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preprint/preprint__5f1d37d721e021a44e5568aa238f1811958abbd8ec4ce4a5f8b339ff2a15068c/images_list.json

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+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Self-referenced timing-tool setup. A ultrashort \\(800\\mathrm{nm}\\) optical pulse is guided through a motorised delay stage \\(\\Delta t_{1}\\) and frequency doubled to \\(400\\mathrm{nm}\\) in a SHG crystal. A SF11 glass block \\(Disp\\) . is used to further chirp the optical pulse duration. The chirped pulse is guided through the Common-Path-Interferometer consisting of two polarisers \\(P_{1,2}\\) and two a-cut \\(\\alpha \\mathrm{BBO}_{1,2}\\) crystals. The optical pulse and the X-ray pulse are temporally and spatially overlapped in the diamond sample \\(S\\) in the center of the CPI, where the X-ray arrival-time is imprinted into the optical pulse. The spectrally encoded arrival time is analyzed with a spectrograph \\(Sp\\) .",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Calculation of electron densities in a \\(50\\mu \\mathrm{m}\\) thick diamond sample for different X-ray pulse energies over a wide range of X-ray photon energies. The carrier densities are calculated for three different X-ray beam diameters: a) \\(20\\mu \\mathrm{m}\\) , b) \\(100\\mu \\mathrm{m}\\) , and c) \\(200\\mu \\mathrm{m}\\) (each FWHM). For details see text.",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Refractive index change in a \\(50\\mu \\mathrm{m}\\) thick diamond sample for different X-ray pulse energies of a broad range of X-ray photon energies. Subfigures a), b), and c) show the expected refractive index change for X-ray pulses with a FWHM beam diameter of \\(20\\mu \\mathrm{m}\\) FWHM, \\(100\\mu \\mathrm{m}\\) FWHM and \\(200\\mu \\mathrm{m}\\) FWHM, calculated with the Drude model. Correspondingly d), e) and f) illustrate the expected refractive index changes calculated with the Maxwell-Garnett theory. For details see text.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Simulated self-referenced arrival-time spectra for different X-ray arrival-times from - 1500 fs to 1500 fs. The arrival-time spectra are shown as solid purple lines, while the full original spectra of the time-sheared pulse are indicated by the shaded purple lines. Due to the chirp of the optical pulse, the arrival-time signals are not exactly symmetric for corresponding positive and negative arrival-times.",
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Analysis of measured X-ray arrival times. Relative arrival times for 6 consecutive pulse trains, with each 100 X-ray pulses, are shown, a) via radiofrequency synchronisation (RFS) of the electron bunches, b) via the optical facility synchronisation (OS) scheme. For each pulse train, a linear function is fitted to indicate the common drift patterns of the relative arrival times within a pulse train. The timing jitter distribution over a time span of 100 s is shown in c) for the RF synchronisation \\((\\Delta t = 154 \\pm 19 \\mathrm{fs})\\) and d) for the optical synchronisation \\((\\Delta t = 83 \\pm 19 \\mathrm{fs})\\) scheme.",
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. The average arrival times of the X-ray pulses within a pulse train are analysed in the center panel for both synchronisation schemes. X-ray pulses within a pulse train are drifting to earlier arrival times if the RFS (orange) is used, while they are drifting to later arrival times within a pulse train for the OS scheme (blue). The intra-train timing distributions are shown on the left (RFS) and on the right (OS), yielding comparable FWHM values when only using 100 pulses within a pulse train.",
+    "footnote": [],
+    "bbox": [
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. Self-referenced arrival time spectra with the \\(0.5\\%\\) highest amplitudes (orange). The average (red) of theses arrival time spectra is used as reference to fit a simulated (blue) arrival time spectrum to the data. The required X-ray-induced refractive index change to fit the simulation is \\(\\Delta n_{\\mathrm{exp}} = -5.7 \\times 10^{-5}\\) . The horizontal shifts of the individual arrival time spectra are caused by the arrival time jitter, while the fluctuating amplitudes are caused by the X-ray pointing instabilities.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Figure 8. Analysis of the expected transient refractive index change with the experimentally used X-ray beam profile. The calculated fluence of the used X-ray beam is shown in a). The expected transient refractive index changes in diamond calculated from the fluence are shown in b) for the Drude model and c) for the Maxwell-Garnett model. Please note the very different scales for each color bar.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_9.jpg",
+    "caption": "Figure 9. Estimation of the transient refractive index change in diamond in the actual experiment. The solid blue curve is is a simulation which recreates the original experimental data with an X-ray-induced refractive index change of \\(\\Delta n = -5.7 \\times 10^{-5}\\) . The solid orange curve a numerical simulation. The orange curve is the simulated arrival time signal, using the Maxwell-Garnet theory. The orange band gives the upper and lower expected transient refractive index change according to the Maxwell-Garnett model when implementing the uncertainty of the X-ray beam focal size of \\(150 \\pm 20 \\mu \\mathrm{m}\\) . The same applies to the purple curve which indicates the calculated values for the same conditions but with the Drude model.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_10.jpg",
+    "caption": "Figure 10. Common-Path-Interferometer principle. The first polariser defines the polarisation of the optical to \\(45^{\\circ}\\) , which can equally be described by two perpendicular polarisation components (1). In the absence of any X-ray pulse no phase-shift is introduced and the two time-delayed PCs (2), generated by the first BC, can be perfectly synchronised behind the second BC. This recreates an \\(45^{\\circ}\\) polarised pulse (3), blocked by the second polariser (4). In the presence of an X-ray pulse (5), a phase-shift is introduced (6), preventing the perfect synchronisation of both PCs behind the second BC and creating an elliptical polarised pulse (7), partly transmitted through the second polariser (8).",
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preprint/preprint__5f1d69d18d2c9eabaa82d0107bd7fe640f17ab334977916cfd30bd64b4fcb9cc/preprint__5f1d69d18d2c9eabaa82d0107bd7fe640f17ab334977916cfd30bd64b4fcb9cc.mmd

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+
+# Progression of a Muscular Dystrophy Due to a Genetic Defect in Membrane Synthesis is Driven by Large Changes in Neutral Lipid Metabolism  
+
+Mahtab Tavasoli Dalhousie University https://orcid.org/0000- 0001- 7962- 3566  
+
+Sarah Lahire University of Reims Champagne- Ardenne  
+
+Stanislav Sokolenko Dalhousie University  
+
+J. Pedro Fernández- Murray1 Dalhousie University  
+
+Kitipong Uaesoontrachoon Dalhousie University/Agada Biosciences  
+
+Abir Lefsay Dalhousie University  
+
+Joyce Rowsell Agada Biosciences  
+
+Sadish Srinivassane Agada Biosciences  
+
+Molly Praest Agada Biosciences  
+
+Alexandra MacKinnon Agada Biosciences  
+
+Melissa Mammoliti Agada Biosciences  
+
+Ashley Maloney Agada Biosciences  
+
+Marina Moraca Agada Biosciences  
+
+Kanneboyina Nagaraju  
+
+Department of Pharmaceutical Sciences, School of Pharmacy and Pharmaceutical Sciences, Binghamton University  
+
+Eric Hoffman  
+
+School of Pharmacy and Pharmaceutical Sciences
+
+<--- Page Split --->
+
+# Christopher McMaster (Christopher.mcmaster@dal.ca) Dalhousie University  
+
+## Article  
+
+Keywords: metabolism, muscular dystrophy, skeletal muscle, lipid, acylcarnitine, triacylglycerol, phosphatidylcholine, peroxisome proliferator- activated receptors (PPAR)  
+
+Posted Date: May 19th, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 64129/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 23rd, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 29270- z.
+
+<--- Page Split --->
+
+## Progression of a Muscular Dystrophy Due to a Genetic Defect in Membrane Synthesis is Driven by Large Changes in Neutral Lipid Metabolism  
+
+Mahtab Tavasoli \(^{1}\) , Sarah Lahire \(^{2}\) , Stanislav Sokolenko \(^{3}\) , J. Pedro Fernandez- Murray \(^{1}\) , Kitipong Uaesoontrachoon \(^{4}\) , Abir Lefsay \(^{5}\) , Joyce Rowsell \(^{4}\) , Sadish Srinivassane \(^{4}\) , Molly Praest \(^{4}\) , Alexandra MacKinnon \(^{4}\) , Melissa Stella Mammoliti \(^{4}\) , Ashley Alyssa Maloney \(^{4}\) , Marina Moraca \(^{4}\) , Kanneboyina Nagaraju \(^{4,6}\) , Eric P. Hoffman \(^{4,6}\) , and Christopher R. McMaster \(^{1}\)  
+
+\(^{1}\) Department of Pharmacology, Dalhousie University, Halifax, Nova Scotia, Canada \(^{2}\) University of Reims Champagne- Ardenne, Reims, France \(^{3}\) Department of Process Engineering & Applied Science, Dalhousie University, Halifax, Nova Scotia, Canada \(^{4}\) Agada Biosciences Inc., Halifax, Nova Scotia, Canada \(^{5}\) Mass Spectrometry Core Facility, Dalhousie University, Halifax, Nova Scotia, Canada \(^{6}\) School of Pharmacy and Pharmaceutical Sciences, Binghamton University, State University of New York (SUNY), Binghamton, NY, USA  
+
+Correspondence christopher.mcmaster@dal.ca
+
+<--- Page Split --->
+
+## Abstract  
+
+CHKB encodes one of two mammalian choline kinase enzymes that catalyze the first step in the synthesis of the major membrane phospholipid, phosphatidylcholine (PC). In humans, inactivation of the CHKB gene causes a recessive form of a rostral- to- caudal congenital muscular dystrophy. Using Chkb knockout mice, we reveal that at no stage of the disease is PC level significantly altered. Instead, at early stages of the disease the level of mitochondrial specific lipids acylcarnitine (AcCa) and cardiolipin (CL) increase 15- fold and 10- fold, respectively. Importantly, these changes are only observed in affected muscle and contribute to the decrease in the skeletal muscle functional output in these mice. As the disease progresses, AcCa and CL levels normalize and there is a 12- fold increase in the neutral storage lipid triacylglycerol and a 3- fold increase in its upstream lipid diacylglycerol. Our findings indicate that the major changes in lipid metabolism upon loss of function of Chkb is not a change in PC level, but instead is an initial inability to utilize fatty acids for energy resulting in shunting of fatty acids into triacylglycerol.  
+
+Keywords – metabolism, muscular dystrophy, skeletal muscle, lipid, acylcarnitine, triacylglycerol, phosphatidylcholine, peroxisome proliferator- activated receptors (PPAR)
+
+<--- Page Split --->
+
+## Introduction  
+
+Phosphatidylcholine (PC) is the major phospholipid present in mammalian cells, comprising approximately \(50\%\) of phospholipid mass. Choline kinase catalyzes the phosphorylation of choline to phosphocholine and is the first enzymatic step in the synthesis of PC \(^{1}\) . There are two genes that encode human choline kinase enzymes, CHKA and CHKB. Monomeric choline kinase proteins combine to form homo- or heterodimeric active forms \(^{2}\) . CHKA and CHKB proteins share similar structures and enzyme activity but display some distinct molecular structural domains and differential tissue expression patterns. Knock- out of the murine Chka gene leads to embryonic lethality \(^{3}\) . Chkb deficient (Chkb \(^{- / - }\) ) mice are viable, but noticeably smaller than their wild type counterparts, and show severe bowing of the ulna and radius at birth. By 2- 3 months of age Chkb \(^{- / - }\) mice lose hindlimb motor control, while the forelimbs are spared \(^{4,5}\) . Inactivation of the Chkb gene in mice would be predicted to decrease PC level, however, reports indicate no, or a very modest, decrease in PC level in Chkb \(^{- / - }\) mice, and this decrease is similar in both forelimb and hindlimb muscle \(^{6,7}\) . The very small decrease in PC mass, and the fact that there is no rostral- to- caudal change in PC, suggest a poor correlation of the anticipated biochemical defects and observed rostral- to- caudal phenotype of this muscular dystrophy \(^{5}\) . It is unclear how a defect in a gene required for the synthesis the major phospholipid in mammalian cells causes a muscular dystrophy, especially in light of the fact that global inactivation of the CHKB/Chkb gene (human or mouse) does not affect the level of the product of its biochemical pathway, PC.
+
+<--- Page Split --->
+
+Muscular dystrophy, congenital, megacomial type (OMIM 602541) is an autosomal recessive dystrophy caused by loss of function of CHKB gene, and is the only defect in phospholipid synthesis that can cause a muscular dystrophy \(^{5,8 - 14}\) . Muscular dystrophies have been mapped to at least 30 different causal genes \(^{15}\) . The most common types of muscular dystrophy result from mutations in genes coding for members of protein complexes which act as linkers between the cytoskeleton of the muscle cell and the extracellular matrix that provides mechanical support to the plasma membrane during myofiber contraction \(^{16,17}\) . Muscular dystrophies result in fibrofatty replacement of muscle tissue, progressive muscle weakness, functional disability and often early death \(^{18,19,20}\) .  
+
+Skeletal muscle accounts for \(20 - 30\%\) of whole body basal metabolic rate \(^{21}\) . Fatty acid oxidation is the major source of ATP for skeletal muscle during the resting state \(^{22}\) . Fatty acids can be synthesized de novo by cells or can be obtained extracellularly, with the bulk of lipids delivered to cells through the circulation via serum albumin or lipoprotein/lipoprotein receptors. For fatty acids to be metabolized they are first activated by esterification to fatty acyl- CoA. Subsequently, they have divergent fates depending on the metabolic status of the cells (Fig. 1). The three major fates of fatty acids are 1. conversion to fatty acyl carnitine for subsequent mitochondrial \(\beta\) - oxidation to provide energy, 2. the synthesis of neutral lipid species for storage as triacylglycerol (TG) rich cytoplasmic lipid droplets, or 3. metabolism into phospholipids, such as PC, to maintain membrane integrity. Fatty acids can also directly bind peroxisome proliferator- activated receptors (PPARs), key players in the regulation of lipid metabolism by altering the expression of genes required for the conversion of fatty acids to fatty acyl-
+
+<--- Page Split --->
+
+CoA for phospholipid and TG synthesis, and for fatty acid activation to acylcarnitine (AcCa) for entry into mitochondria and subsequent fatty acid \(\beta\) - oxidation \(^{23}\) .  
+
+In the present study, we use mouse and cell models to investigate the temporal changes in lipid metabolism in the absence of the Chkb gene. Results demonstrate that PC level remains essentially unchanged. Instead, this genetic defect in PC synthesis drives large fluctuations in mitochondrial lipid metabolism with an inability to use fatty acids for mitochondrial \(\beta\) - oxidation resulting in a temporal shunting of fatty acids into TG and their storage as lipid droplets. These changes were specific to affected muscle. This study provides insight into the surprising biochemical phenotype whereby a genetic block in a lipid metabolic pathway does not directly affect the product of its pathway, and instead alters tangential pathways in a manner that explains the rostral- to- caudal gradient of a genetic disease.  
+
+## Results  
+
+Choline kinase deficient mice display hallmark muscular dystrophy phenotypesTo address the extent that mice lacking Chkb function display gross muscular dystrophy phenotypes, we tested muscle function in \(Chkb^{+/+}\) , \(Chkb^{+/+}\) and \(Chkb^{/-}\) mice from 6 weeks to 20 weeks of age using a grip strength assay and a total distance run to exhaustion test. Body weight was also recorded each week at similar times over the duration of the phenotyping experiments. Body weight of the \(Chkb^{+/+}\) and \(Chkb^{/-}\) mice showed no difference between groups (Fig. 2a). The \(Chkb^{/-}\) mice weighed significantly less than their wild type counterparts at all time points. The average body weight of
+
+<--- Page Split --->
+
+Chkb<sup>-/-</sup> mice was 33% to 42% less than that of Chkb<sup>+/+</sup> mice at week 6 and week 20, respectively.  
+
+Forelimb grip strength measurements were performed at three different timepoints and normalized to body weight. The Chkb<sup>-/-</sup> mice had significantly lower (less than half) the normalized forelimb strength than wild type mice at all three timepoints (week 6, 12 and 18) (Fig. 2b). Another measure of neuromuscular function is the resistance to treadmill running, evaluated as the total distance that each mouse is able to run until exhaustion. The test was performed in all groups at three timepoints (Week 7, 13 and 19). The total distance covered by the wild type mice before exhaustion was similar at all 3 time points (Fig. 2c). There was no significant difference between Chkb<sup>+/+</sup> and Chkb<sup>+/+</sup> groups, these mice maintained the ability to cover the same total distance before exhaustion (week 7 vs. week 19; non- significant). At week 7, the Chkb<sup>-/-</sup> mice showed a basal level of total distance run that was 50% that of the wild type or Chkb<sup>+/+</sup> mice. Moreover, the Chkb<sup>-/-</sup> mice showed a decline in running performance from week 7 to week 19, with an almost complete inability to run observed by week 19. Gross measurements of neuromuscular strength in whole mice demonstrate that mice heterozygous for Chkb gene display similar phenotypes to wild type mice. Notably, mice lacking both copies of the Chkb gene display a significant decrease in overt neuromuscular phenotypes.  
+
+The level of circulating creatinine kinase (CK), a biomarker of sarcolemma injury, was determined in Chkb<sup>+/+</sup>, Chkb<sup>+/+</sup>, and Chkb<sup>-/-</sup> mice. No significant change in the serum level of CK was observed in Chkb<sup>+/+</sup> heterozygous mice when compared to the
+
+<--- Page Split --->
+
+wild type. CK activity was 2.5- fold higher in \(Chkb^{- / - }\) null mice than that of wild type mice (Fig. 2d).  
+
+To determine if the decreased neuromuscular phenotypes observed in the \(Chkb^{- / - }\) mice were due to a direct effect on muscle itself, maximal specific force generated by freshly isolated extensor digitorum longus (EDL) muscle from the hindlimb of \(Chkb^{+ / + }\) , \(Chkb^{+ / - }\) , and \(Chkb^{- / - }\) mice at week 20 was determined. EDL muscle fatigue was measured with 60 isometric contractions for 300 ms each, once every 5 sec, at 250 Hz. There was no significant difference between wild type and heterozygous \(Chkb\) mice in regard to specific force decrease during fatigue and specific force generation, (Fig. 2e, f). \(Chkb^{- / - }\) mice displayed a specific EDL force that was 10% that of \(Chkb^{+ / + }\) or \(Chkb^{+ / - }\) mice. In addition, \(Chkb^{- / - }\) mice were at maximally fatigued levels, that is those observed in \(Chkb^{+ / + }\) or \(Chkb^{+ / - }\) mice after 60 muscle stimulations, at the first stimulation. Hindlimb muscle from \(Chkb^{- / - }\) mice produce less force, and are much more easily fatigued, than that of wild type or \(Chkb\) heterozygous mice.  
+
+Similar to humans \(^{8,10}\) , mice with one functional copy of the \(CHKB\) gene do not possess any obvious overt muscle dysfunction, whereas mice that are homozygous null for functional copies of the \(Chkb\) gene display hallmark muscular dystrophy phenotypes.  
+
+## Chka protein expression is inversely correlated with the rostro-caudal gradient of severity in Chkb-mediated muscular dystrophy  
+
+Consistent with the rostral- to- caudal nature of \(Chkb\) associated muscular dystrophy, transmission electron micrographs of 115 day old \(Chkb^{- / - }\) mice show extensive injury in hindlimb (quadriceps and gastrocnemius) but not the forelimb (triceps) (Supplementary
+
+<--- Page Split --->
+
+Fig. 1a- c). Chkb encodes choline kinase b, the first enzymatic step in the synthesis of PC, the most abundant phospholipid present in eukaryotic membranes. A second choline kinase, Chka is present in mouse (and human) tissues. We investigated whether the lack of dystrophic phenotypes in Chkb+/- mice, and the rostro- caudal gradient of muscular dystrophy in Chkb+/- muscle, can be explained by compensatory changes in Chkb or Chka protein levels using western blot. In Chkb+/- mice, there was a \(\sim 50\%\) decrease in Chkb protein detected in both the forelimb and hindlimb muscles of Chkb+/- mice compared to wild type (Fig. 3a, b). There was no change in Chka protein level in hindlimb muscle of Chkb+/- mice compared to wild type, and a small but statistically insignificant increase in Chka level in forelimb muscle.  
+
+In Chkb+/- mouse forelimb or hindlimb muscle, Chkb protein expression was undetectable consistent with the allele not producing Chkb protein. In forelimb muscle from Chkb+/- mice there was a compensatory upregulation of Chka protein expression to almost 3- fold that observed in wild type mice. In contrast, in hindlimb muscle from Chkb+/- mice Chka protein expression was decreased to less than \(10\%\) that observed in wild type mice. A compensatory level of Chka protein expression inversely correlates with the rostro- caudal gradient of severity in Chkb+/- associated muscular dystrophy.  
+
+## Loss of Chkb activity exerts a major effect on neutral lipid abundance  
+
+PC synthesis is integrated with the synthesis of other major phospholipid classes, as well as AcCa, fatty acids and the neutral lipids diacylglycerol and triacylglycerol (Fig.1). Lipidomics was used to determine if complete loss of Chkb function, and the associated upregulation of Chka in the forelimb but not hindlimb muscle of Chkb+/- mice,
+
+<--- Page Split --->
+
+differentially altered lipid metabolism. The levels of the major glycerophospholipids, neutral lipids and acylcarnitine in hindlimb and forelimb muscle isolated from 12 day old and 30 day old \(Chkb^{+ / + }\) and \(Chkb^{- / - }\) mice were quantified.  
+
+In the forelimb and hindlimb muscle of both 12 day old and 30 day old \(Chkb^{- / - }\) mice, the level of PC was the same as wild type mice (Fig. 4a- d). In 12 day old \(Chkb^{- / - }\) mice the largest change observed was a 15- fold increase in AcCa level in hindlimb muscle, and to a lesser degree ( \(\sim 2\) - fold increase) in forelimb, compared to their wild type littermates. The second largest change in 12 day old mice was a 10- fold increase in the level of cardiolipin (CL) in hindlimb muscle that was not present in forelimb muscle of \(Chkb^{- / - }\) mice. Phosphatidylethanolamine (PE) and phosphatidylinositol (PI) levels were also slightly increased ( \(\sim 1.5\) fold) in both forelimb and hindlimb muscles of 12 day old \(Chkb^{- / - }\) mice. The large changes in lipid levels in hindlimb muscle, versus forelimb, of \(Chkb^{- / - }\) mice are consistent with the rostral- to- caudal nature of the muscular dystrophy observed in these mice.  
+
+Considering the progressive nature of the disease, we tracked the changes in the lipid profile in the hindlimb of 30 day old \(Chkb^{- / - }\) mice, when muscle injury is more pronounced. In sharp contrast to 12 day old mice, AcCa and CL levels were no longer increased and were at the same level as wild type mice. Instead, there was a 12- fold increase in the neutral storage lipid TG and a 3- fold increase in its precursor DG in the hindlimb samples of \(Chkb^{- / - }\) mice (Fig. 4e, f). PE and PS levels were 2- 3- fold higher in the hindlimb samples from 30 day old \(Chkb^{- / - }\) mice compared to wild type littermates. There is a temporal shift from a 12 to 15 fold increase in CL and AcCa, to a similar increase in TG, only in affected muscle in \(Chkb^{- / - }\) mice.
+
+<--- Page Split --->
+
+As AcCa levels are many fold higher than wild type mice in the early stage of Chkb- muscular dystrophy, this implies that the affected muscles are defective in using fatty acids for the production of cellular energy by mitochondrial \(\beta\) - oxidation. As Chkb- muscular dystrophy progresses, the affected muscles appear to adapt to this inability to consume fatty acids by transitioning toward energy storage indicated by the large increase in TG.  
+
+## Increased intramyocellular lipid droplet accumulation and enlarged mitochondria in hindlimb muscles from Chkb- mice  
+
+To understand early ultrastructural pathological changes, and to further explore the nature of the accumulation of TG in affected muscle as Chkb- muscular dystrophy progresses, we performed transmission electron microscopy (TEM) on hindlimb muscles from 12 and 115 day old mice. Consistent with previous reports \(^{5}\) , our transmission electron images of Chkb- mice showed that the muscular dystrophy in forelimb is extremely mild compared to the hindlimb (Supplementary Fig. 1a), while both limbs do display bone abnormalities \(^{24}\) . A closer examination of hindlimb muscle TEM images from 12 day old mice revealed early signs of disrupted sarcomeres, as well as a small increase in the abundance of cytoplasmic lipid droplets, consistent with the small (2- fold) but statistically not significant increase in TG in hindlimb muscle we observed using lipidomics. Interestingly, these lipid droplets were located mainly adjacent to enlarged mitochondria (Fig. 5a). Detailed quantification of randomly imaged lipid droplets in hindlimb muscle from 12 day old Chkb- mice determined that 81% were
+
+<--- Page Split --->
+
+associated with mitochondria (Fig. 5a and Supplementary Fig. 2c). In 115 day old Chkb<sup>-/-</sup> mice, cytoplasmic lipid droplets increased substantially in size (Fig. 5a).  
+
+We also evaluated TG accumulation in muscle using confocal microscopy by staining hindlimb muscle sections of 30 day old Chkb<sup>-/-</sup> mice with BODIPY 493/503 (Fig. 5b). Concanavalin A dye conjugate (CF™ 633) and Dapi were used to stain membrane (Red) and nucleus (Blue) respectively. Consistent with our TEM and lipidomics results, BODIPY- stained lipid droplets were noticeably more frequent and larger in Chkb<sup>-/-</sup> hindlimb muscles compared to the wild type littermates. The same pattern of lipid droplet staining was observed using Nile red staining (Supplementary Fig. 2a, b).  
+
+The lipidomics results point to large changes in mitochondrial specific lipids at the early stages of Chkb associated muscular dystrophy. To further explore the nature of these changes, we investigated the temporal development of morphological changes in mitochondria in hindlimb muscle of Chkb<sup>-/-</sup> mice using standard TEM stereological methods<sup>25</sup>. The results show that at 12 days of age, the size of mitochondria increased (6.2%±0.5 vs 11.4%±1.6; P<0.01; wild type vs Chkb<sup>-/-</sup>) while the number of mitochondria (17.3±2.6 vs 16.3±2.1) and cristae density (21.6±2 vs. 23.3±1.9) remained the same. At 60 days of age, the number of mitochondria (18.1±7.6 vs 1.8±0.5; P<0.01) and the cristae density (27.7±1.9 vs. 5.8±1.2; P<0.01) decreased significantly while the size did not change (7.3%±0.2 vs 8.2% ±2.5). At the early stages of Chkb muscular dystrophy, there is an increase in mitochondrial size but not number or morphology. As the disease progresses, the increase in mitochondrial size remains, however the number of mitochondria, and the cristae within mitochondria, decrease (Supplementary Fig. 3a, b).
+
+<--- Page Split --->
+
+## Chkb deficiency results in increased lipid droplet accumulation in differentiated myocytes in culture  
+
+To address if the observed increase in TG in Chkb- mice was due to muscle specific events or was due to larger physiological changes that then impact muscle physiology, we assessed TG level in primary cultured muscle cells subsequent to myoblast differentiation.  
+
+We first determined if Chkb deficiency alters differentiation in primary myoblasts. Primary muscle cell cultures were examined for their transition from a single cell proliferative condition to differentiated multinucleated myotubes. During the process of differentiation, mononuclear myoblasts fuse to form myocytes (myotubes), which are large multinucleated cells. We isolated skeletal myoblasts from Chkb+/+ and Chkb- mice and induced differentiation by switching to low growth factor serum. Representative light micrographs of cultures of dissociated myogenic cells from skeletal muscle of Chkb+/+ and Chkb- mice at 0, 3 and 5 days after switching to differentiation media show a similar degree of myotube formation (Fig. 6a). Chkb deficiency resulted in a compensatory upregulation of Chka gene expression as well as a significant increase in the markers of myocyte injury, namely lcam1 and Tgfb1 26 (Fig. 6b). We calculated the fusion index, which is nuclei distribution, to determine the extent of myotube differentiation, by immunofluorescence staining. There was no difference between the Chkb+/+ and Chkb- cells in terms of the percentage of nuclei within the myotubes, the average number of nuclei in each myotube, or the distribution of nuclei in myotubes
+
+<--- Page Split --->
+
+(Fig. c, d). Loss of Chkb function does not appear to affect gross myoblast differentiation.  
+
+To assess whether Chkb deficiency modulates TG storage in isolated myotubes, we stained differentiated myotubes with BODIPY 493/503 to visualize neutral lipid droplets. Lipid droplets were noticeably more abundant and larger in Chkb deficient myotubes compared to wild type (Fig. 6e). Quantification of the corrected total cell fluorescence intensity in Chkb- /- myotubes confirmed a significant 2- fold increase in lipid droplet formation (Fig. 6f). The increase in TG level in differentiated muscle cells isolated from Chkb- /- mice is in line with the increased TG and lipid droplet levels observed in isolated hindlimb muscle from older Chkb- /- mice, and implies that the increase in TG in hindlimb muscle due to the loss of Chkb function is a direct effect on lipid metabolism within the muscle cells themselves.  
+
+## Changes in expression of peroxisome proliferator-activated receptors (Ppars) and target genes reinforce the observed changes in lipid levels in Chkb- /- hindlimb muscle  
+
+Our lipidomic data imply a temporal shift from the use of fatty acids for energy to lipid storage in affected muscle of Chkb- /- mice. To further investigate this metabolic shift, we determined the expression of peroxisome proliferator- activated receptors (Ppars) in affected muscle of 30 day old Chkb+/- , Chkb+/- and Chkb- /- mice. Peroxisome proliferator- activated receptors (PPARs) are master regulators of lipid metabolism 27,28. The endogenous ligands for Ppars are fatty acids and their derivatives. There are three Ppar members, each encoded by distinct genes, designated Ppara, Pparb/d and Pparg.
+
+<--- Page Split --->
+
+Ppara and Pparb/d primarily regulate the expression of genes required for fatty acid oxidation, with Pparb/d also regulating genes required for mitochondria biogenesis. Pparg is primarily expressed in adipose tissue and regulates insulin sensitivity and glucose metabolism 27. Using reverse transcription (RT) qPCR, we determined that the expression of Ppara and Pparb/d were 4-fold and 6-fold lower, while Pparg was 2-fold higher, in the hindlimb muscle of 30 day old mice Chkb- mice compared to wild type (Fig. 7a). Consistent with RT qPCR results, assessment of Ppar protein levels by western blot show decreased Ppara and Pparb/d protein expression, and an increase in Pparg protein expression, in Chkb deficient hindlimb muscle compared to wild type (Fig. 7b). Ppar protein levels did not change in Chkb deficient forelimb muscle compared to Chkb+/+(Supplementary Fig. 4) indicating that the Ppar changes are isolated to affected muscle.  
+
+To further evaluate and validate how the Ppar pathway contributes to the lipid metabolic changes observed in Chkb- mice, we utilized a microarray of 82 Ppar regulated genes, along with 4 housekeeping genes, to assess transcriptional changes in the hindlimb muscle of 30 day old mice. As expected, there was no change in the expression of the 4 housekeeping genes. For Ppar receptors to bind to Ppar response elements in gene promoters, Ppars form obligate heterodimers with Retinoid X receptors (Rxr). There are three members of the Rxr family, Rxra, Rxrb, and Rxrg, and their expression was reduced 8-, 5-, and 16-fold in hindlimb muscle of Chkb- mice compared to wild type (Fig. 7c, d). Ppar and Rxr heterodimers are bound to DNA with coactivator molecules 29 and the expression of each co- activator was also decreased from 2.8- to 14.4- fold compared to wild type (Fig. 7c, d). The several fold decrease in
+
+<--- Page Split --->
+
+expression of the Ppars, as well as their obligate co- receptors, aligns well with the observed changes in lipid profiles we observed in affected muscle of Chkb- mice that predict a decreased capacity to import and use fatty acids by mitochondria for \(\beta\) - oxidation.  
+
+Among Ppar associated genes, the expression of 44 genes was decreased statistically significantly (P<0.05) by at least 2- fold in Chkb- mice, while 8 genes were upregulated at least 2- fold (Fig. 7 c- f, Supplementary Fig. 5, Supplementary Table1 and Table2). Carnitine palmitoyltransferase 1b (Cpt1b), the major muscle isoform of Cpt, is involved in the carnitine shuttle as it catalyzes the conversion of cytoplasmic long- chain fatty acyl- CoA and carnitine into AcCa that are translocated across the inner mitochondrial membrane for subsequent mitochondrial fatty acid \(\beta\) - oxidation. The expression of Cpt1b was decreased 7.9- fold in affected muscle of Chkb- mice. In addition, the expression of enzymes required for mitochondrial fatty acid \(\beta\) - oxidation were also decreased several fold in affected muscle of Chkb- mice including several fatty acylCoA synthases/ligases, fatty acid binding proteins, and fatty acid \(\beta\) - oxidation enzymes.  
+
+Ppara and Ppar b/d are the major transcriptional reporters that regulate expression of fatty acid metabolizing genes. The many- fold decrease in the expression of these Ppars that was specific to affected muscle, along with their coreceptors and downstream target genes corroborate the lipidomics data that suggest that the major change in lipid metabolism in Chkb mediated muscular dystrophy is an inability to metabolize fatty acids via mitochondrial \(\beta\) - oxidation resulting in shunting of excess fatty acid into TG rich lipid droplets.
+
+<--- Page Split --->
+
+## Discussion  
+
+Lipid metabolism is highly integrated. Fluctuating levels of lipid metabolites can not only alter shunting of lipids between tangential pathways, but lipids can also directly bind to transcription factors and alter gene expression of lipid metabolic genes. This study highlights these metabolic factors by determining that inactivation of a gene for PC synthesis does not alter PC level. Indeed, the changes in the level of PC do not appear to contribute to the disease phenotype. This study proposes (1) that a change in PC level is not the major metabolic driver behind this disease despite the fact that the genetic defect lies within the major metabolic pathway for the synthesis of PC, (2) a mechanistic model for defective muscle lipid metabolism in Chkb- mice in which the balance between storage and usage of fatty acids is disrupted, and (3) a mechanism for the rostral- to- caudal gradient for Chkb mediated muscular dystrophy.  
+
+Importantly, we report that at an early stage of Chkb mediated muscular dystrophy, there is a 12- to 15- fold increase in the levels of the mitochondrial specific lipids CL and AcCa. Importantly, these changes were observed only in affected muscle of Chkb- mice. As the disease progresses, AcCa and CL levels return to wild type, and a 12- fold increase in the storage lipid TG occurs. The increase in the mitochondrial specific phospholipid CL is quite telling as far as disease progression. Our TEM of mitochondria in affected muscle during the early stage of Chkb mediated muscular dystrophy revealed a similar number of mitochondria with intact cristae in compared to wild type, however, there was a substantive increase in large mitochondria in affected muscle of Chkb- mice. We propose that the large increase in CL in affected muscle of
+
+<--- Page Split --->
+
+Chkb- mice in the early stage of the disease are mainly driven by the increase in mitochondrial size. As the mice aged the level of CL decreased and had returned to that of wild type by 30 days. At 30 days, mitochondrial size was still increased, however, the number of mitochondria, as well as their cristate (where the bulk of CL resides) were substantively decreased, providing a reasonable explanation for CL mass being reduced to wild type level as the Chkb- mice aged. Previous observations of mitochondria in Chkb- mice have only been determined in mice with advanced disease<sup>6,30</sup>, where similar changes in mitochondrial morphological features and numbers were observed. Indeed, one would predict that as Chkb- mice aged there would be a further decrease in CL mass as mitochondrial numbers further decrease.  
+
+Beyond the large increase in CL mass, the other major change in lipid level at the early stage of Chkb mediated muscular dystrophy was a 15- fold increase in AcCa level in affected muscle. This implies that there is either a decreased ability to transport of AcCa into mitochondria for subsequent fatty acid \(\beta\) - oxidation, and/or incomplete \(\beta\) - oxidation resulting in a backup of substrate within this pathway. In support of this idea the expression of many of the enzymes required for fatty acid transport into mitochondria and subsequent fatty acid \(\beta\) - oxidation were decreased many fold in affected muscle of Chkb- mice. The increase in AcCa level at the early stage of Chkb mediated muscular dystrophy, and the decreased expression of genes required for its synthesis and use, is consistent with an inability to import AcCa into mitochondria for fatty acid \(\beta\) - oxidation.  
+
+As Chkb- mice aged, AcCa and CL and levels in hindlimb muscle returned to wild type and by 30 days a dramatic 12- fold increase in TG level was observed. The
+
+<--- Page Split --->
+
+increase in TG level is consistent with impaired AcCa uptake into mitochondria resulting in a shunting of fatty acids from energy source to energy storage \(^{31}\) . This observation is consistent with other reports showing that inhibition of PC biosynthesis in mouse liver, and cell culture, significantly increased TG level \(^{32,33}\) . One interesting additional observation from our study was that \(\sim 80\%\) of the photographed lipid droplets from \(Chkb^{- / - }\) hindlimb muscles were closely associated with mitochondria (Fig. 5a and Supplementary Fig. 2c). A recent study by Benador et al. demonstrated that peri- droplet mitochondria have enhanced bioenergetic capacity and reduced fatty acid oxidation capacity, and that peri- droplet mitochondria promote lipid droplet expansion by providing ATP for triglyceride synthesis \(^{34}\) . Our observation of an increase in peri- droplet mitochondria in \(Chkb^{- / - }\) affected skeletal is consistent with this study, and with our proposal that there is a reprogramming of muscle lipid metabolism from impaired fatty acid usage for energy to fatty acid storage in TG.  
+
+Two perplexing aspects of \(Chkb\) mediated muscular dystrophy are (i) PC level does not change despite the fact that the sole genetic defect is inactivation of a gene that encodes the first step of the PC biosynthetic pathway, and (ii) the rostral- to- caudal gradient of the disease. We propose that the rostral- to- caudal gradient of the disease is due to compensatory effects modulated by a second choline kinase isoform, Chka. In hindlimb muscle of \(Chkb^{- / - }\) mice we observed a marked reduction in Chka protein level, while conversely in the forelimb of \(Chkb^{- / - }\) mice there was a compensatory upregulation of Chka. The ability of an increase in Chka level to protect against \(Chkb\) - mediated muscular dystrophy is consistent with previous work that demonstrated that the viral delivery of the \(Chka\) gene improves dystrophic phenotypes in \(Chkb^{- / - }\) mice with
+
+<--- Page Split --->
+
+comparable potency to rescue by delivery of Chkb \(^{35}\) . One caveat to the above is the fact that PC level was not different between the forelimb and hindlimb muscle of Chkb- mice, nor was it different between wild type and Chkb- mice at any stage of the disease. This suggests that PC supply must be able to be replenished at a step downstream of choline kinase. We further propose that PC level does not change as PC can be replenished via exogenous PC supply. PC is imported into cells from serum via low density lipoproteins (LDL), and enhanced expression of scavenger receptor- B1 (SR- B1) and low- density lipoprotein receptor (LDLR) was previously observed in muscle of Chkb- mice, both of which would be expected to enhance the uptake of plasma PC \(^{7}\) . We propose that the expected decrease in the level of PC in hindlimb muscle of Chkb- mice, due to inactivation of the Chkb gene and downregulation of Chka gene expression, is not observed as this can be compensated for by increased PC uptake from serum. These predictions are consistent with the changes in muscle function along the rostral- to- caudal gradient in Chkb- mice.  
+
+A interesting mechanistic aspect is the transition from an inability to synthesize PC in affected muscle to an increase in Acca. The synthesis of PC requires the consumption of DAG at the final step in the CDP- choline pathway, and this would not occur in affected muscle as the choline kinase step is either inactivated (Chkb) or downregulated (Chka). DAG requires fatty acids for its synthesis, and an inability to synthesize DAG could result in an inability to utilize fatty acids for subsequent DAG synthesis. Indeed, over time we see an increase in DAG mass in affected muscle. The inability to synthesize PC results in a metabolic defect downstream within this pathway that results in major changes in tangential yet connected lipid metabolic pathways over
+
+<--- Page Split --->
+
+time, an inability to use excess fatty acid for energy followed by its storage as neutral lipid.  
+
+## Acknowledgments  
+
+We acknowledge funding support from the Canadian Institutes for Health Research (to CRM) and the Atlantic Innovation Fund (to CRM and EH). We thank Gregory Cox for sharing Chkb mice.  
+
+## AUTHOR CONTRIBUTIONS  
+
+MT, JPFM, KN, EPH, and CRM conceived the study. MT, SL, SS, KU, JR, SS, MP, AM, MSM, AAM and MM performed experiments. MT, JPFM, and CRM wrote the paper.  
+
+## DECLARATION OF INTERESTS  
+
+The authors declare no competing interests.
+
+<--- Page Split --->
+
+## FIGURE LEGENDS  
+
+Fig. 1 | Glycerophospholipid pathway, maintaining the balance between storage and usage of fatty acids. Fatty acids derived from the plasma are first activated by esterification to fatty acyl- CoA. Subsequently, they will either used as energy through mitochondrial beta oxidation or funneled into phosphatidic acid (PA) synthesis. PA is the simplest glycerophospholipid and contains only a phosphate group as a hydrophilic moiety. A pool of PA can either 1. enter CDP- DAG pathway to generate phosphatidylinositol (PI), phosphatidylglycerol (PG) and cardiolipin (CL) or 2. be converted to diacylglycerol (DG). In fact, the majority of the de novo synthesized PA is dephosphorylated into DG. DG can then be used to catalyze the production of triacylglycerides (TG) and stored as energy source in lipid droplets or be converted into the two most abundant membrane phospholipids: phosphatidylcholine (PC) and phosphatidylethanolamine (PE) as well as phosphatidylserine (PS). PC and PE are generated when CDP- choline or CDP- ethanolamine are combined with DG (not shown). The CDP- choline pathway (Kennedy pathway) begins with the uptake of exogenous choline into the cell. The first enzymatic reaction is catalyzed by choline kinases (Chka and Chkb) and involves the phosphorylation of choline to form phosphocholine.  
+
+Fig. 2 | Choline kinase deficient mice display hallmark muscular dystrophy Phenotypes. a, Body weight was recorded each week at similar times over the entire duration of phenotyping experiment for Chkb<sup>+/+</sup>, Chkb<sup>+/-</sup> and Chkb<sup>-/-</sup> mice. b, Grip
+
+<--- Page Split --->
+
+strength measurements were performed at 3 different timepoints and normalized to body weight (BW). c, Total distance run during an exhaustion test for all experimental groups at 3 different timepoints. d, Serum creatine kinase (CK) level measurements of 15- week- old \(Chkb^{+ / + }\) , \(Chkb^{+ / - }\) and \(Chkb^{- / - }\) mice. e, Loss in muscle force as a result of repeated contractions of EDL muscles by direct stimulation of the nerve for each genotype. f, Maximal specific force generated by freshly isolated extensor digitorum longus (EDL) muscle for each genotype All values are expressed as means ± SEM; n=6–13 animals per group. Significance was calculated using one- way ANOVA with Tukey's multiple comparison test for each specific time point. \(*P < 0.01\) vs. all the other groups and #P<0.05 vs. \(Chkb^{+ / + }\) group at each specific timepoint.  
+
+## Fig. 3 | Chka protein expression is inversely correlated with the rostro-caudal gradient of severity in Chkb-mediated muscular dystrophy  
+
+Western blot of a, forelimb (triceps) and b, hindlimb (quadriceps) samples from three distinct (lanes 1–3) \(Chkb^{+ / + }\) , four distinct (lanes 4–7) \(Chkb^{+ / - }\) and three distinct (lanes 8–10) \(Chkb^{- / - }\) mice probed with anti- Chka, anti- Chkb, and anti- Gapdh antibodies. Bottom: densitometry of the WB data shows the ratio of Chka and Chkb to Gapdh. Chka signal is not significantly different in forelimb and hindlimb samples from \(Chkb^{+ / - }\) mice compared to the wild type. Chka is upregulated in forelimb muscles and downregulated in hindlimb muscles from \(Chkb^{- / - }\) mice. Chkb signal is decreased in hindlimb and forelimb muscle samples of \(Chkb^{+ / - }\) mice and is absent in muscle samples of \(Chkb^{- / - }\) mice. Values are means ± SD; n=3- 4 per group. \(*P< 0.01\) vs \(Chkb^{+ / + }\) , \(**P< 0.01\) vs all the
+
+<--- Page Split --->
+
+other groups (one- way ANOVA with Tukey's multiple comparison test). #P< 0.05 vs Chkb<sup>+/+</sup> (Student's t- test).  
+
+Fig. 4 | Loss of Chkb activity exerts a major effect on neutral lipid abundance. Comparison of expression levels of major glycerophospholipids and AcCa between the Chkb<sup>+/+</sup> and Chkb<sup>- /-</sup> mice. The analysis was performed on a- b, 12 days old forelimb (triceps), c- d, 12 days old hindlimb (quadriceps) and e- f, 30 days old hindlimb (quadriceps) samples. b, d and f. Summary of fold change and statistical tests performed on major glycerophospholipids. n=3 mice per group. Pairwise Wilcoxon signed rank test with Bonferroni correction was used to determine the significance of a median pair- wise fold- increase in lipid amounts at an overall significance level of 5%. As the Bonferroni correction is fairly conservative, significant differences are reported at both pre- correction (*) and post- correction (***) significance levels. AcCa, acylcarnitine; TG, triacylglycerol; DG, diacylglycerol; PC, phosphatidylcholine; PE, phosphatidylethanolamine; PG, phosphatidylglycerol; PI, phosphatidylinositol; PS, phosphatidylserine.  
+
+Fig. 5 | Increased intramyocellular lipid droplet accumulation and enlarged mitochondria in hindlimb muscles from Chkb<sup>- /-</sup> mice. a, Transmission electron microscopy (TEM) appearance of the hindlimb muscle samples (quadriceps) of Chkb<sup>+/+</sup> and Chkb<sup>- /-</sup> mice at 12 days and 115 days of age. (representative of 3 mice per group). LD=Lipid droplets. M=Mitochondria. \*=Disrupted sarcomeres. b, Quadriceps muscle sections of 30 days old Chkb<sup>+/+</sup> and Chkb<sup>- /-</sup> mice were fixed and stained with BODIPY-
+
+<--- Page Split --->
+
+493/503 to visualize LDs (Green). Concanavalin A dye conjugate (CF™ 633) and DAPI were used to stain membrane (Red) and nucleus (Blue) respectively. (representative of 3 mice per group).  
+
+Fig. 6 | Chkb deficiency results in increased lipid droplet accumulation in differentiated myocytes in culture. a, Representative image of isolated skeletal myoblasts from \(Chkb^{+ / + }\) and \(Chkb^{- / - }\) mice, cultured on Matrigel® coated culture flasks. At day 0, when the cells reached \(80\%\) confluency, the medium was replaced by differentiation medium and maintained in differentiation media for 5 days. b, RT-qPCR analysis of gene expression in isolated myocytes from \(Chkb^{+ / + }\) and \(Chkb^{- / - }\) mice at day 5 of differentiation. Values are means ± SD; \(n = 3\) independent experiments. \*P<0.05, \*\*P<0.01. Student's t-test. Formaldehyde fixed and immunostained myotubes were categorized into three groups (1 to 3 nuclei, 4 to 10 nuclei, and >10 nuclei per myotube). The distribution of nuclei (c), and number of multinuclear myotubes in the two groups (d) were calculated. e, Isolated primary myocytes from \(Chkb^{+ / + }\) and \(Chkb^{- / - }\) mice were fixed 5 days after differentiation and stained with BODIPY- 493/503 to visualize LDs (Green). DAPI was used to stain nucleus (Blue). f, The corrected total cell fluorescence intensity of lipid droplets was significantly enhanced in \(Chkb^{- / - }\) myotubes. For c, d and f, total \(\sim 100\) cells were quantified per group in 3 independent experiments. Data are mean ± SD. \*p < 0.05. Student's t-test.  
+
+Fig. 7 | Chkb regulates the gene expression of the members of the Ppar family as well as Ppar target genes. a. Relative gene expression of the Ppar family members.
+
+<--- Page Split --->
+
+b. Western blot of hindlimb (quadriceps) samples from three distinct (lanes 1–3) Chkb+/+, four distinct (lanes 4–7) Chkb+/ and three distinct (lanes 8–10) Chkb-/ mice probed with anti-Ppara, anti- Pparb, anti-Pparg, anti-Cpt1b and anti-Gapdh antibodies. Bottom: densitometry of the western blot data shows the ratio of Ppara, Pparb, Pparg and Cpt1b to Gapdh. Values are means ± SD; n=3-4 per group. \*P<0.01 vs Chkb+/+, \*\*P< 0.01 vs all the other groups (one-way ANOVA with Tukey’s multiple comparison test). c, Fold-Change (2^ (- Delta Delta CT)) is the normalized gene expression (2^ (- Delta CT)) in the Chkb deficient hindlimb sample divided the normalized gene expression (2^ (- Delta CT)) in the control sample. Fold-change values greater than one indicates a positive- or an up-regulation. Fold-change values less than one indicate a negative or down-regulation, and the fold-regulation is the negative inverse of the fold- change. The p values are calculated based on a Student’s t-test of the replicate 2^ (- Delta CT) values for each gene in the Chkb+/+ group and Chkb-/ groups. \*p < 0.05, \*\*p<0.01. N=3 samples per group. d, The clustergram of the Ppar family, Rxr family and Ppar coactivators across three genotypes. e, Fold change, normalized gene expression for the genes involved in peroxisomal and mitochondrial beta oxidation in the Chkb deficient hindlimb sample divided the normalized gene expression in the control sample. f, The clustergram of the Ppar family, Rxr family and Ppar coactivators across three genotypes. Average arithmetic mean of the expression of 4 housekeeping genes (Actb, B2m, Gusb and Hsp90ab1) were used to normalize the expression of all the studied genes.
+
+<--- Page Split --->
+
+## Methods  
+
+## Mouse strains.  
+
+All animal procedures were approved by the Dalhousie University's Committee on Laboratory Animals in accordance with guidelines of the Canadian Council on Animal Care Guide to the Care and Use of Experimental Animals (CCAC, Ottawa, ON, Canada: vol. 1, 2nd ed., 1993; vol. 2, 1984. Chkb mutant mice in C57BL/6J background were a kind gift of Professor Gregory A. Cox and were originally generated at the Jackson Laboratory (Bar Harbor, Maine, USA) \(^{5}\) . Male \(Chkb^{+/- }\) mice on the C57BL/6J background were crossed with female \(Chkb^{+/- }\) on the same background to generate \(Chkb^{+/+}\) , \(Chkb^{- / - }\) and \(Chkb^{+/- }\) littermates. The mutation identified in \(Chkb^{+/- }\) mice is a 1.6 kb genomic deletion between exon 3 and intron 9 that results in expression of a truncated mRNA and the absence of Chkb protein expression \(^{5}\) .  
+
+## Mouse genotyping.  
+
+The mutation identified in \(Chkb^{+/- }\) mice is a 1.6 kb genomic deletion between exon 3 and intron 9 \(^{5}\) . AccuStart™ II Mouse Genotyping Kit (Beverly, MA, USA) was used to extract DNA from ear punches and to perform PCR analysis. A single genotyping program was used to amplify both the wild type \(Chkb\) allele between exons 5 and 9 and the truncated \(Chkb\) allele between exons 2 and 10. The primers used for genotyping were purchased from Integrated DNA Technologies (Coralville, IA, USA). The primer sequences to genotype wild type are Forward Primer: 5'- GTG GGT GGC ACT GGC
+
+<--- Page Split --->
+
+ATT TAT - 3'; Reverse Primer: 5'- GTT TCT TCT GTT CCT CTT CGG AGA- 3' (amplicon size 753 bp).  
+
+The primer sequences to genotype the mutants are: Forward Primer: 5'- TAC CCA CGT ACC TCT GGC TTT T - 3' Reverse Primer: 5'- GCT TTC CTG GAG GAC GTG AC 3' (amplicon size 486 bp). For each mouse, one PCR reactions was performed using both the primer sets. If two bands were observed, the mouse was characterized as a heterozygous.  
+
+## In vivo grip strength and fatigability measurements.  
+
+Forelimb grip strength was measured using a grip strength meter (Columbus Instruments, Columbus, OH, USA) at 3 time points (6, 12, 18 weeks old) as previously described 40. All mice were acclimated for a period of five consecutive days before testing. For each time point, Force measurements were collected in the morning hours over a 5- day period, with maximum values for each day over this period averaged to obtain absolute GSM values (Kgf) or normalized to BW (recorded on the first day of testing) for normalized GSM values (Kgf/kg). For the treadmill exhaustion assay, mice are subjected to an enforced running paradigm that tests the resistance level of fatigue in mice. The exhaustion test was performed at 3 time points (7, 13, 19 weeks old) in each group. Groups of mice were made to run on a horizontal treadmill for 5 min at 5 m/min, followed by an increase in the speed of 1m/min each minute. The total distance run by each mouse until exhaustion was measured. Exhaustion was defined as the inability of the mouse to continue running on the treadmill for 30 seconds, despite repeated gentle stimulation.
+
+<--- Page Split --->
+
+## Primary myoblast isolation, culture and differentiation.  
+
+We followed a protocol outlined in Shahini et al. \(^{41}\) for isolation of myoblast by enabling the outgrowth of these cells from muscle tissue fragments of \(Chkb^{+ / + }\) and \(Chkb^{- / - }\) mice. Briefly, the mice were euthanized via CO2, were sprayed with 70% ethanol and transferred to a sterile hood. The forelimb and hindlimb muscles were removed, finely minced into small pieces and transferred to a 50 ml conical tube. 1 ml enzymatic solution of PBS containing collagenase type II (500 U/mL), collagenase D (1.5 U/mL), dispase II (2.5 U/mL), and \(\mathrm{CaCl_2}\) (2.5 mM) was added to the tube. The muscle mixture was placed in a water bath at \(37^{\circ}\mathrm{C}\) for 60 minutes with agitation every 5 minutes. The suspension was centrifuged for 10 minutes at 300 g. Following centrifugation, the supernatant was removed and discarded, and the pellet was resuspended in proliferation medium. Proliferation medium composed of high glucose Dulbecco's Modified Eagle Medium (DMEM, Gibco, Grand Island, NY), 20% fetal bovine serum (FBS, Atlanta Biologicals, Flowery Branch, GA), 10% horse serum (HS, Gibco), 0.5% chicken embryo extract (CEE, Accurate Chemical and Scientific, Westbury, NY), 2.5 ng/mL bFGF (ORF Genetics, Iceland), 10 \(\mu \mathrm{g / mL}\) gentamycin (Gibco), and 1% Antibiotic- Antimitotic (AA, Gibco), and 2.5 \(\mu \mathrm{g / mL}\) plasmonic prophylactic (Invitrogen, San Diego, CA). The re- suspended pellet containing small pieces of muscle tissue was plated on matrigel coated flasks at 10- 20% surface coverage and incubated at \(37^{\circ}\mathrm{C}\) and 5% \(\mathrm{CO_2}\) to allow attachment of the tissues to the surface and subsequent outgrowth and migration of cells. The myogenic cell population was further purified with one round of pre- plating on collagen coated dishes to isolate fibroblasts from myoblasts. To induce
+
+<--- Page Split --->
+
+differentiation into multinucleated myotubes, the cells were seeded at 10000 cells/cm² on plastic coverslip chambers coated with Matrigel and the medium was replaced by differentiation medium containing DMEM with high glucose and 5% HS.  
+
+## Ex vivo force measurement.  
+
+At the end of the in vivo phase (Week 19), mice were deeply anesthetized with ketamine and xylazine (80 and \(10 \text{mg / kg}\) ). The extensor digitorum longus (EDL) muscle of the right hindlimb was removed for comparison of Ex vivo force contractions between groups as previously described \(^{42,43}\) . Briefly, the EDL muscle was securely tied with braided surgical silk at both tendon insertions to the lever arm of a servomotor/force transducer (model 305B) (Aurora Scientific, Aurora, Ontario, Canada) and the proximal tendon was fixed to a stationary post in a bath containing buffered Ringer solution (composition in mM: 137 NaCl, 24 NaHCO₃, 11 glucose, 5 KCl, 2 CaCl₂, 1 MgSO₄, 1 NaH₂PO₄ and 0.025 turbocurarine chloride) maintained at 25°C and bubbled with 95% O₂ - 5% CO₂ to stabilize pH at 7.4. At optimal muscle length, the maximal force developed was measured during trains of stimulation (300 milliseconds, ms) with increasing frequencies up to 250 Hz or until the highest plateau was achieved. The force generated to obtain the highest plateau was used to determine specific force (maximal force normalized to cross-sectional area of the muscle). Finally, the muscle was subjected to a fatigue protocol consisting of 60 isometric contractions for 300 ms each, once every 5 seconds. The frequency at which the EDL muscles were stimulated is 250 Hz. The force was recorded every 10th contraction during the repetitive contractions and again at 5 and 10 min afterward to measure recovery.
+
+<--- Page Split --->
+
+## Creatine kinase (CK) serum levels.  
+
+CK was determined from serum taken from blood samples withdrawn by cheek bleed at 3 time points (5, 10 and 15 weeks old). Blood was centrifuged for 3000 g for 10 min at \(4^{\circ}C\) to obtain the serum. CK determination was performed by standard spectrophotometric analysis, using a CK diagnostic kit (Cat. no. C7522- 450, PONITSCIENTIFIC, Canton, MI, USA) according to the manufacturer instructions.  
+
+## Total RNA isolation, cDNA generation, and quantitative real-time RT qPCR.  
+
+Isolated tissue samples were incubated overnight in pre- chilled RNAlater® (Cat. no. R0901, Sigma- Aldrich, Ontario, Canada) at \(4^{\circ}C\) . Tissues were then homogenized in TRIzol reagent (Cat. no. 15596026, Invitrogen, MA, USA) and total RNA was isolated according to the manufacturer's protocol. Nine hundred nanograms of total RNA was reverse transcribed using High- Capacity cDNA Reverse Transcription Kit® (Cat. no. 4368814, Applied Biosystems, MA, USA). Quantitative real- time RT- PCR assays were performed on the Bio- Rad CFX96 Touch Real- Time PCR Detection (Bio- Rad ®, California, USA) System using TaqMan™ Fast Advanced Master Mix (Cat. no. 4444557) and TaqMan™ Gene Expression Assays (Cat. no. 4331182, ThermoFisher Scientific) for Chka (RRID: Mm00442759_m1), Chkb Cpt1b (Exon boundary7- 8)(RRID: Mm01308102_g1), Cnsk2a2 (RRID: Mm01243455_m1), Cpt1b (RRID: Mm00487191_g1), Gapdh (RRID: Mm9999915_g1), Icam1 (RRID: Mm00516023_m1), Ppara (RRID: Mm00440939_m1), Ppard (RRID: Mm00440940_m1), Pparg (RRID:
+
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+
+Mm00440940_m1) and Tgfb1 (RRID: Mm011778820_m1). Reactions were run in triplicate.  
+
+## Microarray analysis of Ppar targets  
+
+Mature RNA was isolated using Qiagen RNeasy Plus Mini Kit (Cat. no 74134) according to the manufacturer's instructions. RNA quality was determined using a spectrophotometer and was reverse transcribed using a cDNA conversion kit. The cDNA was used on the real- time RT2 Profiler PCR Array (QIAGEN, Cat. no. PAMM- 149Z) in combination with RT2 SYBR® Green qPCR Mastermix (Cat. no. 330529). CT values were exported to an Excel file to create a table of CT values. This table was then uploaded on to the data analysis web portal at http://www.qiagen.com/geneglobe. Samples were assigned to controls and test groups. CT values were normalized based on a/an Manual Selection of reference genes. The data analysis web portal calculates fold change/regulation using delta delta CT method, in which delta CT is calculated between gene of interest (GOI) and an average of reference genes (HKG), followed by delta- delta CT calculations (delta CT (Test Group)- delta CT (Control Group)). Fold Change is then calculated using \(2^{\wedge}\) (- delta delta CT) formula. The data analysis web portal to plot scatter clustergram, and heat map.  
+
+## Lipid extraction  
+
+We performed lipid extractions using the modified Bligh and Dyer extraction for LC- MS analysis of lipids protocol \(^{44}\) . All reagents were of LC- MS grade. Briefly, the muscle tissue ( \(\sim 10 \text{mg}\) ) was homogenized with a steel bead in 1 ml of cold 0.1 N HCl: methanol
+
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+(1:1, v/v) using a TissueLyser II instrument (Qiagen) set at 30 strokes/s for 2–4 min. Based on protein quantification results, all samples were adjusted to the final concentration of \(700 \mu \mathrm{g} / \mathrm{ml}\) and spiked with \(10 \mu \mathrm{l}\) of internal standard (Avanti Polar Lipids Inc; Catalog Number- 330707). \(500 \mu \mathrm{l}\) of chloroform was added to each sample, vortexed for 30 minutes and centrifuged to separate phases (5 minutes at \(6000 \mathrm{rpm}\) ). The bottom organic phase was transferred into a new Eppendorf and dried under a nitrogen stream. Samples were stored at \(- 80^{\circ} \mathrm{C}\) until ready for analysis.  
+
+## UHPLC method for lipid analysis.  
+
+The Accucore C30 column ( \(250 \times 2.1 \mathrm{mm}\) I.D., particle size: \(2.8 \mu \mathrm{m}\) ) was obtained from ThermoFisher Scientific (ON, Canada). The mobile phase system consisted of solvent A (acetonitrile: H2O 60:40 v/v) and solvent B (isopropanol: acetonitrile: water 90:10:1 v/v) both containing \(10 \mathrm{mM}\) ammonium formate and \(0.1\%\) formic acid. C30- RPLC separation was carried out at \(30^{\circ} \mathrm{C}\) (column oven temperature) with a flow rate of \(0.2 \mathrm{mL} / \mathrm{min}\) , and \(10 \mu \mathrm{L}\) of the lipid extraction suspended in the mobile phase solvents mixtures (A:B, \(70:30\%\) ) was injected onto the column. The following system gradient was used for separating the lipid classes and molecular species: \(30\%\) solvent B for 3 min; then solvent B increased to \(50\%\) over 6 min, then to \(70\%\) B in 6 min, then kept at \(99\%\) B for 20 min, and finally the column was re- equilibrated to starting conditions ( \(30\%\) solvent A) for 5 min prior to each new injection.
+
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+
+## High resolution tandem mass spectrometry and lipidomics.  
+
+High resolution tandem mass spectrometry and lipidomics.Lipid analyses were carried out using a Q- Exactive Orbitrap mass spectrometer controlled by X- Calibur software 4.0 (ThermoScientific, MO, USA) with an acquisition HPLC system. The following parameters were used for the Q- Exactive mass spectrometer - sheath gas: 40, auxiliary gas: 5, ion spray voltage: 3.5 kV, capillary temperature: 250 °C; mass range: 200–2000 m/z; full scan mode at a resolution of 70,000 m/z; top- 1 m/z and collision energy of 35 (arbitrary unit); isolation window: 1 m/z; automatic gain control target: 1e5. The instrument was externally calibrated to 1 ppm using ESI negative and positive calibration solutions (ThermoScientific, MO, USA). Tune parameters were optimized using a mixture of lipid standards (Avanti Polar Lipids, Alabama, USA) in both negative and positive ion mode Thermo Scientific™ LipidSearch™ software version 4.2 was used for lipid identification and quantitation. First, the individual data files were searched for product ion MS/MS spectra of lipid precursor ions. MS/MS fragment ions were predicted for all precursor adduct ions measured within ±5 ppm. The product ions that matched the predicted fragment ions within a ±5 ppm mass tolerance was used to calculate a match- score, and those candidates providing the highest quality match were determined. Next, the search results from the individual positive or negative ion files from each sample group were aligned within a retention time window (±0.2 min) and the data were merged for each annotated lipid.
+
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+
+## Data cleanup and statistical analysis of lipids.  
+
+Data cleanup and statistical analysis of lipids.Lipid concentrations extracted from the LipidSearch software were further analyzed with an in- house script using the R programming language. The data was filtered to exclude any peak concentration estimates with a signal to noise ratio (SNR parameter) of less than 2.0 or a peak quality score (PQ parameter) of less than 0.8. If this exclusion resulted in the removal of two observation within a biological triplicate, the remaining observation was also excluded. The individual concentrations were then gathered together by lipid identity (summing together the concentration of multiple mass spectrometry adducts where these adducts originated from the same molecular source and averaging together biological replicates) and grouped within the broader categories of AcCa, TG, DG, PC, PE, PG, CL, PI, PS. The result was nine groups containing multiple lipid concentrations corresponding to specific lipid identities, which were then compared between wild type and KO samples using a (paired, non- parametric) Wilcoxon signed- rank test at an overall significance level of 5% (using the Bonferroni correction to account for the large number of tests performed). As the Bonferroni correction is fairly conservative, significant differences are reported at both pre- correction (\*) and post- correction (***) significance levels.  
+
+## Nile red 550 / 640 nm, BODIPY 493/503 nm and nuclei staining of muscle tissue.  
+
+Quadriceps and gastrocnemius muscles were embedded in Optimal Cutting Temperature™ (Sakura Finetek, Torrence, CA), and were frozen in cooled isopentane in liquid nitrogen and stored at - 80°C. Frozen sections (7 μm thick) were thaw- mounted on SuperFrost Microscope slides (Microm International, Kalamazoo, MI) and air dried.
+
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+
+Tissue sections were then fixed in \(4\%\) (w/v) paraformaldehyde for 15 minutes and incubated with Concanavalin A CF® Dye Conjugates CF™633 (50- 200 μg/mL) for 20 minutes followed by incubation with either Nile red solution in PBS (0.5 μg/mL) or BODIPY 493/503 for 15 minutes. The sections were then washed for 5 times with PBS, each time for 15 minutes and mounted using ProLong™ Gold Antifade Mountant with DAPI (Thermo Scientific™, Cat. no. P36931) and cured overnight in the dark. Slides were observed under a confocal microscope (Leica TCS SP8 with LIGHTNING) using excitation wavelength 633 for Concanavalin A, 550nm for Nile red, 448 nm for BODIPY and 405 for DAPI.  
+
+## BODIPY 493/503 and nuclei staining of primary myocytes.  
+
+Isolated skeletal myoblasts were cultured on Matrigel® coated Glass chamber slides (Thermo Scientific™, Cat. no. 154534) and differentiated into myocyte. 3 days after differentiation, the cells were washed two times with PBS and fixed in \(4\%\) (w/v) paraformaldehyde for 15 minutes. The cells were washed with PBS for 10 minutes and incubated with BODIPY solution in PBS for 15 minutes, at room temperature on a shaker. The cells were then washed for 3 times with PBS, each time for 15 minutes and mounted using ProLong™ Gold Antifade Mountant with DAPI (Thermo Scientific™, Cat. no. P36931) and cured overnight in the dark. Slides were observed under a confocal microscope (Leica TCS SP8 with LIGHTNING) using excitation wavelength 448 nm for BODIPY and 405 for DAPI. Images were converted to 8- bit and the total corrected cellular fluorescence for the green channel was measured in random 100 cells per group using FIJI (NIH) software. The total corrected cellular fluorescence (TCCF) =
+
+<--- Page Split --->
+
+integrated density – (area of selected cell × mean fluorescence of background readings), was calculated and compared between groups \(^{45}\) .  
+
+## Transmission electron microscopy.  
+
+For TEM analysis, \(\sim 5 \times 5 \mathrm{mm}\) cubes of quadriceps, gastrocnemius and triceps were with \(2.5\%\) Glutaraldehyde diluted with \(0.1 \mathrm{M}\) sodium cacodylate buffer and postfixed with \(1\%\) osmium tetroxide in Millonig's buffer solution for \(2 \mathrm{hr}\) , dehydrated, and embedded in epon araldite resin. Ultrathin sections were stained with \(2\%\) uranyl acetate for \(30 \mathrm{min}\) and lead citrate for \(4 \mathrm{min}\) and viewed with a JEOL JEM 1230 Transmission Electron Microscope at \(80 \mathrm{kV}\) . Images were captured using a Hamamatsu ORCA- HR digital camera. Three mice per genotype for each timepoint were evaluated. The mitochondrial content was determined from the images at \(10,000 \times\) magnification using Image J software and calculated as mitochondria count/field by blinded investigators. Point counting was used to estimate mitochondrial volume density and mitochondrial cristae density based on standard stereological methods \(^{46,47}\) . Only mitochondria profiles of acceptable quality defined as clear visibility and no or few missing spots of the inner membrane were included. Using ImageJ software, a point grid was digitally layered over the micrographic images at \(20,000 \times\) or \(40,000 \times\) magnification for mitochondrial volume density and cristae density calculations respectively. Grid sizes of \(85 \mathrm{nm} \times 85 \mathrm{nm}\) and \(165 \mathrm{nm} \times 165 \mathrm{nm}\) were used to estimate mitochondria volume and cristae surface area, respectively. Mitochondria volume density was calculated by dividing the points assigned to mitochondria to the total number of points counted inside the muscle. The mitochondrial cristae surface area per mitochondrial volume (mitochondrial cristae
+
+<--- Page Split --->
+
+density) was estimated by the formula: mitochondrial cristae density = (4/π) BA, where BA is the boundary length density estimated by counting intersections on test lines multiplied by π/2. In brief, we counted the intersections l(imi) between the inner mitochondrial membrane trace and the test lines and measured the total length of the test line within the mitochondria profile to calculate mitochondrial cristae density =2. l(imi)/L(mi).  
+
+## Western blot analysis (WB) and quantification.  
+
+The muscle tissue ( \(\sim 100\mathrm{mg}\) ) was homogenized with a steel bead in 1 ml of cold RIPA buffer containing 1X Proteinase Inhibitor Mix (complete™ Protease Inhibitor Cocktail, Roche, Cat. no.11 697 498 001), 1X PhosStop (Roche, Mannheim Germany, Cat. no.04 906 845 001) using a TissueLyser II instrument (Qiagen) set at 30 strokes/s for 2–4 min. Based on protein quantification results, all samples were adjusted to the final concentration of 2ug/ul and heat- denatured for 5 min at 99°C in 2X Laemmli buffer. Proteins were separated by SDS- PAGE and transferred to nitrocellulose membranes. The membranes were incubated in Odyssey blocking solution for 1 h. Total proteins were detected by probing the membranes with appropriate primary antibodies overnight at 4°C. The following antibodies were used: Chka (1:1000, Abcam Cat#ab88053), Ppara (1:1000, Abcam, Cat#Ab24509), Pparb (1:1000, Biorad, Cat#AHP1272), Cpt1b (1:1000, Proteintech®, Cat#22170- 1- AP), Chkβ (1:250, Santa Cruz, Cat#398957), GAPDH (1:1000, Cell signaling, Cat#398957), Pparγ (1:500, Santa Cruz, Cat# sc- 7273). Proteins were visualized with goat anti- rabbit IRDye- 800- or - 680- secondary antibodies (LI- COR Biosciences) or anti- mouse m- IgGk BP- CFL 790 (Santa
+
+<--- Page Split --->
+
+Cruz, Cat. no.sc- 516181) using an Odyssey imaging system and band density were evaluated using FIJI (NIH).  
+
+## Quantification and statistical analysis.  
+
+All experiments were repeated 3 or more times. Data are presented as mean ± SEM or mean ± SD, as appropriate. For comparison of two groups the two- tailed Student's t- test was used unless otherwise specified. Comparison of more than two groups was done by one- way ANOVA followed by the Tukey's Multiple Comparison test. P values <0.05 were considered significant.  
+
+## Data availability  
+
+All data that support the findings of this study are available from the corresponding authors upon request.
+
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+
+## REFERENCES
+
+<--- Page Split --->
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+17 Michele, D. E. & Campbell, K. P. Dystrophin-glycoprotein complex: post-translational processing and dystroglycan function. J Biol Chem 278, 15457- 15460, doi:10.1074/jbc.R200031200 (2003).18 Cohn, R. D. & Campbell, K. P. Molecular basis of muscular dystrophies. Muscle Nerve 23, 1456- 1471 (2000).19 Gawlik, K. I. At the Crossroads of Clinical and Preclinical Research for Muscular Dystrophy- Are We Closer to Effective Treatment for Patients? Int J Mol Sci 19, doi:10.3390/ijms19051490 (2018).20 Hoffman, E. P. et al. Novel approaches to corticosteroid treatment in Duchenne muscular dystrophy. Phys Med Rehabil Clin N Am 23, 821- 828, doi:10.1016/j.pmr.2012.08.003 (2012).21 Smith, I. C., Bombardier, E., Vigna, C. & Tupling, A. R. ATP consumption by sarcoplasmic reticulum \(\mathrm{Ca}(2)(+)\) pumps accounts for \(40 - 50\%\) of resting metabolic rate in mouse fast and slow twitch skeletal muscle. PLoS One 8, e68924, doi:10.1371/journal.pone.0068924 (2013).22 Casares, D., Escriba, P. V. & Rossello, C. A. Membrane Lipid Composition: Effect on Membrane and Organelle Structure, Function and Compartmentalization and Therapeutic Avenues. Int J Mol Sci 20, doi:10.3390/ijms20092167 (2019).23 Gervois, P., Torra, I. P., Fruchart, J. C. & Staels, B. Regulation of lipid and lipoprotein metabolism by PPAR activators. Clin Chem Lab Med 38, 3- 11, doi:10.1515/CCLM.2000.002 (2000).24 Kular, J. et al. Choline kinase beta mutant mice exhibit reduced phosphocholine, elevated osteoclast activity, and low bone mass. J Biol Chem 290, 1729- 1742, doi:10.1074/jbc.M114.567966 (2015).25 Weibel, E. R. et al. Design of the mammalian respiratory system. IV Morphometric estimation of pulmonary diffusing capacity; critical evaluation of new sampling method. Respir Physiol 44, 39- 59, doi:10.1016/0034- 5687(81)90076- 1 (1981).26 Torres- Palsa, M. J. et al. Expression of intercellular adhesion molecule- 1 by myofibers in mdx mice. Muscle Nerve 52, 795- 802, doi:10.1002/mus.24626 (2015).27 Phua, W. W. T., Wong, M. X. Y., Liao, Z. & Tan, N. S. An aPPARent Functional Consequence in Skeletal Muscle Physiology via Peroxisome Proliferator- Activated Receptors. Int J Mol Sci 19, doi:10.3390/jims19051425 (2018).28 Varga, T., Czimmerer, Z. & Nagy, L. PPARs are a unique set of fatty acid regulated transcription factors controlling both lipid metabolism and inflammation. Biochim Biophys Acta 1812, 1007- 1022, doi:10.1016/j.bbadis.2011.02.014 (2011).29 Viswakarma, N. et al. Coactivators in PPAR- Regulated Gene Expression. PPAR Res 2010, doi:10.1155/2010/250126 (2010).30 Mitsuhashi, S. & Nishino, I. Phospholipid synthetic defect and mitophagy in muscle disease. Autophagy 7, 1559- 1561, doi:10.4161/auto.7.12.17925 (2011).31 Caviglia, J. M., De Gomez Dumm, I. N., Coleman, R. A. & Igal, R. A. Phosphatidylcholine deficiency upregulates enzymes of triacylglycerol metabolism in CHO cells. J Lipid Res 45, 1500- 1509, doi:10.1194/jlr.M400079- JLR200 (2004).32 Jacobs, R. L., Devlin, C., Tabas, I. & Vance, D. E. Targeted deletion of hepatic CTP:phosphocholine cytidylyltransferase alpha in mice decreases plasma high density and very low density lipoproteins. J Biol Chem 279, 47402- 47410, doi:10.1074/jbc.M404027200 (2004).
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+33 Jackowski, S., Wang, J. & Baburina, I. Activity of the phosphatidylcholine biosynthetic pathway modulates the distribution of fatty acids into glycerolipids in proliferating cells. Biochim Biophys Acta 1483, 301- 315, doi:10.1016/s1388- 1981(99)00203- 6 (2000).34 Benador, I. Y., Veliova, M., Liesa, M. & Shirihai, O. S. Mitochondria Bound to Lipid Droplets: Where Mitochondrial Dynamics Regulate Lipid Storage and Utilization. Cell Metab 29, 827- 835, doi:10.1016/j.cmet.2019.02.011 (2019).35 Sayed- Zahid, A. A. et al. Functional rescue in a mouse model of congenital muscular dystrophy with megacomial myopathy. Hum Mol Genet 28, 2635- 2647, doi:10.1093/hmg/ddz068 (2019).36 Poulsen, L., Siersbaek, M. & Mandrup, S. PPARs: fatty acid sensors controlling metabolism. Semin Cell Dev Biol 23, 631- 639, doi:10.1016/j.semcdb.2012.01.003 (2012).37 Wang, Y. X. et al. Peroxisome- proliferator- activated receptor delta activates fat metabolism to prevent obesity. Cell 113, 159- 170, doi:10.1016/s0092- 8674(03)00269- 1 (2003).38 Finck, B. N. et al. The cardiac phenotype induced by PPARalpha overexpression mimics that caused by diabetes mellitus. J Clin Invest 109, 121- 130, doi:10.1172/JCI14080 (2002).39 Finck, B. N. et al. A potential link between muscle peroxisome proliferator- activated receptor- alpha signaling and obesity- related diabetes. Cell Metab 1, 133- 144, doi:10.1016/j.cmet.2005.01.006 (2005).40 Capogrosso, R. F. et al. Ryanodine channel complex stabilizer compound S48168/ARM210 as a disease modifier in dystrophin- deficient mdx mice: proof- of- concept study and independent validation of efficacy. FASEB J 32, 1025- 1043, doi:10.1096/fj.201700182RRR (2018).41 Shahini, A. et al. Efficient and high yield isolation of myoblasts from skeletal muscle. Stem Cell Res 30, 122- 129, doi:10.1016/j.scr.2018.05.017 (2018).42 Rayavarapu, S. et al. Characterization of dysferlin deficient SJL/J mice to assess preclinical drug efficacy: fasudil exacerbates muscle disease phenotype. PLoS One 5, e12981, doi:10.1371/journal.pone.0012981 (2010).43 Quinn, J. L. et al. Effects of Dantrolene Therapy on Disease Phenotype in Dystrophin Deficient mdx Mice. PLoS Curr 5, doi:10.1371/currents.md.e246cf493a7edb1669f42fb735936b46 (2013).44 Bligh, E. G. & Dyer, W. J. A rapid method of total lipid extraction and purification. Can J Biochem Physiol 37, 911- 917, doi:10.1139/o59- 099 (1959).45 McCloy, R. A. et al. Partial inhibition of Cdk1 in G 2 phase overrides the SAC and decouples mitotic events. Cell Cycle 13, 1400- 1412, doi:10.4161/cc.28401 (2014).46 Weibel, E. R. Stereological methods in cell biology: where are we- - - where are we going? J Histochem Cytochem 29, 1043- 1052, doi:10.1177/29.9.7026667 (1981).47 Meinild Lundby, A. K. et al. Exercise training increases skeletal muscle mitochondrial volume density by enlargement of existing mitochondria and not de novo biogenesis. Acta Physiol (Oxf) 222, doi:10.1111/alpha.12905 (2018).
+
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+<center>Fig. 1</center> 
+
+![](images/Figure_2.jpg)
+
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 2 </center>
+
+<--- Page Split --->
+
+<center>Fig. 3</center> 
+
+![](images/Supplementary_Figure_2.jpg)
+
+
+<--- Page Split --->
+![](images/Supplementary_Figure_3.jpg)
+
+<center>Fig. 4 </center>
+
+<--- Page Split --->
+
+<center>Fig. 5</center> 
+
+![](images/Supplementary_Figure_5.jpg)
+
+
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+  
+
+# Supplementary Fig. 1| Ultrastructural abnormalities in skeletal muscles of Chkb deficient mice.  
+
+a and b. Transmission electron microscopy (TEM) appearance of the forelimb (Triceps) (a) and hindlimb (Quadriceps) (b) of 115 days old Chkb- 1 mice showing extensive injury in hindlimb not the forelimb. c, Ultrastructural appearance of lipofuscin granules (arrowheads), heterogeneous in their size and structure observed in gastrocnemius and quadriceps samples from 115 days old Chkb deficient
+
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+![PLACEHOLDER_51_0]
+
+<center>Supplementary Fig. 2| Increased intramyocellular lipid droplet accumulation in hindlimb muscles from Chkb \(^{+/ - }\) mice. a, Quadriceps muscle sections of 30 days old Chkb \(^{+/ + }\) and Chkb \(^{+/ - }\) mice were fixed and stained with Nile Red-550 / 640 nm to visualize LDs (Red). Dapi was used to stain nucleus (Blue). (representative of 3 mice per group). b, Quadriceps muscle sections of 30 days old Chkb \(^{+/ + }\) and Chkb \(^{+/ - }\) mice were fixed and stained with BODIPY-493/503 to visualize LDs (Green). Concanavalin A dye conjugate (CF™ 633) and Dapi were used to stain membrane (Red) and nucleus (Blue) respectively. (representative of 3 mice per group). c, Transmission electron microscopy (TEM) appearance of the hindlimb muscle samples of 12 days old Chkb \(^{+/ - }\) mice showing the high prevalence of peri-droplet mitochondria in hindlimb muscles (representative of 3 mice per group). Scale bar 1μm. LD=Liquid droplets. M=Mitochondria. \(^{*} =\) Disrupted sarcomeres. </center>
+
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+
+<center>Supplementary Fig.3 | Mitochondrial profile quantification. a, transmission electron microscopy (TEM) appearance of the mitochondrial profile of hindlimbs from 12 days old and 60 days old wild-type \((Chkb^{+ / +})\) and Chkb-deficient \((Chkb^{- / -})\) mice (representative of 3 mice per group). b, At 12 days of age hindlimbs from wild type and \(Chkb^{- / -}\) mice had the same number of mitochondria per imaged field however, the volume density of the \(Chkb^{- / -}\) mitochondria was increased and the cristae density was preserved. At 115 days of age, \(Chkb^{- / -}\) mitochondria were fewer in number, and had markedly reduced cristae density and were much larger in size. The increased size of the mitochondria at this age accounts for the preserved volume density. </center>
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+  
+
+Supplementary Fig. 4| Protein expression of the members of the Ppar family in forelimb samples. a, Western blot of forelimb (Triceps) samples from three distinct (lanes 1–3) Chkb<sup>+/+</sup>, four distinct (lanes 4–7) Chkb<sup>+/−</sup> and three distinct (lanes 8–10) Chkb<sup>−/−</sup> mice probed with anti-Ppar<sub>a</sub>, anti-Ppar<sub>b</sub>, anti-Ppar<sub>g</sub>, anti-Cpt1b and anti-Gapdh antibodies. b, densitometry of the WB data shows the ratio of Ppara, Pparb, Pparg and Cpt1b to Gapdh. Values are means ± SD; n=3-4 per group. No significant difference was observed among groups using one-way ANOVA with Tukey's multiple comparison test.
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+<center>Supplementary Fig.5 | Chkb regulates the expression of the members of the Ppar family as well as Ppar target genes. Clustergram showing non-supervised hierarchical clustering of the entire dataset to display a heat map with dendrograms indicating co-regulated genes across groups or individual samples. Sample Dimension: 1D. Join Type: Average. Color Coded: Average Genes. </center>
+
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+Supplementary Table 1| Ppar associated genes under-expressed in Chkb\\*- hindlimb vs. Chkb\\*\\*/ hindlimb.   
+
+<table><tr><td>Gene Symbol</td><td>Fold Regulation</td><td>p-Value</td><td>Description</td></tr><tr><td>Rxxr</td><td>-16.38</td><td>0.000250</td><td>Retinoid X receptor gamma</td></tr><tr><td>Smarcd3</td><td>-14.40</td><td>0.000951</td><td>SWI/SNF related, matrix associated, actin dependent regulator of chromatin, subfamily d, member 3</td></tr><tr><td>Rxra</td><td>-8.78</td><td>0.008824</td><td>Retinoid X receptor alpha</td></tr><tr><td>Ppargc1a</td><td>-8.46</td><td>0.000002</td><td>Peroxisome proliferative activated receptor, gamma, coactivator 1 alpha</td></tr><tr><td>Cpt1b</td><td>-7.93</td><td>0.002692</td><td>Carnitine palmitoyltransferase 1b, muscle</td></tr><tr><td>Pparb</td><td>-6.19</td><td>0.000176</td><td>Peroxisome proliferator activator receptor delta</td></tr><tr><td>Cyp27a1</td><td>-5.58</td><td>0.001538</td><td>Cytochrome P450, family 27, subfamily a, polypeptide 1</td></tr><tr><td>Slc27a5</td><td>-5.43</td><td>0.022345</td><td>Solute carrier family 27 (fatty acid transporter), member 5</td></tr><tr><td>Hspd1</td><td>-5.05</td><td>0.001198</td><td>Heat shock protein 1 (chaperonin)</td></tr><tr><td>Acadm</td><td>-4.95</td><td>0.000659</td><td>Acyl-Coenzyme A dehydrogenase, medium chain</td></tr><tr><td>Rxrb</td><td>-4.80</td><td>0.000043</td><td>Retinoid X receptor beta</td></tr><tr><td>Txnip</td><td>-4.68</td><td>0.008384</td><td>Thioredoxin interacting protein</td></tr><tr><td>Crebpp</td><td>-4.54</td><td>0.000152</td><td>CREB binding protein</td></tr><tr><td>Ppara</td><td>-4.42</td><td>0.000517</td><td>Peroxisome proliferator activated receptor alpha</td></tr><tr><td>Etfdh</td><td>-4.39</td><td>0.000073</td><td>Electron transferring flavoprotein, dehydrogenase</td></tr><tr><td>Apoa5</td><td>-4.07</td><td>0.000064</td><td>Apolipoprotein A-V</td></tr><tr><td>Ep300</td><td>-3.89</td><td>0.000062</td><td>E1A binding protein p300</td></tr><tr><td>Fabp3</td><td>-3.75</td><td>0.000022</td><td>Fatty acid binding protein 3, muscle and heart</td></tr><tr><td>Acs13</td><td>-3.33</td><td>0.000350</td><td>Acyl-CoA synthetase long-chain family member 3</td></tr><tr><td>Ppargc1b</td><td>-3.25</td><td>0.001233</td><td>Peroxisome proliferative activated receptor, gamma, coactivator 1 beta</td></tr><tr><td>Ech1</td><td>-3.24</td><td>0.000023</td><td>Enoyl coenzyme A hydratase 1, peroxisomal</td></tr><tr><td>Tgs1</td><td>-3.23</td><td>0.028174</td><td>Trimethylguanosine synthase</td></tr><tr><td>Acs14</td><td>-3.15</td><td>0.000615</td><td>Acyl-CoA synthetase long-chain family member 4</td></tr><tr><td>Med1</td><td>-3.10</td><td>0.001997</td><td>Mediator complex subunit 1</td></tr><tr><td>Pdpk1</td><td>-3.08</td><td>0.008230</td><td>3-phosphoinositide dependent protein kinase 1</td></tr><tr><td>Creb1</td><td>-3.02</td><td>0.003162</td><td>CAMP responsive element binding protein 1</td></tr><tr><td>Pprc1</td><td>-3.02</td><td>0.000136</td><td>Peroxisome proliferative activated receptor, gamma, coactivator-related 1</td></tr><tr><td>Slc27a2</td><td>-2.98</td><td>0.017603</td><td>Solute carrier family 27 (fatty acid transporter), member 2</td></tr><tr><td>Chd9</td><td>-2.89</td><td>0.000078</td><td>Chromodomain helicase DNA binding protein 9</td></tr><tr><td>Mlycd</td><td>-2.89</td><td>0.010148</td><td>Malonyl-CoA decarboxylase</td></tr><tr><td>Ncoa6</td><td>-2.86</td><td>0.000177</td><td>Nuclear receptor coactivator 6</td></tr><tr><td>Sirt1</td><td>-2.79</td><td>0.001001</td><td>Sirtuin 1 (silent mating type information regulation 2, homolog) 1</td></tr><tr><td>Cpt2</td><td>-2.77</td><td>0.002056</td><td>Carnitine palmitoyltransferase 2</td></tr><tr><td>Acs1</td><td>-2.67</td><td>0.006296</td><td>Acyl-CoA synthetase long-chain family member 1</td></tr><tr><td>Acadl</td><td>-2.54</td><td>0.000127</td><td>Acyl-Coenzyme A dehydrogenase, long-chain</td></tr><tr><td>Clu</td><td>-2.52</td><td>0.000146</td><td>Clusterin</td></tr><tr><td>Acaa2</td><td>-2.48</td><td>0.010777</td><td>Acetyl-Coenzyme A acyltransferase 2 (mitochondrial 3-oxoacyl-Coenzyme A thiolase)</td></tr><tr><td>Klf10</td><td>-2.42</td><td>0.009957</td><td>Kruppel-like factor 10</td></tr><tr><td>Ehhadh</td><td>-2.34</td><td>0.022919</td><td>Enoyl-Coenzyme A, hydratase/3-hydroxyacyl Coenzyme A dehydrogenase</td></tr><tr><td>Pten</td><td>-2.30</td><td>0.000522</td><td>Phosphatase and tensin homolog</td></tr><tr><td>Slc22a5</td><td>-2.13</td><td>0.010148</td><td>Solute carrier family 22 (organic cation transporter), member 5</td></tr><tr><td>Slc27a4</td><td>-2.11</td><td>0.001068</td><td>Solute carrier family 27 (fatty acid transporter), member 4</td></tr><tr><td>Acox1</td><td>-2.04</td><td>0.034786</td><td>Acyl-Coenzyme A oxidase 1, palmitoyl</td></tr><tr><td>Nr1h3</td><td>-2.02</td><td>0.020303</td><td>Nuclear receptor subfamily 1, group H, member 3</td></tr></table>
+
+<--- Page Split --->
+
+Fold Regulation cut off \(= 2\) . p- Value cut off \(= 0.05\) . Fold- Change \((2^{\wedge}\) (- Delta Delta CT)) is the normalized gene expression \((2^{\wedge}\) (- Delta CT)) in the Test Sample divided the normalized gene expression \((2^{\wedge}\) (- Delta CT)) in the Control Sample. Fold- change values less than one indicate a negative or down- regulation, and the fold- regulation is the negative inverse of the fold- change. The p values are calculated based on a Student's t- test of the replicate \(2^{\wedge}\) (- Delta CT) values for each gene in the control group and Chkb deficient groups.
+
+<--- Page Split --->
+
+# Supplementary Table 2 | Ppar associated genes over-expressed in Chkb<sup>-/-</sup> hindlimb vs. Chkb<sup>+/+</sup> hindlimb 
+
+<table><tr><td>Gene Symbol</td><td>Fold Regulation</td><td>p-Value</td><td>Description</td></tr><tr><td>Pck2</td><td>8.55</td><td>0.000216</td><td>Phosphoenolpyruvate carboxykinase 2 (mitochondrial)</td></tr><tr><td>Apoe</td><td>6.77</td><td>0.000851</td><td>Apolipoprotein E</td></tr><tr><td>Angptl4</td><td>4.46</td><td>0.007248</td><td>Angiopoietin-like 4</td></tr><tr><td>Eln</td><td>3.46</td><td>0.002955</td><td>Elastin</td></tr><tr><td>Fabp5</td><td>2.74</td><td>0.009434</td><td>Fatty acid binding protein 5, epidermal</td></tr><tr><td>Pltp</td><td>2.61</td><td>0.030470</td><td>Phospholipid transfer protein</td></tr><tr><td>Cpt1a</td><td>2.29</td><td>0.008722</td><td>Carnitine palmitoyltransferase 1a, liver</td></tr><tr><td>Pparg</td><td>2.24</td><td>0.041818</td><td>Peroxisome proliferator activated receptor gamma</td></tr></table>
+
+Fold Regulation cut off =2. p-Value cut off= 0.05. Fold-Change (2^ (- Delta Delta CT)) is the normalized gene expression (2^ (- Delta CT)) in the Test Sample divided the normalized gene expression (2^ (- Delta CT)) in the Control Sample. Fold-change values more than one indicate a positive or up-regulation. The p values are calculated based on a Student's t-test of the replicate 2^ (- Delta CT) values for each gene in the control group and Chkb deficient groups.
+
+<--- Page Split --->

