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+Peer Review File
+
+Low-field onset of Wannier-Stark localization in a polycrystalline hybrid organic inorganic perovskite
+
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+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Berghoff et al report Wannier-Stark localization in a thin film of hybrid perovskite MAPbI3 achieved via non-resonant excitation with a 20THz electric field. This is achieved in a self-assembled material and at low electric field intensities compared to previous results in GaAs. Given the potential applications in ultrafast optically controlled switching of material properties, the presented results are not only novel but also have a broad interest. The experiment involves ultrafast THz pump – optical probe spectroscopy and supported by extensive and well-crafted calculations, comparing the effect of static and transient electric fields and accounting for the effect of the sample polycrystallinity. This work represents an exciting contribution, and is suitable for publication in Nature Communications. A few minor points to be addressed are as follows:
+1. It would be helpful to clearly note that in the data presented in the main manuscript (Fig.2(a)), the low-field regime refers only to the early delay times before the THz field peak. A separate measurement, with an overall lower THz field, could also be shown for comparison, providing a reference where no localization occurs.
+2. The discussion of figure 2, which shows the main experimental finding of the paper and its interpretation, should be expanded. In particular, panel d is not sufficiently explained in the main text: how are the separate peaks appearing in the absorbance attributed to n=0, +/-1? The possibility of optically controlled switching between 3D materials and QWs is fascinating and could be explored more at length.
+3. Since the low-field onset of Wannier-Stark localization is a key claim of this work, is it possible to provide a confidence interval to the estimation of the THz electric field amplitude? Can it be absolutely calibrated e.g. using a thin (smaller than the coherence length between the EOS probe and all relevant THz wavelengths) electro-optic crystal?
+4. Considering the in-depth discussion of orientations in both real space and Brilloiun space in pages 12-13, a diagram not only of MAPI structure in general but of the specific details being addressed would facilitate understanding (e.g. what Pb-I bond angles? Which direction is \Gamma M?)
+5. Is there a specific reason to consider MAPbI rather than other hybrid perovskites? Could one expect to easily replicate these results in other materials in the same family? Would a softer lattice, e.g. by selecting different cations or substituting a lighter metal for Pb, result in localization at even lower fields?
+A few typos and mistakes in figure presentation should also be corrected:
+* In the section “Experimental observation of Wannier-Stark Localization”, units are incorrect in the sentence: “relatively weak fields, E < 3 MV, for τ < -100 fs”. It should read MV/cm.
+*Is all the data presented (e.g. in fig. S2, S3) measured with a 6MV/cm THz field? Please specify so in captions.
+* The x-axis of figure S1 is labeled incorrectly, it should probably be in eV and not nm
+* Figures S4/S5 are not referred to in the main text
+
+Reviewer #2 (Remarks to the Author):
+
+This work provided an experimental observation of transient Wannier-Stark (WS) localization in a polycrystalline MAPbI3 perovskite based on similar previous work performed in the GaAs/AlGaAs superlattice (Ref. 8 in this manuscript). As the authors emphasized, the main difference is that the field amplitude needed here (3MV/cm) is far less than that in GaAs/AlGaAs (which exceeds 10 MV/cm) due to the large relevant lattice constant, the small width of electronic energy bands, and the coincidence of these two along the same high-symmetry direction. The results and the method discussed here are interesting and the manuscript is well written. However, since similar work has been reported in literature and I did not find enough novelty of current work, I cannot accept the present paper for publication in high level journals like Nat Comm. The authors may want to show and discuss about the novelty and new highlights of their work should they try to submit to similar journals again. For instance:
+1) Further analysis and emphasis of the peculiarity unique to MAPbI3 (such as low field strengths required for WS), and in particular the applications of this feature.
+2) Any other typical physical phenomena not limited to WS localization that are based on the
+transient spectral analysis? The authors developed a direct method to show WS localization in real natural solids. Since such localization has already been extensively studied in previous work, it will be interesting if this method can also be used for the study of other physical phenomena.
+3) MAPbI3 perovskite exhibits wide light absorption range and excellent photo-electronic properties and is considered as a prominent light harvester. In this manuscript, the description and discussion of novel properties of MAPbI3, especially related to this work, seems absent.
+
+Other questions and suggestions:
+1. In this work, the WS localization is created by applying the bias field from the phase-stable THz pulse and can be detected by optical absorption spectra. Is this method generally applicable for single-crystalline and polycrystalline materials?
+2. The observed WS step is slightly lower than the expected value. Is it possible that the step is higher than the theoretical value? Can the disorder of the sample be controlled here, and what is the influence of disorder on the experimental results?
+3. For MAPbI3, transient optical response is in fact dominated by the least dispersive direction of the band structure. Do other polycrystalline materials also have the same feature?
+4. WS ladders and associated phenomena predicted and observed in biased semiconductor superlattices have intrigued scientists for decades (it seems the work of J. Bleuse et al , Phys. Rev. Lett. 60, 220, 1988, should be cited together with [4, 5]). The concept was later introduced and explored also in ultracold atoms ( Phys. Rev. Lett. 76, 4512, 1996) and optical waveguide arrays superimposed with a linear optical potential (Opt. Lett. 23, 1701, 1998; Opt. Lett. 39, 1065, 2014). Since the paper is intended for an interdisciplinary journal like NC, the authors should discuss the broader impact of their work and possible connection to other fields.
+
+Reviewer #3 (Remarks to the Author):
+
+In this manuscript, the authors synthesized a MAPbI3 polycrystalline film and studied ultrafast nonlinear optical responses of the MAPbI3 film by performing THz-pump/NIR to visible-probe spectroscopy and theoretical calculations. They observed a transient absorption change induced by THz pump with a center frequency of 20 THz and assigned its origin to the Wannier-Stark localization. They found that the transient Wannier-Stark localization in a MAPbI3 film can be observed at lower THz field strength than that in a single crystal GaAs, which results from a narrow electronic bandwidth and a large relevant lattice constant of MAPbI3. The finding that its narrow electric bandwidth and large lattice constant make a MAPbI3 film a unique optical nonlinear material would be important for developing novel photonic devices based on halide perovskites. However, the discussions are not enough to guarantee that the observed transient absorption change originates from the Wannier-Stark localization, on which I commented below. Therefore, my opinion is that this manuscript is not suitable for publication in Nature Communications as it stands.
+
+The following points are the reasons why I doubt the interpretation of the data as the Wannier-Stark localization:
+
+On page 4, the authors mentioned that the measured transient absorption change is well explained by a two-band model. However, I question why the higher energy states, such as light and heavy electron states, do not contribute to the optical nonlinear processes. In fact, the previous study [Z. Wei et al., Nat. Commun. 10, 5342 (2019).] reported that light and heavy electron states exist around 2.25 eV and the optical transitions between those states and the band-edge conduction band states significantly contribute to the two-photon absorption processes in a MAPbI3 film. Therefore, I suspect that the observed transient absorption change originates from the Bloch-Siegert shift [E. J. Sie et al., Science 355, 1066 (2017).] in multiple states consisting of the band-edge valence and conduction band states and the higher energy conduction band states. Is it possible for the authors to comment on this?
+
+How much is the spectral width of the THz pump pulses? As the authors stated on page 6, the phonon modes of halide perovskites fall in the low frequency range around several THz. Therefore, if the spectral width is larger than the phonon frequencies, impulsive stimulated Raman scattering
+should occur. As some of the authors reported, driving the phonon modes leads to the similar transient absorption change albeit in a different crystal structure [Fig. 4a in H. Kim et al., Nat. Commun. 8, 687 (2017).]. Is it possible to discuss the contributions of phonons to the observed signals?
+
+On page 13, the authors mentioned that the crystallites are arbitrarily oriented and the theoretical calculations were performed based on this assumption. Is there any possibility that some preferential orientations of the crystallites exist? Do the authors experimentally verify the assumption from, for example, XRD spectra? The detailed sample properties should be described in the Support Information, because the sample is not single crystal but complicated polycrystalline film.
+
+On page 15, the authors claimed that the calculation result shown as a black curve in Fig. 4a is in good agreement with experimental results at high field amplitudes in Fig. 4b. However, the spectral oscillations around 2 eV can be seen only in the experimental results, not in the calculation. In addition, a bleaching signal around 2.2 eV which is expected from the calculation does not appear in the experimental results. What are the reasons for such disagreements?
+
+I suggest some more points for improving manuscript:
+On page 8, why did the authors consider the band gap energy of 2D perovskites with l =2, not l =1, 3 or 4?
+
+With regard to Ref. 25, the authors should cite the published version [J.-C. Blancou et al., Nat. Commun. 9, 2254 (2018).], not that in arXiv.
+Reviewer #1 (Remarks to the Author):
+
+Berghoff et al report Wannier-Stark localization in a thin film of hybrid perovskite MAPbI3 achieved via non-resonant excitation with a 20THz electric field. This is achieved in a self-assembled material and at low electric field intensities compared to previous results in GaAs. Given the potential applications in ultrafast optically controlled switching of material properties, the presented results are not only novel but also have a broad interest. The experiment involves ultrafast THz pump – optical probe spectroscopy and supported by extensive and well-crafted calculations, comparing the effect of static and transient electric fields and accounting for the effect of the sample polycrystallinity. This work represents an exciting contribution, and is suitable for publication in Nature Communications. A few minor points to be addressed are as follows:
+
+1. It would be helpful to clearly note that in the data presented in the main manuscript (Fig.2(a)), the low-field regime refers only to the early delay times before the THz field peak. A separate measurement, with an overall lower THz field, could also be shown for comparison, providing a reference where no localization occurs.
+
+→ First of all, we appreciate the reviewer for very encouraging and constructive comments. We agree with the reviewer’s first suggestion and thus clarified the first regime as follows in the main text:
+
+“More importantly, two distinct regimes can be identified in the time-resolved transient spectrum (Fig. 2(a)). The first regime appears at delay times \( \tau < -100 \) fs, where the field strength is relatively weak (\( E < 3 \) MV/cm), as an induced absorption (blue, \( \Delta T/T < 0 \)) right below and an induced transmission (red, \( \Delta T/T > 0 \)) right above the bandgap of \( E_{\text{gap}} = 1.62 \) eV. The second regime is apparent for field strengths \( E > 3 \) MV/cm, occurring between delay times \( -100 < \tau < 100 \) fs (Fig. 2(b)).”
+
+Regarding the separate measurement, the low-field regime (< 2 MV/cm) has been analyzed in our previous work using a narrower-band optical probe [Nat. Commun. 8, 687] and in another reported work using ~kHz field [ACS Photonics 2016, 3, 1060–1068]. There, one could find the electroabsorption spectra for comparison, where no localization occurs (Franz Keldysh effect).
+
+Nonetheless, we have performed a separate measurement at a slightly lower peak field strength (4 MV/cm) with a different center frequency of 30 THz. In this case, we reproduce the observed transient Wannier Stark localization with lower peak field strength and different THz center frequency. We have added this result and the THz field characteristics in the supplementary figure S5.
+
+2. The discussion of figure 2, which shows the main experimental finding of the paper and its interpretation, should be expanded. In particular, panel d is not sufficiently explained in the main text: how are the separate peaks appearing in the absorbance attributed to n=0, +/-1? The possibility of optically controlled switching between 3D materials and QWs is fascinating and could be explored more at length.
+
+→ Yes, we agree that the detailed explanation of Figure 2 (c, d) would be necessary not only for clarifying the mechanism, but also for strengthening our interpretation. Therefore, we have added the following paragraph in the main text (experimental results):
+"The extended structure of the transient spectral response can be understood with the assistance of Figure 2 (c, d). The localized Wannier-Stark states, equally spaced in energy by an amount eE_{THz}D, are depicted in the real-space along the field direction, z, in Fig 2 (c). D is the lattice period unit length and n the index. This space-dependent energy shift results in differentiating the electronic transition energies within the same site (arrow with n =0, Fig 2 (c)) from those between different sites (arrows with n =±1, Fig 2 (c)). As the difference in the transition energy with respect to the central spatially-direct (n = 0) transition is neE_{THz}D, one could assign the induced absorption below the band gap and above 1.9 eV to be n=-1 and n=0 transitions, respectively (Fig 2 (d)). The reduced absorption right above the band gap stems from the spectral transfer from non-perturbed optical transition to red- (n=-1) and blue- (n=0) shifted transitions (Fig 2 (d)). Depending on the strength of E_{THz} and the degree of localization, |n| > 1 transitions could, in principle, also be observed. In this case (Figure 2(a)), the observed single central step from reduced to increased absorption near the center of the band E_{pr} = 1.9 eV, is a noticeable signature of Stark localization, where the Wannier-Stark states are localized onto one unit cell."
+
+The possibility of optical switching between 3D delocalized and effective-2D localized electronic states is emphasized as follows:
+
+"The large unit cell and the small bandwidths along one direction of this material allows for optical switching with up to ~40 % transmission modulation depth using relatively moderate biasing fields. Also, the optical modulation of the material is extremely fast (sub-20 fs), as demonstrated directly by the quasi-instantaneous response to an electric field oscillating at mid-infrared frequency."
+
+"The polycrystallinity of this material does not impede the optical switching performance of the material, since the least dispersive direction of the band structure dominates the contribution to the optical response, which favors low-cost fabrications. Together with the outstanding photophysical properties of MAPbI_3, this finding highlights the potential of this material in novel photonic applications."
+
+3. Since the low-field onset of Wannier-Stark localization is a key claim of this work, is it possible to provide a confidence interval to the estimation of the THz electric field amplitude? Can it be absolutely calibrated e.g. using a thin (smaller than the coherence length between the EOS probe and all relevant THz wavelengths) electro-optic crystal?
+
+→The reviewer raises an excellent point. In response, we have added the following statements to describe the accuracy of the THz electric field amplitude in the main text. What we would like to emphasize here is that the estimated field amplitude inside the material was even slightly over-estimated because we use the reported refractive index of the material at near-infrared frequency (2.2, by which the estimated peak field amplitude was 6 MV/cm as we report in the manuscript), which it is likely slightly higher in the measured frequency (20 THz). We note that the refractive index at 3 THz is reported to be ~3 (by which the estimated peak field amplitude is ~5 MV/cm). Therefore, we mention that we report the upper limit of the actual field strength.
+
+"The phase-stable THz biasing fields are generated using a difference-frequency generation scheme in GaSe and characterized by ultrabroadband electro-optic sampling. The accuracy for determination of the absolute electric field strength in the center of the pump spot is estimated to be ±15%. The peak field strength at the interior of the MAPbI_3 perovskite sample is obtained using the Fresnel transmission coefficient with the reported refractive index \( n = 2.2 \) at near-infrared frequency, which sets the upper limit of the actual field strength."
+The crystal we have used exhibits a rather flat response function in the relevant frequency range. Consequently, it does not distort the waveform significantly in the time domain. The crystal would be thinner than the coherence length for all relevant THz input frequencies. A detailed description of the procedure for determination of the field is found in the Methods section:
+
+"The electric field transient is characterized by ultrabroadband electro-optic sampling at a 30-\mu m-thick GaSe crystal using balanced detection of an 8-fs probe pulse centered at a wavelength of 1.2 \mu m as the gating pulse. The quantitative value of the field amplitude is obtained by measuring the THz average power, pulse repetition rate and focal spot size. Then, the value at the interior of the MAPbI$_3$ perovskite sample is estimated using the Fresnel transmission coefficient for the THz field at the air–MAPbI$_3$ interface."
+
+4. Considering the in-depth discussion of orientations in both real space and Brillouin space in pages 12-13, a diagram not only of MAPI structure in general but of the specific details being addressed would facilitate understanding (e.g. what Pb-I bond angles? Which direction is Gamma M?)
+
+→ We thank the reviewer for the helpful suggestion. Accordingly, we modified Fig 1a to indicate the exact Pb-I-Pb angle, the Pb-I bond length, and the most relevant direction (Gamma Z) mentioned in the main text on pages 12-13. Also, we refer to the figure when these details are mentioned (highlighted in the main text).
+
+5. Is there a specific reason to consider MAPbI rather than other hybrid perovskites? Could one expect to easily replicate these results in other materials in the same family? Would a softer lattice, e.g. by selecting different cations or substituting a lighter metal for Pb, result in localization at even lower fields?
+
+→ We appreciate the question highlighting the uniqueness of the MAPbI$_3$. In general, Wannier-Stark localization is very challenging to observe in natural crystals due to the small lattice constants, the rapid scattering, and the dielectric breakdown conditions. One of most important messages of our work is that MAPbI$_3$, in particular, has the combination of the narrow bandwidth, the large periodicity, and the coincidence of the two directions. These unique features of its band structure promote this material to the Wannier Stark regime under relatively modest field amplitudes. Therefore, if one could find any other material (including other perovskites) where these conditions are met, we could expect similar results, provided other material-specific disturbances such as interband tunnelings are absent. Regarding the softness of lattice, if it means the lower nuclear vibration energy, there is not necessarily nor always a correlation between the electronic band dispersion near the band gap and a certain phonon frequency.
+
+In the main text, we have tried to emphasize the unique electronic properties of MAPbI$_3$ that enable our observation, including the above-cited (comment #2) sentences:
+
+"The large unit cell and the small bandwidths along one direction of this material allows for optical switching with up to ~40 % transmission modulation depth using relatively moderate biasing fields. Also, the optical modulation of the material is extremely fast (sub-20 fs), as demonstrated directly by the quasi-instantaneous response to an electric field oscillating at mid-infrared frequency."
+A few typos and mistakes in figure presentation should also be corrected:
+* In the section “Experimental observation of Wannier-Stark Localization“, units are incorrect in the sentence: “relatively weak fields, E < 3 MV, for τ < -100 fs”. It should read MV/cm.
+* Is all the data presented (e.g. in fig. S2, S3) measured with a 6MV/cm THz field? Please specify so in captions.
+* The x-axis of figure S1 is labeled incorrectly, it should probably be in eV and not nm
+* Figures S4/S5 are not referred to in the main text
+
+→ We thank the reviewer for thoroughly reviewing our materials and kindly raising the points that we overlooked. We corrected all of them accordingly (highlighted).
+Reviewer #2 (Remarks to the Author):
+
+This work provided an experimental observation of transient Wannier-Stark (WS) localization in a polycrystalline MAPbI3 perovskite based on similar previous work performed in the GaAs/AlGaAs superlattice (Ref. 8 in this manuscript). As the authors emphasized, the main difference is that the field amplitude needed here (3MV/cm) is far less than that in GaAs/AlGaAs (which exceeds 10 MV/cm) due to the large relevant lattice constant, the small width of electronic energy bands, and the coincidence of these two along the same high-symmetry direction. The results and the method discussed here are interesting and the manuscript is well written. However, since similar work has been reported in literature and I did not find enough novelty of current work, I cannot accept the present paper for publication in high level journals like Nat Comm. The authors may want to show and discuss about the novelty and new highlights of their work should they try to submit to similar journals again. For instance:
+
+1) Further analysis and emphasis of the peculiarity unique to MAPbI3 (such as low field strengths required for WS), and in particular the applications of this feature.
+
+→ First of all, we appreciate the reviewer’s critical yet very helpful comments. For highlighting the first point, we have added the following paragraphs to the introduction, and have rewritten the conclusion and abstract:
+
+[Introduction] “Besides their use in solar cells and light-emitting diodes, in this work, we demonstrate that MAPbI3 also has a great potential in photonic applications, including optical modulators, optical switches, and optical signal processing. For any optical amplitude modulator, one of the essential properties is a substantial change of the absorption edge with relatively low required energies in general. We demonstrate that solution-processed, polycrystalline MAPbI3 shows drastic changes in optical properties via Wannier Stark localization, at weak biasing fields. Whereas conventional semiconductors constituting photo-detectors, e.g. Si or InGaAs, require costly manufacturing processes and are limited to traditional rigid type devices, perovskites with distinct crystal structures exhibit ultrafast response (sub-20 fs), while simultaneously supporting cheap and flexible polycrystalline film fabrication.
+…
+The large unit cell and the small bandwidths along one direction of this material allows for optical switching with up to ~40 % transmission modulation depth using relatively moderate biasing fields. Also, the optical modulation of the material is extremely fast (sub-20 fs), as demonstrated directly by the quasi-instantaneous response to an electric field oscillating at mid-infrared frequency.”
+
+[Conclusion] “we have demonstrated that solution-processed, polycrystalline MAPbI3 shows optical transmission change by tens of percent at relatively modest field strengths via transient Wannier Stark localization. The large lattice periodicity, the narrow electronic energy bandwidths, and the coincidence of these two along the same high-symmetry direction promotes this material to the Wannier Stark regime under relatively moderate biasing fields. Polycrystallinity of this material turns out not to hinder the Wannier Stark localization effect as observed, due to the dominant contribution from the least dispersive direction of the band structure, which favors low-cost fabrications with this material as optical modulators. The degree of disorder and relative orientation among crystallites may influence the modulation spectral shape slightly, e.g. the position of the photon energy where the induced transmission to induced absorption happens, which could be finely tuned depending on the desired device performance by further systematic studies.”
+[Abstract] “Methylammonium lead iodide perovskite (MAPbI3), renowned for an impressive power conversion efficiency rise and cost-effective fabrication for photovoltaics, exhibits a huge potential for optical modulation-type applications, in this work. We demonstrate that polycrystalline MAPbI3s undergo drastic changes in optical properties with the modulation depth to be tens of percent at moderate field strengths, via transient Wannier Stark localization with an ultrafast response time. The distinct band structure of this material - the large lattice periodicity, the narrow electronic energy bandwidths, and the coincidence of these two along the same high-symmetry direction – enables relatively weak fields to bring this material into the Wannier Stark regime. Its polycrystalline nature is not detrimental to the optical switching performance of the material, since the least dispersive direction of the band structure dominates the contribution to the optical response, which favors low-cost fabrication. Together with the outstanding photophysical properties of MAPbI3, this finding highlights the potential of this material in novel photonic applications.”
+
+2) Any other typical physical phenomena not limited to WS localization that are based on the transient spectral analysis? The authors developed a direct method to show WS localization in real natural solids. Since such localization has already been extensively studied in previous work, it will be interesting if this method can also be used for the study of other physical phenomena.
+
+→ We thank the reviewer for the suggestion to emphasize the advantage and potential use of our experimental technique and approach. Accordingly, we have added a dedicated paragraph in the conclusion as follows:
+
+“Moreover, the phase stable THz field transients and the ultra-broadband optical pulses of 7 fs duration revealed that the optical modulation of this material has an extremely fast, quasi-instantaneous (sub-20fs) temporal response in visible/near-IR spectral region. This technique could be generalized for realizing transient Wannier Stark localization in other semiconductor solids in a carefully prepared single-crystalline or a polycrystalline form. More generally, this method enables to analyze any ultrafast changes in optical properties induced by the phase-locked and intense electromagnetic field transients, be it resonantly or non-resonantly. While here we used only the electric field of the transients, one could also exploit the magnetic component for exploring ultrafast magneto-optic effects, by enhancing the magnetic field with respect to the electric field with, e.g., a specially designed plasmonic nanoaperture.”
+
+3) MAPbI3 perovskite exhibits wide light absorption range and excellent photo-electronic properties and is considered as a prominent light harvester. In this manuscript, the description and discussion of novel properties of MAPbI3, especially related to this work, seems absent.
+
+→ We thank the reviewer for this suggestion for improving our work. We have added the following paragraph to the introduction to better connect to the cited part of the conclusion:
+
+[Introduction] “Methylammonium lead iodide perovskite (MAPbI3) has become a remarkable material for photovoltaic applications due to the dramatic increase of the power conversion efficiency and the cost-effective fabrication processes. The success of this material has been attributed to large absorption coefficient and the exceptional transport properties such as long carrier diffusion length, high carrier mobilities and defect tolerance.”
+[Conclusion] “Together with the renowned photophysical properties of MAPbI3, such as the long carrier diffusion length, low mid-gap trap density, and large absorption coefficient, this finding of high modulation depth, ultrafast response, and low onset field for Wannier-Stark localization highlights the potential of this material in photonic applications.”
+
+Other questions and suggestions:
+1. In this work, the WS localization is created by applying the bias field from the phase-stable THz pulse and can be detected by optical absorption spectra. Is this method generally applicable for single-crystalline and polycrystalline materials?
+
+→ Yes, it could be generally applicable for single-crystalline and polycrystalline materials. Thus, we added this sentence in the conclusion:
+
+“This technique could be generalized for realizing transient Wannier Stark localization in other semiconductor solids in a carefully prepared single-crystalline or a polycrystalline form.”
+
+2. The observed WS step is slightly lower than the expected value. Is it possible that the step is higher than the theoretical value? Can the disorder of the sample be controlled here, and what is the influence of disorder on the experimental results?
+
+→ First, we would like to point out that the predicted position where the WS step occurs depends on the level of theory. If we compare the Fig 3 and Fig 4(c, d), the step occurs at slightly below 2 and 1.9 eV, respectively, and the experimentally observed position was 1.9 eV. The difference in the theoretical approaches to obtain Fig 3 and Fig 4(c,d) is whether the other direction is taken into account (i.e., with (Fig 4(c,d)) and without (Fig 3) the averaging over the disorder). The disorder of the sample could not be controlled experimentally here, but from this theoretical comparison, what one could learn about the influence of disorder on the experimental results would be indeed the position of the WS step (with ~100 meV range). We strengthened this discussion by adding the following to the discussion and conclusion sections:
+
+[Discussion] “This finding is remarkable because it means the two extreme cases – the completely random orientation of a polycrystalline sample and the perfectly oriented single crystal – are expected to produce very similar optical responses. The only slight difference between the two extremes would be a small shift in the photon energy (~100 meV) where the induced transmission turns to the induced absorption and in the transient spectral shape. The two extremes include partial preferential orientations. We also note that the averaging process using only two extreme directions does not contain any material-specific information, which means that one could expect other polycrystalline materials to behave similarly.”
+
+[Conclusion] “The degree of disorder and relative orientation among crystallites may influence the modulation spectral shape slightly, e.g. the position of the photon energy where the induced transmission to induced absorption happens, which might be finely tuned depending on the desired device performance by further systematic studies.”
+
+3. For MAPbI3, transient optical response is in fact dominated by the least dispersive direction of the band structure. Do other polycrystalline materials also have the same feature?
+
+→ Yes, we believe so, because for the larger bandwidth, the field required for WS localization will be larger. This means that the direction with the smallest dispersion will always be where WS
+localizations occur for the smallest field. While we observe the localization along the least dispersive direction, the contributions from the other directions are negligible, since the transmission changes are smaller for fields below the WS threshold. It is indeed what we observe from the theoretical model, including averaging over the arbitrarily oriented crystallites. Regarding this point, we added this sentence in the main text (discussion section):
+
+“We also note that the averaging process using only two extreme directions does not contain any material-specific information, which means that one could expect other polycrystalline materials to behave similarly.”
+
+4. WS ladders and associated phenomena predicted and observed in biased semiconductor superlattices have intrigued scientists for decades (it seems the work of J. Bleuse et al , Phys. Rev. Lett. 60, 220, 1988, should be cited together with [4, 5]). The concept was later introduced and explored also in ultracold atoms ( Phys. Rev. Lett. 76, 4512, 1996) and optical waveguide arrays superimposed with a linear optical potential (Opt. Lett. 23, 1701, 1998; Opt. Lett. 39, 1065, 2014). Since the paper is intended for an interdisciplinary journal like NC, the authors should discuss the broader impact of their work and possible connection to other fields.
+
+→ We thank the reviewer for this very insightful suggestion to position our work in a broader context and for the listed literature. We have, in our revised manuscript, cited and discussed the suggested literature and make a connection in the introduction as follows:
+
+“Following the initial observations in semiconductor superlattices under static bias fields \(^{8-10}\) Wannier-Stark ladders have been proposed and realized in various physical systems featuring wave propagation in the presence of periodic potentials and a homogeneous force. Examples include ultracold atoms in an accelerating 1D standing wave\(^5\), waveguide arrays with linearly varying propagation constants\(^6\), and self-accelerating optical beams in 1D photonic lattice\(^7\). Several fundamental observations and device applications from the Wannier-Stark localization have been focused on statically biased artificial semiconductor superlattices\(^9-12\). However, in natural homogeneous solids, where the periodicity is dictated by the atomic structure, such an extreme state of matter has never been achieved using static biasing. To resolve optical transitions to individual Wannier-Stark states in, e.g., absorption spectra, their energetic spacing needs to be larger than the (total) linewidth \( \Gamma \), i.e., \( \mathrm{eED} > \Gamma \)^{9,10,13} Due to the small lattice constant of bulk crystals and the large linewidth which results from the scattering of electrons with lattice vibrations and other electrons, the requirement \( \mathrm{eED} > \Gamma \) can typically not be fulfilled under stationary external fields below the strength where the dielectric breakdown occurs\(^{11,12}\).”
+Reviewer #3 (Remarks to the Author):
+
+In this manuscript, the authors synthesized a MAPbI3 polycrystalline film and studied ultrafast nonlinear optical responses of the MAPbI3 film by performing THz-pump/NIR to visible-probe spectroscopy and theoretical calculations. They observed a transient absorption change induced by THz pump with a center frequency of 20 THz and assigned its origin to the Wannier-Stark localization. They found that the transient Wannier-Stark localization in a MAPbI3 film can be observed at lower THz field strength than that in a single crystal GaAs, which results from a narrow electronic bandwidth and a large relevant lattice constant of MAPbI3. The finding that its narrow electric bandwidth and large lattice constant make a MAPbI3 film a unique optical nonlinear material would be important for developing novel photonic devices based on halide perovskites. However, the discussions are not enough to guarantee that the observed transient absorption change originates from the Wannier-Stark localization, on which I commented below. Therefore, my opinion is that this manuscript is not suitable for publication in Nature Communications as it stands.
+
+The following points are the reasons why I doubt the interpretation of the data as the Wannier-Stark localization:
+
+On page 4, the authors mentioned that the measured transient absorption change is well explained by a two-band model. However, I question why the higher energy states, such as light and heavy electron states, do not contribute to the optical nonlinear processes. In fact, the previous study [Z. Wei et al., Nat. Commun. 10, 5342 (2019).] reported that light and heavy electron states exist around 2.25 eV and the optical transitions between those states and the band-edge conduction band states significantly contribute to the two-photon absorption processes in a MAPbI3 film. Therefore, I suspect that the observed transient absorption change originates from the Bloch-Siegert shift [E. J. Sie et al., Science 355, 1066 (2017).] in multiple states consisting of the band-edge valence and conduction band states and the higher energy conduction band states. Is it possible for the authors to comment on this?
+
+→ First of all, we appreciate the reviewer’s critical, yet very constructive comments. We also thank the reviewer for raising this possible alternative explanation, based on which we were able to improve our manuscript substantially. Here we clarify the detailed assignment of each spectral component (in our optical response) based on our mechanism (WS localization), which seem inconsistent with other nonlinear optical processes, and strengthen our interpretation as follows:
+
+“The extended structure of the transient spectral response can be understood with the assistance of Figure 2 (c, d). The localized Wannier-Stark states, equally spaced in energy by an amount \( eE_{THz}D \), are depicted in the real-space along the field direction, z, in Fig 2 (c). D is the lattice period unit length and n the index. This space-dependent energy shift results in differentiating the electronic transition energies within the same site (arrow with n =0, Fig 2 (c)) from between different sites (arrows with n =±1, Fig 2 (c)). As the difference in the transition energy with respect to the central spatially-direct (n = 0) transition is ne\( E_{THz}D \), one could assign the induced absorption below the band gap and above 1.9 eV to be n=-1 and n=0 transitions, respectively (Fig 2 (d)). The reduced absorption right above the band gap stems from the spectral transfer from non-perturbed optical transition to red- (n=-1) and blue- (n=0) shifted transitions (Fig 2 (d)). Depending on the strength of \( E_{THz} \) and the degree of localization, |n| > 1 transitions could, in principle, also be observed. In this case (Figure 2(a)), the observed single central step from reduced to increased
+absorption near the center of the band \( E_{pr} = 1.9 \) eV, is a noticeable signature of Stark localization, where the Wannier-Stark states are localized onto one unit cell.
+
+This observed transient response is clearly distinct from the shift of transition energy due to the presence of photon-dressed states\(^{28}\). Photon-dressed states can shift energies in only one direction (mostly blue-shift) with energy orders of magnitude smaller than the bandwidth. Also, the contribution from the possible higher energy bands within our probe photon energy range\(^{29}\) is negligible. Indeed, we neither observe any additional Franz-Keldysh and/or Wannier-Stark response within our probe energy, nor find any decay of the entire signal as a function of the field strength due to the tunneling to higher energy bands at intense field regime. Therefore, we could consider simple two-band systems to understand our experimental demonstration of Wannier-Stark localization in further detail. As will be shown below, the two-band model explains our observations."
+
+Regarding the first point (in slightly more detail), given the presence of the higher band with the energy difference of around 2.25 eV, there are two possibilities of experimental features one could observe in our result.
+
+The first possibility is the case of tunneling to a higher energy band in the presence of strong THz fields. In that case, the photoexcited electrons and holes could tunnel into an energetically higher band and would then not contribute to WS localization in the lowest bands. Also, the signal could possibly decay as a function of the field amplitude for strong fields (since the tunneling rate has an exponential dependence on the field amplitude). However, we do not see indications in the experiment that this is happening to a significant degree.
+
+In the other possibility, where the tunneling does not occur, if WS localization is also not the origin of our experimental observation, then each band would have shown at least Franz Keldysh effect at one around the primary bandgap of 1.6 eV and the other one at around the secondary gap above 2.25 eV (as the TPA paper reports). Since the Franz Keldysh effect appears as an oscillatory feature only near the gap (within 100 meV in probe phonon energy), in that case one would expect two separate Franz Keldysh features - one in the 1.5~1.7 eV range and another at 2.1~2.3 eV, with no response for energies in between (1.7~2.1 eV). In contrast, we find an induced transparency from 1.6 eV all the way up to 1.9 eV without interruption. The reason we did not observe any response in 2.2eV (even in FKE) could be understood from the different transition probability in the one-photon and two-photon transition processes. Our optical probing scheme involves one-photon transition where the response around 2.2eV is much weaker than the case of two-photon transition. Therefore, we could safely rule out the other scenario, too.
+
+Regarding the second point, the Bloch-Siegert shift is typically very small in magnitude < 1ueV and, in exceptional cases at best comparable to the optical Stark shift (~10 meV in the mentioned literature). Also, such a shift happens in only one direction: typically only blue shift (because this effect originates from the state repulsion). However, in our case, we have induced absorption below and above the band gap, which means that both red-shifted and blue-shifted transitions occur simultaneously, and reduced absorption at around the band gap due to the spectral transfer. These features are unique to Wannier Stark localization.
+How much is the spectral width of the THz pump pulses? As the authors stated on page 6, the phonon modes of halide perovskites fall in the low frequency range around several THz. Therefore, if the spectral width is larger than the phonon frequencies, impulsive stimulated Raman scattering should occur. As some of the authors reported, driving the phonon modes leads to the similar transient absorption change albeit in a different crystal structure [Fig. 4a in H. Kim et al., Nat. Commun. 8, 687 (2017)]. Is it possible to discuss the contributions of phonons to the observed signals?
+
+→ The spectral width of the THz pump pulses is ~ 4 THz. We added the spectrum of the THz pulses of the main result (fig 2a) in the supplementary information (fig. S1). For comparison, we also added the Fourier transform of the time profile in fig 2a in the SI (fig. S4).
+
+As evident in this spectrum (fig S4), the main oscillation around time zero is 40 THz, and there is no distinct oscillation below 4 THz except for the slow envelope of the pulse. More importantly, if there is any phonon coherence, we know that the dephasing times of at least 1 and 2 THz modes are 0.3 and 1 ps, respectively, and both are much longer than the duration of the IR pulse and our experimental window. So if that was the case, we should have seen responses after the overlap of IR pulses and the visible probe (after t = 200 fs). However, we do not see any oscillation immediately after that, which indicates no contribution from phonons within the bandwidth. Thus, the impulsive stimulated Raman scattering could be safely ruled out. We added this argument om the main text as follows:
+
+“It is noteworthy that the bandwidth of the THz pulse is ~ 4 THz (< 40 THz modulation, Fig. S4), so that in principle impulsive stimulated Raman excitation of sub-4 THz modes be possible. However, no oscillatory signal was observed after 150 fs, which is much shorter than the dephasing times of reported phonon modes with frequency up to 4 THz. Therefore, any possibility of coherent phonon contribution to the temporal modulation can be ruled out.”
+
+On page 13, the authors mentioned that the crystallites are arbitrarily oriented and the theoretical calculations were performed based on this assumption. Is there any possibility that some preferential orientations of the crystallites exist? Do the authors experimentally verify the assumption from, for example, XRD spectra? The detailed sample properties should be described in the Support Information, because the sample is not single crystal but complicated polycrystalline film.
+
+→ We understand and appreciate the reviewer’s concern. However, any possibility of preferential orientations of the crystallites does not make any critical effect, as the two extreme cases – completely arbitrary orientation and perfectly single orientation – produce more or less the same THz induced optical spectra. From this theoretical approach, what we learn is that, no matter how much preferential orientation we have (from zero to complete), the contribution from the least dispersive direction dominates the optical response. Although we indeed can not completely rule out the possibility of partial preferential orientation, this possibility does not affect our conclusion. We highlight the point by adding these sentences in the main text:
+
+“The results of Fig. 4(a, b) suggest that, for the randomly oriented crystallites in the film, the overall response is dominated by the response originating from the band dispersion in the \( \vec{T}Z \) direction. This reasoning is substantiated by the averaged field-dependent absorption changes calculated for both a static and a THz field shown in Figs. 4(c) and (d), respectively. This finding is remarkable because it means the two extreme cases – the completely random orientation of a polycrystalline
+sample and the perfectly oriented single crystal – are expected to produce very similar optical responses. The only slight difference between the two extremes would be a small shift in the photon energy (~100 meV) where the induced transmission turns to the induced absorption and in the transient spectral shape. The two extremes include partial preferential orientations.”
+
+Regarding our sample, we added the SEM image of the polycrystalline perovskite MAPbI3 film spin-coated on TOPAS® substrate in the supplementary information (fig S2). We did not measure the XRD data of the measured sample, but we do have the XRD spectra of the perovskite polycrystalline film prepared in the exactly same way [fig S15 of J. Phys. Chem. Lett. 2015, 6, 4991]. There, one could find not only (hh0) but also other Bragg peaks. Besides, even in the case of a complete preferential orientation of a surface, still the most critical orientation is the relative angle between the [001] direction of each crystallite and the THz field polarization, which is not possible to define. The orientations of [001] direction of each crystallite on top of a completely disordered substrate can still be assumed to be arbitrarily oriented and difficult to measure with the currently available resolution of X-ray microscopy (~500 nm in J. Phys. Chem. C. 2017, 121, 7596).
+
+On page 15, the authors claimed that the calculation result shown as a black curve in Fig. 4a is in good agreement with experimental results at high field amplitudes in Fig. 4b. However, the spectral oscillations around 2 eV can be seen only in the experimental results, not in the calculation. In addition, a bleaching signal around 2.2 eV which is expected from the calculation does not appear in the experimental results. What are the reasons for such disagreements?
+
+→ We thank the reviewer for thoroughly examining our results. Yes, the first point, the spectral oscillations around 2 eV, is indeed something we have tried to understand. The oscillation (or repeated peaks) has an interval of 80–100 meV regardless of the THz field strength. Interestingly this interval matches well with our THz photon energy (83 meV). The oscillations are quite stable as function of the field amplitude, however, they do not correspond to Franz-Keldysh and neither to WS. To analyze the possible origin of these oscillations, we did perform additional model calculations. To that end, we, in particular, modified the k/energy dependence of the interband dipole and also considered a complex interband dipole with a symmetric real and an anti-symmetric imaginary part (it was recently shown that such an interband dipole with such a k-dependence gives rise to SHG in two-band models). With such phenomenological model extensions, we do obtain signatures having similarities with THz sidebands in the optical spectra, see Fig. S9 in the supplementary information. However, the obtained results are quite different from the oscillations observed in the experiment and the model assumptions required to obtain them are rather unrealistic.
+
+Regarding the second point, in a 1D model with WS localization, we remove absorption from the band edges, and this concentrates in the band center. Since we average over systems of different bandwidths and lattice constants, the critical field where the transition to WS takes places and also the position of the band center is not fixed but depends on the individual case, i.e., differs for the different f’s. As a result, in Fig. 4(c) and 4(d) the transitions from blue- to red- shift appear at higher energies with increasing field amplitude, since with increasing amplitude also systems with larger bandwidth, i.e., larger f, enter the WS regime. Therefore, with any two-band model one should always see some bleaching near the upper band edge due to the concentration, or in other words, a shift of the oscillator strength towards the center of the band.
+In any case, the precision of our simple modeling involving some fitting of DFT results with few parameters gets more inaccurate with increasing photon energies.
+
+To clarify this, we add an explanation in the main text as follows:
+
+“The averaged graph is in good agreement with the differential spectra at high field amplitudes given very few parameters to describe the entire contributions from complicated actual band structure (i.e. two extreme bandwidths, lattice constants, and linear interpolation of them). The prediction of 1.9 eV, almost exactly where the change from bleaching to induced absorption is observed in the experiment (Fig 4(b), upper curves) is remarkable. A few minor features including the shape at higher photon energy could be improved by modifying the model band curve and oscillations around 2 eV in Fig 4(b) need further studies (Fig S9). More importantly, this position of 1.9eV is very close to the center of the band structure for the \( \overline{TZ} \) direction, 2 eV as the single direction model indicated above.”
+
+I suggest some more points for improving manuscript:
+On page 8, why did the authors consider the band gap energy of 2D perovskites with l =2, not l =1, 3 or 4?
+
+→ It is because of the doubling of the unit cell in the tetragonal phase compared to the cubic phase. It means the double layers (l=2) Pb-I octahedra is the repeating unit, and in turn the spatial range of confinement. That was the reason we particularly compared the probe energy where one could observe the abrupt change of transmittance and the band gap energy of 2D perovskite with l=2. We realized it could be confusing without further clarification. As such, we modified the corresponding sentence in the discussion section as following:
+
+“In the case of (BA)_2(MA)_{1-x}PbIx_{3+1} perovskites, where the PbI_6 octahedral network forms a double layer (l = 2), the same periodicity of the sample along the c axis, the optical band gap is ~2.1 eV, which is comparable to the observed 1.9 eV.”
+
+With regard to Ref. 25, the authors should cite the published version [J.-C. Blancon et al., Nat. Commun. 9, 2254 (2018).], not that in arXiv.
+
+→ We cited this reference accordingly (highlighted).
+Reviewers' comments:
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have addressed all my concerns/comments in the revised manuscript. However, there are two important concerns from other reviewers which are very important. One is the role of the polycrystallinity of the sample. The only way to address this is to perform measurements on single crystals or two have extensive structural characterization of the sample, which are out of the scope of current work. Publication of this manuscript will inspire future work in that direction, I reckon.
+
+The second concern, as reviewer 3 rightly points out, is with regards to possible alternative explanations to the presented experimental results. The authors provide a convincing arguments to discount other possibilities. Some of the explanations provided in the response to reviewer 3 were not included in the manuscript, for example, on why Bloch-Siegert is not a viable explanation. It may be very instructional to expand on this discussion in the main manuscript.
+
+Apart from these very minor comments, the manuscript is suitable for publication in Nature Communications.
+
+Reviewer #2 (Remarks to the Author):
+
+I have read through authors' response, and the revised manuscript.
+I'm okay with authors' response to my comments, and thus I don't have further objection to accept this manuscript for publication in NC.
+
+Reviewer #3 (Remarks to the Author):
+
+I confirmed the replies from the authors, the revised manuscript, and the supporting information. I appreciate the efforts of the authors to answer my questions and comments. However, I still do not think that it is convincing that the origin of the observed nonlinear responses can be attributed to the Wannier-Stark localization. As the authors replied, the theoretical curves shown in Fig. 4a do not fully reproduce the experimental results in Fig. 4b partly because the theoretical model is too simple. Therefore, to make the interpretation as the Wannier-Stark localization solid, it is important to rule out the other possible origins. Although the other possibilities are discussed in the reply letter and the revised manuscript, I am not satisfied with some of those discussions. Thus, I do not recommend publication of the manuscript for Nature Communications as it stands. I suggest that the following points should be considered.
+
+1. On page 9 in the main manuscript, the authors mentioned that the two induced absorption signals shown in Fig. 2d can be assign to n = -1 and n = 0 transitions, whose difference in the transition energy is eE<sub>THz</sub>D partly because the theoretical model is too simple. How much is the value of eE<sub>THz</sub>D? In addition, I cannot read from Fig. 2d what the n = -1 and n = 0 transition energies are.
+
+2. On page 9 in the main manuscript, the authors stated “Photon-dressed states can shift energies in only one direction (mostly blue-shift) ...” However, I do not agree with the statement. If the higher energy levels exist, the Autler-Townes effect can shift the band-edge transitions in both directions, i.e. blue- and red- shifts, as reported in [C.-K. Yong et al. Nat. Mater. 18, 1065–1070 (2019).]. In addition, [G. Yumoto et al. Nat. Commun. 12, 3026 (2021).] recently reported that three-level Autler-Townes effect indeed occurs in halide perovskites. How do the authors comment on the possibility that the Autler-Townes effect can be the origin of the observed optical nonlinear responses?
+
+3. On page 10 in the main manuscript, the authors stated “..., nor find any decay of the entire signal as a function of the field strength due to the tunneling to higher energy bands at intense field regime.” I agree to the authors that the real excitation of carriers cannot explain the data due to the absence of the signal decay. However, the virtual population generated only under the THz-field irradiation should induce additional transitions for probe pulses, which would result in induced absorption signals. Is it possible to comment on this?
+Reviewer #1 (Remarks to the Author):
+
+The authors have addressed all my concerns/comments in the revised manuscript. However, there are two important concerns from other reviewers which are very important. One is the role of the polycrystallinity of the sample. The only way to address this is to perform measurements on single crystals or two have extensive structural characterization of the sample, which are out of the scope of current work. Publication of this manuscript will inspire future work in that direction, I reckon.
+
+The second concern, as reviewer 3 rightly points out, is with regards to possible alternative explanations to the presented experimental results. The authors provide a convincing arguments to discount other possibilities. Some of the explanations provided in the response to reviewer 3 were not included in the manuscript, for example, on why Bloch-Siegert is not a viable explanation. It may be very instructional to expand on this discussion in the main manuscript.
+
+Apart from these very minor comments, the manuscript is suitable for publication in Nature Communications.
+
+→ First of all, we appreciate the reviewer for very encouraging and constructive comments. We agree with the reviewer’s suggestion, and thus, we explicitly include a discussion explaining why these scenarios can be ruled out in this revised manuscript as follows:
+
+“It is important to distinguish this transient Wannier Stark localization from the optical Stark-type effects such as the Autler-Townes effect and the Bloch-Siegert shift. In general, an external electric field affects the optical properties of a semiconductor in two ways: there are spectral and kinetic aspects. Spectral aspects refer to energy shifts and broadenings that arise from mixing two states by the external optical field. The mixing of the wavefunctions results in dressed states and leads to the Stark-type shifts. The magnitude of such shifts increases with the amplitude of the incident field and the interband dipole matrix, but decreases with increasing detuning between the light frequency and the transition frequency. On the other hand, kinetic aspects represent the evolution of the particle distributions in the renormalized states driven by the external field, which is called “intraband acceleration”. This intraband acceleration leads to the Franz Keldysh effect at a moderate field strength and eventually Wannier-Stark localization in the strong-field regime.
+
+Each of these two contributions can be straightforwardly separated in the semiconductor Bloch equations (SBE). Specifically, the third and second terms on the right-hand side of the Eq (1) represent the spectral (optical Stark-type effects) and the kinetic (Wannier Stark localization) aspects, respectively. One can thus directly compare each contribution to the differential optical response. As evident from Supplementary Fig. 6, the THz-induced optical Stark effect is shown to be much weaker (on the order of a few meV) compared to the shifts arising from the Wannier Stark localization which corresponds to approximately half the band width (several 100 meV). Therefore, we conclude that the observed transient response is mainly contributed from the Wannier Stark localization.”
+
+Reviewer #2 (Remarks to the Author):
+I have read through authors' response, and the revised manuscript. I'm okay with authors' response to my comments, and thus I don't have further objection to accept this manuscript for publication in NC.
+
+→ We thank the reviewer very much for the positive comments.
+
+Reviewer #3 (Remarks to the Author):
+
+I confirmed the replies from the authors, the revised manuscript, and the supporting information. I appreciate the efforts of the authors to answer my questions and comments. However, I still do not think that it is convincing that the origin of the observed nonlinear responses can be attributed to the Wannier-Stark localization. As the authors replied, the theoretical curves shown in Fig. 4a do not fully reproduce the experimental results in Fig. 4b partly because the theoretical model is too simple. Therefore, to make the interpretation as the Wannier-Stark localization solid, it is important to rule out the other possible origins. Although the other possibilities are discussed in the reply letter and the revised manuscript, I am not satisfied with some of those discussions. Thus, I do not recommend publication of the manuscript for Nature Communications as it stands. I suggest that the following points should be considered.
+
+→ We appreciate the reviewer for the thorough review and for giving us the opportunity to improve our manuscript even further. We apologize for apparently underestimating this point: we mistakenly felt it inappropriate to devote a substantial part of the discussion in the manuscript to this point. Rather, we tried to convince the reviewer in the rebuttal. However, we take this concern more carefully into account this time, and explicitly include a discussion explaining what are the similarities and differences between these optical Stark-type effects (i.e. Autler-Townes effects and Bloch-Siegert effects) in a theoretical context and how exactly each effect contributes to the experimentally observed optical response. This was also suggested by reviewer #1.
+
+In the strong field regime (like our experiment), the Wannier-Stark localization (WSL) shifts the onset of the energy gap by approximately half the bandwidth, i.e., several hundred meV. Since the THz frequency is much lower than the interband transition frequencies, the optical Stark shift can be described perturbatively and is determined by the square of the Rabi frequency divided by the detuning. For a maximal field amplitude of 10 MV/cm and the interband dipole matrix element, the resulting Stark shifts are on the order of just a few meV, which is orders of magnitude smaller than the shifts arising from the WSL. These arguments are in agreement with and supported by new simulations in which we artificially neglected the intraband acceleration in order to study Stark-type shifts separately (see Supplementary Figure 6 and Supplementary Method).
+
+Therefore, we could further confirm that the Wannier-Stark localization (originating from the intraband acceleration driven by the field) dominates the observed differential transmission. In contrast, the optical Stark-type effects (which leads to the spectral shift of each k-state of the band) have a negligible amplitude compared to the WSL.
+
+We thank the reviewer for the opportunity to revisit the fundamentals and strengthen our interpretation. Further details are covered in our reply to comment #2 below.
+1. On page 9 in the main manuscript, the authors mentioned that the two induced absorption signals shown in Fig. 2d can be assign to n = -1 and n = 0 transitions, whose difference in the transition energy is eE_{THz}D. How much is the value of eE_{THz}D? In addition, I cannot read from Fig. 2d what the n = -1 and n = 0 transition energies are.
+
+→ We agree with the reviewer that the value of energy distance eE_{THz}D is only inferred, and the necessary numbers appear in a rather scattered way (e.g. E_{THz} = 6 MV/cm in page 11, and D = the largest lattice constant along the c axis, 12.5 Å, in page 15). Therefore, we added the figure caption of figure 2d the following sentence:
+
+"In case of E_{THz} = 6 MV/cm in considering the lattice constant D of 12.5 Å, \( \Delta E_{WSL} = eE_{THz}D \) is estimated to be 750 meV, consistent with the spectrum showing that the absorption band of n = -1 and n = 0 are approximately 750 meV apart."
+
+Indeed, the n=-1 and n=0 transitions have certain energy ranges rather than a single transition energy (i.e. two-level systems) since these are “interband” transitions among mini-bands. So the range of transition energies for n=-1 is 1.2~1.62eV, and that for n=0 is 1.95~2.38 eV, and these transition energy ranges are approximately 750 meV apart (figure 2d).
+
+2. On page 9 in the main manuscript, the authors stated “Photon-dressed states can shift energies in only one direction (mostly blue-shift) ...” However, I do not agree with the statement. If the higher energy levels exist, the Autler-Townes effect can shift the band-edge transitions in both directions, i.e. blue- and red- shifts, as reported in [C.-K. Yong et al. Nat. Mater. 18, 1065–1070 (2019).]. In addition, [G. Yumoto et al. Nat. Commun. 12, 3026 (2021).] recently reported that three-level Autler-Townes effect indeed occurs in halide perovskites. How do the authors comment on the possibility that the Autler-Townes effect can be the origin of the observed optical nonlinear responses?
+
+→ We agree with the reviewer that the optical Stark effect (i.e. the Autler-Townes effect) in fact leads to energy splitting. This initially two-level system with energies of \( \epsilon_1 \) and \( \epsilon_2 \) undergoes light-field induced level splitting to \( \epsilon_1 + \frac{\nu}{2} \pm \frac{1}{2} \sqrt{\nu^2 + h^2 \omega_R^2} \) and \( \epsilon_2 - \frac{\nu}{2} \pm \frac{1}{2} \sqrt{\nu^2 + h^2 \omega_R^2} \) respectively, where \( \nu \) is detuning (\( \epsilon_2 - \epsilon_1 - \hbar \omega_{laser} \)) and \( \omega_R \) is the Rabi frequency. The transitions among these split states are observed from singlet (without optical field) to triplet (“Mollow triplet”, with optical field). In case of weak excitation and finite detuning (here we make a Taylor expansion of the square roots, so it’s a perturbative result), the upper sideband \( \epsilon_2 - \epsilon_1 + \frac{1}{2} \frac{\omega_R^2}{\nu} \) is closest to the original resonance. This transition is the one that is observed in the experiment as a small blueshift depending on the intensity of the light field (and the interband dipole matrix element), if the frequency of the exciting light is smaller than the transition frequency. Although by changing the detuning (frequency difference between the light frequency and the transition frequency) it is possible to observe the peak splitting as the reviewer has pointed out, the blue shift is the common signature for large detuning (such as our experiment - for THz field the detuning to an optical transition is very large). [H. Haug & S. W. Koch, “Quantum Theory of the Optical and Electronic Properties of Semiconductors”]
+However, more fundamentally, in a semiconductor, unlike two-level systems (or multi-levels without k-space dispersion), an external field has pronounced influence on the relative motion of optically generated electron-hole pair, going well beyond the field-induced shifts of excitonic resonance. And this is what we demonstrate by separating the contribution of the optical Stark effect and the intraband acceleration: WSL is by far the dominating contribution to the observed differential optical response and produces the spectral shape in very good agreement. In contrast, the optical Stark-type contributions (Autler-Townes effect from the corotating field and Bloch Siegert shift from the counterrotating field) are almost negligible and, moreover, do not agree with the observed spectral shape. Therefore, we added the following paragraph and the supplementary figure 6 showing this additional result:
+
+“It is important to distinguish this transient Wannier Stark localization from the optical Stark-type effects such as the Autler-Townes effect and the Bloch-Siegert shift. In general, an external electric field affects the optical properties of a semiconductor in two ways: there are spectral and kinetic aspects. Spectral aspects refer to energy shifts and broadenings that arise from mixing two states by the external optical field. The mixing of the wavefunctions results in dressed states and leads to the Stark-type shifts. The magnitude of such shifts increases with the amplitude of the incident field and the interband dipole matrix, but decreases with increasing detuning between the light frequency and the transition frequency. On the other hand, kinetic aspects represent the evolution of the particle distributions in the renormalized states driven by the external field, which is called “intraband acceleration”. This intraband acceleration leads to the Franz Keldysh effect at a moderate field strength and eventually Wannier-Stark localization in the strong-field regime.
+
+Each of these two contributions can be straightforwardly separated in the semiconductor Bloch equations (SBE). Specifically, the third and second terms on the right-hand side of the Eq (1) represent the spectral (optical Stark-type effects) and the kinetic (Wannier Stark localization) aspects, respectively. One can thus directly compare each contribution to the differential optical response. As evident from Supplementary Fig. 6, the THz-induced optical Stark effect is shown to be much weaker (on the order of a few meV) compared to the shifts arising from the Wannier Stark localization which corresponds to approximately half the band width (several 100 meV). Therefore, we conclude that the observed transient response is mainly contributed from the Wannier Stark localization.”
+
+3. On page 10 in the main manuscript, the authors stated “…, nor find any decay of the entire signal as a function of the field strength due to the tunneling to higher energy bands at intense field regime.” I agree to the authors that the real excitation of carriers cannot explain the data due to the absence of the signal decay. However, the virtual population generated only under the THz-field irradiation should induce additional transitions for probe pulses, which would result in induced absorption signals. Is it possible to comment on this?
+
+→The original manuscript contained a paragraph on the possible carrier generation by THz (multi-photon processes and impact ionization) in our method section and also the Supplementary figure:
+
+“In this linear-optical regime, we thus neglect carrier generation by multi-photon processes and impact ionization, which does not seem to play a dominant role in the measured transient spectra. Interband tunneling by the THz field could lead to bleaching at later delay times and the slightly
+asymmetric spectral evolution with respect to \( \tau = 0 \) (Fig. 2(A)) (corresponding to the trailing edge of the THz transient in the Supplementary Material of ref [20]). However, significant carrier multiplication does not occur within this experimental window, as shown in Supplementary Fig. 10."
+
+However, in addition to that, we have performed new simulations that include the possible effects of THz-induced generation of virtual and real carriers that may arise from multi-photon transitions by solving a full set of semiconductor Bloch equations, in which the THz field is treated non-perturbatively, and the weak optical probe pulse is considered linearly. The result is shown in the supplementary fig 6, indicating that for the perovskite, the high-order/multi-photon interband effects are basically negligible. Therefore, our simplified model defined by Eq. (1) in the main text captures all the relevant physics. Accordingly, we have added the following statement in the main text:
+
+"Furthermore, to analyze the possible effects of THz-induced generation of virtual and real carriers that may arise from multi-photon transitions, we solve a full set of SBE (Supplementary Methods) in which the THz field is included non-perturbatively and the weak optical probe pulse is considered linearly. The results (Supplementary Figure 6) show that for the considered field amplitudes, such higher-order interband effects arising from the THz fields are negligible, as the results from the full equations are very close to the ones obtained from the simplified Eq. (1)."
+REVIEWERS' COMMENTS
+
+Reviewer #3 (Remarks to the Author):
+
+I appreciate the efforts of the authors to answer my questions and comments. The authors have cleared up my concerns about the interpretation of the observed nonlinear responses by performing new calculations (Supplementary Figure 6) and ruling out the possible interpretations other than the Wannier-Stark localization. Therefore, now I think the manuscript is suitable to publish in Nature Communications.
+Reviewer #3 (Remarks to the Author):
+
+I appreciate the efforts of the authors to answer my questions and comments. The authors have cleared up my concerns about the interpretation of the observed nonlinear responses by performing new calculations (Supplementary Figure 6) and ruling out the possible interpretations other than the Wannier-Stark localization. Therefore, now I think the manuscript is suitable to publish in Nature Communications.
+
+→ We thank the reviewer very much for the thorough reviews and constructive comments.

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+Low-field Onset of Wannier-Stark Localization in a Polycrystalline Hybrid Organic Inorganic Perovskite
+
+Daniel Berghoff
+Paderborn University
+Johannes Bühler
+University of Konstanz
+Mischa Bonn
+Max Planck Institute for Polymer Research
+Alfred Leitenstorfer
+University of Konstanz
+Torsten Meier
+University of Paderborn   https://orcid.org/0000-0001-8864-2072
+Heejae Kim (kim@mpip-mainz.mpg.de)
+Max Planck Institute for Polymer Research
+
+Article
+
+Keywords: Wannier-Stark localization, Electron confinement, Ultrafast Biasing, Optical modulation, Hybrid perovskites
+
+Posted Date: April 8th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-386040/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on September 29th, 2021. See the published version at https://doi.org/10.1038/s41467-021-26021-4.
+Low-field Onset of Wannier-Stark Localization in a Polycrystalline Hybrid Organic Inorganic Perovskite
+
+Daniel Berghoff*1, Johannes Bühler*2, Mischa Bonn3, Alfred Leitenstorfer2, Torsten Meier*1, Heejae Kim*3
+
+1 Department of Physics, Paderborn University, D-33098 Paderborn, Germany
+
+2 Department of Physics and Center for Applied Photonics, University of Konstanz, D-78457 Konstanz, Germany
+
+3 Department of Molecular Spectroscopy, Max Planck Institute for Polymer Research, D-55128 Mainz, Germany
+
+KEYWORDS
+
+Wannier-Stark localization, Electron confinement, Ultrafast Biasing, Optical modulation, Hybrid perovskites
+ABSTRACT
+
+Control over light propagation in a material by applying external fields is at the heart of photonic applications. Here, we demonstrate ultrafast modulation of the optical properties in the room temperature polycrystalline MAPbI3 perovskite using phase-stable terahertz pulses, centered at 20 THz. The biasing field from the THz pulse creates extreme localization of electronic states in the \( ab \) plane – Wannier-Stark localization. This quasi-instantaneous reduction of dimensionality (from 3D to 2D) causes a marked change in the absorption shape, enabling the modulation depth to be tens of percent at moderate field strengths (3 MV/cm). The notably low-field onset results from a narrow electronic bandwidth, a large relevant lattice constant, and the coincidence of the two along the same direction in this tetragonal perovskite. We show that the transient optical response is in fact dominated by the least dispersive direction of the electronic band structure, facilitating a substantial modulation despite the arbitrary arrangement of the individual crystallites. The demonstration of THz-field-induced optical modulation in a solution-processed, disordered, and polycrystalline material is of substantial potential significance for novel photonic applications.
+
+Introduction
+
+The intriguing properties of electrons in periodic potentials in the presence of strong external electric fields are highly relevant for photonic applications, including optical modulators, optical switches, and optical signal processing. Drastic changes in optical properties can be achieved via localization of electronic states using externally applied fields. In the presence of strong external electric fields \( E \), the continuum of electronic energy bands splits into a series of discrete levels in the direction of the field\(^1\), and the corresponding wave functions are confined on a length scale given by \( \Delta/(eE) \), where \( \Delta \) is the energetic width of the electronic band in the absence of biasing.
+These localized states, the Wannier-Stark states\(^{2,3}\), are equally spaced both in energy by an amount \(eED\), and in space by the lattice period \(D\). Since a spatial separation of \(nD\) lattice periods results in an energy shift of \(neED\) with respect to the central spatially-direct (\(n = 0\)) transition, this Wannier-Stark localization leads to strong spectral modulation of the interband absorption continuum below and above the optical band gap.
+
+The quantum confinement induced by external fields is an extreme state of matter and has never been achieved under static biasing in natural solids but only in artificial superlattices\(^{4-8}\). So far, only one natural solid, a single crystal GaAs\(^{8}\) has allowed for achieving the Wannier-Stark localization transiently by virtue of the recent availability of extremely intense and phase-stable pulses of multi-terahertz radiation\(^{9,10}\). The ultrafast biasing fields could reach amplitudes up to several tens of MV/cm\(^{9,10}\), i.e., field strengths comparable to the interatomic fields. For GaAs, an optimally oriented single crystal was required to observe Wannier-Stark localization with the required field strengths exceeding 10 MV/cm\(^{8}\).
+
+Here, we demonstrate the transient Wannier-Stark localization at a substantially lower field strength in a disordered, solution-processed, polycrystalline film of methylammonium lead iodide perovskite (MAPbI\(_3\), Fig. 1(a)). Already at relatively modest field strengths, the thin film's optical transmission is modified by tens of percent. To resolve optical transitions to individual Wannier-Stark states in, e.g., absorption spectra, their energetic spacing needs to be larger than the (total) linewidth \(\Gamma\), i.e., \(eED > \Gamma\) \(^{4,5,11}\) Due to the small lattice constant of bulk crystals and the large linewidth which results from the scattering of electrons with lattice vibrations and other electrons, the requirement \(eED > \Gamma\) can typically not be fulfilled under stationary external fields below the strength where the dielectric breakdown occurs\(^{6,7}\). At room temperature, however, this material exhibits a tetragonal structure with lattice parameters of \(a = 8.8\) Å and \(c = 12.5\) Å by the expansion
+of the cubic perovskite unit cell \(^{12,13}\). The periodicities are nearly twice as large as the lattice parameter \(a = 5.6\) Å of cubic GaAs\(^8\).
+
+We will show that the large relevant lattice constant (Fig. 1(a)), the small width of electronic energy bands (Fig. 1(b)), and the coincidence of these two along the same high-symmetry direction lead to Stark localization in this organic perovskite at field amplitudes as low as 3 MV/cm, i.e., at a fraction of the field strength required to enter this regime in optimally oriented, single-crystalline GaAs. Moreover, the measured differential spectra containing the overall effects from arbitrarily oriented microcrystals are qualitatively well-described by a two-band model with a cosine band structure. By considering different orientations of the microcrystals in our simulations, we demonstrate that the contribution from the direction with the largest periodicity, i.e., the \(\overline{\Gamma Z}\) direction \(c = 12.5\) Å, strongly dominates the transient changes of the optical response. These findings, together with its renowned characteristics, make MAPbI\(_3\) a strong candidate for cost-effective, efficient, fast, and sensitive optical modulator materials.
+Figure 1. Experimental scheme and properties of MAPbI3 perovskite (a) THz pulse geometry with a tetragonal unit cell (black rectangular cuboid) of MAPbI3. (dark grey: Pb, purple: I, brown: C, light blue: N, light pink: H) The THz biasing along the c axis of a crystallite is depicted. (b) Simplified electronic band structure of MAPbI3 in the tetragonal phase along the directions \( \Gamma(0,0,0) \rightarrow Z(0,0,0.5) \) and \( \Gamma(0,0,0) \rightarrow A(0.5,0.5,0.5) \). The bandwidths and the lattice parameters are used from [Ref 12]. (c) Optical absorption spectrum of MAPbI3 in the spectral range of the probe pulses.
+
+Results and Discussion
+
+Experimental observation of Wannier-Stark Localization
+
+For applying the strong transient bias, non-resonant in energy with any of the optical phonons and electronic transitions, we employ phase-stable multi-cycle optical pulses with a center frequency of 20 THz. The pump pulse is generated using a difference-frequency generation
+scheme in GaSe\(^{9,10}\). For comparison, the MAPbI\(_3\) perovskite has a direct bandgap of \(E_{gap} = 1.62\) eV (390 THz, Fig. 1(c)) at room temperature. The phonon modes of Pb-I inorganic sublattice are below 10 THz and methylammonium organic molecular vibrations above 26 THz\(^{14}\). Due to the presence of the organic cation with a low rotational barrier\(^{15}\), the crystal shows some degree of disorder at elevated temperature and a less pronounced periodicity compared to all-inorganic perovskites\(^{15,16}\). The sample is a polycrystalline film with a thickness of \(\sim 300\) nm spin-coated\(^{17,18}\) on a cyclic olefin/ethylene copolymer substrate (TOPAS\textregistered)\(^{19}\). The differential transmission induced by the external electric field transient is probed by near-IR and visible probe pulses, with spectra covering broad interband electronic transition energies between 1.4 eV and 2.4 eV (see Fig. S1). The duration of these probe laser pulses is 7 fs, which is significantly shorter than the half-cycle period of the THz pump transients of 25 fs. Details of the experimental settings are described in the Method section and Ref[8].
+
+Fig. 2(a) shows the differential transmission \(\Delta T/T\) upon applying the THz biasing as a function of delay time between the pump and probe pulses. The peak field strength of the THz pump pulses is 6.1 MV/cm. As expected for the non-resonant THz pulse, the optical response of the material is instantaneous and peaks when the THz field strength is maximal. The modulation occurs at twice the frequency of the THz pulse (Fig. 2(b)), since the measured differential transmission is at least a third-order nonlinear process\(^{20}\). In such a centrosymmetric crystal as the room-temperature tetragonal phase of perovskite MAPbI\(_3\)^{21}, no contribution from the electro-optic effect is expected which is linear in the electric bias field. The clear temporal modulation of differential transmission appears at high fields, -100 < \(\tau\) < 100 fs, as the strong \(E\) field shortens the interband dephasing time in the vicinity of the bandgap to be comparable to the half-cycle period of 25 fs of the THz
+transient. Thus, the precise arrival time of the probe pulse exciting the interband polarization was resolved within the dephasing time.
+
+More importantly, two distinct regimes can be identified in the time-resolved transient spectrum (Fig. 2(a)). For relatively weak fields, \( E < 3 \) MV, for \( \tau < -100 \) fs, an induced absorption (blue, \( \Delta T/T < 0 \)) right below and an induced transmission (red, \( \Delta T/T > 0 \)) right above the bandgap of \( E_{gap} = 1.62 \) eV are observed. The second regime is apparent for field strengths \( E > 3 \) MV/cm, occurring between delay times -100 \( < \tau < 100 \) fs (Fig. 2(b)). Here, the maximum modulation depth becomes as large as 38 % at the probe energy of \( E_{pr} = 1.7 \) eV (Fig. 2(a) and Fig. S2). Also, the transient response covers a significantly extended spectral range, compared to the moderate field regime. The induced transmission (red) above the bandgap now reaches up to \( E_{pr} = 1.9 \) eV, where it abruptly switches to induced absorption (blue, \( \Delta T/T < 0 \)). This negative region of \( \Delta T/T < 0 \) persists at probe energies all the way up to \( E_{pr} = 2.4 \) eV. This one central step from reduced to increased absorption near the center of the band \( E_{pr} = 2 \) eV, is a noticeable signature of Stark localization, where the Wannier-Stark states are localized onto one unit cell.
+
+![Experimental observation of the transient Wannier Stark localization and the visualized diagram](page_158_1042_1267_312.png)
+
+Figure 2. Experimental observation of the transient Wannier Stark localization and the visualized diagram (a) Experimental differential transmission spectra on a polycrystalline film of
+MAPbI₃ perovskite at room temperature, as a function of delay time of probe pulses after THz pump pulses. The THz pulses have a peak field strength of 6.1 MV/cm and a center frequency of 20 THz; the probe pulses have photon energy of 1.4 ~ 2.4 eV. (b) Temporal profile of the applied THz bias transient. (c) Schematic picture of Wannier Stark localization. In the presence of strong external fields along the c axis, electronic states (orange: conduction band, blue: valence band) are localized to a few layers of \( ab \) plane, and energetically separated by \( \Delta E_{WSL} = eE_{THz}c \) between adjacent lattice sites. Black arrows depict the interband transitions within the same site (\( n = 0 \)) and between different sites (\( n = \pm 1 \)). (d) The absorbance with and without the external transient biasing. The Wannier-Stark localization effectively reduces the 3D electronic structure into 2D layered structure along the \( ab \) plane, as depicted in blue together with the simplified 3D structure.
+
+By driving the 3-dimensional (3D) system into Wannier-Stark localization, i.e., localizing it in the field direction, we transiently create an effectively 2D electronic system (Fig. 2(c, d)). Given the unit cell doubling, this optically prepared transient 2D system perpendicular to the c axis may be directly compared to the physically isolated double-layer structure of PbI₆ octahedra. In such 2D perovskites as (BA)₂(MA)₁₋ₓPbI₃ₓI₃⁺₁ perovskites²², the inorganic layers (perpendicular to the c axis in 3D equivalence) are separated by bulky organic layers²³. The bandgap of the 2D quantum well perovskites is widened due to the bandwidth narrowing (mainly due to the zero dispersion along the vertical direction) compared to 3D perovskite²⁴. In the case of (BA)₂(MA)₁₋ₓPbI₃ₓI₃⁺₁ perovskites, where the PbI₆ octahedral network forms a double layer (\( l = 2 \)), the optical band gap is ~2.1 eV, which is comparable to the observed 1.9 eV²⁵. It is noteworthy that the observed Wannier-Stark step at \( E_{pr} = 1.9 \) eV under THz fields is slightly lower than the expected value under static fields due to the spectral broadening induced by the THz modulation, as will be discussed
+below. Therefore, the abrupt shift of the absorption edge from \( E_{pr} = 1.6 \) eV to 1.9 eV at high transient fields (Fig. 2(d)) could be attributed to the transfer of spectral weight from \( \alpha(E_{g,3D} < E_{pr} < E_{g,2D}) \) to \( \alpha(E_{g,2D} < E_{pr}) \). Such a THz-induced reduction of dimensionality from a 3D to a 2D system could enable new applications in both transport and optoelectronics due to the relatively easy access to that regime in these hybrid perovskite materials.
+
+*Simulations considering one orientation*
+
+To capture the essential ingredients responsible for the experimental observations, we carry out theoretical calculations based on different models of increasing complexity. We start with considering perfect alignment of the THz field with the direction along which the joint bandwidth of the highest valence and the lowest conduction band is narrowest. For the case of the tetragonal MAPbI$_3$ perovskite, the narrowest joint bandwidth, \( \Delta_{\overline{\Gamma}Z} = 0.75 \) eV, is along the \( \overline{\Gamma}Z \) direction (Fig. 1(b))$^{12}$. We thus take into account two one-dimensional bands, i.e., one valence and one conduction band with a cosine-like (tight-binding) band structure and the bandgap of 1.62 eV. Thus, the energy difference for interband transitions is taken as \( E_{cv}(k) = 1.62 \) eV + (\( \Delta_{\overline{\Gamma}Z}/2 \))(1 - cos(g(k, \( a^* \))\( ka^* \))) (see Methods section for details of the function g(k,\( a^* \))). For this model, the spectra are obtained by numerically solving the semiconductor Bloch equations $^{26-28}$, as described in the Methods section.
+Figure 3. Numerical simulation of differential absorption spectra (a) Negative change of the optical interband absorption \( -\Delta \alpha_{\Gamma Z} \) for static fields from a cosine band modeling along \( \Gamma Z \) direction. The region of electric field strengths up to 1 MV/cm is enlarged to show Franz-Keldysh oscillations and the transition to the Wannier-Stark regime. (b) Calculated \( -\Delta \alpha_{\Gamma Z} \) spectra for the excitation with a THz pulse with a peak field strength of \( E_0 = 6 \) MV/cm, where the delay \( \tau \) between the THz and the optical pulse is varied. (c) Simulated temporal profile of the applied THz bias transient. The pulse duration \( \bar{T} \) is 240 fs, the THz frequency is 20 THz, and the dephasing time is \( T_2 = 20 \) fs.
+
+Already when considering static fields (Fig. 3(a)), the simulation results obtained by this simple model exhibits substantial qualitative similarities with the transient experimental results shown in Fig. 2(a). For all field strengths, increased absorption is present below the bandgap and reduced absorption directly above the band gap. For rather weak field strengths of up to about 0.5 MV/cm, oscillations arising from the Franz-Keldysh effect are visible, shifting towards the band center with
+increasing field. For fields exceeding ~3 MV/cm, signatures of Wannier-Stark localization become noticeable, as the field-dependent interband transition energies shift to higher and lower energies by \( neED \) with increasing \( E \) (Fig. 2(c)). Starting at around 3 MV/cm, the condition for Stark localization is fulfilled, i.e., \( eED > \Delta/2 \) (meaning that the energy of the (\( n = -1 \)) Wannier-Stark state is in the bandgap region, see Fig. 2(c, d)), and therefore, the dominant feature is the step-like change from reduced absorption to induced absorption in the center of the band at 1.974 eV (this value is the average transition frequency within our model). This step-like change is, in fact, also the main feature visible in the experimental results for sufficiently high fields, i.e., between about -100 < \( \tau \) < 100 fs as shown in Figs. 2 (a).
+
+Besides, by considering pulsed THz fields, the simulated differential spectra with the same model (Fig. 3(b, c)) well describe both spectral and temporal features in the observed transient modulation of differential transmission spectra (Fig. 2(a)). Fig. 3(b) shows the negative change of the transient absorption, \(-\Delta\alpha_{\Gamma_2}\), upon non-resonant biasing with a THz pulse with a peak field strength of \( E_0 = 6 \) MV/cm and a center frequency of 20 THz, as shown in Fig. 3(c). Besides temporal modulation of the entire transient spectra at twice the carrier frequency of the THz transient, the dominant feature at sufficiently large field strengths (-100 < \( \tau \) < 100 fs) is the rapid change from increased to reduced transmission in the center of the band \( E_{pr} = 2 \) eV, which originates from Stark localization. The slightly lower value of the observed central step at \( E_{pr} = 1.9 \) eV and the asymmetric nature of the spectral shape with respect to the central step (Fig. 2(a)) compared to this simplified model (Fig. 3 (b)) can be explained by the polycrystallinity of the system as discussed below. Given the complexity, disorder, and polycrystallinity of the investigated sample, the required field strength at which this step starts to appear is in surprisingly good agreement with the experiment which confirms that the observed response constitutes a clear
+sign of Wannier-Stark localization. Our interpretations are further supported by Fig. S6, which shows how the results of Fig. 3 change if we consider that the THz field is aligned with the \( \overline{\Gamma A} \) direction instead of the \( \overline{\Gamma Z} \) direction. Comparing those two figures clearly shows that due to the larger bandwidth in the \( \overline{\Gamma A} \) direction the Wannier-Stark localization requires higher field amplitudes to develop and furthermore would lead to a transition from reduced to induced absorption at significantly higher energies as observed in experiment. The effects of different field directions and the averaging over them is discussed in more detail below (see Fig. 4).
+
+As demonstrated so far, Wannier-Stark localization starts to occur at the field amplitude as low as 3 MV/cm in the MAPBI$_3$ perovskite, due to the relatively large periodicity, the narrow joint bandwidth, and the coincidence of the two along the same direction. The largest lattice constant of tetragonal MAPBI$_3$ perovskite, along the $c$ axis, $c = 12.5$ Å, is more than twice as large as those of conventional all-inorganic semiconductors crystallizing with strong covalent bonds in the diamond, wurtzite, or zincblende forms (3.5 ~ 6.5 Å at 300 K). This finding arises because (i) the cubic perovskite unit cell is expanded through rotation of ab plane by 45° and cell doubling along c axis in the tetragonal phase; and (ii) the pseudocubic lattice parameter formed by relatively large Pb$^{2+}$ and I$^-$ ions is 6.3 Å$^{13}$, which is at the larger side of the distribution of parameters for cubic lattice parameters. The pseudocubic lattice parameter is large enough to accommodate large organic molecular cations within the void of their network.
+
+The direction of the narrowest joint bandwidth of the conduction and valence bands, \( \overline{\Gamma Z} \), coincides with the $c$ axis. The conduction band is composed of the overlap of Pb(6p)-I(5p) atomic orbitals and the valence band is of that of Pb(6s)-I(5p) orbitals$^{29}$. Thus, the Pb-I bond length as well as the Pb-I-Pb angle could determine the widths of both bands and the magnitude of the band
+gap. In the tetragonal MAPbI$_3$ perovskite, the corner-shared PbI$_6$ octahedra in cubic phase are tilted about the $c$ axis in the opposite direction between successive tilts, which reduces the Pb-I-Pb angle from 180$^\circ$ along the diagonal direction of the a and b axis. The smaller Pb-I-Pb bond angle indicates weaker orbital overlap between Pb and I atoms and thus smaller band dispersion along $\overline{\Gamma M}$ than $\overline{\Gamma Z}$. However, the Pb-I bond lengths along the $c$ axis is known to be longer on average$^{30}$ and has greater effect on the dispersion than the angle due to the $\sigma$ bonding nature, which leads to the coincidence of the direction of the largest lattice constant and the narrowest bandwidth. We note that unlike GaAs, the body diagonal direction exhibits the strongest dispersion ($\overline{\Gamma A}$). Overall, the large ionic diameter and the geometric distortion result in the unusually narrow joint bandwidth, lower than 1 eV.
+
+*Including polycrystallinity by averaging over orientations*
+
+We now account for the system's polycrystallinity by considering contributions to the differential transmittance spectra from crystallites with orientations different from those with the $c$ axis parallel to the THz field polarization. To include arbitrary orientations of the crystallites into our simulations, we take the $\overline{\Gamma Z}$ and the $\overline{\Gamma A}$ directions, i.e., the two extreme directions with the narrowest/broadest bandwidth and simultaneously the smallest/largest distance in k-space (see Fig. 1(b)) and perform an average overall in between bandwidths and extensions of the first Brillouin zone (see Method section), by interpolating between the two limiting cases with a parameter $f$. The simulated absorption changes at a field amplitude of $E_0 = 4$ MV/cm with various interpolation parameters $f$'s are shown in Fig. 4 (a) together with the measured differential spectra at different instantaneous field amplitudes of the THz pulse (Fig. 4 (b)). Here, $f = 0$ denotes the response along the $\overline{\Gamma Z}$ direction (i.e., the $c$-axis), and $f = 1$ along the $\overline{\Gamma A}$ direction.
+Figure 4. Experiments on polycrystalline system and simulations with averaging of cosine band model from ΓZ to ΓA direction. (a) Illustration for the averaging process over the interpolation parameter \( f \) from the ΓZ direction (\( f = 0 \)) to ΓA direction (\( f = 1 \)). The negative absorption changes -\( \Delta \alpha_f \) are calculated for different one-dimensional systems using a THz pulse centered at \( t = 0 \), with an amplitude of \( E_0 = 4 \) MV/cm, a pulse duration of \( \bar{T} = 240 \) fs, and a THz center frequency of 20 THz. (b) Temporal slices of \( \Delta T/T \) as a function of probe photon energy (Fig. 2(a)), at a delay time corresponding to the contour with constant electric field amplitudes \( E \) (Fig. 2(b)). (c) averaged absorption change, -\( \Delta \alpha_{avg} \), for static fields of various strengths. (d) averaged absorption change, -\( \Delta \alpha_{avg} \), for a THz pulse centered at \( t = 0 \) and various field strengths.
+As shown in Fig. 4(a), the absorption changes depend strongly on the interpolation parameter \( f \), i.e., on the bandwidth and the distance to the border of the first Brillouin zone. For \( f = 0 \), which corresponds to the \( \overline{\Gamma Z} \) direction, the field amplitude of \( E_0 = 4 \) MV/cm drives the system into the region of Stark localization. Therefore, for a static field of such an amplitude, one would see a strong induced absorption in the band center at 1.974 eV, which corresponds to an optical transition to the Stark localized state. The transient nature of the THz pulse causes the single negative peak to be split into two peaks and the spectral region of induced absorption to be slightly broadened. With increasing \( f \), both the bandwidth and the distance to the border of the first Brillouin zone increase. As a result, the minimum field strength for which Stark localization is realized increases significantly by approximately a factor \( (c/a_{\overline{\Gamma Z}}^*)(\Delta_{\overline{\Gamma A}}/\Delta_{\overline{\Gamma Z}}) \), equaling about 4.7. Consequently, already for \( f = 0.25 \), the absorption changes show no sign of Stark localization, with several oscillations emerging owing to the THz driving. This trend of overall weaker absorption changes with some oscillatory structure is also present for even larger \( f \). The only feature present in all spectra shown in Fig. 4 (a) is some induced absorption below the bandgap and reduced absorption directly above the bandgap.
+
+However, when averaging over the interpolation parameter \( f \), i.e., over the orientations considered by our modeling, the result (black curve in Fig. 4(a)) reproduces the main features present for \( f = 0 \), with somewhat fewer oscillations. Most importantly, the change from bleaching to induced absorption in the center of the band structure for the \( \overline{\Gamma Z} \) direction at about 1.9 eV is still present. The averaged graph is in good agreement with the differential spectra at high field amplitudes (upper curves in Fig. 4(b)). Thus, in the averaged results, the spectra for small \( f \)
+dominate strongly since (i) the absorption changes are spectrally concentrated in the monitored region due to the small bandwidth, (ii) one is in the regime of Stark localization due to the small extent of the first Brillouin zone, and (iii) for larger \( f \) the rather weak and oscillatory results partly cancel each other. For these reasons, the contribution from the \( \Gamma Z \) direction, corresponding to small \( f \), is enhanced for energies far above the bandgap and dominates the entire phenomenon.
+
+The results of Fig. 4(a, b) suggest that, for the randomly oriented crystallites in the film, the overall response is dominated by the response originating from the band dispersion in the \( \Gamma Z \) direction. This reasoning is substantiated by the averaged field-dependent absorption changes calculated for both a static and a THz field shown in Figs. 4(c) and (d), respectively. As expected, the \( \Gamma Z \) direction dominates the averaged results, which include the contributions from the dispersion in all the other directions. In both cases for strong fields, the dominant feature is a rapid change from reduced to increased absorption, which takes place near the center of the interband absorption that corresponds to the dispersion in the \( \Gamma Z \) direction. Due to the spectral broadening induced by the THz modulation, this transition appears at slightly lower photon energies for the THz field, Fig. 4(c), than for the static field, Fig. 4(d). Thus, Fig. 4(c, d) is consistent with the notion that the step-like sign change in the center of the band for sufficiently strong field amplitudes is a signature of Stark localization for the polycrystalline perovskite sample.
+
+In conclusion, we have demonstrated the onset of transient Wannier-Stark localization in the polycrystalline form of methylammonium lead iodide perovskite at surprisingly low electric field amplitudes. Despite the static and dynamic disorder of the methylammonium molecular cations at room temperature and the arbitrary distribution of crystal domains with respect to the THz field direction, the dominant contribution from the \( \Gamma Z \) direction of the band structure allows for the clear
+signature of Wannier-Stark localization. The ultrafast field-induced transition from 3D to effectively 2D electronic states leads to substantial spectral transfer from the central spatially-direct (\( n = 0 \)) transition (around the optical band gap of 3D) to 0.3 eV red- (blue-)shifted spatially adjacent transitions \( n = +1 \) (\( n = -1 \)), with up to 38 % maximum modulation depth. Instead of semiconductor superlattices, which need expensive high-vacuum manufacturing processes, the solution-processed hybrid perovskites could meet the growing need for cost-effective\(^{31}\), efficient, fast, and sensitive characteristics as optical modulators\(^{32}\). Together with the renowned photophysical properties of MAPbI\(_3\), such as the long carrier diffusion length\(^{33,34}\), low mid-gap trap density\(^{29,34}\), and large absorption coefficient\(^{35}\), this finding of high modulation depth, fast response, and low onset field for Wannier-Stark localization highlights the potential of this material in photonic applications\(^{36,37}\).
+
+Materials and Methods
+
+Experimental details
+
+The phase-stable multi-cycle mid-IR pulses with a peak field strength of \( \sim 10 \)MV/cm are generated using difference frequency mixing (DFG) in GaSe\(^{9,10}\). The regeneratively amplified pulses with 780 nm and 130 fs are used to pump two parallel optical parametric amplifier stages to provide tunable near-infrared pulses with minimum relative phase fluctuation. The two near-IR pulses are then combined and sent to the GaSe nonlinear crystal for the DFG. The thus generated mid-IR pulses are focused onto the sample with off-axis parabolic mirrors of focal length \( \tilde{f} = 15 \) mm and effective NA = 0.2. The electric field transient is characterized by ultrabroadband electro-optic sampling\(^{38}\) at a 30-\(\mu\)m-thick GaSe crystal using balanced detection of an 8-fs probe pulse centered at a wavelength of 1.2 \(\mu\)m as the gating pulse. The quantitative value of the field
+amplitude is obtained by measuring the mid-IR average power and focal spot size. Then, the value at the interior of the MAPbI$_3$ perovskite sample are estimated using the Fresnel transmission coefficient for the mid-IR field at the air–MAPbI$_3$ interface.
+
+For detection of the field-induced differential optical transmittance in broad spectral range, we generate near-IR and visible pulses with the duration of 7 fs by non-collinear optical parametric amplification (Fig. S1)$^{39}$. The probe pulses are combined with the mid-IR pump pulses at a germanium beam splitter so that both pulses co-propagate through the sample. The probe pulses are then dispersed onto a spectrometer coupled to a CCD camera for the spectral resolution. The relative timing between the pump and probe pulses was controlled using an optical delay stage. To detect the differential optical transmission spectra, we modulate the mid-IR pump pulses by an optical chopper operating at 125 Hz, which is synchronized with the 1 kHz laser repetition rate and the readout of the CCD camera. Two subsequent spectra taken from the CCD camera are subtracted by each other and normalized by one spectrum without the pump. The sample compartment in the experimental setup was purged with dry nitrogen in order to avoid degradation. The complete experimental setup and the laser system have been fully illustrated in Ref [8].
+
+Theoretical approach
+
+For calculating the linear optical interband absorption spectra, we numerically solve the semiconductor Bloch equations (SBE), including the intraband acceleration induced by the strong THz field $^{26-28}$. We use here a one-dimensional trajectory in k-space, denoted as the \( \overline{\Gamma} x \) direction where x is an arbitrary point in the 1. Brillouin zone, which is parallel to the polarization direction
+of the incident THz field and goes through the Γ-point of the Brillouin zone. In the linear optical regime, the SBE reduce to the equations of motion for the microscopic polarizations \( p_k^{cv} \) and read
+
+\[
+\frac{\partial}{\partial t} p_k^{cv} = \frac{i}{\hbar} E_{cv}(k)p_k^{cv} + \frac{e}{\hbar} E_{THz}(t)\nabla_k p_k^{cv} - \frac{i}{\hbar} E_{opt}(t)\mu_k^{vc} - \frac{p_k^{cv}}{T_2}
+\]
+
+Dephasing processes are treated phenomenologically by adding the dephasing time \( T_2 \).
+
+For all calculations presented in this paper, we include the intraband dynamics induced by the static or pulsed THz fields to infinite order, whereas the weak optical probe of the interband absorption is considered only to the first order. In this linear-optical regime, we thus neglect carrier generation by multi-photon processes and impact ionization, which does not seem to play a dominant role in the measured transient spectra. Interband tunneling by the THz field could lead to bleaching at later delay times and the slightly asymmetric spectral evolution with respect to \( \tau = 0 \) (Fig. 2(A)) (corresponding to the trailing edge of the THz transient in the Supplementary Material of ref [8]). However, significant carrier multiplication does not occur within this experimental window, as shown in Fig. S3.
+
+For the interband dipole matrix element, we use the usual decay with increasing transition frequency\(^{40}\)
+
+\[
+\mu_k = \mu_0 \frac{1.62\ \mathrm{eV}}{E_{cv}(k)}
+\]
+
+where the choice of \( \mu_0 \) is not relevant here, as it contributes only as a prefactor to the absorption spectra.
+
+For the THz pulses, we use a Gaussian envelope
+\[
+E_{\mathrm{THz}}(t) = E_0 e^{-4 \ln(2) \left(\frac{t-\tau}{\bar{T}}\right)^2} \cos(\omega_{\mathrm{THz}} (t-\tau))
+\]
+
+with the electric-field amplitude \( E_0 \), the pulse duration \( \bar{T} \) (FWHM of the intensity), the time delay \( \tau \), and the THz frequency \( \omega_{\mathrm{THz}} \). The optical probe pulse is modeled as a weak ultrashort delta-like pulse.
+
+The total optical polarization is obtained by summing over the microscopic polarizations \( p_k^{cv} \)
+
+\[
+P(t) = \sum_k \mu_k^* p_k^{cv}(t) + c.c.
+\]
+
+By Fourier transforming the macroscopic polarization \( P(t) \) the linear absorption can be obtained by
+
+\[
+\alpha_{1D,\vec{\Gamma}_X}(\omega) \propto \omega \operatorname{Im}(P(\omega))
+\]
+
+To be able to compare the numerical results for the one-dimensional k-space trajectory to the measured \( \Delta T/T \) spectra, the negative change of the optical absorption in three dimensions -\( \Delta \alpha_{3D} \) is calculated assuming a parabolic electronic dispersion perpendicular to the considered one-dimensional direction. Due to the constant two-dimensional density of states for a parabolic dispersion, the absorption of the corresponding three-dimensional system is easily obtained as Ref [8]
+
+\[
+\alpha_{\vec{\Gamma}_X}(\omega) \propto \int_0^\omega \alpha_{1D,\vec{\Gamma}_X}(\omega') d\omega' .
+\]
+Band structure model and averaging over crystallographic directions
+
+To incorporate both the bandwidth and the effective mass \( m^* \) at the band gap as obtained from ab-initio calculation in Ref [12] into our model, we use an interband energy difference of
+
+\[
+E_{cv}(k) = E_0 + \frac{\Delta}{2} (1 - \cos(g(ka^*)ka^*))
+\]
+
+Here, \( \pi/a^* \) is the distance from the \( \Gamma \)-point to the border of the first Brillouin zone
+
+and the interpolation function
+
+\[
+g(ka^*) = f + (1 - f) \frac{ka^*}{\pi}
+\]
+
+guarantees that \( E_{cv}(0) = E_0 \) and \( E_{cv}(\pm \pi/a^*) = E_0 + \Delta \), meaning the bandgap energy \( E_0 \) and the bandwidth \( \Delta \) are preserved.
+
+The parameter \( f \) is adjusted to obtain the effective mass which corresponds to the second derivative of the band structure at the \( \Gamma \) point:
+
+\[
+m^* = \hbar^2 \left[ \frac{d^2 E_{cv}(k)}{dk^2} \right]_0^{-1}
+\]
+
+as given in Ref [12].
+
+As mentioned before, the polycrystallinity of the system is included by averaging over several differential transmittance spectra.
+
+The transition from the \( \overline{\Gamma}Z \) to the \( \overline{\Gamma}A \) direction is carried out by varying the bandwidth \( \Delta \) from \( \Delta_{\overline{\Gamma}Z} = 0.75 \) eV to \( \Delta_{\overline{\Gamma}A} = 1.55 \) eV, the extent of the first Brillouin zone \( \frac{\pi}{a^*} \) from \( \frac{\pi}{a^*_{\overline{\Gamma}Z}} = \frac{\pi}{c} = \frac{\pi}{1.27} \) nm\(^{-1}\)
+to \( \frac{\pi}{a_{\Gamma A}^*} = \frac{\pi}{a_c} \sqrt{2c^2 + a^2} = \frac{\pi}{0.56} \) nm\(^{-1}\) and the effective mass m\(^*\) from \( m_{\Gamma Z}^* = 0.17m_0 \) to \( m_{\Gamma A}^* = 0.09m_0 \) via a parameter \( f \) which varies from 0 (i.e. the \( \Gamma Z \)-direction) to 1 (i.e. the \( \Gamma A \)-direction)
+
+\( ^{12} \). The interpolation is performed as:
+
+\[
+\Delta(f) = \Delta_{\Gamma Z} + f(\Delta_{\Gamma A} - \Delta_{\Gamma Z})
+\]
+
+\[
+\frac{\pi}{a^*(f)} = \frac{\pi}{a_{\Gamma Z}^*} + f \left( \frac{\pi}{a_{\Gamma A}^*} - \frac{\pi}{a_{\Gamma Z}^*} \right)
+\]
+
+\[
+m^*(f) = m_{\Gamma Z}^* + f(m_{\Gamma A}^* - m_{\Gamma Z}^*)
+\]
+
+where \( f = 0 \) describes the \( \Gamma Z \)-direction and \( f = 1 \) the \( \Gamma A \)-direction, respectively.
+
+The above described averaging of several spectra for the discretized parameter \( f \) is performed via evaluating
+
+\[
+\alpha_{avg}(\omega) = \frac{1}{n} \sum_{f_i} \alpha_{f_i}(\omega), i \in [1, n]
+\]
+
+With the respective absorption \( \alpha_{f=0} = \alpha_{1D,\Gamma Z} \) and \( \alpha_{f=1} = \alpha_{1D,\Gamma A} \) where for convergence \( n \) is typically chosen as 51.
+
+Supporting Information
+
+Fig. S1. Normalized spectra of near-IR (red) and visible (blue) probe pulses.
+
+Fig. S2. Differential transmission changes measured at probe photon energies of 1.7 eV (red line) and 2.0 eV (blue) together with the E\(^2\)(t) of THz pulse profile.
+Fig. S3. Contributions from free carriers generated via interband tunneling.
+
+Fig. S4. Simulations with averaging from the \( \overline{\Gamma Z} \) to the \( \overline{\Gamma A} \) direction for a THz pulse centered at \( t = 0 \) and various field strengths.
+
+Fig. S5. Simulated absorption change, \( -\Delta \alpha_{avg} \), averaged for a pure cosine model band structure (without the function g, see methods, which was introduced to fit the effective mass) from \( \overline{\Gamma Z} \) to \( \overline{\Gamma A} \) direction for a THz pulse centered at \( t = 0 \) and various field strengths.
+
+**Figure S6.** Simulated change of the optical interband absorption \( -\Delta \alpha_{\overline{\Gamma A}} \) from a cosine band modeling along \( \overline{\Gamma A} \) direction for static fields and a pulsed THz field.
+
+AUTHOR INFORMATION
+
+**Corresponding Author**
+
+*Corresponding author. torsten.meier@upb.de; kim@mpip-mainz.mpg.de
+
+**Author Contributions**
+
+The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ‡These authors contributed equally.
+
+**Notes**
+
+The authors declare no competing financial interest.
+ACKNOWLEDGMENT
+
+The authors thank Keno Krewer and Johannes Hunger for helpful discussions. T. M. and D. B. acknowledge financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the Collaborative Research Center TRR 142 (project number 231447078, project A02). M. B. and H. K. thank the DFG for financial support through the Collaborative Research Center TRR 288 (project number 422213477, project B07), the European Union's Horizon 2020 research and innovation program under grant agreement No.658467, and the Max Planck Society for financial support. A. L. and J. B. acknowledge financial support from the European Research Council through ERC Advanced Grant 290876 (UltraPhase) and the Carl Zeiss Foundation through the fellowship program.
+
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+39. Brida, D. et al. Few-optical-cycle pulses tunable from the visible to the mid-infrared by optical parametric amplifiers. J. Opt. 12, 13001 (2009).
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+40. Haug, H. & Koch, S. W. Quantum Theory of the Optical and Electronic Properties of Semiconductors. (WORLD SCIENTIFIC, 2009).
+Figures
+
+(a)
+
+![THz pulse geometry with a tetragonal unit cell diagram](page_186_232_579_496.png)
+
+(b)
+
+![Simplified electronic band structure plot](page_774_120_377_377.png)
+
+(c)
+
+![Optical absorption spectrum plot](page_774_527_377_377.png)
+
+Figure 1
+
+Experimental scheme and properties of MAPbI3 perovskite (a) THz pulse geometry with a tetragonal unit cell (black rectangular cuboid) of MAPbI3. (dark grey: Pb, purple: I, brown: C, light blue: N, light pink: H) The THz biasing along the c axis of a crystallite is depicted. (b) Simplified electronic band structure of MAPbI3 in the tetragonal phase along the directions Γ(0,0,0) ⊥ Z(0,0,0.5) and Γ(0,0,0) ⊥ A(0.5,0.5,0.5). The bandwidths and the lattice parameters are used from [Ref 12]. (c) Optical absorption spectrum of MAPbI3 in the spectral range of the probe pulses.
+
+(a)
+
+![Probe photon energy vs Delay plot](page_186_1202_377_377.png)
+
+(b)
+
+![El. field vs Time plot](page_563_1202_377_377.png)
+
+(c)
+
+![Energy level diagram with THz field](page_940_1202_377_377.png)
+
+(d)
+
+![Absorbance vs Energy plot with THz field](page_1317_1202_377_377.png)
+Figure 2
+
+Experimental observation of the transient Wannier Stark localization and the visualized diagram (a) Experimental differential transmission spectra on a polycrystalline film of MAPbI3 perovskite at room temperature, as a function of delay time of probe pulses after THz pump pulses. The THz pulses have a peak field strength of 6.1 MV/cm and a center frequency of 20 THz; the probe pulses have photon energy of 1.4 ~ 2.4 eV. (b) Temporal profile of the applied THz bias transient. (c) Schematic picture of Wannier Stark localization. In the presence of strong external fields along the c axis, electronic states (orange: conduction band, blue: valence band) are localized to a few layers of ab plane, and energetically separated by ΔEWSL = eETHzc between adjacent lattice sites. Black arrows depict the interband transitions within the same site (n = 0) and between different sites (n = ±1). (d) The absorbance with and without the external transient biasing. The Wannier-Stark localization effectively reduces the 3D electronic structure into 2D layered structure along the ab plane, as depicted in blue together with the simplified 3D structure.
+
+![Experimental observation of the transient Wannier Stark localization and the visualized diagram](page_186_573_1207_496.png)
+
+Figure 3
+
+Numerical simulation of differential absorption spectra. Please see .pdf file for full caption
+Figure 4
+
+. Experiments on polycrystalline system and simulations with averaging of cosine band model from [110] to [111] direction. Please see .pdf file for full caption
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SlfinalNatComm.pdf

011f1f7cdec2740845fc5c2f410ff02c63329260c767801a3ae4c3d8ae57e6f6/peer_review/peer_review.md

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+Peer Review File
+
+WHIM Syndrome-linked CXCR4 mutations drive osteoporosis
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Anginot et al. report on the importance of CXCR4 desensitization in skeletal stem cells (SSCs) in order to allow SSCs to proliferate adequately and differentiate into the osteogenic lineage, whereas chondrogenic and adipogenic differentiation seem not to be affected by gain of function mutation of CXCR4. These novel data certainly increase our understanding on CXCR4 signalling in osteogenic lineage cells. In addition, the authors combined numerous well-designed in vivo and in vitro experiments to elucidate the cellular mechanisms. However, several inconsistencies between the findings are present, especially concerning the effect of CXCR4 desensitization on SSC properties and their osteogenic differentiation potential.
+
+Figure 2B. The decrease in stroma cell number in mutant mice (60 x10^3 versus 100 x 10^3 in WT mice) cannot be explained by the combined decrease in SSC (3 x10^3 versus 5 x10^3) and OPC (7 x10^3 versus 13 x10^3). The question is therefore which other bone cell types are decreased in mutant mice as these other cell types might also contribute to the observed decrease in bone mass. Are endothelial cells decreased (H-type and L-type) in mutant mice as they express CXCR4 and might provide a vascular niche for the SSC?
+
+Figure 2N and 2S. Parameters of TBV and cortical bone should be quantified, preferable by μCT (or quantitative histological analysis). At this moment, only 1 image per condition is shown and this is an Opn staining, which is not considered to be the appropriate approach for quantitative bone measurements. This quantification of bone parameters is especially necessary to verify the bone loss that occurs when recipient mice are WT (Figure 2S), as the bone loss that is induced by transplantation of mutant donor cells in WT recipient mic is hard to be explained only by a reduced number of SSC and OPC, as is now suggested.
+
+Figure 3. The authors suggest that the in vivo observed increase in osteoclasts in mutant mice is linked to an altered BM environment. To strengthen this statement, coculture experiments of osteogenic cells and osteoclast-precursors, in different combinations of WT vs mutant cells (treated with PTH, Pg or 1,25-vitamin D) should be performed. At this moment, the data only describe a discordance between the in vivo and in vitro findings, but do not allow to make any conclusion on whether the decrease in bone mass is partly caused by increased bone resorption.
+
+Figure 3. The histomorphometric data should be confirmed in more mice, as 3 mice per group for histomorphometric analysis is often not sufficient (Figure 3F-H). In addition, the bone formation data are puzzling, as osteoblast surface and osteoid surface are normal, but MS/BS and DB/BS are decreased. The authors interpret these data as a ‘lower number of osteoblasts’ but this statement does not fit with the normal osteoblast surface that is observed. Since dynamic bone formation parameters primarily measure the incorporation of minerals, these data might suggest that the formation of bone matrix by the osteoblasts is normal, but that the mineralisation of this bone matrix is impaired (and likely some osteoblasts are not mineralizing the matrix, whereas others show normal mineralization capacity as MAR is normal). Gene expression analysis might provide some more insight. The gene expression analysis (Figure 3J) is now restricted to genes that typify mature osteoblasts, but the expression of genes involved in mineralization is not analysed. In addition, the
+variation of the gene expression data reported in Figure 3J and M, is rather high and this quantification should be validated with qRT-PCR data and using more mice.
+
+Figure 4. Panel D shows the relative expression of selected genes; are these the most differentially expressed genes between the different genotypes? To appreciate the importance of these differences, it will be important to provide also the unbiased ranked overview/list of pathways which differ the most between genotypes, based on genes involved. In addition, since mutant SSC maintain their potential to differentiate normally to chondrocytes and adipocytes, are SOX9 and Pparg expression normal in mutant SSC? Furthermore, it remains hard to understand that a decrease in OPC number (Figure 2B, Figure 4I) does not affect osteoblast or osteoid surface. How do the authors reconcile these data?
+
+Figure 5 and 3. The data suggest that osteogenic differentiation starting from mutant SSC is reduced (Figure 5E-G), but once mutant SSC become OPC they can differentiate normally (Figure 3L). It should be good to confirm this observation, by performing the same assays on OPC as shown for SSC (Figure 5: differentiation with Alp quantification and gene expression analysis). In addition, it is rather particular that after 21 days of osteogenic differentiation, most of the cells are still SSC (Figure S1), and intermediate cells account only for 15% of the population, whereas the % of ALP+ cells, reported in Figure 5E, seems much higher. Same comment for the low % of mature cells compared to reported homogeneous and abundant alizarin red staining (Figure 5F).
+
+Figure 5 in vivo data. The authors state that especially the cortical bone is rescued in mutant mice, but not the trabecular phenotype, based on lumbar spine BMD data. To validate this statement, μCT analysis of cortex of long bones should be analysed with and without AMD3100 treatment. In addition, these data also suggest that CXCR4 desensitisation in osteogenic lineage cells is likely not responsible for the trabecular bone phenotype, and that other cell types/mechanisms might be involved. This site-specificity should be reflected in the title and in the abstract.
+
+Minor comments
+Perilipin staining should be quantified as the observation that CXCR4 specifically reduces the osteogenic, but not the adipogenic differentiation is interesting, but should be validated by quantitative data.
+
+Figure 1D: it is not clear whether the total number of mice used is 7-14, coming from 3 experiments, or that in each of the 3 experiments there were 7-14 mice, thus 21-42 mice in total. Similar comment to all experiments using mice.
+Figure 2J: the % of apoptotic OPC is around 30%, which is rather high, and should be commented on.
+Reviewer #2 (Remarks to the Author):
+
+WHIM syndrome (WS) is a rare immunodeficiency caused by gain-of-function CXCR4 mutations. The authors have demonstrated for the first time a substantial decrease in bone mineral density in 25% of WS patients and osteoporosis in a WS mouse model. Interestingly, wild-type mice transplanted with bone marrow hematopoietic cells from mice with a WS-linked CXCR4 mutation (Cxcr4+/1013 or Cxcr4 1013/1013) had reduced trabecular bone content compared with wild-type chimeras. On the other hand, transplantation of wild-type bone marrow cells did not rescue the reduced trabecular bone content in the mutant chimeras. Osteogenic differentiation of cultured bone marrow skeletal stem cells (SSCs) from the mutants was impaired in vitro. The CXCR4 antagonist AMD3100 normalized in vitro osteogenic potential of SSCs and reversed an in vivo decrease in Sca-1-PDGFRa-cells in the mutants. These results are interesting and important; however the major concern remains at this time. There is the possibility that osteopenia in mice and patients, which carry the WS-linked CXCR4 mutation, is the result of only enhanced osteoclast function but not reduced osteogenic differentiation of SSCs.
+
+1. As the authors described, it has been shown previously that deletion of CXCR4 in mesenchymal cells, including SSCs, resulted in osteopenia (Tzeng et al., J. Bone Miner. Res. 2018; Zhu et al., J. Biol/Chem. 2011). These results argue against the authors’ conclusion that gain-of-function CXCR4 mutations in SSCs resulted in osteopenia. Thus, I would recommend the authors to generate and analyze the mice, in which mesenchymal cells, including SSCs, but not hematopoietic cells carry WS-linked CXCR4 mutations.
+
+2. The authors show the reduced trabecular bone content of mice with a WS-linked CXCR4 mutation transplanted with bone marrow hematopoietic cells from wild-type mice was not rescued 3 and 16 weeks after transplantation. However, wild-type hematopoietic cells might be able to rescue the reduced trabecular bone content of the mutants earlier in development.
+
+3. The authors describe Sca-1+PDGFRa+ cells as SSCs (Page 8, line 142); however, the major population of bone marrow SSCs is defined as Sca-1-PDGFRa+PDGFRb+LepR+CD31- cells (Omatsu et al., Immunity 2010; Zhou et al., Cell Stem Cell 2014; Seike et al., Genes Dev 2018).
+
+4. The evidence that Sca-1-PDGFRa- cells are committed osteoblasts (OPCs) in the bone marrow would not be convincing (Page 8, line 143).
+Reviewer #4 (Remarks to the Author):
+
+The manuscript by Anginot and colleagues provides novel insights into the role of CXCR4-mediated signaling in skeletal stromal/stem cell osteogenic specification. The authors describe a series of experiments characterizing the anatomic, developmental and functional properties of the skeletal and osteogenic compartment in a knock-in mouse model of the human genetic disorder WHIM syndrome. The significance of the deficits in skeletal remodeling and stem cell differentiation identified in the mouse model in human bone biology are validated in cohort of WHIM syndrome patients carrying gain-of-function mutations in CXCR4. These findings represent a novel contribution elucidating an important new role for CXCR4 in bone biology.
+
+The authors characterized the effects of increased CXCR4 signaling in vivo through standard histomorphometric of bone anatomy and flow cytometric analyses of various progenitor cell populations in the mouse model. The data in Figure 1 are well presented and convincing in regard to the gene-dose dependent skeletal effects as well as the specificity of the changes to cortical and trabecular bone. Figure 2 is overly dense and contains information that could be moved to the supplement without impacting the major findings of the work. In particular, the experiments demonstrating the functional effects of the mutant CXCR4 receptor recapitulate characteristics of CXCR4 C-terminal truncations that have been well studied in other contexts. It would suffice to state that the mutant receptor localization, internalization and intracellular signaling were similar to what has been seen in other contexts and move panels 2E-J to the supplement. The bone marrow reconstitution experiments shown in the remainder of the figure demonstrate clearly the contribution of cell-extrinsic as well as cell-intrinsic factors to the observed skeletal changes. the Similarly, the effects on bone resorption and formation shown in Figure 3 panels C-E can be moved to supplement to better focus on the transcriptional effects shown in the subsequent panels.
+
+The data in Figures 4 and 5 provide compelling data regarding the impact of aberrant CXCR4 signaling on osteogenic specification at the level of transcriptional effects and cell cycle progression. The PCA data shown in Figure 4C is not well explained as the 48 genes used for expression profiling are not described in the text nor the supplement, which lists a smaller number of genes. The data in the subsequent panels are more informative. I would consider removing panel 4C or moving it to the supplement with a better description of the analysis. The experiments shown in Figure 5 document the selective reduction in osteogenic differentiation capacity of stromal stem cells carrying one or two mutant CXCR4 receptors in a dose dependent fashion and the reversal of this phenotype with treatment of the receptor inhibitor AMD3100. The relevance of these data in mice to human bone biology are supported with the data shown in Figure 6 which revealed a selective osteogenic differentiation defect in bone marrow cells derived from WHIM syndrome patients.
+
+With regards to the conclusion that a skeletal phenotype is present in a subset of WHIM syndrome patients, given that treatment of neutropenia with G-CSF is associated with osteopenia as side effect of therapy, it would be useful to know the total number of patients treated with G-CSF in the cohort to address the concern that the enrichment in osteopenic patients is restricted to those patients that have been so treated as well as their ages and genders given the impact of these variables on risk for osteopenia in general.
+Apart from these concerns, the quality of the data presented is good and the conclusions supported by the evidence. The manuscript is well written and the references appropriate, though it was notable that the initial description of the cause of WHIM syndrome as gain-of-function truncation mutations in CXCR4 was not cited, this should be added.
+Point-to-point response to the reviewers’ comments
+
+Reviewer #1 comments:
+
+Anginot et al. report on the importance of CXCR4 desensitization in skeletal stem cells (SSCs) in order to allow SSCs to proliferate adequately and differentiate into the osteogenic lineage, whereas chondrogenic and adipogenic differentiation seem not to be affected by gain of function mutation of CXCR4. These novel data certainly increase our understanding on CXCR4 signalling in osteogenic lineage cells. In addition, the authors combined numerous well-designed in vivo and in vitro experiments to elucidate the cellular mechanisms. However, several inconsistencies between the findings are present, especially concerning the effect of CXCR4 desensitization on SSC properties and their osteogenic differentiation potential.
+
+Major concerns:
+
+1. “Figure 2B. The decrease in stroma cell number in mutant mice (60 x10^3 versus 100 x 10^3 in WT mice) cannot be explained by the combined decrease in SSC (3 x10^3 versus 5 x10^3) and OPC (7 x10^3 versus 13 x10^3). The question is therefore which other bone cell types are decreased in mutant mice as these other cell types might also contribute to the observed decrease in bone mass. Are endothelial cells decreased (H-type and L-type) in mutant mice as they express CXCR4 and might provide a vascular niche for the SSC?”
+We are grateful to the reviewer for this constructive comment and agree that some populations are likely missing in our flow-cytometric analyses. In particular, we did not consider the CD51-Sca1- cell population which is non-hematopoietic (CD45-) and non-vascular (CD31-) but appeared to be decreased in an allele-dose dependent manner in mutant mice. Thus, this stromal population might contribute to the overall decrease in stroma cell number in mutant mice. Because we do not know anything about this population, we propose to remove the stroma quantification panel to better focus on SSCs and OPCs (new Figures 2A and 2B). Whether endothelial cell (EC) numbers are affected is an interesting question raised by the reviewer. Different types of bone marrow (BM) ECs have been phenotypically identified in long bones (see for instance Kusumbe Nature 2014; Balzano Cell Rep 2019). The bone fraction is reported to be enriched for arteriolar ECs (Sca1+CD31+Emcn-), few L-type sinusoidal ECs and CD31hiEmcnhi H-type ECs, a small fraction of the ECs at the end of the CD31+Emcn- arteriolar network. Based on Sca1 and CD31 expression, we observed by flow cytometry a decrease in ECs in the bone fraction of mutant mice (see below Figure 1 for reviewers). Although these preliminary findings are very interesting, we feel that they deserve to be strengthened by adding notably the Endomucin marker to visualize by immunofluorescence the impact of the Cxcr4 mutation on H-type and L-type EC architecture and numbers. This would constitute the subject of another study that will be dedicated to vascular modifications in WS mice. However, the well-established regulatory role of the vascular system on the mesenchymal one has been discussed in the revised version of the manuscript (page 22, lines 474 and 482). In particular, whether vascular cells participate in the defective osteolineage specification of SSCs in Cxcr4^{1013}-bearing mice deserves further investigations.
+
+![Bar graph showing bone cell numbers (x10^3) for SSC, OPC, and EC in WT, +/1013, and 1013/1013 mice](page_104_1342_495_312.png)
+
+Figure 1: Reduced endothelial cells in the bone fraction of mutant mice. Absolute numbers of the indicated stroma cell subsets from bone fractions were determined by flow cytometry in WT, +/1013 and 1013/1013 mice. Data (means ± SEM) are from three independent experiments with 6 mice in total per group. *, P < 0.05; and **, P < 0.005 compared with WT cells. $, P < 0.005 compared with +/1013 cells. (as determined using the two-tailed Student’s t test).
+2. “Figure 2N and 2S. Parameters of TBV and cortical bone should be quantified, preferable by μCT (or quantitative histological analysis). At this moment, only 1 image per condition is shown and this is an Opn staining, which is not considered to be the appropriate approach for quantitative bone measurements. This quantification of bone parameters is especially necessary to verify the bone loss that occurs when recipient mice are WT (Figure 2S), as the bone loss that is induced by transplantation of mutant donor cells in WT recipient mice is hard to be explained only by a reduced number of SSC and OPC, as is now suggested.”
+We are grateful to the reviewer for this helpful suggestion and as requested, we have quantified trabecular and cortical bone parameters by μCT (new Figures 20 and 2P and new supplemental Figure 1G). By this way, we confirmed the bone loss in WT recipient upon transplantation of mutant BM, thereby indicating cell-extrinsic (hematopoietic) Cxcr4-mediated regulation of the skeletal landscape. The text has been modified accordingly (page 11, line 230; page 9, line 183). One can speculate that myeloid cells including OCLs as well as lymphoid cells may actively participate in promoting bone remodeling in BM chimeric WT recipient mice. Indeed, the laboratory of Pr. A. Bozec among others recently reported that prolonged HIF-1α signaling in B cells leads to enhanced RANKL production and OCL formation in the BM (Meng et al., Bone Research 2022). Likewise, BM T cells are known to produce RANKL and to regulate OCL compartment within the BM (see for review for instance Corrado et al., IJMS 2020; Mori et al., Clin Dev Immunol 2013; Zhang et al., Front Endocrinol 2020). Whether the transplantation of mutant BM recreates a pro-osteoclastogenic environment through a remodeling of the lymphoid compartment deserves further investigations. This point has now been discussed in the revised version of the manuscript (page 21, line 459).
+
+3. “Figure 3. The authors suggest that the in vivo observed increase in osteoclasts in mutant mice is linked to an altered BM environment. To strengthen this statement, coculture experiments of osteogenic cells and osteoclast-precursors, in different combinations of WT vs mutant cells (treated with PTH, Pg or 1,25-vitamin D) should be performed. At this moment, the data only describe a discordance between the in vivo and in vitro findings, but do not allow to make any conclusion on whether the decrease in bone mass is partly caused by increased bone resorption.”
+We sincerely thank the reviewer for this very relevant and helpful comment. We fully agree with the point that making a link between osteogenic cells and osteoclast precursors is of importance. As recommended by the reviewer, we addressed it using a co-culture system between in vitro expanded osteogenic cells carrying or not the Cxcr4 mutation and WT OCL precursors, ie., BM CD11b+ myeloid cells. As shown in the new Figure 3L, mutant osteogenic cells promoted exacerbated OCL differentiation compared to WT cells. Soluble factors seem to be not sufficient to explain this bias as the supernatants of stimulated expanded osteogenic cells (WT or mutant) did not induce OCL differentiation. Additionally, transcriptomic analyses of stimulated osteogenic cells carrying or not the Cxcr4 mutation did not reveal any major changes in expression levels of master genes regulating osteoclastogenesis such as the RANKL/OPG balance or the M-Csf cytokine (see new Figure 3M). These findings suggest a juxtacrine function of osteogenic cells toward OCL differentiation that likely relies on direct interactions between both cell types and involves the Cxcl12/Cxcr4 axis. As adding the osteogenic component carrying the Cxcr4 mutation is sufficient to promote in vitro enhancement of OCL differentiation, we propose that the overall decrease in bone mass in mutant mice involves remodeling of osteogenic and osteoclastogenic components leading to decreased bone formation and increased bone resorption. Although the use of a conditional mutant mouse model would be the ideal way to confirm these findings, such a model is not currently available to our knowledge. In such a process, the osteogenic lineage would act as the driver and the OCL one as a passenger. The underlying molecular mechanism(s)
+of this cross-talk remains to be elucidated, but seems to require direct contact between both cell types. The text has been modified accordingly (page 11, line 230; page 21, line 451).
+
+4. “Figure 3. The histomorphometric data should be confirmed in more mice, as 3 mice per group for histomorphometric analysis is often not sufficient (Figure 3F-H). In addition, the bone formation data are puzzling, as osteoblast surface and osteoid surface are normal, but MS/BS and DB/BS are decreased. The authors interpret these data as a ‘lower number of osteoblasts’ but this statement does not fit with the normal osteoblast surface that is observed. Since dynamic bone formation parameters primarily measure the incorporation of minerals, these data might suggest that the formation of bone matrix by the osteoblasts is normal, but that the mineralisation of this bone matrix is impaired (and likely some osteoblasts are not mineralizing the matrix, whereas others show normal mineralization capacity as MAR is normal). Gene expression analysis might provide some more insight. The gene expression analysis (Figure 3J) is now restricted to genes that typify mature osteoblasts, but the expression of genes involved in mineralization is not analysed. In addition, the variation of the gene expression data reported in Figure 3J and M, is rather high and this quantification should be validated with qRT-PCR data and using more mice.”
+As requested by the reviewer, histomorphometric and osteoclast data have been implemented by adding two to three mice per group. These results that are now displayed in Figure 3A-3E confirmed the previous ones, ie. increased OCL surface and number and decreased total and double labelled bone surfaces in mutant mice compared to WT ones. Mineral apposition rate was similar in WT and Cxcr4^{1013}-bearing mice, while bone formation rate is lower in mutant mice. These data prompt us to suggest a decrease in bone formation related to a lower number of OBLs with maintained activity of each individual OBL. In line with preserved intrinsic bone formation capacities of active osteoblastic lineage cells in mutant mice, our RNA-seq analyses of bulks sorted from the bone fraction highlighted in mutant OPCs a gene signature with preserved mineralized matrix potential that has been confirmed by qPCR analyses (see new Figures 3F-H and S1K-M). In agreement, sorted OPCs from mutant mice were as efficient as WT ones in vitro at producing differentiated OBLs and mineralized nodules after 14- or 21-days culture in osteogenic medium as determined by Alkaline phosphatase and Alizarin Red staining respectively (see new Figures 3I and S1N). This was confirmed by qPCR analyses with no changes in expression of genes encoding osteogenic regulators in mutant cultures (see new Figure S1O). These findings are in line with efficient terminal osteogenic differentiation and preserved bone formation and mineralization capacities in Cxcr4^{1013}-bearing mice. The text has been modified accordingly (page 11, lines 208 & 219).
+
+5. “Figure 4. Panel D shows the relative expression of selected genes; are these the most differentially expressed genes between the different genotypes? To appreciate the importance of these differences, it will be important to provide also the unbiased ranked overview/list of pathways which differ the most between genotypes, based on genes involved. In addition, since mutant SSC maintain their potential to differentiate normally to chondrocytes and adipocytes, are SOX9 and Pparg expression normal in mutant SSC? Furthermore, it remains hard to understand that a decrease in OPC number (Figure 2B, Figure 4I) does not affect osteoblast or osteoid surface. How do the authors reconcile these data?”
+We sincerely thank the reviewer for bringing to our attention that unbiased transcriptomic analyses of WT and mutant SSC are needed. As requested, we investigated the impact of the gain-of-Cxcr4-function on the molecular identity of SSCs by performing RNA-seq analyses of sorted bulk cells from WT and mutant bone fractions. Biological processes related to cell cycle and osteogenic differentiation were significantly modulated in 1013/1013 SSCs compared to WT SSCs as determined by GSEA (Gene set enrichment analysis) (see new Figure 4C). The gene signature related to cell cycle progression and regulation was reduced in 1013/1013 SSCs compared to WT
+ones (see new Figures S2A and S2B). Likewise, genes related to osteogenic differentiation appeared to be decreased in mutant SSCs (see new Figures 4D and 4E). In contrast, key genes involved in both adipogenesis and chondrogenesis were not differentially expressed in mutant SSCs (see new Figure S2C). These results were confirmed by microfluidic-based multiplex gene expression analyses (see Figures 4F and 4G and Figure S2D), thus suggesting that proper Cxcr4 signaling is required for regulating osteogenic specification of SSCs at the transcriptional level. The text has been modified accordingly (page 13, line 264). Regarding the last point about our flow-cytometric and histomorphometric results, we agree that decreased OPC number cannot fully be explained by the unremarkable osteoid and osteoblast number. We therefore measured the labelled surfaces and MAR and also calculated the bone formation rate, which are more accurate indices of dynamic bone formation. Indeed, labelled surfaces and bone formation rate are decreased, which is in favor of reduced OBL differentiation, while the MAR remained identical, thus suggesting a maintained capacity of osteoblast to produce matrix once differentiated.
+
+6. “Figure 5 and 3. The data suggest that osteogenic differentiation starting from mutant SSC is reduced (Figure 5E-G), but once mutant SSC become OPC they can differentiate normally (Figure 3L). It should be good to confirm this observation, by performing the same assays on OPC as shown for SSC (Figure 5: differentiation with Alp quantification and gene expression analysis). In addition, it is rather particular that after 21 days of osteogenic differentiation, most of the cells are still SSC (Figure S1), and intermediate cells account only for 15% of the population, whereas the % of ALP+ cells, reported in Figure 5E, seems much higher. Same comment for the low % of mature cells compared to reported homogeneous and abundant alizarin red staining (Figure 5F).”
+We are grateful to the reviewer for this constructive suggestion and as requested we performed Alp quantification and gene expression analyses as already explained in response to the point#4 above. Our novel data showed that sorted OPCs from mutant mice were as efficient as WT ones in vitro at generating bone-making OBLs after 14-days culture in osteogenic medium as determined by Alp staining (see new Figure S1N). This was further confirmed by qPCR analyses with no changes in expression of genes encoding osteogenic regulators in mutant cultures (see new Figure S1O). These findings are in line with efficient terminal osteogenic differentiation and preserved bone formation and mineralization capacities in Cxcr4\( ^{1013} \)-bearing mice. The text has been modified accordingly (page 11, line 219). We fully agree with the reviewer that the yield of immature and mature osteogenic cells recovered by flow cytometry was not as high as expected in light of Alp and Alizarin red staining, and this was likely due to the difficulty we experimented to collect and separate homogenously the cells from the mineralized matrix at the end of the culture. Although real-time quantitative PCR analyses of Sca-1 and PDGFR\( \alpha \) markers corroborated the flow cytometric results (see Figure S2E), these flow cytometric results are rather dispensable for the paper and therefore we propose to remove them to clarify the message. We thank the reviewer for having pointed this inconsistency.
+
+7. “Figure 5 in vivo data. The authors state that especially the cortical bone is rescued in mutant mice, but not the trabecular phenotype, based on lumbar spine BMD data. To validate this statement, \( \mu \)CT analysis of cortex of long bones should be analysed with and without AMD3100 treatment. In addition, these data also suggest that CXCR4 desensitisation in osteogenic lineage cells is likely not responsible for the trabecular bone phenotype, and that other cell types/mechanisms might be involved. This site-specificity should be reflected in the title and in the abstract.”
+We thank the reviewer for this relevant comment. Our original version of the manuscript stated a suggestion for a correcting effect of Cxcr4-dependent signaling dampening on the cortical, rather than trabecular, bone based on BMD values of lumbar spine in mutant mice. Because \( \mu \)CT analyses were not carried out for this experiment, we sought to measure the cortical thickness in paraffin-embedded sections stained with Toluidine Blue. The two cortices were measured using
+histomorphometry software and expressed as mean of both cortices for each sample. As shown in the new Figure 5L, AMD3100 treatment for 3 weeks did not ameliorate the cortical network in mutant mice, thus suggesting that either the treatment procedure should be further optimized in terms of duration and kinetics or, as anticipated by the reviewer, that other cell types/mechanisms might be involved at this stage such as OCLs or perivascular SSCs as recently reported by Jeffery and coll. (Cell Stem Cell, 2022). This warrants further investigations. This point has been mentioned in the revised version of the manuscript (page 16, line 345).
+
+Minor concerns:
+1. “Perilipin staining should be quantified as the observation that CXCR4 specifically reduces the osteogenic, but not the adipogenic differentiation is interesting, but should be validated by quantitative data.”
+We thank the reviewer for bringing to our attention that quantification data would be helpful to strengthen the significance of our findings. As requested, Figure 1H mentioned by the reviewer has been edited with quantification data and shows no change in adipocyte content in the BM of mutant mice, as compared to WT mice (see new Figure 1J). Congruent with immunostaining on bone sections, RNA-seq analyses performed during the reviewing period show that mutant SSCs displayed a gene signature consistent with preserved adipogenic potential (see new Figures S2C and S2D). These cells also differentiated into adipocytes similarly to WT SSCs when cultured in vitro in adipogenic medium (Figure S2G). These results suggest that proper Cxcr4 signaling is required for regulating the osteogenic specification of SSCs specifically. The text has been modified accordingly (page 7, line 130; page 13, line 264, page 15 line 316).
+
+2. “Figure 1D: it is not clear whether the total number of mice used is 7-14, coming from 3 experiments, or that in each of the 3 experiments there were 7-14 mice, thus 21-42 mice in total. Similar comment to all experiments using mice.”
+We thank the reviewer for bringing to our attention that the total number of mice used in each experiment was not clear and we apologize for that. In fact, each number mentioned represents the total number of mice used, in 3 independent experiments or more. The legends have been modified accordingly.
+
+3. “Figure 2J: the % of apoptotic OPC is around 30%, which is rather high, and should be commented on.”
+We thank the reviewer for this relevant comment. Although the reason why the apoptosis rate is high among OPCs is unclear, we obtained similar results using cleaved caspase 3 staining instead of Annexin V staining. One can speculate that experimental procedures make these cells more fragile and prone to undergo apoptosis. In both assays, we were unable to observe differences between WT and mutant OPCs, thus strongly suggesting that increased apoptosis of OPCs does not contribute to bone loss in mutant mice. As requested by the Reviewer#4, this panel has been moved to the supplemental Figure 1 (see Figure S1F).
+
+Reviewer #2 comments:
+
+WHIM syndrome (WS) is a rare immunodeficiency caused by gain-of-function CXCR4 mutations. The authors have demonstrated for the first time a substantial decrease in bone mineral density in 25% of WS patients and osteoporosis in a WS mouse model. Interestingly, wild-type mice transplanted with bone marrow hematopoietic cells from mice with a WS-linked CXCR4 mutation (Cxcr4+/1013 or Cxcr4 1013/1013) had reduced trabecular bone content compared with wild-type chimeras. On the other hand,
+transplantation of wild-type bone marrow cells did not rescue the reduced trabecular bone content in the mutant chimeras. Osteogenic differentiation of cultured bone marrow skeletal stem cells (SSCs) from the mutants was impaired in vitro. The CXCR4 antagonist AMD3100 normalized in vitro osteogenic potential of SSCs and reversed an in vivo decrease in Sca-1-PDGFRα- cells in the mutants. These results are interesting and important; however the major concern remains at this time. There is the possibility that osteopenia in mice and patients, which carry the WS-linked CXCR4 mutation, is the result of only enhanced osteoclast function but not reduced osteogenic differentiation of SSCs.
+
+Major concerns:
+1. “As the authors described, it has been shown previously that deletion of CXCR4 in mesenchymal cells, including SSCs, resulted in osteopenia (Tzeng et al., J. Bone Miner. Res. 2018; Zhu et al., J. Biol/ Chem. 2011). These results argue against the authors’ conclusion that gain-of-function CXCR4 mutations in SSCs resulted in osteopenia. Thus, I would recommend the authors to generate and analyze the mice, in which mesenchymal cells, including SSCs, but not hematopoietic cells carry WS-linked CXCR4 mutations.”
+
+We are grateful to the reviewer for this relevant and constructive comment. Indeed, truncating mutations in CXCR4 which cause the WHIM syndrome (WS) in humans lead in *vitro* to a typical gain-of-function response to CXCL12 as exemplified by enhanced chemotaxis. However, in several cellular contexts (e.g., HSC lymphoid differentiation, B cell development…), we observed that loss of CXCR4 and gain of function of CXCR4 translated into similar phenotypes. This likely relates to the intensity and the strength of CXCR4 signaling that should be tightly regulated to permit the occurrence of physiological functions. Our findings unveil that mutant SSCs from the bone fraction are impaired in their capacities to generate OBLs as illustrated notably *in vitro* thus implying a cell-autonomous effect of the *Cxcr4* mutation in the bone phenotype. In line with this, J. Pereira’s laboratory recently showed using a second mouse model of the WS, carrying the gain-of-function *CXCR4* R334X mutation, that lymphopoiesis is reduced because of a dysregulated transcriptome of mesenchymal stem cell isolated from the flushed marrow fraction and characterized by a switch from an adipogenic to an osteolineage-prone program with limited lymphopoietic activity (Zehentmeier et al., Science Immunology 2022). These results agree with ours and suggest that both hematopoietic and stromal cells are affected by the *Cxcr4* gain of function mutation. The text has been modified accordingly (page 5, line 90; page 19, line 403).
+
+Our reciprocal BM reconstitution experiments support this assumption since transplantation of WT BM into lethally irradiated mutant recipients was not sufficient to rescue the skeletal landscape phenotype, and conversely, transplantation of mutant BM induced bone dysregulation in WT recipient (see Figures 3E-P and S1G). Although we are aware of the fact that BM chimera do not constitute perfect models, we do believe they are informative notably when hematopoietic cells that are engrafted do not carry WS-linked CXCR4 mutations. Moreover, we think that our ubiquitous mouse model is relevant since it closely phenocopies the immune-hematological phenotype of the human pathology in which both hematopoietic and stromal cells harbor the *Cxcr4* mutation. To confirm that, a conditional mouse model would have been ideal and not beyond the scope but we are not aware that such a model exists and it was not feasible *de novo* in the frame of a reviewing period. Rather, as suggested by the Reviewer#1, we set-up a co-culture system between *in vitro* expanded osteogenic cells carrying or not the *Cxcr4* mutation and WT OCL precursors, *ie.*, BM CD11b+ myeloid cells. As shown in the new Figure 3L, mutant osteogenic cells promoted exacerbated OCL differentiation compared to WT cells. Soluble factors do not seem sufficient as the supernatants of such stimulated expanded osteogenic cells (WT or mutant) did not induce OCL differentiation. Additionally, transcriptomic analyses of stimulated osteogenic cells carrying or not the *Cxcr4* mutation did not reveal any major changes in expression levels of master genes regulating osteoclastogenesis such as the RANKL/OPG
+balance (see new Figure 3M). These findings suggest a juxtacrine function of osteogenic cells toward OCL differentiation that likely relies on direct interactions between both cell types and involves the Cxcl12/Cxcr4 axis. As adding the osteogenic component carrying the Cxcr4 mutation is sufficient to promote in vitro enhancement of OCL differentiation, we propose that the overall decrease in bone mass in mutant mice involves remodeling of osteogenic and osteoclastogenic components leading to decreased bone formation and increased bone resorption. In such a process, the osteogenic lineage would act as the driver and the OCL one as a passenger. The underlying molecular mechanism(s) of this cross-talk remains to be elucidated but seems to require direct contact between both cell types. The entire manuscript as well as the title have been modified accordingly (page 11, line 230; page 21, lines 451 & 459) and a graphical abstract has been designed consequently.
+
+2. “The authors show the reduced trabecular bone content of mice with a WS-linked CXCR4 mutation transplanted with bone marrow hematopoietic cells from wild-type mice was not rescued 3 and 16 weeks after transplantation. However, wild-type hematopoietic cells might be able to rescue the reduced trabecular bone content of the mutants earlier in development.”
+We thank the reviewer for this relevant comment. However, we have to stress that currently we do not have the ethical authorization to transplant BM into mice younger than seven/eight weeks but we are aware that it would be interesting to do it. This has been clearly mentioned in the revised version of the manuscript (page 9, line 175).
+
+3. “The authors describe Sca-1+PDGFRa+ cells as SSCs (Page 8, line 142); however, the major population of bone marrow SSCs is defined as Sca-1-PDGFRa+PDGFRb+LepR+CD31- cells (Omatsu et al., Immunity 2010; Zhou et al., Cell Stem Cell 2014; Seike et al., Genes Dev 2018).”
+We are grateful to the referee for pointing out that the phenotype of SSCs we used could be a matter of debate and should be better justified. To the best of our knowledge, there is currently no consensual denomination for the different BM mesenchymal subpopulations and we agree with the reviewer that we should have been more precise on this point. As shown in the paper of Zhou et al. (Cell Stem Cell, 2014), the highest CFU-F clonogenic potential is observed in the Sca1+PDGFRa+ subset and not in the Sca1-PDGFRa+ population. This has been confirmed and extended to SSCs in the periosteum (Jeffery et al., Cell Stem Cell, 2022). Furthermore, 16wks after transplantation of GFP+ Sca1+PDGFRa+ into WT mice (Morikawa et al., JEM 2009), it was shown that among the GFP+ cells recovered, a few were Sca1+PDGFRa+ and most of them were Sca1-PDGFRa+, indicating that Sca1+PDGFRa+ cells are at the top of the hierarchy. This is why we chose to consider the Sca1+PDGFRa+ cells in the bone fraction as skeletal stem cells as compared to Sca1-PDGFRa+ that are more engaged in differentiation, as osteoblast progenitor cells. This point has been mentioned in the revised version of the manuscript (page 8, line 146).
+
+4. “The evidence that Sca-1-PDGFRa- cells are committed osteoblasts (OPCs) in the bone marrow would not be convincing (Page 8, line 143).”
+We apologize for the lack of clarity with this sentence. As explained in the point 3, we consider the CD51+Sca1- population as more differentiated than its Sca1+ counterpart and the sentence has been modified accordingly (page 8, line 146). There was also a typo and we should have referred to the CD51+Sca1- population as PDGFRa+/- as it includes both PDGFRa positive and negative subsets. In line with this, we already consider early OPCs with multipotent adip/o/osteogenic potential in the flushed stromal marrow fraction as Sca-1-negative and PDGFRa-positive (see new Figure 4M). Our previous results showed that the Sca1-PDGFRa-population highly express committed osteoblast markers such as Bglap, Col1a1 and Pth1r1 (see Balzano et al., Cell Reports 2019).
+Reviewer #4 comments:
+
+The manuscript by Anginot and colleagues provides novel insights into the role of CXCR4-mediated signaling in skeletal stromal/stem cell osteogenic specification. The authors describe a series of experiments characterizing the anatomic, developmental and functional properties of the skeletal and osteogenic compartment in a knock-in mouse model of the human genetic disorder WHIM syndrome. The significance of the deficits in skeletal remodeling and stem cell differentiation identified in the mouse model in human bone biology are validated in cohort of WHIM syndrome patients carrying gain-of-function mutations in CXCR4. These findings represent a novel contribution elucidating an important new role for CXCR4 in bone biology.
+
+Major concerns:
+1. “The authors characterized the effects of increased CXCR4 signaling in vivo through standard histomorphometric of bone anatomy and flow cytometric analyses of various progenitor cell populations in the mouse model. The data in Figure 1 are well presented and convincing in regard to the gene-dose dependent skeletal effects as well as the specificity of the changes to cortical and trabecular bone. Figure 2 is overly dense and contains information that could be moved to the supplement without impacting the major findings of the work. In particular, the experiments demonstrating the functional effects of the mutant CXCR4 receptor recapitulate characteristics of CXCR4 C-terminal truncations that have been well studied in other contexts. It would suffice to state that the mutant receptor localization, internalization and intracellular signaling were similar to what has been seen in other contexts and move panels 2E-J to the supplement. The bone marrow reconstitution experiments shown in the remainder of the figure demonstrate clearly the contribution of cell-extrinsic as well as cell-intrinsic factors to the observed skeletal changes. Similarly, the effects on bone resorption and formation shown in Figure 3 panels C-E can be moved to supplement to better focus on the transcriptional effects shown in the subsequent panels.”
+We are grateful to the reviewer for these constructive suggestions and as requested, the panels 2E-J and 3C-E have been moved to the new Supplemental Figure 1 (see panels S1A-S1F and S1H-S1J).
+
+2. “The data in Figures 4 and 5 provide compelling data regarding the impact of aberrant CXCR4 signaling on osteogenic specification at the level of transcriptional effects and cell cycle progression. The PCA data shown in Figure 4C is not well explained as the 48 genes used for expression profiling are not described in the text nor the supplement, which lists a smaller number of genes. The data in the subsequent panels are more informative. I would consider removing panel 4C or moving it to the supplement with a better description of the analysis. The experiments shown in Figure 5 document the selective reduction in osteogenic differentiation capacity of stromal stem cells carrying one or two mutant CXCR4 receptors in a dose dependent fashion and the reversal of this phenotype with treatment of the receptor inhibitor AMD3100. The relevance of these data in mice to human bone biology are supported with the data shown in Figure 6 which revealed a selective osteogenic differentiation defect in bone marrow cells derived from WHIM syndrome patients.”
+We thank the reviewer for bringing to our attention that the PCA data shown in Figure 4C was not clear and we apologize for that. This panel has now been removed. As suggested by Reviewer#1, we decided to investigate the impact of the gain-of-Cxcr4-function on the molecular identity of SSCs by RNA-seq analyses of sorted bulk cells from WT and mutant bone fractions. Biological processes related to cell cycle and osteogenic differentiation were significantly modulated in
+1013/1013 SSCs as determined by GSEA (Gene set enrichment analysis) (see new Figure 4C). The SSC signature in 1013/1013 mice was reduced for genes related to cell cycle progression and regulation (see new Figures S2A and S2B). Likewise, genes related to osteogenic differentiation appeared to be decreased in mutant SSCs (see new Figures 4D and 4E). In contrast, key genes involved in both adipogenesis and chondrogenesis were not differentially expressed in mutant SSCs (see new Figure S2C). These results were confirmed by microfluidic-based multiplex gene expression analyses (see Figures 4F and 4G and Figure S2D), thus suggesting that proper Cxcr4 signaling is required for regulating osteogenic specification of SSCs at the transcriptional level. The text has been modified accordingly (page 13, line 264).
+
+3. “With regards to the conclusion that a skeletal phenotype is present in a subset of WHIM syndrome patients, given that treatment of neutropenia with G-CSF is associated with osteopenia as side effect of therapy, it would be useful to know the total number of patients treated with G-CSF in the cohort to address the concern that the enrichment in osteopenic patients is restricted to those patients that have been so treated as well as their ages and genders given the impact of these variables on risk for osteopenia in general.”
+We thank the reviewer for this very relevant comment. Nineteen WS patients had a baseline bone density scan as part of a drug treatment trial (NCT02231879) comparing 1 year of twice daily filgrastim (Neupogen) versus plerixafor (Mozobil) in a randomized, blinded crossover design. There were 13 women and 6 men with an average age of 30.5 years (range 10-56). Patients had been on filgrastim for an average of 5.7 years prior to enrolling in the trial (range 0-27). Six of the 19 had not used filgrastim regularly prior to trial enrollment. These findings suggest that the enrichment in osteopenic WS patients is not merely due to treatment regimen, age or gender parameters. This point is now mentioned in the revised version of the manuscript (page 22, line 487; page 23, line 507).
+
+4. “Apart from these concerns, the quality of the data presented is good and the conclusions supported by the evidence. The manuscript is well written and the references appropriate, though it was notable that the initial description of the cause of WHIM syndrome as gain-of-function truncation mutations in CXCR4 was not cited, this should be added.”
+We thank the reviewer for this relevant comment and apologize for this oversight. The initial description of inherited CXCR4 mutations in the WS has been reported by Hernandez and collaborators in 2003 (Nature Genetics, PMID: 12692554). The appropriate reference (n°50 in the list of references) has been added accordingly (page 5, line 98).
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors answered adequately to the comments and questions by performing additional experiments and adapting the text. The claims are now well supported by their findings, making it an interesting study providing further insight in the skeletal effects of CXCR4 mutations.
+
+Minor comments:
+Page 11, line 208: the following sentence is difficult to interpret: Cxcr41013-bearing mice exhibited unremarkable bone formation. Not clear what is meant by ‘unremarkable’.
+
+Page 11, line 225: It is mentioned that OBL differentiation is reduced in mutant mice, whereas the previous lines describe normal osteogenic differentiation when cultures are started with OPCs. To avoid misunderstanding, some other wording should be used to describe that the transition of SSCs to OPCs is impaired or that there is reduced osteogenic lineage commitment.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have given a satisfactory response to some of this reviewer’s concerns, improving the manuscript. However, their answers to several issues remain incomplete, and therefore their conclusions are still not convincing.
+
+1. The new data that transplantation of Cxcr4 1013/1013 mutant bone marrow cells markedly reduced trabecular bone content (BV/TV and Tb.Nb) of wild-type recipient mice (Fig. 2P) are interesting and important. The magnitude of the decrease seems to be much larger compared with Cxcr4 1013/1013 mutant mice, suggesting that microenvironments with gain-of-function Cxcr4 1013/1013 mutations increased and rescued trabecular bone content. This is consistent with previous findings that deletion of CXCR4 in mesenchymal cells reduced trabecular bone content (Tzeng et al., J. Bone Miner. Res. 2018; Zhu et al., J. Biol. Chem. 2011).
+
+2. Again I would recommend the authors to generate and analyze the mice, in which mesenchymal cells, including SSCs, but not hematopoietic cells carry WS-linked CXCR4 mutations. However, the authors mentioned that it was not feasible in the frame of a reviewing period. Then, the authors should at least show trabecular bone content (BV/TV and Tb.Nb) of Cxcr4 1013/1013 mutant mice transplanted with bone marrow cells from wild-type mice and compare the results with those of wild-type mice transplanted with mutant bone marrow cells.
+Reviewer #4 (Remarks to the Author):
+
+The authors have addressed all of the issues raised by me adequately. I am satisfied with the responses to the other reviewers as well and have no additional concerns.
+Point-to-point response to the reviewers’ comments
+
+Reviewer #1 comments:
+
+The authors answered adequately to the comments and questions by performing additional experiments and adapting the text. The claims are now well supported by their findings, making it an interesting study providing further insight in the skeletal effects of CXCR4 mutations.
+
+Minor comments:
+1. Page 11, line 208: the following sentence is difficult to interpret: Cxcr41013-bearing mice exhibited unremarkable bone formation. Not clear what is meant by ‘unremarkable’.
+We thank the reviewer for bringing to our attention that the use of the term “unremarkable” was not clear and probably not appropriate. The sentence has been modified as follow: “Cxcr4^{1013}-bearing mice exhibited similar bone formation as revealed by osteoid surface (OS/BS) and osteoblast surface (Obl.S/BS) compared to WT mice (Fig. 3C)”. The text has been modified accordingly (page 11, line 208).
+
+2. Page 11, line 225: It is mentioned that OBL differentiation is reduced in mutant mice, whereas the previous lines describe normal osteogenic differentiation when cultures are started with OPCs. To avoid misunderstanding, some other wording should be used to describe that the transition of SSCs to OPCs is impaired or that there is reduced osteogenic lineage commitment.
+We thank the reviewer for this very relevant comment. The sentence has been changed as follow: “These findings suggest reduced osteogenic lineage commitment in Cxcr4^{1013}-bearing mice”. The text has been modified accordingly (page 11, line 224).
+
+Reviewer #2 comments:
+The authors have given a satisfactory response to some of this reviewer’s concerns, improving the manuscript. However, their answers to several issues remain incomplete, and therefore their conclusions are still not convincing.
+
+1. The new data that transplantation of Cxcr4 1013/1013 mutant bone marrow cells markedly reduced trabecular bone content (BV/TV and Tb.Nb) of wild-type recipient mice (Fig. 2P) are interesting and important. The magnitude of the decrease seems to be much larger compared with Cxcr4 1013/1013 mutant mice, suggesting that microenvironments with gain-of-function Cxcr4 1013/1013 mutations increased and rescued trabecular bone content. This is consistent with previous findings that deletion of CXCR4 in mesenchymal cells reduced trabecular bone content (Tzeng et al., J. Bone Miner. Res. 2018; Zhu et al., J. Biol. Chem. 2011).
+
+We thank the reviewer for these valuable remarks and suggestions. Although it is difficult to compare chimeric and steady state mice, especially considering the whole-body irradiation and the 4-month reconstitution period, it appears indeed that WT mice reconstituted with mutant BM display stronger trabecular bone defects than younger mutant mice at steady state. It is indeed possible that, as put by the reviewer, “microenvironments with gain-of-function Cxcr4 1013/1013 mutations increased and rescued trabecular bone content”. Besides mesenchymal and osteolineage cells, the BM ecosystem contains other possible effector cells including hematopoietic and mature immune cells, but also some radioresistant endothelial cells, and other stromal cells such as adipocytes that all express the CXCR4 receptor, which emerge during bone development and reach homeostasis at the adult stage. One can assume that the gain of CXCR4 function might modulate, positively or negatively, one, or several, BM landscape component(s) that could balance the trabecular bone defect in 1013/1013 mice. This is indeed consistent with
+previous works reporting a cell-autonomous Cxcl12-Cxcr4 signaling on the MSPC osteogenesis but not adipogenesis (Tzeng et al., J. Bone Miner. Res. 2018; Zhu et al., J. Biol. Chem. 2011). Future studies are necessary to identify such cells by tissue-specific CXCR4 targeting, as suggested by the reviewer. This point has been now discussed (page 21, line 469).
+
+The magnitude of the bone loss in WT recipient upon transplantation of mutant BM is surprising but is indicative of cell-extrinsic hematopoietic-driven Cxcr4-mediated regulation of the skeletal landscape. This may be due to the presence of effector mature leukocytes in the BM graft as we suggested previously in response to the point 2 raised by Reviewer#1. Indeed, one can speculate that myeloid cells including OCL progenitors as well as lymphoid cells may actively participate in promoting bone remodeling in BM chimeric WT recipient mice. Indeed, the laboratory of Pr. A. Bozec among others recently reported that prolonged HIF-1α signaling in B cells leads to enhanced RANKL production and OCL formation in the BM (Meng et al., Bone Research 2022). Likewise, BM T cells are known to produce RANKL and to regulate OCL compartment within the BM (see for review for instance Corrado et al., IJMS 2020; Mori et al., Clin Dev Immunol 2013; Zhang et al., Front Endocrinol 2020). Whether the transplantation of mutant BM recreates a pro-osteoclastogenic environment through a remodeling of the lymphoid compartment deserves further investigations.
+
+2. Again I would recommend the authors to generate and analyze the mice, in which mesenchymal cells, including SSCs, but not hematopoietic cells carry WS-linked CXCR4 mutations. However, the authors mentioned that it was not feasible in the frame of a reviewing period. Then, the authors should at least show trabecular bone content (BV/TV and Tb.Nb) of Cxcr4 1013/1013 mutant mice transplanted with bone marrow cells from wild-type mice and compare the results with those of wild-type mice transplanted with mutant bone marrow cells.
+We are grateful to the reviewer for this helpful suggestion and as requested, we have quantified trabecular bone parameters by μCT (see new Figures 2H and 2I). These new analyses extend the flow-cytometric and histological ones and indicate a persistent bone loss in mutant recipient upon transplantation of WT BM, thereby supporting the hypothesis of a cell-intrinsic CXCR4-mediated regulation of the skeletal landscape. However, the extent of the bone loss appears to be less marked compared with WT recipients transplanted with mutant BM cells. As discussed above, this could rely on the modulatory effect due to the gain of CXCR4 function on one, or several, stromal component(s) that could compensate the trabecular bone defect particularly in 1013/1013 mice. As stated in the manuscript, these findings suggest that impaired CXCR4 desensitization in both skeletal and hematopoietic cells have combinatorial effects on bone landscape dysregulation in adult Cxcr4^{1013}-bearing mice.
+
+Reviewer #4 comments:
+
+The authors have addressed all of the issues raised by me adequately. I am satisfied with the responses to the other reviewers as well and have no additional concerns.
+We thank the reviewer for the previous suggestions and are happy that all concerns were addressed.
+REVIEWERS' COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have given a satisfactory response to this reviewer’s concerns, improving the manuscript.
+
+Minor points
+Figure 2I: How about p-values in Tb.Nb? They appear to be significantly less than 0.005 as seen in BV/TV.
+Point-to-point response to the reviewers’ comments
+
+Reviewer #2 comments:
+The authors have given a satisfactory response to this reviewer’s concerns, improving the manuscript.
+
+Minor points
+Figure 2I: How about p-values in Tb.Nb? They appear to be significantly less than 0.005 as seen in BV/TV.
+
+We thank the reviewer for his/her previous constructive comments that have helped us improving greatly the quality of our manuscript. We are glad to read that all concerns were now addressed. Regarding the p-values of the data shown in Figure 2I, they have been determined using the two-tailed Student’s t test and are as follow:
+
+• For the BV/TV parameter:
+WT BM-chimeric CD45.2+ WT vs WT BM-chimeric CD45.2+ +/1013 mice: P= 0.033
+WT BM-chimeric CD45.2+ WT vs WT BM-chimeric CD45.2+ 1013/1013 mice: P = 0.0244
+
+• For the Tb.Nb parameter:
+WT BM-chimeric CD45.2+ WT vs WT BM-chimeric CD45.2+ +/1013 mice: P= 0.0702
+WT BM-chimeric CD45.2+ WT vs WT BM-chimeric CD45.2+ 1013/1013 mice: P = 0.0710
+
+The exact p-values have been now provided in the legend of Figure 2.

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+Peer Review File
+
+Pt nanoshell with ultra-high NIR- ⊙ photothermal conversion efficiency mediates multimodal neuromodulation against ventricular arrhythmias
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+In this manuscript, the authors synthesized Pt nanoshells for cardiac protection through photothermal therapy. The photothermal conversion efficiency of the Pt nanoshells was studied. In the in vitro and in vivo studies, the effect of photothermal therapy on TRPV1 and TREK1 channels were studied. I have the following comments.
+1. The effect of photothermal therapy in the NIR-I window on ventricular arrhythmias was reported by the authors previously. In this study, the authors used the laser irradiation in the NIR-II instead. In fact, the irradiation was directly performed at the NG and LSG with microinjection of the nanoparticles. There is no need to use PTT in the NIR-II. Therefore, this work lacks novelty.
+2. In the supporting information, the authors suggested that the photothermal conversion efficiency of Pt nanoshells was higher than other nanoparticles in previous reports. It is not accurate.
+3. The Pt nanoshells don't have a unique strong absorption peak in the NIR-II range. Therefore, they are not good candidates for PTT in the NIR-II window.
+4. In the in vitro cell study, the PTT study was performed in a 35 mm confocal dish. However, the irradiation diameter of the laser was very small. Most the cells in the dish cannot received the laser irradiation. It should be another concern.
+
+Reviewer #2:
+Remarks to the Author:
+Wang, Zhou and Liu present a paper describing a ~200 nm platinum-based, PEG-modified nanoparticle (NP) with high absorbance of near infra-red (1,000 nm+) light. The synthesised NP has high photothermal efficiency, which the authors used to stimulate heat-sensitive TRPV1 and TREK1 ion channels. First, they demonstrate this using HT-22 hippocampus neuronal cells, they then applied it to a canine myocardial infarction model, stimulating channels in the nodose ganglion (NG) and left stellate ganglion (LSG). The aim is to stimulate the parasympathetic nervous system and inhibit the sympathetic nervous system. The authors then show changes in ventricular electrophysiology and reduced biomarkers of cardiac injury, plus some basic biocompatibility data.
+
+Overall, there are many positive aspects of the work. I find that the paper is very well presented, with nicely laid out, attractive and well designed figures with clear illustrations. The methods section, at the end of the main document, is also very detailed. However, I find that the main manuscript is quite difficult to follow in some places. There are a lot of abbreviations - many are used without first defining them (though they can be found in the methods section). There is also very little introduction or background information given, meaning that the rationale of the study is not very clearly spelled out. No hypothesis or research aims are stated.
+
+I think it is also somewhat unusual that the introduction section starts to describe results (line 54 onwards) and even refers to figures (even if they are just schematic diagrams.)
+
+Similarly, the results section offers very little narrative or explanation of the results, which makes it difficult to follow the rationale of each experiment. For example, Vacht and c-fos staining are introduced with no explanation of what those are, why they are being stained, or what those results actually mean.
+The work appears to be original. The authors have previously used the same canine I/R models and stimulation of the NG and LSG by other means, but I do not find this NP formulation described previously. Statistical tests, sample sizes and P values are mostly clearly annotated and described, and seem appropriate for the types of data being analysed. Sample sizes also seem reasonable, though it not always clear which data points are replicates, independent biological samples, or
+actual experimental repeats.
+
+I do not find any major flaws with the NP synthesis or characterisation aspects, though this is not my specialty. However, I do have a few questions about the canine I/R model:
+
+The text mentions that “The NG was subsequently exposed to NIR-II laser irradiation for a duration of 5 minutes prior to occlusion of the left anterior descending (LAD) coronary artery for reperfusion therapy.” This text, and the diagram in Figures 4B, 5B and 6B, explain that the treatment was done before the I/R was induced. I am curious about why the authors choose a pre-treatment experimental design, rather than initiating the treatment after reperfusion. Obviously investigating only pre-treatment greatly lowers the clinical/therapeutic relevance of the research.
+
+Related to this, why do the authors think there is a reduction of serum troponin and myoglobin? (It is also not clear at what time point these samples were taken. Does this reflect acute cardio protection?) In my opinion, if the authors want to say that the system is cardioprotective (line 292) or protects against cardiac damage (line 350), additional metrics (echocardiography, infarct volume etc) would be required to support this claim.
+Figure 4f and 4g are a little difficult to understand. The Y axis is different between the two graphs, but it seems that the effect on max HR is quite mild? I think it would make sense to put the baseline and laser irradiation groups on the same graph and statistically compare those too.
+
+I am curious about the overall delivery efficiency, and biodistribution of the NPs and whether direct injection into the NG/LSG is clinically applicable.
+I also note that the in vivo comparisons are simply nanoparticles vs. PBS. This can clearly demonstrate that the NPs have some activity; but how do they compare to other methods of stimulating the NG/LSG, or drugs which stimulate the sympathetic/parasympathetic nervous system? Without these sorts of comparison, it is difficult to put the significance of authors’ findings into context. If the authors can demonstrate that their approach is better than other approaches, this could be a lot more convincing.
+
+In terms of overall interest, I think is a good technical demonstration of clever system; but what is the real-world application? Could the authors envisage a way in which this technology can actually be applied to MI patients?
+
+The abstract mentions that the NPs conferred protection against ventricular arrhythmias following MI. However, supplementary figure 25 seems to show that there was no difference in overall VA events.
+
+Minor points:
+Figure 3i is not very easy to read or understand.
+Line 373, I think that more than a few blood tests and some organ histologically is required to make such a strong claim of “unequivocally demonstrate” long-term safety.
+Supplementary figure 6, 13. I think these would be more readable as tables rather than bar charts.
+Supplementary figure 7; this is quite a broad range of nanoparticle sizes. What makes up the smaller (100 nm) particles? Is there aggregation to produce larger particles?
+
+Reviewer #3:
+Remarks to the Author:
+The manuscript describes photothermal neuromodulation via Pt nano-shell nanoparticles. Ga nanoparticles are used as a template for electrocoupling substitution-based synthesis of the Pt nano-shell. Using KOH wet etching, Ga core is etched and a Pt nano-shell structure is obtained. The rough surface topography of the Pt nano-shell structure allows the particles to exhibit high
+optical absorbance. It is claimed that these particles have one of the highest photothermal energy conversion efficiencies. The photothermal conversion of optical irradiation is then utilized for stimulation of target cells and tissues via temperature activated ion channels- TRPV1 and TREK1. The potential application of such photothermal modulation technique in regulating cardiac pulsing is demonstrated with regards to protecting against acute ventricular arrhythmias.
+However, the manuscript does not include proper controls to demonstrate that in-vivo photothermal modulation is achieved exclusively through the Pt nanoparticles. In addition, there are certain claims and results that need to be better corroborated to reach the scientific requirements of the journal. Therefore, I cannot recommend that this manuscript be accepted at Nature Communications in its current form.
+
+1. Abstract: It is claimed that “the autonomic nervous system plays a pivotal role in the pathophysiology of cardiovascular diseases.” This sentence is misleading since the dysregulation of the autonomic nervous system can contribute to cardiovascular diseases. However, it is not the primary contributor to the diseases, autonomous nervous system in fact regulates normal functioning of the cardiovascular system. (see: Purves D, Augustine GJ, Fitzpatrick D, LaMantia AS, McNamara JO, Williams SM. Autonomic regulation of cardiovascular function. Neuroscience. 2001:491-3 AND Gordan R, Gwathmey JK, Xie LH. Autonomic and endocrine control of cardiovascular function. World journal of cardiology. 2015 Apr 4;7(4):204.)
+2. The authors claim that bi-directional reversible autonomic modulation is achieved via NIR-II photothermal modulation using Pt nano-shell nanoparticles. The manuscript presents uni-directional modulation where the target tissues are stimulated. Bi-directionality isn’t demonstrated since in terms of neural interfaces, bi-directionality refers to the ability to record neural activity as well as stimulate (see: Song KI, Seo H, Seong D, Kim S, Yu KJ, Kim YC, Kim J, Kwon SJ, Han HS, Youn I, Lee H. Adaptive self-healing electronic epineurium for chronic bidirectional neural interfaces. Nature communications. 2020 Aug 21;11(1):4195. AND Hughes C, Herrera A, Gaunt R, Collinger J. Bidirectional brain-computer interfaces. Handbook of clinical neurology. 2020 Jan 1;168:163-81.).
+3. It is unclear why the NIR-II range was utilized in this work. This is important for selecting the right materials, models, and experiments. (see: nature.com/articles/s44222-023-00022-y AND nature.com/articles/s41551-022-00862-w).
+4. Instead of using terminologies like “nearly perfect blackbody absorption”, the actual optical properties and metrics should be presented.
+5. Figure 1 presents how the nanoparticles will interact with the biological systems, however it does not show how light pulses/irradiation will be delivered to the target tissues/sites. This should be discussed in the figure and the manuscript since it is important for clinical translation.
+6. Adequate controls should be provided to better compare the physical properties of PtNP-shells. That is, please provide the optical absorbance of GaNPs, Pt coated GaNPs for Figure 2.d; similar controls should be provided for Figure 2.e (including the thermal transients of such the solvent under irradiation.
+7. For the XPS characterization, a survey scan of representative sample should be presented along with the detailed XPS characterization of oxygen (O1s) and potassium (K2p). The elemental composition of the PtNP-shells, Pt coated GaNPs, and GaNPs should be compared as well. This will better elucidate the composition of effectiveness of the synthesis protocols.
+8. The stability of the Pt-nanoshell suspensions should be evaluated as a function of time. Do the nanoparticle aggregate over time? Will this be a concern when the Pt-nanoshells are injected into biological systems.
+9. How does the addition of mPEG-SH5000 effect the photothermal properties of the nanoparticles?
+10. Critical information from the methods section is missing- for example, details regarding the cell culture protocol and photothermal stimulation (such as power and pulse duration of optical irradiation are missing). How long was the ECG data recorded for? What were the exact stimulation conditions for all in-vivo experiments?
+11. For the in-vitro experiments, are the Pt nanoparticles engulfed by the target cells or are they localized in the vicinity of the cell membrane?
+12. Both in-vivo and in-vitro photothermal stimulation experiments require the cells’ microenvironment to reach temperatures greater than 42°C. Does repeated photothermal stimulation using such high temperatures adversely affect cellular health by disrupting the cell membrane or trigger heat shock response?
+13. The claim that Pt-NP shell does not induce significant damage to neurons under controlled NIR-II laser irradiation is incorrect since there is ~10% loss in cellular viability.
+14. It will be recommended that the data presentation in Figure 3.i be changed since the details of the data are difficult to comprehend through a 3-D plot.
+15. For the in-vivo photothermal stimulation experiments, can similar affects be achieved without the presence of the Pt-nanoshell particles? Figure 4.d presents high temperature gradients for the surrounding tissue as well. Stimulation using infra-red radiation has been demonstrated previously, see: doi.org/10.1364/OL.30.000504 and doi.org/10.1117/1.2121772.
+16. The biosafety of Pt-nanoshell particles was evaluated after a rapid excision of the LSG and NG tissues. Can the authors comments on the long-term biosafety of the nanoparticles in passive (without photothermal stimulation) and active (with photothermal stimulation) states?
+17. Page 2, line 21: Please include examples and appropriate references for “conventional international procedures for MI.”
+18. Page 4, line 16: Please change the word “encapsulated on” since Pt is not encapsulated on the surface of GaNPs. Pt is deposited onto of GaNP core then it encapsulates GaNP core.
+Reply to the referees
+
+To Referee #1
+
+First of all, we really appreciate your constructive comments. We have made a point-by-point response to your comments and carefully revised the manuscript as you suggested. For your reference, please find our revisions marked in red color.
+
+Comment 1: In this manuscript, the authors synthesized Pt nanoshells for cardiac protection through photothermal therapy. The photothermal conversion efficiency of the Pt nanoshells was studied. In the in vitro and in vivo studies, the effect of photothermal therapy on TRPV1 and TREK1 channels were studied. I have the following comments. The effect of photothermal therapy in the NIR-I window on ventricular arrhythmias was reported by the authors previously. In this study, the authors used the laser irradiation in the NIR-II instead. In fact, the irradiation was directly performed at the NG and LSG with microinjection of the nanoparticles. There is no need to use PTT in the NIR-II. Therefore, this work lacks novelty.
+
+Author reply: Thank you for your comments. The focus of our research is to utilize PtNP-shell with near-perfect blackbody absorption and high photothermal conversion efficiency, enabling safer and more precise bidirectional deep neural modulation of the nodose ganglion (NG) and the left stellate ganglion (LSG). Moreover, compared to the first near-infrared (NIR-I, 650–900 nm) and visible window, the photons in the second near-infrared window (NIR-II, 900–1700 nm) exhibit reduced tissue scattering and absorption, thereby increasing the maximum allowable exposure (MPE) of biological tissues. This means photons within the NIR-II window exhibit significantly enhanced tissue penetration depths (up to 5–20 mm) (Nat. Nanotech. 2009, 4, 710; Nat. Med. 2012, 18, 1841; Nat. Biomed. Eng. 2017, 1, 0010). We developed PtNP-shell and validated its photothermal neuromodulation efficacy in the NIR-II window both in vivo and in vitro. Given its wavelength independence, further investigations may facilitate the selection of a more suitable laser for achieving deeper tissue penetration while adhering to the MPE range. The exceptional potential of PtNP-shell makes it highly promising for precise neural regulation in deeper tissue. Moreover, NG and LSG are pivotal nodes of the vagal loop and sympathetic loop, respectively. In contrast to previous studies, our approach not only achieves neural activity inhibition but also enables nerve activation for bidirectional reversible modulation. Furthermore, we substantiate the therapeutic efficacy of this strategy in diverse models of cardiac injury.
+
+Comment 2: In the supporting information, the authors suggested that the photothermal conversion efficiency of Pt nanoshells was higher than other nanoparticles in previous reports. It is not accurate.
+Author reply: Thank you for the comment. The PtNP-shell exhibits an exceptionally high photothermal conversion efficiency, surpassing the values reported in Supplementary Table 2 (Table R1). To ensure utmost rigor, we have revised the statement to “among the highest”.
+
+Table R1 | Comparison of photothermal conversion efficiency.
+
+<table>
+  <tr>
+    <th></th>
+    <th>Photothermal conversion efficiency (%)</th>
+  </tr>
+  <tr>
+    <td>This work</td>
+    <td><span style="color:red">73.70</span></td>
+  </tr>
+  <tr>
+    <td>PEDOT:ICG@PEG-GTA<sup>1</sup></td>
+    <td>71.10</td>
+  </tr>
+  <tr>
+    <td>MINDS<sup>2</sup></td>
+    <td>71.00</td>
+  </tr>
+  <tr>
+    <td>PTG NPs<sup>3</sup></td>
+    <td>67.60</td>
+  </tr>
+  <tr>
+    <td>RBC@Cu<sub>2-x</sub>SeNPs<sup>4</sup></td>
+    <td>67.20</td>
+  </tr>
+  <tr>
+    <td>AuDAg<sub>2</sub>S<sup>5</sup></td>
+    <td>67.10</td>
+  </tr>
+  <tr>
+    <td>MAPSULES<sup>6</sup></td>
+    <td>67.00</td>
+  </tr>
+  <tr>
+    <td>Fe<sub>3</sub>O<sub>4</sub>@PPy@GOD NCs<sup>7</sup></td>
+    <td>66.40</td>
+  </tr>
+  <tr>
+    <td>NPPBTPBF-BT<sup>8</sup></td>
+    <td>66.40</td>
+  </tr>
+  <tr>
+    <td>AS1064<sup>9</sup></td>
+    <td>65.92</td>
+  </tr>
+  <tr>
+    <td>Gold Nanoraspberry<sup>10</sup></td>
+    <td>65.00</td>
+  </tr>
+  <tr>
+    <td>P-Pc-HSA<sup>11</sup></td>
+    <td>64.70</td>
+  </tr>
+  <tr>
+    <td>Ultrathin polypyrrole nanosheets<sup>12</sup></td>
+    <td>64.60</td>
+  </tr>
+  <tr>
+    <td>H<sub>x</sub>MoO<sub>3</sub><sup>13</sup></td>
+    <td>60.90</td>
+  </tr>
+  <tr>
+    <td>NiP PHNPs<sup>14</sup></td>
+    <td>56.80</td>
+  </tr>
+  <tr>
+    <td>FP NRs<sup>15</sup></td>
+    <td>56.60</td>
+  </tr>
+  <tr>
+    <td>COF<sup>16</sup></td>
+    <td>55.20</td>
+  </tr>
+  <tr>
+    <td>2MPT+-CB<sup>17</sup></td>
+    <td>54.60</td>
+  </tr>
+  <tr>
+    <td>SPN-PT<sup>18</sup></td>
+    <td>53.00</td>
+  </tr>
+  <tr>
+    <td>Pdots<sup>19</sup></td>
+    <td>53.00</td>
+  </tr>
+  <tr>
+    <td>Pt Spirals<sup>20</sup></td>
+    <td>52.50</td>
+  </tr>
+  <tr>
+    <td>TBDOPV-DT<sup>21</sup></td>
+    <td>50.50</td>
+  </tr>
+  <tr>
+    <td>TiO<sub>2</sub>3@HA NPs<sup>22</sup></td>
+    <td>50.20</td>
+  </tr>
+  <tr>
+    <td>TBDOPV–DT NP<sup>23</sup></td>
+    <td>50.00</td>
+  </tr>
+  <tr>
+    <td>DPP-IID-FA NPs<sup>24</sup></td>
+    <td>49.50</td>
+  </tr>
+  <tr>
+    <td>SPN-DT<sup>18</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>NP<sup>25</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>FTQ nanoparticles<sup>26</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>CNPs<sup>27</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>H-SiO<sub>x</sub> NPs<sup>28</sup></td>
+    <td>48.60</td>
+  </tr>
+  <tr>
+    <td>BETA NPs<sup>29</sup></td>
+    <td>47.60</td>
+  </tr>
+  <tr>
+    <td>CN-NPs<sup>30</sup></td>
+    <td>47.60</td>
+  </tr>
+  <tr>
+    <td>Pt-NDs<sup>31</sup></td>
+    <td>46.90</td>
+  </tr>
+  <tr>
+    <td>MoO<sub>3-x</sub> nanobelts<sup>32</sup></td>
+    <td>46.90</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>Material</th>
+    <th>λ_max (nm)</th>
+  </tr>
+  <tr>
+    <td>P3 NPs<sup>33</sup></td>
+    <td>46.00</td>
+  </tr>
+  <tr>
+    <td>Ni<sub>3</sub>S<sub>8</sub><sup>34</sup></td>
+    <td>46.00</td>
+  </tr>
+  <tr>
+    <td>PtAg nanosheets<sup>35</sup></td>
+    <td>45.70</td>
+  </tr>
+  <tr>
+    <td>Nb<sub>2</sub>C NSs<sup>36</sup></td>
+    <td>45.65</td>
+  </tr>
+  <tr>
+    <td>V<sub>2</sub>C-TAT@Ex-RGD<sup>37</sup></td>
+    <td>45.10</td>
+  </tr>
+  <tr>
+    <td>PEG-TONW NRs<sup>38</sup></td>
+    <td>43.60</td>
+  </tr>
+  <tr>
+    <td>SPNI-II<sup>39</sup></td>
+    <td>43.40</td>
+  </tr>
+  <tr>
+    <td>1T-MoS<sub>2</sub><sup>40</sup></td>
+    <td>43.30</td>
+  </tr>
+  <tr>
+    <td>Bi@C NPs<sup>41</sup></td>
+    <td>43.20</td>
+  </tr>
+  <tr>
+    <td>Au NPL@TiO<sub>2</sub><sup>42</sup></td>
+    <td>42.10</td>
+  </tr>
+  <tr>
+    <td>CT NPs<sup>43</sup></td>
+    <td>42.00</td>
+  </tr>
+  <tr>
+    <td>PPy-PEG NPs<sup>44</sup></td>
+    <td>41.97</td>
+  </tr>
+  <tr>
+    <td>AuPt@CuS NSs<sup>45</sup></td>
+    <td>41.56</td>
+  </tr>
+  <tr>
+    <td>Bi<sub>10</sub>S<sub>27</sub>I<sub>3</sub> nanorods<sup>46</sup></td>
+    <td>41.50</td>
+  </tr>
+  <tr>
+    <td>Cu<sub>3</sub>BiS<sub>3</sub> NR<sup>47</sup></td>
+    <td>40.70</td>
+  </tr>
+  <tr>
+    <td>MPAE-NPS<sup>48</sup></td>
+    <td>40.07</td>
+  </tr>
+</table>
+
+Comment 3: *The Pt nanoshells don’t have a unique strong absorption peak in the NIR-II range. Therefore, they are not good candidates for PTT in the NIR-II window.*
+
+Author reply: The PtNP shell exhibits strong absorption across a broad range of wavelengths, including the NIR-II window. We posit that the PTNP-shell holds promise as an excellent candidate for photothermal therapy (PTT) within the NIR-II window. Given its wavelength independence, further investigations may facilitate selection of a more suitable laser for achieving deeper tissue penetration while adhering to the MPE range, thereby enabling precise and noninvasive neural modulation.
+
+![Absorption curves and mass extinction coefficient plots for PtNP-shell](page_1012_1342_393_246.png)
+
+Fig. R1 | Absorption of PtNP-shell. **a**, Absorption curves of PtNP-shell with different concentrations (10, 25, 50 and 75 \( \mu \)g·mL\(^{-1}\)). **b**, Mass extinction coefficient of PtNP-shell at 1064 nm. Normalized absorbance intensity at \( \lambda = 1064 \) nm divided by the characteristic length of the cell (A/L) at different concentrations (10, 25, 50 and 75 \( \mu \)g·mL\(^{-1}\)).
+Comment 4: In the in vitro cell study, the PTT study was performed in a 35 mm confocal dish. However, the irradiation diameter of the laser was very small. Most the cells in the dish cannot received the laser irradiation. It should be another concern.
+
+Author reply: Thank you for the comment. With reference to previous photothermal research on cells (Nat. Biomed. Eng. 2022, 6, 754; Nano Converg. 2022, 9, 13), we conducted a cell calcium imaging experiment wherein the NIR-II laser was utilized to activate neuron cells within the confocal dish covered by the laser beam. We employed confocal microscopy to capture images of these neuron cells covered by laser beam and make quantitative analysis of calcium imaging. Consequently, the dimensions of the confocal dish did not influence the outcomes of the cellular calcium imaging experiment. A more comprehensive explanation is provided in the “Method” section:
+
+“XYT images in the region of 1064 nm illumination were acquired and collected under a 20x objective lens.”
+To Referee #2
+
+We appreciate your positive evaluation on our manuscript. We have made a point-by-point response to your comments and carefully revised the manuscript as you suggested. For your reference, please find our revisions marked in red color.
+
+Comment 1: Wang, Zhou and Liu present a paper describing a ~200 nm platinum-based, PEG-modified nanoparticle (NP) with high absorbance of near infra-red (1,000 nm+) light. The synthesised NP has high photothermal efficiency, which the authors used to stimulate heat-sensitive TRPV1 and TREK1 ion channels. First, they demonstrate this using HT-22 hippocampus neuronal cells, they then applied it to a canine myocardial infarction model, stimulating channels in the nodose ganglion (NG) and left stellate ganglion (LSG). The aim is to stimulate the parasympathetic nervous system and inhibit the sympathetic nervous system. The authors then show changes in ventricular electrophysiology and reduced biomarkers of cardiac injury, plus some basic biocompatibility data. Overall, there are many positive aspects of the work. I find that the paper is very well presented, with nicely laid out, attractive and well designed figures with clear illustrations. The methods section, at the end of the main document, is also very detailed. However, I find that the main manuscript is quite difficult to follow in some places. There are a lot of abbreviations - many are used without first defining them (though they can be found in the methods section). There is also very little introduction or background information given, meaning that the rationale of the study is not very clearly spelled out. No hypothesis or research aims are stated.
+
+Author reply: Thank you for your recognition of our work. The advices you put forward are very constructive and help a lot for us to improve our manuscript.
+
+We have provided reasonable descriptions of specialized acronyms that appear for the first time to increase readability. In addition, we have followed up on your comments to optimize the “introduction”. The background and rationale for the development and application of this strategy are described in more detail, and our research hypotheses and objectives are added.
+
+“However, left cardiac sympathetic denervation (LCSD), stellate ganglion block (SGB), and renal denervation (RDN) are associated with certain adverse effects, including Horner's syndrome (Circ.-Arrhythmia Electrophysiol. 2015, 8, 1007), inadvertent bleeding, and inconsistent ablation outcomes (N. Engl. J. Med. 2014, 370, 1393). Both conventional low-level vagus nerve stimulation (LL-VNS) and optogenetic neuromodulation necessitate the implantation of in vivo electrical stimulation (JACC-Clin. Electrophysiol. 2017, 3, 929) or light source devices (J. Am. Coll. Cardiol. 2017, 70, 2778). Furthermore, optogenetic neuromodulation requires viral transfection of photosensitive proteins (J. Am. Coll. Cardiol. 2017, 70, 2778), thereby limiting the clinical advancement of these therapeutic approaches.”
+“The light in the second near-infrared window (NIR-II, 900–1700 nm) has reduced tissue scattering and absorption and increased maximum permissible exposure (MPE) for biological tissues compared to the light in the first near-infrared (NIR-I, 650–900 nm) and visible window (Acc. Chem. Res. 2018, 51, 1840). Consequently, this enables non-invasive and non-implantable neuromodulation using NIR-II photothermal.”
+
+“Therefore, the objective of this study is to develop a Pt nanoparticle shell (PtNP-shell) with near-blackbody properties and ultra-high PCE in the NIR-II window (Fig. 1a) and investigate its potential in protecting against MI and myocardial reperfusion injury accompanying intervention through rapid, efficient, and precise multifunctional autonomic neuromodulation (Fig. 1b).”
+
+Comment 2: I think it is also somewhat unusual that the introduction section starts to describe results (line 54 onwards) and even refers to figures (even if they are just schematic diagrams).
+
+Author reply: Following your suggestion, we have revised the introduction by modifying the section describing results into one that outlines research assumptions and objectives, while enhancing the background information and fundamental principles underlying the development and application of this strategy.
+
+“Therefore, the objective of this study is to develop a Pt nanoparticle shell (PtNP-shell) with near-blackbody properties and ultra-high PCE in the NIR-II window (Fig. 1a) and investigate its potential in protecting against MI and myocardial reperfusion injury accompanying intervention through rapid, efficient, and precise multifunctional autonomic neuromodulation (Fig. 1b).”
+
+Comment 3: Similarly, the results section offers very little narrative or explanation of the results, which makes it difficult to follow the rationale of each experiment. For example, Vacht and c-fos staining are introduced with no explanation of what those are, why they are being stained, or what those results actually mean.
+
+Author reply: Thank you for your kind reminding. We have shown immunofluorescence staining in more details:
+
+“Furthermore, immunofluorescence staining for vesicular acetylcholine transporter protein (VACHT), c-Fos, and TRPV1 on histopathological sections of photothermally modulated NGs served to localize parasympathetic neurons and reflect neuronal activity as well as TRPV1 protein expression, respectively (Fig. 4i).”
+
+“Furthermore, immunofluorescence staining was conducted on LSG tissues to examine the expression of tyrosine hydroxylase (TH), c-Fos, and TREK1 (Fig. 6i). Localization of sympathetic neurons by TH proteins and reflection of neuronal activity as well as TREK1 protein expression.”
+Comment 4: The work appears to be original. The authors have previously used the same canine I/R models and stimulation of the NG and LSG by other means, but I do not find this NP formulation described previously. Statistical tests, sample sizes and P values are mostly clearly annotated and described, and seem appropriate for the types of data being analysed. Sample sizes also seem reasonable, though it not always clear which data points are replicates, independent biological samples, or actual experimental repeats.
+
+Author reply: To ensure the reproducibility and accuracy of our study, we repeated the experiment with independent biological samples in vitro and in vivo experiments to obtain the statistical information, including Fig 3d–j, Fig 4f–h, Fig 5e–k, Fig 6f–h, and Fig 7d–i, as well as the corresponding supplemental data.
+
+Comment 5: I do not find any major flaws with the NP synthesis or characterisation aspects, though this is not my specialty. However, I do have a few questions about the canine I/R model: The text mentions that “The NG was subsequently exposed to NIR-II laser irradiation for a duration of 5 minutes prior to occlusion of the left anterior descending (LAD) coronary artery for reperfusion therapy.” This text, and the diagram in Figures 4B, 5B and 6B, explain that the treatment was done before the I/R was induced. I am curious about why the authors choose a pre-treatment experimental design, rather than initiating the treatment after reperfusion. Obviously investigating only pre-treatment greatly lowers the clinical/therapeutic relevance of the research.
+
+Author reply: Thank you for the comment. The clinical management of acute myocardial infarction primarily involves transvascular interventions to restore blood flow in occluded vessels. However, reperfusion during this process can lead to acute ventricular arrhythmic events (Mediat. Inflamm. 2017, 2017, 14). To mitigate these adverse effects through neuromodulation, we performed NIR-II irradiation intervention prior to reperfusion injury simulation, mimicking the clinical practice scenario. Furthermore, photothermal activation or inhibition of nerves exhibits sustained efficacy. This experimental protocol aligns more closely with the clinical significance of reducing reperfusion injury in patients undergoing myocardial infarction treatment.
+
+Comment 6: Related to this, why do the authors think there is a reduction of serum troponin and myoglobin? (It is also not clear at what time point these samples were taken. Does this reflect acute cardio protection?) In my opinion, if the authors want to say that the system is cardioprotective (line 292) or protects against cardiac damage (line 350), additional metrics (echocardiography, infarct volume etc) would be required to support this claim.
+
+Author reply: Thank you for the comment. Serum troponin and myoglobin are the primary and crucial clinical indicators of myocardial injury. Myoglobin levels typically increase within 1 to 2
+hours following myocardial injury, while troponin elevation usually occurs 2 to 3 hours later. These two serum markers of cardiac injury can remain elevated for approximately 12 hours (*Int. J. Cardiol.* **2005**, *98*, 285). By implementing this experimental protocol, which involves collecting and testing blood samples at a time interval of 4 to 5 hours after modeling cardiac injury, accurate detection of myocardial injury in diverse individuals is facilitated.
+
+Furthermore, significant differences in infarct area detection or ultrasound cardiac function testing can be observed in long-term myocardial ischemia models (*Adv. Sci.* **2023**, *10*, 2205551; *Basic Res. Cardiol.* **2022**, *117*, 34). Previous studies have usually indicated the extent of myocardial injury through acute indices, such as biomarkers of myocardial injury, in acute myocardial ischemia models (*Adv. Mater.* **2023**, *35*, 2304620). We utilized serum markers of myocardial injury to reflect the severity of acute myocardial infarction or acute reperfusion injury.
+
+*Comment 7: Figure 4f and 4g are a little difficult to understand. The Y axis is different between the two graphs, but it seems that the effect on max HR is quite mild? I think it would make sense to put the baseline and laser irradiation groups on the same graph and statistically compare those too.*
+
+**Author reply:** Thank you for the comment. We adjusted the Y axis of Fig. 4f (Fig. R2a) to align with Fig. 4g (Fig. R2b), facilitating a direct comparison of neural function between baseline and laser irradiation conditions. Considering our aim to demonstrate the neural functions of both the PtNP-shell group and control group under these two conditions, presenting the data separately would enhance clarity rather than combining them in one graph. This separate presentation allows for visualization that there is no significant difference between the two groups in the baseline condition, while highlighting that after laser irradiation, PtNP-shell significantly enhances neural activity across all levels of stimulation.
+
+![Maximal HR changes of beagle treatment with PtNP-shell or control before and after NIR-II exposure](page_101_1042_1242_377.png)
+
+Fig. R2 | Maximal HR changes of beagle treatment with PtNP-shell or control a, before and b, after NIR-II exposure, n = 6.
+Comment 8: I am curious about the overall delivery efficiency, and biodistribution of the NPs and whether direct injection into the NG/LSG is clinically applicable.
+
+Author reply: The ganglion’s surface is enveloped by a dense connective tissue matrix, facilitating our direct microinjection of PtNP-shell into the ganglion with exceptional efficiency and minimal loss. Long-term biosafety monitoring revealed an absence of NP distribution in histologic examinations of vital metabolic-immune organs such as the heart, liver, spleen, lungs, and kidneys, while liver and kidney functions remained unaffected (Fig. R3 and R4).
+
+In clinical practice, ultrasound-guided injection of nerve blocking drugs into the ganglion enables local ganglion blockage (*Curr. Pain Headache Rep.* **2014**, *18*, 424). Our experimental approach aligns with established techniques for ganglion blocks and thus holds potential applicability in clinical settings.
+
+![Representative images of H&E and TUNEL staining of NG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up.](page_352_670_1042_393.png)
+
+Fig. R3 | Ganglion biocompatibility of targeted injections of PtNP or PBS after NIR-II irradiation and after 30 days of follow-up. **a**, Representative images of H&E and TUNEL staining of NG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up. **b**, Representative images of H&E and TUNEL staining of LSG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up.
+Fig. R4 | Long term biosafety of PtNP-shell microinjection. Long-term in vivo biosafety was assessed by local injection of PtNP-shell into the ganglion of Beagle or by injection of equal doses of PtNP-shell into the tail vein of Sprague-Dawley rats. a, Representative H&E staining of major organs of beagles following different treatments. Blood biochemical analyses including b, ALT, c, AST, d, Urea, e, Crea, f, LDH1, g, TNF-α, and h, IL-6 were performed on Beagles in different treatment groups. i, Representative H&E staining of major organs of rats following different treatments. Blood biochemical analyses including j, ALT, k, AST, l, Urea, m, Crea, n, LDH1, o, TNF-α and p, IL-6 were performed on rats in different treatment groups.
+
+Comment 9: I also note that the in vivo comparisons are simply nanoparticles vs. PBS. This can clearly demonstrate that the NPs have some activity; but how do they compare to other methods of stimulating the NG/LSG, or drugs which stimulate the sympathetic/parasympathetic nervous system? Without these sorts of comparison, it is difficult to put the significance of authors’ findings into context. If the authors can demonstrate that their approach is better than other approaches, this could be a lot more convincing.
+
+Author reply: Thank you for the comment. Currently, β-blockers are the primary pharmacological drugs employed in clinical practice for arrhythmia treatment (J. Am. Heart Assoc. 2018, 7, e007567; Eur. Heart J. 2023, 44, 3720). However, their administration during acute myocardial ischemia remains unclear and is contraindicated in patients with heart failure. Additionally,
+our previous research investigated the local ganglion blockade using botulinum toxin A to protect the heart (*Heart Rhythm* **2022**, *19*, 2095). Nevertheless, its prolonged blocking effect renders it unsuitable for acute myocardial ischemia management. Conversely, PtNP-shell-based photothermal regulation offers reversible modulation within a short timeframe, exhibiting superior efficacy and controllability.
+
+Cardiac sympathetic denervation (CSD) is a clinical procedure aimed at targeting the autonomic ganglia for refractory ventricular arrhythmias treatment. However, ganglion removal can be traumatic for patients and may lead to complications due to the loss of original physiological function (*Eur. Heart J.* **2022**, *43*, 2096).
+
+Therefore, we aim to investigate the precise photothermal neuromodulation strategy facilitated by PtNP-shell as a reversible intervention approach for inhibiting ventricular arrhythmia associated with ganglion dysfunction. Notably, modulation specifically targeting NG has not been reported thus far, while non-invasive reversible neuromodulation strategies against LSG have primarily focused on photothermal modulation. Consequently, our study mainly established control and NP photothermal modulation groups similar to previous investigations (*Adv. Mater.* **2023**, *35*, 2304620; *Adv. Funct. Mater.* **2019**, *29*, 1902128).
+
+**Comment 10:** *In terms of overall interest, I think is a good technical demonstration of clever system; but what is the real-world application? Could the authors envisage a way in which this technology can actually be applied to MI patients?*
+
+**Author reply:** Thank you for the comment. Both myocardial ischemia and reperfusion injury-induced malignant arrhythmic events pose challenges in the treatment of acute myocardial infarction. Photothermal neuromodulation based on PtNP-shell offers a precise, transient, and reversible approach that may serve as an adjuvant therapy to improve patient prognosis. Additionally, ultrasound-guided targeted ganglionic microinjection is suitable for clinical applications. However, it is undeniable that despite the excellent tissue penetration depth of NIR-II photons (5–20 mm) (*Nat. Nanotech.* **2009**, *4*, 710; *Nat. Med.* **2012**, *18*, 1841; *Nat. Biomed. Eng.* **2017**, *1*, 0010), photothermal regulation still encounters challenges in intervening deeper tissues. Considering the presence of blood vessels surrounding the ganglion, which offers an opportunity to reduce the propagation path of photons in tissues, approaching the NIR-II fiber to the ganglion for photothermal modulation through a transvascular route during interventional therapy could be a potential solution for direct clinical translational application.
+
+**Comment 11:** *The abstract mentions that the NPs conferred protection against ventricular arrhythmias following MI. However, supplementary figure 25 seems to show that there was no difference in overall VA events.*
+Author reply: Thank you for the comment. The statistics of ventricular arrhythmia events encompass various forms, including ventricular premature beats (VPBs), ventricular tachycardia (VT), and ventricular fibrillation (VF). VT is defined as the occurrence of three or more consecutive VPBs. As depicted in Fig. R5 (Fig. 7i), the PtNP-shell group exhibited a significantly lower number of VPBs compared to the control group (p<0.05).
+
+![Bar graph showing VF threshold voltage comparison between Control and PtNP-shell groups](page_384_232_368_246.png)
+
+Fig. R5 | Quantitative analysis of VF threshold in different groups. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ***P < 0.001.
+
+Fig. R6 (Supplementary Fig. 28) presents a comparison between groups regarding the frequency and duration of VT occurrences. Although not statistically significant, there was a notable trend towards VT suppression in the NP group when compared to the control group. Supplementary Fig. 25 has been updated to Supplementary Fig. 28.
+
+![Bar graphs comparing number of VTs and duration of sVTs between Control and PtNP-shell groups](page_384_728_368_246.png)
+
+Fig. R6 | Statistical analysis of recorded ventricular arrhythmia events post myocardial ischemia. Quantitative analysis the number of a, VTs and b, the duration of sVT of beagles with MI. Data are shown as the mean ± S.E.M. ns means that the difference is not statistically significant.
+
+Comment 12: Figure 3i is not very easy to read or understand.
+
+Author reply: Thank you for the comment. We conducted a repeated experiment and made modifications to fig3i, transforming the 3D diagram into two 2D diagrams for enhanced
+comprehensibility. Fig. 3i (Fig. R7a) and Fig. 3j (Fig. R7b) depict cell viability following two different power density (0.75 W·cm^{-1} and 1 W·cm^{-1}) NIR-II laser irradiations at varying time intervals, respectively.
+
+![Bar graphs showing cell viability (%) versus laser duration (s) for two power densities](page_246_384_956_312.png)
+
+Fig. R7 | Effect of NIR-II laser irradiation with varying durations on the viability of HT-22 cells treated with PtNP-shell (50 μg·mL^{-1}) (Power densities: **a**, 0.75 W·cm^{-2} and **b**, 1 W·cm^{-2}). The error bar indicates S.E.M.
+
+**Comment 13:** *Line 373, I think that more than a few blood tests and some organ histologically is required to make such a strong claim of “unequivocally demonstrate” long-term safety.*
+
+**Author reply:** Thank you for the comment. In supplementary Figure 27, we first verified neuronal safety by histologic examination of the microinjected ganglion tissue as well as tunnel staining. In addition, we monitored the biosafety of both local tissue-injected beagles and tail vein-injected rats for 1 month. The major organs of these individuals were examined histologically, including the heart, liver, spleen, lungs, and kidneys. The most important routes of elimination, such as liver function and kidney function, were also examined by serology. In addition, we analyzed the effect of PtNP-shell on the inflammatory response in vivo by ELISA assay (Fig. R8). These detailed tests demonstrated the long-term biosafety of the NPs. The corresponding results have been included in the Supplementary Fig. 31g,h,o,p.
+Fig. R8 | Blood biochemical analyses including a, TNF-α, and b, IL-6 were performed on Beagles in different treatment groups. Blood biochemical analyses including c, TNF-α and d, IL-6 were performed on rats in different treatment groups.
+
+Comment 14: Supplementary figure 6, 13. I think these would be more readable as tables rather than bar charts.
+
+Author reply: Thank you for the comment. We have changed Supplementary Fig. 6 and 13 into Supplementary Table 1 (Table R2) and Supplementary Table 2 (Table R3), respectively.
+
+Table R2 | \( \xi \) potential of bare PtNP-shell, PtNP-shell + KOH and PtNP-shell@PEG.
+
+<table>
+  <tr>
+    <th></th>
+    <th>Zata Potential (mV)</th>
+    <th>St Dev(mV)</th>
+  </tr>
+  <tr>
+    <td>PtNP-shell</td>
+    <td>45.8</td>
+    <td>5.8</td>
+  </tr>
+  <tr>
+    <td>PtNP-shell + KOH</td>
+    <td>−25.7</td>
+    <td>4.64</td>
+  </tr>
+  <tr>
+    <td>PtNP-shell@PEG</td>
+    <td>−19.9</td>
+    <td>3.69</td>
+  </tr>
+</table>
+
+Table R3 | Comparison of photothermal conversion efficiency.
+
+<table>
+  <tr>
+    <th></th>
+    <th>Photothermal conversion efficiency (%)</th>
+  </tr>
+  <tr>
+    <td>This work</td>
+    <td style="color:red">73.70</td>
+  </tr>
+  <tr>
+    <td>PEDOT:ICG@PEG-GTA<sup>1</sup></td>
+    <td>71.10</td>
+  </tr>
+  <tr>
+    <td>MINDS<sup>2</sup></td>
+    <td>71.00</td>
+  </tr>
+  <tr>
+    <td>PTG NPs<sup>3</sup></td>
+    <td>67.60</td>
+  </tr>
+  <tr>
+    <td>RBC@Cu<sub>2-x</sub>SeNPs<sup>4</sup></td>
+    <td>67.20</td>
+  </tr>
+  <tr>
+    <td>AuDAg<sub>2</sub>S<sup>5</sup></td>
+    <td>67.10</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>Material</th>
+    <th>Conductivity (S/m)</th>
+  </tr>
+  <tr>
+    <td>MAPSULES<sup>6</sup></td>
+    <td>67.00</td>
+  </tr>
+  <tr>
+    <td>Fe<sub>3</sub>O<sub>4</sub>@PPy@GOD NCs<sup>7</sup></td>
+    <td>66.40</td>
+  </tr>
+  <tr>
+    <td>NPPBTPBF-BT<sup>8</sup></td>
+    <td>66.40</td>
+  </tr>
+  <tr>
+    <td>AS1064<sup>9</sup></td>
+    <td>65.92</td>
+  </tr>
+  <tr>
+    <td>Gold Nanoraspberry<sup>10</sup></td>
+    <td>65.00</td>
+  </tr>
+  <tr>
+    <td>P-Pc-HSA<sup>11</sup></td>
+    <td>64.70</td>
+  </tr>
+  <tr>
+    <td>Ultrathin polypyrrole nanosheets<sup>12</sup></td>
+    <td>64.60</td>
+  </tr>
+  <tr>
+    <td>H<sub>x</sub>MoO<sub>3</sub><sup>13</sup></td>
+    <td>60.90</td>
+  </tr>
+  <tr>
+    <td>NiP PHNPs<sup>14</sup></td>
+    <td>56.80</td>
+  </tr>
+  <tr>
+    <td>FP NRS<sup>15</sup></td>
+    <td>56.60</td>
+  </tr>
+  <tr>
+    <td>COF<sup>16</sup></td>
+    <td>55.20</td>
+  </tr>
+  <tr>
+    <td>2MPT<sup>+</sup>-CB<sup>17</sup></td>
+    <td>54.60</td>
+  </tr>
+  <tr>
+    <td>SPN-PT<sup>18</sup></td>
+    <td>53.00</td>
+  </tr>
+  <tr>
+    <td>Pdots<sup>19</sup></td>
+    <td>53.00</td>
+  </tr>
+  <tr>
+    <td>Pt Spirals<sup>20</sup></td>
+    <td>52.50</td>
+  </tr>
+  <tr>
+    <td>TBDOPV-DT<sup>21</sup></td>
+    <td>50.50</td>
+  </tr>
+  <tr>
+    <td>Ti<sub>2</sub>O<sub>3</sub>@HA NPs<sup>22</sup></td>
+    <td>50.20</td>
+  </tr>
+  <tr>
+    <td>TBDOPV–DT NP<sup>23</sup></td>
+    <td>50.00</td>
+  </tr>
+  <tr>
+    <td>DPP-IID-FA NPs<sup>24</sup></td>
+    <td>49.50</td>
+  </tr>
+  <tr>
+    <td>SPN-DT<sup>18</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>NP<sup>25</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>FTQ nanoparticles<sup>26</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>CNPs<sup>27</sup></td>
+    <td>49.00</td>
+  </tr>
+  <tr>
+    <td>H-SiO<sub>x</sub> NPs<sup>28</sup></td>
+    <td>48.60</td>
+  </tr>
+  <tr>
+    <td>BETA NPs<sup>29</sup></td>
+    <td>47.60</td>
+  </tr>
+  <tr>
+    <td>CN-NPs<sup>30</sup></td>
+    <td>47.60</td>
+  </tr>
+  <tr>
+    <td>Pt-NDs<sup>31</sup></td>
+    <td>46.90</td>
+  </tr>
+  <tr>
+    <td>MoO<sub>3-x</sub> nanobelts<sup>32</sup></td>
+    <td>46.90</td>
+  </tr>
+  <tr>
+    <td>P3 NPs<sup>33</sup></td>
+    <td>46.00</td>
+  </tr>
+  <tr>
+    <td>Ni<sub>9</sub>S<sub>8</sub><sup>34</sup></td>
+    <td>46.00</td>
+  </tr>
+  <tr>
+    <td>PtAg nanosheets<sup>35</sup></td>
+    <td>45.70</td>
+  </tr>
+  <tr>
+    <td>Nb<sub>2</sub>C NSs<sup>36</sup></td>
+    <td>45.65</td>
+  </tr>
+  <tr>
+    <td>V<sub>2</sub>C-TAT@Ex-RGD<sup>37</sup></td>
+    <td>45.10</td>
+  </tr>
+  <tr>
+    <td>PEG-TONW NRs<sup>38</sup></td>
+    <td>43.60</td>
+  </tr>
+  <tr>
+    <td>SPNI-II<sup>39</sup></td>
+    <td>43.40</td>
+  </tr>
+  <tr>
+    <td>1T-MoS<sub>2</sub><sup>40</sup></td>
+    <td>43.30</td>
+  </tr>
+  <tr>
+    <td>Bi@C NPs<sup>41</sup></td>
+    <td>43.20</td>
+  </tr>
+  <tr>
+    <td>Au NPL@TiO<sub>2</sub><sup>42</sup></td>
+    <td>42.10</td>
+  </tr>
+  <tr>
+    <td>CT NPs<sup>43</sup></td>
+    <td>42.00</td>
+  </tr>
+  <tr>
+    <td>PPy-PEG NPs<sup>44</sup></td>
+    <td>41.97</td>
+  </tr>
+  <tr>
+    <td>AuPt@CuS NSs<sup>45</sup></td>
+    <td>41.56</td>
+  </tr>
+  <tr>
+    <td>Bi<sub>19</sub>S<sub>27</sub>I<sub>3</sub> nanorods<sup>46</sup></td>
+    <td>41.50</td>
+  </tr>
+  <tr>
+    <td>Cu<sub>3</sub>BiS<sub>3</sub> NR<sup>47</sup></td>
+    <td>40.70</td>
+  </tr>
+  <tr>
+    <td>MPAE-NPS<sup>48</sup></td>
+    <td>40.07</td>
+  </tr>
+</table>
+Comment 15: Supplementary figure 7; this is quite a broad range of nanoparticle sizes. What makes up the smaller (100 nm) particles? Is there aggregation to produce larger particles?
+
+Author reply: Thank you for the comment. As show in Fig. R9, the smaller PtNP-shell (100 nm) is composed of ultra-small Pt nanoparticles (2–5 nm), similar to the larger PtNP-shell (200 nm).
+
+![TEM image and element mapping of the smaller PtNP-shell (100 nm)](page_340_368_464_246.png)
+
+Fig. R9 | Characterization of the smaller PtNP-shell (100 nm). a, TEM image and b, element mapping of the smaller PtNP-shell (100 nm).
+
+PtNP-shell will not aggregate to produce larger particles. We surface-modified the PtNP-shell with PEG to enhance its biocompatibility and maintain its dispersibility in PBS. Additionally, dynamic light scattering analysis confirmed that the PtNP-shell exhibited little aggregation behavior after being undisturbed for 14 days (Fig. R10). The corresponding results have been included in the Supplementary Fig. 8.
+
+![Hydrodynamic size size of PtNP-shell after 1, 4, 7, and 14 days of standing](page_340_1042_464_246.png)
+
+Fig. R10 | Hydrodynamic size size of PtNP-shell after a, 1, b, 4, c, 7, and d, 14 days of standing (Inset: digital photograph).
+To Referee #3
+
+First of all, we really appreciate your constructive comments. According to your suggestions, we have made corresponding revisions to our manuscript as listed below.
+
+Overall remark: The manuscript describes photothermal neuromodulation via Pt nano-shell nanoparticles. Ga nanoparticles are used as a template for electrocoupling substitution-based synthesis of the Pt nano-shell. Using KOH wet etching, Ga core is etched and a Pt nano-shell structure is obtained. The rough surface topography of the Pt nano-shell structure allows the particles to exhibit high optical absorbance. It is claimed that these particles have one of the highest photothermal energy conversion efficiencies. The photothermal conversion of optical irradiation is then utilized for stimulation of target cells and tissues via temperature activated ion channels- TRPV1 and TREK1. The potential application of such photothermal modulation technique in regulating cardiac pulsing is demonstrated with regards to protecting against acute ventricular arrhythmias. However, the manuscript does not include proper controls to demonstrate that in-vivo photothermal modulation is achieved exclusively through the Pt nanoparticles. In addition, there are certain claims and results that need to be better corroborated to reach the scientific requirements of the journal. Therefore, I cannot recommend that this manuscript be accepted at Nature Communications in its current form.
+
+Author reply: Following your suggestion, we have added appropriate controls to demonstrate that in-vivo photothermal modulation is achieved exclusively through PtNP-shell. Furthermore, we have meticulously validated various propositions and findings with enhanced detail. These comments have been systematically addressed and resolved. For further information, please refer to the one-to-one reply corresponding to each comment.
+
+Comment 1: Abstract: It is claimed that “the autonomic nervous system plays a pivotal role in the pathophysiology of cardiovascular diseases.” This sentence is misleading since the dysregulation of the autonomic nervous system can contribute to cardiovascular diseases. However, it is not the primary contributor to the diseases, autonomous nervous system in fact regulates normal functioning of the cardiovascular system. (see: Purves D, Augustine GJ, Fitzpatrick D, LaMantia AS, McNamara JO, Williams SM. Autonomic regulation of cardiovascular function. Neuroscience. 2001:491-3 AND Gordan R, Gwathmey JK, Xie LH. Autonomic and endocrine control of cardiovascular function. World journal of cardiology. 2015 Apr 4;7(4):204.)
+
+Author reply: Thank you for the comment. We have made a modification: “Autonomic nervous system disorders play a pivotal role in the pathophysiology of cardiovascular diseases.”
+Comment 2: The authors claim that bi-directional reversible autonomic modulation is achieved via NIR-II photothermal modulation using Pt nano-shell nanoparticles. The manuscript presents uni-directional modulation where the target tissues are stimulated. Bi-directionality isn’t demonstrated since in terms of neural interfaces, bi-directionality refers to the ability to record neural activity as well as stimulate (see: Song KI, Seo H, Seong D, Kim S, Yu KJ, Kim YC, Kim J, Kwon SJ, Han HS, Youn I, Lee H. Adaptive self-healing electronic epineurium for chronic bidirectional neural interfaces. Nature communications. 2020 Aug 21;11(1):4195. AND Hughes C, Herrera A, Gaunt R, Collinger J. Bidirectional brain-computer interfaces. Handbook of clinical neurology. 2020 Jan 1;168:163-81.).
+
+Author reply: Targeting the autonomic nervous system, we achieve nerve inhibition and activation through PtNP-shell-mediated photothermal effect, enabling adjustment of autonomic nervous imbalance. Hence, in this sense, we define it as a “bidirectional” neuromodulation.
+
+Comment 3: It is unclear why the NIR-II range was utilized in this work. This is important for selecting the right materials, models, and experiments. (see: nature.com/articles/s44222-023-00022-y AND nature.com/articles/s41551-022-00862-w).
+
+Author reply: Thank you for the comment. In comparison to the first near-infrared (NIR-I, 650–900 nm) and visible window, the photons in the second near-infrared window (NIR-II, 900–1700 nm) exhibits reduced tissue scattering and absorption, thereby increasing the maximum allowable exposure (MPE) of biological tissues. Consequently, photons within the NIR-II window exhibit significantly enhanced tissue penetration depths (up to 5–20 mm) (Nat. Nanotech. 2009, 4, 710; Nat. Med. 2012, 18, 1841; Nat. Biomed. Eng. 2017, 1, 0010). To achieve deep photothermal nerve regulation for cardioprotection, we developed PtNP-shell and validated its photothermal neuromodulation efficacy in the NIR-II window both in vivo and in vitro. Given its wavelength independence, further investigations may facilitate selection of a more suitable laser for achieving deeper tissue penetration while adhering to the MPE range. The exceptional potential of PtNP-shell makes it highly promising for precise neural regulation in deeper tissue and holds significant clinical translational value.
+
+Comment 4: Instead of using terminologies like “nearly perfect blackbody absorption”, the actual optical properties and metrics should be presented.
+
+Author reply: Thank you for the comment. Referring to the study (Nat. Nanotech. 2016, 11, 60), we have obtained the absorption spectra of PtNP-shell, which demonstrate its exceptional blackbody absorption characteristics. In the range of 250–1300 nm, the PtNP-shell exhibits an absorbance close to 1 at 75 \( \mu \)g·mL\(^{-1}\), which is significantly enhanced in the range of 400–1300 nm compared to GaNPs and Ga@Pt NPs (Fig. R11). Additionally, optical images were acquired for comparison purposes.
+Comparing with GaNPs and Ga@Pt NPs, the grayscale feature of PtNP-shell closely approximates the darkest point on the RGB spectrum, providing evidence that PtNP-shell exhibits a strong tendency towards perfect blackbody behavior (Fig. R12).
+
+![UV-vis-NIR absorption spectrum of GaNPs, Ga@Pt NPs and PtNP-shell (75 μg·mL⁻¹).](page_384_232_627_312.png)
+
+Fig. R11 | UV-vis-NIR absorption spectrum of GaNPs, Ga@Pt NPs and PtNP-shell (75 μg·mL⁻¹).
+
+![Measurement of PtNP-shell blackness. a, Visual appearance of GaNPs, Ga@Pt NPs and PtNP-shell at different concentrations. b, Position of each color in the RGB cube, obtained by extracting the relative components of red, green and blue from Fig. R8a.](page_384_579_627_312.png)
+
+Fig. R12 | Measurement of PtNP-shell blackness. a, Visual appearance of GaNPs, Ga@Pt NPs and PtNP-shell at different concentrations. b, Position of each color in the RGB cube, obtained by extracting the relative components of red, green and blue from Fig. R8a.
+
+Comment 5: Figure 1 presents how the nanoparticles will interact with the biological systems, however it does not show how light pulses/irradiation will be delivered to the target tissues/sites. This should be discussed in the figure and the manuscript since it is important for clinical translation.
+
+Author reply: Thank you for the comment. In Fig. 1 (Fig. R13), we have added the laser transmission path towards the target sites. Furthermore, the methodology section of the manuscript has a comprehensive account of the laser transmission process at the target sites.
+
+“Initial vertical irradiation of NIR-II laser (1064 nm) at 0.80 W·cm⁻² was performed on NG and LSG surfaces. The power density of the NIR-II laser was reduced to 0.45 W·cm⁻² for continuous irradiation when the temperature of the NG reached 42.0 °C, and was reduced to 0.6 W·cm⁻² for continuous irradiation when the temperature of the LSG reached 46.0 °C. The NIR-II laser irradiation remains stable with a spot size maintained at 1.0 cm⁻².”
+Fig. R13 | The synthesis steps of the PtNP-shell and the concept of mediating precise photothermal effects for cardioprotection. a, The synthesis steps of PtNP-shell and schematic diagram of photothermal effect. b, Schematic diagram of multifunctional autonomic modulation mediated by photothermal effect of PtNP-shell for precise cardioprotection against myocardial I/R injury and MI-induced VAs.
+
+Comment 6: Adequate controls should be provided to better compare the physical properties of PtNP-shells. That is, please provide the optical absorbance of GaNPs, Pt coated GaNPs for Figure 2.d; similar controls should be provided for Figure 2.e (including the thermal transients of such the solvent under irradiation.
+
+Author reply: Following your suggestion, we supplemented the absorption spectra of GaNPs and Ga@Pt NPs in Fig. 2d (Fig. R14) and compared them with PtNP-shell. It was observed that the absorption of PtNP-shell in the range of 400–1300 nm was significantly higher than that of GaNPs and Ga@Pt NPs at equivalent concentrations. We made corresponding changes in the manuscript:
+
+“In the range of 250–1300 nm, the PtNP-shell exhibits an absorbance close to 1 at 75 \( \mu \)g·mL\(^{-1}\), which is significantly enhanced in the range of 400–1300 nm compared to GaNPs and Pt-coated Ga nanoparticles (Ga@Pt NPs) (Fig. 2d).”
+Fig. R14 | UV-vis-NIR absorption spectrum of GaNPs, Ga@Pt NPs and PtNP-shell (75 \( \mu \)g·mL\(^{-1}\)).
+
+![UV-vis-NIR absorption spectrum of GaNPs, Ga@Pt NPs and PtNP-shell](page_328_120_496_384.png)
+
+In addition, the thermal transient curves of PBS, GaNPs, Ga@Pt NPs and PtNP-shell are supplemented in Fig. 2e (Fig. R15). The results demonstrate that the rate at which PtNP-shell reaches the target temperature is significantly higher compared to that of GaNPs and Ga@Pt NPs. We made corresponding changes in the manuscript:
+
+“Even in vitro, PtNP-shell (50 \( \mu \)g·mL\(^{-1}\)) exhibited rapid temperature elevation, achieving a rise from room temperature to 41.0 °C and 45.0 °C within only 96 s and 133 s, respectively. However, for GaNPs (409 s and over 600 s) and GaIn@Pt NPs (317 s and over 600 s), it took significantly longer time to reach the same temperatures (Fig. 2e).”
+
+Fig. R15 | Temperature elevation curves of PBS, GaNPs, Ga@Pt NPs and PtNP-shell (50 \( \mu \)g·mL\(^{-1}\)) under NIR-II laser irradiation (1 W·cm\(^{-2}\)).
+
+![Temperature elevation curves of PBS, GaNPs, Ga@Pt NPs and PtNP-shell](page_328_682_496_384.png)
+
+Comment 7: For the XPS characterization, a survey scan of presentative sample should be presented along with the detailed XPS characterization of oxygen (O1s) and potassium (K2p). The elemental composition of the PtNP-shells, Pt coated GaNPs, and GaNPs should be compared as well. This will better elucidate the composition of effectiveness of the synthesis protocols.
+
+Author reply: Following your suggestion, we supplemented the XPS survey spectrum of GaNPs, Ga@Pt NPs and PtNP-shell (Fig. R16), and detailed XPS characterization of oxygen (O1s) and potassium (K2p) (Fig. R17). The elemental compositions of GaNPs, Ga@Pt NPs and PtNP-shell were
+compared by high-resolution XPS spectra (Fig. R17). We made corresponding changes in the manuscript and the results have been included in the Supplementary Fig. 5 and Supplementary Fig. 6.
+
+![XPS survey spectrum of GaNPs, Ga@Pt NPs, and PtNP-shell](page_246_312_957_180.png)
+
+Fig. R16 | The XPS survey spectrum of a, GaNPs, b, Ga@Pt NPs and c, PtNP-shell.
+
+![High-resolution XPS spectra and fitting results of GaNPs, Ga@Pt NPs, and PtNP-shell](page_246_573_957_377.png)
+
+Fig. R17 | High-resolution XPS spectra and fitting results of a, GaNPs, b, Ga@Pt NPs and c, PtNP-shell.
+
+“X-ray photoelectron spectroscopy (XPS) analysis reveals the presence of Ga and O in GaNPs, while Ga@Pt NPs and PtNP-shell exhibit the coexistence of Ga, O, and Pt (Supplementary Fig. 5). As depicted in the Supplementary Fig. 6, despite treatment with KOH, no presence of K element was detected in the PtNP-shell. The strong signals of Pt 4f_{5/2} and Pt 4f_{7/2} indicate that the Pt in Ga@Pt NPs and PtNP-shell exists in a metallic state (Nat. Commun. 2017, 8, 15802). In GaNPs, the peak centered at 1118.11 eV is attributed to Ga^{3+} 2p_{3/2}, while the peak centered at 1115.89 eV corresponds
+to Ga 2p_{3/2}. In Ga@Pt NPs, the peak centered at 1118.80 eV is assigned to Ga^{3+} 2p_{3/2}, and the peak centered at 1116.52 eV corresponds to Ga 2p_{3/2}. As for PtNP-shell, the presence of a peak around 1118.56 eV indicates complete oxidation of Ga in PtNP-shell into Ga^{3+} (Adv. Funct. Mater. **2023**, *34*, 2302172). The O 1s spectrum was fitted using two peak functions, which were assigned to Ga–O at 530.44 eV (GaNPs), 530.98 eV (Ga@Pt NPs), 531.74 eV (PtNP-shell) and Ga–OH at 531.71 eV (GaNPs), 532.08 eV (Ga@Pt NPs), 532.74 eV (PtNP-shell) (*ACS Appl. Mater. Interfaces* **2024**, *16*, 4212). Compared to GaNPs and Ga@Pt NPs, the binding energy of the Ga–O and Ga–OH peaks in the PtNP-shell is shifted towards higher values, indicating a lower oxidation degree of the PtNP-shell.”
+
+Comment 8: *The stability of the Pt-nanoshell suspensions should be evaluated as a function of time. Do the nanoparticle aggregate over time? Will this be a concern when the Pt-nanoshells are injected into biological systems.*
+
+Author reply: Thank you for the comment. PtNP-shell exhibit long-term stability without aggregation, ensuring it compatibility for injection into biological systems. After standing for 1, 4, 7 and 14 days respectively, the statistically averaged hydrated nanoparticle size of PtNP-shell was determined using dynamic light scattering (Fig. R18). It is worth noting that the change of the average hydrated nanoparticle size of PtNP-shell remains negligible after 14 days, indicating its excellent stability. The corresponding results have been included in the Supplementary Fig. 8.
+
+![Hydrodynamic size of PtNP-shell after 1, 4, 7, and 14 days of standing (Inset: digital photograph)](page_184_1012_1080_482.png)
+
+Fig. R18 | Hydrodynamic size of PtNP-shell after **a**, **b**, **c**, **d**, 14 days of standing (Inset: digital photograph).
+Comment 9: How does the addition of mPEG-SH5000 effect the photothermal properties of the nanoparticles?
+
+Author reply: Thank you for the comment. The current research indicates that the photothermal effect of mPEG-SH_{5000} itself can be disregarded (ACS Nano **2020**, *14*, 2265; ACS Appl. Energ. Mater. **2021**, *4*, 7710). We supplemented the temperature elevation curves of mPEG-SH_{5000} modified and unmodified PtNP-shell (Fig. R19a). The heating rate of the mPEG-SH_{5000} modified PtNP-shell is significantly higher compared to that of the unmodified PtNP-shell, potentially attributed to the agglomeration tendency of unmodified PtNP-shell at elevated temperatures, leading to a reduction in photothermal performance. Following 600 s of laser irradiation at 1064 nm, the statistically averaged hydrodynamic size for mPEG-SH_{5000}-modified PtNP-shell was measured as 206.5 nm (Fig. R19b), whereas unmodified PtNP-shell exhibited a size of 1517 nm (Fig. R19c). TEM analysis further confirmed the observed agglomeration behavior in unmodified PtNP-shell subsequent to laser irradiation (Fig. R19d). The corresponding results have been included in the Supplementary Fig. 13.
+
+![Temperature elevation curves and hydrodynamic size distributions of PtNP-shell before and after SH-PEG modification, and TEM image of PtNP-shell before SH-PEG modification](page_186_670_1077_496.png)
+
+Fig. R19 | The impact of PEG on the photothermal properties of PtNP-shell. a, Temperature elevation curves of SH-PEG modified and unmodified PtNP-shell. The hydrodynamic size of PtNP-shell b, before and c, after SH-PEG modification (after 600 s of 1064 nm laser irradiation). d, TEM image of PtNP-shell before SH-PEG modification (after 600 s of 1064 nm laser irradiation).
+
+Comment 10: Critical information from the methods section is missing- for example, details regarding the cell culture protocol and photothermal stimulation (such as power and pulse duration of optical irradiation are missing). How long was the ECG data recorded for? What were the exact stimulation conditions for all in-vivo experiments?
+Author reply: Thank you for your kind reminding. We provide a more detailed description of the Method:
+
+“Cell-specific medium was prepared by mixing Dulbecco’s modified Eagle’s medium (DMEM), fetal bovine serum and penicillin-streptomycin mixture at 89%, 10% and 1%, respectively.”
+
+“To induce activation of TRPV1 and TREK1 ion channels, which had been previously studied, (Science 2003, 300, 1284; EMBO J. 2000, 19, 2483) the culture dish was exposed to 1064 nm laser (0.75 W·cm^{-2}, TRPV1: 50 s, TREK1: 80 s), resulting in an elevation of temperature.”
+
+“The same grouping pattern as in part1 was used, with NIR-II irradiation (Heating stage: 0.8 W·cm^{-2}, 12±3 s; Equilibrium stage: 0.45 W·cm^{-2}, 5 min) of the NG before opening the occluded LAD coronary vessel.”
+
+“The in vivo effects of precise photothermal stimulation of the sympathetic nervous system by PtNP-shell under NIR-II irradiation (Heating stage: 0.8 W·cm^{-2}, 25±5 s; Equilibrium stage: 0.6 W·cm^{-2}, 5 min) were explored.”
+
+“Malignant arrhythmic events occurring within 1 hour of MI and I/R injury were assessed by electrocardiographic recordings in a canine model using Lead 7000 Computerized Laboratory System.”
+
+Comment 11: For the in-vitro experiments, are the Pt nanoparticles engulfed by the target cells or are they localized in the vicinity of the cell membrane?
+
+Author reply: The PtNP-shell is partially localized within the target cells, while the remaining portion exhibits distribution around the cell membrane. We supplemented TEM and SEM images of PtNP-shell (50 \( \mu \)g·ml^{-1}) co-cultured with cells for 24 hours. Cross-sectional TEM and SEM images showed that PtNP-shell was randomly distributed inside or on the surface of the cells (Fig. R20). This is attributed to the fact that the PtNP-shell exhibits a particle size of approximately 200 nm, enabling smaller particles to traverse the cell membrane. The corresponding results have been included in the Supplementary Fig.15.
+Fig. R20 | PtNP-shell co-cultured with neurons. a and b, Cross-sectional TEM and c, SEM of the neurons incubated with PtNP-shell particles for 24 h.
+
+Comment 12: Both in-vivo and in-vitro photothermal stimulation experiments require the cells’ microenvironment to reach temperatures greater than 42 \(^\circ\)C. Does repeated photothermal stimulation using such high temperatures adversely affect cellular health by disrupting the cell membrane or trigger heat shock response?
+
+Author reply: The discovery of temperature-sensitive ion channels has given rise to a boom in the modulation of neuronal activity by temperature. Numerous experiments on temperature modulation of neuronal activity have shown that temperatures of 42\(^\circ\) or even above can safely achieve reversible modulation of neural activity (*Nano Converg. 2022, 9, 13; Brain Stimul. 2021, 14, 790*). In addition, our results also indicate that the NPs-mediated photothermal modulation strategy is biologically safe, both at the cellular (Fig R21) and tissue levels (Fig R22 and R23).
+Fig. R21 | a, Cell viability of HT-22 treated with different concentrations of PtNP-shell for 24 h. Effect of NIR-II laser irradiation with varying durations on the viability of HT-22 cells treated with PtNP-shell (50 \( \mu \)g·mL\(^{-1}\)) (Power densities: b, 0.75 W·cm\(^{-2}\) and c, 1 W·cm\(^{-2}\)). The error bar indicates S.E.M.
+
+Fig. R22 | Ganglion biocompatibility of targeted injections of PtNP or PBS after NIR-II irradiation and after 30 days of follow-up. a, Representative images of H&E and TUNEL staining of NG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up. b, Representative images of H&E and TUNEL staining of LSG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up.
+Fig. R23 | Long term biosafety of PtNP-shell microinjection. Long-term in vivo biosafety was assessed by local injection of PtNP-shell into the ganglion of Beagle or by injection of equal doses of PtNP-shell into the tail vein of Sprague-Dawley rats. a, Representative H&E staining of major organs of beagles following different treatments. Blood biochemical analyses including b, ALT, c, AST, d, Urea, e, Crea, f, LDH1, g, TNF-α, and h, IL-6 were performed on Beagles in different treatment groups. i, Representative H&E staining of major organs of rats following different treatments. Blood biochemical analyses including j, ALT, k, AST, l, Urea, m, Crea, n, LDH1, o, TNF-α and p, IL-6 were performed on rats in different treatment groups.
+
+Comment 13: The claim that Pt-NP shell does not induce significant damage to neurons under controlled NIR-II laser irradiation is incorrect since there is ~10% loss in cellular viability.
+
+Author reply: Thank you for your kind reminding. We conducted a repeated experiment. As illustrated in Fig. R24, although there was a slight decrease in cell activity across all laser irradiation groups compared to the control group (laser duration time of 0 s), no statistically significant differences were observed (all P >0.05). Hence, we conclude that “Pt-NP shell does not induce significant damage to neurons under controlled NIR-II laser irradiation”.
+Fig. R24 | Effect of NIR-II laser irradiation with varying durations on the viability of HT-22 cells treated with PtNP-shell (50 μg·mL^{-1}) (Power densities: **i**, 0.75 W·cm^{-2} and **j**, 1 W·cm^{-2}). The error bar indicates S.E.M.
+
+**Comment 14:** *It will be recommended that the data presentation in Figure 3.i be changed since the details of the data are difficult to comprehend through a 3-D plot.*
+
+**Author reply:** Thank you for your kind reminding. We conducted a repeated experiment and made modifications to Fig. 3i, transforming the 3D diagram into two 2D diagrams for enhanced comprehensibility. Fig. 3i (Fig. R25a) and Fig. 3j (Fig. R25b) depict cell viability following two different power density (0.75 W·cm^{-1} and 1 W·cm^{-1}) NIR-II laser irradiations at varying time intervals, respectively.
+
+Fig. R25 | Effect of NIR-II laser irradiation with varying durations on the viability of HT-22 cells treated with PtNP-shell (50 μg·mL^{-1}) (Power densities: **i**, 0.75 W·cm^{-2} and **j**, 1 W·cm^{-2}). The error bar indicates S.E.M.
+
+**Comment 15:** *For the in-vivo photothermal stimulation experiments, can similar affects be achieved without the presence of the Pt-nanoshell particles? Figure 4.d presents high temperature gradients for the surrounding tissue as well. Stimulation using infra-red radiation has been demonstrated previously, see: doi.org/10.1364/OL.30.000504 and doi.org/10.1117/1.2121772.*
+
+**Author reply:** Thank you for the comment. First of all, the aim of our study was to achieve precise, rapid, and reversible neuromodulation for cardioprotection through NPs mediated conversion of light
+energy into thermal energy. Non-invasive intervention was also the goal we pursued, so we chose to use NIR-II, which has a deeper penetration depth, as the light source. Due to the limitations of NIR itself and its inability to radiate energy to deep tissues, the effects of NIR on nerves are not clinically significant when viewed in isolation. The high-temperature gradient observed in Fig. 4d is only the temperature transfer to the fat, muscle, and other tissues around the ganglion, and does not affect the changes in nerve activity and function.
+
+For experimental rigor, we also added changes in ganglion local temperature and neural function before and after NIR irradiation alone at the same parameters. We found limited local temperature elevation (< 2 °C) and no significant changes in nerve function under NIR irradiation alone, including NG (Fig. R26) and LSG (Fig. R27). The corresponding results have been included in the Supplementary Fig.19 and 25.
+
+![Temperature curve and neural function graphs for NG and LSG under NIR-II irradiation](page_384_613_1042_312.png)
+
+Fig. R26 | Direct effect of NIR irradiation of NG. a, Local temperature curve of NG under NIR-II irradiation. b, Neural function of NG before and after NIR-II irradiation.
+
+![Temperature curve and neural function graphs for NG and LSG under NIR-II irradiation](page_384_1012_1042_312.png)
+
+Fig. R27 | Direct effect of NIR irradiation of LSG. a, Local temperature curve of LSG under NIR-II irradiation. b, Neural function of LSG before and after NIR-II irradiation.
+
+Comment 16: The biosafety of Pt-nanoshell particles was evaluated after a rapid excision of the LSG and NG tissues. Can the authors comments on the long-term biosafety of the nanoparticles in passive (without photothermal stimulation) and active (with photothermal stimulation) states?
+Author reply: Thank you for the comment. In Fig. R28, we first verified neuronal safety by histologic examination of the microinjected ganglion tissue as well as Tunel staining. We also showed by neurofunctional testing that PtNP photothermal stimulation is safe and reversible (Fig. R29 and R30). In addition, we monitored the biosafety of both local tissue-injected beagles for 1 month. These detailed tests demonstrated the long-term biosafety of the NPs (Fig. R31).
+
+![Representative images of H&E and TUNEL staining of NG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up.](page_154_370_1142_464.png)
+
+Fig. R28 | Ganglion biocompatibility of targeted injections of PtNP or PBS after NIR-II irradiation and after 30 days of follow-up. a, Representative images of H&E and TUNEL staining of NG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up. b, Representative images of H&E and TUNEL staining of LSG from different treatment groups immediately after NIR-II irradiation or after 30 days of follow-up.
+
+![Maximal HR changes of beagles treatment with PtNP-shell or control from 1 to 3 hours after NIR irradiation.](page_154_1012_1142_246.png)
+
+Fig. R29 | Effect of PtNP-shell photothermal stimulation of NG. Maximal HR changes of beagles treatment with PtNP-shell or control from 1 to 3 hours after NIR irradiation, n = 6. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ns means that the difference is not statistically significant.
+Fig. R30 | Effect of PtNP-shell photothermal inhibition of LSG. Maximal SBP changes of beagles treatment with PtNP-shell or control from 1 to 3 hours after NIR irradiation, n = 6. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ns means that the difference is not statistically significant.
+
+Fig. R31 | Long term biosafety of PtNP-shell microinjection. Long-term in vivo biosafety was assessed by local injection of PtNP-shell into the ganglion of Beagle or by injection of equal doses of PtNP-shell into the tail vein of Sprague-Dawley rats. a, Representative H&E staining of major organs of beagles following different treatments. Blood biochemical analyses including b, ALT, c, AST, d, Urea, e, Crea, f, LDH1, g, TNF-α, and h, IL-6 were performed on Beagles in different treatment groups. i, Representative H&E staining of major organs of rats following different treatments. Blood biochemical analyses including j, ALT, k, AST, l, Urea, m, Crea, n, LDH1, o, TNF-α and p, IL-6 were performed on rats in different treatment groups.
+Comment 17: Page 2, line 21: Please include examples and appropriate references for “conventional international procedures for MI.”
+
+Author reply: We have attached the reference after “Conventional international procedures for MI”, and the reference number is “3”.
+
+Comment 18: Page 4, line 16: Please change the word “encapsulated on” since Pt is not encapsulated on the surface of GaNPs. Pt is deposited onto of GaNP core then it encapsulates GaNP core.
+
+Author reply: Thank you for your kind reminding. We have changed the word “encapsulated on” in the manuscript to “deposited on”.
+
+Finally, we want to thank the referees again for their constructive comments on our work, and we hope our newly revised manuscript can reach the quality expectation to be published in Nature Communications. Please find our revisions marked in red copy of the revised manuscript.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+I have no additional comments.
+
+Reviewer #2:
+Remarks to the Author:
+The authors have addressed many of the comments I gave, such as improving explanations, results narrative, adding supplementary tables and revising some figure layouts for clarity. I also appreciate the new NP characterisation data. However, I still think there are a few points which need to be addressed further:
+
+Comment 5: Please clarify the exact timing of NP and NIR treatment in relation to the surgery. The text says "The NG was subsequently exposed to NIR-II laser irradiation for a duration of 5 minutes prior to occlusion of the left anterior descending (LAD) coronary artery for reperfusion therapy." This means the treatment is given before artery occlusion. However, the authors’ response to my comment is talking about the importance of reducing reperfusion injury (which I agree is very important). However, if preventing reperfusion injury is the goal, why not induce the MI, then give the NIR treatment at the time of artery re-opening and reperfusion? This would simulate the clinical reality where an intervention could be given before, or during reperfusion. If the experimental design indeed is treating the animals before MI, this limitation needs to be clearly mentioned.
+
+Comment 6: The time point of blood sampling for myoglobin and c-TnI measurement is still not clear in the manuscript. The text simply says "after MI and myocardial I/R injury" (line 736). Please specify the exact time points used for data in 5j and 5k.
+
+I also disagree that reductions in these biomarkers is strong enough evidence to demonstrate cardioprotection, which is claimed multiple times throughout the text. This claim can only be made if there are functional tests or at least histological findings (i.e. reduced infarct size). I think claiming the reduction in acute VAs is fair enough, but “cardiac protection” strongly implies preservation of tissue and corresponding functional changes.
+
+Lastly, the authors also did not provide any explanation for *how or why* these markers would be reduced by the NP/NIR treatment. The implication of lower circulating damage markers would be that there is less cardiac muscle loss - but there are no data to support this. Again, this is where functional metrics would be very useful. Still, as a principle, it’s not exactly clear to me how the NP/NIR-II intervention would lower myoglobin/c-TnI release.
+
+Comment 9-10: I think the responses to my comments are fine, but some of these points should go into the manuscript discussion section.
+
+Reviewer #3:
+Remarks to the Author:
+The authors have addressed most of the reviewer comments. Adequate control experiments and results have also been provided.
+However, there are a couple more concerns regarding the revised manuscript-
+1. For neural interfaces, bidirectionality is defined as the ability and record and stimulate neural activity. Therefore, stimulating and inhibiting neural activity should not be defined as bidirectionality of neuromodulation. A more appropriate term will be multi-modal neuromodulation.
+2. All peaks in the XPS spectra should be identified. For example, there is an emergence of peaks (at ca. 400 eV) other than Ga and O in the GaNP samples. The elemental composition should be assessed to better elucidate the chemical composition of each sample.
+Reply to the referees
+
+To Referee #1
+
+    Overall remark: I have no additional comments.
+
+Author reply: We appreciate your positive evaluation on our manuscript.
+To Referee #2
+
+Overall remark: The authors have addressed many of the comments I gave, such as improving explanations, results narrative, adding supplementary tables and revising some figure layouts for clarity. I also appreciate the new NP characterisation data. However, I still think there are a few points which need to be addressed further.
+
+Author reply: We appreciate your positive evaluation on our manuscript. We have made a point-by-point response to your comments and carefully revised the manuscript as you suggested. For your reference, please find our revisions marked in red color.
+
+Comment 1: Please clarify the exact timing of NP and NIR treatment in relation to the surgery. The text says “The NG was subsequently exposed to NIR-II laser irradiation for a duration of 5 minutes prior to occlusion of the left anterior descending (LAD) coronary artery for reperfusion therapy.” This means the treatment is given before artery occlusion. However, the authors’ response to my comment is talking about the importance of reducing reperfusion injury (which I agree is very important). However, if preventing reperfusion injury is the goal, why not induce the MI, then give the NIR treatment at the time of artery re-opening and reperfusion? This would simulate the clinical reality where an intervention could be given before, or during reperfusion. If the experimental design indeed is treating the animals before MI, this limitation needs to be clearly mentioned.
+
+Author reply: Thank you for the comment. Previously for the timing of the intervention in the reperfusion injury model we led to misunderstandings in the text and picture descriptions. In fact, the time point of neuromodulation by NIR irradiation was just 5 min before reperfusion injury, which is consistent with the timing of interventions for clinical application in ischemia-reperfusion injury.
+
+We first performed microinjections of PtNP-shell in ganglia and occluded the left anterior descending (LAD) coronary artery for 1 h to induce myocardial ischemia. Subsequently, NIR-II laser irradiation was applied to NG for 5 min, followed by reperfusion treatment achieved by opening the ligated knot. Consequently, we further refined the corresponding content and Fig. 5b (Fig. R1) to provide a clearer and more direct representation of the treatment time.
+
+![Flowchart of regulating NG to protect against myocardial I/R injury and associated VAs.](page_374_1092_682_120.png)
+
+Fig. R1 | Flowchart of regulating NG to protect against myocardial I/R injury and associated VAs.
+“The left anterior descending (LAD) coronary artery was occluded for 1 h to induce myocardial ischemia. Subsequently, NIR-II laser irradiation was applied to NG for 5 min, followed by reperfusion treatment achieved by opening the ligated knot.”
+
+Comment 2: The time point of blood sampling for myoglobin and c-TnI measurement is still not clear in the manuscript. The text simply says “after MI and myocardial I/R injury” (line 736). Please specify the exact time points used for data in 5j and 5k.
+
+Author reply: Thank you for your kind reminding. Blood samples for myoglobin and c-TnI measurement were collected via jugular vein of each beagle 4–5 h after coronary artery ligation (3–4 h after reperfusion treatment). We have made corresponding changes in the manuscript.
+
+“Serum Elisa assay revealed significantly lower levels of markers of myocardial injury (MYO and c-TnI) at 4–5 h post-infarction in the PtNP-shell group compared to the control group (all p < 0.05, Fig. 5j and k).”
+
+In Methods:
+
+“In myocardial I/R model experiments, 5 mL of venous blood was obtained from the jugular vein of each beagle 4–5 hours after ligation of the coronary vessels (3-4 h after reperfusion treatment).”
+
+Comment 3: I also disagree that reductions in these biomarkers is strong enough evidence to demonstrate cardioprotection, which is claimed multiple times throughout the text. This claim can only be made if there are functional tests or at least histological findings (i.e. reduced infarct size). I think claiming the reduction in acute VAs is fair enough, but “cardiac protection” strongly implies preservation of tissue and corresponding functional changes.
+
+Author reply: Thank you for the comment. We totally agree with your insightful suggestion, and have substituted the term “cardioprotection” with “reduction in the occurrence of ventricular arrhythmias induced by myocardial ischemia or reperfusion injury” in the manuscript.
+
+In this study, we investigated the role of PtNP-shell-mediated photothermal neuromodulation in a myocardial infarction (MI) model and a myocardial ischemia/reperfusion (I/R) injury model. Our findings not only demonstrated a reduction in myocardial injury biomarkers but also revealed that the neuromodulation technique effectively improved cardiac electrophysiological stability, suppressed the occurrence of MI or I/R-induced VAs.
+
+Indeed, serum markers of myocardial injury in acute infarction models and acute reperfusion injury models do not fully reflect cardioprotective effects. Comprehensive cardioprotective effects should be further assessed in the long-term myocardial injury model through its evaluation of cardiac function and infarct area indexes. The relevant content has been incorporated into the discussion
+section of the manuscript.
+
+“In this study, we validated the protective efficacy of PtNP-shell photothermal neuromodulation strategy in models of acute myocardial infarction and acute reperfusion injury to mitigate ventricular arrhythmia incidence. However, further evaluation through experiments such as assessment of cardiac function and infarct area is required to determine the cardioprotective potential of this strategy in chronic myocardial injury models.”
+
+Comment 4: Lastly, the authors also did not provide any explanation for *how or why* these markers would be reduced by the NP/NIR treatment. The implication of lower circulating damage markers would be that there is less cardiac muscle loss - but there are no data to support this. Again, this is where functional metrics would be very useful. Still, as a principle, it’s not exactly clear to me how the NP/NIR-II intervention would lower myoglobin/c-TnI release.
+
+Author reply: Thank you for the comment. In the case of myocardial cell injury, biomarkers such as troponin, indicative of myocardial damage, are released into the bloodstream (JAMA. 2013, 309, 2262). In the guidelines for cardiovascular disease published by the European Society of Cardiology and others, testing for cardiac injury biomarkers is also an important indicator for clinical detection of myocardial injury in patients (Eur. Heart J. 2012, 33, 2551; Eur. Heart J. 2023, 44, 3720). Therefore, we validate the protective efficacy of PtNP-shell mediated photothermal neuromodulation strategy against ischemia and reperfusion injury by assessing the levels of serum myocardial injury markers.
+
+Neurotransmitters released by sympathetic nerves can bind adrenergic receptors in cardiomyocytes to control cardiomyocyte contraction (Annu. Rev. Physiol. 2022, 84, 285). Myocardial ischemia causes activation of sympathetic nerves, releasing large amounts of sympathetic neurotransmitters (Eur. Heart J. 2024, 45, 669). Subsequently, sympathetic activation of adrenergic receptors promotes sarcoplasmic reticulum calcium release from cardiomyocytes, exacerbating calcium overload and causing cardiac electrophysiologic disturbances (J. Am. Coll. Cardiol. 2010, 56, 805). Acute adrenergic receptor activation results in rapid activation of cardiomyocyte-specific inflammatory vesicles, which induces IL-18 activation, promotes cardiac cytokine waterfall response and macrophage infiltration, and leads to myocardial injury and reduced cardiac function (Fig R2) (Eur. Heart J. 2018, 39, 60). Additionally, parasympathetic nerve stimulation can elicit the activation of α-7 nicotinic acetylcholine receptor (α7nAChR), leading to a reduction in inflammatory response and oxidative stress (J. Am. Heart Assoc. 2023, 12, e030539). The activation of α7nAChR has been shown to reverse the up-regulation of myocardial arginase induced by ischemia-reperfusion injury and reduce infarct size (Fig R3) (Acta Physiol. 2017, 221, 174).
+Fig. R2 | Take home figure working model for b-adrenergic activation induced cardiac inflammatory cascade which finally results in cardiac remodeling (left) and therapeutic strategy (right) (Eur. Heart J. 2018, 39, 60).
+
+![Diagram showing the working model for b-adrenergic activation induced cardiac inflammatory cascade and therapeutic strategy](page_154_72_1142_384.png)
+
+Fig. R3 | Myocardial area at risk and infarct size. a, Area at risk expressed as % of left ventricle and b, infarct size (with representative images of infarcted myocardium) expressed as % of the area at risk following 30 min ischaemia and 2-h reperfusion in control animals (Control IR; n = 14), after vagal nerve stimulation (VNS + IR; n = 13), α7 nAChR blockade and VNS (MLA + VNS + IR; n = 7), the arginase inhibitor nor-NOHA and IR (nor-NOHA + IR, n = 5), nor-NOHA+VNS+IR (n = 6) and MLA alone (n = 5). Data are shown as mean ± SEM. Significant differences between groups are shown: *P < 0.05 and ‡P < 0.001 (Acta Physiol. 2017, 221, 174).
+
+![Bar graphs showing area at risk and infarct size for different experimental groups](page_154_668_1142_384.png)
+In summary, neuromodulation (inhibition of sympathetic nerve or activation of parasympathetic nerve) may reduce myocardial injury and decrease serum levels of markers of myocardial injury through mechanisms such as reduction of calcium overload, inflammatory response, and oxidative stress. The corresponding content have been included in the manuscript.
+
+“Serum Elisa assay revealed significantly lower levels of markers of myocardial injury (MYO and c-TnI) at 4–5 h post-infarction in the PtNP-shell group compared to the control group (all p < 0.05, Fig. 5j and k), indicating an improvement in myocardial injury (*JAMA*. **2013**, *309*, 2262). This may be attributed to the activation of α-7 nicotinic acetylcholine receptor by stimulating parasympathetic nerves, thereby alleviating inflammatory reactions and oxidative stress (*J. Am. Heart Assoc.* **2023**, *12*, e030539; *Acta Physiol.* **2017**, *221*, 174).”
+
+Comment 5: Comment 9-10: I think the responses to my comments are fine, but some of these points should go into the manuscript discussion section.
+
+Author reply: Thank you for your kind reminding. Your valuable suggestion has significantly enhanced the depth of our research. The relevant content has been incorporated into the discussion section of the manuscript.
+
+“Cardiac sympathetic denervation (CSD) is a clinical procedure aimed at targeting the autonomic ganglia for refractory ventricular arrhythmias. However, ganglion removal can be traumatic for patients and may lead to complications due to the loss of original physiological function (*Eur. Heart J.* **2022**, *43*, 2096). Currently, β-blockers are the primary pharmacological drugs employed in clinical practice for arrhythmia treatment (*J. Am. Heart Assoc.* **2018**, *7*, e007567; *Eur. Heart J.* **2023**, *44*, 3720). However, their administration during acute myocardial ischemia remains unclear and is contraindicated in patients with heart failure. Additionally, previous research investigated the local ganglion blockade using botulinum toxin A to protect the heart (*Heart Rhythm* **2022**, *19*, 2095). Nevertheless, its prolonged blocking effect renders it unsuitable for acute myocardial ischemia management. Conversely, PtNP-shell-based photothermal neuromodulation offers reversible modulation within a short timeframe, exhibiting superior efficacy and controllability.”
+
+“Simultaneously, exploiting the presence of blood vessels surrounding the ganglion presents an opportunity to minimize photon propagation within tissues. Consequently, photothermal modulation of NIR-II fibers in proximity to the ganglion through vascular routes during interventional therapy emerges as a promising avenue for direct clinical translation.”
+To Referee #3
+
+Overall remark: The authors have addressed most of the reviewer comments. Adequate control experiments and results have also been provided. However, there are a couple more concerns regarding the revised manuscript.
+
+Author reply: We appreciate your positive evaluation on our manuscript. We have made a point-by-point response to your comments and carefully revised the manuscript as you suggested. For your reference, please find our revisions marked in red color.
+
+Comment 1: For neural interfaces, bidirectionality is defined as the ability and record and stimulate neural activity. Therefore, stimulating and inhibiting neural activity should not be defined as bidirectionality of neuromodulation. A more appropriate term will be multi-modal neuromodulation.
+
+Author reply: Thank you for the comment. We have substituted the term “bi-directional” with “multimodal”.
+
+Comment 2: All peaks in the XPS spectra should be identified. For example, there is an emergence of peaks (at ca. 400 eV) other than Ga and O in the GaNP samples. The elemental composition should be assessed to better elucidate the chemical composition of each sample.
+
+Author reply: Following your suggestion, we identified all peaks in the XPS survey spectra (Fig. R4). The peaks at about 400 eV can be identified to Auger peaks of Ga. The corresponding results have been included in the Supplementary Fig. 5.
+
+![Three XPS survey spectra plots labeled a, b, and c, showing binding energy vs intensity for different samples.](page_186_1097_1077_246.png)
+
+Fig. R4 | The XPS survey spectra of a, GaNPs, b, Ga@Pt NPs and c, PtNP-shell.
+
+Finally, we want to thank the referees again for their constructive comments on our work, and we hope our newly revised manuscript can reach the quality expectation to be published in Nature Communications. Please find our revisions marked in red copy of the revised manuscript.
+Reviewers' Comments:
+
+Reviewer #2:
+Remarks to the Author:
+The authors have addressed all comments in the latest version of the manuscript.
+
+Reviewer #3:
+Remarks to the Author:
+The authors have addressed all comments.

