(N = 1, J = 1/2−, F = 0) with a combination of microwave drives and optical pumping
(I). Next, a microwave p-pulse drives the molecules into the N = 2, J = 3/2−, F = 2,
MF = 0 state (II). Lastly, the eEDM measurement state is prepared as a coherent
superposition of the N = 1, J = 1/2−, F = 1, MF = ±1 states with a microwave p-pulse
(III). The states that are optically detectable with the detection light are shown in
black, whereas those not addressed by the detection light are in gray.
→
¼ EZ
^Z and E
size, as described in previous work (15). The
ODT is linearly polarized, and its polarization
ODT defines the ^Z axis, along which we
vector D→
→
¼
also apply magnetic and electric fields, B
^Z , respectively, as depicted
BZ
in Fig. 1A. We first nondestructively image the
molecules in the ODT for 10 ms as normaliza-
tion against variation in the number of trapped
molecules. The molecules are then optically
pumped into the N = 1− levels of the ~X
2Sþ 010ð
Þ
vibrational bending mode (15) (Fig. 1C), and
the trap depth is adiabatically lowered by 3.5
times to reduce the effect of ac Stark shifts
from the trap light and to lower the temper-
ature of the molecules to 34 mK. Any molecules
that were not pumped into N = 1− levels of the
bending mode are heated out of the trap with
a pulse of resonant laser light.
After transfer to the ~X
Þ N ¼ 1(cid:3)
Þ
ð
state, the molecular population is initially
spread across 12 hyperfine Zeeman sublevels in
the spin-rotation components J = 1/2 and 3/2.
To prepare the molecules in a single hyperfine
state, we used a combination of optical pump-
ing and microwave pulses, as shown in Fig. 1C.
We first applied microwaves from the N = 1,
J = 3/2− state up to the N = 2, J = 3/2− state.
Because this transition is parity-forbidden, we
applied a small electric field EZ = 7.5 V/cm to
slightly mix the parity of the N = 1 levels and
provide transition strength. From the N = 2
state, we drove an optical transition to the ex-
cited ~A
Þ; J ¼ 1=2þ state. This
state predominately decays to both the F = 0
2Sþ 010ð
2P 010ð
Þk2S (cid:3)ð
Fig. 2. Spin precession. (A) Spin precession of the eEDM-sensitive state in the presence of a bias magnetic
field. Error bars represent 68% confidence intervals. au, arbitrary units. (B) Magnetic-field sensitivity of
the eEDM state in CaOH as a function of electric field. The field sensitivity is determined by measuring the
spin-precession frequency at different electric fields with an applied magnetic field of BZ = 110 mG. Error bars
are smaller than the markers. The solid curve is the calculated magnetic-field sensitivity in the presence
of trap shifts using known molecular parameters (34).
(the target state) and F= 1 states in the N = 1,
J = 1/2− manifold. After 3 ms of optical pump-
ing, the microwaves were switched to drive
the accumulated N = 1, J = 1/2−, F = 1 pop-
ulation to the same N = 2, J = 3/2− state in
~X 010ð
Þ, where they are excited by the optical
light and pumped into the target F = 0 state.
Once this optical pumping sequence is com-
plete, we adiabatically ramped the electric field
to EZ = 150 V/cm to substantially mix parity,
then drove the population up to the N = 2, J =
3/2−, F = 2, M = 0 state with a microwave p-pulse
(Fig. 1C, II). We cleaned out any remaining
population in the N = 1 state with a depletion
laser that resonantly drives the population to
undetected rotational levels.
Spin precession in an eEDM-sensitive state
To perform spin precession in the eEDM-
sensitive state, we first adiabatically ramped
the electric field to a value EZ, then turned on a
small bias magnetic field BZ. We measured the
electron spin precession frequency using a
procedure analogous to Ramsey spectroscopy
(24, 25). The molecules were prepared by driving
a p-pulse (2.5 ms), with microwaves linearly
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Fig. 3. Coherence time of the spin-precession signal. (A) Measured coherence times t versus BZ at
different electric fields (red and blue markers, which correspond to different magnetic field sensitivities).
The coherence time scales as 1/BZ owing to ac Stark-shift broadening then plateaus at a limit set by the
magnetic field instability dB. This limit increases as the g-factor approaches zero. Solid and dashed curves
are fit to the data. The ambient magnetic field noise determined from the fit is dB ¼ 4
fitted decoherence time due to light shifts is t ¼ 1=BZ
15 mG, near the zero g-factor crossing (0.06 MHz/G; red) and far from the crossing (1.0 MHz/G; blue).
Shaded regions indicate the fitted exponential decay envelope of the oscillations; the 1.0 MHz/G data are
excluded from the top panel for clarity. The spin-precession coherence time is extended by 16 times by
approaching the zero g-factor point.
þ20
(cid:3)10 ms (cid:4) mG. (B) Spin-precession signal, at BZ =
þ2
(cid:3)1 mG, and the
Þ (cid:4) 80
ð
Fig. 4. Effect of trap light on
coherence time. (A) Effective
magnetic moment, meff, as a
function of electric field for several
trap intensities I. The trap light
shifts the location of the zero
crossing in meff. As a result, mole-
cules at a finite temperature
explore different magnetic-field
sensitivities meff. (B) Dependence of
the spin-precession frequency
(scaled by the trap depth U0) on the
position within the trap, where w0 is
the trap waist. At lower magnetic
fields, the relative change in spin-
precession frequency is reduced.
(C) Two spin-precession curves
taken at the same magnetic field
(BZ = 210 mG) but at different
electric fields, showing that the ac
Stark-shift limitation is independent
of the effective g-factor because ac
Stark shifts dominate the coherence
time for large bias fields.
ffiffiffi
2
jM ¼ (cid:3)1i
polarized along the lab ^X axis, into the “bright”
Þ=
ð
superposition state jBi ¼ M ¼ 1iþ
j
p
within the N = 1, J = 1/2+, F = 1, M = ±1
eEDM-sensitive manifold (Fig. 1C, III). The
state begins to oscillate between the bright
state and the “dark” statejDi ¼ M ¼ 1i(cid:3)
jM ¼
at a rate wSP= meffBZ, where the effec-
(cid:3)1iÞ=
tive magnetic moment m
Bgeff ¼ gEm
B
eff
Þ is tuned by means of
ð
(cid:3) hMSi
hMSi
the applied electric field EZ (Fig. 1B). The con-
tribution from the deEeff term in Eq. 1 is neg-
M¼(cid:3)1
¼ m
M¼1
ffiffiffi
2
p
ð
j
ligible in CaOH but could be measured in
heavier molecules with much larger Eeff. After
a given time, a second p-pulse was applied to
stop spin precession and transfer the bright
state to the optically detectable N = 2, J = 3/2−
level. Once the electric field was ramped down,
the population remaining in the eEDM mani-
fold, which has the opposite parity, is not op-
tically detectable. We then imaged the ODT
again and took the ratio of the first and second
images (Fig. 2A). At long spin precession times
(>10 ms), losses from background gas collisions
(~1 s), blackbody excitation (~1 s), and the spon-
taneous lifetime of the bending mode (~0.7 s)
lead to an overall loss of signal, as characterized
in (15). This effect is mitigated with a fixed dura-
tion between the first and second images, making
the loss independent of the precession time.
To map out the location of the zero g-factor
crossing, we performed spin precession mea-
surements at a fixed magnetic field BZ = 110 mG
for different electric fields (Fig. 2B). The spin
precession frequency corresponds to an effec-
tive g-factor at that electric field. We found
that the zero g-factor crossing within the N = 1,
J = 1/2+, F = 1, M = ±1 eEDM manifold occurs
at an electric field of 59.6 V/cm, in agreement
with theory calculations described in (34). We
note that there is another zero g-factor cross-
ing for the N = 1, J = 3/2+, F = 1 manifold at
≈64 V/cm, which has a smaller eEDM sen-
sitivity but the opposite slope of geff versus EZ,
thereby providing a powerful resource to re-
ject systematic errors related to imperfect field
reversals (34). We emphasize that although
the location of these crossings is dependent on
the structure of a specific molecule, their exist-
ence is generic in polyatomic molecules, which
naturally have parity-doublet structure (6).
Coherence time and limitations
A critical component of the spin precession
measurement is the coherence time, which sets
the sensitivity of an eEDM search. Figure 3A
shows the measured coherence time of our
system at different applied fields BZ and EZ.
We characterized two dominant limitations
that wash out oscillations at long times. Var-
iations in the spin precession frequency can
be linearly expanded as dwSP = meff(dBZ) +
(dmeff)BZ. The first term describes magnetic
field noise and drift of the applied bias field,
given by dBZ. The second term describes noise
and drifts in the g-factor, dgeff, which can arise
from instability in the applied electric field,
EZ, or from ac Stark shifts (described below).
Drifts in the bias electric field EZ were found
to be negligible in our apparatus.
Decoherence caused by magnetic field noise,
dBZ, is independent of the applied magnetic
field but is proportional to meff and can be
mitigated by operating near the zero g-factor
crossing. As shown in Fig. 3B, at an electric
field of 90 V/cm, corresponding to a large mag-
netic moment of meff = 1.0 MHz/G, we realized
a magnetic field noise–limited coherence time
of 0.5 ms at BZ ≈ 15 mG (blue points). At an
electric field of 61.5 V/cm, corresponding to
meff = 0.06 MHz/G, which is much closer to the
zero g-factor location, we found a coherence time
of 4 ms at the same BZ (red points in Fig. 3B).
At higher magnetic fields, the primary lim-
itation to the coherence time is ac Stark shifts
from the optical trapping light (Fig. 4). The
intense Z-polarized ODT light leads to a shift
Anderegg et al., Science 382, 665–668 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
in the electric field at which the zero g-factor
crossing occurs. Owing to the finite tempera-
ture of the molecules within the trap, they will
explore different intensities of trap light and
hence have different values of geff. The spread
dgeff causes variation of wSP, which leads to de-
coherence. In contrast to the magnetic field
noise term, this effect is independent of the
electric field EZ but decreases monotonically
with BZ, which scales the frequency sensitivity
to g-factor variations, dwSP = BZdmeff. The insen-
sitivity of g-factor broadening to the exact value
of geff is demonstrated in Fig. 4C. Decoher-
ence caused by ac Stark shifts can be reduced
by cooling the molecules to lower temperatures
or by decreasing BZ. The bias magnetic field
can be reduced arbitrarily far until either trans-
verse magnetic fields or magnetic field noise
becomes dominant. From the decoherence rates
measured in this work, it is expected that ac
Stark shift–limited coherence times of ~1 s
could be achieved at bias fields of BZ ~ 100 mG.
From the above discussion, it is expected
that the longest achievable coherence times
will occur for very small g-factors, geff ≈ 0, and
very small bias fields, BZ ≈ 0. Minimizing BZ
requires reducing the effects of both magnetic
field noise and transverse magnetic fields to
well below the level of the bias-field energy
shifts. We canceled the transverse magnetic
fields to below 1 mG by maximizing the spin
precession period under the influence of trans-
verse B fields only, and actively monitored and
fed back on the magnetic field along each axis
to minimize noise and drifts in BZ. Note that
the stainless-steel vacuum chamber has no mag-
netic shielding, which leads to high levels of
magnetic field noise that would not be present
in an apparatus designed for an eEDM search.
Even under these conditions, we achieved
a coherence time of 30 ms at an electric field of
60.3 V/cm (corresponding to meff = 0.02 MHz/G)
and a bias field of BZ ≈ 2 mG (34). However, at
such a low bias field, the molecules are sensi-
tive to 60-Hz magnetic field noise that is pres-
ent in the unshielded apparatus, which is on
the same order as the bias field. Because the
experiment is phase-stable with respect to the
ac line frequency, this 60-Hz magnetic field
fluctuation causes a time-dependent spin pre-
cession frequency. Nevertheless, our prototype
experiment confirms that long coherence times
are possible. Any future eEDM experiment
would have magnetic shielding that would
greatly suppress nefarious magnetic fields from
the environment. Such shielding could read-
ily enable coherence times that exceed that of
the ~0.5-s lifetime of the bending modes of
similar linear polyatomic molecules with larger
eEDM sensitivity (15).
Discussion and outlook
We have realized coherent control of optically
trapped polyatomic molecules and demonstra-
ted a realistic experimental roadmap for future
eEDM measurements. By leveraging the dis-
tinctive features of the quantum levels in poly-
atomic molecules, we achieved a coherence
time of 30 ms for paramagnetic molecules in a
stainless-steel chamber with no magnetic shield-
ing. With common shielding techniques used
in past EDM experiments, there is a clear path
to reducing stray fields and extending coher-
ence times to >100 ms. At such a level, the
dominant limitation becomes the finite lifetime
of the bending mode (15). Even longer coher-
ence times are possible with the right choice of
parity-doublet states, as found in symmetric or
asymmetric top molecules (6, 13, 35, 36).
Following this roadmap with heavier trap-
ped polyatomic molecules has the potential
to provide orders-of-magnitude improvements
to present bounds on T-violating physics. Using
a recent study of the ~X 010ð
Þ state in YbOH
(37), we identified similar N = 1 zero g-factor
states for eEDM measurements with greatly
improved sensitivity. In addition to the g-factor
tuning demonstrated in this work, polyatomic
molecules provide the ability to reverse the
sign of S without reversing MS, which is a crucial
feature of recent experiments that has greatly
improved the limit on the eEDM (25, 27). For
example, in the N = 1 manifold of CaOH, there
is another zero g-factor crossing at a nearby
electric field value, with 69% smaller values of
S and opposite sign. Because the ratio of eEDM
sensitivity to g-factor versus EZ slope differs be-
tween these two crossings, measurements at
both points could be used to suppress systemat-
ics caused by nonreversing fields that couple to
the electric field dependence of the g-factor (25).
This work provides an experimental dem-
onstration of the advantages of the rich level
structure of polyatomic molecules for preci-
sion measurements. Although we focused here
on spin precession with T-reversed states (M =
±1), many levels of interest can be favorably
engineered for precision measurement exper-
iments. In a recent proposal (9), parity doublets,
magnetically tuned to degeneracy in optically
trapped polyatomic molecules, were shown
to be advantageous for searches for parity-
violating physics. In another recent work (7), a
microwave clock between rovibrational states
in SrOH was proposed as a sensitive probe of
ultralight dark matter, by using transitions
tuned to electric and/or magnetic insensitiv-
ity. In these proposals, and as now experi-
mentally demonstrated in our work, coherent
control and state engineering in polyatomic
molecules can mitigate systematic errors and
enable robust searches for new physics.
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AC KNOWLED GME NTS
A.J. acknowledges helpful discussions with C. Zhang and P. Yu.
Funding: This work was supported by the Air Force Office of
Scientific Research and the National Science Foundation (NSF).
L.A. acknowledges support from the Harvard Quantum Initiative.
N.B.V. from the Department of Defense National Defense Science and
Engineering Graduate fellowship program, and P.R. from the NSF
Graduate Research Fellowship Program. N.R.H. and A.J. acknowledge
support from NSF CAREER program (PHY-1847550), the Gordon
and Betty Moore Foundation (GBMF7947), and the Alfred P. Sloan
Foundation (G-2019-12502). Author contributions: L.A., N.B.V., C.H.,
P.R., and A.J. performed the experiment and analyzed the data. N.R.H.
and J.M.D. directed the study. All authors discussed the results and
contributed to the manuscript. Competing interests: None declared.
Data and materials availability: All data needed to evaluate the
conclusions in this paper are present in the paper or in the
supplementary materials. All data presented in this paper are
deposited at Zenodo (38). License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg8155
Supplementary Text
Figs. S1 to S4
References (39–50)
Submitted 23 January 2023; accepted 29 September 2023
10.1126/science.adg8155
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evidence for sustained human transmission
since at least 2016
Áine O’Toole1*, Richard A. Neher2, Nnaemeka Ndodo3, Vitor Borges4, Ben Gannon5,
João Paulo Gomes4,6, Natalie Groves7, David J. King8, Daniel Maloney1, Philippe Lemey9,
Kuiama Lewandowski5, Nicholas Loman7,10, Richard Myers7, Ifeanyi F. Omah1,11,
Marc A. Suchard12, Michael Worobey13, Meera Chand7,14, Chikwe Ihekweazu3,
David Ulaeto7†, Ifedayo Adetifa3†, Andrew Rambaut1*†
Historically, mpox has been characterized as an endemic zoonotic disease that transmits through
contact with the reservoir rodent host in West and Central Africa. However, in May 2022, human cases of
mpox were detected spreading internationally beyond countries with known endemic reservoirs. When
the first cases from 2022 were sequenced, they shared 42 nucleotide differences from the closest mpox
virus (MPXV) previously sampled. Nearly all these mutations are characteristic of the action of APOBEC3
deaminases, host enzymes with antiviral function. Assuming APOBEC3 editing is characteristic of human
MPXV infection, we developed a dual-process phylogenetic molecular clock that—inferring a rate of
~6 APOBEC3 mutations per year—estimates that MPXV has been circulating in humans since 2016. These
observations of sustained MPXV transmission present a fundamental shift to the perceived paradigm of
MPXV epidemiology as a zoonosis and highlight the need for revising public health messaging around
MPXV as well as outbreak management and control.
S ince 2017, the Nigeria Centre for Disease
Control has been reporting cases of
MPXV (mpox virus) infection in humans
(fig. S1) (1). MPXV, a DNA virus in the
genus Orthopoxvirus; Family Poxviridae,
is often described as being endemic in West and
Central Africa as a zoonotic disease that trans-
mits through contact with the rodent reservoir
host. Since the first human cases were observed
in the 1970s, MPXV infections have been pre-
dominantly associated with infants and children
(2–4). However, of the cases observed in Nigeria
since 2017, very few have been in children, with
the virus mainly affecting adults aged 20 to 50
(79%), 27% of which were in women (5). Genome
sequencing of viruses revealed enough genetic
diversity among cases that distinct zoonotic
events were not ruled out. In May 2022, cases
1Institute of Ecology and Evolution, University of Edinburgh,
Edinburgh EH9 3FL, UK. 2Biozentrum, University of Basel
and Swiss Institute of Bioinformatics, Basel, Switzerland.
3Nigeria Centers for Disease Control and Prevention, Abuja,
Nigeria. 4National Institute of Health Doutor Ricardo Jorge
(INSA), Lisbon, Portugal. 5UK Health Security Agency, Porton
Down, Salisbury SP4 0JG, UK. 6Veterinary and Animal
Research Centre (CECAV), Faculty of Veterinary Medicine,
Lusófona University, Lisbon, Portugal. 7UK Health Security
Agency, London E14 5EA, UK. 8CBR Division, Defence
Science and Technology Laboratory, Salisbury SP4 0JQ,
UK. 9Department of Microbiology, Immunology and
Transplantation, Rega Institute, KU Leuven, Leuven, Belgium.
10University of Birmingham, Birmingham B15 2TT, UK.
11Department of Parasitology and Entomology, Nnamdi Azikiwe
University, Awka, Anambra State, Nigeria. 12Department of
Biostatistics, Fielding School of Public Health, University of
California, Los Angeles, CA 90095, USA. 13Department of
Ecology and Evolutionary Biology, University of Arizona,
Tucson, AZ 85719, USA. 14UKHSA Guys and St Thomas’ NHS
Trust, London SE1 7EH, UK.
*Corresponding author. Email: aine.otoole@ed.ac.uk (Á.OT.);
a.rambaut@ed.ac.uk (A.R.)
†These authors contributed equally to this work.
of MPXV infection were detected spreading
widely across Europe and subsequently across
the globe. The first MPXV genome sequences
from these 2022 cases showed that they had
descended from the clade characterized by cases
diagnosed in Nigeria and Israel, Singapore, and
the UK (6) associated with travel from Nigeria
(fig. S2 and table S1, in bold). These early 2022
genomes are indicated as a triangle within
clade IIb in Fig. 1A and represent lineage B.1 as
per the nomenclature proposed by Happi et al.
(7). Isidro et al. (6) noticed that sequences
within lineage B.1 shared 42 single-nucleotide
differences from the closest earlier MPXV ge-
nomes from 2018. From a 2017 outbreak of
MPXV in chimpanzees, the evolutionary rate of
MPXV was estimated to be 1.9 × 10−6 substi-
tutions per site per year (1.2 × 10−6 to 2.7 × 10−6),
corresponding to ~1 nucleotide change every
3 years (8). Forty-two substitutions in the space
of 3 to 4 years is an unexpectedly large number.
Under the paradigm that MPXV is a zoonotic
virus with limited human-to-human transmis-
sion, one interpretation of this long branch
might be that it represents adaptation to
humans, facilitating the sustained transmission
that is now observed. However, as we show
here, and as was quickly seen when the first
genomes from 2022 were sequenced, it is clear
that these mutations are not the result of errors
by the virus’s replication machinery and occur
at a much higher rate than would be expected
for an orthopoxvirus (6, 9). Specifically, most of
observed nucleotide changes appear to be of a
particular type—a dinucleotide change from
TC→TT or its reverse complement, GA→AA
(9, 10). This particular mutation is characteristic
of the action of the APOBEC3 (apolipoprotein
B mRNA editing enzyme, catalytic polypeptide
3) family of cytosine deaminases. These act on
single-stranded DNA (ssDNA) to deaminate
cytosine to uracil, causing a G→A mutation in
the complementary strand when it is synthe-
sized. Most human APOBEC3 molecules have
a strong bias toward deaminating 5′TC dinu-
cleotides, and APOBEC3-driven deamination
has been demonstrated with many DNA viruses
and retroviruses; (11–18). Furthermore, a recent
study has specifically demonstrated APOBEC3F
editing in cell culture and during human MPXV
infection (19).
We assess the extent to which APOBEC3 has
acted on MPXV and explore whether this is the
source of the elevated mutation rate observed
since 2017. We also explore the evolutionary
consequences of this mechanism driving evo-
lution in MPXV and model the distinct pro-
cesses underpinning the evolution of MPXV in
the human population.
APOBEC3 editing as a signature of MPXV
evolution in the human population
The known diversity of MPXV is decomposed
into three major clades: clades I, IIa, and IIb
(Fig. 1A) (7). Clade I represents MPXV sampled
in Central Africa, and clade IIa is composed of
viruses from human and nonhuman animal sam-
ples taken in or connected to West Africa. Both
of these clades include virus genomes spanning
from the 1970s to the present day, although most
samples were collected within the last 20 years
(fig. S3). Clade IIb has an early sample taken in
1971 (GenBank accession KJ642617), but most of
the sequences in clade IIb are more recent virus
genomes from 2017 to 2022 that Happi et al. (7)
have labeled as hMPXV-1 (Fig. 1A, labeled phy-
logeny in fig. S2). Within the recent diversity of
clade IIb (indicated as the darker box within IIb
in Fig. 1A), we cataloged transmitted mutations
that occurred between 2017 and 2022 with only a
single representative from the 2022 global lineage
B.1 (n = 44 genome sequences, fig. S2) (20).
Within MPXV clade IIb, we observe rates of
molecular evolution far greater than that ex-
pected for double-stranded DNA viruses and
indeed that observed in clades I and IIa of
MPXV (8) and see this excess accumulation of
mutation in samples as early as 2017. The great
majority of these mutations are of the type
G→A or C→T (90.8%) (Fig. 1B), regardless of
sample host species (fig. S4). Comparing MPXV
clade IIb with clade I and IIa emphasizes that
this pattern is not seen outside of clade IIb (Fig.
1B, labeled phylogenies in fig. S5), nor is it seen
when looking at reconstructed mutations within
a phylogeny of 46 variola virus (VARV) genomes,
the human virus responsible for smallpox (fig.
S6). For the other MPXV clades, APOBEC-type
mutations are observed at between 8 and
13% frequency, which fits with the expected
proportion under standard models of nucleotide
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Fig. 1. Specific enrichment of APOBEC3-type mutations in MPXV samples
collected since 2017. (A) MPXV genetic diversity is categorized into clade I
(predominantly sequences from the Democratic Republic of the Congo), clade IIa
(predominantly West African sequences), and clade IIb. Within clade IIb is a
subclade of genomes sampled from 2017 to 2022 that show mutational patterns
distinct from those of the other two clades. (B) We catalog single-nucleotide
mutations across the phylogenies of clade IIb, clade IIa, and clade I (top to
bottom). For clade IIb, we include samples from 2017 to 2022 and only a single
representative of the global lineage B.1. Of 120 reconstructed mutations that
occurred on internal branches of the clade IIb phylogeny (so are observed
transmitted mutations), 109 are consistent with APOBEC3 editing (90.8% of
mutations). Individual proportions of G→A and C→T mutations are shown above
the respective bars. Ancestral state reconstruction performed across clade IIa
and clade I does not produce the same enrichment of mutations consistent
with APOBEC3 editing, with only 27 of 207 observed mutations (13%) and 38 of
463 clade I mutations (8%) fitting the dinucleotide pattern. (C) Observed
heptamers of C→T or G→A mutated sites of clade IIb, IIa, and I phylogenies
(top to bottom). Heptamers associated with G→A mutations have been
reverse-complemented to reflect deamination on the negative strand. For clade
IIb, most C→T mutations are present in a TC dimer context, consistent with
APOBEC3 editing (107 of 115 mutations, or 93%). However, the same is not seen
for clades IIa and I, in which 29 of 149 (19%) mutations and 42 of 256 (16%)
mutations have the dinucleotide context of APOBEC3, respectively, which is
what we would predict under standard models of nucleotide evolution.
*Only mutations occurring on internal branches of the clade IIb phylogeny
are included.
evolution (21, 22) (Fig. 1B). Notably, the hep-
tamers of C→T and G→A mutations that oc-
curred across the clade IIb phylogeny show
that this is a specific enrichment of APOBEC3-
type dimer mutations of the type TC→TT and
GA→AA (Fig. 1C). Similarly, this enrichment
of TC→TT and GA→AA mutations is observed
within the B.1 lineage (fig. S7), where 84.8%
of observed single-nucleotide polymorphisms
are consistent with APOBEC3 editing (fig. S8).
Observed heptamers around the observed C→T
and G→A mutations show a pronounced en-
richment in TC and GA target sites in the ge-
nomes sampled from 2017 to 2022, in contrast
with the rest of MPXV diversity (Fig. 1C), and
this enrichment is also reflected within line-
age B.1 (fig. S9).
Our analysis highlights that evolution within
clade IIb before the emergence of lineage B.1
mirrors that within lineage B.1 but is distinct
from MPXV clade I or IIa. Since 2022, the B.1
lineage has been sampled and sequenced inter-
nationally in the global epidemic of MPXV.
Lineage B.1 is known to be circulating by sus-
tained human-to-human transmission and as
such, mutations that have accumulated in B.1
can be considered characteristic of this mode
of transmission. We suggest that the APOBEC3-
driven evolution of recent clade IIb MPXV is a
signature of a switch to sustained transmission
within the human population. Within the B.1
lineage, believed to be entirely the result of hu-
man infection and transmission, we continue
to see the same pattern of predominantly
APOBEC3 mutations accumulating at a rate
similar to that seen in A lineage genomes since
2017. It is unlikely that, by chance, MPXV evolved
to become susceptible to APOBEC3 action within
the putative rodent reservoir before the emer-
gence of cases and to retain that susceptibility
to human APOBEC3 molecules once transmitting
in humans. Given that all human cases se-
quenced since 2017 share substantial numbers
of APOBEC3 mutations, including nine on the
stem branch leading to hMPXV-1, it is very un-
likely that these represent multiple zoonotic
introductions. APOBEC3 genes emerged in
placental mammals from a duplication of the
ancestral AID gene and have a dynamic recent
evolutionary past, with gene duplication and
loss across phyla (23, 24). APOBEC3 genes in
primates have undergone recent expansion, with
primate genomes now having seven paralogs
of three ancestral genes (25, 26). Rodents, the
reservoir of MPXV, have only a single functional
APOBEC3 protein, resulting from gene loss and
fusion events (25). Rodent APOBEC3 has been
shown to be expressed preferentially in spleen
and bone marrow, with limited expression ob-
served in other tissues (27, 28).
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Fig. 2. Observed APOBEC3-type mutations are not merely a product of
available target sites. (A) Consequence of hypothetical APOBEC3 mutations
at target dimer site (either the C in the TC target site or G in the GA target site)
in the coding regions of the National Center for Biotechnology Information
reference MPXV genome for clade II (accession NC_063383) and those observed
APOBEC3 mutations across the coding regions of the clade IIb phylogeny
(not including the outgroup branch leading to the 1971 genome sequence). These
are categorized into nonsynonymous (altered amino acid), synonymous (amino
acid remaining unchanged), nonsense (editing producing a stop codon), and
intergenic (not present in a coding sequence). (B) The proportion of target
sites edited for each target site percentile window across the MPXV genome.
The teal shaded regions represent the binomial confidence interval around
observations. Masked regions are indicated by vertical gray bars. Observed
edits include data from the clade IIb phylogeny, with a single representative
of lineage B.1 and not including the branch leading to the outgroup 1971 genome
sequence. (C) Hypothetical amino acid changes for codons overlapping
with TC and GA target sites in a reference MPXV genome (GenBank accession
number: NC_063383) if APOBEC3 edited those dimers to TT and AA. Amino
acid changes are colored by Grantham Score (0–50 conservative, dark blue;
51–100 moderately conservative, light blue; 101–150 moderately radical, light red;
>150 radical, dark red; synonymous, gray). Single-letter abbreviations for the
amino acid residues are as follows: C, Cys; D, Asp; E, Glu; F, Phe; G, Gly;
H, His; I, Ile; K, Lys; L, Leu; M, Met; N, Asn; P, Pro; Q, Gln; R, Arg; S, Ser;
W, Trp; and Y, Tyr. Stop codons are indicated with an asterisk (*).
APOBEC3 has a limited repertoire to generate
variation in the MPXV genome
If we assume this observed evolution within
hMPXV-1 is APOBEC3-driven, this may have
implications for its sustained transmission
in the human population. Considering all GA
and TC dimer sites in the clade II reference ge-
nome (accession number NC_063383)—i.e., those
that could be the target of APOBEC3 editing but
had not been by that point—we assessed what
amino acid changes a deamination mutation
at these sites would bring about (Fig. 2). Of the
23,718 such dimers, 61.6% (14,618) would pro-
duce amino acid replacements, 21% (4990)
would be synonymous, 2.9% (692) would in-
duce stop codons, and 14.4% (3418) would occur
outside of coding regions. For the clade IIb ge-
nomes, of the 633 mutations at these dimers
that did occur, 38.7% (245) were amino acid
replacements and 35.7% (226) were synony-
mous, 4.7% (30) were nonsense, and a further
132 APOBEC3 mutations were in intergenic
regions (20.8%). The probability of getting 226
or greater synonymous mutations out of 663
under a simple binomial distribution with 21.0%
chance of a context being synonymous is P =
7.6 × 10−18. We do not see the same enrichment
for synonymous mutations in the mutations that
are not APOBEC3-like, although the quantity of
these mutations is considerably lower (fig. S10).
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There are also more mutations outside of protein-
coding regions than we would expect based on
the location of target dimers (probability of 4.5 ×
10−6 of getting at least 132 noncoding muta-
tions given that only 14.4% of targets are in
these regions). This supports the hypothesis
that what we observe are the residual least
harmful APOBEC3 mutations after natural
selection has eliminated those with substan-
tial fitness costs to the virus. By comparing the
density of observed C→T and G→A mutations
and the density of APOBEC3 target sites (TC
or GA dinucleotides) across the reference ge-
nome, we see that the distribution of muta-
tions is not simply a product of the availability
Fig. 3. Estimating the time of MPXV emergence into the human population
from the accumulation of APOBEC3-type mutations. (A) MPXV genomes
sampled from human infections from 2017 to 2022, with an outgroup sequence
from an outbreak in Nigeria in 1971 (n = 44 genome sequences, including
outgroup). Lineages indicated as per nomenclature proposed by Happi et al. (7).
Mutations along each branch are indicated with circles colored by whether it is
putatively APOBEC3 edited (TC→TT and GA→AA; red) or whether it is another
mutation type (yellow). The break in the basal branch illustrates the assumption
made in the regression model in panel B, that all APOBEC3 mutations occurred after
emerging into the human population; however, we do not know the precise
distribution of red or yellow mutations. (B) APOBEC3 mutations from MPXV
genomes sampled since 2017. The reconstructed most recent common ancestor
(MRCA) of the panel A phylogeny is used as the root in the root-to-tip plot,
and the y intercept is used as a proxy for time of emergence, which is inferred
by fitting a Bayesian regression to the sequence dates from panel A. Intersects
with y = 1, 2, and 3 are also shown as it is likely that a small number of the
APOBEC3-type mutations are actually earlier replication errors and not
induced by APOBEC3. (C) Maximum clade credibility (MCC) phylogeny of MPXV
clade IIb with absolute time shown on the x axis. We separated the alignment
into an APOBEC3 and a non-APOBEC3 partition and modeled the substitution
process in each independently. We used an epoch model with two outgroup
sequences (not shown) representing the first epoch and hMPXV-1 ingroup
sequences representing MPXV post-emergence into the human population
with an exponential growth model. The probability density distributions show the
estimated time of the most recent common ancestor (tMRCA) of the ingroup
as well as the estimated transition time that represents the time of emergence
into the human population. (D) Estimated effective population size of the
outbreak using a nonparametric coalescent Skygrid model with 11 change points
over a period of 8.5 years. This reconstruction falls within the bounds of the
exponential growth model estimated from the second epoch in panel C,
suggesting that the MPXV population has been exponentially growing since
at least 2016.
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of target sites (Kolmogorov-Smirnov test sta-
tistic = 0.07, P = 0.0002; fig. S11, A and B). When
considering synonymous and nonsynonymous
APOBEC3-like mutations separately, there is
a significant difference between the density
of target sites across the MPXV genome and the
distribution of observed APOBEC3-like synon-
ymous and nonsynonymous mutations, respec-
tively (fig. S11, C and D).
The “repertoire” of mutations that APOBEC3
is able to provide as genetic variation on which
natural selection can act is severely restricted.
Only a limited number of dinucleotide contexts
are present, and the repertoire of amino acid
changes that APOBEC3 editing can induce is
also limited (Fig. 2C and fig. S12). Only 13 dif-
ferent amino acid replacements are possible,
and three that give rise to stop codons, and they
are not reversible by the same mechanism. This
means that given the restricted set of positions
at which these mutations occur and the limited
amino acid changes that they can result in, the
elevated rate will not necessarily facilitate adap-
tation of the virus.
APOBEC3 hypermutation is a host-mediated
antiviral mechanism. These molecules act as
the viral genome is being replicated and single
strands are exposed. During repeated rounds
of replication, either strand can be deaminated,
leading to both C→T and G→A changes on the
positive strand, as seen in this study. Thus, it is
likely that the genomes that are extensively mu-
tated by APOBEC3 will simply not be viable and
will not be transmitted further. MPXV replicates
in the cytoplasm likely by means of rolling-circle
amplification (29), and this facilitates exten-
sive continuous genome replication (30). The
high processivity of this mechanism efficiently
produces high copy numbers of MPXV genome
molecules in the cell, potentially saturating the
APOBEC3 enzyme action if the concentration
of MPXV DNA molecules is high enough. This
likely means that many MPXV genomes are un-
affected by APOBEC3 action. Occasionally, how-
ever, a genome, modestly mutated by APOBEC3,
may remain viable and be transmitted. We see
this in the enrichment of observed synonymous
and intergenic mutations relative to available
targets in the MPXV genome. Given the non-
reversibility of the APOBEC3 action, sustained
evolution within the human population may
result in a depletion of lower-consequence target
sites (i.e., synonymous or conservative amino
acid changes) and thus expedite a decrease in
fitness of MPXV over time. This could be both
through a reduction in the number of viable
offspring viruses produced by infected cells and
as a result of the accumulation of moderately
deleterious mutations by genetic drift (i.e., mu-
tation load). However, the timescale on which
this might happen is uncertain and other evolu-
tionary forces such as recombination may act to
restore fitness, and we do not address this fur-
ther in this study. A further uncertainty arises
when considering the variable repertoire of
genes associated with virus infectivity or host
immune modulation in poxvirus genomes. Mu-
tations that alter or abrogate the function of
these genes may have little direct effect on virus
replication machinery but may disrupt the
virus–host interaction. There is precedent for
the naturally occurring inactivation of genes
in VARV contributing to host specificity, and
consequently the loss of function of some MPXV
genes through APOBEC3 activity may poten-
tially have adaptive value for the virus as it repli-
cates and transmits in a new host (31, 32).
Even if the mutations that accumulate through
this process are simply the neutral residue of a
suboptimal antiviral host defense, they have
produced sufficient variability for the phyloge-
netic analysis of the epidemic over the short term.
The initial lineages proposed by Happi et al. (7)
have expanded with the 2022 epidemic B.1
lineage now encompassing 17 sublineages at the
time of writing (33). The rapid and temporally
linear accumulation of mutations means that
genomic epidemiological models and tools
(34, 35), usually used for RNA viruses, may also
have utility for hMPXV-1.
The linear accumulation of APOBEC3-type
mutations since the emergence and spread
of MPXV in humans
Since 2017, the genomes thus far sampled from
clade IIb have accumulated APOBEC3-type
single-nucleotide mutations approximately
linearly over time (Fig. 3, A and B; labeled phylog-
eny in fig. S13). We applied Bayesian regression
analysis on the root-to-tip plot of sequences in
Fig. 3A, which includes one representative B.1
genome, and also separately on the B.1 lineage
(B.1 phylogeny in fig. S1) (20). To ensure that the
elevated temporal signal is specific to APOBEC3
data, we show combinations of APOBEC3 and
non-APOBEC3 mutations on clade IIb data in
fig. S14. The estimated rate of accumulation was
6.18 per year (95% credible intervals of 5.20,
7.16). For the B.1 lineage, the rate was 5.93
per year (2.95, 8.92), suggesting that despite
widespread and rapid transmission within MSM
(men who have sex with men) networks, the rate
of accumulation of APOBEC3 mutations re-
mained the same as it did for the rest of clade
IIb. It is notable that the regression line for B.1
lies substantially above that for the rest of clade
IIb, suggesting that this lineage accumulated
more mutations than expected before the
emergence of B.1. However most of these mu-
tations are also present in the genome from
Maryland, USA (accession number ON676708)
from November 2021 (10), indicating that they
arose and circulated for some months before
the B.1 epidemic (figs. S15 and S16). Extrapolat-
ing back to when the APOBEC3-type mutations
started to accumulate provides an estimate of
when the first APOBEC3 mutations occurred in
the stem of the branch leading to the 2017
epidemic. If we assume that all these mutations
are due to APOBEC3 in humans, then we esti-
mate this date of emergence to be 20 June 2015.
However, we expect a few APOBEC3-like muta-
tions to actually be due to replication errors
during the earlier preemergence epoch. The num-
ber of mutations that we ascribe to this period
will affect our estimate linearly—i.e., if three
mutations were not due to APOBEC3, then the
estimate would shift to 14 December 2015.
To accommodate this uncertainty in our es-
timates, we have developed a more explicit
model of APOBEC3-mediated evolution in the
BEAST software package (20, 34). We estimate
that the action of APOBEC3 on the MPXV pop-
ulation is driving evolution ~28 times faster
than the background evolutionary rate (fig. S17).
Gigante et al. (10) also described an elevated
overall rate of evolution in the A lineage but
did not decompose the APOBEC3 and non-
APOBEC3 contribution to this. The time of the
most recent common ancestor of the post 2017
genomes is estimated to be 23 February 2016
(28 June 2015, 28 September 2016), with the
transition to sustained human-to-human trans-
mission estimated to be 14 September 2015
(21 August 2014, 31 July 2016; Fig. 3C and fig.
S17). Unlike the assumption in Fig. 3B that all
APOBEC3 mutations occurred after emergence,
the BEAST analysis estimates the transition
point integrating over all possibilities. This
allows for the fact that a few of the APOBEC3-
like mutations may actually be due to replica-
tion errors in the earlier evolutionary epoch
and this might explain the slightly more recent
date. We also see evidence of exponential
growth in the number of infections in the epi-
demic before the emergence of lineage B.1 in
2022 (Fig. 3D), despite the decline in cases
reported in 2020 (fig. S1C), albeit the growth
rate is relatively slow, which reinforces the indi-
cation from the demographics of the cases that
this is not a generalized epidemic.
Implications for the global public health
response to mpox cases
Since the identification of the B.1 lineage, a
number of countries have reported other line-
ages that lie outside the diversity of B.1, in-
cluding the United States, United Kingdom,
Portugal, India, and Thailand. In almost all
instances, these cases are reported as having
a history of international travel. The lineages
in which these are placed (designated as A.2.1,
A.2.2, A.2.3, and A.3) can all be phylogenet-
ically traced back to the epidemic in Nigeria
(Fig. 3A). This suggests that at least one in-
stance of sustained human-to-human transmis-
sion is still ongoing outside of the recognized
MSM networks that were the focus of the 2022
global epidemic. Stopping transmission in these
communities, though necessary, will not be
sufficient to eliminate the virus as a human
epidemic. Many countries lack the surveillance
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to detect MPXV cases, and if sustained human-
to-human transmission has been ongoing
since 2015–2016, it is plausible that there are
other populations that are currently enduring
epidemics.
Historically, mpox was considered a zoonotic
disease, and cases have been treated as inde-
pendent spillover events with low levels of cir-
culation in the human population. Thus far,
this continues to be an accurate characteriza-
tion of clade I in Central Africa. For clade IIb,
although some non-B.1 lineage cases may be
new zoonotic infections, most cases since 2016
are likely the result of human-to-human trans-
mission. Although the B.1 lineage across
the world is now diminished—though not yet
eradicated—the human epidemic from which
it arose continues unabated. It is critical that
global public health affords MPXV cases in
countries that are historically considered to
have endemic reservoir species equal attention
and concern to those elsewhere. Surveillance
needs to be global if MPXV is to be eliminated
from the human population and then prevented
from reemerging.
RE FE RENCES AND N OT ES
1. NCDC, “An Update of Monkeypox Outbreak in Nigeria” (Nigeria
Centre for Disease Control, 2017), (available at https://ncdc.
gov.ng/diseases/sitreps/?cat=8).
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ACKN OWLED GMEN TS
We thank those involved in sequencing MPXV genome sequences
and shared data online rapidly, facilitating rapid public health
responses, and also those who have continued to contribute to
open science by sharing their data in open access platforms such
as GenBank. We have provided all data and scripts related to this
manuscript on Zenodo (36). Funding: Wellcome Trust ARTIC
(Collaborators Award 206298/Z/17/Z, ARTIC network) (Á.O.T.,
P.L., M.A.S., A.R.); European Research Council (grant agreement
no. 725422 – ReservoirDOCS) (P.L., M.A.S., A.R.); National
Institutes of Health (R01 AI153044) (P.L., M.A.S., A.R.); David and
Lucile Packard Foundation (M.W.); Research Foundation, Flanders–
Fonds voor Wetenschappelijk Onderzoek–Vlaanderen, G066215N,
G0D5117N and G0B9317N (P.L.); HORIZON 2020 EU grant 874850
MOOD (P.L.); HERA project (grant/2021/PHF/23776) supported
by the European Commission through the European Centre for
Disease Control and Prevention (V.B. and J.P.G.). Crown Copyright
© 2023. The Nigeria Centre for Disease Control and Prevention
receives core funding from the Nigerian government. Author
contributions: Conceptualization: Á.O.T., A.R.; Methodology: Á.O.T.,
R.N., A.R.;
Investigation: N.N., V.B., B.G., J.P.G., N.G., D.K., D.M., K.L.,
R.M., I.F.O., M.W.; Visualization: Á.O.T., R.N., A.R.; Funding acquisition:
A.R., P.L., M.S., M.C., C.I., D.U., I.A.; Supervision: D.U., I.A., A.R.;
Writing–original draft: Á.O.T., R.N., P.L., M.S., M.W., A.R.; Writing–
review and editing: Á.O.T., R.N., N.N., V.B., B.G., J.P.G., N.G., D.K., D.M.,
P.L., K.L., N.L., R.M., I.F.O., M.S., M.W., M.C., C.I., D.U., I.A., A.R.
Competing interests: The authors declare that they have
no competing interests. Data and materials availability: Data, code,
and materials used in the analysis are available from Zenodo (36).
Tables S1 and S2 include details of accession numbers and author
lists for all source genome sequence data used. All except a single
genome sequence were sourced from GenBank on NCBI. Data
partitions of the alignments have been included in the XML files on
Zenodo and GitHub for ease of reproduction. A single sequence
was sourced from GISAID (gisaid.org) and as such was removed
from the XMLs. Supplementary tables include the GISAID identifier,
which can be used to independently source the data, and
instructions for constructing the alignment and addition to the XML
are included. License information: Copyright © 2023 the authors,
some rights reserved, including, where applicable, UK Crown
copyright licensed under the Open Government License v.3.0;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse. In the
interest of rapid dissemination of results with immediate public
health relevance, and because this research was funded in whole
or in part by the Wellcome Trust (Collaborators Award 206298/Z/17/Z,
ARTIC network), a cOAlition S organization, the author will make
the Author Accepted Manuscript (AAM) version available under
a CC BY public copyright license.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg8116
Materials and Methods
Figs. S1 to S17
Tables S1 to S4
References (37–40)
MDAR Reproducibility Checklist
Submitted 23 January 2023; resubmitted 1 June 2023
Accepted 21 September 2023
10.1126/science.adg8116
O’Toole et al., Science 382, 595–600 (2023)
3 November 2023
6 of 6
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10.1126_science.adg2657
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RES EARCH
CHIRAL MATERIALS
A magnetic assembly approach to
chiral superstructures
Zhiwei Li†, Qingsong Fan, Zuyang Ye, Chaolumen Wu, Zhongxiang Wang, Yadong Yin*
Colloidal assembly into chiral superstructures is usually accomplished with templating or lithographic
patterning methods that are only applicable to materials with specific compositions and morphologies
over narrow size ranges. Here, chiral superstructures can be rapidly formed by magnetically assembling
materials of any chemical compositions at all scales, from molecules to nano- and microstructures. We
show that a quadrupole field chirality is generated by permanent magnets caused by consistent field
rotation in space. Applying the chiral field to magnetic nanoparticles produces long-range chiral
superstructures controlled by field strength at the samples and orientation of the magnets. Transferring
the chirality to any achiral molecules is enabled by incorporating guest molecules such as metals,
polymers, oxides, semiconductors, dyes, and fluorophores into the magnetic nanostructures.
S uperstructures of colloidal particles can
assemble with chiral symmetry (1–5).
The driving force for chiral assembly is
that the particles or structures are intrin-
sically chiral or rendered so with ad-
sorbed surface molecules and templates that
create chirality (usually helical structures) or
by lithographic methods (6–8). Chiral super-
structures, especially those made from plas-
monic nanoparticles, have distinctive optical
properties such as circular dichroism (CD)
under circularly polarized light excitation
(9–14) and have the potential for developing
electric and optical sensors and devices (15–20).
Templated assembly and lithography have
been used to create chiral superstructures
for sensing external stimuli through changes
in CD spectra (21, 22). For example, DNA-
templated assembly can transfer the helical
configuration of DNA templates to many nano-
structures (23–26) and be used to monitor
changes in temperature and chemical bind-
ing (27–31).
Controlling the collective orientation of
these chiral structures in either solution or
solid matrices remains challenging for optimiz-
ing chiroptical performance. Additionally, the
existing strategies such as templated assem-
blies and chiral superlattice formation only
work for materials of narrow length scales and
specific chemical compositions or shapes
(32–34). Designing miniature chiroptical de-
vices and understanding light-matter interac-
tions that involve distinct physical principles
would benefit from a general approach for
assembling achiral materials of diverse sizes,
shapes, and chemical compositions into chiral
superstructures with actively tunable chiroptical
responses (35–37).
Department of Chemistry, University of California, Riverside,
CA 92521, USA.
*Corresponding author. Email: yadong.yin@ucr.edu
†Present address: Department of Chemistry and International
Institute for Nanotechnology, Northwestern University, Evanston, IL
60208, USA.
Here, we report the rapid and reversible
assembly of materials of varying compositions
and length scales, from small molecules to
nano- and microstructures, into chiral struc-
tures, and the active tuning of the structural
handedness, collective orientation, and chirop-
tical properties by using the magnetic field of
a permanent magnet. Our analytical model
demonstrates the presence of a quadrupole
field chirality in the gradient magnetic field
of the magnet. Assembling nanorods in such
a magnetic field led to the formation of chiral
superstructures, with their handedness and
chiroptical properties being determined by
magnet position and orientation. The struc-
tural chirality could be transferred to organic
molecules and inorganic compounds by dop-
ing into or coating onto the host magnetic
building blocks, demonstrating a general
approach to chiral superstructures.
The quadrupole field chirality of
permanent magnets
We consider the magnetic field and field dis-
tribution of a cube-shaped permanent mag-
net (fig. S1), with the north pole of the magnet
pointing upward in fig. S1A. The calculated
azimuth of the local magnetic field (mapped in
Fig. 1A) undergoes gradual changes in the field
direction in each quadrant. A differential
magnetic field was calculated by subtracting
magnetic field vectors in two chosen yz cross
sections (fig. S2). In Fig. 1B, the resulting local-
field rotation is indicated by the black arrows,
and the magnitude is color mapped, with the
rotation angle (Dw) being defined as the dif-
ferences between the azimuth of the magnetic
fields in the two cross sections. The differential
field forms a quadrupole, with two left-handed
(positive Dw in red domains) and right-handed
(negative Dw in blue domains) magnetic field
domains. Figure S3 further delineates the
rotation of local fields along a chosen path-
way, demonstrating the helical magnetic field
distribution.
We developed an analytical model to under-
stand the assembly of magnetic nanorods in
such a chiral field (supplementary materials)
that could predict magnetic nanorod align-
ment along the local field to form chiral
superstructures (Fig. 1C and fig. S4). For small
magnetic nanorods (107.6 ± 5.2 nm in length
and 13.0 ± 1.7 nm in diameter), there were no
obvious CD signals in rod dispersion without a
magnetic field or in a magnetic field along
the x axis (Bx), but changing the field direc-
tion from the x axis to the y and z axes cre-
ated CD responses (Fig. 1, D and E). We
observed positive and negative CD peaks of
similar intensity for y (By) and z fields (Bz),
respectively, which suggested chiral super-
structures with opposite handedness. The CD
responses were then measured in an aqueous
solution of glycerol (n = 1.475) with an in-
creasing volume ratio from 0 to 100%. The
increase in effective refractive index (n) of
the solution induced consistent CD-intensity
decrease under the same magnetic fields
(fig. S5). The nanorods’ CD signal weakened
but did not disappear as the solution refractive
index approached that of the silicon dioxide
(SiO2) layers (n = 1.475 ± 0.005) (38). This
refractive index–matching experiment demon-
strates that both the scattering and absorption
of the nanorods contribute to the overall CD
responses. We calculated an optical anisotropic
factor (g factor) of ~0.01 at 400 nm (fig. S6). To
verify the formation of chiral superstructures,
cyanine 3–doped Fe3O4@SiO2 core-shell nano-
rods (322.2 ± 16.5 nm in length, 70.2 ± 4.7 nm in
diameter, and 50.3 ± 1.5 nm in silica thickness)
were used as magnetic building blocks (39, 40)
and fixed in a polymer by photocuring under a
uniform magnetic field. Linear chains were
formed because of magnetic dipole-dipole
interactions and were parallel to the uniform
field with a standard deviation of 0.36° to
minimize the demagnetizing fields (figs. S7
and S8) (41). If a gradient field of a perma-
nent magnet (cube shape, 12 mm in edge
length) was used (fig. S9), the chain alignment
within one yz plane and the chain rotation
between different yz planes were determined
by the local magnetic fields and field rotation,
respectively (figs. S10 and S11). Thus, the chiral
superstructures made of large nanorods show
similar CD responses to magnetic fields (fig.
S12). Additionally, we characterized the chain
alignment in 10 sequential yz layers from x = 1 to
10 mm and in five layers along the y axis using
optical and electron microscopy, confirming the
chain rotation into chiral superstructures as
driven by the quadrupole chiral field (figs. S13
to S17).
Magnetic assembly and active tuning of
plasmonic chiral superstructures
To systematically study the CD dependence
on magnetic fields over a wide spectral range,
Li et al., Science 380, 1384–1390 (2023)
30 June 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. The quadrupole field chirality of a
permanent magnet. (A) Normalized magnetic
field (white arrows) and field-vector azimuth
(color maps) of a permanent magnet (high-
lighted in the middle square) with a cubic
shape and edge length of 2 cm. (B) The field
rotating vectors (black arrows) and field angle
changes (color map) of the magnetic field
along the x axis. Positive rotation angles (Dw)
represent clockwise left-handed rotation of the
magnetic field, and negative rotation angles
represent counterclockwise right-handed field
rotation. deg, degree. (C) Schematic illustra-
tion of the magnetic assembly during CD
measurement and simulated helical super-
structures assembled from magnetic nanorods
under such a chiral magnetic field. (D) Extinction
spectrum and (E) CD spectra of Fe3O4@SiO2
nanorods under different magnetic fields.
Arbitrary units, a.u.; mdeg, millidegree.
A
0
)
m
c
(
Z
-1
-2
-3
90
-90
-4
-3
-2
-1
1
2
3
0
Y (cm)
C
z
x
0o
180o
y
k
x
(0,1,-0.75)
z
x
z
y
B
0
)
m
c
(
Z
−2
(deg)
6.10
−4
−3
−2
−1
0
1
2
3
−6.10
Y (cm)
D
E
n
o
i
t
c
n
i
t
x
E
)
.
.
u
a
(
3
2
1
0
300
)
g
e
d
m
(
D
C
900
0
-900
300
450
600
Wavelength (nm)
750
900
no magnet
By
600
Wavelength (nm)
450
750
Bx
Bz
900
we introduced Fe3O4/Au hybrid nanorods as
building blocks by taking advantage of the
localized surface plasmon resonance (LSPR)
of Au nanorods and the magnetic responses
of Fe3O4 nanorods. The Au nanorods were
synthesized with a space-confined growth
method and had a length of 156.6 ± 15.2 nm
and a diameter of 48.9 ± 4.7 nm (42, 43). As
shown in fig. S18A, Fe3O4@SiO2 nanorods
were introduced (107.6 ± 5.2 nm in length,
13.0 ± 1.7 nm in diameter, and 5.0 ± 0.5 nm in
silica thickness) as initial templates, followed
by Au seed attachment (~2.0 nm in diameter).
During polymer coating, the SiO2 shells were
etched away, and defined gaps were formed
between the Fe3O4 nanorods and polymer
shells. Seeded growth was performed inside
the gaps to prepare the hybrid nanorods, which
comprise one Au nanorod and one Fe3O4
nanorod in a parallel configuration, as shown
in the transmission electron microscopy (TEM)
images (Fig. 2A) and elemental mapping (fig.
S19). Because of the confinement of the poly-
mer shells, radial growth was limited, and
preferable longitudinal growth produced the
Au nanorods. This growth mode allows easy
tuning of the nanorod length (fig. S18, B to E)
and shifts the LSPR of the Au nanorods from
560 to 880 nm (fig. S18F). The parallel align-
ment of the hybrid nanorods allowed the Au
nanorods to assemble into chiral superstruc-
tures under a chiral magnetic field and pro-
duce CD responses (fig. S20, A and B). Switching
the magnet dipole did not alter the CD profile,
but changing the magnet position to the
opposite side of the sample produced a CD
spectrum with an opposite sign (fig. S20C).
Applying two identical magnets in their at-
traction configuration generated a parallel
magnetic field with a reduced field gradient
between the two magnets and reduced the CD
signals (fig. S20, D and E). The disappearance
of CD signals confirmed that linear super-
structures assembled in a uniform magnetic
field could not produce CD signals in our ex-
perimental conditions. We also fixed the hybrid
nanorods under the absence and presence of
uniform and chiral magnetic fields using a
photocuring polymerization method, which
produced random, linear, and chiral struc-
tures, respectively. Although films containing
random and linear structures were not op-
tically active, the film with chiral superstructures
had CD signals. None of the three structures
showed evident responses to a magnet once
fixed in polymer films (fig. S21). These exper-
iments suggested that the observed CD re-
sponses in a single permanent magnet were
not induced by extrinsic chirality, a CD pro-
perty of achiral superstructures (44), or by mag-
netic circular dichroism (45).
We measured the CD spectra of Au nano-
rods while changing the position of the mag-
net vertically (Fig. 2B and fig. S22, A and B).
The CD signal declined gradually after the
magnet was moved from −1.25 to 0 cm along
the z axis (vertical direction) (fig. S22, C and
D), and the spectra changed the sign across
0 cm (Fig. 2C) in response to the field chirality
changes shown in fig. S22, E and F. The
dependence of CD signals on magnet posi-
tion was similar when the magnet dipole was
along the z axis (fig. S23). Changing the samples’
position relative to the magnet was equivalent
but induced a decrease in CD intensity when
the sample-magnet separation increased up to
3.0 cm along the x axis (fig. S24). The CD
spectra of Au nanorods were then measured
by decreasing field strength from 31.2 to 25.1,
18.3, 12.9, and 5.5 mT, which corresponded to
the magnet being 2.3, 2.5, 3, 4, and 5 cm away
from the nanorod dispersion. We observed a
consistent decrease in CD intensity for Au
nanorods with different LSPR positions and
for left- and right-handed chiral superstructures
(Fig. 2, D and E, and fig. S25), which cor-
responded to the decrease in field rotation
when the magnet departed the sample (Fig. 2F).
Detailed field analysis (Fig. 2, G to J) indicated
that the Dw decreased consistently in the four
chiral domains for increasing magnet-sample
separation. The sample in the first quadrant
was in a left-handed field in the By field (Fig. 2,
G and H), which caused the negative signals in
CD spectra. In the Bz field, the chiral field in the
first quadrant produced positive CD signals
(Fig. 2, I and J). The peak intensities of ex-
tinction and CD of the hybrid nanorods were
linearly proportional to Au concentration at
fixed magnet and sample positions (fig. S26),
which was consistent with Beer’s law and
molar ellipticity in CD. To verify the chirop-
tical properties, we modeled the chiral super-
structures and calculated their CD spectra using
a finite element method. The simulated spectra
in fig. S27 demonstrated CD responses of Au
nanorods with large separations. Considering
the lack of nanorod positional order in exper-
iments, complex models were further developed
to resolve the structures in figs. S15 and S17.
These models contain nanorods with random
Li et al., Science 380, 1384–1390 (2023)
30 June 2023
2 of 7
RES EARCH | R E S E A R C H A R T I C L E
A
B
Fe3O4/Au
z
(0,2.5,1.25)
(0,2.5,0)
50 nm
Polymer
(0,2.5,-1.25)
1.25 cm
-1.25 cm
C
400
200
0
-200
)
g
e
d
m
(
D
C
y
k
x
D
)
g
e
d
m
(
D
C
400
300
200
100
0
-100
-200
-300
-400
31.2 mT
25.1 mT
18.3 mT
12.9 mT
5.5 mT By
5.5 mT Bz
12.9 mT
18.3 mT
25.1 mT
31.2 mT
200 300 400 500 600 700 800 900
Wavelength (nm)
G
)
g
e
d
(
3
0
H
−3
0
−2
)
m
c
(
Z
E
n
e
y
p
B
r
e
P
l
a
c
z
i
t
B
r
e
V
7
6
5
4
3
2
1
1
2
3
4
5
6
7
-455.0
F
)
g
e
d
m
(
D
C
5.5
12.9 18.3
25.1
31.2
Field Strength (mT)
455.0
I
)
g
e
d
(
3
0
−3
0
−2
J
)
m
c
(
Z
-400
200 300 400 500 600 700 800 900
Wavelength (nm)
2.3 cm
3 cm
5 cm
6.1
−4
−6
−4
−2
0
Y (cm)
2
4
6
−4
−6
−4
−2
2
4
−6.1
6
0
Y (cm)
Fig. 2. Magnetic assembly of Fe3O4/Au hybrid nanorods into chiral super-
structures. (A) TEM image of the Fe3O4/Au hybrid nanorods wrapped within polymer
shells. (Inset) Schematic structure of the Fe3O4/Au hybrid nanorods. (B) Schematic
illustration of the magnet position during the CD measurement. (C) CD spectra of
the hybrid nanorods measured by changing the magnet position. (D) CD spectra of the
hybrid nanorods under magnetic fields with consistent direction and decreasing
strength. (E) Dependence of CD intensity on the field strength and the rod aspect
ratios. The magnetic fields are defined as By and Bz when the magnet dipole is parallel
to y and z axis, respectively. (F) Simulated field distributions of the cubic
magnet at given distances to the magnet surface. (G and I) Rotation angles
of magnetic fields between two yz cross sections, (–0.2, y, z) and (–0.8, y, z). The
orientation of the magnet is shown in the inset in each plot. (H and J) The
corresponding field rotation angles (color map) and the local magnetic field at
the cross section (–0.2, y, z). The magnet has a horizontal magnetic dipole in (G) and
(H) and a vertical magnetic dipole in (I) and (J). The field rotation is calculated
by Dw(y, z) = w(–0.8, y, z) − w(–0.2, y, z).
positions but constant rotation in different
planes (fig. S28), resembling the nanorod align-
ment in different cross sections in the SEM im-
ages. The simulated CD spectra show rotation
angle–dependent CD responses, which explains
the decrease of CD intensity with the rotation
angles of magnetic fields. We also observed
similar dependence in nanorods of increas-
ing aspect ratios, and the continuous redshift
of CD peaks in fig. S29 is qualitatively consistent
with the measured CD spectra in fig. S25.
Changing the directions of the magnetic
field produced more complex CD responses.
We considered the rotation of the magnet
within the xy and yz planes to explain the
involved mechanisms (Fig. 3A). The alignment
of the magnetic dipole of the magnet relative
to the axes was defined by the azimuth angle
q. The CD spectra showed intensity changes
when q increased to 180° in the xy plane (Fig.
3B), which increased to a saturated value and
decreased again (fig. S30). Given that the
magnet was rotated in the xy plane (fig. S31),
the local magnetic fields and the field distri-
bution were analyzed for different q values.
The schemes in fig. S31 illustrate the magnet’s
constant position and varying orientation.
Because the incident light was along the
x axis, the magnetic fields within the mea-
sured domains in the yz and xz planes were
further plotted in Fig. 3, C and D, respectively.
We observed only slight changes in field di-
rection and field distribution within the yz
plane for different magnet orientations (Fig.
3C). In the xy planes, however, the field dis-
tribution exhibited dramatic changes when q
increased to 90°, which led to excitation of
longitudinal mode with gradually increased
strength (Fig. 3D). For incident light along
the x axis, the plasmonic excitation of Au nano-
rods was determined by and could be predicted
from the nanorod alignment, light incidence,
and light polarization (46). Because of the
changes in magnetic field direction and dis-
tribution shown in fig. S32, there was an
associated change in the LSPR excitation of the
Au nanorods when q increased to 90°. At 0°, the
field was nearly parallel to the x axis, and
the resulting parallel alignment of nanorods
to the incident light suppressed the longitu-
dinal mode. At 90°, the magnetic field being
nearly parallel to the z axis led to the exci-
tation of the longitudinal mode. We could
predict the longitudinal extinction of the
Au nanorods through the equation sin2(ϕ),
where ϕ is the angle between the local-field
direction and the light incident direction.
Figure 3E shows a symmetric trend with maxi-
mum extinction between 60 and 120°. Compar-
ison of the predicted longitudinal extinction
Li et al., Science 380, 1384–1390 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
C
D
y
y
0o
x
z
in x-y
y
in y-z
x
k
(0,-2,-0.5)
z
z
0o
y
y
48.00
B
180
150
120
90
60
30
)
g
e
d
(
l
e
g
n
A
0
200 300 400 500 600 700 800 900
Wavelength (nm)
-147.0
0.5
0.0
)
m
c
(
Z
-0.5
-1.0
0.5
)
m
c
(
Z
0.0
-0.5
-0.5
-0.5
Y (cm)
0.0
-1.0
-0.5
Y (cm)
0.0
-1.0
-0.5
Y (cm)
0.0
-1.0
-0.5
Y (cm)
E
-35
-90
0.0
F
1
0
)
g
e
d
m
(
D
C
50
0
-50
-100
-150
0.0
X (cm)
0.5
-0.5
0.0
X (cm)
0.5
-0.5
0.0
X (cm)
0.5
-0.5
0.0
X (cm)
0.5
690 nm
535 nm
0
30
60
90
120
150
180
Angle (deg)
Fig. 3. Tunable CD spectra of the assembled superstructures. (A) Schematic
illustration of the azimuth changes of a cubic permanent magnet within the xy
and yz plane during CD measurements. (B) CD spectra of the hybrid nanorods
measured by changing the magnet azimuth in the xy plane. (C and D) The
magnetic field of the cubic magnet in (C) yz and (D) xz planes. The azimuth
of the magnet is 0° to 30°, 60°, and 90° from left to right. (E) Predicted
longitudinal extinction of the nanorods based on the analytical solution.
(F) Dependence of the CD intensity on magnetic field q.
with the CD intensity measured at different q
(Fig. 3F) suggested that CD intensity would
depend on the magnet q and that the CD
responses of the assembled superstructures
would be determined by the longitudinal ex-
tinction changes when the magnet azimuth
increased within the xy plane.
Changing the magnet azimuth in the yz
plane altered the field chirality and led to a
different CD response. The measured CD spec-
tra are shown in fig. S33. The CD peaks at 545
and 698 nm simultaneously switch their signs
at about 20° and 110° during the measurement
(Fig. 4A, color map), which suggested changes
in handedness of the assembled superstruc-
tures. To verify this hypothesis, we used the
analytical model to directly map the local-field
rotation direction, chirality, and handedness
(fig. S2). At q = 0°, the sample was 2 cm away
from the magnet center with an upward off-
set of 0.5 cm, which led to an azimuth of
~14° relative to the magnet center (fig. S34).
Understanding the CD spectrum at q = 0° re-
quired access to field properties at this spe-
cific sample location in the yz plane.
The CD changes in response to magnet ro-
tation were studied by analyzing the local-
field properties in different q. In Fig. 4B, the
plots of field distribution and field chirality
within the yz plane showed a similar quadru-
pole field chirality. The normalized field vectors
at x = –0.2 and –0.8 cm were superimposed
in Fig. 4B to illustrate local-field rotation. The
field rotation angles along a trajectory high-
lighted in fig. S34C are shown in Fig. 4C,
which correspond to the field changes during
experimental measurement. The Dw was ini-
tially positive but changed its sign at q = 15°
and 105°, which is consistent with the experi-
mental chirality-transition angles plotted in
Fig. 4D. The Pearson correlation coefficients
between the field rotation angles and CD
intensity at 698 and 545 nm are –0.989 and
0.987, respectively (fig. S35). The strong negative
and positive correlation indicates that the field
chirality changes could explain the dependence
of the superstructure handedness and CD spec-
tra on magnet rotation in the yz plane.
Optical rotatory dispersion
We also studied the optical rotatory disper-
sion (ORD), which measures the polarization
rotation of a linearly polarized light. Left- and
right-handed circularly polarized light interacts
differently with chiral structures and travels
at different speeds inside of them. Because
linearly polarized light comprises two circu-
larly polarized light beams with the same
magnitude but opposite handedness, these
two highly correlated beams will develop a
phase difference, leading to the polarization
rotation of the incident beam (Fig. 4E). The
ORD effect was tested by applying an analyzer
to the incident beam and observing the color
changes. Only light of a specific wavelength
can pass through the analyzer at a polarization
angle (a) when the material is optically active.
Experimentally, a is defined as the angle
between the analyzer polarization direction
and the horizontal baseline, and the polariza-
tion of the polarizer is fixed along the vertical
direction.
Digital images of a nanorod dispersion are
shown in Fig. 4F, before (left) and after (right)
application of a z-directional magnetic field at
a = 3°. The original dispersion appeared dark
without noticeable colors because only mini-
mal light could transmit through the analyzer.
Under a z-directional magnetic field, the top
domain turned yellow, and the bottom turned
red, demonstrating the formation of chiral
superstructures with opposite handedness
in these two domains, which is consistent
with the predicted field chirality in the first
Li et al., Science 380, 1384–1390 (2023)
30 June 2023
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1
0
-1
-2
-3
-4
-5
-3
-2
-1
0
Y (cm)
1
2
3
C
6.1
D
)
g
e
d
m
(
D
C
200
100
0
-100
-200
-300
−6.1
698 nm
545 nm
0
30
60
90
120 150 180
Angle (deg)
-30o
-27o
-24o
-21o
-18o
-15o
-12o
-9o
-6o
-3o
0o 3o 6o 9o 12o 15o 18o 21o 24o 27o 30o
RES EARCH | R E S E A R C H A R T I C L E
A
)
g
e
d
(
l
e
g
n
A
180
150
120
90
60
30
B
180.0
)
m
c
(
Z
0
200 300 400 500 600 700 800 900
Wavelength (nm)
-255.0
E
Polarizer
z
G
Analyzer
α
x
F
y
(Bz)
w/o mag
w/ mag (Bz)
By
Bz
Bx
No
Fig. 4. Tunable CD spectra and optical rotatory dispersion of the assembled
superstructures. (A) CD spectra of the hybrid nanorods measured by changing the
magnet azimuth in the yz plane. (B) The magnetic field rotation (color map) and
the normalized field vectors (arrows) of the cubic magnet. The magnetic field
rotation is calculated by Dw(y, z) = w(–0.8, y, z) – w(–0.2, y, z). The normalized
magnetic field vectors in (–0.8, y, z) are indicated with black arrows, and the field
vectors in (–0.2, y, z) are indicated with orange arrows. (C) Dependence of field
rotation on the magnet field azimuth. (D) Dependence of the CD peak intensity
on the magnet field azimuth. (E) Schematic illustration of the ORD measurement.
The a is introduced as the angle between the polarization direction of the analyzer
and the horizontal direction. (F) Digital images of a hybrid nanorod dispersion in
a cuvette without (w/o mag) and with (w/ mag) a magnetic field. The a is 3°.
(G) Digital pictures of the hybrid nanorod dispersion under different magnetic field
conditions. The analyzer’s a was switched from –30 to 30° during the measurement.
and fourth quadrants of the magnet. This
ORD effect was determined by superstruc-
ture handedness and the angle a. Under a
z-directional magnetic field, we observed sim-
ilar two-color domains when a increased from
–30 to 30° (Fig. 4G), with red-orange-yellow-
green changes in the top domain and oppo-
site color changes in the bottom domain.
Changing the magnetic field to the y axis led
to color switching between the two domains,
corresponding to a field chirality transition.
Nanorod dispersion under the absence and
presence of the x-directional magnetic field
only exhibited contrast changes at different a
because of the negligible CD responses at these
two conditions.
Generalizing the all-scale chiral assembly
The chirality formed by nanoscale magnetic
assembly could be transferred to organic
molecules, polymers, oxides, and semiconduc-
tors. These guest materials were introduced to
the magnetic nanorods through surface-coating
and doping methods, which have the advan-
tages of wide material accessibility and easy
further processing. Starting with Fe3O4@SiO2
nanorods with a length of 107.6 ± 5.2 nm, a
diameter of 13.0 ± 1.7 nm, and silica thickness
of 5.0 ± 0.5 nm, we coated their surface with
Cu2O nanoparticles and resorcinol-formaldehyde
(RF), with the latter being converted into MnO2
by reacting with KMnO4 (47–49). The resulting
Fe3O4@SiO2@MnO2 nanorods (Fig. 5A) under-
went oxidation-induced volume expansion and
created nanogaps between porous MnO2 nano-
shells and Fe3O4@SiO2 cores. The extinction
spectra of these samples in Fig. 5B showed
broad extinction of Fe3O4@SiO2 and Fe3O4@
SiO2@Cu2O nanorods, and extinction peaks of
Fe3O4@SiO2@RF and Fe3O4@SiO2@MnO2
nanorods. These four samples showed evident
CD activities under magnetic fields that can
also be tuned by changing the field directions
(Fig. 5C). The CD peak positions being near
their extinction peak positions indicates that
the chirality in the superstructures transferred
from the host nanorods to the guest mole-
cules. In addition, changing the field direction
from the y axis to the z axis changed the chiral
superstructures from left-handed to right-handed
symmetry.
Transfer of chirality to small molecules was
demonstrated by doping organic dyes into RF
polymeric shells through electrostatic inter-
actions. Figure S36A shows a typical TEM
image of the Fe3O4@SiO2@RF nanorods with
100-nm RF shells that carry negative charges
after a condensation reaction. We chose three
dyes—methylene blue, methylene green, and
neutral red—and their molecular structures
are given in fig. S36B. These dyes develop
positive charges after dissociation of chloride
anions in water and can be doped into porous
RF shells by mixing with the nanorods at room
temperature. The dyed solutions appeared
blue, green, and red after removing the excess
molecules, with extinction spectra exhibiting
distinct peaks after successful doping (Fig. 5D).
Using the green dye–doped nanorods as
an example, we confirmed their CD responses
under different field directions (fig. S36C),
with negligible CD signals under no and
x-directional magnets and opposite CD peaks
in y- and z-directional magnetic fields. The
CD spectra of nanorods doped with all three
dyes (Fig. 5E) showed peaks at their charac-
teristic wavelengths. The observation is con-
sistent with that of plasmonic nanorods and
demonstrated the formation of chiral super-
structures and the successful transfer of chi-
rality from the nanoscale to molecular levels.
The g factor calculated in Fig. 5F has a max-
imum of ~0.003 for methylene blue–doped
nanorods, a value comparable to that of classic
chiral molecules and magnetically assembled
chiral superstructures of inorganic molecules,
polymers, and semiconductors (figs. S37 and
Li et al., Science 380, 1384–1390 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
B
E
200 nm
Fe3O4@RF
Methylene blue
Methylene green
Neutral red
A
D
2.5
2.0
1.5
1.0
0.5
.
)
.
u
a
(
e
c
n
a
b
r
o
s
b
A
0.0
300 400 500 600 700 800 900 1000
400
300
200
100
0
-100
-200
-300
)
g
e
d
m
(
D
C
-400
)
.
u
.
a
(
e
c
n
a
b
r
o
s
b
a
d
e
z
i
l
a
m
r
o
N
Fe3O4@SiO2
Fe3O4@SiO2@CuO2
Fe3O4@SiO2@RF
Fe3O4@SiO2@MnO2
1.0
0.8
0.6
0.4
0.2
C
)
g
e
d
m
(
D
C
d
e
z
i
l
a
m
r
o
N
0.0
300 400 500 600 700 800 900
Wavelength (nm)
F
1
0
-1
Fe3O4@SiO2/By
Fe3O4@SiO2/Bz
Fe3O4@SiO2@Cu2O/By
Fe3O4@SiO2@Cu2O/Bz
Fe3O4@SiO2@RF/By
Fe3O4@SiO2@RF/Bz
Fe3O4@SiO2@MnO2/By
Fe3O4@SiO2@MnO2/Bz
300 400 500 600 700 800 900
Wavelength (nm)
undoped/By
undoped/Bz
blue/By
blue/Bz
green/By
green/Bz
red/By
red/Bz
Methylene blue
Methylene green
Neutral red
7
6
5
4
3
2
1
)
3
-
0
1
(
r
o
t
c
a
f
-
g
0
300 400 500 600 700 800 900
300 400 500 600 700 800 900
Wavelength (nm)
Wavelength (nm)
Wavelength (nm)
Fig. 5. All-scale magnetic assembly of achiral molecules into chiral
superstructures. (A) TEM image of the Fe3O4@SiO2@MnO2 core-shell
nanorods. (B) Extinction spectra of core-shell Fe3O4@SiO2 and Fe3O4@SiO2@RF
nanorods, Fe3O4@MnO2 yolk-shell nanorods, and Fe3O4@SiO2@Cu2O
core-satellite nanorods. (C) The corresponding CD spectra measured under
y- and z-directional magnetic fields. (D) Extinction spectra of the
Fe3O4@SiO2@RF nanorods and nanorods doped with the three organic
dyes. (Insets, left to right) Digital pictures of the nanorods before and after
doping with methylene blue, methylene green, and neutral red. (E) CD
spectra of the doped and undoped nanorods under y- and z-directional
magnetic fields. (F) The g factor of the doped nanorods under a z-directional
magnetic field.
S38). We further demonstrated that the mag-
netic assembly strategy could be extended
to the assembly of fluorophores for generat-
ing circularly polarized luminescence. When
europium-doped NaYF4 nanorods were decor-
ated with Fe3O4 nanoparticles, the fluorescent
nanorods could be assembled into chiral
superstructures and exhibited circularly polar-
ized luminescence (fig. S39).
Discussion
The consistent rotation of the local-field vec-
tors of the cubic permanent magnet forms
the quadrupole field chirality with alternat-
ing left-handed and right-handed magnetic
fields in the four quadrants. Such chiral mag-
netic fields induce the assembly of magnetic
nanorods into chiral superstructures, with
handedness and chirality determined by the
local features of the magnetic fields. This
strategy allows remote, reversible, and instan-
taneous assembly of chiral superstructures
from nanostructures of various chemical com-
pounds (plasmonic materials, polymers, oxides,
metals, semiconductors, fluorescent nanostruc-
tures, and molecular moieties) and active
tuning of their CD responses in a broad range
of spectra and circularly polarized lumines-
cence, as long as they can be properly bound to
the magnetic nanorods. Fixing the chirality of
these chemical compounds at all scales is
possible by embedding the formed super-
structures in polymer substrates, which could
be realized by applying an external magnetic
field during polymerization. This simple
strategy makes the chiral superstructures
nonvolatile without external magnetic fields
and highly accessible for portable chiroptical
devices.
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We thank the Central Facility for Advanced Microscopy and
Microanalysis at University of California Riverside (UCR) for
help with TEM analysis and G. Ung’s group at University
of Connecticut for assistance with measuring the circularly
polarized luminescence. Funding: US National Science Foundation
CHE- 2203972 (Y.Y.). Authors contributions: Z.L. and Y.Y.
conceived and planned this study. Z.L. and Q.F. developed the
methodology for modeling and simulation. Z.L. developed the
synthesis and characterization of nanoparticles. Z.L., Z.Y., and C.W.
performed the CD measurements. Z.W. contributed to the
circularly polarized luminescence studies. All authors discussed
and analyzed the results and contributed to the writing of this
paper. Competing interests: Y.Y. and Z.L. have filed a patent
application related to this work filed by UCR. The anthors declare
that they have no other completing interests. Data and materials
availability: All data needed to evaluate the conclusions in the
paper are present in the paper or the supplementary materials.
The programming code to model magnetic fields and datasets
used to analyze the field chirality are available online at Zenodo
(50). License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-
article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg2657
Materials and Methods
Supplementary Text
Figs. S1 to S39
Table S1
References (51–57)
Submitted 12 December 2022; accepted 22 May 2023
10.1126/science.adg2657
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RES EARCH
IONTRONICS
Cascade-heterogated biphasic gel iontronics for
electronic-to-multi-ionic signal transmission
Weipeng Chen1,2†, Linxin Zhai3†, Suli Zhang4,5†, Ziguang Zhao1,2†*, Yuhao Hu1,2, Yun Xiang1,
Huirong Liu4,5, Zhiping Xu3, Lei Jiang1,2, Liping Wen1,2*
Currently, electronics and iontronics in abiotic-biotic systems can only use electrons and single-species
ions as unitary signal carriers. Thus, a mechanism of gating transmission for multiple biosignals in
such devices is needed to match and modulate complex aqueous-phase biological systems. Here
we report the use of cascade-heterogated biphasic gel iontronics to achieve diverse electronic-to-multi-
ionic signal transmission. The cascade-heterogated property determined the transfer free energy
barriers experienced by ions and ionic hydration-dehydration states under an electric potential field,
fundamentally enhancing the distinction of cross-interface transmission between different ions by
several orders of magnitude. Such heterogated or chemical-heterogated iontronics with programmable
features can be coupled with multi-ion cross-interface mobilities for hierarchical and selective
cross-stage signal transmission. We expect that such iontronics would be ideal candidates for a
variety of biotechnology applications.
I n biological systems, neural networks with
complex morphologies and highly polar-
ized interfacial architectures can support
elaborate bioionic and biochemical signal
communications between different neu-
rons (1, 2). Such structures and functions of
complex neural networks provide inspiration
for designing cascade-gated architectures ca-
pable of implementing neuron-like multivariate
ionic or chemical signal transport that could
interface with and modulate physiological
processes.
Recently, artificial electronic and iontronic
systems, which broke the information barriers
between abiotic and biotic interfaces, have at-
tracted considerable attention for application
in biosensors (3–6), neuroprosthetics (7, 8),
and implantable neuromorphic devices (9–12).
Electronics, especially neuromorphic electron-
ics (11–14), directly use programmable electrical
impulse signals to treat biological interfaces as
signal transducers for modulating physiologi-
cal activities (14–16), whereas iontronics ex-
hibit the capability of individually performing
the conversion between intrinsic ionic and elec-
trical signals for abiotic-biotic systems (17, 18).
However, compared with biological neuronal
networks with diverse biosignal transmission
invoked by neural action potentials (fig. S1),
1CAS Key Laboratory of Bio-inspired Materials and Interfacial
Science, Technical Institute of Physics and Chemistry,
Chinese Academy of Sciences, Beijing 100190, P. R. China.
2School of Future Technology, University of Chinese Academy
of Sciences, Beijing 100049, P. R. China. 3Applied Mechanics
Laboratory, Department of Engineering Mechanics, Tsinghua
University, Beijing 100084, P. R. China. 4Department of
Physiology and Pathophysiology, School of Basic Medical
Sciences, Capital Medical University, Beijing 100069, P. R.
China. 5Beijing Key Laboratory of Metabolic Disorder Related
Cardiovascular Disease, Capital Medical University, Beijing
100069, P. R. China.
*Corresponding author. Email: zhaoziguang@ucas.ac.cn (Z.Z.);
wen@mail.ipc.ac.cn (L.W.)
†These authors contributed equally to this work.
most electronics and iontronics are still re-
stricted by the single-species attributes of signal
carriers (electrons or single ions) that cannot
carry more biocompatible information. These
existing iontronics constructed from conven-
tional gated or nongated materials do not faith-
fully mimic multi-ionic cotransport, thereby
limiting their characteristic signal expression
in matching biological tissues (19). Ionic cur-
rent signal transmission does not even discrim-
inate between various ions in hydrogel-based
iontronics (20–22). In the realm of iontronics,
diverse electronic-to-multi-ionic transmission
and processing in aqueous-phase biological
environments remain a challenge.
Design and fabrication of cascade-heterogated
biphasic gels
Here we report the use of a biphasic gel iontronic
with cascaded heterointerface–gated properties
to construct diverse ionic cross-medium trans-
mission as a signal communication principle
(Fig. 1A). The cascade-heterogated biphasic
gel (HBG) has phase-separated heteronetwork
structures that incorporate opposite binary gel
phases: a microscale ion-enriched internal gel
phase (IE phase) and a low-conductivity contin-
uous gel phase (LC phase) (Fig. 1B). Specifically,
the IE phase features hydrogel microinclu-
sions that can store and transmit hydrated
ions, and the LC phase serves as an organogel
matrix that functions as the partially dehy-
drated ion transmission medium. Ionic cross-
medium transmission can be triggered by
external stimulation of both continuous- and
pulse-based electrical signals, during which
partial shedding and reconfiguration of cat-
ionic hydration shells, acting as ionic partial
hydration and rehydration states (Fig. 1C),
must occur alternately and consecutively. Thus,
biphasic multi-interfaces induce cascade-
heterogated effects that determine how ions
experience transfer free energy barriers (DE)
and local driving force (º DV) under an elec-
tric potential (Fig. 1, D and E). Because of the
association of these factors with ionic hydration-
dehydration energies, the distinction of cross-
interface transmission between multivariate
cations (X+ and Xn+) is enhanced by several
orders of magnitude. By way of the sorting
and control of ionic transfer energy barriers
at heterogated interfaces, the HBG system
can process electronic-to-multi-ionic hierar-
chical transmission and selective ionic cross-
stage transmission.
An in situ phase-separated polymerization
strategy was introduced to fabricate HBG
iontronics in which interfacial covalent inter-
actions could maintain stable heterogated ar-
chitectures (fig. S2). Heterogeneous structures
of HBGs with different phase compositions
were confirmed by confocal laser scanning
microscopy (CLSM) (Fig. 1B and fig. S3) and
scanning electron microscopy (SEM) (fig. S4).
In CLSM images, it was observed that IE micro-
inclusions (blue-stained) were uniformly dis-
persed in the LC phase (orange-stained) and
found that their average diameters increased
from 1.48 to 2.67 mm upon increasing the ratio
of the IE phase (fig. S5). These results indicate
that cascade-heterogated structures are modu-
lated by the microphase separation degree.
Ion species and concentrations did not affect
HBG heterostructure (figs. S6 and S7). These
samples were denoted as HBG-y, where y rep-
resents the volume ratio of the LC phase to
the IE phase (fixed to 1). Desirable mechan-
ical properties and environmental stability of
HBG iontronics ensure high-reliability ion trans-
port in multimedia-based environments (figs.
S8 and S9).
Ionic transmission characteristics
of cascade-heterogated biphasic gels
In nongated hydrogel iontronics, X+ and Xn+
cations are highly hydrated and can contin-
uously move with extremely low viscous restric-
tions in water-rich environments and easily
traverse the neutral hydrogel network in an
electric potential field (Fig. 2A). There is no
obvious differentiation between the DE of hy-
drated X+ and Xn+ cations during homogeneous
transmission (fig. S10). In HBG systems, the
cascade-heterogated mechanism can effective-
ly govern ion transport owing to the ionic in-
trinsic DE under the external stimulation of
continuous or pulse-based electrical signals
(Fig. 2B). In the cascaded cross-interface ion
transmission, the partial shedding and recon-
figuration of cation hydration shells, which
correspond to the ionic partial hydration and
rehydration states, occurs alternately and suc-
cessively. To further illustrate the heterogated
effect derived from asymmetric chemical and
spatial structures, we established the molec-
ular dynamics model of the heterointerface
Chen et al., Science 382, 559–565 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
D
B
Ion-enriched
internal phase
in
int
IE phase
Lo
L
Low-conductive
ow
con
nt
continuous phase
(
(LC phase)
CLSM image
CLSM image
C
Heterogated transmission
Electrical signal
Electrical signalg
IE phase
Hydrated ion2
d ie
Xn+
(Xn+)
Hydrated ion1
e
ed
Hydrateed ion
)
(X+)
Bi h i
Biphasic-gel Iontronics
Biphasic-gel Iontronics
l I
t
i
e
r
u
t
c
u
r
t
S
n
o
i
t
u
b
i
r
t
s
d
i
Aqueous phase
Oleophilic network
Hydrophilic network
Oleophilic phase
IE phase
LC phase
E
CCCr
CroCross-ss ii
aaa
ans imis ision
inii
tntn erfferfaceace trtra
ssmm oonnn
nn
ffrfaff
Cascade-heterogated
network structure
PP
Partially
P
hydrated ion2
dr
(Xn+)
Partially
h
on
hydrated ion1
(X+)
LC phase
Ionic signal
Transfer energy barrier
( E)
Local driving force
( V)
Hydration
Partial hydration Rehydration
Hydration
Partial hydration Rehydration
Hydrated
ion
Partially
hydrated
ion
EXn+
EX+
y
g
r
e
n
e
e
e
r
F
r IE >> r Hydrated ion > r LC > r Partially hydrated ion
Analog ionic transmission path
through the heterogated interface
IE phase
0
LC phase IE phase
Coordinate
e
g
a
t
l
o
V
VX+
VXn+
IE phase LC phase
0
Coordinate
IE phase
Fig. 1. Heterogeneous structures and cross-interface ion transmission of
cascade-heterogated biphasic gel iontronics. (A) Structural illustration
and (B) CLSM image of the HBGs with phase-separation heteronetworks. Scale
bar, 20 mm. (C) Heterogated cross-interface ion transmission. Owing to the
distinct hydration-dehydration energies between different X+ and Xn+, the
cascade-heterogated effects fundamentally enlarged the hierarchy discrepancy
of the ionic transfer energy barriers to construct diverse electronic-to-multi-ionic
signal transmission by the application of electrical signals. (D) Analysis of the
network structure distribution at the heterogated interface and the analog
ionic transmission path through the heterogated interface from the hydrated
state in the IE phase to the partially hydrated state in the LC phase. (E) The
obvious distinction of transfer energy barrier (DE) and the local driving forces
(º DV) of X+ and Xn+ featuring the hydration and partial hydration states across
the heterogeneous interfaces.
to simulate the ionic transmission path and
the related transfer free energy barrier (fig.
S11). Crossing the heterointerface from the
IE phase to the LC phase, the attractive and
repulsive interactions between cation hydra-
tion shells and IE and LC phases, as well as
the steric limitations of heterogated interfaces,
led to a substantial increase in DE. Meanwhile,
the resultant transport resistance could be
counteracted by the local driving force from
the electric field, which was reflected by the
notable DV. Ionic transmission paths in the
IE phase with an average estimated size of
6.60 to 7.26 nm were found to be larger than
those of hydrated ions, and so a partial de-
hydration transformation reduced the effec-
tive size of hydrated ions, allowing them to
access the LC phase, in which the estimated
path size of 1.5 to 3.0 Å was larger than that of
the partially hydrated ions (Fig. 1D and fig.
S12A). The heterogated interface with a high
degree of permeation also acted as a transi-
tion layer to reduce the driving force of ions
across the heterointerface, and the interfa-
cial gating thickness did not affect the ionic
cross-interface energy consumption originating
from its hydration-dehydration transforma-
tion (fig. S13). Subsequently, an energy com-
pensation existed for the disengagement from
the attractive interaction between the ion and
the IE phase, and the partially hydrated ion
with a related high transfer energy in the LC
phase was relayed to the next IE microinclu-
sions, accompanied by an energetically favor-
able reconfiguration to realize ion rehydration.
For one unit of cascaded cross-interface ion
transport (fig. S12B), the ratios of K+, Ca2+, and
Fe3+ hydration-dehydration energies and ion
mobilities between the biphasic system were
simulated to evaluate different cross-interface
Þ of the
DE values DE
three typical ions (fig. S12, C and D). Specifi-
cally, ionic radius, electrostatic force, hydrogen
bonding, and other weak interactions, which
Ca2þ > DEKþ
Fe3þ > DE
ð
together affect the stability of the ionic hydra-
tion shell, were believed to be intrinsic factors
in determining the ionic hydration-dehydration
energy (23, 24). Theoretically, ions with high
charge densities can lead to the strong electro-
static ordering of nearby water molecules to
stabilize their hydration shells, thus necessi-
tating the higher hydration-dehydration ener-
gies to overcome cross-interface transfer energy
barriers (25).
Figure 2, C and D, and fig. S14 show similar
ionic current variations of nongated hydrogels
containing 1 mM K+, Ca2+, or Fe3+ under dif-
ferent voltage gradients, and their comparable
transfer potentials were confirmed in terms
of the corresponding voltage thresholds (all
1 mV). These indiscriminate results demon-
strate that homogeneous networks of non-
gated hydrogels had difficulty recognizing
ionic intrinsic features for the distinction of ion
transport. In contrast, the ionic current prop-
erties of HBGs reflected obviously different
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Fig. 2. Ionic transmission characteristics of nongated hydrogels and cascade-
heterogated biphasic gels. (A) Homogeneous and (B) cross-interface ion
transmission of the nongated hydrogel and HBGs, respectively. Scale bar, 3 mm.
(C and D) Ionic current properties of the nongated hydrogels and (E and F) the
HBGs containing 1 mM K+, Ca2+, or Fe3+ under varied applied voltages. (G) Statistically
normalized ionic signal intensities of the HBGs with different phase compositions
(data are mean ± SD, N = 3). (H) Normalized ionic signal intensities at 5 V of HBG-5
containing 1 mM of different ions. The ionic cross-interface transport capacity
corresponds to the ionic hydration-dehydration energy (data are mean ± SD, N = 3).
(I) Obvious distinction of the pulse-based K+, Ca2+, and Fe3+ ionic current properties
of the HBG-5 under electrical signal stimulations with varying frequencies of 1, 5,
and 10 Hz. (J) Calculated ionic signal intensity (S) ratio of K+/Ca2+ in the cascade-
heterointerface system with different cascade degrees. The inset shows the equivalent
circuit of n cross-interface ionic transmission units.
trends under a range of varied applied volt-
ages (Fig. 2, E and F). The voltage threshold
of HBG-3 with 1 mM K+ was 5 mV, and 40
and 60 mV, respectively, with Ca2+ and Fe3+.
To gain further insight into the relationship
between the ionic cross-interface transmission
and the phase-separation composition, ionic sig-
nal transmission properties of HBGs varying
with cascade-heterogated effects were character-
ized. The ionic currents of the low-conductivity
organogel separated from the biphasic gel pre-
cursors were initially measured. All samples
were in a nonconductive state at 5 V, confirm-
ing that the ions were not stored and then
continuously transported in the LC phase (fig.
S15). The differences in ionic (K+, Ca2+, Fe3+) sig-
nals derived from the heterojunction biphasic
gel with a single and uniform heterointerface
were still rough in comparison with HBGs fea-
turing cascade-heterogated interfaces (figs. S16
and S17). By modulating cascade-heterogated
effects of HBGs, the ratios of on-state transfer
potentials and the normalized signal intensi-
ties between different cations exhibited increas-
ing trends induced by increasing the degrees
of microphase separation (Fig. 2G and figs.
S18 and S19A). Typically, the ratios of voltage
thresholds (K+ to Fe3+ or K+ to Ca2+) of HBG-5
were 66.76 and 53.34. The normalized signal
intensity ratios of K+ to Fe3+ and K+ to Ca2+ in
HBG-5 reached 5162.40 and 2419.57. In con-
trast, the values of K+ to Fe3+ and K+ to Ca2+ in
nongated hydrogels were only 2.19 and 1.74,
respectively. Such homogeneous ion transmis-
sion depended on the ionic intrinsic transfer
coefficients under an electric potential. The
heterogated effect also held for iontronic sys-
tems in the presence of a high cation concen-
tration up to 100 mM (fig. S20). Otherwise, the
normalized signal intensities and related volt-
age thresholds of HBG-5 indicated that different
ionic cross-interface transport capacities were
related to the theoretical trends of their hydration-
dehydration energies (Fig. 2H, fig. S19B, and
table S1). For both isovalent and aliovalent ions,
the ion with low hydration-dehydration energy
corresponded to low cross-interface DE, thus
exhibiting a relatively high ionic signal inten-
sity and a low voltage threshold.
Compared with the homogeneous ion trans-
mission of nongated hydrogels (fig. S21), cascade-
heterogated effects also demonstrated an obvious
distinction between pulse-based K+, Ca2+, and
Fe3+ ionic current properties under electrical
stimulations at frequencies from 0.1 to 100 Hz
(Fig. 2I and fig. S22). The simulated relationship
between ion dynamics and pulse-based frequen-
cies (0.1 to 1000 Hz) at the heterogated interface
was conducted, in which the simulated trans-
mitted ion number and normalized simulated
current were unrelated to the stimulus frequency
(fig. S23). The duration of the high level in a sin-
gle pulse cycle far exceeded the expected time
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Fig. 3. Electronic-to-multi-ionic signal transmission of cascade-heterogated
biphasic gels. (A) Ionic current characteristics of the HBG-5 containing different
ions. The inset showed the corresponding normalized signal intensities at 5 V (data
are mean ± SD, N = 3). (B) Simulated signal intensity ratios of the HBGs with
different mixtures of K+ and Ca2+ to that of the HBG with K+ (blue line), which were
attributed to the different occupation proportions of K+ (Mmix K
concentration ratio) and Ca2+ (Mmix Ca2þ as the Ca2+ molar concentration ratio) at the
heterogated interface, and simulated independent signal intensity ratios of K+ (Smix K
þ)
þ as the K+ molar
to that of Ca2+ (Smix Ca2þ) in the mixed system (orange line). (C) Schematic of
preferential K+ transport and hysteretic Ca2+ transport at the heterogated interface.
(D to F) Normalized conductance of the HBG-5 containing different ions (data are
mean ± SD, N = 3). (G) Hierarchical ionic signal transmission. The pulse-transmitted
ionic signals of the cascade-heterogated iontronics were successively dominated
by K+, Ca2+, and Fe3+ against different electrical pulse signals from 5 to 500 mV
(data are mean ± SD, N = 3). (H) Selective Ca2+ cross-stage transmission derived
from the chemical-heterogated iontronics (data are mean ± SD, N = 3).
Chen et al., Science 382, 559–565 (2023)
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Fig. 4. Bioionic neurohumoral modulation. (A) Conceptual schematic of the
iontronic signal transduction from electronic control circuits to bioionic neural
circuits. (B) In an abiotic-biotic system, the cardiac electrical activities of a bullfrog
heart were modulated by the bioionic neurohumoral signals from the iontronic
transduction devices. Scale bars, 5 mm. (C) Exogenous bioionic neurohumoral
signals modulate the permeability of cardiomyocytes and consequently alter the K+
outflux and the Ca2+ influx in the cell membrane. (D and E) Bioionic neurohumoral
modulation in the cardiac electrical activities of bullfrog hearts based on the cascade-
heterogated (D) or chemical-heterogated (E) iontronic transduction devices (data
are mean ± SD, N = 3).
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RES EARCH | R E S E A R C H A R T I C L E
for the cross-interface transmission of an ion,
indicating that the cross-interface ion trans-
port of HBG systems would be frequency-
independent (1 to 1000 Hz).
To model cascade-heterogating effects, a
series circuit model based on the nonlinear
Poisson-Boltzmann theory was constructed to
illustrate the relationship between cascaded
heterointerfaces and K+/Ca2+ transport dis-
tinction (Fig. 2J) (26, 27). The total energy con-
sumption (º RTot) can be divided into n units.
For one cross-interface unit, the energy con-
sumption can be divided into four sections: the
consumption of transport in the IE phase (RIE),
across the heterogated interface from the IE
phase to the LC phase (RIn), in the LC phase
(RLC), and across the heterogated interface
from the LC phase to the IE phase (ROut) (fig.
S12B). RIE was negligible owing to the weak
resistance in the IE phase; and ROut was also
ignored because the energetically favorable
reconfiguration for rehydration. On the basis
of different cross-interface DE values, the ionic
signal intensity (S) ratio of K+/Ca2+ (which was
equivalent to the total transport resistance ra-
tio of K+ to Ca2+) was expressed as
SKþ =S
Ca2þ ðnÞ ¼ 2
¼ 2
(cid:1)
nRLC Ca2þ
nRLC Kþð
(cid:3)
(cid:1)
þ nRIn Ca2þ
Þþ nRIn Kþð
Þ
(cid:3)
Þ
ð
RLC Ca2þ
RLC Kþð
Þ
ð
þ N RIn Ca2þ
RIn Kþð
1 þ N
Þ
Þ
ð1Þ
where N ¼ RIn Kþð
Þ
Þ, and this N was used to com-
RLC Kþð
pare the inf luence between the heterogated
interface and the LC phase on the ion trans-
port. When N→∞, the system could be regarded
as the ideal cascade-heterointerface limit (de-
noted as the ideal HBG system)
ð
SKþ =S
Ca2þ Cascade (cid:2) heterointerface limit
(cid:4)
¼ 2exp
(cid:1)
DEIn Ca2þ
Þ (cid:2) 2eDVIn Ca2þ
(cid:2) DEIn Kþð
(cid:3)
(cid:1)
kBT
(cid:3)
(cid:1)
RIn Ca2þ
RIn Kþð
Þ
(cid:5)
þ eDVIn Kþð
Þ
Þ ¼ 2
(cid:3)
ð2Þ
In contrast, when N→0, the system could be
regarded as a single interface (denoted as a
heterojunction)
SKþ =S
ð
Ca2þ Single interface
Þ ¼ 2
(cid:3)
(cid:1)
RLC Ca2þ
RLC Kþð
Þ
ð3Þ
In practical conditions, the heterointerface
density (º N) is often limited, and so the ionic
signal intensity ratio of the HBG system cannot
reach the theoretical limit. However, the cascade-
heterogated interface of iontronics was suffi-
ciently dense to ensure a high SKþ =S
Ca2þ .
Electronic-to-multi-ionic signal transmission
of cascade-heterogated biphasic gels
Figure 3A shows the anomalous decrease in
the ionic current and the normalized signal
intensity of HBG-5 containing a mixture of
1 mM K+ and 1 mM Ca2+. The presence of Ca2+
increased the total ion concentration, but the
normalized signal intensity was only 0.025,
which was one-fortieth that with K+ alone.
This result can be attributed to the fact that
K+ has a lower hydration-dehydration energy
and a smaller ion-hydration size than Ca2+, and
so it was transported more favorably across
the heterogated interface to consecutively un-
dergo partial dehydration and rehydration
under the stimulation of an electrical signal,
resulting in relatively efficient ion transmission.
However, the Ca2+ cross-interface mobility re-
quired a greater transfer energy, which reduced
its own transport efficiency and formed inter-
facial occupations, causing steric hindrance
and electrostatic repulsion at the heterogated
interface, thereby further hindering K+ and
Ca2+ transport. Thus, the simulated signal in-
tensity ratio of HBGs with different mixtures of
K+ and Ca2+ to that of HBGs with only the same
concentration of K+ was negatively linearly cor-
related with the Ca2+ occupation ratio (Mmix Ca2+)
at the heterogated interface (Fig. 3B, blue line).
However, despite the decrease of ionic trans-
mission paths resulting from such occupation,
the simulated independent signal intensity ratio
of K+/Ca2+ in the mixed system remained at
greater than three orders of magnitude (as
mix Ca2þ ≤ 0:91) (orange line). Figure 3C shows
M
preferential K+ transport and hysteretic Ca2+
transport DEKþ <
Ca2þ Þ at the heterointer-
ð
face under segmental electrical signal stimula-
tions. The Ca2+ occupation blocked the ion
paths of the heterogated interface, also result-
ing in a relatively low ionic conductance below
~3 V. As the applied electrical signal increased,
the normalized conductance curve suddenly
increased, which was mainly attributed to the
increased transport of hysteretic Ca2+ (Fig. 3D).
This effect was also confirmed in HBGs con-
taining different binary ionic mixtures (Fig. 3,
E and F, and figs. S25 and S26).
DE
Such cascade-heterogatings can fundamen-
tally enlarge the hierarchy discrepancy of multi-
ion transfer energy barriers for hierarchical
signal transmission. The real-time variations in
the transmitted ionic signal strengths derived
from HBGs incorporated with ternary ionic
mixtures were monitored by inductively coupled
plasma mass spectrometry (fig. S27). Figure 3G
and fig. S28 show that pulse-transmitted ionic
signal strengths were successively dominated
by K+, Ca2+, and Fe3+ against different input
voltage signals ranging from 5 to 500 mV. In the
absence of an input voltage signal, the HBGs
maintained stable ion storage and avoided
ion free diffusion to the surrounding aqueous
phase environment. By applying a 5-mV pulse-
based electrical signal with a frequency of 5 Hz,
the transmitted K+ signal of the HBG was trig-
gered, and the transport of Ca2+ and Fe3+ re-
mained hysteretic. After 2 hours, the K+ signal
strength increased from 6 to 400 parts per
billion. Subsequently, by increasing the ap-
plied voltages to 100 and 500 mV, Ca2+- and
Fe3+-dominated signals were observed, respec-
tively. The cascade-heterogated effect allowed
for the preferential transport of multiple ions
by the sorting of ionic transfer energy bar-
riers. Meanwhile, such transmitted ionic signal
strengths of HBGs have already achieved lev-
els compatible with those of specific physio-
logical bioactivities (28, 29). Unlike ion-selective
membranes and hydrogels, our HBGs can store
a stable ion source on demand and efficiently
process intrinsic ionic signals to the ambient
aqueous environment. The hydrogel iontronics
inevitably led to uncontrolled ionic diffusion
into the external environment, making it im-
possible to modulate or regulate ion transmis-
sion (fig. S29).
Considering the advantageous transport or-
der of one type of ion under specific condi-
tions, the hierarchical ion transmission could
be regarded as a form of ion selectivity. We also
designed a chemical-heterogated architecture
to further regulate the ionic transfer energy
barrier hierarchy for ion-selective cross-stage
transmission. Owing to the coordination ef-
fects of specific ligand groups (18-crown-6 to
K+ and carboxylic group to Fe3+) as chemical
assistance in the IE phase (fig. S30A), ionic
migration behaviors tended to be hopping
between ligands to overcome dissociation en-
ergy barriers (30, 31). Thus, the corresponding
total energy consumption (º RTot) continued
to increase, leading to a higher energy con-
sumption in the IE phase than across the het-
erogated interface and breaking the inherence
in ionic transport hierarchies that originated
from their intrinsic hydration-dehydration en-
ergies. Such cascaded chemical-heterogated
effects rendered the total equivalent transfer
energy barriers of K+ and Fe3+ significantly
greater than that of Ca2+, resulting in Ca2+
cross-stage signal and transmission restric-
tions of the other signal (Fig. 3H and fig. S30B).
In contrast, dual-ligand (18-crown-6 and car-
boxylic group) hydrogel iontronics had no Ca2+
selectivity (fig. S31). In the homogeneous hydro-
gel network, chemical ligand effects were unable
to further establish ion-scale confined-gating
properties that governed ion transport.
Bioionic neurohumoral modulation
Neuronal signaling relies on the controlled
transmission of various neurotransmitter mol-
ecules and ions (32, 33). For iontronics, the
aim is to regulate multiple biofunctional ionic
signal transductions to interface with and con-
trol physiological activities in aqueous-based
bioenvironments (34). To that end, the cascade-
heterogated iontronic transduction device devel-
oped in this study to convert electronic input
signals into diverse bioionic signals demon-
strates its potential for application as a biocom-
munication carrier (Fig. 4, A and B). Meanwhile,
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RES EARCH | R E S E A R C H A R T I C L E
the good biocompatibility of the developed sys-
tem was also demonstrated (figs. S32 and S33).
Figure 4, C and D, outlines the transduction of
biofunctional neurohumoral signals by cascade-
heterogated and chemical-heterogated devices
to regulate the permeability of cardiomyocytes
and modulate cardiac electrical activities in
bullfrog hearts. These results were confirmed
by the alterations in the electrocardiogram
(figs. S34 and S35 and movies S1 and S2). For
abiotic-biotic systems, we anticipate that such
iontronics could act as bridges for biocompa-
tible signal processing and transmission between
electronic control circuits and bioionic neural
circuits.
Conclusions
Here we reported cascade-heterogated iontronics
for diverse ionic signal transmission. These gels
integrated opposite binary phase structures to
form cascaded ionic transfer free energy barriers
that were highly correlated with the hydration-
dehydration energies of different ions. More
impressively, cascade-heterogated interfaces
fundamentally enlarged and controlled the
hierarchical discrepancy of ionic transfer en-
ergy barriers to achieve multi-ionic hierarchi-
cal transmission and ion-selective cross-stage
transmission. Until now, ion-gating has been
primarily manifested in one- or two-dimensional
systems; in this work, we developed a cascad-
ing strategy to expand the ion-gating mecha-
nism to three-dimensional intronic systems
for electronic-to-multi-ion transmission. Most
iontronic and electronic devices employing con-
ventional ion-gating or nongating struggle to
effectively process multi-ion signal carriers in
their potential applications (tables S2 and S3);
however, these properties are critical for inter-
facing with and matching complex biological
systems. HBG-based iontronics offer not only
multispecies bioionic signals that are highly com-
patible with aqueous-phase biological systems
but also advance programmable signal trans-
mission functionalities that facilitate the parallel
and multiplexed transmission of various bio-
signals in abiotic-biotic systems. These cascade-
heterogated iontronics serve as diverse platforms
for possible extensions to more-biofunctional car-
riers and other signal transduction mechanisms.
Meanwhile, it would be worthwhile to study the
weight and coupling features of multispecies sig-
nal interchange in these cascade-gating systems.
Despite the long road ahead for the construction
of high-performance artificial neural networks,
we expect that such cascade-heterogated net-
works will be applicable in hardware imple-
mentation for neuromorphic gating features,
while also providing more signal morpholo-
gies and processing.
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AC KNOWLED GME NTS
All animals used in the experiment were approved by the Animal
Protection Ethics Committee of Capital Medical University (Ethics
Number: AEEI-2014-062). We are grateful to X. Dong (Experimental
Center for basic medical teaching, Basic Medical Sciences, Capital
Medical University) for assistance with the biological experiments,
and K. Wang (Capital Medical University) for helpful discussions.
Funding: This research was supported by the National Natural
Science Foundation (21988102, 22275183, 22122207, 11825203),
the National Key R&D Program of China (2022YFB3805904,
2022YFB3805900), the CAS Project for Young Scientists in Basic
Research (YSBR-039), and the China Postdoctoral Science
Foundation (2022M713226). Author contributions: W.C., L.Z.,
S.Z., and Z.Z. contributed equally to this work. Z.Z., L.W., and W.C.
proposed the research direction. Z.Z., L.W., and L.J. guided the
project. W.C. and Z.Z. co-designed and performed the experiments.
L.Z. and Z.X. performed the theoretical calculations. S.Z. and H.L.
performed the biology experiments. Z.Z. and W.C. drafted the
manuscript. All authors joined the data discussion and revised the
manuscript. Competing interests: The authors declare that they
have no competing interests. Data and materials availability:
All data needed to evaluate the conclusions in the paper are
present in the main text or the supplementary materials. The data
that support the findings of this study are available at Zenodo (35).
License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-
article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg0059
Materials and Methods
Supplementary Text
Figs. S1 to S35
Tables S1 to S4
References (36–72)
Movies S1 and S2
Submitted 26 November 2022; resubmitted 22 July 2023
Accepted 22 September 2023
10.1126/science.adg0059
Chen et al., Science 382, 559–565 (2023)
3 November 2023
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RES EARCH
ORGANOMETALLICS
Oxidative addition of an alkyl halide to form a stable
Cu(III) product
Yongrui Luo1†, Yuli Li1†, Jian Wu1, Xiao-Song Xue1*, John F. Hartwig2*, Qilong Shen1*
The step that cleaves the carbon-halogen bond in copper-catalyzed cross-coupling reactions remains
ill defined because of the multiple redox manifolds available to copper and the instability of the high-
valent copper product formed. We report the oxidative addition of a-haloacetonitrile to ionic and neutral
copper(I) complexes to form previously elusive but here fully characterized copper(III) complexes.
The stability of these complexes stems from the strong Cu−CF3 bond and the high barrier for
C(CF3)−C(CH2CN) bond-forming reductive elimination. The mechanistic studies we performed suggest
that oxidative addition to ionic and neutral copper(I) complexes proceeds by means of two different
pathways: an SN2-type substitution to the ionic complex and a halogen-atom transfer to the neutral
complex. We observed a pronounced ligand acceleration of the oxidative addition, which correlates with
that observed in the copper-catalyzed couplings of azoles, amines, or alkynes with alkyl electrophiles.
C opper-mediated cross-coupling reactions
have become some of the most powerful
methods for the construction of carbon-
carbon (C−C) and C−heteroatom bonds
(1–4). Early efforts in this field focused
mainly on the coupling of sp2-hybridized car-
bon electrophiles, and in recent years, research
has expanded to encompass the mild coupling
of sp3-hybridized carbon electrophiles (5, 6).
Much progress has been made recently on
copper-mediated or copper-catalyzed alkynyla-
tion (7–9), alkylation (10–12), arylation (13–15),
and amination (16, 17) of alkyl halides, pro-
viding an alternative and practical method for
the installation of functional groups on alkyl
chains and rings. Despite this expansion of the
scope of the cross-coupling reactions of alkyl
electrophiles that use copper, the mechanism
of these reactions is poorly understood.
Previously, two distinct cycles were proposed
for copper-catalyzed cross-coupling reactions
of alkyl electrophiles. One cycle comprises a
two-electron Cu(I)/Cu(III) manifold, and one
comprises a stepwise Cu(I)/Cu(II) manifold
involving initial single-electron transfer (SET)
between the Cu(I) center and the alkyl electro-
phile to generate a Cu(II) intermediate and an
alkyl radical, followed by transfer of the func-
tional group from the resulting Cu(II) species
to the alkyl radical (18–22) (Fig. 1A). Differen-
tiation of these two pathways is challenging
because the higher-valent copper intermedi-
ates in the reactions, particularly the putative
Cu(III) intermediates, are highly reactive and
typically elude detection (23–26).
1Key Laboratory of Organofluorine Chemistry, Center for
Excellence in Molecular Synthesis, Shanghai Institute of
Organic Chemistry, University of Chinese Academy of
Sciences, Chinese Academy of Sciences, Shanghai 200032,
PR China. 2Department of Chemistry, University of California,
Berkeley, Berkeley, CA 94720, USA.
*Corresponding author. Email: xuexs@sioc.ac.cn (X-S.X.);
jhartwig@berkeley.edu (J.F.H.); shenql@sioc.ac.cn (Q.S.)
†These authors contributed equally to this work.
Consequently, isolable, well-defined alkyl Cu
(III) complexes are rare. In the early 2000s,
seminal work from the groups of Bertz, Ogle
(27–29), and Gschwind (30) demonstrated that
reactions of alkyl iodides with ionic Gilman
reagents generated Cu(III) species, which were
characterized at a temperature below −93°C
with rapid-injection nuclear magnetic reso-
nance (RI-NMR) spectroscopy techniques
(Fig. 1C). Yet, formation of the Cu(III) inter-
mediates, even at this temperature, is fast,
rendering studies on the mechanism of the
reaction of alkyl halides with the Cu(I) species
challenging.
To probe whether a Cu(III) intermediate
could be generated from the reaction of an
alkyl halide with a Cu(I) species and to deter-
mine how such an intermediate would form
from an alkyl electrophile in a copper-mediated
or copper-catalyzed cross-coupling, we rea-
soned that two requirements must be met:
(i) An alkyl electrophile with a high reduc-
tion potential must be used so that forma-
tion of the Cu(III) species from the starting Cu
(I) species is thermodynamically favorable,
and (ii) the barrier for reductive elimination
from the Cu(III) intermediate must be higher
than that for the oxidative addition that forms
the Cu(III) species (Fig. 1B).
The electron-withdrawing, strong-field tri-
fluoromethyl ligand is known to stabilize both
Cu(I) and high-valent Cu(III) metal centers as
a result of p-back donation of electron density
from the d orbitals on copper to the antibond-
ing (s*) orbitals of the C–F group or the con-
tracted bonding (s) orbitals on copper because
of the high electronegativity of the fluorine
(31). In the past three decades, a variety of
well-defined trifluoromethyl Cu(III) complexes
have been reported (26). Recent studies on
the reactivities of these Cu(III) complexes
showed that the barrier for reductive elimi-
nation to form a C(sp3)−CF3 bond from either
the ionic Cu(III) complex [Cu(CF3)3(alkyl)]−
or the five-coordinate neutral Cu(III) complex
[(bpy)Cu(CF3)2(Me)] is high (32–34). In addi-
tion, stable, well-characterized trifluoromethyl
Cu(I) species—including [CuCF3] (35), which
contains no additional ligands; [(Phen)CuCF3]
(36), which contains a dinitrogen-donor ligand;
[(NHC)CuCF3] (37), which contains an N-
heterocyclic carbene (NHC) ligand; and [Cu(CF3)2]−
(38, 39), which is an ionic Cu(I) cuprate—were
reported to react with aryl halides to give tri-
fluoromethylarene products in good yields. In
light of this prior work, we proposed that an
appropriate trade-off between reactivity and
stability of trifluoromethyl Cu(I) and Cu(III)
complexes could meet the aforementioned re-
quirements and provide an opportunity to in-
vestigate the mechanism of the reaction of alkyl
halides with Cu(I) species to form stable Cu(III)
products.
On the basis of the above rationale, we
studied the reactions of alkyl halides with
trifluoromethyl-Cu(I) complexes (Fig. 1). Stable
[Ph4P]+[Cu(CF3)2]− and [(bpy)Cu(CF3)] (bpy,
bipyridine) were chosen initially as the Cu(I)
complexes that represent the ligandless “ate”-
type Cu(I) complex and the neutral bipyridine-
ligated Cu(I) complex, respectively. These
complexes would allow us to probe the dif-
ferences between the reactivity of two differ-
ent types of Cu(I) complexes and the effect of
the nitrogen ligand on the oxidative addition
process. We chose a-haloacetonitrile XCH2CN
[in which X (halogen) is Cl, Br, or I] as the alkyl
electrophile because XCH2CN is more electro-
philic than other alkyl halides, reducing the
barrier for oxidative addition to Cu(I). In ad-
dition, because of the electron-withdrawing
property of the cyano group, the barrier for
C−C bond-forming reductive elimination from
a [(ligand)CuIII(CF3)2(CH2CN)] complex could
be sufficiently high for the product to be ob-
served directly and possibly isolated. We re-
port the isolation of Cu(III) complexes from
oxidative addition of haloacetonitrile to ionic
and neutral trifluoromethyl Cu(I) complexes.
Mechanistic investigation of these reactions,
conducted with a combination of computa-
tional and experimental studies, shows that
anionic and neutral complexes react with
the same alkyl halide by means of distinct
mechanisms.
Isolation and characterization of
Cu(III) products
We initially studied the reactions of [Ph4P]+
[Cu(CF3)2]− (1a) or a neutral Cu(I) complex
[(bpy)Cu(CF3)] (1b) with haloacetonitriles
ClCH2CN (2-Cl), BrCH2CN (2-Br), and ICH2CN
(2-I) or alkyl tosylate TsOCH2CN (2-OTs)
(Fig. 2A). The reaction of 2.0 equivalents of
anion 1a and bromide 2-Br in dimethyl
sulfoxide (DMSO) occurred smoothly at room
temperature after 3.0 hours to give two pre-
viously unknown species in an approximate
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Fig. 1. Mechanism of Cu-mediated cross-coupling. (A) General mechanism for Cu-catalyzed cross-coupling reaction. (B) Strategy that inverted the barrier for
oxidative addition (OA) and reductive elimination (RE) in the catalytic cycle for Cu-catalyzed cross-coupling. (C) State-of-the-art observations of oxidative addition of
alkyl halide to Cu(I) species. M, metal or quasi-metal; X, halogen; Y, dummy ligand; TM, transmetalation.
1:1 ratio in quantitative yield, as determined
by 19F NMR spectroscopy. One species, cor-
responding to chemical shifts of −33.4 and
−34.4 parts per million (ppm) in a 1:2 integral
ratio in the 19F NMR spectrum, was assigned
as the tetracoordinate ionic Cu(III) complex
[Ph4P]+[Cu(CF3)3(CH2CN)]− (3a) (fig. S1). Cu(III)
complex 3a was stable enough to be isolated
and characterized by 1H, 19F, and 31P NMR
spectroscopies and elemental analysis. The
structure of complex 3a was further con-
firmed by single-crystal x-ray diffraction, which
revealed a typical square-planar geometry (Fig.
2C, top). The second complex, corresponding to
a chemical shift at −27.0 ppm in the 19F NMR
spectrum, was assigned as a cuprate(I) spe-
cies, [Ph4P]+[Cu(CF3)(Br)]− (1c). We presume
that complexes 3a and 1c were generated
from transmetalation of the oxidative addi-
tion product [Ph4P]+[Cu(CF3)2(CH2CN)(Br)]−
with Cu(I) complex [Ph4P]+[Cu(CF3)2]− (1a).
It was found that complex 1c was much less
reactive than complex 1a. It reacted with 1.0
equivalent of bromide 2-Br in DMSO, result-
ing in 30% conversion and 9% yield of 3a after
3 hours at room temperature. Thus, the for-
mation of bromocuprate 1c does not affect the
oxidative addition of 2-Br to [Ph4P]+[Cu(CF3)2]−
(1a). As did the reaction of bromide 2-Br, the
reaction of iodide 2-I with cuprate 1a occur-
red smoothly to give Cu(III) complex 3a in
more than 90% yield and [Ph4P]+[Cu(CF3)(I)]−
(1d) in 62% yield, respectively. By contrast, the
reaction of chloride 2-Cl with cuprate 1a was
much slower, and the starting materials re-
mained intact even after 5 hours at room tem-
perature (Fig. 2A). We also studied the reaction
of tosylate 2-OTs with 1a and found that com-
plex 1a was fully converted within 3 hours at
25°C, but the yield for the formation of Cu(III)
complex 3a was much lower (15%) than those
from the reactions of 2-Br or 2-I (Fig. 2A).
The reaction of neutral Cu(I) complex [(bpy)
Cu(CF3)] (1b) with BrCH2CN (2-Br) occurred
much faster than that of ionic Cu(I) complex
[Ph4P]+[Cu(CF3)2]− (1a). The reaction of 1b with
bromide 2-Br in N,N-dimethylformamide
(DMF) generated trans-[(bpy)Cu(CF3)2(CH2CN)]
(trans-4) and cis-[(bpy)Cu(CF3)2(CH2CN)] (cis-
4) in 56 and 4% yields, as well as [(bpy)CuBr],
respectively, after just 1 min at room temper-
ature (Fig. 2B). Complex trans-4 was fully
characterized by 1H and 19F NMR spectros-
copies, as well as elemental analysis.
X-ray diffraction of the single crystal of
trans-4 shows that it adopts a distorted square-
pyramidal geometry. The H2C−Cu−N angle to
the apical nitrogen is 121.9°, and that to the
equatorial nitrogen is 160.2°; the length of the
N−Cu bond at the apical position (2.236 Å) is
considerably longer than that of the N−Cu
bond in the equatorial position (1.987 Å), indi-
cating that the geometry is closer to a square-
based pyramid than a trigonal bipyramid
(Fig. 2C, bottom).
Reaction of complex 1b with iodide 2-I also
occurred quickly to give trans-4 and cis-4 in
67 and 11% yields, respectively, under similar
conditions (Fig. 2B). In contrast to cuprate 1a,
the neutral complex 1b reacted with chloride
2-Cl to give trans-4 in 49% yield at room
temperature after just 1 hour (Fig. 2B). These
rapid rates indicate that the neutral Cu(I) com-
plex 1b is much more reactive toward the alkyl
halide than is ionic Cu(I) complex 1a, reflect-
ing a sizable ligand acceleration (Fig. 2D).
Such a phenomenon has previously been ob-
served in various copper-mediated or -catalyzed
cross-coupling reactions (40, 41).
The large difference in reactivity of ionic
and neutral Cu(I) complexes led us to conduct
Luo et al., Science 381, 1072–1079 (2023)
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reactions that would reveal the mechanisms
by which the two complexes react with alkyl
halides. The reaction of bromide 2-Br with
ionic Cu(I) complex [Ph4P]+[Cu(CF3)2]− (1a)
was sensitive to the polarity of the solvent.
The reactions conducted in polar solvents, such
as DMSO, N,N-dimethylacetamide (DMAc),
and DMF, proceeded to 96, 87, and 76% con-
version at room temperature over 5 hours
and afforded Cu(III) complex 3a in 93, 70, and
60% yields, respectively (table S1), whereas the
same reactions in less-polar solvents, such as
tetrahydrofuran (THF) or CH2Cl2, occurred
more slowly (24 and 12% conversions after
5 hours at room temperature) to give com-
plex 3a in just 13 and 11% yields, respectively
(Fig. 2E). By contrast, the reaction of chloride
2-Cl or bromide 2-Br with the neutral Cu(I)
complex [(bpy)Cu(CF3)] (1b) was not sensitive
to the polarity of the solvent. Reactions of com-
plex 1b with chloride 2-Cl in the more-polar
solvent DMF or the less-polar solvent THF oc-
curred to full conversion after 1 hour at room
temperature to afford Cu(III) complex trans-4
in 59 and 82% yields, respectively (Fig. 2E).
Quantitative assessment of the reaction of chlo-
ride 2-Cl with complex 1b in THF and DMF at
−5°C showed that the rates of the two reac-
tions are similar [(3.02 ± 0.10) × 10−3 M−1·s−1 in
THF and (3.43 ± 0.32) × 10−3 M−1·s−1 in DMF,
Fig. 2. Oxidative addition of alkyl halides to Cu(I) complexes. (A) Oxidative addition of XCH(R)CN with ionic Cu(I) complex [Ph4P]+[Cu(CF3)2]− (1a). (B) Oxidative
addition of XCH(R)CN with [(bpy)Cu(CF3)] (1b). (C) ORTEP (Oak Ridge Thermal Ellipsoid Plot) diagrams of [Ph4P]+[Cu(CF3)3(CH2CN)]− (3a) (countercation
Ph4P+ is omitted for clarity) and trans-[(bpy)Cu(CF3)2(CH2CN)] (trans-4). Ellipsoids are shown at the 50% level. (D) Reaction progress for ionic Cu(I) complex
[Ph4P]+[Cu(CF3)2]− (1a) with BrCH2CN (2-Br) at 298 K (blue) or neutral Cu(I) complex [(bpy)Cu(CF3)] (1b) with BrCH2CN (2-Br) at 298 K (red). (E) Solvent effect on
the reactions of BrCH2CN with [Ph4P]+[Cu(CF3)2]− (1a) (blue) or [(bpy)Cu(CF3)] (1b) (red). DCM, dichloromethane; MeCN, acetonitrile (methyl cyanide).
Luo et al., Science 381, 1072–1079 (2023)
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respectively (fig. S25)]. The different sensitivities
of the ionic and neutral Cu(I) species to sol-
vent polarity indicate that these Cu(I) com-
plexes might react with the alkyl halide through
different mechanisms.
Kinetic studies
To investigate the effect of the properties of
the C−X bond of the haloacetonitriles on the
reactions with cuprate [Ph4P]+[Cu(CF3)2]− (1a)
or neutral [(bpy)Cu(CF3)] (1b), we compared
the rates of reactions of 1a or 1b with XCH2CN
quantitatively by monitoring the 19F NMR sig-
nals corresponding to 1a for reaction of com-
plex 1a and the signals corresponding to trans-4
and cis-4 for the reaction of complex 1b.
These studies showed that reactions of the ate
complex are first order in complex 1a and first
order in bromide 2-Br (Fig. 3A and figs. S3 to
S6). The reaction of complex 1a with iodide
2-I [(8.54 ± 0.04) × 10−3 M−1·s−1] was about
five times as fast as that with bromide 2-Br
[(1.78 ± 0.03) × 10−3 M−1·s−1 at 25°C]. Because
complex 1a reacted with chloride 2-Cl slowly
at room temperature (Figs. 2A and 3A), we
studied the reaction at elevated temperature.
At 60°C, the reaction occurred with a rate
constant of (1.99 ± 0.14) × 10−4 M−1·s−1. The
rate constant for the reaction of complex 1a
with bromide 2-Br at 60°C was estimated to
be 4.05 × 10−2 M−1·s−1 on the basis of the Eyring
analysis in Fig. 3C, which is roughly 200 times
as fast as that with chloride 2-Cl.
The rates of the reactions of the halides with
neutral complex 1b were measured with 19F
NMR spectroscopy below room temperature
because of their high rate. The reaction of bro-
mide 2-Br with [(bpy)Cu(CF3)] (1b) at −30°C
proceeded to full conversion after 20 min.
Kinetic studies showed that this reaction is
first order in both reactants and that the rate
constant at −30°C is (2.63 ± 0.05) × 10−2 M−1·s−1.
At this temperature after 5 min, the reaction of
chloride 2-Cl with [(bpy)Cu(CF3)] (1b) pro-
ceeded to <1% conversion (Fig. 3B). However,
the reaction of chloride 2-Cl with complex 1b
at −5°C occurred with a rate constant of (3.43 ±
0.32) × 10−3 M−1·s−1. According to the Eyring
analysis shown in Fig. 3C, the rate constant for
reaction of complex 1b with bromide 2-Br at
−5°C was estimated to be 0.37 M−1·s−1, which
is roughly 100 times greater than that of the
reaction of complex 1b with chloride 2-Cl. The
rate dependence of these reactions of the ionic
and neutral Cu(I) species on the strength of the
C−X bond and on the leaving group ability of
the alkyl halides is consistent with typical Cu(I)-
catalyzed cross-coupling reactions.
To evaluate the effect of the steric proper-
ties of the alkyl bromide on the reaction of the
Cu(I) complex, we studied the reaction of Cu(I)
complex [Ph4P]+[Cu(CF3)2]− (1a) with the sec-
ondary alkyl halide, 2-bromopropionitrile
2-Br-Me, and the tertiary alkyl halide, 2-methyl-
2-bromopropionitrile 2-Br-Me2 (Fig. 2A). Re-
action of cuprate 1a with 2-bromopropionitrile
2-Br-Me occurred smoothly at room temper-
ature over 5 hours to give Cu(III) complex 3b in
81% yield. Yet, this reaction of the more steri-
cally hindered 2-bromopropionitrile 2-Br-Me
was slower than that of the less-hindered bromo-
acetonitrile 2-Br [(1.15 ± 0.01) × 10−3 M−1·s−1
versus (1.78 ± 0.03) × 10−3 M−1· s−1]. To de-
termine whether the reactions of complex 1a
occurred with inversion of configuration, we
conducted the reaction of 1a with optically
active (R)-2-bromopropionitrile (R)-2-Br-Me,
but the enantiomers of the resulting product
Fig. 3. Kinetic analysis. Kinetic data were fit to the expression of [1a]t = [1a]0e−kobs + c
for (A) and [4]t = A − Be−kobs for (B), in which t is time and kobs are the apparent
(observed) rate constants (pages S12 and S35 to S38 provide details about derivation
of expression of corrected rate constant kcorr from kobs). (A) Kinetic profiles of
oxidative addition of XCH(R)CN (where X is Cl, Br, or I; and R is H or Me) with ionic
Cu(I) complex [Ph4P]+[Cu(CF3)2]− (1a) at 298 K. (B) Kinetic profiles of oxidative
addition of XCH2CN (where X is Cl or Br) with [(bpy)Cu(CF3)] (1b) at 243 K. (C) Eyring
analysis of the temperature dependence of the rate constants of oxidative addition
of BrCH2CN with [Ph4P]+[Cu(CF3)2]− (1a) (blue), oxidative addition of BrCH2CN
with [(bpy)Cu(CF3)] (1b) (green), and oxidative addition of ClCH2CN with
[(bpy)Cu(CF3)] (1b) (red). (D) Effect of added free bipyridine on oxidative addition
of ClCH2CN with [(bpy)Cu(CF3)] (1b) at 268 K.
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Fig. 4. Five proposed pathways for the oxidative addition of haloacetoni-
triles to ionic or neutral Cu(I) complexes and free energies of each
species computed with DFT. The calculated activation free energies for
the oxidative addition of BrCH2CN(2-Br) to the ionic Cu(I) complex
[Ph4P]+[Cu(CF3)2]− (1a) in DMSO are given in blue, and those for oxidative
addition of ClCH2CN (2-Cl) to the neutral [(bpy)Cu(CF3)] (1b) in DMF are
given in red. The energies are in kilocalories per mole and indicate the
relative free energies calculated at the PBE0-D3(BJ)/Def2-TZVP(SMD,
solvent)//PBE0-D3(BJ)/Def2-SVP(SMD,solvent) level. SMD, solvation
model density.
3b did not separate through chiral high-
performance liquid chromatography (HPLC)
column and only weakly absorbed in the ultra-
violet, preventing assessment of the configu-
ration of the product with chromatography or
spectroscopy. The reaction of 1a with the ter-
tiary alkyl halide, 2-methyl-2-bromopropionitrile
2-Br-Me2, did not afford the corresponding
Cu(III) complex from oxidative addition. In-
stead, Cu(III) complex [Ph4P]+[Cu(CF3)4]− and
Cu(I) complex [Ph4P]+[Cu(CF3)(Br)]− formed in
31 and 7% yields, respectively, as determined
by 19F NMR spectroscopy of the reaction mix-
ture, as well as a few unidentified Cu(II) spe-
cies, which were indicated by the color of the
reaction mixture turning green. Analysis of the
reaction mixture showed that isobutyronitrile
6 also formed through hydrodehalogenation.
This observation suggests that the reaction
forms the isobutyronitrile radical, which is too
sterically hindered to combine with the trifluo-
romethyl Cu(II) species and, instead, abstracts
a hydrogen atom from the solvent. The reac-
tion of 2-chloropropionitrile 2-Cl-Me with the
neutral complex [(bpy)Cu(CF3)] (1b) occurred
over 1 hour at 25°C to generate the correspond-
ing Cu(III) complex trans-4b in 12% yield.
This complex was characterized with 19F NMR
spectroscopy because it was too unstable to be
isolated.
Inhibition studies
To probe whether the oxidative additions of
XCH2CN to Cu(I) complexes [Ph4P]+[Cu(CF3)2]−
(1a) and [(bpy)Cu(CF3)] (1b) occur by means
of a radical intermediate and whether a po-
tential radical would form through initial SET,
we first studied the reaction in the presence of
radical inhibitor 2,2,6,6-tetramethylpiperidine-
1-oxyl (TEMPO) and in the presence of SET
inhibitor 1,4-dinitrobenzene. The reaction of 1a
with BrCH2CN 2-Br in the presence of 2.0 equiv-
alents of TEMPO was complete after 3 hours
at room temperature. The yield of this reaction
(64%) was only 29% less than that in the ab-
sence of TEMPO, and only 19% of the radical
adduct TEMPO−CH2CN 5 was isolated (Fig. 2A).
By contrast, TEMPO had a strong effect on the
reaction of 1b with ClCH2CN 2-Cl, resulting in
the formation of trans-4 in 10% yield and
TEMPO-CH2CN 5 in 75% yield (Fig. 2B). SET
inhibitor 1,4-dinitrobenzene did not noticeably
affect the reaction of haloacetonitrile with either
the ionic Cu(I) complex 1a or the neutral Cu(I)
complex 1b. These results suggest that alkyl radi-
cals are generated in the oxidative addition of 1a
or 1b with bromoacetonitrile but that a SET pro-
cess is unlikely to lead to the radical in either case.
Effect of ligand
The bipyridine ligand in complex 1b could in
principle dissociate from the metal center to
create a less sterically hindered intermediate
that reacts with the alkyl halide. If reaction of
ClCH2CN with neutral Cu(I) complex [(bpy)Cu(CF3)]
(1b) occurred through reversible dissociation
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of the bipyridine, addition of free bipyridine
to the reaction should substantially reduce the
rate. The reactions in the presence of varying
amounts of bipyridine (3.0, 6.0, and 10.0 equiv-
alents versus 1b) occurred with nearly equal
rate constants [(2.81 ± 0.01) × 10−3 M−1·s−1,
(3.33 ± 0.21) × 10−3 M−1·s−1, and (2.91 ± 0.12) ×
10−3 M−1·s−1, respectively] and were only slight-
ly slower than the reaction in the absence of
added 2,2′-bipyridine [(3.61 ± 0.08) × 10−3
M−1·s−1] (Fig. 3D). These data imply that re-
versible dissociation of the ligand does not
precede rate-limiting oxidative addition to 1b.
Activation parameters
To determine the enthalpy and entropy of ac-
tivation of both reactions, we studied the ef-
fect of the temperature on the rates. An Eyring
plot of ln(k/T) versus 1/T (where k is the rate
constant and T is temperature) for the reac-
tion of ionic Cu(I) complex [Ph4P]+[Cu(CF3)2]−
(1a) with bromide 2-Br between 25° and 37°C
revealed an activation enthalpy, DH‡, of 17.7 ±
0.4 kcal/mol and an activation entropy, DS‡, of
−12 ± 1 entropy units (e.u.) (Fig. 3C, blue).
Likewise, an Eyring analysis of the reaction
of neutral Cu(I) complex [(bpy)Cu(CF3)] (1b)
with 2-Br over a temperature range of −30° to
−20°C revealed an activation enthalpy, DH‡, of
13.0 ± 0.6 kcal/mol and a similar activation
entropy, DS‡, of −12 ± 2 e.u. (Fig. 3C, green).
The activation entropies of the reactions of 1a
and of 1b with 2-Br were similar, but the ac-
tivation enthalpy for the reaction of 2-Br with
1b was much less than that with 1a. An Eyring
analysis of the reaction of [(bpy)Cu(CF3)] (1b)
with ClCH2CN (2-Cl) between −8° and 4°C
revealed a DH‡ of 15.2 ± 0.8 kcal/mol and a
DS‡ of −13 ± 3 e.u. (Fig. 3C, red), and this value
for DH‡ is similar to, or even slightly less than,
that for oxidative addition of BrCH2CN (2-Br)
to cuprate(I) complex Ph4P+[Cu(CF3)2]− (1a)
(17.7 ± 0.4 kcal/mol), even though the C−Cl
bond in ClCH2CN (2-Cl) (70.5 kcal/mol) is much
stronger than the C−Br bond in BrCH2CN
(2-Br) (56.8 kcal/mol) and the chloride is less
polarizable and is a poorer leaving group than
bromide (42).
To define the mechanism of the reaction of
haloacetonitrile with the ionic or neutral Cu(I)
species further, we performed density func-
tional theory (DFT) calculations with the PBE0-
D3(BJ) functional. On the basis of previous
proposals for the mechanism of copper-mediated
cross-coupling reactions (18–22) and the ex-
perimental results reported in this work, we
proposed five different pathways that could
account for the oxidative addition of haloace-
tonitrile to ionic and neutral Cu(I) complexes
(Fig. 4). The first pathway (pathway A) in-
volves an SN2 step and is a common type of
two-electron oxidative addition of alkyl halides
to late transition metals, such as Pt (43) and
Pd (44). In addition, such a pathway was pro-
posed by Whitesides (45) and Pearson (46) for
the reaction of lithium dialkylcuprates with
alkyl halides (the Corey-Posner reaction) to
generate a Cu(III) intermediate, which would
then undergo fast reductive elimination to
form the C−C bond in the product. In our case,
reaction of 1a through this mechanism would
form Cu(III) species [CuIII(CF3)2(CH2CN)] or
[Ph4P]+[CuIII(CF3)2(X)(CH2CN)]–, which would
then undergo transmetalation with 1a to gen-
erate [Ph4P]+[CuIII(CF3)3(CH2CN)]– (3a) and
[Cu(CF3)X]–. Likewise, reaction with 1b would
give [(bpy)CuIII(CF3)(CH2CN)]+ or [(bpy)CuIII
(CF3)(X)(CH2CN)], which would undergo trans-
metalation with 1b to give [(bpy)CuIII(CF3)2
(CH2CN)] (trans-4 or cis-4) and [(bpy)CuX],
respectively (details about transmetalation are
provided in fig. S31). A second two-electron
mechanism for oxidative addition would be
a concerted addition of the C−X bond to the
metal center (pathway B), and this step would
be the reverse reaction of concerted reductive
elimination from a high-valent Cu center. A
third pathway for oxidative addition of alkyl
halides to a Cu(I) center could occur through
consecutive single-electron steps. One commonly
proposed mechanism for oxidative addition
through single-electron steps is outer-sphere
SET (OSET; pathway C), which dominates the
redox manifolds of first-row transition metals,
including Fe (47) and Ni (48). A fourth path-
way and an alternative mechanism for oxida-
tive addition through single-electron steps is
halogen-atom transfer (XAT; pathway D) (49, 50).
Ligated Cu(I) complexes are widely used in
atom-transfer radical addition or polymeriza-
tion (ATRA or ATRP) processes in which a
XAT to Cu is involved (51). A fifth pathway,
oxidative addition of the alkyl halide to Cu(I),
could occur by initial ligand dissociation to
generate a neutral, ligandless [CuCF3], which
would undergo oxidative addition of the alkyl
halide to generate a Cu(III) intermediate that
would recoordinate the dative ligand and
undergo transmetalation to give the final Cu(III)
complex (pathway E) (52). The energy param-
eters for these pathways were computed and
are shown in Fig. 4. In all five proposed mech-
anistic pathways, the formation of final product
3a from the reaction of 1a and the formation
of trans-4/cis-4 from reaction of 1b involve a
transmetalation step after initial formation of
a Cu(III) complex. The absence of observed in-
termediates before transmetalation and first-
order rate behavior in the Cu(I) species (1a or
1b) rule out both rate-limiting transmetala-
tion for these reactions and the initial gen-
eration of the Cu(III) intermediate through
reaction of two copper complexes.
Evidence for XAT and SN2 pathways
On the basis of the experimental results and
DFT calculations, we concluded that reaction
of the ionic Cu(I) complex [Ph4P]+[Cu(CF3)2]−
(1a) with BrCH2CN (2-Br) likely proceeds by
means of two different pathways, specifically
the major fraction through an SN2-type pro-
cess (pathway A) and the minor fraction through
a XAT process (pathway D). We also con-
clude that the reaction of the neutral Cu(I)
complex [(bpy)Cu(CF3)] (1b) with ClCH2CN
(2-Cl) likely proceeds exclusively through a
XAT process (pathway D). The following analy-
sis of our experimental and computational
data lead to these conclusions.
The experimental observation that both re-
actions were partially or fully inhibited by the
presence of the radical inhibitor TEMPO argues
against a concerted pathway for oxidative ad-
dition of BrCH2CN (2-Br) to ionic Cu(I) com-
plex [Ph4P]+[Cu(CF3)2]− (1a) or for oxidative
addition of ClCH2CN (2-Cl) to neutral Cu(I)
complex [(bpy)Cu(CF3)] (1b) (Fig. 4, pathway
A). In addition, DFT calculations showed that
the computed barrier (42.5 kcal/mol) for oxi-
dative addition of BrCH2CN (2-Br) to complex
1a through a concerted pathway (pathway A)
is much greater than that of the SN2-type path-
way (pathway B; 22.5 kcal/mol) (Fig. 4) or XAT
process (pathway D; 23.8 kcal/mol) (Fig. 4).
Likewise, the computed barrier (36.3 kcal/mol)
for oxidative addition of ClCH2CN (2-Cl) to
complex 1b by pathway A is about 16.0 kcal/
mol greater than the lowest-energy alternative
pathway, in this case the XAT process (path-
way D; 20.3 kcal/mol).
The experimental observation that the addi-
tion of SET inhibitor 1,4-dinitrobenzene did
not greatly affect either oxidative addition
process argues against an OSET pathway (Fig.
4, pathway C). Moreover, the computed bar-
riers for both reactions through an OSET
pathway (39.3 kcal/mol and 24.3 kcal/mol, re-
spectively) are 16.8 kcal/mol and 4.0 kcal/mol
greater than the SN2-type pathway A for reac-
tion with complex 1a or XAT pathway D for
reaction with complex 1b. Thus, both the ex-
perimental and computational data are incon-
sistent with reaction through an OSET pathway
(Fig. 4, pathway C).
By contrast, the relative reactivity of the
alkyl electrophiles toward the ionic Cu(I) complex
1a of ICH2CN > BrCH2CN >> TsOCH2CN >>
ClCH2CN is consistent with an SN2-type path-
way B. In addition, the reaction of the second-
ary alkyl bromide 2-bromopropionitrile 2-Br-Me
with ionic Cu(I) complex 1a, which is 1.5 times
as slow as that of the less-hindered bromoace-
tonitrile 2-Br [(1.15 ± 0.01) × 10−3 M−1·s−1 versus
(1.78 ± 0.03) × 10−3 M−1· s−1], is inconsistent with
OSET or XAT pathways (Fig. 4, pathways C and
D). The reaction of a secondary alkyl halide
through an OSET or XAT pathway would be
faster than that of the primary alkyl halide
because of the greater stability of the second-
ary alkyl radical.
Also consistent with reaction through an
SN2 pathway B, the reactions of complex 1a
Luo et al., Science 381, 1072–1079 (2023)
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with BrCH2CN (2-Br) in polar solvents were
faster than those in less-polar solvents, and the
more sterically hindered 2-bromopropionitrile
2-Br-Me reacted more slowly than did 2-Br.
The generation of TEMPO−CH2CN as a side
product from the reaction of complex 1a with
BrCH2CN (2-Br) in the presence of TEMPO
suggests that an alternative but minor path-
way also occurs during the reaction of the
cuprate 1a. Consistent with this experimental
observation, the barrier for a reaction of 1a
with BrCH2CN (2-Br) through a XAT pathway
D (23.8 kcal/mol) computed with DFT was
only 1.3 kcal/mol greater than that of the SN2-
type pathway B. Furthermore, the calculated
barrier (22.5 kcal/mol for SN2-type pathway
B and 23.8 kcal/mol for XAT pathway D) is
close to the corresponding experimentally ob-
served activation energy (21.3 kcal/mol), which
provides additional evidence to support the
proposed mechanism for reaction of 1a with
haloacetonitrile.
Our data for reaction of the neutral copper
complex 1b are more consistent with XAT
pathway D as the dominant mechanism. The
considerable inhibiting effect of the addition
of TEMPO on the reaction of chloroacetoni-
trile 2-Cl with [(bpy)Cu(CF3)] (1b) suggests
that a free radical •CH2CN is generated. The
barrier for an OSET pathway C computed with
DFT (24.3 kcal/mol) is much higher than that
of the XAT process (pathway D, 20.3 kcal/mol).
In addition, the calculated Gibbs free energy
(DG; 20.3 kcal/mol) is close to the barrier
(18.6 kcal/mol) determined experimentally,
implying that a XAT process (pathway D) is
the most likely pathway involving an alkyl rad-
ical for oxidative addition of alkyl halides to the
neutral Cu(I) complex 1b.
Our experimental and computational data
are most consistent with reaction of the alkyl
halide directly with [(bpy)Cu(CF3)] (1b). The
zero-order dependence on ligand is inconsistent
with reversible ligand dissociation followed
by oxidative addition (Fig. 4, pathway E). Fur-
thermore, the computed DG for dissociation
of bipyridine from complex 1b (17.5 kcal/mol)
is accessible, but the computed barrier for a
XAT process (pathway D) from ClCH2CN to
the resulting ligandless [CuCF3] is an addi-
tional 22.1 kcal/mol. The combination of these
energies is much greater than the computed
DG‡ (20.3 kcal/mol) for direct XAT to 1b (path-
way D).
To gain more insight into the oxidative ad-
dition of the haloacetonitrile to Cu(I) complex
1a and 1b, we conducted natural population
analysis (NPA) on reactants 1a, 1b, 2-Br, and
2-Cl; transition states TS-a-SN2, TS-a-XAT
and TS-b-XAT; and products [LnCuIII(CF3)
− or bpy) (figs.
(X)(CH2CN)] (where Ln is CF3
S33 and S35). These studies showed that a
small amount of positive charge accumulates
on the copper in the transition states (+0.26
for 1a versus +0.35 for [CuIII(CF3)2(Br)(CH2CN)]−)
during the reaction of 1a with 2-Br (53, 54)
and that the negative charge of the CF3 moiety
decreases considerably (−1.26 for 1a versus
−0.59 for [CuIII(CF3)2(Br)(CH2CN)]−). Even
though the change in charge to copper from
starting complex to the intermediate after oxi-
dative addition is small, the sum of the nega-
tive charge of the bromide and cyanomethyl
ligands (−CH2CN) is large (−0.76 e−). The same
trend was also observed for the reaction of 2-Cl
with 1b. These changes in charge show that
electron density flows from the complexes 1a
or 1b overall to the haloacetonitriles during the
reaction, thus demonstrating that reaction of
haloacetonitrile to 1a or 1b can be considered
an oxidative addition process.
Previous proposals for the mechanism of
copper-catalyzed cross-coupling often involve
a Cu(I)/Cu(II) redox cycle, on the basis of the
experimental evidence for the presence of free
radicals, which was typically deduced from
quenching experiments with radical scav-
engers or from racemization or rearrange-
ments of radical clock substrates. Our studies
suggest that a free radical could be involved in
the oxidative addition of an alkyl halide to Cu
(I) to form a Cu(III) intermediate in these
pathways through XAT. Oxidative addition
of the C(sp3)−X bond to a Cu(I) species is
often considered to be the rate-limiting step
of copper-catalyzed cross-coupling reactions
of alkyl electrophiles, but studies of this ele-
mentary step alone are rare, largely because
of the inherent instability of the copper in-
termediate. Thus, the example of oxidative
addition of a C(sp3)−X bond to Cu(I) in the
current study may help develop more efficient
copper-catalyzed cross-coupling reactions of
alkyl electrophiles.
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AC KNOWLED GME NTS
Funding: Q.S. gratefully acknowledges financial support from the
National Key Research and Development Program of China
(2021YFF0701700) and the National Natural Science Foundation of
China (22061160465). X-S.X. acknowledges financial support from
the National Natural Science Foundation of China (22122104).
J.F.H. acknowledges funding from the NIH (R35GM130387). Y. Luo
thanks Syngenta for a PhD scholarship. Author contributions:
Y. Luo performed the experiments and analyzed experimental data.
Y. Li performed the DFT calculations. J.W. assisted in the kinetic
studies. X.-S.X., J.F.H., and Q.S. directed the research. Y. Luo,
J.F.H., and Q.S. wrote the manuscript. Competing interests: The
authors declare that they have no competing interests. Data
materials and availability: Crystallographic data are available free
Luo et al., Science 381, 1072–1079 (2023)
8 September 2023
7 of 8
RES EARCH | R E S E A R C H A R T I C L E
of charge from the Cambridge Crystallographic Data Centre
(CCDC) under CCDC 2236874 (3a), 2236875 (3b), and 2236887
(trans-4). All other data reported in this paper are available in the
manuscript or the supplementary materials. License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg9232
Materials and Methods
Figs. S1 to S36
Tables S1 to S15
References (55–76)
Submitted 26 May 2023; accepted 10 August 2023
10.1126/science.adg9232
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RES EARCH
R E S E A R C H A R T I C L E S U M M A R Y
◥
ANTIMICROBIAL PROTEINS
The mechanism of the phage-encoded protein
antibiotic from FX174
Anna K. Orta†, Nadia Riera†, Yancheng E. Li, Shiho Tanaka, Hyun Gi Yun,
Lada Klaic, William M. Clemons Jr.*
INTRODUCTION: As part of their life cycle, viruses
must escape from their hosts. For bacteriophages,
this process requires breaching the bacterial cell
wall and the peptidoglycan layer. Small, single-
strand DNA and RNA phages have evolved single-
gene lysis proteins that disrupt peptidoglycan
biosynthesis and trigger cell lysis, a mechanism
also used by some antibiotics. The best-studied
of these is protein E from the historically impor-
tant phage ΦX174, a 91–amino acid protein that
contains a conserved N-terminal transmembrane
helix and an extended cytoplasmic C-terminus.
RATIONALE: Mutagenesis studies have dem-
onstrated that the protein E transmembrane
domain is sufficient for lysis, with functional
mutants mapping to one face of the single
transmembrane helix. The strongest pheno-
types were observed for conserved prolines in
this domain of protein E, with one proline being
essential for lysis. Wild-type protein E requires
the constitutively expressed bacterial chaper-
one SlyD (sensitivity to lysis D), which contains
a prolyl isomerase domain and a chaperone
domain. Previous work had identified mutants
The escape of FX174 from its bacterial host. In the membrane is the YES complex [E. coli enzyme MraY
(cyan), phage protein E (yellow), and E. coli chaperone SlyD (purple)] where protein E disrupts peptidoglycan
synthesis by inhibiting MraY and allowing breaching of the cell wall (tan). Assembled FX174 phage particles
are shown in gray. In the background are bacterial cells that are lysing at their septal division point.
in MraY that confer resistance to protein E–
mediated lysis. MraY catalyzes the synthesis
of a peptidoglycan precursor from a soluble
nucleoside-sugar-peptide and a phospholipid
substrate. Although many functional ques-
tions remain about MraY, here we sought to
understand how a phage protein could spe-
cifically inhibit this key enzyme and what role
SlyD performed in the process.
RESULTS: We established that phage protein E
forms a stable complex with the Escherichia
coli proteins MraY and SlyD, designated the
YES complex (MraY, protein E, SlyD). After
solubilizing in detergent, we determined struc-
tures of the YES complex by single-particle elec-
tron cryo–microscopy. In our structures, the
MraY dimer adopts a back-to-back orientation
with the membrane-exposed active sites facing
away from each other. Two SlyD molecules can
be fit into the density on the cytoplasmic side.
The two MraY and SlyD chains are bridged by
two protein E molecules. The transmembrane
helix of protein E occupies a groove on MraY
corresponding to the putative binding site of the
lipid substrate. At the cytoplasmic surface, the
transmembrane domain of protein E bends to
cross the active site, followed by an a-helix that
extends to the chaperone domain of SlyD. The C-
terminus of protein E continues through a
peptide-binding groove in the second SlyD and
into the prolyl isomerase active site. The conse-
quence is that protein E inhibits MraY by block-
ing lipid access to the active site. Previous protein
E mutant phenotypes are explained by the struc-
ture including the essential proline that allows for
a kink in the transmembrane helix. For MraY, we
can resolve the full chain including the conserved
loop between TM1 and TM2. We show that the
N terminus of MraY forms an a-helical stack
with TM2 and identify ordered lipids on the
protein surface. Finally, we provide evidence
that the role of SlyD is to stabilize the complex.
CONCLUSION: Protein E directly inhibits MraY
by obstructing the MraY active site in a stable
complex with SlyD. This structure resolves key
questions about how the model phage FX174
kills bacteria and escapes the cell. In the FX174
genome, the gene encoding for protein E is
evolutionarily constrained by gene D, in which
it is embedded. The YES complex provides a
route for the rational design of protein E beyond
this gene D restraint. Single-gene lysis proteins,
like protein E, serve as useful models for the
development of antibacterial therapies.▪
The list of author affiliations is available in the full article.
*Corresponding author. Email: clemons@caltech.edu
†These authors contributed equally to this work.
Cite this article as A. K. Orta et al., Science 381, eadg9091
(2023). DOI: 10.1126/science.adg9091
READ THE FULL ARTICLE AT
https://doi.org/10.1126/science.adg9091
Orta et al., Science 381, 180 (2023)
14 July 2023
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RES EARCH
R E S E A R C H A R T I C L E
◥
ANTIMICROBIAL PROTEINS
The mechanism of the phage-encoded protein
antibiotic from FX174
Anna K. Orta1†, Nadia Riera1†, Yancheng E. Li1, Shiho Tanaka1, Hyun Gi Yun1,
Lada Klaic1, William M. Clemons Jr.1*
The historically important phage FX174 kills its host bacteria by encoding a 91-residue protein
antibiotic called protein E. Using single-particle electron cryo–microscopy, we demonstrate that protein
E bridges two bacterial proteins to form the transmembrane YES complex [MraY, protein E, sensitivity
to lysis D (SlyD)]. Protein E inhibits peptidoglycan biosynthesis by obstructing the MraY active site
leading to loss of lipid I production. We experimentally validate this result for two different viral species,
providing a clear model for bacterial lysis and unifying previous experimental data. Additionally, we
characterize the Escherichia coli MraY structure—revealing features of this essential enzyme—and the
structure of the chaperone SlyD bound to a protein. Our structures provide insights into the mechanism
of phage-mediated lysis and for structure-based design of phage therapeutics.
T he full realization of phage therapy as
a solution to the antimicrobial resist-
ance problem requires a fundamental
understanding of the mechanisms vi-
ruses use to kill their host (1–4). Nearly
100 years ago, the first medical application
of phages to treat infections used a cocktail
containing the historically important phage
FX174 (5). A rich source of critical discov-
eries in molecular biology (6–9), FX174 is a
member of the Bullavirinae subfamily within
Microviridae. It is found broadly in environ-
ments that contain coliform bacteria, such as
the human gut (10), with Escherichia coli as
its primary host. The 1977 publication of the
FX174 single-stranded 5.4-kilobase DNA ge-
nome was a milestone for genomics, reveal-
ing 11 open reading frames (ORFs) (11). Most
notable was the gene for lysis, E, that is em-
bedded within the ORF of the scaffolding gene
D (12). Expression of E alone is sufficient to kill
bacteria (13). Although a variety of lysis mech-
anisms have been proposed (14–16), the most
likely is that the product of E, protein E, disrupts
peptidoglycan (PG) biosynthesis, culminating
in a breach in the cell wall. In particular, pro-
tein E was demonstrated to directly inhibit the
integral membrane enzyme MraY (16) depen-
dent on the cytoplasmic chaperone SlyD (sen-
sitivity to lysis D) (17, 18).
Phage-derived single-gene lysis (SGL) pro-
teins, such as protein E, trigger cell lysis by
inhibiting PG biosynthesis [reviewed in (19)]
providing a route for killing bacteria. Protein
E includes a conserved N-terminal transmem-
brane domain (TMD), a cytoplasmic C-terminal
1Division of Chemistry and Chemical Engineering, California
Institute of Technology, Pasadena, CA 91125, USA.
*Corresponding author. Email: clemons@caltech.edu
†These authors contributed equally to this work.
domain with conserved positively charged
residues in a predicted amphipathic helix,
and an unstructured tail (Fig. 1A and fig. S1).
Fusions of globular proteins to the C termi-
nus of the TMD have demonstrated that the
TMD is sufficient for lysis (17, 20, 21). Exten-
sive mutational analysis identified key res-
idues in protein E including the essential
proline 21 (P21) (17, 20–23). The mechanism
through which SlyD and MraY work with
protein E to facilitate rupture of the cell wall
remains unknown. MraY, an important target
for antimicrobial drug discovery [reviewed
in (24)], catalyzes the transfer of a phospho-
MurNAc-pentapeptide from “Park’s nucleotide”
(UDP-MurNAc-pentapeptide) onto the phos-
phate group of the 55 carbon polyisoprenyl-
phosphate (C55P) generating lipid I. X-ray
crystal structures of MraY in detergent from
the thermophilic Gram-negative Aquifex aeolicus
(AaMraY) (25, 26) or the Gram-positive Enterocloster
bolteae (EbMraY) (27) revealed a conserved
homodimeric structure, with ten TMDs per
subunit. The structures localized the active
site in a vestibule on the cytoplasmic side of a
membrane-exposed cleft formed by TMDs 4,
5, and 9, which is the predicted access site for
the lipid substrate (28). The constitutively
expressed but nonessential (29) metallocha-
perone (30) SlyD contains two conserved core
domains: an FK506-binding protein (FKBP)
prolyl-isomerase domain and an insertion-in-
flap (IF) domain that binds unfolded peptides
by b-augmentation (18, 31–33). The disordered
SlyD C terminus (31), although important for
metal binding, can be deleted without affect-
ing chaperone activity (34).
In the present study, we resolve the mech-
anism of peptidoglycan biosynthesis inhibition
by protein E. We determined the structure of
the dimeric heterotrimer YES complex (EcMraY,
viral protein E, EcSlyD) revealing that protein
E physically blocks the lipid substrate from
accessing the MraY active site. This work
provides mechanistic insight into all three
proteins and suggests a path toward devel-
opment of antibacterial agents.
The structure of the YES complex
We used the protein E sequence from either the
original phage FX174 or the shorter protein E
isoform from phage ID21 (91 and 76 residues
respectively), both from within Bullavirinae
(Fig. 1A and fig. S1). We coexpressed an affinity-
tagged protein EFX174 and wild-type (WT)
EcMraY. After purification, a stable complex
formed a single peak during size-exclusion
chromatography (SEC) but resolved into four
bands on a gel, two of which corresponded to
the endogenous EcSlyD (fig. S2A). A SlyD variant
with the disordered C terminus removed res-
cued lysis activity in an E. coli DslyD strain (fig.
S2, B to D) and ran as a single band on a gel (Fig.
1B) (18, 30). This truncation, SlyD154, was used
for subsequent work except where noted.
The two protein E isoforms induced lysis at
similar efficiencies when expressed in a WT
E. coli strain (Fig. 1C). For purification, all three
genes in the YES complex (WT EcMraY, protein
E, and truncated EcSlyD) were recombinantly
expressed together in the DslyD strain with
a C-terminal affinity tag on protein E. The
complex was extracted in detergent and ran
as a single peak by SEC with all three proteins
in an apparent stoichiometric complex (Fig.
1B). Structures for both the YESFX174 and
YESID21 complexes were solved using single-
particle electron cryo–microscopy (cryo-EM)
(Fig. 1D and figs. S3 and S4). The final density
maps were obtained following several rounds
of data processing with heterogeneous and ho-
mogeneous refinements (figs. S3 and S4). The
final overall masked resolution was 3.5 Å for
the YESID21 complex and 3.6 Å for the YESFX174
complex (fig. S5). Statistics are provided in
table S2. For both structures, the resolution
was higher for regions in and adjacent to the
membrane (figs. S3 and S4). We unambiguously
built 90% of the protein residues in the complex.
Sequence differences between the protein E
variants are visible in the density (fig. S5), gen-
erally exposed on the surface of the complex.
The YESID21 complex is used as the reference
structure, except where noted.
Within the density map, we could clearly
distinguish two copies of each member of the
YES complex (six separate proteins). When
contoured to remove the detergent micelle,
densities for 22 TMDs are clear, 20 of which
are accounted for by the EcMraY dimer (Fig.
1, D and E). Most of the cytoplasmic density
can be accounted for by two SlyD molecules,
which is the most flexible region of the com-
plex (fig. S6D). The remaining protein den-
sity corresponds to two protein E molecules
Orta et al., Science 381, eadg9091 (2023)
14 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
Transmembrane Domain
Amphipathic Helix
B
C
10
20
30
40
50
X174
ID21 MGHWT L S G I L A F L L L L S L L L P S L L I MF I P L T FRRP A S SWK A RS L QK I L L MA S S
ME RWT L L D I L A F L L L L S L L L P S L L I MF I P S MY K QHA S LWK A RS L A K T L S MA S S
MV RWT LWD T L A F L L L L S L L L P S L L I MF I P S T FK RP V S SWK A L N L RK T L L MA S S
G4 ME HWT L S G I L A F L L L L S L F L P S L L I MF I P L TS K P P V S SWK V L S L P K TS S MV L N
ID8 ME HWT L S G I L A F L L L L S L L L P S L L I MF I P L TS K P P V S SWK V L S L P K TS S MV L N
*
*
*
*
*
*
*
ID21
X174
G4
ID8
D
60
70
80
90
100
V R L K P L S S S R I P CV L RP DS K RR F
A R L TP L S S S R TP CV L K QDS K K L
V R L K P L NCS R L P CV Y A QE T L T F L L TQK K TCV K NY V QK E RCNV
A P L K P L NCS P S L F L FA P E TK I L S V T L K Q TS V NS Y A L K V P CKG L
A Q L RP L NCS P S L FS FV P A TK T L S V MP RQ T FV NNY V L K V S CK Y Y E K I NS P L WW
*
*
MraYB
MraYA
Protein EA
Micelle
Lipids
Empty
ID21
X174
0.10
0.08
0.06
0.04
0.02
)
U
A
(
e
c
n
a
b
r
o
s
b
A
0.00
0
20
40
60
Time (min)
MraY
SlyD154
EID21
MW
25-
20-
15-
10-
E
MraYB
MraYA
4
7
2
3
1
9a
6
8
5
4
10
9b
Protein EA
Periplasm
N
Cytoplasm
C
SlyDB
Protein EB
SlyDA
SlyDB
Protein EB
SlyDA
Fig. 1. The structure of the YES complex. (A) An alignment of a representative
subset of protein E isoforms. Residue coloring is based on ClustalW. Secondary
structure elements are shown above the sequence. Sequences are ordered as in
fig. S1. Residues highlighted with a (*) at the bottom of the alignment are discussed
in the text. (B) SDS-PAGE gel of the purified YESID21 complex. (C) A lysis assay
for protein E expression. Cells containing either empty vector (black line) or the
protein E genes for ID21 (pink line) or FX174 (green line) were induced at time 0 and
the absorbance at 600 nm was monitored over time. Error bars represent the
standard deviation derived from n = 3. (D) Overview density maps of the YESID21
complex viewed in the plane of the membrane. The detergent micelle is highlighted
by gray coloration. The higher contoured map shows the six components of the
twofold complex with density for E. coli MraY (cyan), protein E (yellow), and E. coli
SlyD (purple) highlighted. The pairs of each protein are distinguished as the
B-subunit is light purple. The general coloring scheme is maintained throughout
the figures. Density that is likely lipid is shown in transparent orange. (E) Illustrated
representation of the YESID21 complex oriented and colored as in (D). Foreground
TMDs for the MraYs are numbered and the bilayer is represented by lines.
N terminus and C terminus of protein EA are labeled.
that each contain a kinked TMD and a solu-
ble domain that bridges between MraY and
SlyD. Densities for lipids are visible around
the membrane-exposed surface of the MraY
dimer (Fig. 1D).
For protein E, starting at the N terminus
in the periplasm, the TMD binds in the groove
formed between TM5 and TM9 of MraY end-
ing on the cytoplasmic side where it makes a
sharp turn into the active site pocket (Figs. 1E
and 2A). The TMD is followed by an amphi-
pathic helix that crosses the active site, parallel
to the membrane, presenting a positive face
toward MraY and a hydrophobic face toward
a SlyD IF-domain. The C-terminal residues
adopt an extended conformation that pri-
marily interacts with the second SlyD. This
results in a crossover point between the two
protein Es with each contacting both SlyDs.