preprint/preprint__5f28392c688a860d3ac3f03c9408d9c7770633a9419220a8b07a3f2a5219ab2c/images_list.json

@@ -0,0 +1,77 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1: A model compensating for the sun's movement in the insect's celestial compass. (a) Cryptochrome (CRY), timeless (TIM) and period (PER) proteins are responsible for encoding time in the insect brain. The mRNA level of CRY1 is increased in the butterfly antennas (and eyes in several insects) when they detect blue light, synchronising internal clocks to the light-and-darkness cycle. (b) The mRNA levels of CRY2 (solid line) and TIM (dashed line) proteins increase and decrease with a different phase during the 24-hour light-and-darkness cycle in monarch butterflies [9, 10]. Data replotted from [10]. (c) The mRNA levels of CRY2 and TIM proteins modelled as cosine and sine functions of zeitgeber time encode the hour angle \\((\\omega)\\) . (d) The hour angle, encoded as in (c), is an arrow that rotates clockwise (CW) and completes a full circle daily. The arrow should point east during sunrise, south at noon and west during sunset (assuming twelve hours day and twelve hours night), roughly predicting the solar azimuth. (e) The hour-angle predicts a constant change in the solar azimuth during the day (blue line), but the actual azimuth deviates depending on location and time of year (orange and red lines). The orange lines illustrate the sun's courses in August (dashed) and October (solid) at Michigan \\((\\sim 46^{\\circ}\\mathrm{N})\\) . The red lines show the respective sun's courses in Mexico \\((\\sim 20^{\\circ}\\mathrm{N})\\) . Shaded areas highlight the difference in the sun's course over two months at the same location. (f) Schematic of the connections between neurons in the brain of Drosophila melanogaster. On the left half, we show the first and second-order inputs to the DN1pB (clock) neurons. We show the celestial compass pathway on the right and where the DN1pB neurons join it. (g) The proposed role of the two types of TuBu1 neurons. The spatial encoding of cosine and sine of the solar azimuth across their population is key to the time-compensation mechanism. (h) By combining the activity of the TuBu1 and DN1pB with multiplications and additions, we implement a trigonometric identity and transform the encoding of the solar azimuth into a pattern of activity indicating north.",
+    "footnote": [],
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+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2: Complete model of the sun's movement. (a) The solar declination is the earth's latitude where the sun is exactly at the zenith, which is equivalent to the angle of the line connecting the centres of the earth and sun from earth's equator. (b) The solar declination is represented by a sinusoidal function of time with an annual period. This sinusoidal can be represented as a two-dimensional direction by decomposing it into two sinusoids. (c) The solar declination moves the hour angle oscillation up or down based on the season. (d) The geomagnetic inclination is the angle between the geomagnetic field and the earth's surface. (e) The geomagnetic inclination is a monotonic function of the geometric latitude, which can also be decomposed into two sinusoidal functions that represent a two-dimensional direction. (f) The amplitude of the hour-angle oscillation is proportional to the observer's latitude and flips in the southern hemisphere, allowing for both clockwise (CW) and counter-clockwise (CCW) movements of the sun. (g) The full solar azimuth model. The proposed circuit combines information from the geomagnetic inclination and daily and annual clocks, to accurately estimate the sun's course during the day. This estimate is a vector with a north-most \\((\\alpha_{N})\\) and east-most \\((\\alpha_{E})\\) component.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3: Computer simulated central-place foraging routes. At dawn, the simulated insect searches for food and stores the food location after finding it. It then returns to its nest. It tries to repeat foraging to the food location every hour until sunset, using (a) a model without time compensation, (b) the hour-angle model, or (c) our complete model. (d) Euclidean distance (m) of the search centroid from the feeder (red) or the nest (green) using the three models. The sample size in each box is \\(n = 9\\) . (e) Homing error as a function of foraging duration (normalised for foraging distance). Solid lines show the mean error when using the no-compensation (grey), the hour-angle (blue) or the complete model (yellow). Shaded areas are the 95% confidence interval (CI). In all the results there is 20% added compass noise.",
+    "footnote": [],
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+      ]
+    ],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4: Computer simulations of insect migrations. (a, b) Simulation of a monarch butterfly (Danaus plexippus) during its autumn migration, using the hour-angle model (blue) and complete model (yellow). Haversine distance: \\(3303.01\\mathrm{km}\\) . The Red dashed arrow illustrates the straight line between the start and goal locations. (c, d) Similar simulation for the Bogong moth (Agrotis infusa) during its autumn migration. Haversine distance: \\(1114.65\\mathrm{km}\\) . (e, f, g) Simulation of a globe skimmer dragonfly (Pantal flavescens) during its spring migration. Haversine distance: \\(4859.20\\mathrm{km}\\) . (h) Tortuosity of the migrating route for each model. (i) The Euclidean distance (km) of the simulated insect from the target location at the end of its migration for each model. In (h) and (i) the sample size is \\(n = 10\\) . In all the results there is \\(20\\%\\) added compass noise.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5: Clock neurons in the insect brain. Light is detected by the photoreceptors of the compound eyes, ocelli and antennas, and regulates the clock neurons in the insect brain. In our models, these are the zeitgeber time \\((t_z)\\) and day length \\((T_L)\\) . The antennae of some insects can also detect the magnetic inclination \\((\\mu)\\) , which can also play a role in the compass of insects. The celestial compass involves processes through the dorsal medulla (Me), anterior optic tubercle (AOTu), and bulb (Bu), where it forms an activity bump representing the insect's heading relative to geocentric coordinates. The clock neurons in the brain of Drosophila melanogaster are the dorsal (DNs) and lateral neurons (LNs), which receive indirect input from the photoreceptors, ocelli and antennas, through the accessory medulla (aMe) and other areas. We suggest that their inputs include the insects' hour angle \\((\\phi)\\) , latitude \\((\\phi)\\) , and the solar declination \\((\\delta)\\) . DNs and LNs target different major areas in the insect brain that control the insect's behaviour. These include the ellipsoid body (EB) and fan-shaped body (FB) of the central complex (CX), the mushroom bodies, and the descending neurons. A particular type of DN, the DN1pB, targets the AOTu and the TuBu neurons and therefore is part of the celestial compass pathway. We suggest that this neuron encodes a prediction of the solar azimuth (relative to an absolute coordinate), which integrates with the detected egocentric solar azimuth into a geocentric compass. Shaded nodes in the architecture denote areas modelled in this work. Grey arrows and empty boxes were not directly modelled in this work.",
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preprint/preprint__5f28392c688a860d3ac3f03c9408d9c7770633a9419220a8b07a3f2a5219ab2c/preprint__5f28392c688a860d3ac3f03c9408d9c7770633a9419220a8b07a3f2a5219ab2c.mmd

@@ -0,0 +1,496 @@
+
+# Spatiotemporal computations in the insect celestial compass  
+
+Evripidis Gkanias ev.gkanias@ed.ac.uk  
+
+The University of Edinburgh https://orcid.org/0000- 0003- 3343- 9039  Barbara Webb  The University of Edinburgh  
+
+## Article  
+
+Keywords:  
+
+Posted Date: August 9th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4804050/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 March 22nd, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 57937-w.
+
+<--- Page Split --->
+
+# Spatiotemporal computations in the insect celestial compass  
+
+Evripidis Gkanias \(^{1*}\) and Barbara Webb \(^{1}\)  
+
+\(^{1}\) School of Informatics, University of Edinburgh, Edinburgh, United Kingdom \(^{*}\) Corresponding author: ev.gkanias@gmail.com  
+
+## Abstract  
+
+To obtain a geocentric directional reference from a celestial compass requires compensation for the sun's movement during the day, which also depends on the time of year and the observer's latitude. We examine how insects could solve this problem, assuming they have clock neurons that represent time as a sinusoidal oscillation, and taking into account the known neuroanatomy of their celestial compass pathway. We show how this circuit could exploit trigonometric identities to perform the required spatiotemporal calculations. Our basic model assumes a constant change in sun azimuth (the 'hour angle'), which is recentered on solar noon for changing day lengths. In a more complete model, the time of year is represented by an oscillation with an annual period, and the latitude is estimated from the inclination of the geomagnetic field. We evaluate these models in simulated migration and foraging behaviours and discuss their potential for practical applications in robotics.
+
+<--- Page Split --->
+
+## 1 Introduction  
+
+2 Using the sun (or equivalent celestial cues) as a compass 3 requires a compensation mechanism for its movement dur- 4 ing the day. Taking inspiration from insects, engineers have 5 implemented various forms of celestial compass for use in 6 robot navigation. Typically the robot's deployment has 7 been short enough (less than an hour) for the sun's move- 8 ment to be neglected [1,2]. For longer deployment, system 9 clocks, a global positioning system (GPS) and an accurate 10 model of the solar ephemeris can be used in an algorithm 11 that tracks the sun and uses its position to time- compensate 12 the compass [3]. However, the key use cases for a robot ce- 13 lestial compass would be situations where GPS is unavail- 14 able (such as remote locations or when satellite systems 15 have been compromised). Similarly, insects use an alterna- 16 tive to GPS. While it is implausible to suppose that they 17 have either an absolute time reference or a precise look- up 18 table for the solar ephemeris, they do perform time com- 19 pensation when navigating by celestial cues [4,5]. Here, we 20 propose plausible neural mechanisms by which insects could 21 use their internal sense of time to predict the sun's position, 22 transforming the measured azimuth of the sun into a geo- 23 centric heading reference.  
+
+Internal clocks (processes that track time or external rhythms) are widespread across biological systems. Insects are known to have clock input to multiple circuits [6, 7]. More specifically, clock inputs from the antennae [8- 12] or the accessory medulla (aMe) of the optic lobes [13- 17] (Fig. 1a) affect the celestial compass function. The time- less (TIM) protein is the main clock signal in the brain, and along with the period (PER) protein, it is involved in the encoding of time in insects [18]. Cryptochrome (CRY) proteins are also involved, acting as photoreceptor inputs to the clock mechanism that allows tuning of the PER and TIM mRNA oscillations (also of CRY2 oscillations in monarch butterflies) to the light- darkness rhythms [9- 11]. As Fig. 1b shows, the oscillation phase of CRY2 proteins differ by six hours from TIM's, suggesting that these two signals might respectively encode the sine and cosine function of the same angle [19] (Fig. 1c), which changes with constant rate of \(15^{\circ}\) per hour and thus (like the hour hand of a clock) completes a circle every day (Fig. 1d).  
+
+Inside the insect brain time is represented by clock neurons [6, 7] whose activity depends on the mRNA levels of the above proteins (although their exact relationship is unclear). Similarly to the protein levels, clock neuron activity expresses an endogenous oscillation with periods that can vary from daily to annual [18]. Roughly half of the clock neurons in the insect brain also rely on the blue light sensitive CRY [17]. The only clock neurons that join the celestial compass pathway of fruit flies (Drosophila melanogaster) are the DN1pB [20], which intersect the path before it reaches the navigation- specific circuits of the central complex (CX) [14, 21]. The current assumption is that these neurons allow the celestial compass to compensate for the moving sun by predicting the sun's course during the day [20]. However, the mechanism that allows this compensation and transforms the retinotopic position of the sun into a geocentric compass is still unknown.  
+
+Several mechanisms have been proposed to explain the compensation of a celestial compass for the sun's movement. Some of them do not require a clock and suggest the calibration of the celestial with other compasses [22] or use the sun's elevation to estimate its speed of motion [23]. Others conceptually examine the effects of mappings from different forms of clock input to the estimated sun's position, but without discussing possible biological implementations [24]. One mechanism examined in Massy et al. (2023) [24] is time- averaging, which has been previously linked to properties of clock proteins found in the antennas of butterflies [19]. As already mentioned, the levels of these proteins express a sinusoidal pattern during the day, representing an arrow that encodes time. The proposed mechanism in Schlierman et al. (2016) [19] uses this signal to estimate the sun's movement as a constant speed of \(15^{\circ}\) per hour (the speed at which the earth rotates around its axis) and assumes that the clock resets at sunrise. However, this produces a directional drift in the compass reference as the length of the day (and hence the time of sunrise) changes. A clock synchronised to solar noon would provide a stable reference point, but it is unclear how this could be achieved. Furthermore, depending on the time of year or location on earth, the observed movement of the sun can deviate significantly from a constant speed (Fig. 1e).   
+
+In this paper, we present a neurally plausible mechanism by which a clock signal carried by DN1pB neurons could be used to correct the insect's celestial compass. We propose two alternative models to generate the encoded signal of DN1pB clock neurons, using information available to insects: an hour- angle and a complete solar- azimuth tracker. Our hour- angle model uses the time of the day to accurately predict the earth's rotation around its spin axis and relative to the sun, including adaptation for changing day length. The complete model additionally uses the time of the year and the geomagnetic inclination (detectable by some migrating insects [25]) to calculate the exact course of the sun during the day. Our results suggest that the hour- angle model is sufficient to support the behaviour of migrating and central- place foraging insects. However, the complete model can compensate for the change from clockwise (CW) to counter- clockwise (CCW) movement of the sun in the northern and southern hemispheres of earth respectively, and hence is needed for migrating insects that cross the equator. We suggest that such a model provides a powerful localisation tool independent of GPS signal and could be used on any planet.  
+
+## Results  
+
+## The hour-angle model  
+
+The hour angle ( \(\omega\) ) describes the earth's rotation around its axis relative to the sun as a constant rate of \(15^{\circ}\) per hour. By convention, the hour angle is the longitudinal difference between the observer and the subsolar point (location on earth where the sun is at its zenith). It is zero when the sun is closest to the observer's zenith (solar noon), at which point the sun azimuth indicates south (assuming the observer is in the northern hemisphere). If the time of day is measured from sunrise (zeitgeber time, \(t_z = t - t_{\mathrm{sr}}\) , from
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1: A model compensating for the sun's movement in the insect's celestial compass. (a) Cryptochrome (CRY), timeless (TIM) and period (PER) proteins are responsible for encoding time in the insect brain. The mRNA level of CRY1 is increased in the butterfly antennas (and eyes in several insects) when they detect blue light, synchronising internal clocks to the light-and-darkness cycle. (b) The mRNA levels of CRY2 (solid line) and TIM (dashed line) proteins increase and decrease with a different phase during the 24-hour light-and-darkness cycle in monarch butterflies [9, 10]. Data replotted from [10]. (c) The mRNA levels of CRY2 and TIM proteins modelled as cosine and sine functions of zeitgeber time encode the hour angle \((\omega)\) . (d) The hour angle, encoded as in (c), is an arrow that rotates clockwise (CW) and completes a full circle daily. The arrow should point east during sunrise, south at noon and west during sunset (assuming twelve hours day and twelve hours night), roughly predicting the solar azimuth. (e) The hour-angle predicts a constant change in the solar azimuth during the day (blue line), but the actual azimuth deviates depending on location and time of year (orange and red lines). The orange lines illustrate the sun's courses in August (dashed) and October (solid) at Michigan \((\sim 46^{\circ}\mathrm{N})\) . The red lines show the respective sun's courses in Mexico \((\sim 20^{\circ}\mathrm{N})\) . Shaded areas highlight the difference in the sun's course over two months at the same location. (f) Schematic of the connections between neurons in the brain of Drosophila melanogaster. On the left half, we show the first and second-order inputs to the DN1pB (clock) neurons. We show the celestial compass pathway on the right and where the DN1pB neurons join it. (g) The proposed role of the two types of TuBu1 neurons. The spatial encoding of cosine and sine of the solar azimuth across their population is key to the time-compensation mechanism. (h) By combining the activity of the TuBu1 and DN1pB with multiplications and additions, we implement a trigonometric identity and transform the encoding of the solar azimuth into a pattern of activity indicating north. </center>  
+
+the German for 'time- giver'), the hour angle is given by  
+
+\[\omega (t) = (t_z - \frac{T_L}{2})15^\circ , \quad (1)\]  
+
+where \(T_{L} = t_{\mathrm{ss}} - t_{\mathrm{sr}}\) is the day length, computed as the difference between the sunrise \((t_{\mathrm{sr}})\) and sunset \((t_{\mathrm{ss}})\) times in hours. Supplementary Text S1 describes a possible neural implementation of equation (1), given the neural encoding of the zeitgeber time and day length separately.  
+
+Given their six- hour phase difference (equivalent to \(90^{\circ}\) hour- angle difference; see Fig. 1b), TIM and CRY2 proteins could encode the (negative) sine and cosine of the hour angle as its east- most \((\omega_{\mathrm{E}})\) and north- most \((\omega_{\mathrm{N}})\) components (Fig. 1c). The period of these sinusoids is determined by the  
+
+temporal difference between two consecutive sunrises [26]. Their phase is determined by the day length \((T_{L})\) , which ensures that the sinusoids are centred at the solar noon (see Supplementary Fig. S1). Note that both (east- most and north- most) components are necessary to describe the hour angle. By combining them, we can create an arrow that rotates with time like the hour hand of a clock (Fig. 1d, blue arrow). However, note that the hour- angle model approximates the solar azimuth and that a complete compensation mechanism should consider more factors (Fig. 1e).
+
+<--- Page Split --->
+
+## Estimating the day length  
+
+The blue- light sensitive CRY1 proteins detected in Danaus plexippus monarch butterflies (equivalent to the CRY proteins of \(D\) melanogaster fruit flies) synchronise the clocks to the light- dark rhythm [9,10,17]. We suggest that two kinds of synchronisation co- occur. The first synchronises the zeitgeber time \((t_z)\) to the sunrise, while the second shifts the hour angle relative to \(t_z\) , as described in equation (1) so that it is zero at the solar noon. Thus we assume that the zeitgeber time is always zero at sunrise and increases linearly during the day. However, the required shift relative to solar noon depends on the day length \((T_L)\) , which we assume is a continuously updated estimate as described in the following. A consequence is that \(T_L\) potentially changes during the day, so the hour- angle might not change linearly.  
+
+We propose that the day length \((T_L)\) can be calculated as a function of CRY1, such that an insect could estimate the day length simply from the changing level of skylight irradiance,  
+
+\[\tau_{L}\frac{\mathrm{d}T_{L}}{\mathrm{d}t} = \mathrm{CRY1}(t) + \beta -T_{L}, \quad (2)\]  
+
+where \(\tau_{L}\) is a time- constant, \(\beta\) is a constant input, and \(\mathrm{CRY1}(t) = aI_{\mathrm{sky}}(t)\) is the protein level of CRY1, where \(a\) is a scaling factor (gain) and \(I_{\mathrm{sky}}\) is the overall blue irradiance in the sky. The parameters \(a\) , \(\beta\) and \(\tau_{L}\) were optimised to fit equation (2) to the actual day length (values summarised in Supplementary Table S1). Supplementary Fig. S2a demonstrates the accuracy of this fit, where we simulate the estimated \(T_{L}\) and plot it over the actual day length, assuming continuous light exposure during the day (for migratory insects).  
+
+As central- place foraging insects are exposed to light at varying times (depending on their foraging pattern), we tested how interrupted light exposure might affect the estimates of \(T_{L}\) (note this might also affect their synchronisation of \(t_z\) , but we do not consider that here). We simulated species with different average foraging durations, from one to eight hours per day; foraging each day could vary around this average and occur anytime from sunrise to sunset. Parameters needed to be optimised to fit the different average foraging durations (summarised in Supplementary Table S1): shorter foraging durations require longer time constants \((\tau_{L})\) and higher gains ( \(a\) ) to transform the sky irradiance into CRY1. Using these optimised parameters, central- place foraging insects can estimate the day length with comparable error to migrating insects, with error increasing for shorter foraging times (Supplementary Fig. S2b, grey boxes). This shows that the higher level of skylight irradiance measured (for the same average exposure time) during the summer (compared to winter) suffices to estimate the day length for central- place foragers. Having the same foraging duration and a consistent time window every day would result in smoother estimates. The black lines in Supplementary Fig. S2 suggest that adding processing units in series can smooth the estimates further and make the hour- angle change at a nearly constant rate (see also Supplementary Text S2). However, this also introduces a delayed response, which translates into a constant shift in the phase of the encoded sinusoid. This lag increases the error but is predictable and could be compensated for by  
+
+following the same principle as we describe in the next section for the compass, using a biological implementation of trigonometric identities.  
+
+## Integration with compass neurons  
+
+Dorsal neurons (DNs) and lateral neurons (LNs) are the clock neurons in the brain of \(D\) melanogaster [17,27]. The calcium level of these neurons has an overall increase and decrease during the day. This can be described by a sinusoidal function whose phase varies among the neurons and looks similar to protein levels in Fig. 1b. A pair of DN neurons (DN1pB) target the TuBu1 neurons and provide clock information to the celestial compass pathway [6,7,28] in each hemisphere [17,20]. We hypothesise that the calcium level of DN1pB neurons predicts the solar azimuth \((\alpha)\) and corresponds to the east- most \((\omega_{E})\) and north- most \((\omega_{N})\) components of the hour angle. There are other clock neurons in. nerving the ellipsoid body (EB) and fan- shape body (FB) of the CX, but we would argue that time compensation should occur before the celestial compass integrates with other compasses (such as wind or visual landmarks) in the EPG neurons of the EB. The DN1pB neurons are, so far, the only reported neurons to target the celestial compass pathway upstream of the EB in \(D\) melanogaster [17]. Although they receive limited direct input from sensory- driven clocks in the antennae or retina (see Fig. 1f and Supplementary Table S2, generated using data from the FlyWire database [29]), they receive input from these via multiple interneurons, which might have a role in shaping their response into a smooth sinusoid (Supplementary Text S2).  
+
+Previous computational modelling studies provide a good approximation of how the TuBu1 neurons can encode the solar azimuth [23,30]. In \(D\) melanogaster, polarised light is detected from the dorsal rim area (DRA) and travels to the anterior optic tubercle (AOTu) through the retina and the medulla (Me) (Fig. 1f) [31,32]. Colour information is detected from the remaining dorsal area in the eye. It travels through the dorsal retina and Me to AOTu and the TuBu1 neurons, where it probably integrates with polarisation information and estimates the retinotopic solar azimuth \((\alpha '\) ; which is in egocentric coordinates). As described above, TuBu1 neurons are also terminals for the DN1pB neurons [6,7,20,28]. Thus, we assume that the time- based solar azimuth prediction is combined with the retinotopic solar azimuth estimate at the axons of TuBu1 neurons, transforming it into a geocentric compass in the anterior bulb (Bu \(a\) ).  
+
+There are two types of TuBu1 neurons: TuBu1a, which targets ER4m ring neurons, and TuBu1b, which targets both ER4m and ER5 neurons (see Supplementary Table S3). Calcium recordings of TuBu1 neurons suggest that the two hemispheres independently encode the (retinotopic) solar azimuth in a spatial sinusoidal pattern of activity [32]. We speculate that the TuBu1a and TuBu1b populations express a \(90^{\circ}\) shift in the represented direction of the sun (see Fig. 1g), which we will see is essential for how we implement the time compensation. We also assume that DN1pB \(t_{2}\) gets the TuBu1a population and the DN1pB \(N\) targets the TuBu1b population (Fig. 1h). Finally, the responses of the TuBu1 populations are added together to encode the
+
+<--- Page Split --->
+
+animal's heading in the responses of the ER4m population.  
+
+The above process implements a crucial trigonometric identity that transforms the solar azimuth into a geocentric compass in the ring neurons, described as  
+
+\[\begin{array}{rl} & {\mathrm{ER4m}^n = \sin (\alpha)\cdot \sin (\alpha ' - \phi^n) + \cos (\alpha)\cdot \cos (\alpha ' - \phi^n)}\\ & {\qquad = \cos (\alpha -\alpha ' + \phi^n),} \end{array} \quad (3)\]  
+
+where \(\alpha = \alpha (t) = \omega (t)\) is the prediction of solar azimuth based on time (DN1pB neurons), \(\alpha ' - \phi^n\) is the estimation of the retinotopic solar azimuth (TuBu1 neurons), and \(\phi^n\) is the retinotopic direction of a TuBu1 neuron. The above equation suggests that ER4m ring neurons encode the angular difference between the observed (celestial compass) and predicted (clock neurons) solar azimuth, indicating north. Note that although we use the north as a reference point in our model, the same principles should apply to any arbitrary direction.  
+
+## Complete time compensation  
+
+The earth's spin axis is not aligned with the earth's orbit around the sun. This misalignment causes seasonal shifts in day length and the observed course of the sun across the sky. (Fig. 1e). To accurately compute the sun's location at a given time, we need to know the longitudes and latitudes of both the subsolar point and the observer [3]. The latitude of the subsolar point is also known as the solar declination ( \(\delta\) ; Fig. 2a), which is maximum at \(23.45^{\circ}\) (the angle of earth's spin axis from a vertical axis) in June, minimum at \(- 23.45^{\circ}\) in December, and zero in March and September. This describes an oscillation with an annual period, which can be further decomposed into two sinusoidal functions (Fig. 2b). We assume that a different pair of clock neurons encode these two components. The first component ( \(\delta_N\) ) raises the hour- angle oscillation during the summer and lowers it during the winter, emulating the longer or shorter days of the year (Fig. 2c) in the northern hemisphere (the relationships would be reversed for the southern hemisphere). Because the solar declination is an angle, we need a second component ( \(\delta_Q\) ) to ensure balanced and stable trigonometric computations. Note that solar declination differs from day length ( \(T_L\) ), as the latter also depends on the geometric latitude of the observer. Interestingly, knowing any two of the day length, solar declination and observer's latitude, we can estimate the third one (see Supplementary Text S3).  
+
+Another way we can estimate the geometric latitude of the observer is by measuring the geomagnetic inclination (or magnetic dip, \(\mu\) ), which is the vertical component of the earth's magnetic field and (approximately) depends on the geometric latitude ( \(\phi\) ) at that point (Fig. 2d) [33]. Monarch butterflies respond to magnetic inclination [25] and we suggest that at least some insects can estimate their latitude by detecting the inclination of the local geomagnetic field. We assume that another pair of neurons encode the sine ( \(\phi_N\) ) and cosine ( \(\phi_Q\) ) of the insect's latitude as a function of magnetic inclination (Fig. 2e). Note that \(\phi_N\) is positive in the northern hemisphere and negative in the southern. Thus, we hypothesise that \(\phi_N\) is multiplied with the north- most component of hour- angle oscillation ( \(\omega_N\) ) to flip it when the insect is in the southern hemisphere and transform its rotation from CW to CCW (Fig. 2f). This property becomes crucial for insects that live close to the equator [34, 35], whereas it might be less important for insects which remain in one hemisphere, and \(\phi_N\) could be replaced by a constant value for insects whose latitude does not change much. The role of the other term ( \(\phi_Q\) ) is to ensure stable trigonometric computations. Our hypothesis on the use of geomagnetic inclination fits well with data showing that both the CRY2 proteins and magnetic inclination are regulated by blue light detected at the antennas of monarch butterflies [25]. However, the pathway that transfers this information to the central brain is yet to be explored, and the existence of this sense in other insects is yet to be established.  
+
+crucial for insects that live close to the equator [34, 35], whereas it might be less important for insects which remain in one hemisphere, and \(\phi_N\) could be replaced by a constant value for insects whose latitude does not change much. The role of the other term ( \(\phi_Q\) ) is to ensure stable trigonometric computations. Our hypothesis on the use of geomagnetic inclination fits well with data showing that both the CRY2 proteins and magnetic inclination are regulated by blue light detected at the antennas of monarch butterflies [25]. However, the pathway that transfers this information to the central brain is yet to be explored, and the existence of this sense in other insects is yet to be established.  
+
+The above information is sufficient to accurately estimate the expected solar azimuth at a specific location and time [3]. Again, we assume that a pair of neurons decompose this information into the east- most ( \(\alpha_E\) , negative sine) and north- most ( \(\alpha_N\) , negative cosine) components of an arrow that points towards the solar azimuth ( \(\alpha\) ; Fig. 1d and e). We suggest that these neurons could be the pair of DN1pB, which now respond to the solar azimuth (as opposed to hour- angle) and achieve complete compensation for the sun's movement. A possible circuit that implements the above function is illustrated in Fig. 2g, while the values of \(\alpha_N\) and \(\alpha_E\) for different combinations of magnetic inclination, solar declination and hour angles are plotted in Supplementary Fig. S3. We refer to this as the 'complete model' of the sun's movement and compare it to the 'hour- angle model' in the following simulations of insect navigation.  
+
+## Central-place foraging experiment  
+
+To demonstrate the effectiveness of our time- compensated compass, we simulated a foraging experiment for insects such as bees and ants who forage throughout the day to a familiar food site but can take long breaks between foraging trips (spent in their home's darkness). The simulated insects initially perform a random walk searching for food just after sunrise, followed by single return trips to the food location (stored as a vector memory) every hour until sunset. We then tested how an insect using CX navigation would perform in this task with different model compass inputs: (a) without time compensation, (b) using the hour- angle or (c) the complete model. The CX model we used is a modified version of a well- established path integration model [36], which also incorporates vector memories of salient locations [37]. We then use our proposed compass model as the input heading of the CX with \(20\%\) noise. Figure 3a- c show example foraging routes produced by the three models during a single day.  
+
+Overall, no matter which compass model the insect used, it could return home quite accurately during individual foraging excursions (Fig. 3d, green boxes). The sun's movement during a short excursion (a few minutes in this simulation) is not enough to cause noticeable errors in the continuous integration of the home vector. However, longer foraging durations increase the error without time compensation, and also affect the performance of the hour- angle model significantly (as opposed to the complete model), as its error increases linearly with time (Fig. 3e). More signif
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2: Complete model of the sun's movement. (a) The solar declination is the earth's latitude where the sun is exactly at the zenith, which is equivalent to the angle of the line connecting the centres of the earth and sun from earth's equator. (b) The solar declination is represented by a sinusoidal function of time with an annual period. This sinusoidal can be represented as a two-dimensional direction by decomposing it into two sinusoids. (c) The solar declination moves the hour angle oscillation up or down based on the season. (d) The geomagnetic inclination is the angle between the geomagnetic field and the earth's surface. (e) The geomagnetic inclination is a monotonic function of the geometric latitude, which can also be decomposed into two sinusoidal functions that represent a two-dimensional direction. (f) The amplitude of the hour-angle oscillation is proportional to the observer's latitude and flips in the southern hemisphere, allowing for both clockwise (CW) and counter-clockwise (CCW) movements of the sun. (g) The full solar azimuth model. The proposed circuit combines information from the geomagnetic inclination and daily and annual clocks, to accurately estimate the sun's course during the day. This estimate is a vector with a north-most \((\alpha_{N})\) and east-most \((\alpha_{E})\) component. </center>  
+
+![](images/Figure_3.jpg)
+
+<center>Fig. 3: Computer simulated central-place foraging routes. At dawn, the simulated insect searches for food and stores the food location after finding it. It then returns to its nest. It tries to repeat foraging to the food location every hour until sunset, using (a) a model without time compensation, (b) the hour-angle model, or (c) our complete model. (d) Euclidean distance (m) of the search centroid from the feeder (red) or the nest (green) using the three models. The sample size in each box is \(n = 9\) . (e) Homing error as a function of foraging duration (normalised for foraging distance). Solid lines show the mean error when using the no-compensation (grey), the hour-angle (blue) or the complete model (yellow). Shaded areas are the 95% confidence interval (CI). In all the results there is 20% added compass noise. </center>  
+
+icantly, insects without time compensation could not accurately revisit a known food site (Fig. 3a). This is because the food- site location was stored in the memory relative to the sun's position, and as the sun moves so does this location. Either form of time compensation seems sufficient to navigate back and forth to the food site with relatively good accuracy (Fig. 3b and c). Despite some advantage of the complete model over the other two, it seems likely that foragers using the hour- angle (or even the no- compensation)  
+
+model combined with other cues, such as visual place recognition in the vicinity of the food site, could produce indistinguishable behaviour (for example, see experiments with honeybees Apis mellifera and A. cerana [38,39]).  
+
+In the above experiments, we used the actual day length for equation (1) (orange lines in Supplementary Fig. S2). Supplementary Fig. S4 shows the results when, instead, we use the smoothed day length estimates (black lines in Supplementary Fig. S2), time- shifted to overlay their theo
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4: Computer simulations of insect migrations. (a, b) Simulation of a monarch butterfly (Danaus plexippus) during its autumn migration, using the hour-angle model (blue) and complete model (yellow). Haversine distance: \(3303.01\mathrm{km}\) . The Red dashed arrow illustrates the straight line between the start and goal locations. (c, d) Similar simulation for the Bogong moth (Agrotis infusa) during its autumn migration. Haversine distance: \(1114.65\mathrm{km}\) . (e, f, g) Simulation of a globe skimmer dragonfly (Pantal flavescens) during its spring migration. Haversine distance: \(4859.20\mathrm{km}\) . (h) Tortuosity of the migrating route for each model. (i) The Euclidean distance (km) of the simulated insect from the target location at the end of its migration for each model. In (h) and (i) the sample size is \(n = 10\) . In all the results there is \(20\%\) added compass noise. </center>  
+
+retical values. Although this introduced some extra noise to the system, the foraging performance was not dramatically affected.  
+
+## Migration experiment  
+
+Most foraging insects remain at a similar latitude during their lifetime so it might be expected that the hour- angle model (which adjusts for day length but not solar declination and latitude) would be sufficient for successful behaviour. By contrast, several species of migrating insects travel, within a relatively short time, through multiple latitudes, so it might be expected that they require the complete time- compensation model for their compass system. We therefore simulated migration experiments for three different insect species: the monarch butterfly \(D\) . plexippus, the Bogong moth Agrotis infusa, and globe skimmer dragonfly Pantal flavescens. We selected these species to demonstrate migration in different characteristic locations on earth  
+
+relative to its equator: above ( \(D\) . plexippus), below ( \(A\) . infusa), or across ( \(P\) . flavescens). This way we test our model in locations where the sun moves CW, CCW, or switches its moving pattern during the migration.  
+
+In the CX model, we replaced its memory component with fixed goal coordinates on earth. We modified our simulation for the migration task, taking into account the curvature of the earth's surface. We assumed that the daily travel capacity of insects is eight hours (at \(2.5\mathrm{msec}^{- 1}\) , based on the speed of \(D\) . plexippus), and they need one- hour breaks every hour for feeding or rest. Here, we compared only the hour- angle and complete models, as without time compensation the simulated insects would move in circles around the starting point.  
+
+Figure 4a- b illustrate the southward autumn migration of monarch butterflies using the two models (blue: hour- angle, yellow: complete), which starts at the end of August from Mackinac Island (Michigan) and ends at the end
+
+<--- Page Split --->
+
+of October in Michoacan (Mexico). Figure 4c-d shows the simulated routes of Bogong moths during their autumn migration from Montrose (Australia) south to Mount Bogong. Although Bogong moths are nocturnal animals and use the night sky to navigate (following the Milky Way instead of the sun), we treat them as diurnal animals to demonstrate navigation in the southern hemisphere. Finally, Figure 4e-g shows the simulated routes of the globe skimmer dragonflies during their spring migration from Mbekenyara (Tanzania) to Madirai (India), which is the world's longest transoceanic migration (approximately \(4859\mathrm{km}\) ).  
+
+Overall, the complete model resulted in straighter migrating routes than the hour- angle model (Fig. 4h). However, the deviations induced by the less accurate hour- angle model largely cancel out during the day. As a result, in the single- hemisphere migrations (monarch butterflies and Bogong moths) both models could bring the animals close to their destinations (Fig. 4i). This suggests that the hour- angle model might be sufficient for migrating insects that do not cross the equator. Note that the simulated moths end up closer to the goal coordinates than the simulated butterflies. This is because their migration is shorter so the accumulated heading noise has a smaller overall effect. The hour- angle model fails for the dragonflies crossing the equator (Fig. 4g), which suggests that the complete model might be necessary for this type of migration.  
+
+As before, these results use the actual day length. Substituting the estimated day length, the migrations became slightly more tortuous and less accurate, especially at the start of the migration route (Supplementary Fig. S5). The largest error in the day length estimates seems to come from the initialisation of \(T_{L}\) , which takes some time to converge to the correct value. Although this could be avoided by optimising the initial value as we did with the other parameters, insects might encounter a similar problem.  
+
+## Discussion  
+
+Insects have a celestial compass that combines the detection of the sun's position and correction for its movement during the day (time- compensation) to obtain a consistent geocentric heading estimate. We suggest that this correction relies on standard trigonometric principles for spatial and temporal processing, and show a plausible neural mechanism by which the required trigonometry could be implemented. We compare the efficacy of two alternative models for time compensation: one that makes an approximate correction by assuming a constant change of sun angle with time (the hour- angle model); and one that makes a complete correction for the effects of latitude and declination on the apparent course of the sun relative to an observer in a particular location and time of year. In both cases, the clock is synchronised to solar noon by being reset at sunrise to a value that depends on a running estimate of day length based on skylight irradiance. We test these in central- place foraging and migrating scenarios, showing the necessity for the complete model only arises in tasks that require crossing the equator. Both models use information that is in principle available to insects and predict identifiable connectivity and activity patterns in the brain that can be explored anatomically and physiologically.  
+
+A striking property of the neural mechanism we propose is that it exploits the fact that both space and time are encoded in the insect brain as sinusoidal activity patterns. For example, solar azimuth information represented by the TuBu1 neurons has a characteristic sinusoidal pattern across a population of neurons [31]. Inputs from other neurons (such as TuTu and MeMe) maintain the sinusoid and keep it consistent across the two hemispheres. On the other hand, clock neurons (such as DN1pB) are characterised by periodic activity oscillations, usually described as temporal sinusoidal patterns. This characteristic of the activity and connectivity patterns in the insect brain greatly facilitates trigonometric operations to perform geometric calculations, such as calculating the difference between two angles (combining space and time information) as we describe in equation (3).  
+
+Our model predicts that the influence of clock neurons on their downstream targets (at least for this circuit) is multiplicative, which is necessary to allow the combination of sines and cosines. This could be tested by looking into specific properties in the responses of clock neurons. Traditionally, time information in the insect brain is described in terms of gene expression (tim, per, cry) or the mRNA level of proteins (like TIM, PER, CRY1, CRY2, and vrille (VRI) [17]). In a typical clock protein, the mRNA level increases and decreases once per day, but this can vary from tidal to annual periods [18]. With the development of optogenetic tools for D. melanogaster, the calcium levels of clock neurons have been observed to follow the same pattern as the proteins, but only daily periods have been described so far. Although calcium is often interpreted as a firing- rate signal, it would be useful to clarify how this changing calcium level in clock neurons translates into the membrane potential (for example, following work on PFNA neurons [40]), information which is currently missing from the literature. This is important to understand the potential mechanisms by which clock neurons affect their downstream targets, which could involve neurotransmitter, neuromodulator or neuropeptide release.  
+
+A complete map of clock neurons in fruit flies suggests a circuit architecture where DNs and LNs collect all temporal information and then distribute it to other areas that are responsible for behaviour [17] (Fig. 5). Sensory clocks (from the eyes, ocelli and antennas) tune neurons in the aMe and other neuropils to synchronise rhythms to external light cues by expressing the CRY protein. In our model, we have not mapped the processes we assume to occur before the DNs directly to these anatomical pathways, but we suggest it should be possible to find within this upstream circuit clock neurons (or proteins) that (1) calculate the day length, (2) smooth the estimations, (3) calculate the hourangle and (4) solar declination based on the day and year length respectively, (5) measure the magnetic inclination, and (6) use it to calculate the insect's latitude. Thus, our model suggests that the different clock neurons are tuned to track 'subtle geophysical forces' [41, 42]. More specifically (and testably) we propose that DN1pB neurons combine this information to encode a prediction of the solar azimuth \((\alpha)\) .  
+
+However, our simulations of insect navigation suggest that time compensation of their celestial compass may not
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5: Clock neurons in the insect brain. Light is detected by the photoreceptors of the compound eyes, ocelli and antennas, and regulates the clock neurons in the insect brain. In our models, these are the zeitgeber time \((t_z)\) and day length \((T_L)\) . The antennae of some insects can also detect the magnetic inclination \((\mu)\) , which can also play a role in the compass of insects. The celestial compass involves processes through the dorsal medulla (Me), anterior optic tubercle (AOTu), and bulb (Bu), where it forms an activity bump representing the insect's heading relative to geocentric coordinates. The clock neurons in the brain of Drosophila melanogaster are the dorsal (DNs) and lateral neurons (LNs), which receive indirect input from the photoreceptors, ocelli and antennas, through the accessory medulla (aMe) and other areas. We suggest that their inputs include the insects' hour angle \((\phi)\) , latitude \((\phi)\) , and the solar declination \((\delta)\) . DNs and LNs target different major areas in the insect brain that control the insect's behaviour. These include the ellipsoid body (EB) and fan-shaped body (FB) of the central complex (CX), the mushroom bodies, and the descending neurons. A particular type of DN, the DN1pB, targets the AOTu and the TuBu neurons and therefore is part of the celestial compass pathway. We suggest that this neuron encodes a prediction of the solar azimuth (relative to an absolute coordinate), which integrates with the detected egocentric solar azimuth into a geocentric compass. Shaded nodes in the architecture denote areas modelled in this work. Grey arrows and empty boxes were not directly modelled in this work. </center>  
+
+need to incorporate all 'subtle geographic forces'. The hour angle model diverges from the actual solar azimuth in inverse proportion to the distance of the insect from the equator. Thus, the precision of the simpler hour- angle model increases closer to the poles and decreases closer to the equator, where the complete model becomes more useful (see Fig. 1e). The most critical band for the hour angle model is within \(23.45^{\circ}\) from the equator, where the sun switches biannually between CW and CCW movement. In  
+
+an extreme scenario (when the insect is exactly at the subsolar latitude) the sun moves in a straight line across the zenith. The solar azimuth remains due east until solar noon when it switches within moments to due west, creating the largest error for the hour- angle model; the complete model can compensate for this phenomenon. Seasonal insects (for example, only active during the summer) equipped with the hour- angle model may not face this situation, but we should expect a large variance in their directed behaviour (see Fig. 3b and Fig. 4e). The complete model is critical for seasonal insects within this band that operate during autumn or spring (when the sun switches moving directions), such as the globe skimmer dragonflies.  
+
+For migrating species that remain in one hemisphere, the complete model allows them to maintain a straighter path. However, note that deviations induced by using the hour- angle approximation largely cancel out over each day, making this simpler model sufficient for reaching their destination. Thus insects known to use magnetic inclination for their migration within a hemisphere, such as the monarch butterfly [25], might have evolved this sensitivity for another purpose: to set the goal location when migrating along the latitudinal axis. In this case, the animal would stop migrating when a target value of magnetic inclination was sensed. Having developed such a sense, their clock may have co- opted the information, but as we have shown, they can still migrate with sufficient accuracy without complete time compensation.  
+
+The hour- angle model also appears to be sufficiently accurate for central- place foragers, although there might be some circumstances in which a complete model that reduces the error in return trips to a food source from that shown in Fig. 3b to that in Fig. 3c would be advantageous. For example, Saharan desert ants (Cataglyphis fortis and C. bicolor) that live in featureless salt pans may have few other cues available to correct for error, and longer foraging durations (inducing more error; Fig. 3e) might be expected due to food scarcity [43]. Note, in this case, the complete model could be somewhat simplified by using constant values for the sine and cosine of latitude, rather than requiring latitude to be estimated from magnetic inclination, as the latitude of the animal is relatively constant.  
+
+For insects that only need to use their celestial compass in relatively short trips, compensating a celestial compass for the sun's movement only becomes critical when trips to the same (remembered) location are to be made at different times of the day. In this case, a possible alternative to using an internal clock for time compensation would be to use familiar visual surroundings, a magnetic compass sense [44, 45] or some other constant directional cue to recalibrate the celestial compass at the start of each journey. Experiments with time delays and displacement of ants (C. fortis and C. bicolor [5]) or bees (Apis mellifera [46,47]) to novel locations make it unlikely that terrestrial visual cues are needed to recalibrate the compass. To rule out the possibility that recalibration occurs using a magnetic compass, it is essential to put in conflict their time- compensated celestial compass and their expected magnetic field, which has not yet been attempted.  
+
+Implementing a complete time- compensated celestial compass could also be advantageous for robotics, as it pro
+
+<--- Page Split --->
+
+vides localisation on earth based on an embedded model of geophysical forces and does not require any satellite-network infrastructure. The model's knowledge of geophysical forces adapts by measuring solar declination, day length (combination of solar declination and latitude) and time of day (zeitgeber time). Given the shared characteristics of all planets (round, spin around their axis, orbit around the sun and have some form of atmosphere for accurately detecting the sun's position), our model could be used as an alternative to GPS on any planet. Apart from the robot's heading, it can also provide its latitude (calculated as a function of day length and solar declination) and its longitude (function of the adaptive hour-angle and a clock tuned to the exact period of the planet's spin). This compass could thus be valuable for outdoor robotics for planetary exploration [48] and on earth, providing a robust backup when the magnetic field is distorted and the GPS signal is weak. This includes underwater missions or extreme weather conditions including sandstorms [49]. As our proposed compass estimates time based on subtle geophysical forces, it can survive accidental power-downs of robots, when time and date information (which could otherwise be used directly to predict sun position) could be lost.  
+
+## Materials and methods  
+
+## The celestial compass model  
+
+Our results assume a compass model that accurately returns the solar azimuth. We assume that this is represented in the AOTu by 16 TuBu1 neurons with field of view centred at homogeneously distributed angles in a ring,  
+
+\[\phi^{n} = n22.5^{\circ},\qquad \mathrm{where}\quad n\in \{1,\ldots ,16\} . \quad (4)\]  
+
+The responses of the TuBu1 neurons are then calculated as  
+
+\[\mathrm{MeTu2a}^{n}(t) = \sin (\alpha_{\mathrm{sum}}(t) - \theta (t) - \phi^{n}), \quad (5)\] \[\mathrm{MeTu2b}^{n}(t) = \cos (\alpha_{\mathrm{sum}}(t) - \theta (t) - \phi^{n}), \quad (6)\]  
+
+where \(\theta (t)\) is the heading of the animal at time \(t\) (hours), \(\phi^{n}\) is the preference angle of the \(n^{\mathrm{th}}\) MeTu2 neuron, and \(\alpha_{\mathrm{sum}}(t)\) is the solar azimuth.  
+
+## Models of compensation for the moving sun  
+
+Three models of the compass are used in different parts of our results: the no- compensation, hour- angle and full models (in order of ascending complexity). Each model provides the responses of the ring neurons (ERs) that are used as an input to the CX model.  
+
+## The no-compensation model  
+
+The activity of the ERs is equivalent to the output of the optic lobe (OL) medulla- tubercle (MeTu) neurons,  
+
+\[\mathrm{ER4m}^{n}(t) = \mathrm{TuBu1b}^{n}(t) = \mathrm{MeTu2b}^{n}(t). \quad (7)\]  
+
+## The hour-angle model  
+
+Here, we introduce a basic correction using the hour- angle. The responses of the DN1pB clock neurons relate to the  
+
+hour angle as  
+
+\[\mathrm{DN1pB}_{E}(t) = \omega_{E}(t), \quad (8)\] \[\mathrm{DN1pB}_{N}(t) = \omega_{N}(t), \quad (9)\]  
+
+where \(t\) is the time (hours) since the beginning of the year. The components \(\omega_{E}\) and \(\omega_{N}\) are calculated as  
+
+\[\begin{array}{r}\omega_{\mathrm{E}}(t) = -\sin (\omega (t)),\\ \omega_{\mathrm{N}}(t) = -\cos (\omega (t)), \end{array} \quad (11)\]  
+
+where \(\omega (t)\) is computed by equation (1). Note here that we assume a perfect estimate of the sunrise time \((t_{sr}\) ; used in equation (1) to estimate the zeitgeber time).  
+
+The activity of the tubercle- bulb (TuBu) neurons is then estimated as  
+
+\[\begin{array}{r}\mathrm{TuBu1a}^{n}(t) = -\mathrm{DN1pB}_{E}(t)\cdot \mathrm{MeTu2a}^{n}(t),\\ \mathrm{TuBu1b}^{n}(t) = -\mathrm{DN1pB}_{N}(t)\cdot \mathrm{MeTu2b}^{n}(t). \end{array} \quad (13)\]  
+
+TuBu neurons add up column- wise in the bulb (Bu), where they target the ERs, whose activity is calculated as  
+
+\[\mathrm{ER4m}^{n}(t) = \mathrm{TuBu1a}^{n}(t) + \mathrm{TuBu1b}^{n}(t). \quad (14)\]  
+
+## The complete model  
+
+The complete model also involves solar declination and the insect's latitude. Solar declination is computed as  
+
+\[\delta (t) = 23.45^{\circ}\sin \left(\frac{284 + t / 24}{365} 360^{\circ}\right), \quad (15)\]  
+
+where \(t\) is the time (hours) since the start of the year, and it is further decomposed into  
+
+\[\begin{array}{r}\delta_{N}(t) = \sin (\delta (t)),\\ \delta_{Q}(t) = \cos (\delta (t)). \end{array} \quad (16)\]  
+
+Geometric latitude can be approximated as a function of geomagnetic inclination [33] as  
+
+\[\phi (\mu) = -\tan^{-1}(0.5\tan (\mu)), \quad (18)\]  
+
+where \(\mu\) is the local geomagnetic inclination, and further decomposes into  
+
+\[\begin{array}{r}\phi_{N}(\mu) = \sin (\phi (\mu)),\\ \phi_{Q}(\mu) = \cos (\phi (\mu)). \end{array} \quad (19)\]  
+
+Using the above information, the apparent solar azimuth can be estimated as [3]  
+
+\[\begin{array}{rl} & {\alpha_{\mathrm{E}}(\mu ,t) = \delta_{Q}(t)\omega_{\mathrm{E}}(t),}\\ & {\alpha_{\mathrm{N}}(\mu ,t) = \phi_{Q}(\mu)\delta_{N}(t) + \phi_{N}(\mu)\delta_{Q}(t)\omega_{\mathrm{N}}(t),} \end{array} \quad (22)\]  
+
+corresponding to the solar azimuth's east (negative sine) and north (negative cosine) components.  
+
+We replace the responses of the DN1pB clock neurons with the solar azimuth components,  
+
+\[\begin{array}{r}\mathrm{DN1pB}_{E}(t,\mu) = \alpha_{E}(t,\mu),\\ \mathrm{DN1pB}_{N}(t,\mu) = \alpha_{N}(t,\mu). \end{array} \quad (24)\]  
+
+We simulate the observed magnetic inclination \((\mu)\) using the actual geometric latitude of the animal as  
+
+\[\mu = \tan^{-1}\left(\frac{-2\sin(\phi)}{\cos(\phi)}\right). \quad (25)\]  
+
+The remaining calculations are the same as in the hour- angle model.
+
+<--- Page Split --->
+
+## The central complex model  
+
+As we do not focus on the ring- attractor dynamics or specific neural response of the neurons in the CX, we simplified the model described in Stone et al. (2017) [36] by replacing the processing layers with vectors represented by complex numbers. Thus, we transformed the compass representation of the ER4m neurons as  
+
+\[z_{\mathrm{ER4m}}(t) = \frac{1}{16}\sum_{n = 1}^{16}r_{n^{\prime}}^{n}(t)\mathrm{e}^{\mathrm{i}\phi^{n}} + \epsilon , \quad (26)\]  
+
+where \(\epsilon = \epsilon_{x} + \mathrm{i}\epsilon_{y}\sim \mathbb{U}(-\eta ,\eta)\in \mathbb{C}\) is a random number drawn from a uniform distribution, with real and imaginary components in the range \([-\eta ,\eta ]\) , and \(\eta \in [0,1]\) is the selected noise level. By default, in all our experiments \(\eta = 0.2\)  
+
+The representation of elipsoid- body protocerebral- bridge gall (EPG) neurons can then be approximated as  
+
+\[\mathrm{EPG}(t) = \frac{\mathrm{ER4m}(t) + \epsilon}{|\mathrm{ER4m}(t) + \epsilon|}. \quad (27)\]  
+
+Note that we need to normalise this complex number to ensure that we only keep the direction information, which is the estimated heading of the animal.  
+
+Multiplying the heading with the speed of the animal \((v)\) , we compute its velocity in the protocerebral- bridge fan- shaped- body nodulus (PFN) neurons,  
+
+\[\mathrm{PFN}(t) = \mathrm{EPG}(t)v(t) + \epsilon . \quad (28)\]  
+
+We use the activity pattern of the PFNs to update the working memory (M) of the CX as  
+
+\[\tau_{\mathrm{M}}\frac{\mathrm{d}\mathrm{M}}{\mathrm{d}t} = \mathrm{PFN}(t), \quad (29)\]  
+
+where \(\tau_{\mathrm{M}} = 40\) sec is the time- constant of the memory charge. Similarly, we have a goal memory ( \(\mathrm{G}\in \mathbb{C}\) ) that can be used as the migration target or the foraging site in our experiments, and by default it is zero.  
+
+The allocentric goal direction is computed by fan- shapedbody columnar (FC) neurons, which we implement as  
+
+\[\mathrm{FC2}(t) = \frac{\mathrm{G}(t) - \mathrm{M}(t)}{|\mathrm{G}(t) - \mathrm{M}(t)|}. \quad (30)\]  
+
+Note that here we also normalise with magnitude of the complex number, as this population of neurons represents the allocentric direction only and not the distance of the goal location.  
+
+Finally, the egocentric steering signal is decomposed into two axes, at \(45^{\circ}\) towards the left (L) or right (R), and it is calculated as  
+
+\[\mathrm{PFL3}_L(t) = \mathrm{FC2}(t) - \mathrm{EPG}(t)\cos (-45^{\circ})e^{-\mathrm{i}45^{\circ}} + \epsilon , \quad (31)\] \[\mathrm{PFL3}_R(t) = \mathrm{FC2}(t) - \mathrm{EPG}(t)\cos (45^{\circ})e^{\mathrm{i}45^{\circ}} + \epsilon . \quad (32)\]  
+
+## Simulations  
+
+We run a set of simulations for migrating and central- place foraging insects. The update of the heading direction and position of the animals in all the simulations happens in the same way.  
+
+Based on the above CX model, we calculate the angular velocity of the animal as  
+
+\[\frac{\mathrm{d}\theta}{\mathrm{d}t} = \frac{1}{4} (|\mathrm{PFL3}_L(t)| - |\mathrm{PFL3}_R(t)|), \quad (33)\]  
+
+where \(\theta (t)\) is the heading of the animal. Then we update the linear velocity of the animal as  
+
+\[\frac{\mathrm{d}z_{xy}}{\mathrm{d}t} = v(t)\mathrm{e}^{\mathrm{i}\theta (t)}, \quad (34)\]  
+
+which is used for updating its actual position, \(z_{xy}(t)\) . The speed in the above equation \((v)\) is set to match approximate insect speeds in the following experimental scenarios.  
+
+## Central-place foraging  
+
+For these experiments, we placed the insects in Edinburgh (55.9533°N, 3.1883°W), the United Kingdom, on August 2, 2024. We use local coordinates where the nest is at point zero, which is also the initial location of the insect. The speed of the insect was constant at \(v(t) = 0.5\mathrm{m}\sec^{- 1}\) for all \(t\) that the insect was moving, or \(v(t) = 0\mathrm{m}\sec^{- 1}\) , for those that the insect was resting. This experiment had three phases: searching for a food source, homing, and foraging to a known food site.  
+
+In the initial phase, a random route is generated and the animal is forced to follow it (see 'Defining a random foraging route'). The CX model is updated in each step using the current heading and speed, as computed by the difference between two subsequent points of the route. The final location of the route is stored as the goal vector memory. The insect then alternates the homing and foraging phases, with one hour of rest after every homing phase.  
+
+In the homing phase, the goal location is set to be the zero point (home), and we update the angular and linear velocity of the animal using equations (33) and (34). When the insect approaches its goal location, the CX model automatically creates a characteristic search pattern. In each step, we estimate the probability of the animal expressing such a pattern, by detecting four consecutive turning points (see 'Detecting a turning point'). The centroid of the four turning points approximates the centre of the search, which we interpret as the expressed goal location of the insect  
+
+\[z_{\mathrm{centroid}} = \frac{1}{4}\sum_{c = 1}^{4}z_{\mathrm{turn}}^{c}. \quad (35)\]  
+
+The foraging phase is similar to the homing, but we replace the goal location with the stored vector memory of the known food site.  
+
+## Migration  
+
+For the migration experiments, we assume that insects can travel for a maximum of \(8\mathrm{h}\) per day (only between sunrise and sunset), they need to stop every hour for rest and feeding, and that their stops last for \(1\mathrm{h}\) . The speed of the insects was set to \(v(t) = 2.5\mathrm{m}\sec^{- 1}\) , which is based on the speed of \(D\) . plexippus monarch butterflies (although this might differ in reality among insects), and the time- step used was \(\mathrm{dt} = 50\mathrm{min}\) .
+
+<--- Page Split --->
+
+The simulation for the autumn migration (from August 29 to October 31, 2024) of monarch butterflies (D. plex- . ippus) started close to the Mackinac Island \((45.7627^{\circ}\mathrm{N}\) 84.7210W), Michigan, and finished close to Michoacan (19.5532N, 101.5960W), Mexico, which is 3303.01 km. The autumn migration (from September 4 to October 1, 2024) of Bogong moths (A. infusa) started close to Montrose \((27.0000^{\circ}\mathrm{S}\) , 150.6500E), Australia, and finished close to Mount Bogong \((36.8400^{\circ}\mathrm{S}\) , 148.4600E), Australia, which is 1114.65 km. The spring migration (from February 4 to May 1, 2024) of globe skimmer dragonflies (P. flavescens) started close to Mbekenyera, \((10.0000^{\circ}\mathrm{S}\) 39.0000E), Tanzania, and finished close to Madurai \((10.0000^{\circ}\mathrm{N}\) , 78.0000E), India, which is 4859.20 km.  
+
+For the foraging experiments, we treat the world as a twodimensional plane. For migration, it is necessary to consider the earth's curvature, hence the equations for location and motion must be modified. The initial heading of the animal was calculated as  
+
+\[\theta (t_0) = \tan^{-1}\left(\frac{\sin(\Delta\lambda)\cos(\phi_e)}{\cos(\phi_s)\sin(\phi_e) - \sin(\phi_s)\cos(\phi_e)\cos(\Delta\lambda)}\right),\]  
+
+and the distance between two points on earth (haverisne distance) was calculated as  
+
+\[\rho = 2R\tan^{-1}\left(-\frac{\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_s)\cos(\phi_e)\sin^2\left(\frac{\Delta\lambda}{2}\right)}}{\sqrt{1 - \sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_s)\cos(\phi_e)\sin^2\left(\frac{\Delta\lambda}{2}\right)}}\right)\]  
+
+where \(R = 6378137\mathrm{m}\) is the radius of earth and  
+
+\[\lambda_{s} = \mathrm{start~longitude},\qquad \phi_{s} = \mathrm{start~latitude},\] \[\lambda_{e} = \mathrm{target~longitude},\qquad \phi_{e} = \mathrm{target~latitude},\] \[\Delta \lambda = \lambda_{e} - \lambda_{s},\qquad \Delta \phi = \phi_{e} - \phi_{s}.\]  
+
+where west and south directions were represented as negative angles.  
+
+The location of the animal on earth was transformed into a complex number for consistency as  
+
+\[z_{xy}(t) = \phi (t) + \mathrm{i}\lambda (t). \quad (37)\]  
+
+Thus, in the CX model, the goal location for the migrating experiments is set as  
+
+\[G(t) = \rho \mathrm{e}^{\mathrm{i}\theta (t_0)}. \quad (38)\]  
+
+We transformed the location and direction of the animal into a quaternion, \(q_{xy\theta}\) , to ease spherical computations. We used the Rotation package of the SciPy library in Python to do this (see code for details). So steering was applied as  
+
+\[q_{xy\theta}(t) = q_{xy\theta}(t - \mathrm{d}t)\left(\cos \left(\frac{1}{2}\frac{\mathrm{d}\theta}{\mathrm{d}t}\right) - \mathrm{k}\sin \left(\frac{1}{2}\frac{\mathrm{d}\theta}{\mathrm{d}t} \right)\right), \quad (39)\]  
+
+and forward movement as  
+
+\[q_{xy\theta}(t) = q_{xy\theta}(t - \mathrm{d}t)\left(\cos \left(\frac{v(t)}{2R}\right) + \mathrm{j}\sin \left(\frac{v(t)}{2R}\right)\right), \quad (40)\]  
+
+where j and k are two of the imaginary parts in the quaternion. We always update the heading before moving forward,  
+
+which composes one step in the simulation. Using the same SciPy package, we can transform the quaternion back to the coordinates of the animal on earth and its heading direction. The coordinates are then transformed into a complex number using equation (37).  
+
+Each simulation is run from the start to the end date of the migration, and the insects are allowed to travel only between sunrise and sunset.  
+
+## Defining a random foraging route  
+
+The initial search for food was created using a von Mises distribution and Newtonian physics. The starting point was set as the home location, \(z_{s} = 0\) , and the final point (food source) was \(100\mathrm{m}\) towards east, \(z_{e} = 100\) . We drew 25 000 \(\frac{5.100\mathrm{m}}{(0.5\mathrm{m}\sec^{- 1}\cdot 1\mathrm{sec})}\) bearing directions for the path from von Mises distribution as  
+
+\[\frac{\mathrm{d}\theta}{\mathrm{d}t}\sim \mathrm{VonMises}(\mu = 0,\kappa = 100), \quad (41)\]  
+
+and low- pass filtered to smooth the turns. Subsequently, the position was updated using equation (34). The generated positions were resized and rotated to end at the final point as  
+
+\[z_{xy}(t) = \frac{z_{xy}(t)}{z_{xy}(t_{e}) - z_{xy}(t_{s})} (z_{e} - z_{s}). \quad (42)\]  
+
+The positions were resampled every \(0.5\mathrm{m}\sec^{- 1}\) using linear interpolation. The final heading directions were then calculated as \(\angle \frac{dz_{xy}}{dt}\) , \(\forall t > t_0\) , where \(\mathrm{d}t = 1\) sec.  
+
+## Detecting a turning point  
+
+To detect the search pattern of an insect, we first needed to detect whether the insect changed its heading direction sufficiently. We mark a sufficient change in the heading when its difference from \(25\mathrm{m}\) before is more than \(120^{\circ}\) and no other turning point was detected in the past \(50\mathrm{m}\)  
+
+## Solar ephemeris  
+
+The sun's course during the day depends on the location of the animal on earth and the time of the year. To calculate these, we use the 'skylight' Python package, which implements the solar ephemeris suggested by the Global Monitoring Laboratory (GML) of the US National Oceanic and Atmospheric Administration (NOAA).  
+
+## Optimisation for the day length  
+
+To optimise equation (2), we needed the overall blue irradiance of the skylight \((I_{\mathrm{sky}})\) and the ground- truth day length \((T_{L})\) . Thus, we generated a ground- truth dataset of overall blue skylight irradiance and day length during a calendar year. Then we optimised the free parameters \((\tau_{L},a\) and \(\beta\) ) of equation (2), using the 'curve_fit' method of the 'SciPy' Python package. The function we optimised was the value of \(T_{L}\) over time, which was calculated using the Euler's method for discrete time with \(\mathrm{d}t = 1\mathrm{h}\) and \(T_{L}(0) = 7\mathrm{h}\) as  
+
+\[T_{L}(t) = \sum_{i = 1}^{t}T_{L}(i - 1) + \frac{1}{\tau_{L}} (a I_{\mathrm{sky}}(i) + \beta -T_{L}(i - 1)). \quad (43)\]
+
+<--- Page Split --->
+
+We calculate day length and overall irradiance using the 'skylight' Python package and the sky model described by Vévoda et al. (2022) [50]. The observer was set to be in Edinburgh (55.9533°N, 3.1883°W), from January 1 to December 31, 2024, collecting one sample per hour (8760 samples in total). For each sample, the day length \((T_{L}^{*})\) was calculated as the time between sunrise and sunset (in hours) of the respective day. For the overall skylight intensity \((I_{\mathrm{sky}})\) , we estimated irradiance by using 1000 homogeneously distributed rays from the simulated sky, we extracted the visible-blue light irradiance and calculated the average across rays.  
+
+To simulate the foraging patterns of insects, we randomly selected \(T_{F} / 12\mathrm{h}\) percentile of the 8760 homogeneous \(I_{\mathrm{sky}}\) samples of the year, where \(T_{F}\) is the foraging time. The remaining samples were set as \(I_{\mathrm{sky}} = 0\mathrm{Wm}^{- 2}\mathrm{sr}^{- 1}\) , simulating the time spent indoors. The above method produces random light exposures per day, with on- average \(T_{F}\) per day within a year. This means that we might have \(12\mathrm{h}\) of foraging spread across a day, and no foraging in another day. For the foraging experiments, \(T_{F}\in [1\mathrm{h},2\mathrm{h},4\mathrm{h},8\mathrm{h}]\) , while for migration, \(T_{F} = 12\mathrm{h}\) .  
+
+## Performance evaluation  
+
+Given the total distance travelled (C) and the straight- line distance of the insect from the goal location \((L)\) , the tortuosity of the path at a specific time (t) is  
+
+\[\varsigma (t) = \frac{C(t)}{L(t)}. \quad (44)\]  
+
+The Euclidean distance of the insect from its goal location is calculated as  
+
+\[\epsilon_{z} = |z_{xy} - z_{\mathrm{goal}}|. \quad (45)\]  
+
+In Fig. 4 and 3, all the measurements were taken when the insect was closest to its centre of search.  
+
+Similarly, the error between the estimated \((T_{L})\) and actual day length \((T_{L}^{*})\) is calculated as  
+
+\[\epsilon_{T_{L}}(t) = |T_{L}(t) - T_{L}^{*}(t)|. \quad (46)\]  
+
+## Code availability  
+
+The code that runs all the simulations and generates all the plots is publicly available through Code Ocean (identifier will be set on publication).  
+
+## References  
+
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+<--- Page Split --->
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+[17] Reinhard, N. et al. Synaptic and peptidergic connections of the Drosophila circadian clock. bioRxiv 2023.09.11.557222 (2024).[18] Saunders, D., Steel, C., Vafopoulou, X. & Lewis, R. Rhythms and clocks. In Insect clocks, chap. 1, 1–5 (Elsevier, 2002).[19] Shlizerman, E., Phillips-Portillo, J., Forger, D. & Reppert, S. Neural integration underlying a time-compensated sun compass in the migratory monarch butterfly. Cell Reports 15, 683–691 (2016).[20] Hulse, B. K. et al. A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection. eLife 10 (2021).[21] Sauman, I. et al. Connecting the navigational clock to sun compass input in monarch butterfly brain. Neuron 46, 457–467 (2005).[22] Mitchell, R., Shaverdian, S., Dacke, M. & Webb, B. A model of cue integration as vector summation in the insect brain. Proceedings of the Royal Society B 290, 20230767 (2023).[23] Gkanias, E., Risse, B., Mangan, M. & Webb, B. From skylight input to behavioural output: a computational model of the insect polarised light compass. PLoS Computational Biology 15, e1007123 (2019).[24] Massy, R. & Wotton, K. R. The efficiency of varying methods and degrees of time compensation for the solar azimuth. Biology Letters 19, 20230355 (2023).[25] Guerra, P. A., Gegear, R. J. & Reppert, S. M. A magnetic compass aids monarch butterfly migration. Nature Communications 5, 4164 (2014).[26] Saunders, D., Steel, C., Vafopoulou, X. & Lewis, R. Circadian rhythms in photoperiodism. In Insect clocks, chap. 11, 339–375 (Elsevier, 2002).[27] Liang, X., Holy, T. E. & Taghert, P. H. Circadian pacemaker neurons display cophasic rhythms in basal calcium level and in fast calcium fluctuations. Proceedings of the National Academy of Sciences 119, e2109969119 (2022).[28] Lamaze, A., Kratschmer, P., Chen, K.- F., Lowe, S. & Jepson, J. E. A wake-promoting circadian output circuit in Drosophila. Current Biology 28, 3098–3105.e3 (2018).[29] Dorkenwald, S. et al. FlyWire: online community for whole-brain connectomics. Nature Methods 19, 119–128 (2022).[30] Gkanias, E. et al. Celestial compass sensor mimics the insect eye for navigation under cloudy and occluded skies. Communications Engineering 2, 82 (2023).[31] Kind, E. et al. Synaptic targets of photoreceptors specialized to detect color and skylight polarization in Drosophila. eLife 10, e71858 (2021).  
+
+[32] Hardcastle, B. J. et al. A visual pathway for skylight polarization processing in Drosophila. eLife 10, e63225 (2021).[33] Fowler, C. M. R. The solid earth: an introduction to global geophysics (Cambridge University Press, 1990).[34] Anderson, R. C. Do dragonflies migrate across the western Indian Ocean? Journal of Tropical Ecology 25, 347–358 (2009).[35] Hedlund, J. S. U. et al. Unraveling the world's longest non-stop migration: the Indian Ocean crossing of the globe skimmer dragonfly. Frontiers in Ecology and Evolution 9, 698128 (2021).[36] Stone, T. et al. An anatomically constrained model for path integration in the bee brain. Current Biology 27, 3069–3085.e11 (2017).[37] le Moël, F., Stone, T., Lihoreau, M., Wystrach, A. & Webb, B. The central complex as a potential substrate for vector based navigation. Frontiers in Psychology 10, 690 (2019).[38] Dyer, F. C. & Gould, J. L. Honey bee orientation: a backup system for cloudy days. Science 214, 1041–1042 (1981).[39] Dyer, F. C. Memory and sun compensation by honey bees. Journal of Comparative Physiology A 160, 621–633 (1987).[40] Ishida, I. G., Sethi, S., Mohren, T. L., Abbott, L. & Maimon, G. Neuronal calcium spikes enable vector inversion in the Drosophila brain. bioRxiv 2023.11.24.568537 (2023).[41] Brown, F. A. Response to Pervasive Geophysical Factors and the Biological Clock Problem. Cold Spring Harbor Symposia on Quantitative Biology 25, 57–71 (1960).[42] Brown, F. A. Propensity for Lunar Periodicity in Hamsters and Its Significance For Biological Clock Theories. Proceedings of the Society for Experimental Biology and Medicine 120, 792–797 (1965).[43] Huber, R. & Knaden, M. Egocentric and geocentric navigation during extremely long foraging paths of desert ants. Journal of Comparative Physiology A 201, 609–616 (2015).[44] Fleischmann, P. N., Grob, R. & Rössler, W. Magnetoreception in hymenoptera: importance for navigation. Animal Cognition 1–11 (2020).[45] Fleischmann, P. N., Grob, R. & Rössler, W. Magnetosensation during re-learning walks in desert ants (Cataglyphis nodus). Journal of Comparative Physiology A 1–9 (2021).[46] Dyer, F. C. & Dickinson, J. A. Development of sun compensation by honeybees: how partially experienced bees estimate the sun's course. Proceedings of the National Academy of Sciences 91, 4471–4474 (1994).
+
+<--- Page Split --->
+
+[47] Dyer, F. C. Spatial memory and navigation by hon-eyebees on the scale of the foraging range. Journal of Experimental Biology 199, 147- 154 (1996).[48] Thakoor, S., Morookian, J., Chahl, J., Hine, B. & Zor-netzer, S. BEES: exploring Mars with bioinspired tech-nologies. Computer 37, 38- 47 (2004).[49] Wu, X. et al. Robust orientation method based on atmospheric polarization model for complex weather. IEEE Internet of Things Journal PP, 1- 1 (2022).[50] Vévoda, P., Bashford-Rogers, T., Kolářová, M. & Wilkie, A. A wide spectral range sky radiance model. Computer Graphics Forum 41, 291- 298 (2022).  
+
+## Acknowledgements  
+
+This work was financially supported by the European Union, Horizon Europe, (Project 101046790, InsectNeuro- Nano). Thanks to Stanley Heinze for the insightful discus-sion on the insects' clock inputs, and to Robert Mitchell for his helpful comments on the manuscript.  
+
+## Author contributions  
+
+Evripidis Gkanias: conceptualisation, formal analysis, in- vestigation, methodology, project administration, software, validation, visualisation, writing—original draft, writing—review & editing.  
+
+## Competing interests  
+
+The authors declare no competing interests.  
+
+## Supplementary information  
+
+"Supplementary Information.pdf"
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- 20240725supplementaryinformation.pdf- sp.pdf- nrreportingsummary.pdf
+
+<--- Page Split --->