015d965c0cb0c74c387f9596e3f91c0197ff39a7333b1c0b5bef96993bcbbd18/peer_review/peer_review.md

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+Peer Review File
+
+The emergence of three-dimensional chiral domain walls in polar vortices
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This paper investigates the local polarization within tubular vortex topologies in STO/PTO/STO superlattice by 4D-STEM. Through quantifying the helicity based on polarization, they discussed the domain chirality separated by different domain walls. The authors discovered new pair of triple points with the opposite/same rotation at the junction of achiral and chiral domain walls. They further discussed that all possible configuration of three point topologies with reliable analysis of the origin of the triple points. This article presents an interesting study of topologically driven chiral domain walls in oxide superlattices by using specialized electron microscopy. I have some comments:
+
+1. The polarization measurement based on 4D-STEM is an important basis of the article. The authors briefly mentioned in the article that 4D-STEM can precisely measure polarization in ferroelectrics due to the violation of Friedel's Law, I think it is necessary to further elaborate the principle and quantitative details, which is crucial for this article. For example, why choose the difference between 1, 2, 3, and 4 pairs to map the polarization, and can we get the same results by performing similar operations on other pairs?
+
+2. In fact, 4D-STEM only maps the tetragonality (strain). Although it is usually positively correlated with the polarization, but sometimes it is not. For example, at the surface of PZT, the polarition is suppressed although the tetragonality (strain) is larger (Nature Communications | 7:11318 | DOI: 10.1038/ncomms11318). In the vortex system, I would expect this case is more complicated. I wonder how the author handle this. Related discussion is needed to avoid any misleading.
+
+3. Vortex is a three-dimensional polar structure. Obviously, in the STEM image the polarization along the viewing direction is not uniform for this sample, i.e., near the core and far away from the core should have different polarization. For the conventional HAADF-STEM method without the depth resolution, it is very difficult to precisely measure the in-plane polarization to extract the chirality information. However, I donot see how the 4D-STEM sovle this problem. Did the authors simply ignore this and extract the averaged polarition information? Detailed discussion is needed.
+
+4. I wonder how to determine the position of vortex cores from the BF-STEM image in Fig. 1a, I can only distinguish the dark contrast of the wave shape. How to correlate the bright/dark contrast with the core postions. Besides, it would be better to remove a few red circles to show more details.
+
+5. Both the virtual dark field image and the actual dark field image in Fig. 1c are constructed from diffraction information. Why are these domain walls invisible in virtual dark field images? In addition, the dark field image in Fig. 1c need to clarify the selected diffraction point.
+
+6. Can different domain walls be distinguished by dark field images? e.g., through branching or stripe periodicity.
+
+7. I found some problems in the cited refereces in this manuscript. For example, the authors mentioned the “The first experimental demonstration was in 25, where chirality switches...”. In fact, at the same time another group published an article of switching chirality of poarl vortex at the atomic scale STEM and dark-field TEM, which has been totally ingored in this manuscript. (Sci. China-Phys.Mech. Astron. 65, 237011 (2022), https://doi.org/10.1007/s11433-021-1820-4). Another one is the authors mentioned that “novel polarization textures in ferroelectrics such as merons, polar flux-closure domains,
+vortices……in oxide superlattices", ignoring the representative polar antivortex (Nature Communications | (2021) 12:2054, https://doi.org/10.1038/s41467-021-22356-0), and three-fold polar vertices (Nature Communications | (2022) 13:6340, https://doi.org/10.1038/s41467-022-33973-8)
+
+8. Some minor suggestions: Fig. 1c lacks the scale bar; Fig. 3a lacks the axis; “Once the atoms were identified, the atomic planes were divided into different zone axis such as along [001]o and [001]o” seems to be a typo here.
+
+Reviewer #2 (Remarks to the Author):
+
+S. Susarla et al. reported the chirality engineering of the topological polar vortex via atomic-scale symmetry-breaking operations. In this work, 4D-TEM results display the topology-driven three-dimensional domain walls, and the manuscript was well organized. As the author said, the chirality of the polar vortex is governed by the perpendicular and parallel polarization of the tubular vortex. In my opinion, polarization vector mapping of the vortex region in in-plane geometry will be a more intuitive way to demonstrate the vortex’ chirality. Furthermore, the 4D-TEM data needs to be reanalysed, otherwise it is difficult to support the existing conclusions. Two main concerns are as follows:
+1. In Figure 1b, it is difficult for the reader to locate the vortex center, which is consistent with the position marked by the author.
+2. The combination of Figure 2 a, 2e and Figure 4e, there is a dislocation structure with respect to the tubular vortex across the γ-domain wall, in accordance with Figure 1b shows. However, in Fig. S3 and S4, the virtual image has obviously the same boundary (in the middle of the image) as in Fig.2b, but the author does not identify it as any vortex domain wall. Could authors explain this difference? Perhaps, the polarization vector mapping on HAADF-STEM image will illustrate the issue more directly.
+
+Reviewer #3 (Remarks to the Author):
+
+The manuscript by Susarla et al. presents a structural analysis of the 3D domain wall network in topological polar vortices formed in (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayers grown on SrRuO3-buffered DyScO3 substrates. The microstructure of the films is examined in detail by means 4D-STEM imaging. Thus, lateral and axial polarization maps are obtained by taking the normalized intensity difference be-tween opposite Friedel pair disks. This allows identifying three distinct types of domain wall configurations having different parallel/antiparallel axial/lateral components. Thus, two chiral and one achiral domain walls are identified. Finally, the authors observe that the domain walls meet at triple points, which typically appear in pairs. They hypothesize that these topological defects could lead to unique electrostatic and magnetic properties useful for quantum sensor applications.
+
+The manuscript presents an original and very good experimental and analytical work on the microstructure of domain walls in topological polar vortices. Overall, the manuscript is clearly written and the figures are well elaborated. I enjoyed reading the manuscript, although I suggest introducing a couple of changes to make it a bit more comprehensible. In addition, I am listing also here some minor amendments.
+
+1. In page 4 of the manuscript, "Supplementary Information" should be deleted, as there is no additional information in the SI referring to the trilayer stack.
+2. At the end of page 5, it reads that in Figure 1b "a zig-zag type pattern, giving rise to a net in-plane polarization rotation along [001]o (lateral component) indicated as Px". I have difficulties seeing this net in-plane polarization. Could the authors plot the resulting in-plane polarization by averaging it along the horizontal direction and plotting it next to the image? This is not obvious from the figure. It seems to me that the Px at the top of the PTO film should cancel with the Px at the bottom of the PTO film.
+
+3. Again, in Figure 1b, it seems there are vortex cores also in the bottom STO layer. Can the authors comment on this?
+
+4. The scale is missing in Figure 1c.
+
+5. It is a bit complicated to follow the discussion of the possible triple points depicted in Figure 3b. Could the authors correlate the triple points observed in Figure 3a (and also in the SI) to the triple point pairs represented in Figure 3b? This would make it easier to follow the explanation.
+
+6. In the cation of Figure 4 it reads "The chirality for each type of domain is indicated by a sketched hand", but in the figure there are no sketched hands. Please, remove the sentence.
+
+7. In the Materials and Methods the authors should indicate how was the sample for S/TEM prepared.
+
+8. In page 14, please change "low-pass and high-pass Gaussian filters" for "band-pass Gaussian filters".
+
+Based on my previous comments I recommend the publication of the manuscript of Susarla et al. in Nat. Commun. after minor revisions.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This paper investigates the local polarization within tubular vortex topologies in STO/PTO/STO superlattice by 4D-STEM. Through quantifying the helicity based on polarization, they discussed the domain chirality separated by different domain walls. The authors discovered new pair of triple points with the opposite/same rotation at the junction of achiral and chiral domain walls. They further discussed that all possible configuration of three-point topologies with reliable analysis of the origin of the triple points. This article presents an interesting study of topologically driven chiral domain walls in oxide superlattices by using specialized electron microscopy. I have some comments:
+
+We thank the reviewer for reading our manuscript. We have tried our best to answer the reviewer’s questions.
+
+Question 1. The polarization measurement based on 4D-STEM is an important basis of the article. The authors briefly mentioned in the article that 4D-STEM can precisely measure polarization in ferroelectrics due to the violation of Friedel's Law, I think it is necessary to further elaborate the principle and quantitative details, which is crucial for this article. For example, why choose the difference between 1, 2, 3, and 4 pairs to map the polarization, and can we get the same results by performing similar operations on other pairs?
+
+Response: Friedel law states that the diffraction intensities from (hkl) and (\( \overline{hkl} \)) planes are similar. However, this rule breaks for non-centrosymmetric materials where the opposite Friedel pair disks have differential intensities due to multiple scattering effects. In this work, we have chosen to use the 1,2, 3 and 4 because these are the primary (hkl) directions along which the effect of Friedel’s law breaking is the maximum. The intensity difference between a particular (hkl) Friedel pair is also coupled to the effective polarization along that direction. Since, we were concerned about purely lateral and axial polarization, we choose disks 1, 2, 3 and 4. The other pairs along different directions might have mixed lateral and axial polarization signals and hence it is difficult to interpret the resultant polarization maps.
+
+We have now added a discussion about it in the main manuscript:
+The polarization from the PTO layer can be determined qualitatively by subtracting the intensity of the opposite Friedel pair disks due to the violation of Friedel’s law \(^{30-32}\). This polarization mapping is slightly different from strain mapping where the accurate position of the diffracted disks is calculated\(^{35}\). The method for subtracting the intensities of opposite Friedel’s pair disks would also work for analogous Pb\(_x\)Zr\(_{1-x}\)TiO\(_3\) (PZT) where polarization is suppressed under large tetragonality\(^{36}\). The (hkl) Friedel pairs were chosen along [001]\(_o\) and [1\(\bar{1}\)0]\(_o\) directions to determine pure lateral and axial polarization respectively. We note that the other (hkl) directions may also break Friedel’s law, but the associated polarization will be a combination of lateral and axial component. The polarization maps corresponding to regions delimited by rectangles in Figure 2b are shown in Figure 2d-e.
+
+Question 2. In fact, 4D-STEM only maps the tetragonality (strain). Although it is usually
+positively correlated with the polarization, but sometimes it is not. For example, at the surface of PZT, the polarization is suppressed although the tetragonality (strain) is larger (Nature Communications |7:11318 | DOI: 10.1038/ncomms11318). In the vortex system, I would expect this case is more complicated. I wonder how the author handle this. Related discussion is needed to avoid any misleading.
+
+Response: We agree with the reviewer that the polarization and strain do not always go hand in hand. However, in 4D STEM , we determine the strain by the change in the position of the disks relative to the parent materials. The polarity is associated with the relative change in the intensity of the opposite Friedel pair disks, that measured in our current work. We have now added the discussion in main manuscript as shown in previous question. To help with the discussion, we have also cited the paper mentioned by the reviewer.
+
+Question 3. Vortex is a three-dimensional polar structure. Obviously, in the STEM image the polarization along the viewing direction is not uniform for this sample, i.e., near the core and far away from the core should have different polarization. For the conventional HAADF-STEM method without the depth resolution, it is very difficult to precisely measure the in-plane polarization to extract the chirality information. However, I do not see how the 4D-STEM solve this problem. Did the authors simply ignore this and extract the averaged polarization information? Detailed discussion is needed.
+
+Response: We thank the reviewer for pointing this aspect. Indeed, the polarization varies near and away from the vortex core. Hence, the HAADF-STEM fails in this regard. However, 4D-STEM allows us to image the lateral and axial polarization simultaneously which is not possible the HAADF-STEM. We cannot access the axial polarization directly with accuracy in conventional HAADF-STEM. However, in 4D-STEM we can access the pure axial polarization because it has a different diffraction condition (different Friedel’s diffraction pairs) than lateral polarization. Additionally we primarily observe polarization from the top half of polar vortices in PbTiO$_3$ layer due to the limited depth resolution (http://arxiv.org/abs/2012.04134). Hence, the lateral polarization do not cancel out one another. We can't measure polarization quantitatively, but our qualitative measurements are good enough for the present purposes studying domain boundaries and triple points). We illustrate this better in the following diagram pasted paste in a figure from a previous paper (https://www.nature.com/articles/s41586-019-1092-8) where we can measure the topological polarization texture buried underneath SrTiO$_3$.
+Figure: **a**, **b**, Reversed Ti-displacement vector map (top) based on the atomically resolved plane-view HAADF-STEM image (bottom) of a single skyrmion bubble (marked by a white circle in Extended Data Fig. 6a), showing the hedgehog-like skyrmion structure. The sketch of the superlattice in **b** is overlaid with the planar-view dark-field TEM image and gives a top view of the superlattice. **c**, Ti-displacement vector map (front) based on the atomically resolved cross-sectional HAADF-STEM image (back), showing a cylindrical domain with anti-parallel (up–down) polarization. The sketch in **b** is overlaid with the cross-sectional dark-field TEM image and shows the cross sectional view of the superlattice. **d**, **e**, The 4D-STEM image of a [(PbTiO$_3$)$_{16}$(SrTiO$_3$)$_{16}$]$_8$ superlattice gives the ADF image (**d**) and maps of polar order using the probability current flow (**e**), which were reconstructed from the same 4D dataset. **f**, **g**, Multislice simulations of the beam propagation through the model structure from Fig. 2 show the ADF image (**f**) and the probability current flow (**g**), which were analyzed using the same process as the experimental data. The signals are not simple projections, but weighted by electron beam channelling towards the middle of the skyrmion bubble, where the polarization exhibits a Bloch-like character.
+
+We have also added this discussion in the main manuscript and modified the schematic in Figure 2.
+
+. On the other hand, 4D-STEM allows us to collect a diffraction pattern at each probe position, which can then be used to create precise maps of physical quantities such as strain and polarization. **The diffraction pattern in 4D-STEM offers a unique advantage over HAADF-STEM in polar vortices because direction of polarization can be accurately measured.** For the present experiment, we performed 4D-STEM imaging on a trilayer STO/PTO/STO along the [110]$_o$ zone axis (Figure 2a). We used a probe size of ~7 Å, larger than the STO/PTO unit cell dimensions (~4 Å) to remove the atomic-resolution signal and to estimate the polarization at unit cell resolution.
+[110]₀
+[1\bar{1}0]₀
+[001]₀
+e- beam
+STO
+PTO
+STO
+
+Question 4. I wonder how to determine the position of vortex cores from the BF-STEM image in Fig. 1a, I can only distinguish the dark contrast of the wave shape. How to correlate the bright/dark contrast with the core positions. Besides, it would be better to remove a few red circles to show more details.
+
+Response: BF-STEM is more sensitive to the diffraction contrast. Vortex features are continuous rotation of polarization vectors and hence they are more visible at lower collection angles in BF-STEM mode. In the BF STEM mode, they usually appear as dark cross. For better clarity, we have removed some of the red circles as the reviewer was suggesting.
+
+SrTiO₃
+PbTiO₃
+SrTiO₃
+SrRuO₃
+DyScO₃
+
+Question 5. Both the virtual dark field image and the actual dark field image in Fig. 1c are constructed from diffraction information. Why are these domain walls invisible in virtual dark field images? In addition, the dark field image in Fig. 1c need to clarify the selected diffraction point.
+
+Response: Some of the vortex domain walls may be missing in the virtual dark field images because they do not capture the entire information. Vortex domain walls originate from the change in lateral and axial polarization which can only be determined by difference in the intensity of the opposite Friedel pair disks.
+Here is an example showing all the dark field images taken from disk 1, 2, 3 and 4. Even, if we combine everything, we will still find a few boundaries missing. It is only the normalized subtraction of (1-2) and (3-4) that reveals all of the vortex domain boundaries.
+
+![Dark field images corresponding disks 1-4.](page_186_370_1217_563.png)
+
+Figure S4: Dark field images corresponding disks 1-4.
+
+Question 6. Can different domain walls be distinguished by dark field images? e.g., through branching or stripe periodicity.
+
+Response: No, they cannot be distinguished by just dark field images. This is because the vortex domain walls are *only* identified by change lateral and axial polarization. The lateral and axial polarization cannot be identified by just one dark field image.
+We have now also included the virtual dark field image created from four different disks. We cannot solely identify all of the polarization domain boundaries from just one dark field image.
+
+Question 7. I found some problems in the cited references in this manuscript. For example, the authors mentioned the “The first experimental demonstration was in 25, where chirality switches…”. In fact, at the same time another group published an article of switching chirality of polar vortex at the atomic scale STEM and dark-field TEM, which has been totally ignored in this manuscript. (Sci. China-Phys.Mech. Astron. 65, 237011 (2022), https://doi.org/10.1007/s11433-021-1820-4). Another one is the authors mentioned that “novel polarization textures in ferroelectrics such as merons, polar flux-closure domains, vortices……in oxide superlattices”, ignoring the representative polar antivortex (Nature Communications | (2021) 12:2054, https://doi.org/10.1038/s41467-021-22356-0), and three-fold polar vertices (Nature Communications | (2022) 13:6340, https://doi.org/10.1038/s41467-022-33973-8)
+
+Response: We thank reviewer for the suggestions. We have included all the citations in the introduction of our manuscript.
+
+Question 8.. Some minor suggestions: Fig. 1c lacks the scale bar; Fig. 3a lacks the axis; “Once
+the atoms were identified, the atomic planes were divided into different zone axis such as along [001]o and [001]o” seems to be a typo here.
+
+Response: We have corrected the typo and added the scale bar in Figure 1c.
+
+Reviewer #2 (Remarks to the Author):
+
+S. Susarla et al. reported the chirality engineering of the topological polar vortex via atomic-scale symmetry-breaking operations. In this work, 4D-TEM results display the topology-driven three-dimensional domain walls, and the manuscript was well organized. As the author said, the chirality of the polar vortex is governed by the perpendicular and parallel polarization of the tubular vortex. In my opinion, polarization vector mapping of the vortex region in in-plane geometry will be a more intuitive way to demonstrate the vortex’ chirality. Furthermore, the 4D-TEM data needs to be reanalyzed, otherwise it is difficult to support the existing conclusions. Two main concerns are as follows:
+
+Response: We thank the reviewer for the comments. However the reviewer has not completely understood our motivation behind performing 4D-STEM. Polar vortices have both axial and lateral polarization components, out of which the former cannot be directly measured via HAADF-STEM due to the projection problem. Since 4D-STEM uses two different Friedel pair disks to map out the lateral and axial polarization, it is more intuitive to use 4D-STEM to quantify the polarization. A more detailed description is given in the latter responses.
+
+Question 1. In Figure 1b, it is difficult for the reader to locate the vortex center, which is consistent with the position marked by the author.
+Response: We have now reanalyzed Figure 1b which is shown below:
+
+![Polarization vector maps overlaid on the drift-corrected HAADF-STEM images. The yellow vector indicates the direction of polarization. The underlying red/blue contrast is the curl of the displacement.](page_370_1012_805_367.png)
+
+Figure S1: Polarization vector maps overlaid on the drift-corrected HAADF-STEM images. The yellow vector indicates the direction of polarization. The underlying red/blue contrast is the curl of the displacement.
+We want to clarify that we are marking the vortex center at the maxima/ minima point of the polarization curl which is defined as below:
+
+\[
+\theta = \frac{1}{2} \left( \frac{\partial u}{\partial y} - \frac{\partial v}{\partial x} \right)
+\]
+
+This is how we have marked the center position of the vortices. We have put the zoomed-out version of the polarization maps, and their corresponding in-plane and out-of-plane strain maps in the supplementary information.
+
+![Strain maps (top two) and infinitesimal rotation (bottom) extracted by A-site fitting of atoms in Figure S1.](page_349_682_573_340.png)
+
+Figure S2: Strain maps (top two) and infinitesimal rotation (bottom) extracted by A-site fitting of atoms in Figure S1.
+
+Question 2. The combination of Figure 2 a, 2e and Figure 4e, there is a dislocation structure with respect to the tubular vortex across the γ-domain wall, in accordance with Figure 1b shows. However, in Fig. S3 and S4, the Virtual image has obviously the same boundary (in the middle of the image) as in Fig.2b, but the author does not identify it as any vortex domain wall. Could authors explain this difference? Perhaps, the polarization vector mapping on HAADF-STEM image will illustrate the issue more directly.
+
+Response: We thank the reviewer for pointing out this aspect. We have now reanalyzed the 4D STEM datasets where we have included the missing vortex domain wall that reviewer pointed
+out.
+
+Figure S6: Virtual image, polarization, and helicity maps from different 4D STEM datasets showing the repeatability of different chiral/achiral boundaries in the PTO/STO trilayer. The presence of triple point topologies is evident whenever the chiral and achiral boundaries intersect one another. Scale bar: 20 nm for all panels.
+
+Figure S7: Virtual image, polarization, and helicity maps from different 4D STEM datasets showing the repeatability of different chiral/achiral boundaries in the PTO/STO trilayer. The presence of triple point topologies is evident whenever the chiral and achiral boundaries intersect one another. Scale bar: 30 nm
+The polarization maps on the in-plane HAADF-STEM image will not reveal all types of domain boundaries as the axial polarization cannot the measured directly in the HAADF-STEM.
+
+Reviewer #3 (Remarks to the Author):
+
+The manuscript by Susarla et al. presents a structural analysis of the 3D domain wall network in topological polar vortices formed in (SrTiO3)16/(PbTiO3)16/(SrTiO3)16 trilayers grown on SrRuO3-buffered DyScO3 substrates. The microstructure of the films is examined in detail by means 4D-STEM imaging. Thus, lateral, and axial polarization maps are obtained by taking the normalized intensity difference be-tween opposite Friedel pair disks. This allows identifying three distinct types of domain wall configurations having different parallel/antiparallel axial/lateral components. Thus, two chiral and one achiral domain walls are identified. Finally, the authors observe that the domain walls meet at triple points, which typically appear in pairs. They hypothesize that these topological defects could lead to unique electrostatic and magnetic properties useful for quantum sensor applications.
+
+The manuscript presents an original and very good experimental and analytical work on the microstructure of domain walls in topological polar vortices. Overall, the manuscript is clearly written, and the figures are well elaborated. I enjoyed reading the manuscript, although I suggest introducing a couple of changes to make it a bit more comprehensible. In addition, I am listing also here some minor amendments.
+
+Response: We thank the reviewer for appreciating our manuscript. We have answered almost all of the reviewer questions.
+
+Question 1. In page 4 of the manuscript, "Supplementary Information" should be deleted, as there is no additional information in the SI referring to the trilayer stack.
+Response: This has now been deleted.
+
+Question 2. At the end of page 5, it reads that in Figure 1b "a zig-zag type pattern, giving rise to a net in-plane polarization rotation along [001]o (lateral component) indicated as Px". I have difficulties seeing this net in-plane polarization. Could the authors plot the resulting in-plane polarization by averaging it along the horizontal direction and plotting it next to the image? This is not obvious from the figure. It seems to me that the Px at the top of the PTO film should cancel with the Px at the bottom of the PTO film.
+
+Response: We thank the reviewer for noticing this aspect. We have re-plotted our polarization vector maps in Figure 1b (i) where we observe that the top portion of lateral polarization is not equivalent with the bottom portion of the polarization. Additionally, we have a schematic in
+Figure 1b (ii) explaining the origin of net lateral polarization.
+
+![Diagram showing the origin of net lateral polarization](page_232_186_1047_153.png)
+
+Question 3. Again, in Figure 1b, it seems there are vortex cores also in the bottom STO layer. Can the authors comment on this?
+Response: We apologize to reviewers for this mistake. We had some errors in fitting the A sites. We re-did the A site gaussian fitting and replaced the earlier images better one as new Figure 1b. Refer to our response to reviewer 2 Question#1
+
+![Image showing vortex cores and polarization vectors](page_232_495_1047_312.png)
+
+Question 4. The scale is missing in Figure 1c.
+Response: The scale bar has been added now.
+
+Question 5. It is a bit complicated to follow the discussion of the possible triple points depicted in Figure 3b. Could the authors correlate the triple points observed in Figure 3a (and also in the SI) to the triple point pairs represented in Figure 3b? This would make it easier to follow the explanation.
+
+Response: We thank the reviewers for the response. We have now included the labels in Figure 3b and also indicated their corresponding location in Figure 3a.
+Question 6. In the cation of Figure 4 it reads "The chirality for each type of domain is indicated by a sketched hand", but in the figure there are no sketched hands. Please, remove the sentence.
+Response: We have removed that sentence.
+
+Question 7. In the Materials and Methods the authors should indicate how was the sample for S/TEM prepared.
+Response: We have now added the STEM sample preparation part in Materials and Methods.
+
+STEM Sample preparation: In-plane [(PbTiO3)16/(SrTiO3)16] trilayer grown on SrRuO3/DyScO3 substrate were mechanically polished using a 0.5° wedge in Allied Multiprep. The samples were subsequently Ar ion milled in a Gatan Precision Ion Milling System, starting from 3.5 keV at 4° down to 1 keV at 1° for the final polish. The HAADF-STEM images were acquired using double aberration corrected TEAM I microscope operated at 300 kV under non-monochromated mode.
+
+Question 8. In page 14, please change "low-pass and high-pass Gaussian filters" for "band-pass Gaussian filters".
+Response: We have changed the typos
+
+Based on my previous comments I recommend the publication of the manuscript of Susarla et al. in Nat. Commun. after minor revisions.
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The revised manuscript addresses my concerns regarding the depth resolution problem in 4DSTEM and polarization information extraction, the authors state that the signal primarily originates from the top half of polar vortices in the PbTiO3 layer, as supported by simulation results (http://arxiv.org/abs/2012.04134). The virtual imaging ability and the ability to obtain pure axial polarization in 4DSTEM is indeed a valuable advantage over conventional STEM imaging. I understand that while quantitative measurements of polarization may not be feasible, the qualitative measurements in this work still provide valuable insights into studying domain boundaries and triple points. Overall, I’m happy with the response to all the questions and comments. Thus, I recommend the publication of this manuscript in NC.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have addressed my concerns.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have satisfactorily addressed most of my concerns and I therefore suggest publication of the manuscript by Susarla et al. in Nature Communications.

018ea56f56282342b1a9e7b0cea3a8dc2890bbe74f3ff129238a91951bc7905d/peer_review/peer_review.md

@@ -0,0 +1,388 @@
+Peer Review File
+
+Multiple valence bands convergence and strong phonon scattering lead to high thermoelectric performance in p-type PbSe
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Band convergence is an effective way to improve the electrical properties of thermoelectric materials. Here, the authors reported that multiple valence bands could be activated in p-type PbSe-AgInSe2 system, which is a novel point compared with the traditional two-band convergence. These results will motivate researchers to find more strategies on band structure engineering. AgInSe2 has an intrinsic low lattice thermal conductivity. The introduction of AgInSe2 leads to strong phonon scattering verified by the nano-scale precipitates and dislocations. As a result, a large ZT (~2.1) was achieved in this work and it shows a good reproducible thermoelectric performance. The paper reported an extensive study on p-type PbSe-AgInSe2 and it is well written. Therefore, I recommend the paper to be published in Nature communications. Suggestions or comments are given below.
+
+1. The microstructure study didn’t give a quantitative results on the occupation of Ag and In atoms in this system. So, the sentence -“Local structure and microstructure analysis reveal that about 80 percent of Ag and In atoms form AgInSe2 as nano-scale precipitates”-in the Abstract may make misunderstanding, which should be modified.
+
+2. The temperature-dependent of band-gap may be another evidence for the band convergence. The increase tendency of band gap become unobvious above ~ 500K, which indicate that the heavy valence bands may dominates above this temperature. This phenomenon is also consistent with the temperature-dependent Hall measurement that RH peak appears around 500K (Figure S5).
+
+3. Mechanical property is important for the transport performance of materials. What is the effect on the mechanical property of PbSe with the introduction of AgInSe2?
+
+4. The Lorenz number was calculated assuming acoustic-phonon scattering dominates. How to prove this?
+
+5. What is the uncertainty for the thermoelectric properties measurements?
+
+Reviewer #2 (Remarks to the Author):
+
+In this manuscript, the authors investigated the thermoelectric properties of Pb0.98Na0.02Se-x%AgInSe2 (LISS). An exceptional figure-of-merit ZT of ~2.1 at 873K was achieved. They performed a systematic study on the electrical/thermal transport properties and microstructures for this system. The introduction of AgInSe2 enlarges the band gap, suppressing the bipolar effect. It is very important to achieve high thermoelectric performance at high temperature regime, but has been challenging to obtain. Interestingly, the incorporation of AgInSe2 facilitates the convergence of multiple valence bands, resulting in high weighted mobility and large power factor. The presence of nano-scale AgInSe2 precipitates and dislocations results in strong phonon scattering. As a result, a combination of band convergence and strong phonon scattering gives record-high thermoelectric performance in PbSe. The local structure analysis by XAFS is very interesting, providing a microscopic perspective to understand the role of doped elements. This is a very solid work and it is suitable for the scope of Nature Communications. This work shows that PbSe thermoelectrics can compete with the much expensive PbTe. It is highly recommended to be published in Nature Communications after addressing minor points as given below:
+
+1. In the “Introduction” section, please cite related works when you mentioned the quality factor B (The lattice thermal conductivity is another important parameter for the thermoelectric performance indicated by the quality factor B).
+
+2. It is mentioned that “the tetragonal AgInSe2 is perfectly inserted to the PbSe matrix as nano-scale
+precipitates revealed by the transmission electron microscopy". This sentence can make readers confused because a part of Ag and In atoms occupies Pb sites.
+
+3. The effective masses increase with the introduction of AgInSe2 as indicated by the Pisarenko plot. Please show the effective masses for each sample, which is more straightforward for the readers.
+
+4. The measurement of sound velocities is not mentioned in the experimental section.
+
+5. The heat capacity (Cp) calculated by the Dulong-Petit law will underestimate the thermal conductivity at high temperature. Estimating the Cp by the empirical equation is more accurate. It is not necessary to use the Cp value estimated by the Dulong-Petit law.
+
+Reviewer #3 (Remarks to the Author):
+
+see separate file
+The present manuscript provides interesting data describing the thermoelectric properties of PbSe doped with AgInSe2. This doping / alloying leads to a reduction in the thermal conductivity and an improvement of band convergence enabling a zT value slightly above 2. Thermoelectric materials are considered a viable option to improve energy conversion since they convert waste heat into electrical energy or enable efficient cooling. Hence identifying promising thermoelectric materials is a timely topic, which could be suitable for Nature Communications. Nevertheless, there are several reasons why the present manuscript does not meet my expectations for a manuscript to be published in Nature Communications.
+
+One of the main claims is that there is multi-band convergence. Yet, the nature of these band and how they could possibly be described and explained is missing. One of the main claims of the present manuscript is the idea that more than 3 bands can contribute, yet the proof for this claim and the explanation of the nature of these bands appears rather incomplete. I would like to see very strong and convincing evidence that indeed more than two bands contribute and what their nature is. To mention one option to provide such evidence: several groups have recently employed tight-binding methods to explain the band structure of related chalcogenides [1,2]. Such calculations could be performed to explore the potential nature and more importantly origin of the bands involved. I am not aware of any study that has claimed and proven so far that three bands can provide a contribution to the thermoelectric performance of PbSe.
+
+Then, I am also concerned about the apparent disagreement between theory and experiment. The authors claim that their experiment shows an increase of band gap upon alloying with AgInSe2. Yet, the DFT calculations presented in fig. 5b do not seem to support this conclusion.
+
+Finally, in recent years the thermoelectric properties in lead chalcogenides have been discussed in terms of the underlying bonding mechanism, which must be related to the corresponding band structure [1,3]. A discussion of the fundamental bonding mechanism relevant here is missing. Such a discussion is important since it can help to predict and explain which materials and changes of bonding can improve the performance of a given thermoelectric material.
+
+[1] Chemistry of Materials 32 (22), 9771-9779 (2020)
+
+[2] Advanced Materials 30, 1801787 (2018)
+
+[3] Advanced Materials 32, 202005533 (2020)
+Reviewer #1 (Remarks to the Author):
+General comment:
+Band convergence is an effective way to improve the electrical properties of thermoelectric materials. Here, the authors reported that multiple valence bands could be activated in p-type PbSe-AgInSe2 system, which is a novel point compared with the traditional two-band convergence. These results will motivate researchers to find more strategies on band structure engineering. AgInSe2 has an intrinsic low lattice thermal conductivity. The introduction of AgInSe2 leads to strong phonon scattering verified by the nano-scale precipitates and dislocations. As a result, a large ZT (~2.1) was achieved in this work and it shows a good reproducible thermoelectric performance. The paper reported an extensive study on p-type PbSe-AgInSe2 and it is well written. Therefore, I recommend the paper to be published in Nature Communications. Suggestions or comments are given below.
+
+Response: We appreciate the reviewer 1 for his/her solid summary and affirmation for our work. Your insightful comments will strengthen our work.
+
+Comment 1: The microstructure study didn’t give a quantitative results on the occupation of Ag and In atoms in this system. So, the sentence -“Local structure and microstructure analysis reveal that about 80 percent of Ag and In atoms form AgInSe2 as nano-scale precipitates” -in the Abstract may make misunderstanding, which should be modified.
+
+Response: Thanks for your good suggestions. We have made a revision for this sentence. In addition, we made a change to the “abstract” to meet the requirement of Nature Communications (150 words or fewer).
+
+Revision: Abundant nano-scale precipitates and dislocations result in strong phonon scattering and thus ultralow lattice thermal conductivity. Consequently, we achieve an exceptional \( ZT \) of ~ 1.9 at 873 K in p-type PbSe. This work demonstrates that a combination of band manipulation and microstructure engineering can be realized by tuning the composition, which is expected to be a general strategy for improving the thermoelectric performance in bulk materials.
+
+Comment 2: The temperature-dependent of band-gap may be another evidence for the band convergence. The increase tendency of band gap become unobvious above ~ 500K, which indicate that the heavy valence bands may dominates above this temperature. This phenomenon is also consistent with the temperature-dependent Hall measurement that \( R_H \) peak appears around 500K (Figure S5).
+
+Response: It is a good point. A related discussion has been added in our manuscript.
+
+Revision: The unobvious increase tendency of bandgap above ~ 500K may be attributed to the band convergence, where the heavy valence bands dominate and the
+position of heavy valence bands are almost temperature independent1.
+
+1. Pei, Y. et al. Convergence of electronic bands for high performance bulk thermoelectrics. Nature **473**, 66-69 (2011).
+
+**Comment 3**: Mechanical property is important for the transport performance of materials. What is the effect on the mechanical property of PbSe with the introduction of AgInSe$_2$?
+
+**Response**: Thanks for your comments. We calculated the bulk modulus (\( K \)) as shown in Table S1. There is no significant effect on the mechanical property of PbSe with introducing AgInSe$_2$ because the bulk modulus has no obvious change.
+
+**Revision**: The deduced Grüneisen parameters (\( \gamma \)) and bulk modulus (\( K \)) of LISS have no obvious change (Table S1).
+
+**Supplementary Table 1**. Various parameters (longitudinal sound velocity (\( v_l \)), transverse sound velocity (\( v_t \)), average sound velocity (\( v_{avg} \)), Poisson ration (\( v_p \)), Grüneisen parameter (\( \gamma \)), and bulk modulus (\( K \))) of Pb$_{0.98}$Na$_{0.02}$Se - x% AgInSe$_2$. The Poisson ration (\( v_p \)) is calculated by \( v_p = \frac{1-2(v_t/v_l)^2}{2-2(v_t/v_l)^2} \), the Grüneisen parameter (\( \gamma \)) is obtained using \( \gamma = \frac{3}{2} \left( \frac{1+v_p}{2-3v_p} \right) \) and the bulk modulus (\( K \)) is given by \( K = \rho \left( v_l^2 - \frac{4}{3} v_t^2 \right) \) (\( \rho \) is the density of sample).
+
+<table>
+  <tr>
+    <th>Sample</th>
+    <th>\( v_l \)(m/s)</th>
+    <th>\( v_t \)(m/s)</th>
+    <th>\( v_{avg} \)(m/s)</th>
+    <th>\( v_p \)</th>
+    <th>\( \gamma \)</th>
+    <th>\( K \)(GPa)</th>
+  </tr>
+  <tr>
+    <td>x=0</td>
+    <td>3165.6</td>
+    <td>1708.6</td>
+    <td>1907.1</td>
+    <td>0.294</td>
+    <td>1.74</td>
+    <td>48.9</td>
+  </tr>
+  <tr>
+    <td>x=0.5</td>
+    <td>3192.9</td>
+    <td>1726.9</td>
+    <td>1927.3</td>
+    <td>0.293</td>
+    <td>1.73</td>
+    <td>50.2</td>
+  </tr>
+  <tr>
+    <td>x=1</td>
+    <td>3214.7</td>
+    <td>1726.1</td>
+    <td>1927.4</td>
+    <td>0.297</td>
+    <td>1.75</td>
+    <td>51.2</td>
+  </tr>
+  <tr>
+    <td>x=1.5</td>
+    <td>3151.7</td>
+    <td>1715.4</td>
+    <td>1913.5</td>
+    <td>0.289</td>
+    <td>1.71</td>
+    <td>48.0</td>
+  </tr>
+  <tr>
+    <td>x=2</td>
+    <td>3217.4</td>
+    <td>1720.9</td>
+    <td>1922.1</td>
+    <td>0.299</td>
+    <td>1.77</td>
+    <td>50.9</td>
+  </tr>
+  <tr>
+    <td>x=2.05</td>
+    <td>3148.7</td>
+    <td>1718.3</td>
+    <td>1916.4</td>
+    <td>0.288</td>
+    <td>1.70</td>
+    <td>47.6</td>
+  </tr>
+  <tr>
+    <td>x=2.1</td>
+    <td>3179.8</td>
+    <td>1720.3</td>
+    <td>1919.9</td>
+    <td>0.293</td>
+    <td>1.73</td>
+    <td>48.3</td>
+  </tr>
+  <tr>
+    <td>x=2.15</td>
+    <td>3149.7</td>
+    <td>1718.8</td>
+    <td>1916.9</td>
+    <td>0.288</td>
+    <td>1.70</td>
+    <td>47.4</td>
+  </tr>
+</table>
+
+**Comment 4**: The Lorenz number was calculated assuming acoustic-phonon scattering dominates. How to prove this?
+
+**Response**: Thanks for your comments. The carrier scattering mechanism can be revealed in the log (\( \mu_H \))-log (T) relation. A log (\( \mu_H \))-log (T) plot displays T\(^{-3/2}\) behavior for \( x = 2.05 \) sample when T < 600 K (see below Figure), demonstrating that acoustic-phonon scattering dominates. The deviation from T\(^{-3/2}\) relation at high temperature is due to the increase of effective mass.
+Revision: The \( \kappa_e \) was calculated by the Wiedemann-Franz relation, \( \kappa_e = L \sigma T \), where \( L \) (Figure S7a) is estimated by SPB model assuming acoustic phonon scattering dominates (Figure S6c).
+
+![Three plots showing temperature dependence of Hall coefficient, effective mass, and Hall mobility for Pb0.98Na0.02Se-2.05% AgInSe2 and Pb1-xNaxSe](page_184_320_1080_320.png)
+
+Supplementary Figure 6. (a) Temperature dependence of Hall coefficient (\( R_H \)) of Pb0.98Na0.02Se-2.05% AgInSe2. (b) Effective mass as a function of temperature for Pb0.98Na0.02Se-2.05% AgInSe2 and Pb1-xNaxSe. (c) Temperature-dependent Hall mobility of Pb0.98Na0.02Se - 2.05% AgInSe2, which displays a \( T^{-3/2} \) behavior when T < 600 K, demonstrating that acoustic-phonon scattering dominates. The deviation from \( T^{-3/2} \) relation at high temperature is due to the increase of effective mass.
+
+Comment 5: What is the uncertainty for the thermoelectric properties measurements?
+
+Response: Thanks for your comments. The standard samples were measured and these measurement data are compared with the reference value. The uncertainties of thermoelectric parameters are given below. In Figure 1 and 2, the measurements of thermal diffusivity (\( D \)), electrical resistivity (\( \rho \)) and Seebeck coefficient (\( S \)) are well consistent with their reference values. The error of thermal diffusivity is less than 2% (Figure 1). The uncertainties of electrical resistivity (\( \rho \)) and Seebeck coefficient (\( S \)) are less than 2% and 5%, respectively (Figure 2). The combined uncertainty of all measurements for determining the \( ZT \) is less than 20%.
+
+![Two plots comparing thermal diffusivity and its uncertainty versus temperature](page_184_1040_1080_320.png)
+
+Figure 1. (a) Comparison of thermal diffusivity (\( D \)) between measurement and reference for standard sample (Inconel). (b) The uncertainty of \( D \).
+Figure 2. Comparison of (a) electrical resistivity (\( \rho \)) and (c) Seebeck coefficient (\( S \)) between measurement and standard sample (Constantan), respectively. The corresponding uncertainties are shown in (b) and (d).
+Reviewer #2 (Remarks to the Author):
+General comment:
+In this manuscript, the authors investigated the thermoelectric properties of Pb_{0.98}Na_{0.02}Se-x%AgInSe_2 (LISS). An exceptional figure-of-merit ZT of ~2.1 at 873K was achieved. They performed a systematic study on the electrical/thermal transport properties and microstructures for this system. The introduction of AgInSe_2 enlarges the band gap, suppressing the bipolar effect. It is very important to achieve high thermoelectric performance at high temperature regime, but has been challenging to obtain. Interestingly, the incorporation of AgInSe_2 facilitates the convergence of multiple valence bands, resulting in high weighted mobility and large power factor. The presence of nano-scale AgInSe_2 precipitates and dislocations results in strong phonon scattering. As a result, a combination of band convergence and strong phonon scattering gives record-high thermoelectric performance in PbSe. The local structure analysis by XAFS is very interesting, providing a microscopic perspective to understand the role of doped elements. This is a very solid work and it is suitable for the scope of Nature Communications. This work shows that PbSe thermoelectrics can compete with the much expensive PbTe. It is highly recommended to be published in Nature Communications after addressing minor points as given below:
+
+Response: We thank the reviewer 2 for his/her positive comments and valuable suggestions, which is a publishable justification for our submission.
+
+Comment 1: In the “Introduction” section, please cite related works when you mentioned the quality factor B (The lattice thermal conductivity is another important parameter for the thermoelectric performance indicated by the quality factor B).
+
+Response: Thanks for your comments. References about quality factor B are cited in the sentence.
+
+Revision: The lattice thermal conductivity is another important parameter for the thermoelectric performance indicated by the quality factor \( B \) (\( B \propto \mu_w / k_L \))\(^{30,31}\).
+
+30. Kang, S. D., Snyder G. J. Transport property analysis method for thermoelectric materials material: quality factor and the effective mass model. arXiv:1710.06896 [cond-mat.mtrl-sci] (2017).
+31. Tan, G., Zhao, L.-D. & Kanatzidis, M. G. Rationally Designing High-Performance Bulk Thermoelectric Materials. Chem. Rev. **116**, 12123-12149 (2016).
+
+Comment 2: It is mentioned that “the tetragonal AgInSe_2 is perfectly inserted to the PbSe matrix as nano-scale precipitates revealed by the transmission electron microscopy”. This sentence can make readers confused because a part of Ag and In atoms occupies Pb sites.
+
+Response: We appreciate your comments. This sentence has been modified.
+Revision: The sentence mentioned above is changed to “Nano-scale AgInSe2 precipitates are revealed by the transmission electron microscopy (TEM).”
+
+Comment 3: The effective masses increase with the introduction of AgInSe2 as indicated by the Pisarenko plot. Please show the effective masses for each sample, which is more straightforward for the readers.
+
+Response: Thanks for your good suggestions. The effective masses as a function of AgInSe2 content are given in our manuscript.
+
+Revision: the effective mass (\( m^* \)) of LISS is largely increased from 0.44 \( m_e \) to 0.81 \( m_e \) with the introduction of AgInSe2 (Figure 4a, Figure S1b).
+
+![Hall carrier concentrations and density-of-states effective mass plots for Pb0.98Na0.02Se - x%AgInSe2 (LISS) with increasing AgInSe2 content at 303K.](page_186_573_1077_377.png)
+
+Supplementary Figure 1. (a) Hall carrier concentrations and (b) density-of-states effective mass of Pb0.98Na0.02Se - x%AgInSe2 (LISS) with increasing AgInSe2 content at 303K.
+
+Comment 4: The measurement of sound velocities is not mentioned in the experimental section.
+
+Response: Thanks for your comments. The measurements of sound velocity have added in the experimental section.
+
+Revision: Pulse-echo method was used to measure the speed of sound and the waveforms were recorded using a Tektronix TBS 1102 oscilloscope.
+Comment 5: The heat capacity (C_p) calculated by the Dulong-Petit law will underestimate the thermal conductivity at high temperature. Estimating the C_p by the empirical equation is more accurate. It is not necessary to use the C_p value estimated by the Dulong-Petit law.
+
+Response: We appreciate your good suggestions. We estimated the heat capacity using the empirical equation for all samples. The total thermal conductivity (\( \kappa_{tot} \)), lattice thermal conductivity (\( \kappa_L \)) and the figure-of-merit \( ZT \) have been recalculated.
+
+Revision: we recalculated the total thermal conductivity (\( \kappa_{tot} \)), lattice thermal conductivity (\( \kappa_L \)) and the dimensionless figure-of-merit \( ZT \). Accordingly, Figure 1, Figure 6 and Figure S8 have been revised.
+
+![Schmatic diagram of multi-bands involvement in transport and ZT vs T graph for PbSe-based materials](page_246_670_957_377.png)
+
+Fig. 1 Multiple valence bands enable high \( ZT \) values in p-type PbSe. a Schmatic diagram of multi-bands (L, \( \Sigma \), \( \Lambda \)) involvement in transport. The Brillouin zone shows that the degeneracies at the L, \( \Sigma \), and \( \Lambda \) points are 4, 12, and 8, respectively. b The activated third band \( \Lambda \) enables higher \( ZT \) values compared with the single-band and two-band PbSe-based materials.
+Fig. 6 Thermal transport properties and dimensionless figure-of-merit \( ZT \) as a function of temperature for Pb$_{0.98}$Na$_{0.02}$Se - x% AgInSe$_2$ (LISS) compounds. **a** Total thermal conductivity. **b** Lattice thermal conductivity. Inset shows the room-temperature lattice thermal conductivities departure from the theoretical line calculated by the Callaway model. **c** The average sound velocity (\( v_{avg} \)) versus lattice thermal conductivity (\( \kappa_L \)) for LISS compounds at room temperature. **d** Temperature-dependent \( ZT \) for LISS samples.
+Supplementary Figure 8. Temperature-dependent (a) electrical conductivity, (b) Seebeck coefficient, (c) total thermal conductivity, and (d) dimensionless figure-of-merit \( ZT \) for several \( x = 2.05 \) and \( x = 2.1 \) samples, respectively.
+Reviewer #3 (Remarks to the Author):
+General comment:
+The present manuscript provides interesting data describing the thermoelectric properties of PbSe doped with AgInSe2. This doping / alloying leads to a reduction in the thermal conductivity and an improvement of band convergence enabling a zT value slightly above 2. Thermoelectric materials are considered a viable option to improve energy conversion since they convert waste heat into electrical energy or enable efficient cooling. Hence identifying promising thermoelectric materials is a timely topic, which could be suitable for Nature Communications. Nevertheless, there are several reasons why the present manuscript does not meet my expectations for a manuscript to be published in Nature Communications.
+
+Response: We appreciate your valuable comments and suggestions, which will strengthen our work. Hopefully, our revised manuscript could meet your expectations.
+
+Comment 1: One of the main claims is that there is multi-band convergence. Yet, the nature of these band and how they could possibly be described and explained is missing. One of the main claims of the present manuscript is the idea that more than 3 bands can contribute, yet the proof for this claim and the explanation of the nature of these bands appears rather incomplete. I would like to see very strong and convincing evidence that indeed more than two bands contribute and what their nature is. To mention one option to provide such evidence: several groups have recently employed tight-binding methods to explain the band structure of related chalcogenides [1,2]. Such calculations could be performed to explore the potential nature and more importantly origin of the bands involved. I am not aware of any study that has claimed and proven so far that three bands can provide a contribution to the thermoelectric performance of PbSe.
+[1] Chemistry of Materials 32 (22), 9771-9779 (2020)
+[2] Advanced Materials 30, 1801787 (2018)
+
+Response: Thanks for your insightful comments. Our DFT calculations reveal that a third valence band \( \Lambda \) along \( \Gamma-L \) is activated. The large weighted mobility and effective mass also reflect the multi-band convergence indirectly. A comparison of the density-of-states effective mass for various p-type PbSe-based materials are shown in the Table 1 below.
+
+Indeed, the tight-binding methods are powerful tool to understand the nature of electronic band structure. However, it is hard to employ tight-binding calculations for Ag-In co-doped PbSe since the supercells contain too many atoms. Instead, we calculated the atomic orbital projected band structure by DFT to understand their nature. The conduction and valence bands of PbSe system are dominated by the Pb-p and Se-p states, respectively, which is in line with the tight-binding calculations for PbTe [Brod, M. K., et al. Chem. Mater. 32, 9771-9779 (2020)]. Owing to the rock-salt structure of PbSe, these p-bands are half-filled forming a \( \sigma \)-bond, which is
+characteristic of metavalent bonding [Wuttig, M., et al. Adv. Mater. **30**, e1803777 (2018)]. Similar to PbTe, the valence band maximum (L band) of PbSe is contributed by the p-states. The projected electronic band structure also implies that the third valence band Λ show a large contribution by the Ag 4d state and Se 4p state. This may explain the promoted band convergence in PbSe by alloying with AgInSe₂.
+
+A similar electronic band structure can also be found in Ag-Sr co-doped PbSe system [Luo, Z. Z. *et al.* Angew. Chem. 2021, 133, 272 – 277]. As shown in Figure 2 below, the valence band 2 (Σ) and valence band 3 (Λ) are almost at the same energy level. The energy offset between valence band 1 (L) and the other two valence bands (Σ and Λ) is ~ 0.17 eV. They found a strong band convergence behavior in this system. However, they didn’t mention the underlying multi-band convergence behavior.
+
+Table 1. Density-of-states effective masses (\( m^* \)) for various p-type PbSe-based materials.
+
+<table>
+  <tr>
+    <th>sample</th>
+    <th>\( m^* (m_e) \) at 300K</th>
+    <th>\( m^* (m_e) \) at 773K</th>
+    <th>reference</th>
+  </tr>
+  <tr>
+    <td><b>PbSe-Na-Ag-In</b></td>
+    <td><b>0.81</b></td>
+    <td><b>2.16</b></td>
+    <td><b>This work</b></td>
+  </tr>
+  <tr>
+    <td>PbSe-Na</td>
+    <td>0.28</td>
+    <td>0.7</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>PbSe-Ag-Sr</td>
+    <td>0.4</td>
+    <td>1.1</td>
+    <td>2</td>
+  </tr>
+  <tr>
+    <td>PbSe-Ag-Ba</td>
+    <td>0.4</td>
+    <td>1.0</td>
+    <td>2</td>
+  </tr>
+  <tr>
+    <td>PbSe-Na-Hg</td>
+    <td>0.45</td>
+    <td>1.3</td>
+    <td>3</td>
+  </tr>
+  <tr>
+    <td>PbSe-Cd-Na-Te</td>
+    <td>0.57</td>
+    <td></td>
+    <td>4</td>
+  </tr>
+  <tr>
+    <td>PbSe-Ag</td>
+    <td>0.35</td>
+    <td></td>
+    <td>5</td>
+  </tr>
+  <tr>
+    <td>PbSe-Na-Ca</td>
+    <td>0.56</td>
+    <td></td>
+    <td>6</td>
+  </tr>
+  <tr>
+    <td>PbSe-Na-Ba</td>
+    <td>0.56</td>
+    <td></td>
+    <td>6</td>
+  </tr>
+  <tr>
+    <td>PbSe-Na-Sr</td>
+    <td>0.48</td>
+    <td></td>
+    <td>6</td>
+  </tr>
+</table>
+
+1 Wang, H., Pei, Y., LaLonde, A. D. & Snyder, G. J. Heavily doped p-type PbSe with high thermoelectric performance: an alternative for PbTe. Adv. Mater. **23**, 1366-1370 (2011).
+2 Luo, Z. Z. *et al.* Strong Valence Band Convergence to Enhance Thermoelectric Performance in PbSe with Two Chemically Independent Controls. Angew. Chem. Int. Ed. **60**, 268-273 (2021).
+3 Hodges, J. M. *et al.* Chemical Insights into PbSe- x%HgSe: High Power Factor and Improved Thermoelectric Performance by Alloying with Discordant Atoms. J. Am. Chem. Soc. **140**, 18115-18123 (2018).
+4 Tan, G., Zhao, L.-D. & Kanatzidis, M. G. Rationally Designing High-Performance Bulk Thermoelectric Materials. Chem. Rev. **116**, 12123-12149 (2016).
+5 Wang, S. *et al.* Exploring the doping effects of Ag in p-type PbSe compounds with enhanced thermoelectric performance. J. Phys. D: Appl. Phys. **44**, 475304 (2011).
+6 Lee, Y. *et al.* High-performance tellurium-free thermoelectrics: all-scale
+hierarchical structuring of p-type PbSe-MSe systems (M = Ca, Sr, Ba). J. Am. Chem. Soc. **135**, 5152-5160 (2013).
+
+![Electronic band structures and density-of-states (DOS) for Ag-doped PbSe (a, b), Ag-doped and SrSe-alloyed PbSe (c, d), and Ag-doped and BaSe-alloyed PbSe (e, f).](page_349_370_755_482.png)
+
+Figure 2 in reference [Luo, Z. Z. *et al.* Angew. Chem. 2021, 133, 272 – 277]. Electronic band structures and density-of-states (DOS) for Ag-doped PbSe (a, b), Ag-doped and SrSe-alloyed PbSe (c, d), and Ag-doped and BaSe-alloyed PbSe (e, f).
+
+**Revision:** The electronic band structures of Ag and In doped PbSe were calculated (Figure S2a, S2b) to understand their role in band manipulation. The Ag-doping and In-doping reflect p-type and n-type doping effect, respectively, which are consistent with previous experimental results\(^{42,43}\). Additionally, In-doping has a more important effect on decreasing energy offset (\( \Delta E_{1-2} \)) compared with the Ag-doping (Figure S2c), while Ag-doping plays a major role in enlarging the bandgap (Figure S2d). The orbital projected band structures reveal that the interaction between Pb-p and Se-p orbitals dominate the band structure (Figure S3a, S3b), which is consistent with previous study\(^{44}\). This is a typical feature of the metavalent bonding system\(^{13,45,46}\). The tight binding calculations reveal that the cation states have important effect on the shape of valence band although their orbital projections are not obvious\(^{44}\). Indeed, the Ag-d orbitals play an important role in modulating the third valence band \( \Lambda \) along \( \Gamma \)-L (Figure S3c). A similar phenomenon was also observed in Ag-Sr co-dope PbSe system\(^{47}\). In addition, the cation-site doping can also contribute to the conduction band (Figure S3d) depending on the nature of cation states. Our results indicate that Ag-In co-doping enable multiple valence band convergence, verifying that the cation-site doping is an effective way to modulate the valence band in PbSe. Similar effects can be expected in other materials, such as PbTe and GeTe, by employing the same chemical bonding mechanism as PbSe.
+13. Wuttig, M., Deringer, V. L., Gonze, X., Bichara, C. & Raty, J. Y. Incipient metals: functional materials with a unique bonding mechanism. Adv. Mater. **30**, e1803777 (2018).
+42. Wang, S. *et al.* Exploring the doping effects of Ag in p-type PbSe compounds with enhanced thermoelectric performance. *J. Phys. D: Appl. Phys.* **44**, 475304 (2011).
+43. Androulakis, J., Lee, Y., Todorov, I., Chung, D.-Y. & Kanatzidis, M. High-temperature thermoelectric properties of n-type PbSe doped with Ga, In, and Pb. *Phys. Rev. B* **83** (2011).
+44. Brod, M. K., Toriyama, M. Y. & Snyder, G. J. Orbital chemistry that leads to high valley degeneracy in PbTe. *Chem. Mater.* **32**, 9771-9779 (2020).
+45. Maier, S. *et al.* Discovering electron-transfer-driven changes in chemical bonding in lead chalcogenides (PbX, where X = Te, Se, S, O). *Adv. Mater.* **32**, e2005533 (2020).
+46. Raty, J. Y. *et al.* A quantum-mechanical map for bonding and properties in solids. *Adv. Mater.* **31**, e1806280 (2019).
+47. Luo, Z. Z. *et al.* Strong valence band convergence to enhance thermoelectric performance in PbSe with two chemically independent controls. *Angew. Chem. Int. Ed.* **60**, 268-273 (2021).
+
+![Electronic band structures and energy offsets for Pb26AgSe27 and Pb26InSe27](page_186_1012_1077_627.png)
+
+Supplementary Figure 2. Electronic band structures of (a) Pb26AgSe27 and (b) Pb26InSe27. (c) The energy offset (\( \Delta E_{1-2} \)) between L and \( \Sigma \) valence band. (d) Theoretical bandgaps (\( E_g \)) for pristine, Ag-doped, In-doped and Ag-In co-doped PbSe.
+Supplementary Figure 3. The atomic orbital projected band structure of Pb25AgInSe27. (a) The conduction band is dominated by Pb-p orbitals, while the valence band contain considerable Pb-s character. (b) The Se-p orbital primarily contributes to the valence band. (c) The Ag-d orbitals have a considerable contribution to the valence band. (d) There is distinct In-s character at the conduction band.
+Comment 2: Then, I am also concerned about the apparent disagreement between theory and experiment. The authors claim that their experiment shows an increase of band gap upon alloying with AgInSe$_2$. Yet, the DFT calculations presented in fig. 5b do not seem to support this conclusion.
+
+Response: We are sorry for this confusion. It is not obvious to distinguish the bandgap from the electronic density-of-states (Figure 5b). Actually, our calculation is consistent with the experimental result that the bandgap increases with introducing AgInSe$_2$ in PbSe matrix (Figure 5a). The theoretical bandgap for pure PbSe, Ag-doped PbSe, In-doped PbSe and Ag-In co-doped PbSe are compared in Figure S2d shown below. A possible reason for this phenomenon is given in our manuscript.
+
+![Electronic band structure and DOS plots for Pb27Se27, Pb26AgInSe27, Pb26AgSe27, Pb26InSe27](page_184_635_1080_393.png)
+
+Fig. 5 Electronic band structure. **a** Electronic band structure of Pb$_{27}$Se$_{27}$ (black) and Pb$_{25}$AgInSe$_{27}$ (red). **b** Electronic density of states (DOS) near the Fermi level for Pb$_{27}$Se$_{27}$ (black), Pb$_{26}$AgSe$_{27}$ (green), Pb$_{26}$InSe$_{27}$ (blue) and Pb$_{25}$AgInSe$_{27}$ (red), respectively.
+Supplementary Figure 2. Electronic band structures of (a) Pb26AgSe27 and (b) Pb26InSe27. (c) The energy offset (\( \Delta E_{1-2} \)) between L and \( \Sigma \) valence band. (d) Theoretical bandgaps (\( E_g \)) for pristine, Ag-doped, In-doped and Ag-In co-doped PbSe.
+
+Revision: The experimental bandgap is ~ 0.24 eV for the pristine PbSe, while the bandgap increases obviously with the incorporation of AgInSe2 and a large bandgap ~ 0.33 eV is achieved for the PbSe - 2% AgInSe2 sample (Figure 2d). The small bandgap of PbSe results from its unconventional chemical bonding mechanism (metavalent bonding). For a perfect half-filled p-band, the energy band structures resemble a metallic system. Yet, the bandgap opens due to a small Peierls distortion or charge transfer41. It is the charge transfer between Pb and Se that opens a small bandgap in PbSe given its perfect octahedral arrangements. DFT results show that the enlarged bandgap is mainly attributed to the incorporation of Ag. The eletronegativity difference between Ag and Te (~ 0.62) is larger than that between Pb and Te (~ 0.22). Therefore, the substitution of Ag at Pb sites will strengthen the charge transfer between cation and anion, leading to an enlarged bandgap.
+
+41. Yu, Y., Cagnoni, M., Cojocaru-Mirédin, O. & Wuttig, M. Chalcogenide Thermoelectrics Empowered by an Unconventional Bonding Mechanism. Adv. Funct. Mater. 30, 1904862 (2019).
+Comment 3: Finally, in recent years the thermoelectric properties in lead chalcogenides have been discussed in terms of the underlying bonding mechanism, which must be related to the corresponding band structure [1,3]. A discussion of the fundamental bonding mechanism relevant here is missing. Such a discussion is important since it can help to predict and explain which materials and changes of bonding can improve the performance of a given thermoelectric material.
+[1] Chemistry of Materials 32 (22), 9771-9779 (2020)
+[3] Advanced Materials 32, 202005533 (2020)
+
+Response: Thanks for your valuable suggestions. We have made discussions to understand the nature of electronic band structure and the bandgap behavior in chemical bonding perspective.
+
+Revision:
+Introduction section: Materials with disordered or complex crystal structure\(^{9,10}\), giant anharmonicity\(^{11,12}\), **metavalent bonding**\(^{13}\), and lone pair electrons\(^{14}\) often exhibit intrinsic low lattice thermal conductivity, which are promising candidates for thermoelectric applications.
+
+Bandgap: The small bandgap of PbSe results from its unconventional chemical bonding mechanism (metavalent bonding). For a perfect half-filled p-band, the energy band structures resemble a metallic system. Yet, the bandgap opens due to a small Peierls distortion or charge transfer\(^{41}\). It is the charge transfer between Pb and Se that opens a small bandgap in PbSe given its perfect octahedral arrangements. DFT results show that the enlarged bandgap is mainly attributed to the incorporation of Ag. The eletronegativity difference between Ag and Te (\(~0.62\)) is larger than that between Pb and Te (\(~0.22\)). Therefore, the substitution of Ag at Pb sites will strengthen the charge transfer between cation and anion, leading to an enlarged bandgap.
+
+Electronic band structure: We calculated the orbital projected band structures to understand the nature of electronic band structure in chemical bonding perspective. The orbital projected band structures reveal that the interaction between Pb-p and Te-p orbitals dominate the band structure (Figure S3a, S3b), which is consistent with previous study\(^{46}\). This is a typical feature of the metavalent bonding system\(^{13,45,46}\). The Ag-d orbitals play an important role in modulating the third valence band \( \Lambda \) along \( \Gamma \)-L (Figure S3c). Our results indicate that Ag-In co-doping enable multiple valence band convergence, verifying that the cation-site doping is an effective way to modulate the valence band in PbSe. Similar effects can be expected in other materials, such as PbTe and GeTe, by employing the same chemical bonding mechanism as PbSe. A more detailed discussion is shown above when we answering the comment 1.
+
+Temperature-dependent bandgap: Clearly, the bandgap increases with rising temperature, which is also verified experimentally (Figure 5d). As revealed by Brod et al.\(^{44}\), there is sufficient interaction between Pb-p and Te-p (Se-p in our case) to
+provide the molecular orbitals with the proper s-type symmetry to place the VBM at L point. The weak s-p hybridization is a small addition to this effect. The thermal expansion will lead to a reduction of orbital overlap between p-orbitals\(^{41}\) as well as a weakened s-p hybridization\(^{48}\). As a result, the energy of VBM (L point) in the electronic band structure decreases\(^{49}\), resulting in an enlarged bandgap (\(E_g\)).
+
+13. Wuttig, M., Deringer, V. L., Gonze, X., Bichara, C. & Raty, J. Y. Incipient metals: functional materials with a unique bonding mechanism. Adv. Mater. **30**, e1803777 (2018).
+41. Yu, Y., Cagnoni, M., Cojocaru-Mirédin, O. & Wuttig, M. Chalcogenide Thermoelectrics Empowered by an Unconventional Bonding Mechanism. Adv. Funct. Mater. **30**, 1904862 (2019).
+44. Brod, M. K., Toriyama, M. Y. & Snyder, G. J. Orbital chemistry that leads to high valley degeneracy in PbTe. Chem. Mater. **32**, 9771-9779 (2020).
+45. Maier, S. *et al.* Discovering electron-transfer-driven changes in chemical bonding in lead chalcogenides (PbX, where X = Te, Se, S, O). Adv. Mater. **32**, e2005533 (2020).
+46. Raty, J. Y. *et al.* A quantum-mechanical map for bonding and properties in solids. Adv. Mater. **31**, e1806280 (2019).
+48. Zeier, W. G. *et al.* Thinking like a chemist: intuition in thermoelectric materials. Angew. Chem. Int. Ed. **55**, 6826-6841 (2016).
+49. Cagnoni, M., Fuhren, D. & Wuttig, M. Thermoelectric performance of IV-VI compounds with octahedral-like coordination: a chemical-bonding perspective. Adv. Mater., e1801787 (2018).
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have answered all the raised questions from these three reviewers. I am satisfied with the response. So, I suggest to accept this paper to publish in Nature Communications.
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript has been properly revised to address all the comments by the reviewers. Now it can be published as it is.
+This work is a milestone for PbSe thermoelectrics, which possibly can outperform PbTe thermoelectrics in the near future.
+
+Reviewer #3 (Remarks to the Author):
+
+In the response to the questions and comments from the different reviewers, the authors have addressed all questions and concerns adequately. Hence, the manuscript is acceptable in its present form.

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+Peer Review File
+
+Crowding results from optimal integration of visual targets with contextual information
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This is an outstanding manuscript. The authors propose a novel and fascinating connection between crowding and serial dependence, two extensively studied areas of perception and cognition. They thoroughly test their idea psychophysically and with modeling. The results support the hypothesis and this will stimulate a lot of future research. I know this hypothesis will be provocative in the field, and not everyone will agree (it’s a fairly contentious field), but this is a strength; the manuscript is exceptionally well balanced and approaches the issues in a most constructive way. The crowding field has been somewhat stagnant for years, and the authors’ novel connection is much needed inspiration for researchers to pursue new directions. I expect this paper will motivate a great flurry of new experiments. I have a few minor suggestions below, but these are just requested clarifications, nothing major. Given the broad connections this manuscript makes across fields and the novelty of the idea and results, the manuscript certainly merits publication in Nature Comms.
+
+Minor points:
+
+Flanker Similarity and the (unmentioned) Diagnostic criteria for crowding. There’s a nod to these diagnostic criteria (eg, Whitney & Levi, 2011) but not a direct statement. The critical spacing one is key of course (p. 6)—and the model does a great job predicting that—but it’s not the only one. Another key characteristic directly addressed in the MS is similarity. This is relevant here bc the prior literature had little explanation for why “similarity” matters in the way that it does (eg similarity modulates crowding and dissimilarity releases crowding). The authors’ idea of a connection between serial dependence and crowding, and their model, is very powerful and important in part bc it provides that “why”. In future work it will be interesting to test if other diagnostic criteria like inner-outer flanker asymmetry, upper lower visual field diff, etc also hold. This isn’t necessary here but readers may wonder and the authors could prompt that question and help motivate the important follow up research.
+
+P2, “tasks like or face recognition” delete “or” and perhaps add a reference here. Maybe Farzin et al 2009 (for faces) or the cited reviews (if this is a generic statement about objects).
+
+P3, “qualitatively and qualitatively”. Perhaps one of these was intended to be “quantitatively”?
+
+Fig 1b. Using red outline and blue outline around the respective panels (or at least red and blue color somehow in those two panels) would help readers follow the correspondence between all the Figs; red always indicates high reliability target. Might as well start using that rule in fig 1b.
+
+P.4. “…Formally the modeling section” should be “formally in the…”
+
+P5. “….With difference between…” should have “the” or an “s” after “difference”
+
+Fig 2, abscissa. Add clarification that this axis is “difference” in orientation. It’s not absolute orientation, right?
+
+Fig 2. Where would isolated (single) targets be on this graph?
+
+P.11. Is the “signature” of the “signature function” the derivative-of-Gaussian shape in the SD literature? If so, perhaps mention that or explain what is meant by “signature”
+
+P 12. The first sentence of the “causal inference model” section. That first sentence is too difficult to parse or understand. Not just because the word “form” probably isn’t intended. Rephrasing could help a lot.
+P12. "...the weight assigned of is the..." Rephrase, please.
+
+Aside from these very minor points, this is an excellent manuscript.
+
+Reviewer #2 (Remarks to the Author):
+
+This is a fascinating manuscript, with novel findings that present a new perspective on a widely studied phenomenon. The authors examine visual crowding, the disruptive effect of clutter on object recognition. A large body of research has depicted this effect as the ‘fundamental bottleneck on object recognition’ in peripheral vision especially. As a result, we know a great deal about the way this process affects object recognition and the potential mechanisms. What is much less clear is why crowding occurs in the first place. This manuscript presents an interesting answer to this question by considering its usefulness.
+
+The broad approach here is to compare crowding with properties of ‘serial dependence’, the effect whereby judgements of a stimulus are influenced by the presentation of other stimuli in prior trials. With this comparison, the authors ask whether crowding can be considered to be an efficient/optimal process, rather than reflecting a disruptive bottleneck. Several predictions are made in this case, all of which are ultimately argued to be supported by the data. The authors ask observers to judge the orientation of shapes made from an outline of dots. They first observe greater biases and higher response scatter with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. Second, they note that response scatter is greatest when the orientation of the flankers is close to the target, with a decrease as dissimilarity decreases (that is, performance improves as crowding increases, showing its efficiency). Finally, the pattern of biases follows the mean orientation of flankers rather than an independent combination, which is used to justify a higher-level model. The manuscript is well written and engaging, and presents a provocative view of a widely studied process. If the findings here are true then this presents an important aspect of our understanding. I do have a number of issues with the manuscript as it stands, however.
+
+1. The pattern of response scatter
+
+The main issue concerns the second finding – that response scatter is greatest (i.e. performance is worst) when the orientation of the flankers is most similar to the target. This finding is a key aspect of the proposal that crowding is efficient/optimal, since errors decrease as the strength of crowding increases. If true however, this finding is inconsistent with a large literature on the effect of target-flanker similarity in crowding. More typically, crowding is greatest when target and flanker elements are most similar to one another, decreasing as their dissimilarity increases (the opposite of the current observation). This has been found for a range of stimulus properties including contrast polarity, color, spatial frequency, and direction (Kooi, Toet, Tripathy, & Levi, 1994; Chung, Levi, & Legge, 2001; Gheri, Morgan, & Solomon, 2007), and in particular for orientation judgements (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellemberg, 1997), similar to those used in the present study. In those latter studies, flankers that share similar orientations to the target induce the most crowing, with less crowding as the orientation of the flankers rotates away. Given that a major premise of the current study rests on the opposite finding, this discrepancy needs explanation and/or further exploration. The authors do in fact cite some of these studies to begin the manuscript, describing the patterns above, but the discrepancy with the current results is subsequently ignored. How can this discrepancy be explained, and how does this fit with the central arguments regarding the efficiency/optimality of crowding?
+
+There seem to me at least two possibilities to explain the discrepancy. One is that the authors have not fully measured the range of possible target-flanker differences in orientation. Targets are
+presented at either 35 or 55 degrees rotation, with flankers that differ from these values by up to ±45 degrees. Response scatter peaks at the highest values measured (±45 degrees). It is however possible then that these values may drop again as the differences further increase, up to their maximum of 90 degrees from the target orientation. It is typically these 90 degree values that are compared in order to show target-flanker similarity effects (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellemberg, 1997), and I suspect that if the measurements continued here that performance would drop again. Indeed – patterns of this nature have been reported in a prior study (Solomon, Felisberti, & Morgan, 2004). There, orientation sensitivity is high when flankers are similarly oriented to the target, drops for orientations up to ±45 degrees, and then increases again as the rotation continues to 90 degrees. The same may be true of the present stimuli if a larger range of orientations were tested. Would that not alter the interpretations regarding the efficiency of this process?
+
+A second possibility is the eccentricity – the authors present their stimuli 26 degrees from fixation. Prior observations of target-flanker similarity have tended to use lower eccentricities. Given that some properties of crowding change with eccentricity, e.g. the response biases (Mareschal, Morgan, & Solomon, 2010) and of course the well-known effects of spatial extent (Bouma, 1970), it could be that the present results are something that only arises in the far periphery. Were this the case, however, the question remains – why is efficiency evident in the present results and not these other studies?
+
+To summarize, the results regarding response scatter appear to follow the opposite pattern to a range of well-established and replicated findings in the literature. The premise of the paper rests heavily on this observation. The authors need to demonstrate that this pattern is reliable by extending the range of their measurements in some way and/or by addressing this discrepancy with prior results. If the current results show efficiency, what does that say about all of these other results? If crowding is only efficient in these limited circumstances, is it really efficient?
+
+2. The lack of an unflanked baseline
+
+Part of the issue of interpretation with the above response scatter data also relates to the lack of an unflanked baseline. Typically, performance with flankers is used to measure crowding, with an unflanked baseline (with an isolated element) used to measure uncrowded performance. The authors here take their baseline using flanked performance, using flankers with orientations at the extremes of their range (p14). Given the odd pattern of response scatter (as above), this assumption is problematic. If unflanked performance is more like the values with a flanker difference of 0 degrees, then performance would go from largely unaffected with the 0 degree flankers to impaired with the ±45 degree flankers, rather than from improved with the 0 degree flankers to unaffected with the ±45 degree flankers, as the authors argue. Does that not change the interpretation of the results and their efficiency/optimality substantially?
+
+3. The distinction with ‘low-level’ pooling models of crowding
+
+The authors contrast their findings with ‘low level pooling models’, which do not seem to me to be at odds with the present results. This distinction begins in the abstract (e.g. on line 2), where low level models are contrasted with their ‘alternative hypothesis’, and continues throughout, e.g. on p15 of the discussion, where it is argued that pooling models cannot explaining the effects of flanker orientation. Later on however, the authors describe their model as a pooling process (p17). The mechanism proposed for their model, with large receptive fields in areas like V4 (p16), also sounds very similar to ideas raised in various pooling models. For instance, processes of ‘population pooling’ have attributed the crowding of orientation signals to pooling within receptive fields in area V2 or V4 (van den Berg, Roerdink, & Cornelissen, 2010; Harrison & Bex, 2015). Similar arguments are also made by ‘high dimensional’ pooling models (Rosenholtz, Yu, & Keshvari, 2019). In fact, patterns of bias that are very similar to those in Figure 2A of this manuscript have been reported previously and accounted for via pooling processes (Greenwood & Parsons, 2020). In this latter case, the model accounts for target-flanker similarity effects via variations in the weights applied to the flankers. I don’t see why this is
+inconsistent with the variations shown in the current study.
+
+The authors distinguish between two possible models, both of which seem like pooling models to me. One is a ‘low level’ version in which the interactions happen independently between each flanker and the target, linked with a feedforward local process. The other involves a broader integration in which the flankers have a combined influence on the target, linked with recurrent feedback interactions. The latter does not seem wholly distinct from the operation of the most recent population pooling models (Harrison & Bex, 2015; Greenwood & Parsons, 2020) described above however. In those cases, the flankers affect the target through their combination within a single population response. My feeling is that the results of Experiment 2 in the present study would be entirely consistent with these models – when flanker orientations vary independently, their combined population response would have a shifted mean that would tend to alter the subsequent judgements related to the target. If so, then I do not think these results are inconsistent with pooling, nor do they provide clear evidence for feedback. This is not to take away from the novelty of these findings, however – I agree that the results provide clear evidence that the flankers do not interact independently with the target. The distinction between the two models presented here is certainly interesting, but their physiological basis is clearly overstated.
+
+4. Effects of target reliability
+
+The first result reported in the manuscript is that biases are greater and response scatter higher with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. This effect is attributed to reliability, and explained via a Bayesian framework. Its relation to similar results with alternative explanations is unexplored, however. Most notably, crowding is strongest with flankers of high luminance contrast (Chung, Levi, & Legge, 2001; Pelli, Palomares, & Majaj, 2004). Lowering the target contrast can also increase crowding (Felisberti, Solomon, & Morgan, 2005). Assimilative biases related to orientation judgements are also increased when noise is added to stimuli (Mareschal, Morgan, & Solomon, 2010). Can all of these effects be understood via reliability? It seems to me there is an alternative explanation that crowding is determined by the strength of the target signal, relative to the strength of the flanker signal(s). Could these effects, including those of the present study, be understood as signal strength rather than reliability per se?
+
+5. The relation to serial dependence
+
+Much is made of the similarities between serial dependence and crowding, which I agree is a fascinating link to make. The arguments for efficiency in this context also sound to me like arguments made more broadly in vision for the principles of redundancy reduction (Atteave, 1954), including for processes like adaptation (Clifford, 2002) and surround suppression (Rao & Ballard, 1999). Could the similarities here in fact indicate a broader link in the form of a “canonical computation” across all of visual perception? I wonder if the strong link to serial dependence is a little short-sighted in this sense.
+
+5. The neural basis of crowding
+
+The idea of crowding relating to higher cortical areas like V4 is attributed to Pelli & Tillman (p2), but this idea derives from earlier work (Motter & Simoni, 2007; Motter, 2009). Others have also linked crowding with receptive field sizes in areas like V2 (He, Wang, & Fang, 2019).
+
+6. Stimulus details
+
+Was the rotation of flankers taken from the target orientation on each trial, such that the ±45 degree range differed in terms of absolute orientations for the 35 and 55 degree targets?
+Additionally, can we be sure that the judgements made by observers concern the orientation of these stimuli, rather than another property? Given the dotted nature of the stimuli used in the present task, perhaps observers are not judging orientation, but rather another property like the position of the outermost dots in the elements. This could allow a kind of relative position or Vernier judgement. Prior studies have tended to use line elements or Gabors in this context – if true, could this explain the difference with the studies of target-flanker similarity described above?
+
+References
+
+Andriessen, J. J., & Bouma, H. (1976). Eccentric vision: Adverse interactions between line segments. Vision Research, 16(1), 71-78.
+Attnave, F. (1954). Some informational aspects of visual perception. Psychological Review, 61(3), 183-193.
+Bouma, H. (1970). Interaction effects in parafoveal letter recognition. Nature, 226, 177-178.
+Chung, S. T. L., Levi, D. M., & Legge, G. E. (2001). Spatial-frequency and contrast properties of crowding. Vision Research, 41, 1833-1850.
+Clifford, C. W. G. (2002). Perceptual adaptation: Motion parallels orientation. Trends in Cognitive Sciences, 6(3), 136-143.
+Felisberti, F. M., Solomon, J. A., & Morgan, M. J. (2005). The role of target salience in crowding. Perception, 34(7), 823-833.
+Gheri, C., Morgan, M. J., & Solomon, J. A. (2007). The relationship between search efficiency and crowding. Perception, 36(12), 1779-1787.
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117(14), 8196-8202.
+Harrison, W. J., & Bex, P. J. (2015). A Unifying Model of Orientation Crowding in Peripheral Vision. Current Biology, 25(24), 3213-3219.
+He, D., Wang, Y., & Fang, F. (2019). The critical role of V2 population receptive fields in visual orientation crowding. Current Biology, 29(13), 2229-2236. e2223.
+Kooi, F. L., Toet, A., Tripathy, S. P., & Levi, D. M. (1994). The effect of similarity and duration on spatial interaction in peripheral vision. Spatial Vision, 8(2), 255-279.
+Mareschal, I., Morgan, M. J., & Solomon, J. A. (2010). Cortical distance determines whether flankers cause crowding or the tilt illusion. Journal of Vision, 10(8):13, 1-14.
+Motter, B. C. (2009). Central V4 Receptive Fields Are Scaled by the V1 Cortical Magnification and Correspond to a Constant-Sized Sampling of the V1 Surface. Journal of Neuroscience, 29(18), 5749-5757.
+Motter, B. C., & Simon, D. A. (2007). The roles of cortical image separation and size in active visual search performance. Journal of Vision, 7(2(6)), 1-15.
+Pelli, D. G., Palomares, M., & Majaj, N. J. (2004). Crowding is unlike ordinary masking: Distinguishing feature integration from detection. Journal of Vision, 4(12), 1136-1169.
+Rao, R. P. N., & Ballard, D. H. (1999). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1), 79-87.
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19(7), 1-25.
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+van den Berg, R., Roerdink, J. B. T. M., & Cornelissen, F. W. (2010). A Neurophysiologically Plausible Population Code Model for Feature Integration Explains Visual Crowding. PLoS Computational Biology, 6(1), e1000646.
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14(9), 2057-2068.
+Reviewer #3 (Remarks to the Author):
+
+Cicchini and colleagues put forward the hypothesis that crowding is results from Bayes-optimal integration of visual targets with spatial context. The authors identify four features of their empirical data that are consistent with Bayes-optimal integration: (1) Crowding is strongest for reliable flankers and unreliable targets, (2) Crowding depends on flanker-target similarity (here orientation), (3) precision of orientation judgments increases with increasing flanker-target similarity, and (4) Crowding depends on similarity of targets to average flanker orientation, not individual flanker orientations. The authors present two ideal observer models (a Bayesian ideal observer, and a causal inference model), which can reproduce the above features of the empirical data.
+
+While I find the hypothesis that crowding results from optimal integration intriguing, I am somewhat reserved when it comes to the evidence provided in the current study. I am also not convinced that the behavioral benefits described here can be ascribed to crowding rather than ensemble perception. Please find my detailed points below.
+
+1. The ideal observer models only provide adequate fits when equipped with scaling parameters that account for “sub-optimal” behavior. The required scaling is not negligible, rescaling the optimal integration weights by ~40 to 50%. Therefore, it is not clear whether the observers’ behavior is at all optimal, beyond resembling some qualitative features of the data. The authors could make a much stronger case when quantitatively accounting for the sub-optimal behavior. For instance, how strong would regression to the mean of orientation judgments need to be (put forward by the authors as an explanation of sub-optimality) in order to match this scaling? Is this consistent with the empirical data?
+
+2. Related to point 1, it is not clear in how far the empirical features are exclusively accounted for by Bayes-optimal integration versus other forms of (non-optimal) integration. As the authors note in their discussion feature 1 (orientation uncertainty) could be captured by obligatory integration models. Feature 2 (flanker-target similarity) could be explained by interference between similarly tuned, and therefore more strongly interconnected neural populations. For feature 4 (global vs local context), it seems that one could develop an alternative optimal observer that integrates local instead of global context. That is, I do not understand which optimality consideration would strictly dictate global versus local integration.
+I believe most of these concerns of whether the behavioral features really arise from optimal integration could be mitigated by improving point 1 above, i.e. providing a more detailed quantitative explanation of behavior, rather than absorbing a considerable mismatch between predictions and data into one or two unexplained “sub-optimality” parameters.
+
+3. It is not clear whether the behavioral benefits examined in this experiment are due to crowding or ensemble perception. While these appear to be at least partially distinct phenomena, they can co-occur (“Reexamining the possible benefits of visual crowding: dissociating crowding from ensemble percepts” Bulakowski et al., 2011). Cicchini et al. test the influence of target-distractor distance, and demonstrate that bias depends on distance, as expected for a crowding effect. However, I would contest that increasing flanker-target distance also alters the ensemble, and can therefore also impact ensemble perception. Perhaps one way to address this issue would be to test whether or not similar integration effects occur for more foveally presented stimuli, i.e. in the absence of crowding (albeit under matched conditions of visual uncertainty). If they do, the current observations would perhaps be better explained as resulting from ensemble perception, while crowding merely co-occurs in the current setup.
+
+Minor comments:
+
+Figure 5B. Minimum scatter appears to occur at 0 deg, while the ideal observer models predict the
+minimum to occur at 15 degrees. I am curious whether the authors have any explanation/speculation of why the bias and variance data diverge in this aspect.
+
+In their introduction the authors state “Crowding impacts on many important daily tasks, such as face recognition and reading [...]” I would be curious how the authors reconcile this view that crowding appears to negatively impact perception in real world scenarios (“daily tasks”) with their optimal integration theory.
+GENERAL
+
+We thank the editor and particularly the reviewers for their time and very helpful advice. We have taken all the suggestions on board, definitely resulting in an improved manuscript. We trust it is now acceptable for publication.
+
+We have marked the changes in blue on the revised manuscript.
+
+David Burr
+
+For the authors
+
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This is an outstanding manuscript. The authors propose a novel and fascinating connection between crowding and serial dependence, two extensively studied areas of perception and cognition. They thoroughly test their idea psychophysically and with modeling. The results support the hypothesis and this will stimulate a lot of future research. I know this hypothesis will be provocative in the field, and not everyone will agree (it’s a fairly contentious field), but this is a strength; the manuscript is exceptionally well balanced and approaches the issues in a most constructive way. The crowding field has been somewhat stagnant for years, and the authors’ novel connection is much needed inspiration for researchers to pursue new directions. I expect this paper will motivate a great flurry of new experiments. I have a few minor suggestions below, but these are just requested clarifications, nothing major. Given the broad connections this manuscript makes across fields and the novelty of the idea and results, the manuscript certainly merits publication in Nature Comms.
+
+We thank the reviewer for their kind words, and agree that the findings will be contentious, but hopefully stimulate useful research.
+
+Minor points:
+
+Flanker Similarity and the (unmentioned) Diagnostic criteria for crowding. There’s a nod to these diagnostic criteria (eg, Whitney & Levi, 2011) but not a direct statement. The critical spacing one is key of course (p. 6)—and the model does a great job predicting that—but it’s not the only one. Another key characteristic directly addressed in the MS is similarity. This is relevant here bc the prior literature had little explanation for why “similarity” matters in the way that it does (eg similarity modulates crowding and dissimilarity releases crowding). The authors’ idea of a connection between serial dependence and crowding, and their model, is very powerful and important in part bc it provides that “why”. In future work it will be interesting to test if other diagnostic criteria like inner-outer flanker asymmetry, upper lower visual field diff, etc also hold. This isn’t necessary here but readers may wonder and the authors could prompt that question and help motivate the important follow up research.
+
+Thanks for this important suggestion. We now mention the diagnosis criteria more clearly in introduction, and pick it up again in discussion.
+
+P2, “tasks like or face recognition” delete “or” and perhaps add a reference here. Maybe Farzin et al 2009 (for faces) or the cited reviews (if this is a generic statement about objects).
+
+P3, “qualitatively and qualitatively”. Perhaps one of these was intended to be “quantitatively”?
+
+Fig 1b. Using red outline and blue outline around the respective panels (or at least red and blue color somehow in those two panels) would help readers follow the correspondence between all the Figs; red always indicates high reliability target. Might as well start using that rule in fig 1b.
+
+Excellent idea
+
+P.4. “…Formally the modeling section” should be “formally in the…”
+
+P5. “…With difference between…” should have “the” or an “s” after “difference”
+
+Fig 2, abscissa. Add clarification that this axis is “difference” in orientation. It’s not absolute orientation, right?
+
+Fig 2. Where would isolated (single) targets be on this graph?
+Unfortunately we did not measure the effects without flankers.
+
+P.11. Is the “signature” of the “signature function” the derivative-of-Gaussian shape in the SD literature? If so, perhaps mention that or explain what is meant by “signature”
+
+P 12. The first sentence of the “causal inference model” section. That first sentence is too difficult to parse or understand. Not just because the word “form” probably isn’t intended. Rephrasing could help a lot.
+
+P12. "...the weight assigned of is the..."Rephrase, please.
+
+Aside from these very minor points, this is an excellent manuscript.
+
+Thank you very much, all the minor points have all been dealt with.
+
+Reviewer #2 (Remarks to the Author):
+
+This is a fascinating manuscript, with novel findings that present a new perspective on a widely studied phenomenon. The authors examine visual crowding, the disruptive effect of clutter on object recognition. A large body of research has depicted this effect as the ‘fundamental bottleneck on object recognition’ in peripheral vision especially. As a result, we know a great deal about the way this process affects object recognition and the potential mechanisms. What is much less clear is why crowding occurs in the first place. This manuscript presents an interesting answer to this question by considering its usefulness.
+
+Thank you for the kind words. Thank you also for the very detailed help you have given, providing useful references and encouraging us to make clearer our ideas.
+
+The broad approach here is to compare crowding with properties of ‘serial dependence’, the effect whereby judgements of a stimulus are influenced by the presentation of other stimuli in prior trials. With this comparison, the authors ask whether crowding can be considered to be an efficient/optimal process, rather than reflecting a disruptive bottleneck. Several predictions are made in this case, all of which are ultimately argued to be supported by the data. The authors ask observers to judge the orientation of shapes made from an outline of dots. They first observe greater biases and higher response scatter with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. Second, they note that response scatter is greatest when the orientation of the flankers is close to the target, with a decrease as dissimilarity decreases (that is, performance improves as crowding increases, showing its efficiency). Finally, the pattern of biases follows the mean orientation of flankers rather than an independent combination, which is used to justify a higher-level model. The manuscript is well written and engaging, and presents a provocative view of a widely studied process. If the findings here are true then this presents an important aspect of our understanding. I do have a number of issues with the manuscript as it stands, however.
+
+1. The pattern of response scatter
+
+The main issue concerns the second finding – that response scatter is greatest (i.e. performance is worst) when the orientation of the flankers is most similar to the target. This finding is a key aspect of the proposal that crowding is efficient/optimal, since errors decrease as the strength of crowding increases. It true however, this finding is inconsistent with a large literature on the effect of target-flanker similarity in crowding. More typically, crowding is greatest when target and flanker elements are most similar to one another, decreasing as their dissimilarity increases (the opposite of the current observation). This has been found for a range of stimulus properties including contrast polarity, color, spatial frequency, and direction (Kooi, Toet, Tripathy, & Levi, 1994; Chung, Levi, & Legge, 2001; Gheri, Morgan, & Solomon, 2007), and in particular for orientation judgements (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellenberg, 1997), similar to those used in the present study. In those latter studies, flankers that share similar orientations to the target induce the most crowding, with less crowding as the orientation of the flankers rotates away. Given that a major premise of the current study rests on the opposite finding, this discrepancy needs explanation and/or further exploration. The authors do in fact cite some of these studies to begin the manuscript, describing the patterns above, but the discrepancy with the current results is subsequently ignored. How can this discrepancy be explained, and how does this fit with the central arguments regarding the efficiency/optimality of crowding?
+
+This important comment shows that we need to do a better job explaining our results and ideas. Firstly, we assume that the first sentence was a typo – response scatter is least (precision greatest) when orientations coincide (where crowding is greatest). That may seem counter-intuitive, but it depends on how you measure crowding. Typically it is percent correct, or perhaps contrast sensitivity. We are saying that RMS Errors (which comprise both accuracy and precision) are reduced, because although average accuracy decreases (strong bias), the increased precision more than offsets the bias, resulting in lower RMSE (radial distance in Fig 2C). However, other performance measures need not necessarily improve. For example, simple measures of accuracy (whether the reproduction was near veridical) would be low when the bias is high, as the orientation
+judgement would seldom be “correct”; improved precision would not increase accuracy, and possibly decrease it, all responses become more tightly grouped around the incorrect bias. The only paper to measure separately bias and precision that we know of is Solomon, Felisberti and Morgan (JoV 2004: thanks for the pointer), and they report results very similar to ours (their Figure 4A). Also their data indicate a reduction in RMS Error (although they did not describe their results that way), shown in this figure below derived from their data. We have tried to make the explanations clearer in the results and discussion sections, and have added a brief paragraph discussing the apparent paradox.
+
+![RMSE calculated from Figure 4A of Solomon et al., 2004](page_312_670_823_393.png)
+
+Figure 1: RMSE calculated from Figure 4A of Solomon et al., 2004
+
+There seem to me at least two possibilities to explain the discrepancy. One is that the authors have not fully measured the range of possible target-flanker differences in orientation. Targets are presented at either 35 or 55 degrees rotation, with flankers that differ from these values by up to ±45 degrees. Response scatter peaks at the highest values measured (±45 degrees). It is however possible then that these values may drop again as the differences further increase, up to their maximum of 90 degrees from the target orientation. It is typically these 90 degree values that are compared in order to show target-flanker similarity effects (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellemberg, 1997), and I suspect that if the measurements continued here that performance would drop again. Indeed – patterns of this nature have been reported in a prior study (Solomon, Felisberti, & Morgan, 2004). There, orientation sensitivity is high when flankers are similarly oriented to the target, drops for orientations up to ±45 degrees, and then increases again as the rotation continues to 90 degrees. The same may be true of the present stimuli if a larger range of orientations were tested. Would that not alter the interpretations regarding the efficiency of this process?
+
+See above response for the explanation of apparent discrepancy. It is interesting that precision (but not bias) improved for 90° flankers in Solomon et al. Unfortunately we did not measure out that far. However, it would not change our story, as we are interested in the range where the flankers cause crowding by biasing results; in that range there is a clear trade-off between accuracy and precision for both our and their data. Our data show maximum bias at a lower orientation than theirs (about 20° compared with their 45°), so it did not seem necessary to measure beyond 45°.
+
+A second possibility is the eccentricity – the authors present their stimuli 26 degrees from fixation. Prior observations of target-flanker similarity have tended to use lower eccentricities. Given that some properties of crowding change with eccentricity, e.g. the response biases (Mareschal, Morgan, & Solomon, 2010) and of course the well-known effects of spatial extent (Bouma, 1970), it could be that the present results are something that only arises in the far periphery. Were this the case, however, the question remains – why is efficiency evident in the present results and not these other studies?
+
+It is true that we used a large eccentricity, to maximize the effects, but our results agree with the only other study where efficiency can be calculated (Solomon et al. above figure), who worked at the much lower eccentricity of 3.7° (now mentioned).
+
+To summarize, the results regarding response scatter appear to follow the opposite pattern to a range of well-established and replicated findings in the literature. The premise of the paper rests heavily on this observation. The authors need to demonstrate that this pattern is reliable by extending the range of their measurements in some way and/or by addressing this discrepancy with prior results. If the current results show efficiency, what does that say about all of these other results? If crowding is only efficient in these limited circumstances, is it really efficient?
+We hope the above comments address this seeming paradox to the reviewer’s satisfaction.
+
+2. The lack of an unflanked baseline
+
+Part of the issue of interpretation with the above response scatter data also relates to the lack of an unflanked baseline. Typically, performance with flankers is used to measure crowding, with an unflanked baseline (with an isolated element) used to measure uncrowded performance. The authors here take their baseline using flanked performance, using flankers with orientations at the extremes of their range (p14). Given the odd pattern of response scatter (as above), this assumption is problematic. If unflanked performance is more like the values with a flanker difference of 0 degrees, then performance would go from largely unaffected with the 0 degree flankers to impaired with the ±45 degree flankers, rather than from improved with the 0 degree flankers to unaffected with the ±45 degree flankers, as the authors argue. Does that not change the interpretation of the results and their efficiency/optimality substantially?
+
+Unfortunately we did not measure a baseline. We did not think this is a major problem, but in retrospect it would have been useful to do so.
+
+3. The distinction with ‘low-level’ pooling models of crowding
+
+The authors contrast their findings with ‘low level pooling models’, which do not seem to me to be at odds with the present results. This distinction begins in the abstract (e.g. on line 2), where low level models are contrasted with their ‘alternative hypothesis’, and continues throughout, e.g. on p15 of the discussion, where it is argued that pooling models cannot explaining the effects of flanker orientation. Later on however, the authors describe their model as a pooling process (p17). The mechanism proposed for their model, with large receptive fields in areas like V4 (p16), also sounds very similar to ideas raised in various pooling models. For instance, processes of ‘population pooling’ have attributed the crowding of orientation signals to pooling within receptive fields in area V2 or V4 (van den Berg, Roerdink, & Cornelissen, 2010; Harrison & Bex, 2015). Similar arguments are also made by ‘high dimensional’ pooling models (Rosenholtz, Yu, & Keshvari, 2019). In fact, patterns of bias that are very similar to those in Figure 2A of this manuscript have been reported previously and accounted for via pooling processes (Greenwood & Parsons, 2020). In this latter case, the model accounts for target-flanker similarity effects via variations in the weights applied to the flankers. I don’t see why this is inconsistent with the variations shown in the current study.
+
+The authors distinguish between two possible models, both of which seem like pooling models to me. One is a ‘low level’ version in which the interactions happen independently between each flanker and the target, linked with a feedforward local process. The other involves a broader integration in which the flankers have a combined influence on the target, linked with recurrent feedback interactions. The latter does not seem wholly distinct from the operation of the most recent population pooling models (Harrison & Bex, 2015; Greenwood & Parsons, 2020) described above however. In those cases, the flankers affect the target through their combination within a single population response. My feeling is that the results of Experiment 2 in the present study would be entirely consistent with these models – when flanker orientations vary independently, their combined population response would have a shifted mean that would tend to alter the subsequent judgements related to the target.
+If so, then I do not think these results are inconsistent with pooling, nor do they provide clear evidence for feedback. This is not to take away from the novelty of these findings, however – I agree that the results provide clear evidence that the flankers do not interact independently with the target. The distinction between the two models presented here is certainly interesting, but their physiological basis is clearly overstated.
+
+Indeed most models of crowding since Morgan’s Nature paper involve some sort of obligatory pooling. The two novelty of what we propose are that the pooling is “intelligent”, occurring when it leads to improved efficiency (measured by RMS Error); and that it is relatable to serial dependence, allowing cross-fertilization of the two fields. No previous model that we are aware of predicts this. Certainly there are elements in common, especially with our preferred model involving compulsory (unintelligent) pooling of signals; but the key difference is that this integrated information is not to final output but is combined intelligently with the more local signal. We have tried to make that clearer in the text.
+
+4. Effects of target reliability
+
+The first result reported in the manuscript is that biases are greater and response scatter higher with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. This effect is attributed to reliability, and explained via a Bayesian framework. Its relation to similar results with alternative explanations is unexplored, however. Most notably, crowding is strongest with flankers of high luminance contrast (Chung, Levi, & Legge, 2001; Pelli, Palomares, & Majaj, 2004). Lowering the target contrast can also increase crowding (Felisberti, Solomon, & Morgan, 2005). Assimilative biases related to orientation judgements are also increased when noise is added to stimuli (Mareschal, Morgan, & Solomon, 2010). Can all of these effects be understood via reliability? It seems to me there is an alternative explanation that crowding is determined by the strength of the target signal, relative to the strength of the
+flanker signal(s). Could these effects, including those of the present study, be understood as signal strength rather than reliability per se?
+
+This is a good point, and we have now added those references. Technically, reliability is the inverse of the variance of the underlying noise distribution. Variance will certainly be affected by contrast and by noise in the way suggested (these have been the standard techniques of manipulating reliability in the multi-sensory literature), so yes, signal strength will increase reliability. However, given that our modelling is quantitatively based on reliability of flanker and target, we prefer to remain within that framework.
+
+It is also interesting to note that the stimuli we employ (ellipses defined by dots), on the other hand allow manipulating reliability while keeping more basic parameters (contrast, visibility etc) as matched as possible. This suggests that the framework we chose could be a more general one and could encompass those special cases reported in the literature
+
+5. The relation to serial dependence
+
+Much is made of the similarities between serial dependence and crowding, which I agree is a fascinating link to make. The arguments for efficiency in this context also sound to me like arguments made more broadly in vision for the principles of redundancy reduction (Attneave, 1954), including for processes like adaptation (Clifford, 2002) and surround suppression (Rao & Ballard, 1999). Could the similarities here in fact indicate a broader link in the form of a “canonical computation” across all of visual perception? I wonder if the strong link to serial dependence is a little short-sighted in this sense.
+
+This is a great idea, but we feel it goes beyond this paper. We would prefer to link crowding to a specific and well studied phenomenon, like serial dependence, rather than trying to push our claims too far at this stage. But we expect that the idea of canonical calculation will prove to be correct.
+
+5. The neural basis of crowding
+
+The idea of crowding relating to higher cortical areas like V4 is attributed to Pelli & Tillman (p2), but this idea derives from earlier work (Motter & Simoni, 2007; Motter, 2009). Others have also linked crowding with receptive field sizes in areas like V2 (He, Wang, & Fang, 2019).
+
+Thanks for this feedback, we now have acknowledged these earlier scholars.
+
+6. Stimulus details
+
+Was the rotation of flankers taken from the target orientation on each trial, such that the ±45 degree range differed in terms of absolute orientations for the 35 and 55 degree targets?
+
+Yes it was.
+
+Additionally, can we be sure that the judgements made by observers concern the orientation of these stimuli, rather than another property? Given the dotted nature of the stimuli used in the present task, perhaps observers are not judging orientation, but rather another property like the position of the outermost dots in the elements. This could allow a kind of relative position or Vernier judgement. Prior studies have tended to use line elements or Gabor’s in this context – if true, could this explain the difference with the studies of target-flanker similarity described above?
+
+If we understand correctly the reviewer is asking us to consider the possibility that observers are not judging orientation of the main axis of the ellipse but rather the relative position of the outermost dot of the target object. This quantity could provide a rough proxy for orientation in that when the target exceeds (i.e. it is more to the right) the flankers likely the target is more horizontal (and vice versa if more inmost). If this was the case however in the “rounded target – slim flankers” the target would not exceed the flankers in this metric and reports should lean towards vertical. Conversely in the “slim target – rounded flanker”, condition. These two predictions however are not met as there are no substantial biases.
+Another possibility is that observers were judging the relative orientation (or position) of the two outmost dots of each stimulus. This would enable for instance judging the absolute orientation of the object (whereas previous hypothesis only would inform on relative orientation respect to the flanker). However, this mechanism cannot account for the clear difference of precision between the two types of stimuli.
+References
+
+Andriessen, J. J., & Bouma, H. (1976). Eccentric vision: Adverse interactions between line segments. Vision Research, 16(1), 71-78.
+
+Attenave, F. (1954). Some informational aspects of visual perception. Psychological Review, 61(3), 183-193.
+
+Bouma, H. (1970). Interaction effects in parafoveal letter recognition. Nature, 226, 177-178.
+
+Chung, S. T. L., Levi, D. M., & Legge, G. E. (2001). Spatial-frequency and contrast properties of crowding. Vision Research, 41, 1833-1850.
+
+Clifford, C. W. G. (2002). Perceptual adaptation: Motion parallels orientation. Trends in Cognitive Sciences, 6(3), 136-143.
+
+Felisberti, F. M., Solomon, J. A., & Morgan, M. J. (2005). The role of target salience in crowding. Perception, 34(7), 823-833.
+
+Gheri, C., Morgan, M. J., & Solomon, J. A. (2007). The relationship between search efficiency and crowding. Perception, 36(12), 1779-1787.
+
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117(14), 8196-8202.
+
+Harrison, W. J., & Bex, P. J. (2015). A Unifying Model of Orientation Crowding in Peripheral Vision. Current Biology, 25(24), 3213-3219.
+
+He, D., Wang, Y., & Fang, F. (2019). The critical role of V2 population receptive fields in visual orientation crowding. Current Biology, 29(13), 2229-2236.e2223.
+
+Kool, F. L., Toet, A., Tripathy, S. P., & Levi, D. M. (1994). The effect of similarity and duration on spatial interaction in peripheral vision. Spatial Vision, 8(2), 255-279.
+
+Mareschal, I., Morgan, M. J., & Solomon, J. A. (2010). Cortical distance determines whether flankers cause crowding or the tilt illusion. Journal of Vision, 10(8):13, 1-14.
+
+Motter, B. C. (2009). Central V4 Receptive Fields Are Scaled by the V1 Cortical Magnification and Correspond to a Constant-Sized Sampling of the V1 Surface. Journal of Neuroscience, 29(18), 5749-5757.
+
+Motter, B. C., & Simoni, D. A. (2007). The roles of cortical image separation and size in active visual search performance. Journal of Vision, 7(2)(6), 1-15.
+
+Pelli, D. G., Palomares, M., & Majaj, N. J. (2004). Crowding is unlike ordinary masking: Distinguishing feature integration from detection. Journal of Vision, 4(12), 1136-1169.
+
+Rao, R. P. N., & Ballard, D. H. (1999). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1), 79-87.
+
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19(7), 1-25.
+
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+
+van den Berg, R., Roerdink, J. B. T. M., & Cornelissen, F. W. (2010). A Neurophysiologically Plausible Population Code Model for Feature Integration Explains Visual Crowding. PLoS Computational Biology, 6(1), e1000646.
+
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14(9), 2057-2068.
+
+Reviewer #3 (Remarks to the Author):
+
+Cicchini and colleagues put forward the hypothesis that crowding is results from Bayes-optimal integration of visual targets with spatial context. The authors identify four features of their empirical data that are consistent with Bayes-optimal integration: (1) Crowding is strongest for reliable flankers and unreliable targets, (2) Crowding depends on flanker-target similarity (here orientation), (3) precision of orientation judgments increases with increasing flanker-target similarity, and (4) Crowding depends on similarity of targets to average flanker orientation, not individual flanker orientations. The authors present two ideal observer models (a Bayesian ideal observer, and a causal inference model), which can reproduce the above features of the empirical data.
+
+While I find the hypothesis that crowding results from optimal integration intriguing, I am somewhat reserved when it comes to the evidence provided in the current study. I am also not convinced that the behavioral benefits described here can be ascribed to crowding rather than ensemble perception. Please find my detailed points below.
+
+1. The ideal observer models only provide adequate fits when equipped with scaling parameters that account for "sub-optimal" behavior. The required scaling is not negligible, rescaling the optimal integration weights by ~40 to 50%. Therefore, it is not clear whether the observers' behavior is at all optimal, beyond resembling some qualitative features of the data. The authors could make a much stronger case when quantitatively accounting for the sub-optimal behavior. For instance, how strong would regression to the mean of orientation judgments need to be (put forward by the authors as an explanation of sub-optimality) in order to match this scaling? Is this consistent with the empirical data?
+Thanks for this important suggestion. We were trying to keep our models as simple as possible to be more accessible to the reader, but the calculation proposed is quite simple. Regression to the mean compresses the output by about 30%, which accounts for much of the underestimation. We now need a scaling factor of only 0.7 to fit the data. The main features of the models is that the same models that fit well serial dependence capture the DoG pattern of results (to a scaling factor), but we agree it is more impressive when the scaling factor is close to unity.
+
+2. Related to point 1, it is not clear in how far the empirical features are exclusively accounted for by Bayes-optimal integration versus other forms of (non-optimal) integration. As the authors note in their discussion feature 1 (orientation uncertainty) could be captured by obligatory integration models. Feature 2 (flanker-target similarity) could be explained by interference between similarly tuned, and therefore more strongly interconnected neural populations. For feature 4 (global vs local context), it seems that one could develop an alternative optimal observer that integrates local instead of global context. That is, I do not understand which optimality consideration would strictly dictate global versus local integration.
+I believe most of these concerns of whether the behavioral features really arise from optimal integration could be mitigated by improving point 1 above, i.e. providing a more detailed quantitative explanation of behavior, rather than absorbing a considerable mismatch between predictions and data into one or two unexplained “sub-optimality” parameters.
+
+We trust that the improved absolute fit goes some way towards addressing the referee’s concerns. We do of course accept that mechanisms of the type suggested could be involved, such as interconnections between similarly tuned neural populations (which we now mention, pointing out they are not consistent with the second experiment). However, we believe that our models put considerable constraints on how these mechanisms act. We also believe that it is constructive to relate crowding to serial dependence, which is currently being studied intensely, prompting cross-fertilization of ideas and discussions between the two important fields of research.
+
+3. It is not clear whether the behavioral benefits examined in this experiment are due to crowding or ensemble perception. While these appear to be at least partially distinct phenomena, they can co-occur (“Reexamining the possible benefits of visual crowding: dissociating crowding from ensemble percepts” Bulakowski et al., 2011). Cicchini et al. test the influence of target-distractor distance, and demonstrate that bias depends on distance, as expected for a crowding effect. However, I would contest that increasing flanker-target distance also alters the ensemble, and can therefore also impact ensemble perception. Perhaps one way to address this issue would be to test whether or not similar integration effects occur for more foveally presented stimuli, i.e. in the absence of crowding (albeit under matched conditions of visual uncertainty). If they do, the current observations would perhaps be better explained as resulting from ensemble perception, while crowding merely co-occurs in the current setup.
+
+Thanks for pointing us to this interesting paper, of which we were unaware. It is interesting that ensemble perception and crowding follow partially different rules, opening the way for interesting experiments. In our experiment we only measured crowding (judging orientation of a single target, rather than the average). It would certainly be interesting to do the converse (ensemble judgements) to see if the two phenomena followed similar rules. If they do not, it would be further proof that the two are at least partially different phenomena. This is of course a large new study (which the second author may pursue for his PhD), but we do now mention ensemble perception, and cite the important study mentioned. Thank you
+
+Minor comments:
+
+Figure 5B. Minimum scatter appears to occur at 0 deg, while the ideal observer models predict the minimum to occur at 15 degrees. I am curious whether the authors have any explanation/speculation of why the bias and variance data diverge in this aspect.
+
+Indeed, the prediction was off. However, we had previous calculated variance of the aggregate participant together, so different individual biases added artificially to the variance. We now remove the individual biases from the calculation of scatter (essentially calculating variance separately for each participant and averaging), and the result is far closer to the predicted 15° (see new figure 5B). We explain this procedure in the methods.
+
+In their introduction the authors state “Crowding impacts on many important daily tasks, such as face recognition and reading […]” I would be curious how the authors reconcile this view that crowding appears to negatively impact perception in real world scenarios (“daily tasks”) with their optimal integration theory.
+
+This is a very good point, thank you. Perhaps it goes a bit beyond the scope of this study, but we now add a paragraph discussing how optimizing for one aspect (minimal RMS Errors) may lead to sub-optimal behaviour of others (such as face recognition), as occurs in other forms of Bayesian optimization.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have thoroughly addressed all of the reviewer concerns, and the manuscript is acceptable for publication.
+
+Reviewer #2 (Remarks to the Author):
+
+As in the first submission, this is a fascinating manuscript, with novel findings that present a new perspective on the widely studied phenomenon of crowding. The revisions have done much to clarify the contributions of this work and the nature of the associated analyses. My major issue was previously with the findings regarding response scatter and their relation to prior work, which is now addressed to some extent in the revised manuscript. Many of the other issues have also been resolved. However, there remains one major issue in particular that has been completely ignored in the revisions, along with some minor issues. It is clear to me that this paper presents a novel and useful viewpoint to the literature, but it is especially important that these claims be supported by evidence. At the moment it is still not clear to me that this is the case.
+
+1. The lack of an unflanked baseline
+
+The major shortcoming with the revised manuscript is the lack of an unflanked performance baseline – the authors seek to measure crowding (recognition of a target when surrounded by flankers) but never measure performance in the absence of crowding (a target without flankers). This issue was raised in the first submission, to which the authors responded that it “would have been useful”, but this shortcoming was neither measured nor is its absence acknowledged in the revised manuscript. This absence leads to problematic assumptions about the data, a potentially problematic implementation within the models, and problematic statements about the nature of crowding.
+
+The authors assert at many points that “crowding improves overall performance” (p6), and that they observe “improved perceptual performance” (p16), “a reduction in response scatter [and] total RMS error” (p16), “to improve performance” (p17) and “improved performance” (p20). However, without the measurement of an unflanked baseline where crowding is absent (i.e. measurement of orientation perception for an isolated target without flankers), it is not clear what this improvement is relative to.
+
+In the absence of this measurement, the authors have assumed that the most extreme values of target-flanker difference that were tested correspond to the performance baseline. As noted in my first review, this is not at all clear. Prior studies have shown that the reduction in crowding with increased dissimilarity between target and flankers does not often return performance to the unflanked baseline. This can be seen for instance in the cited studies on orientation judgements (Wilkinson, Wilson, & Ellemberg, 1997; Solomon, Felisberti, & Morgan, 2004) – a target surrounded by orthogonal flankers is not recognized as well as a target presented on its own. In the data of Wilkinson et al, for instance, the threshold elevations (from unflanked) can remain as high as 2.5 times the unflanked baseline, even with dissimilar flanker elements. It is not possible to assume that crowding is absent so long as the flankers remain present, in other words.
+
+If the authors were able to demonstrate that the response scatter with similar flankers (near the middle of Figure 2b) is indeed better than unflanked performance, this would be a convincing demonstration that the presence of crowding improves performance relative to its absence (with a target in isolation). Otherwise, what we are looking at is an improvement in performance when crowding is strong vs. when it is reduced. A far more problematic outcome would be that that the unflanked baseline may in fact yield very low values of response scatter, which would correspond more closely to the values with similar flankers (near the middle). In this case, all of the performance
+with flankers would in fact be a decrement/impairment, rather than an improvement. In other words, the apparent benefits of crowding that are described here would simply be a case of the authors arbitrarily relabelling “up” as “down”. Without these measurements, we can never know. The question of optimality is never truly addressed until we do.
+
+This is not simply a quibble about stimulus details – it it is a key aspect of the measurements being performed here. Without these measurements, the way in which performance with these circumstances is unclear, as reflected in the lack of a meaningful performance comparison in the statements quoted above (i.e. is it that crowding improves performance relative to uncrowded performance, or simply that strong crowding is better than reduced crowding?).
+
+These assumptions regarding performance also carry through to the modelling. On p15 the authors use the extreme points of the dataset as a baseline to estimate optimal sensory reliability. This in turn carries through to key operations of the model (equation 12). If the unflanked reliability is in fact lower than this point, can crowding truly be said to be optimal? Precision (when calculated as in this study) is certainly better when crowded biases are strongest (with small target-flanker differences) compared to when they are reduced, but the authors cannot say whether this is optimal compared to the absence of crowding altogether.
+
+2. Assumptions in the model and optimality
+
+Much has been improved in the discussion of how these findings relate to prior reports of impaired performance in tasks like letter and face recognition (p19). It seems to me however that a key aspect of this discrepancy relates to the assumptions of the model. The text on p11 states that “ideal responses...can be expressed as a linear weighted combination of [the] target and flankers...”. But this is surely suboptimal when the task is to judge the orientation of the target and to ignore the flankers (as in prior studies on letter/face recognition etc). The updated description of the causal inference model makes this assumption more explicit where it is stated (p13) that “…an optimal blend [assumes] that the two curves originate from the same cause” (with a similar comment on p14). With this assumption in place, I could see how these interactions are optimal, and indeed given the structural regularities of the visual scene (that similar orientations, colors, etc are likely to be found together) this is perhaps a sensible assumption for the most part, as exploited by texture/statistical models of peripheral vision and crowding (Freeman & Simoncelli, 2011; Rosenholtz, Yu, & Keshvari, 2019). But it is problematic in tasks where the observer must recognize the target, ignoring the flankers. Although performance may then be optimal given this assumption, it is clearly not optimal given the task being required of observers in (most) crowding paradigms. In these cases, where the task is clearly very different (identify the target face amongst flankers, for instance), is there not therefore an over-application of this principle and thus a suboptimality? I suspect that this again relates back to the lack of an unflanked baseline in the authors’ measurements, and the missing perspective that arises from this.
+
+3. The findings regarding response scatter
+
+The pattern of results obtained with response scatter are much more clear now. However, the authors now describe the discrepancy between the current and previous studies as being due to their separate measurement of bias and precision (p18). The work of Solomon, Felisberti, and Morgan (2004) is cited in this context as ‘the only study to our knowledge’ to have similarly measured bias and precision. A range of other studies have used this approach however, some of which report patterns that do not quite fit with that observed here, to my eye. For instance, Glen and Dakin (2013) report sensitivity and biases for orientation crowding, while Greenwood and Parsons (2020) measured crowded biases and precision/thresholds for color and motion. The patterns there do not quite match those of the current study, with the least precision arising when flankers are most similar to the target, though it could indeed be the case that on the whole the combination of bias and precision leads to a pattern of response scatter similar to that of the current work.
+4. Relation to pooling models
+
+The discussion of the relationship to pooling models is much improved in the introduction and modelling sections. But there is still a statement in the discussion (p16) that the findings are ‘difficult to reconcile’ with pooling models. On the contrary, effects of target-flanker similarity are simulated by pooling models both in Greenwood and Parsons (2020) and in the context of texture pooling models (Rosenholtz, Yu, & Keshvari, 2019). Again, these approaches do not seem so dissimilar to that employed in the current study.
+
+5. Missing references
+
+At points the authors make reference to prior literature without citing the studies being referred to, particularly in the new additions to the manuscript. This occurs on p2 ("Crowding is stronger in the upper than the lower visual field, and for radial than for tangential flankers") and p16 ("the myriad of experiments showing that similarities in shape...cause maximum crowding"). It is particularly unclear to me what studies the latter refers to.
+
+6. Biases
+
+It would help the clarity of the manuscript to have the direction of biases explained somewhere, e.g. on p6 to explain that the errors in Figure 2 follow the orientation of the flankers, and that they presumably go in the opposite direction with some separations in Figure 3.
+
+References
+
+Freeman, J., & Simoncelli, E. P. (2011). Metamers of the ventral stream. Nature Neuroscience, 14, 1195-1201.
+Glen, J. C., & Dakin, S. C. (2013). Orientation-crowding within contours. Journal of Vision, 13, 1-11.
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117, 8196-8202.
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19, 1-25.
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14, 2057-2068.
+
+Reviewer #3 (Remarks to the Author):
+
+I am still not entirely sure whether Nature Communications is the best outlet, as the study puts forward an intriguing idea, but leaves open many questions that would require more data. However, I agree with the authors and fellow reviewers that this is an interesting research direction.
+
+I appreciate the authors’ attempt to minimize the scaling factor, by quantitatively accounting for known suboptimalities due to the oblique bias. I am still not entirely convinced that we are dealing with optimal integration, or whether part of the required scaling is due to suboptimal integration, which would limit the authors’ claim of crowding resulting from optimal integration. If not done in the current manuscript, this will be an important point for future studies.
+
+I realize that I have been somewhat unclear about my previous point about crowding vs ensemble
+perception. My main question was whether the spatial integration observed in the current experiments could perhaps be more general than just occurring for peripheral targets surrounded by flankers (i.e., the conditions under which crowding occurs). For instance, would a similar bias occur for very noisy *foveal* target stimuli surrounded by flankers, in the absence of crowding. That is, would observers generally rely on a weighted average of an ensemble, when visual information about the target is very poor. In the current experiments, crowding might increase the uncertainty/reliability of the target, which might prompt observers to integrate information of the spatial context. In this case, optimal integration would be the *consequence* of crowding, not the *cause* of crowding. If I understand the authors correctly, they claim that optimal integration is the cause of the crowding phenomenon. I would appreciate if the authors could clarify this point.
+
+I also concur Reviewer #2 that an unflanked baseline (or orthogonal flankers) would help to clarify whether maximally similar flankers indeed enhance performance (better than baseline), or whether they are least detrimental (equal or worse performance than baseline).
+Please find enclosed the response to the reviewers and the novel submission with all changes flagged in blue.
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have thoroughly addressed all of the reviewer concerns, and the manuscript is acceptable for publication.
+
+Reviewer #2 (Remarks to the Author):
+
+As in the first submission, this is a fascinating manuscript, with novel findings that present a new perspective on the widely studied phenomenon of crowding. The revisions have done much to clarify the contributions of this work and the nature of the associated analyses. My major issue was previously with the findings regarding response scatter and their relation to prior work, which is now addressed to some extent in the revised manuscript. Many of the other issues have also been resolved. However, there remains one major issue in particular that has been completely ignored in the revisions, along with some minor issues. It is clear to me that this paper presents a novel and useful viewpoint to the literature, but it is especially important that these claims be supported by evidence. At the moment it is still not clear to me that this is the case.
+
+1. The lack of an unflanked baseline
+
+The major shortcoming with the revised manuscript is the lack of an unflanked performance baseline – the authors seek to measure crowding (recognition of a target when surrounded by flankers) but never measure performance in the absence of crowding (a target without flankers). This issue was raised in the first submission, to which the authors responded that it “would have been useful”, but this shortcoming was neither measured nor is its absence acknowledged in the revised manuscript. This absence leads to problematic assumptions about the data, a potentially problematic implementation within the models, and problematic statements about the nature of crowding.
+
+We have now measured baselines for the rounded targets condition (the main one, that leads to the strongest effects). We also measure with orthogonal flankers. The results are shown in Figure 2 as hollow squares/diamonds. The two thresholds are similar to each other, and worse than all the other flanker conditions. We hope this is sufficient for publication now.
+
+The authors assert at many points that “crowding improves overall performance” (p6), and that they observe “improved perceptual performance” (p16), “a reduction in response scatter [and] total RMS error” (p16), “to improve performance” (p17) and “improved performance” (p20). However, without the measurement of an unflanked baseline where crowding is absent (i.e. measurement of
+orientation perception for an isolated target without flankers), it is not clear what this improvement is relative to.
+
+In the absence of this measurement, the authors have assumed that the most extreme values of target-flanker difference that were tested correspond to the performance baseline. As noted in my first review, this is not at all clear. Prior studies have shown that the reduction in crowding with increased dissimilarity between target and flankers does not often return performance to the unflanked baseline. This can be seen for instance in the cited studies on orientation judgements (Wilkinson, Wilson, & Ellemburg, 1997; Solomon, Felisberti, & Morgan, 2004) – a target surrounded by orthogonal flankers is not recognized as well as a target presented on its own. In the data of Wilkinson et al, for instance, the threshold elevations (from unflanked) can remain as high as 2.5 times the unflanked baseline, even with dissimilar flanker elements. It is not possible to assume that crowding is absent so long as the flankers remain present, in other words.
+
+If the authors were able to demonstrate that the response scatter with similar flankers (near the middle of Figure 2b) is indeed better than unflanked performance, this would be a convincing demonstration that the presence of crowding improves performance relative to its absence (with a target in isolation). Otherwise, what we are looking at is an improvement in performance when crowding is strong vs. when it is reduced. A far more problematic outcome would be that that the unflanked baseline may in fact yield very low values of response scatter, which would correspond more closely to the values with similar flankers (near the middle). In this case, all of the performance with flankers would in fact be a decrement/impairment, rather than an improvement. In other words, the apparent benefits of crowding that are described here would simply be a case of the authors arbitrarily relabelling “up��� as “down”. Without these measurements, we can never know. The question of optimality is never truly addressed until we do.
+
+This is not simply a quibble about stimulus details – it it is a key aspect of the measurements being performed here. Without these measurements, the way in which performance with these circumstances is unclear, as reflected in the lack of a meaningful performance comparison in the statements quoted above (i.e. is it that crowding improves performance relative to uncrowded performance, or simply that strong crowding is better than reduced crowding?).
+
+These assumptions regarding performance also carry through to the modelling. On p15 the authors use the extreme points of the dataset as a baseline to estimate optimal sensory reliability. This in turn carries through to key operations of the model (equation 12). If the unflanked reliability is in fact lower than this point, can crowding truly be said to be optimal? Precision (when calculated as in this study) is certainly better when crowded biases are strongest (with small target-flanker differences) compared to when they are reduced, but the authors cannot say whether this is optimal compared to the absence of crowding altogether.
+
+We accept your arguments, thank you, and have added the baseline to the main condition. We agree that this strengthens the manuscript.
+2. Assumptions in the model and optimality
+
+Much has been improved in the discussion of how these findings relate to prior reports of impaired performance in tasks like letter and face recognition (p19). It seems to me however that a key aspect of this discrepancy relates to the assumptions of the model. The text on p11 states that “ideal responses...can be expressed as a linear weighted combination of [the] target and flankers...”. But this is surely suboptimal when the task is to judge the orientation of the target and to ignore the flankers (as in prior studies on letter/face recognition etc). The updated description of the causal inference model makes this assumption more explicit where it is stated (p13) that “…an optimal blend [assumes] that the two curves originate from the same cause” (with a similar comment on p14). With this assumption in place, I could see how these interactions are optimal, and indeed given the structural regularities of the visual scene (that similar orientations, colors, etc are likely to be found together) this is perhaps a sensible assumption for the most part, as exploited by texture/statistical models of peripheral vision and crowding (Freeman & Simoncelli, 2011; Rosenholtz, Yu, & Keshvari, 2019). But it is problematic in tasks where the observer must recognize the target, ignoring the flankers. Although performance may then be optimal given this assumption, it is clearly not optimal given the task being required of observers in (most) crowding paradigms. In these cases, where the task is clearly very different (identify the target face amongst flankers, for instance), is there not therefore an over-application of this principle and thus a suboptimality? I suspect that this again relates back to the lack of an unflanked baseline in the authors’ measurements, and the missing perspective that arises from this.
+
+We now stress that optimization of basic features while optimal strictly speaking, may still impact negatively in higher recognition processes. Indeed it is not uncommon that optimal processes lead to illusions such as the ventriloquist effect and the hollow face illusion
+
+3. The findings regarding response scatter
+
+The pattern of results obtained with response scatter are much more clear now. However, the authors now describe the discrepancy between the current and previous studies as being due to their separate measurement of bias and precision (p18). The work of Solomon, Felisberti, and Morgan (2004) is cited in this context as ‘the only study to our knowledge’ to have similarly measured bias and precision. A range of other studies have used this approach however, some of which report patterns that do not quite fit with that observed here, to my eye. For instance, Glen and Dakin (2013) report sensitivity and biases for orientation crowding, while Greenwood and Parsons (2020) measured crowded biases and precision/thresholds for color and motion. The patterns there do not quite match those of the current study, with the least precision arising when flankers are most similar to the target, though it could indeed be the case that on the whole the combination of bias and precision leads to a pattern of response scatter similar to that of the current work.
+
+Thank you, we were not aware of these studies. We now reference them and point out the differences in results (possibly due to differences in the experimental techniques). But we also take the opportunity to add a penultimate paragraph mentioning that our results may not generalize
+beyond orientation, encouraging experiments along these lines for other features such as motion and color. Thank you for prompting this caveat.
+
+4. Relation to pooling models
+
+The discussion of the relationship to pooling models is much improved in the introduction and modelling sections. But there is still a statement in the discussion (p16) that the findings are ‘difficult to reconcile’ with pooling models. On the contrary, effects of target-flanker similarity are simulated by pooling models both in Greenwood and Parsons (2020) and in the context of texture pooling models (Rosenholtz, Yu, & Keshvari, 2019). Again, these approaches do not seem so dissimilar to that employed in the current study.
+
+Thank you. We have toned down our claims of novelty, but do still want to stress the major difference, of flexible pooling.
+
+5. Missing references
+
+At points the authors make reference to prior literature without citing the studies being referred to, particularly in the new additions to the manuscript. This occurs on p2 (“Crowding is stronger in the upper than the lower visual field, and for radial than for tangential flankers”) and p16 (“the myriad of experiments showing that similarities in shape...cause maximum crowding”). It is particularly unclear to me what studies the latter refers to.
+
+Thank you we now added relevant references
+
+6. Biases
+
+It would help the clarity of the manuscript to have the direction of biases explained somewhere, e.g. on p6 to explain that the errors in Figure 2 follow the orientation of the flankers, and that they presumably go in the opposite direction with some separations in Figure 3.
+
+Thank you we now do.
+
+References
+
+Freeman, J., & Simoncelli, E. P. (2011). Metamers of the ventral stream. Nature Neuroscience, 14, 1195-1201.
+
+Glen, J. C., & Dakin, S. C. (2013). Orientation-crowding within contours. Journal of Vision, 13, 1-11.
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117, 8196-8202.
+
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19, 1-25.
+
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14, 2057-2068.
+
+Reviewer #3 (Remarks to the Author):
+
+I am still not entirely sure whether Nature Communications is the best outlet, as the study puts forward an intriguing idea, but leaves open many questions that would require more data. However, I agree with the authors and fellow reviewers that this is an interesting research direction.
+
+I appreciate the authors’ attempt to minimize the scaling factor, by quantitatively accounting for known suboptimalities due to the oblique bias. I am still not entirely convinced that we are dealing with optimal integration, or whether part of the required scaling is due to suboptimal integration, which would limit the authors’ claim of crowding resulting from optimal integration. If not done in the current manuscript, this will be an important point for future studies.
+
+I realize that I have been somewhat unclear about my previous point about crowding vs ensemble perception. My main question was whether the spatial integration observed in the current experiments could perhaps be more general than just occurring for peripheral targets surrounded by flankers (i.e., the conditions under which crowding occurs). For instance, would a similar bias occur for very noisy foveal target stimuli surrounded by flankers, in the absence of crowding. That is, would observers generally rely on a weighted average of an ensemble, when visual information about the target is very poor. In the current experiments, crowding might increase the uncertainty/reliability of the target, which might prompt observers to integrate information of the spatial context. In this case, optimal integration would be the consequence of crowding, not the cause of crowding. If I understand the authors correctly, they claim that optimal integration is the cause of the crowding phenomenon. I would appreciate if the authors could clarify this point.
+
+We thank the referee for making their point more clear. It is certainly a good point, which we are not able to address at this stage (other than showing in Figure 3 that the assimilative effects disappear at large separations). We do now mention that this is an open question meriting further research (in the penultimate paragraph).
+I also concur Reviewer #2 that an unflanked baseline (or orthogonal flankers) would help to clarify whether maximally similar flankers indeed enhance performance (better than baseline), or whether they are least detrimental (equal or worse performance than baseline).
+
+We too were convinced, and did the extra measurements (open symbols in Figure 2).
+REVIEWERS’ COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have responded comprehensively to issues raised in the previous rounds of submission, and my major issues with the manuscript are resolved. The new baseline measurements (with an additional condition including orthogonally-oriented flankers) are a convincing addition, providing a clear reference for the arguments that crowding can improve the precision of the shape judgements measured by the authors.
+
+As I have said in earlier rounds, this is a fascinating manuscript whose findings present a new perspective on a widely studied phenomenon. I do not agree with everything that is said, but the authors have sufficiently qualified their statements to the extent that the ideas are fully available for the reader to decide. I am sure this will inspire a great deal of future research.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have addressed the remaining issues. I have no further comments.

022065845b0149dd1bde836e14da3448f70c4603767a53533c6448baf134c8c3/preprint/preprint.md

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+Crowding results from optimal integration of visual targets with contextual information
+
+Guido Marco Cicchini
+Consiglio Nazionale delle Ricerche   https://orcid.org/0000-0002-3303-0420
+
+Giovanni D'Errico
+CNR Neuroscience Institute   https://orcid.org/0000-0002-0491-581X
+
+David Burr (dave@in.cnr.it)
+University of Florence   https://orcid.org/0000-0003-1541-8832
+
+Article
+
+Keywords:
+
+Posted Date: March 1st, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1296243/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on September 30th, 2022. See the published version at https://doi.org/10.1038/s41467-022-33508-1.
+Crowding results from optimal integration of visual targets with contextual information
+
+Guido Marco Cicchini¹, Giovanni D’Errico¹ and David C. Burr¹,²
+
+1. Institute of Neuroscience, CNR, via Moruzzi, 1 , 56124 – Pisa (ITALY)
+2. Department of Neurosciences, Psychology, Drug Research and Child Health, University of Florence, viale Pieraccini, 6 – 50139 Firenze (ITALY)
+
+ABSTRACT
+
+Crowding is the inability to recognize peripheral objects in clutter, usually considered a fundamental low-level bottleneck to object recognition. Here we advance and test an alternative hypothesis, that crowding, like “serial dependence”, results from optimizing strategies that exploit redundancies in natural scenes. This notion leads to several testable predictions: (1) crowding should be greatest for unreliable targets and reliable flankers; (2) crowding-induced biases should be maximal when target and flankers have similar orientations, falling off for differences around 20°; (3) flanker interference should be associated with higher precision in orientation judgements, leading to lower overall error rate; (4) effects should be maximal when the orientation of the target is near that of the average of the flankers, rather than to that of individual flankers. All these effects were verified, and well simulated with ideal-observer models that maximize performance. The results suggest that while crowding can impact strongly on object recognition, it is best understood not as a processing bottleneck, but as a consequence of efficient exploitation of the spatial redundancies of the natural world.
+INTRODUCTION
+
+Crowding is the inability to recognize and identify objects in clutter, despite their being clearly visible, and recognizable when presented in isolation¹ (see examples in Figure 1A). It is particularly elevated in the periphery, scaling linearly with eccentricity, such that the minimal spacing between targets and flanking elements for uncrowded vision is equal to about half the eccentricity (Bouma’s law² ). Crowding impacts on many important daily tasks, such as face recognition and reading (for reviews see³,⁴,⁵ ), to the extent it has been considered a major bottleneck to object recognition.
+
+Most popular current models of crowding involve some form of compulsory pooling (or substitution) of targets with flankers. For example, Parkes and colleagues⁶ showed that while the orientation of a single line cannot be determined when embedded in flankers, it does influence the perceived orientation of the ensemble: hence it is merged with the flankers, rather than suppressed. This is reinforced by several studies showing that the targets can take on characteristics of the flanker stimuli⁷-⁹. Pelli and Tillmann³ suggest that the compulsory integration occurs in higher cortical areas, such as V4, which have large receptive fields, appropriately sized to account for Bouma’s law (see also ¹⁰).
+
+However, compulsory integration does not explain all the known facts about crowding. For example, flankers that are similar in size, colour or orientation cause more crowding than dissimilar ones¹¹-¹³. More difficult to explain are the recent demonstrations of Herzog and colleagues¹⁴ of “uncrowding”, where the addition of extra flanking stimuli around the flankers can reduce drastically their crowding effect, particularly if the extra flankers group with the original flankers to form coherent objects. These data do not fit easily with compulsory integration, even with appropriate linear filtering, which could in principle account for other effects, such as orientation or size selectivity.
+
+Crowding has been studied for decades, and usually considered to be a defect in the system, “an essential bottleneck to object perception”¹⁵. Certainly, it impacts heavily on object recognition in tasks like or face recognition: but is it possible that it may reflect processes that are in principle advantageous to perception? Perception is strongly affected by contextual information, particularly temporal context, where recent and longer term perceptual history has been shown to exert a major influence on current perception¹⁶-¹⁹. While the role of context and experience has been appreciated for some time²⁰,²¹, it has
+become particularly topical in recent years within the framework of Bayesian analysis. This approach has revealed an interesting phenomenon termed “serial dependence”, where the appearance of many important attributes of a stimulus (including orientation, numerosity, facial identity, beauty etc) are biased towards previously viewed stimuli\(^{17,18,22,23}\). Counterintuitively, these consistent biases in perception have been shown to reflect an efficient perceptual strategy, exploiting temporal redundancies in natural viewing to reduce overall reproduction errors, despite the biases\(^{24,17,25}\).
+
+Could crowding also be a consequence of efficient integration processes that exploit spatial (rather than temporal) redundancies to improve performance? We investigate this possibility by studying crowding with a similar paradigm used for serial dependence studies. If, like serial dependence, crowding is a by-product of efficient redundancy-reducing mechanisms, it should display several specific signature characteristics. One is that crowding-induced biases should be stronger for targets that are unreliably perceived, and for flankers that are reliably perceived. In addition, crowding should follow the signature pattern seen in serial dependence, highest when the orientations of target and flankers are similar, then steadily falling off. We verify these characteristics qualitatively and qualitatively, and show that crowding, while leading to biases, also improves overall performance. The results fit well with models simulating intelligent combination of signals from a small receptive field centred on the target with signals from a much larger integration region, following the same rules that govern serial dependence. On this view crowding should not be considered a defect, or bottleneck, in the system, but the unavoidable consequence of efficient exploitation of spatial redundancies of the natural world.
+Figure 1
+a) Crowding is a visual phenomenon where items that can be easily identified in isolation are not identifiable if surrounded by similar items. The P and hand symbol on the right are difficult to recognize, while fixating the central red dots.
+b) Stimuli employed in this experiment. Observers judged the orientation of a peripheral target (the central oval), which was flanked above and below by oval stimuli. Two conditions were tested: a rounded target with elongated flankers (Low reliability target, high reliability flankers, at left) or an elongated target with rounded ovals (at right). In the main condition the centre-to-centre distance of flankers and targets was 5.5 deg, and eccentricity 26 degrees, leading to a Bouma ratio of 0.21.
+
+RESULTS
+
+To test if visual crowding follows the rules of optimal integration, which well describe serial dependence^{18,25}, we measured crowding with an orientation reproduction task. Participants reproduced the orientation of oval stimuli, which were either elongated (aspect ratio 1: 2.8) or rounded (aspect 1: 1.4). Targets were presented 26° to the right of fixation, and vertically flanked by similar oval stimuli, elongated if the target was rounded, and vice versa (see Fig. 1B). The orientation of the target was either 35° or 55° (at random). The orientations of the two flankers were yoked together, and varied randomly over a range of ±45° from target orientation. The clear prediction from the efficient integration model^{24} (see Eqn 10) is that the effects of crowding will be far stronger for the rounded targets and elongated flankers than vice versa. The reasons are explained formally the modelling section, but the intuition is that the rounded stimuli have less reliable orientation signals and therefore benefit more from integration with contextual information, especially if it is reliable.
+
+Figure 2A shows the bias in target reproduction as a function of difference in flanker orientation. Clearly, the rounded targets show the strongest contextual effects of crowding,
+with peak biases varying by up to ±5.1°, compared with ±1.9° for the elongated targets. Furthermore, the pattern of bias follows closely that predicted and observed in serial dependence studies25, varying non-linearly with difference between target and flanker orientation, increasing to a maximum around ±20°, then decreasing. These data are well fit by derivative of gaussian functions (eqn. 15, light-coloured lines), commonly used in serial dependence studies18, and expected from a causal inference model (see modelling section26). The dark lines show the predictions of another Bayesian model (eqn. 10), which has also proven successful with serial dependence data17,25. While the models are detailed later, it is worth noting that they are almost entirely anchored by data, down to a simple scaling factor, suggesting that the data are consistent with ideal behaviour.
+
+![Three panels showing bias and scatter plots for flanker orientation effects](page_340_682_1067_312.png)
+
+Figure 2
+a) Average response bias (response minus target orientation) as a function of the orientation of two identical flankers. Low reliability (rounded) targets in blue, high reliability (elongated) in red. Error bars show ±1 SEM. Dark lines show predictions from an ideal-observer Bayesian model which scales the action of flankers according to their reliability and orientation difference (Eqn 10 of model section). Light blue and red curves show predictions for the causal inference model that doses flanker and target information according to their reliability and the probability of originating from a common cause (Eqn 15 of model section).
+b) Response scatter as a function of the orientation of two identical flankers, together with model predictions. Colour coding as in A.
+c) Response Scatter error plotted against bias errors for the two conditions. Dashed circles indicate regions with identical RMSE error (given by the Pythagorean sum of the two types of error). RMSE varies with orientation, and is least around 0°, when target and flankers coincide.
+
+Another important prediction is that the contextual effects should improve performance. Figure 2B plots reproduction scatter (root-variance of reproduction trials) as a function of orientation difference. As expected, at all orientation differences, these are lower for the elongated than the rounded targets. However, for both targets, particularly the rounded
+targets, the scatter decreased as the difference between target and flanker orientation decreased. Figure 2C plots scatter against bias, with points connected to follow the change in orientation. On this plot, total error (the Pythagorean sum of scatter and bias) is the radial distance from the origin. For the points with flanker orientation most distant from the target (near ±45°), the total error is around 15°. Between these extremes, total error falls off, despite the constant bias. When the flankers and targets have similar orientations, the error falls to around 11°, evidence that “crowding” improves overall performance.
+
+If the effects shown in Figure 2 represent visual crowding, they should depend on critical spacing between target and flankers, and follow Bouma’s law¹. We therefore measured the effects as a function of target-flanker spacing, for 5 participants. Figure 3 shows the data for the rounded targets with elongated flankers (which show the strongest effects). For the two smallest spacings (5.5 and 7.5 deg), bias showed the characteristic S-shaped dependency on the orientation of the flankers. For the larger spacings (11.0 and 16.6 deg), however, the effect was much reduced and even inverted at 11 deg. As before, the curves are fit by a derivative of gaussian function (eqn 18), which is the product of a linear regression (illustrated by dashed line in Figure 3A) and a gaussian. The best fitting slope of this regression is an estimate of the weight given to the flankers when judging orientation. Figure 3B plots the fitted weight as a function of target-flanker spacing (lower abscissa), with the upper abscissa showing the Bouma constant, the distance between target and flanker centres divided by the eccentricity (26 deg). The weight drops from 0.5 to 0 for Bouma constants between 0.3 and 0.4, broadly in line with the literature, suggesting that the effects observed here relate to crowding.
+Figure 3
+a) Response bias as function of flanker orientation for various target-flanker distances leading to four different Bouma ratios (distance between flanker and target centres divided by eccentricity. Data are fit with a derivative of gaussian function with free parameters (Eqn 18).
+b) Weight of the flankers (maximal slope of the curves in panel A) as a function of the Bouma ratio (colour-code as before). Error bars show ±1 SEM.
+
+The results so far show that integration is not obligatory, but depends on the reliability of both target and flankers, and on their orientation similarity. A remaining question is how the flankers integrate with the target: each separately, or after combination with each other. Figure 4 illustrates two possibilities (see also modelling section). One is feedforward model where the target integrates independently with low-level, high-resolution neural representations of each of the flankers. The other depicts integration with a broader representation including both flankers, potentially implemented through recurrent feedback.
+Figure 4
+a) Rationale of Experiment 2. Flankers could either act independently on the target (as illustrated by purple arrows in top left panel), or first pooled into a larger RF, which in turn biases the target (illustrated by the large yellow circle and arrow in bottom left panel).
+b) Predictions for the two hypotheses. If the flankers act independently, when one flanker is locked at +15° and the other free to vary, the pattern should be similar to that of the main experiment (centre close to 0°), but raised because of the action of the locked flanker (purple curve). If flankers are first integrated at a more global stage, maximal effect is expected when all the elements in the larger operator average 0°. Since one of the flankers is locked at +15°, this occurs when the other flanker is −15°, leading to a leftward shift of the curve of the main experiment (yellow curve)
+
+To distinguish between these two plausible possibilities, we measured target bias with the orientation of the two flankers varying independently. Specifically, one flanker (randomly top or bottom) was always oriented +15° from the target, while the other varied randomly over the range. The logic is that the gaussian function windowing the contextual effect should be centred where the orientations of target and context coincide. If the integration occurs directly between the target and individual flankers, then the maximum effects should occur when the variable flanker coincides with the target; on the other hand, if the integration is with a broader representation including both flankers, maximum integration should occur when the flanker mean is zero, which occurs when the variable flanker is −15°. These predictions are illustrated in Figure 4B: note that the individual flanker effect also predicts the curve to be higher at all flanker orientations, as the fixed flanker will exert a constant effect at all orientations of the variable flanker.
+
+![Diagram showing flanker action types and corresponding bias curves](page_186_120_1077_495.png)
+The results for the rounded targets with elongated flankers are shown figure 5A. The biases clearly follow the signature pattern, well fit by a derivative of gaussian function. The centre of the function is −12.1°, closer to the 15° predicted by integration with the average orientation of the flankers, than 0° predicted by the individual flanker model. The mean height of the function is 0.5°, close to that observed in the previous experiment (−0.9°), while the individual-flanker integration model predicts a constant average bias 4.7°. Figure 5B shows the scatter for this experiment, which was reduced over the region of bias, well described by an inverted Gaussian.
+
+![Three panels showing bias, response scatter, and histogram data for flanker orientation and center of DoG](page_362_682_1047_312.png)
+
+Figure 5.
+a) Biasing errors as function of a single flanker orientation, while the other flanker was locked at +15°. Colours and conventions as for Figure 2. Thick dark lines refer to the ideal observer model (Eqn 10), thick light blue lines to the causal inference model (Eqn 15). Thin dashed lines show best-fitting derivative of gaussian, with all parameters free to vary (Eqn 18).
+b) Response Scatter as a function of the variable flanker orientation. Conventions as in panel a.
+c) Histogram of the centres of the gaussian derivative for 1000 bootstrap fits.
+
+To test significance, we bootstrapped the data 1000 times (sampling with replacement) and measured the centre of the gaussian derivative on each iteration. The results plotted in the histogram of Figure 5C show that on only 16 out of 1000 iterations (1.6%) was the centre closer to 0° (individual flanker prediction) than to −15° (joint-flanker prediction). This leads to a likelihood ratio (Bayes factor) of 984/16 = 61.5, strong evidence in favour of the joint-flanker-integration model.
+MODELLING
+
+We propose two plausible models to explain the pattern of data. Both are motivated by principles of “optimal cue integration” commonly used in multi-sensory perception\(^{27,28}\), which predict optimal combination of information from multiple sources after appropriate weighting to minimize overall root-mean-square error. The first is based on an ideal-observer model successfully used to model serial dependence\(^{17}\), the second on a “causal-inference” model of multi-sensory integration\(^{26}\). Both models predict well the data.
+
+Ideal Observer
+
+Total RMS error (\(E\)) can be decomposed into bias (\(B\)) and precision (scatter standard deviation: \(S\)), whose squares sum to give total squared error:
+
+\[
+E = \sqrt{B^2 + S^2}
+\] [eq. 1]
+
+The ideal responses (\(R\)) in a pooling model can be expressed as a linear weighted combination of internal representation of target (\(T\)) and flankers (\(F_1\) and \(F_2\)), each weighted by \(w_1\) and \(w_2\).
+
+\[
+R = w_1 F_1 + w_2 F_2 + (1 - w_1 - w_2) T
+\] [eq. 2]
+
+As the two flankers of this study had the same aspect ratio they should be weighted equally, (\(w_1 = w_2 = w\)), so Eqn. 2 simplifies to:
+
+\[
+R = w F_1 + w F_2 + (1 - 2w) T
+\] [eq. 3]
+
+The mean of the responses (\(\mu_R\)) is a simple linear combination of the means of flankers and target (\(\mu_1, \mu_2\) and \(\mu_T\)).
+
+\[
+\mu_R = w \mu_1 + w \mu_2 + (1 - 2w) \mu_T = w(\mu_1 + \mu_2) + (1 - 2w) \mu_T
+\] [eq. 4]
+
+Bias is the difference between the mean estimated response (\(\mu_R\)) and real orientation, \(x_T\); \(B = \mu_R - x_T\). Using equation 4 and considering that the average target representation (\(\mu_T\)) should be unbiased and coincide with target (\(\mu_T = x_T\)) it follows that:
+
+\[
+B = \mu_R - x_T = w(\mu_1 + \mu_2) + \mu_T - 2w \mu_T - x_T = w(\mu_1 + \mu_2 - 2 \mu_T)
+\] [eq. 5]
+The term \( \mu_1 + \mu_2 - 2\mu_T \) can be rearranged as \( 2((\mu_1 + \mu_2)/2 - \mu_T) \) which is twice the distance between the average of the flanker representations, \((\mu_1 + \mu_2)/2\), and the target representation \( \mu_T \). For convenience we define:
+
+\[
+d = (\mu_1 + \mu_2)/2 - \mu_T \tag{eq. 6}
+\]
+
+so that Eqn. 5 becomes:
+
+\[
+B = w(\mu_1 + \mu_2 - 2\mu_T) = 2wd \tag{eq. 7}
+\]
+
+Variance of the linear combination of the flankers and target is itself a linear combination of the flanker and target variances (\( \sigma_F^2 \) and \( \sigma_T^2 \)) with the squared coefficients
+
+\[
+S^2 = w^2 \sigma_F^2 + w^2 \sigma_F^2 + (1-2w)^2 \sigma_T^2 \tag{eq. 8}
+\]
+
+From Eqn 1, 7 and 8 it follows that \( RMSE \) can be written as:
+
+\[
+E = 4w^2 d^2 + w^2 \sigma_F^2 + w^2 \sigma_F^2 + (1-2w)^2 \sigma_T^2 \\
+= 4w^2 d^2 + w^2 \sigma_F^2 + w^2 \sigma_F^2 + (1-4w+4w^2)\sigma_T^2 \tag{eq. 9}
+\]
+
+Since RMSE is a function of second order of \( w \), it is minimized when \( w = \frac{-b}{2a} \), so the optimal weight (\( w_{opt} \)) is obtained at:
+
+\[
+w_{opt} = -\frac{1}{2} \frac{-4\sigma_T^2}{4\sigma_T^2 + 2\sigma_F^2 + 4d^2} = \frac{\sigma_T^2}{2\sigma_T^2 + \sigma_F^2 + 2d^2} \tag{eq. 10}
+\]
+
+This equation has much in common with that of all Bayesian-like integrations used in multi-sensory research and serial dependence: the weight depends directly on *target* variance \( \sigma_T^2 \), so *targets* of low reliability (inverse variance) benefit more from integration, resulting in higher weighting to the *flankers*. Increase in flanker variance (\( \sigma_F^2 \)) has the opposite effect.
+
+The term \( 2d^2 \) is fundamental for the signature function, as the weight of the *flankers* will decrease with angular difference between target and average flanker orientation. This is reminiscent of serial dependence effects, and ensures that contextual cues are used only if they are plausibly similar to the target\(^{24,17,25}\). Importantly, the point that will ensure maximal weight of the flankers is when the target coincides with the average of the flankers (i.e. \( d^2 = 0 \)).
+Together the behaviour of Eqns 3 and 10 define the ideal observer behaviour. In order to accommodate suboptimal behaviour we introduce a scaling factor (\( \alpha \)) which multiplies \( w_{opt} \) and sets the actual weight of the flankers:
+
+\[
+R = \alpha w_{opt} F_1 + \alpha w_{opt} F_2 + (1 - 2\alpha w_{opt}) T
+\]
+
+[eq. 11]
+
+**Causal Inference Model**
+
+An alternative model prescribes that the optimal blend of information can be obtained behaving as if the sources of information originated form one cause times the probability that two sources of information originate from the same cause\(^{26}\). Within this framework the maximal interaction between cues occurs when the two sources coincide, where the weight assigned of is the well known result known in sensory integration literature\(^{27,28}\) (see also eq. 10):
+
+\[
+w_A^{max} = \frac{\sigma_B^2}{\sigma_A^2 + \sigma_B^2}
+\]
+
+[eq. 12]
+
+The probability of the two sources originating from a common cause can be calculated using Bayes’ Theorem as demonstrated in\(^{26}\). Assuming gaussian probability distribution functions (with centres at \( \mu_A \) and \( \mu_B \) and variances \( \sigma_A^2 \) and \( \sigma_B^2 \)), the solution is soluable analytically\(^{26}\):
+
+\[
+p(A,B|C=1) \propto \exp \left( -\frac{1}{2} \frac{(\mu_A-\mu_B)^2 \sigma_P^2 + (\mu_A-\mu_P)^2 \sigma_A^2 + (\mu_B-\mu_P)^2 \sigma_B^2}{\sigma_A^2 \sigma_B^2 + \sigma_A^2 \sigma_P^2 + \sigma_B^2 \sigma_P^2} \right)
+\]
+
+[eq. 13]
+
+This is function of the variances of the two sources (\( \sigma_A^2 \) and \( \sigma_B^2 \)), the centres of the representations (\( \mu_A \) and \( \mu_B \)) and their distance, and the a-prior likelihood of there being one cause (itself gaussian and characterized by mean and variance \( \mu_P \) and \( \sigma_P^2 \)). If no prior knowledge is available (\( \sigma_P^2 \to \infty \)) Eqn 13 simplifies to
+
+\[
+p(A,B|C=1) \propto \exp \left( -\frac{1}{2} \frac{(\mu_A-\mu_B)^2}{\sigma_A^2 + \sigma_B^2} \right)
+\]
+
+[eq. 14]
+
+This is a gaussian peaking when the distribution of the two cues coincide (\( \mu_A = \mu_B \)) and falling off with a space constant related to the sum of their variances (\( \sigma_A^2 + \sigma_B^2 \)).
+
+In the specific case of our experiment we can map the two sources of information to the flanker compound (a gaussian with centre at \( \mu_F = (\mu_1 + \mu_2)/2 \), variance \( \sigma_F^2/2 \)) and the
+target (assumed gaussian with centre \( \mu_T \), and variance \( \sigma_T^2 \). Putting together Eqns 12 and 14, the bias (difference between the response and the target) is given by:
+
+\[
+B = w_F^{max} p(F,T|C=1)(\mu_F - \mu_T) = \frac{\sigma_T^2}{\sigma_F^2 + \sigma_T^2} \exp \left( -\frac{1}{2} \frac{(\mu_F - \mu_T)^2}{\sigma_F^2 + \sigma_T^2} \right) (\mu_F - \mu_T) \tag{eq 15}
+\]
+
+Which is a derivative of gaussian as a function of flanker orientation \( \mu_F \)
+
+It also follows that response scatter is minimized only when the system considers a common cause likely (Eqn 14), predicting U-shaped (gaussian) plots of Figures 2B and 5B.
+
+Again, to allow for suboptimal behaviour we introduced two free parameters that regulate the amplitude of the dependency on the flankers (\( \beta \)) and the breadth of the region of interaction (\( \gamma \)) so that the bias is:
+
+\[
+B = \beta \frac{\sigma_T^2}{\sigma_F^2 + \sigma_T^2} \exp \left( -\frac{1}{2} \frac{(\mu_F - \mu_T)^2}{\gamma^2 (\sigma_F^2 + \sigma_T^2)} \right) (\mu_F - \mu_T) \tag{eq 16}
+\]
+
+Interestingly, comparable behaviour is obtained if, instead of constructing a system which multiplies probabilities as in\(^{26}\), one considers a system that measures the similarity between two distributions via their point-by-point product of the distributions and takes either the peak or area under the distribution.
+
+The product of gaussians is itself a gaussian, is centred at \( \left( \frac{\mu_B \sigma_A^2 + \mu_A \sigma_B^2}{\sigma_A^2 + \sigma_B^2} \right) \), has variance \( \left( \frac{\sigma_A^2 \sigma_B^2}{\sigma_A^2 + \sigma_B^2} \right) \) and peak at:
+
+\[
+\frac{1}{2 \pi \sigma_A \sigma_B} \exp \left( -\frac{(\mu_A - \mu_B)^2}{2(\sigma_A^2 + \sigma_B^2)} \right) \tag{eq. 17}
+\]
+
+So the peak embeds the same behaviour of Eqn. 14. It is easy to demonstrate that also the area under the curve follows the same gaussian dependency on the distance between cues as the area of a gaussian is equivalent to the peak (Eqn. 16) times the standard deviation of the curve (\( \sqrt{\frac{\sigma_A^2 \sigma_B^2}{\sigma_A^2 + \sigma_B^2}} \)) and a constant factor \( 1/\sqrt{2 \pi} \) all of which are constant once the distributions have known width and thus reduce to a scaling factor.
+
+Model Fitting
+
+The predictions of the two modelling approaches are overlayed on the data of Figures 2 and 5 with dark and light colours. To minimize degrees of freedom we derived the values of
+sensory reliability from the data of Figure 2b, assuming that the extreme points (±30° and ±45°) give baseline data, not influenced by flanker integration: this is 17.1 for rounded targets (blue symbols), and 11.7 for elongated targets (red symbols).
+
+We implemented the ideal observer model (Eqn. 11) with only a scaling constant (\( \alpha \)), which allows for sub-optimal behaviour. These fits are particularly good for the rounded targets (with largest effects), with \( R^2 \) of 0.97 and 0.74 (for bias and scatter), and 0.24 and 0.60 for elongated targets) and come about assuming \( \alpha = 0.57 \). One of the key features of the ideal observer model is that it reduces RMSE by leveraging on all available information. Thus it predicts the Global Integration of Figure 4, with centres of the Gaussian derivatives close to −15°. Besides capturing this key feature, the model also provides good quantitative fits to the data of Figure 5a with \( R^2 \) of 0.76 and average fits to those of Figure 5b 0.23 for bias and scatter respectively (\( \alpha=0.32 \)).
+
+We used the same reliability values from Figure 2b to implement the “optimal causality gating model”\(^{26}\), the derivative of gaussian function plotted with light colours in Figures 2 and 5. The sensory reliabilities fix both the maximal slope of the curve (see Eqn 12) and the width of the region of interaction (see Eqn 14). Assuming the same sensory precisions as above (17.1 and 11.7 for the two types of stimuli) maximal slopes should be 0.81 and 0.48 for the two conditions, larger than the real data. Also the widths (27.8 and 33.2) are larger than those predicted by Eqn 14 (19 and 16.8). For this reason we allowed two scaling factors, one enabling lower weighting of the context (\( \beta \)) and the other modulating the width (\( \gamma \)). Setting \( \beta=0.54 \) and \( \gamma=1.46 \) led to good fits with \( R^2 = 0.97 \) and 0.89 for the low reliability target (bias and scatter curves), and 0.67 and 0.79 for the high reliability target (\( \beta=0.26 \) and \( \gamma=1.97 \)). As with the other model, the prediction in Experiment 2 is for large pooling of all available cues, thus the prediction is that of a centre at −15°. This model also provides good fits for response bias (\( R^2=0.89 \)) and acceptable fits for response scatter (\( R^2=0.38, \beta=0.62 \) and \( \gamma=1.37 \)).
+DISCUSSION
+
+The results of this study suggest a novel interpretation of visual crowding: that it is a by-product of efficient Bayesian processes, which lead to improved perceptual performance, minimizing production error. We tested and validated several key predictions of this idea. Firstly, crowding, measured as flanker-induced orientation bias, was greatest when targets had the weakest orientation signals (least reliability) and flankers had the strongest signals, as predicted from most models of optimal cue combination\(^{27,28}\). The magnitude of the bias varied with the difference of target and flanker orientation, following the predicted non-linear pattern, increasing to a maximum of around \(15^\circ\), then falling off for larger orientation differences. Importantly, the interaction of the flankers and target was associated with a reduction in response scatter, which led to a reduction in total RMS error, an index of improved performance. Finally, the results suggest that the bias does not result from direct interactions with individual flankers, but from interaction with a representation of the average orientations of the two flankers. All these results were predicted by optimal feature combination principles, and quantitatively well modelled an ideal-observer model that minimizes reproduction errors.
+
+These results are clearly difficult to reconcile with standard models of obligatory integration\(^{6,29}\). Passive integration systems may be tweaked to explain the stronger effects for more elongated flankers (such as having more Fourier energy at that orientation), but cannot explain the fall off in crowding effects when the difference exceeds \(15^\circ\). Any basic integrator would necessarily combine orientation energy of all angles, not only similar angles. On the other hand, the flexible integrator models proposed here (Eqns 10 and 15) predict both the pattern and the magnitude of the results. Furthermore, the final experiment suggests that this intelligent orientation-dependent integration is unlikely to occur directly within a higher order cell itself, as the orientation-dependent integration function aligns with the average of two disparate flankers, rather than with each individual flanker. This suggests that the integration is between the target and a broad representation that includes both flankers. Mechanisms operating directly between target and individual flankers (such as the proposed “local association field”\(^{30}\)) are not consistent with the results of Figure 5, which shows that flankers are first combined with each other before exerting their effects on the target.
+Combination of target and a broad representation of both flankers could be implemented in several ways. One physiologically plausible mechanism would be feedback from mid-level areas, such as V4, which have large receptive fields, integrating over a wide area. These cells could contain information of both flankers (as well as the target), which could be fed back to low levels (eg V1) to integrate flexibly with finer representations of the target. Within this framework the fine-grain target information is not lost, but combined with broad contextual information in an optimal manner to improve performance. This is analogous to the process of serial dependence, where representations of perceptual history (often termed Bayesian priors) are generated at mid- to high-levels of analysis, but feed back onto fairly low processing levels\(^{31}\). Similar processes could evoke crowding, integrating over space rather than time.
+
+The predictions of the crowding behaviour derive from theoretical minimization of total RMS errors, explained in detail in the modelling section, but readily understood intuitively. There are two orthogonal sources of error, bias (average accuracy) and response scatter (precision), which combine by Pythagorean sum to yield total error. Thus although the contextual effects do lead to inaccuracies (biases), these are more than offset by the decrease in response scatter (Fig. 2C). Clearly, if the effects were to increase continuously with orientation, then the bias would become large, and offset the reduction in scatter, leading to increased error: integration is therefore efficient only over a limited range. Note that the efficiency-driven ideal model gives good fits simultaneous to both bias and scatter data with only one free parameter, a scaling factor. This comes out at around 0.57 for the main data and probably reflects other processes in orientation judgements that we did not control for, such as regression to the mean\(^{32,33}\).
+
+The current experiment shows that under conditions of crowding, information about the target is not necessarily lost. This is consistent with a good deal of previous evidence (see reference\(^{34}\) for review), including studies showing that it can affect the ensemble judgment\(^6\), can cause adaptation\(^{35}\) and that crowding induced biases may not affect grasping\(^{36}\). Even more dramatic are the demonstrations that increasing flanker length\(^{37}\) or adding additional flankers\(^{14}\) can decrease or eliminate crowding. Our study employed simple well controlled stimuli to allow quantitative prediction and measurement of crowding-effects, similar to the studies with serial dependence studies. Thus they do not readily relate
+to the clever uncrowding studies of Herzog and colleagues. However, it is not difficult to envisage extensions to the model incorporating grouping principles within the rules of integration, in the spirit of the general principles of our model: flexible, “intelligent” combination of signals, rather than a rigid integration via “rectify and sum” or similar rules\(^{10}\).
+
+In summary, the current study suggests that crowding may be analogous to serial dependence, pointing to similar function and mechanisms. As serial dependence has been shown to exploit temporal redundancies to maximize performance, crowding may also reflect similar exploitation of redundancies over space. It is worth noting that while the rules governing crowding are flexible, leading to improved performance, crowding remains completely obligatory: no effort of will or deployment of attention can allow us to resolve the crowded objects, or to ignore the contextual effects of the orientated flankers. Indeed, while our proposed pooling process is flexible and “intelligent”, it remains automatic, not subject to voluntary control. This is similar to many of the experience-driven perceptual illusions, such as the “hollow mask illusion”\(^{21}\): no effort of will can cause us to see the inside of a hollow mask as concave, we always see the convex face. However, while visual crowding remains an obligatory limitation to object recognition, we conclude that like the effects of temporal context and experience, it is best understood not as a defect or bottleneck of the system, but the consequence of efficient exploitation of spatial redundancies of the natural world.
+
+METHODS
+
+Participants
+
+Fifteen healthy participants with normal or corrected-to-normal vision were recruited (aged 18-55 years, mean age = 36, 7 females). Experimental procedures are in line with the declaration of Helsinki and approved by the local ethics committee (*Commissione per l’Etica della Ricerca*, University of Florence, 7 July 2020). Written informed consent was obtained from each participant, which included consent to process, preserve and publish the data in anonymous form.
+Stimuli
+
+The stimuli, illustrated in Fig. 1A, were generated with Psychtoolbox for MATLAB (R2016b; MathWorks). They comprised an oval-shaped visual target flanked by oval-shaped upper and lower visual flankers, displayed 26 deg eccentric from the fixation point, with the target close to the horizontal meridian (vertical position was slightly varied from trial to trial to avoid pre-allocation of attention to the target) and flankers 5.5 deg away from the target. Both target and flankers were sketches of oval shapes, defined by 12 dark grey dots (diameter 0.3 deg, 1.4 deg inter-dots distant, 16.8 deg perimeter), presented against a uniform grey background. The target was orientated either +35° or +55° (clockwise) from the vertical, and flanker orientation randomly chosen in steps of 5° from –45° to +45° with respect to the target orientation. The two flankers were 5.5 deg from target, leading to a Bouma ratio of 0.2. We manipulated the reliability of orientation information of target and flanker stimuli by using two different aspect ratios, 2.8 (axes 3.48 and 1.23 deg) and 1.4 (axes 3.19 and 2.28 deg), illustrated in Fig. 1A. The more elongated target was always associated with more rounded flankers, and vice versa. In each experimental session of the three experiments, the two target-flanker combinations were shown both kinds of stimuli in random order.
+
+Procedure
+
+Stimuli were displayed on a linearized 22” LCD monitor (resolution 1920 x 1080 pixels, refresh rate 60 Hz). Observers were positioned 57 cm from the monitor, in a quiet room with dim lighting, and maintained fixation on a small (0.35 deg) black central dot. After a random delay from the observer initiating the trial, the stimulus was displayed for 167 ms. Then a thin rotatable white bar (0.05 x 5 deg with a gaussian profile) was presented at the fixation point with random orientation, and observers matched its orientation to that of the target by mouse control. In the first two experiments, the orientation of the two flankers was yoked, while in the third, one flanker was always +15° (clockwise) while the other varied from -45° to +45°. In the second experiment, the target-flanker distance varied, being 5.5, 7.5, 11.0 and 16.6 deg, leading to Bouma ratios of 0.21, 0.27, 0.4, 0.6.
+
+Ten observers participated in the first experiment, five in the second, thirteen in the third. They contributed for a total of 10699 trials for the first experiment, 14377 for the second (spread across the four flanker-target distances) and 16574 for the last.
+Data analysis
+
+Responses occurred out from the range between 0.5 and 3 seconds after the stimulus offset were removed (for a total of 15.9% trials across the 3 experiments), as were responses with reproduction error greater than 35° (6.9% of trials).
+
+For each target and relative orientation of the flanker, we calculated the average constant error (bias, positive meaning clockwise) and scatter. We then averaged the values for the two targets. Bias functions were fitted by a derivative of gaussian function, which can be considered to be a gaussian of width s multiplied by a straight line of slope a [or w], which can be considered the weighting given to the flankers: 1 means the flankers are weighted equally to the target. Bias is given by:
+
+\[
+B = a \cdot (\theta - m) \exp \left( - \frac{(\theta - m)^2}{s^2} \right) + b
+\]
+
+[eq. 18]
+
+Where \( \theta \) is orientation difference, \( m \) the centre, and \( b \) the vertical offset of the function. \( a \), \( b \) and \( m \) were free to vary.
+
+Scatter (\( S \)) was defined as the average root variance in each condition. The variation with orientation a gaussian function in the form:
+
+\[
+S = a \cdot \exp \left( - \frac{(\theta - m)^2}{s^2} \right) + b
+\]
+
+[eq. 19]
+
+Where \( b \) is the baseline at high orientation differences and \( a \) is the amplitude of the Gaussian. As Bias and Scatter likely originate from the same process, we yoked the parameter \( s \) to best fit both curves.
+
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+Peer Review File
+
+Changes in limiting factors for forager population dynamics in Europe across the Last Glacial-Interglacial Transition
+
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+Reviewers’ Comments:
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+Reviewer #1:
+Remarks to the Author:
+This study aims to identify the limiting climate factors of hunter-gatherer population density in Europe from the LGM to early Holocene, which is a tempting research question that, if answered convincingly, could provide clues in resilience and adaptation strategies of ancient human societies. The authors built statistical models (quantile Generalised Additive Models) of population density versus each of the 18 climate variables based on contemporary hunter-gatherer dataset, and hindcasted population density using paleoclimate outputs from a climate model. This workflow and statistical techniques are not new (e.g. Tallavaara et al. 2015 pnas), but selecting the factor that predicts the lowest population density across space and time, based on the concept of limiting factor, provides a fresh angle of view. However, I have some major concerns about the robustness of the analysis and significance of current results, as outlined below. Based on these, I cannot recommend its publication, at least not in its current form.
+
+Robustness of results:
+Mean temperature of the Warmest Month (MWM) is identified a major limiting factor during all critical periods (Fig. 4), but MWM is the variable that has the most severe non-analogy problem comparing present-day climate space and past climates (Fig. 2 and Supplementary material S2). Although mentioned at Lines 126-128, considering the strong relevance to the main findings, the risk of an unreliable extrapolation out of the range of data used to fit the statistical model is higher than acknowledged here.
+In addition, it is not clear to me why the authors chose 90th percentile of population density to do the hindcast. First, the results, in principle, would not be comparable to previous estimates in literature. Second, does the resulted limiting factors change dependent on the choice of the percentile? Although the general shape of the population density versus climate relationship looks similar across different percentiles for each individual climate factor (Lines 311-312), it is the relative magnitudes between all predicted densities by these factors that ultimately selects the limiting factor. Thus, it is not straightforward whether your results are sensitive to the choice of percentiles.
+Regarding the comparison between hindcasted population density and the archeological population proxy (Fig. 3), I would not say they are “in line with” each other (Lines 139-140). The black curve in Fig. 3 starts to increase already since 18 ka, which is relatively flat in the red curve; the red curve increases significantly during GI1 and GS1, whereas it is stale in the black curve.
+By the way, at Lines 101-103, why do you separate higher and lower predictive accuracy by a threshold of “explained deviances < 0.79”? According to Table 1, these predictors are all so close.
+
+About mechanism insights:
+From the results it is hard to infer mechanisms regarding how the identified limiting factor has constrained population density. This is limited by the fact that only temperature and precipitation and their variants were used as predictors, without direct information about productivity; whereas climate impacts population density via indirect effects on ecosystem attributes like NPP (e.g. Freeman et al. 2020, doi:10.1016/j.jas.2020.105168). Throughout the text the authors have tried to relate some of the factors to environmental productivity, but it was highly speculative. Let me take Lines 185-192 as an example. During 14.7ka to 11.7ka, the importance of ET decreases while importance of MWM and temperature seasonality increases. But all three variables are linked to NPP (and possibly other aspects of the ecosystem). From these changes one still cannot judge what process is taking effect in the end.
+Given this, why not use NPP as a predictor in the first place? Data availability for the hindcast should not be a problem since simulated NPP for the past 21,000 years are publicly accessible from some climate models already.
+
+Significance of the results in archaeological perspective:
+I commend the authors’ effort to put the (more of ecology-oriented) results into archaeological
+context, but currently it is still limited in qualitative descriptions scattered in the text. If the authors could achieve a more systematic compilation of archaeological records regarding how these societies have tackled with the limiting climate factors and find a consistency with your hindcasted results in space and time, it would add much merit to this study, with broader significance and impacts.
+
+Aside from the above concerns, the organization of Results and discussion needs to be improved. Adding sub-headings would help. Besides, descriptions of the results in the text should be more careful. Currently they are sometimes inconsistent with the table or figures. For example, at Lines 104-110, it says seasonal temperature variables are among the lowest explained deviance, which is not the case as listed in Table 1.
+
+A minor point is that the uncertainties/biases in the paleoclimate outputs of the CCSM3 climate model should be discussed.
+
+Code availability: though not mandatory, it is strongly encouraged to make the code readily available so as to enable reproduction of the results.
+
+Table 1: A conceptual confusion: MCM is not “extreme events”. Same for MWM, PDM, and PWM. Extreme events are events that occur with low frequency, not the regular seasonal maxima or minima.
+
+There are a few careless errors in the manuscript, for example:
+Line 266: “16 climatic predictors”: there are 18 climate variables in Table 1.
+Line 289: it says “We use a subsample of 159 hunter-gatherers populations...” in the Reporting summary, while here it says “127 populations”.
+Table 1: Acronym of “Precipitation of the Wettest Month” should be PWM, not PDM.
+Figure caption of Fig. 3: “Minimum temperature of the Coldest Month” should be “Mean…”, and “Maximum temperature of the Warmest Month” should be “Mean…”
+Figure caption of Supplementary material S1: it is not “the six most important environmental factors”. Please check carefully throughout the paper.
+
+Reviewer #2:
+Remarks to the Author:
+This is truly thought-provoking, highly interesting and novel contribution to the hunter-gatherer ecology. I very much like the approach of applying the analysis of ecological limiting factors, for the first time, to prehistoric hunter-gatherers. Below I have highlighted few issues that you could consider to revise to further improve the paper.
+
+Best regards,
+Miikka Tallavaara
+
+1.
+Given that many of the climate predictors are highly correlated (as you also write in the manuscript), they will convey partly the same information. This can potentially make it difficult to differentiate the importance between different climatic variables as limiting factors. I would suggest that you add some more justification for using large number correlated variables in the analysis. Or, alternatively, consider reducing the dimensionality of the data.
+
+2.
+Partly related to the item 1, you could provide justification for using univariate instead of multivariate approach. The effect of a predictor variable can change (sometimes dramatically) when controlled for the effects of other variables by adding them to the model. Therefore, you should explain why you rely on univariate approach, or, alternatively, try to add the best predictor candidates in the same model
+and see how the results would change.
+
+3.
+Binford’s data is notorious for spatial auto-correlation, especially because in particular areas, he has basically split closely living ecologically, demographically and culturally similar groups into smaller units even though one might consider many of those belonging to the same ethnic group. This can lead to inflated performance metrics in traditional cross-validation schemes. The idea of cross-validation is to test the model with data that the model has not seen before, so in the presence of spatial auto-correlation, test data can be “too” similar to training data. Therefore, your performance metrics are quite likely “too good” and I suggest that you could use some kind of spatial block cross-validation scheme, such as h-block cross validation. See, e.g.
+Salonen, J.S., et al, 2016. Calibrating aquatic microfossil proxies with regression-tree ensembles: Cross-validation with modern chronomid and diatom data. The Holocene 26, 1040–1048.
+https://doi.org/10.1177/0959683616632881
+https://quantpalaeo.wordpress.com/2013/12/15/h-block-cross-validation-of-transfer-functions/
+https://cran.r-project.org/web/packages/blockCV/vignettes/BlockCV_for_SDM.html
+
+4.
+Related to the above issue, on page 3 you write that no single environmental variable explained more than 81% of the population density variation among ethnographic foraging societies. It might be because of my ignorance of quantile regression, but I’m not sure if you can really say that quantile regression model can explain some percentage of the variation in a response variable. So clarify this and explain what the explained deviance is measuring in your quantile regressions, is it the goodness of fit of the 90th quantile or what?
+
+I’m also not sure if one can directly compare your performance metrics (explained deviance) to e.g. our metrics (R2) (Tallavaara et al. 2015). Besides, our R2 e.g. for multivariate GAM is clearly smaller (0.6), not marginally better, than any your values. After a lot of exploration with Binford’s data, I also think that it is really difficult to push the R2 of (multivariate) population density models well above 0.7 unless you really overfit the model.
+
+5.
+On page 5, you provide the modelled population size estimates for Europe, which seems to be pretty high. The LGM estimate is twice as large as our previous estimate (which has been argued to be way too large by some) despite we having larger geographical area. However, am I right that your estimates are actually maximum estimates based on the modelled 90th quantile? Whatever the case, this needs to be stated clearly in the text and in the relevant figure captions.
+
+6.
+I might have missed it somehow, but which of the many univariate models you are using when estimating the population size or average density (including figures 3 and 4a–e)? Or is it ensemble of all models? This is nevertheless important information and if it is missing, you should clearly provide the information in the text and also to relevant figure captions.
+
+7.
+Mean temperature of the warmest month seems to be one of the most important limiting factors of hunter-gatherer density in Europe (Table 1, Figure 4). It is therefore interesting that its impact on maximum hunter-gatherer density is negative between 22kyBP and 8kyBP (figure 5B). The figure 1 shows that between 10 and 15 C the 90th quantile of MWM is decreasing, because of couple of outlier points. These kind of “edge effects” are a known problem in GAMs and therefore there are different kinds of constrained GAMs available:
+https://www.researchgate.net/publication/271740857_Shape_constrained_additive_models
+https://arxiv.org/pdf/1812.07696.pdf
+It is nevertheless quite unrealistic to assume that increase of MWM would have had negative impact on forager density from the LGM to Mid Holocene and I therefore suggest that you either try to use more conservative smoothing parameter value to get rid of wiggles or switch to constrained GAM, although I dont know if there are quantile versions available for such techniques. The negative (but unrealistic) effect of MWM is at least one of the reasons why MWM appears to increase its importance as a limiting factor over time in Europe.
+
+8.
+On page 5, you describe your results so that during the LGM the northern limit of human range would have been in central France and southern Germany. However, my reading of figure 4 is that the whole of France would have been within the human range. You use one individual/100km2 as threshold for human occupancy, which is pretty high given that lowest densities in ethnographic data are 0.2–0.25 individuals/100km2. But even with your threshold, the occupied area seems to be clearly bigger than you describe in the text. Why this discrepancy? I would suggest that you bravely stand behind your results and describe them as they are :-)
+
+Reviewer #3:
+Remarks to the Author:
+The manuscript focuses on the relation between the environmental factors explored here and population density. One central assumption that is adopted in this paper is that for foragers, demographic and environmental changes correlate strongly. And that there are causal relations between different environmental variables and human responses through time and Space. They then focus on limiting environmental factor which are defined as the variable predicting the lowest population density at a given place and time and assume that one of these limiting factors, or a combination of several, limited the scarcest recourse, and in turn regulate population sizes and densities. They then identify the dominant climatic constraints for hunter-gatherer population densities and then hindcast their changing dynamics in Europe for the period between 20kyBP to 8kyBP. They detect spatiotemporal variations in these factors in relation to the assessed demographic data for human groups which suggests that European Upper Palaeolithic hunter-gatherers at various regions and periods needed to overcome very different adaptive challenges.
+
+The paper is overall well written and the introduction and Results and Discussion are detailed, and cite a lot of relevant and up to date sources. Moreover, the main caveats associated with their data sources and analyses are mentioned and discussed
+
+I would like to raise three issues which I think can be handled in the revised manuscript.
+
+One is that while I agree that environmental changes seem to have been the main driving force behind evident demographic patterns in the case of human populations and various other species, as the authors indicate, there are also adaptive capacities of humans to buffer and manage at least to some extent, environmental changes and corresponding resource fluctuations. The cited paper by Filho et al. 2021, documents how several African communities deferentially adapted to climate changes. If we assume that at least some of the human groups, during the Last Glacial Maximum and post-LGM period had similar adaptive capacities, it follows that their population sizes, densities an even settlement patterns, will not only reflect a ‘passive’ causal relationship with a specific climatic limiting factor, but also a unique human capacity to buffer and perhaps even overcome some limitation. Some examples include shelters, fire, and projectile technology. Moreover, one of the main mechanisms is mobility and mainly dispersals to refugia with better resources and climatic conditions.
+
+A second issue is the reliance on ethnographic data. The authors cite the article by Bird a& Coddig
+2021, about the Promise and peril of ecological and evolutionary modelling using cross-cultural datasets. While the authors of this paper claim that the promise outweighs the peril. It will be useful for the authors to mention in more details, the potential caveats of drawing the analogy between present day and Upper Palaeolithic hunter-gatherers, since various papers argued that the former are not really a good proxy for the latter.
+
+A third issue is that on page 6, Figure 3, they refer to the date of recolonization of Europe to be 17 kyBP. This is no longer regarded, on the basis of archaeological data, as being the date of onset of the process, as new results indicate that it started around 19 kyBP- see the paper by Maier et al. 2020: https://doi.org/10.1007/s41982-019-00045-1
+
+In sum, the paper is informative and balanced but the above-mentioned points are raised as the way some of the text is worded, it seems that the underlying approach is that human demography is not only affected by environmental shifts, and more specifically climatic changes, but is directly caused only by these. In which case, the assessmentof which specific limiting factor exerted the most impact on a given human populations at a given location and time is indeed informative and interesting. But it should be made clearer that the paper does not test the specific role of human cultural capacities, to buffer and even overcome some limiting factors. Moreover, the spatiotemporal variations are expected to be a reflection of the fact that indeed limiting factors varied and that hunter-gatherers needed to overcome different adaptive challenges, but they cannot shed light on how they actually adapted, or alternatively failed to adapt, to these changes.
+
+Minor comments
+Some of the figures need to be improved in terms of colors and legends.:
+
+Figure 1. What are the abscissa? It is not clear from the figure legend.
+
+Figure 3, Change color for Maximum temperature of the Warmest Month.
+
+Figure 4, side panel legend, should be Population density and not population size
+It is also difficult to understand the panels, what is the difference between each side and the colors are difficult to detect at this scale.
+
+Figure 5, is it assessing population size or population density?
+Final responses:
+
+R1c1: Mean temperature of the Warmest Month (MWM) is identified a major limiting factor during all critical periods (Fig. 4), but MWM is the variable that has the most severe non-analogy problem comparing present-day climate space and past climates (Fig. 2 and Supplementary material S2). Although mentioned at Lines 126-128, considering the strong relevance to the main findings, the risk of an unreliable extrapolation out of the range of data used to fit the statistical model is higher than acknowledged here.
+
+To acknowledge the points made by the reviewer regarding the non-analogy problem with the variable, Mean temperature of the Warmest Month, we remove this variable from the pool of factors used to assess population densities and limiting factors. We explain this in the text in L137-140 and L401-403. We do not consider that removing this variable is a significant problem for our analyses. We reason that our objective is not to determine how a specific variable determines population densities but on the possible processes (as we specify in Table 1) by which climate can determine population densities.
+
+R1c2: It is not clear why the authors chose 90th percentile of population density to do the hindcast. First, the results, in principle, would not be comparable to previous estimates in literature. Second, does the resulted limiting factors change dependent on the choice of the percentile? Although the general shape of the population density versus climate relationship looks similar across different percentiles for each individual climate factor (Lines 311-312), it is the relative magnitudes between all predicted densities by these factors that ultimately selects the limiting factor. Thus, it is not straightforward whether your results are sensitive to the choice of percentiles.
+
+The reviewer’s point regarding the need to justify why we chose the 90th percentile in our analyses is welcomed. We have done all the analyses using the 10th, 50Th, and 90th percentile in this revision. As we now clarify in the text (L62-63; L365-359; L407-412), our goal is not to quantify the population size on each evaluated grid but to indicate what are the potential climatic limiting factors and which could be the expected values (maxi-mum/average/minimum) given this climatic limit. Furthermore, our results and discussion focus on how observed deviations from these estimates can be used to generate hypotheses to how different societies have (or not) tackled these climatic limits, allowing them to have larger population sizes.
+
+R1c3: Regarding the comparison between hindcasted population density and the archaeological population proxy (Fig. 3), I would not say they are “in line with” each other (Lines 139-140). The black curve in Fig. 3 starts to increase already since 18 ka, which is relatively flat in the red curve; the red curve increases significantly during GI1 and GSI, whereas it is stale in the black curve.
+
+While we now acknowledge the nuanced description of the trends by the reviewer in the text (L172-176), we consider that a perfect match on the timing of events cannot be expected as these are variables representing trends at two different resolutions. Having
+said that, the archaeological population proxy and our population density estimates show a strong correlation (rho = -0.7) when aggregated at the same temporal resolution as the archaeological population proxy. We now make this point explicit in our text (L172-176).
+
+R1c4: By the way, at Lines 101-103, why do you separate higher and lower predictive accuracy by a threshold of “explained deviances < 0.79”? According to Table 1, these predictors are all so close.
+We do make this distinction anymore. Now we acknowledge that there are differences in the predictive accuracy between variables, but that accuracy amongst predictors is somewhat similar (L122-124).
+
+R1c5: From the results it is hard to infer mechanisms regarding how the identified limiting factor has constrained population density. This is limited by the fact that only temperature and precipitation and their variants were used as predictors, without direct information about productivity; whereas climate impacts population density via indirect effects on ecosystem attributes like NPP (e.g. Freeman et al. 2020, doi:10.1016/j.jas.2020.105168). Throughout the text the authors have tried to relate some of the factors to environmental productivity, but it was highly speculative. Let me take Lines 185-192 as an example. During 14.7ka to 11.7ka, the importance of ET decreases while importance of MWM and temperature seasonality increases. But all three variables are linked to NPP (and possibly other aspects of the ecosystem). From these changes one still cannot judge what process is taking effect in the end. Given this, why not use NPP as a predictor in the first place? Data availability for the hindcast should not be a problem since simulated NPP for the past 21,000 years are publicly accessible from some climate models already.
+To address the comment, we have done two things:
+First, we no use Net Primary Productivity (NPP) in our work as a predictor. Using the Miami model, we calculate this variable (Lieth, 1972, as described in Table 1). We use this modelling approach instead of other possible NPP products as we want to reduce the potential biases that could come from using environmental datasets from alternative sources. As we do this, NPP as a predictor shows that it is not a significant factor.
+Second, we now refer to Effective Temperature and Potential Evapotranspiration as factors determining energy availability in a broad context (Table 1). NPP relates only to a variable indicating the energy available to hunter-gatherers from primary producers.
+
+R1c6: I commend the authors’ effort to put the (more of ecology-oriented) results into archaeological context, but currently it is still limited in qualitative descriptions scattered in the text. If the authors could achieve a more systematic compilation of archaeological records regarding how these societies have tackled with the limiting climate factors and find a consistency with your hindcasted results in space and time, it would add much merit to this study, with broader significance and impacts.
+Thank you for this comment – naturally, we love to expand on this particular issue. We now provide an extended discussion of how the archaeological record explicitly links to the identified limiting factors and how different forager groups overcame these. We also provide additional references relating to pyrotechnology, shelter, energy capture, etc. (e.g., L223-226 and L262–271).
+
+R1c7: Aside from the above concerns, the organization of Results and discussion needs to be improved. Adding sub-headings would help. Besides, descriptions of the results in the text should be more careful. Currently they are sometimes inconsistent with the table or figures. For example, at Lines 104–110, it says seasonal temperature variables are among the lowest explained deviance, which is not the case as listed in Table 1.
+
+As suggested, we have added subheadings to the Results and discussion section to provide a clear outline of our study results and their implication and relevance. We have now addressed all inconsistencies between the tables, figures and text.
+
+R1c8: A minor point is that the uncertainties/biases in the paleoclimate outputs of the CCSM3 climate model should be discussed.
+
+We would like to evaluate and discuss how CCSM3 SynTrace paleoclimate simulations uncertainties propagate to our population density models and definition of limiting factors. However, the used downscaled and debiased paleoclimatic simulations do not contain uncertainty estimates, and this is a point we acknowledge in our manuscript methods (L394-397).
+
+R1c9: Code availability: though not mandatory, it is strongly encouraged to make the code readily available so as to enable reproduction of the results.
+
+We have now made the code and data used in this study available through a project GitHub site: https://github.com/AlejoOrdonez/PaleoPopDen. This is now part of the data availability statement.
+
+R1c10: Table 1: A conceptual confusion: MCM is not “extreme events”. Same for MWM, PDM, and PWM. Extreme events are events that occur with low frequency, not the regular seasonal maxima or minima.
+
+We have now renamed these as annual limits.
+
+R1c11: Line 266: “16 climatic predictors”: there are 18 climate variables in Table 1.
+
+We have now change these to the current number of predictors.
+
+R1c12: Line 289: it says “We use a subsample of 159 hunter-gatherers populations...” in the Reporting summary, while here it says “127 populations”.
+
+We have corrected this to there is consistency with the Reporting summary.
+
+R1c13: Table 1: Acronym of “Precipitation of the Wettest Month” should be PWM, not PDM.
+
+We have corrected this as suggested.
+R1c14: Figure caption of Fig. 3: “Minimum temperature of the Coldest Month” should be “Mean...”, and “Maximum temperature of the Warmest Month” should be “Mean...”
+We have changed the figure layout to include all used variables and ensure the titles and legend match Table 1
+
+R1c15: Figure caption of Supplementary material S1: it is not “the six most important environmental factors”.
+We have removed this figure as all regressions are now shown in the main text.
+
+R2c1. Given that many of the climate predictors are highly correlated (as you also write in the manuscript), they will convey partly the same information. This can potentially make it difficult to differentiate the importance between different climatic variables as limiting factors. I would suggest that you add some more justification for using large number correlated variables in the analysis. Or, alternatively, consider reducing the dimensionality of the data.
+While we acknowledge in our study that the level of correlation between predictors is high, this level of relationship amongst predictors allows us to “[justify] our grouping of individual variables within groups of possible explanatory mechanisms (as listed in Table 1)” (L69-74; L124-129; and L326-327). We also provide further justifications for this in our response to the reviewer’s flowing point.
+
+R2c2. Partly related to the item 1, you could provide justification for using univariate instead of multivariate approach. The effect of a predictor variable can change (sometimes dramatically) when controlled for the effects of other variables by adding them to the model. Therefore, you should explain why you rely on univariate approach, or, alternatively, try to add the best predictor candidates in the same model and see how the results would change.
+As we now explicitly state in our text, “we are not aiming at determining the best combination of variables to predict population density, but rather at determining the limiting effect of a given environmental driver” (L69-74). This perspective aligns with the core idea of limiting factors behind the current study.
+
+R2c3. Binford’s data is notorious for spatial auto-correlation, especially because in particular areas, he has basically split closely living ecologically, demographically and culturally similar groups into smaller units even though one might consider many of those belonging to the same ethnic group. This can lead to inflated performance metrics in traditional cross-validation schemes. The idea of cross-validation is to test the model with data that the model has not seen before, so in the presence of spatial auto-correlation, test data can be “too” similar to training data. Therefore, your performance metrics are quite likely “too good” and I suggest that you could use some kind of spatial block cross-validation scheme, such as h-block cross validation.
+As suggested, we have used an h-block cross-validation approach (L68; L377-383; L398-401) to determine, for each qGAM model, its’ performance and use these multiple models to control for model specification variability in our estimates of Population Density.
+
+R2c4. Related to the above issue, on page 3 you write that no single environmental variable explained more than 81% of the population density variation among ethnographic foraging societies. It might be because of my ignorance of quantile regression, but I’m not sure if you can really say that quantile regression model can explain some percentage of the variation in a response variable. So clarify this and explain what the explained deviance is measuring in your quantile regressions, is it the goodness of fit of the 90th quantile or what?
+You are right in your assessment that quantile GAMs cannot provide an estimate of the “percentage of the variation in a response variable” (i.e., R2). Our values here refer to the 50th percentile qGAM (or a traditional GAM), a point that was not clear in the original submission. For these, it is possible to determine an R2 value. This revision ensures that the point is explicitly made in the text (L374-377). In both the main text and the method section (L110-120; Table 1), we now also describe the model deviance!
+
+R2c5. I’m also not sure if one can directly compare your performance metrics (explained deviance) to e.g. our metrics (R2) (Tallavaara et al. 2015). Besides, our R2 e.g. for multivariate GAM is clearly smaller (0.6), not marginally better, than any your values. After a lot of exploration with Binford’s data, I also think that it is really difficult to push the R2 of (multivariate) population density models well above 0.7 unless you really overfit the model.
+We agree that a proper comparison between the performance of our models and those in other publications is not so straightforward. Therefore decided to omit this statement in the revised text.
+
+R2c6. On page 5, you provide the modelled population size estimates for Europe, which seems to be pretty high. The LGM estimate is twice as large as our previous estimate (which has been argued to be way too large by some) despite we having larger geographical area. However, am I right that your estimates are actually maximum estimates based on the modelled 90th quantile? Whatever the case, this needs to be stated clearly in the text and in the relevant figure captions.
+We are aware of this, and it is a result of us using the 90th percentile model when describing these trends – as accurately pointed out in the comments. This revision states that “Taken at face value, these figures are gross overestimations of actual sustained and demographically viable human land-use across this timeframe” (L169-170). Furthermore, we state in the text that our goal is NOT to predict population density but rather to show the limiting effects of climate on this important variable (L74-76). Therefore, it makes sense to consider maximum (90th-percentile), average (50th-percentile), and minimum (10th-percentile) values as descriptors of these possible
+limits. These are clarifications we also make when describing our population size/density estimates (L154-169; L177-180).
+
+R2c7. I might have missed it somehow, but which of the many univariate models you are using when estimating the population size or average density (including figures 3 and 4a–e)? Or is it ensemble of all models? This is nevertheless important information and if it is missing, you should clearly provide the information in the text and also to relevant figure captions.
+
+This information was only in the methods in the original submission (L386-397), and now it is part of the main text (L84-89) and the relevant legends.
+
+R2c8. Mean temperature of the warmest month seems to be one of the most important limiting factors of hunter-gatherer density in Europe (Table 1, Figure 4). It is therefore interesting that its impact on maximum hunter-gatherer density is negative between 22kyBP and 8kyBP (figure 5B). The figure 1 shows that between 10 and 15 C the 90th quantile of MWM is decreasing, because of couple of outlier points. These kind of “edge effects” are a known problem in GAMs and therefore there are different kinds of constrained GAMs available.
+It is nevertheless quite unrealistic to assume that increase of MWM would have had negative impact on forager density from the LGM to Mid Holocene and I therefore suggest that you either try to use more conservative smoothing parameter value to get rid of wiggles or switch to constrained GAM, although I dont know if there are quantile versions available for such techniques. The negative (but unrealistic) effect of MWM is at least one of the reasons why MWM appears to increase its importance as a limiting factor over time in Europe.
+
+Thanks for your point regarding the patterns in this variable. This is one of the points we have been discussing in our revision. Given the issues highlighted in this comment and the points raised by Reviewer-1 (the fact that there is a large non-analogy for this variable, especially in the late Pleistocene), we have decided to remove this variable from our analyses. As we discussed in R1C1, we do not consider this a significant problem for our work. Our reasoning is that because our focus is mainly on the “environmental mechanisms” by which climate imposes a limitation to population density (captured usually by two to three variables in our dataset) and not the effect of an individual variable.
+
+R2c9. On page 5, you describe your results so that during the LGM the northern limit of human range would have been in central France and southern Germany. However, my reading of figure 4 is that the whole of France would have been within the human range. You use one individual/100km2 as threshold for human occupancy, which is pretty high given that lowest densities in ethnographic data are 0.2–0.25 individuals/100km2. But even with your threshold, the occupied area seems to be clearly bigger than you describe in the text. Why this discrepancy? I would suggest that you bravely stand behind your results and describe them as they are.
+This text section is now modified (L188-192) to reflect a more detailed discussion of the observed pattern.
+
+R3c1. One is that while I agree that environmental changes seem to have been the main driving force behind evident demographic patterns in the case of human populations and various other species, as the authors indicate, there are also adaptive capacities of humans to buffer and manage at least to some extent, environmental changes and corresponding resource fluctuations. The cited paper by Filho et al. 2021, documents how several African communities deferentially adapted to climate changes. If we assume that at least some of the human groups, during the Last Glacial Maximum and post-LGM period had similar adaptive capacities, it follows that their population sizes, densities an even settlement patterns, will not only reflect a ‘passive’ causal relationship with a specific climatic limiting factor, but also a unique human capacity to buffer and perhaps even overcome some limitation. Some examples include shelters, fire, and projectile technology. Moreover, one of the main mechanisms is mobility and mainly dispersals to refugia with better resources and climatic conditions.
+
+The reviewer points to one of the main points we wanted to showcase with this study, but perhaps it was not clear – that climate sets a stage for human adaptation to “act” (L289-297). You could see this as climate determining a baseline “limit”, where human-populations active interaction with the environment, via behaviour and tools, would result in a deviation from this limit. This is a point we make explicit in our text (L293-297), indicating that deviations from our estimates can be used to signpost which populations had buffering strategies and generate hypotheses as to which could these strategies be.
+
+R3c2. A second issue is the reliance on ethnographic data. The authors cite the article by Bird a& Coddling 2021, about the Promise and peril of ecological and evolutionary modelling using cross-cultural datasets. While the authors of this paper claim that the promise outweighs the peril. It will be useful for the authors to mention in more details, the potential caveats of drawing the analogy between present day and Upper Palaeolithic hunter-gatherers, since various papers argued that the former are not really a good proxy for the latter.
+A paragraph on the inferential limits of the available ethnographic datasets has been added (L148-152). However, we do consider a very detailed discussion of these issues outside of the scope of this particular study, not least because it has been discussed directly in the recent literature, e.g.: Hamilton, M.J., Tallavaara, M., 2022. Statistical inference, scale and noise in comparative anthropology. Nature Ecology & Evolution 6, 122–122. https://doi.org/10.1038/s41559-021-01637-3
+
+R3c3. A third issue is that on page 6, Figure 3, they refer to the date of recolonization of Europe to be 17 kyBP. This is no longer regarded, on the basis of archaeological data, as being the date of onset of the process, as new results indicate that it started
+around 19 kyBP- see the paper by Maier et al.
+2020: https://doi.org/10.1007/s41982-019-00045-1
+
+This text section has been amended (L201-203) and the appropriate reference added.
+
+R3c4. In sum, the paper is informative and balanced but the above-mentioned points are raised as the way some of the text is worded, it seems that the underlying approach is that human demography is not only affected by environmental shifts, and more specifically climatic changes, but is directly caused only by these. In which case, the assessment of which specific limiting factor exerted the most impact on a given human populations at a given location and time is indeed informative and interesting. But it should be made clearer that the paper does not test the specific role of human cultural capacities, to buffer and even overcome some limiting factors. Moreover, the spatio-temporal variations are expected to be a reflection of the fact that indeed limiting factors varied and that hunter-gatherers needed to overcome different adaptive challenges, but they cannot shed light on how they actually adapted, or alternatively failed to adapt, to these changes.
+Thank you for the thoughtful summary of our ideas in our study. We have now added text to ensure the points the reviewer so correctly highlights are even more evident in the text. Notably, the ideas of environmental conditions as factors affecting and determining human demography in the evaluated period (L42-44) determine how technology or behaviour resulted in particular populations overcoming the limitations imposed by the rapid clitic changes of the late-Pleistocene (L74-78).
+
+R3c5. Some of the figures need to be improved in terms of colors and legends.: We have done a substation change in the figures color and legend to clarify their message, and fully explain what the objective of these is.
+
+R3c6. Figure 1. What are the abscissa? It is not clear from the figure legend.
+Figure 1 now show what is the variable in the Abscissa (the same as the title)
+
+R3c7. Figure 3, Change color for Maximum temperature of the Warmest Month.
+In figure-1, we have now plated all the used variables and used a colour scheme that facilitates the readability of the variables.
+
+R3c8. Figure 4, side panel legend, should be Population density and not population size. It is also difficult to understand the panels, what is the difference between each side and the colors are difficult to detect at this scale.
+Figure one has been redrawn, and the density and limiting factors maps have been speared to clarify and enhance the message of each plot.
+
+R3c9. Figure 5, is it assessing population size or population density?
+We now clarify that the top panel shows the changes in the evaluated period (21kyBP to 8kyBP) in the proportion of ice-free cells where a viable is considered the limiting
+factor (predicts the min population density). The bottom panel shows the estimated population density based on the average climatic condition across Europe for each evaluated variable.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+The authors have addressed my major comments by 1) removing the MWM variable in assessing the limiting climate factors so that the serious non-analogy problem can be bypassed; 2) testing NPP as a potential limiting factor in the analysis; and 3) extending the discussion regarding the significance of the results in archaeological perspective. Overall I’m satisfied with these revisions. But there are some points to be clarified in the revised manuscript:
+
+For the variable temperature seasonality, why are the values so large, ~2000 °C (Figure 1F and Figure 2F)? How is it calculated? And for precipitation seasonality, is it the standard deviation of the monthly precipitation?
+
+Table 1: why are the metrics substantially lower than that in the previous version? Is it because now you have used h-block cross validation to address spatial auto-correlation? Besides, why do the deviance explained and R^2 differ so much for some variables like PWM and TAP?
+
+Line 165: what is the threshold of population density to define an occupied grid cell?
+
+Figure 4: It would be more informative if you could overlay the localities of the archaeological sites that correspond to each time interval on the predicted population density maps. It can serve as a qualitative comparison. Besides, the current color legend looks weird – the ticks are not at the boundaries of each color segment.
+
+In addition, there are still quite a few careless errors and inconsistencies in the revised manuscript. Below are some examples.
+Line 110: “most of environmental variable produced models that explaining over 50% of the population density variation” – according to Table 1, the explanatory power of the variables are mostly below 50%.
+Line 230: “PET” here should be TAP?
+Line 234: “PET and TAP were the main limiting factors” – according to Fig. 6, it should be TS and TAP.
+Line 254-255: MWM is no longer used in the prediction.
+Table 1: “TSeson” and “PREC” – inconsistent with those in the text. And check the footnote of Table 1.
+Figure 1: The precipitation has been log-transformed, right? Need to specify it.
+Figure 3 lower panel: why Precip. Dryiest Month is higher than Precip. Wettest Month?
+Figure 5 caption: what is “F-J”?
+
+It is the authors’ job to closely check every sentence, figures and tables to avoid any inconsistency or contradiction!
+
+Reviewer #2:
+Remarks to the Author:
+Authors have successfully revised their manuscript. I have just one follow-up comment because authors might have misunderstood my earlier comment about models having one predictor at a time. My intention was not to suggest to add multiple predictors to achieve better predictive ability, but to take into account the fact that the effect of a predictor can change when one takes into account the effect(s) of other potential predictor(s).
+For example, ET and MCM both appear to be important limiting factors and also representing different kinds of limiting factors, ET relating to energy availability and MCM to annual limits. However, these variables are also highly correlated, which already indicates that it will be difficult to tell apart their
+individual effects. When you include both variables as predictors in the same model it actually turns out that the effect of ET is not statistically significant, response of population density to ET being more or less flat. Similarly, if you add e.g. NPP, ET and TS to the same model their effect (response shapes) are different from their effect when each is the only predictor in the model.
+
+To me, all this suggests that the real limiting effects of climate variables can be different from those you get when you include these variables separately as predictors. However, I don’t know how severe issue this truly is, but I would like to know your thoughts on that. If it really is an issue, one might use PCA to create uncorrelated climate variables and use these as predictors in the models.
+
+Best wishes,
+Miikka Tallavaara
+
+Reviewer #3:
+Remarks to the Author:
+I am fully satisfied with the revised version and with the revised manuscript and the changes.
+REVIEWER COMMENTS
+
+Reviewer #1
+
+R12Co. The authors have addressed my major comments by 1) removing the MWM variable in assessing the limiting climate factors so that the serious non-analogy problem can be bypassed; 2) testing NPP as a potential limiting factor in the analysis; and 3) extending the discussion regarding the significance of the results in archaeological perspective. Overall, I’m satisfied with these revisions. But there are some points to be clarified in the revised manuscript:
+We appreciate your assessment regarding our revision.
+
+R1C1. For the variable temperature seasonality, why are the values so large, ~2000 °C (Figure 1F and Figure 2F)? How is it calculated?
+Thanks for bringing this to our attention. Temperature Seasonality (TS) is estimated as the SD of mean annual temperatures X 100. For Clarity, we have now done two things. First, we now clarify that TS is measured as the SD of mean annual temperatures (so that values are in the same order of magnitude as other temperature variables). Second, we specify how (TS) is calculated in Table 1.
+
+R1C2. And for precipitation seasonality, is it the standard deviation of the monthly precipitation?
+As for TS, we now explain in table 1 how precipitation seasonality (PS) is estimated. In short, yes, it is calculated as the variation in monthly precipitation. However, instead of the SD in monthly precipitation, we use the Coefficient of Variation (CV) as this is the standard when estimating bioclimatic variables. We also clarify this in the “variable” and “units” columns of Table 1.
+
+R1C3. Table 1: why are the metrics substantially lower than that in the previous version? Is it because now you have used h-block cross validation to address spatial autocorrelation? Besides, why do the deviance explained and R^2 differ so much for some variables like PWM and TAP?
+Yes, the values are lower due to using an h-block cross-validation approach to define the random samples. Furthermore, two points explain the lower deviance-explained when compared to the R2 values. First, adding the variable does not add more explanatory power to the model compared to an intercept-only model (hence the low deviance explained and likely low unadjusted R2. Second, we can interpret the higher R2 as the models built on the training dataset can accurately describe the test dataset, which ensures the idea of model transferability. To ensure these points are clear, we add these points of clarification to table 1 legend.
+
+R1C4. Line 165: what is the threshold of population density to define an occupied grid cell?
+A cell was defined as occupied if our model predicted population densities above 0.2 individuals per 100km2 (the lowest densities in the ethnographic dataset). This point is added to the main text (L162-163) and the methods (L405-406).
+
+R1C5. Figure 4: It would be more informative if you could overlay the localities of the archaeological sites that correspond to each time interval on the predicted population density maps. It can serve as a qualitative comparison. Besides, the current color legend looks weird – the ticks are not at the boundaries of each color segment.
+We explored adding the localities of the archaeological sites to figure 4 but decided not to include these as these create an unnecessary layer of complexity for the figure. We also address the point raised by the reviewer regarding the figure colour legend.
+
+R1C6. Line 110: “most of environmental variable produced models that explaining over 50% of the population density variation” – according to Table 1, the explanatory power of the variables are mostly below 50%.
+We appreciate the reviewer catching this inconsistency coming from a legacy text from the first version. We now changed the sentence, so it does not specify a cut-off value (50%) but the range of mean deviance across the 1000 different models (L110).
+
+R1C7. Line 230: “PET” here should be TAP?
+We consider that here the variable to include is PET, as we are building from the idea of a relationship between productivity and Evapotranspiration. This is the case as the second point relates to energy availability, not climate variability. To further justify this link, we add a reference (L232).
+
+R1C8. Line 234: “PET and TAP were the main limiting factors” – according to Fig. 6, it should be TS and TAP.
+We appreciate the reviewer catching this inconsistency coming from a legacy text from the original submission. We now changed the sentence accordingly.
+
+R1C9. Line 254-255: MWM is no longer used in the prediction.
+We appreciate the reviewer catching this legacy text from the first submission. We have rephased this point (L256).
+
+R1C10. Table 1: “TSeson” and “PREC” – inconsistent with those in the text. And check the footnote of Table 1.
+The acronym was changed as suggested in the table for consistency with the text.
+
+R1C11. Figure 1: The precipitation has been log-transformed, right? Need to specify it.
+We have added this clarification to the corresponding axes in figure 1 and table 1.
+
+R1C12. Figure 3 lower panel: why Precip. Dryiest Month is higher than Precip. Wet-test Month?
+We appreciate the reviewer catching this inconsistency. This was a problem in the code calling the different variables after we removed the Temperature of the Warmest Month, which caused a mismatch between the names and the data plotted in the bottom panels of figure 3. The figure now has corrected this.
+
+R1C13. Figure 5 caption: what is “F-J”?
+We appreciate the reviewer catching this legacy text from the first submission. This text was removed.
+
+Reviewer #2.
+
+R2C1. Authors have successfully revised their manuscript. I have just one follow-up comment because authors might have misunderstood my earlier comment about models having one predictor at a time.
+My intention was not to suggest to add multiple predictors to achieve better predictive ability, but to take into account the fact that the effect of a predictor can change when one takes into account the effect(s) of other potential predictor(s).
+For example, ET and MCM both appear to be important limiting factors and also representing different kinds of limiting factors, ET relating to energy availability and MCM to annual limits. However, these variables are also highly correlated, which already indicates that it will be difficult to tell apart their individual effects. When you include both variables as predictors in the same model it actually turns out that the effect of ET is not statistically significant, response of population density to ET being more or less flat. Similarly, if you add e.g. NPP, ET and TS to the same model their effect (response shapes) are different from their effect when each is the only predictor in the model.
+To me, all this suggests that the real limiting effects of climate variables can be different from those you get when you include these variables separately as predictors.
+However, I don’t know how severe issue this truly is, but I would like to know your thoughts on that. If it really is an issue, one might use PCA to create uncorrelated climate variables and use these as predictors in the models.
+
+We thank the reviewer for his positive feedback on our revision and the clarification of his original point. As we now understand the reviewer’s point, the issue is that significant absolute effects from univariate models would not translate into relative effects determined by multivariate models.
+While we agree with the point, we consider that the multiple regression approach does not translate to the idea of limiting factors we are evaluating here. We argue that multiple regression coefficients indicate effects in the context of other variables (hence contingent on which variables are included or omitted in a model). Therefore, these determine how much each variable contributes to the change in population density. To define which variables set a lower boundary, we require a measure of absolute effects provided by univariate approaches. Focusing on the relative effects would not allow us
+to define limiting factors but which variable(s) contribute the most to changes in population density from the "regional" mean.
+Suppose we could build models for change in population density for each evaluated time bin. In that case, we could define the variable that contributes the most to population density at each time bin. Still, this is not a limiting factor but the variable that contributes the most to changes in population density form the regional average (i.e., the model intercept). Last, there is the issue of translating these relative effects into space, which our approach based on univariate models can do.
+Furthermore, while PCA, or other ordination approaches, could be used here to determine "groups of variables" and the variable most representative of such "group", we will still be looking at relative effects when using the two or three most important axes.
+There also be questions about how suitable it is to use the eigenvectors generated by the ordination under current conditions to "reorganize" past climatic surfaces where the correlations between variables change.
+In summary, we consider that using univariate models, while far from perfect, is a practical approach to assessing the absolute effects of each variable and comparing these between variables over time. Also, it allows us to link our models to a process. All these points are now made in the text (L72-80) and the methods (L364-368).
+
+Reviewer #3.
+I am fully satisfied with the revised version and with the revised manuscript and the changes.
+Thanks for your positive assessment.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+I’m satisfied with the revisions and have no further comments.
+
+Reviewer #2:
+Remarks to the Author:
+While I still slightly disagree with you about the effects of univariate vs multivariate models on the results, I’m happy to do so. It is good that you now explain in the manuscript your choices regarding the matter, so I’m fully satisfied with this revised manuscript.
+
+Best,
+Miikka Tallavaara
+REVIEWER COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+While I still slightly disagree with you about the effects of univariate vs multivariate models on the results, I’m happy to do so. It is good that you now explain in the manuscript your choices regarding the matter, so I’m fully satisfied with this revised manuscript.
+
+We appreciate your assessment regarding our revision and your willingness to agree to disagree regarding the effects of univariate vs multivariate models on the results.

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+Peer Review File
+
+Deep learning shows declining groundwater levels in Germany until 2100 due to climate change
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+Review of Deep learning shows declining groundwater levels in Germany until 2100 due to climate change by A. Wunsch, T. Liesch, and S. Broda
+In this work, the authors attempted to assess the potential impact of future climate on groundwater (GW) levels in 118 wells in Germany. To do this, they trained 1D CNN models using historic weekly GW observations from 1950 to 2015 (after gap filling), and then applied the trained CNN models to predict future GW levels by using projected precipitation and temperature as forcing. Although the motivation is good, I’m concerned with the validity of applying this data-driven approach to future climate scenarios.
+1. The known “unknowns” in this case, as the authors mentioned, are “anthropogenic groundwater withdrawals” and “associated with land-use changes”. There’s plenty of evidence suggesting many contemporary global hydrological models couldn’t simulate current-day human intervention very well, not to mention future scenarios. For example, a study by Scanlon et al. (2018) compared the simulated groundwater storage trends to that observed by GRACE satellites for a large number of global river basins and noticed large discrepancies between simulated and observed trends. In the future, as the authors mentioned “the impact of these factors will be exacerbated as water demand increases...” (L54). So the compounding effect caused by climate change and human intervention on GW may not be a linear one. Thus, using P and T to project future GW trend using data driven method is generally not reliable. For the same reason, I also question the main premise on L95-96, “…due to high prediction accuracy in the past, the selected sites are unlikely to be under the influence of strong groundwater withdrawals or comparable effects…” As I elaborate in the next bullet, a good performance on historical data is not a guaranty for future performance.
+
+2. It is well known that data driven methods are not good at extrapolation. In other words, these methods aren’t good at predicting instances that are not seen during training and they are not good at predicting nonstationary time series. If for some reason, there’s a change in trend or there are huge spikes that are out of the training data range, the data-driven methods will usually fail. As a case in mind, Sun et al. (2020) trained numerous machine learning models to predict total water storage in the U.S. However, significant wetting trends occurred in several basins during the “future” phase. The authors showed that the data-driven methods couldn’t capture the trend change well.
+3. Methodology wise, I’m concerned with using 1D CNN for time series forecasting, especially when dealing with long sequences (52 weeks). This is because CNN has a fixed reception field (in their work, the authors used a fixed kernel size 3), which cannot capture multiscale temporal correlations very well. Based on my own experience, LSTM would be a much better choice in terms of forecasting accuracy on time series with long memory.
+4. On data analysis part, data gap filling is a huge issue and almost deserves a separate analysis on its own. Here Figure 6 shows data availability is pretty limited pre-1980. Any interpolation will add artifacts to the time series. The authors treatment of this issue was surprisingly cursory. It’s not clear how the authors assessed the quality of gap filling.
+5. The authors showed temperature is a dominant predictor, which is not new as GW level in humid regions is generally dominated by seasonality. However, this is probably only valid in Germany, not valid in many other arid and semiarid regions that depend more on GW as a critical water supply. Thus, a more meaningful task would be to predict inter-annual GW change instead of full signal that’s dominated by seasonal variations and uncertain trend.
+References:
+Scanlon, B. R., Zhang, Z., Save, H., Sun, A. Y., Schmied, H. M., Van Beek, L. P., ... & Bierkens, M. F. (2018). Global models underestimate large decadal declining and rising water storage trends relative to GRACE satellite data. Proceedings of the National Academy of Sciences, 115(6), E1080-E1089.
+Sun, A. Y., Scanlon, B. R., Save, H., & Rateb, A. (2020). Reconstruction of GRACE Total Water Storage Through Automated Machine Learning. Water Resources Research, e2020WR028666.
+Rodell, M., Famiglietti, J. S., Wiese, D. N., Reager, J. T., Beaudoin, H. K., Landerer, F. W., & Lo, M.
+H. (2018). Emerging trends in global freshwater availability. Nature, 557(7707), 651-659.
+
+Reviewer #2:
+Remarks to the Author:
+Wunsch et al. present in their manuscript “Deep learning shows declining groundwater levels in Germany until 2100 due to climate change” some interesting results on the potential groundwater response on climatic changes. However, there are strong limitations which are currently not addressed and prevent results to be useful. To make valid statements on future groundwater levels it will be necessary to analyse much more the different RCPs and the different sources of uncertainty.
+1. The authors state they use only projections based on RCP 8.5 (l. 87). This is a major constraint and prevents to derive any general future predictions. Usually, the different RCP are used to analyse the bandwidth of potential future changes, therefore, using only the most extreme one (leading to the strongest changes and trends) requires some strong reasoning. Unfortunately, any reasoning or discussion of this point is completely missing in the manuscript. Without considering different RCPs the authors cannot claim to present valid predictions for 2100. However, for most parts of the manuscript this important limitation does not become clear. E.g. many of the results are written like forecasts (“heads will probably decrease”, “expected to show increased values”, etc.). Also, the title exaggerates the findings without mentioning the constraints.
+2. The authors present many results for the selected set of 6 different climate models. However, the climate model is only one source of uncertainty and not necessarily the most important one. Other sources of uncertainty which are probably relevant in this context include: groundwater model uncertainty (from the supplements it is evident that model performance differs between sites and that there are larger uncertainties for the simulation of extremes); scaling uncertainty (grid of 5x5km vs. borehole); statistical analysis uncertainty (limitations of MK-Test and trend analysis), emission scenario uncertainty (see above); etc. While the authors quantify and discuss climate model uncertainty, all the other uncertainties are neglected. However, without a reliable uncertainty analysis results are not useful and cannot depict the expectable changes of groundwater levels in Germany until 2100.
+
+Minor points:
+• I. 89 “represent 80% of the possible future climate signal” -> this high percentage is puzzling given that only one RCP is used in this study and hence a very small proportion of possible future climate signals is covered by the runs.
+• I. 106: Is a linear trend an appropriate functional form to describe the change? For example, in case the real trend at a station is rather exponential, the linear trend could give values that deviate for 2100 quite a bit. In general, the fitted values at the end of the timeseries quite often deviate from actual values.
+• II. 113 f.: unit of mm/y not clear. Seems like a rate of change (i.e. the slope of the trend line), but I guess that is not meant here.
+• II. 140 ff.: All these results are focussed on annual percentiles, correct? Above you mention the different water users and potential water conflicts, also different climatic changes within the year are mentioned -> did you also look on groundwater trends for the different seasons? Based on Figure 3 I can already guess that there are some relevant seasonal differences. These can be also very relevant for water management.
+• Figure 3: From my perspective this figure contains way too many plots which are too small to be readable.
+• I. 454: Probability values of Mann-Kendall are only valid in case of no autocorrelation which is usually not the case for groundwater records. Were autocorrelations calculated and timeseries pre-whitened?
+Reviewer #3:
+Remarks to the Author:
+Comments:
+
+This paper is of great interest not only from a scientific point of view but also for practitioners, as questions about our future water resources are piling up. It is an exciting contribution to study the future climatic impacts on groundwater quantity in the future. Referring to the text I have the following comments and questions:
+
+In my opinion, the title is somewhat misleading, as the paper only focuses on the worst-case scenario (RCP8.5) and ignores all other future projections. Current studies show that even with a 'business as usual' development - regarding CO2-emissions - the bandwidth of projected results will be partly below the range of the RCP8.5 projections, which means the effects for groundwater fluctuations is quite smaller. Therefore, it makes sense to mention the used RCP scenario in the paper title. This points out to the reader right from the start that only parts of the available climate projections was used.
+
+Line 12ff.: ...RCP8.5 scenario ... represent 80% of the bandwidth....
+From my point of view the following details are missing in the paper: Why only RCP8.5 projections are chosen? What does it mean, when 80% of the bandwidth is used? (Here, for example, the authors could refer to the IPCC classification of likelihoods).
+
+Line 28ff.: ...on groundwater and springs...
+It is true that groundwater plays a crucial role in some parts of Germany (and also on the national level in the whole). However, there are also federal states that increasingly use surface water. Perhaps this circumstance should therefore also be mentioned in order to differentiate the significance of the result on a regional level.
+
+Line 34ff.: ...less than 2% of the total withdrawal volume...
+Does this value apply to an average in Germany, or is it a regional figure that applies to all federal states?
+
+Line 41ff.: ...of several degrees...by 2100.
+Here it would be better to use the original literature, where the data were first described, such as by EURO-CORDEX or the Reklies-De project.
+
+Line 43ff.: For Europe...
+Why do the authors go from Germany to Europe, only to return to Germany later?
+
+Line 43ff.: snow dominated regions...
+What role does that play for Germany as a whole. I think that this is only relevant for the South.
+
+Line 43ff.: ...unconfined shallow aquifers...
+What about regions characterised by fractured aquifers or karstic aquifers? You cannot simply ignore the different aquifers with their different characteristics, which are totally different to shallow porous aquifers.
+
+Line 69ff.: ...declines up to 10 m close to the Alps...
+How big was the model error in this study? How good were the statements in relation to the prevailing groundwater thickness? What about areas with aquifers less than 10 m thickness?
+
+Line 81ff.: ...respective uppermost unconfined aquifer...
+How representative are the selected wells and springs for the whole of Germany or selected groundwater landscapes?
+Line 87ff.: ...downscaled 5 x 5 km2...
+How do this resolution and the size of the catchment of selected wells/springs fit together? Was a weighted allocation carried out?
+
+Line 103ff.: ...Germany by 2100...
+The references for the climatic information used are not primary references.
+
+Line 103ff.: ....exact values....
+If results from climate projections are used, there are no exact values but only bandwidths of the entire ensemble.
+
+Line 118ff.:...under the RCP8.5 scenario...
+From my point of view, it would be good to briefly draw a reference to the other scenarios in order to be able to better classify the results. For example, by pointing out that the approach used shows the greatest possible impact, whereas small effects are to be expected when other RCPs are used.
+
+Line 141ff.:...in 2100...
+What does this time indication mean? Since it is a 30-year average, different time periods are possible, such as 2071-2100 or similar. Please specify exactly.
+
+Line 142ff.:...the simulation (2014)....
+Why was 2014 chosen as the start of the simulation? Is this for technical or other practical reasons?
+
+Line 151 and others:.....significant trend...
+How was significant defined? When is a trend called significant? Since there are different approaches for testing the significance of data, further information would be useful.
+
+Line 216:...(2070-2100)...
+I think it should be 2071-2100.
+
+Line 243:... We do not find ....increasing mean trends...
+How does this fit with the statement that the amount of precipitation increases in the year?
+
+Line 272:... Even fewer significant shift...
+Are there any classification steps for significance?
+
+Line 284 and ff:... that temperature is mainly the driving factor for declining groundwater levels...
+It should be explicitly mentioned here that the results only apply to shallow aquifers. It would also make sense to define what is meant by "shallow aquifer". Finally, it could also be helpful to address the issue of the behavior of different aquifer types in the discussion.
+Response to Reviewers
+We thank the reviewers for their comprehensive reviews, and their appreciative and constructive comments. We are happy to read that our paper is described as "of great interest" and used the constructive criticism to substantially improve the manuscript. In the following, please find our answers (red) on the review comments (black). The line numbers in the review comments refer to the originally submitted manuscript, the line numbers in our answers refer to the revised version.
+
+Decision on Nature Communications manuscript NCOMMS-21-14445
+
+Dear Mr Wunsch,
+
+Thank you again for submitting your manuscript "Deep learning shows declining groundwater levels in Germany until 2100 due to climate change" to Nature Communications. We have now received reports from 3 reviewers and, after careful consideration, we have decided to invite a major revision of the manuscript.
+
+As you will see from the reports copied below, the reviewers raise important concerns. We find that these concerns limit the strength of the study, and therefore we ask you to address them with additional work. Without substantial revisions, we will be unlikely to send the paper back to review. In particular, reviewers agree the current approach limits the robustness of the conclusions. To move forward with a revised manuscript, additional analyses using other RCP scenarios is needed. We also agree with Reviewer #2 that a full accounting of sources of uncertainty would strengthen the utility of the results. While we do not require a change in methods, per Reviewer #1’s suggestion for the use of a long short-term memory network, we urge you to provide an expanded justification of the choices made in this analysis and representativeness of the selected wells (Reviewer #3).
+
+If you feel that you are able to comprehensively address the reviewers’ concerns, please provide a point-by-point response to these comments along with your revision. Please show all changes in the manuscript text file with track changes or colour highlighting. If you are unable to address specific reviewer requests or find any points invalid, please explain why in the point-by-point response.
+
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Review of Deep learning shows declining groundwater levels in Germany until 2100 due to climate change by A. Wunsch, T. Liesch, and S. Broda
+
+In this work, the authors attempted to assess the potential impact of future climate on groundwater (GW) levels in 118 wells in Germany. To do this, they trained 1D CNN models using historic weekly GW observations from 1950 to 2015 (after gap filling), and then applied the trained CNN models to predict future GW levels by using projected precipitation and temperature as forcing. Although the motivation is good, I’m concerned with the validity of applying this data-driven approach to future climate scenarios.
+
+Thank you very much for your assessment of the manuscript. We understand your concerns and try to answer in detail to the following statements.
+1. The known “unknowns” in this case, as the authors mentioned, are “anthropogenic groundwater withdrawals” and “associated with land-use changes”. There’s plenty of evidence suggesting many contemporary global hydrological models couldn’t simulate current-day human intervention very well, not to mention future scenarios. For example, a study by Scanlon et al. (2018) compared the simulated groundwater storage trends to that observed by GRACE satellites for a large number of global river basins and noticed large discrepancies between simulated and observed trends. In the future, as the authors mentioned “the impact of these factors will be exacerbated as water demand increases…” (L54). So the compounding effect caused by climate change and human intervention on GW may not be a linear one.
+
+Thank you for this comment. We completely agree with your assessment of the future development. We cannot account for land use changes, increased anthropogenic pumping and other such factors. Because of these reasons we do not state to project the real groundwater level development, but only the direct climatic influence under current boundary conditions. We have now better highlighted this aspect (L. 108-115, 401ff). Until now it remained unclear, what the pure climatically driven development of groundwater for Germany might be, because we do not have a very intuitive development of the climatic key forcings such as precipitation and temperature. T increases clearly but also does P, depending on the region. We try to answer which influence dominates the development (L42f).
+
+Thus, using P and T to project future GW trend using data driven method is generally not reliable. For the same reason, I also question the main premise on L95-96, “…due to high prediction accuracy in the past, the selected sites are unlikely to be under the influence of strong groundwater withdrawals or comparable effects….” As I elaborate in the next bullet, a good performance on historical data is not a guaranty for future performance.
+
+In our opinion, using P and T as inputs is reliable because – as elaborated above – we calculate only the climatic influence under existing boundary conditions. We therefore respectfully disagree to the fact that “using P and T to project future GW trend using data driven method is generally not reliable”. For high prediction accuracy in the past it is necessary that a very strong relationship between climate variables and groundwater level exists for a specific site. If other factors were dominant, the model would produce less accurate results in the past. Concerning the performance in the future, we agree that there is never a guarantee of good performance, not for these models nor any other (e.g. physically-based) models. To account for this, we took several measures to increase the confidence in our models and the produced results (high performance in the past, high dropout rate, SHAP values (e.g. L 523ff.), extrapolation behavior (e.g. 514ff.) etc.). Please see also our elaborations for the next bullet point.
+
+2. It is well known that data driven methods are not good at extrapolation. In other words, these methods aren’t good at predicting instances that are not seen during training and they are not good at predicting nonstationary time series. If for some reason, there’s a change in trend or there are huge spikes that are out of the training data range, the data-driven methods will usually fail. As a case in mind, Sun et al. (2020) trained numerous machine learning models to predict total water storage in the U.S. However, significant wetting trends occurred in several basins during the “future” phase. The authors showed that the data-driven methods couldn’t capture the trend change well.
+
+Thank you for pointing out this important aspect. We agree, the data driven models start to fail at some point of extrapolation. However, we see several reasons that this is not the case for our models using future climate scenario data.
+
+First, we have carefully evaluated our models and performed the mentioned plausibility checks which already used unrealistically high values for P (x4) and T (+5°C) in the past (L. 514ff.). Even for those, the models did not completely fail. Of course, absolute values were not realistic,
+but the models still produced – at least visually – plausible output patterns in the past that correspond to our conceptual understanding. (compare Fig. 9b).
+
+Second, we do not perform an extrapolation in a classical sense with data out of the (absolute) training range. The changes in future climate patterns we see (e.g. increasing temperatures) are changes in mean values and absolute future values usually still are in the range of the training data (e.g. in the future we might see more regular temperatures above 30°C for a certain location, but we have seen these temperatures also in the past, just less often). We therefore hold the opinion that we do not leave the data manifold in the future. As long as we are confident that our models learn the input output relation in a correct manner (conceptually checked by our explainable AI - SHAP value approach), we argue that we can assume that there is meaning in the forecasted values. We have added and discussed this aspect to the newly added uncertainty section and hope that it becomes clearer now (L 535-358)
+
+3. Methodology wise, I’m concerned with using 1D CNN for time series forecasting, especially when dealing with long sequences (52 weeks). This is because CNN has a fixed reception field (in their work, the authors used a fixed kernel size 3), which cannot capture multiscale temporal correlations very well. Based on my own experience, LSTM would be a much better choice in terms of forecasting accuracy on time series with long memory.
+
+Thank you for this comment, and we completely understand your concerns. For the same reason we have conducted a study (Wunsch et al. 2021, see below), where we explore the suitability of different model types on groundwater level prediction. We have shown, that 1D-CNNs mostly outperform LSTMs in case of groundwater level forecasting, which is the reason we used a similar approach here. We agree, that in theory LSTMs are probably more suited, but besides the mentioned performance differences, in our experience, LSTMs are less stable. Moreover, the receptive field of each individual kernel is indeed three, but we use a large number of kernels, where each of them can detect other features in the complete input sequence of up to one year (length is optimized for each site). We have extended the justification of the choice of methods in Lines 59-67.
+
+4. On data analysis part, data gap filling is a huge issue and almost deserves a separate analysis on its own. Here Figure 6 shows data availability is pretty limited pre-1980. Any interpolation will add artifacts to the time series. The authors treatment of this issue was surprisingly cursory. It’s not clear how the authors assessed the quality of gap filling.
+
+Thank you for pointing out this important aspect. We want to point out, that the data availability is indeed limited before 1980 and we think there is a misunderstanding concerning this figure. To clarify, we did not extrapolate the initial length of the time series. The time series length is as shown in the manuscript.
+
+Concerning interpolation of data gaps itself, we used mostly prior knowledge of hydrographs with similar dynamics. This way, we were able to close gaps using the course of a similar hydrographs, not showing a gap in the respective period. Where this was not possible or did not yield plausible results, we used PCHIP interpolation. As part of a previous project, the similarity of the dynamics of several thousand hydrographs all over Germany were analyzed (Wunsch & Liesch 2020), unfortunately the report is only available in German. The results from this report form the basis of our preprocessing strategy. We have added a clarifying statement to the text (Lines 421-428). A paper, which demonstrates the methodology on a subregion of Germany was recently published in Water Resources Management (Wunsch et al. 2021)
+
+Concerning your statement of added artifacts to the time series, we agree, but draw a different conclusion. Based on our knowledge (examples follow) of length and proportion of interpolated data gaps, we think that the added artifacts are neglectable.
+Of all 118 time series, 48 had no missing values, other 44 had less than 2% interpolated values (about 20 values for a hypothetical time series of 20 years of data). Only very few time series show a higher proportion of interpolated values (11 time series > 4%). We have published the complete groundwater dataset (see below) and please feel free to check for each site individually the amount of interpolated data and which method was used. To illustrate, in the following, a figure from the published data set is shown for the time series with by far the largest proportion of interpolated values (14%). As you can see, mostly shorter sections had to be interpolated, which do not strongly influence the overall dynamics, because no high frequency changes can be observed overall. Around 2005 (for example) a larger section has been interpolated based on information of highly correlated neighboring time series and we also yield a very plausible pattern here.
+
+![Groundwater level time series with interpolation points](page_370_613_1097_312.png)
+
+The following figure is from the electronic appendix of Wunsch&Liesch (2020) and shows some of the correlated time series which the interpolation shown above was based on. As you can see, we find very similar dynamic patterns and we can use this information to close data gaps with comparably high reliability.
+
+![Stacked, z-transformed groundwater timeseries](page_370_1012_1097_312.png)
+
+Overall, we hold believe that the interpolation has no negative effect on the result. We have now extended the section on gap filling in the revised manuscript (Lines 421-4289
+
+References:
+
+• Wunsch, A. & Liesch, T. Entwicklung und Anwendung von Algorithmen zur Berechnung von Grundwasserständen an Referenzmessstellen auf Basis der Methode Künstlicher Neuronaler Netze. 191
+https://www.bgr.bund.de/DE/Themen/Wasser/Projekte/laufend/F+E/Mentor/mentor-abschlussbericht-I.pdf?__blob=publicationFile&v=2 (2020)
+
+• Wunsch, A., Liesch, T. & Broda, S. Feature-based Groundwater Hydrograph Clustering Using Unsupervised Self-Organizing Map-Ensembles. Water Resour Manage (2021). https://doi.org/10.1007/s11269-021-03006-y
+
+• Wunsch, A., Liesch, T. & Broda, S. Weekly groundwater level time series dataset for 118 wells in Germany. (2021) doi:10.5281/ZENODO.4683879.
+
+5. The authors showed temperature is a dominant predictor, which is not new as GW level in humid regions is generally dominated by seasonality. However, this is probably only valid in Germany, not valid in many other arid and semiarid regions that depend more on GW as a critical water supply. Thus, a more meaningful task would be to predict inter-annual GW change instead of full signal that's dominated by seasonal variations and uncertain trend.
+
+Thank you very much for this interesting idea of predicting change instead of the actual GWL values. We might incorporate this in our future work. For now, we find a basic problem in predicting changes instead of the full signal. When using the full signal, we are able to judge if at least visually our model produces meaningful outputs. However, when simulating inter-annual changes, we get a result, which is harder to judge, because even though each timestep might yield plausible results, when translating back into a time series, we are significantly biased by cumulative errors.
+
+To illustrate this, we show in the following example the translation of predicted changes into a groundwater level time series (not inter-annual changes but on a weekly basis, but overall a similar problem):
+
+![Time series plot showing simulated and observed GWL values, with confidence intervals](page_186_682_1077_340.png)
+
+This is a time series, for which a highly accurate forecast of the groundwater levels of these two years has been produced by our models (available in the Supplement). In this case, the mere simulation result (not shown), which is changes from timestep to timestep, is not so bad either. However, when translating the changes back into a time series, we are forced to cumulate results from prior steps, which also cumulates prior errors. A correction is only possible if the ground truth (groundwater levels) is known for the test set, which is not until 2100. At the moment, we see no solution to this problem. Therefore, for this specific study, it exceeds the currently possible scope.
+
+Concerning the validity of the results; yes of course, this is only valid for Germany, and even there with all uncertainties and limitations discussed. We do not claim a broader validity or transferability.
+
+Thank you for this compilation of literature. It helped us to illustrate the raised concerns.
+
+References:
+Scanlon, B. R., Zhang, Z., Save, H., Sun, A. Y., Schmied, H. M., Van Beek, L. P., ... & Bierkens, M. F. (2018). Global models underestimate large decadal declining and rising water storage trends relative to GRACE satellite data. Proceedings of the National Academy of Sciences, 115(6), E1080-E1089.
+
+Sun, A. Y., Scanlon, B. R., Save, H., & Rateb, A. (2020). Reconstruction of GRACE Total Water Storage Through Automated Machine Learning. Water Resources Research, e2020WR028666.
+
+Rodell, M., Famiglietti, J. S., Wiese, D. N., Reager, J. T., Beaudoin, H. K., Landerer, F. W., & Lo, M. H. (2018). Emerging trends in global freshwater availability. Nature, 557(7707), 651-659.
+
+Reviewer #2 (Remarks to the Author):
+
+Wunsch et al. present in their manuscript “Deep learning shows declining groundwater levels in Germany until 2100 due to climate change” some interesting results on the potential groundwater response on climatic changes. However, there are strong limitations which are currently not addressed and prevent results to be useful. To make valid statements on future groundwater levels it will be necessary to analyse much more the different RCPs and the different sources of uncertainty.
+
+1. The authors state they use only projections based on RCP 8.5 (l. 87). This is a major constraint and prevents to derive any general future predictions. Usually, the different RCP are used to analyse the bandwidth of potential future changes, therefore, using only the most extreme one (leading to the strongest changes and trends) requires some strong reasoning. Unfortunately, any reasoning or discussion of this point is completely missing in the manuscript. Without considering different RCPs the authors cannot claim to present valid predictions for 2100. However, for most parts of the manuscript this important limitation does not become clear. E.g. many of the results are written like forecasts ("heads will probably decrease", “expected to show increased values”, etc.). Also, the title exaggerates the findings without mentioning the constraints.
+
+Thank you for pointing out these aspects. We now have additionally included RCP4.5 and RCP2.6 in our analyses and have adapted the manuscript accordingly. See especially Lines 226ff and Figures 2 and 3. We admit that our title was a little bit misleading, given that we only investigated RCP8.5. Given our additional analyses for RCPs 2.6 and 4.5 and after careful consideration, we think that the title is adequate now, and does not need to be changed. With the analyses performed, we find declining groundwater levels for all RCP scenarios considered. For most of the wells there are already at least slightly negative trends under RCPs 2.6 and 4.5.
+
+Moreover, we have modified our wording throughout the manuscript and hope that it now better communicates the constraints and limitations, as well as sounds less strongly like as we present precise forecast results.
+
+2. The authors present many results for the selected set of 6 different climate models. However, the climate model is only one source of uncertainty and not necessarily the most important one. Other sources of uncertainty which are probably relevant in this context include: groundwater model uncertainty (from the supplements it is evident that model performance differs between sites and that there are larger uncertainties for the simulation of extremes); scaling uncertainty (grid of 5x5km vs. borehole); statistical analysis uncertainty (limitations of
+MK-Test and trend analysis), emission scenario uncertainty (see above); etc. While the authors quantify and discuss climate model uncertainty, all the other uncertainties are neglected. However, without a reliable uncertainty analysis results are not useful and cannot depict the expectable changes of groundwater levels in Germany until 2100.
+
+Thank you for pointing out this weakness of our manuscript. We have strengthened our results, as we now have taken measures to take care of some mentioned sources of uncertainty. Our analysis now considers different RCP scenarios (RCP2.6, RCP4.5 and RCP 8.5), each with an ensemble of different climate models. We also have included additional statements (e.g. Lines 347-367) to further discuss the uncertainty sources in our manuscript. Further, a newly calculated uncertainty (95% confidence interval) derived from Theil-Sen slopes is now included into the presentation of the results to account for the statistical test uncertainty (e.g. Figure 2 and Figure 3). Scaling uncertainty due to the differences between a single location and the grid cell sizes are certainly present. By achieving high performance in the past using training data in the same grid resolution we can assume that this influence is not severe. We further changed the data selection strategy for the climate projections, by now using 3x3 grid cells instead of 1x1 (directly at the location of each site) (L. 363 and 453). We hereby follow the recommendations of the German Meteorological Service to account for larger scale atmospheric processes that usually do not scale to a single scale of the used data.
+
+Minor points:
+
+• I. 89 “represent 80% of the possible future climate signal” -> this high percentage is puzzling given that only one RCP is used in this study and hence a very small proportion of possible future climate signals is covered by the runs.
+
+Thank you for pointing out this ambiguous wording. We have modified the respective statement to make the meaning clearer (L 95-99). Further, by analyzing also other RCPs the context should also be better understandable.
+
+• I. 106: Is a linear trend an appropriate functional form to describe the change? For example, in case the real trend at a station is rather exponential, the linear trend could give values that deviate for 2100 quite a bit. In general, the fitted values at the end of the timeseries quite often deviate from actual values.
+
+We think that a linear trend analysis is appropriate, because for our simulation results we do not find exponential trends but rather sections of successive years with stronger/weaker changes. It would be hard to grasp and interpret such periodicities, additionally the linear trend analysis considers the whole simulation period of >80y, which circumvents problems of interpreting shorter than 30y periods (which is not recommended).
+
+• II. 113 f.: unit of mm/y not clear. Seems like a rate of change (i.e. the slope of the trend line), but I guess that is not meant here.
+
+Thank you for pointing out. As we are speaking of the total annual precipitation the unit is indeed mm per year. We rewrote this part of the text, but nevertheless removed “per year” from similar statements (Lines 116ff.).
+
+• II. 140 ff.: All these results are focussed on annual percentiles, correct?
+
+Yes, this is correct. The results are all on annual percentiles.
+
+Above you mention the different water users and potential water conflicts, also different climatic changes within the year are mentioned -> did you also look on groundwater trends for the different seasons? Based on Figure 3 I can already guess that there are some relevant seasonal differences. These can be also very relevant for water management.
+Thank you for this suggestion, this would be an interesting extension of our analysis. However, we did not analyze this aspect, because we think that this would exceed the scope of the current study and we already hardly are able to present all results of the current analyses, especially given the additional RCP scenarios that are now included. We will take this suggestion into account for future research.
+
+• Figure 3: From my perspective this figure contains way too many plots which are too small to be readable.
+
+Thank you. We have restructured this figure completely and increased the font size in the new version. We hope this resolves the readability problems.
+
+• I. 454: Probability values of Mann-Kendall are only valid in case of no autocorrelation which is usually not the case for groundwater records. Were autocorrelations calculated and timeseries pre-whitened?
+
+Yes, you are right. MK-Test should not be applied for seasonal data. However, we perform a trend analysis on annual values (e.g. the annual mean), which means that the autocorrelation from typical groundwater seasonality (per year) is not part of the analysis. Therefore, no change in methodology is needed here. To clarify, we have further elaborated this aspect in Line 544ff.
+
+Reviewer #3 (Remarks to the Author):
+
+Comments:
+
+This paper is of great interest not only from a scientific point of view but also for practitioners, as questions about our future water resources are piling up. It is an exciting contribution to study the future climatic impacts on groundwater quantity in the future. Referring to the text I have the following comments and questions:
+
+In my opinion, the title is somewhat misleading, as the paper only focuses on the worst-case scenario (RCP8.5) and ignores all other future projections. Current studies show that even with a 'business as usual' development - regarding CO2-emissions - the bandwidth of projected results will be partly below the range of the RCP8.5 projections, which means the effects for groundwater fluctuations is quite smaller. Therefore, it makes sense to mention the used RCP scenario in the paper title. This points out to the reader right from the start that only parts of the available climate projections were used.
+
+Thank you for this comment. We agree that our title was a little bit misleading, given that we only investigated RCP8.5 We now additionally show results for RCPs2.6 and 4.5 and after careful consideration, we think that the title is adequate now, and does not need to be changed. Our analyses show that for all three RCPs considered, declining groundwater level trends can be found. Even under RCPs 2.6 and 4.5 most of the wells show a slight declining trend.
+
+1. Line 12ff.: ...RCP8.5 scenario ... represent 80% of the bandwidth….
+From my point of view the following details are missing in the paper: Why only RCP8.5 projections are chosen? What does it mean, when 80% of the bandwidth is used? (Here, for example, the authors could refer to the IPCC classification of likelihoods).
+Thank you for pointing out. We applied major changes to our manuscript and included also RCP Scenarios 2.6 and 4.5 into our study (see especially Lines 226ff., Figures 2 and 3). We also clarified what we meant by bandwidth (ensemble spread) (L 96, 449). We still do not use the IPCC classification of likelihoods as this is not what was meant here.
+
+2. Line 28ff.: ...on groundwater and springs…
+It is true that groundwater plays a crucial role in some parts of Germany (and also on the national level in the whole). However, there are also federal states that increasingly use surface water. Perhaps this circumstance should therefore also be mentioned in order to differentiate the significance of the result on a regional level.
+
+Yes, on national scale groundwater indeed plays a crucial role (regarding drinking water supply – what is probably meant in the comment). There are of course local and sometime regional differences, but we do not aim to resolve this aspect on such a spatial scale. However, even for surface water, which is strongly interconnected to groundwater via baseflow, the relevance of these results is still high. As shown by de Graaf et al. (2019) (also cited in the manuscript) even a small decrease of 10cm can have severe consequences for baseflow of rivers in northern Germany. Moreover, groundwater is not only relevant regarding drinking water supply, but also for groundwater dependent ecosystems, and therefore plays a crucial role in general. We therefore do not think, that a relativization is necessary at this point.
+
+Reference:
+
+de Graaf, I. E. M., Gleeson, T., (Rens) van Beek, L. P. H., Sutanudjaja, E. H. & Bierkens, M. F. P. Environmental flow limits to global groundwater pumping. Nature 574, 90–94 (2019).
+
+3. Line 34ff.: ...less than 2% of the total withdrawal volume…
+Does this value apply to an average in Germany, or is it a regional figure that applies to all federal states?
+
+According to the source cited, which is the Federal Environment Ministry (UBA, Umweltbundesamt), this is a number derived from DESTATIS (Federal Statistical Office) data and an overall average for whole Germany.
+
+4. Line 41ff.: ...of several degrees….by 2100.
+Here it would be better to use the original literature, where the data were first described, such as by EURO-CORDEX or the Reklies-De project.
+
+Thank you for this hint. In the further course of the text, we exchanged the literature and the original literature is now cited in Lines 98-99. At this specific point in the text we talk about an analysis of water availability. We therefore think that it is adequate to stick with the cited literature.
+
+5. Line 43ff.: For Europe…
+Why do the authors go from Germany to Europe, only to return to Germany later?
+
+Thank you. We have adapted the respective sentences and hope it is easier to follow now. (L38ff.).
+
+6. Line 43ff.: snow dominated regions…
+What role does that play for Germany as a whole. I think that this is only relevant for the South.
+
+Thank you. We have adapted the respective sentences to better point out that this is only relevant for the South. (L 46f.).
+7. Line 43ff.: …unconfined shallow aquifers…
+What about regions characterised by fractured aquifers or karstic aquifers? You cannot simply ignore the different aquifers with their different characteristics, which are totally different to shallow porous aquifers.
+
+Thank you for raising this important concern. We have also included a smaller number of wells in fractured and karstic aquifers. Please check the “Data” section in the “Methods” part of the manuscript for more details on their positioning. Further, we have limited our analysis to the uppermost aquifer at each site, which often happens to be a porous aquifer. In the overall available data that we selected our wells from, the number of wells in fractured and karstic aquifers is both generally, but especially for the uppermost aquifer, by far smaller than the number of wells in porous aquifers. In the end there was only this small number of fractured and karstic aquifer wells that met our rigorous pre-selection criteria. We would have liked to include more of these, but it was just not possible. From a relevance point of view, you are right, we cannot neglect other aquifers, still, shallow porous aquifers are probably the most important ones when it comes to groundwater extractions or water availability, due to the larger volumes that are available there, and also regarding e.g. water availability for vegetation/groundwater dependent ecosystems.
+
+8. Line 69ff.: …declines up to 10 m close to the Alps…
+How big was the model error in this study?
+
+we have chosen models that fit the data with high accuracy for a test period in the past, see e.g. Fig. 9a. However, the individual model error varies from site to site and can be looked up in the Supplementary. The model uncertainty based on different realizations (derived from Monte Carlo dropout, no uncertainty from inputs included) is usually very small. We hope this answers your question.
+
+8.1 How good were the statements in relation to the prevailing groundwater thickness?
+
+We are sorry, but we usually have no information about this locally and we have not investigated this for the same reason.
+
+8.2 What about areas with aquifers less than 10 m thickness?
+
+Good point, thank you. In principle it is possible that the decline is stronger than physically possible. However, such knowledge is not included into the model, nor in the interpretation, since, as mentioned above, we lack this information.
+
+9. Line 81ff.: …respective uppermost unconfined aquifer…
+How representative are the selected wells and springs for the whole of Germany or selected groundwater landscapes?
+
+Representativity is difficult to judge. We have no possibility to check if a single well is representative for a whole groundwater landscape. At least porous aquifers (which are the most) are more important for GW availability in Germany than the other types (with regional differences, of course). Our selection is thus not representative for all areas, but probably for the majority/or the most important ones. Moreover, it is important to emphasize that the results are not suitable for regionalization.
+
+In Wunsch&Liesch (2020) (Report in German), we performed a comprehensive cluster analysis of groundwater dynamics throughout Germany. Based on these cluster results, we already performed interpolation of data gaps (See our answer on question 4 of Reviewer #2). The only thing we can say is that our 118 wells originate from 52 different clusters, which in total comprise time series of more than 2600 wells. However, we cannot directly draw a conclusion on representativeness from this number, because not all clusters are as
+homogenous as the example shown above, nor are all of our 118 wells similarly representative for their whole cluster. Nevertheless, this is an indicator that our wells represent the dynamics of a certain number of other wells, too. However, this is generally vague and we therefore refrain from adding this to our manuscript.
+
+10. Line 87ff.: ...downscaled 5 x 5 km2…
+    How do this resolution and the size of the catchment of selected wells/springs fit together? Was a weighted allocation carried out?
+
+In the original submission directly the grid cell, which the site lies in was selected. We have changed our approach and now follow the best practice recommendations of DWD by taking the mean of 9 (3x3) cells (L 363.453), with the groundwater well grid cell in the middle. We did not include springs in our dataset, groundwater wells mostly do not have a well-defined catchment area. Thus, we sticked with the 9-cell-mean approach.
+
+11. Line 103ff.: ...Germany by 2100…
+    The references for the climatic information used are not primary references.
+
+Thank you. We have now corrected these references. (L 98,99)
+
+12. Line 103ff.: ….exact values….
+    If results from climate projections are used, there are no exact values but only bandwidths of the entire ensemble.
+
+Yes, you are right. What we meant was “more precise” values. We have corrected the wording., thank you. L 117-118
+
+13. Line 118ff:….under the RCP8.5 scenario…
+    From my point of view, it would be good to briefly draw a reference to the other scenarios in order to be able to better classify the results. For example, by pointing out that the approach used shows the greatest possible impact, whereas small effects are to be expected when other RCPs are used.
+
+Thank you for pointing out. As of the other Reviewers’ comments, we have substantially modified the manuscript and included additional scenarios in our analyses.
+
+14. Line 141ff:….in 2100…
+    What does this time indication mean? Since it is a 30-year average, different time periods are possible, such as 2071-2100 or similar. Please specify exactly.
+
+As we elaborate in the text, we compare the relative change between the simulation start (2014) and the end (2100) (L 148f.). We rephrased the section to clarify what was done. See also Lines 544ff.
+
+15. Line 142ff:….the simulation (2014)….
+    Why was 2014 chosen as the start of the simulation? Is this for technical or other practical reasons?
+
+Thank you for asking. This was for data availability reasons. We have clarified this aspect in the text (L 551)
+
+Line 151 and others:…..significant trend…
+How was significant defined? When is a trend called significant? Since there are different approaches for testing the significance of data, further information would be useful.
+
+We examined each quantity development using Mann-Kendall linear trend test and derived the relative development in percent from a linear fit using Theil-Sen slope. We considered a trend
+significant for p < 0.05. We elaborate this aspect in L 559. Further statements on the significance can be found in Lines 160, 228, Figures 1d, 4d and caption of Figure 2.
+
+16. Line 216:...(2070-2100)...
+    I think it should be 2071-2100.
+
+Thank you. We have corrected this (L 272).
+
+17. Line 243:... We do not find ….increasing mean trends…
+    How does this fit with the statement that the amount of precipitation increases in the year?
+
+As pointed out in the introduction (L 39ff.): [...] analyses based on climate projections show opposing trends in terms of water availability, with a slight increase in annual precipitation sums, i.e. more water, but at the same time a significant temperature increase of several degrees Celsius by 2100, i.e. less water. The resulting effect on groundwater resources is therefore not directly clear and needs to be analyzed" This is the motivation of our study, to find the future GWL trends despite intuitively opposing trends in the groundwater level forcings. Moreover, besides some regional/local differences, especially regarding future precipitation trends, which of the forcings (T or P) is the dominant one also depends on the individual site. We hope this clarifies your question.
+
+18. Line 272:... Even fewer significant shift…
+    Are there any classification steps for significance?
+
+We apologize, this is a misunderstanding. We did not mean less significant but less frequently significant. However, this section is not part of the manuscript anymore.
+
+19. Line 284 and ff…. that temperature is mainly the driving factor for declining groundwater levels…
+    It should be explicitly mentioned here that the results only apply to shallow aquifers. It would also make sense to define what is meant by “shallow aquifer”. Finally, it could also be helpful to address the issue of the behavior of different aquifer types in the discussion.
+
+Thank you for pointing out. We have added this to the respective sentence (L.322). However, we do not think that the small number of fractured and karstic aquifers (especially considering the already existing sources of uncertainty) allow a discussion of behavior differences compared to porous aquifers.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+Please see the pdf file.
+Review of revised manuscript, Deep learning shows declining groundwater levels in Germany until 2100 due to climate change
+
+This study focused on predicting future groundwater levels in Germany using a 1D convolutional neural network (CNN) model. While the study is interesting and touches up future climates, I found its scope is narrow and provides little additional insight to the Nat Comm readers. In particular, I have the following comments.
+
+• Groundwater aquifers are an integral component of the global terrestrial water cycle. Many studies, especially those from the GRACE community (e.g., Rodell et al. 2019; Figure 1 pasted below), have already shown a detectable downward terrestrial water storage (TWS) trend in the Germany/Austria region in recent decades. Further, a recent study conducted by Pokhrel et al. (2021, Figure 1 pasted below) demonstrated the future TWS drying trend for Europe under RCP2.6 and 6.0 by using a large ensemble of global hydrological models. Here the authors only considered shallow unconfined aquifers in a temperate climate. The data-driven projections naturally follow the same trends manifested in the climate forcings (i.e., precipitation and temperature) that the authors used. In other words, putting aside human interventions which the authors didn’t consider, the results mainly reflect the causal relationship between the climate forcing and shallow groundwater storage. This is hydrology 101. However, focusing on a small region using a relatively small dataset and a purely data-driven ML approach also puts the scope of this study less significant for a high-impact journal like Nat. Comm. It’ll be easier for me to recommend the publication of this article on HESS or JoH.
+• Regarding LSTM, I read the HESS algorithm comparison paper published by the same authors in April [Wunsch, A., Liesch, T. & Broda, S. Groundwater level forecasting with artificial neural networks: a comparison of long short-term memory (LSTM), convolutional neural networks (CNNs), and non-linear autoregressive networks with exogenous input (NARX). Hydrology Earth System Sciences 25, 1671–1687 (2021)]. There the authors considered an autoregressive setup, GW_t = f(GW_{t-1,...,t-N}...), namely, they incorporated antecedent GW to predict future GW. It is known (e.g., Selvin et al., 2017) using LSTM in an autoregressive setting may hurt its performance due to noise in data. There are ways to alleviate that effect (e.g., using moving average Feng et al., 2020). Under this work, however, the authors mainly used precip and temperature data to drive the ML model. Using LSTM in the setting of this work has been shown to achieve state-of-the-art performance (Kratzert et al., 2019) compared to physics-based models.
+• I think the power of ML has been underutilized in this work by doing single well predictions. Existing works have already shown the merits of incorporating a large sample dataset to perform many-to-one prediction, which can be especially important given the levels in many wells can be spatially correlated. Existing works have also compared the performance of ML to similar process-based models, or at least adopting a physics-informed ML approach. This work does not possess those elements.
+• One of the main selling points of this work is using a data-driven model to project the future scenarios. However, numerous climate studies already pointed the caveat of this approach in capturing future extremes (https://phys.org/news/2018-07-machine-method-capable-accurate-extrapolation.html). Although the time dimension was extrapolated, the extremes of predicted groundwater levels cannot be extrapolated if they are not part of the historical data used for
+training. A true extrapolation would instead learn the distribution of data (i.e., generative modeling), from which the tails of distribution can be extrapolated. That’s not the approach taken by the authors. In their rebuttal letter, the authors mentioned “The changes in future climate patterns we see (e.g. increasing temperatures) are changes in mean values and absolute future values usually still are in the range of the training data” This is a very irresponsible subjective statement. How can you see the future without validation? If the future patterns are truly like the current days as you mentioned, then what is the point of projection. You can simply apply the groundwater climatology.
+
+![Annotated map of TWS trends. Trends in TWS (in centimetres per year) obtained on the basis of GRACE observations from April 2002 to March 2016. The cause of the trend in each outlined study region is briefly explained and colour-coded by category. The trend map was smoothed with a 150-km-radius Gaussian filter for the purpose of visualization; however, all calculations were performed at the native 3° resolution of the data product.](page_246_678_1092_482.png)
+
+Fig. 1 | Annotated map of TWS trends. Trends in TWS (in centimetres per year) obtained on the basis of GRACE observations from April 2002 to March 2016. The cause of the trend in each outlined study region is briefly explained and colour-coded by category. The trend map was smoothed with a 150-km-radius Gaussian filter for the purpose of visualization; however, all calculations were performed at the native 3° resolution of the data product.
+Fig. 1 | Impact of climate change on TWS. a-d. The changes (multi-model weighted mean) in TWS, averaged for the mid- (2030–2059; a,c) and the late (2070–2099; b,d) twenty-first century under RCP2.6 (a,b) and RCP6.0 (c,d) relative to the average for the historical baseline period (1976–2005). The colour hues show the magnitude of change and the saturation indicates the agreement, among ensemble members, in the sign of change. The graph on the right of each panel shows the latitudinal mean.
+
+References:
+
+Rodell, M., Famiglietti, J. S., Wiese, D. N., Reager, J. T., Beaudoing, H. K., Landerer, F. W., & Lo, M. H. (2019). Emerging trends in global freshwater availability (vol 557, pg 651, 2018). Nature, 565(7739), E7-E7.
+
+Pokhrel, Y., Felfelani, F., Satoh, Y., Boulange, J., Burek, P., Gädeke, A., ... & Wada, Y. (2021). Global terrestrial water storage and drought severity under climate change. Nature Climate Change, 11(3), 226-233.
+
+Selvin, S., Vinayakumar, R., Gopalakrishnan, E. A., Menon, V. K., & Soman, K. P. (2017, September). Stock price prediction using LSTM, RNN and CNN-sliding window model. In 2017 international conference on advances in computing, communications and informatics (icacci) (pp. 1643-1647). IEEE.
+
+Feng, D., Fang, K., & Shen, C. (2020). Enhancing streamflow forecast and extracting insights using long-short term memory networks with data integration at continental scales. Water Resources Research, 56(9), e2019WR026793.
+
+Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., & Nearing, G. S. (2019). Toward improved predictions in ungauged basins: Exploiting the power of machine learning. Water Resources Research, 55(12), 11344-11354.
+Reviewer #2:
+Remarks to the Author:
+The revisions of Wunsch et al. clearly improved the manuscript which benefits from adding RCP 2.6 & 4.5 as well as additional uncertainty analysis (Theil-Sen line) and discussion (II. 347-367). However, from my perspective there remain two points for further revision:
+• The authors use the MK-trend test without pre-whiting. It is important to note that this test is only valid in case of no autocorrelation, otherwise the significance of the test will be overestimated. The authors correctly state that the seasonal autocorrelation is not relevant in the context of their MK-test as they only use annual values. However, apart from seasonal autocorrelation groundwater often exhibits autocorrelation on longer time scales as well. Based on my experience with groundwater data in Germany I would expect at least half of the groundwater records to show significant first-order autocorrelation for the annual values used in this work.
+As an example, I made a quick test and randomly selected one of the wells used for this work (file “NI_40000175_GW-Data.csv” from the repository). After calculating annual time series of the mean and 2.5- and 97.5-percentiles I get first-order autocorrelations of 0.35 (mean), 0.02 (2.5-percentile) and 0.65 (97.5-percentile). The correlations for the mean and the 97.5.-percentile are significant and definitely relevant in the context of MK-trend tests. If the author’s CNN model captures the dynamics of the well correctly, the modelled time series until 2100 will exhibit a similar autocorrelation structure and without appropriate pre-processing the MK-test will overestimate trend significance for this well. Hence, the authors will definitely have to check for autocorrelation and exclude where existent before using MK and characterizing trends as significant.
+• The authors discuss different sources of uncertainty including model uncertainty. However, models are usually trained to match mean conditions best but are much weaker in simulating extremes. Based on Figure 7 this seems to be the case also for the models used in this work as it can be clearly seen that the maxima of the time series are systematically underestimated. The plots in the supplements reveal similar problems for the extremes (mostly the upper extreme, sometimes also the lower extreme) at many stations. Hence, the studies’ results regarding the mean will be more robust than those regarding the extremes. To judge the validity of model results I think it is necessary to evaluate the model performance regarding the different metrics (annual mean, annual 2.5-/97.5-percentile) in more detail.
+
+Reviewer #3:
+Remarks to the Author:
+Comments:
+By revising the paper, the statements were once again clearly sharpened.
+It is now clear which general statements about groundwater development in Germany are possible and where the results still showed larger bandwidths that do currently not allow clear statements.
+With regard to climate impacts, it was clearly shown what influence global warming can have on groundwater availability in Germany. Furthermore, the results also clearly show that any global reduction in CO2-emissions will have a positive impact on groundwater level and groundwater yield. However, the results also show that the resource groundwater will change regionally in the future and that all users must adapt to this.
+
+From my point of view, I only have two small comments:
+
+Line 41 ff.: this sentence is formulated somewhat unclearly. Actually, all models show a robust increase in temperature (i.e. (almost) all climate models agree on this), but there are drier and wetter models for precipitation, depending on the calculation approach. However, these statements cannot be read out of the text clearly.
+
+Line 56: to meet the needs…. Wouldn't it also be important to mention here that climate change, especially higher temperatures, also has an impact on changing water demands (not only in the city).
+This is particularly relevant when considering peak demands. This addition is not an absolute must, but could build an important bridge to practice.
+Response to Reviewers
+
+We thank all Reviewers for the repeated revision of our manuscript. We are glad to read that our revisions from stage one sharpened the results. We will comment on the open questions and concerns in the following. Please find the reviewers comments in black and our answer in red. Line numbers in our answers refer to the newly revised manuscript.
+
+Dear Mr. Wunsch,
+
+Thank you again for submitting your manuscript "Deep learning shows declining groundwater levels in Germany until 2100 due to climate change" to Nature Communications. We have now received reports from 3 reviewers and, on the basis of their comments, we have decided to invite a revision of your work for further consideration in our journal. Your revision should address all the points raised by our reviewers (see their reports below). In particular, Reviewer #1 and #2 raise important technical concerns, such as the presence of autocorrelation and underutilization of the machine learning methods that must be addressed for publication in Nature Communications.
+
+When resubmitting, you must provide a point-by-point response to the reviewers’ comments. Please show all changes in the manuscript text file with track changes or colour highlighting. If you are unable to address specific reviewer requests or find any points invalid, please explain why in the point-by-point response.
+
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Review of revised manuscript, Deep learning shows declining groundwater levels in Germany until 2100 due to climate change
+
+This study focused on predicting future groundwater levels in Germany using a 1D convolutional neural network (CNN) model. While the study is interesting and touches up future climates, I found its scope is narrow and provides little additional insight to the Nat Comm readers. In particular, I have the following comments.
+
+We thank anonymous Reviewer#1 for again reviewing our manuscript. We recognize that no recommendation for publication Nature Communications is provided. With surprise, we found that in the second review stage some new fundamental criticism is raised that (i) has not been mentioned in stage one and (ii) that no constructive comments or propositions are given other than changing the fundamental approach including both data basis and methods. We therefore were not able to change our manuscript accordingly, however, we try to comment on every point in the following.
+
+1. Groundwater aquifers are an integral component of the global terrestrial water cycle. Many studies, especially those from the GRACE community (e.g., Rodell et al. 2019; Figure 1 pasted below), have already shown a detectable downward terrestrial water storage (TWS) trend in the Germany/Austria region in recent decades. Further, a recent study conducted by Pokhrel et al. (2021, Figure 1 pasted below) demonstrated the future TWS drying trend for Europe under RCP2.6 and 6.0 by using a large ensemble of global hydrological models. Here the authors only considered shallow unconfined
+aquifers in a temperate climate. The data-driven projections naturally follow the same trends manifested in the climate forcings (i.e., precipitation and temperature) that the authors used. In other words, putting aside human interventions which the authors didn’t consider, the results mainly reflect the causal relationship between the climate forcing and shallow groundwater storage. This is hydrology 101. However, focusing on a small region using a relatively small dataset and a purely data-driven ML approach also puts the scope of this study less significant for a high-impact journal like Nat. Comm. It’ll be easier for me to recommend the publication of this article on HESS or JoH.
+
+We are pleased that Reviewer #1 recognizes that our models “reflect the causal relationship between the climate forcing and shallow groundwater” as it was one of our main goals during model building and training to ensure that the deep learning models learn the correct relationship. Groundwater dynamics and groundwater recharge seem simple, yet they are complex processes, depending on many boundary conditions and controlling factors, that superimpose each other in time and space (otherwise there would be no need for complex groundwater models). It is therefore not as simple as implied by the statements above, to derive groundwater levels from climate forcings alone. Much more important, we show that precipitation and temperature (depending on the scenario) regionally influence groundwater in possibly contradictory ways (e.g. L. 41-43, and L. 116ff). It is therefore not obvious from the input data alone which direction the future groundwater level development will follow. We further show that the calculated trends and changes in our study indeed do not simply reflect the spatial input data patterns (e.g. for RCP8.5, as mentioned in L. 208–209).
+
+In comparison to global studies, we base our analyses on specifically suitable climate projections, namely the “core-ensemble” of the German Meteorological Service. All members of this ensemble fulfill certain quality and validity criteria for central Europe. We therefore think that our study nicely complements existing studies (such as Pokhrel et al. (2021)) by investigating regional climate change effects with (slightly) reduced input data uncertainty. Especially compared to the mentioned study of Pokhrel et al. (2021), we provide additional insights by investigating three instead of two RCP scenarios and by including more than four (RCP2.6: five, 4.5 and 8.5: six) climate models for each scenario. Thus, we potentially better represent the full range of possible developments across different RCP paths as well within each scenario. In comparison to results focusing on TWS in general, simulation of groundwater levels does not only reveal a reduction in total water availability but allows conclusions on the future variability of the important water resource of groundwater and specific effects on wet and dry periods. Moreover, it is well-known that GRACE derived data (e.g. Rodell et al. 2019) has a much coarser resolution and is therefore not suitable for regional or even local studies.
+
+2. Regarding LSTM, I read the HESS algorithm comparison paper published by the same authors in April [Wunsch, A., Liesch, T. & Broda, S. Groundwater level forecasting with artificial neural networks: a comparison of long short-term memory (LSTM), convolutional neural networks (CNNs), and non-linear autoregressive networks with exogenous input (NARX). Hydrology Earth System Sciences 25, 1671–1687 (2021)]. There the authors considered an autoregressive setup, GW_t = f(GW_{t-1,...t-N}..), namely, they incorporated antecedent GW to predict future GW. It is known (e.g., Selvin et al., 2017) using LSTM in an autoregressive setting may hurt its performance due to noise in data. There are ways to alleviate that effect (e.g., using moving average Feng et al., 2020). Under this work, however, the authors mainly used precip and temperature data
+to drive the ML model. Using LSTM in the setting of this work has been shown to achieve state-of-the-art performance (Kratzert et al., 2019) compared to physics-based models.
+
+We thank Reviewer#1 for reading our HESS study, but we also think there exists a misunderstanding. We therefore would like to point out that while we have investigated an autoregressive setup in the above-mentioned study in the context of short-term forecasting without input data, this setup is of no relevance for the submitted manuscript. The larger part of the HESS study investigated sequence-to-value or sequence-to-one prediction solely based on meteorological input forcings (precipitation, temperature and relative humidity in this case), thus similar to the approach chosen in this manuscript and also comparable to the approach by Kratzert et al. (2019). This is what we refer to and what we base our conclusions on, regarding the appropriateness of CNN models.
+
+3. I think the power of ML has been underutilized in this work by doing single well predictions. Existing works have already shown the merits of incorporating a large sample dataset to perform many-to-one prediction, which can be especially important given the levels in many wells can be spatially correlated. Existing works have also compared the performance of ML to similar process-based models, or at least adopting a physics-informed ML approach. This work does not possess those elements.
+
+We agree that there is plenty of room for improvement in future studies and that our methodology is not the be-all and end-all. However, in our opinion we also demonstrated sufficiently that our results are valid and allow reasonable conclusions on the future groundwater level development in Germany.
+
+It is true that performing many-to-one predictions outperformed existing models in rainfall-runoff modeling (Kratzert et al. 2019), however, we lack comparable data to transfer this approach to our study area and the groundwater domain. Theoretically, therefore, the power of ML was underutilized, but practically it was not. For future studies we are already working on the collection of such data, which, however, is not yet available. Generally, it remains to say that we see advantages of many-to-one approaches not in spatial correlation, but in improved extrapolation capabilities of a model. Especially in the context of climate change, knowledge transfer from locations with historically different conditions can help to estimate the reaction to previously unseen climate at a site. To fully exploit this advantage, one should even include additional regions, other than Germany, to enable the model to learn different climate conditions historically.
+Regarding “physics-informed”, we would argue that this phrase itself is not yet well defined. Many studies sell simple model modifications as physics-informed (e.g. not allowing below-zero output values if physically not reasonable, or even only “physics-informed” input features), while only few studies incorporate true physics (such as mass conservation restraints) in their models. One could even argue that our models are at least physics-controlled, as we used XAI to check the conceptual correctness of our models. We agree, however, that there is great potential to improve simulations using physics in models for the future.
+
+4. One of the main selling points of this work is using a data-driven model to project the future scenarios. However, numerous climate studies already pointed the caveat of this approach in capturing future extremes (https://phys.org/news/2018-07-machine-method-capable-accurate-extrapolation.html). Although the time dimension was extrapolated, the extremes of predicted groundwater levels cannot be extrapolated if they are not part of the historical data used for training. A true extrapolation would
+instead learn the distribution of data (i.e., generative modeling), from which the tails of distribution can be extrapolated. That’s not the approach taken by the authors. In their rebuttal letter, the authors mentioned “The changes in future climate patterns we see (e.g. increasing temperatures) are changes in mean values and absolute future values usually still are in the range of the training data” This is a very irresponsible subjective statement. How can you see the future without validation? If the future patterns are truly like the current days as you mentioned, then what is the point of projection. You can simply apply the groundwater climatology.
+
+We admit that we have used inaccurate wording in our last response letter, as we spoke of “patterns”, which of course are not similar in the future and the past. However, we formulated our manuscript with more caution and would like to refer to the respective sentence there: “[...] because mean values and frequencies of input values change in the future, but the total range of these values is usually already present in the training data.” As we speak of “range” instead of “patterns”, this formulation is more precise and better represents what we tried to express.
+
+![Annotated map of TWS trends. Trends in TWS (in centimetres per year) obtained on the basis of GRACE observations from April 2002 to March 2016. The cause of the trend in each outlined study region is briefly explained and colour-coded by category. The trend map was smoothed with a 150-km-radius Gaussian filter for the purpose of visualization; however, all calculations were performed at the native 3° resolution of the data product.](page_374_682_1092_496.png)
+
+Fig. 1 | Annotated map of TWS trends. Trends in TWS (in centimetres per year) obtained on the basis of GRACE observations from April 2002 to March 2016. The cause of the trend in each outlined study region is briefly explained and colour-coded by category. The trend map was smoothed with a 150-km-radius Gaussian filter for the purpose of visualization; however, all calculations were performed at the native 3° resolution of the data product.
+Fig. 1 | Impact of climate change on TWS. a–d. The changes (multi-model weighted mean) in TWS, averaged for the mid- (2030–2059; a,c) and the late (2070–2099; b,d) twenty-first century under RCP2.6 (a,b) and RCP6.0 (c,d) relative to the average for the historical baseline period (1976–2005). The colour hues show the magnitude of change and the saturation indicates the agreement, among ensemble members, in the sign of change. The graph on the right of each panel shows the latitudinal mean.
+
+References:
+Rodell, M., Famiglietti, J. S., Wiese, D. N., Reager, J. T., Beaudoin, H. K., Landerer, F. W., & Lo, M. H. (2019). Emerging trends in global freshwater availability (vol 557, pg 651, 2018). Nature, 565(7739), E7E7.
+Pokhrel, Y., Felfani, F., Satoh, Y., Boulangé, J., Burek, P., Gádeke, A., ... & Wada, Y. (2021). Global terrestrial water storage and drought severity under climate change. Nature Climate Change, 11(3), 226233.
+Selvin, S., Vinayakumar, R., Gopalakrishnan, E. A., Menon, V. K., & Soman, K. P. (2017, September). Stock price prediction using LSTM, RNN and CNN-sliding window model. In 2017 international conference on advances in computing, communications and informatics (icacci) (pp. 1643-1647). IEEE.
+Feng, D., Fang, K., & Shen, C. (2020). Enhancing streamflow forecast and extracting insights using longshort term memory networks with data integration at continental scales. Water Resources Research, 56(9), e2019WR026793.
+Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., & Nearing, G. S. (2019). Toward improved predictions in ungauged basins: Exploiting the power of machine learning. Water Resources Research, 55(12), 11344-11354.
+
+Reviewer #2 (Remarks to the Author):
+
+The revisions of Wunsch et al. clearly improved the manuscript which benefits from adding RCP 2.6 & 4.5 as well as additional uncertainty analysis (Theil-Sen line) and discussion (ll. 347-367). However, from my perspective there remain two points for further revision:
+
+• The authors use the MK-trend test without pre-whiting. It is important to note that this test is only valid in case of no autocorrelation, otherwise the significance of the test will be overestimated. The authors correctly state that the seasonal autocorrelation is not relevant
+in the context of their MK-test as they only use annual values. However, apart from seasonal autocorrelation groundwater often exhibits autocorrelation on longer time scales as well. Based on my experience with groundwater data in Germany I would expect at least half of the groundwater records to show significant first-order autocorrelation for the annual values used in this work.
+
+As an example, I made a quick test and randomly selected one of the wells used for this work (file “NI_40000175_GW-Data.csv” from the repository). After calculating annual time series of the mean and 2.5- and 97.5-percentiles I get first-order autocorrelations of 0.35 (mean), 0.02 (2.5-percentile) and 0.65 (97.5-percentile). The correlations for the mean and the 97.5.-percentile are significant and definitely relevant in the context of MK-trend tests. If the author’s CNN model captures the dynamics of the well correctly, the modelled time series until 2100 will exhibit a similar autocorrelation structure and without appropriate pre-processing the MK-test will overestimate trend significance for this well.
+
+Hence, the authors will definitely have to check for autocorrelation and exclude where existent before using MK and characterizing trends as significant.
+
+Thank you for raising this important concern. We checked our calculations and first-order autocorrelation had indeed a certain influence on the results presented in our manuscript. We therefore applied 3PW method (mannkendall/Python package) after Collaud Coen et al. (2020). Advantage of this method is the combination of three pre-whitening approaches to overcome shortcomings and assumptions of each approach. Overall, slightly fewer results are considered significant now and some changes are considered a bit weaker; however, the general conclusions of our analyses still remain. We adapted the newly calculated trends to all relevant graphics in the manuscript and the supplement and corrected the text accordingly.
+
+References:
+
+Collaud Coen, M. et al. Effects of the prewhitening method, the time granularity, and the time segmentation on the Mann–Kendall trend detection and the associated Sen’s slope. Atmos. Meas. Tech. 13, 6945–6964 (2020).
+
+Vogt, F. P. A. mannkendall/Python. (Zenodo, 2021). doi:10.5281/ZENODO.4495590.
+
+• The authors discuss different sources of uncertainty including model uncertainty. However, models are usually trained to match mean conditions best but are much weaker in simulating extremes. Based on Figure 7 this seems to be the case also for the models used in this work as it can be clearly seen that the maxima of the time series are systematically underestimated. The plots in the supplements reveal similar problems for the extremes (mostly the upper extreme, sometimes also the lower extreme) at many stations. Hence, the studies’ results regarding the mean will be more robust than those regarding the extremes. To judge the validity of model results I think it is necessary to evaluate the model performance regarding the different metrics (annual mean, annual 2.5-/97.5-percentile) in more detail.
+
+Thank you for pointing out, this indeed deserves a detailed discussion. With validity, we can judge the model performance only for the comparably short testing period of 4 years, which makes it especially difficult to derive conclusions for extreme value performance, as mostly only four highs and four lows occur in four years. Nevertheless, we evaluated the relative model Bias (normalized on the historic Min-Max range), for this period and for all models. We included a discussion of this evaluation in the uncertainty section of our manuscript. We hope that this sharpens the different
+sources of uncertainty for the reader. We agree that in general the estimation of the mean conditions in the future is more robust than for the extreme values. However, we also think that due to the systematic nature of this error (even though difficult to quantify), that relative trends or tendencies derived from these models, still are reasonably interpretable, even for the extreme values.
+
+Reviewer #3 (Remarks to the Author):
+
+Comments:
+By revising the paper, the statements were once again clearly sharpened. It is now clear which general statements about groundwater development in Germany are possible and where the results still showed larger bandwidths that do currently not allow clear statements. With regard to climate impacts, it was clearly shown what influence global warming can have on groundwater availability in Germany. Furthermore, the results also clearly show that any global reduction in CO2-emissions will have a positive impact on groundwater level and groundwater yield. However, the results also show that the resource groundwater will change regionally in the future and that all users must adapt to this.
+
+From my point of view, I only have two small comments:
+
+• Line 41 ff.: this sentence is formulated somewhat unclearly. Actually, all models show a robust increase in temperature (i.e. (almost) all climate models agree on this), but there are drier and wetter models for precipitation, depending on the calculation approach. However, these statements cannot be read out of the text clearly.
+
+Thank you for pointing out. This is indeed an important aspect that should become clear from the text. We have modified this statement to be more precise. L 39-42
+
+• Line 56: to meet the needs.... Wouldn't it also be important to mention here that climate change, especially higher temperatures, also has an impact on changing water demands (not only in the city). This is particularly relevant when considering peak demands. This addition is not an absolute must, but could build an important bridge to practice.
+
+Thank you for pointing out this important aspect. We agree that water demands not only increase in urban areas but also in rural areas for example due to agricultural irrigation. In this sentence we already list growing population/urban areas, industry and agricultural irrigation. It seems that it nevertheless has not become clear that we refer to all of these factors, therefore we now slightly modified the wording. L 56-60
+Response to Reviewers
+
+Please find our statements (red) to the reviewers’ comments (black) in the following.
+
+Reviewer #2 (Remarks to the Author):
+
+I think the authors have replied satisfactorily to all points raised by the referees. The changes have further improved the quality of the paper and I have no other concerns.
+
+Thank you for your constructive criticism during the review process, which helped to improve the manuscript substantially. We are glad to read that there are no more concerns.