Overall, the dimeric complex (two of each of
the heterotrimers) has a near twofold sym-
metry perpendicular to the plane of the mem-
brane. The membrane and periplasmic facing
regions overlay perfectly but the symmetry
is broken at the cytoplasmic face where the
C-termini of the two protein E molecules
cross each other at different residues and the
SlyDs adopt slightly different orientations
(Fig. 1E and fig. S6). Following toward the end
of protein E, we can see continuous backbone
density that positions proline 65 in the ac-
tive site of the FKBP domain. Beyond that, the
density is insufficient to resolve the sequence
and we see little difference between FX174 and
ID21 (fig. S5).
The interaction of protein E with MraY
Functional studies have consistently revealed
the requirement for a proline at position 21
(21, 22, 35). Our structure allows an elegant
explanation for this requirement. The pro-
tein E TMD binds in the cleft of MraY that
is defined by the angled TM9b (Fig. 2A). The
proline at position 21 breaks the hydrogen
bonding and introduces a kink that allows
bending of the TMD around TM9b following
the groove to the active site. Mutation of P21
would result in loss of the kink favoring a
straight TMD that could not bind in the groove.
Residue P29, also completely conserved (Fig.
1A and fig. S1), creates a second bend that com-
pletes the wrap around TM9b and a mutation
at this position results in delayed lysis onset
(21, 22). Additional alanine mutations in the
TMD identified residues that result in de-
layed lysis onset, postulated to decrease the
binding affinity of protein E to MraY (21). In
the present structure, most of these residues
(L19, L20, L23, and M26) (Fig. 2C) make direct
contact with MraY. The exception, F27, appears
Orta et al., Science 381, eadg9091 (2023)
14 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. The interaction of protein E with EcMraY. (A) Illustration of the
YESID21 complex as in Fig. 1E with a 90° rotation except that MraYA is color-
ramped using the Viridis palette that goes from purple to yellow for the N- to
C-terminus, respectively. Prolines are shown in red. The bilayer is modeled in
white. The B-subunits and SlyDs are faded. Boxes indicate regions highlighted in
panels (B to D). Side chains for protein E residues that contact MraY are shown
as sticks. (B) as in (A) with positions of protein E resistance mutants in MraY
highlighted (dark cyan). (C) as in (A) with residues at the interface highlighted
as sticks. (D) The region where the two protein E molecules cross highlighting
the asymmetry colored as in (A) with interacting residues shown as sticks.
Density for the amphipathic helix of protein E shown as a blue mesh. SlyDs are
removed for clarity. (E) Lysis assay of expressed protein EFX174 variants. Error
bars represent the standard deviation derived from n = 3. (F) is similar to (D)
for protein EFX174.
to sterically position M26 into a tight inter-
action with Y134 in MraY, which is conserved
in most Gram-negative bacteria (fig. S7).
At the cytoplasmic interface, protein E res-
idues A36 through M50 form the amphipathic
helix spanning the width of an MraY subunit.
The hydrophilic face of this helix orients toward
the membrane in the MraY active site. The helix
contains conserved positively charged residues
that interact with conserved negatively charged
residues in MraY (Fig. 2D). An example is the
K46 salt bridge where, in our lysis assay, a K46A
mutation resulted in delayed lysis onset (Fig.
2E). Here, isoform differences can be visualized.
For example, position 42 is a leucine in FX174
whereas in ID21 it is an arginine that forms a
salt bridge with E335 in MraY (Fig. 1). The helix
ends at the crossover between the two protein
Es at residue V54 in protein EA and A51 in
protein EB resulting in differing interactions
with residues in MraY, such as the essential
H326 (Fig. 2D).
The Epos (plaques on DslyD) mutations, R3H
and L19F, allow phage propagation in a DslyD
background (23). The R3H mutant of protein
E in FX174 results in a silent mutation in pro-
tein D and is found native to other species
such as ID21 (fig. S8). Previous work reported
that this variant resulted in higher levels of
protein E in the membrane (23). In the present
structure (fig. S5, G and H), this residue does
not make specific contact with MraY. It is
likely that the loss of a positive charge in the
periplasm favors a higher percentage of pro-
tein E molecules that are correctly inserted in
the membrane as a result of the positive-inside
rule. L19F does not result in higher levels of
protein E (21) and likely hastens lysis onset
by having a higher affinity to MraY. Another
phenylalanine mutation at the interface, L23F,
also hastens lysis onset likely by higher affi-
nity, although this is not a general rule as other
leucine to phenylalanine mutants did not af-
fect lysis (21). Both L19 and L23 are near the
conserved F182 in MraY and may add addi-
tional stability through aromatic p interactions
(Fig. 2C). The opposite mutation, phenylala-
nine to leucine, can show loss of binding. For
example, the F288L mutation in MraY (16) is
located at the interface with protein E and re-
sults in a loss of lysis, most likely due to lower
affinity.
All the mutations in MraY that allow re-
sistance to protein E–mediated lysis (P170L,
DL172, G186S, F288L, V291M) (16, 35) are at
the interface with protein E (Fig. 2B). The
mutant F288L, as noted above, lowers affi-
nity to protein E. Residue G186 is at the near-
est approach between the two proteins and a
mutation to serine would prevent protein E
binding. The mutant V291M lies directly at the
interface near L19 in protein E, although a
specific effect for this mutation is not clear.
Finally, P170L and DL172 are located within
periplasmic loop 4-5, which interacts with the
conserved N terminus of protein E. Although
more resistant to lysis, these two mutants are
predicted to still bind protein E, albeit with
lower affinity (35).
The mechanism of inhibition of MraY
by protein E
The YES complex structure allows us to pro-
pose a simple mechanism for inhibition of
MraY by protein E. Superposition with previ-
ous MraY inhibitor complexes (26, 27) on the
YES complex (Fig. 3) shows that the predicted
path of the polyisoprenyl chain of C55P is the
groove formed between TM5 and TM9, which
is occluded by protein E. Therefore, one mech-
anism of inhibition is that protein E prevents
access of the lipid substrate to the active site
(Fig. 3A). Protein E is a noncompetitive inhib-
itor of Park’s nucleotide (36) and, accord-
ingly, the pocket that binds the nucleoside is
fully accessible in the present structure (Fig.
3B). Loop 9-10 in MraY contains catalytic his-
tidines that must move toward the binding
pocket to facilitate catalysis by completing
the active site (28). The cytoplasmic helix of
protein E separates loop 9-10 from the rest of
the active site, blocking this transition and
providing a second mechanism of inhibition.
Overall, protein E blocks access of the lipid
substrate and prevents formation of the active
site upon substrate binding.
Orta et al., Science 381, eadg9091 (2023)
14 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
carbacaprazamycin
tunicamycin
A
EcMraY
B
5
Protein E
4
AaMraY
AaMraY
(inhibited)
Loop 9-10
9b
B
lipid binding site
Loop 1-2
C
RMSD
-
EcMraY
0.966
AaMraY(6OYH)
1.081
AaMraY(4J72)
1.024
EbMraY(5JNQ)
*
N-terminus
Loop 3-4
*
EcMraY
Protein EA
*
Periplasm
EbMraY
*
AaMraY
2
1
2
1
Cytoplasm
nucleoside
binding
site
Fig. 3. The mechanism of inhibition by protein E.
(A) Accessible surface of MraY (colored as in Fig. 2A)
viewed from the cytoplasm looking toward the active
site cleft. Protein E is shown as an illustration. The
structures for the inhibitors tunicamycin (maroon) and
carbacaprazamycin (pink) are shown as sticks based
on a structural alignment to EcMraYA with their
respective complex structures [PDBID: 6OYH (26) and
5JNQ (27)]. (B) Similar to (A) from a slightly different
angle highlighting the catalytic pocket. MraY (dark
cyan) is shown as an illustration. The two substrate
binding sites are highlighted by dashed boxes. Predicted
catalytic residues in MraY are shown as sticks.
Key structural features of MraY
Although there are prior crystallographic MraY
structures (25–27), our YES complex structure
reveals E. coli MraY in a distinct structural
context (fig. S9). There is agreement with the
prior structures when comparing MraY mono-
mers with backbone RMSDs around 1 Å (Fig. 4A
and fig. S10). We can model previously disor-
dered regions of MraY including all the cyto-
plasmic loops that enclose the active site. Loop
1-2 likely adopts distinct conformations during
the catalytic cycle and indeed has two slightly
different conformations in our dimer (fig. S6C).
Loop 9-10 adopts a conformation that is simi-
lar to the reported small-molecule inhibitor
co-crystal structures of MraY (26, 27, 37) but
distinct from the apoprotein structure (Fig. 4
and fig. S10). This conformation of loop 9-10
Fig. 4. Features observed in the EM structure of E. coli MraY. (A) Cytoplasmic view of a structural
alignment of EcMraY (dark cyan) against uninhibited AaMraY [green, PDBID:4J72 (25)] and carbacaprazamycin
inhibited AaMraY [pink, PDBID:6OYH (26)]. RMSDs to monomer A of EcMraY are shown. The color scheme for
the various MraY crystal structures is used throughout the figures. (B) A view in the plane of the membrane
showing the region that includes TM1 and TM2 in backbone ribbons. (Left) The EcMraY structure colored
from the N terminus through TM2 in the Viridis color scheme. (Right) The inhibited AaMraY structure
from (A) and the EbMraY structure [gray, PDBID:5JNQ (27)]. Each structure is aligned to EcMraY. The location of
each N terminus is indicated by an asterisk. (C) Accessible surface of EcMraY (cyan) and unmodeled
densities (orange) that are likely lipids or detergent as well as a putative C55P molecule (purple, see below).
The inset is a view of the periplasmic cavity viewed from a removed monomer.
may be a general feature of MraY complexed
with inhibitors.
In prior crystal structures, the N terminus of
MraY begins at either TM1 or is a helix that
projects away from the structure in an orienta-
tion incompatible with the bilayer (Fig. 4B). In
the YES complex, the N-terminal end of the first
helix (NTH) hydrogen-bonds to the C-terminal
end of TM2, effectively forming a helical stack-
ing structure (Fig. 4B and fig. S9C). A multiple
sequence alignment across bacteria shows
that the NTH in MraY is conserved across gram-
negative bacteria but missing in Gram posi-
tives (figs. S7 and S11). Although this feature is
not found in the crystal structures, AlphaFold
(38) predicts the NTH stacking for E. coli and
other Gram-negative bacteria with slight dif-
ferences in hydrogen bonding and orientation
relative to the cryo-EM structure (fig. S11). For
the AaMraY structures (25, 26), the positioning
of the N terminus is likely a product of crys-
tallization, as AlphaFold predicts the NTH stacks
for this and the related Hydrogenivirga spe-
cies (fig. S11). For Gram-positive bacteria, both
the EbMraY and predicted structures lack the
NTH (27) (Fig. 4B and fig. S11).
Protein E as a general antibacterial protein
Expression of protein E leads to lysis that
results in a subset of killed bacteria becom-
ing “ghosts”—essentially empty cell walls (15).
Ghosts have been used in a variety of contexts
including vaccine development [reviewed in
(39)]. For ghosts to be made, protein E must
inhibit the native MraY of the target bacteria.
Although phage FX174 is restricted to E. coli,
many bacteria have been probed for ghost for-
mation by expression of protein E. All Gram-
negative bacteria tested (fig. S11A) resulted in
the formation of ghosts [reviewed in (40)]. By
contrast, protein E was unable to cause lysis
in the Gram-positive Staphylococcus carnosus
(41). Expression of the Bacillus subtilis MraY
in E. coli prevented cell lysis, suggesting that it
has a low affinity for protein E (35). Compar-
ing the residues in EcMraY that contact pro-
tein E to those in Gram-positive species, there
are no single residue differences that easily
explain the inability to inhibit MraY from gram-
positive species. There are a few residues that
may play a role—such as P170 in EcMraY which
confers resistance when mutated to leucine—
that are absent in Gram-positive MraYs (fig. S7).
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EcMraY residue Y134, which forms a bridge
with protein E M26 in our model (Fig. 2C), is
also missing in Gram-positive species (fig. S7).
Lipids bound to the YES complex
The YES complex was solubilized from its na-
tive environment and, for the YESID21 complex,
the final detergent solution was supplemented
with E. coli lipids. We observe lipid densities
around the membrane surface of MraY (Fig.
1D and fig. S12, A and B). Prior work supports a
functional role for anionic phospholipids with
MraY including stabilizing the dimer (42–44).
We observe substantial lipid density near the
dimer interface with features consistent with
glycerophospholipids, although not all density
can be clearly assigned (fig. S12). As in previous
structures (25, 27), there is a hydrophobic peri-
plasmic cavity within the MraY dimer that con-
tains unexplained density (Fig. 4C). Although
this density has clear structure, we are unable
to fit typical E. coli phospholipids.
Recently, a study using native mass spec-
trometry and molecular dynamics identified
a binding site for C55P at the dimer interface
with the phosphate headgroup predicted to
form a salt bridge to R341 in EcMraY (44). In
our structure, we observed a long tube of den-
sity at the dimer interface (fig. S12A, purple)
that ends at R341 and is consistent with C55P
(fig. S12C). Although we cannot confidently iden-
tify this lipid, the density would be consistent
with C55P, although the role for this binding
site remains to be determined.
The role of SlyD in protein E–mediated lysis
The amphipathic helix of protein E bridges the
two E. coli proteins, MraY and SlyD, which
make no specific contact with each other (Fig.
2A). The IF domain sits on the hydrophobic
face of the protein E helix (Fig. 5A) and con-
tacts the extended C terminus of the oppos-
ing protein E, which then extends to bind
the FKBP domain (Fig. 5B). This results in a
bowtie-like interaction with each SlyD binding
both protein E–soluble domains (Fig. 1E). There
are no contacts between the two SlyD mol-
ecules (fig. S6D). These protein E interfaces
validate structural studies of SlyD where pep-
tides bind to each of the interfaces seen here
including b-augmentation in a groove in the IF
domain (Fig. 5, C and D) (32). The IF domain
binding to an a-helix may be an important
chaperoning interaction. The FKBP domain is
well-ordered but adopts a range of orientations
in our particles (fig. S13) and consequently has
the lowest resolution (fig. S3). This flexibility
relative to the IF domain is consistent with the
NMR structure of SlyD where the orientations
of the two domains are not constrained by each
other (31). The only contact of the FKBP do-
main to the rest of the YES complex is the
flexible linker to the IF domain and binding to
the extended C terminus of protein E. We ob-
serve continuous backbone density that allows
us to place P65 at the FKBP active site. As seen
before for some SlyD-bound peptides (32), pro-
tein E binding to the FKBP domain adopts a
noncanonical orientation. Protein E P65 is not
A
C
B
D
Y68
P65
Y13
P58
F96
Y63
Pro
Y13
S2 peptide
F91
Pro
TtSlyD
PDBID: 7OXI
Fig. 5. Interactions between protein E and SlyD. (A) The amphipathic helix of protein E (yellow) as a
illustration with side chains contacting SlyD shown as sticks. SlyD (purple) is shown as an illustration along
with a transparent accessible surface (B) Full view of SlyD bound to two protein E molecules shown in
different shades of yellow. (C) As in (A) highlighting the b-augmentation of the extended C-terminal protein
E. (D) Structures of SlyD from the YESID21 complex and TtSlyD [PDBID:7OXI (33)] (green) aligned to
the IF domains. The two S2 peptides bound to the TtSlyD are shown in pink.
completely conserved (fig. S1), although other
species have a proline at residue 63 which could
reach the active site with additional tilting of
the FKBP domain. A proline near this posi-
tion may help to localize the chaperone to the
complex and facilitate assembly.
The lack of contacts between SlyD and MraY
suggest that the soluble domain of protein E
alone could form a complex with SlyD. We
coexpressed EcSlyD with N-terminal trunca-
tions of protein E from either ID21 (residues
33 to 76) or the shortest isoform a3 (residues
33 to 75). Both form complexes that could be
purified by an affinity tag on the soluble do-
main (fig. S2E). These observations point to
a high-affinity interaction between SlyD and
the C-terminal domain of protein E.
Protein E is unstable in the absence of SlyD
(18) and is rapidly degraded (23). It has been
speculated that prolyl-isomerization is central
to the lysis mechanism (22), but this idea is not
supported by available evidence. Nonproline
mutations in protein E can rescue lysis in a
DslyD background (18, 45), as well as completely
replace the cytoplasmic domain of protein E
with an unrelated globular protein (20, 21, 45).
We also performed our lysis assay with sev-
eral SlyD variants in the DslyD strain (fig. S2C).
As before, protein EFX174 was unable to pro-
mote lysis in the absence of SlyD, however
lysis could be rescued by expression of either
EcSlyD or EcSlyD154. Thermus thermophilus (Tt)
SlyD has high structural homology to EcSlyD
(Fig. 5D and fig. S2, B, F, and G) and also res-
cued lysis in the DslyD strain (fig. S2C). We
generated an EcSlyD Y68K mutant that sub-
stantially reduces prolyl-isomerase activity
(46) and this too could rescue lysis. Finally,
we purified a complex of protein E using the
Epos rescue mutants (R3H and L19F) (45) in
the DslyD strain. This YE complex was very
unstable and aggregated according to SEC (fig.
S2H). These results support the conclusion that
the primary role of SlyD in promoting lysis is not
prolyl-isomerization, but to protect protein E
and stabilize the YES complex. This does not
obviate a role for proline binding in complex
assembly. Mutation of P65, in the FKBP active
site, creates a slower-lysis phenotype (22), which
may indicate that binding of these residues by
SlyD is key to assembling the YES complex.
Protein E is evolutionarily constrained
Protein E arrived late in the evolution of FX174
and was overprinted into a +1 reading frame
in the ORF for gene D (47, 48). The structure
supports that this embedding constrains the
evolution of protein E (12). Considering the
sequence changes across protein E isoforms,
we note that from the N terminus through
residue 70, with few exceptions, each position
that is not completely conserved is either si-
lent or that there is only a slight change in
protein D (fig. S8A). The silent changes vary
Orta et al., Science 381, eadg9091 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
the codon’s second position, which is the wob-
ble position in the overlapping codon for pro-
tein D. For example, residue W7 in FX174 is
replaced with a Ser or Leu in other species.
Although seemingly substantial changes, each
is coded by the sequence UXG and all three
variations at this position are sampled. These
variable positions generally do not contact
MraY. An exception is found in the G4 isoform
where a phenyalanine occurs at position 19, as
in the Epos mutant, which results in a change
from alanine to serine at position 79 in protein
D. This places a polar residue in the hydro-
phobic core of protein D (fig. S8). This single
nucleotide change increases protein E affinity
to MraY but likely lowers the stability of pro-
tein D and the overall fitness of the virus. In-
troduction of this mutation results in smaller
plaque formation relative to the wild type (23).
The C terminus of protein D and the exten-
sions in the longer isoforms of protein E are
likely disordered and less constrained, hence
the increased sequence variability (fig. S8).
Conclusions
The mechanism for FX174 inhibition of pep-
tidoglycan biosynthesis is suprisingly simple.
Protein E binds in the active site cleft prevent-
ing access of the lipid substrate and blocking
conformational changes needed for catalysis
(fig. S14). The YES complex structure provides
a template for interpreting all the previous
results for lysis by FX174. Notable among these
are that the extensive functional mutations
in protein E and MraY map to the interface
between the two proteins. SlyD binds to the
cytoplasmic domain of protein E to stabilize
the MraY/protein E complex. As we demon-
strated, the requirement for SlyD is based on
the protein binding properties, as distantly re-
lated SlyD homologs can rescue lysis in a DslyD
strain. SlyD in this case does not serve directly
in the mechanism of inhibition of MraY and
can be functionally replaced.
Our structures offer some insights for future
work applying SGL proteins as therapies. Pro-
tein E binding to EcMraY identifies a distinct
mechanism from current inhibitors. Blocking
of the lipid substrate access to the active site in
MraY could be exploited by small molecules,
with structure-based drug design guided by
the protein E structure. Expanding protein E
efficacy to Gram-positive bacteria and, potentially,
other related polyisoprenyl-phosphotransferases
such as bacterial WecA or the mammalian
DPAGT1 could further increase applicability.
SGL proteins, which have distinctly evolved
many times (49), can also be used to improve
the antibacterial potency of bacteriophages. The
use of phages for medical therapies, although
known for a hundred years, has attracted re-
cent attention (1). Improving the efficiency of
FX174 protein E based on structural infor-
mation may help these therapies achieve their
greatest potential in the fight against antimi-
crobial-resistant pathogens.
Materials and Methods
Coexpression of EcMraY, protein E, and EcSlyD
DslyD BL21(DE3)-competent cells were co-
transformed with pET22b-SlyD154 and either
pRSFDuetEcMraY-EID21 or pRSFDuet-EcMraY-
EFX174 and plated in LB-agar containing 35 mg/ml
Kanamycin and 100 mg/mL Ampicillin. Our
pET22b-SlyD154 construct expresses E. coli SlyD,
modified by the removal of the flexible C-
terminus. The pRSFDuet-EcMraY-EID21 plas-
mid contains the ID21 isoform of protein E,
along with a wild-type EcMraY to prevent cell
lysis from the overexpression of protein E. Cells
were grown in 2xYT media at 37°C, 225 r.p.m.,
and induced at an OD600 of 0.9 with 0.4mM
IPTG at 18°C overnight. The culture was har-
vested by centrifugation for 10 minutes at
9000xg, 4°C then frozen or used immediately
for purification.
Purification of the YES complex
The cells were resuspended in lysis buffer (20mM
Tris-HCl pH 7.5, 300 mM NaCl, 10% Glycerol,
5mM b-mercaptoethanol (bME), 0.1mM PMSF,
0.1mM Benzamidine) and homogenized using a
M-110L microfluidizer (Microfluidics). The lysate
was cleared by a 20-minute centrifugation at a
speed of 22,000xg. The supernatant was then
centrifugated at 167,424xg and the resulting
membrane pellet was then solubilized in the
extraction buffer [10 mM HEPES pH 7.5, 300 mM
NaCl, 5% Glycerol, 5mM bME, 0.1mM phenyl-
methylsulfonyl fluoride (PMSF), 0.1mM ben-
zamidine, 10 mM imidazole and 1% dodecyl 4-O-
a-D-glucopyranosyl-b-D-glucopyranoside (DDM)]
After allowing for extraction for 1.5 hours at
4°C, the solution was centrifuged at 167,424xg
for 30 minutes and the remaining lysate was
mixed with 1mL NiNTA resin (Qiagen, Alameda,
CA) then nutated at 4°C for two hours. This
solution was loaded onto a gravity column and
then washed with five column volumes of wash
buffer (10 mM HEPES pH 7.5, 150 mM NaCl,
5% glycerol, 5mM bME, & 0.03% DDM) with
10mM imidazole followed by five column vol-
umes of wash buffer with 30 mM imidazole.
The YES complex was eluted in 20mL of wash
buffer containing 200 mM imidazole. The final
purification step was SEC (Superdex 200 10/300
GL, Millipore Sigma) in 10mM HEPES pH 7.5,
75 mM NaCl, 5% Glycerol, 5mM bME and 0.03%
DDM. Fractions were assessed by SDS-PAGE and
directly used for cryo-EM sample preparation.
Co-expression of EcMraY and protein E in
various SlyD backgrounds
The pRSFDuet-E-EcMraY and pRSFDuet-Epos-
EcMraY expression vectors were transformed
into BL21-Star cells (Novagen). Similarly, the
pRSFDuet-E(C-term)-SlyD154 was transformed
into SlyD-knockout cells. The cultures were
grown at 37 °C to an OD600 0.8 and induced
with 1 mM IPTG. Induced cultures were grown
for 3 hours followed by harvesting by centrifu-
gation at 9,000xg for 20 min. Cell pellets were
resuspended in lysis buffer and lysed by son-
ication. The lysate was then cleared by cen-
trifugation at 22,000xg, followed by a second
centrifugation at 234,78xg for 1 hour to isolate
the membrane fraction. The complex was ex-
tracted in 20 mM Tris-HCl pH 7.5, 300 mM NaCl,
10% Glycerol, 10 mM Imidazole, and 1% n-Decyl-
b-Maltoside (DM) and incubated at 4°C for
1.5 hours. The debris was cleared by centrifu-
gation at 234,788xg for 30 min. The sample was
incubated with 1 mL NiNTA resin for 1 hour,
followed by a wash with 50 column volumes
lysis buffer with 30mM Imidazole. The protein
E complexes were similarly eluted in 300mM
Imidazole. The elutions were concentrated and
further purified by size exclusion chromatogra-
phy (Superdex 200 10/300 GL, Millipore Sigma).
Lysis assays of WT protein E FX174 and ID21
LEMO DE3 competent cells were transformed
with a pRSF-Duet vector either empty, with
protein EFX174, or protein EID21. Cultures were
grown to an OD600 of 0.2 and inoculated into a
Corning 96-well Clear Flat Bottom plates in
100mL triplicate aliquots and induced as de-
scribed previously. Cultures were incubated at
37C with orbital shaking at 220rpm using an
Infinite M Nano+ (Tecan, Switzerland). Readings
were taken in 5-minute intervals for 90 minutes.
Lysis assay for protein E constructs
LEMO DE3 competent cells (New England
Biolabs, MA, USA) were transformed with a
pRSFDuet vector either empty, with C-terminally
FLAG tagged protein EFX174 variants (WT,
P21A, K46A). The lysis assays were performed
in three biological replicates as previously de-
scribed (21). Absorbance readings were recorded
in 5-minute intervals for 1 hour and 30 minutes.
Manual readings were taken using a Biowave
Cell Density Meter CO8000. The values were
plotted using GraphPad Prism version 9.1.1
for macOS.
Lysis assays based on SlyD variants
DslyD (18) cells were transformed with either
a control empty pRSF-Duet vector or pRSFDuet-
ProteinFX174 and either pET22b-EcSlyD, pET22b-
SlyD154, pET22b-EcSlyD Y68K, or pET22b-Thermus
thermophilus SlyD. Cultures were grown in 2xYT
media at 37°C and induced with 0.4mM IPTG
once at an OD600 of 0.2. Absorbance measure-
ments were manually recorded in 5-minute
intervals for 70 minutes. Similarly, DslyD cells
were transformed with either a control empty
pRSF-Duet vector or pRSF-Duet-ProteinID21
either alone, with pET22bEcSlyD, or with pET22b-
EcSlyD154 and induced with 0.4mM IPTG. Read-
ings were recorded using an Infinite M Nano+
plate reader as described above.
Orta et al., Science 381, eadg9091 (2023)
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Sample preparation for cryoEM
The YES complex was diluted to 5.0 mg/mL in
10 mM HEPES pH 7.5, 75 mM NaCl, 5% Glyc-
erol, 5mM bME and 0.03% DDM. Additionally,
the YESID21 sample was supplemented with
1mM E. coli total lipid extract (Avanti Polar
Lipids, 100600P). Quantifoil holey carbon films
R1.2/1.3 300 Mesh, Copper (Quantifoil, Micro
Tools GmbH) grids were glow discharged with
a 2-minute 20Å plasma current using a Pelco
easiGlow, Emitech K100X. Grids were prepared
using a Vitrobot (FEI Vitrobot Mark v4 x2, Mark
v3) by applying 3mL of sample onto the grid
followed by a 3.5 second blot using a +8-blot
force and plunge frozen into liquid ethane.
Data acquisition and analysis
The grids were imaged in a 300 kV cryo-TEM
microscope equipped with a Gatan K3 6k x 4k
direct electron detector and a Gatan Energy Filter
(slit width 20eV) in super-resolution mode using
Serial EM. Datasets were collected at a 105k
magnification with a pixel size of 0.416 Å/pixel.
Movies with 40 frames were recorded with a
total exposure dose of 60 e-/Å2 and a defocus
range of -1.0 to -2.5 mm. For the YESID21 complex,
a total of 12,070 movies were recorded. Movies
were normalized by gain reference and mo-
tion corrected using the patch motion correc-
tion built in function in cryosparc (v3.3.2) with
a twofold bin that resulted in a pixel size of
0.832 Å/pixel (50). The contrast transfer func-
tion (CTF) was estimated using CTFFIND4 (51).
Micrographs were manually curated, and low-
quality images were removed for further analy-
ses. A total of 2,462,335 particles were obtained
followed by the generation of 6 ab-initio mod-
els. Out of the 6 models, two models are se-
lected for classification into “good” and “trash”
volumes. All particles were then sorted in these
two volumes through heterogeneous refinement
using particles extracted with a 4x bin, which
produced 6,589,696 good particles. Heteroge-
neous refinement was used in an iterative man-
ner to sort the particles into the 5 volumes (4
good and 1 trash). The 1,151,777 good particles
were used for non-uniform homogeneous re-
finement to generate a higher resolution vol-
ume. The particles were then extracted with
a 3x bin and sorted into 4 iterations of the
higher resolution volume and 1 trash volume.
Iterative rounds of heterogeneous refinement
at 3x bin produced 935,754 particles. Particles
were then extracted in a 2x bin and heteroge-
neously refined into either high- or low-resolution
volumes. At this point, discerning features in
the soluble region of the model were used to
select the most complete volumes. The volumes
were individually refined through non-uniform
refinement and the particles that composed the
volumes with most complete and highest reso-
lution were used. A total of 122,452 particles
were used for the most complete model obtained
upon non-uniform refinement. The FSC-masked
resolution was 3.5Å, while the unmasked reso-
lution was 3.9Å. The half-maps were then used
for post-processing through DeepEMhancer
(52) with the high-resolution model selected for
our most complete density map. Post-processing
through DeepEMhancer removed the micelle
and improved the features on the soluble por-
tions of the map, however the lipid densities
were also removed. The lipid densities described
in this work are those of the YESID21 map before
post-processing. Notably, the dimer-interface
lipid density was also present in the YESFX174
density map without the supplementation of
E. coli lipid extract. Figure 1D uses the densities
before post-processing for the MraY dimer, mi-
celle and lipid densities, and the DeepEMhancer
post-processed map for protein E and SlyD.
Supplemental figures S9 and S12 were made
with the map before DeepEMhancer sharpen-
ing. The YESFX174 complex dataset was pro-
cessed in this same manner. A total of 10,798
movies were recorded. The model for the YESID21
complex was then used as a template for tem-
plate picking, from which 1,516,368 particles
were picked and curated. Following gradual
un-binning and sorting into good and trash
volumes, 155,270 particles were used for the
final iteration of non-uniform refinement. The
local resolution of both maps was performed
on cryosparc (v3.3.2). The half-maps were then
post-processed using DeepEMhancer as de-
scribed previously.
Model building
For starting models we used the Aquifex aeolicus
un-bound structure (PDBID:4J72) (25) for EcMraY
and the E. coli NMR structure (PDBID:2K8I) (31)
for EcSlyD which were fit using phenix.dock.
SlyD was then split into its two domains, IF
and FKBP, at residues Y68 and G127. Protein E
was modeled de novo up to residue P65 using
Coot 0.8.9.2. The structures of the EcMraY, pro-
tein E, and EcSlyD-IF domain were refined using
phenix.real space refinement and ISOLDE 1.6,
and validated with PHENIX-1.19.2. After the re-
finements of EcMraY, protein E, and the EcSlyD-IF
domain were completed, the FKBP domains
were docked into density using ChimeraX. The
complete YES complex structure was then re-
fined using PHENIX-1.19.2 and ISOLDE 1.6.
RMSDs were calculated using ChimeraX Match-
maker chain alignment. Structure figures were
made using ChimeraX and sequence alignments
using Jalview and ClustalW (53–55).
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AC KNOWLED GME NTS
We are particularly grateful to R. Young and T. Bernhardt for providing
inspiration and feedback during the course of this project. We thank
them, M. Kurosu, and D. Rees for critical feedback on the manuscript.
We further thank R. Young for providing the DslyD strain. (Cryo)
Electron microscopy was done in the Beckman Institute Resource
Center for Transmission Electron Microscopy at Caltech. We are
grateful to S. Chen for help with data collection and processing.
Funding: This work was funded by the following: National Institutes
of Health grant R01GM114611 (to W.M.C. and M.K.); National
Institutes of Health grant DP1GM105385 (to W.M.C.); and the G. Harold
and Leila Y. Mathers Foundation (to W.M.C.) Author contributions:
Conceptualization: S.T. and W.M.C. Methodology: A.K.O., N.R., Y.E.L.,
S.T., H.G.Y., L.K., and W.M.C. Investigation: A.K.O., N.R., Y.E.L., S.T.,
H.G.Y., L.K., W.M.C. Visualization: A.K.O., N.R., S.T., and W.M.C.
Funding acquisition: W.M.C. Project administration: W.M.C.
Supervision: W.M.C. Writing – original draft: A.K.O., N.R., and
W.M.C. Writing – review and editing: A.K.O., N.R., Y.E.L., S.T., H.G.Y.,
L.K., and W.M.C. Competing interests: Authors declare that they
have no competing interests. Data and materials availability: All
experimental data are available in the main text or the supplementary
materials. Coordinates with experimental maps have been
deposited to the RCSB or the EMDB for both the YESID21 (PDB
ID 8G01, EMDB-29641) and YESFX174 (PDB ID 8G02 and EMDB-
29642) complexes. License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American Association
for the Advancement of Science. No claim to original US government
works. https://www.sciencemag.org/about/science-licenses-
journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg9091
Figs. S1 to S14
Table S1
References (56–57)
MDAR Reproducibility Checklist
Movie S1
52. R. Sanchez-Garcia et al., DeepEMhancer: A deep learning
View/request a protocol for this paper from Bio-protocol.
solution for cryo-EM volume post-processing. Commun. Biol. 4,
874 (2021). doi: 10.1038/s42003-021-02399-1;
pmid: 34267316
Submitted 4 February 2023; accepted 23 May 2023
10.1126/science.adg9091
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RES EARCH
PLASTIC UPCYCLING
Chemical upcycling of polyethylene, polypropylene,
and mixtures to high-value surfactants
Zhen Xu1†, Nuwayo Eric Munyaneza1†, Qikun Zhang2, Mengqi Sun1, Carlos Posada1, Paul Venturo1,
Nicholas A. Rorrer3,4, Joel Miscall3,4, Bobby G. Sumpter5*, Guoliang Liu1,6*
Conversion of plastic wastes to fatty acids is an attractive means to supplement the sourcing of these
high-value, high-volume chemicals. We report a method for transforming polyethylene (PE) and
polypropylene (PP) at ~80% conversion to fatty acids with number-average molar masses of up to
~700 and 670 daltons, respectively. The process is applicable to municipal PE and PP wastes and their
mixtures. Temperature-gradient thermolysis is the key to controllably degrading PE and PP into
waxes and inhibiting the production of small molecules. The waxes are upcycled to fatty acids by
oxidation over manganese stearate and subsequent processing. PP b-scission produces more olefin
wax and yields higher acid-number fatty acids than does PE b-scission. We further convert the fatty
acids to high-value, large–market-volume surfactants. Industrial-scale technoeconomic analysis
suggests economic viability without the need for subsidies.
A s the two most widely used commodity
plastics, polyethylene (PE) (Table 1) and
polypropylene (PP) contribute nearly 60%
of the world’s plastic production (~400
million tonnes), primarily for short-
term applications (1). The manufacturing of
PE and PP is associated with the highest en-
ergy consumption among all plastics (1, 2) and
contributes substantially to annual greenhouse
gas emissions (2). Short-term use plastics quickly
turn into waste and cause substantial pollution
(3). To recycle PE and PP, the waste collection
and sorting processes must be economically
efficient to lower the cost (4), and the recycled
products should ideally be high value and high
volume to have a major impact on waste ac-
cumulation. Although PE and PP can be sepa-
rated from heavier-than-water polymers such as
polyvinyl chloride (PVC) and polyethylene ter-
ephthalate (PET) through a sink-float method
that uses water as the medium (Fig. 1A), further
separation of PE and PP is much more chal-
lenging because of their similar structures and
densities. The two polymers are furthermore
incompatible and cannot be blended unless
expensive and sophisticated compatibilizers
are used (5). Finding a generic and profitable
method to recycle or upcycle both PE and PP
while increasing their final product value over
that of virgin plastics is thus imperative (3, 6–8).
1Department of Chemistry, Virginia Tech, Blacksburg, VA 24061,
USA. 2Department of Chemistry, Chemical Engineering and
Materials Science, Ministry of Education Key Laboratory of
Molecular and Nano Probes, Shandong Normal University,
Shandong 250014, PR China. 3Renewable Resources and
Enabling Sciences Center, National Renewable Energy
Laboratory, Golden, CO 80401, USA. 4BOTTLE Consortium,
Golden, CO 80401, USA. 5Center for Nanophase Materials
Sciences, Oak Ridge National Laboratory, Oak Ridge, TN 37831,
USA. 6Department of Chemical Engineering, Department of
Materials Science and Engineering, Macromolecules Innovation
Institute, Virginia Tech, Blacksburg, VA 24061, USA.
*Corresponding author. Email: gliu1@vt.edu (G.L.);
sumpterbg@ornl.gov (B.G.S.)
†These authors contributed equally to this work.
Chemical upcycling increases product value
and is envisioned as a solution that converts
postconsumer wastes into high-value chem-
icals, e.g., the conversion of polystyrene (PS)
into aryl carbonyls and aryl alkyls (9–11). Chem-
ical upcycling of PP and PE, however, is diffi-
cult because of the high ceiling temperatures
involved (12). Moreover, the lack of heteroatom-
associated weak links within the polymer chains
(e.g., esters in PET) provides no selective chain-
scission sites. Product control is thus exception-
ally challenging. Recently, chemical reactions
that use iridium- (13) and platinum-based cat-
alysts (14) and ionic liquids (15) generated fuels
and improved selectivity toward aryl moieties
in the upcycling of PE. On a laboratory scale, PE
can also be converted to propylene by dehydro-
genation and tandem isomerizing ethenolysis
(16, 17). Considering the technoeconomic po-
tential for increased product value and gener-
alizability to both PE and PP, the conversion
of polyolefins to high-value fatty acids or ionic
surfactants is appealing because PE and PP
are aliphatic by nature. In addition, surfactant
products have huge market demands (i.e., com-
parable to plastics) and high economic values
(i.e., higher than fuels, waxes, and regular aro-
matic compounds) (table S1). Moreover, sur-
factant products such as soaps are made from
fatty acids of varying chain lengths and are
often blended with ketones and aldehydes to
soften the product and modulate fragrance
release (18), diminishing the need to remove
ketone and aldehyde by-products in the up-
cycling process of PE and PP. Biodegradation
converts PE to fatty acids by means of micro-
bial strains, but the fermentation period is too
long (>10 days) to be practically deployable
in the chemical industry (19). Chemically, the
Novoloop method and hydrothermal reactions
with strong oxidants quickly degrade PE but
require harsh reaction conditions, such as strong
nitric acid and high pressure (20, 21). Most re-
cently, metallization of PE over Zr and alkyl
aluminum has afforded products with con-
trollable average carbon-chain lengths, and the
catalysts must operate under O2-, CO2-, and
H2O-free conditions (22). Therefore, time- and
material-efficient methods that use noncorro-
sive chemicals, atmospheric pressure, and air-
tolerant reaction conditions are highly sought
to efficiently transform both PE and PP into
large–market-volume fatty acids, preferably with-
out the need for additional sorting and sepa-
ration but with high selectivity and conversion.
Here we report a gradient-temperature ther-
molysis method that can selectively break PE,
PP, and their mixtures into waxes under atmo-
spheric pressure (Fig. 1, A and B). The key is that
the temperature gradient prevents violent pyrol-
ysis reactions, quenches vaporized waxes, and
inhibits complete degradation to small mole-
cules (Fig. 1C and figs. S1 and S2; see discussion
in supplementary materials). PE- and PP-derived
waxes are subsequently transformed into fat-
ty acids with high acid numbers (ANs) and
number-average molar masses of up to ~700
and 670 Da, respectively (Fig. 1D and tables
S2 to S4). Through subsequent saponifica-
tion, we obtain an ionic surfactant product
that contains salts of fatty acids. Simply mix-
ing with additives (e.g., fragrances) can produce
commercial products, such as soap bars and
liquid detergents (examples in Fig. 1A), which
have higher market values than typical chemical
products such as fuels and alkylaromatics (11, 14).
Polyethylene conversion to fatty acids
Initially, pulverized lab-grade PE (~500 mg;
Mw, 97 kDa; polydispersity Ð = 2) was loaded
into a custom-designed quartz reactor (Fig. 1A
and fig. S1) and purged with gases of con-
trolled compositions (N2, 10 vol % O2 in N2, or
air). The degradation was initiated by heating
the bottom of the reactor to ~360°C stepwise
with a step size of ~100°C per 5 min. Polymer
smokes (fig. S2) appeared, indicating the va-
porization of fragmented polyolefins or waxes.
The waxes were condensed in the cold part of
the reactor, preventing further fragmentation
to shorter hydrocarbons. The wax yields from
PE degradation in N2 (PE-N2-wax), 10 vol % O2
(PE-O-wax), or air (PE-air-wax) were 86, 79,
and 55 wt % (Fig. 2A and table S2, experiments
1 to 3, 7 to 9, and 13), respectively. In a control
experiment under N2 without a temperature
gradient, the products were mostly short-chain
hydrocarbons of C8 and below (Fig. 1C).
Gas chromatography–mass spectrometry
(GC-MS) was used to characterize the wax
composition (Fig. 2B), showing mainly solid
waxes with minor fractions of light hydrocar-
bons (~10 wt % of C8 and below, fig. S3). Each
primary peak could be resolved into a doublet
of alkene and alkane with the same carbon
number (figs. S4 and S5), similarly to degrada-
tion in flow reactors (23). In the presence of O2,
Xu et al., Science 381, 666–671 (2023)
11 August 2023
1 of 6
~630 and 540 (fig. S6 and table S3), corre-
sponding to a carbon number of ~45 and 42,
respectively. Despite m/z ranges of 300 to 1000
for PE-N2-wax and 200 to 900 for PE-O-wax (fig.
S6C), the polydispersities were relatively small
(<1.1, table S3). The PE-N2-wax and PE-O-wax
were further characterized by nuclear magnetic
resonance (NMR) spectroscopy through het-
eronuclear multiple bond correlation (HMBC)
and heteronuclear single quantum correlation
(HSQC) experiments (Fig. 2C and figs. S7 and
S8) to investigate the waxes’ structures. NMR
confirmed the presence of unsaturated carbon
in both PE-N2-wax and PE-O-wax, showing pri-
marily 2-propenyl at the chain end (1H NMR d
5.0 and 5.8, 13C NMR d 114 and 138) and minor
internal alkenes (13C NMR d 123 to 131). The
presence of O2 partially oxidized PE-O-wax and
produced ketones, aldehydes, and esters (fig. S8).
Upcycling of the waxes was conducted over
Mn compounds for 10 hours in an airflow at
150°C. Although inorganic MnO2 and KMnO4
have shown effectiveness in paraffin oxidation
(28), they were ineffective in oxidizing PE-derived
wax, probably because of low miscibility,
showing no appreciable carbonyl signals after
24 hours (fig. S9). By contrast, Mn stearate
catalyzed the oxidization of PE-derived wax
much faster owing to the better dispersion of
the catalyst in the organic media (29, 30). The
oxidation rates of PE-N2-wax or PE-O-wax were
similar over Mn stearate (5 wt % loading) un-
der a constant air flow, as shown by the similar
slopes of carbonyl index (CI) changes as a
function of time. PE-O-wax showed a higher
final CI because of the higher initial value than
did PE-N2-wax. We conclude on the basis of
HMBC analysis that the oxidation of PE-O-wax
over Mn stearate intensified the carbonyl con-
centration in the first 6 hours (figs. S9 and S10,
13C NMR d 160 to 206), producing primarily
aldehydes and minor esters, ketones, and car-
boxylic acids. The oxidation likely occurred by
means of a radical addition mechanism (31, 32),
possibly through epoxy intermediate rear-
rangement to aldehydes and ketones (33). The
presence of aldehyde was confirmed by NMR-
HMBC, whereas epoxy signals were too weak to
D
RES EARCH | R E S E A R C H A R T I C L E
PE-O-wax and PE-air-wax exhibited GC-MS
peaks and molecular ion signals similar to
those of PE-N2-wax. PE-O-wax and PE-air-wax
showed stronger intensities at shorter elution
times than PE-N2-wax (Fig. 2B), indicating more
short hydrocarbons and lower average molecu-
lar weights as a result of accelerated degrada-
tion by oxygen radicals (24). The PE-air-wax
yield was too low (~55%), albeit higher than
those in the literature (25, 26), to be practically
useful for generating hydrocarbons suitable for
downstream production of surfactants (Fig.
2A); therefore, no further characterization of
PE-air-wax was conducted. High-temperature
gel permeation chromatography (HT-GPC) con-
firmed the degradation of polymers (fig. S6).
Because HT-GPC cannot resolve the exact mo-
lecular weights in this range, and because GC
cannot detect low-volatility heavy hydrocar-
bons (>C40) (27), atmospheric pressure chem-
ical ionization mass spectrometry (APCI-MS)
was used to analyze the full composition. The
spectra of PE-N2-wax and PE-O-wax showed
waxes of mass/charge ratio (m/z) centered at
A
B
C
Fig. 1. Upcycling of PE and PP to fatty
acids in a temperature-gradient reactor.
(A) Schematic process flow of separation
and upcycling of commercial polyolefins,
including high-density PE (HDPE), low-
density PE (LDPE), and PP to soap products
performed using a custom-designed gradi-
ent thermal reactor. The temperature-
gradient reactor has a hot and cold zone,
preventing complete thermolysis of PE and
PP to small molecules, and is key to
controlling the chain length of fragmented
products. Photographs show representative
PE and PP wastes used in this study (HDPE
container, grocery bags, sandwich bags,
bottle caps, PP centrifuge tubes, and PP
foam), as well as the products of
intermediate waxes, fatty acids, surfactant
solution, and soap molded into various
shapes. The market price per metric ton of
common surfactant products is almost
double that of virgin plastics (table S1).
(B) Reaction schemes of upcycling PE and
PP to fatty acids. (C) Representative
product distributions after PE degradation
in the reactor with and without temperature
gradient. The distribution and intensity were
measured with GC. Signals from 3 to 7 min
overlapped with the toluene solvent and
thus were not shown for clarity. (Inset)
Infrared thermal image of the reactor with
and without temperature gradient. (D) AN of
resulting fatty acids compared with that of
stearic acid (SA, C18) and theoretical
values of fatty acids with average carbon
numbers of C47 for PE and C45 for PP.
The error bars are the standard deviation of
at least three replicates.
Xu et al., Science 381, 666–671 (2023)
11 August 2023
2 of 6
RES EARCH | R E S E A R C H A R T I C L E
be confirmed. The dominance of aldehyde in-
termediates agreed well with the simulation
results. Because aldehydes were susceptible to
further oxidation, they were converted to acids
(Fig. 2D, 13C NMR d 180) in the latter 2 hours
of oxidation and subsequent saponification
in 0.1 M aqueous KOH. The saponification
hydrolyzed minor fatty esters and increased the
amount of fatty acids; it also helped remove
undesired short-chain acids (e.g., acetic acids).
Hydroxyl signals were too weak to confirm
the presence of alcohols in the product. The
saponified solution was neutralized with HCl,
crashing out fatty acid (PE-O-FA). After washing
and drying under a vacuum, PE-O-FA was char-
acterized by HMBC, showing primarily carbox-
ylic acids and minor ketones. Aldehydes were
no longer detectable (fig. S11). The carboxyl in
the fatty acid correlated with two types of pro-
tons (Fig. 2D, 1H NMR d 2.0 and 1.5), poten-
tially indicating a carboxyethyl end group.
The AN of the PE-O-FA was determined by tit-
ration, giving an ordinary AN of 96 mg KOH/g
(Fig. 1D and table S4) that slightly exceeded the
theoretical value of ~80 mg KOH/g for a 700 g/
mol monocarboxylic acid (C47).
Extension to polypropylene and mixtures
After successfully converting PE to fatty acids,
the process was applied to pulverized lab-grade
PP (500 mg; Mw, 158 kDa; Ð=4) under reaction
conditions similar to those used for PE (N2,
10 vol % O2 in N2, and air). Degradation products
in N2 (PP-N2-wax), 10 vol % O2 (PP-O-wax), and
air (PP-air-wax) showed total wax yields of 90,
85, and 87 wt %, respectively (Fig. 3A and table
S2, experiments 4 to 6, 10 to 12, and 14), with a
small amount of coke and gaseous products
(fig. S12). The m/z ranges were 170 to 950 (cen-
tered at 560) for PP-N2-wax and 150 to 700 (cen-
tered at 450) for PP-air-wax (fig. S6C), and the
molecular weight polydispersities were rela-
tively small (table S3). Unlike that for PE, the
PP wax yield remained high in the air, eliminat-
ing the need for controlled gases in the process
and making the method more economically
attractive. Therefore, the degradation of PP
in 10 vol % O2 was not investigated further.
GC-MS analysis of PP-N2-wax showed broad
multimodal distributions of primarily alkene
products in GC-MS (fig. S13). The carbon num-
bers of alkenes were mostly multiples of 3 (or
3n in the range of C9 to C36), and those of the
rest of alkanes, alkenes, and dienes were main-
ly 3n+1. This distribution suggested that the
primary degradation mechanism could be chain
scission on the PP backbone because each PP
repeating unit has three carbons (which is in
agreement with our simulations below). With
air present, the chromatogram of PP-air-wax
became crowded and hard to analyze (fig. S6A).
PP-N2-wax and PP-air-wax were characterized
by APCI-MS (fig. S6, B and C), and the latter
showed a slightly higher proportion of short
Table 1. Abbreviations.
Full name
Abbreviation
Chemicals
.....................................................................................................................................................................................................................
Polyethylene
.....................................................................................................................................................................................................................
Polypropylene
.....................................................................................................................................................................................................................
Polyvinyl chloride
.....................................................................................................................................................................................................................
Polyethylene terephthalate
.....................................................................................................................................................................................................................
High-density PE
.....................................................................................................................................................................................................................
Low-density PE
.....................................................................................................................................................................................................................
Stearic acid
.....................................................................................................................................................................................................................
Wax yielded from PE degradation in N2
.....................................................................................................................................................................................................................
Wax yielded from PE degradation in 10 vol % O2
.....................................................................................................................................................................................................................
Wax yielded from PE degradation in air
.....................................................................................................................................................................................................................
PE-O-wax derived fatty acid
.....................................................................................................................................................................................................................
Wax yielded from PP degradation in N2
.....................................................................................................................................................................................................................
Wax yielded from PP degradation in 10 vol % O2
.....................................................................................................................................................................................................................
Wax yielded from PP degradation in air
.....................................................................................................................................................................................................................
PP-air-wax derived fatty acid
.....................................................................................................................................................................................................................
PE
PP
PVC, or V
PET
HDPE
LDPE
SA
PE-N2-wax
PE-O-wax
PE-air-wax
PE-O-FA
PP-N2-wax
PP-O-wax
PP-air-wax
PP-air-FA
Instrumentation and methods
.....................................................................................................................................................................................................................
Gas chromatography
.....................................................................................................................................................................................................................
Gas chromatography-mass spectrometry
.....................................................................................................................................................................................................................
High-temperature gel permeation chromatography
.....................................................................................................................................................................................................................
Atmospheric pressure chemical ionization mass spectrometry
.....................................................................................................................................................................................................................
Nuclear magnetic resonance spectroscopy
.....................................................................................................................................................................................................................
Heteronuclear multiple bond correlation
.....................................................................................................................................................................................................................
Heteronuclear single quantum correlation
.....................................................................................................................................................................................................................
Proton NMR
.....................................................................................................................................................................................................................
Quantitative NMR
.....................................................................................................................................................................................................................
Flame ionization detector
.....................................................................................................................................................................................................................
Mass selective detector
.....................................................................................................................................................................................................................
Density functional–based tight-binding
.....................................................................................................................................................................................................................
ab initio molecular dynamics
.....................................................................................................................................................................................................................
Fourier transform infrared spectroscopy
.....................................................................................................................................................................................................................
Thermogravimetric analysis
.....................................................................................................................................................................................................................
GC
GC-MS
HT-GPC
APCI-MS
NMR
HMBC
HSQC
1H NMR
q-NMR
FID
MSD
DFTB
AIMD
FTIR
TGA
Parameters
.....................................................................................................................................................................................................................
Number-average molar mass
.....................................................................................................................................................................................................................
Weight-average molar mass
.....................................................................................................................................................................................................................
Polydispersity
.....................................................................................................................................................................................................................
Carbonyl index
.....................................................................................................................................................................................................................
Acid number
.....................................................................................................................................................................................................................
Activation energy
.....................................................................................................................................................................................................................
Pre-exponential factor
.....................................................................................................................................................................................................................
Selectivity of thermolysis (T) or upcycling (U)
.....................................................................................................................................................................................................................
Yield of thermolysis (T) or upcycling (U)
.....................................................................................................................................................................................................................
Concentration of alkenyl groups
.....................................................................................................................................................................................................................
Concentration of total waxes
.....................................................................................................................................................................................................................
Concentration (mmol/g) of acid group in fatty acids
.....................................................................................................................................................................................................................
Concentrations (mmol/g) of alkenyl groups in fatty acids
.....................................................................................................................................................................................................................
Mn
Mw
Ð
CI
AN
Ea
A
sT or sU
aT or aU
cc¼c
cwax
cacid
cc¼c;FA
hydrocarbons because of air-induced oxidation,
which is similar to the finding in a previous re-
port. (34) As with the PE degradation product,
PP-N2-wax and PP-air-wax were primarily com-
posed of terminal alkenes with minor internal
alkenes (Fig. 3B and figs. S14 and S15). The pri-
mary form of the terminal alkene was possibly
2-methyl-2-propenyl, as suggested by the cor-
relations in the HMBC and HSQC. Additionally,
some minor forms of alkenes were detected
in the 13C NMR spectra and could be ascribed
to internal alkenyl structures (fig. S14A). PP-air-
wax contained ketones, aldehydes, and esters
because of partial oxidation (fig. S15), but
the alkenyl region resembled that of the
PP-N2-wax.
As with the PE-derived waxes, upcycling of
PP-N2-wax and PP-air-wax was conducted in air
Xu et al., Science 381, 666–671 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
B
C
Fig. 2. Degradation of PE into intermediate waxes and upcycling into fatty acids. (A) Yields and (B) GC-MS
chromatograms of intermediate waxes after degrading lab-grade PE in N2, 10 vol % of O2 balanced with
N2, or air. (C) NMR-HMBC spectra of PE-N2-wax in deuterated p-xylene. The circles highlight the C-H
correlations of the major and minor alkene products. (D) NMR-HMBC spectrum of the fatty acid derived
from PE-O-wax. The black box highlights the two carboxyl carbon correlations with protons. [Insets in (C) and
(D)] Chemical structures of the major alkene and fatty acid products.
at 150°C over Mn stearate. PP-air-wax oxition
was faster than that for PP-N2-wax; the former
showed a CI of ~0.9 after 4 hours (fig. S9C).
Moreover, a possible epoxy structure was de-
tected in oxidized PP-air-wax (fig. S16), indi-
cating that poxy could be a potential oxidation
intermediate between alkenyl and aldehydes.
The fatty acids (PP-air-FA) that resulted from
hydrolysis were characterized by NMR-HMBC
and showed no detectable aldehyde but stronger
ketone carbonyl signals than those of PE-O-FA.
The acid carbonyl showed three correlations
with protons (Fig. 3C and fig. S17), possibly
indicating a 2-carboxylpropyl terminal structure.
PP-air-FA exhibited an AN of 169 mg KOH/g,
substantially higher than the theoretical value
of 84 mg KOH/g for a monocarboxylic acid at
670 g/mol (C46) (table S4, entry 6), suggesting
the presence of polyacids.
After both PE and PP were successfully con-
verted to wax and fatty acids at high conversions,
municipal PE/PP wastes (obtained in Blacksburg,
VA) were sorted (if labeled), pulverized, and
mixed to mimic a waste stream [high-density
PE (HDPE, 25 wt %), PP (25 wt %), low-density
PE (LDPE, 25 wt %), and PE/PP unsorted
(25 wt %)]. Three batches of the PE/PP waste
mixtures (500 mg per batch) were degraded
into wax, resulting in an average yield of 82% in
N2. The lower wax yield of PE/PP mixtures from
municipal waste streams was ascribed to the
additives, paint, dye, and labels. The wax was
further upcycled to fatty acids, giving an aver-
age AN of 57.3 mg KOH/g (Fig. 1D and table
S4, entry 8). The AN can be improved by tun-
ing the oxygen level during degradation, the
airflow during oxidation, and the upcycling
temperature. Ketones and aldehydes could
potentially be present in the product and
can adjust the product viscosity, function as
soap softeners (35), and modulate fragrance
release (18).
Theoretical simulations
Density functional–based tight-binding (DFTB)
simulations were used to gain a molecular
understanding of the temperature-gradient
degradation of PE and PP and to evaluate the
subsequent oxidative upcycling reactions. DFTB
and the extended tight-binding methods enable
simulations of relatively large systems and rea-
sonable timescales with good accuracy but are
considerably faster than typical ab initio den-
sity functional theory (DFT) methods (36).
Fig. 3. Degradation of PP and PE/PP mixture
into intermediate waxes and upcycling into
fatty acids. (A) The intermediate wax yield of
lab-grade PP upon degradation in N2, N2/O2 mixture
(10 vol % O2), or air, along with the wax yield from
a PE/PP waste mixture (including 25 wt % HDPE,
25 wt % PP, 25 wt % LDPE, and 25 wt % PE/PP
unsorted) upon degradation in N2. The ANs are
shown in table S4. The low wax yield from the
PE/PP waste mixture was due to solid contaminants
such as paper labels, paints, and dyes. (B) NMR-
HMBC spectra of PP-N2-wax in deuterated p-xylene.
(Inset) Chemical structure of the major alkene
product. The circles highlight the C-H correlations
of the major and minor alkene products, respec-
tively. (C) NMR-HMBC spectra of PP-air-FA. (Inset)
Chemical structure of the major fatty acid product.
The black box highlights the three carboxyl
carbon correlations with protons.
Multiple (>10) molecular-dynamics trajectories
were used to evaluate the PP and PE chain be-
havior. The model polymer chains undergo sig-
nificant coiling and dynamical oscillations
during the ab initio molecular dynamics (AIMD)
simulations. The mechanisms of alkene for-
mation from PE and PP are primarily radical
b-scission and secondarily disproportionation
(Fig. 4A and fig. S18), similar to the findings of
previous reports (3, 7, 38). We focus the discus-
sion on PP because it produces more olefin wax
Xu et al., Science 381, 666–671 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 4. Plausible reaction
pathway, thermody-
namics, and kinetics of
b-chain scission in PE
and PP. (A) The thermolysis
of a model polymer chain
into an alkane and alkene
fragment and subsequent
oxidation to a fatty acid, as
captured by the simulations.
(B) b-Scission of a radical in
PE or PP, R=H or CH3.
(C) Thermodynamic parame-
ters and (D) kinetic constants
of PE b-scission and PP
b-scission at 298, 633, and
823 K, as calculated
according to the Benson
group-additivity method
(39, 40).
during degradation than does PE. The results
show that chain scission occurs somewhat ran-
domly along the backbone of the PP chain and
that multiple bonds are broken to form alkene
and alkane fragments (Fig. 4A and fig. S19). We
note that the simulated fragment-size distribu-
tions agree with experimental observation and
that there are more alkenes formed for PP
than for PE. For example, in the experimental
PE degradation, the initial C=C concentration in
PE-N2-wax was ~1.15 mmol/g on the basis of
quantitative NMR (q-NMR, fig. S20 and table
S5). By contrast, the C=C concentration in PP-
N2-wax was ~3.15 mmol/g, showing good
qualitative agreement with the simulation
results.
The degradation fragments from the simu-
lations were then annealed by geometry op-
timization and modeled for reactivity toward
oxygen at reduced temperatures. During the
oxidation step, hydrogen extraction from a
methyl or methylene group in the fragment
was predicted to form a hydroperoxyl radical,
which is prone to react with a readily formed
aldehyde from alkenyl oxidation at the frag-
ment end (Fig. 4A). This sequence initially
produces an alcohol-like intermediate (H is
transferred to carbonyl O on the aldehyde) that
ultimately forms a carboxylic acid, by using a
modified Baeyer-Villiger reaction. After the al-
dehyde accepts a H from the HOO(cid:129), the O-O(cid:129)
binds to the intermediate C-OH to form a car-
boxylic acid. The aldehyde intermediate was
confirmed by the NMR-HMBC experiments on
partially oxidized wax (fig. S16). The primary
intermediates found in this work also agree
with the results of a previous study of paraffin
oxidation over stearate (29), but we cannot
rule out other potential oxidation pathways at
this time.
Applying the qualitative insights from the
DFTB simulations, we then used the Benson
group-additivity method (39, 40) to evaluate the
standard Gibbs free energy (DGo) (Fig. 4B and
table S6) of PE b-scission (DGo
PE = 51.1 kJ/mol)
and PP b-scission (DGo
PP = 45.7 kJ/mol). Thermo-
dynamically, alkene formation from PP and PE
is disfavored at 298 K (Fig. 4C and table S7).
At elevated temperatures (633 K and 823 K),
PE b-scission and PP b-scission become increas-
ingly thermodynamically favorable. Under our
experimental conditions (633 K), the reaction
enthalpies and DGoof PE and PP degradation are
reduced (DHPP;633K = 88.9 kJ/mol and DGPP;633K =
−5.60 kJ/mol; DHPE;633K = 94.3 kJ/mol and
DGPE;633K = 1.20 kJ/mol). However, the process
is still slightly disfavored for PE. Upon increas-
ing the temperature to 823 K, both PE and PP
have favored b-scission pathways (DHPP;823K =
86.9 kJ/mol and DGPP;823K = −33.1 kJ/mol;
DHPE;823K = 92.9 kJ/mol and DGPE;823K =
−26.5 kJ/mol). The kinetic parameters and con-
stants of b-scission were also predicted by using
the group-additivity method on the basis of
model reactions (fig. S21A) (41). PP b-scission
showed lower activation energies and higher
Xu et al., Science 381, 666–671 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
kinetic constants than did PE at all tempera-
tures (Fig. 4D and table S8). In general, alkene
formation from PP b-scission is more favored
and faster than that from PE (this agrees well
with our experiments and simulations above).
Our observation of PE– and PP–b-scission de-
pendence on temperature also agrees well with
the literature, in which the alkene yield from
PE thermolysis increased from ~30% at ~600 K
to ~70% at above 800 K, whereas that from
PP thermolysis stayed high (>70%) regardless
of the temperature (fig. S22) (23, 37, 42–48).
Technoeconomic analysis (TEA) of the process
was assessed on the basis of a 10,000-ton/year
capacity (tables S9 to S14). The total capital
investment was estimated at USD 2.70 million
with an annual net profit of USD 1.03 million,
resulting in an internal rate of return of 39.1%,
a payback period of 2.63 years, and an aver-
age return of investment of 33.0%, with-
out any government subsidies or tax returns
(table S15).
Outlook
The fatty acids produced in this study have a
wide range of applications, either for being kept
in the plastic loop or for downstream uses. The
downstream surfactant products have at least
twice the market value of virgin plastics, rep-
resenting an economically competitive process
for plastic-waste utilization. In addition, sur-
factants have a market volume matching that
of end-of-life plastic wastes, thus representing a
volume-impactful method for plastic-waste re-
moval. Controlled thermolysis in a temperature-
gradient reactor is the key to controlling the
high yield of the wax products relative to small
gaseous molecules. Unlike existing processes
(22), our process tolerates oxygen and requires
no expensive catalysts or stringent reaction con-
ditions. The resulting products show good ANs
for PE- (96 mg KOH/g) and PP-derived fatty
acids (169 mg KOH/g), which can be further
optimized by inhibiting side reactions (figs.
S23 and S24). We anticipate the process to be
amenable to a diverse range of other plastic
wastes for producing high-value, large–market-
volume products (e.g., fatty alcohols and sul-
fates) (49–51).
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AC KNOWLED GME NTS
The authors acknowledge the Chemistry Chromatography Center
at Virginia Tech, especially M. Ashraf-Khorassani, for providing GC
and GC-MS support. The authors also acknowledge the Mass
Spectrometry Incubator at Virginia Tech, especially R. Helm and
K. Ray for their support on APCI-MS. The molecular simulations
were performed at the Center for Nanophase Materials Sciences, a
US Department of Energy (DOE) Office of Science User Facility
operated at Oak Ridge National Laboratory. Funding: G.L.
acknowledges support from the Department of Chemistry and the
Dean’s Discovery Fund at Virginia Tech. This material is partially
based on the work supported by NSF Award DMR-1752611 through
the CAREER award. Mechanistic studies of the deconstruction
processes were partially supported by the US DOE Office of
Science, Materials Sciences and Engineering Division. The
simulations used resources of the Compute and Data Environment
for Science (CADES) at the Oak Ridge National Laboratory,
which is supported by the Office of Science of the US DOE under
contract no. DE-AC05-00OR22725. Funding for N.A.R. and J.M.
was provided in part by the US DOE Office of Energy Efficiency and
Renewable Energy, Advanced Manufacturing Office (AMO) and
Bioenergy Technologies Office (BETO). This work was performed as
part of the BOTTLE Consortium and was supported by AMO and
BETO under contract no. DE-AC36-08GO28308 with the National
Renewable Energy Laboratory, operated by Alliance for Sustainable
Energy. Author contributions: G.L. conceived and supervised the
project. G.L. and Z.X. designed the project. Z.X. and N.E.M. conducted
degradation-upcycling reactions and GC, GC-MS, and FTIR
measurements. Z.X. and P.V. performed NMR experiments. B.G.S.
conducted DFT simulations. Q.Z. performed TEA and heat and mass
transfer analyses. N.E.M. and C.P. performed rheological experiments.
N.R. and J.M. conducted HT-GPC measurements. Z.X. determined the
standard Gibbs free energies for the degradation reactions. M.S.
performed titrations to determine the ANs. N.E.M. evaluated the effect
of temperature gradient on the degradation reactions. G.L., B.G.S., Z.X.,
and N.E.M. analyzed the data, interpreted the results, and wrote the
manuscript. All authors proofread the manuscript. Competing
interests: G.L., Z.X., and N.E.M. are inventors on Provisional Patent
Application no. 63/462,863 pertaining to this work. Data and
materials availability: Data pertaining to this work are available in
the supplementary materials and Dryad (52). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh0993
Figs. S1 to S31
Tables S1 to S18
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Submitted 9 February 2023; accepted 16 June 2023
10.1126/science.adh0993
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RES EARCH
QUANTUM SENSING
Improving metrology with quantum scrambling
Zeyang Li (
Roman Schmied5, Soonwon Choi4, Mikhail Lukin2, Edwin Pedrozo-Peñafiel1, Vladan Vuletić1*
)1, Simone Colombo1, Chi Shu1,2, Gustavo Velez1,3, Saúl Pilatowsky-Cameo4,
Quantum scrambling describes the spreading of information into many degrees of freedom in
quantum systems, such that the information is no longer accessible locally but becomes distributed
throughout the system. This idea can explain how quantum systems become classical and acquire a
finite temperature, or how in black holes the information about the matter falling in is seemingly erased.
We probe the exponential scrambling of a multiparticle system near a bistable point in phase space
and utilize it for entanglement-enhanced metrology. A time-reversal protocol is used to observe
a simultaneous exponential growth of both the metrological gain and the out-of-time-order correlator,
thereby experimentally verifying the relation between quantum metrology and quantum information
scrambling. Our results show that rapid scrambling dynamics capable of exponentially fast
entanglement generation are useful for practical metrology, resulting in a 6.8(4)-decibel gain beyond
the standard quantum limit.
tum metrology, this enables a family of powerful
quantum amplification protocols (17–24) such
as signal amplification through time-reversed
interaction (SATIN) (23). Such protocols can
be robust against many limitations that usual-
ly affect entanglement-enhanced atomic sen-
sors, including imperfect measurements. In the
presence of exponential scrambling dynamics
(Fig. 1A), the SATIN signal is also amplified
exponentially over time.
Experimental setup
The Lipkin-Meshkov-Glick (LMG) Hamiltonian
(24, 25–34) is of particular interest in this con-
text, as it exhibits exponential evolution in
phase space while it can be experimentally
realized in a cavity quantum electrodynamics
(cQED) system. The latter is accomplished by
adding a global rotation term ^S x to the one-
axis-twisting (OAT) (35) Hamiltonian ^Sz
2
ð1Þ
^H ¼ c^Sz
2 þ W^S x
(cid:3)
(cid:1)
Here S ¼ ^S x; ^S y; ^S z
2
represents the total
spin of the system consisting of N ¼ 2S spin-1
particles, c is the shearing parameter for OAT,
and W is the transverse rotation frequency.
Although the time evolution is not chaotic
because of the conservation of ^S 2
, the LMG
Hamiltonian nevertheless features a quantum
Lyapunov exponent for 0 < W= Scð
Þ < 2 due
to an unstable (bifurcating) trajectory in the
system phase space (Fig. 1A) (32, 36, 37).
Our experiments operate with N ¼ 200 171Yb
atoms whose magnetic sublevels ↑; ↓j
i in the
2 sys-
electronic ground state represent a spin- 1
tem. One of the two spin states ( ↑j i) couples to
an electronically excited state ej i via sþ-polarized
light that circulates inside the optical cavity
(Fig. 1B). The coupling between a single atom
and the cavity is characterized by the single-
atom cooperativity h ¼ 8:8 2ð Þ (38). We imple-
ment the LMG Hamiltonian in the rotating
frame by adding an oscillating transverse mag-
netic field to the OAT Hamiltonian (34) [Fig.
1B and supplementary materials (SM) (39)].
The experiments start by initializing the
system in a coherent spin state (CSS) pointing
along the x axis by means of optical pumping
followed by a p=2 spin rotation. Analytical
solutions using the Holstein-Primakoff approx-
Þ < 0 or
imation (40) show that for W= Scð
Þ > 2, the system evolution is periodic
W= Scð
(41). How-
with a frequency w ¼
ever, for 0 < W= Scð
Þ < 2 the frequency w
becomes imaginary, corresponding to an
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
W2 (cid:1) 2ScW
p
E ven though all unitary dynamics of quan-
tum systems are in principle reversible,
it is extremely challenging in practice to
reverse the arrow of time in generic in-
teracting many-body systems. This is be-
cause any small perturbations or imperfections
in the time-reversed dynamics can lead to
highly complicated, nonlocal changes in quan-
tum wave functions, similar to the butterfly
effect in chaos theory. Dubbed information
scrambling (1–3), this quantum-mechanical
effect gives rise to a variety of unusual pheno-
mena and applications ranging from models
of quantum gravity (4, 5) to quantum metrol-
ogy (6). The speed of information scrambling
can be quantified by out-of-time-ordered cor-
relators (OTOCs) (7, 8), which constitute a
measure of how fast the noncommutativity
between two different quantum operations
is established (9). In certain systems, the
OTOC grows exponentially fast over time
elQ t , where lQ > 0 defines the generalized
quantum Lyapunov exponent (8). OTOCs have
been measured (10) and used as probes for
various many-body phenomena, such as ther-
malization (11), quantum phase transitions
(12), many-body entanglement growth (13), and
quantum scrambling (14–16). However, the
observation of exponential scrambling has
remained elusive.
One approach to effective time reversal in-
volves changing the sign of the Hamiltonian
^H → (cid:1) ^H during the evolution of highly engi-
neered quantum systems. In the field of quan-
1Department of Physics, MIT-Harvard Center for Ultracold
Atoms, Research Laboratory of Electronics, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA.
2Department of Physics, Harvard University, Cambridge, MA
02138, USA. 3Department of Electrical Engineering and
Computer Science, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA. 4Department of Physics,
Massachusetts Institute of Technology, Cambridge, MA
02139, USA. 5Viewpointsystem GmbH, 1010 Wien, Austria.
*Corresponding author. Email: vuletic@mit.edu
Fig. 1. Time-reversal–based exponential growth of sensitivity in a system with an unstable fixed point.
(A) Classically, for a trajectory with a positive Lyapunov exponent l1 > 0, an initial signal (displacement) d 0ð Þ
increases exponentially over time. For quantum dynamics, however, an initial overlap between two states is
preserved under unitary evolution. To amplify the signal similarly to the classical case, one needs to evolve the
^
H, resulting in decreased quantum fluctuations along a direction with negative Lyapunov
state under the nonlinear
^
coefficient l2 < 0. A displacement along this direction followed by application of the negative Hamiltonian (cid:1)
H
(such that l1;2→ (cid:1) l1;2) is then used to amplify the signal. The plots represent the evolution on the Bloch
sphere, where the Sy and Sz axes are labeled as in the left subplot of the middle row. (B) Experimental setup. The
LMG Hamiltonian is generated by the interaction of the collective atomic spin with light inside a cavity on the
transition ↑j i→ ej i, while a radiofrequency magnetic field is applied to rotate the atomic spin.
Li et al., Science 380, 1381–1384 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
unstable-fixed-point exponential evolution with
a Lyapunov exponent lQ ¼ wj
j. For a fixed
Sc, choosing W ¼ Sc results in a maximum
Lyapunov exponent lQ ¼ Scj
j.
Metrological gain
Þ
(cid:3)= S=2
ð
≡ maxa var Sað
½
We first measure the antisqueezing {largest
variance x2
Þ} of the col-
þ
lective spin S after an evolution under ^H as
a function of the ratio W= Scð
Þ . The anti-
squeezing x
þconstitutes an upper bound on
the quantum Fisher information (QFI) with
respect to spin rotations (42). As shown in
Fig. 2B, the experimental data for x2
þ agree
with the numerical simulation of the model
(solid red line) and show a peak at W ¼ Sc,
as expected.
We then measure in Fig. 2C how x2
þ grows
with time for the two cases W ¼ 0 (OAT Hamil-
tonian) and W ¼ Sc (critically tuned LMG
Hamiltonian). The OAT data (gray) exhibit
quadratic growth of x2
þ , as expected. The
LMG data (red) show exponential growth of
þ ¼ e2lQ t, with lQ ¼ Sc for times t ≲ ðScÞ(cid:1)1.
x2
For larger times, the growths slows because
of finite particle number and light-induced
decoherence (34, 39). The finite total spin fur-
ther causes the states to turn non-Gaussian,
which we characterize via the Binder cumu-
lant (43) (Fig. 2D).
The time evolution under the critically tuned
(W ¼ Sc) LMG Hamiltonian ^H quickly pre-
pares an entangled collective quantum state.
To implement quantum metrology with the
SATIN protocol, we then apply a small rotation
^U df ¼ e(cid:1)i^S adf, where ^S a ≡ ^S ycosa þ ^S z sina
represents a collective spin operator in the yz
plane. This encodes a signal phase df along
the a direction, with a ¼ p=4 chosen to max-
imize the metrological gain [Fig. 1A and SM
(39)]. To implement (cid:1) ^H, we switch to another
set of laser frequencies incident on the cavity
and flip the sign of the transverse field W [SM
(39)]. This generates an effective backward
evolution in time that amplifies the applied
signal df. The shifted state then undergoes a
bifurcated trajectory for df ≶ 0 (see Fig. 2C),
resulting in an exponentially amplified devia-
tion Gdf from the original position. We mea-
sure the mean spin value h^S ai ¼ Ssin Gdf
Þ to
infer the signal amplification G. As shown in
Fig. 3, the squared signal amplification G2
(orange) increases exponentially with the same
exponent 2lQ as the antisqueezing x2
þ up to
times t ≈ ðScÞ(cid:1)1. The measured quantum noise
N 2 , i.e., the variance of spin projection noise
along the amplification direction ^S a normalized
to the standard quantum limit (SQL) (blue),
remains unity until t ≈ 0:8ðScÞ(cid:1)1 . The subse-
quent increase of the noise N 2 results from
the residual light-atom entanglement (34) and
can be improved in the future by optimizing
the light detuning (39). The improvement of
the metrological gain over the SQL is 6.8(4) dB.
ð
Fig. 2. Collective-spin evolution in the cQED system. (A) Numerical calculation of the normalized variance x2
þ
of the antisqueezed direction as a function of Sct and W=Sc with linecuts representing the measurements in
(B) and (C). (B) Experimentally measured antisqueezing (blue symbols) and theoretical expectation (red line) for
Sct ¼ 1:8 as a function of the rotation strength W. The shaded region indicates exponential growth, whereas
in the other regions the time evolution is either quasi-periodic or growing polynomially. (C) Comparison of
antisqueezing x2
þ between the fastest exponential growth for a critical rotation strength W ¼ Sc, and the
polynomial growth of pure OAT (W ¼ 0). The two Bloch spheres represent the lines of classical evolution in
both situations. The dashed and dash-dotted red lines represent exponential growth based on the theoretically
predicted Lyapunov exponent and the full numerical result, respectively, with no free parameters. The gray dashed
line is calculated for W ¼ 0. (Inset) Logarithmic plot for W ¼ Sc showing the exponential growth of x2
þ.
(D) The Binder cumulant B (characterizing the deviation from a Gaussian distribution for B > 0) for the
antisqueezed direction for the critical LMG condition W ¼ Sc versus time t. (Insets) Measured spin distributions
for Sct ¼ 0 (blue) and Sct ¼ 2 (purple), with the latter being strongly non-Gaussian.
Fig. 3. Metrological gain with
exponential LMG time-reversal
protocol. The squared signal
amplification G2 (pink open circles)
and system noise N2 (blue solid
squares) versus time t. The pink
dashed line represents the exponen-
tial growth of the antisqueezing shown
in Fig. 2, and constitutes an upper
bound to the QFI. The blue dash-dotted
line is the calculated noise (with no
free parameters) due to residual light-
atom entanglement. The maximum
metrological gain is 6:8 4ð Þ dB.
The deviation of G2 from an exponential for
t ≳ ðScÞ(cid:1)1 is due to the nonuniform coupling
between atoms and the cavity light (44), as
well as the residual light-atom entanglement,
both of which can be improved in the future
(34, 45).
Quantum metrology and quantum information
To investigate the quantum information sci-
ence aspect of the time-reversal protocol, we
measure the fidelity OTOC (FOTOC) with quan-
tum state tomography using randomized mea-
surements (39, 46, 47). The FOTOC F tð Þ can
be expressed as the trace between the den-
sity matrix r 0ð Þ of the original state and that
of the state displaced by df evolved back-
t 0ð Þ :¼ ^U t^r 0ð Þ ^Ut†, where
ward in time, r′
^U t :¼ ei ^Hte(cid:1)i^S adfe(cid:1)i ^Ht
D
F tð Þ ≡ ^U t^r 0ð Þ ^U †
(cid:1)
¼ Tr r′
t 0ð Þr 0ð Þ
t ^r 0ð Þ
E
(cid:3)
At fixed forward evolution time t, the FOTOC
F depends on the small displacement df and
ð2Þ
Li et al., Science 380, 1381–1384 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 4. FOTOC and OTOC extracted from quantum state tomography. (A) Experimental Wigner functions
obtained from quantum state tomography after applying the LMG SATIN protocol with different signal
displacements df [for W ¼ Sc and t ¼ 0:57ðScÞ(cid:1)1]. The dashed circle indicates the original CSS state. (B) The
solid blue line is a quadratic fit to the data (open circles), used to extract the OTOC I (see text and Eq. 3).
Fig. 5. Comparison between quantum
information and quantum metrology
parameters for the LMG model. The
purple open circles, solid green squares,
and solid blue diamonds represent the
antisqueezing, metrological gain, and
OTOC, respectively. All quantities increase
initially exponentially with time with a
fitted Lyapunov exponent lQ ¼ 1:01 3ð ÞSc
that agrees well with the theoretical
prediction lQ ¼ Sc. The OTOC error bars
are obtained by using the bootstrapping
method (39, 50). For longer times
t ≳ ðScÞ(cid:1)1, the metrological gain and
OTOC decrease owing to decoherence
caused by light-atom entanglement, as is
well captured by the theoretical model
(solid blue line) without free parameters.
is related to the OTOC I tð Þ by its second de-
rivative (12)
1
2
@2F tð Þ
I tð Þ ≡ (cid:1)
(cid:5)
ð@dfÞ2 jdf¼0
¼ ^S a tð Þ^r 0ð Þ^S a tð Þ^r 0ð Þ
(cid:6)
ð3Þ
with the Hermitian operator ^S a tð Þ :¼ ei ^Ht
^S ae(cid:1)i ^Ht.
Choosing four different evolution times
(such that Sct1 ∈ 0:38; 0:57; 0:77; 0:96
g), we
f
displace the entangled state for each t1 by
several different small angles df. We then
perform the tomographic reconstruction after
a reversed time evolution with (cid:1) ^H to obtain
F t1ð Þ, as shown in Fig. 4A. The OTOC I t1ð Þ is
then extracted from the data by fitting a quad-
ratic function in the displacement df to the
FOTOC (Fig. 4B). We notice that the fitted
quadratic curve is slightly shifted from df ¼ 0
and has slightly reduced peak fidelity. The
shift is likely due to a small difference between
the assumed and actual Larmor frequencies
between the spin states, whereas the reduc-
tion from unit peak fidelity is due to the im-
perfect time reversal associated with residual
light-atom entanglement. The small imperfec-
tions do not reduce the metrological gain ap-
preciably (39).
Figure 5 summarizes our findings regard-
ing the close relation between quantum scram-
bling and time-reversal quantum metrology:
The antisqueezing x2
þ, metrological gain G :¼
G2=N 2, and OTOC I all agree with each other
and scale exponentially with application time
t of the LMG Hamiltonian for t ≲ 0:8ðScÞ(cid:1)1.
The exponential fit yields a Lyapunov exponent
lQ= Scð
Þ ¼ 1:01 T 0:03, in excellent agreement
with the theoretical expectation lQ= Scð
Þ ¼ 1.
Concluding remarks
Our experiments demonstrate a cQED real-
ization of the critically tuned (W ¼ Sc) LMG
model with an exponential evolution in phase
space. We also point out and experimentally
verify that time-reversal protocols represent a
powerful experimental tool giving access not
only to metrological gain beyond the SQL
(22, 23, 48), but also enabling the measure-
ment of quantum information scrambling in
many-body systems. This generalizes the pos-
sibilities of using quantum information science
to enhance quantum metrology (49). Further-
more, we observe exponential growth of both
the OTOC and the metrological gain for the
LMG model, thereby experimentally verify-
ing the intrinsic relation between these two
concepts from different subfields of quantum
science. The demonstrated methods to re-
verse time evolution may enable the exper-
imental investigation of complex many-body
quantum systems in which the information
spreads exponentially fast within many de-
grees of freedom.
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ACKN OWLED GMEN TS
We thank J. Thompson, M. Schleier-Smith, B. Braverman, and
A. Adiyatullin for inspiring discussions. We also thank M. Liu for
helping resolve the subtleties of using bootstrap method to
extract statistical uncertainties. Funding: We acknowledge
financial support from ONR (grant N00014-20-1-2428), the
National Science Foundation through the Center for Ultracold
Atoms (grant PHY-1734011) and NSF QLCI (Award OMA -
2016244), DOE QSA (through grant DE-SC0021013 and LBNL
QSA Center), and ARO (grant W911NF1910517). Author
contributions: Z.L., S. Colombo, C.S., G.V., and E.P. contributed
to building the experimental setup and performed the
measurements. Z.L. and S.Colombo analyzed the data, numerically
simulated the experiments, and contributed to theoretical
interpretation of the results. R.S. contributed to developing the
quantum state tomography method. S.P.-C. and S. Choi
contributed to the theoretical interpretation of the results. All
work was supervised by V.V. All authors discussed the results
and contributed to the manuscript. Competing interests:
The authors declare no competing interests. Data and materials
availability: All data needed to evaluate the conclusions in the
paper are present in the figures of the paper and/or the
supplementary materials. The data can be accessed at Dryad (51).
License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.sciencemag.org/about/science-licenses-
journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg9500
Materials and Methods
Figs. S1 and S2
Tables S1 and S2
References (52–58)
Submitted 1 February 2023; accepted 19 May 2023
10.1126/science.adg9500
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RES EARCH
STRUCTURAL BIOLOGY
Translation dynamics in human cells visualized at
high resolution reveal cancer drug action
Huaipeng Xing1,2, Reiya Taniguchi1, Iskander Khusainov1, Jan Philipp Kreysing1,3,
Sonja Welsch4, Beata Turonˇová1, Martin Beck1,5*
Ribosomes catalyze protein synthesis by cycling through various functional states. These states
have been extensively characterized in vitro, but their distribution in actively translating human cells
remains elusive. We used a cryo–electron tomography-based approach and resolved ribosome structures
inside human cells with high resolution. These structures revealed the distribution of functional states
of the elongation cycle, a Z transfer RNA binding site, and the dynamics of ribosome expansion
segments. Ribosome structures from cells treated with Homoharringtonine, a drug used against chronic
myeloid leukemia, revealed how translation dynamics were altered in situ and resolve the small
molecules within the active site of the ribosome. Thus, structural dynamics and drug effects can be
assessed at high resolution within human cells.
tive positions. By contrast, the elongation
factor bound “eEF1A, A/T, P” state was most
abundant in eukaryotic D. discoideum cells.
In microsomes isolated from human cells,
the membrane-associated elongation cycle has
been resolved, revealing the eEF1A, A/T, P, E
state as the most prominent (8). However, to
which extent these insights are applicable to
actively translating human cells remains unclear.
A
eEF1A, A/T, P
B
Homoharringtonine (HHT) is a natural
compound that binds to the ribosome and in-
hibits protein synthesis (9). It is used to treat
patients with chronic myeloid leukemia clini-
cally and as a reference to study new anticancer
ribosome inhibitors (9, 10). The HHT-bound
ribosome structure has been determined by
incubating the purified 80S ribosome with HHT
in vitro (11, 12), revealing the binding site at
the peptidyl transferase center (PTC). In the
cellular context, it remains unclear how HHT
affects translation dynamics and how exactly
it inhibits protein synthesis. We applied cryo–
focused ion beam (cryo-FIB), cryo-ET and
advanced data processing algorithms to de-
termine the near-atomic structures of ribosomes
and analyzed the abundance and organization
of different ribosome states in untreated and
HHT-treated human cells.
Ribosomes are bound with HHT inside
human cells
To study the 80S ribosome structures inside
human cells, we first prepared cryo–FIB-milled
lamellae from 35 native (untreated) human
embryonic kidney cells (HEK-293) and acquired
358 tilt series (fig. S1A and table S1). We used
template matching to identify ribosomes within
the reconstructed tomograms (fig. S1B and
T he eukaryotic ribosome (80S) consists of
two subunits (60S and 40S) that trans-
late mRNA into proteins (1). Purified 80S
ribosomes have been extensively studied
in vitro, which has elucidated molecular
details of translation (2, 3). The translation
process can be divided into four main stages:
initiation, elongation, termination, and ribo-
some recycling (3). During elongation, the
rotation of the 40S, the association of elonga-
tion factors, and the translocation of tRNAs
are coordinated to synthesize nascent chains
(3). tRNAs have three canonical binding sites
on the ribosome: aminoacyl (A), peptidyl (P),
and exit (E) sites (3). A noncanonical tRNA
binding site called the Z site, located in an
extreme position past the E site, has been
identified in structures of isolated transla-
tionally inactive mammalian ribosomes (4).
It is speculated that the Z site may represent
a late-stage intermediate of tRNA ejection
downstream of the E site with similarity to
internal ribosome entry site interactions, but
the exact physiological relevance remains ob-
scure (4).
The 70S ribosome from Mycoplasma pneu-
moniae and 80S ribosome from Dictyostelium
discoideum and the respective translation
elongation processes have been visualized
inside cells using cryo–electron tomography
(cryo-ET), revealing differences in translation
elongation (5–7). For example, the most abun-
dant elongation intermediate in bacterial
M. pneumoniae cells was the “A, P” state
wherein tRNAs were identified in the respec-
1Department of Molecular Sociology, Max Planck Institute of
Biophysics, 60438 Frankfurt am Main, Germany. 2Faculty of
Biochemistry, Chemistry and Pharmacy, Goethe University
Frankfurt am Main, 60438 Frankfurt am Main, Germany.
3IMPRS on Cellular Biophysics, 60438 Frankfurt am Main,
Germany. 4Central Electron Microscopy Facility, Max Planck
Institute of Biophysics, 60438 Frankfurt am Main, Germany.
5Institute of Biochemistry, Goethe University Frankfurt,
Frankfurt am Main, Germany.
*Corresponding author. Email: martin.beck@biophys.mpg.de
Xing et al., Science 381, 70–75 (2023)
7 July 2023
40S
60S
P
A/T
Codon sampling
Codon recognition
eEF1A
2.7
4.0
5.0
6.0
7.0
8.0
C
D
Sampling
P site
A site
mRNA
A 1824
A 1825
18S rRNA
Fig. 1. 80S ribosome structures in human cells. (A) Color-coded local resolution map of the eEF1A, A/T,
P state identified in the untreated dataset. (B) Superposition of the codon recognition state (PDB 5LZS, cyan)
onto our eEF1A-tRNA ternary complex at the eEF1A, A/T, P state. The atomic model of tRNA (lavender) and
eEF1A (maroon) from PDB 4CXG were fitted into our map for comparison to 5LZS. (C) The mRNA segmented
from the eEF1A, A/T, P state was fitted with PDB 5LZS. Density is more clearly defined at the P site as
compared with the A site. (D) The atomic model (5LZS) of 18S rRNA (A1822 to A1827) was rigid-body–fitted
into the corresponding density of the 80S at the eEF1A, A/T, P state. The decoding nucleotides A1824 and
A1825 in the atomic model are in the flipped-out configuration, which is inconsistent with the observed
density (arrowhead).
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RES EARCH | R E S E A R C H A R T I C L E
movie S1). After classification and refinement,
we determined the ribosome structure at an
overall resolution of ~3.2 Å and locally resolved
features up to 2.5 Å in resolution from un-
treated cells (Fig. 1B and figs. S1 to S3). The den-
sity of ribosomal protein side chains, ribosomal
RNA (rRNA) bases, tRNA bases, and ions were
well-resolved (fig. S1E), indicating the quality of
the map. Using the same approach we processed
352 tilt series from 32 HHT-treated cells. In the
resulting structure the density of HHT was visi-
ble (fig. S1, F and G) and the position of HHT at
the PTC showed a high similarity to previous
in vitro analysis (9, 11). The P-tRNA was poorly
resolved compared with the untreated ribosome
(fig. S1G), suggesting that the translation was
altered after HHT treatment.
Translation elongation cycle in human cells
We next investigated the translation elonga-
tion process. In untreated cells, focused classi-
fication was performed with dedicated tRNA
and elongation factor masks, resulting in eight
ribosome states resolved from 3.4 Å to 16.4 Å
(figs. S2 and S3 and table S2). These states
were well-explained by previously reported
structural models that captured various elon-
gation states (figs. S4 to S6) (4, 8, 13–15). The
eEF1A, A/T, P state was the best resolved,
globally reaching ~3.4 Å (Fig. 1A), and dis-
played structural features characteristic for
tRNA scanning, indicating that codon sampling
A
60S
eEF1A-tRNA
rather than codon recognition is occurring
(Fig. 1B and fig. S4A) (13, 16). Specifically, the
mRNA codon was more clearly resolved at
the P site (Fig. 1C), suggesting that the codon-
anticodon interaction at the A site is not yet
established. Consistently, we observe the decod-
ing nucleotides A1824 and A1825, which are
thought to stabilize the A-site tRNA by a
“flipping out” movement upon codon recogni-
tion (13), in a “flipped in” conformation (Fig. 1D).
In total, six classes—accounting for ~83%
of all identified ribosomes—were assigned to
the translation elongation cycle based on their
similarity to the previously reported structures
(Fig. 2A) (3, 5, 13, 16). The elongation cycle is
thought to start from the non-rotated P state
that was detected but not particularly abun-
dant in our data (5) (Fig. 2A). It is followed by
the eEF1A, A/T, P state discussed above which
was the most prominent, consistent with
in situ analysis of the lower eukaryote Dictyo-
stelium discoideum (7), but in contrast to pre-
vious analysis in bacteria (5). The abundance
of the codon sampling state in human cells
could be important for the higher decoding
fidelity during translation (17). The following
states were the non-rotated A/T, P and A, P
states. At a low contour level of the map a factor-
like density at the eEF1A binding region is seen
in the A/T, P state, but neither an extended nor
compact eEF1A model provides a sufficient
explanation (fig. S4C, Materials and Methods)
(8, 13). As expected, the A, P state displayed the
A1824 and A1825 nucleotides in a flipped out
conformation (fig. S4D). Yet it was less abun-
dant than in bacteria, where it was the most
populated (5). The subsequent state was iden-
tified as eEF2, ap/P, pe/E (18). Next, two
possible sequences of events are conceivable:
eEF2 and E-tRNA could first dissociate from
the ribosome forming the P state that subse-
quently binds the eEF1A-tRNA, or the eEF1A-
tRNA may displace eEF2 with subsequent
departure of the E-tRNA (5) (Fig. 2A). Various
conformational changes of the small subunit
are apparent during the elongation cycle (fig.
S5) and consistent with previous work (16, 18).
Two further states were identified whose
places in the elongation cycle are not obvious
(Fig. 2B). The rotated eEF2 state without tRNA
fitted the previous structural model very well
(15, 19) (fig. S4G), although the eEF2 position
was shifted by ~1.7 nm compared with the
eEF2, ap/P, pe/E state (fig. S4I). The remain-
ing class, which accounts for only 1.6% of all
classified ribosomes (Fig. 2B), was consistent
with the non-rotated eEF1A, A/T, P, Z state,
which has been suggested to be transient (4).
Although the resolution of this state was only
moderate in untreated cells, the observed elec-
tron optical density at the Z site fitted well with
the purified ribosome at the non-rotated P, Z
state (Fig. 2B and fig. S4, H and J) (4). To our
knowledge, alternative factors binding to this
B
R2
eEF2
3.8%
C
60S
Untreated
HHT-treated
N
eEF1A, A/T, P, Z
1.6%
eEF1A-tRNA
Compact eEF2
40S N
P
10.2%
eEF1A
R1+R2
A, P
15.3%
R1+R2
Compact eEF2, A, P
3.4%
40S N
P
4.5%
eEF1A-tRNA
N
eEF1A, A/T, P
39.6%
R2
eEF2, ap/P, pe/E
5.2%
eEF2
N
eEF1A, A/T, P, E
13.0%
R1+R2
A, P
14.1%
N
A/T, P
6.4%
D
R1: Rolled
R2: Rotated
N: Non-rotated and unrolled
R2
eEF2
46.9%
N
eEF1A, A/T, P, Z
6.7%
N
A/T, P, Z
3.3%
Fig. 2. Ribosome states in native untreated and HHT-treated cells. (A) Six
ribosome states are assigned to the elongation cycle in untreated cells. (B) The
eEF2 and eEF1A, A/T, P, Z states in untreated cells. (C) Three potential
translation elongation intermediate states in the HHT-treated cells. The dashed
arrow illustrates how the elongation states may connect. (D) The eEF2,
eEF1A, A/T, P, Z and A/T, P, Z states inside the treated cells. R1, rolled; R2,
rotated; N, nonrotated and unrolled. The information about 40S rolling and
rotation is shown in figs. S5 and S11.
Xing et al., Science 381, 70–75 (2023)
7 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
site have not been identified. More importantly,
we obtained higher resolution in HHT-treated
cells (see below), which further strengthened
this conclusion. We note that ~12% of the
particles identified as ribosomes were not at-
tributed to a specific state by our classification
and may correspond to additional low abun-
dant states or transitions between states. Col-
lectively, our data allowed the detailed analysis
of the translation dynamics inside native hu-
man cells, which exhibited differences compared
with previous ex vivo studies (8, 18), indicating
that the ribosome isolation process may affect
the ability to capture native elongation inter-
mediates (5, 7).
HHT alters the elongation cycle
The anticancer drug HHT blocks peptide
bond formation (9, 20). Previous in vitro analy-
sis of purified ribosomes revealed that HHT
binds in the A-site cleft in the PTC (11, 21).
Upon HHT treatment, one would thus expect
to observe a strong enrichment of ribosomes
with the A- and P-site tRNAs bound (11).
Indeed, M. pneumoniae ribosomes treated
with 0.5 mg/ml (1547.4 mM) chloramphenicol
(Cm), a related antibiotic binding to the PTC of
the 50S, showed over 70% of ribosomes at the
A, P state (5, 22). The effect of HHT on human
ribosome states in cells remains unknown. To
address this, we exposed cells to HHT concen-
trations of 0.055 mg/ml (100 mM) in the medium,
which resulted in a significantly lower cellu-
lar protein concentration than untreated cells
(fig. S7A), implying that protein synthesis was
inhibited. At the time point examined by cryo-EM,
the ATP levels, which serve as an indicator of
cell viability, were not yet reduced (fig. S7B)
and the cell morphology of untreated and
treated cells was indistinguishable (fig. S7C).
Classification, as described above, identified
six ribosome states resolved into the 3.7 Å to
11.5 Å range (figs. S8 to S12 and table S3).
Unexpectedly, the rotated state with eEF2 but
without tRNA accounted for almost half of all
ribosomes in the dataset (Fig. 2, C and D,
and Fig. 3A). This state showed density for
SERPINE1 mRNA-binding protein 1 (SERBP1)
and thus accounts for hibernating ribosomes
(15, 23) (fig. S10G), in which the HHT density
was visible (fig. S8C). The P state increased in
abundance compared with the untreated cells,
whereby the A, P states showed a similar abun-
dance (Fig. 2C). The HHT molecule was also
resolved at the A, P state but not in other less
populated classes as a result of the lower
resolution (Fig. 3B). We therefore combined
the particles from the four remaining less abun-
dant classes. The resulting average also displayed
density for HHT (fig. S8C). The positions of
A-tRNA and P-tRNA at A, P states were simi-
lar in untreated and HHT-treated cells (Fig. 3B)
(9). One of our classes appeared similar to a
potential compact eEF2, A, P state (figs. S10, D,
I, and J, and S11F) (24), although the respective
local resolution prevents a definitive assign-
ment due to a lack of secondary structure.
Finally, two states with Z-tRNA were consider-
ably more abundant compared with untreated
cells (Fig. 2D and fig. S10, C and E), showing
the typical features of tRNA shape at the Z
site (fig. S10, E and H, and movie S3). Thus,
HHT treatment results in the accumula-
tion of ribosome hibernation instead of the
A, P state, which may be representative of
the mechanism of the drug action in cancer
therapy.
To investigate cell-to-cell variability, we ana-
lyzed the distribution of the ribosome states
across individual cells captured by multiple
A
e
g
a
t
n
e
c
r
e
P
e
g
a
t
n
e
c
r
e
P
50
40
30
20
10
0
50
40
30
20
10
0
B
A, P
A, P
Untreated
A 4411
G 3878
G 4413
U 4414
A 4449
G 4451
G 3907
U 4452
HHTHHT
90°
1 2 3 4 5 6 7 8 9 10
Treated
1 2 3 4 5 6 7 8 9 10
Ribosome class
1 eEF1A, A/T, P
4 eEF1A, A/T, P, E
8 eEF1A, A/T, P, Z
2 A/T, P
5 eEF2
9 A/T, P, Z
3 eEF2, ap/P, pe/E
6 P
10 Compact eEF2, A, P
7 A, P
E
P
A
HHT
Fig. 3. Distribution of ribosome states in cells. (A) Percentages of ribosome states in untreated and
HHT-treated cells. (B) The PTC of ribosomes at the A, P state in untreated and treated cells is shown
fitted with PDBs 5AJ0 and 6QZP, respectively. Structural overlay of tRNAs at A, P states with models determined
from previous studies (bottom; materials and methods). The black arrow points to P-tRNA. HHT is colored in cyan.
tomograms. We identified some degree of cell-
to-cell variability (fig. S13A), for example, the
eEF1A, A/T, P state varied from 25 to 56% in
untreated cells (fig. S13B). Overall, the signal
observed in multiple tomograms of the same
cell was similar, with some notable exceptions
that may imply local variability (fig. S13B).
Notably, the abundance of the eEF1A, A/T, P
(class 1) and eEF1A, A/T, P, E (class 4) was
largely anticorrelated in untreated cells (fig.
S13, C and D), whereas the sum of eEF1A-bound
states was relatively consistent, suggesting that
its total concentration may be limited (fig.
S13E). By contrast, the abundance of ribosomes
containing eEF2 was much more diverse be-
tween different cells (fig. S13E).
Polysomes are impaired upon HHT treatment
We analyzed the spatial organization of dif-
ferent ribosome states within polysomes in
treated and untreated cells. The densities ac-
counting for neighboring ribosomes that are
commonly observed in the subtomogram aver-
ages of untreated cells were reduced in HHT-
treated cells (fig. S14A). Furthermore, the
ribosome distribution was more dispersed sub-
sequent to treatment (Fig. 4, A and B), both
implying that polysomes might be largely abol-
ished. To test this hypothesis, we defined poly-
somes based on a distance threshold of 9 nm
from the mRNA exit to entry sites of neighbor-
ing particles (fig. S14B and table S4, Materials
and Methods). Although this arbitrary classifier
will not capture the entirety of polyribosomes
as it could, for example, miss more distantly
spaced ribosomes on a longer transcript, over-
all it performs well in their detection (fig. S15).
Of all ribosomes in untreated cells, 30.2% were
grouped into arbitrary polysomes (Fig. 4C and
fig. S14, C and D), which was considerably higher
than in HHT-treated cells (fig. S15, A to E). In
monosomes the eEF2 state was prevalent (Fig.
4D and fig. S16, A and B) and exhibits much less
neighboring density (fig. S16, C and D), under-
lining the notion that these ribosomes are hi-
bernating. In polysomes, the eEF2, ap/P, pe/E
state (class 3, see Fig. 3A) was less frequent in
the first leading ribosome than the trailing ribo-
somes (fig. S15F). Classification of all untreated
ribosomes with a dedicated mask resolved the
low-resolution structure of the di-ribosome, in
which the mRNA density was visible (fig. S17A)
(25, 26). This di-ribosome resembled the top-
to-top configuration (t-t, the central protuber-
ance of both ribosomes facing a similar direction)
(27, 28) (fig. S17B). Two other arrangements
of pairs were apparent: one with the central
protuberance of the i+1 ribosome toward down
(t-d), the other toward up (t-u) (fig. S17, C and D).
Although the abundance of these configurations
declined in the treated cells (fig. S17, D and E),
the center-to-center and exit-to-entry distance
of these pairs were indistinguishable from un-
treated cells (fig. S17F).
Xing et al., Science 381, 70–75 (2023)
7 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
Untreated
B
HHT-treated
1
2
3
4
5
6
7
C
90°
3’
5’
3’
5’
8
D
e
g
a
t
n
e
c
r
e
P
30
25
20
15
10
5
0
1
2
5
6
7
8
9
10
e
g
a
t
n
e
c
r
e
P
50
40
30
20
10
0
5
7
8
Monosomes
Polysomes
9
10
8
7
6
Ribosome class
HHT-treated
6
5
4
3
Ribosome class
Untreated
Fig. 4. Spatial and functional analysis of polysomes. (A and B) Distribution of ribosome states in a representative tomogram from an untreated (A) and
treated (B) cell. (C) A polysome and the putative mRNA path. The center-to-center distance of the neighboring ribosomes: 27.3 ± 1.8 nm (mean ± SD, n = 8).
(D) Distribution of ribosome states in monosomes and polysomes from 358 tomograms of untreated cells and 352 tomograms of treated cells. Class numbers
are the same as in Fig. 3A.
We classified ribosomes with a mask cover-
ing the region beyond the exit tunnel, thus
capturing both the potential membrane and
the expansion segment ES27L (figs. S18 and
S19, and tables S2 and S3). The analysis re-
vealed that the translation state distributions
of soluble and membrane-bound ribosomes
were similar (fig. S18D). Notably, seven con-
formations of the expansion segment ES27L
were found in cytosolic ribosomes (fig. S19,
Materials and Methods). One of these con-
tains a long stretch of ES27L that associates
with the ErbB3 receptor-binding protein (Ebp1)
on the surface of the 60S and resembles a
previously published in vitro structure (29, 30)
(fig. S19, A and B, and tables S2 and S3). The
percentage of Ebp1-associated ribosomes was
below 20% in most untreated cells, whereas
the abundance was over 25% in all HHT-treated
cells (fig. S20A). Whether Ebp1 is related to spe-
cific translation states remained unclear (29, 30).
Xing et al., Science 381, 70–75 (2023)
7 July 2023
Thus, a subfraction of Ebp1-bound ribosomes is
observed in all apparent intermediates of the
elongation cycle (fig. S20B).
HHT binds the free 60S associated with eIF6
Finally, we investigated the free 60S and 40S
in the cytoplasm of human cells. The free 60S
showed Ebp1 and ES27L density in both data-
sets (Fig. 5, A and B, fig. S21, A and B), which
was similar to the Ebp1-associated 80S ribo-
some. However, the 60S was much more abun-
dant in treated cells than in untreated cells
(Fig. 5C). Eukaryotic initiation factor 6 (eIF6)
binds the 60S to prevent premature 60S bind-
ing with 40S (31, 32). Our data show that the
60S did not contain eIF6 in the cytosol of
native untreated cells, contrasting HHT-treated
cells (Fig. 5D). Thus, it appears that eIF6
prevents the association between large and
small ribosomal subunits in cells (33–35)
(Fig. 5, C and D, and fig. S21, C to E). Furthermore,
the HHT density was resolved in the 60S from
treated cells (Fig. 5E). Thus, we conclude that
HHT can bind not only the PTC of different
states of the 80S ribosome (Fig. 3B and fig.
S8C) but also the free 60S decorated with eIF6,
which may block the assembly of 40S and
60S in the cytosol of the cell.
Discussion
Our extensive cryo-ET analysis stresses the
feasibility of obtaining structures at high res-
olution and visualizes an anticancer drug
inside human cells. The local resolution in the
ribosome core in our study is limited by the
pixel size. This illustrates that technical obsta-
cles that hinder high resolution in cellular to-
mography have been overcome. The combined
improvements in energy filtering (36), image
processing (Warp-RELION-M pipeline) (22)
and tight control over specimen thickness
(37, 38) enable high resolution, as long as the
4 of 6
)
%
(
e
c
n
a
d
n
u
b
a
S
0
6
20
15
10
15.5
5
4.1
0
Untreated
Treated
RES EARCH | R E S E A R C H A R T I C L E
A
D
E
B
C
150°
40°
150°
40°
10.0 Å
90°
ES27L
Ebp1
4.2 Å
Ebp1
90°
Untreated
Treated
eIF6
eIF6
A 4449
A 4449
G 4451
G 3907
G 4451
G 3907
U 4452
HHT
U 4452
HHT
90°
HHT
Fig. 5. Structure of 60S in human cells. (A and B) Structures of free 60S in
the cytoplasm of untreated cells (A) and HHT-treated cells (B). ES27L and Ebp1
(PDB: 6SXO) are fitted into the 60S maps. Although Ebp1 was not confidently
assigned to the 60S from untreated cells as a result of the lower resolution, it
fitted better in comparison to alternative factors (amino-terminal acetyltrans-
ferases and nascent polypeptide-associated complex) binding to the tunnel exit.
(C) Percentage of the 60S in untreated and HHT-treated cells normalized to the
number of 80S ribosomes in the respective dataset. In untreated cells,
abundance = 60S/(60S+80S) = 1,693/(1693+39,402). In treated cells, 60S/
(60S+80S) = 7176/(7176+39,070). (D) The structure of 60S in untreated cells
fitted with PDB 6LSR indicates that eIF6 is missing (left), contrasting HHT-
treated 60S (right). Large subunit GTPase 1 (LSG1), NMD3 and ZNF622 (PDB:
6LSR) are not observed in the HHT-treated 60S structure. (E) The PTC of free
60S from untreated and treated datasets fitted with PDB 6QZP. HHT is colored in cyan.
number of particles that can be obtained is
sufficient. Further improvements in the autom-
atization of specimen preparation techniques
may thus be instrumental in pushing the reso-
lution for other macromolecular assemblies
analyzed inside cells (38–43).
The detailed comparison of ribosome struc-
tures within untreated and HHT-treated cells
revealed that HHT binds to the PTC of the 80S
ribosome in situ (Fig. 3B and figs. S1G and
S8C), where it can block peptide bond forma-
tion as suggested by previous in vitro studies
(9, 11, 21). However, we also observed SERBP1
binding to ribosomes, a factor that functions
downstream of mammalian target of rapamycin
complex 1 (mTORC1) and leads to a dormant
ribosome state (44). Such a dormant ribosome
state can be a result of cellular stress signaling
(44). Further, we uncovered that HHT bound
the free 60S associated with eIF6 (Fig. 5, D and
E), thus likely hampering the assembly of func-
tional 80S ribosomes and in turn further impair-
ing overall protein synthesis. The accumulation
of 60S-eIF6 may be explained by the fact that
the HHT binding site overlaps with that of
the N terminus of Shwachman-Bodian-Diamond
syndrome protein (SBDS) (fig. S21F) and that
the binding of SBDS to 60S is necessary to
release eIF6 (34, 45).
Our study provides insights into the trans-
lation elongation cycle, the coordination of
ribosome activity within polysomes, and the
diverse arrangements of ES27L inside human
cells. The same technology may be used in the
future to investigate ribosome, translation,
and mRNA quality control pathways in the
context of human tissue culture cells and
primary patient-derived cells. Intermediates
that have not yet been observed inside cells
may be enriched by introducing kinetical
bottlenecks through genetic or pharmaceu-
tical perturbation (5, 46, 47). Our study may
set the stage for the analysis of structures
inside mammalian cells and allow characteri-
zation of drug susceptibility of human indi-
viduals at high resolution by cryo-ET.
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ACKN OWLED GMEN TS
We thank P. C. Hoffmann, M. Tuijtel, and T. Majtner from the
Department of Molecular Sociology at the Max Planck Institute of
Biophysics for advice on membrane segmentation, data collection
and data processing. We thank all the members from the Central
Electron Microscopy facility and the Department of Molecular
Sociology at the Max Planck Institute of Biophysics, and
A. Schwarz, E. Schuman and the Department of Synaptic Plasticity
at the Max Planck Institute of Brain Research for support and
advice. We acknowledge the support from the Max Planck
Computing and Data Facility. We thank M. Rodnina, N. Fischer, and
S. Boehm for critical reading of the manuscript. Funding: M.B.
acknowledges funding from the Max Planck Society. Author
contributions: Conceptualization: H.X. and M.B. Methodology:
H.X., B.T., I.K., and J.P.K. Investigation: H.X., R.T., I.K., J.P.K., S.W.,
and B.T. Visualization: H.X., B.T., and M.B. Funding acquisition:
M.B. Project administration: H.X. and M.B. Supervision: H.X. and
M.B. Writing – original draft: H.X., B.T., and M.B. Writing – review and
editing: H.X., R.T., I.K., J.P.K., S.W., B.T., and M.B. Competing
interests: The authors declare no competing interests. Data and
materials availability: The original tilt series have been deposited in
the Electron Microscopy Public Image Archive (EMPIAR-11538). EM
maps have been deposited in the Electron Microscopy Data Bank
(EMDB) under accession numbers: EMD-16721, 16725, 16726, 16727,
16728, 16733, 16734, 16735, 16736, 16737, 16738, 16739, 16740,
16741, 16742, 16743, 16722, 16744, 16748, 16747, 16749, 16750,
16751, 16752, 16754, 16755, 16756, 16757. The codes used for
polysome analysis are part of the cryoCAT repository (48) and are
deposited at Zenodo. All other data are available in the manuscript or
supplementary materials. License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original US
government works. https://www.sciencemag.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh1411
Materials and Methods
Figs. S1 to S21
Tables S1 to S4
References (49–64)
MDAR Reproducibility Checklist
Movies S1 to S3
View/request a protocol for this paper from Bio-protocol.
Submitted 3 March 2023; accepted 5 June 2023
10.1126/science.adh1411
Xing et al., Science 381, 70–75 (2023)
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incarcerations that occurred in the country (16).
Although homicide and incarceration trends
are imperfect because they do not discriminate
between offenses that occurred specifically in
the context of organized crime, they can be
used to estimate cartels’ violence capacity and
the state’s incapacitation against them. In this
work, we build on this intuition and exploit
data on murders, missing persons, and incar-
cerations in Mexico between 2012 and 2022 to
derive cartel size. We propose a mathematical
system to represent their behavior over 10 years
and seek to shed light on the mechanisms with-
in the so-called black box of the cartels.
This work has two main goals. First, we aim
to obtain plausible estimates of the cartels’
population, including their number of mem-
bers and recruitment capacity. Second, we seek
to simulate different policy scenarios (i.e., in-
creased state incapacitation and recruitment
prevention) to disentangle the effects of vary-
ing strategies to curb cartels’ power and, in
turn, violence in the country. Our conceptual
framework is built on the evidence that, de-
spite the high number of murders and incar-
cerations in the past 10 years, cartels have
maintained and even increased their power,
control, and resources, introducing even more
violence in the country. To construct our model,
we gauge data on 150 cartels active in Mexico in
2020, including information on their alliances
and rivalries and data corresponding to homi-
cides, missing persons, and incarcerations.
Methods
We ask two research questions (RQs). RQ1:
What is the size of Mexico’s cartel population,
and what is their capacity to recruit members?
RQ2: To control cartel violence, is a preventive
policy strategy (focused on reducing cartel re-
cruitment efforts) more effective than a reactive
policy strategy (focused on increasing police
efforts to incarcerate cartel members)?
We consider four mechanisms that explain
why cartel size varies: recruitment, incapac-
itation, saturation, and conflict (Fig. 1). We
model the conflict between cartels with a
RES EARCH
CARTELS
Reducing cartel recruitment is the only way to lower
violence in Mexico
Rafael Prieto-Curiel1*, Gian Maria Campedelli2†, Alejandro Hope3‡
Mexican cartels lose many members as a result of conflict with other cartels and incarcerations. Yet,
despite their losses, cartels manage to increase violence for years. We address this puzzle by leveraging
data on homicides, missing persons, and incarcerations in Mexico for the past decade along with
information on cartel interactions. We model recruitment, state incapacitation, conflict, and saturation
as sources of cartel size variation. Results show that by 2022, cartels counted 160,000 to 185,000 units,
becoming one of the country’s top employers. Recruiting between 350 and 370 people per week is
essential to avoid their collapse because of aggregate losses. Furthermore, we show that increasing
incapacitation would increase both homicides and cartel members. Conversely, reducing recruitment
could substantially curtail violence and lower cartel size.
out tasks (both strictly criminal and not) for
cartels (11). Incapacitation measures the abil-
ity of the state to counter cartels through in-
carceration (12). Considering all incarcerations
allows us to avoid the bias of only focusing
on incarcerations for homicides, which are
only a fraction of the offenses committed by
cartel members. Conflict describes the extent
to which cartels clash and fight with each
other (13, 14). Finally, saturation character-
izes internal instability and dropouts, which
lead to organizational fragmentation (4, 15).
Despite Mexican cartels’ economic, social,
and political importance, we lack essential in-
formation to better understand how they func-
tion. In fact, we primarily lack estimates of the
size of these criminal entities. We also lack
systematic estimates of cartel-related killings
and kidnappings and figures related to recruit-
ment trends, which makes it extremely difficult
to deepen our knowledge about their presence,
resources, and goals. The secretive nature of
cartels’ actions, as well as the insufficient amount
of information accessible to map them, makes
them conceptually similar to black boxes, from
which we can only extrapolate imperfect proxies
of activity using, for instance, the daily num-
ber of homicides or the number of drug-related
L atin America is home to only 8% of the
world’s population, but roughly one in
three intentional homicides worldwide
occur in the region (1). Mexico accounts
for a relevant share of such homicides,
primarily because of the long-standing pres-
ence of cartels across many areas of the coun-
try. In 2021, Mexico reported 34,000 victims of
intentional homicide—nearly 27 victims per
100,000 inhabitants—and was ranked among
the least peaceful countries in Latin America
(2). Between 2007 and 2021, the number of
homicides in the country increased by more
than 300% (3), with institutional sources quan-
tifying that between 2006 and 2018, about
125,000 to 150,000 homicides were related to
organized crime in Mexico (4).
The effects of cartels on Mexico’s society are
far-reaching. These entail their presence across
a wide array of illegal activities beyond drug
trafficking (5, 6), the deterioration of human
rights (7), and the weakening of institutional
stability through extensive acts of violence
(8, 9). Furthermore, some cartels have acquired
a transnational dimension, expanding their
business to the United States and beyond (10).
In this context, although cartels lose dozens
of members daily as a result of killings and
state incapacitation through incarcerations,
the violence over the years has not decreased.
We tackle this puzzle by studying cartels’ evo-
lution, deriving their sizes, and considering
four fundamental sources of size variation:
recruitment, incapacitation, conflict, and sat-
uration. These sources capture the different
exogenous and endogenous dynamics explain-
ing why and to what extent cartels grow or
shrink. Recruitment refers to the process of
attracting a new workforce that stably carries
1Complexity Science Hub, Vienna, Austria. 2Department of
Sociology and Social Research, University of Trento, Trento,
Italy. 3Independent Security Analyst.
*Corresponding author. Email: prieto-curiel@csh.ac.at
†Present address: Mobile and Social Computing Lab, Fondazione
Bruno Kessler, Trento, Italy.
‡Deceased.
Fig. 1. Model diagram representing
the four reasons why a cartel
changes in size. Most cartel-related
activities remain undercover, but we
observe some of their by-products in
casualties and incapacitations.
recruitment
conflict
1500 weekly rate
1000
500
incapacitations
missing persons
recruitment
+
incapacitation
−
saturation
−
conflict
2012
2017
casualties
2022
−
n
w
o
n
k
n
u
n
w
o
n
k
Prieto-Curiel et al., Science 381, 1312–1316 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
weighted network, where a node represents
each cartel, and an edge represents a conflict
in some state in Mexico. Similarly, we con-
struct a weighted network of alliances between
cartels across different states. The model is a
system of coupled differential equations, one
for each cartel. Although we cannot observe
most aspects of cartels (such as their recruitment
and internal conflicts), we use the observed
number of casualties and incarcerations to
estimate the model parameters and infer the
size of each cartel. We then use those esti-
mates to forecast different scenarios for the
next 5 years in Mexico. See the supplemen-
tary materials, sections A to F, for details
on methodology.
Results
RQ1: Estimating cartels’ populations
Most cartel-related activities are organized as
dark networks to maintain their operations
and activities covered (17, 18). However, their
human losses caused by homicidal violence
and the state’s action through incapacitation
provide insights into the overall amounts of
such activities. We leverage the trends in homi-
cides, missing persons, and incarcerations over
the past decade to motivate our investiga-
tion of cartels’ sizes in Mexico (supplementary
materials, section A). Not all losses are directly
related to the conflict between cartels (e.g.,
domestic violence), and some are a by-product
of their dispute (e.g., deaths suffered by family
members or bystanders). To study the size and
evolution of the cartel population, we exclu-
sively model homicides between cartel mem-
bers (i.e., homicides in which the victim and
the perpetrator are both cartel members). The
starting point is that cartels have not seen their
power diminished because violence has not re-
duced either. In Mexico, 686 people were killed
each week of 2021, with an additional 137 people
reported as missing and yet to be found, and
more than 2500 people were imprisoned each
week (3, 19, 20).
We use the number of cartel losses to infer
otherwise unknown properties, including their
size and recruitment rate. Data compiled from
open sources by the Programa de Política de
Drogas (PPD) (21) enable us to detect the ex-
istence of k = 150 active cartels in Mexico in
2020. Building on such data, we operationally
define cartels as those criminal organizations
that are found to be active in Mexico, regard-
less of their size and activity (supplementary
materials, section B). Cartels have different
interactions: They can be allies, they can have
no interactions (particularly from distant lo-
cations), or they can fight for territory or re-
sources, creating substantial losses among
both groups. To represent these interdepen-
dencies, we construct two separate weighted
networks—the allies A and rivalries R—to
recreate conflicting and cooperating cartels,
Fig. 2. Rivalries and alliances were observed between 150 active cartels in Mexico in 2020. The size
of the node represents the estimated cartel size. If cartels have at least one state rivalry, nodes are
connected (left). The width of the edge corresponds to the number of states in which cartels fight. Nodes are
connected if they are identified as allies (right). NF Mich., Nueva Familia Michoacana; UTepito, Unión Tepito;
Z, Los Zetas; SRdL, Santa Rosa de Lima.
with weights corresponding to the number of
states in which two cartels interact (Fig. 2).
Major cartels, such as Cártel Jalisco Nueva
Generación (CJNG), the Sinaloa Cartel, and
Nueva Familia Michoacana, are present al-
most at a national level and have alliances with
many satellite organizations forming three main
clusters. These clusters fight against each other,
creating most of the violence between cartels
(16). Smaller organizations are local to one city
and have few interactions (cooperation or con-
flict) with other cartels.
X
The number of members of cartel i at time t,
expressed as Ci(t), increases instantly accord-
ing to rCi, where r is the fixed recruitment rate.
Because of state forces, the size of the cartel
decreases by hCi=
jCj for some h > 0 that
represents the incapacitation rate. Because
of internal instability, dropouts, and dimin-
ishing returns, large groups decrease their
size instantly by wC 2
i for some small value of
w > 0, known as the saturation rate (22, 23).
The impact of conflict between two cartels, i
and j, is modeled according to the number of
homicide offenders between rival groups,
which is assumed to be proportional to car-
tel size, so cartel i suffers instant casualties
according to qCiCj, where q ≥ 0 is the deathly
rate of conflict related to homicide offend-
ers within cartels. Combining recruitment,
incarceration, conflict, and saturation, we
obtain
(cid:2)
C
(cid:3) h
i ¼ rCi
|{z}
recruitment
Ci
C|{z}
incapacitation
Xk
(cid:3) q
CiCjSij
j≠1
|{z}
conflict
ð1Þ
(cid:3) wC 2
i
|{z}
saturation
(cid:2)
where C
i indicates the rate of change in cartel
size i, and Sij ≥ 0 captures the interaction be-
tween cartels. We obtain a system of k = 150
coupled differential equations—one for each
cartel (supplementary materials, section C).
The number of weekly casualties produced by
all cartels is given by d tð Þ ¼ qC⊤SC, where
C = (C1,C2,…,Ck). Cartels recruit rC individuals,
where C ¼
Ci, and i tð Þ ¼ h
are inca-
Xk
X
i¼1
Ci
C
pacitated. In line with previous works on other
types of organizations, we assume that the ini-
tial cartel size is a heavy-tailed distribution (sup-
plementary materials, section D) (24–26). We
use the observed weekly number of casualties
and incapacitations to estimate the time-varying
number of cartel members Ci(t).
Not all observed deaths, missing persons,
and incapacitations in the country are suffered
by cartel members, and most incapacitations
are not linked to the incarcerations of cartel
members. In our analysis, we estimate casual-
ties as the sum of missing persons with mur-
ders and consider that a fraction f = 10% of
the observed weekly deaths and a fraction g =
5% of the incapacitations are cartel members
(supplementary materials, section D). In total,
50,000 casualties and 55,000 incapacitations
directly involve cartel members. On the basis
of these figures, we estimate that in 2012, there
were 115,000 cartel members and that by 2022,
the number increased to 175,000. Thus, despite
efforts from the state to hinder their power, car-
tels have increased their size by 60,000 members
in a decade. Incarcerating nearly 6000 cartel
members each year has not prevented them
from growing into larger organizations. Given
the current conditions, we quantify 120 weekly
cartel-related deaths, with an increase of 77%
between 2012 and 2022. To ensure that our
results are not driven by wrong assumptions
Prieto-Curiel et al., Science 381, 1312–1316 (2023)
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about the number of homicides between cartel
members and incarcerations of cartel affili-
ates, we conduct sensitivity tests considering
the scenarios between 40,000 and 60,000 car-
tel casualties and 45,000 and 65,000 incapa-
citations. By considering the variation of these
two parameters, we obtain that the total pop-
ulation of cartel members in 2022 lies between
160,000 and 185,000 units. At the same time,
additional sensitivity tests were used to try to
quantify the effect of potential missing data at
the network level concerning alliances and
rivalries. Adding 10% more cartels would, on
average, lead to 3.2% more members than the
estimated 175,000. Furthermore, we also pro-
vide evidence that adding 10% more alliances
or rivalries would at most affect the overall
dimension of violence by 5% (supplementary
materials, section E). Even under a conserva-
tive scenario, Mexican cartels have lost around
200 members per week for years (Fig. 3A). Spe-
cifically, we estimate that in a decade, 285,000
people acted as cartel units and that—in total—
37% of them are either deceased (17%) or in-
carcerated (20%).
Despite competition with other cartels and
state forces’ incapacitation, cartels have prevailed
for decades. Between January and December
of 2021, cartels recruited 19,300 individuals,
losing 6500 members as a result of conflict
with other cartels and 5700 members as a
result of incapacitation, which resulted in a
net gain of roughly 7000 members during that
year (supplementary materials, section D). A
similar estimate is observed for each year be-
tween 2012 and 2022. Unless all cartels com-
bined recruit between 350 and 370 people
per week, they would have collapsed as a re-
sult of conflict, incapacitation, and saturation
combined (Fig. 3A).
Given the estimated overall population, all
cartels combined are the fifth largest employer
in Mexico (27) (Fig. 3B). The 10 largest cartels
in Mexico have more than 50% of the active
affiliates in the country, but the conflict be-
tween them only produces 15% of the fatalities
(Fig. 3C). Most cartels are small local organ-
izations playing a critical role in creating vi-
olence in the country, often becoming targets
of more powerful organizations. Previous re-
search has suggested that large cartels fre-
quently adopt fragmented cells of other weaker
and less experienced structures (16). Small car-
tels play a crucial role because they are more
likely to become targets of powerful illicit
organizations rather than fighting organ-
izations of similar sizes. We estimate that
more than half of the country’s casualties
result from the fight between the smallest
140 and the largest 10 cartels (supplemen-
tary materials, section B).
RQ2: Comparing policy scenarios
On the basis of the size of cartels in 2022 and
the trends observed in the past decade, we
predict that the weekly number of casualties
related to organized crime will keep increasing
in the coming years. We estimate that if current
trends continue, cartels will keep increasing
their power, and we could observe 40% more
casualties and 26% more cartel members by
2027. We test the effectiveness of two main pol-
Fig. 3. Current size of cartels and career paths for recruited members. (A) Between 2012 and 2022, we
estimate that 285,000 people took part as cartel members, but only 60% were still active by 2022. The
cartel career is brief and risky. Roughly 17% of them are dead, and 20% are incapacitated. (B) Number
of employees from the top 10 companies in Mexico and the combined size of cartels (27). We estimate that
cartels had between 160,000 and 185,000 members combined. (C) Of the 175,000 active cartel members,
roughly 17.9% are part of CJNG, 8.9% are part of Cartel de Sinaloa, and 6.2% are from Nueva Familia
Michoacana—the top three cartels in size.
icy scenarios designed to reduce future violence
in the country: first, a preventive strategy aimed
at reducing cartel recruitment, and second, a
reactive strategy aimed at increasing incapac-
itation. On the one side, doubling incapacitation,
with all of the associated costs and challenges
in increasing security resources (including po-
lice personnel, army, prisons, etc.), will still
result in an increase of 8% in the number of
casualties and an increase of 6% in the num-
ber of cartel members. Even doubling incar-
cerations will translate to a rise in violence
(Fig. 4). Cartels have a critical equilibrium where
their recruitment compensates for their losses,
maintaining a stable size. Yet, if the recruitment
rate of a cartel is 10% above its equilibrium,
the incapacitation rate must increase by more
than 21% to dismantle it (supplementary ma-
terials, section F).
Conversely, decreasing the cartel’s ability to
recruit by half will reduce the weekly casualties
by 2027 by 25% and cartel size by 11%. Math-
ematically, a preventive strategy is far more
successful than a traditional reactive strategy.
However, the cartel population is so large that,
even in the hypothetical scenario where recruit-
ment drops to zero, it would take 3 years to
return to the—already high—levels of violence
observed in 2012. This further calls for rapid
and timely large-scale initiatives to reduce re-
cruitment in the country.
We also assess the effects of two additional
ancillary policy scenarios. The first one is de-
signed to alter the type of conflict between car-
tels (e.g., pushing for a narcopeace), and the
second one is targeted at modifying cartels’
saturation levels (i.e., making cartels more prone
to fragmentation). Neither of the two strat-
egies outperforms the positive effects that a
reduction in recruitment could produce (sup-
plementary materials, section E). Decreasing
the conflict by 20% reduces the number of ca-
sualties by 8.7%, whereas increasing satura-
tion by 20% lowers the number of homicides
between cartel members by 5.4% (supplemen-
tary materials, section E). In light of the cur-
rent estimated circumstances, the growth of
cartels’ size is impeded mainly by the conflict
existing among organizations rather than the
ability of the state to reduce the levels of vi-
olence in Mexico successfully.
Discussion
For the past 15 years, Mexico has suffered from
staggering levels of violence. Most of the vi-
olence has been perpetrated by cartels fighting
against each other (4). Despite the relevance of
cartels, we lack basic information on their size
and the impact of different policies that seek
to curb their power. To the best of our knowl-
edge, this work represents the first scholarly
attempt to mathematically quantify the size of
the cartel population in Mexico and to compare
policy scenarios intended to decrease violence
Prieto-Curiel et al., Science 381, 1312–1316 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 4. Forecast of the number
of casualties and cartel size
according to four different
strategies. Weekly cartel-related
deaths (top) and cartel size
(bottom) if trends continue, if
incapacitation doubles, if
recruitment is reduced by half,
and if recruitment is reduced
to zero. Estimates for 2027 are
obtained by keeping the 2022
estimates and adjusting the
corresponding values of
incapacitation or recruitment.
in the country. Overall, our work advances the
growing literature on mathematical and sta-
tistical simulations for studying complex crim-
inal phenomena (28–30).
Our simulations yield some key findings. We
estimated that the cartel population counted
160,000 to 185,000 units by 2022 and that, over
the 2012 to 2022 period, 285,000 people acted as
cartel members. Given these figures, we showed
that in 2022, cartels needed to recruit between
350 and 370 units per week to avoid collapse
as a result of joint effects of conflict, incapacita-
tion, and saturation. Furthermore, we assessed
the effectiveness of two main scenarios to curb
cartels’ violence: preventive (intended to pre-
vent recruitment) and reactive (designed to in-
crease incapacitation through incarcerations).
If current levels of incapacitation are doubled,
some violence will be contained, but we would
still expect an increase in the weekly casualties.
Conversely, reducing recruitment by half leads
to a decrease in homicides of 25%. We also tested
the effect of two ancillary scenarios—reducing
the conflict by pushing for cartel agreement
and fragmentation, intended to decrease car-
tels’ power through internal fights (supplemen-
tary materials, section E). Results showed that
the preventive strategy remained substantially
more effective in reducing violence in the coun-
try. Tackling recruitment will have a triple effect
in the future: First, it will lower the number of
cartel members, reducing the violence that it
can create by having fewer killers. Second, it
will lower the number of targets, so fewer people
are vulnerable to suffering more violence. And
third, it will reduce the cartel’s capacity for fu-
ture recruitment.
Although offering policy recommendations
is beyond the scope of this work, our results
can prompt policy-related reflections. Many
initiatives to counter organized crime aim to
increase incapacitation through incarceration.
In this work, we demonstrate how increasing
incapacitation substantially may not necessarily
reduce violence. Contrarily, we offer an alterna-
tive scenario centered around reducing recruit-
ment and suggest how it may have longer-lasting
beneficial effects. More than 1.7 million people
in Latin America are incarcerated, and adding
more people to saturated jails will not solve the
insecurity problem (31).
Despite the contributions of this investigation,
there were some limitations. First and foremost,
although the lack of data on the size of cartels
represents the inherent motivation of this work,
it also represents a structural limitation because
our estimates cannot be meaningfully validated
with real-world information. We took all possi-
ble precautions to obtain statistically consistent
estimates through extensive sensitivity analyses,
but this does not eliminate the core validation
issue. Additionally, a thorough reflection on
other sources of limitation and assumptions is
provided in the supplementary materials, sec-
tion I. These entail (i) temporal variability in
rivalries and alliances, (ii) alternative sources
of cartels’ size variability, and (iii) the lack of a
finite population.
Results highlight the need to devote more
attention to recruitment. Reducing recruit-
ment requires structural efforts at the state
and local levels. This especially applies to areas
with high cartel support, where offering edu-
cational and professional opportunities that
outweigh the short-term benefits offered by
cartels represents a critical goal for the future
of the country (32–35). Future work on this
topic should focus on enriching our model of
cartel size variation with additional sources,
such as cartel fragmentation, and should also
consider the possibility of studying recruit-
ment dynamics using data on finite populations
to obtain mathematical models that consider
individual risk factors (such as age and sex)
in the computation of violence and recruit-
ment trends.
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AC KNOWLED GME NTS
We are grateful for the insightful comments from L. Sánchez,
J. Mohar, and C. A. Pérez Ricart. After submitting this manuscript to
Science, author Alejandro Hope passed away. We acknowledge his
tireless efforts to make Mexico a safer and more peaceful country,
and we hope that this work will honor his memory. Funding: The
research was funded by the Austrian Federal Ministry for Climate
Action, Environment, Energy, Mobility, Innovation and Technology
Prieto-Curiel et al., Science 381, 1312–1316 (2023)
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(2021-0.664.668) and by the Austrian Federal Ministry of the Interior
(2022-0.392.231). Author contributions: R.P.-C. designed the
study. R.P.-C. and G.M.C. analyzed the results. All authors wrote the
manuscript, but A.H. passed away while it was under peer review.
R.P.-C. and G.M.C. completed the revisions. Competing interests:
The authors declare that they have no competing interests. Data and
materials availability: All data are available in the manuscript or the
supplementary materials. A public repository with the processed data
and code to reproduce and extend the results is available on Dryad (36).
License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government works.
https://www.science.org/about/science-licenses-journal-article-reuse
Figs. S1 to S8
Tables S1 and S2
References (37–66)
MDAR Reproducibility Checklist
Spanish Translation of Author Accepted Manuscript
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh2888
Supplementary Text
Submitted 22 February 2023; accepted 2 August 2023
10.1126/science.adh2888
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R E S E A R C H A R T I C L E
◥
COMPARATIVE COGNITION
Songbird species that display more-complex vocal
learning are better problem-solvers and have
larger brains
Jean-Nicolas Audet1,2*, Mélanie Couture1,3, Erich D. Jarvis1,2,3,4*
Complex vocal learning, a critical component of human spoken language, has been assumed to be
associated with more-advanced cognitive abilities. Tests of this hypothesis between individuals
within a species have been inconclusive and have not been done across species. In this work, we
measured an array of cognitive skills—namely, problem-solving, associative and reversal learning, and
self-control—across 214 individuals of 23 bird species, including 19 wild-caught songbird species, two
domesticated songbird species, and two wild-caught vocal nonlearning species. We found that the
greater the vocal learning abilities of a species, the better their problem-solving skills and the relatively
larger their brains. These conclusions held when controlling for noncognitive variables and phylogeny.
Our results support a hypothesis of shared genetic and cognitive mechanisms between vocal
learning, problem-solving, and bigger brains in songbirds.
complex vocal learning behavior overlap with
those long thought to exhibit more-intelligent
cognitive capacities [e.g., humans, cetaceans,
elephants, corvid songbirds, and parrots (3, 4)],
although this has not been quantitatively tested
across species.
The few studies that have tested for rela-
tionships between vocal learning complexity
and cognitive abilities have all been within
species (5). Some studies found positive rela-
tionships (6, 7), whereas others did not (8–10),
and some found negative relationships (7, 11),
which led Searcy and Nowicki (5) to conclude
that there is not good evidence of such relation-
ships. The challenge for these within-species
studies is that it is difficult to tease out whether
individual differences are due to genetic fac-
tors or cultural or life-experience factors, such
as food deprivation (12) or stress (13).
Although vocal learning is often thought of
as a dichotomous trait, considerable variation
in phenotypes has been documented within
lineages, with songbirds being the most speciose
S poken language and problem-solving
are often considered to be components
of intelligence in humans. An essential
and specialized component of spoken
language is vocal production learning,
or the ability to imitate sounds (1, 2). Ad-
vanced vocal learning has been found in only
a handful of taxa, including five mammalian
(humans, elephants, cetaceans, pinnipeds, and
bats) and three avian (songbirds, parrots, and
hummingbirds) clades (1). Interestingly, the
vocal learning taxa that display the most-
1The Rockefeller University Field Research Center, Millbrook,
NY, USA. 2Laboratory of Neurogenetics of Language, The
Rockefeller University, New York, NY, USA. 3The Vertebrate
Genome Laboratory, The Rockefeller University, New York,
NY, USA. 4Howard Hughes Medical Institute, The Rockefeller
University, New York, NY, USA.
*Corresponding author. Email: jaudet@rockefeller.edu (J.-N.A.);
ejarvis@rockefeller.edu (E.D.J.)
Fig. 1. The 23 study species of birds and their vocal learning characteristics.
(A) Phylogenetic tree of the species that were studied based on (42). Inside circle
colors indicate the type of vocal learning, perimeter circle colors indicate
domesticated versus wild species, and circle size is proportional to vocalization
repertoire size. (B) Comparisons of song and call repertoire sizes in open- versus
closed-ended vocal learning songbirds (n = 21 species). (C) Comparison of mimic
and nonmimic species. Black * and ** indicate significant PANOVA at <0.05 and
<0.01, respectively. Green * and ** indicate significant PAOV.PHYLO (ANOVA
accounting for phylogenetic relationships). ns, not significant. Full statistical values
are provided in table S2. Bars are means ± SEM.
Audet et al., Science 381, 1170–1175 (2023)
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Table 1. Summary of MCMCglmm phylogenetic models. Full, separate models were implemented for vocal learning type [closed-ended (reference category),
open-ended, and mimicry]; repertoire size of songs, calls, or both; and vocal learning complexity. All potential covariates were tested first (see tables S4 to S7),
and the models with only the significant variables, when applicable (with species, phylogeny, and capture site as random effects), were rerun to obtain
unbiased effects of vocal learning. Significant effects are highlighted in bold. All measured behaviors are expressed in logged trials; higher numbers represent
lower performance (n = 23 species, 214 individuals). Post.mean, mean of the posterior distribution; CI, confidence interval; pMCMC, MCMCglmm P value.
Cognitive trait
Vocal learning feature
Post.mean
Lower 95% CI
Upper 95% CI
pMCMC
Learning
Problem-solving
Reversal learning
0.0020
Open-endedness
.........................................................................................................................................................................................................................................................................
0.0378
Mimicry
.........................................................................................................................................................................................................................................................................
0.0217
Song repertoire
.........................................................................................................................................................................................................................................................................
0.0216
Call repertoire
.........................................................................................................................................................................................................................................................................
0.0018
Total vocal repertoire
.........................................................................................................................................................................................................................................................................
0.0012
Vocal learning complexity
............................................................................................................................................................................................................................................................................................................................................
0.0889
Open-endedness
.........................................................................................................................................................................................................................................................................
0.3065
Mimicry
.........................................................................................................................................................................................................................................................................
0.6366
Song repertoire
.........................................................................................................................................................................................................................................................................
0.4620
Call repertoire
.........................................................................................................................................................................................................................................................................
0.8780
Total vocal repertoire
.........................................................................................................................................................................................................................................................................
0.3768
Vocal learning complexity
............................................................................................................................................................................................................................................................................................................................................
0.0269
Open-endedness
.........................................................................................................................................................................................................................................................................
0.1634
Mimicry
.........................................................................................................................................................................................................................................................................
0.4115
Song repertoire
.........................................................................................................................................................................................................................................................................
0.7206
Call repertoire
.........................................................................................................................................................................................................................................................................
0.9675
Total vocal repertoire
.........................................................................................................................................................................................................................................................................
0.1978
Vocal learning complexity
............................................................................................................................................................................................................................................................................................................................................
0.7938
Open-endedness
.........................................................................................................................................................................................................................................................................
0.2026
Mimicry
.........................................................................................................................................................................................................................................................................
0.9554
Song repertoire
.........................................................................................................................................................................................................................................................................
0.8932
Call repertoire
.........................................................................................................................................................................................................................................................................
0.9742
Total vocal repertoire
.........................................................................................................................................................................................................................................................................
0.4057
Vocal learning complexity
............................................................................................................................................................................................................................................................................................................................................
0.1571
Open-endedness
.........................................................................................................................................................................................................................................................................
0.0812
Mimicry
.........................................................................................................................................................................................................................................................................
0.0362
Song repertoire
.........................................................................................................................................................................................................................................................................
0.0132
Call repertoire
.........................................................................................................................................................................................................................................................................
0.0013
Total vocal repertoire
.........................................................................................................................................................................................................................................................................
0.0037
Vocal learning complexity
............................................................................................................................................................................................................................................................................................................................................
−1.151
−1.036
−0.174
−0.187
−0.257
−0.090
−0.391
−0.295
0.024
−0.038
−0.009
−0.016
−0.818
−0.607
0.066
−0.029
0.005
−0.037
−0.111
−0.725
0.003
−0.009
0.002
−0.023
0.976
1.971
1.373
1.702
2.297
0.678
−0.517
−0.056
−0.030
−0.032
−0.118
−0.046
0.060
0.297
0.126
0.068
0.106
0.021
−0.133
0.272
0.227
0.140
0.185
0.021
0.667
0.443
0.148
0.147
0.169
0.034
2.362
4.242
2.628
2.989
3.494
1.119
−1.806
−2.015
−0.323
−0.342
−0.395
−0.134
−0.843
−0.890
−0.078
−0.141
−0.124
−0.054
−1.497
−1.469
−0.092
−0.194
−0.173
−0.093
−0.910
−1.928
−0.144
−0.162
−0.160
−0.080
−0.390
−0.248
0.114
0.392
1.125
0.242
Relative brain size
Self-control
and best-characterized clade (1, 14–16). Features
that are believed to reflect more-complex vocal
learning in songbirds include (i) large vocal
repertoires, (ii) lifelong open-ended vocal learn-
ing ability, and (iii) mimicry of other species’
vocalizations (16–18). It is unknown whether
these vocal learning variations are linked with
other cognitive phenotypes.
Cognition has been measured in the labo-
ratory using a variety of behavioral tasks. Of
these, problem-solving is assumed to be one
of the most complex, requiring animals to fig-
ure out the best action to overcome a challenge.
Problem-solving may be relevant for allow-
ing animals to cope with ecological disturbances
(19). Other cognitive assays that are often con-
ceptually linked with intelligence include asso-
ciative learning, reversal learning, and self-control
tasks (20).
In this work, we quantitatively tested whether
there is a linkage between vocal learning com-
plexity and other cognitive traits. We tested
214 individuals from 23 species consisting of 21
wild-caught and two domesticated avian spe-
cies; 21 species were vocal learning songbirds,
and two were vocal nonlearning species (Fig. 1A).
We generated a database of vocal learning char-
acteristics of these species from an extensive
literature of 80 publications (table S1), assessed
species’ performance on a battery of behav-
ioral tasks (fig. S1 and supplementary meth-
ods), and found across-species relationships
between vocal learning complexity, problem-
solving, and relative brain size.
Vocalization repertoire size is associated with
open-endedness and mimicry
Wild birds were caught at the Rockefeller Uni-
versity Field Research Center in New York,
USA, over a 3-year period, and domesticated
species were bred at the same location (zebra
finches) or purchased from a local breeder
(canaries). Birds were opportunistically cap-
tured in mist nets, and species were chosen if
their local abundance allowed for a sufficient
sample size (n ≥ 12) of males (the vocal learn-
ing sex for most species); in addition, for eight
species, we kept and tested one or two animals
each to see whether they would follow a trend.
All birds were habituated individually in cages
for 3 days, where they could hear but not see
other individuals.
For all 23 species, literature exists on their
vocal behavior (table S1). We used these data to
establish a consistently defined profile for each
species in a database that included six vocal
learning characteristics: (i) presence of vocal
learning, (ii) open-ended versus closed-ended
vocal learning, (iii) capacity for vocal mimicry
of other species, (iv) song repertoire size per
individual, (v) call repertoire size per species,
and (vi) total repertoire size of both songs and
calls (supplementary methods and table S1).
Audet et al., Science 381, 1170–1175 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
)
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20
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20
Vocal learning types
Vocalization repertoire size
A
***
B
ns
I
***
Non-learning
Closed-ended
Open-ended
Mimic
P = 0.0003
P = 0.1389
C
ns
D
ns
J
P = 0.1858
P = 0.6506
E
*
F
ns
K
P = 0.0162
P = 0.5029
G
ns
H
ns
L
P = 0.8253
P = 0.7491
Closed-
ended
Open-
ended
Non-
mimic
Mimic
Blue jay (n=13)
Tufted titmouse (n=13)
Black-capped chickadee (n=19)
Cedar waxwing (n=2)
White-breasted nuthatch (n=13)
House wren (n=13)
Gray catbird (n=15)
European starling (n=16)
American robin (n=12)
Veery (n=1)
Zebra finch (n=12)
American goldfinch (n=13)
Canary (n=13)
Yellow warbler (n=1)
American redstart (n=2)
Red-winged blackbird (n=2)
Brown-headed cowbird (n=14)
Chipping sparrow (n=12)
White-throated sparrow (n=12)
Song sparrow (n=1)
Northern cardinal (n=1)
Eastern phoebe (n=13)
Mourning dove (n=1)
R = 0.814
P < 0.0001
ns
R = -0.171
P = 0.4465
ns
R = 0.059
P = 0.7951
ns
R = -0.016
P = 0.9429
20
Vocalization repertoire size (rank)
15
10
5
Fig. 2. Relationships between cognitive traits and vocal learning features.
(A to H) Four cognitive measures (y axes) compared between species grouped
by vocal learning features (x axes: closed-ended, which includes vocal
nonlearning species; open-ended; and nonmimic or mimic). (I to L) Correlation
analyses between the four cognitive behavioral measures (y axes) and
vocalization repertoire size (x axis). Values are ranked means of species
performance from all individuals (sample sizes are shown in the legend). P values
in (A) to (H) are from Wilcoxon tests; R and P values in (I) to (L) are from
Spearman correlations. Regression lines are for illustration purposes to show the
significance and direction of relationships. Images to the left are examples of
birds in the different tasks, which are snapshots from videos taken by the
authors. ***P < 0.001; *P < 0.05; ns, not significant.
We found that, consistent with Robinson et al.
(18), open-ended vocal learning songbirds had
significantly larger song repertoires than closed-
ended vocal learners (Fig. 1B and table S2A).
Using the complete vocalization repertoires
(song and calls) yielded an even greater dif-
ference between open- and closed-ended
vocal learning species (Fig. 1B and table
S2A). Similarly, songbird species that are
capable of vocal mimicry had larger reper-
toires than nonmimics (Fig. 1C and table S2A).
All of these differences increased in significance
when including the two vocal nonlearners
(the mourning dove and suboscine eastern
phoebe; table S2B), which were at the lower
end of the distribution for song and call re-
pertoire sizes (table S1). Nearly all differ-
ences were still significant when accounting
for phylogenetic relationships in the analy-
sis of variance (ANOVA) model, except for
repertoire size between mimic and nonmimic
songbirds, which still approached significance
[phylogenetic ANOVA P value (PAOV.PHYLO) ~
0.07; table S2B]. These findings demonstrate
that relationships exist among different vocal
learning phenotypes.
Species with more-advanced vocal learning
abilities are better problem-solvers
We presented all 214 individuals of the 23 bird
species with seven cognitive tasks after over-
night food deprivation, the duration of which
was adjusted to the night lengths and body
weights of each individual. The tasks occurred
over 6 days in the same sequence, with 5-min
intervals between trials or tasks (supplementary
Audet et al., Science 381, 1170–1175 (2023)
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Fig. 3. Species that
display higher vocal
learning complexity are
better problem-solvers.
(A) PCA on open-ended
capacity, mimicry capacity,
and log of vocalization
repertoire (songs and
calls). PC1 explains 69.9%
of the variance and was
used as our index of
vocal learning complexity.
(B) The higher the vocal
learning complexity, the
better the problem-solving
performance among
species. (C to E) Species’
associative learning (C),
reversal learning (D), and
self-control (E) performances
are not associated with
vocal learning complexity.
Values are ranked means
of species performance
from all individuals (sample
sizes are shown in the
legend). R and P values are
from Spearman correlations.
***P < 0.001; ns, not
significant.
methods). The first four were different obstacle-
removal tasks of increasing complexity, during
which the birds had to figure out how to ac-
cess a food reward (seeds or worms) by either
removing, piercing, or pulling parts of the
apparatuses (fig. S1, F to I, and movies S1 to
S4). We used the average number of trials
required to solve the four problems as our
problem-solving measure. Self-control was eval-
uated using a typical detour-reaching task in
which birds had to access a food reward
without trying to obtain the food through a
transparent barrier (fig. S1J and movies S5 to
S6). Associative learning was measured on a
standard two-color discrimination task in
which birds had to associate a color with a food
reward (fig. S1K and movie S7). The rewarded
color was switched the next day to assess re-
versal learning.
Looking at the categorical vocal learning
variables, we found that species classified as
open-ended vocal learners were significantly
better problem-solvers than the other species
(Fig. 2A). Species capable of vocal mimicry were
at the upper problem-solving performance
range, although the difference was not signif-
icant (Fig. 2B). There were no significant dif-
ferences for open-ended or mimicking vocal
learning species and their associative learning
abilities (Fig. 2, C and D), reversal learning
(Fig. 2, E and F), or self-control (Fig. 2, G and
H), except a largely overlapping, but signif-
icantly better, reversal learning performance
in open-ended vocal learners (Fig. 2E). When
splitting the vocal learning phenotypes into
a more-sensitive multigroup ANOVA analysis,
only problem-solving was significantly better
for both open-ended vocal learners and mim-
ics (fig. S2, A to D).
Looking at the continuous vocal learning
variables, we found a strong and significant
relationship, with species having the largest
repertoires (songs and calls) being the best
problem-solvers (Fig. 2I). We found no signif-
icant correlations or even qualitative signs of
a correlation between vocalization repertoire
size and associative learning, reversal learn-
ing, or self-control (Fig. 2, J to L). Considering
only songs or calls yielded similar significant
relationships with problem-solving, although
the associations were weaker (table S3). Exclud-
ing vocal nonlearning and domesticated species
yielded identical conclusions (fig. S2, F to I).
When excluding the eight species with small
sample sizes, the correlation between vocal-
ization repertoire size and problem-solving re-
mained (Spearman’s correlation R = 0.779; P =
0.0006). Together, these results indicate a posi-
tive association between vocal learning features
and problem-solving among cognitive traits.
Vocal learning complexity better predicts
problem-solving performance
To obtain an estimate of general vocal learn-
ing complexity, we performed a principal com-
ponents analysis (PCA) with the three vocal
learning features (open-endedness, mimicry,
and total vocalization repertoire size) and ex-
tracted the first principal component (PC1),
which explained the majority (69.9%) of the
variance in all three measures (Fig. 3A). We
found a positive and significant relationship
Audet et al., Science 381, 1170–1175 (2023)
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Fig. 4. Relationships
between relative brain size
and vocal learning features.
(A) Open-ended vocal learning
species have significantly
larger relative brain sizes than
the other species. (B) The
difference in brain size between
mimic and nonmimic species is
not significant. (C) Vocalization
repertoire is significantly
associated with relative brain
size. (D) Species’ vocal
learning complexity is also
significantly associated with
relative brain size. Relative
brain sizes are the residuals of
brain volumes with body size
obtained from (43). P values in
(A) and (B) are from Wilcoxon
tests; R and P values in (C) and
(D) are from Spearman corre-
lations, with vocal learning
complexity from PC1 of Fig. 3A.
***P < 0.001; *P < 0.05;
ns, not significant.
between the vocal learning complexity PC1
and problem-solving across species, which
was stronger than with any of the individual
vocal learning features (Fig. 3B versus Fig. 2,
A to B and I). Vocal learning complexity was
unrelated to the other cognitive traits of asso-
ciative learning, reversal learning, or self-control
(Figs. 3, C to E). Again, excluding vocal non-
learning and domesticated species did not
change the outcome of the results (fig. S3).
When excluding the eight species with small
sample sizes, the correlation between vocal
learning complexity and problem-solving re-
mained (R = 0.846; P = 0.0001). These findings
strengthen the conclusion of an association
between vocal learning abilities and problem-
solving across species and provide a means to
summarize overall vocal learning complexity
in one measure.
More-advanced vocal learners have
bigger brains
We sought a biological variable that could ex-
plain our findings and examined relative brain
size (brain to body size residuals), which, al-
though a coarse measure, was available for all
the studied species (21). Previously, relative
brain size was found to vary with counts of
field innovations (22, 23) and higher neuron
numbers (24), and the size of the songbird
high vocal center (HVC) vocal learning nu-
cleus was found to vary positively with song
repertoire size (25, 26). We found that open-
ended vocal learning species had significant-
ly larger relative brain sizes, but there was no
significant difference in mimicking species
(Fig. 4, A and B). Further, there was a signif-
icant positive correlation between vocal re-
pertoire size, as well as overall vocal learning
complexity, and relative brain size (Fig. 4, C
and D). These relationships again held when
excluding vocal nonlearning and domesti-
cated species (figs. S2J and S3E) or species
with low sample size (vocal learning com-
plexity RVLC = 0.714; PVLC = 0.0028). These
findings show that vocal learning complexity,
problem-solving abilities, and relatively larger
brains are all related.
Vocal learning cognitive relationships are not
due to noncognitive factors or phylogeny
We tested whether the relationships that we
discovered could (i) also be found when in-
cluding individual variation, (ii) be explained
by noncognitive factors such as personality
traits and captive conditions, or (iii) be ex-
plained by phylogeny relationships. To address
these factors within the same analysis, we used
generalized linear mixed models of Markov
chain Monte Carlo techniques (MCMCglmm).
The models included phylogenetic relation-
ships between species as a random effect,
personality traits (shyness, or latency to feed
following human disturbance; neophobia, or
latency to feed in the presence of a novel ob-
ject, minus shyness), experimental conditions
(capture site, food deprivation period, body
weight), and captive status (wild or domesti-
cated) on the whole dataset of the 214 indi-
vidual values.
Open-endedness, mimicry, vocalization re-
pertoire size, and vocal learning complexity all
still significantly predicted problem-solving
performance in the MCMCglmm modeling;
they were still not associated with associative
learning, reversal learning, or self-control, ex-
cept for reversal learning, which was marginally
associated with vocal learning open-endedness
(Table 1 and tables S4 to S7). In addition, shy-
ness was negatively associated with problem-
solving and positively associated with reversal
learning and self-control, neophobia was neg-
atively associated with associative learning,
and body weight was negatively associated
with self-control but positively associated
with reversal learning (Table 1 and tables S4
to S7). Although open-ended vocal learning or
mimicry did not predict brain size, repertoire
size and vocal learning complexity were sig-
nificantly associated with relative brain size
in the MCMCglmm modeling (Table 1 and
tables S5 to S7). Excluding species with small
sample sizes yielded similar relationships be-
tween vocal learning complexity and all tested
cognitive traits (table S8). Thus, MCMCglmm
analyses strongly support the existence of a
robust relationship between vocal learning
abilities, problem-solving, and brain size, even
when taking into account individual variation,
phylogeny, and other potential confounding
covariates.
Discussion
Our findings suggest a coevolution between
vocal learning complexity, problem-solving,
and relative brain size. Vocal learning and
innovative problem-solving have separately
been linked with extinction risk, fitness, and
Audet et al., Science 381, 1170–1175 (2023)
15 September 2023
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RES EARCH | R E S E A R C H A R T I C L E
sexual selection (19, 27). Further, both problem-
solving and bird songs vary according to habitat
differences, for example, urbanization (28, 29).
To explain our and these ecological findings,
we suggest that a selective factor links these
traits within a “vocal learning cognitive com-
plex.” This selective factor could be a genetic
component that drives coevolution of vocal
learning complexity, problem-solving, and
relative brain size.
Previous studies that performed within-
species comparisons on vocal learning and
other cognitive traits found no or conflicting
evidence of relationships [(6, 7, 9, 10, 12), re-
viewed in (5)]. A major factor as to why we
find a clear relationship between vocal learn-
ing complexity and problem-solving is likely
greater differences across than within spe-
cies. In addition, some studies trained birds
to first solve problems and then measured
their capacity to repeat the learned solution,
whereas we measured problem-solving on the
first trial. We also generated a new measure
of vocal learning complexity that did not ig-
nore calls that were assumed to be innate but
included calls and songs together. Calls are
increasingly recognized as learned in vocal
learning species (30, 31).
Our finding of a link between vocal learning
complexity and brain size is consistent with
the prior finding that two of the three avian
vocal learning lineages (songbirds and parrots)
have larger relative brain sizes and a higher
density of telencephalic neurons compared
with vocal nonlearners (32). Devoogd et al.
(25) found a relationship between song rep-
ertoire size and the HVC size across songbird
species, but not telencephalon size [confirmed
in (26)]. We hypothesize that the relative in-
crease in brain size across species could be due
to relative increases in the song system and
the adjacent nonvocal motor circuit (33) that
is potentially involved in problem-solving.
Vocal learners can also synchronize body move-
ments to rhythmic sounds of music (dance),
which is thought to be controlled by the sur-
rounding motor circuits (34, 35) and could be
another component of a vocal learning cog-
nitive complex. Another brain region to con-
sider is the caudal-lateral nidopallium (NCL),
or avian prefrontal cortex, which is involved
in complex cognitive processing (36). Regard-
less of specific brain regions, a higher density
of neurons likely provides vocal learners with
more brain computational power.
At the molecular level, expression levels of
different N-methyl-D-aspartate (NMDA) glu-
tamate receptor subunits in song nuclei and
nearby brain regions have been associated with
both complex vocal learning capacity (37, 38)
and problem-solving (39). Thus, this neuro-
transmitter receptor family is a plausible can-
didate to partly explain our discovered cognitive
relationships.
There has been a long-standing assumption
of a link between human spoken language, ad-
vanced cognition, and larger brain size relative
to other species (40). Our study quantitative-
ly tests such a relationship between species
in a vocal learning bird lineage and serves as
a model for testing other avian and mamma-
lian lineages. Testing cognitive abilities across
more-divergent species might be more chal-
lenging because it may require different ap-
paratus designs, whereas this is not the case
for comparative genomic studies across spe-
cies without behavioral testing [e.g., (41)]. For
example, some bird lineages have highly diver-
gent beak shapes (e.g., hummingbirds, pelicans)
or rely mainly on their feet to manipulate ob-
jects (e.g., parrots, birds of prey). Moreover, the
vocal repertoires of many nonsongbird spe-
cies are not as well characterized as those of
songbirds. Nevertheless, it would be interest-
ing to see whether the relationships we discov-
ered here exist for other vocal learning species
and innate repertoires of vocal nonlearning
species. Our results support the continuum
hypothesis of vocal learning within a clade (1).
More broadly, our discoveries open the door
for an unexplored sphere of research on shared
neurobiological, molecular, and physiological
evolutionary foundations of vocal learning and
problem-solving.
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AC KNOWLED GME NTS
We thank G. Smith-Vidaurre for insightful discussions on vocal
learning complexity; S. Ducatez for assisting with the statistical
analyses; L. Lefebvre, M. Davenport, and L. Cauchard for providing
helpful suggestions on the manuscript; C. Scivolette for helping
with bird captures; S. Sepe for helping with the establishment
of wild-bird care protocols; G. Permuy and L. Tchernichovski for
helping with bird care; and W. T. Gale for assisting with the
construction of the behavior laboratory at the Rockefeller University
Field Research Center. Funding: This study was supported by a
Banting postdoctoral fellowship and an NSERC postdoctoral fellowship
to J.-N.A. and by the Howard Hughes Medical Institute and a Keck
Foundation Award to E.D.J. Author contributions: Conceptualization:
J.-N.A., M.C., E.D.J.; Methodology: J.-N.A., M.C.; Investigation: J.-N.A.,
M.C.; Visualization: J.-N.A., M.C.; Funding acquisition: J.-N.A., E.D.J.;
Supervision: J.-N.A., E.D.J.; Writing – original draft: J.-N.A.; Writing –
review and editing: J.-N.A., M.C., E.D.J. Competing interests: The
authors declare that they have no competing interests. Data and
materials availability: The raw dataset and code are available
at Dryad (44). License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh3428
Materials and Methods
Figs. S1 to S3
Tables S1 to S8
References (45–144)
MDAR Reproducibility Checklist
Movies S1 to S7
Submitted 25 February 2023; accepted 14 August 2023
10.1126/science.adh3428
Audet et al., Science 381, 1170–1175 (2023)
15 September 2023
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10.1126_science.adh2526
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Corrected 5 January 2024. See full text.
RES EARCH
ATMOSPHERES
Iodine oxoacids enhance nucleation of sulfuric acid
particles in the atmosphere
Xu-Cheng He1,2,3*, Mario Simon4, Siddharth Iyer5, Hong-Bin Xie6*, Birte Rörup1, Jiali Shen1,
Henning Finkenzeller7,8, Dominik Stolzenburg1,9, Rongjie Zhang6, Andrea Baccarini10,11,
Yee Jun Tham1,12, Mingyi Wang13, Stavros Amanatidis13, Ana A. Piedehierro3, Antonio Amorim14,
Rima Baalbaki1, Zoé Brasseur1, Lucía Caudillo4, Biwu Chu1,15, Lubna Dada1,10, Jonathan Duplissy1,16,
Imad El Haddad10, Richard C. Flagan13, Manuel Granzin4, Armin Hansel17, Martin Heinritzi4,
Victoria Hofbauer2, Tuija Jokinen1,18, Deniz Kemppainen1, Weimeng Kong13, Jordan Krechmer19,
Andreas Kürten4, Houssni Lamkaddam10, Brandon Lopez2,20, Fangfang Ma6, Naser G. A. Mahfouz2,
Vladimir Makhmutov21,22, Hanna E. Manninen23, Guillaume Marie4, Ruby Marten10, Dario Massabò24,
Roy L. Mauldin25,26, Bernhard Mentler17, Antti Onnela23, Tuukka Petäjä1, Joschka Pfeifer23,
Maxim Philippov21, Ananth Ranjithkumar27, Matti P. Rissanen5,28, Siegfried Schobesberger29,
Wiebke Scholz17, Benjamin Schulze13, Mihnea Surdu10, Roseline C. Thakur1, António Tomé30,
Andrea C. Wagner4, Dongyu Wang10, Yonghong Wang1,15, Stefan K. Weber23,4, André Welti3,
Paul M. Winkler31, Marcel Zauner-Wieczorek4, Urs Baltensperger10, Joachim Curtius4, Theo Kurtén28,
Douglas R. Worsnop1,19, Rainer Volkamer7,8, Katrianne Lehtipalo1,3, Jasper Kirkby23,4,
Neil M. Donahue2,20,25,32, Mikko Sipilä1*, Markku Kulmala1,16,33,34*
The main nucleating vapor in the atmosphere is thought to be sulfuric acid (H2SO4), stabilized by
ammonia (NH3). However, in marine and polar regions, NH3 is generally low, and H2SO4 is frequently
found together with iodine oxoacids [HIOx, i.e., iodic acid (HIO3) and iodous acid (HIO2)]. In experiments
performed with the CERN CLOUD (Cosmics Leaving OUtdoor Droplets) chamber, we investigated the
interplay of H2SO4 and HIOx during atmospheric particle nucleation. We found that HIOx greatly enhances
H2SO4(-NH3) nucleation through two different interactions. First, HIO3 strongly binds with H2SO4 in
charged clusters so they drive particle nucleation synergistically. Second, HIO2 substitutes for NH3, forming
strongly bound H2SO4-HIO2 acid-base pairs in molecular clusters. Global observations imply that HIOx is
enhancing H2SO4(-NH3) nucleation rates 10- to 10,000-fold in marine and polar regions.
A erosols influence climate by acting as
cloud condensation nuclei (CCN) and by
scattering solar radiation. Secondary
aerosol and CCN formation continue to
be two of the largest uncertainties hin-
dering accurate projection of climate change (1).
Only a few types of vapors in the atmosphere can
nucleate to form new aerosol particles, which
can further grow to CCN sizes. Sulfuric acid
(H2SO4) is considered to be the primary vapor
(2) driving particle formation in the atmo-
sphere of both polluted environments (3, 4)
and pristine environments (5–7). However, as
H2SO4-H2O binary nucleation is slow, stabilizing
vapors, such as ammonia (NH3), amines, and
oxidized organics, are generally needed to
explain observed particle formation rates
(3–11).
In terms of radiative balance, marine clouds,
especially low-level marine stratocumulus (12),
are key players because they have strong long-
wave emission and efficiently reflect solar radia-
tion back to space. As marine cloud formation
is often limited by low CCN number concen-
trations, it is important to reach a comprehen-
sive understanding of new particle formation
in marine environments. New particle and
subsequent CCN formation in marine regions
is presently thought to be driven by H2SO4 and
methanesulfonic acid (MSA) (8, 13), aided by
NH3 (5, 14). However, a recent global survey of
aerosol acidity suggests that global models
substantially overestimate NH3 concentrations;
in particular, the polar atmosphere and high
altitudes are characterized by low NH3 con-
centrations (15). Assuming solely H2SO4 nucle-
ation, advanced Earth system models struggle
to reproduce aerosol number concentrations
measured by aircraft (16), leading to low con-
fidence for estimates of aerosol radiative forc-
ing. Iodine-driven nucleation (17–21) has not
yet been incorporated into Earth system mod-
els; iodine oxoacids (HIOx, x = 2 to 3 in this
study) can drive rapid particle formation under
low NH3 conditions, and they may play an im-
portant role in polar, marine, and free tropo-
spheric particle formation.