preprint/preprint__5f28392c688a860d3ac3f03c9408d9c7770633a9419220a8b07a3f2a5219ab2c/preprint__5f28392c688a860d3ac3f03c9408d9c7770633a9419220a8b07a3f2a5219ab2c_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 940, 175]]<|/det|>
+# Spatiotemporal computations in the insect celestial compass  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 266, 240]]<|/det|>
+Evripidis Gkanias ev.gkanias@ed.ac.uk  
+
+<|ref|>text<|/ref|><|det|>[[44, 268, 655, 335]]<|/det|>
+The University of Edinburgh https://orcid.org/0000- 0003- 3343- 9039  Barbara Webb  The University of Edinburgh  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 375, 104, 393]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 413, 137, 431]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 451, 310, 470]]<|/det|>
+Posted Date: August 9th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 489, 475, 508]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4804050/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 526, 916, 570]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 588, 535, 607]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 643, 933, 687]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on March 22nd, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 57937-w.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[147, 73, 849, 96]]<|/det|>
+# Spatiotemporal computations in the insect celestial compass  
+
+<|ref|>text<|/ref|><|det|>[[323, 110, 671, 128]]<|/det|>
+Evripidis Gkanias \(^{1*}\) and Barbara Webb \(^{1}\)  
+
+<|ref|>text<|/ref|><|det|>[[234, 146, 763, 175]]<|/det|>
+\(^{1}\) School of Informatics, University of Edinburgh, Edinburgh, United Kingdom \(^{*}\) Corresponding author: ev.gkanias@gmail.com  
+
+<|ref|>sub_title<|/ref|><|det|>[[463, 216, 533, 229]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[91, 234, 905, 350]]<|/det|>
+To obtain a geocentric directional reference from a celestial compass requires compensation for the sun's movement during the day, which also depends on the time of year and the observer's latitude. We examine how insects could solve this problem, assuming they have clock neurons that represent time as a sinusoidal oscillation, and taking into account the known neuroanatomy of their celestial compass pathway. We show how this circuit could exploit trigonometric identities to perform the required spatiotemporal calculations. Our basic model assumes a constant change in sun azimuth (the 'hour angle'), which is recentered on solar noon for changing day lengths. In a more complete model, the time of year is represented by an oscillation with an annual period, and the latitude is estimated from the inclination of the geomagnetic field. We evaluate these models in simulated migration and foraging behaviours and discuss their potential for practical applications in robotics.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[36, 38, 208, 56]]<|/det|>
+## 1 Introduction  
+
+<|ref|>text<|/ref|><|det|>[[35, 71, 490, 384]]<|/det|>
+2 Using the sun (or equivalent celestial cues) as a compass 3 requires a compensation mechanism for its movement dur- 4 ing the day. Taking inspiration from insects, engineers have 5 implemented various forms of celestial compass for use in 6 robot navigation. Typically the robot's deployment has 7 been short enough (less than an hour) for the sun's move- 8 ment to be neglected [1,2]. For longer deployment, system 9 clocks, a global positioning system (GPS) and an accurate 10 model of the solar ephemeris can be used in an algorithm 11 that tracks the sun and uses its position to time- compensate 12 the compass [3]. However, the key use cases for a robot ce- 13 lestial compass would be situations where GPS is unavail- 14 able (such as remote locations or when satellite systems 15 have been compromised). Similarly, insects use an alterna- 16 tive to GPS. While it is implausible to suppose that they 17 have either an absolute time reference or a precise look- up 18 table for the solar ephemeris, they do perform time com- 19 pensation when navigating by celestial cues [4,5]. Here, we 20 propose plausible neural mechanisms by which insects could 21 use their internal sense of time to predict the sun's position, 22 transforming the measured azimuth of the sun into a geo- 23 centric heading reference.  
+
+<|ref|>text<|/ref|><|det|>[[35, 387, 490, 656]]<|/det|>
+Internal clocks (processes that track time or external rhythms) are widespread across biological systems. Insects are known to have clock input to multiple circuits [6, 7]. More specifically, clock inputs from the antennae [8- 12] or the accessory medulla (aMe) of the optic lobes [13- 17] (Fig. 1a) affect the celestial compass function. The time- less (TIM) protein is the main clock signal in the brain, and along with the period (PER) protein, it is involved in the encoding of time in insects [18]. Cryptochrome (CRY) proteins are also involved, acting as photoreceptor inputs to the clock mechanism that allows tuning of the PER and TIM mRNA oscillations (also of CRY2 oscillations in monarch butterflies) to the light- darkness rhythms [9- 11]. As Fig. 1b shows, the oscillation phase of CRY2 proteins differ by six hours from TIM's, suggesting that these two signals might respectively encode the sine and cosine function of the same angle [19] (Fig. 1c), which changes with constant rate of \(15^{\circ}\) per hour and thus (like the hour hand of a clock) completes a circle every day (Fig. 1d).  
+
+<|ref|>text<|/ref|><|det|>[[35, 658, 490, 899]]<|/det|>
+Inside the insect brain time is represented by clock neurons [6, 7] whose activity depends on the mRNA levels of the above proteins (although their exact relationship is unclear). Similarly to the protein levels, clock neuron activity expresses an endogenous oscillation with periods that can vary from daily to annual [18]. Roughly half of the clock neurons in the insect brain also rely on the blue light sensitive CRY [17]. The only clock neurons that join the celestial compass pathway of fruit flies (Drosophila melanogaster) are the DN1pB [20], which intersect the path before it reaches the navigation- specific circuits of the central complex (CX) [14, 21]. The current assumption is that these neurons allow the celestial compass to compensate for the moving sun by predicting the sun's course during the day [20]. However, the mechanism that allows this compensation and transforms the retinotopic position of the sun into a geocentric compass is still unknown.  
+
+<|ref|>text<|/ref|><|det|>[[55, 902, 490, 916], [506, 40, 960, 383]]<|/det|>
+Several mechanisms have been proposed to explain the compensation of a celestial compass for the sun's movement. Some of them do not require a clock and suggest the calibration of the celestial with other compasses [22] or use the sun's elevation to estimate its speed of motion [23]. Others conceptually examine the effects of mappings from different forms of clock input to the estimated sun's position, but without discussing possible biological implementations [24]. One mechanism examined in Massy et al. (2023) [24] is time- averaging, which has been previously linked to properties of clock proteins found in the antennas of butterflies [19]. As already mentioned, the levels of these proteins express a sinusoidal pattern during the day, representing an arrow that encodes time. The proposed mechanism in Schlierman et al. (2016) [19] uses this signal to estimate the sun's movement as a constant speed of \(15^{\circ}\) per hour (the speed at which the earth rotates around its axis) and assumes that the clock resets at sunrise. However, this produces a directional drift in the compass reference as the length of the day (and hence the time of sunrise) changes. A clock synchronised to solar noon would provide a stable reference point, but it is unclear how this could be achieved. Furthermore, depending on the time of year or location on earth, the observed movement of the sun can deviate significantly from a constant speed (Fig. 1e).   
+
+<|ref|>text<|/ref|><|det|>[[506, 385, 960, 696]]<|/det|>
+In this paper, we present a neurally plausible mechanism by which a clock signal carried by DN1pB neurons could be used to correct the insect's celestial compass. We propose two alternative models to generate the encoded signal of DN1pB clock neurons, using information available to insects: an hour- angle and a complete solar- azimuth tracker. Our hour- angle model uses the time of the day to accurately predict the earth's rotation around its spin axis and relative to the sun, including adaptation for changing day length. The complete model additionally uses the time of the year and the geomagnetic inclination (detectable by some migrating insects [25]) to calculate the exact course of the sun during the day. Our results suggest that the hour- angle model is sufficient to support the behaviour of migrating and central- place foraging insects. However, the complete model can compensate for the change from clockwise (CW) to counter- clockwise (CCW) movement of the sun in the northern and southern hemispheres of earth respectively, and hence is needed for migrating insects that cross the equator. We suggest that such a model provides a powerful localisation tool independent of GPS signal and could be used on any planet.  
+
+<|ref|>sub_title<|/ref|><|det|>[[506, 728, 593, 746]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[506, 761, 725, 778]]<|/det|>
+## The hour-angle model  
+
+<|ref|>text<|/ref|><|det|>[[506, 789, 960, 916]]<|/det|>
+The hour angle ( \(\omega\) ) describes the earth's rotation around its axis relative to the sun as a constant rate of \(15^{\circ}\) per hour. By convention, the hour angle is the longitudinal difference between the observer and the subsolar point (location on earth where the sun is at its zenith). It is zero when the sun is closest to the observer's zenith (solar noon), at which point the sun azimuth indicates south (assuming the observer is in the northern hemisphere). If the time of day is measured from sunrise (zeitgeber time, \(t_z = t - t_{\mathrm{sr}}\) , from
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[65, 40, 940, 408]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[57, 418, 941, 690]]<|/det|>
+<center>Fig. 1: A model compensating for the sun's movement in the insect's celestial compass. (a) Cryptochrome (CRY), timeless (TIM) and period (PER) proteins are responsible for encoding time in the insect brain. The mRNA level of CRY1 is increased in the butterfly antennas (and eyes in several insects) when they detect blue light, synchronising internal clocks to the light-and-darkness cycle. (b) The mRNA levels of CRY2 (solid line) and TIM (dashed line) proteins increase and decrease with a different phase during the 24-hour light-and-darkness cycle in monarch butterflies [9, 10]. Data replotted from [10]. (c) The mRNA levels of CRY2 and TIM proteins modelled as cosine and sine functions of zeitgeber time encode the hour angle \((\omega)\) . (d) The hour angle, encoded as in (c), is an arrow that rotates clockwise (CW) and completes a full circle daily. The arrow should point east during sunrise, south at noon and west during sunset (assuming twelve hours day and twelve hours night), roughly predicting the solar azimuth. (e) The hour-angle predicts a constant change in the solar azimuth during the day (blue line), but the actual azimuth deviates depending on location and time of year (orange and red lines). The orange lines illustrate the sun's courses in August (dashed) and October (solid) at Michigan \((\sim 46^{\circ}\mathrm{N})\) . The red lines show the respective sun's courses in Mexico \((\sim 20^{\circ}\mathrm{N})\) . Shaded areas highlight the difference in the sun's course over two months at the same location. (f) Schematic of the connections between neurons in the brain of Drosophila melanogaster. On the left half, we show the first and second-order inputs to the DN1pB (clock) neurons. We show the celestial compass pathway on the right and where the DN1pB neurons join it. (g) The proposed role of the two types of TuBu1 neurons. The spatial encoding of cosine and sine of the solar azimuth across their population is key to the time-compensation mechanism. (h) By combining the activity of the TuBu1 and DN1pB with multiplications and additions, we implement a trigonometric identity and transform the encoding of the solar azimuth into a pattern of activity indicating north. </center>  
+
+<|ref|>text<|/ref|><|det|>[[30, 712, 468, 728]]<|/det|>
+the German for 'time- giver'), the hour angle is given by  
+
+<|ref|>equation<|/ref|><|det|>[[195, 736, 485, 764]]<|/det|>
+\[\omega (t) = (t_z - \frac{T_L}{2})15^\circ , \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[57, 774, 491, 845]]<|/det|>
+where \(T_{L} = t_{\mathrm{ss}} - t_{\mathrm{sr}}\) is the day length, computed as the difference between the sunrise \((t_{\mathrm{sr}})\) and sunset \((t_{\mathrm{ss}})\) times in hours. Supplementary Text S1 describes a possible neural implementation of equation (1), given the neural encoding of the zeitgeber time and day length separately.  
+
+<|ref|>text<|/ref|><|det|>[[57, 845, 491, 916]]<|/det|>
+Given their six- hour phase difference (equivalent to \(90^{\circ}\) hour- angle difference; see Fig. 1b), TIM and CRY2 proteins could encode the (negative) sine and cosine of the hour angle as its east- most \((\omega_{\mathrm{E}})\) and north- most \((\omega_{\mathrm{N}})\) components (Fig. 1c). The period of these sinusoids is determined by the  
+
+<|ref|>text<|/ref|><|det|>[[507, 713, 940, 854]]<|/det|>
+temporal difference between two consecutive sunrises [26]. Their phase is determined by the day length \((T_{L})\) , which ensures that the sinusoids are centred at the solar noon (see Supplementary Fig. S1). Note that both (east- most and north- most) components are necessary to describe the hour angle. By combining them, we can create an arrow that rotates with time like the hour hand of a clock (Fig. 1d, blue arrow). However, note that the hour- angle model approximates the solar azimuth and that a complete compensation mechanism should consider more factors (Fig. 1e).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[60, 40, 319, 58]]<|/det|>
+## Estimating the day length  
+
+<|ref|>text<|/ref|><|det|>[[60, 64, 491, 265]]<|/det|>
+The blue- light sensitive CRY1 proteins detected in Danaus plexippus monarch butterflies (equivalent to the CRY proteins of \(D\) melanogaster fruit flies) synchronise the clocks to the light- dark rhythm [9,10,17]. We suggest that two kinds of synchronisation co- occur. The first synchronises the zeitgeber time \((t_z)\) to the sunrise, while the second shifts the hour angle relative to \(t_z\) , as described in equation (1) so that it is zero at the solar noon. Thus we assume that the zeitgeber time is always zero at sunrise and increases linearly during the day. However, the required shift relative to solar noon depends on the day length \((T_L)\) , which we assume is a continuously updated estimate as described in the following. A consequence is that \(T_L\) potentially changes during the day, so the hour- angle might not change linearly.  
+
+<|ref|>text<|/ref|><|det|>[[60, 264, 490, 320]]<|/det|>
+We propose that the day length \((T_L)\) can be calculated as a function of CRY1, such that an insect could estimate the day length simply from the changing level of skylight irradiance,  
+
+<|ref|>equation<|/ref|><|det|>[[170, 328, 488, 355]]<|/det|>
+\[\tau_{L}\frac{\mathrm{d}T_{L}}{\mathrm{d}t} = \mathrm{CRY1}(t) + \beta -T_{L}, \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[60, 362, 490, 503]]<|/det|>
+where \(\tau_{L}\) is a time- constant, \(\beta\) is a constant input, and \(\mathrm{CRY1}(t) = aI_{\mathrm{sky}}(t)\) is the protein level of CRY1, where \(a\) is a scaling factor (gain) and \(I_{\mathrm{sky}}\) is the overall blue irradiance in the sky. The parameters \(a\) , \(\beta\) and \(\tau_{L}\) were optimised to fit equation (2) to the actual day length (values summarised in Supplementary Table S1). Supplementary Fig. S2a demonstrates the accuracy of this fit, where we simulate the estimated \(T_{L}\) and plot it over the actual day length, assuming continuous light exposure during the day (for migratory insects).  
+
+<|ref|>text<|/ref|><|det|>[[60, 504, 490, 916]]<|/det|>
+As central- place foraging insects are exposed to light at varying times (depending on their foraging pattern), we tested how interrupted light exposure might affect the estimates of \(T_{L}\) (note this might also affect their synchronisation of \(t_z\) , but we do not consider that here). We simulated species with different average foraging durations, from one to eight hours per day; foraging each day could vary around this average and occur anytime from sunrise to sunset. Parameters needed to be optimised to fit the different average foraging durations (summarised in Supplementary Table S1): shorter foraging durations require longer time constants \((\tau_{L})\) and higher gains ( \(a\) ) to transform the sky irradiance into CRY1. Using these optimised parameters, central- place foraging insects can estimate the day length with comparable error to migrating insects, with error increasing for shorter foraging times (Supplementary Fig. S2b, grey boxes). This shows that the higher level of skylight irradiance measured (for the same average exposure time) during the summer (compared to winter) suffices to estimate the day length for central- place foragers. Having the same foraging duration and a consistent time window every day would result in smoother estimates. The black lines in Supplementary Fig. S2 suggest that adding processing units in series can smooth the estimates further and make the hour- angle change at a nearly constant rate (see also Supplementary Text S2). However, this also introduces a delayed response, which translates into a constant shift in the phase of the encoded sinusoid. This lag increases the error but is predictable and could be compensated for by  
+
+<|ref|>text<|/ref|><|det|>[[506, 41, 937, 84]]<|/det|>
+following the same principle as we describe in the next section for the compass, using a biological implementation of trigonometric identities.  
+
+<|ref|>sub_title<|/ref|><|det|>[[506, 108, 841, 124]]<|/det|>
+## Integration with compass neurons  
+
+<|ref|>text<|/ref|><|det|>[[506, 133, 937, 488]]<|/det|>
+Dorsal neurons (DNs) and lateral neurons (LNs) are the clock neurons in the brain of \(D\) melanogaster [17,27]. The calcium level of these neurons has an overall increase and decrease during the day. This can be described by a sinusoidal function whose phase varies among the neurons and looks similar to protein levels in Fig. 1b. A pair of DN neurons (DN1pB) target the TuBu1 neurons and provide clock information to the celestial compass pathway [6,7,28] in each hemisphere [17,20]. We hypothesise that the calcium level of DN1pB neurons predicts the solar azimuth \((\alpha)\) and corresponds to the east- most \((\omega_{E})\) and north- most \((\omega_{N})\) components of the hour angle. There are other clock neurons in. nerving the ellipsoid body (EB) and fan- shape body (FB) of the CX, but we would argue that time compensation should occur before the celestial compass integrates with other compasses (such as wind or visual landmarks) in the EPG neurons of the EB. The DN1pB neurons are, so far, the only reported neurons to target the celestial compass pathway upstream of the EB in \(D\) melanogaster [17]. Although they receive limited direct input from sensory- driven clocks in the antennae or retina (see Fig. 1f and Supplementary Table S2, generated using data from the FlyWire database [29]), they receive input from these via multiple interneurons, which might have a role in shaping their response into a smooth sinusoid (Supplementary Text S2).  
+
+<|ref|>text<|/ref|><|det|>[[506, 490, 937, 730]]<|/det|>
+Previous computational modelling studies provide a good approximation of how the TuBu1 neurons can encode the solar azimuth [23,30]. In \(D\) melanogaster, polarised light is detected from the dorsal rim area (DRA) and travels to the anterior optic tubercle (AOTu) through the retina and the medulla (Me) (Fig. 1f) [31,32]. Colour information is detected from the remaining dorsal area in the eye. It travels through the dorsal retina and Me to AOTu and the TuBu1 neurons, where it probably integrates with polarisation information and estimates the retinotopic solar azimuth \((\alpha '\) ; which is in egocentric coordinates). As described above, TuBu1 neurons are also terminals for the DN1pB neurons [6,7,20,28]. Thus, we assume that the time- based solar azimuth prediction is combined with the retinotopic solar azimuth estimate at the axons of TuBu1 neurons, transforming it into a geocentric compass in the anterior bulb (Bu \(a\) ).  
+
+<|ref|>text<|/ref|><|det|>[[506, 732, 937, 916]]<|/det|>
+There are two types of TuBu1 neurons: TuBu1a, which targets ER4m ring neurons, and TuBu1b, which targets both ER4m and ER5 neurons (see Supplementary Table S3). Calcium recordings of TuBu1 neurons suggest that the two hemispheres independently encode the (retinotopic) solar azimuth in a spatial sinusoidal pattern of activity [32]. We speculate that the TuBu1a and TuBu1b populations express a \(90^{\circ}\) shift in the represented direction of the sun (see Fig. 1g), which we will see is essential for how we implement the time compensation. We also assume that DN1pB \(t_{2}\) gets the TuBu1a population and the DN1pB \(N\) targets the TuBu1b population (Fig. 1h). Finally, the responses of the TuBu1 populations are added together to encode the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[30, 44, 490, 58]]<|/det|>
+animal's heading in the responses of the ER4m population.  
+
+<|ref|>text<|/ref|><|det|>[[30, 59, 490, 101]]<|/det|>
+The above process implements a crucial trigonometric identity that transforms the solar azimuth into a geocentric compass in the ring neurons, described as  
+
+<|ref|>equation<|/ref|><|det|>[[75, 108, 488, 144]]<|/det|>
+\[\begin{array}{rl} & {\mathrm{ER4m}^n = \sin (\alpha)\cdot \sin (\alpha ' - \phi^n) + \cos (\alpha)\cdot \cos (\alpha ' - \phi^n)}\\ & {\qquad = \cos (\alpha -\alpha ' + \phi^n),} \end{array} \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[30, 151, 490, 292]]<|/det|>
+where \(\alpha = \alpha (t) = \omega (t)\) is the prediction of solar azimuth based on time (DN1pB neurons), \(\alpha ' - \phi^n\) is the estimation of the retinotopic solar azimuth (TuBu1 neurons), and \(\phi^n\) is the retinotopic direction of a TuBu1 neuron. The above equation suggests that ER4m ring neurons encode the angular difference between the observed (celestial compass) and predicted (clock neurons) solar azimuth, indicating north. Note that although we use the north as a reference point in our model, the same principles should apply to any arbitrary direction.  
+
+<|ref|>sub_title<|/ref|><|det|>[[30, 311, 347, 327]]<|/det|>
+## Complete time compensation  
+
+<|ref|>text<|/ref|><|det|>[[30, 335, 490, 688]]<|/det|>
+The earth's spin axis is not aligned with the earth's orbit around the sun. This misalignment causes seasonal shifts in day length and the observed course of the sun across the sky. (Fig. 1e). To accurately compute the sun's location at a given time, we need to know the longitudes and latitudes of both the subsolar point and the observer [3]. The latitude of the subsolar point is also known as the solar declination ( \(\delta\) ; Fig. 2a), which is maximum at \(23.45^{\circ}\) (the angle of earth's spin axis from a vertical axis) in June, minimum at \(- 23.45^{\circ}\) in December, and zero in March and September. This describes an oscillation with an annual period, which can be further decomposed into two sinusoidal functions (Fig. 2b). We assume that a different pair of clock neurons encode these two components. The first component ( \(\delta_N\) ) raises the hour- angle oscillation during the summer and lowers it during the winter, emulating the longer or shorter days of the year (Fig. 2c) in the northern hemisphere (the relationships would be reversed for the southern hemisphere). Because the solar declination is an angle, we need a second component ( \(\delta_Q\) ) to ensure balanced and stable trigonometric computations. Note that solar declination differs from day length ( \(T_L\) ), as the latter also depends on the geometric latitude of the observer. Interestingly, knowing any two of the day length, solar declination and observer's latitude, we can estimate the third one (see Supplementary Text S3).  
+
+<|ref|>text<|/ref|><|det|>[[30, 689, 490, 916]]<|/det|>
+Another way we can estimate the geometric latitude of the observer is by measuring the geomagnetic inclination (or magnetic dip, \(\mu\) ), which is the vertical component of the earth's magnetic field and (approximately) depends on the geometric latitude ( \(\phi\) ) at that point (Fig. 2d) [33]. Monarch butterflies respond to magnetic inclination [25] and we suggest that at least some insects can estimate their latitude by detecting the inclination of the local geomagnetic field. We assume that another pair of neurons encode the sine ( \(\phi_N\) ) and cosine ( \(\phi_Q\) ) of the insect's latitude as a function of magnetic inclination (Fig. 2e). Note that \(\phi_N\) is positive in the northern hemisphere and negative in the southern. Thus, we hypothesise that \(\phi_N\) is multiplied with the north- most component of hour- angle oscillation ( \(\omega_N\) ) to flip it when the insect is in the southern hemisphere and transform its rotation from CW to CCW (Fig. 2f). This property becomes crucial for insects that live close to the equator [34, 35], whereas it might be less important for insects which remain in one hemisphere, and \(\phi_N\) could be replaced by a constant value for insects whose latitude does not change much. The role of the other term ( \(\phi_Q\) ) is to ensure stable trigonometric computations. Our hypothesis on the use of geomagnetic inclination fits well with data showing that both the CRY2 proteins and magnetic inclination are regulated by blue light detected at the antennas of monarch butterflies [25]. However, the pathway that transfers this information to the central brain is yet to be explored, and the existence of this sense in other insects is yet to be established.  
+
+<|ref|>text<|/ref|><|det|>[[506, 43, 937, 225]]<|/det|>
+crucial for insects that live close to the equator [34, 35], whereas it might be less important for insects which remain in one hemisphere, and \(\phi_N\) could be replaced by a constant value for insects whose latitude does not change much. The role of the other term ( \(\phi_Q\) ) is to ensure stable trigonometric computations. Our hypothesis on the use of geomagnetic inclination fits well with data showing that both the CRY2 proteins and magnetic inclination are regulated by blue light detected at the antennas of monarch butterflies [25]. However, the pathway that transfers this information to the central brain is yet to be explored, and the existence of this sense in other insects is yet to be established.  
+
+<|ref|>text<|/ref|><|det|>[[506, 228, 937, 469]]<|/det|>
+The above information is sufficient to accurately estimate the expected solar azimuth at a specific location and time [3]. Again, we assume that a pair of neurons decompose this information into the east- most ( \(\alpha_E\) , negative sine) and north- most ( \(\alpha_N\) , negative cosine) components of an arrow that points towards the solar azimuth ( \(\alpha\) ; Fig. 1d and e). We suggest that these neurons could be the pair of DN1pB, which now respond to the solar azimuth (as opposed to hour- angle) and achieve complete compensation for the sun's movement. A possible circuit that implements the above function is illustrated in Fig. 2g, while the values of \(\alpha_N\) and \(\alpha_E\) for different combinations of magnetic inclination, solar declination and hour angles are plotted in Supplementary Fig. S3. We refer to this as the 'complete model' of the sun's movement and compare it to the 'hour- angle model' in the following simulations of insect navigation.  
+
+<|ref|>sub_title<|/ref|><|det|>[[506, 490, 844, 507]]<|/det|>
+## Central-place foraging experiment  
+
+<|ref|>text<|/ref|><|det|>[[506, 516, 937, 773]]<|/det|>
+To demonstrate the effectiveness of our time- compensated compass, we simulated a foraging experiment for insects such as bees and ants who forage throughout the day to a familiar food site but can take long breaks between foraging trips (spent in their home's darkness). The simulated insects initially perform a random walk searching for food just after sunrise, followed by single return trips to the food location (stored as a vector memory) every hour until sunset. We then tested how an insect using CX navigation would perform in this task with different model compass inputs: (a) without time compensation, (b) using the hour- angle or (c) the complete model. The CX model we used is a modified version of a well- established path integration model [36], which also incorporates vector memories of salient locations [37]. We then use our proposed compass model as the input heading of the CX with \(20\%\) noise. Figure 3a- c show example foraging routes produced by the three models during a single day.  
+
+<|ref|>text<|/ref|><|det|>[[506, 775, 937, 916]]<|/det|>
+Overall, no matter which compass model the insect used, it could return home quite accurately during individual foraging excursions (Fig. 3d, green boxes). The sun's movement during a short excursion (a few minutes in this simulation) is not enough to cause noticeable errors in the continuous integration of the home vector. However, longer foraging durations increase the error without time compensation, and also affect the performance of the hour- angle model significantly (as opposed to the complete model), as its error increases linearly with time (Fig. 3e). More signif
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[60, 37, 936, 285]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[55, 298, 941, 469]]<|/det|>
+<center>Fig. 2: Complete model of the sun's movement. (a) The solar declination is the earth's latitude where the sun is exactly at the zenith, which is equivalent to the angle of the line connecting the centres of the earth and sun from earth's equator. (b) The solar declination is represented by a sinusoidal function of time with an annual period. This sinusoidal can be represented as a two-dimensional direction by decomposing it into two sinusoids. (c) The solar declination moves the hour angle oscillation up or down based on the season. (d) The geomagnetic inclination is the angle between the geomagnetic field and the earth's surface. (e) The geomagnetic inclination is a monotonic function of the geometric latitude, which can also be decomposed into two sinusoidal functions that represent a two-dimensional direction. (f) The amplitude of the hour-angle oscillation is proportional to the observer's latitude and flips in the southern hemisphere, allowing for both clockwise (CW) and counter-clockwise (CCW) movements of the sun. (g) The full solar azimuth model. The proposed circuit combines information from the geomagnetic inclination and daily and annual clocks, to accurately estimate the sun's course during the day. This estimate is a vector with a north-most \((\alpha_{N})\) and east-most \((\alpha_{E})\) component. </center>  
+
+<|ref|>image<|/ref|><|det|>[[58, 476, 936, 643]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[55, 656, 941, 756]]<|/det|>
+<center>Fig. 3: Computer simulated central-place foraging routes. At dawn, the simulated insect searches for food and stores the food location after finding it. It then returns to its nest. It tries to repeat foraging to the food location every hour until sunset, using (a) a model without time compensation, (b) the hour-angle model, or (c) our complete model. (d) Euclidean distance (m) of the search centroid from the feeder (red) or the nest (green) using the three models. The sample size in each box is \(n = 9\) . (e) Homing error as a function of foraging duration (normalised for foraging distance). Solid lines show the mean error when using the no-compensation (grey), the hour-angle (blue) or the complete model (yellow). Shaded areas are the 95% confidence interval (CI). In all the results there is 20% added compass noise. </center>  
+
+<|ref|>text<|/ref|><|det|>[[55, 780, 491, 908]]<|/det|>
+icantly, insects without time compensation could not accurately revisit a known food site (Fig. 3a). This is because the food- site location was stored in the memory relative to the sun's position, and as the sun moves so does this location. Either form of time compensation seems sufficient to navigate back and forth to the food site with relatively good accuracy (Fig. 3b and c). Despite some advantage of the complete model over the other two, it seems likely that foragers using the hour- angle (or even the no- compensation)  
+
+<|ref|>text<|/ref|><|det|>[[504, 780, 939, 838]]<|/det|>
+model combined with other cues, such as visual place recognition in the vicinity of the food site, could produce indistinguishable behaviour (for example, see experiments with honeybees Apis mellifera and A. cerana [38,39]).  
+
+<|ref|>text<|/ref|><|det|>[[504, 845, 939, 916]]<|/det|>
+In the above experiments, we used the actual day length for equation (1) (orange lines in Supplementary Fig. S2). Supplementary Fig. S4 shows the results when, instead, we use the smoothed day length estimates (black lines in Supplementary Fig. S2), time- shifted to overlay their theo
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[60, 40, 936, 500]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[58, 509, 940, 624]]<|/det|>
+<center>Fig. 4: Computer simulations of insect migrations. (a, b) Simulation of a monarch butterfly (Danaus plexippus) during its autumn migration, using the hour-angle model (blue) and complete model (yellow). Haversine distance: \(3303.01\mathrm{km}\) . The Red dashed arrow illustrates the straight line between the start and goal locations. (c, d) Similar simulation for the Bogong moth (Agrotis infusa) during its autumn migration. Haversine distance: \(1114.65\mathrm{km}\) . (e, f, g) Simulation of a globe skimmer dragonfly (Pantal flavescens) during its spring migration. Haversine distance: \(4859.20\mathrm{km}\) . (h) Tortuosity of the migrating route for each model. (i) The Euclidean distance (km) of the simulated insect from the target location at the end of its migration for each model. In (h) and (i) the sample size is \(n = 10\) . In all the results there is \(20\%\) added compass noise. </center>  
+
+<|ref|>text<|/ref|><|det|>[[58, 648, 490, 690]]<|/det|>
+retical values. Although this introduced some extra noise to the system, the foraging performance was not dramatically affected.  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 708, 275, 725]]<|/det|>
+## Migration experiment  
+
+<|ref|>text<|/ref|><|det|>[[58, 732, 490, 914]]<|/det|>
+Most foraging insects remain at a similar latitude during their lifetime so it might be expected that the hour- angle model (which adjusts for day length but not solar declination and latitude) would be sufficient for successful behaviour. By contrast, several species of migrating insects travel, within a relatively short time, through multiple latitudes, so it might be expected that they require the complete time- compensation model for their compass system. We therefore simulated migration experiments for three different insect species: the monarch butterfly \(D\) . plexippus, the Bogong moth Agrotis infusa, and globe skimmer dragonfly Pantal flavescens. We selected these species to demonstrate migration in different characteristic locations on earth  
+
+<|ref|>text<|/ref|><|det|>[[506, 648, 938, 705]]<|/det|>
+relative to its equator: above ( \(D\) . plexippus), below ( \(A\) . infusa), or across ( \(P\) . flavescens). This way we test our model in locations where the sun moves CW, CCW, or switches its moving pattern during the migration.  
+
+<|ref|>text<|/ref|><|det|>[[506, 711, 938, 853]]<|/det|>
+In the CX model, we replaced its memory component with fixed goal coordinates on earth. We modified our simulation for the migration task, taking into account the curvature of the earth's surface. We assumed that the daily travel capacity of insects is eight hours (at \(2.5\mathrm{msec}^{- 1}\) , based on the speed of \(D\) . plexippus), and they need one- hour breaks every hour for feeding or rest. Here, we compared only the hour- angle and complete models, as without time compensation the simulated insects would move in circles around the starting point.  
+
+<|ref|>text<|/ref|><|det|>[[506, 859, 938, 915]]<|/det|>
+Figure 4a- b illustrate the southward autumn migration of monarch butterflies using the two models (blue: hour- angle, yellow: complete), which starts at the end of August from Mackinac Island (Michigan) and ends at the end
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 42, 490, 198]]<|/det|>
+of October in Michoacan (Mexico). Figure 4c-d shows the simulated routes of Bogong moths during their autumn migration from Montrose (Australia) south to Mount Bogong. Although Bogong moths are nocturnal animals and use the night sky to navigate (following the Milky Way instead of the sun), we treat them as diurnal animals to demonstrate navigation in the southern hemisphere. Finally, Figure 4e-g shows the simulated routes of the globe skimmer dragonflies during their spring migration from Mbekenyara (Tanzania) to Madirai (India), which is the world's longest transoceanic migration (approximately \(4859\mathrm{km}\) ).  
+
+<|ref|>text<|/ref|><|det|>[[57, 200, 490, 411]]<|/det|>
+Overall, the complete model resulted in straighter migrating routes than the hour- angle model (Fig. 4h). However, the deviations induced by the less accurate hour- angle model largely cancel out during the day. As a result, in the single- hemisphere migrations (monarch butterflies and Bogong moths) both models could bring the animals close to their destinations (Fig. 4i). This suggests that the hour- angle model might be sufficient for migrating insects that do not cross the equator. Note that the simulated moths end up closer to the goal coordinates than the simulated butterflies. This is because their migration is shorter so the accumulated heading noise has a smaller overall effect. The hour- angle model fails for the dragonflies crossing the equator (Fig. 4g), which suggests that the complete model might be necessary for this type of migration.  
+
+<|ref|>text<|/ref|><|det|>[[57, 412, 490, 540]]<|/det|>
+As before, these results use the actual day length. Substituting the estimated day length, the migrations became slightly more tortuous and less accurate, especially at the start of the migration route (Supplementary Fig. S5). The largest error in the day length estimates seems to come from the initialisation of \(T_{L}\) , which takes some time to converge to the correct value. Although this could be avoided by optimising the initial value as we did with the other parameters, insects might encounter a similar problem.  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 560, 183, 578]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[57, 590, 490, 917]]<|/det|>
+Insects have a celestial compass that combines the detection of the sun's position and correction for its movement during the day (time- compensation) to obtain a consistent geocentric heading estimate. We suggest that this correction relies on standard trigonometric principles for spatial and temporal processing, and show a plausible neural mechanism by which the required trigonometry could be implemented. We compare the efficacy of two alternative models for time compensation: one that makes an approximate correction by assuming a constant change of sun angle with time (the hour- angle model); and one that makes a complete correction for the effects of latitude and declination on the apparent course of the sun relative to an observer in a particular location and time of year. In both cases, the clock is synchronised to solar noon by being reset at sunrise to a value that depends on a running estimate of day length based on skylight irradiance. We test these in central- place foraging and migrating scenarios, showing the necessity for the complete model only arises in tasks that require crossing the equator. Both models use information that is in principle available to insects and predict identifiable connectivity and activity patterns in the brain that can be explored anatomically and physiologically.  
+
+<|ref|>text<|/ref|><|det|>[[508, 42, 941, 270]]<|/det|>
+A striking property of the neural mechanism we propose is that it exploits the fact that both space and time are encoded in the insect brain as sinusoidal activity patterns. For example, solar azimuth information represented by the TuBu1 neurons has a characteristic sinusoidal pattern across a population of neurons [31]. Inputs from other neurons (such as TuTu and MeMe) maintain the sinusoid and keep it consistent across the two hemispheres. On the other hand, clock neurons (such as DN1pB) are characterised by periodic activity oscillations, usually described as temporal sinusoidal patterns. This characteristic of the activity and connectivity patterns in the insect brain greatly facilitates trigonometric operations to perform geometric calculations, such as calculating the difference between two angles (combining space and time information) as we describe in equation (3).  
+
+<|ref|>text<|/ref|><|det|>[[508, 272, 941, 598]]<|/det|>
+Our model predicts that the influence of clock neurons on their downstream targets (at least for this circuit) is multiplicative, which is necessary to allow the combination of sines and cosines. This could be tested by looking into specific properties in the responses of clock neurons. Traditionally, time information in the insect brain is described in terms of gene expression (tim, per, cry) or the mRNA level of proteins (like TIM, PER, CRY1, CRY2, and vrille (VRI) [17]). In a typical clock protein, the mRNA level increases and decreases once per day, but this can vary from tidal to annual periods [18]. With the development of optogenetic tools for D. melanogaster, the calcium levels of clock neurons have been observed to follow the same pattern as the proteins, but only daily periods have been described so far. Although calcium is often interpreted as a firing- rate signal, it would be useful to clarify how this changing calcium level in clock neurons translates into the membrane potential (for example, following work on PFNA neurons [40]), information which is currently missing from the literature. This is important to understand the potential mechanisms by which clock neurons affect their downstream targets, which could involve neurotransmitter, neuromodulator or neuropeptide release.  
+
+<|ref|>text<|/ref|><|det|>[[508, 601, 941, 886]]<|/det|>
+A complete map of clock neurons in fruit flies suggests a circuit architecture where DNs and LNs collect all temporal information and then distribute it to other areas that are responsible for behaviour [17] (Fig. 5). Sensory clocks (from the eyes, ocelli and antennas) tune neurons in the aMe and other neuropils to synchronise rhythms to external light cues by expressing the CRY protein. In our model, we have not mapped the processes we assume to occur before the DNs directly to these anatomical pathways, but we suggest it should be possible to find within this upstream circuit clock neurons (or proteins) that (1) calculate the day length, (2) smooth the estimations, (3) calculate the hourangle and (4) solar declination based on the day and year length respectively, (5) measure the magnetic inclination, and (6) use it to calculate the insect's latitude. Thus, our model suggests that the different clock neurons are tuned to track 'subtle geophysical forces' [41, 42]. More specifically (and testably) we propose that DN1pB neurons combine this information to encode a prediction of the solar azimuth \((\alpha)\) .  
+
+<|ref|>text<|/ref|><|det|>[[508, 889, 941, 916]]<|/det|>
+However, our simulations of insect navigation suggest that time compensation of their celestial compass may not
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[80, 40, 490, 336]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[58, 347, 491, 759]]<|/det|>
+<center>Fig. 5: Clock neurons in the insect brain. Light is detected by the photoreceptors of the compound eyes, ocelli and antennas, and regulates the clock neurons in the insect brain. In our models, these are the zeitgeber time \((t_z)\) and day length \((T_L)\) . The antennae of some insects can also detect the magnetic inclination \((\mu)\) , which can also play a role in the compass of insects. The celestial compass involves processes through the dorsal medulla (Me), anterior optic tubercle (AOTu), and bulb (Bu), where it forms an activity bump representing the insect's heading relative to geocentric coordinates. The clock neurons in the brain of Drosophila melanogaster are the dorsal (DNs) and lateral neurons (LNs), which receive indirect input from the photoreceptors, ocelli and antennas, through the accessory medulla (aMe) and other areas. We suggest that their inputs include the insects' hour angle \((\phi)\) , latitude \((\phi)\) , and the solar declination \((\delta)\) . DNs and LNs target different major areas in the insect brain that control the insect's behaviour. These include the ellipsoid body (EB) and fan-shaped body (FB) of the central complex (CX), the mushroom bodies, and the descending neurons. A particular type of DN, the DN1pB, targets the AOTu and the TuBu neurons and therefore is part of the celestial compass pathway. We suggest that this neuron encodes a prediction of the solar azimuth (relative to an absolute coordinate), which integrates with the detected egocentric solar azimuth into a geocentric compass. Shaded nodes in the architecture denote areas modelled in this work. Grey arrows and empty boxes were not directly modelled in this work. </center>  
+
+<|ref|>text<|/ref|><|det|>[[57, 789, 490, 914]]<|/det|>
+need to incorporate all 'subtle geographic forces'. The hour angle model diverges from the actual solar azimuth in inverse proportion to the distance of the insect from the equator. Thus, the precision of the simpler hour- angle model increases closer to the poles and decreases closer to the equator, where the complete model becomes more useful (see Fig. 1e). The most critical band for the hour angle model is within \(23.45^{\circ}\) from the equator, where the sun switches biannually between CW and CCW movement. In  
+
+<|ref|>text<|/ref|><|det|>[[507, 42, 940, 227]]<|/det|>
+an extreme scenario (when the insect is exactly at the subsolar latitude) the sun moves in a straight line across the zenith. The solar azimuth remains due east until solar noon when it switches within moments to due west, creating the largest error for the hour- angle model; the complete model can compensate for this phenomenon. Seasonal insects (for example, only active during the summer) equipped with the hour- angle model may not face this situation, but we should expect a large variance in their directed behaviour (see Fig. 3b and Fig. 4e). The complete model is critical for seasonal insects within this band that operate during autumn or spring (when the sun switches moving directions), such as the globe skimmer dragonflies.  
+
+<|ref|>text<|/ref|><|det|>[[507, 230, 940, 441]]<|/det|>
+For migrating species that remain in one hemisphere, the complete model allows them to maintain a straighter path. However, note that deviations induced by using the hour- angle approximation largely cancel out over each day, making this simpler model sufficient for reaching their destination. Thus insects known to use magnetic inclination for their migration within a hemisphere, such as the monarch butterfly [25], might have evolved this sensitivity for another purpose: to set the goal location when migrating along the latitudinal axis. In this case, the animal would stop migrating when a target value of magnetic inclination was sensed. Having developed such a sense, their clock may have co- opted the information, but as we have shown, they can still migrate with sufficient accuracy without complete time compensation.  
+
+<|ref|>text<|/ref|><|det|>[[507, 444, 940, 643]]<|/det|>
+The hour- angle model also appears to be sufficiently accurate for central- place foragers, although there might be some circumstances in which a complete model that reduces the error in return trips to a food source from that shown in Fig. 3b to that in Fig. 3c would be advantageous. For example, Saharan desert ants (Cataglyphis fortis and C. bicolor) that live in featureless salt pans may have few other cues available to correct for error, and longer foraging durations (inducing more error; Fig. 3e) might be expected due to food scarcity [43]. Note, in this case, the complete model could be somewhat simplified by using constant values for the sine and cosine of latitude, rather than requiring latitude to be estimated from magnetic inclination, as the latitude of the animal is relatively constant.  
+
+<|ref|>text<|/ref|><|det|>[[507, 646, 940, 884]]<|/det|>
+For insects that only need to use their celestial compass in relatively short trips, compensating a celestial compass for the sun's movement only becomes critical when trips to the same (remembered) location are to be made at different times of the day. In this case, a possible alternative to using an internal clock for time compensation would be to use familiar visual surroundings, a magnetic compass sense [44, 45] or some other constant directional cue to recalibrate the celestial compass at the start of each journey. Experiments with time delays and displacement of ants (C. fortis and C. bicolor [5]) or bees (Apis mellifera [46,47]) to novel locations make it unlikely that terrestrial visual cues are needed to recalibrate the compass. To rule out the possibility that recalibration occurs using a magnetic compass, it is essential to put in conflict their time- compensated celestial compass and their expected magnetic field, which has not yet been attempted.  
+
+<|ref|>text<|/ref|><|det|>[[507, 888, 939, 915]]<|/det|>
+Implementing a complete time- compensated celestial compass could also be advantageous for robotics, as it pro
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 42, 491, 369]]<|/det|>
+vides localisation on earth based on an embedded model of geophysical forces and does not require any satellite-network infrastructure. The model's knowledge of geophysical forces adapts by measuring solar declination, day length (combination of solar declination and latitude) and time of day (zeitgeber time). Given the shared characteristics of all planets (round, spin around their axis, orbit around the sun and have some form of atmosphere for accurately detecting the sun's position), our model could be used as an alternative to GPS on any planet. Apart from the robot's heading, it can also provide its latitude (calculated as a function of day length and solar declination) and its longitude (function of the adaptive hour-angle and a clock tuned to the exact period of the planet's spin). This compass could thus be valuable for outdoor robotics for planetary exploration [48] and on earth, providing a robust backup when the magnetic field is distorted and the GPS signal is weak. This includes underwater missions or extreme weather conditions including sandstorms [49]. As our proposed compass estimates time based on subtle geophysical forces, it can survive accidental power-downs of robots, when time and date information (which could otherwise be used directly to predict sun position) could be lost.  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 389, 334, 408]]<|/det|>
+## Materials and methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 420, 341, 437]]<|/det|>
+## The celestial compass model  
+
+<|ref|>text<|/ref|><|det|>[[57, 443, 490, 501]]<|/det|>
+Our results assume a compass model that accurately returns the solar azimuth. We assume that this is represented in the AOTu by 16 TuBu1 neurons with field of view centred at homogeneously distributed angles in a ring,  
+
+<|ref|>equation<|/ref|><|det|>[[110, 508, 488, 526]]<|/det|>
+\[\phi^{n} = n22.5^{\circ},\qquad \mathrm{where}\quad n\in \{1,\ldots ,16\} . \quad (4)\]  
+
+<|ref|>text<|/ref|><|det|>[[57, 535, 490, 550]]<|/det|>
+The responses of the TuBu1 neurons are then calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[128, 557, 488, 595]]<|/det|>
+\[\mathrm{MeTu2a}^{n}(t) = \sin (\alpha_{\mathrm{sum}}(t) - \theta (t) - \phi^{n}), \quad (5)\] \[\mathrm{MeTu2b}^{n}(t) = \cos (\alpha_{\mathrm{sum}}(t) - \theta (t) - \phi^{n}), \quad (6)\]  
+
+<|ref|>text<|/ref|><|det|>[[56, 603, 490, 647]]<|/det|>
+where \(\theta (t)\) is the heading of the animal at time \(t\) (hours), \(\phi^{n}\) is the preference angle of the \(n^{\mathrm{th}}\) MeTu2 neuron, and \(\alpha_{\mathrm{sum}}(t)\) is the solar azimuth.  
+
+<|ref|>sub_title<|/ref|><|det|>[[56, 663, 490, 680]]<|/det|>
+## Models of compensation for the moving sun  
+
+<|ref|>text<|/ref|><|det|>[[56, 686, 490, 757]]<|/det|>
+Three models of the compass are used in different parts of our results: the no- compensation, hour- angle and full models (in order of ascending complexity). Each model provides the responses of the ring neurons (ERs) that are used as an input to the CX model.  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 775, 298, 790]]<|/det|>
+## The no-compensation model  
+
+<|ref|>text<|/ref|><|det|>[[56, 796, 490, 825]]<|/det|>
+The activity of the ERs is equivalent to the output of the optic lobe (OL) medulla- tubercle (MeTu) neurons,  
+
+<|ref|>equation<|/ref|><|det|>[[123, 833, 488, 850]]<|/det|>
+\[\mathrm{ER4m}^{n}(t) = \mathrm{TuBu1b}^{n}(t) = \mathrm{MeTu2b}^{n}(t). \quad (7)\]  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 867, 246, 881]]<|/det|>
+## The hour-angle model  
+
+<|ref|>text<|/ref|><|det|>[[56, 888, 490, 916]]<|/det|>
+Here, we introduce a basic correction using the hour- angle. The responses of the DN1pB clock neurons relate to the  
+
+<|ref|>text<|/ref|><|det|>[[506, 43, 606, 56]]<|/det|>
+hour angle as  
+
+<|ref|>equation<|/ref|><|det|>[[642, 60, 936, 97]]<|/det|>
+\[\mathrm{DN1pB}_{E}(t) = \omega_{E}(t), \quad (8)\] \[\mathrm{DN1pB}_{N}(t) = \omega_{N}(t), \quad (9)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 100, 938, 128]]<|/det|>
+where \(t\) is the time (hours) since the beginning of the year. The components \(\omega_{E}\) and \(\omega_{N}\) are calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[646, 132, 936, 170]]<|/det|>
+\[\begin{array}{r}\omega_{\mathrm{E}}(t) = -\sin (\omega (t)),\\ \omega_{\mathrm{N}}(t) = -\cos (\omega (t)), \end{array} \quad (11)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 174, 938, 217]]<|/det|>
+where \(\omega (t)\) is computed by equation (1). Note here that we assume a perfect estimate of the sunrise time \((t_{sr}\) ; used in equation (1) to estimate the zeitgeber time).  
+
+<|ref|>text<|/ref|><|det|>[[506, 217, 938, 245]]<|/det|>
+The activity of the tubercle- bulb (TuBu) neurons is then estimated as  
+
+<|ref|>equation<|/ref|><|det|>[[546, 248, 936, 285]]<|/det|>
+\[\begin{array}{r}\mathrm{TuBu1a}^{n}(t) = -\mathrm{DN1pB}_{E}(t)\cdot \mathrm{MeTu2a}^{n}(t),\\ \mathrm{TuBu1b}^{n}(t) = -\mathrm{DN1pB}_{N}(t)\cdot \mathrm{MeTu2b}^{n}(t). \end{array} \quad (13)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 289, 938, 318]]<|/det|>
+TuBu neurons add up column- wise in the bulb (Bu), where they target the ERs, whose activity is calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[572, 323, 936, 339]]<|/det|>
+\[\mathrm{ER4m}^{n}(t) = \mathrm{TuBu1a}^{n}(t) + \mathrm{TuBu1b}^{n}(t). \quad (14)\]  
+
+<|ref|>sub_title<|/ref|><|det|>[[506, 354, 679, 368]]<|/det|>
+## The complete model  
+
+<|ref|>text<|/ref|><|det|>[[506, 375, 938, 404]]<|/det|>
+The complete model also involves solar declination and the insect's latitude. Solar declination is computed as  
+
+<|ref|>equation<|/ref|><|det|>[[585, 408, 936, 438]]<|/det|>
+\[\delta (t) = 23.45^{\circ}\sin \left(\frac{284 + t / 24}{365} 360^{\circ}\right), \quad (15)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 442, 938, 471]]<|/det|>
+where \(t\) is the time (hours) since the start of the year, and it is further decomposed into  
+
+<|ref|>equation<|/ref|><|det|>[[650, 475, 936, 511]]<|/det|>
+\[\begin{array}{r}\delta_{N}(t) = \sin (\delta (t)),\\ \delta_{Q}(t) = \cos (\delta (t)). \end{array} \quad (16)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 516, 938, 545]]<|/det|>
+Geometric latitude can be approximated as a function of geomagnetic inclination [33] as  
+
+<|ref|>equation<|/ref|><|det|>[[612, 548, 936, 566]]<|/det|>
+\[\phi (\mu) = -\tan^{-1}(0.5\tan (\mu)), \quad (18)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 571, 938, 599]]<|/det|>
+where \(\mu\) is the local geomagnetic inclination, and further decomposes into  
+
+<|ref|>equation<|/ref|><|det|>[[650, 603, 936, 640]]<|/det|>
+\[\begin{array}{r}\phi_{N}(\mu) = \sin (\phi (\mu)),\\ \phi_{Q}(\mu) = \cos (\phi (\mu)). \end{array} \quad (19)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 644, 938, 673]]<|/det|>
+Using the above information, the apparent solar azimuth can be estimated as [3]  
+
+<|ref|>equation<|/ref|><|det|>[[544, 676, 936, 714]]<|/det|>
+\[\begin{array}{rl} & {\alpha_{\mathrm{E}}(\mu ,t) = \delta_{Q}(t)\omega_{\mathrm{E}}(t),}\\ & {\alpha_{\mathrm{N}}(\mu ,t) = \phi_{Q}(\mu)\delta_{N}(t) + \phi_{N}(\mu)\delta_{Q}(t)\omega_{\mathrm{N}}(t),} \end{array} \quad (22)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 717, 938, 746]]<|/det|>
+corresponding to the solar azimuth's east (negative sine) and north (negative cosine) components.  
+
+<|ref|>text<|/ref|><|det|>[[506, 746, 938, 774]]<|/det|>
+We replace the responses of the DN1pB clock neurons with the solar azimuth components,  
+
+<|ref|>equation<|/ref|><|det|>[[625, 778, 936, 815]]<|/det|>
+\[\begin{array}{r}\mathrm{DN1pB}_{E}(t,\mu) = \alpha_{E}(t,\mu),\\ \mathrm{DN1pB}_{N}(t,\mu) = \alpha_{N}(t,\mu). \end{array} \quad (24)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 819, 938, 848]]<|/det|>
+We simulate the observed magnetic inclination \((\mu)\) using the actual geometric latitude of the animal as  
+
+<|ref|>equation<|/ref|><|det|>[[626, 852, 936, 888]]<|/det|>
+\[\mu = \tan^{-1}\left(\frac{-2\sin(\phi)}{\cos(\phi)}\right). \quad (25)\]  
+
+<|ref|>text<|/ref|><|det|>[[506, 889, 938, 917]]<|/det|>
+The remaining calculations are the same as in the hour- angle model.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[58, 40, 330, 56]]<|/det|>
+## The central complex model  
+
+<|ref|>text<|/ref|><|det|>[[58, 64, 490, 147]]<|/det|>
+As we do not focus on the ring- attractor dynamics or specific neural response of the neurons in the CX, we simplified the model described in Stone et al. (2017) [36] by replacing the processing layers with vectors represented by complex numbers. Thus, we transformed the compass representation of the ER4m neurons as  
+
+<|ref|>equation<|/ref|><|det|>[[149, 155, 488, 196]]<|/det|>
+\[z_{\mathrm{ER4m}}(t) = \frac{1}{16}\sum_{n = 1}^{16}r_{n^{\prime}}^{n}(t)\mathrm{e}^{\mathrm{i}\phi^{n}} + \epsilon , \quad (26)\]  
+
+<|ref|>text<|/ref|><|det|>[[58, 205, 490, 262]]<|/det|>
+where \(\epsilon = \epsilon_{x} + \mathrm{i}\epsilon_{y}\sim \mathbb{U}(-\eta ,\eta)\in \mathbb{C}\) is a random number drawn from a uniform distribution, with real and imaginary components in the range \([-\eta ,\eta ]\) , and \(\eta \in [0,1]\) is the selected noise level. By default, in all our experiments \(\eta = 0.2\)  
+
+<|ref|>text<|/ref|><|det|>[[58, 262, 490, 290]]<|/det|>
+The representation of elipsoid- body protocerebral- bridge gall (EPG) neurons can then be approximated as  
+
+<|ref|>equation<|/ref|><|det|>[[180, 300, 488, 331]]<|/det|>
+\[\mathrm{EPG}(t) = \frac{\mathrm{ER4m}(t) + \epsilon}{|\mathrm{ER4m}(t) + \epsilon|}. \quad (27)\]  
+
+<|ref|>text<|/ref|><|det|>[[58, 340, 490, 383]]<|/det|>
+Note that we need to normalise this complex number to ensure that we only keep the direction information, which is the estimated heading of the animal.  
+
+<|ref|>text<|/ref|><|det|>[[58, 383, 490, 425]]<|/det|>
+Multiplying the heading with the speed of the animal \((v)\) , we compute its velocity in the protocerebral- bridge fan- shaped- body nodulus (PFN) neurons,  
+
+<|ref|>equation<|/ref|><|det|>[[177, 435, 488, 451]]<|/det|>
+\[\mathrm{PFN}(t) = \mathrm{EPG}(t)v(t) + \epsilon . \quad (28)\]  
+
+<|ref|>text<|/ref|><|det|>[[58, 462, 490, 491]]<|/det|>
+We use the activity pattern of the PFNs to update the working memory (M) of the CX as  
+
+<|ref|>equation<|/ref|><|det|>[[208, 500, 488, 530]]<|/det|>
+\[\tau_{\mathrm{M}}\frac{\mathrm{d}\mathrm{M}}{\mathrm{d}t} = \mathrm{PFN}(t), \quad (29)\]  
+
+<|ref|>text<|/ref|><|det|>[[58, 539, 490, 595]]<|/det|>
+where \(\tau_{\mathrm{M}} = 40\) sec is the time- constant of the memory charge. Similarly, we have a goal memory ( \(\mathrm{G}\in \mathbb{C}\) ) that can be used as the migration target or the foraging site in our experiments, and by default it is zero.  
+
+<|ref|>text<|/ref|><|det|>[[58, 595, 490, 623]]<|/det|>
+The allocentric goal direction is computed by fan- shapedbody columnar (FC) neurons, which we implement as  
+
+<|ref|>equation<|/ref|><|det|>[[184, 632, 488, 664]]<|/det|>
+\[\mathrm{FC2}(t) = \frac{\mathrm{G}(t) - \mathrm{M}(t)}{|\mathrm{G}(t) - \mathrm{M}(t)|}. \quad (30)\]  
+
+<|ref|>text<|/ref|><|det|>[[58, 673, 490, 730]]<|/det|>
+Note that here we also normalise with magnitude of the complex number, as this population of neurons represents the allocentric direction only and not the distance of the goal location.  
+
+<|ref|>text<|/ref|><|det|>[[58, 730, 490, 773]]<|/det|>
+Finally, the egocentric steering signal is decomposed into two axes, at \(45^{\circ}\) towards the left (L) or right (R), and it is calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[70, 782, 488, 821]]<|/det|>
+\[\mathrm{PFL3}_L(t) = \mathrm{FC2}(t) - \mathrm{EPG}(t)\cos (-45^{\circ})e^{-\mathrm{i}45^{\circ}} + \epsilon , \quad (31)\] \[\mathrm{PFL3}_R(t) = \mathrm{FC2}(t) - \mathrm{EPG}(t)\cos (45^{\circ})e^{\mathrm{i}45^{\circ}} + \epsilon . \quad (32)\]  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 836, 175, 851]]<|/det|>
+## Simulations  
+
+<|ref|>text<|/ref|><|det|>[[58, 860, 490, 916]]<|/det|>
+We run a set of simulations for migrating and central- place foraging insects. The update of the heading direction and position of the animals in all the simulations happens in the same way.  
+
+<|ref|>text<|/ref|><|det|>[[504, 41, 937, 69]]<|/det|>
+Based on the above CX model, we calculate the angular velocity of the animal as  
+
+<|ref|>equation<|/ref|><|det|>[[592, 78, 937, 108]]<|/det|>
+\[\frac{\mathrm{d}\theta}{\mathrm{d}t} = \frac{1}{4} (|\mathrm{PFL3}_L(t)| - |\mathrm{PFL3}_R(t)|), \quad (33)\]  
+
+<|ref|>text<|/ref|><|det|>[[504, 119, 937, 147]]<|/det|>
+where \(\theta (t)\) is the heading of the animal. Then we update the linear velocity of the animal as  
+
+<|ref|>equation<|/ref|><|det|>[[654, 157, 937, 186]]<|/det|>
+\[\frac{\mathrm{d}z_{xy}}{\mathrm{d}t} = v(t)\mathrm{e}^{\mathrm{i}\theta (t)}, \quad (34)\]  
+
+<|ref|>text<|/ref|><|det|>[[504, 196, 937, 239]]<|/det|>
+which is used for updating its actual position, \(z_{xy}(t)\) . The speed in the above equation \((v)\) is set to match approximate insect speeds in the following experimental scenarios.  
+
+<|ref|>sub_title<|/ref|><|det|>[[506, 255, 694, 270]]<|/det|>
+## Central-place foraging  
+
+<|ref|>text<|/ref|><|det|>[[504, 278, 937, 404]]<|/det|>
+For these experiments, we placed the insects in Edinburgh (55.9533°N, 3.1883°W), the United Kingdom, on August 2, 2024. We use local coordinates where the nest is at point zero, which is also the initial location of the insect. The speed of the insect was constant at \(v(t) = 0.5\mathrm{m}\sec^{- 1}\) for all \(t\) that the insect was moving, or \(v(t) = 0\mathrm{m}\sec^{- 1}\) , for those that the insect was resting. This experiment had three phases: searching for a food source, homing, and foraging to a known food site.  
+
+<|ref|>text<|/ref|><|det|>[[504, 405, 937, 520]]<|/det|>
+In the initial phase, a random route is generated and the animal is forced to follow it (see 'Defining a random foraging route'). The CX model is updated in each step using the current heading and speed, as computed by the difference between two subsequent points of the route. The final location of the route is stored as the goal vector memory. The insect then alternates the homing and foraging phases, with one hour of rest after every homing phase.  
+
+<|ref|>text<|/ref|><|det|>[[504, 521, 937, 660]]<|/det|>
+In the homing phase, the goal location is set to be the zero point (home), and we update the angular and linear velocity of the animal using equations (33) and (34). When the insect approaches its goal location, the CX model automatically creates a characteristic search pattern. In each step, we estimate the probability of the animal expressing such a pattern, by detecting four consecutive turning points (see 'Detecting a turning point'). The centroid of the four turning points approximates the centre of the search, which we interpret as the expressed goal location of the insect  
+
+<|ref|>equation<|/ref|><|det|>[[640, 670, 937, 710]]<|/det|>
+\[z_{\mathrm{centroid}} = \frac{1}{4}\sum_{c = 1}^{4}z_{\mathrm{turn}}^{c}. \quad (35)\]  
+
+<|ref|>text<|/ref|><|det|>[[504, 720, 937, 763]]<|/det|>
+The foraging phase is similar to the homing, but we replace the goal location with the stored vector memory of the known food site.  
+
+<|ref|>sub_title<|/ref|><|det|>[[506, 780, 590, 795]]<|/det|>
+## Migration  
+
+<|ref|>text<|/ref|><|det|>[[504, 803, 937, 916]]<|/det|>
+For the migration experiments, we assume that insects can travel for a maximum of \(8\mathrm{h}\) per day (only between sunrise and sunset), they need to stop every hour for rest and feeding, and that their stops last for \(1\mathrm{h}\) . The speed of the insects was set to \(v(t) = 2.5\mathrm{m}\sec^{- 1}\) , which is based on the speed of \(D\) . plexippus monarch butterflies (although this might differ in reality among insects), and the time- step used was \(\mathrm{dt} = 50\mathrm{min}\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 40, 492, 242]]<|/det|>
+The simulation for the autumn migration (from August 29 to October 31, 2024) of monarch butterflies (D. plex- . ippus) started close to the Mackinac Island \((45.7627^{\circ}\mathrm{N}\) 84.7210W), Michigan, and finished close to Michoacan (19.5532N, 101.5960W), Mexico, which is 3303.01 km. The autumn migration (from September 4 to October 1, 2024) of Bogong moths (A. infusa) started close to Montrose \((27.0000^{\circ}\mathrm{S}\) , 150.6500E), Australia, and finished close to Mount Bogong \((36.8400^{\circ}\mathrm{S}\) , 148.4600E), Australia, which is 1114.65 km. The spring migration (from February 4 to May 1, 2024) of globe skimmer dragonflies (P. flavescens) started close to Mbekenyera, \((10.0000^{\circ}\mathrm{S}\) 39.0000E), Tanzania, and finished close to Madurai \((10.0000^{\circ}\mathrm{N}\) , 78.0000E), India, which is 4859.20 km.  
+
+<|ref|>text<|/ref|><|det|>[[57, 243, 491, 313]]<|/det|>
+For the foraging experiments, we treat the world as a twodimensional plane. For migration, it is necessary to consider the earth's curvature, hence the equations for location and motion must be modified. The initial heading of the animal was calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[60, 317, 491, 353]]<|/det|>
+\[\theta (t_0) = \tan^{-1}\left(\frac{\sin(\Delta\lambda)\cos(\phi_e)}{\cos(\phi_s)\sin(\phi_e) - \sin(\phi_s)\cos(\phi_e)\cos(\Delta\lambda)}\right),\]  
+
+<|ref|>text<|/ref|><|det|>[[28, 360, 490, 389]]<|/det|>
+and the distance between two points on earth (haverisne distance) was calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[60, 395, 496, 450]]<|/det|>
+\[\rho = 2R\tan^{-1}\left(-\frac{\sqrt{\sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_s)\cos(\phi_e)\sin^2\left(\frac{\Delta\lambda}{2}\right)}}{\sqrt{1 - \sin^2\left(\frac{\Delta\phi}{2}\right) + \cos(\phi_s)\cos(\phi_e)\sin^2\left(\frac{\Delta\lambda}{2}\right)}}\right)\]  
+
+<|ref|>text<|/ref|><|det|>[[28, 455, 416, 470]]<|/det|>
+where \(R = 6378137\mathrm{m}\) is the radius of earth and  
+
+<|ref|>equation<|/ref|><|det|>[[100, 479, 456, 530]]<|/det|>
+\[\lambda_{s} = \mathrm{start~longitude},\qquad \phi_{s} = \mathrm{start~latitude},\] \[\lambda_{e} = \mathrm{target~longitude},\qquad \phi_{e} = \mathrm{target~latitude},\] \[\Delta \lambda = \lambda_{e} - \lambda_{s},\qquad \Delta \phi = \phi_{e} - \phi_{s}.\]  
+
+<|ref|>text<|/ref|><|det|>[[28, 559, 490, 587]]<|/det|>
+where west and south directions were represented as negative angles.  
+
+<|ref|>text<|/ref|><|det|>[[28, 588, 490, 616]]<|/det|>
+The location of the animal on earth was transformed into a complex number for consistency as  
+
+<|ref|>equation<|/ref|><|det|>[[200, 624, 490, 641]]<|/det|>
+\[z_{xy}(t) = \phi (t) + \mathrm{i}\lambda (t). \quad (37)\]  
+
+<|ref|>text<|/ref|><|det|>[[28, 650, 490, 680]]<|/det|>
+Thus, in the CX model, the goal location for the migrating experiments is set as  
+
+<|ref|>equation<|/ref|><|det|>[[216, 688, 490, 706]]<|/det|>
+\[G(t) = \rho \mathrm{e}^{\mathrm{i}\theta (t_0)}. \quad (38)\]  
+
+<|ref|>text<|/ref|><|det|>[[28, 715, 490, 772]]<|/det|>
+We transformed the location and direction of the animal into a quaternion, \(q_{xy\theta}\) , to ease spherical computations. We used the Rotation package of the SciPy library in Python to do this (see code for details). So steering was applied as  
+
+<|ref|>equation<|/ref|><|det|>[[70, 780, 490, 815]]<|/det|>
+\[q_{xy\theta}(t) = q_{xy\theta}(t - \mathrm{d}t)\left(\cos \left(\frac{1}{2}\frac{\mathrm{d}\theta}{\mathrm{d}t}\right) - \mathrm{k}\sin \left(\frac{1}{2}\frac{\mathrm{d}\theta}{\mathrm{d}t} \right)\right), \quad (39)\]  
+
+<|ref|>text<|/ref|><|det|>[[28, 825, 250, 838]]<|/det|>
+and forward movement as  
+
+<|ref|>equation<|/ref|><|det|>[[70, 844, 490, 880]]<|/det|>
+\[q_{xy\theta}(t) = q_{xy\theta}(t - \mathrm{d}t)\left(\cos \left(\frac{v(t)}{2R}\right) + \mathrm{j}\sin \left(\frac{v(t)}{2R}\right)\right), \quad (40)\]  
+
+<|ref|>text<|/ref|><|det|>[[28, 888, 490, 916]]<|/det|>
+where j and k are two of the imaginary parts in the quaternion. We always update the heading before moving forward,  
+
+<|ref|>text<|/ref|><|det|>[[505, 40, 938, 112]]<|/det|>
+which composes one step in the simulation. Using the same SciPy package, we can transform the quaternion back to the coordinates of the animal on earth and its heading direction. The coordinates are then transformed into a complex number using equation (37).  
+
+<|ref|>text<|/ref|><|det|>[[505, 113, 938, 155]]<|/det|>
+Each simulation is run from the start to the end date of the migration, and the insects are allowed to travel only between sunrise and sunset.  
+
+<|ref|>sub_title<|/ref|><|det|>[[505, 172, 790, 187]]<|/det|>
+## Defining a random foraging route  
+
+<|ref|>text<|/ref|><|det|>[[505, 194, 938, 280]]<|/det|>
+The initial search for food was created using a von Mises distribution and Newtonian physics. The starting point was set as the home location, \(z_{s} = 0\) , and the final point (food source) was \(100\mathrm{m}\) towards east, \(z_{e} = 100\) . We drew 25 000 \(\frac{5.100\mathrm{m}}{(0.5\mathrm{m}\sec^{- 1}\cdot 1\mathrm{sec})}\) bearing directions for the path from von Mises distribution as  
+
+<|ref|>equation<|/ref|><|det|>[[600, 286, 937, 315]]<|/det|>
+\[\frac{\mathrm{d}\theta}{\mathrm{d}t}\sim \mathrm{VonMises}(\mu = 0,\kappa = 100), \quad (41)\]  
+
+<|ref|>text<|/ref|><|det|>[[505, 325, 938, 380]]<|/det|>
+and low- pass filtered to smooth the turns. Subsequently, the position was updated using equation (34). The generated positions were resized and rotated to end at the final point as  
+
+<|ref|>equation<|/ref|><|det|>[[590, 378, 937, 410]]<|/det|>
+\[z_{xy}(t) = \frac{z_{xy}(t)}{z_{xy}(t_{e}) - z_{xy}(t_{s})} (z_{e} - z_{s}). \quad (42)\]  
+
+<|ref|>text<|/ref|><|det|>[[505, 415, 938, 459]]<|/det|>
+The positions were resampled every \(0.5\mathrm{m}\sec^{- 1}\) using linear interpolation. The final heading directions were then calculated as \(\angle \frac{dz_{xy}}{dt}\) , \(\forall t > t_0\) , where \(\mathrm{d}t = 1\) sec.  
+
+<|ref|>sub_title<|/ref|><|det|>[[505, 473, 723, 488]]<|/det|>
+## Detecting a turning point  
+
+<|ref|>text<|/ref|><|det|>[[505, 495, 938, 566]]<|/det|>
+To detect the search pattern of an insect, we first needed to detect whether the insect changed its heading direction sufficiently. We mark a sufficient change in the heading when its difference from \(25\mathrm{m}\) before is more than \(120^{\circ}\) and no other turning point was detected in the past \(50\mathrm{m}\)  
+
+<|ref|>sub_title<|/ref|><|det|>[[505, 583, 641, 597]]<|/det|>
+## Solar ephemeris  
+
+<|ref|>text<|/ref|><|det|>[[505, 604, 938, 690]]<|/det|>
+The sun's course during the day depends on the location of the animal on earth and the time of the year. To calculate these, we use the 'skylight' Python package, which implements the solar ephemeris suggested by the Global Monitoring Laboratory (GML) of the US National Oceanic and Atmospheric Administration (NOAA).  
+
+<|ref|>sub_title<|/ref|><|det|>[[505, 706, 821, 722]]<|/det|>
+## Optimisation for the day length  
+
+<|ref|>text<|/ref|><|det|>[[505, 729, 938, 870]]<|/det|>
+To optimise equation (2), we needed the overall blue irradiance of the skylight \((I_{\mathrm{sky}})\) and the ground- truth day length \((T_{L})\) . Thus, we generated a ground- truth dataset of overall blue skylight irradiance and day length during a calendar year. Then we optimised the free parameters \((\tau_{L},a\) and \(\beta\) ) of equation (2), using the 'curve_fit' method of the 'SciPy' Python package. The function we optimised was the value of \(T_{L}\) over time, which was calculated using the Euler's method for discrete time with \(\mathrm{d}t = 1\mathrm{h}\) and \(T_{L}(0) = 7\mathrm{h}\) as  
+
+<|ref|>equation<|/ref|><|det|>[[513, 875, 937, 916]]<|/det|>
+\[T_{L}(t) = \sum_{i = 1}^{t}T_{L}(i - 1) + \frac{1}{\tau_{L}} (a I_{\mathrm{sky}}(i) + \beta -T_{L}(i - 1)). \quad (43)\]
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 42, 491, 212]]<|/det|>
+We calculate day length and overall irradiance using the 'skylight' Python package and the sky model described by Vévoda et al. (2022) [50]. The observer was set to be in Edinburgh (55.9533°N, 3.1883°W), from January 1 to December 31, 2024, collecting one sample per hour (8760 samples in total). For each sample, the day length \((T_{L}^{*})\) was calculated as the time between sunrise and sunset (in hours) of the respective day. For the overall skylight intensity \((I_{\mathrm{sky}})\) , we estimated irradiance by using 1000 homogeneously distributed rays from the simulated sky, we extracted the visible-blue light irradiance and calculated the average across rays.  
+
+<|ref|>text<|/ref|><|det|>[[57, 214, 491, 355]]<|/det|>
+To simulate the foraging patterns of insects, we randomly selected \(T_{F} / 12\mathrm{h}\) percentile of the 8760 homogeneous \(I_{\mathrm{sky}}\) samples of the year, where \(T_{F}\) is the foraging time. The remaining samples were set as \(I_{\mathrm{sky}} = 0\mathrm{Wm}^{- 2}\mathrm{sr}^{- 1}\) , simulating the time spent indoors. The above method produces random light exposures per day, with on- average \(T_{F}\) per day within a year. This means that we might have \(12\mathrm{h}\) of foraging spread across a day, and no foraging in another day. For the foraging experiments, \(T_{F}\in [1\mathrm{h},2\mathrm{h},4\mathrm{h},8\mathrm{h}]\) , while for migration, \(T_{F} = 12\mathrm{h}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 375, 292, 392]]<|/det|>
+## Performance evaluation  
+
+<|ref|>text<|/ref|><|det|>[[57, 400, 490, 444]]<|/det|>
+Given the total distance travelled (C) and the straight- line distance of the insect from the goal location \((L)\) , the tortuosity of the path at a specific time (t) is  
+
+<|ref|>equation<|/ref|><|det|>[[228, 454, 490, 485]]<|/det|>
+\[\varsigma (t) = \frac{C(t)}{L(t)}. \quad (44)\]  
+
+<|ref|>text<|/ref|><|det|>[[57, 496, 490, 524]]<|/det|>
+The Euclidean distance of the insect from its goal location is calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[209, 527, 490, 543]]<|/det|>
+\[\epsilon_{z} = |z_{xy} - z_{\mathrm{goal}}|. \quad (45)\]  
+
+<|ref|>text<|/ref|><|det|>[[57, 551, 490, 580]]<|/det|>
+In Fig. 4 and 3, all the measurements were taken when the insect was closest to its centre of search.  
+
+<|ref|>text<|/ref|><|det|>[[57, 581, 490, 610]]<|/det|>
+Similarly, the error between the estimated \((T_{L})\) and actual day length \((T_{L}^{*})\) is calculated as  
+
+<|ref|>equation<|/ref|><|det|>[[186, 620, 490, 638]]<|/det|>
+\[\epsilon_{T_{L}}(t) = |T_{L}(t) - T_{L}^{*}(t)|. \quad (46)\]  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 660, 258, 679]]<|/det|>
+## Code availability  
+
+<|ref|>text<|/ref|><|det|>[[57, 692, 490, 735]]<|/det|>
+The code that runs all the simulations and generates all the plots is publicly available through Code Ocean (identifier will be set on publication).  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 760, 186, 778]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[57, 790, 490, 933]]<|/det|>
+[1] Lambrinos, D., Moller, R., Labhart, T., Pfeifer, R. & Wehner, R. A mobile robot employing insect strategies for navigation. Robotics and Autonomous Systems 30, 39- 64 (2000).  [2] Dupeyroux, J., Viollet, S. & Serres, J. R. An ant- inspired celestial compass applied to autonomous outdoor robot navigation. Robotics and Autonomous Systems 117, 40- 56 (2019).  
+
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+[3] Zhang, T., Stackhouse, P. W., Macpherson, B. & Mikovitz, J. C. A solar azimuth formula that renders circumstantial treatment unnecessary without compromising mathematical rigor: mathematical setup, application and extension of a formula based on the subsolar point and atan2 function. Renewable Energy 172, 1333- 1340 (2021).  
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+[4] Wehner, R. & Lanfranconi, B. What do the ants know about the rotation of the sky? Nature 293, 731- 733 (1981).  
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+[5] Wehner, R. & Müller, M. How do ants acquire their celestial ephemeris function? Naturwissenschaften 80, 331- 333 (1993).  
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+[6] Guo, F., Holla, M., Díaz, M. M. & Rosbash, M. A circadian output circuit controls sleep- wake arousal in Drosophila. Neuron 100, 624- 635. e4 (2018).  
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+[7] Liang, X. et al. Morning and evening circadian pacemakers independently drive premotor centers via a specific dopamine relay. Neuron 102, 843- 857. e4 (2019).  
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+[8] Reppert, S. M. The ancestral circadian clock of monarch butterflies: role in time- compensated sun compass orientation. Cold Spring Harbor symposia on quantitative biology 72, 113- 8 (2007).  
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+[9] Zhu, H. et al. Cryptochromes define a novel circadian clock mechanism in monarch butterflies that may underlie sun compass navigation. PLoS Biology 6, e4 (2008).  
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+[10] Merlin, C., Gegear, R. J. & Reppert, S. M. Antennal circadian clocks coordinate sun compass orientation in migratory monarch butterflies. Science 325, 1700- 1704 (2009).  
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+[11] Guerra, P. A., Merlin, C., Gegear, R. J. & Reppert, S. M. Discordant timing between antennae disrupts sun compass orientation in migratory monarch butterflies. Nature Communications 3, 958 (2012).  
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+[12] Massy, R. et al. Hoverflies use a time- compensated sun compass to orientate during autumn migration. Proceedings of the Royal Society B 288, 20211805 (2021).  
+
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+[13] Heinze, S. & Reppert, S. M. Anatomical basis of sun compass navigation I: the general layout of the monarch butterfly brain. Journal of Comparative Neurology 1599- 1628 (2012).  
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+[14] Heinze, S., Florman, J., Asokaraj, S., Jundi, B. e. & Reppert, S. M. Anatomical basis of sun compass navigation II: the neuronal composition of the central complex of the monarch butterfly. Journal of Comparative Neurology 521, 267- 298 (2013).  
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+[15] el Jundi, B. & Homberg, U. Evidence for the possible existence of a second polarization- vision pathway in the locust brain. Journal of Insect Physiology 56, 971- 979 (2010).  
+
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+[16] el Jundi, B., Pfeiffer, K. & Homberg, U. A distinct layer of the medulla integrates sky compass signals in the brain of an insect. PLoS ONE 6, e27855 (2011).
+
+<--- Page Split --->
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+[17] Reinhard, N. et al. Synaptic and peptidergic connections of the Drosophila circadian clock. bioRxiv 2023.09.11.557222 (2024).[18] Saunders, D., Steel, C., Vafopoulou, X. & Lewis, R. Rhythms and clocks. In Insect clocks, chap. 1, 1–5 (Elsevier, 2002).[19] Shlizerman, E., Phillips-Portillo, J., Forger, D. & Reppert, S. Neural integration underlying a time-compensated sun compass in the migratory monarch butterfly. Cell Reports 15, 683–691 (2016).[20] Hulse, B. K. et al. A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection. eLife 10 (2021).[21] Sauman, I. et al. Connecting the navigational clock to sun compass input in monarch butterfly brain. Neuron 46, 457–467 (2005).[22] Mitchell, R., Shaverdian, S., Dacke, M. & Webb, B. A model of cue integration as vector summation in the insect brain. Proceedings of the Royal Society B 290, 20230767 (2023).[23] Gkanias, E., Risse, B., Mangan, M. & Webb, B. From skylight input to behavioural output: a computational model of the insect polarised light compass. PLoS Computational Biology 15, e1007123 (2019).[24] Massy, R. & Wotton, K. R. The efficiency of varying methods and degrees of time compensation for the solar azimuth. Biology Letters 19, 20230355 (2023).[25] Guerra, P. A., Gegear, R. J. & Reppert, S. M. A magnetic compass aids monarch butterfly migration. Nature Communications 5, 4164 (2014).[26] Saunders, D., Steel, C., Vafopoulou, X. & Lewis, R. Circadian rhythms in photoperiodism. In Insect clocks, chap. 11, 339–375 (Elsevier, 2002).[27] Liang, X., Holy, T. E. & Taghert, P. H. Circadian pacemaker neurons display cophasic rhythms in basal calcium level and in fast calcium fluctuations. Proceedings of the National Academy of Sciences 119, e2109969119 (2022).[28] Lamaze, A., Kratschmer, P., Chen, K.- F., Lowe, S. & Jepson, J. E. A wake-promoting circadian output circuit in Drosophila. Current Biology 28, 3098–3105.e3 (2018).[29] Dorkenwald, S. et al. FlyWire: online community for whole-brain connectomics. Nature Methods 19, 119–128 (2022).[30] Gkanias, E. et al. Celestial compass sensor mimics the insect eye for navigation under cloudy and occluded skies. Communications Engineering 2, 82 (2023).[31] Kind, E. et al. Synaptic targets of photoreceptors specialized to detect color and skylight polarization in Drosophila. eLife 10, e71858 (2021).  
+
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+[32] Hardcastle, B. J. et al. A visual pathway for skylight polarization processing in Drosophila. eLife 10, e63225 (2021).[33] Fowler, C. M. R. The solid earth: an introduction to global geophysics (Cambridge University Press, 1990).[34] Anderson, R. C. Do dragonflies migrate across the western Indian Ocean? Journal of Tropical Ecology 25, 347–358 (2009).[35] Hedlund, J. S. U. et al. Unraveling the world's longest non-stop migration: the Indian Ocean crossing of the globe skimmer dragonfly. Frontiers in Ecology and Evolution 9, 698128 (2021).[36] Stone, T. et al. An anatomically constrained model for path integration in the bee brain. Current Biology 27, 3069–3085.e11 (2017).[37] le Moël, F., Stone, T., Lihoreau, M., Wystrach, A. & Webb, B. The central complex as a potential substrate for vector based navigation. Frontiers in Psychology 10, 690 (2019).[38] Dyer, F. C. & Gould, J. L. Honey bee orientation: a backup system for cloudy days. Science 214, 1041–1042 (1981).[39] Dyer, F. C. Memory and sun compensation by honey bees. Journal of Comparative Physiology A 160, 621–633 (1987).[40] Ishida, I. G., Sethi, S., Mohren, T. L., Abbott, L. & Maimon, G. Neuronal calcium spikes enable vector inversion in the Drosophila brain. bioRxiv 2023.11.24.568537 (2023).[41] Brown, F. A. Response to Pervasive Geophysical Factors and the Biological Clock Problem. Cold Spring Harbor Symposia on Quantitative Biology 25, 57–71 (1960).[42] Brown, F. A. Propensity for Lunar Periodicity in Hamsters and Its Significance For Biological Clock Theories. Proceedings of the Society for Experimental Biology and Medicine 120, 792–797 (1965).[43] Huber, R. & Knaden, M. Egocentric and geocentric navigation during extremely long foraging paths of desert ants. Journal of Comparative Physiology A 201, 609–616 (2015).[44] Fleischmann, P. N., Grob, R. & Rössler, W. Magnetoreception in hymenoptera: importance for navigation. Animal Cognition 1–11 (2020).[45] Fleischmann, P. N., Grob, R. & Rössler, W. Magnetosensation during re-learning walks in desert ants (Cataglyphis nodus). Journal of Comparative Physiology A 1–9 (2021).[46] Dyer, F. C. & Dickinson, J. A. Development of sun compensation by honeybees: how partially experienced bees estimate the sun's course. Proceedings of the National Academy of Sciences 91, 4471–4474 (1994).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[15, 42, 494, 245]]<|/det|>
+[47] Dyer, F. C. Spatial memory and navigation by hon-eyebees on the scale of the foraging range. Journal of Experimental Biology 199, 147- 154 (1996).[48] Thakoor, S., Morookian, J., Chahl, J., Hine, B. & Zor-netzer, S. BEES: exploring Mars with bioinspired tech-nologies. Computer 37, 38- 47 (2004).[49] Wu, X. et al. Robust orientation method based on atmospheric polarization model for complex weather. IEEE Internet of Things Journal PP, 1- 1 (2022).[50] Vévoda, P., Bashford-Rogers, T., Kolářová, M. & Wilkie, A. A wide spectral range sky radiance model. Computer Graphics Forum 41, 291- 298 (2022).  
+
+<|ref|>sub_title<|/ref|><|det|>[[60, 263, 285, 282]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[60, 291, 491, 364]]<|/det|>
+This work was financially supported by the European Union, Horizon Europe, (Project 101046790, InsectNeuro- Nano). Thanks to Stanley Heinze for the insightful discus-sion on the insects' clock inputs, and to Robert Mitchell for his helpful comments on the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[60, 384, 312, 402]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[60, 412, 491, 490]]<|/det|>
+Evripidis Gkanias: conceptualisation, formal analysis, in- vestigation, methodology, project administration, software, validation, visualisation, writing—original draft, writing—review & editing.  
+
+<|ref|>sub_title<|/ref|><|det|>[[60, 534, 300, 553]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[60, 564, 381, 578]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[60, 599, 385, 618]]<|/det|>
+## Supplementary information  
+
+<|ref|>text<|/ref|><|det|>[[60, 629, 306, 643]]<|/det|>
+"Supplementary Information.pdf"
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 43, 312, 71]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[59, 130, 440, 204]]<|/det|>
+- 20240725supplementaryinformation.pdf- sp.pdf- nrreportingsummary.pdf
+
+<--- Page Split --->