0297e09c8c2b5e744ded2ba5e84ab6868857ddbdce0ca65775323250f8a61cea/preprint/preprint.md

@@ -0,0 +1,388 @@
+Deep learning shows declining groundwater levels in Germany until 2100 due to climate change
+
+Andreas Wunsch (andreas.wunsch@kit.edu)
+Karlsruhe Institute of Technology    https://orcid.org/0000-0002-0585-9549
+Tanja Liesch
+Karlsruhe Institute of Technology
+Stefan Broda
+Federal Institute for Geosciences and Natural Resources
+
+Article
+
+Keywords: climate change, groundwater resources, machine learning, groundwater levels
+
+Posted Date: April 22nd, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-420056/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on March 9th, 2022. See the published version at https://doi.org/10.1038/s41467-022-28770-2.
+Abstract
+
+In this study we investigate how climate change will directly influence the groundwater resources in Germany during the 21st century. We apply a machine learning groundwater level prediction framework, based on convolutional neural networks to 118 sites well distributed over Germany to assess the groundwater level development under the RCP8.5 scenario, based on six selected climate projections, which represent 80% of the bandwidth of the possible future climate signal for Germany. We consider only direct meteorological inputs, while highly uncertain anthropogenic factors such as groundwater extractions are excluded. We detected significant declining trends of groundwater levels for most of the sites, revealing a spatial pattern of stronger decreases especially in the northern and eastern part of Germany, emphasizing already existing decreasing trends in these regions. We can further show an increased variability and longer periods of low groundwater levels during the annual cycle towards the end of the century.
+
+Introduction
+
+Climate change is increasingly altering water availability even in generally water-rich areas like Germany, where overall water stress is currently low¹. Nevertheless, hot and dry summers in recent years (especially 2018-2020) led to ongoing exceptional droughts²,³ with severe consequences for agriculture and ecology, such as drought damages in forests, reduced crop yields and extreme low flows in rivers. Drought effects accumulated over years, because winter precipitation did not compensate summer deficits. This applies not only, but especially to groundwater resources, which are of major importance since drinking water supply in Germany is strongly dependent on groundwater and springs (almost 70%)⁴. Declining groundwater levels due to generally reduced groundwater recharge and higher water demand in summer, regionally forced water suppliers to exploit their current maximum capacity during dry periods to meet the demand; locally even water supply shortages occurred. During future dry periods strong usage conflicts can be expected in areas of low water availability between water suppliers and industry (process and cooling water), additionally amplified by increasing agricultural irrigation demand, which currently has only minor significance with less than 2% of the total withdrawal volume¹. Knowledge of future groundwater level development, especially in the long-term, is therefore crucial to develop sustainable groundwater management plans to meet future demands, solve usage conflicts and protect ecosystems.
+
+Climate change affects groundwater in several direct and indirect ways⁵. Major direct drivers are changes in precipitation, snowmelt and evapotranspiration⁶. For Germany, climate projections show opposing trends in terms of water availability, with a slight increase in annual precipitation sums, i.e. more water, but at the same time a significant temperature increase of several degrees Celsius by 2100³⁴,³⁵, i.e. less water. The effect on groundwater resources is therefore not directly clear and needs to be analyzed. For Europe in general, higher precipitation is generally expected during winter, which in combination with a generally decreasing amount of snow, thus increasing direct infiltration, leads to higher groundwater recharge during winter and less in spring. Especially for snow dominated regions this might cause changes of seasonality⁶. Weather extremes are expected to intensify, therefore longer droughts and more frequent intense rainfall events will occur⁵. Generally higher temperatures cause higher atmospheric water demand, thus increasing evapotranspiration, leading to less infiltration and therefore less groundwater recharge. Especially unconfined, shallow aquifers are most
+likely to be sensitive to direct climate change effects\(^7\). Indirect climate change influences on groundwater are mostly related to anthropogenic groundwater withdrawals or associated with land-use changes\(^5\). It is known that the groundwater storage reduction caused by pumping could easily far exceed natural recharge\(^6,8\). The impact of these factors will be exacerbated as water demand increases to meet the needs of regionally growing population (mainly due to growing urban areas), industry and agricultural irrigation.
+
+In recent years, artificial neural network (ANN) approaches have proven their usefulness in predicting groundwater levels\(^9–14\), even using a highly transferable approach with purely climatic input parameters (e.g. ref\(^15\)). In a previous study\(^15\) we showed that 1D-Convolution Neural Networks (CNNs) are a good choice for groundwater level simulation, as they can provide high accuracy and furthermore are fast and reliable. Unlike physically-based models, which usually require a very good knowledge of local conditions and need to be time-consumingly built and calibrated, data-driven models such as ANNs are able to predict a target variable using only relevant driving forces. This makes studies on larger areas easier and is therefore the method of choice for this study. To the authors' knowledge, no comprehensive direct evaluation of groundwater level development until 2100 exists for Germany yet. Besides a rather old small-scale study\(^16\) also a regional-scale study for the Danube basin has been conducted to date\(^17\). The latter uses several dynamically-coupled, process-based model components and the authors found strongly declining groundwater levels with declines of up to 10 m close to the Alps in southernmost Germany for their scenario period (2036–2060). Further, several studies investigated future groundwater recharge in different contexts for subregions of Germany using mainly water balance models or process-based models\(^17–22\). Furthermore, the application of ANNs to study groundwater level development in the long-term and in the context of climate change for a larger area like Germany has not been performed yet. Related studies with applications of ANNs either used a very small number of wells\(^23–25\) and limited time horizons\(^23,24\) or use ANNs without directly presenting future climate signals to the ANN\(^25\). In case of streamflow runoff simulation, however, ANNs have been successfully applied to analyze the future development under climate change influences in several catchments all over California\(^26\) as well as two catchments in China\(^27,28\).
+
+In this study we use a 1D-CNN approach\(^29\) to build 118 site-specific models, well distributed all over Germany in the respective uppermost unconfined aquifer, which are able to predict weekly groundwater levels with high accuracy using only precipitation and temperature as inputs in the past. We visually check the model output plausibility under an artificial extreme climate scenario\(^26\) and investigate how the model has learned input-output relationships using an explainable AI approach (SHAP\(^30\)). We then use the trained CNN models to investigate the future groundwater level development for the selected sites, using precipitation and temperature derived from the RCP8.5 scenario\(^31\) of bias-corrected and downscaled (5 x 5 km\(^2\)) climate projection data\(^32\) from six climate models as inputs. These six climate models were preselected by the German Meteorological Service to represent 80% of the possible future climate signal ("core-ensemble")\(^33\) for Germany. Table 1 lists these projections, which are part of the EURO-CORDEX Ensemble and assigns them an abbreviation that will be used as a synonym in the remaining part of the paper. As we use purely climatic input parameters we can only project the influence of direct climate change effects, while secondary, most certainly stronger indirect effects, such as increased groundwater pumping, are not included in this study. However, due to high prediction accuracy in the past, the selected sites are unlikely to be under the influence of strong groundwater
+withdrawals or comparable effects, and are therefore suitable for predicting that part of the future groundwater level trend that results from direct climatic influences, as long as the basic input-output relationships remain unchanged.
+
+Table 1: Climate projections used in this study and according abbreviations used throughout the text. For more information on the models please visit https://www.euro-cordex.net/ .
+
+<table>
+  <tr>
+    <th>Projection</th>
+    <th>Abbrev.</th>
+  </tr>
+  <tr>
+    <td>CCCma-CanESM2_rcp85_r1i1p1_CLMcom-CCLM4-8-17</td>
+    <td>p1</td>
+  </tr>
+  <tr>
+    <td>ICHEC-EC-EARTH_rcp85_r1i1p1_KNMI-RACMO22E</td>
+    <td>p2</td>
+  </tr>
+  <tr>
+    <td>MIROC-MIROCS5_rcp85_r1i1p1_GERICS-REMO2015</td>
+    <td>p3</td>
+  </tr>
+  <tr>
+    <td>MOHC-HadGEM2-ES_rcp85_r1i1p1_CLMcom-CCLM4-8-17</td>
+    <td>p4</td>
+  </tr>
+  <tr>
+    <td>MPI-M-MPI-ESM-LR_rcp85_r1i1p1_UHOOH-WRF361H</td>
+    <td>p5</td>
+  </tr>
+  <tr>
+    <td>MPI-M-MPI-ESM-LR_rcp85_r2i1p1_MPL-CSC-REMO2009</td>
+    <td>p6</td>
+  </tr>
+</table>
+
+Generally, climate projections show a slight increase in precipitation sums and a significant temperature increase of several degrees Celsius for Germany by 2100^{34,35}, exact values depending on the scenario considered^{35}. Figure 1 shows the change of total annual precipitation (A1-A3) and annual average temperature (B1-B3) for each of the climate projections used in this study in 2100, compared to the start of our investigation in 2014. The change is derived from a linear trend analyses at the 118 sites, that are subject to further investigations in this study. Boxplots (A2, B2) show only significant (p < 0.05) changes, according numbers are shown in subplots A3 and B3, further, the order within subplots A1 and B1 does not correspond to the numbering of the projections but to the strength and direction of the trend. We see that many projections of total annual precipitation do not show any significant trend and are therefore marked in grey (especially p2, p4 and p5, s.a. Figure 1-A3). However, for almost all sites we observe significant declines of up to -450 mm per year for p1, but at the same time increases of up to 296 mm per year for p3 and especially p6. Some projections are therefore diverging until 2100 in terms of precipitation sums, which shows that we cover a large range of a possible climate signal under the RCP8.5 scenario. Despite many non-significant trends, a spatial pattern of significant changes with a decreasing tendency in northwestern Germany and less clear increasing tendency in eastern Germany is visible. Strongest decreases are projected to occur in southernmost Germany; however, especially in southern but also in eastern areas two opposing trends usually occur at one site, so the development is not unambiguous. Compared to precipitation sums, the development of the annual average temperature is more consistent for all projections. Overall, temperature increases between 2.4°C and 5.8°C occur. On average, p1 shows the strongest increases, followed by p4. Together with the decreasing precipitation sums, p1 therefore shows the probably most challenging development in terms of water availability compared to the other projections used in this study. Spatially, we observe lighter temperature increases in north-western Germany, which most certainly is linked to a buffer effect near the coast.
+
+Results
+
+Individual projection results
+
+For each of the examined 118 test sites, we simulated the future weekly groundwater level development based on six climate projections (s.a. Table 1). Since these climate projections differ considerably in detail for individual future time periods, we also obtained six different future groundwater level simulations, which should only be interpreted on the basis of longer time periods (at least 30 years)^{36}. Figure 2 depicts the trend
+as the relative development in percent of the annual mean for each of the six projections (A) as well as the annual upper extreme (97.5%) quantile (B) and the annual lower extreme (2.5%) quantile (D) for all test sites in 2100, compared to the start of the simulation (2014) and normalized on the individual historic range as explained in the methods section. For each site, all relative developments are shown ordered by the strength of the change, the order does therefore not correspond to the numbering of the projections. The given boxplots in Figure 2C provide more detailed information for the three maps as well as on the development of the 25% and the 75% quantiles, relative and absolute values of the presented changes are given in Table 2. The values of the non-significant trends are not shown in the boxplots, which has to be kept in mind for interpretation, especially for quantiles with many non-significant trends (compare Table 2).
+
+In case of the mean, approximately 54% of all simulations (387 of 708, i.e. six projections for each of the 118 sites) show a significant trend until 2100. At least one of the projected developments is always considered significant (p<0.05) for each site, which, however, also means that there are several sites with mainly non-significant trends (grey). The large majority of the significant trends is negative with a median ranging between -23% in case of p1 and -6.6% in case of p6 (Table 2). In Figure 2C we observe that p1 systematically shows the strongest declines until 2100, being significant for 117 of the 118 wells. The overall maximum decline is -46%, clearly indicating the different character of p1 compared to the other projections. Especially projections p3-p5 show more moderate changes of the mean (median ranges from -8% to -13%), with many non-significant trends (35%-54%). Simulations based on p2 and p6 only find significant trends for around 30% of all sites and additionally are moderate in their significant results. Three projections (p2, p3, but mainly p6, compare Table 2) even show some positive developments until 2100, however overall, such developments are rare and occur at sites, where other projections simultaneously show at least non-significant or even negative trends. In absolute numbers the mentioned median changes are in the order of -0.1 m to -0.4 m, which is highly dependent on the individual groundwater level range at each site. Despite many non-significant and some positive trends, there is a clear tendency of declining mean groundwater levels until 2100. Additionally, we can observe a slight spatial tendency with more and stronger significant negative trends in some areas of northern and eastern Germany, where we also find the strongest overall relative declines. In southern Germany many wells show several non-significant trends and also most positive changes can be found scattered in this region, however, some of the southernmost wells show very strong declines for single simulations, comparably to the strong declines in eastern Germany.
+
+In case of the upper extreme value quantile (97.5%) this spatial pattern is partly confirmed. In Figure 2B we clearly observe many significant declines in eastern Germany, while the large majority (>70%) of the trends in whole Germany is considered to be non-significant. Increasing trends are found comparably often for the 97.5% quantiles, with increases up to 20%. Comparing the projections with each other (Figure 2C), we find a similar behavior as before: p1 shows the strongest significant decreases (down to -47%), p3, p4 and p5 tend to move in the moderate negative range (medians around -12%), while p2 and p6 more often show positive trends (positive medians of the significant trends). We therefore observe partly a contradictory development of the upper extreme values compared to the mean. The absolute numbers of the mentioned changes again are in the order of few tens of centimeters upwards and downwards. The strongest simulated absolute increase (max. of p6) is almost 5 meters, however, in a karstic well in southern Germany, which has a high variability anyway.
+The tendency of declining groundwater levels we observed for the mean, gets clearer for the lower extreme values (2.5% quantile) shown in Figure 2D. We still observe 36% non-significant trends, however the remaining 65% show almost exclusively negative changes with a maximum decline of -81% (Table 2). The median change of the 2.5% quantile of all projections ranges between -38% for p1, which again shows the strongest declines, followed by p4 (-21%), as well as p2, p3, p5 and p6 with a median change around -10% each. The latter four, and especially of them p6, contain the majority of non-significant trends, the changes shown in the boxplots therefore tend to be overestimated. There are only few sites where only one result is considered significant. These occur mainly near the Baltic Sea coast, the central and eastern part of northern Germany, and the central area of southern Germany. In the latter, however, there are at the same time quite strong relative decreases, just as we also find them in eastern Germany and in the western part of northern Germany. This pattern is largely consistent with the spatial pattern of the mean mentioned above. Most median decreases (p2-p6) are in the order of -0.1 to -0.4 m, for p1 the median decrease reaches even -0.7 m for the annual lower extreme value quantile. All projections except p6 agree that of all significant changes, at least a decrease of -0.1 m will be observed (max. values for 2.5% quantile in Table 2).
+
+Considering all results, we see a clear tendency toward declining groundwater levels overall, with stronger declines for lower quantiles, i.e. groundwater level lows will occur more frequently and will be more severe in the future. At the same time, mostly no or even increasing trends are found for upper extreme values, which means that the overall variability will increase significantly by the end of the century.
+
+Table 2: Detailed numbers for each projection on relative changes (left), already shown as boxplots (Figure 2C). Right tables show associated absolute changes in meters.
+
+<table>
+  <tr>
+    <th colspan="7">Relative [%]</th>
+    <th colspan="7">Absolute [m]</th>
+  </tr>
+  <tr>
+    <th></th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>mean</th>
+  </tr>
+  <tr>
+    <td>Max</td><td>-18.9</td><td>-18.3</td><td>-23.9</td><td>-13.7</td><td>-13.3</td><td>-20.6</td><td>2.1</td><td>3.1</td><td>0.6</td><td>1.2</td><td>1.2</td><td>4.0</td><td>1.9</td>
+  </tr>
+  <tr>
+    <td>Upper Quartile</td><td>-12.3</td><td>-10.5</td><td>-12.2</td><td>-8.5</td><td>-6.0</td><td>-13.0</td><td>-0.2</td><td>0.2</td><td>0.0</td><td>-0.1</td><td>0.1</td><td>0.5</td><td>0.0</td>
+  </tr>
+  <tr>
+    <td>Median</td><td>-17.8</td><td>-7.5</td><td>-12.0</td><td>-12.3</td><td>-10.7</td><td>-10.7</td><td>-0.3</td><td>0.1</td><td>-0.2</td><td>-0.2</td><td>-0.2</td><td>0.2</td><td>-0.1</td>
+  </tr>
+  <tr>
+    <td>Lower Quartile</td><td>-23.5</td><td>-9.3</td><td>-15.6</td><td>-16.9</td><td>-14.2</td><td>-4.7</td><td>-0.6</td><td>-0.2</td><td>-0.3</td><td>-0.4</td><td>-0.4</td><td>-0.4</td><td>-0.3</td>
+  </tr>
+  <tr>
+    <td>Min</td><td>-46.8</td><td>-16.3</td><td>-30.4</td><td>-31.9</td><td>-30.6</td><td>-16.5</td><td>-2.8</td><td>-1.3</td><td>-0.4</td><td>-0.7</td><td>-0.7</td><td>-0.8</td><td>-0.7</td>
+  </tr>
+  <tr>
+    <td>No. of sign. samples</td><td>45</td><td>20</td><td>31</td><td>34</td><td>32</td><td>39</td><td>45</td><td>20</td><td>31</td><td>34</td><td>32</td><td>39</td><td>201</td>
+  </tr>
+</table>
+
+<table>
+  <tr>
+    <th colspan="7">Relative [%]</th>
+    <th colspan="7">Absolute [m]</th>
+  </tr>
+  <tr>
+    <th></th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>mean</th>
+  </tr>
+  <tr>
+    <td>Max</td><td>18.3</td><td>14.0</td><td>22.9</td><td>12.5</td><td>9.4</td><td>20.2</td><td>2.1</td><td>2.5</td><td>2.0</td><td>1.8</td><td>0.1</td><td>4.8</td><td>2.2</td>
+  </tr>
+  <tr>
+    <td>Upper Quartile</td><td>-10.6</td><td>8.4</td><td>-6.7</td><td>-8.2</td><td>-7.4</td><td>-12.0</td><td>-0.2</td><td>0.1</td><td>-0.1</td><td>-0.1</td><td>0.3</td><td>0.0</td><td>0.0</td>
+  </tr>
+  <tr>
+    <td>Median</td><td>-16.3</td><td>-7.9</td><td>-9.4</td><td>-11.1</td><td>-8.9</td><td>-7.4</td><td>-0.3</td><td>-0.1</td><td>-0.2</td><td>-0.2</td><td>-0.2</td><td>0.2</td><td>-0.1</td>
+  </tr>
+  <tr>
+    <td>Lower Quartile</td><td>-22.2</td><td>-12.2</td><td>-15.3</td><td>-16.6</td><td>-13.1</td><td>-8.0</td><td>-0.6</td><td>-0.2</td><td>-0.3</td><td>-0.3</td><td>-0.1</td><td>-0.1</td><td>-0.1</td>
+  </tr>
+  <tr>
+    <td>Min</td><td>-44.1</td><td>-16.3</td><td>-30.8</td><td>-33.5</td><td>-24.5</td><td>-17.7</td><td>-1.6</td><td>-0.6</td><td>-0.7</td><td>-0.7</td><td>-0.9</td><td>-0.8</td><td>-0.8</td>
+  </tr>
+  <tr>
+    <td>No. of sign. samples</td><td>64</td><td>25</td><td>46</td><td>45</td><td>47</td><td>40</td><td>64</td><td>25</td><td>46</td><td>45</td><td>47</td><td>40</td><td>267</td>
+  </tr>
+</table>
+
+<table>
+  <tr>
+    <th colspan="7">Relative [%]</th>
+    <th colspan="7">Absolute [m]</th>
+  </tr>
+  <tr>
+    <th></th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>mean</th>
+  </tr>
+  <tr>
+    <td>Max</td><td>-6.8</td><td>8.5</td><td>11.7</td><td>-6.5</td><td>-4.3</td><td>15.0</td><td>2.1</td><td>1.5</td><td>1.0</td><td>-0.1</td><td>4.1</td><td>1.1</td>
+  </tr>
+  <tr>
+    <td>Upper Quartile</td><td>-17.8</td><td>-6.4</td><td>7.8</td><td>-9.7</td><td>-8.7</td><td>-6.8</td><td>-0.3</td><td>-0.1</td><td>-0.2</td><td>-0.1</td><td>-0.2</td><td>-0.1</td><td>-0.2</td>
+  </tr>
+  <tr>
+    <td>Median</td><td>-22.9</td><td>-10.6</td><td>-12.7</td><td>-8.4</td><td>-8.6</td><td>-11.6</td><td>-0.4</td><td>-0.1</td><td>-0.2</td><td>-0.2</td><td>-0.1</td><td>-0.2</td><td>-0.2</td>
+  </tr>
+  <tr>
+    <td>Lower Quartile</td><td>-28.1</td><td>-11.9</td><td>-12.8</td><td>-17.5</td><td>-12.1</td><td>-9.3</td><td>-0.6</td><td>-0.2</td><td>-0.3</td><td>-0.5</td><td>-0.3</td><td>-0.4</td><td>-0.4</td>
+  </tr>
+  <tr>
+    <td>Min</td><td>-46.0</td><td>-18.2</td><td>-27.0</td><td>-31.4</td><td>-22.3</td><td>-14.2</td><td>-6.5</td><td>-1.1</td><td>-3.6</td><td>-5.0</td><td>-1.1</td><td>-0.4</td><td>-3.0</td>
+  </tr>
+  <tr>
+    <td>No. of sign. samples</td><td>117</td><td>35</td><td>66</td><td>76</td><td>54</td><td>39</td><td>117</td><td>35</td><td>66</td><td>76</td><td>54</td><td>39</td><td>387</td>
+  </tr>
+</table>
+
+<table>
+  <tr>
+    <th colspan="7">Relative [%]</th>
+    <th colspan="7">Absolute [m]</th>
+  </tr>
+  <tr>
+    <th></th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>mean</th>
+  </tr>
+  <tr>
+    <td>Max</td><td>-12.2</td><td>-5.0</td><td>-4.6</td><td>-7.3</td><td>-5.0</td><td>-10.0</td><td>-0.3</td><td>-0.1</td><td>-0.1</td><td>-0.1</td><td>-0.1</td><td>0.1</td><td>0.1</td>
+  </tr>
+  <tr>
+    <td>Upper Quartile</td><td>-29.9</td><td>-8.3</td><td>-9.1</td><td>-13.4</td><td>-7.8</td><td>-7.7</td><td>-0.5</td><td>-0.2</td><td>-0.2</td><td>-0.2</td><td>-0.1</td><td>-0.2</td><td>-0.2</td>
+  </tr>
+  <tr>
+    <td>Median</td><td>-34.9</td><td>-11.3</td><td>-12.3</td><td>-17.6</td><td>-10.0</td><td>-9.0</td><td>-0.6</td><td>-0.2</td><td>-0.2</td><td>-0.3</td><td>-0.2</td><td>-0.3</td><td>-0.3</td>
+  </tr>
+  <tr>
+    <td>Lower Quartile</td><td>-42.2</td><td>-14.2</td><td>-15.5</td><td>-22.4</td><td>-14.0</td><td>-10.2</td><td>-1.0</td><td>-0.3</td><td>-0.4</td><td>-0.6</td><td>-0.3</td><td>-0.5</td><td>-0.5</td>
+  </tr>
+  <tr>
+    <td>Min</td><td>-67.8</td><td>-23.1</td><td>-51.1</td><td>-41.4</td><td>-28.1</td><td>-15.5</td><td>-12.8</td><td>-3.0</td><td>-3.8</td><td>-7.6</td><td>-1.1</td><td>-2.8</td><td>-1.1</td>
+  </tr>
+  <tr>
+    <td>No. of sign. samples</td><td>118</td><td>53</td><td>66</td><td>65</td><td>51</td><td>38</td><td>118</td><td>53</td><td>66</td><td>65</td><td>51</td><td>38</td><td>410</td>
+  </tr>
+</table>
+
+<table>
+  <tr>
+    <th colspan="7">Relative [%]</th>
+    <th colspan="7">Absolute [m]</th>
+  </tr>
+  <tr>
+    <th></th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>p1</th><th>p2</th><th>p3</th><th>p4</th><th>p5</th><th>p6</th><th>mean</th>
+  </tr>
+  <tr>
+    <td>Max</td><td>-12.6</td><td>-4.2</td><td>-5.1</td><td>-7.5</td><td>-4.0</td><td>-8.0</td><td>-0.3</td><td>-0.1</td><td>-0.1</td><td>-0.1</td><td>-0.1</td><td>0.1</td><td>0.1</td>
+  </tr>
+  <tr>
+    <td>Upper Quartile</td><td>-31.1</td><td>-8.8</td><td>-8.6</td><td>-15.6</td><td>-7.8</td><td>-7.2</td><td>-0.5</td><td>-0.2</td><td>-0.2</td><td>-0.2</td><td>-0.1</td><td>-0.2</td><td>-0.2</td>
+  </tr>
+  <tr>
+    <td>Median</td><td>-37.7</td><td>-11.5</td><td>-12.5</td><td>-17.6</td><td>-10.7</td><td>-9.7</td><td>-0.6</td><td>-0.2</td><td>-0.2</td><td>-0.3</td><td>-0.2</td><td>-0.3</td><td>-0.3</td>
+  </tr>
+  <tr>
+    <td>Lower Quartile</td><td>-45.9</td><td>-15.0</td><td>-14.4</td><td>-25.9</td><td>-12.9</td><td>-11.3</td><td>-1.0</td><td>-0.3</td><td>-0.4</td><td>-0.7</td><td>-0.3</td><td>-0.5</td><td>-0.5</td>
+  </tr>
+  <tr>
+    <td>Min</td><td>-80.8</td><td>-27.6</td><td>-26.7</td><td>-45.1</td><td>-25.1</td><td>-15.5</td><td>-15.6</td><td>-4.1</td><td>-3.4</td><td>-9.9</td><td>-2.0</td><td>-3.7</td><td>-6.3</td>
+  </tr>
+  <tr>
+    <td>No. of sign. samples</td><td>118</td><td>72</td><td>66</td><td>102</td><td>60</td><td>37</td><td>118</td><td>72</td><td>66</td><td>102</td><td>60</td><td>37</td><td>455</td>
+  </tr>
+</table>
+
+Figure 3 shows the detailed development at four selected sites (black boxes in Figure 2). For each site we plot the six projected groundwater level time series for the far future (2070-2100) (A1-D1), as well as the complete simulations, separately as heatmaps with years as row and weeks as columns (A2-D2). The time series plots show the diverging development of some projections in the far future, however, there is no strict sequence of
+projections in terms of absolute groundwater height, the order can change throughout the years. Most heatmaps show the development described above by displaying generally declining groundwater levels (more and darker red, as well as lighter or constant blue shadings towards 2100 in the lower part of the heatmaps). What we additionally see now is that the length of low groundwater levels increases (red shadings get wider) for all sites. The time of higher groundwater levels throughout the year shows two possible developments of either getting shorter (blue shadings get narrower, e.g. B2-p1 or even change to red, e.g. D2-p4) or staying constant in length (width of blue shadings does not change, e.g. A2-p2 and A2-p6), with optionally even increasing peak height (darker blue, e.g. A2-p6). In both plot types we can also recognize sequences of several more extreme years, such as several dry years around 2090 in B1-p4, which also reflects in a dark-red stripe in the corresponding heatmap (B2-p4). Such sequences are especially critical because effects accumulate and dependent ecosystem are not able to recover but are instead particularly vulnerable to further damage in subsequent years due to reduced resilience.
+
+Average projection results
+
+We consolidated the separate projection results for each site into one by calculating the mean of the significant trends shown in Figure 2. Only sites with at least 4 (thus the majority) significant results are included, the rest is depicted as not significant on average. Results are shown in Figure 4. The development of the mean is depicted in the upper left map and we find, that according to the aforementioned definition, 41% of the wells (49 of 118) are considered significant on average and on median show a change of -13%. We do not find any wells with increasing mean trends and observe a similar spatial pattern as before with strongest decreases in eastern Germany. For wells in southern Germany we observe noticeably many non-significant changes. All in all, we simulated significant average decreases between -0.2 m to -2.4 m for about 25 wells, and at least a decrease of -10 cm for all 49 wells in Figure 4A (max. abs. value of the mean in Figure 4D). In case of the upper extreme value quantile (97.5%) we can summarize that the consolidated results show mainly no trends, especially for southern Germany, they will therefore probably remain at their current level. Few sites (5), all of them in northern Germany, are expected to show increased upper extreme values up to a maximum of 15% or 1.5 m, however, we still observe a spatial pattern of decreasing upper extreme values in eastern Germany up to -30% or -0.7 m. Hence, in this area the groundwater levels probably will decrease in every part of the annual cycle and with comparably high certainty (many consistent significant simulations). This applies also to the lower extreme values (2.5% quantile) that show on average significant decreases for more than half of the examined sites all over Germany with median decreases of -19% (equivalent to -0.3 m, comp. Figure 4C, D). On this map, no clear spatial pattern is recognizable any longer.
+
+Annual maximum and minimum timing aspects
+
+Besides the relative and absolute developments of the groundwater height, we also investigated timing aspects of the groundwater dynamics. For a possible shift of the annual minimum (Figure 5) we found significant (p<0.05) results for p1 (41 of 118) and also p4 (33 of 118), with median shifts of 3.4 and 3.1 weeks (positive, i.e. later. A spatial pattern exists, showing significant and stronger shifts with increasing proximity to the coast in the north and no or even negative (i.e. earlier) shifts in the south. However, please note that most results are not significant and the shown pattern may only serve as an indication for further interpretation.
+Even fewer significant shift were found in case of the annual maximum timing (not shown). Especially for snow dominated regions a shift of the peak timing from spring towards the winter is expected in the context of climate change, however, Germany as a whole cannot be considered snow-dominated. This is in accordance with our findings, because we found mainly non-significant shifts (< 10 per projection). Only in case of p4 we detected a slightly larger number of significant shifts (29 of 118). Here, the maximum even occurs on median 4 weeks later during the annual cycle, in contrary to the expected shift for snow-dominated regions.
+
+Model input analysis
+
+From the combined analysis of our groundwater level simulations and the model inputs shown in the introduction, we can conclude, that temperature is mainly the driving factor for declining groundwater levels, rather than precipitation. This applies because mostly no significant or even increasing precipitation is projected, our models, however, still frequently show declining groundwater level tendencies, which therefore most likely are caused by the significantly increased temperature until the end of the century. Therefore, our results are consistent with other studies, which indicate that the reduction in water availability in the future is driven primarily by changes in temperature34.
+
+This reflects also in the model interpretability approach (SHAP values) we used to check the plausibility of our model outputs. The minimum SHAP value for T is mostly lower than the minimum SHAP value observed for P (except for eight sites); i.e. the models have learned that high temperatures can cause stronger decreasing groundwater levels than low precipitation. This is, however, only an interpretation of what was learned, which agrees with our conception. A causality cannot be derived from this.
+
+Discussion
+
+The results of our simulations show a nation-wide decrease in groundwater levels by the end of the century. The absolute changes may seem small, but the fact that we investigated almost exclusively shallow aquifers and sites with very small depths to groundwater, reinforces the importance of the results, predominantly in terms of water availability for vegetation and agriculture. A decline of several tens of centimeters (depending on the projection and the area) can be vital for plants during hot and dry periods, if, as a result, the groundwater is no longer accessible. Furthermore, a related study showed, that for large parts of northern Germany, a decline of the groundwater levels by 10 cm can be considered critical in terms of altered streamflow discharge due to reduced baseflow from groundwater8. This has already been visible during the last two years, when simultaneously to low groundwater levels also extremely low water levels in surface waters (even until running dry) have been observed3. Our results show a clearer tendency of declining groundwater levels in the North and East compared to the South (Figure 4A), which emphasizes the already existing trends and patterns. However, in the southernmost part of Germany, for some individual projections, we find also some of the strongest declines (Figure 2). It is very important to note that the assessed results are only long-term averages of a future development. As recent developments showed, the succession of several dry years is much more critical than the overall trend. In such periods, the projected effects accumulate over consecutive years to extremely low groundwater levels, and thus more severe consequences are to be expected. Such longer dry periods are most likely to be averaged out, in a linear trend analysis, as performed in this study, but their existence can be seen in the examples shown in Figure 3. Future research should pay attention to this aspect more intensively. It is also
+important to recall that we model simply direct climate effects on groundwater levels, thus the change is based on the development of temperature and precipitation until the end of the century only, and we assume that the basic input-output relationship or system behavior does not change. However, it can be expected that in many cases, the system behavior will be influenced by future changes in groundwater extractions, changes in vegetation and land use, as well as surface sealing and other related factors. Groundwater withdrawals in particular, are expected to increase due to regionally growing population especially in metropolitan areas (drinking water demand) and increasing demand for industry, energy and especially irrigated agriculture. As a result, the groundwater level will inevitably drop further if no active measures, such as limitation of withdrawals, avoidance of irrigated agriculture by changing crop types or even artificial recharge by infiltration, are applied. Despite all these limitations, the results give a good impression of the magnitude of changes to be expected purely due to direct climatic influences.
+
+Methods
+
+Data
+
+We used weekly groundwater level data from 118 different sites, well distributed all over Germany (Figure 6A). All wells are located in the unconfined, uppermost (thus mostly shallow) aquifers, which are most likely to be subject to direct climate change effects. Greater depths to groundwater are predominantly found in fractured and karstic aquifers. For additional details on the sites please refer to our supplementary material. Groundwater level records of all sites show very different lengths (Figure 6B), from 15 to 67 years, with a median length of 36 years. Data gaps were closed using information of several related groundwater level time series with highly correlated dynamics\(^{37}\). Information on interpolated values are included into the dataset (see section data availability).
+
+Input parameters for our models are purely climatic: precipitation (P) and temperature (T). They are widely available and easy to measure in the past and present, and also well evaluated in terms of climate projection output. Precipitation serves as proxy for groundwater recharge, temperature for evapotranspiration. Additionally, temperature usually shows a distinct annual cycle, which also provides the models with valuable information on seasonality. Since we specifically selected wells with high forecast accuracy in the past (see Model Calibration and Evaluation), we can assume that groundwater dynamic at these wells is mainly dominated by climate forcings. As long as no fundamental change of the system relations occurs (e.g. newly installed groundwater pumping or severe changes in land use nearby), we can expect reasonable results for our simulations.
+
+Besides the groundwater level data itself, we based our analysis on several datasets. The models were trained using data from the HYRAS dataset\(^{38,39}\), which is a gridded (5x5 km\(^2\)) meteorological dataset based on observed data from meteorological stations ranging from 1951 to 2015. To evaluate the influence of climate change we used RCP8.5 scenario data from six selected climate projections that form the so called core-ensemble defined by DWD\(^{33}\). The core-ensemble is specifically selected for Germany and derived from a larger set of 21 climate projections ('reference-ensemble')\(^{33}\) to represent 80% of the bandwidth of the possible future climate signal. Further, we received the projection data bias adjusted onto the HYRAS dataset and regionalized on a 5x5 km\(^2\) grid by ref\(^{32}\).
+Convolutional neural networks (CNNs)
+
+Convolutional Neural Networks (CNNs)⁴⁰ are commonly used for image recognition and classification tasks but also work well on sequential data, such as groundwater level time series²⁹. The CNNs used in this study comprise a 1D-Convolutional layer with fixed kernel size (3) and optimized number of filters, followed by a Max-Pooling layer and a Monte-Carlo dropout layer, applying a fixed dropout of 50% to prevent the model from overfitting. A dense layer with optimized size follows, succeeded by a single output neuron. We used the Adam optimizer for a maximum of 100 training epochs with an initial learning rate of 0.001 and applied gradient clipping to prevent exploding gradients. Early stopping algorithm with a patience of 15 epochs was applied as another regularization technique to prevent the model from overfitting the training data. Several model hyperparameters (HP) were optimized using Bayesian optimization⁴¹: training batch size (16 to 256); input sequence length (1 to 52 weeks); number of filters in the 1D-Conv layer (1 to 256); size of the first dense layer (1 to 256). All models were implemented using Python 3.8⁴², the deep-learning framework TensorFlow⁴³ and its Keras⁴⁴ API. Further, the following libraries were used: Numpy⁴⁵, Pandas⁴⁶,⁴⁷, Scikit-Learn⁴⁸, BayesOpt⁴¹, Matplotlib⁴⁹, Unumpy⁵⁰ and SHAP³⁰.
+
+Model calibration and evaluation
+
+In this study we used weekly groundwater level time series data of varying length (Figure 6B). To find the best model configuration we split every time series into four parts: training set, validation set, optimization set and test set. The test set uses always the 4-year period from 2012 to 2016 (Figure 7B, s.a. Figure 8A for an example), for few sites where the time series ended slightly earlier, we shifted the test set accordingly. The first 80% of the remaining time series before 2012 were used for training, the following 20% for early stopping (validation set) and for testing during HP optimization (optimization set), using 10% of the remaining time series each (Figure 7B). As acquisition function during HP optimization we chose the sum of Nash-Sutcliffe efficiency (NSE) and squared Pearson r (R²) (compare ref¹⁵), because in this study we used mainly these two criteria to judge the accuracy of the final optimized model in the test section. For each model we used a maximum optimization step number of 150 or stopped after 15 steps without improvement once a minimum of 60 steps was reached. Generally, we scaled the data to [-1,1] and used an ensemble of 10 pseudo-randomly initialized models to reduce the dependency towards the random number generator seed. For each of the ten ensemble members, we applied Monte-Carlo dropout during simulation to estimate the model uncertainty from 100 realizations each. We derived the 95% confidence interval from these 100 realizations by using 1.96 times the standard deviation of the resulting distribution for each time step. Each uncertainty was propagated while calculating the overall ensemble median value for final evaluation in the test set (2012-2016). We calculated several metrics to judge the simulation accuracy: Nash-Sutcliffe efficiency (NSE), squared Pearson r (R²), absolute and relative root mean squared error (RMSE/rRMSE), as well as absolute and relative Bias (Bias/rBias). Note that we calculate NSE with a long term mean GWL before the test set. Please see ref²⁹ for more details on calculation as the same approach was used. We use only wells, at which the models showed a very high forecast accuracy in the test-set (mostly NSE and R² larger than 0.8, compare Figure 7A). Some models were included with slightly lower accuracy (at least NSE and R² larger than 0.7) to improve the spatial coverage resulting in a set of 118 wells from all over Germany. For additional details on the error measures and hyperparameters for all sites please refer to our supplementary material.
+Model plausibility and interpretability
+
+To perform groundwater level simulations until 2100 we retrained all models using the defined hyperparameters and all data until 2014. Hence, we split the time series only in two parts: 80% for training and 20% for early stopping (Figure 7B). Afterwards, we assessed the model stability and the plausibility of the output values in the extrapolated regime accordingly to ref\(^{26}\) by evaluating the model output using artificially altered input data based on historical observed climatology with quadruple precipitation and systematically 5°C higher temperature (Figure 8B). As long as the model output does not “blow up” or produce meaningless outputs\(^{26}\), we hereby improve confidence in the model output when investigating the RCP8.5 climate change scenario. Models showing implausible behavior were not considered for this study. We additionally applied an explainable AI approach to check, whether the models have learned correctly in terms of our hydrogeological understanding. We calculated SHAP\(^{30}\) values that explain the influence (sign and strength) of every input feature value on the model output (Figure 8C). Generally, our models showed that the relationship between input and output was captured plausibly. For example, high precipitation inputs (red) produce high SHAP values and therefore have a strongly positive influence on the model output, which corresponds to our basic understanding of the influence of recharge, leading to increasing groundwater levels. Low or no precipitation (blue) has a comparably very slight negative influence on GWL, whereas high temperature inputs (red) have a strong negative influence on the model output. Again, this corresponds with our basic understanding of the governing processes, where high temperature usually means high evapotranspiration, which causes less recharge or even direct groundwater evaporation in some cases. This sounds trivial, however, during preliminary work for this study we found that not all models capture these relations correctly, which also partly caused erroneous values in the extrapolated regime. Figure 8 exemplarily summarizes the model evaluation (A) and plausibility checks (B, C) for one well. Check the supplement for the respective figures of all other sites.
+
+Evaluation of the groundwater results
+
+For our simulation results until 2100, we examined the relative development of the mean and the following quantiles over time: 2.5% (lower extreme quantile), 25% (lower quartile), 75% (upper quartile), and 97.5% (upper extreme quantile). All were site-specifically calculated on a yearly basis for each individual projection, followed by a linear trend analysis. In doing so, we are able to capture both the range and the individual development of all considered future climate projections. To make comparisons between different sites possible, results are normalized on the individual range of each historic groundwater level time series between the years 2000 and 2014 (start of simulation). Even though all climate projections are bias-adjusted on the HYRAS training dataset, they still do not depict the real climate development for individual years (also historically), which can cause a bias between the end of historic data records and the start of our simulations. We therefore investigated the trend of the aforementioned quantities between the start of the simulation and the end in 2100 and did not directly consider the end of the historic records. We examined each quantity development using Mann-Kendall linear trend test\(^{51}\) and derived the relative development in percent from a linear fit using Theil-Sen slope. We considered a trend significant for p < 0.05.
+
+Declarations
+
+Data availability
+All groundwater level data are available free of charge from the respective websites of the local authorities. We used data interpolated based on previous knowledge and therefore publish the used data with the kind permission of the local authorities under:
+
+https://doi.org/10.5281/zenodo.4683879
+
+All climate data are available on request and free of charge for non-commercial purposes from the German Meteorological Service.
+
+Code availability
+
+The code necessary to reproduce our results is available on GitHub under:
+https://github.com/AndreasWunsch/Long-Term-GWL-Simulations
+
+Author contributions
+
+All authors contributed to conceptualization of this study. AW and TL contributed to the methodology, AW further contributed to writing the software code, validation, formal analysis, investigation, visualization and wrote the original draft. All authors contributed to reviewing and editing the draft. TL and SB both supervised the work and were involved in project administration.
+
+Funding
+
+Open Access funding enabled and organized by Project DEAL.
+
+Competing interests
+
+The authors declare no competing interests.
+
+References
+
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+51. Md. Manjurul Hussain Shourov, Ishtiaq Mahmud & Niemeyer, K. mmhs013/pyMannKendall: v1.4.1. (Zenodo, 2020). doi:10.5281/ZENODO.3876036.
+
+Figures
+Figure 1
+
+Absolute changes of total annual precipitation sums (A) and annual average temperature (B) projected by climate models for the relevant sites used in this study. Single squares depict results of a single projection, ordered by the strength and sign of the change. A2 and B2 summarize all significant (p < 0.05) results from A1 and B1, Tables (A3 and B3) give detailed numbers on the boxplots.
+Figure 2
+
+Change of groundwater level [%] in 2100 relative to 2014 (start of sim.) for each site and each climate projection, based on a linear trend analysis: A) mean, B) 97.5% quantile, D) 2.5% quantile; the order corresponds to the strength and sign of the change. C) Boxplots showing the significant changes for A, B, D as well as the 25% and 75% quantiles. Black boxes mark four sites (A-D) shown in detail in Figure 3.
+Figure 3
+
+Detailed results on four sites (marked by black boxes in Figure 2): Time series plots of the far future (2070-2100) simulation results (A1-D1); Heatmap plots (A2-D2) of the whole simulation for each of the projections with columns as weeks during the year and rows as the year (up: 2104 – down: 2100).
+Figure 4
+
+Means of the significant trends of the mean (A), the 97.5% (B) and the 2.5% (E) quantiles shown also in Figure 2. Subplot C shows the associated boxplots (also for 25% and 75% quantiles) and the corresponding absolute changes (lower boxplots). Tables in D show detailed numbers describing the boxplots.
+Figure 5
+
+Shift of the annual minimum in weeks until 2100 compared to the start of the simulation (2014). Negative means earlier, positive later during the annual cycle.
+
+![Map showing the shift of the annual minimum in weeks until 2100 compared to the start of the simulation (2014) across Germany](page_68_68_793_563.png)
+Figure 6
+
+Position, type of aquifer and depth to groundwater for each study site, B: time series length of all study sites North-South ordered.
+
+Figure 7
+
+A) Model performance of all models for the test-set (2012-2016), B) time series splitting scheme for optimization (upper) and retraining (lower).
+Figure 8
+
+A) Optimized model evaluation in the past for the test set (2012-2016), B) Model output under an artificial extreme climate scenario in the past, C) SHAP Summary plot
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupportingInformation100MB.pdf

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+Peer Review File
+
+Designed Rubredoxin miniature in a fully artificial electron chain triggered by visible light
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The manuscript by Lombardi and co-workers describes a de novo design of a miniature protein with only 28 amino acid residues that mimics the function of rubredoxin in electron transfer. While it’s indeed impressive that the X-ray structure of the artificial protein (with Zn as the metal center) can be resolved at such a high resolution, the current work suffers from several major drawbacks:
+
+1) If the aim is to provide a general methodology for the de novo design of miniature proteins, the authors should have compared the differences and/or advantages of the current method with literature methods (especially with ref 28 and ref 29); if the aim is to obtain a fully functional miniature protein capable of transferring electron, now that the X-ray structure is available, isn’t it the best opportunity to go a step further and do some protein engineering, especially the second coordination sphere residues, to obtain a more robust miniature protein? As this would not only test the authors’ claim that “the designed second-shell interactions are crucial in determining one of the highest potentials amongst the Rd family.”, but more importantly, could even higher redox potential possible via mutagenesis?
+
+2) Redox cycling ability is an important feature for any de novo designed rubredoxin mimics, although the authors claim that “no dramatic loss of the protein signal upon recycling for 9 times”, but as far as this reviewer can see from figure 4b, the Abs at 494 nm decreased very obviously, what is the possible reason? Would it be possible that the the Fe-S center is not so stable during oxidation or dithionite-treatment? Once the Fe ion is lost in the process, what would happen to the Cys residues? This issue is also true for the experiment in Figure 6, as obvious decrease of the Abs at 314 nm for the reduced species can be observed only after the second redox cycling, what if a third of even fourth cycle? Is the protein robust/stable enough in this system?
+
+As such, this reviewer does not think the manuscript fulfill the high publication standards of Nature Communications.
+
+Below are some other minor issues that may be helpful for the author to revise the manuscript for another journal.
+
+1) Why 5 mM of TCEP was included in the EPR sample?
+
+2) In the experiment described in Figure 6, why the second round of light irradiation is only 15 min while the first one is 25 min? And by the way, it looks like only 10 min of the light irradiation was applied in the second round from Figure 6d, is it a drawing mistake?
+
+3) The X-ray structure is resolved only for the Zn-complex, did the author try the Fe-complex instead?
+
+4) In the SI, page 11, Supplementary Fig. 2 in the text should be Fig. 3; SI, page 13, Supplementary Fig. 3 in the text should be Fig. 4.
+
+5) The yield of the peptide synthesis is 65%, is this HPLC yield or isolated yield? ESI-MS spectrum should be given for the purified peptide, rather than the crude, as multiple masses can be observed in the Supplementary Fig. 11.
+
+Reviewer #2 (Remarks to the Author):
+
+Overall, I found the described work to be exciting and relevant to the times. The authors created a novel nano-sized biological photoelectron acceptor that can be used as a tool for broader applications that require electron transport. The designed system contains a single polypeptide chain consisting of
+only 28 residues that contains internal 2-fold symmetry. They effectively created a protein knot to tetrahedrally coordinate metal that is more structurally stable than a Zn-finger. They performed the appropriate biophysical experiments (EPR, mass spectrometry, UV-VIs titrations and circular dichroism) to prove the designed protein coordinated iron such that it could be reduced and oxidized on demand. Then crystallized the the protein with Zn2+ Ultimately, I would prefer the crystal structure contain iron instead of zinc, but I recommend the manuscript be published without any major changes. Below is a list of minor changes that should be made.
+
+To improve the paper, the authors should have a figure of the Cp Rd with its first and second coordination spheres defined. They draw many comparisons to this structure throughout the manuscript and it would be easier for the reader to have a picture instead of having to pull up the structure from the PDB.
+
+I found the crystal packing description on page 8 (last paragraph of section “ZnMETPsc1 crystal structure reveals a handful of secondary motifs”) to be a distraction and should be deleted. The description doesn’t lead to any relevant conclusions. I believe it was to setup the placement of the symmetry related Arg in the second coordination sphere- but is not needed. Also Supplemental, Figure 8: This figure doesn’t add any special information to the paper and can be removed. The figure is too busy to full understand with out being able to rotate it. The placement of the Asp and Arg residues is not obvious. I assume the red balls signify water molecules.
+Figure 2, part d: add the distances for the coordinating bonds.
+
+The rest of the requested changes are typos and bad sentence structure that can easily be corrected.
+
+Page 2: lines 6-9; re write: “We assembled in a as small as 28- residue peptide the quintessential elements required to correctly fold around a single iron redox center, coordinated to four cysteinyl thiolates (FeCys4 site), and to efficiently function in electron- transfer.”
+Page 3: line 14 : put a comma after “ to achieve for the first time in protein design”
+Page 3: line 16: Nature should not be capitalized.
+
+Page3: line 23: clarify the statement about rubrerythrin.
+Page 4: line 16: restate “ half-sized respect to natural Ads”
+Page 4: line 25: “second sphere to second coordination sphere
+Page 5: line 1 : Sulpur should not be capitalized.
+Page 5, line 25: change “identifying” to “identify”
+Page 6, line 4: packer ??
+Figure 1: legend, line 10: change “found with” to “found from”
+Page 7, line 8 & page 9, line 6: change “buldge “ to “bulge”
+Page 7, lines 7, 8 & 9: change “2-residues” to “2-residue”
+Page 7, line 18: Sentence starting with The overall backbone should be rewritten.
+Page8, lines 11 & 12: Why is this sentence important ? ”In addition, interactions between Tyr16 and the equivalent residue of a crystallographic related METPsc1 molecule are observed with a 3.32 Å distance between -OH atom groups. “
+Page 8: the crystal packing information is not relevant.
+Page 8, lines 20 & 21: change “and containing Zn+2” to “that contain Zn+2”
+
+Page 10, line 18: change “(one and two order of magnitude, respect to Zn2+ and Co2+, respectively)” to “(one and two orders of magnitude for Zn2+ and Co2+, respectively)”
+Page 10, line 19: change “most probably attributable to “ to “most likely attributable to ”
+Page 12, Figure 4: define the Fe2+ and Fe3+ species in part b.
+Page 19: line 5: “statistic” to “statistics”
+Page 19 lines 5 & 6: “Crystals presented an orthorhombic unit cell with space group C2221. “ change
+to something like “ Crystals grew in the orthorhombic space group C2221.”
+
+Page 19: line 25 & Page 20, line 10: change “25°C” to “25 °C”
+
+Page 20: line 18: Change “30% of glycerol as glassing agent to an” to “30% glycerol to an”
+Page 21: line 2: move “ under argon” to “All cyclic voltammetry experiments were performed under argon with a Potentiostat…”
+Page 21, line 6: change “For all the measurement” to F”or all measurements“SEP”Page 21: lines 10 & 11: clarify “Cyclic voltammetry experiments on freely diffusing FeMETPsc1 were performed by adapting a previously published procedure, at 15°C“
+
+Page 22, lines 1 & 6: availability misspelled.
+
+Authors need to define acronyms at the first instance of use:
+some examples: Page 3: line 23: define SHE before using acronym
+Page 4; line 7: define METP
+Page 5; line 11: define Cp
+
+Wavelength of data collection differs between main manuscript (1.00 Å) and supplementary table 2 (1.24 Å).
+Resolution of refined structure also differs between main manuscript (1.44 Å) and supplementary table 2 (1.34 Å).
+Items missing from supplementary table 2: redundancy of data, add the RSCC and RSR of Zn ions, add the mol probity score and clashscore, footnotes explaining the terms.
+
+Supplemental, page 6: Define where to find the MASTER software as you did PyMOL.
+Supplemental, page 7: change "grigoryanlab" to "Grigoryan lab "
+Supplemental, Page 11: (Supplementary Fig. 2) should be (Supplementary Fig. 3)
+Supplemental, page 13 (Supplementary Fig. 3) should be (Supplementary Fig. 4)
+
+Supplemental, pages 15 & 16: Change” The C-terminal strand (Strand F) folds in a head-to-tail manner to antiparallelly align with the first strand, “ to “ The C-terminal strand (Strand F) folds antiparallel with respect to the first strand,”
+
+Reviewer #3 (Remarks to the Author):
+
+Designed Rubredoxin miniature in a fully artificial electron chain triggered by visible light by the group of Lombardi and Pavone
+The group has important and valid contributions in designing metal sites into de novo proteins, and in engineering of metalloprotein functions in designed and native scaffolds, in the field of artificial enzymes (heme proteins).
+In this manuscript, the authors assembled a small peptide required to correctly fold around a single iron redox center, coordinated to four cysteinyl thiolates (FeCys4 site), a mimetic compound for Rubredoxins that can participate and function in electron-transfer.
+(Fe3+,Fe2+) METPsc1 and Zn2+-METPsc1 were synthetized with success and the crystal structure Zn2+-METPsc1 was detailed analysed. Fe3+METPsc1 was explored by spectroscopic methods (VIS, CD, EPR) and electrochemical properties determined, always with counterpoint with the ferrous form.
+The high reduction potential compared to natural and designed FeCys4-containing proteins was exploited as a terminal electron acceptor of a fully artificial chain triggered by visible light.
+The work is exciting and deserves to be publish.
+A few points to clarify:
+i) The METPsc1 ligand was obtained in large amounts. Fe and Zn could be reconstituted in the template. This is a fact well known for rubredoxins that can also accept a large number of metals (mainly transition metal) and even Ga can be used as a interesting isomorphous replacement, for Fe3+. Why the crystal structure was extensively done in for and Zn2+-METPsc1? I understand the spectroscopy was conducted for (Fe3+, Fe2+) METPsc, since Zn2+ is silent in EPR and no absorption bands are observed in Vis region (as well no redox).
+
+ii) Table I compares the spectroscopic parameters of FeMETPsc1 and Cp Rd in Fe(II) and Fe(III) oxidation states. There is a clear match.
+
+The EPR data for Fe2+ states should no be indicated as (-) is a S=2 state, as it is looks EPR silent (difficult to be observed by EPR using different modes, and really observed by MB techniques). High-spin integer spin Fe2+ (S = 2) is more difficult to observe by EPR methods and low-spin Fe2+ is EPR silent. Both oxidation states in Rd type proteins are high-spin systems. Mössbauer (MB) spectroscopy is a particularly suitable technique for investigating the valence and spin-states of iron sites in Rd.
+
+iii) Figure 4. FeMETPsc1 redox characterization. a, UV-Vis monitoring of Fe2+-METPsc1 (blue trace) aerobic oxidation to Fe3+-METPsc1 (red trace).
+blue trace or purple trace ???
+
+iv) The FeMETPsc1 possesses significantly high potential value (121 mV vs SHE), exceeding the typical range for prokaryotic Rds (-100/+50 mV). The phrase could be modified ... an high reduction potential value (121 mV vs SHE), slightly higher than the values observed for Rds.
+
+v) Photoinduced electron transfer from ZnMC6* to Fe3+-METPsc1 is an interesting observation, as a possible reaction scheme of the synthetic electron cascade. Other couples could be explored. More details should be given on ZnMC6*.
+
+Reviewer #4 (Remarks to the Author):
+
+This manuscript describes the design and synthesis of a functional artificial rubredoxin (Rd)-like FeCys4-cluster peptide. This miniaturised metallo-'protein' (METPsc1) was designed de novo by dissecting the Fe-binding region from a high-resolution structure of Rd and then searching for the optimal peptide fragment that could bridge the two truncated sequences. The final model was obtained by Monte Carlo sampling. The Rd miniature was synthesised and characterised by X-ray diffraction as the Zn complex. Coordination to the metal closely mirrors that of native Rd and matches exceptionally well onto the computationally modelled structure. Fe binding was then assessed using UV-Vis, CD and EPR; a 1:1 complex is formed with the metal and the cluster gives characteristic LMCT UV-Vis bands and EPR resonances. Reversible redox cycling is also demonstrated. CV of the cluster reveals a high reduction potential relative to native Rds. Finally, Fe-METPsc1 is used as the terminal electron acceptor in a visible-light-mediated artificial electron cascade.
+
+Based on the fact that the Fe-METPsc1 was designed from 'scratch' and very well characterised, including X-ray data, the novelty/originality of this paper is high. The integration of the FeMETPsc1 into an electron cascade further enhances the impact of the publication and points towards potential applications for de novo designed proteins in complex artificial systems. The methods described in the main paper, and details in the SI, are sufficiently detailed to allow reproduction of the results.
+
+The computational design aspect of this work is outside my area of expertise so I will leave it to other reviewers to comment on the method; however, due to the extensive characterisation of the resulting METPsc1, I have no doubt regarding the effectiveness of the approach. My only real concern is in regard to Figure 6c/6d; the UV-Vis LCMT band at 496 is visible only as a flat absorbance next to the large band at around 400 nm from ZnMC6*a. Furthermore, the shift from 311 nm to 314 nm is very slight. These results are complicated by the fact that the ZnMC6*a compound absorbs at 496 nm after
+successive rounds of oxidation and reduction. Since the final results of this paper are based on the disappearance of the 496 nm absorbance and 311 to 314 nm shift, the authors should include the UV-Vis traces (overlaid if clear or with Abs values if not) for all time points of Figure 6d in the SI to show the gradual changes in each peak. It would be ideal if this experiment could be repeated at a higher concentration (if that is possible) to give a more pronounced band at 496, however, this is not necessary if the UV-Vis spectra of the time points from Figure 6d are clear. Finally, it’s not clear to me how the concentration values for the oxidised and reduced clusters are calculated for Figure 6d. Please add this info into the SI.
+
+A few additional points:
+
+The METP abbreviation should be clearly defined on first use.
+
+For Figure 3, the four plots a, b, c, d are positioned clockwise which isn’t standard formatting (compared to c below a and d below b) – a very minor point.
+
+The amount of dithionite added for each redox cycle (Figure 4b) should be stated in the SI – an ‘excess’ is mentioned in the text, but clarity would aid reproduction of the experiments.
+
+Line 6-7 of the abstract (“… in a as small as…”) should be re-worded for clarity.
+
+In my opinion, this manuscript is of significant novelty and impact for publication in Nature Communications, and should be accepted once the above concerns have been addressed.
+We would like to thank the reviewers for their comments and suggestions that have contributed to improve the quality of the manuscript.
+
+We have considered the comments of all Reviewers and accepted all relevant suggestions, also by performing new experiments. In particular, we carried out again the redox cycling characterization (Figure 4), the photoinduced electron transfer experiments (Figure 6), and we acquired new LCMS spectrum of the purified peptide (Supplementary Information).
+
+A detailed point-to-point reply to the Reviewers’ comments, highlighting the changes made in the revised manuscript, is provided in the following.
+
+REVIEWER COMMENTS
+
+AUTHOR RESPONSE
+
+Reviewer #1 (Remarks to the Author):
+
+The manuscript by Lombardi and co-workers describes a de novo design of a miniature protein with only 28 amino acid residues that mimics the function of rubredoxin in electron transfer. While it’s indeed impressive that the X-ray structure of the artificial protein (with Zn as the metal center) can be resolved at such a high resolution, the current work suffers from several major drawbacks:
+
+1) If the aim is to provide a general methodology for the de novo design of miniature proteins, the authors should have compared the differences and/or advantages of the current method with literature methods (especially with ref 28 and ref 29); if the aim is to obtain a fully functional miniature protein capable of transferring electron, now that the X-ray structure is available, isn’t it the best opportunity to go a step further and do some protein engineering, especially the second coordination sphere residues, to obtain a more robust miniature protein? As this would not only test the authors’ claim that “the designed second-shell interactions are crucial in determining one of the highest potentials amongst the Rd family.”, but more importantly, could even higher redox potential possible via mutagenesis?
+
+We thank the Reviewer for pointing this out, giving us the opportunity to clarify our aim and put our work under a better focus. When writing this manuscript, we were primarily motivated to report the remarkable high-resolution structure of an artificial metalloprotein (as the Reviewer has acknowledged), and the impact of the designed and experimentally found interactions in determining a reduction potential that closely matches the highest reported potential in the Rd family. We feel that these are notable results of interest to the chemistry community. Indeed, they allowed us to develop a fully artificial electron transport chain. Thanks to the Reviewer’s comments, we have made changes in the text, to make these points clearer.
+
+1. We have better highlighted the advantages of the adopted design methodology on p. 7 l. 5-7: “Interestingly, this search allowed us to overcome some of the limitations previously encountered to covalently link the two symmetry-related moieties, such as the use of stabilizing long β-hairpins28 or synthetically difficult cyclization steps29,” and on p. 18 l. 12-15: “Our design strategy, differently from previous attempts mimicking Rd28,29, is fully generalizable, because it relies only on the knowledge of the mutual orientation of the C2-related moieties, without using neither a specific super-secondary motif nor cyclization/stapling to link them.”
+
+2. Moreover, thanks to the new experiments we performed, we have been able to demonstrate the high stability of our miniaturized de novo metalloprotein in redox cycling, see p. 13-14 l. 17-20, 1-3, and Supplementary Figure 8: “A FeMETPsc1 solution (40 μM, pH 7) was subjected to at least twelve consecutive and reversible redox cycles, without any loss of the protein signal upon recycling (Fig. 4b), similarly to other redox-cycling Rd mimics27–29. The cycling experiment lasted two days, and the complex was kept under argon atmosphere overnight without any detectable loss of signal and full recycling for two more times the day after (see Supplementary Fig. 8). The last of 12 oxidation
+processes recovered approximately 92% of the expected Fe^{3+}METPsc1 signal, suggesting that more cycles could be performed."
+We are confident that in the next future we and others could apply our simple approach to the design of many other miniaturized metalloproteins. Nonetheless, we agree with the Reviewer about the opportunity to perform a mutagenesis study to modulate the redox potential (such study is currently under course in our lab). However, we respectfully think that the electrochemical study of a conspicuous set of mutants (not only in the second but also in the first coordination sphere, possibly with non-coded amino acids) would deserve a full and more detailed paper, in which we would hopefully be able to expand the reduction potential range of the FeS_4 metal site. We are afraid that by conveying another different “story” in this paper would be misleading for the reader. We hope that the Reviewer could recognize that this manuscript already addresses important challenges.
+
+2) Redox cycling ability is an important feature for any de novo designed rubredoxin mimics, although the authors claim that “no dramatic loss of the protein signal upon recycling for 9 times”, but as far as this reviewer can see from figure 4b, the Abs at 494 nm decreased very obviously, what is the possible reason? Would it be possible that the Fe-S center is not so stable during oxidation or dithionite-treatment? Once the Fe ion is lost in the process, what would happen to the Cys residues? This issue is also true for the experiment in Figure 6, as obvious decrease of the Abs at 314 nm for the reduced species can be observed only after the second redox cycling, what if a third of even fourth cycle? Is the protein robust/stable enough in this system?
+We thoroughly appreciate this comment, which allowed us to deepen and clarify this point. In the experiment reported in the original version of the manuscript, we did not allow the complete oxidation of the Fe-S center, because we used a fixed time for each oxidation cycle. Now, we re-ran the redox cycle experiment several times, allowing each cycle the complete oxidation to the ferric complex. We ran a total of 12 cycles with no apparent iron loss. The 10th cycle was performed overnight, and the next day we performed two more redox cycles to verify the complex stability over a long-time frame. In the revised manuscript, we provide the experimental data as a new Figure 5b and the full time-course with the overnight specification in Supplementary Figure 8. Remarkably, a huge beneficial effect was firstly observed by working with 0.8 eq of iron, thus excluding any effect of free iron to the redox cycling (most probably by Fenton chemistry), and secondly by using a dithionite solution, stored under argon atmosphere (most probably by preventing the formation of sulfides and sulfites by disproportion, which caused iron precipitation after a few additions, and/or sulfonation of the cysteines). We have added these experimental details on p. 21, l. 19-24: “In the redox cycling experiment, a 0.7 mL solution of METPsc1 (50 μM) in HEPES buffer (20 mM) and TCEP (2 mM) at pH 7 was preliminary purged for 5 min with Ar and then a 10 mM Mohr’s salt solution under Ar atmosphere was added to a final concentration of 40 μM. Next, the solution was sequentially purged with air to form the Fe^{3+} complex, then with argon and finally reduced with 0.2 μL of 0.5 M sodium dithionite, prepared under Ar atmosphere, to restore the Fe^{2+} complex”.
+We also recollected data for the light-induced electron transfer experiment in Figure 7, under slightly different experimental conditions (as suggested also by Reviewer #4). In the new experiment, we limited and fixed the irradiation time to 20 minutes for each cycle, to keep the light dose constant over each cycle. We clearly show that FeMETPsc1 is able to perform several redox cycles under these conditions. Moreover, it should be noted that the instability of the ZnMC6*a upon several irradiations is limiting the complete recycling.
+We hope that these new experiments have fulfilled the main concerns of the Reviewer, who might positively reconsider our revised version.
+
+Minor issues:
+1) Why 5 mM of TCEP was included in the EPR sample?
+The Tris(2-carboxyethyl)phosphine (TCEP) is a common reducing agent used in peptide/protein-containing samples. We used it to ensure full reduction of thiol moieties before metal addition. We generally kept a TCEP:METPsc1 ratio in the range 20-30 (TCEP: 1 mM; METPsc1 30-50 μM). In the case of the EPR experiment a higher peptide concentration was needed (0.5 mM). Thus, we used a lower TCEP:METPsc1 ratio (= 10), considering that the sample was freshly prepared and immediately frozen under liquid nitrogen for data acquisition.
+2) In the experiment described in Figure 6, why the second round of light irradiation is only 15 min while the first one is 25 min? And by the way, it looks like only 10 min of the light irradiation was applied in the second round from Figure 6d, is it a drawing mistake?
+We appreciate the comment by the Reviewer as it gave us the opportunity to significantly improve this point in the manuscript. It was not a drawing mistake: under the used experimental conditions (ZnMC6*a: 40 μM; Fe3+METPscI: 50 μM), approximately 25 minutes were sufficient to reduce almost 100% of the FeMETPscI. In the second round, we stopped the irradiation after 10 minutes because the absorption spectrum of the Zn-porphyrin moiety began to change, indicating porphyrin bleaching, and the Fe3+ METPscI reduction was not proceeding any further. In the data we re-collected, we performed the experiment under a different ratio of FeMETPscI-ZnMC6*a of 40μM:5μM, to better highlight and evaluate the redox cycles of the Rd mimic. Moreover, we kept fixed the irradiation time at 20 minutes. Under these conditions, up to four cycles could be performed, even though 100% reduction was not obtained. Nevertheless, we hope that the Reviewer agrees with us that this result is quite valuable, also considering a possible degradation of ZnMC6*a. We believe that our system represents a stimulating proof of principle, even though it deserves further improvements.
+The text was modified on p. 16/17, l. 9-14, 1-14, accordingly to the new findings: “When a solution containing 2 mM TEA, 40 μM Fe3+METPscI, and 5 μM ZnMC6*a was purged with air, a 494 nm band of the oxidized [FeCys4]I- appeared (Fig. 6c,d), demonstrating that iron oxidation at METPscI was not affected by TEA and ZnMC6*a. When the solution was exposed to green light irradiation for 20 minutes under argon atmosphere, almost complete disappearance of the ferric charge-transfer band was observed. A band at 311 nm concomitantly appeared, characteristic of the reduced [FeSf]2+ species (Fig. 6c). As a control, when the system was kept under Ar atmosphere in the dark for 30 minutes, the signal at 494 nm slightly decreased (approximately 10%; Figure 7d, blue box). These results clearly demonstrate Fe3+METPscI reduction upon light exposure. As a final proof of the artificial photo-electron transfer chain, the system was exposed to air and then to green light irradiation for three times. As expected, air oxidized Fe3+METPscI, and then after 20 minutes of irradiation, it was reduced back with formation of a peak at 311 nm. However, only partial disappearance of the band in the visible region could be observed in the following cycles, with a Fe3+METPscI signal corresponding to almost half of the oxidized species (from 35 mM to 15 mM of Fe3+METPscI concentration). Incomplete reduction was indeed accompanied by ZnMC6*a degradation after each cycle (see Supplementary Fig. 9a). In turn, this could be ascribed either to reactive oxygen species that formed during the previous O2 reduction step by FeMETPscI (Fig. 7a), or by formation of radical species due to self-oxidation. ZnMC6*a was therefore exposed to 20 minutes irradiation in the absence of FeMETPscI. Notably, in only one irradiation round, ZnMC6*a was fully converted to degradation byproducts, lacking the characteristic Soret band (Supplementary Fig. 9b). ”.
+
+3) The X-ray structure is resolved only for the Zn-complex, did the author try the Fe-complex instead?
+We would love to solve the Fe-complex crystal structure. We tried to obtain crystals of the iron complex, but we were unlucky until now. We are currently performing both crystallization under a glow box at the synchrotron facility, and soaking experiments from cobalt crystals. We hope to be successful soon.
+
+4) In the SI, page 11, Supplementary Fig. 2 in the text should be Fig. 3; SI, page 13, Supplementary Fig. 3 in the text should be Fig. 4.
+We thank the Reviewer for noting the mistakes, which have been corrected. Many apologizes for this.
+
+5) The yield of the peptide synthesis is 65%, is this HPLC yield or isolated yield? ESI-MS spectrum should be given for the purified peptide, rather than the crude, as multiple masses can be observed in the Supplementary Fig. 11.
+We apologize for the inaccuracy. We revised the text on page 19 (and in the SI) by detailing that 65 % was the yield of the isolated crude: “The isolated crude product was obtained in 65% yield (based on the resin substitution), with 50% HPLC purity.” Moreover, we acquired the LCMS spectrum of the purified peptide (p. 19-21 of the Supplementary Information).
+Reviewer #2 (Remarks to the Author):
+Overall, I found the described work to be exciting and relevant to the times. The authors created a novel nano-sized biological photoelectron acceptor that can be used as a tool for broader applications that require electron transport. The designed system contains a single polypeptide chain consisting of only 28 residues that contains internal 2-fold symmetry. They effectively created a protein knot to tetrahedrally coordinate metal that is more structurally stable than a Zn-finger. They performed the appropriate biophysical experiments (EPR, mass spectrometry, UV-Vis titrations and circular dichroism) to prove the designed protein coordinated iron such that it could be reduced and oxidized on demand. Then crystallized the protein with Zn2+ Ultimately, I would prefer the crystal structure contain iron instead of zinc, but I recommend the manuscript be published without any major changes.
+
+We really thank the Reviewer for the inspiring words of estimation for our work. We hope that the revised version could be of even more interest to her/him.
+
+Below is a list of minor changes that should be made.
+
+To improve the paper, the authors should have a figure of the Cp Rd with its first and second coordination spheres defined. They draw many comparisons to this structure throughout the manuscript and it would be easier for the reader to have a picture instead of having to pull up the structure from the PDB.
+
+We appreciate this suggestion. We added an additional figure (Figure 1) highlighting the first and second coordination sphere of V44A Cp Rd.
+
+I found the crystal packing description on page 8 (last paragraph of section “ZnMETPsc1 crystal structure reveals a handful of secondary motifs”) to be a distraction and should be deleted. The description doesn’t lead to any relevant conclusions. I believe it was to setup the placement of the symmetry related Arg in the second coordination sphere- but is not needed.
+
+The description has been removed as suggested.
+
+Also Supplemental, Figure 8: This figure doesn’t add any special information to the paper and can be removed. The figure is too busy to fully understand without being able to rotate it. The placement of the Asp and Arg residues is not obvious. I assume the red balls signify water molecules.
+
+Supplementary Figure 8 has been removed as suggested.
+
+Figure 2, part d: add the distances for the coordinating bonds.
+
+Figure 2d (Figure 3d in the revised manuscript) has been modified accordingly.
+
+The rest of the requested changes are typos and bad sentence structure that can easily be corrected.
+Page 2: lines 6-9; re write: “We assembled in a as small as 28-residue peptide the quintessential elements required to correctly fold around a single iron redox center, coordinated to four cysteinyl thiolates (FeCys4 site), and to efficiently function in electron- transfer.”
+Page 3: line 14: put a comma after “to achieve for the first time in protein design”
+Page 3: line 16: Nature should not be capitalized.
+Page 3: line 23: clarify the statement about rubrerythrin.
+Page 4: line 16: restate “ half-sized respect to natural Ads”
+Page 4: line 25: “second sphere to second coordination sphere
+Page 5: line 1 : Sulpur should not be capitalized.
+Page 5, line 25: change “identifying” to “identify”
+Page 6, line 4: packer??
+Figure 1: legend, line 10: change “found with” to “found from”
+Page 7, line 8 & page 9, line 6: change “buldge” to “bulge”
+Page 7, lines 7, 8 & 9: change “2-residues” to “2-residue”
+Page 7, line 18: Sentence starting with The overall backbone should be rewritten.
+Page 8, lines 11 & 12: Why is this sentence important? “In addition, interactions between Tyr16 and the equivalent residue of a crystallographic related METPsc1 molecule are observed with a 3.32 Å distance between -OH atom groups.”
+Page 8: the crystal packing information is not relevant.
+Page 8, lines 20 & 21: change “and containing Zn+2” to “that contain Zn+2”
+Page 10, line 18: change “(one and two order of magnitude, respect to Zn2+ and Co2+, respectively)” to “(one and two orders of magnitude for Zn2+ and Co2+, respectively)”
+Page 10, line 19: change “most probably attributable to “ to “most likely attributable to”
+Page 12, Figure 4: define the Fe2+ and Fe3+ species in part b.
+Page 19: line 5: “statistic” to “statistics”
+Page 19 lines 5 & 6: “Crystals presented an orthorhombic unit cell with space group C2221. “change to something like “ Crystals grew in the orthorhombic space group C2221.”
+Page 19: line 25 & Page 20, line 10: change “25°C” to “25 °C”
+Page 20: line 18: Change “30% of glycerol as glassing agent to an” to “30% glycerol to an”
+Page 21: line 2: move “ under argon” to “All cyclic voltammetry experiments were performed under argon with a Potentiostat…”
+Page 21, line 6: change “For all the measurement” to F”or all measurements”
+Page 21: lines 10 & 11: clarify “Cyclic voltammetry experiments on freely diffusing FeMETPsc1 were performed by adapting a previously published procedure, at 15 °C”
+Page 22, lines 1 & 6: availability misspelled.
+Authors need to define acronyms at the first instance of use: some examples:
+Page 3: line 23: define SHE before using acronym
+Page 4; line 7: define METP
+Page 5; line 11: define Cp
+Wavelength of data collection differs between main manuscript (1.00 Å) and supplementary table 2 (1.24 Å). Resolution of refined structure also differs between main manuscript (1.44 Å) and supplementary table 2 (1.34 Å).
+Items missing from supplementary table 2: redundancy of data, add the RSCC and RSR of Zn ions, add the mol probity score and clashscore, footnotes explaining the terms.
+Supplemental, page 6: Define where to find the MASTER software as you did PyMOL.
+Supplemental, page 7: change ”grigoryanlab“ to “Grigoryan lab”
+Supplemental, Page 11: (Supplementary Fig. 2) should be (Supplementary Fig. 3)
+Supplemental, page 13 (Supplementary Fig. 3) should be (Supplementary Fig. 4)
+Supplemental, pages 15 & 16: Change” The C-terminal strand (Strand F) folds in a head-to-tail manner to antiparallely align with the first strand, “ to “ The C-terminal strand (Strand F) folds antiparallel with respect to the first strand,”
+
+We are profoundly grateful to the Reviewer #2 for the deep and careful reading of the manuscript. All these typos and minor issues have been fixed. Many apologizes for this.
+
+Reviewer #3 (Remarks to the Author):
+Designed Rubredoxin miniature in a fully artificial electron chain triggered by visible light by the group of Lombardi and Pavone.
+The group has important and valid contributions in designing metal sites into de novo proteins, and in engineering of metalloprotein functions in designed and native scaffolds, in the field of artificial enzymes (heme proteins).
+In this manuscript, the authors assembled a small peptide required to correctly fold around a single iron redox center, coordinated to four cysteinyl thiolates (FeCys4 site), a mimetic compound for Rubredoxins that can participate and function in electron-transfer.
+(Fe3+, Fe2+) METPsc1 and Zn2+METPsc1 were synthetized with success and the crystal structure Zn2+METPsc1 was detailed analysed. Fe3+METPsc1 was explored by spectroscopic methods (VIS, CD, EPR) and electrochemical properties determined, always with counterpoint with the ferrous form. The high
+reduction potential compared to natural and designed FeCys4-containing proteins was exploited as a terminal electron acceptor of a fully artificial chain triggered by visible light.
+The work is exciting and deserves to be publish.
+We thank the Reviewer for the nice words of appreciation to our work.
+
+A few points to clarify:
+
+i) The METPsc1 ligand was obtained in large amounts. Fe and Zn could be reconstituted in the template. This is a fact well known for rubredoxins that can also accept a large number of metals (mainly transition metal) and even Ga can be used as an interesting isomorphous replacement, for Fe3+. Why the crystal structure was extensively done in for and Zn2+METPsc1? I understand the spectroscopy was conducted for (Fe3+, Fe2+) METPsc, since Zn2+ is silent in EPR and no absorption bands are observed in Vis region (as well no redox).
+We tried to obtain crystals with several metals as well as Ga3+ as a Fe3+ proxy. We were able to get diffracting crystals also with Cd2+ and Co2+, in the same crystallizing conditions of Zn2+. Now, we are trying to get other metals by exchanging the more labile cobalt complex. Some crystallization trials have been set up for iron under a glow box directly at the synchrotron facility, but we are still in the process of getting high resolution data. Nevertheless, we acquired very good NMR data in solution for the Zn2+, Co2+, and Ga3+ complexes, and we will report a deeper characterization in solution in a following manuscript.
+
+ii) Table I compares the spectroscopic parameters of FeMETPsc1 and Cp Rd in Fe(II) and Fe(III) oxidation states. There is a clear match.
+The EPR data for Fe2+ states should not be indicated as (-) is a S=2 state, as it is looks EPR silent (difficult to be observed by EPR using different modes, and really observed by MB techniques). High-spin integer spin Fe2+ (S = 2) is more difficult to observe by EPR methods and low-spin Fe2+ is EPR silent. Both oxidation states in Rd type proteins are high-spin systems. Mössbauer (MB) spectroscopy is a particularly suitable technique for investigating the valence and spin-states of iron sites in Rd.
+The Reviewer is correct in saying that Fe2+ is potentially amenable to EPR investigations, however, as noted by the Reviewer its integer spin state makes EPR detection at conventional frequencies (X- and Q-band) problematic due to large Zero Field Splitting (zfs). The problem can be circumvented by using High field EPR (v ≥ 95 GHz), which has been successfully employed to obtain the full set of spin-Hamiltonian parameters for model systems and Cp Rd. It is worth noting that ferrous iron, despite its integer spin and typically large zfs, is not exactly “EPR silent” at conventional frequencies and in some cases X- and Q-band EPR observations have been possible at very low T and using parallel mode detection (Yoo, S., Meyer, J., Achim, C. et al. JBIC 5, 475–487 (2000). https://doi.org/10.1007/s007750050008). However, detection of such signals is not always possible due to the low intensity and large line widths involved. This was our case, and therefore we inserted the (-) symbol in Table 1. Following the comment of competent Reviewer 3, we modified the Table inserting appropriate references to the literature as noted above.
+
+<table>
+  <tr>
+    <th rowspan="2"> </th>
+    <th colspan="2">Fe<sup>2+</sup> METPsc1</th>
+    <th colspan="2">Fe<sup>2+</sup> Cp Rd</th>
+    <th colspan="2">Fe<sup>3+</sup> METPsc1</th>
+    <th colspan="2">Fe<sup>3+</sup> Cp Rd</th>
+  </tr>
+  <tr>
+    <th>λ/nm (ε/mM-1 cm-1)</th>
+    <th></th>
+    <th>λ/nm (+/-)</th>
+    <th></th>
+    <th>λ/nm (+/-)</th>
+    <th></th>
+    <th>λ/nm (+/-)</th>
+    <th></th>
+  </tr>
+  <tr>
+    <td>UV-Vis</td>
+    <td>311 (7.73),<br>331 (4.43)</td>
+    <td>311 (10.8),<br>333 (6.3)<sup>42</sup></td>
+    <td>345 (7.28),<br>370 (8.33),<br>494 (6.54),<br>570 (3.13),<br>745 (0.33)</td>
+    <td></td>
+    <td>350 (7.00),<br>380 (7.70),<br>490 (6.60),<br>570 (3.20),<br>750 (0.35)<sup>43</sup></td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>CD</td>
+    <td>312(-), 333(+)</td>
+    <td>314(-), 335(+)<sup>44</sup></td>
+    <td>437(+), 502(-),<br>557(+), 632(-)</td>
+    <td></td>
+    <td>437(+), 500(-),<br>560(+), 635(-)<sup>44</sup></td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>EPR</td>
+    <td>g<sub>eff</sub><sup>a</sup></td>
+    <td>a</td>
+    <td>a</td>
+    <td></td>
+    <td>9.15, 4.26</td>
+    <td></td>
+    <td>9.4, 4.3<sup>42</sup></td>
+    <td></td>
+  </tr>
+</table>
+
+a Although the high-spin (S = 2) ferrous iron is a paramagnetic species its integer spin state makes it usually “EPR silent” under normal experimental conditions. Spin-Hamiltonian parameters have been measured by means of high-frequency EPR (HFEPR,
+v ≥ 95 GHz) in references 45–46. An effective gz =2.08±0.01 has been reported from X- and Q-band EPR studies for a variant of Cp Rd 47. Due to low intensity and the large line widths involved, this signal was not observed in our experiments.
+
+iii) Figure 4. FeMETPsc1 redox characterization. a, UV-Vis monitoring of Fe2+METPsc1 (blue trace) aerobic oxidation to Fe3+METPsc1 (red trace). blue trace or purple trace ???
+We were referring to the purple trace. We apologize to the Reviewer for the mistake and thank him for pointing out our oversight. We corrected accordingly in the text.
+
+iv) The FeMETPsc1 possesses significantly high potential value (121 mV vs SHE), exceeding the typical range for prokaryotic Rds (-100/+50 mV). The phrase could be modified … an high reduction potential value (121 mV vs SHE), slightly higher than the values observed for Rds.
+We corrected according to the Reviewer’s suggestion.
+
+v) Photoinduced electron transfer from ZnMC6* to Fe3+METPsc1 is an interesting observation, as a possible reaction scheme of the synthetic electron cascade. Other couples could be explored. More details should be given on ZnMC6*.
+According to the Reviewer remark, we added more details about ZnMC6*a in the introduction (p. 4-5, l 26, 1-2): “In particular, ZnMC6*a is the Zn2+ derivative of MC6*a, the best performing artificial peroxidase model, able to host several metal ions (Fe, Mn, Co), displaying different activities.” We also added more detail about ZnMC6*a degradation during the photoinduced electron transfer cycles (p. 17, l. 8-14 and Supplementary Fig. 9). We hope that in a near future, we and other groups will exploit both ZnMC6*a and METPsc1 as partners in redox processes. In particular, we believe that, given the simplicity of the METPsc scaffold, its engineering in biological electron transport chains could be tested for other biologically-relevant redox partners.
+
+Reviewer #4 (Remarks to the Author):
+This manuscript describes the design and synthesis of a functional artificial rubredoxin (Rd)-like FeCys4-cluster peptide. This miniaturised metallo-“protein” (METPsc1) was designed de novo by dissecting the Fe-binding region from a high-resolution structure of Rd and then searching for the optimal peptide fragment that could bridge the two truncated sequences. The final model was obtained by Monte Carlo sampling. The Rd miniature was synthesised and characterised by X-ray diffraction as the Zn complex. Coordination to the metal closely mirrors that of native Rd and matches exceptionally well onto the computationally modelled structure. Fe binding was then assessed using UV-Vis, CD and EPR; a 1:1 complex is formed with the metal and the cluster gives characteristic LMCT UV-Vis bands and EPR resonances. Reversible redox cycling is also demonstrated. CV of the cluster reveals a high reduction potential relative to native Rds. Finally, Fe-METPsc1 is used as the terminal electron acceptor in a visible-light-mediated artificial electron cascade.
+Based on the fact that the Fe-METPsc1 was designed from ‘scratch’ and very well characterised, including X-ray data, the novelty/originality of this paper is high. The integration of the FeMETPsc1 into an electron cascade further enhances the impact of the publication and points towards potential applications for de novo designed proteins in complex artificial systems. The methods described in the main paper, and details in the SI, are sufficiently detailed to allow reproduction of the results.
+We thank the Reviewer for the encouraging words reserved to our work. We really appreciated them.
+
+The computational design aspect of this work is outside my area of expertise so I will leave it to other reviewers to comment on the method; however, due to the extensive characterisation of the resulting METPsc1, I have no doubt regarding the effectiveness of the approach. My only real concern is in regard to Figure 6c/6d; the UV-Vis LCMT band at 496 is visible only as a flat absorbance next to the large band at around 400 nm from ZnMC6*a. Furthermore, the shift from 311 nm to 314 nm is very slight. These results are complicated by the fact that the ZnMC6*a compound absorbs at 496 nm after successive rounds of oxidation and reduction. Since the final results of this paper are based on the disappearance of the 496 nm absorbance and 311 to 314 nm shift, the authors should include the UV-Vis traces (overlaid if clear or with Abs values if not) for all time points of Figure 6d in the SI to show the gradual changes in each peak. It would be ideal if this experiment
+could be repeated at a higher concentration (if that is possible) to give a more pronounced band at 496, however, this is not necessary if the UV-Vis spectra of the time points from Figure 6d are clear. Finally, it's not clear to me how the concentration values for the oxidised and reduced clusters are calculated for Figure 6d. Please add this info into the SI.
+
+According to the Reviewer request (see also reply to remark 2 of Reviewer 1), we performed again the experiment in Figure 6 under different conditions, and we reported it as a new Figure 6. In this experiment, we changed the ZnMC6*a:FeMETPscI ratio, by fixing their concentrations to 5 \( \mu \)M and 40 \( \mu \)M, respectively. We also kept METPscI peptide concentration in slight excess to be more confident that any free iron could alter or have any role in the electron transport process. Moreover, irradiation time has been kept constant to 20 minutes for each cycle, to maintain a constant light dose. Under these conditions, we are not able to reach full reduction of FeMETPscI in the first cycle (most probably because we decreased the ZnMC6*a:FeMETPscI ratio), nevertheless we were able to perform partial reduction of FeMETPscI for at least 4 cycles before clear bleaching of ZnMC6*a hampered further cycles to occur.
+
+A few additional points:
+
+The METP abbreviation should be clearly defined on first use.
+We have defined acronyms as they first appear in the text. Thank you.
+
+For Figure 3, the four plots a, b, c, d are positioned clockwise which isn’t standard formatting (compared to c below a and d below b) – a very minor point.
+We were aware of this non-standard formatting, we preferred to keep it that way because this allowed us to match UV and CD data for an easier up/down comparison of the spectra. If possible, we would prefer to keep this order.
+
+The amount of dithionite added for each redox cycle (Figure 4b) should be stated in the SI – an ‘excess’ is mentioned in the text, but clarity would aid reproduction of the experiments.
+According to the Reviewer suggestion, we revised the related paragraph in the method section of the main text: “Next, the solution was sequentially purged with air to form the Fe^{2+} complex, then with argon and finally reduced with 0.2 \( \mu \)L of 0.5 M sodium dithionite, prepared under Ar atmosphere, to restore the Fe^{2+} complex.” (p. 21 l. 22-24).
+
+Line 6-7 of the abstract (“… in a as small as…”)) should be re-worded for clarity.
+We reworded as follows: “We assembled into a miniature 28-residue protein the quintessential elements …”
+
+In my opinion, this manuscript is of significant novelty and impact for publication in Nature Communications and should be accepted once the above concerns have been addressed.
+We thank the Reviewer for the kind remarks, and we hope we have satisfied her/his concerns.
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Most of my previous concerns have been nicely addressed (although I would love to see further application of this strategy for a more applicable artificial protein). Nevertheless, this reviewer agrees that the manuscript is now in a good shape for a publication in Nat. Commun.
+
+Reviewer #2 (Remarks to the Author):
+
+They authors have addressed all my previous concerns. I support the publication of this manuscript.
+
+Reviewer #3 (Remarks to the Author):
+
+"Designed Rubredoxin miniature in a fully artificial electron chain triggered by visible light".
+
+I would like to comment, in terms of the comments made (reviewer#3), that I am satisfied with the answers.'
+
+In addition, I would feel more comfortable if the authors avoid in Table I (note) the term "EPR silent" and replace it with "difficult to detect by EPR" since it is an integer spin S=2.
+
+Reviewer #4 (Remarks to the Author):
+
+The authors have addressed my main points of concern in their revised manuscript. In particular, the updated figure 7C now shows the clear disappearance of the 494 nm peak and appearance of a signal at 311 nm. This data is now much clearer than in the original manuscript, leaving no room for doubt concerning this key result.
+
+In my opinion this manuscript should now be accepted without further revision.
+REVIEWER COMMENTS
+
+AUTHOR RESPONSE
+
+Reviewer #1 (Remarks to the Author):
+Most of my previous concerns have been nicely addressed (although I would love to see further application of this strategy for a more applicable artificial protein). Nevertheless, this reviewer agrees that the manuscript is now in a good shape for a publication in Nat. Commun.
+We thank the Reviewer for her/his kind words of appreciation, and we are working hard to deliver to the community an exciting set of designed metalloproteins based on this scaffold.
+
+Reviewer #2 (Remarks to the Author):
+They authors have addressed all my previous concerns. I support the publication of this manuscript.
+We really thank the Reviewer for the very supporting words she/he reserved to our work. And we hope she/he may continue following our work in metalloprotein design in the future.
+
+Reviewer #3 (Remarks to the Author):
+I would like to comment, in terms of the comments made (reviewer#3), that I am satisfied with the answers. 'In addition, I would feel more comfortable if the authors avoid in Table I (note) the term "EPR silent" and replace it with "difficult to detect by EPR" since it is an integer spin S=2,
+We are glad that the Reviewer is satisfied with the answers provided in the previous round of revisions, and we apologize for the misleading comment we included in the note to Table 1. We revised “EPR silent” as suggested with "usually difficult to detect under standard experimental conditions".
+
+Reviewer #4 (Remarks to the Author):
+The authors have addressed my main points of concern in their revised manuscript. In particular, the updated figure 7C now shows the clear disappearance of the 494 nm peak and appearance of a signal at 311 nm. This data is now much clearer than in the original manuscript, leaving no room for doubt concerning this key result. In my opinion this manuscript should now be accepted without further revision.
+We cannot be more enthusiastic to read that now the Reviewer is fully convinced by our data. We really think that the contribution by all the reviewers significantly helped us in pushing further the quality of the manuscript and of the overall scientific soundness of the publication

029b063b4c7e6cb6f98cd7272f8ba5aae91cfdac89a5b03027277558d21a4027/preprint/preprint.md

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+Designed Rubredoxin miniature in a fully artificial electron chain triggered by visible light
+
+Marco Chino
+University of Naples Federico II   https://orcid.org/0000-0002-0436-3293
+Luigi Di Costanzo
+University of Naples Federico II
+Linda Leone
+University of Naples Federico II
+Salvatore La Gatta
+University of Naples Federico II
+Antonino Famulari
+University of Torino
+Mario Chiesa
+University of Torino   https://orcid.org/0000-0001-8128-8031
+Angela Lombardi (alombard@unina.it)
+University of Naples Federico II   https://orcid.org/0000-0002-2013-3009
+Vincenzo Pavone
+Università di Napoli
+
+Article
+
+Keywords: Metalloproteins, de novo design, iron-sulfur cluster, electron cascades, photo-induced 17 electron transfer
+
+Posted Date: April 4th, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1473985/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+Designed Rubredoxin miniature in a fully artificial electron chain triggered by visible light
+
+Marco Chino¹, Luigi Franklin Di Costanzo², Linda Leone¹, Salvatore La Gatta¹, Antonino Famulari³⁴, Mario Chiesa³, Angela Lombardi¹* and Vincenzo Pavone¹*.
+
+1. Department of Chemical Sciences, University of Naples Federico II. Via Cintia 21, 80126 Napoli, Italy.
+2. Department of Agricultural Sciences, University of Naples Federico II. Via Università 100, 80055 - Portici (NA), Italy.
+3. Department of Chemistry, University of Torino. Via Giuria 9, 10125 Torino, Italy.
+4. Department of Condensed Matter Physics, University of Zaragoza, Calle Pedro Cerbuna 12, 50009 Zaragoza, Spain.
+
+Correspondence to: alombard@unina.it; vipavone@unina.it
+Abstract
+
+Designing metal sites into de novo proteins has significantly improved, recently. However, identifying the minimal coordination spheres, able to encompass the necessary information for metal binding and activity, still represents a big challenge, today. Here, we tested our understanding with a benchmark, nevertheless difficult, case. We assembled in a small 28-residue peptide the quintessential elements required to correctly fold around a single iron redox center, coordinated to four cysteinyl thiolates (FeCys4 site), and to efficiently function in electron-transfer. This study represents a milestone in de novo protein design: for the first time the crystal structure of a designed tetra-thiolate metal-binding protein is reported within sub-\AA{} agreement with the intended design. This allowed us to well correlate structure to spectroscopic and electrochemical properties. Given its high reduction potential compared to natural and designed FeCys4-containing proteins, we exploited it as terminal electron acceptor of a fully artificial chain triggered by visible light.
+
+Keywords: Metalloproteins; de novo design; iron-sulfur cluster; electron cascades; photo-induced electron transfer.
+Main
+
+Electron transport chains play a central role in many life-sustaining functions from respiration\( ^{1,2} \), to light harvesting\( ^{3,4} \). They involve two or more redox active metalloproteins, with one or more metal cofactors bound in their interior. These metal cofactors are highly conserved in their first coordination sphere, and the surrounding residues intimately modulate their electronic structure. A wide range of reduction potentials can be achieved, thus generating the driving force of electron cascades. The protein matrix also drives the mutual orientation of these cofactors, by subtly evolved self-assembly processes, fundamentally regulating electron-transfer. Thus, it is imperative in metalloprotein design to develop finely tunable redox-active metal sites, amenable for photo-induced electron trafficking and bioenergy control. Previous work has been focused on charge-separation/recombination at purposely optimized abiotic cofactors\( ^{5,6} \), electron transfer towards natural acceptors\( ^{7,8} \), injection into titanium-based photoanodes\( ^{9} \), as well as intraprotein electron transfer between two different cofactors\( ^{10,11} \). In this work, we explore two small proteins, designed from scratch, to achieve for the first time in protein design the construction of a fully artificial electron chain triggered by visible light.
+
+In Nature, most of the redox proteins involved in electron trafficking and bioenergy control is represented by cupredoxins\( ^{12,13} \), cytochromes\( ^{14,15} \), and iron-sulfur proteins\( ^{16-18} \). Rds represent the simplest and most studied case. They bind a single iron ion through four Cys S\(_\gamma\) with an almost tetrahedral geometry and they can cycle between the oxidation states (II) and (III). Rds (45–55 amino acids) adopt a \(C_2\)-pseudo-symmetric fold constituted by two symmetry-related CXXCX \(\alpha\)-turns\( ^{19} \). Despite well-conserved backbones and sequences (50–60% sequence identity), their reduction potential varies in the range -100/+50 mV in prokaryots and could reach 125 mV (\(vs\) SHE) in eukaryots, as well as in the closely related rubrerythrin\( ^{16} \). Mutagenesis studies have dissected the role of the second coordination sphere in modulating Rds potential\( ^{17,20-22} \), and some double mutants have shown that the effect of mutations is generally additive\( ^{23} \). In this respect,
+several studies of rational redesign and fully de novo design have targeted the Rd system. Among these, some groups have focused on alternative metal ions, using the S4 site as a surrogate of more complex catalysts, such as [NiFe] hydrogenases or molybdoenzymes22,24. Others have installed the tetrahedral FeCys4 site in structurally different natural and de novo proteins25–27. We, and others, have focused on the Rd prototypical structural unit, making use of its intrinsic symmetry to build a miniaturized peptide scaffold28–31.
+
+In this context, we describe the design and characterization of a single-chain high-potential miniaturized electron transfer protein (named METPsc1) based on the FeCys4 metal cofactor. In doing so, we address three challenges in de novo metalloprotein design. First, we implanted a FeS4 site into a de novo protein, closely matching the highest reported reduction potential in the Rd family; secondly, we obtained the first X-ray structure of a tetra-thiolate metalloprotein designed from scratch, within sub-Å agreement with the intended design; thirdly, and most important, we established a fully artificial photo-induced electron cascade, exploiting the newly developed protein as terminal electron acceptor. The photosensitizer unit (ZnMC6*a) used in this process is itself an artificial protein, belonging to the class of synthetic metalloporphyrin-containing proteins, named Mimochromes32–34. Taken together, our results demonstrate that such miniaturized proteins might be exploited in optoelectronics and light-harvesting biodevices.
+
+Results and Discussion
+
+Design of a single-chain miniaturized FeS4 protein
+
+The first goal of this work consists in the design of a high potential miniprotein, leveraging from the wealth of mutagenesis studies on Rds. Rd from Clostridium pasteurianum (Cp) has been a central player in unraveling the factors that affect the reduction potential of the FeCys4 metal site16,17. It was shown that Fe(II) stability can be related to the number and the strength of H-bonds
+involving the coordinating Sγ atoms. Though double and triple mutants of Rd have been reported, several single-point mutations at once may perturb the global fold or alter the expression profile22,23.
+
+More intensive protein engineering routines, such as directed evolution, are generally needed to adapt the protein, and host the desired mutations. De novo design provides a remarkable alternative, which allows incorporating all the desired mutations at once, and generating the most suited structural arrangement for testing and refining folding and functions, such as redox potential.
+
+In our preview studies, the designed protein METP was recognized as a minimal unit needed to reproduce Rds by retrostructural analysis30. Two short undecapeptides are related by a twofold axis around a central metal ion as in Rd. Despite METP spectroscopic characterization indicated the expected structural arrangement when coordinated to different metal ions, its iron complex was unable to perform reversible redox cycles. An auto-redox reaction may account for the observed instability of the Fe(III)-tetrathiolate complex, with Fe(III) reduction to Fe(II), and disulfide formation.
+
+In recent studies, sacrificing symmetry to generate monomeric analogs has been identified as a common strategy to solve this stability issue28,29,35-37. We generated new backbone coordinates by miniaturization and symmetry considerations, following the early METP design. We began from the high-resolution structure of the reduced V44A mutant of Cp Rd, which represents one of the high-potential mutants (Figure 1a, PDB ID: 1c09)21. The segment from Val38 to Glu50 was dissected from the protein, and the \( C_2 \) longitudinal axis was applied (Figure 1b) to generate the dimer coordinates. We then performed a systematic search to find the best fragment linking N- (Val38) and C-termini (Glu50 of the symmetric copy), fixing seven residues as the maximum gap length.
+Figure 1. Design and structural characterization of METPsc1. a, crystal structure of Cp Rd V44A mutant (PDB ID: 1C09). b, miniaturized model, obtained by applying a C2 longitudinal rotation to the Val38-Glu50 fragment of Cp Rd V44A. c, superimposition of the 4-residue loops found with the fragment search. d, single-chain METP prototype, obtained by combination of the C2-symmetric dimer with the type I' beta turn selected from the search. e, designed model of ZnMETPsc1.
+
+We plotted the number of fragments within 1 Å backbone RMSD against the gap length (Extended Data Figure 1), and we found that a 4-residues loop represented the shortest yet designable choice to link the two ends (39 hits out of 158 total hits, Figure 1c). As expected for a 4-residues segment, simple β-turn motifs were found in most cases (29 out of 39). The sequence analysis of the matches revealed that both i+1 and i+2 positions were mainly occupied by Gly residues (Extended Data Figure 2), as typically observed in type I'/III' β turns38. 14 and 3 fragments corresponded to type I' and III' β turns, respectively (Supplementary Table 1). The best matching
+fragment was used to generate an initial backbone model, by grafting the loop coordinates onto the previously generated Val38-Glu50 \( C_2 \)-symmetric dimer (Figure 1d). This structure was then submitted to a preliminary flexible backbone design routine (see Supplementary Information). This step helped identifying some key features in terms of residue propensities at specific positions (see Supplementary Information). Moreover, in this stage we fixed 2-aminoisobutyric (Aib) residues at pseudo-symmetric positions 9 and 24 to induce the \( 3_{10} \)-helix formation, as successfully accomplished in METP design. In a second design round, we instructed the packer with the results from the previous steps, and we further defined the identities of the residues at the corner positions of the CXXC motif (Figure 1e), by limiting them only to hydrophilic residues. This condition aimed at understanding the role of the H-bonding on redox potential by excluding the effect of the local dielectric environment.
+
+*ZnMETPsc1 crystal structure reveals a handful of secondary motifs*
+
+The newly designed 28 residue METPsc1 miniprotein was synthesized in good yield by standard solid phase methods and characterized by X-ray diffraction analysis as zinc complex at high resolution. ZnMETPsc1 crystallizes in the orthorhombic space group C222₁. The asymmetric unit of the cell contains one monomer. All protein residues were clearly identified from the electron density map and correspond to the designed protein sequence, including the N- and C-terminal acetyl and amide protecting groups, respectively (Figure 2a, Supplementary Table 2). The overall monomeric structure is quite identical to the design (Figure 2b, backbone RMSD 0.45 Å), as well as Cys and hydrophobic sidechain packing, while surface exposed sidechains adopt alternative rotamers, probably due to packing and solvation interactions. The monomer folds as a truncated cone shaped molecule (Extended Data Figure 3), with an upper base corresponding to the metal binding site near the surface formed by Cys20-Asp4 and Cys5-Asn19 residues. The hydrophobic residues Aib9, Val12, Aib24 and Ile27, facing each other, with sidechains nearly aligned on a plane, form the lower base. Notably, Cys2 and Cys17, the other two cysteine residues completing the
+coordination sphere, occupy the innermost space of the whole protein. All the remaining residues decorate the external surface of the conical shape, forming a highly hydrophilic surface.
+
+The observed structure is a compelling collection of secondary and super-secondary motifs, all of them collapsed into one small polypeptide chain. The pseudo two-fold symmetry axis is relating two consecutive similar segments formed by a progression of: (1) a small extended 2-residues β-strand; (2) an α-turn with Ser-Asp-Cys as corner residues; (3) Gly β-buldge; (4) a small extended 2-residues β-strand; (5) an incipient 3_{10}-helix with two consecutive β-turns; (6) a small extended 2-residues β-strand; (7) a type I’ β-turn involving two consecutive Gly residues (Figure 2c, Supplementary Table 3 and Supplementary Information). Interestingly, β-strands pair to give two sets of short antiparallel β-sheets.
+
+The shell around the macromolecules is hydrated and the crystal packing is characterized by interactions involving symmetrically related Arg residues. The crystal packing is stabilized by intermolecular salt bridges between a crystallographic related residue of Arg26 and Asp4 (see below). In addition, interactions between Tyr16 and the equivalent residue of a crystallographic related METPsc1 molecule are observed with a 3.32 Å distance between -OH atom groups.
+
+The METPsc1 complex forms two packing large channels (Extended Data Figure 4). One central channel of a larger diameter (~12 Å), around the C-centered midpoint of the space group C222_1, is surrounded by negatively charged Asp residues. The second channel is formed by crystallographic binary axes and aligned by several positively charged Arg residues.
+
+First and second sphere interactions define zinc complex features
+
+Zn^{2+} is tetrahedrally coordinated by four Cys Sγ with average Sγ-Zn distance of 2.34±0.03 Å and Sγ-Zn-Sγ bond angle of 109±4° (Figure 2d), consistently with the geometry found in the twelve ultrahigh resolution rubredoxin structures retrieved from the Protein Data Bank (PDB) and containing Zn^{2+}.
+Figure 2. ZnMETPsc1 structural characterization. a, Metal ion, all sidechains, and N- and C-terminal capping groups are clearly visible in the electron density map (2F_o-F_c map, 1.3 σ level). b, The monomeric X-ray structure of ZnMETPsc1 (cyan, this work, PDB ID: 5sbg) closely matches the designed model (light brown). c, Description of secondary structural elements found in ZnMETPsc1 structure (blue: β-strand; red: α-turn; gray: β-bulge; green: 3_10-helix; orange: type I’ β-turn). Dashed lines represent backbone to backbone H-bonds. d, First coordination sphere shows the expected coordination bond distances between zinc and cysteine sulfur atoms. e, Second coordination sphere involving amide of Ala7 and Ala22 exacerbates H-bond strength with respect to wt Cp Rd. f, The H-bond donors from sidechains of Asn19 and a symmetry-related Arg26 (in cyan) to METPsc1 partners are indicated.
+
+The Cys residues are arranged around the metal center with a clockwise distribution of sidechains in that \( \chi^1 \) are either g+ or t for Cys5/Cys20 and Cys2/Cys17, respectively. The torsion angle Sγ(Cys2)-Zn-Sγ-Cβ(Cys17) is 180° while the pseudo-symmetry-related torsion angle is Sγ(Cys6)-Zn-Sγ-Cβ(Cys20) is 159°.
+
+The second coordination shell is characterized by H-bonds involving Cys Sγ and backbone N-H donors, similarly to natural Rds (Supplementary Table 4). Cys2 accepts H-bonds from backbone amide groups of Asp4 and Cys5, the same occurring for the symmetry related Cys17 (Asn19 and Cys20 backbone amides). The designed sequence presents Ala residues at positions 7 and 22, being sufficiently small to let their own backbone N-H to H-bond Cys5 and Cys20 Sγ, respectively (Figure 2e). The strength of this H-bond has previously been correlated to the reduction potential,
+as shown for Cp Rd mutants of Val4420. Moreover, positions 4 and 19 of METPsc1 (Figure 2f) correspond to position 41 of Cp Rd, the latter being crucial for the solvent accessibility and H-bonding of Cys9 in Cp Rd39. In our model, it is reasonable to hypothesize that Asp4 residue would drive water access towards Cys20. Asn19 residue donates its sidechain amide protons to Cys5 Sy, further decreasing its electron density (Figure 2e). Cys20 Sy accepts a H-bond from sidechain guanidine group of a crystallographically related Arg26, mimicking a water molecule as observed in L41A Cp Rd X-ray structure (Figure 2f).
+
+Structure correlates with function as assessed by spectroscopy and voltammetry
+
+Spectroscopic and electrochemical studies were performed to analyze the METPsc1 behavior in solution and to correlate structural to functional properties. Iron binding and coordination geometry was assessed by a combination of UV-Vis absorption, CD, and EPR spectroscopies (Table 1)40–42. METPsc1 forms a 1:1 complex with Fe^{2+} at pH 6.8, as assessed by Mohr salt titration of the apo peptide, under inert atmosphere (Figure 3a). The data were well described by a binding isotherm with an apparent K_D \leq 300 nM.
+
+<table>
+  <tr>
+    <th rowspan="2"> </th>
+    <th colspan="2">Fe^{2+} METPsc1</th>
+    <th colspan="2">Fe^{2+} Cp Rd</th>
+    <th colspan="2">Fe^{3+} METPsc1</th>
+    <th colspan="2">Fe^{3+} Cp Rd</th>
+  </tr>
+  <tr>
+    <th>UV-Vis</th>
+    <th>\lambda/nm (\varepsilon/mM^{-1} cm^{-1})</th>
+    <th>CD</th>
+    <th>\lambda/nm (+/-)</th>
+    <th>EPR</th>
+    <th>g_{eff}</th>
+    <th>Fe^{3+} METPsc1</th>
+    <th>Fe^{3+} Cp Rd</th>
+    <th>g_{eff}</th>
+  </tr>
+  <tr>
+    <td>UV-Vis</td>
+    <td>311 (7.73), 331 (4.43)</td>
+    <td>311 (10.8), 333 (6.3)<sup>40</sup></td>
+    <td>345 (7.28), 370 (8.33), 494 (6.54), 570 (3.13), 745 (0.33)</td>
+    <td>350 (7.00), 380 (7.70), 490 (6.60), 570 (3.20), 750 (0.35)<sup>41</sup></td>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>CD</td>
+    <td>312(-), 333(+)</td>
+    <td>314(-), 335(+)<sup>42</sup></td>
+    <td>437(+), 502(-), 557(+), 632(-)</td>
+    <td>437(+), 500(-), 560(+), 635(-)<sup>42</sup></td>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>EPR</td>
+    <td></td>
+    <td></td>
+    <td>9.15, 4.26</td>
+    <td>9.4, 4.3<sup>40</sup></td>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+</table>
+
+Table 1. Spectroscopic parameters of FeMETPsc1 and Cp Rd in Fe(II) and Fe(III) oxidation states.
+Figure 3. FeMETPsc1 spectroscopic and electrochemical characterization. a, UV-Vis titration of METPsc1 with Fe^{2+}, absorbances at 311 nm are reported in the inset (black squares) and fitted by a 1:1 binding isotherm (red dashed line). Mohr’s salt (36 mM) aliquots were added to a 30 μM METPsc1 solution in a 20 mM HEPES buffer (pH 7) and 1 mM TCEP. b, c, UV-Vis and CD spectra of the reduced (black line) and oxidized (red line) FeMETPsc1 (40 μM) species. d, X-band CW-EPR spectrum of Fe^{3+}METPsc1 (0.5 mM) in 20 mM phosphate buffer (pH 7) and 5 mM TCEP at 4.5 K. e, Cyclic voltammograms of FeMETPsc1 (80 μM) as a function of scanning rate were recorded in 40 mM HEPES buffer (pH 7) and 0.3 M KCl. Each voltammogram is the last of three consecutive scans.
+
+Such value is dramatically lower than those we previously observed for the dimeric METP (one and two order of magnitude, respect to Zn^{2+} and Co^{2+}, respectively), most probably attributable to the enhanced chelate effect granted by the monomeric protein. METPsc1 is a tighter ligand for iron when compared to other previously designed monomeric constructs^{27,28}, but still looser than a previously reported zinc-finger inspired cyclic scaffold^{29}.
+
+When exposed to air, Fe^{2+} complex readily oxidizes to the ferric state. We collected UV-Vis and CD spectra of both reduced and oxidized forms. Absorption spectra for both oxidation states
+show the Rd characteristic LMCT bands of tetrahedral thiolate donors (Figure 3b). In addition, their extinction coefficients are in striking agreement with those reported for \( Cp \) Rd (Table 1). CD positive and negative Cotton effects alternate as previously reported for the ferric state\(^{42}\) and lead to the assignment of at least six transitions in the visible region (Figure 3c), four of which match those found in \( Cp \) Rd (Table 1), and in other designed models\(^{27,29}\).
+
+The complex was also characterized by X-band Continuous Wave (CW)-EPR spectroscopy (Figure 3d). The observed resonances, \( g_{\text{eff}} = 9.15 \) and 4.26, match those of a high-spin Fe\(^{3+}\) (S=5/2) center, consistent with a rhombic distortion E/D of about 0.22 and a positive D value, as observed for \( Cp \) Rd and sulfur ligated ferric iron model compounds\(^{29,43}\). Taken together, spectroscopic data demonstrate that both Fe\(^{2+}\) and Fe\(^{3+}\) are tightly bound into a tetrathiolate environment as in natural Rds, both in geometry and electronic structure.
+
+Once established the high binding affinity of METPsc1 for iron in both oxidation states, we analyzed whether the protein accomplishes reversible redox cycles. We performed a typical redox-cycling experiment following changes of the characteristic Fe\(^{3+}\)METPsc1 band at 494 nm. We cyclically oxidized iron upon exposure to air, followed by argon purge and reduction by sodium dithionite addition (Extended Data Figure 5). A protein solution (40 \( \mu \)M, pH 7) was subjected to at least nine consecutive and reversible redox cycles, without dramatic loss of the protein signal upon recycling (Extended Data Figure 6), similarly to other redox-cycling Rd mimics\(^{27-29}\). The last of 9 oxidation processes recovered approximately 50% of the expected Fe\(^{3+}\)METPsc1 signal, suggesting that more cycles could be performed. These results demonstrate that FeMETPsc1 can reversibly switch between ferrous and ferric states in diffusion under excess of reductant (dithionite) or oxidant (dioxygen), respectively.
+
+A fundamental test of the correctness of our design came from electrochemical measurements. A double mutant in positions Tyr11 and Val44 of \( Cp \) Rd has never been reported to date (Ala7 and Ala22, respectively in METPsc1), and thus it is of particular interest to analyze METPsc1
+electrochemistry. We, therefore, performed cyclic voltammetry experiments at different scan rates in which a glassy carbon electrode was immersed in a solution of 80 μM FeMETPsc1 (pH 7), using 0.3 M KCl as electrolyte (Figure 3e). FeMETPsc1 gave measurable currents in the range of 2.5 – 50 mV/s, displaying a quasi-reversible behavior with reduction potential centered at \( E^{*0} = 121 \) mV (vs SHE), with \( \Delta E_p \) in the range 59–136 mV. This high potential was our design goal, and it is not surprising considering the crystallographic data. Its value surpasses the classical range for prokaryotic Rds, and closely matches the potential of ruberythrins\(^{16,23}\). The number and strength of H-bonds in the second coordination sphere (Ala7, Ala22, Asn19, Arg27) significantly decrease the electron density of sulfur donors, thus favoring the ferrous state. Randles-Ševčík analysis has been used to evaluate the diffusion coefficients of the reduced and oxidized species (Extended Data Figure 7). They are 0.92 \( 10^{-6} \) and 1.4 \( 10^{-6} \) cm\(^2\) s\(^{-1}\) for the reduced and oxidized forms, respectively, in reasonable agreement with the value calculated from the crystallographic model (1.47 \( 10^{-6} \) cm\(^2\) s\(^{-1}\)).
+
+*Definition of an artificial photo-triggered electron cascade*
+
+FeMETPsc1 possesses a significantly high reduction potential, and the Fe\(^{3+}\) reduction is accompanied by a clear change in the visible spectrum. To test whether FeMETPsc1 could represent the final electron acceptor of an electron transport chain, a photo-triggered reduction experiment was designed (Figure 4a).
+Figure 4. Photoinduced electron transfer from ZnMC6*a (40 μM) to Fe3+METPsc1 (50 μM). a, reaction scheme of the synthetic electron cascade. b, experimental setup showing the LED strip wrapped around the UV cuvette under Ar atmosphere. c, superimposed UV-Vis spectra of Fe3+METPsc1 (black trace) and Fe2+METPsc1 (red trace) in the presence of ZnMC6*a (40 μM) and triethylamine (4 mM). d, redox cycling of FeMETPsc1 monitored at 496 nm and 314 nm. Green boxes correspond to light irradiation.
+
+Triethylamine (TEA) was chosen as sacrificial reductant, and FeMETPsc1 as oxidant, whilst a newly synthesized Zn2+ derivative of Mimochrome VI*a (ZnMC6*a) was used as photosensitizer32. Zinc tetrapyrroles have been already used in designed and engineered metalloproteins, and they showed peculiar time-resolved spectroscopic features41, intra-molecular ET processes5,6,10, and allosteric modulation45. However, this photoactive cofactor has never been used to transfer electrons from one protein to another. Therefore, a simple experiment was carried
+out by following FeMETPsc1 UV/Vis-spectrum differences upon reduction/oxidation due to green light exposition (Figure 4b).
+
+When a solution containing 4 mM TEA, 50 \( \mu \)M Fe\(^{2+}\)METPsc1, and 40 \( \mu \)M ZnMC6*a was purged with air, a 496 nm band of the oxidized [FeCys\(_4\)]\(^{1-}\) appeared (Figure 4c,d), demonstrating that iron oxidation at METPsc1 was not affected by TEA and ZnMC6*a. When the solution was exposed to green light irradiation for 25 minutes under argon atmosphere, complete disappearance of the ferric charge-transfer band was observed. A band at 314 nm concomitantly appeared, characteristic of the reduced [FeS\(_4\)]\(^{2-}\) species, close to the previously observed maximum at 311 nm, with a slight shift due to superposition with the zinc porphyrin spectrum. These results clearly demonstrate Fe\(^{3+}\)METPsc1 reduction upon light exposure. As a final proof of the artificial photo-electron transfer chain, the system was exposed again to air and then to green light irradiation. As expected, air oxidized FeMETPsc1, and then after 15 minutes of irradiation, it was reduced back with formation of a peak at 314 nm. However, complete disappearance of the band in the visible region could not be observed, mostly because spectrum contribution from the zinc porphyrin was significantly altered. In turn, this could be possibly ascribed to reactive oxygen species that formed during the previous O\(_2\) reduction step (Figure 4a, Extended Data Figure 8).
+
+Conclusions
+
+The combination of powerful computational tools\(^{46,47}\), and more recently machine learning\(^{48,49}\), together with the genome palette (e.g., directed evolution and phage/yeast display)\(^{50,51}\) is significantly helping protein designers in increasing success rate. However, direct correlation between single point mutations and metal-dependent function still remains elusive when large scaffolds are adopted\(^{50,52}\). Design of synthetic metalloproteins by miniaturization helps circumventing this problem by limiting the metal surroundings to only a few crucial residues\(^{53}\). To this end, we developed by design and miniaturization a synthetic Rd, METPsc1, capable of keeping the intended structural and functional properties in a small 28-residue peptide. The availability of
+high-resolution structure and its agreement with the designed model at sub-Å level validate the adopted design principles. The designed second-shell interactions revealed crucial in determining one of the highest potentials amongst the Rd family. This result prompted us to generate a synthetic electron transfer chain from a sacrificial electron donor (TEA) to a sacrificial acceptor (O_2) by means of two newly-developed synthetic mini-proteins (FeMETPsc1, ZnMC6*a), whose overall size correspond to ~6.5 kDa.
+
+In perspective, our studies provide a prototype for the generation of nanosized multicomponent mini-protein devices. They should encourage future design of small metalloproteins with predetermined structural and functional properties.
+
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+40. Im, S.-C. & Geoffrey Sykes, A. Kinetic studies on the redox reactions of Clostridium pasteurianum rubredoxin. *J. Chem. Soc. Dalton Trans.* 2219–2222 (1996).
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+41. Xiao, Z. *et al.* The Rubredoxin from Clostridium pasteurianum: Mutation of the Iron Cysteinyl Ligands to Serine. Crystal and Molecular Structures of Oxidized and Dithionite-Treated Forms of the Cys42Ser Mutant. *J. Am. Chem. Soc.* **120**, 4135–4150 (1998).
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+42. Eaton, W. A. & Lovenberg, W. The Iron-Sulfur Complex in Rubredoxin. in *Molecular Properties* 131–162 (Elsevier, 1973). doi:10.1016/B978-0-12-456002-4.50009-5.
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+43. Peisach, J., Blumberg, W. E., Lode, E. T. & Coon, M. J. An Analysis of the Electron Paramagnetic Resonance Spectrum of Pseudomonas oleovorans Rubredoxin: a method for determination of the ligands of ferric iron in completely rhombic sites. *J. Biol. Chem.* **246**, 5877–5881 (1971).
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+44. Polizzi, N. F. *et al.* De novo design of a hyperstable non-natural protein–ligand complex with sub-Å accuracy. *Nat. Chem.* **9**, 1157–1164 (2017).
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+45. Pirro, F. *et al.* Allosteric cooperation in a de novo-designed two-domain protein. *Proc. Natl. Acad. Sci.* **117**, 33246–33253 (2020).
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+47. Zhou, J., Panaitiu, A. E. & Grigoryan, G. A general-purpose protein design framework based on mining sequence–structure relationships in known protein structures. *Proc. Natl. Acad. Sci.* **117**, 1059–1068 (2020).
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+48. Baek, M. *et al.* Accurate prediction of protein structures and interactions using a three-track neural network. *Science* **373**, 871–876 (2021).
+49. Jumper, J. et al. Highly accurate protein structure prediction with AlphaFold. Nature **596**, 583–589 (2021).
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+50. Basler, S. et al. Efficient Lewis acid catalysis of an abiological reaction in a de novo protein scaffold. Nat. Chem. **13**, 231–235 (2021).
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+51. Rocklin, G. J. et al. Global analysis of protein folding using massively parallel design, synthesis, and testing. Science **357**, 168–175 (2017).
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+52. Choi, T. S. & Tezcan, F. A. Overcoming universal restrictions on metal selectivity by protein design. Nature **1–6** (2022) doi:10.1038/s41586-022-04469-8.
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+53. Maglio, O., Nastri, F. & Lombardi, A. Structural and Functional Aspects of Metal Binding Sites in Natural and Designed Metalloproteins. in *Ionic Interactions in Natural and Synthetic Macromolecules* (eds. Ciferri, A. & Perico, A.) 361–450 (John Wiley & Sons, Inc., 2012).
+
+Methods
+
+Computational modelling and simulation methodology is described in the Supplementary Information and in Supplementary Figures 1-4.
+
+Solid-phase peptide synthesis.
+
+METPsc1 was synthesized by automatic solid-phase synthesis, using an ABI 433A peptide synthesizer (Applied Biosystem, Foster City, CA, USA) with standard Fmoc chemistry on a 0.1 mmol scale. The acid labile H-PAL ChemMatrix resin, with a substitution of 0.20 mmol/g, was used as solid support. Amino acids were activated in situ with 2-(7-Aza-1H-benzotriazole-1-yl)-1,1,3,3-tetramethyluronium hexafluorophosphate (HATU) as coupling reagent. The N-terminal amino group was acetylated with a solution of acetic anhydride, 1-hydroxybenzotriazole (HOBr) and diisopropylethylamine (DIEA) in N-methyl-pyrrolidone (NMP). Peptide cleavage from the resin and sidechains deprotection was achieved with a mixture of trifluoroacetic acid/H$_2$O/triisopropylsilane/ethanedithiol 9.4:0.25:0.25:0.1 (v/v/v/v), yielding to amidated C-
+terminal. The crude peptide was precipitated in cold diethyl ether and dried under reduced pressure.
+
+The overall synthesis yield was 65%, based on the resin substitution.
+
+Peptide purification and analysis
+
+Peptide purification was accomplished using a Shimadzu LC-8A preparative HPLC system (Shimadzu, Kyoto, Japan), equipped with a SPD-M10AV UV-Vis detector. A Reverse Phase Vydac C18 column (250 cm x 22 mm; 10 μm) was eluted with a linear gradient of H2O 0.1% TFA (eluent A) and acetonitrile 0.1% TFA (eluent B), from 5% to 70% B over 50 min at a flow rate of 22 mL/min.
+
+Peptide purity and identity were assessed by RP-HPLC-MS analysis (Supplementary Figures 5-7), using a Shimadzu LC-10ADvp equipped with an SPDM10Avp diode-array detector. ESI-MS spectra were recorded on a Shimadzu LC-MS-2010EV system with ESI interface and a quadrupole mass analyzer. A Vydac C18 column (150 mm x 4.6 mm, 5 μm) was used in the LC-MS analyses, eluted with a linear gradient of H2O 0.1% TFA (eluent A) and acetonitrile 0.1% TFA (eluent B), from 5% to 70% B over 60 min at a flowrate of 0.5 mL/min.
+
+Crystallography
+
+The ZnMETPsc1 complex was crystallized by the hanging drop vapor diffusion method at 20 °C. Typically, a drop containing 2.0 μL of 1:1 (v/v) mixture of protein solution (10 mg/mL, 7 mM DTT, 4 mM ZnCl2) and 2.0 μL of precipitant buffer (0.1 M HEPES at pH 7.5, 1.4 M sodium citrate tribasic dihydrate) was equilibrated against 0.5 mL reservoir of precipitant buffer. Crystals of the ZnMETPsc1 complex appeared within 4 days and grew as long needles with typical dimension of 0.15x0.15x0.5 mm³. Crystals were transferred to the same mother liquor solution augmented with 30% MPD solution and flash cooled. These crystals yielded diffraction data to 1.44 Å resolution at the XRD1 beamline (Elettra Synchrotron Light Source, Trieste, Italy), using a wavelength of 1.000 Å, and kept at 100 K. Data were processed using XDS and POINTLESS (version 1.11.21)54,55 with
+a data collection statistic reported in Supplementary Table 2. Crystals presented an orthorhombic unit cell with space group C2221. No twinning was detected.
+
+The structure of the ZnMETPsc1 complex was solved by molecular replacement via Phaser56, run under Phenix suite (version 1.16)57, using the designed model cleaved of the N- and C-terminal residues as a search model. The optimal solution for the positioning of one monomer in the asymmetric unit yielded a total log-likelihood gain of 21, a rotation function Z score (RFZ) = 3.2 and a translational function Z score (TFZ) = 3.7. An initial rigid-body refinement with data at 2.5 Å dropped the R/Rfree to 0.377/0.427. The program PHENIX.refine was used to anisotropically refine the model, and the graphics program COOT58 was used for structural model adjustments and inspection of Fourier residual maps. In the final stage of refinement, a total of 26 water molecules could be located. The data processing and structural refinement statistics are shown in Supplementary Table 2.
+
+Protein Data Bank has been accessed (March 11, 2022) for high-resolution Rd structures in order to determine the average M^{2+}—Sγ distance59. The search settings were: “Uniprot Molecule Name” contains “Rubredoxin”, “Refinement Resolution” > 0.5 and <= 1.2 Å. A total of 25 entries were retrieved. Among them, only 4 contained Zn^{2+} as ligand, for a total of 12 independent models binding zinc in the Cys4 binding site.
+
+UV-Vis Spectroscopy
+
+UV-Vis spectra were acquired on a Cary Varian 60 spectrophotometer, equipped with a thermoregulated cell holder and a magnetic stirrer. All buffer, protein or metal solutions were prepared with MilliQ water and purged with argon. All experiments were performed at 25°C, using rubber sealed quartz cuvettes of 1 cm pathlength. Concentration of METPsc1 was determined using a molar extinction coefficient of \( \varepsilon_{276} = 2980 \ \mathrm{M}^{-1} \ \mathrm{cm}^{-1} \). UV-Vis titration experiments with Fe^{2+} were performed by adding aliquots (~0.1 equiv) of Mohr’s salt to a solution of apo-METPsc1 (30 μM)
+in HEPES buffer (20 mM) pH 7 containing 1 mM TCEP. In the redox cycling experiment, a solution of Fe^{2+}METPsc1 (50 μM) in HEPES buffer (20 mM) and TCEP (1 mM) at pH 7 was sequentially purged with air to form the Fe^{3+} complex, then purged with argon and reduced with an excess of sodium dithionite to restore the Fe^{2+} complex. UV-Vis spectra were acquired every 3 minutes.
+
+Circular Dichroism spectroscopy
+
+CD spectra were recorded at 25°C on a JASCO J-815 dicrograph equipped with a thermoregulated cell holder. All spectra were acquired at 0.2 nm intervals with 20 nm/min scan speed, using quartz cells of 1 cm pathlength. Spectra in the far-UV region (190 - 260 nm) were acquired for apo- and ZnMETPsc1 (50 μM) in phosphate buffer (5 mM) at pH 7 (Supplementary Figure 8). The Zn complex was formed by addition of ZnCl_2 (1.5 equiv) to apoMETPsc1. Spectra in the UV-visible region (300 – 800 nm) were collected for the oxidized and reduced forms of FeMETPsc (40 μM) in HEPES buffer (20 mM) at pH 7. The Fe^{2+} complex was prepared by addition of Mohr’s salt (1.5 equiv) to an argon purged solution of METPsc1. The latter was then purged with air to obtain the Fe^{3+} complex.
+
+Electron Paramagnetic Resonance spectroscopy
+
+For the EPR study, Fe^{3+}METPsc1, in 20 mM phosphate buffer (pH 7) and 5 mM TCEP, was mixed with 30% of glycerol as glassing agent to an approximate final concentration of 0.5 mM. CW-EPR experiments were performed on a Bruker Elexys E580 X-band spectrometer (microwave frequency 9.76 GHz) equipped with a cylindrical dielectric cavity and a helium gas-flow cryostat from Oxford Inc. The spectrum was recorded at 4.5 K and a microwave power of 1 mW, a modulation amplitude of 0.7 mT and a modulation frequency of 100 KHz were used.
+Cyclic Voltammetry
+
+All cyclic voltammetry experiments were performed with a Potentiostat/Galvanostat μAUTOLAB Type III (Metrohm Autolab, Utrecht, The Netherlands) using a three-electrode cell for small volume samples (0.5-2 mL) purchased from BASi (West Lafayette, IN, USA), under argon. Temperature controlled measurements were conducted using a thermo-cryostat R2 (Grant). For all the measurement, a 3 mm-diameter glassy carbon electrode (GCE, BASi) was used as working electrode. A Pt wire and an Ag|AgCl NaCl 3 M electrodes (BASi) were used as counter and reference electrode (E°+= 0.206 V), respectively. Acquired data was processed by GPES software package.
+
+Cyclic voltammetry experiments on freely diffusing FeMETPsc1 were performed by adapting a previously published procedure, at 15 °C60. A 5 μL drop of a 0.76 mM METPsc1 solution in water was deposited on a square piece of a Spectra/Por (Biotech CE MWCO 0.5 – 1 kDa), and 0.2 μL of a 100 mM Mohr’s salt solution were added to it. Then, the polished GCE was pressed against the membrane and an O-ring, to form a solution layer. The electrode was then immersed in 20 mM HEPES buffer and 0.3 M KCl at pH 7 for 5 minutes to reconstitute the protein. The sample volume in the electrochemical cell was 2.0 ml. CV measurements were performed three times in the range 2.5 – 50 mV/s of scan speed, and the third voltammogram was used to perform the analysis. Diffusion coefficient of the crystallographic model was calculated by HYDRONMR71.
+
+Photo-induced electron transfer
+
+ZnMC6*a was synthesized according to previously described procedures.61 A solution of Fe^{2+}METPsc1 (50 μM), ZnMC6*a (40 μM) and triethylamine (4 mM) in HEPES buffer (20 mM) pH 7 was prepared and placed in a rubber sealed UV-Vis cuvette. The solution was first purged with air to form the Fe^{3+}METPsc1 complex, then purged with argon prior to the photoreduction.
+The latter was achieved by wrapping the cuvette with a green led strip (\( \lambda_{\text{max}} \) 570 nm, 5 mW/cm\(^2\) per led bulb) for 25 minutes or 15 minutes during the first or the second cycle, respectively.
+
+Data availabiblity
+
+The crystal structure of ZnMETPsc1 complex has been deposited in wwPDB with the accession code 5sbg.
+
+Acknowledgements
+
+We wish to thank Dr. Maurizio Polentarutti for X-ray data collection and Dr. Artemis Papadaki for performing preliminary designability analysis, Prof. Flavia Nastri and Ornella Maglio for fruitful discussion and Dr. Monica Grasso for administrative support. This work was supported by Campania Region “Programma Operativo FESR Campania 2014-2020, Asse 1” [CUP B63D18000350007] and by Italian MUR, Project SEA-WAVE 2020BKK3W9, [CUP_E69J22001140005].
+
+Author contributions
+
+M.C. and V.P. conceived the project and designed the miniproteins, which S.L.G. and L.L synthesized and purified. M.C. and L.L. performed the spectroscopic characterization and the electrochemical experiments; L.F.D.C., L.L. and S.L.G. conducted the crystallization and L.F.D.C. acquired crystallographic data; L.F.D.C. and M.C. determined the X-ray crystal structure; M.Chiesa and A.F. acquired and analyzed EPR data; M.C. and L.F.D.C prepared the manuscript draft; M.C., V.P. and A.L. interpreted the data, edited and finalized the manuscript with input from all authors; V.P. and A.L. supervised the project.
+
+Competing interests
+
+The authors declare no competing interests.
+References
+
+54. Kabsch, W. XDS. Acta Crystallogr. D Biol. Crystallogr. **66**, 125–132 (2010).
+
+55. Winn, M. D. *et al.* Overview of the CCP4 suite and current developments. *Acta Crystallogr. D Biol. Crystallogr.* **67**, 235–242 (2011).
+
+56. McCoy, A. J. *et al.* Phaser crystallographic software. *J. Appl. Crystallogr.* **40**, 658–674 (2007).
+
+57. Liebschner, D. *et al.* Macromolecular structure determination using X-rays, neutrons and electrons: recent developments in Phenix. *Acta Crystallogr. Sect. Struct. Biol.* **75**, 861–877 (2019).
+
+58. Emsley, P., Lohkamp, B., Scott, W. G. & Cowtan, K. Features and development of Coot. *Acta Crystallogr. D Biol. Crystallogr.* **66**, 486–501 (2010).
+
+59. Burley, S. K. *et al.* RCSB Protein Data Bank: biological macromolecular structures enabling research and education in fundamental biology, biomedicine, biotechnology and energy. *Nucleic Acids Res.* **47**, D464–D474 (2019).
+
+60. Correia dos Santos, M. M. *et al.* Electrochemical studies on small electron transfer proteins using membrane electrodes. *J. Electroanal. Chem.* **541**, 153–162 (2003).
+
+61. Caserta, G. *et al.* Enhancement of Peroxidase Activity in Artificial Mimochrome VI Catalysts through Rational Design. *ChemBioChem* **19**, 1823–1826 (2018).
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformationMETPsc1.pdf

030d32ff9b730af3688e796beaceb960542869b68e0c2941b54bdcec394c4d7e/peer_review/peer_review.md

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+Peer Review File
+
+Capacitive tendency concept alongside supervised machine-learning toward classifying electrochemical behavior of battery and pseudocapacitor materials
+Editorial Note: Parts of this peer review file have been redacted as indicated to maintain the confidentiality unpublished data.
+
+Reviewer #1 (Remarks to the Author):
+
+Reviewer’s general comment: The work focused on a machine learning method with the capacitive tendency for classifying battery and pseudocapacitor materials. The manuscript is within the scope of the Journal. To help improve the paper’s quality, my suggestions and comments are shown below.
+
+1) Abstract:
+
+(1) It is suggested to give a brief description of the current research progress in the forms of the classification of battery and pseudocapacitor electrode materials, especially the efforts in machine learning. Then, please summarize the research gaps, as well as the motivations and advantages of your method.
+
+(2) It is suggested to introduce the mechanism of the proposed methodology in one to two sentences.
+
+(3) Qualitative results with quantitative data are necessary to support the contribution of the work.
+
+2) Introduction:
+
+(1) The definition of capacitive tendency is not clear in the “introduction part”, while the advantages are given. The mechanism of “capacitive tendency” to help classify battery and pseudocapacitor materials is suggested to be further explained.
+
+(2) Introduction: as mentioned in the manuscript, the text-mining algorithms have been developed to efficiently extract various specific information of the materials, like BatteryDataExtractor and Li-ion battery annotated corpus. In this study, the authors applied ML for electrochemical signal interpretation. This belongs to the first application. From this point, the innovation or originality might be questionable.
+
+(3) Original contribution at the end of Introduction needs to be further enhanced.
+
+(4) Compare your approaches used in your study to the others in terms of their advantages and drawbacks.
+
+(5) The proposed algorithm should be tested on different data sources.
+
+3) Methods:
+
+(1) Dataset Construction: according to the paper, 80% of data is used for training, while 20% of data is used for validation. Here the “validation” may be changed into “test”. The “validation” in machine learning is part of the training set, which is used for hyperparameter optimization and model architecture optimization, while the test set is used for model performance evaluation based on data out of the training set.
+(2) Machine-learning for CV/GCD classification procedures: according to the “alternative way to understand the definition of capacitive tendency”, the capacitive tendency is an index that can quantify the difference between the theoretical curves and the actual curves and help tell the classification of the targeted material. However, many methods can be used to quantify the difference between the two curves. Only qualitative description is not convincing. Hence, please explain the necessity of CNN models and give the reference or quantitative comparison results to convey the superiority of the CNN model over traditional methods.
+
+(3) In addition to the detailed mathematical descriptions of methods adopted in the proposed algorithm, the motivations, and reasons why you choose the methods are suggested to be added in detail.
+
+4) Results and Discussion:
+
+(1) In Figure 4, the formula and citation format should be corrected. The same mistakes can be found in Figure 6.
+
+4) Conclusion
+
+(1) point-by-point items with quantitative results will be more effective to convey the main findings of this study.
+
+(2) As mentioned in Conclusion, ‘ML application in distinguishing between these often complex signals’, how to distinguish the database for training, testing and validation?
+
+Other questions:
+
+(1) Supervised ML is a powerful tool for fast and accurate calculation, while the main issue is its poor capability in new knowledge exploration. In other words, it is good at knowledge exploitation within the training database, but fails to classify materials and predict the performance out of the training database boundary. How to address these issues? More discussion on the drawbacks will be wonderful.
+
+Overall, the topic of this study is important. Hope the comments can be helpful to improve the paper’s quality.
+
+Reviewer #2 (Remarks to the Author):
+This Manuscript provides an incredibly useful tool for estimating the percentage of capacitive or battery-like behavior of energy storage materials. Due to the very large number of publications on pseudocapacitive materials and confusion about the appropriate classification, the free-accessible robot tool provided by the group of Olivier Fontaine can be of large interest to the research community.
+
+Nevertheless, often the shape of the cyclic voltammetry or the galvanostatic profile may become similar to “pseudocapacitive” at high scan rate, high current, respectively. How the robot takes in consideration the capacitive tendency with respect to the scan rate or current used?
+
+Reviewer #3 (Remarks to the Author):
+
+The article titled "A Novel Approach for Classifying Battery and Pseudocapacitor Materials Using Capacitive Tendency and Supervised Machine Learning" discusses the use of supervised machine learning techniques to analyse, interpret and classify electrochemical signals in energy storage devices (batteries and supercapacitors). The use of supervised machine learning and the development of an online tool for classification are significant contributions to the field, despite they appear more suitable for a methodology or computational journal rather than for an interdisciplinary one. While the article presents interesting findings and potential applications, it has both major and minor issues that should be addressed.
+
+Major issues:
+
+1) The article recalls the concept of a "continuum spectrum" to describe the transition between capacitive and battery-type signals. However, the authors acknowledge that this concept lacks mathematical support and is merely a postulate. This weakens the scientific rigor of the proposed approach and calls into question the reliability of the findings. The Authors are encouraged to argue on this possible weakness.
+
+2) The validation of the classification architectures used in the machine learning approach is not adequately explained. The article mentions benchmarking the models based on five metrics but does not provide sufficient details or results to assess the performance of the selected models in the main manuscript (only in the Supplementary Information). Please include a picture with main prediction performance for all Processes during both training and validation steps.
+
+3) The article briefly mentions the use of computing techniques and text mining in energy storage research but fails to provide a comprehensive comparison with existing techniques for interpreting
+electrochemical signals. This limits the understanding of how the proposed machine learning approach contributes to the field and whether it outperforms or complements existing methods. Have you conducted any comparative analysis with existing methods to demonstrate the superiority of the capacitive tendency metric? It would be valuable to provide a quantitative comparison and discuss the advantages of your approach over conventional classification techniques in terms of both computational requirements and accuracy.
+
+Minor issues:
+
+1) The article lacks sufficient contextualization within the broader field of energy storage research. While the article discusses the significance of distinguishing between capacitive and battery-type signals, it does not sufficiently connect this research to the current state of the field or highlight how the findings contribute to advancing energy storage technologies. For instance, the use of machine learning approach to analyse the impact of physicochemical features of carbon electrodes on the capacitive performance of supercapacitors could be mentioned.
+
+2) In the article, you mentioned that there can be an overlap between battery and pseudocapacitor signals due to their faradaic nature. It would be beneficial to discuss some examples or case studies where this overlap occurs and how the proposed capacitive tendency metric effectively distinguishes between them. This would provide concrete evidence of the robustness and accuracy of your approach.
+
+3) Could you please elaborate on the dataset used for training the supervised machine learning algorithm? Specifically, how diverse is the dataset in terms of electrode materials and electrochemical behaviours? It would be helpful to understand the representativeness of the dataset and its impact on the performance and generalizability of the proposed classification approach.
+
+4) The article lacks clarity in explaining the methodology used for dataset construction and the specific processes involved in the machine learning classification. Important details such as the selection criteria for training and validation datasets, data preprocessing techniques, and hyperparameter tuning are not sufficiently explained. This hinders reproducibility and makes it challenging for readers to evaluate the methodology. Moreover, in the Methods section, all Processes and Outputs shall be described in chronological order.
+
+5) How GCD and CV pictures are extracted from articles and recognized among other Figures? Did you check that the adopted measure units are the same in these graphs? How did you train Process 1? How did you label the GCD and CV pictures so that they belong to one of these two classes? How did you label the Output 3 into the three types of training sets for Process 3 and 4?
+
+6) “Moreover, cross-validation was performed with the experts in the field with the number of meetings”: what do you mean? Which types of cross-validations were performed? Who were the experts? Please describe such cross-validation with more quantitative arguments.
+
+7) Please better describe why two models (Process 4 and 5) have been trained to predict the capacitive tendency if the output figure of merit is just one. In this sense, Output 4 and 5 seem redundant (they should be complementary with each other).
+8) The subsection “The issues surrounding electrochemical signal identification” appears as a repetition of Introduction rather than a Results. Please improve the readability of the article by removing redundant parts.
+
+9) In the analysis carried out in Figure 7, were the considered articles outside training set?
+
+10) The article briefly mentions the limitation of electrochemical signals deviating from ideal curves, but it does not extensively discuss other potential limitations of the proposed machine learning approach. Furthermore, the article does not provide a detailed discussion on future directions for improving the methodology or addressing these limitations.
+
+11) Please improve English language and correct typos (e.g., caption of Fig. 6, table headings of Fig. 6).
+Responses to Comments raised by Reviewers
+
+“A Novel Approach for Classifying Battery and Pseudocapacitor Materials Using Capacitive Tendency and Supervised Machine Learning”
+
+No.: NCOMMS-23-20980
+
+Nature Communications
+
+For Editor:
+
+Dear Editor and Reviewers,
+
+You will find, in black numerated, the reviewer comment and in blue with this style our explanation
+
+-----------------------------Inserted in manuscript at P.XX Line XX----------------------
+In blue and italic like here
+-----------------------------The content above resides within the manuscript----------------------
+Reviewer 1
+
+Reviewer’s general comment: The work focused on a machine learning method with the capacitive tendency for classifying battery and pseudocapacitor materials. The manuscript is within the scope of the Journal. To help improve the paper’s quality, my suggestions and comments are shown below.
+
+Thank you for your detailed and helpful comments on our manuscript. We have carefully considered your comments and suggestions, the reviewer 1 suggestions improve a lot the present manuscript.
+
+Abstract:
+
+1. It is suggested to give a brief description of the current research progress in the forms of the classification of battery and pseudocapacitor electrode materials, especially the efforts in machine learning. Then, please summarize the research gaps, as well as the motivations and advantages of your method.
+
+Thank you for your comments, and we emphasized more on this point in the Abstract, here the change:
+
+-------------------------------Inserted in manuscript at P.2 Line 22-32-------------------------------
+
+“Up to date, the difficulty lies in determining which group these materials fall into one or another electrode type (battery vs. pseudocapacitor) through simple binary classification as black and white. Recently in the field of energy storage, the famous qualitative term ‘continuum transition’ has been introduced ascribing to the overlapping of the characteristic of electrochemical signals between battery and pseudocapacitor. To overcome this conundrum, we applied supervised machine-learning of image classification towards the electrochemical shape analysis (over 5,500 CVs and 2,900 GCDs) and the confidence percentage of the prediction reflects the shape tendency of the curves, consequently defined as the new maker called “capacitive tendency”. This predictor not only surpasses the limitations of human-based classification but also provides statistical tendencies regarding electrochemical behavior.”
+
+-------------------------------The content above resides within the manuscript----------------------
+2. It is suggested to introduce the mechanism of the proposed methodology in one to two sentences.
+
+We added the mechanism of the proposed methodology in the Abstract.
+
+-------------------------------Inserted in manuscript at P.2 Line 27-30-------------------------------
+
+“To overcome this conundrum, we applied supervised machine-learning of image classification towards the electrochemical shape analysis (over 5,500 CVs and 2,900 GCDs) and the confidence percentage of the prediction reflects the shape tendency of the curves, consequently defined as the new maker called “capacitive tendency”.”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+3. Qualitative results with quantitative data are necessary to support the contribution of the work.
+
+Thank you for your comments, we put the number of data used in this work.
+
+-------------------------------Inserted in manuscript at P.2 Line 27-29-------------------------------
+
+“To overcome this conundrum, we applied supervised machine-learning of image classification towards the electrochemical shape analysis (over 5,500 CVs and 2,900 GCDs)”.
+
+
+-------------------------------The content above resides within the manuscript----------------------
+
+Introduction:
+
+4. The definition of capacitive tendency is not clear in the “introduction part”, while the advantages are given. The mechanism of “capacitive tendency�� to help classify battery and pseudocapacitor materials is suggested to be further explained.
+
+The “capacitive tendency” is defined based on the percentage confidence of the classification between box shaped and peak shaped CV. The percentage confidence ranges from 0-100% that
+the CV is either classified as battery or pseudocapacitor. For example, the CV is classified as pseudocapacitor with 30 % confidence, it simply means that the CV has 30% capacitive tendency. Here the change inside the manuscript:
+
+-------------------------------Inserted in manuscript at P.5 Line 99-105-------------------------------
+
+“So, by this approach, we proposed the new definition call “capacitive tendency” based on the percentage confidence of the classification between box shaped and peak shaped CV, implying the capacitive behavior of electrode materials.”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+5. Introduction: as mentioned in the manuscript, the text-mining algorithms have been developed to efficiently extract various specific information of the materials, like BatteryDataExtractor and Li-ion battery annotated corpus. In this study, the authors applied ML for electrochemical signal interpretation. This belongs to the first application. From this point, the innovation or originality might be questionable.
+
+Previous approaches to data mining of electrochemical, chemical, and physical properties of energy storage materials have focused on text mining or material extraction. Despite the importance of the work, these approaches do not analyze electrochemical signal shape or interpretation.
+
+Our work is the first to use supervised machine learning to interpret electrochemical signal shape, specifically CV and GCD images. This is a significant advancement because the shape of CV and GCD images can tell us about the underlying mechanism of the energy storage material, such as battery, pseudocapacitor, or supercapacitor. To clarify the originality, we rearranged the text in this part in the introduction:
+
+-------------------------------Inserted in manuscript at P.4 Line 78-101-------------------------------
+
+Recently, text-mining algorithms have been developed to efficiently extract various specific information of the materials from the article such as BatteryDataExtractor using bidirectional-encoder representations from transformers (BERT),[11] and Li-ion battery annotated corpus
+(LIBAC) based on ML, natural language processing (NLP), Named Entity Recognition (NER).[2-4] However, the direct interpretation of the image data from figures remain difficult using the above method of data-mining from image. Machine learning has been used to predict the electrochemical mechanism involved in the reaction that expresses through a cyclic voltammogram (CV). Deep learning has also been used to distinguish the mechanism of the electrochemical reaction from CV based on residual neural network (ResNet) architecture. However, the application of machine learning to analyze electrochemical signals in the field of energy storage is still in its early stages and focused on analytical or fundamental electrochemistry.
+
+This study presents the first time that electrochemical signal analysis (CV and GCD) has been performed using a machine learning (ML) approach based on image classification. This approach is well-suited for unlabeled data, noise-tolerant, and capable of handling complex data. Ultimately, this led to the determination of the capacitive behavior of electrode materials from thousands of scientific papers. The originality of this work lies in its use of machine learning (ML) to quickly and accurately interpret electrochemical signal images and transform them into accurate values. This is made possible by the large database of electrochemical energy storage images that is available to the ML model. This approach overcomes the limitations of human ability to interpret data, which can be too complicated in most cases. (Figure 1). So, by this approach, we propose the new definition call “capacitive tendency” based on the percentage confidence of the classification between box shaped and peak shaped CV, implying the capacitive behavior of electrode materials.”
+
+6. Original contribution at the end of Introduction needs to be further enhanced.
+
+We rewritten the text on the originality of the work at the end of Introduction.
+
+“This study presents the first time that electrochemical signal analysis (CV and GCD) has been performed using a machine learning (ML) approach based on image classification. This approach is well-suited for unlabeled data, noise-tolerant, and capable of handling complex
+data. Ultimately, this led to the determination of the capacitive behavior of electrode materials from thousands of scientific papers. The originality of this work lies in its use of machine learning (ML) to quickly and accurately interpret electrochemical signal images and transform them into accurate values. This is made possible by the large database of electrochemical energy storage images that is available to the ML model. This approach overcomes the limitations of human ability to interpret data, which can be too complicated in most cases. (Figure 1). So, by this approach, we propose the new definition call “capacitive tendency” based on the percentage confidence of the classification between box shaped and peak shaped CV, implying the capacitive behavior of electrode materials.”
+
+7. Compare your approaches used in your study to the others in terms of their advantages and drawbacks.
+
+The advantage of our approach is that the fast and simple analysis by only two steps (1) inserting CV or GCD image and (2) click ‘predict’ to obtain the predicted capacitive percentage without pre-processing required. The prediction can tell the tendency of the material to behave like battery or supercapacitor/pseudocapacitor types. However, the drawback can be the lack of data mining of the image data such as the plot label, scan rate, or electrolyte. This requires a huge work and human power to integrate image recognition and text mining out of the image data.
+
+The advantage of other studies is that they can extract electrochemical, chemical, physical properties of the materials directly from the context but not to interpret the electrochemical signal. However, the drawback of this approach is the signal interpretation from the image data of plots such as electrochemical CV/GCD, directly.
+
+We added I the manuscript of the sentences emphasizing this point:
+
+“However, the direct interpretation of the image data from figures remain difficult using the above method of data-mining from image. Machine learning has been used to predict the electrochemical mechanism involved in the reaction that expresses through a cyclic
+voltammogram (CV). Deep learning has also been used to distinguish the mechanism of the electrochemical reaction from CV based on residual neural network (ResNet) architecture. However, the application of machine learning to analyze electrochemical signals in the field of energy storage is still in its early stages and focused on analytical or fundamental electrochemistry.
+
+This study presents the first time that electrochemical signal analysis (CV and GCD) has been performed using a machine learning (ML) approach based on image classification. This approach is well-suited for unlabeled data, noise-tolerant, and capable of handling complex data. Ultimately, this led to the determination of the capacitive behavior of electrode materials from thousands of scientific papers."
+
+-----------------------------The content above resides within the manuscript----------------------
+
+8. The proposed algorithm should be tested on different data sources.
+
+We used three different types of data sources:
+
+(1) Dataset from literature:
+    The major source of image data of CV and GCD (over 5,500 CVs and 2,900 GCDs) were extracted from a number of scientific papers. The image datasets are on Github repository (https://github.com/ice555mee/TB-robot_code-data ). Available for the reader.
+
+(2) Theoretical GCD and CV:
+    In the manuscript (in the part Validation of theoretical CVs and GCDs), we generated the images of CV and GCD using electrochemical equations (Eq. 2-4). The images of different CV and GCD were obtained by varying the shape parameter and finally producing the variation of CV and GCD shaped image data as shown in Figure 5 in the manuscript.
+
+(3) Experimental dataset from experimental data:
+    The last data source is from the experimental image of CV and GCD from co-authors (Prof. Thierry Brousse and his team). We added Figure ESI 22, and ESI 23 in supporting information.
+We added in the manuscript:
+
+-------------------------------Inserted in manuscript at P.7 Line 131-135-------------------------------
+
+“We used three data sources for their study of CV and GCD images. The first source was a large dataset of over 5,500 CVs and 2,900 GCDs extracted from scientific papers. The second source was theoretical CVs and GCDs generated using electrochemical equations. The third source was experimental CVs and GCDs from co-authors.”
+
+-------------------------------The content above resides within the manuscript-------------------------------
+
+Methods:
+
+9. Dataset Construction: according to the paper, 80% of data is used for training, while 20% of data is used for validation. Here the “validation” may be changed into “test”. The “validation” in machine learning is part of the training set, which is used for hyperparameter optimization and model architecture optimization, while the test set is used for model performance evaluation based on data out of the training set.
+
+We changed the word from “validation” to “test”, since the validation was performed by human expertise validation to the ground truth (edited in manuscript at P.7 Line 125). So, the testing data was different dataset from the training dataset and only used to evaluate the performance of the testing model.
+
+10. Machine-learning for CV/GCD classification procedures: according to the “alternative way to understand the definition of capacitive tendency”, the capacitive tendency is an index that can quantify the difference between the theoretical curves and the actual curves and help tell the classification of the targeted material. However, many methods can be used to quantify the difference between the two curves. Only qualitative description is not convincing. Hence, please explain the necessity of CNN models and give the reference or quantitative comparison results to convey the superiority of the CNN model over traditional methods.
+
+Our defined ‘capacitive tendency’ is not for qualifying the difference between the theoretical curves and the actual curves but to tell the tendency of any (either theoretical or experimental)
+CV or GCD curves to be more of the battery or supercapacitor characteristic shapes (box vs peak shape for CV).
+
+And the capacitive tendency is not only the qualitative description but quantitative one based on statistic of the ML classification result that the percentage of confidence of the prediction of the CV shape reflects the probability of the shape of curves, basically like a tendency.
+
+This research gap is about the shape interpretation of electrochemical curves presented in image data form. In conventional way, curve fitting using electrochemical equations is commonly done. But the problem is when the data is too big, for example, over 5000 CVs that need forever to fit all curves by human. Not only, when all these curves are in image form (JPEG, PNG, etc..), the value of all data points need to be extracted from the curve in the image at the first step and only this step need a big human power (number of people and time consuming).
+
+So, only ML for image classification (such as CNN model) is the best way out for the analysis of a large number of images, faster and more accurate than any conventional methods. Nowadays, artificial intelligence is the most powerful approach in terms of performance, time consuming, cost, and resources for calculation, classification big data analysis.
+
+Here, the model was applied to analyze MOF materials with different types of ligands (future work) as shown in Figure R1.
+
+![Heatmap of MOF showing capacitive tendency for various MOF materials and metal nodes](page_374_682_1002_496.png)
+
+Figure R.1. TB robot application on classification of MOF materials with different structures.
+We have calculated preliminary results using a different method (future work) that employs the concept of capacitive tendency. However, without our descriptor, it is impossible to correlate these results with the chemical nature of the materials.
+
+![Experimental Data plot showing number of redox centers per nm^3 vs Z value (in total) for various materials](page_246_370_1057_496.png)
+
+Figure R.2: List of materials classified according to %pseudo (calculated by numerical method).
+
+The Y-axis represents the number of redox centers per nm^3 and the X-axis represents the total number of electrons in the crystal structure.
+
+We added in the manuscript:
+
+------------------------------- Inserted in manuscript at P.5 Line 83-101-------------------------------
+
+"Machine learning has been used to predict the electrochemical mechanism involved in the reaction that expresses through a cyclic voltammogram (CV). Deep learning has also been used to distinguish the mechanism of the electrochemical reaction from CV based on residual neural network (ResNet) architecture, and focused on analytical or fundamental electrochemistry. However, the application of machine learning to analyze electrochemical signals in the field of energy storage is still in its early stages.
+
+This study presents the first time that electrochemical signal analysis (CV and GCD) has been performed using a machine learning (ML) approach based on image classification. This approach is well-suited for unlabeled data, noise-tolerant, and capable of handling complex data. Ultimately, this led to the determination of the capacitive behavior of electrode materials from thousands of scientific papers. The originality of this work lies in its use of machine
+learning (ML) to quickly and accurately interpret electrochemical signal images and transform them into accurate values. This is made possible by the large database of electrochemical energy storage images that is available to the ML model. This approach overcomes the limitations of human ability to interpret data, which can be too complicated in most cases. (Figure 1). So, by this approach, we propose the new definition call “capacitive tendency” based on the percentage confidence of the classification between box shaped and peak shaped CV, implying the capacitive behavior of electrode materials.”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+11. In addition to the detailed mathematical descriptions of methods adopted in the proposed algorithm, the motivations, and reasons why you choose the methods are suggested to be added in detail.
+
+------------------------------- Inserted in manuscript at P.9 Line 165-179-------------------------------
+
+“ResNet50 was exploited in different steps denoted as Processes 1, 2, 3, 4, and 5 (as summarized in Figure 3c) according to the types of inputs and outputs. All the images extracted from scientific papers were then categorized by Process 1 (ResNet50 model) which yielded Output 1, comprising GCDs, CVs and other images (such as optical image). GCDs from Output 1 were then classified using Process 2, and CVs were separately classified by Process 3, thereby providing the resulting prediction (Output 2: classified GCDs, and Output 3: classified CVs) of either battery or pseudocapacitor with a percentage confidence rating of 0 – 100 %, while the errors were monitored and minimized to improve the prediction. Here, the capacitive tendency (0 – 100 %) was first defined by the percentage confidence value, indicating the probability of CV shape as peak (0% capacitive tendency) and box shape (100% capacitive tendency). In the final step (Figure 3b), the classified CVs (in Output 3) were labeled according to four percentage confidence classes — 100 % battery, 50 % battery, 50 % pseudocapacitor and 100 % pseudocapacitor — before being further modeled in Processes 4 and 5 to provide the capacitive tendency based on a percentage confidence of 0 – 100 %.”
+Results and Discussion:
+
+12. In Figure 4, the formula and citation format should be corrected. The same mistakes can be found in Figure 6.
+
+Thank you for your helpful correction. We have made the necessary changes to the formula and citation formats in Figures 4 and 6.
+
+Conclusion:
+
+13. point-by-point items with quantitative results will be more effective to convey the main findings of this study.
+
+We emphasis more of the definition of the ‘capacitive tendency’ that is quantitative description based on statistics and mathematics on classification using ML approach. Our descriptor is the first tool in the energy storage community that can transform information in the CV and GCD images (qualitative information of shape identification) to the certain number as ‘capacitive tendency’ (quantitative information of predicted value by AI).
+
+-------------------------------Inserted in manuscript at P.19 Line 347-353-------------------------------
+“This demonstrates the superiority of machine learning over human-based analysis for the interpretation of electrochemical signal images. Machine-learning is able to quickly and accurately transform the shape information of images into predicted values, while human-based analysis is far slower and more subjective. This is due to the fact that machine learning algorithms are able to learn from large datasets of images and extract patterns that are not visible to the human eye. As a result, machine learning is a more reliable and objective approach to the analysis of electrochemical signal images.”
+
+-------------------------------The content above resides within the manuscript----------------------
+And,
+
+“a first online tool based on our model toward simple CV and GCD image classification via our precise marker, called capacitance tendency (quantitative information presented in percentage),”
+
+14. As mentioned in Conclusion, ‘ML application in distinguishing between these often complex signals’, how to distinguish the database for training, testing and validation?
+
+The database for training is the images of clear box or peak shaped CVs and the straight triangular or plateau shape GCDs, without ambiguity as representatively. For testing dataset, we used both ambiguous and non-ambiguous image data to test the performance of the model, where the performance was evaluated by Accuracy, Sensitivity, Specificity, Precision, and F1-score (Table ESI 2).
+
+We added in the manuscript:
+
+“In the training process of GCD (process 2) and CV (process 3) classification, CV and GCD images were firstly labeled as belonging to one of two classes, namely battery or pseudocapacitor following the criteria of non-ambiguous signal shape (which can be put into four categories: (1) Box shaped CV, (2) Peak shaped CV, (3) Triangular GCD, and (4) Plateau GCD) for 80 % of total data, where 20 % of total data was used as testing data. These training processes is based on binary classification of electrochemical signal, such as the box vs peak shaped CV, and the triangular vs plateau shaped GCD, as represented in Figure ESI 6, where all image datasets used are available on Github.”
+Other questions:
+
+15. Supervised ML is a powerful tool for fast and accurate calculation, while the main issue is its poor capability in new knowledge exploration. In other words, it is good at knowledge exploitation within the training database, but fails to classify materials and predict the performance out of the training database boundary. How to address these issues? More discussion on the drawbacks will be wonderful.
+
+While the training dataset that only contains those non-ambiguous images of CV or GCD, the testing dataset contains both ambiguous and non-ambiguous data to be used to test the classification, where our based model (ResNet50) gave more than 94.07 of F-score and more than 95 % accuracy (Table ESI 2). In our work, we only focus on training the model to distinguish between box and peak shapes for CV curve. In this case, we can use this prediction for understanding the origin of the electrochemical phenomena that can partially originate from redox reaction or electrochemical double layer capacitance. The result will give the possibility of the electrochemical behavior of the electrode materials. However, the other drawback that could be more useful for the better improvement or for the new classifier that to further predict in terms of other electrochemical information the resistive tendency of electrochemical signals.
+
+We added in the manuscript:
+
+"However, a potential drawback of the current classifier is that it can only predict the resistive tendency of electrochemical signals based on CV/GCD image data. A more comprehensive classifier by featuring text-mining of material information of a hidden information such as labels, scan rate, electrolytes in the figure could be an ultimate strategy for future perspectives on artificial intelligence for energy storage technology."
+
+Overall, the topic of this study is important. Hope the comments can be helpful to improve the paper’s quality.
+
+Thank reviewer 1 for their feedback on the paper. The comments are helpful in improving the quality of the paper.
+Reviewer 2
+
+This Manuscript provides an incredibly useful tool for estimating the percentage of capacitive or battery-like behavior of energy storage materials. Due to the very large number of publications on pseudocapacitive materials and confusion about the appropriate classification, the free-accessible robot tool provided by the group of Olivier Fontaine can be of large interest to the research community.
+
+1. Nevertheless, often the shape of the cyclic voltammetry or the galvanostatic profile may become similar to “pseudocapacitive” at high scan rate, high current, respectively. How the robot takes in consideration the capacitive tendency with respect to the scan rate or current used?
+
+Currently, the robot is not able to take into consideration the scan rate, high current, and other "chemical information" concerning the analysis of scientific papers extracted. This is because this part involves the use of text mining. However, future users of the robot can simply input the image of their CV produced at any scan rate or GCD at any current density. The predicted result (capacitive tendency) will relate to the shape of CV or GCD obtained from the experimental condition performed.
+
+We added in the manuscript:
+
+-------------------------------Inserted in manuscript at P.19 Line 358-360-------------------------------
+“Using the present program, all experimental user will be able to correlate chemical information to capacitive tendencies, as the scan rate, the current density.”
+-------------------------------The content above resides within the manuscript----------------------
+Reviewer 3
+
+The article titled "A Novel Approach for Classifying Battery and Pseudocapacitor Materials Using Capacitive Tendency and Supervised Machine Learning" discusses the use of supervised machine learning techniques to analyse, interpret and classify electrochemical signals in energy storage devices (batteries and supercapacitors). The use of supervised machine learning and the development of an online tool for classification are significant contributions to the field, despite they appear more suitable for a methodology or computational journal rather than for an interdisciplinary one.
+
+Firstly, we would like to address the justification of the journal:
+
+This work is significant for a large reader, as electrochemists, materials chemists, computing sciences, data sciences, because it has the potential to change the way that electrode materials are identified. By providing a more accurate and reliable method for understanding electrochemical behavior, our work will accelerate the development of new and improved energy storage technologies. We believe that this work is an interest for a large type of expertise.
+
+While the article presents interesting findings and potential applications, it has both major and minor issues that should be addressed.
+
+Major issues:
+
+1. The article recalls the concept of a "continuum spectrum" to describe the transition between capacitive and battery-type signals. However, the authors acknowledge that this concept lacks mathematical support and is merely a postulate. This weakens the scientific rigor of the proposed approach and calls into question the reliability of the findings. The Authors are encouraged to argue on this possible weakness.
+
+Our manuscript provides a quantitative approach to this postulate, as shown in Figure R.3, by introducing a metric or indicator to assess the degree of deviation from the ideal shape of a capacitor in the CV or GCD plots.
+[redacted]
+
+We understand that Reviewer 3 may have interpreted the Figure R.3b(left) (Figure 5 of ref [16]) as a model, but it is crucial to clarify that it is just a direction and a point of view, as the objective of a perspective paper, in mathematic notified as a conjecture.
+
+To clearly identify our originality vs. the paper published in REF [16], we added in the manuscript, Page 4. And this quantification of the above mentioned figure from Ref[16] was demonstrated in Figure ESI 21, in the manuscript.
+
+-------------------------------Inserted in manuscript at P.4 Line 66-70-------------------------------
+
+“In order to complete this concept of ‘continuum spectrum’ and to provide the real quantitative value to it, we analyze the electrochemical signals with the help of supervised machine-learning for achieving the descriptor, “capacitive tendency” that allows our community to quantify this important spectrum.”
+
+-------------------------------The content above resides within the manuscript----------------------
+2. The validation of the classification architectures used in the machine learning approach is not adequately explained. The article mentions benchmarking the models based on five metrics but does not provide sufficient details or results to assess the performance of the selected models in the main manuscript (only in the Supplementary Information). Please include a picture with main prediction performance for all Processes during both training and validation steps.
+
+The classification architectures were validated by evaluating their performance using the following metrics: accuracy, sensitivity, specificity, precision, and F1-score (see Table ESI 2). These metrics are commonly used in supervised machine learning, so we followed this convention. We further explained the validation of different architecture in the main manuscript and as well referred in the Supplementary Information such as loss curve in Figure ESI 7- ESI 11.
+
+Following reviewer 3 recommendation, we also rearranged this part of information by putting Table ESI 2 in the main manuscript in Figure 3.
+
+3. The article briefly mentions the use of computing techniques and text mining in energy storage research but fails to provide a comprehensive comparison with existing techniques for interpreting electrochemical signals. This limits the understanding of how the proposed machine learning approach contributes to the field and whether it outperforms or complements existing methods.
+
+Using Machine learning to analyse electrochemical signals in the field of energy storage is totally new. But, utilizing machine-learning on electrochemical signal interpretation in fundamental electrochemistry has been done by the other groups:
+
+(1) Alan M. Bond’s group demonstrated the successful application of ML on voltammetric mechanistic studies to predict the electrochemical mechanism involved in the reaction that express through a cyclic voltammogram. The prediction was done by using simulated duck shaped CV images with various simulated conditions.[6-8]
+
+(2) Similarly to the work from Cyrille Costentin’s group using deep learning to distinguish the mechanism of the electrochemical reaction such as interfacial charge transfers (E step) and/or solution reactions (C steps) from CV based on residual neural network (ResNet) architecture.[9]
+In summary, both of these works are significant advances in the field of analytical electrochemistry. They demonstrate the potential of ML to be used for a variety of tasks in this field, and they could lead to new and improved methods for studying electrochemical reactions. However, the previous methods are focused on analytical or fundamental electrochemistry (which is always found in any electrochemical experiment at higher scan rate). So, our main difference is the study of electrochemical energy storage devices.
+
+We added in the manuscript:
+
+-------------------------------Inserted in manuscript at P.5 Line 83-89-------------------------------
+
+“Machine learning has been used to predict the electrochemical mechanism involved in the reaction that expresses through a cyclic voltammogram (CV). Deep learning has also been used to distinguish the mechanism of the electrochemical reaction from CV based on residual neural network (ResNet) architecture, and focused on analytical or fundamental electrochemistry. However, the application of machine learning to analyze electrochemical signals in the field of energy storage is still in its early stages.”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+4. Have you conducted any comparative analysis with existing methods to demonstrate the superiority of the capacitive tendency metric? It would be valuable to provide a quantitative comparison and discuss the advantages of your approach over conventional classification techniques in terms of both computational requirements and accuracy.
+
+In conventional way, the method that has been widely used in energy storage field is based on the relationship \( i = k_1 v + k_2 v^{1/2} \), where \( v \) is scan rate. However, this method was questioning by Costentin et al.,[10] on the inappropriate use based on the limitation of this method including the irreversible process during the voltammetry, as well as the complicate capacitive mechanism such as insertion/intercalation in the case of pseudocapacitor which cannot apply this method.
+
+The paper "To Be or Not To Be Pseudocapacitive?" by Brousse et al. [REF 3] is a seminal work in the field of electrochemical capacitors. It is one of the first papers to clearly identify the difference between pseudocapacitive and battery materials. The authors support
+their thesis by pointing out that the electrochemical signature of pseudocapacitive materials is very different from that of battery materials. Pseudocapacitive materials typically exhibit rectangular CV curves and triangular GCD curves, while battery materials exhibit rounded CV curves and GCD curves. This difference in electrochemical signature is due to the different mechanisms by which charge is stored in the two types of materials, that the apparent capacitive behavior “Anyway if it is pseudo or EDLC” are when:
+
+\[
+\frac{dQ}{dE} = \text{CONSTANT}, \text{ and the CONSTANT is the capacity.}
+\]
+
+Here, we compared the method from the previous studies using the popular v/v^{1/2} scan rate diagnosis and the predicted result using machine-learning in our study in Table R.1. The results clearly demonstrate that the previous approach is not suitable for peak-shaped CV curves, such as those reported in ref[14, 19] in Table R1. Our method suggests that the capacitive tendency in these cases should be a small number.
+
+We added this Table and discussion in supporting manuscript and Table ESI3.
+
+------------------Inserted in supporting manuscript at P.37 Line 373-386------------------
+“Here, we compared the method from the previous studies using the popular v/v^{1/2} scan rate diagnosis and the predicted result using machine-learning in our study in Table ESI3. The results clearly demonstrate the big difference such in the case of ref [14] and ref [19] that the previous approach from literature (v/v^{1/2} scan rate) gave high percentage capacitance, whereas our study suggested the lower percentage of capacitive tendency. Our method suggests that the capacitive tendency in these cases should be a small number since the peak characteristic of CV is dominant. The limitation of the conventional method does not cover some situations as pointed in some references [REF 10 and REF 3]. Unlike the conventional model which relies on a proportionality to scan rate, the present capacitive tendency is a geometric variable that does not indicate whether a dynamic is surface-related or diffusion-related. It is based on an analysis of the signal's shape. It should be noted that the historical concept of pseudocapacitance focuses on this geometric shape more than on a surface vs. diffusion dynamic. Through our approach, we propose to researchers a different indicator, one that is
+more focused on the pure and initial definition."
+
+-------------------------------The content above resides within the manuscript----------------------
+
+Table R.1. The predicted capacitive tendency compared with the result from the articles.
+[Parts of table have been redacted]
+
+<table>
+  <tr>
+    <th>Reference</th>
+    <th>Input CV for the classification</th>
+    <th>Capacitive contribution with scan rate</th>
+    <th>Capacitive tendency</th>
+  </tr>
+  <tr>
+    <td>[12]</td>
+    <td>![CV plot for reference [12]](page_340_563_181_120.png)</td>
+    <td>67%</td>
+    <td>51.90 %</td>
+  </tr>
+  <tr>
+    <td>[13]</td>
+    <td>![CV plot for reference [13]](page_340_700_181_120.png)</td>
+    <td>64%</td>
+    <td>52.04 %</td>
+  </tr>
+  <tr>
+    <td>[14]</td>
+    <td>![CV plot for reference [14]](page_340_837_181_120.png)</td>
+    <td>74%</td>
+    <td>38.27 %</td>
+  </tr>
+  <tr>
+    <td>[15]</td>
+    <td>![CV plot for reference [15]](page_340_974_181_120.png)</td>
+    <td>78%</td>
+    <td>51.94 %</td>
+  </tr>
+  <tr>
+    <td>[10]</td>
+    <td>![CV plot for reference [10]](page_340_1111_181_120.png)</td>
+    <td>64%</td>
+    <td>51.94 %</td>
+  </tr>
+  <tr>
+    <td>[16]</td>
+    <td>![CV plot for reference [16]](page_340_1248_181_120.png)</td>
+    <td>n/a</td>
+    <td>52.10 %</td>
+  </tr>
+  <tr>
+    <td>[17]</td>
+    <td>![CV plot for reference [17]](page_340_1385_181_120.png)</td>
+    <td>n/a</td>
+    <td>51.92 %</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>[18]</th>
+    <td>66%</td>
+    <td>51.90 %</td>
+  </tr>
+  <tr>
+    <th>[19]</th>
+    <td>70%</td>
+    <td>18.26 %</td>
+  </tr>
+  <tr>
+    <th>[20]</th>
+    <td>63%</td>
+    <td>96.03 %</td>
+  </tr>
+  <tr>
+    <th>[21]</th>
+    <td>n/a</td>
+    <td>96.10 %</td>
+  </tr>
+  <tr>
+    <th>[22]</th>
+    <td>93%</td>
+    <td>95.80 %</td>
+  </tr>
+  <tr>
+    <th>[23]</th>
+    <td>66%</td>
+    <td>63.45 %</td>
+  </tr>
+  <tr>
+    <th>[24]</th>
+    <td>93%</td>
+    <td>51.93 %</td>
+  </tr>
+  <tr>
+    <th>[25]</th>
+    <td>n/a</td>
+    <td>51.90 %</td>
+  </tr>
+  <tr>
+    <th>[26]</th>
+    <td>n/a</td>
+    <td>51.97 %</td>
+  </tr>
+  <tr>
+    <th>[27]</th>
+    <td>80%</td>
+    <td>51.98 %</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>[28]</th>
+    <th></th>
+    <th>n/a</th>
+    <th>3.80 %</th>
+  </tr>
+  <tr>
+    <td>[29]</td>
+    <td></td>
+    <td>75%</td>
+    <td>95.47 %</td>
+  </tr>
+  <tr>
+    <td>[30]</td>
+    <td></td>
+    <td>n/a</td>
+    <td>96.20 %</td>
+  </tr>
+</table>
+
+Minor issues:
+
+5. The article lacks sufficient contextualization within the broader field of energy storage research. While the article discusses the significance of distinguishing between capacitive and battery-type signals, it does not sufficiently connect this research to the current state of the field or highlight how the findings contribute to advancing energy storage technologies. For instance, the use of machine learning approach to analyse the impact of physicochemical features of carbon electrodes on the capacitive performance of supercapacitors could be mentioned.
+
+We added further discussion on this point in the manuscript.
+
+---------------------------------------------Inserted in manuscript at P.15 Line 294-299---------------------------------------------
+"The understanding of the origin of the electrochemical behavior is the key point for the deep knowledge and for the future development of the electrode materials. TB robots have been used to study the physicochemical features of a variety of electrode materials, including carbon electrodes, MOFs, COFs, graphite, NMC, and MXenes materials, determining the capacitive tendency of the CV in 'continuum region from the recent papers (as shown in Figure ESI 21).'"
+---------------------------------------------The content above resides within the manuscript--------------------------
+
+6. In the article, you mentioned that there can be an overlap between battery and pseudocapacitor signals due to their faradaic nature. It would be beneficial to discuss some examples or case studies where this overlap occurs and how the proposed capacitive tendency metric effectively distinguishes between them. This would provide
+concrete evidence of the robustness and accuracy of your approach.
+
+The case study of the overlap of electrochemical signal characteristics referred to the paper of the proposed continuum transition between supercapacitor and battery CV characteristics (Nature Energy, Fleischmann et al.[11]).
+
+Overlap region
+
+[redacted]
+
+From the supplementally information in Figure ESI 21aII, and 21bII as shown below, we transform the concrete analysis of the overlap region that is where capacitive behavior is found. Our approach can give a quantitative predicted result with exact percentage of the capacitive tendency of any CV in the transition region.
+Figure ESI 21 | The predicted representative electrochemical signals (from Nature Energy, Fleischmann et al.[11]): a-I) porous carbon with solvated ion adsorption, a-II) porous carbon with partially solvated ion adsorption, a-III) graphite with desolvated Li+ intercalation, b-I) MXene with hydrated Li+ adsorption, b-II) MXene with partially desolvated Li+ intercalation, b-III) layered LiNi1/3Mn1/3Co1/3O2, NMC with desolvated Li+ intercalation, and c) % capacitive tendency.
+
+We added in the manuscript:
+
+---------------------------------------------Inserted in manuscript at P.15 Line 295-299---------------------------------------------
+"The trained model has been used to study the physicochemical features of a variety of electrode materials, including carbon electrodes, MOFs, COFs, graphite, NMC, and MXenes materials, determining the capacitive tendency of the CV in 'continuum region from the recent papers (as shown in Figure ESI 21).'"
+
+---------------------------------------------The content above resides within the manuscript-------------------------
+7. Could you please elaborate on the dataset used for training the supervised machine learning algorithm? Specifically, how diverse is the dataset in terms of electrode materials and electrochemical behaviours? It would be helpful to understand the representativeness of the dataset and its impact on the performance and generalizability of the proposed classification approach.
+
+The logic behind our classification is only based on binary image identification. Since we aimed to distinguish the electrochemical signals (CV and GCD) between battery type vs pseudocapacitor type, we trained the ML model with CV/GCD of these type of electrode materials (especially the non-ambiguous ones). The study only focuses on the identification of the electrochemical signal shapes and shape variation such as the box vs peak shaped CV, and the triangular vs plateau shaped GCD as shown in Figure R5 below.
+
+[redacted]
+Where all images of CV and GCD training datasets were published in Github repository (https://github.com/ice555mee/TB-robot_code-data ):
+
+• Battery CV training data: https://github.com/ice555mee/TB-robot_code-data/tree/main/CV%20classification/CV%20python/CV%20classification%20process%203/Battery%20training%20data
+• Pseudocapacitor CV training data: https://github.com/ice555mee/TB-robot_code-data/tree/main/CV%20classification/CV%20python/CV%20classification%20process%203/Pseudocapacitor%20training%20data
+• Battery GCD training data: https://github.com/ice555mee/TB-robot_code-data/tree/main/GCD%20classification/GCD%20Py/Battery%20training%20data
+• Pseudocapacitor GCD training data: https://github.com/ice555mee/TB-robot_code-data/tree/main/GCD%20classification/GCD%20Py/Pseudocapacitor%20training%20data
+
+We added in the manuscript:
+
+-------------------------------Inserted in manuscript at P.7 Line 125-128-------------------------------
+
+These training processes is based on binary classification of electrochemical signal, such as the box vs peak shaped CV, and the triangular vs plateau shaped GCD, as represented in Figure ESI 6, where all image datasets used are available on Github.
+
+-------------------------------The content above resides within the manuscript----------------------
+
+8. The article lacks clarity in explaining the methodology used for dataset construction and the specific processes involved in the machine learning classification. Important details such as the selection criteria for training and validation datasets, data preprocessing techniques, and hyperparameter tuning are not sufficiently explained. This hinders reproducibility and makes it challenging for readers to evaluate the methodology. Moreover, in the Methods section, all Processes and Outputs shall be described in chronological order.
+
+We explained more details on the methodology of the classification. For data collections, PyMuPDF and OpenCV were used to extract the figures from the articles and only CV and GCD were collected and put into categories (1. Box shaped CV, 2. Peak shaped CV, 3.
+Triangular GCD, and 4. Plateau GCD), which were then used as the training data. The ambiguous shaped CV and GCD is put in the categories of testing data. In the data processing step, we simply collected them without any processing in order to clean the image of CV or GCD such as removing the axis or separating the curve according to the different scan rates or labels. This purpose is that we would like to finally create a tool for any users to just simply input their data (image of CV or GCD) directly without any pre-processing for quick and easy analysis.
+
+8.1 Data collection and model training
+
+We highlighted in the manuscript:
+
+-------------------------------Inserted in manuscript at P.7 Line 117-121-------------------------------
+
+“In the present paper, all datasets are in the form of images extracted using PyMuPDF library in Python language from more than 3,300 scientific papers. The first dataset, or Output 1, was obtained by figures extracting using OpenCV which provides (2,979) GCD, (5,598) CV and other images such as crystal structure image (which will not be used in the further classification steps).”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+We added in the supporting manuscript:
+
+-------------------------------Inserted in supporting manuscript at P.6 Line 111-115-------------------------------
+
+3.Data collection, model training, and classification
+
+The first step was to extract the figures from the scientific paper using the PyMuPDF library in Python. Each figure could contain multiple CVs or GCDs. The OpenCV library was then used to separate each CV or GCD image. The resulting dataset contained CVs, GCDs, and other images, such as the author's image, the journal's logo, and illustrations. This is illustrated in Figure ESI 4.
+[redacted]
+
+Since the number of images extracted from the articles was large, we needed to screen and collect only the CVs and GCDs from the entire image dataset. To do this, we quickly classified the extracted images using the ResNet50 model, which only collects CV and GCD images (this step is called Process 1). This is illustrated in Figure ESI 5. Firstly, the images of CV and GCD were manually labelled by human to be used as the training dataset for Process 1 (distinguishing CV/GCD from the other images). Process1 was then performed (using ResNet50 architecture) to classify and collect only CV and GCD images from all unclassified images. The prediction (Output1) will finally compose of 3 categories:
+
+1. CV
+2. GCD
+3. Other images.
+
+Here, only the CV and GCD were then used for the classification in the next step (Process2, 3, 4, and 5) later.
+[redacted]
+We edited in the manuscript:
+
+-------------------------------Inserted in manuscript at P.7 Line 121-125-------------------------------
+
+In the training process of GCD (process 2) and CV(process 3) classification, CV and GCD images were firstly labeled as belonging to one of two classes, namely battery or pseudocapacitor following the criteria of non-ambiguous signal shape (which can be put into four categories: 1. Box shaped CV, 2. Peak shaped CV, 3. Triangular GCD, and 4. Plateau GCD) for 80 % of total data, where 20 % of total data was used as testing data.
+
+-------------------------------The content above resides within the manuscript----------------------
+
+8.2 Labeling of GCDs and CVs for process 2,3
+
+We added in the manuscript:
+
+-------------------------------Inserted in manuscript at P.7 Line 126-128-------------------------------
+
+“, such as the box vs peak shaped CV, and the triangular vs plateau shaped GCD, as represented in Figure ESI 6, where all image datasets used are available on Github.”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+And,
+
+-------------------------------Inserted in supporting manuscript at P.11-------------------------------
+
+Figure ESI 6 | The representative of training datasets of CV (a) box, (b) peak characteristic, and GCD (c) triangular, and (d) plateau characteristic.
+
+-------------------------------The content above resides within the manuscript----------------------
+8.3 Labeling of GCDs and CVs for process 4,5
+
+We highlighted in the manuscript:
+
+-------------------------------Inserted in manuscript at P.7 Line 129-131-------------------------------
+
+“From Process 3, Output 3 was obtained and categorized into three types of training sets: 100 % battery, 50 % battery/pseudocapacitor, and 100 % pseudocapacitor. This output was then further refined in Processes 4 and 5, as illustrated in Figure 3b.”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+8.4 Classification architecture
+
+Hence, the criteria of choosing the classification architecture are to use the deep layers of ML convolution layers with complex structure to be able to detect those generic informative details such as frame, axis, multiple line, colors, fonts, etc. as shown in Figure R6. So, we chose to test the different architectures as described in the manuscript (Validation of the classification architectures). As shown in Table ESI2, the classification architectures were evaluated and validated according to Accuracy, Sensitivity, Specificity, Precision, and F1-score.
+
+[redacted]
+Table ESI 2 | GCD and CV classification comparison based on evaluation values obtained from five different architectures; ResNet50, MobileNetV2, VGG16, Xception, and 8-Layer CNN.
+
+<table>
+  <tr>
+    <th>CNN-Model</th>
+    <th>Accuracy (%)</th>
+    <th>Sensitivity (%)</th>
+    <th>Specificity (%)</th>
+    <th>Precision (%)</th>
+    <th>F1 -Score</th>
+  </tr>
+  <tr>
+    <th colspan="6">GCD</th>
+  </tr>
+  <tr>
+    <td>ResNet50</td>
+    <td>94.22</td>
+    <td>93.84</td>
+    <td>94.45</td>
+    <td>94.16</td>
+    <td>93.99</td>
+  </tr>
+  <tr>
+    <td>MobileNetV2</td>
+    <td>93.11</td>
+    <td>92.56</td>
+    <td>93.07</td>
+    <td>93.12</td>
+    <td>92.82</td>
+  </tr>
+  <tr>
+    <td>VGG16</td>
+    <td>92.22</td>
+    <td>92.24</td>
+    <td>94.61</td>
+    <td>91.78</td>
+    <td>91.99</td>
+  </tr>
+  <tr>
+    <td>Xception</td>
+    <td>93.77</td>
+    <td>93.98</td>
+    <td>96.49</td>
+    <td>93.33</td>
+    <td>93.60</td>
+  </tr>
+  <tr>
+    <td>8-Layer CNN</td>
+    <td>94.00</td>
+    <td>93.73</td>
+    <td>94.77</td>
+    <td>93.82</td>
+    <td>93.78</td>
+  </tr>
+  <tr>
+    <th colspan="6">CV</th>
+  </tr>
+  <tr>
+    <td>ResNet50</td>
+    <td>95.80</td>
+    <td>93.52</td>
+    <td>96.74</td>
+    <td>94.65</td>
+    <td>94.07</td>
+  </tr>
+  <tr>
+    <td>MobileNetV2</td>
+    <td>94.64</td>
+    <td>92.62</td>
+    <td>96.42</td>
+    <td>93.24</td>
+    <td>92.92</td>
+  </tr>
+  <tr>
+    <td>VGG16</td>
+    <td>94.36</td>
+    <td>93.12</td>
+    <td>97.13</td>
+    <td>91.53</td>
+    <td>92.28</td>
+  </tr>
+  <tr>
+    <td>Xception</td>
+    <td>93.04</td>
+    <td>88.87</td>
+    <td>94.35</td>
+    <td>91.31</td>
+    <td>90.00</td>
+  </tr>
+  <tr>
+    <td>8-Layer CNN</td>
+    <td>93.65</td>
+    <td>89.08</td>
+    <td>94.26</td>
+    <td>92.77</td>
+    <td>90.74</td>
+  </tr>
+</table>
+
+9. How GCD and CV pictures are extracted from articles and recognized among other Figures? Did you check that the adopted measure units are the same in these graphs? How did you train Process 1? How did you label the GCD and CV pictures so that they belong to one of these two classes? How did you label the Output 3 into the three types of training sets for Process 3 and 4?
+
+How GCD and CV pictures are extracted from articles and recognized among other Figures?
+
+In the first step, the figures in the article were extracted using PyMuPDF library in Python language from scientific paper. In one figure could be composed of many CVs or GCDs. Here, OpenCV was used to separate each CV or GCD images. From this step, the overall dataset will contain CV, GCD, and other images such as the image of the author, the logo of the journal, the illustration, etc. as illustrated in Figure EIS 4.
+
+Since the number of images that could be extracted from the articles are large and we need to screen and collect CV and GCD images from the whole image dataset. Hence, these extracted images were quickly classified to collect only CV and GCD images using ResNet50 model (this
+step called Process 1), as illustrated in Figure ESI 5.
+
+Process 1:
+Firstly, the images of CV and GCD were manually labelled by human to be used as the training dataset for Process 1 (distinguishing CV/GCD from the other images). Process1 was then performed (using ResNet50 architecture) to classify and collect only CV and GCD images from all unclassified images. The prediction (Output1) will finally compose of 3 categories:
+4. CV
+5. GCD
+6. Other images.
+Here, only the CV and GCD were then used for the classification in the next step (Process2, 3, 4, and 5) later.
+
+We added in the supporting manuscript:
+
+“3.Data collection, model training, and classification
+
+The first step was to extract the figures from the scientific paper using the PyMuPDF library in Python. Each figure could contain multiple CVs or GCDs. The OpenCV library was then used to separate each CV or GCD image. The resulting dataset contained CVs, GCDs, and other images, such as the author's image, the journal's logo, and illustrations. This is illustrated in Figure ESI 4.
+
+[redacted]
+Since the number of images extracted from the articles was large, we needed to screen and collect only the CVs and GCDs from the entire image dataset. To do this, we quickly classified the extracted images using the ResNet50 model, which only collects CV and GCD images (this step is called Process 1). This is illustrated in Figure ESI 5. Firstly, the images of CV and GCD were manually labelled by human to be used as the training dataset for Process 1 (distinguishing CV/GCD from the other images). Process1 was then performed (using ResNet50 architecture) to classify and collect only CV and GCD images from all unclassified images. The prediction (Output1) will finally compose of 3 categories:
+
+7. CV
+8. GCD
+9. Other images.
+
+Here, only the CV and GCD were then used for the classification in the next step (Process2, 3, 4, and 5) later.
+[redacted]
+
+5.2 Did you check that the adopted measure units are the same in these graphs?
+
+We only took consideration on the shape of CV or GCD, so we did not do any value
+measurement or checking the unit from the figures, since the large number of figures has different axis value and different unit.
+
+How did you train Process 1?
+    As aforementioned in the answer of Question 5.1, in Figure ESI 5, the images of CV and GCD were manually labelled by human to be used as the training dataset for Process 1 (distinguishing CV/GCD from the other images). Process1 was then performed (using ResNet50 architecture) to classify and collect only CV and GCD images from all unclassified images. The prediction (Output1) will finally compose of 3 categories:
+        10. CV
+        11. GCD
+        12. Other images.
+How did you label the GCD and CV pictures so that they belong to one of these two classes? The images of CV and GCD were manually labelled by human that the GCD images normally look like the triangular shape or plateau shape, where CV images normally look like box shape or peak or duck shapes as shown in Figure R5.
+
+[redacted]
+How did you label the Output 3 into the three types of training sets for Process 3 and 4?
+
+We edited the new version of Figure 3, as shown below. The output 3 from Process 3 was then further selectively labeled as 4 categories as 100 % battery, 50 % battery/pseudocapacitor, and 100 % pseudocapacitor, according to the confident percentage from the prediction from Process 3, as illustrated in Figure 3b.
+
+![Flowchart showing the classification processes and outputs](page_246_370_957_682.png)
+
+Figure 3 | (a) CV and GCD datasets obtained after classification by Process 1, splitting them into training and testing datasets for further GCD and CV classification in Process 2 and Process 3, respectively. (b) The outputs from Process 3 are used in this final classification step to obtain the capacitive tendency based on percentage confidence rating of the prediction. (c) Table of processes, inputs and outputs performed/used to obtain these results.
+9. “Moreover, cross-validation was performed with the experts in the field with the number of meetings”: what do you mean? Which types of cross-validations were performed? Who were the experts? Please describe such cross-validation with more quantitative arguments.
+
+The cross-validation was done by using improved training datasets (or using the different training datasets collected by different experts) to optimize the performance of the classification each time.
+
+We edited in the manuscript:
+
+-------------------------------Inserted in manuscript at P.7 Line 135-136-------------------------------
+
+“Moreover, cross-validation was performed with the experts in the field to generate the different training datasets for the optimizing of the classification performance.”
+
+-------------------------------The content above resides within the manuscript-------------------------------
+
+10. Please better describe why two models (Process 4 and 5) have been trained to predict the capacitive tendency if the output figure of merit is just one. In this sense, Output 4 and 5 seem redundant (they should be complementary with each other).
+
+Basically, the training datasets for process 4 and 5 in CV classification were the output from classification in process 3 that the classes of output are categorized by % confidence: (Class I) ~0% confidence, (Class II) ~50% confidence, (Class III) ~100% confidence as pseudocapacitor type as illustrated below:
+Figure R7. CV images classified in process 3 giving three classes of output.
+
+We highlighted in the manuscript:
+
+"From Process 3, Output 3 was obtained and categorized into three types of training sets: 100 % battery, 50 % battery/pseudocapacitor, and 100 % pseudocapacitor. This output was then further refined in Processes 4 and 5, as illustrated in Figure 3b."
+
+11. The subsection “The issues surrounding electrochemical signal identification” appears as a repetition of Introduction rather than a Results. Please improve the readability of the article by removing redundant parts.
+
+We removed this part and integrated it to improve the introduction part.
+“However, some faradaic electrode materials including pseudocapacitors display electrochemical signals similar to those of EDLCs, such as the rectangular/quasi-rectangular CV and the sloping GCD curves,[6, 7] found in a variety of transition metal oxides (RuO2,[8] MnO2[9, 10]), conducting polymers (poly(3,4-ethylenedioxythiophene)[11, 12], polyaniline[13, 14]), and carbides (MXene)[15].”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+And,
+
+-------------------------------Inserted in manuscript at P.3 Line 56-58-------------------------------
+
+“Indeed, electrochemical signals are numerous and complex, varying according to the choice of electrode materials, as shown in Figure 1, hence the difficulty in identifying and categorizing these materials based on electrochemical signals.”
+
+-------------------------------The content above resides within the manuscript----------------------
+
+12. In the analysis carried out in Figure 7, were the considered articles outside training set?
+
+Yes, the analysis was performed by using a number of articles that contain keyword ‘battery’ or ‘pseudocapacitor’ which is outside the training dataset. This method will only compare the results from the image classification of CV and GCD by ML with the type of electrode material defined by the authors.
+
+We added in the manuscript:
+
+-------------------------------Inserted in manuscript at P.16 Line 305-306-------------------------------
+
+“(used articles outside the training dataset)”
+
+-------------------------------The content above resides within the manuscript----------------------
+13. The article briefly mentions the limitation of electrochemical signals deviating from ideal curves, but it does not extensively discuss other potential limitations of the proposed machine learning approach. Furthermore, the article does not provide a detailed discussion on future directions for improving the methodology or addressing these limitations.
+
+The potential drawback of this ML approach can be the lack of data mining of the image data such as the plot label, scan rate, or electrolyte. This requires a huge work and human power to integrate image recognition and text mining out of the image data. The addition of these improvements to overcome these limitations would benefit and give an ultimate tool for this analysis of electrochemical signals.
+
+We discussed more of the limitations and the improvements in the conclusion part.
+
+--------------------------------------Inserted in manuscript at P.19 Line 360-364-------------------------------
+
+“However, a potential drawback of the current classifier is that it can only predict the resistive tendency of electrochemical signals based on CV/GCD image data. A more comprehensive classifier by featuring text-mining of material information of a hidden information such as labels, scan rate, electrolytes in the figure could be an ultimate strategy for future perspectives on artificial intelligence for energy storage technology.”
+
+--------------------------------------The content above resides within the manuscript----------------------
+
+14. Please improve English language and correct typos (e.g., caption of Fig. 6, table headings of Fig. 6).
+
+We have corrected the typos at Figure 6.
+
+Reference
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+32. Zukalová, M., et al., LiNi1/3Mn1/3Co1/3O2 with morphology optimized for novel concept of 3D Li accumulator. International Journal of Energy Research, 2020. **44**(11): p. 9082-9092.
+33. Le Calvez, E., et al., Investigating the Perovskite Ag1-3xLaxNbO3 as a High-Rate Negative Electrode for Li-Ion Batteries. Frontiers in Chemistry, 2022. **10**.
+34. Miranda, J., et al., Revisiting Rb2TiNb6O18 as electrode materials for energy storage devices. Electrochemistry Communications, 2022. **137**: p. 107249.
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Reviewer’s general comment: The work focused on a machine learning method with the capacitive tendency for classifying battery and pseudocapacitor materials. The manuscript is within the scope of the Journal. To help improve the paper’s quality, my suggestions and comments are shown below.
+
+1) There is one article online in research square: A Novel Approach for Classifying Battery and Pseudocapacitor Materials Using Capacitive Tendency and Supervised Machine Learning. The content is almost similar. Please ensure there is no conflict of interest for publication.
+
+(2) The author mention: ‘Our work is the first to use supervised machine learning to interpret electrochemical signal shape, specifically CV and GCD images’. After checking in google scholar, the reviewer found following articles:
+
+K Khosravinia, A Kiani. Unlocking pseudocapacitors prolonged electrode fabrication via ultra-short laser pulses and machine learning
+
+Wang, T., Pan, R., Martins, M.L. et al. Machine-learning-assisted material discovery of oxygen-rich highly porous carbon active materials for aqueous supercapacitors. Nat Commun 14, 4607 (2023).
+
+P Puthongkham, S Wirojsaengthong, A Suea-Ngam. Machine learning and chemometrics for electrochemical sensors: moving forward to the future of analytical chemistry. Analyst, 2021, 146, 6351-6364
+
+The authors need to justify the originality with these works.
+
+(3) As mentioned by authors, ‘The originality of this work lies in its use of machine learning (ML) to quickly and accurately interpret electrochemical signal images and transform them into accurate values. This is made possible by the large database of electrochemical energy storage images that is available to the ML model’. Actually, machine learning (ML) to quickly and accurately interpret images has been widely used in cancer detection. The main difference and breakthrough of ML in electrochemical signal images between cancer detection is better to be provided, so as to justify the contribution of the work.
+
+(4) The manuscript needs to be carefully checked to avoid grammar errors.
+
+(5) Comment 7: Compare your approaches used in your study to the others in terms of their advantages and drawbacks. It is better to add the detailed comparison in the main context with references.
+
+(6) Regarding the generality and universality of the proposed approach, breakthrough out of the training database boundary should be provided, for performance prediction, material classification and etc. Is it possible for authors to add relevant contents on this?
+Reviewer #3 (Remarks to the Author):
+
+The Authors have replied to all raised issues in a convincing way and improved the manuscript accordingly.
+Reviewer 1
+
+Reviewer’s general comment: The work focused on a machine learning method with the capacitive tendency for classifying battery and pseudocapacitor materials. The manuscript is within the scope of the Journal. To help improve the paper’s quality, my suggestions and comments are shown below.
+
+We understand the intentions of reviewer 1 and thank him for this analysis, which enhances the wide audience of Nature communications.
+
+1. There is one article online in research square: A Novel Approach for Classifying Battery and Pseudocapacitor Materials Using Capacitive Tendency and Supervised Machine Learning. The content is almost similar. Please ensure there is no conflict of interest for publication.
+
+There is no conflict of interest. The article in Research Square corresponds to our work, and when we submitted it to the Nature Comm journal, we were offered the possibility of pre-depositing it in Research Square.
+
+2. The author mention: ‘ Our work is the first to use supervised machine learning to interpret electrochemical signal shape, specifically CV and GCD images ’ . After checking in google scholar, the reviewer found following articles:
+
+K Khosravinia, A Kiani. Unlocking pseudocapacitors prolonged electrode fabrication via ultra-short laser pulses and machine learning
+Wang, T., Pan, R., Martins, M.L. et al. Machine-learning-assisted material discovery of oxygen-rich highly porous carbon active materials for aqueous supercapacitors. Nat Commun 14, 4607 (2023).
+
+In the present scientific article, the author uses machine learning to select the best precursor to predict the specific capacitance.
+
+P Puthongkham, S Wirojsaengthong, A Suea-Ngam. Machine learning and chemometrics for electrochemical sensors: moving forward to the future of analytical chemistry. Analyst, 2021, 146, 6351-6364.
+
+This paper is a minireview summarizing recent applications of machine learning and experimental designs in electroanalytical chemistry.
+
+The authors need to justify the originality with these works.
+
+We thank the reviewer for this information. We have added this state of the art to the main manuscript. However, we would like to draw the reviewer’s attention to the fact that these articles focus on the correlation between materials and properties. We emphasize our innovation: the analysis of electrochemical signal shape.
+3. As mentioned by authors, ‘The originality of this work lies in its use of machine learning (ML) to quickly and accurately interpret electrochemical signal images and transform them into accurate values. This is made possible by the large database of electrochemical energy storage images that is available to the ML model’. Actually, machine learning (ML) to quickly and accurately interpret images has been widely used in cancer detection. The main difference and breakthrough of ML in electrochemical signal images between cancer detection is better to be provided, so as to justify the contribution of the work.
+
+The basic concept of image recognition is the same, whatever the technology: transforming an image into pixels and discovering a pattern through learning. The difference between all these types of learning is the particularity of the images to be analyzed. This is what will decide which neural network to use. In the manuscript, we don't think it's appropriate to compare our approach specifically to cancer detection. However, we have added a more general text on image recognition:
+
+Image recognition is used in many fields, such as facial recognition, cancer detection and autonomous cars. All these models have been trained using a supervised or semi-supervised deep learning approach, in order to teach the model, the pattern best suited to the situation. The difference between the techniques lies in the choice of neural network, which must be adapted to the specific problem. In our case, the main difficulty was to differentiate the figures representing a CV and a GCD from the other graphs.
+
+4. The manuscript needs to be carefully checked to avoid grammar errors.
+
+We checked the grammar and found no more issues.
+
+5. Comment 7: Compare your approaches used in your study to the others in terms of their advantages and drawbacks. It is better to add the detailed comparison in the main context with references.
+
+The capacitive tendency represents the shape of the electrochemical signal, this variable is new and different of other previous analysis, mainly the surface and diffusional contribution analysis.
+In the present case, the Capacitive tendency is useful if the reader/ scientist wants to compare different materials and to check the general trend of the electrochemical signal not to extract the surface contribution to the diffusional contribution.
+
+In the main manuscript, we added this sentence:
+
+In comparison to other studies, the capacitive tendency analyses the shape of the electrochemical signal. Unfortunately, the capacitive tendency doesn’t provide the surface contribution or the diffusional contribution inside the cyclic voltammetry.
+
+6. Regarding the generality and universality of the proposed approach, breakthrough out of the training database boundary should be provided, for performance prediction, material classification and etc. Is it possible for authors to add relevant contents on this?
+
+We added the following text in the main manuscript:
+
+The training database boundary is fixed using only scientific data with the pseudocapacitor or battery keywords associated. It is recommended for reader to use the present model to compare signal associated to EDLC, pseudocapacitor and Metal-ion battery. The present model isn’t adapted to redox flow battery, and fuel-cells. Moreover, the present model doesn’t provide any performance predictions. The typical useful application is to compare the same family of materials (i.e., MOF, NMC, MXene) but presenting a different electrochemical behavior. That is the generality and universality of this study.