In the marine atmosphere, iodine and sulfur
precursors emitted from the ocean surface lead
to the formation of both H2SO4 and HIOx (22).
HIOx has generally been observed at con-
centrations similar to or lower than H2SO4
(6, 18, 21, 23). Despite the higher nucleation
potential of HIOx compared with H2SO4 (18),
iodine-driven new particle formation has hith-
erto been considered important only in re-
gions with considerably higher concentrations
of iodic acid (HIO3) than of H2SO4, such as
coastal zones and specific regions in the Arctic
(17, 18, 20, 21, 24, 25). However, new particle
formation from the mixed chemical system
HIOx-H2SO4(-NH3) has not been reported so far.
Particle formation experiments in CLOUD
Here we report laboratory experiments per-
formed in the CERN CLOUD (Cosmics Leaving
OUtdoor Droplets) chamber (5) (see methods
in the supplementary materials for details)
between September 2018 and December 2019
under conditions relevant for marine and polar
environments. We performed particle forma-
tion experiments using HIOx-H2SO4(-NH3) va-
pors produced from the following precursors:
molecular iodine (I2), sulfur dioxide (SO2), ammo-
nia (NH3), ozone (O3), and water vapor (H2O).
1Institute for Atmospheric and Earth System Research/Physics, Faculty of Science, University of Helsinki, 00014 Helsinki, Finland. 2Center for Atmospheric Particle Studies, Carnegie Mellon
University, Pittsburgh, PA 15213, USA. 3Finnish Meteorological Institute, 00560 Helsinki, Finland. 4Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, 60438
Frankfurt am Main, Germany. 5Aerosol Physics Laboratory, Faculty of Engineering and Natural Sciences, Tampere University, 33720 Tampere, Finland. 6Key Laboratory of Industrial Ecology and
Environmental Engineering (Ministry of Education), School of Environmental Science and Technology, Dalian University of Technology, 116024 Dalian, China. 7Department of Chemistry, University
of Colorado Boulder, Boulder, CO 80309, USA. 8Cooperative Institute for Research in Environmental Sciences, University of Colorado Boulder, Boulder, CO 80309, USA. 9Institute for Materials
Chemistry, TU Wien, 1060 Vienna, Austria. 10Laboratory of Atmospheric Chemistry, Paul Scherrer Institute, CH-5232 Villigen, Switzerland. 11Laboratory of Atmospheric Processes and their
Impact, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland. 12School of Marine Sciences, Sun Yat-sen University, 519082 Zhuhai, China. 13Division of Chemistry and
Chemical Engineering, California Institute of Technology, Pasadena, CA 91125, USA. 14CENTRA and Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, Portugal. 15Research
Center for Eco-Environmental Sciences, Chinese Academy of Sciences, 100084 Beijing, China. 16Helsinki Institute of Physics, University of Helsinki, 00014 Helsinki, Finland. 17Institute of Ion
Physics and Applied Physics, University of Innsbruck, 6020 Innsbruck, Austria. 18Climate and Atmosphere Research Centre (CARE-C), The Cyprus Institute, 1645 Nicosia, Cyprus. 19Aerodyne
Research, Inc., Billerica, MA 01821, USA. 20Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA. 21P. N. Lebedev Physical Institute of the Russian
Academy of Sciences, 119991 Moscow, Russia. 22Moscow Institute of Physics and Technology (National Research University),141701 Moscow, Russian Federation. 23CERN, the European
Organization for Nuclear Research, CH-1211 Geneva, Switzerland. 24Department of Physics, University of Genoa, 16146 Genoa, Italy. 25Department of Chemistry, Carnegie Mellon University,
Pittsburgh, PA 15213, USA. 26Department of Atmospheric and Oceanic Sciences, University of Colorado Boulder, Boulder, CO 80309, USA. 27Natural Environment Research Council, British
Antarctic Survey, CB3 0ET Cambridge, UK. 28Department of Chemistry, University of Helsinki, 00014 Helsinki, Finland. 29Department of Applied Physics, University of Eastern Finland, 70211
Kuopio, Finland. 30Instituto Dom Luiz (IDL)–Universidade da Beira Interior, 6201-001 Covilhã, Portugal. 31Faculty of Physics, University of Vienna, 1090 Wien, Austria. 32Department of Engineering
and Public Policy, Carnegie Mellon University, Pittsburgh, PA 15213, USA. 33Joint International Research Laboratory of Atmospheric and Earth System Sciences, School of Atmospheric Sciences,
Nanjing University, 210023 Nanjing, China. 34Aerosol and Haze Laboratory, Beijing Advanced Innovation Center for Soft Matter Science and Engineering, Beijing University of Chemical
Technology, 100029 Beijing, China.
*Corresponding author. Email: xucheng.he@helsinki.fi (X.-C.H.); markku.kulmala@helsinki.fi (M.K.); mikko.sipila@helsinki.fi (M.Sip.); hbxie@dlut.edu.cn (H.-B.X.)
He et al., Science 382, 1308–1314 (2023)
15 December 2023
1 of 6
RES EARCH | R E S E A R C H A R T I C L E
Corrected 5 January 2024. See full text.
A
a
b
NH3 detection limit
B
b
NH 3 concentration
H2SO4 concentration
HIO 3 concentration
HIO 2 concentration
d
c
e
f
g
C
D
9
10
8
10
7
10
6
10
5
10
4
10
10
1
0.1
0.01
0.001
)
3
-
m
c
(
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o
i
t
a
r
t
n
e
c
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o
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1
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7
.
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,
e
t
a
r
n
o
i
t
a
e
c
u
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l
0.0001
00:00
Oct-10,2018
Measured J 1.7
Expected J 1.7 from H 2SO4 + NH 3
01:00
02:00
03:00
04:00
05:00
22:00
23:00
Time (UTC)
00:00
Oct-11,2018
01:00
02:00
9
10
8
10
7
10
6
10
5
10
4
10
10
1
0.1
0.01
0.001
0.0001
Fig. 1. New particle formation from HIOx-H2SO4 and HIOx-H2SO4-NH3
at −10°C. (A and B) vapor concentrations and (C and D) nucleation rates. Solid
black lines show the measured nucleation rates at 1.7 nm and solid red lines
present predicted J1.7 from H2SO4-NH3 nucleation alone (14). Dashed lines
represent vapor concentrations, and vertical gray bars show experimental stages.
The experiments show that the rapid nucleation rates cannot be explained by
the H2SO4-NH3 mechanism alone. HIOx significantly enhances H2SO4-NH3
nucleation at comparable HIO3 and H2SO4 concentrations. The NH3 concentra-
tion in (A) is below the detection limit of the H3O+-CIMS (~4 pptv). An NH3
concentration of 4 pptv is used to conservatively estimate the H2SO4-NH3
nucleation rates in (C). The experimental conditions are 41.1 parts per billion by
volume (ppbv) O3, 63.5% relative humidity (RH), 2.3 ppbv SO2, and 17.4 pptv
I2 [(A) and (C)]; and 40.8 ppbv O3, 62.3% RH, 1.6 ppbv SO2, and 67.2 pptv I2
[(B) and (D)]. Stages a, c, d, e, f, and g enhanced the UVH light intensity
(higher OH production rates), and stage b increased the green light intensity
(higher I2 photolysis rate).
To investigate possible synergies in HIOx-
H2SO4(-NH3) nucleation, green and ultraviolet
light sources were used to drive photochem-
ical production of HIOx and H2SO4 from I2
and SO2. An example experiment at −10°C is
shown in Fig. 1 and fig. S1, and at 10°C in fig.
S2. Experiments were first performed with-
out any added NH3 [<4 parts per trillion by
volume (pptv) contaminant level]; these are
shown in the left-hand panels of Fig. 1 and
figs. S1 and S2. A second set of experiments
were performed with NH3 added to the cham-
ber (right-hand panels of Fig. 1 and figs. S1 and
S2). At both temperatures, a significantly higher
nucleation rate at 1.7 nm, J1.7, is observed in
the presence of HIOx than the J1.7 expected
from H2SO4-NH3 nucleation (5, 14), both with-
out and with added NH3.
In Fig. 2, we present J1.7 for the HIOx-H2SO4
system (hollow markers) and the HIOx-H2SO4-
NH3 system (filled markers) at 10°C (circles) and
−10°C (squares). The concentration ranges of
HIOx and H2SO4 closely match ambient val-
ues, spanning from <106 cm−3 to nearly 108 cm−3
(6, 17, 18, 20, 21, 23). We show the measured J1.7
for these mixed systems for various possible
drivers: H2SO4 (Fig. 2A), HIO3 + H2SO4 (Fig. 2B),
and (HIO3 + H2SO4) × HIO2 (Fig. 2C) (HIO2,
iodous acid). The data at both temperatures be-
come progressively less scattered when plotted
against these variables, as well as more con-
sistent with parameterizations (14, 18). The
H2SO4-NH3 mechanism cannot predict the nu-
cleation rates, even when the HIOx concentra-
tion is much lower than that of H2SO4 (Fig. 2A).
For instance, J1.7 at 10°C from HIOx-H2SO4
with NH3 < 4 pptv (Fig. 2A, hollow circles) is
roughly 60 times faster than J1.7 from H2SO4
with NH3 at 4 pptv; this is as fast as nucleation
from H2SO4 with NH3 at 500 pptv. Therefore,
sub-pptv levels of HIOx are as effective at
stabilizing H2SO4 as 500 pptv of NH3. Hence,
HIOx may replace NH3 as a nucleation driver
in pristine marine and polar environments,
where NH3 concentrations are typically below
a few tens of parts per trillion by volume or
lower (26, 27).
Figure 2B shows the observed J1.7 versus
total acid concentration (HIO3 + H2SO4) and
compares these rates to the values predicted
by the H2SO4(-NH3) parameterizations (14),
applying (HIO3 + H2SO4) as H2SO4. The J1.7 of
the HIOx-H2SO4 system without added NH3
(hollow markers) remains higher than the pre-
diction for H2SO4(-NH3) nucleation. This indi-
cates that HIOx contributes more prominently
to nucleation than by simply increasing the acid
concentration. Moreover, the relatively mild
sensitivity to NH3 suggests that the base sta-
bilization comes from another source. This is
supported by Fig. 2C, which indicates that
HIO2 is effectively providing base stabilization
in the molecular clusters. To further investi-
gate the underlying mechanisms, we studied
the molecular composition of nucleating parti-
cles under neutral (ion-free) and charged (ion-
induced) conditions, as described below.
HIO2 accelerates neutral nucleation
To measure neutral clusters, we used a nitrate
chemical ionization mass spectrometer (nitrate-
CIMS). The concentrations of monomers HIO3,
H2SO4, and HIO2 are presented in Fig. 3A,
together with four product dimers in Fig. 3B.
Although the HIO2 concentration was one to
two orders of magnitude lower than that of
HIO3 or H2SO4, the most prominent dimers,
HIO3-HIO2 and H2SO4-HIO2, both contain HIO2.
He et al., Science 382, 1308–1314 (2023)
15 December 2023
2 of 6
RES EARCH | R E S E A R C H A R T I C L E
Corrected 5 January 2024. See full text.
A
4
2
100
6
4
)
1
-
s
3
-
m
c
(
7
.
1
J
2
10
6
4
,
e
t
a
r
n
o
i
t
a
e
c
u
N
l
2
1
6
4
2
0.1
6
4
2
0.01
4
6 8
106
2
4
6 8
107
H2SO4 (cm-3)
B
HIO3
4
2
8
6
4
2
7
10
6
10
2
4
6 8
108
2
C
–10°C 10°C
HIOx
H2SO4+NH3(500ppt)
H2SO4+NH3(4ppt)
HIOx+H2SO4
HIOx+H2SO4+NH3
ACDC: HIOx+H2SO4(Neutral)
ACDC: HIO3+HIO2 or
H2SO4+HIO2(Neutral)
4
6
8
108
1011
2
4 6
1012
2
4 6
1013
2
4 6
2
1014
(HIO3 + H2SO4) HIO2 (cm-6)
2
4
6
8
107
HIO3 + H2SO4 (cm-3)
Fig. 2. Nucleation rates of HIOx-H2SO4(-NH3) systems. Nucleation rates at
1.7 nm versus (A) H2SO4, (B) HIO3 + H2SO4, and (C) (HIO3 + H2SO4) × HIO2 at
+10° and −10°C. All data points and lines show experiments carried out at
galactic cosmic ray ionization conditions, except for the atmospheric cluster
dynamics code (ACDC) simulations in (C) (orange band and filled diamonds), which
represent the theoretical prediction for the neutral nucleation rates (see methods).
The color bar represents HIO3 concentration (per cubic centimeter). H2SO4-NH3
mechanism fails to predict the overall nucleation rates, even with HIOx is much
lower than H2SO4. The J1.7 from experiments with high H2SO4 is also higher
than that predicted by pure iodine oxoacids (18). The nucleation rates become
less spread when plotted against (HIO3 + H2SO4) × HIO2, as well as more
consistent with parameterizations and ACDC predictions. The results show that
HIO3 and HIO2 have to be considered together with H2SO4 to predict the
nucleation rates in this multicomponent system. H2SO4-NH3 nucleation rates
(dotted and dash-dotted lines) are calculated following Dunne et al. (14), whereas
HIOx nucleation rates (solid lines) are calculated on the basis of J1.7, HIO3, and
recalculated HIO2 from He et al. (18), applying HIO3 × HIO2 as (HIO3 + H2SO4) ×
HIO2, to guide the eye. The experimental conditions for HIOx-H2SO4(-NH3)
experiments are 38.4 to 53.2 ppbv O3, 41.9 to 75.3% RH, 0.6 to 11.2 ppbv SO2,
and 10.0 to 57.7 pptv I2. The NH3 concentrations for the filled squares and filled
circles range from 30 to 42 pptv and from 176 to 261 pptv, respectively. The
error bars show one standard deviation during the data selection periods. Overall
systematic scale errors on the HIO3 concentrations of −33% and +50% and on
the nucleation rates of a factor of 10 are not shown on the data points.
Despite HIO3-HIO2 clusters having been re-
ported before (18, 28), we believe this is the
first observation of H2SO4-HIO2 dimers.
While HIO2 enables H2SO4-HIO2 dimer for-
mation, its role in larger clusters is not clear.
We address this with a combination of quan-
tum chemical calculations and cluster dynam-
ics modeling (29). We optimized the geometries
of H2SO4-HIO2, HIO3-HIO2, and H2SO4-HIO3-
HIO2 clusters and calculated their formation
free energies and evaporation rates (fig. S3).
Clusters containing HIO2 are the most stable
and, moreover, show an exceptionally wide
range of stable combinations of molecules.
The cluster geometries suggest that HIO2 en-
hances H2SO4 neutral nucleation in the same
way as it does for HIO3 neutral nucleation (18).
Specifically, HIO2 accepts the proton donated
either by H2SO4 or HIO3, thereby function-
ing as a base. Furthermore, HIO2 forms strong
halogen bonds with H2SO4 and HIO3, further
enhancing the cluster stability. Clusters includ-
ing HIO2 are even more stable than H2SO4-
DMA (dimethyl amine) clusters (fig. S3), which
is known to cluster at the collision limit for
sulfuric acid with only 4 pptv DMA (3). How-
ever, the predicted neutral nucleation rates
for the H2SO4-HIO2 and HIO3-HIO2 systems
still underestimate our measured nucleation
rates [galactic cosmic ray (GCR) conditions,
the sum of neutral and ion-induced chan-
nels] at −10°C (Fig. 2C, orange band). On the
other hand, the predicted HIOx-H2SO4 neu-
tral nucleation rates approximately agree with
CLOUD observations (Fig. 2C, squares and di-
amonds). The consistency between theoretical
predictions and the CLOUD measurements at
−10°C suggests that neutral nucleation domi-
nates at this temperature, which is also indicated
by the fact that the nucleation rates far exceed
the ion-pair production rate limit (2 to 10 cm−3 s−1).
Additionally, this suggests that the control-
ling mechanism is indeed a synergy of three
molecules (HIO3, H2SO4, and HIO2) and not
simply the combined neutral nucleation of
any two molecules. Given that HIO2 behaves
as a base, we show in Fig. 2C our observed J1.7
versus (HIO3 + H2SO4) × HIO2. This expres-
sion is proportional to the formation rate of the
dimer (H2SO4-HIO2 or HIO3-HIO2), which rep-
resents the initial nucleating cluster. We find
that the HIOx-H2SO4(-NH3) nucleation rates
fall near the prediction from HIOx nucleation
(J1.7 versus HIO3 × HIO2; H2SO4 is absent in
pure iodine oxoacid nucleation, but it is added
to the HIO3 concentration given its identical
role) (18), implying that HIO2 indeed plays the
key role as stabilizer both for HIO3 and H2SO4
and that NH3 plays a minor role.
While the formation mechanism for HIO3
has recently been established (22), the path-
way for HIO2 formation remains uncertain. A
quantum chemical study provided a potential
energy surface describing formation of HIO2
from iodooxy hypoiodite, I2O2 + H2O (30). We
have extended this study with high-level quan-
tum chemical calculations and provide a re-
vised potential energy surface in fig. S4A. We
also present a potential new pathway for HIO2
formation from iodine dioxide (OIO) and the
hydroperoxyl radical (HO2) (fig. S4B). Our cal-
culations show that both the singlet and trip-
let channels are exothermic. Further studies
are needed to quantify the relative importance
in the atmosphere of these two channels.
Because complex reactions are involved in
the formation of HIO3 and HIO2, it is impor-
tant to confirm that the HIO3:HIO2 ratio in the
CLOUD chamber matches ambient conditions.
Figure S5 shows that both the ratio and ab-
solute concentrations of HIO3 and HIO2 fall
within the range measured at Mace Head (17)
and Ny-Ålesund (21), confirming that the results
from our study are relevant to the atmosphere.
HIO3 enhances ion-induced nucleation
Ions can stabilize embryonic molecular clus-
ters, leading to ion-induced nucleation (IIN)
(5, 18, 19, 31, 32). To investigate the influence of
ions on HIOx-H2SO4 nucleation, we increased
the ionization rate in the chamber in three steps
at 10°C: (i) neutral (ion-free), (ii) GCR ion-
ization (∼1000 ion pairs cm−3), and (iii) beam-
enhanced ionization (∼6000 ion pairs cm−3)
(fig. S6). Compared with neutral conditions,
J1.7 at GCR ionization rates is enhanced by
He et al., Science 382, 1308–1314 (2023)
15 December 2023
3 of 6
RES EARCH | R E S E A R C H A R T I C L E
Corrected 5 January 2024. See full text.
Fig. 3. Neutral and charged cluster
composition during HIOx-H2SO4-
NH3 nucleation. Background-
subtracted neutral monomer (A) and
dimer (B) concentrations in HIOx-
H2SO4 nucleation events at +10°C
(pink bars) and −10°C (cyan bars).
(C and D) Negatively charged cluster
compositions of HIOx-H2SO4 nucleation
at +10° and −10°C, respectively.
(E and F) Negatively charged cluster
compositions of HIOx-H2SO4-NH3 nucle-
ation at +10° and −10°C, respectively.
As indicated in (B), the dominant
neutral dimers are H2SO4-HIO2 and
HIO3-HIO2 clusters—despite very low
HIO2 concentrations—which represent
the initial molecular clusters during
neutral nucleation. Ion-induced nucleation
is dominated by charged HIO3-H2SO4 [(C)
and (D)] or HIO3-H2SO4(-NH3) [(E)
and (F)] cluster formation processes.
HIO3-NH3 clusters are not detected,
which suggests that NH3 has a
negligible effect on ion-induced HIO3
cluster formation. The marker size
is shown in the legend (cps, ion
counts per second). The experimental
conditions are 38.5 to 43.9 ppbv O3,
61.6 to 75.2% RH, 0.7 to 11.0 ppbv
SO2, and 14.4 to 44.5 pptv I2.
)
3
-
m
c
(
n
o
i
t
a
r
t
n
e
c
n
o
C
0.2
0.0
-0.2
-0.4
-0.6
0.2
0.0
-0.2
-0.4
-0.6
)
h
T
(
t
c
e
f
e
d
s
s
a
M
A
neutral monomer
B
neutral dimer
+10 °C
10 °C
107
106
105
104
H2SO4
HIO3
HIO2
H2SO4·H2SO4
H2SO4·HIO3
H2SO4·HIO2
HIO3·HIO2
C
HIOx + H2SO4 at +10 °C
D HIO x + H2SO4 at 10 °C
< 0.01 cps
0.01-0.1
0.1-1
1-10
10
E
HIO x + H2SO4 + NH3 at +10 °C
F
HIOx + H2SO4 + NH3 at 10 °C
Other
HIOx and iodine containing
H2SO4 and sulfur containing
HIOx - H2SO4
H2SO4 - NH3
HIOx - H2SO4 - NH3
0
200
400
600
800
1000
0
200
Mass/charge, m/z (Th)
400
600
800
1000
∼50 times at 2 × 107 cm−3 H2SO4 and 5 × 106 cm−3
HIO3. As with HIOx, ion-induced HIOx-H2SO4
nucleation only occurs with negative ions (com-
pare fig. S6A and fig. S6B). Interestingly, six
times larger ion concentrations formed by
the pion beam only enhance J1.7 by a factor of
two. This is likely because the increased ion-
ion recombination rate, and hence the shorter
charge lifetime, neutralizes some clusters be-
fore they have become stable against evapo-
ration when neutral. When NH3 is added to
the HIOx-H2SO4 system, it initiates positive
IIN that is as strong as negative IIN at −10°C
(fig. S1D). Adding NH3 approximately doubles
the overall J1.7.
To measure the molecular composition of
charged clusters, we used an atmospheric pres-
sure interface time-of-flight mass spectrome-
ter. For HIOx-H2SO4 IIN without NH3 injection
(Fig. 3, C and D), we observe a series of charged
clusters with the empirical formula (HIO3)n-
− (cyan triangles), which indicate
(H2SO4)m-HSO4
synergistic IIN of HIO3 and H2SO4. We identify
these clusters as (n+m+1)-mer (which include
the ion; fig. S7). At 10°C, monomers, dimers, and
trimers consist primarily of H2SO4, whereas
HIO3 appears in clusters starting from the tetra-
mers and becomes equal to the H2SO4 mole
fraction already in the hexamers. At −10°C, HIO3
appears in the dimers and becomes equal to the
H2SO4 starting with the tetramers.
In these experiments, the HIO3:H2SO4 ratio
in the gas phase is between 0.3 and 1.4, and the
molar ratios of I:S in the larger clusters tend
toward 1:1. We also know that pure ion-induced
HIO3 nucleation proceeds at the collision limit
(18, 19) but that ion-induced H2SO4 nucleation
is slower than the collision limit (5). We there-
fore conclude that H2SO4 condensation is en-
hanced by HIO3 for a cluster stoichiometry up
to 1:1, beyond which the net rate of H2SO4 con-
densation slows, while HIO3 condensation is
limited by the collision rate under our exper-
imental conditions.
We performed additional experiments in
which NH3 was added to the HIOx-H2SO4 sys-
tem. Notably, none of the charged pure iodine
(i.e., H2SO4-free) clusters contained NH3, which
indicates a negligible role of NH3 in ion-induced
HIO3 nucleation. This was independently con-
firmed by raising NH3 from the background
level (<4 pptv) to 100 pptv in an iodine oxoacid
nucleation experiment without H2SO4 (fig.
S8). The measured nucleation rate at 1.7 nm
remained constant throughout the experi-
ment, indicating that HIO3(-HIO2) nucleation
is unaffected by NH3.
On the other hand, we found a set of clusters
−
with the composition (H2SO4)n-(NH3)m-HSO4
− in the
and (HIO3)n-(H2SO4)m-(NH3)j-HSO4
mass spectra of charged clusters (Fig. 3, E
and F), similar to the clusters reported near
the coast of Antarctica (6). We found that NH3
is only present in charged tetramers and above,
consistent with its behavior in H2SO4-NH3 IIN
(5). The iodine and sulfur molar fraction dis-
tributions remained unchanged after adding
NH3 to the system, likely because the HIO3-
H2SO4 negative IIN had already reached the
collision limit (fig. S7). The presence of NH3
only converted some of the (HIO3)n-(H2SO4)m-
− ions
− to (HIO3)n-(H2SO4)m-(NH3)j-HSO4
HSO4
and gives rise to positive IIN (fig. S1).
Particle growth
Since the atmospheric concentration of HIO2
is less than one-tenth that of HIO3, its role in
particle growth is minor (18). To evaluate the
role of HIO3 and H2SO4 in particle growth, we
compare in fig. S9A our measured growth rates
between 1.8 and 3.2 nm (GR1.8-3.2) with those
calculated assuming condensation of H2SO4
and HIO3 (18, 33) at the collision limit. The
good agreement indicates that H2SO4 and
HIO3 are the main condensing vapors driving
particle growth (18, 33) while other iodine
species contribute little to particle mass. We
show in fig. S9B the measured and predicted
particle survival probability, J2.5/J1.7, which
increases at faster growth rates and approaches
unity above growth rates of ~10 nm hour−1
for the CLOUD chamber (2.2 × 10−3 s−1 wall loss
rate). In the marine atmosphere, condensation
He et al., Science 382, 1308–1314 (2023)
15 December 2023
4 of 6
RES EARCH | R E S E A R C H A R T I C L E
Corrected 5 January 2024. See full text.
78-90N
A
Arctic Ocean: Aug-Sep
Villum: March-Aug
Ny-Ålesund: April-Aug
81N
79N
70N
60N
30N
0
21S
Latitude (°)
34-74S
73S
B
10 4
JHIOx+H2SO4+NH3
JH2SO4+NH3
103
102
10 1
10 0
H2SO4 (cm-3)
108
8
6
4
2
107
8
6
4
2
106
0.1
6 8
2
Värriö: April-Oct
Helsinki: July-Aug
Réunion: April
Southern Ocean: Feb-Mar
Aboa: Dec-Jan
-10 °C 10 °C
HIOx+H2SO4
HIOx+H2SO4+NH3
4
6 8
10
2
4
6 8
2
1
HIO3 : H2SO4 ratio
Fig. 4. HIOx enhancement of H2SO4-NH3 nucleation. (A) Box plot statistics of HIO3:H2SO4 ratios measured
around the globe, showing median values with 10 and 90% percentiles in the whiskers. The gray labels show
the site name and months, with data covering >50% of the days. (B) Nucleation enhancement by HIOx is
calculated by dividing the measured JHIOx(cid:1)H2SO4(cid:1)NH3 to predict JH2SO4(cid:1)NH3 using CLOUD parameterizations (14).
The median ratios at all sites are greater than 0.1, which infers at least a 10-fold nucleation rate enhancement
by HIOx. The enhancement is especially pronounced in polar regions where the HIO3:H2SO4 ratio is consistently
higher than 0.1. Thin symmetric error bars represent one standard deviation during the data selection periods. In the
experiments without NH3 injection (hollow markers), the NH3 concentrations were below the instrument
detection limit (4 pptv), which is adopted as a conservative estimate of JH2SO4(cid:1)NH3. However, the actual NH3
concentration is expected to be below 1 pptv, as all charged clusters are essentially NH3 free (Fig. 3). The
thick asymmetric error bars represent the systematic uncertainty assuming NH3 equals 1 pptv. The NH3
concentrations in experiments with NH3 injection (filled markers) are well measured, and thus without
asymmetric errors. The field observation sites are summarized in the methods.
of other compounds, such as MSA and oxi-
dized organic molecules, can also contribute
to early particle growth, in addition to H2SO4
and HIO3.
Climate implications
Atmospheric observations show that both
iodine oxoacid and sulfuric acid–ammonia
nucleation can be important particle sources
in specific regions of the pristine boundary
layer (6, 17, 18, 20, 21). So far, HIO3 and HIO2
have been thought to be important only in
regions where they are more abundant than
H2SO4. In polar and marine environments, it
is currently thought that H2SO4-NH3 constitutes
the primary source of new particle formation,
despite the perceived scarcity of NH3 (15). This
picture is challenged by our findings. Our data
support the reverse: H2SO4-NH3 nucleation
plays a major role only when H2SO4 is sub-
stantially more abundant than HIO3 and HIO2.
The role of HIOx in atmospheric aerosol nuclea-
tion may have been overlooked, as studies could
easily be deceived by relatively higher H2SO4
than HIOx in parts of the pristine atmosphere.
To assess the atmospheric importance of
HIOx-H2SO4(-NH3) nucleation, we calculated
the J1.7 enhancement factor [the ratio of J1.7
from HIOx-H2SO4(-NH3) to that from H2SO4-
NH3] (14) as a function of the HIO3:H2SO4
concentration ratio (Fig. 4B). The enhance-
ment factors are large, ranging from 10 to 104
for atmospherically relevant HIO3:H2SO4 ra-
tios. Even when the HIO3:H2SO4 ratio is 0.1,
the enhancement factor is 10. Observations at
marine and polar sites from the North Pole to
Antarctica show median HIO3:H2SO4 ratios
larger than 0.1 (Fig. 4A), implying that syn-
ergistic HIOx-H2SO4(-NH3) nucleation may
have global importance and yet has hitherto
been overlooked. This conclusion is supported
by our calculations of sulfuric acid nucleation
enhanced by HIOx, which are shown in fig.
S10. At −10°C, which is representative of the
marine free troposphere, fast nucleation rates
of up to 10 cm−3 s−1 are estimated for ambient
acid concentrations. The pronounced temper-
ature dependence of HIOx-H2SO4(-NH3) nu-
cleation that we find in our study may help
explain why nucleation in the marine bound-
ary is rarely observed, whereas nucleation is
frequently found in the free troposphere or the
upper marine boundary layer after passage of
a cold front (23, 34, 35).
New particle formation from HIOx-H2SO4
has notable implications for the future cli-
mate. Iodine oxoacids may enhance CCN and
cloud formation in the Arctic (20), which would,
in turn, affect both long- and shortwave radia-
tive forcing at the surface (36). The absence
of iodine oxoacid nucleation mechanisms in
climate models may help explain why they
systematically underestimate the CCN number
concentration around the coast of Antarctica
(37, 38). Iodine has also been observed in both
gas and particle phases in the polar and ma-
rine free troposphere and the upper tropo-
sphere and lower stratosphere (39, 40). These
regions are characterized by low temperatures
and extremely low NH3 concentrations (15),
conditions that strongly favor HIOx-H2SO4
or pure HIOx nucleation over H2SO4-NH3 nu-
cleation. While global anthropogenic SO2
emissions continue to fall as a result of emission
policies, iodine emissions have tripled since
the 1950s, and this trend continues (41, 42).
As a result, nucleation mechanisms involv-
ing iodine oxoacids are anticipated to become
even more important in future. To sharpen the
understanding of marine aerosol-cloud radia-
tive forcing, it is important that representa-
tions of new particle formation in global
climate models now include iodine oxoacids
together with sulfuric acid.
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ACKN OWLED GMEN TS
We thank CERN for supporting CLOUD with important technical
and financial resources and for providing a particle beam from the
CERN Proton Synchrotron. We thank the CSC IT Center for Science
in Espoo, Finland, for computing time. Funding: This work was
supported by Research Council of Finland ACCC Flagship nos.
337549 and 337552; Research Council of Finland professorship
(302958); Research Council of Finland Centre of Excellence nos.
346371, 346372, and 346373; Research Council of Finland project
nos. 335844, 334514, 345125, 325656, 316114, 314798, 325647,
353836, 341349, 346372, 296628, and 349659; European Research
Council (ERC) project nos. 742206, 714621, 616075, and 101002728;
Marie Skłodowska-Curie grant agreement nos. 316662, 701647,
895875, and 764991; National Natural Science Foundation of China
grant nos. 42175118 and 22236004; the National Key Research
and Development Program of China (2022YFC3701000, Task 1);
Swiss National Science Foundation grant nos. 200021_169090,
200021_213071, 206021_198140, 200020_172602, and 20FI20_172622;
US National Science Foundation grants nos. AGS-2132089,
AGS-1801897, AGS-1801574, AGS-1801280, AGS-2027252,
AGS-2215522, AGS-1602086, AGS-1801329, and AGS-2215527;
German Federal Ministry of Education and Research (BMBF)
project no. 01LK1601A; and Portuguese Science Foundation project
CERN/FIS-COM/0028/2019. R.C.T. and M.K. thank the Jane and
Aatos Erkko Foundation for funding. M.K. received funding from
Prince Albert Foundation contract no. 2859. M.W. thanks the
Schmidt Science Fellowship for support. X.-C.H. and M.K. thank the
Jenny and Antti Wihuri Foundation for funding. Author contributions:
X.-C.H., J.Kir., M.Sip., and M.K. planned the experiments. X.-C.H.,
M.Sim., B.R., J.S., H.F., D.S., A.B., Y.J.T., M.W., S.A., A.A.P., A.A., R.B.,
Z.B., L.C., B.C., L.D., J.D., I.E.H., R.C.F., M.G., M.H., V.H., W.K.,
J.Kre., A.K., H.L., B.L., N.G.A.M., V.M., H.E.M., G.M., R.M., D.M.,
R.L.M., B.M., A.O., T.P., J.P., M.P., M.P.R., S.S., W.S., B.S., M.Sur., A.T.,
A.C.W., D.W., Y.W., S.K.W., A.W., P.M.W., M.Z.-W., J.Kir., U.B.,
K.L., J.C., R.V., M.Sip., and M.K. prepared the CLOUD facility or
measuring instruments. X.-C.H., M.Sim., S.I., B.R., J.S., H.F., D.S.,
A.B., Y.J.T., A.A., R.B., L.C., L.D., J.D., I.E.H., M.G., M.H., V.H., T.J.,
D.K., W.K., J.Kre., H.L., B.L., N.G.A.M., V.M., H.E.M., G.M., R.M.,
D.M., R.LM., B.M., J.P., A.R., W.S., R.C.T., A.C.W., D.W., S.K.W., M.Z.-W.,
J.Kir., J.C., and R.V. collected the data. X.-C.H., S.I., H.-B.X., H.F., D.S.,
R.Z., Y.J.T., L.C., L.D., R.C.F., F.M., W.S., R.C.T., S.K.W., P.M.W., T.K.
and D.R.W. analyzed the data. X.-C.H., N.M.D. and J.Kir. wrote the
manuscript with contributions from S.I., H.-B.X., B.R. and R.Z. X.-C.H.,
M.Sim., S.I., H.-B.X., B.R., J.S., H.F., D.S., R.Z., A.B., L.D., J.D., I.E.H.,
R.C.F., A.H., H.L., N.G.A.M., T.P., S.S., W.S., R.C.T., A.C.W., J.Kir., U.B.,
K.L., J.C., T.K., D.R.W., R.V., N.M.D., M.Sip. and M.K. commented
on and edited the manuscript. Competing interests: The authors
declare that they have no competing interests. Data and materials
availability: Data for all figures in the main text and supplementary
materials are available at the Zenodo repository (43). Correspondence
and additional requests for materials should be addressed to X.-C.H.
(institutional email: xucheng.he@helsinki.fi; permanent email:
xuchenghe93@gmail.com). License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original US
government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh2526
Materials and Methods
Figs. S1 to S10
References (44–76)
Submitted 20 February 2023; accepted 13 November 2023
10.1126/science.adh2526
He et al., Science 382, 1308–1314 (2023)
15 December 2023
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RES EARCH
R E S E A R C H A R T I C L E
◥
INORGANIC CHEMISTRY
Diberyllocene, a stable compound of Be(I) with
a Be–Be bond
Josef T. Boronski*, Agamemnon E. Crumpton, Lewis L. Wales, Simon Aldridge*
The complex diberyllocene, CpBeBeCp (Cp, cyclopentadienyl anion), has been the subject of numerous
chemical investigations over the past five decades yet has eluded experimental characterization.
We report the preparation and isolation of the compound by the reduction of beryllocene (BeCp2) with
a dimeric magnesium(I) complex and determination of its structure in the solid state by means of x-ray
crystallography. Diberyllocene acts as a reductant in reactions that form beryllium-aluminum and
beryllium-zinc bonds. Quantum chemical calculations indicate parallels between the electronic
structure of diberyllocene and the simple homodiatomic species diberyllium (Be2).
B ecause of the extreme biotoxicity of be-
ryllium, its chemistry is the least well-
developed of all the nonradioactive
elements (1–3). This toxicity is a mani-
festation of beryllium’s particular chem-
ical properties: It forms the smallest of all
metal ions (Be2+; ionic radius, 0.31 Å; com-
pare with that of Li+, 0.60 Å), with unparal-
leled charge density (6.45 Å−1; compare with
that of Li+, 1.67 Å−1). Its bonding interactions
often feature considerable covalent character
on account of the highly polarizing properties
of the dication (2). Given this capacity for co-
valency, the fundamental nature of beryllium-
beryllium bonding has been debated for more
than a century (4–11). Basic molecular orbital
theory predicts that diberyllium (Be2) should
have a bond order of zero, and only recently
has meaningful insight into the true nature of
the beryllium-beryllium interaction in gaseous
Be2 been obtained (12, 13). Moreover, despite
seminal reports of zinc-zinc and magnesium-
magnesium bonds in the early 2000s and a
host of quantum chemical investigations into
the potential stability of beryllium-containing
analogs, the isolation of a compound that fea-
tures a beryllium-beryllium bond in the con-
densed phases has not been achieved (14–17).
Given the dearth of compounds that feature
beryllium-beryllium bonds, in recent years,
synthetic studies have focused on the prep-
aration of low-valent beryllium species sta-
bilized by redox noninnocent carbene ligands
(18–20). Compounds proposed to contain beryl-
lium in the 0 and +1 oxidation states have been
synthesized. However, such descriptions have
proven controversial and are a source of on-
going debate within the literature (21–24). We
recently reported the beryllium-aluminyl com-
Chemistry Research Laboratory, Department of Chemistry,
Oxford, OX1 3TA, UK.
*Corresponding author. Email: josef.boronski@sjc.ox.ac.uk (J.T.B.);
simon.aldridge@chem.ox.ac.uk (S.A.)
plex CpBeAl(NON) [1; NON, 4,5-bis(2,6-diisopro-
pylanilido)-2,7-di-tert-butyl-9,9-dimethylxanthene;
Cp, cyclopentadienyl anion, [C5H5]−], which
displays the reactivity expected from low-
valent, nucleophilic beryllium (25–27). In this
work, we present diberyllocene, CpBeBeCp
(2), an unambiguous beryllium(I) compound
that is stable in the condensed phases and
features a Be–Be bond. The experimentally
determined properties of diberyllocene (which
is stable at 80°C for extended periods) validate
past quantum chemical predictions of its stab-
ility with respect to disproportionation to Be(0)
and BeCp2 (7).
Synthesis and characterization
We previously succeeded in using beryllocene
BeCp2 for the synthesis of beryllium-aluminyl
complex 1 (25, 28). Calculations indicate that
compound 1 features a higher partial positive
charge at aluminum than beryllium. Thus, the
formation of 1 could be viewed as a reduction
of beryllium(II) to beryllium(I) by the aluminyl
anion, with associated one-electron oxidation
of aluminum(I), which forms a covalent Be–Al
bond. We therefore set out to examine the
possibility of reducing beryllocene to form
a covalent Be–Be bond between two beryl-
lium(I) centers. We turned our attention to
di-magnesium(I) reagent [(MesNacnac)Mg]2
{3;MesNacnac, [(MesNCMe)2CH]−; Mes, 2,4,6-
trimethylphenyl}, which has been used for
the controlled reduction of various organo-
metallic compounds (6, 17). At room temper-
ature, under an inert atmosphere, the reaction
of one equivalent of 3 with two equivalents of
BeCp2 in toluene leads to quantitative for-
mation of diberyllocene CpBeBeCp (2) and
(MesNacnac)MgCp, as evidenced by multi-
nuclear nuclear magnetic resonance (NMR)
spectroscopy (Fig. 1 and fig. S5). Both com-
pounds are highly soluble in alkane solvents,
such as pentane and hexane. However, 2 is a
volatile solid and can be purified through sub-
limation at room temperature, which allows
for its isolation in 85% yield.
Compound 2 can be crystallized from a con-
centrated hexane solution, which yields crys-
tals suitable for the elucidation of its structure
by means of single-crystal x-ray diffraction
(Fig. 1B). Compound 2 is shown to feature two
half-sandwich (cyclopentadienyl)beryllium
units linked through a beryllium–beryllium
bond. Zinc is the only other element for which
the dimetallocene structural motif has been
reported—for example, in Cp*ZnZnCp* [4; Cp*,
pentamethylcyclopentadienyl anion (C5Me5)−]—
and the configuration of 2 closely resembles
that of 4 (14, 15). Both 2 and 4 display D5h
symmetry in the solid state, with the cyclo-
pentadienyl ligands adopting a parallel, eclipsed
configuration. At 2.0545(18) Å, where the num-
ber in parentheses is the standard deviation of
the least significant digits, the Be1–Be2 distance
in 2 is in line with the sum of the single-bond
covalent radii for beryllium (2.04 Å) (29). This
value is extremely close to that predicted by
previous computational investigations of this
compound (2.041 to 2.077 Å) (7–9). Examples
of hydride-bridged beryllium compounds of
the form XBe(m-H)2BeX all feature wider Be–Be
separations [range, 2.098(3) to 2.212(8) Å; mean,
2.136 Å] (26, 30–32). The Be–C distances within
2 range from 1.923(2) to 1.938(2) Å (mean, 1.930
Å) and are considerably longer than that of
BeCp2 [range, 1.862(9) to 1.936(8) Å; mean,
1.904 Å] (28). Consistently, the Be-(h5-C5H5)
centroid distances for Be1 and Be2 are both
1.519 Å, which is again longer than that re-
ported for BeCp2 (1.485 Å). These bond metrics
reflect the lower oxidation state and greater
ionic radius of the beryllium(I) centers in 2
compared with those of the beryllium(II) center
in BeCp2.
Compound 2 was investigated by use of
multinuclear NMR spectroscopy. The 1H NMR
spectrum of 2 consists of a single resonance at
5.73 parts per million (ppm), which corre-
sponds to the five equivalent cyclopentadienyl
ligand protons. The 1H NMR resonances of
terminal beryllium-bound hydride ligands are
generally found between 4 and 5 ppm (32, 33).
Thus, 2 shows no signals attributable to Be–H
hydrides in its 1H NMR spectrum, only the
resonance that corresponds to the cyclopenta-
dienyl ligand. Similarly, the 13C NMR spec-
trum of 2 features one signal at 102.7 ppm.
Compound 2 was also investigated by means
of 9Be NMR spectroscopy—which offers a con-
venient probe of the electron density at the
beryllium center—and shows a single high-field
resonance at −27.6 ppm (25, 34). The coordi-
nation of strongly electron-donating anionic
ligands to beryllium generally shifts the 9Be
NMR resonances further upfield as the in-
creasingly electron-rich beryllium center be-
comes more strongly shielded. So, for example,
CpBeCl exhibits a d9Be shift of −19.5 ppm,
Boronski et al., Science 380, 1147–1149 (2023)
16 June 2023
1 of 3
RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Synthesis, crystallographic, and electronic structure of diberyllocene (2). (A) Synthesis of 2
through reaction of magnesium(I) complex 3 and beryllocene. (B) Molecular structure of 2 in the solid state,
as determined with x-ray crystallography. Thermal ellipsoids set at 50% probability. (C) Calculated HOMO for
2 [isovalue, 0.03 arbitrary units (a.u.)].
whereas the corresponding signals of CpBeMe,
CpBeGa(NON), CpBe[Si(CH3)3], and beryllium–
aluminyl compound 1 are found at −20.5, −26.9,
−27.7, and −28.8 ppm, respectively (table S2)
(34). These data suggest that the beryllium center
in 2 is similarly as electron rich as that in 1,
which is consistent with the description of 2
as a metal-metal bonded beryllium(I) com-
pound (25, 34). Moreover, the 9Be NMR shift
for compound 2 also provides evidence against
a bridging hydride formulation for this com-
pound because such a species would be ex-
pected to show a much lower field chemical
shift (fig. S23) (34).
To further argue against the hydride for-
mulation for 2, we measured attenuated total
reflection infrared (ATR IR) spectra for sam-
ples of 2 prepared in both protio and perdeu-
tero toluene solvents (figs. S14 and S15). The
spectra are identical, and neither features an
absorbance band in the 1500 to 2000 cm−1
region where a Be–H stretch might be ex-
pected to be observed (35). The infrared spec-
tra of both 2 and the hypothetical complex
CpBe(m-H)2BeCp were simulated through quan-
tum chemical calculations (figs. S17 and S18).
The experimentally derived ATR IR spectrum
of 2 closely matches the spectrum calculated
for this complex (fig. S19) and differs substan-
tially from that of the hydride-bridged species
(fig. S20), which features a very intense band
at 1527 cm−1 [us(Be–Hb)]. The beryllium(II)
hydride compound (CpBeH)n is thermally frag-
ile and has been reported to undergo ligand
redistribution to form BeCp2 and BeH2 within
minutes at −10°C (35, 36). This reactivity con-
trasts with the relative stability of 2, which
shows no obvious signs of degradation upon
heating in solution at 80°C for 48 hours.
Quantum chemical investigations
Quantum chemical calculations were performed
on 2 (B3LYP D3BJ def2-TZVP def2/J), in light
of the experimental data that had been un-
available for previous theoretical investigations
of this molecule (7–9). Key structural param-
eters align well with those determined crys-
tallographically [for example, d(Be–Be) =
2.046 Å, as compared with 2.0545(18) Å].
These calculations indicate that the energetic
separation between the highest occupied mo-
lecular orbital (HOMO) and lowest unoccupied
molecular orbital (LUMO) is 5.541 eV. The
HOMO of 2 is calculated to be the Be–Be
s-bonding orbital, with some Be–Cp s-bonding
character (Fig. 1C); the lower-lying HOMO − 1 to
HOMO − 4 correspond to the Cp–Be p-bonding
combinations. As with the homodiatomic mo-
lecule Be2, we calculated the Be–Be s* anti-
bonding orbital (LUMO + 1) of diberyllocene
to be markedly lower in energy than the
Be–Be p-bonding orbitals (LUMO + 4 and
LUMO + 5) (figs. S27 and S29) (12, 13). This
implies that further reduction of 2 would
lead to a weakening of the Be–Be interaction.
Indeed, the Be–Be distance in Be2 (2.45 Å) is
considerably longer than that measured for 2
[2.0545(18) Å] (12, 13). As such, the core of 2
could be considered to be a (cyclopentadienyl-
stabilized) dication of diberyllium, [BeBe]2+,
which molecular orbital theory would predict
to feature a beryllium–beryllium s-bond and
a formal bond order of one, as is found here
(37, 38).
We used natural bond orbital (NBO) calcula-
tions to examine the bonding and charge dis-
tribution within 2. Natural population analysis
(NPA) indicates that the 2s valence orbital of
each beryllium atom is substantially populated
[0.98 electrons (e–)], with a non-negligible pop-
ulation of the beryllium 2p orbitals (0.17 e–).
These data are consistent with a formal beryl-
lium(I) oxidation state. NBO calculations sug-
gest that the Be–Be bond comprises 93% 2s
character and 7% 2p character, with each be-
ryllium center contributing equally (50:50).
We calculated a Wiberg bond index (WBI) of
0.90 for the Be–Be bonding interaction, which
is slightly greater than the WBI calculated for
the Al–Be bond of 1 (0.82) (25). The charge
distribution in 2 was probed with both NPA
and quantum theory of atoms in molecules
(QTAIM) calculations. QTAIM analysis indi-
cates that a non-nuclear attractor is present
for the Be–Be interaction, as has been indi-
cated with previous theoretical studies of 2,
and yields a charge of +1.33 for each beryllium
atom (8). The NPA charges at each beryllium
center are lower (+0.84), but these do not take
into account the presence of the non-nuclear
attractor. QTAIM calculations previously per-
formed on 1 provide a charge of +1.39 for the
beryllium center in this compound, which sug-
gests that the beryllium centers in 1 and 2 are
similarly electron rich. This is consistent with
the similar 9Be NMR shifts measured for the
two compounds (25, 34).
Because of the high quality of the x-ray
crystallographic data obtained for 2, we used
quantum-crystallographic methods to gain fur-
ther evidence that this compound does not
feature bridging hydride ligands. Even with-
out using quantum-crystallographic methods,
there is insufficient residual electron density
to account for the presence of bridging hy-
dride ligands (figs. S34 and S35). We employed
Boronski et al., Science 380, 1147–1149 (2023)
16 June 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Reactivity of compound 2 with metal-iodide complexes, which leads to the formation of
beryllium-metal bonded complexes 1 and 5. iPr, isopropyl; tBu, tert-butyl.
the NoSpherA2 method; this technique allows
for refinement of crystallographic data on the
basis of the partitioned wave function of a
molecule, rather than the traditional approach
of refining against a model in which electron
density is considered as point charges asso-
ciated with specific atoms (independent elec-
tron model) (39, 40). By using NoSpherA2,
essentially all electron density in the data col-
lected for 2 is accounted for (figs. S31 and S32).
The electron density associated with the cyclo-
pentadienyl C–H bonds can be clearly identi-
fied (fig. S35), and there is no residual electron
density resulting from bridging hydride ligands
(figs. S31 and S33).
Reactivity studies
In view of the metal–metal bond in 2, we probed
its reactivity as a source of low-valent beryl-
lium. Complex 2 does not react with H2 (one
atmosphere), even at elevated temperatures—
a finding that is consistent with di-magnesium
(I) compounds such as 3, which also do not
react with H2 (17). However, compound 2 re-
duces (NON)AlI to cleanly and quantitatively
yield the known beryllium-aluminyl compound
1 and CpBeI (Fig. 2, left), which evidences the
usefulness of 2 for the synthesis of beryllium-
metal bonds (25). This reactivity would not be
expected from a beryllium(II) hydride com-
pound. The reaction of 2 with (DippNacnac)ZnI
(DippNacnac, [(DippNCMe)2CH]−; Dipp, 2,6-
diisopropylphenyl) was similarly tested to ex-
amine whether the formation of a (hitherto
unknown) Zn–Be bond could be achieved (Fig.
2, right). In a similar fashion, 1H NMR spec-
troscopy indicates the complete consumption
of 2, along with quantitative formation of
CpBeI and a (DippNacnac)-containing species.
Additionally, the formation of a small amount
of dark gray metallic precipitate was observed.
Crystallization from hexane yielded CpBeZn
(DippNacnac) (5), which was structurally au-
thenticated by single-crystal x-ray diffraction
(fig. S21).
The Zn–Be bond within compound 5 repre-
sents a very rare example of a beryllium-metal
bonding combination and provides further evi-
dence for the constitution of 2 itself (25, 27, 41).
The Zn–Be bond distance within 5 [2.169(10) Å]
is in line with the sum of the covalent radii of
Be and Zn (2.20 Å) and is consistent with the
presence of a covalent metal-metal bond (29).
Additionally, 5 exhibits a 9Be NMR resonance
(−27.7 ppm) that is consistent with a very
electron-rich beryllium metal center, similar
to those of 1 and 2 (25, 34). Quantum chemical
calculations performed on 5 (B3LYP D3BJ
def2-TZVP def2/J) yield a similar Zn–Be dis-
tance (2.175 Å) to that determined crystallo-
graphically and indicate that the HOMO is a
Zn–Be s-bonding orbital (fig. S30). On the
basis of the Pauling electronegativities of be-
ryllium (1.57) and zinc (1.65), compound 5 might
be assigned a beryllium(II)/zinc(0) formalism.
However, quantum chemical calculations indi-
cate considerable covalent contributions to
the Zn–Be bonding in this compound, in simi-
lar fashion to the Be–Al bonding in 1 (25). For
example, NPA calculations imply that the va-
lence orbitals of both zinc and beryllium are
substantially populated (Be, 2s, 1.00 e– and 2p,
0.16; Zn, 4s, 1.04 e–). Additionally, NBO analy-
sis suggests that beryllium and zinc make
almost equal contributions to the Zn–Be bond
(Zn:Be, 49.9:50.1). Thus, a beryllium(I)–zinc(I)
formulation seems a more appropriate descrip-
tor for 5.
After half a century, diberyllocene (2) has
been synthesized. The Be–Be distance in 2
[2.0545(18) Å] is in line with all previous quan-
tum chemical investigations of this com-
pound. Moreover, 2 reacts as a reductant
and can be used to synthesize beryllium-metal
bonds.
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AC KNOWLED GME NTS
Funding: J.T.B. thanks St John’s College, Oxford, for a Junior
Research Fellowship. We thank the John Fell Fund (0011792) for
financial support. We thank the EPSRC Centre for Doctoral Training
in Inorganic Chemistry for Future Manufacturing (OxICFM, EP/
S023828/1 studentship for L.L.W. and A.E.C.). Author
contributions: J.T.B.: conceptualization, investigation,
visualization, writing – original draft, writing – review and editing,
funding acquisition, supervision, and project administration. A.E.C.:
quantum-crystallographic investigations, writing – review and
editing. L.L.W.: collection and processing of x-ray crystallographic
data, writing – review and editing. S.A.: supervision, project
administration, and writing – review and editing. Competing
interests: The authors declare no competing interests. Data and
materials availability: X-ray data are available free of charge from
the Cambridge Crystallographic Data Centre under reference
numbers CCDC 2245595 (2), 2245596 (5), and 2246346
[(MesNacnac)MgCp]. All other experimental, spectroscopic,
crystallographic, and computational data are included in the
supplementary materials. Computational data are also available
through Dryad (42). License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh4419
Materials and Methods
Figs. S1 to S35
Tables S1 to S3
References (43–56)
Submitted 6 March 2023; accepted 25 April 2023
10.1126/science.adh4419
Boronski et al., Science 380, 1147–1149 (2023)
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RES EARCH
METALENSES
Extreme ultraviolet metalens by vacuum guiding
Marcus Ossiander1*†, Maryna Leonidivna Meretska1†, Hana Kristin Hampel2†, Soon Wei Daniel Lim1,
Nico Knefz2, Thomas Jauk2, Federico Capasso1*, Martin Schultze2*
Extreme ultraviolet (EUV) radiation is a key technology for material science, attosecond metrology,
and lithography. Here, we experimentally demonstrate metasurfaces as a superior way to focus
EUV light. These devices exploit the fact that holes in a silicon membrane have a considerably
larger refractive index than the surrounding material and efficiently vacuum-guide light with a
wavelength of ~50 nanometers. This allows the transmission phase at the nanoscale to be controlled
by the hole diameter. We fabricated an EUV metalens with a 10-millimeter focal length that supports
numerical apertures of up to 0.05 and used it to focus ultrashort EUV light bursts generated
by high-harmonic generation down to a 0.7-micrometer waist. Our approach introduces the vast
light-shaping possibilities provided by dielectric metasurfaces to a spectral regime that lacks
materials for transmissive optics.
D ielectric metasurfaces consist of trans-
parent nanostructures with subwave-
length separation, which manipulate
the phase of light on the nanoscale (1).
This elaborate control is revolutioniz-
ing modern optics: Metasurfaces can replace
bulk optics by thin and flat elements (2, 3),
combine multiple functions in single optical
elements (4, 5), and be used to realize inno-
vative optical components that induce, for
example, freely designable optical angular
momentum (6) and polarization (7, 8). Tech-
nology, including modern semiconductor
lithography, demands this design liberty for
innovative optical elements for ever-shorter
wavelength radiation, but this development
has been stalled at ultraviolet frequencies
where dielectrics stop being transparent. To
our knowledge, linear metaoptics have only
been demonstrated down to a wavelength of
≈250 nm (9–11). Nonlinear metasurfaces reach
further into the ultraviolet spectrum at the cost
of indirect light-shaping mechanisms and have,
at present, been demonstrated down to a wave-
length of 185 nm (12–15).
Inaccessible to metasurface design has been
extreme ultraviolet radiation (EUV), which
covers the wavelength range from 10 to 121 nm
and corresponds to a photon energy of 10 to
124 eV (16). This wavelength regime receives
appreciable attention as a gateway to achiev-
ing attosecond temporal resolution in ultrafast
spectroscopy (17) and lithographically fabricat-
ing nanometer-scale transistors in state-of-the-
art semiconductor industry (18). However, today,
all fields that use EUV radiation are encumbered
by handling problems that arise from being
limited to reflective or binary optics [e.g., to-
1John A. Paulson School of Engineering and Applied
Sciences, Harvard University, Cambridge, MA 02138, USA.
2Institute of Experimental Physics, Graz University of
Technology, 8010 Graz, Austria.
*Corresponding author. Email: mossiander@g.harvard.edu (M.O.);
capasso@seas.harvard.edu (F.C.); schultze@tugraz.at (M.S.)
†These authors contributed equally to this work.
roidal mirrors or Fresnel zone plates; see (19)
for an overview of existing technology]. Here,
we present a new physical mechanism for meta-
surface design and demonstrate how linear
metasurfaces can be realized at a wavelength
of 50 nm, thus providing the foundation for
general-purpose transmissive optics technology
for EUV radiation.
Principle of vacuum guiding and
metalens design
In the EUV, the strong absorption of most
materials and their near-unity real part of the
refractive indexes (20) usually prevent effective
refraction or waveguiding. The refractive in-
dexes of most dielectrics in the visible spectrum
are determined by electronic transitions in
the ultraviolet, that is, by resonances whose
frequencies are higher than the frequency w
of visible light. In the Drude-Lorentz oscillator
model, this results in a complex refractive index
~n wð Þ ¼ n wð Þ þ ik wð Þ for visible light, with a real
part n ≥ 1, the imaginary unit i, and a negligi-
ble absorption coefficient k. By contrast, EUV
light oscillates faster than these electronic
resonance frequencies, resulting in n ≤ 1 and a
large absorption coefficient k, which renders
conventional transmissive metaoptics design
unfeasible. For the same reason, EUV manip-
ulation must rely on reflective glancing-angle
mirrors in vacuum. The concept for metasur-
face design introduced here is visualized in
Fig. 1: In the EUV spectrum, vacuum or air
(n = 1) has a refractive index that is larger than
that of a pillar made from n < 1 material; there-
fore, the pillar cannot guide or confine light.
However, a void or hole (n = 1), that is, the
absence of material, in a layer with mate-
rial index n < 1 can act as a waveguide core
surrounded by a lower-index cladding. There-
fore, truncated waveguide metasurfaces are
possible in the EUV by following an inverted
design scheme that tunes nanohole dimen-
sions instead of the shapes of free-standing
nanostructures.
Materials with n < 1 that can be used to re-
alize such metasurfaces exist throughout the
EUV; for example, aluminum, silicon, and be-
ryllium allow optics for the wavelength range
from 40 to 90 nm; scandium and boron cover
20 to 40 nm; and rhenium, molybdenum, and
zirconium cover 10 to 20 nm. Figure S1 com-
piles the refractive indexes and the trans-
mission of these materials. Because of the
availability of high-brightness laser-driven tin
plasma sources, 13.5 nm is a wavelength of
major importance for semiconductor lithog-
raphy (18). At this wavelength, for example,
ruthenium has the complex refractive index
~n ¼ 0:88 þ 0:02i (21).
For the implementation of this concept, we
chose a thin membrane of crystalline silicon
as the base material and a cylindrical hole as
the polarization-independent guiding struc-
ture. These are schematically shown (Fig. 1, A
and C) together with the real part of the silicon
refractive index in the EUV (22) and the trans-
mission through a 220-nm-thick silicon layer
(Fig. 1B). To highlight the vacuum-guiding
behavior of the holes, the simulated intensity
profile of light with a vacuum wavelength of
lvac = 50 nm incident on such a perforated
silicon membrane [80-nm hole diameter in a
square 120-nm–by–120-nm unit cell, periodic
boundary conditions; see section 1 of (19) for
simulation details] is plotted in Fig. 1D: At the
center of the membrane (110 nm after its front
surface), 84% of the energy of an incident plane
wave is transmitted within the hole, whereas
16% of its energy is transmitted in the silicon.
However, the hole only covers 34% of the unit-
cell area. Because most power is transmitted in
vacuum, absorption in silicon is limited, and
the overall transmission is enhanced relative to
that of the unstructured film: An unstructured
220-nm-thick silicon membrane transmits 28%
of incoming 50-nm light. Accounting for the
80-nm-diameter hole using its area coverage
would increase transmission to 52%. Vacuum
guiding increases the transmission further
to 67%.
Although perforations have been used in
nano-optics before, the presented guiding
mechanism is fundamentally different from
antiguiding in holes (23), low-index guiding in
air (24), or hollow-core fibers (25). Furthermore,
the enhancement does not require a periodic
structure, which distinguishes the effect from
extraordinary optical transmission (26).
To realize our EUV metasurface (Fig. 1A),
with full design flexibility to emulate the phase
profile of a desired optical element, we numer-
ically created a library of meta-atoms based on
the transmission phase of holes with 20- to
80-nm diameters in a 220-nm-thick silicon
membrane [see section 1 of (19) for simulation
details]. Notably, between wavelengths of 50
and 62 nm, the photon energy–dependent
transmission phase is widely tunable by the
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Fig. 1. Vacuum-guiding enables EUV metalenses. (A) Concept
and simulation of a metalens that is focusing EUV: We impart
the phase profile of an aspheric focusing lens on light pulses
with a vacuum wavelength of 50 nm (purple disks) using
holes through a silicon membrane (rectangular area). Because
the refractive index of silicon is smaller than unity in parts
of the EUV spectrum, holes through silicon concentrate
incoming light. This effect relaxes subwavelength requirements
for creating metasurfaces, allows us to impart a hole size–
dependent phase shift using feature sizes on the order of the
vacuum wavelength, and increases transmission through
the absorbing membrane. The false color plot illustrates this
light concentration in the holes and how the ultraviolet
radiation collapses into a focus after propagating the focal
length. For better visibility, we cut the displayed metasurface
and the light-intensity distribution along a plane that includes
the optical axis. Further simulation details are presented
in Fig. 4. (B) Photon energy–dependent real part of the
refractive index of crystalline silicon [blue line, data from
(22)] in the EUV spectrum and intensity transmission of
a 220-nm-thick silicon membrane (red line). The frequencies
of the bulk wP and surface plasmon wSP are marked in
purple. (C) Schematic and setup for meta-atom simulation:
EUV light (purple arrow) passes through a 220-nm-thick
crystalline silicon membrane (blue) with a hole with diameter
d. We model a single unit cell (120 nm by 120 nm) with
periodic boundary conditions. (D) Finite-difference time-domain simulation of EUV vacuum-guiding through an 80-nm-diameter hole in a 220-nm-thick silicon
membrane. The false color plot shows the transverse beam intensity profile of light with a vacuum wavelength of 50 nm at the midpoint of the silicon membrane along
the propagation direction, that is, 110 nm after the front surface. The hole is indicated as a blue circle. The simulation setup in three dimensions is shown in (C). The
hole covers 34% of the total area; however, 84% of the energy is transmitted within the hole and only 16% of the energy is found in silicon. The intensity decays
exponentially into the silicon cladding because of the refractive index contrast. The overall transmission of the patterned 220-nm-thick silicon membrane is 67%.
Fig. 2. Design and fabrication of an EUV metalens.
(A) Photon energy–dependent transmission phase of holes in a
220-nm-thick silicon membrane (see Fig. 1C for the unit cell),
color coded for different hole sizes. The gray area indicates the
region where hole diameters from 20 to 80 nm offer phase
coverage larger than 1.5p, which is enough to achieve efficient
and diffraction-limited focusing (27). (B) Overall hole diameter–
dependent intensity transmission (purple crosses) and
transmission phase in the forward direction (blue circles) of
the resulting meta-atom library at 50-nm wavelength (25-eV
photon energy). Because the 120-nm–by–120-nm unit-cell size
is comparable to the wavelength, low diffraction orders can
be generated for holes that cause a transmission phase shift
close to p (diameters around 45 nm). When plotting only
the transmission into the zeroth diffraction order (red circles) of
a periodic array of same-diameter holes, this causes a dip
in the transmission. Because hole diameters spatially vary in a
metalens and light from all holes interferes constructively to a focus, the more uniform overall transmission (purple crosses) is a better gauge to judge transmission
uniformity. (C) Target transmission-phase profile (blue line) of a metalens with focal length f = 10 mm at 50-nm wavelength, calculated from Eq. 1 modulo 2p, and
the corresponding matched hole diameter (red circles) using the library of (B) to realize the metalens. (D) Shown at the bottom is a scanning electron microscope (SEM)
picture of a 3-mm–by–0.5-mm portion of the metalens with 1-mm diameter and 10-mm focal length designed for 50-nm wavelength. The position where the picture
was taken on the metalens is marked by the purple arrow in (G). Shown at the top is the design of the metalens in this area [compare with (C)]. (E) Cross section of a
metalens fabricated using the same recipe as the lens in (D) on the silicon-on-insulator carrier wafer obtained using focused-ion-beam milling and SEM. The position
where the picture was taken on the metalens is marked by the purple arrow in (G). (F) Zoomed-out SEM picture of a 34-mm–by–31-mm portion of the metalens.
The position where the picture was taken on the metalens is marked by the green rectangle in (G). The focusing pattern of the metalens is apparent from the ring
segments, which show decreasing width from left to right. Every 10 mm, holes are omitted to increase the stability of the metalens, which is visible as a square scaffolding
pattern. The symmetry of the scaffolding is intentionally different from the symmetry of the metasurface to increase stability. (G) Optical microscope picture of the
final metalens membrane. The metalens (ML) is encircled by the dashed blue line. Because its features are too small to be resolved at this magnification, the metalens
shows a moiré pattern (ring patterns and bright area at the center; an enlarged image is provided in fig. S4). The unpatterned silicon membrane area appears
solid gray (encircled by the dashed red line). Areas with a remaining buried oxide layer appear red and green because of thin-film interference (encircled by the dashed
yellow line). The silicon carrier wafer appears black.
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RES EARCH | R E S E A R C H A R T I C L E
hole diameter and offers more than 1.5p trans-
mission phase coverage with an average trans-
mission of 40% at 50 nm (see Fig. 2A for the
photon energy–dependent transmission phase,
Fig. 2B for the transmission and transmission
phase at 50 nm, and fig. S2 for the photon energy
dependent transmission). This transmission-
phase coverage is enough to achieve efficient
and diffraction-limited focusing, as explored,
for example, in (27). The metasurface unit cell
is shown in Fig. 1C, and the corresponding
library is shown in Fig. 2B.
Experimental results
To experimentally prove that the vacuum-
guiding concept yields viable EUV metalenses,
we forward-designed a focusing EUV metasur-
face by mimicking the wavelength-dependent
transverse hyperbolic phase profile (28)
(cid:4)
2p
lvac
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
r2 þ f 2
ϕ r; lvac
Þ ¼ (cid:2)
ð1Þ
(cid:2) f
p
(cid:3)
ð
p
of an aspheric lens with focal length f = 10 mm
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
x2 þ y2
in vacuum at transverse position r ¼
(x and y are the cartesian coordinates centered
at the beam axis). This analog phase profile
is matched by a simulated digital phase profile
(sampled at positions x, y; x = kDx; y = lDy;
k; l ∈ ℤ; and Dx = Dy = 120 nm; k and l are
integer indexes) using the hole library (Fig.
2B), yielding a recipe for the required hole-
diameter distribution (Fig. 2C). The metalens
is designed for a central vacuum wavelength of
lvac = 50 nm, where silicon features a refractive
index ~n ¼ 0:77 þ 0:02i. The smaller-than-unity
real part at this wavelength partially relaxes the
necessity for true subwavelength patterning,
which facilitates the manufacturing of the meta-
optical element. In the given implementation,
the maximum feature size (80 nm) and unit cell
size (120 nm) correspond to 1.2 and 1.8 times
the inside-silicon wavelength lSi, respectively.
Although this does not entirely prevent the for-
mation of low diffraction orders that contain up
to 53% of the transmitted light, it still allows the
realization of numerical apertures up to NA <
lvac
2Dx ¼ 0:2 following the Nyquist theorem (29).
The demonstration sample, a free-standing
metalens with a 1-mm diameter (numerical
aperture NAmax = 0.05), is realized from silicon-
on-insulator wafers [see section 2 of (19) and
fig. S3 for fabrication details]. Figure 2, D and F,
shows scanning-electron microscopy pictures
of the final sample after metasurface etching
but before membrane isolation. Figure 2G
shows a light microscopy picture of the finished
membrane, with thin-film interference colors
confirming the complete removal of the buried
oxide layer in the lens area. We achieved the
designed hole diameters (see Fig. 2D) using
both diameter-dependent electron beam lithog-
raphy doses and diameter-dependent fabrication
offsets [see section 2 of (19)]. A focused-ion-beam
cut (Fig. 2E) through a sample reveals holes
Fig. 3. Experimental demonstration of EUV metalens focusing. (A) An intense near-infrared femtosecond
laser pulse (red arrow and area) is focused into an argon gas target (green) to generate an attosecond
pulse train (purple arrow and area) by high-harmonic generation. Near-infrared radiation is blocked using
an aluminum filter foil (gray). The attosecond pulse train is then focused using the metalens (blue) pictured
in Fig. 2. At the position of the focus along the propagation direction (marked z), a knife-edge scan is
performed using a razor blade mounted on a piezo stage moving along the transverse beam direction
(marked x). Afterward, the attosecond pulse train’s spectral components are split using a grazing incidence
toroidal grating, and the focal plane is imaged on a charge-coupled device (CCD) camera. (B) EUV beam
profile after the metasurface (false color plot) at 25.3-eV photon energy (21st harmonic of the driving laser at
1030-nm wavelength) detected by the CCD. For comparison, we repeat the outlines from the microscopy
image in Fig. 2G: The dashed blue line marks the metasurface, and the dashed red line marks the
unpatterned silicon area. The granular structure with low intensity is already present in the incoming beam
profile, which is plotted in fig. S5. The focal spot created by the metalens, which is imaged onto the
CCD using the toroidal grating, is marked by the green dashed rectangle. It appears larger than the real focus
because of the limited numerical aperture of the toroidal grating and aberrations caused by the imaging
system. (C) Knife-edge scans for different positions along the propagation direction of the metasurface-
focused beam [movement direction marked z in (A)]. The colored lines show the knife position–dependent
[movement direction marked x in (A)] integrated photon flux detected by the CCD camera in the focus
area. As the razor blade moves into the focus, it blocks part of the transmitted radiation and decreases the
transmitted flux. A large negative derivative of the flux represents a small focus. The error bars represent
the standard deviation of three measurements. The black lines are least-squares fits to the data assuming a
Gaussian focus profile. (D) Same as (C) but in close proximity to the focus. The error bars represent
the standard deviation of 10 measurements. (E) Propagation direction–dependent waist sizes extracted from
the fits in (C) and (D) (blue dots). The error bars represent the 95% confidence interval. The red line
is a fit to the waist sizes assuming Gaussian beam propagation. The inset shows a zoomed-in view of the
propagation direction–dependent waist size close to the focus [extracted only from the fits in (D)]. The
minimum waist sizes reported in the text are marked by the black arrow.
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Fig. 4. Finite-difference time-domain modeling and benefits of an EUV
metalens. (A) Target transverse-phase profile (blue line) of a diffraction-limited
metalens (focusing length f = 10 mm, size 6 mm by 6 mm) designed for incoming
light with 50-nm wavelength (25-eV photon energy) and sampling of this
phase profile with the library presented in Fig. 2 (green crosses). As a comparison,
the transmission profile of a binary intensity Fresnel zone plate with the
same numerical aperture, focal length, and size is also shown (red line). (B) On
the left is a two-dimensional design of a metasurface that realizes the phase
profile in (A). White areas represent a 220-nm-thick silicon membrane, and
blue areas represent holes through the silicon membrane. On the right is a
two-dimensional design of a binary intensity Fresnel zone plate that realizes the
transmission profile in (A). White areas are perfectly transmitting, and red
areas are perfectly absorbing. (C) Modeled transverse intensity cuts through
the focus generated by the metasurface (blue dashed line) and the zone plate
in (B) (red line) for incoming light with 50-nm wavelength (25-eV photon
energy) and illumination by a Gaussian beam with a 2-mm waist. The zone-plate
focus has characteristic side lobes that are not present in the metasurface
focus. (D) Shown on the left is the modeled light-intensity evolution (false color
plot) after the metasurface pictured in (B) focuses the Gaussian beam
described in the caption of (C). Shown on the right is the modeled light-
intensity evolution (false color plot) after the zone plate pictured in (B) focuses
the same Gaussian beam.
with square sidewalls and a partial etch of the
smallest diameter holes. Because of the small
transmission-phase difference between a mem-
brane with small holes and a solid membrane
(see Fig. 2B), the resulting phase error is smaller
than 0.1p and can be corrected during meta-
atom library calculation.
For experimental verification of the focusing
power of the metalens, we generated diverging
EUV attosecond pulse trains through near-
infrared femtosecond laser pulse–driven high-
harmonic generation in argon gas (30–32)
[Fig. 3A and section 3 of (19)]. The frequency
up-conversion extends up to the 35th order
(42.1-eV photon energy, 29-nm wavelength) of
the driving laser pulses (1.2-eV photon energy,
1030-nm wavelength), with spectral power con-
centrated around the laser’s odd harmonics. A
toroidal EUV grating disperses the spectral
components of the attosecond pulse train and
creates a frequency-resolved image of the focal
plane on an EUV-sensitive camera where the
metasurface’s effect at the design wavelength
can be inspected.
Figure 3B shows the beam profile at the focal
plane of the metalens of the 21st harmonic with
25.3-eV photon energy and 49-nm wavelength
(close to the design wavelength of the optics).
The outline of the circular metasurface (dashed
blue line) and features caused by the remaining
silica aperture (dashed red and yellow lines;
compare with Fig. 2G and fig. S4) are also vis-
ible. The bright focal spot at the metasurface
center (dashed green line) presents experi-
mental evidence for the viability of the EUV
metalens to focus incident light.
Because the grazing incidence toroidal im-
aging grating provides a considerably smaller
numerical aperture than the metasurface and
introduces aberrations and astigmatism, the
obtained image does not determine the focal
spot diameter and underestimates the focus-
ing power of the optical element. To deter-
mine the real focal spot size produced by the
metasurface, we implemented a knife-edge
scan [see Fig. 3A and (33)], where part of the
focused beam in the focal plane is gradual-
ly blocked by a razor blade translated along
the x direction indicated in Fig. 3A and the
position-dependent transmitted intensity is
recorded. As focusing concentrates the beam
intensity along the transverse direction, the
negative spatial derivative of the recorded
x-dependent intensity reveals the beam pro-
file. Figure 3, C and D, displays scan results
for different planes along the propagation di-
rection around the focus. Figure 3D includes
a knife-edge scan that features a maximum
negative spatial derivative, which is indic-
ative of the focal plane. Under the assump-
tion of a cylindrically symmetric Gaussian
beam, the corresponding beam size is ex-
tracted by fitting an error function to the data
at each position along the propagation direc-
tion (Fig. 3E) (33).
p
¼ w
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
x2 þ y2
We observe that the metasurface focuses
the illuminating beam to a minimum waist of
= 0.7 ± 0.3 mm [all reported waists
wmetasurface
0
w are measured using the 1/e2 intensity, that is,
(cid:6)
(cid:5)
Þ=e2]. Using
I r ¼
the Rayleigh-Sommerfeld diffraction integral
(34), we calculated the minimum achieva-
= 0.45 mm, assuming
ble waist wdiffractionlimit
0
diffraction-limited focusing of our incoming
beam (see fig. S5), which highlights that the
metalens already performs within 1.6 times of
ð
¼ I r ¼ 0
the diffraction limit. For further comparison,
the measured propagation distance–dependent
waist size w(z) can be fitted to that of a focused
Gaussian beam with minimum waist w0 (35)
in vacuum:
w zð Þ ¼ w0
ð2Þ
s
(cid:7)
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(cid:8)
2
zlvac
pw2
0
1 þ
0
The fit (see Fig. 3E) suggests a minimum pos-
sible waist size of wmetasurface
= 0.56 ± 0.03 mm,
which is even closer to the diffraction limit.
Both results overlap within the experimental
uncertainty. We attribute the deviation from
the diffraction limit to imperfections in the
EUV beam guiding and filtering optics and
possible residual corrugations of the silicon
membrane. For comparison, achieving similar
spot sizes using the near-infrared driving laser
would require close-to-unity numerical aper-
tures; in the EUV, only a numerical aperture of
0.05 is required (36).
Aside from the focusing power, the transmis-
sion properties are crucial for future applica-
tions. Photons with wavelengths shorter than
100 nm possess enough energy to overcome
the bandgap of all known dielectrics; there-
fore, large absorption is unavoidable (37). None-
theless, owing to the vacuum guiding concept,
our sample transmits more than 10% of all
incoming 49-nm light and focuses 48% of the
transmitted 49-nm light, which limits the root-
mean-squared metalens wavefront error (38)
due to fabrication accuracy to lvac/10 [lvac =
49 nm; see section 4 of (19) for details]. Such
fine-granular phase control not only is a pre-
requisite for focusing but also opens the door
for the future demonstration of optical angular
Ossiander et al., Science 380, 59–63 (2023)
7 April 2023
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RES EARCH | R E S E A R C H A R T I C L E
momentum plates and general holograms at
EUV wavelengths.
Simulation of Nyquist-limited focusing
To further explore the potential of EUV meta-
lenses, we investigated a metalens design with
focal length f = 10 mm and overall optics di-
ameter d = 6 mm (see Fig. 4A for the phase
profile and Fig. 4B for the final design). We
then simulated the focusing of a linearly po-
larized Gaussian beam using finite-difference
time-domain modeling [illuminating Gaussian
beam waist willum: = 2 mm, and effective nu-
i
merical aperture NAeff ¼ sin tan(cid:2)1 willum:
willum:
f ¼ 0:2 (36), which corresponds to the max-
imum realizable numerical aperture given by
the Nyquist sampling theorem and our unit cell
size (29); see section 1 of (19) for simulation
details].
(cid:3)
≈
(cid:4)
h
f
0
0
Figure 4D shows the formation of the meta-
surface focus. Even under these challenging con-
ditions, the metasurface focus closely approaches
the diffraction limit (wdiffractionlimit
= 85 nm)
with a minimum beam waist wmetasurface
=
94 nm. The metalens focusing properties for a
light pulse with extended bandwidth are ex-
plored in section 5 of (19) and fig. S6. Having the
unit cell size be of the order of the design wave-
length causes diffraction of ~53% of the inci-
dent power away from the beam axis into the
diffraction orders of the quasi-periodic unit-cell
arrangement. Adding an unpatterned layer of
silicon with a refractive index n = 0.77 and a
thickness on the order of half a wavelength after
the metalens changes the grating condition in
transmission and would prevent the creation of
most of these propagating diffraction orders [be-
cause it limits the grating indices p; q ∈ ℤ that
satisfy the transverse momentum wavevector
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(cid:3) (cid:4)
(cid:6)2 þ 2pq
(cid:5)
2
2pp
Þ2
condition nk0 ¼
Dx
with the overall momentum k0 and the mo-
mentum along the layer normal kz].
ð
þ nkz
r
Dy
,
For thorough comparison, we also modeled
the focal profile of a binary absorption zone
plate with equal numerical aperture (see Fig. 4A
for the absorption profile and Fig. 4B for the
design). The juxtaposition of the focal profiles
generated by the zone plate and the metalens
shown in Fig. 4D highlights notable differences
in focus quality and corroborates the benefit
of the innovative metalens. A comparison with
state-of-the-art technology [see (39) for a zone
plate with comparable outermost zone width
and section 6 of (19) for a summary of EUV
focusing optics] highlights that the zone plate
creates side lobes in its focal plane, which is an
unavoidable property of zone plate foci (40).
By contrast, because the metasurface realizes
the focusing phase profile accurately by sup-
pressing spherical aberrations, no sidelobes are
visible. Furthermore, because vacuum guiding
decreases absorption and no energy is lost to
sidelobes, the maximum intensity in the meta-
surface focus exceeds that of the zone plate by
9%. The transverse focal cuts in Fig. 4C high-
light this behavior: Unwanted features present
in the focal plane are suppressed by more than
10 dB for the metasurface compared with the
zone plate.
Concluding remarks
The transfer of metasurface technology, with
its associated superior design freedom to the
EUV spectral region, provides a general route
to manufacture transmissive optics in this fre-
quency range. This capability should lead to
applications such as microscopy with unprec-
edented spatial and temporal resolution, orbital
angular momentum beams with ultrahigh fre-
quency, and structured light that has direct
access to core-level electronic transitions in
atoms and molecules. EUV lithography has
become the main enabling fabrication tech-
nology that allows us to keep up with Moore’s
law (18); conversely, metasurface-based optics
can be fabricated with deep ultraviolet lithog-
raphy in the same semiconductor foundries
of mainstream complementary metal-oxide-
semiconductor (CMOS) technology (27). This
convergence of semiconductor-processing tech-
nology and optics will expand to the realization
of metaoptics using EUV lithography, further
shrinking feature sizes and increasing the
complexity of nanostructure shapes. In turn,
with metasurfaces operating in the EUV, they
will enable a new generation of lithography
optics.
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AC KNOWLED GME NTS
Funding: This work was performed, in part, at the Center
for Nanoscale Systems (CNS), a member of the National
Nanotechnology Coordinated Infrastructure (NNCI), which is
supported by the NSF under award no. ECCS-2025158. CNS is a
part of Harvard University. The computations in this paper
were run on the FASRC Cannon cluster supported by the FAS
Division of Science Research Computing Group at Harvard
University. M.O. acknowledges funding by the Alexander von
Humboldt Foundation (Feodor-Lynen Fellowship), the Austrian
Science Fund (FWF, Start Grant Y1525), and the European
Union (grant agreement 101076933 EUVORAM). The views and
opinions expressed are, however, those of the author(s) only
and do not necessarily reflect those of the European Union
or the European Research Council Executive Agency. Neither
the European Union nor the granting authority can be held
responsible for them. S.W.D.L. is supported by A*STAR Singapore
through the National Science Scholarship Scheme. F.C.
acknowledges financial support from the Air Force Office of
Scientific Research (AFOSR) under award number FA9550-21-1-
0312. Author contributions: M.O. developed the project,
designed the metalenses, and conducted the numerical
modeling. M.L.M. fabricated the samples. M.L.M., S.W.D.L.,
and M.O. imaged the samples. H.K.H., M.O., N.K., T.J., and
M.S. designed, conducted, and analyzed the experiment. M.O.,
M.S., and F.C. wrote the manuscript. All authors discussed
the final version of the manuscript. Competing interests:
M.O., M.L.M., S.W.D.L., and F.C. have filed a provisional patent
application (US 63/385,066). The authors declare no other
competing interests. Data and materials availability: The data
that support the findings of this study are included in the
manuscript and the supplementary materials and are archived
at figshare (41). License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to
original US government works. https://www.science.org/about/
science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg6881
Materials and Methods
Figs. S1 to S6
References (42–62)
Submitted 15 January 2023; accepted 7 March 2023
10.1126/science.adg6881
Ossiander et al., Science 380, 59–63 (2023)
7 April 2023
5 of 5
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10.1126_science.adg7883
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RES EARCH
STRUCTURAL BIOLOGY
Structure of the R2 non-LTR retrotransposon
initiating target-primed reverse transcription
Max E. Wilkinson1,2,3,4,5, Chris J. Frangieh1,2,3,4,5,6, Rhiannon K. Macrae1,2,3,4,5, Feng Zhang1,2,3,4,5*
Non–long terminal repeat (non-LTR) retrotransposons, or long interspersed nuclear elements (LINEs),
are an abundant class of eukaryotic transposons that insert into genomes by target-primed reverse
transcription (TPRT). During TPRT, a target DNA sequence is nicked and primes reverse transcription
of the retrotransposon RNA. Here, we report the cryo–electron microscopy structure of the Bombyx mori
R2 non-LTR retrotransposon initiating TPRT at its ribosomal DNA target. The target DNA sequence is
unwound at the insertion site and recognized by an upstream motif. An extension of the reverse
transcriptase (RT) domain recognizes the retrotransposon RNA and guides the 3′ end into the RT active
site to template reverse transcription. We used Cas9 to retarget R2 in vitro to non-native sequences,
suggesting future use as a reprogrammable RNA-based gene-insertion tool.
N on–long terminal repeat (non-LTR) ret-
rotransposons are the most abundant
class of mobile genetic element (MGE)
in the human genome, primarily rep-
resented by the LINE-1 and SINE (or
Alu) long and short interspersed nuclear ele-
ments, respectively (1). Despite their prevalence
and contribution to genetic diversity and dys-
regulation through mutagenicity and recombi-
nation (1–3) and their prospective use as gene
insertion tools, there is much left to understand
about the mobility mechanisms of non-LTR
retrotransposons (4). Pioneering research
on the Bombyx mori (silk moth) R2 element
(R2Bm), which selectively inserts into the 28S
ribosomal RNA (rRNA) gene, has contributed
substantially to our understanding of this type
of MGE (5). R2, like all non-LTR retrotranspo-
sons, encodes an open reading frame (ORF)
with DNA binding, endonuclease, and reverse
transcriptase activities (Fig. 1A). The endonu-
clease domain (restriction-like endonuclease,
RLE) nicks the target DNA, and the reverse
transcriptase domain uses the exposed 3′ end
from the nick to prime reverse transcription
of the R2 RNA, resulting in a new genomic
copy of the R2 element (Fig. 1B) (6, 7). This
process is called target-primed reverse tran-
scription (TPRT) and is characteristic of non-
LTR retrotransposons and their group II intron
ancestors (8, 9). The nicked strand that primes
reverse transcription is referred to as the bot-
tom strand. Complementarity between the bot-
tom strand and the 3′ end of the R2 RNA (3′
1Howard Hughes Medical Institute, Cambridge, MA 02139,
USA. 2Broad Institute of MIT and Harvard, Cambridge, MA
02142, USA. 3McGovern Institute for Brain Research,
Massachusetts Institute of Technology, Cambridge, MA
02139, USA. 4Department of Brain and Cognitive Science,
Massachusetts Institute of Technology, Cambridge, MA
02139, USA. 5Department of Biological Engineering,
Massachusetts Institute of Technology, Cambridge, MA
02139, USA. 6Department of Electrical Engineering and
Computer Science, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA.
*Corresponding author. Email: zhang@broadinstitute.org
homology) is not required to initiate reverse
transcription (10). Non-LTR retrotransposons
are specific for reverse transcribing their own
RNA; for R2, this specificity requires an ele-
ment in the 3′ untranslated region (3′UTR),
but the precise motif has not been located (11).
It is also unclear how R2 specifically recog-
nizes the 28S rRNA target gene, or how DNA
nicking is coupled to reverse transcription
within the same protein. To address these
questions, we solved a cryo–electron micros-
copy (cryo-EM) structure of R2Bm initiat-
ing TPRT at the 28S rRNA gene using its own
3′UTR. The structure reveals an extensive in-
terface with the target DNA, a small core re-
gion of the 3′UTR required for TPRT, and shows
that R2Bm can be engineered to reprogram its
insertion site.
Reconstitution and cryo-EM structure of an
R2 TPRT complex
We overexpressed R2Bm in Escherichia coli
and purified it to apparent homogeneity (fig.
S1). The purified protein was active in vitro,
reproducing previously found biochemical ac-
tivities, including RNA-stimulated nicking of
the target DNA bottom strand, site-specific
TPRT when supplied with in vitro–transcribed
3′UTR RNA, and low levels of template jump-
ing (Fig. 1C) (6, 12). It is unclear if 3′ homology
is required for TPRT in vivo; however, con-
sistent with previous findings, we found that
downstream sequences of up to 10 nucleotides
(nt) do not inhibit activity in vitro (Fig. 1C)
(10). Sequencing of TPRT junctions confirmed
that homology-mediated TPRT is more likely
to initiate reverse transcription at the 3′ end
of the 3′UTR rather than skipping bases or
inserting untemplated nucleotides (fig. S2) (10).
To assemble a complex stalled during initiation
of TPRT, we incubated R2Bm with target DNA,
3′UTR RNA, and the chain-terminator nucle-
otide 2′,3′-dideoxythymidine (ddT), which mi-
mics the first nucleotide incorporated in the
TPRT reaction (dT) but does not allow further
elongation. Purified TPRT complexes contained
stoichiometric amounts of R2Bm, 3′UTR RNA,
and target DNA with >99% of the bottom
strand nicked (fig. S1). Initial attempts at cryo-
EM imaging failed owing to the preferred
orientation and flexibility of the complex. To
overcome these issues, we used a carbon sup-
port on the cryo-EM grid and added 5 nt of
downstream 28S rRNA sequence to the 3′ end
of the 3′UTR RNA to stabilize the complex by
forming a primer-template duplex with the
target DNA bottom strand. With these mod-
ifications, we obtained a cryo-EM reconstruc-
tion of the R2 TPRT complex at 3.1-Å resolution
(Fig. 1D, figs. S3 and S4, and table S1).
The core of the R2Bm protein is a reverse-
transcriptase (RT) domain similar to that of
group II intron RTs (13), followed by a C-terminal
a-helical thumb domain and preceded by a
characteristic N-terminal extension domain
(NTE0) implicated in template switching (14),
but the R2Bm RT includes a further N-terminal
extension (NTE-1) that binds the 3′UTR RNA
(Fig. 1, E and F) (15). Preceding the NTE-1
element are two DNA binding domains: the
N-terminal C2H2 zinc finger domain (N-ZnF)
and a Myb domain. C-terminal to the thumb
domain lies an a-helical linker domain that
packs against the thumb, followed by a CCHC
zinc-finger domain (ZnF) conserved in many
LINE ORFs (4). The ZnF then links to the
C-terminal RLE domain, which cleaves the
target DNA. This domain arrangement closely
resembles that of Prp8 (13, 16, 17), the core
protein of the spliceosome, underscoring the
close relationship between pre-mRNA splicing
and retrotransposons.
There are several key interactions between
the R2Bm protein, 3′UTR RNA, and target
DNA (Fig. 1, E and F). The two strands of the
target DNA separate around the ZnF domain,
with the bottom strand feeding into the RLE
active site where the scissile phosphate remains
bound, while the top strand snakes along the
opposing surface of the RLE. The RT active
site contains a heteroduplex formed by the
nicked bottom strand of the target DNA (5′
to the cleavage site) and the 5 nt of 28S rRNA
homology extension beyond the 3′UTR RNA
(Fig. 1G). This target heteroduplex is sur-
rounded by residues important for RT activity
(18), and the cryo-EM density shows incorpo-
ration of the ddT chain terminator nucleotide
into the bottom strand (Fig. 1H). The 5′ end of
the bottom strand remains base-paired to the
top strand as it leaves the RLE, and this down-
stream DNA region has weak cryo-EM den-
sity, suggesting that it is not tightly bound by
R2Bm. The 248-nt 3′UTR RNA is mostly not
resolved in the cryo-EM density except for a
core 40-nt region, which wraps around the
NTE-1 a helix of R2Bm and the 3′ end of
which is guided into the RT active site via the
NTE0 domain.
Wilkinson et al., Science 380, 301–308 (2023)
21 April 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Cryo-EM structure of the R2Bm retrotransposon. (A) Domains of the R2Bm retrotransposon. ZnF, zinc finger; NTE, N-terminal extension; RT, reverse
transcriptase; RLE, restriction-like endonuclease. (B) Schematic of target-primed reverse transcription (TPRT). (C) Denaturing gel of in vitro TPRT reactions on a
labeled 211-bp 28S DNA target. The same gel was visualized by Cy5 fluorescence and toluidine blue staining. (D) Cryo-EM density of the R2Bm TPRT complex.
(E) Cartoon of the cryo-EM structure. Stars represent active sites. (F) Atomic model for the R2Bm TPRT complex. (G) Reverse transcriptase domain and template–
primer duplex. (H) Reverse transcriptase active site. Cryo-EM density is shown as a gray transparent surface.
R2Bm recognizes a sequence motif upstream
of the cleavage site
The target 28S DNA sequence has extensive
interactions with R2Bm (summarized in Fig.
2A). Upstream bases from –38 to –7 and down-
stream bases from +6 to +21 are respectively
paired, whereas the 11 base pairs from –6 to
+5 are melted around the RLE domain (bases
are numbered relative to the bottom-strand
cleavage site). The upstream DNA has a 40°
bend and binds along the surface of the RT,
linker, and thumb domains in a manner sim-
ilar to that of the DNA in a recent group IIC
intron maturase structure (Fig. 2B and figs.
S5 and S6) (19). Many of the contacts between
Wilkinson et al., Science 380, 301–308 (2023)
21 April 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
B
D
F
R958
scissile
+1
A
T
U
A
cDNA
T
A
A
...
+5
G
G
C
T
C
G
A
C
3
+5
+1
248
RT
C
WT:
1:
2:
3:
4:
-34
RUM
-22
RASIN
-27
DNA: WT
1
2
3
4
-35
-30
-25
-20
-15
-10
-7
R198
K149 R151 H673 K675
R119
H130 D761
K844
5
top strand
C G G
G
T
A A A C G G
C G G
G A G T A A C T A T G A C T C T C
RUM
bottom strand
G C C
C A T
T T G C C G C C
C T C A T T G A T A C T G A G A G
3
N1103
R935
A913
R919
C
1
2
6
A
K964
R
7
7
9
R1101
T1100
+1
+5
RLE
T A G C C
A G G
R
9
0
1
Q905
T
T
P
9
1
5
RASIN
-5
R
9
2
4
R
9
2
2
A A T T C C
D902
-1
R1093
L1090
N1098
G957
G1094
+10
A A A T G C C T C
T T T A C G
G A G
3
5
T189 R188
R125
K676
R132 R133
R517
H677
K772 R771
K786
R876
Q949
S1014
R961
V1012
3
base contact
stacking
Myb
RT6a loop
N-ZnF
ZnF
RLE
downstream DNA
+20
+10
3
5
RLE
active site
RASIN
bottom strand
Zn
ZnF
1
6
Linker
~120o
RLE
active site
RASIN
top strand
RLE
-6
-1
NTE0
RT
Myb
Zn
N-ZnF
RT6a
RUM
N-ZnF
NTE-1
upstream DNA
RT
RNA
DNA bottom strand
DNA top strand
upstream DNA
DNA top strand
DNA bottom strand
RUM library
RASIN
Nt.BbvCI
RUM-specific
cleavage
adapter ligation,
amplification,
sequencing
R2Bm
G
N-ZnF
Zn
R125
A(
A(
A(
T(
G(
K149
Myb
RUM
R198
A(
G(
RUM
H
G(
RUM top strand
C(
G(
K675
H673
RT6a
downstream DNA
R2Bm:
R2Bm:
WT
6a
= Cy5 (bottom strand)
28S RUM:
RUM screen:
2
s
1
t
i
b
0
E
I
C
G
AA
A
T
A
T
T
A
A
G
T
T
A
C
T
C
A
GC
C
C
T
G
A
A
T
G
C
34
22
position relative to bottom strand cleavage
27
T
G
A
25
A
T
A
T
30
-34
RUM
-22
RUM-RASIN
distance
-6RASIN
0
0
+3 +2 +1
R2Bm:
= Cy5 (bottom strand)
Fig. 2. Target DNA recognition upstream of the R2 cleavage site. (A) Schematic
of interactions with the target DNA. Bases are numbered relative to the bottom-
strand cleavage site. Positions of protein domains are shown by shaded rectangles.
(B) Structure of R2Bm around the upstream DNA sequences. (C) Effect of
upstream DNA mutations on target cleavage. The schematic shows the sequences
of five DNA sequences tested in top-strand sense; dots represent bases identical
to those of wild type. Red triangle, bottom-strand cleavage site. Denaturing gels
show in vitro TPRT reactions on labeled 211-bp 28S DNA targets. DN, deletion of
N-terminal N-ZnF and Myb domains. DRT6a, deletion of residues 672 to 677
(DGHRKK) of the RT6a loop. (D) Screen for identifying active RUM sequences.
Nicking sites of R2Bm and the restriction endonuclease Nt.BbvCI are shown
by triangles. (E) Sequence logo for sequences enriched in the RUM screen.
(F to H) Details of interactions between the target DNA and the N-ZnF, Myb,
and RT6a loop. (I) Effect of altering the distance between the RUM and RASIN
motifs. Denaturing gel shows in vitro TPRT reactions on labeled 211-bp 28S DNA
targets. Single-letter abbreviations for the amino acid residues are as follows:
A, Ala; D, Asp; E, Glu; F, Phe; H, His; K, Lys; L, Leu; P, Pro; Q, Gln; R, Arg; S, Ser;
T, Thr; V, Val; and Y, Tyr.
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Fig. 3. Target DNA recognition at the R2 cleavage site. (A) Interactions of the
top and bottom strands of the target DNA with the ZnF domain of R2Bm. Star,
RLE active site. (B) Interactions of the DNA bottom strand with the RLE domain.
(C) Interactions of the DNA top strand with the RLE domain. Residues mutated in
the RD>AA mutant are highlighted. (D) RASIN sequence requirements for bottom-
strand cleavage. The labeled 211-bp 28S DNA targets were incubated with R2Bm and
3′UTR RNA in the absence of deoxynucleotide triphosphates (dNTPs). The reactions
were analyzed with a denaturing gel. Mutations are notated in top-strand sense, but
both strands were mutated. (E) Denaturing gel showing R2Bm cleavage and TPRT
activity on partially stranded substrates. Reactions contained a fluorescein-labeled
76-nt bottom strand. Reactions as indicated also contained 17 nt of downstream
top-strand sequence (17d), 32 nt of upstream top strand sequence (32u), or 60 nt
of top-strand sequence fully complementary to the bottom strand spanning the
upstream and downstream regions. RD>AA, R2Bm R901A D902A.
R2Bm and the DNA are via the phosphate
backbone, suggesting that they are not se-
quence specific. Based on the structure, how-
ever, we predicted that two regions are key for
sequence-specific DNA recognition by R2Bm:
a 13-bp upstream motif from –34 to –22, which
is bound by the N-terminal N-ZnF and Myb
domains, and the 7 bp from –6 to +1, which are
bound by the RLE (Fig. 2A). We term these re-
gions the retrotransposon upstream motif
(RUM) and retrotransposon-associated inser-
tion site (RASIN), respectively.
Consistent with the importance of the RUM
region for R2 activity, mutating the entire up-
stream sequence between –38 to –7 eliminated
bottom-strand cleavage, whereas mutating the
downstream sequences between +6 and +37
preserved wild-type levels of bottom-strand
cleavage and TPRT (Fig. 2C) (20). Adding just
the 13-bp RUM region to the upstream mutant
at positions –34 to –22 restored near–wild-
type activity, whereas a point mutant RUM
(G–27 to C) did not rescue activity (Fig. 2C).
This region of the target was strongly pro-
tected in a previous deoxyribonuclease (DNase)
footprinting assay (21). To systematically de-
termine the importance of each base within
the RUM, we performed an R2 cleavage assay
on a DNA target with the upstream region
(–38 to –7) mutated and the RUM (–34 to –22)
replaced with a 13N library (Fig. 2D). Sequenc-
ing of cleaved targets revealed a consensus
RUM sequence A–31WWWGCNNNA–22, where
W is A/T and N is any nucleotide, with minor
preferences in other positions (Fig. 2E). This
consensus is a close match to the wild-type
28S sequence A–31ACGGCGGGA–22, with the
differences shown in bold.
The RUM is recognized by three domains:
N-ZnF, Myb, and an R2-specific insertion “6a”
in the RT domain between motifs 6 and 7 (Fig.
2B and fig. S7). The N-ZnF has the classical
C2H2 fold with a zinc ion coordinated between
an a helix and a b hairpin, but unusually the a
helix binds in the widened minor groove of the
DNA from bases –18 to –23 instead of the typ-
ical major groove (Fig. 2F and fig. S6) (22). The
preference for A at base –22 in the RUM is
likely due to N-ZnF Arg125, which hydrogen
bonds with the minor-groove–facing side of
the A–T base pair (Fig. 2F). The Myb domain
forms a typical three-helix bundle, with the
third helix bound in the major groove from
bases –31 to –34 (22) while its linker to N-ZnF
engages with base –30 (Fig. 2G). This is remi-
niscent of other Myb–DNA structures, in-
cluding telomere-interacting protein Rap1 (23).
The Myb domain recognizes the A at base –31
through hydrogen bonds with Lys149 (Fig. 2G).
Although Arg198 contacts bases at positions
–33 and –34, these contacts appear not to be
sequence specific, as the RUM screen showed
only weak sequence preferences in this region
(Fig. 2, E and G). Deletion of the N-ZnF and
Myb domains together (DN mutant) complete-
ly inhibits target DNA nicking and subsequent
TPRT (Fig. 2C) (20). The central GC of the RUM
is recognized by His673 and Lys675 of the loop
6a of the RT domain (Fig. 2H). Structural pre-
dictions suggest that this loop is specific among
non-LTR RT domains to R2 proteins (fig. S7).
We found that deletion of the 6a loop inhibits
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Fig. 4. Interactions of R2Bm with the 3′UTR RNA. (A) Secondary-structure
diagram of the 3′UTR RNA, based on (26). Thicker strokes represent nucleotides
visible in the cryo-EM density. Nucleotides are numbered from the first base
of the 3′UTR (the base following the stop codon). (B) Structure of the 3′UTR
RNA core and the R2Bm NTE-1 domain. Dotted lines, hydrogen bonds.
(C) Low-pass filtered cryo-EM map. (D) Interactions between 3′UTR bases. Dotted
lines, hydrogen bonds. (E) Secondary structure of the R2 tag RNA. Unshaded bases
are not in the full-length 3′UTR. (F) Denaturing gel of in vitro TPRT reactions on a
labeled 211-bp 28S DNA target using various R2 RNAs. Highlighted mutants are in the
J1/2 region. The same gel was visualized by Cy5 fluorescence and toluidine blue
staining. (G) The R2-tag allows TPRT of cargo RNAs. Denaturing gel shows TPRT
reactions with equimolar amounts of the indicated RNAs and a labeled 211-bp 28S DNA
target. R2 tag (43 nt) was added to the 3′ end of a 239-nt RNA encoding the CMV
promoter or a 764-nt RNA encoding GFP.
target DNA nicking (Fig. 2C). Finally, we found
that the distance between the RUM and the
bottom-strand cleavage site (the RASIN) is im-
portant. Increasing the distance by one base
was tolerated, but further increase or any de-
crease to the distance inhibited target cleavage
(Fig. 2I).
Target DNA interactions at the cleavage and
integration site
The second key region for DNA target recog-
nition by R2Bm is the target site for nicking
by the RLE domain and R2 insertion, which
we term the RASIN. In our structure, the 11 bp
of the RASIN from –6 to +5 are melted around
the RLE domain. The ZnF appears to act as
the “zip,” stacking on the last upstream pair
C–G(–7) with Arg922 and Arg924 and holding
unzipped strands apart (Fig. 3A). Strand melt-
ing may be enhanced by the 40° bend in target
DNA around the RUM (Fig. 1F). Bases –6 to –1
on the bottom strand then follow a cleft be-
tween the ZnF and the RLE, which adopts a
canonical PD-(D/E)xK-family nuclease fold,
but with the characteristic Lys1026 on an a helix
instead of the usual b strand (Fig. 3B) (24). This
lysine, along with catalytic residues Asp996 and
Asp1009, is 4 to 6 Å from the scissile phosphate
of C(–1), suggesting that C(–1) may be close to
its position during catalysis of bottom-strand
cleavage. On the top strand, bases –6 to +2 all
make extensive contacts along a cleft between
the RLE and linker domains, except for A(–4),
which flips out and contacts C126 of the 3′UTR
(Fig. 3C). To determine the relative impor-
tance of the bases in the RASIN, we mutated
each of the 11 bp individually and tested the
effect on bottom-strand cleavage. Mutating
T(+1) to A abolished cleavage entirely, and
mutating T(–6), T(–5), and A(–3) severely de-
creased activity, whereas other changes were
tolerated (Fig. 3D). This suggests the following
RASIN motif for cleavage, given in top-strand
sense: T–6TNANNT+1.
Because only the bottom strand of the RASIN
enters the RLE active site, we tested the ac-
tivity of R2Bm on a single-stranded DNA with
the bottom-strand sequence and found that it
was cut, albeit weakly (Fig. 3E). Endonuclease
activity was strongly stimulated by providing a
60-nt top strand spanning the RASIN and up-
stream and downstream sequences, but was
similarly stimulated by a 32-nt top strand com-
plementary only to the upstream region contain-
ing the RUM. A 17-nt top strand complementary
to the downstream sequence did not stimulate
activity (Fig. 3E). This suggests that the RUM
in a double-stranded state is important for re-
cruiting the R2Bm RLE to the RASIN bottom
strand and that the top strand of the RASIN,
despite its extensive interaction with R2Bm,
is dispensable for specific bottom-strand cleav-
age. However, when we added deoxynucleotides
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Fig. 5. Mechanism and retargeting of first-strand synthesis by R2Bm.
(A) Model for the initial stages of target site cleavage and first-strand synthesis.
(B) Design of R2Bm + Cas9 experiments. (C) Complementation of DNA target site
mutants by Cas9 cleavage in trans and cis. The denaturing gel shows in vitro TPRT
reactions on a labeled 211-bp target corresponding to the wild-type 28S target, or two
235-bp targets: one where the RASIN TAAGGTA is replaced by 31 bp of unrelated
sequence, and another where the 13-bp RUM is additionally scrambled. R2Bm and
SpCas9(H840A) were added in trans, or in cis connected by a 33XTEN linker (fusion
indicated by a shaded box). The sgRNA is complementary to the inserted sequence
and nicks 40 nt from the last RUM base. The R2 RNA is the 3′UTR with 5 nt of
3′ homology to the nick site. (D) Sequences used for retargeting R2Bm to an unrelated
locus from the Drosophila virilis genome. (E) Denaturing gel of in vitro TPRT reactions
on the labeled 192-bp Drosophila virilis target. sgRNAs are numbered as in (D); all R2
RNAs or R2-tagged RNAs have 10 nt of 3′ homology to the nick site of the sgRNA.
to these reactions, TPRT activity was eliminated
in the absence of the top strand from the RASIN
downstream but was partially rescued if the
3′UTR RNA contained 3′ homology to the tar-
get site (Fig. 3E). The top-strand RASIN bases
A(–4), A(–3), and G(–2) are grasped by Arg901
and Asp902 of the R2Bm linker (Fig. 3C). We
mutated these two residues to alanine and
tested TPRT activity on a fully double-stranded
substrate, and found that TPRT activity was
reduced and partially rescued by 3′ homology
(Fig. 3E). These results suggest two important
factors for initiating TPRT when the 3′UTR
RNA lacks 3′ homology: (i) the presence of a
top strand downstream of the RASIN, which
may help retain the nicked bottom strand, and
(ii) contacts between R2Bm and the top-strand
RASIN, which help the nicked bottom strand
“pivot” into the RT active site.
R2Bm binds a small core region of the 3'UTR
R2Bm can only initiate TPRT on RNAs contain-
ing the R2 3′UTR (self-specificity), but the mo-
lecular basis for this is not known (25). Multiple
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models have been proposed for the secondary
structure of the R2 3′UTR, and the divergent
sequences of R2 RNAs have hindered identi-
fication of key bases (26, 27). A model for the
R2 3′UTR secondary structure based on chem-
ical probing is shown in Fig. 4A and has at
least 11 stems (26). In our cryo-EM map, we
resolved density for two stems and their flank-
ing single-stranded regions (Fig. 4B). On the
basis of nomenclature commonly used for struc-
tured RNAs, we name these stems P1 (nu-
cleotides 33 to 38 and 120 to 135) and P2
(nucleotides 131 to 137 and 236 to 242), and
term the single-stranded junction between P1
and P2 as J1/2 and the single-stranded region
preceding P1 as J0/1. The rest of the 3′UTR
may occupy a diffuse cloud of cryo-EM density
next to these core regions (Fig. 4C).
P1 and J1/2 are mainly recognized by an a
helix from the R2Bm NTE-1 domain, which
packs into the major groove of P1 and is wrap-
ped by J1/2 (Fig. 4B). Arg307 recognizes the
Hoogsteen edge of P1 G33, and the interaction
is secured by Arg310 and Arg311. Consistently,
these residues were previously shown to be
essential for RNA binding (15), and the first
45 bases of the 3′UTR are essential for TPRT
activity (11). J1/2 makes numerous sequence-
specific contacts (Fig. 4D): A127 forms a sugar-
edge pair with the Watson-Crick face of J0/1
A32, A128 hydrogen bonds to Leu732 and Lys733
of the R2Bm thumb domain and stacks on
NTE-1 Tyr314, U129 hydrogen bonds to Glu319
and Lys322 of NTE-1, and C126 stacks on and
hydrogen bonds with A(-4) from the top strand
of the DNA target (Fig. 4, B and D).
To test if regions of the R2 3′UTR not clearly
visible in the cryo-EM density are required for
TPRT activity, we designed a 43-nt minimal
3′UTR—“R2 tag”—that contains only the se-
quences visible in the cryo-EM density, linked
by tetraloops (Fig. 4E). The R2 tag was reverse
transcribed as efficiently as the full 248-nt
3′UTR in a TPRT reaction. We tested the impor-
tance of the J1/2 linker by making single-base
transversions and found that A127U reduced
activity and A128U almost completely abol-
ished TPRT activity (Fig. 4F). Mutating G33 to
C to disrupt base pairing at the bottom of stem
P1 also reduced activity but could be rescued
by the compensatory C125G mutation (Fig. 4F).
Mutation of J0/1 A32 to G reduced activity, but
mutations to C or U were tolerated. Equiv-
alents to P1, P2, J0/1, and J1/2 can be identi-
fied in the secondary structures of diverse
R2 elements (26) (fig. S7). The P1 and P2
stems have different sizes and base compo-
sitions, but positions 2 and 3 of J1/2, cor-
responding to A127 and A128, are conserved as
adenosines, consistent with their importance
for TPRT.
Because the R2 tag alone is efficiently in-
tegrated in a TPRT reaction, we tested if ad-
ding the R2 tag to the 3′ end of a “cargo” RNA
would allow its integration at the 28S target
site. We added the R2 tag to the 3′ end of a
239-nt cytomegalovirus (CMV) promoter RNA.
This tagged RNA was used as efficiently as
wild-type R2 3′UTR in a TPRT reaction, whereas
an untagged RNA was not used, nor was an
RNA tagged with an R2-tag A128U mutant
(Fig. 4G). A larger RNA containing the 720-nt
coding sequence for green fluorescent protein
(GFP) and a 3′ R2 tag was also reverse tran-
scribed in a TPRT reaction (Fig. 4G).
R2Bm can be retargeted with CRISPR-Cas9
Our structural and biochemical observations
suggest a multistep model for initiation of
TPRT: The R2Bm N-terminal domains first
detect a RUM sequence, followed by cleav-
age of the bottom strand at the RASIN site,
possible pivoting of the nick around the top
strand into the RT active site, annealing of
any 3′ homology to the nicked bottom strand,
and finally initiation of reverse transcription
(Fig. 5A). This model implies that R2Bm could
prime reverse transcription off an exogenously
nicked bottom strand close to the R2Bm bind-
ing site (Fig. 5B). To test this, we replaced the
RASIN and downstream sequences of the 28S
DNA target with an unrelated sequence con-
taining an efficient SpCas9 target sequence,
but kept the RUM sequence to anchor R2Bm
(Fig. 5B). This substrate could not be cleaved
by R2Bm but was nicked efficiently by an SpCas9
H840A nickase mutant (Fig. 5C). When SpCas9
and R2Bm were added together with a single-
guide RNA (sgRNA) and an R2 3′UTR RNA
with 5 nt of 3′ homology to the sgRNA nick
site, we detected low amounts of TPRT activ-
ity. This activity was enhanced when the R2Bm
and SpCas9 proteins were fused with a 33XTEN
flexible linker (Fig. 5C). The RUM was not re-
quired for Cas9-directed TPRT, as mutating the
RUM did not reduce activity (Fig. 5C). This
suggests that Cas9 might be able to direct
R2Bm to perform TPRT at loci other than the
28S target. We mixed the R2Bm-Cas9(H840A)
fusion protein with a 192-bp target sequence
from Drosophila virilis, various sgRNAs, and
R2 3′UTRs with 10 nt of 3′ homology to the
nick site dictated by the sgRNA (Fig. 5D). We
found TPRT activity at all Cas9 nick sites, with
one sgRNA (guide 2) giving efficient activity
(Fig. 5E). Adding R2Bm and SpCas9(H840A)
as separate polypeptides also yielded efficient
TPRT with guide 2 but was less robust with
other guides (fig. S9). The 239-nt CMV promo-
ter RNA with a 3′ R2 tag and 10 nt of homo-
logy to the guide 2 nick site was also reverse
transcribed efficiently; this activity required
the R2 tag and was reduced in the absence of
3′ homology or with the R2 tag A128U muta-
tion (Fig. 5E). Larger RNAs such as GFP could
also be reverse transcribed at the guide 2 nick
site (fig. S9). In summary, R2Bm can be retar-
geted by Cas9 to perform TPRT at unrelated
loci, and the R2 tag can direct incorporation of
cargo RNAs at these sites.
Discussion
Here we show the structure of a non-LTR ret-
rotransposon during transposition, and we dis-
sect the principles of target DNA and self-RNA
recognition. Our structure suggests that R2Bm
uses its N-ZnF and Myb domains to locate the
endonuclease target sequence, a model that
contrasts with the model for other non-LTR
retrotransposons in which the endonuclease
domain is the only determinant of target site
selection (28, 29). We identified two essential
target site motifs—the RUM and RASIN—that
are recognized by R2Bm, but we note that
searching the B. mori genome with a RUM-
RASIN consensus motif yields many potential
off-target sites outside of the ribosomal DNA
arrays (fig. S10). We examined the sequence of
a previously identified B. mori non-28S inser-
tion in (30) and found that the target site had
limited similarity with 28S but had a TTAAcG|T
RASIN motif (“|” indicates insertion site, low-
ercase denotes deviation from 28S) and a
GCTACTTGCGCAT RUM the correct distance
upstream of the RASIN (fig. S10). Non-28S in-
sertions, however, are rare, so it is likely that
other factors are important in regulating R2Bm
transposition, including chromatin accessibil-
ity, other sequence motifs, or the ability of the
target DNA to bend and melt.
Non-LTR retrotransposons form a diverse
family, and even within the R2 superclade
there are notable differences between elements.
R2Bm is a representative of the R2-D clade of
elements, which have a single C2H2 N-terminal
ZnF domain, but R2-A clade elements have
three tandem N-terminal ZnF domains (31)
that may create a more extensive DNA binding
interface with greater stringency in target site
selection. More broadly, non-LTR retrotrans-
posons can be divided into two types on the
basis of their endonuclease domains: those
that, like R2Bm, use a C-terminal restriction
enzyme-like (RLE) domain, and those that, like
human LINE-1, use an unrelated N-terminal
apurinic or apyrimidinic endonuclease (APE)
domain (32, 33). Structure prediction using
AlphaFold (34) suggests that, in these retro-
transposons, the position of the APE domain
is distinct from that of the RLE domain in
R2Bm, suggesting that there may be mecha-
nistic differences in how target cleavage is
coupled to reverse transcription (fig. S5) (35).
Nonetheless, the similarity between the DNA
interface on the R2Bm thumb domain and the
corresponding interface in the group IIC in-
tron (fig. S5) suggests that this interface might
be conserved among most non-LTR retrotrans-
posons (19). Indeed, the upstream DNA from
R2Bm was easily modeled into an AlphaFold
model of human LINE-1 ORF2, including not
only the thumb interactions but also strand
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separation by the CCHC ZnF domain, which in
LINE-1 ORF2 corresponds to the C-terminal
cysteine-rich domain (fig. S5).
Overall, the results of this work advance our
understanding of transposition by non-LTR
retrotransposons and suggest avenues for en-
gineering these transposons for targeted gene
insertions.
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ACKN OWLED GMEN TS
We thank S. Zhu and M. Walsh for valuable discussions; E. Brignole
and C. Borsa for the smooth running of the MIT.nano cryo-EM
facility, established in part with financial support from the
Arnold and Mabel Beckman Foundation; S. Lövestam for a critical
reading of the manuscript; and the entire Zhang lab for support
and advice. We thank T. H. Eickbush and colleagues for their
inspiring and pioneering work on R2 elements. Funding: Helen Hay
Whitney Foundation Postdoctoral Fellowship (M.E.W.), Howard
Hughes Medical Institute (M.E.W., F.Z.), National Institutes of
Health grant 2R01HG009761-05 (F.Z.), Hock E. Tan and K. Lisa
Yang Center for Autism Research at MIT (F.Z.), K. Lisa Yang and
Hock E. Tan Molecular Therapeutics Center at McGovern (F.Z.),
K. Lisa Yang Brain-Body Center at MIT (F.Z.), Broad Institute
Programmable Therapeutics Gift Donors (F.Z.), the Pershing
Square Foundation, W. Ackman, and N. Oxman (F.Z.),
Asness Family Foundation (F.Z.), BT Charitable Foundation
(F.Z.), the Phillips family (F.Z.), J. and P. Poitras (F.Z.), D. Cheng
(F.Z.), R. Metcalfe (F.Z.). Author contributions: M.E.W. and
F.Z. conceived the project. M.E.W. designed and performed
experiments and solved the cryo-EM structure. C.J.F. generated
and analyzed sequencing data. F.Z. supervised the research and
experimental design with support from R.K.M. M.E.W. wrote the
manuscript with input from all authors. Competing interests:
F.Z. is a scientific adviser for and cofounder of Editas Medicine,
Beam Therapeutics, Pairwise Plants, Arbor Biotechnologies, and
Aera Therapeutics. F.Z. is a scientific adviser for Octant. Data and
materials availability: The cryo-EM map has been deposited in
the Electron Microscopy Data Bank with accession code EMD-
40033. The coordinates for the atomic model have been deposited
in the Protein Data Bank with accession code 8GH6. The raw
cryo-EM data have been deposited in EMPIAR with accession code
EMPIAR-11458. License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.sciencemag.org/about/
science-licenses-journal-article-reuse. This article is subject to
HHMI’s Open Access to Publications policy. HHMI lab heads have
previously granted a nonexclusive CC BY 4.0 license to the public
and a sublicensable license to HHMI in their research articles.
Pursuant to those licenses, the author-accepted manuscript of this
article can be made freely available under a CC BY 4.0 license
immediately upon publication.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg7883
Materials and Methods
Figs. S1 to S10
Tables S1 to S3
References (36–47)
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
Submitted 20 January 2023; accepted 21 March 2023
10.1126/science.adg7883
Wilkinson et al., Science 380, 301–308 (2023)
21 April 2023
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RES EARCH
MOLECULAR BIOLOGY
Structural basis for inactivation of PRC2
by G-quadruplex RNA
Jiarui Song1,2,3, Anne R. Gooding1,2,3, Wayne O. Hemphill1,2,3, Brittney D. Love4,5,6, Anne Robertson4,5,6,7,
Liqi Yao1, Leonard I. Zon4,5,6,7, Trista E. North4,5,6, Vignesh Kasinath1*, Thomas R. Cech1,2,3*
Polycomb repressive complex 2 (PRC2) silences genes through trimethylation of histone H3K27.
PRC2 associates with numerous precursor messenger RNAs (pre-mRNAs) and long noncoding RNAs
(lncRNAs) with a binding preference for G-quadruplex RNA. In this work, we present a 3.3-Å-resolution
cryo–electron microscopy structure of PRC2 bound to a G-quadruplex RNA. Notably, RNA mediates the
dimerization of PRC2 by binding both protomers and inducing a protein interface composed of two
copies of the catalytic subunit EZH2, thereby blocking nucleosome DNA interaction and histone H3 tail
accessibility. Furthermore, an RNA-binding loop of EZH2 facilitates the handoff between RNA and
DNA, another activity implicated in PRC2 regulation by RNA. We identified a gain-of-function mutation
in this loop that activates PRC2 in zebrafish. Our results reveal mechanisms for RNA-mediated regulation
of a chromatin-modifying enzyme.
M any nuclear proteins that bind chro-
matin also bind RNA molecules (1–3).
The binding of RNA has been sug-
gested to facilitate both positive and
negative regulation (e.g., recruitment
to target sites and enzymatic inhibition, re-
spectively). Polycomb repressive complex 2
(PRC2) is a prominent example of a chroma-
tin modifier known to be regulated by RNA
(4, 5). PRC2 is essential for embryonic develop-
ment and cell differentiation (6, 7). Some tu-
mors are PRC2 dependent (e.g., because of
silencing of tumor suppressor genes), making
PRC2 a target for cancer therapeutics (8). PRC2
consists of four core protein components: EZH2
(catalytic subunit), EED [binds histone H3 tri-
methylated at lysine 27 (H3K27me3)], SUZ12
(provides a platform), and RBAP48 (7). Asso-
ciating cofactors define two PRC2 subclasses
(9, 10), of which PRC2.2, containing AEBP2 and
JARID2, is the subject of this study.
PRC2 binds numerous pre-mRNA and long
noncoding RNA (lncRNA) transcripts in vitro
and in vivo (11–13). This broad RNA recogni-
tion can be explained at least in part by PRC2
preferring an RNA G-quadruplex (G4) motif
(14–16), which could be ubiquitous in the tran-
scriptome from intramolecular and perhaps
even intermolecular assemblies (17). Proposed
models of RNA regulation of PRC2 remain
disparate. First, in the “handoff” model, PRC2
requires RNA for recruitment and occupancy
1Department of Biochemistry, University of Colorado Boulder,
Boulder, CO 80303, USA. 2BioFrontiers Institute, University of
Colorado Boulder, Boulder, CO 80303, USA. 3Howard Hughes
Medical Institute, University of Colorado Boulder, Boulder,
CO 80303, USA. 4Stem Cell and Regenerative Biology
Department, Harvard University, Cambridge, MA 02138, USA.
5Stem Cell Program, Division of Hematology/Oncology,
Boston Children’s Hospital and Dana-Farber Cancer Institute,
Boston, MA 02115, USA. 6Harvard Medical School, Boston,
MA 02115, USA. 7Howard Hughes Medical Institute, Harvard
Medical School, Boston, MA 02115, USA.
*Corresponding author. Email: thomas.cech@colorado.edu (T.R.C.);
vignesh@colorado.edu (V.K.)
on a specific subset of targeted chromatin
(18, 19). The direct handoff from RNA to DNA
is an intrinsic property of PRC2, as shown by
recent biophysical analyses (20). Second, the
“eviction” model suggests that nascent RNA
removes PRC2 from actively transcribed chro-
matin to restrict nonspecific activity (14, 21–23).
Third, in the “inhibitor” model, RNA and nu-
cleosome binding of PRC2 are mutually exclu-
sive, so RNA serves as a direct competitor to
prevent PRC2 action (14, 18, 22, 24). Another
version of the inhibitor model proposes that
RNA exploits a regulatory site on PRC2 to abol-
ish H3K27me3 binding to EED, which conse-
quently eliminates allosteric activation of EZH2
(25). Therefore, structural details of PRC2-RNA
interaction have been needed in the field to
provide mechanistic insights and coordinate
those models.
Cryo–electron microscopy (cryo-EM) and x-ray
crystallography have provided visualization of
both substrate-free and nucleosome-bound
PRC2 complexes (26–34). However, solving a
structure of a PRC2-RNA complex has proved
challenging. A streptavidin-biotin–affinity EM
grid approach has been successfully used in
cryo-EM (35), and here we adapt this technique
for ribonucleoprotein (RNP) complexes using
biotinylated RNA. We found that PRC2 can
dimerize following RNA binding with a protein-
protein interface composed of EZH2 CXC
domains. The structure provides a molecular
explanation for how RNA acts as a PRC2 in-
hibitor, and it suggests a mechanism for RNA
facilitation of PRC2 recruitment.
Structure of G-quadruplex RNA-mediated
PRC2 dimer
We prepared six-subunit PRC2.2 complexes with
full-length EZH2, SUZ12, RBAP48, EED, em-
bryonic short-isoform AEBP2, and truncated
JARID2119–450 (Fig. 1A), as well as two G4-forming
RNAs (Fig. 1B) that bind PRC2 in vitro (fig. S1).
We used streptavidin-affinity EM grids to cap-
ture 5′-biotinylated RNAs, which select for
RNA-bound PRC2 complexes and also protect
them from the hydrophobic water-air inter-
face. Because this method had not been ap-
plied to an RNP complex, we validated it by
testing different RNA concentrations with the
same excess of PRC2. The number of particles
observed by negative staining was proportional
to the RNA concentration in most fields (Fig.
1C), indicating that the vast majority of protein
complexes on the grid are bound to RNA. Com-
pared with RNA-free PRC2 (particles ~150 Å in
diameter), the majority of two-dimensional
(2D) class averages from 1G4- and 2G4-bound
PRC2 complexes were larger (particles ~250 Å
in diameter), containing two recognizable PRC2
complexes (Fig. 1D).
We determined the cryo-EM structure of the
dimeric PRC2-1G4 RNA complex at 3.4-Å res-
olution from consensus refinement, and at
3.3 Å from multibody refinement (36) (figs. S2
and S3 and table S1). The two PRC2 protomers
in the RNP complex are nearly identical and
have a conformation previously characterized
as the SANT1 extended form (37) (Fig. 1E and
fig. S4). We identified a protein interface in the
RNA-induced dimer that is a localized EZH2-
EZH2 interaction (described in the dimer in-
terface section below) (movie S1).
Notably, this PRC2 dimer has imperfect C2
symmetry (fig. S5A) associated with differ-
ential occupancy of RNA in the two symmet-
ric sites (fig. S5B). The stronger density has a
volume representative of a G4 RNA (fig. S5, C
and D, and S6D), whereas the symmetric site
has discontinuous density and is not discussed
hereafter. We could not obtain high-quality
RNA density for de novo modeling in either of
the sites from multibody refinement (fig. S5, C
and D) and particle subtraction classification
(fig. S6) (38). We attribute this to the multiple
independent and flexible interactions between
PRC2 and RNA. The G4 RNA is not nestled
into the surface of the protein, as is typically
seen for RNA-protein complexes, but instead
appears to be separated from the protein. The
RNA density is in closest proximity to the EZH2
SANT2 domain (residues 353 to 362), EZH2
CXC domain (residue R532), EZH2 SET domain
(residue N697), the RRM (RNA recognition
motif)–like domain of SUZ12, and an unstruc-
tured region of RBAP48 (residues 92 to 107)
(movie S1). These binding sites, excluding
RBAP48, are supported by previous in vitro
and in vivo studies (25, 26, 39, 40). We were able
to observe density that links regions proximal to
PRC2 and G4 RNA at 3.9-Å resolution from
particle subtraction and classification (de-
scribed in the arginine-rich site section below).
The distance between the two PRC2 proto-
mers is reduced from 51 to 48 Å on the side with
stronger G4 density (Fig. 1E, bottom), which
not only explains the imperfect symmetry, but
Song et al., Science 381, 1331–1337 (2023)
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Fig. 1. Overall structure of a PRC2-1G4 RNP complex. (A) (Left) Schematic of
the proteins in the PRC2.2 six-subunit complex. Transparent N-terminal region
of JARID2 was not included. (Right) Coomassie-stained gel of purified PRC2.
(B) The two RNA oligonucleotides used in this study. (C) Negative-staining EM
images of streptavidin-affinity grids with excess PRC2 and various 1G4 RNA
concentrations. (D) Negative-staining EM provided 2D-class averages of PRC2
alone collected from continuous carbon grids and PRC2-G4 RNAs from
streptavidin-affinity grids. (E) (Top) Cryo-EM density map of PRC2 bound to 1G4
RNA. EZH2 (CXC-SET) of protomer 1 in blue, EZH2 (CXC-SET) of protomer 2
in light blue, and 1G4 RNA in orange. (Bottom) The atomic model of PRC2 bound
to 1G4 RNA. Distances between EZH2 (SANT2) and SUZ12 (RRM-like) are
highlighted by black arrows to emphasize the change from 1G4-binding.
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Fig. 2. G4 RNA induces PRC2 dimerization in solution. (Left) Size-exclusion chromatography of PRC2
preincubated with 1G4, 2G4, and mock (protein only). Abs, absorbance; mAU, milli–absorbance unit.
(Right) Standard curves were used to estimate the molecular weights of PRC2 complexes.
also supports the model of a single G4 being
sufficient for PRC2 dimerization. Although the
stoichiometry of most RNPs is 2 PRC2:1 RNA
in our preparations, we do not reject the pos-
sibility of a PRC2 dimer engaging two inde-
pendent G4 RNAs simultaneously.
G-quadruplex RNA induces PRC2 dimerization
in solution
To validate the dependence of PRC2 dimeriza-
tion on G4 RNA binding in solution, we used
analytical size-exclusion chromatography and
mass photometry. In the absence of RNA, our
six-subunit PRC2 complex chromatographed
as a monomer (Fig. 2), which was consistent
with an absolute molecular weight of 340 kDa
(fig. S7A). Incubating PRC2 with 18-kDa 1G4
RNA or 30-kDa 2G4 RNA led to a large RNP
complex of approximately 720 kDa measured
by both size-exclusion chromatography (Fig. 2)
and mass photometry (fig. S7C), which was
consistent with a dimer. In addition, native gel
electrophoresis of PRC2-G4 RNP cross-linked
with glutaraldehyde indicated that G4 RNA re-
mains bound as part of a cross-linked complex
(fig. S7D). Furthermore, negative-staining EM
reference-free 2D class averages of cross-linked
complexes on conventional carbon-support grids
confirmed the presence of RNA-mediated
PRC2 dimers as observed in the non–cross-
linked streptavidin-affinity grids (fig. S7E).
Together, our results verified the requirement
of RNA for this specific PRC2 dimerization in
solution and provided confidence that the dimer
was not an artifact of streptavidin-affinity
selection.
To test the specificity of G4 structure in me-
diating PRC2 dimerization, we used microscale
thermophoresis (MST) to measure PRC2-RNA
binding in different reaction conditions (fig.
S8). In a G4-favoring KCl buffer, the MST profile
showed two distinguishable stages of thermo-
phoretic mobility. This biphasic binding curve
is typical for two binding events (41), which
suggests that a higher-affinity binding site on
PRC2 is primarily occupied at low PRC2 con-
centrations (1 PRC2:1 RNA), and at higher PRC2
concentrations, lower-affinity binding of a sec-
ond PRC2 follows (2 PRC2:1 RNA). In addition,
we performed the same MST assays in a G4-
destabilizing LiCl buffer or using a G-rich
single-stranded RNA with no G4-forming po-
tential. Neither experiment gave a distinct bi-
phasic curve, indicating that PRC2 dimerizes
specifically on RNA containing at least one
G4 motif.
The dimer interface prevents nucleosome
and H3 tail binding
The PRC2-1G4 RNA dimer has three features
that would be expected to inhibit nucleosome
binding and histone methylation. First, the
residues within the CXC domain of EZH2 in-
teract with the CXC of the second protomer
to form the dimer interface. This dimer inter-
face includes two R566–A569 hydrogen bonds,
two R566–T573 hydrogen bonds, two Q575–
G564 hydrogen bonds, and a K568–K568 hy-
drophobic interaction (Fig. 3A). By contrast,
in a nucleosome-bound PRC2, the CXC domain
facilitates the catalytic activity of the adjacent
SET domain of EZH2, specifically with R566,
K568, T573, and Q575 contributing to interac-
tions with nucleosome DNA and the H3 tail
(Fig. 3B) (27). The disparate functions of the
CXC domain in these different PRC2 structures
are seen by the superposition of our density map
onto the nucleosome-bound PRC2, which shows
clashes with both the DNA and the H3 tail
(Fig. 3C and movie S2). Therefore, we propose
that nucleosome binding and H3 tail loading,
both of which are essential for histone methy-
transferase (HMTase) activity, are mutually
antagonistic with RNA-mediated PRC2 di-
merization. The disruption of nucleosome-PRC2
complexes by 1G4 RNA was confirmed by a
competition-binding assay in solution (Fig. 3D).
Second, the EZH2 bridge helix (residues 500
to 516)—important for nucleosome DNA bind-
ing and channeling H3 tail into the active site
of the EZH2 SET domain (27)—is disordered
in both protomers of our RNP complex (fig.
S9). This is consistent with structures of PRC2
lacking nucleosome substrate. Lastly, the EZH2
C-terminal helix (residues 738 to 742), which
points away from the H3K27 binding site in
nucleosome-bound PRC2, now occludes the
active site in RNA-bound PRC2 (fig. S9) and
appears to serve as an additional mechanism
to prevent H3 tail binding.
To test the importance of the CXC dimer
interface, we purified a mutant (EZH2 R566A
K568A Q575A). Mutation of these residues did
not affect G4 RNA binding (fig. S10, A and B)
or prevent RNA-induced dimerization (fig. S10,
C and D). However, negative-staining EM
with streptavidin-affinity grids classified sub-
stantially more monomer-size particles from
the mutant (59%) than the wild-type (WT) PRC2
(9%) (Fig. 3E and fig. S10E). This suggests that
these EZH2 mutations impacted the overall
stability of the PRC2 dimer by destabilizing
the protein-protein interaction, and consequent-
ly, one protomer more easily dissociated dur-
ing stringent washes (dilutions) in our grid
preparations compared with the WT. Because
streptavidin-affinity grids only retain RNA-bound
complexes, those monomer particles of the mu-
tant could also represent an intermediate stage
of one PRC2 engaging RNA prior to associa-
tion of the second PRC2, which is consistent
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Fig. 3. RNA-mediated PRC2 dimer is
an inactive complex. (A) Cryo-EM
structure of PRC2-1G4 complex with
zoom-in to show the interface of
two EZH2 CXC domains. Interacting
residues (R566, K568, T573, and Q575)
are highlighted in the stick representation.
One set of hydrogen bonds (R566NE-
T573OG1, 2.70-Å distance; R566NH1-A569O,
2.73-Å distance; and Q575NE2-G564O,
2.51-Å distance) is indicated by yellow
dashed lines. The other set of hydrogen
bonds between the same amino acid
pairs in the second PRC2 protomer is not
shown for clarity. Another view of the
same region is shown in fig. S3G.
(B) Structure of PRC2-nucleosome
complex (PDB: 6WKR) with zoom-in to
emphasize the CXC interactions with
nucleosome H3 tail (orange). The same
residues as shown in (A) are high-
lighted in stick representation.
(C) Superposition of the EZH2 CXC
domain of the RNA-bound PRC2 on
the nucleosome-bound PRC2 to empha-
size disparate functions of the CXC
domain. (D) Nucleosome-RNA competi-
tion assay. PRC2 was incubated with
constant amount of radiolabeled trinu-
cleosome and serial dilutions of 1G4 RNA.
Incomplete PRC2-trinucleosome
complexes are indicated by * and **. We
assume two of three nucleosomes were
occupied by PRC2 in *, and one of three
nucleosomes in **. (E) Negative-stain EM
to quantify monomer and dimer particles
of EZH2 R566A K568A Q575A binding
1G4. The number of particles in each
class is indicated above each bar.
(F) Binding affinity of 1G4 RNA or
dsDNA to WT PRC2 and EZH2 R566Y
K568Y W575Y (3Y) measured by FP.
We used a reaction buffer with a lower
salt concentration to achieve higher
binding affinity for the dsDNA (right).
Kd, dissociation constant. (G) Methyl-
transferase activities from figs. S12 to
S15 are plotted against reaction times
for PRC2 (400 nM) preincubated
with 1G4 (400 nM), 2G4 (400 nM),
and mock (protein only). Error bars
represent standard deviations of
three replicates performed on different
days. (H) Methylation of trinucleo-
somes by PRC2 with serial dilutions of
1G4 RNA. (Top) Radiogram that shows
methylation. (Bottom) Coomassie-
stained gel. Single-letter abbreviations
for the amino acid residues are as
follows: A, Ala; C, Cys; D, Asp; E, Glu;
F, Phe; G, Gly; H, His; I, Ile; K, Lys;
L, Leu; M, Met; N, Asn; P, Pro; Q, Gln;
R, Arg; S, Ser; T, Thr; V, Val; W, Trp;
and Y, Tyr.
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Fig. 4. EZH2 loops physically contact G4 RNA and contribute to direct
handoff from RNA to DNA. (A) Map of PRC2-1G4 RNA from particle subtraction
and classification (fig. S6) with zoom-ins to emphasize the observed physical
interactions of PRC2 and G4 RNA. (B) EZH2 structure from AlphaFold predicts
two disordered loops of EZH2. Arginine-rich loop [EZH2(353–362)] and lysine-rich
loop [EZH2(494–502)] are indicated in blue and green, respectively. (C) FP assays to
monitor the transfer kinetics of PRC2 from fluorescently labeled 1G4 RNA to a
dsDNA competitor. The ratio kq/k–1 of the PRC2 RNA-to-dsDNA direct-transfer
rate constant (kq) and the PRC2-RNA dissociation rate constant (k–1) provides a
measure of the propensity of PRC2 to exchange these ligands by the direct transfer
mechanism. WT PRC2 had kq = 90 ± 11 M−1s−1, k–1 = 5.6 ± 0.49 × 104 s−1, and
kq/k–1 = 1.7 ± 0.35 × 105 M−1. EZH2 D353–362 had kq = 48 M−1s−1, k–1 = 12 × 104 s−1,
and kq/k–1 = 0.4 × 105 M−1. EZH2 CR had kq = 130 ± 62 M−1s−1, k–1 = 2.7 ± 0.63 × 104 s−1,
and kq/k–1 = 4.6 ± 1.3 × 105 M−1. koff
obs, dissociation rate constant observed.
with the biphasic binding curve observed in
our MST assays.
We next attempted to disrupt the CXC inter-
face more severely by substituting bulky side-
chains of tyrosine, so we constructed an EZH2
R566Y K568Y Q575Y mutant. Unexpectedly,
this mutant had higher binding affinity to the
G4 RNAs, as determined by fluorescence po-
larization (FP) assays (Fig. 3F, left) and elec-
trophoretic mobility-shift assays (EMSA) (fig.
S11, A and B). Notably, double-stranded DNA
(dsDNA) binding of this mutant was not af-
fected (Fig. 3F, middle and right), which fur-
ther indicates that DNA and RNA use separate
mechanisms to engage PRC2 even though
they bind mutually antagonistically. Although
this mutant PRC2 is a monomer as observed
by negative-staining EM, RNA-bound particles
showed a dominant population of dimer com-
plexes, which is consistent with the increased
RNA binding affinity and the role of RNA in
mediating PRC2 dimerization (fig. S11, C and
D). We propose that the aromatic sidechains
of tyrosine might stack on each other and
therefore stabilize the CXC interface. Thus,
the dimerization interface need not be spe-
cific, and it appears to be RNA binding rather
than protein-protein interaction that drives PRC2
dimerization. Overall, we observed a positive
correlation between the CXC dimer interface
and G4 RNA binding.
RNA-induced PRC2 dimer is inactive
Structural observations on the EZH2 CXC in-
terface prompted us to hypothesize that the
HMTase activity of the G4-induced PRC2 di-
mer would be inhibited. To test this, we per-
formed activity assays to compare free PRC2
with RNA-sequestered dimers (Fig. 3G and
figs. S12 to S15). As expected, we detected sub-
stantial reductions in methylation rates with
all substrates (including recombinant H3) in
response to RNA binding, with stronger inhibi-
tion by the higher-affinity 2G4 RNA (Fig. 3G).
The extent of inhibition was limited by the
RNA concentration because complete inhibi-
tion was achieved with excess 1G4 RNA (Fig.
3H and fig. S16A).
An arginine-rich site of EZH2 binds G4 RNA
and participates in RNA-to-DNA handoff
Applying particle subtraction and classifica-
tion (fig. S6), we identified multiple sites in
EZH2 [EZH2(353–362): KRPGGRRRGR, EZH2
R532, and EZH2 N697] that physically contact
G4 RNA (Fig. 4A). The arginine-rich EZH2(353–
362) has been implicated in binding lncRNA
(25, 39), and similar arginine-rich sequences
in multiple transcription factors have been
linked to RNA binding (42). EZH2 truncation
[EZH2(D353–362)] and a local charge-reversed
EZH2 [EZH2 CR(353–362): DEPGGEEEGE] both
exhibited decreased HMTase activity but showed
no obvious reduction in G4 RNA binding or
G4 RNA-mediated PRC2 dimerization in vitro
(fig. S17). We also generated a double-truncation
mutant [EZH2(D353–362 D494–502)] to remove
an adjacent lysine-rich site (EZH2 494–502)
(Fig. 4B). EZH2 residues 494 to 502 were
previously implicated in binding nucleosome
DNA and G4 RNA (27, 40) and might com-
pensate for RNA binding in the absence of
EZH2 residues 353 to 362. PRC2 containing
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Fig. 5. EZH2 CR is a gain-of-function mutant in rescue of zebrafish develop-
ment. (A) Representative images of injected zebrafish embryos at 48 hours
post fertilization (hpf). Gross phenotypic scoring of anterior-posterior axis growth
was sorted into three categories: normal, reduced, and severely reduced growth.
(B) Scoring of anterior-posterior axis growth at 48 hpf. Zebrafish embryos were
injected with 4-ng ezh2-MO or the same amount of control MO. For rescue
experiments, 100 ng of mRNA encoding WT or mutated human EZH2 was
coinjected with ezh2-MO. At least three clutches were examined for each injection.
Fisher’s exact test was used to determine the P values. (C) Dose-response
experiments with 25, 50, and 100 ng of mRNA coinjected. Statistical analyses were
performed as in (B) by comparing different doses with ezh2-MO alone. ns, not
significant; *P < 0.05; **P < 0.01; ***P < 0.001; ****P < 0.0001.
EZH2(D353–362 D494–502) exhibited a 1.5- to
twofold reduction of binding affinity for G4
RNA (fig. S17G). We attribute this modest re-
duction to the presence of other RNA-binding
regions observed in our structure and sup-
ported by previous studies (25, 40, 43).
PRC2 has the intrinsic ability to directly trans-
fer or hand off from RNA to DNA, without there
ever being a free-enzyme intermediate (20, 44).
We therefore examined whether the arginine-
rich EZH2(353–362) region, in addition to its
role in RNA binding, is important for such
RNA-to-DNA handoff. We found that the
EZH2(D353–362) and EZH2 CR mutants had
a 4.3-fold reduction and a 2.7-fold increase,
respectively, in the propensity for direct trans-
fer from RNA to DNA (Fig. 4C). We rationalized
these results with a model (fig. S18) in which
PRC2 harbors the arginine-rich EZH2(353–362)
and lysine-rich EHZ2(494–502) to form a ternary
intermediate with both RNA and DNA binding.
EZH2(D353–362) and CR mutations of the RNA-
binding region affect the propensity for direct
transfer in different directions.
EZH2 CR is a gain-of-function mutant
in zebrafish development
We used zebrafish to examine the significance
of the EZH2 G4 RNA-binding sites in verte-
brate development. Zebrafish and human EZH2
proteins have high sequence identity, including
the regions responsible for G4 RNA binding
and RNA-induced PRC2 dimerization (fig. S19A).
EZH2 knockdown in zebrafish by antisense
morpholino oligonucleotides (MOs) led to a
severe growth defect (45) represented by gross
alterations in the length of the anterior-posterior
axis (Fig. 5A). As expected, coinjection with
mRNA that encodes human WT EZH2 signif-
icantly rescued the growth defects (P < 0.0001)
(Fig. 5B and fig. S19B). Mutant EZH2 mRNAs
rescued overall development to varying degrees
(fig. S19C). Notably, the EZH2 CR mutant had a
gain-of-function phenotype, giving significant-
ly better rescue than that of WT EZH2 (P <
0.01) and phenotypically mimicking a gain-of-
function mutant (EZH2 Y646F) that is well-
studied in the human system and frequently
found in lymphoma (Fig. 5B) (46–48). Dose-
response assays by coinjecting ezh2-MO and in-
creasing amounts of mRNAs (Fig. 5C) confirmed
that the extent of rescue was consistently similar
between CR and Y646F, whereas the catalyt-
ically dead EZH2(D694–751) gave no rescue.
Therefore, the EZH2 CR mutant, which shows
an increased propensity for direct transfer be-
tween RNA and DNA in vitro, also behaves as a
gain-of-function mutant in zebrafish development.
Discussion
In the past 10 years, lncRNAs and pre-mRNAs
have become prominent in discussions of PRC2
regulation (4, 5). Because of the broad PRC2
transcriptome (11, 12), deciphering molecular
details of PRC2-RNA interaction has been chal-
lenging. PRC2 binds G4 RNA in vitro (14, 15, 23),
PRC2 binding sites on chromatin genome
wide are associated with G-tract motifs (15),
and a well-defined G4-forming RNA TERRA
(telomeric repeat–containing RNA) recruits
PRC2 to telomeres (16). Thus, we focused on G4
RNA in the present study.
By using a biotinylated G4 RNA with streptavidin-
biotin affinity grids, we determined the cryo-EM
structure of an RNA-bound PRC2 complex. This
structure supports the earlier conclusion that
nucleosomal DNA and RNA binding are mutu-
ally antagonistic (22, 24), but it provides a much
more interesting mechanism than just competi-
tion on overlapping sites. Instead, G4 RNA trig-
gers formation of a PRC2 dimer that occludes
the DNA-binding amino acids. Based on the pre-
sent structure and biochemical and biophysical
data, we propose a model that can explain multi-
faceted functions of RNA in PRC2 regulation.
First, actively transcribed loci, which need
to avoid silencing by PRC2, generate nascent
RNA transcripts that have the potential to di-
merize PRC2 among other RNA processing
events. The RNA-induced dimer simultaneously
inactivates two PRC2 complexes (no H3 tail
binding) and evicts them from local chromatin
(no nucleosome DNA binding). Residues of
the EZH2 CXC domain, known to load the H3
tail into the catalytic groove, are occupied in a
protein-protein interaction that reinforces the
dimerization. Dimerization may prevent the
spreading of H3K27me3 across regions near
preexisting H3K27me3 or JARID2 116me3
marks, both of which induce allosteric activa-
tion of PRC2 (31, 49, 50), and therefore, it may
help define heterochromatin boundaries.
Song et al., Science 381, 1331–1337 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Second, the interactions of PRC2 with RNA
are proposed to be important for PRC2 occu-
pancy on chromatin (19, 51). Consistent with this
idea, PRC2 has the intrinsic ability to translocate
onto target chromatin as it simultaneously dis-
sociates from inhibitory RNA (20). To reconcile
the role of RNA in inhibiting and evicting PRC2
from chromatin and its role in promoting PRC2
chromatin occupancy, we propose that EZH2
harbors partially redundant nucleic acid bind-
ing sites that allow PRC2 to transiently engage
both RNA and DNA, thereby facilitating direct
transfer from RNA to DNA. The EZH2 CR mu-
tant, designed to destabilize RNA binding, en-
hances the direct transfer of PRC2 from RNA
to DNA in vitro. This CR mutant rescues the
knockdown of PRC2 in zebrafish better than
WT EZH2. This gain-of-function phenotype is
consistent with a direct transfer from RNA to
DNA, which facilitates PRC2 activity in vivo.
However, the many differences between in vitro
and in vivo experiments warrant a cautious in-
terpretation. The precise mechanism of the
EZH2 CR mutant gain-of-function merits fur-
ther investigation.
Our structure describes one mode of RNA
recognition by PRC2, but there may very well
be others. Other reported RNA-binding sites
include the RNA-binding region (RBR) adja-
cent to the bridge helix of EZH2 (residues 494
to 502) (40), the stimulatory recognition motif
(SRM) of EZH2 (residues 127 to 153) (25), the
EED amino acids close to EZH2 SRM (residues
336 to 355) (25), and the JARID2 RBR (residues
332 to 358) (43). Although we did not obtain
any subclass map having a distinguishable RNA
density in proximity to those regions, this is not
sufficient to reject their RNA-binding potential.
We propose that the numerous RNA-binding
regions within PRC2 explain why mutations
give only modest effects on RNA binding in
this and other studies.
PRC2 has been shown to dimerize without
RNA binding. We consistently find that, in the
absence of RNA, a small fraction of PRC2 mol-
ecules self-associate into dimers at high protein
concentrations, as found for a four-subunit
PRC2 holoenzyme (52) and the six-subunit
PRC2.2 complex (fig. S20A). However, 2D class
averages of self-associated dimers show a dif-
ferent dimer interface than the RNA-induced
dimer (fig. S20B). In addition, two reported
domain-swapped PRC2 dimers—PRC2-PCL
and PRC2:EZH1 (29, 32)—have completely dif-
ferent architectures than our RNA-mediated
dimer.
Aside from PRC2, many chromatin-associated
complexes have been found to interact with
RNA, including other histone modifiers (2),
transcription factors (42, 53, 54), and DNA
methyltransferase (55, 56). Similar to PRC2, they
tend not to have canonical RNA-recognition
motifs and bind RNA broadly, and obtaining
molecular structures of the RNA-protein com-
plexes has been very challenging. Ultimately,
solving additional structures of RNA bound to
epigenetic modifiers will reveal the mechanisms
by which RNA serves direct regulatory roles,
rather than simply serving as a messenger.
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AC KNOWLED GME NTS
We thank R. Yan, Z. Yu, and S. Yang (Janelia Cryo-EM Facility);
C. Moe (University of Colorado Boulder BioKEM Facility); and
S. Zimmermann and G. Morgan (University of Colorado Boulder
Electron Microscopy Service) for microscope operation and data
collection. We thank A. Erbse (University of Colorado Boulder
Shared Instruments Pool RRID SCR_018986) for mass photometer
operation, data acquisition, providing the MST instrument, and help
with MST data interpretation. We thank A. Iragavarapu for help
with plasmid preparation, R. Fenske for help with FP assays,
Y. Long (Weill Cornell Medicine) and C. Lim (University of Wisconsin
Madison) for helpful discussions, and B. Greber for helpful
suggestions related to model refinement. Funding: J.S. is
supported by Howard Hughes Medical Institute (HHMI)–Jane
Coffin Childs postdoctoral fellowship. W.O.H. is supported by NIH
NIGMS postdoctoral fellowship (F32-GM147934). V.K. is supported
by startup funds from University of Colorado Boulder and
NIGMS R00GM132544. T.R.C. and L.I.Z. are HHMI Investigators.
Author contributions: Conceptualization: J.S., V.K., and T.R.C.
Investigation: all authors; Visualization: J.S., A.R.G., W.O.H., B.D.L.,
A.R., and L.Y.; Funding acquisition: L.I.Z., T.E.N., V.K., and T.R.C.;
Project administration: V.K. and T.R.C.; Supervision: L.I.Z., T.E.N.,
V.K., and T.R.C.; Writing – original draft: J.S., V.K., and T.R.C.;
Writing – review and editing: all authors. Competing interests:
T.R.C. is a scientific advisor for Storm Therapeutics, Eikon
Therapeutics, and Somalogic, Inc. L.I.Z. is a founder and
stockholder of Fate Therapeutics, CAMP4 Therapeutics, Triveni Bio,
Scholar Rock, and Branch Biosciences. L.I.Z. is a consultant for
Celularity and Cellarity. The other authors declare no competing
interests. Data and materials availability: All data are available in
the main text or the supplementary materials. Cryo-EM density
maps and fitted models have been deposited in the Electron
Microscopy Data Bank (EMD-29578, consensus map; EMD-29647,
Body1 from multibody refinement; and EMD-29656, Body2 from
multibody refinement) and the Protein Data Bank (PDB: 8FYH).
Requests for reagents, plasmids, cell lines, and zebrafish strains
used in this study should be directed to the corresponding authors.
License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-article-
reuse. This article is subject to HHMI’s Open Access to Publications
policy. HHMI lab heads have previously granted a nonexclusive CC BY
4.0 license to the public and a sublicensable license to HHMI in
their research articles. Pursuant to those licenses, the Author
Accepted Manuscript (AAM) of this article can be made freely
available under a CC BY 4.0 license immediately upon publication.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh0059
Materials and Methods
Figs. S1 to S20
Table S1
References (57–68)
Movies S1 and S2
MDAR Reproducibility Checklist
Submitted 3 February 2023; resubmitted 5 July 2023
Accepted 22 August 2023
10.1126/science.adh0059
Song et al., Science 381, 1331–1337 (2023)
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RES EARCH
NEUROSCIENCE
Volitional activation of remote place representations
with a hippocampal brain–machine interface
Chongxi Lai1*†‡, Shinsuke Tanaka1†‡, Timothy D. Harris1, Albert K. Lee1,2*
The hippocampus is critical for recollecting and imagining experiences. This is believed to involve voluntarily
drawing from hippocampal memory representations of people, events, and places, including maplike
representations of familiar environments. However, whether representations in such “cognitive maps” can
be volitionally accessed is unknown. We developed a brain–machine interface to test whether rats can
do so by controlling their hippocampal activity in a flexible, goal-directed, and model-based manner.
We found that rats can efficiently navigate or direct objects to arbitrary goal locations within a virtual
reality arena solely by activating and sustaining appropriate hippocampal representations of remote
places. This provides insight into the mechanisms underlying episodic memory recall, mental simulation
and planning, and imagination and opens up possibilities for high-level neural prosthetics that use
hippocampal representations.
T he ability to simulate scenarios in one’s
mind is a hallmark of intelligence, as it
facilitates the evaluation of past exper-
iences and future plans. For instance, we
can imagine walking around our previ-
ous workplace, or imagine how our current
workplace might function if we rearranged the
furniture. Such imagination requires an inter-
nal world model that can be flexibly accessed
to construct possible scenarios (1–3).
The hippocampus is a brain region that is
critical for memory and imagination (1, 4–6).
It holds a model of the environment (also called
a cognitive map) (7, 8) that could potentially
be mentally traversed for the purpose of recall
or simulation. In particular, the hippocampus
contains spatial maplike representations of
previously explored environments. Each envi-
ronment’s representation consists of place
cells—neurons that fire selectively whenever
an animal moves through specific locations
(called the “place fields” of those cells) in that
environment (9, 10). This selective firing re-
sults in a distinct multicell activity pattern at
each location in the environment, which, during
physical navigation, can be used to decode the
animal’s current location from the ongoing
pattern of neural activity (11). In contrast, a
key aspect of imagination is the activation of
neural representations that deviate from cur-
rent sensory input, such as those that are non-
local (i.e., represent locations away from one’s
current location). Previous work has shown
brief and intermittent activation of nonlocal
1Janelia Research Campus, Howard Hughes Medical Institute,
Ashburn, VA, USA. 2Howard Hughes Medical Institute and
Department of Neurology, Beth Israel Deaconess Medical
Center, Boston, MA, USA.
*Corresponding author. Email: chongxi.lai@gmail.com (C.L.);
alee31@bidmc.harvard.edu (A.K.L.)
†Present address: Howard Hughes Medical Institute and
Department of Neurology, Beth Israel Deaconess Medical Center,
Boston, MA, USA.
‡These authors contributed equally to this work.
hippocampal spatial representations sugges-
tive of the planning of specific paths within a
cognitive map (12–21). However, it is unknown
whether this activity is volitionally controlled
or rather reflects passive memory–related
processes that are presumably nonvolitional
(22, 23).
To test whether an animal can directly con-
trol its hippocampal activity according to its
model of the world, we used a brain–machine
interface (BMI) approach because, unlike with
humans, we cannot simply ask animals to
imagine scenarios. With BMI methods, we could
reward animals for generating neural activity
resembling the simulation of specific scenar-
ios. More precisely, we could reward them for
the volitional activation of specific nonlocal
representations from the cognitive map—a
fundamental building block of scenario simu-
lation. BMI research has a rich history of di-
rectly testing for volitional control of activity
patterns of neuronal ensembles in the motor
cortex and related areas (24–35). In the hippo-
campus, it has been shown that the activity
level of individual neurons (36, 37) or the pop-
ulation activity related to individual stimuli
(38) can be controlled. However, a real-time
BMI that allows humans or animals to con-
trol their hippocampal population activity in
terms of the content of their cognitive map
(e.g., location representations) has never been
demonstrated.
A hippocampal map–based BMI
We designed a real-time hippocampal BMI
and two BMI tasks to investigate whether rats
could navigate to goals (“jumper” navigation
task), or move external objects to goals while
remaining stationary (“Jedi” object location
control task), within an immersive virtual real-
ity (VR) environment solely by controlling the
activity of a population of place cells. Each
jumper or Jedi BMI experiment consisted of
three phases (Fig. 1A). In phase 1, rats ran to a
succession of arbitrary locations marked by a
tall, visible goal cue placed in a familiar two-
dimensional virtual arena (“running” task).
Upon reaching each cue, liquid reward was
delivered, the trial ended, and the cue moved
to another location for the next trial. Animals
were secured in a harness and could freely
rotate their body and head direction on top of
a spherical treadmill (39) while hippocampal
CA1 neural activity was recorded (Fig. 1B, fig.
S1, and movie S1). We applied a recently de-
veloped field-programmable gate array (FPGA)–
based neural signal processor to perform low-
latency (1 ms) assignment of extracellular spikes
(recorded from 128 channels) to a population
of hippocampal units (40, 41). In the running
task, treadmill movement updated the ani-
mal’s location in the virtual environment, and
many hippocampal units (i.e., place units) dis-
played spatially modulated activity (39, 42–44)
(Fig. 1B, blue arrows) similar to that in real-
world environments (8–11). In phase 2, the
binned spike counts from the most recent 1.5
or 5 s of activity of these place units and the
animal trajectory from the running task
were used to train a decoder (Fig. 1B, green
arrows) that estimates the animal’s current
location from the neural data every 100 ms.
We used a deep neural network for decoding
(fig. S2), allowing the use of data augmenta-
tion for training—a method that improves
both the decoder’s performance given limited
data and its noise robustness. In phase 3, the
treadmill was disconnected from the VR sys-
tem, and the animal’s ability to control its own
or an object’s translational movement was
limited to controlling its hippocampal activity,
which was converted by the decoder into a
specific location output every 100 ms (Fig. 1C).
Note that the decoder was trained to estimate
the animal’s current location in the running
task only, not its location in the subsequent
BMI tasks, but, during BMI periods, the ani-
mal needed to generate activity corresponding
to locations away from its current location.
BMI navigation task
In the jumper task, we tested whether animals
could navigate to arbitrary goal locations as
in the running task, except here by means of
BMI-based first-person teleportation. After
rats performed the running task for ~40 min
(~120 trials) (Fig. 2, A and B, and movie S1),
the data were used to train the decoder, which
accurately estimated the rat’s current location
in the running task [validation set coefficient
of determination (R2) = 0.78 to 0.88] (Fig. 2C).
Jumper trials were identical to running trials,
except the animal’s location was updated to
the BMI-decoded location (smoothed with a
3-s sliding window to help reduce potential
high-frequency visual jitter of the VR updates)
(Fig. 2, D and E, and movie S1). If an animal
did not reach the goal within 62 s, the trial
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RES EARCH | R E S E A R C H A R T I C L E
phase 1: Running task
phase 2: Train decoder
phase 3: BMI tasks
A
B
R
V
e
t
a
d
p
u
Running task
trial 1
trial 2
physically run to goals
Train deep network
population decoder of
current location in
Running task
goal
decoded location
controlled object
phase 1:
Running task
VR projector
raw hippocampal neural data
task 1: BMI navigation (“Jumper”)
task: teleport self to goal
(animal teleported
toward decoded location)
trial 1
trial 2
task 2: BMI object location control (“Jedi”)
trial 1
trial 2
32 electrode groups
1
2
3-32
task: move object to goal
& maintain it there
(animal fixed at center,
object moved toward
decoded location)
spike sort
~40 min data
and select place units
360˚
screen
spherical
treadmill
update location
goal cue
animal’s view
of virtual arena
s
t
i
n
u
e
c
a
p
l
treadmill
movement
phase 2:
Train decoder of
current location
animal
locations
time
0
max
firing rate
spatially tuned activity
of individual place units
sliding window
of spike counts
3
0
2
0
0
1
0
0
s
t
i
n
u
e
c
a
p
l
0
0
0
2
1
0
0
time bins
neural
activity
top view of virtual arena
C
phase 3:
BMI tasks
VR projector
low-latency spike assignment
using spike sorted model (in FPGA)
goal cue
real-time spike trains of
place units
R
V
e
t
a
d
p
u
spherical
treadmill
update location
treadmill
disconnected
decoded location
time
real-time
spike counts
(in PC)
2
0
1
0
1
2
0
2
1
2
0
1
0
1
0
trained
decoder
Fig. 1. Hippocampal map–based brain–machine interface in a virtual reality
system. (A) Steps for performing the two different BMI experiments in this study.
Rats first physically ran to a series of goals (running task), while their hippocampal
neural activity and (virtual) location in a square arena were recorded. This data
was used to train a decoder to take neural activity as input and output the animal’s
current location in the running task. In BMI task 1 (jumper task), animals needed
to generate neural activity that would be decoded as locations they wanted to move
to so that they could reach each goal (to obtain a reward). In BMI task 2 (Jedi
task), animals were fixed at the center of the virtual arena (but could rotate) and
needed to generate activity corresponding to locations where they wanted an
external object to move to so that the object reached the goal, then they needed
to sustain that activity to maintain the object there (to maximize reward).
(B) Schematic of the VR system (left). The animal was free to rotate its body in
the horizontal plane. In the running task, the animal’s location in the virtual arena
environment was updated according to treadmill movement. Simultaneously
recorded spiking from a population of hippocampal CA1 units expressed place
fields—the basis of the cognitive map of the environment (right). Decoder was
then trained using binned spiking activity and location data. (C) In both BMI tasks,
the treadmill no longer updated VR. Instead, the animal or object location was
controlled solely by real-time hippocampal activity. A neural signal processor rapidly
assigned activity to individual units, whose spike counts were fed into the decoder.
VR projection was updated according to locations output by the decoder. In the
jumper (Jedi) task, the animal’s (object’s) virtual location was moved toward the
most recent decoded locations. PC, personal computer.
Lai et al., Science 382, 566–573 (2023)
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Phase 1: Running task
trial 11
1m x 1m arena
trial 10
goal
B
Running trial
D
Jumper BMI trial
20 cm
20 cm
6.4 s
3.4 s
3.5 s
4.2 s
7.6 s
RES EARCH | R E S E A R C H A R T I C L E
A
trial
end
trial
start
3.8 s
trial 14
17.7 s
13.0 s
4.0 s
3.4 s
2.3 s
3.7 s
6.0 s
trials 21-99
Phase 2:
Train decoder of
current location
behavior
decoded
20 cm
e
r
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s
10 s of
trajectory
Y
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(no movement)
)
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rat 2
p = 1.5 × 10-7
rat 3
p = 2.8 × 10-15
100
20
20 cm
5.4 s
125
25
Phase 3: “Jumper” BMI navigation task
1mx1m arena
goal
10.6 s
10.3 s
10.0 s
11.0 s
trial 1
trial 2
G
rat 1
p = 8.2 × 10-11
control
Jumper
trial
end
trial
start
trial 5
7.6 s
8.0 s
16.6 s
5.8 s
6.6 s
11.1 s
14.2 s
9.0 s
120
t
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30
14.6
mean trial duration (s)
50
40
16.3
30
40
50
14.3
30
40
50
H
goal-directedness
of trajectory
0°
0°
0°
45°
-45°
45°
-45°
45°
-45°
11.6 s
7.2 s
12.2 s
90°
-90°
90°
-90°
90°
-90°
trials 13-53
Run
Jumper
135°
-135°
135°
-135°
135°
-135°
180°
180°
180°
Fig. 2. Rats can navigate to goals by controlling their hippocampal activity.
In both the running and jumper BMI tasks, animals were rewarded when they reached
each goal. (A) Animal trajectories in the virtual arena for consecutive running task
trials. Trial duration (time to reach goal) in seconds is shown. (B) Example running
task trial. From top: trajectory, firing rate (z-scored) of individual units (units were
ordered by time of peak activity), treadmill speed, and LFP from one recording channel
and corresponding wavelet spectrogram during trial. (C) Accuracy of trained decoder
of animal’s current location for held-out running task data. Actual and decoded
trajectories during example trial (top left) and across several trials (for x and y
coordinates separately, bottom left). Median decoding error (distance between actual
and decoded locations) with range and quartiles (bottom right). (D) Example jumper
BMI trial with similar trajectory as the running trial in (B). From top: trajectory generated
by the animal controlling its hippocampal activity and the decoder output (animal is
teleported toward decoded location; each gray circle represents the decoded location at
the time the animal is at the corresponding point in the trajectory connected by the
dark line, sampled here every 1 s), firing rate of individual units [using same order of
units as in (B)], treadmill speed, LFP, and spectrogram. (E) Example jumper BMI trial
in which animal did not move the treadmill. Trajectory (left) as in (D). Right, from top: unit
activity, treadmill speed, LFP, and spectrogram. See fig. S10 for all 10 nonmovement
trials. (F) BMI-generated trajectories for consecutive jumper trials. (G) Mean jumper
trial duration (magenta vertical line) is significantly lower than distribution of expected
mean duration for simulated trials if goals were in random locations. (H) Polar distribution
of angle between direction of movement and direction to goal during running and
jumper tasks. Zero corresponds to animal movement directly toward the goal center.