preprint/preprint__5f3b415aff982a510536358770e8c1ff2c485133bc197bbe4dc106f74e752aed/preprint__5f3b415aff982a510536358770e8c1ff2c485133bc197bbe4dc106f74e752aed.mmd

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+
+# Facilitating the design of combination therapy for cancer using multipartite network models: Emphasis on acute myeloid leukaemia  
+
+Mohieddin Jafari (mohieddin.jafari@helsinki.fi) University of Helsinki https://orcid.org/0000- 0002- 6991- 8587  
+
+Mehdi Mirzaie Helsinki University  
+
+Jie Bao Helsinki University  
+
+Famaz Barneh Princess Máxima Center  
+
+Shuyu Zheng University of Helsinki https://orcid.org/0000- 0003- 0624- 8077  
+
+Johanna Eriksson Helsinki University  
+
+Jing Tang Helsinki University  
+
+## Article  
+
+Keywords: drug therapy, cancer treatments, myeloid leukaemia  
+
+Posted Date: June 22nd, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 577256/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 April 19th, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 29793- 5.
+
+<--- Page Split --->
+
+# Facilitating the design of combination therapy for cancer using multipartite network models: Emphasis on acute myeloid leukaemia  
+
+Mohieddin Jafari \(^{1*}\) , Mehdi Mirzaie \(^{1}\) , Jie Bao \(^{1}\) , Farnaz Barneh \(^{2}\) , Shuyu Zheng \(^{1}\) , Johanna Eriksson \(^{1}\) , Jing Tang \(^{1*}\)  
+
+\(^{1}\) Research Program in Systems Oncology, Faculty of Medicine, University of Helsinki, Finland \(^{2}\) Prinses Maxima Center for Pediatric Oncology, 3584 CS Utrecht, the Netherlands  
+
+# Corresponding authors:  
+
+Jing Tang  Tel. +358 45 8689708  Jing.tang@helsinki.fi  Mohieddin Jafari  Mohieddin.jafari@helsinki.fi
+
+<--- Page Split --->
+
+## Abstract  
+
+From the drug discovery perspective, combination therapy is recommended for cancer treatment due to its efficiency and safety compared to the common cytotoxic and single- targeted monotherapies. However, identifying effective drug combinations is time- and cost- consuming. Here, we offer a novel strategy for predicting potential drug combinations and patient subclasses by constructing multipartite networks using drug- response data on patient samples. In this study, we used Beat AML and GDSC, two comprehensive datasets based on patient- derived and cell line- based samples, to show the potential of multipartite network modelling in combinatorial cancer therapy. We used the median values of cell viability to compare drug potency and reconstruct a weighted bipartite network that models the interaction of drugs and biological samples. Then, clusters of network communities were identified in two projected networks based on the topological structure of the networks. Chemical structures, drug- target networks, protein- protein interactions, and signalling networks were used to corroborate the intra- cluster homogeneity. We further leveraged the community structures within the drug- based multipartite networks to discover effective multi- targeted drug combinations and synergy levels, which were supported with more evidence using the DrugComb and ALMANAC databases. Furthermore, we confirmed the potency of selective combinations of drugs against monotherapy in in vitro experiments using three acute myeloid leukaemia (AML) cell lines. Taken together, this study presents an innovative data- driven strategy based on multipartite networks to suggest potential drug combinations to improve AML treatment.
+
+<--- Page Split --->
+
+## Introduction  
+
+Studies on cases with advanced cancers have shown that less than \(10\%\) of patients have actionable mutations, and the improvement of outcomes is unobserved in a randomised trial of precision medicine based on genomic profiles (1). The current limitation of genomics- centric personalised medicine falls short of the enormous heterogeneity and lack of actionable and sustainable treatment options. With a few exceptions, patient genomic signatures with clinical pathology do not typically predict drug responses. More precisely, cancer can principally be considered a signalling disease, not a genetic disease. There is a wealth of data that has validated this hypothesis, including signalling behaviours involved in growth factor and nutrient responses, the process of entering and exiting the cell cycle, ensuring that chromosomes are segregated in an orderly, efficient and accurate manner during mitosis and apoptosis (2, 3). On the other hand, the complexity of crosstalk between signalling pathways necessitates to modify multiple targets in cancer cells; otherwise, a lack of complete response, resistance, and relapse will emerge during the course of treatment.  
+
+Despite the fact that large amounts of small molecules or drugs have been tested on many cell lines or patient- derived samples, using single drugs as monotherapies to cure cancer might not be a promising strategy, as it is known that the complex interactions of various biological components can induce drug resistance during the treatment of cancer (4- 6). As a matter of fact, monotherapy, the slogan of one target one drug—is inefficient in curing complex diseases, such as cancer (7, 8). Combination therapy or polytherapy with synergistic drugs may achieve a more effective and safer outcome by targeting several targets in the same or separate pathways of the complex system (4). To better identify the synergistic drug combination based on precision medicine, we need ex vivo drug screening to decipher the functional impact of cancer genomics at the phenotypic level and to understand their interactions in the context of biological networks (9, 10). Therefore, understanding network biology may provide a unique opportunity to leverage the rich source of drug response data to offer network- based models for combinatorial therapy. These network models have shown promise for developing clinical decision support tools to discriminate functional patient subclasses (11, 12). Even though there are networks reconstructed to model biological mechanisms of diseases and predict drug combination synergies based on molecular data (13- 16), network models have not been systematically applied to patient data, such as the drug response data of patient- derived samples, to predict patient- customised drug combinations (14). Instead, the ex vivo drug response data are straightforwardly translated into the clinic for patient treatment since these individualised
+
+<--- Page Split --->
+
+experiments represent the efficiency of some approved drugs on patient- derived primary cultures (17, 18).  
+
+In 2018, the Beat AML programme reported a cohort of 672 tumour specimens collected from 531 patients, analysing the ex vivo sensitivity for 122 drugs alongside the mutational status and the gene expression signatures of the samples (19). Despite the dearth of large patient- related drug response datasets, some large cell line- based datasets, such as genomics of drug sensitivity in cancer (GDSC) and ALMANAC, can offer a strong source of supporting evidence for predictions. The GDSC database contains the responses of 1001 cancer cell lines to 265 anti- cancer drugs, providing a rich source of information to connect genotypes with cellular phenotypes and to identify cancer- specific therapeutic options (20). The largest publicly accessible dataset for cancer combination drugs, such as ALMANAC, was recently published by the U.S. National Cancer Institute. This data collection contained more than 5,000 combinations of 104 investigational and licensed drugs, with synergies calculated against 60 cancer cell lines, resulting in more than 290,000 synergy scores (21). Moreover, DrugComb (https://drugcomb.org/), a web- based portal for storing and studying drug combination screening datasets, offers a comprehensive visualisation of drug combination susceptibility and synergy, which can significantly aid in the understanding of drug interactions at unique dosage levels. Drugcomb now has 751,498 drug combinations and 717,684 single drug screens from 37 trials, which relate to 2040 cell lines and 216 cancer forms (22).  
+
+In this study, we developed a network pharmacology approach to predict potential drug combinations for acute myeloid leukaemia (AML) based on the Beat AML dataset. We proposed a drug combination strategy using multipartite network modelling of ex vivo drug screening data. By ex vivo drug response data, we directly accessed the individual phenotypes of the patients' cancer cells, and by network modelling, we demonstrated the similarity of drugs and AML patients. Then, we used the community structures within the drug- based multipartite networks to discover effective multi- targeted drug combination regimens. Our predicted drug combinations were only suggested regarding the phenotypic interactions of the cancer cells or patient samples with the drugs without prior understanding of the genetic origin or molecular understanding of the disease.
+
+<--- Page Split --->
+
+## Methods  
+
+Fig. 1 presents the entire workflow of this study. The weighted bipartite network is constructed using the Beat AML dataset. This dataset is a collaborative research programme of 11 academic medical centres providing data on AML samples while offering genomics, clinical, and drug responses. It includes a cohort study of 672 tumour specimens collected from 531 patients and an analysis of 122 drug responses. To construct a weighted bipartite network, the best response read- out of drug potency was defined using information- based measures. Then, two unipartite networks were obtained using network projection on the samples and drugs. Next, communities of two projected networks were extracted, and intra- cluster homogeneity analysis was performed using the similarity of drugs and patients/cell members based on available gene expression profiles for patients, protein- protein interaction network, and biological pathways. The drug candidates for drug combination were selected from two different communities, and a high- throughput drug screening was used to assess their synergetic effects.  
+
+Defining the response read- out for drug screening experiments  
+
+Pharmacogenomic studies require extensive standardisation to avoid inconsistency of drug response data for further research and unbiased predictions (23, 24). Therefore, first, we controlled the quality of cell viability data to select the potent compounds. To achieve this, we examined the raw datasets regarding the availability of replicated data and outlier detection, followed by assessment of distribution, pairwise correlation, and homoscedasticity analyses to select the best response read- out or measure of drug potency. This analysis was performed using information- based nonparametric measures available in the Minerva package (25) by computing the maximal information coefficient (MIC), maximum edge value (MEV), and maximum asymmetry score (MAS). Furthermore, the relative and absolute IC50 (i.e. IC50 measures, which were computed based on the top and bottom plateaus of the curve or based on the blank and the positive control values, respectively), relative inhibition (RI) value, area under curve of drug- response fitted line (AUC), and the median of cell viability in the drug response experiments were
+
+<--- Page Split --->
+
+assessed to select the best measurement. The chosen measurement was later used as a weight value for the edges of the weighted bipartite network reconstruction.  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1: Flowchart of the study </center>  
+
+Data collection started from existing drug response databases, followed by incidence matrix extraction, weighted bipartite network reconstruction, network projection, and community detection. Furthermore, the intra- cluster homogeneity analysis was conducted using the similarity of drug and patient/cell members of all clusters according to available gene expression profiles, drug- target interactions, protein- protein interactions, and biological pathways. Finally, a high- throughput drug screening experiment was used to assess the synergistic behaviour of the proposed drug combinations.  
+
+Reconstruction and analysis of the bipartite network model  
+
+In our bipartite network model, one group of nodes contained drugs and the other group contained cancer cell lines (in GDSC and ALMANAC) or patient samples (in BeatAML). The edges were defined by incidence matrices derived from the min- max normalised values:  
+
+\[Normalised value = \frac{\mathrm{value - minimum(values)}}{\mathrm{maximum(values)} - \mathrm{minimum(values)}}.\]  
+
+This normalisation transforms these values, which indicate the potency of small molecules on cancer cell lines or patient samples, into a decimal between 0 and 1. Next, we projected the bipartite network into two similarity networks: the drug similarity network and sample similarity network. In the network projection, two unipartite graphs were derived from a bipartite graph, resulting in the deduction of a similar node's relationships. In this study, we projected similarity networks that consider the edge weights in the bipartite network. Then, we studied the general properties of the networks, such as network heterogeneity, centralisation,
+
+<--- Page Split --->
+
+and clustering coefficients. The critical step was community detection within the projected networks to discern functionally similar drugs and cells or patients regarding drug response. The modularity index was used to determine the best community detection algorithms, including infomap (26), fast greedy (27), and spinglass (28). Furthermore, we explored the network modules to propose a strategy for drug combination design.  
+
+## Computational corroboration  
+
+Multiple computational methods were applied to validate the predictions of the drug combinations and patient or cell stratification. The validation of the community structures is like the general cluster quality assessment method, and we assessed the clustering performance by matching the clustering structures to prior knowledge. This validation is foundational to possible drug combination designs. Alternatively, the combination of distinct drugs in terms of chemical structure, target profile, and implicated biological pathways is likeliest more efficient than similar drugs (7). Therefore, we used the drug- target network, protein- protein interactions, and signalling networks to justify the similarity of cluster elements. Thus, Chembl (29), drug target commons (DTC) (30), KEGG (31), and the OmniPath database (32) were used to extract prior annotations about the drugs and their targets. To compare the chemical structures of the drugs, a simplified molecular input line entry system (SMILES) of the drug molecules was retrieved and transformed into an extended connectivity fingerprint (ECFP) to assess the Dice similarity of the molecules. The Dice similarity is one of the standard metrics for molecular similarity calculations in which \(S_{A,B} = \frac{2c}{(a + b)}\) , where \(a\) is the number of ON bits in molecule A, \(b\) is the number of ON bits in molecule B, and \(c\) is the number of ON bits in both A and B molecules (33). Also, the corresponding gene expression profiles were used to assess similarity within a patient or cell line modules in the sample similarity networks. For reads per kilobase per million (RPKM) with negative values and counts per million (CPM), we used the Harmonic similarity and Jaccard distance, respectively, as follows:  
+
+\[S_{P,Q} = 2\times \sum_{i = 1}^{n}(P_{i}\times Q_{i}) / (P_{i} + Q_{i}),\]  
+
+\(D_{P,Q} = 1 - \sum_{i = 1}^{n}(P_{i}\times Q_{i}) / (\sum_{i = 1}^{n}P_{i}^{2} + \sum_{i = 1}^{n}Q_{i}^{2} + \sum_{i = 1}^{n}P_{i}\times Q_{i})\) , where \(P = \{P_{1},P_{2},\dots ,P_{n}\}\) and \(Q = \{Q_{1},Q_{2},\dots ,Q_{n}\}\) denote the vector of gene expression values for patients or cell lines, and \(n\) is the number of genes. In all cases, the similarity or distance scores were compared with the random grouping of small molecules or biological samples to perform statistical testing.
+
+<--- Page Split --->
+
+The synergy scores provided by the DrugComb database (34) were used to corroborate synergistic combinations of our network- based predictions, including HSA, Bliss, Loewe, ZIP, CSS, and S. Let us assume that drug 1 at dose \(\mathbf{x}_1\) and drug 2 at dose \(\mathbf{x}_2\) are used to produce the effects of \(\mathbf{y}_1\) and \(\mathbf{y}_2\) , and \(\mathbf{y}_c\) is the effect of their combination. Drug effect is usually measured as a percentage of cell death, and a drug combination is classified as synergetic, antagonistic, or non- interactive (35). The expected effect denoted by \(\mathbf{y}_e\) represents a non- interactive level, and it is quantified based on a reference model. Several mathematical models have been introduced to calculate the expected effect by assuming specific principles. The HSA model (36) considers the expected combination effect as the maximum of single- drug effects, that is, \(\mathbf{y}_e = \max (\mathbf{y}_1,\mathbf{y}_2)\) . The Loewe model (37) assumes that an individual drug produces \(\mathbf{y}_e\) at a higher dose than in the combination. In the Bliss model (38), \(\mathbf{y}_e\) is the effect of the two drugs acting independently. The ZIP model (35) considers the assumptions of the Loewe and Bliss models by assuming that, at the reference model, two drugs do not potentiate each other. CSS determines the sensitivity of a drug pair, and S synergy is based on the difference between the drug combination and the single drug dose- response curves (39).  
+
+Cell culture and reagents  
+
+AML cell lines MOLM- 16, NOMO- 1, and OCI- AML3 were kind gifts from Professor Caroline Heckman (University of Helsinki, Finland). MOLM- 16 and NOMO- 1 were cultured in RPMI- 1640 medium (Gibco/Thermo Fisher Scientific, Waltham, MA, USA) and OCI- AML3 in \(\alpha\) - MEM (with nucleosides; Gibco/Thermo Fisher Scientific) supplemented with GlutaMAX (Gibco CTS/Thermo Fisher Scientific), foetal bovine serum (20% for MOLM- 16 and OCI- AML3; 10% for NOMO- 1), and antibiotics.  
+
+Drug combination testing  
+
+The compounds dissolved in dimethyl sulfoxide (DMSO) were plated using Beckman Coulter Echo 550 Liquid Handler (Beckman Coulter, Indianapolis, IN, USA) combined with seven concentrations for each compound in half- log dilution series with 2.5/7.5/25 nl volumes, covering a 1,000- fold concentration range on black clear- bottom TC- treated 384- well plates (Corning #3764, Corning, NY, USA). All doses were randomised across the plate to minimise any plate effects. As positive (total killing) and negative (non- effective) controls, 100 \(\mu \mathrm{M}\) of benzetohonium chloride and 0.2% DMSO were used, respectively.  
+
+Cells were plated on pre- administered compound plates in 25 \(\mu \mathrm{l}\) (2500, 2000, or 1250 cells per well for MOLM- 16, NOMO- 1, and OCI- AML3 cell lines, respectively) using BioTek MultiFlo FX RAD (5 \(\mu \mathrm{l}\) cassette) (Biotek, Winooski, VT, USA) and incubated for 72 h at 37°C and 5% CO2. Cell
+
+<--- Page Split --->
+
+viability was then determined by dispensing 25 μl of Cell Titre Glow 2.0 reagent (Promega, Madison, WI, USA). Plates were incubated for 5 min and centrifuged for 5 min \((173 \times \mathrm{g})\) before reading luminescence with a PHERAstar FS multimode plate reader (BMG Labtech, Ortenberg, Germany).  
+
+## Results  
+
+Defining the edge weight of bipartite networks  
+
+In the Beat AML dataset, a set of 122 inhibitor drugs was used against 531 patient- derived AML samples. The spectra of low to high potency of drugs were observed across the patient- derived samples. However, this panel of small molecule inhibitors was selected according to their activity against the proteins involved in tyrosine- dependent and non- tyrosine kinase pathways, particularly for AML (19). First, we determined the weight value of the drug- sample interaction to be used in the bipartite network reconstruction. This value should describe the most potent compounds for inhibiting tumour cells regarding the drug sensitivity analysis. Adding to the relative and absolute \(\mathrm{IC}_{50}\) , RI value (39), and AUC, we calculated the median cell viability in the drug response experiments. The distribution of these measures was evaluated in terms of normality, skewness, and modality (Fig. 2) to choose the best measure as a weight in the bipartite network. The relationship of median to AUC was a high positive value (with the highest r Pearson correlation coefficient \(\sim 0.94\) ). The distribution of medians was unimodal in contrast to \(\mathrm{IC}_{50}\) distributions, homoscedastic contrary to RI distribution, and more symmetric (non- skewed) compared to AUC distribution. In addition to investigating the linear relationship, that is, Pearson correlation analysis, we computed MIC, which measures the relationship strength, and MEV to check the closeness of the relationship to being a function. Interestingly, the relationship between median and AUC displayed higher MAS and MEV ( \(\sim 0.75\) ) compared with the relationship of RI and AUC, meaning that median has a stronger association with AUC. Therefore, we have chosen the inverse of the actual median as the weight of the drug- patient interaction.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2: Comparison of different measures for drug response experiments in the Beat AML study. The lower triangle of this pairwise comparison matrix shows the pairwise scatter plots for ic50_abs (Absolute IC50), ic50_rel (Relative IC50), RI (Relative Inhibition), median (the median of cell viability), and AUC (Area Under Curve of cell viability fitted line). The diagonal panel describes the histogram of each measure independently. The upper triangle represents the Pearson correlation coefficients of the corresponding pairwise comparisons. </center>  
+
+## Analysis of bipartite networks  
+
+Furthermore, the maximum square submatrix of patient samples and small molecules was used as the incidence matrix of the bipartite network. Specifically, we selected the list- wise deletion strategy to remove missing values, and we used the complete cases of both variables. The downstream analysis was done on an undirected weighted bigraph comprising 176 (88 + 88) nodes and 7744 edges (Fig. 3A). The distribution of the min- max normalised edge weights indicated positive skewness, indicating that the cells were not highly sensitive to most drugs. All the performed analyses were also carried out for the GDSC dataset as proof of concept. The undirected weighted bigraph of the GDSC dataset comprised 532 (266 + 266) nodes and 70,756 edges (Fig. 3C). The distribution of the min- max normalised edge weights showed positive skewness in this dataset as well (Fig 3D), again indicating low potency for most of the drugs. Therefore, exploring the best combination is not straightforward, and categorising drug- sample
+
+<--- Page Split --->
+
+interactions seems to be required. Following the projection of these bigraphs as outlined in Fig. 3, two projected graphs, the patient similarity network (PSN) and drug similarity network (DSN), were reconstructed, such that each edge was obtained by multiplying the weighted incidence matrix. Thus, the edge weights of the projected graphs indicate the profile similarities of patient samples in PSN and small molecule inhibitors in DSN. Note that the edge weight values in DSNs and PSNs differ due to the different matrix multiplications.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3: Bigraphs of cancer datasets. The general overview of the bipartite graphs for the Beat AML (A) and GDSC (B) datasets is represented with the blue nodes as small molecule inhibitors, and red and green nodes as patient-derived and cell line samples, respectively. The distributions of edge weight values are also depicted using violin plots with scatter plots. </center>  
+
+The PSN and DSN of the Beat AML dataset contained 88 nodes and 3828 edges (Fig. 4), while in the GDSC projected similarity networks, there were 266 nodes and 35,378 edges (data not shown). In Fig. 4, the larger the node size, the more sensitive patient- derived samples and the more potent drugs. In this subset of the Beat AML dataset, without missing data, patient 16- 00627 was found to be the most sensitive and SNS- 032 was the most potent inhibitor (See Supplementary Fig. 1). The community detection was subsequently done for both similarity networks via modularity score optimisation, resulting in two communities for DSN with 50 and 38 small molecules, and two communities for PSN with 39 and 49 patient samples. Alternatively, we identified two clusters of patients with distinctive drug response profiles, suggesting two subcategories of the disease. Also, we detected two clusters of small molecules, which pointed to
+
+<--- Page Split --->
+
+disparate inhibiting patterns on the patient samples. In the following steps, we presented evidence of the consistency of cluster members in both networks using prior knowledge.  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4: Drug and PSNs of the Beat AML dataset. The force-directed layout was selected to depict both networks. The thickness of the edges corresponds to the edge weight of the original bipartite networks after network projection, considering the weight values. The edge thickness represents the weight value of similarity between each pair of patient samples or small molecules. The node size is proportional to the strength of each node, which is the sum of the edge weights of the adjacent edges for each node. </center>  
+
+Intra- cluster homogeneity analysis of similarity networks  
+
+## Drug similarity network  
+
+Focusing on small molecules, we presumed that inhibitory molecules with correlated effects on cell survival tended to have similar structures, purposes, and functions (40- 43). Therefore, we evaluated the similarity of SMILES structures, the analogy of protein targets, and the biological pathways of the detected clusters in the DSNs against random groupings of molecules. The distribution of the Dice similarity of the SMILES structures differed significantly between the random grouping and the clusters based on network topology (Fig. 5A). The statistical test of the median difference also resulted in the lowest p- values for both the pairwise two- sample Wilcoxon and Kruskal- Wallis rank sum test (p- value \(< 2e - 16\) ). Evaluating their target similarities, we explored the protein targets of the small molecule inhibitors and examined the number of target intersections of small molecule pairs within the clusters. In this analysis, DTC
+
+<--- Page Split --->
+
+and OmniPath were applied to explore the binding targets of small molecules and second- order node neighbours (secondary targets) in the signalling network, respectively. Assuming that proteins usually correspond to multiple signalling pathways, the KEGG database was used to check the number of pathway intersections of the protein targets for each pair of small molecules. The median similarity measures of the intersections within the network clusters significantly exceeded those for a large set of random pairs of small molecules (Fig. 5B- D) (p- value \(< 2.2e - 16\) , Kruskal- Wallis rank sum test). Analysis of the GDSC dataset gave similar results (Fig. 6) (p- value \(< 2.2e - 16\) , Kruskal- Wallis rank sum test), suggesting that our method is also reproducible for the analysis of cell line- based datasets.  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5: Beat AML intra-cluster homogeneity analysis. (A) The distribution of SMILE structure similarities of DSN clusters compared to random grouping. (B) The distribution of pairwise intersection size of binding protein targets, (C) corresponding KEGG pathways, and (D) secondary targets in the OmniPath database. </center>
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Figure 6: GDSC intra-cluster homogeneity analysis. (A) The distribution of SMILE structure similarities of DSN clusters compared to random grouping. (B) The distribution of pairwise intersection size of immediate protein targets, (C) corresponding KEGG pathways, and (D) second targets in the OmniPath database. </center>  
+
+## Patient and cell-line similarity network  
+
+Next, we examined the member consistency of the patient clusters in the PSN using other available data from patient samples in the Beat AML dataset. The gene expression data, including the RPKM and CPM of the samples, were utilised to check the pairwise similarity of the cluster members. The similarity measures were also computed for a large set of random pairs of patient samples to compare with our patient stratification using network clustering. When we compared the harmonic mean similarities of the RPKM values, the pairwise similarities of patients within the clusters significantly exceeded those of the randomly selected patients (p- value \(< 2.2e - 16\) , Kruskal- Wallis rank sum test) (Fig. 7A). For the CPM dataset, the distributions of Jaccard distance were shown, where the distances within the clusters were statistically lower than those in the random group (p- value \(= 4.655e - 05\) , Kruskal- Wallis rank sum test) (Fig. 7B). For the GDSC dataset, we used the expression profiles of signature genes provided by the SPEED platform (44). Then, differentially expressed genes were used to provide gene signatures of perturbed cancer- related pathways. In this dataset, there were 11 activity scores to represent the activity levels of 11 well- known pathways for each cell line. Therefore, we compared the distance distributions of the cell line pairs in the clusters to a set of random pairs of cell lines. Our findings indicated that
+
+<--- Page Split --->
+
+the distances within the clusters were much lower than those in the random grouping (p- value = 6.94e- 08, Kruskal- Wallis rank sum test) (Fig. 7C).  
+
+![](images/Figure_7.jpg)
+
+<center>Figure 7: Validation of network communities of PSN. (A) The distribution of similarity of RPKM in the Beat AML dataset. (B) The distribution of distances of CPM in the Beat AML dataset. (C) The distribution of distances of pathway-based activity scores in GDSC dataset. (D) The frequently mutated genes in the clusters of Beat AML patients. The non-benign mutations with the possibility of being damaged in greater than 0.5 were selected to find the intersection of mutated genes. The gene names are shown with the relative frequency of mutated genes in each cluster (e.g. NPM1—0.38 indicates 38% of the patients in cluster 1 have this mutation). The lines between mutated genes illustrate the rank shift in the two clusters. </center>  
+
+The Beat AML study also provided the first detailed view of the mutational landscape in AML. Here, we used a dataset of non- benign gene mutations to characterise both clusters of patient samples. As shown in Fig. 7D, both clusters of patients demonstrate a distinct profile of gene mutations regarding the involved genes and the ranks of genes based on frequency. Previously, Tyner et al. highlighted the importance of TP53 and ASXL gene mutations, both responsible for the broad drug resistance patterns (19). They further showed that mutations in certain genes may identify disease subgroups sensitive to certain inhibitors. For example, they found that patients with FLT3- ITD and NPM1 mutations were sensitive to SYK inhibitors.
+
+<--- Page Split --->
+
+Interestingly, our molecular-independent network-based approach to characterise patient samples also captured the significance of the mutations above. Furthermore, our findings indicate that TP53, DNMT3A, and NRAS were the most frequently mutated genes in one of the patient clusters, while TET2 and NPM1 were the most frequently mutated genes in the other cluster, along with the FLT3- ITD mutation. These results suggest that the phenotype- level information in drug response data can corroborate the genotype- level information to stratify patients more effectively.  
+
+## Inter-cluster design strategy for drug combinations  
+
+We assumed that the best drug combination strategy was the selection of one drug from each cluster to block potential drug resistance mechanisms and cancer recurrence. A common drug combination design could be the use of the most effective drugs of each cluster to prohibit cancer cells more effectively. However, other pharmacologic evidence can encourage the choice of the best combination of drugs more specifically. As the focus in drug combination studies also lies in finding the most synergistic drug combinations, previously reported studies were used to explore the synergy values (i.e. the degree of interactions) of drug combinations. First, we checked if the combinations of the top five drugs (based on the median values of cell viability) of each cluster in the Beat AML and GDSC datasets (Table 1) were found in the DrugComb database. However, there were no reports regarding the 25 possible combinations of these drugs, so we aimed to compare the average synergistic values for these 10 drugs in the whole database. Fig. 8 shows the distributions of synergy values in DrugComb, highlighting the mean of the synergy of the bottom and top five drugs in each network cluster. This analysis revealed the reasonably high potential of the combinations of the top five drugs according to the average median values in both Beat AML and GDSC datasets (p- value = 2.96e- 02 and p- value = 3.56e- 02, Wilcox rank sum test, respectively).  
+
+Table 1: Top five small molecules in each cluster of DSNs   
+
+<table><tr><td></td><td>Cluster 1</td><td>Cluster 2</td></tr><tr><td rowspan="5">Beat AML</td><td>SNS-032 (BMS-387032)</td><td>Dovitinib (CHIR-258)</td></tr><tr><td>Flavopiridol</td><td>Nintedanib</td></tr><tr><td>Panobinostat</td><td>Doramapimod (BIRB 796)</td></tr><tr><td>AT7519</td><td>KI20227</td></tr><tr><td>Bortezomib (Velcade)</td><td>Cabozantinib</td></tr><tr><td></td><td></td><td></td></tr><tr><td>GDSC</td><td>Amuvatinib<br>GSK690693</td><td>Sepantronium bromide (YM-155)<br>Belinostat</td></tr></table>
+
+<--- Page Split --->
+
+
+<table><tr><td></td><td>Vinblastine</td><td>AT-7519</td></tr><tr><td></td><td>AS605240</td><td>CAY10603</td></tr><tr><td></td><td>HG6-64-1</td><td>AR-42</td></tr></table>  
+
+![](images/Figure_8.jpg)
+
+<center>Figure 8: Distribution of drug combination synergy scores in the DrugComb database. The median of synergy zip score for the top and bottom five drugs are represented by dashed lines in Beat AML dataset (A) and the GDSC dataset (B). </center>  
+
+## Synergy analysis of the inter-cluster combination of drugs  
+
+For further validation of our strategy for predicting synergistic drug combinations using network modelling, we focused on the ALMANAC dataset (21), which has 1,892,650 combinations of 103 inhibitors tested on 60 cell lines. The same procedure as described in Fig. 1 was implemented to extract the drug modules in the DSN according to the available single drug experiments in this dataset. The median inhibition values of the single- drug responses on cell lines were used as weight values in the bipartite drug- cell line network. Using the projection of the weighted DSN, clusters of drugs with similar effect profiles on cell lines were extracted.  
+
+According to our predefined assumption, the combinations of drugs from different clusters were used as the positive group and the combinations of drugs within the clusters as the negative group. Then, we retrieved the synergy and sensitivity scores of the combinations for both groups using the DrugComb computed values, especially the highest single agent (HSA), zero- interaction potency (ZIP), Bliss, Loewe, combinational sensitivity score (CSS), and S synergy. Fig. 9A shows that the positive group of drug combinations exhibited a significantly higher value of drug synergy than the negative group. This result was evident for all types of synergy measures, indicating the superiority of the strategy of using inter- cluster drug combinations. These data
+
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+
+also indicate the efficiency of our proposed network- based modelling to discern drugs with similar profile effects on biological samples. Also, our proposed strategy of drug combination using the drugs of contrary clusters is likelier to acquire higher drug synergy and potency.  
+
+## High-throughput drug screening for the proposed drug combinations in AML cell lines  
+
+To further demonstrate the ability of our model in predicting specific and robust drug combinations, experimental corroboration was conducted on a subset of 45 drug combinations for 3 AML cell lines, MOLM- 16, OCI- AML3, and NOMO- 1. Also, 25 out of 45 drug combinations originated from the top five drugs of the two clusters as the positive group, where higher synergy was predicted by our model, while others were the combinations of the top five drugs within each cluster, which transformed into 20 combinations as the negative group. The findings of the experimental validation of 135 drug- drug- cell line triplets is depicted in Fig. 9B using the ZIP, Bliss, HSA, and Loewe models to assess the degree of synergy. The drug combinations predicted by our model in the positive group were validated as more synergistic when considering positive scores as evidence of synergy degree (Fig. 10 and Supplementary Fig. 2). These findings were statistically more significant when using Bliss or HSA measures. Overall, these results demonstrate the robustness of network- based predictions across various experimental setups and synergy scoring models, and the ability of our network- based model to detect new combinations of treatments.
+
+<--- Page Split --->
+![](images/Figure_9.jpg)
+
+<center>Figure 9: Synergy of drug combinations. (A) The combinational sensitivity (CSS) and synergy scores (S, synergy_bliss, synergy_bsa, synergy_loewe, and synergy_zip) of drug combinations in the ALMANAC dataset. The top five drugs of cluster 1 (Cabazitaxel, 5-FU, Cytarabine hydrochloride, Methotrexate, Bleomycin) and cluster 2 (CHEMBL17639, Gefitinib, Ixabepilone, Dexrazoxane, Eloxatin) for inter-cluster and intra-cluster combinations are shown in blue and red as the positive and negative groups, respectively. Each plot contains a scatter plot, a notch box plot, and mean values for each group. The p-value represents the one-sided Student's t-test significance for each score separately. (B) The measured synergy of drug combination scores in the experimental validation of selected drugs based on network modelling of the Beat AML data in three AML cell lines. Four measures of synergy, that is, ZIP, HSA, Bliss, and Loewe, are seen as notch box plots for the experimental confirmation of the 25 chosen predictions in three cell lines. Inter-cluster drug combinations are shown in blue as the positive group, and the intra-cluster combinations are shown in red as the negative group. </center>
+
+<--- Page Split --->
+![](images/Supplementary_Figure_2.jpg)
+
+<center>Figure 10: The top synergistic drug combinations identified in the positive group. These matrices represent the highest synergistic combination based on four measures of synergy. HSA and LOEWE methods indicate that the cabozanitib and AT7519 combination is the highest synergistic combination. The combination of cabozanitib and panobinostat is the most synergistic based on ZIP and Bliss measures. For each combination, the sensitivity landscapes are shown in both 2D and 3D. The complete sensitivity landscapes for all 135 drug combinations can be found in supplementary Fig. 2. </center>  
+
+## Discussion  
+
+The availability of single- drug response datasets for cancer cell lines has prompted us to develop methods for predicting and selecting the most effective combination therapy. Several AI- based combination prediction approaches have recently been introduced that combine high- throughput molecular profiling data with drug response data to improve prediction and validation. To reflect the relationships between drug combinations, Narayan et al. used dose- response data from pharmacogenomic encyclopaedias and represented them as drug atlas (45). Combining with the pathway/gene ontology data, their approach enables the prediction of combinatorial therapy, i.e., vulnerability when attacked by two drugs that can be related to tumour- driving mutations. They repeated the predicted synergies in several tumours, including glioblastoma, breast cancer, melanoma, and leukaemia mouse models, highlighting the cancer-
+
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+
+independent prediction power of drug combination treatment. Ianevski et al. also showed that bulk viability single- agent screening assays had unexpectedly large predictability for AML cell subpopulation co- inhibition effects when combined with scRNA- seq transcriptomic data (18). They developed a machine- learning model by combining single- cell RNA sequencing with ex vivo single- agent testing for AML with a different genetic background. They displayed an accurate prediction of synergistic patient- specific combinations while avoiding the inhibition of non- malignant cells. However, while our biomarker- independent approach relies only on the phenotypic level of information, that is, drug- response data, our predictions were compatible with the molecular profiling and biochemical annotations when it came to assessing the intra- cluster homogeneity of drugs, patients, and cell lines  
+
+Moreover, a training machine- learning model for predicting drug combination response, comboFM, was recently introduced using drug combination screening data as a training dataset (46). comboFM uses a factorisation machine to model cell context- specific drug interactions through higher- order tensors. Julkunen et al. demonstrated that comboFM enables leveraging information from previous experiments performed on similar drugs and cells as training data when predicting responses of new combinations, insofar as untested cells (testing data). They displayed high predictive performance and robust applicability of comboFM in various prediction scenarios using experimental validation of a set of previously untested drugs. However, we expounded that the prediction accuracy of the inter- cluster design strategy of drug combinations based on multipartite networks can be achieved independently from the high- quality training dataset.  
+
+Strictly speaking, in the present study, we revisited the analysis of nominal variables, namely drug name and sample identity, in drug screening results for data mining using graph theory, which we termed the nominal data mining approach. We first considered data quality control, such as outlier detection, outlier treatment, biological and technical replicates. Because of the discrete explanatory independent variable (i.e. drug doses) (47), we assumed that regression- based measurements might even be discarded; hence, we demonstrated that median values can represent an appropriate weight score in comparing drug functionality for network reconstruction. These values were used to quantify and weight the bipartite network, which reflects the interaction strength of the drugs and biological samples. Then, two similarity networks were provided by weighted network projection to detect the topological structure of the network communities. We showed that network communities represent a rationale starting point for proposing a combinational drug regimen. Our computational and experimental
+
+<--- Page Split --->
+
+validation steps amplified the logic of our proposed platform. Hence, while training datasets were not required in this method to predict drug combination, drug response data alone were adequate for the prediction, without integrating prior knowledge of biochemical profiling.  
+
+Noting that the occurrence of synergistic toxicities, which can arise from additive toxicities when targets are shared by the combined drugs, is a major barrier to applying combination therapy in the clinic (48). If drug screening data on healthy cells are available, we suggest that a similar strategy for predicting toxicity without losing efficacy is also essential before future translational experiments. Ianevski et al. previously illustrated the importance of a desired synergy- efficacy- toxicity balance for predicting patient- customised drug combinations (18). Hence, drug- response data on healthy cells are demanded to complement synergistic interactions of drug combinations with toxicity predictions; where drug synergy and toxicity data are optimally matched for combinatorial therapy, stronger and longer- lasting outcomes of drug combinations can be predicted.  
+
+Furthermore, prospective work will necessitate the provision of further patient- derived experimental validations. Despite the fact that our prediction depends solely on the drug sensitivity dataset, our suggested combinations address the common mutational assigned aetiology of AML. Remarkably, this combination was proposed purely on the grounds of the phenotypic response of cancer cells or patient samples to the drugs, with no previous knowledge of the disease's genetic origin.
+
+<--- Page Split --->
+
+## References  
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+
+## Supplementary figures  
+
+Supplementary figure 1: Drug and patient nodes in the projected networks of the Beat AML dataset. The nodes are ordered based on the strength of each node, which is the sum of the edge weights of the adjacent edges for each node.  
+
+Supplementary figure 2: The complete interaction landscapes for all the 135 drug combinations.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+SupplementaryFig1. pdf SupplementaryFig2. pdf
+
+<--- Page Split --->

preprint/preprint__5f3b415aff982a510536358770e8c1ff2c485133bc197bbe4dc106f74e752aed/preprint__5f3b415aff982a510536358770e8c1ff2c485133bc197bbe4dc106f74e752aed_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 106, 901, 210]]<|/det|>
+# Facilitating the design of combination therapy for cancer using multipartite network models: Emphasis on acute myeloid leukaemia  
+
+<|ref|>text<|/ref|><|det|>[[44, 228, 598, 270]]<|/det|>
+Mohieddin Jafari (mohieddin.jafari@helsinki.fi) University of Helsinki https://orcid.org/0000- 0002- 6991- 8587  
+
+<|ref|>text<|/ref|><|det|>[[44, 276, 216, 316]]<|/det|>
+Mehdi Mirzaie Helsinki University  
+
+<|ref|>text<|/ref|><|det|>[[44, 323, 216, 363]]<|/det|>
+Jie Bao Helsinki University  
+
+<|ref|>text<|/ref|><|det|>[[44, 370, 270, 410]]<|/det|>
+Famaz Barneh Princess Máxima Center  
+
+<|ref|>text<|/ref|><|det|>[[44, 416, 598, 457]]<|/det|>
+Shuyu Zheng University of Helsinki https://orcid.org/0000- 0003- 0624- 8077  
+
+<|ref|>text<|/ref|><|det|>[[44, 462, 216, 502]]<|/det|>
+Johanna Eriksson Helsinki University  
+
+<|ref|>text<|/ref|><|det|>[[44, 509, 216, 549]]<|/det|>
+Jing Tang Helsinki University  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 590, 102, 607]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 627, 584, 647]]<|/det|>
+Keywords: drug therapy, cancer treatments, myeloid leukaemia  
+
+<|ref|>text<|/ref|><|det|>[[44, 666, 305, 686]]<|/det|>
+Posted Date: June 22nd, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 704, 463, 724]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 577256/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 741, 910, 784]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 820, 910, 863]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on April 19th, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 29793- 5.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[125, 97, 904, 190]]<|/det|>
+# Facilitating the design of combination therapy for cancer using multipartite network models: Emphasis on acute myeloid leukaemia  
+
+<|ref|>text<|/ref|><|det|>[[92, 197, 910, 243]]<|/det|>
+Mohieddin Jafari \(^{1*}\) , Mehdi Mirzaie \(^{1}\) , Jie Bao \(^{1}\) , Farnaz Barneh \(^{2}\) , Shuyu Zheng \(^{1}\) , Johanna Eriksson \(^{1}\) , Jing Tang \(^{1*}\)  
+
+<|ref|>text<|/ref|><|det|>[[92, 286, 890, 330]]<|/det|>
+\(^{1}\) Research Program in Systems Oncology, Faculty of Medicine, University of Helsinki, Finland \(^{2}\) Prinses Maxima Center for Pediatric Oncology, 3584 CS Utrecht, the Netherlands  
+
+<|ref|>title<|/ref|><|det|>[[93, 362, 316, 380]]<|/det|>
+# Corresponding authors:  
+
+<|ref|>text<|/ref|><|det|>[[92, 388, 340, 504]]<|/det|>
+Jing Tang  Tel. +358 45 8689708  Jing.tang@helsinki.fi  Mohieddin Jafari  Mohieddin.jafari@helsinki.fi
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[93, 87, 181, 103]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[91, 110, 936, 584]]<|/det|>
+From the drug discovery perspective, combination therapy is recommended for cancer treatment due to its efficiency and safety compared to the common cytotoxic and single- targeted monotherapies. However, identifying effective drug combinations is time- and cost- consuming. Here, we offer a novel strategy for predicting potential drug combinations and patient subclasses by constructing multipartite networks using drug- response data on patient samples. In this study, we used Beat AML and GDSC, two comprehensive datasets based on patient- derived and cell line- based samples, to show the potential of multipartite network modelling in combinatorial cancer therapy. We used the median values of cell viability to compare drug potency and reconstruct a weighted bipartite network that models the interaction of drugs and biological samples. Then, clusters of network communities were identified in two projected networks based on the topological structure of the networks. Chemical structures, drug- target networks, protein- protein interactions, and signalling networks were used to corroborate the intra- cluster homogeneity. We further leveraged the community structures within the drug- based multipartite networks to discover effective multi- targeted drug combinations and synergy levels, which were supported with more evidence using the DrugComb and ALMANAC databases. Furthermore, we confirmed the potency of selective combinations of drugs against monotherapy in in vitro experiments using three acute myeloid leukaemia (AML) cell lines. Taken together, this study presents an innovative data- driven strategy based on multipartite networks to suggest potential drug combinations to improve AML treatment.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[93, 87, 224, 104]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[91, 112, 927, 432]]<|/det|>
+Studies on cases with advanced cancers have shown that less than \(10\%\) of patients have actionable mutations, and the improvement of outcomes is unobserved in a randomised trial of precision medicine based on genomic profiles (1). The current limitation of genomics- centric personalised medicine falls short of the enormous heterogeneity and lack of actionable and sustainable treatment options. With a few exceptions, patient genomic signatures with clinical pathology do not typically predict drug responses. More precisely, cancer can principally be considered a signalling disease, not a genetic disease. There is a wealth of data that has validated this hypothesis, including signalling behaviours involved in growth factor and nutrient responses, the process of entering and exiting the cell cycle, ensuring that chromosomes are segregated in an orderly, efficient and accurate manner during mitosis and apoptosis (2, 3). On the other hand, the complexity of crosstalk between signalling pathways necessitates to modify multiple targets in cancer cells; otherwise, a lack of complete response, resistance, and relapse will emerge during the course of treatment.  
+
+<|ref|>text<|/ref|><|det|>[[91, 437, 937, 911]]<|/det|>
+Despite the fact that large amounts of small molecules or drugs have been tested on many cell lines or patient- derived samples, using single drugs as monotherapies to cure cancer might not be a promising strategy, as it is known that the complex interactions of various biological components can induce drug resistance during the treatment of cancer (4- 6). As a matter of fact, monotherapy, the slogan of one target one drug—is inefficient in curing complex diseases, such as cancer (7, 8). Combination therapy or polytherapy with synergistic drugs may achieve a more effective and safer outcome by targeting several targets in the same or separate pathways of the complex system (4). To better identify the synergistic drug combination based on precision medicine, we need ex vivo drug screening to decipher the functional impact of cancer genomics at the phenotypic level and to understand their interactions in the context of biological networks (9, 10). Therefore, understanding network biology may provide a unique opportunity to leverage the rich source of drug response data to offer network- based models for combinatorial therapy. These network models have shown promise for developing clinical decision support tools to discriminate functional patient subclasses (11, 12). Even though there are networks reconstructed to model biological mechanisms of diseases and predict drug combination synergies based on molecular data (13- 16), network models have not been systematically applied to patient data, such as the drug response data of patient- derived samples, to predict patient- customised drug combinations (14). Instead, the ex vivo drug response data are straightforwardly translated into the clinic for patient treatment since these individualised
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[93, 82, 866, 127]]<|/det|>
+experiments represent the efficiency of some approved drugs on patient- derived primary cultures (17, 18).  
+
+<|ref|>text<|/ref|><|det|>[[90, 132, 923, 555]]<|/det|>
+In 2018, the Beat AML programme reported a cohort of 672 tumour specimens collected from 531 patients, analysing the ex vivo sensitivity for 122 drugs alongside the mutational status and the gene expression signatures of the samples (19). Despite the dearth of large patient- related drug response datasets, some large cell line- based datasets, such as genomics of drug sensitivity in cancer (GDSC) and ALMANAC, can offer a strong source of supporting evidence for predictions. The GDSC database contains the responses of 1001 cancer cell lines to 265 anti- cancer drugs, providing a rich source of information to connect genotypes with cellular phenotypes and to identify cancer- specific therapeutic options (20). The largest publicly accessible dataset for cancer combination drugs, such as ALMANAC, was recently published by the U.S. National Cancer Institute. This data collection contained more than 5,000 combinations of 104 investigational and licensed drugs, with synergies calculated against 60 cancer cell lines, resulting in more than 290,000 synergy scores (21). Moreover, DrugComb (https://drugcomb.org/), a web- based portal for storing and studying drug combination screening datasets, offers a comprehensive visualisation of drug combination susceptibility and synergy, which can significantly aid in the understanding of drug interactions at unique dosage levels. Drugcomb now has 751,498 drug combinations and 717,684 single drug screens from 37 trials, which relate to 2040 cell lines and 216 cancer forms (22).  
+
+<|ref|>text<|/ref|><|det|>[[91, 558, 924, 804]]<|/det|>
+In this study, we developed a network pharmacology approach to predict potential drug combinations for acute myeloid leukaemia (AML) based on the Beat AML dataset. We proposed a drug combination strategy using multipartite network modelling of ex vivo drug screening data. By ex vivo drug response data, we directly accessed the individual phenotypes of the patients' cancer cells, and by network modelling, we demonstrated the similarity of drugs and AML patients. Then, we used the community structures within the drug- based multipartite networks to discover effective multi- targeted drug combination regimens. Our predicted drug combinations were only suggested regarding the phenotypic interactions of the cancer cells or patient samples with the drugs without prior understanding of the genetic origin or molecular understanding of the disease.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[93, 85, 183, 101]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[91, 111, 927, 406]]<|/det|>
+Fig. 1 presents the entire workflow of this study. The weighted bipartite network is constructed using the Beat AML dataset. This dataset is a collaborative research programme of 11 academic medical centres providing data on AML samples while offering genomics, clinical, and drug responses. It includes a cohort study of 672 tumour specimens collected from 531 patients and an analysis of 122 drug responses. To construct a weighted bipartite network, the best response read- out of drug potency was defined using information- based measures. Then, two unipartite networks were obtained using network projection on the samples and drugs. Next, communities of two projected networks were extracted, and intra- cluster homogeneity analysis was performed using the similarity of drugs and patients/cell members based on available gene expression profiles for patients, protein- protein interaction network, and biological pathways. The drug candidates for drug combination were selected from two different communities, and a high- throughput drug screening was used to assess their synergetic effects.  
+
+<|ref|>text<|/ref|><|det|>[[93, 414, 640, 433]]<|/det|>
+Defining the response read- out for drug screening experiments  
+
+<|ref|>text<|/ref|><|det|>[[91, 440, 935, 736]]<|/det|>
+Pharmacogenomic studies require extensive standardisation to avoid inconsistency of drug response data for further research and unbiased predictions (23, 24). Therefore, first, we controlled the quality of cell viability data to select the potent compounds. To achieve this, we examined the raw datasets regarding the availability of replicated data and outlier detection, followed by assessment of distribution, pairwise correlation, and homoscedasticity analyses to select the best response read- out or measure of drug potency. This analysis was performed using information- based nonparametric measures available in the Minerva package (25) by computing the maximal information coefficient (MIC), maximum edge value (MEV), and maximum asymmetry score (MAS). Furthermore, the relative and absolute IC50 (i.e. IC50 measures, which were computed based on the top and bottom plateaus of the curve or based on the blank and the positive control values, respectively), relative inhibition (RI) value, area under curve of drug- response fitted line (AUC), and the median of cell viability in the drug response experiments were
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 83, 905, 125]]<|/det|>
+assessed to select the best measurement. The chosen measurement was later used as a weight value for the edges of the weighted bipartite network reconstruction.  
+
+<|ref|>image<|/ref|><|det|>[[213, 135, 808, 440]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[390, 441, 637, 456]]<|/det|>
+<center>Figure 1: Flowchart of the study </center>  
+
+<|ref|>text<|/ref|><|det|>[[92, 461, 935, 584]]<|/det|>
+Data collection started from existing drug response databases, followed by incidence matrix extraction, weighted bipartite network reconstruction, network projection, and community detection. Furthermore, the intra- cluster homogeneity analysis was conducted using the similarity of drug and patient/cell members of all clusters according to available gene expression profiles, drug- target interactions, protein- protein interactions, and biological pathways. Finally, a high- throughput drug screening experiment was used to assess the synergistic behaviour of the proposed drug combinations.  
+
+<|ref|>text<|/ref|><|det|>[[92, 606, 609, 624]]<|/det|>
+Reconstruction and analysis of the bipartite network model  
+
+<|ref|>text<|/ref|><|det|>[[92, 631, 923, 699]]<|/det|>
+In our bipartite network model, one group of nodes contained drugs and the other group contained cancer cell lines (in GDSC and ALMANAC) or patient samples (in BeatAML). The edges were defined by incidence matrices derived from the min- max normalised values:  
+
+<|ref|>equation<|/ref|><|det|>[[139, 705, 606, 734]]<|/det|>
+\[Normalised value = \frac{\mathrm{value - minimum(values)}}{\mathrm{maximum(values)} - \mathrm{minimum(values)}}.\]  
+
+<|ref|>text<|/ref|><|det|>[[91, 740, 922, 911]]<|/det|>
+This normalisation transforms these values, which indicate the potency of small molecules on cancer cell lines or patient samples, into a decimal between 0 and 1. Next, we projected the bipartite network into two similarity networks: the drug similarity network and sample similarity network. In the network projection, two unipartite graphs were derived from a bipartite graph, resulting in the deduction of a similar node's relationships. In this study, we projected similarity networks that consider the edge weights in the bipartite network. Then, we studied the general properties of the networks, such as network heterogeneity, centralisation,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 82, 931, 202]]<|/det|>
+and clustering coefficients. The critical step was community detection within the projected networks to discern functionally similar drugs and cells or patients regarding drug response. The modularity index was used to determine the best community detection algorithms, including infomap (26), fast greedy (27), and spinglass (28). Furthermore, we explored the network modules to propose a strategy for drug combination design.  
+
+<|ref|>sub_title<|/ref|><|det|>[[94, 236, 350, 253]]<|/det|>
+## Computational corroboration  
+
+<|ref|>text<|/ref|><|det|>[[91, 259, 936, 741]]<|/det|>
+Multiple computational methods were applied to validate the predictions of the drug combinations and patient or cell stratification. The validation of the community structures is like the general cluster quality assessment method, and we assessed the clustering performance by matching the clustering structures to prior knowledge. This validation is foundational to possible drug combination designs. Alternatively, the combination of distinct drugs in terms of chemical structure, target profile, and implicated biological pathways is likeliest more efficient than similar drugs (7). Therefore, we used the drug- target network, protein- protein interactions, and signalling networks to justify the similarity of cluster elements. Thus, Chembl (29), drug target commons (DTC) (30), KEGG (31), and the OmniPath database (32) were used to extract prior annotations about the drugs and their targets. To compare the chemical structures of the drugs, a simplified molecular input line entry system (SMILES) of the drug molecules was retrieved and transformed into an extended connectivity fingerprint (ECFP) to assess the Dice similarity of the molecules. The Dice similarity is one of the standard metrics for molecular similarity calculations in which \(S_{A,B} = \frac{2c}{(a + b)}\) , where \(a\) is the number of ON bits in molecule A, \(b\) is the number of ON bits in molecule B, and \(c\) is the number of ON bits in both A and B molecules (33). Also, the corresponding gene expression profiles were used to assess similarity within a patient or cell line modules in the sample similarity networks. For reads per kilobase per million (RPKM) with negative values and counts per million (CPM), we used the Harmonic similarity and Jaccard distance, respectively, as follows:  
+
+<|ref|>equation<|/ref|><|det|>[[139, 744, 450, 766]]<|/det|>
+\[S_{P,Q} = 2\times \sum_{i = 1}^{n}(P_{i}\times Q_{i}) / (P_{i} + Q_{i}),\]  
+
+<|ref|>text<|/ref|><|det|>[[91, 771, 930, 870]]<|/det|>
+\(D_{P,Q} = 1 - \sum_{i = 1}^{n}(P_{i}\times Q_{i}) / (\sum_{i = 1}^{n}P_{i}^{2} + \sum_{i = 1}^{n}Q_{i}^{2} + \sum_{i = 1}^{n}P_{i}\times Q_{i})\) , where \(P = \{P_{1},P_{2},\dots ,P_{n}\}\) and \(Q = \{Q_{1},Q_{2},\dots ,Q_{n}\}\) denote the vector of gene expression values for patients or cell lines, and \(n\) is the number of genes. In all cases, the similarity or distance scores were compared with the random grouping of small molecules or biological samples to perform statistical testing.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[91, 81, 936, 454]]<|/det|>
+The synergy scores provided by the DrugComb database (34) were used to corroborate synergistic combinations of our network- based predictions, including HSA, Bliss, Loewe, ZIP, CSS, and S. Let us assume that drug 1 at dose \(\mathbf{x}_1\) and drug 2 at dose \(\mathbf{x}_2\) are used to produce the effects of \(\mathbf{y}_1\) and \(\mathbf{y}_2\) , and \(\mathbf{y}_c\) is the effect of their combination. Drug effect is usually measured as a percentage of cell death, and a drug combination is classified as synergetic, antagonistic, or non- interactive (35). The expected effect denoted by \(\mathbf{y}_e\) represents a non- interactive level, and it is quantified based on a reference model. Several mathematical models have been introduced to calculate the expected effect by assuming specific principles. The HSA model (36) considers the expected combination effect as the maximum of single- drug effects, that is, \(\mathbf{y}_e = \max (\mathbf{y}_1,\mathbf{y}_2)\) . The Loewe model (37) assumes that an individual drug produces \(\mathbf{y}_e\) at a higher dose than in the combination. In the Bliss model (38), \(\mathbf{y}_e\) is the effect of the two drugs acting independently. The ZIP model (35) considers the assumptions of the Loewe and Bliss models by assuming that, at the reference model, two drugs do not potentiate each other. CSS determines the sensitivity of a drug pair, and S synergy is based on the difference between the drug combination and the single drug dose- response curves (39).  
+
+<|ref|>text<|/ref|><|det|>[[94, 461, 310, 478]]<|/det|>
+Cell culture and reagents  
+
+<|ref|>text<|/ref|><|det|>[[92, 485, 932, 630]]<|/det|>
+AML cell lines MOLM- 16, NOMO- 1, and OCI- AML3 were kind gifts from Professor Caroline Heckman (University of Helsinki, Finland). MOLM- 16 and NOMO- 1 were cultured in RPMI- 1640 medium (Gibco/Thermo Fisher Scientific, Waltham, MA, USA) and OCI- AML3 in \(\alpha\) - MEM (with nucleosides; Gibco/Thermo Fisher Scientific) supplemented with GlutaMAX (Gibco CTS/Thermo Fisher Scientific), foetal bovine serum (20% for MOLM- 16 and OCI- AML3; 10% for NOMO- 1), and antibiotics.  
+
+<|ref|>text<|/ref|><|det|>[[94, 640, 317, 657]]<|/det|>
+Drug combination testing  
+
+<|ref|>text<|/ref|><|det|>[[92, 663, 927, 833]]<|/det|>
+The compounds dissolved in dimethyl sulfoxide (DMSO) were plated using Beckman Coulter Echo 550 Liquid Handler (Beckman Coulter, Indianapolis, IN, USA) combined with seven concentrations for each compound in half- log dilution series with 2.5/7.5/25 nl volumes, covering a 1,000- fold concentration range on black clear- bottom TC- treated 384- well plates (Corning #3764, Corning, NY, USA). All doses were randomised across the plate to minimise any plate effects. As positive (total killing) and negative (non- effective) controls, 100 \(\mu \mathrm{M}\) of benzetohonium chloride and 0.2% DMSO were used, respectively.  
+
+<|ref|>text<|/ref|><|det|>[[92, 839, 928, 909]]<|/det|>
+Cells were plated on pre- administered compound plates in 25 \(\mu \mathrm{l}\) (2500, 2000, or 1250 cells per well for MOLM- 16, NOMO- 1, and OCI- AML3 cell lines, respectively) using BioTek MultiFlo FX RAD (5 \(\mu \mathrm{l}\) cassette) (Biotek, Winooski, VT, USA) and incubated for 72 h at 37°C and 5% CO2. Cell
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 81, 910, 178]]<|/det|>
+viability was then determined by dispensing 25 μl of Cell Titre Glow 2.0 reagent (Promega, Madison, WI, USA). Plates were incubated for 5 min and centrifuged for 5 min \((173 \times \mathrm{g})\) before reading luminescence with a PHERAstar FS multimode plate reader (BMG Labtech, Ortenberg, Germany).  
+
+<|ref|>sub_title<|/ref|><|det|>[[93, 187, 171, 204]]<|/det|>
+## Results  
+
+<|ref|>text<|/ref|><|det|>[[93, 215, 498, 234]]<|/det|>
+Defining the edge weight of bipartite networks  
+
+<|ref|>text<|/ref|><|det|>[[91, 240, 936, 712]]<|/det|>
+In the Beat AML dataset, a set of 122 inhibitor drugs was used against 531 patient- derived AML samples. The spectra of low to high potency of drugs were observed across the patient- derived samples. However, this panel of small molecule inhibitors was selected according to their activity against the proteins involved in tyrosine- dependent and non- tyrosine kinase pathways, particularly for AML (19). First, we determined the weight value of the drug- sample interaction to be used in the bipartite network reconstruction. This value should describe the most potent compounds for inhibiting tumour cells regarding the drug sensitivity analysis. Adding to the relative and absolute \(\mathrm{IC}_{50}\) , RI value (39), and AUC, we calculated the median cell viability in the drug response experiments. The distribution of these measures was evaluated in terms of normality, skewness, and modality (Fig. 2) to choose the best measure as a weight in the bipartite network. The relationship of median to AUC was a high positive value (with the highest r Pearson correlation coefficient \(\sim 0.94\) ). The distribution of medians was unimodal in contrast to \(\mathrm{IC}_{50}\) distributions, homoscedastic contrary to RI distribution, and more symmetric (non- skewed) compared to AUC distribution. In addition to investigating the linear relationship, that is, Pearson correlation analysis, we computed MIC, which measures the relationship strength, and MEV to check the closeness of the relationship to being a function. Interestingly, the relationship between median and AUC displayed higher MAS and MEV ( \(\sim 0.75\) ) compared with the relationship of RI and AUC, meaning that median has a stronger association with AUC. Therefore, we have chosen the inverse of the actual median as the weight of the drug- patient interaction.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[103, 103, 901, 440]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[108, 440, 920, 561]]<|/det|>
+<center>Figure 2: Comparison of different measures for drug response experiments in the Beat AML study. The lower triangle of this pairwise comparison matrix shows the pairwise scatter plots for ic50_abs (Absolute IC50), ic50_rel (Relative IC50), RI (Relative Inhibition), median (the median of cell viability), and AUC (Area Under Curve of cell viability fitted line). The diagonal panel describes the histogram of each measure independently. The upper triangle represents the Pearson correlation coefficients of the corresponding pairwise comparisons. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[94, 593, 355, 610]]<|/det|>
+## Analysis of bipartite networks  
+
+<|ref|>text<|/ref|><|det|>[[91, 625, 930, 897]]<|/det|>
+Furthermore, the maximum square submatrix of patient samples and small molecules was used as the incidence matrix of the bipartite network. Specifically, we selected the list- wise deletion strategy to remove missing values, and we used the complete cases of both variables. The downstream analysis was done on an undirected weighted bigraph comprising 176 (88 + 88) nodes and 7744 edges (Fig. 3A). The distribution of the min- max normalised edge weights indicated positive skewness, indicating that the cells were not highly sensitive to most drugs. All the performed analyses were also carried out for the GDSC dataset as proof of concept. The undirected weighted bigraph of the GDSC dataset comprised 532 (266 + 266) nodes and 70,756 edges (Fig. 3C). The distribution of the min- max normalised edge weights showed positive skewness in this dataset as well (Fig 3D), again indicating low potency for most of the drugs. Therefore, exploring the best combination is not straightforward, and categorising drug- sample
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[91, 82, 930, 227]]<|/det|>
+interactions seems to be required. Following the projection of these bigraphs as outlined in Fig. 3, two projected graphs, the patient similarity network (PSN) and drug similarity network (DSN), were reconstructed, such that each edge was obtained by multiplying the weighted incidence matrix. Thus, the edge weights of the projected graphs indicate the profile similarities of patient samples in PSN and small molecule inhibitors in DSN. Note that the edge weight values in DSNs and PSNs differ due to the different matrix multiplications.  
+
+<|ref|>image<|/ref|><|det|>[[111, 262, 860, 535]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[95, 560, 933, 642]]<|/det|>
+<center>Figure 3: Bigraphs of cancer datasets. The general overview of the bipartite graphs for the Beat AML (A) and GDSC (B) datasets is represented with the blue nodes as small molecule inhibitors, and red and green nodes as patient-derived and cell line samples, respectively. The distributions of edge weight values are also depicted using violin plots with scatter plots. </center>  
+
+<|ref|>text<|/ref|><|det|>[[91, 670, 933, 915]]<|/det|>
+The PSN and DSN of the Beat AML dataset contained 88 nodes and 3828 edges (Fig. 4), while in the GDSC projected similarity networks, there were 266 nodes and 35,378 edges (data not shown). In Fig. 4, the larger the node size, the more sensitive patient- derived samples and the more potent drugs. In this subset of the Beat AML dataset, without missing data, patient 16- 00627 was found to be the most sensitive and SNS- 032 was the most potent inhibitor (See Supplementary Fig. 1). The community detection was subsequently done for both similarity networks via modularity score optimisation, resulting in two communities for DSN with 50 and 38 small molecules, and two communities for PSN with 39 and 49 patient samples. Alternatively, we identified two clusters of patients with distinctive drug response profiles, suggesting two subcategories of the disease. Also, we detected two clusters of small molecules, which pointed to
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 82, 863, 127]]<|/det|>
+disparate inhibiting patterns on the patient samples. In the following steps, we presented evidence of the consistency of cluster members in both networks using prior knowledge.  
+
+<|ref|>image<|/ref|><|det|>[[60, 150, 980, 465]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[95, 472, 933, 574]]<|/det|>
+<center>Figure 4: Drug and PSNs of the Beat AML dataset. The force-directed layout was selected to depict both networks. The thickness of the edges corresponds to the edge weight of the original bipartite networks after network projection, considering the weight values. The edge thickness represents the weight value of similarity between each pair of patient samples or small molecules. The node size is proportional to the strength of each node, which is the sum of the edge weights of the adjacent edges for each node. </center>  
+
+<|ref|>text<|/ref|><|det|>[[93, 596, 591, 614]]<|/det|>
+Intra- cluster homogeneity analysis of similarity networks  
+
+<|ref|>sub_title<|/ref|><|det|>[[93, 626, 302, 643]]<|/det|>
+## Drug similarity network  
+
+<|ref|>text<|/ref|><|det|>[[91, 660, 933, 907]]<|/det|>
+Focusing on small molecules, we presumed that inhibitory molecules with correlated effects on cell survival tended to have similar structures, purposes, and functions (40- 43). Therefore, we evaluated the similarity of SMILES structures, the analogy of protein targets, and the biological pathways of the detected clusters in the DSNs against random groupings of molecules. The distribution of the Dice similarity of the SMILES structures differed significantly between the random grouping and the clusters based on network topology (Fig. 5A). The statistical test of the median difference also resulted in the lowest p- values for both the pairwise two- sample Wilcoxon and Kruskal- Wallis rank sum test (p- value \(< 2e - 16\) ). Evaluating their target similarities, we explored the protein targets of the small molecule inhibitors and examined the number of target intersections of small molecule pairs within the clusters. In this analysis, DTC
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[91, 81, 926, 303]]<|/det|>
+and OmniPath were applied to explore the binding targets of small molecules and second- order node neighbours (secondary targets) in the signalling network, respectively. Assuming that proteins usually correspond to multiple signalling pathways, the KEGG database was used to check the number of pathway intersections of the protein targets for each pair of small molecules. The median similarity measures of the intersections within the network clusters significantly exceeded those for a large set of random pairs of small molecules (Fig. 5B- D) (p- value \(< 2.2e - 16\) , Kruskal- Wallis rank sum test). Analysis of the GDSC dataset gave similar results (Fig. 6) (p- value \(< 2.2e - 16\) , Kruskal- Wallis rank sum test), suggesting that our method is also reproducible for the analysis of cell line- based datasets.  
+
+<|ref|>image<|/ref|><|det|>[[195, 320, 864, 651]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[95, 654, 933, 732]]<|/det|>
+<center>Figure 5: Beat AML intra-cluster homogeneity analysis. (A) The distribution of SMILE structure similarities of DSN clusters compared to random grouping. (B) The distribution of pairwise intersection size of binding protein targets, (C) corresponding KEGG pathways, and (D) secondary targets in the OmniPath database. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[190, 80, 844, 400]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[100, 405, 930, 465]]<|/det|>
+<center>Figure 6: GDSC intra-cluster homogeneity analysis. (A) The distribution of SMILE structure similarities of DSN clusters compared to random grouping. (B) The distribution of pairwise intersection size of immediate protein targets, (C) corresponding KEGG pathways, and (D) second targets in the OmniPath database. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[93, 508, 431, 525]]<|/det|>
+## Patient and cell-line similarity network  
+
+<|ref|>text<|/ref|><|det|>[[91, 527, 932, 897]]<|/det|>
+Next, we examined the member consistency of the patient clusters in the PSN using other available data from patient samples in the Beat AML dataset. The gene expression data, including the RPKM and CPM of the samples, were utilised to check the pairwise similarity of the cluster members. The similarity measures were also computed for a large set of random pairs of patient samples to compare with our patient stratification using network clustering. When we compared the harmonic mean similarities of the RPKM values, the pairwise similarities of patients within the clusters significantly exceeded those of the randomly selected patients (p- value \(< 2.2e - 16\) , Kruskal- Wallis rank sum test) (Fig. 7A). For the CPM dataset, the distributions of Jaccard distance were shown, where the distances within the clusters were statistically lower than those in the random group (p- value \(= 4.655e - 05\) , Kruskal- Wallis rank sum test) (Fig. 7B). For the GDSC dataset, we used the expression profiles of signature genes provided by the SPEED platform (44). Then, differentially expressed genes were used to provide gene signatures of perturbed cancer- related pathways. In this dataset, there were 11 activity scores to represent the activity levels of 11 well- known pathways for each cell line. Therefore, we compared the distance distributions of the cell line pairs in the clusters to a set of random pairs of cell lines. Our findings indicated that
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 82, 926, 127]]<|/det|>
+the distances within the clusters were much lower than those in the random grouping (p- value = 6.94e- 08, Kruskal- Wallis rank sum test) (Fig. 7C).  
+
+<|ref|>image<|/ref|><|det|>[[95, 150, 920, 528]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[95, 531, 934, 675]]<|/det|>
+<center>Figure 7: Validation of network communities of PSN. (A) The distribution of similarity of RPKM in the Beat AML dataset. (B) The distribution of distances of CPM in the Beat AML dataset. (C) The distribution of distances of pathway-based activity scores in GDSC dataset. (D) The frequently mutated genes in the clusters of Beat AML patients. The non-benign mutations with the possibility of being damaged in greater than 0.5 were selected to find the intersection of mutated genes. The gene names are shown with the relative frequency of mutated genes in each cluster (e.g. NPM1—0.38 indicates 38% of the patients in cluster 1 have this mutation). The lines between mutated genes illustrate the rank shift in the two clusters. </center>  
+
+<|ref|>text<|/ref|><|det|>[[91, 703, 914, 898]]<|/det|>
+The Beat AML study also provided the first detailed view of the mutational landscape in AML. Here, we used a dataset of non- benign gene mutations to characterise both clusters of patient samples. As shown in Fig. 7D, both clusters of patients demonstrate a distinct profile of gene mutations regarding the involved genes and the ranks of genes based on frequency. Previously, Tyner et al. highlighted the importance of TP53 and ASXL gene mutations, both responsible for the broad drug resistance patterns (19). They further showed that mutations in certain genes may identify disease subgroups sensitive to certain inhibitors. For example, they found that patients with FLT3- ITD and NPM1 mutations were sensitive to SYK inhibitors.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 82, 896, 252]]<|/det|>
+Interestingly, our molecular-independent network-based approach to characterise patient samples also captured the significance of the mutations above. Furthermore, our findings indicate that TP53, DNMT3A, and NRAS were the most frequently mutated genes in one of the patient clusters, while TET2 and NPM1 were the most frequently mutated genes in the other cluster, along with the FLT3- ITD mutation. These results suggest that the phenotype- level information in drug response data can corroborate the genotype- level information to stratify patients more effectively.  
+
+<|ref|>sub_title<|/ref|><|det|>[[92, 286, 537, 304]]<|/det|>
+## Inter-cluster design strategy for drug combinations  
+
+<|ref|>text<|/ref|><|det|>[[91, 318, 936, 714]]<|/det|>
+We assumed that the best drug combination strategy was the selection of one drug from each cluster to block potential drug resistance mechanisms and cancer recurrence. A common drug combination design could be the use of the most effective drugs of each cluster to prohibit cancer cells more effectively. However, other pharmacologic evidence can encourage the choice of the best combination of drugs more specifically. As the focus in drug combination studies also lies in finding the most synergistic drug combinations, previously reported studies were used to explore the synergy values (i.e. the degree of interactions) of drug combinations. First, we checked if the combinations of the top five drugs (based on the median values of cell viability) of each cluster in the Beat AML and GDSC datasets (Table 1) were found in the DrugComb database. However, there were no reports regarding the 25 possible combinations of these drugs, so we aimed to compare the average synergistic values for these 10 drugs in the whole database. Fig. 8 shows the distributions of synergy values in DrugComb, highlighting the mean of the synergy of the bottom and top five drugs in each network cluster. This analysis revealed the reasonably high potential of the combinations of the top five drugs according to the average median values in both Beat AML and GDSC datasets (p- value = 2.96e- 02 and p- value = 3.56e- 02, Wilcox rank sum test, respectively).  
+
+<|ref|>table<|/ref|><|det|>[[117, 740, 881, 900]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[293, 720, 733, 736]]<|/det|>
+Table 1: Top five small molecules in each cluster of DSNs   
+
+<table><tr><td></td><td>Cluster 1</td><td>Cluster 2</td></tr><tr><td rowspan="5">Beat AML</td><td>SNS-032 (BMS-387032)</td><td>Dovitinib (CHIR-258)</td></tr><tr><td>Flavopiridol</td><td>Nintedanib</td></tr><tr><td>Panobinostat</td><td>Doramapimod (BIRB 796)</td></tr><tr><td>AT7519</td><td>KI20227</td></tr><tr><td>Bortezomib (Velcade)</td><td>Cabozantinib</td></tr><tr><td></td><td></td><td></td></tr><tr><td>GDSC</td><td>Amuvatinib<br>GSK690693</td><td>Sepantronium bromide (YM-155)<br>Belinostat</td></tr></table>
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[118, 82, 880, 135]]<|/det|>
+
+<table><tr><td></td><td>Vinblastine</td><td>AT-7519</td></tr><tr><td></td><td>AS605240</td><td>CAY10603</td></tr><tr><td></td><td>HG6-64-1</td><td>AR-42</td></tr></table>  
+
+<|ref|>image<|/ref|><|det|>[[105, 177, 918, 413]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[91, 421, 933, 480]]<|/det|>
+<center>Figure 8: Distribution of drug combination synergy scores in the DrugComb database. The median of synergy zip score for the top and bottom five drugs are represented by dashed lines in Beat AML dataset (A) and the GDSC dataset (B). </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[92, 520, 587, 537]]<|/det|>
+## Synergy analysis of the inter-cluster combination of drugs  
+
+<|ref|>text<|/ref|><|det|>[[91, 538, 922, 707]]<|/det|>
+For further validation of our strategy for predicting synergistic drug combinations using network modelling, we focused on the ALMANAC dataset (21), which has 1,892,650 combinations of 103 inhibitors tested on 60 cell lines. The same procedure as described in Fig. 1 was implemented to extract the drug modules in the DSN according to the available single drug experiments in this dataset. The median inhibition values of the single- drug responses on cell lines were used as weight values in the bipartite drug- cell line network. Using the projection of the weighted DSN, clusters of drugs with similar effect profiles on cell lines were extracted.  
+
+<|ref|>text<|/ref|><|det|>[[91, 712, 933, 909]]<|/det|>
+According to our predefined assumption, the combinations of drugs from different clusters were used as the positive group and the combinations of drugs within the clusters as the negative group. Then, we retrieved the synergy and sensitivity scores of the combinations for both groups using the DrugComb computed values, especially the highest single agent (HSA), zero- interaction potency (ZIP), Bliss, Loewe, combinational sensitivity score (CSS), and S synergy. Fig. 9A shows that the positive group of drug combinations exhibited a significantly higher value of drug synergy than the negative group. This result was evident for all types of synergy measures, indicating the superiority of the strategy of using inter- cluster drug combinations. These data
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 82, 894, 152]]<|/det|>
+also indicate the efficiency of our proposed network- based modelling to discern drugs with similar profile effects on biological samples. Also, our proposed strategy of drug combination using the drugs of contrary clusters is likelier to acquire higher drug synergy and potency.  
+
+<|ref|>sub_title<|/ref|><|det|>[[92, 172, 825, 190]]<|/det|>
+## High-throughput drug screening for the proposed drug combinations in AML cell lines  
+
+<|ref|>text<|/ref|><|det|>[[90, 191, 930, 533]]<|/det|>
+To further demonstrate the ability of our model in predicting specific and robust drug combinations, experimental corroboration was conducted on a subset of 45 drug combinations for 3 AML cell lines, MOLM- 16, OCI- AML3, and NOMO- 1. Also, 25 out of 45 drug combinations originated from the top five drugs of the two clusters as the positive group, where higher synergy was predicted by our model, while others were the combinations of the top five drugs within each cluster, which transformed into 20 combinations as the negative group. The findings of the experimental validation of 135 drug- drug- cell line triplets is depicted in Fig. 9B using the ZIP, Bliss, HSA, and Loewe models to assess the degree of synergy. The drug combinations predicted by our model in the positive group were validated as more synergistic when considering positive scores as evidence of synergy degree (Fig. 10 and Supplementary Fig. 2). These findings were statistically more significant when using Bliss or HSA measures. Overall, these results demonstrate the robustness of network- based predictions across various experimental setups and synergy scoring models, and the ability of our network- based model to detect new combinations of treatments.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[140, 90, 900, 725]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[97, 729, 933, 896]]<|/det|>
+<center>Figure 9: Synergy of drug combinations. (A) The combinational sensitivity (CSS) and synergy scores (S, synergy_bliss, synergy_bsa, synergy_loewe, and synergy_zip) of drug combinations in the ALMANAC dataset. The top five drugs of cluster 1 (Cabazitaxel, 5-FU, Cytarabine hydrochloride, Methotrexate, Bleomycin) and cluster 2 (CHEMBL17639, Gefitinib, Ixabepilone, Dexrazoxane, Eloxatin) for inter-cluster and intra-cluster combinations are shown in blue and red as the positive and negative groups, respectively. Each plot contains a scatter plot, a notch box plot, and mean values for each group. The p-value represents the one-sided Student's t-test significance for each score separately. (B) The measured synergy of drug combination scores in the experimental validation of selected drugs based on network modelling of the Beat AML data in three AML cell lines. Four measures of synergy, that is, ZIP, HSA, Bliss, and Loewe, are seen as notch box plots for the experimental confirmation of the 25 chosen predictions in three cell lines. Inter-cluster drug combinations are shown in blue as the positive group, and the intra-cluster combinations are shown in red as the negative group. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 110, 839, 524]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[100, 527, 929, 613]]<|/det|>
+<center>Figure 10: The top synergistic drug combinations identified in the positive group. These matrices represent the highest synergistic combination based on four measures of synergy. HSA and LOEWE methods indicate that the cabozanitib and AT7519 combination is the highest synergistic combination. The combination of cabozanitib and panobinostat is the most synergistic based on ZIP and Bliss measures. For each combination, the sensitivity landscapes are shown in both 2D and 3D. The complete sensitivity landscapes for all 135 drug combinations can be found in supplementary Fig. 2. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[94, 630, 204, 647]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[91, 656, 926, 902]]<|/det|>
+The availability of single- drug response datasets for cancer cell lines has prompted us to develop methods for predicting and selecting the most effective combination therapy. Several AI- based combination prediction approaches have recently been introduced that combine high- throughput molecular profiling data with drug response data to improve prediction and validation. To reflect the relationships between drug combinations, Narayan et al. used dose- response data from pharmacogenomic encyclopaedias and represented them as drug atlas (45). Combining with the pathway/gene ontology data, their approach enables the prediction of combinatorial therapy, i.e., vulnerability when attacked by two drugs that can be related to tumour- driving mutations. They repeated the predicted synergies in several tumours, including glioblastoma, breast cancer, melanoma, and leukaemia mouse models, highlighting the cancer-
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 82, 927, 327]]<|/det|>
+independent prediction power of drug combination treatment. Ianevski et al. also showed that bulk viability single- agent screening assays had unexpectedly large predictability for AML cell subpopulation co- inhibition effects when combined with scRNA- seq transcriptomic data (18). They developed a machine- learning model by combining single- cell RNA sequencing with ex vivo single- agent testing for AML with a different genetic background. They displayed an accurate prediction of synergistic patient- specific combinations while avoiding the inhibition of non- malignant cells. However, while our biomarker- independent approach relies only on the phenotypic level of information, that is, drug- response data, our predictions were compatible with the molecular profiling and biochemical annotations when it came to assessing the intra- cluster homogeneity of drugs, patients, and cell lines  
+
+<|ref|>text<|/ref|><|det|>[[91, 333, 936, 602]]<|/det|>
+Moreover, a training machine- learning model for predicting drug combination response, comboFM, was recently introduced using drug combination screening data as a training dataset (46). comboFM uses a factorisation machine to model cell context- specific drug interactions through higher- order tensors. Julkunen et al. demonstrated that comboFM enables leveraging information from previous experiments performed on similar drugs and cells as training data when predicting responses of new combinations, insofar as untested cells (testing data). They displayed high predictive performance and robust applicability of comboFM in various prediction scenarios using experimental validation of a set of previously untested drugs. However, we expounded that the prediction accuracy of the inter- cluster design strategy of drug combinations based on multipartite networks can be achieved independently from the high- quality training dataset.  
+
+<|ref|>text<|/ref|><|det|>[[91, 608, 923, 905]]<|/det|>
+Strictly speaking, in the present study, we revisited the analysis of nominal variables, namely drug name and sample identity, in drug screening results for data mining using graph theory, which we termed the nominal data mining approach. We first considered data quality control, such as outlier detection, outlier treatment, biological and technical replicates. Because of the discrete explanatory independent variable (i.e. drug doses) (47), we assumed that regression- based measurements might even be discarded; hence, we demonstrated that median values can represent an appropriate weight score in comparing drug functionality for network reconstruction. These values were used to quantify and weight the bipartite network, which reflects the interaction strength of the drugs and biological samples. Then, two similarity networks were provided by weighted network projection to detect the topological structure of the network communities. We showed that network communities represent a rationale starting point for proposing a combinational drug regimen. Our computational and experimental
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[92, 82, 934, 152]]<|/det|>
+validation steps amplified the logic of our proposed platform. Hence, while training datasets were not required in this method to predict drug combination, drug response data alone were adequate for the prediction, without integrating prior knowledge of biochemical profiling.  
+
+<|ref|>text<|/ref|><|det|>[[91, 182, 934, 428]]<|/det|>
+Noting that the occurrence of synergistic toxicities, which can arise from additive toxicities when targets are shared by the combined drugs, is a major barrier to applying combination therapy in the clinic (48). If drug screening data on healthy cells are available, we suggest that a similar strategy for predicting toxicity without losing efficacy is also essential before future translational experiments. Ianevski et al. previously illustrated the importance of a desired synergy- efficacy- toxicity balance for predicting patient- customised drug combinations (18). Hence, drug- response data on healthy cells are demanded to complement synergistic interactions of drug combinations with toxicity predictions; where drug synergy and toxicity data are optimally matched for combinatorial therapy, stronger and longer- lasting outcomes of drug combinations can be predicted.  
+
+<|ref|>text<|/ref|><|det|>[[91, 433, 930, 579]]<|/det|>
+Furthermore, prospective work will necessitate the provision of further patient- derived experimental validations. Despite the fact that our prediction depends solely on the drug sensitivity dataset, our suggested combinations address the common mutational assigned aetiology of AML. Remarkably, this combination was proposed purely on the grounds of the phenotypic response of cancer cells or patient samples to the drugs, with no previous knowledge of the disease's genetic origin.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[93, 87, 207, 103]]<|/det|>
+## References  
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+
+<|ref|>sub_title<|/ref|><|det|>[[94, 587, 325, 606]]<|/det|>
+## Supplementary figures  
+
+<|ref|>text<|/ref|><|det|>[[93, 621, 920, 673]]<|/det|>
+Supplementary figure 1: Drug and patient nodes in the projected networks of the Beat AML dataset. The nodes are ordered based on the strength of each node, which is the sum of the edge weights of the adjacent edges for each node.  
+
+<|ref|>text<|/ref|><|det|>[[93, 688, 812, 722]]<|/det|>
+Supplementary figure 2: The complete interaction landscapes for all the 135 drug combinations.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 43, 311, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 290, 177]]<|/det|>
+SupplementaryFig1. pdf SupplementaryFig2. pdf
+
+<--- Page Split --->