030d32ff9b730af3688e796beaceb960542869b68e0c2941b54bdcec394c4d7e/preprint/preprint.md

@@ -0,0 +1,293 @@
+A Novel Approach for Classifying Battery and Pseudocapacitor Materials Using Capacitive Tendency and Supervised Machine Learning
+
+Siraphra Deebansok
+VISTEC
+Jie Deng
+Institute for Advanced Study & College of Food and Biological Engineering, Chengdu University
+Etienne Le Calvez
+University of Nantes
+Yachao ZHU
+ICGM https://orcid.org/0000-0001-8057-3754
+Olivier Crosnier
+Université de Nantes
+Thierry Brousse
+Institut des Matériaux Jean Rouxel, CNRS UMR 6502 - Université de Nantes https://orcid.org/0000-0002-1715-0377
+Olivier Fontaine (olivier.fontaine@vistec.ac.th)
+VISTEC (Vidyasirimedhi Institute of Science and Technology) https://orcid.org/0000-0002-1804-5990
+
+Article
+
+Keywords:
+
+Posted Date: May 29th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2930525/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on February 7th, 2024. See the published version at https://doi.org/10.1038/s41467-024-45394-w.
+A Novel Approach for Classifying Battery and Pseudocapacitor Materials
+
+Using Capacitive Tendency and Supervised Machine Learning
+
+Siraphrapha Deebansok,a Jie Deng,b Etienne Le Calvez,c,d Yachao Zhu,e Olivier Crosnier,c,d Thierry Brousse,c,d Olivier Fontaine*a,f
+
+a Molecular Electrochemistry for Energy laboratory, VISTEC, Institute of Science and Technology, Rayong, 21210, Thailand.
+
+b Institute for Advanced Study & College of Food and Biological Engineering, Chengdu University, Chengdu 610106, China.
+
+c Nantes Université, CNRS, Institut des Matériaux de Nantes Jean Rouxel, IMN, 44000 Nantes, France.
+
+d Réseau sur le Stockage Électrochimique de l’Énergie (RS2E), CNRS FR 3459, 33 rue Saint Leu, 80039 Amiens, France.
+
+e ICGM, Université de Montpellier, CNRS, 34293 Montpellier, France.
+
+f Institut Universitaire de France, 75005 Paris, France.
+
+* Corresponding author. Email: Olivier Fontaine: olivier.fontaine@vistec.ac.th
+Abstract
+
+In recent decades, there have been more than 100,000 scientific articles dedicated to developing electrode materials for supercapacitors and batteries. A heated debate nonetheless persists surrounding the standards for determining electrochemical behavior involving faradaic reactions, since the electrochemical signals produced by the various electrode materials and their different physicochemical properties often complicate matters. The difficulty lies in determining which group these materials fall into through simple binary classification as there can be an overlap between battery and pseudocapacitor signals and because both materials are faradaic in origin. To solve this conundrum, we applied supervised machine-learning toward a statistical analysis of electrochemical signals, and consequently developed a new standard which we called capacitive tendency. This predictor not only surpasses the limitations of human-based classification but also provides statistical tendencies regarding electrochemical behavior. Notably, and of particular importance to the electrochemical energy storage community publishing over a hundred articles weekly, we have created an online tool for easy classification of their data.
+Introduction
+
+In the energy storage research field, batteries are one of the most studied types of devices owing to their use in a wide range of applications including electronic equipment, electric vehicles and for medical and military purposes.[1] On the other hand, pseudocapacitive electrodes have attracted a considerable amount of attention due to their superior power capability.[2] Both of these energy storage systems are generally composed of various types of electrode materials exhibiting electrochemical signals that may or may not resemble one another.[3]
+
+It is common knowledge that electric double layer capacitors (EDLCs) rely on a non-faradaic process without any electron transfer, whereas batteries and pseudocapacitors are governed by faradaic reactions.[4] The latter processes are generally depicted by peaks on Cyclic Voltammograms (CVs) and plateaus on Galvanostatic Charge-Discharge (GCD) curves (Figure 1).[5] Nowadays, some faradaic electrode materials display electrochemical signals similar to those of EDLCs, such as the rectangular/quasi-rectangular CV and the sloping GCD curve.[6, 7] This characteristic has been found in a wide variety of transition metal oxides (RuO₂,[8] MnO₂[9, 10]), conducting polymers (poly(3,4-ethylenedioxythiophene)[11, 12], polyaniline[13, 14]), and carbides (MXene)[15]). Numerous studies are underway focusing on faradaic electrode materials and including the behavior of pseudocapacitors and batteries, where both involve redox reactions, in keeping with the concept proposed by Conway et al.[4]. Currently, owing to the vast amounts of materials studied, guidelines for distinguishing between the two are still largely inadequate, with some studies even contradicting the conventional definition of Conway et al., as later supported by Brousse et al. and other researchers in the field.[7]
+
+Indeed, electrochemical signals are numerous and complex, varying according to the choice of electrode materials, as shown in Figure 1, hence the difficulty in identifying and categorizing
+these materials based on electrochemical signals. Recently, Fleischmann *et al.*[16], in a perspective paper, postulated the importance of a unified understanding when it comes to the electrochemical signals found in capacitors and batteries. The authors proposed the concept of electrolyte confinement that could impact the electrochemical behavior as a transition as a ‘spectrum’ from battery- to capacitor-type signals. It depicts the continuum of the signal from one state to another by altering the degree of confinement depending on, for example, the pore size of the electrode materials or the spacing size between *MXene* layers. Their work highlights the significance of successful quantification in order to move away from the postulate and arrive at a quantifiable spectral variable. It is shown that understanding the overlap and transition in electrochemical signals essentially requires a clear-cut classification of electrode material types based on their electrochemical behaviors (in CV and GCD). Unfortunately, the scientific elements presented by the authors are comparable to a mathematical conjecture, meaning that the proposed continuum is not supported by any mathematical variable or formalism. It is merely the subject of a postulate. Nonetheless, stating that the continuum is necessary does not diminish its importance. However, it becomes apparent that a mathematical variable must be added to quantify and measure this variation within the continuum. In order to metric this concept of ‘continuum spectrum’ and to provide the quantitative value to it, we analyze for the first time to the best of our knowledge the electrochemical signals with the help of supervised machine-learning. Our method is based on data science driven-supervised machine learning for achieving the descriptor, “capacitive tendency” that allows our community to develop metric, as a next step following this postulate.
+Figure 1 | Illustration of CVs and GCD curves of a pseudocapacitor without ambiguity (a and d, respectively), and a battery (c and f, respectively). CV and GCD curve with ambiguity (b and e, respectively).
+
+To date, computing techniques have been used as somewhat satisfactory tools toward ascertaining the charge storage mechanism behind various electrochemical signatures.[17-20] It has been popular in the energy storage community that extracting the information such as electrochemical, chemical, and physical properties from literatures is essential, when big data has been generated with large number of scientific papers every year. Text mining was used to gather information of Li-ion battery research and development involving in several processes such as electrode synthesis, electrochemical performance, processing condition parameters, where the models are based on machine-learning (ML), natural language processing (NLP), Named Entity Recognition (NER).[21, 22] Recently, text-mining algorithms have been developed to efficiently extract various specific information of the materials from the article such as BatteryDataExtractor using bidirectional-encoder representations from transformers (BERT),[23] and Li-ion battery annotated corpus (LIBAC) based on NER.[24] However, using ML for electrochemical signal interpretation has not been done.
+
+In this work, ML approach is used to interpret the CV and GCD signals by way of a supervised ML descriptor aimed at analyzing and determining the capacitive behavior of electrode materials found in thousands of scientific papers, as illustrated in Figure 2. Since our nuanced
+classification is substantially different from the binary identification by human as only being battery or pseudocapacitor among various electrochemical signals, we propose a new definition called capacitive tendency. This tendency is not only able to classify a large majority of relevant materials, but also to depict possible behaviors of the material in question. Hence, this artificial intelligence (AI) power will be the only important tool to help transforming the information from images to accurate values based on big database available in the electrochemical energy storage community. In addition to this, we provide an online tool kit which uses supervised machine-learning to easily classify materials. Today, the large amount of literature sometimes leads to a misuse of the proposed definitions, to reduce this definitional mishap, our work will reduce these errors. Our work thus serves to put forward a new concept toward understanding and labeling the various electrochemical signatures of energy storage devices. Above all, it also offers a unique opportunity to unify the complex electrochemical signatures of more than 100,000 scientific papers through supervised ML.
+
+![Image extraction from scientific papers followed by CV and GCD classifications based on ResNet50 architecture.](page_324_670_1092_388.png)
+
+Figure 2 | Image extraction from scientific papers followed by \( CV \) and \( GCD \) classifications based on *ResNet50* architecture.
+Methods
+
+Dataset Construction
+
+In the present paper, all datasets are in the form of images extracted using PyMuPDF library in Python language from more than 3,300 scientific papers. The first dataset, or Output 1, was obtained by figures extracting using OpenCV which provides (2,979) \( GCD \), (5,598) \( CV \) and other images such as crystal structure image (which will not be used in the further classification steps). The \( GCDs \) and \( CVs \) were then labeled as belonging to one of two classes, namely batteries or pseudocapacitors without ambiguity, to be used for model training (80 \% of total data), as well as for validation (20 \% of total data) in Process 2 and Process 3 for \( GCD \) and \( CV \) classification, respectively. From Process 3, Output 3 was obtained and categorized into three types of training sets: 100 \% battery, 50 \% battery/pseudocapacitor, and 100 \% pseudocapacitor. This output was then further refined in Processes 4 and 5, as illustrated in Figure 3b. Moreover, cross-validation was performed with the experts in the field with the number of meetings.
+Figure 3 | (a) CV and GCD datasets obtained after classification by Process 1, splitting them into training and validation datasets for further GCD and CV classification in Process 2 and Process 3, respectively. (b) The outputs from Process 3 are used in this final classification step to obtain the capacitive tendency based on percentage confidence rating of the prediction. (c) Table of processes, inputs and outputs performed/used to obtain these results.
+
+Validation of classification architectures
+
+In this work, Convolutional Neural Networks (CNNs) were selected for use as the image classification architectures.[25] Benchmarking was conducted on five different CNN models, including ResNet50,[26] MobileNetV2,[27] VGG16,[28] Xception[29] and 8-Layer CNN[25] (see Supplementary Figures ESI 1-2), to compare model performance. It was carried out based on five metrics, including: Accuracy, Sensitivity, Specificity, Precision, and F-Score[30] (see
+Supplementary Figures ESI 3 and Eq. ESI 1-5). During the model training cycles, the number of training and validation iterations can impact the accuracy of the prediction since this is related to the experience gained over time by the ML model. Moreover, binary cross entropy (\(BCE\)) loss,\(^{[31]}\) calculated from the prediction error as shown in **Eq. 1**, was minimized along the number of training iterations to optimize predictor performance.
+
+\[
+L_{BCE} = -\frac{1}{n}(\sum_{i=1}^{n} y_i \cdot \log(\hat{y}_i) + (1 - y_i) \cdot \log(1 - \hat{y}_i))
+\]
+**Eq. 1**
+
+Where \(y_i\) is the ground truth label (0 or 1, in this case battery or pseudocapacitor), \(\hat{y}\) is the predicted value, and n is the output size.\(^{[31]}\)
+
+**Machine-learning for \(CV/GCD\) classification procedures**
+
+The ML architecture displaying the best performance after the validation step (further explained in the Results and Discussion section) was selected for use in this work as will be supervised during classification processes. *ResNet50* was exploited in different steps denoted as Processes 1, 2, 3, 4, and 5 (as summarized in **Figure 3c**) according to the types of inputs and outputs. All of the images extracted from scientific papers were then categorized by Process 1 (*ResNet50* model) which yielded Output 1, comprising *GCDs*, *CVs* and other images (such as optical image). *GCDs* from Output 1 were then classified using Process 2, and *CVs* were separately classified by Process 3, thereby providing the resulting prediction (Output 2: classified *GCDs*, and Output 3: classified *CVs*) of either battery or pseudocapacitor with a percentage confidence rating of \(0 - 100\%\), while the errors were monitored and minimized to improve the prediction. Here, the capacitive tendency (\(0 - 100\%\)) was firstly defined by the percentage confidence value, indicating the probability of CV shape as peak (0% capacitive tendency) and box shape (100% capacitive tendency). In the final step (**Figure 3b**), the classified *CVs* (in Output 3) were labeled according to four percentage confidence classes —
+100 % battery, 50 % battery, 50 % pseudocapacitor and 100 % pseudocapacitor — before being further modeled in Processes 4 and 5 to provide the capacitive tendency based on a percentage confidence of \(0 - 100\%\).
+
+An alternative way to understand the definition of capacitive tendency is to analyse it as the deviation from the ideal of the purely capacitive signal (is easy to recognize). When the trained model is confident that the curve is close to a rectangle (for CV) or a triangle (for GCD), then this implies that the curve is close to an ideal capacitive signal. On the contrary, a curve whose confidence value is close to zero means that the curve has a different contribution. Basically, the capacitive tendency reflects the analysis of the signal shape. It is information based on a geometric shape. Of course, alternatives could be used. However, the use of the classical formalism, as indicated in the "ideal CVs" area in Figure 4a, is impossible when the shape of the electrochemical signal deviates from this ideal. In the purely mathematical domain, the possibility of adding a rectangle to a closed geometric shape (a CV is a closed geometric shape) is a complex mathematical situation. It is the concept of Inscribed rectangular problem in mathematics. Thus, our data science-driven by supervised deep learning approach is a suitable alternative.
+
+Results and Discussion
+
+This section explains how the models for \(CV\) and \(GCD\) classification were established for this specific dataset through the validation of different \(CNN\) architectures. The selection was based on well-known parameters including Accuracy, Sensitivity, Specificity, Accuracy, and F-Score. Moreover, the most accurate model was developed for use as the descriptor in order to determine the capacitive tendency of the various electrochemical behaviors, by applying the experimental data of various electrode materials. Ultimately, the selected model is destined for use by electrochemists as a tool for determining the nature of their materials.
+The issues surrounding electrochemical signal identification
+
+The rapidly increasing number of scientific publications involving the study of capacitive materials over the last decade points to the importance of this field of study (as shown in Figure 4). It was found that the 3,300 papers contain around 5,600 \( CVs \) and 3,000 \( GCDs \), which generates a massive amount of data and thereby renders human-based interpretation extremely challenging. Furthermore, the \( CV \) signals measured by these experiments are mostly performed in complex situations, and thus to not produce the perfect curves obtained in theoretical demonstrations using various common types of electrode materials (Figures 4). This also holds true for \( GCD \) signals acquired from experimental measurements. The whole limitation of the analyses in the field is summarised in figure 4a, most of the electrochemical signals are too far from the ideal signal to be analysed with the tools proposed in the state-of-the-art.
+Figure 4 | Illustration of **a)** experimental *CVs* and *GCDs* of different electrode materials including *MnO$_2$*,[32] *V$_2$C*,[33] *RuO$_x$*,[34] *LaMnO$_3$*,[35] *Ti$_3$C$_2$T$_x$*,[15] *H$_2$TiNb$_6$O$_{18}$*,[36] *Ag$_1$-$_3$x*La$_x$□$_2$x*NbO$_3$*,[37] *Nb$_2$O$_5$*,[38] *nano-MnS$_2$*,[39] *bulk-MoS$_2$*,[39] *TiO$_2$*[40] and *NaFePO$_4$*[41], theoretical **b)** *CVs* and **c)** *GCDs* undergoing different electrochemical processes, and **d)** Number of publications involving capacitive and battery electrode materials from 2012 to 2022. (Google Scholar, August 28$^{th}$, 2022).
+
+In this study, these *CVs* and *GCDs* were analyzed via supervised ML trained with datasets extracted from over 4,000 scientific papers (see DOI in Supplementary Information). In the following section, various Convolutional Neural Network architectures are validated and
+selected based on the evaluations explained in the experimental section, by applying the theoretical \( CV \) and \( GCD \) curves.
+
+Validation of architectures
+
+To select the Convolutional Neural Network architecture best suited to our datasets, the validation of a total of five models (\( ResNet50 \), \( MobileNetV2 \), \( VGG16 \), \( Xception \), and \( 8\text{-Layer CNN} \)) was first performed using Processes 2 and 3 with different types of input and output (**Table ESI 1**). These architectures were chosen based on the reported accuracy ranking ascribed to the models’ performance from *ImageNet* validation.\(^{[42,43]}\) In this step, the prediction was governed by binary classification to obtain only two different outputs, namely (i) battery or (ii) pseudocapacitor, since the model had been trained and supervised with \( CV \) and \( GCD \) datasets without ambiguity. *ResNet50* was found to be the most accurate and precise one out of all the models (**Table ESI 2**) and was thus selected to further prediction in the next step. Moreover, *ResNet50* is more adapted to the variety of data that will be input by the users, for example, plot with different frame and font styles and different color curves.
+
+To demonstrate the efficiency of the model, 5598 \( CVs \) and 2979 \( GCDs \) were randomly selected and entered into the classifier according to Processes 2 and 3. **Figure ESI 9** clearly demonstrates that the majority of predicted datasets showed a 100 % confidence rating, which would suggest that our *ML* model displays a high level of precision and reliability with a negligible risk of error.
+Validation of theoretical CVs and GCDs
+
+In this part, the simulations of CV and GCD images were done using basic equations from theoretical electrochemistry including Faradaic process with peak-shaped CV,[44] and EDLC with box-shaped CV which relies on Eq. 2 and Eq. 3. The simulated images were then classified by the trained model (process 4-5). The equation for CVs showing redox peaks is given as follows:
+
+\[
+\frac{i}{i_{max}} = \frac{\frac{F}{eRT}(E-E^0_{peak})}{1+\left(\frac{F}{eRT}(E-E^0_{peak})\right)^2}
+\]
+
+Eq. 2,
+
+where \( \frac{i}{i_{max}} \) is the normalized current of the peak current function, \( F \) is the Faraday constant, \( R \) is the gas constant, \( T \) is the temperature, \( E \) is the applied potential and \( E^0_{peak} \) is the peak potential. The box-shaped *EDLC* current function is given by:
+
+\[
+\frac{i}{i_{max}} = 1 - e^{-\frac{t}{RC}}
+\]
+
+Eq. 3,
+
+where \( C \) is the capacitance, \( R \) is the resistance and \( t \) is the charging period.[45] It was shown that capacitive behavior is more pronounced the further the CV shape deviates from peaked to rectangular (**Figure 5a**).
+
+Furthermore, simulating number of theoretical *GCD* images with the transition in curvature from straight to plateau feature could be applied with the classification model (process 2) in order to see the region of ambiguity. Using **Eq. 4** by varying M parameter:
+
+\[
+E = M \cdot \left( \frac{R \cdot T}{n \cdot F} \right) \log \left( \frac{\sqrt{\tau} - \sqrt{t}}{\sqrt{t}} \right) + E_{v/4}
+\]
+
+Eq. 4,
+
+where \( E \) is the potential, \( n \) is the number of electron transfers, \( t \) is the charging/discharging time, \( \tau \) is the time constant, \( E_{v/4} \) is the quarter-wave potential and \( M \) is the mathematical factor permitting the manipulation of the galvanostatic curve to show either a plateau feature (as
+found in battery material measurements) or straight line (as in supercapacitor material measurements), the continuum GCD curves were obtained, as shown in Figure 5b (blue, grey, and purple lines).
+
+![Illustration of classified theoretical CVs with Gaussian and box shapes as components, and classified theoretical galvanostatic charge (I) and discharge (II) curves obtained by using Eq 4. with a varying M parameter. The color of each curve is related to the probability of being battery (purple gradient bar) or capacitive material (blue gradient bar).](page_232_370_1016_482.png)
+
+Figure 5 | The illustration of (a) classified theoretical CVs with Gaussian and box shapes as the components, and (b) classified theoretical galvanostatic charge (I) and discharge (II) curves obtained by using Eq 4. with a varying M parameter. The color of each curve is related to the probability of being battery (purple gradient bar) or capacitive material (blue gradient bar).
+
+**Figure 5b(I)** shows that a battery-type signature was found to apply for an \( M \) value range of between 1.6 and 7 (purple zone, with a 90-100% confidence rating), whereas the prediction point to a pseudocapacitor-type for \( M \) values of between 7.1 and 19.6 (blue zone, with a 70-100% confidence rating). Similarly, this result was also observed for theoretical discharging profiles, as shown in **Figure 5b(II)**. However, in the grey zone when M is around
+7.0 during charge and 9.4 during discharge, respectively, the predictor was hesitant to define the signal type, suggesting that a certain ambiguity occurs when the curvature of the \( GCD \) signal is somewhere between a straight line and a plateau, as has already been observed and which is consistent with experimental measurements related to pseudocapacitive materials (Figure 6c). The most pertinent conclusion that can be drawn from this calculation is that our model demonstrated the transition region of \( GCD \) signals in accordance with the continuum transition concept as proposed by Fleischmann *et al.*[16]. Our model clearly demonstrates the source of the confusion for both humans and computers, which stems from the fact that these behaviors all originate from faradaic processes where electron transfer is the elementary step. This explains why the results of theoretical studies only hold true for basic scenarios. More complex behaviors, however, are frequently observed in experimental measurements and account for vast amounts of data, as depicted in **Figure 4**.
+
+**Revealing the nature of electrode materials through supervised machine-learning**
+
+In accordance with the main purpose of this study, namely overcoming human limitations when it comes to understanding electrochemical signals, the objective in this section concerned clarifying the behavior of faradaic electrode materials. To this end, experimental \( CVs \) from **Figure 4** were applied to the model to predict the capacitive tendency behavior of various electrode materials that conventionally can be calculated from dQ/dV= constant in only simple cases such as supercapacitor materials but could be too complex to apply for pseudocapacitors. Well-known pseudocapacitive and battery materials from the literature, such as \( MnO_2 \) and *NMC*, were compared not only to separate the signals produced by Processes 2 and 3 according to the conventional binary classification, but also to establish a new standard that we called capacitive tendency. Processes 4 and 5 broadened the classification range to create a statistical tendency representing an interpretable value: in the range of 0% denoting a
+battery, to 100% being a pseudocapacitor. Finally, we were able to predict the capacitive behavior of various electrode materials from experimental data, as demonstrated in Figure 6.
+
+![Capacitive tendency prediction of experimental voltammograms of (a) the well-known pseudocapacitor and battery electrode materials MnO2 and NMC, compared with the ambiguous CVs of Ag1.3La0.7NbO3 and H2TiNbO18, respectively. Predicted (b) CVs and (c) GCDs of other electrode materials from the literature, as per Figure 4.](page_256_384_946_384.png)
+
+Figure 6 | Capacitive tendency prediction of experimental voltammograms of (a) the well-known pseudocapacitor and battery electrode materials \( MnO_2 \),[46] and \( NMC \),[47] respectively, compared with the ambiguous \( CVs \) of \( Ag_{1.3}La_{0.7}NbO_3 \),[37] and \( H_2TiNbO_{18} \)[36], respectively. Predicted (b) \( CVs \) and (c) \( GCDs \) of other electrode materials from the literature, as per Figure 4.
+
+As previously mentioned, the exemplary rectangular and peak shapes are unfortunately not often present when it comes to systems exhibiting fast charge/discharge behavior or when pseudocapacitive materials are investigated. Electrochemists thus find it difficult to analyze the voltammograms correctly in the face of such a variety of shapes, with even the \( CVs \) of \( V_2C \), \( Nb_2O_5 \) and nano-\( MoS_2 \) electrode materials (**Figure 6b**) displaying a similar capacitive tendency of around 52-53 %. This finding served to emphasize the necessity of using machine-learning
+as a decisive tool for interpreting CV signals displaying a complexity that is beyond human discernment.
+
+The limitation of the binary classification battery vs. pseudocapacitor
+
+During this phase of our research, numerous scientific articles containing the keyword “battery” (2011 articles) or “pseudocapacitor” (1346 articles) (see Supplementary Information for DOI) were analyzed using our supervised ML model to provide a statistical analysis of the number of papers containing a keyword that was in contradiction to their signals. Briefly, the articles were randomly selected and their relevant CV and GCD signals were extracted and then simply classified into either battery or pseudocapacitive type using only Processes 2 and 3. The outputs in Figure 7 depict that around 67 % of the papers with a “pseudocapacitor” keyword are consistent with their experimental observations. Unexpectedly, however, nearly 50% of the articles with a “battery” keyword displayed contradicting signals. These results serve to reinforce the fact that human-based interpretation could greatly benefit from being replaced with computing techniques such as ML. Apparently, our machine-learning classification technique showed the significant portion of the articles using binary keywords (battery or pseudocapacitor) that contradict (mismatched) with their electrochemical signal (Supporting Information Section 8.1-8.6).
+Figure 7 | (a) The methodology behind the title classification of papers as either a battery or pseudocapacitor, followed by (b) CV and \( GCD \) extraction and then (c) the matched/mismatched outputs using our classifiers (Processes 1, 2 and 3). The percentage correlation between titles for pseudocapacitor and battery materials vs. correctly classified \( CVs \) and \( GCDs \).
+
+This result perfectly shows the limit of the binary approach in the field. Because analysing a binary classification leads to this misclassification by the authors. Our approach, using capacitive tendency, allows a unification of the measurements, by including them in a "spectrum" as proposed by Frieshman et al\(^{[16]}\), in a mathematical conjecture.
+Online tool kit for \( CV/GCD \) classification
+
+In order to facilitate the task of users worldwide when it comes to classifying the electrochemical behaviors (battery or pseudocapacitor) of their experimental data (\( CVs \) and \( GCDs \)), we have launched an online tool for analyzing these signals and providing an output in the form of a capacitive trend (or percentage confidence rating). It is publicly available at http://supercapacitor-battery-artificialintelligence.vistec.ac.th, and details are also provided in the Supporting Information.
+
+![Screenshot of the online tool kit for CV and GCD classification, showing a web interface for uploading images and predicting capacitor type](page_370_624_1002_384.png)
+
+Figure 8 | The online tool kit for \( CV \) and \( GCD \) classification based on our model.
+
+Conclusion
+
+The research presented herein has successfully managed to resolve the decades-old conundrum concerning the interpretation of electrochemical signals from \( CVs \) and \( GCDs \) by making full use of advanced computing technology in order to classify the behavior of
+materials as battery-like or pseudocapacitor-like. Specifically, we demonstrated that supervised ML is a powerful and accurate way to distinguish between these often complex signals. Our study also highlights the recurrent issue of the titles of scientific papers often contradicting the results of their own data, especially when it comes to those articles with “battery” in the title. This emphasizes the importance of using computer-based modelling for prediction as opposed to human-based analysis, which is far slower and more subjective and that leads to much unnecessary disagreement and debate. As a major contribution to our peers in the electrochemical energy storage community, we are delighted to announce a unique online tool based on our model toward simple online classification via our distinguishing marker, called capacitance tendency, affording them the possibility of a quick and easy standard to refer to when attempting to determine the nature of their new materials. Last but not least, featuring text-mining of material information with our classification tool could be an ultimate strategy for future perspectives on artificial intelligence for energy storage technology.
+
+Data and code availability
+
+Machine-learning models and datasets are made publicly available at GitHub repository: https://github.com/ice555mee/TB-robot_code-data or contact the author (olivier.fontaine@vistec.ac.th) for more information. The instruction is provided in both supporting information and on Github repository. The website is available via the link: http://supercapacitor-battery-artificialintelligence.vistec.ac.th/
+
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+
+Acknowledgements
+
+Website hosting is supported by Vidyasirimedhi Institute of Science and Technology server.
+
+This work is supported by funding from Thailand Science Research and Innovation (TSRI) (Grant No. FRB660004/0457).
+
+Competing interests
+
+The authors declare no competing interests.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• ESISUB1.docx

0358cbd719cad92a5106a1d23b164c7a9ee9af38881e700bf32a1c27078c4f3f/preprint/preprint.md

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+Red Light-Mediated Photoredox Catalysis Promotes Regioselective Switch in the Difunctionalization of Alkenes
+
+Shoubhik Das
+shoubhik.das@uni-bayreuth.de
+
+University of Bayreuth   https://orcid.org/0000-0002-4577-438X
+Tong Zhang
+University of Antwerp
+
+Article
+
+Keywords:
+
+Posted Date: February 12th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-3910735/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on June 18th, 2024. See the published version at https://doi.org/10.1038/s41467-024-49514-4.
+Red Light-Mediated Photoredox Catalysis Promotes Regioselective Switch in the Difunctionalization of Alkenes
+
+Tong Zhang*a, and Shoubhik Das*a,b
+
+AFFILIATIONS:
+
+a. Department of Chemistry, University of Antwerp, 2020 Antwerp, Belgium
+b. Department of Chemistry, University of Bayreuth, 95447 Bayreuth, Germany
+Corresponding author: shoubhik.das@uni-bayreuth.de
+
+Abstract:
+
+Controlling regioselectivity during difunctionalization of alkenes represents significant challenges, particularly when the installation of both functional groups is involved in radical processes. In this aspect, several functionalized trifluoromethylated (-CF3) compounds have been accomplished via difunctionalization reactions due to their wide importance in the pharmaceutical sectors, however, all these existing reports are limited to afford the corresponding β-trifluoromethylated products. The main reason for this limitation arises from the fact that -CF3 group served as an initiator in those reactions and predominantly preferred to be installed at the terminal (β) position of an alkene. In contrary, functionalization of the -CF3 group at the internal (α) position of alkenes provides valuable products but a meticulous approach is necessary to win this regioselectivity switch. Intrigued by this challenge, we have developed an efficient and highly regioselective strategy where -CF3 group is installed at the α-position of an alkene and at the end, molecular complexity is achieved via the simultaneous insertion of a sulfonyl fragment (-SO2R) at the β-position. This strategy provides the simultaneous installation of two important functional groups such as -CF3 and -SO2R groups and both of these functional groups are the key units to attain or to enhance the bioactivity in organic molecules. A precisely regulated sequence of radical generation using red light-mediated photocatalysis facilitates this regioselective switch from the terminal (β) position to the internal (α) position. Furthermore, this approach demonstrates distinctive regioselectivity, broad substrate scope and industrial potential for the synthesis of pharmaceuticals under mild reaction conditions.
+
+Introduction
+
+Recently, photoredox catalysis has gained tremendous attention in achieving unique synthetic targets under mild reaction conditions.1 In most of these cases, short-wavelength light regions (\( \lambda_{\text{max}} < 460 \) nm) were utilized to achieve these reactions successfully, however, short-wavelength light regions have severe limitations of potential health risk such as photooxidative damage to the retina and furthermore, they can lead to generate undesired side products and thereby, lower the atom economy of that reaction.2-4 Additionally, lower penetration power of short-wavelength light regions causes concern for the scale up of that particular reaction.5 All these limitations have encouraged scientists to move forward to the longer-wavelength regions such as red light or near-infrared (NIR) regions since these are associated with low health risk factor, generate less side products due to their lower energy and have high penetration power in the solution which in turn assist to scale up the reaction.6-9 In longer-wavelength regions as the photocatalysts will be activated by the low-energy, their corresponding redox windows are consequently narrower and that in turn assists to exercise finer control in chemical processes, permitting only specific reactions to take place under defined conditions. Inspired by this, the groups of MacMillan and Rovis have independently developed inspiring photocatalytic strategies for the activation of aryl azide via red light-mediated photoredox catalysis which have been utilized for proximity labeling.10-11 Additionally, the utilization of red light-mediated photocatalysis has been increasingly applied across multiple domains to enhance the control of chemical reactions.12-14 Thus, it is very clear that the red light-mediated photoredox catalysis can uniquely attain many unsolved
+processes which were impossible by the irradiation of ultraviolet (UV) or blue light and that leads to the growing surge of interest in this field, however, it is imperative to acknowledge that still the applications of red light-mediated strategies in organic synthesis are in the early stage of development.
+
+![Diagram showing drug molecules containing trifluoromethyl and sulfonyl groups, site-selective trifluoromethylation of olefin, requirements for control of two distinct radicals, and red light-mediated sulfonyltrifluoromethylation of olefin](page_184_120_1207_1012.png)
+
+<table>
+  <tr>
+    <th>Entry</th>
+    <th>Variations</th>
+    <th>Yield (%)<sup>a</sup></th>
+    <th>Entry</th>
+    <th>Variations</th>
+    <th>Yield (%)<sup>a</sup></th>
+  </tr>
+  <tr>
+    <td>1</td>
+    <td>none</td>
+    <td>76(73<sup>b</sup>)</td>
+    <td>9</td>
+    <td>2.0 equiv. Mes-Umemoto reagent</td>
+    <td>trace</td>
+  </tr>
+  <tr>
+    <td>2</td>
+    <td>2 equiv. NaSO<sub>2</sub>Ph</td>
+    <td>50</td>
+    <td>10</td>
+    <td>2.0 equiv. bpyCu(CF<sub>3</sub>)<sub>3</sub></td>
+    <td>0</td>
+  </tr>
+  <tr>
+    <td>3</td>
+    <td>1.5 equiv. CF<sub>3</sub>-reagent</td>
+    <td>66</td>
+    <td>11</td>
+    <td>20 mol% CuCl</td>
+    <td>51</td>
+  </tr>
+  <tr>
+    <td>4</td>
+    <td>30 mol% bpy ligand</td>
+    <td>0</td>
+    <td>12</td>
+    <td>20 mol% Cu powder</td>
+    <td>0</td>
+  </tr>
+  <tr>
+    <td>5</td>
+    <td>30 mol% 1,10-phen ligand</td>
+    <td>0</td>
+    <td>13</td>
+    <td>MeCN (0.1 M)</td>
+    <td>26</td>
+  </tr>
+  <tr>
+    <td>6</td>
+    <td>2.0 equiv. Togni I</td>
+    <td>trace</td>
+    <td>14</td>
+    <td>No CuCl<sub>2</sub></td>
+    <td>0</td>
+  </tr>
+  <tr>
+    <td>7</td>
+    <td>2.0 equiv. Togni II</td>
+    <td>8</td>
+    <td>15</td>
+    <td>No [O]</td>
+    <td>0</td>
+  </tr>
+  <tr>
+    <td>8</td>
+    <td>2.0 equiv. Umemoto reagent</td>
+    <td>20</td>
+    <td>16</td>
+    <td>No light</td>
+    <td>0</td>
+  </tr>
+</table>
+
+*<sup>a</sup>Yield was determined by <sup>19</sup>F NMR with trifluorotoluene as internal standard. *isolated yields
+
+Figure 1. Design of the sulfonyltrifluoromethylation of olefins via red light-mediated photocatalysis.
+
+Difunctionalization of alkenes is a powerful synthetic strategy to attain molecular complexity from readily available starting materials.<sup>15-21</sup> In this approach, simultaneously two different functional groups are installed across an olefin by the introduction of two new C – C or C – X bonds. Along this direction, tremendous catalytic efforts have been paid to attain molecular complexity to design pharmaceutically relevant compounds.<sup>22-48</sup> However, the simultaneous introduction of the trifluoromethyl (-CF<sub>3</sub>) and the sulfonyl fragment (-SO<sub>2</sub>R) via difunctionalization is highly challenging due to the intricate difficulty in circumventing undesired side reactions, therefore, rarely this challenge has been solved in organic synthesis. On the other hand, these two functional groups (-CF<sub>3</sub> and -SO<sub>2</sub>R) are highly demanding due to their intrinsic capability to enhance the stability, membrane permeability, and metabolism in bioactive molecules and that is reflected in their wide presence as common pharmaceuticals such as CJ-17493 and eletriptan which are served as an NK-1 receptor antagonist, and as a medication for migraine headaches respectively (Figure 1a).<sup>49-54</sup> To the best of our knowledge, only a single report has been published for the simultaneous introduction of these two functional groups across the alkene moiety, however, the position of the -CF<sub>3</sub> group was always in the
+terminal position (β-position).49 Along the same direction, it should be clearly noted that the difunctionalization of alkenes via the introduction of a -CF3 group has frequently been employed, however, -CF3 group mainly acted as an initiator via the formation of a radical and was always installed to the terminal (β) position of an alkene (as depicted by the solid frame in Figure 1b). Followed by this terminal addition, subsequent coupling with other functional groups such as -chloro, -chlorosulfonyl, -amino, -carboxylic acid groups were performed to achieve the difunctionalized products.55-60 In contrary, reverse regioselectivity of the -CF3 group at the internal position (α) in the difunctionalized olefins (indicated by the dashed frame in Figure 1b) is very rare, although this will allow to achieve important pharmaceuticals such as CJ-17493, apinocaltamide and many more. To the best of our knowledge, only the group of Li presented an elegant thermocatalytic strategy by involving copper/N-fluorobenzenesulfonimidate (NFSI) for the introduction of -CF3 group at the internal position of an alkene (Figure 1b).30 In this approach, the N-centered radical, derived from an electrophilic NFSI, served as an initiator to facilitate the addition to the -β position of the olefin and the (bpy)Zn(CF3)2 complex was employed as a nucleophilic -CF3 reagent.
+
+Inspired by all these information, we became interested to design a photoredox system for the first time that should install both the -CF3 and -SO2R groups simultaneously in alkenes where the -CF3 group should be positioned at the internal position (α) in the difunctionalized product. To achieve a success in this site selectivity, meticulous designing of the photoredox strategy during the coupling of two different functional groups is inevitable. This was absolutely orthogonal in the case of Li’s protocol where they worked with only one radical (N-centered radical) in attaining the difunctionalized products.30 Specifically, when both the -CF3 and -SO2R radicals coexist, the -CF3 radical demonstrates higher propensity to attach to the olefin first.37,57 To overcome this obstacle, we argued to ensure: (1) the formation of the -CF3 radical should occur to the subsequent formation of -SO2R radical which will readily initiate the addition to olefins; (2) we also argued to utilize a copper salt as a catalyst to capture the free -CF3 radical since copper-based salts are well known for simultaneous cross-coupling reactions by involving -CF3 radical.25-26 To fulfill these requirements, we attempted to employ a photocatalyst which should be activated by the red light to attain the sulfonyltrifluoromethylated product (Figure 1c).61-62 The reason behind our rationale to use the red light in our reaction was due to the lower energy of the red light compared to the blue light, photocatalysts activated by the red light are expected to exhibit a narrower redox window, enabling a precisely control of radical generation, thereby should facilitate regioselectivity during the addition of two distinct radicals on alkenes. Owing to the narrower redox window of the red light-activated photocatalyst, it was essential to ensure that the excited state of the photocatalyst (PC*) should undergo reduction solely through the sulfinate salts via reductive quenching pathway.44,62 The resulting sulfonyl radical should then be added to the alkene, leading to the formation of the desired carbon-centered radical. At last, the desired product will be achieved by the carbon-centered radical and Cu–CF3 complex via Cu-catalyzed cross-coupling reaction.25-26 In contrast, we rationalized to avoid the oxidative quenching pathway of the PC* since this would have generated free -CF3 radical which would result to the undesired trifluoromethylated side products (-CF3 group at the terminal (β) position).37,57 To accomplish this, the photocatalyst was carefully selected based on the redox potentials of sulfinate salts and -CF3 reagents and the redox potentials should have fulfilled: \( E_{\text{ox}}(\text{RSO}_2^-) < E(\text{PC}^*/\text{PC}^-), \quad E_{\text{red}}(\text{CF}_3^+) < E(\text{PC}^*/\text{PC}^+) \) and \( E(\text{PC}^0/\text{PC}^-) < E_{\text{red}}(\text{CF}_3^+) \) (Figure 1c).
+
+Results
+Reaction optimization
+At the outset of the reaction, 4-vinyl-1,1'-biphenyl (1 equiv.), Os(bptpy)2(PF6)2 (0.8 mol%), NaSO2Ph (3 equiv.) and TTCF3*OTF- (2 equiv.) were employed as the model substrate, photocatalyst, sulfinate salt and -CF3 reagent in the presence of copper chloride (CuCl2, 20 mol%) in dichloromethane (DCM, 0.1 M) to afford the sulfonyltrifluoromethylated product (Figure 1d).56,61-62 We carefully chosen these reagents (Os(bptpy)2(PF6)2, sodium benzenesulfinate (NaSO2Ph) and trifluoromethyl thianthrenium triflate (TTCF3*OTF-)) based on their redox potential values to match with our scientific rationale: \( E([\text{Os}]^{III}/II) = +0.93 \) V vs. Ag/AgCl (3 M KCl), \( E([\text{Os}]^{III}/II) = -0.67 \) V vs. Ag/AgCl (3 M KCl))5, \( E_{\text{ox}}(\text{NaSO}_2\text{Ph}) = +0.6 \) V vs. Ag/AgCl (3 M KCl))57-58, \( E_{\text{red}}(\text{TTCF}_3^*\text{OTF}^-) = -0.69 \) V vs. Ag/AgCl (3 M KCl))63. As expected, the performance of the reaction under these conditions did not generate any trifluoromethylated side products (at the terminal position) and only provided the desired product with 73% of yield. It was also observed that reducing the quantities of NaSO2Ph and TTCF3*OTF-, led to a decrease in the yield of the final product (Figure 1d, entries 2-3). It was necessary to use the excess quantity of sulfinate salts to ensure the faster oxidation of
+sulfinate salt to the -SO2R radical. In addition, due to the lower solubility in DCM, the use of the excess quantity of sulfinate salts was highly necessary as well as the presence of excess quantity of -CF3 reagent accelerated the reaction rate.23,61-62 Furthermore, the addition of ligands such as 2,2′-bipyridine (bpy) and 1,10-phenanthroline (1,10-phen) exerted deleterious effects in the reaction, giving no product under this conditions (Figure 1d, entries 4-5). We assumed that the presence of ligands occupied the coordination sites for -CF3 radical or hindered the binding of -CF3 radical to the Cu-center.25 To verify the importance of the appropriate -CF3 reagent, alternative electrophilic -CF3 sources such as Togni’s reagent, Umemoto’s reagent, and Cu(CF3)3bpy were also applied, albeit substantially lower or negligible yield of the desired product was obtained (Figure 1d, entries 6-10). The rationale behind this could be ascribed to their unsuitable redox potentials, which did not align with Os(bptpy)2(PF6)2 and consequently, failed to meet the requirements. Furthermore, alternative Cu-salts and solvents were also investigated, but lower or negligible yields of the products were obtained (Figure 1d, entries 11-13). Finally, control experiments revealed that the presence of the photocatalyst, Cu-salts and red light were essential for this reaction (Figure 1d, entries 14-16).
+
+In order to exhibit the red light-mediated regioselective gain for this reaction, reaction conditions under the irradiation of blue light were also compared. Similar to the ‘red light system’, the crucial combination of the photocatalyst, sulfinate salt and -CF3 reagent was determined, namely [Ru(bpz)3]PF6·2H2O, NaSO2Ph and 5-(trifluoromethyl)dibenzo-thiophenium triflate (Figure 2b). However, after extensive optimizations via the investigation of each crucial component of this reaction, the highest yield of the desired product reached to 42% and this could be due to the fact that free -CF3 radical was generated faster under these conditions. (See SI 1.3.2). Subsequently, this -CF3 radical underwent an addition reaction with styrene, resulted the formation of the undesired β-substituted trifluoromethylated byproduct and the contrast was notably evident in the 19F NMR spectra (Figure 2c). The ‘blue light system’ exhibited numerous peaks of side products while the spectrum of the ‘red light system’ appeared significantly cleaner and mainly contained the -CF3 reagent and the desired product. This significant difference highlighted the pronounced regioselectivity gain in the sulfonyltrifluoromethylation of alkenes via the red light-mediated photocatalysis.
+
+![Reaction comparison: "blue" vs. "red"](page_184_1047_1207_384.png)
+
+Figure 2. Initial investigation of the reaction under blue and red light with respective photocatalysts.
+
+Substrate scope
+
+With this optimized reaction conditions in hand, we started to evaluate the scope of the sulfonyltrifluoromethylation of alkenes. As shown in the Figure 3, an array of para-substituted styrenes containing diverse electron-donating groups (EDGs) like -methyl, -acetoxy, and -tert-butyl, as well as electron-withdrawing groups (EWGs) such as -halogens provided the corresponding sulfonyltrifluoromethylated products in moderate to excellent yield (Figure 3, 1-8). Specifically, 4-bromostyrene and 4-chlorostyrene were tolerant under our optimized conditions to provide the desired products (6 and 7), thereby, demonstrated the potential for subsequent functionalization via cross coupling
+reactions.\(^{30}\) Furthermore, the reaction demonstrated compatibility with 2- and 3-substituted styrenes (10-13), leading to the formation of products in satisfactory yield, regardless of the presence of -EDGs or -EWGs. In comparison, electron-deficient alkenes (9 and 14) exhibited decreased efficiency, however, the use of \(p\)-chlorophenyl sulfinate led to an improvement in the reaction. In general, the difunctionalization of \(\beta\)-substituted styrenes represents increased difficulty due to the hindrance caused by these \(\beta\)-substituents and this hindrance can impede the addition of initiators, such as sulfonyl radicals in this work.\(^{30}\) However, under our optimized reaction conditions, (E)-\(\beta\)-methylstyrene (15) and indene (16) underwent the difunctionalization reaction smoothly and provided the yield of 46% and 78%, respectively.
+
+![Scope of the sulfonyltrifluoromethylation of olefins](page_184_370_1207_1042.png)
+
+Figure 3. Scope of the sulfonyltrifluoromethylation of olefins.\(^{a}\) Yields are reported as isolated yield. \(^{b}\)dr value was determined by \(^{1}\)H NMR.
+
+Encouraged by these results, an extensive exploration of sulfinate salts was conducted within the optimized reaction conditions. To our delight, a diverse array of \(p\)-substituted phenyl sulfinates, encompassing -methyl, -chloro, -bromo, -nitro, and -cyano groups, demonstrated excellent tolerance, yielding the desired products in yields from
+good to excellent (17-21). Furthermore, aliphatic sulfinates (22 and 23) also proved to be compatible which exhibited strong application potentials in pharmaceutical area such as the modification of azidothymidine which is known as an anti-HIV drug.64 The adaptability of our methodology extended further to sulfinates bearing biphenyl-, cyclopropane-, and thiophene-groups. These substrates smoothly underwent difunctionalization reactions under the irradiation of red light, yielding products in the range of 35-93% (24-26). This exhibited wide generality of our system to afford various sulfones-containing chemicals, thereby making significant contributions to the field of pharmaceuticals, agrochemicals, and it should be also noted that the synthesis of sulfones-containing chemicals is of paramount importance in organic chemistry.44-46
+
+Recently, the focus on late-stage modification has garnered significant interest due to its direct and efficient approach in synthesizing functionalized complex molecules.65-69 The expedite synthesis of highly-functionalized molecules holds strong promise for its potential utility in various scientific disciplines including drug discovery, materials science, and molecular imaging.89 To evaluate the application of our method on complex molecules, a series of drug molecules and natural products derivatives such as estrone, (S)-(+)-naproxen, dexibuprofen, (1S)-(−)-camphanic acid, indomethacin and adapalene were applied (27-32). Under our experimental conditions, these diverse drug derivatives, encompassing a variety of functional groups, exhibited excellent tolerance and compatibility. The resulting products were obtained in yields from 66% to 88%, indicating high reaction efficiency. This demonstrated the potential of our methodology in facilitating the synthesis of more complex sulfonyltrifluoromethylated molecules. We strongly believe that the -trifluoromethyl and -sulfonyl groups in functionalized drug molecules and natural products should not only improve their inherent properties but should also provide the opportunity for further transformation.
+
+![Post-functionalization scheme showing synthetic routes and product transformations](page_184_668_1207_340.png)
+
+Figure 4. Post-functionalization of the sulfonyltrifluoromethylated product.
+
+Application potentials
+
+To further examine the application potential, a 4 mmol-scale reaction was carried out which proceeded smoothly in 4 hours and yielded 0.85 grams of the desired product (Figure 4a). Due to the superior light penetration of red light, it became feasible to directly conduct the upscaling of the reaction within a batch reaction system.5 To further demonstrate the synthetic utility of our strategy, the elimination of the -sulfonyl group was achieved through a straightforward strategy by using a mixture of Cs2CO3 and 7-methyl-1,5,7-triazabicyclo(4.4.0)dec-5-ene (MTBD), resulting in the production of α-trifluoromethyl styrene (33) with a yield of 90% (Figure 4b).62 The mixture of base facilitated the deprotonation and desulfonylation of the sulfonyltrifluoromethylated styrenes to form the α-trifluoromethyl styrenes. In general, α-trifluoromethyl styrene derivatives are highly important as versatile synthetic intermediates for the construction of complex fluorinated compounds which are synthesized through methylation of trifluoromethylketones (Wittig reaction) or via transition metal-catalyzed cross-coupling reactions.70-71 However, compared to these approaches, our strategy enabled the direct synthesis of α-trifluoromethyl styrene derivatives from styrene, eliminating the requirement of Wittig reagents as well as -borylated or -halide reagents in the processes to improve the atom economy. Additionally, the obtained α-trifluoromethyl styrene was further transformed into gem-difluoroalkenes (34) in 86% yield and these fluorinated compounds have strong potential to act as a
+ketone mimic in pharmaceuticals.72-74 In fact, substitution of the carbonyl group by the gem-difluoroalkene moiety has shown to enhance the oral bioavailability of therapeutic agents.72 Furthermore, our strategy generated a key intermediate (35) for the synthesis of apinocaltamide (37), T-type calcium channel blocker from 4-bromostyrene (Figure 4c).75-76 All these approaches clearly demonstrate the strong potential of our strategy for further applications in designing or modifying pharmaceuticals.
+
+![Mechanistic studies: quenching experiments, radical probe experiment via ring-opening reaction, fluorescence quenching experiments, analysis of Cu–CF3 active species, proposed mechanism of this work](page_184_312_1207_693.png)
+
+Figure 5. Mechanistic studies.
+
+Mechanistic investigations
+
+Inspired by all these outcomes, we became interested to validate the reaction mechanism of this unique reaction strategy and a series of mechanistic experiments were conducted to validate our mechanistic proposal (Figure 5). At first, (2,2,6,6-Tetramethylpiperidin-1-yl)oxyl (TEMPO) was added as a radical quenching reagent under the optimized reaction conditions. As expected, trace quantity of the product was obtained and a carbon-centered radical (III) was captured by TEMPO which was detected by the high-resolution mass spectrometry (HRMS) (Figure 5a), indicating that the radical process was involved. To further support the involvement of radicals during the addition of the sulfonyl radical, a radical probe experiment was conducted where the model styrene (39) yielded the ring-opening product 40 (Figure 5b). Upon the addition of sulfonyl radical to 39, a cyclopropylmethyl radical moiety was formed, followed by the rapid ring opening rearrangement relieved the ring strain and finally, resulted the final ring-opening product (40). Additionally, Stern–Volmer fluorescence quenching experiments were conducted, revealing that the sodium sulfinate salt exhibited the highest potential as a quencher for the excited state of the Os-photo-catalyst, which was also corroborated by the electrochemical measurements for redox potentials (Figure 5c, see SI 1.4.1).5 In Figure 5c, it demonstrated that as the concentration of sulfinate salt was increased, there was a notable reduction in fluorescence intensity. However, minimal alterations were detected in the case of the -CF3 reagent, styrene, and CuCl2. This observation was aligned with the anticipated reductive quenching pathway and supported our design that the generation of -sulfonyl radical was prior than the generation of -CF3 radical in the reaction, indicating that no free -CF3 radical was generated and ensured the high regioselectivity switch in this reaction. Furthermore, the form of Cu–CF3 active species was also investigated and to analyze the possible Cu–CF3
+active species, various control experiments were carried out (Figure 5d). Initially, we attempted to detect the active species in the absence of styrene under model reaction conditions, while no new peak corresponding to CuII–CF3 was observed in 1 - 4 h, however, we observed the presence of the CuIII(CF3)4 anion peak (Experiment A in Figure 6). Due to the potential instability of the CuII–CF3 complex, we further attempted the addition of the bpy ligand to detect the potential existence of the CuII–CF3 in Experiment A. However, only peak of TTCF3+OTf− was observed in 19F NMR (Experiment B in Figure 6). The presence of ligands either occupied the available coordination sites of -CF3 radical or impeded the binding of -CF3 radical to the Cu-center.25 To further verify the CuIII(CF3)4 anionic complex, we synthesized stable Me4NCuIII(CF3)4 complex by following the reference article.77 However, no product was obtained by using Me4NCuIII(CF3)4 complex instead of CuCl2 under our optimized reaction conditions (Experiment C in Figure 6). Similarly, to verify the possibility of CuI–CF3 complex as active species, the model reaction was carried out by replacing CuCl2 with fresh copper powder (Cu0) and as expected, no product was obtained under this condition (Experiment D in Figure 6). By analyzing all these experiments, we could assume that the active species Cu–CF3 were not in the form of CuIII–CF3 or CuI–CF3 complexes but possibly were in the form of CuII–CF3 complex.
+
+![NMR spectra of the analysis for Cu–CF3 complex. Experiment A: Model reaction in the absence of styrene after 1 h and 4 h. Experiment B: Experiment A with the addition of bpy (0.5 or 1.5 equiv.) as ligand. Experiment C: Model reaction by replacing CuCl2 with Me4NCuIII(CF3)4 complex. Experiment D: Model reaction by replacing CuCl2 with fresh Cu powder.](page_184_670_1207_496.png)
+
+Figure 6. NMR spectra of the analysis for Cu–CF3 complex. Experiment A: Model reaction in the absence of styrene after 1 h and 4 h. Experiment B: Experiment A with the addition of bpy (0.5 or 1.5 equiv.) as ligand. Experiment C: Model reaction by replacing CuCl2 with Me4NCuIII(CF3)4 complex. Experiment D: Model reaction by replacing CuCl2 with fresh Cu powder.
+
+Based on all these mechanistic studies, we proposed a possible mechanism for the overall reaction system (Figure 5e). The excited state of the photocatalyst [OsIII]* (EIII/II = +0.93 V vs. Ag/AgCl (3 M KCl), EIII/III = -0.67 V vs. Ag/AgCl (3 M KCl))5 was activated by the red light and exclusively underwent reduction by the sulfinate salts, I (Eox = +0.4–0.6 V vs. Ag/AgCl (3 M KCl))61-62 to form the sulfonyl radical II (Path A) rather than oxidation by TTCF3+OTf− IV (Ered = -0.69 V vs. Ag/AgCl (3 M KCl))63 to generate the free -CF3 radical V (Path B), which was consistent with
+the result of fluorescence quenching experiments. The formed sulfonyl radical III was added to the alkene to generate a carbon-centered radical III which was verified by the TEMPO quenching experiment and the radical probe experiment. Later, the CuI-species captured the free -CF3 radical V, generated through the reduction of IV by [Os'] (\( E^{0/1} = -0.82 \) V vs. Ag/AgCl (3 M KCl))\(^{5}\), resulted the formation of the CuI—CF3 complex VI. At last, the final product VII was delivered via the cross-coupling reaction between III and VI.
+
+Conclusions
+
+In summary, we have developed a unique protocol where red light-mediated photocatalysis triggered a regioselective switch during the sulfonyltrifluoromethylation of olefins. This strategy has effectively addressed the challenges associated with regioselective addition of radicals onto alkenes. The broad substrate scope and late-stage transformation demonstrated the high efficiency of these reactions and also proved the excellent tolerance of functional groups. Furthermore, post-functionalization studies highlighted the significant industrial potential of the sulfonyltrifluoromethylated product. Additionally, detailed mechanistic investigations revealed a sequential generation of radicals, followed by Cu-catalyzed cross-coupling reactions. We believe that this strategy will strongly contribute to the regioselective functionalizations and will further inspire the development of additional methods in this field.
+
+Methods
+
+General procedure for sulfonyltrifluoromethylation of olefins. A dried reaction vial with a magnetic stirring bar was charged with Os(bptpy)2(PF6)2 (0.0008 mmol, 0.8 mol%), CuCl2 (0.02 mmol, 20 mol%), TT-CF3*OTf- (0.2 mmol, 2 equiv.) and sodium sulfinate (0.3 mmol, 3 equiv.). After charging all these reagents, the vessel was evacuated by using Schlenk techniques and flushed with N2 for three times. Under nitrogen gas flow, olefin (0.1 mmol, 1 equiv.) (if liquid, otherwise added before flushing cycle) and dry DCM (0.1 M) were added by using a syringe which was flushed with inert gas. The resulting mixture was stirred for 3 - 4 h under the irradiation of red LED light (EvoluChem™ LED 650PF HCK1012-XX-014 650 nm 20 mW/cm\(^2\)) in the EvoluChem PhotoRedOx Box. After the completion of the reaction, the reaction mixture was quenched by adding distilled water (2 mL). The organic phase was extracted and concentrated in vacuo. 1,1,1-Trifluorotoluene was added as internal standard to determine the NMR yield of the functionalized product through \( ^{19}\)F NMR. Purification proceeded via flash column chromatography.
+
+Data availability
+
+All of the data supporting the findings of this study are available within the paper and its Supplementary Information file.
+
+Additional information
+
+Optimization of reactions, Mechanism investigation, General procedure of reactions, characterization of substrates and products and spectra of products could be found in Supporting Information.
+
+Author Contributions
+
+T.Z. and S.D. designed the project. T.Z. developed the reaction, investigated the substrate scope, examined the applications, and studied the reaction mechanism. Finally, T.Z. and S.D. wrote the manuscript.
+
+Competing interests
+
+The authors declare no competing financial interest.
+
+Acknowledgement
+
+S.D. thanks the Francqui start up grant from the University of Antwerp, Belgium, for the financial support. T.Z. thanks FWO SB PhD fellowship for their financial assistance to finish this work. We thank Dr. Rakesh Maiti from University of Bayreuth for helpful discussions. We also thank Mr. Glenn Van Haesendonck from UAntwerpen, Belgium for HRMS measurements.
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supportinginformation5.pdf

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+Peer Review File
+
+Rapid incidence estimation from SARS-CoV-2 genomes reveals decreased case detection in Europe during summer 2020
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+This manuscript presents a new method for estimating the number of SARS-CoV-2 infections over time from dated genome sequence data. There is an enormous number of genome sequences that have been collected from multiple sites around the world, with nearly 2 million currently available through GISAID. Making effective use of these data in a timely manner is critically important. However, the state-of-the-art — arguably Bayesian phylodynamics — does not readily scale to such numbers (notwithstanding the latest improvements to such methods that specifically address this limitation). Thus, the method described in this manuscript is a welcome addition to our analytical toolkit for the current pandemic and for the future.
+
+The method itself is quite simple. However, the authors' explanation of the method is not adequately clear. It is based on a result from theoretical population genetics, specifically a recent analysis of soft selective sweeps by Bhavin Khatri and Austin Burt. First, the authors are making an analogy between SARS-CoV-2 incidence and a selective sweep due to the simultaneous, deterministic growth under positive selection of multiple lineages of independent origins (and that are also fated to reach fixation with probability 2s), carrying the same mutant allele on different genetic backgrounds. This analogy is not made explicit and requires a careful explanation. The exact interpretation of "number of mutant sequences" ($m_b$) and "number of haplotypes" ($h_b$) is unclear. Since the authors' application of the model to incidence does not seem to focus on any particular mutation (relative to a reference genome), does $m$ represent the absolute number of sampled infections (irrespective of sequence) in a given time period (indexed by $b$)? In other words, does $m$ adjust for sampling effort? Does $h$ represent the number of unique genome sequences? If so, how do the authors deal with ambiguous or base calls or incomplete sequence coverage? Figure 1 does help visually explain $h$ and $m$ to some extent, but there needs to be a clearer explanation and rationale integrated into the main text. The term "number of mutant sequences" is particularly confusing.
+
+In addition, their analogy appears to interpret the uninfected susceptible population as wild-type alleles in a population of constant size. The population dynamics of SARS-CoV-2 does not resemble a selective sweep. What are the consequences of non-sigmoidal dynamics in the number of infections? Is the origination of the mutant allele in a new haplotype analogous to the importation of SARS-CoV-2 from an external source to the population, and does this stipulate that the imported infection carries a unique genome sequence? The mutation rate is incorporated into the derivation of Khatri and Burt's result, but it does not make sense if origination corresponds instead to an importation process. I had expected to see these issues addressed substantially in the Discussion, but most of this section was used to review study results rather than discussing the model assumptions and limitations.
+
+The manuscript presents some simulation results, which is a necessary step for validating a new method, since the ground truth is known without error. Population dynamics were simulated by drawing from a Poisson distribution centred on the population size at the previous time point with a deterministic sinusoidal coefficient driving variation over time, instead of a more parametric model (such as an epochal SEIR model). I am somewhat concerned that the authors were not sufficiently critical of their model with respect to its sensitivity to incomplete sampling and importation of cases. For example, incomplete sampling was assessed by censoring infections completely at random (or stratified by time window), but systematic associations between variation in sampling rates and genomic variation (for example, concentrated sampling of a particular district or subpopulation) may induce a more serious bias. Additionally, the impact of importation on model estimates was simulated by adding genomes in which 10% of sites were randomly mutated with respect to the "founder sequence of the local outbreak". This is an excessive amount of mutation. It is not apparent to me whether this simulation setting is meant to be induce a large effect, i.e., make a conservative assessment on sensitivity of the method to importation. Lastly, percent deviation from linearity (supplementary figures) is difficult to interpret as a quantitative outcome of the simulation experiments.
+
+Having raised these issues, I am nonetheless quite impressed with the method presented in the
+manuscript - it seems to work surprisingly well on my test data. I think this will be an important contribution not only to the field of molecular epidemiology, but also for public health applications of sequence analysis. It might be helpful to quantify how much more we learn about the number of unsampled infections from this sequence analysis in comparison to conventional data sources such as test positivity rates, if possible.
+
+Running the program:
+
+I was able to install and run demo code on both macOS Catalina 10.15.7 and Ubuntu 18.04.5. However, I ran into problems when attempting to run GInPipe on a custom data set comprising about 5,000 SARS-CoV-2 genome sequences. First, the snakemake workflow had problems dealing with a relative path to the reference FASTA file in the configuration YAML (the program threw the following exception: "MissingIndexException: Missing input files for rule minimap_index_ref"). I had to move the YAML file into the nested directory and use the filename without any relative path prefix. This input specification needs to be more flexible. Next, I ran into a ValueError exception with the error message "invalid contig" when running the pipeline with NC_045512 as the reference genome. Replacing the sequence header with ">ref" seems to fix this problem, but there is no such requirement specified in the documentation. Overall, I found the pipeline to be quite unforgiving about path specifications and the locations of input files.
+
+The third exception I encountered was associated with "rule run_binning", with "CalledProcessError in line 145". This seems to be associated with an error in the Python script "sam_to_bins_modular.py" on line 260 with "KeyError: 0". At first, I suspected that this was due to one or more incomplete sample collection dates in the inputs. However, I found no such instance when grepping the input files. I then realized that the problem was that I had included spaces around the pipe ('|') delimiter between sample name and collection date fields. My reason for doing so was because the README documentation actually includes a space between "some_name" and the pipe character. Removing the excess spaces resolved this issue. Hence, the documentation needs to be more explicit about how sequence headers in the sample FASTA input should be formatted. Afterwards, I was able to run the pipeline to completion on these data. The locations of peaks in the incidence correlate plot was generally consistent with the first and second waves (with respect to daily numbers of confirmed cases) for the region represented in the data. Since these trends are fairly correlated with sample collection dates (i.e., more samples collected during waves), I also re-ran the analysis with a random permutation of collection dates among sequences to confirm that the same incidence correlate trend could not be recovered. I didn't have time to run more extensive tests.
+
+Source code:
+
+- I appreciate that the authors have released their source code into the public domain under a permissive license (GPLv3). The Python code looks fairly PEP8 compliant.
+
+- Some of the Python scripts are rather unstructured, in that the code is seldom modularized into functions, e.g., `fix_cigars_subprocess.py`. This makes it somewhat more difficult to interpret the code, and prevents users from adapting the functionality of GInPipe into other workflows in a modular fashion. (Same goes for the R scripts - could the developers please consider turning these scripts into a package?)
+
+- Some of the code style is unconventional. For example, the developers make frequent use of string concatenation instead of Python's built-in methods for formatted strings, such as `str.format()` or C-style formatted strings (with '%s' placeholders).
+
+- External programs are being run through the shell, which is generally considered bad practice. For example, a user might be exposed to a shell injection attack if they ran a YAML configuration file with malicious text passed to snakemake parameters. Recommended method is `subprocess.check_call()`.
+- please consider using temporary files via Python module tempfile rather than writing to hard-coded file names like `list_of_files.tsv`.
+
+- clearing the user's workspace with an `rm()` command in the R script is not really user friendly, particularly if a user sources one of these files in an interactive R session.
+
+- many functions in the R scripts need documentation; code style is a bit inconsistent, e.g., varying use of `=` and `<-` assignment operations, varying use of whitespace.
+
+- bam_to_fingerprints.py, lines 103-127 would be more readable code if you used enumerate to iterate over cigar, and then unpacked the tuple into variables, i.e.,
+
+for i, cigtuple in enumerate(cigar):
+    operation, length = cigtuple
+    if operation == 0:  # and so on
+
+Specific comments:
+
+- generally, the manuscript is in a very inconvenient format for review (single-spaced, narrow margins, no line numbering)
+
+- when installing GInPipe on macOS Catalina 10.15.7, I also had to install mamba in order for `conda` to detect `snakemake`, whereas I did not encounter this problem in Ubuntu 18.04, so this doesn't seem to be a Linux-specific issue as implied by the README document.
+
+- the R package mgcv is used in `splineRoutines.R` - shouldn't this be listed as a dependency?
+
+- "the sequences are placed into temporal bins $b$ - this is awkward phrasing, are these bins indexed by variable $b$, or is $b$ the total number of bins?
+
+- p.2, please clearly define "mutant sequences" and "haplotypes" at first use
+
+- p.2 "point estimates are prone to slight underestimation" Please provide quantitative results instead of a qualitative summary.
+
+- p.3, regarding BEAST2, there are some recent advances that should enable users to run larger, low diversity (e.g., SARS-CoV-2) datasets than before, such as PIQMEE
+
+- Figure 1A, y-axis label - why not just say "cumulative number of sequences" instead of using a formula that may frustrate some readers?
+
+- the variant filtering step did not seem to exclude any sequences for either the demonstration data or my own data.
+
+- page 4, "R_e(\tau) estimates for Scotland agree almost exactly" Please provide quantitative results.
+
+- Figure 3, since incidence estimates $\phi$ are correlates, the relation between the two scales ($\phi$ and reported cases) is arbitrary. How did you decide on a proportionality constant for drawing data on these two scales?
+
+- Figure 4, space permitting, it would be helpful to directly label the vertical dashed lines that correspond to different policy changes.
+
+- pages 6-7, much of the text here is essentially describing features of Figure 4; I think this word count would be better invested in describing and discussing the underlying method (i.e., adapting Khatri and Burt's method).
+- page 8, "the vast majority of reconstructed sequence data has been made broadly available through public databases" Unfortunately this is only true for a minority of countries such as Denmark and the UK.
+
+- page 9, "The power of GInPipe lies in the swift reconstruction [...] without requiring [...] masking of problematic sites in the virus genomes." This is not a computationally expensive step and benefits from domain expertise, so why not make use of this filtering step in pre-processing?
+
+- page 9, "The execution time appears to scale linearly with the number of sequences to be analyzed" It would be appropriate to provide some actual results here in supplementary material.
+
+- page 10, "Point mutations appearing less than three times in the whole data set were filtered out, as they may occur due to sequencing errors." This is a problematic assumption. Depending on the size of the data set, a large number of biologically real mutations will fall below this frequency threshold. How sensitive are the results to relaxing this threshold?
+
+- page 10, "we deduced the nucleotide substitutions for each sequence" - so this method excludes indel polymorphisms? Is this justifiable?
+
+- page 11, what convolution filter, exactly?
+
+signed,
+Art Poon
+
+Reviewer #2:
+Remarks to the Author:
+The authors propose a novel method (GInPipe) to estimate the true incidence of SARS-CoV-2 using time-stamped viral genomic data. By analyzing the number and frequency of sequence variants at a given time, they are able to estimate the effective reproductive number and the relative incidence of infection. They validated this method using in silico data, simulating various scenarios including missing/incomplete genomic data, and the introduction of new variants into the population. Subsequently, they validated their model against real-world data from 4 countries: Denmark, Scotland, Switzerland and the Australian state of Victoria. They compared the estimates for Re from BEAST versus GInPipe as well as relative incidence versus the actual number of reported cases in each country/region.
+
+Overall, the manuscript is well written and represents a comprehensive validation of a complementary method to estimate COVID-19 disease incidence. This method will be especially useful when more sensitive diagnostic tests are inadequate relative to the extent of the outbreak. However, it does require the availability of a significant amount of genomic data, which is usually only available in countries with sufficient resources for PCR and sequencing. That said, there important observations that can be inferred from their analysis - when the availability of PCR testing is reduced because of a perceived reduction in the number of cases, the genomic data from those cases may reveal more widespread, cryptic transmission; and while there is utility of rapid antigen testing, widespread use of this less sensitive method may underestimate the true incidence of disease as indicated by genomic data.
+
+It is not clear why the 4 datasets (Denmark, Scotland, Switzerland, and Victoria) were chosen. The a priori rationale for choosing these datasets needs to be stated and justified. This is important for the real-world validity of their results.
+
+The mutation rate is not constant throughout the SARS-CoV-2 genome. There are regions under neutral pressure whereas other regions are under selective pressure. In addition, there are synonymous and non-synonymous mutations. Could the method be improved by using only neutral regions of the genome and/or non-synonymous mutations? Could the authors explain the rationale for grouping by Pango lineage and subsampling within lineages?
+Reviewer #3:
+Remarks to the Author:
+The aims of this paper – to approximate incidence using genetic data alone and to compute changes in the probability of reporting are both important and interesting. Characterising the incidence of cases and even deaths is not simple, especially in the face of detection delays and under-ascertainment. An approach that can circumvent some of these problems would be a valuable addition to the outbreak response toolkit. This paper makes some good progress towards these aims but I have several major concerns around validation and accuracy, which need to be resolved for this analysis/methodology to be convincing.
+
+1. The validation on simulated data is not yet sufficient. This is especially important for a paper proposing a new method. A couple more examples with different dynamics should be included and then some statistics computed to showcase accuracy (e.g., considering the lag and scaling between the true incidence and inferred correlate). In particular, the current example shows clear differences (t = 30-50 and t > 100) that need to be explained and accounted for before the claim of accuracy can be upheld.
+
+2. The approach to simulated epidemics also seems somewhat strange (especially given the use of the Wallinga-Teunis method later). Why not use a renewal model to more accurately simulate what an epidemic might look like (and which is the model behind the Wallinga-Teunis)? The key difference from the current approach would be the use of a generation time distribution (which is better suited for properly considering incidence on daily scales as the paper provides) rather than a simple branching process with fixed generations.
+
+3. The comparisons of Re via BDSky and the Wallinga-Teunis approach do not seem that consistent – more analysis is needed, and the confidence intervals of both approaches do not seem that clear. While the need for piecewise constant Re from BDSky is understandable, there still are discrepancies that warrant a closer look.
+
+4. Why not also compare the Ne with coalescent approaches? It does not appear the Ne from the method chosen has been considered against more standard approaches such as https://academic.oup.com/mbe/article/22/5/1185/1066885. It would be good to know if the correlation between Ne and incidence is general.
+
+5. The methods of https://royalsocietypublishing.org/doi/full/10.1098/rstb.2010.0060 have explicitly investigated relationships among Ne and prevalence/incidence. I think this paper should comment on those links since it proposes another correlation.
+
+6. In the supplement the importance of binning strategies is noted. Can some comment in the main text be given for what selection approach was taken? Is there some good theoretical reason? The bias-variance trade-off of bins is well known at least for Ne https://academic.oup.com/sysbio/article-abstract/68/5/730/5307781. Can some related comment be made in the choices of this approach?
+
+We hypothesize that the genetic data alone holds information about the pandemic trajectory – I would remove this (as it is what makes phylodynamics as a whole useful) and go to the next line, which is the actual hypothesis specifically examined here.
+
+The approach builds on recent work by Khatri and Burt... – could you add a line with some additional explanation here to improve readability for those unfamiliar with this paper? This is particularly helpful since this is a major point underlying the paper.
+
+We observed a strong (r = 0:96)... This correlation is not as informative as it could be. A similar association but done per time point would be more useful to confirm if the seeming lag between the inferred and true Ne is upheld or an artefact. Such lags are important for a method providing incidence estimates given what of the key differences between incidence and reported cases is
+indeed the lag, the influence of which has been debated. E.g., see https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409
+
+Our analyses showed that the method can still accurately reconstruct incidence histories over time, when data is missing or when data sampling is unbalanced – this needs to be better explained and qualified/validated. It seems counterintuitive given that sampling is well known to be a major source of bias both in genetic data and case data (and for estimating either Re or Ne). If this claimed robustness does hold then it is worth including background for why this would be an advance/important trait of the method e.g., for case data/Re see https://academic.oup.com/aje/article/178/9/1505/89262?login=true and for genetic data/Ne https://academic.oup.com/mbe/article/37/8/2414/5719057?login=true
+
+Finally, we evaluated whether introductions of foreign sequences affect the reconstruction of incidence histories – this is another counterintuitive point since introductions/imports affect estimates of key epidemiological parameters as has been found across COVID-19. I think this needs more qualification and detail.
+
+For the second wave, reconstructed incidence histories correspond to the reported cases – this does not seem quite right as reported cases themselves do not correspond with the incidence. Please clarify what should be comparable.
+
+Taken together, these lines of evidence suggest that evolutionary change of SARS-CoV-2, the effective viral population size, and the number of infected people are correlated – could some more detail and intuition be provided to help readers understand why this correlation, which is the main assumption behind the method, is valid?
+
+Finally, we envision that the method will be particularly useful to estimate the extent of the SARS-CoV-2 pandemic in regions where diagnostic surveillance is insufficient for monitoring, but may still yield a few samples for sequencing – has this point been demonstrated as possible?
+
+The reproductive number \( \mathrm{Re}(t) \) ... was drawn from a log-normal distribution ... which is changed to N (48.8;1) after first control measures are implemented in the respective area – can some more intuition and explanation be provided for these choices?
+We thank the reviewers for their constructive comments, which we believe further improved the manuscript. We particularly appreciate the speed in which they delivered their feedback. Based on the reviewers comments, we performed extensive additional experiments. Below is a point-by-point response to all reviewers’ comments and a documentation of all changes and additional experiments. All changes are marked in purple in the ‘manuscript with track changes’ and page and line numbers in the response letter refer to the ‘manuscript with tracked changes’.
+
+Major changes:
+• In response to reviewers #1-3, we performed extensive tests of GlnPipe, which are documented in the extended Supplementary Note 1.
+• In response to Rev. #1, we rewrote parts of the discussion and streamlined the tool.
+• In response to reviewers #2-3, we analysed further countries (Japan, Chile, South Africa, India), documented in Supplementary Figure 3.
+• In response to reviewer #3, we performed further phylodynamic analysis to estimate incidence. Unfortunately, setting up and performing this analysis consumed most time (as stated in the manuscript, setting up and performing phylodynamic analysis requires considerable expertise and computational time to derive meaningful results). We were however able to derive phylodynamically reconstructed incidence profiles for Scotland (using EpilInf), which are shown together with reported cases and the results of GlnPipe in Supplementary Figure 1.
+
+We hope that the reviewers are content with and convinced by the additional analyses.
+
+<table>
+  <tr>
+    <th>REVIEWER</th>
+    <th>COMMENTS</th>
+  </tr>
+  <tr>
+    <td>Reviewer #1</td>
+    <td>(Remarks to the Author):</td>
+  </tr>
+</table>
+
+This manuscript presents a new method for estimating the number of SARS-CoV-2 infections over time from dated genome sequence data. There is an enormous number of genome sequences that have been collected from multiple sites around the world, with nearly 2 million currently available through GISAID. Making effective use of these data in a timely manner is critically important. However, the state-of-the-art — arguably Bayesian phylodynamics — does not readily scale to such numbers (notwithstanding the latest improvements to such methods that specifically address this limitation). Thus, the method described in this manuscript is a welcome addition to our analytical toolkit for the current pandemic and for the future.
+
+-> Many thanks for the very constructive feedback and also for the time that went into the extensive testing of the pipeline. Apologies if the reviewer felt that the pipeline was so unforgiving in its initial state. We are grateful to make the tool more user- and developer-friendly.
+
+1. The method itself is quite simple. However, the authors' explanation of the method is not adequately clear. It is based on a result from theoretical population genetics, specifically a recent analysis of soft selective sweeps by Bhavin Khatri and Austin Burt. First, the authors are making an analogy between SARS-CoV-2 incidence and a selective sweep due to the simultaneous, deterministic growth under positive selection of multiple lineages of independent origins (and that are also fated to reach fixation with probability 2s), carrying the same mutant allele on different genetic backgrounds. This analogy is not made explicit and requires a careful explanation.
+-> Thank you for this critical assessment. We have not clearly pointed out that while the method is motivated by Khatri & Burt’s article, it is actually quite different regarding the points made by the reviewer. We have changed the wording accordingly and also added a paragraph in the discussion (page 8, lines 382ff). We are currently working on the theory, which however will take much more time than can be envisaged during the revision process and may also require a different target audience/journal. Based on our analyses, we do have empirical evidence that the method works (see also response to Rev #2, comment 1; further countries in new Supplementary Figure 3) and thus, we currently view the proposed method as empirical evidence that for SARS-CoV-2 an evolutionary signal exists, from which the incidence trajectory can be deduced. Unarguably, over the next month and years, we will further evaluate the theory, improve and automate the pipelines, and assess if the method works for other respiratory infections. We have added corresponding passages to the discussion explaining the scope of the results, limitations and the outlook on page 9.
+
+We also evaluated the method in scenarios with positive/negative selection (Supplementary Note 1, section SN.1.14, see also Reviewer #2, comment 2). Here also, the method works well.
+
+2. The exact interpretation of "number of mutant sequences" ($m_b$) and "number of haplotypes" ($h_b$) is unclear. Since the authors' application of the model to incidence does not seem to focus on any particular mutation (relative to a reference genome), does $m$ represent the absolute number of sampled infections (irrespective of sequence) in a given time period (indexed by $b$)? In other words, does $m$ adjust for sampling effort?
+
+-> Absolutely, yes: If the population diverged sufficiently from the reference, then $m$ denotes the number of sampled infections within a sequence set (= number of sequences). We believe that $m$ therefore adjusts for the sampling effort. ‘Number of haplotypes’ refers to the number of unique sequences in a sequence set, as stated in the revised manuscript on page 2/3, paragraph ‘Incidence reconstruction’.
+
+3. Does $h$ represent the number of unique genome sequences? If so, how do the authors deal with ambiguous or base calls or incomplete sequence coverage? Figure 1 does help visually explain $h$ and $m$ to some extent, but there needs to be a clearer explanation and rationale integrated into the main text. The term "number of mutant sequences" is particularly confusing.
+
+-> We rephrased “number of mutant sequences”, page 2/3, paragraph ‘Incidence reconstruction’.
+
+If there is incomplete coverage (in more than 10% of the sequence), the sequence will not be aligned by minimap (page 12, line 553). Our pipeline is currently entirely based on point mutations, i.e. InDels are ignored in the current version of the pipeline (missing data below the 10%). Ambiguous bases are:
+
+    (i) either treated as the reference base, if the ambiguous code contains the reference base (e.g. ‘R’ would be replaced by ‘A’, if ‘A’ is the reference), or
+
+    (ii) or the ambiguous does not contain the reference, a random non-ambiguous base is chosen from the set that defines the ambiguous code.
+
+We added this information to the Methods section (page 12, paragraph ‘Data and data pre-processing’) and apologize that it was not provided in the initial version of the manuscript.
+
+-> In the revision process, we also realized that the alignment filter (10% mismatch criteria in minimap) may have falsely excluded some sequences in the simulation studies (particularly during the simulation of introductions). We have adjusted the length of the sequences, as well as the
+difference of the introduced sequences to the founder sequence to avoid sequence exclusion. Interestingly, removing this bug further improved the performance of GInPipe (Fig. 1D-F and Supplementary Note 1).
+
+4. In addition, their analogy appears to interpret the uninfected susceptible population as wild-type alleles in a population of constant size. The population dynamics of SARS-CoV-2 does not resemble a selective sweep. What are the consequences of non-sigmoidal dynamics in the number of infections? Is the origination of the mutant allele in a new haplotype analogous to the importation of SARS-CoV-2 from an external source to the population, and does this stipulate that the imported infection carries a unique genome sequence? The mutation rate is incorporated into the derivation of Khatri and Burt’s result, but it does not make sense if origination corresponds instead to an importation process. I had expected to see these issues addressed substantially in the Discussion, but most of this section was used to review study results rather than discussing the model assumptions and limitations.
+
+-> As stated in the response to comment 1, the analogy with Khatri & Burt may not be as strong as perceived by the reviewer. We apologize if our wording may have given the wrong impression.
+
+-> Non-sinusoidal dynamics: We have tested non-sinusoidal dynamics in the extended Supplementary Note 1, section SN.1.9 (constant effective population size, time-dependent sampling) and in section SN.1.10 (step functions for the effective population size; [= extreme, non-smooth dynamics]). The method appears to cope well.
+
+-> Importation vs. origination: In our simulations, origination and importation are different. Origination depends on the effective population size, importation not. In the extreme scenarios (Supplementary Note 1, section SN.1.8, Figure SN.10 therein) we assessed situations, where importation does not contribute to the effective population size (‘stopped at the border’), i.e. does not evolve after being imported. In other words, importation was a source of ‘noise’ in those simulations. In some extreme cases, this may bias our inference. Thus, there is some empirical evidence that importation is not a driving factor of the proposed method: If sufficient evolution occurs, we observe that the method works: Hence, as long as the “evolutionary signal” is sufficient, the method seems to be able to reconstruct incidence profiles.
+
+-> The mutation rate is not explicitly considered in our equation, yet. As mentioned in response to comment 1, we are currently working out the theory. When we are able to derive an explicit formula that represents the relationship between the mutation rate and \( \phi \), we may also be able to quantify absolute incidences (unlike, as currently, relative changes), which of course is a very high priority for us.
+
+-> We have added a methodological discussion that also refers to the analyses performed in the Supplementary Notes SN.1.8-15 (see also comment 1.), page 8/9 in the Discussion.
+
+5. The manuscript presents some simulation results, which is a necessary step for validating a new method, since the ground truth is known without error. Population dynamics were simulated by drawing from a Poisson distribution centred on the population size at the previous time point with a deterministic sinusoidal coefficient driving variation over time, instead of a more parametric model (such as an epochal SEIR model). I am somewhat concerned that the authors were not sufficiently critical of their model with respect to its sensitivity to incomplete sampling and importation of cases. For example, incomplete sampling was assessed by censoring infections completely at random (or stratified by time window), but systematic associations between variation in sampling rates and genomic
+variation (for example, concentrated sampling of a particular district or subpopulation) may induce a more serious bias.
+
+-> These are very good (and challenging) comments.
+
+-> Choice of model for simulations: For the purpose of analysis, we chose the minimal modelling approach. Essentially, for model simulations, the only interesting quantity in our context is the number of infectious individuals (the 'I' in the SEIR). Moreover, we believe that an SEIR is probably the wrong modelling approach, given that SARS-CoV-2 variants (beta, gamma, delta, lambda, ...) seem to arise that are able to re-infect individuals (PMID: 33515491,33293339; i.e., the 'R' in the SEIR may be incorrect for modelling long-term dynamics). A suitable mechanistic modelling approach would therefore (i) either have to consider the emergence of variants by explicitly considering phenotypes (ability of strain j to infect individuals recovered from infection with strain i) in a multi-variant SEIR model, or (ii) assume that sufficient susceptibles are available at all times (SIS-like model). For the first (i) approach, many assumptions have to be made and even more parameters to be justified. The second approach (ii) may reduce to sampling from a Poisson distribution with time dependent mean (depending on I(t) and some time dependent infection rate constant \( p(t) = b(t) * S \)), whenever the proportion of infected individuals remains in the lower single-digit percent values (consequently \( S(t) \approx S_0 \)). The latter is a very reasonable assumption for SARS-CoV-2, given that the duration of infection is short (e.g. ‘prevalence estimator’ function in https://covidstrategycalculator.github.io/).
+
+-> The reviewer is absolutely right that severely biased sampling, e.g. only of very related cases, may induce a more serious bias in GlnPipe. In essence, if the sampling (and thus the ‘evolutionary signal’) is severely distorted, the method, naturally, cannot work. However, this limitation with regards to biased sampling applies to all methods available (serology, wastewater analysis, phylodynamics, diagnostics). For this reason, we have made the experience that nationally (Germany) and with our international partners (e.g. Insa-Cog, Africa-CDC, WHO), great effort is put into building up genomic surveillance networks that produce representative data.
+
+We have performed the corresponding simulations in Supplementary Note 1, section SN.1.9 and also included this limitation in the discussion (page 8/9). In ongoing work, we are developing methods to detect and set apart such distorted signals and apply automatic filters in the pipeline. With regards to real data, we added further countries, some with very low sequencing capacities in Supplementary Fig. 3 (see also response to reviewer #2, comment 1).
+
+-> We also want to assure the reviewer that we were VERY critically evaluating the method over the last year (note the method was already up and running at the COVID-19 Dynamics and Evolution Conference in Oct. 2020).
+
+6. Additionally, the impact of importation on model estimates was simulated by adding genomes in which 10% of sites were randomly mutated with respect to the "founder sequence of the local outbreak". This is an excessive amount of mutation. It is not apparent to me whether this simulation setting is meant to be induce a large effect, i.e., make a conservative assessment on sensitivity of the method to importation.
+
+-> Yes, the set-up was meant to induce a large effect to test the methods’ limits. We found that the method is quite insensitive to what the imported sequences look like.
+
+-> However, we realized that the original set-up may have introduced a bias by falsely disregarding sequences (see response to comment 3). We altered the settings accordingly to remove this bug, which made GlnPipe’s reconstructions even better.
+7. Lastly, percent deviation from linearity (supplementary figures) is difficult to interpret as a quantitative outcome of the simulation experiments.
+
+-> We apologize for this inconvenience. This measure arose from the fact that, while we know that the effective population size and our estimate \( \varphi \) correlate linearly, we do not know the slope (and thus the true relation) \emph{a priori}. Hence, the best we can do is to infer a slope and to compute the deviation from that slope. However, we also added a scatter plot with regards to the \emph{true} and \emph{inferred} Re in the revised Fig. 1f, as well as a contingency table and an accuracy estimate on the categorical data (see also Rev #3, comment 9).
+
+8. Having raised these issues, I am nonetheless quite impressed with the method presented in the manuscript - it seems to work surprisingly well on my test data. I think this will be an important contribution not only to the field of molecular epidemiology, but also for public health applications of sequence analysis. It might be helpful to quantify how much more we learn about the number of unsampled infections from this sequence analysis in comparison to conventional data sources such as test positivity rates, if possible.
+
+-> Thank you very much for your feedback and enthusiasm, which we share 100%.
+
+Running the program:
+
+I. I was able to install and run demo code on both macOS Catalina 10.15.7 and Ubuntu 18.04.5. However, I ran into problems when attempting to run GinPipe on a custom data set comprising about 5,000 SARS-CoV-2 genome sequences. First, the snakemake workflow had problems dealing with a relative path to the reference FASTA file in the configuration YAML (the program threw the following exception: "MissingIndexException: Missing input files for rule minimap_index_ref"). I had to move the YAML file into the nested directory and use the filename without any relative path prefix. This input specification needs to be more flexible.
+
+-> We apologize for this inconvenience. In the README it says *The specified paths in the config file should either be absolute, or relative to the work environment specified with -d in the snakemake call (see below in Execution)*. We have added more information about running the pipeline directly to the github repo.
+
+II. Next, I ran into a ValueError exception with the error message "invalid contig" when running the pipeline with NC_045512 as the reference genome. Replacing the sequence header with ">ref" seems to fix this problem, but there is no such requirement specified in the documentation. Overall, I found the pipeline to be quite unforgiving about path specifications and the locations of input files.
+
+-> We tried to reproduce this error. Using arbitrary names, including "NC_045512" works, but apparently this error occurs when there are whitespaces in the header. This is also the case for the downloaded fasta file for “NC_045512” from NCBI, which might have caused the crash if the reviewer used it with the full header name. We solved this issue now: the pipeline will only take the reference name up until first whitespace. Also a suggestion to only use reference names with no whitespaces was added to the README.
+
+III. The third exception I encountered was associated with "rule run_binning", with "CalledProcessError in line 145". This seems to be associated with an error in the Python
+script "sam_to_bins_modular.py" on line 260 with "KeyError: 0". At first, I suspected that this was due to one or more incomplete sample collection dates in the inputs. However, I found no such instance when grep'ing the input files. I then realized that the problem was that I had included spaces around the pipe ('|') delimiter between sample name and collection date fields. My reason for doing so was because the README documentation actually includes a space between "some_name" and the pipe character. Removing the excess spaces resolved this issue. Hence, the documentation needs to be more explicit about how sequence headers in the sample FASTA input should be formatted.
+
+-> The description in the README has been changed (by error there was a whitespace after the |; apologies!). The utilized format of the header is adapted to the GISAID format (hence allows application to data downloaded directly from there).
+
+-> We also deposited a utility function that merges meta-data files with the sequence files add_date_from_metadata.py in scripts/utils folder of the main GitHub repository.
+
+IV. Afterwards, I was able to run the pipeline to completion on these data. The locations of peaks in the incidence correlate plot was generally consistent with the first and second waves (with respect to daily numbers of confirmed cases) for the region represented in the data. Since these trends are fairly correlated with sample collection dates (i.e., more samples collected during waves), I also re-ran the analysis with a random permutation of collection dates among sequences to confirm that the same incidence correlate trend could not be recovered. I didn't have time to run more extensive tests.
+
+-> This is a very nice test. Thank you so much for taking the time and for your interest in this work!
+
+V. Source code:
+
+- I appreciate that the authors have released their source code into the public domain under a permissive license (GPLv3). The Python code looks fairly PEP8 compliant.
+
+- Some of the Python scripts are rather unstructured, in that the code is seldom modularized into functions, e.g., `fix_cigars_subprocess.py`. This makes it somewhat more difficult to interpret the code, and prevents users from adapting the functionality of GInPipe into other workflows in a modular fashion. (Same goes for the R scripts - could the developers please consider turning these scripts into a package?)
+
+-> We have considerably restructured the code and turned the respective scripts into packages.
+
+- Some of the code style is unconventional. For example, the developers make frequent use of string concatenation instead of Python's built-in methods for formatted strings, such as `str.format()` or C-style formatted strings (with '%' placeholders).
+
+-> Thank you very much, we have changed everything to the C-style as requested.
+
+- External programs are being run through the shell, which is generally considered bad practice. For example, a user might be exposed to a shell injection attack if they ran a YAML configuration file with malicious text passed to snakemake parameters. Recommended method is `subprocess.check_call()`.
+-> We are not entirely sure whether we understood the remark correctly.
+
+If the reviewer is referring to Snakemake, we have screened the Snakemake documentation and went through various forums. We did not find any discussion that this is bad practice.
+
+If the reviewer is referring to Python calling external programs (e.g. SAM tools), the issue has been largely resolved (however, subprocess.check_call() is still used once for indexing bam files (in erase_empty_bins.py line 45)).
+
+- please consider using temporary files via Python module tempfile rather than writing to hard-coded file names like 'list_of_files.tsv'.
+
+    - This has been changed. The script does not write files with intermediate outputs anymore. Thanks for the remark!
+
+        - clearing the user's workspace with an `rm()` command in the R script is not really user friendly, particularly if a user sources one of these files in an interactive R session.
+
+    - This has been changed. Thanks for the remark!
+
+        - many functions in the R scripts need documentation; code style is a bit inconsistent, e.g., varying use of `=` and `<-` assignment operations, varying use of whitespace.
+
+    - This has been changed. Thank you for the remark!
+
+        - bam_to_fingerprints.py, lines 103-127 would be more readable code if you used enumerate to iterate over cigar, and then unpacked the tuple into variables, i.e.,
+
+            for i, cigtuple in enumerate(cigar):
+                operation, length = cigtuple
+                if operation == 0: # and so on
+
+    - This has been changed. Thanks for the remark!
+
+Specific comments:
+
+- generally, the manuscript is in a very inconvenient format for review (single-spaced, narrow margins, no line numbering)
+
+-> Apologies. Nature Comm. allows a format-independent initial submission. We realized that there were no line numbers and sent a version with line numbers to the editorial office. However, the editors were incredibly quick and the manuscript had already been sent to the reviewers. We fixed this in the revision.
+
+- when installing GlnPipe on macOS Catalina 10.15.7, I also had to install mamba in order for `conda` to detect 'snakemake', whereas I did not encounter this problem in Ubuntu 18.04, so this doesn't seem to be a Linux-specific issue as implied by the README document.
+
+-> We changed the README. The recommended installation for Snakemake using mamba is described in the README and is not system-specific (opposite to what was stated before).
+- the R package mgcv is used in `splineRoutines.R` - shouldn't this be listed as a dependency?
+
+-> We fixed this (this was historical code which was not used anymore)
+
+- "the sequences are placed into temporal bins $b$" - this is awkward phrasing, are these bins indexed by variable $b$, or is $b$ the total number of bins?
+
+-> Apologies. It is indexed by $b$. We rephrased the sentence (page 2/3, paragraph ‘Incidence reconstruction’).
+
+- p.2, please clearly define "mutant sequences" and "haplotypes" at first use
+
+-> done (page 2/3, paragraph ‘Incidence reconstruction’).
+
+- p.2 "point estimates are prone to slight underestimation" Please provide quantitative results instead of a qualitative summary.
+
+-> We reformulated this sentence “\( \varphi \) point estimates have the tendency to yield lower values” (page 3, line 118). The effect is a scaling, similar to the one shown for different filters (third last comment below “Point mutations appearing less than three times in the whole data set were filtered…”). In response to comment 7, we also provide a different assessment of the quality of incidence reconstruction (e.g. Fig.1F).
+
+- p.3, regarding BEAST2, there are some recent advances that should enable users to run larger, low diversity (e.g., SARS-CoV-2) datasets than before, such as PIQMEE
+
+Thank you for raising this point. Through direct correspondence with the PIQMEE developer (VB), we can say that PIQMEE may indeed be suitable for analysis of SARS-CoV-2 data sets. However, a significant increase in the number of sequences analysed (as compared to analysis using BDSKY) would only be possible if the data was sampled at very few sampling points (VB said they have tried no more than 5) and the number of unique sequences should be in the hundreds, not more. Neither is the case here. However, we have adjusted the original statement ("*However, these methods are computationally expensive, so that only moderately sized sequence sets can be used, and advanced knowledge is required to apply them properly to larger data sets.*") to better reflect the possible applications of phylogenetic methods to large data sets (page 4, section Method validation: phylodynamics).
+
+- Figure 1A, y-axis label - why not just say "cumulative number of sequences" instead of using a formula that may frustrate some readers?
+
+-> Thank you, we changed this.
+
+- the variant filtering step did not seem to exclude any sequences for either the demonstration data or my own data.
+
+-> This filtering excludes specific mutations at a specific site and not sequences (page 12, Methods section, paragraph ‘Data and data pre-processing’). We also checked and corrected the ReadMe on github.
+- page 4, "R_e(\tau) estimates for Scotland agree almost exactly" Please provide quantitative results.
+
+-> Specified: “The GInPipe estimate is within 20% of the BEAST2 estimate” (page 4, line 164)
+
+- Figure 3, since incidence estimates \( \phi \) are correlates, the relation between the two scales (\( \phi \) and reported cases) is arbitrary. How did you decide on a proportionality constant for drawing data on these two scales?
+
+-> We used the respective min/max values on both axes.
+
+- Figure 4, space permitting, it would be helpful to directly label the vertical dashed lines that correspond to different policy changes.
+
+-> We had done this in a pre-submission version of the manuscript. However, the figures became very overloaded and hence we decided to put the explanations in the caption.
+
+- pages 6-7, much of the text here is essentially describing features of Figure 4; I think this word count would be better invested in describing and discussing the underlying method (i.e., adapting Khatri and Burt’s method).
+
+-> We have extended the discussion of the method (page 8/9). We found that the underdetection issue is a very nice feature of the method, worth discussing with the presented examples and an important addition to the portfolio of tools to monitor SARS-CoV-2 (and possibly other respiratory infections) in the future.
+
+- page 8, "the vast majority of reconstructed sequence data has been made broadly available through public databases" Unfortunately this is only true for a minority of countries such as Denmark and the UK.
+
+-> Meanwhile, many national genomic surveillance initiatives make their data available, with about 2.3 million sequences on GisAID to date (including Germany; which we are making available, ever since the data was systematically collected, and against all resistances from data protection officers, after lengthy discussions with Peter Bogner and the like ... ;)). We changed “vast majority” to “many” (page 8, line 344).
+
+- page 9, "The power of GInPipe lies in the swift reconstruction [...] without requiring [...] masking of problematic sites in the virus genomes." This is not a computationally expensive step and benefits from domain expertise, so why not make use of this filtering step in pre-processing?
+
+-> The pipeline does not seem to require masking, which is great in terms of reducing manual adjustments by users (which may also take time to perceive and to perform). However, we have added a utility that can mask particular sites (replace them by the reference residue).
+
+- page 9, "The execution time appears to scale linearly with the number of sequences to be analyzed"
+It would be appropriate to provide some actual results here in supplementary material.
+
+-> We included a plot with the runtimes for some analysed countries in the new Supplementary Figure 4 and added a cross reference in the main text (page 10, line 466).
+
+- page 10, "Point mutations appearing less than three times in the whole data set were filtered out, as they may occur due to sequencing errors." This is a problematic assumption. Depending on the size of the data set, a large number of biologically real mutations will fall below this frequency threshold. How sensitive are the results to relaxing this threshold?
+
+-> We made this filter an optional input by the user. We found that applying this filter has a scaling effect (changing the slope of the linear correlation).
+
+- page 10, "we deduced the nucleotide substitutions for each sequence" - so this method excludes indel polymorphisms? Is this justifiable?
+
+-> Our current version of the pipeline focuses only on point mutations (substitutions), comment 3. Substitutions denote frequent mutational events that apparently comprise a sufficient evolutionary signal for incidence reconstruction. InDels however, are less frequent and may imply more severe phenotypic changes. We therefore suspect that Indels negatively affect signal-to-noise.
+
+- page 11, what convolution filter, exactly?
+
+-> We applied a smoothing filter (moving average; R routine ‘filter’ with window size 7, 2-sided). We added the information (page 13, paragraph ‘Reconstructing the incidence history’).
+
+Reviewer #2 (Remarks to the Author):
+
+The authors propose a novel method (GInPipe) to estimate the true incidence of SARS-CoV-2 using time-stamped viral genomic data. By analyzing the number and frequency of sequence variants at a given time, they are able to estimate the effective reproductive number and the relative incidence of infection. They validated this method using in silico data, simulating various scenarios including missing/incomplete genomic data, and the introduction of new variants into the population. Subsequently, they validated their model against real-world data from 4 countries: Denmark, Scotland, Switzerland and the Australian state of Victoria. They compared the estimates for Re from BEAST versus GInPipe as well as relative incidence versus the actual number of reported cases in each country/region.
+
+Overall, the manuscript is well written and represents a comprehensive validation of a complementary method to estimate COVID-19 disease incidence. This method will be especially useful when more sensitive diagnostic tests are inadequate relative to the extent of the outbreak. However, it does require the availability of a significant amount of genomic data, which is usually only available in countries with sufficient resources for PCR and sequencing. That said, there important observations that can be inferred from their analysis - when the availability of PCR testing is reduced because of a perceived reduction in the number of cases, the genomic data from those cases may reveal more widespread, cryptic transmission; and while there is utility of rapid antigen
+testing, widespread use of this less sensitive method may underestimate the true incidence of disease as indicated by genomic data.
+
+1. It is not clear why the 4 datasets (Denmark, Scotland, Switzerland, and Victoria) were chosen. The a priori rationale for choosing these datasets needs to be stated and justified. This is important for the real-world validity of their results.
+
+-> The choice of these countries and regions was to some extent random, but we also did have the following thought in mind: For most of the countries we expected that the pandemic was reasonably tracked by the reported cases, to ensure that the comparison between reported cases and estimated incidence is meaningful. Moreover, the following consideration were made
+
+• Denmark: Many sequences
+• Scotland: Many sequences, ?underdetection at beginning?
+• Victoria: small setting; very few infections, different dynamics/waves at different times in comparison to Europe; good sequencing coverage
+• Switzerland: exploratory.
+
+-> We added a few more countries in Supplementary Figure 3 and added the corresponding text in the Results (page 6, line 240ff), as well as the Discussion (page 10).
+
+• Japan (exploratory: ... olympic games)
+• India (exploratory: probably unmitigated spread, very few sequences in comparison to number infected, emergence of delta variant)
+• Chile (exploratory: very few sequences; high rates of vaccination)
+• South Africa (exploratory: potentially a lot of unnoticed spread, fewer sequences in comparison to number infected, emergence of beta variant)
+
+![Four scatter plots showing sample size vs. reported cases for Japan, Chile, India, and South Africa](page_355_872_1147_496.png)
+2. The mutation rate is not constant throughout the SARS-CoV-2 genome. There are regions under neutral pressure whereas other regions are under selective pressure. In addition, there are synonymous and non-synonymous mutations. Could the method be improved by using only neutral regions of the genome and/or non-synonymous mutations?
+
+-> Practically, whether positions are neutral may not be known a priori, as even synonymous mutations may be selected (non-coding RNA, or codon bias). However, we included a utility in GInPipe that allows us to mask particular sites (see also Rev. # 1, fifth last minor comment).
+
+-> We set up a simulation example (Supplementary Note 1, section SN.1.14), where we also incorporated sites under selective pressure. We chose a parameter setting, such that the average fitness of the viral population would increase up to factor 2 during simulations (Fig. SN.22 in Suppl. Note SN1). Note that the indicated fitness value is similar to the putative fitness advantage of the delta variant over the wild type of approx. factor 2). In summary, the method still works well when some sites are under selection.
+
+Could the authors explain the rationale for grouping by Pango lineage and subsampling within lineages?
+-> The reason for subsampling within Pango lineages for the phylodynamic analysis, as only done for the D.2 lineage in Victoria, was the very high proportion of sequences assigned to D.2 in the data set and the relatively low subsampling percentage. Taken together, this would have led to the loss of most of the non-D.2 sequences, especially those comprising the background during the D.2 outbreak. To account for this non-random subsampling, we model and estimate a separate sampling proportion for lineage D.2 compared to the non-D.2 lineages.
+In general, we subsample the full data sets randomly through time to decrease the total number of sequences to a point at which they can be analysed in a reasonable time with the phylodynamic method used. We then group the sequences in the subsampled data set by Pango lineage in order to roughly approximate independent introductions into the area, such that most transmission events in the trees happened inside of the considered area. Even though the Pango lineages do not provide an exhaustive separation of intra-area clusters, they are defined in a way that new emerging clades within the global SARS-CoV-2 phylogeny are identified, especially when spreading into a new region. We therefore assume that, although we cannot identify all introductions, we are able to separate clusters of potentially different dynamics using this clustering method. We have clarified this in the revised manuscript.
+
+Reviewer #3 (Remarks to the Author):
+
+The aims of this paper – to approximate incidence using genetic data alone and to compute changes in the probability of reporting are both important and interesting. Characterising the incidence of cases and even deaths is not simple, especially in the face of detection delays and under-ascertainment. An approach that can circumvent some of these problems would be a valuable addition to the outbreak response toolkit. This paper makes some good progress towards these aims but I have several major concerns around validation and accuracy, which need to be resolved for this analysis/methodology to be convincing.
+
+-> We thank the reviewer for their appreciation of our work.
+
+1. The validation on simulated data is not yet sufficient. This is especially important for a paper
+proposing a new method. A couple more examples with different dynamics should be included and then some statistics computed to showcase accuracy (e.g., considering the lag and scaling between the true incidence and inferred correlate). In particular, the current example shows clear differences (t = 30-50 and t > 100) that need to be explained and accounted for before the claim of accuracy can be upheld.
+
+-> In Figure 1D, the apparent difference ('lag') may have been visually deceiving due to the scaling of the respective y-axes. We reran the simulations for additional accuracy analyses, this time with longer sequences but same settings. The re-running was necessary, since we found a small bug in the code (mapping filter in minimap), as outlined in response to Rev #1, comment 3. The resulting new Figure 1D-F does not show this “lag”. Other analyses in Supplementary Note 1 did NOT point towards systematic ‘lags’ in GInPipe’s estimates (more below). We also added a more qualitative analysis of apparent differences between simulations and incidence reconstructions in Fig. 1F, see also comment 9.
+
+-> We replaced ‘accurately’ in the manuscript, since accuracy may depend on the goal of the analysis. While we can compute correlation coefficients, we do not know the precise scaling factor between our incidence correlates and the true incidence, hence, it is currently difficult to quantify if, and how much the prediction is off in particular scenarios quantitatively. With regards to qualitative comparisons we added analyses (below and comment 9).
+
+-> More examples and analysis:
+
+a) We included a few additional countries (Supplementary Figure 3; see also response to Rev #2, comment 1), some with rather low sequencing coverage (Chile, India, South Africa). Generally, also based on the additional analyses, we would consider the method to perform well with real data.
+b) In terms of simulations, we performed additional tests, e.g. evaluating whether
+   i) a time-varying, drastic change in the sampling proportion (= sequencing coverage) has effects, Supplementary Note 1, section SN.1.8.
+
+We found that the sampling proportion does not affect the incidence reconstruction
+
+ii) Lag-time: We assessed whether GInPipe can reconstruct non-smooth pandemic dynamics (sudden increases or decreases of the number of infected individuals by several factors), Supplementary Note 1, section SN.1.13.
+
+We found that if the pandemic dynamics are too extreme (step function), a ‘smearing out’ may appear. This was however only observed for drastic increases of the number of infected individuals (Supplementary Note 1, Figure SN.21 therein). However, the tested step functions are likely more extreme than real pandemic curves.
+
+1) Lag times in \( \varphi \) in relation to *increasing population sizes during simulations* can occur when mutation rates are very low (in comparison to the population dynamics). In all applications of the method to real data, we do not observe this type of delay. I.e., \( \varphi \) typically increases before, or coinciding with increases in reported cases. Thus, we are confident that this lag does not occur for SARS-CoV-2.
+
+2) A lag time with regards to *decreasing population sizes during simulations* can arise when the variety of haplotypes persists despite decreasing population sizes. Therefore, this lag arises when the ‘renewal rate’ is low (rate to become noninfectious). The rate to become non-infectious is however large in SARS-CoV-2 (see also comment 5), such that we anticipate
+to observe a small 'lag effect' with SARS-CoV-2. We speculate that the 'apparent lags' when comparing to case reporting date (Fig 3), may actually be a result of the diagnostic behaviour, i.e. underreporting of cases after the peaks when people are 'tired of the pandemic'. For the third wave in Scotland we also performed additional analyses with Epilnf (Supplementary Figure 1; see also comment 4), which also predicted a more long-lasting third wave.
+
+iii) We also tested whether selection affects GlnPipe, Supplementary Note 1, section SN.1.14.
+
+We did not find major effects of selection on GlnPipe.
+
+iv) We tested whether biased sampling affects GlnPipe, Supplementary Note 1, section SN.1.9.
+
+We essentially found that when closely related sequences are more likely to be sampled, we see no systematic effects on GlnPipe. However, if the sampling of diversity changes over time (e.g. a switch from ‘random’ to ‘genetically similar’ sampling) the evolutionary signal becomes temporally distorted and incidence reconstructions are affected. We added some more remarks regarding this last point to the manuscript (see also Rev #1, comment 5).
+
+2. The approach to simulated epidemics also seems somewhat strange (especially given the use of the Wallinga-Teunis method later). Why not use a renewal model to more accurately simulate what an epidemic might look like (and which is the model behind the Wallinga-Teunis)? The key difference from the current approach would be the use of a generation time distribution (which is better suited for properly considering incidence on daily scales as the paper provides) rather than a simple branching process with fixed generations.
+
+-> We used the simulations only to generate data on which we can evaluate the GlnPipe method in silico (Supplementary Note 1). As pointed out by the reviewer, we used a minimalistic modelling approach for these simulation studies (see also Reviewer #1, comment 5). We chose the method (discrete time) because it is computationally efficient. Essentially, for the simulation studies in Supplementary Note 1 , ‘time’ (whether continuous on a real-, or virtual scale, or discrete) is not relevant. To illustrate this argument, we also performed simulations using exponentially distributed generation times (classical Markov Jump Process formalism) in Supplementary Note 1, section SN.1.10. Sampling from more complex generation times is also possible (e.g. PMID: 33899035, Fig. 1C therein, for example using the EXTRANDE algorithm), but will not affect any of the conclusions made in Supplementary Note 1, other than making the simulations more time-consuming. So, in essence, we are convinced that the simulation method is well-suited for the purpose of testing GlnPipe on simulated data.
+
+3. The comparisons of Re via BDSky and the Wallinga-Teunis approach do not seem that consistent – more analysis is needed, and the confidence intervals of both approaches do not seem that clear. While the need for piecewise constant Re from BDSky is understandable, there still are discrepancies that warrant a closer look.
+
+-> We agree with the reviewer that the comparison of Re from BDSky vs. GlnPipe is challenging. We, however, deliberately wanted to include the comparison with an entirely different method (BEAST) that utilizes the same data. Additionally, we are comparing independent measures (here Re) that, no matter the method used to infer them, should agree with one another. There are obvious differences in the methods such as a) the need for a piecewise constant Re in BDSKY vs. the
+ability to derive a continuous function in GInPipe. The largest source of discrepancy particularly early in the pandemic is our relatively crude clustering approach, please see also the answer to the next comment. For better comparability, we have now used our piecewise constant results from BDSKY to infer continuous incidence trajectories using the BEAST2 package Epilnf for Scotland (Supplementary Figure 1).
+
+4. Why not also compare the Ne with coalescent approaches? It does not appear the Ne from the method chosen has been considered against more standard approaches such as https://academic.oup.com/mbe/article/22/5/1185/1066885. It would be good to know if the correlation between Ne and incidence is general.
+
+Thank you for the suggestion. Many tree-based phylodynamic methods such as the one Bayesian coalescent skyline plot (BSP) suggested by the reviewer make the assumption that the phylogeny is a good approximation of the transmission tree. This is one of the reasons for the necessity to split the large country-wise data sets into clusters. In contrast to the BDSKY approach used here, the full data set cannot be analysed by joining all clusters (approximating independent introductions) into a single analysis, because the tree intervals cannot easily be adjusted to certain points in time to ensure the temporal alignment of separate trees. Thus, all sequences have to be analysed in one tree. This leads to the reconstruction of a large number of coalescent events outside the considered region, likely biasing the estimate of the effective population size over time (see also comment 11). We have nevertheless tried running BSP on the full trees, however, the method does not converge properly. This is most likely due to the large number of sequences, requiring the reconstruction of trees with over 2,000 tips.
+
+However, to provide a better comparison to the GInPipe incidence estimates, we have set up the BEAST2 package Epilnf (PMID: 31058982) to infer incidence trajectories over time from the results obtained from the presented BDSKY analyses (see point 3). As stated in the manuscript, setting up and performing phylodynamic analysis requires considerable expertise, fine-tuning and computational time to derive meaningful results, which altogether demanded the majority of time during revision. Therefore, we only did this for one country. The resulting incidence estimates from Epilnf for Scotland are shown in Supplementary Fig. 1. The comparison shows that Epilnf, GInPipe and reported cases agree overall. The Epilnf estimation for the epidemic waves one (April ‘20) seems to lag slightly behind, and wave two (November ‘20) is slightly underestimated in comparison with GInPipe and reported cases. Both Epilnf and GInPipe hint towards a longer lasting third wave (Jan ‘21) in Scotland. We also see an epidemic wave in August ‘20 for Epilnf that is not supported by the reporting data or using GInPipe. We suppose that this may be an artefact that is caused by the crude clustering of the sequences in phylodynamic analysis. As mentioned in the manuscript, the phylodynamic inference is very sensitive to clustering and it may not be possible to find a clustering setting that produces robust results for all different countries that were analysed in the manuscript (we chose one clustering approach for all BEAST analyses). We have revised the manuscript accordingly (Results: page 5, line 188 and Methods: page 14, section ‘Phylodynamic analyses’)
+
+5. The methods of https://royalsocietypublishing.org/doi/full/10.1098/rstb.2010.0060 have explicitly investigated relationships among Ne and prevalence/incidence. I think this paper should comment on those links since it proposes another correlation.
+
+-> If we understand the reviewer and the mentioned paper correctly, it is stated
+
+a) that coalescent times (and generation times * Ne) may correlate with incidence, but not with prevalence, which may be out of phase or temporally shifted.
+For SARS-CoV-2, the duration of infection is typically short, such that the temporal shift is very small (50% of infections are cleared a week after symptom onset (~diagnosis & sampling time), PMID: 33899034). However, we noted that ‘infected individuals’ is sometimes used ambiguously (i.e. referring to the cumulative number of individuals that have been infected). We therefore revised the manuscript and refer to either incidence or actively infected individuals.
+
+b) Secondly “In this model, as the time between infections changes, the use of a single transformation of time to fit the early stages of the epidemic results in an overestimation of the true number of infected individuals in the later stages.” . Please refer to the answer to the next comment.
+
+6. Some studies also noted that the generation time is effectively the time between infections (Pomeroy et al. 2008; van Ballegooijen et al. 2009), and not the duration of infectiousness, but did not recognize that this changes throughout an epidemic. Hence, a single transformation of time, which is commonly used to estimate Ne from temporally sampled sequence data, cannot be used to recover the ‘effective number of infected individuals’
+
+-> We thank the reviewer for this statement and hope that we understood the comment by the reviewer correctly. Regarding GlnPipe and following the discussion in the paper (PMID: 19910379), we agree with statements made therein. [For hepatitis B:] “A reduction in genetic diversity can be due to a decline in the number of infections but also to a shorter generation time or an increase in the average and variance of the number of secondary infections produced by one infective individual”.
+
+Shorter generation times: the statement above refers to an infection (Hepatitis B), which can be onwards transmitted either within weeks, or years after infection, i.e. there is an immense range of evolutionary time and selective pressure that shapes the viral quasispecies, before onwards transmission. Therefore, if the generation time for HBV shortens considerably, for example to weeks, the “evolutionary signal” would also be completely altered, as stated in PMID: 19910379. I.e., a variant that is onwards transmitted at later time points after infection may have diversified considerably from the founder virus, whereas an early transmitted variant may not.
+
+This is entirely different in SARS-CoV-2, where any within-host quasi-species dynamics have comparatively little impact on the transmitted variant (this is why SARS-CoV-2 mutates so little at the population level, compared to the fidelity of the RdRp; A similar observation has been made also for other respiratory infections, e.g. paramyxoviridae in PMID: 18217182). I.e., the virus may usually be transmitted before quasi-species break through, and the transmitted virus may usually be a result of (almost) clonal expansion of the founder virus, or a founder virus that acquired mutations during the first replication cycles. Because the transmitted virus usually already has very few (if at all) mutational differences with regards to the founder virus, further shortening of the generation time does not significantly impact on the genetics of the transmitted variant.
+
+We are aware of these differences between the distinct viruses (e.g. respiratory vs. sexually transmitted), and clearly state that we believe that GlnPipe only works for infections that are passed on within a very short time after infection on page 8. We also added a comment about super-spreaders on page 9 in the discussion.
+
+7. In the supplement the importance of binning strategies is noted. Can some comment in the main text be given for what selection approach was taken? Is there some good theoretical reason? The bias-variance trade-off of bins is well known at least for Ne https://academic.oup.com/sysbio/article-abstract/68/5/730/5307781. Can some related comment be made in the choices of this approach?
+-> Yes, this was potentially hard to find in the Supplementary Note 1 (last paragraph of section SN.1.5 in the original note). Essentially, on the one hand, the bins have to be large enough in order to contain enough mutational information, but on the other hand not too large such that the time resolution is sufficient (e.g. ‘peaks’ and ‘valleys’ within the population dynamic can still be captured). We added a corresponding statement to the methods section, page 12, paragraph ‘Construction of temporal sequence bins’.
+
+In Supplementary Note 1, section SN.15 we also further observe a relation between the mutation rate (~ evolutionary signal) and the bin size: If the mutation rate is lowered, the evolutionary signal per sequence is lowered and hence larger bins need to be chosen to contain enough ‘evolutionary signal’.
+
+8. We hypothesize that the genetic data alone holds information about the pandemic trajectory – I would remove this (as it is what makes phylodynamics as a whole useful) and go to the next line, which is the actual hypothesis specifically examined here.
+
+-> We modified the sentence accordingly without breaking the flow of the text (page 2, lines 47-48).
+
+The approach builds on recent work by Khatri and Burt... – could you add a line with some additional explanation here to improve readability for those unfamiliar with this paper? This is particularly helpful since this is a major point underlying the paper.
+
+-> Khatri & Burt: We have better clarified the relation to the paper by Khatri & Burt, as outlined in response to reviewer #1, comment 1.
+
+9. We observed a strong (r = 0.96)... This correlation is not as informative as it could be. A similar association but done per time point would be more useful to confirm if the seeming lag between the inferred and true Ne is upheld or an artefact. Such lags are important for a method providing incidence estimates given what of the key differences between incidence and reported cases is indeed the lag, the influence of which has been debated. E.g., see https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1008409
+
+-> We thank the reviewer for this feedback. We spend a lot of time investigating the ‘seeming lag’ (response to comment 1, Supplementary Note 1, section SN.1.13) and to better visualize the data. Regarding the latter, we decided to include an additional figure that compares the respective Re(t) estimates (which we estimate for each time point t). In particular, in the new Fig 1F one can see both the qualitative and quantitative congruence of the simulated- vs. reconstructed dynamics, i.e. for the upper right quadrant of Fig. 1F both dynamics are increasing (Re(t) > 1), for the lower right they are both decreasing (Re(t) < 1) and the off-diagonal elements denote qualitative mismatches. We hope that this additional representation satisfies the reviewer.
+
+10. Our analyses showed that the method can still accurately reconstruct incidence histories over time, when data is missing or when data sampling is unbalanced – this needs to be better explained and qualified/validated. It seems counterintuitive given that sampling is well known to be a major source of bias both in genetic data and case data (and for estimating either Re or Ne). If this claimed robustness does hold then it is worth including background for why this would be an advance/important trait of the method e.g., for case data/Re see
+https://academic.oup.com/aje/article/178/9/1505/89262?login=true and for genetic data/Ne https://academic.oup.com/mbe/article/37/8/2414/5719057?login=true
+
+-> Robustness to sampling Bias: We have performed quite a few additional simulations to test the effects of sampling on incidence reconstruction with GInPipe (see also response to comment 1). Basically,
+
+• In Supplementary Note 1, section SN.1.8, we show that the sampling proportion does not introduce any biases with regards to incidence reconstruction using GInPipe. In contrast, the same experiment would introduce biases in standard phylogenetic reconstruction as shown in https://academic.oup.com/mbe/article/37/8/2414/5719057?login=true (pointed out by the reviewer) but can be overcome by the epoch sampling skyline plot (ESP).
+• In Supplementary Figure 3, we show the incidence reconstruction for settings with much fewer viral sequences available (India, South Africa, Chile). In particular for South Africa, where the fewest sequences are available, the incidence reconstruction seems to be particularly good (in India we suspect quite large underreporting).
+• A possible limitation, which we included in the discussion (page 8/9), is sampling that affects the diversity, see also reviewer #1 comment 5. The corresponding simulations were conducted in Supplementary Note 1, section SN.1.9. This type of sampling severely manipulates the input ("evolutionary") signal, hence any method, including phylodynamic reconstruction is likely affected by this kind of manipulation.
+
+-> Importance of the method: We envision that GInPipe could serve as a complementary tool to case reporting data, in particular when the diagnostic surveillance infrastructure may be insufficient. We stated this utility of GInPipe in the abstract.
+
+11. Finally, we evaluated whether introductions of foreign sequences affect the reconstruction of incidence histories – this is another counterintuitive point since introductions/imports affect estimates of key epidemiological parameters as has been found across COVID-19. I think this needs more qualification and detail.
+
+-> Exactly! This is actually a particular strength of the proposed method over phylodynamic reconstructions, which are very sensitive to introductions.
+
+• The sensitivity of the phylodynamic methods with regards to introductions is caused by the attempt to coalesce the lineages. Obviously, introduced lineages would affect coalescent times and consequently estimates of epidemiological parameters derived from them (in our BEAST analyses we circumvented this issues by building separate phylogenies for the distinct lineages), see also comment 4.
+• The proposed method (GInPipe) does not coalesce lineages. Frankly, it does not even consider the relatedness of lineages. In essence, introductions will simply appear as additional haplotypes. In the (quite unrealistic case) that these introduced sequences (haplotypes) do not contribute to the pandemic, and represent a considerable proportion of all haplotypes (e.g. >> 10%; Supplementary Note 1, section SN.1.12, Figure SN.19 therein) the method may overestimate incidence. However, this extreme example is there to test the limits of the method, and very unlikely to ever be encountered with real data.
+
+12. For the second wave, reconstructed incidence histories correspond to the reported cases – this
+does not seem quite right as reported cases themselves do not correspond with the incidence. Please clarify what should be comparable.
+
+-> We reformulated the sentence. We meant to say that the profiles match (page 5, line 226).
+
+13. Taken together, these lines of evidence suggest that evolutionary change of SARS-CoV-2, the effective viral population size, and the number of infected people are correlated – could some more detail and intuition be provided to help readers understand why this correlation, which is the main assumption behind the method, is valid?
+
+-> We realized that the formulation may have been misleading and cryptic. We reformulated the corresponding paragraph and tried to explain better why we think that there is a link between the viral evolution that is observed in patient samples, and the number of infections for SARS-CoV-2. (page 8)
+
+14. Finally, we envision that the method will be particularly useful to estimate the extent of the SARS-CoV-2 pandemic in regions where diagnostic surveillance is insufficient for monitoring, but may still yield a few samples for sequencing – has this point been demonstrated as possible?
+
+-> Yes, thank you for raising this point. We added a few more countries (Japan, India, Chile and South Africa), some of which have little diagnostic surveillance, in Supplementary Figure 3 and added the corresponding text on page 6, starting in line 240 (see also comment 1 and Rev#2, comment 1)
+
+15. The reproductive number Re(t) ... was drawn from a log-normal distribution ... which is changed to N (48.8;1) after first control measures are implemented in the respective area – can some more intuition and explanation be provided for these choices?
+
+-> The reasoning behind the prior distributions that we set for the three epidemiological parameters is the following: Since we want to estimate the reproductive number, we have chosen a distribution that is rather uninformative in the range of parameters that are allowed. Therefore, we used the lognormal distribution, which does not assign any probability mass to values smaller than 0, and parameterized it with 0 and 4, yielding a prior mean for the reproductive number of 1 with a relatively high standard deviation. The become-uninfectious rate, in contrast, we do not aim to estimate and instead constrain it strongly to account for correlations between the BDSKY parameters. For COVID-19, the end of the infectious period lies, on average, at 13.5 days post infection (PMID: 33899034). Therefore, we use a strict prior centered around 27.1 per year (corresponding to a duration of infection of 13.5 days), namely the normal distribution with mean 27.1 and standard deviation 1, in the naive population. However, in all four countries considered here, strict non-pharmaceutical interventions (NPI) were implemented in early 2020 when case numbers continued to rise. These interventions included stay-at-home orders for people with respiratory symptoms and quarantining of infected and contact individuals, which reduces the time span where individuals could infect others. Since the become-uninfectious rate in our model captures the inverse of the effective duration of infectiousness, it is not only determined by the course of the disease, i.e. recovery or death, but also by the possible changes in behaviour leading to a decreased time of infectiousness. Here, we assume that after the implementation of first NPIs, infected individuals are being diagnosed and quarantined or start to self-quarantine on average 7.5 days after being infected. This corresponds to a rate to become uninfected of 48.8 per year.
+
+-> As discussed in response to comment 6, GlnPipe does not require these adjustments for the estimation of the incidence correlate.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+I appreciate the additional work that the authors have put into revising their manuscript and source code. I think there was some misunderstanding about what I meant by making the code more modular (i.e., compartmentalizing blocks of code into functions), but this largely boils down to divergent coding styles. Additionally, there seems to have been confusion about population dynamics that do not correspond to the assumptions of the model. I was referring to "sigmoidal" curves, not "sinusoidal". However, this is tied up in a more direct interpretation of Khatri and Burt's model, and it seems that the analogy is meant to be looser.
+
+I was a bit disappointed to learn that the theoretical underpinnings of the method are not well understood, making the method itself a bit of a "black box". Even so, the simulated and empirical findings are sufficiently convincing, and I look forward to seeing a more detailed investigation of the model in subsequent work.
+
+- Abstract, missing spaces "August2021" and "205million"
+- line 544, it is unusual to use uppercase in "InDels", usually this is written "indels".
+
+AP
+
+Reviewer #2:
+Remarks to the Author:
+I agree with the other reviewers that this paper describes an important and useful method which adds to the tools available for outbreak modelling when genomic-level data is available. The authors have thoughtfully addressed all my concerns.
+
+Reviewer #3:
+Remarks to the Author:
+I am pleased with the depth and focus of this revision. I particularly appreciate that the lag was found to be an artefact (which was a previous major concern) and enjoyed the additional sensitivity tests that were done. Results look much more robust now. One point the authors may consider in future is in upgrading their Re estimates from the classic WT. Recent approaches (e.g. EpiFilter, which appears to combine WT with EpiEstim) might likely smooth some of the fluctuations in Re that they found and aid comparison against BDSky.

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+Peer Review File
+
+Vanishing weekly hydropoeaking cycles in American and Canadian rivers
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+Authors analyze daily observed flow across 100 years over an increasing number of river sites, up to 400 in 2019. They specifically look into the weekly Hydropeaking Index, a novel index to quantify the week-end vs weekday river alterations. The robust statistical analysis demonstrates that the alterations increased from 1920 to about 1990, plateaued for a bit and have decreased since the 2010s. Authors discuss potential reasons for this decrease in the last decade, which include changes in demand, environmental regulation and new generation resources.
+
+Organization
+- The results and discussion section need re-organization. The results section presently focus on plain statistics with no maps, and lead to so many technical questions that are only answered in the SI and with no actually insight of what the actual result to be promoted is.
+- Some section in the methods and SI would actually enhance the flow of the paper. For example, the description of the area is necessary to support the current description in the results section. Also Fig 2 in SI actually tells the story of the paper and is more impactful than some of the maps in the main manuscript that tend to only show the data and support some specific examples.
+Technical Approach and impact of the paper on the community
+- In the introduction (L81-84), authors “conclude” that the “vanishing ” is due to changes in hydropower demand, environmental regulation and new generation resources. However those causes were not fully demonstrated, only discussed. I would suggest the authors to reframe this sentence with “probably due to ..” but most importantly focus on the impact of why it matters. May I suggest that this matters for the hydropower industry long term planning, but also for the power system operators. Specifically ”Does that mean that hydropower is “less flexible” or does that mean that hydropower flexibility is used differently?” The potential reasons brought forward by the authors could be categorized based on “who is affected by that result”, or other ways, to provide more clarity on why this paper is important.
+- The analysis focused on 400 sites, and authors discussed governances. In order to enhance the impact of the paper (who should be concerned by this result), showing trends in WHI by main river basin (hydrology, environmental regulation, level of regulation, etc) and by market regions, or grid, would provide more support to the discussion of potential causes for the regional trends. It would be more informative than by latitude and longitudes.
+- “Hydropower demand” throughout the paper - it would be more accurate to say “electricity demand ” that is changing due to changes in socio-economic development etc. The hydropower contribution (or generation) however is indeed influenced by the changes in generation portfolio, markets, environmental regulation and so on.
+- More potential causes– for example it is possible that with wind and solar the prices differences have changed and hydropower provide new types of services, such as capacity markets, which could affect the WHI index. Socio-economic development is pretty vague and could mean changes in water demands in general?
+- Authors presently mention that “spilling” is the reason for lower WHI during wet years. During a wet year, especially snowmelt period, the hydropower operators generate firm energy, i.e. reduced sub-daily peaking and very limited to none week-end/week day alterations. – it should be revised for completeness in the manuscript.
+
+Editing
+- In concluding remarks, L399, it
+- L429 – specify discharge at a daily time scale.
+- L512-514 – this is a nice and succinct description that could have made its way in the main part of the manuscript along with the description of the domain.
+- L524: DTF – spell out
+- L571 – WHIq was mentioned in the results section with no description. Again, figure 2 of SI would
+help in describing (and synthetizing) the impactful-take home message results.
+
+Reviewer #2:
+Remarks to the Author:
+The manuscript developed a novel weekly hydropoeaking index for quantifying the 1920-2019 intensity and prevalence of hydropoeaking cycles at 400 sites across the United States of America and Canada. The key finding is that there is a recent decline in weekly hydropoeaking cycles in the US and Canada. More importantly, the findings may have a broad impact across multiple disciplines. On one hand, the causes of this declined weekly hydropoeaking cycles can be attributed to factors from changing climate, socioeconomic shifts, alternative energy production, to legislative and policy changes. On the other hand, it has very significant ecohydrological implications. In short, the manuscript has revealed an important area which has a lot of potential to be explored in many ways. The manuscript is overall well-organized and well-written. The new index can be easily adopted in other regions across scales as long as long-term daily streamflows observations are available.
+There are a few areas which can be improved.
+1) It would be nice to compare the WHI before and after reservoir constructions. Since the weekly hydropoeaking cycles are directly driven by reservoir flow regulations, the first thing to check how it has changed after dam construction. Reservoir info can be acquired from databases such as GRanD.
+2) While most reservoirs have multiple functions, the manuscript has attributed the changes of hydropoeaking cycles to hydropower generation. Therefore, additional analysis which compares the WHI downstream of different types of reservoirs (by primary function) would be interesting. For instance, how do the WHI values downstream of irrigation reservoirs compare to those downstream of hydropower reservoirs?
+3) Some more quantitative investigations about the causes of the changed WHI would be necessary. Currently, multiple drivers for the decline have been pointed out. However, there is a lack of evidence on this regard. For instance, it is unclear what time period, spatial domain does the “above average precipitation” refer to. Although the alternative energy has increased, the hydropower generation hasn’t decreased much. In this sense, the flow regulation may not have changed much. Then, how to relate alternative energy to the finding?
+
+From Huilin Gao
+
+Reviewer #3:
+Remarks to the Author:
+place this table by a figure.
+Review of paper “Vanishing weekly hydropeaking cycles in American and Canadian rivers”
+
+The authors propose a new WHI index to analyze weekly fluctuations in daily flows in regulated rivers (400 sites) in the United States and Canada to illustrate the decrease in flows that take place on weekends (Saturday and Sunday) downstream from dams. Results from analyzing flows at 400 sites over the 1920-2019 period show that there is an increase in the number of sites showing such decrease in flows since 1920, reaching a maximum in 1963, followed by a significant decline until 2019. These changes are due to climate- and human-related factors.
+
+Originality of the work
+
+The development of the WHI index and its application to a large number of sites in the United States and Canada in order to highlight this decrease in stream flows is, in my mind, a perfectly original scientific contribution to the study of the impacts of dams worldwide. In addition, the issue of flow fluctuations on weekend days is also an original contribution to the study of the impacts of dams. The authors have shown that this variation in flows results from the interaction of numerous climate and human factors, thereby highlighting the complex nature of factors affecting streamflow downstream from dams. There is no doubt that the results are of great scientific interest for understanding better the impacts of flow management on the function and hydromorphological and hydroecological evolution of stream ecosystems downstream from dams. As such, they are contributing to the development of flow requirements for the management, restauration and conservation of these anthropized ecosystems.
+
+Review of the paper
+
+1. Statistical methods used
+- Regarding the interannual variability of the WHI index, the authors only considered the influence of autocorrelation on the significance of the MK (Mann-Kendall) test even though, when analyzing long data series (1920-2019), they definitely should consider the influence of the persistence phenomenon affecting the long series by applying the LMK test. In fact, the presence of persistence weakens the MK test (see, among others, Kumar et al., 2009; Dinpashoh et al., 2014).
+- The MK method does not detect breaks in mean values nor discriminate between sharp and gradual variance values. A statistical test that allows objective detection of breaks in mean values of the analyzed series (e.g., Pettitt, Lombard test) must be used, making it possible to determine rigorously the dates of shifts in mean values of the WHI index.
+- It would be useful to apply a classification method (e.g., bottom-up hierarchical classification) to WHI index values to subdivide the 400 sites in classes to improve their characterisation and description.
+2. Results
+
+Table 1 should be replaced with a table showing the result of all values of the WHI index derived for the 400 sites. See an example
+
+<table>
+  <tr>
+    <th>Indice</th>
+    <th>Number of sites</th>
+    <th>% of sites</th>
+    <th>Sites in USA (%)</th>
+    <th>Sites in Canada (%)</th>
+  </tr>
+  <tr><td>&gt;3.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>3.0 – 3.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>2.5 – 3.0</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>2.0 – 2.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>1.5 – 2.0</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>1.0 1.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>0.5 – 1.0</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>0.0 – 0.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>-0.5 – 0.0</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>-1.0 --0.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>-1.5 - -1.0</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>-2.0 - -1.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>-2.5 - -2.0</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>-3.0 - -2.5</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>-3.5 - -3.0</td><td></td><td></td><td></td><td></td></tr>
+  <tr><td>&lt; -3.5</td><td></td><td></td><td></td><td></td></tr>
+</table>
+
+N.B. It may be preferable to replace this table by a figure.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Authors analyze daily observed flow across 100 years over an increasing number of river sites, up to 400 in 2019. They specifically look into the weekly Hydropoeaking Index, a novel index to quantify the week-end vs weekday river alterations. The robust statistical analysis demonstrates that the alterations increased from 1920 to about 1990, plateaued for a bit and have decreased since the 2010s. Authors discuss potential reasons for this decrease in the last decade, which include changes in demand, environmental regulation and new generation resources.
+
+We sincerely thank Reviewer #1 for the thoughtful and constructive comments provided in this report on our paper. We address each of Reviewer #1’s comments with a point-by-point response in bold lettering. Thank you for taking the time to carefully read and review our manuscript as we feel that by addressing these comments our paper is now much stronger.
+
+Organization
+
+- The results and discussion section need re-organization. The results section presently focus on plain statistics with no maps, and lead to so many technical questions that are only answered in the SI and with no actually insight of what the actual result to be promoted is.
+
+We acknowledge that the prior version of the manuscript included a considerable amount of statistics on the WHI. Given the WHI is a novel metric introduced in this paper, we judge it critical to report on the overall statistics of the WHI so that the reader can gauge its central tendency, dispersion, and range across the 500 sites of interest and over time. Furthermore, these statistics are first reported in the Results section (now after the study area description) to provide baseline information for the interpretation of the spatio-temporal variability of the WHI across the USA and Canada. Thus the revised text retains a subset of the statistics reported in an earlier version of the paper; however, we have shifted the result of the Shapiro-Wilk test to the Supplementary Information. As well, we have deleted the Cullen and Frey graph (Supplementary Figure 1 in the initial submission), and the skewness and kurtosis values to reduce the amount of statistics presented in the first part of the Results section. Other parts of the paper have also been revised and restructured to further promote the key message of declining WHI trends across the USA and Canada.
+
+Three of the four main figures in the original paper are maps depicting spatial plots of the WHI. Thus there are quite a few maps (along with several others in the Supplementary Information) to visualize and interpret the WHI results aside from the statistics presented in the paper. Due to the strict length limitation of Nature Communications (main text of 5,000 words or less) and our strong desire to provide a comprehensive analysis of the WHI results, many technical aspects are relegated to the Supplementary Information. Our Results section builds strongly the case for the study’s main findings of vanishing weekly hydropeaking cycles in the USA and Canada, namely in the temporal evolution and trend
+analysis subsection. Our findings are further promoted in the Discussion where we invoke several possible reasons for the declines in weekly hydropeaking cycles in the study domain.
+
+Please also see our response to the next comment regarding some additional restructuring of the paper.
+
+- Some section in the methods and SI would actually enhance the flow of the paper. For example, the description of the area is necessary to support the current description in the results section. Also Fig 2 in SI actually tells the story of the paper and is more impactful than some of the maps in the main manuscript that tend to only show the data and support some specific examples.
+
+We agree some of the material in the Supporting Information (previously Supplementary Figure 2) and in the Methods is more appropriate for the main body of the paper. In response to this comment, we have now shifted content describing the study area previously introduced in the Methods to the first paragraph in the Results section (lines 93-105). The plot illustrating the time series of mean annual WHI and other important metrics now forms part of the Results section (as the revised Figure 3) rather than in the Supplementary Information.
+
+Technical Approach and impact of the paper on the community
+
+- In the introduction (L81-84), authors “conclude” that the “vanishing” is due to changes in hydropower demand, environmental regulation and new generation resources. However those causes were not fully demonstrated, only discussed. I would suggest the authors to reframe this sentence with “probably due to ...” but most importantly focus on the impact of why it matters. May I suggest that this matters for the hydropower industry long term planning, but also for the power system operators. Specifically “Does that mean that hydropower is “less flexible” or does that mean that hydropower flexibility is used differently?” The potential reasons brought forward by the authors could be categorized based on “who is affected by that result”, or other ways, to provide more clarity on why this paper is important.
+
+Indeed, our work only discusses possible reasons leading to recent declines in weekly hydropeaking cycles across Canada and the USA. Without an extensive database of electricity generation and other information regarding socioeconomic activity, policy and governance changes (among other factors), it is impossible to pinpoint the exact causes of the recent WHI declines reported in our work. Nonetheless, we anticipate this will motivate other studies that may well tackle these issues in a more comprehensive way, as this remains beyond the scope of the present effort. Note, however, that in response to a comment from Reviewer #2 we have inserted some additional material to back up statements in regards to possible factors leading to recent WHI declines.
+
+To address this comment, we have replaced the word “conclude” with “propose” on line 86 and inserted “likely” before “contributing factors” on line 89 in the final paragraph of the Introduction.
+As raised by Reviewer #1, the previous version of the manuscript did not properly convey why this work is important in the Introduction. In response to this, we have added a sentence at the end of the third paragraph of the Introduction that reads as follows: “Aside from their ecohydrological impacts, changes in hydropoeaking remain key concerns for long term planning within the hydropower industry, system operators, and water resources managers.”
+
+- The analysis focused on 400 sites, and authors discussed governances. In order to enhance the impact of the paper (who should be concerned by this result), showing trends in WHI by main river basin (hydrology, environmental regulation, level of regulation, etc) and by market regions, or grid, would provide more support to the discussion of potential causes for the regional trends. It would be more informative than by latitude and longitudes.
+
+Water management and governance occur on multiple levels leading to complex interactions with impacts to hydropower production and hence hydropoeaking cycles. Indeed, water management and governance occur within and across legislative / political boundaries (e.g. provincial, state-wide, federal), at the watershed scale, and by market regions. Given this work emphasizes hydropoeaking cycles emerging from hydropower production, we have added to the map of the study area the principal power grid interconnections of the USA and Canada (see Supplementary Figure 14a).
+
+To avoid cluttering the plots depicting spatial results for the WHI values, only the map of the study area shows the power grid interconnections. However, the spatial plots retain the primary provincial, state, and federal boundaries to allow interpretation of the results across political jurisdictions. Primary waterways are also identified on the maps to infer results at the watershed scale. The paper retains Supplementary Figure 14b-e illustrating the distribution of latitudes, longitudes, gauged areas and mean annual discharges for the 500 sites as primary metadata to our analyses.
+
+Cross comparison of the primary power grid interconnections (Supplementary Figure 14a) with the map depicting spatial trends in WHI (Figure 5) reveals that most of the negative WHI trends lie within the Western Electricity Coordinating Council (WECC), Northeast Power Coordinating Council (NPCC) and SERC Reliability Corporation (SERC) synchronous grids. Therefore, a statement has been added at lines 232-234 that identifies the primary power grid interconnections where negative WHI trends emerge: “Clusters of negative WHI trends lie primarily within the Western Electricity Coordinating Council, Northeast Power Coordinating Council and SERC Reliability Corporation power grid interconnections.” In a future effort, we anticipate tackling in more detail the causality of recent declines in weekly hydropoeaking cycles including links to market regions and power grid interconnections.
+
+- “Hydropower demand” throughout the paper - it would be more accurate to say “electricity demand” that is changing due to changes in socio-economic development etc. The hydropower contribution (or generation) however is indeed influenced by the changes in generation portfolio, markets, environmental regulation and so on.
+We agree with the reviewer’s comment that it is not only hydropower demand that is changing in response to socioeconomic development and other factors. As such we have replaced the word “hydropower” with “electricity” where relevant to generalize this statement throughout the manuscript.
+
+- More potential causes– for example it is possible that with wind and solar the prices differences have changed and hydropower provide new types of services, such as capacity markets, which could affect the WHI index. Socio-economic development is pretty vague and could mean changes in water demands in general?
+
+Recent reductions in the costs for solar and wind energy production may have resulted in hydropower providing new types of services such as capacity markets. A statement to that effect is now included in the first paragraph of the discussion (see lines 312-314). The term “socioeconomic development” is purposefully vague to account for the multitude of factors (e.g. a shifting manufacturing sector, globalization, lifestyle changes, commercial and industrial activity, etc.). Rather than attempting to provide an exhaustive list of these potential factors, the text retains the term “socioeconomic factors” in several instances.
+
+- Authors presently mention that “spilling” is the reason for lower WHI during wet years. During a wet year, especially snowmelt period, the hydropower operators generate firm energy, i.e. reduced sub-daily peaking and very limited to none week-end/week day alterations. – it should be revised for completeness in the manuscript.
+
+This is a very interesting point raised by Reviewer #1 that certainly merits further investigation. Some preliminary analyses do suggest that the weekly hydropeaking cycles experience seasonality, perhaps as hydropower generating stations shift from peaking plants to firm energy production depending on water availability. We anticipate tackling this issue in a future effort for which we will explore the seasonality of the WHI across all sites depending on water availability. In the meantime, to ensure completeness of the manuscript in regards to the impacts of wet/dry spells on hydropeaking cycles, a statement has been added to the Discussion (lines 333-335) as follows: “Alternatively, wet years may lead utilities to generate continuous baseload energy instead of peaking hydropower, inducing a similar effect.”
+
+Editing
+
+- In concluding remarks, L399, it
+
+It is unclear from this statement what text should be modified on line 399 of the manuscript. As such, no modification to the text is implemented based on this comment.
+
+- L429 – specify discharge at a daily time scale.
+
+We have inserted “daily” prior to “discharge” on line 467.
+- L512-514 – this is a nice and succinct description that could have made its way in the main part of the manuscript along with the description of the domain.
+
+Thank you for this comment, we have incorporated a similar statement in the third paragraph of the Introduction (see lines 80-82): “We show that the WHI captures well the typical weekly rhythm observed in hydropoeaking rivers, with low flows on weekends when hydropower demand wanes then high flows on weekdays when hydropower demand waxes.”
+
+- L524: DTF – spell out
+
+The abbreviation “DFT” for Discrete Fourier Transform has been deleted from the paper including at lines 535, 563, and 565-566.
+
+- L571 – WHIq was mentioned in the results section with no description. Again, figure 2 of SI would help in describing (and synthetizing) the impactful-take home message results.
+
+Thank you for this remark. A definition of the discharge-weighted WHI is now included where this is introduced in the Results section (see lines 174-177). For completeness, the mathematical definition (Equation 5) is retained in the Methods section of the paper (line 617). The plot depicting the time series of various WHI metrics including the discharge-weighted values is now part of the main paper (as revised Figure 3).
+Reviewer #2 (Remarks to the Author):
+
+The manuscript developed a novel weekly hydropeaking index for quantifying the 1920-2019 intensity and prevalence of hydropeaking cycles at 400 sites across the United States of America and Canada. The key finding is that there is a recent decline in weekly hydropeaking cycles in the US and Canada. More importantly, the findings may have a broad impact across multiple disciplines. On one hand, the causes of this declined weekly hydropeaking cycles can be attributed to factors from changing climate, socioeconomic shifts, alternative energy production, to legislative and policy changes. On the other hand, it has very significant ecohydrological implications. In short, the manuscript has revealed an important area which has a lot of potential to be explored in many ways. The manuscript is overall well-organized and well-written. The new index can be easily adopted in other regions across scales as long as long-term daily streamflows observations are available.
+
+Our sincere thanks to Reviewer #2 for this positive overview of our manuscript and for the most helpful and constructive comments provided in this report. We address each of the three comments with point-by-point responses below using bold text. Given in part the request to include some additional results on the impacts of dams and reservoirs on the weekly hydropeaking index (WHI) values, our database has been augmented to 500 sites. By addressing these comments, we firmly believe our paper has significantly improved. Thank you kindly for your time and effort in providing this report on our manuscript.
+
+There are a few areas which can be improved.
+
+1) It would be nice to compare the WHI before and after reservoir constructions. Since the weekly hydropeaking cycles are directly driven by reservoir flow regulations, the first thing to check how it has changed after dam construction. Reservoir info can be acquired from databases such as GRanD.
+
+As we compute the weekly hydropeaking index (WHI) each year at all sites, it responds to the commissioning of new hydropower infrastructure and other factors that impact hydropeaking. This is evident in Supplementary Figure 13 that illustrates how rivers of northern Canada including the Churchill, La Grande, Nelson and Peace, jump from large negative to large positive WHI values once hydropower dams are commissioned. Vertical red lines denoting the years when hydropower facilities were commissioned have been added to this plot to better illustrate this feature in our WHI time series.
+
+Given the importance of hydropower infrastructure on the WHI results, we have added a new paragraph in the Results section addressing the influence of dam commissioning on WHI evolution. Specifically, we now present time series of annual WHI for 1920-2019 at 14 hydroelectric dams operated by the Tennessee Valley Authority (TVA). Most of these dams were built in the early part of the 20th century and upon commissioning yield abrupt inclines in WHI (Supplementary Figure 5 reproduced as Figure R1 below). For instance, the inception of the Blue Ridge Dam on the Toccoa (Ocoee) River induces a sharp rise in WHI from 0.464 in 1930 to 2.684 in 1931, with elevated WHI scores thereafter. At other sites such as Apalachia Dam on the Hiwassee River, however, dam commissioning leads to
+little change in WHI. Apalachia Dam is a run-of-river facility with flows regulated mainly at the upstream Hiwassee Dam that has considerable flood storage capacity (0.253 km^3). Lines 243-252 in the Results section describe how dam commissioning and operation dictate WHI evolution in regulated waterways in the Tennessee Valley.
+
+![Temporal evolution of annual WHI at 14 sites with hydropower dams managed by the Tennessee Valley Authority, 1920-2019. Vertical red lines denote commissioning years of hydropower dams at the gauging site.](page_370_682_1042_496.png)
+
+Figure R1: Temporal evolution of annual WHI at 14 sites with hydropower dams managed by the Tennessee Valley Authority, 1920-2019. Vertical red lines denote commissioning years of hydropower dams at the gauging site (https://www.tva.com/energy/our-power-system/hydroelectric). Note that Great Falls Dam on the Caney Fork River was commissioned in 1916 explaining the absence of a vertical red line in that panel.
+
+2) While most reservoirs have multiple functions, the manuscript has attributed the changes of hydropeaking cycles to hydropower generation. Therefore, additional analysis which compares the WHI downstream of different types of reservoirs (by primary function) would be interesting. For instance, how do the WHI values downstream of irrigation reservoirs compare to those downstream of hydropower reservoirs?
+
+The presence of an upstream reservoir from a gauging site may also influence the weekly hydropeaking cycles. Here, we employ a subset of 14 waterways with different types of reservoirs examined by Ferrazzi et al. (2021). For sites with upstream reservoirs managed, at least in part, for hydropower production, the WHI generally stays elevated at positive values. In contrast, for sites downstream of reservoirs serving other functions (see Table
+R1), WHI oscillates near zero (see Figure R2). Thus the type of reservoir along with dam operations play a distinct role on the temporal evolution of the WHI.
+
+Table R1: Alphabetical list of 14 reservoirs with gauging sites on rivers part of our extended database (information sourced from Ferrazzi et al. 2021).
+
+<table>
+  <tr>
+    <th>Reservoir</th>
+    <th>River</th>
+    <th>Capacity (Mm<sup>3</sup>)</th>
+    <th>Type*</th>
+  </tr>
+  <tr>
+    <td>Allegheny</td>
+    <td>Allegheny</td>
+    <td>1,460</td>
+    <td><b>FPAQRW</b></td>
+  </tr>
+  <tr>
+    <td>Cannonsville</td>
+    <td>WB Delaware</td>
+    <td>362</td>
+    <td>S</td>
+  </tr>
+  <tr>
+    <td>Carters</td>
+    <td>Coosawattee</td>
+    <td>583</td>
+    <td><b>FP</b></td>
+  </tr>
+  <tr>
+    <td>Cave Run</td>
+    <td>Licking</td>
+    <td>757</td>
+    <td>FQRW</td>
+  </tr>
+  <tr>
+    <td>Green</td>
+    <td>Green</td>
+    <td>892</td>
+    <td>FSAQR</td>
+  </tr>
+  <tr>
+    <td>Mark Twain</td>
+    <td>Salt</td>
+    <td>1,760</td>
+    <td><b>FNPRSW</b></td>
+  </tr>
+  <tr>
+    <td>Perry</td>
+    <td>Delaware</td>
+    <td>950</td>
+    <td>FSRWX</td>
+  </tr>
+  <tr>
+    <td>Philpott</td>
+    <td>Smith</td>
+    <td>393</td>
+    <td><b>FPR</b></td>
+  </tr>
+  <tr>
+    <td>Pomme de Terre</td>
+    <td>Pomme de Terre</td>
+    <td>802</td>
+    <td>FRWX</td>
+  </tr>
+  <tr>
+    <td>Raystown</td>
+    <td>Juniata</td>
+    <td>940</td>
+    <td><b>FPRW</b></td>
+  </tr>
+  <tr>
+    <td>Shelbyville</td>
+    <td>Kaskaskia</td>
+    <td>844</td>
+    <td>FSNRW</td>
+  </tr>
+  <tr>
+    <td>Stockton</td>
+    <td>Sac</td>
+    <td>2,060</td>
+    <td><b>FPRW</b></td>
+  </tr>
+  <tr>
+    <td>Waterbury</td>
+    <td>Little</td>
+    <td>46</td>
+    <td><b>FRP</b></td>
+  </tr>
+  <tr>
+    <td>Zoar</td>
+    <td>Housatonic</td>
+    <td>33</td>
+    <td>P</td>
+  </tr>
+</table>
+
+*Reservoir functions are: flood control (F), urban water supply (S), hydropower production (P), low flow augmentation (A), navigation (N), wildlife preservation (W), water conservation and sedimentation (X), water quality control (Q), and public recreation (R).
+Figure R2: Temporal evolution of annual WHI at 14 sites with upstream reservoirs with different functions (see Table R1), 1920-2019. Red lines denote sites with an upstream reservoir managed, at least in part, for hydroelectricity production.
+
+We have added text on the impacts of reservoirs, depending on their functions, to the Results section following the description of dam commissioning and operation, on lines 252-256. Table R1 and Figure R2 are also included in the Supplementary Information (Supplementary Table 7 and Supplementary Figure 6).
+
+3) Some more quantitative investigations about the causes of the changed WHI would be necessary. Currently, multiple drivers for the decline have been pointed out. However, there is a lack of evidence on this regard. For instance, it is unclear what time period, spatial domain does the “above average precipitation” refer to. Although the alternative energy has increased, the hydropower generation hasn’t decreased much. In this sense, the flow regulation may not have changed much. Then, how to relate alternative energy to the finding?
+
+Correct, we invoke in our Discussion a number of potential causes for the recent WHI declines. This includes: 1) a generally wet decade in the 2010s; 2) socio-economic shifts such as increases in commercial and industrial activity on weekends; 3) shifts towards other modes of electricity production (e.g. renewable resources such as wind, wave and solar energy); 4) deregulation of electricity production and power grid interconnections; 5) legislative and policy changes affecting water management (e.g. increased concern for
+ecological, environmental and cultural flows). We concur that providing more concrete evidence for the reductions in WHI is highly desirable; however, obtaining all of the data to undertake these analyses is beyond the scope of the present effort.
+
+To address the Reviewer’s comment, we provide some additional information in regards to points 1), 3), and 4) outlined in the previous paragraph. First, we have added the spatial distribution of the standardized discharge anomalies in the 2010s, which was a wet decade relative to others between the 1920s to 2000s across the northern two-thirds of the study area (see Supplementary Figure 8b included as Figure R3 below). As discussed in the paper, this may have led dam operators to spill greater amounts of water and/or to generate firm energy rather than peaking hydropower, abating the weekly hydropeaking cycles.
+
+![Spatial distribution of decadal standardized discharge anomalies at 500 sites across the USA and Canada, 2010-2019. Negative values indicate relatively dry conditions while positive values denote relatively wet conditions.](page_186_670_1207_670.png)
+
+Figure R3: Spatial distribution of decadal standardized discharge anomalies at 500 sites across the USA and Canada, 2010-2019. Negative values indicate relatively dry conditions while positive values denote relatively wet conditions.
+Furthermore, there has been explosive growth in the generation of electricity from non-hydro renewable resources in the last decade in both the USA and Canada (Figure R4). Indeed, non-hydro renewable energy production jumped from \(203.5 \times 10^6\) kWh in 2010 to \(603.6 \times 10^6\) kWh in 2020 by which time it comprised 12.9% of overall electricity generation in the USA and Canada combined. The emerging availability of renewable sources of electricity such as solar, wind and wave energy diminishes the reliance on hydropower to match peak demand. For instance, solar energy potential peaks during midday when electricity demand is high. It is also evident in Figure R4 that the production of hydroelectricity has remained stable in the USA but continued to expand in Canada through the 2010s. Indeed, the generation of hydropower increased by \(66.0 \times 10^6\) kWh between 2010 and 2020 in the USA and Canada combined even as the weekly hydropeaking cycles diminished in intensity.
+
+![Annual cumulative electricity generation (kWh, left or %, right) for four types of electricity production in (a, b) the USA, (c, d) Canada, and (e, f) the USA and Canada combined, 1980-2020.](page_172_670_1207_627.png)
+
+Figure R4: Annual cumulative electricity generation (kWh, left or %, right) for four types of electricity production in (a, b) the USA, (c, d) Canada, and (e, f) the USA and Canada combined, 1980-2020. Note the different y-axis scales in panels (a), (c) and (e). There is a rapid expansion of non-hydro renewable sources of electricity in the 2010s across all regions. Data are sourced from the U.S. Energy Information Administration (http://iea.org).
+Plotting the annual electricity production from non-hydro renewable sources vs. the mean annual WHI across Canada and the USA over a 40-year period reveals a statistically-significant anti-correlation (Figure R5). While this statistical relationship does not equate to cause and effect, it does suggest that the rapid emergence of non-hydro renewable sources of energy may play a leading role in the diminishing weekly hydropoeaking cycles.
+
+![Scatter plot showing annual non-hydro electricity production vs. mean annual WHI, with a linear regression line and equation Y = -0.000806X + 0.243](page_312_573_900_600.png)
+
+Figure R5: Annual non-hydro electricity production across the USA and Canada combined vs. the mean annual WHI at 500 sites, 1980-2019. The thick line denotes the linear regression with \( R = -0.82, p < 0.05 \).
+Synchronous power grid interconnections, deregulation and the centralization of electricity dispatching may also yield reductions in WHI. As reported in the Discussion, the commissioning of the Churchill Falls hydropower plant in the early 1970s followed by the James Bay Hydroelectric Complex in the early to mid-1980s shifted the presence of hydropeaking from rivers in southern to northern Québec and Labrador. With the continued expansion of electricity exports from Canada to the USA (see Figure R6) through the international power grid interconnections, this also likely precipitated a reduction in the number of hydropeaking sites in the northern USA.
+
+![Line graph showing total annual electricity exports (10^6 kWh) from Canada to the USA, 1980-2019](page_340_563_1002_482.png)
+
+Figure R6: Total annual electricity exports (10^6 kWh) from Canada to the USA, 1980-2019. Data are sourced from the U.S. Energy Information Administration (http://iea.org).
+
+Based on these examples, there is evidence that the relatively wet 2010s, the expansion of non-hydro renewable sources of electricity, and integration within the electricity markets are contributing factors to diminishing weekly hydropeaking cycles in parts of North America. Socioeconomic determinants along with legislative, policy and water management changes do require additional investigation to confirm their role in vanishing weekly hydropeaking cycles. Nevertheless, our study provides two concrete examples on how modifications in water management influences the WHI: 1) the Sturgeon River in northern Michigan’s Upper Peninsula experienced a sharp decrease in WHI when the Prickett hydroelectric facility switched operations from peaking to run-of-river power production
+(Auer et al. 1996); 2) the Churchill River at Churchill Falls Powerhouse in Labrador observed a step decrease in WHI in 1997 related to electricity markets and a change in water management in that system (see Supplementary Figures 10 and 13).
+
+The revised manuscript now includes these additional sources of information to further back the statements on possible causes for the vanishing weekly hydropoeaking cycles in the USA and Canada.
+
+From Huilin Gao
+
+We sincerely thank Dr. Gao for these constructive comments that has led to a much improved paper.
+Reviewer #3 (Remarks to the Author):
+
+Review of paper “Vanishing weekly hydropeaking cycles in American and Canadian rivers”
+
+The authors propose a new WHI index to analyze weekly fluctuations in daily flows in regulated rivers (400 sites) in the United States and Canada to illustrate the decrease in flows that take place on weekends (Saturday and Sunday) downstream from dams. Results from analyzing flows at 400 sites over the 1920-2019 period show that there is an increase in the number of sites showing such decrease in flows since 1920, reaching a maximum in 1963, followed by a significant decline until 2019. These changes are due to climate- and human-related factors.
+
+Originality of the work
+
+The development of the WHI index and its application to a large number of sites in the United States and Canada in order to highlight this decrease in stream flows is, in my mind, a perfectly original scientific contribution to the study of the impacts of dams worldwide. In addition, the issue of flow fluctuations on weekend days is also an original contribution to the study of the impacts of dams. The authors have shown that this variation in flows results from the interaction of numerous climate and human factors, thereby highlighting the complex nature of factors affecting streamflow downstream from dams. There is no doubt that the results are of great scientific interest for understanding better the impacts of flow management on the function and hydromorphological and hydroecological evolution of stream ecosystems downstream from dams. As such, they are contributing to the development of flow requirements for the management, restauration and conservation of these anthropized ecosystems.
+
+Thank you for this positive overview of our manuscript and for highlighting the novel aspects of this research. We address the comments in this report point-by-point below using a bold font. We appreciate the very informative and constructive comments provided by Reviewer #3 on our work, which has led to a much improved paper.
+
+Review of the paper
+
+1. Statistical methods used
+- Regarding the interannual variability of the WHI index, the authors only considered the influence of autocorrelation on the significance of the MK (Mann-Kendall) test even though, when analyzing long data series (1920-2019), they definitely should consider the influence of the persistence phenomenon affecting the long series by applying the LMK test. In fact, the presence of persistence weakens the MK test (see, among others, Kumar et al., 2009; Dinpashoh et al., 2014).
+
+Thank you for this comment on the influence of autocorrelation and long-term persistence on trend detection using the Mann-Kendall test (MKT). Please first note that the MKT is applied only to the focused study period of 1980-2019 and not to the entire century for which at least partial data are available at the selected sites (see Figure 5). Nonetheless, we concur that serial correlation can diminish the true significance of the monotonic trends inferred by MKT. To that end, we follow Yue et al. (2002) in removing the lag-1
+autocorrelation, or AR(1), in the WHI time series when statistically-significant (\( p < 0.05 \)) local trends are inferred.
+
+Following the steps outlined by Yue et al. (2002), we obtain 26 sites where the detrended WHI times series have statistically-significant AR(1) values in the presence of locally statistically-significant MKT trends. After pre-whitening the time series we find that only one site, the English River at Manitou Falls, no longer exhibits a locally statistically-significant trend (\( p = 0.065 \)). Thus mitigating the effects of the lag-1 serial correlation on the trend analysis does not alter our main conclusion that a large number of sites across the USA and Canada exhibit significant declines in WHI from 1980-2019.
+
+As an example, Figure R7 illustrates the original WHI time series at four sites exhibiting statistically-significant lag-1 autocorrelations as well as positive (b and c) and negative (a and d) trends (\( p < 0.05 \)) based on the MKT. The trend-free pre-whitening of the WHI time series according to the methodology outlined by Yue et al. (2002) removes the lag-1 serial correlation component while retaining the linear trends.
+
+![Time series of the original and pre-whitened WHI for four sites](page_340_670_900_600.png)
+
+Figure R7: Time series of the original and pre-whitened WHI for (a) the Chattahoochee River, (b) Colorado River at Lees Ferry, (c) English River at Manitou Falls, and (d) Kootenai River, 1980-2019. While all original, detrended WHI time series exhibit statistically-significant AR(1), none of the pre-whitened time series has AR(1) with \( p < 0.05 \).
+Nonetheless, further analysis of the detrended WHI time series reveals some statistically-significant autocorrelations at lags 2 or higher at six sites where the MKT reveals trends with \( p < 0.05 \). These sites are: the Cowlitz, Michipicoten, Montreal (Lake Superior), Obey, Sacandaga and Tallapoosa rivers (Table R2). Thus the section on the impacts of serial correlation on the trend analysis in the Supplementary Information (lines 290-296) now includes details of the sites where long-term persistence may play a role on the significance of the trend results. A paragraph has been added to address this issue as follows:
+
+“Several studies\(^{5-8}\) suggest that long-term persistence (beyond lag-1 autocorrelation) may also lead to overestimation of trend significance in hydrometeorological variables. Further analysis reveals that only six sites with statistically-significant trends (two positive and four negative) also exhibit autocorrelations with lag-2 or higher with \( p < 0.05 \) in their detrended WHI time series. Thus care is required when interpreting the significance of the trends for the Cowlitz, Michipicoten, Montreal (Lake Superior), Obey, Sacandaga and Tallapoosa rivers given the presence of long-term persistence in their WHI time series.”
+
+Table R2: Six sites where the Mann-Kendall test reveals statistically-significant trends in WHI in the presence of statistically-significant autocorrelations (lag 2 or higher) in detrended WHI time series, 1980-2019.
+
+<table>
+  <tr>
+    <th>Site</th>
+    <th>WHI Trend Magnitude (year<sup>-1</sup>)</th>
+    <th>\( p \)-value</th>
+  </tr>
+  <tr>
+    <td>Cowlitz</td>
+    <td>5.09 × 10<sup>-2</sup></td>
+    <td>8.84 × 10<sup>-5</sup></td>
+  </tr>
+  <tr>
+    <td>Michipicoten</td>
+    <td>-7.40 × 10<sup>-2</sup></td>
+    <td>1.42 × 10<sup>-3</sup></td>
+  </tr>
+  <tr>
+    <td>Montreal (Lake Superior)</td>
+    <td>-4.33 × 10<sup>-2</sup></td>
+    <td>7.58 × 10<sup>-3</sup></td>
+  </tr>
+  <tr>
+    <td>Obey</td>
+    <td>4.70 × 10<sup>-2</sup></td>
+    <td>1.67 × 10<sup>-2</sup></td>
+  </tr>
+  <tr>
+    <td>Sacandaga</td>
+    <td>-5.40 × 10<sup>-2</sup></td>
+    <td>4.59 × 10<sup>-3</sup></td>
+  </tr>
+  <tr>
+    <td>Tallapoosa</td>
+    <td>-3.24 × 10<sup>-2</sup></td>
+    <td>7.76 × 10<sup>-3</sup></td>
+  </tr>
+</table>
+
+Building on the work of Dinpashoh et al. (2014), Khaliq et al. (2009), Kumar et al. (2009) and Zamani et al. (2017), we plan to explore the role of long-term persistence on WHI trend analyses in a future effort; however, this preliminary work suggests only a few sites in our database exhibit long-term persistence that would impact the significance of the detected WHI trends. Indeed, even if consideration of long-term persistence yielded insignificant trends at all six sites listed in Table R2, we would retain 26 positive and 134 negative significant trends in our database of 479 sites with \( n_y \geq 30 \) years across the USA and Canada for 1980-2019.
+
+- The MK method does not detect breaks in mean values nor discriminate between sharp and gradual variance values. A statistical test that allows objective detection of breaks in mean values of the analyzed series (e.g., Pettitt, Lombard test) must be used, making it possible to determine rigorously the dates of shifts in mean values of the WHI index.
+
+Correct, the MKT only distinguishes a linear, monotonic trend irrespective whether it arises from an abrupt or a gradual change in WHI. It is possible that some of the reported
+trends in WHI arise from a sudden change in operation, the commissioning of a new, or the decommissioning of an old, hydropower facility.
+
+![Time series plots of WHI for four rivers, showing mean values before and after statistically-significant change points](page_246_370_1057_496.png)
+
+Figure R8: Time series of the WHI for (a) the Churchill River at Churchill Falls Powerhouse, Labrador, (b) Cowlitz River, (c) Michipicoten River, and (d) South Saskatchewan River, 1980-2019. Horizontal blue and red lines identify mean WHI values before and after, respectively, the detection of a statistically-significant change point through the Pettitt test. Note y-axis scales vary between panels.
+
+In response to this comment, we applied the Pettitt (1979) test to verify if any of the statistically-significant linear trends are associated with break points in the WHI time series. There are indeed 109 sites for which statistically-significant break points are detected by the Pettitt test at sites with MKT trends with \( p < 0.05 \) and at least 30 years of available data during 1980-2019. Figure R8 provides examples of the results of the Pettitt test applied to two sites with statistically-significant positive trends in WHI (Cowlitz and South Saskatchewan rivers) and two sites with statistically-significant negative trends in WHI (Churchill and Michipicoten rivers). This illustrates that the Pettitt test accurately detects years when abrupt changes in WHI appear at all four sites.
+
+For completeness, we have prepared an extra supplementary table with the results of the Pettitt test at all sites with no less than 30 years of available data during 1980-2019. Specifically, Supplementary Table 4 contains results of the Pettitt test statistic U*, the
+corresponding p-value, and the years when a change point is identified. Additionally, the table lists the mean WHI prior to and after the change points. We caution, however, that not all results of the Pettitt test are statistically-significant at the \( p < 0.05 \) level and must be interpreted with care. In this application, the Pettitt test reports only the most significant break point in a time series that can otherwise include several change points or none at all. Where insufficient data (\( n_y < 30 \) years) are available to perform the Pettitt test, “NA” is shown in the table for the test statistics.
+
+Thus application of the Pettitt test is helpful in determining rigorously the inception of new management practices in regulated waterways, commissioning or decommissioning of hydropower infrastructure, among other factors that may induce abrupt changes in WHI. A statement on the results of the Pettitt test has been added to the discussion of the MKT results (lines 240-242). We thank Reviewer #3 for this useful comment that provides added value to the WHI trend results.
+
+- It would be useful to apply a classification method (e.g., bottom-up hierarchical classification) to WHI index values to subdivide the 400 sites in classes to improve their characterisation and description.
+
+Thank you for this suggestion to implement a bottom-up hierarchical classification scheme to the WHI results. Following this suggestion, we implemented the “cluster” package in R and used the “agnes” function to perform agglomerative clustering starting with the 1980-2019 mean WHI values at all 500 sites. Aside from the WHI, the data table contains the relevant metadata for each site: latitude, longitude, gauged area, and mean annual discharge. Given the latter two variables span several orders of magnitude, their base 10 logarithms are instead used in the data table. The data are then standardized prior to the cluster analysis with the “agnes” function. Figure R9 provides a dendrogram of the results from the classification method.
+
+Dendrogram of agnes(x = DD, stand = TRUE, method = "complete")
+
+![Dendrogram of agnes(x = DD, stand = TRUE, method = "complete")](page_370_1042_1067_377.png)
+Figure R9: Dendrogram illustrating the result of a bottom-up hierarchical classification scheme applied to all 500 sites based on the 1980-2019 mean WHI, coordinates, and the base 10 logarithms of gauged area and mean annual discharge.
+
+While this is an interesting idea, we do not find that the bottom-up hierarchical classification of the WHI provides useful interpretation of our results, particularly in addressing the study’s objectives of identifying recent trends in weekly hydropeaking cycles across the USA and Canada. As such, we exclude the results of the bottom-up hierarchical classification from this manuscript but will consider incorporating this in a future effort.
+
+2. Results
+Table 1 should be replaced with a table showing the result of all values of the WHI index derived for the 400 sites. See an example
+
+Indice Number of sites % of sites in USA (%) Sites in Canada (%)
+
+>3.5
+
+3.0 – 3.5
+
+2.5 – 3.0
+
+2.0 – 2.5
+
+1.5 – 2.0
+
+1.0 1.5
+
+0.5 – 1.0
+
+0.0 – 0.5
+
+-0.5 – 0.0
+
+-1.0 - -0.5
+
+-1.5 - -1.0
+
+-2.0 - -1.5
+
+-2.5 - -2.0
+
+-3.0 - -2.5
+
+-3.5 - -3.0
+< -3.5
+
+N.B. It may be preferable to replace this table by a figure.
+
+In response to this comment we have replaced Table 1 with the binned distribution of WHI values for the USA, Canada and all sites over 1980-2019 (reproduced below as Table R3). The bins used, however, are slightly different from those suggested by Reviewer #3. Instead, they follow the same bin sizes (in increments of 0.75) as those used in the spatial plots. Results in this table are now discussed on lines 139-142 of the paper.
+
+Table R3. Number and percentage of sites in 10 WHI bins in increments of 0.75 for all sites, the USA, and Canada, 1980-2019. WHI bins follow those used in Figure 1 in the paper.
+
+<table>
+  <tr>
+    <th>WHI Bin</th>
+    <th>Sites – All</th>
+    <th>Sites – All (%)</th>
+    <th>Sites – USA</th>
+    <th>Sites – USA (%)</th>
+    <th>Sites – Canada</th>
+    <th>Sites – Canada (%)</th>
+  </tr>
+  <tr>
+    <td>&lt; -3.00</td>
+    <td>2</td>
+    <td>0.4</td>
+    <td>0</td>
+    <td>0.0</td>
+    <td>2</td>
+    <td>1.3</td>
+  </tr>
+  <tr>
+    <td>-3.00 to -2.25</td>
+    <td>9</td>
+    <td>1.8</td>
+    <td>0</td>
+    <td>0.0</td>
+    <td>9</td>
+    <td>5.9</td>
+  </tr>
+  <tr>
+    <td>-2.25 to -1.50</td>
+    <td>22</td>
+    <td>4.4</td>
+    <td>2</td>
+    <td>0.6</td>
+    <td>20</td>
+    <td>13.2</td>
+  </tr>
+  <tr>
+    <td>-1.50 to -0.75</td>
+    <td>48</td>
+    <td>9.6</td>
+    <td>23</td>
+    <td>6.6</td>
+    <td>25</td>
+    <td>16.4</td>
+  </tr>
+  <tr>
+    <td>-0.75 to 0.00</td>
+    <td>151</td>
+    <td>30.2</td>
+    <td>113</td>
+    <td>32.5</td>
+    <td>38</td>
+    <td>25.0</td>
+  </tr>
+  <tr>
+    <td>0.00 to 0.75</td>
+    <td>140</td>
+    <td>28.0</td>
+    <td>118</td>
+    <td>33.9</td>
+    <td>22</td>
+    <td>14.5</td>
+  </tr>
+  <tr>
+    <td>0.75 to 1.50</td>
+    <td>65</td>
+    <td>13.0</td>
+    <td>46</td>
+    <td>13.2</td>
+    <td>19</td>
+    <td>12.5</td>
+  </tr>
+  <tr>
+    <td>1.50 to 2.25</td>
+    <td>36</td>
+    <td>7.2</td>
+    <td>26</td>
+    <td>7.5</td>
+    <td>10</td>
+    <td>6.6</td>
+  </tr>
+  <tr>
+    <td>2.25 to 3.00</td>
+    <td>21</td>
+    <td>4.2</td>
+    <td>14</td>
+    <td>4.0</td>
+    <td>7</td>
+    <td>4.6</td>
+  </tr>
+  <tr>
+    <td>&gt; 3.00</td>
+    <td>6</td>
+    <td>1.2</td>
+    <td>6</td>
+    <td>1.7</td>
+    <td>0</td>
+    <td>0.0</td>
+  </tr>
+</table>
+
+The previous Table 1 listing the top 10 WHI scores has been moved to the Supplementary Information document as Supplementary Table 2.
+References:
+
+Auer, N. A. Response of spawning lake sturgeons to change in hydroelectric facility operation. T. Am. Fish. Soc. **125**, 66-77 (1996).
+
+Dinpashoh, Y., Mirabbasi, R., Jhajharia, D., Abianeh, H. Z. & Mostafaeipour, A. Effect of short-term and long-term persistence on identification of temporal trends. *J. Hydrol. Eng.* **19**, 617-625 (2014).
+
+Ferrazzi, M., Woods, R. A. & Botter, G. Climatic signatures in regulated flow regimes across the Central and Eastern United States. *J. Hydrol. Reg. Studies*, **35**, 100809 (2021).
+
+Khaliq, M. N., Ouarda, T. B. M. J. & Gachon, P. Identification of temporal trends in annual and seasonal low flows occurring in Canadian rivers: the effect of short- and long-term persistence. *J. Hydrol*. **369**, 183-197 (2009).
+
+Kumar, S., Merwade, V., Kam, J. & Thurner, K. Streamflow trends in Indiana: Effects of long term persistence, precipitation and subsurface drains. *J. Hydrol*. **374**, 171-183 (2009).
+
+Pettitt, A. N. A non-parametric approach to the change point problem. *J. Appl. Stat.* **28**, 126-135 (1979).
+
+U.S. Energy Information Administration: http://iea.org (2021).
+
+Yue, S., Pilon, P., Phinney, B. & Cavadias, G. The influence of autocorrelation on the ability to detect trend in hydrological series. *Hydrol. Process*. **16**, 1807-1829 (2002).
+
+Zamani, R., Mirabbasi, R., Abdollahi, S. & Jhajharia, D. Streamflow trend analysis by considering autocorrelation structure, long-term persistence, and Hurst coefficient in a semi-arid region of Iran, *Theor. Appl. Climatol*. 129, 33-45 (2017).
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+The manuscript has been improved. Below are just a handful of editorial recommendations for inaccurate statements and which do not require re-review. The paper is great and impactful as is, and is promising to be cited a lot for "the decreasing in weekly hydropoeaking" finding. Without further synthesis however it cannot be cited for any potential reason or regional implications. It seems a bit limited for a Nature paper.
+The authors maintained an analysis throughout the now-500 locations with a rich discussion on the potential reasons for reduction in hydropoeaking without further investigating support for those inferences. I recommend authors to engage in a limited synthesis ( because there is already a lot in the paper) to enhance the impact of the paper. With or without this additional synthesis, I strongly recommend to further work on figure 4 for highlighting and clarifying the synthesis of the finding. Suggestions are also provided below.
+
+1) First paragraph of results section. "While many dams in North America have multiple purposes, hydropower generation remains a principal function" . That is not the case throughout the western USA especially for federal dams were hydropower is the purpose with the least priority. I would remove this statement or rephrase to " Most dams are operated for multi-purposes shaping seasonal and subseasonal patterns. Hydropower remains a principal component for sub-monthly variations along with flood control."
+
+2) "Clusters of negative WHI trends lie primarily within the Western Electricity Coordinating Council, Northeast Power Coordinating Council and SERC Reliability Corporation power grid interconnections". The authors refer to "reliability councils in charge of resource adequacy and arbitrage" when in fact they should refer to the actual interconnects "Western, Northeastern and Southeastern Interconnects".
+
+3) "Recent cost reductions for the production of solar and wind energy may also lead to new types of services offered by hydropower such as capacity markets. Furthermore, the rapid 328 increase in electricity production from non-hydro renewable sources coincides with the sharp decline of weekly hydropoeaking intensity in the 2010s (Supplementary Fig. 12)." The two sentences do not flow together. The second sentence would make more sense coming first, leading to hydro providing new services. I would not mention the cost of wind and solar as those are high subsidized in the US and considered as must-take by the grid.
+
+4) "Alternatively, wet years may lead utilities to generate continuous baseload energy instead of peaking hydropower, inducing a similar effect. The relatively wet climate of the 2010s could account for part of the recent declines in WHI across the USA and Canada." Is there a reference to back up a wet year from a hydropower perspective? 2014-16 was the worse drought in California and 2015 a severe drought in the Northwest, and 2011 the worse drought of record in Texas for water-dependent electricity generation.
+
+5) Figures: figure 4 is very much around showing the data while panels k and l are the most informative supporting the synthesis in the paper. Panel l is very hard to understand without the color legend on the side. The caption says that the week starts on FS while other graphs start on SS. This is a bit inconsistent which contributes the overall lack of clarity for this panel. I understand that authors maintain all the panels, k and l are however those going to be picked up by media and other authors to build on this work. They deserve to be highlighted and more self standing.
+
+6) the overall analysis still focuses on the WHI value at individual locations. Regulation and operations
+( governance) are however at the watershed scale and interconnect scale. The paper has a rich discussion which remains based on inference while using panels k and i from figure 4 by interconnect for example (western US, western canada, ercot, southeastern, MISO, etc) would provide more support on the discussion based on the generation portfolio. Similarly hydrologic regions could be used as well. The manuscript has an impactful message but lacks a synthesis to increase the impact of the paper.
+
+Reviewer #2:
+Remarks to the Author:
+I’d like to thank the authors for fully addressing my comments and improving the manuscript accordingly. The analyses of the WHI temporal evolutions have offered some new insights. The authors have also done a great work investigating the relationship between non-hydropower electricity and WHI. I do not have additional comments for the revised manuscript.
+
+Reviewer #3:
+Remarks to the Author:
+Dear Editor,
+
+I have carefully read the answers to the questions raised by the three reviewers and the corrections made by the authors to their manuscript. As far as I’m concern, I’m happy with the changes made by the authors. I recommend acceptance of the article in its current revised form.
+
+Best Regards,
+Prof. Assani
+RESPONSE DOCUMENT
+
+NCOMMS-21-12638A
+
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The manuscript has been improved. Below are just a handful of editorial recommendations for inaccurate statements and which do not require re-review. The paper is great and impactful as is, and is promising to be cited a lot for "the decreasing in weekly hydroparking" finding. Without further synthesis however it cannot be cited for any potential reason or regional implications. It seems a bit limited for a Nature paper.
+
+The authors maintained an analysis throughout the now-500 locations with a rich discussion on the potential reasons for reduction in hydroparking without further investigating support for those inferences. I recommend authors to engage in a limited synthesis (because there is already a lot in the paper) to enhance the impact of the paper. With or without this additional synthesis, I strongly recommend to further work on figure 4 for highlighting and clarifying the synthesis of the finding. Suggestions are also provided below.
+
+We sincerely thank Reviewer #1 for the additional constructive comments provided in this report on our paper. We address each of Reviewer #1’s comments with a point-by-point response in bold lettering. As outlined below, a limited synthesis of the results is now provided in our final remarks. We anticipate reporting further details (including analyses at different spatio-temporal scales) and synthesizing our results in future publications. Thank you for taking the time to carefully read and review our revised manuscript as we feel that by addressing these comments our paper is now even stronger.
+
+1) First paragraph of results section. "While many dams in North America have multiple purposes, hydropower generation remains a principal function". That is not the case throughout the western USA especially for federal dams were hydropower is the purpose with the least priority. I would remove this statement or rephrase to " Most dams are operated for multi-purposes shaping seasonal and subseasonal patterns. Hydropower remains a principal component for sub-monthly variations along with flood control."
+
+We agree with this statement and have modified the text accordingly. Lines 100-102 now state as follows: “Most dams in North America are operated for multi-purposes shaping seasonal and subseasonal patterns. Hydropower remains a principal component for sub-monthly variations along with flood control.”
+
+2) "Clusters of negative WHI trends lie primarily within the Western Electricity Coordinating Council, Northeast Power Coordinating Council and SERC Reliability Corporation power grid interconnections". The authors refer to "reliability councils in charge of resource adequacy and arbitrage" when in fact they should refer to the actual interconnects "Western, Northeastern and
+Southeastern Interconnects".
+
+As per Reviewer #1’s suggestion, the text on lines 236-237 has been modified to specify that the clusters of negative WHI lie within the Western, Northeastern and Southeastern Interconnects.
+
+3) "Recent cost reductions for the production of solar and wind energy may also lead to new types of services offered by hydropower such as capacity markets. Furthermore, the rapid increase in electricity production from non-hydro renewable sources coincides with the sharp decline of weekly hydropeaking intensity in the 2010s (Supplementary Fig. 12)." The two sentences do not flow together. The second sentence would make more sense coming first, leading to hydro providing new services. I would not mention the cost of wind and solar as those are high subsidized in the US and considered as must-take by the grid.
+
+We concur with this comment and have updated the text on lines 314-319 as follows:
+“Solar and wind energy production activate during favourable weather conditions with hydropower otherwise matching the demand, which may disrupt the typical weekly pattern in regulated flows while allowing hydropower to offer new types of services such as capacity markets. Furthermore, the rapid increase in electricity production from non-hydro renewable sources coincides with the sharp decline of weekly hydropeaking intensity in the 2010s (Supplementary Fig. 12).”
+
+4) "Alternatively, wet years may lead utilities to generate continuous baseload energy instead of peaking hydropower, inducing a similar effect. The relatively wet climate of the 2010s could account for part of the recent declines in WHI across the USA and Canada." Is there a reference to back up a wet year from a hydropower perspective? 2014-16 was the worse drought in California and 2015 a severe drought in the Northwest, and 2011 the worse drought of record in Texas for water-dependent electricity generation.
+
+The statement that 2010-2019 was a relatively wet decade is based on the spatial distribution of the decadal standardized discharge anomalies reported in Supplemental Figure 8b and reproduced below (Figure R1). Based on streamflow data, this illustrates the 2010s was generally a wet decade relative to others between the 1920s to 2000s across the northern two-thirds of the study area. This plot also confirms the Reviewer’s remark in regards to the prolonged drought conditions in the southwestern and southern USA and parts of the Pacific Northwest (Oregon, Idaho) yielding negative discharge anomalies. The southeastern USA (south of Tennessee and North Carolina) also shows predominantly negative standardized discharge anomalies. For the remainder of the study area including the northeastern and north-central USA and Canada, most discharge anomalies are positive, indicating generally wet conditions in the 2010s. This pattern is consistent with recent precipitation anomalies reported across the USA (e.g. https://www.climate.gov/media/13465).
+
+Out of the 500 study sites with available data in the 2010s, 67% showed positive discharge anomalies while 33% reported negative anomalies. Thus the statement about the 2010s
+being a relatively wet decade applies only to two-thirds of the study domain. Thus we have adjusted the text on lines 338-339 to reflect this, as follows:
+
+“The relatively wet climate of the 2010s could account for part of the recent declines in WHI across Canada and the northern half of the conterminous USA.”
+
+![Spatial distribution of decadal standardized discharge anomalies at 500 sites across the USA and Canada, 2010-2019. Negative values indicate relatively dry conditions while positive values denote relatively wet conditions.](page_246_370_1092_670.png)
+
+Figure R1: Spatial distribution of decadal standardized discharge anomalies at 500 sites across the USA and Canada, 2010-2019. Negative values indicate relatively dry conditions while positive values denote relatively wet conditions.
+
+5) Figures: figure 4 is very much around showing the data while panels k and l are the most informative supporting the synthesis in the paper. Panel l is very hard to understand without the color legend on the side. The caption says that the week starts on FS while other graphs start on SS. This is a bit inconsistent which contributes the overall lack of clarity for this panel. I understand that authors maintain all the panels, k and l are however those going to be picked up by media and other authors to build on this work. They deserve to be highlighted and more self standing.
+
+Thank you for these thoughtful suggestions. In response to this comment, we have transferred panels k and l originally in Figure 4 into a separate figure (a new Figure 5) so
+that they stand alone and better highlight a synthesis of our results. Color legends have been added to both plots but the order of the two days of the week has not been modified in the final panel – this is to retain the same vertical layout in the presentation of the results in the bar graph (new Figure 5b) with the legends used in Figure 4. The addition of a legend in this panel should hopefully eliminate any issue with the interpretation of these results. The associated text (lines 214-219) describing these results has also been shifted to a separate paragraph so that these findings stand out better in our paper.
+
+6) the overall analysis still focuses on the WHI value at individual locations. Regulation and operations (governance) are however at the watershed scale and interconnect scale. The paper has a rich discussion which remains based on inference while using panels k and i from figure 4 by interconnect for example (western US, western canada, ercot, southeastern, MISO, etc) would provide more support on the discussion based on the generation portfolio. Similarly hydrologic regions could be used as well. The manuscript has an impactful message but lacks a synthesis to increase the impact of the paper.
+
+We concur that a comprehensive synthesis of the results is lacking in the paper; however, the strict length limitations imposed by Nature Communications prevents us from adding a new section to synthesize our main results. Nevertheless, in response to this comment, we have added a limited synthesis with the following sentences (lines 453-461) in the final part of the Discussion section now titled “Summary and synthesis”:
+
+Our analyses reveal that 29% of sites with at least three decades of available data during 1980-2019 exhibit locally statistically-significant declines in WHI while only 6% show inclines. Moreover, the fraction of sites with WHI \( \geq 1.5 \) dropped by half from the 2000s to the 2010s reverting to a value observed in the 1920s. Major watersheds observing significant declines in weekly hydropeaking include the Alabama, Columbia, Cumberland, Great Lakes-St. Lawrence, and upper Mississippi, which fall within the Eastern and Western Interconnects. Regional clusters of declining WHI highlight hydropower operations and river regulation governed at the watershed-, interconnect- and utility-scale.
+
+We anticipate following up on this study with a more profound regional analysis of WHI trends including at the interconnect- and watershed-scales, and perhaps even at the utility scale, if relevant electricity generation data can be acquired for analysis. Thus we now conclude our paper with the following statement (lines 471-473):
+
+Lastly, detailed investigations at various spatial (e.g., watershed, interconnect, utility) and temporal (e.g., seasonal) scales should be undertaken to elucidate the role of governing agencies and hydroclimate on hydropeaking globally.
+
+Sincere thanks to Reviewer #1 for providing supplemental remarks on our revised manuscript that continue to improve the presentation and interpretation of our results.
+Reviewer #2 (Remarks to the Author):
+
+I’d like to thank the authors for fully addressing my comments and improving the manuscript accordingly. The analyses of the WHI temporal evolutions have offered some new insights. The authors have also done a great work investigating the relationship between non-hydropower electricity and WHI. I do not have additional comments for the revised manuscript.
+
+Our sincere thanks to Reviewer #2 for this positive overview of our revised manuscript and for stating that our revisions have fully addressed the Reviewer’s earlier comments. We sincerely appreciate the Reviewer’s time and effort in assessing the overall revised manuscript and response document.
+
+Reviewer #3 (Remarks to the Author):
+
+Dear Editor,
+
+I have carefully read the answers to the questions raised by the three reviewers and the corrections made by the authors to their manuscript. As far as I’m concern, I’m happy with the changes made by the authors. I recommend acceptance of the article in its current revised form.
+
+Best Regards,
+Prof. Assani
+
+Sincere thanks to Reviewer #3 for a positive overview of our revised manuscript and that the earlier comments were fully addressed in our revisions. We express our deep gratitude to the Reviewer for the time and effort placed into assessing our revised manuscript and our responses to the comments we received from the three referees.

03cad287deb044c05daa550c40716d2819e5af19adf18b7b6e72878c97733fe6/preprint/preprint.md

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+Vanishing weekly hydropeaking cycles in American and Canadian rivers
+
+Stephen J. Dery (sdery@unbc.ca)
+University of Northern British Columbia https://orcid.org/0000-0002-3553-8949
+Marco A. Hernández-Henríquez
+University of Northern British Columbia
+Tricia A. Stadnyk
+University of Calgary https://orcid.org/0000-0002-2145-4963
+Tara J. Troy
+University of Victoria https://orcid.org/0000-0001-5366-0633
+
+Research Article
+
+Keywords: Canada, United States of America, Flow Regulation, Human Intervention, Hydropeaking, Hydropower, Streamflow
+
+Posted Date: April 20th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-441563/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on December 1st, 2021. See the published version at https://doi.org/10.1038/s41467-021-27465-4.
+Vanishing weekly hydropeaking cycles in American and Canadian rivers
+
+Stephen J. Dery¹*, Marco A. Hernández-Henríquez¹, Tricia A. Stadnyk², and Tara J. Troy³
+
+¹Department of Geography, Earth and Environmental Sciences, University of Northern British Columbia, 3333 University Way, Prince George, British Columbia, V2N 4Z9, Canada
+²Department of Geography, University of Calgary, Calgary, Alberta, T2N 1N4, Canada
+³Department of Civil Engineering, University of Victoria, Victoria, British Columbia, V8W 2Y2, Canada
+
+*Corresponding author: Stephen Dery (sdery@unbc.ca), ORCID # 0000-0002-3553-8949
+Email address for Marco Hernández-Henríquez: hernandezhenriquez.m@gmail.com
+Email address for Tricia Stadnyk: Tricia.Stadnyk@ucalgary.ca, ORCID # 0000-0002-2145-4963
+Email address for Tara Troy: jtroy@uvic.ca, ORCID # 0000-0001-5366-0633
+
+CONFIDENTIAL MANUSCRIPT - FOR PEER REVIEW ONLY
+
+31 March 2021
+
+Running head: Vanishing weekly hydropeaking cycles in American and Canadian rivers
+
+Keywords: Canada, United States of America, Flow Regulation, Human Intervention, Hydropeaking, Hydropower, Streamflow
+Abstract
+
+Sub-daily and weekly flow cycles termed ‘hydropeaking’ are common features in regulated rivers worldwide. Weekly flow periodicity arises from fluctuating hydropower demand and production tied to socioeconomic activity, typically with higher consumption during weekdays followed by reductions on weekends. Here, we propose a novel weekly hydropeaking index to quantify the 1920-2019 intensity and prevalence of weekly hydropeaking cycles at 400 sites across the United States of America and Canada. A robust weekly hydropeaking signal exists at 1.1% of sites starting in 1920, peaking at 17.0% in 1963, and diminishing to 3.2% in 2019, marking a 21st century decline in hydropeaking intensity. We propose this decline may be tied to recent, above-average precipitation, socioeconomic shifts, alternative energy production, and legislative and policy changes impacting water management in regulated systems. Vanishing weekly hydropeaking cycles may offset some of the prior deleterious ecohydrological impacts from hydropeaking in highly regulated rivers.
+
+Introduction
+
+In 2019, the United States of America (USA) and Canada generated a combined 674 TWh of hydroelectricity from a total 184 GW of installed capacity, ranking them with China and Brazil in the four largest global producers of hydroelectricity¹. With the proliferation of dam and reservoir construction during the 20th and early 21st centuries²,³, many of the two countries’ main rivers are now moderately or strongly affected by fragmentation, regulation and/or diversions⁴⁻⁶. With increasing demands for renewable sources of energy, additional generating capacity is being developed or planned across Canada. This includes the 1,100 MW Site C Dam on the Peace River in northeastern
+British Columbia (BC), the 824 MW Muskrat Falls development on the lower Churchill River in Labrador, and the 695 MW Keeyask Generating Station on the Nelson River in northern Manitoba¹, with its first of seven units becoming operational in February 2021.
+
+While overall demand for electricity continues to increase, consumption patterns vary depending on socioeconomic activity, short-term weather conditions, seasonal climate fluctuations and long-term climate trends⁷,⁸. In the northern USA and Canada, the winter season usually incurs peak hydroelectric demand due to domestic, commercial and industrial heating and lighting requirements⁹. With climate change, winter cold waves subside while summer heat waves intensify¹⁰,¹¹, shifting some of the demand from winter heating to summer cooling¹²-¹⁴. Apart from seasonality shifts, day-to-day activities influence hydroelectricity demand as well. Similar to many other industrialized countries, North American educational, industrial and commercial activity intensifies on weekdays (Monday through Friday) but abates on weekends, particularly on Sundays⁹.
+
+This weekly rhythm of socioeconomic activity can thus impact water retention and releases in regulated rivers¹⁵. These rapid, frequent and periodic flow fluctuations downstream of regulation points are commonly termed ‘hydropeaking’ events and are known to disrupt a range of ecohydrological processes¹⁶,¹⁷. Yet the characteristics and trends in weekly hydropeaking cycles due to daily variation in hydropower demands remain largely unknown. This is despite the general availability of discharge data at a daily time scale and the distinct weekly rhythm of socioeconomic activity including hydropower production, and hence water releases in regulated waterways, which impact ecohydrological processes.
+To address that knowledge gap and a demand for global attention to hydropeaking rivers\(^{18}\), we assess here the prevalence of weekly hydropeaking cycles for 400 gauging sites along rivers of the USA and Canada spanning a wide range of basin characteristics, regulation, hydrological and climatic regimes. Specifically, we develop a scale-independent and dynamic weekly hydropeaking index (WHI) with both time and frequency domain terms, allowing quantification of weekly flow periodicity. Application of the novel WHI to 1920-2019 time series of river discharge provides evidence of vanishing weekly hydropeaking cycles in many regulated rivers of the USA and Canada with the 2010s comparable to the 1920s for hydropeaking prevalence. We conclude that increased commercial and industrial activity on weekends, a shift towards other modes of energy production, policy changes altering water management practices, electrical grid interconnectivity and deregulation of electricity generation, plus a relatively wet decade in the 2010s are contributing factors to waning weekly hydropeaking cycles.
+
+Results
+
+Overall WHI statistics. The 1980-2019 mean, median, and standard deviation of WHI for the 400 sites reach 0.097, 0.005 and 1.115, respectively (Supplementary Table 1). An application of the Shapiro-Wilk test to the WHI data suggests the distribution is not Gaussian (\(W = 0.974,\ p = 1.32 \times 10^{-6},\ n = 400\)); yet, the low skewness (0.157) and excess kurtosis (0.754) along with a Cullen and Frey graph (Supplementary Fig. 1) infer a reasonable fit. Twenty-five sites attain a mean annual WHI \( \geq 2.0 \) for 1980-2019 with another 49 sites achieving WHI \( \geq 1.0 \). A list of sites with the top ten ranking WHI values reveals their wide regional distribution with foci in the Chattahoochee, Colorado, Columbia, Great Lakes-St. Lawrence, Nelson and upper Tennessee drainage basins
+(Table 1), all of which are heavily dammed. The Chattahoochee River at Buford Dam claims the top WHI score of 3.299 while BC’s Stuart River shows the lowest score of -3.469. Some highly regulated systems such as Manitoba’s Burntwood River, which funnels water diverted from the Churchill River into the Nelson River, exhibit large negative WHI values (-1.892) as Notigi (the upstream point of regulation) is a control structure for a large reservoir operated in a longer term (e.g., seasonal) manner. Similarly, while several large dams impound the Missouri River, they are managed not only for hydropower production but also for flood control, irrigation, navigation and recreational values. As such, the three sites along the Missouri River used in this study exhibit an average WHI = -0.492 revealing an absence of significant weekly hydropeaking cycles.
+
+Spatial analyses. A map of the 1980-2019 WHI values reveals that weekly hydropeaking rivers abound across the USA and Canada. Clusters of high WHI values emerge in the Alabama, Chattahoochee, and Tennessee river basins of the southeastern USA, in waterways draining the Ozark Mountains, the Colorado River and in northern Ontario rivers draining into the Great Lakes (Fig. 1). The Columbia River has several major points of regulation (WHI \( \geq 1.5 \)) from its headwaters in BC to its outlet in the Pacific Ocean. Highly hydropeaking sites (WHI \( \geq 2.0 \)) appear in both small (e.g., Alberta’s Kananaskis River, \( A = 899 \) km\(^2\)) and large (Manitoba’s Nelson River, \( A = 1.1 \times 10^6 \) km\(^2\)) systems. In contrast to their adjacent regulated rivers, free-flowing rivers of northern Canada, particularly those draining into Hudson Bay, exhibit large, negative WHI values. These unregulated rivers manifest strong annual cycles dominated by snowmelt-driven freshets and contain large natural storage capacity in the form of
+extensive lakes, ponds and wetlands. Free-flowing, pluvial rivers of the southeastern USA (e.g. the Choctawhatchee, Ogeechee, Pascagoula, Satilla and Suwanee rivers) also exhibit negative, albeit > -1.5, WHI scores. WHI values diminish moving downstream from a point of regulation. For instance, WHI = 1.437 on the Peace River just downstream of BC’s WAC Bennett and Peace Canyon dams where minimum flows arise on weekends; 400 km downstream from the dams\(^{19}\), however, WHI declines to 0.929 at the community of Peace River in Alberta where minimum flows occur on Mondays/Tuesdays, indicating a 2-day delay in signal propagation. A cascade of dams and reservoirs can amplify or sustain the hydropoeaking signals along waterways (e.g., the Colorado, Columbia, and Tennessee rivers) or attenuate them (e.g., Ottawa River).
+
+Sites with high values of WHI (\( \geq 1.5 \)) also show a preponderance of flow reductions on the weekends (Saturdays/Sundays) as identified by the larger symbols in Fig. 1. Of the 44 sites with WHI \( \geq 1.5 \), 39 experience the two consecutive days with low flows on weekends. In contrast, sites with negative WHI values show a range of low flow days with no distinct pattern emerging. No less than 30.8% of all sites used in this study exhibit low flows on Saturdays/Sundays, more than twice the expected value (Fig. 2). This disproportionate amount of weekend low flows occurs mainly in hydropoeaking rivers (WHI > 0). Weekday combinations show frequencies at, or lower than, the expected value with the Friday/Saturday sequence appearing at only 6.0% of sites. A Chi-Square test applied to the frequency of two consecutive low flow days reveals that the results differ significantly from the expected value of 0.143 (\( \chi^2 = 109.95,\ p < 2.2 \times 10^{-16},\ n = 7 \) with six degrees of freedom). The mean WHI equals 0.292 for 123 sites with
+low flows on weekends while it remains near zero or slightly negative for the six other two-day combinations. The distribution of mean WHI for the two-day combinations differs significantly from a uniform distribution based on a Chi-Square test (\( \chi^2 = 8.43, p = 0.05 \) based on 10,000 replicates with \( n = 7 \)).
+
+Temporal evolution and trend analysis. The temporal evolution of the mean and median WHI shows a rapid increase in hydropeaking intensity from the 1920s to the 1950s at which point they level off and fluctuate near zero (Supplementary Fig. 2). Starting in the 1990s, though, there is a gradual decline in both the mean and median WHI values with a return in the 2010s to statistics first seen in the 1930s (largely pre-regulation), a pattern observed both in the USA and Canada (not shown). The discharge-weighted WHI_Q emphasizes the increasing volumes of regulated flows starting from the 1920s through the 1980s; however, WHI_Q also declines markedly thereafter into the 21st century. In 1920, only 1.1% of available sites rank in the top decile of 1920-2019 WHI values (WHI \( \geq 2.021 \)). This fraction peaks at 17.0% of available sites in 1963 but thereafter diminishes consistently. In 2000, 50 or 13.2% of available sites score in the top decile of 1920-2019 WHI values but these counts fall precipitously to just 12 or 3.2% of the available sites by 2019, marking a 21st century declining pattern in weekly hydropeaking intensity. Trend analysis applied to the overall mean annual WHI reveals a statistically-significant decline of -0.40 over 1980-2019 (Supplementary Fig. 3). These temporal results, however, rely on the availability of discharge data, as the record length averages 78.4 years, ranging from a minimum of 24 years at one site to a full century at 87 sites (Supplementary Fig. 4). The number of available sites increases steadily from 1920 into the early 1990s and peaks at 393 sites
+in 1985 and 1992 but then declines to 373 sites by 1996 thereafter averaging 383±6 sites until 2019. Notable gaps appear in the discharge records starting in the 1990s, particularly for regulated rivers in Ontario and Québec; however, adjusting the time series of mean annual WHI for unavailable sites reveals little difference in the overall pattern and trend of WHI during 1980-2019 (Supplementary Fig. 3).
+
+Data availability also factors in the appraisal of the decadal evolution of hydropeaking intensity across the USA and Canada (Fig. 3a-j). Nevertheless, this shows the gradual inception of hydropeaking cycles during the 1920s and 1930s, particularly in the north-central, northeastern, and southeastern USA and in northern Ontario. The 1940s show an expansion of weekly hydropeaking rivers into the western USA including within the Colorado, Columbia and Sacramento river basins. The 1940s and 1950s mark an intensification of regulation in the Tennessee and Alabama river basins as well as rivers of northern Ontario draining to Lakes Superior and Huron. A pronounced expansion and amplification of the hydropeaking signal appears in the 1960s, particularly across the Great Lakes-St. Lawrence river basin in Ontario and Québec. Some stabilization of the hydropeaking pattern marks the 1970s but a resurgence follows in the 1980s and 1990s when additional hydropeaking rivers emerge in western Canada. The 2000s retain a wide distribution of hydropeaking rivers across both countries; yet, by the 2010s, the number of highly hydropeaking rivers diminishes considerably, particularly in parts of the Great Lakes-St. Lawrence and Tennessee river basins. The decadal distribution of the 10 WHI bins (Fig. 3k) further highlights the peak fraction of sites with WHI \( \geq 1.5 \) attained in the 1960s (19.6%), with nearly matching minimum values in the 1920s
+(6.8%) and 2010s (6.7%). After the 1960s, there is a steady decline in the relative number of sites with low flows either on the Saturday/Sunday or Sunday/Monday combinations, indicating waning differences between weekday and weekend flows across the USA and Canada (Fig. 3l).
+
+The temporal evolution of the annual maximum WHI value shows a rapid increase from ~3.0 in the 1920s to > 4.0 in the 1930s onward (Supplementary Fig. 2d). Annual peak WHI values > 4.0 are generally sustained for the remainder of the 20th century but then fall below that threshold starting in 2003 until 2019. The peak WHI value each year over the study period is distributed among 19 sites, with the Winnipeg River at the outlet of the Lake of the Woods capturing the top spot 12 times in the 1920s to early 1960s (Supplementary Fig. 5). The Colorado River at Hoover Dam dominates the list 25 times between the 1940s into the early 1980s. From the 1960s to 2010s, the Chattahoochee River at Buford Dam ranks first 12 times while in the 1990s and 2000s, the Montreal River that drains to Lake Superior tops the list 10 times. The overall maximum WHI score of 4.587 arises in 1961 at the Winnipeg River at the outlet of Lake of the Woods.
+
+Further statistical analysis reveals an abundance of strong, negative WHI trends interspersed with positive ones for the 380 sites with \( n_y \geq 30 \) years over 1980-2019 (Fig. 4). A total of 104 sites show locally statistically-significant (\( p < 0.05 \)) declines in WHI while 26 show locally statistically-significant inclines. Of the 130 locally-significant trends, 81 remain globally significant. Significant negative WHI trends abound in the southeastern and northeastern USA, the Great Lakes-St. Lawrence basin, and the
+Pacific Northwest while a cluster of positive trends arises in Québec’s Saguenay watershed. While regulated rivers of Newfoundland show increasing WHI values, their unregulated counterparts show similar tendencies. Similarly, in New Brunswick, the regulated St. John River shows a decreasing trend in WHI while the proximal, unregulated Southwest Miramichi River shows an increasing trend. Sixty-four percent of the locally-significant WHI trends arise in hydropeaking rivers (WHI > 0) with fewer locally-significant trends in non-hydropeaking rivers (WHI < 0; Supplementary Fig. 6).
+
+Interannual and interdecadal variability. Water management practices and climate variability, among other factors, yield significant interannual variation in hydropeaking intensity. For example, the Colorado River at Lees Ferry shows marked declines in WHI during high flow years (Supplementary Fig. 7a). Indeed, heavy precipitation during strong El Niño events in the early 1980s induced high flows in the Colorado River including at Lees Ferry. Due to the unusually wet weather, the bypass tubes and spillway at Glen Canyon Dam were used to release additional water downstream, thereby moderating hydropeaking signals from 1983 to 1986\(^{20}\). Similar declines in WHI appear in 1997 and 2011 when flows exceed the recent annual average. Computing the Pearson correlation coefficient between the 1980-2019 annual river discharge and the corresponding WHI yields 81 statistically-significant negative correlations and only 16 statistically-significant positive correlations (Supplementary Fig. 7b). Thus high flows over extended periods attenuate weekly periodicity even in heavily regulated rivers such as the Colorado.
+This analysis suggests that sustained wet periods may attenuate hydropeaking intensity while dry periods may accentuate it. Binned distributions of decadal standardized anomalies in river discharge reveal the contrasting dry 1930s vs. the wet 1970s, the latter coinciding with a suppression of hydropeaking across the USA and Canada (Supplementary Fig. 8). Yet, while the 2010s experienced relatively high flows, 6.7% of sites have WHI \( \geq 1.5 \) whereas in the similarly wet 1990s, 15.6% of sites achieve WHI \( \geq 1.5 \). Of 20 sites with large (> 1), positive standardized discharge anomalies during the 2010s, only three (the Betsiamites, La Grande and Nelson rivers) have WHI > 1, which are likely more in response to enhanced diverted flows rather than high precipitation. Thus it is unlikely interdecadal climate variations alone account for recent WHI declines.
+
+Dispersion of daily flows. Apart from climate variations, changes in day-of-the-week flows may influence WHI trends. Sites with WHI > 0 generally observe greater dispersion of day-of-the-week flows although pluvial and intermittent rivers, particularly in the southern USA, also experience greater day-to-day flow variations (Supplementary Fig. 9a). A trend analysis reveals significant declines in the dispersion of flows across the seven days of the week, concomitant with diminishing WHI values from 1980 to 2019 (Supplementary Fig. 9b). As an example, an abrupt reduction in dispersion of day-of-the-week flows in Labrador’s Churchill River appears in 1997 and is then sustained, suggesting factors other than climate variations are altering daily flows (Supplementary Fig. 10).
+Discussion
+
+Possible factors leading to recent WHI declines. The recent decline in weekly hydropeaking cycles in the USA and Canada emerges as a key finding in this study. Several possible factors may be contributing to this general pattern observed over the study area. Firstly, hydropower demand, production and consumption may have shifted in recent years, thereby diminishing differences between weekdays vs. weekends. For instance, there has been a gradual shift towards more commercial (including e-commerce) and industrial activity on weekends that could alter the weekly discharge patterns in regulated rivers\(^{21,22}\). A shifting manufacturing sector, globalization, and lifestyle changes are all socioeconomic factors modifying electricity demand. Another possible factor is the development and expansion of other modes of energy production such as dispatchable combustion turbines and non-dispatchable solar and wind energy. Solar and wind energy production activate during favourable weather conditions with hydropower otherwise matching the demand, which may disrupt the typical weekly pattern in regulated flows. Regulatory bodies and changing governmental policies may also be altering how utilities manage regulated waterways. Indeed, there is renewed interest for environmental, ecological and cultural (e.g., from a First Nations perspective) flows in human-influenced systems, with emerging regulations and policies supporting their implementation\(^{23}\). For instance, regulatory changes in the operation of the Prickett hydroelectric facility from a peaking to run-of-river site to assist spawning lake sturgeon\(^{24}\) induced a significant WHI decline (of -0.216 decade\(^{-1}\)) along the Sturgeon River in the upper peninsula of Michigan starting in the 1990s. Indeed,
+changes in operation away from peaking hydropower generating stations, whether mandated or voluntary, could influence hydropeaking patterns.
+
+Additionally, the increasing interconnectivity of the North American power grid, deregulation, and centralization of electricity dispatching may further contribute to a recent reduction of hydropeaking intensity. Finally, climate variations may also play a role in hydropower production as wet periods may require greater spillage of water from reservoirs thereby diminishing hydropeaking intensity. The relatively wet climate of the 2010s could account for part of the recent declines in WHI across the USA and Canada. Thus a combination of factors including changing hydropower demand patterns tied to lifestyle factors and socioeconomic activity, the emergence of alternative modes of energy production plus power grid interconnectivity, implementation of regulations and policies, and climate variations may be influencing the day-to-day hydrology of many regulated waterways across the USA and Canada.
+
+Spatio-temporal patterns within and across jurisdictions. Given the vast territory of the USA and Canada, their waterways often drain multiple jurisdictions including international transboundary watersheds (e.g., the Rio Grande, Great Lakes-St. Lawrence, Winnipeg and Columbia rivers). Regional water authorities, inter-jurisdictional water boards, federal, provincial, and state legislation, and international water treaties and commissions all affect how waterways are managed. Furthermore, synchronous inter-jurisdictional power grids (e.g., interconnections) can also affect hydropower generation and hence regulated flows, leading to distinct spatio-temporal
+patterns in hydropeaking intensity. Decadal maps of WHI values reveal the progression of weekly hydropeaking systems from the eastern and central USA to the Pacific Northwest in the 1960s when development in the Columbia River Basin expanded rapidly. The international Columbia River Treaty implemented in 1961 led to the construction of three major dams along the Columbia River (Duncan, Keenleyside and Mica Dams in Canada) plus another on the Kootenai River (Libby Dam in the USA)\(^{25}\). These dams and generating stations expanded the presence of hydropeaking cycles from the lower to the upper Columbia Basin in the 1970s and 1980s (Fig. 3). As such, regulation in the Canadian portion of the Columbia Basin now leads to downstream propagation of hydropeaking into the northern USA where it is regenerated at multiple points of regulation including Grand Coulee Dam and the Dalles.
+
+Another noticeable pattern in the decadal results is the WHI decline in many rivers of southern Québec in the 1970s and 1980s. As the 5,428 MW Churchill Falls generating station in Labrador came online in late 1971 (with hydropower sold mainly to the provincial utility Hydro-Québec)\(^{26}\), followed a decade later by the 17,418 MW James Bay Hydroelectric Complex in northern Québec\(^{15}\), a northward shift in hydropower generation abated the weekly hydropeaking cycles in more southern waterways. Simultaneous reductions in WHI in the northeastern USA (e.g., Hudson and Connecticut Rivers) may also be tied to transboundary power grid interconnections and Hydro-Québec’s large export capacity (7,974 MW in 2019\(^{27}\)). Similar to regional climate trends\(^{28}\), synchronous power grids thus have the capacity to shift the intensity of hydropeaking signals 1000s of kms away from points where hydropower is consumed,
+thereby creating hydropeaking teleconnections with potential for far-reaching social and ecohydrological effects.
+
+Ecohydrological implications. Ecohydrological impacts of hydropeaking are site-specific and may include rapid changes in water temperature (i.e., ‘thermo-peaking’), increases in soil erosion and suspended matter, and habitat degradation, which affect ecosystems, reduce species abundance, and limit biodiversity (e.g., fish, riparian plants, macroinvertebrates)\(^{16,29,30}\). Across the USA and southern Canada, hydropeaking emerged relatively early in the \(20^{\text{th}}\) century with the proliferation of dams and flow regulation in these regions. Starting in the 1960s, hydropower infrastructure expanded northwards into regions previously devoid of any significant flow regulation and hydropeaking. This includes major waterways like BC’s Peace River, Manitoba’s Nelson River, Ontario’s Moose and Abitibi rivers, and Québec’s La Grande Rivière. On these systems, major dams and reservoirs were built from the 1960s to early 1980s, vastly expanding the northern reach of hydropeaking rivers (Supplementary Fig. 11). This shifted potential ecohydrological impacts of hydropeaking to areas also undergoing rapid climate change through Arctic amplification of global warming\(^{31}\). As such, sub-Arctic species of fish (e.g., brook trout, lake sturgeon, northern pike, and walleye), insects and riparian plants may now be exposed to the cumulative impacts of these environmental stressors\(^{17}\). Additionally, winter frazil ice production and ice jams may be precipitated and accentuated downstream of hydroelectric facilities with persistent hydropeaking signals such as in the Peace River\(^{19}\).
+Despite their recent northward expansion, weekly hydropeaking cycles are generally waning across the USA and southern Canada, suggesting a 21st century hydropeaking recovery in some of these river systems. Indeed, prior ecohydrological impacts of hydropeaking may be partially offset, benefiting local biota and ecosystem biodiversity32. For instance, recovery of lake sturgeon in the northern peninsula of Michigan demonstrates some of the benefits of shifting away from peaking hydropower operations24. This is particularly important as evidence is also mounting that hydropeaking influences aquatic species in rivers of Canada33-36. Other aspects of flow regulation, such as sub-daily flow fluctuations and associated ramping up and down cycles not investigated in this study, may negate this hydropeaking recovery16, 17. Additional research is thus needed to explore hydropeaking cycles at other temporal scales to establish their site-specific ecohydrological impacts.
+
+Advantages and limitations of the WHI relative to other metrics. The proposed index to infer weekly hydropeaking signals provides a complementary metric to those developed in other studies5, 37, 38. Advantages of our approach include its scale independence, dynamic response, and relatively simple implementation. The WHI can be applied from small (< \(1 \times 10^3\) km\(^2\)) to large (> \(1 \times 10^6\) km\(^2\)) river basins with available daily discharge data (whether observed, reconstructed or simulated). The WHI responds to interannual variability in climate (e.g., wet/dry periods), changes in water management practices and policies, commissioning of new hydroelectric facilities or decommissioning of old ones, and other factors that affect flows. The use of daily discharge data also avoids the need for extensive databases on dams, reservoirs and
+other infrastructure that influence flows. Its possible implementation for short-term flow predictions emerges as another distinct advantage of the WHI. As an example, a running value of the WHI can be computed on the past year’s daily flows and used to infer the possible deviations in daily flows over a given week based on recent historical patterns. Its computational simplicity, coded in our study in Fortran, allows processing of results for the 400 sites in < 2.5 minutes. As such, it is feasible to implement a version of the code for short-term flow predictions so long as up-to-date daily flow records remain available. It would also be relatively straightforward to adapt the code to explore sub-daily hydropeaking cycles9 if appropriate discharge data are available.
+
+One challenge in implementing the WHI is access to daily discharge records. While considerable gauging stations exist in most of the USA and southern Canada, other waterways are not necessarily well monitored. A late 20th century decline in hydrometric stations due to budget restraints39 and the Water Survey of Canada’s curtailment of data collection combined with stricter quality standards from third parties have exacerbated hydrological data accessibility. As well, private industry and government-owned corporations often record discharge at or near their hydroelectric facilities but may consider these data as sensitive such that they are not released publicly. Thus, acquisition of daily discharge data in regulated systems, particularly as the number of small, private firms operating run-of-river hydroelectric facilities expands3, yields a distinct challenge in accessing flow data. Therefore, remote sensing40, data reconstructions (e.g. from statistical models or machine learning methods41) and
+numerical simulations that incorporate regulation\(^{42}\) are key in filling spatio-temporal gaps where and when *in situ* observations are lacking.
+
+**Concluding remarks.** As hydropower generation and infrastructure development continues to expand across the USA and Canada, it is important to establish how water management practices affect downstream river flows and ecosystems. A common feature in regulated rivers are discharge periodicities associated with hydropower production ebbs and flows including weekly cycles. In this study, a new measure of this weekly rhythm in flows, the weekly hydropeaking index (WHI), is formulated and applied to 400 sites over parts of North America. Our findings reveal vanishing weekly hydropeaking cycles across the USA and Canada in the 2010s, suggesting diminishing differences between discharge on weekends vs. weekdays. Factors possibly yielding this result include increased commercial and industrial activity on weekends, a shift towards other modes of energy production during peak demand hours or days, and policy changes altering water management practices including for ecological and environmental flows. This reduction in weekly hydropeaking also may benefit aquatic species, insects and riparian vegetation that otherwise are susceptible to rapid shifts in flows and water levels. Future efforts should therefore establish the ecohydrological implications of waning hydropeaking cycles. The application of the WHI to other regions over the globe would provide broader perspectives on the commonality of this feature in regulated rivers.
+Methods
+
+Study area. The USA and Canada harbor abundant freshwater resources that include some of the world’s largest rivers (by annual volumetric flows) including the Mississippi, St. Lawrence, Mackenzie, Ohio and Columbia rivers43. Many of these rivers and/or their tributaries have been impounded for hydropower generation, flood control, irrigation, potable water supply, navigation and recreation, leading to fragmented river networks and regulated flows4,6. Indeed, numerous dams have been built across the USA and Canada in the 20th and early 21st centuries2,3. While many dams in North America have multiple purposes, hydropower generation remains a principal function. Distinct weekly patterns mark hydropower production except perhaps at run-of-river facilities and those supplying industries continuously in operation such as aluminum smelters or pulp and paper mills8,9. As such, this study focuses on both regulated and unregulated waterways of the USA and Canada to explore the prevalence and intensity of weekly periodicity in discharge.
+
+Site selection. A total of 400 sites across the USA and Canada ranging 480-1,805,222 km² in gauged area (A), 25-60°N in latitude, 54-132°W in longitude, and 0.11-268.28 km³ in mean annual discharge are selected for this study (Supplementary Fig. 12 and Supplementary Table 2). A primary site selection criterion is discharge data availability for ≥ 24 years between 1920-2019, with ≥ 14 years during the focus period of 1980-2019. The chosen sites span a wide range of hydrological regimes from pluvial rivers in warmer climates (e.g., BC’s Yakoun River) to nival and glacial systems at higher elevations or latitudes in cooler climates (e.g., BC’s Lillooet River)44. Thus, the study area spans regions with little to no snowmelt where sub-annual scales govern temporal
+variability while others are mainly snowmelt-driven with predominant annual cycles\(^{45}\).
+The database also includes intermittent streams in warmer, drier climates such as California’s Santa Ana River and Arizona’s Little Colorado River. Regulated and unregulated rivers are selected (using guidance from Benke and Cushing\(^{43}\)) to allow comparisons between sites. Some sites such as Lees Ferry on the Colorado River include extended records that cover pre- and post-regulation effects on flows.
+
+Data. Data and metadata (station ID, gauge coordinates, and gauged area) are extracted from various sources including publicly accessible databases maintained by federal, provincial and state agencies in addition to proprietary data from private industry, government-owned utilities and international commissions. For most unregulated rivers, daily discharge data are sourced partly from the Water Survey of Canada’s Hydrometric Database (HYDAT), the Centre d’Expertise Hydrique du Québec (CEHQ) and the United States Geological Survey (USGS). For regulated rivers, though, daily discharge data are not necessarily available from these sources or other public repositories as they are partially or entirely collected, quality controlled and archived by government-controlled utilities or private industry (see Supplementary Tables 2 and 3). This includes: Nalcor Energy for the Salmon and Exploits rivers plus the Churchill Falls (Labrador) Corporation Limited for the Churchill River at Churchill Falls Powerhouse in Newfoundland and Labrador; NB Power for the St. John River in New Brunswick; Rio Tinto for the Kemano Powerhouse in BC and the Saguenay and Péribonca rivers in Québec; Hydro-Québec for La Grande Rivière, Betsiamites, Manicouagan, des Outaouais, des Outardes and St-Maurice rivers; Evolugen by Brookfield Renewable for the Coulonge, Lièvre, and Noire rivers in Québec and Mississagi and Aux Sables rivers
+in Ontario; Ontario Power Generation for the Abitibi, English, Kaministiquia, Madawaska, Mattagami (tributary to the Moose River), Montreal and Ottawa rivers; H2O Power for the Abitibi River; Manitoba Hydro for the Nelson and Winnipeg rivers; Transalta for the North Saskatchewan and Kananaskis rivers; and BC Hydro for the Columbia River at Mica Dam. Additional data for gauges along the Rio Grande on the border between the USA and Mexico and the Pecos River are provided by the International Boundary and Water Commission. Data at six sites in the Tennessee River Basin are provided by the Tennessee Valley Authority. Recent records of daily discharge from the US Bureau of Reclamation supplement those from the USGS for sites on the Colorado and upper Rio Grande rivers. Finally, the 1 October to 31 December 2019 daily discharge data for the Snake River at Hells Canyon Dam are sourced from Idaho Power. Potential errors associated with discharge measurements and implications to our results are discussed in the Supplementary Methods.
+
+Time series construction. The overall study period spans 1 January 1920 to 31 December 2019 for which at least partial, extended (\( \geq 24 \) years) records of daily discharge are available at all sites. Time series of daily streamflow (in \( m^3 \ s^{-1} \)) are constructed based on data availability for each site of interest (Supplementary Table 2) and follows D\'ery et al.\(^{46}\) in its approach. Daily discharge data sourced from the USGS, US Bureau of Reclamation, Tennessee Valley Authority, Idaho Power, Nalcor Energy (Exploits River) and NB Power are converted to metric units prior to analysis. For several waterways (e.g., the Nelson and Saguenay Rivers), data furthest downstream are first used, but when unavailable (prior to construction of dams and hydroelectric facilities), are replaced with those from the closest upstream gauging station while
+adjusting the data for the missing contributing area as necessary\(^{46, 47}\). Gaps are in-filled with the mean daily discharge over the period of record; however, any calendar year with \( \geq 10\% \) missing records is excluded from analysis. Supplementary Table 2 lists the percentage of in-filled data at each site (average: 0.02%, maximum: 0.55%) omitting years when \( \geq 10\% \) of the data remain unavailable. Uncertainty in the results associated with data homogeneity and the gap-filling strategy is evaluated and discussed in the Supplementary Methods.
+
+Development of the WHI. Various approaches are commonly used to explore flow alterations in regulated rivers including comparisons of hydrographs pre- and post-regulation\(^{9, 48, 49}\), trends in peak and/or low flows\(^{50}\) or of naturalized versus observed (regulated) flows\(^{51-53}\). A broader approach employs a set of multiple (up to 33) indicators of hydrologic alteration (IHA) to quantify changes over the water year arising from regulation\(^{54-56}\). Another method combines hydrological data, reservoir information and a database of large dams in developing river regulation and fragmentation indices with a matrix of impact for application to all major global watersheds\(^{4, 5}\). Apart from time domain analyses, Discrete Fourier Transforms (DFTs) or wavelet analyses offer additional insights on impacts of flow alterations from human interventions\(^{15, 20, 45, 57}\). Consult Jumani et al.\(^{38}\) for a review of river regulation and fragmentation indices including their applications, advantages and limitations.
+
+While various approaches exist to infer hydrologic alterations from diversions, dam and reservoir operations including sub-daily hydropoeaking cycles\(^{58, 59}\), none focuses on the weekly timescale, a primary periodicity of socioeconomic activity. Therefore, we develop a novel WHI that combines time and frequency domain terms to quantify weekly
+periodicity in river discharge. The time domain term (\( T_T, \% \)) counts the number of weeks (\( D_w \)) in a given calendar year when two consecutive days exhibit flows lower than the corresponding weekly average (\( \overline{Q_{1-7}} \)), followed by five sequential days above the corresponding weekly average:
+
+\[
+T_T = \max \left\{ \frac{100}{52} \sum_{w=1}^{52} D_w , 0.001 \right\}
+\]
+and where
+
+\[
+D_w = \begin{cases}
+1 & \text{if } Q_{1,2} < \overline{Q_{1-7}} \text{ and if } Q_{3,...,7} > \overline{Q_{1-7}} \\
+0.25 & \text{if } Q_1 < \overline{Q_{1-7}} \text{ and if } Q_{2,...,7} > \overline{Q_{1-7}} \\
+0 & \text{if otherwise}
+\end{cases}
+\]
+
+This sequence of daily flows is chosen to emphasize the typical weekly rhythm observed in hydropowering rivers: low flows on weekends when hydropower demand wanes, followed by high flows on weekdays when hydropower demand waxes\(^9\). A partial score of 0.25 is ascribed to sites where six consecutive days above the weekly average follow a single low flow day for that week. As some gauging sites lie downstream from points of regulation such that low flows are shifted later in the week rather than occurring on Saturdays and Sundays, we test all seven possible combinations of two consecutive days (e.g., Saturday/Sunday, Sunday/Monday, ..., Friday/Saturday) and select the one that maximizes WHI at each site over the period of record. This approach for the time domain term attenuates the effects of cyclical (rather than periodic) variations from synoptic-scale storm activity, which otherwise leads to marked weekly cycles in pluvial rivers\(^{45}\).
+An application of DFTs to the daily discharge data provides the frequency domain term. Here we follow Wilks\(^{60}\) in partitioning the daily discharge time series into sine and cosine waves of amplitude \( C_k \) for harmonic \( k \). DFTs are computed for each calendar year with the 52\(^{\text{nd}}\) harmonic representing the weekly timescale of interest here. Then we compute the explained variance of the 52\(^{\text{nd}}\) harmonic (\( T_F \)):
+
+\[
+T_F = \frac{\left( \frac{n}{2} \right) c_{52}^2}{(n-1)s_Q^2}
+\]
+
+where \( n \) is the number of days in a given year (365 or 366 for a leap year), \( C_{52} \) is the amplitude of the 52\(^{\text{nd}}\) harmonic, and \( s_Q \) is the standard deviation in discharge.
+
+After expressing \( T_T \) and \( T_F \) as percentages, we take the base 10 logarithm of their product to obtain an annual WHI:
+
+\[
+\text{WHI} = \log_{10}[B(T_T \times T_F)]
+\]
+
+in which \( B (= 10) \) is a coefficient chosen so that the median WHI \( \approx 0 \) among all 400 sites. Annual WHI values range typically from about -4 to +4 (although WHI values have no theoretical upper or lower bounds), with large positive values indicating strong weekly periodicity attributed to flow regulation at hydropower stations. In contrast, rivers with robust annual cycles with flows dominated by potent snowmelt-driven freshets and/or large (natural) storage capacity within abundant lakes, ponds and wetlands exhibit large negative WHI values. The transition between negative to positive WHI values marks a shift from annual to weekly dominant time scales of variability in flow.
+
+The 1980-2019 mean daily flows (considering the day of the week) for the Stuart River (BC), Mohawk River (New York), and Chattahoochee River at Buford Dam (Georgia)
+illustrate the WHI ranging from the minimum, median, and maximum values (Supplementary Fig. 13). WHI values remain site-specific and must be interpreted with care, particularly moving away (both upstream and downstream) from measurement sites with an intervening body of water, a confluence or another point of regulation altering hydropoeaking intensity.
+
+Statistical analyses. We first compute WHI time series at all 400 sites and develop a ‘climatology’ of index values for 1980-2019, with 14 years \( \leq n_y \leq 40 \) years depending on data availability at each site. Summary statistics (mean, median, standard deviation, etc.) of the 1980-2019 WHI data are tabulated and their distribution tested for normality using the Shapiro-Wilk test. Similar climatological analyses are developed for each decade (1920s to 2010s) with results reported when \( n_y \geq 5 \) years at a given site. The Mann-Kendall test (MKT\(^{61,62}\)) applied to all WHI time series with \( n_y \geq 30 \) years over 1980-2019 yields linear, monotonic trends in hydropoeaking intensity, with \( p < 0.05 \) considered locally statistically-significant. The field (or global) significance of the individual (or local) trend tests is assessed following Wilks\(^{60}\). The approach minimizes the false discovery rate (FDR) by first ranking \( p \)-values in ascending order for all trend tests with \( n_y \geq 30 \) years. Trends are then globally significant if \( p < p_{FDR} \) depending on the distribution of sorted \( p \)-values as:
+
+\[
+p_{FDR} = \max_{i=1,2,...,N} \{ p_i : p_i \leq (i/N)\ \alpha_{global} \}
+\]
+
+in which we set \( \alpha_{global} = 0.10 \). Trend analysis sensitivity to autocorrelation is tested in the Supplementary Methods.
+We assess the 1920 to 2019 annual mean, median and maximum WHI across all sites with available data in a given year to track the overall evolution of hydropeaking intensity across the USA and Canada. We also count the annual number and percentage of sites that fall in the top decile of all 1920-2019 WHI scores. An additional metric reported is the discharge-weighted WHI_{Qj} computed each calendar year (index \( j \)) as:
+
+\[
+\mathrm{WHI}_{Qj} = \sum_{i=1}^{n=400} \mathrm{WHI}_{i,j} \times Q_{i,j} / \sum_{i=1}^{n=400} Q_{i,j}
+\]
+
+where \( Q_{i,j} \) (km\(^3\) yr\(^{-1}\)) denotes the annual discharge and \( i \) is the site index. This yields a relative measure of annual volumetric flows affected by weekly hydropeaking cycles rather than just the number of sites. For monotonic trend analysis, the MKT is applied to time series of overall mean annual WHI over the 1980-2019 focus period. The potential influence of missing data on the evolution of average WHI over 1980-2019 is assessed by substituting incomplete time series with each missing site’s average WHI computed over the remainder of the focus period. This yields an adjusted mean annual WHI time series for a first order assessment of the influence of incomplete data.
+
+A histogram illustrates the distribution of two consecutive days when low flows emerge relative to the expected value of \( 1/7 = 0.143 \) were these randomly distributed. Fractions of the seven possible two-day combinations are partitioned according to \( \mathrm{WHI} \geq 0 \). The histogram also includes the corresponding mean WHI across all rivers for a given two-day combination of low flows. A Chi-Square goodness-of-fit test\(^{63}\) verifies the hypothesis of whether the distribution of low flow days differs significantly from the expected value with threshold \( p = 0.05 \). Similarly, we test if the corresponding mean WHI values for the
+two-day pairs with low flows follow a uniform distribution using a Chi-Square test. The relationship between annual WHI values and mean annual flows over 1980-2019 is evaluated using Pearson’s correlation coefficient with \( p < 0.05 \) considered statistically-significant values. Next, we transform annual discharge time series to standardized anomalies over the period of record at each site (with < 10% missing data in a calendar year). Decadal mean standardized anomalies for all available sites are then computed when \( n_y \geq 5 \) years in a given decade. These decadal average anomalies are binned in increments of 0.25 standard anomaly for comparison with WHI decadal distributions.
+
+To explore possible factors contributing to WHI trends we assess whether the dispersion of flows across the seven days of the week is changing over time. Here we first compile total annual flows (in m\(^3\) s\(^{-1}\)) for each of the seven days of the week, as well as the overall average, over each calendar year. Then we quantify departures (as a percentage) for each day of the week relative to the annual mean. Next, we calculate standard deviations (\( \sigma \)) in the percentage departures for the seven days of the week each year, creating \( \sigma \) time series for all 400 sites over 1980-2019. Finally, application of the MKT on the \( \sigma \) time series (when \( n_y \geq 30 \) years) yields 1980–2019 dispersion trends.
+
+**Data availability**
+
+Data related to this article can be found in the Supplementary Information and Supplementary Data files. Discharge data used in this study are available in the following publicly accessible databases: Centre d’Expertise Hydrique du Québec (http://www.cehq.gouv.qc.ca/hydrometrie/historique_donnees/info_validite.htm), US Bureau of Reclamation (https://data.usbr.gov/), United States Geological Survey
+(https://waterdata.usgs.gov/nwis), Water Survey of Canada’s Hydrometric Database (https://wateroffice.ec.gc.ca), Idaho Power (https://idastream.idahopower.com/Data/) and the International Boundary and Water Commission (https://www.ibwc.gov/Water_Data/). For some regulated rivers, proprietary discharge data can be requested from the following data providers: BC Hydro, Evolugen, H2O Power, Hydro-Québec, International Boundary and Water Commission, Manitoba Hydro, Nalcor Energy, NB Power, Ontario Power Generation, Rio Tinto, Tennessee Valley Authority, and TransAlta (see Supplementary Table 3). Source data are provided with this paper.
+
+Code availability
+The Fortran code used in this study is available online with explanation at http://web.unbc.ca/~sdery/NatComm.zip.
+
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+
+Acknowledgements. Thanks to the Water Survey of Canada and its provincial and territorial partners, the Centre d’Expertise Hydrique du Québec, USGS, BC Hydro, Evolugen by Brookfield Renewable, Transalta, Manitoba Hydro, Ontario Power Generation, H2O Power, Rio Tinto, Hydro-Québec, NB Power, Nalcor Energy, Idaho Power, the Tennessee Valley Authority, the International Boundary and Water Commission and the US Bureau of Reclamation for providing hydrometric data. Thanks to Aseem Sharma (UNBC/NRCan) for preparing the spatial plots, Clyde McLean and Joanna Barnard (Nalcor Energy), Jim Samms (NB Power), Marie Broesky, Kevin Gawne, Kristina Koenig, Phil Slota, Kevin Sydor, Efrem Teklemariam, Mike Vieira and Shane Wruth (Manitoba Hydro), Matt MacDonald (Ontario Power Generation), Erik Richards and Marc Mantha (H2O Power), Samer Alghabra and Mokhtar Moujahid (Hydro-Québec), Bruno Larouche and Richard Loubier (Rio Tinto), Michael Smilski (Transalta), Jim Li, Debbie Rinvold and Stephanie Smith (BC Hydro), Adrian Cortez and
+Delbert Humberson (International Boundary and Water Commission), Kelly Withers and Matti Hanninen (Evolugen) for providing comments on this work and for additional data for regulated rivers, Dwayne Akerman, Amber Brown, Michel Desjardins, Matt Falcone, Samantha Hussey, Lyssa Maurer, Angus Pippy, Melanie Taylor, and Frank Weber (Water Survey of Canada) for sharing supplemental hydrometric data, and Huilin Gao (Texas A&M), John Zhu (Texas Water Development Board), Julie Thériault (UQAM) and Mike Vieira and Kristina Koenig (Manitoba Hydro) for logistical support. This research was supported by the Natural Sciences and Engineering Research Council of Canada, Manitoba Hydro, and partners through funding of the BaySys project.
+
+Author contributions. S.J.D. designed the study, extracted hydrometric data and constructed time series of daily discharge for all rivers, formulated the weekly hydropeaking index, developed the codes, performed the statistical and computational analyses, and drafted line graphs with support from M.A.H.H., T.A.S., and T.J.T. S.J.D. wrote the manuscript with contributions from all co-authors and all contributed to manuscript refinement and revisions.
+
+Competing interests. The authors declare no competing interests.
+Figure Legends
+
+Fig. 1 Map of the 1980-2019 mean WHI values for 400 sites across the USA and Canada. Circle size corresponds to the two consecutive days with low flows beginning with the Saturday/Sunday (SS, largest symbols) combination and ending with the Friday/Saturday (FS, smallest symbols).
+
+Fig. 2 Histogram of the 1980-2019 frequency distribution of low flow days and corresponding WHI values. Black bars denote the two consecutive days with low flows while red bars represent the WHI values for 400 sites across the USA and Canada, 1980-2019. Fractions of the two consecutive days with low flows are partitioned according to positive (solid) and negative (hatched) WHI values. The days of the week begin with the Saturday/Sunday (SS) combination and end with the Friday/Saturday (FS) combination. The horizontal black line denotes the expected value if the two-day low flows were distributed randomly while the horizontal red line marks the mean WHI across the 400 sites.
+
+Fig. 3 Maps of the decadal mean WHI values for 400 sites across the USA and Canada. Maps are shown for a 1920-1929, b 1930-1939, c 1940-1949, d 1950-1959, e 1960-1969, f 1970-1979, g 1980-1989, h 1990-1999, i 2000-2009, and j 2010-2019. Circle size corresponds to the two consecutive days with low flows beginning with the Saturday/Sunday (SS, largest symbols) combination and ending with the Friday/Saturday (FS, smallest symbols). Results are shown only when \( n_y \geq 5 \) years in a given decade. Panels k and l represent the cumulative percentage of sites falling within one of 10 WHI bins and one of seven two-day combinations of low flows, respectively. In k, WHI bins match those used in the spatial plots a-j with a similar color palette (e.g., the maroon bars indicate WHI \( \geq 3.0 \) starting at a zero cumulative percentage). In l, the two-day combinations with low flows start on Friday/Saturday at a zero cumulative percentage (maroon bars) and end on Saturday/Sunday at 100% (black bars).
+
+Fig. 4 Map of the 1980-2019 monotonic trends in WHI at 380 sites across the USA and Canada. Red upward (blue downward) pointing triangles indicate positive (negative) trends. Trend magnitudes are proportional to the triangle sizes and green circles (pink outlines) indicate locally (globally) statistically-significant trends (\( p < 0.05 \)). Results are shown only when \( n_y \geq 30 \) years.
+Fig. 1 Map of the 1980-2019 mean WHI values for 400 sites across the USA and Canada. Circle size corresponds to the two consecutive days with low flows beginning with the Saturday/Sunday (SS, largest symbols) combination and ending with the Friday/Saturday (FS, smallest symbols).
+Fig. 2 Histogram of the 1980-2019 frequency distribution of low flow days and corresponding WHI values. Black bars denote the two consecutive days with low flows while red bars represent the WHI values for 400 sites across the USA and Canada, 1980-2019. Fractions of the two consecutive days with low flows are partitioned according to positive (solid) and negative (hatched) WHI values. The days of the week begin with the Saturday/Sunday (SS) combination and end with the Friday/Saturday (FS) combination. The horizontal black line denotes the expected value if the two-day low flows were distributed randomly while the horizontal red line marks the mean WHI across the 400 sites.
+
+![Histogram showing the frequency distribution of low flow days and corresponding WHI values by day of the week](page_352_670_1047_627.png)
+a 1920-1929
+b 1930-1939
+c 1940-1949
+d 1950-1959
+e 1960-1969
+f 1970-1979
+
+Legend
+[Legend color scale and symbols]
+
+![Map of the United States showing precipitation anomalies by year, with colored dots representing different values across the country](page_184_180_1207_1687.png)
+g 1980-1989
+h 1990-1999
+i 2000-2009
+j 2010-2019
+k
+l
+Fig. 3 Maps of the decadal mean WHI values for 400 sites across the USA and Canada. Maps are shown for a 1920-1929, b 1930-1939, c 1940-1949, d 1950-1959, e 1960-1969, f 1970-1979, g 1980-1989, h 1990-1999, i 2000-2009, and j 2010-2019. Circle size corresponds to the two consecutive days with low flows beginning with the Saturday/Sunday (SS, largest symbols) combination and ending with the Friday/Saturday (FS, smallest symbols). Results are shown only when \( n_y \geq 5 \) years in a given decade. Panels k and l represent the cumulative percentage of sites falling within one of 10 WHI bins and one of seven two-day combinations of low flows, respectively. In k, WHI bins match those used in the spatial plots a-j with a similar color palette (e.g., the maroon bars indicate WHI \( \geq 3.0 \) starting at a zero cumulative percentage). In l, the two-day combinations with low flows start on Friday/Saturday at a zero cumulative percentage (maroon bars) and end on Saturday/Sunday at 100% (black bars).
+Fig. 4 Map of the 1980-2019 monotonic trends in WHI at 380 sites across the USA and Canada. Red upward (blue downward) pointing triangles indicate positive (negative) trends. Trend magnitudes are proportional to the triangle sizes and green circles (pink outlines) indicate locally (globally) statistically-significant trends (\( p < 0.05 \)). Results are shown only when \( n_y \geq 30 \) years.
+
+![Map showing monotonic trends in WHI at 380 sites across the USA and Canada, with colored triangles indicating trend direction and significance.](page_276_370_1092_670.png)
+Table 1 List of sites with the top ten ranking WHI values, 1980-2019.
+
+<table>
+  <tr>
+    <th>Rank</th>
+    <th>Site</th>
+    <th>WHI</th>
+  </tr>
+  <tr>
+    <td>1</td>
+    <td>Chattahoochee R. at Buford Dam (GA)</td>
+    <td>3.299</td>
+  </tr>
+  <tr>
+    <td>2</td>
+    <td>Chattahoochee R. at West Point (GA)</td>
+    <td>3.276</td>
+  </tr>
+  <tr>
+    <td>3</td>
+    <td>Colorado R. at Hoover Dam (AZ/NV)</td>
+    <td>3.222</td>
+  </tr>
+  <tr>
+    <td>4</td>
+    <td>Nelson R. (MB)</td>
+    <td>2.916</td>
+  </tr>
+  <tr>
+    <td>5</td>
+    <td>Niagara R. (ON/NY)</td>
+    <td>2.900</td>
+  </tr>
+  <tr>
+    <td>6</td>
+    <td>Colorado R. at Lees Ferry (AZ)</td>
+    <td>2.844</td>
+  </tr>
+  <tr>
+    <td>7</td>
+    <td>Montreal R. (Lake Superior, ON)</td>
+    <td>2.790</td>
+  </tr>
+  <tr>
+    <td>8</td>
+    <td>Montreal R. (Ottawa Basin, ON)</td>
+    <td>2.716</td>
+  </tr>
+  <tr>
+    <td>9</td>
+    <td>Holston R. at Cherokee Dam (TN)</td>
+    <td>2.675</td>
+  </tr>
+  <tr>
+    <td>10</td>
+    <td>Columbia R. at Grand Coulee Dam (WA)</td>
+    <td>2.662</td>
+  </tr>
+</table>
+
+AZ: Arizona, GA: Georgia, MB: Manitoba, NV: Nevada, NY: New York, ON: Ontario, TN: Tennessee, WA: Washington
+Figures
+
+![Map showing WHI (1980-2019) values for 400 sites across the USA and Canada, with colored circles representing different WHI ranges and symbols indicating days in a week.](page_172_153_1207_1017.png)
+
+Figure 1
+
+Map of the 1980-2019 mean WHI values for 400 sites across the USA and Canada. Circle size corresponds to the two consecutive days with low flows beginning with the Saturday/Sunday (SS, largest symbols) combination and ending with the Friday/Saturday (FS, smallest symbols).
+Figure 2
+
+Histogram of the 1980-2019 frequency distribution of low flow days and corresponding WHI values. Black bars denote the two consecutive days with low flows while red bars represent the WHI values for 400 sites across the USA and Canada, 1980-2019. Fractions of the two consecutive days with low flows are partitioned according to positive (solid) and negative (hatched) WHI values. The days of the week begin with the Saturday/Sunday (SS) combination and end with the Friday/Saturday (FS) combination. The horizontal black line denotes the expected value if the two-day low flows were distributed randomly while the horizontal red line marks the mean WHI across the 400 sites.
+
+![Histogram showing fraction of WHI values by days of the week, with black bars for positive WHI and gray bars for negative WHI, and red bars for WHI values.](page_153_186_1207_1017.png)
+Figure 3
+
+Maps of the decadal mean WHI values for 400 sites across the USA and Canada. Maps are shown for a 1920-1929, b 1930-1939, c 1940-1949, d 1950-1959, e 1960-1969, f 1970-1979, g 1980-1989, h 1990-1999, i 2000-2009, and j 2010-2019. Circle size corresponds to the two consecutive days with low flows beginning with the Saturday/Sunday (SS, largest symbols) combination and ending with the Friday/Saturday (FS, smallest symbols). Results are shown only when ny \( \geq 5 \) years in a given decade. Panels k and l represent the cumulative percentage of sites falling within one of 10 WHI bins and one of seven two-day combinations of low flows, respectively. In k, WHI bins match those used in the spatial plots a-j with a similar color palette (e.g., the maroon bars indicate WHI \( \geq 3.0 \) starting at a zero cumulative percentage). In l, the two-day combinations with low flows start on Friday/Saturday at a zero cumulative percentage (maroon bars) and end on Saturday/Sunday at 100% (black bars).
+Figure 4
+
+Map of the 1980-2019 monotonic trends in WHI at 380 sites across the USA and Canada. Red upward (blue downward) pointing triangles indicate positive (negative) trends. Trend magnitudes are proportional to the triangle sizes and green circles (pink outlines) indicate locally (globally) statistically-significant trends (p < 0.05). Results are shown only when ny \( \geq 30 \) years.
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformation.pdf
+• SupplementaryTable2.xlsx
+• SupplementaryTable3.xlsx
+• WHITimeSeries.xlsx

0417a97ecc0d13717181d9623733f3148d5ba9e7ac583590ea0cf0862739b60a/preprint/preprint.md

@@ -0,0 +1,205 @@
+Hyperuniformity and phase enrichment in vortex and rotor assemblies
+
+Naomi Oppenheimer ( naomiop@gmail.com )
+Tel Aviv University   https://orcid.org/0000-0002-8212-3404
+David Stein
+Flatiron Institute
+Matan Yah Ben Zion
+New York University   https://orcid.org/0000-0002-9876-787X
+Michael Shelley
+Flatiron Institute   https://orcid.org/0000-0002-4835-0339
+
+Article
+
+Keywords: Particle Ensembles, Two-dimensional Fluid, Spontaneous Self-assembly, Hamiltonian Structure, Topological Defects
+
+Posted Date: April 26th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-385285/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on February 10th, 2022. See the published version at https://doi.org/10.1038/s41467-022-28375-9.
+Hyperuniformity and phase enrichment in vortex and rotor assemblies
+
+Naomi Oppenheimer,1,* David B. Stein,2 Matan Yah Ben Zion,3 and Michael J. Shelley2,4,†
+1School of Physics, and the Center for Physics and Chemistry of Living Systems, Tel Aviv University, Tel Aviv 6997801, Israel
+2Center for Computational Biology, Flatiron Institute, New York, NY 10010, USA
+3Laboratoire Gulliver, UMR CNRS 7083, ESPCI Paris, PSL Research University, 75005 Paris, France
+4Courant Institute, New York University, New York, NY 10012, USA
+(Dated: April 13, 2021)
+
+Ensembles of particles rotating in a two-dimensional fluid can exhibit chaotic dynamics yet develop signatures of hidden order. Such “rotors” are found in the natural world spanning vastly disparate length scales — from the rotor proteins in cellular membranes to models of atmospheric dynamics. Here we show that an initially random distribution of either ideal vortices in an inviscid fluid, or driven rotors in a viscous membrane, spontaneously self assembles. Despite arising from drastically different physics, these systems share a Hamiltonian structure that sets geometrical conservation laws resulting in distinct structural states. We find that the rotationally invariant interactions isotropically suppress long wavelength fluctuations — a hallmark of a disordered hyperuniform material. With increasing area fraction, the system orders into a hexagonal lattice. In mixtures of two co-rotating populations, the stronger population will gain order from the other and both will become phase enriched. Finally, we show that classical 2D point vortex systems arise as exact limits of the experimentally accessible microscopic membrane rotors, yielding a new system through which to study topological defects.
+
+Two-dimensional (or nearly so) fluid flows show rich and complex vortical dynamics. These can arise from flow interactions with boundaries (1, 2), the inverse cascades of 2D turbulence (3–5), from Coriolis force dominated atmospheric flows (6), and from quantization effects in super fluid He-II (7, 8). Point vortices have long been staples for the modeling of such inertially dominated inviscid flows. Kirchoff (9) was the first to describe point vortices using a Hamiltonian framework and his work was extended by many others [e.g. (10–13)], notably, Onsager (14) in his statistical mechanics treatment of 2D turbulence as clouds of point vortices.
+
+Remarkably, structurally identical Hamiltonian and moment constraints can arise in the microscopic viscously-dominated realm from a strict balance of dissipation with drive on immersed rotating objects. These objects include models of interacting transmembrane ATP-synthase “rotor-proteins” (15–17), and the planar interactions of rotors — microscopic particles driven to rotate by an external torque (18, 19). We refer to such systems as BDD systems, as in balanced drive and dissipation. In modeling rotational BDD systems other physical effects may also come into play, such as steric interactions, that can yield interesting complexities (17). Interacting assemblies of driven-to-rotate particles has become an area of intensifying interest in the active matter community (18–26)
+
+Here we study both point vortices and a BDD rotor system of rotationally-driven microscopic particles — membrane rotors — immersed in a flat membrane. We show that in both systems, their Hamiltonian conservation laws lead to distinct structural states — hyperuniformity, phase enrichment and crystallization (see Fig. 1), not yet observed for either system. We use the Hamiltonian to derive a bound for spatial correlations requiring hyperuniformity. We demonstrate numerically that rotational dynamics robustly self-assembles particles into a disordered hyperuniform 2D material; This self-assembly is insensitive to the details of the hydrodynamic interactions, steric repulsion, or the presence of impurities in the form of different rotation rates. At steady state, the long wavelength configuration is characterized by an isotropically vanishing structure factor, \( S(\mathbf{q} \to 0) \to 0 \) (where \( \mathbf{q} \) is the wavevector), leading to an isotropic band-gap (27–29).
+
+In classical mechanics, symmetries of the Hamiltonian \( \mathcal{H} \) restrict the phase-space of the conjugate variables, position and momentum. However, in 2D point vortex or BDD point rotor systems, the conjugate variables are the actual spatial coordinates of the ensemble \( \{ x_i \} \) and \( \{ y_i \} \). The conservation laws are therefore geometrical in nature, bounding the proximity and distribution of the particles. For both point vortices and membrane rotors, as well as for a myriad of other 2D rotating systems (18–21, 24, 30), the dynamics are dictated by Hamilton’s equations,
+
+\[
+\Gamma_i \mathbf{v}_i = \partial_i^\perp \mathcal{H},
+\]
+
+where \( \partial_i^\perp = (\partial y_i, -\partial x_i) \), \( \mathbf{v}_i \) is the velocity of rotor \( i \), and \( \Gamma_i \) is the circulation (proportional to the magnitude of the torque for rotors). Our finding, as we will show, is that the spatial arrangements of point vortices, as measured by \( S(\mathbf{q}) \), are dictated by the Hamiltonian,
+
+\[
+\mathcal{H}[\rho(\mathbf{r})] = \frac{N T^2}{4 \pi} \int d\mathbf{q} \frac{S(\mathbf{q})}{q^2}.
+\]
+
+To derive Eq. 2 and to find the Hamiltonian of \( N \) particles, we first describe the flow due to a single vortex in
+FIG. 1. Three different structural states of 2D vortices/rotors - hyperuniformity for Euler point vortices (A) and QG rotors/surface rotors (B), (C) phase enrichment induced by circulation differences where green (black) represents vortices of high (low) circulation, and (D) crystallization arising from hydrosteric interactions. The insets of (A), (B) and (C) show the structure factor, \( S(q) \). In (A) and (B) \( S(q) \) decays to zero at small \( q \), indicating that the distribution is hyperuniform. In (C) the structure factor shows the six distinct peaks of a hexagonal lattice.
+
+an ideal Euler fluid and show its equivalence to a point rotor in a viscous membrane. We then use the linearity of the equations to extend the result to the many-body case. An ideal point vortex is given by a singular vorticity, \( \omega = \nabla \times \mathbf{v} = \delta(\mathbf{r}) \). A 2D incompressible fluid can be described using a stream function \( \Psi \) such that the velocity, \( \mathbf{v} \), is given by \( \mathbf{v} = \partial^\perp \Psi \). This equation, combined with the equation above gives, \( \Psi = -\frac{1}{2\pi} \log r \) (12). The flow, \( \mathbf{v}(r) \), therefore, scales as \( 1/r \), where \( r = |\mathbf{r}| \).
+
+We switch now to a point rotor in a viscous membrane, driven by an external torque \( \tau \). Following Saffman and Delbrück’s seminal work (31), and many others that followed (32–34), we assume that the membrane is incompressible (\( \nabla \cdot \mathbf{v} = 0 \)), and that inertia is negligible. Under these assumptions, the Stokes momentum conservation equation for the membrane reads,
+
+\[
+0 = \eta_{2D} \nabla^2 \mathbf{v} + \eta_{3D} \left. \frac{\partial \mathbf{u}^\pm}{\partial z} \right|_{z=0^\pm} + \tau \partial^\perp \delta(\mathbf{r}),
+\]
+
+where \( \mathbf{v} \) is the 2D velocity in the plane of the membrane, \( \mathbf{u}^\pm \) is the 3D flow in the outer fluids, \( \eta_{2D} \) is the 2D viscosity, and \( \eta_{3D} \) is the viscosity of the outer fluids. The second term on the right hand side is the surface shear stress of the outer fluids, and the third term is the force due to a rotating point object. There is no pressure contribution when the motion is purely rotational. This equation is coupled to the equations of the outer fluids. It is easy to solve the above equations using a 2D Fourier Transform (\( \tilde{F}(\mathbf{q}) = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} F(\mathbf{r}) e^{-i \mathbf{q} \cdot \mathbf{r}} d^2 r \)), giving:
+
+\[
+\tilde{\mathbf{v}}(\mathbf{q}) = \Gamma \partial^\perp \tilde{\Psi} \quad ; \quad \tilde{\Psi} = \frac{1}{q(q+\lambda^{-1})},
+\]
+
+where \( \Gamma = \tau / \eta_{2D} \), and \( \lambda = \eta_{2D}/2\eta_{3D} \) is the Saffman Delbrück length. At small distances (\( r \ll \lambda \)) momentum travels in the plane of the membrane. At large distances (\( r \gg \lambda \)) momentum travels through the outer fluid as well (35, 36). In real space \( \Psi(\mathbf{r}) = 1/4(H_0(r/\lambda) - Y_0(r/\lambda)) \), where \( H_0 \) and \( Y_0 \) are zeroth order Struve function and Bessel function of the second kind respectively.
+
+In the limit of small distances, \( r \ll \lambda \), the stream function is, \( \Psi \approx -\frac{1}{2\pi} \log r \), i.e. exactly the same as for an ideal point vortex. In the opposite limit, \( r \gg \lambda \), the stream function becomes \( \Psi = \frac{1}{2\pi r} \) as in quasigeostrophic (QG) flows — atmospheric or oceanic flows coming from gradients in pressure coupled to the Coriolis force (37), or driven rotors on the surface of a fluid (22). A membrane rotor, therefore, transitions from a point vortex for Euler at small distances to that of QG flow at large distances. The velocity is given by derivatives of \( \Psi \) and is thus proportional to \( 1/r \) (\( 1/r^2 \)) in the limit of small (large) distances (see Fig. 2B). For simplicity, we work primarily in the limit of small distances, \( r \ll \lambda \), since in this limit the dynamics in a membrane converge with those of point vortices (many results still apply to the more general case as shown in the SI). In what follows, we will use “point vortices” when there are only hydrodynamic interactions and “rotors” when the particles have steric interactions in addition to hydrodynamic ones.
+
+The dynamics of \( N \) point vortices follows from the Hamiltonian \( \mathcal{H} = \frac{1}{2} \sum_{i \neq j} \Gamma_i \Gamma_j \Psi(|\mathbf{r}_i - \mathbf{r}_j|) \), where \( \Gamma_i \) is the circulation of vortex \( i \) (in a membrane \( \Gamma_i = \tau_i / \eta_{2D} \)). The Hamiltonian depends on the conjugate variables \( \mathbf{r}_i = (x_i, y_i) \), [normalized by the circulation \( \sqrt{|\Gamma_i|} \mathrm{sgn}(\Gamma_i) \)], i.e. the positions of the vortices (12). The symmetries of the Hamiltonian correspond to conservation laws (39). In this case, we have symmetries with respect to translation in time, space, and rotation, corresponding to conservation of the Hamiltonian itself, and of the first and second moments of the distribution, \( \mathbf{L} = \sum_i \Gamma_i \mathbf{r}_i (= 0 \) wlog), and \( M = \sum_{i,j} \Gamma_i \Gamma_j r_i^2 \). Thus, the initial area cannot change dramatically, particles cannot drift to infinity since the second moment is fixed, nor can they collapse to a point since the Hamiltonian is conserved. These properties are readily observed in simulations. Figure 2D shows typical trajectories of 200 membrane rotors. The initial distribution is random in a predefined finite area, and the dynamics are chaotic (40). The final configuration occupies nearly the same region of space as the initial configuration does, and the conservation laws hold
+FIG. 2. (A) A representation of a membrane rotor — a disk rotating due to a torque \( \tau \) in the plane of the membrane. (B) The velocity field due to a membrane rotor (solid line) which scales as a point vortex \( v \sim 1/r \) at small distances (dotted), \( r/\lambda \ll 1 \), transitioning to a QG behavior at large distances \( v \sim 1/r^2 \) (dashed). (C) Contour dynamics of an ellipse with radii ratios \( r_l/r_s \leq 3 \), where \( r_l \) (\( r_s \)) is the major (minor) axis. Starting from the same contour, the dynamics differ according to the radius relative to the SD length. Blue is in the limit \( r_l \ll \lambda \). In this limit the ellipse is rotating as a rigid body, as predicted by Kelvin (38) for an elliptic patch in an Euler fluid. Black is in the limit \( r_l \gg \lambda \), no longer conserving its shape since the large distance flow is in the quasigeostrophic regime. (D) 200 point membrane rotors, blue is the initial random configuration, black is the final configuration. Solid line shows typical trajectory of an individual vortex. Note that the area did not change considerably since the system of vortices is self-bounding. (E) the relative error in \( \mathcal{H} \) and \( M \) over a few cycle times, \( t_c \).
+
+to high precision in our simulations, as shown in Fig. 2E. This self confining property of vortex dynamics has further consequences, as we now show.
+
+**Hyperuniformity.** Hyperuniformity is the suppression of density-density fluctuations at small wavenumbers (or correspondingly, at large distances) (41–43). Disordered hyperuniformity can emerge due to short ranged interactions such as those that arise in sheared suspensions (30, 44, 45), jammed materials (46), and for spinning particles (47). Here we will show hyperuniformity emerging from long ranged interactions, similar to its emergence in sedimentation of irregular objects (48). A good way to characterize hyperuniformity is the structure factor, defined as \( S(\mathbf{q}) = N^{-1}|\tilde{\rho}(\mathbf{q})|^2 \), where \( \rho(\mathbf{r}) = \sum_i \delta(\mathbf{r} - \mathbf{r}_i) \) is the coarse grained density. In a hyperuniform material, \( S(q) \) goes to zero as a power law at small wavenumbers. We argue that point vortices must be hyperuniform due to the conservation of the Hamiltonian. For a density of rotors, the Hamiltonian is given by \( \mathcal{H}[\rho(\mathbf{r})] \sim \frac{\Gamma^2}{2} \int d\mathbf{r} \int d\mathbf{r}' \rho(\mathbf{r}) \rho(\mathbf{r}') \psi(|\mathbf{r} - \mathbf{r}'|) \). Using the convolution theorem, we find a general relation between the Hamiltonian and the structure factor
+
+\[
+\mathcal{H}[\rho(\mathbf{r})] = \frac{N \Gamma^2}{4 \pi} \int d\mathbf{q} S(\mathbf{q}) \tilde{\Psi}(\mathbf{q}).
+\]
+
+In the case of point vortices, \( \tilde{\Psi}(\mathbf{q}) = 1/q^2 \), which gives Eq. 2. For the integral of Eq. 2 to converge in 2D, \( S(\mathbf{q}) \sim q^\alpha \) near the origin, and we must have \( \alpha > 0 \). In other words, an ensemble of point vortices is hyperuniform (a similar calculation in the QG limit, where \( \tilde{\Psi} = \lambda/q \), yields \( \alpha > -1 \)). Figures 3B and 4C, show an apparent \( \alpha \sim 1.3 \) scaling for point vortices, consistent with the above argument.
+
+Using simulations we show that a set of \( N \) vortices, uniformly distributed within a radius \( R \), evolves to a disordered steady-state with a hidden order visible to the naked eye (compare Figures 3A left and right). We quantitatively characterize the system in steady-state in three ways: **(1)** *The structure factor.* At steady-state \( S(\mathbf{q}) \) shows a distinct cavity, at \( q \approx 0 \), \( S(\mathbf{q}) \to 0 \), for both points vortices (Fig. 3A) and rotors (Fig. 3C). All simulations produce a hyperuniform arrangement. **(2)** *Perturbations.* We demonstrate that hyperuniformity is robust under different perturbations, be it in the form of numerical errors, repulsive interactions, or impurities (in the next section). For point vortices, the steady state appears later and later as the timestep is decreased, suggesting that perturbations are necessary for convergence, here very small but persistent timestepping errors (49). Adding steric interactions, hyperuniformity appears on a timescale that is independent of the timestep. Moreover, with steric interactions, as the area fraction \( \phi \) of the particles is increased, the system transitions from disordered hyperuniform, to an ordered hyperuniform hexagonal lattice at \( \phi \sim 0.5 \), as can be seen in Fig. 3C. The inset of Fig. 3B shows the averaged structure factor where at intermediate area fractions we see Percus-Yevick type features for the structure factor of disks (50). **(3)** *The returnity.* We observe that at late times the ensemble of point vortices rotates almost as a rigid body and each particle goes back to its position at the previous cycle. We measure particle deviations by what we term the “returnity” (see Fig. 3D for details). The system may seem to have reached an absorbing state, but the motion of vortices over many cycles is still chaotic.
+
+**Rotation induced phase enrichment.** We now show that for mixed populations of fast and slow rotating particles, there is phase enrichment of both populations and hyperuniformity of the fast ones. Consider a mixture of two equally numbered populations (\( \rho_f = \rho_h \) at \( t = 0 \)) initially placed within the same radius \( R \). \( \rho_f \) rotates slowly with \( \Gamma_f \ll \Gamma_h \), where \( \Gamma_h \) is the circulation of the second population. Figure 4A shows long-time simulation results for 10,000 point vortices. The two populations behave very differently. The fast vortices remain in
+FIG. 3. Hyperuniformity in ensembles of point vortices and rotors. (A) Snapshots of 10,000 point vortices initially (left) and at steady-state (right). Insets show the structure factor, \( S(q) \) showing a distinct cavity at steady-state. (B) Angular average of the structure factor shown in A, in a log-log scale with solid line showing a \( q^{1.3} \) scaling. Error bars are standard deviation over 10 well separated timesteps. Inset shows the structure factor of the rotors shown in (C) with increasing hue corresponding to increased concentration \( \phi = (0.14, 0.24, 0.37, 0.54) \). Solid line is the same \( \alpha \sim 1.3 \) scaling. (C) Steady state configurations of 2,000 membrane rotors with the corresponding structure factors, showing a transition from disordered hyperuniformity to a hexagonal lattice. (D) A plot of the returnuity measuring the deviation of particle \( i \) at position \( r_i \) from its position at the previous cycle, \( returnuity = \Delta r_i(t_{\text{cyc}})/R \), where \( R \) is the initial radius of the ensemble. The cycle time, \( t_{\text{cyc}} \), is defined at steady state as the distance between two adjacent minima of the function \( f = \sum_i^N \Delta r_i(\Delta t) \), where \( \Delta t \) is the time difference. Color scheme is from blue to yellow with increasing deviation.
+
+a disk of only slightly smaller size than their initial area (Fig. 4B). The slow particle distribution shows a significant expansion. In addition, there is a striking difference when comparing the independently computed structure factors of these two populations, the fast vortices are hyperuniform with the same scaling as before, \( S(q) \sim q^{1.3} \), whereas the slow ones show no signs of hyperuniformity (Fig. 4C). This difference is dramatic enough to be visible in a cursory examination of the separate distributions; see Fig. 4A.
+
+Using a heuristic model, we show that the conservation laws allow two solutions at steady-state. In one solution, the two populations remain confined to a circle of the same radius. In the second solution, the radius of the slower population expands, while the radius of the faster population contracts. We then show that the segregated solution is the one that maximizes the number of states in the system. For simplicity, we assume that the final steady states are uniform (not true for the slow vortices as is clear from Fig. 4B). There are two possible solutions where \( \mathcal{H} \) and \( M \) are conserved — in the first, the initial radius, \( R \), does not change; in the second, the radius of the fast vortices slightly decreases to \( R_h \), allowing the slow vortices to expand to a larger radius \( R_l \) given by \( R_l^2 = (\gamma + 1)R^2 - R_h^2 \gamma \), where \( \gamma = \Gamma_h/\Gamma_l \) (see Fig. 4D). Linearly expanding in \( 1/\gamma \), we find that \( R_h \simeq R(1-\beta/\gamma) \) for the high circulation vortices, where \( \beta \) is a positive prefactor of order 1. The slow vortices asymptote to \( R_l \simeq R\sqrt{1+2\beta}+O(1/\gamma) \). The simulation results indicate that the outer radius indeed asymptotes to a larger valued
+FIG. 4. Two populations of vortices with different circulations showing phase enrichment, \( \Gamma_l = 2\pi \) in black and \( \Gamma_h = 256\pi \) in green. (A) Steady-state configuration for ten thousand point vortices of a circulation ratio \( \gamma = \Gamma_h / \Gamma_l = 128 \). Each inset shows a close-up view of one of the populations within the same physical region. (B) Density of the configuration in (A), \( \rho(r) \), averaged over angle as a function of distance from the center. Note how density fluctuations are suppressed for the high circulation vortices, as is more clearly observed by the averaged structure factor, \( S(q) \), in (C), where the solid green line shows a \( \sim q^{1.3} \) power law. (D) The second moment for \( N = 10,000 \) vortices. Plotted separately for the high (in green) and low (in black) vortices at steady state as a function of \( \gamma \) (i.e. increasing \( \Gamma_h \)). (E) LOSSLESS compression for the two populations showing an increase (decrease) in file size (an estimate of entropy) for the low (high) circulation vortices over a couple of cycles. In blue is the file size for the total system. Solid line is a moving average, time is normalized by an average cycle time \( t_c \).
+
+constant as \( \gamma \) increases and does not increase indefinitely (see Fig. 4D and SI).
+
+A solution with two different radii is therefore possible and is indeed observed at large circulation ratios. Such a solution is favored entropically since it maximizes the available states. Asymptotically at large \( \gamma \), the main entropical contribution is volumetric, \( \Delta S_{volume} = 2N \log(R_{final}/R_{initial}) \). Since the high circulation vortices hardly change radius, \( R_h \xrightarrow{\gamma \to \infty} R_r \), the change in entropy is coming mainly from the expansion of the low circulation vortices and is given by \( \Delta S_{total} \sim N \log(1+2\beta) > 0 \). Coupling the two populations allows one population to expand where before it was bounded (51). The situation is analogous to depletion interactions, where the net entropy of a system increases by condensing the large particles allowing for the small particles to explore a larger volume (52).
+
+A simple way to estimate the entropy in a system is by using LOSSLESS compression, as suggested by Refs. (53, 54). Compressing plots of particle positions in a system of 10,000 point vortices with circulation ratio \( \Gamma_h / \Gamma_l = 128 \) shows an increase in file size for \( \rho_l \) and a decrease for \( \rho_h \), while the combined system is increasing, see Fig. 4E.
+
+Discussion. We have shown that driven particles in a membrane or a soap film, as well as point vortices in an ideal 2D fluid, have geometrical conservation laws which limit their distribution. These conservation laws dictate different possible structural states — namely hyperuniformity and phase enrichment. We have shown that hyperuniformity is robust to several forms of perturbations whether arising due to numerical errors, steric interactions, or impurities in the form of low circulation vortices. For rotors with steric interactions, the unbounded ensemble crystallizes into a hexagonal lattice when the area fraction \( \phi \gtrsim 0.5 \) (see also (17)). We have limited the discussion to membrane rotors and vortices, but the results hold for other settings in which mass is conserved in the 2D plane, e.g. particles at the surface of a fluid (see SI).
+
+What is especially interesting about our particular BDD system is its potential for experimental realizability, its moment and Hamiltonian structure, and that its near-field interactions (i.e. below the Saffman-Delbruck length) are identical to those of Euler point vortices. Further, the far-field interactions of membrane rotors are identical to those of point vortices of the semi-quasigeostrophic equations (37, 55, 56) used to model atmospheric flows. Thus, to observe the interesting dynamical features we describe, one does not need to go to the atmospheric scale, or cool a fluid to near-zero temperature. In principle, one can simply observe microscopic particles on a soap film, in smectic films, a membrane, or even at the surface of a fluid (19, 22, 57, 58).
+
+Methods. Simulations. Simulations were performed in Python. Random initial configurations within the unit disk were found by rejection sampling (points in the unit rectangle were sampled uniformly, transformed to the rectangle \([-1,1]^2\), and those with \( r > 1 \) were discarded). The initial Hamiltonian \( H_0 \) is computed at \( t = 0 \), and the relative error \( \epsilon(t) = |H_t - H_0|/H_0 \) is
+monitored as a measure of fidelity. For simulations of rotors (i.e. with steric repulsion), a 5th order explicit Runge-Kutta method based on the Dormand-Prince scheme (59) with a fixed timestep size of \( \delta t = 10^{-7} \) was used. Long integration times were required for simulations of point vortices, and for these simulations an explicit eighth-order adaptive method based on the Dormand-Prince scheme (60, 61) was used, with both relative and absolute tolerances set to \( 10^{-6} \). The specific implementation of the scheme used was the DOP853 method of scipy.integrate (62). For simulations of 10,000 point vortices with \( \Gamma = 2\pi \), \( \epsilon(t) < 1.6 \times 10^{-3} \) up to \( t \approx 16,000 \) cycles, while for simulations with 5,000 vortices with \( \Gamma = 2\pi \) and 5,000 vortices with \( \Gamma = 256\pi \), \( \epsilon(t) < 5 \cdot 10^{-3} \) up to \( t \approx 10 \) cycles. Time is normalized by the average cycle time, \( t_c \approx 4\pi^2 R^2 / \sum_i \Gamma_i \), where \( R \) is the initial radius.
+
+Steric interactions were taken as the repulsive part of a harmonic potential, i.e. for two particles whose centers are distance \( r_i \) apart, \( F = -k r_{ij} \) if \( r_{ij} < 2a \) and zero otherwise. The use of a harmonic potential, rather than a sharp step function for hard core particles, provided improved numerical stability and convergence. A large \( k \) value was chosen to ensure no overlap between particles, \( k = 1 \cdot 10^6 \), for particles of size \( a = 0.01 \).
+
+Structure factor. To accurately compute the structure factor \( S(\mathbf{q}) \) we use a type-I non-uniform fast-Fourier transform (63). Explicitly, points are restricted to a windowing region which is confined entirely within the unit disk. The frequencies \( \vec{\rho}(\mathbf{q}) \) are computed for the first 512 modes in each direction, and the average value (i.e. \( \vec{\rho}(0) \)) is set to 0. This results in structure factors in the plane, such as those shown in Fig. 3. Except in those cases where crystallization occurs, these structure factors are azimuthally isotropic. To summarize this information, the angular average over the structure factor was calculated by slicing the result to 1000 equal bins between \( q_{\min} \) and \( q_{\max} \) and taking the mean of the results that fell within each slice.
+
+Compression. A plot of the positions of the point vortices was compressed using PNG with AGG backend. Each vortex was plotted by a single pixel. The total size of the plots was kept fixed in time. The figure size was chosen to minimize overlap between neighboring vortices but maintaining a computationally accessible file size.
+
+Acknowledgment We thank Haim Diamant for insightful discussions regarding the emergence of hyperuniformity from the conservation laws, to Martin Lenz for suggesting a simple heuristic model of the phase enrichment, and to Enkeleida Lushi. N.O. acknowledges supported by the Israel Science Foundation (grant No. 1752/20). M.J.S. acknowledges support by the National Science Foundation under Awards Nos. DMR-1420073 (NYU MRSEC), DMS-1620331, and DMR-2004469.
+
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+Figures
+
+Figure 1
+
+Three different structural states of 2D vortices/rotors - hyperuniformity for Euler point vortices (A) and QG ro-tors/surface rotors (B), (C) phase enrichment induced by circulation differences where green (black) represents vortices of high (low) circulation, and (D) crystallization arising from hydrosteric interactions. The insets of (A), (B) and (C) show the structure factor, S(q). In (A) and (B) S(q) decays to zero at small q, indicating that the distribution is hyperuniform. In (C) the structure factor shows the six distinct peaks of a hexagonal lattice.
+
+Figure 2
+
+(A) A representation of a membrane rotor — a disk rotating due to a torque \( \tau \) in the plane of the membrane. (B) The velocity field due to a membrane rotor (solid line) which scales as a point vortex \( v \propto 1/r \) at small distances (dotted), \( r/\lambda << 1 \), transitioning to a QG behavior at large distances \( v \propto 1/r^2 \) (dashed). (C) Contour dynamics of an ellipse with radii ratios \( rl/rs \leq 3 \), where \( rl \) (rs) is the major (minor) axis. Starting from the same contour, the dynamics differ according to the radius relative to the SD length. Blue is in the limit \( rl << \lambda \). In this limit the ellipse is rotating as a rigid body, as predicted by Kelvin (38) for an elliptic patch in an Euler fluid. Black is in the limit \( rl >> \lambda \), no longer conserving its shape since the large distance flow is in the quasigeostrophic regime. (D) 200 point membrane rotors, blue is the initial random configuration, black is the final configuration. Solid line shows typical trajectory of an individual vortex.
+Note that the area did not change considerably since the system of vortices is self-bounding. (E) the relative error in H and M over a few cycle times, tc.
+
+![Panel A: Initial and Steady state point vortices; Panel B: Plot of \( \langle S(q) \rangle \) vs q; Panel C: Steady state rotors; Panel D: Returnity at different cycles](page_186_232_1207_1012.png)
+
+Figure 3
+
+Hyperuniformity in ensembles of point vortices and rotors. Please see manuscript .pdf for full figure caption
+Figure 4
+
+Two populations of vortices with different circulations showing phase enrichment, \( \Gamma = 2\pi \) in black and \( \Gamma h = 256\pi \) in green. (A) Steady-state configuration for ten thousand point vortices of a circulation ratio \( \gamma = \Gamma h / \Gamma = 128 \). Each inset shows a close-up view of one of the populations within the same physical region. (B) Density of the configuration in (A), \( \rho(r) \), averaged over angle as a function of distance from the center. Note how density fluctuations are suppressed for the high circulation vortices, as is more clearly observed by the averaged structure factor, \( S(q) \), in (C), where the solid green line shows a \( \propto q^{1.3} \) power law. (D) The second moment for \( N = 10,000 \) vortices. Plotted separately for the high (in green) and low (in black) vortices at steady state as a function of \( \gamma \) (i.e. increasing \( \Gamma h \)). (E) LOSSLESS compression for the two populations showing an increase (decrease) in file size (an estimate of entropy) for the low (high) circulation vortices over a couple of cycles. In blue is the file size for the total system. Solid line is a moving average, time is normalized by an average cycle time \( t_c \).
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SI.pdf

042a95bb963a3fded623677d176d398a6df7372697fadd494fd320558dfef397/preprint/preprint.md