Lai et al., Science 382, 566–573 (2023)
3 November 2023
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A
Phase 1:
Running task
Phase 2:
Train decoder of
current location
Phase 3:
“Jedi” BMI object location control task
50 cm
goal
5 s
distribution of real-time decoded locations
0
max. density
rat location (fixed at center)
950950950
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population burst event (PBE)
population spike count
treadmill speed
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decode
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rat location
(fixed at center)
3
2
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24
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5 s
20 cm
1 s
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rat location
(fixed at center)
3
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-1
p=5.2 × 10-10
p=7.6 × 10-11
D
78.8% < 1 cm/s
67.4% < 1 cm/s
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Jedi
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rat 1
rat 2
rat 3
F
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C
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treadmill speed (cm/s)
rat 1
0
10
20
30
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10
15
rat 2
rat 3
Fig. 3. Rats can move objects to remote goal locations and maintain
them there by controlling their hippocampal activity. In the Jedi BMI task,
trials did not end when the external controlled object first reached the goal;
instead, animals were rewarded as long as the object was in the goal region
(white circle), for up to 3 min per trial. The animal was always fixed at center of
the virtual arena but could rotate its body and generally turned toward each
goal. (A) Distribution of real-time decoded locations (output every 100 ms)
generated by the animal controlling its hippocampal activity across eight
consecutive Jedi BMI trials for rats 1, 2, and 3. Panels show decoded locations
during each trial (up to 3 min; fig. S11). Periods when the animal’s body
rotated >12°/s were excluded. See text and methods for details. The external
controlled object (which was visible for rats 1 and 2 but invisible for rat 3)
was moved toward the decoded location (fig. S11 shows that the distribution
of object locations was essentially the same as the distribution of decoded
Lai et al., Science 382, 566–573 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
locations). (B) A 40-s-long period during an example trial during which the
animal did not move the treadmill. From top: summed activity across all
units with PBEs identified, treadmill speed, distance of decoded location from
goal (0 means inside goal region), and close-ups of two 5-s periods [as
animal moves object to goal (left) and as animal maintains object at goal
(right); points in the arena represent sequence of decoded locations] with
spike trains of units, LFP, and spectrogram. See fig. S12 for additional
example periods. (C) Mean distance of decoded location from goal across
all trials (magenta vertical line) is significantly lower than mean distance
expected for randomized goal locations. (D) Treadmill speed distribution
during periods shown in (A), illustrating that the animal was generally still
during task performance.
ended and a new goal cue appeared at a ran-
dom location.
Rats successfully navigated by controlling
their hippocampus, generating efficient paths
to each goal (Fig. 2F; see figs. S3 to S5 for all
trials of three rats, and figs. S6 to S8 for all
trials re-decoded using a shorter decoding
window and without smoothing). To check
whether this performance could be attributed
to non-spatially-specific neural activity (e.g.,
modulating global firing rate), we randomly
shuffled the spike trains across place units, ran
the shuffled data through the original decoder
to produce simulated trajectories, then deter-
mined how long it would have taken to reach
the same sequence of goal locations as in the
original experiment. Shuffled-unit mean trial
durations were much longer than the actual
means (P < 10−100, three rats, one session each),
suggesting that performance depended on
generating place field–related activity. To test
whether generating non-goal-directed sequen-
ces of location-specific activity (e.g., random
movement within the cognitive map) could
explain the performance, we randomly shuffled
the goal locations in each trial while preserv-
ing the original BMI trajectories and then de-
termined the time that would have been
needed to reach the shuffled goals. Shuffled-
goal mean trial durations were again much
longer than actual means (P = 2.8 × 10−15 to
1.5 × 10−7) (Fig. 2G), indicating that animals’
BMI trajectories were clearly goal-directed.
Goal-directedness was also apparent from the
distribution of angles between the animal’s
instantaneous direction of BMI-generated
movement and the direction from the animal’s
current location to the goal, which was con-
centrated around a value near 0° (Fig. 2H).
Thus, even though jumper trials took longer
than running trials (mean trial duration across
animals: 15.1 s versus 6.9 s; note, however, that
BMI decoding and smoothing added a few sec-
onds to jumper durations), the animals’ routes
revealed effective, goal-directed, map-based BMI
navigation. Furthermore, such performance
was achieved without extensive BMI training
(Fig. 2F; figs. S3 to S5 show sessions 3, 9, and
2 for rats 1, 2, and 3, respectively; table S1; a
fourth rat failed to perform either BMI task).
Although animals were free to physically run
during the jumper task, such movement was
not necessary for task performance. Initially,
animals ran as in the running task, but in later
trials, animals ran less (fig. S9). In a subset of
trials (10 out of 161 trials) (Fig. 2E and fig. S10),
animals remained still, yet in all cases they
efficiently reached the goal. Moreover, this suc-
cessful navigation did not depend on activity
in population burst events (PBEs), which often
appear during immobility and during which
brief activation of place cell representations
for remote locations has been shown to occur
(13–16, 18, 20, 21, 23).
BMI object location control task
Although episodic memories are encoded and
often retrieved using a first-person perspective,
individuals can also imagine scenarios from a
third-person perspective, with other animate
and inanimate players taking part. Further-
more, imagination often involves holding a
single thought in mind for extended periods.
Therefore, our second BMI task, the Jedi task,
tested whether animals—while remaining in
the same place—could use the same map of
the arena to control the location of a virtual
object, guide it to the goal cue location, and
maintain it nearby. The jumper and Jedi tasks
thus used different forms of feedback: self-
location and the location of an object, respec-
tively. After the same running task and decoder
training phases as in the jumper experiment, the
animals in Jedi were fixed (but could freely turn)
at the arena’s center, and the object’s location
was updated to the BMI-decoded location (with
a 2-s smoothing window). In each trial, the goal
cue remained in the same place, providing re-
ward as long as the object touched it. After 3 min
or the rat having received 0.5 ml of reward in
total, whichever came first, a new goal cue ap-
peared at a distant random location for the
next trial.
Rats could activate and sustain a remote lo-
cation’s representation around the goal for
long periods, until the trial ended, and then
shift attention to the next goal (Fig. 3, A and B;
fig. S11; and movie S1). Performance was mea-
sured using the mean distance (over time) be-
tween the decoded locations and goals. Shuffling
spike trains across units yielded much greater
mean distances than the actual means (P = 2.2 ×
10−5 to 2.6 × 10−3, three rats, one session
each). To assess the goal-directedness of BMI-
generated activity, we shuffled the goal loca-
tions while preserving the locations output
by the decoder. The decoded (and controlled
object’s) location was far more concentrated
around the actual remote goal cue than shuffled
goal locations (P = 1.8 × 10−22 to 5.2 × 10−10)
(Fig. 3C and fig. S11), indicating clear goal-
directed control of activity. Again, such per-
formance occurred without extensive training
(Fig. 3A shows sessions 7, 6, and 3 for animals
1, 2, and 3, respectively). Task performance
was not dependent on PBEs, as there was no
change in performance when all activity in PBEs
was eliminated and the decoder was rerun post
hoc (fig. S11).
Animal movement was generally low when
engaged in the Jedi task (Fig. 3D), and move-
ment was not required for successful perform-
ance. There were many longer periods (≥8 s
long with a treadmill speed of ≤1 cm/s, 38
periods, mean: 17.3 s, maximum: 44.0 s) during
which the animal did not move the treadmill
while it directed the object to the goal and/or
held it there (34 of 38 periods) (Fig. 3B and fig.
S12). Activity during PBEs was also generally
not necessary for performance in these non-
movement segments (fig. S12).
Features of volitionally generated spiking and
local field potential activity
What characteristics did the volitionally gen-
erated activity have? First, mean firing rates per
unit were similar between jumper and run-
ning tasks (fig. S13A). Mean firing rates per
unit were correlated across Jedi and running
tasks, but lower in Jedi (fig. S13B)—consistent
with the decreased physical movement in Jedi.
We then investigated the hypothesis that, to
move themselves or the object toward a given
(decoded) location in the jumper and Jedi
tasks, animals generated a pattern of firing
rates across units (i.e., a population vector, or
PV) similar to the mean PV at that location
over the entire running task (called the refer-
ence PV, or rPV) (Fig. 4A). (Note that the set of
rPVs for all locations is thus equivalent to the
standard place field map across the popula-
tion.) We examined the correlation between
the PV generated at each moment (in every
500-ms window) during jumper or Jedi and
the rPV of the decoded location at that mo-
ment. As a benchmark, we computed the cor-
relation between the 500-ms PVs during the
running task with the rPVs corresponding
to the animal’s actual location at those times
(Fig. 4, B and C, “Run”) as well as the correla-
tion between the running task PVs and the
rPVs of random locations (Fig. 4, B and C,
“randRun”). We then correlated jumper or
Jedi PVs with the rPVs of the decoded locations
at each moment (Fig. 4B for “jumper” and Fig.
4C and fig. S14 for “Jedi”) and with rPVs of ran-
dom locations (“randJumper” and “randJedi”).
Jumper and Jedi PVs were significantly correlated
Lai et al., Science 382, 566–573 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
activity during
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actual location
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no movement (Jedi)
movement (Jedi)
5
10
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frequency (Hz)
Fig. 4. Volitionally generated nonlocal activity is similar to the activity
when the animal is at the corresponding locations and is associated with
theta-band power in the LFP. (A to E) The population vector (PV) of ongoing
spiking activity was compared with the average place field activity (rPV) at
a given location during the running task. (A) Schematic of comparison.
(B) Mean correlation of instantaneous (500-ms window) PV during running or jumper
task with rPV for the current location (in the running task), current decoded
location (in the jumper task), or random location in the running (randRun) or jumper
(randJumper) task. (C) Same as (B) but for the Jedi task. For Jedi, only periods
when decoded location was near (within 5 cm of) the goal were included [also
for (E)]. [(D) and (E)] Correlation of PV with rPV relative to baseline random
value as a function of the time integration window for determining the PV.
(F and G) Evaluation of decoder performance when ground truth activity for each
location, i.e., the rPV, was input into the decoder. (F) Schematic of evaluation
procedure. (G) Comparison of our DNN decoder to Bayesian decoder for different
levels of added noise, with example traces using a specific level of noise (top).
(H) Distribution of decoded location (left) during Jedi task segment with no
treadmill movement (right). Right, from top: summed activity across all units with
PBEs identified, treadmill speed, distance of decoded location (excluding data
during PBEs) from goal, and close-up of LFP with spectrogram. (I) Power spectral
density of z-scored (for pooling across animals) LFP during the Jedi task for
periods of treadmill movement and all long segments (≥8 s) without treadmill
movement. See text and methods in the supplementary materials for details. Here
and elsewhere, all confidence intervals (CIs) are 95% CIs.
Lai et al., Science 382, 566–573 (2023)
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with the rPVs associated with the decoded loca-
tions versus random locations, consistent with
the hypothesis. Furthermore, jumper PV-rPV
correlations were comparable to running task
PV-rPV correlations. In line with this, the ex-
ample running (Fig. 2B) and jumper (Fig. 2D)
trials, which happened to share similar trajec-
tories, showed similar activity patterns across
place units over time. PV-rPV correlation scores
were, unlike in jumper, lower in Jedi than in
the running task using 500-ms windows (Fig.
4C), consistent with noisier generation of non-
local representations and/or lower firing rates
(fig. S13B) in Jedi. However, with longer in-
tegration windows (>500 ms) (Fig. 4, D and
E), the PVs generated during Jedi matched
the rPVs as well as the best match during the
running task (note that longer integration times
work for Jedi because animals activated goal
location representations for extended periods).
These results indicate that, during BMI task
performance, animals generated nonlocal pop-
ulation activity as similar to the corresponding
place field representations as when they ac-
tually visited those locations in the running
task. Were these place field–like (i.e., rPV-like)
patterns what our deep network detected to
decode location? While determining what fea-
tures a deep network uses for decoding is gen-
erally not straightforward, inputting a single
location’s rPV for a brief duration was suffi-
cient to produce accurate location decoding
(Fig. 4, F and G), consistent with the decoder
being tuned to detect rPV-like activity. In ad-
dition, unlike the commonly used Bayesian
decoder (45), our decoder was highly robust to
noise (Fig. 4G) by design because of the use of
data augmentation during training.
Lastly, we analyzed the local field potential
(LFP) activity during BMI task performance
(Fig. 4, H and I). When animals move, the ro-
dent hippocampal LFP is known to display
prominent theta band (∼5 to 12 Hz) power,
which peaked at ~7.3 Hz during periods of
movement in the running and BMI tasks (Fig.
4I). During the extended periods of nonmove-
ment when the animal was performing the
Jedi task, the theta peak shifted down to 6.3 Hz
(Fig. 4I). Note that, unlike the more continuous
theta oscillations during movement, the oscil-
lations during such nonmovement periods
tended to be more intermittent.
Discussion
Previous BMI research has yielded major ad-
vances in the control of robotic arms, com-
puter cursors, and other devices by activity
from the primary motor cortex, premotor cor-
tex, and posterior parietal cortex (24–35). The
hippocampal cognitive map has a code that
represents space in terms of absolute location
in the external environment versus location
relative to (e.g., in front of, or to the right or
left of) the animal (8–11), and it was unknown
whether a subject could control a BMI by
means of this code. With this study, we dem-
onstrated a hippocampal map–based BMI in
which the subject is able to control its location
or that of other objects by activating location
representations in terms of absolute space, in-
dependent of where the animal currently is.
That is, even though animals generally (but
not always) turned their body toward the goal,
the activity that needed to be generated dif-
fered depending on the location of the goal
with respect to the environment. The relative-
ly small amount of training needed for the
animals to perform our BMI tasks is in line
with our use of a biomimetic decoder (35, 46),
that is, one based on the neural code that the
subject naturally employs.
In humans, imagining or recalling objects or
video clips is accompanied by hippocampal
activity in individual neurons similar to that
when viewing the original stimuli (47, 48).
This suggests that the mechanisms allowing
animals to selectively activate their nonlocal
hippocampal spatial representations, as we
have shown here, could also underlie our abil-
ity to actively recall or imagine experiences in
other places. The ability of rodents to perform
these BMI tasks should thus allow imagina-
tion, as well as the voluntary recall of memory,
to be investigated using the range of tools
available for this model system. More gener-
ally, the neural processes engaged here could
underlie our capacity to perform “mental time
travel”—travel back in time by reexperiencing
richly detailed episodic memories and travel
forward in time by generating possible future
scenarios (49). Mental time travel depends
critically on the hippocampus (4–6, 50–52)
and enables subjects to internally simulate new
experiences according to their world model.
This can aid decision-making and facilitate
learning in complex situations where trial and
error is expensive, as shown using artificial
agents (3, 53–55).
Along these lines, the rats in our study could
control their hippocampal map-based activity
on a timescale of seconds, corresponding to
the speed and duration at which humans re-
live past events or imagine new scenarios.
Navigational trajectories each lasted ~10 s,
and a virtual object could be held at a remote
location for several seconds. This contrasts
with the previously described fast (~100 ms)
sequences of nonlocal hippocampal activity in
awake rodents (i.e., awake replay events, which
are associated with population bursts and
sharp wave–ripples) thought to be associated
with planning (12, 16, 18, 21), and which were
not responsible for the performance in our
BMI tasks (analysis in which all PBEs were re-
moved). The content of such replay events,
which can portray specific routes through
the environment starting from the animal’s
current location, has been shown to be corre-
lated with deliberative (12) and future (16, 18, 21)
behavior. However, it is not known whether
this content is—or replay content in general
can be—under an animal’s volitional control.
For instance, hippocampal activity displays
similar fast sequences during sleep (23), thus
nonlocal path generation per se does not ap-
pear to require intention. If awake replay is
volitionally controlled, these events could rep-
resent a brief consideration of alternatives for
making a quick decision and be distinct from
the more comprehensive mental simulations
of possible scenarios that take seconds. Previ-
ous work has also described neurons in the
hippocampus and related areas whose activity
is tuned to the angle to a goal or a salient cue
or object relative to the direction the animal is
facing (56–59). In addition, hippocampal neu-
rons that are tuned to the location of con-
specifics have been found (60, 61). As with
fast sequences, whether these forms of activity
that reflect locations away from the animal are
volitionally controlled is yet to be determined.
Beyond aiding decision-making, the ability
to control the content of the hippocampal
spatial and episodic memory system could help
explain the richness of our inner lives. Finally,
the ability to control hippocampal activity to
guide oneself or objects to intended locations—
and do so with high signal-to-noise readout
using our decoder—could lead to new BMI ap-
plications for restoring or enhancing function
by realizing a subject’s high-level intentions
with respect to their internal world models.
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ACKN OWLED GMEN TS
We thank M. Bolstad for work on the virtual reality software;
W. Bishop, S. Romani, and X. Zhao for valuable discussions
regarding the study; S. Lindo, R. Gattoni, and other members of
the Janelia Vivarium team, and B. Lustig, A. Sohn, S. Sawtelle,
I. Negrashov, B. Foster, J. Osborne, J. Arnold, R. Rogers, and
J. Cohen for technical assistance; and J. Dudman, S. Romani,
A. Hantman, T. Wang, and J. Colonell for valuable comments
on the manuscript. Funding: This work was supported by
the Howard Hughes Medical Institute (A.K.L. and T.D.H.).
Author contributions: Conceptualization: C.L. and A.K.L. Task
design: C.L. BMI and task software and BMI hardware: C.L.
Behavioral and recording hardware: S.T. Experiments: S.T.
and C.L. Data analysis: C.L. and A.K.L. Writing: C.L., A.K.L., and
S.T. Supervision: A.K.L. and T.D.H. Competing interests:
T.D.H. is also affiliated with the Department of Biomedical
Engineering at Johns Hopkins University. Data and materials
availability: All data needed to assess the findings in this study
are publicly available at Zenodo (62). All analysis methods
are described in the main text and supplementary materials,
and the code for building and applying the decoder is publicly
available at Zenodo (62). License information: Copyright ©
2023 the authors, some rights reserved; exclusive licensee
American Association for the Advancement of Science. No claim
to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse. This article is subject
to HHMI’s Open Access to Publications policy. HHMI lab
heads have previously granted a nonexclusive CC BY 4.0 license to the
public and a sublicensable license to HHMI in their research articles.
Pursuant to those licenses, the author-accepted manuscript (AAM) of
this article can be made freely available under a CC BY 4.0 license
immediately upon publication.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh5206
Materials and Methods
Figs. S1 to S14
Table S1
References (63–72)
MDAR Reproducibility Checklist
Movie S1
Submitted 9 March 2023; accepted 22 September 2023
10.1126/science.adh5206
Lai et al., Science 382, 566–573 (2023)
3 November 2023
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RES EARCH
QUANTUM OPTICS
Quantum vortices of strongly interacting photons
Lee Drori†, Bankim Chandra Das†, Tomer Danino Zohar, Gal Winer, Eilon Poem,
Alexander Poddubny, Ofer Firstenberg*
Vortices are topologically nontrivial defects that generally originate from nonlinear field dynamics.
All-optical generation of photonic vortices—phase singularities of the electromagnetic field—requires
sufficiently strong nonlinearity that is typically achieved in the classical optics regime. We report
on the realization of quantum vortices of photons that result from a strong photon-photon interaction
in a quantum nonlinear optical medium. The interaction causes faster phase accumulation for
copropagating photons, producing a quantum vortex-antivortex pair within the two-photon wave
function. For three photons, the formation of vortex lines and a central vortex ring confirms the
existence of a genuine three-photon interaction. The wave function topology, governed by two- and
three-photon bound states, imposes a conditional phase shift of p per photon, a potential resource
for deterministic quantum logic operations.
P hotons do not interact with one another
in the optical regime. An effective inter-
action between photons can be medi-
ated by matter, but, in conventional
optical nonlinear media, this interac-
tion is negligible on the level of individual
photons. It is only at the ultimate limit of quan-
tum nonlinear optics, realized in specially en-
gineered systems, that a single photon can
alter the optical response of the system, ren-
dering an appreciable photon-photon inter-
action (1–4).
The realization of strong photon-photon in-
teractions in atomic ensembles can enable de-
terministic quantum-information processing
for optical qubits, such as single-photon tran-
sistors and phase gates (5–7). It can be used
to generate nonclassical states of light, such
as squeezed, cluster, and repeater states, as a
resource for quantum communication, com-
putation, and sensing (8, 9). It can also mani-
fest in interacting quantum gases and fluids
of photons, allowing the exploration of exotic
many-body physics for light (10–13).
We realize an extreme regime of quantum
nonlinear optics and observe optical quantum
vortices generated by the interaction between
only two or three photons. Quantum vortices—
phase singularities of the wave function—are
typically expected in strongly interacting sys-
tems of many particles, such as nonlinear op-
tical systems (14, 15), superfluids (16–19), and
hybrid light-matter systems (20–24). In this
work, we induce a strong, effective interaction
at the few-photon level by coupling photons to
Rydberg atoms in an ultracold rubidium gas
(Fig. 1, A and B).
The photons propagate through the me-
dium as light-matter polaritons, at 10−6 times the
speed of light. Because of the strong van der Waals
Department of Physics of Complex Systems, Weizmann
Institute of Science, Rehovot 7610001, Israel.
†These authors contributed equally to this work.
*Corresponding author. Email: ofer.firstenberg@weizmann.ac.il
Drori et al., Science 381, 193–198 (2023)
14 July 2023
coupling between the Rydberg atoms, photons
that propagate close to each other—at a dis-
tance smaller than the so-called blockade radius
rb—experience a local change in the refractive
index. For two photons, the optical field can be
described by a wave function y(x1, x2), which
is the probability amplitude of having photons
at coordinates x1 and x2 along the medium (25).
The change in refractive index at x1 (cid:1) x2
j ≤ rb
causes the accumulation of excess local phase
in y(x1, x2), which, under the correct conditions,
produces vortices in y(x1, x2).
j
To understand the vortex formation, we con-
sider a simplified analytical model describing
the evolution of y(x1, x2) in a medium of uni-
form density and length L using the two-photon
Schrödinger equation (25, 26):
i@Ry ¼ (cid:1)
1
2m
@2
r
y þ V 2ð Þ rð Þy
ð1Þ
Here, r = x1 − x2 is the relative coordinate of the
two photons, and the center-of-mass coordi-
nate along the medium R = (x1 + x2 + L)/2 = 0…
L plays the role of time. The incoming, co-
herent probe field dictates homogeneous initial
conditions y(r, R = 0) = 1. The photon-photon
interaction is described by a nearly square
6), where U con-
potential V (2)(r) = U/(1 + r6/rb
stitutes the change in the refraction index due
to the Rydberg blockade, and the (negative)
effective mass m = −U/8 arises from single-
photon dispersion. Because mU < 0, Eq. 1 de-
scribes attraction between photons (25).
A nontrivial prediction of Eq. 1 is the for-
mation of vortex-antivortex pairs in the me-
dium, symmetrically around the potential well
(Fig. 1C). Equation 1 has localized and extended
eigenstates, denoted as bound and scattering
two-photon states (25). Considering a single
bound state ybound(r) with energy E2, which is
the case in our experiment, the initial scatter-
ing component is yscat = 1 – ybound(r). In the
crudest approximation, the phase accumula-
tion of the scattering component can be ne-
glected (27), and the solution to Eq. 1 reduces to
y r; Rð
Þ ¼ e(cid:1)iE2Ry
bound rð Þ þ y
scat
ð2Þ
The phase vortices are formed around y = 0
when the two terms—the bound and scatter-
ing components—cancel each other. This re-
sult is generic and occurs for a sufficiently long
medium and for any number of bound states.
Such an interference mechanism for vortex-
antivortex pair formation is universal and
known from acoustics (28) and atomic col-
lisions (29) to linear (30, 31) and nonlinear (32)
optics. However, such vortex-antivortex pair
formation has not been observed before in
quantum optics because the required strong
and prolonged photon-photon interaction had
been unattainable.
jr2
We quantify the duration and strength of
the interaction by the dimensionless parame-
ters ϕ = UL/2 and l ¼ 2 Umj
b (33), respec-
tively. For vortices to develop, ϕl should be
large. When the interaction is weak, that is, for
l ≪ 1, we find the condition ϕl > ϕ0, with the
threshold phase ϕ0 ≈ 0.94p. For moderate in-
teractions l ≥ 1, the condition is ϕ > ϕ0 [see
section S2.4 in (27)]. These conditions are
illustrated by solid lines in the “phase diagram”
in Fig. 1D, and they compare reasonably well
with the domain of vortex formation calculated
numerically for our experimental, nonuniform
medium (green shading).
In Rydberg polariton systems, the essen-
tial experimental parameters are the total
optical depth OD of the medium (e−OD being
the on-resonance transmission) and the optical
depth of the blockade range ODb = OD·rb/L.
These parameters govern ϕ º OD and l º
2. In our experiment, we reach OD ≈ 110
ODb
and ODb ≈ 22, setting ϕ ≈ 2.7p and l ≈ 3
(blue diamond in Fig. 1D). The moderate inter-
action obtained in previous experiments (ϕ ≈
1.5p and l ≪ 1), albeit being enough to ob-
serve the signatures of photonic bound states
(25, 34, 35), were well below the threshold
for vortex formation.
Observation of two-photon vortices
p
Our experiment starts by compressing and
trapping an ultracold rubidium cloud with a
0e(cid:1)x2=2s2 centered at
Gaussian density profile r
ffiffiffiffiffi
x = 0 and effective length L ¼
s ≈ 75 mm
2p
along the optical axis x. Our maximal peak
density r0 ≈ 5 × 1012 atoms/cm3 is a factor of
three to six higher than that in previous ex-
periments and is the primary source of our
large l º r0
2. We form Rydberg polaritons
using counter-propagating probe and con-
trol fields, which together resonantly couple
the atomic 5S ground level to the 100S Rydberg
level via the 5P level (Fig. 1B). We send, on av-
erage, f ≈ 0.25 probe photons per microsecond.
The probe photons experience the three-
level optical susceptibility, except within the
1 of 6
RES EARCH | R E S E A R C H A R T I C L E
A
C
B
D
Fig. 1. Setup and conditions for generating photon vortices in Rydberg-
mediated quantum nonlinear optics. (A) Counter-propagating probe (red) and
control (blue) fields are focused onto an elongated ultracold atomic cloud (left,
absorption image), held in a crossed optical trap (green). After traversing the
medium, the probe light is split and measured by four single-photon detectors D1
to D3 and Df. Detectors D1 to D3 provide the two-photon and three-photon
correlation functions g(2) and g(3). Detector Df, which measures the interference
beat between the probe and reference light (LO, local oscillator), is correlated
with detectors D1 to D3 to extract the conditional phases f(2) and f(3) (see also
fig. S2). (B) Atomic-level structure for generating polaritons comprising the 100S
Rydberg orbital. The van der Waals interaction (vdW) between two Rydberg
atoms disturbs the propagation of two close polaritons, leading to local
p
ffiffiffiffiffi
12
accumulation of excess propagation phase. (C) Amplitude and phase of the
two-photon wave function, calculated numerically in the Schrödinger approxi-
mation (Eq. 1, with U ¼
=rb), showing the formation of a vortex-antivortex
pair of two interacting photons. (D) Conditions for vortex generation (green
shaded area, calculated numerically for a realistic Gaussian cloud) in terms of the
photon-photon interaction strength l and the accumulated interaction phase in
the finite medium ϕ. The solid curves are minimal conditions calculated
analytically for a uniform cloud under the approximation of Schrödinger evolution
(27). The dotted blue line indicates the available ϕ and l in our experimental
setup, peaking at the blue diamond. Red circles indicate the conditions
achieved in (25, 34, 35). The inset image depicts the phase structure of a
single vortex-antivortex pair.
blockade range rb ≈ 15.3 mm, where they
experience the two-level (5S-5P) susceptibility.
Ideally, we want the difference U between
these susceptibilities to be purely real, render-
ing a conservative photon-photon interaction.
To this end, we first detune the probe from the
atomic transition by D = 9.4G, where G is the
half-width of the 5P level, and then adjust
the control frequency such that the transmis-
sion remains the same outside and inside of the
blockade range (25). This adjustment elimi-
nates the residual nonconserving (dissipative)
part of the interaction and amplifies the con-
serving part U = (OD/L)(qG/D) by the factor
q ≈ 1.4 (27). The atomic density decreases dur-
ing the experimental cycle by a factor of 5.5,
allowing us to study the full range 110 ≥ OD ≥
20 (2.7p ≥ ϕ ≥ 0.5p) and, correspondingly, 22 ≥
ODb ≥ 4.1 (3 ≥ l ≥ 0.1) in each experiment
(dotted line in Fig. 1D).
The vortex-antivortex pair forms in the two-
photon wave function y(r, R) of the probe
inside the medium. Although we cannot di-
rectly measure these vortices within the medium,
we experimentally determine their presence and
structure from the correlations of the outgoing
photons, essentially measuring y(r, R = L) at
the medium’s boundary. We track the depen-
dence of y(r, R = L) on the optical depth OD,
and by varying OD, we effectively vary the
interaction duration. The dependence on OD
at the boundary becomes a proxy for the evo-
lution in the bulk. Whereas OD corresponds
to R, the temporal separation t between the
outgoing photons coarsely corresponds to their
spatial separation r in the medium (36). Ex-
perimentally, we measure the two-photon cor-
relation function g(2)(t) and conditional phase
f(2)(t) of the outgoing probe field for varying
OD and associate them, respectively, with the
squared amplitude and phase of y(r, R = L).
In the experimental results (Fig. 2, A and B),
we first observe the gradual bunching of pho-
tons, g(2)(0) > 1, as the OD increases, accom-
panied by depletion of g(2)(t) at tj j ≈ 0:25 ms
[see cross section (i) in Fig. 2A]. The bunching
and depletion are due to the effective attraction
between the photons, which is governed by a
two-photon bound state and accompanied by
accumulation of conditional phase f(2)(0) < 0
[see (i) in Fig. 2B] (25). At OD ≈ 78, f(2)(0)
reaches −p. A p conditional phase allows for
deterministic, maximally entangling operation
on photonic qubits (7), and here it is obtained
for copropagating photons.
The vortex-antivortex pair is formed around
OD ≈ 80, as manifested by the clockwise and
counterclockwise phase twists in Fig. 2B (or-
ange arrows). These phase twists correspond
to steep steps of f(2)(t) at tj j ≈ 0:25 ms, whose
direction flips when the OD increases [com-
pare (ii) with (iii) in Fig. 2B]. Furthermore,
as expected, the photons are depleted from the
vortex core, where g(2)(t) = 0.24 (global minima
in Fig. 2A). Following the vortex-antivortex for-
mation, f(2)(0) decreases gradually from p to
zero, and the bunching and depletion in g(2)
get smaller. The vortices effectively “unwind
the tension” between the regions of fast and
slow accumulation of phase.
Our experimental results are also corrobo-
rated by numerical simulations based on the
model described in (25, 36). The simulations
use the actual experimental parameters, in-
cluding the Gaussian density profile of the
Drori et al., Science 381, 193–198 (2023)
14 July 2023
2 of 6
RES EARCH | R E S E A R C H A R T I C L E
A
B
C
Fig. 2. Two-photon
vortices. (A and B)
Color maps show the
experimental (A) two-
photon correlation
g(2) and (B) two-photon
phase f(2) as a function
of the time between
photons t and the optical
depth of the atomic
medium OD. Enlarged
views (i) to (iii) explicitly
show the measured
curves g(2)(t) and f(2)(t)
for OD = 49, 78, and 95.
A vortex-antivortex pair
[orange arrows in (B)] is
formed around OD = 80
on the edge of the medium
and is thus captured by
the detectors as a phase
step around |t| = 0.25 ms
and a phase wrap of
f(2)(t = 0) from −p to +p.
At the vortices’ core,
g(2) approaches zero.
(C) Numerically calculated
f(2) for the experimental
conditions. (D and E) Nu-
merically calculated
phase of the stationary,
space-dependent two-
photon wave function,
showing the two-photon
vortices forming (D) deep
inside the medium and (E)
on the edge. Dashed circles
represent the edge (2s) of
the Gaussian cloud.
D
medium and the propagation of the second
photon after the detection of the first photon.
They are presented in Fig. 2C and are in excellent
agreement with the measured data, reproduc-
ing the vortex-antivortex pair and the surround-
ing phase structure in full detail. The 10%
discrepancy in the OD at which the vortices
are observed is due to a slight saturation of our
phase detection scheme and is completely
resolved for a weaker incoming probe (see fig.
S5). We use these simulations to calculate the
conditions for vortex formation in Fig. 1D (green
shaded area).
Moreover, the simulations are able not only
to reproduce the experimentally accessible data
but also to establish the dynamics of the two-
photon wave function y(x1, x2) inside the me-
dium. Figure 2, E and D, presents the phase of
y(x1, x2) for two values of OD. These simu-
lations exhibit the entrance of phase singulari-
ties and eventually the presence of a stationary
pair of quantum vortices in the medium.
Three-photon vortices
The strong interaction, responsible for forming
two-photon vortex-antivortex pairs, leads to an
even richer topological structure of the three-
photon wave function y(x1, x2, x3). We will first
illustrate this by considering only the pairwise
photon interactions. If only two of the three
photons are close together, they attract each
other and form a quasi-bound two-photon state.
Because the third photon remains unbound, the
three pairs of vortices resulting from each of the
three possible quasi-bound states would mani-
fest as six vortex lines in the (x1, x2, x3) space.
To verify this prediction, we measured the
three-photon phase f(3)(t1, t2, t3) and the cor-
responding correlation function g(3)(t1, t2, t3)
over a range of OD. Whereas the stationary
two-photon correlation function depends on
a single time separation t1 − t2, characteriza-
tion of the three-photon wave function requires
two time separations. These are conveniently
parametrized by the Jacobi coordinates
h ¼ t21=
ð
and z ¼ t13 þ t23
, where
tij = ti − tj (37). The three-photon measure-
ments are then given by three-dimensional
(3D) datasets for f(3) and g(3) that depend on h,
z, and OD.
ffiffiffi
6
ffiffiffi
2
Þ=
p
p
(cid:3)
(cid:3)
Figure 3A shows f(3)(h, z) at the critical OD
where vortices appear. We identify cores of
vortex lines with p-phase dislocations: along
(cid:3)
(cid:3) ¼ p region)
the edges of the six-bar star ( f 3ð Þ
and around the center (f(3) = 0 region). Figure
3, B and C, shows the development of the phase
along the lines z = 0 (uniformly separated
photons) and h = 0 (a photon at some distance
from a pair). Notably, f(3)(0, 0) varies mono-
tonically with OD much faster than f(2)(0)
does, as seen by comparing Fig. 3B with Fig. 2B.
Eventually, the vortices structure is best
understood from Fig. 3D, which shows the re-
(cid:3)
(cid:3) ¼ 0:7 rad=ms,
constructed 3D isosurfaces ∇f 3ð Þ
with the phase f(3) indicated by the surface
color. The starlike structure of tubes in Fig.
3D corresponds to six vortex lines, in agree-
ment with our prediction. We can addition-
ally verify that this structure is due only to the
two-photon attraction by constructing it from
the measured two-photon data. This construc-
tion, shown in fig. S4, exhibits a starlike vortex
structure nearly identical to that found in the
three-photon data.
(cid:3)
(cid:3)
¼ y
Þ þ y
Þ þ y
bound r21ð
bound r32ð
bound r13ð
The vortex star structure can be explained
analytically by generalizing Eq. 2 to three pho-
tons. To this end, we replace ybound(r) by a sum
y 2→3
ð
Þ
Þ of
bound
three quasi-bound states (rij = xi – xj), respecting
the bosonic (permutation) symmetry of the three-
photon wave function. For simplicity, we assume
bound rð Þ ¼ 2e(cid:1)2 rj j=a in a
a weakly bound state y
delta potential, where a ≈ rb/l is the scattering
length (25, 38). As shown in Fig. 3E using the
spatial Jacobi coordinates h ¼ r21=
and
ffiffiffi
z ¼ r13 þ r23
, the generalized Eq. 2 gives
6
the six vortex lines. These results support our
ffiffiffi
2
Þ=
p
p
ð
Drori et al., Science 381, 193–198 (2023)
14 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. Three-photon vortex lines and vortex ring. (A to D) Three-photon con-
ditional phase f(3)(h, z) measured at different OD, where h and z are time
separations between the photons in Jacobi coordinates. For each OD, the data are
averaged by assuming a sixfold symmetry; an example of data before averaging is
shown in the inset in (A). We present three cross sections: (A) OD = 79, (B)
z = 0, and (C) h = 0. In all these, the central feature originates from three-photon
interactions. In (D), to reveal the vortex structure, we plot the measured f(3) along
(cid:3)
(cid:3)
(cid:3)
(cid:3), which are themselves derived from the data. We identify six
isosurfaces of rfð3Þ
vortex lines (tubes) and a central vortex ring (torus); note the 2p phase twist around
the cross section of the tubes and torus (inset). (E and F) Analytic calculation
of the three-photon phase arg[y(h, z, R)] using the approximate ansatz in Eq. 3 (E)
without and (F) with the three-photon bound-state term, for E3 = 3E2 and
y 3ð Þ
Þ. The outer vortex lines are due to the generalized two-
bound 0; 0ð
photon bound states, whereas the vortex ring is due to the three-photon bound state.
Þ ¼ (cid:1)3y 2→3
bound 0; 0ð
Þ
ð
interpretation that the vortex lines in the
three-photon wave function are a direct gen-
eralization of the two-photon vortices.
The full three-photon data, however, show
richer behavior, which cannot be reduced to
just independent pairwise photon attraction.
The effect of a third photon approaching a
bound pair is reflected in the central feature in
Fig. 3C and, more clearly, as a torus around h =
z = 0 in Fig. 3D, manifesting a vortex ring. This
inner ring does not originate from two-photon
quasi-bound states but rather from a genuine
three-photon bound state y 3ð Þ
bound (34, 37) that
interferes with the scattering states.
To describe the formation of the ring, we
bound and its
use the following ansatz, adding y 3ð Þ
energy E3 to the generalized Eq. 2:
y h; z; R
ð
Þ ¼ e(cid:1)iE3Ry 3ð Þ
h; z
ð
bound
ð
Þ
þ e(cid:1)iE2Ry 2→3
bound
Þ
þ y
scat
ð3Þ
Þ
ð
scat
bound
bound
h; z
p
Þº e(cid:1)
¼ 1 (cid:1) y 3ð Þ
ffiffi
ffiffi
p
p
j
hþ
j=ae(cid:1)
z
2
3
ð
(cid:1) y 2→3
wherey
bound . As shown in
(34, 39), the wave function of a three-photon weakly
bound state near h = z = 0 can be approximated
ffiffi
ffiffi
p
byy 3ð Þ
j=a.
j
h(cid:1)
jhj=ae(cid:1)
z
2
8
This form can be interpreted as a product of
confined states, with three pairs attracting
each other simultaneously. It is then straight-
forward to check, as shown in Fig. 3F, that the
interference between the first and last terms
in Eq. 3 produces a vortex ring with the same
topology that we observe experimentally.
ffiffi
p
3
Another important result revealed by the
f(3) data in Fig. 3 is that the vortex lines and
ring appear approximately at the same value
of OD ≈ 80. This observation is far from
obvious, allowing us to estimate the relation
between the bound state energies E3 and E2.
An analytical model with only pairwise in-
teraction V (2) predicts E3 = 4E2 (40), which
would result in the vortex ring appearing at
j
a lower OD. Fitting Eq. 3 to the experimental
data yields E3 = 3E2, so that e(cid:1)iE3R ¼ (cid:1)1 forms
a vortex ring simultaneously with e(cid:1)iE2R ¼ (cid:1)1
forming the vortex lines, as shown in Fig. 3F.
The result E3=E2
j < 4 is experimental evi-
dence of a genuine three-photon repulsion
term V (3)(h, z) that attenuates the pairwise
photon attraction (37, 41). This attenuation
follows from the physics of the Rydberg block-
ade, where one photon can “saturate” the in-
teraction and simultaneously block two (or
more) other photons.
The conditional (same-time) phase f 3ð Þ
0
≡
f 3ð Þ 0; 0ð
Þ, which originates from the construc-
tive sum of the vortex lines and ring, is f 3ð Þ
≈
0
(cid:1)2p. This nonzero value is evident from the
monotonic increase of the phase versus OD in
Fig. 3, B and C, or from the phase winding
directions in Fig. 3D. Alternatively, one can
unwrap the f(3) data, as shown in fig. S3, to
find −2p at the center of the ring. Impor-
tantly, given that f 2ð Þ
≡ f 2ð Þ 0ð Þ≈ (cid:1)p, we find
0
f 3ð Þ
0 . This result deviates from the
0
known nonlinear quantum-Kerr phase for n
photons f nð Þ
Þ=2, which ascribes
ð
Kerrn n (cid:1) 1
Kerr
f 3ð Þ
ð2Þ ¼ (cid:1)p (42). Our result
Kerr
Kerr
ð3Þ ¼ 2f 2ð Þ
f
0 agrees with the prediction for sat-
0
urated interaction (34), again indicating the
attenuation of the interaction by the block-
ade saturation.
¼ f 2ð Þ
¼ (cid:1)3p for f
¼ 2f 2ð Þ
The strong three-photon attraction in
the l > 1 regime and the repulsive effect of the
blockade saturation are also evident in the
three-photon correlations g(3) presented in
Fig. 4. Whereas the six crests of g(3) > 1 away
from the center are governed by the two-photon
quasi-bound states, the structure at the center
is substantially modified by the three-photon
bound state. To see this, compare the mea-
sured g(3) data in Fig. 4, A to C, with that
expected from only the pairwise interactions
Þ þ g 2ð Þ t13ð
(3) = g (3) − gd
g 3ð Þ
Þ þ g 2ð Þ t32ð
¼ g 2ð Þ t21ð
Þ (cid:1) 2 in Fig.
d
4, D to F. g 3ð Þ
d is the so-called disconnected part
of the correlations (37). It is evident in all cross
sections that the central peak in g(3), reaching
a maximal value of g(3)(0, 0) = 7.4 ± 0.3, is twice
as narrow as the corresponding peak in g 3ð Þ
d .
This strong three-photon bunching has been
characterized before and attributed to the
tighter confinement of y 3ð Þ
bound compared with
y 2ð Þ
bound (34, 37).
The effect of blockade saturation is best
captured by the connected part of the correla-
(3) in Fig. 4, H and I. We
tions gc
(3) as a manifestation of the
can interpret gc
contribution of the three-photon correction
term V (3), which is repulsive. First, the repul-
sion attenuates the bunching of simultaneous
(3) close
photons, as evident by the negative gc
to the center (blue in Fig. 4, G to I). We observe
a minimal value ofg 3ð Þ
¼ (cid:1)2:5 T 0:2. Second,
as photons are less attracted to the center, we
(3) (at a radius
observe a ring of positive gc
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h2 þ z2
≈ 0:25 ms; red in Fig. 4G), reaching
g 3ð Þ
c;max ¼ 0:9 T 0:1. As expected, with l > 1, both
c;min and g 3ð Þ
g 3ð Þ
c;max are an order of magnitude
larger than the values obtained previously with
l ≪ 1 (34, 35, 43). Finally, gc
(3) is modulated
along that ring, exhibiting six peaks where the
three photons are uniformly separated in time
(e.g., along h, for z = 0). This, too, is due to the
repulsive correction, which favors equally
spaced photons over the asymmetric arrange-
ment of one photon separated from a close
pair (e.g., along z, for h = 0). For larger photon
separations, the regularization effect of V (3)
diminishes, and gc
(3) approaches zero.
c;min
Discussion and summary
Our observation of topological defects—including
quantum vortex-antivortex pairs, vortex lines,
and vortex rings—in the few-body wave function
Drori et al., Science 381, 193–198 (2023)
14 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 4. Three-photon bound-state and blockade saturation. (A to C) Three-photon
correlations g(3)(h, z, OD) (after sixfold averaging), sectioned at (A) OD = 69, (B) z =
0, and (C) h = 0. (D to F) Disconnected part of the correlations gd
calculated from only the g(2)(t, OD) data and representing the two-photon contribution
to the three-photon correlations. The strong confinement of the three-photon
(3)(h, z, OD),
(3) = g(3) − gd
bound state leads to a tighter bunching feature. (G to I) Connected part of the
(3), reflecting the dynamics beyond pairwise interactions.
correlations gc
These dynamics are regulated by the saturation of the blockade interaction, expressed
as an effective, short-range repulsive force. The negative central feature (blue), the
positive ring (red), and the modulation along this ring are all governed by this force.
of interacting photons is enabled predominantly
by realizing a strong interaction between the
photons. The interaction strength is quantified
by the dimensionless parameter l, which is the
ratio between the characteristic interaction and
kinetic energies. Whereas in previous works
this interaction strength was less than unity,
our system reaches l ≈ 3.
The vortices in the n-photon wave function
(n)
determine the maximal conditional phase f0
achievable for copropagating photons. For two
photons, the vortex-antivortex pair develops
(2) ≈ −p. For three photons, these pairs
when f0
connect to form six vortex lines surrounding a
(3) ≈ −2p.
vortex ring, the sum of which gives f0
The deviation from the value −3p expected for a
quantum-Kerr nonlinearity is a manifestation
of the blockade saturation. It demonstrates the
role played by the vortices in controlling the
conditional phase, with important consequences
for deterministic quantum logic operations
(44, 45) and other quantum nonlinear devices
(46, 47) with three or more photons.
Our findings far from exhaust the potential
of exploring many-body polariton physics. Even
for relatively weak interactions, one could
imagine exotic many-body bound states, such
as a cascade of Efimov three-body states with
a scaling-invariant spectrum. Although ini-
tially proposed for 3D structures (48), Efimov
states were later predicted to exist for a
lower number of spatial dimensions (49, 50),
including quasi–1D Rydberg atom clouds
(13), but have not been observed thus far. Fur-
ther, our observation of the genuine three-
body interaction V (3) could be key to the
realization of four-body interactions, which
are important for lattice simulations of gauge
field theories (51).
As opposed to real space, which is limited to
three dimensions, the (x1, x2, …) space studied
in this work can be generalized to more than
three dimensions, where higher-dimensional
topological structures, such as linked and knotted
vortex loops, could be explored. This could
provide an interesting connection to the stud-
ies of nontrivial topological physics in syn-
thetic dimensions (52, 53). It could further be
interesting to examine whether and how the
topological phase singularities of the n-photon
wave function transform to vortices of the mean
field in the nonlinear classical optics description
at n ≫ 1.
Finally, a twofold increase in the atomic
density will realize the regime l > p2, where
higher-order two- and three-photon bound
states should appear (26, 38). A superposition
of vortex series arising from different bound
states would drive complex nonperiodic dynam-
ics of the few-photon wave function with an
intricate phase structure. The three-photon
vortex rings that we observe are a relatively
simple example of how the phase of the n-
photon wave function can be controlled by
an additional (n + 1) photon. Potentially, these
topological phase structures of n-photon wave
function could be harnessed to develop new
multiphoton control tools and deterministic
quantum logic.
Drori et al., Science 381, 193–198 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
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AC KNOWLED GME NTS
We thank C. Avinadav for helpful discussions. Funding: We
acknowledge financial support from the Israel Science Foundation,
the US-Israel Binational Science Foundation (BSF) and the US
National Science Foundation (NSF), European Research Council
starting investigator grant QPHOTONICS 678674, the Minerva
Foundation with funding from the Federal German Ministry for
Education and Research, the Estate of Louise Yasgour, and the
Laboratory in Memory of Leon and Blacky Broder. Author
contributions: L.D., B.C.D., G.W., and O.F. conceptualized the
project. L.D., B.C.D., T.D.Z., and G.W. performed the experiment
and analyzed the data. B.C.D. and A.P. lead the theory work. All
authors contributed to building the methodology and writing the
final manuscript. B.C.D., E.P., A.P., and O.F. supervised the project.
Competing interests: The authors have no competing interests.
Data and materials availability: All data are available in the
manuscript or the supplementary materials or are deposited at
Zenodo (54). License information: Copyright © 2023 the authors,
some rights reserved; exclusive licensee American Association for
the Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-
article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh5315
Materials and Methods
Supplementary Text
Figs. S1 to S6
References
Submitted 9 March 2023; accepted 7 June 2023
10.1126/science.adh5315
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RES EARCH
CELLULAR IMMUNOLOGY
Perforin-2 is a pore-forming effector of endocytic
escape in cross-presenting dendritic cells
Pablo Rodríguez-Silvestre1, Marco Laub1, Patrycja A. Krawczyk1, Alexandra K. Davies2†,
Julia P. Schessner2, Reejuana Parveen1, Benjamin J. Tuck1,3, William A. McEwan3,
Georg H. H. Borner2, Patrycja Kozik1*
During initiation of antiviral and antitumor T cell–mediated immune responses, dendritic cells (DCs)
cross-present exogenous antigens on major histocompatibility complex (MHC) class I molecules.
Cross-presentation relies on the unusual “leakiness” of endocytic compartments in DCs, whereby
internalized proteins escape into the cytosol for proteasome-mediated generation of MHC I–binding
peptides. Given that type 1 conventional DCs excel at cross-presentation, we searched for cell type–
specific effectors of endocytic escape. We devised an assay suitable for genetic screening and identified
a pore-forming protein, perforin-2 (Mpeg1), as a dedicated effector exclusive to cross-presenting cells.
Perforin-2 was recruited to antigen-containing compartments, where it underwent maturation, releasing its
pore-forming domain. Mpeg1−/− mice failed to efficiently prime CD8+ T cells to cell-associated antigens,
revealing an important role for perforin-2 in cytosolic entry of antigens during cross-presentation.
T he integrity of endosomal and lysosomal
membranes is critical to protect the cell
against extracellular pathogens and toxins,
and from the activity of lysosomal hydro-
lases. In dendritic cells (DCs), however,
internalized proteins are delivered from endo-
cytic organelles into the cytosol, where they can
be proteolytically processed for presentation
on major histocompatibility complex (MHC)
class I molecules (1). The ability of DCs to present
exogenous peptides on endogenous MHC-I is
termed cross-presentation. Cross-presentation
is critical for initiation of cytotoxic T cell (CTL)
responses to antigens not expressed in DCs
such as neoantigens or antigens from virally
infected cells (2–4).
Various mechanisms have been suggested
to facilitate endocytic escape and promote
cross-presentation (5–10). Early studies pro-
posed that escape is mediated by protein
channels (such as Sec61) recruited from the
endoplasmic reticulum to endosomes (7, 11).
More recent data suggest that escape occurs
through unrepaired damage to membranes
(e.g., due to reactive oxygen species–driven
lipid peroxidation) (6, 9, 10). Both models
imply that the unusual “leakiness” of endo-
cytic compartments in DCs might not rely on
any cell type–specific effectors, but on the
regulation of ubiquitously expressed proteins
through signaling (12, 13) and trafficking (14)
events specific to cross-presenting cells.
1MRC Laboratory of Molecular Biology, Cambridge, UK.
2Department of Proteomics and Signal Transduction,
Max Planck Institute of Biochemistry, Martinsried, Germany.
3UK Dementia Research Institute at the University of
Cambridge, Department of Clinical Neurosciences,
Cambridge, UK.
*Corresponding author. Email: pkozik@mrc-lmb.cam.ac.uk
†Present address: School of Biological Sciences, Faculty of Biology,
Medicine and Health, Manchester Academic Health Science Centre,
University of Manchester, Manchester, UK.
Here, to identify DC-specific regulators
of endocytic escape, we developed a flow
cytometry–based assay to monitor escape in
individual cells and applied it in a CRISPR-
Cas9–based screen using cells specialized in
cross-presentation, conventional DC1s (cDC1s).
A CRISPR-Cas9 screen identifies Mpeg1
(perforin-2) as a regulator of endocytic escape
To monitor endocytic escape, we used the
28-kDa type I ribosome-inactivating protein
(RIP) saporin (5). Once in the cytosol, RIPs
arrest translation through depurination of the
sarcin-ricin loop in the 28S subunit of the
ribosome (15). In contrast to type II RIPs, such
as ricin, which comprise a domain that facil-
itates entry into the cytosol, cytosolic delivery
of type I RIPs is dependent on the cell-intrinsic
efficiency of endosome-to-cytosol transport (5).
To detect saporin-induced translation inhibi-
tion, we monitored incorporation of puromycin,
a structural analog of aminoacyl tRNAs, into
nascent polypeptides (16). We labeled intra-
cellular puromycylated polypeptides with a
fluorescent 12D10 antibody allowing for flow
cytometry–based readout of translation effi-
ciency and thereby of endocytic escape (Fig. 1A).
cDC1s, a subset of DCs that excels at cross-
presentation in vivo (17), have been reported
to have the most efficient endocytic escape
pathway (17, 18). We thus developed the
saporin-puromycin assay using a murine cDC1-
like cell line, MutuDCs (13, 19, 20) (Fig. 1B and
fig. S1, A and B). We confirmed that saporin
escape is the rate-limiting step in the assay (fig. S1,
C and D) and that the assay recapitulates
previously reported differences in escape effi-
ciency, namely, more efficient escape in cDC1s
compared with cDC2s (fig. S2, A and C) (18, 21)
and enhanced “leakiness” of endocytic com-
partments in cells from lupus-prone MRL/
MpJ-Faslpr/J mice (fig. S2, B and D) (22).
We then used the saporin-puromycin assay
in a CRISPR-Cas9–based screen of 281 genes
highly expressed in cDC1s compared with cDC2s
(fig. S3). We used a mix of Atto550-labeled and
unlabeled saporin, gated on cells with similar
uptake efficiency, and sorted the cells into two
bins: purolow (saporin escape, translation arrest)
and purohigh (saporin retention, efficient trans-
lation) (fig. S3C). In the absence of saporin, none
of the single guide RNAs (sgRNAs) affected the
translation rate (fig. S3E and table S1). The
strongest hit in saporin-pulsed cells was Mpeg1
(Fig. 1C), with the four sgRNAs enriched in
purolow versus purohigh populations (fig. S3F).
Perforin-2 is necessary for endocytic
escape in DCs
Mpeg1 encodes perforin-2, a member of the
membrane attack complex (MAC) and perforin
superfamily (MACPF) of pore-forming proteins
(23). Perforin-2 can form oligomeric pores on
liposomes with an opening of at least 75 Å in
diameter (24–26) (Fig. 1D). It was initially pro-
posed that perforin-2 pores facilitate killing of
intravacuolar bacteria (27), but these results
were not replicated in a recent study (28). Here,
we explored whether perforin-2 can function
as an effector of endocytic escape.
We generated Mpeg1KO MutuDCs and con-
firmed protein depletion in sorted, sgRNA-
expressing blue fluorescent protein (BFP)
cells (fig. S4A). To account for the effect of
passage numbers on MutuDC behavior (20), we
cultured control cells expressing nontargeting
(NT) sgRNA in parallel with the knockout (KO)
line. We first demonstrated that disruption of
Mpeg1 protected the cells from the cytotoxic
effects of saporin and from death induced by
a different RIP, gelonin (fig. S5A). We also tested
the sensitivity of Mpeg1KO DCs to a glycopeptide
chemotherapeutic, bleomycin A2, which induces
DNA damage, but owing to its hydrophilicity
does not enter the cells efficiently (29). We
used automated imaging to monitor MutuDC
growth rate and found that loss of perforin-2
rendered the cells more resistant to bleomycin-
mediated cytotoxicity (fig. S5A). Notably, the
Mpeg1KO cells were not protected against the
effects of poly(I:C), which induces cell death
via endosomal Toll-like receptor 3 (TLR3) (30),
or against membrane-permeable cycloheximide
(fig. S5A).
We next verified that the sensitivity of
perforin-2–expressing DCs to cytosolic toxins
is due to efficient escape rather than due to
efficient uptake. In the saporin-puromycin
assay with Atto550-labeled saporin, endocytic
escape was impaired in Mpeg1KO DCs, even
though they internalized similar amounts of
saporin compared to NT cells (Fig. 1E). The
differences in escape were also not due to
changes in DC activation, because neither NT
nor Mpeg1KO MutuDCs were activated by
saporin (fig. S5B). Finally, we rescued saporin
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Fig. 1. Saporin-puromycin assay to monitor endocytic escape in DCs.
(A and B) Saporin-puromycin assay. (A) Schematic representation. Saporin-
pulsed cells are labeled with puromycin to monitor translation rate. Puromycin
incorporated into nascent peptides is detected with an aPuromycin Ab and
flow cytometry. If saporin is retained within the endosomes, translation remains
high. When saporin escapes into the cytosol, it depurinates ribosomes,
inducing translation arrest. (B) Representative flow cytometry plot. MutuDCs
were incubated with 0.5 mg/ml of saporin followed by 0.01 mg/ml puromycin
(purple histogram), with puromycin alone (yellow), or in media only (gray). Cells
in translation arrest are denoted by the purple, gate. See also fig. S1B.
(C) Volcano plots showing the sgRNA enrichment analysis for the saporin-
puromycin endocytic escape screen. Each of the dots represents one targeted
gene. Data represent the combined mean enrichment scores and the non-
adjusted P values from three independent experiments (Fisher’s method). See
also fig. S3. (D) Schematic representation of the different perforin-2 domains
alongside structures of single-subunit (PDB ID: 6U2K) and the hexadecameric
perforin-2 pore (PDB ID: 6SB5). (E) Quantification of translation arrest in
Mpeg1KO and NT MutuDCs. Cells were pulsed with saporin (11:1 unlabeled:
Atto550-labeled saporin) for 2 hours, and translation was monitored by a
30-min puromycin chase. The x axis represents Atto550 mean fluorescence
intensity (MFI) normalized to the NT MutuDC Atto550 MFI at the highest
saporin concentration. Data represent mean and SEM of three independent
experiments; ns, not significant; **P < 0.01 using a multiple unpaired t test
(two-stage step-up, Benjamini, Krieger, and Yekutieli). Significance symbols in
the plot refer to the differences in proportion of cells in translation arrest.
Differences in saporin Atto550 MFI were not significant. See also fig. S4A.
(F) Mpeg1KO MutuDCs were reconstituted with the indicated Mpeg1 mutants
or with mScarlet only and used in the saporin-puromycin assay with a 2-hour
pulse with 0.1 mg/ml saporin. Data are representative of three independent
experiments. See also fig. S4C.
import without affecting uptake by transducing
Mpeg1KO cells with full-length sgRNA-resistant
Mpeg1 (figs. S4C and S5C).
Next, we addressed whether the pore-forming
ability of perforin-2 is required for endocytic
escape. Perforin-2 forms pores by oligomeriza-
tion and unwinding of two helices in the
MACPF domain into b sheets (shown in red in
Fig. 1D) (24, 25). To test whether this conforma-
tional change is required for endocytic escape,
we generated two mutants: Mpeg1G212V/A213V,
with mutations in the conserved MACPF motif
(31), and Mpeg1K251C/G286C, with a disulfide bond
known to constrain one of the pore-forming
helices preventing pore formation in vitro (24).
Both Mpeg1G212V/A213V and Mpeg1K251C/G286C
were expressed at levels similar to those of
Mpeg1WT, but neither rescued saporin escape
in Mpeg1KO MutuDCs (Fig. 1F and fig. S4C).
Thus, perforin-2 pores mediate endocytic escape
in cross-presenting DCs.
Perforin-2 is sufficient for endocytic escape in
nonimmune cells
Because perforin-2 expression is restricted
to antigen-presenting cells (32, 33), we asked
whether it is sufficient for endocytic escape in
nonimmune cells. We generated human em-
bryonic kidney 293T (HEK293T) and HeLa
cells coexpressing murine Mpeg1 with mScarlet
or BFP, or expressing the fluorescent protein
alone, and used them in a range of escape
assays.
Ectopic expression of perforin-2 was suffi-
cient to promote saporin escape in HEK293Ts
(Fig. 2A). We also monitored escape of 34-kDa
b-lactamase using a cytosolic dye CCF4 (34, 19).
CCF4 consists of fluorescein and 7-hydroxycou-
marin linked by a b-lactam ring, which is
cleaved when b-lactamase escapes into the
cytosol, resulting in a shift in fluorescence
emission (Fig. 2B). Expression of perforin-2
in HeLa cells increased the frequency of cells
with cleaved CCF4 and thus the efficiency of
b-lactamase escape (Fig. 2B and fig. S6). We
then adopted a split luciferase-based assay
to monitor endocytic escape of microtubule-
associated protein, tau (35). We expressed the
large 18-kDa NanoLuc subunit (LgBiT) in the
cytosol of HEK293Ts and pulsed the cells with
oligomers of 42-kDa tau fused to the short
HiBiT peptide. Upon entry into the cytosol,
LgBiT binds HiBiT, resulting in catalytically
active luciferase and luminescence in the pres-
ence of the Nano-Glo(R) substrate. Again, in
perforin-2–expressing HEK293Ts, tau-HiBit
escaped more efficiently compared with the
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Fig. 2. Perforin-2 is sufficient for endocytic escape of cargo in
non-immune cells. (A) HEK293Ts and Mpeg1-complemented HEK293Ts were
pulsed with saporin (11:1 unlabeled:Atto550-labeled saporin) for 2 hours, and
translation was monitored by a 30-min puromycin chase. The x axis represents
Atto550 MFI normalized to the WT cells pulsed with 0.5 mg/ml saporin.
Data represent mean and SEM of three independent experiments; ns, not
significant; ****P < 0.0001 using a multiple t test (Bonferroni-Dunn).
Significance symbols on the plot refer to the differences in cells in translation
arrest. Differences in saporin Atto550 MFI were not significant. (B) Cytosolic
escape of b-lactamase in cells loaded with the CCF4 results in CCF4 cleavage,
loss of fluorescence resonance energy transfer, and shift in emission
fluorescence. HeLa cells expressing either Mpeg1IRES-mScarlet or mScarlet only
were pulsed with b-lactamase for the indicated time. b-lactamase escape was
monitored by measuring the shift in fluorescence emission by flow cytometry.
Data represent mean and SEM of three independent experiments, ns, not
significant; ns, not significant; **P < 0.01; ***P < 0.001 using a multiple t test
(two-stage step-up, Benjamini, Krieger, and Yekutieli) For gating strategy, see
fig. S6. (C) To monitor the escape of tau oligomers, cells expressing NLS-eGFP-
LargeBiT were pulsed with Tau-HiBit oligomers. The escape of Tau-HiBiT into the
cytoplasm allows binding to the 18-kDA luciferase subunit, LgBiT. This results
in reconstitution of catalytic activity and generation of luminescence. NLS-eGFP-
LargeBiT HEK293Ts expressing either Mpeg1IRES-BFP or BFP only were pulsed
with tau-HiBiT for the indicated time. Following substrate addition, luminescence
and cell viability were assessed. Relative luminescent units (RLUs) were then
normalized to viability per well. Data represent mean and SEM of three independent
experiments each with six technical replicates, ***P < 0.001 using a paired t test.
(D) HEK293Ts were plated in the presence or absence of bleomycin and cultured
in an Incucyte for 48 hours to monitor the growth rate. Data represent mean and
SEM of three independent experiments each with four wells per condition; ns, not
significant; *P < 0.5; **P < 0.01; ****P < 0.0001 using a multiple t test (Bonferroni-Dunn).
control line (Fig. 2C). Finally, we demonstrated
that expression of perforin-2 renders HeLa
cells more sensitive to bleomycin-mediated
toxicity (Fig. 2D). Thus, ectopic expression of
perforin-2 is sufficient to drive endocytic es-
cape in nonimmune cells.
Perforin-2 is proteolytically processed
in lysosomes
Given the cytotoxic potential of pore-forming
proteins, we asked how cDC1s regulate pore
formation and restrict it to antigen-containing
compartments (19, 35). Perforin-2 is the only
known mammalian pore-forming protein with
an additional transmembrane domain (TMD)
that is not involved in pore formation (Fig.
1D). The TMD has been proposed to act as
an anchor preventing damage to endogenous
membranes and orientating the pore toward
intravacuolar bacteria (24, 27). We hypothe-
sized that the ectodomain would have to be
proteolytically released to facilitate endocytic
escape.
To investigate the proteolytic processing of
perforin-2, we analyzed a SILAC (stable isotope
labeling by amino acids in cell culture)–based
organellar mapping dataset generated previ-
ously (19). The maps were prepared by mass
spectrometry–based analysis of the fractionated
postnuclear supernatants from MutuDCs (fig.
S7A) (36). In the original maps, perforin-2 had
a profile similar to those of lysosomal proteins.
Here, instead of analyzing protein profiles, we
analyzed each tryptic peptide individually, only
including endo- or lysosomal proteins (Fig. 3, A
and B). Peptides derived from endosome- and
lysosome-resident proteins formed separate
clusters, as did peptides derived from trans-
membrane and luminal proteins in the lyso-
some cluster. Fifteen out of 17 perforin-2–
derived peptides clustered with soluble rather
than transmembrane lysosomal proteins, con-
sistent with the hypothesis that the perforin-2
ectodomain is released from the TMD anchor.
The remaining perforin-2 peptides, p340-372
[within the epidermal growth factor (EGF)–
like domain] and p629-635 (within the TMD-
proximal region), coclustered with endosomal
proteins (such as Vps35, Fig. 3A), suggesting
that they are present in the full-length protein
as it transits through endosomes but are absent
(cleaved) once perforin-2 reaches lysosomes.
We confirmed that perforin-2 was proteo-
lytically processed using antibodies against
the MACPF, P2, and the C-terminal tail (C-term)
(fig. S7, B and C). All three antibodies detected
full-length perforin-2 at 70 kDa. We also iden-
tified a 40-kDa MACPF and a 30-kDa P2 frag-
ments, consistent with the cleavage in the EGF
domain. The aC-term antibody detected only
the full-length protein, indicating that the tail
(and most likely the TMD) are rapidly degraded
after release of the ectodomain. Bafilomycin
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Fig. 3. Perforin-2 undergoes proteolytic cleavage, releasing its pore-
forming domain into the organellar lumen. (A and B) (A) Principal-component
analysis of mass spectrometry–based organellar mapping of MutuDCs (19)
(see also fig. S7A). The maps were prepared from control MutuDCs and cells
treated with drugs that promote lysosomal leakiness, prazosin and tamoxifen.
Peptides derived from lysosomal and endosomal proteins are represented by
filled and empty circles, respectively. The different colors indicate localization
of the protein within the corresponding organelle. Perforin-2 peptides are
displayed as filled black circles regardless of their localization. (B) Mapping of the
different lysosomal and endosomal perforin-2 peptides detected by organellar
mass spectrometry onto the different perforin-2 domains and structure.
(C) Perforin-2 levels in NT MutuDCs treated with 0.5 mM BafA1 for 3 hours
were assessed by immunoblot under reducing conditions using the aMACPF
and aC-terminal tail antibodies. (D) Confocal microscopy images of MutuDCs
stained for perforin-2 with either aC-terminal tail or aMACPF antibodies (red),
Vps35 (green), and lysotracker (blue). Data represent two independent
experiments each with at least 80 cells, ***P < 0.0001 using a Kolmogorov-
Smirnov test. (E) BafA1- and CpG-induced changes in the abundance of
tryptic and semi-tryptic (cleaved) perforin-2 peptides. Control and treated
cells (1 mM BafA1 or 1 mM CpG) were analyzed by mass spectrometry, and
peptide intensities were normalized to the corresponding protein intensities.
Statistical analysis was performed with a two-sided student’s t test. P values
(y axis) and fold change in abundance (line thickness) in treated versus
control cells are shown. The amino acid position indicates the location of the
peptides along the different perforin-2 domains. (F) Differences in the
abundance of tryptic and semi-tryptic (cleaved) perforin-2 peptides
between control and AEPKO MutuDCs (fig. S9B) by full proteome mass
spectrometry. The analysis was performed as in (E).
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Fig. 4. Perforin-2 undergoes pH-dependent maturation in antigen-containing phagosomes.
(A) Schematic representation of the phagoFACS assay. Cells are pulsed with OVA-beads and allowed to
internalize them. After an indicated chase period, noninternalized beads are labeled with an aOvalbumin
antibody. After cell homogenization, phagosomes are stained with antibodies against OVA coupled to
an alternative fluorophore and phagosomal markers. (B) Mpeg1KO and NT MutuDCs were pulsed with OVA-
beads and chased for the indicated time in the presence of either BFA or BafA1. Isolated phagosomes
were stained with antibodies against Lamp1 and either the perforin-2 C-terminal tail (top panel) or MACPF
domain (bottom panel). Data are representative of three independent experiments. See also fig. S11 for
gating strategy, quantification, and additional plots.
A1, a vacuolar-type ATPase (V-ATPase) inhib-
itor that interferes with lysosomal acidifi-
cation, accumulated full-length perforin-2,
consistent with the hypothesis that proteo-
lytic processing occurs in lysosomes (Fig. 3C).
Finally, confocal microscopy confirmed that
the aC-term antibody, which we predicted to
recognize the immature (full-length) perforin-2,
colocalized with Vps35 (Fig. 3D), and the
aMACPF antibody colocalized with lyso-
tracker, but not with Vps35. This result,
together with the organellar mapping data,
suggests that most of the protein is in lysosomes
at steady-state. Thus, full-length perforin-2
resides in (or transits through) endosomes,
and upon reaching low pH compartments,
undergoes maturation involving at least two
cleavage events.
Perforin-2 maturation is controlled by
asparagine endopeptidase (AEP)
We then asked whether perforin-2 maturation
might be regulated by antigen-associated sig-
nals. From a panel of TLR agonists, CpG (TLR9-
agonist) and Toxoplasma profilin (TLR11-agonist)
were most efficient in promoting perforin-2
proteolytic processing (fig. S8). To further
characterize the putative cleavage sites, we
performed comparative proteomics analysis of
tryptic and semi-tryptic peptides from CpG-,
BafA1-, and mock-treated cells (Fig. 3E). Semi-
tryptic peptides are considered to be derived
from proteins that were cleaved in the cell,
before sample processing. The semi-tryptic
peptide p340-349 (within the EGF domain)
was enriched in CpG-treated cells and depleted
in BafA1-treated cells, whereas tryptic peptides
near the TMD, p621-628 and p629-637, were
depleted in CpG-treated cells and enriched in
BafA1-treated cells.
Several of the nontryptic peptides in the
EGF region terminated on asparagine (fig.
S9A), suggesting that perforin-2 processing
might be mediated by AEP (37). Indeed, the
cleavage pattern in the EGF domain was dif-
ferent in AEPKO MutuDCs (fig. S9B) compared
with control cells (see peptides p340-358 and
p340-351, Fig. 3F), suggesting that AEP medi-
ates perforin-2 maturation, but its activity
can be replaced by other enzymes [most likely
cathepsins (38)]. Immunoblot analysis con-
firmed that the EGF cleavage is less efficient
(albeit not completely abolished) in the absence
of AEP, resulting in accumulation of the 60-kDa
ectodomain (fig. S9C). We were also able to
reconstitute this cleavage in vitro using re-
combinant perforin-2 and AEP (fig. S9D).
In summary, perforin-2 maturation is con-
trolled by at least two cleavage events, both oc-
curring at steady-state but stimulated by TLR
signaling. The cleavage in the TMD-proximal
CTT domain releases the ectodomain into the
lysosomal lumen to orient the pore-forming
domain toward the endogenous membranes.
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Fig. 5. Antigen cross-priming is
impaired in vivo in the absence
of perforin-2. (A) Perforin-2
expression was assessed by intra-
cellular staining with an aPerforin-2
antibody and flow cytometry in
Mpeg1+/+ and Mpeg1−/− spleno-
cytes. cDC1s are defined as Lineage
(CD3, CD19, NK1.1)−, F4/80−,
CD11c, XCR1+; cDC2s as Lineage
(CD3, CD19, NK1.1)−, F4/80−,
CD11c, CD172a+; and pDCs as
Lineage (CD3, CD19, NK1.1)−,
F4/80-, CD11cintSiglecH+. For gat-
ing strategies, see fig. S13C.
(B) CD11c+ magnetically enriched
splenocytes from WT and Mpeg1−/−
mice were pulsed with saporin
for 2 hours, and translation was
monitored by a 30-min puromycin
chase. cDC1s are defined as CD11c+,
XCR1+, cDC2s are defined as
CD11c+, CD172a+, and pDCs are
defined as CD11cintSiglecH+. Dot
plots are representative of two
independent experiments. For gat-
ing strategies, see fig. S14E. (C and
D) Wild-type and Mpeg1−/− mice
were intravenously (i.v.) injected
with 0.5 × 106 cell trace violet
(CTV)–labeled magnetically purified
OT-I cells. One day later, mice were
injected i.v. with 1 × 106 UVC-
irradiated (240 mJ/cm2) 3T3 cells,
coated with 10 mg/ml ovalbumin
as antigen source and 0.25 mg/ml
Poly(I:C) as an adjuvant. Three
days later, OT-I proliferation was
assessed by flow cytometry (C).
OT-I are defined as Lineage (CD19,
F4/80, CD11c)−, CD3+, CD4−CD8+,
TCRvb5.1, 5.2+TCRva2+, CTV+. For
gating strategy, see fig. S15A.
(D) Normalized OT-I counts 3 days
after intravenous antigen injection.
Each dot corresponds to an indi-
vidual mouse, with three to five
mice per group. For each experi-
ment, OT-I counts per 1 × 106 splenocytes were normalized to the average of WT controls. Data represent five independent experiments.
ns, not significant; **P < 0.01 using an unpaired t test.
The AEP-mediated cleavage in the EGF region,
which is not required for pore formation in vitro
(24, 39), may provide additional flexibility to
complete pore insertion in vivo or may serve
to inactivate the pores.
Perforin-2 undergoes maturation in
antigen-containing compartments
To test whether perforin-2 undergoes matura-
tion upon recruitment to antigen-containing
compartments or whether antigen-containing
compartments acquire mature perforin-2, we
analyzed perforin-2 processing in phagosomes.
We first confirmed that perforin-2 mediates
the escape of bead-conjugated saporin from
phagosomes into the cytosol (fig. S10). We then
followed perforin-2 maturation in individual
phagosomes by phagoFACS, a technique in which
DCs are pulsed with ovalbumin (OVA)–coated
beads and the resulting phagosomes are an-
alyzed by flow cytometry (Fig. 4A). Using
the aC-term antibody, we demonstrated that
perforin-2 was rapidly recruited to phagosomes,
reaching its highest levels within 30 min (Fig. 4B
and fig. S11, A and B). This rapid acquisition
suggests that perforin-2 is recruited before
phagosome-lysosome fusion (40). Indeed, bre-
feldin A (BFA), an inhibitor of ARF GTPases
that blocks protein trafficking through the
early secretory pathway, inhibited perforin-2
(but not Lamp1) recruitment, consistent with
the delivery of full-length perforin-2 to phago-
somes from the Golgi (Fig. 4B and fig. S11, B
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and C). In phagoFACS experiments with the
aMACPF antibody, perforin-2 acquisition was
also BFA dependent. However, the aMACPF
staining was restricted to Lamp1+ phagosomes
and increased over time, whereas the aC-term
signal was gradually lost (Fig. 4B and fig. S11, A
and B). Thus, during phagosome maturation,
the C-terminal part of perforin-2 is cleaved off
and degraded, whereas the ectodomain under-
goes a conformational change that exposes an
epitope recognized by the aMACPF antibody.
To confirm that perforin-2 maturation in
phagosomes is pH dependent, we first asked
whether MutuDC phagosomes acidify given
the conflicting reports on whether the pH in
DC phagosomes remains high (41–43) or de-
creases (44–46) over time. Using pHrodo-beads,
we found that phagosome acidification in
MutuDCs was abrupt and occurred on a time-
scale comparable to that of Lamp1 acquisition
(fig. S12). Inhibition of phagosomal acidifica-
tion with BafA1 interfered with both gradual
loss of the aC-term signal and acquisition of
the aMACPF signal (Fig. 4B and fig. S11B),
confirming that perforin-2 maturation is
regulated by pH.
The pHrodo experiments also revealed that
phagosomal pH was similar in NT and Mpeg1KO
MutuDC (fig. S12), suggesting that perforin-2
pores are either not permissive to protons, pore
formation is transient, or the cells can compen-
sate for proton loss. Furthermore, these data
suggest that membrane integrity of phagosomes
is not compromised during perforin-2–mediated
escape, in line with the observation that phago-
somes containing OVA-beads do not recruit
galectin-3, a marker of damaged compartments
(6). Consistent with these data, OVA degra-
dation was not affected by knocking out Mpeg1,
confirming that perforin-2 does not drastically
alter the degradative potential of phagosomes
(fig. S11, D and E).
Thus, perforin-2 undergoes pH-dependent
maturation in antigen-containing compartments,
and perforin-2–mediated endocytic escape of
antigens can occur while preserving the overall
integrity of the phagosomal membrane.
Perforin-2 is expressed in antigen-presenting
cells and facilitates cross-presentation
To test whether perforin-2 is involved in the
delivery of antigens for cross-presentation,
we generated Mpeg1−/− mice (fig. S13A and B).
Notably, knocking out Mpeg1 did not result in
any obvious disease phenotype or a change in
immune cell frequencies (fig. S13, C and D).
We used intracellular staining to confirm
that perforin-2 expression is restricted to splenic
cDC1s (Lin−CD11c+XCR1+), as well as other cell
types previously shown to cross-present, includ-
ing splenic macrophages (Lin−F4/80+), plasma-
cytoid DC (pDCs, Lin−F4/80−CD11cintSiglecH+),
and Ly6C+ monocytes (Fig. 5A and fig. S14A)
(47–50). In the spleen, only a small, CX3CR1+
subpopulation of cDC2s expressed perforin-2,
whereas in the lungs, a large fraction of cDC2s
was perforin-2 positive (fig. S14, B and C).
Consistent with perforin-2 expression patterns,
knocking out Mpeg1 decreased the efficiency
of endocytic escape in splenic cDC1s and pDCs,
but not in cDC2s (Fig. 5B).
We also asked whether perforin-2–mediated
escape delivers antigens for cross-presentation.
To assess the efficiency of antigen presentation
in vivo, we adoptively transferred OT-I T cells
(expressing a T cell receptor specific to H2-
Kb MHC-I with OVA257-264 peptide) and mo-
nitored OT-I proliferation after immunization.
Because cross-presentation of soluble OVA,
which can be processed by cell types other than
cDC1s (48, 50), was not significantly affected in
the Mpeg1−/− mice (fig. S15), we used dead cells
as an antigen source. Compared to wild-type
(WT) mice, Mpeg1−/− had fewer OT-I T cells
after immunization with ultraviolet C (UVC)–
irradiated, OVA-coated fibroblasts (Fig. 5C).
Similarly, Mpeg1−/− bone marrow-derived cDC1s
[from FMS-like tyrosine kinase 3 ligand (Flt3 L)
and granulocyte-macrophage colony-stimulating
factor (GM-CSF) cultures] displayed impaired
endocytic escape in the saporin assay and a
reduced capacity to cross-present cell-associated
antigens (fig. S16). Thus, loss of perforin-2 leads
to a defect in cross-presentation of cell-associated
antigens in vitro and in vivo, suggesting that in
cross-presenting cells, endocytic pores provide a
route for cytosolic entry of antigens.
Conclusions
Here, we uncovered a mechanism of endocytic
escape that is governed by a cell type–specific
pore-forming effector protein, perforin-2. The
role of perforin-2 in the delivery of antigens for
cross-presentation suggests that the immune
system evolved to use two related pore-forming
effectors, perforin-1 and perforin-2, during diff-
erent stages of adaptive immune responses.
Perforin-1, expressed by cytotoxic T cells, is a
well-characterized effector used for the deliv-
ery of granzymes into the cytosol of target cells
(51). Our data suggest that perforin-2 delivers
endocytic contents into the cytosol of cross-
presenting DCs to enable generation of MHC-
I:peptide complexes and T cell priming.
We do not exclude the possibility that in
different contexts, membrane destabilization
may also result in antigen delivery for cross-
presentation (6, 9, 52). Membrane integrity is
regulated by a wide range of mechanisms
(53, 54), and different perturbations can result
in leakage of endosomal contents into the
cytosol under pathological conditions. Perforin
2–mediated endocytic escape, however, appears
to occur without compromising the overall
stability of the endocytic compartments.
The restricted expression of Mpeg1 to sub-
sets of professional antigen-presenting cells
points to an important role of perforin-2 during
the initiation of immune responses. The ability
to genetically manipulate perforin-2–mediated
endocytic escape provides a tool for exploring
the contribution of the escape pathway to
anticancer and antiviral immunity in vivo.
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AC KNOWLED GME NTS
We thank members of the Kozik laboratory for discussions and
feedback regarding this work; we also thank G. M. Griffiths and
L. C. James for reading of the manuscript and their feedback. We are
indebted to N. Hacohen and T. Eisenhauer for their help setting up
CRISPR-Cas9 screens and G. Slodkowicz for help with statistical
Rodríguez-Silvestre et al., Science 380, 1258–1265 (2023)
23 June 2023
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RES EARCH | R E S E A R C H A R T I C L E
analysis. We also thank A. Crisp for help with data processing.
We are grateful to M. Mann for his support and I. Paron and
T. Heymann at the Max Planck Institute of Biochemistry for technical
assistance with mass spectrometry. Finally, we thank the animal
facility/ARES staff, genotyping facility, flow cytometry core, and
microscopy core at the MRC Laboratory of Molecular Biology for
their technical assistance. Funding: This work was supported
by the UK Medical Research Council (MRC grant no. MC_UP_1201/
26). P.R.-S. was supported by an MRC CellTech Research
Fellowship (MRF-104-0007-S-RODRI). P.A.K. was supported by the
Boehringer Ingelheim Fonds PhD Fellowship. G.H.H.B., A.K.D., and
J.P.S. were funded by the Max Planck Society for the Advancement
of Science. B.J.T. was supported by the Cambridge Trust Vice
Chancellor Award and Hughes Hall Edwin Leong PhD scholarship.
W.A.M. is a Lister Institute Fellow and supported by a Sir Henry
Dale Fellowship jointly funded by the Wellcome Trust and the Royal
Society (206248/Z/17/Z). W.A.M. was further supported by the
UK Dementia Research Institute, which receives its funding from
DRI Ltd, funded by the UK Medical Research Council, Alzheimer’s
Society, and Alzheimer’s Research UK. Author contributions:
P.R.S. designed and performed experiments and wrote the manuscript.
M.L. designed and performed experiments and contributed to the
manuscript. P.A.K. performed experiments and provided scientific
insight. A.K.D., J.P.S., and G.H.B. carried out mass spectrometry
experiments and proteomics data analysis. R.P. performed
experiments. B.J.T. and W.A.M. carried out Tau-HiBit assay. P.K.
supervised the study, designed and performed experiments, and
wrote the manuscript. Correspondence and requests for materials
should be addressed to Patrycja Kozik (pkozik@mrc-lmb.cam.ac.uk).
Competing interests: The authors declare no competing interests.
Data and materials availability: All data are available in the main
text or the supplementary materials. Data are available via
ProteomeXchange with identifier PXD041861. License
information: Copyright © 2023 the authors, some rights
reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.sciencemag.org/about/science-licenses-
journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adg8802
Materials and Methods
Figs. S1 to S16
Tables S1 to S5
References (55–61)
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
Submitted 27 January 2023; accepted 3 May 2023
10.1126/science.adg8802
Rodríguez-Silvestre et al., Science 380, 1258–1265 (2023)
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RES EARCH
GEOPHYSICS
Tremor signals during fluid injection are generated
by fault slip
Shankho Niyogi1*, Abhijit Ghosh1, Abhash Kumar2, Richard W. Hammack2
Seismic tremor signals, also known as long-period, long-duration signals, have been reported in
several locations where fluid injection for enhanced oil and gas exploration is taking place. However,
the origin of these signals remains poorly constrained. We studied seismic tremor signals in Wellington
Field, Kansas, using a seismic array during a carbon dioxide injection program. We show that these
signals are generated below the surface during the time of carbon dioxide injection. They have a
distinct spectral signature, similar to those observed in glacial and volcanic environments. The tremor
sources are located near the injection site and aligned with preexisting faults. Modeling results imply
that such tremors are generated by frictional slip on fault. These observations may reveal an important
deformation mode, which is useful for studying associated stress, seismicity, and triggering,
as well as for tracking fault activities during injection operations of all fluids, including
supercritical carbon dioxide.
C O2 injection in the subsurface can be
performed both for sequestration and
for enhanced oil recovery purposes. It is
a discipline that has recently witnessed
growth because of increasing efforts to
mitigate global warming and growing energy
demand. When CO2 is injected into an oil reser-
voir, it reduces the viscosity of the residual oil
and expands its volume, facilitating extraction,
extending the productive life of the hydrocarbon
field, and removing the injected CO2 out of
the atmosphere. However, the injection of these
fluids can increase the pore pressure in the
subsurface and potentially cause critically stressed
faults near the injection site to slip. When seismic
events such as earthquakes are generated from
such a mechanism, this is known as induced
seismicity. In contrast to natural earthquakes,
some induced seismic events can show very
different signal characteristics. Such signals are
typically reported as long-period, long-duration
events in several fluid injection sites (1–6).
Physical mechanisms of such events, their
underlying physics, and their relation to the
injected fluid, however, remain enigmatic.
The waveform characteristics of these long-
period, long-duration signals are similar to the
tectonic tremors found in large natural faults.
Contemporary studies report that the pres-
ence of fluids in faults and subduction zones
is one of the factors behind the origin of tectonic
tremors and is largely driven by aseismic slip
(7–9). Laboratory studies have shown that
slow injection rates can accelerate aseismic creep
while maintaining stable slip due to the pressur-
ized zone being confined within a critical size for
an unstable slip in fault gouge samples (10).
Similarly, aseismic deformation was found to
be the dominant response when fluid injections
were performed in natural fault systems in the
1University of California, Riverside, CA, USA. 2National Energy
Technology Laboratory, Pittsburgh, PA, USA.
*Corresponding author. Email: sniyo001@ucr.edu
Low Noise Underground Laboratory [Labora-
toire Souterrain Bas Bruit (LSBB)] of Rustrel,
France, to induce slip (11). We also have evi-
dence of fluid injection–induced earthquakes
exhibiting broader body wave pulses and lower
frequency coda (12), and these characteristics
have been attributed to slower rupture speeds
and lower stress drop values, which makes them
similar to low-frequency earthquakes with regard
to source characteristics.
We observed low-frequency, long-duration,
emergent signals in the seismic monitoring sta-
tions [Incorporated Research Institutions for
Seismology (IRIS) network identifier: ZA] placed
around the injection well 2-32 in Wellington
Field, Kansas, during a supercritical CO2 injec-
tion program (6) (Fig. 1). The supercritical CO2
was injected into the Mississippian carbonate
reservoir in a fluid state (6). Additionally, waste-
water was being disposed of in the deeper,
aquitard-bounded Arbuckle Group Formation.
On the basis of our analysis of the United States
Geological Survey (USGS) earthquake catalogs,
the onset of the injection program did not cause
an increase in local earthquakes, especially around
the injection well. Most earthquakes in the south-
central Kansas region are caused by oil and gas
activities such as wastewater disposal from
both local areas and from northern Oklahoma
caused by far-field pressure diffusion (13). The
locations of these earthquakes show that they
are aligned with the structural features of this
region, like the Humboldt Fault Zone and the
Central Kansas Uplift (Fig. 1). Historical earth-
quakes in Kansas have also taken place on the
faults along these features. The Mississippian
Group of rocks and the Cambro-Ordovician
Arbuckle Group in Wellington Field are the tar-
get lithology for CO2-enhanced oil recovery and
storage, respectively (14). Exploration seismic
data show that both of these formations are con-
nected to the basement faults in Wellington Field
(14). Initial studies of these low-frequency events
suggested aseismic expression of these fault
movements (6). We focused on the coherency and
spectral signatures of these events, which make
them similar to harmonic tremors reported earlier
from volcanic and glacial settings. We explain
the signals using physical models derived from
these sources. For simplicity, we refer to these
long-period, long-duration events as tremors.
Investigation of unknown seismic signals
often involves a separate analysis for looking
into possible anthropogenic sources. We con-
ducted independent analysis of these events
with regard to their origin from freight trains,
vehicular traffic, aerial sources such as helicop-
ters, and machinery equipment such as pumps
and generators on the surface near the seismic
array. The presence of equipment does create
noise, which is shown in the clearly visible parts
of the spectrograms. However, a number of events
with high signal-to-noise ratio clearly establishes
the characteristics of the tremor signal. We have
used that to make a tremor catalog based upon
these well-defined waveform characteristics. A
notable characteristic of these tremor events
are the lines gliding across frequencies between
1 and 5 Hz observed in the spectrograms. For
many of the events displaying similar spectral
characteristics with gliding spectral lines, slow-
ness and back azimuth could not be robustly
determined because of the inherent noise con-
tent. Therefore, we did not include them in our
final analyses. Observations of such kinds of
low-frequency tremor events, their source lo-
cations, and their spatiotemporal distribution
may provide a useful and benign way of track-
ing the migration of injected fluids in the
subsurface. Using an array response function
with a synthetic waveform showed that the
array could perform reasonably well at 1 to
5 Hz, the dominant frequency band of interest,
and up to at least 0.3 s/km, which was suitable
for our analysis.
Background
The Arbuckle Formation consists mainly of
interlayered dolomites and carbonates and
was deposited in a shallow epicontinental sea in
Kansas and Oklahoma during the late Cam-
brian to the Middle Ordovician. Karst formations
within it created permeable zones for waste-
water disposal, sealed by the overlying Devonian
Woodford shale formation. The Mississippian
limestone formations were later deposited in
similar shallow marine environment settings
and are bounded by unconformities. Oil deposits
of the Mississippian formations are mostly a
combination of structural-stratigraphic traps
where the present-day CO2 injection is going
on. Tectonic events such as the Nemaha Uplift
and the Midcontinent Rift event influenced the
structure of the Mississippian and Arbuckle
Formation, creating deep vertical faults in the
subsurface. Subsurface formations in southern
Kansas were strongly affected by these tectonic
Niyogi et al., Science 381, 553–558 (2023)
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events (15–23), and this is where most earth-
quake activity has occurred, including an esti-
mated magnitude 5.1 event in 1867.
Information about subsurface structures in
Wellington Field comes from three-dimensional
seismic reflection data and formation micro-
imaging (FMI) well logs (14). Analyzing the
seismic data shows mostly northeast and some
northwest trending subvertical faults, whereas
FMI data show that most of the fractures were
oriented toward the northwest, with some in
the northeast direction. On the basis of the trend
of the earthquake locations, faults, and fracture
data, the tectonic episodes that created the
Central Kansas Uplift and the Nemaha Ridge
Humboldt Fault Zone also affected Wellington
Field and generated similar structures in that
area as well.
Observations
We found that the long-period, long-duration
events (tremor events) occurred when the CO2
injection was being performed between January
and June of 2016. Kumar et al. (6) suggested that
the filtered waveforms of these signals bear
visual similarity to those of tectonic tremors
found in geologic settings under natural tec-
tonic stresses. These events contain the highest
energy in 1 to 5 Hz, which is part of the 1- to 12-Hz
frequency band in which tectonic tremors are
usually visible. The events are not visible in
regional seismic networks in this region, sug-
gesting their local origin. By beamforming the
tremor signals in 1 to 5 Hz, we showed that they
have a low slowness value (<0.3 s/km), indicat-
ing their subsurface origin. From the initial
catalog of Kumar et al. (6), we selected several
events with high signal-to-noise ratios that passed
our strict quality tests (fig. S3). Using the wave-
form characteristics of these events, we detected
additional events not previously recognized
during the injection period. Most of the signals
had durations ranging from 2 to 5 min. After
conducting thorough quality evaluations on
these events, we ultimately selected 27 to locate
using the beam backprojection technique
(24–27). The locations of the signals were deter-
mined by assuming the depth in which the
supercritical CO2 injections took place. This
assumption is necessary because a single array
cannot constrain depth of the signal indepen-
dently. All of the locations that we obtained
were within 5 km of the injection well. The
spatial pattern of the locations is roughly aligned
along northeast-southwest and northwest-
southeast directions. These trends are also
shared by the faults of the Central Kansas Uplift
and the Nemaha Ridge Humboldt Fault Zone
in this region. Schwab et al. used exploration
seismic data to show that basement faults did
extend to the horizons where the fluids were
being injected (14). Schwab et al. also showed the
presence of natural open fractures in the target
formations, as shown by the FMI data from
Fig. 1. Location of the network in relation to earthquake occurrences and other tectonic structures in
Kansas. (A) Location of the ZA network in Wellington Field. We analyzed three-component seismic data from
December 2015 to July 2016. The area is shown by the blue rectangle in the inset map. (B) Historical and present
earthquake occurrences and main structural elements in Kansas. The red highlighted box indicates Sumner
County, and the yellow circle indicates Wellington Field. Earthquake magnitudes are represented by the area of the
circles, and color indicates the distribution of historical and present-day seismicity. Most of the earthquakes follow
the main structural trends. Figure is modified from Hildebrand et al. (53).
wells 1-28 and 1-32. The northeast and north-
west trend of the source locations of our events
was similar to the distribution of regional earth-
quakes in the USGS catalog and was also shown
by the open fractures in the wells.
We observed that the occurrence of the tremor
signal and local earthquakes had no temporal
correlation between them, even though their
spatial trends were along the same northeast
and northwest directions. No observable in-
crease in the local background seismicity
occurred during or after the supercritical CO2
injection. Most earthquakes in the south-
central Kansas area stem from oil and gas
operations, mainly from the disposal of waste-
water (28, 29). The lack of increase in con-
temporary earthquakes rates during the CO2
injection may indicate that the injection rate
was not high enough to generate additional
earthquakes in the region. However, the dis-
tribution of tremor signals was limited to the
supercritical CO2 injection period, and we did
not detect these signals in the month before or
after the injection period.
The most distinct characteristic of tremor
signals is the presence of narrow, more or less
Niyogi et al., Science 381, 553–558 (2023)
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Fig. 2. Similarity of the spectrogram characteristics between tremors found in this study and those
found in other geologic environments. A spectrogram is a visual representation that shows how the energy
in different frequencies changes over time in the data, with the x and y axes representing time and frequency,
respectively. Here, we show a spectrogram of volcanic tremors (A) reported by Almendros et al. (54) at Arenal
Volcano in Costa Rica, seismic tremors associated with glacial earthquakes (B) at Whilllans Ice Stream in Antarctica
described by Winberry et al. (33), and two examples of the tremor events detected in this study [(C) and (D)].
Note the gliding spectral lines in the spectrogram at 1 to 5 Hz. The presence of analogous spectrogram signatures
within comparable frequency ranges highlights the similarity in the mechanisms generating these events.
evenly spaced bands of frequency that gradu-
ally increase, reach a peak, and then decrease
(Fig. 2). These time-varying spectral lines are
also seen in tremor signals from glacial and vol-
canic regions (30, 31) (Fig. 2). The spectral lines
are characterized by relatively high amplitude
and generally stay within the 1- to 5-Hz range.
The peak frequency often aligns with the peak
amplitude in the waveform in the time domain.
Typically, we observed two spectral lines, al-
though three lines were occasionally visible
in the spectrogram.
A physical model to explain tremors
Mathematical models have been proposed to
explain the occurrence of harmonic tremors de-
tected near volcanoes. Dmitrieva et al. (32), using
the general equations given by Hotovec et al.
(31), derived and then showed that a delta func-
tion with increasing recurrence interval as a
function of stress accumulation rate could
generate the characteristic harmonic tremor
signal seen near volcanoes. Dmitrieva et al.’s
model shows that the signal is generated by
shear slip induced by fluid in the volcanic sys-
tem. In another study, Lipovsky and Dunham
(30) showed that tremors detected by seismo-
meters in Whillans Ice Plain, West Antarctica,
occurred during large-scale sliding events, and
this was confirmed by GPS stations. These
tremor events are also characterized by gliding
spectral lines and can be modeled on the basis
of repeating earthquake patches at the ice-bed
interface. Our tremor events bear similarities
to both volcanic (31) and glacial tremors (30, 33)
in terms of the gliding spectral lines. The sig-
nals for both the volcanic and glacial tremors
are produced by frictional processes. Signals
showing discernable narrow bands of varying
frequency with time are related to a varying re-
currence interval of events, which in turn is
related to the changing stressing rate a on the
fault plane (32). We used the same mathemati-
cal model to show that a pattern of increasing
followed by decreasing stressing rate a can ex-
plain the occurrence of the tremor signals within
the 1 to 5 Hz identified in this study.
According to Dmietrieva et al. (32), the spec-
trum of N repeating events occurring periodi-
cally with a recurrence interval value of T is
given by multiplying an individual spectrum
event by a spectrum of sequence of N delta
functions [as derived in Hotovec et al. (31)]:
υ wð Þ e (cid:2)iw
M0
4prc3r exp
(cid:2) (cid:3)
iwr
c
(cid:2)
exp (cid:2)
wj
jr
2cQ
(cid:3)
sin
(cid:5)
(cid:4)
wNT
(cid:5)
(cid:4)
2
wT
sin
2
where the variable w is the angular frequency,
u(w) is the Fourier transform of particle veloc-
ity u(t), M0 is the seismic moment, r is the
density of the propagating medium, r is the
propagation distance, c is the shear wave speed,
and Q is the quality factor.
Niyogi et al., Science 381, 553–558 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. Analysis of the detected events through examination of nearby
earthquake activities and injection program duration. (A) Source locations
of tremor events as determined by the beam backprojection method (25, 26).
Some tremor locations are aligned with the Central Kansas Uplift (northwest-
southeast) and others with the Humboldt Fault Zone (northeast-southwest).
Regular earthquakes are aligned with the same structures. (B) Modeling of the
tremor signal. Shown is an illustration of a series of earthquakes with temporally
varying recurrence interval times as a result of increasing and decreasing
rates of stress accumulation. (C) Illustration of multiple spectral lines as a
result of the series of earthquakes shown in (B). A quadratic rate of change of
events can simulate the pattern seen in the spectrograms of the observed
tremor signals. (D) Expanded timeline of the histogram of the tremor events.
(E) Occurrence of tremor events (black) plotted in the backdrop of earthquakes
(blue) occurring within 50 km of the injection well. (F) Plot of the maximum
magnitude earthquakes (green), along with the cumulative number of
earthquakes (red).
Dmitrieva et al. (32) showed that the spec-
tral peaks occur when wT/2 becomes an inte-
ger multiple of p. The recurrence interval T is
dependent upon stress t and stress accumula-
tion rate a as T ∼ dt/a. Considering nearly
equal stress drop value for events generated
on a fault plane, an increase in stress accu-
mulation rate a leads to a decrease in T and
vice versa. Any smooth change in the recurrence
interval rate is reflected in the spectrograms of
these events as spectral lines increasing or
decreasing in frequency as a function of time
(equidistant signals are shown in Fig. 2, C
and D, and fig. S3). Winberry et al. (33) reported
the timings of the spectral crests of the observed
tremors, and these match the highest rate of
glacial earthquake occurrences. This compari-
son indicates, as expected, that the occurrences
of tremor signals with gliding frequencies are
not restricted to volcanic environments alone.
We modified some of the parameter values
in Dmitrieva et al. (32) for modeling our tremor
events because the frequency ranges of volcanic
tremors and our events overlap. In our model-
ing, we also assumed a linear and quadratic
change of recurrence interval value T. We found
that multiple spectra with different starting and
ending recurrence intervals generate signals
that most closely resemble the ones seen in
Kansas. As observed in the spectrograms, the
Niyogi et al., Science 381, 553–558 (2023)
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chief characteristics of the signal, the gliding
equidistant spectral lines, can be modeled by
multiple subsequent earthquakes with varying
interevent times.
Results and discussion
Even though earthquakes have increased in
the northern Oklahoma and southern Kansas
region overall due to subsurface fluid injection
(13, 34–42), we found no obvious change of
background seismicity at the beginning of the
CO2 injection program for oil recovery in the
Wellington Field region (Fig. 3E and fig. S2).
We also saw evidence of natural fractures in
those formations from borehole image logs
oriented in the same northeast-southwest direc-
tion as the Humboldt Fault Zone. Previous stud-
ies showed that alterations in pore pressure
resulting from fluid injections can trigger both
seismic and aseismic activity in fault zones
provided that the local stress conditions, hydro-
mechanical coupling, and fluid diffusion pro-
cesses are conducive to such occurrences (43).
Thus, the tremor signals with gliding spectral
lines in our study area can provide an expla-
nation for why faults are releasing some of the
accumulated stress without causing an increase
in regular seismicity, i.e., earthquakes. We have
determined that the characteristics of the wave-
forms and spectra of the signals can be modeled
as a series of shear slip events likely induced
by fluid injection. On the basis of these find-
ings, we infer that these tremor sources are
driven by aseismic slip.
Previous studies have shown that harmonic
tremors are associated with stress state changes
caused by the movement of magma and fluids
in the subsurface (31, 44). Theoretical models
such as those developed by Thomas and Neuberg
(45) are valuable for studying source mechanisms
because they are based on the observations of
harmonic tremors. Therefore, we derived a
physical model that is based on Dmitrieva et al.
(32) and inferred that a temporally varying
stress pattern can generate the tremor signals
with gliding spectral lines observed in this area.
Aseismic movement of faults can occur aided by
increases in pore fluid pressure near the faults
caused by fluid injections. Past studies showed
that frictional properties can change during fluid
injection from rate weakening to rate strength-
ening with increasing fluid pressure, which helps
to maintain aseismic slip (10). A correlation also
exists among earthquakes, aseismic slip, and the
pumping of fluids near subsurface faults, as
shown in areas such as Delaware Basin in west
Texas (46, 47). We relate the lack of increased
seismicity in Wellington Field to aseismic fault
movements that may have driven the localized
tremor sources found in this area.
The occurrences of these tremor events have
implications for the subsurface movement of
injected fluids. Tracking the movement of sub-
surface fluids is usually done through simu-
lations and modeling (48, 49). Observations
of these low-frequency tremor events and their
source locations can help us track deformation,
fracture location, and movement of injected
fluids in the subsurface around the injection
well. Determining the locations of induced
earthquakes is one of the ways to deduce the
extent of subsurface fluid migration from the
injection well (13, 50–52). The injection rate of
fluids for disposal and enhanced oil recovery
purposes is monitored carefully to prevent in-
duced earthquakes from increasing in frequency
and magnitude. Therefore, observations of such
tremor events, their source locations, and their
spatiotemporal distribution may provide a use-
ful and benign way of tracking the migration of
injected fluids.
Conclusions
We analyzed tremor signals and showed that
they originated from the subsurface during a
CO2 injection program in Wellington Field in
Sumner County, Kansas. Using array analyses,
we ruled out surface noises such as freight
trains and helicopters as being the origin of
these tremors. By locating the events using the
beam backprojection method, we were able to
show that all of the events occurred in the
vicinity of the injection well and that they
followed the major structural trends shown by
the Humboldt Fault Zone and the Nemaha
Uplift. This trend was also evident in the spatial
pattern of earthquakes in Kansas over a long
time scale. Based on the similarities in their
waveforms and spectral characteristics, the
closest physical analog of these signals are
tremors with gliding spectral lines found in
volcanic and glacial settings. These tremor sig-
nals are modeled as being generated by a series
of small earthquakes with temporally varying
recurrence interval times. We infer that these
tremors may be driven by aseismic slow slip.
Such induced tremor events provide a way to
track stress distribution and deformation dur-
ing subsurface high-pressure fluid injection.
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ACKN OWLED GMEN TS
We thank the two anonymous reviewers for their dedication and
time in going through the manuscript, highlighting the necessary
changes, and recommending improvements to the text. Their
suggestions have substantially improved this manuscript. Funding:
This work was supported by the University of California Riverside.
Author contributions: S.N. analyzed the data, performed the
experiments, and contributed to the writing of the manuscript. A.G.
conceived the study, planned the experiments, coordinated
the project, and assisted in analyzing the data, interpreting the
results, and writing the manuscript. A.K. and R.H. provided the
waveform data and station metadata and assisted in interpreting
the results. All authors discussed the manuscript and contributed to
the science presented in the article. Competing interests: The
authors declare no competing interests. Data and materials
availability: Waveform data and codes can be accessed at Zenodo
(55). License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government works.
https://www.science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh1331
Materials and Methods
Figs. S1 to S6
References (56–64)
Submitted 13 February 2023; accepted 23 June 2023
10.1126/science.adh1331
Niyogi et al., Science 381, 553–558 (2023)
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RES EARCH
FERROELECTRICS
Atomic-scale polarization switching in
wurtzite ferroelectrics
Sebastian Calderon V1, John Hayden2, Steven M. Baksa2, William Tzou1, Susan Trolier-McKinstry2,
Ismaila Dabo2, Jon-Paul Maria2, Elizabeth C. Dickey1*
Ferroelectric wurtzites have the potential to revolutionize modern microelectronics because they are
easily integrated with multiple mainstream semiconductor platforms. However, the electric fields
required to reverse their polarization direction and unlock electronic and optical functions need
substantial reduction for operational compatibility with complementary metal-oxide semiconductor
(CMOS) electronics. To understand this process, we observed and quantified real-time polarization
switching of a representative ferroelectric wurtzite (Al0.94B0.06N) at the atomic scale with scanning
transmission electron microscopy. The analysis revealed a polarization reversal model in which puckered
aluminum/boron nitride rings in the wurtzite basal planes gradually flatten and adopt a transient
nonpolar geometry. Independent first-principles simulations reveal the details and energetics of the
reversal process through an antipolar phase. This model and local mechanistic understanding are a
critical initial step for property engineering efforts in this emerging material class.
B etween 2019 and 2021, researchers world-
wide demonstrated unexpected ferro-
electricity in solid solutions in the AlN-ScN
(1), AlN-BN (2), GaN-ScN (3), and ZnO-
MgO (4) composition families. These re-
ports disrupted the more than 100-year-old
perspective that wurtzite crystals are pyro-
electric and piezoelectric but cannot be ferro-
electric because the polarization cannot be
switched with an electric field. The important
scientific and technological consequences that
accompanied this understanding were that (i)
we have a previously unknown class of ferro-
electrics that violates the long-standing rela-
tionship linking polarization and ferroelectric
transition temperature (5)—that is, they are
likely not soft-mode ferroelectrics; (ii) the new
physical mechanisms that enable ferroelectricity
1Department of Materials Science and Engineering, Carnegie
Mellon University, Pittsburgh, PA 15213, USA. 2The
Pennsylvania State University, Department of Materials
Science and Engineering and Materials Research Institute,
University Park, PA 16802, USA.
*Corresponding author. Email: ecdickey@cmu.edu
will almost certainly impart different manifes-
tations of physical scaling trends and differ-
ent property dependencies on temperature,
pressure, and time; and (iii) these materials
can be processed at or near room temperature
with a robust property response, and in some
cases (for example, Al1−xBxN) they consist ex-
clusively of elements that are already common
and essential in the silicon complementary
metal-oxide semiconductor (CMOS) front end.
This emerging ability to directly integrate a
strongly hysteretic nonlinear dielectric is trans-
formational for future logic, memory, high-
power, acoustic, or electro-optic devices (6–8).
These ferroelectrics, however, bring their own
challenges, the most notable being that the
margin between the coercive field and break-
down field is uncomfortably small at room tem-
perature. Consequently, devices are operated in
close proximity to their failure thresholds, which
invariably erodes electrical endurance and can
induce degradation pathways.
Lowering the energetic switching barriers is
a principal goal necessary to realize the full po-
tential of ferroelectric wurtzites in electrical,
optical, and acoustic devices. Empirically, we
know that epitaxial tensile strain and an in-
creased dopant concentration can reduce coer-
cive fields in Al1−xScxN (9, 10) and Al1−xBxN (2),
presumably by reducing the energy barriers
that regulate the polarity switch, and that in-
creasing temperature also reduces the coercive
field by thermally activating the nucleation
and switching processes (11). These trends are
based on macroscopic observations—that is, on
measuring millimeter-scale capacitors—and
although the trends demonstrate possibilities
to reduce the coercive field, they do not pro-
vide local mechanistic insight.
Understanding these trends and phenomena
at global and local-length scales is essential so
that the property response of wurtzite ferro-
electrics can be further developed for practical
use. We addressed this challenge by measur-
ing in situ the polarization reversal process at
the atomic scale. Our experimental approach
takes advantage of local electrostatic sample
charging occurring during the illumination of
dielectric materials in the electron microscope,
which can induce the necessarily large local
electric fields (12, 13) for polarization switch-
ing in ferroelectrics (14, 15). We used scanning
transmission electron microscopy (STEM) in
differentiated differential phase contrast mode
(dDPC) to observe in situ polarization inversion
in thin films of the composition Al0.94B0.06N
[(Al,B)N]. Materials in this composition space
have remanent polarization (Pr) values exceed-
ing 125 mC cm–2 while maintaining bandgaps
above 5.8 eV; this is a substantial advantage
relative to other wurtzite-based ferroelectrics,
albeit the coercive fields are also larger (2). Our
experimental analysis documents polarization
switching with quantitative information at
the atomic scale that is coinformed with first-
principles calculations of the same compo-
sition. The first-principles simulation analyses
provide an atomic-scale understanding of the
switching pathways and energetics in these
emerging ferroelectric materials. Covalidation
Fig. 1. Structure of (Al,B)N. (A) dDPC-STEM images for (Al,B)N film. (B) Fast
Fourier transform calculated from the (Al,B)N region of image in (A). (C) dDPC-STEM
image of an (Al,B)N grain oriented along the [110] direction, where the location of
the atomic columns has been highlighted with blue (N) and gray (Al) circles after
Gaussian fitting. “P” with arrow shows the direction of polarization. (D) dDPC image
overlapped with a vector map indicating the calculated polarization at each unit cell.
Calderon et al., Science 380, 1034–1038 (2023)
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of STEM imaging and density functional the-
ory support a switching mechanism in which
a transient antipolar structure mediates the
switching process; the transient structure is
similar to long-standing models for inversion
domain boundaries in III-nitrides.
Effect of boron and wake-up process on
the structure
We show a dDPC-STEM image of an (Al,B)N
film grown by means of reactive pulsed dc sput-
tering on a W electrode, showing a columnar
grain structure with a nominal epitaxial relation
of (Al,B)N <001> // W <110> // growth direction
(Fig. 1). The W electrode is faceted, and we
observed small variations in the orientation of
(Al,B)N grains, leading to the low density of
dislocations that are observed in the image. We
detected the out-of-plane crystalline mosaicity
in the rocking curves of the 002 reflection of the
(Al,B)N films, with full width at half-maximum
(FWHM) values of 1.44° (fig. S1).
From the STEM images, we made structural
polarization measurements to compare with
macroscopic measurements. To quantify the
spontaneous polarization, we acquired dDPC
images along the <110> zone axis (Fig. 1C),
where the growth direction points from the
bottom to the top of the image along the 00(cid:1)1
(cid:2)
direction of (Al,B)N. We determined the polar-
ization orientation from the images by estab-
½
lishing the nitrogen tetrahedral orientation
(Fig. 1C, inset). This orientation is polarization
down—that is, the positive end of the perma-
nent dipole points to the substrate, which is
commonly referred to as an “N-polar” growth
direction. Among the observed regions, the
N-polar orientation is uniform with no evi-
dence of Al-polar orientations, which is consist-
ent with prior studies that show uniformly
N-polar-oriented films (16). The atomic-column
positions of both Al(B) and N were determined
with a Gaussian fitting process on the dDPC
images, which allows precise location of the
atomic-column positions and thus an accurate
quantification of the polarization, as previously
reported (17). The polarization was quantified
by using the Born effective charges calculated
from density-functional perturbation theory
(18). We show a vector-map representation of
the calculated polarization per unit cell for an
as-deposited (Al,B)N film (Fig. 1D), which we
discuss in comparison with other samples.
We constructed a summary comparison of
the calculated polarization per unit cell for
as-deposited pure AlN film (Fig. 2A), an as-
deposited (Al,B)N film (Fig. 2B), and a field-
cycled (Al,B)N film left in the opposite polarity
from the as-deposited film (Fig. 2C). The
sputtered AlN film (Fig. 2A) exhibits an average
polarization magnitude of 1.13 ± 0.07 C m−2.
The standard deviation is close to the measure-
ment uncertainty arising from the atomic-
column fitting process. The average measured
polarization magnitude is 6.6% less than that
of the ideal AlN structural model (1.21 C m−2).
The as-deposited (Al,B)N film (Fig. 2B) exhib-
its an average spontaneous polarization of
1.30 C m−2, 13% larger than the undoped film,
which is in agreement with the trend pre-
dicted by first principles (2). The (Al,B)N film
exhibits peak-to-peak variations of 1.13 to
1.36 C m−2 and a standard deviation of 0.10 C m−2
within the measured area. These variations,
which exceed the measurement error, are
consistent with the chemical and structural
inhomogeneities associated with the 6% B
substitution—for example, FWHM x-ray peak
widths of ~1° in w and 2q circles and a large
radial misfit of B for Al.
Electric field–induced polarization switching
from the as-deposited unipolar state can be
highly frequency dependent. For kilohertz
pulses just above the coercive field, full reversal
per cycle may take many tens of cycles. For
slow cycling (for example, 0.1 Hz), one sweep
can be sufficient. This “wake-up” process that
precedes fast polarization reversal is ascribed
to low initial domain-wall density and mobility
(16). To better understand this wake-up pheno-
menon, we completed the same STEM polar-
ization analysis on a field-cycled sample and
compared those results against bulk electrical
Fig. 2. Polarization evolution. (A to C) dDPC images for (A) pure AlN, (B) (Al,B)N as-deposited, and (C) field-cycled (Al,B)N. (D) Schematic of the structure
modification after boron incorporation and field cycling. dDPC-STEM images showing the full field of view are presented in fig. S2.
Calderon et al., Science 380, 1034–1038 (2023)
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Fig. 3. In situ polarization switching. (A) dDPC-STEM frames at 0, 209, 266,
and 361 s for in situ polarization switching. (B) AlN dumbbell-angle evolution as a
function of time for the corresponding frames in (A). The Roman numerals in
(A) and (B) indicate the different regions in the images going from the top of the
frame (I) to the bottom (IV). The rows of AlN dumbbells in the images are
numbered from 1 to 8 for reference between (A) and (B). (C) Dumbbell-angle
evolution as a function of time for one unit cell. (Inset) The schematics of the
dumbbell angle and the dDPC images at specific times.
measurements. For a fully woken-up sample,
hysteresis loops yield Pr of 1.38 ± 0.01 C m−2,
whereas dDPC-STEM imaging yields 1.40 ±
0.14 C m−2. Furthermore, the STEM-based
polarization measurements allow us to com-
pare the intrinsic spontaneous polarization in
the as-deposited and field-cycled states (Fig.
2, B and C). The similarity of these STEM-
quantified polarization magnitudes (average
values within ~7%) suggests that the wake-up
process does not substantially alter the bulk
material structure.
To further explore this possibility, we ana-
lyzed the average local structure evolution
using two-dimensional vector pair correlation
functions (vPCF) calculated from dDPC-STEM
images that can be found in the supplemen-
tary materials (fig. S3) (19). The relevant param-
eter extracted from vPCF is Dr (Fig. 2D), which
describes the distance between the nearest
(Al,B) basal-plane layers and N layers, also
referred to as the “puckering” of the wurtzite
basal planes. Whereas the average Dr increases
10% on alloying AlN with 6% B, the Dr in as-
deposited and field-cycled (Al,B)N states are the
same within one standard deviation of the
measurement distribution, supporting the con-
clusion of no major structural phase transitions
during the wake-up process. We therefore
infer that the wake-up phenomenon is more
likely associated with interfacial or nucleation
site–based mechanisms than bulk crystal-
structure changes.
In situ switching observations
Electron microscopy can visualize ferroelectric
polarization reversal at length scales that
reveal local atomic and domain structures
(15, 20). In these cases, preparation of extremely
thin parallel-plate capacitor structures that
can be field cycled either in situ or by imple-
menting a nanoprobe that applies a local bias
is common (20). Wurtzite ferroelectrics are
difficult to analyze with these methods because
of the large coercive fields that invariably
accelerate surface migration of atomic species
across the sample surface and create short-
circuit pathways. Alternatively, prior reports
demonstrate that the charge accumulation
from beam-solid interactions in electron and
ion microscopes can create internal fields large
enough to reverse ferroelectric polarization
(14, 15). By using extended beam exposures
during STEM image acquisition, polarization
reorientation can be achieved from the large
lateral electric fields that emerge from the
beam-solid interactions that produce positive
sample charging, as described in detail by
Cazaux (12). For very thin samples, incident
electrons do not contribute substantially to
charge accumulation because they are fully
transmitted. However, some electrons are
scattered inelastically, promoting ionization
and secondary and Auger electron emission
and a net positive charge accumulation for
electrically insulating materials. This super-
imposes additional built-in electric fields, which
can reach the megavolt-per-centimeter range
needed to switch (Al,B)N. Our primary data-
set is an in situ domain switching movie collected
on an (Al,B)N film (movie S1). We summarize
the in situ data with a set of frames spanning
the roughly 7-min experiment (Fig. 3). The
images are indexed from top to bottom with
row numbers and divided into four regions
(I, II, III, and IV), with region I closest to vac-
uum (the top of the sample), where the charge-
induced field is expected to be largest in the
vertical direction (and thus capable of inducing
switching), and region IV closest to the bottom
electrode, which provides a physical path to
Calderon et al., Science 380, 1034–1038 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 4. Nudged-elastic-band simulation of polarization reversal pathways. (A) Nudged-elastic-band simulation of polarization reversal pathways for AlN and
Al15/16B1/16N. (Insets) The structural models at specific stages of the simulation. (B) Structural model of the nonpolar transient state calculated for Al15/16B1/16N
viewed along different projections. (C) Atomic models, STEM image simulations, and experimental images for the N-polar, nonpolar, and Al-polar states.
microscope ground. This distinction is impor-
tant because the electric field in the experiment
will necessarily be spatially heterogeneous in
magnitude and evolve over time; nonetheless,
it serves as an important mechanism to in-
duce switching in these large-coercive-field
samples. Our STEM images are overlayed with
red, white, and blue lines, which indicate quan-
titatively (from image analysis) the dumbbell
angles associated with the bond puckering in
the wurtzite basal plane; red is positive, blue is
negative, and white is 0° on average. We show
four graphs that quantify the average dumb-
bell angles for regions I through IV (Fig. 3B),
each one representing a unit-cell-thick layer.
We note four observations: (i) In region I,
the transition between red and blue is the
most clear and uniform and occurs first; this
observation is consistent with expectations for
maximum charging fields in this zone. (ii) As
one progresses from the top zones to the bot-
tom zones, the dumbbell-angle transition is
less uniform, and the switching process takes
longer; this is again consistent with the antic-
ipated electric-field evolution and gradient
direction. (iii) Region IV and below do not
completely switch, which is attributed to dimin-
ishing electric field toward the bottom of the
sample. (iv) The regions of the sample that
switch do so through a transient state in which
the integrated intensities of all associated
scatterers yield an average dumbbell angle of
0° (Fig. 3C).
We also note the 209-s panel in Figure 3A,
and in particular, the yellow highlighted rectan-
gular region where the largest electric field is
expected. The dumbbell-angle rotation, and
thus switching, initiates first at the top of this
rectangle and progresses laterally and verti-
cally with time; the structure in this region is
identified as a local domain nucleation site
with attendant domain walls.
Last, we show the average AlN dumbbell-
angle progression for one unit cell in the movie
close to the location of maximum anticipated
electric field (Fig. 3C). The angle evolution from
positive to negative values, and thus polariza-
tion down to up, is clearly visible. Figure 3C also
contains inset images of the initial N-polar
(polarization-down) state, the final Al-polar
(polarization-up) state, and the transient inter-
mediate state of this region of the sample.
To further understand the switching path-
way and identify the transient state observed
experimentally, we carried out first-principles
calculations using the nudged-elastic-band
method for determining the minimum energy
pathway for polarization reversal in both AlN
and Al15/16B1/16N, which closely matches the
experimental composition. After structural
optimization, we calculated the polarization
reversal pathways (Fig. 4A). The results high-
light two distinct mechanisms, in which AlN
switches coherently in one step at 0.523 eV/
formula unit (f.u.), whereas Al15/16B1/16N switches
sequentially in nine steps at 0.200 eV/f.u.
The coherent polarization reversal suggests
that pure AlN switches through a nonpolar
hexagonal (h)-BN–like structure, whereas in
Al15/16B1/16N, we observed an average non-
polar supercell in the middle of the switching
process (Fig. 4A, insets). This metastable state
is not a h-BN–like structure but consists of anti-
polar arrangements of wurtzite motifs when
viewed along the [100] direction, as shown in
our atomic models (Fig. 4B). A more convoluted
structure is observed when projecting the
structure along the [110] or [010] orientation
(Fig. 4B), where N-polar and Al-polar unit
cells are overlapped in this projection, which
agrees qualitatively well with the transient
structure observed during the in situ switch-
ing experiments. Both in situ data and first-
principles calculation independently show that
the anion and cation sublattice contribute com-
parable distortions along the switching path.
To correlate the experimental observations
and the first-principles calculations, we carried
out dPDC-STEM image simulations using the
atomic models of the Al15/16B1/16N, at the initial
(N-polar), middle (nonpolar), and final (Al-polar)
step in the simulation (Fig. 4C). The simulated
images correlate well with the experimental
STEM images at different stages during the
switching process, corroborating the nonpolar
state predicted with the nudged-elastic-band
simulations. Similar projected local structures
have been observed with TEM and STEM
images in polarity inversion domain boundaries
(IDBs) in other wurtzite structures (21–23),
and the four- and eightfold rings of bonds that
were found in simulations of IDBs in GaN (24)
are present in this metastable Al15/16B1/16N
structure (fig. S4). The low-energy IDB in GaN
exhibits no interface electronic gap states
because the Ga and N atoms can maintain
similar local coordination as the parent wurtz-
ite phase.
These results provide insight into the induced
ferroelectricity of wurtzite structures such as
AlN, where the incorporation of alloying ele-
ments, such as B, in the parent wurtzite struc-
ture, results in substantial local-bonding and
local-structural distortions, as has been pointed
out in the (Al,Sc)N system (25). We demonstra-
ted that this disorder provides low-energy path-
ways to nucleate the switching process and that
the switching is mediated by a metastable
transient nonpolar state. This nonpolar meta-
stable state maintains a local structure similar
Calderon et al., Science 380, 1034–1038 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
to the parent wurtzite structure and analogous
to the local structure evidenced in IDBs in
numerous nonferroelectric wurtzites. The
chemical and structural disorder in the (Al,B)N
alloys leads to a relatively flat energy land-
scape that facilitates switching.
Our work provides detailed atomic-scale
structure analysis of ferroelectrically active
wurtzite-structured (Al,B)N thin films, reveal-
ing that B doping leads to a larger spontane-
ous polarization relative to pure AlN sputtered
films. The study also unambiguously shows
the domain nucleation and switching pathway
for these emerging ferroelectric materials. The
alloying disorder provides a complex but sub-
stantially lower-energy-barrier switching pathway
to a transient nonpolar state, which engenders
ferroelectricity in the class of technologically
important polar materials. Such wurtzite-
structured materials can be coprocessed with
mainstream semiconductors, providing path-
ways toward CMOS-compatible integrated fer-
roelectrics, piezoelectrics, and electro-optics.
Our insights into the atomic-scale processes of
domain switching provide guidance to ongoing
and future investigations of wurtzite-structured
thin films that can lead to targeted property
performance.
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AC KNOWLED GME NTS
Funding: This material is based on work supported by the Center
for 3D Ferroelectric Microelectronics (3DFeM), an Energy Frontier
Research Center funded by the US Department of Energy, Office
of Science, Office of Basic Energy Sciences Energy Frontier
Research Centers program under award DE-SC0021118. E.C.D. and
S.C. acknowledge the use of the Materials Characterization Facility
at Carnegie Mellon University supported by grant MCF-677785.
Author contributions: Conceptualization: S.C.V. and E.C.D.
Material production: J.H. and J.-P.M. Electron microscope
characterization: S.C.V, W.T., and E.C.D. First-principles
calculations: S.M.B. and I.D. Data interpretation: S.C.V., J.H.,
S.M.B., E.C.D., J.-P.M., I.D., and S.T.-M. Funding acquisition: E.C.D,
J.-P.M., I.D., and S.T.-M. Supervision: E.C.D., J.-P.M., and I.D. Writing –
original draft: S.C.V. Writing – review and editing: All authors
reviewed and edited the draft. Competing interests: The authors
declare that they have no competing interests. Data and
materials availability: TEM data generated in this study are
available at Zenodo (26). First-principles data and models that
support the findings of this study are available at Zenodo (27).
License information: Copyright © 2023 the authors, some rights
reserved; exclusive licensee American Association for the Advancement
of Science. No claim to original US government works. https://
www.science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh7670
Materials and Methods
Figs. S1 to S4
Movie S1
References (28–44)
Submitted 13 March 2023; accepted 10 May 2023
10.1126/science.adh7670
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RES EARCH
ENZYMOLOGY
Trivalent rare earth metal cofactors confer rapid
NP-DNA polymerase activity
Victor S. Lelyveld1,2, Ziyuan Fang1,2,3, Jack W. Szostak1,2,3,4,5,6*
A DNA polymerase with a single mutation and a divalent calcium cofactor catalyzes the synthesis of
unnatural N3′→P5′ phosphoramidate (NP) bonds to form NP-DNA. However, this template-directed
phosphoryl transfer activity remains orders of magnitude slower than native phosphodiester synthesis.
Here, we used time-resolved x-ray crystallography to show that NP-DNA synthesis proceeds with a single
detectable calcium ion in the active site. Using insights from isotopic and elemental effects, we propose that
one-metal-ion electrophilic substrate activation is inferior to the native two-metal-ion mechanism. We found
that this deficiency in divalent activation could be ameliorated by trivalent rare earth and post–transition
metal cations, substantially enhancing NP-DNA synthesis. Scandium(III), in particular, confers highly specific
NP activity with kinetics enhanced by more than 100-fold over calcium(II), yielding NP-DNA strands up to
100 nucleotides in length.
T he principal chemistry at the core of
RNA and DNA metabolism is phospho-
diester synthesis. Polymerases generate
nascent strands of genetic material by
stepwise phosphoryl transfer of nucleo-
tides to primer termini, yielding O3′→P5′ phos-
phodiester linkages. This template-directed
process is conserved across all known biology.
Nucleotide 3′ substitutions have therefore
been widely regarded as chain terminating for
polymerase activity, forming the basis for a
class of nucleoside analog drugs (1, 2).
In recent work, we demonstrated the direct
enzymatic synthesis of an unnatural linkage
by substitution of the 3′-OH nucleophile with
a 3′-amine, extending the chemistry amenable
to polymerase catalysis (1). We reported that
3′-NH2 primer extension can be catalyzed by a
modified DNA polymerase, yielding N3′→P5′
phosphoramidate DNA (NP-DNA; Fig. 1, A
and B). The large fragment of DNA polymerase I
(BF), cloned from the thermophilic soil bacte-
rium Geobacillus stearothermophilus (Bst), ac-
quires nontrivial levels of N3′→P5′ polymerase
activity through two unexpectedly minor sub-
stitutions: a single active-site mutation (F710Y)
and substitution of its divalent Mg2+ cofactors
with Ca2+ (1). However, this level of activity
remained around four orders of magnitude
slower than native phosphodiester synthesis.
Although NP synthesis was detectable in the
presence of several divalent alkaline earth
metal ions, the pattern of metal cofactor activ-
ity was distinct from that found in native phos-
1Center for Computational and Integrative Biology,
Department of Molecular Biology, Massachusetts General
Hospital, Boston, MA 02114, USA. 2Department of Genetics,
Harvard Medical School, Boston, MA 02115, USA.
3Department of Chemistry, University of Chicago, Chicago, IL
60637, USA. 4Howard Hughes Medical Institute, The
University of Chicago, Chicago, IL 60637, USA. 5Howard
Hughes Medical Institute, Massachusetts General Hospital,
Boston, MA 02114, USA. 6Department of Chemistry and
Chemical Biology, Harvard University, Cambridge, MA 02138, USA.
*Corresponding author. Email: jwszostak@uchicago.edu
phodiester activity (3). Crystal structures of the
ground-state NP reaction complex showed a
single metal ion in the active site (1), suggest-
ing a plausible distinction between the NP
mechanism and the classical two-metal-ion
mechanism in native phosphodiester activity
(4). Whether NP catalysis does in fact rely on
a distinct mechanism with a nonclassical co-
factor configuration remains to be established,
as do the critical factors limiting the kinetics of
NP synthesis.
Linearly correlated density dynamics in
reacting BF crystals during NP synthesis
To understand the mechanistic barriers to rapid
enzymatic NP-DNA synthesis, we first sought
to observe NP bond formation through crystal-
lography. In previous x-ray crystal structures
of the fully assembled NP polymerase pre-
insertion complex, we modeled a single divalent
metal ion in the reaction center, occupying a
site distal to the primer-terminal nucleophile (1).
This site is equivalent to the so-called “B site” in
the classical two-metal-ion reaction center and
includes inner sphere ligands from the substrate
triphosphate moiety, the side chains of Asp830
and Asp653, and the backbone amide of Tyr654.
No evidence for an “A-site” metal proximal to
the primer 3′-amino terminus was observed
in these earlier prechemistry model structures,
a finding consistent with the expectation that a
neutral amine is the nucleophile in NP synthe-
sis. However, earlier structures did not fully
recapitulate the active NP reaction center or
the product state (1). The A-site metal ion can
also be poorly ordered even in structures
of the native polymerase reaction complex.
Nakamura et al. reported that accumulation
of an additional metal ion in a “C site” of poly-
merase h, a polymerase Y family member,
occurs in a manner linearly correlated with
bond formation, suggesting that the product
state’s postchemistry metal configuration may
be distinct from that observed in the prechem-
istry reaction complex (5). This observation
was subsequently extended to polymerase X
family members (6, 7). To add evidence that a
single divalent metal ion cofactor catalyzes
unnatural NP synthesis in BF, a polymerase A
family member, we performed a single-nucleotide
primer extension reaction in intact crystals (Fig. 1,
B to D). We crystallized active substrate-bound
BF polymerase F710Y/D598A with a 3′–amino-
terminal DNA primer and DNA template in
the presence of Ca2+ and 2′-deoxyguanosine 5′-
triphosphate (dGTP). Reactions were then ini-
tiated in the intact crystals by a pH shift from
an acidic mother liquor (pH < 6) to a basic
soaking liquor at pH 8.8, and reacting crystals
were quenched at various times by flash freez-
ing (Fig. 1, C and D).
Quantitative analysis of electron density
dynamics is complicated by crystal-to-crystal
variance in diffraction datasets. We therefore
incorporated datasets arising from up to four
crystals at each of six time points after ini-
tiation. By scaling reflections from 19 total crys-
tals (resolution 2.0 to 2.7 Å) across the time
course (0 to 24 hours), we could estimate voxel-
wise first-order rate constants for changes in
real-space electron density across the asym-
metric unit and particularly at the reaction
center (Fig. 1D, bottom left panel). Early time
points show negligible differences in ordered
density between the ground-state complex crys-
tallized under acidic conditions versus the com-
plex after 1 hour of soaking under reaction
conditions, suggesting that the reactant state
and ground state cannot be clearly distin-
guished in this resolution range. By following
the reaction at subsequent times, we observed
monotonic accumulation of nascent NP bond
density between the primer terminal 3′-amino
group and the substrate a-phosphate with con-
comitant loss of electron density between the
a- and b-phosphates with similar first-order
rate constants (Fig. 1D).
By inspecting the kinetics of density changes
at nearby sites, we observed that the most prom-
inent local density dynamics in the active site
had simple linear relationships with nascent
bond formation. Pairwise linear regression
yields the relative slope (b) of density changes
occurring at any two points across the time-
resolved dataset (Fig. 2, A and B). Performing
this regression at all points in the asymmetric
unit versus the nascent bond furnished a field
of b values or “beta map” in real space, which
could be contoured at a desired threshold of
|b| to give isosurfaces for visualization (Fig.
2C). To show that regions with high |b| are also
highly correlated, we produced pairwise Pearson
correlation maps using a similar procedure (Fig.
2D). Regions of local conformational dynamics
were qualitatively in agreement between corre-
lation maps with coefficient r contoured at |r| >
0.9 (Fig. 2D) versus regression maps contoured
at |b| > 0.45 (Fig. 2C). When beta maps were
Lelyveld et al., Science 382, 423–429 (2023)
27 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
B
A
P
O
O
O
O
O
O
O
O
O
N
N
NH
C
D
O
P
O
O
P
O
O
P
O
Y654
D653
D830
NH2
Y710
dGTP
b
m
u
h
T
alm
P
Fingers
Fig. 1. NP polymerase activ-
ity proceeds in crystallo by
a one-metal-ion mecha-
nism. (A) Condensation of
nNTPs generates NP-DNA.
(B) Reaction scheme for
BF-catalyzed primer extension
of a 3′–amino-terminal primer
on a DNA template, yielding
pyrophosphate and an NP-
linked +1 nucleotide extension.
R = OH for in crystallo single-
nucleotide addition of dGTP
with co-crystallized divalent
metal ion cofactor Ca2+,
whereas R = NH2 for multiple
turnover extension in solution
to synthesize NP-DNA poly-
nucleotide strands in the pres-
ence of divalent (M2+) or
trivalent (M3+) metal ion
cofactors. (C) Ribbon cartoons
of BF polymerase ground-state
(GS) holocomplex x-ray crystal
structure with 3′–amino-terminal
DNA primer (green ribbon)
and DNA template (cyan) with
bound dGTP substrate and a
single Ca2+ ion (green atom) in
the canonical metal-B site (left
and middle panels), showing
one of two complexes co-
crystallized in the asymmetric
unit. All analyses performed
here derive from the first
complex (structure chains A
to C), but consistent trends
are seen in both. Dotted circle
indicates the position of a
missing A-site metal in
analogous models of the
canonical phosphodiester
synthesis mechanism but
not observed in closed
conformation GS structures
containing a 3′-NH2 (middle
panel) or in product state (PS)
structures of the in situ synthesized NP bond. (D) Representative time-dependent
difference maps (Fo – Fc) showing density changes in the BF F710Y/D598A
active site during NP bond formation in crystallo. GS crystals containing a 3′-amino-
2′,3′-dideoxycytidine (nC) terminated primer and DNA template were formed
under acidic conditions (pH 5 to 6) in the presence of Ca2+ and dGTP, and
the in situ reaction was initiated by transferring crystals to a solution at
pH 8.8. The reaction in intact crystals was quenched at the indicated times by
e
g
n
a
h
C
y
t
i
s
n
e
D
d
e
z
= 0.21±0.03 h-1
10
Time (h)
Primer
Ca2+
pH
N-P
P-O
N-P
K706
a
m
r
o
N
t=0
D653
E831
nC
P-O
D830
1.0
0.0
0.6
0.8
0.4
0.2
20
i
l
0
Template
Primer
O
N
H2
O
O
R
BF
O
M2+/3+
O
O
P O P
O
OO
O
P
O O
R
O
O
O
P
O
O
O
N
H
O
HO P
OO
O
P
O O
pH
A B
GS
PS
t = 1
t= 2
t = 4
t=24h
t=8
t = 6
flash freezing for subsequent data collection. Positive (aquamarine mesh) or
negative (red mesh) isosurfaces are shown contoured at 2.5 s and superimposed
on the GS model. Bottom left inset: normalized density change extracted
from difference maps at the nascent N–P (aquamarine) and scissile O–P (red)
bonds quantified from 19 crystals (dots). Observed first-order rate constant
estimates, kNP and kPO, for the density changes ± SD are plotted (solid line ±
shaded area).
contoured at |b| > 0.9, we observed that the in-
cluded voxels were tightly constrained to the site
of the nascent NP bond and the scissile Pa–Oa,b
bond (fig. S1A). No other linear density dynamics
were larger in scalar magnitude than the chem-
istry itself during bond formation in crystallo.
Inspecting the isosurfaces contoured at |b| >
0.45, we observed four major density perturba-
tions that were also highly correlated (|r| > 0.9)
with the nascent bond (Fig. 2B, i to iv): (i) dis-
placement of the terminal phosphodiester link-
age between the –1 position and the primer
terminus; (ii) a conformational switch of the
substrate deoxyribose moiety from C2′-endo
to C3′-endo, matching the sugar pucker of the
primer terminus; (iii) a small deflection of the
K706 side chain toward the substrate bridging
a,b-oxygen, homologous to a putative general
acid in the native mechanism (8); and finally (iv)
disordering of the leaving group pyrophosphate
moiety. As apparent from the high correlation
coefficients, maps generated as 1 – p for two-
tailed P values determined for the correlation
field versus the nascent bond show that all of
Lelyveld et al., Science 382, 423–429 (2023)
27 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. One-metal-ion NP catalysis is limited by deficient substrate activa-
tion. (A) Voxelwise linear regression analysis of density dynamics in crystallo.
Difference map (Fo – Fc) densities derived from reacting crystals quenched at
various times yield kinetic traces at a reference point (Ref.) or any query point of
interest. A pairwise linear regression slope (b) of density changes at the
reference versus query points can be estimated for any two points in real space.
(B) Regression statistics of key density dynamics during NP synthesis in BF
F710Y/D598A. Insets i to iv show difference map density derived from individual
crystals at four major active-site blobs indicated in (C). Left panels: first-order
kinetics of density differences from individual crystals (dots) over reaction time,
with values for the estimated rate constant ± SD plotted (solid line ± shaded
area). Right panels: pairwise linear regressions, coefficients of determination
(R2), and correlation coefficients (r) of difference map densities at the indicated
site versus the NP bond across all crystals. (C) Pairwise linear regression “beta”
map calculated at all points versus the nascent NP bond (black wedge) with
positive (aquamarine mesh) or negative (red mesh) b displayed as isosurfaces
superimposed on the GS structure and contoured at |b| > 0.45. (D) Pearson
correlation map of the active site contoured at |r| > 0.9 calculated by pairwise
comparison of all voxels versus the peak of the nascent bond (black wedge), with
positive (aquamarine mesh) or negative (red mesh) correlation displayed as
isosurfaces superimposed on the GS structure. (E) Alternative view of the beta
map contoured at |b| > 0.4, highlighting positive and negative beta peaks at sites
(purple wedges) associated with a conformational change at the side chain of
Lys706 [positive lobe quantified in (B), iii] in the direction of the substrate Oa,b
bridging position and the scissile bond, as well as the conformation change in the
dGTP substrate sugar [gray wedges, positive lobe quantified in (B), ii]. (F) Pairwise
linear regression and correlation statistics versus the nascent bond calculated at
a position equivalent to the absent A-site metal [gray “A” label in (C) and (D)].
(G) Cartoon overlay of GS (peach) and PS (blue) models with indicated
conformational dynamics labeled as in (B) to (E).
these active-site dynamics were highly signifi-
cant with P < 10−6 (fig. S1B). Deflection of K706
toward the substrate a,b-bridging oxygen was
well resolved on the beta map as positive and
negative lobes surrounding terminal atoms of
the side chain (Fig. 2E). This motion is note-
worthy because the site is structurally homol-
ogous to the C-site metal-ion density reported
for X- and Y-family polymerases (5, 6, 7, 9).
Crucially, no well-correlated density changes
were observed at a position equivalent to the
absent A-site metal in the native mechanism
(Fig. 2F).
Conformational changes in both the upstream
and downstream nucleotides flanking the nas-
cent bond were linearly correlated with covalent
bonding (Fig. 2B, i and ii and C and D). The
upstream conformational change at the primer-
terminal linkage was also observable in time-
resolved datasets of native phosphodiester
synthesis in polymerase h (5). The downstream
conformational change in the dGTP substrate
sugar from C2′- to C3′-endo upon product
formation (Fig. 2, B, inset ii, and E), however,
was not observed in an equivalent time-resolved
experiment with the wild-type enzyme, in which
the conformation was stably C3′-endo (fig. S2).
Although interesting, a ground-state confor-
mational change in the deoxynucleotide sub-
strate is unlikely to be relevant to 3′-amino
Lelyveld et al., Science 382, 423–429 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
nucleotides, which already prefer the C3′-
endo conformation due to a mixture of steric
and anomeric effects (see the supplementary
materials) (10).
Isotopic and elemental substitution effects
point toward rate-limiting chemistry with Ca2+
Reacting crystals were sampled on a time scale
vastly slower than that of conformational
dynamics such as furanose pseudorotation. The
crystal data are therefore not directly informa-
tive of the relative sequence and magnitude of
these reaction barriers. To gain more insight
into the rate-limiting step for NP synthesis, we
turned to solution-phase kinetics. Two proton
transfers have been detected in the rate-limiting
step of native polymerase activity using careful
measurements of the solvent deuterium kinetic
isotope effect (SDKIE) (8, 11). In NP synthesis,
it is minimally required that one proton arising
from the 3′-amino nucleophile must ultimately
be transferred out of the reaction center in the
forward reaction, yielding the product phos-
phoramidate. The conserved Asp830 side chain,
proximal to the nucleophilic primer 3′-amine
at ~2.5 Å in refined ground-state structures
(Fig. 3B), is the most likely general base me-
diating this proton transfer. A sterically con-
servative point mutation at this position, D830N,
entirely abolishes activity (1). We found that
the effect of varying mole fraction, n, of D2O
solvent on pre–steady-state NP reaction kinet-
ics was negligible, yielding an SDKIE estimate
of 1.16 for 3′-amino primer extension in the
presence of Ca2+ and dCTP (Fig. 3A). In native
phosphodiester polymerases, this value has
generally been measured in the 2 to 5 range
(8). The substantially lower value measured
here suggests that proton transfer is not a criti-
cal barrier in the NP reaction with Ca2+.
If the chemical step of NP bond synthesis
sets the overall reaction rate, then modulating
the electrophilicity of the substrate should
show an appreciable kinetic effect. We there-
fore measured the nonbridging elemental
thio substitution effect in solution using stereo-
pure Sp or Rp diastereomers of dCTPaS. We
found that the thio effect was kO/kS = 10.6 ± 0.5
(mean ± SD) when substituting the dCTP
substrate with Sp-dCTPaS in pre–steady-state
extension of a 3′-amino terminus at 45°C (Fig. 3,
C and D). Elemental thio effects of similar
magnitude have been observed for native poly-
merase mismatch extension or when the di-
valent cofactors are Mn2+ rather than Mg2+,
both conditions for which the chemical step ap-
pears to be rate limiting (11, 12). The thio effect
was compounded by an additional fourfold
for the Rp substrate versus the Sp substrate
(Fig. 3D), consistent with the coordination
geometry seen in crystal structures (Fig. 3B).
The interpretation of thio effects has long
been a matter of debate in phosphoryl transfer
catalysis, given the potential for complicating
A
1.2
1
0.8
0.6
0.4
0.2
C
°
5
5
@
O
2
H
k
/
n
k
0
0
C
B
nC
Y710
d
G
T
P
pro-Sp
3.8 Å
pro-Rp
Å
5
.
2
D830
0.2
0.4
n
0.6
0.8
1
D2O
E831
D653
3´NH2 F710Y
Ca2+
+1,2,3...
D
dCTP
Sp-dCTP S
Rp-dCTP S
0 1 2 4 8 16 32 min
C
°
5
4
@
)
1
-
n
m
i
(
l
o
p
k
0.08
0.06
0.04
0.02
0
1
0
.
6
±
0
.
5
4.2 ± 0.7
dCTP Sp- S Rp- S
Fig. 3. Probing for rate-limiting chemistry in NP-DNA synthesis in solution. (A) Pre–steady-state
solvent deuterium kinetic isotope effect estimated from the slope of the line kn/kH2O = 1 + n(ϕ-1) for 3′-amino
primer extension with 1 mM dCTP and 10 mM CaCl2 in varying mole fractions, n, of D2O. The quantity 1/ϕ is
the SDKIE, estimated at 1.16 with 95% confidence interval (1.09 to 1.23) in the shaded region. (B) Atomic
model distances in the GS reaction complex for the primer-terminal (nC) 3′-amine to the D830 side chain or
to the substrate Pa. Gray mesh overlay indicates 2Fo – Fc density map contoured at 2.5 s. (C) Effect of
a-phosphorothioate substitution on pre–steady-state Ca2+-activated NP synthesis at 45°C with 500 mM
Sp-aS, Rp-aS, or unmodified dCTP substrates and BF F710Y. Inset: fluorescently labeled primer and template
strand for the experiments in (A), (C), and (D). Representative 15% tris-borate EDTA (TBE)–urea PAGE
separation of quenched reaction samples is shown. Only the first addition to this primer forms an NP or NPS
linkage in the presence of 2′-deoxyribose substrates, yielding subsequent phosphodiester or phosphorothioate
products, including mismatch extension products. (D) Elemental thio effects (labeled arrows, mean ± SD)
estimated from the pre–steady-state rate constants (kpol, error bars indicate SD, n = 3) for reactions with
substrates as in (C).
B
2-
O
A
N+1
O
H
O
N
O
O
O
O
E831
2+
M
A
O
O
D830
K706
OH
O
O
NH3+
O
O P
OO
M
2+
B
O
P
O
O
O
N
H
D653
Y654
P
O O
C
3-
O
K706
NH2
NH3+
O
O P
OO
O
O
P
O
O
M2+
P
O O
N+1
O
H
N
H
O
N
O
O
D830
O
O
O
N
H
D653
Y654
N
O
O
N+1
O
H
N
H
O
D830
2-
O
K706
NH2
NH3+
O
O P
OO
O
O
P
O
P
O O
M3+
O
?
O
O
O
N
H
D653
Y654
Di-divalent (3 -OH)
Mono-divalent (3 -NH2)
Mono-trivalent (3 -NH2)
Fig. 4. Comparison of reaction models for phosphodiester and phosphoramidate synthesis in BF.
(A) Model for the canonical two-metal ion “di-divalent” mechanism for native phosphodiester activity.
(B) Model for the mono-divalent mechanism for Ca2+-catalyzed NP activity. (C) Proposed mono-trivalent
mechanism for REE-catalyzed NP activity. Note that neither inner sphere waters nor exact proton-transfer
pathways have been depicted. Two rate-limiting proton transfers have been detected for native activity
(8, 11), but proton transfer is not rate limiting for mono-divalent NP activity with Ca2+. At least one proton
must nevertheless be transferred to generate the phosphoramidate product from the attacking neutral
amine. In BF, these transfers likely involve deprotonated D830 as a general base and protonated K706 as a
general acid.
Lelyveld et al., Science 382, 423–429 (2023)
27 October 2023
4 of 7
NH2
BF
M3+, nNTPs
55 °C
Sc3+
Lu3+
~100 nt
1 - 2 hr
Sc3+
+100
RES EARCH | R E S E A R C H A R T I C L E
A
C
°
5
5
@
)
1
-
n
m
i
(
l
o
p
k
8
7
6
5
4
3
2
1
0
101
100
10-1
10-2
10-3
C
D
3´NH2
BF
M3+, nCTP
+1,2
B
nCTP + Sc3+
0 7 13 23 31 42 s
Al3+
Ga3+
Er3+
La3+
Yb3+
Gd3+
Eu3+
+71
+70
Ca2+
Ca2+
Y3+
In3+
Lu3+
Sc3+
N.D.
N.D.
3
2.5
2
1.5
1
C
°
5
4
@
)
1
-
n
m
i
(
l
o
p
k
0.5
0
3´NH2
BF, Sc3+
dCTP/dCTP S
+1
0.58 ± 0.07
6
6
±
7
dCTP Sp- S Rp- S
dCTP
Sp-dCTP S
Rp-dCTP S
0 10 30 45 60 120 240 s
0 2 4 8 16 32 64 min
0 2 4 8 16 32 64 128 min
Fig. 5. Trivalent rare earth metal ion cofactors confer rapid NP polymerase
activity. (A) Pre–steady-state kpol estimates for extension of a 3′–amino-
terminal DNA primer on a DNA template (inset cartoon) by BF F710Y/D598A at
55°C in the presence of various 1:1 ammonium citrate–buffered trivalent metal
cations at 5 mM in 40 mM Tris-HCl, pH 8.8, 2 mM bME, in reactions initiated by
addition of 250 mM nCTP. Estimates are displayed in linear (top) and log-scaled
(bottom) axes compared with the level of Ca2+ activity (dotted line). Inset:
representative 15% TBE-urea PAGE of quenched reaction samples from BF
F710Y/D598A 3′–amino primer extension reactions in the presence of 5 mM Sc3+
showing +1 and +2 NP-DNA extension at the indicated times. ND, not detected.
Error bars indicate SEM for n = 4 (Sc3+ and Lu3+) or n = 3 (In3+ and Y3+).
(B) Mixed-sequence NP-DNA synthesis with excess BF F710Y/D598A on a 71-nt
(left image) or 100-nt (right image) DNA-templating region at 55°C from a
5′–fluorescein-labeled 3′–amino-terminal DNA primer in the presence of 1:1
ammonium citrate–buffered 5 mM Sc3+ or Lu3+, as indicated, in 40 mM Tris-HCl,
pH 8.8, 10 mM bME, and 25 mM spermine-HCl. Reactions were initiated by the
addition of a 250 mM concentration of each nNTP, sampled and quenched at
the indicated times, and samples were separated on 10% (left) or 8% (right)
TBE-urea PAGE gels. (C) Elemental thio effects (labeled arrows, mean ± SD) for
Sc3+-activated NP synthesis with 500 mM Sp-aS, Rp-aS, or unmodified dCTP
substrates at 45°C estimated from kpol (error bars indicate SD, n = 3) using a
fluorescently labeled primer and template strand (cartoon at top), yielding
exclusively +1 product due to high NP(S) specificity. (D) Representative 15%
TBE-urea PAGE separation of quenched samples for the reactions in (C).
steric effects with phosphorothioate substrates
(12, 13). Nevertheless, a plausible interpreta-
tion of the observed thio effects is that the
chemical step sets the overall reaction rate
for NP synthesis.
Electrophilic substrate activation as a
probable deficiency in NP catalysis with Ca2+
If the chemical step is in fact rate limiting but
proton transfer is not, then an augmented
barrier to NP versus phosphodiester synthesis
could, at least in part, originate from an altered
metal-ion configuration in the presence of a 3′-
amino primer. In the native reaction center, it
is generally understood that the A-site metal
ion activates the 3′-OH nucleophile by inner
sphere coordination, yielding a metal alkoxide
in the transition state, but numerous crystallo-
graphic models of reaction intermediates also
show that the octahedral ion bound at the A
site forms an additional inner sphere contact
with the substrate pro-Rp a-phosphate non-
bridging oxygen (14). It has been indepen-
dently argued that the role of the conserved
polymerase dinuclear metal center (Fig. 4A) is
to stabilize the transition state electrostatically
on the basis of linear free energy relationships
obtained from Brønsted plots of pre–steady-
state kinetics in polymerase b, harnessing a
series of Ob,g bridge substituent–modified sub-
strate analogs with varying leaving group pKa
(15, 16). The catalytic effect of the A-site metal
in native activity likely encompasses several
effects, but any catalytic effect conferred by
the presence of an A-site metal ion on sub-
strate activation, as opposed to nucleophile
activation, is absent for NP synthesis. The lack
of electron density for an A-site metal ion in
the ground state and at later time points is
also consistent with the expectation of a neu-
tral nucleophile in the NP reaction and the
generally weak affinity of aliphatic amines
for Ca2+. Because neither the apparent bind-
ing constant nor the active-site conforma-
tion is significantly perturbed by the presence
Lelyveld et al., Science 382, 423–429 (2023)
27 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
of a 3′-amino nucleophile (1), a significant
contributor to the kinetic defect for NP ver-
sus phosphodiester synthesis may therefore
be the relative loss of transition state stabi-
lization associated with the missing A-site
metal cofactor for the reaction with an amino
nucleophile.
If the native metal cofactors act, at least in
part, on the native transition state by charge
stabilization, then it is noteworthy that the net
effect of the absence of one divalent ion (with
disengagement of its conserved ligand, Glu831)
would be to decrease the formal net charge of the
transition state complex by 1 (Fig. 4, A and B).
Outer sphere charge mutations may not be able
to compensate for this inner sphere defect, par-
ticularly if the role of the missing metal in
native activity is partially to contribute to
stabilizing the developing charge polarization
across the scissile bond. This view is consistent
with the observation that eliminating the neg-
ative charge on the disengaged native ligand
by the mutation E831Q fails to enhance NP
synthesis kinetics (1).
Trivalent metal ions confer rapid and specific
NP synthesis activity
On the basis of this activation argument and
the observed thio effect, we hypothesized that
substitution of a trivalent cation into the metal
site B might compensate for the electrostatic
component of the catalytic defect resulting
from the absence of the A-site metal, following
the hypothetical reaction structure depicted
in Fig. 4C. Upon screening a series of redox-
stable trivalent metal ions, we indeed found that
an exotic series of trivalent metal ions could act
as polymerase cofactors for rapid catalysis of
NP bond formation (Fig. 5). The diamagnetic
group three trivalent rare earth element (REE)
cations scandium (Sc3+), yttrium (Y3+), and
lutetium (Lu3+), as well as the post–transition
metal ion indium (In3+), all significantly im-
proved single-nucleotide 3′-amino primer exten-
sion (Fig. 5A), as well as NP-DNA polymerization
with all four 3′-amino 2′,3′-dideoxynucleoside 5′-
triphosphates (nNTPs) on mixed-sequence
templates (Fig. 5B and figs. S3 and S4). Sc3+ in
particular accelerated pre–steady-state rate con-
stants for nCTP addition by ~100-fold at 55°C to
7.1 ± 0.5 min−1 (mean ± SEM) versus 0.069 min−1
for Ca2+ (1), suggesting a stabilization effect of
approximately –3 kcal/mol. Lu3+ yielded simi-
lar levels of burst activity, kpol = 6.9 ± 0.7 min−1
(mean ± SEM), but had far weaker multiple
turnover activity in long primer extensions rel-
ative to Sc3+ (Fig. 5B and fig. S3). NP-active tri-
valent ion cofactors have a wide range of pKa
values for the aquo ion, are prone to hydrolysis
under the reaction conditions, and have a ten-
dency to precipitate nucleotides and other phos-
phates. We found that reaction conditions were
optimal when these ions were buffered at ~1:1
stoichiometry with citrate such that all reac-
tion components remain homogeneously solu-
ble (fig. S4). Although the reaction kinetics were
quite sensitive to the metal:citrate stoichiome-
try, they were not appreciably sensitive to the
concentration of 1:1 Sc3+:citrate in the low-
millimolar range (0.5 to 10 mM) in the presence
of 1 mM total nNTPs (fig. S4). However, it is
known that the metal-ligand stoichiometry
of trivalent REE citrate complexes in solution
is diverse (17).
Trivalent metal ion cofactors confer exqui-
sitely specific catalysis of NP versus phospho-
diester chemistry. We found that the pre–
steady-state rate constant for extension of a
native DNA 3′-OH terminus with nCTP in the
presence of Sc3+ was 5.5 ± 0.6 × 10−3 min−1,
which is at least three orders of magnitude
slower than 3′-NH2 extension (fig. S3B).
NP-DNA synthesis activated by Sc3+ was also
inhibited by added Mg2+ in the low millimolar
range optimal for native activity (fig. S5A). The
mutation D830N was completely inactivating,
whereas the adjacent E831Q mutant exhibited
wild-type activity in long extensions (fig. S5B),
consistent with the active-site configuration
proposed in Fig. 4C. Another notable feature
of trivalent NP catalysis is an apparent in-
verse elemental thio effect. We found that the
Sc3+ thio effect was 0.58 ± 0.07 (mean ± SD) at
45°C, indicating a significant preference for
phosphorothioate substrates to yield thio-
phosphoramidate (NPS) linkages (Fig. 5, C
and D). Inverse thio effects are more readily
explained in the context of inverted stereo-
specificity with thiophilic metal cofactor sub-
stitution, but in this case the catalyzed reaction
remained highly specific (66-fold) for the Sp
over Rp substrates at 45°C. Synthesis of the
potentially clinically relevant NPS linkages
under these conditions was confirmed by high-
resolution mass spectrometry (fig. S6).
NP-DNA synthesis on long templates was
aided by the addition of polyamines (fig. S4).
With spermine and Sc3+, full-length products
on mixed-sequence DNA templates up to +71
nucleotides (nt) or, with additional enzyme, up
to +100 nt, could be synthesized in 1 to 2 hours
at 55°C (Fig. 5B and fig. S4). Polyamine rescue
is consistent with linkage-dependent confor-
mational effects on duplex helicity for NP-
DNA:DNA hybrids that arise during long-range
primer extension synthesis, or it might reflect
competition for inhibitory metal coordination
sites. Activation by spermine was optimal at
low micromolar concentrations, consistent
with its reported effects on Klenow activity
previously attributed to helicity effects (18).
Under these conditions, NP-DNA synthesis
remains highly determined by template se-
quence, because omission of any single amino-
nucleotide from the nNTP mixture markedly
stalled extension activity at or immediately
before the first template position complemen-
tary to the missing substrate (fig. S7A and B).
Extension products also show characteristic
features expected from the incorporation of
unnatural NP linkages, such as acid lability at
elevated temperature (fig. S7A and B, HOAc
lanes) and high resistance to 3′-5′ exonuclease
I activity (fig. S7, C and D).
Discussion
Unlike native phosphodiester catalysis, only a
single metal ion cofactor is detectable by crys-
tallography during NP catalysis. Although tran-
sition states and other short-lived intermediates
were not directly observable in our studies, the
totality of the evidence supports a single–metal
ion mechanism with weakened substrate acti-
vation in 3′-amino primer extension by BF.
From this inference, we identified a series of
trivalent metal ion polymerase cofactors with
markedly enhanced reactivity and specificity
for NP-DNA synthesis. Relative to the wild-type
BF DNA polymerase, combining a single active-
site point mutation with trivalent REE cofactor
substitution accelerated NP synthesis by well
over 1000-fold, yielding template-directed NP-
DNA strands of useful lengths in benchtop
enzyme reactions. In the presence of Sc3+
and spermine, overall NP polymerase reaction
time to yield full-length products (~0.9 to
1.3 min/nt at 55°C) was similar to that re-
ported for certain evolved xenonucleic acid
(XNA) polymerases producing OP-linked strands
incorporating synthetic sugars [0.75 to 1.5 min/nt
at 50 to 65°C (19)]. REE-catalyzed NP polymerase
reactions are therefore comparable to those of
extensively mutated polymerases engineered
for alternative phosphodiester synthesis activi-
ties by directed evolution (20). This finding
suggests that the evolutionary distance to ca-
talysis of distinct chemistry may be negligible
when alternative cofactors are present, given a
conservatively modified substrate. By compari-
son, recovering a conserved chemistry with
highly divergent substrates may require a more
extensive search of sequence space.
The considerable catalytic advantage con-
ferred by trivalent metal ion cofactors implies
that a broader family of polymerase activities
may be accessible by directed evolution of sub-
strate specificity given the well-demonstrated
ability of evolutionary methods to optimize
native catalysis on XNA substrates (20, 21).
NP-DNA falls within a class of phosphorami-
date nucleic acids that have long been valued
for their potential utility as nuclease-resistant
antisense oligonucleotides (22). These poly-
mers have also been extensively studied for
their nonenzymatic self-assembly from chemi-
cally activated phosphorimidazolide nucleo-
tide analogs (23–26) on a path to developing
synthetic protocells and model systems for
key aspects of abiogenesis (27, 28). Despite
lacking a 2′-OH group, short synthetic NP-DNA
duplexes adopt a conformational geometry
more similar to RNA than to DNA (10) such that
Lelyveld et al., Science 382, 423–429 (2023)
27 October 2023
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RES EARCH | R E S E A R C H A R T I C L E
these polymers are viable templates for reverse
transcriptase activity (29) but are poor sub-
strates for several classes of nucleases (30, 31).
Whether NP polymers are, like RNA, fully
functional Darwinian polymers remains a mat-
ter of considerable interest. The development
of practical levels of NP polymerase activity is
a crucial step on the path to demonstrating
that this class of synthetic genetic materials is
in fact functional and evolvable.
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ACKN OWLED GMEN TS
We thank the staff at the Advanced Light Source (ALS) beamline
822 and the Advanced Photon Source (APS) beamline 23ID-B for
technical assistance and F. Ng for invaluable research support.
Funding: This work was supported by the Howard Hughes Medical
Institute and Simons Foundation (grant 290363 to J.W.S.). The
Berkeley Center for Structural Biology is supported in part by the
Howard Hughes Medical Institute. The ALS is a Department of
Energy (DOE) Office of Science User Facility supported by
contract no. DE-AC02-05CH11231. The ALS-ENABLE beamlines
are supported in part by the National Institutes of Health (NIH),
National Institute of General Medical Sciences (grant P30
GM124169). GM/CA@APS has been funded by the National
Cancer Institute (grant ACB-12002) and the National Institute of
General Medical Sciences (grant AGM-12006, P30GM138396).
This research used resources of the APS, a DOE Office of
Science User Facility operated for the DOE Office of Science by
Argonne National Laboratory under contract no. DE-AC02-
06CH11357. The Eiger 16M detector at GM/CA-XSD was funded
by NIH grant S10 OD012289. Author contributions: V.S.L. and
J.W.S. conceived the study and designed the research plan.
Z.F. performed crystallizations, data collections, and
refinements. V.S.L. analyzed the structural data, prepared
materials, performed solution phase experiments, and analyzed
the data. V.S.L. and J.W.S. interpreted the data and wrote
the manuscript. Competing interests: A related patent
application regarding enzymatic polymerization of NP-linked
polynucleotides has been filed by V.S.L. and J.W.S. The
remaining author declares no competing interests. Data and
materials availability: Crystallographic data and maps have
been deposited into the Protein Data Bank under PDB codes
8SCG, 8SCI, 8SCJ, 8SCK, 8SCL, 8SCM, 8SCN, 8SCO, 8SCP,
8SCQ, 8SCR, 8SCS, 8SCT, and 8SCU. All other data are
presented in the main text or supplementary materials. License
information: Copyright © 2023 the authors, some rights
reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-
journal-article-reuse. This article is subject to HHMI’s Open
Access to Publications policy. HHMI lab heads have previously
granted a nonexclusive CC BY 4.0 license to the public and a
sublicensable license to HHMI in their research articles.
Pursuant to those licenses, the Author Accepted Manuscript
(AAM) of this article can be made freely available under a CC BY
4.0 license immediately upon publication.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh5339
Materials and Methods
Supplementary Text
Figs. S1 to S7
Tables S1 to S3
References (32–39)
MDAR Reproducibility Checklist
Submitted 23 April 2023; accepted 20 September 2023
10.1126/science.adh5339
Lelyveld et al., Science 382, 423–429 (2023)
27 October 2023
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RES EARCH
BIOCHEMISTRY
Structure of a ribonucleotide reductase R2
protein radical
Hugo Lebrette1,2*†, Vivek Srinivas1†, Juliane John1, Oskar Aurelius1,3, Rohit Kumar1, Daniel Lundin1,
Aaron S. Brewster4, Asmit Bhowmick4, Abhishek Sirohiwal1, In-Sik Kim4, Sheraz Gul4, Cindy Pham4,
Kyle D. Sutherlin4, Philipp Simon4, Agata Butryn5,6‡, Pierre Aller5,6, Allen M. Orville5,6, Franklin D. Fuller7,
Roberto Alonso-Mori7, Alexander Batyuk7, Nicholas K. Sauter4, Vittal K. Yachandra4, Junko Yano4,
Ville R. I. Kaila1, Britt-Marie Sjöberg1, Jan Kern4*, Katarina Roos8§, Martin Högbom1*
Aerobic ribonucleotide reductases (RNRs) initiate synthesis of DNA building blocks by generating a free
radical within the R2 subunit; the radical is subsequently shuttled to the catalytic R1 subunit through
proton-coupled electron transfer (PCET). We present a high-resolution room temperature structure of
the class Ie R2 protein radical captured by x-ray free electron laser serial femtosecond crystallography.
The structure reveals conformational reorganization to shield the radical and connect it to the
translocation path, with structural changes propagating to the surface where the protein interacts with
the catalytic R1 subunit. Restructuring of the hydrogen bond network, including a notably short O–O
interaction of 2.41 angstroms, likely tunes and gates the radical during PCET. These structural results help
explain radical handling and mobilization in RNR and have general implications for radical transfer in proteins.
U ncontrolled or unmitigated free radicals
can cause damage to cells but radicals
are also essential to numerous meta-
bolic pathways and enzyme-mediated
chemistry (1, 2). Ribonucleotide reduc-
tase (RNR) is an archetypal radical enzyme,
and the tyrosyl radical (Y(cid:129)) in the R2 subunit
from Escherichia coli was the first stable pro-
tein radical to be observed, 50 years ago (3).