preprint/preprint__5f44282bdf1db87c38eb7fe0d1af91b67dcf18e457633d14c451199a9f417da2/images_list.json

@@ -0,0 +1,152 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Vision and Design of WalkON (a) Illustration of the envisioned scenario where older adults engage in hiking while benefiting from the support provided by WalkON, thereby enhancing their daily mobility. (b) The design of WalkON comprises a textile structure encompassing a waist belt and two thigh harnesses that can be comfortably worn over regular clothing. The actuation mechanism relies on a tendon-driven transmission, with artificial tendons linked to the front part of the user's legs. These tendons are actuated by motors in accordance with the user's gait cycle. Motor commands deliver assistive forces during the swing phase of each step according to the hip joint kinematics recorded through Inertial Measurement Units (IMUs) in the sagittal plane.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        80,
+        884,
+        325
+      ]
+    ],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Uphill outdoor walking task and metabolic results for young adults. (a) The task involved walking along a steep \\(500\\mathrm{m}\\) uphill trail presenting altitudes of \\(127\\mathrm{m}\\) and \\(184\\mathrm{m}\\) respectively at the starting and ending points. Young adults walked at their preferred pace being unassisted (No Assistance, grey), and using WalkON (navy). (b, c) Metabolic results demonstrated a significant reduction in the cost of transport when using WalkON to perform the walking task. This result is visible from the cost of transport timeseries in (b), where the thick line represents the average across subjects, the shaded area the standard deviation, and from the mean values in (c). (d) The preferred mean walking speed of participants along the trail was not significantly altered when using WalkON. Results are presented as mean \\(\\pm\\) s.e.m. \\*\\*\\* indicates statistical significance with \\(\\mathrm{p}< 0.001\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        80,
+        884,
+        466
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Hip joint motion results for young adults. (a) Representation of the hip flexion angle shape in the sagittal plane along a gait cycle. (b) The raw hip phase portrait averaged across steps and subjects, combining hip angle and velocity measured on the sagittal plane, visually demonstrates that WalkON does not impose any restriction on natural hip motion. (c) The hip range of motion exhibited a significant increase with WalkON compared to the No Assistance condition. The upper row illustrates the mean time series of the hip angle across young adults and steps (shaded area represents the standard deviation), and the lower row shows the averaged hip range of motion (ROM). (d) There were no significant variations in hip velocity peaks with WalkON compared to the No Assistance condition. The upper row displays the mean time series of the hip velocity across young adults and steps (shaded area represents the standard deviation), while the bar plots in the lower row indicate the peak velocity during stance (negative values) and swing (positive values). Results in bar plots are presented as mean \\(\\pm\\) s.e.m. \\* indicates statistical significance with \\(\\mathrm{p}< 0.05\\) . The grey color indicates results for the No Assistance condition and the navy for the WalkON condition.",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        75,
+        884,
+        437
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Sense of Agency results for young adults. The sense of agency assessment for young adults using WalkON involved rating various items about motor control with assistive devices on a Likert scale from 1 to 7, indicating their level of agreement with each statement. Items 2, 3, 6, and 8, which are inversely coded, were re-coded before analysis. Answers distribution for the sense of agency questionnaire is presented in terms of boxplot (the white circle being the median). The mean score \\((\\pm \\mathrm{s.e.m.})\\) across young adults demonstrates that users felt a strong sense of agency when using WalkON. Participants significantly perceived themselves as having greater control over their movements than the device. This significant difference was tested in comparison to the midpoint value of 4 (Neither Agree Nor Disagree) on the Likert scale. \\(\\mathrm{***p}< 0.001\\)",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        90,
+        884,
+        346
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 Efficacy study with older adults. (a) Older participants completed a \\(400\\mathrm{m}\\) walk on a flat athletic track at their preferred speed in two conditions: No Assistance (grey) and with WalkON (navy). (b) Using WalkON significantly reduced the metabolic cost of transport. (c) The linear velocity of walking was unaltered on average across participants. (d, e, f) WalkON allowed for unrestricted hip motion. (g) Older adults reported strong perceived sense of control over voluntary movements while using WalkON. Results in bar plots are presented as mean \\(\\pm\\) s.e.m; timeseries are displayed as mean and standard deviation (shaded area). Sense of agency answers distribution is presented in terms of boxplot (the white circle being the median). \\(^{*}\\mathrm{p}< 0.05\\) , \\(^{**}\\mathrm{p}< 0.01\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        78,
+        875,
+        749
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Intra-participants results for the technology assessment with young adults. For each young adult (YA): (a) mean cost of transport while walking along the \\(500\\mathrm{m}\\) uphill hiking trail; (b) linear velocity of walking across the trial; (c) hip range of motion (ROM) and hip peak velocities as a mean across steps. The shaded bars indicate the average results across participants as presented in the main text (grey = No Assistance; navy = WalkON). The symbol \\* indicates statistical significance between conditions.",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        78,
+        888,
+        275
+      ]
+    ],
+    "page_idx": 39
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Intra-participants results for the efficacy study with older adults. For each older adult (OA): (a) mean cost of transport while walking along the 400m flat athletic track; (b) linear velocity of walking across the trial; (c) hip range of motion (ROM) and hip peak velocities as a mean across steps. The shaded bars indicate the average results across participants as presented in the main text (grey = No Assistance; navy = WalkON). The symbol \\* indicates statistical significance between conditions.",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        78,
+        888,
+        290
+      ]
+    ],
+    "page_idx": 41
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Textile blueprint (a) WalkON waist belt extended. (b) Layer composition of the belt with the back and frontal view in its closed configuration. (c) Thigh textile harness inner view and closed configuration.",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        130,
+        887,
+        682
+      ]
+    ],
+    "page_idx": 42
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 WalkON hardware components. (a) Computer-aided design of WalkON (b) Inertial Measurement Unit (IMU) sensors stream hip motion data via Bluetooth Low Energy to the control unit. This unit runs the controller on a microcontroller. The output is a velocity command sent to the actuators. (c) The textile structure of WalkON is composed by a waist belt and two thigh harnesses. (d) Anchor points are placed on the belt and thigh harness to guide the artificial tendons.",
+    "footnote": [],
+    "bbox": [
+      [
+        130,
+        155,
+        884,
+        555
+      ]
+    ],
+    "page_idx": 43
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 WalkON Controller. The WalkON control system operates across three levels. The High-Level controller determines the gait phase by calculating the polar angle between the hip joint position, \\(\\theta (t)\\) , and velocity, \\(\\dot{\\theta} (t)\\) , during each gait cycle in real-time. It then uses sinusoidal interpolation to create a foundational trajectory for the reference motor position, \\(\\theta_{\\mathrm{r}}(t)\\) . The Mid-Level controller applies a Kalman filter to \\(\\theta_{\\mathrm{r}}(t)\\) to eliminate noise emerging from the phase estimation method. Following this, it uses cubic spline interpolation to create the final trajectory for the final motor position reference, \\(\\theta_{\\mathrm{ref}}(t)\\) . The Low-Level controller actuates tendon displacement based on the motor commands derived from the outputs of the previous levels.",
+    "footnote": [],
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preprint/preprint__5f44282bdf1db87c38eb7fe0d1af91b67dcf18e457633d14c451199a9f417da2/preprint__5f44282bdf1db87c38eb7fe0d1af91b67dcf18e457633d14c451199a9f417da2.mmd

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+
+# Soft robotic shorts improve outdoor walking efficiency in older adults  
+
+Enrica Tricomi  
+
+enrica.tricomi@ziti.uni- heidelberg.de  
+
+Heidelberg University https://orcid.org/0000- 0002- 9117- 4385  
+
+Francesco Missiroli Heidelberg University  
+
+Michele Xiloyannis Akina AG  
+
+Nicola Lotti Heidelberg University  
+
+Xiaohui Zhang Heidelberg University  
+
+Marios Stefanakis Heidelberg University  
+
+Maximilian Theisen Heidelberg University https://orcid.org/0000- 0003- 1596- 805X  
+
+Jurgen Bauer Heidelberg University Hospital  
+
+Clemens Becker Heidelberg University Hospital  
+
+Lorenzo Masia Heidelberg  
+
+Biological Sciences - Article  
+
+Keywords: Soft robotic shorts, aging, mobility, walking assistance, metabolic cost  
+
+Posted Date: February 13th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3744597/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+
+Version of Record: A version of this preprint was published at Nature Machine Intelligence on October 1st, 2024. See the published version at https://doi.org/10.1038/s42256-024-00894-8.
+
+<--- Page Split --->
+
+# Soft robotic shorts improve outdoor walking efficiency in older adults  
+
+Enrica Tricomi \(^{1*}\) , Francesco Missiroli \(^{1\dagger}\) , Michele Xiloyannis \(^{1\ddagger}\) , Nicola Lotti \(^{1}\) , Xiaohui Zhang \(^{1}\) , Marios Stefanakis \(^{3,4}\) , Maximilian Theisen \(^{5}\) , Jürgen Bauer \(^{3,4}\) , Clemens Becker \(^{3,4}\) and Lorenzo Masia \(^{1}\)  
+
+\(^{1}\) Institut für Technische Informatik (ZITI), Heidelberg University, Heidelberg, Germany. \(^{2}\) Akina AG, Zürich, Switzerland. \(^{3}\) Digital Unit, Center for Geriatric Medicine, Heidelberg University Hospital, Heidelberg, Germany. \(^{4}\) Network Aging Research, Heidelberg University, Heidelberg, Germany. \(^{5}\) Psychological Institute, Heidelberg University, Heidelberg, Germany.  
+
+\*Corresponding author. E- mail: enrica.tricomi@ziti.uni- heidelberg.de; Contributing authors: \(\dagger\) These authors contributed equally to this work;  
+
+## Abstract  
+
+As people grow older, their walking efficiency declines, posing constraints on mobility and affecting independence and overall life quality. While wearable assistive technologies are recognized as a potential solution for age- related movement challenges, few have proven effective for older adults, predominantly within controlled laboratory experiments. Here we present WalkON, a pair of soft robotic shorts designed to enhance walking efficiency for older individuals by assisting hip flexion. To assess the impact of WalkON in daily walking activities, we initially conducted a technology assessment with young adults on a demanding outdoor uphill 500m hiking trail. Subsequently, we validated our findings with a group of older adults walking on a flat outdoor 400m track. WalkON significantly reduced the metabolic cost of transport by 17% for young adults during uphill walking. Concurrently, participants reported high perceived control over their voluntary movements (self- reported mean score of 5.67 out of 7 on a Likert scale). Similarly, older adults experienced a 9% reduction in metabolic cost when using WalkON during level ground walking, while retaining a strong sense of movement control (mean score of 5.85 out of 7). These findings emphasize the potential of wearable robotic assistive devices to enhance energy efficiency in daily outdoor walking, suggesting promising implications for promoting physical well- being and advancing mobility, particularly during the later stages of life.  
+
+Keywords: Soft robotic shorts, aging, mobility, walking assistance, metabolic cost
+
+<--- Page Split --->
+
+## 40 Introduction  
+
+In one of the closing scenes of Paolo Sorrentino's acclaimed movie "Youth" 1, 2016, the lead character confronts his own aging process and remarks, "I've become old and I don't know how I got here". This Sorrentinian sentiment profoundly echoes in a society where the escalation in aging populations is becoming a major demographic shift. According to the World Health Organization, by 2030, it is projected that one in six individuals worldwide will have reached the age of 60 and beyond, a paradigm shift from the one in eleven of \(2019^{2}\) . However, aging is not merely a statistical reality but an escalating biological process that changes the very dynamics of day- to- day life. The process of aging is intrinsically linked with an exacerbation in the effort and metabolic cost required to perform everyday motor tasks. Simple activities, such as walking, ascending stairs, or rising from a chair, become more demanding with increasing age, limiting mobility and independence.  
+
+As a reaction to these realities, the scientific community has intensified its efforts to design solutions that enhance mobility, with the ultimate goal of preventing the aging process from creating barriers. In the realm of robotics, this has led to the development of wearable assistive devices supporting movement in various body regions. The first generation of these wearable robots featured rigid actuated links generating large torques parallel to the human joints, best known as traditional exoskeletons. Over time, a select few of these devices have been explicitly designed to strengthen the mobility of older adults, with a specific emphasis on walking, which is typically most affected as people age. However, their use is confined mainly to lab- based experiments due to their weight and size. Incorporation into daily life applications is also limited due to low social acceptance.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Vision and Design of WalkON (a) Illustration of the envisioned scenario where older adults engage in hiking while benefiting from the support provided by WalkON, thereby enhancing their daily mobility. (b) The design of WalkON comprises a textile structure encompassing a waist belt and two thigh harnesses that can be comfortably worn over regular clothing. The actuation mechanism relies on a tendon-driven transmission, with artificial tendons linked to the front part of the user's legs. These tendons are actuated by motors in accordance with the user's gait cycle. Motor commands deliver assistive forces during the swing phase of each step according to the hip joint kinematics recorded through Inertial Measurement Units (IMUs) in the sagittal plane. </center>  
+
+In recent years, there has been a significant shift towards the development of soft, lightweight solutions. Commonly known as “exosuits” \(^{12}\) , these devices feature textile garments and active components working in parallel to the human muscles. They have proven efficacy in various settings, by alleviating muscle strain in upper body joints \(^{14,15,16}\) , and reducing the metabolic expenditure associated with walking or running \(^{17,18,19}\) . Exosuits have showcased comparable usability to rigid exoskeletons, but with superior user satisfaction in terms of weight, effectiveness, and safety \(^{20}\) . Social acceptance is also higher with respect to their rigid counterpart, increasing the likelihood that individuals would incorporate them into daily life applications \(^{20}\) .  
+
+Nonetheless, the widespread adoption of such assistive technologies outside of controlled laboratory settings still poses a substantial challenge. With respect to walking support, foremost among the current limitations is the critical need for assistive devices to be self- contained and capable of adapting to the
+
+<--- Page Split --->
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+variable pace and modes of locomotion encountered in unstructured, real- world environments \(^{21,22}\) . Additionally, from the user perspective, the sensation of precise control over voluntary movements while using such technologies holds paramount importance. This level of control augments the sense of agency resulting in a more unobtrusive and user- inclusive experience \(^{13,23}\) . Addressing these challenges has the potential to encourage a more extensive adoption of such technologies. Ultimately, this can break down the barriers imposed by aging, allowing for an extension of physical activity beyond.  
+
+In this study, we present a pair of lightweight, soft robotic shorts, hereafter referred to as WalkON, designed to be worn over regular clothing and to act as a walking aid for daily use in real- world scenarios. These robotic shorts are intended to facilitate prolonged outdoor walking sessions, accommodating both typical outdoor settings and more challenging hiking- like terrains. The primary goal of this technology is to enhance the autonomy and walking energy efficiency for its users, with a particular focus on providing support to older individuals.  
+
+By design, WalkON assists hip flexion during the swing phase of walking. This feature is particularly important as the hip joint plays a vital role in ground clearance and limb advancement, demanding significant power especially in uphill and upstairs walking \(^{24,25}\) . As people age the role of the hip becomes more critical. Compared to young adults, it exhibits more pronounced kinetics during the push- off phase, resulting in increased mechanical work required for locomotion and reduced energy efficiency \(^{5,26}\) . Given these considerations, preserving hip function emerges as a fundamental strategy for maintaining walking ability, particularly for older adults or individuals facing mobility challenges \(^{5,27}\) .
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Uphill outdoor walking task and metabolic results for young adults. (a) The task involved walking along a steep \(500\mathrm{m}\) uphill trail presenting altitudes of \(127\mathrm{m}\) and \(184\mathrm{m}\) respectively at the starting and ending points. Young adults walked at their preferred pace being unassisted (No Assistance, grey), and using WalkON (navy). (b, c) Metabolic results demonstrated a significant reduction in the cost of transport when using WalkON to perform the walking task. This result is visible from the cost of transport timeseries in (b), where the thick line represents the average across subjects, the shaded area the standard deviation, and from the mean values in (c). (d) The preferred mean walking speed of participants along the trail was not significantly altered when using WalkON. Results are presented as mean \(\pm\) s.e.m. \*\*\* indicates statistical significance with \(\mathrm{p}< 0.001\) . </center>  
+
+WalkON aims to achieve this objective by enabling the propagation of 106 upward leg movement through an actuation method that utilizes artificial tendons. It features a portable and lightweight design and employs a versatile 108 controller that is not limited to specific walking patterns or terrains. The control strategy is grounded in the user's natural leg movement pattern, making 110 it inclusive, adaptable, and resilient to variations in ground surfaces. This versatility makes it well- suited for outdoor use and extended walking sessions. By 112 promoting independence and fostering overall well- being, these shorts aim to 113 transform the aging experience.
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+We hypothesize that WalkON can reduce the metabolic cost during walking compared to unassisted walking. Additionally, we posit that no restriction of the physiological kinematic patterns happens while using the system. Most crucially, we expect that users maintain full control over their voluntary movements, thus reporting a strong sense of agency.  
+
+The contribution of this study is twofold. From a technical standpoint, we tested these hypotheses through a technology assessment that involved young, healthy participants walking on a challenging outdoor uphill path. This allowed us to showcase the biomechanical effects of the system during demanding walking activities. Then, we conducted an efficacy study with our target population, involving participants aged 67 years and older on an outdoor walking track. These steps served to confirm the observed effects and provide a comprehensive understanding of WalkON's impact across different age groups.  
+
+## Results  
+
+## Technology assessment with young adults  
+
+Participants. Seven young and physically fit individuals, comprising four men and three women, were recruited for the technology assessment of WalkON (Fig. 1- (b)). On average, their age was \(25.43 \pm 2.23\) years, with mean height \(172.57 \pm 12.42\) cm, and weight \(67.57 \pm 13.06\) kg (refer to Table 1 in Extended Data Young Adults for individual demographic).  
+
+WalkON significantly reduced the metabolic cost of transport in uphill outdoor walking. The metabolic cost of transport, which measures the amount of metabolic energy required to cover a unit of distance<sup>28</sup>, serves as a crucial indicator of the effectiveness of wearable robotic assistive devices. The seven recruited young adults walked along a panoramic and winding
+
+<--- Page Split --->
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+500m uphill trail encompassing the surrounding hills of the city of Heidelberg 141 (49°24'55.1"N 8°42'00.9"E, Philosophenweg, Heidelberg, Germany). The trail 142 involved an altitude change of 57m between the starting (altitude of 127m) 143 and ending points (altitude of 184m) (Fig 2- (a)). Participants walked at their 144 self- selected pace in two conditions: (1) No Assistance, where they wore the 145 robotic shorts in an unpowered mode, and (2) the WalkON condition, where 146 they received assistance from the system. 147  
+
+Using WalkON, the metabolic demand of traversing the outdoor uphill trail 148 was significantly reduced by \(- 17.04 \pm 3.21\%\) (mean \(\pm\) s.e.m., \(\mathrm{n} = 7\) , \(\mathrm{p} < 0.001\) ) 149 (Fig. 2- (b, c)). The linear walking velocity (Fig. 2- (d)) did not show significant 150 differences between conditions, although there was a noticeable trend towards 151 a \(+5\%\) increase with WalkON compared to No Assistance. Particularly, four 152 out of seven participants increased their walking speed with WalkON. 153  
+
+## Natural hip joint movement was not restricted when using WalkON. 155  
+
+Ensuring that the use of external assistive devices does not restrict or interfere with natural movements is essential, particularly for individuals without significant movement impairments<sup>12</sup>. This principle underpins the use of the device, promoting health and energy optimization without sacrificing movement freedom. 160  
+
+During natural locomotion, the hip angle exhibits a periodic trajectory resembling a sinusoidal waveform, while the hip velocity is shifted by \(\pi /2\) relative to the angle. These variables create a counterclockwise circular orbit in the hip phase portrait, representing the relationship between position and velocity in the gait cycle<sup>29</sup>. The angular separation between these two quantities indicates the leg's progression during walking. The control strategy of WalkON is 166
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Hip joint motion results for young adults. (a) Representation of the hip flexion angle shape in the sagittal plane along a gait cycle. (b) The raw hip phase portrait averaged across steps and subjects, combining hip angle and velocity measured on the sagittal plane, visually demonstrates that WalkON does not impose any restriction on natural hip motion. (c) The hip range of motion exhibited a significant increase with WalkON compared to the No Assistance condition. The upper row illustrates the mean time series of the hip angle across young adults and steps (shaded area represents the standard deviation), and the lower row shows the averaged hip range of motion (ROM). (d) There were no significant variations in hip velocity peaks with WalkON compared to the No Assistance condition. The upper row displays the mean time series of the hip velocity across young adults and steps (shaded area represents the standard deviation), while the bar plots in the lower row indicate the peak velocity during stance (negative values) and swing (positive values). Results in bar plots are presented as mean \(\pm\) s.e.m. \* indicates statistical significance with \(\mathrm{p}< 0.05\) . The grey color indicates results for the No Assistance condition and the navy for the WalkON condition. </center>  
+
+167 based on these principles (refer to the Methods section) which lay the basis for the delivery of assistive forces along the gait cycle.  
+
+Fig. 3- (b) shows the raw mean hip phase portrait for the seven young adults walking along the uphill trail. It is noticeable that wearing WalkON did not restrict the natural progression of hip angle and velocity along the gait cycle.  
+
+The range of motion of the hip joint exhibited a significant increase with  
+
+The range of motion of the hip joint exhibited a significant increase with  
+
+the use of the assistive robotic shorts (Fig. 3- (c)): in the No Assistance condi  
+
+tion the range of motion was \(48.82^{\circ} \pm 0.68^{\circ}\) on average between the two legs
+
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+
+and across subjects, which increased to \(53.21^{\circ} \pm 1.32^{\circ}\) with WalkON (+9.08 175 \(\pm 2.85\%\) , \(\mathrm{n} = 7\) , \(\mathrm{p} < 0.05\) ). Instead, being assisted by the device did not result in a significant change in hip peak velocities throughout the gait cycle (Fig. 177 3- (d)). 178  
+
+The sense of agency was preserved with WalkON. The perception of 180 control over one's movements significantly influences the acceptance of wearable robotic technologies among potential users \(^{23}\) . This concept is commonly 182 referred to as the "sense of agency", which is typically defined as the feeling 183 of being in command of an action \(^{30}\) . 184  
+
+To assess the young adults' sense of agency while using WalkON, we administered a ten- item questionnaire (Fig. 4). Each participant rated their level of 186 agreement with the items on a Likert scale ranging from 1 (strongly disagree) 187 to 7 (strongly agree). After completing the walking task using WalkON, young 188 adults consistently indicated high sense of agency, as reported by answers distribution in Fig. 4. On average, mean self- reported score to the questionnaire 190 was \(5.93 \pm 0.31\) (mean \(\pm\) s.e.m.) out of 7. Such scores resulted significantly 191 higher compared to a midpoint of 4 on the Likert scale ( \(\mathrm{n} = 7\) , \(\mathrm{t} = 6.78\) , 192 \(\mathrm{p} < 0.001\) ), indicating neither agreement nor disagreement with the statements. These results demonstrate that the users' perception of control over 194 their movements was not altered when utilizing WalkON. 195  
+
+## Efficacy study with older adults  
+
+The primary objective of WalkON is to provide support for daily locomotion as 197 individuals age, with the goal of elevating the autonomy, life quality, and overall 198 well- being of its users in the long term. In line with this vision, an efficacy 199 study was conducted to evaluate the effectiveness in improving the metabolic 200
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 Sense of Agency results for young adults. The sense of agency assessment for young adults using WalkON involved rating various items about motor control with assistive devices on a Likert scale from 1 to 7, indicating their level of agreement with each statement. Items 2, 3, 6, and 8, which are inversely coded, were re-coded before analysis. Answers distribution for the sense of agency questionnaire is presented in terms of boxplot (the white circle being the median). The mean score \((\pm \mathrm{s.e.m.})\) across young adults demonstrates that users felt a strong sense of agency when using WalkON. Participants significantly perceived themselves as having greater control over their movements than the device. This significant difference was tested in comparison to the midpoint value of 4 (Neither Agree Nor Disagree) on the Likert scale. \(\mathrm{***p}< 0.001\) </center>  
+
+demands of outdoor walking specifically targeted at WalkON's intended users — older adults.  
+
+Six participants were recruited, whose ages spanned from 67 to 82 years (mean age \(74.50 \pm 6.95\) years), mean height \(172.83 \pm 8.28\) cm and weights \(68.67 \pm 11.17\) kg. The gender distribution was balanced, with an equal number of male and female individuals. According to the LUCAS Functional Ability Index \(^{31}\) , five of the six participants fell into the "robust" category, indicating that they are active individuals for whom health promotion and physical exercise are recommended. The remaining participant was classified as "pre- frail", suggesting a higher likelihood of mobility issues (refer to Table 2 in Extended Data Older Adults for individual characteristics).  
+
+The outdoor walking path was intentionally less challenging for the assessment in order to prevent overexertion among the older users. Here, study
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 Efficacy study with older adults. (a) Older participants completed a \(400\mathrm{m}\) walk on a flat athletic track at their preferred speed in two conditions: No Assistance (grey) and with WalkON (navy). (b) Using WalkON significantly reduced the metabolic cost of transport. (c) The linear velocity of walking was unaltered on average across participants. (d, e, f) WalkON allowed for unrestricted hip motion. (g) Older adults reported strong perceived sense of control over voluntary movements while using WalkON. Results in bar plots are presented as mean \(\pm\) s.e.m; timeseries are displayed as mean and standard deviation (shaded area). Sense of agency answers distribution is presented in terms of boxplot (the white circle being the median). \(^{*}\mathrm{p}< 0.05\) , \(^{**}\mathrm{p}< 0.01\) . </center>
+
+<--- Page Split --->
+
+participants undertook a 400m walk on a flat athletic track (49°25'16.0"N 8°39'37.0"E, Heidelberg, Germany, Fig. 5-(a)) at their preferred speed, both unassisted (No Assistance) and with the support of WalkON.  
+
+Compared to the No Assistance condition, the metabolic cost of transport required for the outdoor walking task was reduced by an average of - 8.90 ± 3.83% (mean ± s.e.m, n = 6, p = 0.035) when using WalkON (Fig. 5-(b)). The linear velocity of walking increased for three out of six participants, resulting in an overall slight average increasing trend of +1.50% (p > 0.05) (Fig. 5-(c)).  
+
+The progression of the raw hip angle and velocity in the hip phase portrait was not altered by the assistive system (Fig. 5-(d)). Neither the physiological range of motion of the hip joint (Fig. 5-(e)), nor the peak velocities achieved at the joint during walking (Fig. 5-(f)) were constrained when compared to the No Assistance condition (p > 0.05).  
+
+Older participants expressed strong sense of agency while utilizing WalkON (Fig. 5-(g)), with an overall mean self- reported evaluation of 5.85 ± 0.41, which was significantly above the scale midpoint of 4 (n = 6, t = 4.90, p = 0.004), signifying their high perception of control over their movements.  
+
+## Discussion  
+
+As the world's population grows older, the issues surrounding the decline of mobility become more pressing, leading to a rising need for assistive mobility solutions. The challenge goes beyond merely extending physical activity; it is about addressing the constraints of aging and empowering individuals to thrive in their later years.  
+
+Back in 2009, Daniel P. Ferris envisioned a promising future for wearable assistive technologies in everyday life, foreseeing that "by 2024, individuals would navigate streets, malls, and homes while wearing robotic exoskeletons"32.
+
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+Yet, despite this visionary perspective, their actual use has remained largely 240 experimental and primarily confined to lab settings \(^{33}\) . 241  
+
+With WalkON, we aspire to actualize Ferris's vision. As sketched in Fig. 242 1- (a), we aim to offer an unobtrusive assistive tool for daily life to address 243 the mobility challenges of aging by enhancing leg swing dynamics and supporting the hip flexor muscles responsible for initiating and maintaining limb 245 advancement. While it may seem theoretically unnecessary to expend substantial mechanical work to swing the legs due to the pendulum model \(^{34}\) , research 247 has shown that leg swinging is, in fact, energetically costly \(^{35}\) . Findings from 248 previous studies revealed that leg swinging can consume up to approximately 249 one- third of the net energy required for walking \(^{36}\) . This energy expenditure is 250 primarily associated with the transition from one stance limb to the next and 251 is linked to the work performed by muscles to move the leg forward \(^{25,35,37}\) . The 252 effects of aging significantly compromise this function \(^{3,27}\) . Numerous investigations have indicated that the strength of lower extremity muscles tends to 254 decline at a rate of 1- 4% per year, beginning around the age of 50 \(^{38}\) . This 255 decline is especially pronounced in the case of the hip flexors, which have been 256 observed to be the first to deteriorate \(^{27}\) . Due to loss in muscle strength, older 257 adults adapt by incrementing the simultaneous co- activation of antagonistic 258 muscles during walking \(^{39}\) . This compensatory mechanism serves to augment 259 joint stiffness and, in turn, enhance overall stability. However, this adjustment 260 comes at notable increase in metabolic expenditure \(^{3,39}\) . 261  
+
+WalkON demonstrated to improve the energy efficiency of walking in older 262 adults, contributing to enhanced mobility. In this study we investigated the 263 physiological and biomechanical advantages of using the system in daily- like 264 tasks by conducting a comprehensive outdoor walking evaluation with a two- 265 fold approach: initially, we carried out a technology assessment with young 266
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+individuals while hiking on an uphill trail; subsequently, we validated these findings in an efficacy study with our primary target population — older adults.  
+
+In trials with young participants, WalkON facilitated energy savings of \(17\%\) on average compared to No Assistance (Fig. 2- (c)), with individual outcomes ranging from \(7.44\%\) to \(33.64\%\) . In older adults, we observed an average decrease in the cost of transport of \(8.90\%\) while using WalkON (Fig. 5- (b)), with individual results ranging from a minimum saving of \(0.23\%\) to a maximum of \(22.38\%\) .  
+
+Metabolic reductions of this magnitude are accomplished without necessitating high power outputs from the system (peak motor power of \(1.52 \mathrm{W / kg}\) during walking). This underscores the high efficiency of the provided assistance. These findings align with prior studies \(^{40}\) that have demonstrated the superior efficiency of assisting hip flexion when compared to other lower- limb movements, such as hip extension \(^{41}\) or ankle plantarflexion \(^{42}\) . Even modest mechanical outputs from the assistive system are sufficient to achieve significant reductions in metabolic costs \(^{40}\) .  
+
+In a broader perspective, optimizing energy efficiency in daily walking tasks can significantly reduce fatigue during extended walks. This enhancement enables individuals to cover greater distances or sustained activity, improving overall endurance \(^{43}\) . Studies indicate that improving walking energy efficiency is pivotal for enhancing mobility, independence, and the overall quality of life for older adults. This is evidenced by positive effects on cardiovascular risk factors, decreased respiratory disease risk, and a general reduction in mortality from various causes \(^{43,44}\) . Beyond physical health benefits, walking
+
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+demonstrates a direct association with a reduced risk of depression, a positive influence on emotional well- being, and various aspects of health- related quality of life<sup>45</sup>.  
+
+Notably, studies demonstrating the effectiveness of wearable assistive technologies in comprehensive outdoor daily life scenarios are very sparse. Then, our ability to draw comparisons with existing literature is quite limited. For instance, Haufe et al.<sup>18</sup> tested the Myosuit, a commercial wearable robot designed to assist hip and knee extension through a tendon- driven mechanism guided by a rigid joint at the knee level, in the context of a 400m uphill gravel path with young participants. Their findings revealed an average metabolic saving of 10.6% compared to an unpowered condition. Instead, in a recent study, Slade et al.<sup>21</sup> introduced an ankle exoskeleton that reduced the cost of transport by an average of 17% in young, healthy subjects. This outcome is particularly relevant considering the crucial role of the ankle, alongside the hip, as a primary power source for the forward propulsion during walking. This metabolic improvement was achieved on a 566m flat path using a rigid system and a control algorithm that required specific adjustments and personalization for each user. While customization and personalization are important for optimizing individual assistance, they often compromise the device's ease of use and "plug- and- play" functionality. Additionally, in both of the mentioned instances, the outdoor tasks were comparatively less strenuous than our hiking activity, tests were conducted only on young and fit individuals, and the outcomes were achieved through systems featuring rigid links or joints. Such design elements typically simplify the characterization process, ensuring direct and predictable transmission of force, preserving component alignment and position, and facilitating ease of control. In contrast, the core design of
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+WalkON revolves around a soft structure that conforms to the body like regular clothing and lacks any rigid joints. This characteristic offers enhanced comfort, wearability, and reduced intrusiveness. However, it does make the final force transmitted to the human body less predictable, necessitating greater attention to system modeling and control. Despite these challenges, our system showcased substantial metabolic advantages in a deliberately demanding and fatiguing task, all without impeding freedom of movement during use.  
+
+When evaluating hip joint movement during uphill hikes, young adults exhibited a range of motion in the hip joint \(9.08\%\) higher while utilizing WalkON (Fig. 3- (c)). From a physiological perspective, uphill walking requires an increase in the hip joint range of motion and a concurrent reduction in knee extension as the swing phase ends \(^{24}\) . The utilization of WalkON might have possibly accentuated this inherent adaptation; however, these enhancements did not result in any disruption of movement and, consequently, contributed to improved metabolic efficiency. Instead, for older individuals walking on level terrain, their natural hip joint movement remained unaltered, indicating the absence of any movement constraints (Fig. 5- (e, f)).  
+
+To date, we have not come across any research that delves into real- world applications of assistive technologies tailored specifically for older adults while quantifying the metabolic advantages and assessing the psychophysical impact. The latter aspect is undeniably of paramount importance and forms a cornerstone of any robotic assistive device. The conscious perception of its value by the user encompasses one of the fundamental pillars for widespread adoption and should be considered a critical evaluation criterion, alongside biomechanical measurements, to gauge the impact of the technology. For the device to be considered valuable by potential users, it must provide an experience that unequivocally demonstrates its worth \(^{46}\) . This aligns with the overarching
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+objective of enhancing the user experience, ensuring that individuals feel in 345 perfect synchronization with the system and retain complete autonomy over 346 their movements. This concept is known in the literature as the “sense of 347 agency”, often described as the sensation of being in control of an action<sup>30</sup>. It 348 encompasses the experience of initiating one’s voluntary actions and, through 349 these actions, influencing the external world<sup>47</sup>.  
+
+Our assessments regarding the sense of agency yielded promising outcomes 351 (Fig. 4, Fig. 5- (g)). Participants reported a strong sense of agency on the 352 administered questionnaire, with mean Likert- scale ratings of 5.67 for young 353 adults and 5.85 for older adults out of a total score of 7. This indicates a notable 354 alignment between their intentions and the system, emphasizing their percep- 355 tion of being the initiators and controllers of their actions. This result can be 356 primarily attributed to the controller of WalkON which synchronizes with the 357 user’s natural motion ensuring that no extraneous actions are imposed upon 358 voluntary movements. The control algorithm is designed to constantly analyze 359 the user’s movement pattern and derive the progression of their leg throughout 360 the gait cycle. It accomplishes this using solely thigh motion data, eliminat- 361 ing the need for personalization or resource- intensive classification algorithms. 362 This guarantees that the assistance provided harmonizes with the user’s natu- 363 ral walking pattern and seamlessly adapts to variations in walking speed. These 364 qualities collectively make WalkON’s controller a plug- and- play solution. Users 365 can incorporate the system into their daily routines without the requirement 366 for extensive setup or customization. This approach not only simplifies the 367 user experience but also reduces usage barriers, making the technology more 368 inclusive and akin to a pair of shorts for everyday use. 369  
+
+The primary limitation of our study lies in the absence of a control mea- 370 surement of metabolic activity without wearing WalkON. Instead, we relied 371
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+on a comparison based on gross metabolic changes, utilizing a condition where the device was worn but turned off as a reference point. While this approach may be less realistic in real- world terms, it was chosen for practical experimental reasons and it is the most widely adopted in the literature \(^{12,18,17,48}\) . This decision allowed us to capture the user's movement during the No Assistance condition for meaningful comparison and to isolate the active biomechanical effect of assistance from the passive effects of wearing the suits. Given the demanding nature of the technology assessment with young adults, we opted not to impose an additional experiment on the participants. It is worth noting that due to the soft structure of the device, the negligible weight (2.93kg) and its positioning closer to the user's center of mass, we do not anticipate any significant impact on the final outcomes \(^{49}\) .  
+
+Even in terms of gross metabolic change, there was a difference in outcomes for the two groups. We believe this was influenced by age- related factors, including a propensity for shorter walking sessions, and variations in experimental protocols. The primary distinction between the experiments arises from the dissimilarities in the walking tasks themselves. Specifically, young individuals were asked to walk in considerably more physically demanding conditions, particularly on steep uphill terrain. Ground incline plays a pivotal role in determining energy expenditure during walking, with costs escalating proportionally as the gradient increases, and this relationship becomes linear for grades exceeding \(15\%\) \(^{50}\) . In such scenarios, the phase of limb advancement becomes more demanding, necessitating greater effort from hip flexors to raise the swinging leg against gravity \(^{5}\) . Consequently, the assistance offered by WalkON may deliver more pronounced benefits in these situations compared to walking on level ground.
+
+<--- Page Split --->
+
+Future research endeavors anticipate conducting a pilot randomized controlled trial involving our target population in an even more ecologically valid setting, such as stair climbing, with an enhanced assessment of the system's impact during everyday use. This will be complemented by a thorough analysis of usability and user acceptance to provide a more comprehensive understanding of the technology's potential and limitations. We envision that prolonged walking sessions with WalkON could yield even greater benefits for our target users and ultimately achieve our long- term objectives. Additionally, we aim to investigate the application of the device in specific clinical populations characterized by restricted aerobic capacity and diminished muscle strength, such as individuals with congestive heart failure and multiple sclerosis.  
+
+Looking toward the future, we anticipate that the advantages of employing WalkON during extended walking sessions, encompassing various terrains from flat surfaces to challenging hiking trails, may become increasingly evident and potentially transformative. Mitigating the metabolic requirements linked to daily tasks like outdoor walks or indoor movement could not only enhance users' physical well- being but also potentially have a positive impact on their mental and emotional health<sup>43</sup>. As a result, older individuals could cover greater distances with reduced fatigue, thereby enhancing their autonomy and mobility. In doing so, we hope to move closer to realizing the vision that echoes that of Ferris – a future in which assistive technologies empower humans to achieve exceptional feats even in old age.  
+
+## References  
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+[31] Ulrike Dapp, Christoph E Minder, Stefan Golgert, Björn Klugmann, Lilli Neumann, and Wolfgang von Renteln- Kruse. The inter- relationship between depressed mood, functional decline and disability over a 10- year observational period within the longitudinal urban cohort ageing study (lucas). J Epidemiol Community Health, 75(5):450- 457, 2021.  
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+<--- Page Split --->
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+of skeletal muscle strength, mass, and quality in older adults: the health, 553 aging and body composition study. The Journals of Gerontology Series 554 A: Biological Sciences and Medical Sciences, 61(10):1059–1064, 2006. 555 
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+[40] Jinsoo Kim, Brendan T Quinlivan, Lou-Ana Deprey, Dheepak Aru-559 mukhom Revi, Asa Eckert-Erdheim, Patrick Murphy, Dorothy Orzel, and 560 Conor J Walsh. Reducing the energy cost of walking with low assis-561 tance levels through optimized hip flexion assistance from a soft exosuit. 562 Scientific reports, 12(1):11004, 2022. 563 
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+[41] Patrick W Franks, Gwendolyn M Bryan, Russell M Martin, Ricardo 564 Reyes, Ava C Lakmazaheri, and Steven H Collins. Comparing optimized 565 exoskeleton assistance of the hip, knee, and ankle in single and multi-joint 566 configurations. Wearable Technologies, 2:e16, 2021. 567 
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+
+<--- Page Split --->
+
+580 [45] Karmel W Choi, Chia- Yen Chen, Murray B Stein, Yann C Klimentidis, Min- Jung Wang, Karestan C Koenen, Jordan W Smoller, et al. Assessment of bidirectional relationships between physical activity and depression among adults: a 2- sample mendelian randomization study. JAMA psychiatry, 76(4):399- 408, 2019. [46] Roberto Leo Medrano, Gray Cortright Thomas, and Elliott J Rouse. Can humans perceive the metabolic benefit provided by augmentative exoskeletons? Journal of NeuroEngineering and Rehabilitation, 19(1):26, 2022. [47] Brianna Beck, Steven Di Costa, and Patrick Haggard. Having control over the external world increases the implicit sense of agency. Cognition, 162:54- 60, 2017. [48] Enrica Tricomi, Mirko Mossini, Francesco Missiroli, Nicola Lotti, Xiaohui Zhang, Michele Xiloyannis, Loris Roveda, and Lorenzo Masia. Environment- based assistance modulation for a hip exosuit via computer vision. IEEE Robotics and Automation Letters, 2023. [49] Guillaume J Bastien, Patrick A Willems, Benedict Schepens, and Norman C Heglund. Effect of load and speed on the energetic cost of human walking. European journal of applied physiology, 94:76- 83, 2005. [50] Luke N Jessup, Luke A Kelly, Andrew G Cresswell, and Glen A Lichtwark. It is not just the work you do, but how you do it: The metabolic cost of walking uphill and downhill with varying grades. Journal of Applied Physiology, 2023.
+
+<--- Page Split --->
+
+## Methods  
+
+## WalkON hardware design  
+
+WalkON is a soft robotic assistive system featuring one motor per leg (AK60- 6, 605 9Nm peak torque, T- Motor, China), each wrapping up an artificial tendon on 606 a spool (diameter of 35mm). This design allows independence between assisted 607 legs, enabling adjustments in the assistance profile to accommodate complex 608 movements and a broad range of motion. The weight of the device is 2.93kg, 609 most of which is located approximately at the level of the user's center of mass 610 to minimize the impact of the extra mass on the metabolic energy expenditure 611 during walking51.  
+
+WalkON is connected to the human body through a compliant textile structure. The textile interface consists of an adjustable waist belt, which is worn 614 at the user's iliac crest level, and two thigh fabric harnesses. Both the belt and 615 the harnesses feature an inner layer of neoprene, offering good tensile strength 616 and hardness while ensuring soft contact with the body. Velcro strips are used 617 to provide a custom fit for a wide range of human body shapes and sizes. A 618 blueprint of the textile components is provided in Extended Data Fig. 3. The 619 textile interface serves as an anchor for the actuation stage and electronics and 620 to guide the tendon- driven transmission.  
+
+The mentioned transmission uses artificial tendons made of Black Braided 622 Kevlar Fiber (KT5703- 06, 2.2 kN max load, USA) to actively assist the user's 623 hip flexion. These tendons run from the actuation stage, located at the back 624 of the belt on a rigid plate, to a proximal anchor point on the front, guided 625 by Bowden cables (Shimano SLR, diameter 5mm, Sakai, Osaka, Japan). From 626 here, the tendons run parallel to each leg and are anchored to a distal anchor 627 point on the thigh textile harness. By shortening the distance between the 628
+
+<--- Page Split --->
+
+proximal and distal anchor points on the suit, assistive forces delivered to the user generate a flexing moment around the hip joint.  
+
+The systems are powered by a portable Lithium Polymer battery (Tattu, 0.4kg, 14.8V, capacity of 3700 mAh). Custom- designed housings for actuation, power, and electronics, as well as anchor points, are fabricated using 3D printing technology with PLA material. Computer- aided design files for such elements are provided as Supplementary Material.  
+
+The controller is executed on a microcontroller (Arduino MKR 1010 WiFi, Arduino, Italy) at a 100Hz frequency, and it obtains information via Bluetooth Low Energy (Feather nRF52832, Bluefruit, Adafruit) protocol from two Inertial Measurements Unit (IMU) sensors (BNO055, Bosch, Germany) placed laterally on the thigh harness. These sensors continuously stream the hip flexion angle of each leg as measured in the sagittal plane, then converted by the control algorithm to an assistance profile according to the leg progression along the gait cycle.  
+
+A complete schematic of WalkON components is provided in Extended Data Fig. 4.  
+
+## WalkON Controller  
+
+WalkON is operated using a control framework designed to actuate tendon displacement based on the kinematics of hip flexion during human locomotion and its progression along the gait cycle. The entire architecture is built so that signals flow along a forward path from the sensing system to the control unit and finally to the actuation unit. This is achieved through a three- tiered approach: a High- Level Controller that estimates the gait phase in real- time from hip kinematic data, a Mid- Level Controller that generates the actuator reference motion based on the user's gait phase, and a Low- Level Controller that provides appropriate assistance to the user based on the previous layer's outputs.
+
+<--- Page Split --->
+
+The control framework is depicted in Extended Data Fig. 5. Detailed information about the algorithm and a pseudocode are provided in the Supplementary Information. 658  
+
+The high- level controller calculates a monotonically increasing gait phase 659 variable from a single inertial sensor on each leg. The underlying approach 660 incorporates the concepts from the general control theory of oscillating dynamical systems. Indeed, during natural locomotion, the angular position of the hip 662 joint, \(\theta (t)\) , has a periodic trajectory that can be approximated as a sinusoidal 663 waveform, similar to an undamped oscillator \(^{52,53}\) . As such, the hip angular 664 velocity, \(\dot{\theta} (t)\) , has a \(\pi /2\) shift with respect to \(\theta (t)\) and the two variables produce a circular orbit in the counterclockwise sense of rotation on the hip phase 666 portrait, i.e., position vs. velocity phase plane. The gait phase, denoted as \(\phi (t) = f([\theta (t),\dot{\theta} (t)])\) , is extracted in real- time by computing the polar angle 668 between these two quantities. For each step, both variables are initially shifted 669 about the origin of the hip phase portrait, and \(\theta (t)\) is re- scaled to match the 670 amplitude of \(\dot{\theta} (t)\) in order to produce a more circular orbit \(^{54}\) . Information 671 about the walking speed are intrinsically present in the gait phase extraction, 672 allowing instant adaptation to changes in walking pattern. To comply with 673 the sinusoidal nature of the hip flexion angular displacement measured on 674 the sagittal plane, sinusoidal interpolation follows the gait phase estimation 675 deriving a signal, \(\theta_{\mathrm{r}}(t)\) , used as basis for the motor reference trajectory. 676  
+
+As the gait phase extraction method shows sensitivity to noise captured 677 from the inertial sensors on unstructured terrains, to filter out such noise from \(\theta_{\mathrm{r}}(t)\) , a Kalman filter is implemented at the Mid- Level controller. Kalman 679 filter parameters have been optimized in preliminary trials to strike a good 680 balance between the noise in the real- time recorded data and the noise in 681 the estimated data. The actuator's final position reference trajectory, \(\theta_{\mathrm{ref}}(t)\) , 682
+
+<--- Page Split --->
+
+is obtained using cubic spline interpolation on the Kalman- filtered \(\theta_{\mathrm{r}}(t)\) . The amplitude of \(\theta_{\mathrm{ref}}(t)\) is determined based on the user's hip range of motion, pulley diameter, and anthropometric considerations.  
+
+At the low- level controller, a feedback position loop compares the actual position of the motor \(\theta_{\mathrm{m}}(t)\) with the reference position \(\theta_{\mathrm{ref}}(t)\) extracted from the previous layer. A Proportional- Differential (PD) controller is used to convert the position error into motor angular velocity. To prevent disturbances or noise in the hip kinematics recordings from translating to unwanted motor commands when a subject stops walking, a stop detection condition is implemented based on the gait speed.  
+
+## Study Protocol  
+
+The first aim of the study is to evaluate the effectiveness of WalkON in enhancing outdoor walking experiences. To achieve this objective, a technology assessment of the system was conducted on uphill hiking- like trails with young adults. The ultimate goal of the research is to propose this system as an effective support for walking in older individuals. To explore this possibility, an efficacy study was undertaken with participants aged over 67 years old.  
+
+Before the study began, all participants provided informed written consent, as well as consent to publish identifiable images. Our research procedures were conducted in accordance with the principles of the Declaration of Helsinki and were approved by the Ethics Committee of Heidelberg University under resolution No. S- 313/2020. During the study, each participant underwent evaluations in multiple conditions, acting as their own control for comparison.
+
+<--- Page Split --->
+
+## Technology assessment with young adults  
+
+Inclusion criteria for young adults (n = 7) recruitment included age between 707 18 and 35 years, no visual or auditory impairments or any neurological, cardiovascular, metabolic, or mental disorders that might interfere with the tasks at hand. 710  
+
+The chosen experimental path was a panoramic snake- like trail up the 711 hills surrounding the city of Heidelberg, Germany, known as Philosophenweg 712 (49°24'55.1"N 8°42'00.9"E). We selected the initial segment of the trail, which 713 is a winding and very steep 500m track with a change of altitude from 127m to 714 184m between the starting and ending points (Fig. 2- (a)). The trail began with 715 108 stairs made of sandstone irregular in shape, followed by an uphill section. 716  
+
+Study participants were instructed to walk at their preferred speed along 717 the trail two times under different conditions: without assistance (No Assis- 718 tance) and with assistance from WalkON. In the No Assistance condition, 719 participants worn the system in unpowered mode in order to allow for record- 720 ings of kinematic data. Given the physically demanding nature of the trial, 721 we conducted the different conditions on separate days to minimize any 722 fatigue- related effects. 723  
+
+After completing the uphill walking, each participant retraced the same 724 path in the opposite direction, going downhill. The walking distance for each 725 condition of the study accounted then for a total of 1 km walked. However, 726 the results for the downhill walking are not included in the main text but 727 rather reported in the Supplementary Information, as the assistance provided 728 by WalkON for hip flexion is less significant during this phase. This is because 729 the swinging leg does not need to be lifted as high during downhill walking for 730 ground clearance<sup>55</sup>. The primary focus of retracing the path was to demonstrate that the assistive system and its weight do not impede motion or impose 732
+
+<--- Page Split --->
+
+a metabolic burden during downhill sections. The Supplementary Information additionally reports a comparative study on two hardware configurations of WalkON used to assess the most efficient design.  
+
+## Efficacy study with older adults  
+
+Older adults enrolled for the efficacy study ( \(\mathrm{n} = 6\) ) were selected based on criteria that included being over 65 years of age, being categorized as either "robust" or "pre- frail" according to the LUCAS Functional Ability Index \(^{56}\) , and not having severe uncorrected visual or auditory impairments or significant neurological, cardiovascular, metabolic, or mental conditions.  
+
+To avoid any physical overload for the frailer subjects of the study, we chose an outdoor path with a shorter distance and a flat ground. Participants were instructed to walk at their preferred speed on a \(400\mathrm{m}\) athletic track on flat ground (located at \(49^{\circ}25'16.0''\mathrm{N}\) \(8^{\circ}39'37.0''\mathrm{E}\) , Heidelberg, Germany, Fig. 5- (a)) under two different conditions: wearing the device in unpowered mode (No Assistance) and with assistance from WalkON. Both conditions were conducted on the same day, with a minimum 20- minute rest period in between to prevent fatigue. The order of the conditions was randomized among participants to eliminate order effects.  
+
+## Data analysis and statistics  
+
+In order to evaluate the use of WalkON in improving walking efficiency, the principal outcome measure was the metabolic cost associated with walking. Oxygen and carbon dioxide consumption data were recorded using a portable respirometer (K5, COSMED, Italy), and the net metabolic cost was deduced using Péronnet and Massicotte's formula \(^{57}\) . For establishing a baseline, participants were instructed to breathe normally for a three- minute period while standing at rest before each experiment began. The mean baseline metabolic
+
+<--- Page Split --->
+
+cost from the final minute was then subtracted from the overall metabolic data 759 to discern the cost of walking for each condition. To account for the different walking speeds across conditions, metabolic data were analyzed in terms 761 of cost of transport \(^{58}\) . This was computed by dividing the net metabolic cost 762 by the product of the participant's weight, gravitational acceleration, and the 763 average speed of walking. The average walking speed was determined by the 764 distance covered over the duration of the experiment. Considering that it takes 765 approximately two minutes for metabolic data to stabilize after any significant 766 changes in physical activity, for the technology assessments involving younger 767 adults, we excluded the initial two minutes of recording and analyzed the 768 remainder of the data. For the efficacy study with older adults, we examined 769 the final two minutes of the trial, since visual inspection of the data demonstrated steady- state behavior during this time segment and the time taken by 771 participants to traverse the walking track was approximately four minutes. 772  
+
+Kinematic evaluations were conducted on the profiles of the hip angle and hip velocity for both the left and right legs, using data recorded from inertial sensors integrated into the system. The raw motion data was divided into steps post low- pass filtering (4th order Butterworth, cut- off frequency 10 Hz). For each participant, we evaluated the range of motion (ROM), along with the average peak velocity during both stance and swing phases across all steps, under both unassisted and assisted condition. 779  
+
+Results are presented as mean \(\pm\) s.e.m (standard error of the mean). Data were tested for normality using a Shapiro- Wilk test and resulted normally distributed. The significance level for all statistical tests was set to be less than 0.05. A linear mixed effects model was used for subsequent statistical analysis of the collected metabolic and motion data, employing the least squares regression method (MATLAB, MathWorks Inc., Natick, MA, USA). The model
+
+<--- Page Split --->
+
+accounted for the "condition" ("No Assistance", "WalkON"), which was presented as dummy- encoded, categorical fixed- effect explanatory variables. A term "participant" (either YA1 to YA7 for young adults or OA1 to OA6 for older adults) was included in the model as a random- effect variable.  
+
+In our analysis of the sense of agency, we asked study participants to answer to a questionnaire consisting of six positively framed items (items 1, 4, 5, 7, 9 10 in Fig. 4 and Fig. 5- (g)) and four negatively framed items (items 2, 3, 6, 8) evaluating the sense of control they had while using WalkON. The items were derived from the theoretical literature on sense of agency and were finetuned to the context of wearable mobility aids59. The negatively framed items were recoded so that higher values indicate higher sense of agency. For items analyses, we calculated a mean score of the scale items. Internal consistency of the questionnaire scale after recoding was good ( \(\alpha = 0.83\) 95%, CI [0.67; 0.92]). To test whether participants felt that their movements were more controlled by themselves or by the device, we tested whether this mean score significantly deviated from the scale midpoint of 4 through a paired- sample t- test twotailed. A mean above the scale midpoint suggested that the participants saw themselves more in control of their movements than the device.  
+
+## Data availability  
+
+All data needed to evaluate the conclusions in the Article are present in Supplementary data 1 and may be reused for ethical, scientific purposes.  
+
+## Code availability  
+
+The exemplary scripts for data processing and analysis for this study are present in Supplementary data 1.
+
+<--- Page Split --->
+
+## References  
+
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+[55] M Kuster, S Sakurai, and GA Wood. Kinematic and kinetic comparison 825 of downhill and level walking. Clinical biomechanics, 10(2):79- 84, 1995. 826  
+
+[56] Ulrike Dapp, Christoph E Minder, Stefan Golgert, Björn Klugmann, 827 Lilli Neumann, and Wolfgang von Renteln- Kruse. The inter- relationship 828 between depressed mood, functional decline and disability over a 10- year 829 observational period within the longitudinal urban cohort ageing study 830 (lucas). J Epidemiol Community Health, 75(5):450- 457, 2021. 831  
+
+[57] François Peronnet, Denis Massicotte, et al. Table of nonprotein respiratory quotient: an update. Can J Sport Sci, 16(1):23- 29, 1991. 833  
+
+[58] Henry J Ralston. Energy- speed relation and optimal speed during 834 level walking. Internationale Zeitschrift für Angewandte Physiologie 835 Einschliesslich Arbeitsphysiologie, 17(4):277- 283, 1958. 836
+
+<--- Page Split --->
+
+[59] Adam Tapal, Ela Oren, Reuven Dar, and Baruch Eitam. The sense of agency scale: A measure of consciously perceived control over one's mind, body, and the immediate environment. Frontiers in psychology, 8:1552, 2017.  
+
+Acknowledgments. The presented results were obtained within the scope of the HeiAge and SMART- AGE projects (P2019- 01- 003) funded by the Carl Zeiss Foundation. We extend our heartfelt gratitude to all the participants that volunteered in the study for their time, feedback and contribution.  
+
+Author contributions. ET designed and implemented the WalkON controller. NL and LM provided feedback to control implementation. ET, FM, NL, XZ, and LM led the design and implementation of the textile interface, actuator unit, and electronics. ET, FM, NL, MX, JB, CB, and LM designed the study. ET, FM, and MS led the study conduct. MT provided the psychophysical evaluation questionnaire and analysed the related data. ET analyzed the data and prepared the figures and manuscript. All authors reviewed the manuscript and provided critical feedback.  
+
+Competing interests. E.T., F.M, N.L., and L.M. are co- inventors of a patent application disclosing the walking assistive systems described herein. The patent application is pending at the time of the submission of the present scientific report.  
+
+Additional information. Supplementary information Supplementary Information is available for this paper. Correspondence and requests for materials should be addressed to Enrica Tricomi.
+
+<--- Page Split --->
+
+# Extended Data Young Adults  
+
+Table 1 Young adults demographic   
+
+<table><tr><td colspan="6">Participant characteristics</td></tr><tr><td>ID</td><td>Height (cm)</td><td>Weight (kg)</td><td>Body-Mass Index (kg/m²)</td><td>Sex (-)</td><td>Age (years)</td></tr><tr><td>YA1</td><td>184</td><td>74</td><td>21.86</td><td>Male</td><td>24</td></tr><tr><td>YA2</td><td>156</td><td>60</td><td>24.65</td><td>Female</td><td>28</td></tr><tr><td>YA3</td><td>171</td><td>60</td><td>20.52</td><td>Male</td><td>23</td></tr><tr><td>YA4</td><td>193</td><td>93</td><td>24.97</td><td>Male</td><td>27</td></tr><tr><td>YA5</td><td>163</td><td>54</td><td>20.32</td><td>Female</td><td>28</td></tr><tr><td>YA6</td><td>171</td><td>70</td><td>23.94</td><td>Male</td><td>23</td></tr><tr><td>YA7</td><td>170</td><td>62</td><td>21.45</td><td>Female</td><td>25</td></tr></table>
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Intra-participants results for the technology assessment with young adults. For each young adult (YA): (a) mean cost of transport while walking along the \(500\mathrm{m}\) uphill hiking trail; (b) linear velocity of walking across the trial; (c) hip range of motion (ROM) and hip peak velocities as a mean across steps. The shaded bars indicate the average results across participants as presented in the main text (grey = No Assistance; navy = WalkON). The symbol \* indicates statistical significance between conditions. </center>
+
+<--- Page Split --->
+
+# Extended Data Older Adults  
+
+Table 2 Older adults demographic   
+
+<table><tr><td colspan="7">Participant characteristics</td></tr><tr><td>ID</td><td>Height (cm)</td><td>Weight (kg)</td><td>Body-Mass Index (kg/m²)</td><td>Sex (-)</td><td>Age (years)</td><td>LUCAS Functional Ability Index</td></tr><tr><td>OA1</td><td>173</td><td>63</td><td>21.05</td><td>Female</td><td>69</td><td>Robust</td></tr><tr><td>OA2</td><td>186</td><td>90</td><td>26.01</td><td>Male</td><td>82</td><td>Robust</td></tr><tr><td>OA3</td><td>168</td><td>58</td><td>20.55</td><td>Female</td><td>78</td><td>Robust</td></tr><tr><td>OA4</td><td>165</td><td>70</td><td>25.71</td><td>Female</td><td>67</td><td>Robust</td></tr><tr><td>OA5</td><td>166</td><td>66</td><td>23.95</td><td>Female</td><td>69</td><td>Robust</td></tr><tr><td>OA6</td><td>179</td><td>65</td><td>20.29</td><td>Male</td><td>82</td><td>Pre-frail</td></tr></table>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Intra-participants results for the efficacy study with older adults. For each older adult (OA): (a) mean cost of transport while walking along the 400m flat athletic track; (b) linear velocity of walking across the trial; (c) hip range of motion (ROM) and hip peak velocities as a mean across steps. The shaded bars indicate the average results across participants as presented in the main text (grey = No Assistance; navy = WalkON). The symbol \* indicates statistical significance between conditions. </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Textile blueprint (a) WalkON waist belt extended. (b) Layer composition of the belt with the back and frontal view in its closed configuration. (c) Thigh textile harness inner view and closed configuration. </center>
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 WalkON hardware components. (a) Computer-aided design of WalkON (b) Inertial Measurement Unit (IMU) sensors stream hip motion data via Bluetooth Low Energy to the control unit. This unit runs the controller on a microcontroller. The output is a velocity command sent to the actuators. (c) The textile structure of WalkON is composed by a waist belt and two thigh harnesses. (d) Anchor points are placed on the belt and thigh harness to guide the artificial tendons. </center>
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 WalkON Controller. The WalkON control system operates across three levels. The High-Level controller determines the gait phase by calculating the polar angle between the hip joint position, \(\theta (t)\) , and velocity, \(\dot{\theta} (t)\) , during each gait cycle in real-time. It then uses sinusoidal interpolation to create a foundational trajectory for the reference motor position, \(\theta_{\mathrm{r}}(t)\) . The Mid-Level controller applies a Kalman filter to \(\theta_{\mathrm{r}}(t)\) to eliminate noise emerging from the phase estimation method. Following this, it uses cubic spline interpolation to create the final trajectory for the final motor position reference, \(\theta_{\mathrm{ref}}(t)\) . The Low-Level controller actuates tendon displacement based on the motor commands derived from the outputs of the previous levels. </center>
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- ManuscriptSupplementaryInformation.pdf- Supplementarydata3Video.mp4
+
+<--- Page Split --->