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+Mapping Intrapatient Response Heterogeneity and Lesion-specific Relapse Dynamics in Metastatic Colorectal Cancer
+
+Jiawei Zhou
+University of North Carolina at Chapel Hill
+
+Amber Cipriani
+University of North Carolina at Chapel Hill https://orcid.org/0000-0003-3596-0581
+
+Yutong Liu
+University of North Carolina at Chapel Hill
+
+Gang Fang
+University of North Carolina at Chapel Hill
+
+Quefeng Li
+University of North Carolina at Chapel Hill
+
+Yanguang Cao (yanguang@unc.edu)
+University of North Carolina at Chapel Hill https://orcid.org/0000-0002-3974-9073
+
+Article
+
+Keywords:
+
+Posted Date: March 28th, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1447896/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+Mapping Intrapatient Response Heterogeneity and Lesion-specific Relapse Dynamics in Metastatic Colorectal Cancer
+
+Jiawei Zhou¹, Amber Cipriani¹,², Yutong Liu³, Gang Fang⁴, Quefeng Li³, Yanguang Cao¹,⁵*
+
+¹Division of Pharmacotherapy and Experimental Therapeutics, School of Pharmacy, University of North Carolina at Chapel Hill, NC 27599, USA; ²UNC Health Medical Center, Department of Pharmacy, Chapel Hill, NC 27514; ³School of Public Health, University of North Carolina at Chapel Hill, NC 27599, USA; ⁴Division of Pharmaceutical Outcomes and Policy, School of Pharmacy, University of North Carolina at Chapel Hill, NC 27599, USA; ⁵Lineberger Comprehensive Cancer Center, School of Medicine, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
+
+Corresponding author:
+
+Yanguang Cao, Ph.D.
+
+Division of Pharmacotherapy and Experimental Therapeutics, UNC School of Pharmacy
+
+2318 Kerr Hall, UNC Eshelman School of Pharmacy
+
+Chapel Hill, NC 27599-7569
+
+E-mail: yanguang@unc.edu
+
+Phone: +1-919-966-4040.
+Abstract
+
+Achieving systemic tumor control across metastases is vital for long-term patient survival but remains intractable in many patients. High intrapatient heterogeneity persists, conferring many dissociated responses across metastatic lesions. Most studies of metastatic disease focus on tumor molecular and cellular features, which are crucial to elucidating the mechanisms underlying intrapatient heterogeneity. However, our understanding of intrapatient heterogeneity on the macroscopic level, such as lesion dynamics in growth, response, and relapse during treatment, remains rudimentary. This study investigated intrapatient heterogeneity through analyzing 116,542 observations of 40,612 lesions in 4,308 metastatic colorectal cancer (mCRC) patients. Despite significant differences in their response and relapse dynamics, metastatic lesions converged on four phenotypes that varied with anatomical site. Importantly, we found that organ-level relapse sequence was closely associated with patient survival, and that patients with the first relapses in the liver often had worse survival. In conclusion, our study provides insights into intrapatient response heterogeneity in mCRC and creates impetus for metastasis-specific therapeutics.
+Introduction
+
+Metastasis is the leading cause of cancer mortality¹. Unfortunately, antitumor therapies are still designed mostly based on the biology of primary tumors, with little consideration of metastases²,³. Achieving systemic tumor control across metastases is critical for long-term survival but remains intractable in many patients. Some metastases respond highly to treatment while others do not at all, resulting in many dissociated and heterogeneous responses within patients⁴⁻⁷. Lesion-level response and relapse heterogeneity are common in many cancer types, but our understanding of such intrapatient heterogeneity and its relevance to prognosis remains rudimentary.
+
+Most investigations of intrapatient lesion heterogeneity focus on tumor genetic mutations, clonal compositions, or transcriptomics ⁸⁻¹⁰. These molecular and cellular characterizations are critical to elucidating the underlying mechanisms of intrapatient response heterogeneity¹¹,¹². However, it is equivalently critical to study intrapatient heterogeneity on the macroscopic level, such as distinct lesion dynamics in growth, response, and relapse during treatment, as well as their potential phenotypic convergence anatomically. These phenotypes would complement molecular and cellular analyses for a holistic view of intrapatient heterogeneity. This study sought to investigate intrapatient response heterogeneity through mapping lesion-specific response and relapse dynamics in metastatic CRC (mCRC).
+
+Colorectal cancer (CRC) is the third leading cause of cancer-related death¹³. About 20% of CRC patients have distant metastases at diagnosis; the five-year relative survival rate is only 14% for these patients¹⁴,¹⁵. Intrapatient response heterogeneity is common in CRC patients treated with either standard chemotherapy alone or in combination with targeted therapy¹⁶. We, along with others, have found that high intrapatient response heterogeneity is associated with worse survival¹⁶⁻¹⁹. Importantly, we also found favorable responses in liver metastases predicted longer patient survival, compared to lesions in the lungs and lymph nodes (LN)¹⁶. Characterizing intrapatient response heterogeneity in mCRC is valuable for prognosis and therapies.
+The local microenvironment selects tumor phenotypes in response to treatment, leading to heterogeneity across anatomically distinct lesions in terms of response and relapse dynamics\(^{20,21}\). Characterizing their phenotypic differences (divergence) or similarities (convergence) could yield insights into tumor ecological features and systemic resistance. To map the lesion-level response and relapse patterns in mCRC, we first applied a mathematical model to capture tumor growth dynamics in 4,308 mCRC patients. Next, individual lesion-specific response and relapse probabilities were mapped to predict their phenotypic divergence and convergence across anatomical sites. Last, we applied a machine learning approach to analyze the relapse sequence across lesions and its relevance to long-term patient survival. Our study provides insights into intrapatient phenotypic heterogeneity in mCRC and yields substantial implications for designing metastasis-specific therapeutics.
+Results
+
+Data Sources and Structure
+
+To evaluate lesion-level response and relapse dynamics in mCRC, we collected longitudinal radiographical measurements of metastatic lesions in colorectal cancer (CRC) patients from Project Data Sphere. In total, 4,308 patients with 40,612 lesions from eight Phase III trials were included. The inclusion and exclusion criteria are presented in Fig. 1a. The distribution of lesion number across organs is shown in Fig. 1b. The total target lesions were 19,180 with 94,174 radiographic measurements, and there were 18,594 nontarget lesions and 2,838 new lesions with response status over time. Additional information including patients’ demographic and clinical characteristics (e.g., age, gender, race, body mass index [BMI], tumor type, treatment history, RECIST response, and KRAS status), progression-free survival (PFS) and overall survival (OS) are reported in Table 1. We also included the tumor longitudinal measurements in a head and neck squamous cell carcinomas (mHNSCC) trial for external validation. The data was also from Project Data Sphere with similar criteria as CRC data (Supplementary Fig. 3a).
+
+Model recapitulated tumor growth dynamics of individual lesions
+
+The tumor growth dynamics of 19,180 target lesions with 94,174 radiographical measurements were recapitulated with a widely adopted growth model\(^{22}\). The three dynamic parameters in the model are the regression rate \(Kd\), the fraction of non-responding cells \(F\), and the progression rate \(Kg\) (Fig. 2a). The model was optimized using a nonlinear mixed effect (NLME) modeling approach, which allows the estimation of three dynamic parameters at the individual level and their inter-lesion variance in the population. Overall, the model adequately recapitulated the longitudinal profiles of tumor radiographic measurements for each lesion. The goodness-of-fit and model visual predictive check plots, as well as representative individual fittings, show good model predictive performance (Supplementary Fig. 1).
+Population estimates and inter-lesion variances in tumor dynamic parameters are summarized in Supplementary Table 1. The parameters for individual lesions significantly differed across organs (p < 0.0001, Fig. 2b). Among all metastases, lesions in the bone exhibited the lowest response depth (1-F), while lesions in the genitourinary and reproductive (GR) system had the fastest progression rates (Kg), and kidney lesions showed the lowest regression rates (Kd). Among three most abundant metastatic sites (liver, lung, and LN), lesions in the liver showed the highest response depth but the fastest progression rates, suggesting the unique growth feature of liver lesions.
+
+Higher treatment-resistant cell fraction F is associated with slower rates of regression (Kd, r = -0.69, p < 0.005) and faster rates of progression (Kg, r = 0.53, p < 0.05, Fig. 2c). Progression rates seemed to be independent of regression rates (Fig. 2c). Remarkably, no significant correlations were observed between baseline tumor burden and all tumor dynamic parameters (Fig. 2d). Large tumor burden, on the individual lesion level, did not necessarily confer slow regression rates, high treatment-resistant fractions, or slow progression rates, implying that tumor burden at baseline is not a robust prognostic factor in mCRC^{23-25}. Notably, metastatic lesions under antibody targeted therapy (bevacizumab and/or panitumumab) plus chemotherapy (FOLFOX or FOLFIRI), compared to standard chemotherapy alone, showed significantly deeper response (effect size = 0.43) and lower progression rates (effect size = 0.26), but had a moderate effect on tumor regression rates (effect size = 0.06, Supplementary Fig. 2).
+
+Response and relapse dynamics suggest phenotypic convergence on organ level
+
+The tumor growth model predicted the longitudinal profiles of response and relapse for each target lesion. Response and relapse times were then derived as the duration from the start of treatment to the time of response or relapse per RECIST v1.1^{26}, respectively. We integrated the response time for both target and non-target lesions and the relapse time for all lesions, including the new ones, into random effect Cox proportional models^{27}. The Cox model predicted the relative probabilities of lesion response or relapse at the organ level. Of note, treatment effects from either chemotherapy or combination therapy were included as a confounding factor in the Cox regression model. With that, we could focus on the organ-
+intrinsic response and relapse characteristics. The hazard ratios for the response and relapse across organs are shown in Fig. 3a and Fig. 3b.
+
+With abdominal lesions as the reference, metastatic lesions in the liver were most likely to respond to treatments, whereas lesions in the brain/central nervous system (CNS) were least likely (Fig. 3a). Lesions in the gastrointestinal (GI) system, skin, and bone were significantly less likely to respond than abdominal lesions. Lesions in the spleen, lung, and peritoneum showed comparable responses. The probability of relapse also differed greatly across anatomical sites (Fig. 3b). The metastatic lesions with the highest likelihood of relapse were those in the brain/CNS, GR system, and liver, while lesions in the GI system, and regional and distal LNs were least likely.
+
+We then integrated organ-specific response and relapse probabilities to investigate their potential phenotypic convergence across anatomical sites. As in Fig. 3c, an anatomical chart of organ-specific response and relapse probabilities was created based on their relative hazards in the Cox model. Four types of phenotypic features emerge in CRC-metastatic organs defined by their associated lesions’ likelihood of response and relapse. Notably, bone and brain lesions had low response and high relapse probabilities (low-high phenotype), while liver lesions had high probabilities of both response and relapse (high-high phenotype). Patients with these metastases, particularly those with low-high phenotype, had much worse survival outcomes (OS median 378 days vs. 561 days, p<0.0001, Supplementary Fig. 3a). On the other side, metastatic lesions in the lung and LN showed high response and low relapse probabilities (high-low phenotypes). Patients who have metastases in high-low phenotype organs only tend to have a better prognosis than patients with other phenotypic metastases do (OS median 770 days vs. 524 days, p<0.0001, Supplementary Fig. 3b).
+
+Interestingly, most metastatic lesions with high relapse probabilities tend to occur in organs known to have immunosuppressive microenvironments, such as the liver, bone, and brain/CNS^{28-31}. To discern the influence of local tissue environment on tumor response phenotype, we performed the same analyses in head and neck squamous cell carcinomas (mHNSCC) to see whether a similar anatomical chart exists
+(Fig. 3d). A total of 393 patients with 1,892 lesions were analyzed, including eleven metastatic organs (Supplementary Fig. 4a and 4b). Patients’ demographics are reported in Supplementary Table 2. The organ-specific hazard ratios for relapse and response were ranked, as we did in mCRC (Supplementary Fig. 4c and 4d). In mHNSCC, metastases in the liver, bone, and brain also showed high relapse potential, in line with what we observed in mCRC. Metastatic lesions in the LNs exhibit a high-low phenotype, consistent with mCRC. Similar anatomical charts across cancer types suggest that organ-intrinsic microenvironmental factors, such as the local physical and immunological components, could be key modulators to the mechanisms underlying the probabilities of tumor response and relapse.
+
+Treatment effects on organ-specific responses were also investigated. For simplicity, treatments were divided into two groups, chemotherapy alone and in combination with antibody targeted therapy. The combined antibody targeted therapies are either panitumumab or bevacizumab, or both. Surprisingly, combination with the antibody targeted therapies did not significantly influence organ-specific response probabilities (Fig. 3e), suggesting low direct cytotoxic effects of antibody-based therapies. Notably, the primary therapeutic benefit of antibody targeted therapies was to decrease relapse potential (Fig. 3f). Relapse hazards significantly decreased in most metastatic organs except for the skin, brain/CNS, spleen, and kidney. Taken together, antibody targeted therapies had the primary effect of decreasing lesion relapse probability but had limited influence on the lesion response probability. Interestingly, high-relapse organs in Fig. 3c also had high relapse probability during cytotoxic chemotherapies in Fig. 3f, suggesting a critical role for local tissue environments in long-term tumor control.
+
+Relapse sequence across organs predicts patient survival
+
+We built a k-means unsupervised clustering model to cluster patients based on their organ-level lesion relapse sequence to investigate their relevance to patient survival. Elbow sum of square\(^{32}\) (Supplementary Fig. 5a) and Silhouette score\(^{33}\) (Supplementary Fig. 5b) were calculated to determine the optimal k (= 5) in the final classification. Five groups of patients were identified with distinct patterns of organ-specific relapse sequences and were stratified by relapsing organ number and first-relapsing
+organ: Mono-Organ (n=1,425), Hetero-Organ (n=801), Lung-First (n=577), Liver-First (n=1,194), and the Other-First (n=888) groups. The clinical demographics and baseline information of each group are summarized in Supplementary Table 3.
+
+Organ-level relapse sequence is significantly correlated with long-term patient survival (p < 0.0001, Fig. 4b). As expected, patients with multiple organ relapses had worse survival than patients with only one organ relapse (OS median Hetero-Organ 385 days vs. Mono-Organ 653 days). Remarkably, despite comparable number of baseline metastases, patients whose first relapses were in the liver had a much worse prognosis than those whose first relapses were in lungs or other sites (OS median Liver-First 450 days vs. Lung-First 679 days vs. Other-First 581 days, Fig. 4b). This is consistent with earlier observations (Fig. 3c) that lesions in the lung had high-low phenotype that is often associated with good patient prognosis. Patients with relapse first in the liver had faster subsequent relapses than patients whose relapses occurred in lungs or other sites, suggesting that relapsing lesions in the liver have high systemic consequences (p<0.0001, Fig. 4c). It also aligns with our previous finding that the response of liver lesions to treatments strongly predicted patient survival16.
+
+Next, we performed k-means unsupervised clustering in the Hetero-Organ group to further investigate relapse patterns in patients with extensive metastases and relapses. Four groups of patients were optimally clustered (Supplementary Fig. 5c and 5d), and one distinctive feature among these clusters was the relapse order of liver lesions (Supplementary Fig. 6a). Despite similar metastases, patients with first or second relapse occurring in the liver had worse survival than those with early relapses occurring in other organs (Supplementary Fig. 6b and 6c). This observation further underlines the importance of liver lesions to systemic response and resistance.
+
+Targeted antibody therapies minimally influence lesion relapse sequence
+
+We compared the relapse sequence in patients under different treatments (chemotherapy alone vs. combination with antibody targeted therapy). In patients with Liver-First, Lung-First or Other-First
+relapse patterns, antibody targeted therapies significantly improved patient overall survival (p < 0.0001, Fig. 5a). However, neither the proportion of patients with each relapsing pattern (Fig. 5b) nor the sequence of relapse across metastatic organs were significantly different (Fig. 5c-5e). Relapses in the GR and pancreas occurred slightly earlier in antibody targeted therapy, which did not seem to translate meaningful difference in patient survival. Despite the similar sequence, patients under antibody targeted therapies had significantly slower first and second relapses, but had non-significant difference in the third or later relapses (Fig. 5f-5g). The average relapse times were much longer in combination therapy compared to chemotherapy alone.
+
+In patients with the Hetero-Organ pattern, antibody targeted therapies did not meaningfully improve overall survival (Supplementary Fig. 7a) compared to chemotherapy alone, and the proportions of patients in each subcluster were similar between the two treatment groups (Supplementary Fig. 7b). Patients’ relapse patterns and lesion relapse time were largely comparable, especially for those who had early liver lesion relapse (Supplementary Fig. 7c-h). Similarly, antibody targeted therapies did not influence lesion relapse sequence. Overall, the primary therapeutic benefit of antibody targeted therapies was to delay relapse in patients with few (< 4) metastatic organs, but not in those with broad metastases.
+
+Machine learning model predicts lesion relapse sequence.
+
+In order to predict patient relapse sequence at the time of diagnosis, we built a gradient boosting model using patient baseline characteristics and metastases profiles34. The model parameters are in Supplementary Table 4. The area under the receiver operating characteristic (ROC) curve of the testing data was 0.91, which indicated fair performance (Supplementary Fig. 8a). The model could predict Mono-Organ and Hetero-Organ groups better than Lung-First, Liver-First, and Other-First groups with higher area under the ROC curve. This indicates that more follow-up information is imperative to accurately predict the relapse sequences of the latter three groups (Supplementary Fig. 8b).
+Discussion
+
+Metastasis is responsible for the majority of cancer-related mortality. Unfortunately, systemic tumor control across metastases remains intractable in many patients. This study investigated inter-lesion heterogeneity by analyzing response dynamics of 40,612 lesions in 4,308 mCRC patients. Unlike most molecular characterizations of metastases, we focused on the phenotypic features associated with lesion response and relapse dynamics as well as the anatomical divergence and convergence of these features. Our analyses yielded several intriguing findings. First, metastases differed considerably in their response to treatment, with depth of response positively correlating with regression rate and negatively correlating with progression rate. Second, metastatic lesions within the same organ exhibited congruent response and relapse dynamics, converging upon four organ-level phenotypes. Metastatic lesions in the liver exhibited high response and high relapse probabilities (high-high phenotype), while lesions in the bone and brain/CNS had low response and high relapse probabilities (low-high phenotype). These phenotypes appear to be consistent across cancers. Third, we found that organ-level relapse sequence was closely associated with patient survival, and patients with the first relapse in the liver had worse survival outcomes compared to patients with first relapse in other sites.
+
+This study quantified the degree of inter-lesion heterogeneity by modeling tumor regression and progression dynamics. By assuming first-order regression of drug-sensitive cancer cells (log-kill hypothesis), the empirical model adequately recapitulated the longitudinal size measurements on the lesion level. The first-order regression implies that drug-sensitive cancer cells may have only one rate-limiting step on the path to cell death\(^{35}\). Baseline tumor burden did not correlate with regression rates in our analyses, restating the first-order regression. Large tumors are often expected to have tumor regression potentially deviating from strict first-order kinetics because of their non-uniform drug distributions inside the tumor or only the surface tumor cells being actively proliferating and sensitive to treatment\(^{36-38}\). Our analyses did not find evidence to support these speculations. In contrast, despite large
+sizes, metastatic lesions in the liver had relatively high regression rates compared to lesions at other organ sites.
+
+The progression rates of drug-resistant tumor cells varied more between lesions than their associated regression rates and accounted the majority of intrapatient heterogeneity. Lesion relapse time was more closely associated with the progression rates than with the regression rates, in line with Stein et al., who reported that progression rates were a stronger predictor of patient survival\(^{39}\). If validated prospectively, the progression rates would offer more appropriate efficacy endpoints in clinical trials than the current ones that focus on the early response and regression, such as response rate and best of response.
+
+Antibody therapies significantly increased response depths and decreased progression rates, but did not considerably affect regression rates. These observations indicate that the primary therapeutic benefit of combined antibody therapies is from growth suppression rather than direct cytotoxicity. In renal cell carcinomas, bevacizumab significantly reduced the growth rate constants, and the effect could become more apparent after relapse, in line with our observations in mCRC\(^{40}\). Interestingly, despite the broad evidence of its antibody-dependent cellular cytotoxicity (ADCC)\(^{41}\) or complement-dependent cytotoxicity in vitro systems\(^{42}\), the other antibody panitumumab in our analyses did not significantly affect tumor regression rates either, suggesting its low direct cytotoxicity in patients. In fact, the magnitude of the ADCC elicited by EGFR-targeting antibodies in patient remains hard to define, especially considering the restricted and highly varying infiltrations of effector cells in tumor beds\(^{43,44}\). Panitumumab (IgG2), compared to another EGFR-targeting antibody cetuximab (IgG1) showed reduced ADCC-dependent therapeutic effect, probably related to the reduced avidity of IgG2 for CD16, as compared to IgG1\(^{45,46}\). Unfortunately, our analyses did not include patients under cetuximab treatment, precluding direct comparison.
+
+Metastatic lesions with lower fractions of resistant cells also had slower progression rates, suggesting consistent fitness of resistant cells before treatment and after relapse. However, metastatic lesions in the liver appear to behave differently; they had higher probability to respond, but also faster progression rates
+than lesions in the LN and lungs, suggesting unique ecological properties of liver lesions. Our analyses highlight the importance of tissue microenvironments to metastatic phenotypes. Metastatic lesions with higher responses were typically found in the liver, spleen, LN, and lungs. These organs have discontinuous or fenestrated endothelial membranes, which may lead to higher drug exposure, potentially conferring high treatment responses\(^{47,48}\). In contrast, the organs bearing poorly-responding lesions are usually those with continuous endothelial membranes and thus more limited drug distribution, such as the muscle and brain/CNS\(^{49-52}\). Some organs that bear poorly-responding metastatic lesions, such as kidney and muscle, have relatively dense tissue matrices. This could limit the growth rate of metastatic lesions within these organs\(^{33,54}\) and render them less responsive to cytotoxic chemotherapy\(^{55,56}\).
+
+On the other hand, organ-specific relapse probabilities seem to closely relate to the local immune microenvironments. Metastatic lesions with higher relapse potentials were found in the liver, bone, and brain/CNS, which either are immune-privileged or tolerogenic organs \(^{20,21,28-31}\). Interestingly, high relapses in these organs also occurred during cytotoxic chemotherapies that primarily work through DNA damage-induced cell death (Fig. 3f). Higher containment of tumor relapses in immunocompetent organs highlights the critical role anticancer immunity plays in long-term tumor control. Patients with highly relapsing lesions, such as lesions in the liver and bones, had much worse survival outcomes and likely require more effective and targeted therapeutics.
+
+Tumor relapse is a serious impediment to cancer treatment, but organ-level relapse patterns remain poorly characterized. We found that early relapses in the liver, compared to early relapses in other sites, predicts worse patient survival and more rapid subsequent relapses. The liver’s anatomical location, as a trafficking hub for CRC cells to spread to other organs, possibly underlies this finding\(^{57}\). By modeling large autopsy data sets in mCRC, Newton et al. highlighted that liver metastases could serve as tumor “spreaders” \(^{58}\), and that there are multidirectional paths of tumor spread during progression\(^{58,59}\). Although we did not estimate transit probabilities from site to site, we speculate it is likely that early relapses in liver metastases could lead to more resistant cells spreading throughout the body and cause more frequent
+subsequent relapses. Our population-level analysis supports this speculation and shows that liver metastases were often associated with a more pronounced tumor spread in the body.
+
+The primary therapeutic benefit of antibody targeted therapies was to delay tumor progression and systemic relapses, without strong preferential effect on any organ-specific metastases. As such, antibody therapies did not affect relapse sequences, and the fraction of patients with the first relapse in the liver were largely comparable to chemotherapy alone. Unfortunately, in patients with multiple relapsed metastases (> 4 relapsed organs), the therapeutic benefit of antibody therapies is minimal, and more effective treatments remain sorely needed to treat patients with broad metastases.
+
+In conclusion, we quantified intrapatient heterogeneity by modeling the longitudinal size measurement of metastatic lesions. This study provided a broad characterization of the phenotypic heterogeneity across metastatic lesions in mCRC, which could complement conventional molecular and cellular analyses to promote a more comprehensive view of intrapatient heterogeneity and yield substantial implications for metastasis-targeting therapies.
+Methods
+
+Data
+
+Multiple mCRC and mHNSCC studies with longitudinal measurements of individual metastatic tumor information were included for the analyses. All datasets are accessible in Project Data Sphere (https://www.projectdatasphere.org/). Patients under one of the following conditions were excluded: (1) no target lesion longitudinal measurements; (2) baseline tumor size measured more than 12 weeks before the treatment. Patients’ demographics and survival information were collected if applicable. The size and anatomical site about target/non-target lesion and occurring time and anatomical sites of new lesions were all recorded and analyzed if any.
+
+All study protocols were approved by institutional review boards at each participating center. All patients have been provided written informed consent before study-related procedures were performed. All data sharing plans have been approved by the data sponsors.
+
+Lesion-specific tumor growth dynamics
+
+The longest diameter was converted to volume assuming the ellipsoidal shape of tumor (*Equation 1*) and the ratio of the tumor long versus short axis as \(1.31^{60}\). An empirical tumor growth model (*Equation 2*) was used to recapitulate lesion-specific tumor growth dynamics.
+
+\[
+V = \frac{(long\ axis) \times (short\ axis)^2}{2} \quad (Equation\ 1)
+\]
+
+\[
+V = V0 \cdot [F \cdot e^{Kg t} + (1 - F) \cdot e^{-Kd \cdot t}] \quad (Equation\ 2)
+\]
+
+\(V\) is the tumor volume, \(V0\) is the tumor baseline volume, \(t\) is the time. The model has three parameters for estimation: \(F\) is the fraction of non-responding tumor cells, with \(1-F\) as the response depth; \(Kg\) is the progression rate and \(Kd\) is the regression rate. We fitted the model for all target lesions simultaneously using the Non-Linear Mixed Effect (NLME) method in Monolix2020R1. Stochastic approximation expectation-maximization (SAEM) algorithm was applied to search global optimum in the estimation. M3
+method61 was applied for quantifying size below the quantification of limit (< 200 mm^3)62. In the NLME method, the model parameters are described in Equation 3-5.
+
+\[
+\ln(Kg^j) = \ln(\theta_{Kg}) + \eta_{Kg^j} \quad (\text{Equation 3})
+\]
+
+\[
+\ln(Kd^j) = \ln(\theta_{Ka}) + \eta_{Ka^j} \quad (\text{Equation 4})
+\]
+
+\[
+\logit(F^j) = \logit(\theta_F) + \eta_{F^j} \quad (\text{Equation 5})
+\]
+
+where \( \theta \) is the population typical value, and \( \eta \) is the random effect with a log-normal distribution describing the difference between individuals and population average for each lesion \( j \). Proportional error model was assumed. The initial values of \( Kg \), \( Kd \) and \( F \) were 0.01 day^{-1}, 0.01 day^{-1}, and 0.1 (unitless).
+
+**Tumor response and relapse times**
+
+Tumor growth dynamic parameters were further taken to predict the longitudinal profiles of response and relapses for each target lesions. The longitudinal response and relapse status for each target or non-target lesion were determined per RECIST V1.126. Target lesion response time (when the lesion size decreases \( \geq 20\% \) from baseline) and relapse time (when the lesion size increases \( \geq 30\% \) from tumor nadir or at least 200 mm^3 increase from nadir) were derived using tumor growth model with NLME-estimated parameters on the individual lesion level. Non-target lesions responded when “partial response” or “complete response” was firstly observed during the treatment and relapsed when “progressive disease” appeared in tumor evaluation. The relapse time for new lesions were defined as the detection time.
+
+**Cox proportional regression model**
+
+Cox proportional models were built to estimate lesion response and relapse probabilities across organs and treatments in R-4.1.0 and RStudio “coxme” package. Inter-patient variability was adjusted in the Cox models as random effect. Lesions without relapse or response during the treatment were labeled as censored by the last day of that patient in the trial. New lesions were considered only in the relapse hazard estimation.
+Relapse pattern classification and prediction
+
+We used the k-means machine learning algorithm to classify all the patients based on their organ relapse sequence in Spyder (Python 3.8) in Anaconda using the SCIKIT-LEARN 1.0.2 software package. Elbow method and Silhouette score were applied to find optimal k. The relapse patterns of patients clustered with different k were compared to help determine the choice of k in the final classification.
+
+Gradient Boosting algorithm was applied to build a relapse pattern predictive model in Spyder (Python 3.8) in Anaconda using the SCIKIT-LEARN 1.0.2 software package. The research samples were randomly divided into a training and testing groups at a ratio of 4:1. The initial value of the hyperparameters used in this model was determined by parameter grid search, using 5-fold cross-validation and F1-score as a metric (Supplementary Table 4). The model outcome is the patient relapse sequence classified in k-means algorithm. Model predictors included patient clinical and demographic characteristics, as well as the baseline metastatic profiles, including the metastatic organs, metastatic numbers, metastatic target lesion baseline volume. Continuous predictors were normalized and categorical predictors were transformed to dummy variables. Performance index accuracy, precision, recall rate and area ROC curves were used to evaluate model performance.
+
+Statistical analysis
+
+Comparisons of continuous variables were performed using the two-tailed Mann–Whitney test or Kruskal–Wallis test. Multiple comparisons were adjusted by Dunn’s test. PFS (defined as the start of therapies until RECIST-defined progression or death) and OS (defined as the start of therapies until patient death) among the groups were depicted using Kaplan–Meier curves and compared using log-rank tests. All the statistical tests were performed in GraphPad Prism 9.
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+Data Availability
+
+The clinical data that support the findings of this study are available in the Project Data Sphere, https://data.projectdatasphere.org/projectdatasphere/html/access. The machine learning algorithms codes were deposited at https://github.com/zhoujw14/Mapping-Metastasis.git. All source data for our model development and plotting will be provided upon request.
+
+Acknowledgements
+
+We thank Mr. Timothy Qi and Dr. Tyler Dunlap from University of North Carolina at Chapel Hill, Eshelman School of Pharmacy for providing valuable suggestions and edits for the manuscript.
+Funding Source: National Institute of Health, R35GM119661
+
+Author Contributions
+
+Conceptualizations: J.Z., and Y.C.; methodology: J.Z., A.C., G.F., Q.L., and Y.C.; formal analysis: J.Z.; investigation: J.Z., Y.L., Q.L., and Y.C.; writing-original draft: J.Z., and Y.C.; writing-reviewing and editing: J.Z., A.C., G.F., Y.L., Q.L., and Y.C.; supervision: Y.C.
+
+Competing Interests
+
+All the authors declare no competing interests.
+
+Correspondence and requests for materials should be addressed to Y.C.
+Table 1. Demographic information of colorectal cancer patients.
+
+<table>
+  <tr>
+    <th>Variable</th>
+    <th></th>
+  </tr>
+  <tr>
+    <td>Age, years (mean, sd)</td>
+    <td>60.2 (10.8)</td>
+  </tr>
+  <tr>
+    <td>Gender (n, %)</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Male</td>
+    <td>2538 (58.9)</td>
+  </tr>
+  <tr>
+    <td>Female</td>
+    <td>1770 (41.1)</td>
+  </tr>
+  <tr>
+    <td>Race (n, %)</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>White/Caucasian</td>
+    <td>3883 (90.1)</td>
+  </tr>
+  <tr>
+    <td>Black/African American</td>
+    <td>104 (2.4)</td>
+  </tr>
+  <tr>
+    <td>Asian</td>
+    <td>142 (3.3)</td>
+  </tr>
+  <tr>
+    <td>Other</td>
+    <td>179 (4.2)</td>
+  </tr>
+  <tr>
+    <td>Body Mass Index, kg/m<sup>2</sup> (mean, sd)</td>
+    <td>26.2 (5.1)</td>
+  </tr>
+  <tr>
+    <td>Tumor Type (n, %)</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Colon</td>
+    <td>2581 (59.9)</td>
+  </tr>
+  <tr>
+    <td>Rectal</td>
+    <td>1359 (31.5)</td>
+  </tr>
+  <tr>
+    <td>Unspecified</td>
+    <td>368 (8.5)</td>
+  </tr>
+  <tr>
+    <td>Prior Surgery (n, %)</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Yes</td>
+    <td>2993 (69.5)</td>
+  </tr>
+  <tr>
+    <td>No</td>
+    <td>1315 (30.5)</td>
+  </tr>
+  <tr>
+    <td>Prior Radiation (n, %)</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Yes</td>
+    <td>445 (10.3)</td>
+  </tr>
+  <tr>
+    <td>No</td>
+    <td>3345 (77.6)</td>
+  </tr>
+  <tr>
+    <td>Unknown</td>
+    <td>518 (12.1)</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>Treatment<sup>1</sup> (n, %)</th>
+    <th></th>
+  </tr>
+  <tr>
+    <td>Bevacizumab plus chemotherapy</td>
+    <td>376 (8.7)</td>
+  </tr>
+  <tr>
+    <td>Bevacizumab plus FOLFOX</td>
+    <td>640 (14.9)</td>
+  </tr>
+  <tr>
+    <td>FOLFIRI alone</td>
+    <td>1303 (30.2)</td>
+  </tr>
+  <tr>
+    <td>FOLFOX alone</td>
+    <td>762 (17.7)</td>
+  </tr>
+  <tr>
+    <td>Panitumumab plus Bevacizumab plus chemotherapy</td>
+    <td>372 (8.6)</td>
+  </tr>
+  <tr>
+    <td>Panitumumab plus FOLFOX</td>
+    <td>441 (10.2)</td>
+  </tr>
+  <tr>
+    <td>Panitumumab plus FOLFIRI</td>
+    <td>424 (9.8)</td>
+  </tr>
+  <tr>
+    <th colspan="2">Response (n, %)</th>
+  </tr>
+  <tr>
+    <td>Complete Response</td>
+    <td>118 (2.7)</td>
+  </tr>
+  <tr>
+    <td>Partial Response</td>
+    <td>1473 (34.2)</td>
+  </tr>
+  <tr>
+    <td>Progressive Disease</td>
+    <td>781 (18.1)</td>
+  </tr>
+  <tr>
+    <td>Stable Disease</td>
+    <td>1806 (41.9)</td>
+  </tr>
+  <tr>
+    <td>Not Evaluable</td>
+    <td>130 (3)</td>
+  </tr>
+  <tr>
+    <th colspan="2">Metastatic organ number (n, %)</th>
+  </tr>
+  <tr>
+    <td>1</td>
+    <td>553 (12.8)</td>
+  </tr>
+  <tr>
+    <td>2</td>
+    <td>1159 (26.9)</td>
+  </tr>
+  <tr>
+    <td>3</td>
+    <td>1146 (26.6)</td>
+  </tr>
+  <tr>
+    <td>≥4</td>
+    <td>1450 (33.7)</td>
+  </tr>
+  <tr>
+    <th colspan="2"><i>KRAS</i> status (n, %)</th>
+  </tr>
+  <tr>
+    <td>Wild-Type</td>
+    <td>795 (18.4)</td>
+  </tr>
+  <tr>
+    <td>Mutant</td>
+    <td>593 (13.8)</td>
+  </tr>
+  <tr>
+    <td>Unknown</td>
+    <td>2920 (67.8)</td>
+  </tr>
+</table>
+
+<sup>1</sup>FOLFOX is the combination of folinic acid, fluorouracil and oxaliplatin. FOLFIRI is the combination of folinic acid, fluorouracil and irinotecan.
+Fig. 1 Data source. a. CONSORT diagram of metastatic colorectal cancer data inclusion and exclusion criteria. b. The number of all lesions (target, non-target and new) and target lesions across organs. GR, Genitourinary and Reproductive; CNS, central nervous system; GI, Gastrointestinal tract; LN, lymph nodes.
+Fig. 2 Tumor response dynamics were recapitulated by modeling. a. Schematic plot of tumor growth model. b. Box plots of model parameters \( Kd, F \) and \( Kg \) across organs. Significance was calculated using Kruskal-Wallis tests. The box extends from the 25th to 75th percentiles and the line in the middle is plotted as the median. The whiskers are drawn down to the 10th percentile and up to the 90th percentile. Points below and above the whiskers represent individual lesions. c. The correlations between model parameters. d. The correlations between model parameters and tumor baseline volume. The size of the dots represents lesion number (reported in panel b). The dashed lines with gray area are the linear
+regression with 95% confidence interval. The correlation coefficients and significance were calculated using two-tailed Pearson correlation tests.
+a  Response
+<table>
+  <tr><th></th><th>Hazard ratios</th><th>p-value</th></tr>
+  <tr><td>Liver (n=18,116)</td><td>0.94</td><td>&lt;0.0001</td></tr>
+  <tr><td>Distal LN (n=5,867)</td><td>0.94</td><td>&lt;0.0001</td></tr>
+  <tr><td>Pancreas (n=23)</td><td>0.94</td><td>&lt;0.0001</td></tr>
+  <tr><td>Abdomen (n=1,090)</td><td>Ref</td><td></td></tr>
+  <tr><td>Chest (n=346)</td><td>0.11</td><td></td></tr>
+  <tr><td>Spleen (n=150)</td><td>0.41</td><td></td></tr>
+  <tr><td>Lung (n=7,270)</td><td>0.023</td><td></td></tr>
+  <tr><td>Peritoneum (n=987)</td><td>0.20</td><td></td></tr>
+  <tr><td>Pelvis (n=508)</td><td>0.78</td><td></td></tr>
+  <tr><td>Regional LN (n=1,278)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>GI (n=383)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Adrenal (n=134)</td><td>0.11</td><td></td></tr>
+  <tr><td>GI (n=881)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Other (n=492)</td><td>0.23</td><td></td></tr>
+  <tr><td>Muscle/Soft Tissue (n=48)</td><td>0.27</td><td></td></tr>
+  <tr><td>Kidney (n=45)</td><td>0.37</td><td></td></tr>
+  <tr><td>Skin (n=57)</td><td>0.40</td><td></td></tr>
+  <tr><td>Bone (428)</td><td>0.51</td><td></td></tr>
+  <tr><td>Brain/CNS (n=24)</td><td>&lt;0.0001</td><td></td></tr>
+</table>
+
+b  Relapse
+<table>
+  <tr><th></th><th>Hazard ratios</th><th>p-value</th></tr>
+  <tr><td>Brain/CNS (n=67)</td><td>Ref</td><td>&lt;0.0001</td></tr>
+  <tr><td>GR (n=44)</td><td>0.27</td><td>&lt;0.0001</td></tr>
+  <tr><td>Liver (n=19,366)</td><td>0.11</td><td>&lt;0.0001</td></tr>
+  <tr><td>Muscle/Soft Tissue (n=55)</td><td>0.78</td><td></td></tr>
+  <tr><td>Adrenal (n=147)</td><td>0.94</td><td></td></tr>
+  <tr><td>Pelvis (n=542)</td><td>0.94</td><td></td></tr>
+  <tr><td>Abdomen (n=1,172)</td><td>Ref</td><td></td></tr>
+  <tr><td>Bone (n=510)</td><td>0.51</td><td></td></tr>
+  <tr><td>Peritoneum (n=1,980)</td><td>0.2</td><td></td></tr>
+  <tr><td>Other (n=545)</td><td>0.23</td><td></td></tr>
+  <tr><td>Spleen (n=167)</td><td>0.41</td><td></td></tr>
+  <tr><td>Lung (n=3,094)</td><td>0.023</td><td></td></tr>
+  <tr><td>Chest (n=398)</td><td>0.11</td><td></td></tr>
+  <tr><td>Skin (n=69)</td><td>0.40</td><td></td></tr>
+  <tr><td>Kidney (n=47)</td><td>0.37</td><td></td></tr>
+  <tr><td>Distal LN (n=6,130)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Regional LN (n=1,324)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>GI (n=880)</td><td>&lt;0.0001</td><td></td></tr>
+</table>
+
+C  mCRC
+![Response probability vs. Relapse probability plot for mCRC](page_184_624_627_312.png)
+
+D  mHNSCC (Validation)
+![Response probability vs. Relapse probability plot for mHNSCC (Validation)](page_1012_624_627_312.png)
+
+e  Response
+<table>
+  <tr><th></th><th>Hazard ratios [log]</th><th>p-value</th></tr>
+  <tr><td>Liver (10,010/8,106)</td><td>-0.0001</td><td></td></tr>
+  <tr><td>Distal LN (3,152/2,715)</td><td>0.13</td><td></td></tr>
+  <tr><td>Pancreas (916/9)</td><td>0.06</td><td></td></tr>
+  <tr><td>Abdomen (650/40)</td><td>0.02</td><td></td></tr>
+  <tr><td>Chest (189/157)</td><td>0.63</td><td></td></tr>
+  <tr><td>Spleen (87/63)</td><td>0.55</td><td></td></tr>
+  <tr><td>Lung (3,514/3,756)</td><td>0.066</td><td></td></tr>
+  <tr><td>Peritoneum (522/465)</td><td>0.027</td><td></td></tr>
+  <tr><td>Pelvis (65/197)</td><td>0.52</td><td></td></tr>
+  <tr><td>Regional LN (659/620)</td><td>0.003</td><td></td></tr>
+  <tr><td>GR (12/27)</td><td>0.96</td><td></td></tr>
+  <tr><td>Adrenal (61/73)</td><td>0.91</td><td></td></tr>
+  <tr><td>GI (388/473)</td><td>0.52</td><td></td></tr>
+  <tr><td>Other (225/267)</td><td>0.99</td><td></td></tr>
+  <tr><td>Muscle/Soft Tissue (4/48)</td><td>0.40</td><td></td></tr>
+  <tr><td>Kidney (15/30)</td><td>0.82</td><td></td></tr>
+  <tr><td>Skin (24/33)</td><td>0.009</td><td></td></tr>
+  <tr><td>Bone (173/255)</td><td>1.00</td><td></td></tr>
+  <tr><td>Brain/CNS (13/11)</td><td>-1.00</td><td></td></tr>
+</table>
+
+f  Relapse
+<table>
+  <tr><th></th><th>Hazard ratios [log]</th><th>p-value</th></tr>
+  <tr><td>Brain/CNS (31/36)</td><td>0.31</td><td></td></tr>
+  <tr><td>GR (12/25)</td><td>0.025</td><td></td></tr>
+  <tr><td>Liver (10,612/6,754)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Muscle/Soft Tissue (575/565)</td><td>0.0047</td><td></td></tr>
+  <tr><td>Adrenal (63/84)</td><td>0.0047</td><td></td></tr>
+  <tr><td>Pelvis (323/219)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Pancreas (5/20)</td><td>0.024</td><td></td></tr>
+  <tr><td>Abdomen (59/473)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Bone (94/146)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Peritoneum (575/515)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Other (239/306)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Spleen (557/2)</td><td>0.068</td><td></td></tr>
+  <tr><td>Lung (3,839/1,197)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Chest (227/177)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Skin (34/35)</td><td>0.87</td><td></td></tr>
+  <tr><td>Kidney (19/32)</td><td>0.059</td><td></td></tr>
+  <tr><td>Distal LN (3,262/2,868)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>Regional LN (678/646)</td><td>&lt;0.0001</td><td></td></tr>
+  <tr><td>GI (394/486)</td><td>&lt;0.0001</td><td></td></tr>
+</table>
+Fig. 3 Organ-level tumor response and relapse probabilities suggest phenotypic convergence. a and b rank the hazard ratio estimates with 95% confidence interval by organs on lesion response and relapse in colorectal cancer patients. c and d are the anatomical charts of organ-specific response and relapse hazard ratios in metastatic colorectal cancer (mCRC) and metastatic head and neck squamous cell carcinomas (mHNSCC). e and f are response and relapse hazard ratio with 95% confidence interval by organs stratified on treatments in mCRC. P-values were calculated by comparing the hazard ratios in antibody targeted therapies plus chemotherapy (TAR+Chemo) vs. chemotherapy alone (Chemo Alone) within each organ.
+Fig. 4 Patient relapse sequence association with patient survival. a. Patients were clustered into five groups based on their lesion relapse sequence. The column labels are the relapse sequence. Color of the heatmap represents the log10 scale of patient number (all plus one to avoid zero values). b. Kaplan-Meier curves of clustered patients overall survival. c. The mean and standard deviation of the first lesion relapse time (1st), time between first and second relapse (2nd-1st), time between second and third relapse (3rd-2nd), time between third and fourth relapse (4th-3rd), and the average relapse time in Lung-First (n=577), Other-First (n=639), and Liver-First (n=930).
+a
+TAR+Chemo (n=1,082)   Chemo Alone(n=1,054)
+OS (%)    p<0.0001
+Days
+
+b
+TAR+Chemo (n=1,082)   Chemo Alone (n=1,064)
+Lung-First
+28.37% 307 Lung-First   25.38% 270 Lung-First
+40.67% 440 Liver-First   46.05% 490 Liver-First
+30.96% 335 Other-First   28.57% 304 Other-First
+
+c
+Lung-First
+TAR+Chemo (n=307)   Chemo Alone (n=270)
+Abdomen-Adrenal-Bone-Brain/CNS-Chest-Distal LN-GI-GR-Kidney-Liver-Muscle/Soft Tissue-Other-Pancreas-Pelvis-Peritoneum-Regional LN-Skin-Spleen-No Relapse
+Log [patient number]
+
+f
+Lung-First
+Time to relapse (days)
+TAR+Chemo   Chemo Alone
+p<0.0001   p=0.02   p=0.52
+1st   2nd-1st   3rd-2nd   Mean
+
+d
+Liver-First
+TAR+Chemo (n=440)   Chemo Alone (n=490)
+Abdomen-Adrenal-Bone-Brain/CNS-Chest-Distal LN-GI-GR-Kidney-Liver-Muscle/Soft Tissue-Other-Pancreas-Pelvis-Peritoneum-Regional LN-Skin-Spleen-No Relapse
+Log [patient number]
+
+g
+Liver-First
+Time to relapse (days)
+TAR+Chemo   Chemo Alone
+p<0.0001   p=0.01   p=0.80
+1st   2nd-1st   3rd-2nd   Mean
+
+e
+Other-First
+TAR+Chemo (n=335)   Chemo Alone (n=304)
+Abdomen-Adrenal-Bone-Brain/CNS-Chest-Distal LN-GI-GR-Kidney-Liver-Muscle/Soft Tissue-Other-Pancreas-Pelvis-Peritoneum-Regional LN-Skin-Spleen-No Relapse
+Log [patient number]
+
+h
+Other-First
+Time to relapse (days)
+TAR+Chemo   Chemo Alone
+p<0.0001   p=0.67   p=0.86
+1st   2nd-1st   3rd-2nd   Mean
+Fig. 5. Targeted therapy decreases average time to relapse but has minimal effect on relapse sequence. **a.** Lung-First, Other-First and Liver-First patients overall survival stratified by treatments. **b.** Lung-First, Other-First and Liver-First patient proportions by treatments. **c, d**, and **e** are patient relapse sequences stratified by treatments. **f, g**, and **h** are the mean and standard deviation of the first lesion relapse time (1st), time between first and second relapse (2nd-1st), time between second and third relapse (3rd-2nd), time between third and fourth relapse (4th-3rd), and the average relapse time by treatments of the groups in **c, d**, and **e**. TAR+Chemo, antibody targeted therapies plus chemotherapy; Chemo Alone, chemotherapy alone.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementary3.13.pdf
+• ClinicalTrialInformationNCOMMS2209853.xlsx

09b108cd9ad0034506ae629f2fb23d3bf7f4cd8c58a23feee09b7b89729c5397/peer_review/peer_review.md

@@ -0,0 +1,218 @@
+Peer Review File
+
+Hydrodynamic manipulation of nano-objects by optically induced thermo-osmotic flows
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The manuscript by Franzl et. al. describes how to harness the contribution of thermo-osmotic flow and the balance between attractive van der Waal’s force and electrostatic repulsion to trap gold nanoparticles in a salt solution. The phenomenon is appreciable when trapping gold nanoparticles due to the weak contribution from repulsive thermophoresis, given the high thermal conductivity of gold. The manuscript is well-written and should be of broad interest to the readers of Nature Communications journal. I have provided some technical comments questions to be addressed below:
+
+1.) Most of the SI videos show the trapping of a single gold NP. Is this trap self-limiting? Can more than one gold NP be trapped? Also, please provide information on the spatial width of the trapping potential well?
+2.) Does the channel height have to be limited to 3um? Can larger channel heights such as 100 um be utilized?
+3.) What is the impact of the channel height on the thermo-osmotic flow and the trapping potential described in this manuscript? Is there a specific reason for limiting the channel height to only 3 microns?
+4.) What is the smallest particle size of gold nanoparticles that can be stably trapped?
+
+Reviewer #3 (Remarks to the Author):
+
+The authors demonstrate interesting manipulation (trapping and driving, with multiplexing) of nanoparticles in thin film fluids using local laser-induced heating.
+They provide experimental data on the influence of the nanoparticle nature (metallic or dielectric) and dissolved species (salt, surfactant…) which are then discussed and compared to simulations, in good agreement providing a comprehensive description of the involved processes.
+This work can be of great interest for the direct use of the demonstrated manipulation technique, and for future development based on the theoretical description.
+Yet, the manuscript shows several weak points, with missing information, as well as statements with no clear enough support.
+Therefore, I would support publication after significant modifications, following the remarks below.
+
+P3:
+“while at lower salt concentrations an enhanced probability (Fig. 2a) of finding the particle near the surface is the cause of the observed diffusion coefficient.”
+Isn’t this effect occurring at c0=10 mM? The particle is trapped near the surface by the potential, and experience there the lower diffusion coefficient.
+At lower concentrations, the particle is almost delocalized over the full height of the film, only with a slight shift towards the surface with increasing c0 inducing a small reduction of the diffusion coefficient. This sentence appears at least not clear enough.
+
+Can <d> be measured experimentally from z position statistics? Histograms of positions as function of c0 could be of interest to compare with model.
+Deviation may be found since calculated p(d) only takes into account the potential, and actual probability density would also be influenced by the dynamics: lower diffusion will increase the effective time of presence near the surface. Can this consideration explain the discrepancy between modeled and experimental diffusion coefficient (lower experimental D// at c0=1 & 3 mM compared to model in fig 2b)?
+
+Fig 2i,k
+There is a significant discrepancy between experiment and simulation for the velocity in the xy plane with r close to 0 and away from the Au surface. Can this be discussed? It is not done in main text, where experimental data are considered to “compare well to simulation results”.
+
+P4:
+“Analysis of the lateral position histograms (inset in Fig. 3c for 1.25 mW) yields an effective stiffness of the trap (Fig. 3a) that well matches the predictions based on the thermo-osmotic flow (Fig. 2i, j).” Figures 2i,j present experimental data of velocities. It is not explained how based on these data, prediction for stiffness are made. In fact, how the experimental and simulated stiffness in Fig 3a are obtained is not presented. Although I do not doubt on the conclusions, the methods for extracting the stiffness (exp and sim) should be clearly described in SI.
+
+SI section 7
+FE modeling for temperature profile with a constant heating flux can show strong dependence with boundary conditions (position and temperature of reservoirs fully drive the temperatures). Is DT=25K (significantly) dependent on the thickness of glass? Is Tamb = 25°C well fixed in experiment (and how)?
+Also, are all the FE modeling conclusions sensitive (or not) to water thickness? It is only discussed for thermal convection. It is important since this value is not measured and not precisely controlled. It is noted in Sample preparation that it is around 5um, while 3 um is considered in all models and schematics...
+
+Below can be found many remarks and suggestions (and I might have missed some).
+Their amount indicates that significant writing effort needs to be done.
+
+Fig 1:
+Value of R could have been indicated in the schematics.
+The “d vs V” graph is not presented at all in caption. It shows a selection of data, not indicating which exactly, only discussed later in fig2a. It should be removed or well introduced and discussed.
+
+Page 1
+z should be defined when it is first introduced in equation (d = z – R) . Definition should explicitly mention that it is the distance of the “center” of the particle from the wall.
+c0 is not defined in main text.
+
+Fig 2:
+a-b-c can be separated from the rest for clarity, as they correspond to a different section in the text.
+d- Caption can mention that glass interfaces are presented as white solid lines at z = 0 and 3 um.
+
+Page 4
+\( \eta \, \zeta \, \epsilon \, AH \) are not defined in main text.
+
+Fig 3
+b- F^O instead of F^OF in the figure
+shaded and dashed areas are not described in caption
+e- The corresponding video could have been included as SI.
+
+Page 6
+Eq 6 and 7, please differentiate the drift velocity symbol “u” in the 2 cases.
+Eq 7, R already corresponds to the AuNP size. c seems to be concentration of SDS (needs to be explicitly mentioned in main text), while c0 is in the equation.
+NA is not defined.
+Please correct « the the »
+Sample preparation:
+Solution where Au particles are dispersed is not indicated
+
+Financial supports are not implemented.
+
+Author contributions:
+"und" instead of and
+
+SI:
+figS14: issue with the curve-color attribution.
+Response to Reviewer Comments
+
+Reviewer #1 (Remarks to the Author):
+
+Thank you very much for the valuable comments and questions!
+
+1.) Most of the SI videos show the trapping of a single gold NP. Is this trap self-limiting? Can more than one gold NP be trapped? Also, please provide information on the spatial width of the trapping potential well?
+
+The trap is not self-limiting, i.e., we can trap more than one gold NP at a single trapping location. To show this, we have added a new Supplementary Video (Video 13). The trapping potential is illustrated the inset in Fig. 3c and its spatial width (\( \sigma \)) in terms of the trapping stiffness \( k = (k_B T)/\sigma^2 \) is plotted as function of the heating power in Fig. 3a. We updated also the figure caption of Fig. 3 highlight this result more directly.
+
+2.) Does the channel height have to be limited to 3 \( \mu \)m? Can larger channel heights such as 100 um be utilized?
+
+There is no limitation to a specific channel height. Channel heights of several 100 \( \mu \)m can be utilized as well. For larger channel height additional convective contributions may arise, which are, however, weak as compared to the thermo-osmotic flows (see Fig. S26).
+
+3.) What is the impact of the channel height on the thermo-osmotic flow and the trapping potential described in this manuscript? Is there a specific reason for limiting the channel height to only 3 microns?
+
+The strength of thermo-osmotic flows at the gold/water interface is not affected by the channel height, but a larger sample height leads to weaker back flows in the center of the liquid film. The sample height of 3 \( \mu \)m was chosen to provide easy experimental access to the z-position of the particles (Fig. S2). At higher sample heights, the particles go out of focus due to the limited depth of field of the microscope objective and the particle intensities become too low to be detected.
+
+4.) What is the smallest particle size of gold nanoparticles that can be stably trapped?
+
+So far, we have achieved a stable trapping of 50 nm AuNPs (Fig. 4a). As the trapping is defined by the strength of the DLVO potential and the optical/hydrodynamic forces that try to push the particle out of the DLVO potential, optimal trapping conditions with different salt concentration can be found also for smaller particles (see “Concentration/Size Dependence” in Supplementary Note 4). Also, the use of depletion forces, as indicated in the manuscript, can further increase the range of particle sizes that can be trapped. Nevertheless, we have not tested the limits of trapping so far.
+Reviewer #3 (Remarks to the Author):
+
+Thank you very much for carefully evaluating our manuscript. We have revised our manuscript according to the questions and comments. Please find additional details below.
+
+P3: “while at lower salt concentrations an enhanced probability (Fig. 2a) of finding the particle near the surface is the cause of the observed diffusion coefficient.”
+Isn’t this effect occurring at c0=10 mM? The particle is trapped near the surface by the potential, and experience there the lower diffusion coefficient.
+At lower concentrations, the particle is almost delocalized over the full height of the film, only with a slight shift towards the surface with increasing c0 inducing a small reduction of the diffusion coefficient. This sentence appears at least not clear enough.
+
+Thank you for pointing out this weak point in the text. As the salt concentration increases, the particle spends more and more time near the surface due to the increasing depth of the DLVO potential.
+However, this increasing time near the surface leads to a strongly decreasing mean distance <d> only for a salt concentration c0>3mM as calculated. At about c0=10 mM the mean distance approximately corresponds to the minimum of the DLVO potential, as shown in Figure 2c. This indicates a stable trapping. At the concentrations between 3mM and 10 mM, the particle would be temporarily trapped for increasing periods of time. We have now reformulated this paragraph and updated also Figure 2c to make the overall message is clearer.
+
+Can <d> be measured experimentally from z position statistics? Histograms of positions as function of c0 could be of interest to compare with model. Deviation may be found since calculated p(d) only takes into account the potential, and actual probability density would also be influenced by the dynamics: lower diffusion will increase the effective time of presence near the surface. Can this consideration explain the discrepancy between modeled and experimental diffusion coefficient (lower experimental D|| at c0=1 & 3 mM compared to model in Fig. 2b)?
+
+<d> can in principle be measured from the z-position, yet the statistics is distorted by non-linearities of the spot size as a function of z-position at small z. Close to the focus, the size of the spot converges nonlinearly to the focal point spread function, which translates into a higher probability density to measure small spot sizes and thus distances. This is less important for the velocity determination (due to the differences it just lowers the measured velocity value), but it strongly affects the mean distance measurement and we have not been able yet to correct for this issue.
+
+Overall, the value of <d> is determined solely by the potential at thermal equilibrium. While diffusion near the interface is slowed down and the residence time is increased, the time required for diffusion to the interface is also longer. Thus, without additional potential, diffusion in thermal equilibrium will always result in a homogeneous density distribution. This is also the result of Eq. 10 in the Appendix when the potential is set to zero. In this case, the particle needs the same time for the path from d_min to d_max as for the path from d_max to d_min, which expresses the validity of the detailed balance.
+
+However, the longer residence times due to slower diffusion make it experimentally more difficult to observe the correct mean distance in an experiment with limited measurement time. We assume that this limitation, together with the uncertainty in the sample height, causes the discrepancy between the theoretical and experimental diffusion coefficients.
+Fig 2i,k: There is a significant discrepancy between experiment and simulation for the velocity in the xy plane with r close to 0 and away from the Au surface. Can this be discussed? It is not done in main text, where experimental data are considered to “compare well to simulation results”.
+
+The discrepancy is caused by the limited spatial accuracy. Very small spatial distances (r = 0) are not well resolved and the particles at this position are very fast. For a particle speed of 60 \( \mu \)m/s, this could be already more than 1 \( \mu \)m, which makes a precise localization and velocity determination very difficult in this region. To improve this, we would need to go to much higher framerates. We added a sentence to discuss the discrepancy in the main text.
+
+P4: “Analysis of the lateral position histograms (inset in Fig. 3c for 1.25 mW) yields an effective stiffness of the trap (Fig. 3a) that well matches the predictions based on the thermo-osmotic flow (Fig. 2i, j).” Fig. 2i,j present experimental data of velocities. It is not explained how based on these data, prediction for stiffness are made. In fact, how the experimental and simulated stiffness in Fig 3a are obtained is not presented. Although I do not doubt on the conclusions, the methods for extracting the stiffness (exp and sim) should be clearly described in SI.
+
+Thank you very much for the comment. As mentioned in the main text, the velocity fields are converted to hydrodynamic forces with \( F = 6\pi \eta R v \). We have added a short explanation to the main text pointing also to a section in the SI, which explains additional details.
+
+SI Section 7: FE modeling for temperature profile with a constant heating flux can show strong dependence with boundary conditions (position and temperature of reservoirs fully drive the temperatures). Is \( \Delta T = 25K \) (significantly) dependent on the thickness of glass? Is Tamb = 25°C well fixed in experiment (and how)? Also, are all the FE modeling conclusions sensitive (or not) to water thickness? It is only discussed for thermal convection. It is important since this value is not measured and not precisely controlled. It is noted in Sample preparation that it is around 5um, while 3 um is considered in all models and schematics…
+
+The limit affecting the thickness of the glass was chosen sufficiently large (50 \( \mu \)m), as indicated in Figure S21 in the Appendix. We find no significant change in the maximum temperature rise with the thickness of the glass. Very small water film thicknesses will reduce the maximum temperature rise due to the greater thermal conductivity of glass compared to water. We have added a paragraph to the SI to explain this further. The ambient temperature is set and measured with a foil heater and an integrated thermistor attached to the lens and controlled with a temperature controller.
+
+The sample height specified in the "Sample preparation" section was incorrect. The samples were prepared with a nominal thickness of 3 \( \mu \)m. Many thanks for indicating this flaw!
+
+Below can be found many remarks and suggestions (and I might have missed some). Their amount indicates that significant writing effort needs to be done.
+
+We thank the reviewer for carefully reading the manuscript. We addressed all mentioned issues.
+
+Fig 1: Value of R could have been indicated in the schematics. The “d vs V” graph is not presented at all in caption. It shows a selection of data, not indicating which exactly, only discussed later in fig2a. It should be removed or well introduced and discussed.
+
+This has been corrected.
+
+Page 1: z should be defined when it is first introduced in equation (d = z – R) . Definition should explicitly mention that it is the distance of the “center” of the particle from the wall. c0 is not defined in main text.
+
+This has been corrected.
+Fig 2: a-b-c can be separated from the rest for clarity, as they correspond to a different section in the text. d- Caption can mention that glass interfaces are presented as white solid lines at z = 0 and 3 \( \mu m \).
+
+We have split Figure 2 into two Figures and extended the figure captions to better reflect all details.
+
+Page 4: \( \eta \) \( \zeta \) \( \varepsilon \) AH are not defined in main text.
+
+This has been corrected.
+
+Fig 3: b- F^O instead of F^OF in the figure shaded and dashed areas are not described in caption
+
+This has been corrected.
+
+e- The corresponding video could have been included as SI.
+
+This has been corrected.
+
+Page 6: Eq 6 and 7, please differentiate the drift velocity symbol "u" in the 2 cases.
+
+This has been corrected.
+
+Eq 7, R already corresponds to the AuNP size.
+
+This has been corrected.
+
+c seems to be concentration of SDS (needs to be explicitly mentioned in main text), while c0 is in the equation.
+
+This has been corrected.
+
+NA is not defined.
+
+This has been corrected.
+
+Please correct « the the »
+
+This has been corrected.
+
+Sample preparation: Solution where Au particles are dispersed is not indicated.
+
+This has been corrected.
+
+Financial supports are not implemented.
+
+We have now indicated financial support.
+
+Author contributions: “und” instead of and.
+
+This has been corrected.
+
+SI: FigS14: issue with the curve-color attribution.
+
+We could not find this issue.
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+I thank the authors for addressing my comments. I recommend acceptance of the manuscript.
+
+Reviewer #3 (Remarks to the Author):
+
+Authors’ response to my comments and corresponding modifications in the manuscript fully fulfill my expectation.
+I therefore recommend publication of this work in Nature Communications.
+Response to Reviewer Comments
+
+Reviewer #1 (Remarks to the Author):
+
+I thank the authors for addressing my comments. I recommend acceptance of the manuscript.
+
+Thank you very much for your positive assessment and the time for reviewing our manuscript.
+
+Reviewer #3 (Remarks to the Author):
+
+Authors' response to my comments and corresponding modifications in the manuscript fully fulfill my expectation. I therefore recommend publication of this work in Nature Communications.
+
+Thank you very much for your positive assessment and the time for reviewing our manuscript.

09b108cd9ad0034506ae629f2fb23d3bf7f4cd8c58a23feee09b7b89729c5397/preprint/preprint.md

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+Hydrodynamic manipulation of nano-objects by optically induced thermo-osmotic flows
+
+Martin Fränzl
+Leipzig University   https://orcid.org/0000-0001-6754-8554
+Frank Cichos (cichos@physik.uni-leipzig.de)
+Leipzig University   https://orcid.org/0000-0002-9803-4975
+
+Article
+
+Keywords: nano-objects, microfluidics, hydrodynamics, thermo-ostic flow
+
+Posted Date: September 24th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-879955/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on February 3rd, 2022. See the published version at https://doi.org/10.1038/s41467-022-28212-z.
+Hydrodynamic manipulation of nano-objects by optically induced thermo-osmotic flows
+
+Martin Fränzl1 and Frank Cichos1,*
+
+1 Peter Debye Institute for Soft Matter Physics, Molecular Nanophotonics Group, Universität Leipzig, Linnéstr. 5, 04103 Leipzig, Germany.
+
+*cichos@physik.uni-leipzig.de
+
+The manipulation of nano-objects at the microscale is of great technological significance to construct new functional materials, to manipulate tiny amounts of liquids, to reconfigure sensorial systems or to detect minute concentrations of analytes in medical screening. It is commonly approached by the generation of potential energy landscapes, for example, with optical fields or by using pressure driven microfluidics. Here we show that strong hydrodynamic boundary flows enable the trapping and manipulation of nano-objects near surfaces. These thermo-osmotic flows are induced by modulating the van der Waals interaction at a solid-liquid interface with optically generated temperature fields. We use a thin gold film on a glass substrate to provide localized but reconfigurable point-like optical heating. Convergent boundary flows with velocities of tens of micrometres per second are observed and substantiated by a quantitative physical model. The hydrodynamic forces acting on suspended nanoparticles and attractive van der Waals or depletion induced forces enable precise positioning and guiding of the nanoparticles. Fast multiplexing of flow fields further provides the means for parallel manipulation of many nano-objects and the generation of complex flow fields. Our findings have direct consequences for the field of plasmonic nano-tweezers as well as other thermo-plasmonic trapping schemes and pave the way for a general scheme of nanoscopic manipulation with boundary flows.
+
+The control and manipulation of nano-objects is a key element for future nanophotonics1–5, material science6,7, biotechnology8,9 or even quantum sensing10. Analytes dissolved in liquids, for example, need to be delivered, concentrated, separated or locally confined for further studies to become eventually processed and removed. Photonic elements including plasmonic nano-structures require precise positioning or controlled rearrangements to serve as adaptive functional structures. Key elements of the control at the micro- and nanoscale are often either pressure driven fluids transporting liquid volume and solutes or the generation of potential energy landscapes or force fields. The latter is achieved with optical1 and plasmonic tweezers11,12, magnetic fields13, or using electrokinetic14 or opto-electronic15 effects. Especially in the field of plasmonic tweezers and nanoantennas where light is used to excite collective electron motion in noble-metals, the Joule losses lead to the unavoidable generation of heat at boundaries as an unwanted side effect16,17. Yet, such optically generated temperature fields seem also suitable for the manipulation of nano-objects in liquids, for example, for the trapping of nanoparticles18 and single molecules19 or protein aggregates20 as well as for manufacturing active particles21–24. Those techniques rely on a drift of molecules and particles in optically generated temperature gradients termed thermophoresis or suggest thermo-electric effects25 relying on a thermally induced charge separation. In addition, thermo-electrohydrodynamic effects using time-varying electric fields have been proposed for rapid particle transport26,27 and convective effects that arise from temperature-induced density changes in the large liquid cells have been reported28–31.
+
+Here we report on a fundamental physical process that is able to provide a versatile trapping and manipulation of nano-objects and fluids near surfaces in the simplest geometries. Contrary to most other techniques, our scheme is based on hydrodynamic flows generated by optically induced thermo-osmosis. Thermo-osmosis relies on a perturbation of the interfacial interactions at a solid-liquid boundary and is present in all experiments involving temperature gradients in plasmonic structures including plasmonic tweezers. We show that local temperature gradients on a thin gold film induce strong interfacial flows of several 10 to 100 \( \mu \)ms\(^{-1}\) in its direct vicinity (10 nm) that results in a flow pattern reminiscent of convection. Based on a fully quantitative analysis of our experimental results we reveal that these thermo-osmotic flows on gold-water interfaces are induced by a temperature-induced perturbation of the van der Waals (vdW) interactions. Nano-objects suspended in the liquid are therefore dragged by the hydrodynamic forces originating from these flows. Utilizing attractive vdW interactions of the nano-object with the gold surface or temperature-induced depletion, we trap and manipulate different types of nano-objects near the surface. The fast heating at small scales allows us to multiplex flow fields and to manipulate multiple objects with great precision. Our detailed analysis of the flow fields, the localization accuracy of nano-objects, and a comparison with numerical and theoretical predictions provide a quantitative understanding of these effects and paves the way for controlling boundary layer dynamics to manipulate objects at the smallest length scales in solutions.
+
+Experimental configuration and working principle Our experiments rely on a simple sample geometry with a gold film (50 nm) that is deposited on a microscopy glass cov-
+Fig. 1: Thermo-hydrodynamic manipulation of Au NPs in NaCl solution. a, The sample consists of two glass slides that confine a 3 μm thin liquid film of gold nanoparticles (AuNPs) dispersed in aqueous NaCl solution. The lower glass slide carries a 50 nm Au film that is locally heated by optical absorption of a focused laser of \( \lambda = 532 \) nm wavelength. b, The experimental setup comprises an inverted optical microscope equipped with an acusto-optical deflector controlled, steerable focused laser with a wavelength of \( \lambda = 532 \) nm. The AuNPs are observed using darkfield illumination with an oil-immersion dark-field condenser (NA 1.2) and a 100× oil-immersion objective set to NA 0.6. Images are recorded with an EMCCD camera.
+
+erslip (Fig. 1a). The sample chamber contains a suspension of gold nanoparticles (AuNPs) or other nano-objects (polystyrene NPs and ellipsoids) with a controlled amount of salt (NaCl), surfactants (SDS, ...) or polymers (PEG). The gold film is heated locally in an inverted microscopy setup by a highly focused laser (532 nm) using beam steering optics (Acusto-Optic-Deflector, AOD). The nano-objects are observed using darkfield illumination with an oil-immersion darkfield condenser (NA 1.2) and a 100× oil-immersion objective set to NA 0.6 (Fig. 1b). Additional details of the experimental setup and sample preparation are provided in the Methods section.
+
+The trapping of nano-objects as detailed in the following is comprising two effects. i) The vertical confinement of the suspended objects as achieved by an attractive interaction of the suspended nano-objects with the gold surface, which is found to be the vdW interaction for gold nanoparticles and can be replaced by depletion forces for other materials. ii) The generation of thermo-osmotic boundary flows that are induced by the local heating and the corresponding perturbation of the liquid-solid interactions. This boundary flow is directed radially inwards to the heated spot and provides a confining hydrodynamic force on suspended objects at the heating spot.
+
+Dynamics of AuNPs close to a Au film Consider a single AuNP with a radius of \( R = 125 \) nm that is suspended in an aqueous solution of NaCl at a 10 mM concentration and diffusing in a thin liquid film of about 3 μm thickness over a 50 nm Au film (Fig. 1a). Exploring the diffusion of the particle we observe a restriction of the z-positions to a thin layer close to the gold film. The gold particle never defocuses under these conditions while it does in deionized (DI) water (Supplementary Video 1). This restricted out-of-plane motion is the result of interactions comprising an attractive vdW contribution, a repulsion of the electrostatic double layers of the particle and surface\(^{32}\) as described by the DLVO theory and the gravitational potential (see Supplementary Information for details).
+
+\[
+V(d, c_0) = V_{E}(d, c_0) + V_{vdW}(d) + V_G(d) .
+\]
+
+The total potential for the experimental situation is depicted in Fig. 2a for different salt concentrations (see SI for parameters) as a function of the surface-to-surface distance \( d = z - R \). The stronger screening of the surface charges at the gold film and the AuNP at higher salt concentration increase the importance of attractive vdW interactions to create this secondary minimum in the DLVO part of the potential. This potential influences the observed dynamics as well as the particle couples with its hydrodynamic flow field to the solid boundary\(^{33}\). The in-plane \( D_\parallel \) (equation 2) and out-of-plane \( D_\perp \) diffusion coefficient (see Supplementary Information for details) are modulated with the distance \( z \) of the particle from the wall.
+
+\[
+\frac{D_\parallel(z)}{D_0} \approx 1 - \frac{9}{16} \frac{R}{z} + \frac{1}{8} \left( \frac{R}{z} \right)^3 \pm \cdots := \gamma_\parallel^{-1}(z)
+\]
+
+Over the course of a diffusion trajectory, the particle samples different regions with different diffusion coefficients according to its probability density \( p(d) \propto \exp(-V(d, c_0)/(k_B T)) \) to be at a distance \( d \) from the surface (filled regions in Fig. 2a). The observed in-plane diffusion coefficient is thus a weighted average of the diffusion coefficient over the different vertical positions \( d \). Using \( p(d) \) we can calculate the corresponding salt concentration dependence of the in-plane diffusion coefficient and compare that to the experimental results. Fig. 2b shows that the experimentally observed \( D_\parallel \) is decreasing with increasing salt concentration due to the hydrodynamic coupling in fair
+Fig. 2: DLVO potential, lateral diffusion analysis, temperature distribution and thermo-osmotic flow field. a, Plot of the DLVO potential, equation (1), between a 250 nm Au NP and a 50 nm Au film on a glass surface as function of surface-surface distance d for different NaCl concentrations c_0. The shaded curves display the calculated probability density for finding the particle at this distance at the different salt concentrations (see Supplementary Information for details). The vertical dashed lines correspond to the mean distance of the particle as calculated from the probability density for a 3 μm liquid film height. b, The measured diffusion coefficient D_0 (blue) scale to the Au NP with respect to the bulk diffusion coefficient D_b as function of NaCl concentration c_0. The symbols correspond to the experimental values. The lines reflect the theoretical prediction including a distance dependent diffusion coefficient for three different Hamaker constants (dotted: \(A_H = 4 \cdot 10^{-20}\) J, dash-dotted: \(5 \cdot 10^{-20}\) J and dashed: \(6 \cdot 10^{-20}\) J) of gold according to a Boltzmann weighting (see text). c, Relation between the mean distance (\(d\)) and the NaCl concentration c_0. The symbols and the horizontal lines denote the calculated distances for measured concentrations. d, Simulation of the relative temperature increment in the xz-plane of the sample. e, Experimentally obtained temperature increment \(ΔT_{max}\) as a function of the incident laser power \(P_0\) (green data points) compared to the simulated values (green curve). f, Measured thermo-osmotic flow field in the xy-plane in close proximity to the gold film (\(z < 500\) nm). g, Measured thermo-osmotic flow field in the xz-plane. h, Illustration of the measured flow field planes in f and g. i, j, The x- and z-component of the measured flow velocities compared to the simulation results in k and l.
+
+agreement with the theoretical predictions (for three different Hamaker constants for the AuNP gold surface interaction). Calculating in addition the mean distance (\(d\)) of the particle from the surface reveals that only in the case of \(c_0 = 10\) mM the particle is confined in the DLVO potential well, while at lower salt concentrations an enhanced probability (Fig. 2a) of finding the particle near the surface is the cause of the observed diffusion coefficient. These calculations help us to estimate the mean distance (\(d\)) of the particle from the surface, which is about 1.5 μm and 0.9 μm for the lowest NaCl concentrations (Fig. 2c). At a concentration of \(c_0 = 10\) mM the particle is hovering at a distance of \(⟨d⟩ = 20\) nm surface. Note that this corresponds to values of \(z/(2R) ≈ 0.58\), which is far below the commonly explored region of the hydrodynamic coupling of colloids to walls\(^{33}\) allowing to experimentally explore new terrains also in the field of hydrodynamic wall coupling of colloids.
+
+Hydrodynamic Particle Confinement When tightly focusing the light of 532 nm wavelength to the gold film, a part of the incident energy (about 30 %) is absorbed and converted into heat that perturbs the liquid-solid interactions. The temperature rise at the gold surface can be determined using a thin nematic liquid crystal (5CB) film and substan-
+tiated by finite element simulations with the complete three-dimensional temperature profile in the solution (see Fig. 2d, e and Supplementary Information for details).
+
+These local temperature perturbations of the solid-liquid interactions at the interface induce a thermo-osmotic flow\(^{34,35}\). Taking a liquid volume element close to the solid from the cold side and exchanging that with one at the hot side would not only transport heat since the liquid volumes have different temperatures, but also additional free energy as the liquid has a different interaction with the solid in these regions. The flow is induced in an ultrathin boundary layer corresponding in thickness to the length scale of liquid-solid interactions. Since the characteristic interaction length of liquid-solid interactions is only a few nanometers, the boundary flow on the substrate can be collapsed into a quasi-slip hydrodynamic boundary condition:
+
+\[
+v_{||} = - \frac{1}{\eta} \int_0^{\infty} z \, h(z) \, dz \, \frac{\nabla_{||} T}{T} = \chi \frac{\nabla_{||} T}{T} ,
+\]
+
+where \(h(z)\) is the excess enthalpy, \(T\) the temperature and \(\nabla_{||} T\) is the temperature gradient parallel to the surface. The integral can be summarized to a thermo-osmotic coefficient \(\chi\). The thermo-osmotic coefficient \(\chi\), therefore, contains all information about the interfacial interaction between the liquid and the solid. If \(\chi < 0\) the liquid is driven to the cold, whereas for \(\chi > 0\), the liquid is driven to the hot. These boundary flows are present at all liquid-solid interfaces with tangential temperature gradients, though, they are commonly overlooked. They become particularly important for plasmonic and thermo-plasmonic trapping\(^{16}\) as those techniques rely on the dynamics of molecules and particles in the direct vicinity of plasmonic nanostructures. The boundary flow drives the flow field inside the fluid film. The resulting volumetric flow field can be tracked experimentally by single AuNPs in DI water, where the particles are not confined to a surface layer as reported above. We analyze the in-plane (\(xy\)) position of the particle and its \(z\)-position, where the latter is estimated from the radius \(r_0\) of the defocussed particle images (see Supplementary Video 2 and Supplementary Information for details). The measured velocity distributions in the \(xy\)-plane near the gold layer and in the \(xz\)-plane are shown in Fig. 2f and g, respectively. The \(x\)- and \(z\)-component of the measured flow velocities are depicted in Fig. 2i, j and compare well to simulation results in Fig. 2k, l. From these measurements, we extract a thermo-osmotic coefficient on the order of \(\chi \sim 10 \cdot 10^{-10} \text{ m}^2 \text{ s}^{-1}\) (see Supplementary Information for details). We can break down the contributions to this value with equations (4) and (5) to estimate the double layer and vdW contributions using the experimental parameters. Note that AuNP do not show thermophoresis due to their high thermal conductivity and thus isothermal surface.
+
+\[
+\chi_E = \frac{\varepsilon \zeta^2}{8 \eta} \approx 0.8 \cdot 10^{-10} \text{ m}^2 \text{ s}^{-1} .
+\]
+
+For the electrostatic contribution we used \(\zeta = -30 \text{ mV}\)\(^{36}\) and \(\varepsilon = 80 \varepsilon_0\) (see Methods section for details). An estimate of the vdW contribution can be given by
+
+\[
+\chi_{vdW} = \frac{A_H \beta T}{3 \pi \eta d_0} \approx 9.3 \cdot 10^{-10} \text{ m}^2 \text{ s}^{-1} ,
+\]
+
+with \(\beta = 0.2 \cdot 10^{-3} \text{ K}^{-1}\) being the thermal expansion coefficient of water and \(d_0 = 0.2 \text{ nm}\) for the cut-off parameter\(^{34}\) (see Supplementary Information for details). The sum of both contributions \(\chi = \chi_E + \chi_{vdW} = 10.1 \cdot 10^{-10} \text{ m}^2 \text{ s}^{-1}\) matches well the experimental result and suggests that thermo-osmosis at gold-water interfaces is governed by vdW interactions. The obtained quasi slip velocities are ranging up to 80 \(\mu\)m/s and provide, due to their omnipresence, a unique tool for nanofluidics. These thermo-osmotic flows are induced without any external pressure difference. They can be controlled by the light intensity heating laser and are quickly switched due to the extremely fast heat conduction at these length scales. Moreover the finding of the vdW dominated thermo-osmotic flows suggest that such contributions must be present in any plasmonic trapping experiment with extended gold structures\(^{12,16,17,27}\).
+
+Using \(F_{||}^{TF} = 6 \pi \eta R \gamma_{||} v_{||}\) and \(F_{\perp}^{TF} = 6 \pi \eta R \gamma_{\perp} v_{\perp}\), where \(\gamma_{||}\) and \(\gamma_{\perp}\) are the correction factors for the friction coefficient of a sphere close to a surface we are able to extract the hydrodynamic forces that are exerted on the AuNP tracers (see equation (2) and Supplementary Information for details). The lateral forces allow to confine objects at the heating spot, yet the hydrodynamic force normal to the surface (\(z\)-direction) is repulsive without any additional interaction. Finally, such boundary flows with substantial vertical velocity gradients also exhibit a vorticity (see Supplementary Information for details) that generates a torque on suspended objects causing them to rotate\(^{37}\).
+
+Single particle trapping and flow field multiplexing The repulsive normal component caused by the hydrodynamic drag is now superimposed with the attractive force due to the DLVO potential when increasing the NaCl concentration. The surface-to-surface distance between AuNP and gold film and the depth of the appearing secondary DLVO potential minimum can be controlled by the NaCl concentration. At a NaCl concentration of about \(c_0 = 10\) mM, the attractive potential has a depth of about \(10 k_B T\) (see Fig. 2a) and is strong enough to compete with the vertical drag force and additional optical forces on the AuNP to trap the particle above the heating spot.
+
+Supplementary Video 3 demonstrates this trapping of an AuNP above the hot spot on the Au surface. This is purely the result of the hydrodynamic drag forces generated by the thermo-osmotic flow and the attractive vdW interaction between the AuNP and the Au film. This observation is substantiated by a quantitative evaluation of the lateral trap stiffness and vertical forces, as depicted in Fig. 3a, b. The fluctuations of the particle in the hydrodynamic flow arise from a balance of the restoring hydrodynamic currents and the diffusive currents. Analysis of the lateral position histograms (inset in Fig. 3c for 1.25 mW) yields an effective stiffness of the trap (Fig. 3a) that well matches the predictions based on the thermo-osmotic flow (Fig. 2i, j). The hydrodynamic trapping stiffness increases linearly up to a heating power of about 1.8 mW. At this power, the vertical forces become strong enough to let the particle escape the secondary DLVO minimum, which is visible from the \(z\)-position time traces displayed in Fig. 3d. The AuNPs are then observed to move vertically out of the DLVO potential to follow the flow inside the sample and to eventually return
+Fig. 3: Forces on trapped NPs in 10 mM NaCl. a, The lateral trap stiffness obtained from the experimental position histograms (blue data points) as function the laser power \( P_0 \) compared to the simulation result (blue solid line). b, The z-component of the thermo-osmotic drag force \( F_z^{TF} \) (blue line), the optical force \( F_z^O \) (green line) and the total force \( F_z^{DLVO} + F_z^{TF} \) (black dashed line) as function the incident laser power \( P_0 \) for a NP located at \( x = 0, d = 30 \) (\( z = d + R \)). The attractive DLVO force \( F_z^{DLVO} \) is independent of the incident laser power and depicted as horizontal, red line. c, Trajectory of a AuNP for a heating laser power of 1.25 mW (see Supplementary Video 2 for details). The inset shows the corresponding lateral distribution histogram. d, Time traces of the z-position for three different laser powers. e, Trajectory of a AuNP for a heating laser power of 2.5 mW, which is above the threshold power of 2.25 mW.
+
+to the boundary flow via sedimentation (Fig. 3e, Supplementary Video 4). The forces which eject the particle from the potential comprise the hydrodynamic and the optical forces due to the radiation pressure from the heating laser leaked through the film. We have evaluated the individual contributions in simulations. They are shown together with the hydrodynamic force and the total vertical force as compared to the attractive force of the DLVO potential (Fig. 3b) and provide quantitative agreement (threshold heating power of 2.25 mW) with our experimental results. Note that while the stationary distribution of particles in the vertical direction is not influenced by the diffusive dynamics, the escape rate from the potential well is heavily altered by the fact that the vertical diffusion coefficient \( D_z \) of the particle is decreasing to zero when approaching the gold film. This is enhancing the trapping times considerably (see Supplementary Information for details) but also increases the time required for the particle to enter the DLVO minimum by diffusion.
+
+The observed trapping is, hence, a vDW assisted thermo-hydrodynamic process. Vertical confinement is achieved by vDW attraction and double layer repulsion, while lateral confinement is the result of thermo-osmotic flows induced in an ultra-thin sheet of liquid at the interface. No additional contributions, for example, due to convective flows with similar flow patterns (see Supplementary Information for details) or thermo-electric effects are required for a quantitative description\(^{25,31,38,39}\). Precise tuning of the DLVO potential enables the trapping of even smaller Au NPs (Fig. 4a, Supplementary Video 5).
+
+The speed of heat diffusion, which is about 4 orders of magnitude faster than the particle diffusion\(^{40}\) allows us to introduce a flow field multiplexing. We switch the heating location between different positions inducing thermo-osmotic flow fields for time periods of about 100 μs. With the help of this multiplexing, we are able to hold multiple \( R = 125 \) nm AuNPs (Fig. 4b, c) at distances of less than 1 μm, which would not be possible with continuous heating of close-by locations (Supplementary Videos 6 and 7). A trapped AuNP can also be guided along the predefined path over the Au film as fast as 10 μms\(^{-1}\) (Fig. 4d, Supplementary Video 8). At larger manipulation speeds (\( f > 100 \) Hz) and higher heating power (\( P_0 > 10 \) mW) the thermo-osmotic attraction to the heating spot is combined with thermo-viscous flows\(^{41,42}\). These flows originate from the temperature dependent viscosity \( \eta(T) \) of the liquid and are directed opposite to the scanning direction of the laser\(^{42}\). The result of this combination of thermo-osmosis and thermo-viscous flows is a rotating ring-like particle structure (Fig. 4e and Supplementary Video 9).
+
+These different effects that can be exploited in a simple planar geometry give rise to numerous applications including for example a freely configurable nanoparticle on mirror geometry for plasmonic sensing\(^{43}\). The multiplexing of local flow field may be be helpful to construct more complex effective flow fields for an efficient transport of analytes without external pressure.
+
+Beyond thermo-osmotic van der Waals trapping So far, the presented manipulation is based on thermo-osmotic flows that drive the lateral motion of suspended colloids and a vertical confinement due to the secondary minimum of the DLVO potential between AuNP and Au film. While the thermo-osmotic flows are characteristic for all systems containing a heated gold/water interface including all previous studies on thermo-plasmonic trapping, the DLVO potential minimum is much weaker for other materials like polymer colloids or macromolecules due to their smaller vDW attraction. Often, those system even show a repulsion from the heat source due to thermophoresis, which is not present for AuNP. A more generalized strategy therefore needs additional attractive contributions, which confine suspended colloids or molecules to regions close to the gold surface to take advantage of the thermo-osmotic flow.
+
+Such attractive contributions can arise from depletion interactions\(^{21,44}\). Thereby a temperature gradient repels dissolved molecules from the heated regions generating a concentration gradient that drives suspended nano-objects to the heating spot. To demonstrate this effect we use the surfactant sodium dodecyl sulfate (SDS) at a concentration of 5 mM well below the critical micelle concentration
+(8.2 mM) to avoid complications of micelle formation. We suspend additional polystyrene particles (PS) and AuNPs of the same size (\( R = 125 \) nm) in the solution and compare their dynamics to a solution with AuNPs and PS particles without SDS but 10 mM NaCl. Remarkably, the heated spot is attractive for both AuNPs and for PS NPs (Fig. 4f, Supplementary Video 10) in the SDS solution showing even PS colloidal crystal growth, while only the AuNP is trapped in the NaCl solution and the PS particles are repelled by thermophoresis (Fig. 4g, Supplementary Video 11).
+
+The observations in NaCl are readily explained by the fact that the AuNP is confined in the DLVO minimum as demonstrated above but the PS particle is not due to a 10 times lower Hamaker constant (see Supplementary Information for details). The PS particle samples the whole liquid film thickness equally and not preferentially the region close to the Au film and experiences an additional thermophoretic drift velocity given by
+
+\[
+u = -\frac{2}{3} \chi \frac{\nabla T}{T} = -D_T \nabla T,
+\]
+
+where \( D_T \) is the thermophoretic mobility\(^{34}\) and \( \nabla T \) the temperature gradient (Fig. 4g, Supplementary Video 11). For \( \chi > 0 \) the particle is driven to the cold. From equation (4) we find \( \chi \approx \chi_E = 1.28 \cdot 10^{-10} \) m\( ^2 \) s\( ^{-1} \) and \( D_T \approx 0.3 \) \( \mu \)m\( ^2 \) K\( ^{-1} \) s\( ^{-1} \), where we have used a measured zeta potential of \( \zeta \approx -38 \) mV. The vdW contribution, \( \chi_{vdW} \) to either the thermophoretic drift or the attraction to the gold surface can be neglected due to the smaller Hamaker constant of PS. From the stationary probability distribution of the PS NP we find a Soret coefficient of \( S_T \approx 0.24 \) K\( ^{-1} \) (see Supplementary Information for details) in agreement with our theoretical prediction \( S_T = D_T/D_0 \approx 0.21 \) K\( ^{-1} \).
+
+In the SDS solution, the additional surfactant molecules now undergo thermophoresis to yield a concentration gradient in which suspended colloidal particles drift. The lower concentration in the heated regions promotes an effective attractive interaction of suspended colloids with the gold surface due to depletion forces. The drift velocity is described by an additional term to the thermodiffusion coefficient \( D_T \), that is, the second term in brackets in equation (7)\(^{31,34,44}\).
+
+\[
+u = -\left( D_T - \frac{k_B}{3\eta} R^2 c_0 N_A \left( TS_T^{SDS} - 1 \right) \right) \nabla T
+\]
+
+Here \( R \) is the size of the SDS molecule, \( c \) the concentration in units of mol/l and \( S_T^{SDS} \) the Soret coefficient of SDS. For \( R = 2 \) nm\(^{45}\), \( c_0 = 5 \) mM and \( S_T^{SDS} = 0.03 \) K\(^{-1}\)\(^{46}\) we find \( -0.43 \) \( \mu \)m\( ^2 \) K\( ^{-1} \) s\( ^{-1} \) for the additional depletion contribution, which exceeds the thermophoretic mobility, \( D_T \approx 0.3 \) \( \mu \)m\( ^2 \) K\( ^{-1} \) s\( ^{-1} \), rendering the overall mobility negative. The PS NPs and the AuNPs are thus driven to the the heated Au film surface (Fig. 4f, Supplementary Video 10) which allows for further transport in the thermo-osmotic
+
+![Manipulation of AuNPs over a Au film in NaCl and SDS solution.](page_120_1042_1209_1042.png)
+
+Fig. 4: Manipulation of AuNPs over a Au film in NaCl and SDS solution. a, A AuNP with 50 nm radius trapped at a NaCl of 30 mM (Supplementary Video 5). b, Manipulation of two AuNPs by a multiplexed laser beam (Supplementary Video 6). c, Control of three AuNPs (Supplementary Video 7). d, Actuation of a single AuNP on a circular trajectory by a steerable laser beam (Supplementary Video 8). The green and white dashed arrows denote the moving direction of the laser focus and particle, respectively. e, Generation of thermoviscous flows by rotating the laser focus on a circle with a rotation frequency of 500 Hz at high laser power (Supplementary Video 9). Note that this laser-driven rotation and the thermal flow (within dashed area) are of opposite directions. f, Attraction of a AuNP and PS NPs in 5 mM SDS due to depletion (Supplementary Video 10). g, An AuNP (125 nm radius) trapped in an ensemble of polystyrene (PS) NPs of the same size at 10 mM NaCl (Supplementary Video 11), where the PS-particles are repelled due to thermophoresis. h, Attraction of PS ellipsoids (2.39 \( \mu \)m major-axis length, 0.34 \( \mu \)m minor-axis length) in 5 mM SDS (Supplementary Video 12).
+boundary flow. Additional contributions, as for example thermo-electric fields may even enhance the attractive components. Overall, this concept is readily transferred to other objects as shown in Figure 4h and Supplementary Video 12, where we have trapped ellipsoidal PS particles in a 5 mM solution of SDS. Note that as compared to other schemes, our approach always includes thermo-osmotic boundary flows.
+
+Conclusion In conclusion, we have demonstrated that thermo-hydrodynamic boundary flows can manipulate nano-objects with unprecedented flexibility in a very simple sample geometry. These flows are the key for future thermo-optofluidic implementations with an extensive range of applications in the fields of i) nanoparticle sorting and separation; ii) assembly of nanophotonic circuits57 and plasmonic quantum sensors45,58; iii) biotechnology on-chip laboratories48 and iv) manufacturing of nanomaterials16 and functional nanosurfaces49,50. We have substantiated our experimental findings of thermo-osmotic flow assisted trapping with a quantitative theoretical description. A flow field multiplexing scheme has been further developed to allow for the simultaneous manipulation of many individual nano-objects and the generation of complex effective flow patterns. Our concept can be combined with other thermally induced effects such as thermophoresis, depletion forces and thermoviscous flows to form a fully-featured nanofluidic system-on-a-chip. Besides direct consequences for the field of plasmonic nano-tweezers and other thermoplasmonic trapping schemes, the use of thermo-hydrodynamic flows as a tool for nanofluidic applications will extend the limits at the forefront of nanotechnology and help to develop AI and feedback controlled schemes for the material synthesis.
+
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+[43] R. Chikkaraddy, B. de Nijs, F. Benz, S. J. Barrow, O. A. Scherman, E. Rosta, A. Demetriadou, P. Fox, O. Hess, and J. J. Baumberg, Single-Molecule Strong Coupling at Room Temperature in Plasmonic Nanocavities, Nature 535, 127–130 (2016).
+[44] Y. T. Maeda, A. Buguin, and A. Libchaber, Thermal Separation: Interplay between the Soret Effect and Entropic Force Gradient, Phys. Rev. Lett. 107, 038301 (2011).
+[45] O. Syshchyk, D. Afanasenka, Z. Wang, H. Kriegs, J. Buitenhuis, and S. Wiegand, Influence of Temperature and Charge Effects on Thermophoresis of Polystyrene Beads, Eur. Phys. J. E 39, 129 (2016).
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+
+Methods
+
+Experimental setup  The experimental setup (Figure S19) consists of an inverted microscope (Olympus, IX71) with a mounted piezo translation stage (Physik Instrumente, P-733.3). The microparticles are heated by a focused, continuous-wave laser at a wavelength of 532 nm (CNI, MGL-III-532). The beam diameter is increased by a beam expander and sent to an acousto-optic deflector (AA Opto-Electronic, DT5X1-400-532) and a lens system to steer the laser focus in the sample plane. The deflected beam is focused by an oil-immersion objective (Olympus, UPlanApo 100/1.35, Oil, Iris, NA 0.5–1.35) to the sample plane (\( w_0 \approx 0.5 \) μm) and was in the sample plane. The sample is illuminated with an oil-immersion darkfield condenser (Olympus, U-DCW, NA 1.2 – 1.4) and a white-light LED (Thorlabs, SOLIS-3C). The scattered light is imaged by the objective and a tube lens (250 mm) to an EMCCD (electron-multiplying charge-coupled device) camera (Andor, iXon DV858LC). The variable numerical aperture of the objective was set to a value below the minimum aperture of the darkfield condenser. The dichroic beam splitter (D) was selected to reflect the laser wavelength (Omega Optical, 560DRLP) and a notch filter (F) is used to block any remaining back reflections from the laser (Thorlabs, NF533-17). The acousto-optic deflector (AOD), as well as the piezo stage, are driven by an AD/DA (analogue-digital/digital-analogue) converter (Jäger Messtechnik, ADwin-Gold II). A LabVIEW program running on a desktop PC (Intel Core i7 2600 4 × 3.40 GHz CPU) is used to record and process the images as well as to control the AOD feedback via the AD/DA converter.
+
+Sample preparation  The sample consists of two glass coverslips (22 mm × 22 mm) confining a thin liquid film. First, the coverslips were thoroughly cleaned by rinsing successively with acetone, isopropyl and Milli-Q water and dried with a nitrogen gun. Subsequently, the edges of one coverslip were covered with a thin layer of PDMS (polymethylsiloxane) for sealing. The particle solution used for the experiments was prepared by dispersing 0.250 μm diameter gold particles (Cytodiagnostics) in ... solution. Finally, 0.5 μl of the mixed particle suspension is pipetted in the middle of one of the coverslips and the other is placed on top. Depending on the area covered by the liquid, typically about (10 mm × 10 mm), the resulting liquid film height is about 5 μm.
+
+Acknowledgement
+
+The authors acknowledge financial support by ...
+
+Author contributions
+
+M.F. and F.C. designed the experiments. M.F. performed the experiments. M.F. and F.C. analyzed the experimental data. M.F. und F.C. implemented and evaluated the numerical calculations. M.F. and F.C. wrote the manuscript. All authors discussed the results and commented on the manuscript.
+Competing interests
+
+The authors declare no competing interest.
+
+Additional information
+
+Supplementary information is available for this paper at https://doi.org ...
+
+Correspondence and requests for materials should be addressed to F.C.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Video6.mp4
+• SI.pdf
+• Video3.mp4
+• Video2.mp4
+• Video8.mp4
+• Video7.mp4
+• Video1.mp4
+• Video5.mp4
+• Video4.mp4

09b35197b5ad4345c614483e5c88cb8e2e52505854eacc518df23d1042b94777/peer_review/peer_review.md

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+Peer Review File
+
+Deep learning-based high-accuracy quantitation for lumbar intervertebral disc degeneration from MRI
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+This paper proposes a semantic segmentation network (BianqueNet) to achieve high-precision segmentation of intervertebral disc(IVD) related areas and a quantitative method to calculate the signal intensity difference (ASI) in IVD, average disc height (DH), disc height index (DHI), and disc height-to-diameter ratio (DHR). The method in this paper is evaluated in a dataset contains 1051 MRI images collected from four hospitals around China. The merit of this paper is that its evaluation is implemented on quite a large dataset. However, the main drawback of this paper is it lacks methodology innovations. For example:
+1. What is the advantage of the proposed method compared with the widely-used semantic segmentation method such as U-net?
+2. What are the innovation parts in the proposed swin transform skip connection (ST-SC) module? Also, there are some issues in writing the paper:
+3. Fig. 1 and 2 contain too much information, while the most important information is lost. For example, the proposed ST-SC module accounts for only a small proportion in Fig. 2; its modules, i.e., LN and W-MSA are not stated anywhere in the caption or in the text.
+4. The paper does not describe how the signal intensity difference (ASI) in IVD, average disc height (DH), disc height index (DHI), and disc height-to-diameter ratio (DHR) are calculated after segmenting the intervertebral disc. Even if these calculation methods are not originally proposed by the authors, they should at least briefly describe how they are implemented.
+5. In the experimental part, there seem to be no qualitative illustrations of the segmentation results. Also, the authors do not show how the segmentation results are used to analyze the correlation with IVD degeneration grading.
+
+Reviewer #2:
+Remarks to the Author:
+This paper utilized CNN for lumbar spine segmentation to evaluate the intervertebral disc degeneration.
+
+1. It is great to collect the dataset which may benefit the community. I'd like to ask if the dataset will be released or not?
+
+2. The main contribution of this paper is utilizing a network for lumbar spine segmentation. The segmentation network showed in Fig.2, why do we need the ST-SC module? The multi-head self-attention mechanism can indeed model the long-range information dependency, while you have already used multi-scale information in the network, so I'm wondering if you indeed need the high-computational cost ST-SC module or not.
+
+3. In Fig. 1, the pipeline shows that you input two datasets into the network, that's fine for data from these sites. However, then how do you guarantee your model works fine for data collected a new site.
+
+4. Is that really good to input different resolution images in the network? How about upsampling them to 512x512 for training and test on different resolution images? Why do we need multi-scale input in the training phase.
+
+5. What's the significance of this work? The segmentation model (I don't think so) or the truth you proved that neural network can work well on evaluating the intervertebral disc degeneration?
+
+6. What's the novelty of this work?
+
+7. The main issue is that this kind of work (maybe the works are not about intervertebral disc degeneration but on other tasks, but they have proved the possibility of using networks for analyzing some diseases) has been vastly done before.
+Reviewer #3:
+Remarks to the Author:
+Thank you for the opportunity to review this manuscript. The broad goal of developing accurate quantitative measures of IVD degeneration using deep learning is important in my opinion. Without these measures it will not be possible to work towards differentiating degeneration due to aging compared to clinically important degeneration. This is a major gap in the back pain field. I have very limited understanding of the deep learning methods described in this paper, so am unable to comment on the quality of many the methods undertaken. My comments are limited to other aspects of the manuscript.
+1. The aim is unclear to me and does not capture the big picture of what this work could achieve. While the long-term potential clinical use is important but I am not sure the current study has this aim/purpose.
+2. Abstract refers to reliability with Pfirrmann. I think correlation is a better term to describe the study.
+3. In the Implications for patient care I believe the authors have extrapolated beyond their study results too far. For example, they should not talk about assessing risk of disc herniation. This is inappropriate based on current study. In general the conclusions need to be more limited the study design and results. This study lays a foundation to later test the clinical importance of MRI measures of disc degeneration, but does not investigate this clinical aspect. This should be clearer throughout.
+4. There are a reasonable number of small expression issues.
+5. I cannot assess if the methods to test if the approach works well across different MRI machines is valid. A radiologist review of this would be important.
+6. The methods do not provide adequate information on the process for assessing Pfirrmann scores. There is also no refence for the modified scale. The reader needs to understand this scale to interpret much of the findings. Was reliability of Pfirrmann assessed. Line 126 reports “discussed together”. This is unclear. Were those doing Pfirrmann measures blinded to the quantitative measures?
+7. It does not seem that any normalisation was performed for disc height. Interpreting the raw score requires this to make it cleanly useful. The nice graphs in figure 4 suggest that individuals can be compared to normal values, means etc based on age, disc level etc. More discussion of this would be good as this demonstrates how the findings could be applied in clinical practice and assessed for ability to predict important outcomes in future studies.
+8. How many images were manually segmented to compare and train the automatic segmentation. As mentioned, I have little expertise in this area but it would be good if the processes could eb made easier to read for an average reader especially clinical experts who will want to understand this work.
+9. What exactly is “signal intensity difference”. Why is it not just signal intensity? IS this value the mean SI in the region of interest or max value etc. Given how critical the signal intensity difference and the 3 measures of DH are to the paper, they should be more clearly defined and explained.
+10. Line 244 describes nearly 1/3 of potential participants being excluded. It seems this would limit the generalisability of the results.
+11. It seems odd that DH increases with age (line 258). Please explain or discuss.
+12. More clearly state reference groups for analyses in table 5
+13. Many values (e.g those in table 5) are described based on statistical significance. It would be helpful to understand how much some of the variables influences the outcome (e.g disc height). Can values like R2 be provided. So how much is the difference based on gender for example. Is it likely to be important?
+14. Please define BMP
+15. Third limitations is unclear line 329
+16. Figure 3 described Pfirrmann in grade 1-5 which does not appear to match the modified version used.
+Reply to editors and reviewers
+
+Hello Dear editors and reviewers,
+
+Thank you for your kind suggestions and comments. I’ve revised this manuscript to address all of the reviewer comments.
+
+My point-by-point reply is as follows:
+
+Reviewers' comments:
+
+Reviewer #1:
+
+Manuscript Summary:
+
+This paper proposes a semantic segmentation network (BianqueNet) to achieve high-precision segmentation of intervertebral disc (IVD) related areas and a quantitative method to calculate the signal intensity difference (\( \Delta SI \)) in IVD, average disc height (DH), disc height index (DHI), and disc height-to-diameter ratio (DHR). The method in this paper is evaluated in a dataset contains 1051 MRI images collected from four hospitals around China. The merit of this paper is that its evaluation is implemented on quite a large dataset. However, the main drawback of this paper is it lacks methodology innovations. For example:
+
+1. What is the advantage of the proposed method compared with the widely-used semantic segmentation method such as U-net?
+
+Reply to Reviewer: This point is well taken. Please forgive us for not making this point clearer in the first submission. The most important advantage of the proposed network is higher accuracy in segmentation. As shown in the figure and table below, compared with U-Net, higher segmentation may contribute better feature extraction, which is important in IVD degeneration quantitation.
+
+Performance of BianqueNet compared with other semantic segmentation method
+
+<table>
+  <tr>
+    <th rowspan="2">model</th>
+    <th colspan="2">Vertebral body</th>
+    <th colspan="2">IVD</th>
+    <th colspan="2">Lumbar spine</th>
+  </tr>
+  <tr>
+    <th>mDice</th>
+    <th>mIoU</th>
+    <th>mDice</th>
+    <th>mIoU</th>
+    <th>mDice</th>
+    <th>mIoU</th>
+  </tr>
+  <tr>
+    <td>U-Net</td>
+    <td>0.9159</td>
+    <td>0.8732</td>
+    <td>0.8886</td>
+    <td>0.8260</td>
+    <td>0.9020</td>
+    <td>0.8460</td>
+  </tr>
+  <tr>
+    <td>PSPnet</td>
+    <td>0.9334</td>
+    <td>0.8849</td>
+    <td>0.9066</td>
+    <td>0.8389</td>
+    <td>0.9135</td>
+    <td>0.8520</td>
+  </tr>
+  <tr>
+    <td>BianqueNet</td>
+    <td><b>0.9703</b></td>
+    <td><b>0.9425</b></td>
+    <td><b>0.9480</b></td>
+    <td><b>0.9019</b></td>
+    <td><b>0.9470</b></td>
+    <td><b>0.9035</b></td>
+  </tr>
+</table>
+Figure 2. The segmentation performance of BianqueNet in three typical cases and the influence of different segmentation accuracy on feature point detection and calculation.
+
+Fig.2 in the revised paper shows the importance of segmentation accuracy.
+
+Similar to U-NET, BianqueNet is an encoder-decoder network architecture.
+
+In the encoder section, we adopted the method of Deeplabv3 +, feature extraction network (applying empty convolution in deep separable) and added a DFE module (extracting richer global semantic information).
+
+In the decoder section, compared with U-Net, we proposed ST-SC module (extracting more accurate contour details) to replace the original Skip Connection Section to obtain the final denser prediction results by means of integrating the feature map information of each stage from up-sampling process.
+
+2. What are the innovation parts in the proposed Swin-Transform skip connection (ST-SC) module?
+
+Reply to Reviewer: In the revised paper, we described the innovation parts in detail (Line 437-462).
+
+To obtain more accurate segmentation information of IVDs and vertebral bodies, down-sampling-origin feature maps information needed to be selectively transferred to
+the up-sampling paths. Swin-Transformer blocks containing multi-headed self-attention mechanisms were added to the Skip Connection (see text for more details on the structure) to achieve the selective transfer function more efficiently and with less complexity.
+
+To verify this idea, we output feature maps from both network with and without ST-SC module as shown in Fig.5 f, g.
+
+![Feature maps from both network with and without ST-SC module](page_324_613_1097_482.png)
+
+Feature maps in the upper row are output from network with ST-SC module, and those in the bottom row are output from network with 1*1 convolution.
+
+For high-resolution and low-path feature maps (left column), there are not significantly difference in the visualization between these two networks.
+
+However, for middle-path feature maps (middle column), boundary information of vertebral bodies and cerebrospinal fluid presents clearer from the network with ST-SC module.
+
+For low-path feature maps (right column), boundary information of IVDs and cerebrospinal fluid presents clearer from the network with ST-SC module.
+Notably, this method may be the first one to be introduced into spine MR image segmentation tasks. In general, the innovation of our method is reflected in the compatibility and accuracy improvement of application in lumbar MR images quantitation.
+
+Also, there are some issues in writing the paper:
+3. Fig. 1 and 2 contain too much information, while the most important information is lost. For example, the proposed ST-SC module accounts for only a small proportion in Fig. 2; its modules, i.e., LN and W-MSA are not stated anywhere in the caption or in the text.
+
+Reply to Reviewer: Thank you for pointing out these issues. Considering that there is too much information in Fig.1 and Fig.2, we redrew Fig.1 with a clearer study design and workflow, as shown below.
+
+![Study design and clinical workflow diagram](page_184_670_1080_563.png)
+
+Figure 1. Study design and clinical workflow.
+
+Meanwhile, we separated Fig.2 into two separate figures (Fig.5 for network architecture, Fig.6 for feature extraction calculation).
+Figure 5. The proposed Bianque-net consists of segmentation CNNs with DFE module and SW-SC module.
+Figure 6. Schematic diagram of IVD parameters calculation.
+
+In addition, further explanations were added in the revised manuscript (Line 407-558).
+
+4. The paper does not describe how the signal intensity difference (\( \Delta SI \)) in IVD, average disc height (DH), disc height index (DHI), and disc height-to-diameter ratio (DHR) are calculated after segmenting the intervertebral disc. Even if these calculation methods are not originally proposed by the authors, they should at least briefly describe how they are implemented.
+
+Reply to Reviewer: Thank you for your comment. A long and detailed calculation description for every parameter has been provided in the Supplemental file, while there was less information of the detailed method in the main text, which may have confused the reader as to the important parts.
+
+Thus, in the revised paper, we put these parts briefly into the main text (Line 484-558) and used Fig.6 to help readers understand the details.
+
+5. In the experimental part, there seem to be no qualitative illustrations of the segmentation results. Also, the authors do not show how the segmentation results are used to analyze the correlation with IVD degeneration grading.
+
+Reply to Reviewer: We only calculated segmentation performance of different networks in the previous submission, which may have failed to make clear the segmentation performance differences.
+
+In the revised paper, we added Fig.2 to show vital differences in segmentation between BianqueNet and U-Net network, and made a certain analysis of the role of
+each module (Table 1).
+
+Based on segmentation, we extracted the signal intensity and geometric characteristics of the IVDs (see Methods/Lumbar IVD quantitative analysis/ Parameters Calculation based on IVD-related area segmentation for details).
+
+On the other hand, all IVDs were manually graded according to the modified Pfirrmann grading guidelines.
+
+For the correlation analysis of ΔSI and degeneration grade, considering that there is no difference in signal intensity values of grades 5-8, we combined grades 5-8 into one class and conducted a correlation analysis test for disc ΔSI parameters and corresponding degeneration grade (1, 2, 3, 4, 5-8).
+
+For the correlation analysis of geometric parameters and degenerative grade, we classified grade 1-5 into one class, given that the IVD height between grade 1 and grade 5 are basically equal (no collapse occurs).
+
+Fig.7 was added to the revised paper to present the different geometric characteristics and signal intensity among all kinds of IVD degeneration grades.
+
+![Schematic of IVD degeneration quantitation.](page_186_670_1077_393.png)
+
+Figure 7. Schematic of IVD degeneration quantitation.
+Reviewer #2:
+
+Manuscript Summary:
+
+This paper utilized CNN for lumbar spine segmentation to evaluate the intervertebral disc degeneration.
+
+1. It is great to collect the dataset which may benefit the community. I'd like to ask if the dataset will be released or not?
+
+Reply to Reviewer: We do realize that if this dataset is released publicly, it may be used by others to perform important research. However, for ethical reasons its release has to be limited. Even so, publication of the current study should help popularize this efficient and consistent method among the research community to help establish a consistently growing and updated dataset with proper privacy protections in place.
+
+2. The main contribution of this paper is utilizing a network for lumbar spine segmentation. The segmentation network showed in Fig.2, why do we need the ST-SC module? The multi-head self-attention mechanism can indeed model the long-range information dependency, while you have already used multi-scale information in the network, so I'm wondering if you indeed need the high-computational cost ST-SC module or not.
+
+Reply to Reviewer: We appreciate the comment. Please forgive us as the details and novelty of our segmentation network were not described clearly in the previous manuscript, which has now been clarified in the revised paper (Line 407-483).
+
+As one of the most important parts of our work, segmentation provides a basis for quantitative features automatic extraction. As we know, the feature maps from depth feature extraction module contain rich multi-scale semantic information and little boundary detail information. Considering that deconvolution operation presents limited capacity in recovering detail information from target image, and the use of skip connection can better improve this problem. Furthermore, the multi-head self-attention mechanism in the skip connection module (SC module) can selectively transfer the down-sampling feature map information to the up-sampling path, providing more accurate details of target images for the up-sampled path.
+
+To verify this idea, we output feature maps from both networks, with and without an ST-SC module, as shown in Fig. 5f, g.
+Feature maps in the upper row are output from network with ST-SC module, and those in the bottom row are output from network with 1*1 convolution.
+
+For high-resolution and low-path feature maps (left column), there are no significant differences in the visualization between these two networks.
+
+However, for middle-path feature maps (middle column), boundary information of vertebral bodies and cerebrospinal fluid is presented clearer from the network with ST-SC module.
+
+Likewise, for low-path feature maps (right column), boundary information of IVDs and cerebrospinal fluid is presented clearer from the network with ST-SC module.
+We also compared final segmentation outputs and their related feature points in Fig.2.
+
+Case1 and Case2 show that our network may predict the boundary information of IVDs and vertebral bodies better.
+
+On the other hand, compared with global self-attention mechanism, computational complexity of ST-SC module is lower. As a major contributor for computational complexity in ST-SC module, W-MSA (SW-MSA) calculates self-attention based on local windows, which are arranged to evenly partition the image in a non-overlapping manner. Supposing each window contains M×M patches, the computational complexity of a global MSA module and a window based one on an image of hw patches are:
+
+\[
+\Omega(MSA) = 4hwC^2 + 2(hw)^2C
+\]
+
+\[
+\Omega(W\text{-}MSA) = 4hwC^2 + 2M^2hwC
+\]
+
+where the global MSA module is quadratic to patch number hw, and the latter is linear when M is fixed. Global self-attention computation is generally unaffordable for a large hw, while the window based self-attention is scalable.
+
+3. In Fig. 1, the pipeline shows that you input two datasets into the network, that's
+fine for data from these sites. However, then how do you guarantee your model works fine for data collected a new site.
+
+Reply to Reviewer: The pipeline in the previous manuscript was not clear enough. To better explain our study design and workflow, we redrew the pipeline in Fig. 1
+
+![A detailed pipeline diagram showing segmentation training phase, performance evaluation phase, and data analysis phase for IVD degeneration quantification using BianqueNet.](page_246_370_1057_496.png)
+
+As shown in Fig.1 above, both Data Set A (resolution of 512*512) and Data Set B (resolution of 320*320) are from two machines in the Longhua hospital, Shanghai University of TCM. Model A and Model B were trained with images at different resolutions.
+
+Considering that the resolutions of MR images from different hospitals are not consistent (320*320, 512*512, 640*640, 960*960, etc), we proposed to adjust all the MR images to a uniform resolution of 512*512 to improve model’s universality. Furthermore, we carried out a validation test to determine whether the adjustment of MR images resolution may affect the accuracy of IVD degeneration quantitation or not, whose results were described in the section (Quantitation performance in different MR images with different resolutions, Line 149-168).
+
+The results show that Model A could still accurately calculate IVD degeneration parameters after MR images resolution were adjusted to 512*512 (Table 3).
+Table 3 Consistency analysis of intervertebral disc parameters calculated by MRI of different sizes
+
+<table>
+  <tr>
+    <th rowspan="2">Measure</th>
+    <th colspan="2">Intraclass Correlation<sup>b</sup></th>
+  </tr>
+  <tr>
+    <th>ICC<sup>a</sup></th>
+    <th>95%CI</th>
+  </tr>
+  <tr>
+    <td>\( \Delta SI \)</td>
+    <td>.874***</td>
+    <td>(.840, .902)</td>
+  </tr>
+  <tr>
+    <td>DHI</td>
+    <td>.958***</td>
+    <td>(.943, .968)</td>
+  </tr>
+  <tr>
+    <td>HDR</td>
+    <td>.956***</td>
+    <td>(.886, .978)</td>
+  </tr>
+</table>
+
+Therefore, the subsequent characteristic parameters of IVD degeneration were segmented and calculated by Model A.
+
+The reason why we set MR images resolution to 512*512 for final model input is because a large proportion of images present resolution of 512*512 among all collected MR images. Considering that using an interpolation method may miss or change information from an image by reducing or enlarging images sizes, we finally chose the middle image resolution of 512*512 to retain the original information of MR images to the most extent.
+
+To ensure that this network can perform well in other data sets, unrestricted histogram equalization operation and data enhancement operation were used to improve the generalization performance of the model in the training phase.
+
+In addition, MR images were randomly selected from the other three hospitals, adjusted resolution to 512*512, and evaluated consistency with Model A, as shown in Table 2.
+
+Table 2. Segmentation Performance on other MR images from different sites
+
+<table>
+  <tr>
+    <th rowspan="2">Cites</th>
+    <th colspan="2">Vertebral body</th>
+    <th colspan="2">IVD</th>
+    <th colspan="2">Lumbar spine</th>
+  </tr>
+  <tr>
+    <th>mDice</th>
+    <th>mIoU</th>
+    <th>mDice</th>
+    <th>mIoU</th>
+    <th>mDice</th>
+    <th>mIoU</th>
+  </tr>
+  <tr>
+    <td>Dongzhimen Hospital, Beijing University of CM</td>
+    <td>0.9567</td>
+    <td>0.9214</td>
+    <td>0.9198</td>
+    <td>0.8567</td>
+    <td>0.9193</td>
+    <td>0.8620</td>
+  </tr>
+  <tr>
+    <td>Guangdong Provincial Hospital of CM</td>
+    <td>0.9656</td>
+    <td><b>0.9498</b></td>
+    <td>0.9337</td>
+    <td><b>0.9046</b></td>
+    <td>0.9365</td>
+    <td>0.8888</td>
+  </tr>
+  <tr>
+    <td>Shenzhen Pingle Orthopedics Hospital</td>
+    <td>0.9654</td>
+    <td>0.9445</td>
+    <td>0.9334</td>
+    <td>0.8952</td>
+    <td>0.9269</td>
+    <td>0.8763</td>
+  </tr>
+  <tr>
+    <td>Longhua Hospital, Shanghai University of TCM *</td>
+    <td><b>0.9703</b></td>
+    <td>0.9425</td>
+    <td><b>0.9480</b></td>
+    <td>0.9019</td>
+    <td><b>0.9470</b></td>
+    <td><b>0.9035</b></td>
+  </tr>
+</table>
+
+* MR images from Longhua Hospital, Shanghai University of TCM were used to train the model as data set and to evaluate the accuracy of segmentation performance as control.
+
+The segmentation performance for MR image from Dongzhimen Hospital was
+acceptably moderate, while those for other two hospitals showed no significant difference with training set (Longhua Hospital).
+
+4. Is that really good to input different resolution images in the network? How about upsampling them to 512x512 for training and test on different resolution images? Why do we need multi-scale input in the training phase?
+
+Reply to Reviewer: Thank you for your comment. We apologize for our mistake in the previous pipeline. We have revised them in the current manuscript.
+
+Please see our explanation above as to the reason why we set MR images resolution of 512*512 for the final model input.
+
+5. What's the significance of this work? The segmentation model (I don't think so) or the truth you proved that neural network can work well on evaluating the intervertebral disc degeneration?
+
+Reply to Reviewer: I’m sorry for the misunderstanding.
+
+The significance of this work is to propose a segmentation-based and automatic quantitative analysis method for IVD parameters. To achieve quantitative evaluation of IVD degeneration, MR images of large sample were collected from several hospitals to extract parameters and establish baseline characteristics of lumbar IVDs in different subgroups (age, gender, segment, and Pfirrmann grade) as IVD degeneration grading criterion. The segmentation network or neural network were only used to obtain the geometric feature information of IVD-related areas as the input for the subsequent IVD features extraction. According to grading criterion, we achieved automatic grade IVD degeneration with quantitative features of IVDs as Fig.4.
+Figure 4. Quantitative analysis results of typical cases.
+
+6. What's the novelty of this work?
+
+Reply to Reviewer: The innovations can be summarized in three points:
+
+1) We propose an improved Deeplabv3 + semantic segmentation network.
+
+2) Based on accurate and consistent segmentation, we propose an automatic quantitative method in IVD degeneration feature extraction.
+
+3) We establishe a baseline characteristic of IVD in different subgroups (age, gender, segments and degeneration grades) among a large population.
+
+7. The main issue is that this kind of work (maybe the works are not about intervertebral disc degeneration but on other tasks, but they have proved the possibility of using networks for analyzing some diseases) has been vastly done before.
+Reply to Reviewer: We apologize for not making this point clearer in the previous version of the paper. Previous CNN were mainly proposed as a degeneration level classifier, while our network is proposed to automatically quantify IVD degeneration, which is the major difference from other medical deep learning-based networks.
+
+Indeed, many studies were focused on IVD degeneration. Some quantitative studies proposed some semi-automatic quantitative analysis with general medical image processing software, while other deep learning studies proposed some classifiers for automatic IVD degeneration grading, which were similar to some auxiliary diagnostic neural networks, such as the segmentation of brain tumors and the classification of tumor types, etc.
+
+Compared with other quantitative analysis studies on IVD degeneration, our work can achieve both automatic extraction of IVD degeneration parameters and quantitative analysis IVD degeneration.
+
+Compared with other CNN studies on auxiliary diagnosis, our work embodies not only the deep learning neural network approach, but also a good correlation between characteristics of IVD parameters and IVD degeneration grades, which may improve the interpretability of diagnostic results.
+
+In terms of method, different from most methods in other studies, segmentation network is only a part to achieve automatic IVD feature extraction. Subsequently, an automatic quantitative feature calculation method is proposed to comprehensively analyze the geometric characteristic (DH, DHI, HDR) and signal intensity (\( \Delta SI \)) of IVD based on segmentation, which may quantitatively reflect structural collapse and water content loss with the process of IVD degeneration.
+Reviewer #3:
+
+Manuscript Summary:
+
+Thank you for the opportunity to review this manuscript. The broad goal of developing accurate quantitative measures of IVD degeneration using deep learning is important in my opinion. Without these measures it will not be possible to work towards differentiating degeneration due to aging compared to clinically important degeneration. This is a major gap in the back pain field. I have very limited understanding of the deep learning methods described in this paper, so am unable to comment on the quality of many the methods undertaken. My comments are limited to other aspects of the manuscript.
+
+1. The aim is unclear to me and does not capture the big picture of what this work could achieve. While the long-term potential clinical use is important but I am not sure the current study has this aim/purpose.
+
+Reply to Reviewer: Thank you for pointing out this issue. We didn’t clearly state our research aim and main function of our network in the previous manuscript. We have now described all of the study design in detail (Line 374-398) and redrew Fig.1 to better illustrate our workflow.
+
+![Workflow diagram showing segmentation training phase, performance evaluation phase, and data analysis phase for IVD degeneration quantification](page_256_682_1344_482.png)
+In this study, we propose an improved deeplabv3+ segmentation network with newly designed modules and a quantitative method to automatically quantify IVD degeneration.
+
+Firstly, we test its performance in automatic segmentation (accuracy) and calculation (consistency)
+
+Secondly, we test its adaptability (segmentation and quantitation) from other machine in different hospitals.
+
+Thirdly, IVD parameters were extracted from lumbar MR images by proposed network. According to large population subgroups (age, gender, segment, degeneration grade), we established a baseline criterion of IVD parameters characteristic for IVD degeneration automatic classification.
+
+![Quantitative analysis results of typical cases.](page_184_670_1082_563.png)
+
+Figure 4. Quantitative analysis results of typical cases.
+This study proposed a consistent, accurate and efficient deep learning network to achieve automatic lumbar IVD degeneration quantitation. We believe that the popularization of this method will greatly transfer MR images into data to establish a quantitative index system.
+
+2. Abstract refers to reliability with Pfirrmann. I think correlation is a better term to describe the study.
+
+Reply to Reviewer: Thank you for pointing this out. We used the wrong expression in the sentence ‘while signal intensity in IVD degeneration had excellent reliability according to the modified Pfirrmann Grade (macroF1=90.63%~92.02%)’.
+
+MacroF1 value was used to evaluate the classification accuracy of proposed model. What we originally meant to express is that our method is very accurate in classification, but it is admittedly improper to express its use as ‘reliable’.
+
+3. In the Implications for patient care I believe the authors have extrapolated beyond their study results too far. For example, they should not talk about assessing risk of disc herniation. This is inappropriate based on current study. In general the conclusions need to be more limited the study design and results. This study lays a foundation to later test the clinical importance of MRI measures of disc degeneration but does not investigate this clinical aspect. This should be clearer throughout.
+
+Reply to Reviewer: Thank you for your suggestion. In the previous version, we did extrapolate the application of our network.
+
+As we mentioned in the Introduction, the progressive process of IVD degeneration may hardly be described by traditional degeneration grade. As an early phase of spine degenerative disease, IVD degeneration should be screened with more accurate data extracted from MRIs to prevent progressive outcomes. Although manual measurement on IVD is convenient to learn and apply, it may take several attempts and a high degree of concentration to ensure accuracy in its measurements. As a result of these man-power issues, data from spine MRIs haven’t been fully and widely used in some clinical practices and clinical trials with large populations. Due to the nature of its automation our method may provide more precise information for clinical practice (lumbar MR image structural report), clinical trials (efficacy assessment) and mechanism investigation (biomechanics research and finite element analysis).
+
+4. There are a reasonable number of small expression issues.
+
+Reply to Reviewer: Thank you. We have carefully checked and improved the English
+grammar and syntax in the revised manuscript.
+
+5.I cannot assess if the methods to test if the approach works well across different MRI machines is valid. A radiologist review of this would be important.
+
+Reply to Reviewer: Thank you for your comment and agree with your concern. To test the model performance, especially in clinical settings, we designed three different evaluations for a human-machine comparison, as described in the Methods (Line 588-628).
+
+Evaluation of model performance
+    Accuracy evaluation on IVD segmentation performance
+    Consistency evaluation on IVD parameter quantitation
+    Validity evaluation on IVD degeneration quantitation
+
+In the segmentation phase, we compared manual segmentation with model segmentation. mDice and mIoU were used to assess the similarity between regions segmented by machines and regions defined by residents.
+
+In the quantitation phase, we compared manual measurements with model calculation. IVD parameters measured by a senior radiologist and orthopedic residents are important as a control standard. A 4th-year radiology resident, and a 4th-year orthopedic resident measured and calculated all the IVD parameters (HDR and DHI) among these 15 MR images randomly selected from data set B.
+
+Each IVD was measured and recorded three times, from which mean values of three-time measurements were used to compare with each other. In additions, to avoid fatigue in long-term measurement, these residents were asked to take a 20-minute rest after measuring every two MR images.
+Average IVD height:
+\( h_{IVD} = a1/d1 \)
+
+Core area of IVD (a1)
+Core diameter of IVD (d1)
+Total diameter of IVD (d2)
+
+HDR = \( \frac{h_{IVD}}{d2} \)
+
+VB height:
+\( h_{VB} = a2/d3 \)
+
+Area of vertebral body (a2)
+Diameter of vertebral body (d3)
+
+DHI = \( \frac{2 * h_{IVD}}{h_{upperVB} + h_{lowerVB}} \)
+
+Supplement Fig.2 Schematic diagram of manual measurement of IVD
+
+The intraclass correlation coefficient (ICC) was used to analyze the consistency between the IVD parameters extraction and IVD manual measurement. Results were reported in the revised manuscript (Line 169-196).
+
+Finally, in the IVD degeneration classification phase, to test the validity of signal intensity quantitation on IVD degeneration, 50 MR images randomly selected from data set A and data set B, respectively, were used to automatically grade IVD degeneration levels. Meanwhile, a research team, composed of a 4th-year radiology resident, two 8th-year orthopedic residents and three 4th-year orthopedic residents, graded all the IVD degeneration levels independently, according to the modified Pfirrmann Grading System. They were all blinded to the automatic quantitative measures. Disagreements were resolved by consensus with additional two 10th-year orthopedic residents.
+
+MacroF1-score and Kendall coefficient were used to analyze the validity between the automatic grade results and final manual grade results. Results were reported in the revised manuscript (Line 222-253).
+6. The methods do not provide adequate information on the process for assessing Pfirrmann scores. There is also no refence for the modified scale. The reader needs to understand this scale to interpret much of the findings. Was reliability of Pfirrmann assessed. Line 126 reports “discussed together”. This is unclear. Were those doing Pfirrmann measures blinded to the quantitative measures?
+
+Reply to Reviewer: We apologize for this issue as some important details were omitted in the previous manuscript, but we have added this information in the revised paper.
+
+Regarding the modified Pfirrmann Grade, we inserted a related reference and included an illustration of different grades of IVD degeneration in Fig.7, as shown below (lower right part)
+
+![Scheme of IVD degeneration quantitation.](page_349_563_1047_388.png)
+
+Figure 7. Scheme of IVD degeneration quantitation.
+
+To ensure the reliability of Pfirrmann grading, a research team, composed of a 4th-year radiology resident (DW Kong), two 8th-year orthopedic resident (J Chen, XF Ma), and three 4th-year orthopedic resident (YL Sun, YP Lin, MC Yin), graded all the IVD degeneration levels independently according to the modified Pfirrmann Grading System. They were all blinded to the automatic quantitative measures. Disagreements were resolved by consensus with additional two 10th-year orthopedic residents (XJ Cui and YJ Wang). In the revised version, we added more details about “discuss together” (Line 623-628).
+7. It does not seem that any normalisation was performed for disc height. Interpreting the raw score requires this to make it cleanly useful. The nice graphs in figure 4 suggest that individuals can be compared to normal values, means etc based on age, disc level etc. More discussion of this would be good as this demonstrates how the findings could be applied in clinical practice and assessed for ability to predict important outcomes in future studies.
+
+Reply to Reviewer: Thank you very much for your suggestion. Of course, there is no way to compare our IVD height (DH) with other measured DH in previous studies, because our DH is calculated with the number of pixels in specific segments, which depends on the MRI resolution (The larger the resolution of the image, the more pixel values, the larger the calculated DH).
+
+To ensure the comparability of DH, the only thing we did for normalization was to adjust all the images to a fixed resolution (512*512), so that the number of pixels per unit area was kept consistent.
+
+However, DH value calculated by our model is still an intermediate variable, which may be influenced by a number of other individual factors. According to the application of these two parameters (DHI, HDR) in previous studies, we calculated them with heights and diameters of IVD and VB for normalization and comparison.
+
+Regarding future clinical practice and assessment, we will insert this network into MR image system and export a structural lumbar MRI report like Fig.4 for doctors, patients, and researchers. Compared with traditional text description MRI report, our quantitative report may provide more accurate IVD parameters to reflect height collapse and water content loss with IVD degeneration. According to IVD baseline characteristic criteria in each age, gender, and segments, deviation of IVD geometric parameters and pfirrmann grade based on signal intensity will be obtain automatically to reflect both structural collapse status and water content loss in IVD comprehensively, which may provide more precise information for clinical practice (lumbar MR image structural report), clinical trials (efficacy assessment) and mechanism investigation (biomechanics research and finite element analysis). Notably, this baseline characteristics will be updated dynamically as these MR image data are collected and summarized.
+
+8. How many images were manually segmented to compare and train the automatic segmentation. As mentioned, I have little expertise in this area but it would be good if the processes could be made easier to read for an average reader especially clinical experts who will want to understand this work.
+
+Reply to Reviewer: Thank you very much for this good suggestion. We have revised the manuscript to include this information.
+In this study, we trained two models for segmentation using MRIs with different resolutions. The data set for Model A contains 223 participants' MRIs, including 303 images in the training set and 80 images in the test set. The data set for Model B contains 63 participants’ MRIs, including 93 images in the training set and 24 images in the test set. The training set and test set were randomly assigned. The training images of two data sets were enhanced with data enhancement. (Specific values are also shown in Fig.1)
+
+9. What exactly is “signal intensity difference”. Why is it not just signal intensity? IS this value the mean SI in the region of interest or max value etc. Given how critical the signal intensity difference and the 3 measures of DH are to the paper, they should be more clearly defined and explained.
+
+Reply to Reviewer: Thank you for your comment. In the previous submission, there’s a long and detailed calculation description for every parameter uploaded as Supplemental file, while there’s less information of the detailed methodology in the main text, which we understand now may confuse the reader. In the revised paper, we outlined these parts briefly in the main text (Line 484-558) and used Fig.6 to illustrate the calculation process.
+
+10. Line 244 describes nearly 1/3 of potential participants being excluded. It seems this would limit the generalizability of the results.
+
+Reply to Reviewer: We appreciate this concern. This does limit the versatility of this network to a certain extent. However, among the 1508 MRIs screened in 4 sites around China, there’re 73 excluded for unaligned outlines (diagnosed as lumbar spondylolisthesis), 45 excluded for abnormal signal intensity distribution (diagnosed as spine tumors), 364 excluded for irregular structures (diagnosed as IVD herniation or vertebral body ossification), and only 144 excluded for imaging quality (segmentation results and corner detection did not meet the requirements of parameter calculation), and finally a total of 1051 individuals were collected (Line 198-203).
+
+Even though BianqueNet's performance is very good, future work will continue to optimize segmentation performance. There are generally two strategies to improve segmentation performance:
+
+1) To improve the generalization performance of segmentation algorithm, one of the more reliable methods is to increase training samples, but this costs a lot of time.
+
+2) To study more powerful segmentation algorithms. These measures may broaden the scope of our approach.
+
+11. It seems odd that DH increases with age (line 258). Please explain or discuss.
+Reply to Reviewer: Thank you very much for your concern. According to our statistical results, this is indeed the trend, which is similar with the age trend of peak bone mass.
+
+![A line graph showing bone acquisition/loss over age for male and female, with key points labeled for puberty, active bone growth, peak bone mass, bone loss due to menopause, and age-related bone loss. The x-axis is labeled 'Age (year)' and the y-axis is labeled 'Bone acquisition/loss'. There is a legend indicating the points and a note about suboptimal lifestyle factors and increasing risk of osteoporosis/fracture.](page_246_370_1017_495.png)
+
+According to the figure^4, turning point for peak bone mass is age of 36. In our study, we found that the turning point for ‘peak IVD height’ is in age range of 50-60, which may be a secondary degenerative process. Due to changes in vertebral osteoporosis, the endplate of the vertebral body becomes more depressed, which may make the IVD sink into the vertebral body, resulting in lower vertebral height and higher disc height^{1,3}.
+
+Also, there are many studies on the relationship between age and height of IVD and vertebral bodies. H.S. Monoo-Kuofi et al^{2} concluded that IVD height increases with age, but not in a linear fashion, with alternating periods of overgrowth and thinning, and a significant decrease of 2.5% after age 50. These studies support our results.
+
+In the future, we will continue to collect data from more MRIs and possibly investigate these IVD parameters as a function of aging.
+
+12. More clearly state reference groups for analyses in table 5
+
+Reply to Reviewer: Thank you for your suggestion.
+
+This experiment is to investigate the influence of age, gender, and segments on these IVD parameters in degeneration progress. For each factor, when a reference group was selected in the Stata software, group of other factors was analyzed as controls. For example, when male factor is selected as the reference group, all data with female are included into the control group.
+For age, 20-30 was selected as the reference group.
+
+For segment, L4-L5 was selected as the reference group.
+
+13. Many values (e.g those in table 5) are described based on statistical significance. It would be helpful to understand how much some of the variables influences the outcome (e.g disc height). Can values like R2 be provided. So how much is the difference based on gender for example. Is it likely to be important?
+
+Reply to Reviewer: Our \( R^2 \) results showed that for the 4 IVD parameters, our model and actual values have a high goodness of fit.
+
+<table>
+  <tr>
+    <th></th>
+    <th>\( \Delta SI \)</th>
+    <th>DH</th>
+    <th>DHI</th>
+    <th>HDR</th>
+  </tr>
+  <tr>
+    <td>Prob&gt;F</td>
+    <td>0.0000</td>
+    <td>0.0000</td>
+    <td>0.0000</td>
+    <td>0.0000</td>
+  </tr>
+  <tr>
+    <td>R-squared</td>
+    <td>0.4226</td>
+    <td>0.4770</td>
+    <td>0.3909</td>
+    <td>0.3078</td>
+  </tr>
+  <tr>
+    <td>Adj R-squared</td>
+    <td>0.4191</td>
+    <td>0.4739</td>
+    <td>0.3872</td>
+    <td>0.3036</td>
+  </tr>
+  <tr>
+    <td>Root MSE</td>
+    <td>22.253</td>
+    <td>1.7014</td>
+    <td>0.04576</td>
+    <td>0.02744</td>
+  </tr>
+</table>
+
+Here, multiple regression analysis was standardized to investigate the influence of different factors (age, gender, segments) on IVD degeneration (\( \Delta SI \), DH, DHI, HDR). The greater absolute value of the normalized coefficient (only significant regression coefficient was concerned), the higher these dependent factors may influence on IVD degeneration.
+
+For example, gender and other factors have no significant influence on \( \Delta SI \). For DH parameters, segment and gender had greater influence than age.
+
+14. Please define BMP
+
+Reply to Reviewer: BMP, short for Bitmap, is a standard image file format in The Windows operating system. It is supported by various Windows applications and widely used with the popularity of Windows operating system and the development of rich Windows applications.
+
+15. Third limitations is unclear line 329
+
+Reply to Reviewer: Thank you for your suggestion. What we mean is that this retrospective study may be subject to potential selection bias. We have revised all the limitations as below:
+
+Our study has some limitations. First, this retrospective study may be subject to potential selection bias. Some prospective studies should be rigorously conducted to test the clinical utility of this proposed model. Second, our deep learning model was
+trained and tested using a single ethnic group (namely, Chinese patients), so its reproducibility among different ethnic groups should be further evaluated.
+
+In the future, it will be important to combine radiomics and prospective design and integrate all kinds of clinical examination, fluid flow biomechanics, and molecular approaches to improve accuracy in IVD degeneration evaluation.
+
+16. Figure 3 described Pfirrmann in grade 1-5 which does not appear to match the modified version used.
+
+Reply to Reviewer: According to the Modified Pfirrmann grading guidelines, the characteristics of IVD signal intensity are the same among grade 5 to 8, so IVD degeneration grade of 5 to 8 are combined as one (grade 5).
+
+![Illustration of different grades of IVD degeneration and corresponding signal intensity descriptions](page_246_670_1012_393.png)
+
+We inserted a related reference and drew an illustration of different grades of IVD degeneration in Fig.7, as shown above (lower right part)
+
+References
+
+1. Berlemann, U., Gries, N. C. & Moore, R. J. The relationship between height, shape and histological changes in early degeneration of the lower lumbar discs. Eur. Spine J. 7, 212–217 (1998).
+2. Amonoo-Kuofi, H. S. Morphometric changes in the heights and anteroposterior diameters of the lumbar intervertebral discs with age. J. Anat. **175**, 159–68 (1991).
+
+3. Twomey, L. & Taylor, J. Age changes in lumbar intervertebral discs. *Acta Orthop.* **56**, 496–499 (1985).
+
+4. Zhu X, Zheng H. Factors influencing peak bone mass gain. Front Med. 2021 Feb;15(1):53-69.
+Reviewers' Comments:
+
+Reviewer #1:
+Remarks to the Author:
+My questions are answered.
+
+Reviewer #3:
+Remarks to the Author:
+The authors have responded to my previous comments and suggestions adequately. Responses were detailed but the changes were not highlighted so difficult to check if and when the additional information was added to the manuscript. A few minor ongoing comments:
+
+- regarding my previous comment 13. The authors state the values are standardised values. This is not clear when I read the table. Please add this as a footnote etc.
+
+- Regarding my previous comment 9. The authors have added additional descriptions as requested but I must say I still don’t understand the description of signal intensity. Why is the SI measure a difference between 2 peaks? This is most likely my lack of expertise in the methods used in the paper; however, it does raise the potential issue that many readers will find this paper too dense to understand and this may detract from the potential value of the study. Please consider trying to simply some of the reporting for people who are not experts in the methods but may be the researchers or clinicians who apply these findings in the future.
+Reply to editors and reviewers
+Hello Dear editors and reviewers,
+Thank you for your kind suggestions and comments. I’ve revised this manuscript to address all of the reviewer comments.
+My point-by-point reply is as follows:
+Reviewer #3’ comments:
+The authors have responded to my previous comments and suggestions adequately. Responses were detailed but the changes were not highlighted so difficult to check if and when the additional information was added to the manuscript. A few minor ongoing comments:
+Reply to Reviewer: Thank you for your kind suggestion. Please forgive us for not highlighting changes clearer in the revised version, because it has been extensively rewritten with outline rearrangement.
+1. Regarding my previous comment 13. The authors state the values are standardised values. This is not clear when I read the table. Please add this as a footnote etc.
+Reply to Reviewer: This point is well taken. Thanks. In the latest version, a footnote has been added in the Table 4 as below:
+Table 4 Correlations between IVD parameters and modified Pfirrmann Grading
+
+<table>
+  <tr>
+    <th rowspan="2">lumbar level</th>
+    <th colspan="2">ΔSI</th>
+    <th colspan="2">DH*</th>
+    <th colspan="2">DHI</th>
+    <th colspan="2">HDR</th>
+  </tr>
+  <tr>
+    <th>female</th>
+    <th>male</th>
+    <th>female</th>
+    <th>male</th>
+    <th>female</th>
+    <th>male</th>
+    <th>female</th>
+    <th>male</th>
+  </tr>
+  <tr>
+    <td>L1/L2</td>
+    <td>-.421***</td>
+    <td>-.296**</td>
+    <td>-.304***</td>
+    <td>-.235***</td>
+    <td>-.473***</td>
+    <td>-.397***</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>L2/L3</td>
+    <td>-.966***</td>
+    <td>-.481***</td>
+    <td>-.417***</td>
+    <td>-.354***</td>
+    <td>-.398***</td>
+    <td>-.575***</td>
+    <td>-.455***</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>L3/L4</td>
+    <td>-.639***</td>
+    <td>-.470***</td>
+    <td>-.530***</td>
+    <td>-.443***</td>
+    <td>-.626***</td>
+    <td>-.539***</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>L4/L5</td>
+    <td>-.656***</td>
+    <td>-.696***</td>
+    <td>-.560***</td>
+    <td>-.665***</td>
+    <td>-.709***</td>
+    <td>-.758***</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>L5/S1</td>
+    <td>-.701***</td>
+    <td>-.687***</td>
+    <td>-.641***</td>
+    <td>-.664***</td>
+    <td>-.744***</td>
+    <td>-.778***</td>
+    <td></td>
+    <td></td>
+  </tr>
+</table>
+
+*** p<0.01 ** p<0.05 * p<0.1
+r. Spearman rank correlation coefficients
+a. DH is the only parameter that is not standardized, while ΔSI can be applied to MRI at different centers, and DHI and HDR can be applied to different types of imaging means and physical measurements.
+
+2. Regarding my previous comment 9. The authors have added additional descriptions as requested but I must say I still don’t understand the description of signal intensity. Why is the SI measure a difference between 2 peaks? This is most likely my lack of expertise in the methods used in the paper; however, it does raise the potential issue that many readers will find this paper too dense to understand and this may detract from the potential value of the study. Please consider trying to simply some of the reporting for people who are not experts in the methods but may be the researchers or clinicians who apply these findings in the future.
+Reply to Reviewer: Thank you for your kind suggestion. It is very important to simply some of the reporting for people, especially for popularization of cutting-edge technology.
+Regarding to SI measure, please forgive us for not explaining clearly. We added some details in the Method section in the latest manuscript as below.
+Signal intensity represent the magnitude of each pixel in a grayscale, and we follow this statement from previous studies on histogram features of intervertebral discs13. The histogram feature is used to quantify different signal intensity distribution in different areas from MRI, in which X-axis represents different signal intensities, and Y-axis represents the corresponding number of pixels. A two-peak distribution has been analyzed in healthy IVD from MRI, because the sharpness of the boundary between the NP and the AF can be well characterized with large amounts pixel with two major signal intensities (Fig. 5d)13, With IVD degeneration, water content loss in NP can be measured in histogram feature distribution changes, which presents that previous higher signal intensity (light) in the IVD area gradually becomes lower (dark) (Fig. 5g). The difference in pixel numbers corresponding to different signal intensities can well describe the degeneration state.
+Reference
+13. Waldenberg, C., Hebelka, H., Brisby, H. & Lagerstrand, K. M. MRI histogram analysis enables objective and continuous classification of intervertebral disc degeneration. Eur. Spine J. 27, 1042–1048 (2018).

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+Deep Learning Approach for Evaluating Lumbar Intervertebral Disc Degeneration: Achieving High Accurate Segmentation for Quantitative Analysis on MRI
+
+Hua-dong Zheng
+Shanghai University
+Yue-li Sun (yueli_sun@foxmail.com)
+Longhua Hospital, Shanghai University of Traditional Chinese Medicine
+De-wei Kong
+Department of Radiology·Longhua Hospital of Shanghai University of TCM
+Meng-chen Yin
+Longhua Hospital, Shanghai University of TCM
+Jiang Chen
+Dongzhimen Hospital of BeijingUniversity of Chinese Medicine
+Yong-peng Lin
+Dongzhimen Hospital, Beijing University of Chinese Medicine
+Xue-feng Ma
+Shenzhen Pingle Orthopedics Hospital (Shenzhen Pingshan District Hospital of TCM)
+Hong-shen Wang
+Guangdong Provincial Hospital of Chinese Medicine
+Guangjie Yuan
+Shanghai University
+Min Yao
+Longhua Hospital, Shanghai University of TCM
+Xue-jun Cui
+Longhua Hospital, Shanghai University of TCM
+Yingzhong Tian
+Shanghai University
+Yongjun Wang
+Shanghai University of Traditional Medicine   https://orcid.org/0000-0001-9333-2423
+Keywords: lumbar disc degeneration, intervertebral disc degeneration, MRI, deep learning and image processing technology
+
+Posted Date: September 2nd, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-864336/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on February 11th, 2022. See the published version at https://doi.org/10.1038/s41467-022-28387-5.
+Abstract
+
+Purpose: Using deep learning and image processing technology, a standardized automatic segmentation and quantitation network of lumbar disc degeneration based on T2MRI was proposed to help residents accurately evaluate the intervertebral disc (IVD) degeneration.
+
+Materials and Methods: A semantic segmentation network (BianqueNet) consist of self-attention mechanism skip connection module and deep feature extraction module was proposed to achieve high-precision segmentation of IVD related areas. A quantitative method was used to calculate the signal intensity difference (\( \Delta SI \)) in IVD, average disc height (DH), disc height index (DHI), and disc height-to-diameter ratio (DHR). Quantitative ranges for these IVD parameters in a larger population was established among the 1051 MRI images collected from four hospitals around China.
+
+Results: The average dice coefficients of BianqueNet for vertebral bodies and intervertebral discs segmentation are 97.04% and 94.76%, respectively. This procedure was suitable for different MRI centers and different resolution of lumbar spine T2MRI (ICC=.874~.958). These geographic parameters of IVD degeneration have a significant negative correlation with the modified Pfirrmann Grade, while signal intensity in IVD degeneration had excellent reliability according to the modified Pfirrmann Grade (macroF1=90.63%~92.02%).
+
+Conclusion: we developed a fully automated deep learning-based lumbar spine segmentation network, which demonstrated strong versatility and high reliability to assist residents on IVD degeneration evaluating by means of IVD degeneration quantitation.
+
+Implication for Patient Care: Deep learning–based approaches have the potential to maximize diagnostic performance for detecting disc degeneration and assessing risk of disc herniation while reducing subjectivity, variability, and errors due to distraction and fatigue associated with human interpretation.
+
+Introduction
+
+The intervertebral disc (IVD) plays an important role in distributing loads and absorbing shock in the spine, which is comprised of a gel-like nucleus pulposus (NP), collagenous annulus fibrosis (AF) layers, and ring-like cartilaginous endplates (EP). Identifying IVD structural changes, including IVD deformation, NP dehydration and EP ossification, due to chronic degeneration or acute injury, in patients undergoing MRI of the lumbar spine has many important clinical implications \( ^1 \). It has been determined that IVD degeneration is a consequence of aging. Accumulated compressive overload usually lead to functional fatigue fractures in endplates and subsequently IVD herniation\( ^{2-4} \), which may lead to increased inflammation\( ^5 \), nerve compression\( ^6 \) and release of pain factors\( ^7 \). Lifestyle modifications and surgical interventions are likely to be most effective for treating IVD degeneration or herniation, but it is more important to initiate screening and prevention during the earliest stages of the disease process.
+MRI with morphologic cartilage imaging sequences has been shown to have high specificity but only moderate sensitivity for detecting dehydration and deformation within the IVD degeneration\(^{2,4}\). Diagnostic performance is highly dependent on the level of reader expertise, and only moderate interobserver agreement between readers has been reported in most studies \(^2\). Quantitative analysis is efficient and comprehensive in evaluating IVD degeneration by measuring the signal intensity and geometric information. Early research on quantitative measurement of intervertebral discs used general image processing programs for manual measurement\(^{8-10}\). However, there is still no universal automatic IVD degeneration analysis tool in this field. The lack of a universal and widely accepted standard definition of IVD degeneration is one of the main reasons.
+
+There has been much recent interest in using deep learning methods in medical imaging \(^{11}\). With the wide-spread application of convolutional neural network classifiers in medical images, many studies use the rectangular box surrounding the lumbar IVD as input, and the corresponding degeneration level as the label to train the classifier for learning degenerative features by neural network. However, the input rectangular bounding box of the intervertebral disc needs to be segmented artificially or detected automatically using complex algorithms\(^{1,12-17}\). There are also some studies on the quantitative measurement of intervertebral discs based on deep learning, which did not use quantitative data to evaluate intervertebral disc degeneration\(^{18,19}\).
+
+In this study, a fully automated deep learning-based lumbar spine segmentation network (LSSN) has been developed at our institution by using a deep convolutional neural network (CNN) with the self-attention skip connection, deep feature extraction module and the corresponding loss function. According to IVD degeneration features (water content loss and height decrease) \(^{20}\), signal intensity difference and geometric parameters of IVD are calculated and validated with the modified Pfirrmann grading system. Finally, baseline ranges of lumbar IVD parameters among different gender and age and lumbar level was established based on a large population around China for quantitative and structured report. The diagram of this study is illustrated in Fig. 1.
+
+Materials And Methods
+
+MRI Data Sets
+
+This study was approved by Institutional Review Board (IRB) in all the participating sites. All retrospective subject data were obtained with a waiver of consent under IRB approval. The data were anonymized before being shared.
+
+Data sets for segmentation training (Data set A & B)
+
+Training and validation of the proposed lumbar spine semantic segmentation method was carried out by performing an institutional review board–approved retrospective analysis of lumbar spine images from
+286 subjects who underwent MR imaging in the Longhua Hospital, Shanghai University of TCM between January 1, 2019, to December 31, 2020. Among these, there’re 223 subjects using a 1.5-T MRI unit (MAGNETOM Aera XJ, SIEMENS) and 63 subjects using another 1.5-T MRI unit (MAGNETOM Avanto, SIEMENS), which were trained two separate segmentation networks for different resolution of 512*512 (Data set A) and 320*320 (Data set B). Mid-sagittal T2 images of different resolution were exported from Data set A and Data set B respectively, being randomly allocated into each training set or test set (Fig.1). All images in the segmentation data set were labeled by LabelMe (version 3.3.6, CSAIL, Massachusetts Institute of Technology) \(^{21}\). Based on the structural features mentioned in the modified Pfirrmann grading system, the segmentation area of 14 parts, included 5 vertebral bodies (L1-L5), 5 lumbar IVDs (L1/L2-L5/S1), sacrum (S1), pre-iliac fat area, cerebrospinal fluid area in the spinal canal, and background as Fig. 2a.
+
+Data set for quantitative analysis (Data set C)
+
+The proposed LSSN was used to extracted 1051 lumbar spine images as Data set C in four hospitals around China, including Longhua Hospital, Shanghai University of TCM, Guangdong Provincial Hospital of Chinese Medicine, Shenzhen Pingle Orthopedics Hospital, and Dongzhimen Hospital, Beijing University of Chinese Medicine between January 1, 2019, and March 30, 2021. The imaging parameters of all sites are summarized in Table 1.
+
+Table 1 Imaging Parameters for the MRI Sequences in the 4 Sites
+<table>
+  <tr>
+    <th>Site</th>
+    <th>City</th>
+    <th>Strength of the Magnet</th>
+    <th>Company</th>
+    <th>Model</th>
+    <th>Coil</th>
+  </tr>
+  <tr>
+    <td>Longhua Hospital, Shanghai University of TCM</td>
+    <td>Shanghai</td>
+    <td>1.5-Tesla</td>
+    <td>SIEMENS</td>
+    <td>MAGNETOM Aera XJ</td>
+    <td>18-channel Spine Tim 4G coil</td>
+  </tr>
+  <tr>
+    <td>Guangdong Provincial Hospital of Chinese Medicine</td>
+    <td>Guangzhou</td>
+    <td>3-Tesla</td>
+    <td>SIEMENS</td>
+    <td>TIM Systems</td>
+    <td>32-channel Spine Tim coil</td>
+  </tr>
+  <tr>
+    <td>Shenzhen Pingle Orthopedics Hospital</td>
+    <td>Shenzhen</td>
+    <td>1.5-Tesla</td>
+    <td>SIEMENS</td>
+    <td>MAGNETOM Essenza</td>
+    <td>8-channel quadrature body coil</td>
+  </tr>
+  <tr>
+    <td>Dongzhimen Hospital, Beijing University of Chinese Medicine</td>
+    <td>Beijing</td>
+    <td>1.5-Tesla</td>
+    <td>SIEMENS</td>
+    <td>MAGNETOM Amira</td>
+    <td>24-channel quadrature body coil</td>
+  </tr>
+</table>
+
+A research team, composed of a 4-year radiology resident (DW Kong), two 8-year orthopedic resident (J Chen, XF Ma), two 4-year orthopedic resident (YL Sun, YP Lin) and a 2-year orthopedic resident (MC Yin), discussed together for the final segment and Pfirrmann grade for each MR image.
+
+Lumbar Spine Segmentation from MR Images
+
+Convolutional Neural Network (CNN) Training
+
+The critical component of LSSN is an improved deeplabv3+ segmentation network\(^{22}\) with backbone ResNet-101\(^{23}\), called BianqueNet. The BianqueNet was built on the basis of deep feature extraction to extract richer semantic information and denser features. An illustration of this semantic segmentation network is shown in **Fig. 2**. The entire network consists of a swin transform skip connection (ST-SC) module and a deep feature extraction (DFE) module. Swin Transform is a hierarchical transform calculated by shifting the window, which has the advantages of high efficiency and low complexity\(^{24}\). The skip connections structure designed in this study uses two successive Swin-Transformer blocks, with 1*1 convolutional layers in parallel at the same time, and finally the two output features are spliced. Through the pyramid pooling module, feature information of different depths through pooling operations
+of different scales can be obtained. By repeating check with feature map of 4096 channels multi-scale information \(^{25}\), the network can achieve efficient features extraction with a dense semantic feature map of 256 channels.
+
+32-depth BMP images were exported from raw MRI to train the LSSN as input. In the upsampling phase, a modified upsampling operation with a deconvolution decoder was used to recover more detailed features of the segmentation target. In the feature extraction phase, the feature maps of different resolutions were obtained by down-sampling and output to the ST-SC module, which splices images and extracts features from different resolutions. According to feature pyramid\(^{26}\), feature maps with low-resolution and high-resolution were integrated to extract more semantic and spatial information, in which a 3*3 double convolutional layer was used for the fused feature map to improve the feature. Finally, a double upsampling operation was performed to obtain a dense prediction image.
+
+Weighted Dice Loss Function
+
+A weighted dice loss function as below was proposed to enhance segmentation performance by estimating difficulties in difference images with typical or atypical structure, which ensured consistent in segmentation:
+
+\[
+L_{wdice} = \frac{1}{C} \sum_{j=1}^{C} \xi_j \left( 1 - \frac{2 \sum_{i=1}^{N} p_{1i} g_{1i}}{2 \sum_{i=1}^{N} p_{1i} g_{1i} + \sum_{i=1}^{N} p_{0i} g_{1i} + \sum_{i=1}^{N} p_{1i} g_{0i}} \right)
+\]
+
+This formula was used in the output of the softmax layer, where the is the probability of voxel (target) and is the probability of voxel (non-target). So was for and . represents different segmentation areas, represents the total number of channels, which is taken as 14. represent the weight of different segmentation channels. According to the experimental analysis results, channels weight was set to 0.9, 0.8 and 1 for vertebral body, IVD and the other respectively, which may achieve the best segmentation performance.
+
+For avoiding that the subsequent feature extraction operations are affected, corrosion and expansion operations were used to remove the burrs (**Fig. 2b**).
+
+Lumbar IVD Quantitative Analysis
+
+Parameters Calculation based on Pfirrman Grading System
+
+Based on previous studies \(^{18,25-27}\), some extraction and calculation methods were modified with histogram features of IVD. signal intensity difference (\(\Delta SI\)) was obtained to quantify the blurring degree of boundary between NP and AF, which indicating water content in IVD. Average disc height (DH), disc
+height index (DHI), and disc height-to-diameter ratio (DHR) were obtained to quantify structural collapse in IVD degeneration. Specific calculation methods for each parameter are described in the Supplement File 1.
+
+Versatility Test for Images with Different Origins
+
+IVD parameters extracted by LSSN in mid-sagittal lumbar MR images with different resolutions were compared with each other. In the data set B, 46 images with resolution of 320*320 were randomly selected to be segmented and quantified by model B. Meanwhile, these images were adjusted to 512*512 for segmentation and quantitation by model A. IVD parameters extracted from these two models were used for versatility test. If IVD parameters from LSSN shows good consistency under different origins of imaging, LSSN will be used into a larger population (Data set C) with different machines and models to establish degenerative ranges of IVD parameters in different people.
+
+Quantitation for IVD Degeneration
+
+Relationship between IVD parameters (including ΔSI, DH, DHI, and HDR) and demographic information (including gender, age, and segment) and correlation between IVD parameters and IVD degeneration (based on the modified Pfirrmann grading system) were analyzed respectively in Data set C. Based on these results, a baseline of IVD degeneration in larger population was established, which may indicate a qualitative IVD degeneration in different population with accordance to the modified Pfirrmann grading system. Details in quantitative protocols were shown in the Supplement File 2.
+
+Statistical analysis
+
+The intraclass correlation coefficient (ICC) was used to analyze the consistency between the IVD parameters calculated using the original resolution (320*320) from the data set B and the adjusted resolution (512*512). The macroF1-score and the Kendall correlation coefficient were used to test sensitivity and specificity in IVD degeneration grading performance among deep learning methods and 3 residents in the two data sets with different resolution according to the modified Pfirrmann grading system. An absolute value of r of 0-0.4 was considered as weak correlation, 0.4-0.6 as moderate correlation, and greater than 0.6 as strong correlation.
+
+Spearman rank correlation coefficient between IVD signal intensity and grading score has been calculated via SPSS (version 26, IBM, USA). Multiple regression analysis was performed on IVD quantitative parameters (, DH, DHI, HDR) and baseline information (including gender, age, segment) to describe some characters in larger population via Stata (version 15.1, USA).
+
+Results
+Segmentation Performance
+
+The BianqueNet provided good segmentation performance of IVD-related areas. The mean Dice coefficients (mDice) and mean intersection over Union (mIoU) were 94.45% and 89.88% for whole lumbar spine, 96.71% and 93.66% for vertebral body, 94.38% and 89.43% for IVD. Based on deeplabv3+, Adding the three modules of DFE, ST-SC and FPN improved segmentation significantly as shown in Table 2. The average training time for BianqueNet was 10 hours in each data set. Segmentation of vertebral bodies and IVDs on the mid-sagittal MRI image for a patient took approximately 1 seconds with the trained network.
+
+Table 2 BianqueNet shows superior segmentation effectiveness demonstrated by the pixel-level Dice and IoU coefficient
+
+<table>
+  <tr>
+    <th rowspan="2">Model</th>
+    <th colspan="2">Module</th>
+    <th colspan="2">Vertebral body</th>
+    <th colspan="2">IVD</th>
+    <th colspan="2">Lumbar spine</th>
+  </tr>
+  <tr>
+    <th>DFE</th>
+    <th>ST-SC</th>
+    <th>mDice</th>
+    <th>mIoU</th>
+    <th>mDice</th>
+    <th>mIoU</th>
+    <th>mDice</th>
+    <th>mIoU</th>
+  </tr>
+  <tr>
+    <td>DeepLabv3+</td>
+    <td></td>
+    <td></td>
+    <td>0.9671</td>
+    <td>0.9366</td>
+    <td>0.9438</td>
+    <td>0.8943</td>
+    <td>0.9445</td>
+    <td>0.8988</td>
+  </tr>
+  <tr>
+    <td>DeepLabv3++DFE</td>
+    <td>√</td>
+    <td></td>
+    <td>0.9681</td>
+    <td>0.9384</td>
+    <td>0.9444</td>
+    <td>0.8960</td>
+    <td>0.9455</td>
+    <td>0.9006</td>
+  </tr>
+  <tr>
+    <td>DeepLabv3++DFE+ST-SC</td>
+    <td>√</td>
+    <td>√</td>
+    <td>0.9692</td>
+    <td>0.9405</td>
+    <td>0.9458</td>
+    <td>0.8982</td>
+    <td>0.9468</td>
+    <td>0.9028</td>
+  </tr>
+  <tr>
+    <td>DeepLabv3++DFE+ST-SC+FPN (BianqueNet)</td>
+    <td>√</td>
+    <td>√</td>
+    <td>√</td>
+    <td><b>0.9703</b></td>
+    <td><b>0.9425</b></td>
+    <td><b>0.9480</b></td>
+    <td><b>0.9019</b></td>
+    <td><b>0.9470</b></td>
+    <td><b>0.9035</b></td>
+  </tr>
+</table>
+
+Versatility test for different resolution
+
+A total of 230 IVDS and 276 vertebral bodies of 46 subjects were segmented after resolution of MRI-exported images had been adjusted from 320*320 to 512*512. The results showed a good consistency in using different parameter calculation algorithms for different resolution of MRI-exported images. Among them, the measurement of intervertebral disc geometric parameters DHI and DWR have extremely high ICC values, which are 0.958 (p=0.000) and 0.956 (p=0.000), respectively, and the ICC value of the \( \Delta S/ \) is 0.874 (p=0.000), as shown in Table 3.
+
+Table 3 Consistency analysis of intervertebral disc parameters calculated by MRI of different sizes
+
+<table>
+  <tr>
+    <th>Measure</th>
+    <th>Intraclass Correlation<sup>b</sup></th>
+    <th>95%CI</th>
+  </tr>
+  <tr>
+    <td>ICC<sup>a</sup></td>
+    <td>.874***</td>
+    <td>.840-.902</td>
+  </tr>
+  <tr>
+    <td>\( \Delta S/ \)</td>
+    <td>.958***</td>
+    <td>.943-.968</td>
+  </tr>
+  <tr>
+    <td>DHI</td>
+    <td>.958***</td>
+    <td>.943-.968</td>
+  </tr>
+  <tr>
+    <td>HDR</td>
+    <td>.956***</td>
+    <td>.886-.978</td>
+  </tr>
+</table>
+Two-way mixed effects model where people effects are random and measures effects are fixed. ICC, intraclass correlation coefficient; 95% CI, 95% confidence interval;
+
+a. The estimator is the same, whether the interaction effect is present or not.
+
+b. Type A intraclass correlation coefficients using an absolute agreement definition.
+
+Characteristics of IVD Parameters in a Larger Population
+
+After screening 1508 MRI images in 4 sites around China, a total of 1051 individuals were collected, in which there're 144 excluded for imaging quality and 313 excluded for irregular structures (especially in vertebral bodies). The demographic information (including age and gender) distributed evenly as shown in Table 4, which were integrated to conduct correlation analysis with IVD parameters.
+
+Table 4 Included Patient Demographic Information from the Four Sites around China
+
+<table>
+  <tr>
+    <th rowspan="2">Site</th>
+    <th rowspan="2">Number</th>
+    <th colspan="7">Age(F/M)</th>
+  </tr>
+  <tr>
+    <th>20-29</th>
+    <th>30-39</th>
+    <th>40-49</th>
+    <th>50-59</th>
+    <th>60-69</th>
+    <th>70-89</th>
+  </tr>
+  <tr>
+    <td>Longhua Hospital, Shanghai University of TCM</td>
+    <td>433</td>
+    <td>32/21</td>
+    <td>52/51</td>
+    <td>49/45</td>
+    <td>34/35</td>
+    <td>53/39</td>
+    <td>12/10</td>
+  </tr>
+  <tr>
+    <td>Shenzhen Pingle Orthopedics Hospital</td>
+    <td>222</td>
+    <td>16/18</td>
+    <td>20/20</td>
+    <td>19/20</td>
+    <td>18/21</td>
+    <td>13/23</td>
+    <td>9/25</td>
+  </tr>
+  <tr>
+    <td>Guangdong Provincial Hospital of Chinese Medicine</td>
+    <td>246</td>
+    <td>19/24</td>
+    <td>20/15</td>
+    <td>23/17</td>
+    <td>22/17</td>
+    <td>18/15</td>
+    <td>22/34</td>
+  </tr>
+  <tr>
+    <td>Dongzhimen Hospital, Beijing University of Chinese Medicine</td>
+    <td>150</td>
+    <td>7/8</td>
+    <td>13/18</td>
+    <td>21/17</td>
+    <td>13/8</td>
+    <td>12/11</td>
+    <td>8/14</td>
+  </tr>
+  <tr>
+    <th>Total</th>
+    <th>1051</th>
+    <th>74/71</th>
+    <th>105/104</th>
+    <th>112/99</th>
+    <th>87/81</th>
+    <th>96/88</th>
+    <th>51/83</th>
+  </tr>
+</table>
+
+Supplement Figure (1-4) and Table 5 shows comprehensive distribution of IVD parameters in a larger population and multiple regression analysis result among IVD parameters and each demographic information respectively. \( \Delta S/\) in IVDs decreased with age, while DH, DHI and DHR of IVDs increased with age, reaching peak at the age of 50-60 (\(P<0.01\)). There're no significant different between male and
+female in in IVDs, while DH, DHI and DHR of IVDs were significantly higher in males than those in females (\(P<0.01\)). In additions, DH, DHI and DHR were significantly higher in lower segmental IVDs (L3-L4, L4-L5 and L5-S1) than upper ones (L1-L2 and L2-L3), and disc height of L4-L5 IVDs was highest(\(P<0.01\)). In the further analysis of all the IVD height parameters, the influence of segments on the parameters is greater than those of age. For the IVD height, the influence of gender is greater than age. For DHI and HDR, gender and age have similar effects.
+
+Table 5 The results of multiple regression analysis of signal intensity peak difference, DH, DHI, HDR and gender, different ages, and different disc positions
+
+<table>
+  <tr>
+    <th>N=1651</th>
+    <th>\( \Delta S/ \)</th>
+    <th>DH</th>
+    <th>DHI</th>
+    <th>HDR</th>
+  </tr>
+  <tr>
+    <td>female</td>
+    <td>-0.0279</td>
+    <td>-0.2541***</td>
+    <td>-0.1121***</td>
+    <td>0.1115***</td>
+  </tr>
+  <tr>
+    <td>male</td>
+    <td>0.000</td>
+    <td>0.000</td>
+    <td>0.000</td>
+    <td>0.000</td>
+  </tr>
+  <tr>
+    <td>20-30</td>
+    <td>0.000</td>
+    <td>0.000</td>
+    <td>0.000</td>
+    <td>0.000</td>
+  </tr>
+  <tr>
+    <td>30-40</td>
+    <td>-0.1669***</td>
+    <td>0.0796***</td>
+    <td>0.0557*</td>
+    <td>0.1100***</td>
+  </tr>
+  <tr>
+    <td>40-50</td>
+    <td>-0.3802***</td>
+    <td>0.1110***</td>
+    <td>0.0927***</td>
+    <td>0.0980***</td>
+  </tr>
+  <tr>
+    <td>50-60</td>
+    <td>-0.4826***</td>
+    <td>0.1612***</td>
+    <td>0.1577***</td>
+    <td>0.0440</td>
+  </tr>
+  <tr>
+    <td>60-70</td>
+    <td>-0.6002***</td>
+    <td>0.1427***</td>
+    <td>0.1687***</td>
+    <td>0.0099</td>
+  </tr>
+  <tr>
+    <td>70-90</td>
+    <td>-0.5137***</td>
+    <td>0.0328</td>
+    <td>0.0806***</td>
+    <td>-0.0674***</td>
+  </tr>
+  <tr>
+    <td>L1-L2</td>
+    <td>0.2800***</td>
+    <td>-0.7181***</td>
+    <td>-0.6708***</td>
+    <td>-0.4932***</td>
+  </tr>
+  <tr>
+    <td>L2-L3</td>
+    <td>0.1719***</td>
+    <td>-0.3832***</td>
+    <td>-0.4155***</td>
+    <td>-0.2912***</td>
+  </tr>
+  <tr>
+    <td>L3-L4</td>
+    <td>0.0907***</td>
+    <td>-0.1593***</td>
+    <td>-0.1942***</td>
+    <td>-0.1122***</td>
+  </tr>
+  <tr>
+    <td>L4-L5</td>
+    <td>0.000</td>
+    <td>0.000</td>
+    <td>0.000</td>
+    <td>0.000</td>
+  </tr>
+  <tr>
+    <td>L5-S1</td>
+    <td>0.1526***</td>
+    <td>-0.0520**</td>
+    <td>-0.0312</td>
+    <td>0.1105***</td>
+  </tr>
+</table>
+
+*** p<0.01 ** p<0.05 * p<0.1
+
+Correlation with IVD Degeneration Grading
+
+Considering structural collapse with IVD degeneration according to the modified Pfirrmann grading system, a regression analysis was conducted to investigate correlation between its certain grading (For analyzing the correlation between degeneration segments and \( \Delta S/ \), the corresponding grading were 1, 2, 3, 4, and (5-8). For analyzing the correlation between the degeneration segments and geometric parameters, the corresponding grading are (1-5), 6, 7, 8)) and IVD parameters in different age, gender and segments. As shown in Table 6, IVD parameters showed a good accordance to the modified Pfirrmann grade.
+Table 6 Correlations between IVD Parameters and Modified Pfirrmann Grading
+
+<table>
+  <tr>
+    <th rowspan="2">lumbar level</th>
+    <th rowspan="2">\( \Delta S_I \)</th>
+    <th colspan="2">DH</th>
+    <th colspan="2">DHI</th>
+    <th colspan="2">HDR</th>
+  </tr>
+  <tr>
+    <th>female</th>
+    <th>male</th>
+    <th>female</th>
+    <th>male</th>
+    <th>female</th>
+    <th>male</th>
+  </tr>
+  <tr>
+    <td>L1/L2</td>
+    <td>.966***</td>
+    <td>.421***</td>
+    <td>-.296***</td>
+    <td>-.304***</td>
+    <td>-.235***</td>
+    <td>-.473***</td>
+    <td>-.397***</td>
+  </tr>
+  <tr>
+    <td>L2/L3</td>
+    <td></td>
+    <td>-.481***</td>
+    <td>-.417***</td>
+    <td>-.354***</td>
+    <td>-.398***</td>
+    <td>-.575***</td>
+    <td>-.455***</td>
+  </tr>
+  <tr>
+    <td>L3/L4</td>
+    <td></td>
+    <td>-.639***</td>
+    <td>-.470***</td>
+    <td>-.530***</td>
+    <td>-.443***</td>
+    <td>-.626***</td>
+    <td>-.539***</td>
+  </tr>
+  <tr>
+    <td>L4/L5</td>
+    <td></td>
+    <td>-.656***</td>
+    <td>-.696***</td>
+    <td>-.560***</td>
+    <td>-.665***</td>
+    <td>-.709***</td>
+    <td>-.758***</td>
+  </tr>
+  <tr>
+    <td>L5/S1</td>
+    <td></td>
+    <td>-.701***</td>
+    <td>-.687***</td>
+    <td>-.641***</td>
+    <td>-.664***</td>
+    <td>-.744***</td>
+    <td>-.778***</td>
+  </tr>
+</table>
+
+*** p<0.01 ** p<0.05 * p<0.1
+
+r, Spearman rank correlation coefficients
+
+Regarding water content loss with IVD degeneration, result from a further regression analysis showed a stronger correlation between the modified Pfirrmann grade (1, 2, 3, 4, and (5-8)) and \( \Delta S_I \) (R=-0.966, \( P=0.000 \)). Specific ranges of according to the modified Pfirrmann grade (1, 2, 3, 4, and (5-8)) were calculated and listed in Table 7.
+
+Table 7 Quantitative ranges of \( \Delta S_I \)/according to the modified Pfirrmann Grade (1-8)
+
+<table>
+  <tr>
+    <th>modified Pfirrmann Grade</th>
+    <th>1</th>
+    <th>2</th>
+    <th>3</th>
+    <th>4</th>
+    <th>5-8</th>
+  </tr>
+  <tr>
+    <td>Number</td>
+    <td>154</td>
+    <td>1130</td>
+    <td>1622</td>
+    <td>1315</td>
+    <td>1034</td>
+  </tr>
+  <tr>
+    <td>(mean±SD)</td>
+    <td>121.97±9.96</td>
+    <td>95.34±7.20</td>
+    <td>72.34±7.81</td>
+    <td>44.63±8.49</td>
+    <td>20.60±9.28</td>
+  </tr>
+</table>
+
+According to the results of multiple regression analysis, gender and segments have significant correlations with \( \Delta S_I \), while age, gender and segments have significant correlations with geometric parameters. Fig.3 and Supplement Table (1-4) showed comprehensive distribution of IVD parameters in a larger population.
+
+Discussion
+Our study described a fully automated deep learning–based lumbar IVD quantitative system utilizing a CNN with the self-attention skip connection, deep feature extraction module and the corresponding loss function for segmenting IVD-related areas to extract geometric and signal parameters. The proposed deep learning approach achieved high accuracy for segmentation and measurement. More specifically, our method showed high consistency with the modified Pfirrmann grading system.
+
+Compared with previously reported conventional image processing methods for lumbar spine MRI, our method is focus on quantitative measurement other than degeneration grade classification. Standard and accurate ranges of \( \Delta S/ \) in IVD was established to quantify IVD degeneration, which has strong applicability and accuracy for grading IVD degeneration (macroF1: 92.02% and 90.63% in two data sets) as shown in Table 8.
+
+Table 8 Accuracy of IVD degeneration grading with \( \Delta S/ \) in IVD
+
+<table>
+  <tr>
+    <th rowspan="2">Modified Pfirrmann Grade</th>
+    <th colspan="5">1</th>
+    <th>5-8</th>
+    <th>macro-average (%)</th>
+    <th>macroF1(%)</th>
+  </tr>
+  <tr>
+    <th>1</th>
+    <th>2</th>
+    <th>3</th>
+    <th>4</th>
+    <th>5-8</th>
+    <th>macro-average (%)</th>
+    <th>macroF1(%)</th>
+  </tr>
+  <tr>
+    <td>Data set A</td>
+    <td>Precision (%)</td>
+    <td>60.76</td>
+    <td>97.28</td>
+    <td>99.40</td>
+    <td>97.89</td>
+    <td>89.08</td>
+    <td>88.89</td>
+    <td>92.02</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Recall (%)</td>
+    <td>100</td>
+    <td>90.96</td>
+    <td>97.84</td>
+    <td>90.05</td>
+    <td>98.15</td>
+    <td>95.40</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Data set B</td>
+    <td>Precision (%)</td>
+    <td>/</td>
+    <td>81.82</td>
+    <td>93.55</td>
+    <td>100</td>
+    <td>85.71</td>
+    <td>90.27</td>
+    <td>90.63</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Recall (%)</td>
+    <td>/</td>
+    <td>90.00</td>
+    <td>90.63</td>
+    <td>83.33</td>
+    <td>100</td>
+    <td>90.99</td>
+    <td></td>
+  </tr>
+</table>
+
+By means of LSSN, all the IVD parameters will be extracted and quantified from MR images in about half of second, which may describe water content loss and structural collapse in IVD, indicating degeneration process. Fig.4 shows a potential application for structural MRI report output from the IVD degeneration quantitative analysis.
+
+Pfirrmann grading system, as the most used IVD imaging grading method, was designed based on symptomatic patients with an average age of about 40 years old \( ^{15} \). Therefore, its reliability for early IVD degeneration or IVD degeneration in the elderly people may be unsatisfied. This study proposed an automatic quantitative method for IVD degeneration assessment in asymptomatic patients of different ages. In addition, multiple quantitative sequences in imaging are generally used together to accurately evaluate IVD degeneration or lesions, which are too time-consuming to popularize MR imaging quantitative analysis in IVD. Our LSSN may meet both patients’ affordability and clinical diagnosis needs.
+
+Our study has limitations. First, we only included MR images with relatively regular outline in IVD-related areas, most of which were accurately segmented by LSSN. Second, accuracy of LSSN is dependent on the depth of BMP exported from MR imaging system. Third, the subjects included in this study did not take symptoms (such as low back pain) into account, lacking clinical validation on IVD degeneration.
+Finally, as a retrospective study, IVD parameters extracted from Data set C did not exactly represent the real-world setting. Further research is needed to determine the applicability of this LSSN in a prospective multi-institutional study in patients with low back pain.
+
+In conclusion, we developed a fully automated deep learning-based lumbar spine segmentation network, which demonstrated strong versatility and high reliability to assist residents on IVD degeneration grading by means of IVD degeneration quantitation.
+
+Declarations
+
+Acknowledge
+
+This study was supported by the National Natural Science Foundation of China (81930116, 81804115, 81873317, and 81704096).
+
+Author contributions
+
+Guarantor of integrity of entire study, YL Sun, YJ Wang; study concepts/study design or data acquisition or data analysis/interpretation, all authors; manuscript drafting or manuscript revision for important intellectual content, all authors; approval of final version of submitted manuscript, all authors; agrees to ensure any questions related to the work are appropriately resolved, all authors; literature research, HD Zheng, MC Yin, M Yao, XJ Cui; clinical studies, YL Sun, DW Kong, MC Yin, J Chen, YP Lin, XF Ma; experimental studies, YZ Tian, HS Wang, GJ Yuan; statistical analysis, HD Zheng, M Yao, XJ Cui; and manuscript editing, HD Zheng, YL Sun, YJ Wang.
+
+Disclosure of Conflict of Interest
+
+All author disclosed no relevant relationships.
+
+References
+
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+
+**Figures**
+Figure 1
+
+The flowchart of the study process
+Figure 2
+
+The fully automatic IVD quantitative analysis system based on semantic segmentation network. The proposed method consisted of segmentation CNNs with SW-SC module and DFE module, histogram-based signal intensity quantitation, and area-based fully automated geometric measurement. (a) Segmentation label of lumbar spine related area, (b) Each image channel output by the model corresponds to a segmentation area, (c) The outline of the segmented area is displayed on the original
+image. Signal intensity histogram calculation (d) Cerebrospinal fluid area, (e) Presacral fat area, (f) L3L4 intervertebral disc area. (g) Intervertebral disc parameter calculation, (h) Vertebral body corner detection result (red point) and feature point calculation result (green point), (i) 80% area extraction result of the intervertebral disc center.
+
+![Six line plots showing various IVD parameters and their distributions by age, gender, and segment](page_120_367_1347_355.png)
+
+Figure 3
+
+Characteristics of IVD Parameters ( (a) The mean and standard deviation (\( \sigma \)) of the \( \Delta SI \) of each the Modified Pfirrmann Grading System (level 1, 2, 3, 4, 5), \( \Delta SI \) (b), DH (c), DHI (d) and HDR (e)) in different age, gender, and segments
+Figure 4
+
+Quantitative analysis results of typical cases. (a) 23-year-old male(Longhua Hospital); (b) 49-year-old female(Dongzhimen Hospital, Beijing University of Chinese Medicine); (c) 63-year-old male(Guangdong Provincial Hospital of Chinese Medicine); (d) 81-year-old male(Shenzhen Pingle Orthopedics Hospital).
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementFigures.pdf
+• SupplementFile1signalintensityandgeographicmeasurementinIVD.docx
+• SupplementFile2IVDquantitativeanalysiswithPfirrmannGrading.docx
+• SupplementTable1.docx
+• SupplementTable2.docx
+• SupplementTable3.docx
+• SupplementTable4.docx

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+Peer Review File
+
+Functional architecture of executive control and associated event-related potentials in macaques
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Review – Sajad et al. Functional architecture of executive control and associated event-related potentials.
+
+The manuscript by Sajad and colleagues describes a study in which the authors sought to extend existing knowledge of the contribution of supplementary eye fields (SEF) to performance monitoring and adaptive control by carrying out laminar recordings during a modified version of the well-studied saccade countermanding paradigm to characterize the response properties of single SEF neurons across cortical layers. Event-related potentials were also recorded at the cortical surface and the contribution of single neurons to the ERP N2/P3. They describe several patterns of response properties during the task, and their laminar distributions: 1) Conflict neurons, modulated after the SSRT in a manner consistent with coactivation of GO and STOP processes, distributed across all cortical layers, 2) Time Keeping neurons, modulated in a manner consistent with representation of timing of task events and interval durations. A subset of these neurons exhibiting ramping activity showed some laminar differentiation, although in general this type was found across all layers, and 3) Goal Maintenance neurons, revealed by the modification of the task used here which required the animals to maintain fixation on the visual stop signal until a tone signaled that a saccade to the target was permitted to obtain reward. These neurons exhibited sustained activity during this time period consistent with short-term retention of the task goal. In contrast to the other two neuronal types, Goal Maintenance neurons were found most commonly in layers 2/3 rather than layers 5/6, and more of these neurons were characterized as narrow spiking putative interneurons. Finally, the authors also observed an N2/P3 ERP component on successful stopping trials, consistent with findings in human participants. N2 polarization was found to be predicted by spiking activity in layers 2/3 but not 5/6. P3 polarization was predicted by the spiking activity of goal maintenance neurons in layers 2/3 but not 5/6.
+
+Overall, this is an excellent manuscript and the data represent a significant and timely advance. The laminar distributions and broad and narrow-spiking classifications together with knowledge of the response profiles during the countermanding task are new contributions, and are critical for advancing knowledge and developing models of cortical microcircuits and their contributions to cognitive processes more generally. Indeed, a very detailed model of this sort is presented in the discussion of the manuscript. The authors employ a well-established and thoroughly modeled behavioral paradigm requiring response inhibition and response monitoring, which has been studied extensively in human participants as well as non-human primates and thus has much value in the translation of findings. The addition of the ERP component to the study makes this particularly so, since an electrophysiological link between the two species is established as well. Studies of this sort are of immeasurable value in understanding the neural basis of response inhibition and cognitive control.
+
+The quality of the data are excellent, and all analyses are thorough and appropriate. The laboratory of the senior author is expert in the countermanding paradigm, the SEF, and all other procedures employed here. I am happy to recommend publication of the manuscript with no major revisions.
+
+I have only one minor comment with respect to the Goal Maintenance neurons described here. The authors ascribe the sustained activity they observed to a mnemonic process representing the task goal. I wonder if there were any trials on which the animals broke fixation prior to the tone and whether this type of activity was absent in this case ?
+Reviewer #2 (Remarks to the Author):
+
+Summary
+The authors recorded EEG and neural spiking over and in the supplementary eye field (SEF) of macaques during a saccade countermanding task, to better understand the neural circuitry and laminar structure that implements executive control and eventually broadcasts event-related potentials (ERPs) to the brain surface. They found functionally different neuronal groups important for various task elements such as conflict monitoring, time keeping and goal maintenance. Particular N2 and P3 ERP components were predicted by the different neuronal groups in different cortical layers. These findings provide valuable information about the origins of scalp-recorded ERPs, and demonstrate how to combine multiple scales of electrophysiology (EEG, single-unit spiking activity).
+
+Major concerns/criticisms
+- Line 121-123, 167, 398-401, 912-914, 921-923. It’s not clear why activity on canceled trials is compared to no stop-signal trials if you want to find out what is associated with successful response inhibition. The comparison between canceled and non-canceled trials is ignored in these cases, but is relevant for studying successful response inhibition, as this comparison shows the inhibition-specific activity. As the authors decided to leave this comparison out in almost the entire manuscript it needs proper justification why this comparison is not relevant according to them. Nevertheless, my suggestion would be to at least include this comparison in the main analyses and add the non-canceled trials to the figures as suggested in the minor concerns/criticisms.
+
+- I’m confused about how p(error) is computed. Is this calculated per-session? Or over a running history of the previous N trials? Or per RT bin?
+
+- I was surprised that the authors did not compute the N2/P3 in the silicon probe. Isn’t that the best intermediate step in between the spikes and the EEG? According to the methods section, the LFP data were recorded.
+
+- The authors equate p(error) with conflict, but ‘conflict’ in the cognitive control literature typically indicates a competition between two (or more) different responses, with one being automatic and the other being task-driven (as typified by Stroop, Simon, and flanker tasks). The stop-signal task has only one action at a time, which is fully engaged or canceled. Clearly this task requires cognitive control and inhibition, but it’s not the same kind of conflict as in many other tasks. (It’s also worth noting here that the Yeung/Botvinick model of conflict=a1*a2 has not held up to empirical scrutiny.) I suggest to rename this to something else, e.g., “p(error) neurons” or “difficulty-encoding neurons.” I realize that the authors might disagree (cf Schall and Boucher 2007), but at the least, a serious discussion needs to be added that the term ‘conflict’ is used here in a different way than other parts of the literature.
+Relatedly, I don’t mean to be too pedantic here, but increased errors are not necessarily coupled to increased conflict. Errors rates also vary by time pressure, task complexity, working memory load, attentional demands, time-on-task and other factors. The point is that calling neurons whose activity varies with p(error) ‘conflict neurons’ seems inappropriately speculative for the Results section. I guess they used this cognitive label to link to the N2, but that seems more a Discussion section point than a Results section label.
+
+Minor concerns/criticisms
+- In Figure 2a, 3a, 4a and 5a I would like to also see the line for the non-canceled trials. It’s easy put them in and gives a more complete view of the contrasts between the different trial types. The contrast between canceled and non-canceled trials is relevant, as it shows which part of activity is specific to the successful execution of countermanding. This will also make the figure more convincing, as now it seems like the authors hide these non-canceled trials for an unwanted reason.
+
+- In the first paragraph of the Discussion section the authors refer to Figure 6. However, I prefer the explanation of this figure to be embedded in the Discussion instead of having an entirely separate paragraph in the figure description. This will make it more of a complete single story, instead of having
+a separate story in the figure description.
+
+- Line 876-878. It is unclear why the set of SSDs for the different monkeys have different separation sizes (40-60 ms vs. 100 ms). This needs explanation.
+- Wouldn’t it be easier to call ‘no stop signal’ trials ‘go’ trials? The authors use the term ‘go’ several other times in the manuscript.
+- Figure 2c doesn’t really seem to be a ‘representative’ neuron considering its peak responses is later than most of the neurons shown in Figure 2b. Is it possible to show more data? Perhaps examples of putative pyramidal and inhibitory cells that peak around SSRT vs later? Maybe you can highlight the specific ‘representative’ neuron by highlighting it in Figure 2b.
+- Same comment for Figure 3c. In fact, from looking at Figure 3b, I cannot tell which neuron 3c comes from. Maybe you can highlight the specific neuron in Figure 3b, like suggested for Figure 2b.
+
+Line edits
+- Please have a native English speaker smooth out the manuscript. Some sentences read like notes rather than full sentences (e.g. line 53), and there are many minor mistakes that could be corrected, like missing articles (e.g. line 17, 40, 51, 606, 610).
+
+Reviewer #3 (Remarks to the Author):
+
+This paper is an important step toward a better understanding of cortical microcircuitry involved in executive control. As a continued effort to dissect laminar organization of medial frontal cortex during stop-signal task (Sajdad et al., Nat. Neuro. 2019), this paper focused on more critical trial types (canceled) and task epochs (around SSRT) and found interesting functional dissociations across different neuronal groups. In particular, it is noteworthy finding that “goal maintenance” narrow-spiking neurons are specifically localized in L2/3. Furthermore, the report of N2/N3 in the monkey model is novel and its relation to neural spiking activates is an important addition to the field. The paper has solid and convincing results. That said, I have some suggestions that can potentially improve the paper.
+
+- Major points
+More justification is needed for the approach of classifying individual neurons into distinct groups – conflict monitoring, event timing, goal maintenance. While it is justified in terms of previous findings (e.g., for conflict neurons) and behavioral demands, this classification seems arbitrary, post-hoc, and not based on first principles (i.e., derived from theory or model). Why are there three, not two or not four, categories? Even clustering results in Supplementary figure 1 do not speak to this issue.
+
+Another way to ask this question is, how should readers interpret the different number of neurons in each group? Does it matter? Because there is a relatively smaller number of goal-maintenance neurons, should we conclude that SEF is involved more in conflicting monitoring and time keeping? Or does SEF do everything including the processing of gain and loss (Sajdad et al., Nat. Neuro. 2019)? How these different groups of neurons interact and what is the population-level understanding? I know this is a high-level question that may need brand-new analyses (like population-level decoding or state-space/dynamical-systems approach). But at least, this issue should be thoroughly discussed as medial frontal cortex has notoriously heterogeneous neural populations in their sensorimotor selectivity.
+
+Another key question is, is this classification a distinct category or more like a continuum? The latter is more likely given their overlapped dynamics (Fig. 5b, Sup. Fig. 1e). The difference between conflict and maintenance neurons is only about how long the neurons sustain their activities (e.g., transient versus persistent) and so not clear cut at all. Specifically, maintain neurons can be well considered as conflict monitoring and vice versa. This issue seems to become more problematic as even predictions between models are similar – as mentioned in methods, model predictions and parameters are correlated (e.g., SSD, p(error), conflict, and time to tone) and it is not clear how “random variations”
+(across single trials?) can differentiate these models.
+
+Along the line of the previous comment, model comparison results should be presented better. In particular, details of alternative models are buried in the text/supplementary and hard to digest. It’d be useful to have a figure showing predictions from different models (well explained in method, “mixed-effects model”) and to bring a simplified version of Sup. Table 2 into the main manuscript.
+
+Another big question is, what is the behavioral relevance of these activities in stop-signal task. More specifically, the behavioral relevance of conflict monitoring is not directly tested. In discussion, it is mentioned that conflict monitoring can be useful for post-stopping slowing but this interesting idea is not tested at all. For instance, was the go RT slower in the next trial after the conflict-monitoring neurons showed a higher firing rate? Does animal use timing information in ‘time-keeping neurons’ to predict SSD and adjust behavior accordingly?
+
+Given that no specificity was found for conflict neurons in terms of laminar and spiking width (X^2 analyses), the conclusion that those neurons are broad-spiking and in L3/5 (in abstract, Line 23-25) is not warranted. This is just a by-product of sampling neurons in SEF. The valid conclusion is that no specificity was found.
+
+Motivation for classifying neurons into broad-spiking and narrow-spiking is also not clear. It’d be useful to provide backgrounds or hypotheses in the introduction. For example, is there any previous anatomical study suggesting inhibitory interneurons are more common in L2/3? It seems to be the case in Supp. Fig. 1.
+
+It’d be useful to explicitly state the null hypothesis when linking N2/P3 and spiking activities across layers. Is it somewhat obvious that ERPs would be better predicted by upper layers as they are closer? Also, due to their match in timing, isn’t it obvious that monitoring/timing neurons better predict N2 and maintenance neurons better predict P3? One way to tackle the former question is to test how well the cranial EEG is predicted by LFP signals across layers.
+
+- Minor points
+In figure 2.3, and 4, the bottom plots in panel (a) have a confusing label, P(active). Because p(active) is different between left and right panels, it’d be better to use a separate y-axis label.
+
+I can easily imagine, to readers naïve to the stop-signal task, the paper is written a bit difficult to follow and jargon-heavy fashion. If it is written without assuming prior knowledge, the paper will receive a wider readership.
+
+Y-axis Label of the right panel in fig. 3c should be pre-SSRT, to be consistent with left panel shades and legends.
+
+Why did conflict neurons show higher activity right before feedback tone (Fig. 2a, Sup. Fig. 3b)?
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Review – Sajad et al. Functional architecture of executive control and associated event-related potentials.
+
+The manuscript by Sajad and colleagues describes a study in which the authors sought to extend existing knowledge of the contribution of supplementary eye fields (SEF) to performance monitoring and adaptive control by carrying out laminar recordings during a modified version of the well-studied saccade countermanding paradigm to characterize the response properties of single SEF neurons across cortical layers. Event-related potentials were also recorded at the cortical surface and the contribution of single neurons to the ERP N2/P3. They describe several patterns of response properties during the task, and their laminar distributions: 1) Conflict neurons, modulated after the SSRT in a manner consistent with coactivation of GO and STOP processes, distributed across all cortical layers. 2) Time Keeping neurons, modulated in a manner consistent with representation of timing of task events and interval durations. A subset of these neurons exhibiting ramping activity showed some laminar differentiation, although in general this type was found across all layers, and 3) Goal Maintenance neurons, revealed by the modification of the task used here which required the animals to maintain fixation on the visual stop signal until a tone signaled that a saccade to the target was permitted to obtain reward. These neurons exhibited sustained activity during this time period consistent with short-term retention of the task goal. In contrast to the other two neuronal types, Goal Maintenance neurons were found most commonly in layers 2/3 rather than layers 5/6, and more of these neurons were characterized as narrow spiking putative interneurons. Finally, the authors also observed an N2/P3 ERP component on successful stopping trials, consistent with findings in human participants. N2 polarization was found to be predicted by spiking activity in layers 2/3 but not 5/6. P3 polarization was predicted by the spiking activity of goal maintenance neurons in layers 2/3 but not 5/6.
+
+Overall, this is an excellent manuscript and the data represent a significant and timely advance. The laminar distributions and broad and narrow-spiking classifications together with knowledge of the response profiles during the countermanding task are new contributions, and are critical for advancing knowledge and developing models of cortical microcircuits and their contributions to cognitive processes more generally. Indeed, a very detailed model of this sort is presented in the discussion of the manuscript. The authors employ a well-established and thoroughly modeled behavioral paradigm requiring response inhibition and response monitoring, which has been studied extensively in human participants as well as non-human primates and thus has much value in the translation of findings. The addition of the ERP component to the study makes this particularly so, since an electrophysiological link between the two species is established as well. Studies of this sort are of immeasurable value in understanding the neural basis of response inhibition and cognitive control.
+
+The quality of the data are excellent, and all analyses are thorough and appropriate. The laboratory of the senior author is expert in the countermanding paradigm, the SEF, and all other procedures employed here. I am happy to recommend publication of the manuscript with no major revisions.
+
+We thank the reviewer for their kind comments and appreciation of the manuscript.
+
+I have only one minor comment with respect to the Goal Maintenance neurons described here. The authors ascribe the sustained activity they observed to a mnemonic process representing the task goal. I wonder if there were any trials on which the animals broke fixation prior to the tone and whether this type of activity was absent in this case?
+
+Thank you for this idea. Indeed, we had examined this but had not included it in the manuscript because the number of useful aborted canceled trials was too small to support a confident conclusion. However, because both reviewers 1 and 3 have asked this question, we are now showing these results in Supplementary Figure 6f and report the finding in the Results section, Page 11, Lines 328-330.
+
+We examined the activity of neurons on trials in which fixation was successfully maintained (i.e., canceled trials) against trials in which the fixation was broken by a saccade or a blink (i.e., aborted) in a period between SSRT and feedback tone. Because we had not conceived of analyzing aborted trials, on these trials only the TrialStart event was saved. So, we reconstructed the timing of saccades, fixation breaks, and blinks that aborted the trials relative to this time. We included only a subset of the aborted trials in which we identified a saccade or blink confidently during the period between SSRT and feedback tone, and the proportions of trials were matched
+for SSD. Only 14/54 Goal Maintenance neurons had \( \geq 5 \) trials for meaningful comparison of neural activity. These neurons showed reduced activity on fixation break trials compared to successful stop trials.
+
+We recently completed sampling neural activity from two other monkeys doing this task. As shown in the figure below, we replicated the basic observations of these neurons.
+
+![Three line plots showing neural activity over time for Goal maintenance, Event timing, and Conflict, with different trial types (Canceled vs No-stop) and error rates (Low, Mid, High).](page_328_670_927_495.png)
+Reviewer #2 (Remarks to the Author):
+
+Summary
+The authors recorded EEG and neural spiking over and in the supplementary eye field (SEF) of macaques during a saccade countermanding task, to better understand the neural circuitry and laminar structure that implements executive control and eventually broadcasts event-related potentials (ERPs) to the brain surface. They found functionally different neuronal groups important for various task elements such as conflict monitoring, time keeping and goal maintenance. Particular N2 and P3 ERP components were predicted by the different neuronal groups in different cortical layers. These findings provide valuable information about the origins of scalp-recorded ERPs, and demonstrate how to combine multiple scales of electrophysiology (EEG, single-unit spiking activity).
+
+We are pleased that the reviewer appreciated our contribution.
+
+Major concerns/criticisms
+
+- Line 121-123, 167, 398-401, 912-914, 921-923. It’s not clear why activity on canceled trials is compared to no stop-signal trials if you want to find out what is associated with successful response inhibition. The comparison between canceled and non-canceled trials is ignored in these cases, but is relevant for studying successful response inhibition, as this comparison shows the inhibition-specific activity. As the authors decided to leave this comparison out in almost the entire manuscript it needs proper justification why this comparison is not relevant according to them. Nevertheless, my suggestion would be to at least include this comparison in the main analyses and add the non-canceled trials to the figures as suggested in the minor concerns/criticisms.
+
+We appreciate this comment and have revised the text to clarify why the Logan race model of countermanding performance guides the trial comparisons that we used. In short, including the error non-canceled trials would be misleading for two reasons:
+
+(1) Erroneous non-canceled trials happen because the GO process was too fast producing shorter RT. Correct canceled trials happen because the GO process happened to be slow enough to be interrupted by the STOP process. This fundamental property is the basis of the Logan race model and is reflected clearly in the patterns of neural activity observed in motor structures (Hanes et al. 1998 J Neurophysiol; Paré & Hanes, 2003 J Neurosci). Consequently, comparing neural activity between non-canceled and canceled trials is confounded by differences in the visual and motor processes producing the earlier and the later parts of RT distributions. The standard approach in this literature is to “latency-match” non-canceled trials with no-stop trials with RT < SSD + SSRT and canceled trials with no-stop trials with RT > SSD + SSRT. This approach is used in studies of spiking as well as ERPs (e.g., see Figure 2 in Kok, A., Ramautar, J. R., De Ruiter, M. B., Band, G. P., & Ridderinkhof, K. R. (2004). ERP components associated with successful and unsuccessful stopping in a stop-signal task. Psychophysiology, 41(1), 9-20).
+
+(2) As reported previously (Stuphorn et al. 2000; Sajad et al. 2019), neural activity in SEF on non-canceled trials has an additional error component that can confuse the interpretation (see Supplementary Figure 2b).
+
+We have clarified the rationale for not including non-canceled trials in the Results (Pages 4-5, Lines 95-105) and in a new Supplementary Figure 2. Nevertheless, we now show the spiking activity on non-canceled trials in Supplementary Figure 2b for the 3 neuron classes described in this manuscript.
+
+- I’m confused about how p(error) is computed. Is this calculated per-session? Or over a running history of the previous N trials? Or per RT bin?
+
+We thank the reviewer for highlighting this ambiguity. We have thoroughly revised the text in the Results (page 5, Lines 106-128) and Methods (page 28, Lines 886-890) and explain the models in revised Figure 1, We also changed the nomenclature for the conflict model to \( p(\text{NC} \mid \text{SSD}) \) and
+the error-likelihood model to \( p(NC_{error} \mid SSD) / p(SS_{seen} \mid SSD) \). We did not calculate a running history of N trials, but we will look at this in the future. For the conflict model we combine data within each session based on the parameters of the inhibition function for each stop-signal delay bin. For the error likelihood model we combine data within each session for each stop-signal delay bin.
+
+- I was surprised that the authors did not compute the N2/P3 in the silicon probe. Isn’t that the best intermediate step in between the spikes and the EEG? According to the methods section, the LFP data were recorded.
+
+Thank you for this suggestion. Certainly, the laminar LFPs offer an important perspective. In fact, this is the focus of an ongoing collaboration to describe the biophysical origin of the EEG signal. (Herrera B, Sajad A, Woodman GF, Schall JD, Riera JJ. A minimal biophysical model of neocortical pyramidal cells: Implications for frontal cortex microcircuitry and field potential generation. J Neurosci. 2020 Oct 28;40(44):8513-8529). Manuscripts are in preparation now characterizing the laminar patterns of LFP in SEF during this task. In parallel with Sajad et al. 2019, we restricted the scope of this manuscript to the relationship between EEG signals and concomitant laminar patterns of neural spiking. We have revised the text to clarify this distinction (Page 13, Lines 394 - 396).
+
+- The authors equate p(error) with conflict, but ‘conflict’ in the cognitive control literature typically indicates a competition between two (or more) different responses, with one being automatic and the other being task-driven (as typified by Stroop, Simon, and flanker tasks).
+The stop-signal task has only one action at a time, which is fully engaged or canceled. Clearly this task requires cognitive control and inhibition, but it’s not the same kind of conflict as in many other tasks. (It’s also worth noting here that the Yeung/Botvinick model of conflict=a1*a2 has not held up to empirical scrutiny.) I suggest to rename this to something else, e.g., “p(error) neurons” or “difficulty-encoding neurons.” I realize that the authors might disagree (cf Schall and Boucher 2007), but at the least, a serious discussion needs to be added that the term ‘conflict’ is used here in a different way than other parts of the literature.
+
+We appreciate the nuanced understanding revealed by this comment and acknowledge that the literature has evolved from the simple “conflict = a1*a2” framework. We have revised the text and supplementary information to clarify and justify the utility of this framework in the description of these data. Our implementation of the concept of conflict flows directly from the interactive race model (Boucher L, Palmeri TJ, Logan GD, Schall JD. Inhibitory control in mind and brain: an interactive race model of countermanding saccades. Psychol Rev. 2007 Apr;114(2):376-97; Logan GD, Yamaguchi M, Schall JD, Palmeri TJ. Inhibitory control in mind and brain 2.0: blocked-input models of saccadic countermanding. Psychol Rev. 2015 Apr;122(2):115-47), which by the way applies to perceptual decision-making tasks with competing response tendencies (Middlebrooks PG, Zandbelt BB, Logan GD, Palmeri TJ, Schall JD. Countermanding perceptual decision-making. iScience. 2020 Jan 24;23(1):100777). As demonstrated in revised Figure 1 and Supplementary Figure 3, the GO and STOP units are co-active before and after SSRT, so “conflict = a1*a2” yields interpretable values. In Results and Discussion, we test alternative interpretations of surprise and salience and as the reviewer suggested acknowledge that this may be related to encoding difficulty (Page 15, Line 440-472).
+
+We must observe, though, that many other investigators have used the stop-signal task to investigate conflict. Originally, Brown & Braver (2005, Learned predictions of error likelihood in the anterior cingulate cortex, Science, 307(5712):1118-21) used a modified stop signal task (stop-change or double-step task) to evaluate conflict and error detection and develop their error-likelihood theory of ACC function. We note that Braver was a co-author of Botvinick et al. 2001. Subsequently, Stahl & Gibbons (2007, Dynamics of response-conflict monitoring and individual differences in response control and behavioral control: an electrophysiological investigation using a stop-signal task. Clin Neurophysiol. 118(3):581-96), motivated by the Yeung, Botvinick & Cohen 2004 description of conflict in the interpretation of the ERN, investigated the ERN in a stop-signal task and observed, “However, independently of response type Ne/ERN also increased with
+increasing stop-signal delay. Since longer delay invokes stronger response conflict, results specifically support the notion of Ne/ERN reflecting response-conflict monitoring”. Similarly, Aron, Behrens., Smith, Frank, and Poldrack (2007, Triangulating a cognitive control network using diffusion-weighted magnetic resonance imaging (MRI) and functional MRI, J Neurosci. 27(14):3743-52) used a conditional stop-signal paradigm to examine behavioral and neural signatures of conflict-induced slowing. The comprehensive model of Wiecki & Frank (2013, A computational model of inhibitory control in frontal cortex and basal ganglia, Psychol Rev, 120(2):329-55) incorporates the conceptual framework that we are evaluating in this manuscript. Consider their statement of the problem, “In the current model, conflict is computed explicitly by the dorsal anterior cingulate cortex (dACC), which detects when multiple competing FEF response units are activated concurrently, and in turn activates the STN to make it more difficult to gate any response until this conflict is resolved. (page 332)”. Finally, most recently, Kleinsorge (2021, Stimulus-response conflict tasks and their use in clinical psychology, Int J Environ Res Public Health, 18(20):10657) wrote, “Although the stop-signal task is not a typical stimulus-response conflict task, it induces conflict between a go- and a stop-signal that can be pitted against each other in a methodologically elegant way that has yielded important conceptual insight into the nature of ‘automaticity’...” We trust that this brief review justifies conceptually our employment of this concept. We turn now to the empirical justification.
+
+Relatedly, I don’t mean to be too pedantic here, but increased errors are not necessarily coupled to increased conflict. Errors rates also vary by time pressure, task complexity, working memory load, attentional demands, time-on-task and other factors. The point is that calling neurons whose activity varies with p(error) ‘conflict neurons’ seems inappropriately speculative for the Results section. I guess they used this cognitive label to link to the N2, but that seems more a Discussion section point than a Results section label.
+
+We understand the reviewer’s point and agree that performance errors can arise for many different reasons. A utility of the stop-signal task is that most errors can be explained by the race of the GO and STOP processes. The original Botvinick measure of conflict is easily derived from the time course of activation of the GO and STOP process that are governing performance. That quantity happens to relate in an intelligible manner to the inhibition function, which characterizes error rate in this task. To clarify the presentation, we are happy to revise the nomenclature for the conflict model. We believe this change in nomenclature clarifies that we do not equate conflict simply with error and thus addresses the reviewer’s very useful comment.
+
+Minor concerns/criticisms
+- In Figure 2a, 3a, 4a and 5a I would like to also see the line for the non-canceled trials. It’s easy put them in and gives a more complete view of the contrasts between the different trial types. The contrast between canceled and non-canceled trials is relevant, as it shows which part of activity is specific to the successful execution of countermanding. This will also make the figure more convincing, as now it seems like the authors hide these non-canceled trials for an unwanted reason.
+
+For reasons we detailed above, the direct comparison between canceled and non-canceled trials is not valid and can be misleading. However, in revised Supplementary Figure 2b we plot activity on non-canceled trials for comparison.
+
+- Line 876-878. It is unclear why the set of SSDs for the different monkeys have different separation sizes (40-60 ms vs. 100 ms). This needs explanation.
+
+We have explained this in the revised Methods section and cited relevant literature on Page 25, Lines 797-798; Page 3, Line 57-58. The key aspect of the stop-signal task is to have a set of SSDs that probe response inhibition low to high error rates. Monkeys, like people, are idiosyncratic, so different SSD values must be used.
+- Wouldn’t it be easier to call ‘no stop signal’ trials ‘go’ trials? The authors use the term ‘go’ several other times in the manuscript
+
+We avoid the term to ‘go’ to avoid the following confusions:
+
+(1) In the literature ‘go’ trials refer to other manipulations and the saccade response in other conditions (e.g., GO/NO-GO task).
+
+(2) The term “no-stop signal trial” is consistent with the terminology used in the stop-signal task literature.
+
+(3) In this literature the term GO refers to the race model GO processes that results in the generation of the saccade. Conceptually, this is not equivalent to no-stop trials.
+
+As requested by the reviewer we have now made the terminology consistent throughout the manuscript.
+
+- Figure 2c doesn’t really seem to be a ‘representative’ neuron considering its peak responses is later than most of the neurons shown in Figure 2b. Is it possible to show more data? Perhaps examples of putative pyramidal and inhibitory cells that peak around SSRT vs later? Maybe you can highlight the specific ‘representative’ neuron by highlighting it in Figure 2b.
+- Same comment for Figure 3c. In fact, from looking at Figure 3b, I cannot tell which neuron 3c comes from. Maybe you can highlight the specific neuron in Figure 3b, like suggested for Figure 2b.
+
+We now include additional example neurons for each type in the Main text figures. These examples were chosen to be complementary by illustrating neurons in different layers with different spike widths and modulation times. In the time-depth plots (panel b of each figure), we added an arrow identifying the example neurons.
+
+Regarding Figure 3, although the lower panel of Fig 3a shows the recruitment of significant activity for the entire population, Fig 3b shows this only for sessions in which we could confidently assign neurons to layers. Therefore, not every neuron shown in panel a is also in panel b.
+
+- In the first paragraph of the Discussion section the authors refer to Figure 6. However, I prefer the explanation of this figure to be embedded in the Discussion instead of having an entirely separate paragraph in the figure description. This will make it more of a complete single story, instead of having a separate story in the figure description.
+
+Seeking to balance word count and clarity, we wrote the caption of Figure 6 to be self-sufficient. To address the reviewer’s comment, we have now isolated the conjecture on microcircuitry, which overlaps with Figure 6, in a new section, Cortical Microcircuitry of Executive Control (Page 17-20). We have also added some text from the figure 6 caption to the main text of the Discussion to ensure all the material in Figure 6 is also present there. We understand that making this change increases our word count.
+
+Line edits
+- Please have a native English speaker smooth out the manuscript. Some sentences read like notes rather than full sentences (e.g. line 53), and there are many minor mistakes that could be corrected, like missing articles (e.g. line 17, 40, 51, 606, 610).
+
+As requested, we have revised the manuscript to improve the flow and correct grammar and spelling. Native English speakers have also reviewed the manuscript.
+Reviewer #3 (Remarks to the Author):
+
+This paper is an important step toward a better understanding of cortical microcircuitry involved in executive control. As a continued effort to dissect laminar organization of medial frontal cortex during stop-signal task (Sajad et al., Nat. Neuro. 2019), this paper focused on more critical trial types (canceled) and task epochs (around SSRT) and found interesting functional dissociations across different neuronal groups. In particular, it is noteworthy finding that “goal maintenance” narrow-spiking neurons are specifically localized in L2/3. Furthermore, the report of N2/N3 in the monkey model is novel and its relation to neural spiking activates is an important addition to the field. The paper has solid and convincing results. That said, I have some suggestions that can potentially improve the paper.
+
+We thank the reviewer for their kind comments and appreciation of the manuscript.
+
+- Major points
+More justification is needed for the approach of classifying individual neurons into distinct groups – conflict monitoring, event timing, goal maintenance. While it is justified in terms of previous findings (e.g., for conflict neurons) and behavioral demands, this classification seems arbitrary, post-hoc, and not based on first principles (i.e., derived from theory or model). Why are there three, not two or not four, categories? Even clustering results in Supplementary figure 1 do not speak to this issue.
+
+The reviewer is asking a core question. Our approach is motivated by the comprehensive understanding of the early visual pathway derived from characterizing and distinguishing neuron types (e.g., Rowe MH, Stone J. The interpretation of variation in the classification of nerve cells. Brain Behav Evol. 1980;17(2):123-51). We have revised the manuscript to explain how our approach emphasizes unbiased clustering methods and evaluates all neurons through converging constraints derived from the principles of quantitative models used to describe executive control (Page 4, Lines 91-108). Figure 1 and associated supplementary figures were thoroughly revised to clarify our approach.
+
+Another way to ask this question is, how should readers interpret the different number of neurons in each group? Does it matter? Because there is a relatively smaller number of goal-maintenance neurons, should we conclude that SEF is involved more in conflicting monitoring and time keeping? Or does SEF do everything including the processing of gain and loss (Sajad et al., Nat. Neuro. 2019)? How these different groups of neurons interact and what is the population-level understanding? I know this is a high-level question that may need brand-new analyses (like population-level decoding or state-space/dynamical-systems approach). But at least, this issue should be thoroughly discussed as medial frontal cortex has notoriously heterogeneous neural populations in their sensorimotor selectivity.
+
+We appreciate these questions because we ask them ourselves. Here we address the questions in the order they were asked: We address the first question about sample numbers on page 21 of Discussion, in the first paragraph of a new section called Incidence and Multiplexing of Signals. In short, we believe that conclusions derived from relative sampling frequencies are too risky given the uncertainties inherent in extracellular spike sampling.
+
+We address the question about state-space/dynamical systems approach also in that section (Page 21, Lines 654-671). We are also describing how signals reported in this study multiplexed with those reported before in Sajad et al 2019. (Page 7, Lines 172-179; Page 9, Lines 257-262; and Page 11-12, Lines 335-339). In short, the population-level state-space/dynamical-systems analysis methods treat neurons as equivalent, but decades of previous research have demonstrated that functional differences among neurons within and across layers correspond to differences in morphology, biophysics, and connectivity. Therefore, we believe a catalogue of functional differences is most informative now. Certainly, future research can employ alternative approaches to investigate these data.
+
+Another key question is, is this classification a distinct category or more like a continuum? The latter is more likely given their overlapped dynamics (Fig. 5b, Sup. Fig. 1e). The difference between conflict and maintenance neurons is
+only about how long the neurons sustain their activities (e.g., transient versus persistent) and so not clear cut at all. Specifically, maintain neurons can be well considered as conflict monitoring and vice versa. This issue seems to become more problematic as even predictions between models are similar – as mentioned in methods, model predictions and parameters are correlated (e.g., SSD, p(error), conflict, and time to tone) and it is not clear how “random variations” (across single trials?) can differentiate these models.
+
+The reviewer raises two important points:
+
+1) Are categories discrete or continuous? Indeed, neuron classification has always been a non-trivial problem in neurophysiology (see Rowe and Stone citation above). Even in sensorimotor areas with robust sensory- and motor-related responses the distinction between sensory and motor neurons has proven to be a challenge. But many studies draw the line based on objective criteria, acknowledging that there can be a gray zone. In this study, we have drawn the line between the two facilitated neuronal classes based on objective criteria as well. We acknowledge that there is a gray zone and there can be some degree of misclassification, but these two populations exhibited other differences beyond their duration that justifies their separation into two distinct neuronal populations. We have now emphasized these differences in the Results (Page 10, Lines 285-287; Lines 294-296; Page 10-11, Lines 302-304; Page 12, Lines 350-351). We have also added a new Supplementary Figure 6e that illustrates that Goal Maintenance and Conflict neurons exhibited an opposite overall relationship to performance parameters.
+
+2) Are the model tests decisive? We have addressed this in Methods (Page 28, Lines 886-890) and have plotted the degree of difference between the tested models in our new Supplementary Figure 3b. In short, the association of the different neuron modulation patterns with different models can be determined with Bayesian reliability because task performance and derived behavioral parameters varied across sessions.
+
+Along the line of the previous comment, model comparison results should be presented better. In particular, details of alternative models are buried in the text/supplementary and hard to digest. It’d be useful to have a figure showing predictions from different models (well explained in method, “mixed-effects model”) and to bring a simplified version of Sup. Table 2 into the main manuscript.
+
+We have revised the manuscript substantially based on this suggestion. We moved a substantial portion of Supplementary Figure 2 to Figure 1 to explain the models. In Figures 2, 3, 4, and 5 we have moved from previous Supplementary Table 2 the panels showing the model-comparison results. We have clearly defined the models based on their mathematical descriptions and provided a summary for our nomenclature in our new Supplementary Table 2. We have added a new Supplementary Figure 3a explaining different hazard rate models in more detail. We have added a new Supplementary Figure 3b showing how parameters related to different models differ from each other. We have revised the text in the Results section to orient the reader to the different models with simpler language (Page 5-6, Lines 99-145). Finally, when reporting model comparisons in Results, we report which model was the best and remind the reader which models were excluded.
+
+Another big question is, what is the behavioral relevance of these activities in stop-signal task. More specifically, the behavioral relevance of conflict monitoring is not directly tested. In discussion, it is mentioned that conflict monitoring can be useful for post-stopping slowing but this interesting idea is not tested at all.
+For instance, was the go RT slower in the next trial after the conflict-monitoring neurons showed a higher firing rate? Does animal use timing information in ‘time-keeping neurons’ to predict SSD and adjust behavior accordingly?
+
+We thank the reviewer for this important question. We now describe the relationships of the neural signals to adjustments in RT on Page 6-7, Lines 167-170, Page 9, Lines 249-255, and Page 11, Lines 331-333, with the Methods (Page 28, Lines 904 - 908). We also report in
+Results (page 11, Lines 328-330) and show in Supplementary Figure 6f that the activity of Goal Maintenance neurons was lower when monkeys aborted canceled trials.
+
+Given that no specificity was found for conflict neurons in terms of laminar and spiking width (X^2 analyses), the conclusion that those neurons are broad-spiking and in L3/5 (in abstract, Line 23-25) is not warranted. This is just a by-product of sampling neurons in SEF. The valid conclusion is that no specificity was found.
+
+We thank the reviewer for this astute comment and have revised the text in the Abstract. We would note here that our statistical analysis for the laminar distribution of neurons does account for the sampling bias (Supplementary Table 1). Also, we trust that the reviewer agrees with us that the interpretability and importance of the results do not depend on the laminar distribution being different from the sampling distribution.
+
+Motivation for classifying neurons into broad-spiking and narrow-spiking is also not clear. It would be useful to provide backgrounds or hypotheses in the introduction. For example, is there any previous anatomical study suggesting inhibitory interneurons are more common in L2/3? It seems to be the case in Supp. Fig. 1.
+
+We have clarified the motivation in Results where we first report broad- vs. narrow-spiking neurons (Page 7, Lines 181-184). When describing the spiking widths of the other neuron types, we now state that this is to inform the contribution of neurons within the microcircuitry. We trust that the reviewer agrees that this information is useful to constrain microcircuit models that can enact different functions (e.g., Michael X Cohen, Trends in Neuroscience, 2014).
+
+It’d be useful to explicitly state the null hypothesis when linking N2/P3 and spiking activities across layers. Is it somewhat obvious that ERPs would be better predicted by upper layers as they are closer? Also, due to their match in timing, isn’t it obvious that monitoring/timing neurons better predict N2 and maintenance neurons better predict P3? One way to tackle the former question is to test how well the cranial EEG is predicted by LFP signals across layers.
+
+We have addressed this in Discussion (Page 20-21, Line 631-644).
+
+- Minor points
+In figure 2,3, and 4, the bottom plots in panel (a) have a confusing label, P(active). Because p(active) is different between left and right panels, it’d be better to use a separate y-axis label.
+
+We appreciate this suggestion and have edited the figures.
+
+I can easily imagine, to readers naive to the stop-signal task, the paper is written a bit difficult to follow and jargon-heavy fashion. If it is written without assuming prior knowledge, the paper will receive a wider readership.
+
+We have revised the text throughout. Major changes were made in the beginning of Results where we introduce the task and models (Page 3, Line 52-62; Page 4-6, Lines 94 - 143), explaining the testing procedures in the main text (Results, Figure 1), and revising the Supplementary material to provide a more thorough explanation of concepts relevant to our analyses (Supplementary Figures 1-3). We are anxious to learn if the reviewer finds the manuscript more accessible to the general reader.
+
+Y-axis Label of the right panel in fig. 3c should be pre-SSRT, to be consistent with left panel shades and legends.
+
+Thank you. We have now corrected this in the new panel Figure 3e
+Why did conflict neurons show higher activity right before feedback tone (Fig. 2a, Sup. Fig. 3b)?
+
+We are not sure whether the Reviewer is asking about the activity on no-stop trials that appear on panels 2a and Supplementary Fig 3b or is asking about the activity on canceled trials. We address both in turn:
+
+1) The activity of neurons aligned on tone, on no-stop trials (figure 2a, and Sup. Fig 3b) during the pre-tone interval can be larger than that on Canceled trials simply because of post-saccadic activity bleeding into this time period. Therefore, this appearance of modulation is incidental to other effects. We have now added this in the figure captions (e.g., Fig 2a and Supplementary Figure 4b).
+
+2) With respect to the activity of Conflict neurons on Canceled trials prior to tone, it was observed as a weak modulation in a low proportion of neurons. We were not confident proposing a definite interpretation, but we included the right panel in Fig 2b for transparency and consistency with the other figures. The most conservative interpretation must parallel that of the Goal Maintenance neurons. But as we have explained in the manuscript there is some degree of multiplexing that can also explain this.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have adequately addressed my questions and I am happy to recommend this manuscript for publication.
+
+Reviewer #2 (Remarks to the Author):
+
+We thank the authors for their diligent efforts to improve the quality and readability of their manuscript.
+
+We have one final point, which is about this comment:
+
+"Line 876-878. It is unclear why the set of SSDs for the different monkeys have different separation sizes (40-60 ms vs. 100 ms). This needs explanation."
+
+Your reply: "We have explained this in the revised Methods section and cited relevant literature on Page 25, Lines 797-798; Page 3, Line 57-58. The key aspect of the stop-signal task is to have a set of SSDs that probe response inhibition low to high error rates. Monkeys, like people, are idiosyncratic, so different SSD values must be used."
+
+The authors misunderstood our comment. The question was why the experimental manipulation differed between the two monkeys? We do understand the SSD titration procedure, and why it's needed, but we missed why the resolution of the titration for one monkey was twice that of the other monkey. Please clarify.
+
+Reviewer #3 (Remarks to the Author):
+
+I appreciate the authors' thorough response to the points raised by me and the other reviewers. More specifically, the paper is significantly improved by the unbiased clustering of neuronal types, better presentation of model comparisons, and also written better to address the reviewer’s concerns. I fully support publication.
+
+I just have two minor suggestions: 1) I do not see panel f in supplementary figure 6, which might be lost due to technical issues during editing. 2) For the time-keeping neuron (figure 3), isn’t it much more straightforward to present data from the time of Go signal (i.e., as a function of SSD)? I understand the current plot ("time from SSRT") is more consistent with how the other types of neurons are shown but I expect readers would wonder why activities in figure 3a reflect time-keeping. If the activities are plotted as a function of time from Go, time-keeping/ramping in those neurons would be much more clearly shown as their main feature.
+Sajad Errington Schall – Response to reviews
+
+REVIEWERS' COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have adequately addressed my questions and I am happy to recommend this manuscript for publication.
+
+    We are pleased to have satisfied the reviewer and appreciate the helpful comments.
+
+Reviewer #2 (Remarks to the Author):
+
+We thank the authors for their diligent efforts to improve the quality and readability of their manuscript.
+
+    We are pleased to have satisfied the reviewer and appreciate the helpful comments.
+
+We have one final point, which is about this comment:
+
+"Line 876-878. It is unclear why the set of SSDs for the different monkeys have different separation sizes (40-60 ms vs. 100 ms). This needs explanation."
+
+Your reply: "We have explained this in the revised Methods section and cited relevant literature on Page 25, Lines 797-798; Page 3, Line 57-58. The key aspect of the stop-signal task is to have a set of SSDs that probe response inhibition low to high error rates. Monkeys, like people, are idiosyncratic, so different SSD values must be used."
+
+The authors misunderstood our comment. The question was why the experimental manipulation differed between the two monkeys? We do understand the SSD titration procedure, and why it's needed, but we missed why the resolution of the titration for one monkey was twice that of the other monkey. Please clarify.
+
+    We apologize for the misunderstanding.
+
+The revised text reads, “The selection of SSDs was adjusted to the idiosyncrasies of each subject to ensure performance satisfying key criteria for stop-signal task. Different SSD values were used for the two subjects to account for between-subject differences in stopping performance 1.”
+
+In running various participants (human or monkey) on this task adjustments of SSD parameters to account for individual differences is common. The key criteria satisfied by all participants is successful stopping in 50% of stop signal trials and \( RT_{noncanceled} < RT_{no-stop-signal} \). Now, we have not addressed why monkeys X and Eu were different because we do not have enough information. The difference is most likely derived from the incident different training histories of the two monkeys. If the reviewer wishes us to expand on this, we are happy to, but every macaque
+behavior neurophysiology study includes idiosyncratic differences like this.
+
+Reviewer #3 (Remarks to the Author):
+
+I appreciate the authors’ thorough response to the points raised by me and the other reviewers. More specifically, the paper is significantly improved by the unbiased clustering of neuronal types, better presentation of model comparisons, and also written better to address the reviewer’s concerns. I fully support publication.
+
+I just have two minor suggestions: 1) I do not see panel f in supplementary figure 6, which might be lost due to technical issues during editing.
+
+    We apologize. Panel f is now included in Supplementary Fig 6.
+
+2) For the time-keeping neuron (figure 3), isn’t it much more straightforward to present data from the time of Go signal (i.e., as a function of SSD)? I understand the current plot ("time from SSRT") is more consistent with how the other types of neurons are shown but I expect readers would wonder why activities in figure 3a reflect time-keeping. If the activities are plotted as a function of time from Go, time-keeping/ramping in those neurons would be much more clearly shown as their main feature.
+
+    We agree with the reviewer about the advantages of the suggested illustration. However, such an alignment would obscure the pronounced suppression of these neurons after SSRT. To address this comment, though, the revised figure now explicitly marks when the GO signal appeared. We would also note that interested readers can construct such a plot easily from the code and data deposited in the OSF repository.

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+Peer Review File
+
+Volumetric extrusive rates of silicic supereruptions from the Afro-Arabian large igneous province
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+This is an incredibly well written and organised manuscript with a concise, systematic narrative that provides exciting new insights into the temporal evolution of what is arguably one of the greatest episodes of silicic magmatism in Earth history. I find this manuscript to be impactful for a number of reasons:
+• The timing, rates and durations of magmatic processes are fundamental, underpinning knowledge necessary for creating and testing ideas about topics ranging from geodynamics to climate change. Accordingly, these authors have constructed one of the most finely, temporally tuned records for large-scale silicic volcanism anywhere. Such a record and dataset provide key constraints on concepts about volcanisms role in shaping Earth surface environments, including as a calibration standard for understanding processes that require being assessed within robust geochronological frameworks.
+• Specific to my latter point above, this manuscript refines the palaeomagnetic time scale during a pivotal time in Earth history, i.e. the Eocene-Oligocene transition that archives Earth’s initiation and decent into our current ice age. This will be a great dataset by which to connect and correlate ocean-based records (e.g. ODP cores) with land-based records reliant on palaeomag as a proxy for absolute time calibration.
+• A current ‘hot topic’ is the role of volcanism in altering climate and influencing (generally adversely) societal functioning. The data presented in this manuscript reveals that Earth-system-scale perturbations are not necessarily an inevitable outcome to (super)volcanic eruptions. There is an ever-expanding body of research focussing on documenting and assessing the magnitude of climate change linked to volcanos---to date, evidence seems to indicate that even the most violent recorded eruptions result in hemispherically restricted climatic disturbances that operate on human-scale time scales. Nevertheless, it remains a strongly held view that volcanism is a mechanism that can induce nuclear-winter style climatic response and wholesale global change. This work shows that the timing of the Yemeni eruptions, some of the undoubtedly largest explosive volcanic events of the Phanerozoic, have little to no correspondence with well documented environmental change deduced from marine stable isotope records spanning early-mid Tertiary time. This is a significant finding for use by the Earth science community interested in understanding drivers of Earth system change on a planetary scale. In fact, the authors have provided an exemplar case study that shows how due diligence and circumspection must be undertaken before too glibly invoking ‘volcanic cause’ for ‘climate-change effect’.
+• I am, to use a rather colourful term, ‘gobsmacked,’ at the rapidity of magmatic differentiation these workers appear to have documented via the evolving REE and incompatible element ratios tied to specific zircons that are resolvable-y different in age. Perhaps this is a well-established truism in petrology circles but to non-petrology-afficionados, who I assume are many such as myself, my understanding of magmatic longevity is that there are proponents who champion magmatic processes that remain operative on 106-7 yr and even longer time scales and another set of proponents who have generated data sets that indicate much shorter durations. This dataset nails down magmatic differentiation occurring over time scales 1000’s-10,000’s yr and perhaps even shorter. This strikes me as having the potential to inform models and modellers interested in continental crust evolution.
+• Lastly, the Yemen region has been far-less studied than its neighbouring African counterparts. The authors have addressed that shortcoming and provide important insights into the geodynamical evolution of a hallmark tectonic region, namely, the Ethiopian-Gulf rift system, a region that researchers worldwide study to gain knowledge about mantle-crust process-response.
+
+For these reasons I consider this manuscript to be apropos for Nature Communications, it would have wide appeal to a broad swath of researchers interested in linking Earth’s internal processes to the drivers of environmental change on Earth’s surface, it provides fundamental new and exciting data from a key but vastly understudied region for investigating plate tectonic phenomena, and the geochronological and geochemical data the authors have amassed goes far beyond simply accurate and precise dating-rocks-in-Yemen and will be used for studies ranging from volcanism and climate
+change, to petrological processes in silicic melts, to calibrating absolute time for a pivotal period of Earth system change. I do have a few minor comments and, once those are dealt with by the authors, I recommend publication.
+
+There is an issue with reference numbering. Starting at about line 156, the numbers appear to be off by 1, i.e. in line 156 ref 18 should be ref 17, in line 156 ref 17 should be ref 16, etc. untikl the end of the manuscript, including in the Methods section. Also, I thinbk ref 17 in line 155 should be ref 15.
+
+CL should be defined before citing it as an acronym---I think the first mention of CL is line 72
+
+Fig 1. Are the labels for Upper Bimodal Phase and Main Basalts Phase reversed on the figure? In the figure legend (below map) you should give Uskins Peate et al. (2205) and Baker et al. (1996) superscripted reference numbers to tie them to the reference list. Also, define ‘Ig’ as ignimbrite in the figure caption.
+
+Fig. 2. There are two versions of this figure; the one included with the caption is a bit pixelated and fuzzy but the 2nd version at the end of the manuscript is clear and sharp---make certain that is the one that is used for the published figure. Again, provide superscript reference numbers for the references listed on the figure. Perhaps define what you mean by ‘basement’ (pre-Oligocene rocks?). Line 443: change “unknown” to “uncertain”, this term has a somewhat more ‘positive’ connotation. Line 449: insert ‘in’ after ‘reported’
+
+Fig. 3. Same comment as above: there are two versions of this figure; the one included with the caption is rather pixelated and fuzzy but the 2nd version at the end of the manuscript is clear and sharp---make certain that is the one that is used for the published figure.
+
+Lines Fig. 4. This is a fascinating result with implications regarding the rate of crystal growth in magmas. If you are correct in identifying these trends as indicative of magmatic differentiation, is it possible to do a back-of-the-envelope style calculation to estimate the amount of feldspar that needs to form in order to reduce Eu/Eu* and increase Th/Y by the amounts shown, and does the mineralogical composition of the successively younger ignimbritic units show a compatible/corroborative increase in feldspar component? One wee issue with the figure: your letter designations on the figure are in lower case but are given as upper case in the caption; these should be consistent.
+
+Review by: Tony Prave, School of Earth and Env. Sciences, University of St Andrews, Scotland
+
+Reviewer #2:
+Remarks to the Author:
+Editorial Office, Nature Communications
+Topic: Review of Thines et al. 2021 (m/s no. NCOMMS-21-16463)
+
+Dear Editorial Office,
+
+This letter accompanies my formal review of the manuscript '"Magma flux of silicic supereruptions from the Afro-Arabian large igneous province" by Dr Thines and colleagues.
+
+The manuscript presents new zircon age and trace element data for a series of supereruptions produced from the Afro-Arabian large igneous province during the Oligocene. The authors find that there is very little time between the main period of volcanism and calculate extreme eruption rates for this period, the highest known on Earth. These findings are exciting, the data are of excellent quality and the manuscript is reasonably well written. CA-TIMS is not an easy method and this is a robust
+data set that produces some very nice results. However, I think that some of the terminology is misleading and there are a few points that need to be changed.
+
+I have made detailed comments on the combined manuscript pdf, but also provide some general comments below:
+
+1. Terminology. The main point of the paper is to calculate the ages of these events, which can then be used to calculate how much magma was erupted. The term magma flux is a bit misleading in this case. I've pointed out where I think these types of terms should be changed for consistency.
+
+2. Eruption volume accuracy. These eruption deposits are very large and the estimates of volume are not the precise given the many unknowns like total area, caldera infill and erosion. In many places and in figures these eruption volumes are quoted to the nearest km3. Please address this issue.
+
+3. Introduction. Doesn't really convey why this topic and area is of global interest and importance. The paper calculates the highest ever eruption rate for silicic volcanism (perhaps by an order of magnitude). This section needs to be improved.
+
+4. Discussion. I've highlighted areas that I think need further consideration. Particularly around the calculation of magma evolution. I also struggle to see what the environmental impacts section brings to the paper.
+
+5. Reference order. There are many places where the incorrect reference number is called. This may be an issue with numbers being mixed up. Please check.
+
+Thank you for the opportunity to review, I am happy to be contacted for further comments or reviews.
+
+Kind regards,
+Simon Barker
+July 21, 2021
+
+Dear Reviewers,
+
+I am grateful for the thoughtful and constructive reviews provided on the manuscript. These comments have significantly helped to improve the quality and clarity of my paper. I have revised the manuscript to address the feedback from the reviewers. Below, I provide point-by-point responses (in italics) to the comments from each reviewer with reference to the original and revised manuscript where appropriate. Basic grammatical and referencing errors from both reviewers have been addressed in the revised manuscript.
+
+Reviewer #1 Comments:
+
+Fig 1. Are the labels for Upper Bimodal Phase and Main Basalts Phase reversed on the figure? In the figure legend (below map) you should give Ukstins Peate et al. (2005) and Baker et al. (1996) superscripted reference numbers to tie them to the reference list. Also, define ‘Ig’ as ignimbrite in the figure caption.
+R: *The labels were switched and is corrected in the revised version of the figure. The figure legend has been corrected with the subscripted reference numbers. ‘Ig.’ has also been defined in the figure caption [line 493 of revised manuscript].*
+
+Fig. 2. There are two versions of this figure; the one included with the caption is a bit pixelated and fuzzy but the 2nd version at the end of the manuscript is clear and sharp---make certain that is the one that is used for the published figure. Again, provide superscript reference numbers for the references listed on the figure. Perhaps define what you mean by ‘basement’ (pre-Oligocene rocks?). Line 443: change “unknown” to “uncertain”, this term has a somewhat more ‘positive’ connotation. Line 449: insert ‘in’ after ‘reported.’
+R: *There was an error with the way the figures were linked to the manuscript document that caused them to appear blurry. I have re-added the figures to mitigate this but the submitted PDFs are the high-quality versions. The figure legend has been corrected with the subscripted reference numbers. Where present in outcrop, the Northern Yemen volcanic units overly sedimentary basement from the Tawilah Group (Ukstins Peate et al., 2005; doi:10.1007/s00445-005-0428-4). As the basement is not discussed in the manuscript itself, no further detail has been added [line 506 of revised manuscript].*
+
+Fig. 3. Same comment as above: there are two versions of this figure; the one included with the caption is rather pixelated and fuzzy but the 2nd version at the end of the manuscript is clear and sharp---make certain that is the one that is used for the published figure.
+R: *Same as above.*
+
+Fig. 4. This is a fascinating result with implications regarding the rate of crystal growth in magmas. If you are correct in identifying these trends as indicative of magmatic differentiation, is it possible to do a back-of-the-envelope style calculation to estimate the amount of feldspar that needs to form in order to reduce Eu/Eu* and increase Th/Y by the amounts shown, and does the mineralogical composition of the successively younger ignimbritic units show a compatible/ corroborative increase in feldspar component? One wee issue with the figure: your
+letter designations on the figure are in lower case but are given as upper case in the caption; these should be consistent.
+
+R: Single mode fractional crystallization modelling using the experimental partition coefficients of Rubatto and Hermann (2007; doi: 10.1016/j.chemgeo.2007.01.027) and the fractionating assemblage from Ukstins Peate et al. (2008; doi: 10.1016/j.lithos.2007.08.015) demonstrate that the evolution of Eu/Eu* in zircon is consistent with previous estimates (Ukstins Peate et al., 2008; doi: 10.1016/j.lithos.2007.08.015) of 50-60% fractional crystallization in these rhyolites [lines 123-129 of revised manuscript].
+
+Reviewer #2 Comments:
+
+[Line 1] Here and throughout the paper. There is a bit of an issue with mixing terms here. MAGMA FLUX is very different from VOLCANIC FLUX (i.e. eruption rate). This is particularly relevant for silicic systems where large amounts of partial melt stay in the crust. I would suggest changing this title to avoid confusion as most of what you calculate is volcanic flux.
+
+R: The terminology throughout the manuscript has been adjusted such that ‘magma flux’ is now ‘long-term volumetric extrusive rate’ and ‘short-term accumulation rate’ is now ‘magma flux rate’ to reflect common use in the literature (e.g., Rivera et al., 2016; doi:10.1093/petrology/egw053; White et al., 2006; doi: 10.1029/2005GC001002).
+
+[Line 12] Here and elsewhere. Be careful with the precision you are claiming with volume estimates. I would say that this is probably +/- 50% so to say eruptions are 2667 km^3 exactly is not really appropriate. Maybe round to nearest 100 km^3 at least? Might be worth also discussing the uncertainty in these volume estimates?
+
+R: Throughout the manuscript text, estimated minimum total eruptive volumes have been rounded to the nearest 100^th for all units except the Green Tuff (~60 km^3 DRE) and Escarpment Ignimbrite (~360 km^3 DRE). I have also recalculated the long-term volumetric extrusive rates using the rounded volume estimates. Figure 3 still shows the original volume estimates from Ukstins Peate et al. (2005; doi: doi:10.1007/s00445-005-0428-4) and Bryan et al. (2010; doi: 10.1016/j.earscirev.2010.07.001) for reference. A short discussion on the volume estimates in regards to the calculation of the long-term volumetric extrusive rates was added to the ‘Long-Term Volumetric Extrusive Rates’ section [lines 206-212 of revised manuscript].
+
+[Line 19] By more than 2 orders of magnitude! Maybe express this in km^3 per kyr?
+
+R: Volumetric extrusive rates are calculated in km^3/yr in agreement with Rivera et al. (2016; doi:10.1093/petrology/egw053) and White et al. (2006; doi: 10.1029/2005GC001002).
+
+[Line 24] No mention of lack of environmental impacts?
+
+R: Statements regarding the environmental change (or lack thereof) in relation to the Northern Yemen eruptions have been added to the ‘Abstract’ and ‘Background’ [lines 22-24 and 81-86 of revised manuscript, respectively].
+[Line 25] I think that the beginning of the Background section doesn't really cover the importance of the subject and the relevance of large silicic eruptions (supereruptions) and eruption rate/flux.
+R: A statement regarding the importance of long-term volumetric extrusive rates of silicic magmas in the context of LIPs has been added to the 'Background' [lines 34-37 of revised manuscript].
+
+[Line 16] This is a little misleading as none of the 13 Quaternary supereruptions have come from a LIP. This would also be a good place to introduce the definition of a supereruption.
+R: While it is true that the many of the recent silicic supereruptions are not from large igneous provinces, the exceptions are the 2.08 Ma Huckleberry Ridge Tuff and 0.63 Ma Lava Creek Tuff from the Columbia River-Snake River Plain-Yellowstone Plateau LIP. The occurrence of LIPs is rare compared to other volcanic events and the Afro-Arabian LIP is among the youngest currently identified (Bryan and Ernst, 2008; doi: 10.1016/j.earscirev.2007.08.008). Even so, the volcanic record is biased towards younger events and some of the main hindrances to the identification of silicic supereruptions are erosion, burial, tectonic fragmentation, and distal ash dispersal (Bryan et al., 2010; doi: 10.1016/j.earscirev.2010.07.001), an attribute that makes this study especially relevant. A succinct definition of supereruptions has been added to the 'Background' [lines 40 of revised manuscript].
+
+[Line 65] Need to clarify why your study is novel and different from these.
+R: Perhaps the most notable attribute of the Northern Yemen is the well-constrained stratigraphy that preserves a series of these silicic supereruptions. Previous paleomagnetism and \(^{40}\)Ar/\(^{39}\)Ar studies (Riisager et al., 2005; doi: 10.1016/j.epsl.2005.06.016; Ukstins et al., 2002; doi: 10.1016/S0012-821X(02)00525-3) and correlations to distal tephra layers (Ukstins Peate et al., 2008; doi: 10.1016/j.lithos.2007.08.015) strengthen the robustness of the findings [lines 49-53, and 206-213 of revised manuscript].
+
+[Line 68] I found it a bit of a jump from the last section to here, with no details of the methods employed etc. I know these have been forced to the end in normal nature style but it might be good to have a line in the last sections saying "Here we use high-precision CA-TIMS to refine the timing of eruptions and show that...
+R: I completely agree. Brief statements on the methods have been added to the end of the 'Background' and 'Results' to provide a smoother transition [lines 81-91 of revised manuscript].
+
+[Line 84] First mention on LA-ICPMS. Need to explain why this was done (i.e. to look for crystal inheritance), xenocrysts etc. as mentioned below.
+R: I think it is more appropriate to introduce the concepts of xenocrysts and antecrysts during the discussion of the LA-ICP-MS data itself after the context of the zircon morphologies has been given. A brief mention was made in lines 88-91 of the revised manuscript and expanded upon in lines 107-114.
+
+[Line 97] Check number of significant figures in this file for the various trace elements. No point in having REE's to 4 DP.
+R: The data in 'Supplemental Information 2' is now reported to the appropriate number of significant figures.
+[Line 108] On the basis of CL? How to you decide whether or not to cull these data points? How would these impact on your mean age?
+R: The decision was made primarily based on the \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) CA-TIMS zircon ages of the underlying units. The weighted mean age of the Escarpment Ignimbrite is \(29.755 \pm 0.023\) Ma. The oldest dated zircon from the overlying SAM Ignimbrite is older than the \(29.755 \pm 0.023\) Ma age of the Escarpment Ignimbrite and was therefore excluded from the calculation of the final weighted mean date. The same thought process was used for the three oldest zircons from the Sana’a Ignimbrite and all of the dated zircons from Iftar Alkalb. While the inclusion of the single rejected zircon from the SAM Ignimbrite yields a final age that is stratigraphically feasible (\(29.733 \pm 0.030\) Ma; MSWD = 2.40), the inclusion of the three rejected zircons from the Sana’a Ignimbrite does not (\(29.793 \pm 0.042\) Ma; MSWD = 8.96). Furthermore, the MSWD of the final ages that include the rejected zircons [lines 142-144 of revised manuscript] are anomalously high, further supporting the original approach.
+
+[Line 114] Some of the CL images seem to be distinct? Mention these?
+R: In most respects, Iftar Alkalb was an outlier in this study whose complexities are interesting and require additional work to understand [lines 150-152 and 180-183 of revised manuscript].
+
+[Line 118] Perhaps explain why this is important to give context of these recalculations?
+R: The main purposes of including the previous \(^{40}\mathrm{Ar}/^{39}\mathrm{Ar}\) ages recalculated with the updated monitor age is to demonstrate that the new zircon ages are compatible with the preexisting stratigraphic framework and provide a single place with all of the current dates for the Northern Yemen volcanic units [lines 161-163 of revised manuscript].
+
+[Line 128] Accumulation is the wrong term here. For silicic eruptions accumulation is often used to refer to the build up of a melt dominant body prior to eruption. You are looking at rhyolite magma evolution timescales.
+R: ‘Short-term accumulation rates’ is now discussed in terms of ‘timescales of magma differentiation’ and ‘magma flux rate’ to clear up confusion.
+
+[Line 134] I don’t agree with this approach. CA-TIMS gives a bulk age on the zircon and is very precise but is an average of the whole grain. You should at least point this out as a limitation here. The LA-ICPMS data are from single points and therefore the age of that particular region of the grain may not match the average TIMS age.
+R: Ideally I would have at least one core and rim LA-ICP-MS spot per zircon crystal but the majority of the zircon crystals were either too small for multiple 15\( \mu \)m laser ablation spots and/or had too many Fe-Ti oxide and apatite inclusions to obtain clean data [lines 178-180 of revised manuscript].
+
+[Line 137] This is not clear from the figure. Can you plot age vs trace elements if this is your main argument here?
+R: The goals of Figure 4 are to show both the evolution of the zircon in terms of Th/Y and Eu/Eu* and show the age distribution within each unit. Both could not be achieved by changing one of the axes to age and an additional figure would be redundant. Further clarification has
+been added to Figure 4 by adding the difference in age between the most and least zircon in each unit as discussed in the text [lines 171-174 of revised manuscript].
+
+[Line 140] This is also misleading and has little context. The magmas didn't contain zircon throughout their evolution, it would have only crystallised once the melt reached Zr saturation. You don't have the resolution of U/Th dating as many of the studies you refer to.
+R: While there are limitations to the current approach, this is the first study of its kind on the silicic component of the Afro-Arabian LIP and provides evidence for rapid differentiation of the large-volume silicic magmas, an ongoing debate within the geologic community. A discussion of these limitations has been added to tone down the original argument while still presenting the evidence.
+
+[Line 144] What is the basis for using these values? not clear. Is the maximum related to the time since mafic volcanism?
+R: These values are based on the age difference between the most and least evolved zircon crystals in each discussed in the previous paragraph - 0.01 ± 0.16 Ma for the Escarpment Ignimbrite, 0.02 ± 0.09 Ma for the SAM Ignimbrite, and 0.07 ± 0.17 Ma for the Sana’a Ignimbrite. These are related to the time since the magmas reached zircon saturation. Previous fractional crystallization modelling of ash shards from the correlated distal tephras (Ukstins Peate et al., 2008; doi: 10.1016/j.lithos.2007.08.015) demonstrate that the rhyolites were generated from extreme fractional crystallization of mafic magma. The evolution of Eu/Eu* in these zircons is also consistent with this finding [lines 123-129 of revised manuscript].
+
+[Line 171] But there is no discussion of why your volume estimates are so good?
+R: More information about the Northern Yemen section was added to the ‘Background’ and reiterated in the ‘Long-Term Volumetric Extrusive Rate’ section for clarification [lines 49-53 and 206-208 of revised manuscript].
+
+[Line 193] I'm not really sure what this section adds to the paper? There is not really the temporal resolution to assess environmental change as demonstrated in Fig. 2. This section needs to be explained in more detail or dropped as it doesn't really add much beyond previous studies e.g. Prave et al. 2016
+R: While I didn’t find evidence that these silicic supereruptions resulted in major global environmental change, at least some discussion on the matter is still warranted following the publication of the 2020 Geologic Time Scale and the new \( \delta^{18}O \) and \( \delta^{3}C \) curves (Speijer et al., 2020; doi: 10.1016/B978-0-12-824360-2.00028-0). Eruptions from LIPs (both basaltic and rhyolitic) are sufficiently large to have global impacts yet there is a growing consensus that many did not result in global thermal perturbations (Bryan and Ferrari, 2013; doi: 10.1130/B30820.1). The key to establishing this correlation (or lack thereof) is both high-resolution geochronologic data and climate proxy data. Due to the high number of well-documented cooling events in the Oligocene, this section is more of a cautionary tale of the importance for these high-resolution data and another demonstrating that large volcanic eruptions do not necessarily result in global climate change on scales observable in the geologic record.
+[Line 202] Not clear in fig 2 as to the degree of the perturbation. It seems like 29.7 Ma does have a small step but it is hard to tell from the resolution and scale.
+
+R: While there does appear to be small perturbations in both \( \delta^{18}O \) and \( \delta^{3}C \) at ~29.7 Ma, the current age of the Bayt Mawjan Ignimbrite is too imprecise to make a strong argument for any causality. Figure 2 shows that is a potential area of interest for future consideration and is beyond the scope of this study.
+
+[Line 205] Over long time scales. They would undoubtedly have climate impacts but they are not preserved in the resolution of the climate proxy you show. I don't see how this section adds to the paper and it is not even mentioned in the abstract.
+
+R: The original manuscript was not clear enough about why this section is important and was lacking an adequate discussion on the precision of the climate proxy data. The topic has now been introduced in the 'Abstract' [lines 22-24 of revised manuscript] and 'Background' [lines 75-78 of revised manuscript] with a more thorough discussion in the 'Afro-Arabian Volcanism and Oligocene Environmental Change' section [lines 235-258 of revised manuscript].
+
+Sincerely,
+
+Jennifer E. Thines
+
+Jennifer E. Thines, Ph.D.
+University of Iowa, Dept of Earth & Environmental Sciences
+115 Trowbridge Hall
+Iowa City, IA 52242 U.S.A.