RNR provides the only pathway for de novo
synthesis of deoxyribonucleotides and repre-
sents a drug target for both cancer and infec-
tious diseases (4, 5). Aerobic RNR (class I)
depends on the ferritin-like R2 subunit to gen-
erate a catalytic radical in an oxygen-dependent
reaction; the radical must be transferred back
and forth with the catalytic R1 subunit, which
performs the ribonucleotide reduction (6). Radi-
cal translocation between the subunits proceeds
through reversible long-range proton-coupled
electron transfer (PCET) in a transient R1-R2
complex (7). Radical transfer initiation in-
volves redox-induced structural changes in R2
(8, 9), conformational gating (10), short-range
1Department of Biochemistry and Biophysics, Stockholm
University, Arrhenius Laboratories for Natural Sciences,
Stockholm, Sweden. 2Laboratoire de Microbiologie et
Génétique Moléculaires, Centre de Biologie Intégrative,
CNRS, Université Toulouse III, Toulouse, France. 3MAX IV
Laboratory, Lund University, Lund, Sweden. 4Molecular
Biophysics and Integrated Bioimaging Division, Lawrence
Berkeley National Laboratory, Berkeley, CA, USA. 5Diamond
Light Source Ltd, Harwell Science and Innovation Campus,
Didcot, UK. 6Research Complex at Harwell, Harwell Science
and Innovation Campus, Didcot, UK. 7LCLS, SLAC National
Accelerator Laboratory, Menlo Park, CA, USA 8Department of
Cell and Molecular Biology, Uppsala University, Uppsala,
Sweden.
*Corresponding author. Email: hugo.lebrette@univ-tlse3.fr (H.L.);
jfkern@lbl.gov (J.K.); hogbom@dbb.su.se (M.H.)
†These authors contributed equally to this work.
‡Present address: Macromolecular Machines Laboratory, The Francis
Crick Institute, London, UK.
§Present address: Sprint Bioscience, Huddinge, Sweden.
proton transfer (11) coupled to long-distance
electron transfer (12), and regulation by R1 (7).
Recently, the structure of an R1-R2 holo-
complex was determined by cryo–electron mi-
croscopy (cryo-EM) (7) providing a picture of
the long-range radical transfer pathway. How-
ever, atomic resolution snapshots of the radi-
cal state and the conformational gating taking
place at the R2 active site remain unresolved.
Most R2 proteins harbor a conserved tyro-
sine residue oxidized to Y(cid:129) by an oxygen-
activated metal center in the catalytically active
state. In a recently discovered active metal-free
R2 subclass, denoted R2e, this tyrosine residue
is post translationally meta-hydroxylated to a
3,4-dihydroxyphenylalanine (DOPA) which serves
as the radical-harboring residue (13, 14). Oxygen
activation of R2e and metal-containing R2 pro-
teins display analogous pathways consisting
of a nonactivated state, a catalytically active
radical state, and a radical-lost ground state
(Fig. 1A).
From an experimental point of view, R2e
from Mesoplasma florum (MfR2) represents an
attractive model to study active radical states
in RNRs. Its radical state is metal-independent
which simplifies sample preparation and ex-
cludes partial occupancy or mismetalation of
the metal site often encountered with metallo-
enzymes in vitro (15). In addition, in absence
of protein R1 its radical state is stable with no
decay observed after more than six hours at 25°C
(13). However, as with any radical state, it is
expected to be highly sensitive to photoreduction
as x-ray radiation damage generates free radicals
that spread through protein crystals (16). This
obstacle renders the structural characteriza-
tion of a protein radical state using standard
x-ray crystallography methods unfeasible (17, 18).
Though many crystal structures of iron- and
manganese-containing R2 proteins from dif-
ferent organisms have been obtained, they
describe either the nonactivated state, the
radical-lost ground state (often referred to as
the “met” state) or partially reduced states. Crys-
tal structures of R2e have been solved from two
different organisms (13, 14), likewise showing
signs of x-ray–induced photoreduction.
Discrepancies between R2 crystal structures
and spectroscopic data of radical states have
been observed, leading to contradictory theo-
retical models regarding the conformation of Y(cid:129)
and its environment (8, 19–21). In the present
study, by rapid protein production, microcrys-
tallization and x-ray free-electron laser (XFEL)
serial femtosecond crystallography, using the
diffraction-before-destruction principle (22),
we have determined the atomic structure of
MfR2 in the active radical state at room tem-
perature. Compared with the structure of the
radical-lost ground state, also presented here,
the radical state structure reveals a notably
short hydrogen bond and a critical rearrange-
ment of conserved residues upon acquisition of
the radical. Based on these two distinct states,
we propose a mechanism for structural recog-
nition of the radical state and a model for
redox-coupled conformational gating as a pro-
logue to the radical transfer. This mechanism
defines central aspects of the PCET process and
may be conserved in aerobic RNRs.
Structure of the radical-lost ground state of MfR2
In the catalytically active radical state, the
radical-harboring meta-hydroxylated tyrosyl
(from here denoted DOPAY126(cid:129)) in MfR2 exhib-
its a characteristic absorbance peak at 383 nm
and colors the protein blue (13). The catalytic
radical can be chemically quenched by hydro-
xyurea, a known RNR radical scavenger used
for decades as an antitumor drug (23) pro-
posed to inactivate R2 through PCET (24). Im-
portantly, hydroxyurea causes a reversible
inactivation of MfR2 as the enzyme can recover
activity upon reoxidation by NrdI (13). Thus,
the protein is not permanently inactivated or
damaged but resides in a radical-lost ground
state (Fig. 1A).
To ensure an accurate depiction of the
radical-lost ground state of MfR2, we solved the
crystal structure at 1.35 Å resolution of the pro-
tein chemically quenched by incubation with
hydroxyurea before crystallization. This treat-
ment abolished the 383-nm absorbance peak
and rendered the protein colorless (13). The
electron density map clearly shows the post
translational modification in the meta posi-
tion of DOPAY126 (Fig. 1B). The two oxygen-
containing functional groups of DOPAY126 in
the para and meta positions (denoted para-O
and meta-O, respectively) form hydrogen bonds
(H-bond) with D88. Notably, the meta-O is in-
volved in an unusually short interaction (Fig.
1B). Using END/RAPID error analysis (25), the
O–O distance between DOPAY126 and D88 was
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Fig. 1. Radical state and radical-lost ground state of MfR2. (A) Outline of
the proposed activation pathway of metal-free R2e, including the nonactivated
state, catalytically active radical state, and radical-lost ground state (also known
as “met” in canonical R2). The two states determined in this work are indicated
in green. The structure of R2e in the nonactivated state has been determined
previously (13, 14). For clarity, chemical reactions are not strictly balanced.
(B) Structure of MfR2 in the radical-lost ground state obtained after chemical
quenching by hydroxyurea (monomer A is shown). (C) Structure of MfR2 in the
radical state obtained from XFEL serial femtosecond crystallography showing
a reorganization of the site compared with the ground state including a coupled
movement of the DOPAY126-D88 dyad, the presence of a new water w1, and
the inward conformation of K213. The short H-bond is highlighted in orange.
(D) Superimposition of the ground and radical states. The 2-Å displacement of
the DOPA para-O is marked in purple. Nitrogen and oxygen atoms are shown
in blue and red, respectively. Carbons are shown in gray and cyan for the radical-
lost ground state and radical state, respectively. Distance between atoms involved in
H-bond interactions are in Å. Simulated annealing composite Omit 2Fo−Fc electron
density maps are shown in green and contoured at 2 s. The structural changes
are further illustrated in movie S1. (E and F) Using quantum mechanical calculations
on the XFEL structure, the short H-bond between DOPAY126 and D88 can be
reproduced by a DOPA radical state with the radical mainly located on the para-O
and the proton located on meta-O (E) (neutral DOPA radical state) or D88 (F)
(negatively charged DOPA radical state). For clarity, only a subset of residues
included in the calculations is presented on the figure (see fig. S3 for full details).
calculated to 2.43 ± 0.04 Å, a length which
could correspond to a low-barrier or single-
well H-bond (26, 27). In addition, DOPAY126
does not interact with any water, nor with
K213 whose e-ammonium group is facing
away from DOPAY126 (Fig. 1B). Compared with
previous R2e structures, differences and al-
ternate conformations are observed through-
out the structures, particularly variations in
the conformation of DOPAY126, D88, and K213
(fig. S1A).
Structure of the radical state of MfR2 by
serial femtosecond crystallography
To circumvent photoreduction artifacts, we used
XFEL serial femtosecond crystallography to
determine the structure of the catalytically
active radical state of MfR2 at atomic reso-
lution. The active radical-harboring protein
was batch crystallized to produce a suspension
of blue microcrystals used to collect room tem-
perature serial femtosecond diffraction data at
an XFEL source. The resulting dataset produces
a model of the protein at 1.5-Å resolution, and
the electron density map allows unambiguous
interpretation (Fig. 1C). A short H-bond be-
tween DOPAY126 meta-O and D88 is present
with a O–O distance calculated to 2.41 ± 0.05 Å
using END/RAPID error analysis (25) (see
Methods for details). A short H-bond is ob-
served in both states of the protein and may
play a special structural role as suggested in
other cases (28), contributing to maintaining
the integrity of the enzyme active site (29).
The short H-bond may stabilize the interaction
between DOPAY126 and D88 to ensure that no
hydrogen is available to mediate a putative pro-
ton transfer from D88 to the DOPAY126 para-O,
which would annul productive PCET. We note
that this H-bonding structure results in a sit-
uation analogous to canonical R2 proteins in
which a deprotonated aspartate is involved in
metal coordination and not in proton transfer,
thus forcing the latter to occur with a different
nearby proton donor, suggested to be a metal-
bound water molecule (11). Furthermore, it is
tempting to speculate that this short H-bond is
involved in redox tuning. By preventing the
radical delocalization between the meta-O and
para-O, the DOPA radical becomes electroni-
cally more similar to a tyrosyl radical, rather than
a DOPA-semiquinone radical, in agreement with
previous characterization of MfR2 by electron
paramagnetic resonance (EPR) (13).
A notable conformational shift takes place
upon radical acquisition between DOPAY126 and
D88: the dyad undergoes a coupled coplanar
(but not coaxial) rotation of ~22°, with an ad-
ditional rotation of the aromatic ring of ~12°
along the Cb-C1 axis. It results in a 2-Å dis-
placement of the para-O carrying the main
radical spin density away from D88 and a re-
organization of the interaction pattern around
DOPAY126 (Fig. 1D). The aspartate residue cor-
responding to D88 in MfR2 is strictly con-
served as the N-terminal metal-coordinating
residue in Y(cid:129)-harboring canonical R2 proteins
and exhibits redox-induced conformational
changes in metal-containing R2 proteins
(8, 17, 30, 31). Furthermore, coupled movements
of the conserved radical-harboring Y have been
observed to be redox-induced in R2b from
Bacillus anthracis (17). For R2a from E. coli
(EcR2a), the conserved aspartate is proposed
to form a H-bond with the reduced Y in the
ground state. By contrast, single-crystal EPR
experiments suggest that the Y(cid:129) rotates away
in the radical state, leading to a ~1-Å displace-
ment of the radical-harboring oxygen and
breaking the connection with the aspartate
(8). A displacement of the Y(cid:129) could also be
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RES EARCH | R E S E A R C H A R T I C L E
hypothesized from discrepancies observed
between crystal structures and spectroscopic
data for R2 proteins from Bacillus anthracis
(32), Salmonella typhimurium (33), Coryne-
bacterium ammoniagenes (30) and mouse (19).
This type of rearrangement upon acquisition
of the radical is principally similar to what
we observe in MfR2 structures and is less
pronounced than movements proposed in
other studies, which involve either translation
of the main chain or larger Y(cid:129) displacement by
several Å (20, 21, 24).
In addition, a clearly defined water molecule
(w1) mediates a new H-bond between DOPAY126
and the e-ammonium group of K213, which
displays a different orientation facing toward
DOPAY126 (Fig. 1C). K213 adopts a single well-
defined conformation different from previously
published structures of active R2e determined
using synchrotron radiation (13) (fig. S1B). The
presence of a water molecule at a position sim-
ilar to w1 has been observed previously in other
RNR systems (34, 35), and seems to be de-
pendent on the redox state (17) (fig. S2). More-
over, superimposition with structures of R2
proteins shows that the new location of the
K213 e-ammonium group corresponds to the
position of another water molecule that is metal-
coordinated in canonical R2 proteins (fig. S2).
This water is proposed to transfer a proton to Y(cid:129)
in the conformational gate initiating the PCET
(11, 36, 37). Residue K213 was recently suggested
by density functional theory to be a proton
donor for radical transfer in R2e (38). There-
fore, it may represent the water-equivalent
proton donor in the case of R2e, and thus its
conformational change could effectuate a com-
parable conformational gate.
Comparing the structures of the defined rad-
ical and radical-lost states determined here to
previously solved structures of R2e proteins
shows that no previous structure fully repre-
sents either the radical state or the radical-
lost state (fig. S1). Although the proteins in
prior work may have originally crystallized in
the “active form,” they appear to have suffered
different degrees of x-ray–induced photo-
reduction during synchrotron data collection.
The XFEL structure can be reproduced in
silico by a radical state
To evaluate whether the crystal structure ob-
tained by XFEL femtosecond crystallography
theoretically corresponds to a radical state,
calculations were performed on the crystal struc-
ture active site. Based on quantum chemical
geometry optimizations, the short interaction
between DOPAY126 and D88 could be reproduced
with the main radical character on the para-O.
The proton could reside on either DOPAY126 or
D88 as both states produced a short O–O dis-
tance (Fig. 1, E and F, and fig. S3, A and B). The
calculated energy difference of 3 kcal/mol be-
tween the two states suggests that both states
are accessible with slight favoring of the proton
residing closer to DOPAY126(cid:129). In addition, var-
ious alternative DOPAY126 states were modeled
by quantum mechanical calculations, none of
them agreeing well with the experimental ob-
servations. In particular, a longer hydrogen bond
with D88 is observed when DOPAY126 is modeled
as a neutral DOPA, a DOPA quinone, or with
the radical located on the meta-O (fig. S3, C to
E). Furthermore, the calculated spin population
of DOPAY126(cid:129) in the protein active site models
revealed an asymmetric distribution closer to
a meta-substituted Y(cid:129) than the fully delocalized
character of an ortho-semiquinone, based on
comparisons with calculated distributions in
smaller models. This is fully consistent with
spectroscopic data of the radical (13, 14) and
indicates a possible role for the short DOPAY126-
D88 hydrogen bond to destabilize the other-
wise potentially too stable semiquinone radical
in the protein.
Molecular dynamics simulation starting from
the XFEL structure of the radical state but with
induced loss of the radical in silico, showed
DOPAY126 movement with the dynamics domi-
nated by the position of the radical-lost ground
state, forming two H-bonds to D88 (fig. S3, F
to H), consistent with the crystal structure.
Altogether, our calculations support that the
structure obtained by XFEL corresponds to
the catalytically active radical state of the MfR2
protein and are in agreement with previous
EPR and UV–vis spectroscopic results (13),
showing that the spin density distributes sim-
ilar as in a meta-substituted tyrosyl radical ra-
ther than as in an ortho-semiquinone.
Specific protein rearrangements upon
radical acquisition
The radical acquisition in MfR2 leads to two
major protein rearrangements that are of par-
ticular interest as they can be directly impli-
cated in radical generation, stabilization, and
transfer. The first major protein rearrangement
takes place within the activating-oxidant path.
The channel connecting the NrdI flavin cofactor
to the R2b metal site (39, 40), proposed as the
(cid:129)− route for activation, seems to be con-
O2
served in R2e (14). In the radical-lost ground
state of MfR2, in place of the metal center
present in canonical R2, a continuous chain of
well-defined H-bonded water molecules cre-
ates the link between the putative oxidant
route and the DOPAY126-D88 dyad. By contrast,
in the radical state of MfR2, this water network
is disrupted by Q91 which undergoes a large
sidechain flip toward D88 (Fig. 2 and movie
S1). In the radical-lost ground state, Q91 is
involved in a H-bond network conserved in the
R2b subclass (Q70 in R2b from E. coli), which
lines the channel for oxidant transport to the
MnII
2 active site (40). Our data suggest that
Q91 could play a key role as it obstructs the
putative oxidant channel in the radical state,
preventing radical quenching by further oxi-
dant access to the active site.
The second major protein rearrangement
upon radical acquisition concerns the PCET
route. In the immediate vicinity of the side chain
of DOPAY126, residues L183 and F187 undergo
large conformational changes in the radical
Fig. 2. Major conformational changes between the radical-lost ground
state and the radical state. (A) Structure of MfR2 in the radical-lost ground
state obtained after chemical-quenching by hydroxyurea. (B) Structure of MfR2
in the radical state obtained from XFEL serial femtosecond data showing
reorganization of the site compared with the radical-lost ground state, including
conformational changes of Q91, L183, and F187. In the radical state, Q91
displaces two water molecules, breaking the water H-bond network toward
DOPAY126. Structural movements of L183 and F187 leave space for 3 water
molecules interacting with D88, DOPAY126, and K213. Simulated annealing
composite Omit 2Fo−Fc electron density maps are shown in green and contoured
at 1.5 s. (C) Superimposition of the structures of MfR2 in the radical state
(cyan) and radical-lost ground state (gray).
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state of MfR2, leaving space for the position-
ing of three water molecules (including w1)
and creating a water-mediated H-bond net-
work between DOPAY126, D88, K213, and Q91
(Fig. 2 and movie S1). Residues L183 and F187
belong to helix aE which forms a distorted
p-helix conserved across many ferritin super-
family members. The p-helix conformation of
helix aE is believed to play a functional role
(41, 42), and is known to undergo redox-induced
structural rearrangements (17, 30, 34). Resi-
dues L183 and F187 are conserved in all R2
proteins, the position of L183 being either F
or L (in 91 and 9% of sequences, respectively)
and F187 being conserved in 99% of the se-
quences. In none of the R2 crystal structures
solved to date do these residues exhibit con-
formations resembling those in the MfR2 rad-
ical state (fig. S4). In the first solved structure
of R2, it was noted that the radical-harboring
tyrosyl oxygen was surrounded by a conserved
hdrophobic pocket formed by residues F208,
F212, and I234 in EcR2a (equivalents to L183,
F187, and I209 in MfR2, respectively) (43). The
major function of these residues was proposed
through mutational studies to contribute to
the tyrosyl radical stability by insulating the
radical-harboring tyrosyl oxygen (44). Our ob-
servation of hitherto unseen movements of
these radical-shielding residues further impli-
cates them in radical control and suggests their
involvement in gating of the ribonucleotide
reductase PCET mechanism. The specific local
rearrangements at the radical site also trans-
late to movements of the protein backbone and
global structural changes of the protein scaffold
protruding to the R1 interaction surface and the
radical transfer path (movie S2). It has previ-
ously been shown that the active R1-R2 complex
exhibits tighter binding after radical initiation
(45–47). We propose that these global structural
changes observed in R2 provide a mechanism
by which the R1-R2 binding properties can be
modulated during the catalytic cycle.
Model of conformational gating for radical
transfer initiation
In MfR2, the catalytically active radical state and
the radical-lost ground state are interconvertible
by quenching the radical and through NrdI-
mediated reoxidation of DOPAY126 (Fig. 1A).
Based on our structural data, we propose a
model of the conformational gating orches-
trated by R2 after radical acquisition, which is
a prelude to the radical translocation to the R1
subunit (Fig. 3). This model proceeds in three
steps. First, the oxidation of DOPAY126 leads
to a repulsion between its para-O and D88
due to the removal of the H-bonding hydro-
gen atom, resulting in the 2-Å displacement
of the DOPAY126 para-O (Fig. 3A). Secondly, this
triggers a cascade of structural changes to
shield the radical and prepare its transfer: Q91
blocks the access to further oxidant, L183 and
F187 reshape the insulating pocket around the
radical, and water w1 connects the DOPAY126
radical-carrying oxygen with the PCET route
(Fig. 3B). This also leads to global structural
rearrangements of protein R2, including the
R2-R1 interaction surface and binding of
protein R1 (Fig. 3C and movie S2). Thirdly, the
formation of the R1-R2 complex results in the
ordering of the full R2 C-terminal tail at
the R1-R2 interface [as demonstrated in (7)],
completing the electron transfer path and in-
ducing the injection of an electron to reduce
DOPAY126(cid:129), e.g., through the conserved W52
and/or Y325 (corresponding to W48 and Y356
in EcR2a), as previously suggested (12) (Fig. 3D).
Coupled to this event, a proton transfer from
K213 to DOPAY126(cid:129) occurs by means of the water
w1 [as proposed in (38)] and initiates the long-
range radical translocation. Figure 3 summarizes
the proposed steps of conformational gating in
R2e. The interaction with R1 is modeled based
on a superposition of the cryo-EM structure of
the R1-R2 holocomplex from E. coli (7).
This conformational gating model for ini-
tiating the radical translocation could be com-
mon to class I RNR systems. In PCET, proton
Fig. 3. Model of conformational gating and radical transfer during PCET
in R2e. (A) Oxidation of the radical-lost ground state DOPAY126 (gray) displaces
DOPAY126-D88 and introduces a water molecule (w1) to facilitate the proton
transfer from the redirected amino group of K213 (cyan). (B) Concurrently, the
cavity surrounding the generated DOPAY126 radical is reshaped, shown in
surface representation (radical-lost state and radical state in gray and cyan,
respectively). Primarily, Q91 flips away from Y163 to block access of any further
oxidant from NrdI through the R2-NrdI channel and L183 and F187 flip to reshape
the cavity and facilitate electron transfer from W52 to DOPAY126. (C) Structure
superposition of MfR2 in the radical (cyan) and radical-lost (gray) states at
the R1 binding interface. Reshaping of the pockets surrounding the DOPAY126
leads to conformational changes protruding to the R2-R1 interaction surface and
binding to protein R1 completes the PCET pathway. (D) PCET is initiated by a
proton transfer (PT) from the amino group of K213 to DOPAY126 mediated by w1,
and simultaneously an electron transfer from W52 to DOPAY126, thus trans-
locating the radical toward the active site C394 of R1. R1 (represented in red)
is modeled in complex with the radical-state MfR2 using the cryo-EM structure of
the R1-R2 holocomplex from E. coli (PDB ID: 6w4x) (7).
Lebrette et al., Science 382, 109–113 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
transfer occurs through H-bond networks and
requires the proton donor and acceptor to be
within a standard ~2.8-Å H-bond distance (48).
As a displacement of the radical-harboring
Y upon radical acquisition is also observed by
spectroscopy in other R2 proteins (8, 19, 30, 32, 33),
an intermediary may be required between the
metal-bound water and Y(cid:129). In MfR2 the ad-
ditional water w1 gained upon radical acquisi-
tion represents the missing piece of the puzzle,
connecting the radical to K213 (Fig. 3D). We
note that an analogous binding site for water
has been observed in other R2 proteins (fig.
S2), and that the e-ammonium group of K213
is located at the position of the metal-bound
water in metal-containing R2s (fig. S2). There-
fore, we speculate that, similarly as in R2e, a
water in this position links the radical to the
metal-bound water proposed to be the proton
donor in canonical R2 proteins and gates the
first proton transfer to initiate radical translo-
cation to R1.
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ACKN OWLED GMEN TS
We thank R. Bolotovsky and I. D. Young for help with data
processing and the staff at LCLS. We acknowledge the Paul
Scherrer Institute, Villigen, Switzerland for provision of synchrotron
radiation beamtime (proposals 20161653 and 20182304), and the
staff of beamline X06SA (PXI) at the Swiss Light Source for
assistance. We acknowledge SOLEIL for provision of synchrotron
radiation facilities (proposal 20180270) and we thank the staff
of beamlines PROXIMA 1 and PROXIMA 2A for assistance.
Research was carried out at the Linac Coherent Light Source
(LCLS), SLAC National Accelerator Laboratory (proposal LU50),
supported by the DOE Office of Science, OBES under contract
DE-AC02-76SF00515. XFEL data processing was performed in part
at the National Energy Research Scientific Computing Center,
supported by the DOE Office of Science, contract DEAC02-
05CH11231. The Rayonix detector used at LCLS was supported by
the NIH grant S10 OD023453. Experiments at the LCLS were
supported by the NIH grant P41GM139687. D.L. acknowledges the
Centre for Ecology and Evolution in Microbial model Systems –
EEMiS, Linnaeus University. A.S. and V.R.I.K. acknowledge the
National Academic Infrastructure for Supercomputing in Sweden
(NAISS 2023/1-31) for computational resources. Funding: The
authors acknowledge financial support of this work by the Swedish
Research Council (2021-03992 to M.H. and 2019-01400 to
B.-M.S.), by the European Research Council (HIGH-GEAR 724394
to M.H.), by the Knut and Alice Wallenberg Foundation (2017.0275
and 2019.0436 to M.H., 2019.0251 to V.R.I.K.), by the Swedish
Cancer Foundation (20 1210 PjF to B.-M.S.), by the Swedish
Foundation for Strategic Research (ICA16-0040 to K.R.), by the
Swedish National Infrastructure for Computing (SNIC 2021/5-137
to K.R.), by the Director, Office of Science, Office of Basic Energy
Sciences (OBES), Division of Chemical Sciences, Geosciences,
and Biosciences (CSGB), Department of Energy (DOE) (to J.Y.,
V.K.Y., and J.K.), by the National Institutes of Health (NIH) grants
GM133081 (to K.D.S.), GM055302 and 1R35GM149528-01
(to V.K.Y.), GM110501 (to J.Y.) GM126289 (to J.K.), GM117126
(to N.K.S.), by Diamond Light Source, the UK Science and Technology
Facilities Council (STFC), and Biotechnology and Biological Sciences
Research Council (to A.M.O., P.A., and A.Bu.), by a Wellcome
Investigator Award (210734/Z/18/Z to A.M.O.), by a Royal Society
Wolfson Fellowship (RSWF\R2\182017 to A.M.O.), and by an
EMBO Long-Term Fellowship (ALTF 952-2022 to A.S.). Author
contributions: H.L. performed crystallography, processed and
analyzed synchrotron and XFEL data, and wrote the manuscript;
V.S. performed protein production and crystallography; M.H.
conceived and led the study; K.R., A.S., and V.R.I.K. performed
computational studies; H.L., V.S., J.J., R.K., J.K., K.R., and M.H.
edited the manuscript; D.L. performed bioinformatics; B.-M.S.
performed study design; C.P., I.-S.K., S.G., A.M.O., F.D.F., and J.K.
developed, tested and ran the XFEL sample delivery system; H.L.,
A.S.B., K.D.S., A.Bh., A.Bu., and N.K.S. processed and analyzed XFEL
data; F.D.F., R.A.-M., and A.Ba. operated the MFX instrument; H.L.,
J.J., O.A., C.P., I.-S.K., A.S.B., S.G., K.D.S., A.Bh., P.S.S., A.Bu., P.A.,
A.M.O., F.D.F., A.Ba., N.K.S., V.K.Y., J.Y., J.K., and M.H. performed the
XFEL experiment at LCLS. Competing interests: Authors declare
that they have no competing interests. Data and materials
availability: Atomic coordinates and structure factors have been
deposited in the Protein Data Bank (PDB) with the following codes:
catalytically active radical state solved by XFEL, 8bt3; radical-lost
ground state, 8bt4. In silico models and output are available at
the SciLifeLab Data Repository (49). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse. This research was
funded in whole or in part by the Wellcome Trust (grant 210734/Z/
18/Z). The author will make the Author Accepted Manuscript (AAM)
version available under a CC BY public copyright license.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh8160
Materials and Methods
Figs. S1 to S5
Table S1
References (50–66)
MDAR Reproducibility Checklist
Movies S1 and S2
Submitted 17 March 2023; accepted 30 August 2023
10.1126/science.adh8160
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RES EARCH
HERBIVORY
Plant size, latitude, and phylogeny explain
within-population variability in herbivory
The Herbivory Variability Network*†
Interactions between plants and herbivores are central in most ecosystems, but their strength
is highly variable. The amount of variability within a system is thought to influence most aspects of
plant-herbivore biology, from ecological stability to plant defense evolution. Our understanding
of what influences variability, however, is limited by sparse data. We collected standardized surveys of
herbivory for 503 plant species at 790 sites across 116° of latitude. With these data, we show that
within-population variability in herbivory increases with latitude, decreases with plant size, and is
phylogenetically structured. Differences in the magnitude of variability are thus central to how
plant-herbivore biology varies across macroscale gradients. We argue that increased focus on
interaction variability will advance understanding of patterns of life on Earth.
P lant-herbivore interactions, which involve
more than half of macroscopic biodiver-
sity and 90% of macroscopic biomass
(1), are believed to shape macroscale
biological patterns and processes, such
as plant and herbivore biodiversity gradients,
biomass distributions, community structure,
species coexistence, and trait evolution (2–4).
Biologists have studied the role of herbivory
at macroscales by quantifying how the mean
herbivore damage level covaries with latitude,
biome, functional traits, and phylogeny (5–7).
However, macroscale patterns have not always
matched expectations. For example, despite
the paradigm that herbivore pressure increases
toward the equator owing to more-benign envi-
ronmental conditions, empirical patterns have
been weak or inconsistent (8–10). Similarly,
despite the expectation that closely related
plant species should face similar pressures
from herbivores, phylogenetic signal in mean
herbivore damage is often undetectable or
restricted to certain groups (5, 11). We suggest
that our understanding of macroscale patterns
in herbivory can be improved by considering
patterns in the magnitude of variability in
herbivory rather than only mean interaction
strength.
Variability is a hallmark of plant-herbivore
interactions (12). Within populations, patterns
in damage are often highly skewed, with most
plant individuals receiving very low levels of
damage, and a few plants receiving high levels
(13). Although there are limited data on the
drivers and consequences of this variability,
theory indicates that within-species variation
in traits or interactions can be as important
as the mean for biological processes ranging
from population viability to evolutionary dy-
namics (14, 15). For example, spatial variability
can stabilize plant-herbivore dynamics by giving
plants refuges from overexploitation (16), can
increase the importance of competition among
herbivores (17), can maintain diversity by fa-
cilitating the evolutionary coexistence of al-
ternative strategies (18), and can drive disease
dynamics by causing superspreading events
(19). Variation in damage among plant indi-
viduals also indicates the potential pattern of
selection by herbivores, which drives plant
defense evolution (20). Variability has been
hypothesized to favor inducible plant defenses
over constitutively expressed defenses—a cen-
tral dichotomy in defense evolution (21). Des-
pite the central role that variability likely
plays in the ecology and evolution of plants
and herbivores, macroscale patterns of var-
iability remain uncharacterized. In this work,
we propose and test three hypotheses for pat-
terns in the magnitude of variation in herbi-
vore damage among individuals within plant
populations.
First, we hypothesize that herbivory varia-
bility within populations increases with distance
from the equator owing to shorter growing
seasons and less-stable abiotic conditions at
higher latitudes reducing the time available
for herbivore foraging. A latitudinal variability
gradient could help explain how herbivores
have influenced global patterns of plant bio-
diversity despite the weak latitudinal gradient
in mean herbivory (22, 23). Herbivory may
maintain plant diversity at low latitudes not
just by being more intense on average but by
being a more-consistently important force
within plant populations. Second, we hypothe-
size that herbivory is more variable among
small plants compared with large plants. Large
*Corresponding author. Email: william.wetzel@montana.edu
†Herbivory Variability Network authors and affiliations are listed in the
supplementary materials.
low
400
B
C
high
even
uneven
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0
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Mean herbivory
(proportion damage)
1.0
100
50
i
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l
t
n
a
p
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e
b
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0.0
0.5
Variability in herbivory
(Gini coefficient)
1.0
i
y
r
o
v
b
r
e
h
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n
o
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t
r
o
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C
1.0
0.5
0.0
Gini coefficient
1.0
0.5
0.0
0.0
1.0
0.5
Cumulative proportion of plants
Fig. 1. Mean and variability in plant-herbivore interactions. (A) Histogram of
the number of plant species with different mean proportion leaf area damaged
by herbivores. (B) Histogram of the Gini coefficient values for all plant
species in our dataset. (C) Lorenz curves from all 790 population surveys
in our dataset. Each curve shows the cumulative proportion of herbivory
across the cumulative proportion of plants, ordered by increasing herbivory,
for one plant population. Curves closer to the 1:1 line (gray dashes) indicate
more-even distributions. Lorenz curves form the basis for the calculation
of the Gini coefficient of inequality, which ranges from 0 (a perfectly
even distribution) to 1 (a perfectly uneven distribution). Curves are colored
by their Gini coefficient [as in (B)]. Sample sizes are 790 surveys of
503 plant species.
Robinson et al., Science 382, 679–683 (2023)
10 November 2023
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RES EARCH | R E S E A R C H A R T I C L E
plants, which represent a greater sampling
area, should average over small-scale random
variation in herbivory, resulting in values closer
to the population mean, whereas small plants
should be more likely to escape herbivory
entirely or be highly damaged by a few events.
If supported, this hypothesis would expand
our understanding of long-studied differences
in defenses between trees and herbs (24), with
consistent damage on large plants explaining
why trees invest a greater proportion of their
biomass in constitutive defenses (25). Third,
we hypothesize that variability in herbivory is
phylogenetically structured, with more-closely
related plants displaying more-similar levels
of variability. This pattern, which has been
documented for mean herbivory (5), would
indicate that variability is influenced by species-
level traits and is not simply random, as it has
often been treated.
To characterize macroscale patterns in
population-level mean and variability in her-
bivory, 127 research teams in 34 countries used
a standardized protocol (26) to sample plants
and quantify aboveground herbivore damage
for 790 populations of 503 species in 135 fami-
lies. This sample comprised more than 50,000
A
B
i
y
r
o
v
b
r
e
h
n
i
y
t
i
l
i
b
a
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r
a
V
i
)
t
n
e
c
i
f
f
e
o
c
i
i
n
G
(
1.0
0.5
0.0
0
Gini
coefficient
1.0
0.5
0.0
C
i
y
r
o
v
b
r
e
h
n
a
e
M
)
n
o
i
t
r
o
p
o
r
p
(
1.0
0.5
0.0
20
40
60
Latitude (absolute value)
Biome
0
20
40
60
Latitude (absolute value)
D
i
y
r
o
v
b
r
e
h
n
i
y
t
i
l
i
b
a
i
r
a
V
)
t
i
n
e
c
i
f
f
e
o
c
i
i
n
G
(
0.8
0.7
0.6
0.5
0.4
0.025
0.050
0.075
Mean herbivory (proportion)
Tundra
Boreal Forests/Taiga
Montane Grasslands & Shrublands
Temperate Grasslands, Savannas & Shrublands
Temperate Broadleaf & Mixed Forests
Temperate Conifer Forests
Mediterranean Forests, Woodlands & Scrub
Tropical & Subtropical Moist Broadleaf Forests
Deserts & Xeric Shrublands
Tropical & Subtropical Dry Broadleaf Forests
Tropical & Subtropical Grasslands, Savannas & Shrublands
Fig. 2. Global patterns of variability in herbivory within plant populations.
(A) The geographic distribution of our sampling sites, colored by variability in
herbivory among individuals within populations (Gini coefficient). Points are
slightly jittered for visibility. (B and C) Variability in herbivory increased (B) and
mean herbivory decreased (C) with latitude across our sampling extent. Lines
show predicted means and 50, 80, and 95% credible intervals from Bayesian
phylogenetic beta regressions. (D) The 11 biomes in our study can be characterized
by their mean and variability in herbivory. Herbivory variability and mean showed
an inverse relationship across biomes [r = −0.67 (−0.94 to −0.08)], but there were
also differences in variability between biomes with similar means. Error bars show
50 and 80% credible regions. Sample size is 790 surveys of 503 species. Legend in
(D) is ordered by Gini coefficient.
Robinson et al., Science 382, 679–683 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
plant individuals distributed across six con-
tinents and 116° of latitude. Past macroscale
studies that have focused on differences in
means typically examined relatively few indi-
viduals per population (5). By contrast, we
sampled 60 individuals per population, which
allowed us to analyze patterns in population-
level variability. For each plant individual, we
recorded plant size (height for most species, or
canopy diameter for prostrate species) and vis-
ually estimated the cumulative proportion of
leaf tissue damaged by invertebrate and verte-
brate herbivores. We quantified the variability
in herbivory among individuals within popu-
lations using the Gini coefficient—a commonly
used scale-invariant metric that ranges from 0
to 1 (perfectly even to perfectly uneven) (27). We
tested our hypotheses by quantifying associa-
tions between each macroscale factor and
the Gini coefficient or mean herbivory using
Bayesian phylogenetic beta regressions.
Overall, within-population variation in her-
bivore damage was very high [mean Gini
coefficient = 0.61 (95% confidence interval: 0.40
to 0.78)] (Fig. 1). On average, the most-damaged
individual in each plant population lost 34.2%
(32.4 to 36.0%) of its leaf area to herbivory,
whereas 27.9% (25.9 to 29.9%) of individuals
completely or essentially escaped herbivory
(<0.5% damage). Half of the damage in each
population was concentrated on 11.3% (10.7 to
11.9%) of its individuals on average. The level
of variation within populations also varied sig-
nificantly across populations and species, with
the Gini coefficient ranging from 0.03, an almost
perfectly even distribution of damage, to 1.0,
a perfectly uneven distribution with all damage
on one plant (Fig. 1, B and C). Even though the
Gini coefficient normalizes by the mean, it
can nevertheless be correlated with it. Mean
herbivory and the Gini coefficient were nega-
tively correlated, with Gini coefficients being
low for the 3.9% of populations with very high
(>25%) mean herbivory, whereas populations
with lower mean herbivory exhibited the full
range of Gini coefficients (r = −0.46) (fig. S1).
Geographic patterns of variability
We found strong support for the latitudinal
variability gradient hypothesis (Fig. 2, A and B).
Variation was lowest at the equator [Gini = 0.51
(0.33 to 0.69)] and increased toward 70°N and
70°S (70°N/S) [Gini = 0.70 (0.54 to 0.84);
Bayesian coefficient of determination (R2) =
5%; posterior probability (pp) = 1.0; Bayes factor
(BF) = 2.0 × 104]. Mean herbivory, by contrast,
declined with latitude, from 8.0% (4.1 to 12.3%)
at the equator to 2.9% (1.4 to 4.7%) at 70°N/S;
this relationship was less predictable than the
one for the Gini coefficient (R2 = 2%; pp = 1.0;
BF = 2.9 × 104) (Fig. 2C, figs. S2 and S3, and
tables S1 to S3). Thus, plants at higher latitudes,
with shorter growing seasons and lower tem-
peratures (26), receive less herbivory on average,
and that herbivory is concentrated on fewer
individuals. This result could conceivably be an
artifact of the negative mean–Gini coefficient
correlation. We therefore repeated our analysis
with mean herbivory included as a covariate.
The estimated latitudinal variability gradient
was still strongly positive, though it was lower
in magnitude, with a 20% (6 to 38%) increase
in the Gini coefficient from the equator to 70°
N/S (R2 = 23%; pp = 1.0; BF = 14.5) (fig. S4).
This relationship captured differences among
biomes: Higher latitude and higher elevation
biomes had higher Gini coefficients and lower
mean herbivory (Fig. 2D and fig. S5). Whereas
there was a negative correlation between the
mean and Gini coefficient among biomes [r =
−0.68 (−0.95 to −0.10)], there were also large
differences in the Gini coefficient between
biomes with similar mean herbivory. This sug-
gests that interaction variability could be a fun-
damental characteristic differentiating biological
systems across macroscales.
Debate over the contribution of herbivory to
global patterns of plant evolution has been
contentious (3, 6, 8, 10, 22, 23). Our data show
strong evidence of a meaningful, although noisy,
latitudinal decline in mean levels of herbivore
damage. They also show that herbivory becomes
more variable with increasing latitude. This
pattern is consistent with our hypothesis that
herbivory influences plant evolution at low
latitudes not just by being more intense on
average, but also by being more consistently
important within a plant population. Theory
predicts that the relationship between the
strength of antagonistic interactions and the
intensity of selection is concave down (saturat-
ing) at low mean interaction strengths (28),
which means that variability at high latitudes,
where mean herbivory is low, should erode
selection through nonlinear averaging (14), all
else being equal. Our finding is also consistent
with the hypothesis that inducible defenses
are more common among temperate com-
pared with tropical plants (29, 30) because
greater variation in herbivory is predicted to
select for inducibility (21). In addition to sea-
sonality and climate, other mechanisms for
the latitudinal variability gradient could in-
clude greater predation pressure on herbivores
at low latitudes (3) suppressing localized out-
breaks and high tropical herbivore diversity
and specialization (31) evening out damage
patterns across plant individuals. More gen-
erally, our results confirm the long-held view
that biotic interactions are more consistent
in the tropics, perhaps owing to longer grow-
ing seasons or greater species diversity and
specialization (3).
Variability and plant size
We also found strong support for the size-
mediated variability hypothesis. Populations
of larger individuals exhibit less variability in
Fig. 3. Plant size shapes variability in herbivory.
(A) Variability in herbivory among individuals
within populations declines with the average size
(height or canopy diameter for prostrate species)
of plants in the population (R2 = 13.3%; pp = 1.0;
BF = 4.6 × 107; 735 surveys of 472 species).
(B) Variability in herbivory, however, is only
weakly related to plant growth form (R2 = 2.8%),
with woody plants having 10.9% (2.9 to 19.1%)
lower Gini coefficients compared with herbaceous
species (790 surveys of 503 species). Lines,
shaded regions, and large points show predicted
means and 50, 80, and 95% credible intervals
from phylogenetic Bayesian beta regressions.
Each small gray point is one survey.
herbivory among individuals. A 2-m increase
in mean plant size (from 0.05 to 2.05 m, en-
compassing ~90% of our populations) resulted
in a 32.7% (20.6 to 44.7%) decrease in the Gini
coefficient [from 0.70 (0.54 to 0.85) to 0.47
(0.29 to 0.66); R2 = 13.3%; pp = 1.0; BF = 4.6 × 107]
(Fig. 3A and fig. S6). This relationship held
even after accounting for the decline in plant
size with increasing latitude and differences
in plant abundance (which ranged from 2 to
100% cover in our dataset) (tables S4 and S5)
(32). Woody species, which averaged 4.1 times
as large as herbs in our dataset, had 10.9% (2.9
to 19.1%) lower Gini coefficients compared
with herbaceous species [0.56 (0.37 to 0.76)
versus 0.63 (0.44 to 0.81); BF = 4.25]. How-
ever, the overall variance explained by growth
form, including climber and graminoid catego-
ries, was low (R2 = 2.8%) (Fig. 3B and fig. S7),
which suggests that mean size is a more-
important determinant of herbivory patterns
than growth form. Mean herbivory, by contrast,
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RES EARCH | R E S E A R C H A R T I C L E
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Fig. 4. Phylogenetic patterns of mean and variability in herbivory. Variability in herbivory among plants within populations (Gini coefficient) show greater
phylogenetic signal [Pagel’s l = 0.51 (0.45 to 0.52); P < 0.001] compared with mean herbivory levels [Pagel’s l = 0.07 (0.06 to 0.08); P > 0.1]. For clarity, this
tree includes only the 240 species from the 11 best-represented plant families (≥8 species per family). Our analyses included all 503 species in the dataset
(see fig. S10 for the full tree).
was unrelated to mean size or growth form
(figs. S8 and S9).
We posit that lower among-individual vari-
ability in herbivory on large plants results from
the law of large numbers, which says that
processes that involve more random events
produce values closer to the overall mean. In
other words, large plants, which have a greater
number of potential herbivory events, average
over within-plant variability and receive values
closer to the population mean on average. Small
plants, by contrast, are more likely to escape
herbivory entirely or be severely damaged by
a few events, which results in high variability.
A key implication of this phenomenon is that
Robinson et al., Science 382, 679–683 (2023)
10 November 2023
4 of 5
RES EARCH | R E S E A R C H A R T I C L E
larger species (and larger stages within species)
should experience greater selection for high
concentrations of constitutive defenses or
tolerance. Smaller species (and stages), by con-
trast, should experience greater selection for
inducible defenses and low concentrations
of metabolically cheap toxins to save resources
in the absence of herbivory and repel herbivores
when encountered. This dichotomy in defense
evolution has been the focus of decades of
research on differences in defenses between
trees and herbs (24) and across ontogenetic
stages (33). Whereas previous work has in-
voked complex biological explanations for
these differences—such as how apparent plants
are to herbivores (24)—our results suggest
that patterns are more parsimoniously ex-
plained by the statistical consequences of mean
plant size.
Phylogenetic patterns of variability
Finally, we tested the hypothesis that variability
in herbivory is phylogenetically structured. The
Gini coefficient exhibited significant phyloge-
netic signal [Pagel’s l = 0.51 (0.45 to 0.52);
P < 0.001], indicating that more-closely re-
lated species display more-similar variability
levels (Fig. 4 and fig. S10). Mean herbivory, by
contrast, did not show meaningful phyloge-
netic signal [l = 0.07 (0.06 to 0.08); P = 1.0].
These results were robust to tree topology and
species sampling (supplementary materials).
Our findings suggest that the mean damage
level across species changes relatively rapidly
in response to evolutionarily labile plant traits,
whereas the variability is more strongly de-
termined by traits that are phylogenetically
conserved. Traits thought to influence the
amount of herbivore damage, such as chemi-
cal defenses, diverge as plants escape their
herbivores by evolving novel defenses (2, 34),
whereas characteristics such as geographic lo-
cation and plant size, which we find relate to
variability, tend to be less labile. High varia-
bility in some families (e.g., Apocynaceae and
Plantaginaceae) invites further investigation
and could help reveal drivers of these conserved
patterns. To examine macroevolutionary pat-
terns, we fit Brownian motion and Ornstein-
Uhlenbeck models to test for differences in
rates of evolution and the strength of stabiliz-
ing selection. The best-fitting models included
optima for variability and mean herbivory in
tropical versus temperate systems and woody
versus herbaceous growth forms (tables S6
and S7), which indicates that the evolution
of variability in herbivory seems to be driven
by conserved plant traits and is therefore a
biologically informative feature rather than
random noise.
Conclusions
The assumption that plant-herbivore interac-
tions are highly variable has long dominated
ecology and evolution, with foundational works
on so-called variable plants and herbivores
(12) and theory exploring the consequences
of variable herbivory (21). Our data confirm
this assumption but also reveal a pattern that
had not been previously documented: strong
differentiation across systems in the level of
variability itself. Variation in herbivory co-
varied with factors central to the ecology and
evolution of plant-herbivore interactions, such
as latitude, biome, plant size, and phylogeny.
These macroscale patterns were often stronger
than patterns for mean herbivory levels. This
suggests that the level of variability could be
important for driving differences in plant-
herbivore biology around the planet, between
species with different traits and across phylo-
geny. Although the importance of varia-
bility in interactions has been recognized by
a few fields, such as epidemiology (19), the
central role of interaction variability in shap-
ing macroscale patterns of life on Earth has
been underappreciated. Our global dataset
is evidence for the ubiquity and predictabil-
ity of variability in one biotic interaction and
highlights the promise of further explorations
of the causes and consequences of interaction
variability.
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AC KNOWLED GME NTS
The authors thank A. Agrawal, J. Thaler, J. Conner, J. Lill,
M. Weiss, N. Sanders, and M. Meek for helpful discussions
and comments on different versions of the analyses and
manuscripts. Any use of trade, firm, or product names
is for descriptive purposes only and does not imply
endorsement by the US government. The findings and
conclusions in this publication are those of the authors and
should not be construed to represent any official US
Department of Agriculture (USDA) or US government
determination or policy. Funding: The authors acknowledge
funding for central project coordination from NSF Research
Coordination Network grant DEB-2203582; the Ecology,
Evolution, and Behavior Program at Michigan State
University; and AgBioResearch at Michigan State University.
Site-specific funding is listed in the supplementary materials.
Author contributions: This project was conceptualized
by W. C. Wetzel and N. Underwood. It was coordinated by
W. C. Wetzel, M. L. Robinson, P. G. Hahn, B. D. Inouye,
N. Underwood, S. R. Whitehead, K. C. Abbott, E. M. Bruna,
N. I. Cacho, and L. A. Dyer. Other author contributions
are listed in the supplementary materials. Competing
interests: The authors declare that they have no competing
interests. Data and materials availability: The dataset
generated and analyzed in this study is available at Dryad (35).
Our code is archived at Zenodo (36). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of
Science. No claim to original US government works. https://
www.science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh8830
Herbivory Variability Network Authors
Materials and Methods
Supplementary Text
Figs. S1 to S10
Tables S1 to S7
References (37–58)
MDAR Reproducibility Checklist
17. R. F. Denno, M. S. McClure, J. R. Ott, Annu. Rev. Entomol. 40,
297–331 (1995).
Submitted 26 March 2023; accepted 27 September 2023
10.1126/science.adh8830
Robinson et al., Science 382, 679–683 (2023)
10 November 2023
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RES EARCH
BIOPHYSICS
MyoD-family inhibitor proteins act as auxiliary
subunits of Piezo channels
Zijing Zhou1,2†, Xiaonuo Ma3,4†, Yiechang Lin5, Delfine Cheng1,2, Navid Bavi6, Genevieve A. Secker7,
Jinyuan Vero Li1,2, Vaibhao Janbandhu1,2, Drew L. Sutton7,8, Hamish S. Scott7,8,9, Mingxi Yao10,
Richard P. Harvey1,2,11, Natasha L. Harvey7,8, Ben Corry5, Yixiao Zhang3,4*, Charles D. Cox1,12*
Piezo channels are critical cellular sensors of mechanical forces. Despite their large size, ubiquitous
expression, and irreplaceable roles in an ever-growing list of physiological processes, few Piezo channel–
binding proteins have emerged. In this work, we found that MyoD (myoblast determination)–family inhibitor
proteins (MDFIC and MDFI) are PIEZO1/2 interacting partners. These transcriptional regulators bind to
PIEZO1/2 channels, regulating channel inactivation. Using single-particle cryogenic electron microscopy, we
mapped the interaction site in MDFIC to a lipidated, C-terminal helix that inserts laterally into the PIEZO1
pore module. These Piezo-interacting proteins fit all the criteria for auxiliary subunits, contribute to
explaining the vastly different gating kinetics of endogenous Piezo channels observed in many cell types,
and elucidate mechanisms potentially involved in human lymphatic vascular disease.
T o decode mechanical cues, cells are en-
dowed with a palette of molecular force
sensors. Among these sensors, Piezo ion
channels (1) have emerged as critical force
sensors that participate in determining
how cells sense their physical environment.
Piezo channels assemble as trimers that pos-
sess all the structural requirements for mecha-
nosensitivity (2, 3). However, native PIEZO1
channels can display nonuniform subcellu-
lar localization (4–7) and exhibit different
gating kinetics—principally, slower inactiva-
tion (1, 8–13)—in many cell types when com-
pared with heterologous expression systems.
These observations could be explained by dif-
ferences in lipid composition (14, 15), curvature-
dependent sorting (5, 7), or protein-protein
interactions. Many ion channels interact with
auxiliary subunits (16, 17) to modify their
cellular location and gating properties. Ion-
1Victor Chang Cardiac Research Institute, Sydney, NSW
2010, Australia. 2School of Clinical Medicine, Faculty of
Medicine and Health, University of New South Wales,
Sydney, NSW 2052, Australia. 3Interdisciplinary Research
Center on Biology and Chemistry, Shanghai Institute of
Organic Chemistry, Chinese Academy of Sciences, Shanghai
200032, China. 4State Key Laboratory of Chemical Biology,
Shanghai Institute of Organic Chemistry, Chinese Academy
of Sciences, Shanghai 200032, China. 5Research School
of Biology, Australian National University, Acton, ACT 2601,
Australia. 6Department of Biochemistry and Molecular
Biophysics, University of Chicago, Chicago, IL 60637, USA.
7Centre for Cancer Biology, University of South Australia and
SA Pathology, Adelaide, SA 5001, Australia. 8Adelaide
Medical School, University of Adelaide, Adelaide, SA 5005
Australia. 9Department of Genetics and Molecular Pathology,
SA Pathology, Adelaide, SA 5000, Australia. 10Department
of Biomedical Engineering, Southern University of Science
and Technology, Shenzhen 518055, China. 11School of
Biotechnology and Biomolecular Science, University of
New South Wales Sydney, Kensington, NSW 2052, Australia.
12School of Biomedical Sciences, Faculty of Medicine and
Health, University of New South Wales Sydney, Kensington,
NSW 2052, Australia.
*Corresponding authors. Email: c.cox@victorchang.edu.au (C.D.C.);
yzhang@mail.sioc.ac.cn (Y.Z.).
†These authors contributed equally to this work.
channel auxiliary subunits are commonly defined
by four criteria: (i) they are non–pore-forming
subunits, (ii) they have a direct and stable in-
teraction with the pore-forming subunit, (iii)
they modulate channel properties in heterol-
ogous systems, and (iv) they regulate endoge-
nous channel activity in native cells (17). Despite
substantial effort, to our knowledge, no Piezo
channel–binding partners or auxiliary subunits
have emerged that fit these criteria.
Identification of Piezo channel–binding proteins
To identify binding partners for Piezo channels
we used two complementary affinity-capture
mass spectrometry (AC-MS) strategies in con-
junction with two CRISPR-Cas9–edited, PIEZO1-
expressing, human dermal fibroblast (hDF)
lines (Fig. 1, A to F, and fig. S1). The reason we
chose fibroblasts lies in the previously reported
slower inactivation kinetics of PIEZO1 in this
cell type (10, 12, 13). Our pipeline consisted of
three comparator groups: (i) hDF with PIEZO1
ablated with CRISPR/cas9 (that were com-
pared with wild-type cells in which PIEZO1
was enriched through a conventional anti-
PIEZO1 antibody strategy), (ii) hDF with a
HaloTag added into the endogenous PIEZO1
loci (P1-Halo) where PIEZO1 was enriched with
HaloTrap resin, and (iii) primary human car-
diac fibroblasts (hCF) in which PIEZO1 was
enriched through a conventional anti-PIEZO1
antibody strategy. We then stringently ana-
lyzed the resulting MS data to identify PIEZO1-
interacting proteins present in all three groups
that were not present in any of their respective
negative controls. Using these criteria, we only
identified two proteins, the first of which was
PIEZO1 (Fig. 1E). This provided strong val-
idation for both affinity-capture strategies.
The second protein identified was the sparsely
studied transcriptional regulator MyoD (myo-
blast determination) family–inhibitor domain-
containing protein (MDFIC) (18, 19). MS provided
39 ± 14% coverage of MDFIC protein averaged
over the three groups (Fig. 1F).
Using RNA expression data, we identified many
cell types in addition to fibroblasts that coex-
press Piezo channels and the MyoD-family in-
hibitor proteins, MDFIC or MDFI (fig. S2, A and
B) (20). We then validated the protein-protein
interaction by expressing N-terminally hemag-
glutinin (HA)–tagged MDFIC together with
PIEZO1 in human embryonic kidney 293 cells
with SV40 large-T antigen (HEK293T). Using a
coimmunoprecipitation (co-IP) assay, we could
reciprocally capture PIEZO1 with MDFIC and
found that the complex was present under
mechanical (shear stress) or chemical [10 mM
Yoda-1 (21)] activation of PIEZO1 (fig. S2C),
which indicated the stability of the interac-
tion. We also confirmed that PIEZO1 interacted
with the closely related MDFI (fig. S2D) (22).
PIEZO2 has high sequence similarity with
PIEZO1, so we next tested whether MDFIC se-
lectively interacted with PIEZO1/2 channels
using native gels. We identified MDFIC at the
size of the respective PIEZO1/2 trimers but not
in oligomeric complexes of other structurally
unrelated channels such as TRPM4 (tetramer) or
TREK-1 (dimer) (fig. S2E). In doing so, we found
that PIEZO1 enhanced the protein amounts of
both MDFIC and MDFI by greater than three-
to fourfold (fig. S2, C to E). To determine the
specificity of this effect, we coexpressed MDFIC
with PIEZO1 and PIEZO2 and compared the
amount of MDFIC when expressed alongside
other unrelated ion channels. Coexpression of
MDFIC with green fluorescent protein (GFP),
TRPM4, TRPV4, or TREK-1 did not enhance
the amount of MDFIC (fig. S3, A and B). To
understand the mechanism, we used a cyclo-
heximide chase assay to observe the degrada-
tion time course of MDFIC. In cells treated for
4 to 8 hours with the protein synthesis inhib-
itor cycloheximide, we observed using Western
blotting that the protein amount of MDFIC fell
much more rapidly in the absence of PIEZO1
(fig. S3, C and D). This suggests that interacting
with PIEZO1 decreased MDFIC turnover.
MDFIC binds the PIEZO1 pore module
To provide molecular details of the interaction,
we coexpressed mouse PIEZO1 (mPIEZO1) with
N-terminally FLAG-tagged mouse MDFIC and
purified the complex using FLAG resin. Using
single-particle cryogenic electron microscopy
(cryo-EM), we determined the structure of the
PIEZO1-MDFIC complex at an overall resolu-
tion of 3.66 Å (Fig. 2, A and B, and fig. S4). We
resolved the C-terminal 21 amino acids of MDFIC
(Fig. 2, A to D), whereas the N-terminal portion
displayed little or no density, presumably ow-
ing to local dynamics. The resolved region of
MDFIC (residues 225 to 246) consists of an
amphipathic helix that sits parallel to the
membrane at the membrane interface (Fig.
2C). This helix inserts laterally into the PIEZO1
Zhou et al., Science 381, 799–804 (2023)
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A
D
RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. AC-MS identifies a newly characterized
family of Piezo-channel binding partners.
Groups for AC-MS consisted of: (A) WT and
PIEZO1-edited (knockout, KO) human
dermal fibroblasts (hDF; n = 2), (B) WT and
PIEZO1-HaloTag (P1-Halo) hDF (n = 2), and
(C) primary human cardiac fibroblasts (hCF; n = 2).
(D) Affinity-captured protein lysates were run
on SDS–polyacrylamide gel electrophoresis
(SDS-PAGE) gels and sectioned into quadrants
(red dashed lines). Each quadrant was subjected to
in-gel protein digestion, peptide extraction and
liquid chromatography (LC), and MS, in that order.
(E) Venn diagram illustrating proteins identified in
each experimental group that had ≥2 distinct
peptides that were absent from negative control
replicates. (F) Two proteins were identified in
all positive control replicates: PIEZO1 and MDFIC.
Alignment of distinct MDFIC peptides identified
with MS.
Group 1
B
Group 2
C
P1-KO hDF
WT hDF
WT hDF
P1-Halo hDF
Group 3
hCF
Negative
control
+
Piezo1 antibody
+
Halo Trap Agarose beads
+
Mouse IgG Piezo1 antibody
Antibody affinity capture
HaloTag affinity capture
Antibody affinity capture
KO
WT
PIEZO1
E
hCF
F
2. MDFIC
1. PIEZO1
2. MDFIC
6
2
0
0
3
0
9
In-gel
protein
digestion
+
peptide
extraction
260
160
80
60
50
40
30
20
15
10
LC-MS/MS Analysis
Gene Annotation
hDF
WT vs KO
hDF
P1-Halo vs WT
0 peptides in control
>2 unique peptides
C
outer leaflet
cap
inner leaflet
MDFIC
IH
OH
α2
α1
α3
G
L2127
OH
OH
I2195
α1
F2120
E229
K2184
D232
S230
E235
V2187
K2183
E239
S231
L234
H2116
F2120
~90°
H2116
~90°
V2187
K2184
K2183
R2169
α3
T2171
W2140
S2148
L2149
S2150
α3
M238
S247
Q2123
α1
F2484
F245
B
90°
F
A
MDFIC
E
blade
IH
F2485
I2195
OH
M2191
V2187
F2484
C244
F245
I243
C241
C240
L2127
Q2123
α1
C237
I236
M238
F2120
H2116
C233
L234
I2186
S230
D
H
OH
α1
IH
α1
IH
90°
OH
OH
IH
α1
MDFIC
α3
N2161
F2494
α1
I2164
P246
M2493
E2495
S247
F245
α3
S2150
L2149
OH
Fig. 2. Structural elucidation of the PIEZO1-MDFIC complex. (A and B) Cryo-EM
density maps of the mouse PIEZO1-MDFIC complex at 3.66-Å nominal resolution
viewed from the top (A) and side (B), with the resolved MDFIC region colored green.
(C) The distal C-terminal of MDFIC resides parallel to the bilayer between the anchor
domain (a1 to a3) and the outer helix (OH). The cytoplasmic constriction residues
Met2493 and Phe2494 are shown in cyan. (D) The C-terminal region of MDFIC
penetrates deep into the pore module of PIEZO1, approaching the inner helix (IH).
(E to H) The interactions between PIEZO1 and MDFIC from the (E) membrane-facing
view, (F) lateral view, and (G and H) cytoplasmic-facing view. Variants linked to
lymphatic malformations (mPIEZO1 V2187 and mMDFIC F245) are labeled in bold.
pore module, nestling between the anchor do-
main and the outer helix of PIEZO1 (Fig. 2, C
and D), making contacts with His2116, Phe2120,
and Gln2123 from the a1 helix of the anchor
domain; Val2187, Met2191, and Ile2195 from the
outer helix; and Phe2484 and Phe2485 at the base
of the inner helix that lines the PIEZO1 pore
(Fig. 2E). The amphipathic helix of MDFIC con-
sists of a sequence of five cysteines that point
toward the bilayer interior (Fig. 2, E and F) and
a sequence of four negatively charged residues
that point toward the solvent, forming salt
bridges with multiple lysine residues (Fig. 2, F
and G). The MDFIC C terminus penetrates far
enough to come close to the cytoplasmic con-
striction formed by Met2493 and Phe2494 (Fig.
2H) and residues critical for voltage-dependent
inactivation, Lys2479 and Arg2482 (23, 24). Despite
its central location, MDFIC binding did not
influence the closed structure of the PIEZO1
pore module (fig. S4I).
Because both PIEZO1 and MDFIC are es-
sential for lymphatic development in mice and
humans (19, 25, 26), we investigated using the
ClinVar database whether any disease-causing
mutations were located within this binding
interface. We found mutations in both PIEZO1
(human V2171f; Fig. 2, E and G) and MDFIC
(human F244L; Fig. 2, E and H) associated with
human lymphatic disease.
MDFIC and MDFI regulate Piezo gating
Given the location of MDFIC binding, we next
tested whether human MDFIC and MDFI-
modified human PIEZO1 (hPIEZO1) gating in
HEK293T cells. MDFIC and MDFI expressed
Zhou et al., Science 381, 799–804 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. MyoD-family inhibitor proteins regulate PIEZO1 and PIEZO2 channel
gating. (A to E) Representative cell-attached patch-clamp recordings from
hPIEZO1 (A) control and hPIEZO1 in the presence of (B) hMDFIC, (C) hMDFI,
(D) the conserved C terminus of MDFIC (hMDFIC C-81), and (E) with MDFIC
lacking its C-terminal 20 amino acids (hMDFIC DC20) all at a holding potential
of –65 mV. (F to H) Quantification of (F) peak currents per patch, (G) percent
current remaining, and (H) normalized current 1 s after pressure release
(normalized Ipost) for replicates of cell-attached recordings shown in (A) to (E).
(I to L) Representative cell-attached recordings from (I) hPIEZO2 control and
hPIEZO2 in the presence of hMDFIC and hMDFI, and [(J) to (L)] quantification of
replicates. (M to O) Representative cell-attached patch-clamp recordings from
mouse cardiac fibroblasts isolated at E16.5 from (M) WT, (N) heterozygous, and
(O) homozygous MdficM131fs* mice. (P to R) Quantification of (P) peak current per
patch, (Q) percent current remaining, and (R) normalized Ipost for replicates
of cell-attached recordings shown in [(M) to (O)] All data are displayed as mean ± SEM
or as maximum-to-minimum box-and-whiskers plot. P values are noted above
the plots and were determined with one-way analysis of variant (ANOVA) and
either Dunnett’s or Tukey’s multiple comparison test. ns, not significant.
Zhou et al., Science 381, 799–804 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
alone did not generate stretch-activated cur-
rents (fig. S5, A to D). Compared with hPIEZO1
alone, coexpression with MDFIC resulted in a
mild right shift in the pressure response curve
[from 14.5 ± 3.2 mmHg (n = 9 cells) to 23.9 ±
3.9 mmHg (n = 6)] (fig. S5, E to G), a marked
increase in the peak stretch-evoked currents, a
substantial slowing of channel inactivation,
and continued channel gating even after the
pressure was released (Fig. 3, A to H, and fig.
S5). We quantified the latter of these effects
using the current that remained 1 s after ap-
plication of stretch (Ipost). Neither MDFIC nor
MDFI influenced mRNA TMEM150c, demon-
strating that these inactivation effects were in-
dependent of TMEM150c (fig. S5N) (27). MDFIC
did not influence PIEZO1 protein amounts in
either HEK293T or LNCaP cells transfected
with MDFIC (fig. S6, A to D) but did increase
PIEZO1 single-channel conductance from 26 ±
3pS (n = 4) to 48 ± 8 pS (n = 4) (fig. S6, E to G).
Thus, the increase in stretch-activated cur-
rents in the presence of MDFIC is likely driven
by changes in conductance and its strong
-+
-
+ +
--
+ +
+
+ +
+
+
+
+
D
+hPIEZO1-HaloTag
HA-Tag
WGA
-HA-
hMDFIC
+HA-
hMDFIC
<0.0001
<0.0001
G
125
100
)
x
a
m
I
%
(
H
<0.0001
t
s
o
p
t
n
e
r
r
u
c
g
n
n
a
m
e
R
i
i
75
50
25
0
<0.0001
1.0
0.8
0.6
0.4
0.2
0.0
I
d
e
z
i
l
a
m
r
o
N
K
(9)
5C-S
(9) (10)
5C-A
hMDFIC
hMDFIC
hMDFIC
(9)
5C-S
(9) (10)
5C-A
hMDFIC
hMDFIC
hMDFIC
A
B
E
C241
C237
C244
C240
C233
S230
C
HAM
PIEZO1
HA-hMDFIC
mPEG-Mal10kDa
HAM
- +
- +
10000
F
hMDFIC
hMDFIC 5C-A
hMDFIC 5C-S
100 pA
20 pA
20 pA
)
A
p
(
t
n
e
r
r
u
c
k
a
e
P
c/a
0
500 ms
500 ms
500 ms
-60 mmHg
-60 mmHg
-60 mmHg
1000
0.004
0.002
100
10
(9)
5C-S
(9) (10)
5C-A
hMDFIC
hMDFIC
hMDFIC
I
PIEZO1 pore
MDFIC
(lipidated)
J
MDFIC
POPC bilayer
MDFIC
(unmodified)
)
%
(
y
c
n
a
p
u
c
c
O
t
c
a
t
n
o
C
100
80
60
40
20
Lipidated
5C-S
Unmodified
Inner helix
0
L2121
G2124
V2128
P2129
L2197
F2198
A2201
A2201
I2202
V2471
L2475
V2477
F2480
V2481
L2475
F2480
V2481
MDFIC
(lipidated)
Fig. 4. C-terminal lipidation of MDFIC underlies regulation of PIEZO1 channel
gating. (A) Cryo-EM density map showing extension of density on cysteine residues
within the C terminus of MDFIC. (B) Representative immunoblot (IB) with Avidin
(top) or anti-HA (bottom) from acyl biotin exchange showing lysate ± hydroxylamine
(HAM). Blots show a band at the correct size for HA-tagged MDFIC, but the biotinylated
MDFIC can only be seen in the HAM-treated group, which indicates palmitoylated-
MDFIC (palm-MDFIC). (C) Mass-tagging of MDFIC with methoxy-polyethylene glycol
(mPEGylated) maleimide reveals at least three palmitoylation sites labeled 1 to 3
(* represents a nonspecific band in all groups). (D) Membrane-localized HA-tagged MDFIC
in PIEZO1-HaloTag expressing HEK293T cells and the wheat germ agglutinin (WGA)–
delineated membrane. (E) Representative cell-attached recordings of hPIEZO1 in
the presence of WT MDFIC and mutation of the five C-terminal cysteine residues
to either alanine (5C-A) or serine (5C-S), which abolishes the regulatory effects
of MDFIC. (F to H) Quantification of (F) peak currents per patch, (G) percent
current remaining, and (H) normalized Ipost for replicate recordings shown in (E).
(I) All-atom molecular dynamic simulations of the mPIEZO1 pore module in
complex with unmodified (green), 5C-S mutant (purple), and lipidated MDFIC (pink)
C-termini. (J and K) Contact occupancy for MDFIC monomers with PIEZO1 residues
from replicate simulations and a snapshot of the location of three inner helix
residues important for inactivation that interact with lipidated MDFIC for
prolonged periods. P values are noted above the plots and were determined with
one-way ANOVA and Dunnett’s multiple comparison test. ns, not significant.
Zhou et al., Science 381, 799–804 (2023)
18 August 2023
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RES EARCH | R E S E A R C H A R T I C L E
effect on inactivation. The slow “closure” after
pressure release—identified in single-channel re-
cordings (fig. S6, H to J) and from macrocurrents—
was more pronounced at hyperpolarizing volt-
ages (fig. S7, A and B), which suggests an effect
on the structural transition–governing voltage-
dependent inactivation (23, 24). Consistent with
this, the channel could be rapidly closed by
flipping the voltage to depolarizing potentials
(fig. S7, C and D). We identified slower inactiv-
ation in both cell-attached and whole-cell modes
(fig. S8). Additionally, MDFIC expression did
not influence the function of mechanosensitive
TREK-1 channels, ruling out nonspecific effects
(fig. S9).
The C termini of MDFIC and MDFI are highly
homologous, whereas the N termini bear little
resemblance and have no known function (fig.
S10A); therefore, we asked whether the MyoD-
inhibitor domain of MDFIC (residues 165 to
246, which we name C-81) expressed alone could
modify PIEZO1 function. Despite being unsta-
ble, this domain reduced channel inactivation
(Fig. 3, D and G, and fig. S10B). Moreover, the
amount of C-81 protein was dramatically in-
creased when coexpressed with PIEZO1 (fig.
S10, C and D). Conversely, truncation of the C-
terminal 20 residues (DC20) prevented MDFIC
from regulating PIEZO1 gating (Fig. 3, E to G).
This truncation reduced the interaction with
PIEZO1, and MDFIC DC20 protein amounts
were only marginally affected by PIEZO1 (fig.
S10, D and E). Thus, functional regulation of
the PIEZO1-MDFIC complex depends on the
conserved C terminus of MDFIC.
Given the homology of PIEZO1 and PIEZO2
in the MDFIC-binding region, we additionally
showed that the same regulation occurs for
both hPIEZO2 and mouse Piezo orthologs
(Fig. 3, I to L, and fig. S11). Moreover, the ex-
pression of MDFIC and MDFI correlated with
the native inactivating phenotype of PIEZO1
in multiple human and mouse cell lines (fig.
S12). This included HEK293T, in which fast
PIEZO1 inactivation was seen, and prostate
cancer cell lines (LNCaP and DU145), in which
differential stretch-activated kinetics were pre-
viously reported (9). HEK293T and LNCaP have
almost undetectable amounts of MDFIC and
MDFI and display fast inactivation, whereas
DU145 has notable amounts of MDFI at the
mRNA level and inactivates slowly (fig. S12, A
to F). Overexpression of MDFIC in LNCaP cells
markedly slowed inactivation of native PIEZO1
channels (fig. S12, B to F). In mouse embryonic
fibroblasts and C2C12 myoblasts, we detected
MDFIC, and both cell types displayed slow
PIEZO1 inactivation indicated by larger cur-
rent remaining at the end of pressure pulses (fig.
S12, G to I). By contrast, in Neuro2A (N2A) cells,
PIEZO1 channels exhibited rapid inactivation with
undetectable expression of MDFIC and MDFI.
We next asked whether genetic loss of MDFIC
could modify the kinetics of native PIEZO1 cur-
rents. To investigate this, we used a mouse mod-
el of a complex lymphatic anomaly known as
central conducting lymphatic anomaly, bear-
ing a truncated variant of MDFIC that lacked
the complete conserved C-terminal but retained
the N-terminal region (19). Our assessment of
PIEZO1 activity in embryonic cardiac fibro-
blasts isolated from embryonic day 16.5 (E16.5)
wild-type (WT/WT), heterozygous (WT/M131fs*),
and homozygous mice (M131fs*/M131fs*) re-
vealed that fibroblasts harboring C-terminally
truncated MDFIC had smaller PIEZO1 cur-
rents that inactivated more rapidly (Fig. 3,
M to R). This effect on inactivation was pheno-
copied by silencing MDFIC in fibroblasts
with small interfering RNA (siRNA) (fig. S13,
D to J).
PIEZO1 regulation requires MDFIC lipidation
Cryo-EM maps of MDFIC revealed extra den-
sities on Cys233, Cys237, Cys240, Cys241, and Cys244
(Fig. 4A). Given that this helix is situated at the
membrane interface and contains motifs for
cysteine lipidation (28), we hypothesized that
these extra densities resulted from lipidation,
which is the covalent addition of acyl chains to
amino acids (29). A second cryo-EM complex
of the MDFIC mutant Cys240Ala (3.68 Å) spe-
cifically lacked the extra density at Cys240, which
is consistent with posttranslational modification
(fig. S14). Acyl biotin exchange confirmed that
MDFIC was palmitoylated (Fig. 4B). Mass tagging
with polyethylene gycol–modified (PEGylated)
maleimide (increases mass per palmitoylated
site) showed that there were at least three sites
for lipidation on MDFIC (Fig. 4C), that two were
in the distal C terminus (fig. S15), and that like
most lipidated proteins, MDFIC associated with
the plasma membrane (Fig. 4D).
To check whether MDFIC lipidation is func-
tionally relevant, we mutated all five C-terminal
cysteines to alanine or serine. MDFIC with
Cys233/237/240/241/244Ala (5C-A) or Cys233/237/
240/241/244Ser (5C-S) bound to PIEZO1, but nei-
ther mutant influenced PIEZO1 activity, which
suggests that the lipidation of the MDFIC
C terminus is critical for PIEZO1 regulation
(Fig. 4, E to H, and fig. S15C).
To probe the role of lipidation, we used all-
atom molecular-dynamics simulations of the
PIEZO1 pore module (residues 1956 to 2547) in
complex with the MDFIC C terminus (Fig. 4, I
to K, and fig. S16). Simulations consisted of
three MDFIC monomers: one unmodified, one
lipidated at all five cysteine residues in the
helix, and one where each cysteine was mutated
to serine (5C-S mutants) (Fig. 4I). All variations
of the MDFIC C terminus remained stably bound
(fig. S16, A and B). An overlay of a snapshot
from simulations shows that the acyl chains
coincide with the additional MDFIC cryo-EM
densities (fig. S16C). We compared all inter-
actions that occurred in either unmodified or
lipidated MDFIC monomers with those in the
5C-S mutant, which we know binds to but does
not modulate PIEZO1 function (Fig. 4J and fig.
S16). Interactions between the unmodified and
5C-S MDFIC were indistinguishable, which sup-
ports the critical role of MDFIC lipidation in
modulating PIEZO1 function. By contrast, the
lipidated MDFIC had multiple distinct inter-
actions with inner-helix residues (Fig. 4, J and
K, and fig. S16, D and E). Some of these resi-
dues within the inner helix are critical for in-
activation, including Leu2475 (30), making
this the likely pathway for functional modifi-
cation. Given that MDFIC would need to stay
bound throughout the PIEZO1 conformational
cycle, we also examined whether MDFIC could
bind to the flattened state of PIEZO1 (31). When
MDFIC was aligned to the same pocket, sim-
ulations showed that it interacted with the
inner helix and remained stably bound (fig.
S16, F to H).
Discussion
Using AC-MS, we have identified a family of
Piezo-channel binding partners—the MyoD-
family inhibitor proteins, MDFI and MDFIC—
that fit all the criteria for Piezo-channel aux-
iliary subunits. Although our study does not
resolve full-length MDFIC or its native mem-
brane topology, it does reveal that MDFIC binds
to the PIEZO1 pore module through its con-
served C terminus, which regulates channel
inactivation. The regulation of Piezo-channel
inactivation critically involves palmitoylation
of the distal C-terminal of MDFIC. Because
palmitoylation is a reversible lipid addition (29),
this adds the potential for dynamic spatiotem-
poral regulation of Piezo inactivation by MDFIC.
Although we identified few other Piezo-channel
binding-partner candidates with our “fibroblast-
centric” screen, we speculate that the binding
region of MDFIC could form a conserved bind-
ing site for alternate membrane-associated Piezo
regulators or auxiliary subunits. In support of
this hypothesis, the PIEZO1 lysine residues
that form salt bridges with MDFIC have been
proposed to interact with other proteins (32).
Despite PIEZO1 channels being able to func-
tion as independent mechanosensors in sim-
plified systems (2), ample evidence suggests
that Piezos, particularly PIEZO2, may receive
force through molecular tethers (33). Given
the location of binding, it seems unlikely that
MDFIC could act as a tethering molecule.
It remains to be seen how ubiquitous this
regulatory mechanism is; MDFIC and MDFI
are absent from many cell types with rapidly in-
activating PIEZO1 channels, including LNCaP
(9) and N2A (1), but are expressed in others,
including fibroblasts (10, 12, 13) and endothe-
lial cells that exhibit slower PIEZO1 inactiva-
tion (8, 11, 14). We isolated cardiac fibroblasts
from mice that harbored a truncated MDFIC
lacking the C terminus (19), in which PIEZO1
exhibited faster inactivation than in wild-type
Zhou et al., Science 381, 799–804 (2023)
18 August 2023
5 of 6
RES EARCH | R E S E A R C H A R T I C L E
fibroblasts. Thus, MDFIC- or MDFI-mediated
regulation of Piezo channels could be widely
used. Despite our study not defining a PIEZO1-
MDFIC complex in lymphatic endothelial cells,
the similar lymphatic phenotypes associated
with loss of function of MDFIC (19) and PIEZO1
(25, 26) means that this interaction may unearth
molecular aspects underlying lymphatic vas-
cular disease. Furthermore, both MDFIC and
MDFI bind to transcription factors (19, 34) [in-
cluding GATA2, a master regulator of lymphatic
valve development (35)]. Whether PIEZO1/2
channels influence this aspect of their func-
tion is unknown but may lay the foundation
for the unveiling of a direct mechanosignaling
pathway by means of Piezos to transcription
through GATA2 or other transcription factors.
Thus, our structural and functional data not
only reveal a family of Piezo-channel auxiliary
subunits but may also reveal a conserved bind-
ing site for other membrane-associated pro-
teins that modulate Piezo-channel function
and, in doing so, the basis for an alternate Piezo-
dependent mechanosignaling pathway.
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ACKN OWLED GMEN TS
We thank B. Martinac, E. Perozo, J. Xu, and the Patapoutian Lab
for useful scientific input and Y. Zhang and Y. Yuan for mass spec
support. We thank the Cryo-EM Center at the Interdisciplinary
Research Center on Biology and Chemistry of the Shanghai
Institute of Organic Chemistry for help with data collection.
Funding: This work was supported by Australian Research Council
(ARC) Future Fellowship FT220100159 (C.D.C.); STI2030-Major
Projects 2022ZD0207400, Shanghai Municipal of Science and
Technology Project 20JC1419500, and Shanghai Municipal Science
and Technology Major Project 2019SHZDZX02 (Y.Z.); National
Health and Medical Research Council Ideas Grant 2021260 and the
Lymphatic Malformation Institute (N.L.H.); ARC DP200100860
(B.C.); and Medical Research Future Fund grant GHFM76777
(H.S.S.). Research was undertaken with the assistance of resources
and services from the National Computational Infrastructure,
supported by the Australian Government. Author contributions:
Z.Z., M.Y., and D.C. generated cell lines and performed biochemical
and imaging experiments. Z.Z., N.B., and C.D.C. performed
electrophysiology. G.A.S., D.L.S., H.S.S., V.J., R.P.H., and N.L.H.
generated animal models and isolated cells. Z.Z. and J.V.L.
generated reagents. X.M. and Y.Z. performed cryo-EM structural
studies. B.C. and Y.L. performed molecular dynamics simulations.
C.D.C. and Y.Z. conceived of and supervised the project. All
authors wrote and approved the manuscript. Competing
interests: C.D.C. and Z.Z. note an Australian provisional patent
application #2023902096 entitled “Piezo channel regulators.”
Data availability: The composite map of the PIEZO1-MDFIC
complex has been deposited in the Electron Microscopy Data Bank
under the accession code EMD-35577. The composite map may
contain artificial features near the boundaries of the masks. The
consensus map, masked refined cap map, masked refined TMD map,
and the map of PIEZO1-MDFIC (C240) have been deposited under
the accession codes EMD-36241, EMD-36242, EMD-36243, and
EMD-36244. The atomic coordinates have been deposited in the
Protein Data Bank under the accession code 8IMZ. All data are
available in the main text or the supplementary materials. License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh8190
Materials and Methods
Supplementary Text
Figs. S1 to S16
Tables S1 to S3
References (36–47)
Submitted 16 March 2023; accepted 19 July 2023
10.1126/science.adh8190
Zhou et al., Science 381, 799–804 (2023)
18 August 2023
6 of 6
|
10.1126_science.adi1071
|
Post date 6 June 2024
Retraction
On 8 December 2023, Science published the Research Article “Drought sensitivity in mesic forests heightens
their vulnerability to climate change” (1). In January 2024, Stefan Klesse, William Anderegg, John Abatzoglou,
and Margaret E. K. Evans alerted the authors to errors in an R script on which they had relied to calculate
potential evapotranspiration and climatic water deficit using a heat load–modified Thornthwaite equation.
In response, the authors updated to the newest, corrected version of this script and reran their analysis.
Although many results remained unchanged after these corrections, the statistical significance of some conclu-
sions, and the results of some robustness tests, did change. In addition, the paper’s primary result was not
robust to the use of an alternate climate input dataset that calculated potential evapotranspiration using the
Penman-Monteith equation. As a result, all authors agree to retract the paper. The authors thank S. Klesse, W.
Anderegg, J. Abatzoglou, and M. E. K. Evans for quickly detecting and raising these issues.
Robert Heilmayr1,2*, Joan Dudney1,2, Frances C. Moore3
1Environmental Studies Program, University of California, Santa Barbara, Santa Barbara, CA, USA. 2Bren
School of Environmental Science and Management, University of California, Santa Barbara, Santa Barbara, CA,
USA. 3Department of Environmental Science and Policy, University of California, Davis, Davis, CA, USA.
*Corresponding author. Email: rheilmayr@ucsb.edu
REFEREN C E S A N D N OTES
1. R. Heilmayr, J. Dudney, F. C. Moore, Science 382, 1171 (2023).
SCIENCE science.org
RETRACTION POST DATE • 6 JUNE 2024 1
10.1126/science.adq4537
RES EARCH
FOREST ECOLOGY
Drought sensitivity in mesic forests heightens their
vulnerability to climate change
Robert Heilmayr1,2*, Joan Dudney1,2, Frances C. Moore3
Climate change is shifting the structure and function of global forests, underscoring the critical need to
predict which forests are most vulnerable to a hotter and drier future. We analyzed 6.6 million tree rings
from 122 species to assess trees’ sensitivity to water and energy availability. We found that trees
growing in wetter portions of their range exhibit the greatest drought sensitivity. To test how these
patterns of drought sensitivity influence vulnerability to climate change, we predicted tree growth
through 2100. Our results suggest that drought adaptations in arid regions will partially buffer trees
against climate change. By contrast, trees growing in the wetter, hotter portions of their climatic range
may experience unexpectedly large adverse impacts under climate change.
F orests cover approximately 30% of Earth’s
land surface (1), absorb more carbon than
all other terrestrial ecosystems (2, 3), and
provide trillions of dollars’ worth of eco-
system services (4, 5). Climate change,
however, is causing pronounced changes in
forests, including drought-induced diebacks
and declines in productivity. Scientists warn
that forests will continue to shift from carbon
sinks to sources as climate change–related dis-
turbances increase (6–8). To effectively man-
age and respond to these changes, there is a
critical need for accurate predictions that de-
tail which forests will be most vulnerable to
drier and hotter conditions (9, 10).
Precise estimates of forest vulnerability to
drought depend on an understanding of how
spatial variation in drought sensitivity inter-
acts with anticipated changes in drought expo-
sure (Fig. 1) (11–13). Will forests located near
their dry-range edge be pushed beyond their
physiological limits or can drought adapta-
tion in drier regions insulate forests against
hotter droughts? Answering this question rests
on a clear understanding of trees’ relative sen-
sitivity to dry conditions across their range.
However, past research exploring variation in
drought sensitivity has yielded contradic-
tory results, supporting either a “dry-range–
sensitive” or a “drought-naïve” hypothesis.
The dry-range–sensitive hypothesis predicts
that trees growing in drier portions of their
range are the most drought sensitive. Trees
growing in resource-poor conditions—for ex-
ample, shallow soils, steep slopes, and aspects
exposed to greater solar radiation—are often
more climate and drought sensitive (14–16).
Similarly, many studies have observed greater
reductions in radial growth during drought at
drier sites than at more-mesic sites (15, 17–22).
One explanation for these patterns is that in-
creasing aridity in drier regions could exceed
species’ physiological limits, leading to marked
declines in growth in response to drought
(10, 23).
By contrast, the drought-naïve hypothesis
predicts that trees growing in wetter portions
of their range are the most drought sensitive
(10). Drought-naïve effects have been found
in forests in the Pacific Northwest (24), pine
forests in the Eastern Mediterranean (25),
European beech trees (Fagus sylvatica) (26),
and ponderosa pine (Pinus ponderosa) pop-
ulations in North America (27). Higher drought
sensitivity in wetter regions may reflect fewer
drought adaptations as a result of lower drought
exposure. Long-term drought exposure, which
is often higher in arid regions, can shift pheno-
typic plasticity (26, 28), tree density (29, 30),
and heritable traits that together confer greater
drought resilience (31). Reconciling whether
dry-range–sensitive or drought-naïve dynam-
ics are more prevalent at a global scale can
advance our ability to predict forest vulner-
ability to climate, which is fundamental to
1Environmental Studies Program, University of California,
Santa Barbara, Santa Barbara, CA, USA. 2Bren School of
Environmental Science and Management, University of
California, Santa Barbara, Santa Barbara, CA, USA.
3Department of Environmental Science and Policy, University
of California, Davis, Davis, CA, USA.
*Corresponding author. Email: rheilmayr@ucsb.edu
Sensitivity
A
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Δ
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Exposure
Vulnerability
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Standardized aridity
(Deviation from species mean)
1
2
-2
-1
0
Standardized aridity
(Deviation from species mean)
2
1
-2
-1
0
Standardized aridity
(Deviation from species mean)
1
2
H0: Consistent
H1: Dry-range
H2: Drought-naïve
Fig. 1. Hypothesized vulnerability to climate change. (A) Three hypothesized
patterns of heterogeneity in drought sensitivity across an aridity gradient: (H0) Trees
show a consistent drought response across their species’ climatic range (consistent
sensitivity; green line); (H1) trees growing in more-arid portions of their range are more
drought sensitive (dry-range sensitive; gray line); and (H2) trees growing in more-
mesic portions of their range are more drought sensitive (drought-naïve; purple line).
Sensitivity (y axis) is defined as a change in annual growth (measured using RWI) in
response to interannual fluctuations in water availability (measured using CWD).
Standardized aridity (x axis) is defined as the historic average CWD at a given location
relative to the mean CWD experienced across a species’ range. (B) Increases in
CWD are widespread but anticipated to be highest in more-arid regions. Bar heights
illustrate average increases in CWD CMIP5 models by 2100. (C) The interaction
between sensitivity (A) and exposure (B) drives predicted changes in RWI, which we
used as a measure of vulnerability. Colored lines and corresponding bars represent
hypothesized patterns of vulnerability (change in RWI) when different patterns of
sensitivity (A) interact with anticipated increases in drought exposure (B).
Heilmayr et al., Science 382, 1171–1177 (2023)
8 December 2023
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RES EARCH | R E S E A R C H A R T I C L E
Data preparation
Step 1
Step 2
Estimation
Step 3
Step 4
Step 5
Step 6
Prediction
Fig. 2. Methodological approach, using data for P. ponderosa as an illustration. Step 1: We extracted
tree-ring width measurements from ITRDB sites (pink dots, with two example sites highlighted in purple
and green) and downloaded geographic species ranges for all species in the ITRDB (P. ponderosa
distribution shown in gray). Then, we detrended raw ring width measurements into RWI. Step 2: We
downloaded global climate data and calculated annual CWD and PET, which we standardized for
each species using the historic climate experienced across the species’ geographic range. The figure
shows the distribution of mean PET and CWD between 1901 and 1980 across the ponderosa pine’s full
range (contours) and within ITRDB sites (dots). Step 3: We estimated sensitivity within each site.
Step 4: We estimated heterogeneity in sensitivity across historic standardized CWD and PET using
site-level sensitivity estimates. Although this figure illustrates this approach for the subset of PIPO sites,
the primary model specification discussed in the rest of this paper conducts this analysis across all
species. Step 5: We predicted sensitivity across the geographic range of all species. Step 6: We
predicted change in RWI as a function of predicted sensitivities and CMIP5 predictions of changes
in CWD and PET.
developing effective management strategies
(32–34).
We address this long-standing debate by
(i) identifying where trees exhibit the greatest
sensitivity to changes in water and energy
availability and (ii) predicting where forests
will be most vulnerable to climate change. To
quantify trees’ sensitivity to weather fluctua-
tions, we drew upon two large databases of
annual tree-ring measurements: the Interna-
tional Tree Ring Data Bank (ITRDB) and the
US Forest Service’s Forest Inventory and Analy-
sis (FIA) tree-ring dataset (35). The ITRDB
data we analyzed includes 6.6 million annual
observations of tree growth from 3775 sites
spanning 122 species (listed in table S1). In
addition to its geographic and taxonomic scope,
an important benefit of the ITRDB is that
the distribution of observed climatic condi-
tions provides a fairly representative sample
of macroscale climatic variation experienced
across tree species’ full geographic ranges
(fig. S2). However, the ITRDB exhibits known
biases toward trees growing in marginal con-
ditions that exhibit relatively strong climate
signals (36, 37), which may overstate trees’
sensitivity to weather (15). To ensure that our
results were not an artifact of ITRDB biases,
we replicated our analysis using FIA tree cores.
Though FIA data are more geographically and
taxonomically limited than those of the ITRDB,
FIA tree cores are drawn from a systematic
sampling design, thereby enabling a more
representative understanding of ecological
processes.
We analyzed these data using six steps (Fig. 2)
(38). First, we detrended all tree-ring width
measurements using standard dendrochrono-
logy approaches to generate annual observations
of ring width index (RWI), a standardized mea-
sure of tree growth. Second, we characterized
each tree species’ climatic niche by extracting
historic weather data across the entirety of each
species’ geographic range. We characterized
weather and climate using potential evapo-
transpiration (PET) and climatic water deficit
(CWD), two variables drawn from climatic water
balance equations that emphasize the inter-
acting roles that water and energy availa-
bility play in constraining tree species’ ranges
(39–41). Specifically, PET describes the atmo-
spheric demand for water from vegetation,
which is primarily a function of the amount
of energy available to plants. By contrast, CWD
quantifies shortages in water availability rela-
tive to this atmospheric demand. To enable
comparisons across species, we standardized
CWD and PET values using the distribution of
historic CWD and PET experienced across the
species’ full range (fig. S1). Third, for each ITRDB
site, we regressed annual, tree-level observa-
tions of RWI (step 1) on fluctuations in species-
standardized weather (step 2) to estimate the
sensitivity of individual sites to interannual
Heilmayr et al., Science 382, 1171–1177 (2023)
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RETRACTED 6 June 2024. See Retraction. RES EARCH | R E S E A R C H A R T I C L E
A
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(Deviation from species mean)
1
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Fig. 3. Variation in sensitivity to CWD and PET across species’ climatic niches. (A and D) Marginal effects
of CWD (A) and PET (D) from site-specific, first-stage models, averaged within bins distributed across the
standardized, historic CWD-PET climate space. First-stage coefficients represent the sensitivity of RWI to
changes in CWD (high CWD sensitivity in dark red and low CWD sensitivity in gray). Sensitivity is measured as
the change in RWI that would result from a 1-SD increase in CWD or PET. (B, C, E, and F) Second-stage
models were used to summarize heterogeneity in sensitivity to CWD across a gradient of historic CWD (B)
and PET (C) and heterogeneity in sensitivity to PET across historic CWD (E) and PET (F). Shading represents
the 2.5 to 97.5% interquantile range from the block-bootstrapped second-stage model.
changes in CWD and PET. Fourth, we quan-
tified how the sensitivities estimated in step 3
varied across sites along a gradient of his-
toric, species-standardized climate. Fifth, using
this estimate of heterogeneity in sensitivity
along a climatic gradient, we predicted cli-
matic sensitivities across each species’ full
geographic range. Finally, we estimated how
climate change will shift tree growth across
species’ ranges by combining predicted sen-
sitivities (step 5) with climate predictions
from the Representative Concentration Path-
way 6.0 scenario (RCP 6.0) of the Coupled Model
Intercomparison Project Phase 5 (CMIP5).
To ensure that our final results reflected the
combined uncertainty of steps 3 to 6 of this
analysis, we propagated uncertainty using a
combination of Monte Carlo simulation and
block bootstrapping.
Effects of CWD and PET on tree growth
Most ITRDB sites exhibited positive growth re-
sponses to increases in either water or energy
availability (fig. S3), a pattern that is consis-
tent with ecological theory and previous studies
(9, 10, 24, 40). Specifically, a site that exper-
ienced a 1 SD decline in CWD (relative to the
distribution of CWD across the species’ full
range) experienced a 3.2% decline (95% confi-
dence interval: −10.1 to −1.1) in RWI in the same
year. The site-level, marginal effect of CWD
was significantly negative (p < 0.05) for 54.6%
of sites, whereas only 10.6% of sites exhibited
a significantly positive relationship (fig. S3A).
By contrast, the relationship between PET and
growth varied greatly across sites, with signif-
icant positive relationships in 39.7% of sites
and significant negative relationships in 25.3%
of sites (fig. S3B). Site-level, distributed lag
models provided further evidence that nega-
tive CWD shocks and positive PET shocks led
to increases in growth, with the strongest ef-
fects occurring in the year of the shock rather
than in lagged years (fig. S3, C and D).
Drier sites exhibit less sensitivity to drought
Consistent with the drought-naïve hypothesis,
trees located in drier parts of their species’
climatic range exhibited less sensitivity to
drought than those in more mesic sites (Fig. 3).
For example, our estimates of site-level sensi-
tivity to CWD indicate that drier-than-average
sites experienced a 12.8% decline (−22.3 to
−6.0%) in annual growth in response to a 1-SD
increase in CWD (Fig. 3A). By contrast, wetter-
than-average sites experienced a larger 22.1%
decline (−34.4 to −11.2%) in growth from a
1-SD increase in CWD. To summarize this
variability in CWD sensitivity, we modeled
sensitivity as a quadratic function of historic
CWD and PET (Fig. 3, B and C). The regression
results highlight that observed sensitivity de-
clined with increasing CWD [slope at the spe-
cies’ mean, historic CWD = 0.015 (0.006 to
0.059)]. This slope indicates that a 1-SD in-
crease in CWD leads to an approximately 1.5
percentage point greater decline in growth
in sites located at their species’ mean CWD
than in a site that is 1 SD drier.
Trees also exhibited heterogeneity in their
responses to annual increases in energy avail-
ability (Fig. 3, D to F). In the most energy-
limited portions of species’ ranges, trees often
experienced large increases in growth in response
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Fig. 4. Predicted changes in
CWD and PET. (A) Spatial
distribution of the mean
predicted change in
CWD through 2100. (B and
C) Predicted increases in
CWD (B) and PET (C) are
largest in regions of high
historic CWD and PET.
(D) Predicted changes in
CWD would push most
species’ historic ranges above
their historic mean CWD.
All plots compare changes
between the historic
(1970–2000) and end-of-
century (2091–2100) predic-
tions according to the average
of CMIP5’s 47 model runs
for the RCP 6.0 scenario.
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to increased PET. For example, in the coldest
10% of sites (<1.5 SD below the species’ his-
toric mean PET), growth increased 18.7% (8.7
to 25.1%) in response to a 1-SD increase in PET.
However, this positive growth response to in-
creased annual PET quickly declined across
a gradient of historic PET (Fig. 3F). In sites
with above-average historic PET, increased an-
nual PET was associated with an insignificant
decline in growth.
Our main conclusion—that tree sensitivity
to CWD decreases across an aridity gradient—
is robust to a variety of alternate models and
datasets (38). For example, fig. S6 contrasts
estimates of heterogeneity derived from system-
atically sampled, FIA tree-ring data against
results derived from comparable ITRDB data.
The similarity in results indicates that the
drought-naïve effect we observed is unlikely to
be the result of biases in ITRDB site selection.
In addition, we found that the drought-naïve
effect persists under a wide variety of alternate
approaches to data processing and analysis
(fig. S5). Finally, although drought-sensitivity
patterns vary across the 10 most common genera
in the ITRDB, most exhibited a significant
drought-naïve pattern of CWD sensitivity,
whereas none of the genera exhibited a sig-
nificantly higher sensitivity in the dry portions
of their range (fig. S4). The results provide
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C
Predicted change
in CWD (std)
E
Predicted
change in RWI
Predicted
sensitivity
to CWD
−0.05
−0.06
−0.07
−0.08
Predicted
sensitivity
to PET
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0.05
0.00
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1
2
Fig. 5. Predicted changes in tree growth through 2100. (A and B) Predicted mean sensitivity of RWI to interannual changes in CWD (A) and PET (B) aggregated
across the historic climatic ranges of all ITRDB species. Sensitivity is measured as the change in RWI that would result from a 1-SD increase in CWD or PET.
(C and D) Forecasted changes in CWD (C) and PET (D) between CMIP5 RCP 6.0’s historic (1970–2000) and end-of-century (2090–2100) periods, measured in standard
deviations. (E) Resulting predictions of the impacts of climate change on tree growth (RWI) across species’ historic climatic ranges.
further support for our conclusion that CWD
sensitivity declines along a gradient of his-
toric CWD.
Climatic changes across species ranges
Tree species will generally face much warmer
and drier conditions by 2100 (Fig. 4). Specif-
ically, CMIP5 model ensembles predict that
the entirety of every species’ range analyzed
will experience increases in both mean PET
and CWD (Fig. 4, B and C). On average, the
mean PET across a species’ range is antici-
pated to increase by 1.39 SD (0.45 to 3.05),
whereas CWD is anticipated to increase by
1.41 SD (0.34 to 3.78). Supporting concerns
about the emergence of “novel climates” (42, 43),
11% of the average species’ range will be drier
than anywhere in that species’ historic, cli-
matic range (Fig. 4D). For some species (e.g.,
Pinus pinea and Quercus faginea), more than
half of their current range is projected to be
drier than the driest parts of their historic
range.
Although the greatest increases in tem-
perature are expected to occur in northern
latitudes as a result of snow and ice albedo
feedbacks (44), CMIP5 models predict higher
rates of drying in warmer, lower latitudes (Fig.
4A). An important mechanism driving this
pattern is the nonlinear effect of temperature
on the water-holding capacity of the atmo-
sphere (45, 46). As a result of this nonlinear
effect, PET is anticipated to increase more
rapidly in hotter locations (Fig. 4C). Fore-
casted changes in annual precipitation across
most ITRDB sites are not sufficient to offset
warming-induced increases in atmospheric
water demand, leading to pervasive increases
in CWD. These increases in CWD are also antic-
ipated to be most pronounced in dry and hot
locations.
The largest growth declines are predicted to
occur in wet and hot regions
Combining our estimates of sensitivity to CWD
and PET with predicted changes in climate, we
estimate that by 2100, tree growth will decline
by 10.4% (−37.3 to +0.7%). More forests are
predicted to experience declines in growth
than increases in growth. Specifically, 51.2% of
grid cells (representing the combination of a
species and location) are predicted to experi-
ence a significant (>95% of Monte Carlo itera-
tions) decline in growth. By contrast, only
0.6% of grid cells are predicted to experience a
significant increase in growth. These results
highlight that a hotter, drier planet will likely
lead to major shifts in the health of global
forests and their ability to sequester carbon.
Predictions of RWI changes through 2100
highlight that climate change may have a sur-
prisingly pronounced and negative impact
on trees growing in wetter, warmer portions of
their range, whereas cooler parts of species’ dry-
range edges may be unexpectedly resilient to
climate change. Figure 5 illustrates how spatial
variation in sensitivity (Fig. 5, A and B) inter-
acts with climate change exposure (Fig. 5, C
and D) to yield heterogeneity in predicted RWI
declines (Fig. 5E). The wetter but hotter-than-
average portions of species’ ranges are pro-
jected to experience a 17.2% decline in growth
(−51.9 to −1.4%). By contrast, drier but cooler-
than-average locations are predicted to experi-
ence a smaller 11.0% decline in growth (−33.9%
to +0.3%). Grid cells predicted to experience in-
creases in growth are primarily located in very
energy-limited parts of species’ historic ranges.
Capturing heterogeneity in sensitivity in eco-
logical models is important to accurately pre-
dict the impacts of climate change. For example,
a neutral model, in which predicted sensitivity
to PET and CWD is constant across species’
climatic ranges, would yield contrasting results
to our model, which allows for spatial hetero-
geneity. Specifically, the neutral model would
likely underestimate the negative impact of cli-
mate change in wetter regions but overestimate
the negative impact in drier regions when com-
pared with our model (fig. S7). These results
highlight that the spatial heterogeneity in trees’
climatic sensitivities will likely play a critical
role in mediating the response of the world’s
forests to climate change.
Discussion
Trees growing in wet and warm portions of
their range will likely experience the greatest
declines in growth under climate change. This
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pattern of vulnerability captures the inter-
action of heterogeneity in both exposure and
sensitivity—historically wet forests are more
sensitive to drier conditions, whereas hot
forests will be exposed to the greatest in-
creases in CWD. Though drought-induced de-
clines in tree growth frequently occur in dry
regions (15, 19, 47), our results support the
hypothesis that the vulnerability of wetter
forests to climate change is greatly under-
appreciated (48).
The drought-naïve pattern exhibited across
ITRDB and FIA sites is likely the result of
long-term adaptations to local climatic condi-
tions. Drought adapted traits—for example,
higher resistance to cavitation, lower leaf-area
index, higher water-use efficiency, and wider
hydraulic safety margins (49, 50)—often e-
merge in regions that experience higher aridity
and drought frequency (51–53). In theory,
drought adaptations could occur at the scale of
individuals (e.g., phenotypic plasticity) or local
communities (e.g., tree density) or through
evolutionary processes that occur across gen-
erations. Recent research, however, suggests
that most climate adaptation develops over
longer timescales than an individual tree’s life
span (54). This suggests that genetic adap-
tation is an important mechanism that pro-
tects trees from climate change, but it also
highlights the risk that rapid warming may
outpace the rate of adaptation.
Although sensitivity patterns for many gen-
era are consistent with the drought-naïve
effect (fig. S4), the sign, magnitude, and signif-
icance of this effect varies across taxa. Some
of this variability is likely due to differences in
tree traits (e.g., turgor loss point, xylem struc-
ture, leaf size) and mechanisms of acclimation
(e.g., canopy thinning, trait plasticity, shifts in
water allocation) (23, 48). Interestingly, Quercus
and Taxodium, the two genera that exhibited
opposite (although insignificant) patterns of
drought sensitivity, both have hotter species
ranges than the other commonly sampled gen-
era (fig. S4). This suggests that taxonomic
differences in drought sensitivity may be partly
explained by trade-offs between investments
in heat and drought tolerance (55), as well as
the physiological limits of climate adaptation.
Future research that disentangles the primary
mechanisms of drought and heat tolerance
will improve estimates of species-level vulner-
ability to climate change.
The prevalence of drought-naïve effects is
relevant for understanding climate change
impacts across many scales of biological or-
ganization. Organisms and ecosystems with
prior exposure to extreme weather (e.g., droughts
and heat waves) are often less sensitive to
extreme events than entities that lack past
exposure. This pattern has been found across
diverse systems, including soil microbial com-
munities (56), insect species (57), bird popula-
tions (58), agricultural production (59), human
mortality (60), and even biomes (61). Though
the mechanisms that enable adaptation vary
by system, relatively consistent patterns of sen-
sitivity underscore the important role that
adaptation could play in moderating the ef-
fects of climate extremes.
Because we quantified vulnerability using
tree growth rather than mortality, our analysis
provides incomplete insights into patterns of
mortality under climate change. Declines in
RWI have been shown to predict tree mortal-
ity (62, 63), and the primary mechanisms of
drought-induced mortality—hydraulic failure,
carbon starvation, and defensive failure (23)—
can be linked to changes in tree growth (64).
Therefore, our predictions of growth declines
in mesic regions suggest that increases in tree
mortality may be surprisingly widespread.
Nevertheless, declines in RWI can be an un-
reliable predictor of mortality (64, 65). A tree’s
age, genotype, functional traits, and mecha-
nisms of acclimation (64, 66, 67) are all im-
portant determinants of growth responses to
drought, which can decouple the relationship
between RWI and mortality. Importantly, our
predictions of vulnerability might understate
the risk of mortality at dry-range edges if there
are thresholds in the relationship between tree
growth and mortality (68). For example, trees
likely require a minimum amount of growth
to survive (68); therefore, the same percent-
age growth decline could be more harmful for
slow-growing trees located at their dry-range
edge than for trees growing in mesic areas
(10). Future research that characterizes these
nonlinear responses to drought could improve
predictions of climate impacts (42, 43).
Finally, our findings have important policy
implications, both for conserving forests and
managing terrestrial carbon sinks. Policy-makers
who seek to protect forests from climate change
may need to expand the focus of conservation
interventions beyond species’ dry-range edges.
By contrast, drought adaptations in popula-
tions from drier regions could be useful for
management interventions, including assisted
migration into wetter regions. Additionally,
although dynamic global vegetation models
are increasingly sophisticated (69–72), very
few, if any, account for the spatial variation in
the climate sensitivity of carbon capture. Fail-
ing to account for drought-naïve effects can
lead to overestimates of the resilience of car-
bon sinks in wetter regions. Improving fore-
casts of climate-change impacts on terrestrial
carbon sinks by accounting for the variability in
drought sensitivity will facilitate more-effective
global policies aimed at reducing carbon emis-
sions (73, 74).
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ACKN OWLED GMEN TS
We thank R. Huezo for help parsing the ITRDB database and
M. Leung for support in compiling our database of species range
maps. We express our appreciation to the many contributors to
the ITRDB. In addition, we thank S. Klesse and J. Shaw for providing
access to the US Forest Service’s National Forest Inventory and
Analysis Program’s Interior West tree-ring dataset. Funding:
J.D. acknowledges support from the David H. Smith Conservation
Research Fellowship. F.C.M. acknowledges support from the
National Science Foundation (NSF award no. 1924378). Author
contributions: R.H., J.D., and F.C.M. all contributed to the
conceptualization, data curation, formal analysis, writing (original
draft), and writing (review and editing) of this paper. Competing
interests: The authors declare that they have no competing
interests. Data and materials availability: All code used to
clean data, conduct the analysis, and generate figures and results
is available at this paper’s Open Science Framework (OSF)
repository (75). This repository also includes the preprocessed
data necessary to reproduce all results, figures, and tables.
Raw input data are available from the ITRDB (76), the Climate
Research Unit (77), and the Coupled Model Intercomparison Project
(78). License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government works.
https://www.science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi1071
Materials and Methods
Figs. S1 to S7
Table S1
References (79–91)
MDAR Reproducibility Checklist
Submitted 7 April 2023; accepted 26 October 2023
10.1126/science.adi1071
Heilmayr et al., Science 382, 1171–1177 (2023)
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RES EARCH
3D PRINTING
Self-enhancing sono-inks enable deep-penetration
acoustic volumetric printing
Xiao Kuang1†, Qiangzhou Rong2†, Saud Belal2†, Tri Vu2, Alice M. López López1, Nanchao Wang2,
Mehmet Onur Arıcan1, Carlos Ezio Garciamendez-Mijares1, Maomao Chen2,
Junjie Yao2*, Yu Shrike Zhang1*
Volumetric printing, an emerging additive manufacturing technique, builds objects with enhanced
printing speed and surface quality by forgoing the stepwise ink-renewal step. Existing volumetric
printing techniques almost exclusively rely on light energy to trigger photopolymerization in transparent
inks, limiting material choices and build sizes. We report a self-enhancing sonicated ink (or sono-ink)
design and corresponding focused-ultrasound writing technique for deep-penetration acoustic
volumetric printing (DAVP). We used experiments and acoustic modeling to study the frequency and
scanning rate–dependent acoustic printing behaviors. DAVP achieves the key features of low acoustic
streaming, rapid sonothermal polymerization, and large printing depth, enabling the printing of
volumetric hydrogels and nanocomposites with various shapes regardless of their optical properties.
DAVP also allows printing at centimeter depths through biological tissues, paving the way toward
minimally invasive medicine.
T hree-dimensional (3D) printing is at-
tracting increasing attention with its
ability to directly fabricate geometrically
complex constructs for prototypes (1),
high-performance materials (2, 3), multi-
material parts (4, 5), flexible electronics (6, 7),
medical devices (8), and engineered tissues
(9, 10). Various printing modalities, such as
extrusion printing, inkjet printing, stereolithog-
raphy, and powder-bed fusion, have been de-
veloped to print different materials, including
thermoplastics, liquid photoinks, and solid
polymer powders, among others (11, 12). These
printing methods use light or photothermal
heating as energy sources to trigger selective
material solidification in a layer-by-layer fash-
ion. A build platform controlled by a linear
translation stage is usually required to support
the stepwise material solidification. Emerg-
ing printing techniques accompanied by new
photocurable inks have been developed to
improve printing speed (13, 14), printing res-
olution (15–17), and printout functionality
(18, 19). Volumetric printing that creates 3D
constructs without a build platform or an
ink-renewal step can substantially improve
printing speed and surface quality (20–23).
The existing volumetric printing techniques
use light to achieve selective photopolymer-
ization in the volumes of optically transparent
inks (24–26). However, the light attenuation
by inks themselves, the presence of functional
additives (e.g., photoabsorbers and fillers),
or/and already-cured parts have imposed con-
1Division of Engineering in Medicine, Department of Medicine,
Brigham and Women’s Hospital, Harvard Medical School,
Cambridge, MA 02139, USA. 2Department of Biomedical
Engineering, Duke University, Durham, NC 27708, USA.
*Corresponding author. Email: junjie.yao@duke.edu (J.Y.);
yszhang@bwh.harvard.edu (Y.S.Z.)
†These authors contributed equally to this work.
straints on the material choices and the build
sizes for light-based volumetric printing. Al-
though infrared (IR) light can be used to im-
prove light penetration to several millimeters
(26–28), it remains technically challenging
to deliver light deep into optically scattering
media, such as biological tissues. Therefore,
light-based volumetric printing has intrinsic
limitations for application in deep-penetration
digital manufacturing schemes and, further,
in minimally invasive fabrication scenarios
(29, 30).
Compared with light, ultrasound waves
(<10 MHz) can penetrate >100 times deeper
into optically scattering materials and thus
hold promise for depositing energy to trigger
polymerization at depths (31). By means of an
ultrasound bath or horn-based reactors, ultra-
sound waves can generate reactive oxygen spe-
cies (ROS; i.e., hydroxyl and peroxide radicals)
by cavitation of water, enabling vinyl mono-
mer polymerization for hydrogel formation in
several to tens of minutes (32, 33). Ultrasound
waves can also be focused into a small volume
using a focused ultrasound (FUS) transducer.
A FUS transducer can generate acoustic waves
with positive and negative pressures alternat-
ing at megahertz frequency and propagating
along the depth direction, and the high acous-
tic energy can be delivered into the focal zone
with high precision. Previously, cavitation-
based ultrasound printing was achieved by
curing a polydimethylsiloxane resin (34). How-
ever, a build platform was required, and only
relatively simple geometries could be printed,
because the intense acoustic streaming by the
high acoustic pressure disturbed the local ink
at the focus region.
Here, we report phase-transition viscoelastic
sonicated inks (hereafter, sono-inks) that simul-
taneously allow deep acoustic penetration, low
acoustic streaming, and rapid sonothermally
induced radical polymerization, collectively
enabling deep-penetration acoustic volumet-
ric printing (DAVP) (Fig. 1A). DAVP takes ad-
vantage of rapid material solidification by the
sonothermal effect of the FUS focus in a visco-
elastic sono-ink, which provides the building
voxel to construct 3D objects without the need
for a build platform. In DAVP, the FUS waves
deliver deep-penetration acoustic energies
with pressures up to several tens of mega-
pascals to the local region at a distance of up
to 64 mm (focal length) (Fig. 1B). The small
oval-shaped FUS focal zone (full width at
half maximum of the acoustic pressure field:
0.3 to 0.7 mm) is further narrowed by the
nonlinear acoustic propagation effect at high
acoustic pressure (35), collectively facilitating
fast, high-resolution printing (Fig. 1C and fig.
S1). Consequently, DAVP allows us to print
geometrically complex materials precisely and
volumetrically, even through nontransparent
and optically scattering materials.
DAVP principle and self-enhancing
sono-ink design
Traditionally, ultrasound-mediated cross-linking
of the vinyl-based hydrogel precursors is slow,
because of the low concentration of ROS gen-
erated by ultrasound-induced cavitation (see
supplementary text in the supplementary mate-
rials). Besides, ROS can be rapidly quenched
or diluted by robust acoustic streaming. Our
simulation results showed that high-viscosity
fluids could significantly reduce the acoustic
streaming velocity (Fig. 1D and fig. S2). How-
ever, highly viscous ink feedstocks usually
exhibit high acoustic attenuations and thus
substantially reduce acoustic penetration (36).
We hypothesized that a meticulously designed
multicomponent viscoelastic sono-ink should
suppress acoustic streaming while facilitating
a fast sonothermal effect and thus trigger
rapid and spatial radical polymerization of
vinyl precursors for a deep-penetration fabri-
cation scheme.
To formulate such a proof-of-concept sono-
ink, we selected a vinyl oligomer of poly
(ethylene glycol) diacrylate (PEGDA) as the
base component, agar microparticles as the
rheology modifier, poly(N-isopropyl acrylam-
ide) (PNIPAm) as the self-enhancing acoustic
absorber, and ammonium persulfate (APS) as
the thermal initiator (fig. S3). Compared with
PEGDA ink, PEGDA-based sono-ink (PEGDA/
agar/PNIPAm at, for example, 20/10/3 wt/wt/
wt % ratio) showed enhanced viscosities ow-
ing to the coil-to-globule phase transition of
PNIPAm [transition temperature (Tt) = 34° to
36°C] (Fig. 1E and fig. S4). The viscosity of
the sono-ink increased 92-fold, from 2.0 to
185.3 Pa·s, when heated from 25°C to 40°C
at low shearing (0.05 Hz) (fig. S4C). Mean-
while, the sono-ink showed prominent shear
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Fig. 1. Working principle of DAVP and design of self-enhancing sono-ink.
(A) Scheme showing acoustic printing of constructs by selective curing of
sono-ink using deep-penetration FUS. The sonothermal effect enhanced by the
phase-transitioning acoustic absorber triggers the decomposition of the initiator
for local polymerization of acrylate oligomers into polymer networks at the
heating zone. (B) Simulated acoustic pressure field in water for the 3.41-MHz FUS
transducer with an acoustic power of 50 W, using the nonlinear acoustic model.
(C) Lateral pressure distribution of the 3.41-MHz FUS transducer with an output
voltage (Vp) of 192 V. The shaded regions show the full width at half maximum of
the positive and negative pressures (0.3 to 0.7 mm). (D) Simulated maximum velocity
in the focal region versus the dynamic viscosity of the sono-ink. Inset acoustic
streaming simulation shows the velocity field of fluids with a viscosity of 2.5 Pa·s.
(E) Oscillation temperature sweep shows the enhanced moduli and viscosity of
PEGDA-based sono-ink at a transition temperature (33° to 36°C) due to coil-to-globule
transition of PNIPAm. (F) Acoustic streaming in different fluids at the focal region
of 3.41-MHz FUS for 2-s exposure: 20 wt % PEGDA (i) and PEGDA/agar/PNIPAm
sono-ink (ii). Scale bars: 5 mm. (G) Acoustic properties of the PEGDA/agar/PNIPAm
sono-ink and its key components under 3.41-MHz FUS at 25° and 37°C: acoustic
attenuation coefficient in linear scale (i) and penetration depth in log scale (ii).
(H) Peak temperature in sono-ink at the heating zone near the FUS focus as a
function of exposure time, at an environment temperature of 24°C. (I) Gelation
time measured by rheology as a function of the curing temperature for PEGDA-based
sono-ink supplemented with 1.0 w/w% APS. Orange squares represent the
experiment data, and the solid blue line is the fitting curve by the Arrhenius law.
thinning, as reflected by an 87% reduction in
viscosity under 100-Hz shearing at 25°C (fig.
S4). This sono-ink design concept was gen-
eralizable to different formulations, includ-
ing those using vinyl oligomers from natural
polymers [e.g., gelatin methacryloyl (GelMA)]
(fig. S4) or different phase-transition poly-
mers with tunable transition temperatures
(Tt,offset = 20.9° to 38.5°C) (fig. S5 and table
S1), as well as formulations adding various
nanoparticles (table S2). Our sono-ink de-
sign resolved the long-standing dilemma be-
tween acoustic penetration depth and acoustic
streaming. On the one hand, the shear thin-
ning facilitated deep acoustic penetration under
high-frequency acoustic waves. On the other
hand, the viscosity enhancement by phase tran-
sition substantially reduced acoustic stream-
ing. In contrast to the violent streaming in the
PEGDA solution, the self-enhancing sono-ink
exhibited negligible fluid flow at the FUS focus
(Fig. 1F, fig. S6, and movie S1), as supported by
the simulation (Fig. 1D).
To investigate the sono-ink’s self-enhanced
acoustic attenuation effect, we measured the
acoustic attenuation coefficient (a) of the proof-
of-concept sono-ink and key components at
various temperatures (fig. S7). Because of the
phase transition, the a of the PNIPAm (3 wt %)
aqueous solution and PEGDA-based ink at the
ultrasound frequency of 3.41 MHz increased
with the temperature, for example, by 600 and
100%, respectively, from 25°C to 37°C (Fig. 1G).
The a of the sono-ink (containing both PEGDA
and PNIPAm) was 25.2 nepers per meter (Np m−1)
at a temperature of 37°C, which was 86-fold
larger than that of 20 wt % PEGDA alone but
still much lower than the a of soft biological
tissues under the same conditions (table S3).
Despite the self-enhanced acoustic attenuation,
the acoustic waves could still achieve a large
penetration depth (Dp = 1/a) of 40 mm into
the sono-ink at 37°C (Fig. 1G).
As a direct result of self-enhanced acoustic
attenuation and viscosity, the phase-transition
sono-ink exhibited a fast and self-enhanced
heating effect. The PNIPAm solution and the
sono-ink could be rapidly heated up to between
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60° and 80°C at the heating zone after sec-
onds of FUS exposure at mild input powers
(<100 W) (fig. S8 and movie S2). PNIPAm
played a critical role in achieving fast sono-
heating, in contrast to the negligible heating of
the 20 wt % PEGDA solution. To further in-
vestigate the self-enhanced heating effect, the
heating-zone temperatures as a function of
FUS exposure time were monitored by an IR
thermal camera during FUS exposure at dif-
ferent environmental temperatures (Tenv). At a
Tenv of 24°C—far below the Tt, offset of PNIPAm
—the peak temperature at the heating zone
first showed a slow heating rate (4.8°C s−1) and
then, after the temperature leap at 36°C, a
much-enhanced heating rate (11.3°C s−1), as
a result of the phase transition (Fig. 1H). The
slow heating period, called the induction period,
was reduced from 0.5 s to 0.1 s by raising the
Tenv to 33°C (close to Tt, offset) and entirely elim-
inated at Tenv = 35°C (>Tt, offset) (fig. S9 and
movie S3). In our printing technique, Tenv was
set slightly lower than Tt, offset to allow for
confined sonoheating at the FUS focus. It is
worth noting that, as in thermal-based tissue
ablation (37), our self-enhancing sono-ink en-
abled a prominent sonothermal effect under a
high-duty cycle of 90%. We did not observe
FUS-induced cavitation activities, as validated
by active cavitation mapping (fig. S10 and
movie S4). Therefore, it was concluded that
FUS-induced cavitation is not responsible for
the sono-ink solidification.
The self-enhanced sonothermal effect was
leveraged to trigger the radical polymeriza-
tion of vinyl oligomers for fast gelation. The
gel-point conversion of the PEGDA-based sono-
ink was ~0.3, as measured by Fourier trans-
form infrared spectroscopy (fig. S11). In the
presence of APS, the sono-inks proceeded
with (sono)thermal-induced gelation, as illu-
strated by the rheological measurement (fig.
S12). The temperature-sensitive gelation time
(tgel) followed the Arrhenius law, revealing a
high activation energy (171 kJ mol−1) (eq. S10).
Consequently, long shelf life (tgel = 167 days
at 4°C) and on-demand fast curing (tgel =
1.9 s at 80°C) were simultaneously achieved
(Fig. 1I).
DAVP printing-resolution characterizations
We developed a 3D FUS printer, which was
equipped with a FUS transducer at three ultra-
sound frequencies (2.05, 3.41, and 6.86 MHz),
a 3D motorized translation stage, and a print-
ing control system (fig. S13; see materials and
methods in the supplementary materials for
further details). We first studied the single-
point printing resolution of DAVP. Upon FUS
exposure in the sono-ink, a whitening region
formed and quickly expanded beyond the FUS
heating zone (fig. S14 and movie S5), as PNIPAm
simultaneously acted as the self-enhancing
acoustic absorber and the temperature indi-
cator (38). IR thermal images of the sono-ink
surface showed a clear temperature increase
forming a heating zone (Fig. 2A). The heated
surface area (diameter of up to 4 mm) was larger
than the focal zone of the FUS transducer
(0.45 mm at 3.41 MHz) because of the rapid
thermal diffusion. Upon cooling, a piece of
opaque solid formed at the center of the heat-
ing zone, and the uncured sono-ink returned
to its original color. By comparing the curing
size with the heating-zone temperature pro-
file, we found that the curing temperature
threshold was Tc = 67°C for the PEGDA-based
sono-ink supplemented with 0.5 w/w% APS.
Because of heat diffusion by the low-power
cumulative FUS, the curing size increased with
input power (or peak acoustic pressure) and
exposure time (Fig. 2B and fig. S15). The non-
linear acoustic effect resulted in elevated acous-
tic intensity at the FUS focus by increasing the
peak pressure and reducing the focal region
(39, 40), as shown by our nonlinear acoustic
modeling (fig. S16). The simulation also cap-
tured the nonlinear acoustic propagation in
the sono-ink, exhibiting weak reflection and
scattering by different boundaries (such as
plastics and tissues) in the far field (fig. S17),
and negligible acoustic reflection and scatter-
ing at the interface formed by the sono-ink
phase transition (fig. S18). Using the numer-
ically modeled temperature map and the
measured Tc, we investigated the increasing
single-point curing size (0 to 4 mm in diam-
eter) as a function of peak acoustic pressure
(35 to 55 MPa) and exposure time (0 to 5 s) (Fig.
2C, fig. S19, and movie S6). Tc of the sono-inks
could be readily reduced from 67°C to 62°C
by increasing the APS concentration, because
of the enhanced reaction rate (fig. S20 and eq.
S8). Additionally, increasing the PEGDA con-
centration (40 wt %) increased the apparent Tc
of the sono-ink, likely owing to additional
heating by the exothermic effect of polymeri-
zation and reduced viscosity (fig. S21).
We further investigated the printing resolu-
tions of DAVP by continuously scanning a line
under different printing settings. An expand-
ing heated region instantly formed at the front
of the scanning FUS focus, as a result of the
thermal diffusion within the ink, which was
also confirmed by sonothermal modeling (Fig.
2D, fig. S22, table S4, and movie S7). The sono-
ink was cross-linked only at the center of the
heating zone, where the temperature increased
above the curing threshold, forming aniso-
tropic filaments. We also investigated the de-
pendence of the curing size on several key
parameters, including the scanning speed of
the FUS focus, the FUS frequency and power,
and thermal diffusion (figs. S23 to S25 and
movie S8). Modeling results showed that the
thin ink tank (6 mm) caused heat accumula-
tion at the tank boundary, whereas a thicker
tank (>10 mm) allowed for normal thermal
diffusion around the focal region (fig. S26).
Therefore, we used the 10-mm-thick ink tank
to quantify the curing sizes (or printing reso-
lutions) (Fig. 2E). First, increasing the scan-
ning speed can improve the printing resolution.
We observed overcuring in the longitudinal
dimension (larger than design) at a slow scan-
ning speed with all three ultrasound frequen-
cies (2.05, 3.41, and 6.86 MHz), owing to excess
heat accumulation. In comparison, undercur-
ing (lower than design) was observed at high
scanning speeds because of inadequate tem-
perature increase at the two ends. The in-
plane curing size was determined by the joint
effect of the FUS scanning speed and thermal
diffusion. For instance, the in-plane curing
size at 3.41 MHz was improved from 7.6 mm to
1.6 mm by increasing the scanning speed from
0.4 mm s−1 to 0.8 mm s−1. Similarly, the axial
curing size was mostly determined by the FUS
depth of focus and thermal diffusion. As an
example, the 6.86-MHz FUS had a smaller
depth of focus (1.69 mm) than the 2.05-MHz
FUS (5.58 mm), but the sono-ink had a 10-fold
acoustic absorption at 6.86 MHz and thus
much higher heating efficiency. Eventually,
the axial curing size ranged from 5.0 to 9.9 mm
for the investigated printing parameters. The
depth of focus here is defined as the size of
the focal zone along the acoustic axis, in which
the acoustic pressure drops to half of the peak
value (table S5).
The printing resolution of DAVP can be
flexibly adjusted by optimizing the FUS scan-
ning speed, frequency, and power. Generally,
the printing anisotropy (ratio of the axial and
in-plane curing size) increased with the print-
ing speed, mostly as a result of the decreased
in-plane curing size (Fig. 2F). For example,
when printing at 0.8 mm s−1 by the 6.86-MHz
FUS, the cross section of printed filaments ex-
hibited an oval shape with an axial size of
8.8 mm, which was 100% larger than the in-
plane curing size (Fig. 2, G and H). The sono-
thermal curing mechanism also led to different
microstructures within the FUS heating zone.
The cured hydrogels displayed sub-micrometer
pores in the PEGDA/PNIPAm matrix due to
polymerization-induced phase separation, as
shown by scanning electron microscopy (SEM)
(Fig. 2I). SEM images suggested melting of
agar microparticles owing to a high tempera-
ture of >85°C at the center of the heating zone
(Fig. 2I, panel ii). However, the agar micro-
particles maintained a granular shape outside
the center of the focal zone at various printing
speeds and frequencies, similar to that achieved
by bulk heating at 60° to 70°C (figs. S28 and
S29). These results further excluded the pres-
ence of FUS-induced cavitation and confirmed
the heat accumulation–based curing mecha-
nism. Meanwhile, the enhanced surface qua-
lity of the printed filaments was confirmed by
the uniform and smooth surface (fig. S29D).
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Fig. 2. Characterizations of DAVP printing resolution. (A) Typical surface
temperature profile near the FUS focal region. The IR thermal image shows the
in-plane temperature map (i) and temperature diagram at the cross section (ii).
The inset shows the cured solid after 3-s FUS exposure (3.41 MHz) with the
curing threshold temperature of 67°C. (B) In-plane curing size of printed solids
versus FUS exposure time using PEGDA-based sono-ink (0.5 w/w% APS) at
different Vp, as labeled. (C) Color-contour of modeled in-plane curing size at
3.41 MHz as a function of acoustic pressure and exposure time. (D) Snapshots of
photographs (i) and IR thermal images (ii) near the FUS focal zone, as well as
modeled temperature map on the focal plane (iii) at different time points during
line printing using PEGDA-based sono-ink (1.0 w/w% APS) (FUS frequency:
3.41 MHz; printing speed: 1.5 mm s−1). (E) Curing sizes for single-line DAVP
printing using different printing speeds at various FUS frequencies as labeled:
longitudinal size (i), in-plane size (ii), and z-axial size (iii). (F) Axial-to-lateral
curing size ratio as a function of printing speed using various FUS frequencies, as
labeled. (G) Photographs of printed filaments by single-line DAVP (6.86-MHz
FUS at a speed of 0.8 mm s−1): in-plane size (i) and axial size (ii). (H) Cross-sectional
micrographs of printed filaments in (G) with three different marked regions.
(I) SEM images of dried hydrogels in (H) at different regions: top (i), center (ii),
and bottom (iii). Scale bars: 2 mm [(A), (D), (G), (H)] and 2 mm (I).
When performing multipath printing, the
axial printing size (or printing thickness) in-
creased, as a result of repeated FUS exposure
along the acoustic axis at the scanned regions;
however, the printing lengths were less sensi-
tive to the number of printing paths (fig. S30).
Additionally, the printing performance of DAVP
was independent of the line-scanning direc-
tion of the 3D FUS printer. There were no
significant differences in printing fidelity and
mechanical properties (e.g., Young’s moduli:
1.4 ± 0.1, 1.2 ± 0.3, and 1.3 ± 0.1 MPa) using
different scanning directions (0°, 45°, and 90°,
respectively) (fig. S31). Moreover, the printed
sample at the 0° infill angle showed signifi-
cantly higher stiffness than that by bulk heat-
ing (0.9 ± 0.1 MPa), likely because of the high
temperature–induced fast matrix curing and
agar welding.
DAVP of volumetric constructs and
material generality
Deep penetration is the primary advantage of
DAVP over conventional light-based 3D print-
ing (Fig. 3A). For example, in a black-dyed
sono-ink (0.5 w/w%), the penetration depths
for the 2.05-, 3.41-, and 6.86-MHz ultrasound
waves were 295.2, 86.8, and 28.2 mm at room
temperature, respectively, which were, respec-
tively, 600, 180, and 60 times as large as those
for the 405-nm light (Dp = 0.48 mm) (Fig. 3B).
As such, a large curing depth of 24 mm in the
dyed sono-ink was achieved in 26 s at an axial
scanning speed of 1 mm s−1 and 3.41-MHz FUS,
whereas only a thin solid (2.4 mm) in the dye-
stained photoink was obtained after photo-
curing for 165 s (fig. S32). The large penetration
depth of DAVP, regardless of the optical prop-
erties of the ink, allowed us to volumetrically
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Fig. 3. DAVP performance and material generality. (A) Schematic illustrations for
photocuring of photoinks (i) and FUS-curing of sono-inks (ii) with different
penetration capabilities. (B) Penetration depth as a function of black-dye content for
UV light (405 nm) and FUS at different frequencies, as labeled. (C to F) Design
models (i), top-view (ii), and tilt-view photographs (iii) of printed constructs of
various shapes using PEGDA-based sono-ink: honeycomb (C), vessel network
(D), 3D hand (E), and spider (F). (G to J) Photographs of printed constructs
using various sono-inks: multicolor three-part gear set (i) and a three-part wheel
set (ii) by dye-stained PEGDA-based sono-inks consisting of different colors (G),
vascular network model by a fluorescence-stained PEGDA-based sono-ink (0.1 w/w%
rhodamine B) (H), tree-shaped model by a PEGDA-based nanocomposite sono-ink
(10 wt % nanoclay) (I), and layered heart-shaped model by a GelMA-based protein
sono-ink (J). (K to M) In vitro cytocompatibility of GelMA-based sono-inks and
cured hydrogels: representative fluorescence micrographs of live (green)/dead (red)
cells (NIH/3T3 fibroblasts) after 30-min exposure to DPBS (control) and GelMA-
based sono-ink (K), quantitative cellular viability values of NIH/3T3 fibroblasts after
30-min exposure to GelMA-based sono-ink (i) and at day 7 after seeding on GelMA-
based hydrogel (ii) (L), fluorescence micrographs showing F-actin staining of cells
at day 7 after seeding on the GelMA/PNIPAm hydrogel using two cell types: human
mesenchymal stem cells (hMSCs) (i) and human umbilical vein endothelial cells
(HUVECs) (ii). F-actin, red; nucleus, blue. ns, no significant difference. Scale bars:
10 mm [(C) to (J)] and 100 mm [(K) and (M)].
print nontransparent 2D and 3D hydrogel con-
structs with different sizes and geometrical
complexities, including letters and lattices with
sharp corners and spirals and vessels with
smooth surfaces and transitions (fig. S33, table
S6, and movie S9). For example, a 10-layer
honeycomb and a vascular network were
printed at 3.41 MHz (Fig. 3, C and D, and table
S6). A complex 3D hand model (67 mm by 53 mm
by 10 mm) and a spider model (52 mm by 43 mm
by 10 mm) were also printed at 6.86 MHz (Fig.
3, E and F; fig. S34; and table S6).
Using dye-stained PEGDA-based sono-inks,
we printed opaque-colored hydrogel compos-
ites for prototypes, including a set of three
gears of different sizes and an assembled wheel
set of three colored parts (Fig. 3G and fig. S35).
Altering the phase-transition polymers with
higher Tt, such as poly(N-isopropylmethacrylamide)
(PNIPMAm), could facilitate printing at body
temperature (37°C) (fig. S35D). Additionally,
fluorescence-stained sono-ink (0.1 wt % rho-
damine B) was used to print a high-fidelity
branched vascular network shape (81 mm by
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Fig. 4. DAVP for proof-of-concept through-tissue printing and minimally
invasive therapy. (A) Scheme of minimally invasive therapy by through-tissue
manufacturing of scaffolds on target lesions and tissues. (B to D) Tissue
phantoms with marked thicknesses (i) and printed objects with associated
digital models (ii) for through-tissue manufacturing: a bone-shaped model
printed under porcine belly (B), a lattice printed under porcine liver (C), and
a heart-shaped model printed under porcine kidney (D). Printing was
performed with 2.05-MHz FUS at 0.6 mm s−1. (E and F) DAVP for LAA closure
for a 12-mm-thick goat heart: scheme and printing process at different
time points (E), and stretching of closed LAA (F). (G and H) DAVP for
defective bone reconstruction: scheme and photographs showing the
procedures of manufacturing a nanocomposite filler material on a bone defect
through 10-mm-thick skin and muscle (G), and ultrasound images of the
bone defect (i) and the reconstructed bone (ii) (H). (I to K) DAVP for chemotherapy
drug delivery for a 14-mm-thick porcine liver: scheme and photographs showing
the procedure of printing drug-eluting hydrogels using a doxorubicin-loaded
sono-ink on a liver lesion (I), cross-sectional photograph showing the printed
hydrogel-liver interface (J), and fluorescence micrograph showing drug diffusion
from the printed drug-eluting filler hydrogel to the liver at 1500-s contact (K).
Scale bars: 10 mm [(B) to (J)] and 200 mm (K).
70 mm by 3 mm) (Fig. 3H). Further, a nano-
composite sono-ink consisting of 10 wt %
nanoclay was exploited to print a four-layer
tree shape (2 mm in thickness) (Fig. 3I). DAVP
was also used to print protein-based biomate-
rials, as suggested by the tough-hydrogel heart
model using the GelMA-based sono-ink (Fig.
3J and fig. S35, E and F). Both PEGDA- and
GelMA-based sono-inks and their key compo-
nents exhibited zero to low cytotoxicity using
NIH/3T3 fibroblasts as a model cell line. High
cell viability (>99%) similar to the control [using
Dulbecco’s phosphate-buffered saline (DPBS)]
was observed after direct and indirect expo-
sure to the sono-ink for up to 30 min (Fig. 3, K
and L, and fig. S36). Moreover, similar to the
control cultured in a petri dish, the GelMA-
based hydrogel enabled high viability (>99%)
and healthy attachment and proliferation of
postseeded mammalian cells of different types
(Fig. 3M and fig. S37), indicating its favorable
bioactivity.
DAVP for through-tissue printing and
constructive minimally invasive medicine
As a proof of concept, we applied DAVP for
high-speed and high-resolution through-tissue
manufacturing and minimally invasive medi-
cine (Fig. 4A). First, we illustrated the ex vivo
through-tissue printing using soft tissues of
different types and dimensions (fig. S38 and
table S7). For through-tissue printing, thick
tissues (up to 17 mm thick) were placed on
top of the sono-ink chamber in the FUS near
field. We printed a bone-shaped construct at
2.05 MHz through an ex vivo porcine tissue
phantom consisting of a skin layer (3 mm), a
fat layer (5 mm), and a muscle layer (7 mm) (Fig.
4B). High-fidelity honeycombs were printed
through a 15-mm-thick porcine tissue con-
sisting of skin and muscle or a 17-mm-thick
porcine liver tissue (Fig. 4C). Similarly, a hol-
low heart-shaped model was printed through
a 17-mm-thick porcine kidney tissue (Fig. 4D
and movie S10).
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Nonvalvular atrial fibrillation is a prevalent
cardiovascular disease related to the left atrial
appendage (LAA) (41, 42). Open-chest surgery
or transcatheter procedures can seal off the
LAA to reduce the risk of thromboembolism.
However, surgical LAA closure is severely in-
vasive, and the treatment is often incomplete
(41). We demonstrated proof-of-concept DAVP-
assisted LAA closure (Fig. 4E). We delivered the
sono-ink through a catheter to the LAA of an
ex vivo goat heart placed in the printing cham-
ber. The sono-ink was then solidified using the
3D FUS printer at 3.41 MHz through a 12-mm-
thick heart wall. Precise FUS focus scanning en-
abled selective curing of the sono-ink within the
entire LAA volume while sparing surrounding
heart tissues (fig. S39 and movie S11). After
treatment, the cured hydrogels completely oc-
cluded the LAA and bonded well with the tissue
wall, which could tolerate reasonable distortions
that mimicked the heart beating (Fig. 4F).
We further explored the potential of the
DAVP technique for tissue reconstruction and
regeneration, such as treating large bone de-
fects (43). As an illustration, the PEGDA/agar/
PNIPMAm nanocomposite sono-ink consist-
ing of 5 w/w% hydroxyapatite (HAp) nanopar-
ticles was formulated to print a bone scaffold
for a hypothetical bone loss treatment (Fig.
4G and movie S12). We used a chicken leg to
create a fibula bone defect model (1 cm long).
After injecting the nanocomposite sono-ink,
we printed a beam-shaped HAp-laden com-
posite material through the skin and muscle
tissues (10 mm thick) to reshape the defec-
tive volume. The nanocomposite material could
reconstruct the bone with seamless bonding
to the native parts without influencing the
surrounding tissues, as confirmed by ultra-
sound imaging (Fig. 4H).
We also demonstrated DAVP for therapeu-
tic drug delivery by printing drug-eluting filler
hydrogels on liver lesions (Fig. 4I). Doxorubi-
cin, a clinical chemotherapy drug for treating
a wide range of cancers, such as breast cancer
and hepatocellular carcinoma, was used as a
model drug (44). PEGDA/agar/PNIPMAm sono-
ink consisting of 1 mg ml−1 of doxorubicin was
formulated for printing chemotherapy drug-
eluting hydrogels at the liver lesion sites at 37°C
using FUS at various frequencies (fig. S40).
DAVP enabled through-tissue printing and
selective curing, as shown by the intimate
hydrogel-tissue interfacial bonding (front side)
and negligible burning of the intervening tis-
sue (back side) (Fig. 4J and movie S13). The
drug in the hydrogel gradually released and
diffused into the liver tissue (effective diffu-
sivity: 8.7 × 108 cm2 s−1), forming an ~3-mm-
thick effective therapeutic layer [5.8 mg ml−1
concentration (44)] within 7 days by modeling
(Fig. 4K and fig. S41). We anticipated that this
method could be used as postablative chemo-
therapy to improve cancer treatment.
We note that relatively high FUS energies
were needed for through-tissue printing, main-
ly because of the acoustic attenuation by the
intervening tissues. The acoustic energy loss
might possibly result in overheating of the in-
tervening tissues. To mitigate the risk of tissue
overheating and to improve future in vivo
printing efficiency, we developed a confocal-
DAVP system in which the 3D FUS printer
used two FUS transducers aligned in a cross-
beam pattern, with their acoustic axes 90°
apart and their foci overlapping (fig. S42).
Taking advantage of the energy superposition
of two acoustic foci, confocal-DAVP can achieve
the curing temperature threshold in the com-
bined foci, using roughly half of the output
energy from each FUS transducer. Such a con-
focal configuration has two advantages: (i) the
acoustic energy deposition in the local inter-
vening position is reduced by ~50%, and thus
the overheating risk is minimized; (ii) the
printing resolution and speed can be improved,
owing to better sonothermal confinement
within the overlapped foci. Indeed, the axial
printing resolution was improved to 0.7 mm,
and the printing speed reached 8 mm s−1 (fig.
S42). Accordingly, complex models, including
a leaf-shaped structure (55 mm by 35 mm) and
a vessel-like network (75 mm by 25 mm), were
successfully printed using the confocal-DAVP,
taking only 20 and 83 s, respectively (fig. S43,
table S8, and movie S14).
Conclusions
Leveraging the deep-penetration capability of
FUS waves, low acoustic streaming, and rapid
sonopolymerization of the viscoelastic self-
enhancing sono-inks, we have developed a
DAVP technique that can volumetrically build
constructs with high printing fidelity and
resolution in the absence of a build platform.
The use of a thermally responsive adaptive
acoustic absorber resolves the conflict be-
tween acoustic streaming and deep penetra-
tion upon FUS exposure. The self-enhancing
sono-ink and nonlinear acoustic propaga-
tion collectively enhanced the sonothermal
heating at the FUS focus for fast and se-
lective material solidification as the building
voxel. The heat accumulation–based curing
mechanism resulted in anisotropic printing
resolution at a millimeter scale, which may
be further improved by optimizing printing
parameters of FUS frequency and scanning
speed and by using the confocal dual-transducer
configuration. The deep penetration of FUS
waves allows the volumetric fabrication of
opaque (nano)composites and printing through
centimeter-thick tissues that are not attain-
able through state-of-the-art light-based print-
ing techniques (table S9). The self-enhancing
sono-ink design can be generalized for differ-
ent systems, greatly expanding the materials
library for acoustic printing techniques.
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AC KNOWLED GME NTS
This work was performed in part at the Center for Nanoscale
Systems (CNS) at Harvard University, a member of the National
Nanotechnology Infrastructure Network (NNIN), which is supported
by the National Science Foundation under award number
ECS0335765. We also thank D. A. Weitz from Harvard University
for rheometer access, and P. Zhong from the Department of
Mechanical Engineering and Materials Science at Duke University
for assistance with acoustic cavitation mapping. Funding: This
work is supported by the National Institutes of Health
(R21EB025270, R01HL153857, R01HL165176, R01HL166522, and
R01CA282451), the National Science Foundation (CBET-EBMS-
1936105), and the Brigham Research Institute, all to Y.S.Z.;
National Institutes of Health (NIH) [R21EB027981, R21EB027304,
RF1NS115581 (BRAIN Initiative), R01NS111039, R01EB028143,
R21EB027981, and R01EB031629], National Science Foundation
Kuang et al., Science 382, 1148–1155 (2023)
8 December 2023
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RES EARCH | R E S E A R C H A R T I C L E
CAREER award 2144788, and Chan Zuckerberg Initiative Grant
2020-226178, all to J.Y. M.O.A. acknowledges funding support from
the TÜBİTAK 2214-A Program (1059B141801395). Author
contributions: X.K., J.Y., and Y.S.Z. conceived of the idea. X.K.
designed the materials and methods. Q.R., S.B., X.K., M.C.,
T.V., and C.E.G.-M. designed the printer setup. X.K., A.M.L.L., and
M.O.A. prepared the materials and conducted material
characterizations. Q.R., S.B., T.V., N.W., and X.K. performed the
printing and acoustic characterizations. Q.R. and X.K. developed
the numerical models and conducted the simulations. X.K., Q.R., S.B.,
T.V., N.W., and C.E.G.-M. analyzed the results and processed
visualizations. X.K., J.Y., and Y.S.Z. wrote the manuscript, with input
from all authors. Y.S.Z. and J.Y. supervised the study. Competing
interests: Y.S.Z. consults for Allevi by 3D Systems and sits on the
scientific advisory board and holds options of Xellar, neither of which,
however, participated in or biased this work. Data and materials
availability: All data needed to evaluate the conclusions in the
study are present in the paper and/or the supplementary materials.
G-codes for printing and simulation codes for diffusion analysis are
provided on Zenodo (45). License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original US
government works. https://www.science.org/about/science-licenses-
journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi1563
Materials and Methods
Supplementary Text
Figs. S1 to S43
Tables S1 to S9
References (46–81)
MDAR Reproducibility Checklist
Movies S1 to S14
Submitted 6 April 2023; accepted 13 October 2023
10.1126/science.adi1563
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RES EARCH
QUANTUM SIMULATION
Direct observation of nonlocal fermion pairing in an
attractive Fermi-Hubbard gas
Thomas Hartke*, Botond Oreg, Carter Turnbaugh, Ningyuan Jia, Martin Zwierlein
The Hubbard model of attractively interacting fermions provides a paradigmatic setting for fermion
pairing. It features a crossover between Bose-Einstein condensation of tightly bound pairs and
Bardeen-Cooper-Schrieffer superfluidity of long-range Cooper pairs, and a “pseudo-gap” region where
pairs form above the superfluid critical temperature. We directly observe the nonlocal nature of
fermion pairing in a Hubbard lattice gas, using spin- and density-resolved imaging of ~1000 fermionic
potassium-40 atoms under a bilayer microscope. Complete fermion pairing is revealed by the vanishing
of global spin fluctuations with increasing attraction. In the strongly correlated regime, the fermion
pair size is found to be on the order of the average interparticle spacing. Our study informs theories of
pseudo-gap behavior in strongly correlated fermion systems.
L ong-range Cooper pairs form in a Fermi
gas for even the weakest attraction be-
tween fermions. With increasing inter-
action, fermion pairs become more tightly
bound, as the system undergoes a smooth
crossover from Bardeen-Cooper-Schrieffer (BCS)
superfluidity toward a Bose-Einstein conden-
sate (BEC) of molecular pairs (1–3). In the BCS
limit, pair formation and the onset of super-
fluidity occur at the same temperature, but in
the crossover, pairs are expected to form at
temperatures above the critical temperature
Tc for superfluidity; the onset pair-formation
temperature is usually called T (cid:1) . In this so-
called “pseudo-gap” regime, the pair size should
be on the order of the interparticle spacing and
pairing strongly affected by many-body effects
(4, 5). The character of this strongly correlated
regime, situated between a Fermi liquid and
a normal Bose liquid, is a matter of debate,
whose resolution should affect understanding
of other strongly coupled fermion systems,
such as the high-Tc cuprates and twisted bi-
layer graphene (6–8). The rich physics of the
BEC-BCS crossover is captured by the attractive
Fermi-Hubbard model, a spin-1/2 gas of fer-
mions hopping on a lattice with on-site inter-
actions between unlike spins (9–17). Through
a particle-hole transformation, it stands in
one-to-one correspondence with the repulsive
Hubbard model (18, 19), which under charge
doping is believed to hold the key toward un-
derstanding high-temperature superconduc-
tivity. The model can be realized using neutral
fermionic atoms in optical lattices with tun-
able interactions. Recent investigations have
found spectral gaps (20), correlations between
local pairs (21), and evidence for interspin cor-
relations from density profiles (22).
In this work, we observe the formation and
spatial ordering of nonlocal fermion pairs in the
pseudo-gap regime of an attractive Hubbard
gas confined to two dimensions. We use bilayer
quantum gas microscopy to detect the in situ
location and spin of each fermion in every exper-
imental shot (23–25). Access to microscopic spin
and density correlations reveals the formation
of nonlocal pairs, the development of long-
range spatial correlations between pairs, and
the interplay of pair fluctuations with this
density-wave order.
Department of Physics, MIT–Harvard Center for Ultracold
Atoms, and Research Laboratory of Electronics, MIT,
Cambridge, MA 02139, USA
*Corresponding author. Email: hartke@mit.edu
Fig. 1. Atom-resolved detection of an attractive
Fermi-Hubbard gas. (A) Qualitative phase diagram
of the attractive Fermi-Hubbard model versus
on-site attraction U=t and temperature T=t at
density n≈0:8 (9–13). Below a critical temperature
Tc, attractive fermions form a BCS or BEC
superfluid (SF). In the pseudo-gap regime between
Tc and pairing temperature T(cid:1), accessed in this
work (white shading), increasing attraction
drives pair formation, with pairs exhibiting charge
density wave (CDW) and superfluid correlations.
(B) Measured doublon density d (circles) at
fixed density n versus U=t, from the noninteracting
limit d ¼ ðn=2Þ2 (triangles) to the fully paired
limit d ¼ n=2 (squares), with representative
images of the full density in ~20 × 20 site regions
shown above. (C) Snapshot of full spin-and-
density readout of a strongly correlated gas at
U=t ¼ 8:4 4ð Þ and T=t ¼ 0:36 5ð Þ. The spin up
(blue), spin down (red), and combined images
(rightmost panel) are obtained via bilayer quantum
gas microscopy (23, 25).
Hartke et al., Science 381, 82–86 (2023)
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Simulating the attractive Fermi-Hubbard model
The phase diagram of the attractive Fermi-
Hubbard model is shown in Fig. 1A as a func-
tion of the attractive on-site interaction strength
U , tunneling amplitude t, and temperature
T (9–13). For weak attraction U ≪ t, a BCS
superfluid of long-range fermion pairs forms
with Tc ¼ T (cid:1) , reflecting the exponentially
weak pair binding. In the opposite limit of
strong attraction U ≫ t, all fermions are bound
into local on-site pairs below a dissociation
temperature T (cid:1) ∼ U . These pairs condense
at the critical temperature of Bose-Einstein
condensation Tc, proportional to the pair
density np and pair tunneling rate tp ∼ t2=U.
A peak of the condensation temperature
Tc=t ≈ 0:2 is expected to occur at U =t ≈ 6 and
density n ≈ 0:8 (9–13). Above the transition
temperature, superfluid correlations compete
with the formation of a checkerboard charge
density wave (CDW) (21). At half-filling (den-
sity n ¼ 1), this competition persists down
to T ¼ 0 and prevents condensation. In this
work we use a filling n ≈ 0:8, staying in a
regime where the ground state is a paired
superfluid (9, 15).
We here experimentally realize the attractive
Fermi-Hubbard model using a two-species gas
of degenerate fermionic 40 K atoms trapped
within an optical lattice (23, 25). The Hubbard
tunneling amplitude t is controlled by the
lattice depth, and the interaction strength U is
tuned via the magnetic field. A bilayer quan-
tum gas microscope reveals the location of each
fermion.
As a first measure of strong pairing in the
attractive Hubbard gas, we detect the density
d of doublons (doubly occupied lattice sites) for
increasing interaction strength U =t across the
phase diagram in Fig. 1A. At fixed density n, d
increases from the noninteracting limit d ¼
ðn=2Þ2 of random encounters of unlike spins to
the fully paired limit d ¼ n=2 (Fig. 1B) (17). At
intermediate attraction, strong checkerboard
ordering of doublons is observed, shown in
Fig. 1C at U =t ¼ 8:4 4ð Þ and T =t ¼ 0:36 5ð Þ.
Multiple neighboring sites containing a sin-
gle spin up and spin down are present among
doublons in Fig. 1C. These correlated pairs of
single spins are evidence of the nonlocal na-
ture of fermion pairs. The microscopic mech-
anism is the virtual dissociation of a doublon
into spatially separate pairing partners, with
matrix element t and intermediate energy cost
U, which perturbatively lowers the energy of
a pair by 4t2=U. Because pairs are composed
of fermions, dissociation can only occur if a
nearby site does not already contain a like spin.
This leads to effective nearest-neighbor repul-
sive interactions between pairs (23), which
in turn are the source of long-range CDW order.
The presence of these delocalized pairs also
demonstrates that the doublon density d is an
incomplete measure of pairing.
Fig. 2. Observation of nonlocal fermion pairing. (A) Experimental snapshots of the Fermi gas at U=t ¼ 0,
U=t ¼ 5:8 3ð Þ, and U=t ¼ 8:4 4ð Þ (left to right), showing the formation of nonlocal pairs and on-site pairs with
increasing attraction. Schematics above highlight the physics dominating spin correlations in each image,
and shaded bonds suggest possible pair correlations. (B) Correlation maps h ^mi
^miþdi
m ¼ n↑ (cid:3) n↓ at various U=t. (C) Total magnetization fluctuations
^miþdi
c of the magnetization
c (blue circles) and on-site
h ^mi
X
→
d
fluctuations (black squares) versus U=t. Total fluctuations equal the product of magnetic susceptibility c
temperature T via the fluctuation-dissipation theorem (23). Vanishing total spin fluctuations for U=t ≥ 6
(orange shading) indicate full pairing and vanishing c
of total fluctuations at n ¼ 0:85, from T=t ¼ 0:3 to T=t ¼ 0:4 (23). The pairing temperature T(cid:1) crosses
T ≈ 0:35t at U=t ≈ 2:5. Nonlocal pairing is reflected in the singlon fraction per total density s=n (upper inset),
which scales as ~8t2=U2 (gray line) at large attraction. Fluctuations at U=t ¼ 5:8 3ð Þ (lower inset) extend
beyond the interparticle spacing 1=
bootstrapping greater than 50 images of atomic clouds with imaging loss correction (23).
m. Blue shading shows quantum Monte Carlo simulations
(dotted line). All data and error bars are obtained from
m and
ffiffiffiffiffiffiffi
pn↑
p
Detecting fermion pairing
A true signature of pairing that accounts for
these nonlocal pairs is the vanishing of total
spin fluctuations. Indeed, a system in contact
with a surrounding particle bath will generally
display fluctuations of the total magnetiza-
tion M ¼
X
i
h ^mii, where the magnetization
m ¼ n↑ (cid:3) n↓. However, pair formation sup-
presses spin fluctuations, as pairs do not
contribute to M, and thus in a fully paired
system the variance s2
M vanishes. This variance
Hartke et al., Science 381, 82–86 (2023)
7 July 2023
2 of 5
RES EARCH | R E S E A R C H A R T I C L E
^niþdi
c reflect the crossover from
Fig. 3. Charge density wave ordering of pairs. (A) Density correlations h^ni
a noninteracting gas (left), to a fully paired gas with CDW order (center), to a weakly ordered gas of
ð(cid:3)1Þdxþdy are well
local pairs (right). (B) At U=t ¼ 8:4 4ð Þ, the nonlocal rectified correlations h^ni
p
ffiffiffiffiffiffiffi
described by long-range exponential decay. Dotted line shows the interparticle spacing 1=
pn↑
density response c
n (red circles) and interspin response c↑↓ (blue squares) at wave vector k
order parameters for CDW correlations. These susceptibilities are obtained via the fluctuation-dissipation
(cid:3)
theorem c
ccos k
→(cid:3) (cid:4)
n k
at U=t ¼ 0 (black) and U=t ¼ 8:4 4ð Þ (red). (D) Fluctuation thermometry: The measured
(cid:3)
ccos k
→
versus k
→(cid:3) (cid:4)
n k
h^ni↑^niþd↓i
and c↑↓ k
. (C) The
^niþdi
c
¼ 1=Tð
¼ 1=Tð
Þ serve as
(23). Inset:
¼ p; pð
^niþdi
→(cid:3) (cid:4)
→
(cid:4) d
→
(cid:4) d
h^ni
X
X
(cid:4)
(cid:4)
c
→
d
→
d
Þ
Þ
→
→
→
h^ni
^niþdi
c (top) and uniform compressibility @n=@m ¼ c
(cid:3)
→
n k
(cid:4)
Þ
¼ 0; 0ð
(middle)
X
density fluctuations
→
d
are combined to directly obtain the temperature T=t (bottom).
is measured locally in our quantum gas mi-
croscope through the sum of connected cor-
relations s2
c, where
h ^mi ^miþdi
h ^mi ^miþdi
M = Area
ð
→
d
¼ h ^mi ^miþdi (cid:3) h ^miih ^miþdi.
Þ ¼
X
c
The magnetization fluctuations are directly
connected to the magnetic susceptibility cm ¼
@m=@h, the response of the magnetization to a
global magnetic field h, through the fluctuation-
c (23).
dissipation theorem cmT ¼
h ^mi ^miþdi
X
→
d
An energy gap for spin excitations, which ex-
ponentially suppresses excess spins and thus
X
c, also exponentially suppresses
h ^mi ^miþdi
→
d
cm (26).
Figure 2 reports a crossover to full fermion
pairing beyond an interaction strength U =t ≈ 6
at n ¼ 0:8 1ð Þ and T =t ¼ 0:35 5ð Þ, determined
by in situ observation of magnetization fluc-
tuations. The reduction in fluctuations is in
good agreement with theoretical predictions
for these parameters (12–14). Figure 2A high-
lights the physical mechanisms that determine
spin fluctuations at various U =t . At vanishing
interactions, Pauli exclusion separately reduces
the density fluctuations of each spin, and there-
Hartke et al., Science 381, 82–86 (2023)
7 July 2023
by also reduces total spin fluctuations. With
increasing attraction, nonlocal pairs form in
which spins are subject to a competition of
Pauli exclusion and attraction, while deep in
the on-site pair regime spin fluctuations reflect
virtual hopping onto neighboring sites. From
statistical averages over more than 50 spin
configurations, as shown in Fig. 2A for each in-
teraction strength, we obtain the two-dimensional
(2D) magnetization correlation maps h ^mi ^miþdi
c,
shown in Fig. 2B. To detect pairing, Fig. 2C
presents the sum of these correlation maps, the
total magnetization fluctuations, which are
fully suppressed beyond U =t≈6. Already at
zero interactions, Pauli exclusion reduces total
fluctuations by 68 5ð Þ% compared to the high-
temperature expectation n 1 (cid:3) n=2
Þ. This re-
flects the substantial degeneracy of the Fermi
gas (T =TF ≈ 0:1, where TF is the Fermi tem-
perature). Increasing attraction reduces mag-
netization fluctuations further, and the fraction
of unpaired spins is less than 1:5 1:8ð
Þ% at
X
U =t ¼ 5:8 3ð Þ, where
c gives the
h ^mi ^miþdi
→
d
density of unpaired spins. This full suppression
is dual to the formation of a Mott insulator for
repulsive interactions (18, 19, 23, 25).
ð
The suppression of fluctuations in Fig. 2C
with increasing U =t signifies the development
of an energy gap for spin excitations (26). The-
ory predicts (10–14, 27, 28) a pairing tem-
perature T (cid:1) ≈ 0:25U in the crossover regime
(23). This predicted T (cid:1) crosses T ≈ 0:35t near
U =t ≈ 2:5, explaining the near-complete sup-
pression of fluctuations beyond U =t ≈ 6. The
corresponding expected spin excitation gap
far exceeds the two-body binding energy Eb,
highlighting the many-body nature of pairing.
Within this regime of full pairing, the two
atoms within a pair have a finite probability
of being located on separate lattice sites be-
cause of quantum fluctuations, in which case
they appear as isolated single atoms (called
singlons). This probability is measured by the
ratio of the singlon density to the total density,
s=n (Fig. 2C, upper inset). The observed scaling
of s=n with t2=U 2 at strong attraction is ex-
pected from perturbation theory already for
a Fermi-Hubbard double well (25, 29). At
U =t ¼ 5:8 3ð Þ, the nonlocal portion of the pairs
amounts to ~20%. The effective size of fermion
pairs can be obtained as the spatial extent of
nonlocal spin fluctuations. With full pairing at
U =t ¼ 5:8 3ð Þ, spin fluctuations are present be-
yond the single-spin interparticle spacing (Fig.
2C, lower inset), indicating that fermion pairs
overlap substantially.
Measuring charge correlations
Characteristic for the pseudo-gap regime is a
predicted strong departure from Fermi liquid
behavior, in which spin and charge fluctua-
tions are similar (4, 5). Having established the
existence of nonlocal fermion pairs through
vanishing magnetization fluctuation, we there-
fore now explore charge (i.e., density) correla-
tions of the gas. Whereas for weak interactions
charge and spin correlations are closely asso-
ciated, for stronger attraction we instead find
spatial ordering into a CDW across the phase
diagram of Fig. 1A. Previously, evidence for
CDW order has only been observed in doublon-
doublon correlations and at a fixed interaction
strength (21). In Fig. 3A, beginning without
interactions, we observe negative nonlocal den-
sity correlations h^ni ^niþdi
c for nearest-neighbor
and diagonal correlations. These correlations
are a simple and direct manifestation of the
Pauli hole experienced by a single spin (25, 30).
Indeed, here h^ni ^niþdi
c is precisely equal to
h^ni↑ ^nj↑i
c + h^ni↓ ^nj↓i
c because the measured in-
terspin correlations h^ni↑ ^nj↓i
c vanish (23). For
increasing attraction, the Pauli hole gives way
to the positive checkerboard long-range density
correlations, shown versus distance in Fig. 3B
at U =t ¼ 8:4 4ð Þ. Further increase in U =t re-
duces the observed CDW strength, likely as a
result of smaller effective repulsion between
more-localized pairs (Fig. 2B). Notably, we
measure a negative sum of nonlocal inter-
spin correlations h^ni↑^niþd↓i
c for any attractive
3 of 5
RES EARCH | R E S E A R C H A R T I C L E
A
Pair Fluctuation
Tunneling
Superfluid
Charge-Density
Wave
_ _
Flipped
SF Phase
Reduced
CDW Strength
B
Bare Correlations
vs
Conditioned
on Singlon or
C
=
D
(cid:4)
D
E
(cid:3)
^
di (cid:3) ^
hi
the CDW strength, defined as
Fig. 4. Interplay of nonlocal pairs and many-body order. (A) When local pairs in a strongly correlated
attractive system virtually fluctuate into spatially separated single spins, further tunneling can disturb the
underlying many-body ordered state. (B) Polaronic correlations are observed by measuring disturbances of
(cid:4)
ð(cid:3)1Þdxþdy, in the vicinity of a single spin. Whereas a
(cid:3)
diþd (cid:3) ^
^
peak in the background CDW strength is observed near U=t ≈ 8 for various displacements d
a strong reduction in CDW strength is observed after conditioning on the presence of a nearby isolated spin
(right panel). Right inset shows the relative location of the single spin (purple circle) and CDW bond. (C) The
relative change in CDW strength DCDW reveals the spatial extent of polaronic correlations at U=t ¼ 8:4 4ð Þ.
(cid:6)
→(cid:6)
(cid:6)r
(cid:6) from the singlon to the CDW bond. The shaded region represents the extent of
DCDW decays with distance
the disturbance to the background order. (D) A symmetrized 2D map of (C), with lattice sites represented by
black dots and the isolated spin at center. In the CDW strength,
^
^
hi) denotes a doublon (hole, or empty site).
di (
(left panel),
hiþd
→
c
interaction (23), revealing that a single ↑ atom
in total repels spin ↓ atoms on all other sites.
This constitutes a strong direct signature of
effective repulsion between pairs.
¼ p; pð
The development and destruction of CDW or-
der across the phase diagram of Fig. 1 can be cap-
tured by the density response cn at wave vector
→
k
Þ (Fig. 3C), which reflects the preva-
lence of low-energy states with checkerboard
order. Highlighting the power of quantum gas
microscopy, this thermodynamic property can be
Hartke et al., Science 381, 82–86 (2023)
7 July 2023
measured in equilibrium using the fluctuation-
dissipation theorem for density perturbations,
cn k
, and
h^ni ^niþdi
(cid:3)
ccos k
¼ 1=Tð
(cid:3) (cid:4)
→
→
(cid:4) d
X
(cid:4)
Þ
→
→
d
→
(cid:4)
Þ
¼ 0; 0ð
(cid:3)
the measured uniform density compressibility
cn k
¼ @n=@m (Fig. 3D) (25). This
(cid:3) (cid:4)
→
same method allows measurement of cn k
throughout the Brillouin zone (Fig. 3C, inset)
and provides a model-independent measure-
ment of temperatureT (Fig. 3D) (25, 31). The latter
enables obtaining the magnetic susceptibility
→
→
(cid:4) d
c
m from the measured spin fluctuations with-
out applying a magnetic field (23, 32). As ex-
pected from the phase diagram in Fig. 1, the
peak in CDW order occurs near U =t ≈ 6. Also
displayed are the interspin correlations, obtained
(cid:4)
X
from c↑↓ k
Þ
.
h^ni↑ ^niþd↓i
(cid:3)
ccos k
¼ 1=Tð
(cid:3) (cid:4)
→
→
d
Although opposite spins are uncorrelated at
U =t ¼ 0, they are seen to almost fully carry the
CDW order beyond U =t ≈ 6. Because density,
magnetization, and interspin correlations are re-
¼ 4h^ni↑ ^niþd↓i
(cid:3) h ^mi ^miþdi
lated byh^ni ^niþdi
c,
the relative agreement of cn and c↑↓ illustrates
the strength of density order as compared to
→
Þ. The pronounced
¼ p; pð
magnetic order at k
CDW peak is also a signature of strong super-
fluid correlations within the crossover regime,
as CDW correlations away from half-filling
serve as a lower bound for superfluid correla-
tions (21, 33).
c
c
Polaronic correlations
Given simultaneous charge and spin measure-
ments, we finally explore the interplay of non-
local pair fluctuations and the CDW order of
other pairs, revealing the existence of polar-
onic correlations in the CDW order of the
attractive Hubbard model. Polaronic corre-
lations occur in the regime of highly nonlocal
pairs, where further tunneling of a separated
pair can dislocate the CDW checkerboard or
flip the sign of superfluid correlations (Fig. 4A).