preprint/preprint__5f44282bdf1db87c38eb7fe0d1af91b67dcf18e457633d14c451199a9f417da2/preprint__5f44282bdf1db87c38eb7fe0d1af91b67dcf18e457633d14c451199a9f417da2_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 812, 175]]<|/det|>
+# Soft robotic shorts improve outdoor walking efficiency in older adults  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 170, 214]]<|/det|>
+Enrica Tricomi  
+
+<|ref|>text<|/ref|><|det|>[[54, 222, 466, 240]]<|/det|>
+enrica.tricomi@ziti.uni- heidelberg.de  
+
+<|ref|>text<|/ref|><|det|>[[44, 269, 600, 288]]<|/det|>
+Heidelberg University https://orcid.org/0000- 0002- 9117- 4385  
+
+<|ref|>text<|/ref|><|det|>[[44, 293, 243, 333]]<|/det|>
+Francesco Missiroli Heidelberg University  
+
+<|ref|>text<|/ref|><|det|>[[44, 339, 210, 377]]<|/det|>
+Michele Xiloyannis Akina AG  
+
+<|ref|>text<|/ref|><|det|>[[44, 385, 243, 425]]<|/det|>
+Nicola Lotti Heidelberg University  
+
+<|ref|>text<|/ref|><|det|>[[44, 431, 243, 470]]<|/det|>
+Xiaohui Zhang Heidelberg University  
+
+<|ref|>text<|/ref|><|det|>[[44, 477, 243, 516]]<|/det|>
+Marios Stefanakis Heidelberg University  
+
+<|ref|>text<|/ref|><|det|>[[44, 523, 600, 563]]<|/det|>
+Maximilian Theisen Heidelberg University https://orcid.org/0000- 0003- 1596- 805X  
+
+<|ref|>text<|/ref|><|det|>[[44, 570, 321, 609]]<|/det|>
+Jurgen Bauer Heidelberg University Hospital  
+
+<|ref|>text<|/ref|><|det|>[[44, 616, 321, 655]]<|/det|>
+Clemens Becker Heidelberg University Hospital  
+
+<|ref|>text<|/ref|><|det|>[[44, 662, 175, 700]]<|/det|>
+Lorenzo Masia Heidelberg  
+
+<|ref|>text<|/ref|><|det|>[[44, 747, 288, 765]]<|/det|>
+Biological Sciences - Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 784, 750, 803]]<|/det|>
+Keywords: Soft robotic shorts, aging, mobility, walking assistance, metabolic cost  
+
+<|ref|>text<|/ref|><|det|>[[44, 821, 336, 840]]<|/det|>
+Posted Date: February 13th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 859, 474, 878]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3744597/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 896, 912, 937]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 100, 925, 142]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Machine Intelligence on October 1st, 2024. See the published version at https://doi.org/10.1038/s42256-024-00894-8.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[159, 93, 836, 156]]<|/det|>
+# Soft robotic shorts improve outdoor walking efficiency in older adults  
+
+<|ref|>text<|/ref|><|det|>[[139, 184, 931, 264]]<|/det|>
+Enrica Tricomi \(^{1*}\) , Francesco Missiroli \(^{1\dagger}\) , Michele Xiloyannis \(^{1\ddagger}\) , Nicola Lotti \(^{1}\) , Xiaohui Zhang \(^{1}\) , Marios Stefanakis \(^{3,4}\) , Maximilian Theisen \(^{5}\) , Jürgen Bauer \(^{3,4}\) , Clemens Becker \(^{3,4}\) and Lorenzo Masia \(^{1}\)  
+
+<|ref|>text<|/ref|><|det|>[[140, 268, 931, 374]]<|/det|>
+\(^{1}\) Institut für Technische Informatik (ZITI), Heidelberg University, Heidelberg, Germany. \(^{2}\) Akina AG, Zürich, Switzerland. \(^{3}\) Digital Unit, Center for Geriatric Medicine, Heidelberg University Hospital, Heidelberg, Germany. \(^{4}\) Network Aging Research, Heidelberg University, Heidelberg, Germany. \(^{5}\) Psychological Institute, Heidelberg University, Heidelberg, Germany.  
+
+<|ref|>text<|/ref|><|det|>[[168, 400, 830, 432]]<|/det|>
+\*Corresponding author. E- mail: enrica.tricomi@ziti.uni- heidelberg.de; Contributing authors: \(\dagger\) These authors contributed equally to this work;  
+
+<|ref|>sub_title<|/ref|><|det|>[[448, 463, 548, 480]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[167, 485, 831, 830]]<|/det|>
+As people grow older, their walking efficiency declines, posing constraints on mobility and affecting independence and overall life quality. While wearable assistive technologies are recognized as a potential solution for age- related movement challenges, few have proven effective for older adults, predominantly within controlled laboratory experiments. Here we present WalkON, a pair of soft robotic shorts designed to enhance walking efficiency for older individuals by assisting hip flexion. To assess the impact of WalkON in daily walking activities, we initially conducted a technology assessment with young adults on a demanding outdoor uphill 500m hiking trail. Subsequently, we validated our findings with a group of older adults walking on a flat outdoor 400m track. WalkON significantly reduced the metabolic cost of transport by 17% for young adults during uphill walking. Concurrently, participants reported high perceived control over their voluntary movements (self- reported mean score of 5.67 out of 7 on a Likert scale). Similarly, older adults experienced a 9% reduction in metabolic cost when using WalkON during level ground walking, while retaining a strong sense of movement control (mean score of 5.85 out of 7). These findings emphasize the potential of wearable robotic assistive devices to enhance energy efficiency in daily outdoor walking, suggesting promising implications for promoting physical well- being and advancing mobility, particularly during the later stages of life.  
+
+<|ref|>text<|/ref|><|det|>[[167, 842, 830, 870]]<|/det|>
+Keywords: Soft robotic shorts, aging, mobility, walking assistance, metabolic cost
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[70, 77, 319, 101]]<|/det|>
+## 40 Introduction  
+
+<|ref|>text<|/ref|><|det|>[[110, 121, 888, 504]]<|/det|>
+In one of the closing scenes of Paolo Sorrentino's acclaimed movie "Youth" 1, 2016, the lead character confronts his own aging process and remarks, "I've become old and I don't know how I got here". This Sorrentinian sentiment profoundly echoes in a society where the escalation in aging populations is becoming a major demographic shift. According to the World Health Organization, by 2030, it is projected that one in six individuals worldwide will have reached the age of 60 and beyond, a paradigm shift from the one in eleven of \(2019^{2}\) . However, aging is not merely a statistical reality but an escalating biological process that changes the very dynamics of day- to- day life. The process of aging is intrinsically linked with an exacerbation in the effort and metabolic cost required to perform everyday motor tasks. Simple activities, such as walking, ascending stairs, or rising from a chair, become more demanding with increasing age, limiting mobility and independence.  
+
+<|ref|>text<|/ref|><|det|>[[110, 515, 888, 867]]<|/det|>
+As a reaction to these realities, the scientific community has intensified its efforts to design solutions that enhance mobility, with the ultimate goal of preventing the aging process from creating barriers. In the realm of robotics, this has led to the development of wearable assistive devices supporting movement in various body regions. The first generation of these wearable robots featured rigid actuated links generating large torques parallel to the human joints, best known as traditional exoskeletons. Over time, a select few of these devices have been explicitly designed to strengthen the mobility of older adults, with a specific emphasis on walking, which is typically most affected as people age. However, their use is confined mainly to lab- based experiments due to their weight and size. Incorporation into daily life applications is also limited due to low social acceptance.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 80, 884, 325]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[112, 331, 884, 461]]<|/det|>
+<center>Fig. 1 Vision and Design of WalkON (a) Illustration of the envisioned scenario where older adults engage in hiking while benefiting from the support provided by WalkON, thereby enhancing their daily mobility. (b) The design of WalkON comprises a textile structure encompassing a waist belt and two thigh harnesses that can be comfortably worn over regular clothing. The actuation mechanism relies on a tendon-driven transmission, with artificial tendons linked to the front part of the user's legs. These tendons are actuated by motors in accordance with the user's gait cycle. Motor commands deliver assistive forces during the swing phase of each step according to the hip joint kinematics recorded through Inertial Measurement Units (IMUs) in the sagittal plane. </center>  
+
+<|ref|>text<|/ref|><|det|>[[111, 482, 933, 774]]<|/det|>
+In recent years, there has been a significant shift towards the development of soft, lightweight solutions. Commonly known as “exosuits” \(^{12}\) , these devices feature textile garments and active components working in parallel to the human muscles. They have proven efficacy in various settings, by alleviating muscle strain in upper body joints \(^{14,15,16}\) , and reducing the metabolic expenditure associated with walking or running \(^{17,18,19}\) . Exosuits have showcased comparable usability to rigid exoskeletons, but with superior user satisfaction in terms of weight, effectiveness, and safety \(^{20}\) . Social acceptance is also higher with respect to their rigid counterpart, increasing the likelihood that individuals would incorporate them into daily life applications \(^{20}\) .  
+
+<|ref|>text<|/ref|><|det|>[[111, 783, 932, 894]]<|/det|>
+Nonetheless, the widespread adoption of such assistive technologies outside of controlled laboratory settings still poses a substantial challenge. With respect to walking support, foremost among the current limitations is the critical need for assistive devices to be self- contained and capable of adapting to the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[66, 80, 888, 312]]<|/det|>
+variable pace and modes of locomotion encountered in unstructured, real- world environments \(^{21,22}\) . Additionally, from the user perspective, the sensation of precise control over voluntary movements while using such technologies holds paramount importance. This level of control augments the sense of agency resulting in a more unobtrusive and user- inclusive experience \(^{13,23}\) . Addressing these challenges has the potential to encourage a more extensive adoption of such technologies. Ultimately, this can break down the barriers imposed by aging, allowing for an extension of physical activity beyond.  
+
+<|ref|>text<|/ref|><|det|>[[111, 321, 888, 552]]<|/det|>
+In this study, we present a pair of lightweight, soft robotic shorts, hereafter referred to as WalkON, designed to be worn over regular clothing and to act as a walking aid for daily use in real- world scenarios. These robotic shorts are intended to facilitate prolonged outdoor walking sessions, accommodating both typical outdoor settings and more challenging hiking- like terrains. The primary goal of this technology is to enhance the autonomy and walking energy efficiency for its users, with a particular focus on providing support to older individuals.  
+
+<|ref|>text<|/ref|><|det|>[[110, 561, 887, 853]]<|/det|>
+By design, WalkON assists hip flexion during the swing phase of walking. This feature is particularly important as the hip joint plays a vital role in ground clearance and limb advancement, demanding significant power especially in uphill and upstairs walking \(^{24,25}\) . As people age the role of the hip becomes more critical. Compared to young adults, it exhibits more pronounced kinetics during the push- off phase, resulting in increased mechanical work required for locomotion and reduced energy efficiency \(^{5,26}\) . Given these considerations, preserving hip function emerges as a fundamental strategy for maintaining walking ability, particularly for older adults or individuals facing mobility challenges \(^{5,27}\) .
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 80, 884, 466]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[112, 470, 884, 613]]<|/det|>
+<center>Fig. 2 Uphill outdoor walking task and metabolic results for young adults. (a) The task involved walking along a steep \(500\mathrm{m}\) uphill trail presenting altitudes of \(127\mathrm{m}\) and \(184\mathrm{m}\) respectively at the starting and ending points. Young adults walked at their preferred pace being unassisted (No Assistance, grey), and using WalkON (navy). (b, c) Metabolic results demonstrated a significant reduction in the cost of transport when using WalkON to perform the walking task. This result is visible from the cost of transport timeseries in (b), where the thick line represents the average across subjects, the shaded area the standard deviation, and from the mean values in (c). (d) The preferred mean walking speed of participants along the trail was not significantly altered when using WalkON. Results are presented as mean \(\pm\) s.e.m. \*\*\* indicates statistical significance with \(\mathrm{p}< 0.001\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[111, 633, 931, 895]]<|/det|>
+WalkON aims to achieve this objective by enabling the propagation of 106 upward leg movement through an actuation method that utilizes artificial tendons. It features a portable and lightweight design and employs a versatile 108 controller that is not limited to specific walking patterns or terrains. The control strategy is grounded in the user's natural leg movement pattern, making 110 it inclusive, adaptable, and resilient to variations in ground surfaces. This versatility makes it well- suited for outdoor use and extended walking sessions. By 112 promoting independence and fostering overall well- being, these shorts aim to 113 transform the aging experience.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 885, 222]]<|/det|>
+We hypothesize that WalkON can reduce the metabolic cost during walking compared to unassisted walking. Additionally, we posit that no restriction of the physiological kinematic patterns happens while using the system. Most crucially, we expect that users maintain full control over their voluntary movements, thus reporting a strong sense of agency.  
+
+<|ref|>text<|/ref|><|det|>[[110, 230, 886, 463]]<|/det|>
+The contribution of this study is twofold. From a technical standpoint, we tested these hypotheses through a technology assessment that involved young, healthy participants walking on a challenging outdoor uphill path. This allowed us to showcase the biomechanical effects of the system during demanding walking activities. Then, we conducted an efficacy study with our target population, involving participants aged 67 years and older on an outdoor walking track. These steps served to confirm the observed effects and provide a comprehensive understanding of WalkON's impact across different age groups.  
+
+<|ref|>sub_title<|/ref|><|det|>[[111, 485, 234, 508]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[111, 530, 672, 553]]<|/det|>
+## Technology assessment with young adults  
+
+<|ref|>text<|/ref|><|det|>[[110, 570, 886, 714]]<|/det|>
+Participants. Seven young and physically fit individuals, comprising four men and three women, were recruited for the technology assessment of WalkON (Fig. 1- (b)). On average, their age was \(25.43 \pm 2.23\) years, with mean height \(172.57 \pm 12.42\) cm, and weight \(67.57 \pm 13.06\) kg (refer to Table 1 in Extended Data Young Adults for individual demographic).  
+
+<|ref|>text<|/ref|><|det|>[[110, 752, 886, 893]]<|/det|>
+WalkON significantly reduced the metabolic cost of transport in uphill outdoor walking. The metabolic cost of transport, which measures the amount of metabolic energy required to cover a unit of distance<sup>28</sup>, serves as a crucial indicator of the effectiveness of wearable robotic assistive devices. The seven recruited young adults walked along a panoramic and winding
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 80, 931, 283]]<|/det|>
+500m uphill trail encompassing the surrounding hills of the city of Heidelberg 141 (49°24'55.1"N 8°42'00.9"E, Philosophenweg, Heidelberg, Germany). The trail 142 involved an altitude change of 57m between the starting (altitude of 127m) 143 and ending points (altitude of 184m) (Fig 2- (a)). Participants walked at their 144 self- selected pace in two conditions: (1) No Assistance, where they wore the 145 robotic shorts in an unpowered mode, and (2) the WalkON condition, where 146 they received assistance from the system. 147  
+
+<|ref|>text<|/ref|><|det|>[[111, 291, 931, 465]]<|/det|>
+Using WalkON, the metabolic demand of traversing the outdoor uphill trail 148 was significantly reduced by \(- 17.04 \pm 3.21\%\) (mean \(\pm\) s.e.m., \(\mathrm{n} = 7\) , \(\mathrm{p} < 0.001\) ) 149 (Fig. 2- (b, c)). The linear walking velocity (Fig. 2- (d)) did not show significant 150 differences between conditions, although there was a noticeable trend towards 151 a \(+5\%\) increase with WalkON compared to No Assistance. Particularly, four 152 out of seven participants increased their walking speed with WalkON. 153  
+
+<|ref|>sub_title<|/ref|><|det|>[[111, 500, 930, 522]]<|/det|>
+## Natural hip joint movement was not restricted when using WalkON. 155  
+
+<|ref|>text<|/ref|><|det|>[[111, 530, 930, 672]]<|/det|>
+Ensuring that the use of external assistive devices does not restrict or interfere with natural movements is essential, particularly for individuals without significant movement impairments<sup>12</sup>. This principle underpins the use of the device, promoting health and energy optimization without sacrificing movement freedom. 160  
+
+<|ref|>text<|/ref|><|det|>[[111, 682, 930, 854]]<|/det|>
+During natural locomotion, the hip angle exhibits a periodic trajectory resembling a sinusoidal waveform, while the hip velocity is shifted by \(\pi /2\) relative to the angle. These variables create a counterclockwise circular orbit in the hip phase portrait, representing the relationship between position and velocity in the gait cycle<sup>29</sup>. The angular separation between these two quantities indicates the leg's progression during walking. The control strategy of WalkON is 166
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 75, 884, 437]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 442, 885, 658]]<|/det|>
+<center>Fig. 3 Hip joint motion results for young adults. (a) Representation of the hip flexion angle shape in the sagittal plane along a gait cycle. (b) The raw hip phase portrait averaged across steps and subjects, combining hip angle and velocity measured on the sagittal plane, visually demonstrates that WalkON does not impose any restriction on natural hip motion. (c) The hip range of motion exhibited a significant increase with WalkON compared to the No Assistance condition. The upper row illustrates the mean time series of the hip angle across young adults and steps (shaded area represents the standard deviation), and the lower row shows the averaged hip range of motion (ROM). (d) There were no significant variations in hip velocity peaks with WalkON compared to the No Assistance condition. The upper row displays the mean time series of the hip velocity across young adults and steps (shaded area represents the standard deviation), while the bar plots in the lower row indicate the peak velocity during stance (negative values) and swing (positive values). Results in bar plots are presented as mean \(\pm\) s.e.m. \* indicates statistical significance with \(\mathrm{p}< 0.05\) . The grey color indicates results for the No Assistance condition and the navy for the WalkON condition. </center>  
+
+<|ref|>text<|/ref|><|det|>[[60, 677, 884, 728]]<|/det|>
+167 based on these principles (refer to the Methods section) which lay the basis for the delivery of assistive forces along the gait cycle.  
+
+<|ref|>text<|/ref|><|det|>[[110, 736, 884, 787]]<|/det|>
+Fig. 3- (b) shows the raw mean hip phase portrait for the seven young adults walking along the uphill trail. It is noticeable that wearing WalkON did not restrict the natural progression of hip angle and velocity along the gait cycle.  
+
+<|ref|>text<|/ref|><|det|>[[110, 795, 884, 815]]<|/det|>
+The range of motion of the hip joint exhibited a significant increase with  
+
+<|ref|>text<|/ref|><|det|>[[110, 825, 884, 845]]<|/det|>
+The range of motion of the hip joint exhibited a significant increase with  
+
+<|ref|>text<|/ref|><|det|>[[110, 855, 884, 874]]<|/det|>
+the use of the assistive robotic shorts (Fig. 3- (c)): in the No Assistance condi  
+
+<|ref|>text<|/ref|><|det|>[[110, 884, 884, 904]]<|/det|>
+tion the range of motion was \(48.82^{\circ} \pm 0.68^{\circ}\) on average between the two legs
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 931, 194]]<|/det|>
+and across subjects, which increased to \(53.21^{\circ} \pm 1.32^{\circ}\) with WalkON (+9.08 175 \(\pm 2.85\%\) , \(\mathrm{n} = 7\) , \(\mathrm{p} < 0.05\) ). Instead, being assisted by the device did not result in a significant change in hip peak velocities throughout the gait cycle (Fig. 177 3- (d)). 178  
+
+<|ref|>text<|/ref|><|det|>[[110, 230, 931, 373]]<|/det|>
+The sense of agency was preserved with WalkON. The perception of 180 control over one's movements significantly influences the acceptance of wearable robotic technologies among potential users \(^{23}\) . This concept is commonly 182 referred to as the "sense of agency", which is typically defined as the feeling 183 of being in command of an action \(^{30}\) . 184  
+
+<|ref|>text<|/ref|><|det|>[[110, 381, 931, 702]]<|/det|>
+To assess the young adults' sense of agency while using WalkON, we administered a ten- item questionnaire (Fig. 4). Each participant rated their level of 186 agreement with the items on a Likert scale ranging from 1 (strongly disagree) 187 to 7 (strongly agree). After completing the walking task using WalkON, young 188 adults consistently indicated high sense of agency, as reported by answers distribution in Fig. 4. On average, mean self- reported score to the questionnaire 190 was \(5.93 \pm 0.31\) (mean \(\pm\) s.e.m.) out of 7. Such scores resulted significantly 191 higher compared to a midpoint of 4 on the Likert scale ( \(\mathrm{n} = 7\) , \(\mathrm{t} = 6.78\) , 192 \(\mathrm{p} < 0.001\) ), indicating neither agreement nor disagreement with the statements. These results demonstrate that the users' perception of control over 194 their movements was not altered when utilizing WalkON. 195  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 727, 544, 750]]<|/det|>
+## Efficacy study with older adults  
+
+<|ref|>text<|/ref|><|det|>[[111, 767, 931, 878]]<|/det|>
+The primary objective of WalkON is to provide support for daily locomotion as 197 individuals age, with the goal of elevating the autonomy, life quality, and overall 198 well- being of its users in the long term. In line with this vision, an efficacy 199 study was conducted to evaluate the effectiveness in improving the metabolic 200
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[110, 90, 884, 346]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 352, 884, 495]]<|/det|>
+<center>Fig. 4 Sense of Agency results for young adults. The sense of agency assessment for young adults using WalkON involved rating various items about motor control with assistive devices on a Likert scale from 1 to 7, indicating their level of agreement with each statement. Items 2, 3, 6, and 8, which are inversely coded, were re-coded before analysis. Answers distribution for the sense of agency questionnaire is presented in terms of boxplot (the white circle being the median). The mean score \((\pm \mathrm{s.e.m.})\) across young adults demonstrates that users felt a strong sense of agency when using WalkON. Participants significantly perceived themselves as having greater control over their movements than the device. This significant difference was tested in comparison to the midpoint value of 4 (Neither Agree Nor Disagree) on the Likert scale. \(\mathrm{***p}< 0.001\) </center>  
+
+<|ref|>text<|/ref|><|det|>[[58, 515, 884, 563]]<|/det|>
+demands of outdoor walking specifically targeted at WalkON's intended users — older adults.  
+
+<|ref|>text<|/ref|><|det|>[[110, 575, 884, 836]]<|/det|>
+Six participants were recruited, whose ages spanned from 67 to 82 years (mean age \(74.50 \pm 6.95\) years), mean height \(172.83 \pm 8.28\) cm and weights \(68.67 \pm 11.17\) kg. The gender distribution was balanced, with an equal number of male and female individuals. According to the LUCAS Functional Ability Index \(^{31}\) , five of the six participants fell into the "robust" category, indicating that they are active individuals for whom health promotion and physical exercise are recommended. The remaining participant was classified as "pre- frail", suggesting a higher likelihood of mobility issues (refer to Table 2 in Extended Data Older Adults for individual characteristics).  
+
+<|ref|>text<|/ref|><|det|>[[110, 845, 884, 896]]<|/det|>
+The outdoor walking path was intentionally less challenging for the assessment in order to prevent overexertion among the older users. Here, study
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 78, 875, 749]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 748, 884, 878]]<|/det|>
+<center>Fig. 5 Efficacy study with older adults. (a) Older participants completed a \(400\mathrm{m}\) walk on a flat athletic track at their preferred speed in two conditions: No Assistance (grey) and with WalkON (navy). (b) Using WalkON significantly reduced the metabolic cost of transport. (c) The linear velocity of walking was unaltered on average across participants. (d, e, f) WalkON allowed for unrestricted hip motion. (g) Older adults reported strong perceived sense of control over voluntary movements while using WalkON. Results in bar plots are presented as mean \(\pm\) s.e.m; timeseries are displayed as mean and standard deviation (shaded area). Sense of agency answers distribution is presented in terms of boxplot (the white circle being the median). \(^{*}\mathrm{p}< 0.05\) , \(^{**}\mathrm{p}< 0.01\) . </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 80, 886, 162]]<|/det|>
+participants undertook a 400m walk on a flat athletic track (49°25'16.0"N 8°39'37.0"E, Heidelberg, Germany, Fig. 5-(a)) at their preferred speed, both unassisted (No Assistance) and with the support of WalkON.  
+
+<|ref|>text<|/ref|><|det|>[[108, 171, 886, 310]]<|/det|>
+Compared to the No Assistance condition, the metabolic cost of transport required for the outdoor walking task was reduced by an average of - 8.90 ± 3.83% (mean ± s.e.m, n = 6, p = 0.035) when using WalkON (Fig. 5-(b)). The linear velocity of walking increased for three out of six participants, resulting in an overall slight average increasing trend of +1.50% (p > 0.05) (Fig. 5-(c)).  
+
+<|ref|>text<|/ref|><|det|>[[108, 319, 886, 465]]<|/det|>
+The progression of the raw hip angle and velocity in the hip phase portrait was not altered by the assistive system (Fig. 5-(d)). Neither the physiological range of motion of the hip joint (Fig. 5-(e)), nor the peak velocities achieved at the joint during walking (Fig. 5-(f)) were constrained when compared to the No Assistance condition (p > 0.05).  
+
+<|ref|>text<|/ref|><|det|>[[108, 472, 886, 582]]<|/det|>
+Older participants expressed strong sense of agency while utilizing WalkON (Fig. 5-(g)), with an overall mean self- reported evaluation of 5.85 ± 0.41, which was significantly above the scale midpoint of 4 (n = 6, t = 4.90, p = 0.004), signifying their high perception of control over their movements.  
+
+<|ref|>sub_title<|/ref|><|det|>[[110, 605, 283, 629]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[108, 652, 886, 794]]<|/det|>
+As the world's population grows older, the issues surrounding the decline of mobility become more pressing, leading to a rising need for assistive mobility solutions. The challenge goes beyond merely extending physical activity; it is about addressing the constraints of aging and empowering individuals to thrive in their later years.  
+
+<|ref|>text<|/ref|><|det|>[[108, 803, 886, 885]]<|/det|>
+Back in 2009, Daniel P. Ferris envisioned a promising future for wearable assistive technologies in everyday life, foreseeing that "by 2024, individuals would navigate streets, malls, and homes while wearing robotic exoskeletons"32.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 930, 133]]<|/det|>
+Yet, despite this visionary perspective, their actual use has remained largely 240 experimental and primarily confined to lab settings \(^{33}\) . 241  
+
+<|ref|>text<|/ref|><|det|>[[108, 139, 933, 737]]<|/det|>
+With WalkON, we aspire to actualize Ferris's vision. As sketched in Fig. 242 1- (a), we aim to offer an unobtrusive assistive tool for daily life to address 243 the mobility challenges of aging by enhancing leg swing dynamics and supporting the hip flexor muscles responsible for initiating and maintaining limb 245 advancement. While it may seem theoretically unnecessary to expend substantial mechanical work to swing the legs due to the pendulum model \(^{34}\) , research 247 has shown that leg swinging is, in fact, energetically costly \(^{35}\) . Findings from 248 previous studies revealed that leg swinging can consume up to approximately 249 one- third of the net energy required for walking \(^{36}\) . This energy expenditure is 250 primarily associated with the transition from one stance limb to the next and 251 is linked to the work performed by muscles to move the leg forward \(^{25,35,37}\) . The 252 effects of aging significantly compromise this function \(^{3,27}\) . Numerous investigations have indicated that the strength of lower extremity muscles tends to 254 decline at a rate of 1- 4% per year, beginning around the age of 50 \(^{38}\) . This 255 decline is especially pronounced in the case of the hip flexors, which have been 256 observed to be the first to deteriorate \(^{27}\) . Due to loss in muscle strength, older 257 adults adapt by incrementing the simultaneous co- activation of antagonistic 258 muscles during walking \(^{39}\) . This compensatory mechanism serves to augment 259 joint stiffness and, in turn, enhance overall stability. However, this adjustment 260 comes at notable increase in metabolic expenditure \(^{3,39}\) . 261  
+
+<|ref|>text<|/ref|><|det|>[[110, 742, 932, 883]]<|/det|>
+WalkON demonstrated to improve the energy efficiency of walking in older 262 adults, contributing to enhanced mobility. In this study we investigated the 263 physiological and biomechanical advantages of using the system in daily- like 264 tasks by conducting a comprehensive outdoor walking evaluation with a two- 265 fold approach: initially, we carried out a technology assessment with young 266
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[106, 80, 885, 161]]<|/det|>
+individuals while hiking on an uphill trail; subsequently, we validated these findings in an efficacy study with our primary target population — older adults.  
+
+<|ref|>text<|/ref|><|det|>[[106, 170, 886, 342]]<|/det|>
+In trials with young participants, WalkON facilitated energy savings of \(17\%\) on average compared to No Assistance (Fig. 2- (c)), with individual outcomes ranging from \(7.44\%\) to \(33.64\%\) . In older adults, we observed an average decrease in the cost of transport of \(8.90\%\) while using WalkON (Fig. 5- (b)), with individual results ranging from a minimum saving of \(0.23\%\) to a maximum of \(22.38\%\) .  
+
+<|ref|>text<|/ref|><|det|>[[106, 352, 886, 583]]<|/det|>
+Metabolic reductions of this magnitude are accomplished without necessitating high power outputs from the system (peak motor power of \(1.52 \mathrm{W / kg}\) during walking). This underscores the high efficiency of the provided assistance. These findings align with prior studies \(^{40}\) that have demonstrated the superior efficiency of assisting hip flexion when compared to other lower- limb movements, such as hip extension \(^{41}\) or ankle plantarflexion \(^{42}\) . Even modest mechanical outputs from the assistive system are sufficient to achieve significant reductions in metabolic costs \(^{40}\) .  
+
+<|ref|>text<|/ref|><|det|>[[106, 592, 886, 822]]<|/det|>
+In a broader perspective, optimizing energy efficiency in daily walking tasks can significantly reduce fatigue during extended walks. This enhancement enables individuals to cover greater distances or sustained activity, improving overall endurance \(^{43}\) . Studies indicate that improving walking energy efficiency is pivotal for enhancing mobility, independence, and the overall quality of life for older adults. This is evidenced by positive effects on cardiovascular risk factors, decreased respiratory disease risk, and a general reduction in mortality from various causes \(^{43,44}\) . Beyond physical health benefits, walking
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 80, 931, 161]]<|/det|>
+demonstrates a direct association with a reduced risk of depression, a positive influence on emotional well- being, and various aspects of health- related quality of life<sup>45</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[110, 169, 933, 858]]<|/det|>
+Notably, studies demonstrating the effectiveness of wearable assistive technologies in comprehensive outdoor daily life scenarios are very sparse. Then, our ability to draw comparisons with existing literature is quite limited. For instance, Haufe et al.<sup>18</sup> tested the Myosuit, a commercial wearable robot designed to assist hip and knee extension through a tendon- driven mechanism guided by a rigid joint at the knee level, in the context of a 400m uphill gravel path with young participants. Their findings revealed an average metabolic saving of 10.6% compared to an unpowered condition. Instead, in a recent study, Slade et al.<sup>21</sup> introduced an ankle exoskeleton that reduced the cost of transport by an average of 17% in young, healthy subjects. This outcome is particularly relevant considering the crucial role of the ankle, alongside the hip, as a primary power source for the forward propulsion during walking. This metabolic improvement was achieved on a 566m flat path using a rigid system and a control algorithm that required specific adjustments and personalization for each user. While customization and personalization are important for optimizing individual assistance, they often compromise the device's ease of use and "plug- and- play" functionality. Additionally, in both of the mentioned instances, the outdoor tasks were comparatively less strenuous than our hiking activity, tests were conducted only on young and fit individuals, and the outcomes were achieved through systems featuring rigid links or joints. Such design elements typically simplify the characterization process, ensuring direct and predictable transmission of force, preserving component alignment and position, and facilitating ease of control. In contrast, the core design of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 81, 886, 283]]<|/det|>
+WalkON revolves around a soft structure that conforms to the body like regular clothing and lacks any rigid joints. This characteristic offers enhanced comfort, wearability, and reduced intrusiveness. However, it does make the final force transmitted to the human body less predictable, necessitating greater attention to system modeling and control. Despite these challenges, our system showcased substantial metabolic advantages in a deliberately demanding and fatiguing task, all without impeding freedom of movement during use.  
+
+<|ref|>text<|/ref|><|det|>[[110, 291, 886, 584]]<|/det|>
+When evaluating hip joint movement during uphill hikes, young adults exhibited a range of motion in the hip joint \(9.08\%\) higher while utilizing WalkON (Fig. 3- (c)). From a physiological perspective, uphill walking requires an increase in the hip joint range of motion and a concurrent reduction in knee extension as the swing phase ends \(^{24}\) . The utilization of WalkON might have possibly accentuated this inherent adaptation; however, these enhancements did not result in any disruption of movement and, consequently, contributed to improved metabolic efficiency. Instead, for older individuals walking on level terrain, their natural hip joint movement remained unaltered, indicating the absence of any movement constraints (Fig. 5- (e, f)).  
+
+<|ref|>text<|/ref|><|det|>[[110, 592, 886, 883]]<|/det|>
+To date, we have not come across any research that delves into real- world applications of assistive technologies tailored specifically for older adults while quantifying the metabolic advantages and assessing the psychophysical impact. The latter aspect is undeniably of paramount importance and forms a cornerstone of any robotic assistive device. The conscious perception of its value by the user encompasses one of the fundamental pillars for widespread adoption and should be considered a critical evaluation criterion, alongside biomechanical measurements, to gauge the impact of the technology. For the device to be considered valuable by potential users, it must provide an experience that unequivocally demonstrates its worth \(^{46}\) . This aligns with the overarching
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 931, 253]]<|/det|>
+objective of enhancing the user experience, ensuring that individuals feel in 345 perfect synchronization with the system and retain complete autonomy over 346 their movements. This concept is known in the literature as the “sense of 347 agency”, often described as the sensation of being in control of an action<sup>30</sup>. It 348 encompasses the experience of initiating one’s voluntary actions and, through 349 these actions, influencing the external world<sup>47</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[110, 261, 933, 825]]<|/det|>
+Our assessments regarding the sense of agency yielded promising outcomes 351 (Fig. 4, Fig. 5- (g)). Participants reported a strong sense of agency on the 352 administered questionnaire, with mean Likert- scale ratings of 5.67 for young 353 adults and 5.85 for older adults out of a total score of 7. This indicates a notable 354 alignment between their intentions and the system, emphasizing their percep- 355 tion of being the initiators and controllers of their actions. This result can be 356 primarily attributed to the controller of WalkON which synchronizes with the 357 user’s natural motion ensuring that no extraneous actions are imposed upon 358 voluntary movements. The control algorithm is designed to constantly analyze 359 the user’s movement pattern and derive the progression of their leg throughout 360 the gait cycle. It accomplishes this using solely thigh motion data, eliminat- 361 ing the need for personalization or resource- intensive classification algorithms. 362 This guarantees that the assistance provided harmonizes with the user’s natu- 363 ral walking pattern and seamlessly adapts to variations in walking speed. These 364 qualities collectively make WalkON’s controller a plug- and- play solution. Users 365 can incorporate the system into their daily routines without the requirement 366 for extensive setup or customization. This approach not only simplifies the 367 user experience but also reduces usage barriers, making the technology more 368 inclusive and akin to a pair of shorts for everyday use. 369  
+
+<|ref|>text<|/ref|><|det|>[[111, 832, 930, 881]]<|/det|>
+The primary limitation of our study lies in the absence of a control mea- 370 surement of metabolic activity without wearing WalkON. Instead, we relied 371
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 81, 887, 433]]<|/det|>
+on a comparison based on gross metabolic changes, utilizing a condition where the device was worn but turned off as a reference point. While this approach may be less realistic in real- world terms, it was chosen for practical experimental reasons and it is the most widely adopted in the literature \(^{12,18,17,48}\) . This decision allowed us to capture the user's movement during the No Assistance condition for meaningful comparison and to isolate the active biomechanical effect of assistance from the passive effects of wearing the suits. Given the demanding nature of the technology assessment with young adults, we opted not to impose an additional experiment on the participants. It is worth noting that due to the soft structure of the device, the negligible weight (2.93kg) and its positioning closer to the user's center of mass, we do not anticipate any significant impact on the final outcomes \(^{49}\) .  
+
+<|ref|>text<|/ref|><|det|>[[110, 442, 887, 853]]<|/det|>
+Even in terms of gross metabolic change, there was a difference in outcomes for the two groups. We believe this was influenced by age- related factors, including a propensity for shorter walking sessions, and variations in experimental protocols. The primary distinction between the experiments arises from the dissimilarities in the walking tasks themselves. Specifically, young individuals were asked to walk in considerably more physically demanding conditions, particularly on steep uphill terrain. Ground incline plays a pivotal role in determining energy expenditure during walking, with costs escalating proportionally as the gradient increases, and this relationship becomes linear for grades exceeding \(15\%\) \(^{50}\) . In such scenarios, the phase of limb advancement becomes more demanding, necessitating greater effort from hip flexors to raise the swinging leg against gravity \(^{5}\) . Consequently, the assistance offered by WalkON may deliver more pronounced benefits in these situations compared to walking on level ground.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 933, 404]]<|/det|>
+Future research endeavors anticipate conducting a pilot randomized controlled trial involving our target population in an even more ecologically valid setting, such as stair climbing, with an enhanced assessment of the system's impact during everyday use. This will be complemented by a thorough analysis of usability and user acceptance to provide a more comprehensive understanding of the technology's potential and limitations. We envision that prolonged walking sessions with WalkON could yield even greater benefits for our target users and ultimately achieve our long- term objectives. Additionally, we aim to investigate the application of the device in specific clinical populations characterized by restricted aerobic capacity and diminished muscle strength, such as individuals with congestive heart failure and multiple sclerosis.  
+
+<|ref|>text<|/ref|><|det|>[[110, 411, 933, 733]]<|/det|>
+Looking toward the future, we anticipate that the advantages of employing WalkON during extended walking sessions, encompassing various terrains from flat surfaces to challenging hiking trails, may become increasingly evident and potentially transformative. Mitigating the metabolic requirements linked to daily tasks like outdoor walks or indoor movement could not only enhance users' physical well- being but also potentially have a positive impact on their mental and emotional health<sup>43</sup>. As a result, older individuals could cover greater distances with reduced fatigue, thereby enhancing their autonomy and mobility. In doing so, we hope to move closer to realizing the vision that echoes that of Ferris – a future in which assistive technologies empower humans to achieve exceptional feats even in old age.  
+
+<|ref|>sub_title<|/ref|><|det|>[[112, 755, 288, 779]]<|/det|>
+## References  
+
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+[1] P. Sorrentino and N.S. Thompson. Youth. 2016. [2] World population prospects 2022: Summary of results. United Nations, 2022.
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+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[120, 80, 888, 162]]<|/det|>
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+
+<--- Page Split --->
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+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 80, 888, 225]]<|/det|>
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+
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+
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+
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+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 933, 223]]<|/det|>
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+[29] Dario J Villarreal, Hasan A Poonawala, and Robert D Gregg. A 522 robust parameterization of human gait patterns across phase- shifting perturbations. IEEE Transactions on Neural Systems and Rehabilitation 524 Engineering, 25(3):265- 278, 2016. 525
+
+<--- Page Split --->
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+[30] Valerian Chambon, Nura Sidarus, and Patrick Haggard. From action intentions to action effects: how does the sense of agency come about? Frontiers in human neuroscience, 8:320, 2014.  
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+[32] Daniel P Ferris. The exoskeletons are here. Journal of neuroEngineering and rehabilitation, 6(1):1- 3, 2009.  
+
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+[33] Hugh Herr. Exoskeletons and orthoses: classification, design challenges and future directions. Journal of neuroengineering and rehabilitation, 6:1- 9, 2009.  
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+[34] N Rashevsky. A note on energy expenditure in walking on level ground and uphill. The bulletin of mathematical biophysics, 24:217- 227, 1962.  
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+[35] Richard L Marsh, David J Ellerby, Jennifer A Carr, Havalee T Henry, and Cindy I Buchanan. Partitioning the energetics of walking and running: swinging the limbs is expensive. Science, 303(5654):80- 83, 2004.  
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+[36] Jiro Doke, J Maxwell Donelan, and Arthur D Kuo. Mechanics and energetics of swinging the human leg. Journal of Experimental Biology, 208(3):439- 445, 2005.  
+
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+[37] Jinger S Gottschall and Rodger Kram. Energy cost and muscular activity required for leg swing during walking. Journal of Applied Physiology, 99(1):23- 30, 2005.  
+
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+[38] Bret H Goodpaster, Seok Won Park, Tamara B Harris, Steven B Kritchevsky, Michael Nevitt, Ann V Schwartz, Eleanor M Simonsick, Frances A Tylavsky, Marjolein Visser, and Anne B Newman. The loss
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[156, 80, 931, 161]]<|/det|>
+of skeletal muscle strength, mass, and quality in older adults: the health, 553 aging and body composition study. The Journals of Gerontology Series 554 A: Biological Sciences and Medical Sciences, 61(10):1059–1064, 2006. 555 
+
+<|ref|>text<|/ref|><|det|>[[113, 172, 931, 255]]<|/det|>
+[39] Omar S Mian, Jeanette M Thom, Luca P Ardigo, Marco V Narici, and 556 Alberto E Minetti. Metabolic cost, mechanical work, and efficiency during 557 walking in young and older men. Acta physiologica, 186(2):127–139, 2006. 558 
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+[40] Jinsoo Kim, Brendan T Quinlivan, Lou-Ana Deprey, Dheepak Aru-559 mukhom Revi, Asa Eckert-Erdheim, Patrick Murphy, Dorothy Orzel, and 560 Conor J Walsh. Reducing the energy cost of walking with low assis-561 tance levels through optimized hip flexion assistance from a soft exosuit. 562 Scientific reports, 12(1):11004, 2022. 563 
+
+<|ref|>text<|/ref|><|det|>[[113, 413, 931, 523]]<|/det|>
+[41] Patrick W Franks, Gwendolyn M Bryan, Russell M Martin, Ricardo 564 Reyes, Ava C Lakmazaheri, and Steven H Collins. Comparing optimized 565 exoskeleton assistance of the hip, knee, and ankle in single and multi-joint 566 configurations. Wearable Technologies, 2:e16, 2021. 567 
+
+<|ref|>text<|/ref|><|det|>[[113, 533, 931, 641]]<|/det|>
+[42] Juanjuan Zhang, Pieter Fiers, Kirby A Witte, Rachel W Jackson, 568 Katherine L Poggensee, Christopher G Atkeson, and Steven H Collins. 569 Human-in-the-loop optimization of exoskeleton assistance during walking. 570 Science, 356(6344):1280–1284, 2017. 571 
+
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+[43] Zoltan Ungvari, Vince Fazekas-Pongor, Anna Csiszar, and Setor K Kunt-572 sor. The multifaceted benefits of walking for healthy aging: from blue 573 zones to molecular mechanisms. GeroScience, pages 1–29, 2023. 574 
+
+<|ref|>text<|/ref|><|det|>[[113, 743, 931, 881]]<|/det|>
+[44] Elaine M Murtagh, Linda Nichols, Mohammed A Mohammed, Roger 575 Holder, Alan M Nevill, and Marie H Murphy. The effect of walking on 576 risk factors for cardiovascular disease: an updated systematic review and 577 meta-analysis of randomised control trials. Preventive medicine, 72:34–43, 578 2015. 579
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 78, 888, 771]]<|/det|>
+580 [45] Karmel W Choi, Chia- Yen Chen, Murray B Stein, Yann C Klimentidis, Min- Jung Wang, Karestan C Koenen, Jordan W Smoller, et al. Assessment of bidirectional relationships between physical activity and depression among adults: a 2- sample mendelian randomization study. JAMA psychiatry, 76(4):399- 408, 2019. [46] Roberto Leo Medrano, Gray Cortright Thomas, and Elliott J Rouse. Can humans perceive the metabolic benefit provided by augmentative exoskeletons? Journal of NeuroEngineering and Rehabilitation, 19(1):26, 2022. [47] Brianna Beck, Steven Di Costa, and Patrick Haggard. Having control over the external world increases the implicit sense of agency. Cognition, 162:54- 60, 2017. [48] Enrica Tricomi, Mirko Mossini, Francesco Missiroli, Nicola Lotti, Xiaohui Zhang, Michele Xiloyannis, Loris Roveda, and Lorenzo Masia. Environment- based assistance modulation for a hip exosuit via computer vision. IEEE Robotics and Automation Letters, 2023. [49] Guillaume J Bastien, Patrick A Willems, Benedict Schepens, and Norman C Heglund. Effect of load and speed on the energetic cost of human walking. European journal of applied physiology, 94:76- 83, 2005. [50] Luke N Jessup, Luke A Kelly, Andrew G Cresswell, and Glen A Lichtwark. It is not just the work you do, but how you do it: The metabolic cost of walking uphill and downhill with varying grades. Journal of Applied Physiology, 2023.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[113, 77, 257, 101]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[116, 122, 466, 145]]<|/det|>
+## WalkON hardware design  
+
+<|ref|>text<|/ref|><|det|>[[111, 162, 933, 395]]<|/det|>
+WalkON is a soft robotic assistive system featuring one motor per leg (AK60- 6, 605 9Nm peak torque, T- Motor, China), each wrapping up an artificial tendon on 606 a spool (diameter of 35mm). This design allows independence between assisted 607 legs, enabling adjustments in the assistance profile to accommodate complex 608 movements and a broad range of motion. The weight of the device is 2.93kg, 609 most of which is located approximately at the level of the user's center of mass 610 to minimize the impact of the extra mass on the metabolic energy expenditure 611 during walking51.  
+
+<|ref|>text<|/ref|><|det|>[[110, 403, 933, 664]]<|/det|>
+WalkON is connected to the human body through a compliant textile structure. The textile interface consists of an adjustable waist belt, which is worn 614 at the user's iliac crest level, and two thigh fabric harnesses. Both the belt and 615 the harnesses feature an inner layer of neoprene, offering good tensile strength 616 and hardness while ensuring soft contact with the body. Velcro strips are used 617 to provide a custom fit for a wide range of human body shapes and sizes. A 618 blueprint of the textile components is provided in Extended Data Fig. 3. The 619 textile interface serves as an anchor for the actuation stage and electronics and 620 to guide the tendon- driven transmission.  
+
+<|ref|>text<|/ref|><|det|>[[110, 673, 932, 876]]<|/det|>
+The mentioned transmission uses artificial tendons made of Black Braided 622 Kevlar Fiber (KT5703- 06, 2.2 kN max load, USA) to actively assist the user's 623 hip flexion. These tendons run from the actuation stage, located at the back 624 of the belt on a rigid plate, to a proximal anchor point on the front, guided 625 by Bowden cables (Shimano SLR, diameter 5mm, Sakai, Osaka, Japan). From 626 here, the tendons run parallel to each leg and are anchored to a distal anchor 627 point on the thigh textile harness. By shortening the distance between the 628
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[60, 81, 886, 132]]<|/det|>
+proximal and distal anchor points on the suit, assistive forces delivered to the user generate a flexing moment around the hip joint.  
+
+<|ref|>text<|/ref|><|det|>[[110, 140, 886, 285]]<|/det|>
+The systems are powered by a portable Lithium Polymer battery (Tattu, 0.4kg, 14.8V, capacity of 3700 mAh). Custom- designed housings for actuation, power, and electronics, as well as anchor points, are fabricated using 3D printing technology with PLA material. Computer- aided design files for such elements are provided as Supplementary Material.  
+
+<|ref|>text<|/ref|><|det|>[[110, 291, 886, 522]]<|/det|>
+The controller is executed on a microcontroller (Arduino MKR 1010 WiFi, Arduino, Italy) at a 100Hz frequency, and it obtains information via Bluetooth Low Energy (Feather nRF52832, Bluefruit, Adafruit) protocol from two Inertial Measurements Unit (IMU) sensors (BNO055, Bosch, Germany) placed laterally on the thigh harness. These sensors continuously stream the hip flexion angle of each leg as measured in the sagittal plane, then converted by the control algorithm to an assistance profile according to the leg progression along the gait cycle.  
+
+<|ref|>text<|/ref|><|det|>[[110, 531, 885, 582]]<|/det|>
+A complete schematic of WalkON components is provided in Extended Data Fig. 4.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 607, 385, 629]]<|/det|>
+## WalkON Controller  
+
+<|ref|>text<|/ref|><|det|>[[110, 646, 886, 910]]<|/det|>
+WalkON is operated using a control framework designed to actuate tendon displacement based on the kinematics of hip flexion during human locomotion and its progression along the gait cycle. The entire architecture is built so that signals flow along a forward path from the sensing system to the control unit and finally to the actuation unit. This is achieved through a three- tiered approach: a High- Level Controller that estimates the gait phase in real- time from hip kinematic data, a Mid- Level Controller that generates the actuator reference motion based on the user's gait phase, and a Low- Level Controller that provides appropriate assistance to the user based on the previous layer's outputs.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 80, 931, 160]]<|/det|>
+The control framework is depicted in Extended Data Fig. 5. Detailed information about the algorithm and a pseudocode are provided in the Supplementary Information. 658  
+
+<|ref|>text<|/ref|><|det|>[[110, 169, 933, 706]]<|/det|>
+The high- level controller calculates a monotonically increasing gait phase 659 variable from a single inertial sensor on each leg. The underlying approach 660 incorporates the concepts from the general control theory of oscillating dynamical systems. Indeed, during natural locomotion, the angular position of the hip 662 joint, \(\theta (t)\) , has a periodic trajectory that can be approximated as a sinusoidal 663 waveform, similar to an undamped oscillator \(^{52,53}\) . As such, the hip angular 664 velocity, \(\dot{\theta} (t)\) , has a \(\pi /2\) shift with respect to \(\theta (t)\) and the two variables produce a circular orbit in the counterclockwise sense of rotation on the hip phase 666 portrait, i.e., position vs. velocity phase plane. The gait phase, denoted as \(\phi (t) = f([\theta (t),\dot{\theta} (t)])\) , is extracted in real- time by computing the polar angle 668 between these two quantities. For each step, both variables are initially shifted 669 about the origin of the hip phase portrait, and \(\theta (t)\) is re- scaled to match the 670 amplitude of \(\dot{\theta} (t)\) in order to produce a more circular orbit \(^{54}\) . Information 671 about the walking speed are intrinsically present in the gait phase extraction, 672 allowing instant adaptation to changes in walking pattern. To comply with 673 the sinusoidal nature of the hip flexion angular displacement measured on 674 the sagittal plane, sinusoidal interpolation follows the gait phase estimation 675 deriving a signal, \(\theta_{\mathrm{r}}(t)\) , used as basis for the motor reference trajectory. 676  
+
+<|ref|>text<|/ref|><|det|>[[110, 712, 932, 883]]<|/det|>
+As the gait phase extraction method shows sensitivity to noise captured 677 from the inertial sensors on unstructured terrains, to filter out such noise from \(\theta_{\mathrm{r}}(t)\) , a Kalman filter is implemented at the Mid- Level controller. Kalman 679 filter parameters have been optimized in preliminary trials to strike a good 680 balance between the noise in the real- time recorded data and the noise in 681 the estimated data. The actuator's final position reference trajectory, \(\theta_{\mathrm{ref}}(t)\) , 682
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[108, 80, 886, 161]]<|/det|>
+is obtained using cubic spline interpolation on the Kalman- filtered \(\theta_{\mathrm{r}}(t)\) . The amplitude of \(\theta_{\mathrm{ref}}(t)\) is determined based on the user's hip range of motion, pulley diameter, and anthropometric considerations.  
+
+<|ref|>text<|/ref|><|det|>[[108, 170, 886, 374]]<|/det|>
+At the low- level controller, a feedback position loop compares the actual position of the motor \(\theta_{\mathrm{m}}(t)\) with the reference position \(\theta_{\mathrm{ref}}(t)\) extracted from the previous layer. A Proportional- Differential (PD) controller is used to convert the position error into motor angular velocity. To prevent disturbances or noise in the hip kinematics recordings from translating to unwanted motor commands when a subject stops walking, a stop detection condition is implemented based on the gait speed.  
+
+<|ref|>sub_title<|/ref|><|det|>[[110, 397, 320, 420]]<|/det|>
+## Study Protocol  
+
+<|ref|>text<|/ref|><|det|>[[108, 437, 886, 608]]<|/det|>
+The first aim of the study is to evaluate the effectiveness of WalkON in enhancing outdoor walking experiences. To achieve this objective, a technology assessment of the system was conducted on uphill hiking- like trails with young adults. The ultimate goal of the research is to propose this system as an effective support for walking in older individuals. To explore this possibility, an efficacy study was undertaken with participants aged over 67 years old.  
+
+<|ref|>text<|/ref|><|det|>[[108, 617, 886, 789]]<|/det|>
+Before the study began, all participants provided informed written consent, as well as consent to publish identifiable images. Our research procedures were conducted in accordance with the principles of the Declaration of Helsinki and were approved by the Ethics Committee of Heidelberg University under resolution No. S- 313/2020. During the study, each participant underwent evaluations in multiple conditions, acting as their own control for comparison.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[113, 80, 636, 102]]<|/det|>
+## Technology assessment with young adults  
+
+<|ref|>text<|/ref|><|det|>[[111, 119, 931, 230]]<|/det|>
+Inclusion criteria for young adults (n = 7) recruitment included age between 707 18 and 35 years, no visual or auditory impairments or any neurological, cardiovascular, metabolic, or mental disorders that might interfere with the tasks at hand. 710  
+
+<|ref|>text<|/ref|><|det|>[[111, 240, 931, 410]]<|/det|>
+The chosen experimental path was a panoramic snake- like trail up the 711 hills surrounding the city of Heidelberg, Germany, known as Philosophenweg 712 (49°24'55.1"N 8°42'00.9"E). We selected the initial segment of the trail, which 713 is a winding and very steep 500m track with a change of altitude from 127m to 714 184m between the starting and ending points (Fig. 2- (a)). The trail began with 715 108 stairs made of sandstone irregular in shape, followed by an uphill section. 716  
+
+<|ref|>text<|/ref|><|det|>[[111, 420, 931, 620]]<|/det|>
+Study participants were instructed to walk at their preferred speed along 717 the trail two times under different conditions: without assistance (No Assis- 718 tance) and with assistance from WalkON. In the No Assistance condition, 719 participants worn the system in unpowered mode in order to allow for record- 720 ings of kinematic data. Given the physically demanding nature of the trial, 721 we conducted the different conditions on separate days to minimize any 722 fatigue- related effects. 723  
+
+<|ref|>text<|/ref|><|det|>[[111, 631, 931, 891]]<|/det|>
+After completing the uphill walking, each participant retraced the same 724 path in the opposite direction, going downhill. The walking distance for each 725 condition of the study accounted then for a total of 1 km walked. However, 726 the results for the downhill walking are not included in the main text but 727 rather reported in the Supplementary Information, as the assistance provided 728 by WalkON for hip flexion is less significant during this phase. This is because 729 the swinging leg does not need to be lifted as high during downhill walking for 730 ground clearance<sup>55</sup>. The primary focus of retracing the path was to demonstrate that the assistive system and its weight do not impede motion or impose 732
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[58, 81, 886, 162]]<|/det|>
+a metabolic burden during downhill sections. The Supplementary Information additionally reports a comparative study on two hardware configurations of WalkON used to assess the most efficient design.  
+
+<|ref|>sub_title<|/ref|><|det|>[[58, 189, 515, 210]]<|/det|>
+## Efficacy study with older adults  
+
+<|ref|>text<|/ref|><|det|>[[110, 227, 886, 369]]<|/det|>
+Older adults enrolled for the efficacy study ( \(\mathrm{n} = 6\) ) were selected based on criteria that included being over 65 years of age, being categorized as either "robust" or "pre- frail" according to the LUCAS Functional Ability Index \(^{56}\) , and not having severe uncorrected visual or auditory impairments or significant neurological, cardiovascular, metabolic, or mental conditions.  
+
+<|ref|>text<|/ref|><|det|>[[109, 378, 886, 639]]<|/det|>
+To avoid any physical overload for the frailer subjects of the study, we chose an outdoor path with a shorter distance and a flat ground. Participants were instructed to walk at their preferred speed on a \(400\mathrm{m}\) athletic track on flat ground (located at \(49^{\circ}25'16.0''\mathrm{N}\) \(8^{\circ}39'37.0''\mathrm{E}\) , Heidelberg, Germany, Fig. 5- (a)) under two different conditions: wearing the device in unpowered mode (No Assistance) and with assistance from WalkON. Both conditions were conducted on the same day, with a minimum 20- minute rest period in between to prevent fatigue. The order of the conditions was randomized among participants to eliminate order effects.  
+
+<|ref|>sub_title<|/ref|><|det|>[[110, 664, 482, 686]]<|/det|>
+## Data analysis and statistics  
+
+<|ref|>text<|/ref|><|det|>[[109, 704, 886, 907]]<|/det|>
+In order to evaluate the use of WalkON in improving walking efficiency, the principal outcome measure was the metabolic cost associated with walking. Oxygen and carbon dioxide consumption data were recorded using a portable respirometer (K5, COSMED, Italy), and the net metabolic cost was deduced using Péronnet and Massicotte's formula \(^{57}\) . For establishing a baseline, participants were instructed to breathe normally for a three- minute period while standing at rest before each experiment began. The mean baseline metabolic
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 933, 494]]<|/det|>
+cost from the final minute was then subtracted from the overall metabolic data 759 to discern the cost of walking for each condition. To account for the different walking speeds across conditions, metabolic data were analyzed in terms 761 of cost of transport \(^{58}\) . This was computed by dividing the net metabolic cost 762 by the product of the participant's weight, gravitational acceleration, and the 763 average speed of walking. The average walking speed was determined by the 764 distance covered over the duration of the experiment. Considering that it takes 765 approximately two minutes for metabolic data to stabilize after any significant 766 changes in physical activity, for the technology assessments involving younger 767 adults, we excluded the initial two minutes of recording and analyzed the 768 remainder of the data. For the efficacy study with older adults, we examined 769 the final two minutes of the trial, since visual inspection of the data demonstrated steady- state behavior during this time segment and the time taken by 771 participants to traverse the walking track was approximately four minutes. 772  
+
+<|ref|>text<|/ref|><|det|>[[110, 501, 933, 701]]<|/det|>
+Kinematic evaluations were conducted on the profiles of the hip angle and hip velocity for both the left and right legs, using data recorded from inertial sensors integrated into the system. The raw motion data was divided into steps post low- pass filtering (4th order Butterworth, cut- off frequency 10 Hz). For each participant, we evaluated the range of motion (ROM), along with the average peak velocity during both stance and swing phases across all steps, under both unassisted and assisted condition. 779  
+
+<|ref|>text<|/ref|><|det|>[[110, 712, 933, 882]]<|/det|>
+Results are presented as mean \(\pm\) s.e.m (standard error of the mean). Data were tested for normality using a Shapiro- Wilk test and resulted normally distributed. The significance level for all statistical tests was set to be less than 0.05. A linear mixed effects model was used for subsequent statistical analysis of the collected metabolic and motion data, employing the least squares regression method (MATLAB, MathWorks Inc., Natick, MA, USA). The model
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[110, 80, 886, 192]]<|/det|>
+accounted for the "condition" ("No Assistance", "WalkON"), which was presented as dummy- encoded, categorical fixed- effect explanatory variables. A term "participant" (either YA1 to YA7 for young adults or OA1 to OA6 for older adults) was included in the model as a random- effect variable.  
+
+<|ref|>text<|/ref|><|det|>[[110, 201, 887, 613]]<|/det|>
+In our analysis of the sense of agency, we asked study participants to answer to a questionnaire consisting of six positively framed items (items 1, 4, 5, 7, 9 10 in Fig. 4 and Fig. 5- (g)) and four negatively framed items (items 2, 3, 6, 8) evaluating the sense of control they had while using WalkON. The items were derived from the theoretical literature on sense of agency and were finetuned to the context of wearable mobility aids59. The negatively framed items were recoded so that higher values indicate higher sense of agency. For items analyses, we calculated a mean score of the scale items. Internal consistency of the questionnaire scale after recoding was good ( \(\alpha = 0.83\) 95%, CI [0.67; 0.92]). To test whether participants felt that their movements were more controlled by themselves or by the device, we tested whether this mean score significantly deviated from the scale midpoint of 4 through a paired- sample t- test twotailed. A mean above the scale midpoint suggested that the participants saw themselves more in control of their movements than the device.  
+
+<|ref|>sub_title<|/ref|><|det|>[[111, 639, 336, 660]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[110, 678, 885, 728]]<|/det|>
+All data needed to evaluate the conclusions in the Article are present in Supplementary data 1 and may be reused for ethical, scientific purposes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[111, 754, 340, 775]]<|/det|>
+## Code availability  
+
+<|ref|>text<|/ref|><|det|>[[110, 794, 885, 844]]<|/det|>
+The exemplary scripts for data processing and analysis for this study are present in Supplementary data 1.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[112, 77, 288, 101]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[110, 120, 932, 202]]<|/det|>
+[51] MJ Myers and K Steudel. Effect of limb mass and its distribution on the energetic cost of running. Journal of Experimental biology, 116(1):363- 373, 812 1985. 813  
+
+<|ref|>text<|/ref|><|det|>[[110, 211, 932, 295]]<|/det|>
+[52] Eric R Westervelt, Jessy W Grizzle, Christine Chevallereau, Jun Ho 814 Choi, and Benjamin Morris. Feedback control of dynamic bipedal robot 815 locomotion. 2018. 816  
+
+<|ref|>text<|/ref|><|det|>[[110, 303, 932, 415]]<|/det|>
+[53] Dario J Villarreal, Hasan A Poonawala, and Robert D Gregg. A 817 robust parameterization of human gait patterns across phase- shifting perturbations. IEEE Transactions on Neural Systems and Rehabilitation 819 Engineering, 25(3):265- 278, 2016. 820  
+
+<|ref|>text<|/ref|><|det|>[[110, 422, 932, 536]]<|/det|>
+[54] David Quintero, Daniel J Lambert, Dario J Villarreal, and Robert D 821 Gregg. Real- time continuous gait phase and speed estimation from a single 822 sensor. In 2017 IEEE Conference on Control Technology and Applications 823 (CCTA), pages 847- 852. IEEE, 2017. 824  
+
+<|ref|>text<|/ref|><|det|>[[110, 544, 932, 597]]<|/det|>
+[55] M Kuster, S Sakurai, and GA Wood. Kinematic and kinetic comparison 825 of downhill and level walking. Clinical biomechanics, 10(2):79- 84, 1995. 826  
+
+<|ref|>text<|/ref|><|det|>[[110, 604, 932, 747]]<|/det|>
+[56] Ulrike Dapp, Christoph E Minder, Stefan Golgert, Björn Klugmann, 827 Lilli Neumann, and Wolfgang von Renteln- Kruse. The inter- relationship 828 between depressed mood, functional decline and disability over a 10- year 829 observational period within the longitudinal urban cohort ageing study 830 (lucas). J Epidemiol Community Health, 75(5):450- 457, 2021. 831  
+
+<|ref|>text<|/ref|><|det|>[[110, 754, 931, 806]]<|/det|>
+[57] François Peronnet, Denis Massicotte, et al. Table of nonprotein respiratory quotient: an update. Can J Sport Sci, 16(1):23- 29, 1991. 833  
+
+<|ref|>text<|/ref|><|det|>[[110, 813, 931, 896]]<|/det|>
+[58] Henry J Ralston. Energy- speed relation and optimal speed during 834 level walking. Internationale Zeitschrift für Angewandte Physiologie 835 Einschliesslich Arbeitsphysiologie, 17(4):277- 283, 1958. 836
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 80, 887, 193]]<|/det|>
+[59] Adam Tapal, Ela Oren, Reuven Dar, and Baruch Eitam. The sense of agency scale: A measure of consciously perceived control over one's mind, body, and the immediate environment. Frontiers in psychology, 8:1552, 2017.  
+
+<|ref|>text<|/ref|><|det|>[[57, 231, 887, 343]]<|/det|>
+Acknowledgments. The presented results were obtained within the scope of the HeiAge and SMART- AGE projects (P2019- 01- 003) funded by the Carl Zeiss Foundation. We extend our heartfelt gratitude to all the participants that volunteered in the study for their time, feedback and contribution.  
+
+<|ref|>text<|/ref|><|det|>[[57, 360, 887, 591]]<|/det|>
+Author contributions. ET designed and implemented the WalkON controller. NL and LM provided feedback to control implementation. ET, FM, NL, XZ, and LM led the design and implementation of the textile interface, actuator unit, and electronics. ET, FM, NL, MX, JB, CB, and LM designed the study. ET, FM, and MS led the study conduct. MT provided the psychophysical evaluation questionnaire and analysed the related data. ET analyzed the data and prepared the figures and manuscript. All authors reviewed the manuscript and provided critical feedback.  
+
+<|ref|>text<|/ref|><|det|>[[57, 609, 886, 720]]<|/det|>
+Competing interests. E.T., F.M, N.L., and L.M. are co- inventors of a patent application disclosing the walking assistive systems described herein. The patent application is pending at the time of the submission of the present scientific report.  
+
+<|ref|>text<|/ref|><|det|>[[57, 736, 886, 811]]<|/det|>
+Additional information. Supplementary information Supplementary Information is available for this paper. Correspondence and requests for materials should be addressed to Enrica Tricomi.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[113, 78, 592, 101]]<|/det|>
+# Extended Data Young Adults  
+
+<|ref|>table<|/ref|><|det|>[[181, 140, 805, 288]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[113, 296, 460, 312]]<|/det|>
+Table 1 Young adults demographic   
+
+<table><tr><td colspan="6">Participant characteristics</td></tr><tr><td>ID</td><td>Height (cm)</td><td>Weight (kg)</td><td>Body-Mass Index (kg/m²)</td><td>Sex (-)</td><td>Age (years)</td></tr><tr><td>YA1</td><td>184</td><td>74</td><td>21.86</td><td>Male</td><td>24</td></tr><tr><td>YA2</td><td>156</td><td>60</td><td>24.65</td><td>Female</td><td>28</td></tr><tr><td>YA3</td><td>171</td><td>60</td><td>20.52</td><td>Male</td><td>23</td></tr><tr><td>YA4</td><td>193</td><td>93</td><td>24.97</td><td>Male</td><td>27</td></tr><tr><td>YA5</td><td>163</td><td>54</td><td>20.32</td><td>Female</td><td>28</td></tr><tr><td>YA6</td><td>171</td><td>70</td><td>23.94</td><td>Male</td><td>23</td></tr><tr><td>YA7</td><td>170</td><td>62</td><td>21.45</td><td>Female</td><td>25</td></tr></table>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 78, 888, 275]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 279, 884, 366]]<|/det|>
+<center>Fig. 1 Intra-participants results for the technology assessment with young adults. For each young adult (YA): (a) mean cost of transport while walking along the \(500\mathrm{m}\) uphill hiking trail; (b) linear velocity of walking across the trial; (c) hip range of motion (ROM) and hip peak velocities as a mean across steps. The shaded bars indicate the average results across participants as presented in the main text (grey = No Assistance; navy = WalkON). The symbol \* indicates statistical significance between conditions. </center>
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[113, 77, 581, 101]]<|/det|>
+# Extended Data Older Adults  
+
+<|ref|>table<|/ref|><|det|>[[115, 135, 874, 298]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[113, 307, 454, 323]]<|/det|>
+Table 2 Older adults demographic   
+
+<table><tr><td colspan="7">Participant characteristics</td></tr><tr><td>ID</td><td>Height (cm)</td><td>Weight (kg)</td><td>Body-Mass Index (kg/m²)</td><td>Sex (-)</td><td>Age (years)</td><td>LUCAS Functional Ability Index</td></tr><tr><td>OA1</td><td>173</td><td>63</td><td>21.05</td><td>Female</td><td>69</td><td>Robust</td></tr><tr><td>OA2</td><td>186</td><td>90</td><td>26.01</td><td>Male</td><td>82</td><td>Robust</td></tr><tr><td>OA3</td><td>168</td><td>58</td><td>20.55</td><td>Female</td><td>78</td><td>Robust</td></tr><tr><td>OA4</td><td>165</td><td>70</td><td>25.71</td><td>Female</td><td>67</td><td>Robust</td></tr><tr><td>OA5</td><td>166</td><td>66</td><td>23.95</td><td>Female</td><td>69</td><td>Robust</td></tr><tr><td>OA6</td><td>179</td><td>65</td><td>20.29</td><td>Male</td><td>82</td><td>Pre-frail</td></tr></table>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[110, 78, 888, 290]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 294, 885, 383]]<|/det|>
+<center>Fig. 2 Intra-participants results for the efficacy study with older adults. For each older adult (OA): (a) mean cost of transport while walking along the 400m flat athletic track; (b) linear velocity of walking across the trial; (c) hip range of motion (ROM) and hip peak velocities as a mean across steps. The shaded bars indicate the average results across participants as presented in the main text (grey = No Assistance; navy = WalkON). The symbol \* indicates statistical significance between conditions. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[110, 130, 887, 682]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 685, 885, 730]]<|/det|>
+<center>Fig. 3 Textile blueprint (a) WalkON waist belt extended. (b) Layer composition of the belt with the back and frontal view in its closed configuration. (c) Thigh textile harness inner view and closed configuration. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[130, 155, 884, 555]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 558, 884, 645]]<|/det|>
+<center>Fig. 4 WalkON hardware components. (a) Computer-aided design of WalkON (b) Inertial Measurement Unit (IMU) sensors stream hip motion data via Bluetooth Low Energy to the control unit. This unit runs the controller on a microcontroller. The output is a velocity command sent to the actuators. (c) The textile structure of WalkON is composed by a waist belt and two thigh harnesses. (d) Anchor points are placed on the belt and thigh harness to guide the artificial tendons. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 135, 886, 519]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[111, 523, 884, 651]]<|/det|>
+<center>Fig. 5 WalkON Controller. The WalkON control system operates across three levels. The High-Level controller determines the gait phase by calculating the polar angle between the hip joint position, \(\theta (t)\) , and velocity, \(\dot{\theta} (t)\) , during each gait cycle in real-time. It then uses sinusoidal interpolation to create a foundational trajectory for the reference motor position, \(\theta_{\mathrm{r}}(t)\) . The Mid-Level controller applies a Kalman filter to \(\theta_{\mathrm{r}}(t)\) to eliminate noise emerging from the phase estimation method. Following this, it uses cubic spline interpolation to create the final trajectory for the final motor position reference, \(\theta_{\mathrm{ref}}(t)\) . The Low-Level controller actuates tendon displacement based on the motor commands derived from the outputs of the previous levels. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 131, 451, 177]]<|/det|>
+- ManuscriptSupplementaryInformation.pdf- Supplementarydata3Video.mp4
+
+<--- Page Split --->

preprint/preprint__5f717dfa9444b7081dcae9e03379b59567ffe8be0ba96f631c317dca0ad72be5/images_list.json

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+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Relationships between the dates of leaf senescence (DFS) and precipitation changes. A represent the partial correlations between DFS and total precipitation, controlling only temperature and radiation, and B by additionally controlling precipitation frequency. C is partial correlations between DFS and precipitation frequency, controlling temperature, radiation and total precipitation. D shows the changes between significant positive and negative correlations with the Sankey diagram. E represents the results classified by plant functional types (See methods). F shows the same analysis using flux measurements. P and N represent positive and negative, respectively. Significance was set with \\(p< 0.05\\) .",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Mechanisms for the correlation between precipitation frequency and the dates of leaf senescence (DFS). A shows the structural equation model (SEM) analysis. B and C represent the changes of drought response lag and drought recovery time with precipitation frequency. D shows the moving window approach with respect of positive and negative sensitivities of DFS to precipitation frequency over 1982-2022 (see Methods). E shows the relationship between precipitation frequency and the maximum daily precipitation size (N and P represent negative and positive correlations). F represents the correlation between DFS and root zone soil moisture variability using coefficients of variation (%). \\* and \\*\\* represent \\(p<0.05\\) and \\(p<0.01\\) , respectively.",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. The test of Earth system models in reproducing the observed relationship between the dates of leaf senescence (DFS) and precipitation frequency. A shows the overall proportions of significant positive and negative correlations. B represents the sensitivity of DFS to precipitation frequency changes. C is the comparison on the signs of correlation for each pixel. Four shared socioeconomic pathways (SSPs) were included for CMIP6 models, including SSP126, SSP245, SSP370, and SSP585, respectively. -- and ++ represent consistent negative and positive observations. Significance was set with p<0.05.",
+    "footnote": [],
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+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Extended Figure 1. Spatial distribution of the correlation coefficients \\((\\mathbf{R}^2)\\) with respect to total precipitation and its frequency. (a) Total precipitation \\((\\mathbf{P}_{\\text{total}})\\) and dates of leaf senescence (DFS). (b) Precipitation frequency \\((\\mathbf{P}_{\\text{freq}})\\) and DFS.",
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+  },
+  {
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+    "img_path": "images/Figure_2.jpg",
+    "caption": "511 Extended Figure 2. Relationships between drought response lag and (A)",
+    "footnote": [],
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+      [
+        220,
+        88,
+        775,
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+      ]
+    ],
+    "page_idx": 27
+  }
+]

preprint/preprint__5f717dfa9444b7081dcae9e03379b59567ffe8be0ba96f631c317dca0ad72be5/preprint__5f717dfa9444b7081dcae9e03379b59567ffe8be0ba96f631c317dca0ad72be5.mmd