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+Magma flux of silicic supereruptions from the Afro-Arabian large igneous province
+
+Jennifer Thines (jennifer-thines@uiowa.edu)
+University of Iowa   https://orcid.org/0000-0001-9589-960X
+Ingrid Ukstins
+University of Auckland
+Corey Wall
+Boise State University
+Mark Schmitz
+Boise State University
+
+Article
+
+Keywords: volcanos, earth science, silicic supereruptions, magma
+
+Posted Date: May 13th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-469569/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on November 2nd, 2021. See the published version at https://doi.org/10.1038/s41467-021-26468-5.
+Magma flux of silicic supereruptions from the Afro-Arabian large igneous province
+
+Jennifer E. Thines*1, Ingrid A. Ukstins2, Corey Wall3 & Mark Schmitz3
+
+1Department of Earth and Environmental Sciences, University of Iowa, 115 Trowbridge Hall, Iowa City, IA 52242 USA
+2School of Environment, The University of Auckland, Private Bag 92 019, Auckland, New Zealand
+3Department of Geosciences, 1295 University Drive, Boise State University, Boise, ID 83706, USA
+
+Abstract
+
+The Main Silicics phase of the Afro-Arabian large igneous province preserves some of the largest volcanic eruptions on Earth, with six units totaling >8,600 km^3 dense rock equivalent (DRE). The large volumes of rapidly emplaced individual eruptions present a case study for examining the tempo of generation and emplacement of voluminous silicic magmas. We use high-precision ^{206}Pb/^{238}U zircon dating to differentiate individual eruption ages and show that the largest sequentially dated eruptions occurred within a timeframe of 48 ± 34 kyr (29.755 ± 0.023 Ma to 29.707 ± 0.025 Ma), yielding a maximum magma flux of 3.09 × 10^{-1} km^3/yr for 4,339 km^3 DRE and making this sequence the highest known flux of silicic volcanism on Earth. The Main Silicics phase of volcanism occurred within a timeframe of 130 ± 150 kyr (29.80 ± 0.80 Ma to 29.67 ± 0.13 Ma), yielding a maximum magma flux of 3.05 × 10^{-2} km^3/yr. We also provide a robust tie-point for calibration of the geomagnetic polarity timescale by integrating
+recalculated \(^{40}\)Ar/\(^{39}\)Ar data with our high-precision \(^{206}\)Pb/\(^{238}\)U ages to yield new constraints on the duration of the C11n.1r Subchron.
+
+Background
+
+Many of the largest silicic eruptions on Earth occur in large igneous provinces (LIPs), with total eruptive volumes often exceeding 1,000 km\(^3\) dense rock equivalent (DRE) for individual events, which are likely to be emplaced in rapid succession\(^{1-3}\). Although LIPs are generally considered to represent the most productive magmatic systems on Earth\(^4\), uncertainty about volume estimates and imprecise or inaccurate age data for individual events often preclude robust estimates of magma flux and volcanic output rates. The Northern Yemen section of the Afro-Arabian LIP is an ideal testbed for using high-15 \(^{206}\)Pb/\(^{238}\)U zircon dating to quantify the magma flux of a series of flood volcanic eruptions, with three silicic supereruptions occurring within a 70 to 310 kyr timeframe at ca. 29.7 Ma\(^{5-7}\). Previous paleomagnetism and \(^{40}\)Ar/\(^{39}\)Ar studies\(^{5-7}\) indicate these are a set of normal to reversed polarity units that encompass the duration of the C11n.1r Subchron, although overlapping ages for individual eruptions, due to analytical uncertainties, are currently unable to distinguish between the geomagnetic polarity timescale (GPTS) of Cande and Kent\(^8\) and Huestis and Acton\(^9\). In contrast to existing \(^{40}\)Ar/\(^{39}\)Ar ages, the 0.1% precision of state-of-art chemical abrasion thermal ionization mass spectroscopy (CA-TIMS) U-Pb ages of zircons can distinguish between the ages of these units outside analytical uncertainty.
+
+Oligocene volcanism in Northern Yemen (Fig. 1) has been divided into three phases based on field observations, whole rock geochemical correlations, and \(^{40}\)Ar/\(^{39}\)Ar dating\(^{5-7,10}\): Main Basalts (31 to 29.7 Ma), Main Silicics (29.7 to 29.5 Ma), and Upper Bimodal
+(29.6 to 27.7 Ma). The Main Basalts phase is characterized by effusive basaltic volcanism and volumetrically represents 60 to 70% of the total erupted volume of Afro-Arabian lavas\(^{10,11}\). The Main Silicics phase saw the rapid emplacement of seven silicic pyroclastic units and the Upper Bimodal phase includes small-volume basaltic and rhyolitic eruptions\(^{10}\).
+
+We focus on the Main Silicics phase, which contains some of the largest known silicic eruptions on Earth, with an estimated minimum eruptive total volume of 8,633 km\(^3\) DRE emplaced in present-day Yemen and Ethiopia over a period from 29.7 to 29.5 Ma\(^{1,10}\). Volcano-stratigraphic correlations in Yemen\(^{10}\) suggest the emplacement of the Jabal Kura’a Ignimbrite (1,627 km\(^3\) DRE; ~29.6 Ma) and Escarpment Ignimbrite (358 km\(^3\) DRE; ~29.6 Ma) was followed by a brief period of subsidence and erosion, and then the rapid emplacement of the Green Tuff (58 km\(^3\) DRE; \(^{40}\)Ar/\(^{39}\)Ar age = 29.59 ± 0.12 Ma\(^7\); Fig. 2), SAM Ignimbrite (2,330 km\(^3\) DRE; \(^{40}\)Ar/\(^{39}\)Ar age = 29.47 ± 0.14 Ma\(^7\), Sana’a Ignimbrite (1,593 km\(^3\) DRE; ~29.5 Ma; Fig. 2), and Iftar Alkalb caldera collapse mega-breccia (2,667 km\(^3\) DRE; \(^{40}\)Ar/\(^{39}\)Ar age = 29.48 ± 0.13 Ma\(^5\); Fig. 2). The Green Tuff has been interpreted as representing the initial airfall deposit preceding the emplacement of the SAM Ignimbrite based on the sharp upper contact between the units with no evidence of a time gap during emplacement\(^{10}\). These bracketed \(^{40}\)Ar/\(^{39}\)Ar ages indicate all four units, with a cumulative estimated minimum total eruptive volume of ~6,650 km\(^3\) DRE, were emplaced in rapid succession within a timeframe of 70 to 310 kyr\(^{5,7,10}\) but there are no robust estimates of magma generation rates or magma flux over this time interval.
+Results
+
+The Escarpment Ignimbrite contains elongate prismatic crystals (typically 50 to 120 μm in length and, rarely, up to 150 μm) and smaller equant crystals (50 to 75 μm in length). Some prismatic crystals have oscillatory zoning with U-rich non-luminescent cores (CL dark). The SAM Ignimbrite contains elongate prismatic crystals that are both smaller (30 to 75 μm, rarely up to 125 μm) and less numerous than those found in the Escarpment Ignimbrite. Few crystals have subtle oscillatory zoning and one larger crystal ~120 μm in length has a non-luminescent, oscillatory zoned core with a lighter overgrowth rim. Crystals in the SAM Ignimbrite have a weakly paramagnetic behavior, likely due to abundant Fe-Ti oxide and apatite inclusions. The Sana’a Ignimbrite contains small elongate prismatic crystals (30 to 75 μm) with subtle to no oscillatory zoning. Zircon is abundant in Iftar Alkalb as anhedral to euhedral elongate prismatic and equant crystals that range in length from 30 to 120 μm. Internal morphologies are variable with populations of non-luminescent and luminescent crystals with no oscillatory zoning, crystals with non-luminescent cores and lighter rims, and a few crystals with strong oscillatory zoning (see Supplementary Information 1 for CL images).
+
+In total, 273 laser ablation spot analyses were conducted on 79 crystals from the Escarpment Ignimbrite, 46 crystals from the SAM Ignimbrite, 31 crystals from the Sana’a Ignimbrite, and 95 crystals from Iftar Alkalb. The median uncertainty of a single LA-ICP-MS \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) spot analysis is 3 Ma, too imprecise to distinguish antecrust populations (crystals that grew in an earlier pulse and were later incorporated in a different pulse\(^{12,13}\)) for this magmatic system but adequate to determine older xenocrystic zircon crystals. Every unit except the Escarpment Ignimbrite contains >10%
+zircon crystals with LA-ICP-MS \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) ages >33 Ma. The Sana’a Ignimbrite and Iftar Alkalb contain significant proportions of older zircons (30% and 29% respectively), although in the Sana’a Ignimbrite this may be due to the low sample number (\(n = 31\)). There is no correlation between age and trace element (U, Th, Y, HREE) concentrations. CL dark zircon crystals in the Escarpment Ignimbrite and Iftar Alkalb have among the highest HREE concentrations and europium anomalies (Eu/Eu*) in each respective unit (Supplementary Information 2).
+
+32 grains that showed no sign of inclusions and yielded consistent U-Pb laser ablation dates were plucked from their respective grain mounts for high-precision CA-ID-TIMS geochronology (Supplementary Information 2). Preference was given to zircon crystals that captured the full range of compositions found in each unit. Six zircon crystals from the Escarpment Ignimbrite yielded a weighted mean \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) date of 29.755 ± 0.023 Ma (MSWD = 0.62; Fig. 3). Excluding the oldest zircon crystal from the SAM Ignimbrite (which was older than 29.778 Ma, and inferred to be an antecryst), the remaining eight zircon crystals yielded a weighted mean date of 29.728 ± 0.017 Ma (MSWD = 0.34). Six zircon crystals from the Sana’a Ignimbrite yielded a weighted mean date of 29.707 ± 0.025 Ma (MSWD = 0.65; Fig. 3), excluding three zircon crystals older than 29.745 Ma, also inferred to be antecrysts. The weighted mean \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) dates have been interpreted as the eruption age of each respective unit. Although Iftar Alkalb is the stratigraphically youngest unit dated, nine zircon crystals were consistently older (29.731 ± 0.089 Ma to 30.320 ± 0.094 Ma; Fig. 3) than the weighted mean ages of the other units and so no date was assigned; we attribute this to the emplacement mechanism of the caldera collapse breccia with abundant mega-clasts of underlying
+stratigraphy contributing xenolithic material or antecrysts that are recording an earlier stage of zircon crystallization.
+
+Sanidine from the Green Tuff, SAM Ignimbrite, and Iftar Alkalb were previously dated via the \(^{40}\)Ar/\(^{39}\)Ar method\(^{5,7}\). Those dates have been recalculated using a 28.201 Ma monitor age for the Fish Canyon sanidine\(^{14}\). Recalculations (Supplementary Information 3) yield a 29.78 ± 0.12 Ma age for the Green Tuff, 29.66 ± 0.14 Ma age for the SAM Ignimbrite, and 29.67 ± 0.08 Ma age for Iftar Alkalb (Fig. 2). Previous \(^{40}\)Ar/\(^{39}\)Ar ages\(^{5,7,11}\) from the Shibam Kawkabam Ignimbrite (30.35 ± 0.13 Ma), Kura’a Basalt (30.22 ± 0.26 Ma), Akraban Andesite (29.80 ± 0.08 Ma), an overlying small-volume rhyolitic tuff (28.58 ± 0.14 Ma) and ignimbrite (28.18 ± 0.10 Ma), and the Bayt Mawjan Ignimbrite (27.85 ± 0.12 Ma) have also been recalculated and are compiled and presented here as a revised chronostratigraphy of the Northern Yemen flood volcanics (Fig. 2).
+
+Discussion
+
+Short-Term Accumulation Rates
+
+Elements that are normally incompatible during magma differentiation (e.g., U, Nb, Th, Y and Hf) and the europium anomaly (Eu/Eu*) in rare earth element patterns resulting from feldspar fractionation are useful indicators of magma differentiation. Assuming both elements remain incompatible, more differentiated rhyolites will evolve towards higher Th/Y ratios while Eu/Eu* will decrease with continued feldspar crystallization\(^{15}\). With a few exceptions, zircons dated via CA-TIMS for these units show the same trend: the least evolved zircon with the highest Eu/Eu* and lowest Th/Y values
+are older than the most evolved zircon by 0.01 ± 0.16 Ma in the Escarpment Ignimbrite, 0.02 ± 0.09 Ma in the SAM Ignimbrite, and 0.07 ± 0.17 Ma in the Sana’a Ignimbrite. Thus ages for zircon crystals spanning the full geochemical ranges are statistically indistinguishable, suggesting that these large volume magmas were rapidly differentiated within \(10^3\) to \(10^4\) years. Eu/Eu* and Th/Y are not correlated for zircons in the Iftar Alkalb mega-breccia and there is no age relationship between the most and least evolved zircons (Fig. 4), further supporting that the zircons in Iftar Alkalb are of a mixed xenolithic or antecrystic origin.
+
+Short-term accumulation rates were calculated for 50, 100, and 400 kyr of residence for the Escarpment, SAM, and Sana’a Ignimbrites based on the trace element concentrations and CA-TIMS U-Pb zircon dates. For 50 kyr residence, short-term accumulation rates are \(7.2 \times 10^{-3}\) km\(^3\)/yr, \(4.8 \times 10^{-2}\) km\(^3\)/yr, and \(3.2 \times 10^{-2}\) km\(^3\)/yr for the Escarpment, SAM, and Sana’a Ignimbrites, respectively. For 100 kyr residence, short-term accumulation rates are \(3.6 \times 10^{-3}\) km\(^3\)/yr, \(2.4 \times 10^{-2}\) km\(^3\)/yr, and \(1.6 \times 10^{-2}\) km\(^3\)/yr for the Escarpment, SAM, and Sana’a Ignimbrites, respectively. For 400 kyr residence, short-term accumulation rates are \(9.0 \times 10^{-4}\) km\(^3\)/yr, \(6.0 \times 10^{-3}\) km\(^3\)/yr, and \(4.0 \times 10^{-3}\) km\(^3\)/yr for the Escarpment, SAM, and Sana’a Ignimbrites, respectively. Upper estimates of \(7.2 \times 10^{-3}\) to \(3.2 \times 10^{-2}\) km\(^3\)/yr for 50 kyr residence and \(3.6 \times 10^{-3}\) to \(2.4 \times 10^{-2}\) km\(^3\)/yr for 100 kyr residence are similar to those calculated for other rapidly assembled large-volume silicic systems (e.g., Yellowstone supereruptions\(^{16,17}\) and Oruani eruption within the Taupo volcanic zone\(^{18}\)). The most conservative estimates using 400 kyr residence (\(9.0 \times 10^{-4}\) to \(6.0 \times 10^{-4}\) km\(^3\)/yr) are similar to but lower than the minimum calculated magma flux from Yellowstone (\(2.8 \times 10^{-3}\) km\(^3\)/yr for the 280 km\(^3\) Mesa Falls Tuff\(^{17}\)).
+Long-Term Magma Flux
+
+U-Pb zircon dating shows that three sequential eruptions of Afro-Arabian silicic volcanics – the Escarpment Ignimbrite, the Green Tuff and SAM Ignimbrite, and Sana’a Ignimbrites – were collectively emplaced within a timespan of 48 ± 34 kyr (calculated using the square root of the sum of the uncertainties), yielding a magma flux of 5.29 x \(10^{-2}\) to 3.09 x \(10^{-1}\) km\(^3\)/yr for 4,339 km\(^3\) DRE. The estimated minimum total eruptive volume for the entirety of the Main Silicics phase is 8,633 km\(^3\) DRE over a duration of 130 ± 150 kyr, constrained by the ages of the Akraban Andesite and Iftar Alkalb, which yield a lower magma flux of 3.05 x \(10^{-2}\) to 6.64 x \(10^{-2}\) km\(^3\)/yr. Magma flux for other regions of the Afro-Arabian province, such as the Ethiopian stratigraphy, are difficult to constrain. While there was wide-scale silicic volcanism following the termination of the main pulse of flood basalt emplacement\(^{19,20}\), unit volume estimates outside of Northern Yemen remain sparse due to poor exposure and post-emplacement tectonic disruption.
+
+Notably, a series of silicic supereruptions in the Tana Basin, Ethiopia\(^{21}\) have recently been dated at 31.108 ± 0.020 to 30.844 ± 0.027 Ma with an estimated minimum eruptive volume of 2,000 to 3,000 km\(^3\), corresponding to a magma flux of 0.8 to 1.1 x \(10^{-2}\) km\(^3\)/yr.
+
+Magma fluxes of basaltic and andesitic systems are thought to be higher than those of silicic systems by up to two orders of magnitude\(^4\). Average fluxes in silicic systems are calculated to be highest for continental arcs (\(4.90 \pm 0.15 \times 10^{-3}\) km\(^3\)/yr) followed by oceanic arcs (\(4.50 \pm 0.79 \times 10^{-3}\) km\(^3\)/yr), continental rifts (\(4.48 \pm 0.86 \times 10^{-3}\) km\(^3\)/yr), continental hotspots (\(1.29 \pm 0.25 \times 10^{-3}\) km\(^3\)/yr), and continental volcanic fields (\(6.47 \pm 1.96 \times 10^{-4}\) km\(^3\)/yr). The magma flux of the Main Silicics phase of the Northern Yemen
+section of the Afro-Arabian province is most similar to - but notably higher than - the magma fluxes of Taupo (1.15 x \(10^{-2}\) km\(^3\)/yr; ref. 22), the silicic portion of Kamchatka (1.05 x \(10^{-2}\) km\(^3\)/yr, ref. 23) and Quaternary phonolites from the Kenya rift valley (1.20 x \(10^{-2}\) km\(^3\)/yr; ref. 22). Our findings are consistent with observations at other large-volume silicic systems that record rapid periods of differentiation and magma reservoir assembly superimposed on lower background fluxes. While some silicic systems have produced more voluminous individual eruptions (e.g., Fish Canyon Tuff with 4,500 km\(^3\) DRE\(^{24}\)), and larger cumulative eruptive volumes over longer time intervals (e.g., Paraná-Etendeka LIP with 20,000 to 35,000 km\(^3\) over 6 Myr\(^{25,26}\)), the eruptions of the Main Silicics phase in Northern Yemen represent the largest long-term flux of silicic volcanism on Earth.
+
+Afro-Arabian volcanism and Oligocene Environmental Change
+
+Some volcanic provinces appear to coincide with major global environmental change and mass extinctions (e.g., Siberian Traps, Karoo-Ferrar, Emieshan and Central Atlantic LIPs), yet others, even those with silicic supereruptions (e.g., Paraná-Etendeka LIP), do not\(^{27}\). Afro-Arabian silicic volcanism represents the greatest flux of large-volume silicic magma eruption on Earth and is correlated to 10 to 15 cm thick tephra layers located >2,700 km away in the Indian Ocean\(^{28}\) (Fig. 2), suggesting volcanic fallout on a near-global scale. The timing of these supereruptions in relation to several Rupelian-aged cooling events that have been identified in Chrons C12 (Oi1a, Oi1b, and Oi2\(^{29,30}\)) and C10 (Oi2* and Oi2a\(^{29,30}\)) indicate that the perturbations in \(δ^{18}O\) and \(δ^{13}C\) pre-date the eruptions\(^{31,32}\) (Fig. 2). Other silicic supereruptions, such as the ~31 Ma caldera-forming eruptions in the Tana Basin\(^{21}\) and ~28 Ma eruption of the Fish Canyon Tuff\(^{24}\), likewise
+do not coincide with global cooling events. Challenges remain in discerning the various roles of the tempo, volatile budget, eruption mechanism, and volume of magma extruded from large igneous provinces and their effect on global environmental change. However, robust temporal constraints continue to provide critical insight into this relationship.
+
+Implications for Geomagnetic Polarity Time Scale
+
+Previous efforts have been made to correlate Oligocene Afro-Arabian volcanic deposits with the geomagnetic polarity time scale\( ^{5,33} \) but those were unable to unambiguously distinguish between the GPTS of Cande and Kent\(^8\) and Huestis and Acton\(^9\). Recent studies on the Oligocene magnetic polarity sequence have utilized astronomical age models\(^{29}\), radio-isotope age models\(^{30}\), recalculations of the Cande and Kent\(^8\) GPTS using updated \(^{40}\mathrm{Ar}/^{39}\mathrm{Ar}\) flux monitor ages\(^{34}\), and a combination of all three\(^{30}\). One of the lingering issues with distinguishing between an appropriate method for determining the Rupelian age (33.9 to 28.1 Ma) is the lack of tie points from radio-isotopic dates. The Rupelian/Chattian boundary Global Boundary Stratotype Section and Point (GSSP) records a nearly continuous record of astronomically-tuned magnetostratigraphy for the Oligocene but only provides one tie-point for the Rupelian for the uppermost Chron C12r with a gap between 31.8 ± 0.2 Ma and 27.0 ± 0.1 Ma\(^{30,35}\). The 2012 Geologic Time Scale for the Paleogene\(^{30}\) favored an integrated radio-isotope, GPTS, and cyclostratigraphy model with 6\(^{\text{th}}\)-order polynomial fit to produce a complete C-sequence. The C11n.1r Subchron is estimated to have a duration of 0.050 Ma with a -0.654 Ma discrepancy between radio-isotopic and astronomic age models\(^{30}\). The only discrepancy between the combined age model of the 2012 Geologic Time Scale and
+new 2020 Geologic Time Scale for the time range of interest is a shift of the base of Chron C12n to 30.977 Ma from 31.034 Ma^{30,36}.
+
+We propose that the 29.728 ± 0.017 Ma \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) zircon age of the SAM Ignimbrite and 29.67 ± 0.13 Ma \(^{40}\mathrm{Ar}/^{39}\mathrm{Ar}\) sanidine age of Iftar Alkalb - further constrained to 29.67 ± 0.13 Ma by the 29.707 ± 0.025 Ma \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) age of the Sana’a Ignimbrite - can be used as tie-points for the GPTS. Our chrono- and magnetostratigraphy are definitively in agreement with the Cande and Kent^{8} GPTS (Fig. 2). Discrepancies between our results and the 2020 Geologic Time Scale arise from the sparsity of radio-isotope dates for the Rupelian coupled with the short duration of the C11n.1r Subchron. Our findings are within the 0.654 Ma discrepancy between the radio-isotopic and astronomic age models and could thus serve as robust tie points for future time scale calibrations.
+
+Methods
+
+Samples from the Sana’a area of Northern Yemen were previously collected and described^{10} (Fig. 1). Paleomagnetic data was measured on 587 oriented drill cores collected at 71 sites^{5} (Fig. 1). Zircon U-Pb petrochronology was undertaken at the Boise State University Isotope Laboratory. Zircon crystals from the Escarpment, SAM, and Sana’a Ignimbrites, and Iftar Alkalb were separated using standard magnetic and heavy liquid techniques and annealed at 900\(^\circ\)C for 60 hours. Zircons were imaged using a JEOL T-300 scanning electron microscope (SEM) fitted with a Gatan Mini cathodoluminescence (CL) detector and JEOL back-scattered electron (BSE) detector under 15 kV probe current and 2 mA accelerating voltage operating conditions (Supplementary Information 1). Trace element analyses and preliminary U-Pb dating for 31 to 95 crystals per unit (Supplementary Information 2) were performed using a
+ThermoElectron X-Series II quadrupole inductively coupled plasma mass spectrometer (ICP-MS) and New Wave Research UP-213 Nd:YAG UV (213 \( \mu \)m) laser ablation system with a 10 Hz at 5 J/cm\(^2\) pulsed laser and 15 \( \mu \)m spot size. NIST SRM-610 and SRM-612 glasses were used as standards for trace element concentrations and Plešovice zircon standard\(^{37}\) was used for U-Pb calibration. Zircon standards were measured every 10 unknowns; glass standards were analyzed at the beginning of two 109-spot cycles.
+
+A total of 32 crystals from the four units were selected for CA-TIMS analysis on the basis of morphology, zoning, chemistry, and preliminary \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) dates. After chemical abrasion\(^{38}\) in a single aggressive high-temperature step, residual crystals were rinsed and spiked with ET535 tracer solution\(^{39,40}\), dissolved in concentrated HF, converted to a chloride matrix, and U and Pb purified by ion chromatography following the detailed procedures described in Macdonald et al.\(^{41}\). High-precision isotope dilution U and Pb isotope ratio measurements were made using a single Re filament silica gel technique on an Isotopx Isoprobe-T multi-collector thermal ionization mass spectrometer (TIMS) equipped with an ion-counting Daly detector (Supplementary Information 2). Dates are calculated using the decay constants of Jaffey et al.\(^{42}\). Analytical uncertainties on dates are reported to 2\( \sigma \) and propagated using the algorithms of Schmitz and Schoene\(^{43}\).
+
+**Data Availability**
+
+Supplementary Information 1 contains cathodoluminescence (CL) images of zircon crystals analyzed by LA-ICP-MS and CA-TIMS. Supplementary Information 2 contains details on the calculation of CA-TIMS \(^{206}\mathrm{Pb}/^{238}\mathrm{U}\) dates and zircon LA-ICP-MS
+geochronologic and trace element concentrations. Supplementary Information 3 contains details on the recalculation of \(^{40}\mathrm{Ar}/^{39}\mathrm{Ar}\) ages.
+
+References
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+
+**Acknowledgments**
+
+This material is based upon work supported by the National Science Foundation under Grant Nos. EAR-1759200 and EAR-1759353. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. We thank the AGeS program, members of the Boise State University Isotope Geology Laboratory for support with sample preparation, and B.D. Cramer for insightful discussions.
+Author Contributions
+
+J.E.T., I.A.U, and M.S. designed the research project as part of the AGeS2 Geochronology Program. Sample material was provided by I.A.U. C.W. and J.E.T. prepared samples and analyzed the data with help from M.S. J.E.T. wrote the manuscript with support from I.A.U. Progress was overseen by I.A.U, the PhD thesis advisor of J.E.T.
+
+Competing Interests
+
+The authors declare no competing interests.
+
+Additional Information
+
+Correspondence and requests for materials should be addressed to J.E.T.
+Figure 1. Schematic volcanic stratigraphy and paleomagnetic sampling profiles of volcanic units emplaced during Oligocene bimodal volcanism in Northern Yemen (after ref. 5,10). Section abbreviations, from west to east, are: ESC: Escarpment, BM: Bayt Mawjan, A: Section A, BB: Bayt Baws, JS: Jabal Shahirah, SK: Shibam Kawkabam, WD: Wadi Dhar, and JK: Jabal Kura’a. Sites are annotated with magnetic polarity data5 where white and black are reverse and normal polarity, respectively. Sites outlined in boxes denote those dated by \(^{40}\)Ar/\(^{39}\)Ar (ref. 5,7,11) or \(^{206}\)Pb/\(^{238}\)U geochronology (data presented here) and ages are shown in detail Fig. 2. Ages and sites denoted with an asterisk (*) are from correlative units in Ethiopia7.
+![Stratigraphic column and age diagram showing volcanic units, ages, and magnetic polarity](page_186_232_1207_1536.png)
+Figure 2. Composite stratigraphy of Northern Yemen bimodal flood volcanic units is shown using the average thickness of each unit\(^{10}\). Four units have been correlated to Indian Ocean tephra layers\(^{28}\) and are annotated by the colored symbols. Paleomagnetic data\(^{5}\) are indicated where white = reverse polarity and black = normal polarity. Dashed lines show the approximate locations of the paleomagnetic reversals in the stratigraphy. Minor Unit #4 and AMPH 2 are from different sample localities and both underlie the Bayt Mawjan Ignimbrite, but their stratigraphic order relative to each other is unknown. Symbols for \(^{40}\)Ar/\(^{39}\)Ar ages\(^{5,7,11}\) are colored based on polarity. The grey field highlights the \(^{40}\)Ar/\(^{39}\)Ar and \(^{206}\)Pb/\(^{238}\)U ages with associated uncertainties of two pulses of Afro-Arabian silicic volcanism. The Escarpment Ignimbrite, Green Tuff, SAM and Sana’a Ignimbrites, and Iftar Alkalb are a set of normal to reversed polarity that encompass the duration of the C11n.1r Subchron and are compared to the GPTS of Cande and Kent\(^{8}\) as reported the 2020 Geologic Time Scale\(^{36}\). Benthic foraminiferal \(^{18}\)O and \(^{13}\)C curves are from the 2020 Geologic Time Scale\(^{36}\).
+Figure 3. \(^{40}\)Ar/\(^{39}\)Ar and \(^{206}\)Pb/\(^{238}\)U ages for the main silicic units from the Northern Yemen section of the Afro-Arabian volcanic province (subset A). The grey field highlights the ages and associated uncertainties (2\( \sigma \)) of the Escarpment Ignimbrite, Green Tuff, SAM and Sana’a Ignimbrites, and Iftar Alkalb. Ranked single-zircon and \(^{206}\)Pb/\(^{238}\)U dates are shown for the Escarpment, SAM, and Sana’a Ignimbrites. Horizontal grey bars outlined in black indicate the weighted mean \(^{206}\)Pb/\(^{238}\)U ages with 95% confidence interval. B. Minimum total eruptive volume DRE (\( \text{km}^3 \)) values are from on-land and correlated deep-sea tephra layers found in Ocean Drilling Program cores from the Indian Ocean, Leg 115\(^{1,10,28}\).
+Figure 4. Bivariate plots showing Th/Y versus Eu/Eu* for zircon crystals are denoted by age, dating method, and inclusion in final age calculations. Zircons >33 Ma (from preliminary LA-ICP-MS dating, average \(2\sigma\) uncertainty \(±\) 3 Ma) are denoted by diamond symbols. Non-luminescent (CL-dark) zircon crystals from the Escarpment Ignimbrite and Iftar Alkalb are denoted by black symbols. Subsets B-E show Th/Y versus Eu/Eu* in detail for the Escarpment Ignimbrite (subset B), SAM Ignimbrite (subset C), Sana’a Ignimbrite (subset D), and Iftar Alkalb (subset E).
+Figures
+
+![Schematic volcanic stratigraphy and paleomagnetic sampling profiles of volcanic units emplaced during Oligocene bimodal volcanism in Northern Yemen](page_128_153_1047_693.png)
+
+Figure 1
+
+Schematic volcanic stratigraphy and paleomagnetic sampling profiles of volcanic units emplaced during Oligocene bimodal volcanism in Northern Yemen (after ref. 5,10). Section abbreviations, from west to east, are: ESC: Escarpment, BM: Bayt 429 Mawjan, A: Section A, BB: Bayt Baws, JS: Jabal Shahirah, SK: Shibam Kawkabam, WD: Wadi Dhar, and JK: Jabal Kura’a. Sites are annotated with magnetic polarity data5 where white and black are reverse and normal polarity, respectively. Sites outlined in boxes denote those dated by 40Ar/39Ar (ref. 5,7,11) or 206Pb/238U geochronology (data presented here) and ages are shown in detail Fig. 2. Ages and sites denoted with an asterisk (*) are from correlative units in Ethiopia7.
+Figure 2
+
+Composite stratigraphy of Northern Yemen bimodal flood volcanic units is shown using the average thickness of each unit10. Four units have been correlated to Indian Ocean tephra layers28 and are annotated by the colored symbols. Paleomagnetic data5 are indicated where white = reverse polarity and black = normal polarity. Dashed lines show the approximate locations of the paleomagnetic reversals in the stratigraphy. Minor Unit #4 and AMPH 2 are from different sample localities and both underlie the
+Bayt Mawjan Ignimbrite, but their stratigraphic order relative to each other is unknown. Symbols for 40Ar/39Ar ages5,7,11 are colored based on polarity. The grey field highlights the 40Ar/39Ar and 206Pb/238U ages with associated uncertainties of two pulses of Afro-Arabian silicic volcanism. The Escarpment Ignimbrite, Green Tuff, SAM and Sana’a Ignimbrites, and Iftar Alkalb are a set of normal to reversed polarity that encompass the duration of the C11n.1r Subchron and are compared to the GPTS of Cande and Kent8 as reported the 2020 Geologic Time Scale36. Benthic foraminiferal o18O and o13C curves are from the 2020 Geologic Time Scale36
+
+![Bar and line graph showing ages and eruptive volumes for various volcanic units](page_186_370_1017_496.png)
+
+Figure 3
+
+40Ar/39Ar and 206Pb/238U ages for the main silicic units from the Northern Yemen section of the Afro-Arabian volcanic province (subset A). The grey field highlights the ages and associated uncertainties (2) of the Escarpment Ignimbrite, Green Tuff, SAM and Sana’a Ignimbrites, and Iftar Alkalb. Ranked single-zircon and 206Pb/238U dates are shown for the Escarpment, SAM, and Sana’a Ignimbrites. Horizontal grey bars outlined in black indicate the weighted mean 206Pb/238U ages with 95% confidence interval. B. Minimum total eruptive volume DRE (km3) values are from on-land and correlated deep-sea tephra layers found in Ocean Drilling Program cores from the Indian Ocean, Leg 1151,10,28.
+Figure 4
+
+Bivariate plots showing Th/Y versus Eu/Eu* for zircon crystals are denoted by age, dating method, and inclusion in final age calculations. Zircons >33 Ma (from 4preliminary LA-ICP-MS dating, average 2 uncertainty ± 3 Ma) are denoted by diamond symbols. Non-luminescent (CL-dark) zircon crystals from the Escarpment Ignimbrite and Iftar Alkalb are denoted by black symbols. Subsets B-E show Th/Y versus Eu/Eu* in detail for the Escarpment Ignimbrite (subset B), SAM Ignimbrite (subset C), Sana’a 468 Ignimbrite (subset D), and Iftar Alkalb (subset E).
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformation1.docx
+• SupplementaryInformation2.xlsx
+• SupplementaryInformation3.docx

0b813482168c9364c8a5829646c9bed96c4d8b16dc8516b90be2106af51fc4ec/peer_review/peer_review.md

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+Peer Review File
+
+Genomic signatures of pre-resistance in Mycobacterium tuberculosis
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This is a well conducted and very interesting piece, and the authors should be congratulated. They use a number of sound techniques to argue that lineage 2 strains acquire resistance faster than lineage 4 strains. They also identify 3 variants in lineage 4 that are associated with an increased risk of resistance acquisition.
+
+I do however have a small number of questions based around two themes:
+
+1. The claim sampling dates stretch over 17 years is true, but the spirit of the claim is somewhat undermined by the data presented in the appendix where the reader learns that almost 2/3 of samples were from a single year. What are the sampling years for L2 and L4 strains? In the introduction the authors outline the risk of 'insufficient temporal span' in a data set. Can they please reassure me that the extremely uneven sampling times in this data set overcome the described pitfalls? If not, this needs to be listed explicitly as a limitation in the discussion.
+
+2. In line 261 the authors claim to have 'conclusively' shown that L2 acquired resistance faster than L4. I agree that a good case has been made but I would quibble with the claim that it is conclusive. There are potential confounders that have not been mentioned. For example, do we know if L2 and L4 affect different populations, such as different age groups? A lineage introduced more recently might be more strongly associated with younger patients. Different behaviours between patient groups could be a confounder. Do the authors have data on patient ages? Following on from this, is it known when L2 was introduced to Peru? The authors touched briefly on immigration patterns in the discussion, but is more known? It remains entirely possible that resistance in L2 was 'nurtured' in a different country, under different health care system conditions, and imported. The L2 tree appears quite narrow, suggesting relatively close genomic linkage between strains. Was there a founder effect for these samples? Some of this is touched upon in the discussion, but It would be helpful to say more.
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript Genomic signatures of Pre-Resistance in Mycobacterium tuberculosis was well written and will be of interest to both researchers in the field and to a wider audience. I have no major concerns about the results and these will be of some importance.
+
+My only (minor) concerns are:
+
+The sharing of sample metadata and associated accession numbers. Apart from project IDs that can be used to access the raw sequence data, unless I missed it, the authors have not provided sample metadata in the form of a supplementary file. This should be rectified before submission as this will be a dataset that will be useful to researchers around the world
+
+The authors have not made any of their code available online. I would encourage the authors to avoid using a statement like “Variants that did not meet the quality criteria were filtered using a combination of BCFtools filter and custom scripts in Python v3.7.3” without making the code available for review. It would also be useful to see the R code used to perform the analyses in the study, particularly that which made use of the BactDating and Survival packages.
+
+I’m unclear how the genome wide association analysis was performed. Did you use a package like pyseer or was this also done in R?
+
+In the discussion the authors state “Here we demonstrate conclusively that lineage 2 acquired resistance to antibiotics more rapidly than lineage 4.” Isn't this the other way round?
+
+Figure 1: Would it be possible to show the 95% CI for each node as error bars as per BEAST?
+
+Figure 2: In the legend the authors wrote Arrows represent the approximated time of antibiotic distribution.” Did they mean antibiotic introduction?
+Reviewer #3 (Remarks to the Author):
+
+The manuscript presents the analysis of a large collection of culture positive samples from Perú, some belonging to a population-based study in an area in Lima and the remaining belonging to sparse sampling in Perú over 17 years. The authors reconstruct the phylogenetic relationships between strains and then track the emergence of drug resistance associated mutation combining mutation mapping to the phylogenetic branches and different association analyses. The aim is to identify mutations predisposing for acquisition of additional resistance (pre-resistance). The authors identify several patterns including: 1) the role of mono-INH in amplifying drug resistance; 2) lineage 2 is associated with resistance and 3) identification of a region in lppP involved in pre-resistance.
+
+While the approach used by the authors is novel (scanning a dated phylogenetic tree to identify emergence of resistance at the single nucleotide level) the results fall sort in terms of what is stated in the title and abstract. Below I will try to clarify my concerns and help the authors to improve the manuscript:
+
+MAJOR
+
+1.)While scientifically correct I don’t find the novelty in two of the conclusions. INH precedes RIF and this has been known for a while. It is also one of the reasons why GenExpert focuses on RIF (the other is that mutations for RIF are highly concentrated in rpoB and have high explanatory power).
+
+2)The authors focus a lot on the missing INH monoresistance cases when using Xpert (which only looks for RIF) (L277). However they don’t explain that culture DST is still gold standard and carried out in many places (albeit with the known diagnostic delays problems). To be fair, authors should mention that INH monoresistance can be detected in most places using culture DST but given the diagnostic delays associated this maybe too late to avoid amplification of resistance
+
+3)The other observation, lineage 2 is associated with resistance, is also known for a while although it is always difficult to distinguish between social and host factors of TB settings where lineage 2 predominates or pathogen factors. The present analysis shows in a controlled manner that under similar conditions lineage 2 is still associated with, what is a nice corroboration.
+
+4)Sampling biases are of course always a danger in this kind of analysis. The authors recognized and showed how they match-and-mix different dataset to achieve enough temporal signal. However while the 2009 population-based analysis looks unbiased, probably is not the same for the rest of samples which are taken from convenience datasets. Can the authors break down in a table all datasets and specify the % susceptible, % rif monoresistance, % INH monoresistance, % MDR/XDR. A well balanced susceptible/resistance dataset is important to avoid over/under-representation of drug resistant associated branches.
+
+5)The fact that the authors find a good correlation between introduction of a drug and their estimated timing of drug associated mutations is a nice proof of concept that their dating approach works. In the same lines, and if possible, can the authors comment on the timing for fitness compensatory mutations in rpoc? I think it will be novel to add some idea on when compensatory mutations started to circulate in the dataset and this is something that has not been shown before. In other words, are compensatory mutations associated branches arising shortly after the introduction of RIF or are they a more recent phenomenon and why?
+
+6)Some questions worth exploring in your datasets. You say that rif mono-resistance is not frequent (L215). In many settings frequency is usually associated with relapse cases and also to rare rpoB mutations. When you say it is not frequent is that based on DST or on WGS predictions?. Rare mutations can cause false negative results (historically called “disputed mutation”) in some systems and you may have missed some if not looking for those mutations?
+
+7)In general, is there a good correlation between your DST and WGS-based DST?
+
+8)I am still worried about a major assumption that may bias the analyses. The analysis assumes that the great majority of cases are not imported and thus not biasing the timing of emergence of drug resistance associated branches. But this is difficult to confirm as there is no data from the authors about this. Can
+the authors specify how much information they have around imported cases in the dataset? I understand that particularly for the convenience samples it is difficult to tell. In that case maybe a phylogeny of the dataset with globally representative isolates may discern introductions (particularly those generating new drug resistance branches) from local emergence of resistance?
+
+9) Not sure if survival analysis is adequate in this case, as it assumes that you start with a known number of individuals/populations and you can follow them through time. But here the starting population is unknowns and thus results will be highly biased by sampling. I am wondering how robust is to the use fo subsets. For example if you downsample the 2009 dataset?
+
+10) Then I will focus on the most interesting part of the work which is the identification of pre resistance mutations. What makes susceptible Mtb strains predisposed to acquire resistance mutations? The authors scan the phylogeny to identify such mutations in a novel approximation also combined with survival analysis. The authors identify lppP , esxO and an intergenic SNP. My first concern is that one of the two hits is a synonymous SNP in esxO. First, how do the authors explain a hit in a synonymous SNP? If this hit is spurious (as no effect is expected from a syn SNP) then it calls into question the approach to identify hits?. One explanation maybe that the hit generates a new transcriptional start site, is there any hint by looking at the sequence data that a new regulatory region has been created? Is it homoplastic (what will reinforce the notion that is associated with selection)? Alternatively, esX family gene members align poorly when using short reads because repeated sequences along the genome. Can the authors look at individual alignments and confirm there is no such error here? Otherwise how do the authors explain a synonymous hit?
+
+11) About lppP- it is only present in 1.7%. By itself has a low explanatory power and not sure if enough to justify the title of the manuscript (which is basically based on this hit).
+
+12) In addition. This hit and others cannot be validated using the Russian dataset which is understandable given the sample size and that the genetic make up of the Russian dataset is really different. Is there any evidence (even if not statistically significant) for the presence of any of the hits in the Russian dataset?
+
+13) However an extraordinary claim needs extraordinary evidence. I suggest the authors look for alternative validations of the hit. I can think in several ways but one relatively easy (if you have access to the isolates) is to measure and show that isolates carrying that particular mutation have a higher MIC for INH that phylogenetically related isolates without the mutation. Alternatively authors may look for publications in which mutant libraries (with transposon) are tested against first line drugs. Authors can also identify alternative datasets where this can be tested as there are many around nowadays or at the very least authors can look in the global database and see the prevalence of the mutation across continents. The ideal validation will be a KO mutant or an allelic mutant but I understand this is extraordinarily difficult and time-consuming in the case of Mtb.
+
+14) In general, and maybe reflecting my ignorance, looks like p-values in the analysis of pre-resistance mutations are extremely low. This suggests a clear link and in this case also a strong effect. This is good but given that many groups have been working on this and had problems to identify these regions I wonder where the difference resides to obtain such large effects?
+
+15) Regarding the Russian dataset I don't see the full value of incorporating the analysis. It confirms some of the findings but looks like it has more problems than advantages for your purposes. It cannot be used to validate as discussed above. But also it is not dated and thus it is difficult to compare to the main dataset like in Fig4 where one panel is based on years and the other on branch lengths. It is not possible to compare the trajectories in such a case.
+
+16) Even if comparable the Kaplan Meier curve is quite different in both cases and I am struggling to understand why? One explanation is different biases in the dataset (being enriched in MDR/XDR and very few sensitive and monoresistant?). In general Figure 4 should be in the same scale so it can be properly compared and interpret
+
+Minor
+
+1) Can you specify the substitution rate obtained for each lineage and see if it compares well with published rates?
+2)L127. The authors should clarify that 1% frequency refers to the SNP in the analysed dataset and not in the bulk sequencing of individual cultures
+3)L428. Additional details on the ancestral reconstruction algorithm would be welcome, i.e. reversion penalties
+Response to reviewers' comments:
+
+We would like to thank the reviewers for their time and insightful and constructive comments. We believe the paper has been improved as a result, which is reflected in the fact that many of their suggestions have now been included as main figures, tables or entire sections.
+
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This is a well conducted and very interesting piece, and the authors should be congratulated. They use a number of sound techniques to argue that lineage 2 strains acquire resistance faster than lineage 4 strains. They also identify 3 variants in lineage 4 that are associated with an increased risk of resistance acquisition.
+
+I do however have a small number of questions based around two themes:
+
+R1.1. The claim sampling dates stretch over 17 years is true, but the spirit of the claim is somewhat undermined by the data presented in the appendix where the reader learns that almost 2/3 of samples were from a single year. What are the sampling years for L2 and L4 strains? In the introduction the authors outline the risk of 'insufficient temporal span' in a data set. Can they please reassure me that the extremely uneven sampling times in this data set overcome the described pitfalls? If not, this needs to be listed explicitly as a limitation in the discussion.
+
+The reviewer raises an important point regarding the possible biases when calibrating a phylogeny using the time of collection of the isolates at the tips of the tree. As the reviewer points out, most of our samples were collected as part of a population level study in 2009-2010. Even though the root-to-tip regression for assessing temporal signal can be biased by a very uneven sampling time, by performing the date-randomization test we clearly show that we can confidently infer evolutionary parameters using our phylogeny, an evolutionary model and the study’s sampling window when compared to a random permutation of sampling dates. We discuss this point further in the Results section, “Phylogenetic analysis and drug resistance emergence” subsection, line 151: “Before time calibration of the phylogeny, the presence of enough evolutionary change to reliably infer the model parameters was tested. First, a linear regression of the number of substitutions from the root and the sampling times was fitted to confirm a positive association between time and evolutionary change. As an uneven sampling may bias the root-to-tip regression [28], a date-randomization test was additionally performed using the full Bayesian model implemented in BactDating [29] on the original dataset and in 100 randomizations where the sampling times were permuted, representing the expectations of the model parameters in the absence of temporal signal. The substitution rate estimated for the original dataset and for the 100 randomizations was compared to verify a lack of overlap between the 95% credible intervals.” The confirmation of a temporal signal both with linear regression and with BactDating permutation as described make us confident that we have overcome any bias due to uneven temporal sampling.
+As suggested, to show lineage-specific sampling times we have now added the distribution of sampling times as histograms separately for lineage 2 (L2) and Lineage 4 (L4) as Supplementary Figure 2, referenced on line 115: “Both lineage 2 and lineage 4 showed a similar distribution of sampling dates (Supplementary Fig. 2)”
+
+R1.2. In line 261 the authors claim to have ‘conclusively’ shown that L2 acquired resistance faster than L4. I agree that a good case has been made but I would quibble with the claim that it is conclusive. There are potential confounders that have not been mentioned. For example, do we know if L2 and L4 affect different populations, such as different age groups? A lineage introduced more recently might be more strongly associated with younger patients. Different behaviours between patient groups could be a confounder. Do the authors have data on patient ages?
+
+To account for some of the potential confounders described by the reviewer, we have additionally explored the age distribution of the patients for L2 and L4 in a linear model. The mean age for patients with L4 was 33.3 (22-41 IQR), while for L2 the mean age was 30.4 (21-36 IQR). To explore the age differences further, we fitted a quasi-Poisson model, showing an incident rate on age higher for lineage 4 when compared to lineage 2, though with a very low estimate (lineage 4 estimate = 0.09, p = 0.001). Additionally, we explored whether age was associated to a higher risk of drug resistance acquisition by fitting a logistic regression model, and showed that age was not significantly associated with a higher risk of drug resistance acquisition in a logistic model (OR 0.999, 95%CI 0.994-1.003, p=0.69). We are grateful to the reviewer for this pertinent comment and feel that by addressing it with this further analysis we strengthened the paper. Indeed, given these new results, it is not probable that age is an important confounder in drug resistance acquisition for our dataset. This is reported in Results, subsection “Between lineage differences in drug resistance acquisition”, paragraph 4, as well as supplementary figure 9.
+
+In spite of the potential confounders included in the analysis, we agree with the reviewer that there can be other cofactors influencing the patterns we observe. Therefore, as suggested, we removed the word “conclusively” from the discussion.
+
+R1.3 Following on from this, is it known when L2 was introduced to Peru? The authors touched briefly on immigration patterns in the discussion, but is more known? It remains entirely possible that resistance in L2 was ‘nurtured’ in a different country, under different health care system conditions, and imported. The L2 tree appears quite narrow, suggesting relatively close genomic linkage between strains. Was there a founder effect for these samples? Some of this is touched upon in the discussion, but It would be helpful to say more.
+
+We agree with the reviewer that this is an important point, and therefore we added a phylogenetic tree showing the global context of our Peruvian dataset alongside publicly available samples from different countries. We subsetted the dataset as described in the Methods section, line L586. The results are shown in figure 4 and the subsection “Phylogeographic history of Mycobacterium tuberculosis in Peru”. We time calibrated the phylogeny and inferred the time of introduction, which for the biggest clades predated the
+advent of antibiotics. Given this analysis, we concluded that importation of drug resistant strains from different countries and health systems has not been wide enough to explain the differential patterns in drug resistance acquisition between lineage 2 and lineage 4. Apart from this, we acknowledge we may be missing important key importation events, and therefore we caution that this could still affect our results in the Discussion.
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript Genomic signatures of Pre-Resistance in Mycobacterium tuberculosis was well written and will be of interest to both researchers in the field and to a wider audience. I have no major concerns about the results and these will be of some importance.
+
+My only (minor) concerns are:
+
+R2.1 The sharing of sample metadata and associated accession numbers. Apart from project IDs that can be used to access the raw sequence data, unless I missed it, the authors have not provided sample metadata in the form of a supplementary file. This should be rectified before submission as this will be a dataset that will be useful to researchers around the world
+
+Sample metadata is now provided as part of Supplementary Data File 1. Any other metadata will be available upon request.
+
+R2.2 The authors have not made any of their code available online. I would encourage the authors to avoid using a statement like “Variants that did not meet the quality criteria were filtered using a combination of BCFtools filter and custom scripts in Python v3.7.3” without making the code available for review. It would also be useful to see the R code used to perform the analyses in the study, particularly that which made use of the BactDating and Survival packages.
+
+We agree with the reviewer on the importance of making code available, which was missing in our previous manuscript. All custom code is publicly available on GitHub (https://github.com/arturotorreso/mtb_pre-resistance.git), and the link is properly referenced in both Methods and Code Availability sections.
+
+R2.3 I’m unclear how the genome wide association analysis was performed. Did you use a package like pyseer or was this also done in R?
+
+The Cox regression GWAS was done in R, using the survival package. The code is available on GitHub https://github.com/arturotorreso/mtb_pre-resistance.git.
+
+R2.4 In the discussion the authors state "Here we demonstrate conclusively that lineage 2 acquired resistance to antibiotics more rapidly than lineage 4." Isn't this the other way round?
+
+The statement highlighted by the reviewer is correct: the results show that lineage 2 acquires resistance faster than lineage 4, which is shown in the Kaplan-Meir curves where the probability of remaining susceptible decreases earlier and faster for lineage 2.
+R2.5 Figure 1: Would it be possible to show the 95% CI for each node as error bars as per BEAST?
+
+To address this point we have included confidence intervals of the most relevant nodes (e.g., root, drug resistance nodes) in the main text and tables. Given the size of the phylogenetic tree, most nodes are very close to each other and thus adding confidence intervals onto nodes in the tree would make the graphic noisy and difficult to interpret.
+
+R2.6 Figure 2: In the legend the authors wrote Arrows represent the approximated time of antibiotic distribution.” Did they mean antibiotic introduction?
+
+Yes, although we acknowledge that the time of introduction of various drugs to different countries may vary, as well as the time for widespread use. Finding such historical data can be challenging, but the confidence interval around resistance emergence estimates should encompass the wide range of possible drug introduction dates. We have changed the legend of Figure 2 to use the more appropriate term “Introduction”, as suggested by the reviewer.
+
+Reviewer #3 (Remarks to the Author):
+
+The manuscript presents the analysis of a large collection of culture positive samples from Perú, some belonging to a population-based study in an area in Lima and the remaining belonging to sparse sampling in Perú over 17 years. The authors reconstruct the phylogenetic relationships between strains and then track the emergence of drug resistance associated mutation combining mutation mapping to the phylogenetic branches and different association analyses. The aim is to identify mutations predisposing for acquisition of additional resistance (pre-resistance). The authors identify several patterns including: 1) the role of mono-INH in amplifying drug resistance; 2) lineage 2 is associated with resistance and 3) identification of a region in lppP involved in pre-resistance.
+
+While the approach used by the authors is novel (scanning a dated phylogenetic tree to identify emergence of resistance at the single nucleotide level) the results fall sort in terms of what is stated in the title and abstract. Below I will try to clarify my concerns and help the authors to improve the manuscript:
+
+MAJOR
+
+R3.1 While scientifically correct I don't find the novelty in two of the conclusions. INH precedes RIF and this has been known for a while. It is also one of the reasons why GenExpert focuses on RIF (the other is that mutations for RIF are highly concentrated in rpoB and have high explanatory power).
+
+As the reviewer points out, several phylogenetic studies acknowledged in our work have shown that the emergence of INH resistance tends to precede that of RIF. But in our view those studies do not show that there is a higher risk of additional RIF resistance when isolates carry mutations that confer INH resistance, which our work shows by directly comparing the risk of emergence of RIF between INH-Resistance isolates and drug-susceptible ones. INH may historically have preceded RIF emergence because of other factors, including the earlier introduction of INH as
+treatment for tuberculosis. Our findings highlight that the likely consequence of the failing to detect INH monoresistance with the GenExpert is the rapid evolution of MDRTB.
+
+R3.2 The authors focus a lot on the missing INH monoresistance cases when using Xpert (which only looks for RIF) (L277). However they don’t explain that culture DST is still gold standard and carried out in many places )albeit with the known diagnostic delays problems). To be fair, authors should mention that INH monoresistance can be detected in most places using culture DST but given the diagnostic delays associated this maybe too late to avoid amplification of resistance
+
+We have now changed the discussion to reflect this point, specifically line L401: “Globally, rapid drug resistance surveillance is focused primarily on rifampicin, with the widely implemented GeneXpert MTB/RIF PCR based assay unable to detect isoniazid mono-resistance. Although drug susceptibility testing (DST) is the current gold standard for identification of drug resistance isolates and can detect isoniazid mono-resistance, known diagnostic delays associated with it may limit its use in reducing mono-resistance amplification [40,41].”
+
+R3.3 The other observation, lineage 2 is associated with resistance, is also known for a while although it is always difficult to distinguish between social and host factors of TB settings where lineage 2 predominates or pathogen factors. The present analysis shows in a controlled manner that under similar conditions lineage 2 is still associated with, what is a nice corroboration.
+
+We agree with the reviewer that some studies, both laboratory and epidemiological ones, have shown a differential rate of drug resistance acquisition between lineages, but many analyses have also contradicted this idea (eg., Glynn et al. 2002, Werngren et al. 2003). In our view, it remained unclear whether there was a lineage effect on drug resistance acquisition at the population level and over a large time span, and therefore we believe our analysis represents more than a corroboration of earlier results.
+
+1. Glynn, J. R., Whiteley, J., Bifani, P. J., Kremer, K. & van Soolingen, D. Worldwide Occurrence of Beijing/W Strains of Mycobacterium tuberculosis : A Systematic Review.Emerging Infectious Diseases 8,843–849 (2002).
+2. Werngren, J. & Hoffner, S. E. Drug-susceptible Mycobacterium tuberculosis Beijing genotype does not develop mutation-conferring resistance to rifampin at an elevated rate. Journal of Clinical Microbiology 41,1520–1524 (2003). 13
+
+R3.4 Sampling biases are of course always a danger in this kind of analysis. The authors recognized and showed how they match-and-mix different dataset to achieve enough temporal signal. However while the 2009 population-based analysis looks unbiased, probably is not the same for the rest of samples which are taken from convenience datasets. Can the authors break down in a table all datasets and specify the % susceptible, % rif monoresistance, % INH monoresistance, % MDR/XDR. A well balanced susceptible/resistance dataset is important to avoid over/under-representation of drug resistant associated branches.
+
+As the reviewer points out, a dataset enriched for resistance may bias the results. We have now added a supplementary table (supplementary table 1) with the information required by the reviewer regarding the rates of drug resistance isolates in each study. We have also replicated our analysis in a tree with only the 2009 population level dataset to confirm our results
+(supplementary figure 9). Our results show that, even though part of the dataset is enriched for drug resistance samples (in particular multi-drug resistance ones), the inclusion of a sufficiently high number of drug susceptible isolates reduces the potential biases.
+
+R3.5 The fact that the authors find a good correlation between introduction of a drug and their estimated timing of drug associated mutations is a nice proof of concept that their dating approach works. In the same lines, and if possible, can the authors comment on the timing for fitness compensatory mutations in rpoC? I think it will be novel to add some idea on when compensatory mutations started to circulate in the dataset and this is something that has not been shown before. In other words, are compensatory mutations associated branches arising shortly after the introduction of RIF or are they a more recent phenomenon and why?
+
+The reviewer raises an interesting point, and we agree that it would be relevant to understand the temporal dynamics of well known compensatory mutations, which could in turn help find novel ones. We have thus added a new subsection to Results: “The emergence of compensatory mutations”, and a main figure (Figure 3). As the reviewer suggested, and since it’s the best (if only) well known compensatory mechanism, we focused on non-synonymous mutations in the rpoC gene. We analyzed the emergence of non-synonymous rpoC mutations along the phylogeny, and found that the vast majority of mutations appear shortly after rifampicin resistance has been acquired, and keep accumulating through time.
+
+R3.6 Some questions worth exploring in your datasets. You say that rif mono-resistance is not frequent (L215). In many settings frequency is usually associated with relapse cases and also to rare rpoB mutations. When you say it is not frequent is that based on DST or on WGS predictions?. Rare mutations can cause false negative results (historically called “disputed mutation”) in some systems and you may have missed some if not looking for those mutations?
+
+Acknowledging that rifampicin resistance emergence can be caused by rare mutations, we compared the incidence of rifampicin resistance by MODS or by the proportion method in agar. The proportion or Rif mono resistance by DST was 2.77% (87/3134) and the proportion of Rif mono resistance by genotypic determination was 2.1% (65/3134). The differences between the two proportions are mostly due to the presence of isoniazid resistance conferring mutations when using molecular genotyping as has previously been described. Moreover, DST and molecular typing were congruent in 96% of the samples for rifampicin resistance. Given the strong correlation between phenotypic and genotyping resistance testing for Rif we believe that the impact of rare Rif mutations on our findings is not significant. This is now reflected in the text, Results section, subsection “Phylogenetic analysis and drug resistance emergence”, paragraph 2: “In addition to molecular typing of drug resistance, all isolates included in the analysis had drug susceptibility testing performed either by MODS or by the proportional method in agar. DST and molecular typing showed consistent results for 96% of the samples for rifampicin resistance and 92% for isoniazid”
+R3.7 In general, is there a good correlation between your DST and WGS-based DST?
+
+DST and molecular typing showed consistent results for 96% of the samples for rifampicin resistance and 92% for isoniazid. Most differences are caused by isoniazid resistance conferring mutations detected by molecular typing but showing a susceptible phenotype by DST.
+
+R3.8 I am still worried about a major assumption that may bias the analyses. The analysis assumes that the great majority of cases are not imported and thus not biasing the timing of emergence of drug resistance associated branches. But this is difficult to confirm as there is no data from the authors about this. Can the authors specify how much information they have around imported cases in the dataset? I understand that particularly for the convenience samples it is difficult to tell. In that case maybe a phylogeny of the dataset with globally representative isolates may discern introductions (particularly those generating new drug resistance branches) from local emergence of resistance?
+
+We strongly agree with the reviewer that the publication will greatly improve if we address the assumption that all drug resistance is acquired in Peru. Therefore, we have now included a phylogeny containing representatives of our lineages alongside a publicly available global dataset of Mycobacterium tuberculosis (Supplementary Data File 2). The results are shown in Figure 4 and subsection “Phylogeographic history of Mycobacterium tuberculosis in Peru”. In short, the main clades of our dataset are the result of introductions pre-dating the advent of antibiotics, and thus the influence of imported resistance is likely to be limited. Nevertheless, as stated in the Discussion, a possible bias cannot be completely ruled out.
+
+R3.9 Not sure if survival analysis is adequate in this case, as it assumes that you start with a known number of individuals/populations and you can follow them through time. But here the starting population is unknown and thus results will be highly biased by sampling. I am wondering how robust is to the use fo subsets. For example if you downsample the 2009 dataset?
+
+We agree with the reviewer that the method could potentially be biased by very uneven sampling of isolates, especially in drug resistance clusters. We repeated the analysis only on the population level 2009 dataset to address R3.4 point, and found similar results than when using the entire dataset.
+
+We use the last sensitive speciation event as the starting population for each occurrence of drug resistance. The proportional hazard assumption implies that hazard ratios are constant over time, and therefore as long as this assumption is not violated the method would still be valid even if the starting time is not completely known.
+
+R3.10 Then I will focus on the most interesting part of the work which is the identification of pre resistance mutations. What makes susceptible Mtb strains predisposed to acquire resistance mutations? The authors scan the phylogeny to identify such mutations in a novel approximation also combined with survival analysis. The authors identify lppP , esxO and an intergenic SNP. My first concern is that one of the two hits is a synonymous SNP in esxO. First, how do the authors explain a hit in a synonymous SNP? If this hit is spurious (as no effect is expected from a syn SNP) then it calls into question the approach to identify hits?. One explanation maybe that the hit generates a new transcriptional start site, is there any hint by looking at the sequence data that a new regulatory region has been
+created? Is it homoplastic (what will reinforce the notion that is associated with selection)? Alternatively, esX family gene members align poorly when using short reads because repeated sequences along the genome. Can the authors look at individual alignments and confirm there is no such error here? Otherwise how do the authors explain a synonymous hit?
+
+As pointed out in the Discussion, synonymous homoplastic polymorphisms in esx genes have been identified in the past, but we agree their relevance is still unknown, and further studies (including gene expression assays) should be performed.
+
+Regarding the quality of the alignments, we have now added Supplementary figure 12 showing the alignment of the short-reads around the GWAS hits. The visual inspection suggests the alignments are of good quality.
+
+R3.11 About lppP- it is only present in 1.7%. By itself has a low explanatory power and not sure if enough to justify the title of the manuscript (which is basically based on this hit).
+
+To increase the number of putative regions associated with drug resistance in inferred susceptible nodes, we have complemented the SNP based GWAS with a gene-based analysis, aggregating non-synonymous mutations. This method has been proved useful in funding drug resistance associated mutations in Mycobacterium tuberculosis (see Coll et al 2018 and Farhat et al 2019). We have also added a step of sequence base imputation to account for SNPs that may have been overlooked in the previous analysis. Overall, we think that these associations can be used as a “proof of concept”, but we agree with the reviewer that further analyses are needed, which is now also noted in the Discussion section.
+
+Regarding lppP, we confirmed its presence in a global dataset (Supplementary Data File 3) where its frequency was as high as 9%, indicating its global prevalence and suggesting a role in drug resistance acquisition. Such a big difference in frequency with our dataset may either be due to the mutation not being very prevalent in Peru, or due to the global dataset being more enriched with drug resistant isolates. We replicated the analysis on the global dataset, where the lppP deletion was associated with a higher risk of drug resistance in inferred susceptible nodes.
+
+1. Coll, F., Phelan, J., Hill-Cawthorne, G.A. et al. Genome-wide analysis of multi- and extensively drug-resistant Mycobacterium tuberculosis. Nat Genet 50, 307–316 (2018).
+2. Farhat, M.R., Freschi, L., Calderon, R. et al. GWAS for quantitative resistance phenotypes in Mycobacterium tuberculosis reveals resistance genes and regulatory regions. Nat Commun 10, 2128 (2019).
+R3.12 In addition. This hit and others cannot be validated using the Russian dataset which is understandable given the sample size and that the genetic make up of the Russian dataset is really different. Is there any evidence (even if not statistically significant) for the presence of any of the hits in the Russian dataset?
+
+We replicated the analysis in a global dataset of 1573 publicly available isolates (see R3.11), which was enriched with drug resistance samples. The frequencies of all the hits, as well as the results of the analysis, are discussed in the Results section, subsection “Genomic signatures of drug resistance acquisition”, paragraph 2. In short, The lppP deletion had a frequency of 9% and had a hazard ratio 3.6 times greater than those without the deletion (HR 3.6, 95% CI 1.9-6.9, p-value = 8.7e-5).The esxO mutation had a frequency of 10% had a risk of acquiring drug resistance 3.1 times higher than those with the reference genotype (HR 3.1, 95% CI 1.3-7.3, p-value = 0.009).
+
+R3.13 However an extraordinary claim needs extraordinary evidence. I suggest the authors look for alternative validations of the hit. I can think in several ways but one relatively easy (if you have access to the isolates) is to measure and show that isolates carrying that particular mutation have a higher MIC for INH that phylogenetically related isolates without the mutation. Alternatively authors may look for publications in which mutant libraries (with transposon) are tested against first line drugs. Authors can also identify alternative datasets where this can be tested as there are many around nowadays or at the very least authors can look in the global database and see the prevalence of the mutation across continents. The ideal validation will be a KO mutant or an allelic mutant but I understand this is extraordinarily difficult and time-consuming in the case of Mtb.
+
+We agree with the reviewer that further work and evidence it’s needed to validate these hits as well as to add future genotypes.
+
+Given that our aim is to identify polymorphisms in drug sensitive backgrounds that increase the risk of acquiring drug resistance; we hypothesize that comparing the MIC’s of closely related mutant/wild type strains in-vitro is unlikely to demonstrate a difference in MIC’s. Rather our differences are more likely to manifest in vivo when exposed to selection pressure from drugs and host immunity combined. Despite the limitations of in vitro work, we are working on laboratory confirmation of these mutations using fluctuation assays, as well as GWAS analysis in global and more diverse datasets.
+
+As the reviewer suggests, we have also checked the prevalence of the main GWAS hits in the global dataset used to time the importation events of TB in Peru. This is described in the Results section, subsection “Genomic signatures of drug resistance acquisition”, paragraph 2 (see R3.11 and R3.12). In short, the three polymorphisms described in our work are present in the global dataset and in higher frequency. This could be explained by the higher proportion of drug resistance isolates in the publicly available data. Both lppP and esxO were associated with a higher risk of drug resistance in the global data set. These points have been reflected in the Results and Discussion.
+R3.14 In general, and maybe reflecting my ignorance, looks like p-values in the analysis of pre-resistance mutations are extremely low. This suggests a clear link and in this case also a strong effect. This is good but given that many groups have been working on this and had problems to identify these regions I wonder where the difference resides to obtain such large effects?
+
+We are not aware of any group working on this concept, especially in a phylogenetic context. We believe the differences may be caused by the presence of more susceptible samples in our dataset. Given that we are looking for mutations in genotypes inferred to be susceptible, a large number of susceptible isolates is required for the inference. Many GWAS collections are very enriched with drug- and multidrug-resistant samples, and therefore they may lack sufficient resolution to infer the susceptible ancestral genotypes correctly. For instance, many of the mutations described in our work may occur alongside drug resistance conferring mutations, and therefore they will be masked by them.
+
+R3.15 Regarding the Russian dataset I don't see the full value of incorporating the analysis. It confirms some of the findings but looks like it has more problems than advantages for your purposes. It cannot be used to validate as discussed above. But also it is not dated and thus it is difficult to compare to the main dataset like in Fig4 where one panel is based on years and the other on branch lengths. It is not possible to compare the trajectories in such a case. Even if comparable the Kaplan Meier curve is quite different in both cases and I am struggling to understand why? One explanation is different biases in the dataset (being enriched in MDR/XDR and very few sensitive and monoresistant?). In general Figure 4 should be in the same scale so it can be properly compared and interpret.
+
+The Samara dataset represents an interesting comparison, as it is the other largest population level project in a setting where lineage 2 is the major lineage. We acknowledge that the different proportion of drug resistance between datasets makes them harder to compare, but even so, the Samara dataset and the Peruvian one both show that lineage 2 acquires resistance faster than lineage 4, either when measured in years or genetic distance.
+
+Minor
+
+R3.m1 Can you specify the substitution rate obtained for each lineage and see if it compares well with published rates?
+
+The posterior density distribution for the substitution rate for each lineage is shown as violin plots in Figure 1b. As pointed out in Results, subsection “Phylogenetic analysis and drug resistance emergence”, line 151-152 of the original manuscript, these estimates are consistent with previous published ones.
+
+R3.m2 L127. The authors should clarify that 1% frequency refers to the SNP in the analysed dataset and not in the bulk sequencing of individual cultures
+
+The sentence at line L127 has now been changed to: “Most SNPs were not widely distributed across the population, and only 8088 variants had a frequency in the dataset higher than 1%”
+R3.m3 L428. Additional details on the ancestral reconstruction algorithm would be welcome, i.e. reversion penalties
+
+Marginal ancestral states for the sequences were estimated by maximum likelihood by optimizing the transition rate matrix and the rates and finding the state at each node that maximizes the likelihood of the data. This has now been clarified in Methods.
+REVIEWERS' COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have given extensive, well thought through and well evidenced replies to my comments. I am satisfied with the changes that have been made. I have no further comments.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have addressed the concerns raised by the reviewers. Particularly important is the validation in another cohort. Some very minor comments
+
+1) Their evolutionary approach to detect "pre-resistance" is sound and complements efforts to identify candidate loci and mutations associated to higher likelihood to develop additional resistance, for example through mechanisms like drug tolerance mediated by prpR which the authors may want to cite (https://www.nature.com/articles/s41564-018-0218-3).
+
+2) I also thank the authors their new analysis about compensatory mutations. A minor comments is whether the same early identification of rpoC mutations remain true when you discreate the data between S450L and non-S450L rpoB mutation. The reason is that there has been observed a strong association between S450L and compensatory mutations although S450L has by far the lowest fitness cost of all rpoB mutations. The reasons are not clear (one hypothesis is that only those mutations with small fitness costs can be compensated while the others are beyond compensation). A different emergence dynamics in the two subgroups will reinforce the view of S450L being preferentially compensated. It is just a suggestions as I know non-S450L compensated strains are not that common.
+Response to reviewers' comments:
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have given extensive, well thought through and well evidenced replies to my comments. I am satisfied with the changes that have been made. I have no further comments.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have addressed the concerns raised by the reviewers. Particularly important is the validation in another cohort. Some very minor comments
+
+1) Their evolutionary approach to detect "pre-resistance" is sound and complements efforts to identify candidate loci and mutations associated to higher likelihood to develop additional resistance, for example through mechanisms like drug tolerance mediated by prpR which the authors may want to cite (https://www.nature.com/articles/s41564-018-0218-3).
+
+We have now included this relevant reference in the 5th paragraph of the Discussion. We thank the reviewer for pointing out conditional drug tolerance as another mechanism of increasing the risk of drug resistance acquisition.
+
+2) I also thank the authors their new analysis about compensatory mutations. A minor comments is whether the same early identification of rpoC mutations remain true when you disgregate the data between S450L and non-S450L rpoB mutation. The reason is that there has been observed a strong association between S450L and compensatory mutations although S450L has by far the lowest fitness cost of all rpoB mutations. The reasons are not clear (one hypothesis is that only those mutations with small fitness costs can be compensated while the others are beyond compensation). A different emergence dynamics in the two subgroups will reinforce the view of S450L being preferentially compensated. It is just a suggestions as I know non-S450L compensated strains are not that common.
+
+We agree with the reviewer that it would be interesting to analyze the dynamics of emergence of compensatory mutations in S450L strains vs non-S450L ones. As the reviewer points out, we confirmed that isolates with S450L rpoB had a higher probability of acquiring rpoC mutations when compared to non-S450L. This has been added to the subsection “The emergence of compensatory mutations”, first paragraph: “Overall, 62% of rifampicin resistant isolates carried Ser450Leu rpoB mutations (525/842). Rifampicin resistant isolates harboring Ser450Leu rpoB mutations had a higher probability of carrying non-synonymous mutations in the rpoC gene (52%, 272/525) than isolates with other rpoB mutations (6%, 19/317) in a logistic regression model (OR=16.86, 95% CI 10.55-28.50, p<0.001)”. On the other hand, both Ser450Leu and non-Ser450Leu showed similar temporal dynamics, as it is now shown in the new Supplementary Figure 6, although with high uncertainty given the low number of non-Ser450Leu rifampicin resistant isolates.

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+Genomic Signatures of Pre-Resistance in Mycobacterium tuberculosis
+
+Arturo Torres Ortiz
+Imperial College   https://orcid.org/0000-0002-2492-0958
+Jorge Coronel
+Universidad Peruana Cayetano Heredia
+Julia Rios Vidal
+Ministerio de Salud, Lima, Peru
+Cesar Bonilla
+Ministerio de Salud, Lima, Peru
+David Moore
+London School of Hygiene and Tropical Medicine   https://orcid.org/0000-0002-3748-0154
+Robert Gilman
+Johns Hopkins Bloomberg School of Public Health
+Francois Balloux
+University College London   https://orcid.org/0000-0003-1978-7715
+Onn Min Kon
+Imperial College
+Xavier Didelot
+University of Warwick
+Louis Grandjean (l.grandjean@ucl.ac.uk)
+University College London
+
+Article
+
+Keywords: Tuberculosis, phylogenetics, drug resistance, AMR
+
+Posted Date: May 25th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-364747/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+Version of Record: A version of this preprint was published at Nature Communications on December 15th, 2021. See the published version at https://doi.org/10.1038/s41467-021-27616-7.
+Genomic signatures of Pre-Resistance in Mycobacterium tuberculosis
+
+Arturo Torres Ortiz¹, Jorge Coronel², Julia Rios Vidal³, Cesar Bonilla³,⁴, David AJ Moore⁵, Robert H Gilman⁶, Francois Balloux⁷, Onn Min Kon⁸, Xavier Didelot⁹, Louis Grandjean¹,¹⁰*
+
+¹ Imperial College London, Department of Infectious Diseases, London, UK
+² Universidad Peruana Cayetano Heredia, Lima, Perú
+³ Unidad Técnica de Tuberculosis MDR, Ministerio de Salud, Lima, Perú
+⁴ Universidad Privada San Juan Bautista, Lima Perú
+⁵ London School of Hygiene and Tropical Medicine, London, UK
+⁶ Johns Hopkins Bloomberg School of Public Health, Baltimore, Maryland, USA
+⁷ UCL Computational Genomics Institute, London, UK
+⁸ Respiratory Medicine, National Heart and Lung Institute, Imperial College London, UK
+⁹ University of Warwick, School of Life Sciences and Department of Statistics, Warwick, UK
+¹⁰ UCL Department of Infection, Institute of Child Health, London, UK
+
+*Corresponding author l.grandjean@ucl.ac.uk
+Institute of Child Health, 30 Guilford Street, London, WC1N 1EH
+
+Keywords: Tuberculosis, phylogenetics, drug resistance. AMR
+Abstract
+
+Recent advances in bacterial whole-genome sequencing have resulted in the identification of a comprehensive catalogue of genomic signatures of antibiotic resistance in Mycobacterium tuberculosis. With a view to pre-empting the emergence of drug-resistance, we hypothesized that pre-existing balanced polymorphisms in drug susceptible genotypes ("pre-resistance mutations") could increase the risk of acquiring antimicrobial resistance in the future.
+
+In order to identify a pathogen genomic signature of future drug resistance we undertook whole-genome sequencing on 3135 culture positive isolates from different patients sampled over a 17-year period in Lima, Peru.
+
+Reconstructing ancestral whole genomes on time-calibrated phylogenetic trees we identified no single drug resistance in Peru predating 1940. Moving forward in evolutionary time through the phylogenetic tree from 1940, we apply a novel genome-wide survival analysis to determine the hazard of drug resistance acquisition at the level of lineage, mono-resistance state, and single-nucleotide polymorphism. We demonstrate that lineage 2 has a significantly higher incidence of drug resistance acquisition than lineage 4 (HR 3.36, 95% CI 2.10 - 5.38, p-value = \(4.25 \times 10^{-7}\)) and estimate that the hazard of evolving rifampicin following isoniazid resistance acquisition is 14 times that of genomes with a susceptible background (HR 14.45, 95% CI 8.46 - 15.50, p-value < \(10^{-15}\)). Our findings are validated in a separate publicly available dataset from Samara, Russia. After controlling for population structure, we also show that a deletion in a gene coding for the cell surface protein lppP predisposes to the acquisition of drug resistance in susceptible genotypes (HR 6.71, 95% CI 4.82-11.22, p-value = \(1.17 \times 10^{-9}\)).
+
+Prediction of future drug resistance in susceptible pathogens together with targeted expanded therapy has the potential to prevent drug resistance emergence in Mycobacterium tuberculosis and other pathogens. Prospective cohort studies of participants with and without these polymorphisms should be undertaken with a view to implementing personalized pathogen genomic therapy. This approach could be employed to preempt and prevent the emergence of drug resistance and other important traits in other organisms.
+Introduction
+
+Mycobacterium tuberculosis is estimated to have killed 1 billion people over the last 200 years [1] and remains one the world’s most deadly pathogens [2]. Drug resistance in bacteria, particularly the Enterobacteriaceae and Mycobacterium tuberculosis, imposes an unsustainable burden on health programs worldwide with some strains so extensively resistant that they are untreatable with existing antibiotic therapy [3]. Although recent advances in bacterial whole-genome sequencing have significantly improved the identification of drug resistance [4], post hoc approaches to diagnosis miss the opportunity to preempt the emergence of drug resistance and implement preventive measures prior to the acquisition and spread of antibiotic resistant disease.
+
+An increased risk of drug resistance emergence is often attributed to inadequate implementation of control measures [5], but bacterial factors have also been proposed as potential contributors to drug resistance [6]. Evidence of differential drug resistance acquisition at the Mycobacterium tuberculosis sublineage level is conflicting. Epidemiological and in vitro studies have suggested that the Beijing family, belonging to lineage 2, is hyper-mutable [7] with a propensity to develop resistance at a higher frequency than other lineages [8][11], while others cite evidence to the contrary [12][13]. Pre-existing resistance to one antibiotic (mono-resistance) is another factor that may influence the acquisition of multidrug-resistance [14]. Mono-resistance to isoniazid or rifampicin have been associated with increased rates of further development of multidrug-resistance [15][16], but the relative risk of either remains unclear. Similarly, phylogenetic analyses suggest a stepwise progression towards multidrug-resistance, where mutations conferring isoniazid resistance tend to precede those linked to rifampicin resistance [17][20].
+
+Phylogenetic trees have been increasingly used to study pathogen dynamics and evolutionary processes of a wide range of phenotypes of epidemiological interest, including virulence or drug resistance acquisition [21][22]. A necessary focus on improving the molecular diagnosis of drug resistance has led to the generation of large strain collections of drug resistant pathogens. However, unrepresentative samples of this kind enriched for drug-resistant isolates limit the ability to characterize the evolution and dynamics of drug resistance from a diverse background of ancestral susceptible strains. Inadequate sampling without comprehensive population level coverage or sufficient temporal span compounds this problem, while the monomorphic nature of the tuberculosis genome makes constructing time-calibrated phylogenetic trees particularly challenging. As a consequence, a single mutation rate is often applied to the data, but this assumption inappropriately forces lineages and sub-lineages to conform to the same global mutation rate, thus limiting the inferences that can be made from the data.
+
+Overcoming these issues, we present findings from samples collected over a 17-year time span with population level coverage in the hyperendemic suburbs of Lima, Peru. We apply a novel genome-wide survival analysis to a time-calibrated phylogeny of 3135 tuberculosis
+strains and show the existence of pre-resistance mutations among drug susceptible genotypes that increase the risk of future drug resistance emergence in tuberculosis. We demonstrate clear differences in the acquisition of drug resistance between lineages, on mono-resistant backgrounds, and at the level of nucleotide polymorphisms. Our findings are then tested and replicated in an independent publicly available data set of 1000 whole genomes collected in Samara, Russia, to demonstrate that they can be globally generalized.
+Results
+
+Population structure, genomic analysis, and patient demographics
+
+A total of 3432 Mycobacterium tuberculosis genomes from Lima (Peru) were analyzed, of which 3135 passed genomic quality filters. Of this, 2037 were part of a population level study carried out in 2009 where sputum samples were taken from all patients presenting tuberculosis symptoms in the Lima areas of Callao and Lima South [23]. Comparison of drug resistance prevalence between the population level sampling and reports of epidemiological data in Peru [2] are consistent: 1.5% (32/2037) of samples were rifampicin mono-resistant; 5% were isoniazid mono-resistant (105/2037), and 13% were multidrug-resistant (269/2037). The remaining samples were collected from cohort studies covering a 17-year period of research in the regions of Lima and Callao in order to achieve a sufficient temporal span in our sampling window (Supplementary Fig. 1).
+
+The isolates were first aligned to the reference genome H37Rv, then lineages and sublineages were assigned using clade specific SNPs [24]. Lineage 4 (L4, Euro-American) consisted of 2807 samples, while lineage 2 (L2, Beijing) had 327 isolates (Table 1). There was a single representative of lineage 1 (Indo-Oceanic), which was used to root the phylogenetic tree. The remaining samples from the data set, which included 5 Mycobacterium caprae isolates, were not used in the downstream analysis. Lineage 4 had the highest diversity, comprising 1235 isolates from lineage 4.3 (LAM), 935 from lineage 4.1.2.1 (Haarlem), 271 from lineage 4.1.1 (X-Type), and 312 from lineages denoted as Type T, which encompasses lineages 4.5, 4.7, 4.8 and 4.9. Other minor sublineages included lineage 4.2.2 (TUR) and lineage 4.4. All isolates from Lineage 2 were part of the Beijing sublineage (lineage 2.2), mainly from the sublineage 2.2.1 or Modern Beijing, and with only one representative of the sublineage 2.2.2 or Asia Ancestral [25] (Table 1).
+
+The alignment of the isolates to the reference genome resulted in 64,586 SNPs, of which 18,022 were singletons (28%). Most SNPs were not widely distributed across the dataset, and only 8,088 variants had a frequency higher than 1%. A total of 59,789 SNPs (16,934 singletons, 28%) were identified for lineage 4, and 4,821 SNPs (1,370 singletons, 28%) for lineage 2. Similarly, we applied the same analysis to a publicly available data set from Samara, Russia, as a validation set where, unlike the Peruvian dataset, lineage 2 constitutes the main lineage. We identified a total of 28,414 SNPs, consistent with previous publications of this data [19].
+
+Patient demographic metadata was available for 2220 samples, of which 88% were smear positive, 27% were previously treated for tuberculosis, and 2.8% were HIV positive, consistent with previous population level estimates in Peru [26]. The median age was 28 years (IQR 21–41). In our cohort, 86% of lineage 2 and 89% of lineage 4 were smear positive.
+Phylogenetic analysis and drug resistance emergence
+
+The maximum likelihood phylogeny constructed using these alignments grouped the isolates by lineage similarly to previously published global data sets [24] (Fig. 1a, Supplementary Fig. 2). To study the temporal dynamics of drug resistance acquisition at the population level, the maximum likelihood phylogeny was time-calibrated using the sampling dates of the isolates, which extended from 1999 to 2016. Dated phylogenies were built separately for lineage 2 and lineage 4 in order to avoid the confounding effect of the temporal and population structures [27]. Both datasets had a clear temporal signal (Supplementary Fig. 3), and thus model parameters could be confidently inferred from the data [28, 29]. We used the relaxed clock model implemented in BactDating [30], allowing the mutation rate to vary in each branch independently. We ran the MCMC until convergence of the chains was achieved, with an effective sample size (EES) of at least 100 (Supplementary Fig. 4). The estimated rate for lineage 2 was 0.45 substitutions per genome per year (0.32;0.57 95% CI), while lineage 4 had a clock rate of 0.299 (0.25;0.36 95% CI) (Fig. 1b). The estimates of the molecular clock for both lineages were consistent with previous reports [31]. The most common recent ancestor (tMRCA) for our samples was placed at 565 CE (263;826 95% CI) for lineage 4 (Fig. 1c), while lineage 2 had a tMRCA in 1325 CE (1070;1499 95% CI) (Fig. 1d).
+
+Drug resistance was inferred for all isolates at the tips of the phylogenetic tree using well-established drug resistance associated SNPs [32]. The time of emergence of drug resistant mutations was inferred by reconstructing the ancestral sequences of the internal nodes in the phylogenetic tree. The time of emergence of a specific antibiotic resistance mutation was approximated to the inferred year of the internal node where such mutation first appeared. The phylogenetic estimates of the emergence of drug resistance conferring mutations in lineage 4 occurred around the time of the known introductions of the corresponding drug. In contrast the emergence of drug resistance in lineage 2 was observed to have arisen many years after the introduction of antituberculous drugs. This is consistent with the geographic spread of lineage 4 in Europe together with early widespread use of drugs in this region (Table 2, Fig. 2). For both lineage 2 and lineage 4, the earliest inferred occurrence of resistance was to isoniazid, by the Ser315Thr mutation in the gene KatG, around 1957 (1928;1978 95% CI) for lineage 2, and 1942 (1913;1960 95% CI) for lineage 4, in line with the reported wide introduction of isoniazid in 1952 [33]. The rifamycins were first isolated in 1957 [33], and we estimate the date for the first acquisition of resistance to rifampicin due to the rpoB mutation Ser450Leu to be around 1951 (1931;1971 95% CI) for lineage 4 and 1974 (1953;1987.8 95% CI) for lineage 2. None of the drug resistant nodes reverted to susceptible along the branches of the two phylogenetic trees.
+
+Between lineage differences in drug resistance acquisition
+
+The risk of acquiring drug resistance was calculated as the Cox Proportional Hazard Ratio (HR) using the time between sensitive internal nodes and the first drug resistant node in the
+time-calibrated phylogenetic trees. Lineage 2 was characterized by a higher incidence of drug resistance acquisition when compared to lineage 4 in both the Peruvian dataset (HR 3.36, 95% CI 2.10 - 5.38, Likelihood ratio test p-value = \(4.25 \times 10^{-7}\); Fig. 3a), and the Samara dataset (HR 4.82, 95% CI 3.74 - 6.21, Likelihood ratio test p-value < \(10^{-15}\); Fig. 3b). Similarly, the incidence of drug resistance acquisition was also higher in lineage 2 when compared to all sublineages of lineage 4 in the Peruvian dataset (All p-values for comparison < 0.05; Fig. 3c). To assess the adequacy of our data to the proportional hazard assumption, we calculated the relationship between the Schoenfeld residuals against time. In all cases, a non-significant association between the Schoenfeld residuals and time supported the use of the proportional hazards model (Supplementary Fig. 5).
+
+Since previous treatment with antituberculous drugs has been associated to an increased risk of acquiring drug resistance [34], we tested the association between previous treatment and the different sublineages of our cohort. A total of 2236 samples contained metadata regarding previous treatment of tuberculosis. We found no significant association between Mycobacterium tuberculosis sublineages and previous treatment with antituberculous drugs in a logistic regression model (n = 2236, all p-values > 0.1), suggesting that the between lineage differences in drug resistance acquisition observed in the survival analysis are not confounded by a differential distribution of antibiotics between sublineages. Similarly, we found no significant association between Mycobacterium tuberculosis sublineages and HIV and smear positivity in a logistic regression model (n = 2133, all p-values > 0.1).
+
+In order to evaluate the robustness of our maximum likelihood phylogeny, we repeated both the dating and the survival analysis on 100 phylogenetic bootstrap replicates. In both lineage 2 and lineage 4, the Cox Proportional Hazard ratio was not significantly different between the maximum likelihood phylogeny and the bootstrap replicates (Supplementary Fig. 6a,b). Additionally, the Kaplan-Meier curve of the 100 replicates was similar to that of the maximum likelihood tree (Supplementary Fig. 6c,d).
+
+The risk of developing MDR TB from isoniazid mono-resistance
+
+To determine the effect of mono-resistance on the acquisition of further multidrug-resistance, the hazard ratio of acquiring rifampicin resistance was calculated for isoniazid mono-resistant ancestral genotypes versus susceptible ancestral strains. Genotypes with an isoniazid mono-resistant background had 15 times the hazard of developing rifampicin resistance tuberculosis relative to wild type susceptible strains (HR 15.12, 95% CI 10.54 - 21.69, Likelihood ratio test p-value < \(10^{-15}\); Fig. 4a). A larger hazard ratio was obtained in the Samara dataset (HR 37.28, 95% CI 18.81 - 73.88, Likelihood ratio test p-value < \(10^{-15}\); Fig. 4b), although the low prevalence of mono-resistance clades in the Samara set may bias this estimate.
+
+Due to the infrequent occurrence of rifampicin mono-resistance prior to multidrug-resistance emergence, the risk of developing multidrug-resistance from a rifampicin mono-resistance
+Genomic signatures of drug resistance acquisition
+
+Genome-wide survival analysis was performed using a Cox Proportional Hazard regression model to identify genetic variants in phylogenetic nodes inferred to be drug susceptible but associated with a higher risk of progression towards drug resistance. Resistant nodes were defined as those inferred to be resistant to any antibiotic in order to identify common pathways of increased risk of acquiring resistance regardless of the specific antibiotic. The association analysis was performed in lineage 4 and lineage 2 separately, and we further corrected for population structure using a kinship matrix, which reduced the genomic inflation factor (\( \lambda \)) to 1.21 (Supplementary Fig. 7).
+
+Three variants in drug susceptible ancestral genotypes were associated with a higher risk of acquiring drug resistance in lineage 4 after population and multiple testing correction, two of which were in previously annotated genes (Fig. 5a). The variant with the lowest p-value corresponded to a 9bp deletion at location 2,604,157 in the locus \( lppP \), which encodes for a lipoprotein and has been predicted to be required for growth in macrophages [35]. This deletion had a frequency of 1.7% in the population, and it evolved 12 times independently along the phylogenetic tree. Genotypes with this variant had a hazard ratio 6.7 times greater than those with an intact \( lppP \) (Fig. 5b, HR 6.71 95% CI 4.82-11.22, p-value = \( 1.17 \times 10^{-9} \)). A synonymous polymorphism at position 2,626,011 in the gene \( esxO \) (HR 1.64, 95% CI 0.9-3.33 p-value = \( 3.23 \times 10^{-6} \)) with a frequency in the population of 5% had the second lowest p-value. The \( esxO \) gene is part of a family of protein secretion systems described to be critical for growth, pathogenesis, and mycobacterial–host interactions [36].
+
+No significant associations were identified for lineage 2 after correcting for population structure, possibly due to the lower diversity of lineage 2 as well as the strong lineage effect on the phenotype. The analysis could not be replicated in the Samara dataset as the Samara dataset was significantly smaller and hence lacked sufficient statistical power.
+Discussion
+
+This study represents the largest population level genomic analysis of Mycobacterium tuberculosis to date. Our 17-year sampling time frame provided a unique opportunity to study drug resistance acquisition dynamics and evolution. To our knowledge this is the first description and evaluation of pathogen pre-resistance (pre-existing balanced polymorphisms that predispose to the acquisition of future drug resistance).
+
+Using a novel ancestral state genome-wide survival analysis to move in time through the phylogenetic tree, we show that Mycobacterium tuberculosis is predisposed to acquire drug resistance mutations at the lineage level, after mono-resistance, and at the level of nucleotide polymorphisms. Identifying pathogen genetic factors that predispose strains to evolve drug resistance could help prevent the acquisition and spread of resistance as well as treatment failure by expanding treatments to those strains most likely to become resistant in the future.
+
+Previous studies of acquired drug resistance at the sublineage level in Mycobacterium tuberculosis have led to contradictory outcomes, with small sample sizes in fluctuation assays [7, 12] or using amalgamated sub-population level samples. Here we demonstrate conclusively that lineage 2 acquired resistance to antibiotics more rapidly than lineage 4. There were no significant differences observed in drug resistance acquisition between the sub-lineages of the most diverse lineage 4. Even though lineage 2 showed an increased risk in drug-resistance acquisition, lineage 4 evolved resistance earlier than lineage 2 for almost all drugs analyzed, with the exception of streptomycin. This may be explained by the Euro-American distribution of lineage 4 and the earlier widespread implementation of antibiotics in these regions.
+
+The identification and control of mono-resistant strains is a key component of tuberculosis public health infection prevention and control efforts. Mono-resistance is associated with worse clinical outcomes [37] and an increased probability of progressing to multidrug-resistance [15]. At the population level, our study quantifies this risk and shows that isoniazid mono-resistant strains have at least 15 times the hazard of developing multidrug-resistance relative to wild type susceptible strains. Despite the use of new therapeutics, multi-drug resistant tuberculosis continues to require polypharmacy with increased toxicity and longer treatment duration [2]. Globally, drug resistance surveillance is focused primarily on rifampicin, with the widely implemented GeneXpert MTB/RIF PCR based assay unable to detect isoniazid mono-resistance. Inadequate diagnosis of isoniazid mono-resistance will inevitably lead to inappropriate treatment and could fuel rapid evolution of multidrug-resistance, thus posing a significant threat to tuberculosis control.
+
+We also identified three genomic loci associated with higher risk of future drug resistance acquisition. To remain polymorphic these variants must be under balancing selection and only be positively selected once exposed to drug therapy. Rather than causing resistance directly, these variants could promote resistance acquisition by compensating for the fitness
+costs of resistance in vivo [38].
+
+The variant with the lowest p-value corresponded to a 9bp deletion in the gene lppP present at a frequency of 1.7% in the population and arising 12 times independently. Deletions in lipoproteins have been well characterized in the past [39], and lppP has been predicted to be required for growth in macrophages [35]. Lipoproteins can act as antigenic proteins [39], and thus deletions in the genes encoding them may alter the interaction between the bacilli and the macrophages, potentially conferring a selective advantage in the presence of drug and increasing the probability of acquiring drug resistance.
+
+An additional variant was identified in the gene esxO, which encodes for the ESAT-6-like protein esxO. The gene esxO is part of a family of genes that code for immunogenic secreted proteins that play a role in mycobacterial growth, pathogenesis, and host-pathogen interactions [36]. Moreover, esxO has been associated with pathogenesis by inducing autophagy in infected macrophages [40]. Synonymous homoplasic variants in ESX genes have been previously identified [23], but their phenotypic effects are still unclear.
+
+This study benefited from an unbiased population level coverage of both drug resistant and drug susceptible strains that enabled us to reliably correct for the founder effect and control for the influence of pre-existing population diversity. The large sampling size and time frame — a consequence of 17-years of continued research in the same location — allowed us to generate time-calibrated phylogenies without imposing a global mutation rate. This was a pre-requisite for the downstream analyses and our novel GWAS survival analysis approach. We were also able to validate our sublineage and mono-resistance dependent hazards of acquired resistance in the smaller Samara dataset. However, the time scale and size of this publicly available data was insufficient to allow us to confirm the effect of the lppP deletion in a second independent dataset.
+
+Although our phylogenetic analysis reveals trends of drug resistance acquisition over evolutionary time, prospective cohort studies are required to determine the effect of these mutations at the individual patient and household level. There was no difference observed in the proportion of patients receiving previous antituberculous treatment between the two lineages. This makes our findings unlikely to be influenced by differential exposure to drugs among lineages. There was no difference in sputum smear grade between lineages, suggesting that our findings are not a consequence of increased pathogenicity of lineage 2 in comparison to lineage 4. Significant immigration to Peru occurred well before the advent of antibiotics [41], which limits the influence of imported drug resistant strains. Nevertheless, it is possible that some resistance events may have arisen as a result of importation of resistant strains from countries with different drug selection pressures.
+
+In summary, this population wide 17-year long epidemiological study of Mycobacterium tuberculosis genetics provides the first description and evaluation of pre-resistant balanced
+polymorphisms in susceptible genotypes that predispose to the acquisition of future drug resistance. Prediction of future drug resistance in susceptible pathogens together with targeted expanded therapy has the potential to prevent drug resistance emergence in Mycobacterium tuberculosis and other pathogens. Prospective cohort studies of participants with and without these polymorphisms should be undertaken to inform clinical trials of personalized pathogen genomic therapy. This novel ancestral state genome-wide survival analysis could also be employed to predict and prevent the emergence of resistance or indeed any important trait of interest in other organisms.
+Materials and methods
+
+Study design and sample selection
+
+Samples were selected from previous projects taking place across the region of Lima. The first project consisted of a population level study carried out between 2008 and 2010 as part of the population level implementation of Microscopic Observation Drug Susceptibility (MODS) testing [42] [43]. A total of 2,139 unselected patients of tuberculosis were collected. Of these patients, 284 were analyzed in previous studies (PRJEB5280) [23], while 1855 were processed as part of this project.
+
+A second set of 213 MDR-TB samples was obtained from a 3-year long household follow-up study conducted between 2010–2013 [34], of which 185 randomly selected samples underwent whole-genome sequencing (PRJEB5280) [23].
+
+Additionally, 42 unpublished whole-genome sequences of samples collected from 1999 to 2007 in different regions of Lima were added to the study, as well as 575 samples that were collected between 2003 and 2013 as part of the CRyPTIC Consortium (PRJEB32234) [44], and 489 samples from the TANDEM Consortium (PRJEB23245) [45] taken between 2014 and 2016.
+
+All samples without collection date, as well as reference clinical samples, were excluded from the final list. Drug susceptibility testing (DST) was performed either by MODS [43] or by the proportions method on agar [46].
+
+To replicate our findings, all the analyses were repeated in a publicly available independent dataset from Samara, Russia (PRJEB2138), as the sampling was also representative of the population [19].
+
+Whole-genome sequence analysis
+
+Quality analysis of the raw reads was performed using FastQC [47]. A de-novo assembly of the short reads was done with SPAdes genome assembler v3.14.0 [48] across kmers of size 21, 33, 45, 55, 65, 75, 81, 101, 111, and 121. The resulting assembly contigs were mapped to the well annotated H37Rv reference genome (Gene bank: AL123456) using minimap2 [49] with the asm20 option. Single nucleotide polymorphisms (SNPs) and small insertions and deletions (indels) were identified with BCFtools mpileup and BCFtools call v1.9 [50] using the multiallelic calling algorithm, keeping the information about every single site in the genome in a VCF file. Lastly, indels were left-aligned and normalised using BCFtools norm. A consensus sequence was created from the VCF file. In order to determine the quality of the variants, the raw reads were mapped against the resulting consensus sequence using the mem algorithm implemented in BWA v0.7.17 [51], after which the alignments were sorted
+using SAMtools v1.9 [52] and filtered for possible PCR and optical duplicates using Picard v2.19.0 [53]. Local realignment around indels was performed using the GATK v3.8-1-0 ‘IndelRealigner’ module [54]. The mean coverage for each sample was calculated as the number of mapped bases (excluding soft-clipped bases) divided by the genome size. Samples with a mean coverage lower than 15x were excluded from subsequent analysis. SNPs and indels were detected as described in the previous step.
+
+Variants that did not meet the quality criteria were filtered using a combination of BCFtools filter and custom scripts in Python v3.7.3 with the following cutoffs: minimum Phred-scaled quality score (QUAL) of 20; minimum mapping quality (MQ) of 20; minimum genotype quality (QG) of 20; minimum read position bias (RPB), mapping quality bias (MQB), and strand bias (SP) of 0.001; minimum depth (DP) of 10 and a maximum of 5 times the mean coverage; minimum of reads supporting the alternate allele (AD) of 75% of the total depth in that position, with no less than two reads in the forward (ADF) and the reverse (ADR) strands. Additionally, SNPs within 2bp of an indel and indels within 3bp of another indel were removed, as both situations can be indicative of mapping artifacts. Positions that did not meet the quality criteria were annotated using the IUPAC ambiguity codes [55]. Samples with more than 25 high quality heterozygous calls were removed to avoid the inclusion of putative mixed infections. Finally, variants that overlapped 100bp intervals around known hypervariable regions, such repetitive elements and transposases [56], were removed from the analysis as this may affect the reliability of the alignment. Similarly, recombinant regions in genes coding for proline-glutamate (PE) or proline-proline-glutamate (PPE) [57], and SNPs implicated in drug resistance [32] were excluded in order to minimize homoplasies that could disrupt the tree topology. The resulting sequences were concatenated to generate a multiple sequence alignment. Sites with a proportion of ambiguous bases higher than 10% were excluded from the analysis. Finally, samples with a proportion of ambiguous sites in the alignment higher than 5% were excluded.
+
+Phylogenetic analyses
+
+All the phylogenetic analyses were performed based on the alignment containing both lineage 4 and lineage 2 samples, as well as separately for each lineage.
+
+A maximum likelihood phylogeny was inferred using RAxML-NG [58] with the GTR model, 20 starting trees (10 random and 10 parsimony), 100 bootstrap replicates, and a minimum branch length of \(10^{-9}\). A Lineage 2 sample randomly selected from our dataset was selected as an outgroup for the Lineage 4 phylogeny. Likewise, a random Lineage 4 isolate was used as a root for the Lineage 2 phylogeny. The tree containing both lineage 4 and lineage 2 samples was rooted using a lineage 1 isolate.
+
+In order to construct a time-calibrated phylogeny, we tested whether there was a detectable amount of evolutionary change between samples collected at different times [28, 29].
+This was done in lineage 4 and lineage 2 separately in order to avoid population structure confounding in the temporal signal [27]. Two different tests of the temporal signal were applied: the root-to-tip regression method and the date-randomization test [59]. For the former, BactDating [30] was used to perform a linear regression between the collection dates and their root-to-tip genetic distance in the maximum likelihood tree. Additionally, we carried out a date-randomization test, where evolutionary rates estimated by BactDating [30] were compared between the observed data set and 100 data sets obtained by permutation of sampling dates [60].
+
+BactDating [30] was used to time-calibrate the tree using the mixed model for \(10^7\) iterations to achieve both convergence of the MCMC chains and an effective sample size of at least 100.
+
+The subsequent phylogenetic analysis was performed using the R package ape [61]. Ancestral sequence reconstruction was carried out by maximum likelihood as implemented in Phangorn [62], including gaps and ambiguity codes [55].
+
+Time-to-event analysis
+
+Time-to-event analysis was performed on the tree using the R package Survival [63]. The time was measured for all pairs of nodes as the distance between the older and the younger node in the time-calibrated phylogeny. An observation was defined as censored if both nodes were drug sensitive. On the other hand, an event occurred if the older node was drug sensitive and the younger node was drug resistant. Only the first acquisition of resistance was considered. Observations taking place before 1940 were discarded. The survival curve and the Cox proportional hazard ratio were calculated. The entire pipeline was repeated for 100 phylogenetic bootstrap replicates.
+
+Genome-wide association of predisposition to drug resistance
+
+Association analysis was performed using the variant sites alignment for the tips of the phylogenetic tree, as well as the reconstructed sequences of the internal nodes. The phenotype was defined as leading to resistance in the phylogenetic tree, and thus only drug susceptible nodes that immediately preceded the first resistant node of each branch were considered. Variants with a frequency in the population (tips of the tree) lower than 1% and a proportion of ambiguous bases higher than 5% were excluded. Furthermore, only those variants that were polymorphic at the node level were used. Genome-wide association was performed using the Cox proportional hazard model and the time between nodes. In order to correct for population structure, a genetic distance matrix was calculated using SNPs with a frequency in the population higher than 5%, and the eigenvectors were used as covariates in the Cox regression model. The p-values were corrected for multiple testing using a Bonferroni correction.
+Data availability
+
+All raw sequencing data are available with accession numbers listed in Materials and Methods. Samples sequenced as part of this study have been submitted to the European Nucleotide Archive under accession PRJEB39837.
+References
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+Acknowledgements
+
+LG was supported by the Wellcome Trust (201470/Z/16/Z), the National Institute of Allergy and Infectious Diseases of the National Institutes of Health under award number 1R01AI146338 and by the GOSH/ICH Biomedical Research Centre. OMK was supported by the Imperial Biomedical Research Centre (NIHR Imperial BRC, grant P45058). We thank the CRyPTIC project and the Tandem project for making whole-genome data available in the public domain. All authors acknowledge UCL Computer Science Technical Support Group (TSG) and the UCL Department of Computer Science High Performance Computing Cluster.
+
+Author Contributions
+
+ATO, LG, XD, OMK, FB, JRV, RG, CB, and DM conceived and designed the study. JC performed and supervised tuberculosis cultures, DNA extraction, laboratory, and sequencing work. LG, XD, FB, and OMK jointly supervised the research. ATO, LG, FB, and XD performed and advised on computational analyses. ATO, and LG wrote the manuscript with input from all co-authors. All authors read and approved the final manuscript.
+
+Competing interests
+
+The authors declare no competing financial interests
+
+Ethics declarations
+
+Ethical approval was obtained for all individual studies from which this data was derived.
+Figures
+
+![Phylogenetic analysis of Mycobacterium tuberculosis isolates from Lima, Peru](page_184_232_1207_693.png)
+
+Figure 1: Phylogenetic analysis of 3134 *Mycobacterium tuberculosis* isolates from Lima, Peru
+Colors represent different lineages and sublineages. (a) Maximum likelihood phylogeny. Scale in number of substitutions per genome. (b) Posterior density for the inferred substitution rate in substitutions per genome per year for lineage 4 (blue) and lineage 2 (red). (c) Time-calibrated phylogeny of lineage 4. (d) Time-calibrated phylogeny of lineage 2.
+Tree estimation of TB drug resistance emergence
+
+Rifampicin    Isoniazid    Ethambutol    Pyrazinamide
+
+Lineage 4
+Lineage 2
+
+Distribution of new TB compounds
+
+Figure 2: Inferred posterior density distribution of the earliest occurrence of resistance to first line antituberculous drugs
+Posterior density distribution inferred using a time-calibrated phylogeny for both lineage 4 and lineage 2. Arrows represent the approximated time of antibiotic distribution.
+Figure 3: Hazard ratio and Kaplan-Meier curve for different sublineages of Mycobacterium tuberculosis
+(a-c) Top: Hazard ratio (HR). Bottom: Kaplan-Meier curve and numbers at risk. Y-axis represents the probability of remaining susceptible to any antibiotic, while the X-axis shows the time in years or the distance in branch length. (a) depicts the HR of lineage 2 compared to lineage 4 in the Peruvian dataset (HR 3.36, 95% CI 2.10 - 5.38, Likelihood ratio test p-value = \(4.25 \times 10^{-7}\)) and the different Kaplan-Meier curve for lineage 2 and lineage 4 (p<0.0001). (b) same metrics for the Samara dataset (HR 4.82, 95% CI 3.74 - 6.21, Likelihood ratio test p-value < \(10^{-15}\); Kaplan-Meier curve p<0.0001). (c) shows HR between lineage 2 and the different sublineages of lineage 4 found in the Peruvian dataset (LAM9, LAM3, LAM11, Haarlem, X type and T type), using LAM3 as a reference. Statistical significance of the hazard ratio differences presented next to the CI bars (*, p<0.05; **, p<0.01; ***, p<0.001)
+Figure 4: Hazard ratio and Kaplan-Meier curve for rifampicin acquisition (a-b) Top: Hazard ratio (HR). Bottom: Kaplan-Meier curve and numbers at risk. Y-axis represents the probability of remaining susceptible to rifampicin, while the X-axis shows the time in years or the distance in branch length. (a) depicts the risk of acquiring rifampicin resistance from an already isoniazid mono-resistant background compared to a drug susceptible one (HR 15.12, 95% CI 10.54 - 21.69, Likelihood ratio test p-value < \(10^{-15}\)) and the Kaplan-Meier curves for the different backgrounds (p<0.0001). (b) same metrics for the Samara dataset (HR 37.28, 95% CI 18.81 - 73.88, Likelihood ratio test p-value < \(10^{-15}\); Kaplan-Meier curve p<0.0001). Statistical significance of the hazard ratio differences presented next to the CI bars (*, p<0.05; **, p<0.01; ***, p<0.001)
+Figure 5: Genome-Wide association study (GWAS) results. (a) Manhattan plot for GWAS on increased risk of drug resistance acquisition in lineage 4. The red line represents the Bonferroni corrected p-value threshold of \(3.37 \times 10^{-5}\). Labels show the genes where the significant hits are located. Colors indicate the hazard ratio, with a scale of blue representing hazards ratio lower than 1 and a scale of reds for hazard ratios higher than 1. (b) Kaplan-Meier curve and numbers at risk of a 9bp deletion in the gene *lppP* comparing the probability of remaining susceptible between those nodes without the deletion (blue) and those with it (red).
+Table 1: Population structure.
+
+<table>
+  <tr>
+    <th>Clade name</th>
+    <th>Number</th>
+  </tr>
+  <tr>
+    <td><b>Lineage 1</b></td>
+    <td>Indo-Oceanic</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td><b>Lineage 2</b></td>
+    <td>East-Asian</td>
+    <td>327</td>
+  </tr>
+  <tr>
+    <td>Lineage 2.2.1</td>
+    <td>Beijing</td>
+    <td>319</td>
+  </tr>
+  <tr>
+    <td>Lineage 2.2.1.1</td>
+    <td>Beijing</td>
+    <td>7</td>
+  </tr>
+  <tr>
+    <td>Lineage 2.2.2</td>
+    <td>Beijing</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td><b>Lineage 4</b></td>
+    <td>Euro-American</td>
+    <td>2807</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.1.1</td>
+    <td>X Type</td>
+    <td>271</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.1.2.1</td>
+    <td>Haarlem</td>
+    <td>935</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.2.2</td>
+    <td>TUR</td>
+    <td>3</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.3.1</td>
+    <td>LAM</td>
+    <td>5</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.3.2</td>
+    <td>LAM3</td>
+    <td>328</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.3.3</td>
+    <td>LAM9</td>
+    <td>676</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.3.4</td>
+    <td>LAM11</td>
+    <td>226</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.4</td>
+    <td>-</td>
+    <td>51</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.5</td>
+    <td>T Type</td>
+    <td>4</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.7</td>
+    <td>T Type</td>
+    <td>31</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.8</td>
+    <td>T Type</td>
+    <td>86</td>
+  </tr>
+  <tr>
+    <td>Lineage 4.9</td>
+    <td>T Type</td>
+    <td>12</td>
+  </tr>
+  <tr>
+    <td>Lineage 4<sup>1</sup></td>
+    <td>T Type</td>
+    <td>179</td>
+  </tr>
+</table>
+
+Lineages and sublineages defined using clade specific SNPs [24].
+<sup>1</sup> Clade name assigned phylogenetically.
+Table 2: First emergence of drug resistance conferring mutations in Lima, Peru.
+
+<table>
+  <tr>
+    <th>Drug</th>
+    <th>Lineage</th>
+    <th>Gene</th>
+    <th>Year</th>
+    <th>Mutation</th>
+  </tr>
+  <tr>
+    <td>RIF</td>
+    <td>Lineage 4</td>
+    <td>rpoB</td>
+    <td>1951.7 [1931.7 - 1970.7]</td>
+    <td>p.Ser450Leu</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Lineage 2</td>
+    <td>rpoB</td>
+    <td>1974.4 [1953.2 - 1986.8]</td>
+    <td>p.Ser450Leu</td>
+  </tr>
+  <tr>
+    <td>INH</td>
+    <td>Lineage 4</td>
+    <td>KatG</td>
+    <td>1941.6 [1913.6 - 1959.7]</td>
+    <td>p.Ser315Thr</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Lineage 2</td>
+    <td>KatG</td>
+    <td>1957.5 [1928.3 - 1977.4]</td>
+    <td>p.Ser315Thr</td>
+  </tr>
+  <tr>
+    <td>ETH</td>
+    <td>Lineage 4</td>
+    <td>embB</td>
+    <td>1973.7 [1967.8 - 1980.8]</td>
+    <td>p.Gly406Ala</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Lineage 2</td>
+    <td>embB</td>
+    <td>1983.1 [1967.0 - 1994.1]</td>
+    <td>p.Met306Val</td>
+  </tr>
+  <tr>
+    <td>PZA</td>
+    <td>Lineage 4</td>
+    <td>pncA</td>
+    <td>1962.4 [1942.6 - 1972.2]</td>
+    <td>p.His51Arg</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Lineage 2</td>
+    <td>pncA</td>
+    <td>2002.1 [1997.0 - 2005.5]</td>
+    <td>c.-11A&gt;C</td>
+  </tr>
+  <tr>
+    <td>STR</td>
+    <td>Lineage 4</td>
+    <td>rpsL</td>
+    <td>1974.5 [1955.9 - 1986.2]</td>
+    <td>p.Lys43Arg</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td>Lineage 2</td>
+    <td>rpsL</td>
+    <td>1958.1 [1934.6 - 1975.1]</td>
+    <td>p.Lys43Arg</td>
+  </tr>
+</table>
+
+Emergence of drug resistance conferring mutations for the 5 antibiotics historically used as first line drugs for the treatment of tuberculosis. RIF: rifampicin; INH: isoniazid; ETH: ethambutol; PZA: pyrazinamide; STR: streptomycin. Year presented as a point estimate with the highest posterior density interval.
+Supplementary material
+
+![Bar chart showing the temporal distribution of sample cohorts by year, with different colored bars representing different projects. The y-axis is labeled 'Number of samples' and the x-axis is labeled 'Sampling year'. The legend indicates project types: CRyPTIC (green), Household (red), Other (orange), Population (blue), Tandem (brown). Sample counts for each year are shown above the bars.](page_246_312_1097_563.png)
+
+Supplementary Figure 1: Sample cohort
+Temporal distribution of the 3134 samples included in the study.
+Supplementary Figure 2: Maximum likelihood phylogeny of the Samara (Russia) data set
+Phylogeny of the Samara data set for (a) lineage 4 and (b) lineage 2.
+
+![Maximum likelihood phylogeny of the Samara (Russia) data set](page_186_134_1207_495.png)
+Supplementary Figure 3: Temporal signal analysis
+The presence of measurable evolution (temporal signal) within the lineage 2 (top) and lineage 4 (bottom) was tested by a root-to-tip regression (left) and by a date randomization test (right). In the root to tip regression the distance from the tips to the root of the phylogenetic tree (y-axis) are plotted against the sampling dates (x-axis). The mutation rate and the time of the most recent common ancestor (MRCA) are calculated from the linear regression. The date randomization test is performed by comparing the substitution rate of the original dataset (black) with a set of randomized data sets obtained by permutating the sampling dates (grey). Error bars represent 90% confidence intervals. The date randomization test is passed if the estimates from the original data don’t overlap with the randomization sets.
+Supplementary Figure 4: BactDating MCMC chain convergence
+BactDating trace output for lineage 2 and lineage 4 in three independendet MCMC chains. Parameters shown are posterior probabilities, likelihood, prior probabilities, date of MRCA, substitution rates, coalescent time unit and relaxation parameters. Three independent chains were run for each dataset.
+Supplementary Figure 5: Scaled Schoenfeld residuals
+(a-e) Schoenfeld residuals plotted against time. In all cases, the proportional hazard assumption is supported by a non-significant association between residuals and time, thus the proportional hazards model can be assumed. Test and plots modified from the survminer R package. (a) Residuals for lineage 2 and lineage 4 in Peru. (b) Residuals for lineage 2 and several sublineages of lineage 4 in Peru. (c) Residuals for sensitive and isoniazid mono-resistant background in Peru. (d) Residuals for lineage 2 and lineage 4 in Samara. (e) Residuals for sensitive and isoniazid mono-resistant background in Samara.
+Supplementary Figure 6: Hazard ratio and Kaplan-Meier curve of 100 phylogenetic bootstrap replicates
+100 phylogenetic bootstrap replicates were performed in parallel to the maximum likelihood phylogeny. Blue color represents the lineage 4 phylogeny while the red color shows the lineage 2 phylogeny. No statistical differences are found between the results obtained using the maximum likelihood tree and those using the phylogenetic bootstrap replicates. (a, b), Hazard ratio for the maximum likelihood tree (dark point) and 100 phylogenetic bootstrap replicates (light colored points). (c, d), Kaplan-Meier curve for the maximum likelihood tree (dark solid lines) with the 95% CI interval (dark dotted lines), and 100 phylogenetic bootstrap replicates (light colored lines).
+Supplementary Figure 7: Population correction for Genome-Wide association study (GWAS)
+Quantile-quantile (QQ) for the raw p-values (grey), and the p-values corrected for population structure (black). Red line indicates the null hypothesis of uniformly distributed p-values. Lambda represents the genomic inflation factor.
+
+![Quantile-quantile plot showing observed vs expected -log10(p) values for raw and corrected GWAS p-values, with a red line indicating the null hypothesis.](page_324_186_627_495.png)
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• suppMaterialpreresistancearticle.pdf

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+Peer Review File
+
+Seasonal antigenic prediction of influenza A H3N2 using machine learning
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The proposed goal of the study is to develop a machine learning model to predict virus phenotype (~hemagglutination inhibition data) from genotype. The random forest model incorporates minimal genetic information (HA1 similarity), and metadata (avidity, potency, passage history) to predict virus-antiserum cross-reactivity. The authors argue that the “seasonal approach” to training the model is novel, prevents overfitting, and when integrated with metadata has resulted in improved model performance. The authors integrate a significant amount of public HI and sequence data to train the model and apply it to “rank” the importance of individual amino acid sites on virus phenotype.
+
+This contribution is well written, the visualization of the data are strong, the validity/approach taken to build the model is robust (perhaps one-hot encoding the amino acid data without the AAindex step could be considered) and this is an important problem. However, the methods applied are standard and not competed against the state-of-the-art in machine learning, the provided “software” is reproducible for a computational biologist but not for a bench-scientist unfamiliar with these analyses (i.e., it has limited utility), the identification of amino acid sites associated with phenotypic change largely restate prior studies, and the improvement/classification performance represents a marginal improvement. There were intriguing avenues and directions mentioned in the introduction and discussion (e.g., epistasis, the role of sites and genes outside of the HA1, the impact of the immunity landscape on the emergence of antigenic variants) but these were not explored and there was limited empirical testing of the model or an extensive empirical application of the model to provide some form of unique insight into a biological problem.
+
+Consequently, I would suggest that the work be revised to consider and compete against alternate approaches, develop some sort of software beyond the jupyter notebooks so that it could be implemented easily, and an empirical test of the work to address a biological problem should be developed.
+
+Specifically, 1) the proposed model is competed – briefly – with a single method that is integrated in nextstrain. The work would be significantly strengthened if alternate methods were applied, so that this contribution could be better assessed relative to other approaches/the state of the art. Specifically, the RF approach is well studied, and understanding what major advancements are made within this study is difficult. See a handful of recent studies here: Hie, et al 2021. Science, 371(6526), pp.284-288; Huddleston, et al., 2020. Elife, 9, p.e60067; Zeller,et al. MSphere, 6(2), pp.e00920-20.
+
+2) Some form of experiment should be conducted, e.g., what would the impact be on vaccine strain selection should this approach be adopted? Does this approach work for H1 data? Does the emergence of antigenic variants change over time with well-matched/poorly matched vaccines? Is it
+amino acid identity, or simply the position that is important, e.g., are all amino acid mutations at 189 equally important?
+
+And 3) the value of a machine learning model – in this context – is that it could be easily deployed by someone with some raw HI data – the git repo is nicely curated, but for a bench-scientist the application of this approach would be very difficult. A suggestion would be a better worked example, create a software that is installed via PyPi or conda, and making it generalizable, e.g., can this be adapted for a virus that is not influenza?
+
+Reviewer #2 (Remarks to the Author):
+
+This study developed a random-forest model for predicting the antigenic variation of influenza A(H3N2) viruses using both the HA sequence and meta data in HI experiments including virus avidity, antiserum potency and passage category of virus isolates and antisera. The novelty of the model lies in the integration of meta data in the model. The study was well designed and the manuscript was written clearly. The reviewer has some major concerns about the study.
+
+1 Lots of computational models have been developed to predict the antigenic variation of influenza viruses. It is not enough to demonstrate the superity of the model by only comparing it to nextflu. The model had an average accuracy of 0.85 which is not high enough comparing to previous studies.
+
+2 The model relies on metadata in the prediction, which significantly limit its uage in applications.
+
+3 The antigenic evolution of the influenza virus is cluster-wise. It is important to consider the virus population when studying the evolution of the virus.
+
+4 As a new framework for predicting antigenic variation of influenza viruses, it is necessary to test its performance in other subtypes such as A(H1N1) and influenza B virus.
+RESPONSE TO REVIEWERS’ COMMENTS
+
+Seasonal antigenic prediction of influenza A H3N2 using machine learning
+(NCOMMS-23-22338-T)
+
+We thank the reviewers for providing constructive comments. In addressing these comments, we feel the paper has been improved substantially. Our point-by-point responses are detailed below. Changes made to the manuscript are indicated in blue.
+
+Reviewer #1 (Remarks to the Author):
+
+The proposed goal of the study is to develop a machine learning model to predict virus phenotype (~hemagglutination inhibition data) from genotype. The random forest model incorporates minimal genetic information (HA1 similarity), and metadata (avidity, potency, passage history) to predict virus-antiserum cross-reactivity. The authors argue that the “seasonal approach” to training the model is novel, prevents overfitting, and when integrated with metadata has resulted in improved model performance. The authors integrate a significant amount of public HI and sequence data to train the model and apply it to “rank” the importance of individual amino acid sites on virus phenotype.
+
+This contribution is well written, the visualization of the data are strong, the validity/approach taken to build the model is robust (perhaps one-hot encoding the amino acid data without the AAindex step could be considered) and this is an important problem. However, the methods applied are standard and not competed against the state-of-the-art in machine learning, the provided “software” is reproducible for a computational biologist but not for a bench-scientist unfamiliar with these analyses (i.e., it has limited utility), the identification of amino acid sites associated with phenotypic change largely restate prior studies, and the improvement/classification performance represents a marginal improvement. There were intriguing avenues and directions mentioned in the introduction and discussion (e.g., epistasis, the role of sites and genes outside of the HA1, the impact of the immunity landscape on the emergence of antigenic variants) but these were not explored and there was limited empirical testing of the model or an extensive empirical application of the model to provide some form of unique insight into a biological problem.
+
+Consequently, I would suggest that the work be revised to consider and compete against alternate approaches, develop some sort of software beyond the Jupyter notebooks so that it could be implemented easily, and an empirical test of the work to address a biological problem should be developed.
+
+Response:
+
+Thank you for the comments and suggestions. We have now made revisions to the manuscript to address these points. We outline these changes in the following, where we respond to the corresponding, albeit more detailed, review comments.
+
+One specific comment that we address up front (since it is not covered in the comments below), is the use of one-hot encoding to encode the genetic differences between sequences of a virus-antiserum pair. We agree that this is a useful further comparison. Hence, we have now implemented the one-hot encoding scheme into the proposed model. In the revised manuscript, we have incorporated this into Supp. Fig. 3c and updated its caption. We found that in comparison to other genetic encoding schemes, this scheme provided the fourth-best average MAE over four validation seasons (Supp. Fig. 3c). This encoding scheme is explained in updated text in subsection ‘Encoding genetic and metadata information’ under section ‘Methods’, which reads as:
+"In the one-hot encoding scheme, for each virus-antisera pair, at each HA1 site the amino acids in the two sequences were initially represented as binary vectors of length 20 (corresponding to 20 valid amino acids), as per standard one-hot encoding. Subsequently, a logical OR operation was applied between these two vectors to encode the amino acid differences. Consequently, at each HA1 site, distinct amino acids in a virus-antisera pair are encoded as a binary vector of length 20 with a pair of ones, each representing a one-hot encoded amino acid. For the alternative case in which the amino acids are the same at a given site, these are encoded into a binary vector of length 20 with a single one, preserving the amino acid information. With this one-hot encoding strategy together with logical OR combining, the genetic difference for each virus-antisera pair produces an encoded binary vector of length 20×329."
+
+For the remaining review comments, our point-by-point responses are detailed below.
+
+Specifically,
+1) the proposed model is competed – briefly – with a single method that is integrated in nextstrain.
+The work would be significantly strengthened if alternate methods were applied, so that this contribution could be better assessed relative to other approaches/the state of the art. Specifically, the RF approach is well studied, and understanding what major advancements are made within this study is difficult. See a handful of recent studies here: Hie, et al 2021. Science, 371(6526), pp.284-288; Huddleston, et al., 2020. Elife, 9, p.e60067; Zeller,et al. MSphere, 6(2), pp.e00920-20.
+
+Response:
+
+Thank you for the constructive comment. The novelty of our results lies in the demonstration of accurate seasonal antigenic prediction protocols for influenza, which has not been shown previously. This is practically important and relevant to periodic influenza surveillance and vaccine selection. Numerous alternative predictive algorithms to a random forest (RF) approach can nonetheless also be adopted in our seasonal framework. In the original manuscript, we provided a comparison with NextFlu (implemented in our seasonal framework) since it is a widely known method and is incorporated into the NextStrain prediction framework. It is also a linear method, and hence, comparison with NextFlu enabled us to assess the potential advantages of relaxing a linear constraint by adopting a nonlinear RF approach.
+
+We have now implemented and evaluated multiple machine learning (ML) methods in our seasonal prediction framework; see Figure R1 (Supp. Fig. 6 in the revised manuscript). Specifically, along with the RF and NextFlu algorithms considered earlier, we have implemented two additional tree-based learning methods, adaptive boosting (AdaBoost) (also used in the quoted reference (Zeller et al., 2021), albeit in a non-seasonal framework) and extreme gradient boosting (XGBoost), as well as two neural network methods, multilayer perceptron (MLP) and residual neural network (ResNet). In all cases, passage-based metadata features (Fig. 1b) were incorporated, and we optimized the hyperparameters with respect to a set of amino acid mutation matrices in the AAindex2 database. With this new analysis, we found that the AdaBoost model performed the best among all methods (Figure R1). As such, in the revised manuscript, we have selected AdaBoost as our proposed model for seasonal antigenic prediction of influenza A virus (IAV) H3N2 (rather than RF, considered previously).
+
+For the AdaBoost model, we have re-run all simulations and updated all figures and corresponding results in the paper. The performance results are generally improved compared with our earlier analysis, however, the qualitative results and conclusions remain consistent. The main changes are provided in the revised manuscript in Results subsections 'Machine learning model for seasonal antigenic characterization of IAV H3N2' and 'Optimized model accurately performs seasonal antigenic characterization', Methods subsections 'AdaBoost model', and 'Alternate methods'. See also the updated Figures 1 to 4, Supplementary Figures 2 to 8, the new Supplementary Figures 9 to 10, and Supplementary Table 1.
+Figure R1. Performance comparison of ML and NN models for antigenic prediction of IAV H3N2 under the seasonal framework. Comparison of the proposed AdaBoost model with a linear model (NextFlu substitution model), tree-based ML models (RF and XGBoost), and NN models (MLP and ResNet). See Methods for implementation details of these models. The "AdaBoost (NextFlu-matched-params)" model is based on AdaBoost, with parameters tailored to match those of the NextFlu model that uses binary-encoded genetic differences and only two metadata features: virus avidity and antisera potency. For each model, MAE was computed for 14 test seasons from 2014NH to 2020SH.
+
+We have also considered the quoted articles by Hie et al., 2021 and Huddleston et al., 2020. However, the approaches in these articles are not directly applicable to the seasonal antigenic prediction problem that we address. Specifically, the model presented by Hie et al., 2021 defined the semantic change (corresponding to antigenic change) as the L1 norm between the wild-type sequence and a single-residue mutant, and the model is trained in an unsupervised fashion without HI titre data. Hence, it cannot predict the outcome of HI assays. The model designed by Huddleston et al., 2020 is an extension of the NextFlu method that forecasts the genetic composition of the future season’s influenza population. Hence, rather than predicting HI titres, this model predicts the amino acid sequence that will likely dominate in the next influenza season.
+
+2) Some form of experiment should be conducted, e.g., what would the impact be on vaccine strain selection should this approach be adopted? Does this approach work for H1 data? Does the emergence of antigenic variants change over time with well-matched/poorly matched vaccines? Is it amino acid identity, or simply the position that is important, e.g., are all amino acid mutations at 189 equally important?
+
+Response:
+
+Considering these points, we have now conducted further experiments, as we describe in the following.
+
+Starting with the extension to H1 data, this is indeed possible. While our study is focused on seasonal H3N2, the proposed seasonal antigenic prediction method and framework is general and can be easily applied to other influenza subtypes, provided sufficient data is available for model training and evaluation. To demonstrate this, we have now applied our method to a publicly available data set that has been made available for seasonal IAV H1N1 (Gregory et al., 2016) spanning 18 influenza seasons from 2001NH to 2009SH. We evaluated the performance of our AdaBoost-based seasonal prediction approach on this data set, with results shown in Figure R2. Note that this H1N1 data set lacked comprehensive passage information, and hence, passage meta-data was excluded. On average, the H1N1 system achieved a comparable but higher average MAE compared with H3N2 (0.75 versus 0.70). This higher average MAE is likely attributed to the lack of passage information, particularly given that the passage information was found to significantly improve prediction performance for H3N2 (Supp.
+Fig. 3a). Seasonal fluctuations in performance were also more pronounced for H1N1, with season 2005SH achieving a significantly low MAE, while seasons 2003NH and 2007NH exhibited relatively high MAEs (Figure R2). These fluctuations can be attributed to the observed antigenic drift during those seasons (Figure R3). Specifically, seasons 2004SH and 2005SH displayed a minor antigenic drift (Figure R3b and Figure R3c), while season 2007NH showed a more substantial antigenic drift (Figure R3d). In the case of season 2003NH, although the antigenic drift appears to be small (Figure R3a), the higher predicted MAE may also be influenced by the limited availability of circulating isolates during that season (Supp. Fig. 9a).
+
+We have included this result in the revised text in the ‘Discussion’ section and added Figure R2 as a (new) Supplementary Fig. 9b.
+
+![Bar chart showing MAE values for each influenza season from 2001NH to 2009SH, with an 'Average' cell indicating the score averaged over the 20 seasons.](page_232_384_1016_120.png)
+
+Figure R2. The MAE performance of the proposed AdaBoost model for seasonal antigenic prediction of IAV H1N1 over 20 influenza seasons from 2001NH to 2009SH. The ‘Average’ cell on the right indicates the score averaged over the 20 seasons. The darker colour cells indicate better performance.
+
+![Four scatter plots labeled a-d, showing antigenic drift in circulating isolates compared to previous two recent seasons. Each plot contains red circles (current season) and grey points (previous two seasons).](page_232_624_1016_480.png)
+
+Figure R3. Antigenic maps for IAV H1N1 to visualize the antigenic drift in circulating isolates compared to isolates from the previous two recent seasons. (a-c) Small antigenic drift in seasons 2003NH, 2004SH, and 2005SH. (d) Large antigenic drift in season 2007NH. Each square in a grid indicates antigenic difference of two units, corresponding to a four-fold dilution of the antibody in the HI assay. Large antigenic drift is indicated by presence of circulating isolates (red circles) dispersed far from past isolates (grey points).
+Regarding the dependence of antigenic variant changes on vaccine match, we agree that this is an interesting question to explore. In our original manuscript, with the help of antigenic cartography tools, we had demonstrated that the level of seasonal antigenic drift had an effect on the performance of our model (Fig. 3). More specifically, we showed that prediction accuracy was inversely related to the level of drift experienced in a season. Prompted by the reviewer’s query, we conducted further analysis to assess whether there was any association between the performance of our prediction method (and consequently, with the level of antigenic drift) and the match of the seasonal IAV H3N2 vaccine strain. Following Qiu et al., 2020, we utilized a simple empirical measure called the ‘vaccine similarity’ metric to estimate the level of match between the vaccine and circulating viruses. This metric quantifies the percentage of virus-vaccine pairs that exhibit antigenic similarity, indicated by NHT values of two or less. We note that this vaccine similarity metric is only a coarse approximation of vaccine match, and its accuracy is influenced by the number of virus-vaccine pairs reported in a particular season in the WIC reports. The accuracy of this metric may also be affected by potential “selection biases”, since the isolates that have been evaluated with HI titres in each season may not represent a completely random sampling of circulating viruses in that season. Nevertheless, using this definition, our analysis revealed a weak negative correlation between prediction accuracy of our approach and vaccine similarity (**Figure R4**). This correlation was however not statistically significant (P>0.05). This data also suggests that there is also no clear association between the level of antigenic drift and vaccine similarity. To see this more clearly, we refer to the antigenic cartography plots given in Fig. 3 of our manuscript, which show that the 2016NH and 2019NH seasons experience high antigenic drift, while the 2017SH and 2020SH seasons experience low antigenic drift. From **Figure R4**, there is no clear association between the level
+
+![Line graph showing vaccine similarity (%) and MAE (virus-vaccine pairs) for each season from 2014NH to 2020SH.](page_384_670_1012_482.png)
+
+<table>
+  <tr>
+    <th>Correlation coefficient</th>
+    <th>virus-vaccine pairs</th>
+    <th>p value</th>
+  </tr>
+  <tr>
+    <td>Pearson</td>
+    <td>-0.41</td>
+    <td>0.14</td>
+  </tr>
+  <tr>
+    <td>Spearman</td>
+    <td>-0.46</td>
+    <td>0.1</td>
+  </tr>
+</table>
+
+**Figure R4. Seasonal vaccine similarity versus the seasonal predictive performance of our model.**
+For each season from 2014NH to 2020SH, the vaccine similarity is plotted with a blue line, with its scale shown on the left y-axis. For each season, vaccine similarity is defined as the percentage of antigenically similar virus-vaccine pairs based on the normalised HI titre data for that season. For each test season from 2014NH to 2020SH, the MAE performance of the AdaBoost model for virus-vaccine pairs is respectively plotted in orange. The MAE scale is shown on the right y-axis. The Pearson and Spearman correlation coefficients between vaccine similarity and MAE performance are shown in the table. Both results were statistically insignificant.
+of antigenic drift and vaccine similarity in these seasons. Overall, our data suggests that the prediction accuracy of our model is related to the level of antigenic drift experienced in an influenza season but is not obviously related to the match of the vaccine strain in each season. The level of drift in a season and the vaccine match also do not appear to show any clear relationship.
+
+Regarding the potential impact of our proposed method on influenza vaccine strain selection, there are various ways in which the proposed prediction framework may be applied. These include:
+
+- Informing targeted HI experimentation: Our approach can be applied to make rapid sequence-based predictions that suggest which subset of circulating viruses should be tested experimentally with HI assays in a season.
+- Providing complementary HI data predictions: Noting that only a subset of circulating viruses is tested with HI assays due to practical constraints (e.g., animal availability, resources, cost), our approach could be used to provide normalized HI titre estimates for all sequenced circulating viruses in a season. This would provide a more comprehensive picture of the antigenic landscape of viruses circulating in each season and could provide complementary input when making vaccine strain selection decisions. (Note: These complementary predictions are expected to be particularly accurate, as suggested by Supp. Fig. 7 in the manuscript.)
+- Predicting the efficacy of existing vaccines, or candidate vaccines, in a forthcoming influenza season: When used together with influenza evolutionary forecasting tools that predict the dominant clade/influenza quasispecies in a forthcoming influenza season, our approach can be used to predict antigenic differences between putative circulating strains in that season and strains used in existing or candidate vaccines. This could provide important input when deciding on the need for a vaccine update and for optimal vaccine strain selection.
+
+We have updated the Discussion section of the manuscript to make these points clear.
+
+Regarding the importance of amino acid substitutions, the amino acid mutation matrix encoding that we employ encodes the positional information of amino acids, however it lacks the resolution to determine the importance of individual amino acid substitutions at specific positions. We point out this limitation of our model in the section, ‘Limitations of the study’. We also point out that this limitation could be addressed in the future by including amino acid substitutions as features of the model, which will further require re-optimization of the model such as selection of the top performing metadata features and re-optimization of the model hyperparameters. The updated text is as follows:
+
+Third, since the model uses amino acid sites as features, it can determine the importance of individual sites (Fig. 4), but not specific amino acid substitutions. Hence, our model cannot rank different amino acid substitutions that occur at the same site. This may be addressed in future work by using amino acid substitutions as features for the AdaBoost model.
+
+3) And the value of a machine learning model – in this context – is that it could be easily deployed by someone with some raw HI data – the git repo is nicely curated, but for a bench-scientist the application of this approach would be very difficult. A suggestion would be a better worked example, create a software that is installed via PyPi or conda, and making it generalizable, e.g., can this be adapted for a virus that is not influenza?
+
+Response:
+
+Thanks for raising this point that will add to the value of this work. For a bench-scientist, we believe that an appropriate and broadly accessible use case would be to provide a system that takes as input one or more test virus-antisera pairs for an influenza season, and reports the predicted normalised HI titre values for these pairs. To facilitate this, we have developed a user-friendly web application with a
+graphical user interface (GUI) (Figure R5). This web application allows bench-scientists to (i) directly input sequences of test virus-antisera pairs and corresponding (optional) metadata information, or (ii) upload the same data for multiple virus-antisera pairs using a CSV file. Based on the season of the virus isolates being tested, the web application allows the user to select the appropriate model trained up to (but excluding) the test season. To demonstrate its usage, an example and instructions for preparing an input CSV file are also provided. The web application is hosted on the Hugging Face Spaces platform, accessible at https://huggingface.co/spaces/sawshah/SAP_H3N2. This web server eliminates the need for scientists to install and run an application via PyPi or conda, making it more convenient and accessible. We refer to the web application and provide a link to access it in the ‘Results’ section, while the specific details and information about the web application are explained in the ‘Methods’ section.
+
+In addition to this web application, the updated codes in the form of Jupyter notebooks are provided over GitHub (https://github.com/saws-lab/SAP_H3N2_ML) and can be cloned via Git. These notebooks currently reproduce the results for IAV H3N2 and IAV H1N1 present in the manuscript. Research scientists can use these notebooks to retrain the model on user’s data as well as can modify them for other viruses. For example, for viruses having neutralization assay data such as SARS-CoV-2, dengue virus, and hepatitis C virus, the provided notebooks can be modified to take as input neutralization data instead of HI assay data. This extension would be worth considering in a future study. As the focus of this work is on IAV H3N2 and we have also showed its adaptability for IAV H1N1, we pointed out in the ‘Discussion’ section of the manuscript that this approach could be used for other viruses with appropriate adaptation.
+
+![Screenshot of the user-friendly GUI-based web application for the developed model.](page_374_682_1092_496.png)
+
+Figure R5. Snapshot of the user-friendly GUI-based web application for the developed model.
+Reviewer #2 (Remarks to the Author):
+
+This study developed a random-forest model for predicting the antigenic variation of influenza A(H3N2) viruses using both the HA sequence and meta data in HI experiments including virus avidity, antiseraum potency and passage category of virus isolates and antisera. The novelty of the model lies in the integration of meta data in the model. The study was well designed and the manuscript was written clearly. The reviewer has some major concerns about the study.
+
+1) Lots of computational models have been developed to predict the antigenic variation of influenza viruses. It is not enough to demonstrate the superity of the model by only comparing it to nextflu. The model had an average accuracy of 0.85 which is not high enough comparing to previous studies.
+
+Response:
+
+Thank you for the comments. Regarding the novelty of the approach, the incorporation of meta-data (particularly passage information), is indeed a distinction of our method compared with other predictive strategies in the literature. As we show in Section “Model training, optimization, and validation”, this can lead to considerable improvement in prediction accuracy. It is important to emphasize however that the novelty of our manuscript is not restricted to the inclusion of meta-data. The problem that we address in this work – predicting HI titres in an influenza season from sequence and meta data alone – has not been addressed previously. This is a highly relevant problem for influenza surveillance and vaccine strain selection. It seeks to characterise the antigenic distinction of circulating viral strains compared with strains from previous seasons, including vaccine strains. Most previous attempts of predicting HI titres address a different problem, in which HI titres are predicted that are randomly selected in time, and typically, they seek to predict strains in the past, based on future HI data. This is a considerably easier prediction problem compared with predicting the antigenic properties of newly circulating strains when they arise in a new season. Our approach is the first to demonstrate that HI titres can be predicted for circulating strains, on a season-by-season basis, which we believe is a key novel aspect of our work and is important in practice.
+
+With the above in mind, it is true that alterative prediction methods can be substituted and evaluated in the seasonal prediction framework that we consider. Our initial analysis provided a comparison with NextFlu since this is a widely known method and is incorporated into the NextStrain framework. It is also a linear method, and hence, comparison with NextFlu enabled us to assess the potential advantages of relaxing a linear constraint by adopting a nonlinear RF approach. We have now implemented and evaluated multiple machine learning and neural network methods in our seasonal prediction framework; with results reported in Figure R1 (Supp. Fig. 6 in the revised manuscript). Specifically, along with the RF and NextFlu algorithms considered earlier, we have implemented two additional tree-based learning methods, adaptive boosting (AdaBoost), and extreme gradient boosting (XGBoost), as well as two neural network methods, multilayer perceptron (MLP) and residual neural network (ResNet). In all cases, passage-based metadata features (Fig. 1b) were incorporated, and we optimized the hyperparameters with respect to a set of amino acid mutation matrices in the AAindex2 database. With this new analysis, we found that the AdaBoost model performed the best among all methods (Figure R1). As such, in the revised manuscript, we have selected AdaBoost as our proposed model for seasonal antigenic prediction of influenza A virus (IAV) H3N2 (rather than RF, considered previously). For the AdaBoost model, we have re-run all simulations and updated all figures and corresponding results in the paper. The performance results are generally improved compared with our earlier analysis, however the qualitative results and conclusions remain consistent. The main changes are provided in the revised manuscript in Results subsections ‘Machine learning model for seasonal antigenic characterization of IAV H3N2’ and ‘Optimized model accurately performs seasonal antigenic characterization’, Methods subsections ‘AdaBoost model’, and ‘Alternate methods’. See also the updated Figures 1 to 4, Supplementary Figures 2 to 8, the new Supplementary Figures 9 to 10, and Supplementary Table 1.
+Figure R1. Performance comparison of ML and NN models for seasonal antigenic prediction of IAV H3N2 under the seasonal framework. Comparison of the proposed AdaBoost model with a linear model (NextFlu substitution model), tree-based ML models (RF and XGBoost), and NN models (MLP and ResNet). See Methods for implementation details of these models. The "AdaBoost (NextFlu-matched-params)" model is based on AdaBoost, with parameters tailored to match those of the NextFlu model that uses binary-encoded genetic differences and only two metadata features: virus avidity and antisera potency. For each model, MAE was computed for 14 test seasons from 2014NH to 2020SH.
+
+![Boxplot comparing MAE of various ML and NN models for seasonal antigenic prediction](page_370_186_695_377.png)
+
+Regarding the accuracy of our approach, initially we demonstrated an average MAE of 0.74 (normalized HI titre regression) and AUROC of 92% (antigenic variant classification). Notwithstanding some fluctuations over different seasons, these results overall (Figure 2) show a clear ability of our approach to accuracy classify antigenically distinct variants for each influenza season. The MAE of 0.74 also reflects accurate estimation of NHTs, particularly considering that antigenic distinction is routinely considered as NHTs greater than 2 antigenic units. Our newly updated results with AdaBoost show slightly further improved performance also.
+
+We believe that our performance results cannot be meaningfully compared with previous antigenic accuracy results presented in the literature, which deal with a different prediction problem as described in our comments above. We further point out in the Discussion section of our manuscript that for such prior analyses based on a non-seasonal prediction framework, the testing data may comprise isolates having antigenic changes that the model has already learned during training, which can lead to overfitting and inflate model performance. To demonstrate these points more explicitly, we have conducted further analysis using the NextFlu model. Under a non-seasonal prediction framework following that considered in the original NextFlu publication (Neher et al., 2016), the NextFlu model achieved an average MAE of 0.502 (Figure R6). This is substantially lower than the MAE achieved with NextFlu when implemented in the seasonal antigenic prediction framework considered in our paper (0.819 MAE; see Supp. Fig. 6). Since these prediction frameworks are very different, we believe it is not meaningful to draw performance comparisons between them.
+Figure R6. Under the non-seasonal framework, the prediction accuracy of the adapted NextFlu substitution model (MAE = 0.502) matches with the original model (MAE = 0.5). The NHTs predicted by the NextFlu substitution model (y-axis) correlated well with the measured NHTs (x-axis). The evaluation strategy was set similar to that reported in the original work. Specifically, genetic and antigenic data in the 12-year timeframe 2003 – 2015 corresponding to only cell passage category was considered. The data was then randomly divided into 90% training and 10% test datasets in order to train and evaluate the performance of the model, respectively.
+
+2) The model relies on metadata in the prediction, which significantly limit its usage in applications.
+
+Response:
+
+The incorporation of meta-data enhances model prediction, and in practice, we do not expect this to be a limiting factor. The meta-data information encoded in our model, which includes virus avidity, antiserum potency, and passage, simply involves the name and passage information of the two viruses used in each HI assay (i.e., the virus used to generate antiserum and that used for testing). For H3N2, this information is readily available in the Crick Institute WHO reports, and it is routinely reported as part of influenza surveillance based on HI assays.
+
+In terms of testing or applying our trained model in practice to predict the outcomes of HI assays (and more specifically, normalized HI titres), users would simply provide the HA1 sequences for the two viruses to be used in the HI assay, along with the names of those viruses and associated passaging system used for virus culturing (e.g., egg or cell). For the latter, a user could test different inputs to explore a variety of passaging approaches, or they could input their passage of choice (e.g., based on what passaging system may be available to them or their lab in practice). Our prediction system will also function, albeit with performance degradation, if no meta-data information is provided (see Supp. Fig. 3(a)). This flexibility is further highlighted in a web-based application that we have now developed, which seeks to enable scientists (including wet-lab scientists) to make HI assay predictions using our trained algorithm. This system asks users to input a pair of HA1 sequences for the virus isolate and antiserum, and optionally the names and passaging information of both. The system will then report the predicted normalized HI values. Based on the season of the virus isolates being tested, the web application allows the user to select the appropriate model trained up to (but excluding) the test season. The web application is hosted on the Hugging Face Spaces platform, accessible at https://huggingface.co/spaces/sawshah/SAP_H3N2.
+
+While not an issue for H3N2, for any specific data sets where complete meta-data information is not available for model training, the approach is also easily adaptable. This is demonstrated in a model that we have now implemented based on a H1N1 dataset (see the response to the Comment 4 below), for which comprehensive passage information was not available.
+3) The antigenic evolution of the influenza virus is cluster-wise. It is important to consider the virus population when studying the evolution of the virus.
+
+Response:
+
+The antigenic evolution of H3N2 has indeed been shown in prior studies to undergo some level of punctuated, or cluster-wise, antigenic evolution. Most notable is the seminal work by Smith et al., 2004, which reported 10 antigenic cluster transitions over the span of 35 years, where on average a cluster remained dominant for 3.3 years. Cluster transitions are related to large antigenic drift of virus isolates in a season with respect to virus isolates from previous seasons. The results of Smith et al., 2004 demonstrate that cluster transitions do not occur frequently, and for most influenza seasons the antigenic evolution is more mild. While to our knowledge antigenic clusters have not been clearly reported in more recent influenza seasons, analysis of our dataset shows a few specific seasons for which large antigenic drift occurred; namely, the 2016NH and 2019NH seasons (Fig. 3a) between 2016 to 2020.
+
+As far as our predictive model is concerned, if a cluster transition were to occur in a season, the system would simply make prediction for circulating viruses with relatively large antigenic drift. A characteristic feature of our model is that it adapts to new data as it becomes available (since it is progressively trained each season as new antigenic data becomes available), with the past two seasons carrying the most predictive power (see Supp. Fig. 8). This ensures that the model is continually updated in line with the antigenic evolution of influenza, regardless of whether a large (cluster defining) antigenic change or more mild antigenic drift occurs in individual seasons. Moreover, by evaluating performance for every season from 2014NH to 2020SH, we see that the model gives robust predictions in all cases, irrespective of whether a putative cluster-transition event occurs or not. For the two seasons where large antigenic drift most clearly occurs (2016NH and 2019NH), our model performance degrades slightly, but we show that this can be greatly improved with partial HI titre data in the season (see Fig. 3b).
+
+Hence, while our model does not explicitly incorporate cluster-transition information, it does capture and adapt to cluster-transition events and continues to provide robust predictions.
+
+4) As a new framework for predicting antigenic variation of influenza viruses, it is necessary to test its performance in other subtypes such as A(H1N1) and influenza B virus
+
+Response:
+
+Thank you for the suggestion. While our study is focused on seasonal H3N2, the proposed seasonal antigenic prediction method and framework is general and can be easily applied to other influenza subtypes, provided sufficient data is available for model training and evaluation. To demonstrate this, we have now applied our method to a publicly available data set that has been made available for seasonal IAV H1N1 (Gregory et al., 2016) spanning 18 influenza seasons from 2001NH to 2009SH. For this data set, comprehensive passage information was not available, hence only virus avidity and antiserum potency were encoded as meta-data (based on the virus names). We evaluated the performance of our AdaBoost-based seasonable prediction approach on this dataset, with results shown in Figure R2. On average, the H1N1 system achieved a comparable but higher average MAE compared with H3N2 (0.75 versus 0.70). This higher average MAE is likely attributed to the lack of passage information, particularly given that the passage information was found to significantly improve prediction performance for H3N2 (Supp. Fig. 3a). Seasonal fluctuations in performance were also more pronounced for H1N1, with season 2005SH achieving a significantly low MAE, while seasons 2003NH and 2007NH exhibited relatively high MAEs (Figure R2). These fluctuations can be attributed to the observed antigenic drift during those seasons (Figure R3). Specifically, seasons 2004SH and 2005SH displayed a minor antigenic drift (Figure R3b and Figure R3c), while season 2007NH showed a more
+substantial antigenic drift (Figure R3d). In the case of season 2003NH, although the antigenic drift appears to be small (Figure R3a), the higher predicted MAE may also be influenced by the limited availability of circulating isolates during that season (Supp. Fig. 9a).
+
+We have included this result in the revised text in the 'Discussion' section and added Figure R2 as a (new) Supplementary Figure 9b.
+
+Currently, there is a lack of available antigenic data for influenza B. Compared with H3N2, the antigenic evolution of influenza B has been less investigated. Once sufficient data for influenza B becomes available, a similar seasonal predictive model for this subtype can be developed.
+
+![Bar chart showing MAE performance for AdaBoost model across 20 influenza seasons, with 'Average' cell indicating overall score](page_414_678_627_120.png)
+
+Figure R1 The MAE performance of the proposed AdaBoost model for seasonal antigenic prediction of IAV H1N1 over 20 influenza seasons from 2001NH to 2009SH. The 'Average' cell on the right indicates the score averaged over the 20 seasons. The darker colour cells indicate better performance.
+
+![Scatter plots showing antigenic drift in circulating isolates compared to previous two seasons](page_153_1012_1142_377.png)
+
+Figure R3 Antigenic maps for IAV H1N1 to visualize the antigenic drift in circulating isolates compared to isolates from the previous two recent seasons. (a-c) Small antigenic drift in seasons 2003NH, 2004SH, and 2005SH. (d) Large antigenic drift in season 2007NH. Each square in a grid indicates antigenic difference of two units, corresponding to a four-fold dilution of the antibody in the HI assay. Large antigenic drift is indicated by presence of circulating isolates (red circles) dispersed far from past isolates (grey points).
+REFERENCES
+
+Gregory, V. et al. (2016) 'Human former seasonal Influenza A (H1N1) haemagglutination inhibition data 1977-2009 from the WHO collaborating centre for reference and research on influenza, London, UK'.
+Hie, B. et al. (2021) 'Learning the language of viral evolution and escape', Science, 371(6526), pp. 284–288.
+Huddleston, J. et al. (2020) 'Integrating genotypes and phenotypes improves long-term forecasts of seasonal influenza A/H3N2 evolution', Elife, 9, p. e60067.
+Neher, R.A. et al. (2016) 'Prediction, dynamics, and visualization of antigenic phenotypes of seasonal influenza viruses', Proceedings of the National Academy of Sciences, 113(12), pp. E1701–E1709.
+Qiu, T. et al. (2020) 'A benchmark dataset of protein antigens for antigenicity measurement', Scientific Data, 7(1), pp. 1–8.
+Smith, D.J. et al. (2004) 'Mapping the antigenic and genetic evolution of influenza virus', Science, 305(5682), pp. 371–376.
+REVIEWERS’ COMMENTS
+
+Reviewer #3 (Remarks to the Author):
+
+In my opinion, the authors have thoroughly addressed both of the previous reviewers' concerns.

0ba2b4d6f85b2eb6eefa9be26b42505c765a3dba58e4a3b2a285bc42de9f220c/preprint/preprint.md

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+Seasonal antigenic prediction of influenza A H3N2 using machine learning
+
+Syed Awais Wahab Shah
+Hong Kong University of Science and Technology
+Daniel Palomar
+Hong Kong University of Science and Technology
+Ian Barr
+WHO Collaborating Centre for Reference and Research on Influenza https://orcid.org/0000-0002-7351-418X
+Leo Poon
+University of Hong Kong https://orcid.org/0000-0002-9101-7953
+Ahmed Abdul Quadeer
+Hong Kong University of Science and Technology
+Matthew McKay
+matthew.mckay@unimelb.edu.au
+University of Melbourne
+
+Analysis
+
+Keywords:
+
+Posted Date: May 24th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2924528/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on May 7th, 2024. See the published version at https://doi.org/10.1038/s41467-024-47862-9.
+Seasonal antigenic prediction of influenza A H3N2 using machine learning
+
+Syed Awais W. Shah¹, Daniel P. Palomar¹,², Ian Barr³,⁴, Leo L. M. Poon⁵,⁶, Ahmed Abdul Quadeer¹,*, and Matthew R. McKay⁴,⁷,*
+
+¹Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China
+²Department of Industrial Engineering & Decision Analytics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR, China
+³WHO Collaborating Centre for Reference and Research on Influenza, Melbourne, Victoria, Australia
+⁴Department of Microbiology and Immunology, University of Melbourne, at The Peter Doherty Institute for Infection and Immunity, Melbourne, Victoria, Australia
+⁵School of Public Health, LKS Faculty of Medicine, The University of Hong Kong, Hong Kong SAR, China
+⁶Centre for Immunology & Infection, Hong Kong Science Park, Hong Kong SAR, China
+⁷Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne, Victoria, Australia
+*Corresponding authors: Ahmed Abdul Quadeer (eeaaquadeer@ust.hk) and Matthew R. McKay (matthew.mckay@unimelb.edu.au).
+ABSTRACT
+
+Antigenic characterization of circulating influenza A virus (IAV) isolates is routinely assessed by using the hemagglutination inhibition (HI) assays for surveillance purposes. It is also used to determine the need for annual influenza vaccine updates as well as for pandemic preparedness. Performing antigenic characterization of IAV on a global scale is confronted with high costs, animal availability, and other practical challenges. Here we present a machine learning model that accurately predicts (normalized) outputs of HI assays involving circulating human IAV H3N2 viruses, using their hemagglutinin subunit 1 (HA1) sequences and associated metadata. Each season, the model learns an updated nonlinear mapping of genetic to antigenic changes using data from past seasons only. The model accurately distinguishes antigenic variants from non-variants and adaptively characterizes seasonal dynamics of HA1 sites having the strongest influence on antigenic change. Antigenic predictions produced by the model can aid influenza surveillance, public health management, and vaccine strain selection activities.
+
+INTRODUCTION
+
+Genetic changes accumulated in the influenza virus population may alter their antigenic properties, resulting in antigenic drift\(^1\). Antigenically drifted influenza strains may escape immunity induced by previous infection or vaccination\(^2\), leading to increase in morbidity and mortality\(^1\). To counter antigenic drift, influenza virus strains included in the human influenza vaccine are regularly updated. The World Health Organization (WHO) holds vaccine composition meetings (VCMs) twice each year to recommend vaccine strains for the upcoming northern hemisphere (NH) and southern hemisphere (SH) influenza seasons\(^3\). Genetic and antigenic characteristics of circulating isolates are considered when recommending vaccine strains at each meeting\(^3\).
+
+Antigenic characteristics of circulating isolates are primarily determined through hemagglutination inhibition (HI) assays utilizing ferret post-infection antisera, although assessments using both human pre- and post-vaccination antisera are also conducted\(^3\). The HI assay measures the cross-reactivity of a test virus isolate to a serum raised against a reference virus isolate in ferrets or against the vaccine viruses in humans. Ferret antisera are produced in naïve animals and hence have high specificity compared to human sera who generally have extensive cross-reactive antibodies due to encountering multiple infections or vaccinations against influenza. Large-scale antigenic characterization of circulating isolates using HI assays incur high cost and are time and labour intensive\(^4,5\).
+Computational methods that predict ferret HI titres of influenza viruses using genetic sequence data may help to reduce these burdens\(^{1,6}\). Accurate sequence-based models could enable more comprehensive antigenic surveillance of circulating virus isolates without the need for increased experimental resources\(^1\). The efficiency of evolutionary monitoring and vaccine selection procedures may be improved by providing targeted sets of isolates for experimental evaluation. Furthermore, by learning the complex map from genetic to antigenic changes, accurate prediction methods could yield new insights into influenza evolution and the processes underpinning antigenic drift\(^{2,7}\).
+
+Here we develop a machine learning (ML) model that predicts antigenic properties of influenza A virus (IAV) H3N2 isolates circulating in a season using their HA1 sequences and associated metadata, while being trained on data from past seasons only. The model is designed and evaluated for predicting, on a season-by-season basis, HI titres of virus-antisera pairs involving viruses sequenced globally as part of WHO’s seasonal influenza surveillance. This approach is distinct from previous sequence-based HI titre prediction methods\(^{4,7–11}\), which in many cases have considered the problem of predicting HI titres of virus-antisera pairs randomly selected over time. For training and testing our model, we use the IAV H3N2 antigenic data of influenza seasons from 2003 – 2021 reported by the Worldwide Influenza Centre at the Francis Crick Institute\(^{12}\), genetic data available at influenza sequence databases\(^{13,14}\), and their associated metadata. The model predicts HI titres of virus-antisera pairs with a mean absolute error (MAE) of 0.738 antigenic units (where 1 antigenic unit \( \approx \) 2-fold change in HI titre) per season and exhibits a strong discriminatory ability in distinguishing antigenic variants across seasons. The RF model is a data-driven model that captures nonlinear effects in the relation between IAV H3N2 antigenic and genetic changes, which has been suggested by recent experimental studies\(^{15,16}\). We show that the model's predictive power is robust to limiting training data per season. Moreover, incorporating a small amount of antigenic data from circulating isolates in model training significantly enhances its accuracy, particularly for seasons associated with strong antigenic drift. The model identifies key sites with the strongest impact on IAV antigenic change, most of which are located in HA1 epitopes, and reveals how they vary across different seasons. Overall, accurate prediction of HI titres by the developed model across seasons shows its viability for seasonal antigenic characterization of IAV H3N2.
+RESULTS
+
+Machine learning model for seasonal antigenic characterization of IAV H3N2
+Our ML method for seasonal antigenic characterization of IAV H3N2 (Fig. 1a) was designed to mimic the WHO VCM protocols12 (Supp. Fig. 1). The NH VCM is held each February and considers antigenic data for circulating isolates from the preceding September to January, while the SH VCM is held each September and considers isolates from the preceding February to August. Each of these periods constitutes an influenza season. For any given season, our model is trained using genetic, antigenic, and metadata information available prior to that season. The trained model predicts antigenic data for the current season based on genetic data of isolates circulating in that season, along with metadata (Fig. 1a).
+
+The model employs a random forest (RF) approach (Fig. 1b) which learns a nonlinear mapping from the encoded data that predicts the antigenic difference (defined as normalized HI titre (NHT); Materials and Methods) between isolates in a virus-antisera pair, based on their HA1 genetic sequence and metadata information. Pairwise genetic differences in the HA1 gene of isolates in a virus-antisera pair are encoded using a mutation matrix from the amino acid index 2 (AAindex2) database17, while metadata is represented using one-hot-encoding (Materials and Methods, Fig. 1c). The metadata includes virus avidity7, antiserum potency7, and passage category (egg or cell) of virus isolates and antisera.
+
+Model training, optimization, and validation
+For model training, optimization, and evaluation, we compiled HI titre data of IAV H3N2 from reports published by the Worldwide Influenza Centre (WIC) at the Francis Crick Institute, London12 and genetic data from influenza sequence databases, GISAID13 and IVR14. The processed dataset included NHTs of 36,709 virus-antisera pairs with corresponding metadata, spanning 37 influenza seasons from 2003NH to 2021SH (Materials and Methods). Data availability was limited in the early seasons and increased progressively over time (Supp. Fig. 2a). Preliminary assessment using a baseline model (Materials and Methods) revealed sufficient data for reliable predictive performance from the 2012NH season onwards (Supp. Fig. 2b). The four seasons 2012NH to 2013SH were selected as validation seasons to perform feature selection and model optimization.
+
+Using the validation seasons, it was found that incorporating all four metadata features provided optimal performance (MAE of 0.788) (Supp. Fig. 3a) and substantially outperformed the baseline model trained with no metadata (MAE of 0.996). The metadata capture distinct
+information: virus avidity and antiserum potency account for experimental variations among HI assays7, while passage category informs about antigenicity-altering mutations incurred during in vitro propagation of virus isolates using cell or egg lines1,18. Further optimization refined the model hyperparameters and selected the optimal amino acid mutation matrix for data encoding (Supp. Fig. 3b and c; for details see Materials and Methods).
+
+Optimized model accurately performs seasonal antigenic characterization
+
+The performance of the optimized model in predicting NHTs was evaluated for each of the 14 test seasons (2014NH to 2020SH). This yielded a MAE, averaged across seasons, of 0.738 antigenic units (Fig. 2a). Predictions were generally more accurate in more recent influenza seasons, likely due to the increased availability of data over time (Supp. Fig. 2a). Further experiments assessed the robustness of our model to variations in the training data. Prediction accuracy was retained even under conditions where there is substantially less antigenic data for training (Supp. Fig. 4a and b). Minimal effects on performance (compromised performance for a single season only) were observed when omitting HI titre data from an entire season (Supp. Fig. 4c).
+
+The ability of our model to detect antigenic variants was also examined. An influenza virus is considered antigenically distinct from the virus used to generate the antiserum if a more than 4-fold reduction in HI titres is observed against the antiserum4,19. Our model classified antigenic variants and non-variants with an average area under the receiver operating characteristic (AUROC) of 92% across the 14 test seasons (Fig. 2b). Additional metrics (e.g., sensitivity and specificity) further demonstrated classification accuracy (Supp. Fig. 5a).
+
+To further calibrate model performance, we assessed an alternative approach based on the NextFlu linear substitution model7 (Materials and Methods). NextFlu is a widely used model that has demonstrated good capacity to predict NHTs under a non-seasonal framework, where the model was trained on data spanning all time periods and the predictions were made for randomly selected historical NHTs. Here, when evaluated under the seasonal prediction framework (Fig. 1a), the NextFlu linear substitution model returned a higher average MAE (0.819) compared with the RF model (0.738) (Supp. Fig. 6a).
+
+Partial antigenic information of circulating isolates alleviates antigenic drift effects
+
+Disregarding the initial seasons of 2014, the MAE of the RF model was well below average in two seasons: 2016NH and 2019NH (Fig. 2a). This appears to be attributed to a larger antigenic drift observed in these seasons (Fig. 3a). Importantly, performance was recuperated in subsequent seasons and degradation was not carried forward (Fig. 2a).
+While significant antigenic drift makes prediction more challenging, access to partial antigenic data for circulating virus isolates in a season may help overcome this challenge. Further analysis confirmed this hypothesis. For each test season, including as little as 10% of the antigenic data for circulating isolates in the model training improved performance uniformly, with the most significant gains observed in those seasons with large antigenic drift (Fig. 3b and Supp. Fig. 7). Access to a small amount of antigenic data can therefore help ensure high prediction accuracy irrespective of the level of drift experienced by IAV H3N2.
+
+Antigenically important sites identified by the model are temporally associated with HA1 epitopes
+
+Analysis of historical data has demonstrated that antigenic evolution of influenza is strongly influenced by mutations at a subset of sites within HA1\(^{7,20,21}\). Our model enables identification of the specific HA1 sites that have the greatest effect on antigenic changes during a given season, providing insights into the seasonal dynamics of these sites. Such sites can be predicted based on their feature importance\(^{22}\) scores from the model (*Materials and Methods*). Aggregating the top 20 sites identified for seasons 2014NH to 2020SH revealed 37 important sites in total (**Fig. 4a**). Of these, 32 were located within established HA1 epitopes\(^{20,23,24}\) (A, B, C, D, and E). Substitutions in these epitope regions are known to have a dominant effect on the antigenic evolution of IAV H3N2\(^{2,20}\). Epitopes A, B, and D were statistically significantly enriched among the identified 37 sites, with enrichment in A and B being highly significant (p < 0.005). This supports previous findings that epitopes A and B are the most immunodominant\(^{21,24}\).
+
+Seasonal analysis (**Fig. 4b**) revealed seven sites within epitopes that were consistently ranked in the top 20 sites over all 14 seasons from 2014NH to 2020SH. These comprised three sites in epitope A (140, 144, 145), three in B (158, 186, 189), and one in E (62). The relative importance of epitopes A and B persisted across all seasons; though epitope A appears to have become more important more recently (**Fig. 4b and c**). Outside epitopes A and B, epitope D has seemingly decreased in importance in the more recent seasons, while epitope C has increased in importance (**Fig. 4b and c**). In epitope E, site 62 is particularly noteworthy. This site has increased significantly in importance, achieving the highest importance score (among all sites) for the most recent season investigated, 2020SH (**Fig. 4b**). Site 62 is located near the functionally important glycosylation site 63 (ref \(^{25}\)), and it was previously identified as a substitution responsible for a past antigenic cluster transition\(^{2}\).
+
+Of the 37 important sites identified across seasons, five did not belong to any known epitope (**Fig. 4a**). Among these, four sites are in close proximity (with distance between carbon-alpha atoms < 8Å) to the known epitopes: sites 223 and 241 are located close to epitope D, site 269
+is located close to epitope E, while site 225 is close to both epitopes A and D (**Fig. 4c**). Two of these sites, 183 and 225, are part of the functionally important receptor binding sites (RBS)\(^{24}\). Site 225 was consistently ranked in the top 20 important sites across all seasons considered (**Fig. 4b**). Mutations at site 225 can alter the fitness landscape of epitope B\(^{26}\), and a mutation at this site was linked to egg-passaging adaptation in isolates circulating from 2019 to 2021\(^{27}\).
+
+Overall, our model identified HA1 sites, predominantly within known epitopes (but also some outside), that contributed significantly to the antigenic evolution of IAV H3N2 in the last decade, and characterized the dynamics of these antigenic “drivers” over time.
+
+**DISCUSSION**
+
+We have presented a machine learning model that can accurately predict antigenic properties (in terms of NHTs) of IAV H3N2 isolates circulating in an influenza season using only their genetic sequence data and associated metadata. The model was trained and tested under a seasonal framework (**Fig. 1a**), mimicking the periodic influenza surveillance process followed by WHO for annual vaccine strain selection. The model remained robust under data-limited scenarios.
+
+Computational methods have been developed previously for antigenic characterization of IAV. These include the well-known antigenic cartography\(^2\) method, a multi-dimensional scaling approach that is helpful to visualize and study the relationship among virus isolates and antisera in two dimensions. Other sequence-based models have also been developed\(^{1,6}\), most of which considered a non-seasonal framework\(^{4,7-11}\), distinct from the seasonal framework adopted in this work. The non-seasonal framework disregards season/time information and randomly distributes HI titres (or virus isolates) in the multi-seasonal HI data among training and test datasets. Under this framework, the testing data may comprise isolates having antigenic changes that the model has already learned during training, which can lead to overfitting and inflate model performance. In addition to sequence data, information such as structural and physicochemical properties of HA have also been used for IAV antigenic prediction\(^{10,11}\).
+
+Antigenic changes in influenza HA have been shown to be nonlinearly related to genetic changes in recent experimental studies\(^{15,16}\). These studies demonstrated that epistatic interactions or specific HA backgrounds can affect the antigenicity of HA substitutions. Thus, linear or additive models that assume independent effects of HA substitutions on antigenicity might be suboptimal for capturing the genetic-to-antigenic relation for HA. By adopting a data-
+driven ML approach, our model captures nonlinearities in the mapping between genetic and antigenic changes. This is shown to yield improved performance when compared to a linear prediction model7 (Materials and Methods, Supp. Fig. 6a), even when our RF model’s parameters are matched to those of the linear model (Supp. Fig. 6b).
+
+Previous studies7,11,28 have demonstrated the value of incorporating virus avidity and antiserum potency in computational antigenic characterization of IAV H3N2. Our findings highlight the importance of using passage history categories of virus isolates and antisera (e.g., if ferret antisera were raised to cell-propagated or egg-propagated virus isolates), as additional metadata features in model development. Using passage categories alone leads to performance improvement similar to that of using virus avidity and antiserum potency, and we show that incorporating all of these features together leads to significantly improved model performance (Supp. Fig. 3a).
+
+The model’s predictive power is robust to variations in the training data (Supp. Fig. 4a and b). Omitting data from a complete season degrades model performance in the following two seasons, but not beyond that (Supp. Fig. 4c). This indicates that errors due to a lack of data in specific seasons are not retained in later seasons, and only affect the model’s accuracy for a maximum of one or two test seasons. Additional tests showed that training with data from only the two most recent seasons performed similarly to training based on all historical seasons (Supp. Fig. 8). This is in line with the observed rate of antigenic drift of 1.2 units per year2 (equivalent to two seasons) for IAV H3N2, which infers that the antigenicity of H3N2 isolates would differ substantially beyond two seasons and thereby the corresponding data would likely contribute less to predicting antigenicity of the isolates in the current season.
+
+Some clades of H3N2, e.g., 3C.2a, failed to react in HI assays in the past as they had lost the ability to agglutinate red blood cells (RBC)29. To avoid such issues, HI assays are complemented with virus neutralization assays3. In comparison to HI assay data, neutralization assay-based antigenic data has been rarely used5 for developing computational models. This is because the HI assay is still considered the gold standard for characterizing IAV antigenicity, given its well-established protocols and high level of reproducibility and reliability, and in the last few years very few H3N2 viruses do not bind avian or mammalian RBC. Nonetheless, our model can be adapted to predict neutralization titres, a worthwhile problem to pursue in a future study.
+
+To predict NHTs, we used genetic information from the HA1 subunit of the HA protein since it contains the key antibody binding sites (epitopes)1,2. Recent research has shown high rates of amino acid substitutions outside the HA1 epitope region as well as in the other influenza surface protein (neuraminidase, NA), possibly indicating positive selection by host immunity1.
+The proposed model could be augmented with genetic information of the HA2 subunit and NA protein for potentially improving prediction accuracy and for examining the role (and temporal dynamics) of HA2 and NA in driving further antigenic changes in IAV H3N2. We focused on IAV H3N2 due to the availability of rich HI titre data for this subtype, as compared to other human influenza viruses\(^{1,19}\). Our findings, which show that ML-based methods can predict IAV H3N2 HI titres on a seasonal basis, motivate development of methods to track the antigenic evolution of other influenza subtypes, such as A (H1N1) pdm09 or influenza B viruses, provided sufficient antigenic data is available.
+
+Serological data is useful not only for guiding IAV vaccine strain selection during VCMs, but also for building computational models addressing general questions related to influenza evolution. These include models for identifying antigenic clusters\(^{2,30,31}\), and predicting relative growth of viral clades (genetically related isolates stemming from a common ancestor) and forecasting the clades that will likely proliferate in the next season\(^{5,32-35}\). The predictions produced by our model can augment experimentally available serological data and can, in turn, be incorporated into models of influenza evolution that use antigenic data.
+
+Seasonal influenza poses a significant threat to global public health, with high mortality and morbidity rates. The virus's ability to evolve and evade population-level immunity developed from past infections and vaccinations underscores the importance of continued antigenic surveillance for controlling future influenza outbreaks. ML-based models, like the one proposed in this work, offer powerful tools for complementing existing antigenic characterization efforts, enabling comprehensive global influenza antigenicity monitoring, improved vaccine strain selection, and effective public health management.
+
+LIMITATIONS OF THE STUDY
+
+The RF model designed for seasonal antigenic characterization has several limitations. First, like any ML model, its performance is contingent on the availability of training data (**Supp. Fig. 2b**). Given the limited training data available before 2012 (**Supp. Fig. 2a**), we evaluated the model’s performance for seasons after 2012 only. Second, regardless of the amount of training data, the model’s performance is reduced in seasons with large antigenic drift (**Fig. 3a**). A small amount of antigenic information of circulating virus isolates (e.g., as low as 10% of the available data) for model training can help to largely overcome this issue (**Fig. 3b**). Third, since the model uses amino acid sites as features, it can determine the importance of individual sites (**Fig. 4**), but not the specific amino acid substitutions. This may be addressed in future work by using amino acid substitutions as features for the RF model. Lastly, while the RF model can learn a non-linear genotype-to-phenotype mapping and identify important amino
+acid sites individually, it cannot explicitly identify collective effects of amino acid sites (i.e., epistasis) on antigenicity. Interpretable artificial intelligence techniques, such as Shapley Additive exPlanations (SHAP)\(^{36}\), may potentially be explored to study the effect of interactions between amino acid sites.
+
+CODE AVAILABILITY
+
+Source codes implementing the proposed RF model and the results presented in this paper can be accessed from GitHub (https://github.com/saws-lab/SAP_H3N2_ML). HI data can be downloaded from the Francis Crick Institute website\(^{12}\). HA protein sequences can be downloaded from the GISAID\(^{13}\) and the IVR\(^{14}\) databases.
+
+SUPPLEMENTARY INFORMATION
+
+The accession numbers of used genetic sequences are provided in Supplementary Table 1.
+
+ACKNOWLEDGEMENT
+
+We thank all the World Health Organization National Influenza Centres, comprising the WHO Global Influenza Surveillance and Response System (GISRS), for their continuous monitoring of influenza strains around the world. We especially acknowledge the Worldwide Influenza Centre at the Francis Crick Institute, London, for sharing influenza antigenic data through reports on their webpage\(^{12}\), without which this research would not have been possible. We acknowledge all researchers at the originating and submitting laboratories that sequenced influenza viruses and made them available at GISAID and IVR databases.
+
+S.A.W.S and D.P.P. were supported by the General Research Fund (16201620) of the Hong Kong Research Grants Council. L.L.M.P. was supported by the Theme-Based Research Scheme (T11-712/19-N) of the Hong Kong Research Grants Council. A.A.Q. and M.R.M. were supported by the Australian Research Council through Discovery Project (DP230102850). M.R.M. is the recipient of an Australian Research Council Future Fellowship (FT200100928) funded by the Australian Government.
+MATERIALS AND METHODS
+
+Antigenic and genetic datasets of IAV H3N2
+
+We obtained the antigenic HI titre data for IAV H3N2 from 35 biannual reports published during 2003 – 2021 by the Worldwide Influenza Centre (WIC) at the Francis Crick Institute, London12. A total of 82,776 HI titre values against virus-antisera pairs were extracted from these reports, where in each pair the virus represents the circulating/test virus isolate and the antiseraum represents the reference virus isolate against which the post-infection ferret antiseraum was raised. From these reports, we also extracted the metadata information of virus isolates including their names, passages, and collection dates. Based on the passage information, we labelled each virus isolate with either a cell or egg passage category. We used both the name and passage to represent a unique virus isolate. Invalid HI titers37 and HI titres of antiserum-virus pairs with passage category other than egg or cell were removed. Following standard practices of the WHO2,7, we computed NHT-based antigenic differences for each virus-antiseraum pair from the compiled HI titre values. NHT is defined as the difference of the 2-folds dilutions of the homologous and heterologous titre values as follows2,7
+
+\[
+d_{ab} = \log_2(T_{b\beta}) - \log_2(T_{a\beta}),
+\]
+
+where the homologous titre \( T_{b\beta} \) and the heterologous titre \( T_{a\beta} \) represent the reciprocal of the maximum dilution of antiseraum \( \beta \) that is required to inhibit cell agglutination by the reference virus isolate \( b \) and the test virus isolate \( a \), respectively. In case the homologous titre was unavailable, we used the maximum titre value available for that antiseraum2. We removed the virus-antiseraum pairs against which sequences were not found in the influenza genetic databases and used the remaining antigenic data for seasonal antigenic characterization. This included a total of 36,709 NHTs corresponding to 3,737 virus isolates paired with 268 antisera.
+
+In addition to NHT, Archetti Horsfall Titre (AHT)9,38 is also used to characterize antigenic difference between virus isolates. AHT measurement is a two-way analysis39 that requires four HI assays, and antiseraum must be raised against each virus isolate in a pair. AHT is not used by WHO40 and thus was not considered in this work. We also note that HI assays are dependent on agglutination of red blood cells. The source of these red blood cells has varied from chicken to turkey and then to guinea pig over the course of time, due to changes in receptor binding sites41 of IAV H3N2. While these variations are present in the dataset that we consider, the insensitivity of the model to these variations shows that they are likely taken care of by the model parameters of virus avidities and antiseraum potencies7.
+
+For the virus isolates and antisera in this data, we downloaded the corresponding HA protein sequences from the GISAID13 and the IVR14 databases. We aligned the HA protein sequences
+using MAFFT42 with the full-length HA protein (566 amino acids) of A/Beijing/32/1992 (isolate ID: AAA87553)7 as a reference. We restricted our model to the HA1 subunit (amino acid sites 17 to 345) of the HA protein, as this subunit forms globular head of the HA protein containing key epitopes known to be important for antigenicity of IAV H3N21,2.
+
+Encoding genetic and metadata information
+To provide inputs in numeric form to the RF model, we encoded the genetic sequences of virus isolates using the amino acid mutation matrices in AAindex2 database17, and the metadata information of virus isolates using one-hot encoding scheme (Fig. 1c). The encoded genetic and metadata information was used as input features of the RF model.
+
+The AAindex2 database contains 94 20×20 amino acid mutation matrices, where each numeric entry of a matrix describes the rate at which an amino acid in a protein sequence is replaced by another amino acid over evolutionary time. These numerical values are based on the physiochemical and biochemical properties of pairs of amino acids. Of these 94 matrices, two matrices (MEHP950101 and MEHP950103) were discarded for being incomplete as they included gaps in their entries. Thus, the remaining 92 matrices and a binary encoding scheme were investigated for encoding the genetic information of isolates. Specifically, for each virus-antisera pair, we computed genetic difference from a reference (antisera) to test virus isolate by encoding the amino acid mutations at each site of their HA1 protein sequences using the numeric entry of the corresponding amino acid pairs in mutation matrices as described in ref.38. Briefly, for a specific mutation matrix M, the encoded genetic difference between the sequences of a virus v and an antiserum a at HA1 position i is given by:
+
+\[
+g_i = m_{v_i,v_i} + m_{a_i,a_i} - 2m_{a_i,v_i},
+\]
+
+where \( v_i \) and \( a_i \) are respectively the amino acids at position i in the virus and antiserum sequence, and \( m_{j,k} \) is the entry of the matrix M corresponding to amino acids j and k.
+
+In the binary encoding scheme, for each virus-antisera pair, the amino acid differences at each HA1 site were encoded as '1' and otherwise '0'. Any ambiguous amino acid or gap in the protein sequences was also encoded as zero to avoid mapping of ambiguous genetic information to antigenicity. To sum, for each virus-antisera pair, the encoded genetic difference was represented by a numeric vector of length 329 corresponding to the length of the HA1 protein sequence.
+
+Each metadata information of isolates—including their virus avidities, antiserum potencies, and passage categories—was considered as categorical data and converted to numeric data using one-hot encoding scheme in Scikit-learn43. The encoded vector corresponding to each
+virus-antisera pair represents virus avidity, antiserum potency, and passage categories of virus and antiserum. The virus avidity of an isolate is represented by a binary sparse vector of length equal to the number of unique virus isolates in the training dataset, wherein all entries are '0' except a '1' at the position of that isolate in an array of all the virus isolates sorted by their collection dates, names and passages. Similar procedure was followed to represent the antiserum potencies corresponding to antisera. For instance, if the training dataset contains 100 unique virus isolates and 10 unique antisera, and considering the two passage categories (cell/egg) for isolates corresponding to both virus and antiserum, the one-hot encoding corresponding to each virus-antisera pair will result in a binary vector of length \(100+10+2+2 = 114\). Hence, the one-hot encoding scheme resulted in a sparse binary vector of length equal to the number of categories in each metadata information for the corresponding virus-antisera pairs in the training dataset. It is worth noting that when predicting the antigenicity of a circulating virus isolate against an antiserum, the virus avidity is represented by a zero vector. This is because the virus itself is not available during the model's training process under the seasonal framework.
+
+Training, validation, and test datasets
+
+The compiled dataset consisted of 37 influenza seasons from 2003NH to 2021NH. Under the seasonal framework (**Fig. 1a**), initially we considered each of these seasons as a test season and plotted the distribution, specifically the number of data samples of corresponding training and test datasets (**Supp. Fig. 2a**). For each test season \( s \), the training dataset includes the NHTs corresponding to past virus-antisera pairs starting from the earliest season 2003NH to the most recent season \( s - 1 \), while the test dataset includes NHTs of the isolates circulating in the test season \( s \) paired with the past antisera.
+
+We selected four seasons from 2012NH to 2013SH as validation seasons, which were used for model optimization. The next 14 seasons from 2014NH to 2020SH were selected as test seasons for model evaluation. This selection was based on the stable performance of a baseline model (explained below) over these seasons. Note that virus-antisera pairs available for the 2021NH season were very limited (**Supp. Fig. 2a**). Thus, this season was excluded from the analysis to allow reliable model evaluation. Unlike prior works\(^{19,40,44,45}\) that used the entire dataset (including test seasons) for model optimization, our model was optimized solely using the data of past seasons to prevent data leakage issues\(^{46}\) that could inflate model performance\(^{40}\).
+RF model
+
+In the designed RF model, the encoded genetic difference at each site of the HA1 protein sequences was treated as an input feature that nonlinearly contributes toward the computation of the NHT. The remaining features of the RF model consist of binary identifiers for the virus and antiserum related metadata information, including virus avidity, antiserum potency, and their passage categories (Fig. 1c). The designed RF model is an ensemble of decision trees in which each tree was trained on a bootstrap sample that was a subset of the training dataset. At each splitting node of a tree, the candidate set of features was a random subset of the features (including encoded genetic difference at each site of the HA1 protein sequences and one-hot encoded metadata information). The predicted NHT by the RF model is the average NHT by an ensemble of decision trees.
+
+The baseline model was based on the RF model with default hyperparameters within the module RandomForestRegressor in Scikit-learn43, where we used a random seed equal to 100 for reproducibility. No metadata information was provided to this model and binary encoding scheme was used. Hence, in this case, the NHTs were predicted based on only the binary encoded genetic difference at each site of the HA1 protein sequences of virus-antiserum pair.
+
+To optimize the RF model, we performed hyperparameter optimization independently for each of the 92 amino acid mutation matrices and for binary encoding. We considered six hyperparameters in the module RandomForestRegressor in Scikit-learn43 with each hyperparameter optimized over a search space defined as follows: n_estimators43—ranging from 50 to 1000 in steps of 25; max_features43— ranging from 0.1 to 0.75; max_depth43—ranging from 50 to 200 in steps of 10; min_samples_leaf43—ranging from 1 to 5 in steps of 1; min_samples_split43—ranging from 2 to 30; and bootstrap43—binary choice of true or false. The values of hyperparameter max_features43 were sampled from a uniform distribution, while the rest of the hyperparameters were sampled from a quantized uniform distribution47. Bayesian optimization procedure termed as the Tree of Parzen Estimator (TPE)47 under module hyperopt47 was used to automate the process of hyperparameter optimization over 100 runs on the defined search space. The MAE varied between 0.844 to 0.765, depending on the choice of the mutation matrix (Supp. Fig. 3c). This performance variation occurs because each mutation matrix incorporates specific amino acid attributes. The optimized RF model consisted of genetic difference encoded using the AZAE97010117 amino acid mutation matrix and the hyperparameters as n_estimators = 125, max_features = 0.376, max_depth = 200, min_samples_leaf = 1, min_samples_split = 10, and bootstrap = true. To ensure reproducibility, we maintained a fixed random state of 100 for each Python package across all simulations.
+Performance metrics
+
+To assess the performance of the developed model in a particular season, we computed the MAE between the measured \( d \) and predicted \( \hat{d} \) NHTs as
+
+\[
+MAE_S = \frac{\sum_{(i,j)\in S}|d_{ij} - \hat{d}_{ij}|}{\#(S)}.
+\]
+
+Here, \( S \) denotes the set of virus-antisera pairs \( (i,j) \) in a season and \( \#(S) \) represents the cardinality of the set \( S \).
+
+To compute the average performance of the model over \( N \) test seasons, we used the weighted average of the \( MAE_{S_n} \) obtained for the season \( n \), with the weights equal to the cardinality of the dataset in the season \( n \). This is given by
+
+\[
+\text{Average } MAE = \frac{\sum_{n=1}^N \#(S_n) \, MAE_{S_n}}{\sum_{n=1}^N \#(S_n)}.
+\]
+
+To compute the classification scores, the NHTs were converted to binary labels using a threshold of 2 antigenic units\(^{4,19}\) (equivalent to 4-folds change in HI titres). Thus, a virus-antisera pair was classified as either antigenic variant (NHT > 2) and assigned a binary label '1' or antigenically similar (NHT \( \leq 2 \)) and assigned a binary label '0'. The ability of the model to classify antigenic variants was then determined using standard classification metrics including accuracy, sensitivity, specificity, MCC, and AUROC. Similar to MAE, classification performance of the model across seasons was computed using a weighted average. Note that the classification threshold can be chosen to improve the classification performance for either antigenic variants or antigenically similar virus-antisera pairs, considering the target problem. For example, in the scenarios when both sensitivity and specificity are equally important, the threshold can be optimized to maximize Youden's index (sensitivity + specificity - 1) averaged over the most recent three seasons for a given test season (Supp. Fig. 5b).
+
+Antigenic cartography
+
+To observe antigenic drift of IAV H3N2 isolates across seasons (**Fig. 3a**), we performed antigenic cartography of these isolates using R's (version 4.2.0) *Racmacs* package\(^{48}\) (version 1.1.35). *Racmacs* uses the multidimensional scaling procedure, proposed in ref.\(^2\), to position virus isolates and antisera on a lower-dimensional space (2D in our case) based on their HI titres. The 2D coordinates of virus isolates were obtained using default settings of *Racmacs* with 1000 optimizations and setting parameter *minimum_column_basis* to 'none'.
+Feature importance scores of the RF model
+
+In a random forest model, the importance of a feature is calculated by each tree based on its ability to increase leaf purity through variance reduction\(^{22}\). The importance scores from each tree are averaged and normalized to a sum of one. The relatively high scores indicate more important features. We computed feature importance scores for all HA1 sites in the proposed RF model using the built-in function *feature_importances_* in Scikit-learn\(^{43}\). To compute these scores, the RF model was trained on subsets of training data from 2003NH to \( x \) (\( x \) ranges from 2014NH to 2020SH). For each subset, out of the 329 HA1 sites, we selected the top 20 sites corresponding to highest feature importance scores.
+
+Statistical significance of epitope enrichment in top sites (p-values)
+
+Epitope enrichment in the 37 important sites, identified using feature importance scores across seasons (**Fig. 4**), was calculated using a P value. It represents the probability of observing at least \( i \) sites out of \( j \) epitope sites in the set of important sites, where the set of important sites comprises 37 sites out of a total of 329 HA1 sites. Mathematically, this can be written as
+
+\[
+P = \sum_{q=i}^{\min(j,n)} \frac{\binom{j}{q} \left( \frac{329-j}{37-q} \right)}{\binom{329}{37}}.
+\]
+
+The null hypothesis that \( i \) epitope sites were observed in the 37 important sites by a random chance was rejected if \( P < 0.05 \).
+
+Structural analysis
+
+We used *Pymol* (www.pymol.org) for representing the identified important sites over the three-dimensional HA structure of IAV H3N2 A/Brisbane/10/2007 (available in the Protein Data Bank; PDB ID: 6aou\(^{49}\)). To calculate the distance between an epitope and an identified important site that did not lie in any known epitope, we measured the 3D distance between the carbon-alpha of each epitope site and that of the identified site. The identified site was considered close to the epitope if the calculated distance was less than eight Angstroms for at least one of the epitope’s sites.
+
+Linear prediction model (NextFlu)
+
+To benchmark our model's ability to capture non-linearities in the genetic-to-antigenic mapping, we employed the NextFlu substitution model, a well-known linear model for antigenic prediction. In the original work\(^7\), this model was evaluated under a non-seasonal framework. We adapted its implementation (available at https://github.com/nextstrain/augur/blob/master/augur/titer_model.py) to fit our seasonal
+framework (**Fig. 1a**) and input data format. Our adapted version, like the original, did not incorporate passage information and modelled NHT as a linear combination of genetic difference, virus avidity, and antiserum potency.
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+Fig. 1 Overview of the seasonal framework and the designed ML method for seasonal antigenic characterization of IAV H3N2.
+
+(a) Seasonal division of data into training and test datasets respectively for training and evaluation of computational methods in a time-series fashion. Under this framework, historical genetic, antigenic, and metadata information of virus isolates from past seasons are included in the training dataset, while genetic and metadata information of virus isolates from the current season form the test dataset.
+
+(b) The trained RF model was used to predict NHTs using only encoded genetic difference and metadata information of virus-antisera pairs.
+
+(c) Details of the encoding performed at the input of the RF model. The HA1 sequences of isolates in each virus-antisera pair were encoded using amino acid mutation matrix available in the AAindex2 database. One-hot encoding was used to represent the metadata information, which includes virus avidity, antisera potency, and passage category of isolates. The encoded genetic difference and metadata of each virus-antisera pair were used as input features of the RF model. Each training virus-antisera pair was labelled by NHT-based antigenic difference (see Materials and Methods).
+Fig. 2 Performance of the optimized model for seasonal antigenic characterization of IAV H3N2.
+
+(a-b) Model prediction and classification performance is shown in terms of (a) MAE and (b) AUROC respectively over 14 test seasons from 2014NH to 2020SH. The optimized model consisted of encoded genetic difference using the best-performing amino acid mutation matrix AZAE970101, optimized hyperparameters, and all features in the metadata information (virus avidity, antiserum potency, and passage category (egg or cell) of virus isolates and antisera) (Supp. Fig. 3). The classification score AUROC was obtained by converting the measured and predicted NHTs to binary labels such that if NHT was greater than 2 units it was assigned a binary label 1, otherwise 0. The ‘Average’ cell in (a-b) indicates the score averaged over 14 test seasons from 2014NH to 2020SH. The darker colour cells indicate better performance.
+Fig. 3 Partial antigenic information mitigates effects of seasonal antigenic drift.
+
+(a) Antigenic maps48 to visualize the antigenic drift in circulating isolates compared to isolates from the previous two recent seasons (see Materials and Methods). The maps on the left show two instances of large antigenic drift in the 2016NH (top-left) and 2019NH (bottom-left) seasons, while the maps on the right show two instances with small antigenic drift in the 2018SH (top-right) and 2020SH (bottom-right) seasons. Each square in a grid indicates antigenic difference of two units, corresponding to a four-fold dilution of the antibody in the HI assay. Large antigenic drift is indicated by presence of circulating isolates (red circles) dispersed far from past isolates (grey points).
+
+(b) The MAE performance of the model evaluated over 14 test seasons, ranging from 2014NH to 2020SH. The top panel displays the MAE performance of the model trained on data from 2003NH up to the corresponding test season. The bottom panel shows the MAE performance of the model when data of randomly selected 10% circulating isolates was included in model training. For each test season, average scores of 50 Monte Carlo runs are reported.
+a
+
+<table>
+  <tr>
+    <th>Epitope</th>
+    <th>Important HA1 sites aggregated across seasons</th>
+  </tr>
+  <tr>
+    <td>A<sup>*</sup></td>
+    <td>131, 135, 138, 140, 142, 144, 145</td>
+  </tr>
+  <tr>
+    <td>B<sup>*</sup></td>
+    <td>128, 158, 159, 160, 186, 189, 194, 196, 197</td>
+  </tr>
+  <tr>
+    <td>C</td>
+    <td>53, 278, 311, 312</td>
+  </tr>
+  <tr>
+    <td>D<sup>*</sup></td>
+    <td>121, 171, 173, 203, 208, 212, 213, 214, 219</td>
+  </tr>
+  <tr>
+    <td>E</td>
+    <td>62, 94, 261</td>
+  </tr>
+  <tr>
+    <td>Unknown</td>
+    <td>183, 223, 225, 241, 269</td>
+  </tr>
+</table>
+
+*P value < 0.005; *P value < 0.05
+
+b
+
+![Heatmap showing feature importance for HA1 sites across training data from 2003NH to 2020SH](page_246_320_1000_600.png)
+
+c
+
+![Surface representations of influenza hemagglutinin with labeled receptor binding sites (RBS) and buried sites](page_246_1040_1000_300.png)
+
+# receptor binding sites (RBS)
+* buried sites
+Fig. 4 Model-inferred important sites: Correspondence with known epitopes and seasonal dynamics.
+
+(a) Majority of the 37 important sites identified by the model based on the feature importance scores lie in known IAV H3N2 epitopes. The sites are color-coded according to epitopes. The sites that do not lie in any known epitope are referred as unknown. P value indicates the statistical significance of epitope enrichment within the identified important sites (see Materials and Methods).
+
+(b) The RF-based feature importance scores for the 37 important sites are analysed across subsets of training data from 2003NH to x (x ranges from 2014NH to 2020SH), with the top 20 sites based on the feature importance scores listed for each subset. The darker colour cells indicate higher importance score of a site.
+
+(c) Change in the set of important sites, color-coded by epitopes, across two seasons (2014NH and 2020SH) is displayed over the HA structure (Protein Data Bank ID: 6aou; A/Brisbane/10/2007). The sites in epitopes A and D are labelled in the top-view (left panel) while the sites in epitopes C, E, and the unknown region are labelled in the front-view (right panel). HA1 subunit is shown in white and the HA2 subunit is coloured grey.
+Supp. Fig. 1 The WHO framework for seasonal antigenic characterization of human influenza viruses.
+
+As an example, the framework is shown for the Northern Hemisphere and Southern Hemisphere vaccine composition meetings held respectively in the last week of Feb. 2021 and Sep. 2021. In each season, genetic characterization is performed for most of the circulating isolates. A few representative isolates are then selected for antigenic characterization.
+Supp. Fig. 2 Data distribution and the performance of baseline model over multiple influenza seasons.
+
+(a) Under the seasonal framework (Fig. 1a), the data is distributed into training and test datasets for each of the 37 seasons from 2003NH to 2021NH. Upper panel shows the number of virus-antisera pairs in the training dataset for each season, whereas lower panel depicts the same for the test dataset.
+
+(b) The performance of the baseline model in terms of mean absolute error (MAE) for each test dataset in 35 seasons from 2005NH to 2021NH. The baseline model is an RF model with unoptimized hyperparameters, binary encoded genetic difference, and without any metadata information. The vertical dashed line indicates the season after which the baseline model started to provide reliable predictive performance.
+Supp. Fig. 3 Optimization of RF model based on metadata information, model hyperparameters, and amino acid attributes.
+
+(a) MAE performance of the baseline model when a specific feature or group of features are incorporated in the metadata information. The MAE score was averaged over four validation seasons from 2012NH to 2013SH.
+
+(b) MAE performance of the baseline model (including all the metadata information) with unoptimized and optimized hyperparameters (see Materials and Methods).
+
+(c) Variation in MAE performance of the baseline model (including all the metadata information) over the 92 amino acid mutation matrices as well as for binary encoding. The hyperparameters were optimized independently for each of the 92 RF models corresponding to mutation matrices. The top five mutation matrices with the best MAE performance are highlighted and listed.
+Supp. Fig. 4 Robustness of the model’s predictive capability to changes in training data.
+
+(a-b) Performance of models trained over a subset of training data containing (a) only 20-80% randomly selected HI titres, or (b) all the HI titres of only 20-80% randomly selected virus isolates, in each historical season from 2003NH up to the test season. Each boxplot shows the variation in the MAE performance of the models over 14 test seasons from 2014NH to 2020SH. The average MAE, mentioned over each boxplot, is the average over 50 Monte Carlo runs, where each of these 50 values represent average MAE over 14 test seasons.
+
+(c) Performance of the model when training data of the most recent season is excluded from model training. For each test season, ‘Reference’ indicates the MAE performance of the model trained on the complete training dataset starting from the earliest season 2003NH up to the test season. In the heatmap, each row corresponds to a season excluded from the training data. Each cell in a column shows the change in the MAE performance of the model in comparison to the ‘Reference’ cell in the same column. The darker cell colour indicates the worse MAE performance.
+<table>
+  <tr>
+    <th></th>
+    <th>2014NH</th>
+    <th>2014SH</th>
+    <th>2015NH</th>
+    <th>2015SH</th>
+    <th>2016NH</th>
+    <th>2016SH</th>
+    <th>2017NH</th>
+    <th>2017SH</th>
+    <th>2018NH</th>
+    <th>2018SH</th>
+    <th>2019NH</th>
+    <th>2019SH</th>
+    <th>2020NH</th>
+    <th>2020SH</th>
+    <th>Average</th>
+  </tr>
+  <tr>
+    <th>Accuracy</th>
+    <td>0.87</td>
+    <td>0.90</td>
+    <td>0.85</td>
+    <td>0.86</td>
+    <td>0.81</td>
+    <td>0.86</td>
+    <td>0.87</td>
+    <td>0.87</td>
+    <td>0.80</td>
+    <td>0.77</td>
+    <td>0.85</td>
+    <td>0.82</td>
+    <td>0.85</td>
+    <td>0.84</td>
+    <td>0.85</td>
+    <td>0.85</td>
+  </tr>
+  <tr>
+    <th>Sensitivity</th>
+    <td>0.78</td>
+    <td>0.89</td>
+    <td>0.83</td>
+    <td>0.88</td>
+    <td>0.78</td>
+    <td>0.84</td>
+    <td>0.90</td>
+    <td>0.90</td>
+    <td>0.84</td>
+    <td>0.84</td>
+    <td>0.90</td>
+    <td>0.95</td>
+    <td>0.97</td>
+    <td>0.96</td>
+    <td>0.89</td>
+    <td>0.89</td>
+  </tr>
+  <tr>
+    <th>Specificity</th>
+    <td>0.98</td>
+    <td>0.92</td>
+    <td>0.89</td>
+    <td>0.85</td>
+    <td>0.87</td>
+    <td>0.89</td>
+    <td>0.83</td>
+    <td>0.81</td>
+    <td>0.73</td>
+    <td>0.61</td>
+    <td>0.70</td>
+    <td>0.47</td>
+    <td>0.55</td>
+    <td>0.59</td>
+    <td>0.78</td>
+    <td>0.78</td>
+  </tr>
+  <tr>
+    <th>MCC</th>
+    <td>0.76</td>
+    <td>0.78</td>
+    <td>0.70</td>
+    <td>0.72</td>
+    <td>0.63</td>
+    <td>0.73</td>
+    <td>0.73</td>
+    <td>0.71</td>
+    <td>0.57</td>
+    <td>0.46</td>
+    <td>0.60</td>
+    <td>0.50</td>
+    <td>0.62</td>
+    <td>0.63</td>
+    <td>0.67</td>
+    <td>0.67</td>
+  </tr>
+</table>
+
+<table>
+  <tr>
+    <th></th>
+    <th>2014NH</th>
+    <th>2014SH</th>
+    <th>2015NH</th>
+    <th>2015SH</th>
+    <th>2016NH</th>
+    <th>2016SH</th>
+    <th>2017NH</th>
+    <th>2017SH</th>
+    <th>2018NH</th>
+    <th>2018SH</th>
+    <th>2019NH</th>
+    <th>2019SH</th>
+    <th>2020NH</th>
+    <th>2020SH</th>
+    <th>Average</th>
+  </tr>
+  <tr>
+    <th>Accuracy</th>
+    <td>0.88</td>
+    <td>0.90</td>
+    <td>0.84</td>
+    <td>0.86</td>
+    <td>0.76</td>
+    <td>0.84</td>
+    <td>0.86</td>
+    <td>0.87</td>
+    <td>0.79</td>
+    <td>0.78</td>
+    <td>0.83</td>
+    <td>0.84</td>
+    <td>0.77</td>
+    <td>0.81</td>
+    <td>0.83</td>
+    <td>0.83</td>
+  </tr>
+  <tr>
+    <th>Sensitivity</th>
+    <td>0.80</td>
+    <td>0.91</td>
+    <td>0.87</td>
+    <td>0.91</td>
+    <td>0.67</td>
+    <td>0.74</td>
+    <td>0.91</td>
+    <td>0.90</td>
+    <td>0.82</td>
+    <td>0.82</td>
+    <td>0.85</td>
+    <td>0.90</td>
+    <td>0.75</td>
+    <td>0.79</td>
+    <td>0.84</td>
+    <td>0.84</td>
+  </tr>
+  <tr>
+    <th>Specificity</th>
+    <td>0.98</td>
+    <td>0.88</td>
+    <td>0.79</td>
+    <td>0.79</td>
+    <td>0.93</td>
+    <td>0.98</td>
+    <td>0.78</td>
+    <td>0.82</td>
+    <td>0.75</td>
+    <td>0.68</td>
+    <td>0.75</td>
+    <td>0.66</td>
+    <td>0.81</td>
+    <td>0.84</td>
+    <td>0.82</td>
+    <td>0.82</td>
+  </tr>
+  <tr>
+    <th>MCC</th>
+    <td>0.78</td>
+    <td>0.78</td>
+    <td>0.66</td>
+    <td>0.71</td>
+    <td>0.57</td>
+    <td>0.71</td>
+    <td>0.70</td>
+    <td>0.72</td>
+    <td>0.56</td>
+    <td>0.49</td>
+    <td>0.57</td>
+    <td>0.57</td>
+    <td>0.52</td>
+    <td>0.60</td>
+    <td>0.65</td>
+    <td>0.65</td>
+  </tr>
+</table>
+
+Supp. Fig. 5 Classification performance of the optimized model.
+
+(a) Performance of the model with a classification threshold of 2 antigenic units. The darker cell colour indicates better performance. The ‘Average’ cell indicates the classification scores averaged over 14 test seasons from 2014NH to 2020SH.
+
+(b) Performance of the model with an optimized classification threshold. For each test season from 2014NH to 2020SH, the classification threshold was optimized to maximize the Youden’s index (sensitivity + specificity - 1) for the previous three seasons. As the Youden’s index keeps a balance between the two classes, it therefore decreases the sensitivity and improves the specificity in comparison to the scores in (a).
+Supp. Fig. 6 Comparison with a linear prediction model under the seasonal framework.
+
+(a) Comparison of the optimized RF model with a linear prediction model (NextFlu substitution model; see Materials and Methods for implementation details). For each model, MAE was computed for 14 test seasons from 2014NH to 2020SH. The NextFlu model predicts NHTs of virus-antisera pairs based on a linear function of the substitution of amino acids in their HA1 sequences, virus avidity, and antiserum potency.
+
+(b) Performance of a RF model with parameters matched to the NextFlu model. This RF model used binary-encoded genetic differences and only two metadata features: virus avidity and antiserum potency.
+Supp. Fig. 7 Performance of the model when partial antigenic information of circulating virus isolates is available.
+
+The model was trained on dataset consisting of genetic and antigenic information of historical isolates as well as x% of randomly selected circulating isolates, where x was varied from 10% to 50%. The simulations were repeated for 50 Monte Carlo runs. The MAE performance of the model was computed for 14 test seasons from 2014NH to 2020SH, where the average MAE over these seasons is mentioned above each boxplot.
+Supp. Fig. 8 Performance of models trained over subsets of training data containing only one to five most recent seasons.
+
+For reference, 'all' denotes the case when the complete training dataset is used. Each boxplot shows the variation in the MAE performance of the models over 14 test seasons from 2014NH to 2020SH, and the average MAE over these seasons is mentioned above each boxplot. For each test season \( s \), the \( x \) recent seasons represents the case when the model was trained over a subset of training data consisting of \( x \) seasons starting from season \( s - x \) to season \( s - 1 \).
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SuppTable1.csv

0c34a8e31faa7739408a5ccd9d2f5e997e03e8f8f88c468ddded81aa6cf416eb/preprint/preprint.md

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+Diversity and evolution of the vertebrate chemoreceptor gene repertoire
+
+Maxime Policarpo
+University of Basel
+Maude Baldwin
+Max-Planck Institute
+Didier Casane
+CNRS
+Walter Salzburger ( walter.salzburger@unibas.ch )
+University of Basel https://orcid.org/0000-0002-9988-1674
+
+Article
+
+Keywords:
+
+Posted Date: May 15th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2922188/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on February 15th, 2024. See the published version at https://doi.org/10.1038/s41467-024-45500-y.
+Diversity and evolution of the vertebrate chemoreceptor gene repertoire
+
+Maxime Policarpo1*, Maude W. Baldwin2, Didier Casane3,4 and Walter Salzburger1*
+
+1Zoological Institute, Department of Environmental Sciences, University of Basel, Basel, Switzerland
+2Evolution of Sensory Systems Research Group, Max Planck Institute for Biological Intelligence, Seewiesen, Germany
+3Université Paris-Saclay, CNRS, IRD, UMR Évolution, Génomes, Comportement et Écologie, Gif-sur-Yvette, France.
+4Université Paris Cité, UFR Sciences du Vivant, Paris, France.
+
+*Correspondence:
+e-mail: maxime.policarpo@unibas.ch, walter.salzburger@unibas.ch
+
+Abstract
+Chemoreception – the ability to smell and taste – is an essential sensory modality of most animals. The number and type of chemical stimuli that animals can perceive depends primarily on the diversity of chemoreceptors they possess and express. In vertebrates, six families of G protein-coupled receptors form the core of their chemosensory system, the olfactory/pheromone receptor gene families \( OR \), \( TAAR \), \( VIR \) and \( V2R \), and the taste receptors \( TIR \) and \( T2R \). Here, we provide the most comprehensive study to date of the vertebrate chemoreceptor gene repertoire and its evolutionary history. Through the examination of 2,210 vertebrate genomes, we uncover substantial differences in the number and composition of chemoreceptors across vertebrates. We show that the chemoreceptor gene families are co-evolving, highly dynamic, and characterized by lineage-specific expansions (for example, \( OR \) in tetrapods; \( TAAR \), \( TIR \) in teleosts; \( VIR \) in mammals; \( V2R \), \( T2R \) in amphibians) and losses. Overall, amphibians, followed by mammals, are the vertebrate clades with the largest chemoreceptor repertoires. While marine tetrapods feature a convergent reduction of chemoreceptor numbers, the number of \( OR \) genes correlates with habitat in mammals and birds and with migratory behavior in birds, and the taste receptor repertoire correlates with diet in mammals and with aquatic environment in fish.
+Introduction
+
+The survival of animals depends heavily on their ability to perceive their surroundings, for example, to orient themselves, to navigate through the environment, to find food, to escape from predators, and to identify and select mating partners1–3. These vital tasks are typically achieved by one or several of their sensory systems3,4. Different sensory modalities exist in animals that allow them to detect and interpret external or self-induced cues: photoreception for the detection of light, electoreception for the detection of electric signals, magnetoreception for the detection of magnetic fields, and chemoreception for the detection of chemical cues.
+
+The chemosensory system combines the senses of smell (olfaction) and taste (gustation). In vertebrates, four multigene families are responsible for olfaction: olfactory receptor (OR) genes5, trace amine-associated receptor (TAAR) genes6, and the vomeronasal receptor gene families V1R and V2R7–9. In tetrapods, OR and TAAR genes are primarily expressed in olfactory sensory neurons in the main olfactory epithelium, whereas V1R and V2R genes are expressed in the sensory epithelium of the vomeronasal organ10, excepted in ray-finned fishes where these genes – often referred to as ORA and OlfC in this clade – are expressed in the olfactory epithelium11. Gustation, on the other hand, is achieved through the taste receptor gene families T1R (sweet and umami taste receptors) and T2R (bitter taste receptor), which are expressed in the taste buds12. Overall, the range of molecules that can be recognized by a species depends in large part on the richness of the chemoreceptor gene repertoire11,13. Like the visual opsin genes that are at the core of the visual sensory system, the olfactory and gustatory receptor genes encode for G protein-coupled receptors (GPCRs)4. However, unlike the visual opsin genes, which are well characterized in vertebrates1–3, the extent of the chemoreceptor gene repertoire as well as the evolutionary history of the different chemoreceptor gene families are only known for selected species or clades. To date, no overarching examination of the chemoreceptor gene repertoire exists across vertebrates, which is largely due to the sheer size of some of the chemoreceptor gene families and the application of different gene mining methodologies in previous studies, hampering comparisons between species and evolutionary lineages.
+
+Here we examined the dynamics of chemoreceptor gene evolution across vertebrates. Making use of a newly developed computational pipeline, we mined 2,210 vertebrate genomes for the six chemoreceptors gene families (OR, TAAR, V1R, V2R, T1R and T2R) in order to characterize the evolutionary history and diversification of these genes in unprecedented detail. In addition, we tested for associations between the chemoreceptor gene repertoires and eco-morphological proxies in the three largest vertebrate clades, ray-finned fishes, mammals and birds.
+Results
+
+Characterization of the vertebrate chemoreceptor gene repertoire. By applying a standardized procedure to detect chemoreceptor genes in 2,210 vertebrate genome assemblies (and examining two datasets with different quality thresholds, at 80% and 90% complete BUSCO genes, retaining 1,531 and 1,180 genomes, respectively; Supplementary Table 1 and Supplementary Figs. 1-5), we found that the number of chemoreceptor genes is extremely variable across vertebrates (Figs. 1 and 2). Within olfactory and pheromone receptors (*OR*, *TAAR*, *V1R* and *V2R* genes combined), amphibians had the highest number of complete (that is, with a complete coding sequence [CDS]) genes (mean: 1060.3; minimum: 781; maximum: 1,717; 20 species examined), followed by turtles (966.7; 258 to 1,716; 26 species), mammals (854; 33 to 2,514; 440 species), lepidosaurs (539.7; 56 to 1,035; 53 species), crocodiles (326; 16 to 743; 4 species), ray-finned fishes (238.7; 20 to 1,388; 483 species), agnathans (121.4; 48 to 205; 5 species), birds (94; 4 to 1,089; 488 species) and cartilaginous fishes (43.8; 20 to 62; 10 species). The lungfish (*Protopterus annectens*) and the coelacanth (*Latimeria chalumnae*) featured 989 and 280 complete olfactory receptor genes, respectively. Remarkably, with a mean number of 109.1 complete genes (minimum: 5; maximum: 268), amphibians also had the most extensive taste receptor gene repertoire (*T1R* and *T2R* genes combined) by far of any vertebrate clade. Except for the coelacanth (81 complete genes), the genomes of the other vertebrate groups contained less than one-fourth the number of complete taste receptor genes compared to amphibians: 4.1 (2 to 5) in cartilaginous fishes, 5.8 (0 to 24) in birds, 7.8 (5 to 12) in crocodiles, 9.1 (0 to 31) in ray-finned fishes, 11.8 (1 to 17) in turtles, 12.8 (0 to 61) in lepidosaurs, 23.4 (0 to 91) in mammals, and 24 in the lungfish. Amphibians thus emerge as the vertebrate group with the largest number of chemoreceptor genes per genome, followed by mammals and turtles (Fig. 2). The extended repertoire of chemoreceptor genes in amphibians is not primarily the result of whole genome duplication events in some of their representatives, as exemplified by the genus *Xenopus*: The diploid *X. tropicalis* had a very similar number of taste receptors (52) and an even higher number of olfactory receptors (1,717) than the tetraploid species *X. laevis* (51 and 1,265, respectively) and *X. borealis* (59 and 849, respectively).
+
+Overall, we found positive correlations between the numbers of complete genes across the four different olfactory receptor gene families, suggesting that the evolution of these gene families has not been driven by compensatory gains and losses (Fig. 1b, Extended Data Fig. 1). We further tested for compensatory changes in repertoire size of olfactory and taste receptors, as these can have an overlapping function, in particular in ray-finned fishes, where in some species taste buds are located across the body surface as well as in the oral cavity\textsuperscript{16}. We again found a positive correlation between the number of olfactory receptor genes and the number of taste receptor genes in ray-finned fishes, mammals and birds (Fig. 1b, Extended Data Fig. 1 and Supplementary Fig. 6), suggesting that these sensory modalities also evolve concertedly and that their evolution may be driven by the same life history traits and/or ecological factors. In addition, we found moderately positive correlations between the number of complete or total (sum of complete, pseudogenes and truncated genes) genes in each chemoreceptor family and genome size (Supplementary Figs. 7 and 8). Taking genome size into account, the number of complete genes were still correlated across chemoreceptor families, except between *OR* and *TAAR* genes in birds (Supplementary Table 2).
+Fig. 1 | Co-evolution of chemoreceptor gene repertoires in vertebrates. a, Phylogeny of 1,532 vertebrate species, for which a genome assembly with more than 80% complete BUSCO genes was available (Sceloporus occidentalis is represented in the phylogeny but was excluded from the analysis; see Methods for details). The branches are colored according to the vertebrate (sub)class. The number of OR, TAAR, VIR, V2R, T1R and T2R genes for every species is shown as bars, color-coded as in the lower left panel. Independent marine colonization events by tetrapods (indicated by black arrows) are, for most parts, associated with decreases in chemoreceptor repertoire sizes. It is unknown whether the remaining genes in these species are functional in the context of chemoreception or used for other functions, as is the case for extranasal OR genes17,18. Phylogenies with full species names and sub-trees for each vertebrate (sub)class are available in Supplementary Figs. 9 and 10, respectively. Animal silhouettes were obtained from PhyloPic.org. b, Correlations between the number of complete genes of the different chemoreceptor families, or between the number of complete olfactory (OLR) and the number of complete taste receptors (TR) (BUSCO80 dataset; see Supplementary Fig. 6 for the results with the BUSCO90 dataset). Circles indicate \( P_{PGLS}<0.05 \) and are color-coded according to the pGLS R^2-values, absence of a circle indicates \( P_{PGLS}>0.05 \). The association between OR and TAAR genes in birds (marked with an “**”) is the only one that became non-significant when correcting for genome size.
+Evolution of OR and TAAR genes in vertebrates. The mean number of OR genes per genome ranged from 8.7 in Chondrichthyes (6 to 13) to 953.4 in turtles (252 to 1,698), with an overall mean across vertebrates of 339.5 (Fig. 2a). The species with the highest number of complete OR genes was the short-beaked echidna (Tachyglossus aculeatus: n = 2,399), closely followed by the Asian (Elephas maximus indicus: n = 2,331) and the African elephant (Loxodonta africana: n = 2,278) (see Supplementary Fig. 11 for details). We confirm previous results19 that the OR gene repertoire of tetrapods is almost exclusively composed of genes belonging to the α-, β- and γ-subclades, while the α- and γ-subclades are either completely lacking or present in very low numbers in most ray-finned fishes (Fig. 3a, Extended Data Fig. 2). The OR gene repertoire of ray-finned fishes is, in turn, dominated by genes of the δ- and η-subclades, and to a lesser extent of the ζ-subclade. Whereas the coelacanth and the lungfish also featured genes of the ζ-subclade, these genes were lost in the evolutionary lineage leading to tetrapods. Genes of the η- and δ-subclades were also well represented in the coelacanth and lungfish genomes as well as in amphibians, but were lost before the most recent common ancestor (MRCA) of amniotes (Fig. 3a). The ε-subclade was only retrieved in ray-finned fishes and amphibians, suggesting several independent losses of the ε-subclade, namely in cartilaginous fishes, in the coelacanth, in lungfishes, and before the MRCA of amniotes.
+
+Trace amine-associated receptor (TAAR) genes were found in elevated numbers primarily in the genomes of ray-finned fishes, whereas their numbers were consistently low in tetrapods (Fig. 2b). The mean number of complete TAAR genes ranged from 1.6 (0 to 4) in birds to 51.8 in ray-finned fishes (3 to 497), with an overall mean of 19.7. The two Polypteriformes Erpetoichthys calabaricus and Polypterus senegalus featured by far the highest numbers of TAAR genes (n = 497 and n = 445, respectively), followed by the four-eyed sleeper Bostrychus sinensis (n = 307). On the other hand, some tetrapods completely lost their TAAR genes, such as the garter snake Thamnophis elegans (as opposed to 2 to 5 TAAR genes in all other snakes), the northern gundi (Ctenodactylus gundi), the four-striped grass rat (Rhabdomys dilectus) and several bird species. The comparatively large number of TAAR genes in Actinopterygii is largely due to an expansion of the B4-subclade, which is also present in coelacanth and lungfish, but absent in tetrapods (Fig. 3b, Extended Data Fig. 3 and Supplementary Fig. 12). We further found that tetrapods only have TAAR genes belonging to three subclades (A3, B1 and B3), one of which (B3) was lost in teleosts. TAAR-like genes, the sister subclade to all other TAAR genes and the only ones found in agnathans, are present in all vertebrate groups except amniotes (Fig. 3b).
+Fig. 2 | Number of chemoreceptor genes in vertebrates. For each vertebrate (sub)class (colored as in Fig. 1), the number of olfactory and taste receptor genes is shown as boxplots (first quartile - 1.5 interquartile range; first quartile; mean; third quartile; third quartile + 1.5 interquartile range). For each chemoreceptor gene family, the names of the three species with the highest number of genes, and their silhouettes, are shown. a, OR genes; b, TAAR genes; c, VIR genes; d, V2R genes; e, TIR genes; f, T2R genes. The species with the highest number of complete olfactory receptor genes is Tachyglossus aculeatus (2,514) closely followed by Elephas maximus indicus (2,383) and Loxodonta africana (2,329), while the species with the highest number of complete taste receptor genes is Glandirana rugosa (268). Note that the high number of complete OR genes found in Tachyglossus aculeatus could potentially represent an artifact, as we also retrieved an unusually high number (nearly 9,000) of incomplete genes in this species (Supplementary File 1).
+Fig. 3 | Evolutionary history of OR and TAAR genes in vertebrates. a, Schematic of the OR gene tree (top) indicating the subclades within the OR gene family in vertebrates. Gene duplication events leading to subclade divergence are indicated as triangles on the respective branches in the schematic vertebrate phylogeny (left), subclade losses are indicated with the cross symbol below the branches. The numbers refer to nodes in the gene tree. Circles on the right indicate the presence of a particular subclade in a given evolutionary lineage, whereby the size of each circle corresponds to the mean number of complete OR genes per species in the respective subclade and lineage. The OR gene tree is shown in Extended Data Fig. 2. b, Schematic of the TAAR gene tree (top) indicating the subclades within the TAAR gene family in vertebrates. Gene duplication events are indicated as triangles on the respective branches in the schematic vertebrate phylogeny (left), subclade losses are indicated with the cross symbol. The numbers refer to nodes in the gene tree. Circles on the right indicate the presence of a particular subclade in a given evolutionary lineage, whereby the size of each circle corresponds to the mean number of complete TAAR genes per species in the respective subclade and lineage. The TAAR gene tree is shown in Extended Data Fig. 3. Subclades present in non-teleost fish but absent in teleosts (α-subclade for ORs and B3-clade for TAARs) are marked with an "*".
+Evolution of vertebrate vomeronasal receptors (*V1R* and *V2R*). The mean number of complete *V1R* genes per genome ranged from 0.01 (0 to 1) in birds to 38.1 in mammals (0 to 276), with an overall mean of 13.1 (Fig. 2c). The number of complete *V1R* genes was particularly high in the platypus (*Ornithorhynchus anatinus*: \( n = 276 \)) and in rodents (*Mus musculus*: \( n = 241 \); *Arvicanthis niloticus*: \( n = 187 \)) (Fig. 2c and Supplementary Fig. 13). The comparatively large *V1R* gene repertoire of mammals resulted primarily from an expansion of a single subclade (*V1RII*) in their ancestor, whereas in amphibians, which also have an extensive *V1R* gene repertoire, no major expansion in any particular subclade occurred, but they retained representatives of most subclades instead (Fig. 4a and Extended Data Fig. 4). It is of note that the lungfish is characterized by a rather large *V1R* gene repertoire with 163 complete genes, which is primarily due to an expansion of the *V1R9* subclade. Most teleosts, on the other hand, retained only six *V1R* genes (*ORA1-ORA6*). We previously showed that this reduced repertoire is due to a series of gene losses before the MRCA of ray-finned fishes, followed by additional gene losses that occurred before the MRCA of teleosts and before the MRCA of clupeocephalans\(^{20}\). Contrary to what has previously been thought\(^{21}\), we found that *V1R* genes are not entirely lacking from the genomes of crocodiles and birds, as one gene of the *V1R7* subclade was retained in some birds, and one gene each of the *V1R7* and *V1R10* subclades were retained in all crocodile species investigated. We further document here that the substantial reduction of *V1R* genes in birds occurred gradually, with many gene losses occurring before the MRCA of amniotes, followed by a gradual loss of the remaining subclades (Fig. 4a).
+
+The mean number of *V2R* genes per species was found to be higher than that of *V1R* genes, ranging from 1.3 in turtles (0 to 3) to 140.6 in amphibians, with an overall mean of 23 across vertebrates (Fig. 2d and Supplementary Fig. 14). The *V2R* gene repertoire is particularly large in the lungfish (\( n = 493 \)) as well as in two amphibians (*X. tropicalis*: \( n = 578 \), *X. laevis*: \( n = 388 \)). *V2R* genes are separated in two main subclades, *V2RC* and *V2RD*. The *V2RC* subclade appears to have diversified before the MRCA of lungfishes and tetrapods, with several additional expansions detected in the lungfish (*V2RC6, V2RC7, V2RC8, V2RC9* and *V2RC10*), amphibians (mainly in *Xenopus; V2RC13*), mammals, and lepidosaurs (two independent expansions of *V2RC14*) (Fig. 4b and Extended Data Fig. 5). The *V2RD* subclade, on the other hand, has diversified before the MRCA of jawed vertebrates. However, most of these genes were lost in the lineage leading to tetrapods, suggesting that genes of this subclade are specialized to detect waterborne molecules. *V2R* genes are absent in most (263 out of 392) mammal species, as well as in all birds and crocodiles. In turtles, we found evidence for one to three complete *V2R* genes, except for nine turtle species – including the marine clade – that lacked *V2R* genes entirely.
+
+In general, we found that the diversification of vomeronasal receptor genes is tightly connected with the evolution of the vomeronasal system itself. For example, the expansion and diversification of *V2RC* genes in the common ancestor of lungfishes and tetrapods coincides with the appearance of the vomeronasal organ\(^{22}\). In mammals, we found that *V1R* and *V2R* gene numbers are strongly correlated (\( R^2 = 0.42; P < 2.2e-16 \)) and that groups known for their well-developed vomeronasal organs – such as rodents, lagomorphs, monotremes and marsupials – had comparatively larger *V1R* and *V2R* gene repertoires (Extended Data Fig. 1 and Supplementary Figs. 13 and 14). On the other hand, we provide evidence for a near-complete loss of *V1R* and *V2R* genes in turtles, crocodiles and birds, which either lack a vomeronasal
+Fig. 4 | Evolutionary history of VIR and V2R genes in vertebrates. a, Schematic of the VIR gene tree (top) indicating the subclades within the VIR gene family in vertebrates. Gene duplication events leading to subclade divergence are indicated as triangles on the respective branches in the schematic vertebrate phylogeny (left), subclade losses are indicated with the cross symbol below the respective branches. The numbers refer to nodes in the gene tree. Circles on the right indicate the presence of a particular subclade in a given evolutionary lineage, whereby the size of each circle corresponds to the mean number of complete VIR genes per species in the respective subclade and lineage. The VIR gene tree is shown in Extended Data Fig. 4. b, Schematic of the V2R gene tree (top) indicating the subclades within the V2R gene family in vertebrates. Gene duplication events are indicated as triangles on the respective branches in the schematic vertebrate phylogeny (left), subclade losses are indicated with the cross symbol. The numbers refer to nodes in the gene tree. Circles on the right indicate the presence of a particular subclade in a given evolutionary lineage, whereby the size of each circle corresponds to the mean number of complete V2R genes per species in the respective subclade and lineage. The V2R gene tree is shown in Extended Data Fig. 5. Subclades present in non-teleost fishes but absent in teleosts are marked with an “**” (ancVIR, VIR3, VIR8, VIR9, V2RC3 and V2RD1). Subclades present in osteoglossomorph and elopomorph but absent in clupeocephalans (VIR10) are marked with an “#”.
+system entirely or in which its presence is under debate9. To examine the co-evolution of pheromone receptors and the vomeronasal organ, we collected data on the presence/absence of an accessory olfactory bulb (AOB) in chiropteran23–26. We show that bats with an accessory olfactory bulb (AOB) have significantly more *T1R* genes than species without an AOB (*P*PGLS = 1.8e-5; Extended Data Fig. 6).
+
+**Evolution of vertebrate taste receptors (**T1R** and **T2R**).** Contrary to the four olfactory receptor gene families, which emerged in or before the vertebrate ancestor, we did not find any taste receptor gene in agnathans (Fig. 2e, f). This suggests either a secondary loss of *T1R* and *T2R* genes in jawless vertebrates, or – much more plausibly – an origin of taste receptors in the evolutionary lineage leading towards gnathostomes, possibly in association with the emergence of the jaw apparatus itself and the subsequent diversification in feeding strategies27,28.
+
+In contrast to all other chemoreceptor gene families, which are highly dynamic with respect to gene duplications and losses across vertebrates, the number of *T1R* genes is rather stable, in particular in tetrapods, which typically feature three *T1R* genes: the umami and sweet receptor subunits (*T1R1A* and *T1R2*, respectively) and their co-receptor (*T1R3*) (Fig. 2e). Birds and teleosts independently lost their *T1R2* genes. The genomes of Actinopterygii, on the other hand, contain an additional *T1R* subclade that was lost before the MRCA of Sarcopterygii, which we named *T1R1B* (Fig. 5a and Extended Data Fig. 7). Previous studies have treated this clade as part of the *T1R2* subclade29. However, our phylogeny suggests a possibly more complicated evolutionary scenario, and whether this clade is part of the *T1R1* or *T1R2* clade is not entirely clear. This ray-finned fish clade is more dynamic than other *T1R* subclades, resulting in ray-finned fishes having a greater number of *T1R* genes compared to all other vertebrate clades (Fig. 2e and Supplementary Fig. 15). The species with the highest number of complete *T1R* genes were the Chinese sleeper (*P. glenei*: *n* = 18) and the spinyhead croaker (*Collichthys lucidus*: *n* = 18), followed by the jewelled blenny (*Salarias fasciatus*: *n* = 16) (Fig. 2e). Several lineages completely lost their *T1R* genes, such as the genus *Xenopus*, cetaceans, pinnipeds, the marine turtle *Dermochelys coriacea*, most snakes (which also exhibited a reduced *T2R* gene repertoire with 0 to 2 complete genes), and two bird orders (Sphenisciformes [penguins] and Tinamiformes) (Fig. 5a and Supplementary Fig. 16).
+Fig. 5 | Evolutionary history of TIR and T2R genes in vertebrates. a, Schematic of the TIR gene tree (top) indicating the subclades within the TIR gene family in vertebrates. Gene duplication events leading to subclade divergence are indicated as triangles on the respective branches in the schematic vertebrate phylogeny (left), subclade losses are indicated with the cross symbol below the respective branches. The numbers refer to nodes in the gene tree. Circles on the right indicate the presence of a particular subclade in a given evolutionary lineage, whereby the size of each circle corresponds to the mean number of complete TIR genes per species in the respective subclade and lineage. The TIR gene tree is shown in Extended Data Fig. 7. The TIRA subclade present in non-teleost fish but absent in teleosts is marked with an “*”. An alternative, but overall similar, scenario for TIR evolution was proposed by Nishihara et al.30 b, Schematic of the T2R gene tree (top) indicating the subclades within the T2R gene family in vertebrates. Gene duplication events are indicated as triangles on the respective branches in the schematic vertebrate phylogeny (left), subclade losses are indicated with the cross symbol. The numbers refer to nodes in the gene tree. Circles on the right indicate the presence of a particular subclade in a given evolutionary lineage, whereby the size of each circle corresponds to the mean number of complete T2R genes per species in the respective subclade and lineage. The T2R gene tree is shown in Extended Data Fig. 8.
+It has previously been hypothesized (but was not formally tested) that the evolution of T1R genes in mammals was shaped by diet specializations31,32. In our analyses, we identified 17 independent losses of T1R2 on carnivore branches within mammals, 6 on herbivores and 2 on omnivores (Fig. 6), resulting in more than half (63 in a total of 117) of the mammalian carnivore species lacking the sweet receptor subunit (T1R2). Using a combination of BayesTrait analysis and simulations, we found that, in mammals, carnivores were significantly more prone to lose T1R2 compared to herbivores and omnivores (\( P_{\text{BayesTrait}} = 6e-4 \); Supplementary Tables 3 and 4), and experienced significantly more T1R2 losses than what would be expected at random (\( P_{\text{Simulations}} = 5e-4 \); Fig. 6 and Supplementary Figs. 17 and 18). This association holds true when removing pinnipeds and cetaceans, which may have lost their T1R genes in response to their transition to a marine lifestyle rather than their diet (as observed for other chemoreceptor genes). We would also like to note that, although the loss of T1R2 genes is not reversible, a transition from carnivore to omnivore/herbivore diet33 could potentially involve shifts in taste receptor function, as has been shown for hummingbirds34. No significant association was found between T1R1 gene losses and diet preference in mammals (eight in carnivores, nine in herbivores, and five in omnivores) nor between T1R3 gene losses and diet (six in carnivores, nine in herbivores, and six in omnivores). Most species that lack a complete T1R3 gene lost the T1R1 and/or the T1R2 subunits (43 species, 86%), while 7 species (14%) still have intact T1R1 and T1R2 subunits. Sirens, which – just like pinnipeds and cetaceans – experienced a massive loss of olfactory receptors and of T2R (see below), retained an intact T1R repertoire.
+
+Whereas the T2R gene repertoires of ray-finned fishes and the lungfish are relatively small, a diversification and expansion of this gene family occurred in the lineage leading to tetrapods, followed by subsequent expansions of two subclades in amphibians (T2RE3 and T2RE5) and two other subclades in mammals (T2RE12 and T2RE13) (Fig. 5b and Extended Data Fig. 8). With a mean number of 106.2 complete genes, amphibians had a remarkably large T2R gene repertoire (ranging from 3 in Geotrypetes seraphini to 264 in Glandirana rugosa), followed by mammals with a mean number of 21.1 complete T2R genes (0 to 54) (Fig. 2e). Some tetrapods completely lost the T2R gene repertoire secondarily, such as Sphenisciformes and some cetaceans. With the identification of a single T2R gene in most cartilaginous fishes, we can reject the prevailing view of an origin of T2R genes in bony fishes35,36.
+
+Similar to what has been suggested for the evolution of T1R in mammals, it has previously been proposed that the vertebrate T2R gene repertoire evolved in response to diet preferences, with herbivores having more T2R genes than carnivores in order to detect toxic compounds in plants37. To examine this hypothesis, we retrieved the diet preferences of ray-finned fishes38, birds39 and mammals40. We found a correlation between the number of complete T2R genes and diet categories in mammals (\( P_{\text{BUSCO80}} = 0.006; P_{\text{BUSCO90}} = 0.014 \); Extended Data Fig. 9), which holds true when cetaceans and pinnipeds are removed at the 80% BUSCO completeness threshold (but not at 90%). However, there was no such association in ray-finned fishes (\( P_{\text{BUSCO80}} = 0.46; P_{\text{BUSCO90}} = 0.25 \)) nor in birds and crocodiles (\( P_{\text{BUSCO80}} = 0.05; P_{\text{BUSCO90}} = 0.06 \)). It should also be emphasized that amphibians, which are all carnivores, have an extensive T2R repertoire (Fig. 2f).
+Fig. 6 | Repeated loss of TIR2 in carnivore mammals. a, Phylogeny of mammals, for which a genome assembly with more than 80% complete BUSCO genes was available (392 species). Terminal branches are color-coded according to the diet preference taken from the MammalDiet database40. Diet preferences of internal branches were inferred with PastML. The status of each gene (TIR1, TIR2, TIR3) in each species is indicated (according to the four categories shown; see Methods for details). TIR loss events, inferred by shared loss-of-function mutations across species, are indicated on the respective branches. Large clades with TIR losses, or individual species that have lost all TIR genes, are highlighted with a silhouette. b, Simulation result where TIR2 genes were randomly pseudogenized in the mammalian tree. The histogram represents the results of the simulations (with the x-axis representing the number of randomly drawn branches in the simulations) and the dashed lines represent the observed number of independent TIR2 loss per diet group (same color code as in the phylogeny). The P-value reported above each dashed line correspond to the number of simulations where the same or a greater number of independent TIR2 losses occurred than observed for the same branch category (carnivore, omnivore or herbivore), divided by the total number of simulations (10,000). All simulation result for TIR1, TIR2 and TIR3 are shown in Supplementary Fig. 18.
+The eco-morphology of chemoreceptor evolution in vertebrates. We examined correlations between ecological traits (from existing databases\(^{38,39,41,42}\)) as well as diet preferences and chemoreceptor gene repertoire sizes (this study) across the three vertebrate groups with most genome assemblies available: mammals, birds and ray-finned fishes. Our analyses revealed a strong association between the number of complete \(OR\) genes and habitat in both mammals (\(P_{BUSCO80} = 3e-5; P_{BUSCO90} = 2e-6\)) and birds (\(P_{BUSCO80} = 6e-9; P_{BUSCO90} = 0.02\)), but not in ray-finned fishes (Supplementary Fig. 19). For birds, we further detected a strong correlation between the number of complete \(OR\) genes and migratory behavior (\(P_{BUSCO80} = 5.4e-3, P_{BUSCO90} = 7e-4\)), with non-migratory species having fewer \(OR\) genes than migratory ones. We also found an association between their primary lifestyle (aerial, terrestrial, aquatic or in sessorial, i.e., species spending much of the time perching above the ground) and the number of complete \(OR\) genes (\(P_{BUSCO80} = 2.3e-3; P_{BUSCO90} = 0.07\)). In Actinopterygii, the number of \(TIR\) genes was associated with the primary aquatic habitat (fresh, brackish or salt water, or combinations thereof; \(P_{BUSCO80} = 4e-3; P_{BUSCO90} = 8e-3\)). When using the more strictly filtered dataset (BUSCO90), we further found a correlation between the number of \(T2R\) genes and migratory behavior in birds (\(P_{BUSCO90} = 8e-4\)) (Supplementary Fig. 19).
+
+The transition of tetrapods towards a marine lifestyle appears to have a particularly strong impact on the number of chemoreceptor genes in a given genome\(^{43-47}\). We consistently found a reduction of chemoreceptor genes across marine groups (cetaceans, pinnipeds and sirenians in mammals; penguins in birds; marine turtles; marine snakes of the genera *Hydrophis* and *Laticauda*) (Fig. 1 and Extended Data Fig. 10). Finally, we support the previously suggested association between the number of \(OR\) genes and the morphology of the olfactory organ\(^{20,48,49}\). More specifically, we found positive correlations between the number of complete \(OR\) genes and the relative size of the olfactory bulb in birds\(^{50}\) (pGLS: \(R^2 = 0.14, P = 0.024\)) and mammals\(^{51}\) (pGLS: \(R^2 = 0.11, P = 0.01\)), and between the number of complete \(OR\) as well as the number of complete \(V2R\) genes and the number of lamellae in the olfactory epithelium in ray-finned fishes (pGLS: \(R^2 = 0.17, P = 3.8e-5\) for \(OR\) genes; pGLS: \(R^2 = 0.07, P = 0.01\) for \(V2R\) genes) (Supplementary Fig. 20). Interestingly, we found that, in mammals, the number of complete *TAAR* genes – although not prominent nor very dynamic – is also positively correlated with the relative olfactory bulb size (pGLS: \(R^2 = 0.56, P = 2.8e-7\)). Finally, our results support the correlation between the number of \(OR\) gene and the number of olfactory turbinals in mammals\(^{52}\) (pGLS: \(R^2 = 0.28, P = 8.5e-5\), Supplementary Fig. 5).
+Discussion
+
+In this study, we characterize the chemoreceptor gene repertoires of vertebrates using a novel gene mining approach and applying it to 2,210 vertebrate genome assemblies. We provide an updated nomenclature of vertebrate olfactory/pheromone and taste receptor genes based on extensive phylogenetic analyses across all vertebrate (sub)classes and chemoreceptor multigene families, reconstruct the dynamic evolution of vertebrate chemoreceptor genes, and identify ecological and morphological correlates of chemoreceptor evolution.
+
+First of all, we show here that the sizes of the six chemoreceptor gene families – the olfactory and pheromone receptor gene families \( OR \), \( TAAR \), \( VIR \) and \( V2R \) and the taste receptors \( T1R \) and \( T2R \) – differ greatly among vertebrate species (Fig. 1). Likewise, we found substantial differences across vertebrate (sub)classes with respect to the total number of complete genes they possess from the six different chemoreceptor gene families (Fig. 2), and in the group-specific compositions of chemoreceptors (Figs. 3-5). Turtles, closely followed by amphibians and mammals, have the highest median numbers of complete \( OR \) genes per genome (Fig. 2a). In terms of the \( OR \) subclades, however, the genomes of aquatic and semi-aquatic vertebrate (sub)classes contain a greater \( OR \) subclade diversity compared to terrestrial (that is, amniote) lineages (Fig. 3a). Ray-finned fishes (and above all Polypteriformes), together with the lungfish, stand out by their comparatively large number of \( TAAR \) genes (Fig. 2b); the genomes of ray-finned fishes also show the greatest \( TAAR \)-subclade diversity (Fig. 3b). Mammals, followed by amphibians, have the highest numbers of the vomeronasal chemoreceptor genes \( VIR \) (Fig. 2c), while amphibians, closely followed by lepidosaurs, have the highest numbers of the vomeronasal receptors \( V2R \) (Fig. 2d). The lungfish has a high number of both \( VIR \) and \( V2R \) (Fig. 2c, d), making it the vertebrate with the highest number of vomeronasal chemoreceptor genes. Aquatic and semi-aquatic vertebrate (sub)classes, in particular amphibians, have a much greater \( VIR \) subclade diversity than terrestrial ones (Fig. 4a). With respect to \( V2R \), the lungfish has the greatest subclade diversity, sharing the C-subclade with tetrapods and the D-subclade with its aquatic ancestors (Fig. 4b). The genomes of ray-finned fishes, together with the coelacanth and the lungfish, feature the highest numbers of the taste receptor genes \( T1R \) (Fig. 2e), while amphibian genomes contain the by far largest \( T2R \) gene repertoire (Fig. 2f). While the \( T1R \) subclade diversity is similar across vertebrate clades (Fig. 5a), the \( T2R \) subclade diversity is much greater in the semi-terrestrial amphibians and in the terrestrial amniotes (Fig. 5b). Overall, amphibians turn out to be the clade with the largest chemoreceptor gene repertoire within vertebrates and it is reasonable to assume that the greater number of chemoreceptor genes and the greater representation of subclades of chemoreceptor gene families in amphibian genomes is due to their semi-aquatic (as larvae) / semi-terrestrial (as adults) lifestyle, requiring adaptations to both realms, in combination with their intermediate phylogenetic position between aquatic and primarily terrestrial vertebrate clades. That, at least at the (sub)class level, the number of olfactory receptor genes correlates with the number of taste receptors (Extended Data Fig. 1) argues against compensatory mechanisms between olfaction and gustation and highlights the importance to jointly consider both chemoreceptor subtypes.
+
+Our study also reveals morphological and ecological correlates of chemoreceptor evolution in vertebrates. In agreement with the one neuron/one receptor rule, we confirm that
+the olfactory receptor gene repertoire of ray-finned fishes is associated with the complexity of their olfactory epithelium20. Likewise, we confirm previous results42,43 that olfactory bulb size is positively correlated with the number of olfactory receptor genes in birds and mammals. Whether such associations are also true for other vertebrate clades, for which limited data with respect to their olfactory organ’s sizes are available, is an open question. It is also unknown if the increase in the size of the olfactory epithelium, or the olfactory bulb size, has driven the expansion of olfactory receptor genes or vice versa, or if they co-evolved. We further uncover a strong correlation between the OR gene repertoire and habitat in mammals and birds, and between OR (and to some extent T2R) genes and migratory behavior in birds, and show that carnivorous mammals are more prone to T1R2 (sweet receptor) gene losses than omnivorous or herbivorous ones. The transition towards a marine lifestyle appears to have had a particularly strong impact on the chemoreceptor genes in tetrapods, with marine species generally featuring an impoverished repertoire (Figs. 1, 6 and Extended Data Fig. 10). For example, cetaceans and pinnipeds completely lack T1R genes. It has previously been suggested that the loss of T1R genes in marine mammals is due to the high sodium concentration in oceans53,54. However, we show here that T1R genes are still present in sirenians, casting doubts on this hypothesis and suggesting instead that T1R losses in marine mammals are associated with dietary adaptations. In yet another aspect of convergent evolution between these evolutionary lineages, penguins have also lost their T1R (and T2R) genes. This has previously been associated with their life in cold environments47. However, that the genomes of other representatives of cold-adapted tetrapods – such as the muskox (Ovibos moschatus) and the reindeer (Rangifer tarandus), and in particular the carnivore species snowy owl (Bubo scandiacus), arctic fox (Vulpes lagopus), and polar bear (Ursus maritimus) – contain T1Rs and typically many T2Rs makes it more plausible that the loss of taste receptors in penguins is connected to their semi-marine lifestyle and their sea-based feeding habits.
+
+In summary, we highlight the relevance of examining the six chemoreceptor families together in vertebrates, and provide novel insights into ecological factors driving the chemoreceptor repertoire. Our dataset and gene mining procedure will be a valuable resource for future chemoreceptor studies, especially in the light of more and more genome assemblies becoming available.
+Methods
+
+Genome data. To download all vertebrate genomes available at the NCBI public database as of 31 July 2022, we used the program genome_updater with the options -T “7742” (corresponding to the taxonomic ID of vertebrates at NCBI), -d "refseq,genbank" (to browse both the RefSeq and Genbank databases), and -A 1 (to retain only one genome assembly per species). In total, we downloaded 2,386 vertebrate genomes, of which 176 were removed as their assembly were described as “partial genome assembly” in NCBI, leading to a final dataset comprising 2,210 vertebrate genomes (Agnatha: 5; Chondrichthyes: 14; Actinopterygii: 900; Dipnoi: 2; Coelacanth: 1; Amphibia: 32; Mammalia: 555; Lepidosauria: 66; Testudines: 27; Crocodilia: 4; Aves: 604).
+
+Phylogenies. To obtain a phylogenetic hypothesis for the vertebrate species included in this study, we merged available phylogenies for different vertebrate (sub)classes into a single tree. The phylogenetic tree for Agnatha was retrieved on TimeTree.org55. Phylogenetic trees for Amphibia, Mammalia, Aves, Lepidosauria and Chondrichthyes were downloaded from https://vertlife.org/56-60. We followed the suggestion by61 and downloaded 1000 trees for each (sub)class and summarized these into a 50% majority-rule consensus tree using the sumtree.py script in the Dendropy package62. The phylogeny of Actinopterygii was obtained from https://fishtreeoflife.org/63. For Crocodilia and Testudines, we used previously published phylogenies64,65. For 161 taxa, species names had to be modified in order to match the ones from our genomic dataset (Supplementary File 1; verified using https://www.itis.gov/, https://www.marinespecies.org/ and https://avibase.bsc-eoc.org/). We also inferred the phylogenetic position of 59 species for which a genome was available, but which were not included in the available phylogenies, using genus information (Supplementary File 1). Among the 2,210 species with a genome available, a total of 222 species were excluded because they were hybrid or extinct species, or because it was not possible to infer their phylogenetic position. The different phylogenies were combined with the coelacanth and the two Dipnoi species with the bind.tree function (which can also bind a single tip into a tree) in ape v5.066, using the divergence times available from TimeTree.org55, for a final tree containing 1,988 vertebrate species.
+
+Genome completeness assessment. The completeness of the vertebrate genomes used for this study was assessed with BUSCO v5.1.267 using the vertebrata odb10 database (Supplementary File 1, Supplementary Table 1, Supplementary Fig. 1), except for three extremely large genomes (Dipnoi: Protopterus annectens and Neoceratodus forsteri; Amphibia: Ambystoma mexicanum), for which BUSCO results were retrieved from previous studies68–70. Since it is expected that genomes with a large proportion of missing BUSCO genes will produce biased estimates for the number of chemoreceptor genes, we only selected high-quality genome assemblies on the basis of two different BUSCO score thresholds: 80% and 90% complete BUSCO genes. In jawed vertebrates, 1,532 genome assemblies featured at least 80% complete BUSCO genes (referred to as BUSCO80) and 1,181 genome assemblies contained at least 90% complete BUSCO genes (referred to as BUSCO90).
+
+We noticed that this BUSCO filtering strategy was not applicable to jawless fish. All five agnathan genome assemblies had very low BUSCO scores (between 49.5 and 62.4%; Supplementary Fig. 1), despite the fact that three of them are chromosome-level assemblies. We further observed that the same set of 1,014 BUSCO genes was consistently found to be
+missing or fragmented in these genomes (Supplementary Fig. 2a). To assess if the high number of common missing or fragmented BUSCO genes in agnathans is a true biological result, due to assembly or sequencing artifacts, or due to chance, we performed two rounds of simulations (with 10,000 replications each) in which we randomly extracted N genes, for every agnathan species, in the vertebrata_odb10 database (whereby N was the number of missing/fragmented genes in each species) and then calculated the number of genes that the five species have in common. In one round of simulations the probability of extracting a gene was weighted by gene length (as, in case of assembly artifacts, long genes are more likely to become fragmented or missing than shorter ones). In the other round, all genes had that same probability. The number of common missing genes in both simulations was much lower than the observed number of 1,014 genes (Supplementary Fig. 2b), suggesting that the absence of these genes is likely a biological reality. It is also unlikely that these genes are missing in the genome assemblies due to the programmed DNA elimination known to occur in the somatic cells of lamprey and hagfishes71, as the Reissner and sea lamprey (Lethenteron reissneri and Petromyzon marinus) assemblies are based on germline sequencing72,73. Instead, it seems that the BUSCO gene set is not a suitable quality criterion for jawless fish. We thus decided to include the five agnathan genomes in our analyses, despite their low BUSCO scores.
+
+Finally, we removed one lepidosaur species (Sceloporus occidentalis) from our analyses, as we systematically retrieved chemoreceptor subclades from this genome assembly that were not found in any other lepidosaurs genome but instead matched amphibian sequences in the NCBI nr database with high confidence. To further investigate this, we used all available lepidosaur chemoreceptor genes as queries in a BLASTN search against a database composed of all available amphibian chemoreceptor genes and a default e-value of 10. Whenever there was at least one blastn match, we extracted the lepidosaur query and the amphibian best-hit sequences, translated them to proteins, and aligned them with MAFFT74. PAL2NAL75 was then used to reverse translate these protein alignments into DNA alignments. The function “seqidentity” of the R package ‘bio3d’76 was then used to compute the sequence identity between the lepidosaurs queries and their amphibian best-hits. Chemoreceptor sequences extracted from the S. occidentalis genome that did not have orthologues in other lepidosaurs had a much greater sequence identity to amphibian chemoreceptors than any other chemoreceptors (Supplementary Fig. 3).
+
+Chemoreceptor gene mining. Chemoreceptor genes were mined in all genomes using two different procedures, one adapted for the single-exon gene families, and one for the multi-exon genes. Note that for the VIR gene family, both procedures were used, depending on the clade. This is because the VIR genes of ray-finned fishes (commonly referred to as ORA genes in this group) have several exons, while VIR genes of all other species consist of only one exon. The efficiencies of our procedures were assessed by comparing the number of genes retrieved in the same species in previous studies. Although different estimates of the number of genes are expected due to the methodology used (for example, different gene length thresholds, different blast e-values) and different genome assemblies (for which we could not get information in most studies surveyed), we still found a very similar number of chemoreceptors per species (Supplementary Fig. 4 and Supplementary Fig. 5). All scripts implementing these procedures and the required databases are available on GitHub (https://github.com/MaximePolicarpo/Vertebrate_Chemoreceptors_mining).
+Single-exon genes (OR, TAAR, VIR in non-ray-finned fishes and T2R). Known protein sequences from previous studies\(^{20,37,77–82}\) were used as queries in a tblastn\(^{83}\) search against every genome, with an e-value of 1e-5. Non-overlapping best-hit regions were extracted and extended 1,000 bp upstream and downstream using samtools faidx\(^{84}\). We then extracted open reading frames (ORFs) present in these regions using EMBOSS getorf\(^{85}\), with a length threshold of 750bp for OR and T2R genes\(^{86,87}\), or 810bp and 850bp for VIR and TAAR genes (which is a bit lower than the length of the smallest known gene in these families: 820bp and 870bp, respectively). As recent studies have shown that some OR and TAAR genes can also, in rare cases, have two or three exons\(^{81,88,89}\), we used EXONERATE\(^{90}\) to search for potential multiple exons in regions in which no ORF was detected. All extracted DNA sequences were then translated into protein sequences with EMBOSS transeq and used as a query in a blastp search against a custom database of GPCR protein sequences. This database was constructed using known chemoreceptor genes and non-chemoreceptor GPCR genes extracted from UniProt\(^{91}\). Sequences that best matched to a member of the desired family were then kept and further aligned with known protein sequences of this family (which consist of a representative subset of the sequences used in the initial tblastn search) as well as with outgroup sequences. Outgroup sequences used for each chemoreceptor family can be found in Supplementary File 1. A maximum-likelihood tree was then computed with IQ-TREE\(^{92}\) and sequences that clustered with known chemoreceptor genes were kept and classified as \((i)\) ‘complete’ genes. In order to identify incomplete sequences, these complete genes as well as chemoreceptors from previous studies were used as queries in a second round of tblastn searches against the genome, this time with a more stringent e-value of 1e-20. Again, nonoverlapping best-hit regions were extracted and incomplete gene sequences were predicted in these regions using a combination of tblastn and EXONERATE. These sequences were then used as queries in a blastx search against our custom GPCR database and only sequences that best matched a member of the desired family were retained. These incomplete sequences were classified in three categories: \((ii)\) ‘pseudogene’, if at least one loss-of-function (LoF) mutation was found; \((iii)\) ‘truncated’, if no LoF was found and if the sequence was not near a contig or scaffold border; or \((iv)\) ‘edge’, if the sequence was close to a contig or scaffold border, which is indicative of an assembly artifact. Finally, Phobius\(^{83}\) and TMHMM\(^{84}\) were used to detect the presence of a seven-transmembrane domain typical for GPCR in all complete sequences. All sequences – complete or incomplete – that had at-least one ambiguous nucleotide were classified as ‘ambiguous’.
+
+Multi-exon genes (V2R, VIR of ray-finned fishes and T1R). Known protein sequences from previous studies\(^{20,36,78,95,96}\) were used as queries in a tblastn search against each genome, with an e-value of 1e-5. All blast hits were then extended 30,000bp upstream and downstream and resulting non-overlapping genomic regions were extracted using samtools faidx. EXONERATE was then used to predict chemoreceptor sequences in these regions. In order to avoid extracting a gene prediction that overlapped with two or more real genes, we used an iterative approach to sort EXONERATE results. First, we discarded EXONERATE predictions if the number of exons was higher than the number of exons inferred from tblastn results (that is, the number of non-overlapping tblastn hits that are at least 50bp long and at least 100bp distant form each other). Then, we applied a length threshold, keeping only EXONERATE predictions in which the length was equal or higher than the mean expected gene length (900bp for VIR genes and 2,700bp for V2R and T1R genes). Finally, if two overlapping predictions met these criteria, we kept the one with the best EXONERATE score. We repeated this process
+decreasing the threshold length until no EXONERATE prediction was found any more. EXONERATE-predicted sequences were then classified into four categories: (i) ‘complete’, if a proper CDS was found with a length of at least 810bp, 2,100bp and 2,200bp for \( V1R \), \( V2R \) and \( T1R \) genes, respectively; (ii) ‘pseudogene’, if at least one LoF mutation was detected; (iii) ‘truncated’, if no proper CDS and no LoF mutation was found; or (iv) ‘edge’, if no proper CDS was found and the sequence was close to a contig or scaffold border. The sequences were then translated into protein sequences with EMBOSS transeq (first removing LoF mutations present in pseudogenes) and used as queries in a blastp search against our custom GPCR database. Predictions that best matched a chemoreceptor of the desired family were then aligned with known chemoreceptor proteins and outgroup sequences. A maximum-likelihood tree was computed with IQ-TREE2 and sequences that did not cluster with known chemoreceptor genes were discarded. We also discarded \( V2R \) and \( T1R \) sequences smaller than 400bp, due to difficulties in assigning these to a chemoreceptor family in the light of our blast and phylogeny filtering procedure. In a final step, we used Phobius and TMHMM to detect the presence of a seven-transmembrane domain in the complete sequences. All sequences – complete or incomplete – that had at-least one ambiguous nucleotide were classified as ‘ambiguous’.
+
+Chemoreceptor gene trees and gene delineation. Given the large number of retrieved complete gene sequences in each chemoreceptor family, we first used MAFFT v7.467\(^{74}\) to generate a template alignment for each gene family, using protein sequences retrieved in previous studies as well as outgroup sequences. We then added all retrieved complete sequences with a seven-transmembrane domain predicted by Phobius and/or TMHMM to these template alignments using the option “-add” in MAFFT. FastTree2\(^{97}\) with default options was used to infer near maximum likelihood phylogenies from these large alignments, with local support values computed with a Shimodaira-Hasegawa test. Phylogenetic trees were visualized using the R package ggtree\(^{98}\). Complete sequences without a predicted seven-transmembrane domain, as well as incomplete (in the categories ‘pseudogene’, ‘truncated’ and ‘edge’) and ambiguous sequences were classified based on their best blastx match. In addition to the phylogenetic evidence, we wanted to confirm that the \( T2R \) genes found in cartilaginous fish and the \( V1R \) genes found in birds were also best-matching against known \( T2R \) and \( V1R \) genes, respectively. We thus used the complete \( T2R \) genes of cartilaginous fish as a query in a blastp search against the NCBI nr database and against the NCBI nr database with all cartilaginous fish sequences removed (taxid:7777) (Supplementary Table 5). In a similar way, complete \( V1R \) genes of birds were used as a query in a blastp search against the NCBI nr database and against the nr database but with all bird sequences removed (taxid:8782) (Supplementary Table 6).
+
+Ecological and morphological data (for mammals, birds, ray-finned fishes). Ecological data of mammals were extracted from the EltonTraits\(^{41}\) and PanTHERIA\(^{42}\) databases. Ecological data of birds were extracted from AVONET\(^{39}\) and ecological data on fishes were taken from fishbase\(^{38}\) (Supplementary File 1, Supplementary Table 7). Diet preference of mammals and birds were retrieved from the MammalDIET and the AVONET databases, respectively. For ray-finned fishes, diet preferences were inferred from the trophic levels retrieved from fishbase, following their recommendations (https://www.fishbase.se/manual/English/fishbasethe_ecology_table.htm). Thus, species with a trophic level \( \leq 2.19 \) were classified as herbivores, species with a trophic level \( \geq 2.2 \) and \( \leq 2.79 \) were classified as omnivores, and species with a trophic level \( \geq 2.8 \) were classified as
+carnivores. We inferred the ancestral diet preference for all branches of the mammalian phylogeny with PastML100 using the Felsenstein81 model and the MPPA (marginal posterior probabilities approximation) prediction method. Data on the relative olfactory bulb size of mammals and birds, the mean number of turbinates in mammalian olfactory epithelium as well as the mean number of lamellae in the olfactory epithelium of fishes were taken from previous studies21,51–53 (Supplementary File 1). Data on the presence/absence of an accessory olfactory bulb in bats were taken from24–27. The correlation between the AOB presence/absence in bats and the number of TIR genes could only be done with BUSCO80 species, as the removal of Miniopterus schreibersii (BUSCO score of 89%) would result in a single clade with the presence of an AOB.
+
+TIR loss analysis in mammals. We reclassified TIR genes of mammals (in species with at least 80% complete BUSCO genes) in four categories: (i) ‘complete’, if the gene was complete in the genome assembly, or if we could retrieve the complete CDS by merging gene fragments (‘truncated’ and ‘edge’ sequences), or if the complete CDS was present in another genome assembly of the same species; (ii) ‘high confidence loss, if the gene was found as a pseudogene in the genome assembly, and if there were at least two distant LoF mutations in the CDS, and/or if the same LoF mutation(s) were found in another genome assembly of the same species, and/or if the same LoF mutation was shared with at-least one closely related species; we also classified as ‘high confidence losses’ those cases, where the gene was completely missing from an assembly, while the flanking genes were both found and were on the same scaffold, indicating that the TIR loss most likely represents a true deletion; (iii) ‘low confidence loss’, if the gene was found as a pseudogene in the genome assembly but with only one LoF mutation that we could not verify in another genome assembly of the same species; we also classified as ‘low confidence losses’ those cases, where a gene was completely missing from the genome assembly but where the flanking genes were also not retrieved, or scattered on different scaffolds; (iv) ‘undetermined’, if the gene was initially categorized as ‘edge’, ‘truncated’ or ‘ambiguous’ and if we were not able to retrieve the complete CDS by merging these fragments nor retrieve it in another genome assembly of the same species. Branches on the mammalian phylogeny where TIR losses occurred were inferred using the LoF mutations. For example, all cetaceans shared at least one LoF mutation in TIR1 and TIR3, but no common LoF mutation was found in TIR2, except between Mysticeti (baleen whales) and between Odontoceti (toothed whales).
+
+To test if, in mammals, carnivore species lost TIR2 significantly more often than omnivore and/or herbivore ones, we first counted the number of independent TIR2 losses that occurred on carnivore branches in the mammalian phylogeny as well as the number of carnivore branches with an intact TIR2 gene (which is equal to the total number of carnivore branches in the tree minus the branches where a TIR2 loss occurred as well as all their daughter branches). The same was done for omnivore and herbivore branches, as well as for TIR1 and TIR3 genes (Supplementary Fig. 17). Count data were the compared with a Chi-squared and Fisher’s Exact tests. This strategy is more appropriate than performing a rough count of the number of branches with a TIR2 loss versus the number of branches with an intact TIR2, as it corrects for phylogenetic signal. We then used BayesTraits101, which allows to test the co-evolution between two binary traits to be tested. Accordingly, we assigned two binary traits to each terminal branch of the tree: TIR2 complete (1) or pseudogene (0) or undetermined (-); Carnivore (1) or Herbivore/Omnivore (0). We ran BayesTraits with three models: Model1
+where the two traits evolve independently; Model2 where both traits co-evolve; Model3 where the T1R2 state depends on the diet state but not the other way around. For each model, the transition rate of T1R2 from 0 to 1 (pseudogene to complete gene) was set to 0 and the maximum likelihood algorithm was run 10,000 times to ensure stable results (option MLTries = 10000). Model2 and Model3 were then compared with Model1 by means of a likelihood ratio test. The same procedure was repeated for T1R1 and T1R3. Finally, to complement the two statistical tests described above, we performed simulations, using the empirical data (25 independent T1R2 losses in the mammalian phylogeny) as a basis. To do so, we initially assigned a complete T1R2 gene state to each branch. Then, 25 branches with a complete T1R2 gene were drawn at random and sequentially, and each time a branch was drawn, this branch and all its daughter branches were assigned a non-functional T1R2 gene state. If all branches of a tree were assigned a non-functional T1R2 gene state before the 25 losses could be distributed, the simulation was discarded. We repeated this procedure until 10,000 simulations were performed. Then, the P-value for T1R2 losses in carnivores was defined as the number of simulations where the same number (or more) of independent T1R2 losses occurred than observed on carnivore branches, divided by the total number of simulations. This was repeated two times: once without considering branch length and once with the drawing probability weighted by branch lengths. The same procedure was followed for T1R1 and T1R2 genes, but in these cases adjusting the number of sequential draws to 22 for T1R1 and to 21 for T1R3.
+
+Phylogenetic comparative analyses. The function pglS of the R package caper102 was used to perform all phylogenetic generalized linear models presented in this study. Phylogenetic tree manipulations were done with the R packages phytools103 and ape67. The graphical representation of phylogenetic trees were done with the R package ggtree99. All other plots were done with ggplot2104. Animal silhouettes used in this study were retrieved from http://phylopic.org/ (full links for each silhouette can be found in Supplementary File 1).
+
+Impact of species trees topologies on pGLS. We assessed the impact of the species phylogenies on the pGLS performed in this study. For mammals, we first extracted the 1,000 most represented BUSCO genes only considering species with at least 80% complete BUSCO genes. For each gene, a protein sequence alignment was made using MAFFT and the alignment was trimmed using trimAl105 and the option “-automated1”. We then generated fifty concatenated alignments, taking twenty of the single gene alignments at random without replacement, using AMAS106. A maximum likelihood phylogeny was computed from each concatenated alignment, using IQ-TREE2 and the LG+F+G4 model. Finally, the least square dating method was used to calibrate these trees using three calibration dates retrieved from TimeTree.org (Supplementary File 1). Each tree was used to re-compute pGLS, and we also computed its Robinson–Foulds distance from the reference tree used in the study using phangorn107. The same procedure was followed for birds and actinopterygians. We found that the species tree topologies had very little or no impact on the results (Supplementary Fig. 21-23).
+Data availability
+All data and results from this study are available on FigShare (https://figshare.com/projects/Diversity_and_evolution_of_the_vertebrate_chemoreceptor_ge ne_repertoire/166226). This includes nucleotide sequences of all chemoreceptor sequences (fasta) and their clades (txt); chemoreceptor alignments (fasta); chemoreceptor phylogenetic trees (newick); all species phylogenetic trees (newick) used in this study; PastML results for mammals diet preferences; fifty random concatenated alignments (fasta); and calibrated species trees (newick) for mammals, birds and ray-finned fishes.
+
+Acknowledgements
+We would like to thank the members of the Salzburger lab for valuable suggestions and comments on this study. All calculations were performed at sciCORE (http://scicore.unibas.ch/) scientific computing centre at University of Basel (with support by the SIB/Swiss Institute of Bioinformatics). This work was funded by the Swiss National Science Foundation (SNSF; grants 189970 and 208002) to W.S.
+
+Author contributions
+M.P. and W.S. designed this study, with input from M.W.B. and D.C. M.P. performed all data analyses. M.P. and W.S. wrote the manuscript with input from all authors.
+
+Competing interests
+The authors declare no competing interests.
+
+Additional information
+Extended data is available for this paper
+Supplementary information is available for this paper
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+Extended Data Fig. 1 | Correlations between the numbers of complete chemoreceptor genes across chemoreceptor families. Correlations are shown for OR versus TAAR (a), OR versus V2R (b), OR versus V1R (c), TAAR versus V2R (d), TAAR versus V1R (e), V1R versus V2R (f), between the two taste receptor families T1R and T2R (g) and between the number of complete olfactory receptors (OLR) and the number of complete taste receptors (TR) (h). Phylogenetic linear regression lines, as well as their slope-intercept equation, R-squared and \( P \)-values are shown with the colors associated to the species classes (only shown if significant). Dashed lines represent slope = 1. The number of chemoreceptors per species can be found in Supplementary File 1.
+
+● Agnatha   ● Chondrichthyes   ● Actinopterygii   ● Coelacanth   ● Dipnoi   ● Amphibia
+● Mammalia   ● Lepidosauria   ● Testudines   ● Crocodilia   ● Aves
+
+![Scatter plots showing correlations between numbers of complete chemoreceptor genes across chemoreceptor families, with phylogenetic linear regression lines and equations.](page_349_682_1057_1402.png)
+
+Legend:
+Afrosoricida   Lagomorpha
+Artiodactyla   Macroscelesida
+Carnivora   Microbiotheria
+Chiroptera   Monotremata
+Cingulata   Perissodactyla
+Dasyuromorph   Pholidota
+Dermoptera   Pilosa
+Didelphimorph   Primates
+Diprotodontia   Proboscidea
+Eulipotyphla   Rodentia
+Hyracoida   Sirenia
+Extended Data Fig. 2 | Vertebrate OR gene tree. a, Near maximum likelihood phylogeny of OR genes in vertebrates with branches colored according to the vertebrate (sub)class. b, Clade tree generated from (a) with local support values indicated at each node (according to a Shimodaira-Hasegawa test). All clades defined by Niimura20 in his earlier study of vertebrate OR genes were retrieved as monophyletic. We thus kept the previously proposed clade nomenclature, with Type 1 OR genes being composed of δ, α, β, ζ, ε and γ genes, and Type 2 OR genes being composed of λ, κ, θ and η genes. Three additional Type 2 OR clades were found in this study: clade A, which is restricted to agnathans; clade B, which is restricted to agnathans, the Australian ghostshark (Callorhinichus milii) and the coelacanth; and clade C, which is restricted to agnathans and the ghostshark. The tree in newick version, as well as all sequences and the alignment file can be found in FigShare. Sub-trees for each vertebrate (sub)class are shown in Supplementary Fig. 10.
+
+![Near maximum likelihood phylogeny of OR genes in vertebrates with branches colored according to the vertebrate (sub)class](page_347_682_1057_627.png)
+
+![Clade tree generated from (a) with local support values indicated at each node](page_347_1342_1057_393.png)
+Extended Data Fig. 3 | Vertebrate TAAR gene tree. a, Near maximum likelihood phylogeny of TAAR genes in vertebrates with branches colored according to the vertebrate (sub)class. b, Clade tree generated from (a) with local support values indicated at each node (according to a Shimodaira-Hasegawa test). The gene tree topology was similar to the one presented by Dieris et al.81. However, we renamed the TAAR gene clades, as the former “class II” clade was not monophyletic according to our analyses. Thus, class I genes are split into four clades, named A1 to A4, while “class II” genes are split into three clades, named B1 to B3. Note that former “class III” clade was retrieved as monophyletic, but we renamed it as B4 in coherence with our new nomenclature. We also kept the name for the TAAR-like genes, which is the sister clade of all other vertebrate TAAR genes. The tree in newick version, as well as all sequences and the alignment file can be found in FigShare. Sub-trees for each vertebrate (sub)class are shown in Supplementary Fig. 11.
+
+![Circular phylogenetic tree showing vertebrate TAAR gene clades and branch support values](page_256_384_947_627.png)
+
+![Clade tree diagram with local support values](page_256_1024_947_312.png)
+Extended Data Fig. 4 | Vertebrate *V1R* gene tree. **a**, Near maximum likelihood phylogeny of *V1R* genes in vertebrates with branches colored according to the vertebrate (sub)class. **b**, Clade tree generated from (**a**) with local support values indicated at each node (according to a Shimodaira-Hasegawa test). We kept the clade name for *ancV1R*, which denotes “ancestral V1R” as proposed by Suzuki et al.\(^{108}\). In our gene tree, this clade is the sister clade to all other *V1R* genes, while in the latter study, *ancV1R* genes were clustered together with the *ORA5* and *ORA6* clades. While Suzuki et al. suggested that *ancV1R* originated before the MRCA of bony vertebrates, we found that *ancV1R* genes most likely originated before the MRCA of all vertebrates, followed by a loss in jawless and in cartilaginous fishes. All other *V1R* clades, which were only poorly characterized in previous studies, were renamed *V1R1* to *V1R11*, while we kept the former *ORA* clade nomenclature (*ORA1* to *ORA6*) for teleosts. The tree in newick version, as well as all sequences and the alignment file can be found in FigShare. Sub-trees for each vertebrate (sub)class are shown in Supplementary Fig. 12.
+
+![Near maximum likelihood phylogeny of V1R genes in vertebrates with branches colored according to the vertebrate (sub)class](page_324_670_1092_670.png)
+
+![Clade tree generated from (a) with local support values indicated at each node](page_324_1340_1092_340.png)
+Extended Data Fig. 5 | Vertebrate *V2R* gene tree. **a**, Near maximum likelihood phylogeny of *V2R* genes of vertebrates with branches colored according to the vertebrate (sub)class. **b**, Clade tree generated from (**a**) with local support values indicated at each node (according to a Shimodaira-Hasegawa test). The *V2R* gene tree was consistent with previous studies, in particular the one by Zhang et al.109. As our extensive species sample allowed us to define new clades that were only partially or not at all described in previous studies, we also renamed all these clades. Thus, the formerly described *t-V2R* (tetrapods-V2R) clade was split into fourteen clades named *V2RC1* to *V2RC14*, while the former *f-V2R* (fish-V2R; that is, *Olfc*) clade was split into eleven clades, named *V2RD1* to *V2RD11*. The tree in newick version, as well as all sequences and the alignment file can be found in FigShare. Sub-trees for each vertebrate (sub)class are shown in Supplementary Fig. 13.
+
+![Circular phylogenetic tree showing vertebrate V2R gene clades, with branches colored by vertebrate class and labeled by clade name.](page_186_370_1077_627.png)
+
+![Clade tree diagram showing branching order and support values for vertebrate V2R gene clades.](page_186_1012_1077_370.png)
+Extended Data Fig. 6 | Co-evolution of the *V1R* gene repertoire and the accessory olfactory bulb (AOB). **a**, Phylogeny of bat species included in our dataset, for which the information on the AOB was available from the literature (absence: light blue; presence: red). **b**, Box-blots showing the number of compete *V1R* genes in bats with (red) and without (blue) an AOB (*P*<sub>PgLS</sub>; *n* = 15, *P* = 1.775e-05). Assuming that a loss of the AOB is not reversible, the phylogeny suggests at least four independent losses, indicated by light blue stars.
+
+![Phylogenetic tree and boxplots showing V1R gene numbers in bats with and without accessory olfactory bulb](page_246_384_956_670.png)
+
+**a** Phylogenetic tree
+
+**b** Boxplot of number of complete V1R genes by Accessory olfactory bulb
+Extended Data Fig. 7 | Vertebrate TIR gene tree. a, Near maximum likelihood phylogeny of TIR genes of vertebrates with branches colored according to the vertebrate (sub)class. b, Clade tree generated from (a) with local support values indicated at each node (according to a Shimodaira-Hasegawa test). We kept the former clades names T1R1 (umami receptor subunit), T1R2 (sweet receptor subunit) and T1R3. We also describe here a ray-finned fish specific clade (T1R1B), which may be part of T1R1 or T1R2 (the support value is too low to distinguish between these scenarios). Furthermore, we found three additional clades: T1RA, which is specific to Polypteryiformes; T1RB, which is specific to amphibians and lepidosaurs; and T1RC, which is specific to cartilaginous fishes. Note that the presence of the T1RC clade was already suggested by Angotzi et al.30. An alternative, but rather similar TIR topology has recently been proposed by Nishihara et al31. The tree in newick version, as well as all sequences and the alignment file can be found in FigShare. Sub-trees for each vertebrate (sub)class are shown in Supplementary Fig. 14.
+
+![Near maximum likelihood phylogeny of TIR genes of vertebrates with branches colored according to the vertebrate (sub)class](page_186_563_1077_693.png)
+
+![Clade tree generated from (a) with local support values indicated at each node](page_186_1272_1077_312.png)
+Extended Data Fig. 8 | Vertebrate T2R gene tree. a, Near maximum likelihood phylogeny of T2R genes of vertebrates with branches colored according to the vertebrate (sub)class. b, Clade tree generated from (a) with local support values indicated at each node (according to a Shimodaira-Hasegawa test). For T2R genes, we completely redefined the nomenclature, as no proper gene topology with representative vertebrate species are available as of yet. The tree in newick version, as well as all sequences and the alignment file can be found in FigShare. Sub-trees for each vertebrate (sub)class are shown in Supplementary Fig. 15.
+
+![Circular phylogenetic tree showing vertebrate T2R gene relationships, with branches colored by vertebrate class and local support values indicated.](page_176_349_1102_670.png)
+
+![Clade tree diagram with local support values at each node.](page_176_1047_1102_312.png)
+Extended Data Fig. 9 | Association between the number of *T2R* genes and diet preferences in vertebrates. Diet preferences were retrieved for every species from various databases (see Methods). To examine if the *T2R* gene repertoire was shaped by diet preferences in mammals, birds and ray-finned fishes, we performed pGLS analyses between the number of complete *T2R* genes and the diet. pGLS *P*-values are indicated above each boxplot and each test were performed twice, taking BUSCO80 (left) or BUSCO90 (right) species. For mammals, we further tested the impact of the two carnivore marine clades on the pGLS results.
+
+![Boxplots showing associations between number of complete T2R genes and diet preference for different vertebrate groups](page_176_354_1096_1442.png)
+Extended Data Fig. 10 | The chemoreceptor gene repertoire in marine tetrapods and closely related species. Phylogeny of marine tetrapods and closely related species, displaying the number of olfactory and taste receptors (BUSCO80 dataset). Genes are colored according to their chemoreceptor family. The names of the marine species and the associated branches in the phylogeny are colored in blue, while the names of non-marine species and the respective branches are colored in brown. Marine clades feature a reduction in the number of olfactory and taste receptor genes. All marine clades, excepted sirenians, have lost their T1R genes; T2R genes are completely lacking from the genomes of Sphenisciformes and some cetaceans.
+
+![Phylogeny of marine tetrapods and closely related species, displaying the number of olfactory and taste receptors](page_374_654_1092_410.png)
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• PolicarpoetalSupplementary.pdf
+• PolicarpoetalSupplementaryFile1.xlsx