These tunneling events prevent the virtual
delocalization of other pairs across the bonds
where the order has been reversed, costing
an additional 4t2=U per bond in the strong-
coupling limit and further confining spatially
separated pairs (34). This mechanism is di-
rectly complementary (18, 19, 23) to the mag-
netic polaron mechanism of the repulsive
Fermi-Hubbard model (35, 36), though here
polaronic correlations dress the individual
spins of a spatially separated fermion pair,
rather than excess dopants.
In Fig. 4B, we compare the CDW correlations
surrounding single spins to those present in the
background. We quantify the underlying CDW
strength as hð^d i (cid:3) ^hiÞð^d iþd (cid:3) ^hiþdÞi
ð(cid:3)1Þdxþdy
c
→
for a given displacement d
, which is positive for
→
any d
for a gas possessing checkerboard doublon-
hole correlations. This underlying CDW strength
peaks near an interaction strength U =t ≈ 8. By
contrast, for various U =t values, the measured
CDW strength is strongly reduced after con-
ditioning on the presence of a single nearby
isolated spin. This reduction substantially ex-
ceeds the lowest-order expectation of single-
pair fluctuation events depicted in Fig. 4A, e.g.,
→
Þ and 50% for
25% for a displacement d
→
Þ. The measurements directly
Þ or 2; 0ð
d
reveal the spatial extent of these polaronic effects,
captured by the relative change DCDW
of
conditioned to unconditioned CDW strength
(Fig. 4, C and D). Virtual pair fluctuations disturb
ð
¼ 0; 1
ð
¼ 1; 1
r→(cid:6)
(cid:6)
(cid:6)
(cid:7)
(cid:6)
(cid:5)
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RES EARCH | R E S E A R C H A R T I C L E
the CDW order over a range of ∼2 sites at U =t ¼
8:4 4ð Þ, with complete reduction or even re-
versal of the CDW order on nearby bonds. In
future work, measurements of four-point cor-
relations (36) around pairs of spins will further
elucidate the internal structure of these quan-
tum fluctuations.
Conclusions
Our real-space observations of nonlocal fermion
pairing and its interplay with CDW order il-
lustrate the richness of the pseudo-gap regime
of the attractive Hubbard model. Similar com-
peting or intertwined orders are predicted for
the repulsive Hubbard model. The methods
can be extended further to study polaronic
physics and superfluidity (37), pairing in mo-
mentum space as measured in bulk 2D gases
(38), to detect the p phase shift of CDW order
across stripes (39), and to directly measure the
BCS condensate fraction through pair correla-
tions (40).
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AC KNOWLED GME NTS
Funding: This work was supported by the NSF through the Center
for Ultracold Atoms and grant PHY-2012110, AFOSR (grant
no. FA9550-16-1-0324 and MURI on molecules no. 2GG016303 PO
No15323), and the Vannevar Bush Faculty Fellowship (ONR
no. N00014-19-1-2631). Authors contributions: The experiment
was designed by all authors. T.H., B.O., C.T., and N.J. collected and
analyzed the data. All authors contributed to the manuscript.
Competing interests: The authors declare no competing financial
interests. Data and materials availability: The data and code
for this manuscript are available on Dataverse (41). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
sciencemag.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.ade4245
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resonant electric dipole-dipole coupling for
coherent exchange of rotational angular mo-
mentum between pairs of laser-cooled CaF
molecules individually trapped in optical twee-
zers. With the ability to tune the angle of the
molecular quantization axis in the lab frame,
our system realizes both ferromagnetic and
antiferromagnetic couplings in a quantum XY
spin-exchange model by effectively encoding a
spin-1
2 system into molecular rotational states.
Using this spin-exchange Hamiltonian, we per-
formed iSWAP two-qubit gate operations. An
iSWAP gate, when sequentially combined with
single-qubit operations, can generate bipartite
entanglement deterministically and form a
universal set of quantum gates, which is the
essential resource for all quantum information
applications (12, 43). We found that the fidelity
of generated Bell states is presently limited by
the thermal motion of molecules within the
tweezer traps. Finally, we demonstrate the use
of an interleaved dual tweezer-array system,
which allows for robust single-site address-
ability and fast gate operations between mo-
lecules. This, combined with expected improved
molecular cooling (44), has the potential to
greatly increase the fidelity of two-qubit ope-
rations in this system. This work is parallel and
concurrent with that of another study (45).
Initial-state preparation of CaF molecules in a
1D optical tweezer array
We began the experiment by loading CaF mol-
ecules from a cryogenic buffer gas beam source
(46) into a radio-frequency magneto-optical
trap (14). Next, we loaded the molecules into a
1D optical lattice using L-enhanced gray molasses
D
RES EARCH
R E S E A R C H A R T I C L E
◥
QUANTUM INFORMATION
Dipolar spin-exchange and entanglement between
molecules in an optical tweezer array
Yicheng Bao1,2*, Scarlett S. Yu1,2, Loïc Anderegg1,2, Eunmi Chae3, Wolfgang Ketterle2,4,
Kang-Kuen Ni1,2,5, John M. Doyle1,2
Ultracold polar molecules are promising candidate qubits for quantum computing and quantum simulations.
Their long-lived molecular rotational states form robust qubits, and the long-range dipolar interaction
between molecules provides quantum entanglement. In this work, we demonstrate dipolar spin-exchange
interactions between single calcium monofluoride (CaF) molecules trapped in an optical tweezer array. We
realized the spin-1
2 system into the rotational states of
the molecules and used it to generate a Bell state through an iSWAP operation. Conditioned on the verified
existence of molecules in both tweezers at the end of the measurement, we obtained a Bell state fidelity
of 0.89(6). Using interleaved tweezer arrays, we demonstrate single-site molecular addressability.
2 quantum XY model by encoding an effective spin-1
(28, 31, 39, 40). In this work, we report the
entanglement of pairs of molecules—the crit-
ical ingredient in quantum computing and
simulation based on molecules—by leverag-
ing long molecular coherence and intrinsic
dipolar interactions with individual parti-
cle addressability.
A key step toward using ultracold polar mol-
ecules for quantum simulations and multi-
particle quantum gates is the generation of
coherent dipole-dipole couplings between
molecules (12, 41), which has been shown in
sparsely filled three-dimensional (3D) lattices
(27) and 2D layers (42) and in a molecular
quantum gas microscope (33). Here, we used
A
B
C
Q uantum entanglement is one of the key
ingredients that fundamentally distin-
guishes quantum mechanics from clas-
sical mechanics (1). It is considered an
essential resource for quantum informa-
tion processing but remains generally challeng-
ing to create experimentally. One mechanism
of realizing quantum entanglement between
particles is using the electric dipole-dipole
interaction, as demonstrated in systems such
as Rydberg atoms (2) and silicon quantum
dots (3). Polar molecules possess permanent,
long-range, and spatially anisotropic electric
dipoles whose interaction could be harnessed
for high-fidelity entanglement generation. There-
fore, they have been proposed as a powerful
platform for realizing quantum simulations
of strongly interacting many-body dynamics
(4–7) and for scalable quantum computing
(8–12). Ultracold molecules can be produced
through either direct laser cooling (13–17),
assembly of individual ultracold atoms (18–24),
or optoelectrical Sisyphus cooling (25, 26). Cur-
rent experimental progress has established the
capability of preparing and manipulating ultra-
cold molecules with high fidelity (27–33). In
particular, rearrangeable tweezer arrays offer
an attractive quantum platform owing to their
scalability and potential for single-site address-
ability (24, 34–38). Toward this aim, molecules
have been demonstrated to have long qubit
(rotational and hyperfine state) coherence
times, which are substantially longer than the
predicted molecule-molecule dipolar gate times
1Department of Physics, Harvard University, Cambridge, MA
02138, USA. 2Harvard-MIT Center for Ultracold Atoms,
Cambridge, MA 02138, USA. 3Department of Physics, Korea
University, Seongbuk-gu, Seoul 02841, South Korea.
4Department of Physics, Massachusetts Institute of
Technology, Cambridge, MA 02139, USA. 5Department of
Chemistry and Chemical Biology, Harvard University,
Cambridge, MA 02138, USA.
*Corresponding author. Email: bao@g.harvard.edu
Fig. 1. Experimental setup and relevant energy levels. (A) The image of averaged fluorescence from a
20-site optical tweezer array of CaF molecules. (B) An illustration of the optical tweezers and the coordinate
system used in this work. For visual clarity, only four sites of the realized 20-site array are depicted.
→
(C) An illustration showing the relative angle between the applied bias magnetic field B
→
and the intermolecular vector r
hyperfine (F) states in the ground electronic state of CaF.
. The tweezer light propagates along Z. (D) Relevant rotational (N) and
(in the XY plane)
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RES EARCH | R E S E A R C H A R T I C L E
cooling on the electronic X 2Sþ–A2P1=2 tran-
sition (47, 48) and optically transported them
into a glass cell using a focus-tunable moving
lattice, as characterized previously (49).
We used a microscope objective with 0.6 nu-
merical aperture to project a 1D optical tweezer
array in the glass cell, as well as collect fluo-
rescence from the molecules during L-imaging
(47). The array is formed by passing single-
frequency 776-nm laser light through a shear-
mode acousto-optic deflector (AOD) driven with
a multitone waveform (37), which is generated
by a high-speed arbitrary waveform generator
(AWG). This allows for control of the position
of individual optical tweezer sites as well as trap
depth. We started with a 20-site array formed by
a single AOD (Fig. 1A).
We loaded the molecules into the tweezers
by overlapping the array with a transported mol-
ecular cloud that is held in an optical dipole trap
in the presence of the L-cooling light. We ob-
served an average probability of 35% for loading
a single site with a single molecule. After loading
the array, we applied a L-imaging pulse and
collected fluorescence onto a camera to identify
the tweezer sites that are loaded with single
molecules in the ground electronic and vibra-
tional state (or empty) with a detection fidelity
of 98(1)% and nondestructive detection fidelity
of 94(1)% (37, 47). Because the L-cooling tech-
nique relies on closed photon cycling between
the X, N = 1 and A, J = 1/2 manifolds (N is the
rotational angular momentum, and J is the
total angular momentum, excluding nuclear
spin), only molecules in the X, N = 1 rotational
manifold can be loaded into the tweezers and
detected in this phase of the experiment.
Imaging distributes the population of mol-
ecules over all 12 hyperfine states. To prepare
the molecules in a single quantum state, we
used a combination of optical pumping and
microwave transfer. Using short X−A laser
pulses resonant with all hyperfine levels in
the X, v = 0, N = 1 manifold except the
X ; N ¼ 1; F ¼ 0; mF ¼ 0
i state (v is the vib-
j
rational quantum number; F is the total angu-
lar momentum, including nuclear spin; and
mF is the magnetic quantum number of F), we
pumped most of the molecular population
into the latter state. We then linearly ramped
down the trap depth of the tweezers in 5 ms
and applied a bias magnetic field of ≈3.2 G.
A subsequent microwave p-pulse transfers the
population from X ; N ¼ 1; F ¼ 0; mF ¼ 0
i to
the X ; N ¼ 0; F ¼ 1; mF ¼ 0
i state (Fig. 1B).
Finally, we applied an X−A laser pulse that
contains frequencies to drive all the hyperfine
components in order to remove any molec-
j
j
j
ular population left over in the X, N = 1 man-
ifold. In the end, all the remaining molecules
in the array were in the X ; N ¼ 0; F ¼ 1;
mF ¼ 0i state, initializing the qubits and ef-
fectively encoding a spin- 1
2 model in the sub-
space spanned by the X ; N ¼ 0; F ¼ 1; mF ¼
j
0i ≡ ↑j i and X ; N ¼ 0; F ¼ 1; mF ¼ 0
i ≡ ↓j i
states (Fig. 1B). The total state preparation
and detection efficiency is 60(2)%, which is
limited by the residual population in other
hyperfine states within X, N = 1 and imperfect
imaging fidelity. This state preparation effici-
ency can be improved by an optimized optical
pumping scheme (45).
j
Single-molecule rotational coherence time
To observe high-fidelity dipolar spin-exchange
interactions, a long rotational coherence time
comparable to the timescale of the dipolar
interaction is required. With a sample of mol-
ecules at finite temperature in optical tweezers,
it is important to control the differential ac
Stark shift broadening caused by the molecule’s
thermal motion in the tweezer trap (28, 50–52).
To suppress this broadening, the tweezer laser
is linearly polarized at a “magic” angle relative
to the quantization axis that is defined by the
applied bias magnetic field, as detailed previous-
ly (31) (Fig. 1A). To maximize the single-qubit
A
XY8 Block
X
π/2
X
π
Y
π
X
π
Y
π
Y
π
X
π
Y
π
X
π
X
π/2
B
0.4
)
.
u
.
a
(
t
s
a
r
t
n
o
C
0.3
0.2
0.1
0
0
D
80
60
40
20
)
z
H
(
h
/
J
0
1.5
Bare Ramsey
= 3.6(6) ms
C
Spin Echo
= 33(5) ms
C
XY8
C
= 630(90) ms
100
200
300
Time (ms)
400
500
600
2
Tweezer Spacing ( m)
2.5
C
n
o
i
t
c
a
r
F
n
o
i
t
c
a
r
F
n
o
i
t
c
a
r
F
n
o
i
t
c
a
r
F
0.4
0.2
0
0.4
0.2
0
0.4
0.2
0
0.4
0.2
0
0
R=1.5 m,
D
=35(10) ms, T=35(2) ms
R=1.75 m,
D
=75(17) ms, T=53(2) ms
R=2.0 m,
D
=96(21) ms, T=77(2) ms
R=2.25 m,
D
=159(29) ms, T=105(2) ms
50
100
150
200
250
Time (ms)
Fig. 2. Rotational coherence and dependence of dipolar interactions on
tweezer spacing. (A) The Ramsey sequence with XY8 dynamical decoupling
used in this work. Xp/2 represents a p
2-pulse, which rotates the quantum state
around the x axis of the Bloch sphere by 90°. Similarly, Xp (Yp) represents a 180°
rotation around the x axis (y axis) on the Bloch sphere. At the top, “×N” means that
the block of XY8 pulses is repeated multiple times during the evolution time.
(B) Measured single-molecule rotational coherence time between ↑j i (N = 1)
and ↓j i (N = 0) using Ramsey, single–p-pulse spin echo, and the XY8 dynamical
decoupling sequences. The coherence time is fitted as a Gaussian 1/e decay time
constant. (C) Dipolar spin-exchange oscillation at various tweezer spacings,
with fitted decay-time constant and oscillation period shown in the legends.
→j.
(D) Dipolar spin-exchange interaction strength J versus the tweezer spacing jR
The dashed orange line is the theoretical prediction of J at zero temperature.
The solid blue line is the simulated result of J with the thermal motion of the
molecules taken into account (59). In (B) and (C), error bars represent
one standard deviation of uncertainty.
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RES EARCH | R E S E A R C H A R T I C L E
n
o
i
t
c
a
r
F
0.5
0.4
0.3
0.2
0.1
0
0
= 54.7°
= 0°,
D
= 90°,
D
= 30(7) ms, T = 46(3) ms
= 96(21) ms, T = 77(2) ms
50
100
150
200
250
Time (ms)
Fig. 3. Dipolar spin-exchange interaction at different angles. Shown are the data for q = 0°, 54.7°, and
90°. The q = 0° and q = 90° data are fitted to an exponentially decaying sinusoidal model, with decay-time
constant tD and oscillation cycle time T shown in solid lines. Error bars represent one standard deviation of
uncertainty.
coherence time, it is beneficial to adiabatically
lower the trap depth as much as possible
without unduly spilling molecules from the trap.
However, this is not optimal for maximizing
the number of observed dipolar spin-exchange
oscillation cycles. At finite temperature, the
instantaneous dipolar interaction strength fluc-
tuates owing to thermal motion, which becomes
more prominent in a shallow trap. This is the
main mechanism of dephasing. To mitigate
this issue, we confined the molecules more
tightly by operating the tweezer at a higher trap
light intensity for which the magic angle is
close to 90°. The work described in this man-
uscript was performed under these conditions.
We measured the rotational qubit coherence
time under conditions of three different micro-
wave pulse sequences used to drive transitions
between ↑j i and ↓j i and observed the pop-
ulation in ↑j i. With a Ramsey sequence, we
observed a single-qubit coherence time of tc =
3.6(6) ms. By adding a single p spin-echo pulse,
tc is extended to 33(5) ms. We used active mag-
netic field cancellation to remove long-term
drift on the order of 10 mG, but the system
we used does not remove magnetic field fluc-
tuation within a power line cycle time of less
than 1/(60 Hz). This limits the effective interval
between spin-echo pulses to an integer multiple
of 60 Hz, making it difficult to measure fast
dipolar oscillations with only a single p-pulse.
Instead, we used dynamical decoupling schemes
to preserve the qubit coherence. This technique
is used in a variety of quantum information
systems (53, 54), including molecular systems
(27, 30, 45). We chose the XY8 dynamical de-
coupling sequence (Fig. 2A) with a cycle length
of 1.6 ms (55), which is much shorter than 1/
(60 Hz), and achieved a coherence time of tc =
630(90) ms. This dynamical decoupling was
used for all of our measurements except
where noted. Figure 2B shows the measured
contrast versus time for single-particle oscil-
lations between ↑j i and ↓j i, from which tc is
determined.
Coherent dipolar spin-exchange interaction
The dipolar spin-exchange interaction Hamiltonian
(41) is
(cid:1)
J
Hdip ¼
þ
þ
(cid:2)
(cid:2)^S
þ ^S
^S
^S
2
1
2
1
(cid:3)
x
y
y^S
x þ ^S
^S
2
1
2
1
(cid:1)
2
¼ J ^S
(cid:3)
ð1Þ
þ
(cid:2)
, ^Si
x, ^Si
where, respectively, ^Si
(^Si
y) is the spin- 1
2
raising (lowering, Pauli-X, Pauli-Y) operator
for molecule number i in a tweezer pair. J is
the dipolar interaction strength that can be
further expressed as
ð2Þ
J ¼
(cid:5)
(cid:4)
d2
4pD0r3 1 (cid:2) 3cos2q
where d is the transition dipole moment be-
tween the ↑j i and ↓j i state (d ≈ 1 Debye), D0 is
the vacuum permittivity, r is the intermolecular
spacing, and q is the angle between the quan-
tization axis and the intermolecular axis direc-
tion. Apart from molecular systems (27, 30, 33),
this XY spin Hamiltonian was previously stu-
died with Rydberg atoms in optical tweezers
(56) and atoms in optical lattices (57, 58).
We set the bias magnetic field perpendicu-
lar to both the k-vector of the tweezer light
and the direction of the 1D tweezer array. The
polarization of the linearly polarized tweezer
light is rotated to the tweezer array direction
(i.e., a magic angle close to 90°). This config-
uration provides the largest “magic trap depth”
(the tightest confinement) at a given magnetic
field.
We first prepared pairs of tweezers spaced
→j∼5 mm, with each site loaded with a
at jR
single molecule prepared in the ↓j i state (or
empty), yielding the ↓↓j
i state. At this sepa-
ration, the dipolar interaction strength J is
negligible (J/h < 3 Hz, where h is Planck’s
constant). In a time period of ~1 ms, we then
i
ð
ð
p
p
Þ=
Þ=
ffiffiffi
2
i þ ↑↓j
moved the even numbered sites toward the odd
numbered sites by sweeping the AOD frequency
tones of the even sites, which reduces the sep-
aration and has the effect of increasing the
dipolar interaction strength. We then applied a
p
2-pulse to prepare both molecules in the super-
position state ↑j i þ ↓j i
Þ=
. Then, we applied
XY8 dynamical decoupling sequence of micro-
wave pulses. Under the time evolution of dipolar
spin-exchange Hamiltonian (Hdip), a relative
p
ffiffiffi
phase accumulated between ↓↑j
2
ffiffiffi
and ↑↑j
ð
i þ ↓↓j
i
. (Because the XY8 se-
2
quence only contains p-pulses, it will not affect
the phase accumulation during the evolution
under Hdip.) After a wait time, we applied an-
other p
2-pulse and then moved the molecules
apart. To read out the final qubit state, we
used a second L-imaging pulse to project the
system to ↑↑j
i. We selected the data where
both sites in a tweezer pair are initially loaded
with single molecules. Our measurement
yielded the probability P↑↑ of detecting both
molecules in the ↑j i state. To summarize,
starting from the initial state ↓↓j
i, a microwave
pulse sequence creates a final state that evolves in
i
h
(cid:1)
(cid:1)
time as y tð Þ ¼ 1
1 þ e(cid:2)i Jt
1 (cid:2) e(cid:2)i Jt
↑↑j
i
,
2
resulting in the probability P↑↑ ¼ cos2 Jt
4ħ ¼
(cid:5)
(cid:4)
2 1 þ cos Jt
1
, which oscillates at an angular
2ħ
frequency of wJ ¼ J
2ħ , where ħ is reduced
Planck’s constant.
i (cid:2)
↓↓j
(cid:3)
(cid:3)
2ħ
2ħ
At smaller tweezer spacings, we observed
increased wJ because of the stronger dipolar
interaction between the two molecules (Fig. 2C).
By fitting the data to an exponentially decaying
sinusoidal model, we extracted the dipolar oscil-
lation cycle period T and contrast decay time
constant tD. The dipolar spin-exchange strength
J at different tweezer spacings can then be cal-
culated from T (Fig. 2D). We found that the
measured J is slightly smaller than the theo-
retical prediction and deviates more as the
spacing decreases. This can be explained by the
finite temperature of the molecules causing
(cid:7)
the effective intermolecular spacing r→(cid:7)
(cid:7) to be
→j. We used
larger than the tweezer spacing jR
Monte Carlo simulations to describe the behav-
ior of the molecules in the tweezer, including
the thermal motion of the molecules, and show
in Fig. 2D that the simulated results agree with
the experimental data. Additionally, the sim-
ulation captures that the thermal motion re-
duces the observed number of coherent dipolar
oscillations as tweezer spacing is decreased (59).
(cid:7)
Anisotropy of the dipolar interaction
The general dipole-dipole Hamiltonian described
in Eqs. 1 and 2 is inherently anisotropic owing to
the q-dependent term. We studied the effect of
the anisotropy of spin exchange experimentally
by varying the angle q and measuring the cor-
responding dipolar interaction strength. The
angle q is varied by rotating the quantization
axis relative to the line between the centers
of the tweezers. The quantization axis is set by
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RES EARCH | R E S E A R C H A R T I C L E
the applied bias magnetic field and can be
changed by tuning the current through two pairs
of magnetic field coils while simultaneously ro-
tating the tweezer light polarization to maintain
the same magic angle.
In Fig. 3, we show P↑↑ at three characteristic
angles q = 0°, 54.7°, and 90°, all taken with a
→j ¼ 2 mm tweezer spacing. We observed di-
jR
polar spin-exchange oscillations in both the
q = 0° and q = 90° configurations, with the oscil-
lation at q = 0° being at twice the frequency as
that at q = 90°. No clear oscillation is observed for
the q = 54.7° configuration, which was as ex-
pected because the dipolar interaction averages
to zero at this angle. These results agree with
the absolute value of the magnitude of the anis-
otropic term in each configuration. We also ob-
served a larger number of oscillation cycles at
q = 90° than at q = 0°. Our Monte Carlo sim-
ulation indicated that thermal motion dephas-
ing is the dominant cause. At q = 0°, the larger
motional wave function spread in the more-
weakly trapped axial direction of the optical
tweezers results in a large fluctuation of the
instantaneous value of q. The q = 90° config-
uration is less affected because of the tight
confinement of the optical tweezers in the ra-
dial direction.
Fidelity of created Bell states
Dipolar spin-exchange can be used in a two-
qubit iSWAP gate to generate entanglement
between molecules in neighboring tweezers
(12). At a dipolar spin-exchange interaction
time of t = T/4 = 19.2 ms, where T is the
oscillation period of the spin-exchange oscilla-
tion, the system has evolved into a maximally
entangled state known as a Bell state. To test
the fidelity of the Bell state that was generated
in our system, we applied a third p
2-pulse (see
Fig. 4 legend) around a variable rotation axis
on the Bloch sphere (angled f relative to the x
axis on the equatorial plane) (Fig. 4A). By vary-
ing f and measuring the survival probability of
all four possible final-state outcomes, one can
construct the parity quantity P (43, 60):
D
¼ ^S
(cid:8) (cid:9)
P ¼ ^P
E
z
z
^S
2
1
¼ P↑↑ þ P↓↓ (cid:2) P↑↓ (cid:2) P↓↑
ð3Þ
Here,hi denotes averaging over all occurrences
where both sites in a tweezer pair are initially
loaded with single molecules, and ^Si
represents
the Pauli-Z operator on the number i molecule
in a pair.
z
Starting from a Bell state, this sequence will
result in a 4p oscillation in P as f is varied
from 0 to 2p (61). In Fig. 4B, P is displayed
for both the q = 0° and q = 90° configu-
rations. Extracting the contrast of the oscil-
lation for the q = 90° case, we measured a Bell
state fidelity of F ¼ 0:32 2ð Þ and a state prep-
aration and measurement (SPAM)–corrected
fidelity of F SPAM ¼ 0:89 7ð Þ. The phase of the
parity oscillation reveals the sign of the aniso-
tropic term (1 – 3cos2q), also seen previously (45).
Our data show that the q = 0° configuration
leads to a negative J, which corresponds to a
ferromagnetic interaction, and the q = 90° con-
figuration leads to a positive J, which corre-
sponds to an antiferromagnetic interaction.
j
ð
F SPAM is measured to be significantly higher
than F, with imperfect state preparation and
detection being the surmised cause. In detail,
during initial-state preparation, molecules that
fail to be prepared in the desired N ¼ 0; F ¼ 1;
mF ¼ 0i ↓j i
Þ state are intentionally removed
by a resonant laser pulse, resulting in an empty
trap or traps. During the final readout, if the
molecule is in the ↓j i state or the trap is simply
empty, both would appear dark. We used a
p-pulse and additional imaging pulse (Fig. 4C)
to distinguish between these two cases. If the
molecule is in the ↓j i state, it will be trans-
ferred to the ↑j i state and detected, whereas an
empty trap will remain dark. This information
is used to exclude the cases of empty traps during
the final readout, which improves the contrast of
the parity oscillation (Fig. 4D). The resulting Bell
state fidelity corrected for measurement error
is determined to be F ex ¼ 0:89 6ð Þ, which is
higher than the threshold of F th ¼ 0:5 (60),
showing, under these conditions, the conditional
preparation of entanglement of two molecules in
a tweezer pair. The evolution of the system to
create a Bell state is an iSWAP operation, and,
although we have not fully characterized the
system as an iSWAP gate, the Bell state fidelity
indicates how it would perform.
XY8 Block
X
π/2
π/2 #2
X
π
#3
90° Parity, Empty Traps Excluded, A = 0.81(6)
A
B
X
π/2
1
0.5
0
-0.5
-1
y
t
i
r
a
P
XY8 Block
X
π/2
π/2 #2
0° Parity, A = -0.31(7)
90° Parity, A = 0.31(4)
C
D
y
t
i
r
a
P
X
π/2
1
0.5
0
-0.5
-1
0
45
90
135
180
(Degrees)
225
270
315
360
0
45
90
135
180
(Degrees)
225
270
315
360
Fig. 4. Parity measurements showing the creation of Bell state pairs.
(A) The microwave pulse and detection sequence used in the parity oscillation
p
measurement. The XY8 block is the same as that in Fig. 2A. fp/2 denotes a
2
-pulse with a microwave phase shifted by f relative to the first Xp/2 pulse in
the sequence, effectively rotating the quantum state around an axis that is
angled f relative to the x axis on the Bloch sphere. The pulse in yellow with a
camera symbol represents imaging of the molecules. Note that the first imaging
pulse for tweezer-loading identification, as well as the microwave pulses for
initial-state preparation, are applied before this sequence and not shown in
this figure. (B) Parity oscillation at q = 0° and q = 90°. A is the fitted parity
oscillation amplitude. (C) With the addition of a p-pulse and a third imaging
step to the sequence shown in (A), molecules are verified to be present
throughout the entanglement and readout process. (D) Parity oscillation for
q = 90°, with empty traps excluded and corrected for measurement error,
using the sequence depicted in (C). In (B) and (D), error bars represent one
standard deviation of uncertainty.
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RES EARCH | R E S E A R C H A R T I C L E
A
n
o
i
t
c
a
r
F
0.8
0.6
0.4
0.2
0
-0.2
0
|
|
, T = 21(2) ms
, T = 22(2) ms
B
0.6
0.5
0.4
0.3
0.2
0.1
n
o
i
t
c
a
r
F
Odd Sites
Even Sites
5
10
15
Time ( s)
20
25
30
0
0
10
20
30
40
Time (ms)
50
60
70
Fig. 5. Single-site–resolved state preparation. (A) Rabi oscillation after preparation of the molecular pair in ↓↑j
↑↓j
i state at q = 90°. Shown here is the outcome of ↓↑j
i. In (A) and (B), error bars represent one standard deviation of uncertainty.
i and ↑↓j
i. (B) Dipolar spin-exchange oscillation with an initial
Toward arbitrary initial-state preparation
Motivated by the desire to perform robust
single-site addressing, instead of using a single
AOD to generate all sites in the array, we
switched to using one AOD to generate the odd
numbered sites and another AOD to generate
the even numbered sites. This allowed for conve-
nient independent trap-depth control over each
molecule in a pair and uniformity across the
array. Additionally, by offsetting the frequency
of the tweezer light of the even and odd sites,
molecules can be moved in close proximity
without experiencing the heating that can arise
in a single AOD system (34, 38). For a given
trap depth, the differential ac Stark shift results
in molecules in even numbered sites being away
from the resonance of the ↑j i→ ↓j i microwave
transition, therefore allowing separate micro-
wave addressing of the odd sites. By applying a
microwave p-pulse when odd sites are detuned
away, we could prepare an antiferromagnetic
i. Under Hdip, an initial state ↑↓j
initial state ↑↓j
i
(cid:7)
(cid:7)
evolves as y tð Þ ¼ cos Jt
2ħ ↑↓i (cid:2) isin Jt
j
2ħ ↓↑i
, and
(cid:5)
(cid:4)
2 1 þ cos Jt
P↓↑ ¼ cos2 Jt
2ħ ¼ 1
will thus oscillate
ħ
at an angular frequency of J
ħ.
To demonstrate individual addressing, we
first prepared the molecules (both in the even
and odd sites) in initial state ↓↓j
i . We then
adiabatically ramped the trap depth of the odd
sites to seven times that of the even sites, so as
to detune the transition of the molecules in
the odd sites out of resonance. The microwave
p-pulse then only transfers the molecules in
the even sites from ↓j i to ↑j i. This creates an
antiferromagnetic state ↓↑j
i. By then applying
a microwave pulse with variable length of time
and detecting molecules in the ↑j i state, we ob-
served Rabi oscillations in both even and odd
sites with opposite phase (Fig. 5A). To observe
dipolar spin exchange, we moved the tweezers
→j ¼ 2 mm). As with the
to a smaller spacing (jR
single AOD system, we applied the XY8 dynam-
ical decoupling pulses and then separated the
pairs for detection. The resultant outcome pro-
babilities are shown in Fig. 5B, with a clear dis-
play of spin exchange.
Conclusions and outlook
We observed dipolar spin-exchange interac-
tions and created Bell-state entangled pairs
with single CaF molecules trapped in optical
tweezers. We studied the dipolar interaction
and entanglement by tuning the spacing of the
optical tweezers and the angle of the electric
dipole quantization axis. By applying detection
at the end of the entanglement sequence to
include only cases where two molecules are
present, we determined a Bell state fidelity
of F ex ¼ 0:89 6ð Þ through a parity oscillation
measurement. Parity measurements confirm
that the interaction in this system can be tuned
between ferromagnetic and antiferromagnetic.
The coherence time of dipolar interactions
and the single-molecule rotational coherence
time are both limited by the finite tempera-
ture of the molecules. Implementation of fur-
ther cooling using other techniques, for example,
Raman sideband cooling (44), would substan-
tially reduce motional dephasing, extend the
single-qubit rotational coherence time (31), and
thus increase the two-qubit gate fidelity (12).
The approach presented in this work can be
extended to ultracold polyatomic molecules,
which have robust parity doublet states that
give rise to an advantageous Stark level struc-
ture (62, 63).
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ACKN OWLED GMEN TS
We thank M. D. Lukin and N. Y. Yao for carefully reading the
manuscript. Funding: This material is based upon work supported
by the US Department of Energy, Office of Science, National
Quantum Information Science Research Centers, Quantum
Systems Accelerator. Additional support is acknowledged from the
Air Force Office of Scientific Research, the Asian Office of
Aerospace Research and Development, the Army Research office,
and the National Science Foundation (NSF). S.S.Y. acknowledges
support from the NSF Graduate Research Fellowships Program.
L.A. and S.S.Y. acknowledge support from the Harvard Quantum
Initiative (HQI). E.C. acknowledges support from the National
Research Foundation of Korea (2020R1A4A1018015,
2021M3H3A1085299, 2022M3E4A1077340, and
2022M3C1C8097622). Author contributions: Y.B., S.S.Y., L.A.,
E.C., W.K., K.-K.N., and J.M.D. contributed to the experimental
effort. All authors discussed the results and contributed to the
manuscript. Competing interests: The authors declare no
competing interests. Data and materials availability: All data
needed to evaluate the conclusions in this paper are present in
the paper or in the supplementary materials. All data presented in
this paper are deposited at Zenodo (65). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science. No
claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf8999
Supplementary Text
Figs. S1 to S3
Reference (66)
Submitted 18 November 2022; accepted 12 October 2023
10.1126/science.adf8999
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RES EARCH
MOLECULAR BIOLOGY
Human POT1 protects the telomeric ds-ss DNA
junction by capping the 5′ end of the chromosome
Valerie M. Tesmer, Kirsten A. Brenner, Jayakrishnan Nandakumar*
Protection of telomeres 1 (POT1) is the 3′ single-stranded overhang-binding telomeric protein that
prevents an ataxia telangiectasia and Rad3–related (ATR) DNA damage response (DDR) at chromosome
ends. What precludes the DDR machinery from accessing the telomeric double-stranded–single-stranded
junction is unknown. We demonstrate that human POT1 binds this junction by recognizing the
phosphorylated 5′ end of the chromosome. High-resolution crystallographic structures reveal that the
junction is capped by POT1 through a “POT-hole” surface, the mutation of which compromises junction
protection in vitro and telomeric 5′-end definition and DDR suppression in human cells. Whereas
both mouse POT1 paralogs bind the single-stranded overhang, POT1a, not POT1b, contains a POT-hole
and binds the junction, which explains POT1a’s sufficiency for end protection. Our study shifts the
paradigm for DDR suppression at telomeres by highlighting the importance of protecting the
double-stranded–single-stranded junction.
N ucleoprotein complexes called telomeres
cap chromosome ends to ensure genome
integrity. Human telomeric DNA contains
~10 to 15 kb of tandem 5′-GGTTAG-3′/3′-
CCAATC-5′ repeats. Although telomeric
DNA is primarily double-stranded (ds), all
chromosomes terminate in a 50- to 500-
nucleotide (nt) single-stranded (ss) G-rich
telomeric overhang (Fig. 1A, bottom) (1). The
six-protein shelterin complex coats telomeric
DNA to protect chromosome ends from being
recognized as dsDNA breaks by the ataxia
telangiectasia and Rad3–related (ATR) kinase–
and ataxia-telangiectasia mutated (ATM)
kinase–mediated DNA damage response (DDR)
machineries (2, 3). ATR signaling involves
multiple protein factors and coordinated recog-
nition of both the ss and the adjacent ds-ss
junction of its DNA substrates (4). Protection
of telomeres 1 (POT1) is a shelterin component
that binds the ss G-rich overhang with high
affinity and sequence specificity and prevents
ATR signaling at telomeres (2, 5, 6). POT1
recognizes ssDNA through its DNA bind-
ing domain (DBD), which consists of two
oligonucleotide/oligosaccharide-binding (OB)
domains (Fig. 1A). Previous studies have re-
ported a decanucleotide TTAGGGTTAG within
two telomeric ss repeats, 1GGTTAGGGTTAG12,
to be sufficient for high-affinity binding to hu-
man POT1 (hPOT1) (7). The first OB domain
(OB1) of hPOT1 binds 3TTAGGG8 (OB1DNA),
whereas its second OB domain (OB2) binds
9TTAG12 (OB2DNA) (Fig. 1, A and B) (7). Homologs
of POT1 are identifiable across eukaryotes
(5, 8–15), and deleting the POT1 paralog in
mice that is involved in chromosome-end pro-
tection (POT1a) is embryonic lethal (14, 15).
Department of Molecular, Cellular and Developmental
Biology, University of Michigan, Ann Arbor, MI 48109, USA.
*Corresponding author. Email: jknanda@umich.edu
The current model for ATR suppression at
telomeres invokes the prevention by POT1 of
replication protein A (RPA) loading onto the ss
overhang, through POT1’s high affinity for
telomeric ssDNA and its tethering to the rest
of shelterin at telomeric dsDNA (2, 6, 16). Yet,
multiple observations suggest that addition-
al features of POT1 are involved in ATR rep-
ression. First, mouse POT1 paralogs POT1a
and POT1b display indistinguishable ssDNA-
binding activity, but only POT1a is sufficient for
chromosome-end protection (6, 15, 17), whereas
POT1b regulates chromosome-end processing
and replication activities (16, 18–21). Replac-
ing the DBD of POT1b with that of POT1a or
hPOT1 enables ATR repression at telomeres
(17). Second, replacing the DBD of POT1a with
that of ssDNA-binding protein RPA70 is not
sufficient to fully repress ATR signaling at
telomeres in mouse cells that lack POT1a
(16). Moreover, POT1’s binding to the G-rich
ss overhang does not explain how it dictates
the 5′ end of the C-rich strand, which terminates
predominantly in ATC-5′ in mammals (22, 23)
(Fig. 1A, bottom). These observations are con-
sistent with the DBD of hPOT1 and mouse POT1a
carrying out an additional function relevant to
ATR suppression.
Results
Human POT1 binds a 5′-phosphorylated
telomeric ds-ss DNA junction
We hypothesized that hPOT1 binds to the telo-
meric ds-ss junction after we reanalyzed its pub-
lished DNA binding-site preferences. Two classes
of POT1 binding sites emerged from previous
SELEX (systematic evolution of ligands by ex-
ponential enrichment) analysis, one of which
was the expected 3TTAGGGTTAG12 (OB1DNA and
OB2DNA) site (Fig. 1B, Class I) (24). A second class
contained OB1DNA, an upstream tri-K (“K” indi-
cates a G or T nucleotide), and a seemingly non-
telomeric (NT) sequence implicated in binding
to OB1 (consensus: CTCCAGCAGGGG3TTAGGG8)
(Fig. 1B, Class II) (24). Junction binding was
suspected on the basis of the observation that
the tri-K GGG motif corresponds to the telo-
meric repeat sequence upstream of OB1DNA,
and NT sequences in the Class II hits could fold
into a hairpin (hp) containing a 2-base-pair (bp)
stem −1GG0/−6CC−7 and a variable tetraloop
(positions −5 to −2) (Fig. 1B and fig. S1, A and B).
In this interpretation, G0 and C−7 represent the
first base pair at the ds-ss junction (with C−7
corresponding to the 5′ end of the mammalian
chromosome), and the 3′ overhang initiates in
the GGTTAG register (Fig. 1, A and B, and fig. S1,
A and B). We conducted a quantitative electro-
phoretic mobility shift assay (EMSA) with puri-
fied hPOT1 DBD (hDBD) (fig. S2A) and a 5′-32P–
labeled hp oligonucleotide derived from the
Class II consensus terminating in a C at the
5′ end and containing a 3′ overhang of sequence
1GGTTAGGG8 (hp-ss1-8) (Fig. 1C). The absence
of OB2DNA from the Class II consensus atten-
uates the affinity of hDBD for ssDNA (7), allow-
ing us to assess DNA affinity of POT1 for the
ds-ss junction. hDBD bound strongly to hp-ss1-8
[dissociation constant (Kd) = 2.6 ± 0.3 nanomolar
(nM)] but not to a similar target (no_hp-ss1-8)
that lacks the ability to form a hairpin (Fig. 1, C
and D). The natural telomeric ds-ss junction
ends in a 5′-phosphate (5′-P), which has been
previously exploited to determine the 5′-terminal
nt of chromosomes by using DNA ligase-
mediated methods (25). To test the importance
of this phosphate in binding hPOT1, we per-
formed a competition experiment mixing
5′-32P-hp-ss1-8 with either nonradiolabeled
5′-phosphorylated hp-ss1-8 or 5′-OH-hp-ss1-8 be-
fore binding to hDBD. The 5′-P was required to
effectively outcompete POT1 binding to the
radiolabeled DNA (Fig. 1E). The absence of a
5′-P at the DNA junction in past in vitro
studies may have prevented the detection of
this previously unappreciated POT1 DNA-
binding activity (17, 26–29). POT1 bound to
a telomeric ds-ss junction in vivo is poised to
engage both OB1DNA and OB2DNA. Extension of
the overhang of the hp to include OB2DNA (hp-
ss1-12) resulted in a higher affinity for hDBD
[Kd = 70 picomolar (pM)] (Fig. 1, C and F)
compared with either ss1-12 (Kd = 190 pM)
(Fig. 1C and fig. S2B) or hp-ss1-8 (Fig. 1, C and D).
We confirmed that a heterodimer of full-length
hPOT1 and shelterin partner TINT1-PTOP-PIP1
(TPP1) (by using the TPP1N truncation con-
struct), which approximates the context of
hPOT1 coating the ss overhang in vivo (30, 31),
exhibited robust binding to 5′-P-hp-ss1-12
(Fig. 1G). DBD bound a two-stranded DNA
(duplex reinforced with 30 bp of arbitrary,
nontelomeric sequence) terminating in 5 bp of
native ds telomeric junction sequence and an
8-nt overhang (long_ds-ss1-8) with an affinity
that was approximately one order of magni-
tude greater than observed with hp-ss1-8, likely
Tesmer et al., Science 381, 771–778 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Human POT1 recognizes the 5′-phosphorylated
ds-ss junction of telomeres. (A) (Top) Schematic
of hPOT1 includes binding domains for ssDNA
(hDBD) and TPP1 (TPP1-BD). hDBD (PDB: 1XJV) is
composed of OB1 and OB2. The current model
suggests that POT1 outcompetes the ssDNA-binding
RPA complex to prevent ATR signaling at telomeres.
HJRL, Holliday junction resolvase-like. (Bottom)
Mammalian chromosomes end in a ds-ss junction
containing ATC-5′ (predominantly) and a ss
G-rich overhang. Numbering starts with the first
overhang nucleotide. (B) A previous SELEX study
revealed two hPOT1-binding DNA classes (24).
Class I harbors the known sites for OB1 and OB2,
denoted as OB1DNA (cyan) and OB2DNA (pink),
respectively. Class II revealed a consensus containing
a seemingly nontelomeric (NT) sequence upstream of
OB1DNA that can potentially fold into a hp; “K”
indicates a G or T nucleotide, and the shaded area
indicates the sequence of the first bp at the telomeric
ds-ss junction. (C) Annotated name, sequence,
predicted hp structure [with Tm (where Tm is the
temperature at which 50% of dsDNA is denatured)
calculated by the UNAFold web server], and mean Kd
and SD (of binding to hDBD) of the oligonucleotides
used in EMSA analysis. NA indicates not applicable.
(D to H) EMSA of indicated proteins (hDBD or POT1-
TPP1N heterodimer) and 5′-32P–labeled DNA oligo-
nucleotides. (D), (F), (G), and (H) indicate direct
binding experiments, and (E) indicates a competition
experiment. In (D), 0.1 nM 5′-32P-hp-ss1-8 was used;
the number of experimental replicates n = 5 for
hp-ss1-8 (full and partial titrations); n = 3 for no_hp-ss1-8.
In (E), 100 nM hDBD and 0.1 nM 5′-32P–labeled hp-ss1-8
were incubated with indicated amounts of unlabeled
hp-ss1-8 (cold DNA) containing either a 5′-OH or a 5′-P;
n = 3. In (F), 0.001 nM 5′-32P-hp-ss1-12 was used; n = 3.
In (G), 0.01 nM 5′-32P-hp-ss1-12 was used; n = 3. (H)
0.001 nM 5′-32P-long_ds-ss1-8 was used; n = 3. Circled
red “P” indicates radiolabeled; circled black “P”
indicates nonradiolabeled. Bound (B) indicates DNA
bound to protein; Free (F) indicates free, unbound DNA.
reflecting the greater stability of the more phys-
iologically representative duplex DNA versus
that of the hp (Fig. 1, C and H). Our data dem-
onstrate that the telomeric ds-ss junction is a
previously unappreciated high-affinity binding
site for hPOT1.
High-resolution structures reveal how human
POT1 caps the phosphorylated 5′ end of a
telomeric junction
To determine the structural basis for hPOT1’s
telomeric ds-ss junction–binding activity, we
formed complexes of hDBD with two sub-
strates that mimic the telomeric ds-ss junction—
5′-P-ds-ss1-12 (DNA containing a 5-bp arbitrary,
nontelomeric tether upstream of GTTAG/CAATC-
5′-P native telomeric ds sequence extending into a
12-nt 3′ overhang) (fig. S2, C and D) and 5′-P-hp-
ss1-12 (Fig. 1C)—and solved their structures
using x-ray crystallography (Fig. 2, A and B).
The hDBD-bound 5′-P-ds-ss1-12 and 5′-P-hp-ss1-12
structures were solved to 2.60- and 2.16-Å res-
olution, respectively (table S1). Both struc-
tures are similar to each other (fig. S3D) and
recapitulate the previously reported hDBD-ss
DNA-binding interface with minor differences
(fig. S3, A to C, and E to J) (7). These structures
reveal how hPOT1 binds the phosphorylated 5′
end of the telomeric ds-ss junction (Fig. 2). An
electropositive pocket of four amino acids (Y9,
R80, H82, and R83) in the hPOT1 OB1 domain
that we name the “POT-hole” caps the 5′-P-
cytidine nucleotide by means of a network of
stacking and electrostatic interactions (Fig. 2,
D to F, and fig. S4A). R83 acts as the linchpin
by forming an ionic interaction with the 5′-P,
Tesmer et al., Science 381, 771–778 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Structural basis of telomeric junction
5′- end protection by human POT1. (A and B)
Cartoon representation of high-resolution crystal
structures of complexes of (A) hDBD with 5′-P-ds-
ss1-12 and (B) 5′-P-hp-ss1-12, showing OB1 (cyan)
and OB2 (pink) bound to DNA [gray, with the
exception of the 5′-P, whose atoms are shown as
spheres and in Corey-Pauling-Koltun (CPK) coloring].
A boxed schematic of the DNA is shown below the
structure, with the ds sequence found naturally at
the telomeric ds-ss junction shaded gray, the 5′-P in
red, and residues in the G-rich 3′ overhang colored
to indicate binding by OB1 and OB2, respectively.
(C) Cartoon and (E) electrostatic surface (blue
is electropositive and red is electronegative) repre-
sentations of the hDBD-5′-P-ds-ss1-12 structure shown
in a view orthogonal to that in (A). The 5′-P occupies
a pocket in POT1 that is complementary in shape
and charge. Single-letter abbreviations for the amino
acid residues are as follows: H, His; R, Arg; and
Y, Tyr. (D) The POT-hole-DNA interface within the
hDBD-5′-P-hp-ss1-12 structure is shown with POT-hole
side chains (carbon in cyan) and the nucleotides
(carbon in light gray) near the junction shown as
sticks. A water molecule bridging hPOT1 R80 to
the 5′-P is shown as an orange sphere. The dashed
lines indicate H-bonds and ionic interactions, the
double-headed arrow indicates stacking of the hPOT1
R83 side chain with the 5′-C at the junction
(numbered C0), and N indicates the N terminus of
hDBD resolved in the crystal structure. (F) Interaction
map of hDBD with the ds-ss junction.
stacking against the 5′-cytosine base, and form-
ing hydrogen bonds (H-bonds) with the ribose-
ring oxygen of the 5′-cytidine nucleoside (5′-C)
(Fig. 2, D and F, and fig. S4A). R83 also forms
an H-bond with Y9, which along with H82
interacts with the 5′-P. R80 forms a water-
mediated H-bond with the 5′-P. We observed
that the POT-hole is not optimally sized to
accommodate a bulkier adenine (purine in-
stead of a pyrimidine) or thymine (methyl group
on the base) at the 5′ end because of steric clashes
(fig. S5, A to C). Furthermore, the fixed distance
between the POT-hole and the ssDNA-binding
region of hPOT1 dictates the preference for the
naturally occurring ATC-5′ versus alternative
5′-C iterations: ATCC-5′ and ATCCC-5′ (fig. S5D).
In addition to interactions involving the POT-
hole, junction recognition is fortified by con-
tacts made by the backbone amides of hPOT1
amino acids 121 to 124 with the phosphodiester
group penultimate to the 5′-C (Fig. 2F and fig.
S4B), as well as S99 with G2 (Fig. 2F and fig.
S3, K and L). These data provide the structural
basis for binding of the telomeric ds-ss junction
by hPOT1.
The POT-hole dictates telomeric DNA junction
binding and inhibits DDR at telomeres
We evaluated the importance of the POT-hole
in binding the telomeric ds-ss junction in vitro
using purified hDBD variants with alanine
mutations at Y9, R80, H82, and R83 (fig. S6A).
We also engineered an R83E charge-reversal
mutant to test the importance of the ionic R83-
5′-P interaction. Alanine substitution of F62, a
residue in hPOT1 OB1 that is indispensable
for binding telomeric ssDNA (32), was included
as a control to disrupt binding to both ssDNA
and the ds-ss junction. In agreement with the
structural data, little to no DNA binding was
observed for any POT-hole mutant with the
5′-P-hp-ss1-8, even at concentrations 100-fold
greater than the Kd with wild-type (WT) hDBD
(Fig. 3A, left). By contrast, POT-hole mutants
bound 5′-P-ss1-12 with an affinity similar to that
of wild type (Fig. 3A, right, and fig S6, B and C).
F62A failed to bind either oligonucleotide,
which is consistent with binding to OB1DNA
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Fig. 3. Separation-of-function POT-hole mutations abrogate ds-ss DNA
junction binding in vitro and result in a DDR at human telomeres.
(A) EMSA to detect direct binding of WT or indicated mutant hDBD constructs
with 5′-32P-hp-ss1-8 (0.1 nM; lanes 1 to 22) and 5′-32P-ss1-12 (0.1 nM; lanes 23 to
30); n = 3. (B) Schematic conveying how POT-hole mutations would disrupt
binding to the ds-ss junction but not coating of the ss overhang by POT1.
(C) Scheme for deletion of endogenous POT1 and complementation with lentivirally
transduced hPOT1-Myc to assess the ability of mutants to suppress TIF formation
in a HEK 293E–based cell line (34). (D) TIF analysis of cell lines after 4-OHT and dox
(1000 ng/ml; 25 ng/ml in “low dox” wild type) treatment as described in (C) performed
with peptide nucleic acid fluorescent in situ hybridization (PNA-FISH) for telomeres
(green) and immunofluorescence (IF) for Myc (hPOT1; cyan) and 53BP1 (red). 4′,6-
diamidino-2-phenylindole (DAPI) was used to stain the nucleus (blue). Overlap of
the telomeric and 53BP1 foci (and Myc foci, if applicable) in the “Merge” panel
indicates TIFs. (Inset) Magnified view of the boxed area within the image; arrowheads
indicate TIFs. (E) Quantitation of TIF data of which (D) is representative. Mean
and SD (n = 3 for all conditions except WT −dox, for which n = 5; each +dox set
containing >75 nuclei and each −dox set containing >50 nuclei) for TIFs are plotted
for the indicated cell lines. P values calculated with a two-tailed Student’s t test
for comparisons against WT +dox data are indicated above the bars.
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Fig. 4. Presence of the POT-hole dictates POT1 paralog choice for
chromosome-end protection in mice. (A) Human POT-hole residues are conserved in
mouse POT1a but not mouse POT1b. (B) Electrostatic surface comparisons of
hDBD (from hDBD-5′-P-ds-ss1-12 structure) and POT1a and POT1b DBD (Alphafold
models), with the phosphorylated 5′-C of the hDBD-bound structure shown in
sticks. (C and D) EMSA analysis of indicated mouse POT1a and POT1b DBD
constructs with the indicated 5′-32P–labeled oligonucleotides [0.1 nM for (C)
and (D), right; 0.01 nM for (D), left]; n = 3. (E) EMSA analysis of indicated
human and mouse POT1 DBD constructs with 0.001 nM 5′-32P-long_ds-ss1-8
two-stranded DNA; n = 3. (F) (Top left) Names and sequences of the two DNA
oligonucleotides, hp-ss1-24 and ss1-24, used to evaluate 5′-end–binding prefer-
ence. Both DNAs were labeled at the 5′ end with 32P for EMSA analysis. (Bottom
left) Three possible DNA-binding registers for the first DBD molecule are
shown with the center-binding register precluding the binding of a second DBD
molecule. (Right) EMSA analysis of POT1a DBD with hp-ss1-24 (discrete slow-migrating
band with increasing concentrations of protein; 2×B) and ss1-24 (smeary band;
mixture of B and 2×B), DNA at 0.1 nM; n = 3. (G) EMSA analysis of indicated POT1a
DBD constructs with 0.1 nM hp-ss1-24. YHR, triple mutant Y9S-H82Q-R83G; n = 3.
being critical for both DNA-binding modes.
These data highlight the importance of the POT-
hole in 5′-end binding and provide separation-
of-function mutants to test the importance
of hPOT1’s junction-binding activity in cells
(Fig. 3B).
Loss of POT1 binding at the 3′ overhang re-
sults in telomere dysfunction–induced foci (TIF),
which signify the recognition of telomeres by
the DDR machinery (33). To determine the bio-
logical importance of the POT-hole binding to
the telomeric junction, we used a previously
described cell line in which POT1 can be deleted
in an inducible fashion (POT1 KO) (34) to test
the ability of transduced WT and mutant hPOT1
Myc-tagged constructs to compensate for the
loss of endogenous POT1 (materials and meth-
ods). Transduced cells were treated first with
4-OHT to delete POT1 and then either treated
with doxycycline (dox) to induce exogenous
hPOT1 expression (“+dox”) or left untreated
(“−dox”) (Fig. 3C). In the absence of dox,
4-OHT treatment resulted in a robust TIF
phenotype, characterized by colocalization of
the DDR factor 53BP1 at telomeres (fig. S6, E
and F). hPOT1 wild type and “low dox” wild
type, but not hPOT1 F62A, suppressed TIFs
(Fig. 3, D and E). POT-hole mutants Y9A,
R83A, and R83E were defective in TIF sup-
pression compared with wild type, with R83E
being the most deleterious (Fig. 3, D and E).
This trend emphasizes the importance of the
ionic interaction between R83 and the 5′-P.
Clones isolated from 6X-Myc–tagged hPOT1 WT,
F62A, and R83E cell populations also reca-
pitulated the TIF phenotypes (fig. S7, A to D).
Furthermore, TIFs were smaller (Fig. 3D, inset)
and less frequent (Fig. 3, D and E) in POT-hole
mutant cells compared with those in F62A
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Fig. 5. Maintenance of the ATC-5′ end of chromo-
somes by the POT-hole. (A) Schematic of the
modified STELA technique for determining the
chromosomal 5′-terminal nucleotide in human cell
lines. Step 1: DNA ligation of genomic DNA 5′-P ends
with telorettes ending in each of the six possible
repeat registers at the 3′-OH ends. Step 2: PCR
amplification of the ligation products performed with
a forward primer (PCR-F) targeting the subtelomere
of chromosome XpYp and a reverse primer (PCR-R)
targeting a sequence shared by all telorettes. The
products are visualized with Southern blot analysis
performed with a 5′-32P–labeled XpYpB2 reverse
primer. (B) STELA-based determination of the
chromosomal 5′-terminal nucleotide in the HEK
293E–based POT1 KO parental cell line (−4-OHT
and +4-OHT) and hPOT1-Myc WT– or R83E-
complemented clonal cell lines treated with both
4-OHT and dox. (C) Quantitation of ATC-5′ preference
calculated as the ratio of the total band intensity in the
primer 3 lane over the total intensity over all six
lanes. Mean and SD for n = 4 replicates of which B is
representative are plotted. P values were calculated
with a two-tailed Student’s t test for comparisons
against parental −4-OHT data (for parental +4-OHT) or
hPOT1-Myc WT clones (for hPOT1-Myc R83E clones).
(D) (Left) TRF analysis of cell lines used in (B)
performed first under native conditions with a
5′-32P–labeled telomeric C-probe (CTAACC)4 to detect
the ss G-rich overhang. (Right) TRF analysis after
denaturing the DNA on the same gel and reprobing it to
detect the total telomeric DNA signal; n = 1. (E) Model
for ATR inhibition at telomeres by POT1. The ssDNA-
binding of hPOT1 prevents the loading of RPA to curb
ATR recruitment to the 3′ overhang. Protection of the
ds-ss junction by hPOT1 prevents loading of the
9-1-1/Rad17-RFC clamp and clamp-loader complex and
ATR activator TOPBP1. In mice, both POT1 paralogs
coat the ss overhang, but only POT1a protects the ds-ss
junction. The shelterin proteins protecting the telomeric
dsDNA are expected to keep POT1-TPP1 tethered to
the ss overhang, facilitated by protein-protein
interactions and the conformational flexibility within
the proteins (29) and the telomeric DNA.
cells. This finding suggests that both junction-
and ssDNA-binding activities of hPOT1 must
be compromised to trigger a full DDR (see
Discussion). Our results demonstrate that junc-
tion binding, which should involve a single
POT1 molecule per chromosome end (Fig. 3B),
is critical for chromosome-end protection.
The POT-hole differentiates mouse POT1
paralogs and enables POT1a to protect the
telomeric junction
Despite being strictly conserved in other mam-
malian POT1 homologs, including mouse POT1a,
each of the four POT-hole amino acids is re-
placed with a structurally disparate residue in
mouse POT1b (Fig. 4A and fig. S8A). By contrast,
the residues used in ss DNA binding are con-
served in all mammalian POT1 homologs, in-
cluding POT1b (fig. S8A). Aligning Alphafold
predictions (35) of POT1a and POT1b DBDs
with the junction-bound structure of hDBD
illustrates that the shape and electropositive
nature of the POT-hole are predicted to be lost
in POT1b (Fig. 4B and fig. S8, B and C). We
hypothesized that POT1a, but not POT1b, pro-
tects the 5′ end at the junction. Indeed, POT1a-
and POT1b-DBD proteins bound ss1-12, but only
POT1a DBD engaged a telomeric ds-ss junction
with high affinity (Fig. 4, C to E, and fig. S8, D
and E). POT1a replaced with POT1b residues in
the POT-hole (except R80; fig. S8F legend
explains rationale) retained affinity toward ss1-12
(Fig. 4C) but failed to bind the junction (Fig. 4D,
right, and E, and fig. S8D).
To measure junction-binding in the presence
of multiple ss DNA-binding sites, we developed
an EMSA-based “POT1 packing” assay with two
DNA targets, each containing four telomeric
ss repeats (24 nt) spanning three possible
Tesmer et al., Science 381, 771–778 (2023)
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POT1-binding registers. The 5′ and 3′ registers
are compatible with the packing of two POT1
molecules, whereas binding to a central reg-
ister precludes the loading of a second POT1
(Fig. 4F, left). hp-ss1-24 includes a ds-ss junction
upstream of this ss region, whereas ss1-24 does
not. A fully packed 2:1 DBD-DNA complex
would produce a sharp, slow-migrating band
at higher DBD concentrations, whereas a mix
of 2:1 and 1:1 complexes (of various binding
registers) would generate a smear. POT1a DBD
binding resulted in a sharp band for hp-ss1-24
but not ss1-24, suggesting that the protein packs
preferentially against a ds-ss junction but that
there is no end-binding bias to dissuade it from
binding to the central site of ss1-24 (Fig. 4F,
right). POT1a POT-hole mutants R83G and
triple mutant YHR lost the ability to pack at the
junction (Fig. 4G), which is consistent with R83
capping the 5′ terminus (Fig. 2, D and F) and
repressing TIFs (Fig. 3, D and E). hDBD and
mouse POT1b DBD formed a discrete complex
with not only hp-ss1-24 but also ss1-24, which is
consistent with a 3′-end–binding preference
(fig. S9, A and B) (7). Our results demonstrate
that the POT-hole allows POT1a to preferen-
tially bind the telomeric junction.
The POT-hole helps maintain the 5′-end identity
of human chromosomes
Consistent with the structures we solved, the
POT-hole of hDBD and mouse POT1a DBD pro-
tect the 5′-P end from 5′ exonucleolytic action
in vitro (fig. S10, A to F). We next asked whether
the POT-hole helps maintain the 5′-terminal
sequence of the chromosomes in cells. We used
a modified single telomere length analysis
(STELA) approach that uses ligation-mediated
polymerase chain reaction (PCR) amplification
to determine the abundance of each of the six
possible chromosomal 5′-end permutations
(Fig. 5A) (23). Genomic DNA extracted from the
parental human embryonic kidney (HEK) 293E
cell line displayed the expected ATC-5′ prefer-
ence that is lost after POT1 deletion (Fig. 5, B
and C). WT hPOT1, but not R83E hPOT1, was
able to restore the ATC-5′ bias to untreated
(parental –4-OHT) levels, demonstrating that
the POT-hole helps maintain the 5′ end of the
human chromosome (Fig. 5, B and C, and fig.
S10G). The 5′-end scrambling of hPOT1 R83E
was less severe than that of POT1 KO. This dif-
ference may be explained by the unleashing of 5′
exonuclease activity at telomeres completely
devoid of POT1 (36). Terminal restriction frag-
ment (TRF) analysis reproduced previously
characterized phenotypes (15, 34, 37), including
the accumulation of slow-migrating species
(denatured and native blots) and an increase
in the G-rich ss signal (native blot) upon POT1
deletion, which were suppressed by expression
of hPOT1 wild type but not F62A (Fig. 5D and
fig. S10H). R83E recapitulated the WT pheno-
types, suggesting that the end-protection func-
tion of the POT-hole is separable from hPOT1’s
role in bulk-telomere or overhang-length main-
tenance. Thus, the POT-hole helps maintain
ATC-5′ ends without acutely influencing telo-
mere length.
Discussion
The major pathway of ATR activation requires
RPA binding to exposed ssDNA and recogni-
tion of the ds-ss junction by the 9-1-1/Rad17-RFC
(RAD9–RAD1–HUS1/Rad17-RFC2–RFC3–RFC4–
RFC5) clamp and clamp loader, which with the
MRN (MRE11-RAD50-NBS1) complex recruit
TOPBP1 (DNA topoisomerase 2-binding pro-
tein 1) to activate ATR (Fig. 5E) (4, 38). The struc-
ture of human 9-1-1/Rad17-RFC bound to a ds-ss
junction revealed a basic pocket in Rad17 that
is poised to bind the 5′-phosphorylated end of
a junction by using a mechanism similar to
that of POT1 (fig. S11, A and B) (39). Con-
sistent with a competition between POT1
and 9-1-1/Rad17-RFC in binding the ds-ss
junction, subunits of the 9-1-1 and MRN com-
plexes, as well as TOPBP1, are enriched at
telomeres in the absence of hPOT1 (34). We
therefore propose that POT1 not only out-
competes RPA at the telomeric ss overhang
but also prevents ATR activation by denying
9-1-1/Rad17-RFC access to the telomeric ds-ss
junction (Fig. 5E).
The duplication of POT1 (40), the conserva-
tion of the POT-hole in POT1a (fig. S12A), the
disruption of the POT1-hole in POT1b (fig. S12B),
and the retention of CTC1-STN1-TEN1 (CST)–
binding motifs in POT1b (40) within the Muri-
dae and Cricetidae families of the Rodentia
order provide support to the hypothesis that
POT1b relinquished junction binding to facili-
tate processes at the 3′ end. We propose that
POT1a wards off 9-1-1/Rad17-RFC at the junc-
tion, although both POT1a and POT1b paralogs
could counter RPA at the overhang in mouse
cells (Fig. 5E).
The POT-hole is conserved in species dis-
tant to mammals, such as Sterkiella nova and
Caenorhabditis elegans (fig. S13A). The precisely
defined S. nova macronuclear telomere contains
a 5′-C at the ds-ss junction and a 16-nt overhang
that binds one telomere end–binding protein
(TEBP)a/b complex (homologous to the POT1-
TPP1 complex) (41). TEBPa has been crystal-
lized with a sulfate ion bound in a manner
indistinguishable from how the 5′-P binds hDBD
in our junction-bound structures (fig. S13B) (42).
Indeed, like hPOT1, TEBPa binds the telomeric
ds-ss junction more strongly than it binds telo-
meric ssDNA (8). These observations point to a
single TEBPa/b complex simultaneously pro-
tecting the 5′ and 3′ ends of the chromosome
(8, 41, 42). Schizosaccharomyces pombe, in which
a POT-hole is not obvious (fig. S13, A and C)
(5, 43), and eukaryotes whose chromosomes do
not end in a 5′-C, must have evolved alternative
approaches for junction protection.
We updated the model for how telomeres
avert detection by the DDR machinery to include
a critical role of POT1 in binding the telomeric
ds-ss junction. Thus, POT1 protects both DNA
strands at human chromosome ends by coating
the G-rich ss overhang and recognizing the phos-
phorylated 5′ end of the C-rich strand.
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AC KNOWLED GME NTS
We thank S. Padmanaban (Nandakumar laboratory) for input on
the design of the cell-based experiments; G. Glousker and
J. Lingner [Ecole Polytechnique Fédérale de Lausanne (EPFL),
Tesmer et al., Science 381, 771–778 (2023)
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Switzerland] for graciously gifting the POT1-inducible KO HEK 293E
cell line and the pCW22_TREtight_MCS_UBC_rtTA_IRES_Blast
lentiviral vector for dox-inducible expression and for sharing
detailed protocols and troubleshooting tips for these resources;
J. Schmidt (Michigan State University, USA) for the 53BP1 antibody;
the beamline staff at the Life Sciences Collaborative Access Team
(LS-CAT) beamline of the Argonne National Laboratory for help
with x-ray diffraction data collection [use of the Advanced Photon
Source, an Office of Science User Facility operated for the US
Department of Energy (DOE) Office of Science by Argonne National
Laboratory, was supported by the US DOE under contract no.
DE-AC02-06CH11357]; F. C. Lowder and L. Simmons (University of
Michigan at Ann Arbor, USA) for helpful suggestions for the
exonuclease protection experiment carried out with fluorophore-
labeled DNA and for preparation of an RNA ladder; T. de Lange and
S. Cai (Rockefeller University, USA), J. Schmidt (Michigan State
University, USA), H. Shibuya (University of Gothenburg, Sweden),
and J. Williams (Nandakumar laboratory) for helpful comments on
the manuscript; and G. Sobocinski for help with microscopy.
Funding: This study was supported by NIH grants R01GM120094,
R01HD108809, and R35GM148276 (J.N.) and by American Cancer
Society Research Scholar grant RSG-17-037-01-DMC (J.N.).
Author contributions: Conceptualization: V.M.T. and J.N.
Methodology: V.M.T., K.A.B., and J.N. Investigation: V.M.T. and
K.A.B. Visualization: V.M.T., K.A.B., and J.N. Funding acquisition: J.N.
Project administration: V.M.T. and J.N. Supervision: V.M.T. and J.N.
Writing – original draft: V.M.T. and J.N. Writing – review and editing:
V.M.T., K.A.B., and J.N. Competing interests: The authors declare that
they have no competing interests. Data and materials availability:
All data are available in the main and supplementary figures. All material
generated in this study, such as plasmids for protein expression and
cell lines, are available upon request. Coordinates and structure
factors of the crystal structures of hDBD with 5′-P-hp-ss1-12 and 5′-P-
ds-ss1-12 are deposited in the Protein Data Bank (PDB) under
accession codes 8SH0 and 8SH1, respectively. License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi2436
Materials and Methods
Figs. S1 to S13
Tables S1 and S2
References (44–55)
MDAR Reproducibility Checklist
Submitted 19 April 2023; accepted 19 July 2023
10.1126/science.adi2436
Tesmer et al., Science 381, 771–778 (2023)
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RES EARCH
HOST-GUEST CHEMISTRY
Disequilibrating azobenzenes by visible-light
sensitization under confinement
Julius Gemen1, Jonathan R. Church2, Tero-Petri Ruoko3, Nikita Durandin3, Michał J. Białek4,
Maren Weißenfels1, Moran Feller1, Miri Kazes1, Magdalena Odaybat5, Veniamin A. Borin2,
Rishir Kalepu1, Yael Diskin-Posner6, Dan Oron1, Matthew J. Fuchter5, Arri Priimagi3,
Igor Schapiro2*, Rafal Klajn1,7*
Photoisomerization of azobenzenes from their stable E isomer to the metastable Z state is the basis of
numerous applications of these molecules. However, this reaction typically requires ultraviolet light,
which limits applicability. In this study, we introduce disequilibration by sensitization under confinement
(DESC), a supramolecular approach to induce the E-to-Z isomerization by using light of a desired
color, including red. DESC relies on a combination of a macrocyclic host and a photosensitizer, which
act together to selectively bind and sensitize E-azobenzenes for isomerization. The Z isomer lacks
strong affinity for and is expelled from the host, which can then convert additional E-azobenzenes to
the Z state. In this way, the host–photosensitizer complex converts photon energy into chemical
energy in the form of out-of-equilibrium photostationary states, including ones that cannot be
accessed through direct photoexcitation.
(18, 19). For example, deep-sea fishes install a
chlorophyll antenna next to the opsin-bound
retinal (20, 21). This antenna captures red light
and sensitizes the nearby retinal by means of a
triplet-energy transfer (TET) mechanism (22).
The subsequent photoisomerization of retinal
induces a large conformational change in the
surrounding opsin protein, ultimately enabling
the fish to detect red light (23).
Similar to retinal, azobenzene can be switched
through TET (24–26). Unfortunately, this process
has long (27, 28) been known to unidirectionally
convert E–Z mixtures to the thermodynamically
stable E isomer. This directionality originates
from i) the higher tendency of Z (over E) to act
as a triplet-energy acceptor (29) and ii) the
preferential [by a factor of >50 (28)] relaxa-
tion of the triplet excited state of azobenzene
to E over Z. Therefore, whereas various photo-
sensitizers can rapidly and efficiently facilitate
the equilibration of the high-energy Z isomer
into the stable E state, the reverse reaction—
i.e., sensitized disequilibration—is far more
challenging and has remained elusive.
The concept of disequilibration
by sensitization under confinement
We hypothesized that sensitized disequilibration
might be achieved by using a photosensitizer
(PS) that acts on the E isomer of azobenzene
with high selectivity (Fig. 1B). We have previously
shown that (i) the water-soluble, palladium-
containing macrocyclic host H (30) (Fig. 1C)
binds two molecules of various E-azoarenes
(which are planar and readily stack on top of
A zobenzene and its derivatives are arguably
the simplest and most widely studied
photoswitchable compounds (1–3). Upon
exposure to ultraviolet (UV) light, the pla-
nar (4), nonpolar E isomer of azobenzene
isomerizes to the metastable Z form (Fig. 1A),
which is nonplanar and substantially more
polar. The Z→E back-isomerization occurs
spontaneously and can be accelerated with
visible (blue) light. Owing to the highly re-
versible nature of E⇄Z photoswitching, azo-
benzenes and other azoarenes (5) have found
applications in energy storage systems (6, 7),
switchable catalysis (8, 9), controlled release
(10, 11), and photopharmacology (12, 13), to
name but a few (14, 15). However, the necessity
to rely on UV light to generate the metastable
Z isomer has severely limited the applicability
of these compounds. Shifting E-azobenzene’s
absorption band to the visible range can be
achieved by decorating it with various sub-
stituents (16, 17), but this approach requires
additional synthetic effort and affects the com-
pound’s identity.
Natural systems evolved an alternative, supra-
molecular strategy to extend the absorption
spectral range of photoswitchable molecules
1Department of Molecular Chemistry and Materials Science,
Weizmann Institute of Science, Rehovot 7610001, Israel.
2Fritz Haber Center for Molecular Dynamics Research,
Institute of Chemistry, The Hebrew University of Jerusalem,
Jerusalem 9190401, Israel. 3Faculty of Engineering and
Natural Sciences, Tampere University, P.O. Box 541, 33101
Tampere, Finland. 4Department of Chemistry, University of
Wrocław, 14 F. Joliot-Curie St., 50383 Wrocław, Poland.
5Department of Chemistry, Molecular Sciences Research Hub,
White City Campus, Imperial College London, 82 Wood Lane,
London W12 7SL, UK. 6Department of Chemical Research
Support, Weizmann Institute of Science, Rehovot 76100, Israel.
7Institute of Science and Technology Austria, Am Campus 1,
3400 Klosterneuburg, Austria.
*Corresponding author. Email: rafal.klajn@ista.ac.at (R.K.);
igor.schapiro@mail.huji.ac.il (I.S.)
Fig. 1. Disequilibration by sensitization under confinement (DESC). (A) The transformation of the stable
E isomer of azobenzene to the metastable Z isomer traditionally relies on the use of ultraviolet
(l ≈ 350 nm) light. (B) The mechanism of DESC is as follows: (i) formation of the ternary inclusion complex
(E·PS)⊂H (PS, photosensitizer; H, host); (ii) absorption of a photon of visible light by the PS followed by
intersystem crossing (ISC); (iii) triplet-energy transfer (TET) and the formation of triplet azobenzene, followed by
its relaxation (iv) to Z-azobenzene or (iv') back to E-azobenzene (corresponding to internal conversion); and (v)
disassembly of the unstable (Z·PS)⊂H inclusion complex. (C) Components of the supramolecular system used for
DESC include macrocyclic host H coassembled from six Pd2+ ions and four triimidazole ligands, and a
photosensitizer (e.g., BODIPY ps1). (D) Structural formulae of azoarenes 1 to 9 investigated in this study.
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each other to form noncovalent homodimers),
but only one molecule in the Z configuration
(31, 32) [because of its nonplanar (33) geom-
etry]; (ii) host H can also encapsulate—and
thus, induce noncovalent dimerization of—guests
structurally similar to E-azobenzene (i.e., planar
aromatic molecules), including various dyes
(34, 35); and (iii) mixing two different inclusion
complexes (each binding two molecules of a
given guest) induces a rapid guest exchange
between the hosts, affording heterodimeric
complexes, whereby the host encapsulates two
different guest molecules (36). Taken together,
we speculated that host H could coencapsu-
late the E isomer of azobenzene and a PS (thus
bringing them in close proximity) while pro-
hibiting close encounters of the same PS with
the Z-azobenzene (which is bound as a sole
guest). We call this approach disequilibration
by sensitization under confinement (DESC).
The concept of DESC is illustrated in Fig. 1B.
The addition of an encapsulated PS [i.e., (PS)2⊂H]
to E-azobenzene induces the formation of a
ternary complex (E⋅PS)⊂H (step i). Upon expo-
sure to visible light, PS is promoted to a singlet
excited state, which relaxes to a triplet state
through intersystem crossing (ISC) (step ii). In
step iii, PS transfers its triplet energy to the co-
confined E-azobenzene. The resulting triplet
azobenzene—which cannot be generated by di-
rect photoexcitation—can either decay to the
initial E isomer (step iv′) or transform into the
Z state (step iv). The former case regenerates
(E⋅PS)⊂H, which can be reexcited. By contrast,
the latter case results in (Z⋅PS)⊂H, which is an
unstable complex because Z-azobenzene is too
bulky to coexist with the PS inside H. At the
same time, Z as a sole guest is bound relatively
weakly (fig. S103); hence, it is expelled from
the host and effectively removed from the equi-
librium. Thus, the azobenzene-free inclusion
complex of the PS is regenerated (step v) and
available for transforming additional mole-
cules of E- into Z-azobenzene.
To verify our hypothesis, we initially focused
on the parent azobenzene E-1 and the proto-
typical boron–dipyrromethene (BODIPY) dye
ps1 (Fig. 1, C and D). Both E-1 and ps1 form
homodimers within H’s cavity, as previously
elucidated by several techniques including
x-ray diffraction, nuclear magnetic resonance
(NMR), and UV-visible (vis) absorption spec-
troscopy (31, 32, 34). Figure 2B shows the UV-
vis spectrum (dotted brown line) obtained after
mixing aqueous solutions of the two homo-
dimers, (E-1)2⊂H and (ps1)2⊂H, in a 1:1 molar
ratio. The absorption profile in the visible range
is practically identical to that of pure (ps1)2⊂H
(blue dotted line), indicating a minute fraction
of the (E-1⋅ps1)⊂H heterodimer (i.e., the equi-
librium shown in Fig. 2A heavily favors the
two homodimers). However, exposing this so-
lution to low-intensity green light (wave-
length at maximum intensity, lmax = 525 nm;
2.5 mW cm–2) resulted in a substantial (by
~35%) decrease of absorption in the near-UV
region (Fig. 2B), indicating the E→Z isom-
erization of 1. This result suggests that the
small amount of (E-1⋅ps1)⊂H in equilibrium
with the homodimers absorbs green light, the
energy of which is eventually used to generate
a large amount of the metastable Z isomer (Fig.
1B). The low illumination intensities used in
our studies exclude the possibility of two-photon
isomerization (37, 38), which we confirmed di-
rectly through power-dependence experiments
(fig. S108).
To determine the scope of DESC, we extended
our studies to a diverse portfolio of azobenzenes
and other azoarenes, including derivatives
with charged groups and electron-donating
and -withdrawing substituents (Fig. 1D, 2 to
9). All of these compounds were encapsulated as
homodimers within host H, which was con-
firmed by NMR spectroscopy (supplementary
materials). Similar to 1, most of these guests
preferably existed as E2⊂H homodimers even
in the presence of excess (ps1)2⊂H. However,
azobispyrazole 9 (39) [and, to some extent,
azopyrazole 8 (40)] showed a strong tendency
to form a heterodimer with ps1, as manifested
by the intense 509-nm peak in the absorption
spectrum (Fig. 2C, dotted brown line). The
high fraction of the heterodimer allowed us
to grow single crystals and determine the struc-
ture by x-ray diffraction, revealing E-9 and ps1
bound tightly inside the cavity of the host (Fig.
2D). Exposure of (E-9⋅ps1)⊂H to 525-nm light
quenched its near-UV absorption, consistent
with the E→Z isomerization (Fig. 2C). The
putative (Z-9⋅ps1)⊂H heterodimer is unstable,
forcing ps1 into homodimers, which explains
why the 400- to 600-nm portion of the spec-
trum at the end of the reaction is nearly iden-
tical to that of pure (ps1)2⊂H (Fig. 2C). Similar to
1 and 9, compounds 2 through 8 also switched
to their Z isomers when exposed to 525-nm
light in the presence of (ps1)2⊂H (fig. S79).
The vastly different heterodimer populations
in 1 + ps1 versus 9 + ps1 mixtures do not trans-
late into major differences in the reaction kinet-
ics: The former comprises only ~2% heterodimer
but requires only twice as much time as the
latter (which has a heterodimer fraction of
~80%) to reach a photostationary state (PSS).
This finding reflects the rapid guest-exchange
kinetics between hosts (36), which led us to
hypothesize that DESC should work efficiently
also with catalytic amounts of the PS. Indeed,
decreasing the amount of (ps1)2⊂H to only
0.05 equiv. with respect to (E-9)2⊂H extended
the time required to reach the PSS fourfold
(Fig. 2E), but did not markedly affect its
composition.
The finding that E-9 and ps1 form a het-
erodimer in a near-quantitative yield allowed us
to determine the quantum yield (QY) of DESC
for this pair. Here, we note that ps1 within
(E-9⋅ps1)⊂H is highly emissive, but its fluores-
cence in (ps1)2⊂H is largely quenched (34).
Therefore, exposing (E-9⋅ps1)⊂H to a 515-nm
pulsed laser led to a gradual decrease of emis-
sion (Fig. 2F, empty markers). When the ex-
periment was repeated in the presence of an
extra 2 and 4 equiv. of (E-9)2⊂H, however, we
observed lag periods of ~8 and ~18 min, re-
spectively. The stable fluorescence, despite the
ongoing E→Z isomerization of 9, indicates that
the concentration of (E-9⋅ps1)⊂H remains
steady, which confirms the rapid exchange
kinetics in our system: as soon as the isom-
erized Z-9 is expelled from the host, it is re-
placed by another copy of E-9 (if available).
By assessing the mean number of absorbed
photons required to convert the excess of E-9,
we found that each successful E→Z isomeriza-
tion event requires 17 photons on average (de-
rivation can be found in the supplementary
materials), which corresponds to a QY of ~6%,
a notably high value, given the number of steps
separating the excitation of ps1 from the for-
mation of Z-9 (Fig. 1B).
Once generated by DESC, the Z isomer can
be back-isomerized to E through direct excita-
tion with blue light (435 nm), and the process
can be repeated for many cycles. To demon-
strate the robustness of DESC, we subjected
compound 9 to >100 switching cycles and did
not observe any noticeable fatigue: both 9 and
ps1 retained their initial absorbance values
(Fig. 2G).
Time-resolved spectroscopic and
computational studies of DESC
In solution, BODIPY dyes as simple as ps1 are
poor triplet sensitizers (41, 42); therefore, the
finding that ps1 acts as an efficient photo-
sensitizer in DESC is unexpected. To obtain
mechanistic insights into DESC, we performed
transient absorption spectroscopy (TAS) and
computational studies (Fig. 3). First, we studied
the photoinduced dynamics of the (ps1)2⊂H
homodimer using femtosecond TAS (fs-TAS).
Figure 3A shows the fs absorption changes at
two different wavelengths following excitation
of (ps1)2⊂H with a 500-nm laser. The initial
(<1 ps) ground-state bleach at 483 nm accom-
panied by excited-state absorption at 412 nm
is indicative of the transition from the ground
state (S0) to the singlet excited state (S1) in ps1.
At delay times >100 ps, the 412-nm absorp-
tion increases further and the 483-nm bleach
becomes more pronounced, which can be at-
tributed (43) to ISC from the S1 state to the
triplet excited state (T1). Using microsecond
TAS (ms-TAS), we found the resulting triplet
state to be remarkably stable, with a mono-
exponential lifetime of 16.5 ± 0.5 ms under
ambient conditions (fig. S114A). As expected
from a triplet state, the lifetime is strongly de-
pendent on the amount of oxygen in the sol-
vent; decreasing the amount of O2 by bubbling
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Fig. 2. Following DESC by steady-state absorption and emission spectros-
copy. (A) Equilibrium between (top) homodimeric inclusion complexes of
a PS and an E-azoarene—(PS)2⊂H and E2⊂H, respectively—and (bottom) the
heterodimeric complex (E·PS)⊂H. Only E residing within the heterodimer, but not
the homodimer, can be switched with visible light. The resulting Z is encapsulated
as a sole guest (if enough host is available) and cannot be sensitized either.
(B) Absorption spectrum of a 1:1 mixture of (ps1)2⊂H and (E-1)2⊂H (dotted
brown line) and changes in the spectra accompanying irradiation with green light
(lmax = 525 nm, denoted by green shading). The dotted blue line represents the
absorption spectrum of (ps1)2⊂H. (C) Absorption spectrum of a 1:1 mixture of
(ps1)2⊂H and (E-9)2⊂H [dotted brown line; predominantly (E-9·ps1)⊂H] and
changes in the spectra accompanying irradiation with green light (lmax = 525 nm,
denoted by green shading). The dotted blue line represents the absorption
spectrum of (ps1)2⊂H. (D) The x-ray crystal structure of the heterodimeric
complex (E-9·ps1)⊂H (from the left: front view, side view, and top view; light gray,
host H; dark gray, E-9; green, ps1; water molecules, counterions, and host
protons omitted for clarity). (E) Graph following DESC of 9 in the presence of
different equiv. of ps1 (the data were normalized to the 0 to 1 range, except the
experiment with no PS; raw spectra can be found in fig. S76). Abs., absorbance.
(F) Evolution of the emission intensity of ps1 under 515-nm light (used both
to induce DESC and excite fluorescence) as a function of the amount of 9. Em.
int., emission intensity. (G) More than 100 cycles of reversible photoisomerization of
9 induced solely by visible light (E→Z, DESC with 525-nm light for 2 min; Z→E,
direct photoexcitation using 435-nm light for 30 s). The amount of the E isomer
is proportional to absorbance at 353 nm; the absorption at 480 nm originates
from the (ps1)2⊂H homodimer. norm., normalized.
N2 for 4 min and 10 min extended the lifetime
of the T1 state of ps1 to 160 ± 4 ms and 10.1 ±
0.5 ms, respectively (fig. S114B).
When the fs-TAS experiment was repeated
for a 1:2 mixture of (ps1)2⊂H and (E-9)2⊂H (i.e.,
a pair with a high tendency to form a hetero-
dimer), the bleach at 483 nm was substantially
less pronounced (Fig. 3B, inset), indicating a
TET to E-9 (Fig. 1B, step iii). Notably, the TET
and the subsequent formation of Z-9 occur in
the nanosecond time regime—i.e., much faster
than the lifetime of the ps1 triplet state—which
explains why DESC does not require exclusion
of oxygen. In fact, we found the process to be
equally efficient in strictly deoxygenated ver-
sus thoroughly oxygenated water (fig. S91).
We also studied the E-9–ps1 pair under
ambient conditions by ms-TAS (Fig. 3C) and
found the intensity of transient absorption at
430 nm within 0.1 ms after excitation (DAbs*430)
to be inversely proportional to the amount of
E-9. This finding was consistent with the quench-
ing of ps1’s triplet state by its E-9 co-guest by
means of TET. The resulting triplet-9 can either
relax to the initial E-9 isomer or switch to Z-9,
which absorbs at 430 nm, hence the increasing
steady-state absorption (DAbs∞
430). This intimate
relationship between the degree of ps1 triplet
state quenching and the extent of E→Z isom-
erization identified by ms-TAS further confirms
that DESC proceeds by means of TET between
the ps1 donor and E-9 acceptor.
To gain further insights into DESC, we studied
various azoarene–PS combinations as nonco-
valent heterodimers by using quantum chem-
ical simulations. We consistently found that
the lowest-energy triplet state within these
heterodimers was localized on the PS (there-
fore, we refer to it as TPS) and the second-lowest
triplet state was localized on the azoarene (i.e.,
Tazo), which indicates that the TPS→Tazo tran-
sition is an endothermic process (25, 44) (e.g.,
Fig. 3D shows the energy diagram for 1⋅ps1.
These results led us to hypothesize that the
experimentally observed TET might be facili-
tated by thermal fluctuations of molecules, as
suggested previously for other triplet donor–
acceptor pairs (25, 26, 45, 46). Therefore, we
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Fig. 3. Time-resolved spectroscopic and computational studies of DESC.
(A) Normalized decays of fs transient absorption of ps1 at 412 nm and 483 nm
within the (ps1)2⊂H homodimer (excitation wavelength, lexc = 500 nm). Points,
raw data; lines, four-exponential fits (details can be found in the supplementary
materials). norm., normalized. (B) Normalized transient-absorption decays of ps1
at 483 nm (lexc = 500 nm) in (ps1)2⊂H versus the (E-9·ps1)⊂H heterodimer
(linear scale in the 0 to 1 ps time range; logarithmic scale beyond 1 ps). (Inset)
The same data plotted on the linear scale. (C) Decays of ms transient absorption
at 430 nm (lexc = 510 nm) in (ps1)2⊂H in the presence of increasing amounts
of (E-9)2⊂H. The thin and thick lines correspond to experimental data and
biexponential fits, respectively. (Inset) The inverse correlation between DAbs*430
(absorbance at 430 nm immediately after photoexcitation) and DAbs∞
(steady-state absorbance after photoswitching). All the TAS results presented
here were collected under ambient (nondeoxygenated) conditions. (D) The
calculated energies of the E-1·ps1 heterodimer's lowest excited states: the bright
singlet state (Sps1) and the two lowest triplet states, localized on ps1 and
430
E-1 (Tps1 and TE-1, respectively) (details can be found in fig. S116). The arrows
indicate the sequence of events (“hn” indicates a photoinduced transition; the
gray arrow indicates an endothermic process). (E) Ground-state relaxed scan
along the C–N=N–C dihedral angle F in 1 within the 1·ps1 heterodimer. The
gray line denotes the ground state (S0), the red line denotes the Sps1 state,
and the blue lines denote the TE-1 and Tps1 states. The circular and triangular
markers correspond to the localization of the excited state on the donor (ps1)
and acceptor (E-1), respectively. (F) Ground-state relaxed scan of F in 1 within
the (1·ps1)⊂H heterodimer (orange trace). The blue trace shows the energies
that correspond to the same configurations of 1 and ps1 after removing the host
and its interactions. (i), (ii), and (iii) correspond to DF values 0°, +165°, and
–170°, respectively. (G) Optimized geometries of (1·ps1)⊂H for the three DF
values indicated in (F) (left, side views; right, top views). The distances between
the indicated equatorial Pd nodes describe the degree of host deformation;
the larger the difference between the two Pd–Pd distances, the greater the transition
of H from a tube-like conformation into a bowl-like conformation.
studied the dependence of the 1⋅ps1 excited-
state energies on the C–N=N–C dihedral angle
(F) in azobenzene 1 (which is substantially
more flexible than ps1). Figure 3E shows a
relaxed scan for the 1⋅ps1 heterodimer, demon-
strating that an 18° twist in F is sufficient to
invert the energetic order of Tps1 and TE-1,
making TET energetically favorable. We sep-
arately studied the dynamics of the (1⋅ps1)⊂H
heterodimer by multiscale molecular dynamics
simulations (fig. S121 and movie S1). These
simulations revealed that thermal fluctuations
readily allow 1 to adopt conformations with DF ≥
18° at room temperature.
We performed additional multiscale simu-
lations to better understand the relative insta-
bility of the (Z⋅PS)⊂H heterodimers versus
(E⋅PS)⊂H (Fig. 1B), which lies at the heart of
efficient DESC. The starting point of the sim-
ulations was (E-1⋅ps1)⊂H with a perfectly planar
geometry of E-1. We performed a relaxed scan by
changing F in steps of 5° in both senses of
rotation; the resulting energies are plotted in
Fig. 3F in orange. The blue curves in Fig. 3F cor-
respond to the same geometries while neglecting
the host and its interactions; therefore, the
energetic difference between the two curves
(highlighted with gray shading) quantifies the
instability of the inclusion complex. We found
that rotating F in one direction affords a highly
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unstable supramolecular architecture (Fig. 3G, ii)
that is ~0.35 eV (~8 kcal/mol) higher in energy
than free Z-1⋅ps1 (Fig. 3F). Notably, rotating F in
the opposite direction gave rise to a geometry
where the host did not markedly increase the
energy (Fig. 3, F and G, iii). However, in this struc-
ture, host H assumes a bowl-like conformation,
and Z-1 extrudes from the cavity, facilitating its
expulsion to the solution (movies S5 and S6).
The high conformational flexibility of H (47) is
an important requirement for DESC; indeed, the
cavities of rigid coordination cages (48) and other
confined environments (49, 50) were shown to
render azobenzene nonphotoswitchable under
all wavelengths of light.
Tuning the excitation wavelength of DESC
Encouraged by the unexpected sensitization
potency of ps1 under confinement, we consid-
ered DESC with other, more red-shifted dyes,
including ones not previously known to act as
triplet sensitizers. To this end, we first focused
on the fluorinated BODIPY ps2 (Fig. 4A), with
an absorption peak centered at 553 nm (51)
(compared with 499 nm for ps1). We found
that ps2 exhibited a higher affinity than ps1 to
form heterodimers with various azoarenes and
hypothesized that the increased PS–azoarene
interactions should further promote DESC.
Indeed, Fig. 4B shows that ps2 induces a near-
quantitative E→Z conversion of an equimo-
lar amount of azobenzene 4 within only 90 s
of low-intensity (2.5 mW cm–2) yellow-light
(561 nm) irradiation. The more efficient DESC
allowed us to decrease the PS loading further:
At only 0.01 equiv. of (ps2)2⊂H with respect to
(E-4)2⊂H, the PSS was reached within ~20 min
(Fig. 4C).
In general, ps2 is a more efficient DESC agent
than ps1. However, we found one exception:
Fig. 4. Extending the concept of DESC to red-shifted photosensitizers. (A) Structural formulae of
fluorinated BODIPY ps2, resorufin ps3, and resazurin ps4. (B) Changes in the absorption spectra of encapsulated
E-4 in the presence of an equimolar amount of encapsulated sensitizer ps2 under yellow light (lmax = 561 nm;
2.5 mW cm–2). (C) DESC (here, for E-4) in the presence of substoichiometric amounts of ps2. (D) Changes
in the absorption spectra of encapsulated E-1 in the presence of an equimolar quantity of encapsulated
sensitizer ps3 under orange light (lmax = 599 nm; 0.8 mW cm–2). (E) DESC (here, for E-1) in the presence of
substoichiometric amounts of ps3. (F) Changes in the absorption spectra of encapsulated E-2 in the presence
of an equimolar quantity of encapsulated sensitizer ps4 under red light (lmax = 635 nm; 3.4 mW cm–2). (G) DESC
(here, for E-2) in the presence of substoichiometric amounts of ps4. The data in (C), (E), and (G) were normalized
to the 0 to 1 range, except for the experiments with no PS; raw data can be seen in figs. S85G, S93F,
and S98G, respectively. norm., normalized.
ps2 proved unable to induce the switching
of azobispyrazole E-9. To understand this re-
sult, we resorted to quantum chemical simu-
lations and found the TPS–Tazo energy gap for
the E-9–ps2 heterodimer to be exceptionally
high (1.03 eV; compared with 0.26 eV for E-1–ps1
in Fig. 3D). Relaxed scans analogous to those
in Fig. 3E showed that F in 9 must twist by
38°—a prohibitively large distortion—for the
energies of these two triplet states to equalize
(fig. S122D). These computational results not
only rationalize the experimental findings but
also provide further (although indirect) sup-
port for the involvement of the TET mechanism
in our system.
We also worked with resorufin ps3 and res-
azurin ps4 (Fig. 4A), both of which were pre-
viously reported to form inclusion complexes
of the (PS)2⊂H type (35). These two dyes are
red-shifted even further than is ps2; for ex-
ample, the absorption maxima of their respec-
tive heterodimers with E-1 appear at 587 and
616 nm, with absorption extending into the
red spectral range. To our satisfaction, exciting
the absorption bands on these heterodimers
with orange and red light, respectively, resulted
in a highly efficient E→Z isomerization of
nearly all azoarene–PS combinations (Fig. 4
and figs. S95 and S100).
The performance of DESC is showcased in
Fig. 5A, which lists the PSS compositions (blue
font) for all the nine model azoarenes shown
in Fig. 1D (encapsulated within H in water
with 0.05 equiv. of the selected sensitizer: ps2
for 1 to 7 and ps1 for 8 and 9). The reactions
were performed on the NMR scale (i.e., mil-
ligram quantities of 1 to 9) and can readily be
scaled up to obtain the Z isomers on the pre-
parative scale (tens of milligrams). As control
experiments (red font), we irradiated 1 to 9
under the same conditions and in the pres-
ence of the PS, but without host H (hence, in
an organic solvent). In the absence of H, the E
isomers could not be co-confined with the PS,
which resulted in negligible amounts of Z-
isomer formation by direct photoexcitation
[only azobenzene 6, known for its visible-
light-responsiveness (17), afforded a small
(14%) amount of Z]. The positively charged
azobenzene (52) 5 [often recognized as a proto-
typical photopharmacophore (13, 53)] showed
a particularly impressive contrast in behavior
between the presence and absence of the host,
giving rise to 98% of Z. Notably, such a Z-rich
PSS cannot be achieved by direct photoisom-
erization [of neither (E-5)2⊂H nor free 5] with
any wavelength of light (the same is true for
compounds 1, 3, and 6) because of the partial
overlap of the absorption bands of the two
isomers (54). By contrast, the PSS composition
in DESC is dictated by the tendency of the two
isomers to form the ternary (azo⋅PS)⊂H com-
plex, and this tendency is overwhelmingly higher
for the E isomer.
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 5. Performance and selectivity of DESC. (A) Numbers in blue represent
the composition of the PSS of azoarenes 1 to 9 subjected to DESC on the
millimolar scale in the presence of 0.05 equiv. of the PS (ps2 under 561-nm light
for 1 to 7; ps1 under 525-nm light for 8 and 9). Numbers in red represent the
PSS compositions of the same azoarene–PS mixtures under identical illumination
conditions, but in the absence of the host (CDCl3 was used as the solvent for
all azoarenes except 3 and 5, for which CD3OD was used). Illumination times
were 15, 12, 35, 12, 40, 24, 45, 4, and 9 min for 1 to 9, respectively. n.d., not
detected (i.e., the amount of Z was below the NMR detection limit). (B) Evolution
of absorption spectra during red-light irradiation of E-3 in water in the
presence of 0.005 equiv. of (ps4)2⊂H. The resulting PSS contains 88% Z-3.
(C) Selective switching of the negatively charged E-3 with 561-nm light in the
presence of the positively charged E-5 on the micromolar scale. (D) UV-vis
absorption spectra for the experiment shown in (C). Dotted line, PSS under
561-nm light; dashed line, PSS after the subsequent exposure to 365-nm light
(where both azobenzenes isomerize to a similar extent). (E) Selective switching
of E-4 with 561-nm light and (ps2)2⊂H in the presence of a UV-dimerizable
anthracene. (F) UV-vis absorption spectra for the experiment shown in (E).
Dotted line, PSS under 561-nm light; dashed line, after the subsequent exposure
to 365-nm light.
Having demonstrated that the positively
charged E-5 can be successfully transformed
into Z-5 despite its low affinity to the like-
charged H, we speculated that other water-
soluble azobenzenes may also be efficiently
disequilibrated with a substoichiometric amount
of not only the PS but also the host. Figure 5B
shows the result of an experiment in which an
aqueous solution of the negatively charged 3
was exposed to red light in the presence of
0.005 equiv. of (ps4)2⊂H. The absorption spec-
trum of this solution is dominated by the intense
absorption peak of E-3 in the near-UV region;
the small amount of the sensitizer appears as a
weak band at ~600 nm (Fig. 5B). Remarkably,
exciting this band with low-intensity 635-nm
light resulted in a near-complete disappearance
of the much more prominent and distant peak
originating from another species (E-3). We found
that the PSS contained 88% of Z-3 (versus ~0%
in the absence of either H or ps4), which indi-
cated that each molecule of H hosted more than
180 E→Z isomerization events on average.
Photoswitching selectivity enabled by DESC
To further demonstrate the potential of DESC,
we explored the charge (+12) and cavity size of
host H to discriminate between photoreac-
tive compounds with overlapping absorption
bands, which otherwise cannot be converted
selectively. To this end, we mixed E-3 and E-5
in a 1:3 ratio and added (ps2)2⊂H (0.5 equiv.
with respect to 3) (Fig. 5C). At low (micromo-
lar) concentrations, only the negatively charged
3 exhibits affinity to H; 5 is not encapsulated
owing to the Coulombic repulsion. Indeed,
yellow-light (561 nm) illumination of this mix-
ture led to a highly selective switching of E-3
(despite the threefold excess of E-5) (Fig. 5D
and fig. S104). By contrast, exposure to UV light
induced nonselective isomerization of both
azobenzenes by direct excitation. In the sec-
ond example, we worked with a mixture of E-4
and 9-bromoanthracene, both in the form of
homodimers encapsulated within H. Upon
exposure to UV light, the encapsulated an-
thracene rapidly dimerizes to afford the cor-
responding dianthracene (36) under the same
irradiation conditions that triggered the direct
E→Z photoisomerization of 4 (Fig. 5E, dashed
arrow). However, exposing the same mixture
Gemen et al., Science 381, 1357–1363 (2023)
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to yellow light in the presence of (ps2)2⊂H
induced highly selective photoisomerization of
azobenzene, leaving the anthracene intact (Fig.
5F, dotted line).
Discussion
From a thermodynamic perspective, our sys-
tem acts as a light-driven supramolecular ma-
chine that converts light into chemical energy
in the form of out-of-equilibrium photosta-
tionary states. DESC relies on the selective
coencapsulation of the stable E isomer of an
azobenzene with a dye that acts as an antenna,
absorbing visible light energy that is ultimately
used to generate the metastable Z isomer. The
absorption of light promotes the dye from the
ground state to the singlet excited state. Con-
finement inside of the host increases the dye’s
ability to undergo intersystem crossing, pop-
ulating the dye’s triplet state and turning it
into a potential triplet sensitizer. Quantum
chemical simulations reveal that although the
triplet state of azobenzene is higher than that
of the dye, a small dihedral angle twist in
azobenzene lowers its triplet energy while in-
creasing the triplet energy of the coencapsu-
lated dye to the extent that the two energy levels
converge. Therefore, the dye-to-azobenzene
triplet-energy transfer can become favorable
owing to azobenzene dynamics (25, 44). Once
in the triplet state, the azobenzene can either
dissipate energy or switch to the Z isomer.
Z-azobenzene is nonplanar and can no longer
be co-confined with the photosensitizer; thus,
it is expelled from the host and cannot be re-
sensitized. In this way, DESC shifts the equi-
librium toward the metastable Z state without
the need to populate azobenzene’s singlet ex-
cited state, which is relatively high in energy
and requires the absorption of UV light.
Although we focused on a particular host
and one class of photoswitchable molecules
(H and azoarenes, respectively), our results
allow us to establish general design principles
for other DESC systems: (i) The host should have
an affinity for a photoswitch and a photosen-
sitizer, and its cavity should be large enough to
simultaneously encapsulate the photosensitizer
and the thermodynamically stable isomer of
the photoswitch; (ii) the host’s affinity for the
metastable form of the photoswitch must be
substantially lower (because of its different
shape and/or polarity) so as to render coencap-
sulation with the photosensitizer unfavorable;
and (iii) an open cavity and/or conformational
flexibility should promote rapid guest-binding
and -release kinetics by the host for fast eatalytic
turnover and to ensure that once generated, the
metastable form of the photoswitch is expelled
from the cavity before it is resensitized.
In principle, DESC is applicable to other classes
of photoswitchable compounds, although larger
or differently shaped hosts may be required.
Self-assembly through metal–ligand coordination
offers an attractive approach to generating a
wide range of hosts from simple components
in a modular fashion.
As demonstrated in this work, DESC is a ro-
bust process that works with catalytic amounts
of sensitizers, under ambient conditions (no
oxygen exclusion necessary), and for a wide
range of azobenzenes and heterocyclic azoarenes.
We envision that DESC will become a powerful
tool to control chemical reactivity through a com-
bination of light irradiation and confinement.
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AC KNOWLED GME NTS
Funding: We acknowledge funding from the European Union’s
Horizon 2020 Research and Innovation Program [European
Research Council grants 820008 (Ra.K.) and 101045223 (A.P.) and
Marie Skłodowska-Curie grants 812868 (J.G.) and 101022777
(T.-P.R.)], the Academy of Finland [Center of Excellence
Programme LIBER grant 346107 (A.P.), Flagship Programme
PREIN grant 320165 (A.P.), and Postdoctoral Researcher grant
340103 (T.-P.R.)], Zuckerman STEM Leadership Program
Fellowship (J.R.C.), President’s PhD Scholarship (M.O.), and the
EPSRC [Established Career Fellowship grant EP/R00188X/1 (M.J.F.)].
Author contributions: Conceptualization: A.P., I.S., and Ra.K.;
Methodology: J.G., J.R.C., T.-P.R., N.D., D.O., A.P., I.S., and Ra.K.;
Investigation: J.G., T.-P.R., N.D., M.J.B., M.W., M.F., M.K., M.O.,
V.A.B., Ri.K., and Y.D.-P.; Funding acquisition: M.J.F., A.P., I.S., and
Ra.K.; Project administration: Ra.K.; Supervision: D.O., M.J.F., A.P.,
I.S., and Ra.K.; Writing: J.G., J.R.C., T.-P.R., N.D., A.P., I.S., and Ra.K.
Competing interests: The authors declare no competing interests.
Data and materials availability: Crystallographic data for
inclusion complexes (E-9)2⊂H, (E-9⋅ps1)⊂H, and (TX)2⊂H have
been deposited in the Cambridge Crystallographic Data Centre
(CCDC) with accession codes 2240153, 2227254, and 2227255,
respectively. All other data are available in the main text or the
supplementary materials. Raw data underlying the plots have been
deposited at Dryad (55). License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adh9059
Materials and Methods
Supplementary Text
Figs. S1 to S122
Tables S1 to S5
References (56–93)
Movies S1 to S6
(2019).
33. A. Mostad et al., Acta Chem. Scand. 25, 3561–3568 (1971).
Submitted 21 March 2023; accepted 22 August 2023
10.1126/science.adh9059
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RES EARCH
NEUROSCIENCE
Wide-field fluorescence lifetime imaging of neuron
spiking and subthreshold activity in vivo
Adam J. Bowman1*, Cheng Huang2,† Mark J. Schnitzer2,3,4, Mark A. Kasevich1*
The development of voltage-sensitive fluorescent probes suggests fluorescence lifetime as a promising
readout for electrical activity in biological systems. Existing approaches fail to achieve the speed
and sensitivity required for voltage imaging in neuroscience applications. We demonstrated that
wide-field electro-optic fluorescence lifetime imaging microscopy (EO-FLIM) allows lifetime imaging at
kilohertz frame-acquisition rates, spatially resolving action potential propagation and subthreshold
neural activity in live adult Drosophila. Lifetime resolutions of <5 picoseconds at 1 kilohertz were
achieved for single-cell voltage recordings. Lifetime readout is limited by photon shot noise, and the
method provides strong rejection of motion artifacts and technical noise sources. Recordings revealed
local transmembrane depolarizations, two types of spikes with distinct fluorescence lifetimes, and
phase locking of spikes to an external mechanical stimulus.
R ecording the electrical activity of neu-
rons at high spatial and temporal reso-
lution is central to understanding brain
function. Fluorescent probes of cal-
cium activity enable optical studies of
large neuron populations in vivo (1, 2). How-
ever, the response time of calcium indicators
is much slower than the underlying electri-
cal signals. Fluorescent voltage sensors are a
complementary approach, providing direct
readout of neuron membrane potential with
the capability to resolve action potentials.
Although voltage probes have rapidly devel-
oped with a variety of genetically encoded
(3–7) and chemical dyes (8) in use, there re-
main considerable challenges to their appli-
cation in vivo because of low sensitivity, rapid
photobleaching, and motion artifacts. To
achieve high-speed recording and sufficient
signal-to-noise ratios (SNRs), most voltage
probes use fluorescence intensity to read out
an underlying sensing mechanism on the basis
of absorption, Förster resonance energy trans-
fer (FRET), or quenching.
We applied an alternative strategy for de-
tecting fast probe dynamics that is based on
lifetime imaging (9). Voltage sensors that use
FRET and quenching mechanisms modulate
the probe’s nonradiative decay rate, intrinsi-
cally connecting fluorescence intensity with
nanosecond excited-state lifetime. Lifetime is
a promising readout for voltage imaging, es-
pecially because of its capability to provide an
absolute indication of membrane potential
(10). Recent results have validated fluorescence
1Physics Department, Stanford University, Stanford, CA 94305,
USA. 2James H. Clark Center, Stanford University, Stanford,
CA 94305, USA. 3CNC Program, Stanford University, Stanford,
CA 94305, USA. 4Howard Hughes Medical Institute, Stanford
University, Stanford, CA 94305, USA.
*Corresponding author. Email: abowman2@stanford.edu (A.J.B.);
kasevich@stanford.edu (M.A.K.)
†Present address: Department of Neuroscience, Washington Univer-
sity School of Medicine, St. Louis, MO 63110, USA.
lifetime for static measurements of membrane
potential in vitro (11). However, existing life-
time detectors—for example, single-photon
counters or cameras with modulated pixels
(12)—fall short of the requirements for detect-
ing fast dynamics and imaging neurons in vivo,
either because of their limited photon through-
put or because of prohibitively high noise.
EO-FLIM technique
We demonstrated an approach that uses electro-
optic fluorescence lifetime imaging micros-
copy (EO-FLIM), an all-optical technique for
lifetime imaging that is based on nanosecond
gating of a wide-field image (13, 14). EO-FLIM
allows efficient photon collection and is com-
patible with detection on high-speed, low-
noise scientific cameras. With this method, we
achieved lifetime imaging of action potentials
in vivo.
EO-FLIM enables significant suppression of
intensity artifacts, allowing robust imaging
in the presence of tissue motion and fluctua-
tions in illumination intensity. Such artifacts
are ubiquitous in recordings of neural activity
from awake, behaving animals (15, 16). This
has two consequences: (i) It enables faithful
recording of subthreshold voltage waveforms,
and (ii) it improves the SNR by suppressing
high-frequency intensity noise. These follow
from the fact that EO-FLIM estimates lifetime
from the ratio of a pair of simultaneously
recorded intensity channels derived from a
common optical source. In conventional ap-
proaches, corrections for intensity noise use
ratios of measurements that are nonsimulta-
neous and easily corrupted by high-frequency
noise or slower motion artifacts. Optical sen-
sors of neuron activity are typically reported
by DF =F , referencing fast intensity changes
(DF) to a nonsimultaneous, average fluores-
cence baseline (F ). Fluorescence lifetime can
read out an intensity-optimized sensor with
improved temporal noise performance and
long-term stability without sacrificing acqui-
sition speed.
We implemented our approach through in-
corporation of a Pockels cell into the fluorescence
detection path of a standard epifluorescence
microscope (Fig. 1A, fig. S1, and materials and
methods). The Pockels cell design was optimized
for resonant drive and wide-field imaging, in-
corporating thermal control and transverse
crystal geometry to cancel off-axis birefrin-
gence. A high-voltage modulation was applied
to the Pockels cell with a resonant transformer
(figs. S2 and S3), resulting in a fast polariza-
tion rotation that was synchronous with the
excitation pulses from a 100-ps laser source.
Fluorescence from the sample was first po-
larized, then polarization was modulated with
the Pockels cell and finally split with a polariz-
ing beamsplitter into two wide-field images on
a scientific complementary metal-oxide semi-
conductor (sCMOS) camera corresponding
to gated (G) and ungated (U) intensity. These
two images encoded nanosecond time infor-
mation in their intensity ratio. Because gating
was performed with a beamsplitter, it was pos-
sible to capture the entire fluorescence decay
with photon efficiency limited by optical coat-
ings. In this study, we modulated one input
polarization and discarded half of the avail-
able signal on a first polarizer. This can be
avoided in the future through addition of a
second beam path (13). The fluorescence de-
cay at each pixel was convolved with the tem-
poral gating function of the Pockels cell and
then sampled at a single modulation phase
relative to the excitation laser (Fig. 1B). Each
image thus provided a lifetime estimate for
every pixel in parallel at the frame rate of the
scientific camera. When imaging genetically
targeted neurons in vivo, this technique al-
lowed for 1-kHz–frame rate recordings with
a lifetime sensitivity of 2.53 ± 0.48 ps with
0.7 × 107 to 1.4 × 107 detected photons per
frame (Fig. 1C), indicating a substantial im-
provement in throughput over previous FLIM
recordings of cellular dynamics. EO-FLIM
approaches fundamental sensitivity limits
for estimating lifetimes between 1 and 4 ns
(fig. S2).
Results
We used EO-FLIM to image a genetically en-
coded voltage indicator (GEVI) in Drosophila
melanogaster. We expressed pAce positive
polarity GEVI in a subtype of fly mushroom
body output neuron (MBON), MBON-g1pedc>ab.
pAce works through FRET and is a fusion of
the bright fluorescent protein mNeonGreen
with a voltage-sensitive opsin from Acetabularia
(3). We surgically prepared Drosophila before
imaging to provide optical access to the brain
(17, 18). Action potentials and subthreshold
dynamics were readily resolved with action
potentials corresponding to a 20- to 50-ps
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Lifetime imaging of action potentials.
(A) Schematic of EO-FLIM microscope. Wide-field
fluorescence images were modulated with a Pockels
cell (PC) placed between crossed polarizers (P
and PBS) and driven at 20 MHz by a high-voltage
resonant transformer. Two spatially offset output
images were simultaneously captured after a second
polarizing beamsplitter (PBS) on a sCMOS camera,
corresponding to gated (G) and ungated (U)
intensities. (B) Instrument response function (IRF)
and fluorescence traces for the U channel were
measured by varying the Pockels-cell drive phase
relative to the excitation laser. The pAce GEVI was fit
to 2.2-ns lifetime. For kilohertz imaging, a single
optimal phase point was captured (vertical line
at 0-ns delay), and the G/U image intensity ratio
was converted to a lifetime estimate (fig. S1).
(C) Histogram of measurements (highpass filtered)
obtained at 1 kHz for a single neuron in vivo
demonstrate a lifetime sensitivity of 3 ps (full trace in
Fig. 2A). (D) Wide-field image of a neuron with
structures indicated. Scalebar, 25 mm. (E) Whole-cell
lifetime trace resolves action potentials and sub-
threshold transitions. (F and G) Average spike shape
is plotted in intensity and lifetime from color-coded
regions. (H) Frames from an interpolated lifetime
movie demonstrate spike propagation, averaging the
signal from ~300 individual spikes. The point of
initiation is indicated by the arrow, and bidirectional
propagation was observed both along the axon
and backward toward soma and dendrites (movies S1
to S3). Spike propagation was also imaged directly
without averaging (movies S4 and S5). (I) Applying a
10-frame moving average allowed subthreshold
signals to be localized to neuron structures (movies
S6 and S7). Example frames demonstrate localization
in the dendrite for both positive and negative
subthreshold signals.
shift in the fluorescent lifetime (Fig. 1, D and
E). Average spike readouts in lifetime and in-
tensity for different neuron subregions were
in strong agreement both in their relative tim-
ing and amplitudes (Fig. 1, F and G).
The donor fluorescence lifetime of a FRET
GEVI depends on radiative decay rate, kf, and
the voltage-sensitive nonradiative decay rate,
knr(V), associated with FRET as t ¼
1
kf þ knrðV Þ
(10, 19). In pAce, the Ace opsin acts as acceptor
and provides voltage sensitivity. The donor’s
fluorescence intensity is directly quenched by
FRET, giving a signal, DF º sDknr, where s
is the donor excitation cross section. For an
ð
ideal FRET process, one expects to find Dt=t ¼
DF =F. pAce gave a linear but attenuated life-
ÞDF =F (fig. S4).
time response of 0:70 T 0:07
This may indicate components of the GEVI
response in intensity—for example, modulation
of cross section s—that did not affect lifetime
readout.
Wide-field lifetime imaging correlates neu-
ron activity with spatial structure. The point
of action potential initiation in the axon is
resolved along with bidirectional propagation
along the axon and backward toward the den-
drite and soma (20). Action potentials were
attenuated and broadened in the dendrites
and soma (Fig. 1, F and G, and figs. S5 and S6).
Spike propagation is shown in movies S1 to
S3 with still frames from movie S1 displayed
in Fig. 1H, generated with spike-triggered av-
eraging over ~300 spikes and interpolating
between frames. We also observed individ-
ual spikes and spike propagation in real time
without temporal averaging (movies S4 and
S5). Comparison of recordings from multiple
neuronal subregions revealed local depolari-
zations in the axons, which fail to initiate
action potentials across the entire cell. These
depolarizations were not resolved in inten-
sity readout but are clearly visible in lifetime
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Fig. 2. Lifetime suppresses intensity noise and improves fidelity of subthreshold
recording. Six example MBON neurons are shown comparing lifetime (blue)
with DF=F intensity recordings (black). Recordings were obtained by averaging
over high-resolution images shown at far left. Scalebar, 25 mm. Shaded boxes
highlight some notable regions of the traces for improved lifetime readout. For
each example, the distributions of spike SNR are compared for intensity and
lifetime, with calculated spike detection fidelity d′ indicated. (A and B) Two
examples of flies without motion demonstrate improvement of technical noise
floor at high frequencies by up to 7 dB. The noise power spectra for the traces
are compared at far right, with dotted lines indicating the photon shot-noise
limits. (C to E) Three examples of flies having low-frequency noise associated with
motion artifacts. Lifetime improves noise power spectrum across temporal
frequencies, rejecting intensity noise by up to 9 dB at low frequencies (further
analysis is provided in Fig. 3). (F to J) Lifetime provided an improved readout of
two spike amplitudes in response to mechanical stimulus at 60 Hz. Large-amplitude
(L) spikes showed an enhanced lifetime responsivity and tripled detection SNR
and d′ over the small-amplitude (S) spikes. L spikes occurred independent of
subthreshold waveform level but synchronized with spiking on plateaus shown in
the inset in (F). (G) and (H) show average spike waveforms for color-coded
regions. The point of initiation for S spikes was a central region of the axon
(consistent with movies S1 and S2), whereas L spikes were diffuse and associated
with background fluorescence. L spikes also correspond to local spikes in the
dendrite and soma in (H). The L-spike background component possibly resulted
from out-of-focus neurons (movies S8 and S9). In (I) and (J), histograms of action
potential amplitudes are compared. In intensity, the L and S populations were not
resolved and strongly overlap, but they were clearly separated in lifetime.
Lifetime is used to identify the spikes, and the intensity histogram in (I) is shaded
with two colors to show overlapping populations. (K) A polar histogram demonstrates
strong phase locking of the L spikes to mechanical stimulus by referencing
phase to a bandpass-filtered lifetime trace. S spikes do not show phase locking.
icos qið Þ=NAP, is plotted versus bandpass
(L) The average phase vector length,
center frequency to show narrow-band locking response.
P
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recordings (figs. S5 and S6). When we then
applied a 10-frame moving average, the spatial
distribution of slower subthreshold voltage
signals could also be studied. Subthreshold
signals were often strongest and localized in
the dendrites (movies S6 and S7). Still frames
from these movies are shown in Fig. 1I and
figs. S7 and S8.
By measuring a ratio of simultaneous in-
tensities, EO-FLIM removes noise sources that
are common mode to both the modulated
channels. In Fig. 2, we show example record-
ings of MBON-g1pedc>a=b neurons from six
flies, comparing intensity DF =F with lifetime
readouts. In all recordings, lifetime detec-
tion enhanced the SNR for action potential
detection by approximately twofold. This SNR
was quantified by comparing spike ampli-
tude with the high-frequency noise floor. We
also analyzed traces by using the spike de-
tection fidelity, d′, a discriminability index
that quantifies spike detection by comparing
the statistical distributions of spike ampli-
tudes and background-noise fluctuations (21).
Lifetime detection improved d′ by 1.5 to 2.4
times (Fig. 2, A to E).
Noise power was also compared across tem-
poral frequencies, demonstrating broad sup-
pression of intensity noise (Fig. 2, A to E) and
showing that EO-FLIM approaches the pho-
ton shot-noise limit. To allow a direct compar-
ison of noise power spectrum, the responsivity
of spikes in intensity and lifetime channels
was normalized. For flies not displaying much
motion (Fig. 2, A and B), lifetime primarily
reduced technical noise at high frequencies
that resulted from the excitation laser (4 to
7 dB). Even in these well-behaved examples,
lifetime readout resulted in improved SNR
and d′.
Lifetime recordings also improved long-term
stability in the voltage readout. Intensity-based
voltage imaging often displays strong motion
artifacts, which degrade stability. In Drosophila,
these artifacts result from movements such as
extension of the proboscis. For flies displaying
motion (Fig. 2, C to E, and fig. S9), lifetime
readout suppressed artifacts at low frequen-
cies by up to 9 dB as compared with intensity
readout (in these examples, subthreshold wave-
forms may only be resolved in lifetime). Figure 3
shows trace stability quantified according to
the spike-amplitude distribution and the uni-
formity of threshold voltage level at action
potential locations. Histograms of mean nor-
malized spike heights and mean normalized
subthreshold level are plotted for each spike,
showing that lifetime improves spike unifor-
mity by up to 2.5 times and threshold unifor-
mity by up to 5.8 times.
With the improved readout stability af-
forded by lifetime recording, we observed
two spike amplitudes (Fig. 2, F to L). The
small-amplitude (S) spikes occurred on top
Fig. 3. Lifetime improves uniformity in action potential amplitude and threshold level. (A to D). Histograms
of action potential amplitudes (lifetime in blue) and action potential levels on the subthreshold waveform
(lifetime in green) are plotted for each activity trace, overlayed on the same histograms for intensity (gray).
Action potential amplitudes are normalized to the mean. Subthreshold level is also mean normalized as
(cid:3)
(cid:2)
=(cid:1)
L (cid:2) (cid:1)
L, where L is the spike’s corresponding level on a low-pass filtered trace, and its distance is
L
(cid:1)
measured relative to the mean level of all other spikes,
L. A perfectly uniform threshold would thus result in
L = 0 for all spikes. In each histogram, the ratio of standard deviation between intensity and lifetime readouts,
sF=st, is given as a figure of merit for uniformity. (A) and (B) to (D) correspond to Fig. 2, A and C to E,
respectively.
of subthreshold voltage plateaus, whereas
large-amplitude (L) spikes were observed in
bursts that were independent of subthresh-
old voltage level. In this sample, the fly was
mechanically stimulated with sound waves
near a resonance of the microscope stage.
Figure 2, I and J, show histograms of spike
heights in both intensity and lifetime. The
two spike populations were clearly distin-
guished by using lifetime readout but were
not separable with intensity readout. The L
spikes showed enhanced lifetime responsiv-
ity (1.34 DF =F, compared with 0.68 DF =F for
S spikes). The difference in responsivity may
indicate kinetic differences in the GEVI re-
sponse to different action potential waveforms
(3). Spike-triggered averages (movies S8 and
S9) showed that the L spikes originated dif-
fusely across the image, whereas the S spikes
initiated in a local area of the axon, as shown
in movies S1 and S2. The L spikes may be as-
sociated with out-of-focus neurons displaying
off-target GEVI expression and were also syn-
chronous with spiking of the targeted neuron
(Fig. 2, F to H). The L spikes displayed strong
phase locking in response to mechanical stim-
ulus, whereas the S spikes did not. A histogram
of phases is displayed in Fig. 2K, where phase
is determined by each spike’s location on a
trace that has been filtered at the stimulus
frequency. Narrow-band locking response is
demonstrated in Fig. 2L. Similar L spikes were
also observed during the mechanical stimulus
sweep (Fig. 4C).
To further demonstrate the noise-rejection
capabilities of lifetime detection, we placed
the fly on a piezoelectric stage to provide
mechanical shaking in the xy plane. This
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Fig. 4. Phase locking of spikes to direct mechanical stimulus. (A) Lifetime
provided strong rejection of intensity noise associated with shaking the
sample (40-Hz square wave, ~0.8 mm peak-to-peak). (B) Intensity noise at the
stimulus frequency and second harmonic were attenuated by 21 and 20 dB.
(C) A spectrogram of the lifetime trace is plotted as stimulus is swept from
50 to 150 Hz. Vertical lines of activity in the spectrogram correspond to
spike bursts in the lifetime trace. Mechanical cross-talk is seen as the diagonal
line sweep, and phase locking appears as increased frequency content at
the stimulus frequency during spike bursts. (D) To show phase locking
visually, a sliding window autocorrelation of the lifetime trace is plotted with
a 150-ms window. Phase locking may be seen by observing alignment of
autocorrelation peaks during activity bursts to the peaks resulting from
mechanical cross-talk signal. Examples of bursts showing phase locking are
highlighted (blue vertical bars).
direct mechanical stimulus resulted in high
levels of intensity noise that obscured neu-
ron activity, but lifetime readout suppressed
this noise by up to 21 dB (Fig. 4, A and B).
Using this direct stimulus, we could observe
phase-locked spiking behavior from 30 to
>100 Hz (Fig. 4 and fig. S10). As shown in
these figures, we observed phase locking
through increased spectral power at the stim-
ulus frequency in a spectral waterfall plot as
the excitation frequency was swept. This
phase locking may also be visualized with
the autocorrelation of the lifetime trace (Fig.
4, C and D). These observations are consis-
tent with previous studies on mechanical
and auditory effects in Drosophila that iden-
tified a broad auditory response across the
central brain (22) and responses to substrate
vibrations (23, 24).
Discussion
EO-FLIM may be applied to both existing
lifetime-sensitive probes and to donor read-
out of FRET-based biosensors. Standard FRET
sensors are read out by the ratio of optical
intensities in spectrally separated donor and
acceptor channels (25), requiring an acceptor
molecule with high quantum yield. Two-color
readout frequently limits detection sensitivity
because of spectral cross-talk and also pre-
vents probe multiplexing (26). Lifetime mea-
surement removes these limitations and allows
quantitative FRET measurements with only the
donor channel. In voltage imaging, lifetime will
enable improved measurement of FRET-opsin
(3, 7), hybrid FRET (6), and dye indicators (8).
We also anticipate application to imaging cal-
cium (27), neurotransmitters (28, 29), and cyclic
adenosine monophosphate (30).
Use of GEVIs in vivo is often accompanied
by a large fluorescence background that re-
sults from protein expression outside the cel-
lular membrane (31) or leaky gene expression
from nontargeted cells (32). This background
signal had a different fluorescence lifetime
and photobleaches at a different rate, resulting
in slow drifts of the measured lifetime traces
(fig. S11). (We expect that in vitro studies will
not be affected by such backgrounds.) To mea-
sure absolute voltage, signal and background
populations would need to be unmixed by
discriminating between two closely spaced ex-
ponential decays. For this reason, we focus on
the improved stability and noise performance
afforded by lifetime measurement rather than
on absolute quantification. In our current im-
plementation, we measured the population-
weighted average lifetime by acquiring images
at a single modulation phase. In the future,
multiple modulation phases can be combined
to unmix lifetime components and improve
absolute measurement.
We have shown that EO-FLIM enables flu-
orescence lifetime imaging of neuron activity
in vivo, overcoming the throughput and sensi-
tivity limitations of existing FLIM techniques.
We expect straightforward application to other
systems, including mammalian brains, which
feature both larger neurons and action poten-
tials as compared with those of Drosophila
(3, 7). Voltage imaging in neuroscience is one
example application, but membrane potential
is also broadly interesting throughout biology,
from bacteria (33, 34) and plants (35) to car-
diac (36–38) and muscle tissue (39). The ability
of EO-FLIM to strongly reject motion noise in
vivo is relevant for brain- and cardiac-imaging
applications in which it is challenging to faith-
fully distinguish voltage dynamics from mo-
tion and hemodynamic artifacts (15, 16, 36, 37).
It may become possible to perform voltage
imaging during natural movements such as
insect flight, or while tracking a freely moving
organism (40). Further, recent advances in
GEVI probes have enabled voltage imaging of
populations of neurons (3, 5). Lifetime imag-
ing will establish accurate long-term readout
of subthreshold activity across a neural cir-
cuit, allowing functional connectivity mapping
where spike activity may be correlated with
subthreshold modulation of downstream neu-
rons. Last, by using lifetime detection in com-
bination with optogenetic tools (4, 41), it will
be possible to improve techniques for targeted
optical activation and control (42) of neuron
membrane potential.
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AC KNOWLED GME NTS
Funding: We acknowledge funding from the Gordon and Betty
Moore Foundation; the US Department of Energy, Office of Science,
Office of Biological and Environmental Research, under award
DE-SC0021976; NIH grant U01NS120822 (M.J.S. and G. Vasan);
and NSF NeuroNex grant DBI-1707261 (M.J.S. and K. Deisseroth).
A.J.B. acknowledges support from the NSF Graduate Research
Fellowship under grant 1656518 and the Stanford Graduate
Fellowship. Author contributions: A.J.B. developed the microscope.
C.H. prepared Drosophila for imaging. A.J.B. and C.H. performed the
experiments. A.J.B. and M.A.K. analyzed data and wrote the
manuscript. All authors contributed to experiment conception and
manuscript revision. Competing interests: A.J.B. and M.A.K. are
inventors on PCT/US2019/062640, US17/153438, and US17/
898093. Data and materials availability: All data are available in
the manuscript, in the supplementary material, or deposited at
Dryad (43). Code is available at Zenodo (44). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adf9725
Materials and Methods
Figs. S1 to S11
Movies S1 to S9
MDAR Reproducibility Checklist
View/request a protocol for this paper from Bio-protocol.
Submitted 23 November 2022; accepted 16 May 2023
10.1126/science.adf9725
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RES EARCH
FISHERIES
Large females connect Atlantic cod spawning sites
Esben Moland Olsen1,2*, Ørjan Karlsen3, Jon Egil Skjæraasen3
The Earth’s ecosystems are increasingly deprived of large animals. Global simulations suggest
that this downsizing of nature has serious consequences for biosphere functioning. However, the
historical loss of large animals means that it is now often impossible to secure empirical data
revealing their true ecological importance. We tracked 465 mature Atlantic cod (Gadus morhua)
during their winter spawning season and show that large females (up to 114 centimeters in length),
which are still found in mid-Norway, were characterized by more complex movement networks
compared with smaller females. Large males were sparse but displayed similar movement patterns.
Our finding implies that management programs promoting large fish will have positive impacts
on population resilience by facilitating the continued use of a diversity of spawning habitats and the
connectivity between them.
C urrent ecosystems are often character-
ized by an absence of large animals. This
downsizing of nature is part of the on-
going biodiversity crisis and involves the
loss of larger species as well as the larger
individuals within a species, both of which can
be linked to historic and ongoing harvesting
practices by humans (1). Such signatures of
human activity can be traced back for millen-
nia (1–3), which makes it difficult to infer the
potential role of larger animals in intact eco-
systems. Model simulations suggest that larger
animals could have major influences on pop-
ulation dynamics, ecosystem functioning, and
resilience to environmental change (4), and
therefore they should be the focus of biodiver-
sity restoration programs (5). For instance,
large predators may impose strong top-down
control and prevent destabilizing grazer out-
breaks (6) and even promote genetic diversity
at lower trophic levels (7). Large animals could
also play a particularly important role in con-
necting ecosystems (8).
Here, we describe the role of large female
Atlantic cod (Gadus morhua), which are com-
parable in body size to those typically reported
in archaeological studies of cod bones dating
back at least one millennium (2, 9), in con-
necting coastal spawning sites. The Atlantic
cod is a potentially dominant predator in
North Atlantic coastal ecosystems, and indi-
viduals can grow to reach a body length well
beyond 1 m (2, 10). However, cod is also a prized
catch in fisheries, and many populations have
been seriously overfished, in some cases col-
lapsed to a state where recovery is expected
to be slow or even unlikely (11). Size-selective
and intense fishing has also changed the life
history of this fish and caused major trun-
cations of historic age and size distributions
1Institute of Marine Research; Flødevigen, Arendal 4817,
Norway. 2Centre for Coastal Research, Department of
Natural Sciences, University of Agder; Kristiansand 4604,
Norway. 3Institute of Marine Research; Bergen 5817, Norway.
*Corresponding author. Email: esbenmo@imr.no
(9, 12). Larger female cod are highly fecund
and may spawn >10 million eggs during a sea-
son (13, 14). Larger females also typically pro-
duce higher-quality eggs and could therefore
play an important role in population replen-
ishment compared with the smaller conspe-
cifics typically observed in today’s populations
(14–17). Females are thought to visit male ter-
ritories for pairing and spawning (18, 19), and
multiyear homing to specific spawning grounds
is known (20–22). One study also detected in-
dividual movements among spawning sites
(23). However, the environmental and pheno-
typic predictors of such behavior remain un-
clear. The potential for reproduction to happen
at multiple locations clearly exists because fe-
male cod are batch spawners. Typically, portions
of eggs are matured and spawned approximate-
ly every 2 to 4 days throughout the spawning
season (15), with the number of batches increas-
ing with maternal body size (16).
We used acoustic telemetry (24) to map how
individual female cod move during the spawn-
ing season within a network of coastal spawn-
ing sites in mid-Norway (Fig. 1). The spawning
sites were identified as traditional fishing
grounds where cod will aggregate during spawn-
ing and by scientific surveys on cod egg and
juvenile distributions (25). At the onset of three
consecutive spawning seasons (2017 to 2019), a
total of 213 mature female cod were captured,
tagged, and tracked within these spawning
habitats (table S1) (26). The female cod ranged
in body size from 42 to 114 cm and from 0.8 to
15.1 kg. A total of 24% (n = 50) of the tracked
females were 80 cm or larger (27).
Effects of cod body size on connectivity
Whereas the smaller females were typically de-
tected at a few neighboring sites only, the larger
females were more mobile and were detected
at more, and sometimes distant, sites (Fig. 1).
These basic observations were confirmed by
statistical analyses using a network approach
in which the acoustic receivers deployed at
fixed sites represent the nodes, and fish move-
ments between receiver sites represent the
links (26–28). In our study, each fish was as-
signed a connectivity score representing the
number of specific links detected during the
spawning season (29). A residency index (RI),
defined as the number of days that a particular
cod was detected within the telemetry array
during the spawning season (30), was included
as a covariate in the statistical models. This was
to account for the fact that some individuals
are likely to be less strongly associated with
the chosen study area or moving outside the
listening range of the receivers for parts of the
study duration. In our case, 21% of the females
(n = 45) were detected for ≥75% of the days
during the spawning season, whereas 49% (n =
104) were detected for <25% of the spawning
season days. After an initial filtering (26), data
on all females across observed sizes and resi-
dencies were included in the same statistical
model selection (table S2 and fig. S2). The most
parsimonious model for predicting a connectiv-
ity score included an effect of body size, whereas
alternative models excluding the effect of body
size received very little support and were thus
not considered for inference (table S2). A posi-
tive effect of body size on movement among
sites was very clear for resident individuals
having a stronger overall association to the
area covered by the telemetry array, and it was
less clear for individuals only detected for mi-
nor parts of the spawning period (Fig. 2). The
model predicted a connectivity score of 3.3 links
[95% confidence interval (CI) = 2.6 to 4.2] for
resident females (RI = 0.75) with a body size of
50 cm, compared with a predicted connectivity
score of 8.2 links (95% CI = 5.9 to 11.3) for large
(100 cm) resident females (table S3). A 100%
increase in female cod body size was thus as-
sociated with a 148% increase in connectivity
score. There was also a moderately negative
correlation between female cod body size and
residency (Pearson correlation coefficient =
–0.20, P = 0.004), indicating that large females
tended to move beyond the spawning sites in-
cluded in our study area. Note that this cor-
relation between the two predictor variables
did not introduce a serious issue of collinearity
when interpreting model predictions (variance
inflation factor = 1.04).
In a second step, we analyzed the tracked
movements of the 252 male cod included in the
study (table S1 and fig. S2). These males ranged
in body size from 42 to 110 cm, although only
5% (n = 12) were 80 cm or larger. A total of
30% (n = 75) of the males had an RI of ≥0.75,
whereas 38% (n = 95) had an RI <0.25. As for
females, the larger males tended to have more
extensive movement networks compared with
smaller males (Fig. 1). For small and resident
males (length = 50 cm, RI = 0.75), the model
predicted a connectivity score of 3.4 links
(95% CI = 2.8 to 4.1; Fig. 2). By comparison,
for large and resident males (length = 100 cm,
Olsen et al., Science 382, 1181–1184 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Connectivity among Atlantic cod spawning sites. (A) Individual cod were tracked using acoustic telemetry in the Smøla region of northwestern Norway (red
dot). (B to E) Red lines represent the combined movement networks (links) contributed by the 10 largest females [(B), 91 to 114 cm] versus the 10 smallest females
[(C), 42 to 54 cm], the 10 largest males [(D), 79 to 110 cm], and the 10 smallest males [(E), 42 to 50 cm] present during at least 20% of the spawning season,
inferred from detections stored by moored acoustic receivers (blue dots).
RI = 0.75), the predicted connectivity score
was 7.1 links (95% CI = 5.5 to 9.3; Fig. 2 and
table S3). In contrast to the females, there was
no clear evidence that larger males were less
resident than smaller males (Pearson correla-
tion coefficient = –0.03, P = 0.61).
Cod tracked in this study were captured and
released at five different locations within the
study area (26). In a separate analysis, we ex-
amined the probability of cod moving among
these more distant locations. In contrast to the
finer-scale network analyses described above,
each of the release locations refers to a larger
area associated with multiple acoustic receiv-
ers (fig. S1). A total of 38% (n = 80) of the tagged
female cod were detected at more than one
release location during the spawning season.
The probability of being detected at multiple
release locations increased significantly with
body length, estimated at 0.26 (SE = 0.06) for a
50-cm female compared with 0.56 (SE = 0.09)
for a 100-cm female (table S4). A total of 27%
(n = 68) of the tagged male cod were detected
at multiple release locations. The probability
of being detected at multiple release locations
increased significantly with body length, esti-
mated at 0.11 (SE = 0.03) for a 50-cm male
compared with 0.83 (SE = 0.09) for a 100-cm
male (table S4).
Connectivity and productivity of populations
Our study suggests that the contribution of
large female fish to population productivity
and stability may go beyond what is already
recognized from their high-reproductive-energy
output (17, 31). From a population perspective,
a network of spawning sites can indeed act
to stabilize overall recruitment of broadcast
spawning fish through a connectivity portfolio
effect in which some sites are successful in
some years, whereas other sites are successful
in other years (32). Similarly, for Atlantic cod,
the exact location where the pelagic eggs are
spawned will influence in which habitats the
juveniles eventually settle for growth and sur-
vival (33, 34). There is evidence for spatial
asynchrony in recruitment and juvenile growth
of cod occurring on a scale of only a few tens of
kilometers, including our study region (25, 35),
suggesting that what stands out as the most
favorable spawning site varies temporally.
From the perspective of individual fitness and
adaptive evolution, batch spawning by cod func-
tions as part of a bet-hedging strategy that is
advantageous in unpredictable environments
such as the ocean (31). Recent modeling studies
suggest that female cod can increase their fit-
ness by spreading the risk across several re-
productive events through a spawning season
(36, 37). Our study shows that this bet-hedging
strategy likely involves spreading the risk in
space as well as over time. Potential costs asso-
ciated with such strategies might include reduced
offspring quality in the batches spawned toward
the end of the season (16). Furthermore, maxi-
mum body size can relate to life history traits
such as growth, age and size at maturation, and
longevity (38–40). Natural- and human-induced
mortality and selection acting on these life his-
tory traits may therefore also influence the
bet-hedging strategy and level of connectivity
displayed by female cod. Linked to life his-
tories, age and level of experience could also play
a role in determining which spawning sites
are visited and used by cod. There are many
examples of social learning among fish (41),
and it has been suggested that smaller cod
may follow the lead of larger conspecifics on
their migrations (42). Although age and size
of cod are correlated, we do not know the exact
age of the fish tracked in our study. The reason
is that cod age is usually determined from
seasonal growth zones in their otoliths (ear
bones), and this technique requires that fish
are euthanized.
Increased spatial bet hedging (i.e., spawn-
ing at multiple sites during a season) among
larger females is, in our opinion, a parsimonious
Olsen et al., Science 382, 1181–1184 (2023)
8 December 2023
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. Connectivity response
to cod body size. Shown are
Atlantic cod movement links as
predicted for resident females
[(A), RI = 0.75, detected 75% of
spawning season], females with
low residency [(B), RI = 0.25],
resident males [(C), RI = 0.75],
and males with low residency
[(D), RI = 0.25] showing the
mean prediction (black lines) and
95% CI (gray shading) within
the range of observed body
lengths. The structure of the
underlying statistical models and
associated parameter estimates
are provided in tables S2
and S3.
interpretation of the observation that larger
females tended to have a higher connectiv-
ity score. In addition, other mechanisms might
also be playing out. Earlier studies on spawn-
ing cod in captivity have revealed a complex
mating behavior in which male courtship
displays and vocalizations precede pairing
and spawning during characteristic “ventral
mounts” (18, 43). These behaviors potentially
allow females to assess male quality and to ex-
hibit nonrandom mate choice (43). Therefore,
it is possible that larger females were more
active in seeking out and assessing potential
mates while not necessarily spawning dur-
ing all visits to all locations. Their behavior
would nevertheless add to the spatial complex-
ity of the mating system.
The mating system of the cod has been de-
scribed as a lek, in which at least some domi-
nant males form clustered mating territories
and engage in aggressive interactions toward
other males, and male dominance is positively
associated with body size (18, 43). Our finding
that male movements among sites was com-
parable to that of females suggests that the
exact location of their territory is not fixed, but
rather may shift during a spawning season,
and that larger males are exploring more sites.
Similarly, a study from the Gulf of Maine con-
cluded that male cod probably do not remain
faithful to a specific site when they form tem-
porary individual territories (19).
Our study shows that downsizing of cod by
fisheries, a widespread phenomenon, may con-
tribute to substantially reduced connectivity
and a fragmentation of spawning habitat use,
which is likely to have a negative impact on the
overall population productivity (44). At a larger
spatial scale and population level, catch data
from fisheries that were collected across one
century suggest that depletion of old-growth
age structure is associated with a long-term
truncation of the spawning migration of North-
east Arctic cod (45) and a concurrent decline
in recruitment success (46). Fisheries are pre-
dicted to disarm cod risk-spreading strategies
by selecting against the largest individuals (37)
and perhaps also by selecting directly against
exploratory behaviors (47, 48). Fishing may
also effectively disrupt cod spawning aggre-
gations (49). Furthermore, populations of At-
lantic cod that are severely depleted by fisheries
provide evidence for Allee effects in which the
per capita population growth rate declines at
low population densities, which will impair
the ability of the population to recover should
fishing pressure be reduced (11). Allee effects
could be caused by mating systems becoming
increasingly dysfunctional as population den-
sity decreases (50). In particular, cod spawning
aggregations tend to be male dominated (51),
so connectivity by large females may have an
important influence on the operational sex ratio
and therefore the functioning of the mating sys-
tem at a given point in time.
We acknowledge that the importance of large
individuals for population productivity, and
thus the appropriate management and conser-
vation measures, is still a matter of debate. For
instance, Andersen et al. (52) pointed out
that the largest female fish will usually be rare,
so by accounting for typical fish demography,
their expected impact on population replen-
ishment will be limited. Similarly, a recent
field study linking parents and offspring of
a long-lived reef fish found that whereas re-
productive success increased markedly with
maternal body size, the numerous small ma-
ture females were responsible for a relatively
large proportion of offspring replenishment
even though the parents were sampled from
protected sites within marine reserves (53). The
latter study therefore advocated traditional
minimum size limits as a useful management
tool to complement the benefits offered by ma-
rine reserves. By contrast, another recent study
concluded that for 32 of the world’s largest
fisheries, the typical assumption that egg pro-
duction is simply proportional to spawner bio-
mass will underestimate the contribution of
larger individuals and, consequently, substan-
tially overestimate the population reproduc-
tive potential (54). For northern cod found off
Newfoundland and Labrador, the egg contri-
bution from older females (≥10 years of age)
has declined from an estimated 30 to 40% in
the 1960s to a negligible level in more recent
postcollapse years (31). To restore a safe op-
erating space (55) for fisheries, strategies for
maintaining the full potential of fish spawn-
ing habitat use, set by ecological and evolu-
tionary constraints (56), should be integrated
into management and conservation plans. To
that end, a widely supported recommenda-
tion for rebuilding size and age structures is
to implement slot-size limits in fisheries and
fully protected marine reserves connected by
seascape movement corridors (44, 54, 57, 58).
Conclusions
The mobility expressed by large female cod
during the spawning season shows that these
fish can play an important role in facilitating
connectivity among spawning habitats. Man-
agement actions directed toward rebuilding
fish life histories could therefore be a mean-
ingful way of improving overall population re-
silience. Even though the populations of cod
in mid- and northern Norway are harvested
and far from pristine (59), the continued ex-
istence of some very large individuals presents
a valuable glimpse of what fully expressed and
naturally adapted life histories may add in
terms of movement behavior diversity. Unless
the genetic basis for such life histories and
behaviors has also been eroded by fisheries
(48, 60), our finding offers a positive perspec-
tive for conservation programs aimed at re-
building more severely depleted populations
and species.
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the Norwegian Seafood Research Fund (grant 901230 to J.E.S.).
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Materials and Methods
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Submitted 8 April 2023; accepted 31 October 2023
10.1126/science.adi1826
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RES EARCH
PHYSICS
Ergodicity breaking in rapidly rotating C60 fullerenes
Lee R. Liu1,2*, Dina Rosenberg1,2, P. Bryan Changala1,2†, Philip J. D. Crowley3, David J. Nesbitt1,2,4,
Norman Y. Yao3, Timur V. Tscherbul5, Jun Ye1,2*
Ergodicity, the central tenet of statistical mechanics, requires an isolated system to explore all available
phase space constrained by energy and symmetry. Mechanisms for violating ergodicity are of interest
for probing nonequilibrium matter and protecting quantum coherence in complex systems. Polyatomic
molecules have long served as a platform for probing ergodicity breaking in vibrational energy transport.
Here, we report the observation of rotational ergodicity breaking in an unprecedentedly large molecule,
12C60, determined from its icosahedral rovibrational fine structure. The ergodicity breaking occurs
well below the vibrational ergodicity threshold and exhibits multiple transitions between ergodic and
nonergodic regimes with increasing angular momentum. These peculiar dynamics result from the
molecule’s distinctive combination of symmetry, size, and rigidity, highlighting its relevance to emergent
phenomena in mesoscopic quantum systems.
I solated systems that break ergodicity have
been explored in a variety of experimental
settings, including spin glasses (1), ultra-
cold neutral atoms (2, 3) and ions (4), and
photonic crystals (5). These systems ex-
hibit ergodicity breaking of spin configura-
tions and momentum or spatial distributions.
By contrast, gas-phase polyatomic molecules
provide opportunities to probe the ergodicity
breaking of collective (rotational and vibra-
tional) excitations in a finite quantum system.
In this context, a topic of major interest has
been the transport of energy deposited into
molecular vibrations by optical pumping or
collisions. Intramolecular vibrational redis-
tribution (IVR) sets in once a critical thresh-
old, defined by the product of vibrational
coupling and the local density of vibrational
states (which has a power-law scaling with
vibrational energy), is exceeded (6–11). This
vibrational ergodicity transition has been
studied vigorously in the context of under-
standing and controlling unimolecular reac-
tion dynamics (12).
Among polyatomic molecules, buckmin-
sterfullerene (12C60) is notable for its structural
rigidity and high degree of symmetry, which
suppress IVR and allow for spectroscopic res-
olution (13) and optical pumping (14) of indi-
vidual rovibrational states—an unusual and
fortuitous situation for a molecule with 174
vibrational modes. Its small rotational con-
stant and stiff, cage-like structure ensure that
1JILA, National Institute of Standards and Technology and
University of Colorado, Boulder, CO 80309, USA.
2Department of Physics, University of Colorado, Boulder, CO
80309, USA. 3Department of Physics, Harvard University,
Cambridge, MA 02135, USA. 4Department of Chemistry,
University of Colorado, Boulder, CO 80309, USA.
5Department of Physics, University of Nevada, Reno, NV
89557, USA.
*Corresponding author. Email: lee.richard.liu@gmail.com (L.R.L.);
ye@jila.colorado.edu (J.Y.)
†Present address: Center for Astrophysics, Harvard and Smithsonian,
Cambridge, MA 02138, USA.
Liu et al., Science 381, 778–783 (2023)
18 August 2023
hundreds of rotational states are populated
even when vibrational excitations are largely
frozen out, which can be achieved with mod-
est buffer gas cooling to ~120 K. Thus, a ther-
mal ensemble of 12C60 can reveal extensive,
state-resolved rotational perturbations span-
ning hundreds of rotational quanta by elimi-
nating vibrational “hot bands.”
First observed and understood in atomic
nuclei (15–22), rotational perturbations can
arise from spherical symmetry breaking in the
frame fixed to a rotating self-bound deform-
able body (23), which lifts the degeneracy of
different body-fixed projections of the total
angular momentum vector J. Such perturba-
tions, also called “tensor interactions” because
of their anisotropic nature, manifest in fine-
structure splitting of the total angular momen-
tum (J) multiplets in rovibrational spectra and
encode rich dynamics such as rotational bi-
furcations (18, 24), as previously observed in
tetrahedral SnH4, CD4, CF4, SiH4, and SiF4 and
octahedral SF6 molecules (25–33). Nevertheless,
observing icosahedral tensor interactions, first
predicted for 12C60 over three decades ago (34),
has remained an elusive goal, because there
are far fewer examples of icosahedral mole-
cules, nonspherical interactions occur only at
higher orders of interactions, and icosahedral
molecules are necessarily larger than lower-
symmetry spherical top molecules, implying a
smaller rotational constant.
In this work, we observed these icosahedral
tensor interaction splittings, revealing rota-
tional ergodicity transitions in 12C60 at energies
well below its IVR threshold (10). Specifically,
as the molecule “spins up” to higher J, the
dynamics of the angular momentum vector J
in the molecule-fixed frame switches between
ergodic and nonergodic regimes. In the non-
ergodic regime, distinct vector J trajectories
exist in the same energy range but remain
separated by energy barriers. In the limit of
high J, the tunneling between these trajecto-
ries is too weak to restore ergodicity, leaving
a characteristic signature in the fine-structure
level statistics. This phenomenon differs from
IVR in three key respects: (i) It involves the
“transport” of the molecule frame orientation
of vector J instead of vibrational energy; (ii) it
can occur well below the IVR threshold; and
(iii) it switches back and forth multiple times
between ergodic (described by a 6th rank ten-
sor interaction) and nonergodic (described by
a 10th rank tensor interaction) regimes as the
angular momentum is varied. This peculiar
dynamical behavior arises from multiple
avoided crossings with other vibrational states,
which induce nonmonotonic variations in the
molecule’s anisotropic character as J is varied.
The rotational ergodicity transitions bear some
similarity to those studied in asymmetric top
molecules in a static electric field (35, 36) in
that both concern the transport of angular
momentum in the molecule frame. However,
unlike in (35, 36), the rotational ergodicity
transitions in 12C60 are induced by intramolec-
ular rovibrational coupling in the freely rotat-
ing molecule, rather than by an externally
applied electric field.
Effective 12C60 rovibrational Hamiltonian
The rovibrational structure of C60 can be de-
scribed by a field-free molecular Hamiltonian
H ¼ Hscalar þ Htensor
ð1Þ
The scalar Hamiltonian Hscalar contains only
those combinations of vector J and vibrational
angular momentum ‘ that preserve their spheri-
cal degeneracy (37)
Hscalar ¼ n0 þ BJ2 þ DJ4 þ ⋯ (cid:2) 2BzJ (cid:3) ‘ ð2Þ
where n0 is the vibrational band origin, B is
the rotational constant, D is the scalar cen-
trifugal distortion constant, and z is the Coriolis
coupling constant.
Rovibrational fine structure is encoded in the
tensor Hamiltonian Htensor. For simplicity, we
considered a pure rotational tensor Hamiltonian
consisting of the two lowest-order “icosahe-
dral invariants.” These invariants are linear
combinations of spherical tensors of the same
rank that transform according to the totally
symmetric irreducible representation in the
icosahedral point group (Ih) (38). They can be
expressed (39) in the basis of spherical har-
monics Y k
Þ of degree k and order q, which
depend explicitly on the molecular frame’s
polar q and azimuthal f angles (Fig. 1A). The
first two nontrivial (anisotropic) icosahedral
invariants, with ranks 6 and 10, are given by
q q; fð
T 6½ (cid:4) q; fð
Þ ¼
p
ffiffiffiffi
11
Y 6
Þ
0 q; fð
5
p
ffiffiffi
(cid:3)
7
5
Y 6
5 q; fð
þ
Þ (cid:2) Y 6
Þ
(cid:2)5 q; fð
(cid:4)
ð3Þ
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RES EARCH | R E S E A R C H A R T I C L E
A
B
0.5
0
-0.5
C
π/4
D
π
E
π/4
F
π
165
170
175
180
165
170
175
180
165
170
0.4
0.2
0
0
0.5
1
0
0.5
1
0
175
J
0.5
r
180
165
170
175
180
165
170
175
180
1
0
0.5
1
0
0.5
1
Fig. 1. Rotational energy surfaces and eigenvalues corresponding to icosahe-
dral invariant spherical tensors. (A) Symmetries of C60. (Left to right) (1) Ball-
and-stick model of C60, with the three different types of rotational symmetry axes
that label stationary points on the rotational energy surface (RES). The degeneracies
of the stationary points are listed in parentheses. Color and plot marker coding
for each type of rotational symmetry axis are shown. (2) Body-fixed coordinates:
polar q and azimuthal f angles. (3–5) View along C5, C3, and C2 rotational
Þ ¼
symmetry axes. (B to F) (Top panels) RESs, defined by their radii r q; fð
Þ
ð
Þ=2, for n ranging from 0 to p. Eigenvalues of 1 þ H 6þ10
1 þ H 6þ10
tensor nð Þ=2
ð
tensor n; q; f
ð
Þ
calculated for the fully symmetrized J ¼ 174 subspace are plotted on the surface
as radial contours, colored corresponding to their dominant rotational symmetry
character. (Center panels) Tensor energy defects [eigenvalues of H 6þ10
tensor nð Þ] over a
range of J. The gray vertical line highlights J ¼ 174. Eigenvalues are plotted using
the marker corresponding to their dominant C5, C3, or C2 character (A). Near
the separatrices, the assignment is somewhat ambiguous owing to strong mixing.
(Bottom panels) Distribution p rð Þ of energy gap ratios r (see text) calculated from
tensor energy defect spectra aggregated over J = 0 to 400. Away from n ¼ 0; p [(C)
to (E)], the finite value of p rð Þ as r → 0 is a signature of ergodicity breaking.
Þ
ð
T 10½
(cid:4) q; fð
Þ ¼
(cid:2)
p
p
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3 (cid:3) 13 (cid:3) 19
75
ffiffiffiffiffiffiffiffiffiffiffiffi
11 (cid:3) 19
25
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
3 (cid:3) 11 (cid:3) 17
75
(cid:3)
p
Y 10
0 q; fð
Þ
Y 10
5 q; fð
Þ (cid:2) Y 10
Þ
(cid:2)5 q; fð
(cid:4)
(cid:4)
(cid:3)
10 q; fð
Y 10
þ
Þ þ Y 10
(cid:2)10 q; fð
ð4Þ
which are combined to construct a truncated
tensor Hamiltonian
Þ
ð
H 6þ10
tensor
Þ
(cid:5)
(cid:4)
¼ g cosnT 6½ (cid:4) þ sinnT 10½
(cid:6)
ð5Þ
This Hamiltonian is parameterized by an
overall scaling factor g and mixing angle n such
that n ¼ 0 and n ¼ p=2 correspond to pure T 6½ (cid:4)
and pure T 10½
(cid:4), respectively.
All operators that are incompatible with
icosahedral point group symmetry, including
any spherical harmonics of rank 1 to 5, 7 to 9,
11, 13, 14,... (40), vanish from the Hamiltonian.
The use of full rovibrational tensor operators
is unlikely to change the picture qualitatively,
particularly when J (~100 to 300) is much
greater than the vibrational angular momentum
quantum number ‘ ¼ 1 (38). These polyhedral
invariants are similar to those used to describe
the crystal field splitting of electronic orbitals
owing to an external lattice environment (41)
or the ligand field splitting in transition-metal
complexes (42).
The energetic correction, or tensor energy
defect, associated with orienting J in different
directions in the molecule frame can be vi-
sualized by the altitude of a semi-classical “rota-
tional energy surface” (RES), defined at a fixed
J. Various possible icosahedral RESs, defined
Þ=2,
by their radii r q; fð
corresponding to different mixing angles n, are
plotted for J ¼ 174 in the top panels of Fig. 1, B
to F. Stationary points always lie on C2, C3, or
ð
Þ
Þ ¼ 1 þ H 6þ10
ð
tensor n; q; f
C5 rotational symmetry axes. However, as n
varies, they change in character between mini-
ma, maxima, and saddle points. The RES dic-
tates the dynamics of J in the molecule frame
(30, 43–46), analogous to how an adiabatic
potential energy surface steers the relative
motions of nuclei (47). During free evolution,
the trajectory of J follows an equipotential
contour of the RES.
In a full quantum-mechanical treatment,
the perturbation H 6þ10
Þ
ð
leads only to discrete
tensor
tensor energy defects ei given by the eigen-
values of H 6þ10
ð
Þ
in a fully symmetrized fixed-J
tensor
subspace. These orbits trace out the closed
contours on the RES in Fig. 1. The orbits may
also be obtained directly from the RES: They
are the trajectories that both (i) satisfy a Bohr
quantization condition (44, 48) and (ii) trans-
form according to the totally symmetric irreduc-
ible representation of the icosahedral point
group (38). The latter condition accounts for the
Liu et al., Science 381, 778–783 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
quantum indistinguishability of each bosonic
nucleus in the 12C60 isotopolog (13, 49) and
is analogous to the selection of odd or even
rotational states in ortho- or para-hydrogen
molecules, respectively. The tensor energy de-
fects are plotted for a range of J in the center
panels of Fig. 1, B to F, and may be expected
to appear in the rovibrational fine structure
of 12C60.
Resolving 12C60 rovibrational fine structure
In the preceding discussions, we have focused
solely on the geometric effects of icosahedral
symmetry. In general, however, the measured
tensor defect spectra may exhibit additional
J-dependent scaling and offsets, which depend
on intramolecular couplings specific to 12C60.
To resolve rovibrational perturbations in 12C60,
in this work, we explored the P-branch region
of the 1185 cm−1 T1u (3) band, first identified
as a region of potential interest in (13). Using
cavity-enhanced continuous-wave (cw) spec-
troscopy with a quantum cascade laser (QCL)
source, we achieved a minimum absorption
sensitivity amin ¼ 2:1 (cid:5) 10(cid:2)10cm(cid:2)1 Hz(cid:2)1=2, or
1000-fold better detection sensitivity per spec-
tral element than in (13) (amin ¼ 2:2 (cid:5) 10(cid:2)7
cm(cid:2)1 Hz(cid:2)1=2 per comb mode). We acquired
600-MHz-wide absorption spectra by simulta-
neously scanning the QCL frequency and free
spectral range of the enhancement cavity across
molecular absorption lines, and recording the
frequency-dependent absorption. These spec-
tra were stitched together by a combination of
direct calibration of the QCL frequency with
a Fourier transform spectrometer and com-
parison to matching spectral features in the
broadband, low signal-to-noise (SNR) frequency
comb spectrum of (13). We obtained an absolute
frequency accuracy of ∼6 MHz throughout the
entire measured frequency range, limited by
the resolution of the reference frequency comb
spectrum. Finally, to ensure consistency of
the absorption signal over multiple days of
data collection, we have periodically remea-
sured the molecular absorption feature at
R(J ¼ 181) at n ¼ 1186:27 cm−1 and normalized
all data taken around the same time to its line
strength and measured cavity finesse.
Assigning 12C60 rovibrational fine structure
The culmination of these efforts is the infrared
spectrum in Fig. 2, spanning the spectral re-
gion from 1182.0 to 1184.7 cm−1. At J ≲ 70, there
is a regular progression of rotational lines,
similar to those in the R-branch (13). They
rapidly split into intricate patterns before
merging at and beyond J ≈ 300. Zooming into
the region labeled B), the rotational line cen-
ters could be fit to the scalar part of Eq. 1, as
was done in (13).
nP Jð Þ ¼ n0 þ B′ J (cid:2) 1
Þ
ð
(cid:2) B″J J þ 1
ð
Þ
Þ J þ 2z
ð
ð6Þ
where J here refers to the ground-state total
angular momentum. The scalar centrifugal dis-
tortion term was not significant at our spec-
tral precision and range of J . The fit yielded
B″ = 0.0028 cm(cid:2)1 for the ground-state rota-
ð
Þ , where B ¼ B′ þ B″
tional constant, B′ ¼ B″ (cid:2) 2:876 (cid:5) 10(cid:2)7 cm−1
for the excited-state rotational constant, z ¼
(cid:2)0:37538 for the Coriolis coupling constant,
and n0 ¼ 1184:85 cm−1. Equation 6 yields a
progression of rotational lines with a spacing
of ∼2B 1 (cid:2) z
Þ=2 . The
ð
spectroscopic constants were underdetermined
and only served to facilitate J -assignment of
the peaks in a manner consistent with the
R-branch assignments of (13). The extrapo-
lated P-branch spectral line positions based
on this scalar fit are plotted as gray vertical
lines in Fig. 2, B to F, with every fifth J value
labeled in red. The agreement with the mea-
sured line positions is excellent in the region
J < 70 , where the spectrum appears unper-
turbed (Fig. 2B).
To confirm our J assignment, we compared
the peak absorption cross sections to the nu-
clear spin weights of the ground-state rota-
tional levels and found that they match well.
Finally, we applied a frequency-dependent
scaling factor to the raw absorption spectrum
ð2J þ 1Þ(cid:2)1eB″J Jþ1
Þ=kBT . This scaling removes
the effects of lab frame angular momentum
degeneracy and the thermal ensemble, em-
phasizing the dynamics in the molecule-fixed
frame.
ð
The peaks were identified manually and
circled in blue. Figure 2, C and D, show two
representative regions, at J ∼ 90 and J ∼ 170,
respectively, where peaks could still be indi-
vidually resolved. The local peak density again
matches the predicted nuclear spin weights
(in blue), confirming that the rovibrational
A
B
C
E
D
F
.
.
.
.
.
.
.
.
Fig. 2. Direct continuous-wave (cw) absorption spectroscopy of C60
P-branch. (A) Complete normalized cw spectrum of P-branch to expose
the J dependence of the nuclear spin weights. Red highlighted regions are
shown in greater detail in subsequent panels. (B to F) Enlargement of
red highlighted regions in (A). (B) Enlargement of low-J region of the P-branch.
This relatively unperturbed region of the P-branch is fit to a rigid-rotor
ð
Hamiltonian to obtain the rotational spacing 2B 1 (cid:2) z
are indicated by the gray vertical grid lines, with J labeled in red. Blue
numbers denote calculated nuclear spin weights, which match the measured
peak intensities well. In (C) and (D), peaks are resolvable and marked with
blue circles. In (E) and (F), spectral congestion prohibits identification
of individual peaks.
Þ. Fitted line positions
Liu et al., Science 381, 778–783 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
fine-structure splitting originates from icosahe-
dral tensor interactions of Eq. 5 that lift K -
degeneracy. Figure 2, E and F, show two
regions where the peaks have begun to merge,
and individual peaks can no longer be easily
identified (J > 247).
Interpreting the tensor splittings requires
assigning each absorption peak to a partic-
ular J. We began by assigning each peak to
its nearest J value according to the scalar fit
of Eq. 6. Subtracting the scalar contribution
(Eq. 6) from the central frequency of each
peak generated a single “period” of a Loomis-
Wood-like defect plot in Fig. 3A. There remains
some ambiguity in the defect assignments, as
illustrated in the inset of Fig. 3A: Each defect is
Þ,
constrained to the line with slope 2B 1 (cid:2) z
which passes through its current position.
ð
By carefully rearranging individual defects
according to these discrete allowed “moves,”
we unwrapped five distinct regions that ex-
hibit continuous-looking patterns (Fig. 3B).
Because of the discontinuities at J ≃ 80, 110,
160, and 220, there was still some ambigu-
ity in the overall shift of the four perturbed
sections labeled (i) to (iv). To remove this
ambiguity, we recognized each section’s dom-
inant pure-rank tensor character as follows:
(i) (cid:2)T 6½ (cid:4) ; (ii) T 10½
(cid:4) ; (iii) T 6½ (cid:4) ; (iv) (cid:2)T 6½ (cid:4) .
Eigenvalue spectra in Fig. 1, B, D, and F, show
that the extremal eigenvalues associated with
Cn rotational symmetry axes occur when J is
an integer multiple of n. The J -assignment
depicted in Fig. 3B satisfies this condition
for all sections simultaneously. This final J-
assignment was confirmed by the excellent
agreement between J -resolved peak counts
and calculated nuclear spin weight far from
the discontinuities Fig. 3C.
Rotational ergodicity transitions
The J-dependent tensor energy defects imply
rovibrational dynamics of 12C60. To infer these
dynamics, we parameterized each of the four
perturbed regions (i) to (iv) in Fig. 3B in terms
of a mixed tensor (Eq. 5), J-dependent scaling
b Jð Þ, and J-dependent scalar offset a Jð Þ:
a Jð Þ þ b Jð Þ (cid:5) e n; J; K
ð
Þ
ð7Þ
where e n; J; K
Þ are the J-dependent tensor
ð
splittings as plotted in the lower panels of Fig. 1,
B to F.