@@ -0,0 +1,304 @@
+
+# Declining precipitation frequency drivers earlier leaf senescence by intensifying drought stress and enhancing drought acclimation  
+
+Chaoyang Wu wucy@igsnrr.ac.cn  
+
+Institute of Geographic Sciences and Natural Resources Research https://orcid.org/0000- 0001- 6163- 8209  
+
+Xinyi Zhang Institute of Geographic Sciences and Natural Resources Research  
+
+Xiaoyue Wang The Key Laboratory of Land Surface Pattern and Simulation, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences https://orcid.org/0000- 0002- 9950- 2259  
+
+Constantin Zohner ETH Zurich https://orcid.org/0000- 0002- 8302- 4854  
+
+Josep Penuelas CSIC, Global Ecology Unit CREAF- CSIC- UAB, Cerdanyola del Valles 08193, Catalonia, Spain https://orcid.org/0000- 0002- 7215- 0150  
+
+Yang Li University of Arizona https://orcid.org/0000- 0002- 6463- 6441  
+
+Xiuchen Wu Beijing Normal University https://orcid.org/0000- 0003- 0396- 7439  
+
+Yao Zhang Peking University https://orcid.org/0000- 0002- 7468- 2409  
+
+Huiying Liu East China Normal University https://orcid.org/0000- 0001- 8903- 6103  
+
+Pengju Shen Institute of Geographic Sciences and Natural Resources Research  
+
+Xiaoxu Jia Chinese Academy of Sciences  
+
+Wenbin Liu  
+
+Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Science and Natural Resources Research, Chinese Academy of Sciences https://orcid.org/0000- 0002- 9569- 6762
+
+<--- Page Split --->
+
+# Dashuan Tian  
+
+Institute of Geographic Sciences and Natural Resources Research, CAS https://orcid.org/0000- 0001- 8023- 1180  
+
+## Article  
+
+# Keywords:  
+
+Posted Date: May 20th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4203122/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 January 21st, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 56159- 4.
+
+<--- Page Split --->
+
+Declining precipitation frequency drives earlier leaf senescence by intensifying drought stress and enhancing drought acclimationXinyi Zhang<sup>1,2</sup>, Xiaoyue Wang<sup>1,2\*</sup>, Constantin M. Zohner<sup>3</sup>, Josep Peñuelas<sup>4,5</sup>, Yang Li<sup>6</sup>, Xiuchen Wu<sup>7</sup>, Yao Zhang<sup>8</sup>, Huiying Liu<sup>9</sup>, Pengju Shen<sup>1,2</sup>, Xiaoxu Jia<sup>1,2</sup>, Wenbin Liu<sup>1,2</sup>, Dashuan Tian<sup>5,2</sup>, Chaoyang Wu<sup>1,2\*</sup>1. The Key Laboratory of Land Surface Pattern and Simulation, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China;2. University of the Chinese Academy of Sciences, Beijing 100049, China;3. Department of Environmental Systems Science, Institute of Integrative Biology, ETH Zurich; Zurich, Switzerland;4. CSIC, Global Ecology Unit CREAF-CSIC-UAB, Bellaterra, Barcelona 08193, Catalonia, Spain;5. CREAF, Cerdanyola del Valles, Barcelona 08193, Catalonia, Spain;6. School of Natural Resources and the Environment, University of Arizona, Tucson, Arizona, USA;7. State Key Laboratory of Earth Surface Processes and Resource Ecology, Faculty of Geographical Science, Beijing Normal University, Beijing, China;8. Sino-French Institute for Earth System Science, College of Urban and Environmental Sciences, and Laboratory for Earth Surface Processes, Peking University; Beijing 100871, China;9. Institute of Eco-Chongming (IEC), East China Normal University, Shanghai, China;*Corresponding authors: wucy@igsnrr.ac.cn (C. Wu) and wangxy@igsnrr.ac.cn (X.W)
+
+<--- Page Split --->
+
+Abstract: Precipitation is an important factor influencing the date of leaf senescence (DFS), which in turn affects carbon uptake of terrestrial ecosystems. However, the temporal patterns of precipitation frequency ( \(\mathrm{P_{freq}}\) ) and its impact on DFS remain largely unknown. Using both long-term carbon flux data and satellite observation of DFS across the Northern Hemisphere, here we show that, after excluding impacts from of temperature, radiation and total precipitation, declining \(\mathrm{P_{freq}}\) drives earlier DFS from 1982 to 2022. A decrease in \(\mathrm{P_{freq}}\) intensified drought stress by reducing root- zone soil moisture and increasing atmospheric dryness, and limit the photosynthesis necessary for sustained growth. The enhanced drought acclimation also explained the positive \(\mathrm{P_{freq}}\) - DFS relationship. We found plants experiencing decreased \(\mathrm{P_{freq}}\) showed a more rapid response to drought, as represented by a shorter drought response lag, a measure of the time between a drought event and the most severe reduction in vegetation growth. In particular, increased evapotranspiration with shorter drought response lag was observed, further implying an enhanced water acquisition strategy representing drought acclimation as showing in strengthening roots system to deeper water resources. Finally, we found 30 current state- of- art Earth system models largely failed to capture the sensitivity of DFS to changes in \(\mathrm{P_{freq}}\) and incorrectly predicted the direction of correlations for approximately half of the northern global lands, in both historical simulations and future predictions under various shared socioeconomic pathways (SSPs). Our results therefore highlight the critical need to include precipitation frequency, rather than just total precipitation, into models to accurately forecast plant phenology under future climate change.
+
+<--- Page Split --->
+
+## Main  
+
+Plant phenology is greatly affected by ongoing changing climate \(^{1 - 3}\) . While warming typically leads to earlier spring leaf- out \(^{4}\) , predicting temporal changes in the dates of autumn leaf senescence (DFS) is more complex due to the various drivers involved, leading to mixed observations and model predictions of either earlier or later DFS across northern terrestrial ecosystems \(^{5 - 6}\) . For example, rising temperatures late in the season can delay DFS given sufficient water availability \(^{7}\) . Conversely, warmer conditions can also speed up seasonal development, resulting in earlier DFS \(^{8}\) . Moreover, water availability plays a crucial role in autumn phenology, with severe droughts causing earlier DFS \(^{9}\) . Thus, understanding the impact of water availability on DFS changes is becoming increasingly vital in the context of climate change \(^{10}\) , especially with the expectation of more frequent and severe droughts in the future \(^{11 - 12}\) .  
+
+Precipitation is essential for plant growth, particularly through the replenishment of soil moisture \(^{13}\) . However, its impact on DFS varies widely, with both positive and negative effects reported. This inconsistency is likely due to local environmental factors, such as the amount of annual precipitation, and geophysical conditions like topography \(^{14}\) . The complexity of these patterns and the lack of a clear understanding of the underlying processes make it challenging to accurately model the effects of precipitation on DFS. We propose that the focus should not be solely on the amount of precipitation but also on its temporal patterns, such as frequency. Emerging evidence suggests that variations in the timing and intensity of precipitation can greatly impact plant growth \(^{15 - 16}\) . Therefore, we
+
+<--- Page Split --->
+
+aimed to explore the responses and the underlying reasons of DFS to changes in precipitation frequency across the Northern Hemisphere. To this end, we used both long- term flux measurements and satellite observations (Figure S1, Table S1- S2), combined with precipitation frequency data from gridded meteorological datasets (both ERA5 and CRU) (Figure S2). Additionally, we evaluated the capability of current state- of- the- art Earth system models to reproduce the observed relationships between DFS and precipitation frequency (Figure S3, Table S3- S4).  
+
+## Results  
+
+We observed a widespread decline in \(\mathrm{P}_{\mathrm{freq}}\) across the Northern Hemisphere between 1982 to 2022 from both the ERA5 and CRU data (Figure S4). By controlling autumn temperature and radiation, we observed negative correlations between DFS and total precipitation at higher latitudes (>50 degrees), whereas positive correlations between DFS and precipitation were more common at lower latitudes (Figure 1 A). Overall, the proportions of significantly negative and positive DFS- precipitation correlations were 15.6% and 9.5%, respectively. These proportions slightly changed to 17.4% vs. 8.8% when accounting for the effects of precipitation frequency using partial correlation (Figure 1 B). In comparison, \(\mathrm{P}_{\mathrm{freq}}\) was mostly positively correlated with DFS, with 57.7% of correlations being positive and 14.9% being significantly positive, about double the proportion of significant negative correlations (7.8%) (Figure 1 C). Further analysis, illustrated in a Sankey diagram, showed that considering the impact of \(\mathrm{P}_{\mathrm{freq}}\) significantly reduced the strength of negative DFS- precipitation relationships. This trend remained consistent
+
+<--- Page Split --->
+
+across different plant functional types (Figure 1 E). We also plotted the distributions of the total precipitation- DFS and \(\mathsf{P}_{\mathrm{freq}}\) - DFS correlations in the total precipitation and frequency space (Extended Figure 1). We found earlier DFS with increased total precipitation often occurred when precipitation frequency exceeded an empirical threshold of 15. In comparison, the positive correlations between precipitation frequency and DFS were overall broadly consistent, and earlier DFS with increased frequency was observed only for low precipitation frequency but with extreme total precipitation. Flux measurements showed similar patterns: The correlation between PF and DFS was predominantly positive (23.1% positive vs. 5.7% negative, Figure 1 F), whereas the correlation between \(\mathsf{P}_{\mathrm{freq}}\) and DFS was equally positive and negative (15.8% positive vs. 15.3% negative).
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Relationships between the dates of leaf senescence (DFS) and precipitation changes. A represent the partial correlations between DFS and total precipitation, controlling only temperature and radiation, and B by additionally controlling precipitation frequency. C is partial correlations between DFS and precipitation frequency, controlling temperature, radiation and total precipitation. D shows the changes between significant positive and negative correlations with the Sankey diagram. E represents the results classified by plant functional types (See methods). F shows the same analysis using flux measurements. P and N represent positive and negative, respectively. Significance was set with \(p< 0.05\) . </center>
+
+<--- Page Split --->
+
+We used a structural equation model (SEM) to explore the underlying mechanisms that may explain the predominantly positive correlation between \(\mathsf{P}_{\mathsf{freq}}\) and DFS (Figure 2 A). We found that both total precipitation and \(\mathsf{P}_{\mathsf{freq}}\) significantly decreased radiation (path effect of - 0.42, - 0.43, respectively). In comparison, root zone soil moisture was more strongly affected by \(\mathsf{P}_{\mathsf{freq}}\) than by total precipitation (0.50 vs. 0.44, P<0.01). In particular, atmospheric dryness increased significantly with declined \(\mathsf{P}_{\mathsf{freq}}\) than with total precipitation, with path effects of - 0.51 (P<0.01) and - 0.35 (P<0.05), respectively. This suggests that declines in precipitation frequency have a more severe impact on plant drought stress than changes in total precipitation, which in turn causes earlier leaf senescence in many regions.  
+
+We also found a significantly positive relationship between \(\mathsf{P}_{\mathsf{freq}}\) and the drought response lag ( \(\mathsf{R}^2 = 0.40\) , p<0.05), indicating that plants acclimate to drought more quickly with decreased \(\mathsf{P}_{\mathsf{freq}}\) , necessitating longer recovery times from drought ( \(\mathsf{R}^2 = 0.82\) , p<0.05, Figure 2 B- C). Using a moving window approach, we observed an increasing importance of \(\mathsf{P}_{\mathsf{freq}}\) in regulating DFS changes over the past four decades, indicated by increases in the slope values (Figure 2 D). We further found that decreased \(\mathsf{P}_{\mathsf{freq}}\) was often associated with a smaller size of a single rain event (11.7% and 0.9% for positive and negative correlations, respectively), reducing soil moisture accumulation (Figure 2 E) and thereby contributing to the increased soil moisture variability and earlier DFS consequently ( \(\mathsf{R}^2 = 0.64\) , P<0.01, Figure 2 F).
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Mechanisms for the correlation between precipitation frequency and the dates of leaf senescence (DFS). A shows the structural equation model (SEM) analysis. B and C represent the changes of drought response lag and drought recovery time with precipitation frequency. D shows the moving window approach with respect of positive and negative sensitivities of DFS to precipitation frequency over 1982-2022 (see Methods). E shows the relationship between precipitation frequency and the maximum daily precipitation size (N and P represent negative and positive correlations). F represents the correlation between DFS and root zone soil moisture variability using coefficients of variation (%). \* and \*\* represent \(p<0.05\) and \(p<0.01\) , respectively. </center>
+
+<--- Page Split --->
+
+We further tested if the positive impacts of \(\mathsf{P}_{\mathsf{freq}}\) on DFS could be reproduced by current state- of- the- art Earth system models. This included both Trendy models for historical simulations and CMIP6 models for future projections under various shared socioeconomic pathways (SSPs), including SSP126, SSP245, SSP370, and SSP585. We found that Trendy models overall captured the relationship between DFS and precipitation frequency, with larger proportions of significant positive correlations (Figure 3 A). Similarly, among the 14 CMIP6 models, only three failed to reproduce the observed patterns (ACCESS- ESM1- 5, BCC- CSM2- MR and TaiESM1). However, when assessing the sensitivity of DFS to changes in \(\mathsf{P}_{\mathsf{freq}}\) (i.e., how DFS changes per unit variation in \(\mathsf{P}_{\mathsf{freq}}\) ), we observed substantial differences among models (Figure 3 B). Only seven out of 16 Trendy models demonstrated positive sensitivities, and even fewer CMIP6 models showed positive sensitivities. Additionally, we assessed the accuracy of these models in predicting the sign of the DFS- \(\mathsf{P}_{\mathsf{freq}}\) relationship at each pixel level, comparing these predictions with observations (Figure 3 C). About half of all pixels showed mismatches, highlighting the models' limited accuracy in capturing the DFS- \(\mathsf{P}_{\mathsf{freq}}\) correlations.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. The test of Earth system models in reproducing the observed relationship between the dates of leaf senescence (DFS) and precipitation frequency. A shows the overall proportions of significant positive and negative correlations. B represents the sensitivity of DFS to precipitation frequency changes. C is the comparison on the signs of correlation for each pixel. Four shared socioeconomic pathways (SSPs) were included for CMIP6 models, including SSP126, SSP245, SSP370, and SSP585, respectively. -- and ++ represent consistent negative and positive observations. Significance was set with p<0.05. </center>
+
+<--- Page Split --->
+
+## Discussion  
+
+Our research has revealed a positive correlation between DFS and \(\mathsf{P}_{\mathsf{freq}}\) . Accordingly, the widespread declines in the \(\mathsf{P}_{\mathsf{freq}}\) over the past four decades have led to earlier DFS in northern ecosystems. The impact of these changes varies among plant functional types, reflecting the diversity of strategies plants use to adapt to local environments and respond to climate change factors \(^{17 - 18}\) . Limited soil moisture due to reduced \(\mathsf{P}_{\mathsf{freq}}\) can cause drought stress, negatively affecting soil organic carbon (SOC) levels and soil respiration \(^{19 - 20}\) . Conversely, excessive moisture can also hinder respiration by reducing oxygen availability, which may explain observations of earlier DFS in regions with increased precipitation \(^{21}\) . The interaction between soil moisture, heat, SOC, soil microorganisms, as well as soil geochemical characteristics defines the optimal conditions for plant growth \(^{22 - 23}\) . These conditions are the result of long- term adaptation strategies developed by plants. Changes in \(\mathsf{P}_{\mathsf{freq}}\) alter these soil properties and this may prompt plants to adjust their DFS to enhance survival in changing environments. This adjustment may also reflect the increased demand for soil resources, particularly soil moisture, to sustain photosynthetic activity in a warming climate. Overall, our findings underscore the importance of considering seasonal precipitation patterns, rather than just total amounts, in understanding leaf senescence timing. This insight is crucial for incorporating temporal changes in precipitation into future ecosystem models to better understand the impacts of climate change on plant phenology and growth.  
+
+In our study, we aimed to elucidate the mechanisms behind the observed trend of
+
+<--- Page Split --->
+
+earlier DFS with decreased \(\mathsf{P}_{\mathsf{freq}}\) , a task complicated by the interactive effects of precipitation amount and variability on terrestrial ecosystem processes<sup>24</sup>. Using partial correlation and SEM techniques, we identified that the primary driver for earlier DFS under reduced \(\mathsf{P}_{\mathsf{freq}}\) may be the intensified water constraints on photosynthesis through significant reductions in root- zone moisture and increases in VPD. A lower frequency of rainfall events implies longer drought periods. Consequently, soil moisture gradually declines, particularly in the surface layers where the majority of a plant's roots are concentrated. This poses a challenge for plants to access adequate water supply, especially after prolonged drought periods. Experimental studies have indicated that plant photosynthesis and primary productivity are significantly impacted by changes in \(\mathsf{P}_{\mathsf{freq}}^{15}\) . Reduced \(\mathsf{P}_{\mathsf{freq}}\) , often coupled with smaller precipitation events, adversely affects soil moisture recharge and increases soil moisture variability, which in turn drives earlier leaf senescence. The increase in atmospheric dryness further accelerates the cessation of photosynthesis.  
+
+A pivotal finding of our research is the identification of a significantly shortened drought response lag associated with decreased \(\mathsf{P}_{\mathsf{freq}}\) , a process representing drought acclimation. In particular, we found a significant negative correlation between drought response lag and evapotranspiration (ET) (Extended Figure 2 A). Such results implies an enhanced water- use strategy of plants that further supports plant adaptation and acclimation, probably by strengthening the growth of root systems to extend downstream for deeper water sources under droughts<sup>25</sup>. This reason has been supported by our results showing
+
+<--- Page Split --->
+
+increased root depth with lower drought response lag (Extended Figure 2 B). The enhanced drought acclimation is likely linked to the adaptive strategy of plants that have been exposed to prolonged periods of drought, including more effective water management and utilization. Plants can rapidly reduce water loss or increase water uptake when water availability is scarce through morphologically deeper roots and an enhanced tolerance to drought physiologically by accumulating osmoprotectants and other regulatory substances<sup>26</sup>. Our observations, encompassing a wide range of species with varied plant functional types and local climatic backgrounds, therefore confirm and extend the critical role of \(\mathrm{P_{freq}}\) on vegetation growth beyond site- level experiments.  
+
+We show that while current Earth system models were able to reproduce the overall trend in the correlation between DFS and \(\mathrm{P_{freq}}\) , they inaccurately represent the sensitivity of DFS to changes in \(\mathrm{P_{freq}}\) . A pixel- by- pixel analysis showed that these models incorrectly predict the sign of the DFS- \(\mathrm{P_{freq}}\) correlation for half of the regions examined. This discrepancy may be primarily due to the models' reliance on the link between total precipitation and soil moisture, overlooking the significant effects of \(\mathrm{P_{freq}}\) on ecosystem functions. However, the timing, frequency and duration of precipitation events are determinants of ecosystem processes during autumn<sup>27- 29</sup> and therefore important for leaf senescence, as shown by our observations. Therefore, current Earth system models, driven by basic conceptual frameworks that ignore the effects of \(\mathrm{P_{freq}}\) on plant hydraulics, fall short in reproducing the temporal effects of \(\mathrm{P_{freq}}\) on DFS<sup>30</sup>. Including \(\mathrm{P_{freq}}\) —a key measure of precipitation variability—into ecosystem models therefore has large potential
+
+<--- Page Split --->
+
+to improve future predictions of drought impacts on ecosystems, especially given the expectation that future droughts will intensify in several dimensions, including magnitude, duration, timing, and frequency<sup>11,31</sup>.  
+
+## References  
+
+1. Peaucelle, M., Peñuelas, J. & Verbeeck, H. Accurate phenology analyses require bud traits and energy budgets. Nat. Plants 8, 915-922 (2022). https://doi.org/10.1038/s41477-022-01209-8  
+
+2. Li, Y., Zhang, W., Schwalm, C.R. et al. Widespread spring phenology effects on drought recovery of Northern Hemisphere ecosystems. Nat. Clim. Chang. 13, 182-188 (2023). https://doi.org/10.1038/s41558-022-01584-2  
+
+3. Shen, M., Wang, S., Jiang, N. et al. Plant phenology changes and drivers on the Qinghai-Tibetan Plateau. Nat Rev Earth Environ 3, 633-651 (2022). https://doi.org/10.1038/s43017-022-00317-5  
+
+4. Piao, S. L. et al. Leaf onset in the northern hemisphere triggered by daytime temperature. Nat. Commun. 6, doi:10.1038/ncomms7911 (2015).  
+
+5. Stuble, K. L., Bennion, L. D. & Kuebbing, S. E. Plant phenological responses to experimental warming—A synthesis. Glob. Change Biol. 27, 4110-4124, doi:https://doi.org/10.1111/gcb.15685 (2021).  
+
+6. Zani, D., Crowther, T. W., Mo, L., Renner, S. S. & Zohner, C. M. Increased growing-season productivity drives earlier autumn leaf senescence in temperate trees. Science 370, 1066-1071, doi:10.1126/science.abd8911 (2020).  
+
+7. Chen, L. et al. Leaf senescence exhibits stronger climatic responses during warm than during cold autumns. Nat. Clim. Chang. 10, 777-780, doi:10.1038/s41558-020-0820-2 (2020).  
+
+8. Zohner, C. M. et al. Effect of climate warming on the timing of autumn leaf senescence reverses after the summer solstice. Science, 381, eadf5098. doi:10.1126/science.adf5098 (2023).
+
+<--- Page Split --->
+
+9. Xu, C. G. et al. Increasing impacts of extreme droughts on vegetation productivity under climate change. Nat. Clim. Chang. 9, 948–953, doi:10.1038/s41558-019-0630-6 (2019).  
+
+10. Peñuelas, J. et al. Complex spatiotemporal phenological shifts as a response to rainfall changes. New Phytol. 161, 837-846, doi:10.1111/j.1469-8137.2004.01003.x (2004).  
+
+11. Knapp, A.K., et al. Field experiments have enhanced our understanding of drought impacts on terrestrial ecosystems—But where do we go from here? Functional Ecology, 38, 76-97 (2024).  
+
+12. Zhang, Y., Parazoo, N. C., Williams, A. P., Zhou, S. & Gentine, P. Large and projected strengthening moisture limitation on end-of-season photosynthesis. Proc. Natl. Acad. Sci. U. S. A. 117, 9216–9222, doi:10.1073/pnas.1914436117 (2020).  
+
+13. Kannenberg, S.A., Anderegg, W.R.L., Barnes, M.L. et al. Dominant role of soil moisture in mediating carbon and water fluxes in dryland ecosystems. Nat. Geosci. 17, 38–43 (2024). https://doi.org/10.1038/s41561-023-01351-8  
+
+14. Wu, C., Peng, J., Ciais, P. et al. Increased drought effects on the phenology of autumn leaf senescence. Nat. Clim. Chang. 12, 943–949 (2022). https://doi.org/10.1038/s41558-022-01464-9  
+
+15. Knapp, A.K., et al. Rainfall Variability, Carbon Cycling, and Plant Species Diversity in a Mesic Grassland. Science, 298, 2202–2205 (2002).  
+
+16. Wang, J., Liu, D., Ciais, P. et al. Decreasing rainfall frequency contributes to earlier leaf onset in northern ecosystems. Nat. Clim. Chang. 12, 386–392 (2022). https://doi.org/10.1038/s41558-022-01285-w  
+
+17. Zhang, Y., Gentine, P., Luo, X. et al. Increasing sensitivity of dryland vegetation greenness to precipitation due to rising atmospheric \(\mathrm{CO_2}\) . Nat Commun 13, 4875 (2022). https://doi.org/10.1038/s41467-022-32631-3  
+
+18. Seddon, A., Macias-Fauria, M., Long, P. et al. Sensitivity of global terrestrial ecosystems to climate variability. Nature 531, 229–232 (2016).  
+
+https://doi.org/10.1038/nature16986
+
+<--- Page Split --->
+
+19. Jackson, R. B. et al. The ecology of soil carbon: pools, vulnerabilities, and biotic and abiotic controls. Annu. Rev. Ecol. Evol. Syst. 48, 419-445 (2017).
+20. Huang, N., et al. Spatial and temporal variations in global soil respiration and their relationships with climate and land cover. Science Advances, 6, doi:10.1126/sciadv.abb8508
+21. Buitenwerf, R., Rose, L. & Higgins, S. Three decades of multi-dimensional change in global leaf phenology. Nature Clim Change 5, 364-368 (2015). https://doi.org/10.1038/nclimate2533
+22. Knapp, A. K., Ciais, P., & Smith, M. D. (2017). Reconciling inconsistencies in precipitation-productivity relationships: Implications for climate change. New Phytologist, 214, 41-47.
+23. Fu, Z., Ciais, P., Prentice, I.C. et al. Atmospheric dryness reduces photosynthesis along a large range of soil water deficits. Nat Commun 13, 989 (2022). https://doi.org/10.1038/s41467-022-28652-7
+24. Felton, A.J., et al. Precipitation amount and event size interact to reduce ecosystem functioning during dry years in a mesic grassland. Glo. Chan. Bio. 26, 658-668 (2020). https://doi.org/10.1111/gcb.14789
+25. Li, D. et al. Declining coupling between vegetation and drought over the past three decades. Glo. Chan. Bio. 30, (2024). https://doi.org/10.1111/gcb.17141
+26. Zhou, H. et al. Climate warming interacts with other global change drivers to influence plant phenology: A meta-analysis of experimental studies. Ecology Lett. 26, 1370-1381 (2023).
+27. Pierre, K. J. L., et al. Global change effects on plant communities are magnified by time and the number of global change factors imposed. Proc. Natl. Acad. Sci. U. S. A. 116, 17867-17873 (2019). DOI:10.1073/pnas.1819027116
+28. Jiao, W., Wang, L., Smith, W.K. et al. Observed increasing water constraint on vegetation growth over the last three decades. Nat Commun 12, 3777 (2021). https://doi.org/10.1038/s41467-021-24016-9
+
+<--- Page Split --->
+
+29. Jin, H., Vicente-Serrano, S.M., Tian, F. et al. Higher vegetation sensitivity to meteorological drought in autumn than spring across European biomes. Commun Earth Environ 4, 299 (2023). https://doi.org/10.1038/s43247-023-00960-w30. Paschalis, A., et al. Rainfall manipulation experiments as simulated by terrestrial biosphere models: Where do we stand? Glo. Chang. Biolo. 26, 3336-3355. doi:10.1111/gcb.15024.31. Donat, M., Lowry, A., Alexander, L. et al. More extreme precipitation in the world's dry and wet regions. Nature Clim Change 6, 508-513 (2016). https://doi.org/10.1038/nclimate2941
+
+<--- Page Split --->
+
+## Methods  
+
+## 1. Study area  
+
+Northern Hemisphere (NH) encompasses a wide range of ecosystems that are essential for maintaining the global carbon balance and limiting global warming. Monitoring the dynamics of vegetation in the NH is crucial for understanding and mitigating climate. In this study, we focused on middle and high latitude regions of Northern Hemisphere \((>30^{\circ}\mathrm{N})\) , where vegetation dynamic has an evident seasonality (Figure S1).  
+
+## 2. Site-level DFS from flux data  
+
+The site- level phenology observations were derived from daily gross primary productivity (GPP) based on the eddy- covariance flux measurements. We removed sites with insufficient observations \((< 8\) yr). As a result, 52 flux sites with a total of 662 year- site records of daily GPP from the FLUXNET database were selected (Table S2). We used a dynamic threshold of \(10\%\) of the annual maximum GPP to determine DFS.  
+
+## 3. Satellite derived DFS  
+
+The long time series of continuous NDVI dataset from the GIMMS- 3G+ product was used to derive DFS. This dataset was based on corrected and calibrated measurements from Advanced Very High Resolution Radiometer (AVHRR) data<sup>32</sup> with a spatial resolution of 0.0833 degree and a half- month interval for 1982 to 2022.
+
+<--- Page Split --->
+
+To better capture the seasonal signals of vegetation while eliminating the interference of atmospheric effects and snow cover, the NDVI time series was fist reconstructed by weighted Whittaker algorithm<sup>33</sup>. Then a seven- parameter double logistic function<sup>34</sup> was used to fit the NDVI time series and DFS was determined based on inflection method<sup>35</sup>.  
+
+\[f(t) = m_{1} + (m_{2} - m_{7}\cdot t)\left(\frac{1}{1 + e^{(m_{3} - t)/m_{4}}} - \frac{1}{1 + e^{(m_{5} - t)/m_{6}}}\right) \quad (1)\]  
+
+where, m1 is background NDVI; m2 is the difference between summer- time NDVI and background value; m3 and m5 are the midpoints in the days of the year of the transitions of spring green- up and autumn senescence, respectively; m4 and m6 are normalized slope coefficients for these transitions; m7 is summer green- down parameter. DFS was defined as the time when the curvature changing rate reached its last local maximum value.  
+
+## 4. Simulated DFS from Trendy and CMIP6  
+
+We simulated DFS based on output GPP from 16 Trendy models during 1983- 2021 and 14 CMIP6 models under different shared socioeconomic pathways (SSP- 126, SSP- 245, SSP- 370, and SSP- 585) during 2016- 2100 (Table S3). DFS was determined using the same inflection method as the NDVI- based DFS.  
+
+## 5. Climate data  
+
+We derived monthly total amount (Ptotal) and frequency (Pfreq) of precipitation from two independent datasets: 1) the Climatic Research Unit Time- Series (CRU TS 4.07) and 2) the fifth generation European Centre for Medium- Range Weather Forecasts reanalysis of
+
+<--- Page Split --->
+
+the global climate (ERA5). The CRU dataset is produced by the interpolation from extensive networks of climatic station observations and provides several climate variables on a \(0.5^{\circ} \times 0.5^{\circ}\) spatial resolution and a monthly temporal resolution<sup>36</sup>. We used wet day frequency, which defined as days with \(\geq 0.1\) mm precipitation, as \(P_{\text{freq}}\). The ERA5 product provides hourly estimates of various climate variables with a spatial resolution of \(0.1^{\circ}\) based on vast amounts of historical observations<sup>37</sup>. We obtained total precipitation from the monthly aggregated datasets and calculated the number of rainy days per month based on the daily precipitation \((\geq 0.1 \text{mm})\). We used the mean value of \(P_{\text{total}}\) and \(P_{\text{freq}}\) from CRU and ERA5 as final \(P_{\text{freq}}\) and \(P_{\text{total}}\) for 1982–2022 to reduce the uncertainty from a single dataset. Monthly mean temperature was obtained from CRU and surface net solar radiation was accessed from ERA5. Vapor pressure deficit (VPD) and evapotranspiration (ET) data for 1982–2022 were obtained from TerraClimate with a monthly temporal resolution and a 1/24 degree spatial resolution. The monthly root- zone soil moisture from 1982 to 2022 was obtained from Global Land Evaporation Amsterdam Model (GLEAM) with a spatial resolution of \(0.25^{\circ}\).  
+
+## 6. Identification of drought events, drought recovery and drought response lag  
+
+Drought response lag and recovery time were obtained from Li et al. (2023)<sup>2</sup>. Extreme drought events were identified by examining monthly SPEI- 3 (Standardized Precipitation- Evapotranspiration Index at a 3- month scale) values below the threshold of - 2. Drought recovery is defined as the duration (months) starting from the month with the deepest suppression of NDVI to the month when NDVI returns to within 95% of the
+
+<--- Page Split --->
+
+long- term average baseline in each pixel. The monthly SPEI3 and NDVI time series were first smoothed by a 3- month forward moving window, they were then sequentially deseasonalized and linearly detrended. To avoid lengthening the drought recovery duration due to algorithm design, if vegetation recovery extending through the dormant season and into subsequent year, the drought recovery was calculated as the total length of the recovery period minus the length of the dormant season. We measured response lag in months, which is the time between the lowest SPEI3 value and the most significant drop in NDVI caused by drought. We calculated both drought response lag and recovery time for each pixel individually.  
+
+## 7. Analysis  
+
+Precipitation, along with temperature and radiation, collectively regulate DFS<sup>38</sup>. In addition, covariate effects exist among these climatic variables as well. Therefore, we applied partial correlation analysis to explore the impacts of \(P_{\text{total}}\) and \(P_{\text{freq}}\) on DFS. We performed partial correlation analysis under three scenarios: (1) partial correlation between DFS and \(P_{\text{total}}\), removing the effects of temperature and radiation (scenario 1); (2) partial correlation between DFS and \(P_{\text{total}}\), removing the effects of temperature, radiation, and \(P_{\text{freq}}\) (scenario 2); (3) partial correlation between DFS and \(P_{\text{freq}}\), removing the effects of temperature, radiation, and \(P_{\text{total}}\) (scenario 3). According to previous studies, preseasonal forcings have a better predictive strength on phenology than fixed seasonal climate forcing alone<sup>39- 40</sup>. We thus used the preseason mean values of each climatic variable in the partial correlation analysis. For example, the preseason length of \(P_{\text{freq}}\) was defined as
+
+<--- Page Split --->
+
+the period when the absolute value of partial correlation coefficient between \(\mathsf{P}_{\mathsf{freq}}\) and DFS was at its maximum. For each pixel, the preseason periods of 0 to 6 months prior to the multi- year mean DFS were examined (Figure S5).  
+
+To investigate the temporal changes in the sensitivity of DFS to \(\mathsf{P}_{\mathsf{freq}}\) , we used a moving window method. We conducted tests on a variety of window sizes, ranging from 10 to 20 years. For each window size, we calculated the sensitivity of DFS to \(\mathsf{P}_{\mathsf{freq}}\) based on multilinear regression within each moving window. Then we calculated the percentages of significant sensitivity ( \(P < 0.05\) ) and fitted these values to obtain the optimal window size with the largest \(R^2\) . As a result, the optimal window size was set as 19 years to perform subsequent analyses (Figure S6).  
+
+\[DFS = a\cdot P_{freq} + b\cdot P_{total} + c\cdot Temperature + d\cdot Radiation + \epsilon \quad (2)\]  
+
+where, a, b, c and d are regression coefficients and represent the sensitivity of DFS to \(\mathsf{P}_{\mathsf{freq}}\) , \(\mathsf{P}_{\mathsf{total}}\) , temperature, and radiation, respectively. \(\epsilon\) is the residual error. All the climate variables used in the regression were the mean values during preseason.  
+
+To explore the potential mechanisms by which precipitation affects DFS, we performed structural equation modeling. Considering that precipitation patterns may affect DFS by influencing solar radiation and drought conditions, we selected radiation, VPD, and root- zone soil moisture to construct structural equation model.
+
+<--- Page Split --->
+
+32. Pinzon, J., & Tucker, C. (2014). A Non-Stationary 1981–2012 AVHRR NDVI3g Time Series. Remote Sensing, 6, 6929-6960.  
+
+33. Kong, D., Zhang, Y., Gu, X., & Wang, D. (2019). A robust method for reconstructing global MODIS EVI time series on the Google Earth Engine. Isprs Journal of Photogrammetry and Remote Sensing, 155, 13-24  
+
+34. Elmore, A.J., Guinn, S.M., Minsley, B.J., & Richardson, A.D. (2012). Landscape controls on the timing of spring, autumn, and growing season length in mid-Atlantic forests. Global Change Biology, 18, 656-674  
+
+35. Zhang, X., Friedl, M.A., Schaaf, C.B., Strahler, A.H., Hodges, J.C.F., Gao, F., Reed, B.C., & Huete, A. (2003). Monitoring vegetation phenology using MODIS. Remote sensing of environment, 84, 471-475  
+
+36. Harris, I., Osborn, T.J., Jones, P., & Lister, D. (2020). Version 4 of the CRU TS monthly high-resolution gridded multivariate climate dataset. Scientific Data, 7, 109  
+
+37. Hersbach, H., et al. (2020). The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146, 1999-2049  
+
+38. Liu, Q., Fu, Y.S.H., Zhu, Z.C., Liu, Y.W., Liu, Z., Huang, M.T., Janssens, I.A., & Piao, S.L. (2016). Delayed autumn phenology in the Northern Hemisphere is related to change in both climate and spring phenology. Global Change Biology, 22, 3702-3711  
+
+39. Piao, S., Tan, J.G., Chen, A.P., Fu, Y.H., Ciais, P., Liu, Q., Janssens, I.A., Vicca, S., Zeng, Z.Z., Jeong, S.J., Li, Y., Myneni, R.B., Peng, S.S., Shen, M.G., & Pennuelas, J. (2015). Leaf onset in the northern hemisphere triggered by daytime temperature. Nature Communications, 6  
+
+40. Wu, C., Wang, X., Wang, H., Ciais, P., Peñuelas, J., Myneni, R.B., Desai, A.R., Gough, C.M., Gonsamo, A., Black, A.T., Jassal, R.S., Ju, W., Yuan, W., Fu, Y., Shen, M., Li, S., Liu, R., Chen, J.M., & Ge, Q. (2018). Contrasting responses of autumn-leaf senescence to daytime and night-time warming. Nature Climate Change, 8, 1092-1096
+
+<--- Page Split --->
+
+## Data availability  
+
+All data used in this study are available online. The specific links for each dataset are presented in Supplementary Tables S1.  
+
+## Code availability  
+
+All data analyses and modeling were performed using Python and R. The codes for the phenological models are available at https://doi.org/10.5281/zenodo.5829780.  
+
+Acknowledgements: This work was funded by the National Natural Science Foundation of China (42125101, 42271034). X.W. was funded by the Youth Innovation Promotion Association of Chinese Academy of Sciences (2022051). C.M.Z. was funded by SNF Ambizione grant PZ00P3_193646. J.P. was funded by the TED2021- 132627B- I00 grant funded by the Spanish MCIN, AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR, the Fundación Ramón Areces project CIVP20A6621 and the Catalan government grant SGR221- 1333.  
+
+Author contributions: C.W. designed the research. C.W. and X.W. wrote the first draft of the manuscript. X.Z. and X.W. performed the data analysis. All authors assessed the research analyses and contributed to the writing of the manuscript.  
+
+Competing interests: The authors declare no competing financial interests.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Extended Figure 1. Spatial distribution of the correlation coefficients \((\mathbf{R}^2)\) with respect to total precipitation and its frequency. (a) Total precipitation \((\mathbf{P}_{\text{total}})\) and dates of leaf senescence (DFS). (b) Precipitation frequency \((\mathbf{P}_{\text{freq}})\) and DFS.</center>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>511 Extended Figure 2. Relationships between drought response lag and (A) </center>  
+
+512 evapotranspiration, and (B) root depth.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+ExtendedFigure1. jpg  ExtendedFigure2. jpg  Supplementaryinformation.pdf
+
+<--- Page Split --->

preprint/preprint__5f717dfa9444b7081dcae9e03379b59567ffe8be0ba96f631c317dca0ad72be5/preprint__5f717dfa9444b7081dcae9e03379b59567ffe8be0ba96f631c317dca0ad72be5_det.mmd

@@ -0,0 +1,391 @@
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+# Declining precipitation frequency drivers earlier leaf senescence by intensifying drought stress and enhancing drought acclimation  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 245, 275]]<|/det|>
+Chaoyang Wu wucy@igsnrr.ac.cn  
+
+<|ref|>text<|/ref|><|det|>[[44, 302, 944, 345]]<|/det|>
+Institute of Geographic Sciences and Natural Resources Research https://orcid.org/0000- 0001- 6163- 8209  
+
+<|ref|>text<|/ref|><|det|>[[44, 350, 630, 393]]<|/det|>
+Xinyi Zhang Institute of Geographic Sciences and Natural Resources Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 397, 940, 462]]<|/det|>
+Xiaoyue Wang The Key Laboratory of Land Surface Pattern and Simulation, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences https://orcid.org/0000- 0002- 9950- 2259  
+
+<|ref|>text<|/ref|><|det|>[[44, 466, 560, 507]]<|/det|>
+Constantin Zohner ETH Zurich https://orcid.org/0000- 0002- 8302- 4854  
+
+<|ref|>text<|/ref|><|det|>[[44, 512, 840, 576]]<|/det|>
+Josep Penuelas CSIC, Global Ecology Unit CREAF- CSIC- UAB, Cerdanyola del Valles 08193, Catalonia, Spain https://orcid.org/0000- 0002- 7215- 0150  
+
+<|ref|>text<|/ref|><|det|>[[44, 581, 595, 623]]<|/det|>
+Yang Li University of Arizona https://orcid.org/0000- 0002- 6463- 6441  
+
+<|ref|>text<|/ref|><|det|>[[44, 628, 636, 670]]<|/det|>
+Xiuchen Wu Beijing Normal University https://orcid.org/0000- 0003- 0396- 7439  
+
+<|ref|>text<|/ref|><|det|>[[44, 675, 567, 716]]<|/det|>
+Yao Zhang Peking University https://orcid.org/0000- 0002- 7468- 2409  
+
+<|ref|>text<|/ref|><|det|>[[44, 721, 670, 763]]<|/det|>
+Huiying Liu East China Normal University https://orcid.org/0000- 0001- 8903- 6103  
+
+<|ref|>text<|/ref|><|det|>[[44, 768, 630, 810]]<|/det|>
+Pengju Shen Institute of Geographic Sciences and Natural Resources Research  
+
+<|ref|>text<|/ref|><|det|>[[44, 815, 323, 856]]<|/det|>
+Xiaoxu Jia Chinese Academy of Sciences  
+
+<|ref|>text<|/ref|><|det|>[[44, 861, 144, 878]]<|/det|>
+Wenbin Liu  
+
+<|ref|>text<|/ref|><|det|>[[44, 881, 925, 945]]<|/det|>
+Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Science and Natural Resources Research, Chinese Academy of Sciences https://orcid.org/0000- 0002- 9569- 6762
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[44, 42, 165, 60]]<|/det|>
+# Dashuan Tian  
+
+<|ref|>text<|/ref|><|det|>[[44, 64, 940, 106]]<|/det|>
+Institute of Geographic Sciences and Natural Resources Research, CAS https://orcid.org/0000- 0001- 8023- 1180  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 147, 104, 165]]<|/det|>
+## Article  
+
+<|ref|>title<|/ref|><|det|>[[44, 185, 135, 203]]<|/det|>
+# Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 223, 297, 242]]<|/det|>
+Posted Date: May 20th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 261, 474, 281]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4203122/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 298, 915, 341]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 359, 535, 379]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 414, 944, 457]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on January 21st, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 56159- 4.
+
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+Declining precipitation frequency drives earlier leaf senescence by intensifying drought stress and enhancing drought acclimationXinyi Zhang<sup>1,2</sup>, Xiaoyue Wang<sup>1,2\*</sup>, Constantin M. Zohner<sup>3</sup>, Josep Peñuelas<sup>4,5</sup>, Yang Li<sup>6</sup>, Xiuchen Wu<sup>7</sup>, Yao Zhang<sup>8</sup>, Huiying Liu<sup>9</sup>, Pengju Shen<sup>1,2</sup>, Xiaoxu Jia<sup>1,2</sup>, Wenbin Liu<sup>1,2</sup>, Dashuan Tian<sup>5,2</sup>, Chaoyang Wu<sup>1,2\*</sup>1. The Key Laboratory of Land Surface Pattern and Simulation, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China;2. University of the Chinese Academy of Sciences, Beijing 100049, China;3. Department of Environmental Systems Science, Institute of Integrative Biology, ETH Zurich; Zurich, Switzerland;4. CSIC, Global Ecology Unit CREAF-CSIC-UAB, Bellaterra, Barcelona 08193, Catalonia, Spain;5. CREAF, Cerdanyola del Valles, Barcelona 08193, Catalonia, Spain;6. School of Natural Resources and the Environment, University of Arizona, Tucson, Arizona, USA;7. State Key Laboratory of Earth Surface Processes and Resource Ecology, Faculty of Geographical Science, Beijing Normal University, Beijing, China;8. Sino-French Institute for Earth System Science, College of Urban and Environmental Sciences, and Laboratory for Earth Surface Processes, Peking University; Beijing 100871, China;9. Institute of Eco-Chongming (IEC), East China Normal University, Shanghai, China;*Corresponding authors: wucy@igsnrr.ac.cn (C. Wu) and wangxy@igsnrr.ac.cn (X.W)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 92, 854, 857]]<|/det|>
+Abstract: Precipitation is an important factor influencing the date of leaf senescence (DFS), which in turn affects carbon uptake of terrestrial ecosystems. However, the temporal patterns of precipitation frequency ( \(\mathrm{P_{freq}}\) ) and its impact on DFS remain largely unknown. Using both long-term carbon flux data and satellite observation of DFS across the Northern Hemisphere, here we show that, after excluding impacts from of temperature, radiation and total precipitation, declining \(\mathrm{P_{freq}}\) drives earlier DFS from 1982 to 2022. A decrease in \(\mathrm{P_{freq}}\) intensified drought stress by reducing root- zone soil moisture and increasing atmospheric dryness, and limit the photosynthesis necessary for sustained growth. The enhanced drought acclimation also explained the positive \(\mathrm{P_{freq}}\) - DFS relationship. We found plants experiencing decreased \(\mathrm{P_{freq}}\) showed a more rapid response to drought, as represented by a shorter drought response lag, a measure of the time between a drought event and the most severe reduction in vegetation growth. In particular, increased evapotranspiration with shorter drought response lag was observed, further implying an enhanced water acquisition strategy representing drought acclimation as showing in strengthening roots system to deeper water resources. Finally, we found 30 current state- of- art Earth system models largely failed to capture the sensitivity of DFS to changes in \(\mathrm{P_{freq}}\) and incorrectly predicted the direction of correlations for approximately half of the northern global lands, in both historical simulations and future predictions under various shared socioeconomic pathways (SSPs). Our results therefore highlight the critical need to include precipitation frequency, rather than just total precipitation, into models to accurately forecast plant phenology under future climate change.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[147, 96, 192, 111]]<|/det|>
+## Main  
+
+<|ref|>text<|/ref|><|det|>[[144, 130, 854, 520]]<|/det|>
+Plant phenology is greatly affected by ongoing changing climate \(^{1 - 3}\) . While warming typically leads to earlier spring leaf- out \(^{4}\) , predicting temporal changes in the dates of autumn leaf senescence (DFS) is more complex due to the various drivers involved, leading to mixed observations and model predictions of either earlier or later DFS across northern terrestrial ecosystems \(^{5 - 6}\) . For example, rising temperatures late in the season can delay DFS given sufficient water availability \(^{7}\) . Conversely, warmer conditions can also speed up seasonal development, resulting in earlier DFS \(^{8}\) . Moreover, water availability plays a crucial role in autumn phenology, with severe droughts causing earlier DFS \(^{9}\) . Thus, understanding the impact of water availability on DFS changes is becoming increasingly vital in the context of climate change \(^{10}\) , especially with the expectation of more frequent and severe droughts in the future \(^{11 - 12}\) .  
+
+<|ref|>text<|/ref|><|det|>[[144, 576, 853, 891]]<|/det|>
+Precipitation is essential for plant growth, particularly through the replenishment of soil moisture \(^{13}\) . However, its impact on DFS varies widely, with both positive and negative effects reported. This inconsistency is likely due to local environmental factors, such as the amount of annual precipitation, and geophysical conditions like topography \(^{14}\) . The complexity of these patterns and the lack of a clear understanding of the underlying processes make it challenging to accurately model the effects of precipitation on DFS. We propose that the focus should not be solely on the amount of precipitation but also on its temporal patterns, such as frequency. Emerging evidence suggests that variations in the timing and intensity of precipitation can greatly impact plant growth \(^{15 - 16}\) . Therefore, we
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 93, 852, 335]]<|/det|>
+aimed to explore the responses and the underlying reasons of DFS to changes in precipitation frequency across the Northern Hemisphere. To this end, we used both long- term flux measurements and satellite observations (Figure S1, Table S1- S2), combined with precipitation frequency data from gridded meteorological datasets (both ERA5 and CRU) (Figure S2). Additionally, we evaluated the capability of current state- of- the- art Earth system models to reproduce the observed relationships between DFS and precipitation frequency (Figure S3, Table S3- S4).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 392, 215, 407]]<|/det|>
+## Results  
+
+<|ref|>text<|/ref|><|det|>[[144, 426, 860, 892]]<|/det|>
+We observed a widespread decline in \(\mathrm{P}_{\mathrm{freq}}\) across the Northern Hemisphere between 1982 to 2022 from both the ERA5 and CRU data (Figure S4). By controlling autumn temperature and radiation, we observed negative correlations between DFS and total precipitation at higher latitudes (>50 degrees), whereas positive correlations between DFS and precipitation were more common at lower latitudes (Figure 1 A). Overall, the proportions of significantly negative and positive DFS- precipitation correlations were 15.6% and 9.5%, respectively. These proportions slightly changed to 17.4% vs. 8.8% when accounting for the effects of precipitation frequency using partial correlation (Figure 1 B). In comparison, \(\mathrm{P}_{\mathrm{freq}}\) was mostly positively correlated with DFS, with 57.7% of correlations being positive and 14.9% being significantly positive, about double the proportion of significant negative correlations (7.8%) (Figure 1 C). Further analysis, illustrated in a Sankey diagram, showed that considering the impact of \(\mathrm{P}_{\mathrm{freq}}\) significantly reduced the strength of negative DFS- precipitation relationships. This trend remained consistent
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 94, 852, 445]]<|/det|>
+across different plant functional types (Figure 1 E). We also plotted the distributions of the total precipitation- DFS and \(\mathsf{P}_{\mathrm{freq}}\) - DFS correlations in the total precipitation and frequency space (Extended Figure 1). We found earlier DFS with increased total precipitation often occurred when precipitation frequency exceeded an empirical threshold of 15. In comparison, the positive correlations between precipitation frequency and DFS were overall broadly consistent, and earlier DFS with increased frequency was observed only for low precipitation frequency but with extreme total precipitation. Flux measurements showed similar patterns: The correlation between PF and DFS was predominantly positive (23.1% positive vs. 5.7% negative, Figure 1 F), whereas the correlation between \(\mathsf{P}_{\mathrm{freq}}\) and DFS was equally positive and negative (15.8% positive vs. 15.3% negative).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[156, 92, 812, 655]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 666, 852, 905]]<|/det|>
+<center>Figure 1. Relationships between the dates of leaf senescence (DFS) and precipitation changes. A represent the partial correlations between DFS and total precipitation, controlling only temperature and radiation, and B by additionally controlling precipitation frequency. C is partial correlations between DFS and precipitation frequency, controlling temperature, radiation and total precipitation. D shows the changes between significant positive and negative correlations with the Sankey diagram. E represents the results classified by plant functional types (See methods). F shows the same analysis using flux measurements. P and N represent positive and negative, respectively. Significance was set with \(p< 0.05\) . </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 93, 854, 447]]<|/det|>
+We used a structural equation model (SEM) to explore the underlying mechanisms that may explain the predominantly positive correlation between \(\mathsf{P}_{\mathsf{freq}}\) and DFS (Figure 2 A). We found that both total precipitation and \(\mathsf{P}_{\mathsf{freq}}\) significantly decreased radiation (path effect of - 0.42, - 0.43, respectively). In comparison, root zone soil moisture was more strongly affected by \(\mathsf{P}_{\mathsf{freq}}\) than by total precipitation (0.50 vs. 0.44, P<0.01). In particular, atmospheric dryness increased significantly with declined \(\mathsf{P}_{\mathsf{freq}}\) than with total precipitation, with path effects of - 0.51 (P<0.01) and - 0.35 (P<0.05), respectively. This suggests that declines in precipitation frequency have a more severe impact on plant drought stress than changes in total precipitation, which in turn causes earlier leaf senescence in many regions.  
+
+<|ref|>text<|/ref|><|det|>[[144, 500, 852, 855]]<|/det|>
+We also found a significantly positive relationship between \(\mathsf{P}_{\mathsf{freq}}\) and the drought response lag ( \(\mathsf{R}^2 = 0.40\) , p<0.05), indicating that plants acclimate to drought more quickly with decreased \(\mathsf{P}_{\mathsf{freq}}\) , necessitating longer recovery times from drought ( \(\mathsf{R}^2 = 0.82\) , p<0.05, Figure 2 B- C). Using a moving window approach, we observed an increasing importance of \(\mathsf{P}_{\mathsf{freq}}\) in regulating DFS changes over the past four decades, indicated by increases in the slope values (Figure 2 D). We further found that decreased \(\mathsf{P}_{\mathsf{freq}}\) was often associated with a smaller size of a single rain event (11.7% and 0.9% for positive and negative correlations, respectively), reducing soil moisture accumulation (Figure 2 E) and thereby contributing to the increased soil moisture variability and earlier DFS consequently ( \(\mathsf{R}^2 = 0.64\) , P<0.01, Figure 2 F).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[198, 95, 797, 730]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 734, 850, 900]]<|/det|>
+<center>Figure 2. Mechanisms for the correlation between precipitation frequency and the dates of leaf senescence (DFS). A shows the structural equation model (SEM) analysis. B and C represent the changes of drought response lag and drought recovery time with precipitation frequency. D shows the moving window approach with respect of positive and negative sensitivities of DFS to precipitation frequency over 1982-2022 (see Methods). E shows the relationship between precipitation frequency and the maximum daily precipitation size (N and P represent negative and positive correlations). F represents the correlation between DFS and root zone soil moisture variability using coefficients of variation (%). \* and \*\* represent \(p<0.05\) and \(p<0.01\) , respectively. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 92, 854, 636]]<|/det|>
+We further tested if the positive impacts of \(\mathsf{P}_{\mathsf{freq}}\) on DFS could be reproduced by current state- of- the- art Earth system models. This included both Trendy models for historical simulations and CMIP6 models for future projections under various shared socioeconomic pathways (SSPs), including SSP126, SSP245, SSP370, and SSP585. We found that Trendy models overall captured the relationship between DFS and precipitation frequency, with larger proportions of significant positive correlations (Figure 3 A). Similarly, among the 14 CMIP6 models, only three failed to reproduce the observed patterns (ACCESS- ESM1- 5, BCC- CSM2- MR and TaiESM1). However, when assessing the sensitivity of DFS to changes in \(\mathsf{P}_{\mathsf{freq}}\) (i.e., how DFS changes per unit variation in \(\mathsf{P}_{\mathsf{freq}}\) ), we observed substantial differences among models (Figure 3 B). Only seven out of 16 Trendy models demonstrated positive sensitivities, and even fewer CMIP6 models showed positive sensitivities. Additionally, we assessed the accuracy of these models in predicting the sign of the DFS- \(\mathsf{P}_{\mathsf{freq}}\) relationship at each pixel level, comparing these predictions with observations (Figure 3 C). About half of all pixels showed mismatches, highlighting the models' limited accuracy in capturing the DFS- \(\mathsf{P}_{\mathsf{freq}}\) correlations.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[180, 156, 816, 690]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[78, 700, 911, 833]]<|/det|>
+<center>Figure 3. The test of Earth system models in reproducing the observed relationship between the dates of leaf senescence (DFS) and precipitation frequency. A shows the overall proportions of significant positive and negative correlations. B represents the sensitivity of DFS to precipitation frequency changes. C is the comparison on the signs of correlation for each pixel. Four shared socioeconomic pathways (SSPs) were included for CMIP6 models, including SSP126, SSP245, SSP370, and SSP585, respectively. -- and ++ represent consistent negative and positive observations. Significance was set with p<0.05. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[147, 95, 245, 111]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[144, 123, 854, 824]]<|/det|>
+Our research has revealed a positive correlation between DFS and \(\mathsf{P}_{\mathsf{freq}}\) . Accordingly, the widespread declines in the \(\mathsf{P}_{\mathsf{freq}}\) over the past four decades have led to earlier DFS in northern ecosystems. The impact of these changes varies among plant functional types, reflecting the diversity of strategies plants use to adapt to local environments and respond to climate change factors \(^{17 - 18}\) . Limited soil moisture due to reduced \(\mathsf{P}_{\mathsf{freq}}\) can cause drought stress, negatively affecting soil organic carbon (SOC) levels and soil respiration \(^{19 - 20}\) . Conversely, excessive moisture can also hinder respiration by reducing oxygen availability, which may explain observations of earlier DFS in regions with increased precipitation \(^{21}\) . The interaction between soil moisture, heat, SOC, soil microorganisms, as well as soil geochemical characteristics defines the optimal conditions for plant growth \(^{22 - 23}\) . These conditions are the result of long- term adaptation strategies developed by plants. Changes in \(\mathsf{P}_{\mathsf{freq}}\) alter these soil properties and this may prompt plants to adjust their DFS to enhance survival in changing environments. This adjustment may also reflect the increased demand for soil resources, particularly soil moisture, to sustain photosynthetic activity in a warming climate. Overall, our findings underscore the importance of considering seasonal precipitation patterns, rather than just total amounts, in understanding leaf senescence timing. This insight is crucial for incorporating temporal changes in precipitation into future ecosystem models to better understand the impacts of climate change on plant phenology and growth.  
+
+<|ref|>text<|/ref|><|det|>[[163, 872, 850, 890]]<|/det|>
+In our study, we aimed to elucidate the mechanisms behind the observed trend of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 93, 853, 595]]<|/det|>
+earlier DFS with decreased \(\mathsf{P}_{\mathsf{freq}}\) , a task complicated by the interactive effects of precipitation amount and variability on terrestrial ecosystem processes<sup>24</sup>. Using partial correlation and SEM techniques, we identified that the primary driver for earlier DFS under reduced \(\mathsf{P}_{\mathsf{freq}}\) may be the intensified water constraints on photosynthesis through significant reductions in root- zone moisture and increases in VPD. A lower frequency of rainfall events implies longer drought periods. Consequently, soil moisture gradually declines, particularly in the surface layers where the majority of a plant's roots are concentrated. This poses a challenge for plants to access adequate water supply, especially after prolonged drought periods. Experimental studies have indicated that plant photosynthesis and primary productivity are significantly impacted by changes in \(\mathsf{P}_{\mathsf{freq}}^{15}\) . Reduced \(\mathsf{P}_{\mathsf{freq}}\) , often coupled with smaller precipitation events, adversely affects soil moisture recharge and increases soil moisture variability, which in turn drives earlier leaf senescence. The increase in atmospheric dryness further accelerates the cessation of photosynthesis.  
+
+<|ref|>text<|/ref|><|det|>[[144, 650, 852, 890]]<|/det|>
+A pivotal finding of our research is the identification of a significantly shortened drought response lag associated with decreased \(\mathsf{P}_{\mathsf{freq}}\) , a process representing drought acclimation. In particular, we found a significant negative correlation between drought response lag and evapotranspiration (ET) (Extended Figure 2 A). Such results implies an enhanced water- use strategy of plants that further supports plant adaptation and acclimation, probably by strengthening the growth of root systems to extend downstream for deeper water sources under droughts<sup>25</sup>. This reason has been supported by our results showing
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 94, 852, 410]]<|/det|>
+increased root depth with lower drought response lag (Extended Figure 2 B). The enhanced drought acclimation is likely linked to the adaptive strategy of plants that have been exposed to prolonged periods of drought, including more effective water management and utilization. Plants can rapidly reduce water loss or increase water uptake when water availability is scarce through morphologically deeper roots and an enhanced tolerance to drought physiologically by accumulating osmoprotectants and other regulatory substances<sup>26</sup>. Our observations, encompassing a wide range of species with varied plant functional types and local climatic backgrounds, therefore confirm and extend the critical role of \(\mathrm{P_{freq}}\) on vegetation growth beyond site- level experiments.  
+
+<|ref|>text<|/ref|><|det|>[[144, 464, 852, 892]]<|/det|>
+We show that while current Earth system models were able to reproduce the overall trend in the correlation between DFS and \(\mathrm{P_{freq}}\) , they inaccurately represent the sensitivity of DFS to changes in \(\mathrm{P_{freq}}\) . A pixel- by- pixel analysis showed that these models incorrectly predict the sign of the DFS- \(\mathrm{P_{freq}}\) correlation for half of the regions examined. This discrepancy may be primarily due to the models' reliance on the link between total precipitation and soil moisture, overlooking the significant effects of \(\mathrm{P_{freq}}\) on ecosystem functions. However, the timing, frequency and duration of precipitation events are determinants of ecosystem processes during autumn<sup>27- 29</sup> and therefore important for leaf senescence, as shown by our observations. Therefore, current Earth system models, driven by basic conceptual frameworks that ignore the effects of \(\mathrm{P_{freq}}\) on plant hydraulics, fall short in reproducing the temporal effects of \(\mathrm{P_{freq}}\) on DFS<sup>30</sup>. Including \(\mathrm{P_{freq}}\) —a key measure of precipitation variability—into ecosystem models therefore has large potential
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 94, 852, 185]]<|/det|>
+to improve future predictions of drought impacts on ecosystems, especially given the expectation that future droughts will intensify in several dimensions, including magnitude, duration, timing, and frequency<sup>11,31</sup>.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 243, 247, 259]]<|/det|>
+## References  
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+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[90, 88, 850, 333]]<|/det|>
+29. Jin, H., Vicente-Serrano, S.M., Tian, F. et al. Higher vegetation sensitivity to meteorological drought in autumn than spring across European biomes. Commun Earth Environ 4, 299 (2023). https://doi.org/10.1038/s43247-023-00960-w30. Paschalis, A., et al. Rainfall manipulation experiments as simulated by terrestrial biosphere models: Where do we stand? Glo. Chang. Biolo. 26, 3336-3355. doi:10.1111/gcb.15024.31. Donat, M., Lowry, A., Alexander, L. et al. More extreme precipitation in the world's dry and wet regions. Nature Clim Change 6, 508-513 (2016). https://doi.org/10.1038/nclimate2941
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[142, 95, 224, 110]]<|/det|>
+## Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[142, 132, 261, 147]]<|/det|>
+## 1. Study area  
+
+<|ref|>text<|/ref|><|det|>[[144, 168, 852, 372]]<|/det|>
+Northern Hemisphere (NH) encompasses a wide range of ecosystems that are essential for maintaining the global carbon balance and limiting global warming. Monitoring the dynamics of vegetation in the NH is crucial for understanding and mitigating climate. In this study, we focused on middle and high latitude regions of Northern Hemisphere \((>30^{\circ}\mathrm{N})\) , where vegetation dynamic has an evident seasonality (Figure S1).  
+
+<|ref|>sub_title<|/ref|><|det|>[[144, 428, 410, 445]]<|/det|>
+## 2. Site-level DFS from flux data  
+
+<|ref|>text<|/ref|><|det|>[[144, 465, 852, 630]]<|/det|>
+The site- level phenology observations were derived from daily gross primary productivity (GPP) based on the eddy- covariance flux measurements. We removed sites with insufficient observations \((< 8\) yr). As a result, 52 flux sites with a total of 662 year- site records of daily GPP from the FLUXNET database were selected (Table S2). We used a dynamic threshold of \(10\%\) of the annual maximum GPP to determine DFS.  
+
+<|ref|>sub_title<|/ref|><|det|>[[144, 687, 346, 703]]<|/det|>
+## 3. Satellite derived DFS  
+
+<|ref|>text<|/ref|><|det|>[[144, 724, 852, 852]]<|/det|>
+The long time series of continuous NDVI dataset from the GIMMS- 3G+ product was used to derive DFS. This dataset was based on corrected and calibrated measurements from Advanced Very High Resolution Radiometer (AVHRR) data<sup>32</sup> with a spatial resolution of 0.0833 degree and a half- month interval for 1982 to 2022.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 94, 852, 220]]<|/det|>
+To better capture the seasonal signals of vegetation while eliminating the interference of atmospheric effects and snow cover, the NDVI time series was fist reconstructed by weighted Whittaker algorithm<sup>33</sup>. Then a seven- parameter double logistic function<sup>34</sup> was used to fit the NDVI time series and DFS was determined based on inflection method<sup>35</sup>.  
+
+<|ref|>equation<|/ref|><|det|>[[162, 231, 832, 269]]<|/det|>
+\[f(t) = m_{1} + (m_{2} - m_{7}\cdot t)\left(\frac{1}{1 + e^{(m_{3} - t)/m_{4}}} - \frac{1}{1 + e^{(m_{5} - t)/m_{6}}}\right) \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[144, 279, 852, 483]]<|/det|>
+where, m1 is background NDVI; m2 is the difference between summer- time NDVI and background value; m3 and m5 are the midpoints in the days of the year of the transitions of spring green- up and autumn senescence, respectively; m4 and m6 are normalized slope coefficients for these transitions; m7 is summer green- down parameter. DFS was defined as the time when the curvature changing rate reached its last local maximum value.  
+
+<|ref|>sub_title<|/ref|><|det|>[[145, 538, 497, 556]]<|/det|>
+## 4. Simulated DFS from Trendy and CMIP6  
+
+<|ref|>text<|/ref|><|det|>[[144, 575, 852, 705]]<|/det|>
+We simulated DFS based on output GPP from 16 Trendy models during 1983- 2021 and 14 CMIP6 models under different shared socioeconomic pathways (SSP- 126, SSP- 245, SSP- 370, and SSP- 585) during 2016- 2100 (Table S3). DFS was determined using the same inflection method as the NDVI- based DFS.  
+
+<|ref|>sub_title<|/ref|><|det|>[[145, 761, 276, 777]]<|/det|>
+## 5. Climate data  
+
+<|ref|>text<|/ref|><|det|>[[144, 797, 852, 890]]<|/det|>
+We derived monthly total amount (Ptotal) and frequency (Pfreq) of precipitation from two independent datasets: 1) the Climatic Research Unit Time- Series (CRU TS 4.07) and 2) the fifth generation European Centre for Medium- Range Weather Forecasts reanalysis of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 92, 852, 632]]<|/det|>
+the global climate (ERA5). The CRU dataset is produced by the interpolation from extensive networks of climatic station observations and provides several climate variables on a \(0.5^{\circ} \times 0.5^{\circ}\) spatial resolution and a monthly temporal resolution<sup>36</sup>. We used wet day frequency, which defined as days with \(\geq 0.1\) mm precipitation, as \(P_{\text{freq}}\). The ERA5 product provides hourly estimates of various climate variables with a spatial resolution of \(0.1^{\circ}\) based on vast amounts of historical observations<sup>37</sup>. We obtained total precipitation from the monthly aggregated datasets and calculated the number of rainy days per month based on the daily precipitation \((\geq 0.1 \text{mm})\). We used the mean value of \(P_{\text{total}}\) and \(P_{\text{freq}}\) from CRU and ERA5 as final \(P_{\text{freq}}\) and \(P_{\text{total}}\) for 1982–2022 to reduce the uncertainty from a single dataset. Monthly mean temperature was obtained from CRU and surface net solar radiation was accessed from ERA5. Vapor pressure deficit (VPD) and evapotranspiration (ET) data for 1982–2022 were obtained from TerraClimate with a monthly temporal resolution and a 1/24 degree spatial resolution. The monthly root- zone soil moisture from 1982 to 2022 was obtained from Global Land Evaporation Amsterdam Model (GLEAM) with a spatial resolution of \(0.25^{\circ}\).  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 688, 811, 707]]<|/det|>
+## 6. Identification of drought events, drought recovery and drought response lag  
+
+<|ref|>text<|/ref|><|det|>[[145, 724, 852, 890]]<|/det|>
+Drought response lag and recovery time were obtained from Li et al. (2023)<sup>2</sup>. Extreme drought events were identified by examining monthly SPEI- 3 (Standardized Precipitation- Evapotranspiration Index at a 3- month scale) values below the threshold of - 2. Drought recovery is defined as the duration (months) starting from the month with the deepest suppression of NDVI to the month when NDVI returns to within 95% of the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[144, 93, 852, 410]]<|/det|>
+long- term average baseline in each pixel. The monthly SPEI3 and NDVI time series were first smoothed by a 3- month forward moving window, they were then sequentially deseasonalized and linearly detrended. To avoid lengthening the drought recovery duration due to algorithm design, if vegetation recovery extending through the dormant season and into subsequent year, the drought recovery was calculated as the total length of the recovery period minus the length of the dormant season. We measured response lag in months, which is the time between the lowest SPEI3 value and the most significant drop in NDVI caused by drought. We calculated both drought response lag and recovery time for each pixel individually.  
+
+<|ref|>sub_title<|/ref|><|det|>[[144, 465, 243, 481]]<|/det|>
+## 7. Analysis  
+
+<|ref|>text<|/ref|><|det|>[[144, 500, 852, 892]]<|/det|>
+Precipitation, along with temperature and radiation, collectively regulate DFS<sup>38</sup>. In addition, covariate effects exist among these climatic variables as well. Therefore, we applied partial correlation analysis to explore the impacts of \(P_{\text{total}}\) and \(P_{\text{freq}}\) on DFS. We performed partial correlation analysis under three scenarios: (1) partial correlation between DFS and \(P_{\text{total}}\), removing the effects of temperature and radiation (scenario 1); (2) partial correlation between DFS and \(P_{\text{total}}\), removing the effects of temperature, radiation, and \(P_{\text{freq}}\) (scenario 2); (3) partial correlation between DFS and \(P_{\text{freq}}\), removing the effects of temperature, radiation, and \(P_{\text{total}}\) (scenario 3). According to previous studies, preseasonal forcings have a better predictive strength on phenology than fixed seasonal climate forcing alone<sup>39- 40</sup>. We thus used the preseason mean values of each climatic variable in the partial correlation analysis. For example, the preseason length of \(P_{\text{freq}}\) was defined as
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 93, 852, 188]]<|/det|>
+the period when the absolute value of partial correlation coefficient between \(\mathsf{P}_{\mathsf{freq}}\) and DFS was at its maximum. For each pixel, the preseason periods of 0 to 6 months prior to the multi- year mean DFS were examined (Figure S5).  
+
+<|ref|>text<|/ref|><|det|>[[145, 241, 852, 483]]<|/det|>
+To investigate the temporal changes in the sensitivity of DFS to \(\mathsf{P}_{\mathsf{freq}}\) , we used a moving window method. We conducted tests on a variety of window sizes, ranging from 10 to 20 years. For each window size, we calculated the sensitivity of DFS to \(\mathsf{P}_{\mathsf{freq}}\) based on multilinear regression within each moving window. Then we calculated the percentages of significant sensitivity ( \(P < 0.05\) ) and fitted these values to obtain the optimal window size with the largest \(R^2\) . As a result, the optimal window size was set as 19 years to perform subsequent analyses (Figure S6).  
+
+<|ref|>equation<|/ref|><|det|>[[164, 500, 829, 520]]<|/det|>
+\[DFS = a\cdot P_{freq} + b\cdot P_{total} + c\cdot Temperature + d\cdot Radiation + \epsilon \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[145, 538, 852, 631]]<|/det|>
+where, a, b, c and d are regression coefficients and represent the sensitivity of DFS to \(\mathsf{P}_{\mathsf{freq}}\) , \(\mathsf{P}_{\mathsf{total}}\) , temperature, and radiation, respectively. \(\epsilon\) is the residual error. All the climate variables used in the regression were the mean values during preseason.  
+
+<|ref|>text<|/ref|><|det|>[[145, 687, 852, 816]]<|/det|>
+To explore the potential mechanisms by which precipitation affects DFS, we performed structural equation modeling. Considering that precipitation patterns may affect DFS by influencing solar radiation and drought conditions, we selected radiation, VPD, and root- zone soil moisture to construct structural equation model.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[142, 112, 834, 160]]<|/det|>
+32. Pinzon, J., & Tucker, C. (2014). A Non-Stationary 1981–2012 AVHRR NDVI3g Time Series. Remote Sensing, 6, 6929-6960.  
+
+<|ref|>text<|/ref|><|det|>[[144, 170, 830, 245]]<|/det|>
+33. Kong, D., Zhang, Y., Gu, X., & Wang, D. (2019). A robust method for reconstructing global MODIS EVI time series on the Google Earth Engine. Isprs Journal of Photogrammetry and Remote Sensing, 155, 13-24  
+
+<|ref|>text<|/ref|><|det|>[[144, 254, 801, 329]]<|/det|>
+34. Elmore, A.J., Guinn, S.M., Minsley, B.J., & Richardson, A.D. (2012). Landscape controls on the timing of spring, autumn, and growing season length in mid-Atlantic forests. Global Change Biology, 18, 656-674  
+
+<|ref|>text<|/ref|><|det|>[[144, 338, 850, 414]]<|/det|>
+35. Zhang, X., Friedl, M.A., Schaaf, C.B., Strahler, A.H., Hodges, J.C.F., Gao, F., Reed, B.C., & Huete, A. (2003). Monitoring vegetation phenology using MODIS. Remote sensing of environment, 84, 471-475  
+
+<|ref|>text<|/ref|><|det|>[[144, 422, 850, 470]]<|/det|>
+36. Harris, I., Osborn, T.J., Jones, P., & Lister, D. (2020). Version 4 of the CRU TS monthly high-resolution gridded multivariate climate dataset. Scientific Data, 7, 109  
+
+<|ref|>text<|/ref|><|det|>[[144, 478, 812, 526]]<|/det|>
+37. Hersbach, H., et al. (2020). The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146, 1999-2049  
+
+<|ref|>text<|/ref|><|det|>[[144, 534, 841, 636]]<|/det|>
+38. Liu, Q., Fu, Y.S.H., Zhu, Z.C., Liu, Y.W., Liu, Z., Huang, M.T., Janssens, I.A., & Piao, S.L. (2016). Delayed autumn phenology in the Northern Hemisphere is related to change in both climate and spring phenology. Global Change Biology, 22, 3702-3711  
+
+<|ref|>text<|/ref|><|det|>[[144, 644, 856, 747]]<|/det|>
+39. Piao, S., Tan, J.G., Chen, A.P., Fu, Y.H., Ciais, P., Liu, Q., Janssens, I.A., Vicca, S., Zeng, Z.Z., Jeong, S.J., Li, Y., Myneni, R.B., Peng, S.S., Shen, M.G., & Pennuelas, J. (2015). Leaf onset in the northern hemisphere triggered by daytime temperature. Nature Communications, 6  
+
+<|ref|>text<|/ref|><|det|>[[144, 755, 856, 884]]<|/det|>
+40. Wu, C., Wang, X., Wang, H., Ciais, P., Peñuelas, J., Myneni, R.B., Desai, A.R., Gough, C.M., Gonsamo, A., Black, A.T., Jassal, R.S., Ju, W., Yuan, W., Fu, Y., Shen, M., Li, S., Liu, R., Chen, J.M., & Ge, Q. (2018). Contrasting responses of autumn-leaf senescence to daytime and night-time warming. Nature Climate Change, 8, 1092-1096
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[147, 90, 285, 107]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[147, 121, 850, 177]]<|/det|>
+All data used in this study are available online. The specific links for each dataset are presented in Supplementary Tables S1.  
+
+<|ref|>sub_title<|/ref|><|det|>[[147, 233, 291, 250]]<|/det|>
+## Code availability  
+
+<|ref|>text<|/ref|><|det|>[[147, 269, 850, 325]]<|/det|>
+All data analyses and modeling were performed using Python and R. The codes for the phenological models are available at https://doi.org/10.5281/zenodo.5829780.  
+
+<|ref|>text<|/ref|><|det|>[[147, 380, 851, 622]]<|/det|>
+Acknowledgements: This work was funded by the National Natural Science Foundation of China (42125101, 42271034). X.W. was funded by the Youth Innovation Promotion Association of Chinese Academy of Sciences (2022051). C.M.Z. was funded by SNF Ambizione grant PZ00P3_193646. J.P. was funded by the TED2021- 132627B- I00 grant funded by the Spanish MCIN, AEI/10.13039/501100011033 and by the European Union NextGenerationEU/PRTR, the Fundación Ramón Areces project CIVP20A6621 and the Catalan government grant SGR221- 1333.  
+
+<|ref|>text<|/ref|><|det|>[[147, 678, 851, 771]]<|/det|>
+Author contributions: C.W. designed the research. C.W. and X.W. wrote the first draft of the manuscript. X.Z. and X.W. performed the data analysis. All authors assessed the research analyses and contributed to the writing of the manuscript.  
+
+<|ref|>text<|/ref|><|det|>[[147, 828, 745, 845]]<|/det|>
+Competing interests: The authors declare no competing financial interests.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[180, 90, 810, 320]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 336, 852, 429]]<|/det|>
+<center>Extended Figure 1. Spatial distribution of the correlation coefficients \((\mathbf{R}^2)\) with respect to total precipitation and its frequency. (a) Total precipitation \((\mathbf{P}_{\text{total}})\) and dates of leaf senescence (DFS). (b) Precipitation frequency \((\mathbf{P}_{\text{freq}})\) and DFS.</center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[220, 88, 775, 430]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[90, 444, 850, 464]]<|/det|>
+<center>511 Extended Figure 2. Relationships between drought response lag and (A) </center>  
+
+<|ref|>text<|/ref|><|det|>[[90, 483, 477, 501]]<|/det|>
+512 evapotranspiration, and (B) root depth.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[42, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 131, 353, 203]]<|/det|>
+ExtendedFigure1. jpg  ExtendedFigure2. jpg  Supplementaryinformation.pdf
+
+<--- Page Split --->

preprint/preprint__5f8246d879234f23ce9477cb2233369223f308285c11c4c8512f61f7b194c230/images_list.json