0c8593c3aaadfa5001f0acfc92a8abf82f0aaaa844821bcfadafe8a834f26c72/preprint/preprint.md

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+Ports’ criticality in international trade and global supply-chains
+
+Jasper Verschuur (jasper.verschuur@keble.ox.ac.uk)
+University of Oxford https://orcid.org/0000-0002-5277-4353
+Elco Koks
+Vrije Universiteit Amsterdam https://orcid.org/0000-0002-4953-4527
+Jim Hall
+University of Oxford https://orcid.org/0000-0002-2024-9191
+
+Article
+
+Keywords: ports, global economy, supply chain, international trade
+
+Posted Date: March 31st, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-106378/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on July 27th, 2022. See the published version at https://doi.org/10.1038/s41467-022-32070-0.
+Ports’ criticality in international trade and global supply-chains
+
+J.Verschuur1,*, E.E. Koks1,2 and J.W. Hall1
+
+1 Environmental Change Institute, University of Oxford, Oxford, United Kingdom
+2 Institute for Environmental Studies, Vrije Universiteit Amsterdam, Amsterdam, Netherlands
+*corresponding author: jasper.verschuur@keble.ox.ac.uk
+Environmental Change Institute, 3 South Parks Road, OX1 3QY, Oxford, United Kingdom
+
+Abstract
+
+Ports form the backbone of the global economy. By combining a vast database of ship tracking data with bilateral trade data and input-output tables, we highlight the critical role of specific ports in global supply chains and economies. For some countries, we find that 43.5% of economic activity is dependent on trade going through a single port. The top ten global ports influence 9.3% of the global economy, of which the port of Shanghai alone embeds 1.7% of global output. Ports are even more critical in some sectors, such as the mining and quarrying sector, for which 82% of trade is transported by maritime transport. We estimate how changes in final demand will be routed through ports, revealing that for every US$1000 increase in final demand a country’s ports experience a US$18.3 increase in imports on average, and up to US$108 increase in low income countries and small islands.
+Introduction
+
+Reliable port infrastructure is pivotal for the facilitation of international trade flows\(^{1,2}\). Nowadays, around 80% of global trade in terms of volume is transported by means of maritime transport\(^3\). Developments in inter-country and inter-industry trade flows are becoming increasingly global, extensive and complex\(^{4,5}\), relying ever more on maritime transport. Additionally, ports are becoming more embedded into these complex supply-chains through integrated logistics services that connect ports to their hinterland networks\(^{6,7}\). Future demand scenarios project a near tripling of maritime trade volume by 2050\(^8\), thereby exceeding the current capacity of many port areas\(^9\), requiring large investments to ensure the continuous movements of goods.
+
+Recent research has examined the evolution of international trade and supply-chain interconnectivity\(^{4,5,10}\). This development is backed by advances in the provision of Multi-Regional Input-Output (MRIO) tables that constitute the inter-, and intra-industry dependencies within countries and between countries\(^{11-14}\). Although MRIO tables provide extensive descriptive data on inter-, and intra-industry trade flows, at national and regional scales, it does not provide insights into the domestic and international transportation systems that are used for these trade flows. Nor does it precisely geolocate the locations of imports and exports of particular goods. Another strand of literature has analysed the network structure and evolution of maritime transport networks through a complexity science lens\(^{15-22}\). This research, however, focused solely on the shipping connections between ports, without incorporating information on the goods that are carried by maritime vessels and how these goods are used in the economy. Hence, to date, there is no globally consistent analysis of the use of maritime transport in international trade by country and sector. In addition, we lack a global-scale analysis of the
+the port embeddedness in global trade, which we define as the criticality of a given port for supply chains and economic activity, domestically and internationally. Such spatially explicit supply-chain insight inform economic decisions\(^{23}\). For instance, information on the port embeddedness in trade and supply-chains could help better understand the geographical distribution of trade flows across supply-chains\(^{24,25}\), connect environmental footprints with commodity flows\(^{23,26}\), predict future port demand, in terms of volume and space required, as economies grow\(^9\), allocate maritime emissions (~2.6% global greenhouse gas emissions in 2012) to countries and sectors\(^{27,28}\), and assess the potential supply-chain losses due to port disruptions\(^{29,30}\).
+
+In this study, we set out a complete methodology to provide a globally consistent assessment of the port embeddedness in maritime trade (1172 ports across 177 countries) and global supply-chains (1132 ports across 157 countries). We establish the link between ports and the economy by estimating maritime trade flows between ports and by linking this trade network data to a global MRIO (Methods). To do so, we first estimate the freight modal split globally (i.e. the percentage trade in goods per transport mode) and use this to estimate the share of maritime trade in every bilateral trade flow at a commodity level (HS6). These estimates of bilateral trade flows are then linked to the global port network using a novel downscaling approach based on the Automatic Identification System (AIS) signals of vessels in combination with a trade estimation algorithm developed in previous research\(^{31}\). This allows us to create new insights into the geolocation of sector-level trade and core-periphery structures in the port-to-port trade network. To identify the domestic and global economic dependencies on trade flows through ports, we link the commodities that flow through ports to intermediate demand and final consumption using the EORA MRIO table\(^{13}\). Two metrics are constructed to capture these dependencies (1) the port-level output coefficient (PLOC) that captures to what extent industry
+output is reduced (both domestically and globally) if a particular port is hypothetically extracted from the I-O table, and (2) the port-level import coefficient (PLIC) that measures the increase or decrease in port-level trade flows when demand changes in an economy, and. Throughout this paper, we will adopt an 11 sector classification system (Methods) corresponding to the 11 economic sectors in the EORA MRIO (Supplementary Table 1). This analysis paves the way for a better understanding of the key links, dependencies and feedbacks between port and maritime infrastructure systems and the economy.
+
+Results
+
+Share of maritime transport in global trade
+
+The results of the global modal split (Methods) are included in Fig. 1, showing the percentage of maritime transport in total imports (Fig. 1a) and total exports (Fig. 1b). The mode of transport is defined as the dominant transport mode (longest distance) in the supplier-consumer connection, which explains why landlocked countries can still have a share (although small) of maritime transport (see Methods). In total, we estimate that 55.0% of bilateral trade in terms of value is maritime, although with large differences between sectors (Supplementary Fig. 1 and 2). For instance, 83.5% of trade in mining and quarrying products (sector 3) is by means of maritime transport, whereas manufacturing of electrical products and machinery (sector 9) and manufacturing of transport equipment (sector 10) only transport 52.2% and 48.9%, respectively, of their trade using maritime transportation. Small island states and countries in Africa rely disproportionally on maritime transport for both imports and exports (Fig. 1a-b), whereas Middle-Eastern and South American rely more on maritime transport for their exports compared to their imports. European countries have a much lower share of maritime transport, mainly due to the large flows between European countries that use road, rail and inland
+waterway transport to move goods over relatively short distances\(^{32,33}\). The countries with the highest share of maritime transport in their imports are the Marshall Islands (99.2%), Guinea (97.9%), Liberia (97.6%), Mauritania (97.5%) and Sierra Leone (97.5%), while the countries with the lowest shares are Laos (8.7%), Bhutan (9.7%), Andorra (11.5%), Austria (12.1%) and Switzerland (12.7%). For exports, countries with the highest shares of maritime trade are Equatorial Guinea (99.7%), Solomon Islands (99.5%), Trinidad and Tobago (99.4%), Algeria (99.1%) and Saint Vincent and the Grenadines (98.7%), whereas the lowest export shares are found for Mongolia (5.9%), Kyrgyzstan (10.3%), Bosnia and Herzegovina (10.3%), Laos (11.6%) and Serbia (12.7%). The dominance or absence of maritime transport for trade is mainly determined by the geographical location of trading partners (e.g. distance, island state), the presence of alternative (fast and cheaper) modes, the value to weight ratio of the commodities, and the income of the importing country (i.e. ability to afford air transport)\(^{34}\). For instance, low-income countries mainly export low value bulk goods, for which maritime transport is the only viable option, and relatively few high valued goods that are typically transported by aeroplane\(^{35}\). Even within the same continent, such as in Africa, maritime transport is often the only feasible mode of transport as the road infrastructure lacks the reliability and capacity for efficient trucking, and passing of border crossings are often time-consuming\(^{36}\). Fig. 1c shows the share of maritime transport in total and sector-specific imports grouped by the income level of countries (using the World Bank classification). Low-income and lower-middle income countries import on average 1.6-1.7 times more by means of maritime transport compared to high income countries (79% versus 48%). The difference is largest for the manufacturing sectors (sector 9, 10 and 11) with low-income and lower-middle income countries having maritime shares 1.67-2.14 times and 1.48-1.77 times higher than high income countries, respectively. Therefore, the integration of low and lower-middle income countries into complex manufacturing supply-chains, which critically depend on just-in-time logistics
+services\(^7\), could be hindered by their overreliance on maritime transport, which is considerably slower than air transport\(^{37,38}\).
+
+**Distribution of trade flows per port**
+
+Using a downscaling approach based on AIS data (Methods), we derived a port-to-port trade network, which distinguishes the origin and destination ports of trade per industry (Supplementary Fig. 3 and 4). Altogether, ports import and export 7.8 billion USD (based on 2015 trade data), with the distribution of imports and exports shown in Fig. 2a-b. The top 5 largest ports (top 20 ports highlighted in Fig. 2a) in terms of imports are Los Angeles-Long Beach (277 million USD), Hong Kong (193 million USD), New York-New Jersey (175 million USD), Shanghai (165 million USD) and Singapore (149 million USD). Large importing ports are located in North-America, Western Europe and Asia that serve the populated hinterlands. The top 5 exporting ports (top 20 ports highlighted in Fig. 2a) are Shanghai (442 million USD), Ningbo (353 million USD), Qingdao (197 million USD), Ulsan (175 million USD) and Hamburg (174 million USD). Large exports originate from industrial hubs such as petrochemicals in the Gulf of Mexico region (Houston), the German car manufacturing (Bremerhaven, Hamburg) and Asian manufacturing hubs (China, South-Korea, Vietnam and Taiwan).
+
+On a sector-level, maritime trade flows are highly concentrated in a relatively small number of ports that are either connected to important hinterland transport networks\(^{39}\), or closely located to large sector-specific industry clusters\(^{39}\). Fig. 2c shows the geographical location of the 50 largest importing and exporting ports per sector, showing clear geographical clustering of trade flows. In particular, the exports of textiles and wearing apparel (sector 5) are highly clustered in India, Bangladesh, Thailand and China, while the manufacturing of electronics and
+machinery (sector 9) is highly clustered in China, South-Korea, Vietnam and Taiwan. Agriculture trade has clear origin ports in the United States, Brazil and Argentina, serving ports in Europe and across Asia. Wood and paper manufacturing (sector 6) has large exporting ports in Scandinavia, Canada, Brazil and China, that export products to ports in the United Kingdom, Japan and the Middle-East. The import and export hotspots of mining and quarrying (sector 3) and food and beverages (sector 4) are more spread across the globe, reflecting the export specialisation of different regions (e.g. oil in Middle-East, iron ore and coal in Australia, food products in Indonesia).
+
+This trade unevenness can be expressed as the percentage of ports (relative to the total number of 1172 ports) that handle 50% (90%) of trade (Supplementary Table 2). Exports are more concentrated than imports with 4.9% (28.9%) of ports versus 6.3% (34.1%) of the ports handling 50% (90%) of global maritime trade. Some industries are more concentrated than others. The largest unevenness is found for the exports of textiles and wearing apparel (sector 5), manufacturing of electronics and machinery (sector 9) and other manufacturing (sector 11) with the 50% (90%) share of trade flows concentrated in 0.6% (7.7%), 1.2% (11.4%) and 0.5% (7.7%) ports, respectively. On the contrary, the lowest level of concentration is found for the imports of food and beverages (sector 4) with the concentration of trade in 5.5% (29.2%) ports, and petroleum, chemical and non-mineral products (sector 7) with 5.4% (29.1%) ports covering 50% (90%) of maritime trade flows.
+
+Core-periphery structures
+
+The large unevenness in terms of trade flows suggest a hierarchical structure of trade within the port-to-port trade network. Previous research on country-to-country trade networks\(^{40,41}\) and maritime transport networks\(^{21,22}\) have shown that both networks have a clear core-periphery structure, in which core nodes (ports) are densely connected with each other, while periphery
+nodes are mainly connected to core nodes but sparsely to other periphery nodes. Core-periphery structures within port and transport systems reflect the agglomeration and dispersion of the industries and markets they serve, with core regions demanding a diversified set of products while periphery regions house more specialised industries\(^{42-44}\). Moreover, ports are a driver of a core-periphery structure itself by lowering the transportation costs to access international markets\(^{45}\). In line with this, previous research has posed the hypothesis that core ports are more diversified, while periphery ports are more specialised\(^{43,44}\).
+
+We classified ports according to their degree of specialisation (using the normalised Gini coefficient of trade flows) and the coreness (based on a core-periphery detection algorithm) across industries (Methods and Supplementary Fig. 5), which help to explain the underlying structure of, and role of the port in, the maritime trade network. We find a negative correlation (Spearman rank correlation: -0.36) between the degree of specialisation and the coreness of ports, suggesting that core ports are more diversified, while periphery ports are more specialised (Fig. 3 ‘All’). China, the United States, United Kingdom, India and the Philippines have a clear core-periphery structure within their national port network with a small number of large diversified core ports alongside specialised peripherical ports (Fig. 3). However, other countries have a distinctly different pattern (Fig. 3). For instance, Japan has alongside their high coreness diversified ports (ports of Nagoya, Yokohama and Kobe) a number of highly specialised, large coreness, ports such as the ports of Mikawa, Kanda, Hiroshima (all important ports for vehicle manufacturing). Major exporting countries like Australia, Brazil and South Africa have their specialised exporting ports as the largest core ports. For Australia, the largest coreness is found for the ports of Port Hedland, Newcastle and Port Walcott, all exporting mainly iron ore or coal, followed by the port of Brisbane and Melbourne as diversified ports. For South Africa, the largest coreness port is the port of Richards Bay (largest coal exporting port of Africa) followed
+by the diversified port of Durban, whereas Brazil has the large mining ports of Itaqui and Belem (iron ore exporting ports) as highest coreness ports alongside the diversified importing ports of Santos and Rio de Janeiro. The core-periphery structures we find reflect a hierarchical spatial structure shaped by spatial location of industries and urban areas, the structure of transportation system, and the organisation of logistic services, illustrating how trade flows through ports may change as any of these drivers change.
+
+Port-level output coefficient
+
+The products that are imported through a port are directly consumed in a country or are used in production processes to produce goods for domestic consumption or export. Additionally, goods exported through a port are being used in production processes, or directly consumed, elsewhere. To understand the importance of the trade facilitation function of ports for domestic and global supply-chains, we developed a metric, called the port-level output coefficient (PLOC), that captures the total industry output directly or indirectly dependent on the trade flows through a port, either in absolute terms (PLOCA) or relative to the amount of trade going through a port (PLOCR). This is done by removing the trade flows going through a port from the I-O table and quantifying the output changes to the domestic and global economy (see Methods).
+
+In absolute terms (PLOCA), some ports are important for the domestic economy, while others are more important for the global economy, as can be observed from Fig. 4a, which show the top 10 ports in terms of domestic output and in terms of global output that depend on the trade flow going through this port. In total, 41.9% of global industry output depends on the trade flows going through ports, which, again, are highly concentrated in a few key ports (Fig. 4b). The ports of Shanghai (China, 1.66% of global output), Ningbo (China, 1.19 of global output)
+and Hamburg (Germany, 1.00% of global output) being most of important ones for the economy. Overall, 9.3% of the total industry output depends upon trade flowing through only the top 10 ports, 33.4% to the global economy depends upon flows through the top 100 ports. An average (maximum) of 2.01% (43.50%) of domestic industry output depends on maritime trade going through a single port. Examples of ports that are particularly important to the domestic economy but negligible on a global scale (dark blue or purple markers Fig. 4a) are the ports of Pointe-Noire (Congo, 20.3% of domestic output), Marsaxlokk (Malta, 21.2% of domestic output), Port Louis (Mauritius, 30.6% of domestic output), Reykjavik (Iceland, 20.6% domestic output) and Dar Es Salaam (Tanzania, 25.7% of domestic output). The ports of Singapore, Hong Kong, Mina Al Ahmadi, Laem Chabang and Kaohsiung (red markers Fig. 4a) are found to be essential for both domestic and global economy.
+
+In relative terms (PLOCR), every dollar of trade going through a port influences on average (5-95th quantile) 4.16 (3.41 – 4.97) dollar of industry output to the global economy (Supplementary Fig. 5) . However, the goods that flow through a port can be relatively more embedded in domestic or foreign production processes, and relatively more through forward linkages or backward linkages. The relatively importance of these four components therefore determine how ports are positioned differently within the global supply-chain network, and also provides an indication how port disruptions (i.e. natural disasters, labour strike) can propagate through the economic system. In Fig. 5, we show the relative forward and backward linkages of port-level trade flows, and the degree to which output is linked to domestic or global supply-chains. The ports of Rotterdam, Singapore, Los Angeles-Long Beach, Bremerhaven, Houston and Shanghai are all among the largest ports in terms of total trade (in value terms), but can be found at opposite sides of the spectrum. Rotterdam and Singapore have large global dependencies and balanced forward and backward linkages (relative to other ports), mainly due to their role as
+petrochemicals hub and imports of final consumption goods (which embed products produced in other countries). Shanghai, Yokohama and Bremerhaven, on the other hand, have higher domestic dependencies and larger backward linkages. These ports are highly integrated with domestic manufacturing supply-chains (e.g. car manufacturing for Bremerhaven and Yokohama, and electronics and other manufacturing for Shanghai). The port of Los Angeles-Long Beach has high global dependencies while also having high backward linkages, illustrating that it mainly imports final consumption goods. Similar characteristics are found for the port of Jeddah and Buenos Aires, which are the major container ports that serve Saudi Arabia and Argentina. The port of Houston has higher forward linkages and higher domestic dependencies, indicating that the domestic supply-chains produce goods that are mainly exported and used into upstream production processes (e.g. petrochemical and oil refinery products). Port Hedland (Australia) and Mina Al Ahmadi (Kuwait) have large forward linkages, implying they mainly export goods that are used in production stages downstream in the supply-chain (oil for Mina Al Ahmadi, iron ore for the Port Hedland).
+
+The PLOC metrics illustrate how domestic and global supply-chains are tied to the port, and how ports are differently positioned in the global supply-chain network. This measure therefore helps to understand how demand shocks (e.g. pandemic) ripple through the economy and helps to evaluate the potential losses within supply-chains networks if ports are disrupted by a trade shock (e.g. natural disaster or labour strike).
+
+Port-level import coefficient
+
+To meet the final demand (i.e. domestic consumption and exports) in an economy, imports are necessary, which are facilitated (alongside alternative modes) by a country’s port infrastructure. Due to an increasing fragmentation (i.e. different stages of production in different countries)
+and globalisation (i.e. global expansion) of supply-chains\(^{10,46}\), the reliance on imports to support final demand is increasing. Using the EORA MRIO table, we can find the direct and indirect (through interindustry dependencies) imports per port needed to produce the domestic consumption and (re-)exports in an economy. The port-level import coefficient (PLIC, see Methods) expresses this import need as a fraction of the final demand (Fig. 6a), quantifying the marginal increase or decrease in imports that flows through a port for every dollar increase or decrease in final demand (see Methods).
+
+On average, every 1000 dollar increase in final demand of an economy leads to an additional 2.2 dollar of imports going through a given port. Fig. 6a highlights the 15 ports with the largest PLIC values, indicating how large PLIC values are found for the smaller ports of Male (Maldives, 108.2), Victoria (Seychelles, 73.1), Banjul (Gambia, 53.5) and Paardenbaai (Aruba, 51.7), the medium-sized ports of Kampong Saom (Cambodia, 61.6), Toamasina (Madagascar, 41.2), Dar Es Salaam (Tanzania, 37.8), Paramaribo (Suriname, 37.5), and the larger ports of Ho Chi Ming City (Vietnam, 44.4), Macau (Macau, 39.7), Singapore (Singapore, 32.1) and Colombo (Sri Lanka). In general, the larger PLIC values are found for ports in countries that have a limited number of importing ports and have a high overall trade openness, i.e. they rely disproportionally on foreign products to meet their domestic consumption and for use in domestic production processes that are later exported to other countries. Overall, specialised ports have lower PLIC (Spearman’s rank correlation: -0.24), while the coreness positively scales with the PLIC (Spearman’s rank correlation: -0.50). This can be explained by the fact that more diversified ports (that have higher coreness) tend to handle manufacturing products, which have higher sector-specific PLIC values due to the larger dependencies on imports for their production (see Supplementary Fig. 7).
+Fig. 6b show the country-level import coefficients (CLIC), indicating the dollar increase in country-wide maritime imports due to a dollar increase in final demand. On a country-level, for every 1000 dollar increase in final demand, ports (i.e. all ports in a country) will experience a mean (maximum) 18.3 (108.3) dollar increase in maritime imports. However, a large variation is seen across groups of countries. Countries in Asia and Oceania tend to have an average CLIC that is 1.94 and 1.34 times higher, respectively, compared to the global average, while countries in Europe have a CLIC that is 0.51 times the global average. Small-island developing nations (SIDS), characterized by large dependencies on other economies to meet final demand, tend to have a 1.62 times higher CLIC (Fig. 6c). Moreover, low-income countries have a 1.5 times higher CLIC-values than high-income countries (Fig. 6d), illustrating how maritime trade may rise steadily in low-income countries as economies grow and become more diversified.
+
+The imports coefficients (on a port and country level) help to quantify how future trade flows through ports will change as countries develop (e.g. demand grows), supply-chains further fragment (e.g. higher import coefficients), and if the sector composition in a country shifts (e.g. low-income countries demanding more manufacturing products).
+
+Discussion
+
+This study presents the first global analysis of the embeddedness of ports in international trade and global supply-chains. We make use of a novel downscaling approach that disaggregates global sector-specific bilateral trade flows to the port-level, which allows us to evaluate the share of maritime transport in global trade flows. We create a new classification system of ports based on their degree of specialisation and core-periphery structure. Moreover, we connect this port-to-port network to a global MRIO in order to analyse the domestic and global industry dependencies on trade flows passing a port.
+We find that the approximately 55.0% of global trade by value is via maritime transport, although higher values are found for the agriculture (63.9%) and mining and quarrying (83.5%) sectors. Maritime trade flows are concentrated in a small number of highly diversified ports that benefit from economies of scale and are well-integrated with the hinterland networks. Many countries have a clear core-periphery structure in their port system, with a set of core ports that tend to be diversified alongside a number of periphery specialised ports. This fact confirms a long-standing view in maritime economics and economic geography\(^{44,47}\).
+
+Low-income economies and small island developing states depend disproportionally on their port infrastructure for trade. Low-income countries import 1.7 times more by means of maritime transport than high-income countries, and further require 1.5 times more imports through their ports for every 1 dollar increase in final demand. Therefore, investments in reliable port infrastructure in low-income countries and small island developing states are essential if further economic growth is not to be inhibited by port capacity\(^{48}\). The benefits of increasing trade facilitation provided by ports may reach beyond the port boundaries, as ports tend to attract industry clusters\(^{45,49}\) and lower transaction costs in trade, which could lead to indirect benefits through access to, and integration in, international markets (e.g. food availability, expending exports markets)\(^{50-52}\).
+
+Port are further found to be essential to integrate domestic and global supply-chains. An average (maximum) of \(2.01\%\) (43.50\%) of domestic industry output depends on maritime trade going through a single port. 9.3% of the global industry output depends upon trade flowing through the top 10 ports, with the port of Shanghai found as most critical port for the global economy (1.7% of global output depends on good going through Shanghai). In relative terms, every dollar flowing through a port embeds on average 4.17 dollar to industry output in the economy (both
+domestic and global). The position of ports within supply-chains depends on the relative importance of domestic versus foreign supply-chains, and forward versus backward linkages. Similar ports in terms of size may be found at different ends of the spectrum, which has important implications for the feedback between the economy and trade flows through ports, and for evaluating the potential magnitude and spatial extent of supply-chains losses if ports are disrupted. This highlights how expressing the importance of a port only in terms of the value of trade passing through it hides some key distinctive features of ports in terms of their supply-chain embeddedness.
+
+Future research can build on the framework developed here in various ways. First, our disaggregated analysis of global trade flow could allow estimating the carbon emissions embedded into maritime transportation, which can help allocate these emissions to countries and sectors\(^{27,53}\). Second, recognising that ports are integrated within port-hinterland transport networks\(^{2,39}\), the current framework could be extended to a full intermodal (e.g. road, rail, air, inland waterway) transport network that connects the origin and destinations locations of supply-chains. Third, by analysing future trade flows, the current analysis could help refine the future investment needs of port infrastructure and evaluate the changing dependencies between ports and the economy. At last, by coupling this framework to a disaster impact model\(^{54}\), the economic-wide losses (domestic and global) from port disruptions could be assessed, including the future losses due to climate change (e.g. sea-level rise, increased frequency of flooding). This could help understand the climate change adaptation needs of ports, and its financial viability, by weighting the costs (e.g. land elevation, breakwater construction) and benefits (e.g. reduced delays, physical damages, and business interruptions) of continues functionality.
+In conclusion, ports are closely tied to the economy by facilitating trade flows that connect global supply-chains networks. Therefore, there is a clear need to integrate long-term infrastructure planning of port infrastructure with a system-wide perspective of the interconnectivities between the transport and the economic system. Given the large investments associated with the maintenance, replacement and expansion of port infrastructure needed to meet future demand, evaluating the key links, feedbacks and dependencies between ports and the economy is imperative for the sustainable development of economies.
+
+Data availability
+
+All data to reproduce the results in this study can be accessed via Mendeley Data (link will be added upon acceptance).
+
+Acknowledgements
+
+The authors would like to thank the United Nations Statistical Division and the UN Global Working Group on Big Data for Official Statistics, in particular Markie Muryawan and Ronald Jansen, for providing the mode of transport data and the AIS data. Moreover, we like to thank Lóri Tavasszy for discussions that helped improve the methodology. J.V. acknowledges funding from the Engineering and Physical Sciences Research Council (EPSRC) under grant number EP/R513295/1.
+
+Author contribution
+
+J.V. E.K. and J.H. designed the study. J.V. performed the analysis with input from E.K. and J.H. All authors contributed to the writing and reviewing of the paper.
+
+Competing Interests
+
+The authors declare no competing interests.
+Method (3000 words)
+
+Modal choice model
+
+We develop a global modal choice (or modal split) model to predict the share of maritime trade in every bilateral trade flow. A model choice model intends to predict the allocation of freight transport flows for a given Origin-Destination (O-D) over alternative and competing transport modes\(^{55}\). In order to set-up a model, we have collected mode of transport data from UN Comtrade\(^{56}\) for the period 2016-2018, which describes the share of every mode of transport per bilateral trade flow on a commodity level (HS6). In total, 50 countries report mode of transport data. We filter out trade flows between non-landlocked countries in order to avoid misclassification of the mode of transport (e.g. Switzerland reports trade from Argentina as being road, because it uses road transport to enter the country) and remove trade flows that are specified as road, but where no road connection is present (e.g. trade from Brazil through the Port of Rotterdam to Germany is classified as road or rail). This results in 6.8 million bilateral trade flows between ~12,000 unique country pairs.
+
+We consider, maritime, air and road transport, due to the availability of global data and given that 93% of trade in our sample is by means of these three modes. The model is set up to predict the share of maritime trade given the availability of maritime, air and (if possible) road transport. We adopt a multinomial logit formulation, as is common practise into transport modelling\(^{55,57,58}\), which is based on the concept of utility maximisation given a set of explanatory variables related to the mode of transport (e.g. distance, time), the importing and exporting country (e.g. income level, neighbouring countries), and the commodity (e.g. weight to value ratio). We estimate the modal split per economic sector \( s \) (grouped into 11 sectors, see
+Supplementary Table 1) to account for the heterogeneity in commodity types and because fitting parameters may vary between sectors.
+
+After testing various possible forms (see Supplementary Note 1), we adopt the following formulation to estimate the % of maritime trade for trade flow \( n \) of goods within sector \( s \) given the mode alternatives \( i \)
+
+\[
+LN \left( \frac{1}{\%_{ns,mar}} - 1 \right)
+\]
+\[
+= \beta_1 (C_{ns,air} - C_{ns,mar} + C_{ns,road} - C_{ns,mar})
+\]
+\[
++ \beta_2 (t_{ns,air} - t_{ns,mar} + t_{ns,road} - t_{ns,mar}) + \beta_3 Weight + \beta_4 Value + \beta_5 GDPcap
+\]
+\[
++ Neighb + \gamma_s + C
+\]
+
+with \( C_{ns,i} \) the generalised cost function:
+
+\[
+C_{ns,i} = (d_{ns,i} T_i + t_{ns,i} V_i)
+\]
+
+In this formulation, \( d_{ns,i} \) is the mode-specific distance in km, \( T_i \) the mode-specific transport costs per tonnes per km (US$/t/km), \( t_{ins} \) the mode-specific transit time in h, \( V_i \) the mode-specific value of time per tonnes per hour (US$/t/h), \( Weight \) the total transported weight in tonnes, \( Value \) the value per tonnes of the good in US$, \( GDPcap \) the GDP/capita of the importing country, \( Neighb \) is a dummy variable set to 1 if the countries are neighbours, \( \gamma_s \) a dummy for commodity type (based on HS2 code) and \( C \) a constant. In case road transport is not an alternative (e.g. island states), all parameters with index road drop from Equation 1. For consistency across datasets, the origin and destination of every country pair is determined based on the geographical location of the capital city.
+
+For air transport, the geographical distance between capital cities are derived from the CEPII GeoDist database\(^{59}\). For the transit time, we use data from an air cargo O-D database\(^{60}\) to know which country pairs have direct flight connections and which pairs need transhipment. We
+assume that every country pair can be connected using one transhipment, which add 18h hours to the transit time\(^{60}\). We add a dwell time (time goods spend at an airport) to the airports are set in line with previous research\(^{34}\), and summarized in Supplementary Table 3.
+
+The road transport layer is extracted from the gROADSv1 global road network\(^{61}\). Using this network, we create a routable unidirectional network connecting the road segments (with the length of a segment as weight). We can create shortest paths between all country pairs using Dijkstra’s shortest path algorithm\(^{62}\), which is set to zero if no connection is found. The transit time between countries is based on different speed per road type, which are taken from Martínez et al.\(^{34}\), and summarized in Supplementary Table 3. We run the same shortest path algorithm again, but now using the time (speed times distance) as the weight.
+
+Maritime distance between country pairs are based on the CERDI sea distance dataset\(^{63}\). In this database, the maritime distances between country’s major seaports are estimated based on the 2005 shipping network. In addition, the road distance between the capital city and the major seaport is included. The maritime time between countries is based on actual ship movement data (Automatic Identification System) by create a port-to-port dataset of visits for a year of data (04-2019 until 04-2020, see *Trade distribution approach* section for data specification). We create an unidirectional network with the median transit time between countries. For landlocked countries (which are not included in the port-to-port dataset), we use the road network to connect landlocked countries to the closest 15 ports in 15 countries, to allow landlocked countries to use ports in different countries (e.g. Switzerland can use the an Italian port for trade from Asia and a port in Germany for trade from Scandinavia). We include potential transhipments by adding a transhipment time of 2 days in every node (country). Again, using a shortest path algorithm, we find the transit time between all country pairs. We add the
+turn-around time (time spend in port) to every port visit, which are also found using the AIS data, and the transit time between the port and capital city (for all non-landlocked countries). Lastly, we add a dwell time at the origin and destination ports (time of goods in ports before being loaded in vessel or picked by truck) based on previous work\(^{34}\), and again included in Supplementary Table 3.
+
+To estimate the mode-specific distance costs and the value of time, we test a range of values based on previous research\(^{64-66}\). Given the range of values reported in the literature, we test the sensitivity of the results to variations in the value of time and distance parameters for maritime transport and choose the combination of parameters that yield the best goodness-of-fit values (based on the MSE). The selected values are included in Supplementary Table 4.
+
+Data on the GDP per capita are extracted from the World Development Indicators database\(^{67}\), value-to-weight and total weight values are taken from the BACI trade data for 2015-2017\(^{68}\), and the Neighbouring country dummies are taken from the GeoDist database\(^{59}\).
+
+We perform a validation of the data on a sector level, with scatterplots included in Supplementary Fig. 8. The fitted parameters are included in Supplementary Table 5. The correlation coefficients range from 0.44-0.99, whereas R-squared values range from 0.18-0.99. Moreover, we compare the final fitted maritime shares for the United States, New Zealand and Europe to external databases, which show an overall good result (Supplementary Note 2 and Supplementary Table 6).
+
+To create a harmonized maritime trade dataset, we fit the model with the 2015 BACI harmonized trade data\(^{68}\), which has commodity-specific (HS6) trade data on 7.5 million
+bilateral trade flows between ~24,000 unique country pairs. We use 2015, given that we later couple this data to the EORA MRIO table, which has 2015 as its most recent year.
+
+Trade distribution approach
+
+The country-to-country maritime trade flows are disaggregated to the port-level. We aggregate the HS6-level maritime trade flows to sector-level in line with the sector-classification used in this study. We do this analysis for a total of 1172 ports across 177 (maritime) countries. We take a step-wise approach to assign trade flows to ports. First, for every vessel that sends out AIS signals, we create a database of port visits (port calls) in order to understand which ports are connected to each other on a liner connection (i.e. sequence of port visits for a particular vessel). We analysed a database of 3.2 million ports calls from around 100,000 different vessels. Second, we estimate the port-level imports and exports on that liner connection based on an algorithm developed, and validated, in earlier work\(^{31}\) that estimates the trade flows (in tonnes) based on the vessel characteristics, draft changes, and some correction factors. In principle, every port in a liner connection can trade with each other. We approximate that the likelihood that ports trade with each other scales with the size of trade within a liner connection (i.e. largest importing port trades with largest export port). Moreover, previous work has estimated a conversion factor (\(f_s\)) that estimates the likelihood that a type of vessel transports good from a particular sector (\(s\))\(^{31}\) in combination with a country-specific correction factor for the import (\(f_i\)) and export of goods (\(f_e\)) that reflect that similar types of vessels carry different goods depending on the trade composition of a country. We assume that the type of good that is likely transported between the two countries relates to the weighted correction factors \(f_i\) and \(f_e\). At last, we use a conversion from weight to value (\(f_v\)) based on the country pair. In short, we can write the sector-specific trade scaling factor (\(TSF_{s,e,o,id}\)) of a vessel type on a liner connection
+between an exporting (\( e \)) port in a origin country (\( o \)) and an importing (\( i \)) port in the destination country (\( d \)):
+
+\[
+TSF_{s,eo, id} = E_{eo, id} * I_{eo, id} * f_s * f_{v, od} * \frac{f_{i, d} + f_{e, p}}{2}
+\]
+
+Given all liner connections between ports, we can disaggregate the share of maritime trade for every sector for a bilateral country pair (\( \%_{s,o,d} \)) to the port-level of these countries (\( \%_{s,eo, id} \)) by comparing the \( TSF_{s,eo, id} \) of the port-pair to the total TSF over all port combinations (\( TSF_{s,o,d} \)):
+
+\[
+\%_{s,eo, id} = \frac{TSF_{s,eo, id}}{\sum_{k \in K} \sum_{s \in S} TSF_{s,k o, sd}} * \%_{s,o,d}
+\]
+
+with \( K \) and \( S \) the set of ports in both the origin and destination countries that are connected to each other through liner connections. Using this formulation, we can distribute 97% of all trade flows. For the last 3% where there are no direct liner connections (transhipment is needed), we assume that the distribution is equal to the total TSF of the ports (e.g. the largest importing port in a country and largest exporting port in another country trade disproportionally with each other).
+
+We validate how the well the disaggregation method captures the distribution of sector-specific imports and exports for a country as a whole. We collected port-level trade statistics for 2019 for the United Kingdom, the United States, New Zealand, Brazil and Japan and convert all data to the same sector classification. The validation is included in Supplementary Fig. 9, and shows a good agreement for most sectors and countries, although the methodology generally concentrates to much trade in smaller ports. This deficiency can be attributed to the accuracy of the trade prediction algorithm, which tend to overpredict trade in smaller ports, due to difficulties of capturing trade flows in small ports with large trade imbalances\(^{31}\).
+Port classification
+
+The port classification consists of two factors: (1) the inequality in sector-specific trade flows to capture the degree of specialisation and (2) the core-periphery structure of the port in the trade network. We use the Gini-coefficient as a measure of trade inequality (hence specialisation). For the 11 sectors (s), we measure its proportion to total trade \( T \) (\( T = \) imports + exports), which we first normalise (\( \overline{T} \)) to account for the fact that some sector encompass more valuable goods than others. Hence, the Gini coefficient (using the Brown equation\(^{69}\)) can be derived from the cumulative share of trade (\( C_s = \mathrm{cum}(\overline{T}_s / \overline{T}) \)):
+
+\[
+Gini = \left| 1 - \sum_{s=0}^{10} (X_{s+1} - X_s)(C_{s+1} + C_s) \right|
+\]
+
+with \( X \) the cumulative proportion of sectors (e.g. 1/11, 2/11, etc.).
+
+Core-periphery structure is a meso-scale structure that is found in many transportation systems and in country-to-country trade flows\(^{21,40,70}\). A network can be decomposed into core ports, which are densely connected to other core ports, and periphery ports, that are sparely connected to other periphery ports and connected with some probability to core ports\(^{21,40}\). The core-periphery structure of ports also reflects the hinterland they serve, as core economic regions import more high-value goods, while low-value bulky good tend to be more concentrated in periphery regions\(^{43,44}\). Moreover, core-periphery structure in trade can originate due to the location of industry (e.g. trade between to car manufacturing plants in Japan and Germany), specialisation within supply-chains (e.g. iron ore or oil ports) and the strategic alliances/vertical consolidation of liner companies (e.g. specialised stevedoring companies certain ports owned by a large liner company).
+
+We construct a weighted network per sector using the derived port-to-port trade flows with the weight set to total trade \( T \). We detect core and periphery ports using the continues core-periphery algorithm of Rossa et al.\(^{40}\), which is based on the behaviour of a random-walker in a
+network. We find a coreness value per port per sector and construct the total coreness value of the port by taking the mean of the coreness values across sectors. Hence, large coreness ports are either ports that have high coreness in most sectors, or have very large coreness in a small number of sectors and low coreness in others.
+
+Link to Input-Output tables
+
+To connect the maritime trade flows to an I-O table, we use the latest EORA MRIO\(^{13}\) (2015), which describe the intercountry and interindustry dependencies for 190 countries. Of the 177 countries included in the port-to-port trade network, 157 countries are included in the MRIO, leaving us with 1132 ports for the analysis. Trade flows included in the MRIO table are not always similar as those included in the BACI trade database\(^{68}\), and hence we can only modify overlapping trade flows for this analysis (since we only derive maritime percentages for these specific trade flows).
+
+The import coefficient is derived in line with the work of Hummels et al.\(^{46}\), that used the concept of import coefficients to quantify the amount of imports embedded in the export of a country (i.e. vertical specialisation). Although the methodology of Hummels et al.\(^{46}\) was developed for a single country I-O table, Dietzenbacher\(^{71}\) showed that the same result holds for a MRIO. Our port-level import coefficient (PLIC) metric quantifies the amount of imports through a port (\(p\)) of country (\(k\)) that are embedded in exports (\(\mathbf{e}\), vector of exports) and domestic final consumption (\(\mathbf{c}\), vector of consumption). In a MRIO table, the input coefficients matrix (\(\mathbf{A}\)) for country is derived from its interindustry trade (\(\mathbf{Z}\)) and industry output (\(\mathbf{x}\)). For a country \(k = 1\), this consists of \(\mathbf{A}^{11} = \mathbf{Z}^{11}(\hat{\mathbf{x}})^{-1}\) for domestically produced inputs and \(\mathbf{A}^{k1} = \mathbf{Z}^{k1}(\hat{\mathbf{x}})^{-1}\) for inputs imported from country k (\(k \neq 1\)).
+
+The domestic outputs necessary for \(\mathbf{e}\) is \((\mathbf{I} - \mathbf{A}^{11})^{-1}\mathbf{e}\) and for \(\mathbf{c}\) is \((\mathbf{I} - \mathbf{A}^{11})^{-1}\mathbf{c}\), which require imports \(\mathbf{M} = \sum_{c=2}^{k} \mathbf{A}^{c1} (\mathbf{c} = 2\) to k means input from other countries). Hence, the total imports
+to meet \( \mathbf{e} \) is \( s'M(I - A^{11})^{-1}\mathbf{e} \) and to meet \( \mathbf{c} \) is \( s'M(I - A^{11})^{-1}\mathbf{c} \), with \( s \) a summation vector.
+
+To find imported goods going through a port, we modify the \( \mathbf{M} \) matrix using the port-to-port trade network, by first making \( \mathbf{M} = 0 \), and filling the \( \mathbf{M} \) matrix with the fraction of country-to-country trade (share x trade flow) that goes through a port per sector (\( s \)) (with \( \mathbf{A}_p^{cl} \) the port-level imports from country c to country l to port p). This results in a new \( \mathbf{M}_p \) per port that covers the input coefficients from country k to the host country of the port (country \( c = 1 \)), which are being transported through this port. Using this, we can find the PLIC metrics by
+
+\[
+PLIC_{dom} = \frac{s'M_p(I - A_p^{11})^{-1}\mathbf{c}}{s'\mathbf{c}}
+\]
+
+and
+
+\[
+PLIC_{exp} = \frac{s'M_p(I - A_p^{11})^{-1}\mathbf{e}}{s'\mathbf{e}}
+\]
+
+The total import multiplier for a country is found by aggregating the PLIC-measures to a country scale (\( PLIC = PLIC_{dom} + PLIC_{exp} \)). The sector-specific import multipliers on a country-level are found by replacing \( \mathbf{c} \) and \( \mathbf{e} \) with a vector with a 1 for the specific sector and a zero otherwise, and summing over all ports in the country.
+
+The port-level output coefficient (PLOC) metric is a variation of the Hypothetical Extraction Method (HEM)\(^{72-74}\) used in I-O analysis, in which a sector is hypothetically set to zero (the i-th row and j-th column of matrix \( \mathbf{A} \)) in order to evaluate the interindustry dependencies and importance for the economy through changes in the industry output. For the PLOC, we quantify the output changes to the economy by removing the trade flows going through a port from the I-O table. To do this, we use both supply-driven (Ghosh) and demand-driven (Leontief) versions of the I-O table to find the forward (supply-driven) and backward (demand-driven) linkages. Using a Ghoshian model is justified here as we look at reductions in industry output (see Rose and Wei for a discussion\(^{29}\)). The PLOC metric is derived by (1) modifying the interindustry trade matrix (\( \mathbf{Z} \)) and (2) the final demand matrix (\( \mathbf{y} \)) to account for the trade flows
+going through a port. First, we remove the port-level trade flows (both import and export) from \( \mathbf{Z} \) and re-evaluate the new \( \mathbf{A}_{p,1} \) using the demand-driven model and the new \( \mathbf{B}_{p,1} \) using the supply-driven model (\( \mathbf{B}_{p,1} = \mathbf{x}^{-1} \mathbf{Z} \)). We find the backward losses in industry output (\( \Delta x_{p,1,ind,b} \)) by re-calculating industry output (\( x_{p,1,ind} \)) with the modified direct requirement matrix:
+
+\[
+\Delta x_{p,1,ind,b} = x - (I - A_{p,1})^{-1} y
+\]
+
+And the new industry output for the forward linkages (\( \Delta x_{p,1,ind,f} \)):
+
+\[
+\Delta x_{p,1,ind,f} = x - v (I - B_{p,1})^{-1}
+\]
+
+with \( v \) the vector of value-added. The changes in industry output is the addition of the changes in domestic output (\( \Delta x_{dom,ind,b} ; \Delta x_{dom,ind,f} \)) and change in output on the rest of the economy (\( \Delta x_{glob,ind,b} ; \Delta x_{glob,ind,f} \)). Moreover, we evaluate the changes industry output due to the port-level trade embedded in direct consumption. This is done by modifying the demand matrix (\( y \)) with the equivalent reduction in domestic final consumption (imports) and the reduction in final consumption in other countries (exports). Output losses associated with changes in final consumption in a port in country 1 (\( y_{p,1} \)) can be found by solving:
+
+\[
+\Delta x_{p,1,con,b} = x - (I - A)^{-1}(y - y_{p,1})
+\]
+
+From \( \Delta x_{p,1,con,b} \) we can find changes in domestic output (\( \Delta x_{dom,con,b} \)) and changes in output for the rest of the economy (\( \Delta x_{glob,con,b} \)) in a similar fashion as described above. The forward losses associated with trade in final consumption are simply the trade flows of final consumption, with imports leading to a reduction of domestic output (\( \Delta x_{dom,con,f} \)) and exports leading to a reduction in foreign output (\( \Delta x_{glob,con,f} \)).
+
+This yields the PLOCA metric, which can be derived from changes in domestic and global output:
+\[
+PLOCA = (\Delta x_{dom,ind,b} + \Delta x_{dom,con,b}) + (\Delta x_{dom,con,f} + \Delta x_{dom,ind,f}) + (\Delta x_{glob,ind,b} + \Delta x_{glob,con,b}) + (\Delta x_{glob,con,f} + \Delta x_{glob,ind,f})
+\]
+
+from which PLOCR can be derived:
+
+\[
+PLOCR = \frac{PLOCA}{I + E}
+\]
+
+The relative importance of the global versus domestic losses and forward versus backward can be derived the components of PLOCA. The losses relative to the domestic and global economy are found by dividing the relevant components by the total domestic and global industry output.
+
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+Fig. 1 | The share of maritime transport in global trade. (a-b) Country’s percentage of maritime imports (a) and exports (b) based on the 2015 trade network. (c) Boxplots of the percentage maritime imports per economic sector with countries grouped by income level (based on the World Bank income classification).
+Fig. 2 | The origin and destination ports of trade flows. (a-b) The aggregated imports (a) and exports (b) per port. The top 20 ports are highlighted with the top 5 ports annotated. (c) the location of the 50 largest importing (blue) and exporting (red) ports per sector.
+Fig. 3 | Relationship between port coreness and specialisation. The core-periphery structure in the global ('All') and nine national port systems based on the coreness value of the sector-specific port-to-port network and the degree of specialisation of the port (based on the inequality of sector-specific trade). The dots represent the individual ports, whereas the line is created using a locally weighted scatterplot smoothing (LOWESS) of the data. Note the logarithmic x-axis.
+
+![Scatterplots showing the relationship between port coreness and specialisation for 'All', China, United States, United Kingdom, Japan, Australia, Brazil, India, Philippines, South Africa](page_120_186_1207_495.png)
+Fig. 4 | Global distribution of the port-level output losses as a fraction of domestic and global industry output. (a) The port-level output coefficient (PLOCA) grouped according to the domestic output losses as a percentage of total domestic output and the global output losses as a percentage of total global output. The ten ports with the largest relative influence on domestic and global output are highlighted together with the associated percentage value (domestic in blue, global in red). (b) The cumulative distribution plot of port’s influence on global industry output as a function of the rank of the port. The cumulative output for the top 10, 50 and 200 ports are indicated in the grey scale. Note the logarithmic x-axis.
+Fig. 5 | The relative importance of forward/backward and domestic/foreign port-industry linkages. The total output losses (\( \Delta x \)) per port subdivided into forward and backward losses, and domestic and foreign losses, capturing the relative importance of the four components. The size of the dot corresponds to the total output losses. The black dotted line depicts the equal importance of both components, whereas the red dotted line depicts the median values across all ports. Ports highlighted in blue and annotated are mentioned in the text.
+
+![Scatter plot showing the relative importance of forward/backward and domestic/foreign port-industry linkages, with labeled ports and output sizes.](page_120_180_1208_799.png)
+Fig. 6 | Global distribution of the country-level and port-level import coefficient. (a) The global distribution of the port-level import coefficient (PLIC), expressing the dollar increase in imports for every 1000 dollar increase in final demand. The top 15 ports are highlighted and annotated. (b) The country-wide maritime import coefficient (CLIC) per region. The bar plot illustrates the mean value, with the error bar depicting the 5-95 percentiles. (c) Same as (b) but comparing the global average CLIC to the CLIC of the Small Island Developing States (SIDS). (d) Same as (b) and (c) but the global average CLIC to the CLIC of the countries grouped by income level (based on the World Bank income classification). LI: low income, LMI: lower middle income, UMI: upper middle income, HI: high income.
+Figures
+
+Figure 1
+
+The share of maritime transport in global trade. (a-b) Country’s percentage of maritime imports (a) and exports (b) based on the 2015 trade network. (c) Boxplots of the percentage maritime imports per economic sector with countries grouped by income level (based on the World Bank income classification). Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.
+Figure 2
+
+The origin and destination ports of trade flows. (a-b) The aggregated imports (a) and exports (b) per port. The top 20 ports are highlighted with the top 5 ports annotated. (c) the location of the 50 largest importing (blue) and exporting (red) ports per sector. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its
+authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.
+
+![Scatterplots showing the relationship between port coreness and specialisation for various countries, including All, China, United States, United Kingdom, Japan, Australia, Brazil, India, Philippines, and South-Africa. Each plot includes a line representing a locally weighted scatterplot smoothing (LOWESS) of the data.](page_120_340_1347_563.png)
+
+Figure 3
+
+Relationship between port coreness and specialisation. The core-periphery structure in the global ('All') and nine national port systems based on the coreness value of the sector-specific port-to-port network and the degree of specialisation of the port (based on the inequality of sector-specific trade). The dots represent the individual ports, whereas the line is created using a locally weighted scatterplot smoothing (LOWESS) of the data. Note the logarithmic x-axis.
+Figure 4
+
+Global distribution of the port-level output losses as a fraction of domestic and global industry output. (a) The port-level output coefficient (PLOCA) grouped according to the domestic output losses as a percentage of total domestic output and the global output losses as a percentage of total global output. The ten ports with the largest relative influence on domestic and global output are highlighted together with the associated percentage value (domestic in blue, global in red). (b) The cumulative distribution plot of port’s influence on global industry output as a function of the rank of the port. The cumulative output for the top 10, 50 and 200 ports are indicated in the grey scale. Note the logarithmic x-axis. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.
+Figure 5
+
+The relative importance of forward/backward and domestic/foreign port-industry linkages. The total output losses (\( \Delta x \)) per port subdivided into forward and backward losses, and domestic and foreign losses, capturing the relative importance of the four components. The size of the dot corresponds to the total output losses. The black dotted line depicts the equal importance of both components, whereas the red dotted line depicts the median values across all ports. Ports highlighted in blue and annotated are mentioned in the text.
+
+ROT - Rotterdam
+SIN - Singapore
+MAA - Mina Al Ahmadi
+PHL - Port Hedland
+HOU - Houston
+SHA - Shanghai
+BRE - Bremerhaven
+YOK - Yokohama
+BUA - Buenos Aires
+LOA - Los Angeles-Long Beach
+JDH - Jeddah
+Figure 6
+
+Global distribution of the country-level and port-level import coefficient. (a) The global distribution of the port-level import coefficient (PLIC), expressing the dollar increase in imports for every 1000 dollar increase in final demand. The top 15 ports are highlighted and annotated. (b) The country-wide maritime import coefficient (CLIC) per region. The bar plot illustrates the mean value, with the error bar depicting the 5-95 percentiles. (c) Same as (b) but comparing the global average CLIC to the CLIC of the Small Island Developing States (SIDS). (d) Same as (b) and (c) but the global average CLIC to the CLIC of the countries grouped by income level (based on the World Bank income classification). LI: low income, LMI: lower middle income, UMI: upper middle income, HI: high income. Note: The designations employed and the presentation of the material on this map do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. This map has been provided by the authors.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementaryinformation.docx

0cada618bb488f1258412c269438e0dbe8f9b287946d4660b5442737b0d7019d/preprint/preprint.md

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+Sondheimer oscillations as a probe of non-ohmic flow in type-II Weyl semimetal WP2
+
+Maarten van Delft (maarten.vandelft@epfl.ch)
+Institute of Materials (IMX), Ecole Polytechnique Federale de Lausanne (EPFL) https://orcid.org/0000-0002-6952-9418
+Yaxian Wang
+Harvard University
+Carsten Putzke
+Laboratory of Quantum Materials https://orcid.org/0000-0002-6205-9863
+Jacopo Oswald
+IBM Research
+Georgios Vamavides
+Harvard University
+Christina Garcia
+Harvard University https://orcid.org/0000-0002-9259-3880
+Chunyu Guo
+Ecole Polytechnique Federale de Lausanne (EPFL)
+Heinz Schmid
+IBM Research - Zurich https://orcid.org/0000-0002-0228-4268
+Vicky Süß
+Max Planck Institute for Chemical Physics of Solids
+Horst Borrmann
+Max Planck Institute for Chemical Physics of Solids https://orcid.org/0000-0002-1397-3261
+Jonas Diaz
+École Polytechnique Fédérale de Lausanne
+Yan Sun
+Max Planck Institute for Chemical Physics of Solids https://orcid.org/0000-0002-7142-8552
+Claudia Felser
+Max Planck Institute for Chemical Physics of Solids
+Bernd Gotsmann
+IBM Research - Zurich https://orcid.org/0000-0001-8978-7468
+Prineha Narang
+Harvard University https://orcid.org/0000-0003-3956-4594
+Philip Moll
+École Polytechnique Fédérale de Lausanne https://orcid.org/0000-0002-7616-5886
+Article
+
+Keywords: Non-ohmic Electron Flow, Electron Scattering, Conduction Regime, Magnetoresistance Oscillations, Momentum Exchange
+
+Posted Date: February 11th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-131719/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on August 10th, 2021. See the published version at https://doi.org/10.1038/s41467-021-25037-0.
+Sondheimer oscillations as a probe of non-ohmic flow in type-II Weyl semimetal WP$_2$
+
+Maarten R. van Delft$^{1,*}$, Yaxian Wang$^2$, Carsten Putzke$^1$, Jacopo Oswald$^3$, Georgios Varnavides$^2$, Christina A. C. Garcia$^2$, Chunyu Guo$^1$, Heinz Schmid$^3$, Vicky Süss$^4$, Horst Borrmann$^4$, Jonas Diaz$^1$, Yan Sun$^4$, Claudia Felser$^4$, Bernd Gotsmann$^3$, Prineha Narang$^{2,*}$, and Philip J.W. Moll$^{1,*}$
+
+$^1$Laboratory of Quantum Materials (QMAT), Institute of Materials (IMX), École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland
+$^2$Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
+$^3$IBM Research - Zurich, 8803 Rüschlikon, Switzerland
+$^4$Max Planck Institute for Chemical Physics of Solids, Nöthnitzer Strasse 40, 01187 Dresden, Germany
+*e-mail: maarten.vandelft@epfl.ch; prineha@seas.harvard.edu; philip.moll@epfl.ch
+
+ABSTRACT
+
+As conductors in electronic applications shrink, microscopic conduction processes lead to strong deviations from Ohm’s law. Depending on the length scales of momentum conserving ($l_{MC}$) and relaxing ($l_{MR}$) electron scattering, and the device size ($d$), current flows may shift from ohmic to ballistic to hydrodynamic regimes and more exotic mixtures thereof. So far, an *in situ*, in-operando methodology to obtain these parameters self-consistently within a micro/nanodevice, and thereby identify its conduction regime, is critically lacking. In this context, we exploit Sondheimer oscillations, semi-classical magnetoresistance oscillations due to helical electronic motion, as a method to obtain $l_{MR}$ in micro-devices even when $l_{MR} \gg d$. This gives information on the bulk $l_{MR}$ complementary to quantum oscillations, which are sensitive to all scattering processes. We extract $l_{MR}$ from the Sondheimer amplitude in the topological semi-metal WP$_2$, at elevated temperatures up to $T \sim 50$ K, in a range most relevant for hydrodynamic transport phenomena. Our data on $\mu$m-sized devices are in excellent agreement with experimental reports of the large bulk $l_{MR}$ and thus confirm that WP$_2$ can be microfabricated without degradation. Indeed, the measured scattering rates match well with those of theoretically predicted electron-phonon scattering, thus supporting the notion of strong momentum exchange between electrons and phonons in WP$_2$ at these temperatures. These results conclusively establish Sondheimer oscillations as a quantitative probe of $l_{MR}$ in micro-devices in studying non-ohmic electron flow.
+
+Main text
+
+In macroscopic metallic wires, the flow of electric current is well described by Ohm’s law, which assigns a metal a spatially-uniform ‘bulk’ conductivity. The underlying assumption is that the complex and frequent scattering events of charge carriers occur on the microscopic length scale of a mean-free-path, which is much smaller than the size of the conductor, $d$, leading to diffusive behavior. In addition to the scattering processes of bulk systems, the resistance of microscopic conductors is mostly
+dominated by boundary scattering, thereby masking the internal scattering processes of the bulk in resistance measurements. Here, we present a method to uncover these bulk processes in micro-scale metals, which are of technological importance for fabrication of quantum electronic devices, and simultaneously critical to a fundamental understanding of microscopic current flow patterns. It is instructive to classify the bulk scattering processes into two categories: those that relax the electron momentum, such as electron-phonon, Umklapp or inelastic scattering, occurring at length-scale \( l_{MR} \); and those that conserve the electron momentum, such as direct or phonon-mediated electron-electron scattering, associated with a length scale \( l_{MC} \).
+
+Within a kinetic theory framework, these three length scales, namely \( d \), \( l_{MR} \), and \( l_{MC} \), can be used to describe the current flow in micro-scale conductors. When momentum-conserving interactions are negligible, ohmic flow at the macro-scale (\( l_{MC} \gg d \gg l_{MR} \)) gives way to ballistic transport in clean metals where \( l_{MR}, l_{MC} \gg d \). Conversely, when momentum-conserving interactions occur over similar or smaller length scales to momentum-relaxing interactions, a third regime of ‘hydrodynamic’ transport (\( l_{MR} \gg d \gg l_{MC} \)) is observable\(^{1,2}\). In this regime, the static transport properties of electron fluids can be described by an effective viscosity that captures the momentum diffusion of the system\(^{2,3}\). These electron fluids exhibit classical fluid phenomena such as Poiseuille flow, whereby the current flow density is greatly decreased at the conductor boundary. Recently, advances in both experimental probes and theoretical descriptions have enabled direct observation of these effects using spatially-resolved current density imaging, and have hinted towards the rich landscape of electron hydrodynamics in micro-scale crystals\(^{3-5}\).
+
+While such local-probe experiments provide means of quantifying electron-electron interactions, and thus extracting \( l_{MC} \), direct measurement of the intrinsic momentum-relaxing processes (\( l_{MR} \)) within micron-scale conductors remains elusive, yet is greatly needed. From a practical perspective, \( l_{MR} \) describes the overall scattering from impurities and the lattice vibrations within the metallic microstructure, which at low temperature is an important feedback parameter of quality control in fabrication. Furthermore, given both the reduction of sample size and the improved crystal quality, seemingly exotic transport scenarios where \( l_{MR} \gg d \gg l_{MC} \) is satisfied are expected to become more prevalent in technology. An accurate description of these length scales is necessary to predict the overall resistance and thus voltage drops and heat dissipation in the nanoelectronic devices. For example, the resistive processes in a hydrodynamic conductor occur at the boundaries rather than homogeneously distributed in the bulk, which alters the spatial distribution of Joule heating and thereby has significant impacts on thermal design.
+
+Real devices will operate at some intermediate state in the \( d \), \( l_{MR} \), and \( l_{MC} \) parameter space, departing from the well-understood limiting cases of ohmic, ballistic and hydrodynamic flow. Rich landscapes of distinct hydrodynamic transport regimes are predicted depending on the relative sizes of the relevant length scales\(^{6}\). Effective understanding, modeling and prediction of transport requires an experimental method to estimate these parameters reliably in every regime. In large, ohmic conductors, the bulk mean-free-path \( l_{MR} \) can be simply estimated from the device resistance using a Drude model. Yet when \( l_{MC}, l_{MR} \gtrsim d \), boundary scattering dominates the resistance, and hence estimates of the bulk scattering parameters are highly unreliable. This leaves the worrying possibility of misinterpreting the transport situation in a conductor, in that the microfabrication itself may introduce defects or changes in the bulk properties that remain undetected by macroscopic observables such as the resistance, but have profound impact on the microscopic current distribution. These effects are already noticeable in state-of-the-art transistors, owing to the low carrier density of semi-conductors\(^{7}\), but have similarly been reported in metallic conductors\(^{5}\). With the increased technological interest in quantum and classical electronics operating at cryogenic temperatures, such questions about unconventional transport regimes are also of practical relevance in next generation
+electronics.
+
+In this context, we propose to exploit a magneto-oscillatory phenomenon, Sondheimer oscillations (SO), as a self-consistent method to obtain the transport scattering length \( l_{MR} \) *in-situ*, even in constricted channels when \( l_{MR} \gg d \). In general, a magnetic field (\( \vec{B} \)) applied perpendicular to a thin metal forces the carriers on the Fermi surface to undergo cyclotron motion. Those on extremal orbits of the Fermi surface are localized in space due to the absence of a net velocity component parallel to the magnetic field. These localized trajectories can become quantum-coherent, and their interference causes the well-known Shubnikov-de Haas oscillations. The states away from extremal orbits also undergo cyclotron motion, yet they move with a net velocity along the magnetic field, analogous to the helical trajectories of free electrons in a magnetic field (Fig. 1). These states are responsible for the Sondheimer size effect which manifests itself as a periodic-in-*B* oscillation of the transport coefficients, as discovered in the middle of the past century for clean elemental metals\(^9\).
+
+For any given state, the magnitude of \( \vec{B} \) sets the helical radius and thus determines how many revolutions the electron completes while travelling from one surface to the other in a microdevice. If an integer number of revolutions occur, the charge carrier will have performed no net motion along the channel, and hence is semi-classically localized (Fig. 1a). However, if the number of revolutions is non-integer, a net motion along the channel exists, delocalizing the carriers, resulting in oscillatory magnetotransport behavior. Large-angle bulk scattering events dephase the trajectory, hence the strong sensitivity of SO to the *bulk* \( l_{MR} \) even in nanostructures. These SO are an inherent property of mesoscale confined conductors in three dimensions and have no counterpart in 2D metals like graphene.
+
+The period of the SO is derived by considering a classical charged particle on a helical trajectory between two surfaces perpendicular to the magnetic field\(^{10}\). One compares the time it takes to travel the distance \( d \) between the surfaces, \( t_d = d / v_{||} \), to the time to complete a single cyclotron revolution, \( \tau_c = 2\pi / \omega_c = 2\pi m^*/eB \) (*m*\*: effective mass, *e*: electron charge, \( \omega_c = eB/m^* \): cyclotron frequency). Their ratio describes the number of revolutions of the trajectory. For certain fields the helix is commensurate with the finite structure and the number of revolutions is integer, *n*, such that \( t_d = n \tau_c \). This occurs periodically in field, with the period given by:
+
+\[
+\Delta B = \frac{2\pi m^* v_{||}}{ed} = \frac{\hbar}{ed} \left( \frac{\partial A}{\partial k_{||}} \right).
+\]
+
+The useful identity \( v_{||} = \frac{\hbar}{2\pi m^*} \left( \frac{\partial A}{\partial k_{||}} \right) \), derived by Harrison\(^{11}\), directly relates the SO period to the Fermi surface geometry, where \( v_{||} \) and \( k_{||} \) denote the velocity and momentum component parallel to the magnetic field and \( A \) is the Fermi surface cross-sectional area encircled by the orbit in k-space. Note the contrast to conventional quantum oscillations which appear around extremal orbits, where \( \frac{\partial A}{\partial k_{||}} = 0 \).
+
+All conduction electrons undergo cyclotron motion, yet depending on \( \frac{\partial A}{\partial k_{||}} \), they experience different commensurability fields with a structure of given size *d*. Hence oscillatory contributions to the total conductivity are washed out, unless a macroscopic number of states share the same \( v_{||} \propto \left( \frac{\partial A}{\partial k_{||}} \right)_{E_f} \)^{10}. In earlier days of Fermiology\(^{12}\), geometric approximations for Fermi surfaces, such as elliptical endpoints, were introduced to identify those generalized geometric features that lead to extended regions of constant \( \frac{\partial A}{\partial k_{||}} \). The computational methods available nowadays allow a more modern approach to the problem. Fermi surfaces calculated by ab-initio methods can be numerically sliced in order to calculate their cross-section \( A(k_{||}) \). We propose to extend this routine procedure, used to find extremal orbits relevant for quantum oscillations \( \left( \frac{\partial A}{\partial k_{||}} = 0 \right) \), to
+identify SO-active regions \( \left( \frac{\partial^2 A}{\partial k_z^2} \sim 0 \right) \), based on the Fermi-surface slicing code SKEAF\( ^{13} \) (see the supplementary information for details on implementation).
+
+SO are caused by the real-space motion of charge carriers and hence also pose some conditions on the shape of the conductor. First, surface scattering needs to be mostly diffusive. If an electron undergoes specular scattering \( N \) times before scattering diffusively, it contributes towards the SO as if the sample had an effective thickness \( Nd^{14} \), leading to overtones. Naturally, SO vanish in the (unrealistic) limit of perfectly specular boundary conditions, as such ideal kinetic mirrors remove any interaction of the electron system with the finite size of the conductor. Secondly, the conductor must feature two parallel, plane surfaces perpendicular to the magnetic field to select only one spiral trajectory over the entire structure. The parallelicity requirement is simply given by a fraction of the pitch of the spiral at a certain field (\( \Delta d < v_{||} \tau_e = d \frac{\Delta B}{B} \))\( ^{10} \). These requirements are naturally fulfilled in planar electronic devices.
+
+It is instructive to briefly compare SO to the more widely known quantum oscillations of resistance, the Shubnikov-de Haas effect (SdH). Both are probes of the Fermi surface geometry based on cyclotron orbits, yet the microscopics are strikingly different. While quantum oscillation frequencies are exclusively determined by Fermi surface (FS) properties via the Onsager relation and are thus independent of the sample shape, SO are finite-size effects. SO emerge from extended regions on the FS, unlike SdH oscillations to which only states in close vicinity of extremal orbits contribute. While SdH oscillations are quantum interference phenomena, SO are semi-classical, which is key to their use as a robust probe of exotic transport regimes. If both can be observed, powerful statements on the scattering microscopics can be made, as SdH is sensitive to all dephasing collision events and SO separates out the large-angle ones\( ^{15} \). However, the much more stringent conditions of phase coherence in SdH severely limit their observations at higher temperatures. SO are observable up to relatively high temperatures at which the rapidly shrinking \( I_{MR}(T) \) leads to a transition into an ohmic state, when \( I_{MR}(T) < d \). As such, they are ideally suited to explore the exotic transport regimes in which, for example, hydrodynamic effects occur.
+
+We apply these theoretical considerations to experimentally investigate the scattering mechanisms in micron-sized crystalline bars of the type-II Weyl semimetal WP\( _2 \)^{16} exploiting the Sondheimer effect. Bulk single crystals of WP\( _2 \) are known for their long \( l_{MR} \), in the range of 100-500 \( \mu m \)^{17–19}, comparable to the elemental metals in which SO were initially discovered\( ^{20–23} \). These are an ideal test case for non-ohmic electron flow, as hydrodynamic transport signatures and nontrivial electron-phonon dynamics have been observed in various topological semimetals\( ^{17,18,24–26} \). These ultra-pure crystals are then reduced in size by nanofabrication techniques into constricted channels, to study hydrodynamic or ballistic corrections to the current flow.
+
+Here we employ Focused Ion Beam (FIB) micromachining\( ^{27} \), which allows precise control over the channel geometry in 3D. In this technique, we accelerate Xe ions at 30 kV to locally sputter the target crystal grown by chemical vapor transport (CVT)\( ^{19,28} \) until a slab of desired dimensions in the \( \mu m \)-range remains. This technique leads to an amorphized surface of around 10 nm thickness, yet has been shown to leave bulk crystal structures pristine\( ^{29} \). Naturally, reducing the size of a conductor even without altering its bulk mean-free-path significantly changes the device resistance at low temperatures due to finite size corrections\( ^{30} \). Hence, measurements of the constricted device resistance alone cannot exclude the possibility of bulk degradation due to the fabrication step. Thus far, one could only argue based on size-dependent resistance studies that the values smoothly extrapolate to the bulk resistivity value in the limit of infinite device size\( ^{18,31} \). Measuring SO directly in the microfabricated devices themselves, however, quantitatively supports that the ultra-high purity of the parent crystal remains unchanged by our fabrication. We note that the fundamental question of the bulk parameters is universal in mesoscopic
+Figure 1. Introduction to Sondheimer oscillations. a Illustration of the Sondheimer effect. Left: the applied magnetic field is \( B = n \Delta B \) and the electron (red) makes an integer number of rotations, with no contribution to transport. Right: \( B \neq n \Delta B \). The electron hits the top surface at a different position than its origin on the bottom surface, leading to a contribution to the conductivity. b Resistivity as function of temperature for a WP$_2$ microdevice. Inset: false-color SEM image of a typical device used in this study. c Sondheimer oscillations seen in the Hall resistivity of a WP$_2$ microdevice, for different temperatures. The oscillation period of \( \Delta B = 1.6 \) T is highlighted.
+
+conducting structures irrespective of the fabrication technique, and these considerations are thus equally applicable to structures obtained by mechanically or chemically thinned samples as well as epitaxially grown crystalline films. SO should provide general insights into the material quality in the strongly confined regime, allowing to contrast different fabrication techniques.
+
+At high temperatures, the resistivity measured in \( \mu m \)-confined devices agrees well with previous reports on high quality bulk crystals, as expected given the momentum relaxing limited mean-free-path of charge carriers in this regime (Fig. 1b). Yet in the low temperature limit, the device resistance exceeds those of bulk crystals by more than an order of magnitude\(^{17,19,32}\). Conversely, the residual resistance ratios in our devices (RRR\( \approx \)160-300) are also considerably lower than in bulk crystals\(^{32}\). The main question we address by SO is whether this excess resistance points to fabrication-induced damage, finite size corrections, or a mixture thereof. At low temperatures around 3 K, a drop in resistance signals a superconducting transition. As WP$_2$ in bulk form is not superconducting, this likely arises from an amorphous W-rich surface layer due to the FIB fabrication similar to observations made in NbAs\(^{33}\) and TaB\(^{34}\). In Fig. 1c, we show the Hall resistivity, \( \rho_{xy} \), of one of our devices as a function of the magnetic field, for different temperatures. The Hall signal comprises oscillations with a period of \( \Delta B = 1.6 \) T, resolved above approximately \( B = 2 \) T.
+
+A hallmark signature of SO is their linear frequency dependence on the device thickness perpendicular to the field. For this reason, we fabricated crystalline devices with multiple sections of different thickness to study the \( d \)-dependence in a
+Figure 2. The staircase device. a, False color SEM image of a staircase device, used to measure Sondheimer oscillations for different thicknesses. The crystal is colored in purple, and gold contacts in yellow. b, Main: Schematic of the staircase device, illustrating all possible measurement configurations as well as the thickness of each section. Top left: SEM image of the lamella that will become the device shown in a, prior to extracting it from its parent crystal. Bottom right: SEM image of the same lamella, glued down onto a sapphire substrate, ready to define the device geometry. The lamella and glue are covered in gold (not colored) throughout the full field of view. The magnetic field is applied perpendicular to the structure, aligned along the crystallographic [011] direction.
+
+consistent manner. This ‘staircase’ device allows the simultaneous measurement of transport on 5 steps of different thickness \( d \), as illustrated in Fig. 2. SO appear in all transport coefficients, magnetoresistance and Hall effect alike, yet here we focus on the Hall effect for two practical reasons. First, the step edges induce non-uniform current flows, and hence the device would need to be considerably longer to avoid spurious voltage contributions from currents flowing perpendicular to the device in a longitudinal resistance measurement. Second, WP\(_2\) exhibits a very large magnetoresistance yet a small Hall coefficient, as typical for compensated semi-metals. Therefore, the SO are more clearly distinguishable against the background in a Hall measurement, but they are also present in the longitudinal channel (see Supplementary Information).
+
+The fabrication process of our WP\(_2\) devices follows largely the same procedure as described in Ref. 27. However, for the staircase device, a few key changes were made. In the first fabrication step, the FIB is used to cut a lamella from a bulk WP\(_2\) crystal. One side is polished flat, and the other side polished into five sections, each to a different thickness (Fig. 2b). It is then transferred, flat side down, into a drop of araldite epoxy on a sapphire substrate and electrically contacted by Au sputtering (Fig. 2b). In a second FIB step, the staircase slab is patterned laterally into its final structure (Fig. 2a).
+
+All segments of the staircase devices show pronounced \( B \)-periodic oscillations in the Hall channel, from which the linear background is removed by taking second derivatives. (Fig. 3). At the lowest fields, a weak, aperiodic structure is observed. In this regime, the cyclotron diameter does not fit into the bar, preventing the formation of the Sondheimer spirals. Note that in all devices of different thickness, this onset field of the SO is the same. This is a natural consequence of the fact that the lateral size, perpendicular to the magnetic field, by design, is the same for all steps of the staircase. Each step, however, differs in thickness \( d \) parallel to the magnetic field, and the period varies accordingly between steps (Fig. 3b). At even higher fields, the
+onset of regular SdH oscillations hallmarks a transition into a different quantized regime. The Sondheimer oscillation frequency \( F = 1/\Delta B \) varies linearly with \( d \) as expected (Fig. 3c, Eq. 1).
+
+Next we identify the Sondheimer-active region on the Fermi surface from the ab-initio band structure, which was calculated by density functional theory (DFT) with the projected augmented wave method as implemented in the code of the Vienna ab-initio Simulation Package (VASP)\(^{35}\). The FS of WP\(_2\) consists of two types of spin-split pockets: dogbone shaped electron pockets and extended cylindrical hole pockets (see Fig. 4 and supplementary Fig. S2 for a complete picture of the FS).
+
+Only one area quantitatively agrees with the observed SO periodicity: the four equivalent endpoints of the dogbone (colored orange in Figs. 3f). Slicing all Fermi-surfaces using SKEAF\(^{13}\), their cross-sections \( A(k_{||}) \) are obtained. While in quantum oscillation analysis this information is discarded once the extremal orbits are identified, it forms the basis of the SO analysis. As the dogbone is sliced from the endpoints, the area continuously grows until the two endpoint orbits merge and the area abruptly doubles. Slicing further, the area grows until the maximum orbit along the diagonal is reached. Inversion symmetry enforces then a symmetric spectrum when slicing further beyond the maximum. The quasi-linear growth at the endpoints signals an extended area of Sondheimer-active orbits. Averaging the near-constant derivative in this region, \( \frac{\partial A}{\partial k_{||}} \), provides via Eq. 1 a tuning-parameter-free prediction of the thickness dependence of the SO frequency. This ab-initio prediction (red line in Fig. 3c) is in excellent agreement with the observed thickness dependence.
+
+Next the temperature-dependence of the SO amplitude is used to gain direct information about the microscopic scattering processes acting on this region of the Fermi surface. In Fig. 4a,b, we plot this temperature dependence and highlight two regimes: that of quantum coherence and that of purely Sondheimer oscillations. In the first regime, quantum coherence leads to SdH oscillations; however, for typical effective masses \( m^* \approx m_e \), as in WP\(_2\), they are only observable at very low temperatures (\( T < 5 \) K). Importantly, their quick demise upon increasing temperature is not driven by the temperature dependence of the scattering time, but rather by the broadening of the Fermi-Dirac distribution. This is apparent as their temperature dependence is well described by the Lifshitz-Kosevich formalism based on a temperature-independent quantum lifetime, \( \tau_q \).
+
+This strong temperature-suppression of quantum oscillations severely limits their use to probe scattering mechanisms at elevated temperatures. SO, on the other hand, do not rely on quantum coherence and are readily observed to much higher temperatures, up to 50 K in WP\(_2\), while their temperature decay allows a direct determination of the transport lifetime, \( \tau_{MR} = l_{MR}/v_F \). Hence SO make an excellent tool to study materials in the temperature range pertinent to exotic transport regimes like ballistic or hydrodynamic. They self-evidence non-diffusive transport as they only vanish when \( l_{MR} \sim d \), and hence are only absent in situations of conventional transport within a given device.
+
+Key to observable SO is that electrons do not undergo large-angle scattering events on their path between the surfaces. We therefore have the condition that \( l_{MR} > d^{36,37} \). As \( l_{MR}(T) \) decreases with increasing temperature and the boundary scattering is assumed to be temperature-independent, the SO amplitude is suppressed as \( e^{-d/l_{MR}(T)} \) which allows us to estimate the bulk transport mean-free-path within a finite-size sample, even when \( d \ll l_{MR} \). It is extracted as\(^{36}\):
+
+\[
+\frac{1}{l_{MR}(T)} = -\frac{1}{d} \ln \frac{A(T)}{A(0)},
+\]
+
+where \( A(T) \) is the SO amplitude at temperature \( T \). \( A(T=0) \) is simply estimated by extrapolation, which is a robust procedure as the SO amplitude saturates at low but finite temperatures. This is analogous to the saturation of the resistivity of bulk metals
+Figure 3. Analysis of Sondheimer oscillations in WP2. **a.** Second derivative of the Hall resistivity shown in Fig.1c at \( T = 4 \) K. Inset: Fast Fourier Spectrum (FFT) corresponding to this data. **b.** Second derivatives of the Hall resistivity at three different thicknesses, \( d = 4.3,\ 2.7 \) and \( 2.0\ \mu m,\ T = 4 \) K. **c.** FFTs corresponding to the data in **b.** **d** Dependence of the Sondheimer frequency on \( d \). The red dashed line is calculated from the Fermi surface as determined from DFT. **e** Cross-sectional area, \( A \), of the dogbone Fermi surface pocket of WP2 as a function of \( k \) parallel to the field direction of our experiments (top), and its derivative (bottom). **f** Location of observed Sondheimer orbits drawn on the dogbone-shaped Fermi surface pocket. The magnetic field is applied along the [011]-direction, perpendicular to the current, as indicated by the red line.
+
+at low temperatures, once bosonic scattering channels are frozen out and temperature-independent elastic defect scattering becomes dominant.
+
+In the following discussion, we focus on the scattering time \( \tau_{MR} \) to facilitate comparison of our results with literature and theory, using the average Fermi velocity on the dogbone Fermi surface determined from our band structure calculations
+self-consistently, \( v_F = 3.6 \times 10^5 \) m/s. The \( \tau_{MR}(T) \) obtained from all devices quantitatively agrees, despite their strong difference in thickness and hence SO frequency, further supporting the validity of this simple analysis (see Fig. 4c and Fig. S5). The lifetimes on the SO devices furthermore agree with measurements on bulk crystals\(^{18}\), evidencing that the increased resistivity compared to bulk can be wholly attributed to finite size corrections rather than to any fabrication-induced damage, and that FIB fabrication does not introduce significant changes to the bulk properties of WP\(_2\) that might cause misinterpretations of the scattering regime.
+
+For our WP\(_2\) devices, a standard Dingle analysis\(^{15}\) of the quantum oscillations yields a quantum scattering time \( \tau_q \sim 10^{-13} - 10^{-12} \) s (Fig. 4c), in agreement with published values for bulk crystals WP\(_2\)\(^{19}\). As \( \tau_q \) is sensitive to all dephasing scattering events, but \( \tau_{MR} \) only to large-angle momentum relaxing scattering, the microscopics of the scattering processes in WP\(_2\) are brought to light. The four orders of magnitude of difference between \( \tau_{MR} \) and \( \tau_q \) reflects a common observation in topological semi-metals such as Cd\(_3\)As\(_2\)\(^{38}\), PtBi\(_2\)\(^{39}\) or TaAs\(^{40}\).
+
+Long \( \tau_{MR} \), together with a high quality, clean sample, enables the realization of the hydrodynamic regime where the momentum conserving scattering dominates. These quantitative measurements of \( \tau_q \) and \( \tau_{MR}(T) \) can now be directly compared to theoretical models of scattering. We consider an initial electronic state with energy \( \epsilon_{n\mathbf{k}} \) (where \( n \) and \( \mathbf{k} \) are the band index and wavevector respectively) scattering against a phonon with energy \( \omega_{qV} \) (where \( V \) and \( \mathbf{q} \) are the phonon polarization and wavevector respectively), into a final electronic state with energy \( \epsilon_{m\mathbf{k}+\mathbf{q}} \). The electron-phonon scattering time \( \tau_{e-ph} \) describing such an interaction can be obtained from the electron self energy using Fermi’s golden rule:
+
+\[
+\tau_{e-ph}^{-1}(n\mathbf{k}) = \frac{2\pi}{\hbar} \sum_{mV} \int_{BZ} \frac{d\mathbf{q}}{\Omega_{BZ}} |g_{mn,V}(\mathbf{k},\mathbf{q})|^2 \times \left( n_{qV} + \frac{1}{2} \mp \frac{1}{2} \right) \delta \left( \epsilon_{n\mathbf{k}} \mp \omega_{qV} - \epsilon_{m\mathbf{k}+\mathbf{q}} \right),
+\]
+
+where \( \Omega_{BZ} \) is the Brillouin zone volume, \( f_{nk} \) and \( n_{qV} \) are the Fermi-Dirac and Bose-Einstein distribution functions, respectively, and the electron-phonon matrix element for a scattering vertex is given by
+
+\[
+g_{mn,V}(\mathbf{k},\mathbf{q}) = \left( \frac{\hbar}{2m_0 \omega_{qV}} \right)^{1/2} \langle \psi_{m\mathbf{k}+\mathbf{q}}| \partial_{qV} V | \psi_{n\mathbf{k}} \rangle.
+\]
+
+Here \( \langle \psi_{m\mathbf{k}+\mathbf{q}}| \) and \( |\psi_{n\mathbf{k}} \rangle \) are Bloch eigenstates and \( \partial_{qV} V \) is the perturbation of the self-consistent potential with respect to ion displacement associated with a phonon branch with frequency \( \omega_{qV} \). Plotting these state-resolved electron-phonon lifetimes at \( \sim 10 \) K on the Fermi surface reveals the distribution of scattering in the SO-active regions (Fig. 4(d)). Equation 3, however, accounts, to first order, for all electron-phonon interactions, irrespective of the momentum transfer or equivalently the scattering angle. To remedy this, we augment the scattering rate with an ‘efficiency’ factor\(^{42}\) given by the relative change of the initial and final state momentum (\( 1 - \frac{v_{nk} \cdot v_{nk}}{|v_{nk}| |v_{nk}|} = 1 - \cos \theta \)), where \( v_{nk} \) is the group velocity and \( \theta \) is the scattering angle:
+
+\[
+(\tau_{e-ph}^{mr}(n\mathbf{k}))^{-1} = \frac{2\pi}{\hbar} \sum_{mV} \int_{BZ} \frac{d\mathbf{q}}{\Omega_{BZ}} |g_{mn,V}(\mathbf{k},\mathbf{q})|^2 \times \left( n_{qV} + \frac{1}{2} \mp \frac{1}{2} \right) \delta \left( \epsilon_{n\mathbf{k}} \mp \omega_{qV} - \epsilon_{m\mathbf{k}+\mathbf{q}} \right) \times \left( 1 - \frac{v_{nk} \cdot v_{nk}}{|v_{nk}| |v_{nk}|} \right).
+\]
+
+At low temperatures, the thermally activated phonon modes have a tiny \( \mathbf{q} \), therefore the initial and final electronic states only differ from a small angle. It is thus important to take this momentum-relaxation efficiency factor into account in addition to \( \tau_{e-ph} \), in order to estimate \( \tau_{MR} \) which determines the electron mean free path in the SO-active regions. In the SO measurements,
+Figure 4. Extraction of scattering times from the Sondheimer amplitude. a, FFTs of the SO at different temperatures for thicknesses of 4.3, 2.7 and 2.0 \( \mu \)m. b, Temperature dependence of the Sondheimer and SdH oscillation amplitudes, for different sample thicknesses. The dashed lines are fits used to extrapolate to the amplitude at zero temperature, \( A(0) \) (see the Supplementary Information for details). The dotted line is a Lifshitz-Kosevich fit, giving an effective mass of \( 1.1 m_e \). Two regimes are highlighted: that of quantum coherence, where SdH oscillations exist alongside SO, and that of Sondheimer, where only SO exist. c, Scattering times extracted for WP$_2$ using Eq. 2 and the Fermi velocity from Ref.$^{18}$. An approximate quantum lifetime extracted from the SdH oscillations as well as data from Refs.$^{18,41}$ are included for comparison. d Calculated scattering time for all electron-phonon scattering (\( \tau_{e-ph} \)) and e the scattering efficiency determining the momentum-relaxing scattering lifetimes (\( \tau_{MR} \)) projected onto the Fermi surface at \( T = 10 \) K.
+
+the electron orbits are located on the endpoints of the dogbone-shaped electron pockets (Fig. 3f), therefore we highlight the scattering efficiency distribution on the electron Fermi surface in Fig. 4e. Indeed, when the orbit is aligned along the diagonal direction, the Fermi surface cross section features very low scattering efficiency with an averaged \( 1 - \cos\theta < 0.1 \). This supports our observation of frequently scattering electrons with long transport lifetimes in the SO measurement.
+These results demonstrate the power of the Sondheimer size effect for the extraction of the momentum relaxing mean-free-path in mesoscopic devices when \( d \ll l_{MR} \) via their temperature dependence. Combined with first-principles theoretical calculations we were able to locate the states contributing to the helical motion to the elliptical endpoints of a particular Fermi surface of WP$_2$. We note however that such analysis as well as the thickness dependence are only relevant for the academic purpose of robustly identifying these oscillations as SO. Once this is established, the relevant lifetimes may straightforwardly be obtained from the resistance oscillations at a single thickness. Hence, Sondheimer oscillations promise to be a powerful probe to obtain the bulk mean-free-path in devices with \( \mu m \)-scale dimensions without relying on any microscopic model assumptions. This analysis is a clear pathway to identify scattering processes in clean conductors within operating devices. It thereby provides important feedback of the materials quality at and after a micro-/nano-fabrication procedure and disentangles the roles of bulk and surface scattering that are inseparably intertwined in averaged transport quantities of strongly confined conductors, such as the resistance. As their origin is entirely semi-classical, they are not restricted by stringent criteria such as quantum coherence and thus span materials parameters of increased scattering rate. In particular, they survive up to significantly higher temperatures and thereby allow microscopic spectroscopy in new regimes of matter dominated by strong quasiparticle interactions, such as hydrodynamic electron transport. With this quantitative probe, it will be exciting to test recent proposals of exotic transport regimes and create devices that leverage such unconventional transport in quantum materials.
+
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+Acknowledgements
+M.R.v.D. acknowledges funding from the Rubicon research program with project number 019.191EN.010, which is financed by the Dutch Research Council (NWO). This project was funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant no. 715730, MiTopMat). Y.W. is partially supported by the STC Center for Integrated Quantum Materials, NSF Grant No. DMR-1231319 for development of computational methods for topological materials. 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 U.S. Department of Energy under Contract No. DE-AC02-05CH11231 as well as resources at the Research Computing Group at Harvard University. P.N. is a Moore Inventor Fellow and gratefully acknowledges support through Grant No. GBMF8048 from the Gordon and Betty Moore Foundation. C.A.C.G. acknowledges support from the NSF Graduate Research Fellowship Program under Grant No. DGE-1745303. We acknowledge financial support from DFG through SFB 1143 (project-id 258499086) and the Würzburg-Dresden Cluster 274 of Excellence on Complexity and Topology in Quantum Matter – ct.qmat (EXC 2147, project-id 39085490). B.G. acknowledges financial support from the Swiss National Science Foundation (grant numner CRSII5_189924). H.S and B.G thank J. Gooth for
+discussion and K. Moselund, S. Reidt, and A. Molinari for support, and received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement ID 829044 "SCHINES".
+
+Author contributions
+
+MRvD, CP, JO, CG, JD performed the transport experiments, as well as the microfabrication in collaboration with BG and HS. The crystals were grown by VS and CF, and crystallographically analyzed by HB. YS and CF calculated the band structures, and YW, GV, CACG, PN performed the electron-phonon scattering calculations. BG, CF, PN and PJWM conceived the experiment, and all authors contributed to writing of the manuscript.
+
+Competing interests
+
+The authors declare no competing financial interest.
+
+Supplementary information
+Figures
+
+a)
+
+![Illustration of the Sondheimer effect. Left: the applied magnetic field is B = 3ΔB and the electron (red) makes an integer number of rotations, with no contribution to transport. Right: B ≠ nΔB. The electron hits the top surface at a different position than its origin on the bottom surface, leading to a contribution to the conductivity.](page_120_120_1347_384.png)
+
+b)
+
+![Resistivity as function of temperature for a WP2 microdevice. Inset: false-color SEM image of a typical device used in this study.](page_120_563_627_496.png)
+
+c)
+
+![Sondheimer oscillations seen in the Hall resistivity of a WP2 microdevice, for different temperatures. The oscillation period of ΔB =1.6 T is highlighted.](page_788_563_627_496.png)
+
+Figure 1
+
+Introduction to Sondheimer oscillations. a Illustration of the Sondheimer effect. Left: the applied magnetic field is B = 3ΔB and the electron (red) makes an integer number of rotations, with no contribution to transport. Right: B ≠ nΔB. The electron hits the top surface at a different position than its origin on the bottom surface, leading to a contribution to the conductivity. b Resistivity as function of temperature for a WP2 microdevice. Inset: false-color SEM image of a typical device used in this study. c Sondheimer oscillations seen in the Hall resistivity of a WP2 microdevice, for different temperatures. The oscillation period of ΔB =1.6 T is highlighted.
+Figure 2
+
+The staircase device. a, False color SEM image of a staircase device, used to measure Sondheimer oscillations for different thicknesses. The crystal is colored in purple, and gold contacts in yellow. b, Main: Schematic of the staircase device, illustrating all possible measurement configurations as well as the thickness of each section. Top left: SEM image of the lamella that will become the device shown in a, prior to extracting it from its parent crystal. Bottom right: SEM image of the same lamella, glued down onto a sapphire substrate, ready to define the device geometry. The lamella and glue are covered in gold (not colored) throughout the full field of view. The magnetic field is applied perpendicular to the structure, aligned along the crystallographic [011] direction.
+Figure 3
+
+Analysis of Sondheimer oscillations in WP2. a, Second derivative of the Hall resistivity shown in Fig.1c at T = 4 K. Inset: Fast Fourier Spectrum (FFT) corresponding to this data. b, Second derivatives of the Hall resistivity at three different thicknesses, d = 4.3, 2.7 and 2.0 μm, T = 4 K. c, FFTs corresponding to the data in b. d Dependence of the Sondheimer frequency on d. The red dashed line is calculated from the Fermi surface as determined from DFT. e Cross-sectional area, A, of the dogbone Fermi surface pocket of WP2 as a function of k parallel to the field direction of our experiments (top), and its derivative (bottom). f Location of observed Sondheimer orbits drawn on the dogbone-shaped Fermi surface pocket. The
+magnetic field is applied along the [011]-direction, perpendicular to the current, as indicated by the red line.
+
+![FFT amplitude vs frequency plots for different thicknesses and temperatures](page_184_120_1096_377.png)
+
+![Temperature dependence of Sondheimer and SdH oscillation amplitudes](page_184_527_496_377.png)
+
+![Scattering times vs temperature plot](page_740_527_496_377.png)
+
+![3D surface plot of τ_{e-ph} vs sample thickness](page_184_934_496_377.png)
+
+![3D surface plot of <1-cosθ> vs sample thickness](page_740_934_496_377.png)
+
+Figure 4
+
+Extraction of scattering times from the Sondheimer amplitude. a, FFTs of the SO at different temperatures for thicknesses of 4.3, 2.7 and 2.0 μm. b, Temperature dependence of the Sondheimer and SdH oscillation amplitudes, for different sample thicknesses. The dashed lines are fits used to
+extrapolate to the amplitude at zero temperature, A(0) (see the Supplementary Information for details). The dotted line is a Lifshitz-Kosevich fit, giving an effective mass of 1.1me. Two regimes are highlighted: that of quantum coherence, where SdH oscillations exist alongside SO, and that of Sondheimer, where only SO exist. c, Scattering times extracted for WP2 using Eq. 2 and the Fermi velocity from Ref.18. An approximate quantum lifetime extracted from the SdH oscillations as well as data from Refs.18, 41 are included for comparison. d Calculated scattering time for all electron-phonon scattering (\( \tau_{e-ph} \)) and e the scattering efficiency determining the momentum-relaxing scattering lifetimes (\( \tau_{MR} \)) projected onto the Fermi surface at T =10 K.
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementaryinformation.pdf

0d5d236ca2db4837436a59c800cfcd8d4634bf4e1db39c00ce4a07df353e91c4/preprint/preprint.md

@@ -0,0 +1,337 @@
+Human centromere formation activates transcription and opens chromatin fibre structure
+
+Nick Gilbert (nick.gilbert@ed.ac.uk)
+University of Edinburgh https://orcid.org/0000-0003-0505-6081
+Catherine Naughton
+The University of Edinburgh
+Covadonga Huidobro
+MRC Human Genetics Unit at The University of Edinburgh https://orcid.org/0000-0001-9823-3846
+Claudia Catacchio
+University of Bari, Department of Biology
+Adam Buckle
+MRC Human Genetics Unit at The University of Edinburgh
+Graeme Grimes
+MRC Human Genetics Unit at The University of Edinburgh
+Ryu-Suke Nozawa
+MRC Human Genetics Unit at The University of Edinburgh
+Stefania Purgato
+University of Bologna, Department of Pharmacy and Biotechnology
+Mariano Rocchi
+University of Bari, Department of Biology
+
+Article
+
+Keywords:
+
+Posted Date: January 18th, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1061218/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on September 24th, 2022. See the published version at https://doi.org/10.1038/s41467-022-33426-2.
+Human centromere formation activates transcription and opens chromatin fibre structure
+
+Catherine Naughton1, Covadonga Huidobro1, Claudia R. Catacchio1,2, Adam Buckle1, Graeme R. Grimes, Ryu-Suke Nozawa1, Stefania Purgato1,3, Mariano Rocchi2, Nick Gilbert1*
+
+1MRC Human Genetics Unit, The University of Edinburgh, Crewe Rd, Edinburgh, EH4 2XU 2Department of Biology, University of Bari, Via Orabona 4, 70125 Bari, Italy 3Department of Pharmacy and Biotechnology, University of Bologna, 40126 Bologna, Italy
+
+*Nick.Gilbert@ed.ac.uk
+
+Abstract
+
+Human centromeres appear as constrictions on mitotic chromosomes and form a platform for kinetochore assembly in mitosis. Biophysical experiments led to a suggestion that repetitive DNA at centromeric regions form a compact scaffold necessary for function, but this was revised when neocentromeres were discovered on non-repetitive DNA. To test whether centromeres have a special chromatin structure we have analysed the architecture of a neocentromere. Centromere formation is accompanied by RNA pol II recruitment and active transcription to form a decompacted, negatively supercoiled domain enriched in 'open' chromatin fibres. In contrast, centromerisation causes a spreading of repressive epigenetic marks to surrounding regions, delimited by H3K27me3 polycomb boundaries and divergent genes. This flanking domain is transcriptionally silent and partially remodelled to form 'compact' chromatin, similar to satellite-containing DNA sequences, and exhibits genomic instability. We suggest transcription disrupts chromatin to provide a foundation for kinetochore formation whilst compact pericentromeric heterochromatin generates mechanical rigidity.
+Introduction
+
+Centromeres are highly specialized genomic loci necessary to maintain genome stability. Cytogenetically they are the primary constriction of a metaphase chromosome and functionally provide an assembly site for the kinetochore, a multiprotein structure that forms attachments to the microtubules of the mitotic and meiotic spindles1. In mitosis the kinetochore is composed of a trilaminar structure with an outer layer binding to microtubules, but the architecture of the underlying chromatin fibre is unknown2.
+
+Human centromeric chromatin is assembled from CENP-A nucleosomes3 and repetitive α-satellite DNA sequences that span 250-5000 Kb4,5. Mouse acrocentric chromosomes have a similar organisation but, in this case, a small centromeric domain of minor satellite is flanked by a larger region of major satellite, which in interphase coalesces to form large dense chromocentres, enriched in heterochromatic marks and HP1 protein6. A prevailing hypothesis is that repetitive satellite sequences at centromeres form compact heterochromatin which provides a stable scaffold for the kinetochore. This idea is supported by biophysical experiments: (i) analysis of satellite containing mouse and human centromeric chromatin by sucrose gradient sedimentation shows that it sediments more rapidly than expected for its size, indicating that is has a compact chromatin structure, analogous to a rigid rod7; (ii) in different species nucleosomes are positioned regularly on satellite sequences consistent with the assembly of chromatin fibres having a regular and stable structure8,9; (iii) in vitro pulling experiments indicate that regularly folded chromatin has the biophysics properties of a stiff spring10.
+
+In contrast to biophysical data that indicates satellite containing centromeric chromatin has a uniform compact architecture, immunofluorescence analysis on extended interphase chromatin fibers11-12 show that it is divided into core and pericentromeric domains. The centromere core domain is enriched in active histone modifications indicative of transcription, whilst the surrounding pericentromeric regions are marked by repressive histone marks12. The centromere core, which is epigenetically defined by the variant histone CENP-A, interacts with CENP-C through the LEEGLG motif at the extreme C terminus14 and RNA15,16 to form an anchor for kinetochore formation, whilst the pericentromere recruits cohesin and condensin to regulate chromatin stiffness17. Whilst mechanisms for CENP-A recruitment are slightly different between species, it appears that a function of transcription at the core is to facilitate the incorporation of CENP-A containing nucleosomes18. Furthemore, studies in S. pombe indicate that chromatin remodelers spread from the centromeric core to surrounding pericentromeric regions19. This two-domain organisation appears critical for centromere stability, as experiments disrupting either transcription levels, or heterochromatic marks, affect chromatin compaction and result in mitotic defects20-25.
+
+Higher eukaryotic centromeres are typically located on repetitive DNA sequences, but they can also be found at euchromatic sequences26. These neocentromeres often form in response to chromosome instability in cancer which deletes the canonical centromere, but can also occur congenitally. Neocentromeres that have been inherited through generations and become fixed in the population are described as evolutionary new centromeres (ENC’s) and have often been inferred from studying the chromosome architecture between similarly related species27. Historically molecular analyses of centromeres have been challenging due to the repetitive nature of the underlying DNA, however as neocentromeres are formed on unique DNA sequences they provide a useful model to interrogate centromeric chromatin structure and provide insight into the properties of canonical centromeres. For example, examination of ENCs imply α-satellite DNA may be acquired over time at neocentromeres as they mature28-30, neocentromeres lacking pericentromeric heterochromatin in cis may establish interactions to distal heterochromatin in trans31; neocentromere formation promotes H3K9me3 loss and RNA polymerase II accumulation at the CENP-A core32, suggesting that chromatin is remodelled to accommodate a functional centromere.
+
+To reconcile results from biophysical and imaging based studies we have used a neocentromere as a model system to determine whether centromeres have a special chromatin structure. Centromere formation is accompanied by epigenetic and chromain fibre remodelling: the CENP-A defined core becomes enriched in active epigenetic marks, RNA polymerase, and negatively supercoiled DNA, consistent with transcription. To examine the biophysical properties of the chromatid fibre, sedimentation analysis shows that it has a transcription dependent disrupted chromatin fibre structure. These structural changes of core centromeric chromatin further affect the large-scale chromatin fibre folding of this region which becomes decompacted in a transcription dependent manner. Strikingly, there is pronounced epigenetic remodelling and transcriptional silencing of a large 5 Mb region surrounding the centromeric core. Although there is no concomitant change in nucleosome positioning at the centromere there is evidence for partial remodelling of the flanking
+pericentromeric heterochromatin to form 'compact' chromatin. As this region is genomically unstable we propose that further remodelling of the pericentromeric region to form compact heterochromatin occurs as the neocentromere matures. Overall, our data indicates that centromeres are remodelled to have a special chromatin structure: chromatin fibres at the centromere core have a disrupted structure that we suggest provides a suitable foundation to attach the kinetochore components whilst flanking sequences form a compact heterochromatin-like structure that has mechanical rigidity.
+Results
+Epigenetic remodelling at a human neocentromere
+
+To understand how new centromeres are accommodated in chromosomes and to investigate whether centromeres have a special chromatin structure required to form a stable kinetochore we used a previously identified neocentromere at 3q24 as a model system33. This neocentromere has been propagated across multiple generations, indicating it is stable through the germline, and is located in the vicinity of two genes but within a relatively gene poor segment of the genome. As the parental lymphoblastoid cells are heterozygous for the neocentromere at 3q24 the chromosome harbouring the neocentromere, Neo3, was genetically isolated from the normal counterpart in a human-hamster hybrid cell line (HybNeo3; Fig 1A) and compared to a human-hamster hybrid cell line, GM10253A, which has a single normal human chromosome 3, termed HSA3. No genetic changes were apparent in Neo3 and there was no evidence for repetitive DNA at 3q24 by deep sequencing, whilst as reported for other neocentromeres34–36 α-satellite persisted at the original centromere location (Fig. 1A).
+
+The position of the neocentromere was confirmed by using DNA fluorescence in situ hybridization (FISH) with probes to 3q24 (Supplementary Fig. 1A-C) and high-resolution mapped using ChIP with antibodies to CENP-A and CENP-C in the parental cells (Supplementary Fig. 1D), revealing a centromere core domain of 130 kb, similar to other synthetically derived neocentromeres32. In the derivatized human-hamster HybNeo3 cell line the centromere had drifted ≈ 30kb away from the telomere and had spread to encompass a ≈ 190kb domain. Centromere drift is apparent in horse and fission yeast37,38, and may represent a natural event controlled in part by the constitutive centromere-associated network (CCAN) and buffered by repetitive satellite DNA39.
+
+We set out to investigate how the chromatin fibre is remodelled in response to centromere formation and reasoned there could be two distinct possibilities (i) neocentromeres form at a genomic location that already has the features required for centromere function or (ii) neocentromeres have the capacity to remodel the local epigenetic environment. To discriminate between these two scenarios we examined the epigenetic repertoire of 3q24 using ChIP for active (H3K27ac, H3K4me2, H4K20me1) and repressive (H3K9me3, H3K9me2) epigenetic marks. A small block of GC-rich DNA in the vicinity of the neocentromere amplified aberrantly and was blacklisted (Supplementary Fig. 1E).
+
+The canonical 3q24 locus on HSA3 was decorated with active marks (Fig. 1B-C) coincident with actively transcribed genes in a euchromatic region, whilst repressive heterochromatic marks were absent. In contrast, after neocentromerisation, a large 5 Mb heterochromatin domain marked by H3K9me2/3 formed around the centromere on Neo3 (Fig. 1B, yellow box). Focal active marks in the vicinity of genes were absent and there was a significant loss of H3K27ac, a marker of CBP/P300 activity40. The upstream and downstream pericentromeric regions had the epigenetic hallmarks of heterochromatin consistent with the idea that centromeres are remodelled into a repressive state, even in the absence of repetitive DNA, demonstrating that special DNA sequences are not required for heterochromatin formation. At the centromeric core (Fig. 1B-C, blue box), coincident with CENP-C binding, the chromatin was remodelled to a state distinct from the flanking pericentromeric domains, devoid of heterochromatin marks and enriched for H4K20me1. This data suggests that instead of neocentromeres adopting the local epigenetic landscape they can remodel the local chromatin environment32 to form distinct centromeric and pericentromeric domains (Fig. 1B, blue and yellow boxes, respectively).
+Fig.1. Epigenetic remodelling after centromere formation. (A) Schematic detailing experimental model system. Left; human lymphoblastoid cells (Parental) harbouring a canonical human chromosome 3 (HSA3; purple frame) and a chromosome 3 with a neocentromere located at 3q24 (Neo3; orange frame) were genetically manipulated to isolate Neo3 in a human-hamster hybrid (HybNeo3) for comparison to a human-hamster hybrid (GM10253A) with a single HSA3 chromosome. Middle, DNA FISH with α-satellite specific probe (red) and a fosmid probe (green) for 3q24. The primary constriction (arrow) coincides with the α-satellite array in HSA3 but is located at 3q24 in Neo3. Chromosomes were counterstained with DAPI. Bar is 5 μm. Right, chromosome 3 ideogram to indicate centromere and α-satellite locations on HSA3 and Neo3. (B) Distribution of active (H3K4me2, H3K27ac) and repressive (H3K9me3, H3K9me2) epigenetic marks measured by ChIP-chip at the 3q24 neocentromere region on HSA3 and Neo3 chromosomes. Neocentromere is marked in solid blue, equivalent position in HSA3 is marked in open blue box and remodelled pericentromeric heterochromatin domain is marked in yellow. Bottom, position of genes at 3q24 locus. (C) Detailed view of active (H4K20me1) and repressive (H3K9me2/3) epigenetic marks surrounding the neocentromere.
+Transcriptional landscape at a neocentromere
+
+To understand the molecular basis for the distinct centromeric and pericentromeric domains, patterns of transcription were examined. By RT-qPCR active genes at 3q24 on HSA3 were all silenced upon centromere formation, as far as the distal DIPK2A and HLTF genes (Supplementary Fig. 2), suggestive of a spreading activity emanating from the centromere core domain. RNA sequencing was used to further explore the landscape and showed transcriptional repression over a 5 Mb pericentromeric domain on Neo3 (Fig. 2A). Recent data has indicated that (neo)centromeres are transcriptionally active in mitosis\(^{32,41}\) and in interphase in model organisms\(^{18,19,42}\). ChIP for RNA polymerase II showed it was absent from the pericentromeric domain in Neo3, but statistically significant levels of polymerase were apparent at the centromeric core in both interphase (Fig. 2B) and metaphase (Fig. 2C) cells. However, no transcripts were detected within the centromeric core domain on Neo3 even after exosome knockdown (Fig. 2D-E). Similarly, very deep sequencing for either short RNA transcripts, long RNA transcripts or nascent transcripts could not identify specific RNA species. This led us to speculate that transcription was at a very low level and dispersed across the centromeric core domain with multiple transcription initiation sites, but sufficient to remodel the local chromatin landscape.
+Fig. 2. RNA pol II binding at a functioning human centromere.
+(A) Normalised transcription across HSA3 and Neo3 analysed by RNA-seq. (B) RNA pol II (CTD domain, Diagenode) (green) and CENP-C (gift, W. Earnshaw) (red) immunofluorescence staining on a metaphase spread from parental cells (HSA3, purple; Neo3, orange). Bar is 5 μm. (C) Western blot confirming EXOSC3 protein (arrow) knockdown following 72 h RNAi treatment in GM10253A cells. (D) Distribution of nascent transcripts (normalised RPKM) in 600 kb window around neocentromere (blue), mapped using TT-seq. Top panels correspond to RNAi control, bottom panels are for exosome RNAi knockdown. (E) Distribution of RNA pol II binding at 3q24 for Neo3 (orange) and HSA3 (purple) chromosomes. Top, RNA pol II CTD antibody (D2, Diagenode), bottom, RNA pol II CTD antibody from Hiroshi Kimura (HK1). Horizontal line (arrows) corresponds to a sampled background model with p = 0.01. Significant peaks (p<0.001) called using the Ringo package for Neo3 (orange) and HSA3 (purple) are shown below tracks.
+Distinct pericentromeric domain boundaries
+
+Centromerisation triggered epigenetic remodelling to form a repressive pericentromeric domain (Fig. 1B). To characterise how the domain was delimited we examined facultative epigenetic marks across the locus and identified strong H3K27me3 enrichment at the telomeric end of the domain and a weak enrichment for H3K36me3 at the other end (Fig. 3A). H3K27me3 is a mark indicative of polycomb activity, whilst H3K36me3 is added by Set2 at active genes but is also reported as a facultative mark at heterochromatin43. These features suggest that the repressive pericentromere activity spreads until it reaches these boundaries, but raises the question as to what defines them? CTCF is an abundant protein associated with GC-rich DNA sequences and provides boundary activity for marking chromatin interaction domains measured by 3C techniques44,45. Although CTCF was present throughout the pericentromeric domain there were strong peaks located at both ends of the region (Fig. 3B). More strikingly and consistent with a recent study in budding yeast46 the pericentromeric domain was also delimited by the first convergently transcribed gene encountered moving away from the centromere (Fig. 3B). These results reveal a pronounced two domain structure at centromeres with a core and pericentromeric domain flanked by boundary sites defined by convergent genes and CTCF binding.
+Fig.3. Facultative heterochromatin and convergent genes mark transcriptionally silenced pericentromeric domain.
+(A) Distribution of facultative heterochromatin (H3K27me3 and H3K36me3) marks measured by ChIP-chip on HSA3 and Neo3 chromosomes. (B) Top, ChIP-chip showing distribution of CTCF at pericentromeric boundaries on Neo3 chromosomes. Bottom, schematic showing gene orientation at 3q24, convergent gene boundary marked in red. Vertical blue line corresponds to the neocentromere and repressive pericentromeric heterochromatin domain in yellow.
+Local chromatin fibre remodelling after centromere formation
+
+In gene-rich euchromatin nucleosomal DNA is packaged into chromatin fibres which have a disrupted or 'open' configuration47, a structure that is particularly conspicuous at transcription start sites48. In contrast, the specialised chromatin found at centromeres is formed from alpha satellite 4and CENP-A containing nucleosomes3. Alpha satellite makes up 3% of the human genome and positions nucleosomes precisely in vivo6 and in vitro9. Sedimentation studies to examine the biophysical properties of satellite containing chromatin indicate that it has the characteristics of a rigid rod-like particle which may enable it to fold into an ordered or crystalline array7,49. To establish the biophysical properties of centromeric chromatin (Fig. 4A) soluble chromatin was prepared from nuclei containing HSA3 and Neo3 chromosomes and fractionated by sucrose gradient sedimentation and pulsed-field gel electrophoresis47 (PFGE) (Supplementary Fig. 3A). Subsequently DNA corresponding to 'open' or disrupted chromatin was isolated from the agarose gel (Supplementary Fig. 3B) and used to map the chromatin fibre structure in the centromeric domain. Chromatin fibres located at the neocentromere were substantially remodelled to have a pronounced 'open' configuration (Fig. 4B) which was restricted to the CENP-C containing core, and is similar to the characteristics observed at transcription start sites48. Due to the presence of low-level RNA polymerase in the centromeric domain (Fig. 2A) we speculated that chromatin remodelling was linked to transcription, as has been observed in model organisms18,19,42. Concomitantly transcription inhibition completely abrogated the formation of disrupted chromatin fibres (Fig. 4B) demonstrating that centromeric chromatin is remodelled to have a transcription dependent 'open' structure.
+
+Previous studies have suggested that CENP-A containing chromatin is folded differently and this could be linked to DNA supercoiling50. If DNA is twisted in a right-handed direction it becomes over-wound (positive supercoiling) whilst twisting in the opposite direction it adopts an under-wound (negatively supercoiled) configuration51. Our earlier work showed that the level of supercoiling is transcription dependent52 so we hypothesised that low level RNA polymerase II activity could impact the local DNA configuration. Using biotinylated 4,5,8-trimethylpsoralen (bTMP) as a DNA structure probe52 centromeric chromatin was found to be enriched in negatively supercoiled DNA (Fig. 4C), in a transcription dependent manner. These data further indicate that RNA polymerase is not present as a static component but is engaged in active transcription that remodels DNA and local chromatin fibre structure.
+Fig.4. Centromeric chromatin has a transcription dependent underwound and disrupted chromatine fibre structure.
+(A) Top, schematic indicating the lack of understanding of chromatin structure at canonical centromeric chromatin (HSA3) and after centomerisation (Neo3). (B) Distribution of disrupted chromatine fibres across a 1.2 Mb region on HSA3 and Neo3, in the presence or absence of transcription inhibition (5 h a-amanitin treatment). (C) Organisation of negative (under-wound) and positive (over-wound) supercoils mapped by bTMP binding before or after transcription inhibition (5 h a-amanitin treatment).
+Centromere formation is not accompanied by nucleosome repositioning
+
+Satellite-containing pericentromeric chromatin fibres found at canonical centromeres have a rigid rod-like structure7 that may facilitate kinetochore formation and increase the fidelity of chromosome segregation. In contrast, neocentromeres do not have repetitive α-satellite DNA sequences34–36 to precisely position nucleosomes, so it was important to ask if centromerisation, per se, affected nucleosome positioning within the core or flanking DNA sequences. Mono and di-nucleosome fragments prepared from HSA3- and Neo3-containing nuclei using DFF nuclease (Supplementary Fig. 4A-B) were selected using biotinylated baits (Supplementary Fig. 4C) and deep sequenced. After centromerisation the size of the nucleosomal fragments did not change, despite centromeric nucleosomes being enriched in CENP-A (Supplementary Fig. 4D-F) and no difference in nucleosome positioning (Fig. 5A) or periodicity (Supplementary Fig. 4G) was observed.
+
+Despite no apparent change in the nucleosomal arrangement we speculated that over time pericentromeric chromatin may be remodelled to adopt a more compact configuration (scenario 2; Fig. 5B), analogous to the structure observed at canonical pericentromeres7. Consistent with this idea a 250 kb region at the pericentromeric boundary had a compact chromatin fibre structure (Fig. 5B) coincident with H3K36me3 (Fig. 3A) a mark that has previously been observed at constitutive and facultative heterochromatin43. This indicates that H3K9me2/3 heterochromatin marks are not sufficient to generate a compact chromatin fibre structure, but pericentromeric chromatin can be remodelled to form a structure analogous to canonical satellite-containing pericentromeric chromatin.
+Fig. 5. Compact heterochromatin in pericentromeric domain
+(A) Nucleosome dyad coverage on the HSA3 and Neo3 chromosome at the neocentromere domain (blue) with enlarged region (below) (B) Top, diagram showing potential scenarios for chromatin remodelling at pericentromere after centromerisation. Bottom, distribution of disrupted chromatin fibres, across the 3q24 locus in the HSA3 and Neo3 chromosomes. Blue bar corresponds to neocentromere and the yellow domain marks the silenced pericentromeric region.
+Decompacted large-scale centromeric chromatin
+
+As previous studies indicated an inter-relationship between different levels of chromatin organisation\(^{47,48,52}\), we speculated that after centromere formation local changes in chromatin structure might be propagated and influence large-scale chromatin compaction\(^{53}\). To directly test this hypothesis 3D DNA FISH, with pairs of differentially labelled fosmid probes \( \approx 300 \) kb apart (Supplementary Table 1), was used to ascertain large-scale chromatin compaction at the core and pericentromeric chromatin domains (Fig. 6A). In the hamster-hybrid cells harbouring HSA3 and Neo3 chromosomes there was no apparent change in compaction in pericentromeric regions but a pronounced decompaction at the centromeric core (Fig. 6B). To ensure this difference was not a consequence of comparing different cell lines the analysis was repeated in the parental cells using CENP-C immuno-FISH to discriminate between the Neo3 and HSA3 chromosomes. This similarly revealed a significant large-scale chromatin decompaction after centromerisation (Supplementary Fig. 5A-B) showing that remodelling occurs at multiple levels of centromere organisation. Centromeric large-scale chromatin structure was also transcription dependent, with both \( \alpha \)-amanitin and flavopiridol treatment causing chromatin compaction (Fig. 6C; Supplementary Fig. 5C). As bleomycin treatment (introduces nicks) also caused large-scale chromatin to compact (Fig. 6C), this suggested the fibres were under topological strain, consistent with being negatively supercoiled (Fig. 3C). Although we were unable to find evidence for centromeric derived transcripts (Fig. 2D) we speculated that transcripts may act locally to impact chromatin structure\(^{54}\). Consistent with this idea, RNase H treatment (hydrolyses RNA in the context of a DNA/RNA hybrid) compacted centromeric but not pericentromeric chromatin structure (Fig. 6D) suggesting that a transcription-dependent RNA component stabilised decompacted centromeric chromatin.
+Fig.6. Large-scale neocentromere chromatin fibre decompaction.
+(A) Diagram showing fosmid FISH probes (grey circles) surrounding the CENPC-marked centromeric core domain (blue). (B) Top, representative images of 3D-FISH on HSA3 and Neo3 chromosomes hybridized to probe B (red) and C (green) in single chromosome human-hamster hybrid nuclei, counterstained with DAPI. Bar is 5 μm. Bottom, boxplot showing interprobe distance measurements (μm) for pairs of fosmid probes. Horizontal line, median; whiskers, 1.5 interquartile range; p-values are for a Wilcoxon test; *, p < 0.05; **, p < 0.01; ***, p < 0.001; ****, p < 0.0001. (C) Boxplot showing interprobe distance (μm) between the BC (centromere) fosmid probes in HSA3 (white) and Neo3 (grey) chromosomes in GM10253A and HybNeo3 cell lines respectively, after treatment with α-amanitin (5 h), flavopiridol (3 h) or bleomycin (10 min). (D) Boxplot showing interprobe distance (μm) for the BC (centromere) and DG (pericentromere) pairs of fosmid probes on HSA3 or Neo3 chromosomes following RNase H treatment.
+Inherent genome instability at a neocentromere
+
+Whilst neocentromeres form fully functional kinetochores that are stably propagated\(^{55}\), they are still associated with higher chromosome mis-segregation rates and mitotic errors\(^{56,57}\). To quantify neocentromere stability we examined the chromosome architecture and copy number of the centromeric and pericentromeric domains in cells propagated for different amounts of time (Fig. 7A-B). At low passage almost all chromosomes had a normal structure (Fig. 7B and Supplementary Fig. 6A) but after approximately 50 passages the pericentromeric region upstream of the neocentromere had undergone break and or fusion events in 70% of cells. Copy number analysis was used to estimate the position of breakage events (Supplementary Fig. 6B) which were predominantly in the vicinity of the centromere. However, a region of pronounced DNA amplification was visible near the DIPK2A gene located proximal to the pericentromere boundary (Supplementary Fig. 6C). FISH of the cell population with the border fosmid indicated this region was amplified and located on other chromosomes but strikingly was rarely visible (2%) after chromosome breakage and fusion events (Supplementary Fig. 6D) indicating that breaks occurred in the pericentromeric chromatin domain upstream of the neocentromere.
+Fig.7. Neocentromere chromosome instability.
+(A) Neo3 ideogram and BAC probe used to analyse chromosome stability. (B) Left, Representative 2D DNA FISH images of Neo3 chromosome architecture. Neo3 chromosomes were hybridized with a human chromosome 3 paint (green) and neocentromere BAC probe (red) and scored as normal or abnormal (displaying neocentromere instability in the form of breaks, fusions to hamster chromosomes (dark grey) or duplications). Right, graph quantifying loss in chromosome stability as passage number increased. Bar is 2 µm. (C) Model showing transcription dependent centromere remodelling to a disrupted euchromatin state (grey) and pericentromeric chromatin repression to form heterochromatin (yellow). We suggest that disrupted euchromatin provides a suitable foundation for a high-fidelity kinetochore whilst heterochromatin and the accumulation of satellite sequences generates surrounding mechanical rigidity.
+Discussion
+
+For efficient and accurate chromosome segregation kinetochores must assemble onto CENP-A-containing chromatin. This happens in two stages, initially the constitutive centromere-associated network (CCAN)\(^{58}\) binds to centromeric chromatin via CENP-C\(^{14}\). Then, in mitosis, the complete kinetochore is assembled to provide an attachment site for the microtubules. To achieve these two steps with high fidelity it has been speculated that the underlying chromatin must adopt a special or distinct chromatin structure\(^2\) (Fig 7C).
+
+Previous studies have indicated that centromeric chromatin is associated with histone marks that are reflective of actively transcribed chromatin\(^{12,59}\). After centromere formation we observe a strong enrichment of active histone marks (Fig. 1) and a significant recruitment of RNA polymerase (Fig. 2). Concomitantly the chromatin fibre is remodelled to form a disrupted or 'open' structure (Fig. 4A); but what are the mechanisms for forming disrupted chromatin and what role might it play in kinetochore formation and function? Gene-rich\(^{47}\) and transcriptionally active\(^{48}\) chromatin are reported to form disrupted chromatin fibre structures, through a combination of mechanisms. At typical euchromatic regions irregularly positioned nucleosomes are less able to fold into an organised chromatin structure, but at centromeric regions it is known that satellite DNA sequences position nucleosomes regularly and form a rigid chromatin fibre\(^{7,10}\). After centromere formation there was no apparent remodelling of nucleosomes (Fig. 5A) suggesting that this is not the basis for the disrupted chromatin fibre. Alternatively, it is reported that CENP-A nucleosome tails bind DNA less tightly to form more dynamic nucleosomal structures and may also interfere with linker histone binding, to promote chromatin fibre opening\(^{60}\). Although CENP-A nucleosome properties might influence chromatin fibre folding it appears that the disrupted chromatin structure is strongly transcription dependent (Figure 4B). We therefore speculate that transcription could disrupt nucleosome positioning through the activity of RNA polymerase and recruitment of chromatin remodelling machines.
+
+At centromeres disrupted chromatin fibres may serve two purposes. Firstly, a disrupted structure might increase the likelihood of proteinaceous components of the CCAN, such as CENP-C, bind to CENP-A-containing centromeric nucleosomes\(^{14}\) but may also facilitate other structural components such as RNA to interact due to increased access to histone proteins. Our data indicates that centromere chromatin structure is RNA dependent demonstrating that additional nucleic acids may play a structural role (Fig. 6). This is consistent with previous studies which show that RNA can interact with HP1 to facilitate heterochromatin folding\(^{54}\). Secondly, depending on the nature of centromeric chromatin, a flexible fibre might be able to adopt a structure that is able to form a better scaffold for kinetochore formation. For example, in one model it has been suggested that centromeric chromatin might form a layered configuration termed a boustraphedon \(^{61}\) whilst in an alternate model the centromeric chromatin might be folded into small loops \(^3\), creating an invaginated structure that CCAN proteins can securely attach to. Presumably both large-scale structures would form more readily from a flexible chromatin fibre.
+
+Another recent idea posits that heterochromatin can undergo liquid-liquid phase separation (LLPS)\(^{62,63}\) to form a gel-like microenvironment\(^{64}\) that could facilitate kinetochore assembly. LLPS often occurs through non-covalent interactions that can be modulated by the local concentration of RNA and proteinaceous components such as HP1 or the long tails of histones\(^{65,66}\), so might be facilitated by a disrupted underlying chromatin structure.
+
+This study indicates that the centromeric chromatin core has a flexible disrupted structure (Fig 1 and 4) flanked by transcriptionally repressed pericentromeric chromatin (Fig 1 and 5), to form a two-domain model (Fig. 7C). At a newly formed (neo)centromere these flanking regions are epigenetically remodelled and transcriptionally repressed (Fig 1), presumably by an activity emanating from the core, but epigenetic remodelling was insufficient to completely compact chromatin fibre structure (Fig. 5), as observed for satellite-containing heterochromatin\(^7\). Evidence from evolutionary new centromeres (ENCs) indicate that satellite sequences accumulate over a long period\(^{28-30}\). Consistently only a small region of pericentromeric chromatin had a compact structure (Fig 5), showing that the neocentromere at 3q24 is young and has not yet matured to adopt a compact structure. Concomitantly, it exhibited a low level of aneuploidy suggesting that ENCs recruit satellite DNA sequences over time to progressively form a stable chromatin platform\(^7\) (Fig. 7C). We therefore suggest that centromere formation is accompanied by significant transcriptional, epigenetic and chromatin fibre remodelling to form a suitable environment for kinetochore assembly, and that over time the chromatin fibre structure matures to support high fidelity chromosome segregation in mitosis.
+Acknowledgements
+
+We would like to thank all members of our groups for useful discussions and to Alison Pidoux and Jim Allan for critical comments on the manuscript. This work was funded by the UK Medical Research Council (MR/J00913X/1; MC_UU_00007/13).
+
+Author Contributions
+
+C.N., C.H., C.R.C., A.B., R-S.N., and S.P. undertook experiments; C.N., G.R.G. and N.G. analysed data; M.R. and N.G. designed experiments; C.N. and N.G. wrote the manuscript with input from all authors.
+
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+69. Trazzi, S. et al. The C-terminal domain of CENP-C displays multiple and critical functions for mammalian centromere formation. PloS one 4, e5832 (2009).
+70. Li, H. et al. The Sequence Alignment/Map format and SAMtools. Bioinformatics (Oxford, England) 25, 2078–2079 (2009).
+71. Quinlan, A. R. & Hall, I. M. BEDTools: a flexible suite of utilities for comparing genomic features. Bioinformatics (Oxford, England) 26, 841–842 (2010).
+72. Liao, Y., Smyth, G. K. & Shi, W. featureCounts: an efficient general purpose program for assigning sequence reads to genomic features. Bioinformatics (Oxford, England) 30, 923–930 (2014).
+Methods
+
+Cell lines
+The human parental lymphoblastoid cell line was grown in RPMI 1640 with L-Glutamine (Life Technologies) supplemented with 20% FCS, penicillin (100 U.ml\(^{-1}\)) and streptomycin (100 \( \mu \)g.ml\(^{-1}\)). Human/Hamster hybrid cell lines GM10253A and HybNeo3, harbouring HSA3 and Neo3 respectively, were grown in the same media but with 10% FCS. All cells were maintained at 37 °C in an atmosphere of 5% CO2 and subjected to regular mycoplasma testing. Transcription was blocked by adding \( \alpha \)-amanitin (50 \( \mu \)g.ml\(^{-1}\)) or flavopiridol (100 \( \mu \)M) to cells for the times indicated.
+
+DNA fluorescence in situ hybridization (FISH)
+FISH was performed on both metaphase chromosome spreads and interphase nuclei. Metaphase chromosomes were prepared by treating cells with 0.1 \( \mu \)g.ml\(^{-1}\) Colcemid (Life Technologies, Cat No 15210-040) for 30 min (hybrid cells) or 4 hr (parental lymphoblastoid cells) prior to harvest to induce mitotic arrest and increase the number of mitotic cells. Cells were recovered by trypsin treatment and washed in PBS. Hypotonic solution, containing 75 mM KCl was added drop wise to a final 5 ml volume. Hypotonic treatment was performed at room temperature for 10 min, after which cells were pelleted by centrifugation at 1200 rpm (250g) for 5 min and fixed three times in 5 ml of a freshly prepared solution of 3:1 ratio (v/v) methanol: acetic acid (MAA). The MAA fixative was added to the cell pellet dropwise with constant agitation. Chromosome preparations were stored at ~20°C. To prepare slides with metaphase spreads, metaphase chromosome preparations were dropped onto glass slides. The glass slides were pre-treated in a dilute solution of HCl in Ethanol for at least one hour prior to use. The chromosome preparations were pelleted by centrifugation at 1500 rpm (350g) for 5 min and resuspended in freshly prepared MAA solution until the suspension became cloudy. Two drops of the suspension were dropped onto a pre-treated glass slide from a height of 20 cm and dried at room temperature overnight before staining or hybridization.
+
+For 3D FISH on interphase nuclei hybrid cells were grown overnight on glass slides whilst parental non-adherent lymphoblastoid cells (3 x 10\(^{4}\) cells) were cytopsued onto glass slides at 600 rpm (50g) for 10 min. Slides were rinsed with PBS and fixed in 4% paraformaldehyde (PFA) for 10 min. Slides were then rinsed with PBS and cells were permeabilized for 10 min on ice with PBS supplemented with 0.2% triton. After rinsing, slides were stored in PBS (for immunohistochemistry) or 70% ethanol (for FISH) at 4 °C. For chromatin nicking and RNase H treatment cells were grown on slides overnight, rinsed gently whilst still in the slide tray three times with PBS and then treated with bleomycin (100 \( \mu \)M) in PBS or RNase H (100U.ml\(^{-1}\), NEB MO297S) in PBS supplemented with 0.1% triton, 1mM Ca\(^{2+}\) and 1mM Mg\(^{2+}\) for 10 min at 37°C. Slides were then rinsed with PBS and PFA fixed as before.
+
+FISH was carried out as described\(^{52}\) except that MAA fixed metaphase spreads were denatured for 1 min in 70% formamide in 2× SSC, pH 7.5, at 70°C and interphase cells (grown on glass slides or cytopsued) were 4% PFA fixed and were denatured for 45 min at 80 °C. Following denaturation, slides were submerged in ice-cold 70% ethanol for 2 min and then dehydrated through 90% and 100% ethanol for 2 min each at room temperature. Fosmid and BAC clones (BACPAC Genomics) were labelled by nick translation with digoxigenin-11-dUTP (Roche, #11093070910) or biotin-16-dUTP (Roche, #11093088910) for antibody based detection as previously described or alternatively directly labelled with Green 500 dUTP (Enzo-42845) or red-dUTP (ChromaTide Alexa Fluor 594-5-dUTP C11400). α-satellite probe p82H\(^{67}\) was labelled by nick translation. For hybridization, 150 ng of labelled probe was combined with 5 \( \mu \)g salmon sperm and 10 \( \mu \)g human C\(_o\)t1 DNA (Invitrogen, Cat No 15279011). Two volumes of ethanol were added and the probe mix was collected by centrifugation and dried. Dried probes were resuspended in 10 \( \mu \)l of hybridization buffer containing 50% formamide (v/v), 1% Tween-20 and 10% dextran sulfate (Sigma Aldrich, Cat No D8906-100G) in 2 × SSC. Chromosome 3 paint (XCP3 Green, Metasystems) was supplied already labelled with a green fluorophore and dissolved in hybridization solution and ready to use. Probes were denatured at 70°C for 5 min and re-annealed at 37°C for 15 min and chilled on ice. Probes were pipetted onto slides and hybridization was performed at 37°C overnight. Coverslips were removed and slides were washed four times in 2 × SSC at 45°C for 3 min and four times in 0.1 × SSC at 60°C for 3 min. Slides were blocked in 5% milk in 4 × SSC for 5 min at RT. Detection of biotin label was performed with sequential layers of fluorescein (FITC)-conjugated avidin, biotinylated anti-avidin and a further layer of FITC-avidin. Digoxigenin was detected with sequential layers of Rhodamine-conjugated anti-digoxigenin and Texas-Red (TR) –conjugated anti-sheep IgG. Slides were DAPI stained, mounted in Vectashield (Vector Laboratories, Cat No H-1000) Epifluorescent images were acquired using a Photometrics Coolsnap HQ2 CCD camera on a Zeiss Axioplan II fluorescence microscope
+with a Plan-neofluar/apochromat 100x objective (Carl Zeiss, Cambridge, UK), a Mercury Halide fluorescent light source (Exfo Excite 120, Excelitas Technologies) and Chroma #83000 triple band pass filter set (Chroma Technology Corp., Rockingham, VT) with the single excitation and emission filters installed in motorised filter wheels (Prior Scientific Instruments, Cambridge, UK). Data was collected using Micromanager software and analyzed using custom scripts in iVision.
+
+For four-color 3D Immuno-FISH immunocytochemistry for CENP-C was performed prior to FISH. Slides stored in PBS were blocked in 5% horse serum then incubated overnight with anti-CENP-C antibody (1:200, gift, W. Earnshaw) before 1 hr incubation with Texas Red labelled anti-rabbit (1:100, Jackson ImmunoResearch Laboratories) secondary antibody. CENP-C signal was fixed with 4% PFA for 45 min followed by denaturation with 50% formamide in 2× SSC, pH 7.5, at 80°C for 45 min. Slides were then dipped briefly in 2 x SSC followed by incubation overnight at 37°C with pairs of labelled fosmid probes. Slides were then washed and processed as above. Epifluorescent images were acquired using a Photometrics Coolsnap HQ2 CCD camera and a Zeiss Axiolmager A1 fluorescence microscope with a Plan Apochromat 100x 1.4NA objective, a Nikon Intensilight Mercury based light source (Nikon UK Ltd, Kingston-on- Thames, UK) and a Chroma 89000ET single excitation and emission filters (Chroma Technology Corp., Rockingham, VT) with the excitation and emission filters installed in Sutter motorised filter wheels (Sutter Instrument, Novato, CA). A piezoelectrically driven objective mount (PIFOC model P-721, Physik Instruments GmbH & Co, Karlsruhe) was used to control movement in the z dimension. Hardware control, image capture and analysis were performed using Nikon Nis-Elements software (Nikon UK Ltd, Kingston-on-Thames, UK) and Velocity (Perkinelmer, Inc.). Images were deconvolved using a calculated point spread function with the constrained iterative algorithm of Velocity. Image analysis was carried out using Imaris software that calculate the distance between two fosmid probe signals. The significance of compaction between pairs of probes was tested using the nonparametric Wilcoxon test for paired samples, \( P < 0.05 \) was considered significant. FISH probes are described in Supplementary Table 1.
+
+Immunocytochemistry
+Metaphase chromosome spreads derived from parental cells were rinsed in PBS, blocked in 5% horse serum then incubated overnight with anti-CENP-C antibody (1:200, gift from W. Earnshaw) and anti-RNA pol II (1:1000, Abcam Ab24758) antibody. Secondary antibodies were FITC-conjugated anti-mouse and Texas Red-conjugated anti-rabbit antibodies (1:150, Jackson ImmunoResearch Laboratories). Slides were DAPI stained, mounted in Vectashield (Vector Laboratories, Cat No H-1000) and imaged on a Zeiss epifluorescence microscope using a 100x objective.
+
+Chromatin immunoprecipitation
+ChIP was done as described\(^{68}\) except that a Soniprep 150 (Sanyo) was used for sonication. In brief, cells (5-6 x 10^6 in 10 cm dishes) were cross-linked with 10 ml 1% formaldehyde (Sigma) in medium for 5 min at room temperature and then incubated in 10 ml 200mM glycine in medium for 5 min. Cells were rinsed twice with PBS and incubated with 7 ml lysis buffer (10 mM Tris-HCl (pH 7.5), 10 mM NaCl and 0.5% NP-40) for 10 min at room temperature with mild rotation. This lysis buffer was then aspirated off and cells were scraped into 1 ml lysis buffer and centrifuged at 3000 rpm for 3 min at 4°C. Cell pellet was resuspended in 100 μl SDS lysis buffer (50 mM Tris-HCl (pH 7.5), 10 mM EDTA and 1% SDS) and mixed by pipetting. 400 μl ChIP dilution buffer (50 mM Tris-HCl (pH 7.5), 167 mM NaCl, 1.1% Triton X-100, 0.11% sodium deoxycholate and protease inhibitor cocktail (complete EDTA-free; Roche)) was added before sonication (fifteen times for 20 seconds at 2 μm). After centrifugation at 13,000 rpm for 15 min at 4°C to remove the insoluble material the supernatant was removed to a new 1.5 ml tube and the volume made up to 500 μl with ChIP dilution buffer. 50 μl was removed as input for ChIP and the rest of the sample was incubated with antibody-bound Dynabeads overnight at 4°C with rotation. Dynabeads were prepared in advance by taking 50 μl of beads and washing three times with 500 μl cold RIPA-150 mM NaCl buffer (50 mM Tris-HCl (pH 7.5), 150 mM NaCl, 1 mM EDTA, 1% Triton X-100, 0.1% SDS, 0.11% sodium deoxycholate and protease inhibitor cocktail). Beads were then incubated with 500 μl cold RIPA-150 mM NaCl buffer plus antibody for 2 hr at 4°C with rotation. Beads were then washed three times with 500 μl cold RIPA-150 mM NaCl buffer and were then ready for overnight incubation with the ChIP sample. Beads were washed sequentially with 1 ml cold RIPA- 500 mM NaCl (50 mM Tris-HCl (pH 7.5), 500 mM NaCl, 1 mM EDTA, 1% Triton X-100, 0.1% SDS, 0.11% sodium deoxycholate and protease inhibitor cocktail) and twice with 1 ml TE (10 mM Tris-HCl (pH 8.0) and 1 mM EDTA). DNA was eluted by the addition of 200 μl ChIP direct elution buffer (10mM Tris-HCl (pH8.0), 300 mM NaCl, 5mM EDTA and 0.5% SDS) and incubated overnight at 65°C. Samples were then treated with DNase-free RNase (Roche; 5 μg.ml^{-1}; 37°C; 30 min) and proteinase K (250 μg.ml^{-1}; 55°C; 1 hr). DNA was extracted with phenol-chloroform-isoamyl
+alcohol (25:24:1) and ethanol precipitated with carrier (1μl glycogen, Invitrogen) on dry ice for 30 min. Following 70% ethanol wash the DNA pellet was resuspended in 20 μl water and quantified using a NanoDrop. For microarray hybridization, immunoprecipitated DNA was amplified using whole-genome amplification (Sigma).
+
+Magnetic sheep anti-mouse IgG beads (Dynabeads, Invitrogen, 11201D) were used for mouse antibodies and protein G beads were used for rabbit antibodies (Dynabeads, Invitrogen, 10004D). Antibodies used were to CENP-A69 and CENP-C (gift from W. Earnshaw), H3K27ac (Abcam, Ab4729), H3K4me2 (Millipore, 07-030), H3K9me2 (Millipore, 07-212), H3K9me3 (Abcam, Ab8898), H3K27me3 (Abcam, Ab6002), H3K36me3 (Abcam, Ab9050), CTCF (D31H2) (Cell Signaling Technology, 3418), RNA Polymerase II (Diagenode, C15100055), RNA Polymerase II (gift from H. Kimura). All antibodies were characterized using western blots, and ChIP was optimized using quantitative PCR assays.
+
+Analyzing changes in DNA supercoiling
+Biotinylated psoralen (bTMP) uptake was used to analyse DNA supercoiling as previous described52. Cells were treated with 500 μg.ml⁻¹ of bTMP in PBS for 20 min at room temperature in the dark. bTMP was UV cross-linked to DNA at 360 nm for 10 min. DNA was purified from cells using SDS and proteinase K digestion and extracted using phenol-chloroform-isoamyl alcohol (25:24:1). DNA was fragmented by sonication (thirteen times for 30s at 2 μm). Biotin incorporation into DNA was detected by dot blotting using alkaline phosphatase-conjugated avidin as a probe. The bTMP–DNA complex in TE was immunoprecipitated using avidin conjugated to magnetic beads (Dynabeads MyOne Streptavidin Invitrogen, 65001) for 2 h at room temperature and then overnight at 4°C. Beads were washed sequentially for 5 min each at room temperature with TSE I (20 mM Tris-HCl, pH 8.1, 2 mM EDTA, 150 mM NaCl, 1% Triton X-100 and 0.1% SDS), TSE II (20 mM Tris-HCl, pH 8.1, 2 mM EDTA, 500 mM NaCl, 1% Triton X-100 and 0.1% SDS) and buffer III (10 mM Tris-HCl, pH 8.1, 0.25 M LiCl, 1 mM EDTA, 1% NP40 and 1% deoxycholate). Beads were then washed twice with TE buffer for 5 min. To extract DNA and to release psoralen adducts, the samples were boiled for 10 min at 90°C in 50 μl of 95% formamide with 10 mM EDTA. Samples were then made up to 200 μl with water, and the DNA was purified using a Qiagen MinElute PCR purification kit. bTMP bound DNA was amplified using whole-genome amplification (Sigma) prior to microarray hybridization.
+
+Chromatin Fractionation
+Disrupted or ‘open’ chromatin was isolated as described previously48. In brief, cell nuclei were digested with micrococcal nuclease and soluble chromatin released overnight followed by fractionation on a 6-40% isokinetic sucrose gradient in 80 mM NaCl, 0.1 mM EDTA, 0.1 mM EGTA and 250 μM PMSF. DNA purified from gradient fractions was analyzed by electrophoresis through 0.7% agarose in 1 × TPE buffer (90 mM Tris-phosphate, 2 mM EDTA) with buffer circulation. Preparative fractionation of DNA from gradient fractions was carried out by pulsed-field gel electrophoresis (PFGE) (CHEF system, Biorad) through 1% low melting point agarose in 0.5 × TBE, at 180 V, for 40 hr, with a 0.1–2 s switching time. Size markers were 1 kb (Promega) and λ-HindIII (NEB) DNA ladders. EtBr-stained gels were scanned using a 473 nm laser and a 580 nm band-pass filter on a Fuji FLA-3000. DNA of ~ 20 kb, corresponding to “open” chromatin, was isolated by β-agarase (NEB) digestion and amplified by whole genome amplification (Sigma) prior to microarray hybridization.
+
+Microarray hybridization, data processing and analysis
+Whole-genome amplified DNA (ChIP/bTMP/open’ chromatin) was labelled and hybridised as previously (NSMB) to custom 180K Agilent microarrays ) (7 Mb spanning the neocentromere domain (chr3:142781158-149782213; GRCh38 (hg38). In brief, 500 ng DNA was random prime labeled (ENZO) with Cy3 (Sample DNA) or Cy5 (Input DNA) and purified on a MinElute PCR purification column (Qiagen). Labeled DNA was diluted in hybridization buffer (Agilent) and hybridized to arrays for 24 h at 65°C. Slides were washed according to the manufacturer’s instructions and scanned on a Nimblegen Microarray scanner at 2 μm resolution generating a TIFF file.
+
+Spot signal intensity was extracted from the TIFF files using Agilent Feature Extraction software and were pre-processed in R using the RINGO bioconductor package to give the raw Cy5 and Cy3 signal intensities for each spot. Individual Cy5 and Cy3 channels were normalized to each other and between arrays using a variance stabilizing algorithm (for bTMP arrays) and loess, vsn (for ChIP arrays) or nimblegen (“open” chromatin arrays) normalized and scaled, using the standard Bioconductor LIMMA package. All arrays were quality controlled by checking array hybridization patterns, analyzing signal profiles and using MA plots. For data analysis log2(sample/input) data was loaded in to the ZOO package in R and for display the data was
+smoothed using a rolling median.
+
+RNA extraction and RNA-Seq
+Total RNA was extracted from cells using RNeasy mini kit (Qiagen) with on-column DNase I digestion (RNase-Free DNase Set, Qiagen). For RT-qPCR RNAs were reverse transcribed (Superscript II, Invitro-gen) using random primers and quantified by qPCR (Fast start SYBR green, Roche). Primer sequences are described below. Ribosomal RNA was depleted using Illumina® Ribo-Zero Plus rRNA Depletion Kit (Illumina, 20040526) following the manufacturer’s instructions and libraries for RNA-seq were prepared and indexed using NEBNext® Ultra™ II DNA Library Prep Kit for Illumina® (NEB #E7645L) and NEBNext Singleplex Oligos for Illumina (NEB #E7335, E7500) following the manufacturer’s instructions. Libraries were sized and quality controlled on a D1000 Tapestation tape (Agilent). Single-end RNA-seq of 50-bp read length was performed on Illumina Hi-Seq 2000 (UMC, Amsterdam). FASTQ sequence files were obtained and the RNA-seq reads were aligned to the human reference genome (hg38) using TopHat v2 and processed with Samtools v1.6\(^{70}\) and the Bedtools “genome coverage” tool\(^{71}\). Aligned BAM files were processed with the Subread v1.5 “feature counts” tool\(^{72}\) to generate FPKM scores against hg38 RefSeq genes.
+
+TT-seq
+Nascent RNA was labelled by adding 500 \( \mu \)M 4-thiouridine (4sU)(Sigma, T4509) to cells harbouring HSA3 and Neo3 in T75 flasks and incubating at 37°C for 10 min. Media was aspirated and RNA extraction was performed with TRIzol (Invitrogen) following the manufacturers’ instructions. After DNase treatment (Turbo DNase, Thermo Fisher Scientific) RNA concentration and purity were determined using a NanoDrop. RNA (70 \( \mu \)g) was fragmented in 100 \( \mu \)l H\(_2\)O to <1.5kb by 20 cycles of 30 seconds on/30 seconds off at high power in a Biorupter plus and RNA size assessed by agarose gel electrophoresis. Fragmented 4sU labelled RNA was biotinylated by adding 140 \( \mu \)l of EZ-Link Biotin-HPDP (1mg.ml\(^{-1}\) in dimethylformamide; Pierce, 21341), 70 \( \mu \)l of 10 x biotinylation buffer (100 mM Tris-HCl pH 7.5, 10 mM EDTA) and H\(_2\)O to a final volume of 700 \( \mu \)l. This was incubated at room temperature for 1.5 h with rotation. Unincorporated biotin-HPDP was removed by two rounds of chloroform extraction with 2 ml Phase lock gel heavy tubes (Eppendorf). RNA was precipitated with 1/10 volume of 5M NaCl and an equal volume of Isopropanol. This was inverted to mix and incubated at room temperature for 10 min followed by centrifugation at 10,000g for 20 min at room temperature. RNA pellet was washed with 80% EtOH and centrifuged at 13,000 rpm for 10 min at 4°C. RNA was resuspended in 100 \( \mu \)l H\(_2\)O and dissolved by heating to 40°C for 10 min with agitation. RNA was then immediately placed on ice and RNA concentration determined by Nanodrop spectrophotometer. Biotinylated 4sU labelled RNAs were then recovered using μMACS Streptavidin MicroBeads (Miltenyi, 130-074-101) and separation on a μMACS Separator. For the concentration of total RNA in \( \mu \)g per sample an equal amount in \( \mu \)l of Streptavidin microbeads was added. This was incubated at room temperature for 15 min with rotation. μMacs columns were equilibrated with 900 \( \mu \)l room temperature washing buffer (100 mM Tris-HCl pH 7.5, 10 mM EDTA, 1 M NaCl, 0.1% Tween20). The RNA/streptavidin bead solution was then applied to the column followed by three washes with 900 \( \mu \)l of washing buffer at 65°C and three washes with 900 \( \mu \)l of washing buffer at room temperature. RNA was eluted with 2 x 100 \( \mu \)l of fresh elution buffer (100 mM dithiothreitol in RNase-free H\(_2\)O ) directly into 2 ml lobind tubes (Eppendorf) containing 700\( \mu \)l Buffer RLT (RNeasy MinElute Cleanup Kit, Qiagen). 500 \( \mu \)l of 100% ethanol was added to the RNA solution, and mixed thoroughly by pipetting before RNA was purified through RNAeasy MinElute Spin Columns. RNA concentration was determined using a Nanodrop and libraries for RNA-seq were prepared and indexed using NEBNext® Ultra™ II Directional RNA Library Prep Kit for Illumina® (NEB #E7645L) and NEBNext Singleplex Oligos for Illumina (NEB #E7335, E7500) following the manufacturer’s instructions. Libraries were sized and quality controlled on a D1000 Tapestation tape (Agilent) and Illumina sequencing (paired-end RNA-seq of 50-bp read length) was performed on NovaSeq S1 (Edinburgh Genomics). FASTQ sequence files were obtained and the RNA-seq reads were aligned to a Human(hg38) /Hamster (GCA_003668045.1) hybrid reference genome using Bowtie2 and processed with Samtools v1.6\(^{70}\), and the deepTools “bamCoverage” tool\(^{71}\) with RPKM normalisation.
+
+Exosome RNA interference
+For siRNA treatment, cells (GM10253A and HybNeo3; 10%-20% confluent) were transfected with 10 nM Silencer Select Pre-designed siRNA targeting EXOSC3 (Ambion, Life Technologies) using Lipofectamine RNAi MAX (ThermoFisher) 24 h after seeding and again 48 h later. After a further 48 h exosome knockdown was confirmed by western blotting and TTseq was performed. Silencer Select RNA sequence for EXOSC3 were GAGATATATTCAAAGTGTGA, part number s83102. The control RNA was Stealth RNAi siRNA Negative Control (ThermoFisher). For western blotting cells were suspended in NuPAGE LDS sample buffer (ThermoFisher) with 10 mM DTT, incubated at 100°C for 5 min and sonicated briefly. Protein samples were
+resolved on 12% bis-tris gels (ThermoFisher) and transferred to Immobilon-P PVDF 0.45 mm membrane (Merck Millipore) by wet transfer. Membranes were probed with anti-EXOSC3 antibody (Abcam, Ab156683) using standard techniques and detected by enhanced chemiluminescence.
+
+Shallow DNA Sequencing
+The hybrid HSA3 and Neo3 cell lines were shallow sequenced to confirm copy number. Genomic DNA was prepared from cells and 500 ng DNA was fragmented using a Covaris sonicator. Genomic DNA libraries were prepared using Illumina TruSeq Nano DNA LT sample prep kit as per manufacturer’s instructions and Illumina sequencing (50-bp, single end reads) was performed on Illumina Hiseq 4000 (VUMC Cancer Centre, Amsterdam). FASTQ sequence files were obtained and reads were aligned to the human reference genome (hg19) using BWA and processed with Samtools v1.670. In R the BAM files were loaded into the Bioconductor package QDNAseq for copy number analysis. Human reference genome HG19 was used here as QDNAseq has pre-calculated bin annotations for genome build hg19.
+
+Neocentromere capture DNA sequencing
+NimbleGen Sequence Capture technologies were employed for targeted deep sequencing of the neocentromere domain. Capture probes tiling a 1.5Mb domain across the neocentromere were designed using Nimblegen capture design software and sequence capture performed using this custom SeqCap EZ Choice probe pool and SeqCap EZ HE-Oligo Kit A and SeqCap EZ Accessory Kit (Nimblegen) according to manufacturer’s instructions. In brief, genomic DNA (gDNA) from the parental lymphoblastoid cell line was fragmented to ~200-500bp with 20 cycles of 30 seconds on/30 seconds off on a Biorupter. 1 μg gDNA was then used to prepare the gDNA sample library using NEBNext® Ultra™ II DNA Library Prep Kit for Illumina® (NEB #E7645L) following the manufacturer’s instructions. The neocentromere domain was captured by hybridising this gDNA library with the biotinylated SeqCap EZ library. 342ng of gDNA library was mixed with 5μg C6t1 DNA, 1000 pmol of SeqCap HE Universal Oligo 1 and 1000 pmol SeqCap HE Index Oligo, 7.5 μl 2 X Hybridisation Buffer and 3μl Hybridisation Component A. This was vortexed for 10 seconds and centrifuged at maximum speed for 10 seconds before denaturing at 95°C for 10 min. This gDNA/C6t1/Oligo/Hybridisation cocktail was then combined with the SeqCap EZ library (provided as 4.5μl single-use aliquots in 0.2ml tubes), vortexed for 3 seconds and centrifuged at maximum speed for 10 seconds. Hybridization was then performed on a thermocycler at 47°C and incubated for 70 hours. Each hybridization reaction was then bound to streptavidin beads from SeqCap EZ Pure Capture Bead Kit and washed with SeqCap EZ Hybridization and Wash Kit (Nimblegen), following the manufacturer’s protocol. Captured libraries were re-amplified using Post LM-PCR oligos (Nimblegen) and Q5 High-Fidelity DNA polymerase (NEB) directly from the beads. A mastermix consisting of 65 μl 2 × NEBNext Ultra II Q5 Master Mix NEB, 50 μl captured library (beads in H2O), 13 μl LM-PCR Oligo mix (Oligo 1 & 2, 2μl final concentration of each)(Nimblegen) was made up to 50 μl with H2O, vortexed to mix and then split into 2 × 65 μl samples for PCR using the following PCR cycling conditions. Initial incubation at 98°C for 30 seconds, 14 cycles of 98°C for 10 seconds, 65°C for 30 seconds and 72°C for 30 seconds. Final incubation of 72°C for 5 min and hold at 4°C. The two PCR reactions were recombined and the captured DNA was purified using 1.8:1 AMPure XP Beads: DNA ratio. Capture efficiency was determined to be between 94 and 117 fold using a Nimblegen Sequence Capture control locus qPCR assay. Neocentromere captured DNA libraries were sized and quality controlled on a D1000 Tapestation tape (Agilent), and paired-end sequenced (50 bp) on an Illumina MiSeq (Edinburgh Genomics).
+
+Nucleosome positioning
+Nuclei were extracted from cells carrying HSA3 and Neo3 as described7 and resuspended in NB-R (85 mM KCl, 10 mM Tris-HCl [pH 7.6], 5.5% (w/v) sucrose, 1.5 mM CaCl2, 3 mM MgCl2, 250 μM PMSF). Nuclei (800 μl at 5A260) were digested with DFF nuclease (PMID: 17626049) for increasing amounts of time (100 μl of digested nuclei were removed to a new tube after 1, 2, 4, 8, 16 and 32 min digestion) at room temperature in the presence of 100 μg.ml-1 RNaseA. Digestion was stopped by adding EDTA to 10 mM. DNA was purified with SDS/Protease K digestion, phenol/chloroform extraction and ethanol precipitation. Agarose gel electrophoresis of DFF digested nuclei confirmed digestion to mono and di-nucleosomes. The 4 min and 8 min samples and the 16 min and 32 min samples were pooled and ran on 2.5% LMP GTG agarose in 1 × Sybr Safe (Thermo Fisher) dye. Mono and di-nucleosome DNA bands were excised from the gel and purified by β-agarase (NEB) digestion followed by phenol/chloroform extraction and ethanol precipitation. 500ng DNA samples (50ng from the 4 and 8 min DFF digestion pool plus 450 ng of the 16 and 32 min DFF digestion pool) were concentrated to 55 μl volume using 2:1 AMPure XP Beads: DNA ratio for the mono nucleosome samples and 1.6:1 AMPure XP Beads: DNA ratio for the di nucleosome samples. Genomic DNA sample
+libraries were then prepared using NEBNext® Ultra™ II DNA Library Prep Kit for Illumina® (NEB #E7645L) following the manufacturer’s instructions. This included adaptor-ligated DNA size selection of between 100-200 bp for the mono nucleosome samples and 300-400 bp for the di nucleosome samples. DNA library yield was increased by a further round of PCR with Post LM-PCR oligos (Nimblegen) and Q5 High-Fidelity DNA polymerase (NEB). The PCR reaction consisted of 30 µl of the mono or di nucleosomal DNA libraries (150-270 ng), 50 µl 2 × NEBNext Ultra II Q5 Master Mix NEB, 5 µl Post LM-PCR oligo mix (Oligo 1 & 2, 2 µM final concentration of each; Nimblegen) and 15 µl H₂O. PCR cycling conditions were an initial incubation at 98°C for 30 seconds, 5 cycles of 98°C for 10 seconds and 65°C for 75 seconds and a final incubation of 65°C for 5 min. DNA was purified using 1.8:1 AMPure XP Beads: DNA ratio and libraries were quantified and sized on a D1000 Tapestation tape (Agilent). Libraries, representative of mono and di nucleosome positions throughout the genome, were pooled in equimolar amounts (150 nM) and then subjected to neocentromere capture (as above) to examine nucleosome positioning across the neocentromere region. 1.25 µg of the mono and di nucleosome library pool was mixed with 5µg Cₐt₁ DNA, 1000 pmol of SeqCap HE Universal Oligo 1 and 1000 pmol SeqCap HE Index Oligos 14, 16, 18 and 19, 7.5 µl 2 × Hybridisation Buffer and 3µl Hybridisation Component A. This was vortexed for 10 seconds and centrifuged at maximum speed for 10 seconds before denaturing at 95°C for 10 min. This gDNA/Cₐt₁/Oligo/Hybridisation cocktail was then combined with the SeqCap EZ library (provided as 4.5µl single-use aliquots in 0.2 ml tubes), vortexed for 3 seconds and centrifuged at maximum speed for 10 seconds. Hybridization was then performed on a thermocycler at 47°C and incubated for 70 hours. Each hybridization reaction was then bound to streptavidin beads from SeqCap EZ Pure Capture Bead Kit and washed with SeqCap EZ Hybridization and Wash Kit (Nimblegen), following the manufacturer’s protocol. Captured libraries were re-amplified using Post LM-PCR oligos (Nimblegen) and KAPA High-Fidelity DNA polymerase (KAPA Biosystems) directly from the beads. 25 µl 2 × KAPA HiFi Hot-Start ReadyMix, and 5 µl LM-PCR Oligo mix (Oligo 1 & 2, 2µM final concentration of each; Nimblegen) was added to the 20 µl captured library (beads in H₂O), vortexed to mix and PCR amplified using the following PCR cycling conditions. Initial incubation at 98°C for 45 seconds, 14 cycles of 98°C for 15 seconds, 60°C for 30 seconds and 72°C for 30 seconds. Final incubation of 72°C for 1 min and hold at 4°C. Captured DNA was purified using 1.8:1 AMPure XP Beads: DNA ratio. Capture efficiency was determined to be between 120 and 240 fold using a Nimblegen Sequence Capture control locus qPCR assay. Neocentromere captured DNA libraries were sized and quality controlled on a D1000 Tapestation tape (Agilent), and paired-end sequenced (50 bp) on an Illumina MiSeq (Edinburgh Genomics).
+
+Nucleosome positioning analysis
+Paired end sequencing reads were mapped to hg38 using Bowtie 2 with high quality (mq > 20) and paired reads selected for further analysis. Start and end positions of reads were extracted from bamfiles using bedtools bamtobed function and analysed in R. The NucelR package was used to calculated nucleosomal dyad positions with 40 bp trimming and coverage, data was formatted in the ZOO package and plotted using the lattice package. The acf function in R was used to calculate nucleosome autocorrelation.
+Supplementary Fig. 1. Cell line model system used to interrogate centromeric chromatin structure and mapping of neocentromere mapping to 3q24 (relates to Figure 1).
+(A) Parental human lymphoblastoid cells with one canonical chromosome 3 (HSA3, purple frame) and one chromosome 3 with the centromere relocated to form a neocentromere at 3q24 (Neo3, orange frame). DNA FISH with α-satellite specific probe (red) and a 3q24 fosmid probe (green). (B) The Neo3 chromosome was retained after fusion of the parental cell line with a hamster cell to create a hybrid line called “HybNeo3”. Metaphase spread of HybNeo3 hybridized with human C₀t-1 DNA (green) identifying the seven human chromosomes present in this human/hamster hybrid (4,6,8,11,13,18, X and Neo3 (orange frame)) and a human α-satellite specific FISH probe (red). (C) The GM10253A hybrid cell line has a single canonical human chromosome 3 (HSA3). Metaphase spread of GM10253A hybridized with a human chromosome 3 paint (green; purple frame). Nuclei are counterstained with DAPI. Bar is 5 μm. (D) Top, ideogram depicting chromosomes HSA3 and Neo3. Bottom, distribution of CENP-A and CENP-C ChIP signal in parental and hybrid cells at 3q24. (E) Top, signal for control IgG ChIP-chip and bottom microarray probe GC composition (%). Blacklisted region (chr3: 147324413-147482213; hg38) is marked by red dashed lines. Neocentromere core (chr3: 147400413-147591023) defined from CENP-C (panel A) is marked in blue.
+Supplementary Fig. 2. Transcription repression at the pericentromeric domain (Relates to Figure 2)
+Top, diagram showing individual genes at 3q24, yellow block corresponds to pericentromere domain, blue is the neocentromere. Bottom, RT-qPCR expression data for genes within and bordering the pericentromeric heterochromatic domain, showing expression from HSA3 and gene silencing on Neo3.
+Supplementary Fig. 3. Isolation of “open” chromatin probes (Relates to Figure 4).
+Soluble chromatin isolated from hybrid cell nuclei by micrococcal digestion was fractionated by size and structure on a sucrose gradient. (A) Top, agarose gel electrophoresis of DNA purified from sucrose gradient fractions. (B) DNA from gradient fractions was size selected by PFGE. DNA fragments ≈10 kb longer than the bulk of the DNA signal, corresponding to “open” or disrupted chromatin, was purified from gel slices (yellow boxes).
+A
+
+Time   HSA3   Neo3
+
+1 kb
+200 bp
+
+B
+
+HSA3   Neo3
+
+400 bp
+200 bp
+
+Gel purified fragments
+
+C
+
+Position (Mb)  0  40  80  120  160  200
+HSA 3
+Neo 3
+Hybrid Cell
+Log2(ChIP/npq)
+CENP-C
+CENP-C
+Baits
+Chromosome 3 (Mb)
+
+D
+
+Frequency
+Fragment size (bp)
+HSA3 (mono) n = 62M
+HSA3 (di) n = 67M
+Neo3 (mono) n = 26M
+Neo3 (di) n = 31M
+
+E
+
+10,000 bp windows
+Nucleosome size (bp)
+Chromosome 3 (Mb)
+Neo3 (mono)
+HSA3 (mono)
+
+F
+
+1,000 bp windows
+Nucleosome size (bp)
+Interquartile range (bp)
+Chromosome 3 (Mb)
+Neo3 (mono)
+HSA3 (mono)
+Median=12
+Neo3 (mono)
+HSA3 (mono)
+Median=12
+
+G
+
+Neo3 (Mb)
+146  147  148
+CENP-C
+Left flank   Core   Right flank
+Log2(ChIP/npq)
+Left flank   Core   Right flank
+Autocorrelation Function
+Lag (bp)
+HSA3   Neo3
+
+Supplementary Fig. 4
+Legend over page
+Supplementary Fig. 4. Arrangement of nucleosomes around neocentromere (Relates to Figure 5).
+(A) Agarose gel electrophoresis of DFF digested nuclei isolated from HSA3 and Neo3 containing cells. Mono and di-nucleosome fragments were excised, and the DNA extracted using β-agarase. (B) Agarose gel electrophoresis of purified mono- and di-nucleosomes fragments used for nucleosome mapping. (C) Top, ideogram depicting HSA3 and Neo3 chromosomes with enlargement of 3 Mb region around the neocentromere (marked by CENP-C). Bottom, genomic location of the capture baits used to enrich for 1.5 Mb of neocentromeric region. (D) Size distribution of mono and di nucleosomes (bp) isolated from HSA3 and Neo3 cells for 1.5 Mb around the region corresponding to the neocentromere. (E) Mono nucleosome size distribution in 10 kb windows across the 1.5 Mb captured domain (neocentromere marked in blue). (F) Left, mono nucleosome size (median) in 1 kb windows across the 1.5 Mb captured domain and focussed region covering the neocentromere (marked in blue). Right, variance (interquartile range) in mono nucleosome size in 1 kb windows across the 1.5 Mb captured domain and focussed region covering the neocentromere (marked in blue). (G) Autocorrelation of nucleosome dyad coverage at left flank, centromere core and right flank for different lag (bp).
+Supplementary Fig. 5. Large scale chromatin is decompacted at the neocentromere in the parental cell line (Relates to Figure 6).
+(A) Top, chromosome 3 ideogram indicating CENP-C immunofluorescence signal (yellow) and the neocentromere specific FISH probes (green and red). Bottom right, representative image of 4 colour 3D immuno-FISH for identifying the chromosome 3 harbouring a neocentromere at 3q24 due to the presence of the CENP-C signal proximal to one pair of fosmid probes. Below left, three colour representation of the same image used for measuring interprobe distance. (B) Boxplot showing interprobe distance measurements (\( \mu m \)) between the pair of fosmid probes (B and C, see Fig 6A) for the HSA3 and Neo3 chromosomes in the parental lymphoblastoid cells. (C) RT-qPCR expression data for genes in the pericentromere region flanking the neocentromere domain in cells carrying the HSA3 and Neo3 chromosomes, following transcription inhibition with a-amanitin (5h) or flavopiridol (3h).
+Supplementary Fig. 6. Neocentromere associated genome instability (Relates to Figure 7)
+(A) Left, representative FISH images of Neo3 metaphase chromosomes hybridised to a human chromosome 3 paint (green) and BAC (red) located at the neocentromere. Chromosome morphology was scored as normal or showing instability: deletions, fusions or duplications. Bar is 2μm. Right, quantification (%) of different chromosome morphologies with increasing passage number (low ~ 10, high ~ 100) over time. P values are for a \( \chi^2 \) test compared to low passage. (B) High passage Neo3 Chromosome copy number (RPKM), with a zoom in of the 3 Mb region around the neocentromere (blue). (C) High passage Neo3 Chromosome copy number (RPKM), with a zoom in of the 7 Mb region around the neocentromere (blue). Locations of DNA FISH probes are shown, neocentromere BAC probe (green) and border fosmid (red). (D) Left, representative FISH images of Neo3 metaphase chromosomes hybridised to a BAC (green) located at the neocentromere and a fosmid (red) located at the border. Bar is 2μm. Right, chromosome morphology was scored and quantified (%) with increasing passage number over time. Loss of the border probe signal was coincident with fusion of human Neo3 fragment (light grey) to a hamster chromosome (dark grey). Bar is 2μm.

0db09a99923f418955497d1d6f55a2130a934dc119e9b2f2f18766ecb87dc1ff/preprint/preprint.md

@@ -0,0 +1,426 @@
+Not final yet: a minority of final stacks yields superior amplitude in single-particle cryo-EM
+
+Jianying Zhu
+Tsinghua university
+Qi Zhang
+Tsinghua university
+Hui Zhang
+Yanqi Lake Beijing Institue of Mathematical Sciences and Applications
+Zuoqiang Shi
+Tsinghua university
+Mingxu Hu
+Tsinghua University   https://orcid.org/0000-0003-3603-3966
+Chenglong Bao (clbao@tsinghua.edu.cn)
+Tsinghua University   https://orcid.org/0000-0002-1201-1212
+
+Article
+
+Keywords: cyro-EM, single particle analysis, particle sorting, final stacks
+
+Posted Date: May 29th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2921474/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on December 10th, 2023. See the published version at https://doi.org/10.1038/s41467-023-43555-x.
+Not final yet: a minority of final stacks yields superior amplitude in single-particle cryo-EM
+
+Jianying Zhu$^{1\dagger}$, Qi Zhang$^{3,4,5,6\dagger}$, Hui Zhang$^2$, Zuoqiang Shi$^{1,2*}$, Mingxu Hu$^{3,4,5,6*}$ and Chenglong Bao$^{1,2*}$
+
+$^1$Yau Mathematical Sciences Center, Tsinghua University, Beijing, China.
+$^2$Yanqi Lake Beijing Institute of Mathematical Sciences and Applications, Beijing, China.
+$^3$Key Laboratory of Protein Sciences (Tsinghua University), Ministry of Education, Beijing, China.
+$^4$School of Life Science, Tsinghua University, Beijing, China.
+$^5$Beijing Advanced Innovation Center for Structural Biology, Beijing, China.
+$^6$Beijing Frontier Research Center for Biological Structure, Beijing, China.
+
+*Corresponding author(s). E-mail(s): zqshi@tsinghua.edu.cn; humingxu@mail.tsinghua.edu.cn; clbao@tsinghua.edu.cn;
+†These authors contributed equally to this work.
+
+Abstract
+Cryo-electron microscopy (cryo-EM) is widely used to determine near-atomic resolution structures of biological macromolecules. Due to the extremely low signal-to-noise ratio, cryo-EM relies on averaging many images. However, a crucial question in the field of cryo-EM remains unanswered: how close can we get to the minimum number of particles required to reach a specific resolution in practice? The absence of an answer to this question has impeded progress in understanding sample behavior and the performance of sample preparation methods. To address this issue, we have developed a new iterative particle sorting and/or sieving method called CryoSieve. Extensive experiments demonstrate that CryoSieve outperforms other cryo-EM particle sorting algorithms and reveals that most particles are unnecessary in final
+stacks. The minority of particles remaining in the final stacks yield superior high-resolution amplitude in reconstructed density maps. For some datasets, the size of the finest subset approaches the theoretical limit.
+
+Keywords: cyro-EM, single particle analysis, particle sorting, final stacks
+
+1 Introduction
+
+The transformative impact of cryo-EM single-particle analysis (SPA) on the field of structural biology has been widely recognized by the scientific community [1]. Cryo-EM has advanced significantly due to a series of technological innovations [2–7], enabling the technique to provide macromolecular structures with up to atomic resolution at an unprecedented rate. This technological progress is commonly referred to as the resolution revolution [8]. Cryo-EM involves using electron microscopy images of biomolecules embedded in vitreous, glass-like ice [9], which are then combined to generate three-dimensional (3D) density maps. These maps provide valuable insights into the function of macromolecules and their role in biological processes.
+
+The stability and electron-optical performance of electron microscopes do not hinder the use of cryo-EM [10]. However, biological samples studied in cryo-EM are radiation-sensitive [11, 12]. Therefore, a trade-off must be made between improving the signal-to-noise ratio (SNR) and limiting radiation damage [13, 14]. It was concluded that statistically well-defined three-dimensional (3D) structures could not be obtained from individual biological macromolecules at atomic resolution [15, 16]. Instead, increasing the SNR by averaging image data from many identical macromolecules is the only way to progress [13, 17, 18]. Over two decades ago, Henderson estimated that structures could be determined at a resolution of near 3 Å by merging data from approximately 12,000 particles, even for particles as small as approximately 40 kDa [19]. Later, Rosenthal and Henderson argued that the electron microscopy community should adopt the same threshold criterion for structure factor quality as the X-ray protein crystallography community, which was set at a figure-of-merit of 0.5 corresponding to a phase error of 60 degrees [16].
+
+The theoretical limit of the minimum number of particle images required to achieve a specific resolution can be calculated using the theory proposed by Henderson and Rosenthal [16, 19], given the B-factor of the instrument (e.g., electron microscopy and camera) [13, 14, 20]. In practice, the final stacks of cryo-EM still far fall short of the theoretical limit, indicating a considerable gap between what can be accomplished and the physical limit of what cryo-EM can do [21]. The initial particle datasets obtained by particle picking from micrographs undergo multiple rounds of laborious 2D and 3D classification to generate the final stack for model determination. The final stacks, which yield atomic or sub-atomic resolution density maps, typically comprise several orders of magnitude fewer particles than the original datasets. Therefore, the
+cryo-EM field faces the long-standing question of how close we can approach the theoretical limit in practice. The lack of an answer to this open question has hindered the quantification of the performance of various underdeveloped sample preparation methods and impeded the investigation of trends and the understanding of the underlying mechanisms of sample behavior.
+
+To answer the question of how close cryo-EM can approach its theoretical limit, it is crucial to determine the minimum number of particles required to achieve a high-resolution 3D reconstruction within a given dataset. In this study, we introduce CryoSieve, an iterative particle sorting and/or sieving algorithm that identifies the smallest subset of particles necessary to generate high-resolution density maps, which we call the finest subset. CryoSieve compares the high-frequency components of synthetic and observed particle images. A higher CryoSieve score indicates superior quality rather than typical cryo-EM damage or artifacts (Section 2.1). Extensive experiments show that CryoSieve outperforms other particle sorting algorithms in various metrics and reveals that most particles in final stacks are futile (Section 2.2). The finest subsets generate 3D density maps with better high-resolution amplitude, using much fewer particles than the final stacks (Section 2.3). We propose that CryoSieve removes radiation-damaged particles within cryo-EM datasets, supported by experiments on simulated radiation damage particles (Section 2.4). Lastly, we compare the minimum particles required in theory with the size of the finest subsets obtained by CryoSieve, finding that some datasets come close to the theoretical limit after being sieved by CryoSieve (Section 2.5). We conclude that, for these datasets, the primary opportunity for further improvement lies in generating fewer futile particles during sample preparation rather than further improving the quality of the particle images that constitute the finest subset.
+
+2 Results
+
+2.1 Design of CryoSieve.
+
+We have developed a particle sorting and/or sieving model called CryoSieve that alternatively performs 3D reconstruction and particle selection, eliminating futile particles during each iteration. In CryoSieve, a cryo-EM single-particle reconstruction software selected by the user is used to reconstruct a new density map with the retained particle images, which is then used in the subsequent iteration. The retained particle images in each iteration form a subset of those from the previous iteration, as shown in the following formula:
+
+\[
+\left\{ i_1^{(k)}, i_2^{(k)}, \ldots, i_{n^{(k)}}^{(k)} \right\} \subset \left\{ i_1^{(k-1)}, i_2^{(k-1)}, \ldots, i_{n^{(k-1)}}^{(k-1)} \right\},
+\]
+
+where \( n^{(k-1)} \) represents the number of retained particles. At each iteration, let \( b_j \) be the \( j \)-th particle image, \( A_j \) be its forward operator defined by the estimated parameters and \( x^{(k-1)} \) be the reconstructed density map from the
+retained particle images in the previous iteration, particles are sieved out based on their CryoSieve score, which is defined as follows:
+
+\[
+g_j := \left\| H^{(k)} b_j \right\|^2_2 - \left\| H^{(k)} (b_j - A_j x^{(k-1)}) \right\|^2_2, \quad j \in \left\{ i_1^{(k-1)}, i_2^{(k-1)}, \cdots, i_{n^{(k-1)}}^{(k-1)} \right\}.
+\]
+
+Here, \( H^{(k)} \) is the high-pass operator at the \( k \)-th iteration, and its threshold frequency increases as the iteration progresses.
+
+The CryoSieve score estimates the similarity between a particle and a reference projection above a given frequency. A higher CryoSieve score indicates that the particle and the reference projection share a higher proportion of signal energy, indicating better particle quality. As radiation damage mainly affects the high-frequency range, the CryoSieve score includes a high-pass operator to extract the high-frequency part. We have demonstrated that the CryoSieve score can identify particles with incorrect pose parameters or components in the high-frequency range through theoretical analysis and simulation verification. Assuming that noise in particles follows a Gaussian distribution, we have shown that, with high probability, the CryoSieve score is an ideal indicator of particle image quality, distinguishing it from typical cryo-EM damage or artifacts (Supplementary Material I). Furthermore, when simulating radiation damage as high-frequency random phasing, the CryoSieve score exhibits remarkable accuracy in selecting particles even with a very low signal-to-noise ratio (approximately 0.001), achieving a precision rate of around 90% (Supplementary Material I).
+
+2.2 Majority of the particles are futile in final stacks.
+
+We demonstrate the versatility of our method by applying it to six experimental datasets (Table 1). The first dataset is derived from the human TRPA1 ion channel (EMPIAR-10024) [22]. The second dataset is from influenza hemagglutinin trimer (EMPIAR-10097) [23], of which the preferred orientation necessitated 40-degree tilts during data acquisition. The third dataset involves LAT1-CD98hc bound to MEM-108 Fab (EMPIAR-10264) [24], while the fourth features membrane-bound pfCRT complexed with Fab (EMPIAR-10330) [25]. Both of these datasets utilized signal subtraction during data processing. The fifth dataset is from CS-17 Fab-bound TSHR-Gs (EMPIAR-11120) [26], and the sixth is from TRPM8 bound to calcium (EMPIAR-11233) [27]. All datasets were obtained using a voltage of 300 kV and an amplitude contrast of 0.07 or 0.1. The TEM systems and electron detectors used in the experiments are listed in Table 1, along with additional metadata such as the number of particles in the final stacks, spherical aberration and molecular symmetry.
+
+All of the datasets are deposited in the Electron Microscopy Public Image Archive (EMPIAR) as final stacks. These final stacks, which also contain
+Table 1  Microscopic imaging parameters of six experimental datasets along with their associated metadata.
+
+<table>
+  <tr>
+    <th>dataset</th>
+    <th>TEM</th>
+    <th>electron detector</th>
+    <th>number of particles</th>
+    <th>spherical aberration (mm)</th>
+    <th>symmetry</th>
+  </tr>
+  <tr>
+    <td>TRPA1</td>
+    <td>TF30 Polara</td>
+    <td>Gatan K2 Summit</td>
+    <td>43,585</td>
+    <td>2.0</td>
+    <td>\( C_4 \)</td>
+  </tr>
+  <tr>
+    <td>hemagglutinin</td>
+    <td>Titan Krios</td>
+    <td>Gatan K2 Summit</td>
+    <td>130,000</td>
+    <td>2.7</td>
+    <td>\( C_3 \)</td>
+  </tr>
+  <tr>
+    <td>LAT1</td>
+    <td>Titan Krios</td>
+    <td>FEI FALCON III</td>
+    <td>250,712</td>
+    <td>2.7</td>
+    <td>\( C_1 \)</td>
+  </tr>
+  <tr>
+    <td>pfCRT</td>
+    <td>Titan Krios</td>
+    <td>Gatan K2 Qutuamn</td>
+    <td>16,905</td>
+    <td>0.001</td>
+    <td>\( C_1 \)</td>
+  </tr>
+  <tr>
+    <td>TSHR-Gs</td>
+    <td>Titan Krios</td>
+    <td>Gatan K3 Qutuamn</td>
+    <td>41,054</td>
+    <td>2.7</td>
+    <td>\( C_1 \)</td>
+  </tr>
+  <tr>
+    <td>TRPM8</td>
+    <td>Titan Krios</td>
+    <td>Gatan K2 Summit</td>
+    <td>42,040</td>
+    <td>2.6</td>
+    <td>\( C_4 \)</td>
+  </tr>
+</table>
+the corresponding refined Euler angles, were used to generate the final published reconstructions. The final stacks are generated by manually selecting significantly smaller subsets through multiple rounds of 2D/3D classification, resulting in a substantial reduction in the number of particles compared to the original particle stacks. For example, the final stack of the CS-17 Fab-bound TSHR-Gs dataset consists of 41,054 particles selected from a pool of 2,742,080 particles, representing a reduction by a factor of approximately 67 [26].
+
+We employed CryoSieve to process the six experimental datasets. CryoSieve removed 20% of the particles in each iteration, resulting in a retaining ratio of 80.0%, 64.0%, 51.2%, and so on. The retained particles in different iterations were then used for ab initio reconstruction to determine the finest subset of particles. The finest subset only contained 26.2% to 32.8% of the particles in the final stack. However, the quality of the reconstructed map from the finest subset was consistent with that obtained from all particles in the final stack, as demonstrated in Figure 1. These results indicate that CryoSieve can effectively eliminate over half of the particles with unreliable high-frequency signals without negatively affecting the final reconstruction. Therefore, CryoSieve is highly effective in selecting the most informative particles.
+
+We performed a comparative analysis of CryoSieve with other cryo-EM particle sorting criteria or software currently used in the field, including the normalized cross-correlation (NCC) method [28] and the angular graph consistency (AGC) approach [29]. In our experiments, we used final stacks composed of relatively high-quality particles. NCC retains an equal number of particles compared to CryoSieve at each iteration, while AGC’s retaining ratio is self-determined. However, AGC’s retaining ratio was mainly over 90%, resulting in only a small fraction of particles being removed. Thus the quality of the reconstructed map using the retained particles did not improve or worsen (Supplementary Table 1), as these tested final stacks are composed of relatively high-quality particles. Additionally, we randomly selected the same number of particles from the tested final stacks at each iteration to observe the baseline effect of particle number reduction.
+
+For all the aforementioned methods (CryoSieve, NCC, AGC, and random), we discarded the published refined Euler angles deposited on EMPIAR to avoid the Eisenstein-from-noise effect [30]. Instead, the retained particles were used for ab initio reconstruction by CryoSPARC to obtain refreshed sets of Euler angles and density maps. Several metrics, including FSC-based resolution [16] and Q-score [31], were used to measure the quality of the refreshed density maps. Comprehending these metrics, our analyses reveal that CryoSieve effectively sieves out 67.2% to 73.8% (varying based on datasets) of particles from the final stacks without deteriorating the yielded density maps (Figure 2). Meanwhile, subsets of equal size retained by the other methods failed to reconstruct density maps of the same quality as the original (Figure 2). Therefore, CryoSieve significantly outperforms other particle sorting algorithms, demonstrating that majority of the particles are dispensable in the final stacks.
+Fig. 1 CryoSieve is capable of maintaining resolutions after removing the majority of particles in the final stacks. For all six experimental datasets, density maps of the CryoSieve-retained particles (steel blue) and all particles in the final stack (medium purple) were compared, obtained from CryoSPARC’s ab initio reconstruction after discarding the published refined Euler angles deposited on EMPIAR to avoid the Eisenstein-from-noise effect. The density maps were first FSC-weighted (based on FSCs given by CryoSPARC), and then B-factor sharpened using equivalent B-factors for the same protein: −90Ų for TRPA1, −180Ų for hemagglutinin, −100Ų for LAT1, −60Ų for pFCRT, −70Ų for TSHR-Gs, and −80Ų for TRPM8. The central bars indicate the proportions of the retained and removed particles.
+
+cisTEM [5] is capable of reporting a score for each single particle image after 3D reconstruction, though it is not a particle sorting criterion. Due to differences in alignment and other image processing workflows between cisTEM and cryoSPARC, cisTEM cannot be strictly compared with CryoSieve. Therefore, we compared Cryosieve with cisTEM by sorting single particles by cisTEM score and retaining the same number of particle images for ab initio reconstruction using cryoSPARC. CryoSieve outperformed cisTEM in all six experimental datasets (Supplementary Material II and Supplementary Figure 2).
+
+Moreover, we analyzed the differences between the particle images retained and removed using CryoSieve by performing 2D classification of the particles into 50 classes using CryoSPARC. To ensure a comparable number of particles for both retained and removed groups, iteration 3 was chosen for such analysis, with a retention ratio of 51.2% and a removal ratio of 48.8%. CryoSPARC
+reported the 2D resolution of each class, along with the number of particle images belonging to it. The particles retained by CryoSieve (Figure 3, steel blue) were distributed at a higher resolution compared to those removed by it (Figure 3, crimson). In five out of the six datasets, particle images with the highest resolution, i.e., 8.5–9.6 Å in hemagglutinin, 6.6–8.2 Å in LAT1, 7.2–11.6 Å in pfCRT, 7.2–8.5 Å in TSGH-Gs, and 11.6–7.5 Å in TRPM8, were entirely retained by CryoSieve. Therefore, our analysis suggests that CryoSieve selectively retained the higher-quality particle images in the final stack while discarding lower-quality ones.
+
+2.3 Better high-resolution amplitude with much fewer particles.
+
+B-factors, also known as Debye-Waller factors or temperature factors, reflect the rate at which the amplitude of high-resolution information decreases [16]. Lower B-factors indicate that the high-resolution signal has been better preserved during sample preparation, imaging, and image processing, implying that the particle images are of higher quality. B-factors are widely used to measure image quality in cryo-EM quantitatively [32–36]. In our six experimental datasets, the finest subset, comprising only 26.2% to 32.8% of particles in the final stack, yields 3D density maps with B-factors reduced by 18.0\AA^2 to 71.2\AA^2 compared to those produced by the original final stacks (Table 2, column B and C). In other words, the density maps reconstructed from the finest subset have a better high-resolution amplitude, meaning they contain a greater high-resolution intensity, despite the fact that the finest subsets only contain a small fraction of particles in the final stack. This indicates that CryoSieve significantly reduced the temperature factor and alleviated the amplitude contrast decay, suggesting that high-quality particles contribute to the density map and can be effectively selected by CryoSieve.
+
+2.4 CryoSieve can effectively detect radiation-damaged particles.
+
+We hypothesize that some particle images in the final stacks have been subject to some degree of radiation damage and cannot be screened out by conventional methods. These particles do not contribute positively to the reconstructed density map. To verify the possibility of this conjecture, we generated simulated particle images using InSilicoTEM [37], with varying degrees of radiation damage, and screened them using CryoSieve.
+
+The atomic model of E. coli 50S ribosome bound to VM2 (PDB 6PCQ) [38] was employed to generate particle images, with defocus ranges from 1800 nm to 2800 nm, an electron dose of 40 e^{-} \AA^{-2}, a Falcon I detector, a box size of 450×450, and a pixel size of 1.04Å. Radiation damage was simulated by varying the motion blur factor from 0 to 4 (Figure 4a). Each set of the simulated single particles contained 8,000 particles, and the projection directions followed a random distribution.
+Table 2 The finest subsets alleviate high-resolution amplitude decay, along with a comparison to their theoretical number of particle limit.
+
+<table>
+  <tr>
+    <th>dataset</th>
+    <th>A†</th>
+    <th>B*</th>
+    <th>C*</th>
+    <th>D</th>
+    <th>E</th>
+    <th>F</th>
+  </tr>
+  <tr>
+    <td>TRPA1</td>
+    <td>3.90</td>
+    <td>141.9</td>
+    <td>78.1(63.8-)</td>
+    <td>521</td>
+    <td>11,426(51.9×)</td>
+    <td>43,585(83.7×)</td>
+  </tr>
+  <tr>
+    <td>hemagglutinin</td>
+    <td>3.62</td>
+    <td>232.0</td>
+    <td>160.8(71.2-)</td>
+    <td>975</td>
+    <td>34,078(35.6×)</td>
+    <td>130,000(133.3×)</td>
+  </tr>
+  <tr>
+    <td>LAT1</td>
+    <td>3.11</td>
+    <td>132.6</td>
+    <td>96.0(36.6-)</td>
+    <td>6,697</td>
+    <td>65,687(9.8×)</td>
+    <td>250,712(37.4×)</td>
+  </tr>
+  <tr>
+    <td>pCRT</td>
+    <td>3.37</td>
+    <td>85.1</td>
+    <td><b>49.5(35.6-)</b></td>
+    <td>4,212</td>
+    <td><b>4,429(1.01×)</b></td>
+    <td>16,905(4.0×)</td>
+  </tr>
+  <tr>
+    <td>TSHR-Gs</td>
+    <td>2.96</td>
+    <td>92.9</td>
+    <td><b>61.7(31.2-)</b></td>
+    <td>9,205</td>
+    <td><b>13,465(1.46×)</b></td>
+    <td>41,054(4.5×)</td>
+  </tr>
+  <tr>
+    <td>TRPM8</td>
+    <td>2.98</td>
+    <td>94.7</td>
+    <td>76.7(18.0-)</td>
+    <td>2,200</td>
+    <td>13,789(6.3×)</td>
+    <td>42,040(19.1×)</td>
+  </tr>
+</table>
+
+† (A), half-maps resolution of the CryoSieve-retained particles (Å); (B), B-factor obtained from all particles in the final stacks (Å^2); (C), B-factor obtained from the CryoSieve-retained particles with temperature decrease (compared with all particles) in brackets (Å^2); (D), theoretical number of particles limit at \( B = 50 \text{Å}^2 \); (E), number of the CryoSieve-retained particles with folds of theoretical limit in brackets.; (F), number of particles in final stacks with folds of theoretical limit in brackets.
+* B-factors were reported by cryoSPARC auto-postprocessing.
+
+We compared the retention behavior of CryoSieve and NCC for particles with different simulated degrees of radiation damage, with random retention as the baseline. As the number of iterations increased, the retention rate decreased, and CryoSieve demonstrated a greater ability to screen out particles with higher levels of radiation damage (Figure 4b). While NCC outperformed the random retention baseline, it was still inferior to CryoSieve in terms of screening accuracy (Figure 4b). Additionally, we compared CryoSieve with cisTEM and found that although cisTEM performed acceptably for particles with high radiation damage, it still exhibited inferior performance to CryoSieve for particles with relatively low radiation damage. (Supplementary Material II and Supplementary Figure 2). These results imply that CryoSieve could effectively removes radiation-damaged particles to improve the quality of the final density maps.
+
+2.5 The finest subsets may be close to the theoretical number of particles limit.
+
+The theoretical number limit of particle images, given by Rosenthal and Henderson [16], is
+
+\[
+N_{\text{particles}} = \frac{1}{N_{\text{asym}}} \frac{\frac{S^2}{N^2} 30 \pi}{N_e \sigma_e d} \exp \left( \frac{B}{2d^2} \right),
+\]
+
+where \( N_{\text{asym}} \), \( \frac{S}{N} \), \( N_e \), \( \sigma_e \), \( d \), \( B \) stand for the number of asymmetric units, the signal-to-noise threshold criteria of the resolution, the electron dose, the elastic cross-section for carbon, the resolution, and the overall temperature factor, respectively. In the above formula, \( \frac{S}{N} = \frac{1}{\sqrt{3}} \), which is equivalent to phase error of 60 degrees or 0.143-threshold of half-maps FSC [16]. Meanwhile, \( N_e = 5e^{-\text{\AA}^{-2}} \), which is believed to be the limiting dose due to radiation
+damage for features near-atomic resolution [16, 19, 39, 40]. The electron dose used in practice is typically a fold higher than the limiting dose. Although the additional dose does not contribute to the structure factor amplitudes at near atomic resolution, it may have increased the signal up to the resolution limit of the final map, thus making the determination of particle parameters easier [16]. This conjecture agrees with the observation in the study of micrograph movie stack dose weighting, which found that only the initial few frames, not the subsequent frames, contribute to near atomic features [41–43]. Finally, \( \sigma_e = 0.004\text{\AA}^2 \) is the elastic cross-section for carbon at 300kV [44].
+
+The overall temperature factor, or Rosenthal and Henderson’s B-factor, is the dominant factor in estimating the theoretical limit. Here, we proposed a simplified and crude assumption that limits only exist on instruments (TEM and electron detector) and that no other resolution-limiting factors exist. In other words, we assumed that all other procedures or techniques were ideal. For example, vitrified non-amorphous ice is perfectly flat and of ideal thickness, there is no beam-induced motion, and orientations of particles follow a uniform distribution, and there is no electron-charging effect. Therefore, B-factor represents a summary of all resolution-limiting factors of a given electron microscope, and describes the overall quality of the instrumental setup. Holger Stark and his colleagues have summarized the current knowledge on existing state-of-the-art commercial EM hardware and their B-factors [45]. For the standard Titan Krios, they concluded that its B-factor is 50\(\text{\AA}^2\), which was determined by re-evaluating data from EMPIAR-10216 as described by [46], with modifications to account for off-axial aberrations by splitting the micrographs into nine subsets [47]. Therefore, we computed the theoretical number of particle limits at \( B = 50\text{\AA}^{-2} \) (Table 2, column D). The sizes of the finest subsets obtained by CryoSieve were compared with such theoretical limits (Table 2, column E).
+
+Out of the six datasets examined, two (pfCRT and TSHR-Gs) were found to be close to their theoretical limits (Table 2, column E, emphasized by bold font). However, the TRPA1 dataset fell short of the theoretical limit by approximately 52. This could be due to the lower resolution capabilities of the TF30 Polara TEM used in the study compared to more advanced models like the Titan Krios. It is possible that the assumed B-factor of 50 \( \text{\AA}^2 \) for the TF30 Polara is relatively low and does not accurately reflect the properties of the TEM. Additionally, the sample preparation techniques used in 2015 when the TRPA1 study was conducted may not have been fully optimized to achieve the highest resolution possible. Hemagglutinin also fell short of the theoretical limit by a factor of approximately 36 due to using a tilt-collection strategy to account for preferred orientation, resulting in a larger effective ice thickness and a decrease in the quality of particle images. Finally, LAT1 and TRPM8 fell short of the theoretical limit by a factor of 9.8 and 6.3, respectively, indicating that there is still room for improvement in sample preparation for these datasets.
+3 Discussion
+
+In this study, we introduced the CryoSieve algorithm, which has the ability to estimate the minimum number of particles in a dataset, referred to as the finest subset. CryoSieve demonstrated that most particles in the final stacks are superfluous and do not contribute to reconstructing density maps. On the other hand, the minority of particles that remain in the final stacks yields superior high-resolution amplitude. We also discovered that for some datasets, the size of the finest subset comes close to the theoretical limit. Therefore, CryoSieve can, to some degree, provide insight into a long-standing question in the cryo-EM field: how close can we approach the theoretical limit in practice?
+
+Despite technical advancements that have made cryo-EM more accessible to structural biologists, sample preparation remains a major bottleneck in the workflow. Scientists and engineers are thus focusing their efforts on this challenge [48]. In single-particle analysis (SPA), sample preparation consists of two crucial steps: sample optimization and grid preparation. The former involves purifying the specimen while maintaining its optimal biochemical state. The latter entails preparing the sample for analysis in the microscope, including chemical or plasma treatment of the grid, sample deposition, and vitrification. Numerous techniques have been proposed to address macromolecular instability, but the efficacy of one approach over another depends on the sample’s characteristics [48, 49]. Currently, grid preparation results are heavily influenced by the user’s expertise and experience, which can make the process time-consuming and challenging [21, 50]. The numerous variables encountered in sample and grid preparation pose challenges in establishing cause-and-effect relationships, as researchers can only assess the sample at the molecular level using the microscope. As a result, quantitative statistics from comparisons of different sample and grid preparation protocols are still lacking, and a systematic approach is necessary to investigate trends and comprehend the fundamental mechanisms of sample behavior [51].
+
+CryoSieve has the potential to establish a metric for the quantitative evaluation of various sample preparation techniques by measuring image quality based on the gaps between the theoretical limits and the size of the finest subsets. One of the possible future directions is to address the variables encountered during sample and grid preparation and establish cause-and-effect relationships. Resolving these issues, among others, cryo-EM could become a more versatile and an even more influential technology in structural biology, potentially addressing new research questions and aiding the growth of novel methodologies as the field advances [52].
+
+Acknowledgements
+
+This work was supported by the National Key R&D Program of China (No.2021YFA1001300) (to C.B.), the National Natural Science Foundation of China (No.12271291) (to C.B.), the Advanced Innovation Center for Structural Biology (to M.H.), the Beijing Frontier Research Center for Biological
+Structure (to M.H.), and the National Natural Science Foundation of China (No.12071244) (to Z.S.). We also would like to express our gratitude to Shouqing Li and Ranhao Zhang for generously sharing their expertise and experiences in particle selection and density map reconstruction in Cryo-EM.
+
+Data availability
+
+The raw final stack datasets analyzed in this study were downloaded from the EMPIAR repository (EMPIAR-10024, EMPIAR-11233, EMPIAR-10097, EMPIAR-11120, EMPIAR-10264, EMPIAR-10330). Atomic coordinates from Protein Data Bank 6PCQ were used for the generation of simulated particles using InSilicoTEM. The finest subsets of these six experimental datasets obtained by CryoSieve can be found as Supplementary Material III.
+
+Code availability
+
+CryoSieve will be open-source upon publication and is also available upon request during the review process.
+
+Contribution
+
+C.B., M.H., and Z.S. initiated the project. M.H., Q.Z., and J.Z. developed CryoSieve and carried out testing. H.Z. provided support in using InSilicoTEM. J.Z. and M.H. analyzed the data. M.H., J.Z., and C.B. wrote the manuscript.
+
+Competing interests
+
+All other authors declare no competing interests.
+
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+Fig. 2 CryoSieve outperformed other algorithms in terms of FSC-based resolutions and Q-scores. We compared the density maps reconstructed from retained particles obtained by CryoSieve (indigo) and NCC (green), along with random (orange) as the baseline, at different retention ratios. Density maps were ab initio reconstructed by CryoSPARC after discarding the published refined Euler angles deposited on EMPIAR. Four metrics were employed for measuring density map quality: FSC-based resolutions, including model-to-map (solid lines with squares) and two-half-maps (solid lines with diamonds) resolutions, are shown in the first column; meanwhile, Q-scores of the raw maps (dashed lines with circles) and the sharpened maps (solid lines with circles) are shown in the second column, as Q-score varies by the B-factor used for sharpening. B-factors for sharpening were self-determined by CryoSPARC. The iterations where CryoSieve obtained the finest subset, determined by comprehending these metrics, are labeled with hatched bars.
+
+![Line plots comparing FSC resolution and Q-score for various density maps, with CryoSieve, NCC, and random as baselines, across different retention ratios.](page_186_349_1077_1012.png)
+Fig. 3 The two-dimensional resolution distribution between retained and removed particles was compared. The third iteration of CryoSieve achieved a retention ratio of 51.2% and a removal ratio of 48.8%, resulting in a similar number of particles for retention and removal. These two categories underwent CryoSPARC 2D clustering and averaging, i.e., 2D classification, with the number of 2D classes set to 50. All six experimental datasets were tested. CryoSPARC reported the 2D resolution of each 2D class, along with the number of particle images belonging to it. We statistically analyzed the number of particles belonging to each 2D resolution and plotted histograms, demonstrating the difference between retained (steel blue) and removed (crimson) particles in terms of 2D resolution distribution.
+Fig. 4 CryoSieve prioritizes the removal of radiation-damaged particles. (a), InSilicoTEM generated simulated particle images with different levels of radiation damage. The parameter \( M_b \) in InSilicoTEM, ranging from 0 to 4, mimicked different levels of radiation damage, with higher \( M_b \) leading to weaker high-frequency signals and blurrier particles (clean, upper row). Noise, also generated by InSilicoTEM through physical process simulation, was then added to the clean particles to obtain noisy particles for testing (noisy, lower row). (b), The proportions of particles with varying levels of radiation damage (distinguished by colors) in retained particles at different retention ratios (labeled on the left) are shown. The retained particles obtained by CryoSieve (left horizontal bars) and NCC (right horizontal bars) were compared. NCC performed acceptably for particles with high radiation damage, but was unable to distinguish particles with relatively low radiation damage. Meanwhile, CryoSieve sequentially sieved out particles from high to low radiation damage. The accuracy (the proportion of zero radiation damage particles) of CryoSieve was 91.7% at iteration 7, while that of NCC was only 61.5%. (c), Side chains of density maps reconstructed by cryoSPARC using retained particles obtained by CryoSieve (indigo) and NCC (green) were compared. The atomic model (PDB 6PCQ) was fitted into the density maps. The two reconstruction maps are compared at an identical contour. Red arrows emphasize differences between the two maps. (d) Model-to-map FSCs of reconstructed density maps using retained particles were compared, with retention ratio of 21.0% (iteration 7). Retention particles were obtained by CryoSieve (indigo), NCC (green) and random (baseline method, orange), respectively. The FSC threshold (FSC = 0.5) was depicted as a horizontal dashed line.
+Methods
+
+Details of comparing the performance of particle sorting algorithms.
+
+Since cryo-EM single-particle image processing software has experienced rapid development in the past few years, some of the final stacks deposited in EMPIAR can be better processed by state-of-the-art algorithms. To eliminate effects from different refinement software and their versions, ensuring fair comparisons between various particle sorting algorithms, the final stacks deposited on EMPIAR were reprocessed under a standard workflow using CryoSPARC v4.1.0 following a standard workflow. For hemagglutinin, the initial model was generated by low-pass filtering its atomic model to 30Å, while for the other proteins, initial models were generated by arbitrary random initialization using CryoSPARC. Then, uniform refinement was applied for TRPA1, TRPM8, hemagglutinin and LAT1, while non-uniform refinement was applied for pICRT and TSHR-Gs.
+
+To enable unbiased comparisons of density maps before and after particle sorting, the retained particles obtained from each particle sorting algorithm underwent identical refinement procedures, as previously described using CryoSPARC v4.1.0 in the standard workflow. The reconstructed density maps were used for subsequent measurements. To avoid the potential influence of the ”Einstein-from-noise” effect, the former Euler angles were discarded, and new sets of Euler angles were determined through refinement of the retained particles. Moreover, in order to maintain independence between the two half sets and ensure that the Fourier Shell Correlation (FSC) served as the golden standard, half-set splits were preserved throughout the subsequent procedure by turning off the option “Force re-do GS split”.
+
+The reconstructed density maps were evaluated by several metrics, including FSC-based resolution and Q-score. CryoSPARC produced two raw half maps and an auto-postprocessed density map (FSC-weighted, B-factor sharpened, two half sets averaged), accompanied by reporting half-maps FSC.
+
+FSC-based metric includes half-maps FSC (directly reported by CryoSPARC) and model-to-map FSC. Map-to-model FSC resolution was calculated using the following procedure, with the auto-postprocessed density map as input. The corresponding atomic model of the dataset was converted to the ground-truth density map by the molmap function of Chimera at Nyquist resolution. The mask was generated from the ground-truth density map (after low-pass filtering to 8 Å, extending by 4 pixels and applying a cosine-edge of 4 pixels) using Relion. Model-to-map FSC curves were determined between the input density map (obscured by the mask) and the ground-truth density map. The resolution threshold of the map-to-model FSC was set to 0.5.
+
+As Q-score is sensitive to B-factor sharpening, the Q-scores of both the raw maps and the auto-postprocessed maps were measured. The auto-postprocessed maps were directly provided by CryoSPARC, while the raw maps were obtained by first averaging the two raw half maps provided by
+CryoSPARC, then low-pass filtering them to an appropriate resolution, in order to eliminate the impact of varying noise intensities on the density maps. The low-pass filtering threshold frequency ranged from 0.3Å to 0.5Å higher than the CryoSPARC reported half-maps FSC resolution, thus ensuring the retention of useful signals. Specifically, the threshold frequency for TRPA1 was 3.5Å, for TRPM8 and TSHR-Gs it was 2.7Å, for hemagglutinin it was 3.4Å, for pfCRT it was 3.0Å, and for LAT it was 2.8Å. Q-score was calculated using the MAPQ plugin for UCSF Chimera, with all parameters set to their default values.
+
+All conversions between CryoSPARC and Relion were performed using the pyem script.
+
+CryoSieve’s parameters.
+
+CryoSieve iteratively performs 3D reconstruction and particle sieving, while maintaining independence between two half sets by independently sieving each set of particles. 3D reconstructions of each subset were performed using Relion v4.0-beta-2, with the option “--subset” to preserve the half-set splitting. A mask, generated from the atomic model using RELION (low-pass filtered to 8 Å), was applied to the reconstructed raw density map to obtain \( x^{(k-1)} \) in Equation 2.1 of the CryoSieve score. The same mask was applied to other particle sorting algorithms such as NCC and AGC, to ensure fair comparisons. Subsequently, particles were sieved out based on the ascending order of the CryoSieve score. In total, nine iterations were carried out, with each iteration retaining 80% of the particles from the previous iteration. The cutoff frequency of the highpass operator \( H^{(k)} \) increased linearly as the iteration progressed. For all datasets, except for LAT1, the initial cutoff frequency was set at 40Å, and the final cutoff frequency was 3Å. For LAT1, the initial cutoff frequency was 50Å, and the final cutoff frequency was also 3Å.
+
+AGC’s particle removal.
+
+Incorrectly oriented particle removal by AGC was carried out using Scipion v3.0.12, following the instructions provided in its user manual. The initial volumes required for Scipion’s AGC algorithms were the reconstructed maps of all particles in final stack using Relion v4.0-beta-2, applied with a mask identical to that used in CryoSieve and NCC. The “symmetry group” parameter of AGC was set to the corresponding symmetry of the structure, while the remaining parameters were set to their default values. Since the number of particles in the LAT1 dataset is too large to perform AGC without reporting error, we partitioned them into quarter-datasets and performed AGC algorithm within each subset. The remaining particles in the quarter-datasets were used for ab initio reconstruction in cryoSPARC. Particle removal of other datasets were performed using all particles in final stacks as a whole.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementalmaterial.pdf

0db7a7b09a74a339902dc4b181b4ce940d0055363f3a89dccc6cc3d69449e21f/peer_review/peer_review.md

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+The mitochondrial mRNA-stabilizing protein SLIRP regulates skeletal muscle mitochondrial structure and respiration by exercise-recoverable mechanisms
+
+Corresponding Author: Dr Lykke Sylow
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+Pham and colleagues aimed to identify a mechanism of mitochondria regulation in skeletal muscle, involving the mitochondria mRNA stabilization through exercise and modulation of SLIRP expression. The authors demonstrate an increase in SLIRP expression after exercise stimuli. Knocking down its expression leads to mitochondria fragmentation and reduced function, with a rescue of function and morphology by exercise training.
+
+General comment
+
+The manuscript is well written and brings interesting information using exercise models in flies, mice, and humans to investigate the role of LRPPRC/SLIRP complex in mitochondrial function in skeletal muscle. However, there are several points that need to be addressed to strengthen the findings.
+
+Major issues
+
+In the figure 1, using muscle samples, the authors confirmed previous studies and showed that LRPPRC/SLIRP complex controls mtRNA encoded by mtDNA. This action could be important for mitochondrial complexes assembly or function. However, it is not clear, how LRPPRC/SLIRP complex is involved in the control of mitochondrial proteins related to structural and morphological properties, once nuclear LRPPRC/SLIRP complex seems not be involved in the stabilization of nuclear-encoded mRNA regulators, including TFAM, TFB1M, and TFB2M, nor in the stabilization of the nuclear-encoded OxPhos subunits (PMID: 19680543). This issue must be carefully addressed.
+
+It is important to point out that mRNA levels/stability are strongly modulated in the first exercise sessions and protein content stabilized in response to a few weeks or months of training (PMID: 27508878). It would be interesting to monitor mtRNA levels/stability in response to acute exercise in the absence of SLIRP.
+
+SLIRP is not a exclusive mitochondrial protein, so, mitochondrial and nuclear SLIRP and LRPPRC fractions must be monitored under rest and after exercise.
+
+The figure 1B is hard to follow. In the results, methods, and legend figure section I could not find if adenovirus was injected in control and/or in KO mice. Based on the phrase“due to downregulation of endogenous SLIRP protein”, I supose that the experiment was conducted in KO mice, however, different from figure 1B, SLIRP protein content was clearly detectable in fig 1C. The number of animals used in this experiment needs to be informed.
+
+In the figures 1C and D it is not clear why FDB and gastrocnemius muscle was used for analyzes. SLIRP content was not determined in FDB muscle the initial screening (Fig1A),and SLIRP is poorly expressed in the gastrocnemius muscle. It would be expected that these experiments would be conducted on the soleus muscle.
+
+In figure 4, the chronic exercise protocol increased SLIRP and LRPPRC protein content in muscle of WT mice (4H), but mtRNA levels were not changed in these animals (4E). How may the authors conciliate these results with the study
+hypothesis?
+
+In mtDNA copy number assessment(Fig 4. lines 311-313), it is not clear how crucial SLIRP would be in maintaining RNA stability. A reliable technique to evaluate RNA stability would be measuring the mRNA kinetics through transcription inhibition in vivo.
+
+Figure 5 E-H. The redox response framework involves a large number of proteins and mechanisms. It is not clear why PRDX3 content is reduced in SLIRPKO mice. It seems superficial to state that exercise restored oxidative stress defense systems by evaluating only monomeric levelsof PRDX3. Acutely exercise can activate other mechanisms, including the mitochondrial-unfoldedresponse (UPRmt) (PMID: 37821006) and integrated stress response (ISR) (PMID:38242693) to reduces the mitochondrial stress and improves the milochondrial quality and function. This issue should be explored appropriately, and the activation of these alternative mechanisms induced by exercise to improves mitochondrial quality control should be at least discussed.
+
+Minor points
+
+The SLIRP and LRPPRC interaction, functionand importance was superficially described in the introduction. The role of the nuclear SLIRP/LRPPRC complex should be mentioned.
+
+In figure 1H, the authors describe the evaluation of maximal respiratory capacity of the mitochondria by the addition of glutamate and succinate. This analysis of glutamate+succinate+ADP give us the OXPHOS capacity. The maximal respiratorycapacity is assessed by adding an uncoupler(eg. CCCP, FCCP).
+
+Line 157 typo doubling the word “in”
+
+In the legend of Fig1B, the author mentioned that recombinant adeno-associated virus (rAAV6:SLIRP) and rAAV6:eGFP were used. Probably this informationis related to Figure 1C.
+
+Please replaceComplex V (CV) to ATPase complex or ATPase.
+
+Line 309 please change 4F to 4E.
+
+Reviewer #2
+
+(Remarks to the Author)
+Summary.
+
+This paper examines the role of the mitochondrial mRNA stabilizing protein, SLIRP1, in regulating skeletal muscle energy metabolism at baseline and in response to exercise training. The investigators’ interest in this protein stems from their previous work wherein a proteomics analyses of mouse muscles revealed that SLIRP1 is upregulated in in response to exercise training. SLIRP1 forms a complex with LRPPRC, and together these proteins are known to regulate mt-mRNA stability and polyadenylation of mt-DNA encoded transcripts in cells other than myocytes. The biology and physiological relevance of SLIRP1 has yet to be elucidated in skeletal muscle. Considering that adaptations and perturbations in muscle mitochondrial function are central to the biology of exercise training, aging, and various metabolic diseases; these investigators sought to explore the role of SLIRP1 in muscles of sedentary and exercise trained mice using a mouse model with global knockout (KO) of the gene/protein.
+
+Investigators report that SLIRP1 and LRPPRC protein levels in muscle increase in response to exercise training in both mice and humans, due in part to signaling mechanisms involving Pgc1a. KO of SLIRP1 in mouse muscles resulted in diminished abundance of mitochondrially-encoded mRNAs along with structurally abnormalities in muscle mitochondria detected by transmission electron microscopy. Nonetheless, exercise training-induced improvements in respiratory function remained evident in KO muscles, despite low mt-mRNA levels. The investigators proposed a working model wherein the SLIRP1/LRPPRC complex stabilizes mt-mRNAs to regulate mitochondrial respiratory function at baseline, whereas exercise training bypasses this level of regulation by increasing mitoribosomal translation, thereby enhancing mitochondrial structure and function.
+
+General comments.
+
+The findings are interesting and provocative; and help to elucidate SLIRP1-dependent and independent regulation of mitochondrial function in skeletal muscle. While the report addresses a relatively novel and clinically significant area of investigation, in its current form, the conclusions put forth are not fully supported by the evidence provided. The findings show that loss of SLIRP1 lowers LRPPRC and mRNA levels of mtDNA transcripts, but this molecular signature had minimal impact on function, both at baseline and in response to exercise training. The mechanisms underlying the maintenance and exercise responsiveness of mitochondrial respiratory function in KO mice would be of strong interest to the metabolic research community. Overall, the work was viewed as original, and the findings are intriguing, but in its current form the science is largely descriptive and the conclusions remain speculative.
+
+Specific comments.
+1. The narrative implies that loss of SLIRP1 compromises mitochondrial quality and function. While the EM images reveal some structural differences, the functional measures (Figure 1H and 1I and S. Fig 2) show minimal differences between genotypes. Likewise, the KO does not appear to affect body composition, lean mass, muscle weights, blood lactate, muscle fat oxidation, and exercise tolerance (Figure S2). Therefore, there is very little evidence that KO of SLIRP1 and the resulting degradation of LRPPRC has much, if any, functional impact.
+
+2. Did the KO of SLIRP1 and diminished levels of mtDNA-encoded mRNAs result in lower levels of mitochondria and/or mt-encoded proteins? (i.e. westerns to match Figure 1J).
+
+3. The results described in Figure 4 (ExTr experiment) showed very little effect of the exercise training intervention in the WT group, both functionally and at a molecular level. In this experiment, the ET-induced increases in SLIRP1 and LRPPRC in WT mice were not so convincing (4C), and the western blot (4H) does not appear to be representative of the average response. These results conflict with those shown in Figure 2F and confuse the overall interpretation.
+
+4. The results described in Figure 6 show that exercise training increases SLIRP and LRPPRC in humans. Did the change in these proteins correlate with mt-RNA levels (Fig 6F), mitochondrial proteins (S. Fig 3) and/or other functional outcomes?
+
+5. The report relies on one piece of evidence–the increase in MRPL11 protein in muscles of ET/KO mice (Fig 5B), to support speculation that mitoribosome capacity is enhanced in KO muscles, which in turn is proposed to maintain or augment mitochondrial respiratory function. Further evidence to bolster the conclusions pertaining to mitoribosome capacity could significantly enhance the mechanistic aspect and overall value of the paper.
+
+Minor
+
+1. Figure 1 or S1. Please provide a western blot analysis of SLIRP1 proteins in tissues from the KO mice, similar to Fig 1a for the WT mice. Additionally, it would be helpful to provide assessment of SLIRP1 protein in isolated mitochondrial from the various muscles listed in Fig1a to clarify whether the low levels in some muscles (e.g. gastroc) reflects mitochondrial content or mitochondrial protein composition.
+
+Reviewer #3
+
+(Remarks to the Author)
+Overall, I find this paper interesting and likely to be of interest to many readers too. The roles of LRPPRC-SLIRP complex in mt-mRNA stabilization and polyadenylation were well-known, but using Slirp KO mice and human, the authors showed the plasticity of muscle SLIRP level upon exercise, the role of SLIRP in glucose level maintenance, and the effect of exercise on mitochondrial morphology and insulin secretion even upon Slirp KO, which were surprising and intriguing. There are, however, many points that need further investigations and/or toning down of overstatements, as described below.
+
+Major points:
+
+1. The phenotypes of Slirp KD flies are interesting but the fly investigations are insufficiently performed. I am not sure if the SLIRP homologs in flies are really equivalent to human/mouse SLIRP. Does Slirp KD in flies result in reduction of mt-mRNAs steady-state levels? (or is there previous report on this?) If mt-mRNAs are not decreased in Slirp KD flies, the whole fly results need to be omitted from the paper (even with that, I think that mouse and human results provide enough insights).
+
+2. Fly results (weaker muscle strength implied from climbing experiment) cannot be extended to mammals. To investigate to what extent Slirp KO affects macroscopic mouse muscle functions, the authors should perform additional forced muscle tests like mouse treadmill test (other than spontaneous running test). Considering that Slirp KO mice clearly show changes in glucose tolerance and insulin responses, I think that even if there is no clear difference in treadmill test, it is OK. Nevertheless, it is important to show how much Slirp KO does or does not affect muscle functions.
+
+3. In Slirp KO mice, mt-mRNAs steady-state levels were decreased (Fig. 1J). From this result alone, the author cannot say 'suggesting that SLIRP stabilizes mt-mRNA' (line 163). The reduced mRNA steady-state levels might be due to decreased transcription, rather than increased degradation. Although it is well-known that SLIRP downregulation accelerates mt-mRNA degradation in other cells, considering that the authors are discussing in the muscle context, they should at least check if the levels of mt 16S-rRNA and 12S-rRNA (and preferably mt-tRNAs too) are or are not reduced while mt-mRNA steady-state levels are reduced. This is because mt 12S rRNA, 16S rRNA, and mt-mRNAs and many tRNAs are polycistronically transcribed as the common precursor and can give implications on whether mRNAs are exclusively destabilized.
+
+4. PGC-1alpha is known as the master regulator for the transcription of various mitochondria-related protein genes. In Figure 2A, the reason why PGC1alpha1 overexpression was associated with increase in SLIRP protein although Slirp mRNA was not increased, is perplexing. Various previous studies have shown that SLIRP protein is stabilized by LRPPRC protein as the authors have mentioned. Thus, the authors should check the Lrpprc mRNA level and LRPPRC protein level upon PGC1alpha1 OE, to gain implications on a possibility on whether SLIRP protein increase was caused via Lrpprc mRNA increase, LRPPRC protein increase, and LRPPRC-mediated SLIRP protein increase.
+
+5. Related to the above point 4, in lines 301-303, the authors wrote that “both SLIRP and concomitantly LRPPRC were upregulated by exercise training in the gastrocnemius muscle in WT but not Slirp KO mice (Fig. 4C, D)”. However, Looking
+at Figure 4C and 4H, LRPPRC protein seems to be increased even in Slirp KO mice upon training. Of course, LRPPRC protein level is low, because SLIRP is knocked out, but LRPPRC protein appears to have increased upon exercise. For the experiment in Figure 4C, the authors should check and show Lrpprc mRNA levels to gain implications on how mt-mRNAs are regulated, considering that SLIRP is a tiny protein with just one RNA regoniction motif (RRM) domain and LRPPRC is a big protein with many PPR motifs that bind to RNAs.
+
+6. Related to the above point 5, In Figure 4E, the mt-mRNA levels appear to be increased in Slirp KO mice upon training compared to the resting mice, although the authors wrote in lines 307-309 “downregulation of mt-mRNA transcripts in SED Slirp KO muscle … remained reduced in ET Slirp KO mice relative to WT ET mice”. Upon exercise, increased PGC1alpha might increase mt-mRNA stabilizing protein LRPPRC and perhaps mitochondrial transcription factors too. I think that the result is interesting, but I am afraid that the authors’ interpretations and descriptions may be inappropriate.
+
+7. Lines 330-331: “Exercise training increases mitochondrial protein translational capacity by elevating mitoribosome mass” is a strong overstatement, overstating in two ways. First, the authors have only checked the amount of 12S rRNA and MRPL11 protein. 12S rRNA and MRPL11 cannot be regarded as representatives of “mitoribosome mass”. How about 16S rRNA (large subunit rRNA) and >50 mitoribosomal proteins? Second, upon exercise, PGC1alpha is increased and this might cause increase in mitochondrial transcription via upregulation of mitochondrial transcription-related proteins that produce polycistronic precursor RNA. And, the polycistronic RNA is cleaved at intervening tRNAs to produce the 12S rRNA, 16S rRNA, mRNAs and many tRNAs (tRNA punctuation model). Thus, increased 12S rRNA implies possibilities including increased transcription of the mitochondrial precursor RNA (or decreased mitochondrial RNA degradation by PNase-SUPV3L1 complex). In such case, increased mt-tRNAs may also contribute to increased mitochondrial protein levels. Therefore, the authors should 1) check the amount of “mitoribosome mass” (maybe by proteomics? to check mitoribosomal protein levels, and 16S rRNA RT-qPCR) and also 2) perform mt-tRNA quantification by northern blots or mt-tRNA sequencing.
+
+Minor points:
+1. Why is there a stronger effect of Slirp2 KD in the climbing test than Slirp1 KD but less effect on starvation tolerance or lifespan? Possibilities or hypotheses should be described somewhere.
+
+2. Lines 328-329 “These findings point towards unidentified mechanisms by which ET improves translational efficiency to dictate final protein content”: increased protein level does not “suggest” improved translation. Increased protein level might be due to decreased protein degradation. The description is an overstatement and needs to be appropriately toned down.
+
+3 I think that rather than “protein translation”, words like “mRNA translation” or “protein synthesis” are more widely used and accepted by many researchers in the field of protein synthesis.
+
+Reviewer #4
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #5
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Version 2:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The current version sounds better.
+The authors addressed almost all issues raised by this reviewer, except the measuremet of mRNA stability in the absence of Slirp1 in vivo, once SLIRP KO mouse line has been discontinued.
+In addition, they performed additional analysis including, the cytosolic and mitochondrial fraction analysis of SLIRP1, mt-mRNA evaluation in female mice and the ISR and UPRmt evaluation in the skeletal muscle, as requested.
+Finally, the minor issues were totally addressed.
+I have no additional question.
+
+Reviewer #2
+(Remarks to the Author)
+In their responses to the reviewers, the authors agreed that complete loss of SLIRP/LRPPRC complexes in KO mice resulted in surprisingly mild functional consequences, despite the marked reduction in mt-mRNA. They also offered unpublished observations that functional impact becomes more evident as animals age, but unfortunately these data are not reported. Overall, many of the key interpretations and takeaways remain weakly supported by the data provided in the manuscript. The investigators are encouraged further temper their language and conclusions.
+
+The revised manuscript highlights the following conclusions:
+
+1. SLIRP regulates mitochondrial structure, respiration, and mtDNA-encoded-mRNA pools in skeletal muscle.
+
+As acknowledged by the authors, the impact of the SLIRP KO on mitochondrial structure and function is quite modest. The finding that stands out most is that, despite complete loss of SLIRP/LRPPRC and marked reductions in mtDNA-encoded mRNA pools, baseline mitochondrial function in skeletal muscle is only modestly reduced, while muscle fat oxidation and whole-body physiological function remain unaffected.
+
+2. We identify a mechanism of post-transcriptional mitochondrial regulation in muscle via mitochondrial mRNA stabilization.
+
+As noted by reviewer 1, the report does not include direct measures of mRNA stability, although the data are certainly suggestive of this mechanism.
+
+3. Exercise training effectively counteracts mitochondrial defects caused by loss of LRPPRC/SLIRP loss, despite sustained low mtDNA-encoded-mRNA pools, by increasing mitoribosome translation capacity and mitochondrial quality control.
+
+This conclusion remains speculative. At a descriptive level, the interpretation aligns with changes in mitochondrial OXPHOS and mitoribosome proteins measured in male mice, but it’s contradicted by the same measures made in female mice, even though the modest baseline deficits in mitochondrial respiration were fully rescued by low volume wheel running in both males and females. The conflicting results in figures 4-5 (male) vs S. figure 3 (female) imply that enhanced mito ribosome translation capacity and mito quality control are not required for the recovery, and/or the underlying mechanisms are sexually dimorphic.
+
+4. Muscle levels of SLIRP and LRPPRC are upregulated by exercise training, but SLIRP is dispensable for most whole-body adaptations to exercise training, aside from improvements in blood glucose regulation (in male mice only).
+
+Unfortunately, the exercise stimulus and corresponding adaptations were very modest in this study due to the low volume of voluntary wheel running. This low volume wheel running did not upregulate protein levels of SLIRP and LRPPRC in the corresponding exercise training study. The results show that adaptations to low volume/low intensity exercise training do not require SLIRP. However, still unanswered is whether training-induced adaptations in response to a more vigorous exercise regimen (one that causes more robust induction of both SLIRP and mitochondrial biogenesis) would be affected by SLIRP KO.
+
+Also, considering that the only metric of glucose homeostasis affected by total body SLIRP KO was fasting blood glucose in males, perhaps this points to regulation at the level of hepatic glucose output rather than muscle glucose uptake and metabolism.
+
+Summary
+
+In aggregate, the findings show that SLIRP is crucial for regulating mito-encoded mRNA pools in skeletal muscle. The observations that complete loss of SLIRP/LRPPRC and marked reductions in mtDNA-encoded mRNA pools had only modest effects on baseline mitochondrial respiration, skeletal muscle function and whole-body physiology; along with the finding the low-volume exercise can rescue mild genetic defects in mitochondrial function despite the remarkable depletion of mtDNA-encoded mRNA pools, are important findings that support the notion that habitual physical activity can overcome at least some modest mitochondrial defects. The role of SLIRP in regulating muscle energy metabolism during aging and higher volume/intensity exercise remains uncertain and is certainly worthy of future study.
+
+Conclusions pertaining to exercise-induced upregulation of mtDNA-encoded OXPHOS proteins, mito quality control, and mitoribosome translation capacity were supported by findings in male but not female mice, implying yet unknown mechanisms and/or some level of sexual dimorphism.
+
+Reviewer #3
+
+(Remarks to the Author)
+My previous concerns have nicely been addressed. Additional data filled in the previous gaps or strengthened the authors’ conclusions, and sentences were also carefully improved. How exercise improved the various aspects of mitochondrial and even cytoplasmic proteostasis and quality control (mitoribosomal components, LONP1, and even phosphorylated eIF2alpha) in Slrp KO mice was amazing.
+I could smoothly read the revised manuscript with a lot of excitement and without feeling concerns. I look forward to seeing this paper to be published and the insights be shared to the world.
+
+Reviewer #4
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #5
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Version 3:
+
+Reviewer comments:
+
+Reviewer #2
+
+(Remarks to the Author)
+The authors addressed the concerns noted previously through editorial revisions. No additional comments.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Pham and colleagues aimed to identify a mechanism of mitochondria regulation in skeletal muscle, involving the mitochondria mRNA stabilization through exercise and modulation of SLIRP expression. The authors demonstrate an increase in SLIRP expression after exercise stimuli. Knocking down its expression leads to mitochondria fragmentation and reduced function, with a rescue of function and morphology by exercise training.
+
+General comment
+
+The manuscript is well written and brings interesting information using exercise models in flies, mice, and humans to investigate the role of LRPPRC/SLIRP complex in mitochondrial function in skeletal muscle. However, there are several points that need to be addressed to strengthen the findings.
+
+We thank the reviewer for taking the time to provide constructive feedback on our manuscript and for the useful suggestions. We have now addressed all the comments and believe that this has improved the manuscript and strengthened the conclusions. Please see below our point-by-point replies on how we have addressed the issues raised.
+
+Major issues
+
+In the figure 1, using muscle samples, the authors confirmed previous studies and showed that LRPPRC/SLIRP complex controls mtRNA encoded by mtDNA. This action could be important for mitochondrial complexes assembly or function. However, it is not clear, how LRPPRC/SLIRP complex is involved in the control of mitochondrial proteins related to structural and morphological properties, once nuclear LRPPRC/SLIRP complex seems not be involved in the stabilization of nuclear-encoded mtRNA regulators, including TFAM, TFB1M, and TFB2M, nor in the stabilization of the nuclear-encoded OxPhos subunits (PMID: 19680543). This issue must be carefully addressed.
+
+We thank the reviewer for raising this valid concern, which is a highly interesting biological question. Unfortunately, the mouse line has been discontinued but with the samples already collected we have now included measures on mitochondrial quality control (this new data is added in Fig. 5, Supplementary Fig. 3 and 4). Moreover, we have toned down our interpretation of the effect of SLIRP loss on mitochondrial structure, as the effect may be isolated to IMF mitochondria, whereas subsarcolemmal mitochondria were unaffected, at this age of the mice.
+
+Line 484-489: “Interestingly, the young full-body Slirp KO mice only have a mild molecular phenotype and appear overall healthy, despite the significant decrease in mt-mRNA levels, respiration, and mitochondrial morphology. The effects of Slirp KO on mitochondrial morphology further seemed to be isolated to IMF mitochondria, whereas subsarcolemmal mitochondria were unaffected at this age. Yet, detrimental physiological long-term consequences are suggested by the flies lacking SLIRP1 given their much shorter life span.”
+
+It is important to point out that mRNA levels/stability are strongly modulated in the first exercise sessions and protein content stabilized in response to a few weeks or months of training (PMID: 27508878). It would be interesting to monitor mtRNA levels/stability in response to acute exercise in the absence of SLIRP.
+Thank you for this great suggestion. We are unable to directly measure mt-mRNA stability in the absence of SLIRP as the SLIRP KO mouse line has been discontinued but we have instead monitored muscle mt-mRNA levels in response to an acute exercise bout and over a time course (Fig. 2E).
+
+Concomitant with Slirp and Ppargc1a mRNA levels, mtDNA-encoded mt-Nd1 transcripts mt-Nd1 were significantly increased 1.5-fold 6h post-exercise, but not mt-Cox1, mt-Cox2, and mt-Atp6. While correlative, these data suggest that there may be a coordinated regulatory mechanism linking SLIRP, PGC-1a and the simultaneous upregulation of mt-Nd1 mRNA transcripts.
+
+Line 225-228: “Concomitant with Slirp and Ppargc1a mRNA levels, mtDNA-encoded mt-Nd1 mRNA transcripts were increased 1.5-fold 6h post-exercise, but not mt-Cox1, mt-Cox2, and mt-Atp6 (Fig. 2E). These results indicate a coordinated regulatory mechanism linking SLIRP, PGC-1a and the simultaneous upregulation of mt-Nd1 mRNA transcripts.”
+
+SLIRP is not a exclusive mitochondrial protein, so, mitochondrial and nuclear SLIRP and LRPPRC fractions must be monitored under rest and after exercise.
+
+We thank the reviewer for raising this valid concern, which we have addressed by i) providing new data measuring SLIRP localization in response to muscle contraction, and ii) added text in the introduction stating that SLIRP is not an exclusive mitochondrial protein.
+
+i) Line 229-242: “SLIRP is a nuclear-encoded protein primarily targeted to mitochondria by a specific signal sequence, we next determined if muscle contractions increased the mitochondrial localization of SLIRP in cytosolic and mitochondrial fractions. To investigate this, we excised quadriceps muscles from WT mice 2 h after electrically-induced in situ contraction, using the contralateral leg muscle as a rested control, and performed an adapted subcellular fractionation assay on frozen tissue1, 2 to isolate cytosolic and mitochondrial fractions. COX4 protein was used as mitochondrial marker, and GAPDH as cytosolic marker, respectively, to assess the purity of the fractions.
+
+On a whole-tissue lysate level, SLIRP protein remained unchanged in response to contraction (Fig. 2F). SLIRP protein content tended to be 1.2-fold and 1.3-fold enriched in the cytosolic and mitochondrial fraction, respectively, following in situ muscle contraction (Fig. 2F), indicating that muscle contractions increase protein synthesis in the cytosolic and mitochondrial localization of SLIRP. Interestingly, and with the same sample input, we were able to detect SLIRP protein in the cytosolic fraction, indicating that SLIRP may not be exclusive to mitochondria in skeletal muscle. These data suggest that muscle contraction elicits a subcellular redistribution of SLIRP towards the mitochondria.“
+
+ii) Line 84-86: “SLIRP and LRPPRC, encoded by nuclear DNA, are primarily targeted to mitochondria. In addition, SLIRP may also regulate nuclear receptors by binding to steroid receptor RNA activator3, and LRPPRC may activate nuclear genes through interaction with PGC-1α4.”
+
+The figure 1B is hard to follow. In the results, methods, and legend figure section I could not find if adenovirus was injected in control and/or in KO mice. Based on the phrase“due to
+downregulation of endogenous SLIRP protein", I supose that the experiment was conducted in KO mice, however, different from figure 1B, SLIRP protein content was clearly detectable in fig 1C. The number of animals used in this experiment needs to be informed.
+
+Thank you for noting this, we have now revised the results, methods and figure legend for improving clarity that the injection was solely performed in wildtype mice.
+
+Line 128-132: “To confirm co-stabilization, we administered intramuscular injections of recombinant adeno-associated viral serotype 6 (rAAV6):Slirp into the tibialis anterior (TA) muscle of wild-type (WT) mice, while injecting a control vector into the contralateral TA muscle. As expected, in the absence of injecting vectors to concomitantly upregulate LRPPRC, total SLIRP protein content did not increase because endogenous SLIRP protein was degraded (Fig. 1C).”
+
+In the figures 1C and D it is not clear why FDB and gastrocnemius muscle was used for analyzes. SLIRP content was not determined in FDB muscle the initial screening (Fig1A),and SLIRP is poorly expressed in the gastrocnemius muscle. It would be expected that these experiments would be conducted on the soleus muscle.
+
+Thank you for bringing this to our attention. We utilized FDB muscles as they are optimized for our method. We regret that we did not initially include FDB muscles in Figure 1A. We agree with the reviewer that conducting experiments on the soleus muscle would be ideal due to its high abundance of SLIRP content. Nevertheless, we chose to use the gastrocnemius because, like the quadriceps, SLIRP is indeed expressed, and it is one of the muscle groups most responsive to the exercise training intervention. Additionally, its size allows for multiple analyses within the same muscle, enabling more conclusive interpretations. Using only the soleus would have required more mice in poor alignment with the principle of the 3Rs (Replacement, Reduction, and Refinement) in animal research ethics.
+
+In figure 4, the chronic exercise protocol increased SLIRP and LRPPRC protein content in muscle of WT mice (4H), but mtRNA levels were not changed in these animals (4E). How may the authors conciliate these results with the study hypothesis?
+
+Thank you for highlighting this important issue. We collected muscle tissue after locking the running wheels of the mice overnight to distinguish between the effects of acute exercise and exercise training.
+
+We have now included new data on the levels of mt-mRNA in female mice in Supplementary Fig. 3B, which clearly shows that mt-mRNA per se are highly responsive towards exercise training, an effect completely abrogated in the Slirp KO mice, supporting our hypothesis. The lack of observation in male mice may be owed to the running volume differences between male and female mice, which ran twice as much than their male counterparts. We have emphasized this fact in the results. Locking the wheels for the male mice, was done to single out the effects of the exercise training without the lingering effects of the last exercise bout. In hindsight, that may have compromised our ability to measure changes in mt-mRNA transcript levels in response to exercise training, as levels were comparable to sedentary controls.
+
+The following text and data have now been added:
+Line 335-338: “The sustained reduction in mt-mRNA transcripts upon Slirp KO is clearer in female mice, where exercise training significantly increased mt-mRNA transcript levels in WT mice, a response completely abrogated in Slirp KO mice (Supplementary Fig. 3B).”
+
+In mtDNA copy number assessment (Fig 4. lines 311-313), it is not clear how crucial SLIRP would be in maintaining RNA stability. A reliable technique to evaluate RNA stability would be measuring the mRNA kinetics through transcription inhibition in vivo.
+
+Thank you for raising this very important point. We acknowledge that direct measurements of RNA stability by inhibiting transcription in vivo would provide clarity on this issue. As we are unable to perform this measurement directly, we have instead measured mtDNA content for ND1 and ND6 (Fig. 1K, Supp. Fig. 2J and K). These new data reveal a slight increase under sedentary conditions in Slirp KO muscle and no change under trained conditions, thereby eliminating the possibility that the observed reduced mt-mRNA levels are attributable to decreases in mtDNA content. This suggests that the reduction in mt-mRNA levels occurs post-transcriptionally, consistent with observations in other tissues such as the heart, liver, and kidney 5.
+
+We have emphasized these results in the results section for enhanced clarity and have included them in the discussion as well.
+
+Line 166-168: “Additionally, there was an increased mtDNA copy number, estimated by measuring Nd1 and Nd6 (Fig. 1K). Those results indicate that SLIRP stabilizes mt-mRNA, and its loss adversely affects MTCO1 and MTATP6 protein content in skeletal muscle.”
+
+Line 527-529: “As mtDNA copy number was either increased in SED Slirp KO or unchanged in ET Slirp KO mice, these findings give rise to the possibility that mt-mRNAs are produced in excess in vivo5.”
+
+Figure 5 E-H. The redox response framework involves a large number of proteins and mechanisms. It is not clear why PRDX3 content is reduced in SLIRPKO mice. It seems superficial to state that exercise restored oxidative stress defense systems by evaluating only monomeric levelsof PRDX3. Acutely exercise can activate other mechanisms, including the mitochondrial-unfoldedresponse (UPRmt) (PMID: 37821006) and integrated stress response (ISR) (PMID:38242693) to reduces the mitochondrial stress and improves the mitochondrial quality and function. This issue should be explored appropriately, and the activation of these alternative mechanisms induced by exercise to improves mitochondrial quality control should be at least discussed.
+
+Thank you for raising this very important point. We have now measured markers of the integrated stress response (i.e. pEIF2a S51, EIF2A) and mitochondrial quality control (YMEI1L1, LONP1) and added these new data to the manuscript. Intriguingly, we find that exercise activates other mechanisms that can ultimately improved mitochondrial respiratory function conjointly. Thank you for your important suggestion.
+
+Line 531-549: “In response to exercise training, the mitoribosomal components, MRPL11, MRPL12, MRPS18B, 12S rRNA, and 16S rRNA were upregulated, indicating increased mitoribosome biogenesis and capacity for mitochondrial protein synthesis. These adaptations to exercise training may help sustain protein synthesis and normal physiology, even in the presence of low mt-
+mRNA abundance. The greater increase in OXPHOS, mt-rRNA, and mitoribosomal proteins in Slirp KO ET mice indicates that exercise training may be more effective in the presence of mitochondrial dysfunction, providing exciting avenues for exploring the use of exercise training in conditions of mitochondrial dysfunction. Exercise training also upregulated LONP1 and YME1L1, both important regulators of mitochondrial quality control and proteostasis, and PRDX3, linked to peroxide scavenging. While mitoribosomal protein content, \(12S\) rRNA, \(16\) S rRNA, LONP1, YME1L1, and PRDX3 may not directly control translation efficiency, their roles in the mitoribosomal makeup and improved mitochondrial quality control can influence the overall cellular environment where protein synthesis occurs. Albeit limited by not directly measuring mitochondrial translational rate, this working hypothesis is supported by findings in human skeletal muscle showing that mitochondrial protein synthesis and upregulation of mitoribosome biogenesis is at the core of exercise training-induced benefits\(^6\). That mitochondrial stress was effectively relieved via exercise training is suggested by the marked reduction in phosphorylation of EIF2a at S51, an integral marker of the ISR selectively in Slirp KO mice. This suggests a unique interaction between mitochondrial damage and the ISR, highlighting the heightened sensitivity of Slirp KO mice to exercise training."
+
+Minor points
+
+The SLIRP and LRPPRC interaction, functionand importance was superficially described in the introduction. The role of the nuclear SLIRP/LRPPRC complex should be mentioned.
+
+    Thank you. We have included evidence of nuclear SLIRP/LRPPRC in the introduction.
+
+Line 83-85: “SLIRP and LRPPRC, encoded by nuclear DNA, are primarily targeted to mitochondria. In addition, SLIRP may also regulate nuclear receptors by binding to steroid receptor RNA activator\(^3\), and LRPPRC may activate nuclear genes through interaction with PGC-1α\(^4\).”
+
+In figure 1H, the authors describe the evaluation of maximal respiratory capacity of the mitochondria by the addition of glutamate and succinate. This analysis of glutamate+succinate+ADP give us the OXPHOS capacity. The maximal respiratory capacity is assessed by adding an uncoupler(eg. CCCP, FCCP).
+
+    Thank you for raising this point, we have corrected accordingly in the results and removed the word “maximal”.
+
+Line 157 typo doubling the word “in”
+
+    Thank you for spotting this mistake, we have corrected it.
+
+In the legend of Fig1B, the author mentioned that recombinant adeno-associated virus (rAAV6:SLIRP) and rAAV6:eGFP were used. Probably this informationis related to Figure 1C.
+
+    Thank you for spotting this mistake, we have corrected it.
+Please replaceComplex V (CV) to ATPase complex or ATPase.
+
+    We have replaced Complex (CV) by ATPase in text and figures.
+
+Line 309 please change 4F to 4E.
+
+    Thank you for spotting this mistake, we have corrected it.
+
+Reviewer #2 (Remarks to the Author):
+
+Summary.
+
+This paper examines the role of the mitochondrial mRNA stabilizing protein, SLIRP1, in regulating skeletal muscle energy metabolism at baseline and in response to exercise training. The investigators’ interest in this protein stems from their previous work wherein a proteomics analyses of mouse muscles revealed that SLIRP1 is upregulated in in response to exercise training. SLIRP1 forms a complex with LRPPRC, and together these proteins are known to regulate mt-mRNA stability and polyadenylation of mt-DNA encoded transcripts in cells other than myocytes. The biology and physiological relevance of SLIRP1 has yet to be elucidated in skeletal muscle. Considering that adaptations and perturbations in muscle mitochondrial function are central to the biology of exercise training, aging, and various metabolic diseases; these investigators sought to explore the role of SLIRP1 in muscles of sedentary and exercise trained mice using a mouse model with global knockout (KO) of the gene/protein.
+
+Investigators report that SLIRP1 and LRPPRC protein levels in muscle increase in response to exercise training in both mice and humans, due in part to signaling mechanisms involving Pgc1a. KO of SLIRP1 in mouse muscles resulted in diminished abundance of mitochondrially-encoded mRNAs along with structurally abnormalities in muscle mitochondria detected by transmission electron microscopy. Nonetheless, exercise training-induced improvements in respiratory function remained evident in KO muscles, despite low mt-mRNA levels. The investigators proposed a working model wherein the SLIRP1/LRPPRC complex stabilizes mt-mRNAs to regulate mitochondrial respiratory function at baseline, whereas exercise training bypasses this level of regulation by increasing mitoribosomal translation, thereby enhancing mitochondrial structure and function.
+
+General comments.
+
+The findings are interesting and provocative; and help to elucidate SLIRP1-dependent and independent regulation of mitochondrial function in skeletal muscle. While the report addresses a relatively novel and clinically significant area of investigation, in its current form, the conclusions put forth are not fully supported by the evidence provided. The findings show that loss of SLIRP1 lowers LRPPRC and mRNA levels of mtDNA transcripts, but this
+molecular signature had minimal impact on function, both at baseline and in response to exercise training. The mechanisms underlying the maintenance and exercise responsiveness of mitochondrial respiratory function in KO mice would be of strong interest to the metabolic research community. Overall, the work was viewed as original, and the findings are intriguing, but in its current form the science is largely descriptive and the conclusions remain speculative.
+
+We wish to thank the reviewer for reviewing our manuscript. We greatly appreciate the feedback and useful suggestions. Please find below details on how we have addressed all the excellent concerns raised and we believe that the changes have provided basis for more robust conclusions and mechanistic explanations.
+
+Specific comments.
+
+1. The narrative implies that loss of SLIRP1 compromises mitochondrial quality and function. While the EM images reveal some structural differences, the functional measures (Figure 1H and 1I and S. Fig 2) show minimal differences between genotypes. Likewise, the KO does not appear to affect body composition, lean mass, muscle weights, blood lactate, muscle fat oxidation, and exercise tolerance (Figure S2). Therefore, there is very little evidence that KO of SLIRP1 and the resulting degradation of LRPPRC has much, if any, functional impact.
+
+Thank you for raising this very important point. We agree with the reviewer that the functional consequences of loss of SLIRP/LRPPRC complexes in these young mice show only mild effects, despite the marked reduction in mt-mRNA. We have now toned down our interpretation accordingly.
+
+In parallel, but unpublished, work in inducible skeletal muscle-specific LRPPRC knockout mice, we observe strong age-dependent effects. When the mice are young, they are fully able to compensate for the mitochondrial genetic insult, yet as the mice age, body composition, lean mass, muscle weights and strength are markedly impaired. This shows that the loss of LRPPRC/SLIRP has long-term consequences which at younger age can be mitigated through compensatory mechanisms.
+
+The long-term consequences of lack of muscle SLIRP are illustrated by our fly data which show reduced life span in flies lacking SLIRP. Those data underscore that lack of muscle SLIRP long-term has a negative impact on muscle function and life span.
+
+We have now added a discussion of this interplay in the discussion as described below:
+
+Line 484-489: “Interestingly, the young full-body Slirp KO mice only have a mild molecular phenotype and appear overall healthy, despite the significant decrease in mt-mRNA levels, respiration, and mitochondrial morphology. The effects of Slirp KO on mitochondrial morphology further seemed to be isolated to IMF mitochondria, whereas subsarcolemmal mitochondria were unaffected at this age. Yet, detrimental physiological long-term consequences are suggested by the flies lacking SLIRP1 given their much shorter life span.”
+2. Did the KO of SLIRP1 and diminished levels of mtDNA-encoded mRNAs result in lower levels of mitochondria and/or mt-encoded proteins? (i.e. westerns to match Figure 1J).
+
+We have now included the Westerns to match the mt-mRNA levels in Fig. 1J.
+
+3. The results described in Figure 4 (ExTr experiment) showed very little effect of the exercise training intervention in the WT group, both functionally and at a molecular level. In this experiment, the ET-induced increases in SLIRP1 and LRPPRC in WT mice were not so convincing (4C), and the western blot (4H) does not appear to be representative of the average response. These results conflict with those shown in Figure 2F and confuse the overall interpretation.
+
+Thank you for your comment. As described in the text (now Line: 266), we have mentioned that the mice in our exercise training intervention on average ran 2.4 km/day, which is lower than what mice usually run. We speculate that this is an age-dependent decline in voluntary running. This may have resulted in a lower ET-induced increase in SLIRP and LRPPRC in WT mice. On this basis and the difference in voluntary running between cohorts of mice, we respectfully disagree that Fig. 4 and Fig. 2 are conflicting. Yet, we understand that it may seem confusing and hence, added an additional sentence to underline that Fig. 4 is to be interpreted under the framework of relatively low volume of voluntary wheel running.
+
+Line 270-272: “It is important to consider that the running distance observed in our study of 18-week old mice is shorter than those reported in other exercise training studies using ~ 10-week-old mice, which typically run 6-8 km/day on average7-9.”
+
+4. The results described in Figure 6 show that exercise training increases SLIRP and LRPPRC in humans. Did the change in these proteins correlate with mt-RNA levels (Fig 6F), mitochondrial proteins (S. Fig 3) and/or other functional outcomes?
+
+We have now included correlation analyses between SLIRP protein, and LRPPRC, and OXPHOS proteins (Supplementary Fig. 5B). This new data shows that there is a positive correlation, albeit at different degrees, between SLIRP, LRPPRC and the OXPHOS proteins in human skeletal muscle.
+
+Line 446-449: “Our correlation analysis in this cohort revealed that SLIRP protein content was positively associated with LRPPRC (r^2=0.2901) and several OXPHOS proteins, specifically NDUFB8 (r^2=0.1487), SDHB (r^2=0.4020), UQCRC2 (r^2=0.1110), MT-CO2 (r^2=0.0528), and ATP5A (r^2=0.1141, Supplementary Fig. 5).”
+
+5. The report relies on one piece of evidence–the increase in MRPL11 protein in muscles of ET/KO mice (Fig 5B), to support speculation that mitoribosome capacity is enhanced in KO muscles, which in turn is proposed to maintain or augment mitochondrial respiratory function. Further evidence to bolster the conclusions pertaining to mitoribosome capacity could significantly enhance the mechanistic aspect and overall value of the paper.
+
+Thank you for pointing this out. We have now included new data on additional mitoribosomal proteins, both of small and large subunits, to support our speculation that mitoribosome biogenesis and capacity was enhanced in the KO muscles upon training.
+We have also now included measures on ISR (i.e. pEIF2a S51, EIF2A), and mitochondrial quality control (YMEIL1, LONP1) into the manuscript and show that exercise indeed activates other mechanisms that can ultimately augment mitochondrial respiratory function conjointly.
+
+Line 531-549: “In response to exercise training, the mitoribosomal components, MRPL11, MRPL12, MRPS18B, 12S rRNA, and 16S rRNA were upregulated, indicating increased mitoribosome biogenesis and capacity for mitochondrial protein synthesis. These adaptations to exercise training may help sustain protein synthesis and normal physiology, even in the presence of low mt-mRNA abundance. The greater increase in OXPHOS, mt-tRNA, and mitoribosomal proteins in Slirp KO ET mice indicates that exercise training may be more effective in the presence of mitochondrial dysfunction, providing exciting avenues for exploring the use of exercise training in conditions of mitochondrial dysfunction. Exercise training also upregulated LONP1 and YME1L1, both important regulators of mitochondrial proteostasis, and PRDX3, linked to peroxide scavenging. While mitoribosomal protein content, 12S rRNA, 16 S rRNA, LONP1, YME1L1, and PRDX3 may not directly control translation efficiency, their roles in the mitoribosomal makeup and improved mitochondrial quality control can influence the overall cellular environment where protein synthesis occurs. Albeit limited by not directly measuring mitochondrial translational rate, this working hypothesis is supported by findings in human skeletal muscle showing that mitochondrial protein synthesis and upregulation of mitoribosome biogenesis is at the core of exercise training-induced benefits6. That mitochondrial stress was effectively relieved via exercise training is suggested by marked reduction in phosphorylation of EIF2a at S51, an integral marker of the ISR selectively in Slirp KO mice. This suggests a unique interaction between mitochondrial damage and the ISR, highlighting the heightened sensitivity of Slirp KO mice to exercise training.”
+
+Minor
+
+1. Figure 1 or S1. Please provide a western blot analysis of SLIRP1 proteins in tissues from the KO mice, similar to Fig 1a for the WT mice. Additionally, it would be helpful to provide assessment of SLIRP1 protein in isolated mitochondrial from the various muscles listed in Fig1a to clarify whether the low levels in some muscles (e.g. gastroc) reflects mitochondrial content or mitochondrial protein composition.
+
+    We thank the reviewer for this relevant comment. Unfortunately, addressing the reviewer’s concern directly will not be feasible, as the mouse line has been discontinued.
+
+    However, we will address this issue in an upcoming manuscript where we are investigating the effects in inducible muscle-specific Lrpprc knockout mice on mitochondrial and muscle function.
+
+Reviewer #3 (Remarks to the Author):
+Overall, I find this paper interesting and likely to be of interest to many readers too. The roles of LRPPRC-SLIRP complex in mt-mRNA stabilization and polyadenylation were well-known, but using Slirp KO mice and human, the authors showed the plasticity of muscle SLIRP level upon exercise, the role of SLIRP in glucose level maintenance, and the effect of exercise on mitochondrial morphology and insulin secretion even upon Slirp KO, which were surprising and intriguing. There are, however, many points that need further investigations and/or toning down of overstatements, as described below.
+
+We thank the reviewer for bringing some important issues to our attention and we have revised the manuscript accordingly. Thank you for taking the time and effort to review our manuscript and provide constructive feedback. We believe that by addressing the raised concerns, the manuscript has been improved and the conclusions strengthened.
+
+Major points:
+
+1. The phenotypes of Slirp KD flies are interesting but the fly investigations are insufficiently performed. I am not sure if the SLIRP homologs in flies are really equivalent to human/mouse SLIRP. Does Slirp KD in flies result in reduction of mt-mRNAs steady-state levels? (or is there previous report on this?) If mt-mRNAs are not decreased in Slirp KD flies, the whole fly results need to be omitted from the paper (even with that, I think that mouse and human results provide enough insights).
+
+Thank you for pointing this out. It has been repeatedly shown by Nils-Göran Larssons group that in Drosophila the loss of SLIRP/LRPPRC leads to a reduction in mt-mRNA steady state levels elicited^{10-12}, and we therefore believe that these data can stand on their own.
+
+We have included this in the results for clarification, including references.
+
+Line 179-182: ‘The functions of the mammalian SLIRP is carried out by two proteins in flies: *SLIRP1* and *SLIRP2*, which have been shown to interact with the fly orthologue proteins *LRPPRC1* and *LRPPRC2*, respectively, to regulate mt-mRNA polyadenylation and maturation, and coordinating mitoribosomal translation^{10-12}’
+
+2. Fly results (weaker muscle strength implied from climbing experiment) cannot be extended to mammals. To investigate to what extent Slirp KO affects macroscopic mouse muscle functions, the authors should perform additional forced muscle tests like mouse treadmill test (other than spontaneous running test). Considering that Slirp KO mice clearly show changes in glucose tolerance and insulin responses, I think that even if there is no clear difference in treadmill test, it is OK. Nevertheless, it is important to show how much Slirp KO does or does not affect muscle functions.
+
+We are showing a forced treadmill test in Supp. Fig. 2E, and G, which show no genotype-specific difference between WT and *Slirp* KO mice. We completely agree that the *Slirp* KO mice at this age show and are generally healthy, a point which we also make in the manuscript.
+
+At the age, we are investigating the *Slirp* KO mice, they are still relatively young – hence defects on mitochondrial morphology and respiration, and muscle strength are mild.
+We have now altered the wording to the following:
+
+Line 484-489: “Interestingly, the young full-body Slirp KO mice only have a mild molecular phenotype and appear overall healthy, despite the significant decrease in mt-mRNA levels, respiration, and mitochondrial morphology. The effects of Slirp KO on mitochondrial morphology further seemed to be isolated to IMF mitochondria, whereas subsarcolemmal mitochondria were unaffected at this age. Yet, detrimental physiological long-term consequences are suggested by the flies lacking SLIRP1 given their much shorter life span.”
+
+3. In Slirp KO mice, mt-mRNAs steady-state levels were decreased (Fig. 1J). From this result alone, the author cannot say ‘suggesting that SLIRP stabilizes mt-mRNA’ (line 163). The reduced mRNA steady-state levels might be due to decreased transcription, rather than increased degradation. Although it is well-known that SLIRP downregulation accelerates mt-mRNA degradation in other cells, considering that the authors are discussing in the muscle context, they should at least check if the levels of mt 16S-rRNA and 12S-rRNA (and preferably mt-tRNAs too) are or are not reduced while mt-mRNA steady-state levels are reduced. This is because mt 12S rRNA, 16S rRNA, and mt-mRNAs and many tRNAs are polycistronically transcribed as the common precursor and can give implications on whether mRNAs are exclusively destabilized.
+
+Thank you for raising this valid concern. We have now analyzed and included new data on both 12S rRNA and 16S rRNA in Fig. 5A. These show that transcription was normal in sedentary Slirp KO mice, which interestingly suggest that the reduction in mt-mRNA steady state are likely attributable to processes downstream of transcription. This is particularly evident under trained conditions, where the reductions in mt-mRNA steady-state levels remain reduced, but 12S rRNA and 16S rRNA are markedly upregulated.
+
+Furthermore, we have assessed mtDNA content for ND1 and ND6 (Supp. Fig. 2J and K). Thes new results reveal a slight increase under sedentary conditions and no change under trained conditions, thereby eliminating the possibility that the observed reduced mt-mRNA levels are attributable to decreases in mtDNA content. This suggests that the reduction in mt-mRNA levels occurs post-transcriptionally, consistent with observations in other tissues such as the heart, liver, and kidney5.
+
+We have emphasized these new results in the results section for enhanced clarity and have included them in the discussion as well.
+
+Line 166-168: “Additionally, there was an increased mtDNA copy number, estimated by measuring Nd1 and Nd6 (Fig. 1K), suggesting that SLIRP stabilizes mt-mRNA, and its loss adversely affects MTCO1 and MTATP6 protein content in skeletal muscle.”
+
+Line 531-537: “In response to exercise training, the mitoribosomal components, MRPL11, MRPL12, MRPS18B, 12S rRNA, and 16S rRNA were upregulated, indicating increased mitoribosome biogenesis and capacity for mitochondrial protein synthesis. These adaptations to exercise training may help sustain protein synthesis and normal physiology, even in the presence of low mt-mRNA abundance. The greater increase in OXPHOS, mt-rRNA, and mitoribosomal proteins in Slirp KO ET mice indicates that exercise training may be more effective in the presence of mitochondrial dysfunction,
+providing exciting avenues for exploring the use of exercise training in conditions of mitochondrial dysfunction."
+
+4. PGC-1alpha is known as the master regulator for the transcription of various mitochondria-related protein genes. In Figure 2A, the reason why PGC1alpha1 overexpression was associated with increase in SLIRP protein although Slirp mRNA was not increased, is perplexing. Various previous studies have shown that SLIRP protein is stabilized by LRPPRC protein as the authors have mentioned. Thus, the authors should check the Lrpprc mRNA level and LRPPRC protein level upon PGC1alpha1 OE, to gain implications on a possibility on whether SLIRP protein increase was caused via Lrpprc mRNA increase, LRPPRC protein increase, and LRPPRC-mediated SLIRP protein increase.
+
+Thank you for raising this valid concern. We are currently investigating the relationship between PGC1a1 and LRPPRC in another manuscript where we have explored the Lrpprc mRNA (left bar graph below) and LRPPRC protein (right bar graph below) levels in PGC1a1 overexpressing (OE) mice. For the reviewer's reference, we are including the data here, which shows that Lrpprc mRNA levels are similar in PGC1a1 OE muscle, but there is an increase in protein content, consistent with our observations for SLIRP. If the reviewer insists on including these data in the current manuscript, we will comply, but we respectfully request to reserve these findings for our upcoming manuscript that aims to explore the functional role of LRPPRC in skeletal muscle.
+
+![Bar graphs showing Lrpprc mRNA and LRPPRC protein levels in WT and PGC-1α1 OE muscles](page_355_682_740_312.png)
+
+5. Related to the above point 4, in lines 301-303, the authors wrote that “both SLIRP and concomitantly LRPPRC were upregulated by exercise training in the gastrocnemius muscle in WT but not Slirp KO mice (Fig. 4C, D)”. However, Looking at Figure 4C and 4H, LRPPRC protein seems to be increased even in Slirp KO mice upon training. Of course, LRPPRC protein level is low, because SLIRP is knocked out, but LRPPRC protein appears to have increased upon exercise. For the experiment in Figure 4C, the authors should check and show Lrpprc mRNA levels to gain implications on how mt-mRNAs are regulated, considering that SLIRP is a tiny protein with just one RNA regoniction motif (RRM) domain and LRPPRC is a big protein with many PPR motifs that bind to RNAs.
+Thank you for raising this valid concern and we appreciate our shared interest in SLIRPs binding partner, LRPPRC. In connection to our response above, we are currently investigating the role of LRPPRC in exercise training mediated adaptations in another manuscript where we will look at the Lrpprc mRNA, LRPPRC protein levels and mt-mRNA in inducible muscle-specific LRPPRC knockout mice in exercise training settings. We respectfully request to reserve these findings for our upcoming manuscript that aims to explore the functional role of LRPPRC in skeletal muscle.
+
+6. Related to the above point 5, In Figure 4E, the mt-mRNA levels appear to be increased in Slirp KO mice upon training compared to the resting mice, although the authors wrote in lines 307-309 “downregulation of mt-mRNA transcripts in SED Slirp KO muscle … remained reduced in ET Slirp KO mice relative to WT ET mice”. Upon exercise, increased PGC1alpha might increase mt-mRNA stabilizing protein LRPPRC and perhaps mitochondrial transcription factors too. I think that the result is interesting, but I am afraid that the authors’ interpretations and descriptions may be inappropriate.
+
+Thank you for your important comment.
+
+To strengthen the basis of our interpretation, we have now included new data on the levels of mt-mRNA in female mice in Supplementary Fig. 3B, which clearly shows that mt-mRNA per se are responsive towards exercise training, and where the downregulated mt-mRNA transcripts in Slirp KO mice remain reduced in ET Slirp KO mice.
+
+It is possible that exercise training could elevate residual LRPPRC protein content. For mt-ND5/6 and mt-Co1 transcript levels it may look like that exercise training could partially elevate mt-mRNA levels, although our statistical analyses reveal no differences.
+
+We have now included these additional data in the results section:
+
+Line 332-340: “Indeed, the marked downregulation of mt-mRNA transcripts in SED Slirp KO muscle, also shown in Fig. 1J, remained largely reduced in ET Slirp KO mice relative to WT ET mice (Fig. 4E). Visually, there appeared to be a partial rescue of mt-Nd5/6 and mt-Co1 in ET Slirp KO mice, though this observation was not statistically confirmed. The sustained reduction in mt-mRNA transcripts upon Slirp KO is clearer in female mice, where exercise training significantly increased mt-mRNA transcript levels in WT mice, a response completely abrogated in Slirp KO mice (Supplementary Fig. 3B). The differences in mt-mRNA transcript levels in response to exercise training between sexes are likely due to the variation in running volume, with female WT mice running twice as much as male WT mice (4.8 km/day vs. 2.4 km/day; Fig. 3B).”
+
+7. Lines 330-331: “Exercise training increases mitochondrial protein translational capacity by elevating mitoribosome mass” is a strong overstatement, overstating in two ways. First, the authors have only checked the amount of 12S rRNA and MRPL11 protein. 12S rRNA and MRPL11 cannot be regarded as representatives of “mitoribosome mass”. How about 16S rRNA (large subunit rRNA) and >50 mitoribosomal proteins? Second, upon exercise, PGC1alpha is increased and this might cause increase in mitochondrial transcription via upregulation of mitochondrial transcription-related proteins that produce polycistronic precursor RNA. And, the polycistronic RNA is cleaved at intervening tRNAs to produce the 12S rRNA, 16S rRNA, mRNAs and many tRNAs (tRNA punctuation model). Thus, increased 12S rRNA implies possibilities including increased transcription of the mitochondrial precursor RNA (or decreased mitochondrial RNA degradation by PNase-SUPV3L1 complex). In such case, increased mt-tRNAs may also contribute to increased mitochondrial
+protein levels. Therefore, the authors should 1) check the amount of “mitoribosome mass” (maybe by proteomics? to check mitoribosomal protein levels, and 16S rRNA RT-qPCR) and also 2) perform mt-tRNA quantification by northern blots or mt-tRNA sequencing.
+
+Thank you for raising this valid concern.
+
+We have now measured both 12S rRNA and 16S rRNA and included these new data in Fig. 5A. These results show that transcription was normal, which strengthens our interpretation that the reduction in mt-mRNA steady state are likely attributable to processes downstream of transcription. This is particularly evident under trained conditions, where the reductions in mt-mRNA steady-state levels remain reduced in the Slirp KO muscles, but 12S rRNA and 16S rRNA are markedly upregulated.
+
+Furthermore, we have now measured mtDNA content for ND1 and ND6 (Supp. Fig. 2J and K). These new results reveal a slight increase under sedentary conditions and no change under trained conditions, thereby eliminating the possibility that the observed reduced mt-mRNA levels in the Slirp KO muscles are attributable to decreases in mtDNA content. This suggests that the reduction in mt-mRNA levels occurs post-transcriptionally.
+
+Moreover, we have now included measures on additional mitoribosomal proteins, both of small and large subunits, to support our speculation that mitoribosome biogenesis and capacity was enhanced in the Slirp KO muscles upon training.
+
+We have also now included measures on integrated stress response (i.e. pEIF2a S51, EIF2A) and mitochondrial quality control (YMEIL1, LONP1) into the manuscript. These new results confirm that exercise indeed activates other mechanisms that can ultimately augment mitochondrial respiratory function conjointly.
+
+Line 531-549: “In response to exercise training, the mitoribosomal components, MRPL11, MRPL12, MRPS18B, 12S rRNA, and 16S rRNA were upregulated, indicating increased mitoribosome biogenesis and capacity for mitochondrial protein synthesis. These adaptations to exercise training may help sustain protein synthesis and normal physiology, even in the presence of low mt-mRNA abundance. The greater increase in OXPHOS, mt-tRNA, and mitoribosomal proteins in Slirp KO ET mice indicates that exercise training may be more effective in the presence of mitochondrial dysfunction, providing exciting avenues for exploring the use of exercise training in conditions of mitochondrial dysfunction. Exercise training also upregulated LONP1 and YME1L1, both important regulators of mitochondrial quality control and proteostasis, and PRDX3, linked to peroxide scavenging. While mitoribosomal protein content, 12S rRNA, 16 S rRNA, LONP1, YME1L1, and PRDX3 may not directly control translation efficiency, their roles in the mitoribosomal makeup and improved mitochondrial quality control can influence the overall cellular environment where protein synthesis occurs. Albeit limited by not directly measuring mitochondrial translational rate, this working hypothesis is supported by findings in human skeletal muscle showing that mitochondrial protein synthesis and upregulation of mitoribosome biogenesis is at the core of exercise training-induced benefits6. That mitochondrial stress was effectively relieved via exercise training is suggested by the marked reduction in phosphorylation of EIF2a at S51, an integral marker of the ISR selectively in Slirp KO mice. This suggests a unique interaction between mitochondrial damage and the ISR, highlighting the heightened sensitivity of Slirp KO mice to exercise training.”
+Minor points:
+
+1. Why is there a stronger effect of Slirp2 KD in the climbing test than Slirp1 KD but less effect on starvation tolerance or lifespan? Possibilities or hypotheses should be described somewhere.
+
+Thank you for raising this valid concern. We have included possibilities in the results as follows:
+
+Line 494-499:" SLIRP1 has been demonstrated to interact with the fly orthologue protein LRPPRC1 to regulate mitochondrial mRNA polyadenylation and maturation, while SLIRP2 interacts with LRPPRC2 to coordinate mitochondrial translation\(^{10, 11, 13}\). It has been shown that SLIRP1/LRPPRC1 and SLIRP2/LRPPRC2 complexes have distinct essential roles in the regulation of mtDNA expression. This distinction likely accounts for the varying impacts on climbing ability, starvation tolerance, and lifespan observed when SLIRP1 or SLIRP2 is lost."
+
+2. Lines 328-329 "These findings point towards unidentified mechanisms by which ET improves translational efficiency to dictate final protein content": increased protein level does not “suggest” improved translation. Increased protein level might be due to decreased protein degradation. The description is an overstatement and needs to be appropriately toned down.
+
+    We have rephrased accordingly:
+
+Line 363-365: “These findings point towards unidentified mechanisms by which exercise training modulates translational efficiency or protein degradation pathways to dictate final protein content.”
+
+3 I think that rather than “protein translation”, words like “mRNA translation” or “protein synthesis” are more widely used and accepted by many researchers in the field of protein synthesis.
+
+    Thank you. We have modified the manuscript accordingly and changed “protein translation” to “protein synthesis”.
+
+References
+
+1. Dias, P.R.F., Gandra, P.G., Brenzikofer, R. & Macedo, D.V. Subcellular fractionation of frozen skeletal muscle samples. *Biochem Cell Biol* **98**, 293-298 (2020).
+2. Dimauro, I., Pearson, T., Caporossi, D. & Jackson, M.J. A simple protocol for the subcellular fractionation of skeletal muscle cells and tissue. *BMC Res Notes* **5**, 513 (2012).
+3. Hatchell, E.C. *et al.* SLIRP, a small SRA binding protein, is a nuclear receptor corepressor. *Mol Cell* **22**, 657-668 (2006).
+4. Cooper, M.P. *et al.* Defects in energy homeostasis in Leigh syndrome French Canadian variant through PGC-1alpha/LRP130 complex. *Genes Dev* **20**, 2996-3009 (2006).
+5. Lagouge, M. *et al.* SLIRP Regulates the Rate of Mitochondrial Protein Synthesis and Protects LRPPRC from Degradation. *PLoS Genet* **11**, e1005423 (2015).
+6. Robinson, M.M. *et al.* Enhanced Protein Translation Underlies Improved Metabolic and Physical Adaptations to Different Exercise Training Modes in Young and Old Humans. *Cell Metab* **25**, 581-592 (2017).
+7. Kleinert, M. et al. Quantitative proteomic characterization of cellular pathways associated with altered insulin sensitivity in skeletal muscle following high-fat diet feeding and exercise training. Sci Rep **8**, 10723 (2018).
+8. Raun, S.H. et al. Housing temperature influences exercise training adaptations in mice. Nat Commun **11**, 1560 (2020).
+9. Brandt, N. et al. The impact of exercise training and resveratrol supplementation on gut microbiota composition in high-fat diet fed mice. Physiol Rep **6**, e13881 (2018).
+10. Baggio, F. et al. Drosophila melanogaster LRPPRC2 is involved in coordination of mitochondrial translation. Nucleic Acids Res **42**, 13920-13938 (2014).
+11. Bratic, A. et al. The bicoid stability factor controls polyadenylation and expression of specific mitochondrial mRNAs in Drosophila melanogaster. PLoS Genet **7**, e1002324 (2011).
+12. Matsushima, Y. et al. Drosophila protease ClpXP specifically degrades DmLRPPRC1 controlling mitochondrial mRNA and translation. Sci Rep **7**, 8315 (2017).
+13. Ruzzenente, B. et al. LRPPRC is necessary for polyadenylation and coordination of translation of mitochondrial mRNAs. EMBO J **31**, 443-456 (2012).
+REVIEWER COMMENTS
+
+We wish to express our gratitude to all reviewers for dedicating their time to provide feedback on our manuscript for the second time. We sincerely appreciate their invaluable input. Please find below our point-by-point response outlining the specific actions we have taken to improve the manuscript based on Reviewer 2’s comments.
+
+Reviewer #1 (Remarks to the Author):
+
+The current version sounds better.
+The authors addressed almost all issues raised by this reviewer, except the measuremet of mRNA stability in the absence of Slrp1 in vivo, once SLIRP KO mouse line has been discontinued.
+In addition, they performed additional analysis including, the cytosolic and mitochondrial fraction analysis of SLIRP1, mt-mRNA evaluation in female mice and the ISR and UPRmt evaluation in the skeletal muscle, as requested.
+Finally, the minor issues were totally addressed.
+I have no additional question.
+
+Reviewer #2 (Remarks to the Author):
+
+In their responses to the reviewers, the authors agreed that complete loss of SLIRP/LRPPRC complexes in KO mice resulted in surprisingly mild functional consequences, despite the marked reduction in mt-mRNA. They also offered unpublished observations that functional impact becomes more evident as animals age, but unfortunately these data are not reported. Overall, many of the key interpretations and takeaways remain weakly supported by the data provided in the manuscript. The investigators are encouraged further temper their language and conclusions.
+
+We would like to express our gratitude for the opportunity to undergo a second revision, and to the Reviewer for their valuable input. In response to the Reviewer's comments, we have made additional revisions. We have taken care to specify throughout the manuscript that some of the effects at baseline were mild and we have toned down the conclusions accordingly.
+
+The revised manuscript highlights the following conclusions:
+
+1. SLIRP regulates mitochondrial structure, respiration, and mtDNA-encoded-mRNA pools in skeletal muscle.
+
+As acknowledged by the authors, the impact of the SLIRP KO on mitochondrial structure and function is quite modest. The finding that stands out most is that, despite complete loss of SLIRP/LRPPRC and marked reductions in mtDNA-encoded mRNA pools, baseline mitochondrial function in skeletal muscle is only modestly reduced, while muscle fat oxidation and whole-body physiological function remain unaffected.
+
+We have now rephrased and modified the descriptions.
+
+Line 118, Subheading: “Slrp knockout lowers mt-mRNA levels and results in modest defects in mitochondrial structure and respiratory capacity in mouse muscle.”
+Line 466-468: “First, lack of Slirp led to mild mitochondrial network disruption, mitochondrial fragmentation, and reduced respiratory capacity in skeletal muscle in mice. Second, SLIRP deficiency impaired muscle functionality, and reduced lifespan in flies.”
+
+Line 476-477: “Our first finding indicates that SLIRP is a hitherto unrecognized player in regulating mitochondria content, structure, and respiration in skeletal muscle.”
+
+Line 481-483: “However, despite the stark similarities, mitochondrial respiration was mildly compromised in Slirp KO skeletal muscle, but not in heart or liver, underscoring SLIRP’s functional importance within skeletal muscle relative to other tissues.”
+
+Line 574, Fig. 1: “Slirp knockout caused mild defects in mitochondrial structure and respiratory capacity, and reduced lifespan”
+
+2. We identify a mechanism of post-transcriptional mitochondrial regulation in muscle via mitochondrial mRNA stabilization.
+
+As noted by reviewer 1, the report does not include direct measures of mRNA stability, although the data are certainly suggestive of this mechanism.
+
+We have modified our statements accordingly.
+
+Abstract, Line 59: Our data points to a mechanism of post-transcriptional mitochondrial regulation in muscle via mitochondrial mRNA stabilization, offering insights into how exercise enhances mitoribosome capacity and mitochondrial quality control to alleviate defects.
+
+Discussion, Line 561-563: Taken together, our findings not only imply that mt-mRNA stabilization via SLIRP/LRPPRC is needed for the regulation of basal mitochondrial function in skeletal muscle, but also highlight an incredible exercise training –stimulated plasticity of mitochondria in skeletal muscle facing mitochondrial defects.
+
+3. Exercise training effectively counteracts mitochondrial defects caused by loss of LRPPRC/SLIRP loss, despite sustained low mtDNA-encoded-mRNA pools, by increasing mitoribosome translation capacity and mitochondrial quality control.
+
+This conclusion remains speculative. At a descriptive level, the interpretation aligns with changes in mitochondrial OXPHOS and mitoribosome proteins measured in male mice, but it’s contradicted by the same measures made in female mice, even though the modest baseline deficits in mitochondrial respiration were fully rescued by low volume wheel running in both males and females. The conflicting results in figures 4-5 (male) vs S. figure 3 (female) imply that enhanced mito ribosome translation capacity and mito quality control are not required for the recovery, and/or the underlying mechanisms are sexually dimorphic.
+
+Thank you for your very important comment. We agree that the underlying mechanisms appear to be sexually dimorphic, with the improvement in mitoribosome translation and quality control being more pronounced in males. However, we cannot completely exclude the role of these processes in females. It is still unclear how females compensate for low mt-mRNA levels, and further research is needed to fully understand these compensatory mechanisms. The sexual dimorphism discussion, included in the last revision, has now been further expanded.
+
+Line 522-526: “Sexual dimorphism in response to metabolic challenges, including exercise training, has been frequently reported in mouse models. In both sexes, exercise training
+circumvented SLIRP to induce mitochondrial and metabolic adaptations in skeletal muscle, despite sustained low mitochondrial transcript levels. However, we observed differences in mechanisms by which male and female mice compensated for the lack of SLIRP, illuminating an exciting area of further investigation.”
+
+4. Muscle levels of SLIRP and LRPPRC are upregulated by exercise training, but SLIRP is dispensable for most whole-body adaptations to exercise training, aside from improvements in blood glucose regulation (in male mice only).
+
+Unfortunately, the exercise stimulus and corresponding adaptations were very modest in this study due to the low volume of voluntary wheel running. This low volume wheel running did not upregulate protein levels of SLIRP and LRPPRC in the corresponding exercise training study. The results show that adaptations to low volume/low intensity exercise training do not require SLIRP. However, still unanswered is whether training-induced adaptations in response to a more vigorous exercise regimen (one that causes more robust induction of both SLIRP and mitochondrial biogenesis) would be affected by SLIRP KO.
+
+Thank you for raising this important point. We agree that a more vigorous exercise regimen could lead to more robust conclusions. However, despite the modest exercise training volume in our study, likely due to the age of the mice, it was sufficient to improve glucose tolerance, exercise capacity, citrate synthase activity (indicative of elevated mitochondrial biogenesis) and elevate the expression of several known exercise-responsive proteins (OxPhos proteins). This has already been addressed in the manuscript following the previous round of revisions.
+
+Additionally, the exercise training volume did, in fact, increase the protein content of SLIRP and LRPPRC in the male mice. However, this effect was not detected by 2way-ANOVA because the analysis included both the KO and WT samples. When comparing only the WT untrained and trained groups, the effect of exercise becomes statistically significant.
+
+Also, considering that the only metric of glucose homeostasis affected by total body SLIRP KO was fasting blood glucose in males, perhaps this points to regulation at the level of hepatic glucose output rather than muscle glucose uptake and metabolism.
+
+Great point. We have now stated that “the mechanism by which SLIRP inhibited ET-induced enhanced glucose tolerance was not established in the present study”.
+
+Line 518-521: “The mechanism by which SLIRP influences glucose metabolism was not established in the present study, although this could be due to decreased intramyocellular insulin signaling, reduced insulin-independent glucose uptake, capillarization, and/or blood flow.”
+
+Summary
+
+In aggregate, the findings show that SLIRP is crucial for regulating mito-encoded mRNA pools in skeletal muscle. The observations that complete loss of SLIRP/LRPPRC and marked reductions in mtDNA-encoded mRNA pools had only modest affects on baseline mitochondrial respiration, skeletal muscle function and whole-body physiology; along with the finding the low-volume exercise can rescue mild genetic defects in mitochondrial function despite the remarkable depletion of mtDNA-encoded mRNA pools, are important findings
+that support the notion that habitual physical activity can overcome at least some modest mitochondrial defects. The role of SLIRP in regulating muscle energy metabolism during aging and higher volume/intensity exercise remains uncertain and is certainly worthy of future study.
+
+Conclusions pertaining to exercise-induced upregulation of mtDNA-encoded OXPHOS proteins, mito quality control, and mitoribosome translation capacity were supported by findings in male but not female mice, implying yet unknown mechanisms and/or some level of sexual dimorphism.
+
+Reviewer #3 (Remarks to the Author):
+
+My previous concerns have nicely been addressed. Additional data filled in the previous gaps or strengthened the authors’ conclusions, and sentences were also carefully improved. How exercise improved the various aspects of mitochondrial and even cytoplasmic proteostasis and quality control (mitoribosomal components, LONP1, and even phosphorylated eIF2alpha) in Slirp KO mice was amazing.
+I could smoothly read the revised manuscript with a lot of excitement and without feeling concerns. I look forward to seeing this paper to be published and the insights be shared to the world.
+
+Reviewer #4 (Remarks to the Author):
+
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #5 (Remarks to the Author):
+
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.