First, a Jð Þ was obtained from the observed
mean defect of each section. Next, by perform-
ing a point-cloud registration (50–52) to the
theoretical eigenvalue spectra and the mea-
sured defect plot, we assigned a best-fit mixing
angle n to each section: (i) p; (ii) 0.45p; (iii) 1.9p;
and (iv) p (38). Finally, b Jð Þ was obtained from
a least-squares fit to a polynomial in J (38).
The resulting reconstructed defect plot for re-
gions (i) to (iv) is shown in Fig. 3D.
The abrupt changes in mixing angles n are
associated with transitions between ergodic
and nonergodic rotational dynamics as the mo-
lecule “spins up” to higher J. These dynamics
)
1
-
m
c
(
t
c
e
f
e
d
)
1
-
m
c
(
t
c
e
f
e
d
40
60
80
20
0.01
0
-0.01
0.01
A
0.02
0.01
0
-0.01
-0.02
20
s
t
n
u
o
c
10
5
0
20
0
-0.01
125 130 135 140
100
120
140
160
180
200
220
240
260
280
B
40
C
60
60
80
100
120
140
160
180
200
220
240
260
280
nuclear spin weight
peak counts
C
40
60
80
100
120
140
160
180
200
220
240
260
280
ν = π
0.45π
1.9π
π
D
0.02
0.01
0
-0.01
-0.02
)
1
-
m
c
(
t
c
e
f
e
d
20
40
60
80
100
120
140
160
180
200
220
240
260
280
J
Fig. 3. Obtaining P-branch tensor energy defects versus J. (A) Plot of
experimental energy defects from nearest-neighbor J assignment. Peaks are
assigned to nearest J according to rigid rotor model (gray vertical grid lines in
Fig. 2, B to F). Red defect points (J > 247) correspond to peaks in the absorption
spectrum that are no longer individually resolved. Their peak centers are
obtained from fitting to a cluster of Voigt lineshapes (38). (Inset) Unwrapping
procedure follows a series of allowed “moves” that simultaneously translate
points in vertical steps of ±2B(1− z) and horizontal steps of ±1. (B) “Unwrapped”
defect plot. Four avoided crossings with varying strengths are seen at J ≃ 80, 110,
160, and 220. Defect patterns resemble eigenvalue spectra of icosahedral invariant
tensors. (C) Calculated nuclear spin weights overlaid with measured peak counts.
Blue highlighted sections show excellent agreement between calculated nuclear spin
weights of C60 and assigned peak counts. (D) Reconstruction of perturbed sections of
P-branch spectrum based on eigenvalue spectra of mixed tensor operator H 6þ10
Four perturbed portions of (B) are reproduced with four mixing angles n.
ð
Þ
tensor (n).
Liu et al., Science 381, 778–783 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
transition from ergodic for region (i), to
nonergodic for region (ii), and back again for
regions (iii) and (iv).
The origin of this ergodicity breaking can
be understood semi-classically using the RESs
in Fig. 1, B, D, and F. The dynamics of vector
J are ergodic when time evolution explores
the full space of symmetry-allowed states at
the same energy. For region (iii), the dominant
tensor character is T 6½ (cid:4). Naïvely, the existence
of 12 disconnected trajectories encircling the
C5 axes breaks ergodicity. However, these traj-
ectories cannot be distinguished in 12C60: Ow-
ing to the indistinguishability of the 12C nuclei,
all 12 semi-classical trajectories correspond
to a single quantum state given by their fully
symmetric superposition. As such, the vector
J dynamics do explore the full range of states
at a given energy, and hence are ergodic. The
same argument applies for regions (i) and
(iv), which differ from (iii) only in the sign of
tensor energy defects (Fig. 1F).
By contrast, for region (ii), the dominant
(cid:4). The C5 and C3 axes
tensor character is T 10½
both correspond to peaks on the RES and to
host trajectories over the same range of ener-
gies (Fig. 3D). Trajectories encircling the C5
and C3 axes are distinguishable, and hence cor-
respond to distinct quantum states. The quan-
tum tunneling between these trajectories is
unable to restore the ergodicity: The tunneling
integral between C5 and C3 is exponentially
small in J (53, 54), whereas the level spacing
only scales as 1=J. The scaling of the tunnel-
ing integral follows from standard Wentzel–
Kramers–Brillouin (WKB) results (55), and the
scaling of level spacings can be seen by compar-
ing the relatively fixed bandwidth of tensor en-
ergy defects (Fig. 3B) with the nuclear spin weight
∼ 2J þ 1
Þ=60. Consequently, for our measured J
ð
(well within the large-J limit), tunneling correc-
tions are typically only perturbative.
Energy-level statistics provide a simple probe
of this ergodicity breaking in molecular spec-
tra (56, 57). Quantum ergodicity is associated
with eigenstates extended in phase space that
can be strongly coupled by local perturbations,
inducing energy-level repulsion. By contrast,
ergodicity breaking is associated with the ex-
istence of localized eigenstates, which are not
strongly coupled by perturbations and whose
energies are uncorrelated (58). Ergodic and
nonergodic dynamics are therefore respec-
tively associated with level repulsion and its
absence (59). A useful diagnostic tool is the
distribution p rð Þ, where r is the ratio of consec-
utive level spacings ei (60, 61):
si(cid:2)1
si
ri ¼ min
si
si(cid:2)1
ð8Þ
(cid:7)
(cid:8)
;
si ¼ eiþ1 (cid:2) ei
ð9Þ
In the limit of r → 0, level repulsion in an
ergodic system causes p rð Þ → 0, and for a non-
ergodic system p rð Þ → constant. Similar energy-
level statistics have been used to analyze systems
as diverse as nuclear spectra (59), ultracold
atomic scattering (62), and many-body local-
ization (63).
Figure 4, A to C, show the energy-gap ratios
computed from sections (i) to (iii), respec-
tively, of the experimental defect plot (Fig. 3B).
Here, sections (i) and (iii) exhibit persistent
level repulsion characteristic of ergodicity,
whereas section (ii) does not, indicating non-
ergodicity. We aggregated the energy-gap ratios
over each one of sections (i) to (iii) and their
respective distributions in Fig. 4, D to F. These
distributions confirm the presence of level re-
pulsion in sections (i) and (iii) and its absence
in section (ii).
Þ
The physical origin of rovibrational tensor
energy defects in 12C60 can be inferred from
Fig. 3B. The defects arise from rovibrational
coupling between the bright P-type excited
þð
1u 3ð Þ state and a background of perturb-
T
ing dark states. Specifically, both the disconti-
nuities and excess observed peaks at specific
J values are characteristic of avoided cross-
ings with perturbing zero-order dark vibrational
þð Þ
1u 3ð Þ from
combination states. As they cross T
below, rovibrational coupling lifts the degen-
þð
1u 3ð Þ state, im-
eracy of J multiplets in the T
parting tensor character that depends on the
identity of the perturbing vibrational state.
þð
1u 3ð Þ state (spe-
The tensor character of the T
cifically the fitted n values) is stable in between
Þ
Þ
avoided crossings, suggesting that each of
these sections is dominantly affected by just
one perturbing state at a time. At the avoided
crossings, this assumption breaks down, as
made particularly evident by the rapid change
in mixing angle just before and after the
avoided crossing at J ¼ 160 of Fig. 3B. There
is no apparent structure to the changes in
mixing angle and coupling strength induced
by the different avoided crossings, suggesting
that the perturbing dark states are distinct
and not part of the same Coriolis manifold.
Finally, using the observed local density of per-
≈ 2=cm(cid:2)1 and average mea-
turbing states robs
sured vibrational coupling strength (bandwidth
of the avoided crossings) of bavg ≈ 2(cid:5) 10(cid:2)2 cm(cid:2)1
(38), we arrive at an IVR threshold parameter
(10) T Eð Þ ¼
robsbavg ≈ 0:06 ≪ 1.Our 12C60
rotational ergodicity transitions are observed
well below the IVR threshold, a conclusion sup-
ported by the spectroscopically well-resolved
T1u 3ð Þ band. This further highlights the fact
that, although the rotational ergodicity tran-
sition relies on intramolecular vibrational cou-
pling, it is completely distinct from IVR.
ffiffiffiffiffiffiffiffiffiffi
2p=3
p
Conclusion
We have measured and characterized icosahe-
dral tensor rovibrational coupling in 12C60.
Analysis of the spectrum of rovibrational ten-
sor energy defects revealed that as the mol-
ecule is spun up to higher J, there is a series
of transitions in the dynamical behavior of
J in the fixed body frame. Specifically, vec-
tor J switches between ergodic and nonergodic
behavior at particular J values, leaving a char-
acteristic imprint on the defect-level statistics.
These ergodicity transitions arise from dark
vibrational combination states that cross the
þð
1u 3ð Þ state at particular J values, transferring
T
þð
Þ
1u 3ð Þ
their anisotropic character onto the T
state through rovibrational coupling.
Þ
Our measurements open the door to a rich
hierarchy of emergent behavior in C60 isotopo-
logs, accessible at ever-higher spectral resolution.
The small nuclear spin-rotation interaction—
for example, in 13C-substituted isotopologs of
C60—can have a magnified effect owing to the
small superfine splittings near RES extrema.
A
1
r
0.1
0.01
1
B
1
1
C
1
i)
0.5
0.1
ii)
0.5
0.1
90
100
J
0
0 0.2 0.4
p(r)
0.01
120
140
J
0
0 0.2 0.4
p(r)
0.01
180
J
1
0.5
0
0 0.2 0.4
p(r)
iii)
200
Fig. 4. Energy-level statistics in ergodic and nonergodic regimes. (A to C) (Left panels) Gap ratio r as a function of J calculated from sections (i) to (iv) of the
defect spectrum (Fig. 3B). Gap ratios are only plotted at J values for which the peak counts match the calculated nuclear spin weight (Fig. 3C). (Right panels)
Normalized distribution p rð Þ of gap ratios aggregated over sections (i) to (iii). Note the change from logarithmic to linear r scale between left and right panels. Sections
(i) and (iii) exhibit level repulsion, a signature of ergodicity, whereas section (ii) does not, indicating nonergodicity.
Liu et al., Science 381, 778–783 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Such “hyperfine” coupling can lead to spon-
taneous symmetry breaking in a finite system
(31, 64). These insights could prove useful for
exploiting the exotic orientation state space
of C60 for quantum information processing
(65) and for investigating the quantum-to-
classical transition of information spreading
(66). Ultimately, spectroscopy of C60 isotopo-
logs at ever-higher spectral resolution promises
to uncover deeper insights into the emergent
dynamics of mesoscopic quantum many-body
systems.
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AC KNOWLED GME NTS
We gratefully acknowledge comments on the manuscript from
A. W. Young and Y.-C. Chan. Funding: This research was supported
by AFOSR grant no. FA9550-19-1-0148; the National Science
Foundation Quantum Leap Challenge Institutes (grant QLCI OMA-
2016244); the National Science Foundation (grant Phys-1734006);
and the National Institute of Standards and Technology. Support is
also acknowledged from the US Department of Energy, Office of
Science, National Quantum Information Science Research Centers,
Quantum Systems Accelerator. D.R. acknowledges support from
the Israeli council for higher education quantum science fellowship
and is an awardee of the Weizmann Institute of Science–Israel
National Postdoctoral Award Program for Advancing Women in
Science. P.J.D.C. and N.Y.Y. acknowledge support from the AFOSR
MURI program (FA9550-21-1-0069). D.J.N. acknowledges support
from the US DOE (DE-FG02-09ER16021) and NSF (CHE 2053117).
T.V.T. acknowledges support from the NSF EPSCoR RII Track-4
Fellowship no. 1929190. Author contributions: L.R.L., D.R., and
J.Y. designed, discussed, and performed the experiment and
analyzed the data. L.R.L., D.R., P.B.C., P.J.D.C., D.J.N., N.Y.Y.,
T.V.T., and J.Y. participated in theory discussions and calculations
and in writing of the paper. Competing interests: None
declared. Data and materials availability: Data for raw absorption
spectra and unwrapped tensor energy defect plots are deposited
in Harvard Dataverse (67). All other data needed to evaluate
the conclusions in the paper are present in the paper or the
supplementary materials. License information: Copyright © 2023
the authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.sciencemag.org/about/
science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi6354
Supplementary Text
Figs. S1 to S3
Table S1
Reference (68)
Submitted 9 May 2023; accepted 23 June 2023
10.1126/science.adi6354
27. J. P. Aldridge et al., J. Mol. Spectrosc. 58, 165–168 (1975).
Mater. Phys. 75, 155111 (2007).
Liu et al., Science 381, 778–783 (2023)
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RES EARCH
NEUROSCIENCE
Climbing fiber multi-innervation of mouse Purkinje
dendrites with arborization common to human
Silas E. Busch1 and Christian Hansel1*
Canonically, each Purkinje cell (PC) in the adult cerebellum receives only one climbing fiber (CF) from
the inferior olive. Underlying current theories of cerebellar function is the notion that this highly
conserved one-to-one relationship renders Purkinje dendrites into a single computational compartment.
However, we discovered that multiple primary dendrites are a near-universal morphological feature in
humans. Using tract tracing, immunolabeling, and in vitro electrophysiology, we found that in mice ~25%
of mature multibranched cells receive more than one CF input. Two-photon calcium imaging in vivo
revealed that separate dendrites can exhibit distinct response properties to sensory stimulation,
indicating that some multibranched cells integrate functionally independent CF-receptive fields. These
findings indicate that PCs are morphologically and functionally more diverse than previously thought.
S1 and S2) and did not depend on zonal pattern-
ing by zebrin II expression (15) (fig. S3). Physical
constraints, however, might play a role in the
spatial distribution of PC dendrite morphologies
by foliar subregion (7). Indeed, the multiple
dendrites of Split and Poly PCs predominantly
ramified in a horizontal orientation (defined
by <30° angle deviation from the PC layer, fig.
S4, A and B; see materials and methods) in the
sulcus of human folia (80%) while this occurred
much less frequently in the bank and gyrus (23
and 25%, respectively; fig. S4D). This effect was
not present in mice (fig. S4, C and D). In human
PCs—where dendritic size expands strongly
(Fig. 1, A and D)—the horizontal orientation
follows the inward curvature of the sulcus, pos-
sibly indicating a developmental response to
physical constraints on growth. Because the
physiological implications cannot be readily
studied in humans, we turn to the corresponding
mouse cells for further characterization.
I nputs to the cerebellar cortex are integrated
by the dendrites of Purkinje cells (PCs), its
sole cortical output neuron. Despite their
well-characterized position in what is consid-
ered a conserved and stereotypical circuit
(1), PCs exhibit diverse dendritic morphology
in rodents (2) and it is not known how specific
features of dendritic arborization may affect
their function.
Human PC morphology remains even more
elusive. Studies of human PC morphology,
which date back more than 120 years to the
iconic illustrations of Golgi and Ramón y Cajal
(3, 4), typically investigate small numbers of
cells (5–7). Although no quantitative infor-
mation on frequency and distribution of mor-
phological types is available, it can be observed
that human PCs are often “multibranched,”
having either numerous trunks emerging from
the soma or a proximal bifurcation of a single
trunk. These features produce highly segregated
dendritic compartments, raising the question
of whether this confers functional properties
that have gone unreported.
We specifically asked whether the existence
of several primary dendrites enables multiple
climbing fiber (CF) innervation in the adult
cerebellum. During development, the early
growth of a primary dendrite provides struc-
tural support for the ramification of a “winner”
CF amidst competitive elimination of surplus
CFs (8–10). Weaker CF inputs fail to translocate
to the dendrite, possibly as a result of compet-
itive processes resembling adult bidirectional
synaptic plasticity (11–14). In PCs where mul-
tiple primary dendrites conceivably offer a
means to evade competition from other CFs, is
the elimination pressure reduced enough to
allow multiple CFs to be maintained? Would
multi-innervation provide functionally inde-
1Department of Neurobiology and Neuroscience Institute,
University of Chicago, Chicago, IL 60637, USA.
*Corresponding author. Email: chansel@bsd.uchicago.edu
pendent receptive fields to distinct dendri-
tic compartments?
A majority of human, but not murine, PCs
have multiple primary dendrites
Multiple CFs may innervate separate
primary dendrites
We used fluorescent calbindin immunolabel-
ing to visualize PCs in postmortem human
tissue (Fig. 1A). Based on proximal primary
dendrite structure, which articulates the con-
tours of the entire arbor, we define one stan-
dard structural category—Normative, in which
one primary dendrite may have a distant bifur-
cation (beyond a two-somatic diameter thresh-
old of 40 mm in mice and 50 to 70 mm in humans)–
and two multibranched categories—Split, in
which there is one trunk that bifurcates into
multiple primary dendrites proximal to the soma
(below the somatic diameter threshold) and
Poly—, in which multiple trunks emerge directly
from the soma (Fig. 1A and fig. S1; see mate-
rials and methods). Although these categories
translate to mice (Fig. 1D), we found that mice
diverged significantly from humans in that they
had fewer Split PCs (35.9 versus 44.8%) and far
fewer Poly PCs (16.6 versus 51.2%; Fig. 1G and
fig. S2A). Instead, in mice Normative PCs con-
stituted the largest PC category (47.5%) in con-
trast to humans (4.0%).
We manually marked the distribution of
dendritic morphologies of collectively ~8000
cells across whole parasagittal reconstructions
of brain slices from the mid-hemisphere in hu-
mans and mice (Fig. 1, B and E, and fig. S2, B
and C). In posterior lobules of humans, there is
a higher percentage of Poly PCs (53.8 versus
40.9%) and a lower percentage of Normative
PCs (3.5 versus 6.1%) than in anterior lobules
(Fig. 1C, fig. S2A, and table S1). Although the
total rate is far lower, Poly PCs are relatively
more prevalent in posterior lobules of mice as
well (21.2 versus 10.3%; Fig. 1, F and G, fig. S2A,
and table S2).
The broad morphological distributions were
consistent across nonpathological human and
mouse individuals (fig. S2, B and C, and tables
CF activity causes complex spike firing in PCs
(16, 17), which is reciprocally related to simple
spike firing (17, 18) and exerts powerful control
over dendritic integration and PF plasticity
(19–26). Though many studies cite the critical
importance of one-to-one CF to PC connec-
tivity in cerebellar function, as well as abnormal
connectivity in dysfunction, some work has
shown CF multi-innervation in ~15% of PCs in
adult rodents (27–29).
To test whether multiple CF innervation can
be found in mature PCs, we combined a sparse
dextran tracer (DA-594) labeling of inferior
olivary (IO) neurons (Fig. 2A) with immuno-
labeling of CF terminal boutons (VGluT2) and
PCs (calbindin). Because all CF terminals are
marked by VGluT2, but only some will express
DA-594, this method allows for the identifica-
tion of multiple CF inputs from distinct IO neu-
rons onto single PCs (9, 30). Figure 2B shows a
Poly PC (P87) that was indeed innervated by
two CFs on its separate primary dendrites.
Quantification of CF multi-innervation in
mature PCs
We obtained a quantitative measure of CF
multi-innervation across the PC population by
using whole-cell patch-clamp recordings in
murine cerebellar slices (Fig. 2C). We adjusted
current intensity and stimulus electrode posi-
tion in the granule cell layer—subadjacent to
each patched PC—to identify any ascending CF
inputs and their stimulus thresholds. Mono-
innervated PCs had a single, discrete excitatory
post-synaptic current (EPSC) amplitude whereas
multi-innervated PCs exhibited two or more dis-
crete EPSC amplitudes selectively evoked by
distinct stimulus intensities (Fig. 2C, bottom,
and fig. S5, A and B). About 15% of all PCs in
mature animals (P20-66) received multiple CFs
Busch et al., Science 381, 420–427 (2023)
28 July 2023
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A
e
v
i
t
a
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o
N
t
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l
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RES EARCH | R E S E A R C H A R T I C L E
B
IV
Intraculminate
V
Primary
VI
Superior Posterior
VIIAfolium
Crus I
Horizontal
III
Preculminate
Anterior
Posterior
2 = 170.18
p < 0.001
C
s
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80
80
60
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40
40
40
20
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0
0
0
L3 L4 L5 L6 CrusI
L3 L4 L5 L6 CrusI
L3 L4 L5 L6 CrusI
CrusII
CrusII
CrusII
L7B L8A L8B
L7B L8A L8B
L7B L8A L8B
E
VI
Human
Mouse
50µm
50µm
N
S
P
IV/V
III
II
2 = 106.83
p < 0.001
F
s
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60
40
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***
***
***
***
***
***
***
***
VIIB
***
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
N
one lobule
S
—
—
—
—
P
Percents of total cell counts
47
36
17
45
51
5 mm
G
80
80
80
Mouse
Human
60
60
60
s
s
s
l
l
l
l
l
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e
e
c
c
c
f
f
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t
t
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c
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r
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P
P
P
40
40
40
20
20
20
0
0
0
2 = 55.27
p < 0.001
M
H
4
Fig. 1. Comparative morphology and regional variability in human and
mouse cerebellar PCs. (A) Immunolabeling of PCs in humans reveals a range of
dendritic morphologies, categorized by primary dendrite geometry as Normative,
Split, or Poly. (B) Human mid-hemisphere reconstruction demonstrating the
spatial distributions of each morphological type. As a result of variable
preservation of tissue some anterior lobules and intervening posterior sub-
lobules had a lower density of labeled PCs. (C) Morphology demographics
across lobules (n = 3 individuals >86 years old, 6640 cells; see table S1).
(D) PCs filled with dye during a patch experiment in mice to scale with human
cells also exhibit Normative, Split, and Poly morphology. (E and F) as in (B and
C), but in mice (n = 3 mice >P50, 1350 cells; see table S2). (G) Morphological
category distribution counted by lobule (top) in human (n = 20, 21, and
21 lobules) and mouse (n = 30, 30, 29) reveals a consistent increase in the
number of Split and Poly PCs in human matching the rates of the whole cell
population (bottom). Average lines depict median lobule value. *P < 0.05,
**P < 0.01, ***P < 0.001.
(Fig. 2D, left). CF competition for survival is
complete by P20 (8, 9, 28, 31). In keeping with
this, we did not find an effect of age on the rate
of multi-innervation (fig. S6L).
Combining this technique with fluorescent
dye loading and confocal imaging revealed that
multi-innervation was largely restricted to PCs
with multi-branched structures (23/24 PCs) and
occurred in ~25% of cells in this group (1/64
Normative, 15/61 Split, and 8/34 Poly PCs; Fig.
2D). The summed CF EPSC of multi-innervated
PCs was larger, on average, than the amplitude
of individual CF inputs to mono-innervated PCs
(Fig. 2E). The amplitude of the smaller CF (at
−30 to −10 mV holding potential) was typically
>200 pA (Fig. 2E). This indicates that, under
physiological membrane potentials, even the
weakest of multiple CFs will likely deliver
sufficient current to the soma to influence out-
put (32). The amplitude of weaker CFs in-
creased with age (fig. S5M), which may denote
a delayed or elongated maturation period of
these inputs relative to the completed develop-
ment of single CF inputs or the more dominant
of multiple CFs (fig. S5N). The relative EPSC am-
plitude ratio between dominant and smaller CFs
varied widely, but smaller CFs most often had
Busch et al., Science 381, 420–427 (2023)
28 July 2023
2 of 8
RES EARCH | R E S E A R C H A R T I C L E
A
B
Cerebellum
(Cb)
Tracer (+) VGluT2
Tracer (-) VGluT2
Calbindin
DA-594
VGluT2
25µ m
Inferior Olive
(IO)
C
25µ m
D
100
135
63
25µ m
2 = 15.71 p = 0.003
46
26
)
%
(
s
l
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C
75
50
25
0
22
2
1 2 3
14
1
1
1 2 3
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Number of CFs
7
1
1 2 3
A
p
0
0
5
20ms
Mono-CF (1)
Multi-CF (2+) Sum
2+ Weak
*
Mono-innervation
1 CF EPSC
Multi-innervation
2 CF EPSCs
A
p
0
0
5
20ms
F
Split distance ( m)
***
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11111111111111111111111111111111111111111111111
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111
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1 CF
2+ CFs
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100
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2+
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2+
Fig. 2. CF multi-innervation of mature multibranched PCs. (A) Schematic of tracer (DA-594) injection.
(B) A Poly PC after immunolabeling for PCs (calbindin) and CF terminals (VGluT2). The tracer label
distinguishes CFs with distinct olivary origin on the left and right trunks. (C) Scheme of whole-cell patch-
clamp in cerebellar slices and CF EPSCs recorded from either a mono- or multi-innervated PC. (D) Number
of mono- versus multi-innervated PCs as a combined population (left). Categorizing by morphology reveals
that effectively all multi-innervation occurs in multibranched PCs (n = 50 animals, 159 cells). (E) Summed
multi-CF EPSCs are larger than mono-CF EPSCs (n = 135 and 24 cells). The weaker of multiple CFs typically
provides >200 pA signals. Holding potential: −10 to −30mV (n = 24 cells). (F) Multi-innervated PCs have
earlier dendrite bifurcations (n = 135 and 24 cells). (G) Among PCs with a bifurcated primary dendrite,
multi-innervated cells have a wider distance between compartments (n = 85 and 9 cells). (H) Multi-innervated
Poly PCs have a wider angle between emerging trunks (n = 26 and 8 cells). Summary points indicate
mean ± SEM. *P < 0.05, **P < 0.01, ***P < 0.001.
>25% the relative amplitude of the dominant
CF (fig. S5O). This ratio differed across foliar
sub-areas (fig. S5P) and correlated with the angle
between Poly PC trunks (fig. S5Q), further em-
phasizing the relationship between morphol-
ogy and CF input properties.
The prevalence of multi-innervation was
correlated with proximity of bifurcation and
angle of separation between emerging trunks
in Split and Poly PCs, respectively (Fig. 2, F
and H, and fig. S5, D and F). Multi-CF PCs also
had wider dendritic arbors in the parasagittal
plane (Fig. 2G and fig. S5G), but did not differ
in the angle of bifurcation (fig. S2E) or soma
size (fig. S5H).
CF multi-innervation was present across cere-
bellar regions and foliar sub-areas (fig. S6, A
to I). Posterior lobules had a higher frequency
of multi-innervation (fig. S6I), possibly due to
increased prevalence of Poly PCs (fig. S6, H and
J), matching our finding in immunolabeled tis-
sue (Fig. 1F and fig. S2A). We did not observe
a preferential rate of multi-innervation within
the sulcus as a general pattern [but see (29) for
more detailed analysis within vermis].
CF multi-innervation produces heterogeneous
Ca2+ signals across dendrites in vivo
Do multiple converging CFs provide function-
ally distinct inputs to a single PC? How would
this affect dendritic signaling in vivo? To answer
these questions, we examined whether CF multi-
innervation produces heterogeneous Ca2+ sig-
nals across separate dendritic branches. CF
input triggers massive Ca2+ entry into PC den-
drites through voltage-gated Ca2+ channels (33),
NMDA receptors (34), and release from internal
stores (35), which can be locally modulated by
ion conductance plasticity (33, 36) and inter-
neuron inhibition (37, 38). These mechanisms
contribute to the calcium events that we moni-
tor here in vivo and to their modulation (39–41).
We obtained a sparse PC expression of the
Ca2+ indicator GCaMP6f and used two-photon
imaging of mice in a state of quiet wakefulness
(awake; no detected motion) to record non-
evoked “spontaneous” Ca2+ signals from primary
dendrite compartments in small populations
of <10 cells (Fig. 3, A and B; see materials and
methods). Volumetric scans visualized cellular
morphology and permitted manual tracing of
compartment ROIs (Fig. 3, B and D, and Figs.
4A and 5A) so fluorescence signals were ex-
tracted and deconvolved separately to contrast
event amplitude and frequency across branches
(Fig. 3, C and E). In this configuration, non-evoked
Ca2+ signals beyond the micro-compartment
scale are almost entirely CF-dependent (42, 43)
and Ca2+ event amplitude reflects the number
of spikes in the presynaptic CF burst (44). This is
confirmed by our observed ~1.2 Hz spontaneous
Ca2+ event frequency (fig. S7D) that matches an
expected CF input frequency moderately greater
than 1 Hz (17).
Busch et al., Science 381, 420–427 (2023)
28 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
0.5% AAV-L7-CRE + 20% AAV-FLEX-GCaMP6f
B
Branch 1
Branch 2
20µm
Simplex
513nm
920nm
Crus I
Crus II
D
G
20µm
)
%
(
s
t
n
e
v
e
l
a
c
o
L
100
75
50
25
0
E
1.5
1
0.5
0
1
2
0.5
B
-
0
1
B
0.5
-1
p = 0.087
***
***
H
p
m
A
2
B
1.000
2
R
j
d
A
0.100
0.010
0.001
20µm
3s
3s
Normative
1.5
0.5
F/F0
1
0.5
0
1
Split
0.5
F/F0
0.5
**
***
*
I
p < 0.05
p > 0.05
0
0.5
-1
2 = 9.8
p = 0.007
J
t
u
o
h
t
i
w
s
l
l
e
C
)
%
i
(
p
h
s
n
o
i
t
a
l
e
r
h
c
n
a
r
b
50
40
30
20
10
0
)
v
e
d
t
s
(
l
e
a
c
s
p
m
A
0.5
0.4
0.3
0.2
0.1
0.5
F/F0
0.5
F/F0
2s
2
C
1.5
1
2s
0.5
0
1.5
1
2
0.5
B
-
0
1
B
-0.5
-1
-1.5
Poly
Branch 1 Dominates
Branch 2 Dominates
F
***
)
0
F
F
/
(
e
d
u
t
i
l
p
m
a
n
a
e
M
R2 = 0.099
p < 0.001
l
)
v
e
d
t
s
(
e
a
c
s
p
m
A
0.4
0.2
0.0
K
1.00
0.75
0.50
0.25
0.00
Global
Local
R2 = 0.078
p = 0.002
N
S
P
B1 Amp
N
S
P
20 40 60 80 100120
Split distance ( m)
50 100 150 200 250
Dendrite width ( m)
Fig. 3. Two-photon imaging in vivo reveals Ca2+ signal heterogeneity
across PC dendrites. (A) Schematic of experimental preparation.
(B) Example imaging plane and three-dimensional reconstruction of a Poly PC.
(C) Spontaneous signal and deconvolved events (circles) by branch with
difference trace below demonstrates heterogeneous global event amplitude scale
and branch-specific events. (D and E) Another recording from a Normative and
Split PC highlights homogeneous versus heterogeneous signaling. (F) Local
events are moderately smaller than global events (n = 15 animals, 95 cells).
(G) Branch-specific local events as a percentage of total events in each cell by
morphology (n = 15 animals; n = 32, 55, and 8 cells). (H) Linear regressions
on branch cross-correlation quantifies branch similarity (left). Model fit R2 values
(right) reveals that cells with low branch signal similarity are predominantly
Split and Poly PCs (n = 32, 55, and 8 cells). Bordered points indicate
nonsignificant covariance. (I) Cells lacking detectable relationship using
regression on interbranch amplitudes are all Split or Poly PCs. (J and K)
Interbranch amplitude variation by Split distance (n = 105 cells) and total
parasagittal width of the dendrites (n = 109 cells). Summary points
indicate mean ± SEM. *P < 0.05, **P < 0.01, ***P < 0.001.
We first identified local Ca2+ peaks detected
in only one branch of each cell (Fig. 3, C, F, and G
and movie S1), which were moderately smaller
than globally expressed events on average (Fig.
3F). We also compared the inter-event cross-
correlation of Ca2+ events across branches, for
which the fit and significance of a linear re-
gression describes the interbranch covariation
(Fig. 3, H and I).
Most PCs had homogenous Ca2+ signals
with linear inter-event covariance relationships
across branches (Adj R2 > 0.1) and low numbers
of local events (Fig. 3, G and H). However, some
PCs exhibited Ca2+ signal heterogeneity char-
acterized by a linear regression of inter-event
covariation with low Adj R2 < 0.1 that was not
significant (0, 15, and 38% of Normative, Split,
and Poly PCs, respectively; Fig. 3, H and I) or a
higher ratio of local events (17.4, 36.6, and 51%;
Fig. 3G). High variability of inter-event ampli-
tude scale between branches, another measure
of heterogeneity, correlated with the bifurcation
distance and total parasagittal dendritic width
(Fig. 3, J and K, and fig. S7C). This further links
heterogeneity to underlying morphological con-
tours defined by primary dendrite geometry.
Confirming that local events are the product of
additional CF input, PCs with high local event
rates had higher mean (fig. S7, G, H, and P)
and maximum total event rates (fig. S7, L and
M), producing a larger dynamic range (fig. S7, N
and O). Our observations link the occurrence of
local CF events to underlying morphological
contours defined by primary dendrite geometry,
although other factors, such as inhibition by
molecular layer interneurons (MLIs), are likely
to contribute as well (37, 42).
CFs convey distinct whisker receptive fields to
separate primary dendrites
To identify CF receptive fields (RFs) and their lo-
calization on PC dendrites, we took advantage of
the discrete organization of whiskers as a sen-
sory input array (45, 46). We anaesthetized ani-
mals to stimulate untrimmed individual whiskers
at 2 Hz for 50 s periods while recording Ca2+
activity of PCs in medial Crus I (Fig. 4A and fig.
S8A; see materials and methods). Most PCs had
Busch et al., Science 381, 420–427 (2023)
28 July 2023
4 of 8
RES EARCH | R E S E A R C H A R T I C L E
A
B1
B2
2Hz stimulation of C3 whisker
B
0.3
0.2
0.1
0
0.2
0.1
2
B
0
-
1
B
0.1
5s
B1
B2
5s
0.1
F/F0
0.1
F/F0
ns
***
**
s
e
s
n
o
p
s
e
r
l
a
c
o
l
n
a
e
M
r
e
k
s
i
h
w
r
e
p
10
5
0
C
E
G
N
S
P
Global
Response
Lateralized
Response
B1
B2
B1
B2
ns
*
*
Unresponsive
Global
Lateralized
)
m
(
e
c
n
a
t
s
i
d
t
i
l
p
S
90
60
30
0
ns
*
*
N
S
P
2 = 6.73
p = 0.035
Unresponsive
Global
Lateralized
19
46
10
10
38
28
4
10
4
N
S
P
R2 = 0.046
p = 0.005
eD
c
n
e
r
e
f
f
i
d
r
e
k
s
i
h
w
-
r
e
t
n
I
15
10
5
0
F
100
s
l
l
e
c
f
o
t
n
e
c
r
e
P
75
50
25
0
H
100
)
%
(
s
t
n
e
v
e
l
a
c
o
L
75
50
25
0
1
0
2
Receptive field (whiskers)
4
3
Fig. 4. Branch-specific whisker receptive fields produced by CF multi-innervation of multibranched
PCs. (A) Schematic of the imaging configuration and whisker stimulation under anesthesia. (B) Sample
traces and deconvolved events by branch during 50 s whisker stimulation. Each whisker is tested twice;
data from both periods are combined. Responsiveness of one branch and not the other drives an enhanced
local event rate in B1 during the stimulus period. (C) Mean number of local branch events in response
windows during stimulus periods of each tested whisker (n = 13 animals P95-120, n = 33, 112, and 24 cells).
(D) Difference in local event number between whiskers eliciting maximum and minimum local responses
(n = 33, 112, and 24 cells). (E) Schematic of global versus lateralized responses. (F) Percentage of PCs by
dendritic response profile and morphological category. Fewer Normative PCs have lateralized responses than
multibranched PCs (n = 169 cells). (G) Cells with lateralized responses have shorter Split distances
(n = 75, 42, and 52 cells). (H) Cells with more spontaneous local events respond to a higher number of
whiskers (n = 151 cells). Summary points indicate mean ± SEM. *P < 0.05, **P < 0.01, ***P < 0.001.
only global events identically represented across
primary dendrites (figs. S8, A2, and A3). How-
ever, some PCs had high numbers of local events
in response windows during the stimulus pe-
riod (Fig. 4, B and C, and fig. S8 A4) that varied
in magnitude between distinct whisker stimuli
(Fig. 4D), indicating RF selectivity.
Anaesthetized activity is sparsened, so re-
sponses were determined using the z-scored
response probability during the experimentally
bootstrapped high-frequency stimulus (fig. S8,
B to D). Comparing the z-scored response
probability of each dendrite, we observed a
“lateralized” response in some PCs, in which
local events of one branch constituted a whisker
response not observed in the other branch
(Fig. 4, E and F). Nearly all lateralized responses
arose in Split and Poly PCs (48/52 cells, 92%;
Fig. 4F) and in PCs with more spontaneous
signal heterogeneity, which map to Split and
Poly PCs as in previous experiments (fig. S8F).
Furthermore, PCs with lateralized responses
had more proximal dendrite bifurcations than
PCs with only global responses (18.73 mm versus
28.24 mm; Fig. 4G). Notably, PCs with higher rates
of branch-specific spontaneous events also ex-
hibited responses to more whiskers, denoting
an integration of more whiskers into their RFs
(Fig. 4H). This supports the hypothesis that
heterogeneous signals represent distinct, con-
verging RFs such that heterogeneous PCs are
sampling more upstream RFs carried by func-
tionally independent CF inputs.
CF-induced branch-specific representations
of stimulus modality in awake mice
Although anesthesia provided excellent con-
trol and precision for single whisker stimula-
tion, even subanesthetic ketamine alters network
activity (47). To confirm that PC primary den-
drites can differentially represent CF RFs in a
more naturalistic state, we exposed awake ani-
mals to uni- and multisensory stimuli (Fig. 5A).
As a major hub for sensory integration during
associative learning, PC dendrites are an impor-
tant model for how converging input profiles are
represented across dendrites. The amplitude
and duration of CF-induced dendritic Ca2+ spikes
depend on stimulus strength (43, 48), which
is reflected in CF burst behavior (44) and also
on synaptic connectivity and weight of the CF
input itself (49).
We stimulated awake animals with light
(488 nm, ipsilateral), sound (12 kHz tone, bila-
teral), and peri-oral air puff (10 psi, ipsilateral)
stimuli either alone or in multimodal combi-
nations while recording response properties
in PC primary dendrites. Sensory-evoked events,
more than spontaneous, typically produced a
global dendritic signal with consistent intertrial
amplitude ratio between branches (Fig. 5B1).
However, we also observed complex sensory-
evoked bursts of CF input with heterogeneous
amplitudes between branches (Fig. 5, B2 and
Busch et al., Science 381, 420–427 (2023)
28 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
Light
488nm
B2
C
B1
50µm
Sound
12kHz
Puff
10psi
0.5
F/F0
2s
Global Response
)
%
(
s
t
n
e
v
e
l
a
c
o
l
x
a
M
Uni
*
100
Multi
***
75
50
25
0
N
S/P
N
S/P
D
L
l
a
c
o
L
t
n
e
c
r
e
P
50
LP
100
P
LPS
LPS
LS
L
0
C
S
LP
SP
P
C
LS
S
SP
E
Branch Response
BR (%) =
B1Local - B2Local
Branch 1 Dominates
B1
B2
B1/2Global + B1Local + B2Local
Dendrite
Modality Response Profile
Profile
Mean/Range
Putative
CF RF space
L
LPSP
S
P
LP
LS
SP
Mean
Range
More B1
Local
BR
+100%
More B2
Local
0%
No
difference
BR
-100%
F
)
%
(
e
g
n
a
r
R
B
125
100
75
50
25
0
G
**
)
%
(
n
a
e
m
R
B
50
25
0
-25
-50
-75
Bilateral
low
mean
high
range
Unilateral
high
mean
high
range
Global
low
mean
low
range
or
H
Range - Mean
*
ns
)
%
(
y
t
i
l
a
r
e
t
a
l
i
b
R
B
100
50
0
Branch 2 Dominates
Branch 2 Alone
B1
1.5
1
0.5
0
1
0
-1
B2
1.5
1
0.5
0
1
0
-1
B3
1.5
1
0.5
0
1
0
-1
B4
1.5
1
0.5
0
1
0
-1
Fig. 5. Branch-specific multisensory receptive fields. (A) Scheme of imaging and sensory stimulation
of awake animals. (B) Sample traces showing combinations of inter-branch responses to different stimulus
modalities. (C) The maximum number of local events observed for a stimulus of any category in Normative vs
Split and Poly (S/P) PCs (here and below: n = 12 animals, n = 24 and 38 cells). (D) The percentage of
responses having a local component, regardless of branch identity, across control (C), uni-, or multisensory
trials. Lines connect values for each PC. (E) Calculation of DBR (top) between the stimulus types most
favoring opposite branches. DBR values of each modality are calculated for each cell (bottom, schematic
points) to map the DBR profile across stimuli and identify the mean and range. (F) The range is more
pronounced in S/P cells (n = 24, 38). (G) No group difference in ΔBR mean (n = 24, 38). (H) Response profile
bilaterality is the subtraction of DBR mean from the range. S/P PCs exhibit more bilaterality due to high
ranges and low means (n = 24, 38). Summary points indicate mean ± SEM. *P < 0.05, **P < 0.01, ***P < 0.001.
B3) and either branch-specific responses alone
(Fig. 5B4) or combined with a global response
(Fig. 5B2). Whereas PCs with multiple primary
dendrites [Split and Poly (S/P)] had similar
total response probabilities as Normative PCs
(fig. S9C), a larger share of responses were
branch-specific in S/P PCs across stimulus
modalities (Fig. 5, C and D, and fig. S9, A and B).
To assess the relationship between uni- and
multimodal stimuli, we identified the maximum
branch-specific responses to stimuli of each
category (fig. S9D), obtained the difference
between uni- and multisensory maxima, and
found an enhanced rate of local responses in
S/P but not Normative PCs (fig. S9F). This re-
vealed that multisensory stimuli could enhance
the differential representation of CF RFs across
primary dendrites in putatively multi-innervated
PCs while failing to influence mono-innervated
Normative PCs.
While the previous analyses were blind to
branch identity, we next asked how much the
differential representation of each stimulus
could favor one branch over the other (fig. S9E).
We generated a D Branch Response (DBR) index
for each stimulus modality by calculating the
difference in branch-specific, local responses
as a fraction of total responses (Fig. 5E, top).
Absolute DBR indicates the reliability of local
responses on either branch whereas the sign of
the DBR indicates which branch over-represented
the modality. This allowed us to generate a pro-
file of branch-specific representation across all
stimulus modalities, which could be quantified
by the DBR mean and range for each cell (Fig. 5E,
bottom). In this way, PCs could be distinguished
as having one of three classes of multisensory
response profiles: global, with identical repre-
sentation across branches in all cases; unilateral,
with one branch exhibiting a larger RF repre-
sentation than the other; and bilateral, with
both branches capable of differentially repre-
senting unique stimulus modalities.
On average, S/P cells had a wider range, de-
noting branch-specific (e.g., unilateral or bilat-
eral) representations that were more distinct
across modalities (Fig. 5F and fig. S9, G to I).
Cells for which only one branch exhibits local
responses—that is, unilateral—would have both
a large DBR range but also a DBR mean that de-
viates from zero to favor that branch. To better
characterize whether some PCs had bilateral
representation profiles, we calculated the bilat-
erality of the RF profile by subtracting the
DBR mean from the range. The local responses
of S/P cells, more than Normative, produced
RF profiles wherein a larger percentage of local
signaling produced bilateral representations
across sensory modalities (Fig. 5H and fig. S9,
G, H, and K). Collectively, this shows that PCs
with multiple primary dendrites can differen-
tially represent RFs of distinct CF inputs across
their separate dendrites in awake, mature mice
(for a summary of heterogeneous signaling
Busch et al., Science 381, 420–427 (2023)
28 July 2023
6 of 8
RES EARCH | R E S E A R C H A R T I C L E
observed in our two-photon recordings across
the three dendrite morphologies in mouse PCs,
see fig. S10).
Discussion
We found that noncanonical CF multi-innervation
of PCs does occur in the mature murine cere-
bellum and is dependent on primary dendrite
morphology. Nearly all observed multi-innervation
occurred in neurons with multiple primary
dendrites. Based on a quantitative categoriza-
tion of >6000 PCs from three human brains,
we report that this type of PC dendritic struc-
ture is predominant in the human cerebellum.
By contrast, we detected that only a minority
of murine PCs fall into the Split or Poly cate-
gory. Within these morphological groups, about
25% of PCs were innervated by two or more CFs
in the mouse.
Our two-photon recordings suggest that most
multi-innervated PCs have the capacity for
branch-specific CF signaling and have distinct
CF RFs. Our data do not allow us to conclude
that the same results would be found in hu-
man PCs if such recordings were possible.
However, they do describe a new motif in PC
dendritic compartmentalization: separate den-
dritic subfields with their own assigned CF
inputs may emerge when early branching forms
a multibranched architecture. Variable CF burst
frequency and modulation of CF input ampli-
tude by MLIs may further contribute to com-
partmentalization (37, 42).
CFs provide instructive signals in cerebellar
function and plasticity (17) by encoding signals
related to error (19, 50), sensory omission (51),
as well as reward or reward-prediction (52, 53).
Our findings constitute a substantial shift from
the currently held belief that one CF innervates
each PC. Instead, our observations suggest that
one CF innervates each primary dendrite.
The consequences for dendritic integration
and, ultimately, the activation of target cells in
the cerebellar nuclei (54) are potentially multi-
fold. Here, we discuss those that immediately
result from geometric considerations. Multi-
branched structure often increases dendritic
width in the sagittal plane (Fig. 3K), in some
cases even opening a cleft between compart-
ments (see Fig. 1, A and D, Figs. 3B and 4E, fig.
S1, B and C, and fig. S4B). This configuration
inevitably leads to a wider physical gap between
innervating PF bundles and thus to a potential
functional separation of the contextual infor-
mation they provide (55, 56). It is therefore
conceivable that PCs drive spike output from
a multitude of contextual input combinations
that expand with increased dendrite size and
complexity. Multiple CF innervation that, as
we describe here, occurs at an elevated rate in
multibranched PCs may serve several critical
purposes. First, it may enhance PC function as
a supervised associative learning perceptron
that optimizes synaptic weights (57) by provid-
ing RF-matched CF inputs—and thus relevant
errors and instructive signals—to the different
PF inputs that convey specific contextual infor-
mation (fig. S11A). In this way, the perceptron
orchestrates synaptic weight optimization based
on compartmentalized, rather than all-dendritic,
instructive signals. Thus, in receiving multiple
CF inputs, some PCs are permitted to fully capi-
talize on diverse context representations surveyed
by their multibranched architecture. Second,
multiple CF innervation may enable more com-
plex PC computations, such as multiplexing
and conveying input from a wider array of
sensory modalities (fig. S11B). In this scenario,
individual multibranched PCs may pair differ-
ent contexts presented by their PF inputs with
instructive information collected from a multi-
modal environment.
In both the human and mouse cerebellum,
multibranched PCs are more prevalent in the
posterior cerebellar hemisphere, a region linked
to cognitive and affective roles (58–60). Whether
or not the multibranched architecture enables
such complex functions through the gained
computational power that is postulated here
needs to be investigated in future studies.
On the other hand, excessive CF-PC strength
resulting from disrupted synaptic pruning and
ectopic innervation of distal PC dendrites is
linked to pathological dysfunction in autism
model mice (27, 49) mouse and human essen-
tial tremor (61). The preferential targeting of
distinct primary dendrites by multiple CFs (Fig.
2B) may bring computational advantages while
avoiding disruptive enhancement of CF inputs
to individual dendritic compartments.
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AC KNOWLED GME NTS
For valuable advice and technical support, we thank Hansel lab
members T. F. Lin, A. Silbaugh, and T. Pham. We thank R. A. Eatock
and P. Mason (UChicago Neurobiology) for insightful discussions.
For crucial feedback on the manuscript, we thank W. Wei and
M. Sheffield (UChicago Neurobiology) as well as S. S. Wang
(Princeton). M. Sheffield and S. S. Wang also provided preliminary
viral tools. Human tissue made available by the Anatomical Gift
Association of Illinois. Funding: This work was supported by the
following: National Institutes of Health (NINDS) grant R21NS124217
(to C.H.); National Institutes of Health (NINDS) grant F31NS129256
Busch et al., Science 381, 420–427 (2023)
28 July 2023
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RES EARCH | R E S E A R C H A R T I C L E
(to S.E.B.); and The University of Chicago Pritzker Fellowship (to S.E.B.)
Author contributions: S.E.B. and C.H. designed the experiments.
S.E.B. performed the investigation, formal analysis, visualization,
and wrote the original draft. S.E.B. and C.H. acquired funding and
edited the text. C.H. supervised the work. Competing interests:
Authors declare that they have no competing interests. Data and
materials availability: All data are available in the manuscript or
the supplementary materials. Data and post-processing analysis
code are publicly available in a Dryad archive (62). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
sciencemag.org/about/science-licenses-journal-article-reuse
Figs. S1 to S11
Tables S1 to S10
References (63–66)
MDAR Reproducibility Checklist
Movie S1
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi1024
Materials and Methods
Submitted 3 April 2023; accepted 16 June 2023
10.1126/science.adi1024
Busch et al., Science 381, 420–427 (2023)
28 July 2023
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10.1126_science.adi8237
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RES EARCH
R E S E A R C H A R T I C L E S U M M A R Y
◥
NEUROSCIENCE
Associative and predictive hippocampal codes
support memory-guided behaviors
Can Liu†, Ralitsa Todorova†, Wenbo Tang, Azahara Oliva, Antonio Fernandez-Ruiz*
INTRODUCTION: The brain generates models of
the environment that are used to guide flexible
behaviors. This process requires learning the
states of the world (such as specific locations)
as well as the transitional relationships be-
tween those states (e.g., successive locations
along often-traveled trajectories). The hippo-
campal cognitive map is believed to be one
such internal model, supporting a variety of
behaviors, including associative learning, nav-
igational planning, and inference. It remains
unknown which facets of hippocampal coding
are required for these different behaviors and
how they support both associative and predic-
tive memory functions.
RATIONALE: We hypothesize that two modes of
hippocampal activity support learning of world
states and state transitions, respectively. On
one hand, the synchronous coactivity of groups
of hippocampal neurons—cell assemblies—may
encode features of individual states, forming
an associative code. On the other hand, the
ordered activation of these cell assemblies into
behaviorally relevant sequences may encode
the relational structure between states, form-
ing a predictive code. Previous research has
not been able to dissociate these two dynamic
codes or provide evidence of their specific
functions. We leveraged an optogenetic ap-
proach to dissociate these two coding schemes,
with the goal of disrupting the predictive code
(hippocampal sequences) while preserving the
associative code (rate coding and coactivity
dynamics) in behaving rats. This dissociation
allowed us to examine the different memory
functions of these two codes.
RESULTS: We optogenetically perturbed the
fine temporal coordination of hippocampal
place cell firing as rats navigated specific spa-
tial trajectories in a novel maze. This manip-
ulation disrupted properties of the predictive
code (such as temporally compressed place cell
sequences and anticipatory place field shifts),
but global network dynamics and single-cell
spatial tuning and rate coding properties were
preserved.
During sleep after the novel experience, we
observed that task-related cell assemblies en-
Associative code
Predictive code
Optogenetic
perturbation
Associative code
Predictive code
Coactivity,
theta sequences
Reactivation,
replay
Coactivity,
No theta sequences
Reactivation,
No replay
Unaffected by
perturbation
n.s.
e
c
n
a
m
r
o
f
r
e
P
Disrupted by
perturbation
***
e
c
n
a
m
r
o
f
r
e
P
Flexible navigation
Associative learning
Associative and predictive codes in the hippocampus. Our optogenetic manipulation perturbed hippocampal
sequences without affecting cell coactivity, thus selectively disrupting the predictive code. After learning,
cell assemblies were reactivated, but their order was not preserved, abolishing sequential replay (right). Perturbing
the predictive code had no effect on associative learning (bottom left) but did disrupt the flexible learning of
novel optimal trajectories on a maze (bottom right). [Rat illustrations: Yu Kang]
coding discrete maze locations were reacti-
vated in sharp wave–ripples (SWRs), un-
affected by the manipulation. However, their
sequential structure did not reproduce the
order in which they were active in the task,
resulting in impaired sequential replay for
the perturbed trajectories. This result shows a
dissociation between assembly reactivation and
sequence replay, two phenomena previously
assumed to reflect the same underlying pro-
cess. The same manipulation did not disrupt
replay of familiar trajectories, suggesting that
the precise temporal coordination of place cell
firing during learning mediates initial plasticity
required for subsequent replay. Computational
simulations suggest that distinct Hebbian plas-
ticity mechanisms mediate assembly reactiva-
tion and sequence replay.
We tested the functional role of the predic-
tive code by deploying our optogenetic manip-
ulation in two different hippocampal-dependent
memory tasks. Context-reward associative learn-
ing in a conditioned place preference task was
unaffected and thus does not require a predic-
tive map or memory replay. On the other hand,
flexible memory–guided navigation in a forag-
ing task was perturbed by the manipulation
and thus depends on hippocampal predic-
tive coding.
CONCLUSION: Our results provide a mechanis-
tic and functional dissociation between coac-
tivity and sequence codes in the hippocampus.
Hippocampal cells with similar responses to
behavioral variables fire together, forming func-
tional assemblies during learning, which are
reactivated in SWRs during subsequent sleep.
These cell assemblies encode discrete states in
the environment, an associative code that is
sufficient for some types of episodic memories.
As these cell assemblies are activated in a spe-
cific order during behavior, they form tempo-
rally compressed hippocampal sequences and
promote Hebbian plasticity. This process en-
ables the replay of behaviorally relevant se-
quences during SWRs. Hippocampal sequences
thus encode transitional structures of world
states, generating a predictive model on top
of the associative code of individual assem-
blies. This new framework contributes to our
understanding of how memory associations
develop into predictive representations of the
world and helps reconcile previously dis-
parate views on hippocampal function.▪
Department of Neurobiology and Behavior, Cornell University,
Ithaca, NY, USA.
*Corresponding author. Email: afr77@cornell.edu
†These authors contributed equally to this work.
Cite this article as C. Liu et al., Science 382, eadi8237
(2023). DOI: 10.1126/science.adi8237
READ THE FULL ARTICLE AT
https://doi.org/10.1126/science.adi8237
Liu et al., Science 382, 283 (2023)
20 October 2023
1 of 1
RES EARCH
R E S E A R C H A R T I C L E
◥
NEUROSCIENCE
Associative and predictive hippocampal codes
support memory-guided behaviors
Can Liu†, Ralitsa Todorova†, Wenbo Tang, Azahara Oliva, Antonio Fernandez-Ruiz*
Episodic memory involves learning and recalling associations between items and their spatiotemporal
context. Those memories can be further used to generate internal models of the world that enable
predictions to be made. The mechanisms that support these associative and predictive aspects
of memory are not yet understood. In this study, we used an optogenetic manipulation to perturb
the sequential structure, but not global network dynamics, of place cells as rats traversed specific spatial
trajectories. This perturbation abolished replay of those trajectories and the development of predictive
representations, leading to impaired learning of new optimal trajectories during memory-guided
navigation. However, place cell assembly reactivation and reward-context associative learning were
unaffected. Our results show a mechanistic dissociation between two complementary hippocampal
codes: an associative code (through coactivity) and a predictive code (through sequences).
L earning associations from experience and
using this knowledge to make novel pre-
dictions are integral features of memory-
guided behavior. Learning the structure
of one’s environment can be conceptual-
ized as two separate processes: learning the
states in the world and learning the likely
transitions between those states. The hippo-
campus has been implicated in both processes
because it has been shown to be fundamental
for encoding spatial-temporal associations
(1–5) and supporting flexible memory–guided
behaviors, planning, and inference (6–11). Such
involvement in diverse types of memory has led
to different theories of hippocampal function
focused either on its role in the formation and
recall of episodic memories (12–15) or in the
generation of predictive models to guide behav-
ior (10, 16, 17), while some proposals high-
lighted the intrinsic relationship between
these functions (18, 19). However, it is unclear
which facets of hippocampal coding are required
for these different behaviors. One prominent
candidate is the short-timescale (~10 to 30 ms)
coincidental firing of hippocampal neurons
with selective responses to external variables
(e.g., place cells encoding the same location).
This synchronous activation of “cell assemblies”
can lead to the strengthening of their connec-
tions through Hebbian plasticity, forming a
coactivity code (20–22). In addition, hippocampal
cell assemblies organize into sequences. During
navigation, temporally compressed neuronal
sequences on the timescale of a single cycle
of the theta oscillations (6 to 12 Hz; i.e., “theta
sequences”) sweep ahead of the animal’s cur-
rent position to encode future routes (23–25).
During rest periods, the sequential activation
of place cells “replays” past spatial trajectories
(26, 27). Coactivity and sequential hippocam-
pal dynamics have been traditionally consi-
dered conjoined aspects of the same under-
lying process, supported by common circuit and
synaptic mechanisms to the extent that they
are regarded as nondissociable. An alternative
possibility is that coactivity and sequential dy-
namics of hippocampal place cells represent
distinct coding schemes (Fig. 1). First, assem-
blies of coactive cells would encode individual
associations, or discrete states in the world.
Second, assemblies can be concatenated into
sequences reflecting either experienced or in-
ferred behaviorally relevant state transitions,
forming a predictive code. Although multiple
studies have found deficits in memory-guided
behavior by disrupting hippocampal activity
(28–32), none have been able to dissociate these
two dynamic modes and provide evidence of
the specific role of hippocampal sequences in
behavior. To overcome this limitation and test
our hypothesis, we selectively disrupted hippo-
campal sequences in rats while preserving
place cell expression and coactivity dynamics
and investigated their specific contribution to
predictive coding and flexible spatial learning.
Results
Disruption of hippocampal theta sequences
impairs the formation of a predictive map
To dissociate assembly coactivation and the
sequential organization of assembly activity,
we sought to specifically disrupt place cell
sequence dynamics while preserving their
tuning and coactivity properties in the main
hippocampal output region, CA1. Timing of CA1
place cell firing relies on inputs from the me-
dial entorhinal cortex (MEC) (33–35). However,
silencing or inactivating the MEC profoundly
Department of Neurobiology and Behavior, Cornell University,
Ithaca, NY, USA.
*Corresponding author. Email: afr77@cornell.edu
†These authors contributed equally to this work.
A
B
C
D
Fig. 1. Two hypothesized memory codes in the hippocampus. (A) As a rat
learns to navigate a maze to find a reward, place cells activate along its spatial
trajectory (color areas represent place fields). (B) During navigation, but also
during offline periods, place cells with overlapping fields are active together,
forming functional assemblies (top), and these assemblies form a sequence that
reproduces an animal’s learned trajectory (bottom). (C) We propose that the
coactivity of cell assemblies represents an associative code to learn discrete
states in the world, while their sequential activation forms a predictive code to
learn behaviorally relevant state transitions. (D) An associative memory code
may be sufficient for some types of memory, such as associating a place with a
reward. Other types of memory-guided behavior, such as flexibly navigating a
complex environment, would require a predictive model.
Liu et al., Science 382, eadi8237 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
interferes with hippocampal physiology, affect-
ing place cell expression, coactivity, and phase
coding, and thus lacks the necessary specificity
to test the role of sequences (36–39). To over-
come these limitations, we expressed channel-
rhodopsin (ChR2) in rat MEC g-aminobutyric
acid–releasing (GABAergic) cells to optogen-
etically entrain them at an artificial gamma
frequency (40, 41). With this approach, we
selectively perturbed the fine temporal struc-
ture of MEC outputs while simultaneously
recording hippocampal population activity
(Fig. 2A and fig. S1). In contrast to previous
manipulations (33, 36), our optogenetic pertur-
bation spared theta power, frequency, and the
theta phase modulation of CA1 unit firing (fig.
S1). To evaluate the effect of our optogenetic
perturbation on CA1 place cell properties, we
delivered light while rats (n = 5) ran in one
direction (“Stim ON”) but not in the opposite
direction (“Stim OFF”) on a novel linear track.
We aimed to disrupt specific sequences that
encoded part of the experience and to leave
other sequences intact as a control. The forma-
tion, stability, and firing properties of CA1 place
cells at the single cell and population levels
were preserved for both the Stim ON and
Stim OFF directions (Fig. 2, B to F, and figs.
S2 to S4). Place cells in the two directions had
similar properties and formed a highly direc-
tional code such that Stim OFF and Stim ON
trajectories could be decoded separately (fig.
S3A), and on the population level, the compo-
sition, spatial properties, and stability of place
cell assemblies were similar in the Stim OFF
and Stim ON directions (figs. S4, E to H).
Despite preserved place cell tuning curves, the
progressive shift in their spike timing in rela-
tion to the phase of global theta rhythm
[“phase precession” (42)] was impaired in the
Stim ON direction (Fig. 2D and fig. S5). More-
over, the sequential firing of pairs of place cells
at the theta timescale was disrupted in Stim
ON (Fig. 2, G and H). In contrast, across theta
cycles, cofiring of CA1 cells was preserved in
both directions (Fig. 2, G and I).
In our framework, the formation of place
fields (PFs) in a novel environment reflects
learning the states in the world (e.g., loca-
tions), whereas the formation of a predictive
map develops as an animal learns the likely
transitions between those states (e.g., succes-
sive locations along often-traveled trajectories).
To test whether the predictive code could be
dissociated from the encoding of the individ-
ual states with our manipulation, we examined
the evolution of place cells and hippocampal
predictive coding features in the novel maze.
We found that place cell properties in both
Stim OFF and Stim ON directions showed
experience-dependent development. Place
field quality in both directions improved across
laps, as measured by both their spatial infor-
mation (Fig. 3B) and the decoding accuracy
of animal position from place cell population
activity (fig. S3), indicating that spatial maps
were formed and developed with experience,
unaffected by our optogenetic perturbation.
We then examined the development of a
predictive code in two ways. We first analyzed
theta sequences, because they are temporally
compressed representations of spatial trajec-
tories, reflecting short-term predictions of the
immediate future (43–46). In contrast to the
preserved spatial map formation, theta se-
quences were impaired in the Stim ON direc-
tion (Fig. 3A). Moreover, we observed a specific
experience-dependent development of theta
sequences in the Stim OFF direction, such that
they became more prospective across laps (en-
coding longer distances ahead of the animal)
(Fig. 3C), a process that could reflect the for-
mation of increasingly predictive internal rep-
resentations of the maze. This development
was not observed in the Stim ON direction
(Fig. 3C). Another property of the hippocampal
predictive map is the progressive backward
shift of place fields toward past states (or loca-
tions) with experience (47), so that the early firing
reflects the expectation of upcoming states (17).
We observed a progressive backward shift
across laps of place fields only in the Stim OFF
direction, as expected, not the Stim ON direc-
tion (Fig. 3, D and E). These changes in the pre-
dictive code were not due to differences in animal
behavior between the two trajectories (fig. S3G).
Impaired replay with preserved reactivation of
a novel experience
Memory formation in the hippocampus is typ-
ically measured as both the reactivation of
short-timescale coactivity patterns (“assem-
blies”) and the replay of neuronal sequences
during sharp wave–ripples (SWRs) (48–50).
We first examined sequential replay of a running
experience on a novel linear track. During pauses
between track running and during sleep after
the task, we observed SWR-associated replay
events reproducing place cell sequences of the
Stim OFF direction (Fig. 4, A and B). However,
replay sequences of the Stim ON trajectory,
where hippocampal predictive coding was dis-
rupted, were impaired (Fig. 4B). Compared
with baseline sleep sessions before the task,
the fraction of SWRs that expressed signifi-
cant replay of the Stim OFF trajectory and their
sequence scores were considerably increased,
but no experience-dependent enhancement was
observed for the Stim ON trajectory (Fig. 4C
and fig. S6). This effect cannot be explained by
differences in single neuronal activity during
SWRs or decoding quality (fig. S7). Stim ON
replay sequences were not observed in either
the forward or the reverse direction (fig. S6, B
and C), and this result was replicated with
different replay methods and decoding param-
eters (figs. S6 and S7). We also tested whether
this disruption of replay of specific trajectories
was due to the impaired formation of a predic-
tive map (i.e., encoding the relevant state tran-
sitions). We conducted an experiment in which
rats (n = 3) first explored a linear track without
manipulation to form a predictive map with-
out perturbation and, in a subsequent session,
experienced optogenetic perturbation in one
direction as previously described. Theta se-
quences were still impaired in the Stim ON
direction, but we observed intact replay for
both Stim ON and Stim OFF trajectories (fig.
S8), confirming that although predictive cod-
ing is key in the initial stages of encoding
novel experiences, once the predictive map is
established, it does not require further repeti-
tions to generate replay of recent experience.
In the novel linear track experience, we next
examined reactivation of task coactivity pat-
terns by detecting synchronous cell assemblies
that encoded discrete positions along both
Stim OFF and Stim ON trajectories (fig. S9).
The composition, spatial properties, and sta-
bility of assemblies were similar in the Stim
OFF and Stim ON directions (fig. S4, E to H).
Surprisingly, Stim OFF and Stim ON assem-
blies reactivated with similar strength during
SWRs (Fig. 4, A and B), significantly increasing
their activity compared with the preceding sleep
(Fig. 4D and fig. S9, B to D). This result indi-
cates an intact memory reactivation of loca-
tions along both trajectories, which was also
confirmed using other canonical metrics of
memory reactivation (Fig. 4E and fig. S9A).
We wondered how these stark differences in
reactivation and replay can coexist. A closer
look at the temporal dynamics of cell assem-
blies revealed an important difference. Assem-
blies from the Stim OFF trajectory reactivated
during SWRs in a temporal sequence that re-
produced the order of their encoded spatial
locations in the maze (Fig. 4 and fig. S9A).
However, while individual assemblies for the
Stim ON trajectory reactivated during SWRs
with similar strength to those for the Stim
OFF trajectory, their task sequential structure
was not preserved in these reactivation events
(Fig. 4B and fig. S9E), resulting in the impair-
ment of sequence replay and the preservation
of reactivation of the Stim ON trajectories. In-
deed, although the strength of assembly reac-
tivation and replay for the Stim OFF direction
were correlated at the level of individual SWRs,
this correlation was absent for the Stim ON
direction (Fig. 4F), dissociating reactivation
from replay in the absence of a predictive code.
Associative and predictive codes support
different memory-guided behaviors
Next, we asked whether the associative (coac-
tivity) and predictive (sequences) hippocam-
pal codes have different functional roles. A
predictive model of the environment would be
required to learn tasks that necessitate flexible
navigation. To test this prediction, we trained
Liu et al., Science 382, eadi8237 (2023)
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A
E
F
800
600
400
200
)
F
F
O
m
i
t
S
y
b
d
e
r
e
d
r
o
(
D
I
l
l
e
c
B
C
G
Stim OFF
Stim ON
D
Stim OFF
800
600
400
200
)
N
O
m
i
t
S
y
b
d
e
r
e
d
r
o
(
D
I
l
l
e
c
1 m
min
max
firing rate
Stim ON
H
density
14× mean
0
100
I
)
s
m
(
g
a
l
e
m
i
t
50
0
-50
-100
100
50
0
-50
-100
)
s
m
(
g
a
l
e
m
i
t
-100
0
field distance (cm)
001
-100
0
field distance (cm)
001
Fig. 2. Optogenetic perturbation of MEC gamma timing impairs temporal
but not rate coding features of CA1 place cells. (A) Histological sections
showing (top) expression of mDlx-ChR2-mCherry in MEC GABAergic cells (red)
and optic fibers’ tracks (dashed lines) and (bottom) probe locations in CA1.
(B) Rate maps for CA1 pyramidal cells (n = 815) in the Stim OFF and Stim ON
directions. (C) Example Bayesian decoding of CA1 population spike trains
during running behavior. Dashed cyan line represents animal’s actual position.
The color map indicates probability of a decoded location. (D) Representative
place cells for the Stim OFF (top) and Stim ON (bottom) directions. (Top) Firing
rate as a function of spatial positions. (Bottom) Theta phase–position raster of
place cell spikes. Red line represents the linear circular regression. (E) Spatial
information was not significantly different between cells in the Stim OFF and Stim
ON directions (P = 0.39; Wilcoxon signed-rank test). (F) Representation stability
as measured by the population vector (PV) correlation between even and odd
trials in both directions was higher than shuffled data (OFF/ON versus shuffle:
P = 6 × 10−8/P = 6 × 10−8, Wilcoxon signed-rank test) and not different between the
ON and the OFF directions (P = 0.35, Wilcoxon signed-rank test). (G) Examples of
theta firing relationships for cell pairs with overlapping place fields in OFF (top)
and ON (bottom) directions. The cells cofired in the same theta cycles in both
cases, but the order of firing (AB) is only consistent in the OFF direction.
(H) Average normalized density plot between place field distance and theta
timescale firing lag for all overlapping place cell pairs in OFF (top) and ON
(bottom) running directions. Theta compression was disrupted in Stim ON only
(P = 9 × 10−5, Wilcoxon signed-rank test between theta compression slopes; see
methods). Circles indicate the cell pairs shown in (G). (I) Cofiring of overlapping
place cells in the same theta cycles was preserved in both directions
(overlapping versus nonoverlapping place cells in OFF/ON: P = 1 × 10−4/P =
9 × 10−5, Wilcoxon signed-rank test; OFF versus ON: P = 0.067). ***P < 0.001.
rats (n = 5) to learn a novel spatial configura-
tion of rewards in a familiar “cheeseboard”
maze (8, 41, 51). Rats learned to find three
hidden water rewards in different locations on
the maze, with the reward locations changing
every day (Fig. 5, A and B). Each trial started
with the animal in the home box and ended
when they retrieved the three rewards and
came back to the box. The most efficient strat-
egy for the animal in this task was thus to find
the optimal route that connected all three re-
ward locations by learning to sequentially
Liu et al., Science 382, eadi8237 (2023)
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A
E
B
C
D
Fig. 3. Impaired development of place cell theta sequences and predictive
properties. (A) (Top) Example theta sequences. (Bottom) Average (n = 20
sessions in five rats) decoded position estimated across different theta phases,
relative to the actual animal position (dashed black line). Stim ON theta
sequences were impaired (Stim OFF versus Stim ON quadrant scores: P =
7 × 10−141; weighted correlation: P = 4 × 10−22, Wilcoxon rank sum test,
n = 17,992/13,265 theta cycles). (B) Increase in spatial information of place
cells across laps in both Stim ON (blue) and Stim OFF (black) conditions (***P =
1.8 × 10−11/1.2 × 10−5 for Stim OFF/ON, Wilcoxon rank sum tests comparing
the 1st versus the 15th lap). (C) Increase in theta sequence look-ahead index in
the Stim OFF (***P = 4.0 × 10−6), but not the Stim ON, direction (P = 0.71,
Wilcoxon signed-rank tests). (D) Backward shifting of PF center-of-mass (COM)
overlaps on the Stim OFF trajectory (***P = 1.3 × 10−69) but not the Stim ON
trajectory (P = 0.16, Wilcoxon signed-rank tests). COM shift relative to the first
lap is shown (>0, forward shifting to future; < 0, backward shifting to past).
(E) Example place cells showing backward shifting place fields on the Stim OFF
trajectory (top) and stable fields on the Stim ON trajectory (bottom). Arrows depict
the animal’s running direction. Curves on top show smoothed firing rate for the first
and last laps, and raster plots below show spikes across all laps. For all these analyses,
n = 20 sessions from five rats were used.
navigate from one reward to the next. On half
of the days, we performed the same optoge-
netic perturbation during learning trials (Stim
ON sessions), whereas in the other half there
was no stimulation (Stim OFF sessions). We
observed an intact formation of place fields
(fig. S10) and impaired theta sequences (Fig.
5D) in Stim ON sessions. Animal learning per-
formance was impaired in Stim ON compared
with Stim OFF sessions (Fig. 5C and fig. S10),
supporting a role of the predictive code in the
efficient learning of novel optimal trajecto-
ries in a familiar environment. We next asked
whether replay would be preserved despite the
disruption of theta sequences in this familiar
environment. We first examined replay of the
novel trajectory learned by the end of the cur-
rent day’s training session. In Stim OFF sessions,
we found robust replay in both awake SWRs
(during intertrial periods in the home box) and
in the post-learning sleep session (Fig. 5F and
fig. S11A). In contrast, replay of the novel route
to the new goal locations was impaired in Stim
ON sessions (Fig. 5F and fig. S11A), suggesting
that when learning a new optimal route to
goals, even in familiar environments, the tran-
sitional structure between locations of the route
encoded by theta sequences is required for
its subsequent replay. Replay of the familiar
routes to previously learned locations was pre-
served in both Stim OFF and Stim ON sessions
(fig. S11B). These effects were not due to dif-
ferences in SWR properties, single-unit firing
dynamics during SWRs, or decoding accuracy
of animal position between Stim OFF and Stim
ON sessions (figs. S11, D and E, and S10C). The
two-dimensional (2D) place field properties of
individual cells were also preserved, similar to
those on the 1D linear track (fig. S10E).
In contrast to the impaired Stim ON replay,
reactivation of cell assemblies was maintained
in both Stim OFF and Stim ON sessions (Fig.
5G and fig. S11), replicating our results from
the linear track. Finally, we tested whether im-
pairment of hippocampal sequences with pre-
served place cell expression and coactivity
affected subsequent memory recall. Memory
recall measured 2 and 22 hours after learning
was disrupted in Stim ON compared with Stim
OFF sessions (Fig. 5H), and animals spent less
time exploring around the reward locations
after Stim ON than after Stim OFF sessions
(fig. S10B). Furthermore, while performance on
the 2- and 22-hour tests during Stim OFF ses-
sions remained on par with the final perform-
ance reached during learning, in Stim ON
sessions, performance was further deteriorated
(fig. S10A).
Our hypothesis predicted that in contrast to
“model-based” behaviors that require a pre-
dictive code, an associative memory code im-
plemented by the coactivity of hippocampal
cells would be sufficient to support other types
of episodic memory, such as associating spatial
context with rewards. We trained rats (n = 5) on
a conditioned place preference (CPP) paradigm
(Fig. 5I), which depends on intact hippocampal
function. Rats were trained to associate one of
the two halves of a cheeseboard maze with the
presence of water rewards at random locations.
After four pairing trials, we tested their pref-
erence for either of the two halves of the maze
(without reward present). In half of the ses-
sions, we delivered the optogenetic perturba-
tion during all running periods during pairing
trials. In line with our previous results, we de-
tected similar assembly reactivation during
sleep after both Stim OFF and Stim ON pairing
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Fig. 4. Impaired replay with preserved reactivation of a novel experience.
(A and B) Examples of replay and reactivation for (A) the Stim OFF and (B)
the Stim ON experience, respectively. (Top) Decoded position during replay events
(color coded by decoded position). (Middle) Raster plots of neuronal firing;
colored circles indicate activations of assemblies composed of neurons with nearby
place fields (colored ticks; colors of assemblies reflect their peak activation position).
(Bottom) Assembly reactivation strength curves. (C) Increase in proportion
significant replay (left) and sequence scores (right) of SWRs in post-task sleep as
compared with pre-task sleep. Unlike the OFF direction, there was no significant replay
in the ON direction (n = 4437 events; Stim OFF: student’s t test, ***P = 7 × 10−11;
Stim ON: P = 0.29 for proportions; and Wilcoxon signed-rank test: OFF ***P = 3 × 10−17
and ON P = 0.29 for scores). Only the first session in the maze was included (n = 5 sessions).
(D) Reactivation strength of task-related assemblies centered on post-task sleep
SWR, increased relative to baseline (Stim OFF post-task sleep versus baseline sleep during
SWRs: Wilcoxon signed-rank test, n = 31 components, **P = 0.0096; Stim ON post-task
sleep versus baseline sleep during SWRs: Wilcoxon signed-rank test, n =
27 components, **P = 0.0026). (E) Reactivation of pairwise neuronal correlation as
measured by explained variance (EV) in post-task sleep was significant for both directions
(Stim OFF: *P = 0.031; Stim ON: Wilcoxon signed-rank test, *P = 0.031;
Stim OFF versus Stim ON, Wilcoxon signed-rank test, P = 0.81; n = 5 sessions).
(F) Correlation between replay scores and assembly reactivation strength for post-task
SWRs computed independently for Stim OFF and Stim ON replay events. Reactivation and
replay were correlated in Stim OFF (Pearson’s correlation coefficient
r = 0.11, ***P = 3 × 10−12) but not in Stim ON (Pearson’s r = −0.028, P = 0.06).
trials (fig. S12). Population activity during
SWRs formed distinct memory representations
for both contexts (rewarded and nonrewarded
maze halves) in both Stim OFF and Stim ON
sessions, consistent with an intact associative
code (fig. S12). Because the CPP task involves
boundaries, it gave us the opportunity to quan-
tify a critical signature of hippocampal predic-
tive coding, which is the elongation of place
fields along obstacles in 2D mazes, reflecting
the topological structure of the space (17, 52).
Similar to previous reports (53, 54), fields near
the boundary of our maze tended to elongate
parallel to the wall in Stim OFF sessions (Fig.
5K and fig. S12). However, this effect was dis-
rupted during Stim ON (Fig. 5K and fig. S12),
providing further support that the predictive
map was impaired. To assess replay in the ab-
sence of stereotypical trajectories, we exam-
ined the degree to which the sequential order
of firing in post-task sleep SWRs resembled
the sequential order in behavior. The sequen-
tial order was preserved in post-task sleep in
Stim OFF sessions but not in Stim ON sessions
(fig. S12, F and G). Despite these changes in
the predictive code, on the test session, where
no reward or stimulation was delivered, rats
showed an enhanced preference for the pre-
viously rewarded context in both Stim OFF
and Stim ON conditions (Fig. 5, J and L), con-
firming that an associative memory code was
sufficient for the formation and retrieval of a
context-reward association.
Circuit mechanisms for coactivity and sequence
memory codes
Given this dissociation, we wondered which
distinct circuit mechanisms support the reac-
tivation and replay of memories. The main
inputs that modulate the firing dynamics of
CA1 pyramidal cells are excitatory projections
from CA3 and the entorhinal cortex as well
as perisomatic inhibition (Fig. 6A). The rela-
tive strength of each of these inputs during
behavior can be estimated by measuring layer-
specific gamma oscillations (34, 35, 55, 56). MEC
optogenetic perturbation specifically disrupted
midfrequency gamma oscillations (gammaM)
in the distal CA1 dendrites, the domain in-
nervated by MEC axons (Fig. 6B and fig. S13),
while other CA1 gamma oscillations, elicited
respectively by CA3 inputs and local inhibition
(34, 35, 55–57), remained unaltered (Fig. 6B
and fig. S13). The coupling of CA1 spikes to
gammaM, but not to the other two gamma
oscillations, was also impaired (fig. S13), con-
sistent with the notion that our manipulation
disrupted CA1 pyramidal cell entrainment by
MEC inputs but not by CA3 or local interneur-
ons. The disruption of theta sequences during
initial experience led to the impairment of re-
play but not the reactivation of assemblies,
raising the question of which mechanisms link
these processes. To answer this question, we
turned to computational modeling.
Previous work has suggested that the highly
recurrent CA3 hippocampal region with its
auto-associative network structure is respon-
sible for both the coactivation of CA1 cells
forming functional assemblies (22, 58) and the
generation of sequential activity (24, 59, 60).
We implemented a spiking CA3-CA1 network
model capable of generating spontaneous re-
play. Our CA3 network consisted of recurrent-
ly connected leaky integrate-and-fire pyramidal
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Fig. 5. Internally generated sequences are needed for memory-guided
behavior. (A) Task structure of the cheeseboard task: Each day, animals learned a
novel trajectory to get three hidden rewards in a circular arena. (B) Schematic of
the cheeseboard setup. (C) Learning performance measured as distance traveled
relative to optimal trajectory. ANOVA with repeated measures showed a significant
main effect of group (F1,43 = 133.4, P < 10−10; n = 33 and 11 sessions for Stim OFF
and Stim ON, respectively). (D) Average decoded position versus theta phase,
relative to actual animal position (dashed black line). Stim ON theta sequences
were degraded (quadrant scores were lower in Stim ON than in Stim OFF: n =
5958/2695 cycles for Stim OFF and Stim ON, respectively, P = 2 × 10−3; weighted
correlations were lower in Stim ON than in Stim OFF: P = 3 × 10−4, rank sum
test). Two cycles are shown for visibility. (E) Example of a decoded replay event.
Decoded linearized position (top), spike raster (middle), and assembly reactivation
strength (bottom) were shown for the same replay event. (F) Increase in replay
score in post-task sleep as compared with pre-task sleep. Unlike the Stim OFF
condition, there was no significant replay in the Stim ON condition (Stim OFF:
P = 3 × 10−20; signed-rank test, n = 11,460 events; Stim ON: P = 0.41, n = 8689
events). (G) Reactivation strength of task-related assemblies centered on post-
task sleep SWR (Stim OFF post-task sleep versus baseline sleep during SWRs: n = 36
components, P = 4.71 × 10−4 ; Stim ON post-task sleep versus baseline sleep during
SWRs: n = 22 components, P = 3.19 × 10−3, signed-rank test). (H) Memory
performance during 2 and 22 hour post-learning recall tests (P = 6.8 × 10−4/7.9 × 10−4
for 2 and 22 hour tests, rank sum test; n = 25/11 for Stim OFF/ON sessions from
five rats). (I) Task structure of CPP task. (J) Example rat paths for Stim OFF (left) and Stim
ON (right) baseline and testing sessions on CPP task. The side rewarded during pairing
is highlighted in yellow. (K) Example place fields near the boundary for Stim OFF (left)
and Stim ON (right) conditions, illustrating place field elongation along the boundary,
which was disrupted in the Stim ON condition. Red circles emphasize the shape of
the place field. (L) CPP memory performance: both Stim ON and Stim OFF training
resulted in animals spending more active time in rewarded versus unrewarded
side (Stim OFF: paired t test, n = 5 sessions, P = 2.85 × 10−4; Stim ON: paired t test,
n = 6 sessions, P = 2.10 × 10−5).
cells and interneurons (61). This network was
connected in a feedforward manner to a CA1
network, with a similar composition but lack-
ing recurrent excitation, so every CA1 pyram-
idal cell integrated inputs from multiple CA3
pyramidal cells (Fig. 6C). We first simulated
a learning phase, akin to a rat running on a
novel linear track, in which place cells received
random spatial inputs. In accordance with
experimental observations, CA3-CA1 synaptic
weights were updated according to an asym-
metric (62, 63) spike time–dependent synap-
tic plasticity (STDP) rule, whereas CA3-CA3
weights followed a symmetric (64) STDP rule
(Fig. 6C). On the basis of our experimental
findings, we simulated a Stim OFF condition,
in which place cells displayed phase preces-
sion and robust theta sequences (Fig. 6D and
fig. S14). In a Stim ON condition (mimicking
the effects of our optogenetic MEC perturba-
tion), place cells were phase-locked to theta
oscillation but lacked phase precession and
theta sequences (Fig. 6D and fig. S14), repro-
ducing our experimental findings. We also
simulated offline epochs [akin to non–rapid
eye movement (non-REM) sleep] before and
after spatial learning; in such periods, the
network received low-level stochastic spiking
inputs to drive activity. We examined CA1
spiking patterns after learning and quanti-
fied replay and reactivation as we did with
our experimental data. In the Stim OFF con-
dition, synapses between overlapping place
cells were potentiated by STDP (fig. S14). Place
cell sequences experienced in the learning
phase were spontaneously replayed in the fol-
lowing offline epoch (Fig. 6, E and F). In the
Stim ON condition, disorganized timing within
theta cycles disrupted CA3-CA1 STDP, which
relies on a consistent timing between pre- and
postsynaptic spike pairs (fig. S14). CA3-CA3 STDP
was preserved due to place cell coactivity
within theta cycles, regardless of their precise
temporal ordering (fig. S14). These effects re-
sulted in an impairment of replay in the
Stim ON condition (Fig. 6, E and F) but robust
reactivation of place cell assemblies in both
conditions (Fig. 6, E and G), mirroring our ex-
perimental results. The dissociation between
reactivation and replay in our model suggests
that reactivation and replay are differently
mediated by STDP at CA3 and CA1 synapses,
providing a plausible circuit-level mechanism
for our findings.
Discussion
In this study, we described two complemen-
tary hippocampal circuit mechanisms that sup-
port the formation of memory associations and
the generation of predictive representations of
the environment. First, the coactivity of place cell
assemblies encoded discrete states in the envi-
ronment and, with their subsequent reactivation,
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Fig. 6. Circuit mechanisms for coactivity and sequence hippocampal
dynamics. (A) Schema depicting the inputs to CA1 pyramidal neurons stratified
along their somatodendritic axis. Local inhibitory inputs are dominant in the
pyramidal layer (st. pyr.), CA3 inputs target proximal apical dendrites in the
stratum radiatum (st. rad.), and entorhinal inputs target distal dendrites in
the stratum lacunosum-moleculare (st. l-m.). (B) Gamma amplitude-theta phase
comodulograms for each layer-specific LFP component (see methods)
displayed modulation in a specific gamma sub-band (averaged data from n = 10
sessions from four rats): CA1pyr in gammaF (100 to 160 Hz), rad in gammaS
(30 to 60 Hz), and LM in gammaM (60 to 110 Hz). (Right) MEC perturbation
selectively impaired LM gammaM but not CA1pyr or rad oscillations (**P = 0.002,
Wilcoxon signed-rank test; n = 13 sessions from five rats). (C) (Left) Model
schematic depicting a subnetwork of CA3 cells projecting to a subnetwork of CA1
cells. Triangles represent pyramidal neurons, and circles represent inhibitory
interneurons. (Right) STDP rules used to train different synapses within the
network during learning trials. (D) In Stim OFF simulations (top), place cells
displayed phase precession and prominent theta sequences. In Stim ON
simulations (bottom), phase precession was disrupted, and theta sequences
were abolished. (E) Example replay events simulated by the model after Stim
OFF (left) and Stim ON (right) learning. Decoded position, spike raster, and assembly
reactivation strength as in Fig. 4. (F) Increase in proportion of “SWR” events with
significant replay in post-task “sleep” epochs in Stim OFF and Stim ON protocols.
Replay improvement was above chance levels in Stim OFF but not Stim ON
simulations (Stim OFF: P = 0.0039, Wilcoxon signed-rank test, n = 6585 events;
Stim ON: P = 0.19, n = 6031 events). (G) Reactivation strength of task-related
assemblies centered on post-task sleep SWR-like events increase relative to
baseline (Stim OFF post-task sleep versus baseline sleep during SWR-like events:
Wilcoxon signed-rank test, n = 362 components, ***P = 5 × 10−44; Stim ON
post-task sleep versus baseline sleep during SWR-like events: Wilcoxon signed-
rank test, n = 312 components, ***P = 1 × 10−27).
supported associative memory. Second, tempo-
rally compressed hippocampal sequences en-
coded transitional structures of states in the
environment, supporting the formation of a
predictive map. Replay of these sequences
provided a mechanism to update and exploit
this predictive map, but only after intact en-
coding of transitional structures of task states
during learning. Disruption of trajectory-specific
theta sequences impaired their subsequent
replay but did not affect the reactivation of
neuronal assemblies representing those same
locations. Reactivation and sequence replay
are therefore dissociable neural processes.
The dependence of replay on learning environ-
ment transitional structures through theta se-
quences was highly specific for both space and
time: Neither disruption of theta sequences
for the same trajectory traveled in the opposite
direction nor disruption of previously expe-
rienced trajectories affected replay. Further-
more, these results indicate that encoding the
specific transitions between place cells along
behaviorally relevant trajectories, rather than
place field formation per se or global theta-
timescale dynamics alone, is an instrumental
mechanism for replay, explaining and extending
previous observations on the relationship between
theta population dynamics and replay (65–67).
The disruption of temporally compressed hippo-
campal sequences impaired flexible memory–
guided navigation but did not affect the for-
mation and recall of contextual associations.
Our results advance a framework to unify
previously disparate views of hippocampal
function, including encoding cognitive maps
for spatial and episodic memory (68–70), pre-
dictive maps for flexible navigation and plan-
ning (10, 16, 17), and multimodal memory
representations for relational processing (18, 71).
We argue that the hippocampal role in encoding
episodic memories relies on two complementary
Liu et al., Science 382, eadi8237 (2023)
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mechanisms. First, the synchronous coactivity
of cell assemblies binding different features
of experience into cohesive representations
enables the fast encoding of discrete states in
the world and supports associative memory.
Second, the formation of a predictive map is
supported by internally generated hippocampal
sequences, binding discrete successor states into
a relational structure. Moreover, our results can
account for two independent lines of evidence
supporting previous theories of hippocampal
predictive coding: predictive sequences and
“successor representation” place fields. Our
manipulation impaired the development of
theta and replay sequences. Previous studies
have shown that both theta and replay se-
quences not only reproduce animal recent ex-
periences but can also construct novel predictive
representations. Theta sequences encode trajec-
tories ahead of the animal’s current location
and can represent alternative paths at decision
points (44–46). Replay sequences can repro-
duce never-experienced paths (72, 73) and
dynamically change to reflect learned task
contingencies (11, 74–76) or represent available
paths not yet taken (77, 78). In both cases,
internally generated hippocampal sequences
could be conceptualized as a sampling process
between a series of possible future states from
a probabilistic generative model, and they
were both impaired by our manipulation. In
addition, experience-dependent backward ex-
pansion and deformation around obstacles of
place fields are believed to reflect the encoding
of a predictive map over the locations the
animal expects to occupy in the near future
(17, 52). These features were disrupted by our
manipulation, in contrast to place field forma-
tion and stability, which may be supported by
different plasticity mechanisms (79). Together,
these effects of our manipulation suggest that
all these “generative” features of hippocampal
representations are linked by common circuit
mechanisms.
Although numerous processes could con-
tribute to the generation of replay sequences
(80–83), our results suggest that initial theta
sequence–mediated STDP is necessary for the
replay of newly learned spatial trajectories but
not for memory reactivation. These results
suggest a hierarchical organization of hippo-
campal assembly and sequence dynamics.
Previous work investigating the postnatal
development of hippocampal dynamics sup-
ports this dissociation. Synchronous cell as-
semblies are already present around postnatal
day 17 in rats, with their reactivation in SWRs
reflecting encoding of individual locations on
a maze (84). However, theta sequences and
replay encoding animal spatial trajectories ap-
pear only after postnatal day 21 (66, 84).
The present findings agree with previous
studies that investigated the contribution of
the temporal coordinatization of hippocampal
spike timing to memory. Pharmacological dis-
ruption of place cell theta rhythmicity and co-
ordination, while preserving their rate coding
properties, impaired spatial memory (85, 86).
In addition, disruption of the behavioral time-
scale (on the order of seconds) sequential struc-
ture of CA1 firing responses during temporal
delays also impaired memory (31, 87). These
studies highlight the importance of the precise
temporal coordination of hippocampal spike
timing for memory.
Additional research is still needed to eluci-
date the precise contribution of different input
pathways and cell types in the entorhinal-
hippocampal network to temporal coding and
sequence generation. MEC inputs reach CA1
via direct projections from layer III and also
indirectly via layer II inputs to the dentate
gyrus, CA3, and CA2 (88). Our manipulation
was not restricted to either of these input path-
ways and therefore cannot precisely determine
their contributions to the generation of CA1
sequences. Furthermore, a small subset of MEC
GABAergic cells send direct long-range pro-
jections to CA1 (89). It is possible that our
manipulation also affected these projections;
however, their sparsity and the fact that the
stronger GABAergic projections to CA1 arise
from the lateral rather than the medial en-
torhinal cortex (90) limit their potential con-
tribution to the results described here.
Overall, this study suggests the coexistence
of complementary associative and predictive
codes in the hippocampus. This dual code could
account for the wide range of behavioral func-
tions attributed to this brain structure in learn-
ing, memory, navigation, and planning.
Materials and methods
Surgical procedures
Rats (adult male Long-Evans, 300 to 500 g, 3
to 6 months old) were kept in the vivarium on
a 12 hour light/dark cycle and were housed
two per cage before surgery and individually
after it. All experiments conformed to guide-
lines established by the National Institutes of
Health and have been approved by the Cornell
University Institutional Animal Care and Use
Committee.
Silicon probe implantation was performed
as described previously (41, 51, 91). Animals
were anesthetized with isoflurane anesthesia
and craniotomies were carried out under ste-
reotaxic guidance. Silicon probes (NeuroNexus,
Cambridge Neurotech, or Diagnostic Biosig-
nals) were mounted on custom-made 3D-printed
microdrives to allow precise adjustment of
the vertical position of sites after implantation.
The probes were inserted above the target re-
gion. Craniotomies were sealed with sterile
wax. Two stainless steel screws were placed
bilaterally over the cerebellum to serve as
ground and reference electrodes. Several addi-
tional screws were driven into the skull and
covered with dental cement to strengthen the
implant. Finally, a copper mesh mounted on a
3D-printed resin base was attached to the skull
with dental cement and connected to the ground
screws to act as a Faraday cage, attenuating
the contamination of the recordings by envi-
ronmental electric noise and protecting the
headgear. Three doses of analgesic were
administered, with the first dose administered
prior to surgery in order to cover 72 hours
total. After post-surgery recovery, probes were
moved gradually in 50- to 150-mm steps per day
until the desired position was reached. Hippo-
campal layers were identified physiologically
by unit activity and characteristic local field
potential (LFP) patterns (34, 92).
A variety of different silicon probes were im-
planted in the dorsal hippocampus [−4.0 to
4.5 mm anteroposterior (AP) from Bregma and
2.6 mm from midline (ML)]. Data from some
of the animals included in this study have also
been included in a previous study, and surgical
procedures have been described in more detail
there (41).
For optogenetic experiments, rats were also
implanted with custom-made optic fiber arrays
(three 200-mm core multimode fibers each,
~500 mm apart, connected to a single 2.5-mm
steel ferrule; Doric Lenses) in both hemispheres
over the MEC (–7.7/–8.4/–9.1 AP; ± 4.6 ML and
4.7/ 4.3/3.2 mm from the surface of the brain,
for each fiber respectively).
Optogenetic experiments
For optogenetic experiments, rats were in-
jected with custom-prepared AAV5-mDlx-
hChR2(H134R)-mCherry from AddGene [plasmids
were a gift from Dr. Gord Fishell (40)]. Three
injections per hemisphere were performed
along the dorsoventral MEC as follows: (i)
−7.7 AP, ±4.6 ML, 4.7 mm depth, 200 nl; (ii)
−8.4 AP, ±4.6 ML, 4.3 mm depth, 400 nl; (iii) −9.1
AP, ±4.6 ML, 3.2 depth, 700 nl. After injection,
craniotomies were sealed, and animals recov-
ered in the vivarium for 3 weeks. After this
period, a second surgical procedure for im-
planting optic fibers and electrodes was per-
formed, as described above. Optic fiber arrays
were implanted in the same craniotomies per-
formed previously for virus injection. For opto-
genetic stimulation, fiber array ferrules were
connected with mating sleeves to 450-nm blue
light-emitting laser diodes coupled to 2.5mm
steel ferrules (PL-450, Osram).
Optogenetic perturbations were performed
by delivering blue light, modulated with a pos-
itive 53 Hz current sinusoid using an isolated
current driver (Thorlabs). Light intensity was
calibrated for each animal during home cage
recordings by analyzing the suppression of LFP
gamma power in the stratum lacunosum-
moleculare during stimulation. A minimum
and maximum power of 3 and 6 mW, respec-
tively, was used. In the linear maze task, light
Liu et al., Science 382, eadi8237 (2023)
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stimulation was triggered when the animal
crossed an infrared sensor near the end of the
track (but before the reward port located at
the very end of it) and stopped when it crossed
a similar sensor at the other end, resulting in
stimulation only during running periods. In the
cheeseboard maze and CPP tasks, the same opto-
genetic stimulation was applied during all runn-
ing periods in the maze during learning trials.
Behavioral and electrophysiological recordings
After surgery, animals were handled daily and
accommodated to the experimenter, recording
room, and cables for 1 week before the start of
the experiments. Before the start of the behav-
ioral experiment, the animals were water-
restricted. Electrophysiological recordings
were conducted using Intan RHD2000 inter-
face board or Recording Controller (IntanTech)
and 64-channel digital headstages (IntanTech
or Diagnostic Biochips), sampled at 20 kHz. For
all behavior tasks, animal position was re-
corded with an overhead camera (Basler) and
tracked with DeepLabCut (93) and custom codes.
Linear track task
In the linear track, rats were trained to run
back and forth to collect small sugar water re-
wards at both ends. Animals typically per-
formed between 30 and 80 trials per day. The
session was terminated when the animal was
satiated, typically after 40 min. The linear track
was placed 1 meter above the floor and was
300 cm long and 7 cm wide with 5- to 10-cm-high
walls. Water rewards were automatically de-
livered in reward wells at both ends of the track.
Baseline and post-task sleep were recorded in the
home cage before and after the task, respectively.
Cheeseboard maze task
The cheeseboard maze was a circular platform
(120 cm diameter), where the animals learned
to find three goal wells that contained water
rewards. A trial was completed once the ani-
mal had retrieved all rewards and returned
to the start box to collect an additional food
pellet reward. The locations of the goal wells
changed daily but were fixed during a given
session. This strategy required the animals to
update their memory for the new goal loca-
tions in an otherwise familiar environment
during each session. Note that between trials,
there was always a delay of ∼30 s. If the rat could
not find all three rewards within 2 min, the
trial was terminated, and the animal was re-
turned to the start box. A pre-task test session
of five trials (with the same configuration as
the previous day) was run every day to assess
whether the animal remembered the previous
day’s positions, followed by a 2-hour sleep ses-
sion. Next, a 30-trial learning session was con-
ducted (with or without light stimulation).
After a 2-hour sleep session after the learning
trials, a five-trial post-task test session (with
the newly learned reward configuration) was
also conducted to examine whether the animal
remembered the newly learned locations. Learn-
ing performance was evaluated as the distance
traveled from the start box to collect the three
rewards and divided by the optimal trajectory
(shortest possible path). A value of 1 then indi-
cates an optimal path taken by the animal.
Performance in the post-task test sessions was
computed in the same way (Fig. 5H), and ad-
ditionally it was compared directly with the
learning performance on the final learning trial
(fig. S10A). An additional measure of perform-
ance was computed as the proportion of ex-
ploration time spent within 5 cm the correct
wells (fig. S10B). Stim OFF and Stim ON ses-
sions were alternated in a counterbalanced
manner across animals. The inclusion of data
for the analysis required that the animal be
pretrained for a week in this task.
Conditioned place preference task
The CPP task was performed in the same maze
as in the cheeseboard maze task but separated
into two compartments by a 30-cm-high wall
in the midline. Animals had free access to both
compartments connected by a common corri-
dor at one end of the maze (Fig. 5I). The task
included three stages spanning 3 days: base-
line, pairing, and testing. For the baseline stage
on day 1, animals were allowed to freely ex-
plore the two compartments for 15 min with
no reward. A baseline place preference was
then measured as the difference in active ex-
ploratory time spent in the two compartments.
The compartment that animals explored less
was selected as the rewarded side for the sub-
sequent pairing sessions. Pairing sessions in-
cluded one session after the baseline session
on day 1, two sessions on day 2, and one ses-
sion before the testing session (see below) on
day 3. During the pairing sessions, animals
explored the maze for 20 min, with hidden
water reward delivered at random locations
on the rewarded side. On day 3, after the final
pairing session, a testing session was per-
formed, during which animals again explored
the maze without reward for 15 min and the
place preference was measured as was done
during the baseline session. Optogenetic stim-
ulation was delivered when animals actively
explored the maze during pairing sessions.
Each CPP session was flanked by sleep record-
ings (around 2 hours) in the home cage. Learn-
ing performance of the CPP task was measured
by comparing the place preference during the
baseline versus the testing session (Fig. 5L).
Tissue processing and immunohistochemistry
After the termination of the experiments, ani-
mals were deeply anesthetized and perfused
transcardially, first with 0.9% saline solution
followed by 4% paraformaldehyde solution.
The brains were sectioned into 70-mm-thick
slices (Leica Vibratome). The sections were
washed and mounted on glass slides with a
fluorescence medium [Fluoroshield with DAPI
(4′,6-diamidino-2-phenylindole), product no.
F6057, Sigma, USA]. A confocal microscope (Zeiss
LSM 800) was used to obtain high-quality photos.
Computational model
Architecture
We built a simplified network model consist-
ing of 1250 pyramidal cells (PYR) and 100 in-
hibitory interneurons (INT) in area CA3 and
1250 pyramidal cells and 100 inhibitory inter-
neurons in area CA1 using the Brian2 simu-
lation environment (94). Each neuron was
modeled as an adaptive exponential leaky
integrate-and-fire unit with cellular adapta-
tion (61). Briefly,
Cm
dV tð Þ
dt ¼ (cid:2)ðgL V tð Þ (cid:2) Vrest
ð
Þ (cid:2)
(cid:1)
gLDT exp
(cid:3)
V tð Þ (cid:2) q
DT
þ Isyn tð Þ þ w tð ÞÞ
where V(t) is the membrane potential, Cm is
the membrane capacitance, gL is the leak con-
ductance, Vrest is the reversal potential of the
linear leak current, q is the spike threshold, DT
is the threshold sharpness, Isyn is the synaptic
current, and w(t) is the adaptation current,
described by
dw tð Þ
dt ¼ a V tð Þ (cid:2) Vrest
ð
tw
Þ (cid:2) w tð Þ
where the parameter a describes the strength
of the subthreshold adaptation. The synaptic
current Isyn was computed as
Isyn tð Þ ¼ gAMPA tð Þ V tð Þ (cid:2) Eexc
ð
Þ þ
gGABA tð Þ V tð Þ (cid:2) Einh
ð
Þ
where Eexc = 0 mV and Einh = −70 mV are the
reversal potentials of excitatory and inhibitory
currents, respectively. Synapses were modeled
as conductances with biexponential kinetics (61).
Synapses
Within each area, PYR→INT connectivity oc-
curred at 10% probability, and INT→INT and
INT→ PYR connectivity occurred at 25% prob-
ability. Whereas PYR→PYR connectivity was
absent from CA1, CA3 PYR cells projected at 10%
probability to PYR from both CA3 and CA1, mod-
eling recurrent CA3 connectivity and CA3 in-
puts into CA1, respectively. Synaptic parameters
were used as previously reported (61), with
the modification that synaptic weights were
initialized to follow a lognormal distribution
exp(N(0,1)) × winit, where wCA3→CA3
¼ 0:3 and
where wCA3→CA1
¼ 0:7. To simulate learning as
a result of the activity during exploration, STDP
init
init
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RES EARCH | R E S E A R C H A R T I C L E
was modeled for PYR→PYR synapses alone,
where synaptic weights are updated according
to an additive pair-based learning rule as follows
(cid:3)
(cid:1)
Dwþ ¼ Aþ exp (cid:2)
at tpost if tpre < tpost
Dt
tþ
(cid:1)
Dw(cid:2) ¼ A(cid:2) exp (cid:2)
(cid:3)
Dt
t(cid:2)
at tpre if tpre > tpost
CA3→CA3 STDP followed a symmetric rule,
where A+ = A− = 80 pA, and t+ = t− = 62.5 ms,
while CA3→CA1 STDP followed an asymmetric
rule, where A+ = 800 pA, A− = −A+ × 0.4, tþ ¼
20 ms, and t(cid:2) ¼ 40 ms. All weights were
cropped at wmax = 40 nS.
Exploration phase
Spike trains of PYR cells during exploration
were generated as previously described (61).
Briefly, 10% of all pyramidal cells in each re-
gion were designated as place cells, and place
fields were randomly distributed along a 3-m-
long simulated linear track. Exploration was
simulated as 10 min of exploration time while
the rat ran along the linear track at 50 cm/s.
Silent cells (nonplace cells) fired at 0.01 Hz,
and place cell spikes were sampled from a
Poisson process at 20 Hz, with the sampling
procedure ensuring an inhomogeneous Pois-
son process with a time-dependent rate l(t),
which was the product of a Gaussian tuning
curve (representing the neuron’s place field)
with width s = 7 cm (yielding l = 30 cm place
fields) and a theta component. The theta com-
ponent was either a phase precession compo-
nent to simulate the sequences of the Stim
OFF condition or a phase-locking component
to simulate the lack of sequences but preserved
theta-cycle coactivity in the Stim ON condition.
The Stim OFF theta component was
(cid:1)
qOFF tð Þ ¼ cos 2pfqt þ
(cid:3)
(cid:5)
(cid:4)
x tð Þ (cid:2) xi
p
2p (cid:3) Q
where Q represents the proportion of the
linear track that the place field spans and
takes numeric value of 30-cm field over 300-cm
linear track or 0.1, and xi is the position of the
place field of cell i.
The Stim ON theta component was a phase-
locking component designed to yield the same
phase-locking value as the other condition’s
theta precessing component but abolishing
sequential order of spikes
(cid:1)
qON tð Þ ¼ cos 2pfqt þ
(cid:3)
(cid:7)
p
2p (cid:3) Q
(cid:6)
N p
2
; s
l
(cid:5)
where l is the length of the track (3 m), and
(cid:4)
N p
is a normal distribution with mean p
2
2
and standard deviation s
l.
; s
Offline phase
Before and after exploration-triggered STDP,
the network was simulated using Brian2 to
respectively model pre (baseline) and post
“sleep” sessions. To drive the network, each
CA3 pyramidal cell received random inputs
in the form of uncorrelated Poisson spike
trains with a pooled mean rate of 15 Hz.
Under these conditions, the network spon-
taneously generated population burst events
(akin to SWRs).
Analysis
All the modeling steps described above were
performed n =10 times with different random-
ly generated initial conditions determining
place field locations, initial weights, etc. This
resulted in n = 10 simulated sessions, in which
theta sequences, replay, and reactivation were
analyzed applying the same methodology and
parameters as we did to analyze experimental
data described above.
Spike sorting and unit classification
Spike sorting was performed semiautomatical-
ly with KiloSort (95) (https://github.com/cortex-
lab/; KiloSort), followed by manual curation
using the software Phy (https://github.com/
cortex-lab/phy) and custom designed plug-ins
(https://github.com/petersenpeter/phy-plugins)
to obtain well-isolated single units. Cluster
quality was assessed by manual inspection of
waveforms and autocorrelograms, and by the
isolation distance metric. Multiunit, noise clus-
ters, or poorly isolated units were discarded for
analysis. Well-isolated units were classified
into putative cell types using the Matlab pack-
age CellExplorer (96) (https://github.com/
petersenpeter/CellExplorer). Spiking char-
acteristics, including the autocorrelograms,
spike waveforms, and putative monosynap-
tic connections derived from short-term cross-
correlograms, were used to select and charac-
terize well-isolated units. Three cell types were
assigned: putative pyramidal cells, narrow
waveform interneurons, and wide waveform
interneurons. Two key metrics used for this
separation were burst index and trough-to-
peak latency. Burst index was determined by
calculating the average number of spikes in
the 3- to 5-ms bins of the spike autocorrelo-
gram divided by the average number of spikes
in the 200- to 300-ms bins. To calculate the
trough-to-peak latency, the average waveforms
were taken from the recording site with the
maximum amplitude for the averaged wave-
forms of a given unit.
Detection of brain states
State scoring was performed as previously de-
scribed (41, 51). Briefly, the LFP was extracted
from wide-band data by lowpass filtering (sync
filter with a 450 Hz cutoff band) and down-
sampling to 1250 Hz. Broadband LFP, nar-
row-band theta frequency LFP, and estimated
electromyogram (EMG) were used for state
scoring. Spectrograms were computed from
broadband LFP with a fast Fourier transform
in 10-s sliding windows (at 1 s), and a principal
components analysis was computed after a
Z-transform. The first principal component
reflected power in the low (<20 Hz) frequency
range, with oppositely weighted power at
higher (>32 Hz) frequencies. Theta dominance
was quantified as the ratio of powers in the 5
to 10 Hz and 2 to 16 Hz frequency bands. EMG
was estimated as the zero-lag correlation be-
tween filtered (300 to 600 Hz) signals across
recording sites (55). Soft sticky thresholds on
these metrics were used to identify states. High
LFP principal component 1 and the low EMG
were considered non-REM, the high theta and
low EMG were considered REM, and the remain-
ing data were taken to reflect the waking state.
For analysis of neural activity during active
behavior (e.g., place cell and theta sequence
analysis), only periods in which the animals
run faster than 5 cm/s were included.
SWR detection
To detect SWRs, one channel around the CA1
pyramidal layer was chosen for the ripple de-
tection, and one channel from CA1 stratum
radiatum was chosen for sharp wave detection.
The difference between the two channels was
used as the basis for SWR detection. This dif-
ference signal was filtered with a low-pass filter
at 55 Hz, and then local minima were detected
as candidate events. The corresponding ripple
power (amplitude of the difference signal in the
bandpass 80 to 250 Hz) for each candidate
event was recorded. A true event was considered
when both a sharp wave and ripple oscillation
were detected in the same window. K-means
clustering was used to define clustering of SWR
from non-SWR events, and manual curation
was used to better define the boundary and
remove outliers. The events were then expanded
until the (nonclipped) ripple power fell below
1 SD; short events (<15 ms) and longer events
(>400 ms) were discarded.
To refine the detection of SWR start and
end points for reactivation and replay analyses
(in order to avoid including empty bins), we
detected population burst events as periods
when the instantaneous population firing
rate (binned in 1-ms bins and smoothed with a
Gaussian kernel with 10-ms width) reached a
peak of >2 SD and remained greater than the
mean. The SWR start and end time points
were set as the start and end time points of the
population burst within the respective SWR,
and SWRs without population bursts were
discarded.
Place cell analysis
Spiking data and the tracked animal’s posi-
tion were binned into 3-cm-wide segments of
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RES EARCH | R E S E A R C H A R T I C L E
the camera field projected onto the maze floor,
generating raw maps of spike counts and oc-
cupancy. A Gaussian kernel (SD = 3 cm) was
applied to both raw maps of spike and oc-
cupancy, and a smoothed rate map was con-
structed by dividing the spike map by the
occupancy map. Independent rate maps were
constructed for the different running direc-
tions in the mazes. Only periods in which the
animal velocity was >4 cm/s were included.
A place field was defined as a continuous re-
gion of at least 15 cm2, where the mean firing
rate was >10% of the peak rate in the maze,
and the peak firing rate was >3Hz.
Spatial information (SI) for individual place
cells was obtained from the linearized rate
maps (97)
SI ¼
XN
i¼1
pi
li
l
log2
li
l
where N is the total number of spatial bins,
pi is the probability of occupancy, and li is
the firing rate in the ith spatial bin, and l the
average firing rate of the cell. To measure the
experience-dependent change of SI across laps
in each condition, the mean and standard de-
viation of SI across all cells within a condition
group were calculated, and the SI was then
z-scored for that condition (Fig. 3B).
To identify cells that discriminate between
the two sides of the CPP task, we constructed a
vector for each cell containing the mean firing
rate for every movement interval that the ani-
mal spent in each of the two halves. We then
performed a one-tailed Wilcoxon rank sum test
between the firing vectors in the two halves,
and cells for which this comparison was sig-
nificant were identified as cells with firing
specific to that respective half. To quantify
discrimination in post-task sleep, pairwise post-
task sleep correlations (CPOST, see below) were
compared between pairs of cells specific for the
same half versus pairs of cells that were specific
for opposite halves of the environment.
Population vector analysis
To estimate the stability of the population
code in the Stim OFF and Stim ON conditions,
we performed population vector analysis as
described previously (98). Briefly, we measured
the correlation between the population firing
curves in even and in odd trials for each run-
ning direction, and we compared this value
with the value obtained in surrogate data, in
which cell identity was shuffled across even
and odd trials.
In addition, we performed a cross-correlation
between the population firing curves in even
and odd trials separately for each pair of spa-
tial bins (fig. S3, A and B). To estimate rep-
resentation stability, we computed the “error”
defined as the distance between the peak
correlation for each spatial bin (each of the
columns of the matrix) to the diagonal. To
statistically test the directionality of the hippo-
campal code, we compared the representation
stability within a given direction (even versus
odd trajectories in the same direction) to the
stability of the representation between the two
directions of movement (even trajectories in
one direction versus odd trajectories in the
other direction).
COM shift
To measure PF shifting across laps (Fig. 3D),
we used place cells that had PFs on the linear
track, and calculated the center-of-mass (COM)
of PFs for each lap n (COMn) (99)
COMn ¼
X
FRixiX
FRi
i
i
where FRi is the firing rate in the spatial bin i,
and xi is the distance of the spatial bin i from
the start of the running trajectory. For each
lap, COM shift was then measured as the dif-
ference between the first lap and the current
lap. To prevent any edge effect, only PFs with a
peak location outside the two ends of the track
(i.e., defined by 20% of the track length) were
included. For place cells with multiple PFs,
only the primary PF (with the maximal peak
rate) was included.
Place field eccentricity
To calculate the eccentricity of 2D place fields
in the CPP task (fig. S12), we first defined the
PF boundary on the 2D rate maps. PF was first
defined as the area with firing rates larger
than 40% of the peak rate. This area was fur-
ther refined with a series of morphological
operations: opening, closing, and infill, with
Matlab functions imopen, imclose, and imfill,
respectively. PF boundary was then detected
on the resulting binarized image using the
Matlab function bwboundaries. The eccentric-
ity of the detected PF was measured using the
Matlab function regionprops. For place cells
with multiple PFs, only the primary PF (with
the maximal peak rate located within the PF
boundary with the maximal size) was included.
The boundary and nonboundary cells were
defined as the cells with the peak of the pri-
mary PF located within and outside 15 cm of
the wall, respectively.
Phase precession
Phase precession analysis was performed as
previously described (34, 100). Circular-linear
regression between relative position within
the place field and theta phase was applied
to calculate the phase-precession slope and
correlation strength (101). The slope and cor-
relation strength (r2) of phase precession were
derived from this circular-linear regression
analysis.
Theta compression
Theta compression analysis was performed as
described previously (102), independently for
the Stim OFF and the Stim ON direction.
Briefly, for each pair of overlapping place cells,
we computed (i) the distance between their
place field peaks and (ii) the theta time lag.
To qualify pairs with a significant theta time
lag, we computed a coarse cross-correlogram
for each cell pair using for durations T1 s using
5-ms bins. Cell pairs with a peak in this coarse
correlogram within ±100 ms with at least five
spikes in the peak bin were deemed signifi-
cant, and other cell pairs were excluded from
this analysis. To compute the theta time lag
for the selected cell pairs, cross-correlograms
were restricted to in-field spikes during run-
ning periods of the respective direction (Stim
OFF versus Stim ON) using 1-ms bins, and
each cross-correlogram was filtered with a
bandpass filter between 2 and 30 Hz. The
time of the cross-correlogram peak was defined
as the theta time lag of the pair of place cells.
Theta compression slopes were computed by
performing linear regression between the dis-
tance between the place field peaks and the
theta time lags.
Linearizing positions on the cheeseboard maze
Positions on the cheeseboard maze were lin-
earized along an optimal trajectory, connecting
the start box with the three rewarded loca-
tions for that session (with the closest reward
locations connecting directly to the start box).
The animal’s linearized position was defined
as the relative position along the optimal
trajectory closest to the animal’s current
position. To decode animal position from neu-
ronal activity (for theta sequence and replay
analyses), we only retained periods when this
linearized position described the current ani-
mal’s position well, defined as periods in
which (i) the error distance between the opti-
mal trajectory and the actual animal position
was within 20 cm and (ii) the animal running
speed along the optimal trajectory was at
least 10 cm/s. To decode replay of familiar
routes to previously learned trajectories (fig.
S7), we modified the above procedure to de-
fine the linearized trajectory: Instead of using
the three currently rewarded locations, we used
the three rewarded locations from the previ-
ous day’s session.
Decoding animal position from neuronal activity
To decode position from place cell activity
during both theta states and replay, we used a
Bayesian reconstruction approach as described
previously (65). Briefly, we computed the aver-
ON(x)
age firing rate probability li
for each pyramidal cell i at position x as the
normalized firing rate curve (spatial bin size:
1.5 cm) of the cell during running epochs in
the OFF and the ON direction, respectively,
OFF(x) and li
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which constituted the training step in our
decoder. To then decode the animal posi-
tion from the neuronal activity as expressed
by the firing rate vector n in a particular
window of width ts, we estimate the proba-
bility P(x|n)
P xjnð
Þ ¼
P njxð
Þ (cid:3) P xð Þ
P nð Þ
where spikes are assumed to fire as indepen-
dent Poisson processes
P njxð
Þ ¼
YN
i¼1
ni
Þ
ð
li xð Þ (cid:3) t
n!
i
e(cid:2)li xð Þ(cid:3)t
We applied the same procedure to decode
linearized positions on the cheeseboard maze,
using periods of movement along the line-
arized trajectory in which the animal stayed
within 20 cm of the optimal trajectory to train
the decoder.
Theta sequences
Theta reconstruction matrices
To decode the animal position during theta
cycles, we trained Bayesian decoders for the
OFF and the ON directions as described above
and decoded the animal position during run-
ning periods in the OFF and the ON direction,
respectively, using t = 20 ms bins with 5-ms
sliding window. We then computed theta re-
construction matrices for each theta cycle while
the animal was running in the OFF and the ON
direction by dividing the cycle in 500 temporal
bins and interpolating the respective (OFF or
ON) decoded position. The same procedure
was applied to construct theta reconstruction
matrices for Stim OFF and Stim ON cheese-
board sessions using the linearized cheeseboard
position during periods of movement along the
linearized trajectory and stayed within 20 cm
of the optimal trajectory.
Theta cycles
To detect theta cycles, we first detected deep
and superficial CA1 sublayers using the depth
profile of SWRs as described previously (51)
and selected the deep CA1 channel with the
highest theta power in the normalized spec-
trum. Theta cycles were defined as the peaks
in the LFP filtered in the theta band during
running periods, and cycles shorter than 100 ms
or longer than 200 ms were excluded from
further analyses. To correct for the phase shift
that can occur in different sublayer depth of
the theta channel, the final theta cycles were
shifted to ensure that the theta peaks were de-
fined as the phase of maximal uncertainty of
the theta reconstruction matrices, where un-
certainty u was defined as u ¼ (cid:2)maxx
g.
Theta peaks correspond 0° (0 rad.) and 360°
(2p rad.) and troughs at 180° (p rad.) and 540°
(3p rad.) of theta waves.
P xjnð
f
Þ
Theta sequences
To quantify theta sequence, we applied the
measures of quadrant scores and weighted
correlation on the theta reconstruction mat-
rices for each cycle. To compute the quadrant
score, we divided the central region in the
theta reconstruction matrix that was within
50 cm of the animal’s current location and
within 1
2 p of the theta trough (p) into four
equal quadrants, and computed the ratio be-
tween the probability within quadrants II and
IV (representing directions consistent with
the animal’s running direction) and the prob-
ability within quadrants I and III (represent-
ing directions incongruent with the animal’s
running direction). The weighted correlation
measured the correlation between time t and
location l weighted by the decoded probability
values p within the reconstruction matrix
w ¼
p
cov t; ljp
Þ
ð
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Þcov l; ljp
cov t; tjp
Þ
ð
ð
where
cov t; ljp
ð
m tjpð
Þ ¼
X
Þ ¼
X
pitiX
pi
i
i
pi ti (cid:2) m tjpð
X
ð
i
Þ li (cid:2) m ljpð
Þ
ð
pi
Þ
Þ
,
i
, and m ljpð
Þ ¼
X
piliX
pi
i
.
i
The look-ahead index of theta sequences is
calculated as in previous reports (46). In brief,
we recomputed the reconstruction matrix quad-
rants, this time extending the reach to use all
decoded probabilities within 1 m of the ani-
mal’s current location. The look-ahead index
was measured by comparing the probabilities
in the quadrants ahead (quadrant IV, future)
and behind (quadrant I, past) in the second
half of theta phases, as (IV – I)/(IV + I).
Replay analysis
Candidate replay events
We first detected periods of elevated pyra-
midal cell population activity as defining periods
when the instantaneous firing rate (1-ms bins,
smoothed with a Gaussian kernel of width
10 ms) was greater than the mean and reached
a peak of >2 SD above the mean during the
session. Candidate events were between 100
and 500 ms in duration, and they each over-
lapped with an independently detected SWR;
otherwise they were excluded from further
analyses.
Quantifying replay
We decoded the animal position for the OFF
and the ON direction during each candidate
replay event using non-overlapping t = 20 ms
bins (but see fig. S7A for replay results with t =
40 ms and t = 60 ms). OFF and ON direction
replay were scored independently. To assess
replay quality, we computed trajectory scores
of the reconstruction matrices (103). Briefly,
each reconstruction matrix was fitted with a
line (of slope a and intercept b) maximizing
the average likelihood R that the animal is
located within a distance d (set to 22.5 cm) of
the linear trajectory defined by the slope a
and intercept b
R v; rð
Þ ¼
1
m
Xm(cid:2)1
k¼0
P jpos (cid:2) r (cid:2) v (cid:3) k (cid:3) Dxj≤ d
ð
ð
Þ
Þ
The score of each event was normalized by
subtracting the mean and dividing by the stan-
dard deviation of a distribution of 500 shuf-
fled scores obtained by independently shifting
each of the columns of the event’s reconstruc-
tion matrix along the spatial dimension by a
random distance. An event with a score ex-
ceeding the scores of 95% of its shuffled scores
was considered significant. To quantify replay,
we normalized the proportion of significant
events during awake behavior or post-task
sleep by subtracting the mean proportion of
significant events in pre-task sleep.
In a control analysis, we corrected for the
differences in decoding quality between Stim
OFF and Stim ON trajectories (fig. S7C). For
this purpose, downsampled units before decod-
ing the Stim OFF trajectories by progressively
dropping units until the average decoded
error in Stim OFF trajectories was larger than
the average decoded error in Stim ON trajec-
tories, and we recomputed replay events for
Stim OFF trajectories using this more limited
sample (fig. S7C).
We performed an additional quantification
of replay, where for each replay event we com-
puted the weighted correlation and the jump
distance. The weighted correlation measures
the correlation coefficient between time and
decoded space, and jump distance was defined
as the maximum distance between the peak
decoded positions in two successive time bins of
the same event. Trajectory events were defined
as the events with high weighted correlation
(>0.6) and low jump distance (<75 cm), and to
assess whether the number of trajectory events
exceeded chance, we compared the number
trajectory events in the recorded data with the
number of trajectory events in surrogate data
where cell identities were shuffled 500 times.
This comparison yielded a P value (the propor-
tion of shuffled datasets with as many or more
trajectory events than those observed in the
original dataset), and we generated a signifi-
cance matrix of P values for progressively stricter
weighted correlation thresholds (0.6, 0.65, 0.7,
0.75, 0.8, 0.85, 0.9, 0.95) and jump distance
thresholds (75 cm, 62.5 cm, 50 cm, 37.5 cm,
25 cm, 12.5 cm).
Pairwise bias correlations
The above replay analyses test for the replay of
stereotypical trajectories and are not directly
applicable to the trajectory-free behavior in the
Liu et al., Science 382, eadi8237 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
CPP task. To assess whether the order of unit
spiking in behavior is preserved in these se-
ssions, we computed the similarity between
behavioral sequences and SWR sequences
using a pairwise bias correlation method
(65). Briefly, we computed a bias matrix Bk for
each sequence k
Bk ¼
nk i; j
ð
nk ið Þ (cid:3) nk jð Þ
Þ
where nk(i) is the number of spikes emitted by
neuron i in the kth sequence, and nk(i, j) is the
number of times neuron i spiked before neu-
ron j in the kth sequence (see fig. S12F for an
example). Bk(i, j) therefore reflects the bias of i
to spike before j in the kth sequence, taking
values between 0 (i never precedes j) and 1 (i
always precedes j), with 0.5 representing no
bias (i precedes j half of the time). The cor-
relation between two sequences can be esti-
mated as the cosine between their skew-bias
matrices as each bias matrix is unwrapped
into a vector 2Bk – 2 (this normalization is to
achieve a range of values between −1 and 1,
assuring that two mirror sequences would
have opposite signs with vectors pointing
in opposite directions). The activity of cells
that are not common to the two sequences
is ignored.
To test whether the order of firing in be-
havior was preserved in post-task sleep, we
computed the mean bias matrix of all se-
quences taking place in theta cycles during
the task in a given recording session. We com-
puted the correlation (cosine) between this
bias matrix and each of the bias matrices de-
scribing sequences in post-task sleep SWRs.
We compared this correlation with a shuffled
distribution obtained by recomputing the cor-
relation after shuffling the spikes sequence n =
100 times and deemed as significant those se-
quences with correlations whose absolute value
exceeded 5% of the shuffled distribution. We
normalized the proportion of significant events
by subtracting the mean proportion of signifi-
cant events in pre-task sleep.
Coactivity and reactivation analysis
Cofiring
Each spike train was binned in individual theta
cycles, and the cofiring of a pair of cells was
defined as the Pearson correlation coefficient
of the binned firing rates of the two cells
across all theta cycles in the recorded session.
The matrix of Pearson correlation coefficients
was called the cofiring matrix C.
Explained variance
Explained variance (EV) was quantified as pre-
viously described (104). Briefly, for each session,
we computed the proportion of the variance
in the population spiking activity in post-task
sleep that is explained by task-related activity,
after taking into account correlations pre-
existing in sleep before the experience
0
B
B
@
r
EV ¼
1
2
rC;CPOST (cid:2) rC;CPRE
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(cid:7)
(cid:6)
(cid:6)
1 (cid:2) r2
1 (cid:2) r2
rCPOST;CPRE
(cid:7)
CPOST;CPRE
C;CPRE
C
C
A
where C, CPRE, and CPOST refer to the cofiring
matrix and the correlation matrices across
SWRs in pre- and post-task sleep, respectively,
and rA,B describes the correlation coefficient
between the pairwise correlation matrices A
and B. EV was computed for each recorded
session separately, and it was compared with
the control value of reverse explained variance
(REV) obtained by recomputing EV after swap-
ping CPRE and CPOST.
Pairwise reactivation
For the pairwise reactivation analyses, we
used linear regression between CPOST and CPRE
to remove the portion of the variance in CPOST
that can be explained by preexisting pat-
terns, and we correlated the resultant resid-
uals CRESIDUAL with C (105).
For the CPP reactivation analysis, we iden-
tified cells that had a preference for each of the
two sides of the maze by computing each cell’s
firing rate for every movement period that the
animal spent moving in each of the two sides
of the maze. Cells with a significant preference
(Wilcoxon rank sum test, alpha a = 0.05) were
divided according to the sign of their prefer-
ence between rewarded-side responsive cells
and unrewarded-side responsive cells. We then
compared CRESIDUAL (see above) in pairs of
rewarded-side responsive cells versus pairs of
unrewarded-side responsive cells.
Cell assembly analyses
For detecting cell assembly patterns, we used
an unsupervised statistical framework based
on a hybrid principal components analysis (PCA)
followed by independent component analysis
(ICA) as previously reported (49, 106–108). In
brief, spike trains of each neuron were binned
in 25-ms intervals for the whole session (in-
cluding only task periods during movement),
the matrix of firing correlation coefficients for
all pairs of neurons were constructed. Next, we
calculated the number of assemblies on the
basis of those principal components whose
eigenvalues exceeded the threshold for ran-
dom firing correlations (using the Marchenko-
Pastur law). This method provides a number
of significant patterns smaller than the num-
ber of neurons. Each of these patterns explained
more variance of the spike train correlation ma-
trix than other patterns that would result from
independently firing neurons. Independent
component analysis (fast-ICA algorithm) was
then used to determine for each assembly
(component) the vector of weights with which
each neuron’s firing contributes to that as-
sembly. The strength of each assembly i’s ac-
tivation for a given time bin k was computed
as follows
Sik ¼ Z T
k PZk
where Z is the population activity matrix of the
z-scored firing rate of each unit, and P is the
outer product of the component i’s weights, in
which the diagonal has been set to zero so that
isolated spikes from individual units do not
contribute to S.
Most of the detected assembly patterns con-
sisted of a few neurons with high weights and
a large group of neurons with weights around
zero. Assembly members were thus consi-
dered those cells whose weight exceeded the
mean weight of the assembly by two standard
deviations (107).
To produce the assembly activity profiles in
fig. S9B, we took the assembly activation strength
during the last hour of cumulative baseline
sleep and the first hour of cumulative post-
task sleep, excluding periods outside of non-
REM sleep. During the task, we took the
assembly activation strength during running
in Stim OFF and Stim ON trajectories sepa-
rately. Because the exploration time is variable
between sessions, instead of absolute elapsed
time, we divided the Stim OFF and Stim ON
exploration time into quantiles.
Assembly activation events were detected as
peaks in the assembly activation strength ex-
ceeding a value of 5 (109). The point process of
assembly activation events during behavior in
the task was used to compute the spatial infor-
mation content of assembly activity in fig. S4G.
The order of assembly activation events in
SWRs was analyzed in fig. S9E as follows. For
each SWR in which at least three assemblies
were active, we correlated the timing of assem-
bly activations within an event to the respec-
tive positions (that is, the location of peak
activity for a given assembly). We took the
absolute value of the Spearman’s rank-order
correlation coefficient r to account for reverse
replay. To correct for coefficient variation with
the number of assemblies (e.g., fewer points
yield higher correlation coefficients) and the day
of the recording, we subtracted from each
n defined as the
coefficient r a baseline value r0
mean r of SWRs recorded pre-task sleep of the
same session with a matching number n of
assembly activations.
Spectral analysis, cross-frequency coupling, and
spike-LFP coupling
To obtain the phase of the theta rhythm, one
LFP channel was selected as explained above.
LFP was bandpass-filtered in the range of 5 to
15 Hz. Theta phase was then computed using
the Hilbert transform of the filtered LFP.
Liu et al., Science 382, eadi8237 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Cross-frequency coupling
To perform spectral analysis at a high resolu-
tion in time and frequency, the complex wave-
let transform (CWT) of the LFP (or ICs) was
calculated using complex Morlet wavelets.
Wavelets were calculated using a logarith-
mically spaced frequency vector in the band
of interest (25 to 200 Hz). Phase-amplitude
cross-frequency coupling for a given LFP re-
cording was assessed using the modulation
index measure (MI) (110). Phase time-series
were binned into phase intervals and the mean
wavelet amplitude was calculated for each of
them. The MI was obtained by measuring the
divergence of the observed amplitude distribu-
tion from the uniform distribution. The sta-
tistical significance of the MI values (P value)
was assessed by a surrogate analysis (n = 1000
surrogates) with random shifts between the
phase and amplitude time series. For the pres-
ented plots, grand averages were calculated as
the mean across all animals, unless otherwise
indicated, and MI reported were significant
[P < 0.01 compared with surrogate distribu-
tion (34, 55)].
Spike-LFP coupling
The phase-locking of spikes to LFP features at
each frequency was measured for individual
units using the wavelet phase from 25 to 200 Hz
(30 logarithmically spaced wavelet scales) at
the time of each spike (34, 55). Only neurons
that fired at least 100 spikes during the se-
lected task intervals were included in the analy-
sis. Reference LFP was taken 200 to 400 mm
away from the electrode, where the unit was
recorded to minimize spike energy leakage into
the LFP. Modulation indices were calculated
using the mean resultant length of the phases,
and significance was estimated using the Ray-
leigh test for nonuniformity (P < 0.05) using
circular statistics. Preferred frequency of mod-
ulation was determined as the largest mean
vector length of each significantly modulated
neuron. The mean angle of the phases for a
given neuron’s spikes was taken as the pref-
erred phase.
Independent component and current
source density analysis of LFPs
To separate the different sources that con-
tribute to the LFP mixed signal, we used an
approach based on independent component
analysis (ICA) that has been described and
validated previously for hippocampal record-
ings (41, 55, 111). Here, we applied ICA to
spatially contiguous LFP channels after
filtering in the gamma band (25 to 200 Hz).
The ICA algorithm (runinca) (112) takes a
time series of data with dimension equal to
the number of recording sites and returns a
time series of the same dimensionality, but
rotated so that each dimension represents a
different IC. The inverse of the mixing matrix
that transforms the LFP data into the ICs gives
the channel weight of each component that
is captured for each recording site. When
projected back to the anatomical location of
the recording site, this corresponds to the
spatial voltage loadings of each IC (41, 55, 111).
Once ICs have been extracted from the raw
LFP traces, they can be analyzed as if they
were active independently from activities at
other locations.
Hierarchical bootstrap
Hierarchical bootstrap (113) was performed to
analyze data with hierarchical structure. Briefly,
bootstrap datasets were created by resampling
with replacement following levels of hierar-
chical order (in the order of animals followed
by sessions). The mean of each resampled boot-
strap data was calculated each time, in a total
of 1000 resampling times. The final statistics
were done on the populations of resampled
data from the different experimental condi-
tions. P value indicated the test result that the
values of one condition were higher than the
values of the other condition after controlling
for the other nesting variables.
Statistical analyses
Statistical analyses were performed with MATLAB
functions or custom-made scripts. No specific
analysis was used to estimate minimal popu-
lation sample or group size, but the number of
animals, sessions, and recorded cells was larger
or similar to those used in previous related
works (41, 65, 66, 75, 92). The unit of analysis
was typically identified as single neurons or
assemblies. In a few cases, the unit of analysis
was sessions or animals, and this is stated in the
text. Unless otherwise noted, nonparametric
two-tailed Wilcoxon rank sum (equivalent to
Mann-Whitney U test) or Wilcoxon signed-
rank test was used for unpaired and paired
data, respectively. For multiple comparisons
following analysis of variance (ANOVA), Tukey’s
honest significant difference post-hoc test was
used. All statistical tests were two-sided, unless
otherwise specified. Throughout the manuscript,
statistical significance is indicated by asterisks:
*P < 0.05, **P < 0.01, ***P < 0.001.
On box plots, the central mark indicates the
median; bottom and top edges of the box
indicate the 25th and 75th percentiles, respec-
tively; and whiskers extend to the most extreme
data points not considered outliers. Outliers are
not displayed in some plots but were included
in statistical analysis. Owing to experimental
design constraints, the experimenter was not
blind to the manipulation performed during
the experiment (i.e., optogenetic manipulation).
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AC KNOWLED GME NTS
The authors thank R. Harvey, H. Robison, L. Sjulson, J. Goldberg,
I. Ellwood, W. Sun, M. Zugaro, and D. Nitz for useful comments
on the manuscript and M. R. Warden for providing access to
the confocal microscope. Funding: This work was supported by
NIH grant 4R00MH120343, a Sloan Fellowship, a Whitehall
Research Grant, and a Klingenstein-Simons Fellowship (A.F.-R.);
NIH grant 4R00MH122582 (A.O.); an Eric and Wendy Schmidt
AI in Science Postdoctoral Fellowship (a Schmidt Futures program)
and a Philippe Foundation grant (R.T.); and a Klarman Fellowship
(W.T.). Author contributions: All authors conceived of and
designed the experiments and analyses and wrote the
manuscript. C.L., W.T., and A.F.-R. performed the experiments.
R.T., C.L., W.T., and A.F.-R. analyzed the data. R.T. performed the
simulations. First authorship order was determined by coin toss.
Competing interests: The authors declare that they have no
competing interests. Data and materials availability: All data are
available in the main text or the supplementary materials. Custom
scripts used in this study can be downloaded from Zenodo (114).
License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-
article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi8237
Figs. S1 to S14
MDAR Reproducibility Checklist
Submitted 19 May 2023; accepted 21 August 2023
10.1126/science.adi8237
Liu et al., Science 382, eadi8237 (2023)
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RES EARCH
ORGANIC CHEMISTRY
Multiplicative enhancement of stereoenrichment by a
single catalyst for deracemization of alcohols
Lu Wen†, Jia Ding†, Lingfei Duan†, Shun Wang, Qing An, Hexiang Wang, Zhiwei Zuo*
Stereochemical enrichment of a racemic mixture by deracemization must overcome unfavorable entropic
effects as well as the principle of microscopic reversibility; recently, photochemical reaction pathways
unveiled by the energetic input of light have led to innovations toward this end, most often by ablation
of a stereogenic C(sp3)–H bond. We report a photochemically driven deracemization protocol in which a
single chiral catalyst effects two mechanistically different steps, C–C bond cleavage and C–C bond
formation, to achieve multiplicative enhancement of stereoinduction, which leads to high levels of
stereoselectivity. Ligand-to-metal charge transfer excitation of a titanium catalyst coordinated by a
chiral phosphoric acid or bisoxazoline efficiently enriches racemic alcohols that feature adjacent and
fully substituted stereogenic centers to enantiomeric ratios up to 99:1. Mechanistic investigations
support a pathway of sequential radical-mediated bond scission and bond formation through a common
prochiral intermediate and reveal that, although the overall stereoenrichment is high, the selectivity
in each individual step is moderate.
U biquitous C(sp3)–C(sp3) bonds in organic
compounds have recently been exploited
as unconventional functional handles
for rapid complexity generation through
skeletal editing (1–5). This logic presents
intriguing opportunities for stereogenic bond
construction via asymmetric catalysis. Most
commonly, stereogenic C–C bonds are formed
by facially selective addition to a prochiral start-
ing material (Fig. 1A) (6–8). Critically, the overall
enantioselectivity of this process is thus a direct
function of the stereodifferentiation of the two
prochiral faces in the single stereodefining step
[enantiomeric ratio (er) = kR/kS, where kR is the
rate of formation of the (R)-enantiomer and kS is
the rate of formation of the (S)-enantiomer]. As
a result, exceptionally high degrees of stereo-
induction are required in this irreversible addi-
tion step to achieve synthetically useful results
(kR >> kS). An alternative paradigm can be en-
visioned transiting through a prochiral inter-
mediate to enable a formally reversible C–C bond
formation process, which can convert a mixture
of racemates into enantiomerically pure com-
pounds (Fig. 1B). This approach would enable a
broader purview for catalytic deracemization
because C–C bonds constitute the fundamental
three-dimensional skeleton of complex mole-
cules. Through stereoisomerization of the molec-
ular core, as opposed to the peripheral C–H bonds,
consecutive or fully substituted stereogenic cen-
ters could be directly enriched by using this cycle
of stereocenter-ablating C–C bond scission and
stereocenter-generating C–C bond formation,
State Key Laboratory of Organometallic Chemistry, Shanghai
Institute of Organic Chemistry, University of Chinese
Academy of Sciences, Chinese Academy of Sciences,
Shanghai 200032, China.
*Corresponding author. Email: zuozhw@sioc.ac.cn
†These authors contributed equally to this work.
which would provide a powerful platform for
enantioenrichment via catalytic deracemization.
Within this framework, we recently won-
dered whether one catalyst could be directly
responsible for each of these stereoselective
steps by means of different mechanisms, which
would thus allow for deracemization. The multi-
plicative nature of stereoinduction would lead
to amplification of the enantiodifferentation
ability of the catalyst, in analogy to the Horeau
principle in which multiple asymmetric steps
do not necessarily need rigid stereocontrol to
obtain highly enantioenriched diastereomers
(9–11). However, in this case, because one of
the stereodifferentiating steps in the catalytic
cycle involves stereoablation, the same multi-
plicative enhancement could be achieved in
the context of enantioinduction of even a sin-
gle stereocenter (er = kRk–S/kSk–R). To achieve
synthetically useful levels of enantioinduction
[>90% enantiomeric excess (ee)], the single cat-
alyst would only be required to achieve roughly
60% ee in each of the stereocenter-ablating and
stereocenter-generating steps.
Although conceptually simple and synthet-
ically intriguing, the development of such pro-
cesses has been hindered by the principle of
microscopic reversibility (12–18). To address
this critical issue, previous studies have opted
to use a single chiral catalyst for deracemiza-
tion through a two-step process that consists of
a nonselective step and a stereodifferentiating
step. Notable early studies on redox-driven de-
racemizations by Toste et al. (19) and Zhou et al.
(20), as well as recent breakthroughs in photo-
chemical deracemization such as Bach et al.’s
seminal works that used enantioselective trip-
let sensitization (18, 21–23) and several other
elegant systems with reversible C–H bond
formation (24–29), have demonstrated the
effectiveness of this approach (30, 31). Very
recently, Knowles and Miller and co-workers
used an elegantly designed tricatalytic sys-
tem that consisted of one chiral base for C–H
bond breakage and a chiral thiol catalyst for
C–H bond formation, which exploited the syn-
ergistic effect of two chiral catalysts for the
photocatalytic deracemization of cyclic ureas
(32). It is important to note that using one
chiral catalyst to effect asymmetric induction
in both bond-breaking and bond-making events
will result in an overall equilibrium of racemate
because of the shared energy surface (33, 34),
unless distinct reaction pathways can be re-
alized by a single catalyst.
Recently, we have applied ligand-to-metal
charge transfer (LMCT) excitation in an or-
chestrated sequence of in situ coordination,
LMCT homolysis, and alkoxy radical–mediated
b-scission to the catalytic activation of C–C
bonds of free alcohols for fragment couplings
(35–38). Driven by the thermodynamic stabil-
ity of radicals, both strained and unstrained
C–C bonds can be selectively and irreversib-
ly cleaved into a carbonyl unit and a carbon-
centered radical (39). Notably, high-valent
metal ions, including commonly used Lewis
acids, can be directly used for LMCT catalysis
(40–45), which led us to consider the possibil-
ity of photocatalytic deracemization using chiral
ligand–coordinated, LMCT-competent Lewis
acid catalysts (Fig. 1C). Conceivably, asymmetric
LMCT catalysts could leverage the chiral recog-
nition of racemic alcohols in the coordination
step to preferentially form one diastereomeric
metal alkoxide complex, initiating enantiose-
lective C–C bond scission, even if the b-scission
process may not respond to asymmetric induc-
tion. The concurrent generation of a carbonyl
fragment and a transient carbon-centered
radical would set the stage for single-electron
reduction and enantioface-differentiating ad-
dition to rebuild the stereogenic C–C bond, which
could be facilitated by the lower-valent chiral
metal complex generated in the photoexcita-
tion event (46–55). In this work, we realize this
design plan and describe an LMCT-enabled
deracemization platform that uses a single
chiral Ti-catalyst to induce decoupled and
enantioselective C–C bond cleavage and for-
mation, which results in high stereoselectivity
through multiplicative enhancement of stereo-
induction. By exploiting the photocatalytic
properties of a common Lewis acidic Ti(IV)
catalyst ligated by chiral phosphoric acid or
bisoxazoline, racemic alcohols—including those
that feature adjacent and fully substituted ste-
reogenic centers—can be efficiently converted
into their enantioenriched forms with pro-
nounced selectivity.
Catalyst optimization with cyclic alcohols
We selected the cis isomer of 2-phenylcyclo-
pentanol (1) as the model substrate to explore
LMCT catalysis for deracemization (Fig. 2). Ex-
tensive evaluation of high-valent metal catalysts
Wen et al., Science 382, 458–464 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 1. Catalytic deracemization paradigms via enantioselective bond scission and formation. Multiplicative enhancement of two distinct enantioinduction steps
enables high levels of stereoselectivities in deracemization. (A) Established enantioselective C–C bond formations. (B) Catalytic deracemization via enantioselective
C–C bond scission and formation. (C) Deracemization of free alcohols enabled by asymmetric LMCT catalysis. Bn, benzyl; Boc, t-butyloxy carbonyl; hv, photon energy;
L*, chiral ligand; Me, methyl; Ts, p-toluenesulfonyl; Ph, phenyl; Re, R prochiral face.
Fig. 2. Reaction optimization. Reactions were performed on a 0.05-mmol scale. Yields, dr, and er (given for major diastereomers) were determined by high-performance
liquid chromatography (HPLC) analysis. C6F5, pentafluorophenyl; EtN(iPr)2, diisopropylethylamine; Tf, trifluoromethanesulfonyl; TRIP, 2,4,6-triisopropylphenyl.
with chiral ligands under the irradiation of
light-emitting diodes (LEDs) (peak wavelength,
395 nm; light intensity, 0.8 W/cm2) at 20°C
(see fig. S1 for detailed experimental setup)
revealed the combination of TiCl4 and chiral
phosphoric acid (CPA) as an effective cata-
lyst combination for photocatalytic deracem-
ization. This chiral Lewis acid combination has
been previously used by Leibfarth to control
enantiodifferentiating C–C bond formation
for stereoselective cationic polymerization (56).
In practice, we found that the combination
of 4 mol % TiCl4 and 16 mol % (S)-L1 in the
presence of substoichiometric Na2CO3 achieved
optimal efficiency and selectivity, generating
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Fig. 3. Reaction scope of cycloalkanols. Yields and dr and er values were determined based on isolated products and were the average of three parallel reactions.
*4 mol % TiCl4 with 16 mol % L1. †2 mol % TiCl4 with 8 mol % L6. ‡4 mol % TiCl4 with 16 mol % L6. §2 mol % TiCl4 with 8 mol % L5. ¶−40°C. #0°C. See
supplementary materials for experimental details. C10F7, heptafluoronaphthyl; C12F9, nonafluorobiphenyl; Et, ethyl.
cis (1S,2S)-1 with high efficiency and notable
enantioselectivity (93% yield, 99:1 er, entry 1).
Under these mild and redox-neutral condi-
tions, only a small amount of trans isomer was
obtained along with the desired cis isomer
[8.8:1 diastereomeric ratio (dr)], without the
observation of side products such as aldehyde
from photocatalytic ring-opening processes,
ketone from 2e oxidations, or alkene from de-
hydration (see fig. S2). The steric environment of
the CPA has a notable influence on the stereo-
chemical outcome. Replacing the sterically hin-
dered tri-iso-propylphenyl rings of L1 with
trimethylphenyl (L2) resulted in markedly
diminished stereoselectivity (entry 2), where-
as phosphoric acids bearing electron-deficient
arene substituents (L3, L4, L5, or L6) re-
sulted in rather low selectivities (entries 3 to
6). Use of the more acidic but less coordinat-
ing N-triflyl phosphoramide L7 in place of L1
resulted in markedly lower stereoselectivity
(3.2:1 dr, 21:79 er) despite similar steric envi-
ronments (entry 7). Organic base diisopropyl-
ethylamine was also found to be effective for
the desired deracemization (entry 8). Chang-
ing the loading of CPA relative to Ti from 4:1
to 2:1 had little effect on the efficiency and
stereoselectivity (see table S3), and the 4:1
ratio was adopted for best reproducibility on
small-scale parallel reactions. A linear corre-
lation between the enantioenrichment ob-
served in the reaction and the ee value of CPA
was identified (see fig. S4), and the absence
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 4. Deracemization of acyclic alcohols. Yields and dr and er values were determined on the basis of isolated products and were the average of three parallel
reactions. *8 mol % TiCl4 with 20 mol % L8. †12 mol % TiCl4 with 30 mol % L8. ‡Dichloromethane (DCM) and benzotrifluoride (PhCF3) (1:1). §PhCF3 instead of DCM.
of a nonlinear effect in this deracemization
indicated that a single CPA is presumably in-
volved at the Ti center (57). Use of (R)-L1 re-
sulted in identical values of stereoselectivity
with opposite configuration, supporting the
catalyst-controlled stereoselectivity (entry 9).
Furthermore, deracemization of the second-
ary alcohol was not observed when swapping
TiCl4 with CeCl3 or FeCl3 (entries 10 and 11), and
instead, a trace amount of 5-phenylpentanal
was observed, indicating that Ce and Fe LMCT
catalysts are capable of C–C bond scission but
not effective at promoting C–C bond–forming
addition. Moreover, control experiments re-
vealed that L1, TiCl4, and an LED light are
essential for the deracemization (entries 12
to 14).
As demonstrated in Fig. 3, this Ti-LMCT–
enabled photocatalytic deracemization can
be carried out on structurally diverse cyclo-
alkanols of varying ring sizes, indicating that
ring strain is not a decisive factor. In cyclo-
pentanol and cyclohexanol substrates, we found
that the deracemization is somewhat insen-
sitive to the electronic nature of the b-aromatic
rings. Excellent enantioselectivities could be
obtained for a series of diverse substituents
on the para, ortho, and meta positions, with
trivial differences in the diastereoselectivities.
Even in the presence of large aromatic rings
such as naphthalene (11), benzothiophene (12),
and dibenzofuran (13), the thermodynamical-
ly less-stable cis isomers were preferentially
formed for cyclopentanols. Regarding the six-
membered ring system, enantioenriched trans
isomers were selectively generated, presumably
by virtue of a chair-like cyclic transition state
for C–C bond formation. We found that (R)-
L6 was most effective for the deracemization
of trans-2-substituted cyclohexanols. Notably,
enantioenriched 3-hydroxy piperidine (23),
an essential building block for the syntheses
of important marketed pharmaceuticals such
as zamifenacin, piperidolate, and benidipine, can
also be selectively obtained with this straight-
forward protocol (58). Critically, enantioen-
riched synthesis of a-tertiary alcohols with
fully substituted stereogenic carbons could be
facilely achieved by this deracemization plat-
form. With the catalytic combination of TiCl4
and (S)-L5, a variety of tertiary 3-hydroxy pi-
peridines could be obtained with high levels
of enantioenrichment, regardless of the elec-
tronic nature of the a-aromatic rings. Tertiary
alcohols with a-methyl substituents can also
be accommodated, which renders structurally
diversified piperidine scaffolds with excellent
stereoselectivity. Further studies revealed that
larger alkyl groups at the a-position, including
ethyl and isobutyl groups, resulted in somewhat
lower er (see table S10). The stereochemistry of
tertiary alcohols 24 and 34 has been unam-
biguously assigned by single-crystal x-ray dif-
fraction. Even b-substituted cyclobutanols were
compatible with this deracemization paradigm
and generated enantioenriched cyclobutanols
35 to 38 with good enantioselectivities through
enantioselective C–C bond scission and reforma-
tion of the highly strained four-membered ring.
The generation of aldehyde byproducts through
a photocatalytic ring-opening process was ob-
served in those strained substrates, which re-
sulted in declined yields of deracemization.
Secondary and tertiary alcohols embedded in
seven-membered carbocycle or azepane scaf-
folds were also compatible, albeit with mod-
erate selectivities. We conducted a scaled-up
deracemization of cyclohexanol 14 at 1 mmol
scale by using a simple and easily assembled
photoflow system (see section 5.1 in the sup-
plementary materials), which rendered (−)-14
with similar levels of selectivities as the stan-
dard conditions (91% yield, 7.2:1 dr, 95:5 er).
Extension to acyclic alcohols
This protocol is not limited to cyclic hydroxyl-
ated scaffolds because the deracemization of
acyclic alcohols has been validated on 1,2-diaryl
aminoalcohols, a privileged scaffold for chiral
ligand synthesis (Fig. 4). Under similar cata-
lytic conditions as for the cyclic substrates, with
chiral bisoxazoline L8 as the ligand (see table
S11 for the ligand evaluation), enantioenriched
(+)-41 can be obtained with excellent yield and
stereoselectivity (20:1 dr, 98:2 er). A variety of
substitution patterns on the a- and b-aromatic
rings proved compatible, and high yields and
excellent stereoselectivities have been obtained
with no sensitivity to the electronic property
of the aromatic rings. This deracemization has
provided a practical approach to enantio-
enriched aminoalcohols with electronically
differentiated aryl rings on two different car-
bon termini (59, 60). Moreover, we conducted
1-mmol-scale reactions with 41 and 43, which
delivered enantiopure alcohols with identi-
cal selectivities to the standard condition at
prolonged reaction time (10 hours). Compound
(+)-43 can be elaborated via deprotection and
double condensation to generate a differen-
tially arylated bisoxazoline ligand, the para-
chloro substituted version of L8 (see section
5.2 in the supplementary materials).
Mechanistic investigations
We carried out mechanistic investigations to
elucidate the reaction pathway. Using C–H-
deuterated cylopentanol 50 and aminoalcohol
51 delivered nearly identical stereochemical
outcomes as the unlabeled analogs without
eroding the deuteration ratio, which precludes
hydrogen atom transfer (HAT) or stepwise oxi-
dation reduction as possible deracemization
pathways (Fig. 5A). With the same ligand, en-
antioconvergent transformations that used the
trans isomer of 1 or the opposite enantiomer
(1R,2R)-1 resulted in the same (1S,2S)-1 product
with identical stereoselectivity, supporting a
common, prochiral intermediate generated by
the C–C bond scission (Fig. 5B). This conclusion
can also be drawn from the same set of exper-
iments with aminoalcohol 41 (fig. S8).
The LMCT-homolysis behavior of Ti(IV) com-
plexes has been validated by steady-state photol-
ysis experiments by using an in situ–generated
putative complex [Ti(IV)L(OR)] (Fig. 5C). We
used a mononuclear [TiIV(L8)Cl4] complex, char-
acterized by x-ray diffraction, in the ligand
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 5. Preliminary mechanistic investigations. (A) Isotope labeling experiments. (B) Enantioconvergent transformations. (C) Steady-state photolysis
experiments. a.u., arbitrary unit; GC-MS, gas chromatography–mass spectrometry. (D) Spin-trapping EPR experiments. Exp, experimental; Sim, simulation.
(E) Crossover experiment. (F) Time-course study. (G) Decoupled radial-mediated bond formation and photocatalytic bond scission. THF, tetrahydrofluoran.
Wen et al., Science 382, 458–464 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
exchange with an equimolar amount of 46 for
the in situ generation of [TiIV(L8)(OR)]. The
1H nuclear magnetic resonance (NMR) spec-
trum displayed characteristic signals that can
be assigned to the bisoxazoline L8 and alk-
oxide ligands in a 1:1 ratio, and diffusion or-
dered spectroscopy (DOSY) NMR experiments
confirmed that the obtained species are mono-
meric complex and not higher aggregates (fig.
S10). In the same vein, the putative complex
generated from TiCl4 with an equimolar amount
of L1 and 14 was prepared (fig. S12). Both
complexes exhibited substantial absorptions
in the proximity of 395 nm. Under the irra-
diation of a 395-nm laser, with the gradual
decay of the absorption band ranging from
300 to 400 nm, a weakly absorbing band in
the 500- to 800-nm region started to emerge
as the originally light yellow solution turned
blue, which is indicative of the generation of
Ti(III) species (43). Upon exposure to air, the
blue solution was swiftly bleached to the
yellow Ti(IV) complex with the ultraviolet to
visible spectrum fully recovered. Aldehyde 52,
formed by radical-mediated bond scission,
was detected by gas chromatography–mass
spectrometry and 1H NMR, supporting the
generation of alkoxy radicals. Regarding the
cycloalkanols, the proposed alkyl radical gen-
eration by rapid alkoxy radical b-scission was
monitored by operando electron paramagnetic
resonance experiments with 5,5-dimethyl-1-
pyrroline N-oxide (DMPO) and a-phenyl-N-tert-
butylnitrone (PBN) as spin-trapping reagents.
As depicted in Fig. 5D, the characteristic sig-
nals of alkyl radical adduct with DMPO [hyper-
fine splitting constant AN = 14.4 G, AH = 20.9 G,
spectroscopic splitting factor (g) = 2.0061] or
PBN (AN = 14.6 G, AH = 2.4 G, g = 2.0062) can be
clearly distinguished, whereas alkoxy radical ad-
duct was not detected, indicating a fast b-scission
process that favors the C–C bond cleavage or
a concerted oxidation with C–C bond scission
(61, 62). Moreover, we further confirmed the
alkyl radical generated in the b-scission by the
isolation and characterization of the 2,2,6,6-
tetramethylpiperidin-1-oxyl (TEMPO) adduct.
We rationalized that within the same mech-
anistic framework, the aromatic aldehyde gen-
erated from the b-scission process of acyclic
aminoalcohols could be exchanged with a
more reactive exogenous aldehyde for the C–C
bond formation event to generate another
aminoalcohol product. Indeed, under the same
catalytic conditions for deracemization, cross-
over experiments with racemic 46 and para-
fluorobenzaldehyde 53 resulted in a newly
formed aminoalcohol 42 that contained a
parafluorophenyl group (Fig. 5E). The newly
generated aminoalcohol 42 underwent de-
racemization to reach the same level of en-
antioenrichment as the standard condition
(99:1 er). The yield of 42 can be further en-
hanced at the expense of deracemization
product 46 with increased concentration of
aldehyde 53. The foregoing results collec-
tively and unambiguously support the inter-
mediacy of aldehydes and carbon-centered
radicals generated by b-scission as the shared
intermediate in this deracemization paradigm.
The high efficiency of the desired cyclobutane
ring formation in the deracemization of cyclo-
butanols is notable because direct intramolec-
ular radical addition to the carbonyl to form a
four-membered ring is energetically unfa-
vorable, considering the high exothermicity
and low activation barrier of cyclobutoxy cleav-
age (39, 63). There are two seemingly reason-
able pathways for this cyclization that account
for the ability of Ti(III) to mediate such a rad-
ical bond formation: (i) reductive capture of the
formed alkyl radical by photogenerated Ti(III)
preceding a stereodifferentiating 1,2-addition
with the carbonyl group via a six-membered
cyclic transition state; or (ii) reversible reduction
of the carbonyl to a transient Ti-ketyl radical
followed by radical-radical coupling. Although
the relative 1,2-stereochemistry observed for
cyclobutanol (trans), cyclopentanol (cis), and
cyclohexanol (trans) substrates is reminiscent
of pseudoequitorial positioning of bulky groups
in cyclic transition states (fig. S18), the precise
nature of this ring closure warrants further
investigation.
Insight into the level of asymmetric induc-
tion incurred in the C–C bond–forming events
can be gleaned by tracking the time course of
the deracemization of the syn-46, which re-
sults in enantioenriched anti-46 (Fig. 5F). In
the first 20 min, the bond cleavage of syn-46
and bond formation step to generate anti-46
results in a steady er value of 75:25. As the
concentration of newly generated anti-46 ap-
proaches that of syn-46, the er value of anti-
46 gradually increases as the deracemization
of the formed major diastereomer takes place,
eventually reaching an equilibrium value of
97:3 er. The steady er value of anti-46 during
the initial 20 min indicates that the newly
formed anti-46 is not yet substantially in-
volved in the bond cleavage cycle, and the
enantiofacial-determining ratio of the bond
formation step can be estimated as 75:25, which
results in kR/kS ratio of 3:1. This approximate
value is supported by a 77:23 er (kR/kS ratio of
3.3:1) obtained for the inefficient reductive cou-
pling of aldehyde 52 and imine 54 under dark
conditions with L8-ligated TiCl3, despite pre-
dominant pinacol coupling (Fig. 5G) (51, 53, 64).
Conversely, we could directly probe the bond
scission of aminoalcohol 46 by the introduc-
tion of a large amount of radical trapping re-
agent 55, which would lead to kinetic resolution
based on enantioselective C–C bond cleavage.
The asymmetric induction of the C–C bond
scission step can be established as a k−S/k−R
ratio of 8.1:1, with the (S)-enantiomer preferen-
tially consumed. The predicated er value based
on the multiplicative effect (er = kRk–S/kSk–R)
of these two isolated processes is 96:4, in ex-
cellent agreement with the experimental value
in the deracemization reaction (97:3) (see fig.
S17 for a discussion on cyclic alcohol 1).
The LMCT catalytic paradigm enables the use
of one chiral Ti catalyst to induce two enantio-
selective events in a single catalytic cycle. The
multiplicative enhancement of stereoinduction,
validated in consecutive stereocenter-ablating
C–C bond scission and stereocenter-generating
C–C bond formation, enables high levels of
stereoselectivities with two moderate enantio-
inductions. This mechanistic paradigm holds
promise for the development of a wide array
of asymmetric catalytic reactions through the
statistical upgrading of stereoenrichment.
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ACKN OWLED GMEN TS
Funding: We thank the National Natural Science Foundation of
China (grant nos. 22125111 and 21971163), National Key R&D
Program of China (grant no. 2021YFA1500100), the Shanghai Pilot
Program for Basic Research – Chinese Academy of Science,
Shanghai Branch, and SIOC for financial support. We also thank
J. Lipshultz for thoughtful discussions and J. Wu for assistance
with the NMR experiments. Author contributions: L.W., J.D., and
L.D. contributed equally to this work. Z.Z. conceived and directed
the research; Z.Z., L.W., J.D., L.D., and S.W. designed the
experiments. L.W., J.D., L.D., S.W., Q.A., and H.W. performed and
analyzed the reactions; Z.Z., L.W., and S.W. prepared the
manuscript, which was approved by all authors. Competing
interests: The authors declare no conflicts of interest. Data and
materials availability: Data are available in the manuscript and
supplementary materials. The supplementary crystallographic data
for this paper are available free of charge from the Cambridge
Crystallographic Data Centre (CCDC) under accession numbers
2265923, 2265930, 2266206, and 2287759. License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science.
No claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adj0040
Materials and Methods
Supplementary Text
Figs. S1 to S20
Tables S1 to S42
References (65–69)
Submitted 1 June 2023; accepted 4 September 2023
10.1126/science.adj0040
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RES EARCH
MACHINE LEARNING
Backpropagation-free training of deep physical
neural networks
Ali Momeni1, Babak Rahmani2, Matthieu Malléjac1, Philipp del Hougne3, Romain Fleury1*
Recent successes in deep learning for vision and natural language processing are attributed to
larger models but come with energy consumption and scalability issues. Current training of
digital deep-learning models primarily relies on backpropagation that is unsuitable for physical
implementation. In this work, we propose a simple deep neural network architecture augmented
by a physical local learning (PhyLL) algorithm, which enables supervised and unsupervised training
of deep physical neural networks without detailed knowledge of the nonlinear physical layer’s
properties. We trained diverse wave-based physical neural networks in vowel and image classification
experiments, showcasing the universality of our approach. Our method shows advantages over
other hardware-aware training schemes by improving training speed, enhancing robustness, and
reducing power consumption by eliminating the need for system modeling and thus decreasing
digital computation.
D eep learning has emerged as a break-
through technology with outstanding
success (1, 2) that primarily operates on
traditional von Neumann computing
hardware. This technology is currently
facing high energy consumption, such as the
1.3–gigawatt-hour (GWh) electricity usage of
GPT-3 (3), and low computing speed (4). Be-
cause of these challenges, researchers are
exploring alternative physical platforms for
artificial neural networks (ANNs), including
optics (5–9), spintronics, (10, 11), nanoelectronic
devices (12–15), photonic hardware (5), and
acoustic systems (16, 17).
Two primary methods currently dominate
neural network hardware design. The first in-
volves designing hardware to implement trained
mathematical transformations through strict
operation-by-operation mathematical iso-
morphism, primarily targeting the inference
phase of deep learning (18–21). The second
category, deep physical neural networks (PNNs),
focuses on training the hardware’s physical
transformations directly to perform the de-
sired computations. PNNs hold the promise
of more scalable, energy-efficient, and faster
neural network hardware by exploiting phys-
ical transformations and eliminating the
conventional software-hardware separation
(22, 23).
So far, the training of PNNs has predom-
inantly relied on backpropagation (BP) (24).
Yet, there are several reasons why BP is not a
suitable choice for PNNs, one of which is the
complexity and lack of scalability in the phys-
ical implementations of BP operations in the
1Laboratory of Wave Engineering, Department of Electrical
Engineering, EPFL, Lausanne CH-1015, Switzerland.
2Microsoft Research, Cambridge CB4 0AB, UK. 3University
of Rennes, CNRS, IETR - UMR 6164, F-35000 Rennes,
France.
*Corresponding author. Email: romain.fleury@epfl.ch
hardware (25–28). Commonly, PNN proposals
use in silico training, performing BP calcu-
lations on an external computer with a digital
twin of the physical system. However, this meth-
od may result in potential simulation-reality
gaps as a result of inaccurate representation of
the physical system (6–8, 10, 13, 14, 20, 29, 30).
Moreover, physics-aware training methods based
on BP (PA-BP) (22) offer improvements over
traditional in silico methods but still neces-
sitate a differentiable digital model for the
backward pass. Additionally, PA-BP–trained
PNNs may face challenges when subjected to
strong perturbations, potentially rendering fine-
tuned models unusable and necessitating re-
training from scratch.
Another important drawback of BP is its re-
liance on having complete knowledge of the
computation graph carried out during the
forward pass to accurately compute deriva-
tives (23, 31–34). When a black box is inserted
in the forward pass, BP becomes infeasible.
Therefore, alternative training methods for
PNNs have proved advantageous. For exam-
ple, an approach explored for training physical
networks is the augmented direct feedback
alignment (DFA) method (23), which aims to
avoid the need for a differentiable digital mod-
el. However, this method is only compatible
with certain physical networks, where it is
possible to separate the nonlinear and linear
layers.
Local learning has been extensively studied
for training digital neural networks, from
early work on Hebbian contrastive learning in
Hopfield models (35) to recent biologically
plausible frameworks (31, 34, 36, 37), block-
wise BP (38, 39), and contrastive representa-
tion learning (40, 41). Inspired by this concept
and to address the limitations of BP-based PNN
training, we proposed a simple and physics-
compatible PNN architecture augmented by
a physical local learning (PhyLL) algorithm.
The proposed method enables supervised and
unsupervised contrastive learning training of
arbitrary PNNs locally without the need to
know the nonlinear physical layers and train a
digital twin model. In this BP-free method, the
standard backward pass, typically performed
by a digital computer, is replaced with an ad-
ditional single forward pass through a physical
system. This substitution can improve training
speed, power consumption, and memory usage
during the training phase of wave-based PNNs
by eliminating the extra overhead incurred
because of the digital twin modeling phase
present in other hardware-aware frameworks.
We showed the robustness and adaptability of
the proposed method, even in systems ex-
posed to unpredictable external perturbations.
To showcase the universality of our approach,
we performed experimental vowel and image
classification using three wave-based systems
that differ in terms of the underlying wave
phenomenon and the type of nonlinearity in-
volved (a detailed description of each system
can be found in the supplementary text, sec-
tions 2.3 to 2.5).
PhyLL
Figure 1A shows a simple and physics-compatible
deep PNN including N nonlinear physical
data transformers augmented by trainable
linear multiplications. Each nonlinear phys-
ical data transformer performs a nonlinear
mapping between the input and output fol-
lowed by an augmented trainable linear multi-
plication to classify distinct classes through
a local training algorithm. The output of each
layer is then passed to the next layer. The sub-
sequent layer then carries out the same pro-
cess hierarchically on the output of the previous
layer. The proposed architecture shares some
similarities with conventional deep reservoir
computing systems (42); see supplementary
text, section 2.9, for further details on their
differences.
h
The training algorithm is inspired by the
recently proposed forward-forward algorithm
(31) and local training proposals (38–41) in
digital neural networks, which has been ex-
tended and adapted to the supervised and un-
supervised model-free physical learning of PNNs.
Each nonlinear physical system performs a non-
linear transformation on input data (Fig. 1),
i
which can be expressed as h lð Þ ¼ f lð Þ
,
N
where x lð Þ, W lð Þ
N correspond to the
physical inputs (e.g., optical intensity, electric
voltage, and vibration), the physical intercon-
nections (e.g., optical, electrical, or mechan-
ical coupling) in the physical system, and the
physical nonlinearity (e.g., nonlinear opti-
cal, magnetic, or mechanical effects) in layer
l, respectively.
Here, W lð Þ
N denote the mixing oper-
ation and nonlinear kernel of the l−th physical
p , and f lð Þ
p and f lð Þ
p x lð Þ
W lð Þ
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RES EARCH | R E S E A R C H A R T I C L E
t
systems, respectively (supplementary text, sec-
tions 2.6 and 2.7). The output of layer l can be
expressed as the multiplication of h lð Þ by the
augmented trainable weight matrix W lð Þ
—i.e.,
t
y lð Þ ¼ W lð Þ
h lð Þ. Such trainable matrix multi-
plications can be performed either digitally or
through physical systems, for instance using
Mach-Zehnder interferometer (MZI)–integrated
photonics (43) or spatial light modulators
(SLMs) in optics (21, 44). The goal is to train
W lð Þ
locally without the need to know the non-
t
linear physical layer. Instead of a forward and
backward pass, we use two physical forward
passes: a positive and a negative forward pass
through the physical system, each running on
different physical inputs. The positive physical
W lð Þ
pass, y lð Þ
i
, uses positive
pos ¼ W lð Þ
p x lð Þ
pos
h
f lð Þ
N
t
t
neg
f lð Þ
N
p x lð Þ
h
W lð Þ
i
, uses negative inputs
inputs that include the input dataset and the
correct labels, and the negative physical pass,
neg ¼ W lð Þ
y lð Þ
that include the input dataset and the incor-
rect labels (Fig. 1A). In each layer, we calculate
the so-called goodness function, defined as the
cosine similarity between the positive and
negative activities. Eventually, for each layer l,
W lð Þ
is trained by minimizing the following
t
loss function
L lð Þ ¼ log 1 þ exp q cossim ypos; yneg
f
ð
ð
½
Þ
(cid:2)
g
Þ ð1Þ
In supervised learning, the goodness func-
tion is defined as the cosine similarity between
the activities of the layer and a random vector
drawn from normal distribution, both for the
Deep physical neural networks
positive and negative physical passes. In this
case, the loss function reads
h
n(cid:2)
L lð Þ ¼ log 1 þ exp (cid:3)q cossim ypos; x lð Þ
h
h
cossim yneg; x lð Þ
o(cid:3)i
i
i
(cid:3)
ð2Þ
In the equations above, cossim is the cosine
similarity defined as the cosine of the angle
between the two arguments, q is a scale factor,
and xl is the random vector for the layer l. The
original forward-forward algorithm uses only
the difference of the positive and negative
squared activities, hence necessitating layer
normalization to be applied to the data before
proceeding to subsequent layers (31). Converse-
ly, our algorithm avoids incorporating layer
A
Positive
data
Correct
labels
Input
Negative
data
Incorrect
labels
Input
B Acoustics
Input
Sources
Nonlinear
membranes
Parameters
Parameters
Nonlinear physical data transformer
Trainable linear multiplication
g
n
i
t
a
d
p
U
Output 1
Goodness
Local loss
Physical data transformers
C Microwave
Output
Metasurface
g
n
i
t
a
d
p
U
Output N
Goodness
Local loss
D Optics
Laser
Antennas
Input
(Metasurface config.)
Output
(Transfer func. Intensity)
SLM
Input
Lenses
MMOC
CCD
Rigid
scatterers
Frequency
Output
Fig. 1. Deep PNNs. (A) A simple and physics-compatible deep neural network that
uses a sequence of nonlinear physical data transformers augmented by trainable
matrix multiplications, trained by the supervised PhyLL technique (refer to
supplementary text, section 2.1.1, for additional explanations). At each layer, the
nonlinear physical data transformer conducts nonlinear mapping between input
and output spaces to separate positive and negative data by maximizing the cosine
similarity of the positive data to a random vector x and minimizing the cosine
similarity of the negative data to the same vector. We considered three physical
systems that vary in terms of the underlying wave phenomenon and the type
of nonlinearity. (B) In acoustics, input data are encoded into the intensity of sound
waves at different frequencies injected on the left side of the cavity. Sound waves
propagate through a chaotic cavity that comprises multiple rigid cylindrical diffusers
and nonlinear membranes. The transformed waveforms are received by multiple
microphones. (C) In the chaotic microwave cavity, input data are encoded into the
programmable metasurface configuration inside the metallic disordered cavity.
The outputs are obtained from the waves’ spectra (transfer function). (D) In the
optical setup, input data are encoded onto the SLM, and after passing through
a multimodal optical cavity (MMOC), the resulting optical intensity is measured on
the charge-coupled device (CCD) camera [numerical experiment based on
experimentally acquired data from Rahmani et al. (56)].
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normalization into the architecture because
its hardware-based implementation is a deep
challenge. During the inference phase, we in-
put a particular label into the PNNs and ac-
cumulate the goodness values for all layers.
This process is repeated for each label sepa-
rately. The label with the highest accumulated
goodness value is then selected as the output
(see supplementary text, section 2.1, for more
details). In unsupervised contrastive learning,
a single linear layer maps representations from
pretrained hidden layers to labels (supplemen-
tary text, section 2.1.1). For details on data gen-
eration, refer to supplementary text, section 2.2.
Diverse PNNs for vowel and image classification
Figure 1 presents three deep PNN classifiers
for various standard datasets, including vowel,
A
B
Input layer
Physical layer
Topology of PNN
C
100
y
c
a
r
u
c
c
a
t
s
e
T
90
80
70
60
50
40
30
20
10
In silico
Ideal BP
PhyLL
0
50
100
Epoch
150
200
NL membrane Rigid scatterers
Sources
D
100
y
c
a
r
u
c
c
A
90
80
70
60
50
40
30
20
0
50
100
Epoch
150
98.88 %
97.31 %
E
s
e
u
a
v
l
e
u
r
T
Train
Test
200
ae
ah
aw
uw
er
iy
ih
ae
ah
aw
uw
Predicted values
er
F
s
e
u
a
v
l
e
u
r
T
ae
ah
aw
uw
er
iy
ih
iy
ih
ae
ah
1.0
0.8
0.6
0.4
0.2
0.0
iy
ih
aw
uw
Predicted values
er
Fig. 2. Acoustic-PNN. (A) The topology of the acoustic-PNN consists of a two-layer PNN with skip connections. Each layer comprises an acoustic-PNN augmented
by trainable matrix multiplication. (B) Photograph of the experimental setup. NL, nonlinear. (C) Comparison of test accuracy versus training epoch with in silico,
ideal BP, and PhyLL algorithm for the vowel recognition task. (D) The train and test classification accuracy versus training epoch for the vowel recognition task. (E and
F) The confusion matrix for the PNN on the train (E) and test (F) sets.
A
C
100
y
c
a
r
u
c
c
A
90
80
70
60
50
40
30
Input layer
Physical layer
Topology of PNN
98,74 %
97.31 %
D
s
e
u
a
v
l
e
u
r
T
Train
Test
aeae
ahah
awaw
uwuw
erer
iyiy
ihih
0
20
40
60
Epoch
80
100
aeae
ahah
B
Programmable Metasurface
Antennas
Disorder
E
s
e
u
a
v
l
e
u
r
T
ae
ah
aw
uw
er
iy
ih
iyiy
ihih
ae
ah
1.0
0.8
0.6
0.4
0.2
0.0
iy
ih
aw
uw
Predicted values
er
awaw
uwuw
Predicted values
erer
Fig. 3. Microwave-PNN. (A) The topology of the microwave-PNN consists of a three-layer PNN with skip connections. Each layer comprises a microwave-PNN
augmented by trainable matrix multiplication. (B) Photograph of the experimental setup. (C) Train and test classification accuracy versus training epoch for the vowel
recognition task. (D and E) Confusion matrix for the PNN on the train (D) and test (E) sets.
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digit, fashion Mnist, and CIFAR10, based on
three distinct physical systems, each featur-
ing a distinctive source of nonlinearity (ma-
terials and methods and supplementary text,
sections 2.3 to 2.5). Although there have been
proposals that explore wave-based analog com-
puting for linear operations, such as multi-
plication and convolution (43, 45–53), it is
important to note that PNNs require non-
linearity to effectively handle regression and
classification tasks. We evaluated the per-
formance of PhyLL in these media (refer to
tables S1 and S2 in the supplementary mate-
rials) against in silico and BP methods under
both supervised and unsupervised contras-
tive training schemes using an end-to-end
surrogate forward model of the systems for
benchmarking purposes.
Acoustic chaotic cavity with nonlinear scatterers
In acoustics, an air-filled multimode cavity
composed of multiple nonlinear meta-scatterers
randomly placed on the cavity top wall and
multiple rigid scatterers inside the cavity was
used (materials and methods and supplemen-
tary text, section 2.3). The nonlinear meta-
scatterers were designed to provide a nonlinear
relation between pressure and particle velocity
with controllable power law. The positive and
negative data were encoded onto the ampli-
tude of each frequency component composing
the excitation waveforms, which were then in-
jected into the nonlinear system through loud-
speakers positioned on the right side of the
cavity. The output of the physical system was
measured using microphones below the meta-
scatterers. We investigated the vowel classifi-
cation performance of two-layer acoustic-PNN
(Fig. 2A). To compare the results of PhyLL
with ideal BP and in silico training, we accu-
rately modeled the forward pass of acoustic-PPN
by a digital neural network (supplementary
text, section 2.1). When trained using PhyLL,
the acoustic-PNN achieved a classification
accuracy of 98.88% and 97.31% for train and
test datasets, respectively (Fig. 2, D to F).
Figure 2C shows the comparison of the clas-
sification results obtained for PhyLL, ideal BP,
Input layer
Physical layer
Topology of PNN
Vowel dataset
97.14 %
97.21 %
A
B
100
y
c
a
r
u
c
c
A
90
80
70
60
50
40
0
20
40
60
Epoch
80
Train
Test
100
E
Positive data
Layer-wise training with cos-similarity
Negative data
1
k
s
a
M
2
k
s
a
M
Mapping representations to labels
C
y
c
a
r
u
c
c
A
98
97
96
95
94
93
92
0
Supervised learning
Digit-MNIST dataset
97.19 %
96.36 %
Train
Test
100
200
300
Epoch
Unsupervised learning
Supervised learning
Unsupervised learning
Label
Data
Label
Data
Output
Output
Fashion-MNIST dataset
92.27 %
87.79 %
Train
Test
100
200
Epoch
300
400
Digit-MNIST dataset
97.59 %
96.51 %
Train
Test
50
100
Epoch
150
200
D
98
y
c
a
r
u
c
c
A
96
94
92
90
88
86
84
82
80
0
F
y
c
a
r
u
c
c
A
99
98
97
96
95
94
93
92
0
Fig. 4. Optics-PNN. (A) The topology of the optics-PNN consists of a two-layer PNN. Each layer comprises an optics-PNN augmented by trainable matrix multiplication.
The right panel shows examples of input encoding for supervised and unsupervised contrastive versions along with the corresponding output on a CCD camera for the digit
Mnist dataset. (B to D) The train and test classification accuracy versus training epoch for the vowel (B), digit (C), and fashion Mnist (D) tasks. (E) Schematic of the
unsupervised version for PNNs (supplementary text, section S2). (F) The classification accuracy on the training and test sets versus training epoch for the unsupervised
contrastive version of PhyLL on the digit Mnist dataset.
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RES EARCH | R E S E A R C H A R T I C L E
A
B
Input layer
Physical layer
Topology of PNN
Transmission matrix
Transmission matrix
e
t
a
t
s
m
e
t
s
y
S
Hard perturb
Hard perturbation
Time
D
100
Perturbation
PhyLL
C
100
PA-BP
80
Perturbation
y
c
a
r
u
c
c
a
t
s
e
T
60
40
20
0
0
20
40
60
80
Iteration
100
120
140
160
y
c
a
r
u
c
c
a
t
s
e
T
80
60
40
20
0
0
20
40
60
80
Iteration
100
120
140
160
Fig. 5. Robustness of deep PNNs against unpredictable external perturbations. (A) A deep PNN consists of six layers of optics-PNN augmented by trainable
matrix multiplication. The deep PNN is trained on vowel datasets and is currently in the inference phase. (B) Applying hard perturbation by adding Gaussian noise with
the mean of m and standard deviation of s to the transmission matrix of MMF. (C and D) A comparison between PA-BP (22) (C) and the proposed PhyLL method (D) is
presented, with the focus on their ability to recover the classification accuracy after applying perturbation.
and in silico training. A schematic of the afore-
mentioned methods is provided above Fig. 2C.
The complete comparison between different
hardware-based training methods is provided
in the supplementary text, section 2.1.
As demonstrated in Fig. 2C, in silico training
performed poorly, reaching only a maximum
vowel classification accuracy of ~50%. When
there was a gap between the reality and the sim-
ulation of a physical system (called the reality-
simulation gap), the accuracy of inference would
decrease. By contrast, PhyLL succeeded in accu-
rately training the acoustic-PNN, performing
similarly to the ideal BP algorithm used as a base-
line. The key advantage of PhyLL stems from
the execution of both forward passes through
the physical hardware rather than simulations.
Microwave massively parametrized chaotic
cavity with structural nonlinearity
In the microwave regime, we leveraged a “struc-
tural nonlinearity” such that we could imple-
ment nonlinear mathematical operations at
low power levels with a linear scattering sys-
tem. Our system consisted of a chaotic cavity
that was massively parametrized by covering
one of its walls with a programmable meta-
surface. For each meta-atom and each polari-
zation, the programmable metasurface offered
two possible local boundary conditions. Our
setup is shown in Fig. 3B and further detailed
in the supplementary text, section 2.4. Although
the setup resembles that recently used to im-
plement with high fidelity and in situ repro-
grammability desired linear transfer functions
for signal differentiation (53) and routing (54),
in this case we sought a nonlinear mapping.
Hence, we defined the metasurface configu-
ration as the input and the transfer function
as the output of our mathematical operation.
This relation is in general nonlinear because
of the mutual coupling between meta-atoms
caused by their proximity and, notably, the
reverberation (55). We embrace reverbera-
tion to maximize the nonlinearity, whereas
previous work (50) has sought to limit the
reverberation to implement a linear trans-
formation with the same input-output defi-
nition (see supplementary text, section 2.4,
for further discussion).
We randomly grouped our programmable
metasurface’s 152 degrees of freedom into 40
macropixels because our mathematical opera-
tion necessitated 40 input values. We defined
our mathematical operation’s outputs as the
transfer function intensities at 20 decorrelated
frequencies within the bandwidth of operation
of the programmable metasurface (400 MHz
around 5.2 GHz). Thereby, in addition to the
structural nonlinearity, we added a readout
nonlinearity by considering the transfer func-
tion’s intensity. To flexibly evaluate the pro-
posed approach, we learned a digital surrogate
forward model of the configuration to trans-
fer function intensity mapping (supplemen-
tary text, section 2.4). Then, we constructed
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RES EARCH | R E S E A R C H A R T I C L E
the three-layer microwave-PNN shown in
Fig. 3A and trained it according to the PhyLL.
The training converged after roughly 20 epochs,
and the achieved classification accuracy on the
unseen test data reached 97.31% (Fig. 3, C to E).
Optical multimode fiber with readout nonlinearity
In the optics example, we used the experimen-
tal transfer matrix data of an optical system
that comprised an SLM, a scattering medium
consisting of a step-index multimode fiber
(MMF), and a complementary metal oxide
semiconductor (CMOS) camera (Fig. 1D and
materials and methods) (56). The data were
encoded onto the SLM, and after passing
through the MMF, the resulting optical inten-
sity was seen on the camera. The physical
optical system performed a complex spatial
transformation. Although this transformation
was linear in the complex domain, the process
became nonlinear as a result of the data being
encoded onto the phase (SLM) and the sub-
sequent measurement of the intensity squared
on the camera.
We used an optics-PNN to perform classifi-
cation tasks on different datasets: vowel, digit,
and fashion Mnist (see Fig. 4; table S1; and
supplementary text, section 2.5, for further
details). The two-layered optics-PNN achieved
high classification accuracy on both the vowel
and Mnist dataset. For vowel, we obtained
97.21% and 97.14% accuracy on the training
and test sets, respectively. Using only the two-
layer optics-PNN, the model achieved 97.19%
and 96.36% accuracy on the training and test
sets of Mnist, respectively. To implement a
deeper optics-PNN, we trained it with six layers
on the fashion Mnist dataset, achieving train-
ing and test accuracies of 92.27% and 87.79%,
respectively (see corresponding results in Fig.
4, B to D). In addition, the unsupervised con-
trastive learning version of PhyLL is tested on
three layers of optics-PNN (Fig. 4E). The mod-
el achieved training and test accuracies of
97.59% and 96.51%, respectively (Fig. 4F and
table S2). Results were also consistent with a
recent preprint for a similar experiment that
directly implemented the original forward-
forward algorithm, leading to slightly lower
efficiency (57).
Real-time adaptable learning
In this work, we investigated the robustness
of PhyLL in the context of real-time and adapt-
able learning, where the physical data trans-
former may undergo changes as a result of
the slow dynamics of the physical system dur-
ing the runtime or external hard perturba-
tions (see also supplementary text, section 2.8).
Let us consider a deep optics–PNN with six
layers, as depicted in Fig. 5A, which has al-
ready been trained on vowel datasets and is
currently in the inference phase. The trans-
formation function of each physical system is
f0(q), where q is the physical input. We per-
turbed the physical systems at a specific time
(examples of such perturbations include changes
in the MMF state or the positions of lenses or
masks, etc.), which results in a change in the
transformation function of each physical sys-
tem from f0(q) to fp(q) (Fig. 5B). To show this,
we perturbed the transmission matrix of the
optical setup by adding a Gaussian noise with
mean m and standard deviation s. As observed
in Fig. 5D, the test accuracy dropped as ex-
pected after applying the perturbation. The
question now is whether the training meth-
od can restore the accuracy by retraining the
optics-PNN. We compared our results with
the PA-BP method (22), which uses a digital
model for the backward pass and the physical
system for the forward pass. PA-BP struggled
to restore accuracy with increasing perturba-
tion intensity (Fig. 5C). For instance, the test
accuracy oscillated around 55% for a small per-
turbation (red dots in Fig. 5C) and worsened
further for more intense perturbations. By
contrast, the proposed PhyLL could easily re-
cover accuracy after a few epochs, regardless of
the intensity of the perturbation applied (Fig.
5D). This adaptability could be attributed to
PhyLL executing both forward passes through
the physical hardware rather than digital
models. By contrast, the PA-BP method relied
on a digital model that lost its accuracy when
subjected to hard perturbation, necessitating
retraining from scratch or comprehensive hy-
perparameter tuning.
Discussion
Because of the unprecedented growth in the
size of ANNs, such as large language models
(LLMs) that are expected to increase unceas-
ingly, the costs of both the training and infer-
ence phases of these networks have increased
exponentially. Specialized hardware, such as
PNNs, have the potential to drastically de-
crease these costs. Anderson et al. (21) recently
projected an inference–time energy–efficiency
advantage of ~8000× compared with that of
digital-electronic processors for large-scale
future transformer models. The training meth-
od proposed in this paper could serve as a
viable candidate for training these optical
LLMs, potentially offering substantial energy
efficiency and speed advantages. We further
examine these in the supplementary text, sec-
tion 2.10. Implementing large-scale LLMs with
optics still faces a few challenges, such as the
current SLM capacity limited to a few million
parameters—far from the billions required.
However, there are no fundamental roadblocks
to achieving billion-parameter optical archi-
tectures and energy-efficient PNNs.
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ACKN OWLED GMEN TS
A.M. and M.M. thank X. Guo for useful discussions. B.R. acknowledges
that all materials pertaining to the optical experiment presented in
this manuscript have been sourced from previously published material
that is publicly available and were acquired during his tenure at the
Laboratory of Applied Photonics Devices at EPFL. This work has no
connection to his current employer in any capacity or form. Funding:
A.M. and R.F. acknowledge funding from the Swiss National Science
Foundation under the Eccellenza grant no. 181232. P.d.H. and R.F.
acknowledge funding from the ANR-SNF PRCI program (project
“MetaLearn”: ANR-22-CE93-0010-01). Author contributions: A.M.
conceived the idea, designed the computational engine, and carried
out both the theoretical and numerical simulations as well as a part of
the acoustic experiment. B.R. provided the optics data and
interpretation of machine learning results. M.M. carried out the
acoustic experiment. P.d.H. carried out the microwave experiment.
R.F. supervised the project. All authors contributed to the
interpretation of the results and the writing of the manuscript.
Competing interests: The authors declare no competing interests.
Data and materials availability: Materials and methods to
evaluate the conclusions in the paper are present in the
supplementary materials. All other software and data for running
the simulations and experiments are available through Github
(58). Data underlying the figures are available through Zenodo
(59). License information: Copyright © 2023 the authors, some
rights reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-
article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi8474
Materials and Methods
Supplementary Text
Figs. S1 to S18
Tables S1 to S6
References (60–69)
Submitted 22 May 2023; resubmitted 25 September 2023
Accepted 7 November 2023
Published online 23 November 2023
10.1126/science.adi8474
Momeni et al., Science 382, 1297–1303 (2023)
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RES EARCH
GLYCOSYLATION
Palladium catalysis enables cross-coupling–like
SN2-glycosylation of phenols
Li-Fan Deng1†, Yingwei Wang2†, Shiyang Xu1, Ao Shen1, Hangping Zhu1, Siyu Zhang1,
Xia Zhang1, Dawen Niu1*
Despite their importance in life and material sciences, the efficient construction of stereo-defined
glycosides remains a challenge. Studies of carbohydrate functions would be advanced if glycosylation
methods were as reliable and modular as palladium (Pd)-catalyzed cross-coupling. However, Pd-catalysis
excels in forming sp2-hybridized carbon centers whereas glycosylation mostly builds sp3-hybridized
C–O linkages. We report a glycosylation platform through Pd-catalyzed SN2 displacement from phenols
toward bench-stable, aryl-iodide–containing glycosyl sulfides. The key Pd(II) oxidative addition
intermediate diverges from an arylating agent (Csp2 electrophile) to a glycosylating agent (Csp3
electrophile). This method inherits many merits of cross-coupling reactions, including operational
simplicity and functional group tolerance. It preserves the SN2 mechanism for various substrates and is
amenable to late-stage glycosylation of commercial drugs and natural products.
T he utility of glycosides in medicinal chem-
istry, materials, and biological science
is well appreciated (1, 2) but difficulties
in their synthesis by glycosylation pose
substantial obstacles to exploring their
functions. Both reactants in glycosylation—
the glycosyl donors and acceptors—are often
structurally complex, and the properties of
products are profoundly affected by the ab-
solute configuration of glycosidic centers. There-
fore, an ideal glycosylation method needs to
simultaneously address chemo- and stereo-
selectivity issues, two persistent challenges
in synthesis.
Glycoside synthesis has been propelled by
the introduction of new donors and their ac-
tivating approaches. Most reported glycosylation
methods proceed under (Lewis) acid-promoted
conditions, which convert glycosyl donors to
(equivalents of) oxocarbenium ions for sub-
sequent trapping by acceptors (3, 4). These
techniques have been the cornerstones in car-
bohydrate synthesis and have allowed for pre-
paration of complex structures (5–8). However,
controlling or predicting stereoselectivity re-
mains nontrivial as the glycosylation mechanism
often shifts within the SN1/SN2 continuum (9),
depending on the properties of reactants and
reaction parameters (10). Issues can also arise
when labile donors or harsh activating con-
ditions are needed, complicating reaction setup.
Among the venues to overcome these obsta-
cles, developments include the Yu group (11),
which exploits selective gold-alkyne interac-
tions; the Jacobsen group (12, 13), which ex-
plores mild hydrogen-bond catalysis; the Miller
1State Key Laboratory of Biotherapy and Cancer Center,
West China Hospital, and School of Chemical Engineering,
Sichuan University, Chengdu, China. 2Department of Nuclear
Medicine & Laboratory of Clinical Nuclear Medicine, West
China Hospital, Sichuan University, Chengdu, China.
*Corresponding author. Email: niudawen@scu.edu.cn
†These authors contributed equally to this work.
group (14, 15), which harnesses the strong Ca–F
bond-forming energy; the Nguyen group (16)
that employs Lewis base catalysis; and the
Codée (17), Takemoto (18), and Loh groups (19),
which utilize halogen-bond catalysis, and others
based on transition metal catalysis (20, 21). We
have reported radical activation of glycosyl
donors (22). Despite this progress, there is
still a high demand for methods with a gen-
eral scope to prepare stereodefined glycosides
in a simple and predictable manner, which
continues to fuel mechanistic and methodo-
logical advancements.
The modularity and reliability inherent in
Pd-catalyzed cross-coupling reactions have
made them indispensable tools in organic
synthesis (23, 24). If O-glycosylation could be
as straightforward and robust as Pd-catalyzed
cross coupling, the downstream exploration of
glycosides would be greatly facilitated. However,
Pd-catalysis is typically effective in activating and
forging sp2-hybridized carbon centers, whereas
glycosidic bonds are mostly sp3-hybridized C–O
linkages. Strategies that can bridge this gap
and channel the power of Pd-catalyzed cross
coupling into the field of glycoside synthesis
hold considerable potential. O’Doherty and
others have applied Pd-catalyzed allylic substi-
tution, followed by alkene (di)hydroxylation,
for the de novo synthesis of O-glycosides (25, 26).
Here, we report a Pd-catalyzed SN2 glycosyl-
ation method that commences with the oxida-
tive addition (OA). The utility of this approach
is showcased in a general and simple SN2 gly-
cosylation of phenols, a prominent challenge
in O-glycoside synthesis.
Reaction design
General and straightforward methods for syn-
thesizing stereodefined phenolic O-glycosides
are highly valuable but remain nontrivial
(14, 27, 28). Phenols—glycosylated or not—are
abundant in both naturally occurring and man-
made compounds (Fig. 1A) (29). Introducing
carbohydrate moieties into phenols has proven
to be an effective approach for modifying their
physical and biological properties in drug dis-
covery endeavors. Glycosylation of phenols (3)
is complicated as they exhibit modest nucleo-
philicity compared with alcohols under acidic
conditions (1 to 2; Fig. 1B). Moreover, phenols
are ambident nucleophiles, potentially resulting
in either O-glycosylated (4) or C-glycosylated
products (5).
Pd-catalyzed cross-coupling reactions
(Fig. 1C, left cycle) are usually initiated by
Pd(0)-mediated OA (6 to 7), followed by ligand
exchange (7 to 8) and reductive elimination
(8 to 9) to give the desired products (here O-
arylated phenols 9). Recognizing the limita-
tion of this cycle in activating/building Csp3
centers (30), we designed a strategy (Fig. 1C,
right cycle) that uses bench-stable, ortho-
iodobiphenyl–substituted sulfides (31, 32)
11 as glycosyl donors. The aryl iodide unit in
11 readily undergoes oxidative addition with
Pd(0) catalysts, forming an OA complex 12
that acts as an effective glycosyl (Csp3) elec-
trophile, likely driven by its tendency to un-
dergo Csp2–S reductive elimination (indicated
by dashed lines). Nucleophilic attack to 12
by phenoxides 10 proceeds through a clean
and general SN2 mechanism, resulting in in-
version of the glycosyl center and genera-
tion of 13.
As a result of the donor activation mechanism,
this glycosylation method exhibits a notable
tolerance toward functional groups and al-
lows using unprotected glycosyl donors. No
O-arylation side products are observed from
the process (Fig. 1C), indicating that our ap-
proach directs the Pd-containing OA complex
(such as 12) to transition from an arylating
agent (Csp2) to a glycosylating agent (Csp3),
unveiling an unprecedented reactivity. The
OA complex 12 behaves uniformly as an SN2
electrophile, from fully oxygenated to fully
deoxygenated donors, a rarity in carbohydrate
chemistry. This method grants access to either
isomer of the phenolic O-glycoside products in
a predictable manner, many of which were pre-
viously challenging to obtain. The transforma-
tion occurs under mildly basic conditions and
can be performed as easily as a Pd(0)-catalyzed
cross-coupling reaction.
Reaction validation and condition optimization
Our study commenced with the model reaction
between sulfide 14 or 15 and 4-methoxy phenol
(16) to make O-glycoside 17 or 18 (Fig. 2). The
stereoselective synthesis of 2-deoxyglycosides
of phenols (e.g., 17/18) has been difficult due to
the lack of a C2-substituent as a stereodirect-
ing auxiliary and the susceptibility of the
2-deoxyglycoside products to acid-promoted
hydrolysis. Guided by the reaction design
in Fig. 1C, we established conditions to make
Deng et al., Science 382, 928–935 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
Ph
O
O
HO
HO
O
O
OH
O
HO
HO
O
O
OMe
OH
O
R
O
O
N
N
OH
OMe
O
O
HO
O
O
HN
O
O
O
NH
HN
S
HO
O
OH
OH
O
N
N
R = Me, Scrophuloside C
R = OH, Scrophuloside D
Glycosylated Genistein
Afeletecan (Phase I, anticancer)
HO
RO
O
LG
RO
O
3
RO
O
O
+
RO
1
or equivalents
2
4
O
5
OH
B
C
O
9
= oIB
This Work
Csp3
N2)
I
6
Pd(0)-L
O
I
S
RO
11
Classical
Csp2
Csp3
?
O
Pd
L
8
L
I
Pd
S
O
I
Pd
L
RO
7
12
O
RO
10
O
O
13
Fig. 1. Glycosylated phenols: background and synthetic approaches. (A) Representative examples of glycosylated phenols. (B) Glycosylation of phenols:
challenges and limitations. (C) Comparison of Pd-catalyzed C–O cross-coupling and Pd-catalyzed SN2 glycosylation (this work). FG, functional group.
O-glycosides 17/18 from 14/15 in high yields,
with dibenzothiophene (19) formed as a
byproduct. The b-O-glycoside 17 was obtained
from the a-S-glycoside 14, and a-O-glycoside 18
formed if b-S-glycoside 15 was employed. The
clean inversion of the glycosidic centers in 14/15
suggests that this Pd-catalyzed glycosylation pro-
ceeds by means of an SN2-type mechanism. Gen-
eral and operationally simple SN2-glycosylation
methods remain rare, despite their high value
as tools (12, 34–36) to access stereodefined
glycosides. Even scarcer are methods that can
afford both stereoisomers, as accessing the cor-
responding donors with defined and stable con-
figurations is not always simple. In our case,
sulfide donors (with general structure 11) could
be prepared from the corresponding 1-glycosyl
thioacetates in one pot at decagram scales (see
SM section 3) and stored for months without
precautions to avoid air or moisture. Employ-
ing the Pd(0)-mediated OA as a donor-activating
Deng et al., Science 382, 928–935 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
OBn
O
BnO
BnO
SoIB
14 (1.0 equiv.)
OBn
O
SoIB
BnO
BnO
15 (1.0 equiv.)
OBn
O
O
BnO
BnO
Pd(0)-Xantphos (2 mol%)
K2CO3 (2.0 equiv.)
OMe
17 (95% yield,
: < 1:19)
HO
OMe
16 (1.5 equiv.)
BnO
BnO
OBn
O
O
18 (90% yield,
: > 19:1)
OMe
Entry
Divation from standard Conditions
(with 15 used)
Conversion
Yield ( : )
none
no Pd(0)-Xantphos
no K2CO3
100%
92% (>19:1)
0%
7%
0%
5% (>19:1)
Cs2CO3 instead of K2CO3
100%
94% (>19:1)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
TEA instead of K2CO3
TMG instead of K2CO3
K2CO3 aq.
room temperature
MeCN instead of Toluene
no XantPhos
NiXantPhos instead of XantPhos
DavePhos instead of XantPhos
dppb instead of XantPhos
Addition of TEMPO
45%
79%
87%
21%
41%
77%
100%
67%
100%
100%
Ligands
O
H
N
O
PPh2
PPh2
PPh2
PPh2
PCy2
Ph2P
PPh2
4
NMe2
Xantphos
Ni-Xantphos
Davephos
dppb
Fig. 2. Reaction validation and condition optimization. Reactions in this table were performed at 0.05 mmol
scale at 0.1 M concentration for 24 hours. Yields and conversions are determined by 1H NMR analysis using 1,3,5-
trimethoxy benzene as an internal standard. Diastereomeric ratios were determined by NMR analysis of crude
reaction mixture. TMG, 1,1,3,3-tetramethylguanidine; TEMPO, (2,2,6,6-tetramethylpiperidin-1-yl)oxyl; Bn, benzyl.
approach, this method provides either isomer of
the phenolic O-glycosides. The reaction proceeds
at 60°C and only requires K2CO3 as base and a
catalytic amount (2 mol%) of Pd(0) catalyst as-
sembled from Pd(dba)2 and Xantphos.
We conducted control experiments to iden-
tify factors influencing the performance of this
method. Little reaction occurred in the absence
of Pd(0) catalyst (entry 2) or a suitable base
(entry 3). Inorganic bases K2CO3 (entry 1) and
Cs2CO3 (entry 4) exhibited better effects than
organic bases such as Et3N (entry 5) and TMG
(entry 6). A saturated aqueous solution of K2CO3
could be used (entry 7), suggesting that the re-
action has a good tolerance to water. When the
reaction is conducted at room temperature
20% (>19:1)
54% (2:3)
71% (9:1)
19% (>19:1)
40% (1:1)
75% (>19:1)
85% (4:1)
56% (>19:1)
90% (3:1)
91% (10:1)
Byproduct
S
19
(roughly 25°C), the conversion is relatively low
within the same time period (entry 8). The use
of more polar solvents such as MeCN greatly
eroded the stereochemical purity of products
(entry 9). The added ligands exert pronounced
effects on the reaction efficiency (entries 10 to
13), likely through modulating the properties
of OA complex such as 12 in Fig. 1C. Unlike
phosphine-based ligands, nitrogen-based ligands
and N-heterocyclic carbene ligands we tried
were less effective (see SM, section 4). Addition
of a stoichiometric amount of TEMPO was fully
tolerated, essentially excluding a radical-based
mechanism (entry 14) (22, 37).
Substrate scope
It is rare for a glycosylation method to hold
high efficiency for a broad array of substrates
as the reaction mechanism (and outcome) often
varies with the reactivities of donors and ac-
ceptors (38–41). Our method accommodates
diverse glycosyl units (Fig. 3), providing ei-
ther of the two possible stereoisomers with high
purities (22a-m). For example, donors bearing
benzyl (22a, 22k, 22l), acetyl (22b, 22f),
benzylidene (22d) and silyl–protecting groups
(22c, 22e) could all be used. Various other
2-deoxypyranosyl groups (22f-j) were in-
stalled with similar efficiencies. Our meth-
od could be adopted to construct the more
electron-rich furanosyl linkages: both iso-
mers of 2-deoxyribosides were generated
cleanly (22k). This method is not limited to
2-deoxy sugars, and the SN2 mechanism op-
erates with fully oxygenated (22l and 38g/h
in Fig. 4) and fully deoxygenated tetrahydro-
pyranyl (22m) donors. 2-O-acetyl or 2-N-acetyl
protected donors were unsuccessful, likely be-
cause of interference from these neighbor-
ing participating groups (fig. S6). Aliphatic
alcohols are almost inert under the current
conditions, allowing the use of unprotected
glycosyl donors, as shown by examples 22g-j.
The results attest to the exceptional func-
tional group tolerance of this OA-initiated
glycosylation method. It is worth highlight-
ing that many of the glycosyl units in Fig. 3
are deoxygenated and electron rich. To obtain
the corresponding O-glycosides with high
stereochemical purities would be tedious
by conventional methods, due to dearth of
suitable donors, lack of stereo-directing auxil-
iaries, and susceptibility of products to acid-
promoted hydrolysis.
Both electron-rich (22w, 22ae, 22ah) and
electron-deficient phenols (22n-r) were ac-
commodated, with no product arising from
C-glycosylation observed. Phenols bearing an
ortho-substituent were competent substrates
(22u-w, 22y-z). Functional groups such as
aldehydes (22q), esters (22r), secondary amides
(22af), nitriles (22p), and ketones (22x) were
tolerated. The terminal alkene group in 22v did
not isomerize to conjugate with a phenyl ring.
Deng et al., Science 382, 928–935 (2023)
24 November 2023
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RES EARCH | R E S E A R C H A R T I C L E
O
SoIB
HO
Pd(0)-Xantphos (2 mol%)
O
O
RO
+
20
N
N
21
K2CO3 (2.0 equiv.)
Toluene (0.1 M), 60 °C
RO
N
22
Scope of donor, acceptor = 16 or 4-CO2MePhOH
OBn
O
BnO
BnO
OBn
O
BnO
BnO
OAc
O
AcO
AcO
OAc
O
AcO
AcO
OTBS
O
HO
HO
OTBS
O
HO
HO
Ph
O
O
HO
Ph
O
O
O
HO
O
22a-
90% ( : > 19:1)
22a-
95% ( : < 1:19)
22b-
88% ( : = 8:1)a
22b-
71% ( : = 1:13)a
22c-
57% ( : > 19:1)
22c-
70% ( : = 1:17)
22d-
78% ( : > 19:1)
22d-
63% ( : = 1:13)
tBu
tBu
tBu
Si
O
O
HO
tBu
O
Si
O
O
HO
O
AcO OAc
O
AcO
AcO OAc
O
AcO
Me
HO
O
OH
Me
HO
O
OH
Me
O
Me
O
OH
HO
OH
HO
22e-
81% ( : = 15:1)
22e-
69% ( : = 1:10)
22f-
89% ( : = 5:1)a
22f-
78% ( : = 1:8)a
22g-
67% ( : = 5:1)
22g-
72% ( : = 1:16)
22h-
68% ( : = 6:1)
22h-
77% ( : = 1:10)
HO
HO
O
HO
HO
O
O
OH
HO
O
HOOH
BnO
O
BnO
O
OBn
OBn
22i-
84% ( : = 8:1)
22i-
51% ( : = 1:10)
22j-
77% ( : = 10:1)
22j-
73% ( : = 1:6)
22k-
56% ( : = 6:1)
22k-
77% ( : = 1:10)
BnO
BnO
OBn
O
BnO
22l-
71% ( : > 19:1)a
22l-
86% ( : < 1:19)a
Scope of acceptor, donor = 14/15
O
O
O
O
O
O
Br
CF3
CN
CHO
CO2Me
Bpin
O
22m
92% (95:5 er)
O
O
O
22n-
96% ( : > 19:1)
22n-
83% ( : = 1:14)
Br
O
22u-
82% ( : > 19:1)
22u-
83% ( : < 1:19)
O
N
22ab-
85% ( : > 19:1)
22ab-
72% ( : < 1:19)
22o-
87% ( : > 19:1)
22o-
88% ( : < 1:19)
22p-
93% ( : = 15:1)b
22p-
88% ( : < 1:19)b
22q-
73% ( : = 10:1)b
22q-
68% ( : = 1:10)b
O
O
OMe
O
Me
O
22w-
72% ( : > 19:1)c
22w-
80% ( : = 1:16)c
22x-
95% ( : > 19:1)
22x-
74% ( : < 1:19)
22r-
94% ( : > 19:1)
22r-
73% ( : = 1:11)
O
F
Br
Me
22y-
95% ( : > 19:1)
22y-
84% ( : < 1:19)
22v-
76% ( : = 7:1)
22v-
85% ( : < 1:19)
O
N
Cl
F
22ac-
88% ( : > 19:1)
22ac-
65% ( : = 1:16)
O
N
O
22ad-
72% ( : > 19:1)
22ad-
80% ( : < 1:19)
O
O
O
N
BocHN
CO2Me
22ae-
69% ( : > 19:1)
22ae-
85% ( : = 1:17)
22af-
90% ( : > 19:1)
22af-
95% ( : < 1:19)
22ag-
62% ( : = 10:1)c
22ag-
70% ( : < 1:19)c
22ah-
80% ( : = 10:1)
22ah-
78% ( : = 1:14)
22s-
81% ( : > 19:1)
22s-
67% ( : < 1:19)
22t-
96% ( : > 19:1)
22t-
88% ( : < 1:19)
O
Cl
Cl
O
N
S
22z-
92% ( : > 19:1)
22z-
89% ( : < 1:19)
22aa-
79% ( : > 19:1)
22aa-
88% ( : < 1:19)
Me
Me
O
O
O
OMe
OMe
OMe
Fig. 3. Substrate scope. Unless otherwise noted, reactions in this table were performed at 0.1 or 0.2 mmol scale in toluene (0.1 M) for 24 hours, using Pd(PPh3)4
(2 mol%), Xantphos (4 mol%), and K2CO3. Isolated yields are reported. Diastereomeric ratios were determined by NMR analysis of crude reaction mixture. The
areaction was run at 80°C; bNi-XantPhos was used instead of XantPhos; cCs2CO3 as base. See SM, section 5 for experimental details.
Potentially chelating heterocycles including
dioxolanes (22t), thiazoles (22aa), quinolines
(22ab), pyridines (22ac), oxazoles (22ad), and
morpholines (22ae) were incorporated. Protic
hydrogen atoms in secondary amides (22af)
were compatible. Tyrosine derivatives could
be glycosylated (22af), and the a-stereocenter
in the amino acid backbone stayed intact. Aryl
bromides/chlorides (22n, 22u, 22y-z) did
not interfere with this method, likely because
the oxidative addition to aryl iodide units in
donor 14 or 15 is a faster process. The remain-
ing aryl halide groups could serve as handles
for further derivatizations (see below). Partic-
ularly noteworthy is that aryl boronic esters
(22s) survived the reaction conditions with-
out undergoing a Suzuki-Miyaura reaction,
highlighting the distinctive reactivity of our
Deng et al., Science 382, 928–935 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
A
OBn
O
BnO
BnO
OBn
O
BnO
BnO
O
O
Ph
O
OH
O
O
O
BnO
BnO
OBn
O
O
OBn
O
O
BnO
BnO
MeO
CHO
S
N
Me
23 from Chrysin
52% ( : > 19:1)
24 from 2-Hydroxy-anthraquinone
72% ( : = 6:1)
25 from Vanillin
70% ( : > 19:1)
26 from Rotigotine
73% ( : < 1:19)
Ph
O
O
HO
O
O
OTBS
O
O
HO
HO
H
H
H
OMe
H
H
H
BnO
BnO
Me OH
OBn
O
O
MeO
Me
Me
H
N
O
BnO
BnO
OBn
O
O
MeO
BnO
BnO
OBn
O
O
Ph
Me
N
iPr
iPr
27 from Tolterodine
69% ( : < 1:19)
OBn
O
BnO
BnO
O
O
O
28 from Estrone
66% ( : > 19:1)
29 from Ethynylestradiol
73% ( : = 1:14)a
30 from Capsaicin
74% ( : = 1:19)
31 from Eugenol
78% ( : < 1:19)
32 from 7-Hydroxycoumarin
82% ( : < 1:19)
OBn
BnO
BnO
O
O
OH
Me
N
Me
OTBS
O
O
HO
HO
Cl
O
Cl
Cl
OBn
O
O
BnO
BnO
O
O
OBn
O
O
BnO
BnO
Me
OMe
Me
O
O
O
N
F
N
O
F
OH
36 from Ezetimibe
74% ( : < 1:19)
33 from O-desmethylvenlafaxine
86% ( : < 1:19)
34 from Triclosan
76% ( : = 1:18)a
35 from Mycophenolate mofetil
69% ( : = 1:5)
BnO
BnO
OBn
O
Me
Me
O
O
OMe
O
OH
O
O
O
BnO
OBn
OBn
Me
O
N
N
TESO
O
O
Me
37 from Icaritin
68% ( : > 19:1)
SN-38 derivatives
=
BnO
BnO
OBn
O
OBn
O
BnO
BnO
BnO OBn
O
BnO
BnO OBn
O
BnO
38a 64% ( : < 1:19)
38b 75% ( : > 19:1)
38c 84% ( : = 1:11)
38d 64% ( : > 19:1)
BnO
O
BnO
O
OBn
OBn
Me
O
OBn
BnO
OBn
O
OBn
OBn
BnO
38e 60% ( : < 1:19)
38f 74% ( : > 10:1)
38g 51% ( : > 19:1)b
38h 50% ( : < 1:19)b
B
BnO
BnO
OBn
O
O
40
35% yield
OBn
O
O
BnO
BnO
42
55% yield
CO2Me
NHBoc
One pot, multistep reactions
Pd(0)-Xantphos
K2CO3
60 to 100 °C
Glycosylation/
Suzuki-Miyaura
OBn
O
SoIB
BnO
BnO
HO
Br
14 or 15
(1.0 equiv.)
+
39
(1.5 equiv.)
Me
Glycosylation/
Buchwald-Hartwig
Bpin
H2N
H
N
O
Pd(0)-Brettphos
K2CO3
60 to 100 °C
the 3rd coupling partner (2.0 equiv.)
Pd(0)-Xantphos
K2CO3
60 to 100 °C
Glycosylation/
Suzuki-Miyaura
Glycosylation/
Sonogashira
Pd(0)-Xantphos
K2CO3
60 to 100 °C
BnO
BnO
OBn
O
O
41 from Loratadine
50% yield
N
N
OEt
O
OBn
O
BnO
BnO
H
H
O
MeH
O
Me
HO
43 from ethisterone
61% yield
Fig. 4. Synthetic application. (A) Glycosylation of natural products and commercial drugs. (B) One-pot, multistep, multicomponent reactions. Reactions in this table
were performed at 0.1 or 0.2 mmol scale in toluene (0.1 M) for 24 hours, using Pd(PPh3)4 (2 mol%), Xantphos (4 mol%), and Cs2CO3. Isolated yields are reported.
Diastereomeric ratios were determined by NMR analysis. aK2CO3 used as base; bReaction performed at 100 °C. See SM sections 6 and 7 for experimental details.
Pd(II) OA complexes (i.e., 12 in Fig. 1C) as
glycosyl (Csp3) electrophiles.
Synthetic application
To demonstrate the utility of this method, we
applied it in the modification of natural prod-
ucts and commercial drugs (Fig. 4A). Simple
phenols such as vanillin (25) and triclosan (34)
were glycosylated smoothly. Internal alkene
groups are accommodated, as exemplified by
the formation of 30-31 and 35. The tertiary
amine groups in drug molecules may inter-
fere with acid-promoted glycosylation meth-
ods, but show excellent compatibility with our
conditions (26-27, 33). Under our conditions,
protection of aliphatic alcohols is unnecessary
(29, 33). In the case of chrysin (23), the C7-
OH is glycosylated with high regioselectivity.
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RES EARCH | R E S E A R C H A R T I C L E
OAc
O
S
I
44
A
AcO
AcO
B
Pd(PPh3)4
CH2Cl2
71% yield
OAc
AcO
AcO
O
I
Ph3P
Pd
S
TS-I
AcO
AcO
OAc
O
I
Ph3P
Pd
45
1
S
1.87 Å
=
X-Ray structure
CCDC 2283248
(H atoms omitted)
1.39 Å
1
+
OH
OMe
16
K2CO3
Toluene
AcO
AcO
OAc
O
O
OMe
22b
Without Ligand
70% yield,
: = 1:5
XantPhos
73% yield,
: = 1:11
AcO
AcO
23.3
31.5
11.2
B3LYP-D3/def2-tzvp/SMD(toluene)//B3LYP-D3/def2-svp
G (kcal/mol)
OAc
O
S
Int-I
46
-10.7
Ph3P
S
Pd
TS-III
-3.6
7.1
Ph3P
S
Pd
+
I-
+
OAc
O
O
AcO
AcO
47
Int-II
-20.8
Ph3P Pd
+
S
19
Internal competition
(both 3 and 48 are added)
External competition
(only 48 is added)
ln krel
CO2Me
conversion (%) of 15
@ 90 min
CF3
Br
of R
OMe
H
Me
R
R =
OMe Me
H
Br
CF3 w/o 48
45
+
0
O
46
OAc
O
O
AcO
AcO
I
Ph3P
Pd
S
C
OH
3
OH
R
48
+ 15
Pd(PPh3)4 (2 mol%)
Xantphos (4 mol%)
K2CO3 (2.0 equiv.)
Toluene (0.1 M)
TS-II
OBn
O
O
49
+
OBn
O
O
50
BnO
BnO
BnO
BnO
Fig. 5. Mechanistic studies. (A) OA complex 45, formation, isolation, structure and reactivity. (B) Computed energetics for potential reaction pathways. Free
energies are computed by B3LYP-D3/def2-tzvp/SMD(toluene)//B3LYP-D3/def2-svp. (C) Reactivity of various phenols. Procedures to determine relative rate krel:
phenol (0.1 mmol), substituted phenol 48 (0.1 mmol) and glycosyl donor 15 (0.1 mmol) are allowed to react under standard conditions and stopped at ~30%
conversion. krel, conversion of substituted phenol divided by conversion of phenol. The results are the average of three runs. Error bars represent standard deviations.
See SM section 8 for experimental details.
For polyphenols such as icaritin (37), two gly-
cosyl units can be installed at a time, both with
high selectivities. Glycosylated anthraquinones
are ubiquitous in nature and we show that
2-hydroxylanthraquinone is a competent sub-
strate in our reaction (24). O-glycosylated cou-
marins are frequently employed as fluorescent
probes for detection of glycosidases (42), and
coumarins are glycosylated cleanly (32). Ster-
iodal phenols such as estrone (28) and estradiol
(29) are modified. A glycosyl unit was installed
onto ezetimibe (36), a cholesterol absorption
Deng et al., Science 382, 928–935 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
inhibitor containing a sensitive b-lactam unit.
SN-38 is a potent anticancer agent derived from
camptothecin (43) but is poorly soluble in wa-
ter. Conjugation with a sugar may improve the
pharmacological profile of the parent molecule;
see Afeletecan in Fig. 1A. We mounted an array
of glycosyl units, including both C2-deoxygenated
(38a-f) and C2-oxygenated sugars (38g-h), onto
an SN-38 derivative (Fig. 4A).
Pd-catalyzed SN2 glycosylation could be
performed in tandem with other Pd-catalyzed
cross-coupling reactions, affording carbohydrate-
containing compounds by one-pot, multistep
processes in which a single Pd(0)-complex
catalyzes two distinct steps (Fig. 4B). Mixing
glycosyl donor 14 or 15, m-bromo phenol (39),
and aryl boronic ester in one pot with a Pd(0)-
catalyst and a base, the Pd-catalyzed glycosyla-
tion and the Suzuki-Miyaura coupling proceed
in sequence, to give loratadine derivative 41
or L-tyrosine derivative 40 in useful overall
yields. The glycosylation could also be merged
with Buchwald-Hartwig (44, 45) coupling if
the ligand is switched to Brettphos (46) and
m-toluamide as the third coupling partner;
consecutive formation of Csp3–O and Csp2–N
bonds delivered 42 smoothly. Lastly, a sequence
composed of glycosylation/Sonogashira cou-
pling provides ethisterone-sugar conjugate
43 in 61% overall yield. These examples il-
lustrate selectivity of our Pd-catalyzed glyco-
sylation and suggest a rapid approach to make
glycoconjugates.
Mechanistic studies
Acetyl-protected sulfide donor 44 reacted with
Pd(PPh3)4 smoothly, and the OA complex 45
could be isolated from the mixture by column
chromatography (Fig. 5A). The facility of the
OA step may be attributable to the sulfur atom
in 44, which could pre-coordinate with Pd(0).
Complex 45 is a crystalline solid and its mo-
lecular structure was verified by x-ray crystal-
lography. Similar to other classical Pd(II) OA
complexes (47), the Pd center in 45 adopts a
(slightly twisted) square planar configuration,
with the two neutral ligands (i.e., sulfur and
phosphine atoms) occupying para positions.
From the solid-state structure of 45, we noted
that the C1–S bond is slightly elongated (1.83 to
1.87 Å) and the C1–O bond is shortened (1.41 to
1.39 Å) from their normal lengths (48), indicating
buildup of a positive charge at the C1 position.
Treating 45 with 4-methoxy phenol (16) in
the presence of K2CO3 afforded 22b with de-
cent efficiency and inverted configuration. Ad-
dition of external ligand Xantphos gave similar
results. A small amount of 45 (2 mol%) could
catalyze the reaction between 44 and 16 to
form 22b. These results support 45 as a re-
active intermediate in our process.
We next performed DFT calculations (B3LYP-
D3/def2-tzvp/SMD(toluene)//B3LYP-D3/def2-svp)
employing 45 and phenoxide 46 (or cesium
phenoxide, see SM section 9) as model sub-
strates (Fig. 5B). Two potential pathways were
examined: In principle, reductive elimination
of C–S bond in 45 to yield sulfonium Int-I (by
means of TS-I), followed by phenoxide attack
from 46 could afford glycoside 47. Alterna-
tively, direct attack of phenoxide 46 toward
45 by means of TS-II, followed by reductive
elimination of the C–S bond (45) in Int-II
would provide 47 as well, affording 19 as a
byproduct and regenerating Pd(0) catalyst.
Upon comparing the free energies of species
TS-I and TS-II (note: with different charge
states), we observed that the pathway through
TS-II exhibits lower barriers. Presumably, co-
ordination of the sulfur atom to the Pd center
polarized the C–S bond in 45 and made it
electrophilic enough toward phenoxide attack.
We also considered a scenario where the iodine
anion dissociates early from 45 before SN2 dis-
placement by 46 (see SM, section 9).
We also compared the relative reactivities
of various phenols bearing different para-
substituents (48) in our glycosylation reaction
(Fig. 5C). In internal competition experiments,
those with electron-withdrawing substituents
(49) react at faster rates, presumably because
they are more easily deprotonated under basic
conditions. By external competition experi-
ments, we found that the turnover frequency,
as inferred from the conversion of 15, increases
with the electron-withdrawing ability of the
para-substituent. The absence of phenol 48
resulted in essentially no reaction. These re-
sults indicate the involvement of phenoxide
nucleophiles in the turnover-determining step
and in turn lend some further support for
the pathway through TS-II. Although addi-
tional experiments are warranted to elucidate
mechanistic details, the ability of Pd-containing
OA complex to serve as a glycosyl (Csp3) elec-
trophile was quite general (see examples in
Figs. 3 and 4).
Conclusions
We developed a strategy that exploits Pd(0)-
mediated oxidative addition—the initial step
in classical cross-coupling reactions—as a tool
to activate glycosyl donors. The key to this
success was the use of aryl iodide-containing
glycosyl sulfides as donors, which upon re-
action with Pd(0)-catalysts furnished Pd(II)-
containing OA complexes that act as glycosyl
(Csp3) electrophiles. The following glycosidic
bond-forming stage caused clean inversion of
the glycosyl centers in donors, and either ste-
reoisomer could be obtained in a predictable
manner. This approach enabled a general meth-
od for SN2-glycosylation of phenols, allowing
for the synthesis of phenolic O-glycosides that
were previously challenging to access.
The mechanism grants this reaction oper-
ational simplicity and functional group tol-
erance. No acid or cryogenic conditions are
required, and the reaction can be set up sim-
ilarly to other Pd-catalyzed C–O cross-coupling
reactions. Moreover, the method is amenable
to late-stage glycosylation of a wide range of
commercial drugs and natural products. The
generality and mildness of the method is fur-
ther showcased in several one-pot, multistep,
multicomponent reactions. We anticipate that
this study will bring opportunities in Pd-mediated
glycosylation reactions, enabling advancements
in carbohydrate synthesis and its application in
various fields.
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ACKN OWLED GMEN TS
We acknowledge P. Yu (SusTEC) for helpful discussions and
computational resources. We also thank J. Yang (SCU) for helpful
suggestions. Funding: D.N. is supported by National Natural
Science Foundation of China (T2221004 and 21922106). Author
contributions: D.N. conceived the idea, guided the project, and
wrote the manuscript with feedbacks from other authors. L.-F.D. and
Y.W. made the initial observations and analyzed the results. L.-F.D.,
Y.W., A.S., S.Z., and H.Z. explored substrate scope. L.-F.D. and Y.W.
performed the mechanistic studies. Under the guidance of X.Z. and
D.N, S.X. performed DFT calculations. Competing interests: The
authors declare no competing interests. Data and materials
availability: Crystallographic data for compound 45 are available
from the Cambridge Crystallographic Data Center under reference
number CCDC 2283248. All other data discussed in this paper
are available in the main text or Supplementary Materials. License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement
of Science. No claim to original US government works. https://
www.sciencemag.org/about/science-licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adk1111
Materials and Methods
Supplementary Text
Figs. S1 to S9
References (50–63)
Submitted 4 August 2023; accepted 24 October 2023
10.1126/science.adk1111
Deng et al., Science 382, 928–935 (2023)
24 November 2023
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RES EARCH
PHYSICAL CHEMISTRY
Direct observation of chirality-induced spin
selectivity in electron donor–acceptor molecules
Hannah J. Eckvahl1†, Nikolai A. Tcyrulnikov1†, Alessandro Chiesa2†, Jillian M. Bradley1,
Ryan M. Young1, Stefano Carretta2*, Matthew D. Krzyaniak1*, Michael R. Wasielewski1*
The role of chirality in determining the spin dynamics of photoinduced electron transfer in donor-
acceptor molecules remains an open question. Although chirality-induced spin selectivity (CISS) has
been demonstrated in molecules bound to substrates, experimental information about whether this
process influences spin dynamics in the molecules themselves is lacking. Here we used time-resolved
electron paramagnetic resonance spectroscopy to show that CISS strongly influences the spin dynamics
of isolated covalent donor–chiral bridge–acceptor (D-Bc-A) molecules in which selective photoexcitation
of D is followed by two rapid, sequential electron-transfer events to yield D(cid:129)+-Bc-A(cid:129)–. Exploiting
this phenomenon affords the possibility of using chiral molecular building blocks to control electron
spin states in quantum information applications.
M olecules offer a wide variety of quan-
tum properties that could potentially
be exploited in qubit architectures for
quantum information science (QIS)
(1, 2). Moreover, molecules afford the
ability to tailor these properties as applications
dictate while controlling structure with atomic
precision. One such property of growing in-
terest is molecular chirality, which plays an
essential role in many chemical reactions and
nearly all biological processes. Naaman, Waldeck,
and coworkers presented evidence of the rela-
tionship between molecular chirality and electron
spin (3, 4) when they observed that electrons
photoemitted from a gold surface coated with
a thin film of DNA have a preferred spin state,
a phenomenon now known as chirality-induced
spin selectivity (CISS) (5). Subsequent experi-
ments with molecules bound to metallic, semi-
conductor, or magnetic substrates have confirmed
a connection between electron motion and spin
projection along the chiral axis, which is se-
lected to be parallel or antiparallel to the motion
depending on the handedness of the chiral
molecule (5–9). The spin selectivity of the ef-
fect can be very high, even at room tempera-
ture, and its theoretical foundations are still
being explored (10–17). However, a key prob-
lem hindering a fundamental understand-
ing of CISS is that it is difficult to separate
the role of the substrate from that of the chi-
ral molecule.
Hence, it is crucial to investigate how CISS
affects electron spin dynamics in molecules
undergoing electron transfer that are not bound
1Department of Chemistry, Center for Molecular Quantum
Transduction and Paula M. Trienens Institute for
Sustainability and Energy, Northwestern University, Evanston,
IL 60208-3113, USA. 2Università di Parma, Dipartimento di
Scienze Matematiche, Fisiche e Informatiche, I-43124 Parma, Italy.
*Corresponding author. Email: m-wasielewski@northwestern.edu
(M.R.W.); mdkrzyaniak@northwestern.edu (M.D.K.);
stefano.carretta@unipr.it (S.C.)
†These authors contributed equally to this work
to substrates. Achieving this understanding would
make the design of chiral molecular building
blocks to manipulate electron spin states pos-
sible, which has potential for QIS applications.
In particular, the occurrence of CISS at the
molecular level has been proposed as an en-
abling technology for quantum applications,
e.g., solving key issues like single-spin read-
out and high-temperature spin qubit initial-
ization (6).
In this work, we show direct evidence of CISS
in isolated covalent donor–chiral bridge–acceptor
(D-Bc-A) molecules in which selective photo-
excitation of D to its lowest excited singlet state
(1*D) is followed by two rapid, sequential electron-
transfer events: 1*D-Bc-A → D(cid:129)+-Bc(cid:129)–-A → D(cid:129)+-
Bc-A(cid:129)– (Fig. 1A). If formation of D(cid:129)+-Bc-A(cid:129)– occurs
in ≲1 ns and the effect of chirality is neglected,
the resulting entangled electron spin pair is
prepared initially in a nearly pure singlet state,
1(D(cid:129)+-Bc-A(cid:129)–). These states are commonly re-
ferred to as spin-correlated radical pairs (SCRPs)
and have been studied in systems ranging from
photosynthetic proteins (18–21) and related mod-
el systems (22–25) to DNA hairpins (26–30).
However, in all these cases, no consideration
was given to the possible influence of chirality
on SCRP spin dynamics.
To demonstrate the occurrence of CISS, we
have synthesized pairs of covalent D-Bc-A
enantiomers, (R)-1-h9 (-d9) and (S)-1-h9 (-d9),
where D is either nondeuterated (-h9) or fully
deuterated (-d9) peri-xanthenoxanthene (PXX)
(31), Bc is a pair of naphthalene-1,8-dicarboximides
that are linked at their 4-positions to form
an enantiomeric pair of axially chiral dimers
(R)-NMI2 and (S)-NMI2 (32), and A is naphthalene-
1,8:4,5-bis(dicarboximide) (NDI) (supplemen-
tary materials; figs. S1 and S2). The structures of
(R)-1-h9 (-d9) and (S)-1-h9 (-d9) and the corre-
sponding achiral reference molecules 2-h9 (-d9)
are shown in Fig. 1B. The enantiomers were sepa-
rated by HPLC with a chiral stationary phase
(fig. S3), and their circular dichroism spectra are
given in fig. S4. We have characterized the charge
separation and recombination dynamics of these
molecules with transient optical absorption (TA)
spectroscopy, and the CISS effect on their spin
dynamics with time-resolved electron paramag-
netic resonance (EPR) spectroscopy using either
continuous (TREPR) or pulsed microwave ra-
diation (pulse-EPR).
We found that CISS yields characteristic
features in the TREPR spectra of the photo-
generated PXX(cid:129)+- NMI2-NDI(cid:129)– SCRP in (R)-
1-h9 (-d9) and (S)-1-h9 (-d9), which are absent
in achiral 2-h9 (-d9), when the direction of
electron transfer is oriented orthogonal to the
applied static magnetic field direction, in
agreement with simulations. Conversely, the
corresponding spectra of PXX(cid:129)+-NMI2-NDI(cid:129)–
are practically identical when the field is paral-
lel to the electron-transfer direction.
Time-resolved EPR spectroscopy
Samples of (R)-1-h9 (-d9), (S)-1-h9 (-d9), and
2-h9 (-d9) were each prepared in the nematic
liquid crystal 4-cyano-4'-(n-pentyl)biphenyl
(5CB), which was aligned in a magnetic field
at 295 K, then rapidly frozen to 85 K, which
aligns the long axes of these molecules along
the magnetic field. The orientation of the mol-
ecules aligned in frozen 5CB can then be ro-
tated relative to the applied magnetic field
direction. Because solid 5CB is an optically
scattering medium, to assess the photo-driven
charge-separation dynamics of these molecules
at low temperature, we used both femtosecond
and nanosecond TA spectroscopy, substitut-
ing glassy butyronitrile for 5CB at 105 K. Tran-
sient absorption spectra and kinetics are
given in figs. S5 and S6. The data show that in
each case, ultrafast two-step charge separation
occurs in ≲ 0.2 ns to give PXX(cid:129)+-NDI(cid:129)–, which
recombines to its ground state in time constant
t = 46 to 66 ms, providing ample time for TREPR
measurements. The presence of a ~0.35-T sta-
tic magnetic field in the TREPR experiments
does not affect the ultrafast electron-transfer
reactions because the Zeeman interaction
(~0.3 cm−1) at that field strength is much less
than the adiabatic energy gaps (~20 to 80 cm−1)
for these reactions (see table S1 and the sup-
plementary materials for details).
We used pulse-EPR techniques to assess
the quality of the alignment of (R)-1-h9 (-d9),
(S)-1-h9 (-d9), and 2-h9 (-d9) in 5CB by mea-
suring the isotropic exchange (J) and dipolar
(D) spin-spin interactions for their photogen-
erated SCRPs, where D(q) = d(1 – 3cos2q) and
d = 52.04 MHz (cid:1) nm3=r3
DA in the point-dipole
approximation, which gives detailed distance
and orientation information as defined by
the Hamiltonian in eq. S3. If photogenera-
tion of the SCRP is followed by a Hahn echo
microwave pulse sequence (p/2 pulse – delay
t – p pulse – delay t – spin echo) and t is scanned,
coherent oscillations between the eigenstates
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RES EARCH | R E S E A R C H A R T I C L E
iand FBj
of the SCRP Hamiltonian FAj
i (see
below) that are related to both J and D(q)
modulate the spin-echo amplitude (21, 33–37).
When this experiment is performed on spin-
coherent SCRPs, the echo appears out of phase—
i.e., in the detection channel in quadrature to
the one in which it is expected—and is there-
fore termed out-of-phase electron spin echo en-
velope modulation (OOP-ESEEM) (21, 33–37).
For large SCRP distances, rDA, J can be neg-
lected and the OOP-ESEEM oscillation fre-
quency is approximately 2d when q = 0°, and
d when q = 90°. Thus, OOP-ESEEM can be used
to measure SCRP distances for a given angle
of the dipolar axis relative to the magnetic field
(28, 36–38). The dipolar axis in SCRPs con-
nects the centroids of the spin distributions
of the two radicals. Figures S7 and S8 show
the OOP-ESEEM data for (R)-1-h9 (-d9), (S)-1-
h9 (-d9), and 2-h9 (-d9), assuming that their
dipolar axes are aligned parallel or perpen-
dicular to the magnetic field. Fitting the
OOP-ESEEM data showed that the measured
(cid:129)+-NDI(cid:129)– distances of (R)-1-h9, (S)-1-h9,
PXX-h9
and 2-h9 were 2.48 ± 0.01, 2.48 ± 0.01, and
2.28 ± 0.01 nm, respectively, whereas the cor-
(cid:129)+-NDI(cid:129)– distances of (R)-1-
responding PXX-d9
d9, (S)-1-d9, and 2-d9 were 2.53 ± 0.01, 2.51 ±
0.01, and 2.29 ± 0.02 nm, respectively (table
S2). These experimental distances are con-
sistent with the center-to-center distances
between PXX and NDI determined from
density functional-theory calculations on (R)-
1-h9, (S)-1-h9, and 2-h9, where rDA = 2.59,
2.60, and 2.40 nm, respectively (fig. S9 and
tables S3 to S5). The agreement between
the experimental and calculated distances
shows that the D(cid:129)+-Bc-A(cid:129)– SCRPs are well-
aligned along the magnetic field direction in
frozen 5CB.
The TREPR spectra of aligned (R)-1-h9, (S)-
1-h9, and 2-h9 were obtained by photoexciting
the samples with a 450-nm, 7-ns laser pulse
and monitoring the magnetization with con-
tinuous microwaves by using direct detection
(supplementary materials). The spectra ob-
tained 100 ns after the laser pulse are shown
in Fig. 2. When the long axes of these mol-
ecules are aligned parallel to the magnetic
field direction (q = 0°), both enantiomers as
well as the achiral reference molecule gave
the same spectra (Fig. 2, A and C). Rotating
the samples so that the long axes of (R)-1-h9,
(S)-1-h9, and 2-h9 are aligned perpendicu-
lar to the magnetic field direction (q = 90°)
resulted in the appearance of outer wings in
the spectra of chiral (R)-1-h9 and (S)-1-h9 (Fig.
2B). No such enhancement was observed for
achiral 2-h9. As explained below, we posit
that these new features result from the con-
tribution of CISS to the formation of the SCRPs
in (R)-1-h9 and (S)-1-h9. Deuteration of PXX(cid:129)+
narrows the overall linewidth of (R)-1-d9,
(S)-1-d9, and 2-d9 while retaining the same
Fig. 1. Electron transfer pathways and molecular structures. (A) Electron transfer and intersystem-crossing
pathways in a D-Bc-A system with no applied magnetic field, where kCS1 and kCS2 are the charge-separation rate
constants, kST is singlet-triplet mixing rate constant, and kCRS and kCRT are the charge recombination rates through the
singlet and triplet channels, respectively. (B) Structures of chiral (R)-1 and (S)-1 and achiral 2. The steric constraints
imposed by linking the two NMI groups in (R)-1 and (S)-1 result in stable enantiomers that have axial chirality.
orientation dependence of the signal (Fig. 2,
C and D).
Effect of CISS on radical pair spin dynamics
In the molecules described here, the D(cid:129)+-A(cid:129)–
distances are ≳23 Å, so that the spin-spin
interactions J and D are small relative to the
~0.35-T applied magnetic field. Thus, the
Zeeman term is by far the leading term in
the SCRP spin Hamiltonian (eq. S3), so that
the SCRP wavefunctions Sj i ¼ 1ffiffi
↑↓j
Þ
i
p
2
Þ, which are magnetic
↑↓j
and T0j
field invariant, remain close in energy, where-
i are well sepa-
j
i and T(cid:3)1
j
as Tþ1
rated in energy from both Sj i and T0j
i. In
i are eigen-
particular, both Tþ1
states of the spin Hamiltonian, whereas Sj i
and T0j
i are not eigenstates because of the
different electronic g factors and hyperfine
i and T(cid:3)1
i ¼ 1ffiffi
p
2
i ¼ ↓↓j
i ¼ ↑↑j
i þ ↓↑j
i (cid:3) ↓↑j
i
ð
ð
j
j
i yields FAj
i ¼ cosf Sj i þ sinf T0j
i ¼ (cid:3)sinf Sj i þ cosf T0j
fields of the two spins. Coherent mixing of Sj i
and T0j
i and
i (Fig. 3A), which
FBj
are eigenstates of the spin Hamiltonian, where
the angle f in the mixing coefficients is de-
rived from the magnetic parameters of the
SCRP (supplementary materials) (39–41).
i and FBj
In the ultrafast electron-transfer regime ob-
served here, the initial spin state for an achiral
SCRP is the entangled singlet Sj i state that
yields populations only on FAj
i .
Therefore, four allowed transitions occur be-
i and the initially un-
i and FBj
tween FAj
i states, giving rise
j
i and T(cid:3)1
j
populated Tþ1
to a spin-polarized (out-of-equilibrium) EPR
spectrum. When q = 0°, this results in a typ-
ical (e, a, e, a) spin-polarization pattern (low to
high field, where a = enhanced absorption
and e = emission) because D(q) < 0 (39–41).
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 2. TREPR spectra. TREPR spectra of (R)-1-h9, (S)-1-h9, and 2-h9 (A and B) and (R)-1-d9, (S)-1-d9,
and 2-d9 (C and D) oriented in the nematic liquid crystal 5CB at 85 K and 100 ns after a 450-nm, 7-ns laser
pulse with the long axis of each molecule 0° [(A) and (C)] and 90° [(B) and (D)] relative to the applied
magnetic field direction. (Insets) The spectra are shown with their intensities expanded to highlight features
characteristic of CISS. TDAF, time after laser pulse.
Conversely, when q = 90°, the pattern is re-
versed (a, e, a, e) because D(q) > 0. Because the
g tensors of PXX(cid:129)+ and NDI(cid:129)– are very similar—
i.e., [2.0045, 2.0045, 2.0031] (42) and [2.0047,
2.0047, 2.0027] (43), respectively—the expected
SCRP polarization patterns (e, a, e, a) or (a, e,
a, e) are reduced to broadened (e, a) or (a, e)
patterns, as observed experimentally for the
achiral reference molecules 2-h9 and 2-d9
(Fig. 2, blue traces). Our OOP-ESEEM results
show that the dipolar axis of each SCRP is well
aligned with the long axis of each molecule so
that the dipolar axis and the chirality axis of
(R)-1-h9 (-d9) and (S)-1-h9 (-d9) are nearly
parallel. The angle q between this axis and
the applied magnetic field (B0) direction is
depicted in Fig. 3, B and E, for the parallel
and perpendicular orientations, respectively.
CISS mixes triplet character into the initial
singlet SCRP, thus the initial populations of
FAj
i and the corre-
i , and T(cid:3)1
sponding transition intensities are predicted
to change as well (44–47). If CISS is the sole
contribution to the spin dynamics and q = 0°
(Fig. 3D), then the state following electron
i, depending on
transfer would be ↑↓j
the chirality of the enantiomer and whether B0
is parallel or antiparallel to the electron mo-
tion. Given that the typical alignment of linear
D-B-A molecules within nematic liquid crys-
tals is not unidirectional, B0 has equal prob-
ability of being parallel or antiparallel to the
i or ↓↑j
j
i, Tþ1
i, FBj
j
electron motion and hence, if coherences are
lost, the initial state is an equal mixture of ↑↓j
i
and ↓↑j
i and is thus equivalent to having a
pure initial Sj i state. This situation is shown
schematically in Fig. 3C, where the blue and
red traces depict the idealized TREPR spectra
expected when CISS contributes 0 and 100%,
respectively. Indeed, the observed spectra of
both enantiomers as well as the achiral ref-
erence molecule are practically identical for
q = 0° (Fig. 2, A and C).
j
j
i, and T(cid:3)1
By contrast, when the chirality axis is ortho-
gonal to B0 (Fig. 3E), the initial state is very dif-
ferent in the presence or absence of CISS. In
particular, the CISS contribution initially pop-
i (Fig. 3G and eq. S12).
ulates Tþ1
Therefore, if the SCRP spin state has a 100%
CISS contribution, the TREPR spectra have a
nearly opposite intensity pattern with re-
spect to the case in which CISS does not
contribute. This is shown in Fig. 3F where
the blue and red lines in the idealized TREPR
spectra correspond to the intensity for the
pure Sj i (IS) and pure CISS (ICISS) initial con-
ditions, respectively.
Starting from recent theoretical models
(44–47) that describe the influence of CISS
on SCRP spin dynamics in cases for which
the CISS contribution is not 100%, the initial
state will be a superposition or a mixture of
Sj i, and T0j
i along the chiral axis direction,
making the detection of CISS less obvious. In
fact, the spectral line intensities in this case
are the weighted sum of IS and ICISS, which
occur at the same resonance fields and tend
to cancel out (see details in the supplementary
materials). The key to unraveling CISS and
pure singlet contributions to the SCRP spin
state in the molecules studied here is the ob-
servation of a larger EPR linewidth that occurs
when CISS contributes. Indeed, the sum of the
two contributions (Fig. 3F, black trace) yields
a signal that displays lateral wings of opposite
sign and central features that are narrower
than those produced in the absence of CISS,
exactly as observed experimentally in Fig. 2, B
and D. These features are unambiguous signa-
tures of CISS because they cannot be produced
starting from an initial Sj i state, where the
polarization pattern is fixed to (a, e) for q = 90°
by the sign of D(q) (39–41).
i and FBj
The larger linewidth obtained for the CISS
initial state arises from the very different
dependence of IS and ICISS on the degree of
coherent mixing in the eigenstates. Indeed,
|ICISS| increases with increasing entanglement
(f→0) whereas |IS| decreases (fig. S10). Explor-
ing the variation of the intensity by varying
the composition of the FAj
i eigen-
states is made possible by the presence of sev-
eral nuclear spins and by distributed magnetic
parameters, e.g., dipolar couplings, often termed
strain. Therefore, moving from the center of
each transition, i.e., the center of the distribu-
tions of the magnetic parameters and hyperfine
fields, to the tail of the lineshape corresponds to
changing the composition of the eigenstates,
which produces different linewidths for different
initial states. If entanglement in the eigenstates
is larger in the tails of the spectrum, the CISS
contributions result in magnetic field–dependent
broadening, giving rise to lateral contributions to
the lineshape of opposite sign with respect to the
central features (Fig. 3F, black trace).
To confirm this interpretation, we considered
the spectra of partially deuterated (R)-1-d9 and
(S)-1-d9. By strongly diminishing the hyperfine
couplings on one of the two radicals, we changed
the distribution of the eigenstate composition
and probed its effect on the lineshape. The mea-
sured spectra for q = 0 and 90° are shown in
Fig. 2, C and D, respectively. Although no quali-
tative effect is visible in the parallel direction
as expected, the lateral wings are substantially
reduced in the perpendicular orientation. These
spectra were simulated with a minimal SCRP
model with either one spin-½ nucleus (hydro-
gen atom) on both NDI(cid:129)– and PXX+ or only on
NDI(cid:129)–, the latter of which is the partially deu-
terated case. For reasonable values of the hyper-
fine couplings, the simulations shown in Fig. 4
reproduce the experimental behavior.
The intensities of the lateral wings are cor-
rectly reproduced by combining IS and ICISS with
weights of 41 and 59%, respectively (Fig. 4).
Although a 59% CISS contribution is remarkable,
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. The CISS effect on the spin states of
SCRPs. (A) SCRP spin states in the absence of
CISS and in the presence of a static magnetic field
B0 that is much greater than J, D, and the hyperfine
interactions in both radicals for a singlet precursor.
The enhanced absorptive (a) and emissive (e)
microwave-induced EPR transitions are indicated.
(B) Schematic of chiral molecules aligned parallel to
B0. (C) TREPR spectra with q = 0° expected for
an achiral SCRP (blue trace) and for a chiral SCRP
with an initial state having a 100% (red trace)
or partial CISS contribution (black trace). (D) SCRP
spin states for q = 0° where the initial state has a
100% CISS contribution. (E) Schematic of chiral
molecules aligned perpendicular to B0. (F) TREPR
spectra with q = 90° expected for an achiral SCRP
(blue trace) and for a chiral SCRP with an initial
state having 100% CISS contribution (red trace)
or a partial CISS contribution (black trace, rescaled).
(G) SCRP spin states for q = 90° where the initial
state has a 100% CISS contribution. The widths
of the energy levels in (A), (D), and (G) indicate
the population of the initial state, whereas the
relative arrow thicknesses in the boxes depict the
transition probabilities.
it must be stressed that this is a minimal model
in which the effect of the nuclei is accounted for
only qualitatively, and a full spectral simulation
with all nuclear spins in the fully protonated
molecules is very demanding. However, we
have been able to perform the simulation for
the deuterated case, which includes all four
1H and two 14N nuclei coupled to the electron
spin in NDI(cid:129)– and effects of dipolar strain. In
this case, the experimental behavior is very well
reproduced with a 47% CISS contribution, which
is still considerable.
Further evidence for the validity of this in-
terpretation was obtained by investigating the
time dependence of the TREPR spectra, which
reflected the time evolution of the D(cid:129)+-Bc-A(cid:129)– spin
states under the combined effect of coherent and
incoherent terms as described by the stochastic
Liouville equation and the presence of the mi-
crowave field (supplementary materials). Indeed,
figs. S11 and S12 show that the dependence of the
observed intensity of the wings of the spectra
are similar to that of the main peaks, which is
in agreement with our numerical simulations.
The CISS contribution to the spin dynamics
of (R)-1-h9 (-d9) and (S)-1-h9 (-d9) is similar to
the ~50% spin polarization that was recently
reported for an axially chiral binaphthalene
derivative covalently linked to a gold film de-
posited on nickel (48). Although this single
comparison suggests that the observed CISS
effect for the binaphthalene attached to the gold
surface may be largely due to the chiral molecule,
Fig. 4. Simulations of the TREPR spectra with a minimal model of the SCRP. The model places one
hydrogen nuclear spin-½ on both PXX(cid:129)+ and NDI(cid:129)– (A and B), or only on NDI(cid:129)– (C and D). The nuclear spins
are coupled to each radical with isotropic hyperfine couplings aNDI = 6.3 MHz and aPXX = 10 MHz. (Insets) The
simulations are shown with their intensities expanded to highlight features characteristic of CISS. The
complete list of simulation parameters is given in table S7.
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additional comparative work is needed on a
variety of systems to warrant such a conclusion.
Conclusions
We have found direct evidence of the CISS
effect on the spin dynamics of photogenerated
radical ion pairs in molecular electron donor–
acceptor molecules. The observation of CISS
in these systems affords possibilities both for
increasing our understanding of this important
phenomenon and for its possible applications.
These results show that the substrates or elec-
trodes with their possibly large spin-orbit coupl-
ings are not needed for CISS to occur, and that
TREPR spectroscopy can directly access the spin
dynamics that result from CISS. This provides key
information to guide theoretical investigations and
makes possible many new targeted experimental
studies. In addition, observing CISS at the mo-
lecular level is the first step required to trans-
form this fundamental phenomenon into an
enabling technology for quantum applications.
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AC KNOWLED GME NTS
Funding: This work was supported by the National Science
Foundation award CHE-2154627 (M.R.W.; synthesis, transient
optical, and EPR measurements); the Center for Molecular
Quantum Transduction, an Energy Frontier Research Center
funded by the US Department of Energy, Office of Science, Basic
Energy Sciences (BES) award DE-SC0021314 (M.D.K., EPR data
analysis); and cofunded by the European Union (ERC-SyG CASTLE,
project no. 101071533) (S.C.; calculations). However, views and
opinions expressed are those of the authors only and do not
necessarily reflect those of the European Union or the European
Research Council. Neither the European Union nor the granting
authority can be held responsible for them. Additional funding was
provided by the Foundazione Cariparma (S.C.; calculations). 1H
nuclear magnetic resonance spectroscopy and mass spectrometry
were conducted in IMSERC facilities at Northwestern University, which
have received support from the Soft and Hybrid Nanotechnology
Experimental (SHyNE) Resource (NSF ECCS-2025633), NSF
CHE-1048773, Northwestern University, the State of Illinois, and the
International Institute for Nanotechnology. Author contributions:
Conceptualization: M.R.W.; Methodology: H.J.E., N.A.T., J.M.B.,
M.D.K., A.C., S.C., R.M.Y., and M.R.W.; Investigation: H.J.E., N.A.T.,
J.M.B., M.D.K., A.C., S.C., R.M.Y., and M.R.W.; Visualization:
H.J.E., N.A.T., A.C., R.M.Y., and M.R.W.; Funding acquisition:
M.R.W. and S.C.; Project administration: M.R.W.; Supervision:
M.R.W., M.D.K., and S.C.; Writing – original draft: M.R.W., M.D.K.,
H.J.E., N.A.T., S.C., and A.C.; Writing – review and editing:
M.R.W., M.D.K., H.J.E., N.A.T., S.C., and A.C. Competing interests:
The authors declare that they have no competing interests.
Data and materials availability: All data are available in the main
text, the supplementary materials, and Dryad (49). License
information: Copyright © 2023 the authors, some rights reserved;
exclusive licensee American Association for the Advancement of
Science. No claim to original US government works. https://www.
science.org/about/science-licenses-journal-article-reuse. This
research was funded in whole or in part by ERC-Synergy project
CASTLE 101071533. The author will make the Author Accepted
Manuscript (AAM) version available under a CC BY public
copyright license.
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SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adj5328
Materials and Methods
Supplementary Text
Figs. S1 to S12
Tables S1 to S7
References (50–60)
spin selectivity in electron donor-acceptor molecules, Dryad (2023);
https://doi.org/10.5061/dryad.fbg79cp1r.
Submitted 1 July 2023; accepted 23 August 2023
10.1126/science.adj5328
Eckvahl et al., Science 382, 197–201 (2023)
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RES EARCH
INORGANIC CHEMISTRY
An all-metal fullerene: [K@Au12Sb20]5−
Yu-He Xu1, Wen-Juan Tian2, Alvaro Muñoz-Castro3, Gernot Frenking4,5, Zhong-Ming Sun1*
The C60 fullerene molecule has attracted tremendous interest for its distinctive nearly spherical structure. By
contrast, all-metal counterparts have been elusive: Fullerene-like clusters composed of noncarbon elements
typically suffer from instability, resulting in more compact geometries that require multiple embedded atoms
or external ligands for stabilization. In this work, we present the synthesis of an all-metal fullerene cluster,
[K@Au12Sb20]5−, using a wet-chemistry method. The cluster's structure was determined by single crystal x-ray
diffraction, which revealed a fullerene framework consisting of 20 antimony atoms. Theoretical calculations
further indicate that this distinct cluster exhibits aromatic behavior.
T he study of all-metal clusters reveals the
delicate balance between electronic shells
and structural geometry: The quantum
confinement of electrons (1, 2) gives rise
to a rich diversity of atomic arrange-
ments with intriguing bonding characteristics
(3–5). The discovery of buckminsterfullerene
(C60), which marked a major milestone in the
exploration and application of stable three-
dimensional cages, has sprouted new research
disciplines in chemical, physical, and material
science (6, 7). The distinct near-spherical struc-
ture of fullerenes along with the surface of
delocalized p electrons produces many nota-
ble properties and enables a wide range of
applications in biology, medicine, electron-
ics, and photovoltaics (8, 9). What’s more, the
internal cavity of fullerenes provides a space
for hosting a variety of atoms and molecules,
giving rise to a class of endohedral clusters
termed endofullerenes (10–13). The rapid prog-
ress in fullerene-related clusters and extensive
applications of fullerene-based materials have
prompted the exploration of analogous hollow
sphere molecules composed of other main-
group or transition metal elements known as
inorganic fullerenes (14). In74 with D3h sym-
metry and In48Na12 with D3d symmetry are
fullerene-like constructs found in the solid-
state Zintl phase Na96In97Z2 (Z = Ni, Pd, Pt);
both constitute the outermost shell of a four-
layer onion-like structure rather than existing
as hollow cages (15). Additionally, theoretical
calculations have predicted the stability of an
all-gold fullerene Au32, structurally very sim-
ilar to C60 (16). However, experiments produced
8+ cluster featuring a compact configura-
an Au32
tion of Au12@Au20, which was different from
the previously anticipated fullerene, and the
cationic cluster was protected by organic li-
gand (17, 18). Another ligand-protected dodeca-
hedral silafullerane was also reported, which
encapsulated one chloride ion (19). Obtaining
ligand-free C60 analogs with heavier atoms may
be constrained by their susceptibility to re-
arrangement into alternative, more stable
structures, as evidenced by previous theo-
retical studies. In this work, we report the
isolation and characterization of an all-metal
endohedral fullerene, [K@Au12Sb20]5− through a
solution-based method in which only one K+ ion
resides in a bare dodecahedral cage compris-
ing 12 Au and 20 Sb atoms with distinct struc-
tural features. Each Au atom sits in the center
of an Sb pentagonal plane without breaking the
structure of Sb20 cage, but rather stretching the
cage size. The [K@Au12Sb20]5− cluster is held
together exclusively by Au–Sb bonds exploit-
ing the icosahedron-dodecahedron duality,
thereby retaining an icosahedral, near-spherical
geometry with similar size to C60, but com-
posed of 32 atoms.
Synthesis and characterization
Compound [K(2,2,2-crypt)]5[K@Au12Sb20] was
synthesized by reacting the Zintl phase K8SnSb4
with precursor Au(PPh3)Me in an ethylene-
diamine solution, which was facilitated by the
presence of [2.2.2]crypt (see the supplemen-
tary materials). After stirring at room tem-
perature for 7 hours, the color of the reaction
1State Key Laboratory of Elemento-Organic Chemistry,
Tianjin Key Lab of Rare Earth Materials and Applications,
School of Materials Science and Engineering, Nankai
University, Tianjin 300350, China. 2Institute of Molecular
Science, Shanxi University, Taiyuan 030006, China.
3Facultad de Ingeniería, Arquitectura y Diseño, Universidad
San Sebastián, Bellavista 7, Santiago 8420524, Chile.
4Institute of Advanced Synthesis, School of Chemistry and
Molecular Engineering, State Key Laboratory of Materials-
Oriented Chemical Engineering, Nanjing Tech University,
Nanjing 211816, China. 5Fachbereich Chemie, Philipps-
Universität Marburg, Hans-Meerwein-Strasse 4, 35043
Marburg, Germany.
*Corresponding author. Email: sunlab@nankai.edu.cn
Fig. 1. Molecular structure of the [K@Au12Sb20]5– cluster. (A) Thermal ellipsoid plot (50% probability) of the cluster. (B) Front side view of (A). (C) Space-filling
representation of the crystal structure. (D) Top view of (A). (E) A typical Sb5 pentagon face centered by a gold atom in the cluster (with Sb–Sb bond lengths marked).
K is represented by cyan, Au by gold, and Sb by blue.
Xu et al., Science 382, 840–843 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
mixture was observed to change from brown-
red to brown-gold, and the stirring was stopped.
The reaction vial was stored in a refrigerator at
10°C for about 5 days, and black block-shaped
crystals were isolated from the bottom of the
vial in a yield of 25% based on Au(PPh3)Me. The
resulting complex was characterized by single-
crystal x-ray diffraction, which revealed its crys-
tallization in the triclinic space group P-1. The
asymmetric unit contained five [K(2,2,2-crypt)]+
charge-balancing cations. Additionally, energy-
dispersive x-ray spectroscopy (EDS) was used
to determine the elemental composition of the
compound. The obtained atom values for Au
and Sb were in good agreement with the the-
oretical values calculated for Au12Sb20. Many
attempts were made to obtain mass spectral in-
formation, but to no avail. Because of the high
negative charge of the cluster, it is extremely
unstable in the air, and a distinct gray precipi-
tate was observed in the crystal solution once
exposed to air, which generated great difficul-
ties in mass spectral detection.
As shown in Fig. 1, the anion [K@Au12Sb20]5−
exhibits the overall structure of a slightly flat-
tened dodecahedron with each Sb5 pentagonal
face centered by one Au atom. The average
short axis of the cage measures 7.30 Å (the
distance between two opposing Au@Sb5 pen-
tagonal faces) (Fig. 1, A to C), slightly exceeding
the diameter of C60 (7.1 Å) (20), whereas the
longest axis measures 9.03 Å (the distance be-
tween the two farthest Sb atoms on the cage)
(Fig. 1D), which is comparable to the calcu-
lated diameter of the theoretically predicted
Au32 (9.0 Å) (16). In all twelve planes, the sum
of the angles between the central Au atom and
the five vertices of the Sb5 ring is close to 360°,
indicating that the gold atom lies on the sur-
face of cyclo-Sb5 (in the Sb5 plane in Fig. 1E, for
example, the sum of the angles is 359.9°). Such
a planar pentacoordinate motif is unusual.
Theoretical studies predicted a planar hexa-
2−,
coordinate carbon atom in the anion CB6
which has not yet been synthesized (21). Sim-
ilarly, an iron-centered planar cation [FeSb5]+
was predicted, in which the Sb5 ring is aroma-
tic with equal-length Sb–Sb bonds of 2.973 Å
(22). However, the Sb–Sb bond distances in
[K@Au12Sb20]5− span a wide range from 3.114
to 3.436 Å (average of 3.227 Å), which are sig-
nificantly longer than that of [FeSb5]+ as well
as typical Sb–Sb single bonds (2.81 to 2.98 Å)
(23–25), denoting distinct structural features.
Additionally, the Sb20 dodecahedral shell is
expanded compared with that of the reported
[Sb@Ni12@Sb20]− compounds (where the aver-
age Sb–Sb distance is 3.11 Å), potentially owing
to the influence of the Au atom in the plane
enlarging the Sb5 pentagon (26). All Au–Sb
bonds are located on the faces of the dodeca-
hedron, with a relatively narrow range of 2.698
to 2.798 Å, which is considerably longer than
the bonds observed in [Au2Sb16]4− (2.67 to 2.71 Å)
and [Sb3Au3Sb3]3− (2.59 to 2.61 Å) (27, 28). The
central K+ ion is coordinated by twelve Au
atoms, supporting their positioning on the
Sb5 faces. The K–Au contacts range between
3.493 and 3.756 Å, indicating predominantly
electrostatic interactions. Nevertheless, the
presence of K+ as template cations remains
crucial for the overall cluster stability.
Theoretical analysis
To gain insights into the chemical bonding in
the [K@Au12Sb20]5− cluster, theoretical anal-
ysis was conducted. The optimized structure for
[K@Au12Sb20]5– revealed Au–Au distances of
4.002 Å, mediated by Au–Sb bonds of 2.773 Å,
which compared well to the x-ray structure
(Au–Au, 3.914 Ǻ; Au–Sb, 2.747 Ǻ). Comparison
Fig. 2. AdNDP bonding patterns and canonical molecular orbitals for [K@Au12Sb20]5−. (A) Sb 5s, Au 5d lone pairs, and the four-center two-electron (4c–2e) s
bonds over each Sb2Au2 quadrilateral. ON, occupation number. (B) Selected canonical molecular orbitals with their superatomic features (S, P, and D) indicated.
Xu et al., Science 382, 840–843 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
Fig. 3. Magnetic behavior for [K@Au12Sb20]5–. (A) Three-dimensional and
(B) contour-plot representation of NICS and the induced magnetic field under
certain orientations of the external field. (C) Streamline representation from
GIMIC calculations of the current density over spheres with radii of 3.0, 4.5, and
6.0 Å, with the 6.0-Å sphere given in side and top views, and a cut plane at the
center of the spherical cluster that denotes the magnitude of current density
vector field in nA/T. Isosurface values set at ±3 ppm. Blue represents shielding
and red represents deshielding.
between the calculated energies of a D5d-symmetry
and Ih-symmetry structure indicated that the
latter is favored by 5.4 kcal mol−1, suggesting
that the experimentally characterized D5d-
structure may be influenced by counterions
and crystal packing effects. The resulting Au12
icosahedron enclosed an inner spherical cavity
of diameter 7.491 Ǻ, which is significantly
larger than the Au12 cage found in ligand-
protected gold clusters of about 5.4 Å (29, 30).
This suggests that the cage structure is sup-
ported by Au–Sb bonds, providing a larger
interior volume, which thus presents a promis-
ing strategy for designing larger hollow clusters.
The endohedral K+ atom was stabilized by a
calculated encapsulation energy of –375.8 kcal
mol−1, which was primarily driven by electro-
static interactions that accounted for 90% of
the stabilizing forces (table S6). The calculated
highest occupied molecular orbital–lowest
occupied molecular orbital (HOMO-LUMO)
gap amounted to 2.57 eV at the hybrid PBE0
level. Vibrational analysis denoted a bouncing
motion for the endohedral K+ atom between
70 and 30 cm−1. A theoretical comparison be-
tween [K@Au12Sb20]5– and its hypothetical com-
pact counterpart with Au–Au distances of
3.045 Å (fig. S7b) reveals an energetic preference
for the characterized structure of 55.9 kcal mol−1.
To effectively allocate the 238 valence elec-
trons, we used the adaptive natural partition-
ing (AdNDP) analysis with the AdNDP 2.0
code (31). The advantage of using the AdNDP
method is its capacity to elucidate the chem-
ical bonding arrangement, encompassing both
Lewis bonding constituents [including lone
pairs (1c2e) and two-center two-electron (2c2e)
bonds] and delocalized bonding constituents.
In addition to the 20 Sb 5s lone pairs and 60 Au
5d lone pairs, there are 30 pairs of 4c–2e s
bonds distributed evenly over each butterfly-
shaped Au2Sb2 quadrilateral, covering the sur-
face of the [K@Au12Sb20]5– cluster (Fig. 2A). The
occupation numbers of these bonds range from
1.91 to 1.94 |e|. The remaining 18 electrons are
allocated to nine orbitals with superatomic
features (S, P, and D), satisfying the 3D aromatic
requirement of 2(n + 1)2 (n = 2) (Fig. 2B). These
electron distributions contribute to the overall
stability and distinct properties of the cluster.
The natural atomic orbitals analysis provided
valuable insights into the contribution of each
atom to the orbitals (32). Table S4 presents the
total contribution of each atom to these orbi-
tals, revealing that nearly all atoms make sub-
stantial contributions.
The natural population analysis conducted
on the optimized structure of [K@Au12Sb20]5–
revealed that the central K atom carries a
charge of +0.85 |e|, indicating the presence of
electrostatic interactions between the inner K
atom and the outer Au12Sb20 shell. Moreover, the
detailed energy decomposition analysis results
at the PBE0/STO-TZ2P-ZORA level, as shown
in table S6, further support the ionic nature of
the system. The analysis revealed that electro-
static interactions dominate the K+-cage bond-
ing, contributing more significantly (DEelstat,
89.6%) compared with orbital interactions (DEorb,
7.4%) in attracting local charges and stabiliz-
ing the system.
To evaluate the aromatic properties of
[K@Au12Sb20]5–, the overall magnetic behavior
was given by the three-dimensional represen-
tation of nucleus-independent chemical shift
(NICS) which accounted for the orientational-
ly averaged behavior resulting from the exper-
imental molecular tumbling in solution (Fig. 3).
The NICS isosurface exhibits a shielding con-
tour at the spherical cage, which suggests a
spherical aromatic behavior (33, 34). To over-
come the NICS exaltation near to heavy nuclei,
we focused our analysis on the long-range char-
acteristics of the induced magnetic field at the
low-electron density limit. (35) Moreover, the
representation of the magnetic response un-
der specific orientation of the external field
(Bind
i; i = x, y, z) provides a picture of the
shielding and deshielding regions that ac-
count for the possible global aromatic char-
acteristics in [K@Au12Sb20]5–. As a result, from
Bind
i, an enhanced long-range shielding region
aligned to the applied field for different orien-
tations was obtained, complemented with a de-
shielding region in a perpendicular plane, which
accounts for the shielding cone property inher-
ent to aromatic species (29, 36). The long-range
shielding region exhibited calculated values of
–20.0 ppm at 7.5 Å from the center of the struc-
ture, and of –2.6 ppm at 15.0 Å (Fig. 3b), thus
supporting the spherical aromatic behavior
of [K@Au12Sb20]5– and leading to an enhanced
Xu et al., Science 382, 840–843 (2023)
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RES EARCH | R E S E A R C H A R T I C L E
shielding region. In addition, the current density
upon a z-aligned external field was given from
gauge-including magnetically induced currents
(GIMIC) calculations, denoting a collective of
parallel currents around the cluster that were
observed at inner regions (3.0 Å of radius), at
the structure contour (4.5 Å), and outside of
the spherical shell. This analysis supports the
formation of a long-range shielding region ow-
ing to the presence of aromatic currents upon an
external field. Integration of the induced current
strength denoted values of 9.8 nanoamperes
per tesla (nA/T), contributed by +158.4 nA/T
from diatropic and –148.6 nA/T from para-
tropic currents, which is sizable in comparison
to the prototypical planar aromatic species
given by benzene, with a value of 12.1 nA/T at the
PBE0/def2-tvpz level. At the PBE0/LanL2DZ
level, a value of 21.2 nA/T was obtained, denot-
ing dependence of the level of theory.
The Au–Sb heterobonds play a crucial role
in maintaining the structural integrity of the
cage, whereas the endohedral cation acts as a
template for structure formation. Future in-
vestigations will focus on exploring alternative
synthetic strategies that leverage the interplay
between cage composition and endohedral
templates, thereby enabling the rational and
controlled synthesis of larger all-metal fullerenes.
These superatoms hold great potential for the
design and fabrication of precisely engineered
nanostructures owing to their atomically pre-
cise near-spherical structures.
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AC KNOWLED GME NTS
We are grateful for the valuable discussions with X.-B. Wang
(PNNL), J. Xu (NKU), and N. Li (Rigaku Beijing Co., Ltd.). Funding:
This work was supported by the National Natural Science
Foundation of China (nos. 92161102 and 22371140), the Natural
Science Foundation of Tianjin City (no. 21JCZXJC00140), and 111
project (B18030) from China (MOE). A.M.-C. acknowledges
financial support from ANID FONDECYT Regular 1221676. Author
contributions: Conceptualization: Z.-M.S.; Methodology: A.M.-C.
and Z.-M.S.; Investigation: Y.-H.X.; Visualization: Y.-H.X., W.-J.T.,
A.M.-C., and Z.-M.S.; Funding acquisition: A.M.-C. and Z.-M.S.; Project
administration: Z.-M.S.; Supervision: Z.-M.S.; Writing – original
draft: Y.-H.X, W.-J.T., A.M.-C., and Z.-M.S.; Writing – review and
editing: Y.-H.X, W.-J.T., A.M.-C., G.F., and Z.-M.S. Competing
interests: The authors declare no competing interests. Data and
materials availability: X-ray data are available free of charge from
the Cambridge Crystallographic Data Centre under reference
numbers CCDC 2269174 (method 1) and 2291088 (method 2).
All other experimental, spectroscopic, crystallographic, and
computational data are included in the supplementary materials.
License information: Copyright © 2023 the authors, some rights
reserved; exclusive licensee American Association for the
Advancement of Science. No claim to original US government
works. https://www.science.org/about/science-licenses-journal-
article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adj6491
Materials and Methods
Figs. S1 to S9
Tables S1 to S6
References (37–53)
1. A. W. Castleman Jr., S. N. Khanna, J. Phys. Chem. C 113,
(2015).
2664–2675 (2009).
29. X. Kang, H. Chong, M. Zhu, Nanoscale 10, 10758–10834
2. H. Häkkinen, Chem. Soc. Rev. 37, 1847–1859 (2008).
(2018).
Submitted 8 July 2023; resubmitted 3 September 2023
Accepted 4 October 2023
10.1126/science.adj6491
Xu et al., Science 382, 840–843 (2023)
17 November 2023
4 of 4
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10.1126_science.adi3038
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RES EARCH
VOLCANOLOGY
Fast and destructive density currents created by
ocean-entering volcanic eruptions
Michael A. Clare1*†, Isobel A. Yeo1*†, Sally Watson2, Richard Wysoczanski2, Sarah Seabrook2,
Kevin Mackay2, James E. Hunt1, Emily Lane2, Peter J. Talling3, Edward Pope3, Shane Cronin4,
Marta Ribó5, Taaniela Kula6, David Tappin7, Stuart Henrys8, Cornel de Ronde8, Morelia Urlaub9,
Stefan Kutterolf9, Samuiela Fonua10, Semisi Panuve10, Dean Veverka11, Ronald Rapp12,
Valey Kamalov13, Michael Williams2
Volcanic eruptions on land create hot and fast pyroclastic density currents, triggering tsunamis or
surges that travel over water where they reach the ocean. However, no field study has documented
what happens when large volumes of erupted volcanic material are instead delivered directly into the
ocean. We show how the rapid emplacement of large volumes of erupted material onto steep submerged
slopes triggered extremely fast (122 kilometers per hour) and long-runout (>100 kilometers) seafloor
currents. These density currents were faster than those triggered by earthquakes, floods, or storms, and
they broke seafloor cables, cutting off a nation from the rest of the world. The deep scours excavated by
these currents are similar to those around many submerged volcanoes, providing evidence of large
eruptions at other sites worldwide.
E xplosive volcanism poses a wide range of
hazards, with more than a third of vol-
canic fatalities attributed to fast (up to
hundreds of kilometers per hour) and
high-temperature pyroclastic density cur-
rents triggered by phreatic explosions, pyro-
clastic fountaining, lateral blasts, caldera and
dome collapses, and the vertical collapse of
eruption columns where they contact the
ground (1–6). Study of the behavior of pyro-
clastic density currents on land has revealed
a spectrum from dense to dilute and turbulent
modes of flow, across which a range of hazards
exists (1–3). This spectrum also relates to other
types of particulate density currents, including
snow avalanches and underwater sediment–
laden flows called turbidity currents (7–9).
Where terrestrially initiated pyroclastic density
currents reach the ocean, they create different
hazards. Such currents can generate tsunamis,
create phreatic explosions as hot currents in-
teract with water, travel over the sea, and/or
rapidly cool and transition into a turbidity
current, damaging seafloor infrastructure
1National Oceanography Centre, Southampton, UK. 2National
Institute of Water and Atmospheric Research (NIWA),
Auckland, Aotearoa New Zealand. 3Department of Geography
and Department of Earth Sciences, Durham University,
Durham, UK. 4School of Environment, University of
Auckland, Auckland, Aotearoa New Zealand. 5Department of
Environmental Science, Auckland University of Technology,
Auckland, Aotearoa New Zealand. 6Ministry of Lands and
Natural Resources, Nuku‘alofa, Kingdom of Tonga. 7British
Geological Survey, Keyworth, UK. 8GNS Science, Lower Hutt,
Aotearoa New Zealand. 9GEOMAR Helmholtz Centre for
Ocean Research Kiel, Kiel, Germany. 10Tonga Cable Ltd,
Nuku‘alofa, Kingdom of Tonga. 11Southern Cross Cable
Network, North Ryde, New South Wales, Australia.
12SubCom, Newington, NH, USA. 13Valey Kamalov LLC,
Gainesville, FL, USA.
*Corresponding author. Email: michael.clare@noc.ac.uk (M.A.C.);
i.yeo@noc.ac.uk (I.A.Y.)
†These authors contributed equally to this work.
and devastating marine biological communi-
ties (10–15).
Repeat terrestrial surveys and sampling
after the occurence of pyroclastic density cur-
rents have enabled reconstruction of flow prop-
erties from the resultant deposits, characterizing
the associated hazards (16–18). However, field-
scale observations of density currents linked
to volcanic eruptions in marine settings are
rare, owing to often-remote locations and in-
accessibility of in situ deposits. The behavior
of terrestrially initiated pyroclastic density
currents that cross land to enter the ocean
has only been documented at a single field site
after a small (0.19 km3) eruption (12–14), where-
as no equivalent study has shown what happens
when an eruption directly delivers volcanic
material into the ocean. We address this knowl-
edge gap with observations of underwater vol-
caniclastic density currents triggered during
the eruption of the partially submerged Hunga
Tonga–Hunga Ha‘apai volcano (hereafter re-
ferred to as Hunga volcano) in the Kingdom
of Tonga. We use the term “volcaniclastic den-
sity current,” which encompasses a spectrum
of density currents linked to a volcanic erup-
tion, from hot gas–supported pyroclastic den-
sity currents to cold fluid–supported turbidity
currents.
A key control on the hazard posed by any
type of density current is its velocity (9, 19–22).
Although recent advances in technology have
enabled the direct measurement of turbidity
currents and snow avalanches, no velocity
measurements exist for underwater volcani-
clastic density currents (9, 19–21). These lim-
itations are notable, considering the distinct
hazards posed by partially or fully submerged
volcanoes, which account for more than three-
quarters of active volcanoes worldwide (6).
Consequently, our knowledge relies on studies
of ancient ocean-entering eruptions (23, 24),
scaled-down laboratory modeling (25), and anal-
ysis of geomorphic features around submerged
volcanoes to infer the behavior of past erup-
tions (26, 27). Fields of large sediment waves
and scours, commonly observed radiating around
submerged flanks of volcanoes, are thought to
be diagnostic of catastrophic eruptions (26–28).
However, this hypothesis remains untested be-
cause of a lack of repeat seafloor surveys before
and after a large eruption. These uncertain-
ties severely limit the understanding of the
behavior and associated risks at submerged
volcanoes.
We present observations of voluminous vol-
caniclastic density currents that were triggered
by the 15 January 2022 eruption of Hunga vol-
cano in the Kingdom of Tonga. This eruption
was the most explosive in more than a century
and had worldwide impacts (29–35). The erup-
tion plume entered the mesosphere (57 km
high), tsunamis traveled across the Pacific
Ocean and caused 19- to 20-m runups in Tonga,
and a pressure wave encircled the globe mul-
tiple times (29–31, 33, 34). More than 1 hour
after the main eruption, Tonga’s only interna-
tional subsea telecommunications cable was
severed (Fig. 1), disconnecting the entire nation
from global digital communications at a critical
time for disaster response (36). Such an inci-
dent has wider implications because subsea
cables carry >99% of all international data
traffic, including the internet and trillions of
dollars per day in financial transactions (37).
The >6 km3 eruption expelled a volume of
material equivalent to the annual sediment
flux from all the world’s rivers combined, much
of which directly entered the ocean through
eruption column collapses (15, 38). The rapid
escalation in explosivity and the resultant
hazards were unexpected, exposing a gap in
understanding of many similar, yet unmoni-
tored, volcanoes along the Tonga-Tofua arc and
volcanic settings worldwide (6, 29, 30, 39).
By integrating datasets that document their
timing and extent, we determined the behavior
of underwater volcaniclastic density currents
triggered by the 2022 eruption of Hunga vol-
cano. These currents traveled >100 km and
caused extensive damage to seafloor cables,
from which we could estimate their velocity,
which reached up to 122 km/hour. These cur-
rents differ markedly from those triggered by
terrestrially initiated pyroclastic density currents
that enter the ocean, and their velocity is higher
than that recorded for other underwater den-
sity currents, including those triggered by ter-
restrial floods, large earthquakes, or ocean
waves (Table 1). The currents created distinc-
tive scours around Hunga volcano, excavating
>100-m-deep regions into the volcanic edifice
(Fig. 2), which were evident by comparing sur-
veys 3 months after the eruption to pre-eruption
surveys performed in 2016. Bedforms like these
Clare et al., Science 381, 1085–1092 (2023)
8 September 2023
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RES EARCH | R E S E A R C H A R T I C L E
are generated by, and thus probably record,
large explosive eruptions.
Extensive damage to seafloor cables
At 03:47 (all times UTC) on 15 January 2022, a
low eruptive plume was observed at Hunga
volcano, marking the onset of the main erup-
tive phase, with a steady narrow plume rising
to a height of >10 km (34) (Fig. 1). At 04:15
(T0a), a large explosion occurred [volcanic ex-
plosivity index of between 5 and 6 (35)], which
transformed the plume. High eruption rates
rapidly increased the height and width of an
expanding umbrella-shaped eruption plume
(34) (fig. S6). The plume reached a height of
between 16 and 18 km at 04:17. A second major
explosion (T0b) occurred at 04:21, with addi-
tional explosions generating sonic booms until
04:25 (inception of the atmospheric pressure
wave). By this time, the umbrella cloud had
expanded to a width of at least 120 km, and
the central plume was >15 km wide. Plume
collapses into the ocean below the umbrella
cloud occurred soon after 04:17, especially
from 04:20 onward (34) (fig. S6). By 04:50 to
04:55, the central high plume ceased rising
and was dispersed by the wind. However, the
eruption continued vigorously with a lower
plume (~17 to 21 km high) formed beneath
the larger 57-km-high plume.
Both subsea cables laid near Hunga volcano
were broken on 15 January, but the timing of
this damage lagged after the two most in-
tense explosions (T0a and T0b) by 9 to 15 min
for the domestic cable (at 04:30) and by 83
to 89 min for the international cable (05:44)
(table S1). The timing of these breaks is
known to the nearest minute, on the basis of
loss of data transmission, ultimately with
complete loss of internet capacity when the
international cable was severed. The dis-
tance of the first point of cable damage from
shore was determined immediately using
optical time-domain reflectometry, but the
full extent could not be assessed until a cable
repair ship retrieved the intact ends of the
cable on either side of the damaged zone.
The international cable repair took 5 weeks,
as the closest repair ship was 2500 km away, in
Papua New Guinea, and >100 km of replace-
ment cable was required. Communications were
limited across the kingdom until the domestic
cable was finally repaired, 18 months after the
eruption.
Prior to repair, cable damage was thought to
be caused by local seabed landslides; however,
the extent of damage was far greater than antic-
ipated. More than 89 km of the international
cable was broken and/or buried to a depth
beyond recovery, while 105 km of the domestic
cable was affected. Moreover, the international
cable was recovered at a distance of 5 km to the
north of its originally laid position, closer toward
the volcano. This incident was the largest length
Fig. 1. Extensive damage caused to seafloor cables by volcaniclastic density currents generated by
column collapse at Hunga volcano. (A) Locations and extent of cable damage on the domestic and
international seafloor cables resulting from the volcaniclastic density currents (pathways shown as arrowed
lines) plotted on bathymetric data acquired 3 months after the eruption. The thickness of volcaniclastic
density current deposits as sampled by multicoring is depicted as size-scaled solid circles, showing that
these currents deposited material at least 108 km away from the caldera. Actual sampled thickness of
volcaniclastic density current deposit is annotated. Where the base of the density current deposit was not
sampled, the thickness is given as >X cm. (B) Internet capacity shown for typical periods (in gray) compared
with the sudden loss of internet traffic, which flatlined at 05:44 on 15 January 2022, when the international
cable was broken. (C) Enhanced timeline of the main eruptive phase of Hunga volcano on 15 January 2022,
including the two major eruptions that caused ocean-entering column collapses. The timings of the two cable
breaks are marked with stars, showing that they occurred after the main explosive eruptions.
Clare et al., Science 381, 1085–1092 (2023)
8 September 2023
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RES EARCH | R E S E A R C H A R T I C L E
of cable damage since telegraph cables were
buried by the >200-km3 Grand Banks landslide
offshore Newfoundland in 1929 (40) and the
longest single cable repair in the modern fiber-
optic era (Fig. 1). We did not find evidence
within the resolution of imaging of slope fail-
ures on the deep-water volcano flanks around
the cables and surrounding slopes. We therefore
relate the cable damage to powerful and long
runout volcaniclastic density currents triggered
by the effective delivery of large volumes of
erupted pyroclastic material directly into the
ocean.
Insights into underwater density currents
triggered by eruption column collapse
Dense and highly erosive proximal regime
Linear gullies and trains of crescentic scours,
incised up to 100 m, radiate from the caldera
(Fig. 2), accounting for 3.5 km3 of erosion (15)
and representing an additional removed mass
of >50% of the original erupted volume. Ero-
sional features include scours of up to 2 km in
width and upslope-asymmetric bedforms (30 to
60 m wave height, 500 to 2000 m wavelength)
seen in pre-eruption surveys, which migrated up
to 1.5 km upslope. Pronounced erosion observed
from the post-eruption survey occurs within a
radius of <9.2 km from the caldera rim and
only on the steepest slopes (>10°, locally >40°;
Fig. 2). Recovery of material by seafloor coring
was not successful on such proximal slopes,
presumably owing to the presence of competent
Table 1. Reported velocities of fast-moving (>4 m/s) submerged particulate density currents worldwide. Values based on sequential seafloor cable
breaks or acoustic monitoring. Also compared are subaerial density currents, including pyroclastic density currents and snow avalanches.
Location
Volume
Interpreted trigger
Minimum runout
distance (km)
Maximum recorded
transit velocity (m/s)
Velocity calculation
based on
Submarine particulate density currents, including turbidity currents and volcaniclastic density currents
............................................................................................................................................................................................................................................................................................................................................
1979 Nice Airport,
Mediterranean (58)
0.008 km3
Mediterranean (59)
Not known
1929 Grand Banks
landslide, Newfoundland (40)
>200 km3
Canyon, Taiwan (37)
earthquake, Algeria (60)
Canyon, Taiwan (37)
Not known
Not known
Not known
2009 Gaoping
Canyon, Taiwan (37)
Not known
............................................................................................................................................................................................................................................................................................................................................
Gioia Canyon,
15
4.5
............................................................................................................................................................................................................................................................................................................................................
120
7
Seafloor cable
breaks
800
19.1
Seafloor cable
breaks
............................................................................................................................................................................................................................................................................................................................................
2006 Gaoping
............................................................................................................................................................................................................................................................................................................................................
1954 Orleansville
............................................................................................................................................................................................................................................................................................................................................
2009 Gaoping
............................................................................................................................................................................................................................................................................................................................................
Not known
380
380
20
20.5
10.3
............................................................................................................................................................................................................................................................................................................................................
2020 Deep-sea
Cable breaks
and moored
acoustic Doppler
current profiler array
............................................................................................................................................................................................................................................................................................................................................
Low spring
tide after large
river flood
Congo Canyon,
West Africa (19)
2.675 km3
1130
8
650
16.6
Seafloor cable
breaks
50
7.2
Moored acoustic
Doppler current
profiler array
50
8
2015–17 Monterey
Canyon, California (55)
Not known
Canyon, northeast
Atlantic (61)
2022 Hunga
volcano, Tonga
(this study)
Not known
>6.3 km3 [based on
deposited volume
on slopes outside
of the caldera (15)]
............................................................................................................................................................................................................................................................................................................................................
2019–20 Whittard
............................................................................................................................................................................................................................................................................................................................................
Eruption column collapse
>100
33.8
Cable breaks
............................................................................................................................................................................................................................................................................................................................................
Subaerial particulate density currents
............................................................................................................................................................................................................................................................................................................................................
Largest snow
avalanches (22, 62)
0.01 km3
Various
3 to 5
70
............................................................................................................................................................................................................................................................................................................................................
Terrestrial
pyroclastic density
currents
Dome or flank
collapse or
phreatomagmatic eruption
Up to tens of kilometers
7 to 210
See table S4 (52)
Up to 5.5 km3 for
those with
reported speeds,
but can exceed
hundreds of cubic
kilometers
............................................................................................................................................................................................................................................................................................................................................
Clare et al., Science 381, 1085–1092 (2023)
8 September 2023
3 of 7
Construction activity; slope
failure during
airport extension
Construction activity; slope
failure near port
Magnitude 7.2
earthquake triggered
continental slope failure
Magnitude 7.0
Pingtung earthquake
Magnitude 6.7
Orleansville earthquake
Large river
flood after typhoon
Large river
flood during
typhoon
Oceanographic
trigger related
to along-shelf
transport
Oceanographic trigger
related to across-shelf
transport
Seafloor cable
breaks
Seafloor cable
breaks
Seafloor cable
breaks
Seafloor cable
breaks
Moored acoustic
Doppler current
profiler array
Radar and
pressure plate
measurements
RES EARCH | R E S E A R C H A R T I C L E
B
+100
]
m
[
e
g
n
a
h
c
n
o
i
t
a
v
e
l
E
0
-100
B
0
E'
A
B'
Depositional
obel
C'
C
8
4
Distance [km]
Distance [km]
0.5
1.0
'
C
12
Deeply
incised
gully
B
B
B
D'
D'
D'
D
D
D
Collapsed
caldera
F
F
F
-60
D
D'
Erosional
regime
Depositional
regime
Domestic
cable
20
10
0
F
'
6
Distance [km]
12
]
s
e
e
r
g
e
d
[
t
n
e
i
d
a
r
G
Erosion
Deposition
Erosional
regime
Depositional
regime
6
Distance [km]
12
]20
s
e
e
r
g
e
d
[
10
10
0
0
t
n
e
i
d
a
r
G
'
B
Depositional
obe
l
E
n
o
i
t
a
v
e
l
E
E
]
m
[
e
g
n
a
h
c
Crescentic
scours
Up to 22 m
deposition
on domestic
cable
20
E
E'
0
0
Distance [km]
4
F'
]
m
[
e
g
n
a
h
c
n
o
i
t
a
v
e
l
E
>+50 m
<-50 m
'
S
"
0
0
4
°
0
2
4 km
175°20'0"W
H
NE channel
E channel
NW channel
International cable
Other volcanoes (Pope et al., 2017)
Hunga volcano
(This Study)
]
m
[
t
h
g
i
e
h
e
v
a
W
100
10
1
Small-scale bedforms
Large-scale scours
Large-scale bedforms
- 001
0
100
10
100
1000
10000
Change in seabed elevation [m]
Wavelength [m]
Fig. 2. Sculpting of the seafloor by powerful volcaniclastic density cur-
rents on the slopes proximal to Hunga volcano. (A) Elevation-difference map
generated between pre- (2017) and post-eruption (April to June 2022)
bathymetric surveys shows localized but major seafloor changes. The domestic
cable is shown as a red line. (B to F) Elevation changes shown for selected
locations in cross section, including the incision of deep (locally >120 m) gullies
and upslope-migrating crescentic scours on steep (>10°) slopes [(B), (E), and
(F)] and the deposition of thick (up to 40 m) lobes [(C) and (D)] where slopes
shallow. (G) Cross plot of change in seabed elevation and local seafloor gradient
(based on pre-eruption bathymetry) illustrating how erosion dominates on the
steepest slopes, whereas deposition is largely restricted to slopes <10°.
(H) Comparison of bedform morphometrics observed on the proximal flanks of
Hunga volcano and around the area of the damage to the international cable
with those from a database based on 17 volcanic islands worldwide (8) to
show that the large-scale scours and bedforms plot within the range of those
previously interpreted to relate to large explosive eruptions.
Clare et al., Science 381, 1085–1092 (2023)
8 September 2023
4 of 7
C
n
o
i
t
a
v
e
l
E
]
m
[
e
g
n
a
h
c
40
C
20
0
00
0
0
D
n
o
i
t
a
v
e
l
E
]
m
[
e
g
n
a
h
c
-120
F
]
m
[
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g
n
a
h
c
n
o
i
t
a
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e
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E
+100
0
F
-100
0
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]
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r
g
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d
[
e
p
o
l
s
d
e
b
a
e
s
l
a
c
o
L
30
20
10
0
-200
RES EARCH | R E S E A R C H A R T I C L E
A
40
<18 km from
Hunga volcano
Runout not
reported
<70 km from
Hunga volcano
30
20
10
0
1
]
s
/
m
[
y
t
i
c
o
l
e
v
d
e
d
r
o
c
e
r
.
x
a
M
B
Initiation Mechanism
Earthquake
River flood
Oceanographic
Construction
Eruption column
collapse
120
80
40
/
]
r
h
m
k
[
y
t
i
c
o
l
e
v
d
e
d
r
o
c
e
r
.
x
a
M
10
1000
100
Minimum runout distance [km]
0
10000
Eruption column collapse at submerged edifice
e.g. Hunga volcano
Rapid collapse of large
volume and tall eruption
column
>6 km3
Up to
45 degree
slope
Direct, vertical entry
of pyroclastic
the sea
material
into
up to 122 km/hr
C
River flood
e.g. Congo Canyon, W Africa
Gaoping Canyon, SW Taiwan
<5 degree
slope
A) Plunging of dense sediment-laden flood
water or B) Flushing event during low
Spring tide after flood
Up to ~3 km3
up to ~70 km/hr
D
Continental slope failure
e.g. Grand Banks, Newfoundland
Externally-triggered (e.g. earthquake
or construction) landslide
Up to 100s km3
up to ~70 km/hr
<5 degree
slope
E
Subaerial dome collapse
e.g. Montserrat, Caribbean
Subaerial pyroclastic density currents
travel over land and then enter the sea
<1 km3
<8 degree
slope
Velocity not known
F Volcanic flank collapse
e.g. Hawai’i, Canary Islands
Failure of volcanic flank,
generates a density flow
as collapsed material
disintegrates
No reported velocities
Up to 100s km3
10s of
degree
slope
Fig. 3. Density currents triggered by the Hunga volcano eruption are the
fastest reported for any submerged particulate density current to date.
(A) Measured velocities and minimum runout distances for different underwater
particulate density currents, categorized according to their triggers (as detailed
in Table 1). Precise runout distances cannot be presented, as the current
often ran out beyond the monitoring array or the location of seafloor cables.
(B to F) Schematics illustrating the inception mechanisms for different
submerged density currents: (B) rapid-eruption column collapse, causing vertical
plunging of dense pyroclastic material onto an exceptionally steep slope, as
seen at Hunga volcano; (C) river flood–triggered turbidity currents that enter
the ocean either laterally (where sediment is flushed offshore) or obliquely
(where dense sediment–laden flood water plunges), as observed in the
Gaoping and Congo canyons; (D) continental slope collapses that are
initiated by external ground disturbances, such as large earthquakes or
construction activity, which can initiate on very low angle slopes; (E) initiated
by subaerial volcanic dome collapse entering the ocean obliquely, as
in the case of Montserrat; (F) initiated by the collapse of volcanic island
flanks.
volcanic rock and/or coarse granular material.
Deposition occurs as slope angles reduce (<10°),
where well-defined lobes (up to 40 m thick
and 7 km wide) accumulated downstream of
two of the erosional chutes. As this lobate
deposition occurs on relatively steep slopes,
a dense granular current with high basal fric-
tion was likely responsible for the proximal
depositional lobes (41–43). This is in stark
contrast to turbidity currents, which typically
do not deposit on steep slopes or, where they
do, leave only very thin deposits (44). Indeed,
some turbidity currents only deposit on slopes
of less than 0.05° (45).
The intense erosion on steep slopes (Fig. 2)
caused currents to increase their sediment mass
substantially, thereby enhancing their power
and mobility (46). For context, the eroded volume
is 0.5 km3 greater than the largest known his-
torical volcanic landslide [3 km3, Mount St.
Helens (47)] and ~1 km3 greater than the sedi-
ment volume eroded by the longest monitored
turbidity current that traveled >1000 km along
the deep-sea Congo Canyon (19). Stepped trains
of upslope-migrating crescentic scours and large-
scale bedforms on steep slopes evidence Froude-
supercritical currents undergoing a series of
hydraulic jumps (48–50). Similar scours and
bedforms are a common feature proximal to
the initiation of other large-volume particulate
density currents, including those in nonvolcanic
settings [e.g., the 1 km3 earthquake-triggered
turbidity current in Kaikōura Canyon (51)] and
are of similar scale to those thought to diagnose
past large explosive eruptions on submerged
volcanic flanks (25–28) (Fig. 2H). We confirm
this previously hypothesized link, showing
that multiple radial chutes and bedforms can
be formed during an individual explosive erup-
tion, which has important implications for as-
sessing hazards from seabed geomorphology
at other submerged volcanoes worldwide.
Depositional distal regime
The remaining surveyed area is characterized
by widespread, relatively featureless blanketed
deposition, with an average of +2.8 m eleva-
tion change (i.e., net depositional). In the
valley southeast of Hunga volcano (location
of the domestic cable), slopes rapidly reduce
to <1.5°, and ponded deposition occurred (up
to 27 m thick). Even where elevation change
was not resolvable from repeat seafloor surveys
in deep water, sampling (up to 108 km from
Clare et al., Science 381, 1085–1092 (2023)
8 September 2023
5 of 7
RES EARCH | R E S E A R C H A R T I C L E
the caldera) recovered volcaniclastic deposits
emplaced by density currents (Fig. 1). Density
current deposits are generally of decimeter
thickness; comprise sand to granule–sized vol-
canic material that fines upward, with internal
lamination, ripples, and sharp bases; and are
geochemically linked to the 2022 Hunga vol-
canic eruption (16). Those deposits are over-
lain by thinner deposits interpreted as ash
fallout (52) (fig. S2 and table S2). The area
around the international cable was not cov-
ered by preexisting bathymetric data; how-
ever, detailed seafloor backscatter data reveal
trains of bedforms (1 to 2 m wave height, 100
to 200 m wavelength) within a valley be-
tween seamounts (fig. S1). These bedforms
evidence a complex flow pathway, as corrob-
orated by modeling (15). So intense was the
topographic steering, that the cable was moved
5 km toward the volcano by the density current
(fig. S1).
Contrasting behavior of underwater
volcaniclastic density currents
These depositional and erosional patterns con-
trast with observations from repeat seafloor
surveys and sampling of terrestrially initiated
pyroclastic density currents that entered the
ocean offshore Montserrat in the Caribbean
(12–14). Deposits offshore Montserrat formed
in two parts: (i) coarse-grained ridges up to
60 m thick within 3 to 4 km of the ocean-
entry point formed by a dense granular current;
and (ii) a broader deep-water lobe, comprising
centimeters-thick fine-grained deposits related
to a dilute turbidity current (12–14). The prox-
imal deposition of ridges offshore Montserrat
contrasts with the erosional chutes, scours,
and asymmetric bedforms we observe on Hunga
volcano. Further, the lobes at Hunga volcano are
much higher relief, thicker (tens of meters thick
rather than centimeters thick), on steeper slopes
(up to between 8° and 10° compared with <2°),
and likely composed of coarser material, with
deposits sampled at least 108 km from the edi-
fice, compared with 40 km offshore Montserrat
(Fig. 1). Seafloor cores show that coarse granular
deposits were deposited at least 80 km from
the Hunga edifice, indicating that currents
maintained high densities over this distance,
also in contrast with the dilute flow origin
for distal finer-grained deposits offshore
Montserrat (12–14).
Fast and long-runout underwater
volcaniclastic density currents
Large volumes of pyroclastic material were
delivered into the ocean during the eruption
at Hunga volcano, creating dense underflows
that were steered down its steep flanks. It is
most likely that the pyroclastic material was
predominantly derived from partial collapses
of the eruption column, but we cannot fully
preclude that currents may have been fed in
part by other eruption processes, including
jetting or fountaining. Initially, these volca-
niclastic density currents would have been a
dominantly gas-particle mixture, transitioning
into a water-particle mixture as they cooled
and mixed with seawater (23). We cannot dis-
cern the precise extent of that transition,
underlining our broader use of “volcaniclastic”
rather than “pyroclastic” density current. Vol-
caniclastic density currents were initially steered
along preexisting relief into a valley 15 km
southeast of the caldera. In this location, cur-
rents intersected with the domestic cable
side-on and were deflected to the north and
south (i.e., parallel to the cable) by the topog-
raphy. On the basis of the time between the first
collapses of the eruptive column into the ocean
(T0a and T0b) and severing of the domestic
cable, we calculate a distance-averaged tran-
sit (front) flow velocity of 63 to 122 km/hour
(17.6 to 33.8 m/s; table S1). This observation is
notable, given the inherent challenges in un-
derwater monitoring, particularly during an
ongoing large eruption.
Despite the higher resistance provided by
the surrounding seawater compared with air,
the velocities of volcaniclastic density currents
offshore Hunga volcano fall within the range
measured for pyroclastic density currents on
land (20) (table S4). The velocities at Hunga
volcano are higher than previously documented
for underwater density currents elsewhere in
the ocean, including turbidity currents triggered
by large-magnitude earthquakes, river floods,
and oceanographic processes (Table 1 and Fig.
3). The fastest transit velocities for turbidity
currents are up to 72 km/hour [20 m/s; based
on cable breaks during the 1929 Grand Banks
landslide (40) and the 2006 Pingtung earth-
quake offshore Taiwan (37)]. The volcaniclastic
density currents at Hunga volcano were steered
into deeper water along tortuous paths created
by irregular volcanic topography, where they
severed the international cable 70 km from the
volcano (Fig. 1). Assuming this current was the
same one that also broke the domestic cable in-
dicates a transit velocity of 32 to 51 km/hour (8.9
to 14.2 m/s). This is extraordinarily fast given the
distance traveled. However, our data do not en-
able us to determine how many currents were
triggered at Hunga volcano. It is plausible that
damage to the international cable resulted from
currents triggered by eruption collapses con-
siderably later in the eruption cycle (after T0a
and conceivably after T0b), in which case these
distal velocities are underestimates.
What explains the fast current speeds?
The sheer mass and manner of delivery of
material to the ocean (i.e., direct and rapid
vertical entry of a fast-collapsing plume) at
Hunga volcano is distinct from other mecha-
nisms of particulate density current generation,
such as river plumes that enter the ocean later-
ally, and landslide-triggered turbidity currents
that initiate on far lower angle slopes and
where material in the parent flow must first
disintegrate and mix (Fig. 3). The dominantly
downward rather than lateral trajectory toward
and through the air-ocean boundary also makes
the ocean-entry mechanism of dense pyroclas-
tic material at Hunga volcano distinct from
terrestrially initiated, ocean-entering pyro-
clastic density currents such as those observed
at Montserrat. The pyroclastic density currents
that entered the ocean at Montserrat first trav-
eled 4 km laterally over land, along the Tar
River valley, after a dome collapse (12–14). In
contrast, the formative mechanism at Hunga
volcano is better described as a vertical jet or
fountain collapse of a gas-particle mixture (53),
wherein a huge sediment load of dense volcanic
pyroclasts [up to 2.8 g/cm3 (52)] fell vertically
from considerable height (several kilometers)
as the eruption column collapsed into the ocean
(Fig. 3).
According to the modified Chézy equation
[a simplified approach often used to model
behavior of turbidity currents (52)], to main-
tain the high current velocities observed at
Hunga volcano would require a combination
of a steep slope, thick current, and/or high
sediment concentrations (expressed as the
“depth averaged” value for a vertical profile
through the current) (52, 54). Assuming pre-
viously accepted basal and upper friction values
for underwater density currents (54), to attain
the high transit velocities on the edifice flanks
requires current thicknesses on the order of
tens of meters, with depth-averaged sediment
concentrations of up to 5%, or else even-thicker
currents (hundreds of meters thick) with lower
depth-averaged sediment concentrations (1
to 2% concentration by volume). Near-bed
sediment concentrations are likely substan-
tially higher than these depth-averaged values
(8, 55). These concentrations are particularly
high for underwater particulate density cur-
rents (55), as evidenced by the deposition of
lobes on steep (up to ~10°) slopes of the edifice,
implying a dense granular basal layer (41–43).
Currents at Hunga volcano had sufficient inertia
to flow upslope in some areas (and overtop relief
of up to 860 m), such as south of the domestic
cable break and to reach the international cable
(figs. S4 and S5). This inertia was provided by
their initial velocity and concentration and by
additional entrained mass due to the substan-
tial seafloor erosion. We conclude that fast ve-
locities proximal to Hunga volcano result from
(i) the potential energy generated from the di-
rect, vertical entry of dense and large-volume
pyroclastic fluxes into the ocean; (ii) the ex-
tremely steep (up to 45°) submerged edifice
flanks, which were the location of the impact
zone for the collapsed material (53); and (iii)
the additional mass gained by the currents as
they eroded into the edifice flanks.
Clare et al., Science 381, 1085–1092 (2023)
8 September 2023
6 of 7
RES EARCH | R E S E A R C H A R T I C L E
Implications for hazards assessment
13. J. Trofimovs, R. S. J. Sparks, P. J. Talling, Sedimentology 55,
A push to enhance telecommunications links
across the South Pacific and Caribbean will
necessitate the crossing of volcanically active
regions by new subsea cable routes with a need
to assess threats posed to remote coastal com-
munities and the international communica-
tions infrastructure that serves them. This
requires more-extensive seafloor mapping to
identify submerged volcanoes that may ex-
perience similar eruptions, while offshore
monitoring, such as using fiber-optic sensing
along telecommunications cables (56, 57), is
required to provide early warning. We show
that volcaniclastic density currents triggered
when an eruption collapses into the ocean
can maintain high densities over distances of
>100 km and attain speeds up to 122 km/hour,
providing a fundamentally new view of their
behavior and associated hazards. We con-
firm that bedforms observed on many other
shallow submerged volcanoes worldwide can
be produced by powerful eruptions, demon-
strating that the hazards experienced at Hunga
volcano can occur elsewhere (4, 8, 27). Explo-
sive eruptions from these often unsurveyed and
unmonitored submerged volcanoes can produce
high-energy submarine density currents and
warrant far greater consideration as tsunami-
genic sources and as primary threats to vul-
nerable coastal communities and critical subsea
infrastructure.
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AC KNOWLED GME NTS
We thank the Kingdom of Tonga for allowing us to undertake
this research and the Nippon Foundation-GEBCO Seabed 2030
project and their alumni for their support. This work would not
have been possible without the captain, crew, and scientists
aboard RV Tangaroa (Voyage TAN2206) and the use of SEA-KIT
International’s USV Maxlimer for mapping the caldera. We extend
our gratitude to everyone involved in these voyages and for
assistance in processing the results. We thank B. Sugar of South
Sea Charters, Nuku’alofa, for providing the photographs of the
eruption plume that appear in fig. S6. The staff of the British
Ocean Sediment Core Research Facility (BOSCORF), including
C. McGuire, R. Garnett, M. Charidemou, and M. Edwards, are
thanked for supporting MSCL-CIS data collection and for providing
logistical support to receive and store cores in the UK. We thank
R. Williams and two anonymous reviewers for their constructive
comments and suggestions. Funding: This work was supported by
Natural Environment Research Council grant NE/X00239X/1
(M.A.C. and I.A.Y.); Natural Environment Research Council grant
NE/X003272/1 (J.E.H., M.A.C., and I.A.Y.); Natural Environment
Research Council grant NE/X002454/1 (D.T.); International Cable
Protection Committee (M.A.C. and I.A.Y.); and the Nippon
Foundation grant: NIWA-Nippon Foundation Tonga Eruption
Seabed Mapping Project (S.W., R.W., S.S., K.M., E.L., and M.W.).
Author contributions: Conceptualization: M.A.C., I.A.Y., P.J.T., E.P.,
K.M., R.W., S.W., T.K., S.H., C.d.R., M.U., S.K., S.F., S.P., D.V., R.R.,
and V.K. Methodology: K.M., M.W., I.A.Y., M.A.C., J.E.H., S.F., S.P.,
S.W., S.S., P.J.T., and E.P. Investigation: S.S., S.W., K.M., M.W.,
M.A.C., I.A.Y., J.E.H., S.C., and M.R. Visualization: M.A.C., I.A.Y., S.W., J.E.H.,
and S.C. Funding acquisition: M.A.C., I.A.Y., J.E.H., M.W., K.M., and
D.T. Project administration: M.A.C., M.W., and K.M. Writing – original
draft: M.A.C. and I.A.Y. Writing – review & editing: S.W., R.W., S.S., K.M.,
J.E.H., E.L., P.J.T., E.P., S.C., M.R., T.K., D.T., S.H., C.d.R., M.U., S.K.,
S.F., S.P., D.V., R.R., V.K., and M.W. Competing interests: M.A.C. is the
marine environmental adviser to the International Cable Protection
Committee. The other authors do not have any competing
interests. Data and materials availability: Core logs, photographs,
and coordinates are provided in the methods section of the
supplementary materials. The pre- and post-eruption bathymetric
data can be accessed in Zenodo (63). License information:
Copyright © 2023 the authors, some rights reserved; exclusive
licensee American Association for the Advancement of Science.
No claim to original US government works. https://www.science.org/
about/science-licenses-journal-article-reuse. This research was funded
in whole or in part by the Natural Environment Research Council
(NE/X00239X/1, NE/X003272/1, NE/X002454/1), a cOAlition S
organization. The author will make the Author Accepted Manuscript
(AAM) version available under a CC BY public copyright license.
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adi3038
Materials and Methods
Figs. S1 to S6
Tables S1 to S5
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Submitted 17 April 2023; accepted 1 August 2023
10.1126/science.adi3038
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RES EARCH
PHOTONICS
Ultrafast mode-locked laser in nanophotonic
lithium niobate
Qiushi Guo1,2,3*, Benjamin K. Gutierrez4, Ryoto Sekine1, Robert M. Gray1, James A. Williams1,
Luis Ledezma1,5, Luis Costa1, Arkadev Roy1, Selina Zhou1, Mingchen Liu1, Alireza Marandi1,4*
Mode-locked lasers (MLLs) generate ultrashort pulses with peak powers substantially exceeding their
average powers. However, integrated MLLs that drive ultrafast nanophotonic circuits have remained
elusive because of their typically low peak powers, lack of controllability, and challenges when integrating
with nanophotonic platforms. In this work, we demonstrate an electrically pumped actively MLL in
nanophotonic lithium niobate based on its hybrid integration with a III-V semiconductor optical amplifier. Our
MLL generates ~4.8-ps optical pulses around 1065 nm at a repetition rate of ~10 GHz, with energies
exceeding 2.6 pJ and peak powers beyond 0.5 W. The repetition rate and the carrier-envelope offset
frequency of the output can be controlled in a wide range by using the driving frequency and the pump
current, providing a route for fully stabilized on-chip frequency combs.
M ode-locked lasers (MLLs), which gen-
erate intense and coherent ultrashort
optical pulses on picosecond and femto-
second timescales, have enabled nu-
merous sciences and technologies in
photonics such as extreme nonlinear optics (1),
supercontinuum generation (2), optical atomic
clocks (3), optical frequency combs (4), biological
imaging (5), and photonic computing (6). Today’s
state-of-the-art MLLs are based on discrete fiber-
based and free-space optical components and
are expensive, power demanding, and bulky.
Realizing MLLs on integrated photonic plat-
forms promises widespread use of ultrafast
photonic systems that are currently limited
to table-top laboratory experiments. However,
the performance of integrated MLLs has not
been on par with their table-top counterparts,
lacking the required peak intensities and de-
grees of controllability required for on-chip
ultrafast optical systems (7). A major challenge
lies in the simultaneous realization of large
laser gain and an efficient mode-locking mech-
anism on integrated photonic platforms. Al-
though III-V semiconductor gain media can
be electrically pumped and exhibit a very high
gain per unit length and high saturation powers
(8), the conventional method of achieving mode-
locking and short pulse generation on the same
semiconductor chip requires a narrow range of
pumping current, thus substantially limiting
the output power and the tunability of the in-
tegrated MLLs (9, 10).
To realize high-peak-power integrated MLLs,
a promising approach consists of the hybrid
integration of a semiconductor gain medium
and an external mode-locking element based
on electrooptic (EO) or nonlinear optical effects.
Thin-film lithium niobate (TFLN) has emerged
as a promising integrated nonlinear photonic
platform with access to power-efficient and
high-speed EO modulation (11, 12) and strong
quadratic [c(2)] optical nonlinearity (13, 14).
1Department of Electrical Engineering, California Institute
of Technology, Pasadena, CA, USA. 2Photonics Initiative,
Advanced Science Research Center, City University of
New York, NY, USA. 3Physics Program, Graduate Center,
City University of New York, New York, NY, USA. 4Department
of Applied Physics, California Institute of Technology,
Pasadena, CA, USA. 5Jet Propulsion Laboratory, Pasadena,
CA, USA.
*Corresponding author. Email: qguo@gc.cuny.edu (Q.G.);
marandi@caltech.edu (A.M.)
A
D
Reflector
RF signal
Output coupler
Turning point
B
Intracavity phase
gain
PM
Laser cavity length (L)
0
C
Amplitude
gain
f
m
f0
…
f
-n
Turning point
loss
…
f
n
t
f
RF signal
50 Ω load
III-V gain chip
Reflector
ground
signal
ground
Loop mirror
TFLN
SiO2
Silicon
Fig. 1. Principle and design of integrated actively MLL laser. (A) Diagram of active mode-locking through intracavity phase modulation. (B) Illustration of mode-
locking in the time domain. (C) Illustration of mode-locking in the frequency domain. (D) Schematic of the integrated actively MLL.
Guo et al., Science 382, 708–713 (2023)
10 November 2023
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RES EARCH | R E S E A R C H A R T I C L E
Hybrid integration of semiconductor gain
with TFLN enables a strong interplay between
the laser gain and the EO or nonlinear effects
to achieve active or passive mode-locking with
high efficiency and tunability. Moreover, many
of the nonlinear and ultrafast optical function-
alities such as supercontinuum generation (15),
optical parametric oscillation (16–18), pulse
shortening (19), all-optical switching (20), and
quantum squeezing (21) can be realized in
quasi–phase-matched LN nanophotonic devices
with orders-of-magnitude lower peak powers
compared with other platforms. Therefore, de-
veloping high-peak-power MLLs integrated
into nanophotonic LN can enable a suite of
nonlinear and ultrafast optical phenomena
on a chip, promising integrated photonic sys-
tems with unprecedented performance and
functionalities. In this work, we demonstrate a
high-peak-power, electrically pumped, inte-
grated, actively MLL by hybrid integration of
III-V semiconductors and LN nanophotonics.
Our MLL exploits the high laser gain of III-V
semiconductors and the efficient active optical
phase modulation in LN nanophotonic wave-
guides as the mode-locking mechanism. Such
a design eliminates the complexities associated
with realizing gain and saturable absorption on
the same semiconductor chip, allowing a much
higher output power and a wider tunability of
the laser.
Mode-locked laser operating principle
and design
Figure 1A shows the concept of active mode-
locking by intracavity EO phase modulation. In
the time domain, when a phase modulator (PM)
is driven by a sinusoidal radio frequency (RF)
signal at a frequency fm, the intracavity phase
modulation is equivalent to the cavity length
modulation. Therefore, the laser cavity can be
considered as having a moving end mirror
with a sinusoidal motion at frequency fm. When
an optical signal inside the cavity strikes this
moving end mirror and gets reflected back,
its optical frequency acquires a Doppler shift.
After successive round trips, these Doppler
shifts will accumulate, resulting in no steady-
state solution. However, when a short circulat-
ing pulse strikes the end mirror at either of the
“turning points” where the mirror reverses its
direction (the extremum of the phase varia-
tion as shown in Fig. 1B), it will not acquire a
Doppler frequency shift, but instead, a small
quadratic phase modulation or chirp (22). Thus,
a steady-state optical pulse can be maintained
in the laser cavity after successive round trips.
Although in principle, optical pulses can occur
at either of the two phase modulation extrema
and acquire chirps of different signs, the dis-
persion in the cavity can compensate for the
chirp imposed by the PM at one extremum,
and further chirp the pulse formed at another
extremum (23). The mode-locking mechanism
can also be understood in the frequency do-
main (Fig. 1C). When the intracavity phase
modulation frequency fm matches the cavity
free spectral range (FSR), the sidebands pro-
duced by each of the running axial modes are
injected into the adjacent axial modes, result-
ing in the phase locking of adjacent modes.
Notably, in MLLs, these modes will lase be-
cause of the presence of laser gain within the
cavity, whereas in EO comb sources, they are
generated by dispersing the energy from a
single pump laser line (24–27).
Figure 1D shows the design of our integrated
MLL based on this principle. In our MLL, an
electrically pumped single-angled facet (SAF)
GaAs gain chip is butt-coupled to a TFLN chip
that contains an integrated EO PM and a
broadband loop mirror. A Fabry-Perot laser
cavity configuration is formed between the
reflective facet on the left end of the SAF gain
chip and the broadband loop mirror on the
TFLN chip. Here, an integrated PM is preferred
over a Mach Zehnder interferometer (MZI)–
C
D
Ground
Signal
Ground
10 µm
50 µm
5 µm
A
|E|
1.0
B
E
)
m
µ
(
Y
2
0
-2
F
2 µm
SiO2
SiO2
0
|E|
1.0
H
-8
-4
0
X (µm)
4
8
-8
-4
0
X (µm)
4
8
0.0
G
III-V gain chip
TFLN chip
50 µm
500 µm
Fig. 2. Integrated actively MLL laser on TFLN. (A) Cross-sectional view of the PM
region and the distribution of microwave field (white arrows) at 10 GHz and the optical field
of the fundamental TE mode (color map) at 1065 nm. The RF electrodes are marked in
yellow. |E|, normalized electric field. (B) False-colored SEM image of the PM region in the
fabricated device. The RF electrodes are marked in yellow and the optical waveguide is
marked in blue. (C) SEM image of the broadband loop mirror. (D) The curved coupling
region of the broadband loop mirror. (E and F) The fundamental TE mode profile at
1065 nm in both the (E) SAF gain chip waveguide and (F) TFLN waveguide taper.
(G) Optical microscope image showing the coupling region between the two chips.
(H) Dark-field optical microscope image of the integrated MLL when operating.
Guo et al., Science 382, 708–713 (2023)
10 November 2023
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RES EARCH | R E S E A R C H A R T I C L E
A
B
C
D
Fig. 3. Characterization of integrated actively MLL. (A) Schematic
of the experimental setup. CTL, continuously tunable CW laser;
FPD, fast photodetector; OSA, optical spectrum analyzer; ESA, electrical
spectrum analyzer; YDFA, ytterbium-doped fiber amplifier. (B) The optical
spectrum of the MLL output as a function of the RF driving frequency fm.
(C) Intensity autocorrelation of the MLL output as a function of the fm.
(D) Laser average output power versus Idrive when fm = 10.17 GHz.
Ith, threshold driving current.
based intensity modulator (IM) because the
PM offers a lower insertion loss and avoids
effects from the dc bias drift of the MZI mod-
ulator (28). For the PM, we used an RF coplanar
waveguide (CPW) design with ground-signal-
ground (GSG) configuration to ensure the
transmission of the RF wave with minimal
radiative loss.
Characterization of mode-locked lasers
We fabricated our devices on a 700-nm-thick
X-cut magnesium oxide (MgO)–doped TFLN
on a SiO2/Si substrate. In the PM region (Fig.
2A), the RF CPW was fabricated on top of the
SiO2 cladding layer. Such a design allowed us to
achieve high modulation efficiency (simulated
VpL = 1.1 V(cid:1)cm) by having a small gap (4 mm
here) between the ground and signal electrodes
and a significant overlap between the RF field
and the optical field in the waveguide (12, 29).
We designed the geometry of the RF CPW to
ensure a 50-W impedance around 10 GHz.
Figure 2, B to D, shows the scanning electron
microscope (SEM) images of the fabricated
PM and the loop mirror. We adopted a curved
coupling-region design in the loop mirror to
ensure broadband reflection (see supplemen-
tary materials section I for details). Based on
the length (1.5 mm) and the refractive index
of the SAF gain chip around 1065 nm, we es-
timate that a ∼3-mm-long TFLN waveguide in-
cluding the loop mirror section can lead to a
laser cavity FSR of ∼10 GHz.
Figure 2E shows the 1065-nm fundamental
transverse electric (TE)–mode profile in the wave-
guide of the SAF gain chip. To minimize the
coupling loss between the SAF gain chip and
the TFLN chip, the top width of the input facet
of the TFLN waveguide was tapered out to be
10.3 mm. The 1065-nm fundamental TE-mode
profile in the tapered TFLN waveguide is shown
in Fig. 2F. This design ensures a maximal over-
lap with the optical mode produced by the SAF
gain chip. We estimate a chip coupling loss of
3.4 to 3.9 dB in our experiments (see supple-
mentary materials section II for details). The
chip coupling loss can be further reduced by
using a mode-size converter based on an in-
verted taper edge coupler embedded in a poly-
mer waveguide (30, 31). Figure 2G shows the
microscope image of the chip coupling region
after the alignment. When the SAF gain chip
is electrically pumped with a driving current
(Idrive) of 160 mA, we observed green light (the
second harmonic of the 1065-nm light) inside
the laser cavity (Fig. 1H), which indicated a
high intracavity power around 1065 nm and a
good alignment between the two chips.
We characterized the integrated actively MLL
using the optical setup shown in Fig. 3A. We
applied a ~280-mW sinusoidal RF signal to the
left end of the CPW of the PM using the RF
probe. The right end of the CPW is terminated
Guo et al., Science 382, 708–713 (2023)
10 November 2023
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RES EARCH | R E S E A R C H A R T I C L E
Reference
f
1
f
2
…
A
r
e
w
o
P
B
…
Optical frequency
D
)
m
B
d
(
r
e
w
o
P
E
f
m=10.17 GHz
RF on
RF off
f
3dB=0.35 nm
0
-10
-20
-30
-40
-50
-60
1060
1062
1064
1066
Wavelength (nm)
1068
1070
f
m=10.17 GHz
4.81 ps
8
6
4
2
W/ Pulse shaper
W/O Pulse shaper
Gaussian fit
Gaussian fit
5.03 ps
.
)
.
u
a
(
n
o
i
t
l
a
e
r
r
o
c
o
t
u
A
0
-60 -50 -40 -30 -20 -10
0
Time (ps)
10
20
30
40
50
60
C
)
m
B
d
(
r
e
w
o
P
-40
-60
-80
-100
-120
3
f
1=3.68 GHz
y0 = -1.92456E-10, xc = 3.68371E9
w = 4115238.93752, A = 0.02817
H = 4.35836E-9
4)
W
n
(
2
r
e
w
o
P
3.95 MHz
0
3.67
3.68
3.69
3.70
RF frequency (GHz)
25
20
15
10
5
0
)
W
n
(
r
e
w
o
P
f2=6.49 GHz
y0 = -9.2114E-10, xc = 6.49094E9
w = 4074667.13986, A = 0.11225
H = 1.75378E-8
f
m=10.17 GHz
3.91 MHz
6.48
6.50
6.49
RF frequency (GHz)
4
5
6
7
8
9
10
RF frequency (GHz)
Fig. 4. Finding the mode-locking regime of integrated MLL. (A) Illustration
of the generation of heterodyne beat notes. (B) Evolution of heterodyne
beat notes with the fm. The mode-locking regime is marked by the white dashed
box. (C) Heterodyne beat notes measured at fm = 10.17 GHz. (Insets) Zoomed-in
view of the two beat notes at f1 = 3.68 GHz and f2 = 6.49 GHz. Blue symbols
represent measured data and solid red curves indicate Lorentz fits. (D) Output
optical spectra of the MLL when the RF drive at 10.17 GHz is on (red) and off
F
7)
s
p
(
i
h
t
d
w
e
s
u
P
l
6
5
4
P-0.125
RF
reference
100
200
PRF (mW)
300
400
500
(blue). The side lobes around 1062.7 and 1067 nm can be due to the reflections
in the gap between the gain chip and the TFLN chip. The fast modulation can be due
to the reflections within the gain chip. (E) Intensity autocorrelation traces of the
MLL output measured at fm = 10.17 GHz with (red) and without (blue) the external
pulse shaper. Symbols represent measurement data and solid curves indicate
Gaussian fits. a.u., arbitrary units. (F) Dependence of pulse width on PRF. The red
dashed line represents the 1=
scaling law according to the HME.
p
8
ffiffiffiffiffiffiffi
PRF
by another RF probe with a commercially avail-
able 50-W load resistor. While the gain chip was
pumped with an Idrive of 185.2 mA, we simul-
taneously collected the laser output spectra, the
intensity autocorrelation of the laser output,
and the heterodyne beat notes between two
neighboring laser emission lines and a narrow-
linewidth (~10 kHz) reference continuous wave
(CW) tunable laser. As shown in Fig. 3B, when
we scanned the fm, the laser output exhibited a
clear spectral broadening between 10.1 and
10.4 GHz (labeled by the white dashed box).
Within this fm range, two distinct intensity
autocorrelation peaks separated by ~98 ps
emerged (Fig. 3C), indicating that optical
pulses are formed. At an fm of 10.17 GHz, we
measured the laser output power from the
output facet of the TFLN chip. As shown in
Fig. 3D, the laser exhibits a low threshold Idrive
of 22 mA. Given the measured coupling loss of
~11 dB between the TFLN waveguide and the
single-mode lensed fiber, the on-chip laser out-
put average power is more than 50 mW when
the Idrive is greater than 180 mA.
Heterodyne beat notes were used to char-
acterize the mode-locking and resulting fre-
quency comb. As illustrated in Fig. 4A, when the
frequency of the reference CTL is resting in be-
tween the two neighboring comb lines of the
MLL near the center of its spectrum, two RF
beat notes at f1 and f2 are generated on the fast
detector. As shown in Fig. 4B, when fm is be-
tween 10.165 and 10.173 GHz, as labeled by the
white dashed box, two spectrally narrow beat
notes are observed. This suggests that within
this range of fm, the laser operates in the mode-
locked regime, producing ultrashort optical
pulses with high coherence. When fm is slightly
detuned between 10.165 and 10.173 GHz, f1 and
f2 can shift significantly with fm (Fig. 4B). This
indicates that the carrier frequency of the MLL
sensitively depends on fm. However, when the
fm is further detuned from the cavity FSR, the
MLL exhibits a transition to a turbulent re-
gime (32), which is manifested by multiple
noisy beat notes around f1 and f2 in Fig. 4B. In
the turbulent regime, the laser can still emit
ultrashort pulses as shown in Fig. 3C, albeit
with low coherence.
As shown in Fig. 4C, at fm = 10.17 GHz, we
obtained two spectrally narrow RF beat notes
at f1 = 3.68 GHz and f2 =6.49 GHz, with full
width at half maximum (FWHM) linewidths
of 3.95 and 3.91 MHz, respectively. Given that
the RF drive has a very small phase noise, and
no active locking of the laser cavity was used
here, the linewidths of the heterodyne beat
notes can be mainly limited by the drift of
pulse carrier frequency. As shown in Fig. 4D,
when a 280-mW RF drive at 10.17 GHz was
applied to the PM, significant spectral broad-
ening was observed. The pulse spectrum was
centered at 1064.9 nm and the FWHM of the
spectrum was 0.35 nm. Meanwhile, the inten-
sity autocorrelation trace (Fig. 4E) indicated
that the MLL produced one strong pulse at
one of the modulation turning points, where-
as the other pulse was significantly suppressed.
We fit the intensity autocorrelation trace with
a Gaussian function becasue active mode lock-
ing produces Gaussian pulses according to the
Haus master equation (HME) (33). The fitting
yielded a pulse width of 4.81 ps with the ex-
ternal pulse shaping, and 5.03 ps without. Be-
cause the pulse shaper can compensate for the
chirp on the output pulse and the additional
chirp imposed by the fibers and the YDFA, we
expect the output pulse width directly after the
Guo et al., Science 382, 708–713 (2023)
10 November 2023
4 of 6
RES EARCH | R E S E A R C H A R T I C L E
A
220
200
180
160
140
120
100
80
60
)
A
m
(
e
v
i
r
d
I
C
)
m
B
d
(
r
e
w
o
P
-60
-80
-100
-120
Power (dBm)
B
0
-10
-20
-30
-40
-50
)
A
m
(
e
v
i
r
d
I
220
200
180
160
140
120
100
80
60
Autocorrelation (a.u.)
9
8
7
6
5
4
3
-20 -10 0
10 20
Time (ps)
194.6 mA
193.6 mA
192.6 mA
191.6 mA
190.6 mA
189.6 mA
D
)
z
H
G
10.20
(
m
f
10.15
m
u
m
i
t
p
O
10.10
10.05
1055
1060
1065
1070
Wavelength (nm)
2
4
RF frequency (GHz)
6
8
10
140
160
I
180
drive (mA)
200
Fig. 5. Current tuning of integrated actively MLL. (A) The optical spectrum of the MLL output as a
function of Idrive. (B) Autocorrelation trace of the MLL output as a function of Idrive. a.u., arbitrary units.
(C) Tuning of the heterodyne beat notes by the Idrive. In (A) to (C), fm is fixed at 10.18 GHz. (D) Dependence
of optimum fm for mode-locking on Idrive.
MLL facet to be between 4.81 ps and 5.03 ps. The
pulse width of 4.81 ps after pulse shaping cor-
responds to a time-bandwidth product of 0.445,
which is very close to the transform-limited
time-bandwidth product (0.44) of a Gaussian
pulse (34). To conservatively estimate the pulse
energy and peak power, we used the measured
output average power of 53 mW at Idrive =
185.2 mA and assumed that both pulses exist
in the cavity. Hence, the output pulse energy
of our MLL was at least 2.6 pJ and the pulse
peak power was greater than 0.51 W.
8
p
We further studied the pulse width limits of
our MLL. First, we found that the measured
pulse only slightly decreased when the RF
driving power PRF was increased (Fig. 4F),
ffiffiffiffiffiffiffiffi
which is in good agreement with the 1=
PRF
scaling law (red dashed line) according to the
HME (35). We also found that further increas-
ing the RF power will not shorten the pulse
significantly. Instead, it can lead to laser in-
stability due to RF heating. The HME with cavity
group velocity dispersion, neglecting non-
linear effects within the laser cavity, predicts a
minimum pulse width of ~2.5 ps (36). The ex-
perimentally measured pulse width was wider,
likely due to several factors that are not cap-
tured by the HME such as the complex carrier
dynamics and two-stage gain recovery in the
III-V gain medium (37) and gain bandwidth
narrowing from intracavity etalon (22) or hole
burning effects (38) (see supplementary mate-
rials section IV for detailed analysis).
Electrical tuning of mode-locked lasers
The Idrive can serve as an important tuning knob
of our MLL. Figure 5, A and B, shows the de-
pendence of the output spectra and autocor-
relation of the MLL on the Idrive with 280-mW
RF drive fixed at 10.17 GHz. Within a wide
range of Idrive (140 to 205 mA), optical pulses
can be formed inside the laser. In addition, the
carrier frequency of the MLL blueshifted by
~0.3 nm as the Idrive was increased from 140
to 200 mA (Fig. 5A). This was likely caused
by the blueshift of the peak wavelength of
the gain spectrum owing to band filling and
screening effects induced by carrier injection
(39). We also investigated the effect of Idrive on
the coherence property and the frep of the
laser. We kept the RF drive fixed at 280 mW
and 10.18 GHz. As the Idrive was tuned from
189.6 to 194.6 mA, the laser transitioned from
the turbulent to the mode-locked regime, and
then back to the turbulent regime (Fig. 5C).
These results suggest that, with a frequency-
stable reference CW laser and active feedback
on Idrive, it may be possible to lock the carrier
frequency of the MLL and operate the device
as a stable frequency comb, as the repetition
rate (frep) of the MLL has already been locked
by the external RF oscillator. As shown in Fig.
5D, when we widely varied Idrive from 144 to
204 mA, the optimum fm that enables mode-
locking with high coherence could be varied
from 10.04 to 10.23 GHz, indicating that the frep
of the laser could also be adjusted by ~200 MHz.
Moreover, the optimum fm increased almost
linearly with Idrive, which resulted from an
increase of the cavity FSR caused by carrier
injection in the gain medium. Although fur-
ther increasing the Idrive would not lead to laser
output power saturation, we did not observe
pulse formation at higher Idrive beyond 205 mA.
This is likely attributed to the significant de-
tuning of the cavity FSR or the instability of
laser mode-locking due to more pronounced
self-phase modulation in the gain medium (37).
Conclusions and outlook
We have demonstrated an integrated actively
MLL in nanophotonic lithium niobate oper-
ating around 1065 nm, which offers the high-
est output pulse energy and peak power of any
integrated MLLs in nanophotonic platforms
(fig. S9 and table S2). Our MLL allows for a
wide tuning range of the laser frep of ~200 MHz
and precise control of the laser’s coherence
properties. The current tuning capability of
our MLL indicates that active feedback to
Idrive can achieve simultaneous locking of the
carrier frequency and frep of the MLL. This
allows the MLL to operate as a stable fre-
quency comb with locked carrier frequency
offset (fCEO) and frep. Finally, seamless integra-
tion of our high–peak power MLL with other
c(2) nonlinear optical functionalities provided
by TFLN offers opportunities for realizing
new integrated photonic systems, such as fully
integrated supercontinuum sources, self-referenced
frequency combs, and atomic clocks.
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ACKN OWLED GMEN TS
The device nanofabrication was performed at the Kavli
Nanoscience Institute (KNI) at Caltech. The authors thank
K. Vahala for loaning equipment. Q.G. thanks M.Xu for the helpful
discussions. Funding: The authors acknowledge support from
ARO grant no. W911NF-23-1-0048, NSF grant nos. 1846273 and
1918549, AFOSR award FA9550-23-1-0755, and NASA JPL.
The authors thank NTT Research for their financial and technical
support. Author contributions: Q.G. and A.M. conceived the
project. Q.G. fabricated the devices with assistance from R.S. Q.G.
performed the measurements and numerical simulation. R.S.,
J.W., B.K.G., R.M.G., L.L., L.C., and S.Z. assisted with the
measurements. B.K.G., R.M.G., A.R., and M.L. helped with the
numerical simulation and data analysis. Q G. wrote the manuscript
with input from all authors. A.M. supervised the project.
Competing interests: Q.G. and A.M. are inventors on a patent
application (US patent application no. 17/500,425) that covers the
concept and implementation of the actively MLL in this work.
L.L. and A.M. are involved in developing photonic integrated
nonlinear circuits at PINC Technologies Inc. L.L. and A.M. have an
equity interest in PINC Technologies Inc. The remaining authors
declare no competing interests. Data and materials availability:
All data are available in the manuscript or the supplementary
materials. The data files supporting the plots in the main text
and the computer code for simulating the MLL are available at
Figshare (36). License information: Copyright © 2023 the
authors, some rights reserved; exclusive licensee American
Association for the Advancement of Science. No claim to original
US government works. https://www.science.org/about/science-
licenses-journal-article-reuse
SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.adj5438
Materials and Methods
Supplementary Text
Figs. S1 to S9
Tables S1 and S2
References (40–48)
Submitted 2 July 2023; accepted 4 October 2023
10.1126/science.adj5438
Guo et al., Science 382, 708–713 (2023)
10 November 2023
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