0dc4159524178aa2b8818e1cd5a2fb769cdeba272c79bb5ec67f5f1a67e0d9b5/preprint/preprint.md

@@ -0,0 +1,322 @@
+Knowledge-graph-based cell-cell communication inference for spatially resolved transcriptomic data with SpaTalk
+
+Xin Shao
+Zhejiang University   https://orcid.org/0000-0002-1928-3878
+Chengyu Li
+Zhejiang University   https://orcid.org/0000-0003-3144-9460
+Haihong Yang
+Zhejiang University
+Xiaoyan Lu
+Zhejiang University
+Jie Liao
+Zhejiang University   https://orcid.org/0000-0002-6697-8998
+Jingyang Qian
+Zhejiang University
+Kai Wang
+Zhejiang University
+Junyun Cheng
+Zhejiang University
+Penghui Yang
+Zhejiang University
+Huajun Chen
+Zhejiang University
+Xiao Xu
+Zhejiang University
+Xiaohui Fan (fanxh@zju.edu.cn)
+Zhejiang University   https://orcid.org/0000-0002-6336-3007
+
+Article
+
+Keywords:
+
+Posted Date: April 22nd, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1576678/v1
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on July 30th, 2022. See the published version at https://doi.org/10.1038/s41467-022-32111-8.
+Knowledge-graph-based cell-cell communication inference for spatially resolved transcriptomic data with SpaTalk
+
+Xin Shao1,3, †, Chengyu Li3, †, Haihong Yang2,4, †, Xiaoyan Lu3, Jie Liao3, Jingyang Qian3, Kai Wang1, Junyun Cheng3, Penghui Yang3, Huajun Chen2,4, *, Xiao Xu1,5, *, Xiaohui Fan1,3, 5, *
+
+1Key Laboratory of Integrated Oncology and Intelligent Medicine of Zhejiang Province, Department of Hepatobiliary and Pancreatic Surgery, Affiliated Hangzhou First People’s Hospital, Zhejiang University School of Medicine, Hangzhou 310006, China.
+2Hangzhou Innovation Center, Zhejiang University, Hangzhou 310058, China
+3Pharmaceutical Informatics Institute, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, China
+4College of Computer Science and Technology, Zhejiang University, Hangzhou 310027, China
+5Westlake Laboratory of Life Sciences and Biomedicine, Hangzhou 310003, China.
+
+†These authors should be regarded as Joint First Authors
+
+*Corresponding author: Dr. Huajun Chen (huajunsir@zju.edu.cn), Dr. Xiao Xu (E-mail: zxjxu@zju.edu.cn) and Dr. Xiaohui Fan (E-mail: fanxh@zju.edu.cn, Tel/Fax: 86-571-88208596)
+Abstract
+
+Spatially resolved transcriptomics (ST) provides genetic information in space toward elucidation of the spatial architecture in intact organs and the spatially resolved cell-cell communications mediating tissue homeostasis, development, and disease. To facilitate inference of spatially resolved cell-cell communications from ST data, we here present SpaTalk, which relies on a graph network and knowledge graph to model and score the ligand-receptor-target signaling network between spatially proximal cells, decomposed from ST data through a non-negative linear model and spatial mapping between single-cell RNA-sequencing and ST data. The performance of SpaTalk benchmarked on public single-cell ST datasets was superior to that of existing cell-cell communication inference methods. SpaTalk was then applied to STARmap, Slide-seq, and 10X Visium data, revealing the in-depth communicative mechanisms underlying normal and disease tissues with spatial structure. SpaTalk can uncover spatially resolved cell-cell communications for single-cell and spot-based ST data universally, providing new insights into spatial inter-cellular dynamics.
+Introduction
+
+Cell-cell communications via secreting and receiving ligands frequently occur in multicellular organisms, which is a vital feature involving numerous biological processes¹. Standard algorithms for inferring cell–cell communications mediated by ligand–receptor interactions (LRIs) primarily incorporate a database of known LRIs and single-cell transcriptomic data by delineating cell populations and their lineage relationships²,³. One common strategy is to integrate the abundance of ligands and receptors for the inference of signals from senders to receivers based on the premise that highly co-expressed ligands and receptors are likely to mediate inter-cellular communications⁴,⁵. Another strategy applies the downstream targets triggered by LRIs in receivers to enrich and score the ligand-receptor-target (LRT) signaling network⁶⁻⁸. Although single-cell transcriptomic data can provide information on the genes contributing to cell-cell communications, the spatial information of cells is inevitably lost when dissociating tissues into single cells, thereby hindering the extension of current tools to investigate cell-cell communications in tissues with spatial structure⁹.
+
+Recent technological advances in spatially resolved transcriptomics (ST) benefiting from spatial barcoding and imaging-based approaches have enabled the measurement of whole or mostly whole transcriptomes while retaining the spatial information¹⁰,¹¹, which have been increasingly adopted to generate new insights in the biological and biomedical domains, with dramatically improved accuracy and reliability in the inference of spatially proximal cell-cell communications¹². Given the space-constrained nature of juxtacrine and paracrine signaling, such spatial gene expression information is vital to understand cell-cell communications mediating tissue homeostasis, development, and disease¹³,¹⁴.
+Several methods have recently emerged to decode the mechanisms of cell-cell communications in space\(^{15}\). For example, Giotto utilizes preferential cell neighbors over single-cell ST datasets for each pair of cell types with an enrichment test to evaluate the likelihood of a given LRI based on proximal co-expressing cells and infer cell-cell communication in space\(^{16}\). SpaOTsc applies structured optimal transport mapping between scRNA-seq and ST data to assign a spatial position for each cell, resulting in a cell–cell distance as a transport cost to infer the ligand–receptor signaling network that mediates space-constrained cell–cell communication\(^{17}\). However, Giotto and SpaOTsc are limited to infer inter-cellular communications over single-cell ST data rather than the spot-based ST data and between paired cell types rather than paired cells. It still lacks of methods that can infer and visualize spatially resolved cell-cell communications at single-cell resolution over ST data to date, posing a great challenge for decoding spatial inter-cellular dynamics underlying disease pathology.
+
+To address this challenge, we herein proposed SpaTalk, a spatially resolved cell-cell communication inference method by creatively integrating the principles of the ligand–receptor proximity and ligand–receptor–target (LRT) co-expression to model and score the LRT signaling network between spatially proximal cells relying on the graph network and knowledge graph approaches\(^{18}\). The performance of SpaTalk was evaluated on benchmarked datasets with remarkable superiority over other methods. By applying to STARmap\(^{19}\), Slide-seq\(^{20,21}\), and 10X Visium\(^{22}\) datasets, SpaTalk revealed the in-depth communicative mechanisms underlying normal and disease tissues with spatial structure. Collectively, these results demonstrate SpaTalk as a useful and universal method that can help to uncover spatially resolved cell–cell communications for both single-cell and spot-based ST data, providing insights into the understanding
+Results
+
+Overview of the SpaTalk method. Fig. 1 provides an overview of the workflow for developing and testing SpaTalk, comprising two main components: (1) dissect the cell-type composition of ST data and (2) infer spatially resolved cell–cell communications over decomposed single-cell ST data (Fig. 1a). In the first component, the non-negative linear model (NNLM)\(^{23-25}\) was applied to decode the cell-type composition for a single-cell or spot-based ST data matrix using the scRNA-seq data matrix with k cell types as the underlying reference. By incorporating Lee’s multiplicative iteration algorithm and relative entropy loss\(^{25}\), the model was trained with default hyperparameters until convergence, producing a weight matrix representing the optimal proportion of cell types for each cell/spot. For single-cell ST data, the cell type with the maximum weight was assigned to label each cell. For spot-based ST data, the cell types with different weights were used as the reference to project the cells from scRNA-seq data onto the spatial spot (Fig. 1b). Through random sampling and deep iteration processes, the optimal cellular combination that most resembled the spatial spot was refined to reconstruct the single-cell ST data for spot-based ST data.
+
+The second component of SpaTalk is to infer spatially resolved cell–cell communications and downstream signal pathways. To identify possible communications among cells mediated by LRIs, the principles of ligand–receptor proximity and ligand–receptor–target (LRT) co-expression were incorporated based on a recent review\(^{12}\). In detail, the KNN algorithm is first applied to each cell in space to construct the cell graph network. For the ligand of the sender (cell type A) and the
+receptor of the receiver (cell type B), the number of LRI pairs is obtained from the graph network by counting the 1-hop neighbor nodes of receivers for each sender. A permutation test filters and scores the significantly enriched LRIs, generating the inter-cellular score (Fig. 1c).
+
+![Overview of SpaTalk workflow and visualization](page_246_370_1057_1092.png)
+
+Fig. 1 Workflow of the SpaTalk method and visualization. a Overview of SpaTalk, including the input, intermediate process of decoding spatially resolved cell–cell communications, and output. b Conceptual framework of cell-type decomposition with SpaTalk. Five different spatial technologies and datasets were selected and analyzed: spot-based ST data (Slide-seq and 10X Visium) and single-cell ST data (STARmap, MERFISH, and seqFISH+). NNLM was used to dissect the optimal proportion of cell types for the projection of cells from scRNA-seq reference data onto the spatial cells/spots, generating single-cell ST data with known cell types. c Schematic representation of SpaTalk to infer spatially resolved cell–cell communications
+mediated by LRIs. The inter-cellular and intra-cellular scores were obtained and combined from the cell–cell graph network and the LRT-knowledge graph (KG), respectively, by integrating the KNN, permutation test, and random walk algorithms. L, ligand; R, receptor; TF, transcription factor; T, target. d Visualization of spatially resolved cell–cell communications, including a heatmap, Sankey plot, and diagram of the LRI from senders to receivers in space, as well as ligand-receptor-target (LRT) signaling pathways over the reconstructed single-cell ST data.
+
+The knowledge graph (KG) was then introduced to model the intracellular signal propagation process. In practice, LRIs from CellTalkDB26, pathways from Kyoto Encyclopedia of Genes and Genomes (KEGG) and Reactome, and TFs from AnimalTFDB27 were integrated to construct the LRT-KG, wherein the weight between entities represents the co-expressed coefficient. Taking the receptor as the query node, we incorporated the random walk algorithm28 into the LRT-KG to filter and score the downstream activated TFs and calculate the intracellular score of the LRI from senders to receivers. Inter-cellular and intra-cellular scores are combined to rank the LRIs that mediate spatially resolved cell-cell communications.
+
+SpaTalk also includes numerous visualization functions to characterize the cell-type composition and spatially resolved cell–cell communications, such as the diagram of the LRI from senders to receivers in space and LRT signaling pathways, over the reconstructed single-cell ST data (Fig. 1d). Five broad ranges of different spatial technologies and corresponding representative datasets were analyzed and visualized: spot-based ST data (Slide-seq20,21 and 10X Visium22) and single-cell ST data (STARmap19, MERFISH29, and seqFISH+30).
+
+Performance comparison of SpaTalk with other methods. The cell-type decomposition by SpaTalk is the foundation for subsequent analyses. To evaluate its performance, four single-cell ST datasets from the mouse cortex, hypothalamus,
+olfactory bulb, and sub-ventricular zone were utilized (Supplementary Fig. 1a). All cells were split according to the fixed spatial distance and then merged into simulated spots as the benchmark datasets (Fig. 2a). The quality of predicted cell-type decompositions and expression profiles was evaluated by Pearson’s correlation coefficient and the root mean square error (RMSE) based on the ground truth, wherein SpaTalk exhibited fantastic performance over the benchmark datasets (Supplementary Fig. 1b, c). Although the majority of existing cell-type deconvolution methods (RCTD^{31}, Seurat^{32}, SPOTlight^{33}, deconvSeq^{34}, and Stereoscope^{35}) can achieve a decent correlation coefficient and low RMSE on spot deconvolution, SpaTalk outperformed these methods on most benchmark datasets with the top-ranked performance, except for the MERFISH dataset (Fig. 2b). The MERFISH dataset only includes 155 genes, whereas the STARmap and seqFISH+ datasets cover 1020 and 10,000 genes per cell, respectively, suggesting that SpaTalk is potentially more effective for spatial data with higher gene coverage.
+
+We next compared the performance of SpaTalk with that of existing cell–cell communication inference methods (Supplementary Fig. 2a). Consequently, most methods exhibited a large fraction of overlapped predictions with the rest of the methods despite the different number of inferred cell-cell communications (Supplementary Fig. 2b, c), indicating the reproducible inference across these methods. Regarding the inferred LRIs (Supplementary Fig. 2d), we reasoned that the spatial distances of the inferred LRI between sender–receiver pairs will be shorter than those between all cell–cell pairs and thus the inferred LRI will be more co-expressed in local space as cells that are close are more likely to signal (Fig. 2c). The one-sided Wilcoxon test was performed to evaluate the spatial proximity significance of the inferred LRIs,
+and the co-expressed percentage of the LRI was calculated as the co-expression level using the cell–cell graph network. Although most LRIs inferred by other methods showed significantly closer spatial distances between sender–receiver pairs than that between all cell–cell pairs, superior performance of SpaTalk was observed, ranking first for both evaluation indices for STARmap datasets (Fig. 2d). Similarly, SpaTalk obtained a higher median –\( \log_{10} P \) value and co-expression percent on the seqFISH+ OB and SVZ datasets but not for SpaOTsc (Fig. 2e).
+
+![Schematic diagram and performance comparison plots for SpaTalk and other methods](page_349_678_1047_563.png)
+
+Fig. 2 Superior performance of SpaTalk over existing methods. **a** Schematic diagram for generating simulated spot data. Cells were split according to the fixed spatial distance and then merged for the single-cell ST data with known cell types. **b** Performance comparison of SpaTalk with other existing cell-type deconvolution methods (RCTD, Seurat, SPOTlight, deconvSeq, Stereoscope). The asterisk represents the top-ranked method for each dataset. NA, not available. **c** Schematic illustration of the procedure and rationale for single-cell ST data to evaluate predicted LRIs that mediate spatially resolved cell–cell communications. **d** and **e** Performance comparison of SpaTalk with existing cell–cell communication inference methods (Giotto, SpaOTsc, NicheNet, CytoTalk, and CellCall) on the STARmap and seqFISH+ datasets. The \( P \) value
+represents the difference of spatial distances between sender–receiver and all cell–cell pairs assessed with the Wilcoxon test. f Schematic illustration of the procedure and rationale for single-cell ST data to evaluate predicted downstream target and pathways underlying LRIs. g Performance comparison of SpaTalk on the inferred downstream targets with other methods (NicheNet, CytoTalk, and CellCall) over the STARmap and seqFISH+ datasets. The \( P \) value represents the significance of enriched pathways or biological processes from the KEGG and Reactome databases using inferred downstream targets with the Fisher exact test.
+
+We compared the performance of SpaTalk for inference of intra-cellular signal pathways of the receiver cell type triggered by the LRI with those of NicheNet\(^6\), CytoTalk\(^7\), and CellCall\(^8\) that also infer the downstream targets of LRIs. We reasoned that a more accurate method would be more likely to enrich the receptor-related biological processes or pathways using the inferred downstream target genes in the receiver cell type (Fig. 2f); hence, the Fisher-exact test was adopted for pathway enrichment analysis with the KEGG and Reactome databases on target genes in receivers. The target genes inferred by all methods enriched the most intra-cellular pathways or biological processes triggered by the inter-cellular LRI (Fig. 2g). Nevertheless, SpaTalk exhibited the top-ranked performance over three benchmarked datasets, exceeding other existing methods in inference of the LRT signal network.
+
+**Identification of signal transmission among neurons and non-neuronal cells.** SpaTalk was first applied to investigate and visualize the cell–cell communications over the STARmap ST dataset of the mouse visual cortex (Fig. 3a), including data of 1020 sequenced genes for 973 cells in space covering the spatial axis of excitatory neurons (eL2/3, eL4, eL5, eL6, annotated by anatomic cortical layers); *Pvalb*, *Reln*, *Sst*, and *Vip*-expressing neurons; and non-neuronal cells, including astrocytes (Astro), endothelial cells (Endo), microglia (Micro), oligodendrocytes (Oligo), and smooth muscle cells
+(SMCs) from layers L1 though L6 to the corpus callosum and hippocampus. As shown in Fig. 3b, SpaTalk identified the spatial signal transmission among excitatory and inhibitory neurons and non-neuronal cells such as Sst–Sstr2, Inhba–Acvr1c, and Cort–Sstr2. For example, the direct cell–cell communication mediated by the Sst–Sstr2 interaction was observed between Sst-expressing neurons and Pvalb-expressing neurons (Supplementary Fig. 3a), which are known to regulate neuron activity via non-synaptic, inter-neuronal communication\(^{36, 37}\). Concordantly, these identified LRIs among neurons and non-neuronal cells are associated with multiple biological processes and pathways that play vital roles in the regulation of physiological neural development and the balance of excitatory/inhibitory transmission in the central nervous system\(^{38, 39}\), including growth hormone synthesis, secretion, and action; neuroactive ligand-receptor interaction; signaling by activin; and the transforming growth factor (TGF)-beta signaling pathway (Fig. 3c).
+
+Notably, Astro were relatively abundant across space of the L5 layer and colocalized with numerous excitatory neurons, exhibiting direct cell–cell communication with eL2/3, eL5, and eL6 (Supplementary Fig. 3b). Given the Cort–Sstr2 interaction between eL5 and Astro, eL5 highly expressed and secreted the CORT ligand to interact with the SSTR2 receptor on Astro with a highly overlapped distribution density of eL5 and Astro in the constrained space, wherein the spatial distances of Cort and Sstr2 in eL5–Astro pairs were significantly closer than those in all cell–cell pairs (Fig. 3d). Focusing on the intra-cellular signal pathway of the Cort–Sstr2 interaction reconstructed by SpaTalk, two downstream TFs were identified, Egr1 and Smad3, which are involved in canonical TGF-beta signaling, in line with previous findings\(^{40}\).
+
+Despite the relatively low-rise co-expression of target genes in receivers, the intra-
+cellular signal triggered by the Cort–Sstr2 interaction successfully propagated to the target genes, reaching a high percentage of cells expressing most target genes (Fig. 3e). The Fisher exact test showed significant enrichment with receptor-related pathways (Fig. 3f), indicating the reliability of eL5–Astro communications mediated by the Cort–Sstr2 interaction.
+
+We then applied SpaTalk to another spot-based ST dataset of the mouse cortex (Slide-seq v2), including 17,545 unique genes among 42,550 spots in space, reaching up to 4000 expressed genes per spot. Leveraging previously published adult mouse cortical cell taxonomy by scRNA-seq data\(^{41}\) (Supplementary Fig. 3c), SpaTalk reconstructed the spatial transcriptomics atlas at the single-cell resolution for Slide-seq data, which showed consistent spatial localization of neurons and non-neuronal cells across different layers, including the major excitatory and inhibitory neurons and Oligo (Fig. 3g). Compared to STARmap data, oligodendrocyte progenitor cells, and \( lgtp \)-, \( Ndnf \)-, and \( Smad3 \)-expressing neurons were also observed in the Slide-seq data. Concordantly, most cell–cell communications in STARmap data were also found in Slide-seq data except for those of distinct cell types in the two datasets (Supplementary Fig. 3d). For example, the eL5–Astro communications mediated by the Cort–Sstr2 interaction in space and the downstream targets such as SMAD3 were also observed in Slide-seq data (Fig. 3h), suggesting the universality of the spatially resolved cell-cell communications inferred by SpaTalk. In addition, the direct communications among Pvalb neurons, eL6, and Oligo were also significantly enriched, in accordance with the fact that neuron-oligo communication controls the oligodendrocyte function and myelin biogenesis (Supplementary Fig. 3e).
+Fig. 3 Identification of spatial inhibitory signal transmission among neurons and non-neuronal cells. a STARmap single-cell ST dataset of the mouse visual cortex involving 973 cells and 1020 genes. Astro, astrocytes; eL2/3, eL4, eL5, eL6, excitatory neuron subtypes; Endo, endothelial cells; HPC, hippocampus; Micro, microglia; Oligo, oligodendrocytes; SMC, smooth muscle cells; cc, corpus callosum. b Significantly enriched LRs that mediate cell–cell communications among neurons and non-neuronal cells inferred by SpaTalk with \( P < 0.05 \). The \( P \) value represents the significance of spatial proximity of LRs using the permutation test. c Sankhy plot of the associations among ligands, receptors, and biological processes or pathways in the KEGG and Reactome databases that mediate cell–cell communications in the central nervous system. d Spatial distribution and intra-cellular signaling pathways of the Cort–Sstr2 pairs between the eL5 senders and Astro receivers. \( P \) values were calculated with the Wilcoxon test. e Co-expression of target genes in receivers and the percentage of expressed cells for target genes. f Significantly enriched biological processes and pathways with the ligand-receptor-target genes using the Fisher exact test. g Slide-seq spot-based ST dataset of the mouse visual cortex involving 42,550 spots and 22,542 genes. OPC, oligodendrocyte progenitor cell. h Communications of eL5–Astro mediated by the Cort–Sstr2 interaction in space and the intra-cellular signal pathway
+inferred by SpaTalk over Slide-seq data.
+
+Metabolic modulation of periportal hepatocytes on pericentral hepatocytes. We applied SpaTalk to the Slide-seq ST dataset of the mouse liver covering 17,545 unique genes among 25,595 spots in space (Fig. 4a). To explore the cell-type composition of Slide-seq data, a mouse liver scRNA-seq reference integrating the non-parenchymal cells from the Mouse Cell Atlas (MCA)42 and the parenchymal hepatic cells from the GSE125688 dataset43 were utilized (Supplementary Fig. 4a), containing 6029 cells, including major immune cells such as macrophages (Macro), and the pericentral and periportal hepatocytes. The reconstructed single-cell ST atlas was perfectly accordant with the original outcome obtained by Slide-seq (Fig. 4b), wherein the expression of known marker genes44 and the percent for each cell type were highly correlated across spots (Supplementary Fig. 4b, c, d), such as the pericentrally and periportally zonated genes Cyp2e1 and Pck1 (Fig. 4c). Immune cells were hardly observed in each spot, with pericentral and periportal hepatocytes accounting for the major proportion across spots (Supplementary Fig. 4e); the same phenomenon was observed in recently published ST data of the healthy liver45.
+
+The cell–cell communications between pericentral and periportal hepatocytes were further explored by SpaTalk (Fig. 4d). Both hepatocyte types secrete and receive multiple ligands for their communication, forming spatially distributed metabolic cascades to cooperatively optimize the metabolic environment. For instance, with the gradient expression of enzymes in sequential lobule layers, pericentral hepatocytes perform the primary steroid, alcohol, and lipid metabolic processes, while periportal hepatocyte mainly carry out the small-molecule and monosaccharide biosynthetic processes, amino acid and triglyceride metabolic processes, and gluconeogenesis (Fig.
+4e, f), in line with the variable functions of zonated hepatocytes residing in the central and portal veins\(^{46}\). Notably, the periportal hepatocytes substantially expressed more ligands, including epidermal growth factor (\(Egf\)), transforming growth factor alpha (\(Tgfa\)), heparin-binding EGF-like growth factor (\(Hbegf\)), insulin-like growth factor 1 (\(Igf1\)), and vascular endothelial growth factor A (\(Vegfa\)), to promote the growth of pericentral hepatocytes. As the blood flows from the portal vein toward the central vein, this could reflect the fact that periportal hepatocytes respire most of the oxygen, leading to decreased oxygen concentrations along the lobule axis; thus, periportal hepatocytes secrete numerous growth factors via paracrine signaling to modulate the pericentral hepatocytes for the prevention of hypoxia and the maintenance and amelioration of pericentrally metabolic functions\(^{46}\).
+
+Taking the LRI of \(Apob–Cd36\) as an example, the spatially resolved cell–cell communications between periportal and pericentral hepatocytes mainly occurred across the mid-lobule layers (Fig. 4g). The gene product of \(Apob\) is an apolipoprotein of chylomicrons and low-density lipoproteins highly involved with the regulation of lipids and fatty acids metabolism through CD36, indicating the modulation of periportal hepatocytes on the metabolic microenvironment sensed by pericentral hepatocytes. From the reconstructed intra-cellular signal propagation network triggered by the \(Apob–Cd36\) interaction (Fig. 4h), sequential target TFs were activated, including \(Ahr\) that regulates xenobiotic-metabolizing enzymes such as cytochrome P450, and \(Nr1h4\) that regulates the expression of genes involved in bile acid synthesis and transport, in agreement with the corresponding module score of pericentral hepatocytes in space (Fig. 4i). The LRT network was also remarkably enriched in the AMPK and PPAR signaling pathways, which play crucial roles in the regulation of energy
+and metabolic homeostasis, suggesting the spatially fine-tuned cell–cell communications along the portal–central lobule axis for minimizing risks to pericentral hepatocytes.
+
+![Slide-seq spatial data, SpaTalk decomposition, correlation matrix, enriched pathways, and gene expression heatmaps for pericentral and periportal hepatocytes](page_324_370_1096_1012.png)
+
+Fig. 4 Modulation of periportal hepatocytes on the metabolic microenvironment sensed by pericentral hepatocytes. a Slide-seq spot-based ST dataset of the mouse liver involving 25,595 spots and 17,545 genes. b Cell-type decomposition by SpaTalk. PC, pericentral; PP, periportal; Hep, hepatocytes. c Scaled Pearson’s correlation coefficients between the expression of known marker genes and the percent for each cell type. DC, dendritic cell; Macro, macrophages. d Enriched LRIs that mediate cell–cell communications between pericentral and periportal hepatocytes. e Significant differentially expressed genes (DEGs) between periportal and pericentral hepatocytes assessed with the Wilcoxon test and the corresponding significantly enriched biological processes and pathways determined with the Metascape web tool. Representative DEGs are labeled beside the heatmap. f Significantly activated pathways in pericentral (up) and periportal (down) hepatocytes determined by Gene Set Enrichment Analysis (GSEA). g Communications from periportal hepatocytes to
+pericentral hepatocytes mediated by the Apob–Cd36 interaction in space. h Intra-cellular signal pathway inferred by SpaTalk over Slide-seq data and the significantly enriched pathways over the ligand-receptor-target network. i Inferred module score of each hepatocyte type over the pathway signatures determined with Seurat.
+
+Spatial characterization of cell types over 10X Visium data. Given the widely used 10X Visium tool in ST studies, we applied SpaTalk to a human skin squamous cell carcinoma (SCC) ST dataset published by Ji et al.22, who profiled SCC and matched normal tissues via 10X scRNA-seq and used Visium to identify a tumor-specific keratinocyte (TSK) in the tumor (Fig. 5a). Using the matched SCC scRNA-seq data of patient 2 as reference, the optimal cell-type composition for each spot was deconvoluted by SpaTalk, which exhibited a similar characterization with that histologically assessed from hematoxylin and eosin-stained frozen sections (Fig. 5b). The percent of TSK inferred by our method was compared to the TSK score based on markers (e.g., MMP10, PTHLH, LAMC2, and IL24) defined by Ji et al. across 646 spots (Fig. 5c). A high correlation between the TSK percent and score was observed (Fig. 5d). Moreover, the percent of inferred cell types was prominently associated with the expression of known marker genes, indicating the accuracy of SpaTalk for cell-type decomposition (Supplementary Fig. 5a, b).
+
+Next, we reconstructed the single-cell ST profile by assuming a total of 30 cells in each spot according to a recent review12, which covered the main epithelial cells, including differentiating, cycling, and basal keratinocytes; melanocytes; fibroblasts (FB); Endo; natural killer (NK) cells; and T cells (Fig. 5e). Despite the asymmetrical distribution for most cell types, TSK, FB, and Endo showed specific patterns of locations in space, which were highly adjacent in some tumor areas (Fig. 5f), forming direct cell–cell communications in the tumor microenvironment (TME). By filtering cells from the TSK leading spots (score ≥ 0.8), we found that TSKs reside within a fibrovascular niche,
+resulting in high colocalization of TSKs, FB, and Endo at the TSK leading spots (Fig. 5g), in line with the previous findings\(^{22}\). Moreover, we used SpaTalk to investigate the cell-type composition over the ST data of another SCC patient. Despite a low percentage across 621 spatial spots, most TSKs centered on a handful of corner spots in space, exhibiting a highly consistent distribution with TSK scores (Fig. 5h and Supplementary Fig. 5c). Unsurprisingly, the fibrovascular niche was also observed in the TSK leading spots of patient 10 with clear spatial co-localization (Supplementary Fig. 5d), indicating the close cell–cell communication among TSKs, FB, and Endo in the TME underlying the occurrence and development of SCC.
+
+![Spatial characterization of tumor and stromal cells in human squamous cell carcinoma](page_374_682_1092_1012.png)
+
+Fig. 5 Spatial characterization of tumor and stromal cells in human squamous cell
+carcinoma Visium data with SpaTalk. a Visium spot-based ST dataset of human skin SCC in patient 2 with the matched scRNA-seq dataset involving the main keratinocytes (KC), stromal cells, and immune cells. b Cell-type decomposition by SpaTalk. Cyc, cycling; Diff, differentiating; NK, natural killer; FB, fibroblast. c TSK percent and TSK score across spatial spots. The expression of known TSK markers is plotted. d Pearson’s correlation coefficient between the TSK percent and TSK score. f Contour plot of TSK, FB, and Endo based on the reconstructed single-cell ST atlas by SpaTalk. g TSK leading spots with a TSK score > 0.8 in space. The bar chart represents the number of different cell types and the line chart represents the number of neighbors adjacent to TSKs among the TSK leading spots. h Visium spot-based ST dataset of human skin SCC in patient 10 and the cell-type decomposition by SpaTalk showing the percent of TSKs across 621 spatial spots.
+
+Reconstruction of TSK–stroma communications in space. To dissect the underlying LRI mediating the spatially resolved cell–cell communications between TSKs and stromal cells of the fibrovascular niche in the TME, we applied SpaTalk to infer the communications between TSK–FB and TSK–Endo pairs over the decomposed single-cell ST data of SCC in patient 2, including the top-ranked 20 LRIs based on the integrated inter-cellular and intra-cellular scores (Fig. 6a). Consistent with a TSK–fibrovascular niche, prominent TSK signaling to FB and Endo was mediated by several common ligand–receptor pairs, including VEGFA–NPR1, VEGFB–NPR1, PGF–SDC1, and CDH1–ITGAЕ, associated with tumor angiogenesis. Additionally, TSKs modulate FB through secreting matrix metallopeptidase (MMP)1 and MMP9, which are linked to tumor metastasis via cellular movement and extracellular matrix (ECM) disassembly. Conversely, FB and Endo prominently co-expressed numerous ligands such as MDK, HGF, HMGB1, and THBS1, matching TSK receptors that promote the proliferation and differentiation of TSKs (Fig. 6b). Further supporting TSKs as an epithelial mesenchymal transition (EMT)-like population, SpaTalk predicted that the widely expressed TGFB1 regulates TSKs. TSK receptors corresponding to additional ligands from FB and Endo
+included several integrins (e.g., ITGA5 and ITGB6) and nectins (e.g., NECTIN1 and NECTIN2), highlighting other pathways associated with EMT and epithelial tumor invasion\(^{47,48}\).
+
+![Reconstruction of cell–cell communications between TSK subpopulations and stromal cells in space with SpaTalk.](page_320_370_1009_1042.png)
+
+Fig. 6 Reconstruction of cell–cell communications between TSK subpopulations and stromal cells in space with SpaTalk. **a** Top 20 inferred LRIs that mediate cell–cell communication from the TSK senders to the FB and Endo receivers. Colored blocks represent the known ligand–receptor pairs in CellTalkDB. The asterisk represents the significantly enriched LRIs determined by SpaTalk. **b** Top 20 inferred LRIs that mediate cell–cell communication from the FB and Endo senders to TSK receivers. **c** Region of interest (ROI) covering 42 spatial spots in space with a high total score of TSK, FB, and Endo according to their signature genes. The point plot shows the decomposed single-cell ST atlas determined by SpaTalk. **d** Expression of known cancer-associated fibroblast (CAF) markers across TSKs, FB, Endo, and other cells. **e** Differentially expressed genes (DEGs) between EMT-like and EMT-unlike TSKs and the corresponding
+enriched biological processes and pathways. Representative DEGs are labeled beside the point. f Number of cell-cell pairs over the LRs from the EMT-like and EMT-unlike TSKs to CAFs. g Communications from EMT-like and EMT-unlike TSKs to CAFs mediated by the MMP1–CD44 interaction in space. h Comparison of communications among CAFs, Endo, EMT-like TSKs, and EMT-unlike TSKs with respect to the number of cell-cell pairs in space over the matched LRs evaluated with a paired t test.
+
+Next, we focused on a region of interest (ROI) covering 42 spatial spots in space for in-depth exploration of TSK-stroma communications, which exhibited a high total score of TSK, FB, and Endo according to their signature genes, occupying the major part in the ROI (Fig. 6c). By mapping cancer-associated fibroblast (CAF) markers to the cells in space, the majority of FB in the ROI highly expressed the known CAF marker genes (e.g., VIM, FAP, POSTIN, and SPARC) (Fig. 6d), hinting at the transformation of FB to CAFs induced by the adjacent TSKs and conversely supporting the stemness of TSKs via direct cell-cell communication in space (Supplementary Fig. 6a). Notably, the TSKs appear to be extremely heterogeneous with respect to the broad range of EMT scores in the ROI; thus, TSKs were further classified into 268 EMT-like and 268 EMT-unlike populations (Supplementary Fig. 6b). By comparing their differentially expressed genes, EMT-like TSKs were dramatically enriched with ECM organization, proteoglycans in cancer, regulation of cell adhesion, and the VEGFA-VEGFR2 signaling pathway, representing more invasive properties compared with EMT-unlike TSKs (Fig. 6e).
+
+Additionally, EMT-like TSKs appear to be more communicative with surrounding CAFs in the TME in light of the greater number of cell-cell pairs over the LRs that prominently mediate TSK–stroma communications in space, such as LAMB3-ITGB1, LAMA3-ITGB1, LAMC2-ITGB1, and MMP1-CD44 (Fig. 6f and Supplementary Fig. 6c, d, e). Metastasis-related laminins are essential for formation and function of the
+basement membrane, whereas MMPs are involved in ECM breakdown, both contributing to the aggravated malignancy of tumors. Moreover, CD44 expression on CAFs plays a supporting role in the induction of cellular stemness, wherein CAFs have a preference of cell–cell communications with EMT-like TSKs in space (Fig. 6g). Interestingly, EMT-unlike TSKs notably exhibited more communicative cell–cell pairs with Endo, whereas EMT-like TSKs exhibited significantly more communicative cell–cell pairs with CAFs over the matched LRIs (Fig. 6h), consistent with the observed contribution of CAFs to EMT in a broad range of tumors19, 50.
+
+Discussion
+
+We have demonstrated the capabilities of SpaTalk to infer and visualize spatially resolved cell–cell communications mediated by significantly enriched LRIs under normal and disease states over existing representative datasets, including the single-cell ST data generated from STARmap, MERFISH, and seqFISH+, and the spot-based ST data obtained via Slide-seq and 10X Visium.
+
+There are two principles to decode the mechanisms of cell–cell communications: ligand-receptor proximity and LRT co-expression12. In a given tissue niche, cells are more likely to communicate with each other when they are spatially adjacent and activate downstream target genes in the receiving cell triggered by the LRI in proximal cells; thus, ST data are well suited to apply the two principles for inferring inter-cellular communications. Accordingly, our proposed SpaTalk realizes the integration of these two principles by incorporating the KNN and cell–cell graph network to filter spatially proximal cell pairs and corresponding LRIs, followed by utilizing the knowledge graph algorithm to model the LRT signal propagation process. Consequently, the
+performance of SpaTalk was superior to that of other methods over the benchmarked ST datasets with respect to several evaluation indices, demonstrating the reliability of the two principles in decoding cellular cross-talk, especially for juxtacrine and paracrine communication.
+
+Importantly, SpaTalk is applicable to either single-cell or spot-based ST datasets generated from mainstream ST technologies. For the former, SpaTalk assigns a label to each cell by selecting similar cell types with the top-ranked weight via NNLM for single-cell ST data, generating the ST atlas at single-cell resolution with known cell types for the subsequent inference of cell–cell communications. For spot-based ST data, SpaTalk selects and maps the optimal combination of cells in accordance with the decomposed optimal weight/percent of cell types via NNLM and the transcriptome profiles of spatial spots to reconstruct the ST atlas at single-cell resolution with known cell types. Notably, applications of SpaTalk to the mouse cortex and liver datasets sequenced by STARmap and Slide-seq, respectively, revealed the evidential LRIIs in space that mediate the spatially resolved cell–cell communications contributing to normal physiological processes. Moreover, exploration of SpaTalk on the human skin SCC dataset obtained from 10X Visium identified the variable preference of communication among tumor subpopulations, CAF, and Endo. These cases convincingly demonstrate the universality of SpaTalk in decoding the mechanism of cell–cell communications in space underlying normal and disease tissues for single-cell and spot-based ST data.
+
+As unmatched scRNA-seq and ST data would directly influence the cell-type decomposition, an important feature of SpaTalk is the ability to assign a spot/cell into an unsure category considering the unseen cell types in the scRNA-seq reference. For
+example, the scRNA-seq reference for the Slide-seq mouse cortex ST data was obtained from another repository for the same tissue, resulting in numerous unsure cells by assuming one cell in each spot in terms of the high resolution (10 \( \mu \)m) of Slide-seq technology that almost approaches single-cell resolution. Additionally, the extremely low gene coverage of several spatial spots severely affects the regression model, which were regarded as the unsure type by SpaTalk. However, with respect to the human skin SCC datasets, SpaTalk removed the unsure type for the matched scRNA-seq and ST data. As the matched multi-modal datasets will undoubtedly become greater in number, application of SpaTalk and similar methods will be required for accurate inference of spatially resolved cell–cell communications.
+
+Additionally, SpaTalk characterizes the spatial distribution for each cell type within the reconstructed ST at single-cell resolution through the contour plot of cellular density in space, which enables analyzing the proximal relationship between paired cell types. Moreover, SpaTalk enables the statistical analyses and visualization of spatially proximal LRIs in space, forming a dynamic cell–cell communication network. Currently, it is hard to analyze and visualize the LRI at single-cell resolution for scRNA-seq data, wherein the common practice is to interpret the LRI for paired cell types. By incorporating spatial information, SpaTalk displays the enriched LRI at single-cell resolution via the spatially proximal co-expressed cell pairs, offering an informatively brand-new approach for the analysis and visualization of the LRI and its mediated cell–cell communication underlying the disease pathology from a novel perspective, as shown in the application of SpaTalk to the human skin SCC datasets.
+
+Adding spatial constraints in cell–cell communication inference is critical to the spatial analysis of juxtacrine and paracrine communications. However, this constraint
+inevitably causes the failure of inferring long-range communications such as endocrine and telecrine signaling. Classification of LRIs into short-range and long-range communications with prior knowledge might be helpful to infer the comprehensive communication categories computationally. Moreover, it is potentially beneficial to include other omics data with the increasing multi-modal datasets generated from state-of-the-art technologies such as 10X Multiome and Digital Spatial Profiling\(^{51}\) in studying spatially regulated cell–cell communications. Thus, more reliable computational models might be needed for more accurate integration of multi-modal data and inference.
+
+Methods
+
+Datasets. For STARmap, the single-cell ST data of the mouse cortex (20180410-BY3_1kgenes) was obtained from a public data portal (https://www.dropbox.com/sh/f7ebheru1lbz91s/AABYSSJSTppBmVmWl2H4sKa?dl=0). For MERFISH, the single-cell ST data of the naive female mouse (Animal_ID: 1, Bregma: 0.26) hypothalamic preoptic region was downloaded from Dryad (https://datadryad.org/stash/dataset/doi:10.5061/dryad.8t8s248). For seqFISH+, the single-cell ST data of the mouse cortex and olfactory bulb were retrieved from the Github repository (https://github.com/CaiGroup/seqFISH-PLUS). For Slide-seq, the spot-based ST data of the mouse liver (Puck_180803_8) and somatosensory cortex (Puck_200306_03) were obtained from the Broad Institute Single Cell Portal (https://singlecell.broadinstitute.org/single_cell/study/SCP354/slide-seq-study) and (https://singlecell.broadinstitute.org/single_cell/study/SCP815/highly-sensitive-spatial-transcriptomics-at-near-cellular-resolution-with-slide-seqv2), respectively. For
+10X Visium, the spot-based ST data and scRNA-seq data of human SCC were downloaded from the Gene Expression Omnibus (GEO) repository (GSE144240). The mouse liver scRNA-seq data of non-parenchymal and parenchymal hepatic cells were refined from the MCA (https://figshare.com/articles/MCA_DGE_Data/5435866) and GSE125688, respectively. The mouse cortex scRNA-seq data were obtained from GSE71585.
+
+Data processing. For the liver scRNA-seq datasets, the non-parenchymal cells and parenchymal hepatic cells were collected from the MCA and GSE125688, respectively, wherein hepatocytes were classified into pericentral and periportal hepatocytes with principal component analyses and clustering analysis. For the MERFISH dataset, ependymal cells were excluded due to the limited cell number in the section (<2). For other datasets, all cells were included in the filtered matrices. Human and mouse gene symbols were revised in accordance with NCBI gene data (https://www.ncbi.nlm.nih.gov/gene/) updated on June 30, 2021, wherein unmatched genes and duplicated genes were removed. For all ST and scRNA-seq datasets, the raw counts were normalized via the global-scaling normalization method LogNormalize in preparation for running the subsequent scDeepSort pipeline.
+
+SpaTalk algorithm. The SpaTalk model consists of two components: cell-type decomposition and spatial LRI enrichment. The first component is to infer cell-type composition for single-cell or spot-based ST data, and the second component is to infer spatially proximal ligand–receptor interactions that mediate cell–cell communications in space.
+
+Cell-type decomposition. To dissect the cell-type composition for the ST data matrix \( T[n \times s] \) (\( n \) genes and \( s \) spots/cells), NNLM was first applied to obtain the
+optimal proportion of cell types using the scRNA-seq data matrix \( S[n \times c] \) (\( n \) genes and \( c \) cells) as the reference with \( k \) cell types. Let \( Y = \{y_1,\ y_2,...,\ y_n\} \) be the expression profile for each spot/cell to establish the following linear model:
+
+\[
+Y = X\beta + \varepsilon
+\]
+
+where \( X = [n \times k] \) is the average expression profile generated from \( S \) and \( \varepsilon \) represents random error. Mean relative entropy loss was then used to measure the difference between the predicted and observed values. Therefore, the objective function can be written as:
+
+\[
+\argmin \{\beta \geq 0\} L(Y - X\beta) + \lambda_1 R_1(\beta) + \lambda_\alpha R_\alpha(\beta) + \lambda_2 R_2(\beta)
+\]
+
+where \( R_1 \), \( R_\alpha \) and \( R_2 \) represent the L1, angle, and L2 regularization with non-negative \( \lambda_1 \), \( \lambda_\alpha \) and \( \lambda_2 \) initialized by zero\(^{23},\ ^{24}\). The model was trained with the above objective function using Lee’s multiplicative iteration algorithm\(^{25}\) with default hyperparameters until convergence or after 10,000 iterations to generate the coefficient matrix \( C[k \times s] \).
+
+For single-cell ST data, the cell type with the maximum coefficient was assigned to each cell. For spot-based ST data, let \( M \) be the maximum cell number for each spot, which was set to 30 for 10X Visium data and was set to 1 for Slide-seq data according to a recent review. In practice, the optimal cellular combination \( \omega \) for each spot was determined by the following function:
+
+\[
+\omega_i (i \in \{1, 2, ..., k\}) = \begin{cases}
+[M\beta_i] + 1 & (\{M\beta_i\} \geq 0.5) \\
+[M\beta_i] & (\{M\beta_i\} < 0.5)
+\end{cases}
+\]
+
+wherein \( [M\beta_i] \) and \( \{M\beta_i\} \) represent the integer and fractional parts of \( M\beta_i \), respectively. For each spot, we randomly selected \( m \) (\( m = \sum_{i=1}^k \omega_i \)) cells from \( S \) to compare their merged expression profile \( \epsilon \) with the ground truth according to the
+following function:
+
+\[
+\underset{m \leq M}{\operatorname{argmin}} \sum_{i=1}^{n} (Y_i - \sum_{j=1}^{m} \epsilon_i^j)^2
+\]
+
+To assign a coordinate \((x,\ y)\) to each sampled cell, we applied stochastic \(\alpha \in [0,\ 1]\) and \(\theta \in [0,\ 360]\) in spot \((x_0,\ y_0)\) to locate the cell into the space detailed in the following function:
+
+\[
+\begin{align*}
+x &= x_0 + \alpha d_{min} \cos(\theta \pi / 180) \\
+y &= y_0 + \alpha d_{min} \sin(\theta \pi / 180)
+\end{align*}
+\]
+
+where \(d_{min}\) represents the spatial distance of the closest neighbor spot. By integrating the optimal cellular combinations for all spots, ST data at single-cell resolution were reconstructed for the spot-based ST data.
+
+Spatial LRI enrichment. To generate the cell–cell distance matrix \(D\), the Euclidean distance between cells was calculated using the single-cell spatial coordinates of ST data. The KNN algorithm was then applied to each cell to select the \(K\) nearest cells from \(D\) to construct the cell graph network. For ligand \(i\) of the sender (cell type A) and receptor \(j\) of the receiver (cell type B), the number of LRI pairs (\(P_{Ai,Bj}^0\)) was obtained from the graph network by counting the 1-hop neighbor nodes of receivers for each sender. The permutation test was then performed by randomly shuffling cell labels to recalculate the number of LRI pairs. By repeating this step \(Z\) times, a background distribution \(P = \{P_{Ai,Bj}^1,\ P_{Ai,Bj}^2,\ ...,\ P_{Ai,Bj}^Z\}\) was obtained for comparison with the real interacting score, and the \(P\) value was calculated as follows:
+
+\[
+P_{Ai,Bj} = crad\{x \in P \mid x \geq P_{Ai,Bj}^0\}/Z
+\]
+
+where \(P_{Ai,Bj}\) values less than 0.05 were filtered to calculate the intercellular score of LRI from senders to receivers (\(S_{Ai,Bj}^{inter} = 1 - P_{Ai,Bj}\)). To further enrich the LRIs that activate downstream TFs, target genes, and the related pathways of receivers, the
+knowledge graph was introduced to model the intracellular signal propagation process.
+
+In practice, LRIs from CellTalkDB, pathways from KEGG and Reactome, and TFs from AnimalTFDB were integrated to construct the ligand–receptor–TF knowledge graph (LRT-KG), wherein the weight between entities represents the co-expressed coefficient. Taking the receptor as the query node, we incorporated the random-walk algorithm into the LRT-KG to filter and score the downstream activated \( t \) TFs with no more than 10 steps and Z iterations; thus, the probability \( p \) for each TF can be calculated with the ratio of successful hits from the query node to the target TF during the Z random walks. By integrating the co-expressed TFs and the corresponding target genes from the LRT-KG, the intracellular score of LRI from senders to receivers can be written as:
+
+\[
+S_{Ai,Bj}^{intra} = \sum_{k=1}^{t} \theta_k \times p_k / \eta_k
+\]
+
+where \( \theta \) represents the number of targeted genes, \( \eta \) represents the step from the receptor to the TF in the LRT-KG. By the sigmoid transformation for \( S_{Ai,Bj}^{intra} \), the final score of the LRI from cell type A to cell type B can be written as:
+
+\[
+S_{Ai,Bj} = \sqrt{S_{Ai,Bj}^{inter} \times S_{Ai,Bj}^{intra}}
+\]
+
+**Comparison with other methods.** STARmap, MERFISH, and seqFISH+ ST data were used to compare the performance of SpaTalk with other existing cell-type decomposition methods. For these single-cell ST data, all cells were split according to the fixed spatial distance and then merged into simulated spots as the benchmark datasets. RCTD, SPOTlight, Seurat, deconvSeq, and Stereoscope were benchmarked with the default parameters and evaluated with Pearson’s correlation coefficient and RMSE over the predicted and real cell-type composition for each spot.
+
+Given the limited genes of MERFISH ST data, STARmap and seqFISH+ single-cell ST
+data (including 1020 and 10,000 genes, respectively) were used as the benchmark datasets to compare the performance of SpaTalk with other cell–cell communication inference methods (Giotto, SpaOTsc, NicheNet, CytoTalk, and CellCall). The one-sided Wilcoxon test was performed to evaluate the spatial proximity significance of the inferred LRIs by comparing the number of expressed LRIs between sender–receiver pairs and all cell–cell pairs, and the co-expressed percent of the LRI was calculated to evaluate the co-expression level by counting the number of expressed LRIs from senders to receivers from the cell–cell graph network. All methods were benchmarked with the default parameters and all inferred LRIs were unbiasedly evaluated with the above criteria except for the LRIs from SpaOTsc since the number of inferred LRIs was much larger than that of the other methods; thus, the top 1000 LRIs for each cell–cell communication were selected from SpaOTsc according to the final score. Given the significantly enriched biological processes or pathways in the receiver cell type, the Fisher exact test was adopted for pathway enrichment analysis with the KEGG and Reactome databases on the activated genes in receivers using the following function:
+
+\[
+P = \binom{a+b}{a} \binom{c+d}{c} / \binom{n}{a+c}
+\]
+
+where \( n = a + b + c + d \); \( a \) is the number of inferred target genes that match a given pathway, \( b \) is the number of given pathway genes that exclude \( a \), \( c \) is the number of inferred target genes that unmatch a given pathway, and \( d \) is the number of all genes excluding \( a \), \( b \), and \( c \). NicheNet, CytoTalk, and CellCall were benchmarked with the default parameters and the inferred target genes for each LRI were evaluated according to the significance of pathway enrichment.
+
+Pathway and biological process enrichment. The Metascape web tool
+(https://metascape.org/) was used to perform the enrichment analysis of pathways and biological processes, wherein the top 100 highly expressed genes were selected according to the fold change of the average gene expression. Gene Set Enrichment Analysis (GSEA) was performed using the ranked gene list with the clusterprofiler tool to enrich the significantly activated pathways and biological processes, whose signatures were obtained from the Molecular Signatures Database v7.4 (MSigDB, http://www.gsea-msigdb.org/gsea/msigdb), including the gene sets from Gene Ontology (GO) and the canonical pathway gene sets derived from the KEGG, Reactome, and WikiPathways pathway databases.
+
+Module scoring of hallmarks and signatures. Hallmark scoring of metabolism of xenobiotics by cytochrome P450, synthesis of bile acids and bile salts, TSK, and EMT was performed using the “AddModuleScore” function in Seurat with default parameters. Hallmark pathways and EMT were obtained from MSigDB, and the signature genes of the TSK were download from the original publication by Jin et al.
+
+Statistics. R (version 4.1.1) and GraphPad Prism 8 were used for all statistical analyses.
+
+Data and code availability
+
+No new data was generated for this study. All data used in this study is publicly available as previously described. Source codes for the SpaTalk R package and the related scripts are available at github (https://github.com/ZJUFanLab/SpaTalk).
+
+Acknowledgements
+
+This work was supported by the National Natural Science Foundation of China (81973701), the Key Program, National Natural Science Foundation of China
+(81930016), the Key Research and Development Program of China (2021YFA1100500), the Major Research Plan of the National Natural Science Foundation of China (No.92159202), the Natural Science Foundation of Zhejiang Province (LZ20H290002), the China Postdoctoral Science Foundation (2021M702828) and Westlake Laboratory (Westlake Laboratory of Life Sciences and Biomedicine).
+
+Author contributions
+
+X.F., X.X., and H.C. conceived and designed the study. C.L., X.L., J.L., J.Q., and K.W. collected and analyzed the scRNA-seq and ST data. X.S., H.Y., J.C, and P.Y. implemented the algorithm of SpaTalk. X.S., C.L., and H.Y. developed the package of SpaTalk. All authors wrote the manuscript, read and approved the final manuscript.
+
+Competing interests
+
+The authors declare no competing interests.
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryFigures.pdf

0e6380fd5cbe3c0c7e8a39f2b23083f37592c615a5adfd5421239921c07e585d/preprint/preprint.md

@@ -0,0 +1,364 @@
+Midlatitude Mesoscale Thermal Air-sea Interaction Enhanced by Greenhouse Warming
+
+Xingzhi Zhang
+zhangxingzhi@ouc.edu.cn
+Ocean Univeristy of China
+
+Xiaohui Ma
+Ocean University of China   https://orcid.org/0000-0001-9937-3859
+
+Lixin Wu
+Ocean University of China   https://orcid.org/0000-0002-4694-5531
+
+Peiran Yang
+Laoshan Laboratory
+
+Fengfei Song
+Ocean University of China   https://orcid.org/0000-0002-3004-1749
+
+Zhao Jing
+Ocean University of China   https://orcid.org/0000-0002-8430-9149
+
+Hui Chen
+Ocean University of China
+
+Yushan Qu
+Ocean Univeristy of China
+
+Man Yuan
+Ocean Univeristy of China
+
+Zhaohui Chen
+Ocean University of China   https://orcid.org/0000-0002-0830-2332
+
+Bolan Gan
+Ocean University of China   https://orcid.org/0000-0001-7620-485X
+
+Article
+
+Keywords:
+
+Posted Date: February 19th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-3932615/v1
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on September 4th, 2024. See the published version at https://doi.org/10.1038/s41467-024-52077-z.
+Midlatitude Mesoscale Thermal Air-sea Interaction Enhanced by Greenhouse Warming
+
+Xiaohui Ma1,2, Xingzhi Zhang1,*, Lixin Wu1,2, Peiran Yang2, Fengfei Song1,2, Zhao Jing1,2, Hui Chen1, Yushan Qu1, Man Yuan1, Zhaohui Chen1,2, Bolan Gan1,2
+
+1. Frontiers Science Center for Deep Ocean Multispheres and Earth System and Key Laboratory of Physical Oceanography, Ocean University of China, Qingdao, China.
+2. Laoshan Laboratory, Qingdao, China.
+*Corresponding author. E-mail: zhangxingzhi@ouc.edu.cn
+
+Abstract
+
+The influence of greenhouse warming on mesoscale air-sea interactions, crucial for modulating ocean circulation and climate variability, remains largely unexplored due to the limited resolution of current climate models. This study addresses this gap by analyzing eddy-resolving high-resolution climate simulations and observations, focusing on the coupling between mesoscale sea surface temperature (SST) and latent heat flux (LHF) in winter. Our findings reveal a consistent increase in mesoscale SST-LHF coupling in the major western boundary current regions under warming, characterized by a heightened nonlinearity between warm and cold eddies and a more pronounced enhancement in the northern hemisphere. To understand the dynamics, we develop a theoretical framework that links mesoscale thermal coupling changes to large-scale factors, which indicates that the projected changes are collectively determined by historical background wind, SST, and the rate of SST warming. Among these factors, the large-scale SST and its warming rate are the primary drivers of hemispheric asymmetry in mesoscale coupling intensification. This study introduces a simplified approach for assessing the projected mesoscale thermal coupling changes and implies a growing significance of mesoscale air-sea interaction in shaping weather and climate patterns in a warming world.
+(WBC) regions in the midlatitudes, play a critical role in modulating extratropical weather and climate systems (Chelton et al., 2004; Small et al., 2008; Bryan et al., 2010; Czaja et al.,2019; Seo et al.,2023). The interaction between mesoscale oceanic eddies and the atmosphere actively impacts precipitation, storms, large-scale atmospheric circulations, and provides feedback to the ocean, influencing oceanic circulations and climate variability (Xie, 2004; Skyllingstad et al., 2007; Chelton and Xie, 2010; Frenger et al., 2013; Souza et al., 2014; Ma et al.,2016, 2017; Foussard et al., 2019; Renault et al.,2019; Gan et al.,2023). A key aspect of this interaction is the coupling between sea surface temperature and turbulent heat flux (SST-THF), hereafter denoted as thermal coupling. In terms of the atmosphere, thermal coupling acts as an energy source, which is crucial for the genesis and development of weather systems and deep troposphere response (Parffit et al 2016; Chen et al., 2017; Sheldon et al., 2017; Jiang et al., 2019; Zhang et al., 2019; Liu et al., 2021). In terms of the ocean, thermal coupling serves as an energy sink, which is the key to dissipating oceanic eddy energy and driving oceanic circulation response (Ma et al., 2016; Jing et al., 2020).
+
+How greenhouse warming will impact mesoscale oceanic eddies remains uncertain, let alone mesoscale air-sea coupling. Satellite observations reveal a rise in eddy activity in the WBC regions during recent decades, while climate models project heterogeneous eddy variations in different WBC regions under warming (Martínez-Moreno et al.,2021; Beech et al.,2022). Additionally, the theoretical framework for predicting the mesoscale thermal coupling change in response to greenhouse warming is currently absent. Thermodynamically, the SST warming and the associated water vapor increase governed by the Clausius–Clapeyron (C-C) relation, appear to strengthen the thermal air-sea coupling (primarily through the enhancement of latent heat flux) in a warming climate. Dynamically, the non-uniform warming between the upper and lower troposphere under anthropogenic forcing tends to increase
+atmospheric stability, inhibiting the vertical momentum transfer and thereby suppressing the surface wind and thermal air-sea coupling. This is further complicated by significant uncertainties in atmospheric circulation responses under climate change, introducing additional perturbations to SST-THF coupling. It is noteworthy that the aforementioned oceanic and atmospheric changes discussed within a conventional large-scale framework may not necessarily manifest at mesoscales. Physical processes governing the response of mesoscale thermal coupling to greenhouse warming are multifaceted, making it challenging to pinpoint the ultimate dominant factor.
+
+Utilizing an unprecedented set of high-resolution Community Earth System Model (referred to as CESM-HR, Methods) with ~0.25° atmosphere and ~0.1° ocean components that can explicitly resolve the mesoscale oceanic eddies and their coupling with the atmosphere, we investigated the impact of greenhouse warming on mesoscale thermal coupling in eddy-rich WBC regions. We then constructed a theoretical framework for estimating the mesoscale thermal coupling change in response to greenhouse warming through the decomposition of contributing factors. We further assessed the robustness of the findings by extending the analyses to High-Resolution Model Intercomparison Project (HighResMIP, Methods) models.
+
+Mesoscale thermal coupling during the observational period
+
+We first evaluated the model’s capability in representing the mesoscale thermal coupling in the CESM-HR simulations against observational data (Methods), in four major WBC regions, i.e., the Kuroshio Extension (KE), the Gulf Stream Extension (GS), the Agulhas Return Current (ARC) and the Brazil-Malvinas Confluence Region (BMC), by detecting eddies using sea surface height anomalies and constructing composite analyses with a reference frame centered on the eddy (see details in Methods). The model shows high fidelity in representing the statistical characteristics of eddies, such as the averaged number, amplitude and size, as detailed in Tab. S1. It also successfully reproduces the eddy-induced turbulent heat fluxes
+(including both sensible and latent components) along with their seasonality, for both anticyclonic warm and cyclonic cold eddies (Fig. S1). It is noted that the coupling strength peaks during the winter month. Furthermore, the eddy-induced sensible heat flux (SHF) is approximately half that of latent heat flux (LHF) and remains relatively stable between historical and future simulations (Fig. S2). Consequently, our subsequent analyses will focus on the mesoscale SST-LHF coupling in the hemispheric winter season — DJF for the Northern Hemisphere (NH) and JJA for the Southern Hemisphere (SH).
+
+To assess the potential impact of anthropogenic warming on mesoscale thermal coupling, we analyzed the decadal trend of mesoscale SST-LHF coupling in the observational periods based on high-pass spatial filtering fields (Methods). A significant intensification of mesoscale SST-LHF coupling at an approximate rate of 1.5 W/m^2/°C per decade is detected in the WBCs over the past four decades, with the most pronounced increase observed in the GS and KE regions of the NH (Fig. 1a). The CESM-HR successfully simulates the enhanced mesoscale thermal coupling in the WBCs with a magnitude slightly higher than that recorded in the observations (Fig. 1b). The model also captures the north-south hemispheric asymmetry of the changes. The alignment between model simulated and observational trends in the past lends credence to the use of CESM-HR for investigating the mesoscale coupling response under climate change.
+
+Mesoscale thermal coupling under greenhouse warming
+
+A linear regression between mesoscale SST and LHF based on eddy composites averaged across four WBC regions, yields an estimated coupling coefficient of approximately 28 W/m^2/°C for both anticyclonic warm and cyclonic cold eddies in historical simulations (1956-1975, Fig. 1c,d). The nonlinearity between warm and cold eddies appears to be minimal during the historical period. Under the high greenhouse forcing scenario of Representative Concentration Pathway 8.5, future simulations (2063-2082) project an approximate 13%
+enhancement in mesoscale SST-LHF coupling to 32 W/m^2/°C (Fig. 1d). A detailed examination of the four WBCs reveals a consistent increase in coupling strength by 6% to 20% in future simulations compared to historical simulations (Fig. 1e). Importantly, future simulations project a greater increase of mesoscale SST-LHF coupling strength for warm eddies than for cold eddies, indicating heightened nonlinearity in a warming climate. The increase in nonlinearity is expected to amplify net heat flux from mesoscale oceanic eddies (Ma et al. 2015; Foussard et al., 2019), thereby impacting future weather and climate systems more significantly. Additionally, the projected increase in mesoscale SST-LHF coupling in the GS and KE is twice that of the ARC and BMC, pointing to a more substantial intensification in the NH than in the SH. Combined with the findings in the observational periods, the results indicate that the hemisphere discrepancy in mesoscale SST-LHF coupling is likely to not only persist but also to become more pronounced with ongoing climate warming.
+
+Decomposition of contributing factors
+
+The LHF is proportional to both the surface wind and the humidity difference at the air-sea interface according to the Bulk formula (Large and Yeager 2004). To estimate the mesoscale SST-LHF coupling associated with oceanic eddies, we decompose the relevant fields into large-scale background and mesoscale components in line with previous studies (Yang et al.,2018; Yuan et al, 2023). The mesoscale SST-LHF coupling coefficient can be quantified using the following relationship (see detailed derivation in Methods):
+
+\[
+\frac{dq'_L}{dSST'} = \bar{\rho}_a \bar{A}_v \bar{C}_e [\overline{U}_{10} (\frac{dq'_s}{dSST'} - \frac{dq'_a}{dSST'}) + \frac{du'_{10}}{dSST'} (\bar{q}_s - \bar{q}_a)]
+\]
+
+Here, the prime (') represents mesoscale anomalies defined by the high-pass spatial filtering, and the overbar (̄) denotes large-scale background excluding the mesoscale signal.
+
+The mesoscale SST-LHF coupling coefficient (\( \frac{dq'_L}{dSST'} \)) is determined by two components: the thermodynamic adjustment to mesoscale SST multiplied by the largescale wind
+\(
+(\overline{U}_{10} (\frac{dq'_s}{dSST'} - \frac{dq'_a}{dSST'}), \text{ hereafter denoted as mesoscale thermodynamic adjustment term}), \text{ and the dynamic adjustment to mesoscale SST multiplied by the large-scale humidity difference } (\frac{du'_{10}}{dSST'} (\overline{q}_s - \overline{q}_a ), \text{ hereafter denoted as mesoscale dynamic adjustment term}). \text{ Evaluation of historical and future simulations in the WBC regions reveals an increase in both terms due to greenhouse forcing (bars with black borders in Fig. 2a-d). Particularly, the enhancement of the thermodynamic adjustment term is about 3 to 5 times that of the dynamic adjustment term across all four WBCs (Fig. 2a-d), indicating the dominant contribution of the thermodynamic adjustment term to mesoscale SST-LHF coupling modulation. A further decomposition of the thermodynamic adjustment term reveals that the large-scale wind change between historical and future simulations is negligible (bars with magenta borders in Fig. 2a-d), while the predominant influence arises from the mesoscale moisture response to oceanic eddies, especially the specific humidity change at the ocean surface (\( \frac{dq'_s}{dSST'} \) is an order of magnitude greater than \( \frac{dq'_a}{dSST'} \)). Collectively, the results suggest that the amplification in mesoscale moisture response is the principal driver for the strengthened mesoscale SST-LHF coupling under climate change.
+
+The above analyses indicate that changes in mesoscale SST-LHF coupling due to warming can be effectively estimated via the mesoscale moisture adjustment process. Nonetheless, this estimation still relies on the availability of both mesoscale and large-scale fields from historical and future simulations. To circumvent this, we apply a Taylor series expansion to the mesoscale moisture derivative (see detailed derivation in Methods). The resultant expression provides a simplified approach to assess mesoscale SST-LHF coupling change using large-scale fields:
+
+\[
+\left( \frac{dq'_f}{dSST'} \right)_{(F-P)} = (\bar{\rho}_a \bar{A}_v \bar{C}_e)_{(P)} \cdot \overline{U}_{10(P)} \left( \frac{d^2 q_s(T)}{dT^2} |_{T=SST(P)} \cdot \Delta SST \right)
+\]
+
+Here, 'F' represents future values and 'P' represents historical values in the past. It is evident
+that changes in mesoscale SST-LHF coupling are collectively affected by the large-scale wind and the curvature of the C-C scaling from the historical simulations, along with the projected warming of large-scale SST. Note that the curvature of the C-C scaling is inherently linked with the background SST, with higher temperature corresponding to a more pronounced moisture-temperature sensitivity. The relationship suggests that projections of future mesoscale SST-LHF coupling are significantly influenced by the historical large-scale oceanic and atmospheric conditions. Given that the large-scale wind and the curvature of the C-C scaling stay positive, it can be inferred that the direction of mesoscale SST-LHF coupling is exclusively determined by the sign of projected SST changes, leading to consistent intensification in line with the warming of underlying SST.
+
+We then assessed the regional variations in mesoscale SST-LHF coupling responses among the four WBC regions using Eq. (2), with emphasis on the north-south hemisphere asymmetry. The simplified relationship efficiently captures the more pronounced increase in coupling strength within the KE and GS regions compared to the ARC and BMC regions (Fig. 3a), consistent with the projected intensification of mesoscale SST-LHF coupling between future and historical simulations. Detailed examination of contributing factors in CESM-HR demonstrates consistently higher values for large-scale wind and SST in the KE and GS regions in the NH from historical simulations, alongside a more rapid SST warming rate (Fig. 3c), all of which jointly contribute to the enhanced augmentation in mesoscale coupling strength in the NH under climate change. The historical large-scale wind in the KE is approximately 30% stronger than that in the ARC and BMC, and the background SST in the GS is 7°C higher than in the BMC, corroborated by observations (Fig. 3d). Additionally, the accelerated SST warming trend in the NH is also confirmed by the observational data (Fig. 3d). Further decomposition of the three factors indicates their respective contribution to the overall hemispheric discrepancy (Fig. 3b), with the large-scale SST warming rate being the dominant
+factor, followed by the background SST.
+
+Validations in HighResMIP
+
+We extend the analyses to HighResMIP simulations (Methods) and to different warming periods (2030-2050), aiming to verify the robustness of the findings. All models examined show an increase in mesoscale SST-LHF coupling in response to greenhouse warming across four WBCs by the year 2050 (Tab. 1). A more pronounced intensification of this coupling is projected in the NH compared to the SH, in line with CESM-HR results (Fig. 1e), albeit with a generally lower magnitude of change. The magnitude discrepancy is due to the HighResMIP projections here terminating in 2050, whereas CESM-HR projections shown in Fig 1 extend to a later period of the century (2080).
+
+The effectiveness of the proposed theoretical framework for estimating changes in mesoscale SST-LHF coupling due to greenhouse warming was also evaluated across different models. A comparison between the coupling strength changes estimated by the theoretical framework and those projected by CESM-HR reveals a significant linear relationship across four WBCs (Fig. S3). The estimated and actual projected changes in mesoscale SST-LHF coupling are highly correlated, with a correlation coefficient of around 0.7 in the KE and GS, and 0.5 in the ARC and BMC (Tab. 1). Similar linear correlations, ranging generally from 0.5 to 0.8 (Tab. 1), are found between estimated and projected mesoscale coupling strength changes in HighResMIP models, confirming the broad applicability of the simplified framework across diverse climate models.
+
+Conclusions and Discussions
+
+How greenhouse warming will influence mesoscale air-sea interactions remains an open question. Utilizing eddy-resolving high-resolution CESM simulations, supported by observational and HighResMIP data, we found a ubiquitous intensification (approximately 15%) of mesoscale SST-LHF coupling in WBC regions by the end of the 21st century under the
+RCP8.5 warming scenario. The intensification is characterized by an increased nonlinearity between warm and cold eddies and a more pronounced enhancement in the NH. Our findings suggest an increasingly important role of mesoscale oceanic processes in shaping weather and climate systems in a warming climate, especially in the NH. This underscores the critical need for climate models to incorporate mesoscale air-sea interaction for more reliable climate projections.
+
+We found that the mesoscale moisture response is the key factor driving the strengthened mesoscale SST-LHF coupling under climate change. To further understand the dynamics, we developed a theoretical framework to estimate the mesoscale moisture change. The framework builds a linkage between mesoscale coupling changes and large-scale fields, revealing that the projected mesoscale moisture changes can be estimated by the interplay among historical background wind, SST, and projected SST warming. The direction of mesoscale SST-LHF coupling changes is exclusively determined by the sign of projected SST changes. Given a scenario of SST warming, the mesoscale SST-LHF coupling will invariably exhibit intensification. The relationship highlights the importance of C-C scaling in determining changes in mesoscale SST-LHF coupling, suggesting that higher large-scale SST, determined either by historical baselines or future warming rates, are associated with greater rates of moisture increase and thereby enhanced augmentation of mesoscale SST-LHF coupling.
+
+The effectiveness of the proposed theoretical framework was evaluated across CESM-HR and HighResMIP models. The analysis reveals a robust linear correlation between estimated and projected changes in mesoscale SST-LHF, suggesting the broad applicability of the theoretical framework within major WBC regions. However, it is important to acknowledge that the prerequisite conditions for the theoretical framework to work are the mesoscale moisture adjustment significantly surpasses the mesoscale wind adjustment, the mesoscale moisture adjustment at the ocean surface significantly exceeds that at the atmospheric surface,
+and the large-scale wind changes due to warming is minimal. These conditions may not hold outside the WBCs, potentially undermining the framework’s applicability.
+
+Methods
+
+CESM-HR, HighResMIP Simulations and Observations
+
+We utilized the high-resolution Community Earth System Model (CESM-HR) simulations with ~0.25° atmosphere and ~0.1° ocean components developed by the National Center for Atmosphere Research (NCAR) (Chang et al.,2020). The simulations include a 500-year preindustrial control simulation and a 250-year historical and future simulation from 1850-2100. Historical radiative forcing is applied from 1850 to 2005 while the Representative Concentration Pathway 8.5 (RCP8.5, a high greenhouse gas emission) warming forcing is switched from 2006 onwards. Two 20-year periods with high-frequency (daily) output were chosen to assess the mesoscale thermal coupling response to greenhouse warming in CESM-HR: a historical period from 1956 to 1975 (referred to as HIS) and a future period from 2063 to 2082 (referred to as RCP).
+
+Five HighResMIP simulations with relatively high oceanic resolution were selected: CMCC-CM2-VHR4 (0.25° atmosphere and 0.25° ocean), HadGEM3-GC31-HH (0.5° atmosphere and 0.08° ocean), EC-Earth3P-HR (0.5° atmosphere and 0.25° ocean), CNRM-CM6-1-HR (1° atmosphere and 0.25° ocean), MPI-ESM1-2-XR (0.5° atmosphere and 0.5° ocean). We note that only one model (HadGEM3-GC31-HH) has comparable oceanic resolutions with CESM-HR, yet its atmospheric resolution is coarser. All these selected models include a 100-year historical and future (under RCP8.5 scenario) simulation from 1950-2050. For a consistent comparison between CESM-HR and HighResMIP simulations, 1950-1969 for historical and 2031-2050 for future projections were selected for the corroborative analysis shown in Tab. 1.
+Daily sea surface height (SSH) derived from Copernicus Marine Environment Monitoring Service (CMEMS) during 2003-2007 was used to identify eddies in observations (Tab. S1). Concurrently, SST obtained from the National Oceanic and Atmospheric Administration daily Optimum Interpolation SST (NOAA-OISST) and heat fluxes derived from Japanese Ocean Flux Data Sets with Use of Remote Sensing Observations version3 (J-OFURO3) during the same period were employed to construct observational eddy composites (Fig. S1). ERA5 reanalysis (the fifth generation European Centre for Medium-Range Weather Forecasts atmospheric reanalysis, Hersbach et al., 2020) with an extended temporal span from 1979 to 2022 was utilized to examine the decadal trend of mesoscale coupling strength (Fig. 1a).
+
+Eddy detection, Eddy Composites and High-pass Filtering
+
+In both CMEMS observations and CESM-HR simulations, mesoscale eddies were detected using daily SSH anomalies derived by applying high-pass spatial filtering (20° longitude x 10° latitude) to remove the large-scale signal, following previous studies (Faghmous et al., 2013; Qu et al., 2022). Cyclonic (anticyclonic) eddies are classified by closed contours of SSH anomalies that include a single minimum (maximum), with an SSH anomaly increment (decrement) of 0.05 cm between successive contours. The edge of an eddy is delineated by the outmost closed contour of SSH anomalies. The radius of an eddy corresponds to the radius of a circle with an equivalent area to that enclosed by the outmost contour. The amplitude of an eddy is defined by the SSH anomaly difference between the eddy’s peak and its defined edge. Only eddies with a radius ranging from 70 to 200 km and an amplitude exceeding 3cm are included in the analysis.
+
+Eddy composites were constructed by aligning associated variables to the reference coordinate of the eddy core. The variables were normalized by the individual eddy radius and oriented to the prevailing direction of the large-scale background surface wind, in line with
+previous research (Frenger et al., 2013). Variables within twice the eddy radius were included for composite analysis.
+
+In addition to eddy composite analysis, we also applied a high-pass Loess Filter with a cutoff wavelength of 30° longitude x 10° latitude (similar to a 5°x5° box car average, Bryan et al. 2010, Ma et al. 2016) in ERA5, CESM-HR and HighResMIP, to isolate mesoscale SST and LHF and examined the spatial distribution of their coupling strength (Fig. 1a,b and Fig S3). The coupling strength at each grid point was computed using the linear regression coefficient between high-pass filtered monthly SST and LHF over a spatial domain of 4°x4°. It was noted that applying a high-pass filter directly to monthly data yields a coupling coefficient comparable to that obtained when the filter is first applied to daily data, which is then aggregated into a monthly mean before calculating the coefficient. The former method was selected for its computational efficiency. To highlight regions with pronounced mesoscale SST-LHF coupling, mesoscale signals where the SST anomaly fell below 0.4°C in ERA5 and below 0.6°C in CESM-HR were excluded when computing the decadal trend in coupling strength (Fig. 1a, b).
+
+Decomposition of mesoscale SST-LHF coupling
+
+According to Bulk formula (Large and Yeager 2004), the latent heat flux \( Q_L \) is determined by the equation:
+
+\[
+Q_L = \rho_a \; \Lambda_v \; C_e \; U_{10} (q_s - q_a)
+\]
+
+Here, \( \rho_a \) is the surface air density, \( \Lambda_v \) is the latent heat of vaporization, and \( C_e \) is the transfer coefficients for evaporation. \( U_{10} \) is the 10m wind speed, \( q_s \) is the saturated specific humidity at the ocean surface, and \( q_a \) is air specific humidity at 2m.
+
+Following previous studies (Yang et al.,2018; Yuan et al, 2023), equation (1) can be decomposed into large-scale background and mesoscale components. The mesoscale component of latent heat flux is estimated as follows:
+\[
+Q'_L = \bar{\rho}_a \bar{A}_v \bar{C}_e [\bar{U}_{10}(q'_s - q'_a) + U'_{10}(\bar{q}_S - \bar{q}_a)]
+\] (2)
+
+Here, the prime (') represents mesoscale anomalies defined by the high-pass spatial filtering, and the overbar (\( \bar{} \)) denotes large-scale background excluding the mesoscale signal.
+
+By differentiating with respect to SST, the mesoscale SST-LHF coupling is expressed as:
+
+\[
+\frac{dq'_L}{dSST'} = \bar{\rho}_a \bar{A}_v \bar{C}_e [\bar{U}_{10} (\frac{dq'_s}{dSST'} - \frac{dq'_a}{dSST'}) + \frac{dU'_{10}}{dSST'} (\bar{q}_S - \bar{q}_a)]
+\] (3)
+
+Based on calculations, the second term \( \frac{dU'_{10}}{dSST'} (\bar{q}_S - \bar{q}_a) \) on the right-hand side of Eq. (3) is an order of magnitude smaller than the first term \( \bar{U}_{10} (\frac{dq'_s}{dSST'} - \frac{dq'_a}{dSST'}) \). Furthermore, \( \frac{dq'_a}{dSST'} \) is an order of magnitude smaller than \( \frac{dq'_s}{dSST'} \). Disregarding the relatively smaller terms and assuming the changes in \( \bar{\rho}_a \bar{A}_v \bar{C}_e \) is minimal under global warming, the mesoscale SST-LHF coupling changes is predominately influenced by \( \bar{U}_{10} \frac{dq'_s}{dSST'} \), which can be represented as:
+
+\[
+\left( \frac{dq'_L}{dSST'} \right)_{(F-P)} = (\bar{\rho}_a \bar{A}_v \bar{C}_e)_{(P)} [\bar{U}_{10(F)} \left( \frac{dq'_s}{dSST'} \right)_{(F)} - \bar{U}_{10(P)} \left( \frac{dq'_s}{dSST'} \right)_{(P)}]
+\] (4)
+
+Where 'F' represents future values and 'P' represents historical values in the past. As the large-scale wind, \( \bar{U}_{10(F)} \) and \( \bar{U}_{10(C)} \), experience minimal changes in the WBCs, Eq. (4) can be further simplified as:
+
+\[
+\left( \frac{dq'_L}{dSST'} \right)_{(F-P)} = (\bar{\rho}_a \bar{A}_v \bar{C}_e)_{(P)} \cdot \bar{U}_{10(P)} [ \left( \frac{dq'_s}{dSST'} \right)_{(F)} - \left( \frac{dq'_s}{dSST'} \right)_{(P)} ]
+\] (5)
+
+Applying a Taylor expansion, the right-hand side term can be approximated as:
+
+\[
+\left( \frac{dq'_s}{dSST'} \right)_{(F)} - \left( \frac{dq'_s}{dSST'} \right)_{(P)} = \frac{d^2 q_s(T)}{dT^2}|_{T=\overline{SST}_{(P)}} \cdot \Delta SST
+\] (6)
+
+Substituting (6) into (5) yields:
+
+\[
+\left( \frac{dq'_L}{dSST'} \right)_{(F-P)} = (\bar{\rho}_a \bar{A}_v \bar{C}_e)_{(P)} \cdot \bar{U}_{10(P)} \frac{d^2 q_s(T)}{dT^2}|_{T=\overline{SST}_{(P)}} \cdot \Delta SST
+\] (7)
+
+Where \( \frac{d^2 q_s(T)}{dT^2} \) is determined by C-C scaling and exhibits an exponential increase with
+temperature. Note that the composite coefficient (\( \bar{\rho}_a \overline{A}_v \bar{C}_e \)) is retained to align the estimated coupling strength changes with magnitude analogous to the actual projections.
+Data Availability
+
+CMEMS data can be obtained through https://data.marine.copernicus.eu/products. NOAA-OISST can be accessed through https://www.ncei.noaa.gov/products/optimum-interpolation-sst. J-OFURO3 can be achieved through https://www.j-ofuro.com/en/. ERA5 reanalysis can be downloaded from https://doi.org/10.24381/cds.bd0915c6. The CESM simulations can be achieved through https://ihesp.github.io/archive/products/ds_archive/Sunway_Runs.html. The HighResMIP data can be downloaded from https://pcmdi.llnl.gov/CMIP6/.
+
+Code Availability
+
+MATLAB codes to reproduce the analyses are available upon request from the corresponding author or can be accessed through the link https://zenodo.org/records/10610386.
+
+Acknowledgments
+
+This research is supported by the National Natural Science Foundation of China (42376025), Science and Technology Innovation Program of Laoshan Laboratory (LSKJ202300302, LSKJ202202503), Shandong Provincial Natural Science Foundation (ZR2022YQ29), Taishan Scholar Funds (tsqn202103028). We thank Sunway TaihuLight High-Performance Computer (Wuxi), Laoshan Laboratory in Qingdao and the National Supercomputing center in Jinan for providing the high resolution CESM simulations and high-performance computing resources that contributed to the research results reported in this paper.
+
+Author Contributions
+
+X. M. and X. Z conceived the study. X. M. instructed the investigation and wrote the manuscript. X. Z. performed the analyses and produced all figures. L. W. supervised the project. P. Y., F. S. and M. Y. contributed to the discussion of mesoscale thermal coupling decomposition. Y. Q and H. C. offered insights into eddy detection. Z. J., Z. C. and B. G. contributed to interpreting the results and improving the manuscript.
+
+Competing Interests statement
+The authors declare no competing interests.
+
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+Figures
+
+![Observed and simulated trends in mesoscale SST-LHF coupling. Global distribution of the decadal trends of mesoscale SST-LHF coupling strength as derived from ERA5 (a) and CESM-HR (b) during 1979-2022. The coupling strength is computed using the linear regression coefficient between high-pass filtered monthly SST and LHF (Methods) with trends significant at a 99% confidence level indicated by black dots. (c) Composites of SST (color shading) and LHF (contours) anomalies associated with mesoscale oceanic eddies during historical periods (1956-1975) in CESM-HR. Shown are winter season mean anomalies in warm minus cold eddy composites within four WBC regions (outlined by red boxes in a, b). The white circle represents one eddy radius and the white dot marks the eddy center. (d) Mesoscale SST-LHF coupling strength during historical (1956-1975) and future (2063-2082) periods in CESM-HR for warm (red) and cold (blue) eddies averaged across four WBC regions. The coupling strength is computed using the linear regression coefficient between SST and LHF anomalies within twice the radius of eddy composites. (e) Differences in mesoscale SST-LHF coupling strength between future and historical periods in CESM-HR for warm (red bars) and cold (blue bars) eddies in the KE, GS, ARC and BMC regions, with fractional differences labeled atop the respective bars.
+Fig. 2 Decomposition of mesoscale SST-LHF coupling response under greenhouse warming. (a) Differences in thermodynamic and dynamic adjustments between future and historical periods in CESM-HR in the KE region. From left to right, the terms plotted are thermodynamic adjustment \( \overline{U}_{10} (\frac{dq'_s}{dSST'} - \frac{dq'_a}{dSST'}) \), dynamic adjustment \( \frac{du'_{10}}{dSST'} (\overline{q}_S - \overline{q}_a) \), large-scale surface wind (\( \overline{U}_{10} \)) and moisture adjustment \( (\frac{dq'_s}{dSST'} - \frac{dq'_a}{dSST'}) \). (b-d), as for a, but for the GS, ARC and BMC regions, respectively.
+Fig. 3 Decomposition of mesoscale moisture response under greenhouse warming. (a) Estimated changes in mesoscale SST-LHF coupling between future and historical periods in CESM-HR according to Eq. 2 in the KE GS, ARC and BMC regions. The large-scale SST averaged in the WBCs are displayed on the bottom axis for each respective region. Black lines denote the standard deviations of the corresponding variables. (b) Contributions of \( \bar{U}_{10}, \frac{d^2 q_s(T)}{dT^2} \) and \( \Delta SST \) to the north-south hemispheric asymmetry in the KE GS, ARC and BMC regions. The total deviation from the hemispheric mean due to three terms in a specific region is approximated by \( (ABC)' \approx A'\bar{B}\bar{C}+B'\bar{A}\bar{C}+C'\bar{A}\bar{B} \). Here, A, B, and C denotes the three terms; the overbar denotes a mean component (the average across the four WBCs); the prime denotes an anomaly component (the deviation from the hemispheric mean for each specific WBC region). (c) The historical large-scale surface wind, SST and the projected SST warming within the four WBC regions in CESM-HR. (d) as for c, but for observational data. Surface wind is derived from ERA5 and SST is derived from NOAA-OISST. \( \Delta SST \) is computed based on the warming trend observed over the last 40 years.
+Table. 1 Projected and estimated mesoscale SST-LHF coupling changes in CESM-HR and HighResMIP models.
+
+<table>
+  <tr>
+    <th rowspan="2"></th>
+    <th colspan="4">Projected coupling changes (RCP-HIS) (W·m<sup>−2</sup>·°C<sup>−1</sup>)</th>
+    <th colspan="4">Correlation between projected and estimated changes</th>
+  </tr>
+  <tr>
+    <th>KE</th>
+    <th>GS</th>
+    <th>ARC</th>
+    <th>BMC</th>
+    <th>KE</th>
+    <th>GS</th>
+    <th>ARC</th>
+    <th>BMC</th>
+  </tr>
+  <tr>
+    <td>CESM-HR</td>
+    <td>3.2<br>(10.26%)</td>
+    <td>3.5<br>(15.34%)</td>
+    <td>1.9<br>(6.68%)</td>
+    <td>1.5<br>(6.72%)</td>
+    <td>0.71</td>
+    <td>0.69</td>
+    <td>0.45</td>
+    <td>0.49</td>
+  </tr>
+  <tr>
+    <td>CMCC-CM2-VHR4</td>
+    <td>4.1<br>(14.27%)</td>
+    <td>2.5<br>(11.97%)</td>
+    <td>1.5<br>(6.65%)</td>
+    <td>0.07<br>(0.35%)</td>
+    <td>0.76</td>
+    <td>0.65</td>
+    <td>0.60</td>
+    <td>0.54</td>
+  </tr>
+  <tr>
+    <td>HadGEM3-GC31-HH</td>
+    <td>3.2<br>(11.95%)</td>
+    <td>2.0<br>(8.76%)</td>
+    <td>2.8<br>(11.34%)</td>
+    <td>2.4<br>(11.88%)</td>
+    <td>0.78</td>
+    <td>0.66</td>
+    <td>0.58</td>
+    <td>0.61</td>
+  </tr>
+  <tr>
+    <td>MPI-ESM1-2-XR</td>
+    <td>2.9<br>(14.06%)</td>
+    <td>2.0<br>(10.14%)</td>
+    <td>1.6<br>(9%)</td>
+    <td>0.9<br>(5.24%)</td>
+    <td>0.41</td>
+    <td>0.69</td>
+    <td>0.72</td>
+    <td>0.78</td>
+  </tr>
+  <tr>
+    <td>EC-Earth3P-HR</td>
+    <td>2.0<br>(8.37%)</td>
+    <td>2.4<br>(11.24%)</td>
+    <td>1.5<br>(6.41%)</td>
+    <td>0.5<br>(2.72%)</td>
+    <td>0.72</td>
+    <td>0.76</td>
+    <td>0.69</td>
+    <td>0.66</td>
+  </tr>
+  <tr>
+    <td>CNRM-CM6-1-HR</td>
+    <td>2.2<br>(10.1%)</td>
+    <td>2.4<br>(12.4%)</td>
+    <td>1.2<br>(7.52%)</td>
+    <td>0.9<br>(3.58%)</td>
+    <td>0.69</td>
+    <td>0.7</td>
+    <td>0.67</td>
+    <td>0.58</td>
+  </tr>
+</table>
+
+Note that mesoscale SST-LHF coupling strength changes analyzed here correspond to differences between the historical period of 1950-1969 and the mid-21st century projections for the period of 2031-2050.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SI.pdf

0e85f9efde7d6b5ff7517772dbef871099da6254a7b2b3ce7363284a60076323/peer_review/peer_review.md

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+Peer Review File
+
+Microbial interactions shape cheese flavour formation
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewer #1 (Remarks to the Author):
+
+Melkonian et al provides new insights into inter-species metabolic interactions in cheese flavour formation during ripening. This study has highlighted strain interactions and how their population dynamics in a mixture can shape the metabolic interactions and overall flavour profile of cheese. Streptococcus thermophilus seems to drive Lactococcus lactis growth in cheeses older than 3 months, through the export of amino acids. However, the discussion of cheese flavour compounds should be related back to the metabolic influence between the species, to reinforce the basis of the interactions.
+
+The genomes of the individual strains were used to predict metabolic flux values. Then metatranscriptomics data were obtained from simplified communities used to evaluate up and down regulation of transcripts to validate metabolic regulation. Peptide profiles, free amino acids and SPME-GC-MS data were used for compound profiling of cheese aged to 1 year (5 time points). The authors should clarify what was done in milk fermentations compared to cheese aging.
+
+The conclusions of the paper could be made clearer with a distinct separation between the hypotheses and the findings in the study.
+
+More literature could be cited throughout to complement and confirm some findings of the study. For example, a recent article by first author Ozcan (including Bas Teusink, DOI: 10.1002/bit.27565) was published in 2020 but this work is not cited in the current manuscript. The previous publication cites the current first author, Melkonian, among others, for support (discussion and advice). The previous research points to proteolysis and amino acid exchange as one of the important interactions, citing the yogurt protocooperation between S. thermophilus and L. bulgaricus. In the previous work, genome scale metabolic models were used, while the experimental work was done in chemically-defined medium (CDM), not milk, and the strains used were MG1363 for L. lactis subsp. cremoris and IL1403 for L. lactis subsp. lactis (both non-PrtP strains). There should be some major differences between this previous work and the results obtained in the current study, especially using proteolytic and lactose-utilizing lactococci (if the isolates have been tested for these activities).
+
+The overall design could also be clearer, especially between the Lactococcus lactis blend and individual strains. How did the authors select the strains used in this study from the original industrial strain culture (the defined S-LAB culture) and what was the rationale behind their selection?
+
+Minor revisions are needed throughout the text on clarity of conclusions, experimental design, and spelling/grammar of text. Overall, this manuscript represents a detailed and in-depth analysis of metabolic interactions between starter bacteria in cheese ripened to one year. It would be beneficial to state the cheese type that represents the process used.
+
+Specific comments:
+The word “different” should be replaced by the actual relationship. Example: “different metabolic re-routing”; how is this different between L. cremoris and other L. lactis?
+
+L78: Not clear what peptides are being talked about.
+L89: Any reasons why the metabolic effects become more evident over 3 months of ripening?
+L46: Mention the specific hypotheses to be investigated in the introduction.
+L54: We used for variations of starter cultures; do you mean four?
+L83: need clarification on result and “significant” influence on non-growing yet active cells during long-term cheese ripening.
+L92: We “hypothesize” that this will happen, I do not think it is being used in the right context here, as this is what the study found.
+L97: controlled vs additional strains that were removed- need clarification on this experimental design.
+L115: strain activity referring to the stress tolerance from acidification at different temperatures?
+L147: make sure figures are correctly cited for what is being referred to in the text.
+L205: what is the proteolytic activity of Lactococcus? Do the strains of either species have PrtS (S. thermophilus) or PrtP (Lactococcus). The literature should be referenced a bit more here on complementary proteolysis.
+L218: which compounds were significantly altered? Add some statistics to the text?
+L222: What is meant by “donate”? This should be explained in terms of cross-feeding metabolism. Where is this coming from?
+L247: cite literature.
+L250: Would this section be more like the conclusions of the study?
+L264: not very clear- trying to say that activity and flavour profile is Lactococcus strain-dependent when mixed with S. thermophilus?
+L273: Methods do not state anything about the temperature stress results and how PCC was calculated (data analysis), also more can be reported on what statistical analysis was done as results mention ANOVA only. Perhaps refer to the supplementary material for details on the statistical analysis and tools used.
+L279: What is the inoculation rate of each bulk?
+L280: spelling “S. thermophils”
+L280-281: How was the Lactococcus blend made? How much of each strain was added to the blend?
+L283: Should this original SLAB composition be added at the beginning of methods? As this is where the rationale of all bulks comes from.
+L318: Culture inoculation rates?
+L381: Not clear that two culture inoculations were used in L293-L295.
+L408: No volatile profile for cheese at 2 weeks? Make clear throughout when each analysis was done with respect to the time points.
+L481: Explain the parameters from the metabolic modelling packages. Does the difference between export and import from fluxes come from here, and what does the frequency scale mean?
+L483: Any statistics with this analysis?
+Figure 1: Strain names should be added to the legend.
+Figure 5: Correct the spelling of “stain”.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors present a comprehensive work of high significance combined genomics, metatranscriptomics, metabolomics and metabolic modelling to uncover key microbial interactions in Cheddar cheese-making using industrially relevant SLAB strains. The introduction part is brief and clearly clarifies the main scope of the work. Materials and methods as well as Results are well-presented and adequately detailed, showing how strain-specific metabolic interactions between microbes shape the biochemical profile of cheese using a multi omics-approach. Finally, the Discussion section is brief and sufficiently substantiated by the Results. Overall, I believe that this work can be published in Nature Communications.
+
+Reviewer #3 (Remarks to the Author):
+
+In this study, the authors combined genomics, metatranscriptomics, metabolomics, and metabolic modelling to study key microbial interactions in Cheddar cheese-making by using industrial strains and a full cycle of year-long cheese ripening. The authors reported competitive and cross-feeding metabolic interactions between the lactic acid bacteria used in Cheddar cheese production. Their main findings are following, L. cremoris strain competes with L. lactis for citrate, resulting in accumulation of key metabolites in the final product. In addition, they showed that S.
+thermophilus provides the necessary nitrogen source to the Lactococcus community, which explained one-year long growth of the Lactococcus population and the different final cheese metabolome profile. This is a comprehensive study into interspecies interactions of microbial communities underlying cheese flavor formation.
+
+While the efforts and the data presented in the paper are greatly appreciated, the significance of the work is limited to cheese microbiomes. It is specific, and does not confer broad intellectual significance expected for a publication in the journal.
+
+Additionally, there have been a series of prior studies which harness native food microbiome as well-defined model systems to elucidate the structure, interaction and dynamics of microbial communities. In fact, several of these earlier studies exactly used cheese microbiomes as experimental systems. Thus, the paper also lacks conceptual innovation on that front either.
+
+Specific comments
+1. The background of industrial SLAB culture should be elaborated more. For instance, it is unclear the original/initial abundance of different LAB or characteristics of each species.
+2. Experiments are needed to verify the microbial interaction agents of different LAB from omics sequencing and metabolic modelling, after identifying metabolic factors.
+3. Fig. 2: Why were the flavor-related compounds missing between 2 weeks and 3 months in Fig. 2f?
+4. Fig. 2h and Supplementary Fig. 3a are duplicated.
+5. There are many typos and minor errors in the paper, including but not limited to:
+   - Fig 1: “Additinal” shall be “Additional”
+   - Fig2: “HP-all” or “HP_All”
+   - Line 327: “Lactococcus spp.” should be “Lactococcus spp.”
+   - Line 329: “thermophilic cocci” should be “Thermophilic cocci”
+   - Line 338: “33mM”, “48mM”. Space needed.
+   - Line 535: “150bp”. Space needed.
+   - Line 153-174: check the figure numbers here. Fig. 3 is irrelevant to modelling and simulation.
+Point-by-point response to the reviewers’ comments.
+
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Melkonian et al provides new insights into inter-species metabolic interactions in cheese flavour formation during ripening. This study has highlighted strain interactions and how their population dynamics in a mixture can shape the metabolic interactions and overall flavour profile of cheese. Streptococcus thermophilus seems to drive Lactococcus lactis growth in cheeses older than 3 months, through the export of amino acids. However, the discussion of cheese flavour compounds should be related back to the metabolic influence between the species, to reinforce the basis of the interactions.
+We thank the reviewer for positive feedback and for providing constructive suggestions. Additional discussions regarding how metabolic interactions connect to flavour is added at L97-102, L242-246 and we rewrote part of the conclusion based on reviewer’s comments, L283-293.
+
+The genomes of the individual strains were used to predict metabolic flux values. Then metatranscriptomics data were obtained from simplified communities used to evaluate up and down regulation of transcripts to validate metabolic regulation. Peptide profiles, free amino acids and SPME-GC-MS data were used for compound profiling of cheese aged to 1 year (5 time points). The authors should clarify what was done in milk fermentations compared to cheese aging.
+There is a separation between the two experiments, indicated by "in cheese" or "in milk" in the titles of the respective method sections. Furthermore, Figure 1 aims to clarify the specific procedures carried out in milk fermentation versus the cheese aging experiment. Although metabolomics was conducted in both experiments, different approaches were employed. It is important to note that peptides were not measured in the milk experiment (which were devised to investigate specific mechanisms in a reduced complexity context). To provide further details, the caption of Figure 1 has been expanded to describe the approaches used, and the metabolomics icons have been color-coded differently. Specifically, in relation to cheese, the caption now includes the phrase "measuring acids, sugars, flavor-related organic compounds, and peptides." Regarding milk, the caption specifies "(i.e., acids, sugars, flavor-related organic compounds)." For more in-depth information, readers are encouraged to refer to the method sections and consult our GitHub repository.
+
+The conclusions of the paper could be made clearer with a distinct separation between the hypotheses and the findings in the study.
+Thank you for the suggestion. We rewrote the conclusion based on reviewer’s comment: L283-293.
+
+More literature could be cited throughout to complement and confirm some findings of the study. For example, a recent article by first author Ozcan (including Bas Teusink, DOI:
+10.1002/bit.27565) was published in 2020 but this work is not cited in the current manuscript. The previous publication cites the current first author, Melkonian, among others, for support (discussion and advice). The previous research points to proteolysis and amino acid exchange as one of the important interactions, citing the yogurt protocooperation between S. thermophilus and L. bulgaricus. In the previous work, genome scale metabolic models were used, while the experimental work was done in chemically-defined medium (CDM), not milk, and the strains used were MG1363 for L. lactis subsp. cremoris and IL1403 for L. lactis subsp. lactis (both non-PrtP strains). There should be some major differences between this previous work and the results obtained in the current study, especially using proteolytic and lactose-utilizing lactococci (if the isolates have been tested for these activities).
+We acknowledge that we missed this important publication which corroborates our findings. Now we cite the suggested publication at introduction L32 and with additional text at L225-227 “A previous study conducted in a chemically-defined medium has identified proteolysis and amino acid exchange as significant interactions between S. thermophilus and L. lactis”. Furthermore, we added additional discussion and cited more literature across the manuscript. Regarding the PrtS and PrtP activity, genomic and transcriptomics inspection indicated the presence of transcribed PrtS for ST and the presence of transcribed PrtP for 19 Lactococcus strains, including the 3 major strains. In-depth analysis to investigate the proteolytic activity of the strains was not performed, but it was shown before that the presence of PrtS/PrtP correlates with fast acidifications [1,2].
+
+1) Karlsen ST, Vesth TC, Oregaard G, Poulsen VK, Lund O, Henderson G, et al. (2021) Machine learning predicts and provides insights into milk acidification rates of Lactococcus lactis. PLoS ONE 16(3): e0246287. https://doi.org/10.1371/journal.pone.0246287
+2) Dandoy D, Fremaux C, de Frahan MH, Horvath P, Boyaval P, Hols P, Fontaine L. The fast milk acidifying phenotype of Streptococcus thermophilus can be acquired by natural transformation of the genomic island encoding the cell-envelope proteinase PrtS. Microb Cell Fact. 2011 Aug 30;10 Suppl 1(Suppl 1):S21. doi: 10.1186/1475-2859-10-S1-S21. Epub 2011 Aug 30. PMID: 21995822; PMCID: PMC3231928.
+
+The overall design could also be clearer, especially between the Lactococcus lactis blend and individual strains. How did the authors select the strains used in this study from the original industrial strain culture (the defined S-LAB culture) and what was the rationale behind their selection?
+
+We have used an existing commercial SLAB culture widely used in cheddar cheese production. The text at methods were extended at L332-335 to clarify the SLAB composition as well as a new supplementary table 15.
+In general, the rationale includes the addition of S. thermophilus to accelerate the acidification and Lactococcus Blend as additional genetic background to act as a defense against potential phage attack. More details on the rationale about the specific strains and relative proportion in the culture fall under confidential legislation. Also, how to design SLAB communities fall outside the scope of this manuscript and it is subject to future work. We decided to choose a formulation
+that is relevant for commercial production. Nevertheless, more information can be found in literature about the rationale behind such SLAB culture [3].
+
+3) Høier, E., Janzen, T., Rattray, F., Sørensen, K., Børsting, M. W., Brockmann, E., & Johansen, E. (2010). The Production, Application and Action of Lactic Cheese Starter Cultures. In Technology of Cheesemaking (pp. 166–192). Wiley-Blackwell. https://doi.org/10.1002/9781444323740.ch5
+
+Minor revisions are needed throughout the text on clarity of conclusions, experimental design, and spelling/grammar of text. Overall, this manuscript represents a detailed and in-depth analysis of metabolic interactions between starter bacteria in cheese ripened to one year. It would be beneficial to state the cheese type that represents the process used.
+The cheese type is cheddar, which serves as a keyword and is referenced in the abstract, at the end of the introduction, and a total of six times throughout the manuscript.
+
+Specific comments:
+The word “different” should be replaced by the actual relationship. Example: “different metabolic re-routing”; how is this different between L. cremoris and other L. lactis?
+We replaced “different” by providing more information at the abstract and at the end of introduction L50-51.
+
+L78: Not clear what peptides are being talked about.
+A reference to Supplementary Fig. 2 has been added, indicating an example of six peptides with their corresponding amino acid sequences. Additionally, the amino acid sequences of the peptides presented in Figure 2 have been included in the caption. For even more in-depth view code and proceed data are provided in the accompanied github repository:
+https://github.com/Chrats-Melkonian/mi_cheese/tree/main/code/02_Figure02_R
+
+L89: Any reasons why the metabolic effects become more evident over 3 months of ripening? Discussion is added at L97-102 regarding why the metabolic effects become more evident over 3 months of ripening flavour compound regarding metabolic influence between the species and more literature is cited.
+
+L46: Mention the specific hypotheses to be investigated in the introduction.
+Text is added at L46-48 to clarify the aim/hypotheses of the second experiment, controlled milk fermentations, in relation to the findings from the first experiment, a one-year long cheese making experiment.
+
+L54: We used for variations of starter cultures; do you mean four?
+Yes, corrected to four.
+
+L83: need clarification on result and “significant” influence on non-growing yet active cells during long-term cheese ripening.
+We rewrote the sentence for clarity in L88-90.
+L92: We “hypothesize” that this will happen, I do not think it is being used in the right context here, as this is what the study found.
+Replaced with “conclude”.
+
+L97: controlled vs additional strains that were removed- need clarification on this experimental design.
+Reference to Fig. 1b is added.
+
+L115: strain activity referring to the stress tolerance from acidification at different temperatures?
+Rewritten as “acidification potential”.
+
+L147: make sure figures are correctly cited for what is being referred to in the text.
+Thank you for spotting this; checked and corrected.
+
+L205: what is the proteolytic activity of Lactococcus? Do the strains of either species have PrtS (S. thermophilus) or PrtP (Lactococcus). The literature should be referenced a bit more here on complementary proteolysis.
+We cited Kunji, E.R.S., Mierau, I., Hagting, A. et al. The proteolytic systems of lactic acid bacteria. Antonie van Leeuwenhoek 70, 187–221 (1996). https://doi.org/10.1007/BF00395933 and a review published in Food Microbiology and Biotechnology (FMB), 2018 by Gabriela Mariana Rodríguez-Serrano et. al. under the name “Proteolytic System of Streptococcus thermophilus” to support our hypothesis.
+
+L218: which compounds were significantly altered? Add some statistics to the text?
+We have included a reference to Supplementary Figure 9-10 and Supplementary Section 0.3 to ensure better correspondence with the text. The statistics have been indicated on the figures and in their respective figure captions. For even more in-depth view on the altered compounds the reader can look into our github repository:
+https://github.com/Chrats-Melkonian/mi_cheese/blob/main/code/07_Figure5panelA_C.R
+And
+https://github.com/Chrats-Melkonian/mi_cheese/blob/main/code/08_Figure05PanelE_supp_plots.R
+
+L222: What is meant by “donate”? This should be explained in terms of cross-feeding metabolism. Where is this coming from?
+We have rewritten this section, specifically at L237-241, providing an explanation in terms of cross-feeding interactions and substrate competition.
+
+L247: cite literature.
+We added literature: Jeroen Hugenholtz, Citrate metabolism in lactic acid bacteria 1993. Yaqi Wang et. al Metabolism Characteristics of Lactic Acid Bacteria and the Expanding Applications in Food Industry 2021 and reuse Blaya J, et. al. Symposium review: Interaction of starter cultures and non starter lactic acid bacteria in the cheese environment.. 2018
+L250: Would this section be more like the conclusions of the study?
+We followed the journal guidelines by naming the sections as Results and Discussion.
+Nevertheless, we agree with the reviewer and change the Discussion section into Conclusions also we modify Results into Results & Discussion. We will rely on the Journal and editor for the final decision.
+
+L264: not very clear- trying to say that activity and flavour profile is Lactococcus strain-dependent when mixed with S. thermophilus?
+We wrote as follows at L284-285: “In addition, we have identified that different strains of Lactococcus affect the activity of S. thermophilus differently.” Based on results presented on Fig. 3
+
+L273: Methods do not state anything about the temperature stress results and how PCC was calculated (data analysis), also more can be reported on what statistical analysis was done as results mention ANOVA only. Perhaps refer to the supplementary material for details on the statistical analysis and tools used.
+We added text in methods regarding temperature stress results L542-544 and regarding the PCC calculations as well as other statistical analysis we introduce a new method section under the name “General statistical and computational analysis” L595-608.
+
+L279: What is the inoculation rate of each bulk?
+We have provided the proportion fo the culture in the new supplementary tables 15.
+L280: spelling “S. thermophils”
+Corrected
+
+L280-281: How was the Lactococcus blend made? How much of each strain was added to the blend?
+As mentioned before, the details of the rationale of Lactococcus blend falls under commercially sensitive confidential information. Nevertheless, we can share that in the Lactococcus blend the strains are in equal proportion. Our research focuses on mechanistically understanding how the different components in a complex system interact with each other and how those interactions affect the final cheese flavor. This is what we demonstrated.
+
+L283: Should this original SLAB composition be added at the beginning of methods? As this is where the rationale of all bulks comes from.
+We believe this part has to be at the end as the reader first needs to understand each component and the different conditions before reading about the rationale.
+
+L318: Culture inoculation rates?
+We added new supplementary table 15 to reflect the ratio of each component used in the cheese experiments. In the main text at methods L329-333 the total inoculation of each culture is reported.
+L381: Not clear that two culture inoculations were used in L293-L295.
+We are not sure what the reviewer refers to in this comment. L381 is in the section “Free amino acids in cheese”. We believe the additional information now gives a clear view of the two experiments, the SLAB culture, their conditions and compositions.
+
+L408: No volatile profile for cheese at 2 weeks? Make clear throughout when each analysis was done with respect to the time points.
+Volatile analysis at 2 weeks was not conducted as development of volatile compounds in Cheddar cheese at such an early stage is limited, compared to Cheddar cheeses with an age of 3, 6, 9 or 12 months. The development of many of the volatile compounds in cheeses depends on the conversion of free amino acids by, e.g. aminotransferases. The low level of free amino acids identified at 2 weeks supports that the volatile compound would also be limited. That is why we do not find it relevant to do the analysis of volatiles at week 2. Indeed, the reason for a long maturation time is to allow for flavour formation. Additional text was added at L446-447.
+
+L481: Explain the parameters from the metabolic modelling packages. Does the difference between export and import from fluxes come from here, and what does the frequency scale mean?
+The differences between export and import fluxes comes from the fact that we are simulating models under different media compositions (specified in Figure 4a), and also from the fact that models are gapfilled under different media compositions (see supplementary figure 6d). The frequency simply refers to the number of times across the above-specified-simulation conditions where we observed a given compound to be imported or exported by a given community member.
+
+For individual GEM simulations with cobrapy and reframed see script (https://github.com/Chrats-Melkonian/mi_cheese/blob/main/code/04_individual_GEM_sims.py ). Detailed documentation is available online (https://cobrapy.readthedocs.io/en/latest/, https://reframed.readthedocs.io/en/latest/ )
+
+For community simulations with SMETANA see script (https://github.com/Chrats-Melkonian/mi_cheese/blob/main/code/04_community_GEM_sims.sh )
+• --verbose : outputs more information
+• --detailed : detailed algorithm outputs interactions between species
+• -o ${simMedia}_${modelSet} : specify output file name, simMedia refers to a given media composition used for simulation e.g. milk (aerobic), and modelSet refers to the community members metabolic models gapfilled under a given media composition e.g. milk (anaerobic)
+• --mediadb media_db.tsv : specify media database file to read from
+• -m $simMedia : specify media composition to use for simulation
+• models/$modelSet/*.xml: specify set of models to simulate community interactions
+The parameters are explained in further detail in the SMETANA documentation (https://smetana.readthedocs.io/en/latest/usage.html).
+
+L483: Any statistics with this analysis?
+No statistical analysis was employed here due to the qualitative nature of the metabolic modeling approach, i.e. we are exploring the possible exchanged metabolites across different media compositions, rather than e.g. making claims about significant differences in the distributions of absolute flux values across media compositions / conditions. Furthermore, the main finding is that Valine exchange stood out as being a key metabolite for community growth across multiple simulation conditions (i.e. SMETANA score of 1).
+
+Figure 1: Strain names should be added to the legend.
+Added.
+
+Figure 5: Correct the spelling of “stain”.
+Corrected.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors present a comprehensive work of high significance combined genomics, metatranscriptomics, metabolomics and metabolic modelling to uncover key microbial interactions in Cheddar cheese-making using industrially relevant SLAB strains. The introduction part is brief and clearly clarifies the main scope of the work. Materials and methods as well as Results are well-presented and adequately detailed, showing how strain-specific metabolic interactions between microbes shape the biochemical profile of cheese using a multi omics-approach. Finally, the Discussion section is brief and sufficiently substantiated by the Results. Overall, I believe that this work can be published in Nature Communications.
+We thank the reviewer for the positive assessment.
+
+Reviewer #3 (Remarks to the Author):
+
+In this study, the authors combined genomics, metatranscriptomics, metabolomics, and metabolic modelling to study key microbial interactions in Cheddar cheese-making by using industrial strains and a full cycle of year-long cheese ripening. The authors reported competitive and cross-feeding metabolic interactions between the lactic acid bacteria used in Cheddar cheese production. Their main findings are following, L. cremoris strain competes with L. lactis for citrate, resulting in accumulation of key metabolites in the final product. In addition, they showed that S. thermophilus provides the necessary nitrogen source to the Lactococcus community, which explained one-year long growth of the Lactococcus population and the different final cheese metabolome profile. This is a comprehensive study into interspecies interactions of microbial communities underlying cheese flavor formation.
+While the efforts and the data presented in the paper are greatly appreciated, the significance of the work is limited to cheese microbiomes. It is specific, and does not confer broad intellectual significance expected for a publication in the journal.
+
+Additionally, there have been a series of prior studies which harness native food microbiome as well-defined model systems to elucidate the structure, interaction and dynamics of microbial communities. In fact, several of these earlier studies exactly used cheese microbiomes as experimental systems. Thus, the paper also lacks conceptual innovation on that front either. We thank the reviewer for the comments. To our knowledge, our study is the first that addresses the effect of interactions between members of LAB culture on the development of cheese flavour and under an industrially relevant conditions (including an year long experiment). In addition our integrative multi-omics alongside experimental design was not done before. Although Cheese microbiomes were studied as experimental systems, our view is that we are only at the start of understanding how the complex biochemical reactions governed by polymicrobial activity affect the final cheese formation and its flavour. Thus, a focus on a clear functional aspect of the complex cheese microbial interactions and not merely compositional dynamics is a distinguishing feature of our study,
+
+Specific comments
+1. The background of industrial SLAB culture should be elaborated more. For instance, it is unclear the original/initial abundance of different LAB or characteristics of each species.
+We added additional text that references supplementary table 15 (L332-333) to indicate the ratio of the SLAB cultures across the conditions for the cheese experiments.
+
+2. Experiments are needed to verify the microbial interaction agents of different LAB from omics sequencing and metabolic modelling, after identifying metabolic factors.
+We would like to note that given the challenges posed by microbial ecosystems in complex environments as cheese, our study has progressed from dynamics to key mechanistic insights relevant for a key community-scale output - flavour. Any additional work by other researchers will be welcome. Our current study, based on reviewer's assessment, already “presents a comprehensive investigation into the interspecies interactions of microbial communities underlying cheese flavor formation.”
+
+3. Fig. 2: Why were the flavor-related compounds missing between 2 weeks and 3 months in Fig. 2f?
+Volatile analysis at 2 weeks was not conducted as development of volatile compounds in Cheddar cheese are very limited as compared to Cheddar cheeses with an age of 3, 6, 9 or 12 months. Indeed, this is the reason why the experiment was a year-long. The development of many of the volatile compounds in cheeses depends on the conversion of free amino acids by i.e. aminotransferases. The low level of free amino acids identified at 2 weeks supports that the volatile compound would also be limited. That is why we do not find it relevant to do the analysis of volatiles at week 2. Additional text was added at L446-447.
+
+4. Fig. 2h and Supplementary Fig. 3a are duplicated.
+The reviewer is correct. We would like to retain this duplication because the 2h panel highlights a single example, while the 3a panel provides a correspondence between cheese and milk experiments.
+
+5. There are many typos and minor errors in the paper, including but not limited to:
+- Fig 1: “Additinal” shall be “Additional”
+- Fig2: “HP-all” or “HP_All”
+We went through the manuscript to identify and correct typos.
+For Fig. 2 “HP” is correct, as HP is not a removal condition, instead it is hand packed inoculation of the original complete culture. We modified text and figures accordingly.
+
+- Line 327: “Lactococcus spp.” should be “Lactococcus spp.”
+We rephrase Lactococcus spp. to Mesophilic cocci (Lactococcus) to better describe what the method measures.
+
+- Line 329: “thermophilic cocci” should be “Thermophilic cocci”
+Done.
+
+- Line 338: “33mM”, “48mM”. Space needed.
+Done.
+
+- Line 535: “150bp”. Space needed.
+Done.
+
+- Line 153-174: check the figure numbers here. Fig. 3 is irrelevant to modelling and simulation.
+Done.

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+Electrochemically induced crystalline-to-amorphization transformation in sodium samarium silicate solid electrolyte for long-lasting all-solid-state sodium metal batteries
+
+Ge Sun
+Key Laboratory of Physics and Technology for Advanced Batteries (Ministry of Education), State Key Laboratory of Superhard Materials, College of Physics, Jilin University
+
+Chenjie Lou
+Center for High Pressure Science and Technology Advanced Research
+
+Zhixuan Wei
+Jilin University
+
+Shiyu Yao
+Jilin University
+
+Ziheng Lu
+University of Cambridge
+
+Gang Chen
+Jilin University
+
+Ze Shen
+Nanyang Technological University   https://orcid.org/0000-0001-7432-7936
+
+Mingxue Tang
+Center for High Pressure Science & Technology Advanced Research
+
+Fei Du (dufei@jlu.edu.cn)
+Jilin University   https://orcid.org/0000-0001-6413-0689
+
+Article
+
+Keywords:
+
+Posted Date: March 7th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2623650/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on October 16th, 2023. See the published version at https://doi.org/10.1038/s41467-023-42308-0.
+Electrochemically induced crystalline-to-amorphization transformation in sodium samarium silicate solid electrolyte for long-lasting all-solid-state sodium metal batteries
+
+Ge Sun¹⁴, Chenjie Lou²⁴, Zhixuan Wei¹, Shiyu Yao¹, Ziheng Lu³*, Gang Chen¹, Zexiang Shen¹, Mingxue Tang²*, Fei Du¹*
+
+¹Key Laboratory of Physics and Technology for Advanced Batteries (Ministry of Education), State Key Laboratory of Superhard Materials, College of Physics, Jilin University, Changchun, 130012, China.
+
+²Center for High Pressure Science and Technology Advanced Research (HPSTAR), Beijing 100193, China.
+
+³Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom
+
+⁴These authors contributed equally: Ge Sun, Chenjie Lou.
+
+*Email: zluag@connect.ust.hk (Z. L.); mingxue.tang@hpstar.ac.cn (M. T.); dufei@jlu.edu.cn (F. D.)
+Abstract
+
+Exploiting solid electrolyte (SE) materials with high ionic conductivity, good interfacial compatibility, and ultraconformal contact with electrode are essential for solid-state sodium metal batteries (SSBs). Here we report a crystalline Na5SmSi4O12 SE which features high room-temperature ionic conductivity of \(2.90 \times 10^{-3}\) S cm\(^{-1}\) and a low activation energy of 0.15 eV. All-solid-state symmetric cell with Na5SmSi4O12 delivers excellent cycling life over 800 h at 0.15 mA h cm\(^{-2}\) and high critical current density of 1.4 mA cm\(^{-2}\). Such excellent electrochemical performance is attributed to an electrochemically induced *in-situ* crystalline-to-amorphous (CTA) transformation propagating from the interface to the bulk during repeated deposition and stripping of sodium, which lead to faster ionic transport and superior interfacial properties. Impressively, the Na3V2(PO4)3||Na5SmSi4O12||Na SSBs achieves a remarkable cycling performance over 4000 cycles (6 months) with no capacity loss. These results not only identify Na5SmSi4O12 as a promising SE, but also emphasize the potential of the CTA transition as a promising mechanism towards long-lasting SSBs.
+
+Introduction
+
+All-solid-state batteries (ASSBs) are expected to provide key improvements over today’s rechargeable batteries owing to the inherent merits of solid electrolytes (SEs) such as high safety, long-lasting life, and high energy density\(^{1,2}\). Among them, sodium-based ASSBs are drawing ever-increasing interest because of the abundant resource in nature, beneficial to cost saving and sustainability\(^{3,4}\). Despite the progress of sodium-
+based ASSBs in the past few years, it is still a significant challenge to exploit low-cost and facile synthesized SEs with high ionic conductivity, excellent mechanical and chemical stability. Moreover, the poor wetting of the solid-solid interface with sluggish interfacial kinetics is a big hurdle to future Na-ASSBs development5,6.
+
+Generally, Na-based inorganic SEs can be divided into two categories, e.g., sulfides like Na3SbS4, Na11Sn2PS12, Na7P3S11 and oxides including Na-β"-Al2O3, NASICON-type7. Sulfide electrolytes feature higher ionic conductivity and better ductility than the oxides SEs8,9. However, their chemical instability against air and narrow electrochemical window are likely to induce complex side reaction, leading to shortened cycling lives10,11. In contrast, NASICON-type oxides could deliver high thermal and chemical stability, and low thermal expansion12,13. Nevertheless, large grain boundary resistance and harsh synthesis conditions are critically challenging for their application14,15. Recently, our group reported a novel structure of SE, Na5YSi4O12, with a high room-temperature ionic conductivity of \(1.59 \times 10^{-3}\) S cm\(^{-1}\), comparable with the sulfide SEs16. Furthermore, in comparison with the NASICON-type materials, Na5YSi4O12 can be synthesized at a lower temperature which is beneficial to cost- and energy-saving. More impressively, the stable structure provides sufficient freedom of materials optimization and design by substituting the Y sites by for instance, In, Sc, and the rare earth Lu-Sm, to further enhance the ionic conductivity and understand the ion-conducting behavior of this class of materials17,18.
+
+Besides the difficulty in the SEs exploration, another challenge of developing Na-ASSBs lies in the electrode-electrolyte interfaces, in the mechanics throughout the cell,
+and in processing at scale\(^{19}\). To begin with, the poor ductility and crystallographic orientation-dependent ionic transport properties of oxide SEs likely induce a large interfacial resistance and sluggish kinetics\(^{20},\ ^{21}\). In addition, during the continuous dissolution of sodium, the formation of pores at the sodium metal anode interface will further worsen the interfacial physical contact and generate unavoidable surface defects that could disturb sodium-ion flux and work as the nucleation center, leading to rapid dendrite nucleation and growth\(^{22},\ ^{23}\). Moreover, most SEs are intrinsically thermodynamically unstable against sodium metal, which induces degradation and forms mixed conducting interphases, further accelerating the dendrite propagation\(^{24},\ ^{25}\).
+
+To address these issues, many approaches are employed to fabricate an artificial layer on the surface of sodium metal to improve sodium wetting, chemical stability, and thus reduce interfacial impedance, such as TiO\(_2\)\(^{26}\), SnS\(_2\)\(^{27}\), etc\(^{28},\ ^{29}\). However, they face practical limitations, such as complex synthesis procedures and difficulty in controlling the thickness and achieving acceptable adhesion. Even worse, the artificial interface layer is likely to introduce additional interfacial issues with bulk SEs, such as unexpected phase transition, uneven ion flux distribution, and electrostatic potential drop and formation of “space-charge layer”, seriously limiting the ion transport and reducing the cycle life of ASSBs\(^{30}\).
+
+Herein, we report a new member of the Na\(_5\)MSi\(_4\)O\(_{12}\) family with M=Sm. It has the highest room-temperature ionic conductivity of \(2.90 \times 10^{-3}\) S cm\(^{-1}\) among the Na\(_5\)MSi\(_4\)O\(_{12}\) family that have been reported. Interestingly, we observe an electrochemically induced crystalline-to-amorphous (CTA) transformation of
+Na5SmSi4O12 SE during repeated deposition and stripping of Na. This CTA transition is attributed to the lattice stress generated upon Na+ transportation rather than phase transformation due to chemical instability. When applied in a Li symmetric cell with the same cell configuration (Li||Na5SmSi4O12||Li), this CTA process is speeded up because of the mismatch between Li+ and Na+ ionic radius, which further improves the selectivity of the Li ASSBs. Beneficial from the enhanced mechanical properties, decreased ion mobility activation energy, and lower interfacial energy of amorphous material and interface than crystalline Na5SmSi4O12, symmetric Na cells deliver a low overpotential of ~26 mV and ultra-stable cycling performance over 800 h at 0.15 mA cm^{-2}. Moreover, the amorphous Na5SmSi4O12 facilitates intimate contact of SE with Na metal and brings essentially improved critical current density (CCD) of 1.4 mA cm^{-2} in comparison with the initial crystalline stage (0.6 mA cm^{-2}). By virtue of the decreased resistance of sodium metal anode, the assembled quasi-solid-state Na3V2(PO4)3||Na5SmSi4O12||Na cell demonstrates an ultra-long cycle lives over 4000 cycles with ~100% Coulombic efficiency and capacity retention, indicative of the promising application of Na5SmSi4O12 SE in future large-scale energy storage.
+Results
+
+Synthesis and characterization of crystalline Na5SmSi4O12.
+
+Hexagonal-prismatic crystalline Na5SmSi4O12 was successfully synthesized via two-step solid-state reaction, first at 800 °C for 8 h and then 950 °C for 20 h, according to the stoichiometric mixtures of Na2CO3, Sm2O3 and SiO2. As compared in the XRD patterns before and after the second sintering (Supplementary Fig. 1), pure Na5SmSi4O12 can form after the first sintering. And the second sintering helps to achieve a dense ceramic pellet with few interfacial and bulk pores (Supplementary Fig. 2), beneficial to lower the grain boundary resistance and increase the ionic conductivity.
+
+Note that the sintering temperature of Na5SmSi4O12 is lower than other oxide SEs (Supplementary Table 1), such as Na5YSi4O12, Na-β"-Al2O3, Na3Zr2Si2PO12 and its derivatives, etc., good for the cost- and energy-saving. As shown in Fig. 1a, X-ray diffraction (XRD) was taken to identify the structural property of Na5SmSi4O12, and the Rietveld refined parameters are listed in Supplementary Table 2. All the diffraction peaks can be indexed into a hexagonal system with space group \( R-3c \), and the lattice parameters are calculated as \( a = b = 22.14609 \) Å and \( c = 12.68858 \) Å. Energy dispersive X-ray spectroscopy (Supplementary Fig. 3) suggests all the elements of Na, Sm, Si and O are uniformly dispersed in the as-prepared Na5SmSi4O12.
+
+The ionic conductivity of Na5SmSi4O12 was then studied by the alternating current (AC) impedance spectra. The Nyquist plot at room temperature is, as presented in Fig. 1b, composed with a semicircle at high frequency and a tail at low frequency. Via fitting the bulk and grain boundary resistance, the total ionic conductivity of Na5SmSi4O12 is
+calculated as \(2.90 \times 10^{-3}\) S cm\(^{-1}\), among the highest values in the existing ceramic electrolytes (Supplementary Table 1). Activation energy (\(E_a\)) of Na\(_5\)SmSi\(_4\)O\(_{12}\) was further evaluated via temperature-dependent AC impedance spectra, as displayed in Fig. 1b. With increasing temperature, the high frequency semicircle gradually vanishes, indicative of enhanced Na\(^+\) transport across the grain boundaries. By fitting the Arrhenius plot (Fig. 1c), \(E_a\) is calculated as small as 0.15 eV, indicative of a rapid ion hoping. In addition, the electronic conductivity of Na\(_5\)SmSi\(_4\)O\(_{12}\) was measured as about \(5.8 \times 10^{-10}\) S cm\(^{-1}\) via a direct current (DC) polarization measurement (Supplementary Fig. 4). The intrinsic electronic insulation can effectively reduce the self-discharge of batteries and suppress dendrite growth, enabling Na\(_5\)SmSi\(_4\)O\(_{12}\) as a good candidate for sodium based ASSBs\(^{31}\). Besides the merits of high ionic and low electronic conductivities, Na\(_5\)SmSi\(_4\)O\(_{12}\) demonstrates superior moisture stability, whose XRD pattern shows no change after soaking in deionized water for 48 h (Supplementary Fig. 5) or exposing to air for 45 days (Supplementary Fig. 6), showing great potential in future industrial application.
+
+To further reveal the ion conduction mechanism, molecular dynamics simulation was carried out. As shown in Fig. 1d-g, Na ions in Na\(_5\)SmSi\(_4\)O\(_{12}\) can be characterized by their mobility, i.e., the non-mobile ones Na1, Na2, Na3 and the mobile ones Na4, Na5, Na6. The conductivity is contributed by a percolating conduction pathway in the mobile region, whereas the rest of Na ions serve as a pillar to hold the structure together. Such a behavior was also proposed in the same family of materials from our previous work\(^{16}\). Interestingly, along the ion conduction pathway, three distinctive sites are
+revealed where Na ions can stably sit in, denoted as sites A, B, and C. These sites are connected to each other via the zigzag like channel as observed from the molecular dynamics simulation trajectory. Furthermore, the diffusion barrier of Na ions between these sites are found to be ~0.3 eV, which is relatively low in comparison with other reported solid ion conductors\(^{32,33}\). However, such a value is larger than the activation energy from experiment. We assign such a deviation to the concerted Na hopping behavior. The ~0.3 eV barrier was calculated by assuming a vacancy-mediated uncorrelated conduction mechanism, while the Na concentration is relatively high and concerted motion is favored. The case of concerted motion is further estimated by assuming a two-ion correlated hopping mechanism, as shown in Fig. 1h. According to such a mechanism, the diffusion barrier along the same path dropped to ~0.19 eV, close to the experimental value.
+
+Furthermore, solid-state \(^{23}\)Na nuclear magnetic resonance (NMR) measurements were carried out to reveal the atomic local structure and dynamics mobility\(^{34,35,36}\). As exhibited in Fig. 1i, the pristine Na\(_5\)SmSi\(_4\)O\(_{12}\) conductor shows multiple \(^{23}\)Na resonances, which can be further deconvoluted into six types of signals. Via the aid of crystal structure and the proportion of sodium, the peak at 8.8 ppm is assigned to the mobile sodium at Na5 site, the resonance at 4.5 ppm and 1.6 ppm are attributed to Na1 and Na3, the signal at -16.8 ppm is from Na4, and the rest peaks at -23.4 ppm and -28.6 ppm are assigned to sodium at Na2 and Na6 sites, respectively. The simulated details are listed in Supplementary Table 3, from which the proportion of each Na atom agrees with the theoretical results. To obtain more information about Na\(^+\) dynamics properties,
+NMR spectra at different temperatures were performed. As displayed in Supplementary Fig. 7, the Na5SmSi4O12 show similar spectra upon increasing temperature from 213 K to 367 K, except decrease in signal due to Boltzmann distribution. No obvious change is observed for spectral configuration, possibly attributed to the stable structure caused by the non-mobile Na ions at Na1, Na2, and Na3 sites. Therefore, we turn to a more temperature sensitive parameter, spin-lattice relaxation (SLR) time (\( T_1 \)). Since the strong quadrupole interaction is observed for \( ^{23}\mathrm{Na} \) NMR spectrum in our system, saturation recovery technique is employed to determine \( T_1 \) values\(^{37}\). Via fitting the spectral intensity vs. saturation recovery period measured at room-temperature (Fig. 1j), two relaxation time values of 0.5 and 20 ms are obtained for the non-mobile and mobile Na ions, respectively\(^{38}\). Here, the data analysis is simplified to non-mobile and mobile for convenience. According to Eq. (1), the fitting of the relaxation times as a function of temperature yields an activation energy \( E_a \approx 0.13 \) eV for the mobile Na\(^+\), which is in good agreement with the results from AC impedance (0.15 eV).
+
+\[
+R_1 = 1/T_1 \propto \omega_0^\beta \exp[-E_a/(kT)]
+\]
+
+Where \( R_1 \) is NMR spin-lattice relaxation rate, the reciprocal of \( T_1 \), \( \omega_0 \) is resonance frequency, \( \beta \) is modified exponent, \( E_a \) is activation energy, \( k \) is Boltzmann constant, \( T \) is the absolute temperature in K. Note that the derivate data points marked by hollow circle, as displayed in Fig. 1k, were excluded from the fits since the \( R_1 \) rates (\( 1/T_1 \)) recorded at low temperature range are mainly governed by non-diffusive background effects, such as lattice vibrations or coupling by paramagnetic impurities\(^{39, 40, 41}\).
+Fig. 1. Crystal structure and sodium-ion conduction characteristic of crystalline Na5SmSi4O12.
+a Rietveld refinement based on the powder XRD. b Nyquist plots of Na5SmSi4O12 from 25 to 175 °C.
+c Arrhenius plot of the conductivity values for Na5SmSi4O12. d Top-down and e perspective view of crystal structures of crystalline Na5SmSi4O12. f-g Molecular dynamics simulation trajectories of Na5SmSi4O12. h Minimum potential energy path along Na+ diffusion route in crystalline Na5SmSi4O12. i Solid-state 23Na NMR spectrum and its simulation for the crystalline Na5SmSi4O12. The gray line is experimental data and the green-dashed line is the sum of simulation. j Saturation recovery fitting curve for the data obtained at room temperature. k Temperature dependence of 23Na NMR relaxation rate as a function of temperature in K^{-1}. The solid line is the fit according to Eq. (1). The derivation of the data is not used for the fit.
+
+Electrochemical performance and crystalline-to-amorphous (CTA) transition of Na5SmSi4O12 solid electrolyte.
+To further evaluate the chemical and electrochemical stability of SE against Na metal, symmetric all-solid-state Na cell using Na5SmSi4O12 as the electrolyte was fabricated and tested by the repeatedly galvanostatic stripping and plating at different current densities. The charge/discharge profiles of Na||Na5SmSi4O12||Na without any interfacial modification were recorded at a current density ranging from 0.05 to 0.15 mA cm^{-2} with 120 min per cycle (Fig. 2a). The cell displays stable and long cyclic performance which maintains an overvoltage of ~26 mV at 0.15 mA cm^{-2} with negligible fluctuations over 800 h, indicating sodium dendrite-free plating/stripping and excellent kinetic stability of the Na5SmSi4O12 against Na metal. Afterwards, electrochemical impedance was collected from the symmetric cell after cycling 150, 200 and 300 h to reveal the changes in the internal resistance, as illustrated Fig. 2b and Supplementary Table 4. The resistance of SE (both R_b and R_{GB}) remains nearly unchanged as the sodium plating/stripping proceeding. In contrast, the interfacial resistance (R_{int}) between sodium metal and SE decreases at initial few cycles and then stabilizes at a relatively low value, demonstrating excellent compatibility between Na5SmSi4O12 and sodium metal. This phenomenon is quite different from most of reported SEs without surface modification, whose R_{int} increases gradually with increasing cycling times with the result of the excessive internal resistance and failure of the cells due to interfacial side reactions or the formation of holes^{25, 28, 42}.
+
+Scanning electron microscopy (SEM) images of the electrodes at different plating/stripping stages are shown in Fig. 2c and 2d, which demonstrates an interesting tendency of gradually vanishing gap at the interface between Na and Na5SmSi4O12 after
+cycling and an ultraconformal interfacial contact was created. XRD pattern after cycling 200 h suggests a transformation from the crystalline Na5SmSi4O12 SE into the amorphous state (Fig. 2e). Such CTA transition starts from the surface and then gradually propagates into the bulk of the SE pellets since there is no clear reflection peaks from the depth-profiled XRD pattern (Supplementary Fig. 8). To further confirm the CTA transition, HRTEM and SAED measurements were undertaken before (Supplementary Fig. 9) and after cycling (Fig. 2f-g). There are no observed lattice fringe and diffraction spot for the cycled SE sample, confirming the electrochemistry-induced CTA transition. Because of the amorphous state, it is difficult to determine the possible local coordination based on the XRD measurement. Therefore, Raman spectra were then used to examine the short-range vibration changes. As displayed in Supplementary Fig. 10, crystalline Na5SmSi4O12 exhibits seven vibration peaks\(^{43}\): the bands in the 900-1100 cm\(^{-1}\) region are assigned to Si-O\(^-\) stretching vibrations, the symmetrical band at ~624 cm\(^{-1}\) is corresponding to O-Si-O bending mode. The low-frequency bands (<550 cm\(^{-1}\)) are attributed to Sm-O and Na-O bond vibrations in their polyhedral. Though the cycled Na5SmSi4O12 SE loses its long-term ordering (Fig. 2e-g), it maintains nearly all the vibrational peaks that confirms no chemical reaction between the interface of SE and Na metal. While the disappearance of the peak at 1041 cm\(^{-1}\) might be related to the damage of the fracture of Si-O bond by the amorphous transition. Furthermore, X-ray photoelectron spectroscopy (XPS) suggests that there are no changes in the Sm 3d, Na 1s and Si 2p XPS spectra after cycling, indicative of no redox reaction occurred between sodium metal and Na5SmSi4O12 (Supplementary
+Fig. 11). Thus, it can be concluded that Na5SmSi4O12 SE demonstrates an interesting CTA transition with an excellent electrochemical stability that enables it as the ideal SE for sodium based ASSBs.
+
+![Cycling performance plots and SEM images of Na metal/Na5SmSi4O12 interfaces](page_370_384_1002_670.png)
+
+Fig. 2. Characterization of interfacial evolution and Na5SmSi4O12 after cycling in Na||Na5SmSi4O12||Na symmetric cells. a Cycling performance of Na||Na5SmSi4O12||Na at room temperature. b Nyquist plots of the SE-based symmetric cell after cycling for different times. Cross-sectional SEM images of the Na metal/Na5SmSi4O12 interfaces: c pristine and d 100 h cycling. e XRD profiles of Na5SmSi4O12 after cycling for different times. f HRTEM and g SAED patterns of Na5SmSi4O12 after cycling.
+
+Electrochemical performances of solid-state-batteries.
+
+Critical current density (CCD) and long-term cycling performance of Na||Na5SmSi4O12||Na with a long single deposition time were further measured to evaluate the capability of amorphous materials and interface in suppressing dendrite growth. As displayed in Fig. 3a, CCD for Na||amorphous Na5SmSi4O12||Na cell is
+achieved as 1.4 mA cm\(^{-2}\) at 1.4 mA h cm\(^{-2}\), higher than the CCD for Na||crystalline Na\(_5\)SmSi\(_4\)O\(_{12}||\)Na (0.4 mA h cm\(^{-2}\), Supplementary Fig. 12). This behavior is mainly because the uneven metal deposition leads to rapid growth of sodium dendrites along the crystalline Na\(_5\)SmSi\(_4\)O\(_{12}\) grain boundary with a large deposition current and hence results in the short circuit rapidly. In addition, as shown in Supplementary Fig. 13a, under a large area capacity, the overpotential increases during the cycling and drops suddenly less than 25 h, which suggests that crystalline Na\(_5\)SmSi\(_4\)O\(_{12}\) can be easily penetrated by sodium dendrites. By contrast, if a low area capacity of 0.05 mA h cm\(^{-2}\) is applied in advance to make the electrolyte transition to an amorphous state, the Na||amorphous Na\(_5\)SmSi\(_4\)O\(_{12}||\)Na cell displays a stable and long cycling performance which maintains the overvoltage at around 20 mV over 500 h (Supplementary Fig. 13b). All these results indicate the strong capability of amorphous Na\(_5\)SmSi\(_4\)O\(_{12}\) in suppressing Na dendrite formation.
+
+To further emphasize the superiority of amorphous interface and bulk materials, a Na\(_3\)V\(_2\)PO\(_4\)$_3$ (NVP)||Na\(_5\)SmSi\(_4\)O\(_{12}||\)Na SSB was constructed and evaluated at room temperature, as illustrated in the schematic figure (Fig. 3b). The cyclic voltammetry (CV) curve of stainless steel (SS)||Na\(_5\)SmSi\(_4\)O\(_{12}||\)Na cell in Fig. 3c shows that Na\(_5\)SmSi\(_4\)O\(_{12}\) possesses a wide electrochemical stability window more than 5 V, which is high enough to ensure that the electrolyte does not undergo phase transition within the working voltage range. As shown in Supplementary Fig. 14a, quite flat charge-discharge voltage profiles at 2.3-3.9 V with an initial discharge capacity of 112 mA h g\(^{-1}\) were observed, which matches well with the characteristic NVP redox plateaus in
+liquid electrolyte (Supplementary Fig. 14b). In addition, the high initial Coulombic efficiency of 99% indicates that there is no irreversible side reaction between Na5SmSi4O12 and Na anode or NVP cathode. Meanwhile, an excellent cycling performance is achieved with a high-capacity retention of 95% after 100 cycles (Fig. 3d). Furthermore, specific capacities of 102 mA h g\(^{-1}\), 98 mA h g\(^{-1}\) and 93 mA h g\(^{-1}\) can be obtained at 0.5, 0.75 and 1 C-rates, respectively, suggestive of a superior rate capability (Fig. 3e). Finally, the long-term cycling stability was estimated at a current rate of 2 C (Fig. 3f). Impressively, there is no obvious capacity loss during the repeated 4000 cycles (6 months). The capacity remained to be ~95 mA h g\(^{-1}\). All these features verify the unique interface properties between Na5SmSi4O12 and sodium, which can not only enable sufficient contact with sodium metal, but also inhibit the side reaction and the dendrite growth during cycle process.
+
+![A set of five subfigures labeled a-e, showing various plots and diagrams related to sodium battery performance, including voltage vs. current plots, schematic cell structure, and cycling performance graphs.](page_186_1012_1077_496.png)
+Fig. 3. The electrochemical performance of solid-state batteries. a Potential response of Na||Na5SmSi4O12||Na cell during the CCD measurement with a low area capacity of 0.05 mA h cm−2 is applied for 150 h in advance. b Schematic illustration of Na3V2(PO4)3||Na5SmSi4O12||Na. c CV curve of SS||Na5SmSi4O12||Na cell at a scanning speed of 5 mV s−1. d Cycling performance at 0.5 C-rate (1 C corresponds to 118 mA g−1). e Rate capability at 0.2, 0.5, 0.75 and 1 C-rate. f Long-term cycle life at 2 C-rate.
+
+Discussion
+
+Cell stabilization by CTA transition.
+
+According to the above-mentioned results, the electrochemical-induced CTA transition plays a key role in stabilizing the interfacial properties, suppressing the dendrite formation, and thus increasing the long-term stability and high-rate capability. This superiority of the amorphous stage from the interface to the bulk SE material can be understood in terms of the following two aspects. Firstly, the ionic conductivity of amorphous bulk material was improved. The pathway and the ion transport properties of amorphous Na5SmSi4O12 were investigated in detail by solid-state NMR. Figure 4a shows the 23Na NMR spectra before and after metallic Na cycling by using crystalline Na5SmSi4O12 as electrolyte. The 23Na NMR spectrum did not change significantly before and after cycling, except changes of the mobile ions (Na4, Na5, and Na6), indicative of their slight redistribution upon cycling. Nevertheless, NMR results demonstrate the non-mobile and mobile segments for Na migration within stable structure. In addition, spin-lattice relaxation time \( T_1 \) of \( ^{23}\mathrm{Na} \) were measured at different temperatures for amorphous Na5SmSi4O12, as shown in Fig. 4b and Supplementary Fig. 15. The activation energy of the mobile Na+ of amorphous Na5SmSi4O12 is calculated as 0.07 eV lower than that of the pristine crystalline state (0.13 eV in Fig. 1k). The decrease in the active energy strongly suggests an enhanced Na+ hopping ability for the
+amorphous Na5SmSi4O12 with higher ionic conductivity. Secondly, the interfacial issues, such as high interfacial resistance and metal dendrite growth, are strongly alleviated. The schematic illustration of sodium deposition is provided in Fig. 4d. A locally solid-solid contact induces a heterogeneous sodium-ion flux, whereas a tight interfacial contact of amorphous Na5SmSi4O12 lead to uniform deposition of sodium. As mentioned above in Fig. 2b, there is obvious decrease in the R_{int} upon cycling at different plating/stripping stages. The interesting phenomenon can be attributed to ultraconformal interfacial contact between Na metal and electrolyte due to the increased contact area (Fig. 2c-d). Furthermore, the isotropic surface of amorphous material could enhance the wettability with significantly reduced interface resistance and eliminates the influence of crystallographic orientation-dependent ionic transport since the interfacial energy of amorphous Na5SmSi4O12 is calculated as 0.33 J m^{-2} with sodium, lower than the crystalline Na5SmSi4O12 (0.56 J m^{-2}) (Supplementary Fig. 16). In addition, the amorphous-Na5SmSi4O12 deliver the high mechanical strength, beneficial to inhibiting the dendrite growth. As shown in Fig. 4c, nanoindentation technique was employed to evaluate the Young’s modulus \( E \) and hardness \( H^{44, 45} \). As for the amorphous sample, the \( E \) and \( H \) are calculated to be ~79.9 GPa and ~3.8 GPa, respectively, higher than the crystalline Na5SmSi4O12 (~72.6 GPa and ~2.8 GPa). In summary, the intrinsic microstructural and compositional homogeneity, as well as low electronic conductivity, alleviate the potential fluctuations at local positions in the SE and suppress sodium propagation and penetration into amorphous Na5SmSi4O12.
+Fig. 4. The superiority of amorphous bulk materials and interface. a Solid-state \(^{23}\)Na NMR of the pristine crystalline and the cycled amorphous Na5SmSi4O12. b \(^{23}\)Na NMR relaxation rate of Na cycled Na5SmSi4O12 as a function of temperature in K\(^{-1}\). c Nanoindentation load-displacement curves of crystalline Na5SmSi4O12 and amorphous Na5SmSi4O12. d Schematic of interface morphology evolution during sodium plating/striping.
+
+Mechanism of CTA transition.
+
+Electrochemically-induced solid-state amorphization (SSA) transformations are popular in the alloying type anode, like the transition from nano Si into amorphous Li-Si phases after electrochemical lithiation\(^{46, 47}\). Nevertheless, this kind of SSA process usually undergoes a chemical phase transition, which is disastrous for SEs. To the best of our knowledge, it is the first observation about the electrochemically induced CTA transformation in oxide SEs during alkali metal plating/striping without chemical phase transition. Generally, the SSA transformation depends on the thermodynamic driving force (pressure, defects, internal stress, etc.), and the existence of kinetic constraints (mainly because of the low experimental temperature) that prevent the
+formation of full equilibrium crystalline phases\(^{48, 49, 50}\). For example, when ion conduction is non-homogeneous, the local variance may lead to large local stress, which could in turn lead to the collapse of the structure. Through cycling, SSA transformation may occur. In this case, we calculate the formation energies of the crystalline and the amorphous phases sampled from quenched melts. As shown in Supplementary Fig. 17, the crystalline phases are thermodynamically favored which an energy ~60 meV atom\(^{-1}\) lower than the amorphous structures. This indicates that kinetics may play a critical role in the SSA. One way to magnify such kinetic driving force is to apply large lattice strain on the system. In this context, we computationally substitute the Na ions to Li ions in the structures and further compute the energy difference between the crystalline and the amorphous phases. Interestingly, when the Li concentration reaches ~2/5, the energy difference significantly drops to <10 meV atom\(^{-1}\). This further supports our assumption that the driving force led by the large lattice strain could be the origin of the SSA.
+
+Following the above results, a Li-Na exchange process is captured by atomistic simulations, since the ionic radius of Li\(^+\) (76 pm) is smaller than Na\(^+\) (102 pm) that could induce much larger lattice strain. Large-scale molecular dynamics is run on the hypothetical Na\(_5\)SmSi\(_4\)O\(_{12}\)/Li\(_5\)SmSi\(_4\)O\(_{12}\) using a machine-learned forcefield, as shown in Fig. 5a. Interestingly, the Li ions first exchanges with the mobile Na ions at the reaction front followed by mixing with the non-mobile ones, see Fig. 5b-e. When the pillar Na ions are replaced by smaller Li ions, the structure start to collapse. During the initial exchange process, crystalline Na\(_5\)SmSi\(_4\)O\(_{12}\) and Na\(_{5-x}\)Li\(_x\)SmSi\(_4\)O\(_{12}\) could co-exist.
+We computationally evaluated how Li substitution affects the ion diffusion. As shown in Fig. 5f, when all mobile Na ions are replaced by Li, Li diffusion barrier along the original zig-zag route dropped from ~0.3 eV to ~0.25 eV, indicating a faster diffusion kinetics, which may in turn, result in faster SSA during Li exchange. In conclusion, lattice strain induced by ion intercalation is the main driving force of amorphous transformation. Once the thermodynamic driving force is present, the kinetic hindrance at room-temperature prevents the transition back to amorphous Na5SmSi4O12.
+
+Guided by the computational results, a hybrid symmetric cell of Li||Na5SmSi4O12||Li was fabricated to accelerate this SSA transition. As shown in Supplementary Fig. 18, the cell reveals uniform plating and stripping overpotential profiles with an increased current density. This phenomenon suggests that hybrid movement of Li+/Na+ within the bulk of Na5SmSi4O12 and an effective plating/stripping of Na+ at Li anode. As expected, Na5SmSi4O12 exhibits a much shorter amorphous time within 100 h (Fig. 5g and Supplementary Fig. 19), confirming that the CTA transition of Na5SmSi4O12 is mainly triggered by the lattice strain and speeded up because of the mismatch between Li+ and Na+ ionic radius. Furthermore, an obvious reflections shift and weakening can be observed in the XRD patterns after experiencing different cycling time (Supplementary Fig. 20). This shift indicates the existence of microscopic strain in the lattice, and the gradual accumulation of stress leads to the break of more bonds. Thus, with the increase of cycling time, the crystallinity of Na5SmSi4O12 weakens, and the intensity of XRD peaks decreases gradually. To assess the cationic electrochemical exchange mechanism, XPS analysis of SE operating in the hybrid cell
+was carried out after cycling. As shown in Supplementary Fig. 21, the decrease in Na 1s peak and appearance of Li 1s peak prove that Li\(^+\) ions can successfully replace part of Na\(^+\) ions and the strong Li\(^+\) mobility within hexagonal-prismatic Na\(_5\)SmSi\(_4\)O\(_{12}\). In addition, there is no observed new Raman peaks after cycling in the hybrid symmetric cell (Supplementary Fig. 22), which indicates that Na\(_5\)SmSi\(_4\)O\(_{12}\) SE demonstrates an excellent thermodynamic stability with Li metal.
+
+Figure 5h shows the \(^{23}\)Na spectra of Na\(_5\)SmSi\(_4\)O\(_{12}\) cycled with Li metal under different times, from which the stripped Li will exchange with Na on its way when across the electrolyte. The signals at -16.8 ppm -23.4 ppm, being assigned to sodium at Na4 and Na6 sites, significantly weakened, reflecting the transport activity of Na4 and Na6 sodium sites during polarization. In addition, the signal at 8.8 ppm, which is assigned to sodium at Na5 site, is weakened but fluctuates in intensity at different cycle times, indicating it likely serves as ‘bridge’ for transporting Na/Li ions during polarization. These results further conclude that there is a possible 3D pathway of Na\(_5\)SmSi\(_4\)O\(_{12}\) between Na4-Na5-Na6. Figure 5i and Supplementary Fig. 23 display the \(^7\)Li NMR spectrum of Na\(_{5-x}\)Li\(_x\)SmSi\(_4\)O\(_{12}\) after Li cycled different times (100 and 200 h). The \(^7\)Li NMR spectrum of the electrolyte cycled for 200 h is broader than that for 100 h, indicating the growth of amorphous phase. \(^6\)Li NMR spectrum after Li cycling is shown in Supplementary Fig. 24. Both \(^7\)Li and \(^6\)Li NMR spectra present two components, corresponding to the different mobile Na sites, such as Na4 and Na6.
+Fig. 5. CTA mechanism. a Structure of the Na5SmSi4O12||Li5SmSi4O12 interface model b molecular dynamics trajectories of the interface model. Molecular dynamics simulation trajectories of crystalline c Li5SmSi4O12 d Na5SmSi4O12 and e Li3Na2SmSi4O12. f Minimum potential energy path along Li diffusion route in crystalline Na3-xLi3SmSi4O12. g XRD profiles of Na5-xLi3SmSi4O12 after cycling for different times. Solid-state h 23Na and i 7Li NMR of the Na5SmSi4O12 with different cycling times.
+
+In summary, dense crystalline Na5SmSi4O12 was prepared and exhibits a high room-temperature conductivity of \(2.90 \times 10^{-3}\) S cm\(^{-1}\). Driven by microscopic strain in the lattice, the Na5SmSi4O12 undergoes an amorphous transformation during the cycling in both symmetric Na||Na5SmSi4O12||Na and Li||Na5SmSi4O12||Li cells. On the one hand, the increased contact area greatly reduces the interfacial resistance between sodium metal and electrolyte and promotes the homogeneous deposition of sodium. On the other, the isotropic ionic transport feature of amorphous Na5SmSi4O12 eliminates the ion-blocking crystallographic orientation, uniform distribution of the current and homogeneous metal nucleation at the anode interface will be promoted. Thus, the
+sodium symmetrical cells manifest stable cycling performance for 800 h at 0.15 mA cm\(^{-2}\)@1 h and 500 h at 0.05 mA cm\(^{-2}\)@5 h (25 °C). Furthermore, the successful operation of Na\(_3\)V\(_2\)PO\(_4\)$_3$||Na\(_5\)SmSi\(_4\)O\(_{12}\)||Na solid-state sodium batteries with excellent electrochemical performance further implies the superiority of Na\(_5\)SmSi\(_4\)O\(_{12}\) electrolyte.
+
+Methods
+
+Materials synthesis:
+
+The Na\(_5\)SmSi\(_4\)O\(_{12}\) pellets were synthesized by a solid-state sintering method using Na\(_2\)CO\(_3\), Sm\(_2\)O\(_3\) and SiO\(_2\) as the starting materials. First, the raw materials of analytical grade were mixed by ball-milling at a milling speed constant of 600 rpm for 15 h. The mixture was dried at 80 °C for 12 h and calcined at 800 °C for 8 h. Then the powder was put into a cylindrical pressing mold with diameter of 15 mm and pressed under a pressure of 300 MPa. The pressed pellets were then sintered at 950 °C for 20 h. Finally, buff pellets were obtained after sintering.
+
+The Na\(_3\)V\(_2\)PO\(_4\)$_3$ (NVP) cathode material was prepared by the sol-gel method according to our previous work (Supplementary Fig. 25)\(^{51}\). Firstly, the stoichiometric amount of Na\(_2\)CO\(_3\), NH\(_4\)VO\(_3\) and NH\(_4\)H\(_2\)PO\(_4\) with a molar ratio of 3 : 4 : 6 was dissolved in deionized water. Secondly, 0.02 M aqueous citric acid [HOC(COOH)(CH\(_2\)COOH)$_2$] solution was added dropwise into the solution until the ratio of vanadium: citric acid equals to 2: 1. Then the gel could be acquired by drying the precursor in an oven at 120 °C for 12 h. Finally, the NVP/C powder can be acquired after heat treatments in two steps, first at 350 °C for 5 h and then at 750 °C for 12 h under a nitrogen atmosphere.
+Characterization method:
+
+X-ray diffraction (XRD) patterns were recorded by a Bruker D8 Advance diffractometer with Cu Kα radiation and RigaKu D/max-2550 diffractometer (1.6 kW, Cu Kα radiation, \( \lambda = 1.5406 \) Å), followed by Rietveld refinement using Fullprof software for the crystal structure analysis. The microscopy characteristics of the samples were investigated by Hitachi Regulus8100 FESEM, high resolution transmission electron microscope (HRTEM, talos F200X) and selected area electron diffraction (SAED). The elemental mapping was used to analyze the element distribution of the samples. X-ray photoemission spectrum (XPS) was carried out on a thermo scientific NEXSA spectrometer. Raman spectra were examined using a Renishaw Raman microscope (model 2000) with Ar-ion laser excitation. Prior to analysis the interface properties between Na/Li metal and Na₅SmSi₄O₁₂ electrolyte after cycling, emery paper was employed to remove any residual metal on the surface. All \( ^6\mathrm{Li} \), \( ^7\mathrm{Li} \) and \( ^{23}\mathrm{Na} \) magic angle spinning (MAS) NMR experiments were acquired on Bruker 400 MHz (9.4 T) magnets with AVANCE NEO consoles using Bruker 3.2 mm HXY MAS probe. The samples were filled into rotors inside Argon glove box. The Larmor frequencies for \( ^6\mathrm{Li} \), \( ^7\mathrm{Li} \) and \( ^{23}\mathrm{Na} \) were 58.89, 155.53 and 105.86 MHz, respectively. All spectra were acquired by using one-pulse program and were referenced to 1 M LiCl (\( ^6\mathrm{Li} \) and \( ^7\mathrm{Li} \)) and 1 M NaCl (\( ^{23}\mathrm{Na} \)) solutions with chemical shifts at 0 ppm. The spinning rate \( v_{rot} \) was set to 14 kHz. \( ^{23}\mathrm{Na} \) spin-lattice relaxation times (\( T_1 \)) were recorded by using the saturation recovery pulse sequence. The varying temperature experiments were protected by \( \mathrm{N}_2 \) atmosphere. Nanoindentation
+measurement was taken on a nanoindentation tester (Agilent Nano Indenter G200) equipped with a three-sided pyramidal Berkovich diamond indenter. The applied standard loading, holding, and unloading times were 10, 5, and 10 s, respectively. During the testing, the load-displacement curves up to pellet cracking were recorded and utilized to calculate the Young’s modulus \( E \) and hardness \( H \) using the Oliver-Pharr method. Indentations with maximum indentation load of 1 mN are conducted on the surface of SE pellets. The reduced modulus \( E_r \) was determined by the unloading stiffness and projected contact area. By assuming a Poisson’s ratio of 0.3 for samples and 0.07 for single crystalline diamond, their Young’s moduli were estimated.
+
+**Impedance spectrum test:**
+
+For the conductivity measurement, silver was spread on both sides of the ceramic pellets as blocking electrodes. AC impedance spectra were recorded using a Solartron 1260 impedance analyzer over a frequency range of 5 MHz to 1 Hz, with an applied root mean square AC voltage of 30 mV. The temperature dependence of the conductivity was measured in the same way at several specific temperatures ranging from 25 to 175 °C. For conductivity test at each temperature, the samples were allowed to equilibrate for 2 h prior to measurements. The resistances of the Na||Na5SmSi4O12||Na symmetric cells were tested under the same conditions.
+
+**Electrochemical measurement:**
+
+To obtain NVP cathode, NVP active material (70 wt.%), Super P conductive additive (20 wt.%) and carboxymethyl cellulose (CMC) binder (10 wt.%) were dissolved in water to form a homogeneous slurry, and then uniformly coated onto an aluminum foil
+current collector. After drying for 12 h at 80 °C, the electrode was punched into 1 cm diameter wafers for use with the loading mass of 1.0-1.5 mg cm^{-2}. Sodium foil was employed as anode. The Na5SmSi4O12 pellet was used as both separator and electrolyte. 20 μL 1 M NaClO4 in ethylene carbonate (EC) and propylene carbonate (PC) (1:1 v/v) with the addition of 5 vol.% fluoroethylene carbonate (FEC) was added as the interfacial wetting agent at the cathode side. The 2032-type coin cells were assembled in an argon-filled glovebox. Galvanostatic charge-discharge tests were performed in a cutoff potential window of 2.3-3.9 V by using Land-2100 automatic battery tester. All-solid-state Na||Na5SmSi4O12||Na and Li||Na5SmSi4O12||Li symmetric cells were assembled to test the sodium/lithium metal stripping/platting at 25 °C and 50 °C, respectively. In addition, electrochemical stable window of electrolytes was examined by cyclic voltammetry (CV) measurement with the stainless steel||Na5SmSi4O12||Na cell in the voltage range of -1 to 8 V at a scanning rate of 5 mV s^{-1}. The direct current (DC) polarization measurement was performed on Ag||Na5SmSi4O12||Ag cell with a 300 mV potential and the current response was measured for 100 min at ambient temperature. The CV measurement and the DC measurement were performed using a Bio-Logic electrochemical workstation.
+
+**Computational methods:**
+
+Density functional theory calculations were carried out using the VASP6.3^{52,53} package following the setup we used in previous work^{54, 55, 56}. Briefly, the PBE exchange-correlation functional was adopted with a planewave basis and a cutoff energy of 520 eV. The reciprocal space was sampled using Monkhorst-Pack grids with a spacing of
+0.04 Å^{-1}. The convergence for electron self-consistent computations and structural optimizations are set to \(10^{-4}\) eV atom^{-1} and \(10^{-3}\) eV atom^{-1}, respectively. Due to the need of large-scale molecular dynamics simulations, we trained a machine learning forcefield based on *ab initio* molecular dynamics simulations (AIMD)\(^{54,55}\). Trajectories from smaller systems with 5 compositions sampled evenly between Na$_5$SmSi$_4$O$_{12}$ and Li$_5$SmSi$_4$O$_{12}$ were collected at high temperatures together with their relaxation trajectories. The energy and forces were used as the label to train the model. The production MD simulations were carried out using such a forcefield. The systems were equilibrated at 600 K for 100 ps and gradually dropped to 300 K with a period of another 100 ps under an NPT thermostat at ambient pressure. Then an NVT production run was carried out at 300 K for 200 ps. The time step was 1 fs. For the interface model, we adopted a universal machine learning model which can capture the ground state structures and their energy. Two interface models were built to mimic the interaction between the Li electrode and the crystalline and amorphous SE. The models were first equilibrated at 500 K for 1000 fs followed by energy minimization. The interfacial energy was calculated by subtracting the energy of the interfaces from the sum of energies of independent bulk phases.
+
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+Acknowledgments
+
+This work was supported by the National Natural Science Foundation of China with Grant No. 12274176, 51972142, and 21974007. We also would like to thank the support from the Department of Science and Technology of Jilin Province with Grant No. 20220201118GX and 20210301021GX.
+
+Author contributions
+
+G. S. and C. L. contributed equally to this work. F. D., M. T. and Z. L. designed and supervised the project. G. S. performed materials synthesis, electrochemical tests, and wrote the manuscript. C. L. and M. T. performed NMR experiments and analyses. Z. L. performed and discussed DFT calculation results. Z. W., S. Y., G. C., and Z. S. revised the manuscript. All the authors participated in the discussion and provided constructive advice for the experimental design.
+
+Competing interests
+
+All other authors declare they have no competing interests.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• supplementarymaterials.pdf

0f38253e04174167d6d03bbdbbc7f1a3288595a100abf195116c81c963341bb8/preprint/preprint.md

@@ -0,0 +1,381 @@
+Microspectroscopic visualization of how biochar elevates the soil organic carbon ceiling
+
+Zhe (Han) Weng
+University of Queensland
+Lukas Van Zwieten (lukas.van.zwieten@dpi.nsw.gov.au)
+NSW Department of Primary Industries https://orcid.org/0000-0002-8832-360X
+Michael Rose
+NSW Department of Primary Industries
+Bhupinder Pal Singh
+NSW Department of Primary Industries
+Ehsan Tavakkoli
+NSW Department of Primary Industries
+Stephen Joseph
+University of New South Wales
+Lynne Macdonald
+CSIRO
+Stephen Kimber
+NSW Department of Primary Industries
+Stephen Morris
+NSW Department of Primary Industries
+Terry James Rose
+Southern Cross University
+Bráulio Archanjo
+Instituto Nacional de Metrologia, Qualidade e Tecnologia
+Caixian Tang
+La Trobe University
+Ashley Franks
+La Trobe University https://orcid.org/0000-0003-1664-6060
+Hui Diao
+The University of Qld
+Peter Kopittke
+The University of Queensland https://orcid.org/0000-0003-4948-1880
+Annette Cowie
+NSW Department of Primary Industries / University of New England https://orcid.org/0000-0002-3858-959X
+Article
+
+Keywords: soil carbon, soil organic carbon, biochar
+
+Posted Date: September 10th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-860309/v1
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on September 2nd, 2022. See the published version at https://doi.org/10.1038/s41467-022-32819-7.
+Microspectroscopic visualization of how biochar elevates the soil organic carbon ceiling
+
+Zhe (Han) Weng1,2,3,4, Lukas Van Zwieten1,5*, Michael T. Rose1, Bhupinder Pal Singh6, Ehsan Tavakkoli7, Stephen Joseph8, Lynne M. Macdonald9, Stephen Kimber1, Stephen Morris1, Terry J. Rose5, Braulio S Archanjo10, Caixian Tang3, Ashley Franks11,12, Hui Diao13, Peter M. Kopittke4, Annette Cowie2,14
+
+1NSW Department of Primary Industries, Wollongbar Primary Industries Institute, Wollongbar, NSW 2477, Australia
+2School of Environmental and Rural Sciences, University of New England, Armidale, NSW 2351, Australia
+3Department of Animal, Plant & Soil Sciences, Centre for AgriBioscience, La Trobe University, Melbourne, Vic 3086, Australia
+4School of Agriculture and Food Sciences, The University of Queensland, St. Lucia, Queensland 4072, Australia
+5Southern Cross University, East Lismore, NSW 2480, Australia
+6NSW Department of Primary Industries, Elizabeth Macarthur Agricultural Institute, Woodbridge Rd, Menangle, NSW 2568, Australia
+7NSW Department of Primary Industries, Wagga Wagga Agriculture Institute, Wagga Wagga, NSW 2650, Australia
+8University of New South Wales, Sydney, NSW 2052, Australia
+9CSIRO Agriculture & Food, Waite campus, Glen Osmond, SA 5064, Australia
+10Divisão de Metrologia de Materiais - DIMAT, Instituto Nacional de Metrologia, Normalização e Qualidade Industrial - INMETRO, Duque de Caxias, RJ, 25250-020, Brazil
+11Department of Physiology, Anatomy and Microbiology, La Trobe University, Melbourne, Vic 3086, Australia
+12Centre for Future Landscapes, La Trobe University, Melbourne, Vic 3086, Australia
+13Centre for Microscopy and Microanalysis, The University of Queensland, QLD, 4072, Australia
+14NSW Department of Primary Industries/ University of New England, Armidale, NSW 2351, Australia
+
+*e-mail: lukas.van.zwieten@dpi.nsw.gov.au
+The soil carbon saturation concept suggests an upper limit to store soil organic carbon (SOC), set by the mechanisms that protect soil organic matter from decomposition. Biochar has the capacity to protect new C including rhizodeposits and microbial necromass. However, the decadal scale mechanisms by which biochar influences the molecular diversity, spatial heterogeneity, and temporal changes of SOC persistence remain unresolved. Here we show that the soil C saturation ceiling of a Ferralsol under subtropical pasture could be elevated by 2 Mg (new) C ha\(^{-1}\) by the application of *Eucalyptus saligna* biochar 8.2 years after the first application. Using one, two-, and three-dimensional analyses, significant increases were observed in the spatial distribution of root-derived \(^{13}\)C in microaggregates (53-250 \( \mu \)m, 11 %) and new C protected in mineral fractions (<53 \( \mu \)m, 5 %). Microbial C-use efficiency was concomitantly improved by lowering specific enzyme activities, contributing to the decreased mineralization of native SOC by 18 %. We provide evidence that the global SOC ceiling can be elevated using biochar in Ferralsols by 0.01-0.1 Pg new C yr\(^{-1}\).
+
+Main
+
+Human activities risk releasing 260 Pg of carbon (C) as carbon dioxide (CO\(_2\)) globally that is irrecoverable on a timescale relevant to avoiding profound climate impacts\(^{1,2}\). Agricultural soils contribute an average of 2 Mg C lost ha\(^{-1}\) yr\(^{-1}\) globally\(^{3,5}\). It has been estimated that 122 Mg soil organic C (SOC) ha\(^{-1}\) to 1 m depth has been lost over 1 Mha of land converted to tropical grasslands\(^{6}\), with 40 % of this area occurring on Ferralsols\(^{7}\). To meet the Paris Agreement of limiting global warming to below 2\(^\circ\)C, the Intergovernmental Panel on Climate Change has shown that CO\(_2\) removal (CDR) techniques are urgently needed\(^{8,9}\).
+
+Soil C management\(^{4-6}\) and the application of biochar\(^{10}\) are appealing CDRs\(^{9,11}\) as they also improve soil health, sustain agricultural productivity\(^{12,13}\), and increase resilience of ecosystem services\(^{14,15}\). Protecting and rebuilding soil C could draw down 5.5 Pg CO\(_2\) yr\(^{-1}\), representing 25 % of the potential of natural climate solutions to deliver CDR through conservation, restoration, and improved land
+management practices6. However, there are biophysical and socio-economic barriers to CDR with SOC management4,6,16,17.
+
+Biochar is recognized as a CDR because of its persistence9,11 in the environment. The pyrolysis of biomass can deliver bioenergy outcomes, as well as agronomic and non-CO2 greenhouse gas benefits through use of biochar as a soil amendment18-22. Biochar systems generally show life cycle climate change impacts of emissions reduction in the range of 0.4 -1.2 Mg CO2e Mg-1 dry feedstock23.
+
+Organo-mineral interactions can increase SOC persistence, in some cases over a millennial timescale24,25. There is a general understanding of the effect of microbial activity26 and mineral protection27 on SOC storage. However, there are knowledge gaps on the contribution of molecular diversity of organic compounds, fine-scale spatial heterogeneity, and temporal variability in soil conditions. Such composition-space-time interactions influence the accessibility of decomposer communities to the substrate28,29. Here, we propose a mechanism by which biochar acts as a bio-catalyst to accelerate the formation of organo-mineral and organo-organic interfaces in microaggregates (53-250 μm) and mineral protection of SOC (Fig. 1). Biochar can sorb root-derived C (rhizodeposits) and form biofilms on its surfaces. The very fine layer of soil minerals that subsequently builds on the surfaces of biochar as it ages in soil30-32 protects rhizodeposits from microbial metabolism33,34, and at the same time incorporates microbial necromass35-38. This coating can desorb from the surface during aggregate turnover or in response to a change in soil conditions such as pH, redox and moisture39. The rhizodeposits and microbial necromass are then captured in microaggregates35,40,41 (e.g. <250 μm). A new coating can then form in its place. These processes repeat, building rhizodeposits in soil over time (Fig. 1). We examine these processes in detail to quantify the potential of biochar to elevate the SOC storage ceiling. To do this, we applied Eucalyptus saligna biochar (550°C) to a historic field site established in 200641 (Ferralsol under managed subtropical pasture). The mechanisms (Fig. 1) that we tested included the negative priming via higher microbial C-use efficiency and restricted access to substrates, and enhanced mineral protection via
+catalytic biochar surfaces. We demonstrate the importance of fine-scale spatial heterogeneity and temporal variability of diverse C functional groups in association with mineral fractions for building and protecting rhizodeposits over a decade.
+
+Elevating SOC storage capacity
+
+We hypothesize that biochar enhances the protective mechanisms for soil organic matter (SOM), and that a greater C storage capacity can therefore be obtained through strategic applications of biochar. The field site was converted to managed pasture from subtropical forest 100 years ago. This led to a loss of 17 % of the original soil C stock compared to the adjacent native rainforest (data not shown). To quantify elevated C storage capacity, we measured soil C stocks in the managed pasture over 9.5 years (Table S1) from four treatments: (1) biochar applied to a part of the historical biochar plots 8.2 years after the trial was established (“recent + historical”); (2) biochar applied to a part of the control plots 8.2 years after the trial was established (“recent”); (3) biochar applied 8.2 years previously (“historical”); and (4) nil biochar plots (“control”).
+
+All field plots were managed via annual fertilizer application at the start of winter, coinciding with over sowing by annual ryegrass (Methods). The total soil C stock in the unamended pasture soil (control) did not change over 9.5 years\(^{41,42,43}\) (Fig. 2a; \(P > 0.05\)) and remained at 35 Mg C ha\(^{-1}\) in the 0-100 mm layer when sampled at 8.2 and 9.5 years after the field trial was set-up. The original application of *Eucalyptus saligna* biochar (550\(^\circ\)C) in 2006 resulted in a rapid increase in soil C to 40 Mg C ha\(^{-1}\) (10 Mg biochar ha\(^{-1}\), 76 % C, 7.6 Mg biochar-C) and SOC continued to increase, plateauing at 50 Mg C ha\(^{-1}\) at 8.2 years (“historical”). When recent biochar amendment was incorporated into the plots at the same dose after 8.2 years following the original application (“recent + historical”), the C stock immediately increased from 50 to 56 Mg C ha\(^{-1}\) (Fig. 2a) because of the C added from biochar. The C stock then continued to increase further to 58 Mg C ha\(^{-1}\) between 8.2 and 9.5 years. This additional 2 Mg C ha\(^{-1}\) was accumulated because of the increased protection mechanisms for new C provided by the biochar, thus elevating the C storage ceiling (Fig. 2a).
+The additional 2 Mg new C ha\(^{-1}\) (Fig. 2a) can be explained by negative priming of SOC mineralization (Fig. 2b). Comparing the net cumulative SOC mineralization where there was a recent application of biochar to the control (defined as priming in this study), the recent biochar amendment to the historical plots ("recent + historical") lowered SOC mineralization (\emph{i.e.} negative priming) by 89 g CO\(_2\)-C m\(^{-2}\) compared with the recent biochar amendment to the control ("recent") which lowered SOC mineralization by 55 g CO\(_2\)-C m\(^{-2}\) (\(P<0.05\), Fig. 2b). Recent biochar initiated a small (3 g CO\(_2\)-C m\(^{-2}\)) positive priming effect, whilst recent + historical biochar immediately triggered negative priming (Fig. 2b). Neither recent + historical or recent had an impact on total respiration or root respiration compared to the control (\(P>0.05\), Figs. S1 & S2). As a portion of the total CO\(_2\) flux, root respiration remained relatively consistent (30-32 %) and was unaffected by treatments (\(P>0.05\), Table S2).
+
+The additional 2 Mg C ha\(^{-1}\) that accumulated between 8.2 and 9.5 years because of the recent application of biochar to the historical biochar plots ("recent + historical") accrued through the stabilization of rhizodeposits and microbial necromass (Fig. 3). Recent + historical biochar had a similar proportion of total recovered \(^{13}\)C (58 ± 5.7 %, Fig. 3a) compared to the historical biochar plots ("historical") (60 ± 9.8 %), with this being around 18 % greater than the control (42 ± 7.3 %) and the recent biochar amendment ("recent") (45 ± 4.5 %; Fig. 3b) after the pulse-labelling event at 9.5 years (\(P<0.05\); Table S3). The increase in belowground \(^{13}\)C recovery could be largely explained by an increase in mineral-protected soil organic matter (M-SOM) associated \(^{13}\)C (14 %, \(P<0.05\), Table S4). Initially, recent + historical biochar nearly doubled the \(^{13}\)C retention in the occluded particulate organic matter (O-POM) fractions (5 mg \(^{13}\)C m\(^{-2}\)) of microaggregates (< 250 µm) and M-SOM fractions (14 mg \(^{13}\)C m\(^{-2}\)) of macroaggregates (250-2000 µm) at 8.9 years compared to the recent biochar (Figs. S3a & b). The root-derived \(^{13}\)C from rhizodeposition was accumulated gradually into O-POM in macroaggregates and M-SOM at 9.2 years (Figs. S3c & d), which was in turn transformed into M-SOM fractions in micro- and macroaggregates by 9.5 years (Figs. S3 e & f).
+
+Microbial contribution and responses to stabilization of rhizodeposits
+To determine the microbial contribution to the increased SOC storage capacity, we quantified catabolic enzyme activities, metabolic quotient of native SOC (bulk soil) and rhizodeposition (\(^{13}\mathrm{C}\) content), and specific enzyme activity (the ratio of enzyme activity-to-microbial biomass) comparing a recent biochar amendment to the control ("recent") and to the historical biochar plots ("recent + historical"). Microbial biomass was increased by 11 % in the recent + historical biochar compared to the recent biochar between 8.9 and 9.5 years (Table S5a). This might result from the stimulation of microbial co-metabolism\(^{31}\) of biochar-C, root-C and SOC which induced initial positive priming in the recent biochar amendment (Fig. 2b). The recent + historical biochar had increased substrate-induced respiration for citric, oxalic and malic acids compared to the recent biochar (Microresp, Fig. S4; Table S6). No differences were detected for 12 other substrates. This greater respiration induced by carboxylic acids (e.g. root exudates) may partially explain the higher metabolic quotient associated with bulk SOC and rhizodeposition in the recent biochar *cf.* the recent + historical biochar (Table S5b & c). The recent + historical biochar might result in higher substrate-use efficiency which supports an earlier establishment of negative priming compared to the recent biochar (Fig. 2b). It was previously shown that the recent biochar significantly increased bacterial diversity and the relative abundance of nitrifiers and bacteria consuming biochar C after one year, but the soil bacterial communities from the recent + historical plots did not differ from the control\(^{33}\). This suggests that the microbial accessibility to SOM might be limited in the recent + historical biochar plots, whereas in the recent biochar, the soil microorganisms had to cope with changes in C-substrate type and availability\(^{45}\).
+
+The ratio of enzyme activities to total microbial biomass was lower in both recent + historical biochar and recent biochar compared to the control (Table S7) despite no difference in enzyme activities (Table S8). This suggests that for a given amount of microbial biomass, less enzymes were produced in the biochar-amended soil. A low ratio of extracellular enzymes to microbial biomass can slow down the degradation of native SOC\(^{46}\). This is consistent with increased microbial C-use efficiency (Tables S4b & c), which may indirectly contribute to the negative priming. It has been suggested that the presence of opportunistic microbes that meet their energy and nutrient demands by exploiting the
+catalytic activities of decomposers could lower the specific enzyme activity\(^{46}\). The spatial arrangement between microbes and substrates is critical to this process.
+
+Spatial examination of organo-mineral interactions
+
+To better understand the process of negative priming following biochar application, we examined whether the stabilization of rhizodeposits may be facilitated via protection with the abundant Fe and Al in soil. Root exudates can interact with Fe oxides in the soil to promote the formation organo-mineral complexes. Aluminum may also protect root-C from biodegradation. The development of organo-mineral complexes was assessed using three-dimensional focused ion beam (FIB) coupled with scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (3D-FIB-SEM-EDS) on intact representative soil aggregates from the recent + historical biochar (Fig. 3c) where C retention co-located with clay minerals, but, not in the recent biochar (Fig. 3d).
+
+To provide a deeper insight into the molecular diversity of organic compounds and the temporal and lateral arrangement with respect to organo-mineral interfaces, we conducted *in situ* spectromicroscopic analysis of free water-stable microaggregates (53-250 \( \mu \)m) and organo-mineral fractions (<53 \( \mu \)m) of the recent + historical biochar and recent biochar, and of field-extracted biochars at micro- and nanoscale. The C functional groups, examined using synchrotron-based soft X-ray (SXR) analyses, from the microaggregates (53-250 \( \mu \)m) were dominated by quinones (284.1 eV), aromatic C (285.2 eV, 1s-\( \pi^* \) transitions of conjugated C=C), and aliphatic C (287.3 eV) (Fig. 4a). For the mineral-protected fractions (<53 \( \mu \)m), two prominent features were the low intensity of quinones and high intensity of aliphatic C (Fig. 4a). The dominant peaks of aliphatic, amide and carboxylic C (287-289 eV) are the direct consequence of deposition of microbial metabolites or debris, exopolysaccharides, and root exudates onto mineral surfaces\(^{27,47,48}\). These align with the micro-spatial maps produced from the synchrotron-based infrared (IR) microspectroscopy (Fig. 4b). The close correlation between clay minerals and microbial metabolites on the biochar surface supports SOC stabilization, and highlights the importance of clay minerals for the protection of SOC and the control of microbial activity.
+The correlation between C forms and clay minerals, confirmed by the IR maps, was further examined on a nanometer scale by directly analyzing the chemical composition of the organo-mineral coatings at the surface and in the pores of field-extracted biochars. Greater intensities of quinones (284.1 eV) and carboxyl C–OOH (288.6 eV) were observed in the 9.5-year aged biochar compared with the 1-year aged biochar (Fig. 5a). A high magnification image of the area where the fungi were located inside a biochar fragment shows a high concentration of irregular pores and a coating of organic material (Figs. 5b & c). Fungi can mine nutrients from minerals by exuding acids\(^{49,50}\) which may cause the observed microporosity of organo-mineral-biochar interfaces (Figs. 5b, d, f, h & Fig. S5). Energy dispersive X-ray spectroscopy (EDS) analysis showed that complex changes had occurred on the surface of the biochar over the one-year period (Figs. 5c, 5g). Positively charged nanoparticulate minerals rich in Al, Si, Ca, P, Fe and other cations were attracted to the surface of the negatively charged areas on the biochar. These positively-charged minerals and elements subsequently attracted negatively-charged organic molecules with detectable concentrations of C=C, C-OH, C-N/C=N, C=O, COOH functional groups, quinone bonds and anions thus initiating a process whereby porous clusters are formed on the biochar surface (Figs. 5e, 5i). Similarly, exudates from plants and microorganisms can be deposited around mineral surfaces on the biochar, and cations and minerals can be attracted to these organic molecules. Recent biochar amendment to historical biochar plots would provide unoccupied surfaces and pores in the soil to increase sorption capacity for root exudates\(^{51}\), which would then serve as binding agents to further enhance aggregate formation\(^{52}\). As these clusters are built up, they may also be detached from the biochar either through fluctuating redox conditions and interaction with microbes or perturbation caused by soil invertebrates\(^{30}\).
+
+These biochar micro-sites have a high concentration of free radicals with labile easily-mineralizable organic C and/or inorganics dissolved from the biochar (Table S9). Colloidal biochar particles, leachate, dissolved native OM and rhizodeposits may be further stabilized separately or held together via cation bridging with Ca\(^{2+}\), or with Al and Fe oxyhydroxides\(^{53,54,55}\) and organo-organic interactions at the nanometer scale\(^{56}\) (Figs. 5e, 5i). These processes may be encouraged by oxidation of the biochar
+surface as it ages in soil36,37. This is supported by our LC-OCD results where dissolved hydrophobic C fractions and building blocks (medium molecular weight) were greater in the recent + historical biochar compared to the recent biochar (Fig. 5j; Table S10). The analysis of the surface of the 9.5-year aged biochar by C-edge EELS and XPS indicated that most of the oxidized C species were formed in the organo-mineral coating. The concentrations of the different functional groups appear to be influenced by the presence of nanophase Fe, Si and Al oxides56 (Fig. 5i).
+
+Global impact of elevating the soil carbon ceiling
+
+Building SOC is a global priority9, and our results showed that the SOC storage ceiling can be elevated through single or multiple applications of biochars. We observed a plateau in rhizodeposit accumulation rate over 9.5 years in the historical biochar plots (Fig. 2a; y = 4.24ln(x) + 17.6; R^2= 0.95) which implies that the system was approaching a new (16 % higher) equilibrium for SOC storage, ten years after the initial application. We showed that a strategic application of 10 Mg biochar ha^{-1} after 8.2 years raised the SOC storage ceiling by a further 2 Mg C ha^{-1}. In summary, this Rhodic Ferralsol under the managed pasture had a C storage capacity of 35 Mg C ha^{-1} in the surface soil, which increased to 44 Mg C ha^{-1} one year following the application of biochar, which further increased to 50 Mg C ha^{-1} after nearly a decade. The C storage ceiling was further raised to 59 Mg C ha^{-1} where biochar was applied to the historically amended field plots. Of this C storage, 7.6 Mg C ha^{-1} was attributed to the addition of C from biochar, while 2 Mg C ha^{-1} was attributed to the stabilization of new C.
+
+The long-term stabilization of rhizodeposits by biochar after 9.5 years has significant implications for elevating the SOC ceiling. Plants release ~50 % of photosynthetically fixed C into the soil, which is available for microbial growth57-59. Global grasslands annually contribute 0.04 Pg C to SOC6. The retention and stabilization of belowground C by biochar could play an important part in a natural climate solution for tropical grasslands, which occupy 0.7 Gha of land with an estimated global C content of 30 Pg C. Here we showed a 16 % increase in retention of new C in the recent + historical plots compared with the control via the stabilization of root-derived \(^{13}\)C in microaggregates (53-250
+μm, 11 %) and microbial products and rhizodeposits protected in mineral fractions (<53 μm, 5 %) (Fig. 3). To demonstrate the potential of raising the C saturation ceiling, we extrapolated this 16 % increase in stabilization based on the global projected biochar production. We estimated the strategic application of biochar can increase SOC storage capacity in Ferralsols by 0.01-0.1 Pg C yr\(^{-1}\) worldwide (Supplementary information). This mechanism would increase the global mitigation potential using biochar as a soil amendment, estimated at 1.3 Pg C yr\(^{-1}\) (centurial average; Woolf et al. 2010), by another 0.8-7.7 %.
+
+In our study, we raised the SOC storage capacity in a subtropical pasture with a strategic application of a *Eucalyptus saligna* biochar (550°C) 8.2 years following the original biochar application. Of importance to building soil C stocks, the strategic application of biochar in the aged plots resulted in 16 % more new C (*i.e.* microbial products and rhizodeposits) being stored as soil C in both microaggregates (53-250 μm) and mineral fractions (<53 μm). Microbial C-use efficiency was improved by lowering the specific enzyme activity and slowing down degradation of SOC and rhizodeposits (negative priming). Our *in situ* spectromicroscopic analyses suggest that the catalytic biochar surfaces accelerated the micro- and nanoscale heterogeneity and temporal variability for new C storage.
+
+Methods
+
+Field site details
+
+The field experiment was situated at the Wollongbar Primary Industries Institute (28°49′S, 153°23′E, elevation: 140 m), Wollongbar, New South Wales, Australia. The classification and properties of the soil can be found in Weng et al. (2015). Briefly, the Rhodic Ferralsol is fine-textured and Fe-rich mineral soil dominated by kaolinite, gibbsite and goethite. The 100-mm topsoil had a pH\(_{CaCl_2}\) of 4.5 with total C of 35 g kg\(^{-1}\), total Fe 84 g kg\(^{-1}\), and total Al 67 g kg\(^{-1}\). Details of the initial field site setup in 2006 can be found in Slavich et al. (2013). The treatments (n=3) included (1) *Eucalyptus saligna* biochar incorporated into the topsoil (0-100 mm) at 10 t ha\(^{-1}\) (eq. 1 % w/w, bulk density of 1 g cm\(^{-3}\)) plus NPK
+fertilizer and (2) NPK only (control). The biochar was derived from a single source of above-ground biomass of mature Eucalyptus saligna and pyrolyzed at 550 °C with a residence time of 30 mins (Pacific Pyrolysis, NSW, Australia). The physicochemical properties of the biochar can be found in Slavich et al. (2013). A tetraploid annual ryegrass (Lolium multiflorum) was broadcast at a seeding rate of 35 kg ha\(^{-1}\) and repeated annually. Urea was applied at 46 kg N ha\(^{-1}\) on six occasions (276 kg ha\(^{-1}\) in total) between winter and spring each year following manual cuts of the pasture to simulate grazing. Basal nutrients were applied annually at sowing (Slavich et al. 2013).
+
+In April 2014, the control (NPK only) and 8.2-year-old biochar (Eucalyptus saligna) plots were superimposed with nine subplots (0.5 m × 0.5 m) (Weng et al. 2017). Four treatments were: (1) Recent biochar to historical biochar plots (biochar applied to a part of the historical biochar plots 8.2 years after the trial was established; “recent + historical”); (2) Recent biochar amendment (biochar applied to a part of the control plots 8.2 years after the trial was established, “recent”); (3) Historical biochar amendment (biochar applied 8.2 years previously, “historical”); and (4) Control (nil biochar plots). There was one subplot per field replicate and a total of three field replicates. The biochar added to the control and aged plots was taken from the biochar ‘batch’ applied in 2006, which had been air-dried and archived in sealed 200 L steel containers at room temperature. The details of the subplot set up and installation of belowground respiration collars can be found in Weng et al. (2015). Bulk density of the biochar was 0.332 g cm\(^{-1}\) measured using a method described in Quin et al. (2014). The weight of soil-biochar mixture in the topsoil (100-mm) was determined based on the bulk density assessed in each treatment. Before application, the biochar was sieved to <2 mm. The soil/biochar mixture was carefully packed into the subplots. The control subplots were also excavated and repacked to a bulk density of 1 g cm\(^{-3}\). A root signature sand collar (50 mm diameter) was installed in each of the control subplots to measure the \( \delta^{13}C \) signature of root respiration. It was packed with acid-washed sand and planted with ryegrass (*i.e.* a down-sized version of the soil plus root respiration collar). Similarly, a biochar+root signature sand collar was packed with a biochar-sand mixture (1 % w/w) in each of the recent + historical biochar subplots. To maintain the root growth into the collars,
+NPK fertilizers were applied at the same dose as in Slavich et al. (2013). This study employed the same pasture management regime as Slavich et al. (2013), in terms of ryegrass sowing, NPK applications and weed control.
+
+Periodic \(^{13}\)C pulse labelling to quantify SOC mineralization and root respiration
+
+To understand how plant-biochar-soil interactions affect SOC priming, \(^{13}\)CO\(_2\) pulse labelling campaigns were conducted on three occasions: 12 June 2014, 01 August 2014 and 30 July 2015. The procedure of the pulse labelling experiment and a detailed description of quantification of SOC mineralization and root respiration using three-pool C partitioning can be found in Weng et al. (2015, 2018).
+
+Soil sampling was carried out at 8.9, 9.2 and 9.5 years following the first biochar application in 2006. Intact soil cores (40 mm in diameter) were sampled to 80 mm depth within each subplot but outside the respiration collar area to reduce disturbance. The sampled areas were avoided in the ensuing sampling events. The sample was mixed evenly and analyzed for pH, total soil organic C, and microbial biomass carbon (MBC). Soil pH was measured on the samples prepared for the enzyme assay (1:5 w/w ratio in distilled water with constant stirring using a vortex) using an IntelliCAL PHC101 pH probe on a Hach HQ40d portable meter (Loveland, Colorado, USA). The analytical procedures for SOC and MBC can be found in Weng et al. 2015. The remaining soil was stored at -20°C.
+
+At the 15-month soil sampling event, fresh soil was also taken from the soil respiration collars (\emph{i.e.} unplanted) and soil+root respiration collars (\emph{i.e.} planted) to quantify the effect of plant-biochar-soil interactions on catabolic enzyme activity, substrate-induced respiration, and MBC. The MBC was analyzed using the chloroform fumigation method (Van Zwieten et al. 2010). Metabolic quotient of total C or rhizodeposits was then quantified as the ratio of respiration (native SOC or \(^{13}\)C-labelled root respiration) over the total MBC. The metabolic quotient has been used as an indicator of C-use efficiency (Fang et al., 2018). Detailed calculations for determining rhizodeposit-derived respiration are given in Weng et al. (2015).
+SOC priming in the plant-biochar-soil systems
+
+The rhizosphere priming of native SOC from the biochar-plant-soil interactions was quantified using a three-pool C partitioning model. Specialized respiration collars were used to isolate soil plus root respiration from shoot respiration\(^{41,42}\). Native SOC mineralization was separated using the \( \delta^{13}C \) signature of biochar plus root (biochar plus root sand collars, Supplementary Information) and total respiration (biochar plus soil plus root collars) after pulse labelling. Moisture content was maintained between 60-80 % field capacity in the root collars to minimize potential C isotopic fractionation during photosynthesis caused by water stress \(^{44}\). The \( \delta^{13}C \) signatures of extracted field-aged biochar and fresh biochar (the same biochar archived in a sealed container for 8.2 years) were both -25 ± 0.1 ‰. Any interactive effect of biochar and root on the \( \delta^{13}C \) signature of soil would be surpassed by a greater level of \( \delta^{13}C \) enrichment of the root component compared with any isotopic signature contribution from soil and biochar to the \( \delta^{13}C \) signature of the total respiration. A sensitivity analysis of C source partitioning was performed to assess the impact of plant-biochar (C\(_3\)-dominated)-soil interactions on \( \delta^{13}C \) signatures of soil (a mixture of C\(_3\) and C\(_4\) pools). Errors generated from isotopic partitioning were propagated using the first order Tyler series approximations of the variances of native SOC mineralization.
+
+The recovery of \( ^{13}C \) in various SOC pools at time t (\( i.e. \) \( A^{13}C_{i,t} \), in %) was calculated by dividing the amount of \( ^{13}C \) (g m\(^{-2}\)) in a specific C pool (\( i.e. \) C\(_i\)) by the initial amount of total added \( ^{13}CO_2 \) (g m\(^{-2}\)) at each labelling event (\( i.e. \) \( ^{13}C_{added} \)):
+
+\[
+A^{13}C_{i,t} = (^{13}C_{excess,t} \times C_i) / \ ^{13}C_{added} \times 100
+\]
+
+where \( _i \) represents soil plus root respiration, root biomass, soil aggregates or its associated fractions, \( ^{13}C_{excess,t} \) indicates the increment of the \( ^{13}C \) atom % of an individual C pool from its natural abundance level at a specific sampling time, t.
+The mineralization of native SOC (C_S) was calculated using the \(^{13}\mathrm{C}\) signature of biochar+root (\(^{13}\mathrm{C}_{\mathrm{B+R}}\), sand collar) from the plant-biochar-soil systems after pulse labelling:
+
+\[
+C_S(\%) = 100 \times (\delta^{13}\mathrm{C}_T - \delta^{13}\mathrm{C}_{\mathrm{B+R}})/(\delta^{13}\mathrm{C}_S - \delta^{13}\mathrm{C}_{\mathrm{B+R}})
+\] (1)
+
+where \( \delta^{13}\mathrm{C}_T \): \(^{13}\mathrm{C}\) signature of the total respiration from the planted system after pulse labelling;
+\( \delta^{13}\mathrm{C}_S \): \(^{13}\mathrm{C}\) signature of the soil-derived CO$_2$-C evolved from the unplanted control soil without pulse labelling.
+
+The percentage of soil-derived CO$_2$-C in the total respiration from the planted control soil (C_S(\%)) was determined (Weng et al. 2015):
+
+\[
+C_S(\%) = 100 \times (\delta^{13}\mathrm{C}_T - \delta^{13}\mathrm{C}_R)/(\delta^{13}\mathrm{C}_S - \delta^{13}\mathrm{C}_R)
+\] (2)
+
+where \( \delta^{13}\mathrm{C}_T \): \(^{13}\mathrm{C}\) signature of the total respiration from the planted control; \( \delta^{13}\mathrm{C}_S \): the \(^{13}\mathrm{C}\) signature of the unplanted control soil; \( \delta^{13}\mathrm{C}_R \): the \(^{13}\mathrm{C}\) signature of roots, which was determined from root respiration from the root sand collar as described in Weng et al. (2017).
+
+Similarly, the percentage of soil-derived CO$_2$-C in the total respiration from the unplanted biochar-amended soil (C_S'(\%)) was determined:
+
+\[
+C_{S'}(\%) = 100 \times (\delta^{13}\mathrm{C}_{T'} - \delta^{13}\mathrm{C}_B)/(\delta^{13}\mathrm{C}_S - \delta^{13}\mathrm{C}_B)
+\] (3)
+
+where \( \delta^{13}\mathrm{C}_{T'} \): the \(^{13}\mathrm{C}\) signature of the total respiration from the unplanted biochar soil. \( \delta^{13}\mathrm{C}_S \): the \(^{13}\mathrm{C}\) signature of the unplanted control soil; \( \delta^{13}\mathrm{C}_B \): the \(^{13}\mathrm{C}\) signature of either fresh (-25.02 ± 0.13 %) or aged biochar (-25.04 ± 0.11 %). Biochars were recovered by hand from field soil samples, thoroughly rinsed with distilled water on a 100 µm sieve and oven-dried at 50°C for 24 h.
+
+Rhizosphere priming was calculated in two systems:
+
+i. Unamended system (Planted vs. Unplanted)
+SOC_{planted, unamended}: soil C mineralization in the planted control calculated by \(^{13}\)C-enriched root end-member
+
+SOC_{unplanted, unamended}: soil C mineralization in the unplanted control
+
+Rhizosphere priming in the control soil:
+
+\[
+\Delta \mathrm{SOC}_{\text{unamended}} = (\mathrm{SOC}_{\text{planted, unamended}}) - (\mathrm{SOC}_{\text{unplanted, unamended}})
+\]
+
+ii. Biochar-amended system (Planted vs. Unplanted)
+
+SOC_{planted, amended}: soil C mineralization in the planted biochar soil partitioned from \(^{13}\)C-enriched 'Biochar+Root' end-member
+
+SOC_{unplanted, amended}: soil C mineralization in the unplanted biochar soil partitioned from biochar end members
+
+Rhizosphere priming in the biochar system:
+
+\[
+\Delta \mathrm{SOC}_{\text{amended}} = (\mathrm{SOC}_{\text{planted, amended}}) - (\mathrm{SOC}_{\text{unplanted, amended}})
+\]
+
+SOC priming was the difference in native SOC mineralization between the biochar-amended and control soils:
+
+\[
+\Delta \mathrm{SOC} = (C_s(\%)*C_T_{planted} - C_s(\%)*C_T_{unplanted})/100
+\] (4)
+
+where \(C_T_{planted}\) and \(C_T_{unplanted}\) are the total respiration in planted and unplanted systems either with biochar amendment or the control.
+
+Calculated \(^{13}\)C atom % ( %):
+
+\[
+^{13}\mathrm{C\ atom\ \%} = [(\delta^{13}\mathrm{C}+1000)*R_{PDB}]*100/[(\delta^{13}\mathrm{C}+1000)*R_{PDB}+1]
+\] (5)
+
+where \(R_{PDB} = 0.01118\).
+Sensitivity analysis of isotopic partitioning
+
+Because of the uncertainty of the direction of biochar-induced priming of soil carbon and/or rhizodeposits, the contribution of biochar on the \(^{13}\)C endmember of (\( \delta^{13}C_S \)) was assessed. Therefore, three alternative scenarios of three-pool C partitioning were evaluated:
+
+1) dominant positive priming of new C from the C\(_3\) pasture, where \( \delta^{13}C_S = -27\ \%_{\text{o}} \) (i.e. the upper boundary, grey dashed line, Fig. 2b);
+
+2) equal native SOC priming and rhizosphere priming, hence, the same \(^{13}\)C signatures of soil+root in the biochar and control plots, where \( \delta^{13}C_S = \delta^{13}C_S \) (i.e. solid lines in Fig. 2b);
+
+3) dominant positive priming of the native C\(_4\)-dominant SOC, where \( \delta^{13}C_{S+R} = -13\ \%_{\text{o}} \) (i.e. the lower boundary, grey dashed line, Fig. 2b).
+
+The boundary conditions were calculated from the published \(^{13}\)C signatures for Scenarios 1 and 3 (Farquhar et al. 1989). The 95 % confidence intervals were the combination of the lowest and highest scenarios (n =3). First order Tyler series of the variances of the percentage of soil respiration, C\(_S\) ( %), were approximated to propagate errors from isotopic partitioning (Derrien et al. 2014).
+
+\[
+\sigma^2 C_S(\%) = (\sigma^2 \delta^{13}C_T - \sigma^2 \delta^{13}C_S) / (\delta^{13}C_T - \delta^{13}C_S)^2
+\]
+
+Enzyme activity and substrate-induced respiration
+
+The determination of catabolic enzyme activities using a soil suspension method is described in Weng et al. (2017). Six treatments were derived from the control, the recent + historical biochar and recent biochar plots in both the unplanted (i.e. soil respiration collar) and planted (i.e. soil+ root respiration collar) systems (Table S5, Weng et al., 2017). After 7-d incubation at 40 % water-holding capacity (WHC), the activities of four C-degrading enzymes: \( \beta \)-glucosidase, xylosidase, cellulase, and N-acetyl-glucosaminidase, in the soils were analysed using a fluorescent microplate reader (BMG labtech FLUOstar Omega). Specific C enzyme activity was obtained by dividing the activity of individual
+enzymes over the total MBC at each sampling time. These ratios provided an indication of the C-turnover efficiency of the soil microbial community (Kaiser et al., 2015). Substrate-induced respiration was used to measure Community level physiological profiles using the MicroResp™ method (Campbell et al., 2003) with minor modifications. Fresh soil samples, packed in 96-deepwell plates (around 0.5 g per well), were prepared in the same manner as the enzyme experiment (i.e. incubation conditions). Each treatment per field replicate was sub-replicated eight times for measurement. The experimental protocol is detailed in Weng et al. (2017). Fifteen C substrates (Table S6) were selected to represent a broad range of soil and root exudates (Campbell et al. 2003; Chapman et al. 2007).
+
+Aggregate size and density fractionation
+
+Aggregate size (dry sieving) and density fractionation was conducted based on the method described by Weng et al. (2018). No large macroaggregates (> 2000 μm) was found in this study. Macroaggregates (250-2000 μm) and microaggregates (< 250 μm) were fractioned into free POM (F-POM, \( \rho < 1.6 \) kg m\(^{-3}\)), occluded POM (O-POM, (> 53 μm), and mineral-protected soil organic matter (M-SOM, combining silt- and clay-bound SOM, <53 μm).
+
+Belowground \(^{13}\)C pools
+
+The C and N content, and \( \delta^{13}\)C signatures of bulk soil, aggregates and fractions were measured using a PDZ Europa ANCA-GSL elemental analyzer interfaced to a PDZ Europa 20-20 isotope ratio mass spectrometer (Sercon Ltd., Cheshire, UK) (Weng et al., 2015).
+
+3D-FIB-SEM-EDS
+
+The serial section and EDS Mapping of the soil particle was prepared in a FEI SCIOS focused ion beam/scanning electron microscope (FIB/SEM) DualBeam system. The SCIOS FIB/SEM DualBeam system has a vertical mounted SEM column and an ion column sitting at an angle of 52 degrees with respect to the electron column. The particle was located with the aid of the electron beam. Before
+any milling, one micrometre thick platinum layer was deposited on the sample surface covering the area of interest to prevent it from damage caused by the ion bombardment in the following steps. The smooth finish of the Pt layer would also help to reduce the curtaining effect during the following milling procedure. The serial sectioning of the volume was carried out at 3nA and 30kV ion beam current and the EDS mapping were collected at 5kV and 6.4nA electron beam current. The voxel size of the SEM images is 84 nm(x) × 84 nm(y) × 1000 nm (z, slicing thickness).
+
+Synchrotron soft X-ray
+
+Synchrotron-based soft X-ray (SXR) analysis was performed at the SXR Spectroscopy beamline (14ID) at the Australian Synchrotron on the microaggregate (53-250 μm) and mineral fractions (<53 μm) from 1) recent biochar-amended plots, and 2) the historically biochar-amended plots; and then biochar recovered from the soil, that is: i) 1-year (aged) and ii) 9.5-year (aged) biochar. The samples were ground to fine powder and mounted on double sided carbon tape affixed to a stainless steel ruler.
+
+The SXR spectra were collected at an angle of 100° to the beam over a photon energy range of 275-325 eV with a step size of 0.1 eV. The energy was calibrated using a graphite standard in the beamline which was collected simultaneously with the I_0 and sample SXR spectra. The double normalization and a pre- and post-edge linear subtraction (background) were conducted using the Athena software (Stöhr 2013).
+
+Synchrotron IR
+
+For infrared microspectroscopy, approximately ~30 free water-stable microaggregates (53–250 μm) and mineral fractions (<53 μm) were hand-picked on a glass fibre filter paper and humidified gently over 18 hours (Lehmann et al. 2017; Hernandez-Soriano et al. 2018). The aggregates and fractions were frozen at –20 °C before being cryo-ultramicrotomed at 200 nm using a diamond knife. No embedding media was used. The multiple sections per sample (n >2) were directly collected on CaF_2 windows (IR transparent).
+The sections on CaF$_2$ were directly scanned at the IR beamline at the Australian Synchrotron using a Bruker Hyperion 3000 infrared microscope and a V80v Fourier transform infrared spectrometer. The detail of the microscope was described in Hernandez-Soriano et al. (2018). The spectral maps were produced in transmission mode from 64 scans with a resolution of 4 cm$^{-1}$, step size of 5 µm. Multiple maps were acquired for each treatment to represent the heterogeneity of the sample.
+
+Maps were processed using the software OPUS 8.2 (Bruker Optik GmbH, Germany), targeting absorbance at 3630 cm$^{-1}$ (O–H groups of clays), 2920 cm$^{-1}$ (aliphatic-C), 1600 cm$^{-1}$ (aromatic-C), and 1035 cm$^{-1}$ (polysaccharides-C)(Hernandez-Soriano et al. 2018). The area of these four absorbance peaks was integrated to the map. A linear regression was conducted to assess the correlation between clay content and the selected C functional groups.
+
+STEM-EDS-EELS and XPS
+
+Forty biochar particles were extracted from the soil samples per plot and were examined using a Zeiss Sigma Scanning electron microscope. Detailed analysis of 5 particles was carried using a Bruker X-ray Dispersive analyser (EDS). A Cs-corrected FEI Titan 80/300 scanning transmission electron microscope (STEM) working at 80 keV, equipped with a Gatan imaging filter Tridiem and an EDX analyzer was utilised to determine the structure and composition of the organo-mineral clusters that had formed on the surface of the aged biochar. Twenty biochar particles were sonicated in ethanol and then a sample of this was placed on a lacey carbon grind as described by Archanjo et al (2017). Detailed examination of 2 clusters was carried out using energy electron loss spectroscopy (EELS) and EDS. X-ray photoelectron spectroscopy (XPS) examination of both whole and crushed (< 0.5 mm) 1-year aged particles of biochar was undertaken. Carbon 1s photoelectron peak was decomposed in five components: C1-C5 (Table S9). The first one (C1) centered in 284.6 eV, typical of electrons in carbon sp$^2$ bounds (C=C), *i.e.*, delocalized sp$^2$ electrons. For this component, an asymmetrical line shape was used to fit. The asymmetry of the C1 component, known as a “defect peak”, is related to the localized sp$^2$ electrons. Electrons of C-C or C-H bounds typically appear with a binding energy shift of 0.9 eV in
+relation to sp^2 delocalized electrons, causing a broadening in the first component. The component C2, centered in 286.2±0.2 eV may be attributed to C-OH (phenol or hydroxyl groups), ether (C-O-C) or pyrrolic groups (C-N). Some authors also attribute this component to Csp^3 free radicals. The component C3 is attributed to carbonyl groups (C=O) centered in 287.5±0.4 eV, the component C4 is attributed to the carboxyl groups (COOH) centered in 289.1 ± 0.3 eV, and the last one, the component C5 in 291.4 eV is attributed to the shake-up satellite peak, characteristic of \( \pi \rightarrow \pi^* \) transition of electrons delocalized sp^2.
+
+The concentration of DOC and its fractions, measured by LC-OCD
+
+Dissolved organic carbon (DOC) in a water solution was analysed using liquid chromatography – organic carbon detection (LC-OCD). Two major fractions were: chromatographable organic carbon (CDOC) and hydrophobic organic carbon (HOC). CDOC (hydrophilic fraction) can be categorized into five fractions as a factor of retention time and molecular weight: i) biopolymers, ii) persistent C-like substances, iii) building blocks, iv) low molecular weight acids and v) low molecular weight neutrals. Samples were extracted in distilled water with a ratio of 1:10 (w/v). The solutions were regularly stirred at 50 °C for 24 hours before filtration to differentiate solid and liquid phases.
+
+Calculation and statistical analysis
+
+The cumulative SOC, biochar-C mineralization, and root respiration over 466 d were calculated as the area of a linear interpolation across all measurement points. All statistical analyses were conducted within the R environment (R development core team 2012). When significant F-tests were obtained (\( P = 0.05 \)), means were separated using a least significant difference (LSD) test at the 0.05 probability.
+
+Calculations of global implication for increasing soil carbon sink
+
+Projection for wood biochar production is estimated at 4.8 - 8.3 Pg, based on the total annual production of 5.5 to 9.5 Pg biochar by 2100 (Lehmann et al. 2011) with 87 % of the feedstock as
+wood (Jirka and Tomlinson 2013). Using the same application rate in this current study (10 t ha\(^{-1}\)), all wood biochar is assumed to be applied to 0.5 - 0.8 Gha in 2100, accounting for up to 100 % of tropical Ferralsol and 36 % of tropical grasslands (Lal 2004). The global C sequestration rate in grasslands is reported between \(1.3 \times 10^{10}\) and \(7.6 \times 10^{10}\) Pg C ha\(^{-1}\) yr\(^{-1}\) (Minasny et al. 2017). The range of C sequestration in grasslands before biochar amendment in 2100 would be around 0.07-0.61 Pg C (\(i.e.\) 0.5 or 0.8 Gha at \(1.3 \times 10^{10}\) and \(7.6 \times 10^{10}\) Pg C ha\(^{-1}\) yr\(^{-1}\)). We found a 16 % increase in retention of new C in the recent + historical plots compared with the control. This would lead to an additional soil C sink potential of 0.01-0.1 Pg C (\(i.e.\) 16 % of 0.07 or 0.61 Pg C).
+
+Figure Captions
+
+Fig. 1 Conceptual diagram of the formation of organo-mineral coatings on catalytic biochar surfaces over time in a Rhodic Ferralsol. Biochar can act as a bio-catalyst to accelerate formation of organo-mineral microaggregates (53-250 µm) and mineral-protected soil organic matter (<53 µm) on its surfaces and induce negative priming of soil organic carbon. Microbes, fungal hyphae and root hairs can further mine minerals within pores via exudation and dissolution. Microbial necromass covered with minerals is then incorporated into the organo-mineral (<250 µm) and organo-organic (< 100 nm) interfaces. Following wetting-drying and plant growth cycles, organo mineral and organo-organic aggregates break-off from organic matter because of weak bonding. Once these aggregates break off, new mineral layers can form.
+
+Fig. 2 Belowground carbon dynamics in the longest continuous biochar field experiment. a, Changes in total soil organic carbon (SOC, Mg C ha\(^{-1}\)) in the control and biochar-amended soils over 9.5 years (n=3, LSD = 1.1). Total SOC was measured in the 0-100 soil layer on an equivalent mass basis using Dumas combustion. b, Rhizosphere priming as difference in cumulative SOC mineralization between planted and unplanted “recent” biochar amended soil or soil with the “recent + historical” biochar. “Recent” biochar is biochar applied to a part of the control plots 8.2 years after the trial was established (closed triangles). The “recent + historical” amendment is biochar applied to a part of the historical biochar plots 8.2 years after the trial was established (open triangles). Confidence intervals (95%) of “recent” biochar and “recent + historical” biochar amendments are plotted in dashed lines and normalized against the mean squares across all treatments at each sampling event (n=3). For biochar amendment, the CI was based on a sensitivity analysis (Online Method Section), which considers the extreme scenarios of contrasting SOC pools (C3 vs. C4 dominated) by differences in \(δ^{13}C\) signatures. The six arrows represent nitrogen fertilizer additions.
+
+Fig. 3 Allocation and retention of rhizodeposits (\(^{13}\)C-enriched) and three-dimensional elemental distribution in a biochar-amended Ferralsol at 9.5 years. a, 8.2 years after the first application, the biochar-amended soil received a recent dose of biochar at 10 Mg ha\(^{-1}\) to the historical plots (“recent + historical”). The same total amount (190 mg \(^{13}\)C m\(^{-2}\)) was supplied in each treatment plot (n=3). b, Recent biochar (“recent”) was mixed in top 100 mm of soil at 10 Mg ha\(^{-1}\) one year before measurement. c, 3D FIB-SEM-EDS of an intact soil aggregate (30 µm × 25 µm × 24 µm) from the “recent + historical” biochar plots. d, 3D FIB-SEM-EDS of an intact soil aggregate (30 µm × 20 µm ×
+30 μm) from the “recent” biochar plots. Soil sampling was conducted before and 15 days after labelling. The total recovery of \(^{13}\mathrm{C}\) labelling is given, including soil + root respiration, root biomass, free- and occluded particulate matter and mineral fractions.
+
+Fig. 4 Synchrotron-based spectromicroscopic analysis of microaggregates (53-250 μm) and mineral fractions (<53 μm) in the unamended control and historical biochar-amended plots with recent biochar addition. a, Average SXR spectra of microaggregates (53-250 μm) and mineral fractions (<53 μm) with the “recent + historical” and “recent” biochar amendments (n=9, CV% < 3%). b, Semi-thin (200 nm) sections of free water-stable microaggregates (53-250 μm) and mineral fractions (<53 μm) isolated from the Ferralsol with the “recent + historical” and “recent” biochar amendments analysed using synchrotron-based IR-microspectroscopy. Spectral maps showing the distribution of polysaccharide-C (1035 cm\(^{-1}\)), aromatic-C (1600 cm\(^{-1}\)), aliphatic-C (2920 cm\(^{-1}\)), and mineral-OH (3650 cm\(^{-1}\)) were obtained from 64 co-added scans (4 cm\(^{-1}\) resolution), lateral resolution 5 μm (bars: 50 μm). The signal intensity for each molecular group varied according to the colour scale shown. The images on the left are optical micrographs of the semi-thin sections.
+
+Fig 5. In situ spectromicroscopic analysis of the organo-mineral coating on biochar surfaces and pores over time. a, Average SXR spectra of field-extracted “recent” (1-yr aged) and “historical” (9.5-yr aged) biochars (n=9, CV% < 3%). b, high magnification secondary electron image of a pore where fungi exist. c, EDS spectrum of the area in b. d, STEM-HAADF image of organo-mineral clusters on the “recent” biochar surface; e, its EELS spectra. f, High resolution image of the surface of the organomineral layer inside the pore of the “historical” biochar. g, EDS spectrum of the area in f. h, HAADF image of a deposit attached to the surface of the “historical” biochar. i, its EELS spectra. j, DOC of bulk soils from the “recent + historical” and “recent” biochar amendments analysed with LCOCD. The hydrophilic fraction is further sub-divided into five categories, i: biopolymer, ii: persistent C, iii: building blocks, iv: low molecular weight acids and v: low molecular weight neutrals.
+
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+
+Acknowledgements
+
+The authors thank the Australian Government, Department of Agriculture and Water Resources for supporting the National Biochar Initiatives (2009–2012, 2012–2014) which co-funded this research.
+
+We are particularly grateful to Dr. Peter Slavich, as one of the key founders of this long–term field experiment for providing insightful comments on the initial draft. Part of this research was undertaken on the Soft X-ray spectroscopy beamline and the Infrared microscopy beamline at the Australian Synchrotron, part of ANSTO (grant numbers AS1_SXR_15754 and AS1_IRM_15940). We thank the beamline scientists, Drs Bruce Cowie and Lars Thomsen, for their technical support on the soft x ray analysis and Drs Mark Tobin, Annaleise Klein and Jitraporn (Pimm) Vongsvivut, for their technical support on the infrared microscopy analysis. Part of the research is funded by La Trobe University’s Research Focus Area in Securing Food, Water and the Environment (Grant Ready: SFWE RFA 2000004295; Collaboration Ready: SFWE RFA 2000004349). We also appreciate the technical support from Scott Petty and Josh Rust for maintaining this field experiment over the past decade, and laboratory support from Nichole Morris. We also thank Dr Carlos Achete from INMETRO, Brazil and Dr
+Bin Gong from the University of New South Wales, Australia, for performing XPS analysis of biochars and soils, Dr Sarasadat Taherymoosavi from the University of New South Wales, Australia, for technical assistance in LC-OCD analysis. We acknowledge the intellectual contribution from Prof Johannes Lehmann for discussions on the potential mechanisms of biochar–induced stabilization of rhizodeposits.
+
+Author contributions
+
+ZW drafted and wrote the manuscript, experimental design, set-up and conducted experiments, and data collection and analysis; LVZ, BPS and LMM wrote the manuscript, aided in experimental design, critical revision of the article; SJ, ET, BSA and MTR collected and analyzed data, critical revision of the article; TJT, CT, AF, PMK, SK, SM and AC provided critical revision of the article. All authors provided final approval of the revision to be published.
+
+Correspondence and requests for materials should be addressed to LVZ via email: lukas.van.zwieten@dpi.nsw.gov.au
+Figures
+
+![Conceptual diagram of the formation of organo-mineral coatings on catalytic biochar surfaces over time in a Rhodic Ferralsol.](page_120_184_1347_654.png)
+
+Figure 1
+
+Conceptual diagram of the formation of organo-mineral coatings on catalytic biochar surfaces over time in a Rhodic Ferralsol. Biochar can act as a bio-catalyst to accelerate formation of organo-mineral microaggregates (53-250 μm) and mineral-protected soil organic matter (<53 μm) on its surfaces and induce negative priming of soil organic carbon. Microbes, fungal hyphae and root hairs can further mine minerals within pores via exudation and dissolution. Microbial necromass covered with minerals is then incorporated into the organo-mineral (<250 μm) and organo-organic (< 100 nm) interfaces. Following wetting-drying and plant growth cycles, organo mineral and organo-organic aggregates break-off from organic matter because of weak bonding. Once these aggregates break off, new mineral layers can form.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Videoabstract3DFIBSEMEDXofrhizodepositsretentioninaggregate.mp4
+• SupplementaryInformation.pdf