@@ -0,0 +1,197 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Overview of the dynamical network optimisation framework. (a) Model Generation: Experimental devices are driven under random inputs, their observable states are recorded, and these data are used to fit models of device dynamics. (b) Network Simulation: A neural network is constructed where each node replicates the dynamics of the original device, using the trained model. Parameters controlling device interactions (network weights) are optimised for a task via backpropagation through time (BPTT) or truncated-BPTT on the interacting digital twins. (c) Experimental Transfer: The parameters optimised in simulation are transferred like-for-like to experimental networks where each node is a real device, and task performance evaluated",
+    "footnote": [],
+    "bbox": [
+      [
+        95,
+        103,
+        902,
+        420
+      ]
+    ],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Modelling and optimising dynamic behaviours. (a) Schematic analogy of temporal dependencies. Altering an action in the past has consequences for all future actions. Similarly, for backpropagation through time, changes to the final output caused by all past inputs and states must be taken into consideration. (b) Schematic showing samples from distributions of initial conditions, which subsequently affect the predicted trajectory. Grey clouds show the distribution of all gathered data for a given random input sequence, while red lines highlight specific trajectories. (c) Schematic diagram of the Neural-SDE architecture. Inputs of device states (activities), external driving stimuli, and auxiliary variables feed into a pair of distinct neural networks that handle the deterministic (upper network) and stochastic (lower network) behaviours. The output of these networks feeds into a numerical ODE solver, generating predictions of both activities and auxiliary variables for the next timestep. The results are recursively fed back as inputs to the next timestep prediction, generating predicted trajectories from initial conditions and external driving signals. Black arrows show forward propagation of activities; orange arrows show backward propagation of gradients. (d) Comparison between predictions generated via neural-ODE and neural-SDE models. The neural-ODE produces a single deterministic outcome for a given set of initial conditions and input stimuli, shown by the yellow line. The neural-SDE instead generates sampled trajectories from a distribution based on the learned noise characteristics. The black lines show 100 generations of a signal via the neural-SDE, while red lines show real experimental data from repeated identical input sequences. As in (b), blue circles represent selected initial conditions and the grey clouds represent the distributions observed across all experiments.",
+    "footnote": [],
+    "bbox": [
+      [
+        105,
+        80,
+        888,
+        508
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Temporal classification benchmarks (Partially-observable MNIST/ Neuroprosthetic movement classification). (a) The tasks consist of a variant of the MNIST classification and neuroprosthetic gesture recognition. The MNIST task, presented as sequences of images, has been adapted into a temporal problem by partially obscuring the images at each time step, requiring the system to integrate information over time for accurate classification. The neuroprosthetic gesture recognition task is characterized by input channels that vary over time. (b) Example responses from the network's physical nodes, showing experimentally measured responses (red) and digital twins' responses (black) for different nodes across two layers. The gray areas represent the distribution of responses from the digital twins, while the dashed arrows illustrate the flow of information from the input through the layers to the output. The horizontal bars indicate the output activations of different physical devices representing classes compared to the model output, with the correct class highlighted in red. (c) Transferred performance of nanoring array networks using Neural-ODEs and Neural-SDEs as digital twins in the MNIST benchmark. The deterministic Neural-ODE models exhibit unrealistically high performance in simulation, which significantly deteriorates in experiments. In contrast, the noise-aware training provided by Neural-SDEs maintains high performance on physical devices, demonstrating effective exploitation of node dynamics and robustness during device transfer. (d) Performance of the Neural-SDE models on neuroprosthetic gesture recognition, demonstrating the framework's potential in addressing real-world tasks. The black line represents the error as a percentage across iterations. The inset shows the final performance, comparing simulation results with those after transfer to the physical device.",
+    "footnote": [],
+    "bbox": [
+      [
+        100,
+        144,
+        900,
+        620
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Cascade learning and regression benchmarking (Mackey–Glass future prediction). (a) Schematic overview of the methodology employed for sequentially training network layers with intermediate data gathering. The boxes represent steps performed in simulations, with red shading indicating ASVI twins/experiments in the first layer (L1) and blue shading representing NRAs in the second layer (L2). Initially, a single ASVI layer is connected to a simulated output neuron and trained for the regression task. Once trained, the connectivity from the input to the ASVI layer is transferred to the physical device. Experimental data is then collected to serve as input for training the connectivity to the subsequent layer, consisting of NRAs. This process can, in principle, be extended to accommodate any number of layers. Retraining the digital twin is not required; intermediate data are used solely to adjust the connectivity between the new and the previous layer. (b) Mean-squared error between ground truth and experimental network predictions for the Mackey–Glass future prediction task as the number of future steps increases. Circles/squares represent networks with two/three hidden layers, while dark/light colors compare direct training of the entire network to networks trained using cascade learning, as presented in panel (a). Comparison between model prediction and ground-truth data for the five-timestep future prediction of the Mackey–Glass equation in (c) two-layer and (d) three-layer networks. White circles represent the ground truth data, red lines show the transferred PNN prediction, and pink shading indicates the difference between the ground truth and the network prediction.",
+    "footnote": [],
+    "bbox": [
+      [
+        92,
+        87,
+        905,
+        540
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Modelling of simulated and experimental dynamical systems. Panel (a) illustrates a simulated example of a partial derivative of the acceleration \\((f_{2})\\) with respect to position for the Duffing oscillator. The surface represents the partial derivative as position \\((x_{1}(t))\\) and velocity \\((x_{2}(t))\\) of the system vary. The example trajectories compare the gradient over time, calculated both analytically (red) and via differentiation of the Neural-SDE model (black), for two input sequences, showing excellent agreement. Panel (b) provides a more general view of the model's ability to act as a surrogate for device gradients; here, we adopt eligibility traces that accumulate gradient information (see Main text and Supplementary Information for more details). The difference between the desired and modelled eligibility traces increases due to error accumulation. Panel (c) compares responses generated via the Neural-SDE model (black and yellow lines) and experimentally gathered data of the NRA device (red lines, white circles) for 100 repetitions of a random input sequence. Panel (d) illustrates the Neural-SDE's ability to model the high-dimensional, experimentally measured responses of an artificial spin-vortex-ices (ASVI) device. Here, the x-axis corresponds to the different output dimensions of the device responses, while the colours reflect the temporal evolution. Even for this multivariate system, the model (coloured lines) accurately captures the system behaviour (dots).",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        85,
+        880,
+        545
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. a A scheme of the process of gathering a dataset used to fit an N-DE model. The trajectories are organised such that the concatenation of \\(\\mathbf{s}(t_0)\\) and \\(\\mathbf{y}(t_0)\\) are the initial conditions of the N-DE model, which is asked to produce trajectories that mimic the output \\(\\mathbf{y}(t + \\delta t)\\) across time. The process is depicted in panel \\(\\mathbf{b}\\) for an example segment of trajectories. The initial conditions are depicted in blue and correspond to the starting activities of the N-DE, whose generated response is reported in black. The optimisation process of a neural-ODE typically involves minimisation of the mean-squared error of \\(\\delta (t)\\) , which is simply the difference between the generated and target activities, over the mini-batch of segments considered.",
+    "footnote": [],
+    "bbox": [
+      [
+        97,
+        80,
+        860,
+        476
+      ]
+    ],
+    "page_idx": 19
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. The figure aims to illustrate the importance of capturing coloured noise for an improved expressivity of the neural-SDE. The dynamic system in question is a simple non-linear leaky integrator, where its stochasticity lies on a slower timescale in comparison to its leakage term, which defines its deterministic temporal kernel. Panels a and c (b and d) correspond to a neural-SDE without (with) augmentation of the auxiliary variables. a and c report examples of generated trajectories (black) compared to the corresponding system dynamics (red), where the blue area reflects the dispersion of the distribution of the dynamic process. Given that both models can capture the dispersion of the process, the dynamics generated by the neural-SDE of panel a exhibit rapidly changing stochastic behaviour, not capturing the smoother trends of the reference system. This translates into an inaccurate reproduction of the autocovariance structure, shown in panel c, where the different trends correspond to the diverse reference times over which the autocovariance function is computed. In contrast, the dynamics of the augmented neural-SDE are in considerably improved agreement with the process under study (panel b and d). Despite the simplicity of this example, the result shows how augmentation of the neural-SDE model can strongly improve its expressivity, and it might be necessary to capture stochastic behaviours that are not completely entangled to the temporal kernel of its deterministic component.",
+    "footnote": [],
+    "bbox": [
+      [
+        150,
+        81,
+        849,
+        364
+      ]
+    ],
+    "page_idx": 20
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Figure 8. Scheme of the network of devices (a) and of neural-SDEs (b) illustrating the formalism adopted (see text for more details). The central neural-SDE of panel b has been expanded to show inputs and outputs, highlighting the backward paths to estimate the dependencies (coloured arrows).",
+    "footnote": [],
+    "bbox": [
+      [
+        179,
+        77,
+        768,
+        592
+      ]
+    ],
+    "page_idx": 22
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_9.jpg",
+    "caption": "Figure 9. Comparison between generated and target dynamics for the analytical systems considered, in particular for the leaky integrator (left) and Duffing oscillator (right). In each panel, the systems have been driven by an external signal \\(\\mathbf{s}(t)\\) , while different panels correspond to different external signals. The trajectories generated by the neural-SDE are in black, while the reference trajectories are depicted in red. In each panel, the average response is also highlighted for comparison between the model (yellow line) and the analytical system (circles), where the average is conditioned to a specific bifurcating dynamic for the Duffing oscillator. Despite the variability in the deterministic and stochastic behaviours of the systems for different external signals and the presence of bifurcations, the neural-SDE is in striking agreement with the data.",
+    "footnote": [],
+    "bbox": [
+      [
+        163,
+        84,
+        835,
+        528
+      ]
+    ],
+    "page_idx": 24
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_10.jpg",
+    "caption": "Figure 10. Performance surface of a single-layer network (a and b) and a two-layer network (c and d) for interacting analytical leaky integrators. The reference networks are illustrated in panels b and d, while the twin networks are in a and c. Panel e reports the performance of a multilayer perceptron showing the quick decay in accuracy when the system does not have memory sources.",
+    "footnote": [],
+    "bbox": [
+      [
+        160,
+        323,
+        844,
+        604
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_11.jpg",
+    "caption": "Figure 11. a Reference performance on the MNIST variation for two-layer networks of the analytical models. While the Neural-SDEs are accurate predictor of the systems behaviours and lead to optimised parameters that are robust with respect to stochasticity, the neural-ODEs fail short for the noisy variants of the systems. b Example distributions of input weights taken from (orange) a multi-layer perceptron trained via the digital twin approach, and (blue) a parameter-matched Laplace distribution used for the extreme learning machine frameworks. c Performance of a network of digital twins composed by neural-ODEs in simulation and after transferring to the experiment. The models 70k and 30k refer to networks trained for \\(3\\times 10^{5}\\) and \\(710^{5}\\) learning updates with a batch size of 50. While further optimisation lead to improved performance in simulation, parameters transferred from the Model 70k were unable to obtain a meaningful classification. This is showcased for the two-layer network and \\(25\\%\\) visibility. The result can be interpreted in the following way: as optimisation progresses, the parameters become more dependent on the deterministic responses provided by the neural-ODE, tending to amplify the simulation-reality gap. For this reason, we had to stop the optimisation process before convergence (at \\(3\\times 10^{5}\\) ) for acceptable performance with transferred parameters. As shown in the main text, the noise-aware optimisation of the neural-SDE removes this difficulty.",
+    "footnote": [],
+    "bbox": [
+      [
+        90,
+        180,
+        901,
+        612
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_12.jpg",
+    "caption": "Figure 12. Experimental and reference performance on the neuroprosthetic task as the classification time varies, for optimised networks of nanoring arrays (black), random connectivities of nanoring arrays (red), and software neural networks with small memory buffers (blue). Training is performed over a window containing the most meaningful.",
+    "footnote": [],
+    "bbox": [
+      [
+        185,
+        368,
+        810,
+        580
+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_13.jpg",
+    "caption": "Figure 13. Comparison between generated and target dynamics for the physical systems considered, NRA (left) and ASVI (right). In each panel, the systems have been driven by an external signal \\(\\mathbf{s}(t)\\) , while different panels correspond to different external signals. Similarly to Figure 9, the trajectories generated by the neural-SDE are in black, while the reference trajectories are depicted in red. The right panels corresponding to the ASVI illustrate the dynamics of different frequencies.",
+    "footnote": [],
+    "bbox": [
+      [
+        170,
+        230,
+        833,
+        700
+      ]
+    ],
+    "page_idx": 29
+  }
+]

preprint/preprint__5fbf0de3b241f4ee45e767edca02b1abbbc24f76a5f988443d4aa0a5a8adec71/images_list.json

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+    "caption": "Figure 1. Schematic illustration of synthesis and water splitting mechanism of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) . (a) The synthesis process of Pt single atom anchored NiO/Ni heterostructure nanosheets on Ag nanowires network. (b) The mechanism of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) network as an efficient catalyst towards large-scale water electrolysis in alkaline media.",
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Structural characterization of the fabricated \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) catalyst. (a) XRD patterns of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , \\(\\mathrm{NiO / Ni}\\) , and Ag NWs. (b-c) SEM images of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) . (d) HAADF-STEM image of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) . (e-f) Magnified HAADF-STEM image of \\(\\mathrm{Pt_{SA} - NiO / Ni} \\mathrm{and} \\mathrm{g}\\) the corresponding DFT simulated image, showing the atomically dispersed Pt atoms at Ni position (circles in (e)). (h) HRTEM images of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) and the insert in (h) shows the related FFT image of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) . (i-j) Dark-field TEM images of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) with different magnifications and (k-n) the mapping of the corresponding elements.",
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+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Electronic state and atomic structure characterization. (a) Pt \\(4f\\) spectra, (b) XANES spectra, and (c) calculated Pt oxidation states derived from \\(\\Delta\\) XANES spectra of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , \\(\\mathrm{Pt_{SA} - NiO}\\) , and \\(\\mathrm{Pt_{SA} - Ni}\\) , and Pt foil is given as a reference. (d) Corresponding FT-EXAFS curves of Figure 3b. (e) EXAFS fitting curve of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , \\(\\mathrm{Pt_{SA} - NiO}\\) , and \\(\\mathrm{Pt_{SA} - Ni}\\) \\(R\\) -space. (f) EXAFS wavelet transform plots of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , \\(\\mathrm{Pt_{SA} - NiO}\\) , \\(\\mathrm{Pt_{SA} - Ni}\\) , and Pt foil.",
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+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Theoretical investigations. Computational models and localized electric field distribution of (a) \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , (b) \\(\\mathrm{Pt_{SA} - NiO}\\) and (c) \\(\\mathrm{Pt_{SA} - Ni}\\) . (d) Calculated PDOS of \\(\\mathrm{NiO / Ni}\\) and \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , with aligned Fermi level. (e) Calculated Pt 5d band of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , \\(\\mathrm{Pt_{SA} - NiO}\\) , and \\(\\mathrm{Pt_{SA} - Ni}\\) . (f) The orbital alignment of the surficial sites for \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) binding with \\(\\mathrm{H_2O}\\) molecule. (g) Calculated OH-binding energies \\((\\Delta E_{\\mathrm{OH}})\\) and H-binding energies \\((\\Delta E_{\\mathrm{H}})\\) for Ni, pure NiO, and O vacancies modified NiO surface. (h) Calculated energy barriers of water dissociation kinetic and (i) adsorption free energies of \\(\\mathrm{H^*}\\) on the surface of the \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , \\(\\mathrm{Pt_{SA} - NiO}\\) , and \\(\\mathrm{Pt_{SA} - Ni}\\) catalysts, respectively.",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Electrocatalytic alkaline HER performances of the catalysts in 1 M KOH electrolyte. (a) HER polarization curves of \\(\\mathrm{Pt_{SA} - NiO / Ni}\\) , \\(\\mathrm{Pt_{SA} - NiO}\\) , \\(\\mathrm{Pt_{SA} - Ni}\\) , NiO/Ni, and \\(\\mathrm{Pt / C}\\) . (b) The comparison",
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+    "page_idx": 15
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+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
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+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2",
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+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
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+    "page_idx": 30
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+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5",
+    "footnote": [],
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preprint/preprint__5fbf0de3b241f4ee45e767edca02b1abbbc24f76a5f988443d4aa0a5a8adec71/preprint__5fbf0de3b241f4ee45e767edca02b1abbbc24f76a5f988443d4aa0a5a8adec71.mmd

@@ -0,0 +1,354 @@
+
+# Tailoring Water Dissociation Energy by Platinum Single-Atom Catalyst Coupled with Transition Metal/metal Oxide Heterostructure for Accelerating Alkaline Hydrogen Evolution Reaction  
+
+Changbao Han ( cban@bjut.edu.cn )  
+
+Beijing University of Technology  
+
+Kailing Zhou Beijing University of Technology  
+
+Qianqian Zhang Beijing University of Technology  
+
+Jingbing Liu Beijing University of Technology  
+
+Hui Yan Beijing University of Technology  
+
+Xiaoxing Ke Institute of Microstructure and Properties of Advanced Materials, Beijing University of Technology, Beijing 100124  
+
+Zelin Wang Beijing University of Technology  
+
+Hao Wang Beijing University of Technology  
+
+Changhao Wang Beijing University of Technology  
+
+Yuhong Jin Faculty of Materials and Manufacturing, Beijing University of Technology  
+
+## Article  
+
+Keywords: single- atom catalysts (SACs), NiO/Ni heterostructure, water dissociation, alkaline media, hydrogen evolution reactions (HER)  
+
+Posted Date: February 3rd, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 155535/v1
+
+<--- Page Split --->
+
+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 June 18th, 2021. See the published version at https://doi.org/10.1038/s41467-021-24079-8.
+
+<--- Page Split --->
+
+# Tailoring Water Dissociation Energy by Platinum Single-Atom Catalyst Coupled with Transition Metal/metal Oxide Heterostructure for Accelerating Alkaline Hydrogen Evolution Reaction  
+
+Kai Ling Zhou,†a Zelin Wang,†a Chang Bao Han,∗a Xiaoxing Ke,∗a Changhao Wang,a Yuhong Jin, a Qianqian Zhang, a Jingbing Liu, a Hao Wang∗a and Hui Yan a  
+
+a Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, P. R. China  E- mail: cbhan@bjut.edu; kexiaoxing@bjut.edu.cn; haowang@bjut.edu.cn  † These authors contributed equally.  
+
+## Abstract  
+
+High- activity catalysts in alkaline media are compelling for durable hydrogen evolution reaction (HER). Single- atom catalysts (SACs) provide an effective approach to reduce the amount of precious metals meanwhile maintain their catalytic activity. However, the sluggish activity of SACs for water dissociation in alkaline media has extremely hampered advances in highly efficient hydrogen production. Herein, we developed a platinum SAC immobilized NiO/Ni heterostructure (Pt<sub>SA</sub>- NiO/Ni) as an alkaline HER catalyst. It was found that Pt SACs coupled with NiO/Ni heterostructure enable the tunable binding abilities of hydroxyl ions (OH\*) and hydrogen (H\*), which efficiently tailors the water dissociation energy for accelerating alkaline HER. In particular, the dual active sites consisting of metallic Ni sites and O vacancies modified NiO sites near the interfaces of NiO/Ni in Pt<sub>SA</sub>- NiO/Ni have preferred adsorption affinity for H\* and OH\* groups, respectively, which efficiently lowers the energy barrier of water dissociation of Volmer step. Moreover, anchoring Pt single atoms at the interfaces of NiO/Ni heterostructure induces more free electrons on Pt sites due to the
+
+<--- Page Split --->
+
+elevated occupation of the Pt \(5d\) orbital at the Fermi level and reaches a near- zero H binding energy ( \(\Delta G_{\mathrm{H}^*}\) , 0.07 eV), which further promotes the H\* conversion and \(\mathrm{H}_2\) evolution. Further enhancement of alkaline HER performance was achieved by constructing \(\mathrm{Pt_{SA}}\) - NiO/Ni nanosheets on the Ag nanowires to form a hierarchical threedimensional (3D) morphology that provides abundant active sites and accessible channels for charge transfer and mass transport. Consequently, the fabricated \(\mathrm{Pt_{SA}}\) - NiO/Ni catalyst displays extremely high alkaline HER performances with a quite high mass activity of \(20.6\mathrm{A}\mathrm{mg}^{- 1}\) for Pt at the overpotential of \(100\mathrm{mV}\) , which is 41 times greater than that of the commercial Pt/C catalyst, significantly outperforming the reported catalysts.  
+
+Keywords: single- atom catalysts (SACs), NiO/Ni heterostructure, water dissociation, alkaline media, hydrogen evolution reactions (HER)  
+
+## Introduction.  
+
+Hydrogen \(\mathrm{(H_2)}\) has been regarded as the most promising energy carrier alternative to fossil fuels due to the environmental friendliness nature and high gravimetric energy density. \(^{1,2}\) Electrocatalytic water splitting powered by wind energy or solar technologies for hydrogen generation is considered a sustainable strategy. \(^{3}\) For an optimal electrocatalyst, minimizing the energy barrier and increasing the active sites are desirable for boosting the hydrogen evolution reaction (HER). \(^{4 - 6}\) Despite the significant progress that has been presented in nonprecious catalysts, the HER performances are still second to platinum (Pt)- based materials due to its optimal binding ability with hydrogen. \(^{7 - 10}\) However, the high cost and scarcity of Pt extremely hamper its large- scale application in electrolyzers for \(\mathrm{H}_2\) production. Single- atom catalysts (SACs) provide an effective approach to reduce the amount of Pt meanwhile maintain its high intrinsic activity. \(^{11 - 14}\) Recently, electrocatalytic HER in an alkaline condition has attracted more attention because catalyst systems are generally unstable in acidic media, resulting in safety and cost concerns in practice. Unfortunately, the alkaline HER activity of Pt- based catalysts is approximately two orders of magnitude lower than that in the acidic
+
+<--- Page Split --->
+
+condition caused by the high activation energy of the water dissociation step. \(^{15 - 18}\) Alkaline HER process involves two electrochemical reaction steps: (step (i)) electron- coupled \(\mathrm{H}_2\mathrm{O}\) dissociation to generate adsorbed hydrogen hydroxyl (OH\*) and hydrogen (H\*) (Volmer step), and (step (ii)) the concomitant interaction of dissociated H\* into molecular \(\mathrm{H}_2\) (Heyrovsky or Tafel step). \(^{19,20}\) In particular, the additional energy in step (i) is required to overcome the barrier for splitting strong OH- H bond, leading to a hamper of Pt SACs for alkaline HER application. Therefore, reducing the water dissociation energy in Volmer step (step (i)) for Pt single- atom catalyst in alkaline media becomes vital for large- scale \(\mathrm{H}_2\) production of industrialization.  
+
+Some strategies have been developed to improve Pt SACs HER activity. For instance, employing the microenvironment engineering to immobilize single Pt atoms in MXene nanosheets ( \(\mathrm{Mo}_2\mathrm{TiC}_2\mathrm{T}_x\) ) and onion- like carbon nanospheres supports could greatly reduce the H adsorption energy ( \(\Delta G_{\mathrm{H}}\) ) and, thus, facilitates the release of \(\mathrm{H}_2\) molecular. \(^{21,22}\) Besides, Pt single atoms anchored alloy catalysts (Pt/np- \(\mathrm{Co}_{0.85}\mathrm{Se}\) SAC) were constructed as an efficient HER electrocatalyst, \(^{23}\) in which np- \(\mathrm{Co}_{0.85}\mathrm{Se}\) can largely optimize the adsorption/desorption energy of hydrogen on atomic Pt sites, thus improving the HER kinetics. Furthermore, by utilizing the electronic interaction between the Pt atoms and the supports, single- atom Pt anchored 2D \(\mathrm{MoS}_2\) ( \(\mathrm{Pt}_{\mathrm{SA}}\) - \(\mathrm{MoS}_2\) ), \(^{24}\) nitrogen- doped graphene nanosheets ( \(\mathrm{Pt}_{\mathrm{SA}}\) - \(\mathrm{NGNs}\) ) \(^{25}\) and porous carbon matrix ( \(\mathrm{Pt}(\mathrm{\overline{a}PCM})^{26}\) show enhanced electrocatalytic HER efficiency due to the higher \(d\) band occupation near Fermi level, which can provide more free electrons for boosting the H\* conversion. Despite significant progress in Pt SACs, these methods are difficult to decrease the energy barrier of water dissociation in the Volmer step (step (i)). Generally, the \(\mathrm{H}_2\mathrm{O}\) dissociation and H\* conversion happen on different catalytic sites. \(^{27}\) Especially, the HER activities of Pt- based catalysts in alkaline conditions are governed by the binding ability of hydroxyl species (OH\*), \(^{28 - 30}\) and the alkaline HER kinetics could be optimized by independently regulating the binding energy of reactants (OH and H\*) on dual active sites. \(^{31 - 33}\) Inspired by these findings, the energy barrier of Pt SACs for \(\mathrm{H}_2\mathrm{O}\) dissociation in Volmer step (step (i)) in alkaline media could be decreased by incorporating or creating the dual active sites in the catalyst to independently modulate
+
+<--- Page Split --->
+
+the binding energy of reactants (OH\* and H\*).  
+
+In this work, we developed a three- dimensional (3D) nanostructured electrocatalyst consisting of two- dimensional (2D) NiO/Ni heterostructure nanosheets supported single- atom Pt attached on one- dimensional (1D) Ag nanowires (Ag NWs) conductive network (PtSA- NiO/Ni). Density functional theory (DFT) calculations reveal that the dual active sites consisting of metallic Ni sites and O vacancies modified NiO sites near the interfaces of NiO/Ni heterostructure in PtSA- NiO/Ni show the preferred adsorption affinity toward OH\* and H\*, respectively, which efficiently facilitates water adsorption and reaching a barrier- free water dissociation step with a lower energy barrier of 0.11 eV in Volmer step (step (i)) for PtSA- NiO/Ni in the alkaline condition compared with that of PtSA- NiO (0.34 eV) and PtSA- NiO (1.27 eV) catalysts. Additionally, anchoring Pt single atoms at the interfaces of NiO/Ni heterostructure induces more free electrons on Pt sites due to the elevated occupation of the Pt 5d orbital at Fermi level and the more suitable H binding energy ( \(\Delta G_{\mathrm{H}^*}\) , 0.07 eV) than that of Pt atoms at the NiO ( \(\Delta G_{\mathrm{H}^*}\) , 0.93 eV) and Ni ( \(\Delta G_{\mathrm{H}^*}\) , 0.26 eV), which efficiently promotes the H\* conversion and H2 desorption, thus accelerating overall alkaline HER. (step (ii)). Furthermore, the Ag NWs supported 3D morphology provides abundant active sites and accessible channels for charge transfer and mass transport. As a result, the fabricated PtSA- NiO/Ni catalyst exhibits outstanding HER activity with a quite lower overpotential of 26 mV at 10 mA cm- 2 in 1 M KOH. The mass activity of PtSA- NiO/Ni is 20.6 A mg- 1 Pt at the overpotential of 100 mV, which is 41 times greater than that of the commercial Pt/C catalyst, significantly outperforming the reported catalysts. This work provides a new design principle toward single- atom catalyst systems for efficient alkaline HER.  
+
+## Results  
+
+Synthesis and characterization of PtSA- NiO/Ni catalyst. The fabrication process of PtSA- NiO/Ni on Ag NWs is illustrated in Figure 1. In brief, the synthesized Ag NWs by a typical hydrothermal method<sup>34</sup> were first loaded on the flexible cloth to form a
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Schematic illustration of synthesis and water splitting mechanism of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (a) The synthesis process of Pt single atom anchored NiO/Ni heterostructure nanosheets on Ag nanowires network. (b) The mechanism of \(\mathrm{Pt_{SA} - NiO / Ni}\) network as an efficient catalyst towards large-scale water electrolysis in alkaline media. </center>  
+
+conductive network. Then Ni/NiO composite is attached to the Ag network by the facile electrodeposition process. \(^{35}\) In detail, the Ag NWs network loaded cloth is immersed in nickel acetate aqueous solution followed by an electrochemical process with - 3.0 V versus SCE (saturated calomel electrode) for 200 s (Figure S1), forming the uniformly distributed nanosheets on the Ag network (Figure S2). Transmission electron microscopy (TEM, Figure S3a- b) images, high- resolution TEM (HRTEM, Figure S3c) image, fast Fourier transform (FFT, Figure S3d), and elements mapping (Figure S4) images clearly show that the metallic Ni nanoparticles uniformly embed in amorphous NiO nanosheets. Besides, the X- ray diffraction (XRD, Figure S5) pattern shows that only metallic Ni signal without the peaks of NiO can be detected, and X- ray photoelectron spectroscopy (XPS, Figure S6) spectra suggest both metallic Ni and Ni oxide exists in Ni/NiO sample, further confirming the composition of metallic Ni on amorphous NiO. Interestingly, the deposited composition can be facilely controlled by performing various voltage in the nickel acetate aqueous solution. \(^{35}\) Specifically, as above discussion, a high voltage of - 3 V versus SCE will generate the Ni/NiO
+
+<--- Page Split --->
+
+composite on Ag NWs (NiO/Ni), whereas a lower voltage of - 1 V versus SCE could prepare the amorphous NiO on Ag NWs (NiO, Figure S7- 9). Besides, the pure metallic Ni on Ag network (Ni, Figure S10- 13) was fabricated by a traditional electrodeposition method with 1.2 V for 200 s in a mix solution containing 0.10 M NiCl2 and 0.09 M \(\mathrm{H}_3\mathrm{BO}_3\) . Afterward, the single- atom Pt immobilized NiO/Ni (PtSA- NiO/Ni) is obtained by sequentially electroreduction process with cyclic voltammetry in 1 M KOH solution containing low- concentration Pt metallic salts. Abundant voids and O vacancy defects at the surface- exposed interfaces of NiO/Ni heterostructure induced by crystal- lattice dislocation and phase transition<sup>36-38</sup> will provide efficient sites for trapping Pt single atom. The water dissociation of Volmer step in alkaline media is expected to be accelerated by O vacancies modified NiO near the interfaces interacted strongly with OH and metallic Ni interacted with H for H- OH bond destabilization (step (i)). Apture from the Volmer step, NiO/Ni heterostructure supported single- atom Pt sites could show more suitable H binding ability for the conversion and deabsorption of dissociated H (step (ii)), further accelerating overall HER kinetics of PtSA- NiO/Ni in an alkaline condition.  
+
+The phase evolution of samples is investigated by XRD pattern as shown in Figure 2a, in which no Pt characteristic peaks are detected, implying the absence of Pt cluster and particles in PtSA- NiO/Ni. The scanning electron microscopy (SEM, Figure 2b- c) images show the well- distributed and open 3D nanosheets morphology for PtSA- NiO/Ni. Compared with the original NiO/Ni (Figure S2), the exposed PtSA- NiO/Ni nanosheets morphology on Ag NWs should be attributed to the \(\mathrm{H}_2\) - assisted delamination effect during Pt electro- reduction process in alkaline condition,<sup>21,34</sup> which will provide more sites for Pt atoms immobilization and improve the HER performance. The scanning transmission electron microscopy (STEM, Figure S14) images suggest that the exfoliated nanosheets consist of few NiO/Ni layers for PtSA- NiO/Ni. The high- angle annular dark- field STEM (HAADF- STEM, Figure 2d) image displays bright spots along with the interfaces of NiO/Ni heterostructure, corresponding to heavy constituent atoms species, which efficiently confirms the immobilization of atomically dispersed Pt atoms in the NiO/Ni nanosheets. The magnified HAADF- STEM image (Figure 2e)
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Structural characterization of the fabricated \(\mathrm{Pt_{SA} - NiO / Ni}\) catalyst. (a) XRD patterns of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{NiO / Ni}\) , and Ag NWs. (b-c) SEM images of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (d) HAADF-STEM image of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (e-f) Magnified HAADF-STEM image of \(\mathrm{Pt_{SA} - NiO / Ni} \mathrm{and} \mathrm{g}\) the corresponding DFT simulated image, showing the atomically dispersed Pt atoms at Ni position (circles in (e)). (h) HRTEM images of \(\mathrm{Pt_{SA} - NiO / Ni}\) and the insert in (h) shows the related FFT image of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (i-j) Dark-field TEM images of \(\mathrm{Pt_{SA} - NiO / Ni}\) with different magnifications and (k-n) the mapping of the corresponding elements. </center>  
+
+suggests that the single Pt atoms are exactly immobilized at the interfaces of the NiO/Ni heterostructure. Based on these findings, a STEM simulation was performed to explore the atomic environment of Pt atom via the DFT- optimized structure (Figure 2f- g), and the simulated result suggests that the Pt atoms are fixed at the Ni positions by binding with O atom and Ni atoms near the interfaces of the NiO/Ni heterostructure. Further, the high- resolution TEM (HRTEM) shows one distinct lattice fringes of 0.18 nm, matching well with metallic (200) crystallographic planes (Figure 2h). The
+
+<--- Page Split --->
+
+selected- area electron diffraction pattern (inset in Figure 2h) shows four distinct rings: the red ring corresponds to the metallic Ni (200) plane, \(^{39}\) and the yellow rings with a highly diffused halo are assigned to the amorphous NiO phase. \(^{35,40}\) These results further confirm the formation of single- atom Pt anchored NiO/Ni composition, and the interfacial coupling of Pt single atom with NiO/Ni does not change the phase structure of NiO/Ni. Moreover, the elemental mapping (Figure 2i- n and Figure S15) shows that Pt atoms are uniformly dispersed throughout NiO/Ni nanosheets. Besides, as a comparison, Pt<sub>SA</sub>- NiO and Pt<sub>SA</sub>- Ni were fabricated under the same conditions as Pt<sub>SA</sub>- NiO/Ni but replacing NiO/Ni with NiO and Ni, respectively. The corresponding HAADF- STEM images (Figure S16) confirm the atomically dispersed Pt in the NiO and metallic Ni phase.  
+
+The electronic state evolution of the single Pt atoms in NiO/Ni, NiO, and Ni supports is explored by XPS as shown in Figure 3a. The Pt \(4f\) spectrums of Pt<sub>SA</sub>- NiO/Ni, Pt<sub>SA</sub>- NiO, and Pt<sub>SA</sub>- Ni are close to Pt<sup>0</sup> but show some positive shift with different extents compared with Pt foil, confirming the electrochemical reduction of PtCl<sub>6</sub><sup>2- </sup>and the electronic interaction by charge transfer from Pt sites to the supports (NiO/Ni, NiO, and Ni). \(^{41}\) Specifically, the Pt<sub>SA</sub>- NiO shows the largest positive shift in Pt \(4f\) spectrum, suggesting the maximum electron loss of Pt species. \(^{42,43}\) Besides, the fitting curve of Pt XPS spectrums display Pt(IV) species in the samples, which derives from the adsorbed PtCl<sub>6</sub><sup>2- </sup>ions on the surface of the sample. \(^{44,45}\) Further, the electronic state of Pt atoms in NiO/Ni, NiO, and Ni supports are further verified by performing X- ray absorption fine structure measurements. As shown in Figure 3b, the evolutions of Pt \(L_{3}\) - edge X- ray absorption near edge structure (XANES) spectra with different supports are distinguished, in which the intensity of white- line peaks corresponds to the transfer of the Pt \(2p_{3/2}\) core- electron to \(5d\) states, and thus is used as an indicator of Pt \(5d\) - band occupancy. \(^{46,47}\) The overall white- line intensity gradually decreases as the change of support from NiO, NiO/Ni to metallic Ni, corresponding to the increase of \(5d\) occupancy of Pt. Hence, higher \(5d\) occupancy indicates the less charge loss of the single- atom Pt after coordinating with the supports, which is consistent with the results of XPS analysis in Figure 3a.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. Electronic state and atomic structure characterization. (a) Pt \(4f\) spectra, (b) XANES spectra, and (c) calculated Pt oxidation states derived from \(\Delta\) XANES spectra of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) , and Pt foil is given as a reference. (d) Corresponding FT-EXAFS curves of Figure 3b. (e) EXAFS fitting curve of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) \(R\) -space. (f) EXAFS wavelet transform plots of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , and Pt foil. </center>  
+
+To quantitate the electronic state structural information, the white- line peak evolution of Pt can be clearly described by the differential XANES spectra ( \(\Delta\) XANES, Figure S17) by subtracting the spectra from that of Pt foil. The valence state of Pt can be quantitatively examined by the integration of the white- line peak in \(\Delta\) XANES spectra. As shown in Figure 3c, the average valence state of Pt increase from \(+0.29\) , \(+0.73\) , to \(+1.23\) for the \(\mathrm{Pt_{SA} - Ni}\) , \(\mathrm{Pt_{SA} - NiO / Ni}\) , and \(\mathrm{Pt_{SA} - NiO}\) catalysts, respectively. The evolution of the atomic coordination configuration of Pt was further revealed by extended X- ray absorption fine structure spectroscopy (EXAFS, Figure 3d), in which the typical Pt- Pt contribution peak of Pt foil at about \(2.7 \mathring{\mathrm{A}}\) is absent for the fabricated \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) catalysts, strongly confirming the single Pt atoms dispersion. Further, the first- shell EXAFS fitting of \(\mathrm{Pt_{SA} - NiO / Ni}\) sample (Figure 3e and Table S1) gives a coordination number (CN) of 1.3 for Pt- O contribution and 5.8 for Pt- Ni contribution. For \(\mathrm{Pt_{SA} - NiO}\) , the fitting results of EXAFS spectra suggested CN about
+
+<--- Page Split --->
+
+2.4 for Pt-O contributions and 2.1 for \(CN\) for Pt-Ni contributions. Whereas Pt-Ni contribution with 4.9 for \(CN\) and no Pt-O contributions are found in the fitting of \(\mathrm{Pt_{SA}}\) - Ni EXAFS spectra. Combining the DFT-optimized structure (Figure S18), the Pt atoms are mainly immobilized at the interfacial Ni positions by coordinating with one O atom and 5 Ni atoms in \(\mathrm{Pt_{SA}}\) - NiO/Ni, which is consistent with the conclusion of HAADF-STEM analysis (Figure 2d-g). To more precisely clarify the atomic dispersion and coordination conditions of Pt, the wavelet transform (WT) analysis was carried out due to its more efficient resolution ability in \(K\) spaces and radial distance, \(^{48,49}\) in which the atoms at similar coordination conditions and distances could be discriminated. \(^{50,51}\) As shown in Figure 3f, \(\mathrm{Pt_{SA}}\) - NiO/Ni displays a different intensity maximum with \(\mathrm{Pt_{SA}}\) - NiO and \(\mathrm{Pt_{SA}}\) - Ni, and especially, the intensity maximum at 7.6 \(\mathrm{\AA^{-1}}\) for \(\mathrm{Pt_{SA}}\) - NiO/Ni is lower than that of \(\mathrm{Pt_{SA}}\) - NiO (8.5 \(\mathrm{\AA^{-1}}\) ), but high than that of \(\mathrm{Pt_{SA}}\) - Ni (7.4 \(\mathrm{\AA^{-1}}\) ), further confirming the interfacial coordination conditions for Pt atoms immobilized in NiO/Ni. Besides, the intensity maximum at 11.5 \(\mathrm{\AA^{-1}}\) corresponding to Pt-Pt coordination is absent in the fabricated catalysts; further confirming the successful loading of single Pt atoms in Ni, NiO/Ni, and NiO supports.  
+
+Theoretical investigations. Based on the above structure analysis, theoretical investigations were performed to disclose the influences of the evolved coordinate configurations of the Pt atom on the electronic structure and catalytic activity of the catalysts. According to the HAADF- STEM and EXAFS measurements, the models for \(\mathrm{Pt_{SA}}\) - NiO/Ni were shown in Figure 4a. Based on the calculated charge density distributions, an increased charge density area along the interface of NiO/Ni heterostructure was induced (Figure S19a- b). After coupling Pt single atom with NiO/Ni heterostructure, an electronic structure redistribution at the interfaces of the heterostructure is caused due to the different electronegativity of atoms (3.44 for O atom, 1.91 for Ni, and 2.28 for Pt). Especially, charge delocalizing from Pt to the bonded O atom and charge localizing from adjacent Ni atoms to Pt are displayed. Consequently, a locally enhanced electric field with a half- moon shape area around the Pt site was generated (Figure S19c- d), which is more intensive than that of \(\mathrm{Pt_{SA}}\) - NiO
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Theoretical investigations. Computational models and localized electric field distribution of (a) \(\mathrm{Pt_{SA} - NiO / Ni}\) , (b) \(\mathrm{Pt_{SA} - NiO}\) and (c) \(\mathrm{Pt_{SA} - Ni}\) . (d) Calculated PDOS of \(\mathrm{NiO / Ni}\) and \(\mathrm{Pt_{SA} - NiO / Ni}\) , with aligned Fermi level. (e) Calculated Pt 5d band of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) . (f) The orbital alignment of the surficial sites for \(\mathrm{Pt_{SA} - NiO / Ni}\) binding with \(\mathrm{H_2O}\) molecule. (g) Calculated OH-binding energies \((\Delta E_{\mathrm{OH}})\) and H-binding energies \((\Delta E_{\mathrm{H}})\) for Ni, pure NiO, and O vacancies modified NiO surface. (h) Calculated energy barriers of water dissociation kinetic and (i) adsorption free energies of \(\mathrm{H^*}\) on the surface of the \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) catalysts, respectively. </center>  
+
+(Figure 4b) and \(\mathrm{Pt_{SA} - Ni}\) (Figure 4c), suggesting Pt single atom coupled with NiO/Ni heterostructure could possess the more free electrons to promote the adsorbed H conversion and \(\mathrm{H}_2\) evolution. \(^{22,44}\) Moreover, the projected density of states (PDOS, Figure 4d, and Figure S20) of the single- atom Pt immobilized NiO/Ni heterostructure shows higher occupation than that of the pure NiO/Ni near the Fermi level, suggesting a promoted electron transfer and higher conductivity of \(\mathrm{Pt_{SA} - NiO / Ni}\) . The contrast between the PDOS of NiO/Ni and \(\mathrm{Pt_{SA} - NiO / Ni}\) reveals that the increased DOS of the \(\mathrm{Pt_{SA} - NiO / Ni}\) near the Fermi level mainly derives from the contribution of Pt \(d\) orbitals (Figure 4d). These results suggest that the NiO/Ni heterostructure coupled single- atom Pt can effectively enhance the total \(d\) - electron domination of the catalyst near the Fermi level, which will benefit the activation of \(\mathrm{H}_2\mathrm{O}\) and lead to energetically catalytic activity. \(^{21,52}\) Moreover, the \(d\) - band features of the Pt atom in NiO/Ni, NiO and Ni
+
+<--- Page Split --->
+
+coordinated configurations are investigated. The wider \(5d\) band and higher density near the Fermi level for NiO/Ni supported Pt atom than that of \(\mathrm{Pt_{SA} - NiO}\) and \(\mathrm{Pt_{SA} - Ni}\) ((Figure 4e and Figure S21) suggest that the NiO/Ni coupled Pt atom can induce more free electrons near Pt sites than \(\mathrm{Pt_{SA} - NiO}\) and \(\mathrm{Pt_{SA} - Ni}\) , which is more favorable for the H reactants adsorption and transfer. Besides, the Pt- \(5d\) band of \(\mathrm{Pt_{SA} - NiO / Ni}\) also shows a substantially broad range for overlapping with H- \(1s\) and \(\mathrm{H_2O - 2p\pi}\) orbitals (Figure 4f). Therefore, the Pt- site could play a protecting role for stabilizing the Ni valence state and a distributive role by binding OH and H species to low the deactivation of absorption sites in case of over- binding of intermediates on the active sites for NiO/Ni heterostructure coupled single- atom Pt. \(^{53}\)  
+
+Based on the above finding, we further explore the reaction barrier of the fabricated catalysts for \(\mathrm{H_2O}\) splitting in alkaline conditions, consisting of the dissociation of \(\mathrm{H_2O}\) molecule of Volmer step and the subsequent conversion of H to \(\mathrm{H_2}\) , which mainly depends on how OH and H bond to the active sites on the surface of the catalysts. \(^{54}\) We found that both H and OH bind weakly to the pure NiO surface. While metallic Ni surface shows a preference for stabilizing H, and O vacancies modified NiO facilitates the adsorption of OH species (Figure 4g and Figure S22). For NiO/Ni composition, the O vacancies on the interfaces of the NiO/Ni heterostructure (Figure S23) are induced by the crystal- lattice dislocation and phase transition. \(^{36,37,55}\) As an integration, NiO/Ni coupled single- atom Pt catalyst demonstrates the strongest \(\mathrm{H_2O}\) adsorption ability (Figure S24) and largest energy release of - 0.24 eV for water dissociation in Volmer step (Figure 4h). Moreover, \(\mathrm{Pt_{SA} - NiO / Ni}\) hybrid catalyst only need the minimum energy barriers (0.11 eV) for the dissociation of \(\mathrm{H_2O}\) into OH and H under the assistance of NiO/Ni interfaces (Figure S25), confirming the critical role of surface- exposed NiO/Ni interfaces for the \(\mathrm{H_2O}\) dissociation of Volmer step in alkaline media. In the subsequent step, the NiO/Ni supported single- atom Pt sites at the NiO/Ni interfaces act as the proton- acceptor for the recombination of the dissociated proton (H\*) and \(\mathrm{H_2}\) evolution due to its near- zero H binding energy (0.07 eV, Figure 4i and Figure S26) and strong electron supply capacity deriving from locally enhanced charge distribution (Figure 4a) and the higher occupation of Pt \(5d\) band near Fermi lever
+
+<--- Page Split --->
+
+(Figure 4e). Consequently, the overall steps of \(\mathrm{Pt_{SA} - NiO/Ni}\) hybrid catalyst for HER in alkaline media are significantly accelerated.  
+
+Electrocatalytic alkaline HER performances. Based on the structural characterizations and theoretical investigations, the Pt single- atom catalyst coupled with NiO/Ni heterostructure possesses the best intrinsic HER activity in alkaline media among the fabricated catalysts. Thus, the electrocatalytic activities of \(\mathrm{Pt_{SA} - NiO/Ni}\) for alkaline HER was measured in \(1\mathrm{M}\) KOH solution. As a comparison, the HER performance of \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , NiO/Ni, and \(20\%\) Pt/C were also tested under the same conditions. As shown in Figure 5a, the \(\mathrm{Pt_{SA} - NiO/Ni}\) shows the highest HER performance among all catalysts, and only needs a quite low overpotential of 26 and 85 mV to achieve the current density of 10 and \(100\mathrm{mAcm}^{- 2}\) , respectively, significantly superior to the \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , NiO/Ni and the Pt/C catalyst (Figure 5b). Moreover, the mass activity of \(\mathrm{Pt_{SA} - NiO/Ni}\) normalized to the loaded Pt mass (1.14 wt%, inductively coupled plasma- mass spectrometry) at an overpotential of \(100\mathrm{mV}\) is 20.6 \(\mathrm{Amg^{- 1}}\) , which is 2.4, 2.3, and 41.2 times greater than that of \(\mathrm{Pt_{SA} - NiO}\) (8.5 \(\mathrm{Amg^{- 1}}\) ), \(\mathrm{Pt_{SA} - Ni}\) (9.0 \(\mathrm{Amg^{- 1}}\) ) and the commercial Pt/C catalyst (0.5 \(\mathrm{Amg^{- 1}}\) ), respectively. These results suggest that single Pt atoms coupled with NiO/Ni can extremely maximize the alkaline HER activity of Pt- based catalysts, leading to a significant reduction in cost. Additionally, the \(\mathrm{Pt_{SA} - NiO/Ni}\) exhibits a smaller Tafel slope of \(27.07\mathrm{mVdec^{- 1}}\) than \(\mathrm{Pt_{SA} - NiO}\) (37.54 mV dec \(^{- 1}\) ), \(\mathrm{Pt_{SA} - Ni}\) (37.32 mV dec \(^{- 1}\) ), NiO/Ni (58.67 mV dec \(^{- 1}\) ), and Pt/C catalyst (41.69 mV dec \(^{- 1}\) ), which suggests a typical Volmer- Tafel mechanism for alkaline HER and implies that the rate- determining step of \(\mathrm{Pt_{SA} - NiO/Ni}\) is the \(\mathrm{H_2}\) desorption (Tafel step) rather than the \(\mathrm{H_2O}\) dissociation (Volmer step). \(^{56,57}\) Besides, \(\mathrm{Pt_{SA} - NiO/Ni}\) catalyst exhibits a 2.0 and, 2.4- fold enhancement in the double- layer capacitance \((C_{\mathrm{dl}})\) over \(\mathrm{Pt_{SA} - NiO}\) and \(\mathrm{Pt_{SA} - Ni}\) (Figure S27), respectively, suggesting the favorable nanostructure with more sites for Pt atoms immobilization and HER. Furthermore, the charge transfer resistance \((R_{\mathrm{ct}})\) of \(\mathrm{Pt_{SA} - NiO/Ni}\) (0.61 ohm, Figure 5e) is extremely low than that of \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , and NiO/Ni catalysts, which mainly originates from the introduction of Ag NWs and enhanced electronic structure of single
+
+<--- Page Split --->
+
+Pt atoms coupled with NiO/Ni.  
+
+For real applications, HER catalyzing stability is another essential factor. As present in Figure 5f, the \(\mathrm{Pt_{SA} - NiO / Ni}\) shows high durability in the alkaline electrolyte with negligible loss in HER performance for 5000 cycles or 30 hours. The characterizations of \(\mathrm{Pt_{SA} - NiO / Ni}\) after the stability test, including HAADF- STEM image, elements mapping, and double- layer capacitance (Figure S28- 30), suggest the negligible structure changes and single- atom dispersion for \(\mathrm{Pt_{SA} - NiO / Ni}\) after long- term alkaline HER. Moreover, the turnover frequencies (TOFs) per Pt atom site are analyzed, and the TOFs of \(\mathrm{Pt_{SA} - NiO / Ni}\) (5.71 \(\mathrm{H_2 s^{- 1}}\) ) is 2.02, 1.99, and 38.06 times higher than that of \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , and \(\mathrm{Pt / C}\) catalyst, respectively (Figure 5g). To our knowledge, the electrocatalytic HER performances of our \(\mathrm{Pt_{SA} - NiO / Ni}\) catalyst in the alkaline media are almost optimal among the reported SACs, and are comparable with the performances of catalysts in acid media (Figure 5h and Table S2), confirming the advance by the constructing single- Pt sites in NiO/Ni hybrid system.  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5. Electrocatalytic alkaline HER performances of the catalysts in 1 M KOH electrolyte. (a) HER polarization curves of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , NiO/Ni, and \(\mathrm{Pt / C}\) . (b) The comparison </center>
+
+<--- Page Split --->
+
+of overpotentials required to achieve \(10\mathrm{mAcm}^{- 2}\) for various catalysts. (c) The mass activity of the Pt- based catalysts. (d) Corresponding Tafel slope originated from LSV curves. (e) EIS (Electrochemical Impedance Spectroscopy) Nyquist plots of the catalysts. (f) Stability test of \(\mathrm{Pt_{SA}}\) - NiO/Ni through cyclic potential scanning and chronoamperometry method (Inset in f). (g) TOFs plots of the Pt- based electrocatalysts. (h) Comparison of the HER activity for \(\mathrm{Pt_{SA}}\) - NiO/Ni with reported catalysts, originating from Table S2.  
+
+## Discussion  
+
+In summary, we reported a novel single- atom Pt \(\mathrm{(Pt_{SA})}\) immobilized NiO/Ni heterostructure nanosheets on Ag NWs network nanocomposite by the facile electrodeposition strategy, which serves as an efficient electrocatalyst for vigorous hydrogen production in alkaline media. Theoretical calculations revealed that the Pt SACs coupled with NiO/Ni heterostructure could efficiently tailoring water dissociation energy for accelerating alkaline HER. In particular, the dual active sites consisting of metallic Ni sites and O vacancies modified NiO sites near the interfaces of NiO/Ni have the preferred adsorption affinity toward both \(\mathrm{OH^*}\) and \(\mathrm{H^*}\) , which facilitates water adsorption and reaches a barrier- free water dissociation step with the lowest energy barrier of \(0.11\mathrm{eV}\) in Volmer step (step (i)) for \(\mathrm{Pt_{SA}}\) - NiO/Ni compared with that of \(\mathrm{Pt_{SA}}\) - NiO (0.34 eV) and \(\mathrm{Pt_{SA}}\) - NiO (1.27 eV) catalysts. Besides, fixing Pt atoms at the NiO/Ni interfaces induce a higher occupation of the Pt \(5d\) band at the Fermi level and the more suitable H binding energy \((\Delta G_{\mathrm{H}^*}, 0.07\mathrm{eV})\) than that of Pt atoms at the NiO \((\Delta G_{\mathrm{H}^*}, 0.93\mathrm{eV})\) and Ni \((\Delta G_{\mathrm{H}^*}, 0.26\mathrm{eV})\) , which efficiently promotes the \(\mathrm{H^*}\) conversion and \(\mathrm{H}_2\) desorption, thus accelerating overall alkaline HER. The further enhancement of alkaline HER performance was achieved by introducing Ag NWs network into 2D \(\mathrm{Pt_{SA}}\) - NiO/Ni nanosheets to construct a seamlessly conductive 3D nanostructure. The unique nanostructural feature and highly conductive Ag NWs network provide abundant active sites and accessible channels for electron transfer and mass transport. Consequently, the 3D \(\mathrm{Pt_{SA}}\) - NiO/Ni catalyst shows outstanding HER performances in alkaline conditions with a quite low overpotential of \(26\mathrm{mV}\) at a current density of \(10\mathrm{mAcm}^{- 2}\) and extremely high mass activity of \(20.6\mathrm{Amg}^{- 1}\) Pt in \(1\mathrm{MKOH}\) , significantly outperforming the reported catalysts. This study opens an efficient avenue for the advance of single- atom catalysts by introducing a water dissociation kinetic-
+
+<--- Page Split --->
+
+oriented material system.  
+
+## Methods  
+
+Synthesis of Ag NWs. An oil bath method was used to synthesize Ag NWs according to our previous report. \(^{58}\) Specifically, a mix solution consisting of ethylene glycol, \(\mathrm{FeCl}_3\) (7.19 mM), \(\mathrm{AgNO}_3\) (0.051 M), and polyvinylpyrrolidone (0.012 M) was heat and maintained under an oil bath pan with \(110^{\circ}\mathrm{C}\) for 12 hours. After that, the generated precipitate was washed with acetone and alcohol to get the pure Ag NWs. Subsequently, the Ag NWs were uniformly dispersed on a flexible cloth fabric by spray coating technology to fabricate a conductive network.  
+
+Synthesis of NiO/Ni on Ag NWs. Ni/NiO is grown on Ag NWs network by a facile electrodeposition process in the aqueous electrolyte of \(20\mathrm{mM}\mathrm{C}_4\mathrm{H}_6\mathrm{NiO}_4\cdot 4\mathrm{H}_2\mathrm{O}\) according to the recent report. \(^{35}\) The electrodeposition process was performed by chronoamperometry method with - 3 V vs SCE for 200 s under a standard three- electrode system, in which graphite sheet acted as a counter electrode, SCE acted as a reference electrode, and the fabricated Ag NWs network loaded on the cloth was directly used as working electrode. The obtained samples were washed with deionized water and then dried at room temperature.  
+
+Synthesis of NiO on Ag NWs. NiO is grown on Ag NWs network by the electrodeposition process with - 1 V vs SCE for 600 s in an aqueous electrolyte of 20 mM \(\mathrm{C}_4\mathrm{H}_6\mathrm{NiO}_4\cdot 4\mathrm{H}_2\mathrm{O}\) . The obtained samples were washed with deionized water and then dried at room temperature.  
+
+Synthesis of Ni on Ag NWs. Metallic Ni is grown on Ag NWs network by the electrodeposition process in an aqueous solution consisting of \(0.10\mathrm{M}\mathrm{NiCl}_2\) , \(0.09\mathrm{M}\mathrm{H}_3\mathrm{BO}_3\) , and a solvent containing ethanol and deionized water with 2:5 in volume ratio. The electrodeposition process was performed by chronoamperometry with - 1.2 V vs SCE for 200 s. The obtained samples were washed with deionized water and then dried at room temperature.
+
+<--- Page Split --->
+
+Synthesis of \(\mathbf{PtsA - NiO / Ni}\) on Ag NWs. \(\mathrm{PtsA - NiO / Ni}\) on Ag NWs was fabricated by the electrochemical reduction process in the three- electrode system, in which the fabricated \(\mathrm{NiO / Ni}\) on Ag NWs was performed as the working electrode, graphite sheet acted as a counter electrode, saturated calomel electrode acted as a reference electrode. The corresponding electrochemical process was carried out by multi- cycle cathode polarization in \(1\mathrm{M}\) KOH solution containing \(50\mu \mathrm{M}\mathrm{H}_2\mathrm{PtCl}_6\) with a scan rate of \(50\mathrm{mV}\) \(\mathrm{s}^{- 1}\) between 0 V and - 0.50 V versus reversible hydrogen electrode (RHE) for 200 cycles.  
+
+Synthesis of \(\mathbf{PtsA - NiO}\) on Ag NWs. \(\mathrm{PtsA - NiO}\) on Ag NWs were fabricated by multicycle cathode polarization in \(1\mathrm{M}\) KOH solution containing \(50\mu \mathrm{M}\mathrm{H}_2\mathrm{PtCl}_6\) with a scan rate of \(50\mathrm{mV}\mathrm{s}^{- 1}\) between 0 V and - 0.50 V versus RHE for 200 cycles.  
+
+Synthesis of \(\mathbf{PtsA - Ni}\) on Ag NWs. \(\mathrm{PtsA - Ni}\) on Ag NWs were fabricated by multicycle cathode polarization in \(1\mathrm{M}\) KOH solution containing \(50\mu \mathrm{M}\mathrm{H}_2\mathrm{PtCl}_6\) with a scan rate of \(50\mathrm{mV}\mathrm{s}^{- 1}\) between 0 V and - 0.50 V versus RHE for 200 cycles.  
+
+Characterizations. The morphology measurement of the synthesized catalysts was performed by SEM (GeminiSEM 300). HRTEM images, HAADF- STEM images, and STEM- EDX mapping images were obtained by a TEM coupled with an energy spectrum analyzer (JEOL JEM2100). The Pt contents in the catalysts were measured by inductively coupled plasma optical emission spectrometry (ICP- OES). The XPS spectra of elements were tested by a surface analysis system (ESCALAB250Xi). The phase and crystal information were obtained by Cu \(K\alpha\) radiation in an X- ray diffractometer (XRD, Bruker, D8 Advance Davinci). The EXAFS measurement of the \(\mathrm{PtsA - NiO / Ni}\) , \(\mathrm{PtsA - NiO}\) , and \(\mathrm{PtsA - NiO / Ni}\) at the Pt \(L_3\) - edge was performed at 1W1B station at the Beijing Synchrotron Radiation Facility (BSRF). Data analysis and fitting were performed with Athena and Artemis in the Demeter package.  
+
+Electrochemical measurements. All electrochemical measurements were finished by an electrochemical workstation (CHI 660E) with a three- electrode configuration, in which fabricated catalysts were directly employed as the working electrode, graphite sheet acted as a counter electrode, saturated calomel electrode acted as a reference
+
+<--- Page Split --->
+
+electrode. All the presented potential in this work was transferred to RHE according to an experimental method. \(^{59}\) LSV with \(95\%\) iR- corrections were tested under the potential range from 0.05 to - 0.5 V and the scan rate of \(5\mathrm{mV}\mathrm{s}^{- 1}\) . EIS was obtained by a frequency range from \(100\mathrm{k}\) to \(0.1\mathrm{Hz}\) with an overpotential of \(230\mathrm{mV}\) vs RHE. For the preparation of 3D Pt/C@Ni foam, \(5\mathrm{mg}20\mathrm{wt}\%\) Pt/C was dispersed in \(0.9\mathrm{mL}\) alcohol containing \(0.1\mathrm{mL}5\mathrm{wt}\%\) Nafion solution to form a homogeneous ink. Then, the obtained ink was coated on the Ni foam and dried in air to form a porous Pt/C@Ni foam electrode.  
+
+DFT theoretical calculations. All the structural optimizations, charge density difference analysis, Bader charge analysis, and energy calculations were carried out based on DFT as implemented in the Vienna Ab- initio Simulation Package (VASP). \(^{60 - }\) \(^{62}\) The projector- augmented- wave (PAW) method was implemented to calculate the interaction between the ionic cores and valence electrons. \(^{63,64}\) The Perdew- Burke- Ernzerhof approach of spin- polarized generalized gradient approximation (GGA- PBE) was used to describe the exchange- correlation energy. \(^{65}\) Calculations were performed with the cut- off plane- wave kinetic energy of \(500\mathrm{eV}\) , and \(8\times 4\times 1\) \(k\) - mesh grids were employed for the integration of the Brillouin zone. Electronic relaxation was undertaken to utilize the conjugate- gradient (CG) method \(^{66}\) with the total energy convergence criterion being \(10^{- 5}\mathrm{eV}\) . Geometry optimization was employed by the quasi- Newton algorithm \(^{67,68}\) until all the residual forces on unconstrained atoms less than \(0.01\mathrm{eV / \AA}\) . Climbing image nudge elastic band (CI- NEB) calculations \(^{69}\) were employed for finding transition barriers with the initial configuration of \(\mathrm{H}_2\mathrm{O}\) absorbed on the catalyst surface and final configuration of \(\mathrm{OH} + \mathrm{H}\) absorbed on the catalyst surface. To ensure the initial configuration correctly, an \(\mathrm{H}_2\mathrm{O}\) molecule was deposited on the catalyst surface and relaxed for calculating its local minimum total energy on different sites, and the last one is the initially stable configuration. The final configuration is also found by relaxing \(\mathrm{OH}\) and \(\mathrm{H}\) near the \(\mathrm{H}_2\mathrm{O}\) absorbed site of the initial configuration. Next, The equation for calculating adsorption enthalpy \(\Delta E_{\mathrm{H}^*}\) as the following:
+
+<--- Page Split --->
+
+\[\Delta E_{\mathrm{H}^*}{=}E_{\mathrm{slab + H}}{-}E_{\mathrm{slab}}{-}\frac{1}{2} E_{\mathrm{H}_2}\]  
+
+Where the \(E_{\mathrm{slab + H}}\) is the total enthalpy of H adsorbing on the catalysts, the enthalpy of the catalysts is \(E_{\mathrm{slab}}\) , and the \(\mathrm{H}_2\) enthalpy is \(E_{\mathrm{H}_2}\) .  
+
+The H and \(\mathrm{H}_2\mathrm{O}\) absorbing on the slabs were investigated by comparing the formation energy of different sites. The equation for calculating adsorption enthalpy \(\Delta E_{\mathrm{H}^*}\) as the following:  
+
+\[\Delta E_{\mathrm{H}^*}{=}E_{\mathrm{slab + H}}{-}E_{\mathrm{slab}}{-}\frac{1}{2} E_{\mathrm{H}_2}\]  
+
+Where the \(E_{\mathrm{slab + H}}\) is the total enthalpy of H adsorbing on the catalysts, enthalpy of the catalysts is \(E_{\mathrm{slab}}\) , the \(\mathrm{H}_2\) enthalpy is \(E_{\mathrm{H}_2}\) . As similar, the equation for calculating the \(\mathrm{H}_2\mathrm{O}\) adsorption enthalpy \(\Delta E_{\mathrm{H}_2\mathrm{O}^*}\) as the following:  
+
+\[\Delta E_{\mathrm{H}_2\mathrm{O}^*}{=}E_{\mathrm{slab + H}_2\mathrm{O}^-}E_{\mathrm{slab}^-}E_{\mathrm{H}_2\mathrm{O}^*}\]  
+
+The free energy of adsorbed H and \(\mathrm{H}_2\mathrm{O}\) as follows:  
+
+\[\Delta G_{\mathrm{H}^*}{=}\Delta E_{\mathrm{H}^*}{+}\Delta E_{\mathrm{ZPE}}{-}T\Delta S\] \[\Delta G_{\mathrm{H}_2\mathrm{O}^*}{=}\Delta E_{\mathrm{H}_2\mathrm{O}^*}{+}\Delta E_{\mathrm{ZPE}}{-}T\Delta S\]  
+
+where \(\Delta E_{\mathrm{H}^*}\) represent the H adsorption energy and \(\Delta E_{\mathrm{H}_2\mathrm{O}^*}\) represent the \(\mathrm{H}_2\mathrm{O}\) adsorption energy, and \(\Delta E_{\mathrm{ZPE}}\) represents the difference related to the zero- point energy between the gas phase and the adsorbed state.  
+
+## Acknowledgments  
+
+This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 52070006, 11804012), the Scientific and Technological Development Project of the Beijing Education Committee (No. KZ201710005009), and the Beijing Municipal Education Commission (Grant No. KM201910005009).  
+
+## Notes and references  
+
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+<--- Page Split --->
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+
+<--- Page Split --->
+
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+
+<--- Page Split --->
+
+## Figures  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+Schematic illustration of synthesis and water splitting mechanism of PtSA- NiO/ Ni. (a) The synthesis process of Pt single atom anchored NiO/ Ni heterostructure nanosheets on Ag nanowires network. (b) The mechanism of PtSA- NiO/ Ni network as an efficient catalyst towards large- scale water electrolysis in alkaline media.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+Structural characterization of the fabricated PtSA- NiO/Ni catalyst. (a) XRD patterns of PtSA- NiO/Ni, NiO/Ni, and Ag NWs. (b- c) SEM images of PtSA- NiO/Ni. (d) HAADF- STEM image of PtSA- NiO/Ni. (e- f) Magnified HAADF- STEM image of PtSA- NiO/Ni and (g) the corresponding DFT simulated image, showing the atomically dispersed Pt atoms at Ni position (circles in (e)). (h) HRTEM images of PtSA- NiO/Ni and the insert in (h) shows the related FFT image of PtSA- NiO/Ni. (i- j) Dark- field TEM images of PtSA- NiO/Ni with different magnifications and (k- n) the mapping of the corresponding elements.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>  
+
+Electronic state and atomic structure characterization. (a) Pt 4f spectra, (b) XANES spectra, and (c) calculated Pt oxidation states derived from \(\Delta\) XANES spectra of PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni, and Pt foil is given as a reference. (d) Corresponding FT- EXAFS curves of Figure 3b. (e) EXAFS fitting curve of PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni R- space. (f) EXAFS wavelet transform plots of PtSA- NiO/Ni, PtSA- NiO, PtSA- Ni, and Pt foil.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4 </center>  
+
+Theoretical investigations. Computational models and localized electric field distribution of (a) PtSAniO/Ni, (b) PtSA- NiO and (c) PtSA- Ni. (d) Calculated PDOS of NiO/Ni and PtSA- NiO/Ni, with aligned Fermi level. (e) Calculated Pt 5d band of PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni. (f) The orbital alignment of the surficial sites for PtSA- NiO/Ni binding with H2O molecule. (g) Calculated OH- binding energies (ΔEOH) and H- binding energies (ΔEH) for Ni, pure NiO, and O vacancies modified NiO surface. (h) Calculated energy barriers of water dissociation kinetic and (i) adsorption free energies of H\* on the surface of the PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni catalysts, respectively.
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5 </center>  
+
+Electrocatalytic alkaline HER performances of the catalysts in 1 M KOH electrolyte. (a) HER polarization curves of PtSA- NiO/Ni, PtSA- NiO, PtSA- Ni, NiO/Ni, and Pt/C. (b) The comparison of overpotentials required to achieve 10 mA cm- 2 for various catalysts. (c) The mass activity of the Pt- based catalysts. (d) Corresponding Tafel slope originated from LSV curves. (e) EIS (Electrochemical Impedance Spectroscopy) Nyquist plots of the catalysts. (f) Stability test of PtSA- NiO/Ni through cyclic potential scanning and chronoamperometry method (Inset in f). (g) TOFs plots of the Pt- based electrocatalysts. (h) Comparison of the HER activity for PtSA- NiO/Ni with reported catalysts, originating from Table S2.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- Supportinginformation.docx
+
+<--- Page Split --->

preprint/preprint__5fbf0de3b241f4ee45e767edca02b1abbbc24f76a5f988443d4aa0a5a8adec71/preprint__5fbf0de3b241f4ee45e767edca02b1abbbc24f76a5f988443d4aa0a5a8adec71_det.mmd

@@ -0,0 +1,458 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 940, 243]]<|/det|>
+# Tailoring Water Dissociation Energy by Platinum Single-Atom Catalyst Coupled with Transition Metal/metal Oxide Heterostructure for Accelerating Alkaline Hydrogen Evolution Reaction  
+
+<|ref|>text<|/ref|><|det|>[[44, 262, 400, 283]]<|/det|>
+Changbao Han ( cban@bjut.edu.cn )  
+
+<|ref|>text<|/ref|><|det|>[[52, 286, 338, 305]]<|/det|>
+Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 310, 338, 352]]<|/det|>
+Kailing Zhou Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 357, 338, 399]]<|/det|>
+Qianqian Zhang Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 403, 338, 445]]<|/det|>
+Jingbing Liu Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 450, 338, 491]]<|/det|>
+Hui Yan Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 496, 900, 560]]<|/det|>
+Xiaoxing Ke Institute of Microstructure and Properties of Advanced Materials, Beijing University of Technology, Beijing 100124  
+
+<|ref|>text<|/ref|><|det|>[[44, 565, 338, 607]]<|/det|>
+Zelin Wang Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 611, 338, 653]]<|/det|>
+Hao Wang Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 658, 338, 700]]<|/det|>
+Changhao Wang Beijing University of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 704, 688, 747]]<|/det|>
+Yuhong Jin Faculty of Materials and Manufacturing, Beijing University of Technology  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 787, 102, 805]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 824, 900, 867]]<|/det|>
+Keywords: single- atom catalysts (SACs), NiO/Ni heterostructure, water dissociation, alkaline media, hydrogen evolution reactions (HER)  
+
+<|ref|>text<|/ref|><|det|>[[44, 884, 322, 904]]<|/det|>
+Posted Date: February 3rd, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 922, 463, 942]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 155535/v1
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 44, 910, 87]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 123, 913, 167]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on June 18th, 2021. See the published version at https://doi.org/10.1038/s41467-021-24079-8.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[147, 88, 850, 268]]<|/det|>
+# Tailoring Water Dissociation Energy by Platinum Single-Atom Catalyst Coupled with Transition Metal/metal Oxide Heterostructure for Accelerating Alkaline Hydrogen Evolution Reaction  
+
+<|ref|>text<|/ref|><|det|>[[148, 306, 849, 348]]<|/det|>
+Kai Ling Zhou,†a Zelin Wang,†a Chang Bao Han,∗a Xiaoxing Ke,∗a Changhao Wang,a Yuhong Jin, a Qianqian Zhang, a Jingbing Liu, a Hao Wang∗a and Hui Yan a  
+
+<|ref|>text<|/ref|><|det|>[[147, 382, 840, 468]]<|/det|>
+a Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing 100124, P. R. China  E- mail: cbhan@bjut.edu; kexiaoxing@bjut.edu.cn; haowang@bjut.edu.cn  † These authors contributed equally.  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 496, 240, 514]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[147, 527, 852, 909]]<|/det|>
+High- activity catalysts in alkaline media are compelling for durable hydrogen evolution reaction (HER). Single- atom catalysts (SACs) provide an effective approach to reduce the amount of precious metals meanwhile maintain their catalytic activity. However, the sluggish activity of SACs for water dissociation in alkaline media has extremely hampered advances in highly efficient hydrogen production. Herein, we developed a platinum SAC immobilized NiO/Ni heterostructure (Pt<sub>SA</sub>- NiO/Ni) as an alkaline HER catalyst. It was found that Pt SACs coupled with NiO/Ni heterostructure enable the tunable binding abilities of hydroxyl ions (OH\*) and hydrogen (H\*), which efficiently tailors the water dissociation energy for accelerating alkaline HER. In particular, the dual active sites consisting of metallic Ni sites and O vacancies modified NiO sites near the interfaces of NiO/Ni in Pt<sub>SA</sub>- NiO/Ni have preferred adsorption affinity for H\* and OH\* groups, respectively, which efficiently lowers the energy barrier of water dissociation of Volmer step. Moreover, anchoring Pt single atoms at the interfaces of NiO/Ni heterostructure induces more free electrons on Pt sites due to the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 852, 357]]<|/det|>
+elevated occupation of the Pt \(5d\) orbital at the Fermi level and reaches a near- zero H binding energy ( \(\Delta G_{\mathrm{H}^*}\) , 0.07 eV), which further promotes the H\* conversion and \(\mathrm{H}_2\) evolution. Further enhancement of alkaline HER performance was achieved by constructing \(\mathrm{Pt_{SA}}\) - NiO/Ni nanosheets on the Ag nanowires to form a hierarchical threedimensional (3D) morphology that provides abundant active sites and accessible channels for charge transfer and mass transport. Consequently, the fabricated \(\mathrm{Pt_{SA}}\) - NiO/Ni catalyst displays extremely high alkaline HER performances with a quite high mass activity of \(20.6\mathrm{A}\mathrm{mg}^{- 1}\) for Pt at the overpotential of \(100\mathrm{mV}\) , which is 41 times greater than that of the commercial Pt/C catalyst, significantly outperforming the reported catalysts.  
+
+<|ref|>text<|/ref|><|det|>[[148, 390, 853, 436]]<|/det|>
+Keywords: single- atom catalysts (SACs), NiO/Ni heterostructure, water dissociation, alkaline media, hydrogen evolution reactions (HER)  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 464, 283, 482]]<|/det|>
+## Introduction.  
+
+<|ref|>text<|/ref|><|det|>[[147, 496, 852, 905]]<|/det|>
+Hydrogen \(\mathrm{(H_2)}\) has been regarded as the most promising energy carrier alternative to fossil fuels due to the environmental friendliness nature and high gravimetric energy density. \(^{1,2}\) Electrocatalytic water splitting powered by wind energy or solar technologies for hydrogen generation is considered a sustainable strategy. \(^{3}\) For an optimal electrocatalyst, minimizing the energy barrier and increasing the active sites are desirable for boosting the hydrogen evolution reaction (HER). \(^{4 - 6}\) Despite the significant progress that has been presented in nonprecious catalysts, the HER performances are still second to platinum (Pt)- based materials due to its optimal binding ability with hydrogen. \(^{7 - 10}\) However, the high cost and scarcity of Pt extremely hamper its large- scale application in electrolyzers for \(\mathrm{H}_2\) production. Single- atom catalysts (SACs) provide an effective approach to reduce the amount of Pt meanwhile maintain its high intrinsic activity. \(^{11 - 14}\) Recently, electrocatalytic HER in an alkaline condition has attracted more attention because catalyst systems are generally unstable in acidic media, resulting in safety and cost concerns in practice. Unfortunately, the alkaline HER activity of Pt- based catalysts is approximately two orders of magnitude lower than that in the acidic
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 852, 330]]<|/det|>
+condition caused by the high activation energy of the water dissociation step. \(^{15 - 18}\) Alkaline HER process involves two electrochemical reaction steps: (step (i)) electron- coupled \(\mathrm{H}_2\mathrm{O}\) dissociation to generate adsorbed hydrogen hydroxyl (OH\*) and hydrogen (H\*) (Volmer step), and (step (ii)) the concomitant interaction of dissociated H\* into molecular \(\mathrm{H}_2\) (Heyrovsky or Tafel step). \(^{19,20}\) In particular, the additional energy in step (i) is required to overcome the barrier for splitting strong OH- H bond, leading to a hamper of Pt SACs for alkaline HER application. Therefore, reducing the water dissociation energy in Volmer step (step (i)) for Pt single- atom catalyst in alkaline media becomes vital for large- scale \(\mathrm{H}_2\) production of industrialization.  
+
+<|ref|>text<|/ref|><|det|>[[147, 333, 853, 917]]<|/det|>
+Some strategies have been developed to improve Pt SACs HER activity. For instance, employing the microenvironment engineering to immobilize single Pt atoms in MXene nanosheets ( \(\mathrm{Mo}_2\mathrm{TiC}_2\mathrm{T}_x\) ) and onion- like carbon nanospheres supports could greatly reduce the H adsorption energy ( \(\Delta G_{\mathrm{H}}\) ) and, thus, facilitates the release of \(\mathrm{H}_2\) molecular. \(^{21,22}\) Besides, Pt single atoms anchored alloy catalysts (Pt/np- \(\mathrm{Co}_{0.85}\mathrm{Se}\) SAC) were constructed as an efficient HER electrocatalyst, \(^{23}\) in which np- \(\mathrm{Co}_{0.85}\mathrm{Se}\) can largely optimize the adsorption/desorption energy of hydrogen on atomic Pt sites, thus improving the HER kinetics. Furthermore, by utilizing the electronic interaction between the Pt atoms and the supports, single- atom Pt anchored 2D \(\mathrm{MoS}_2\) ( \(\mathrm{Pt}_{\mathrm{SA}}\) - \(\mathrm{MoS}_2\) ), \(^{24}\) nitrogen- doped graphene nanosheets ( \(\mathrm{Pt}_{\mathrm{SA}}\) - \(\mathrm{NGNs}\) ) \(^{25}\) and porous carbon matrix ( \(\mathrm{Pt}(\mathrm{\overline{a}PCM})^{26}\) show enhanced electrocatalytic HER efficiency due to the higher \(d\) band occupation near Fermi level, which can provide more free electrons for boosting the H\* conversion. Despite significant progress in Pt SACs, these methods are difficult to decrease the energy barrier of water dissociation in the Volmer step (step (i)). Generally, the \(\mathrm{H}_2\mathrm{O}\) dissociation and H\* conversion happen on different catalytic sites. \(^{27}\) Especially, the HER activities of Pt- based catalysts in alkaline conditions are governed by the binding ability of hydroxyl species (OH\*), \(^{28 - 30}\) and the alkaline HER kinetics could be optimized by independently regulating the binding energy of reactants (OH and H\*) on dual active sites. \(^{31 - 33}\) Inspired by these findings, the energy barrier of Pt SACs for \(\mathrm{H}_2\mathrm{O}\) dissociation in Volmer step (step (i)) in alkaline media could be decreased by incorporating or creating the dual active sites in the catalyst to independently modulate
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 90, 526, 107]]<|/det|>
+the binding energy of reactants (OH\* and H\*).  
+
+<|ref|>text<|/ref|><|det|>[[147, 115, 853, 750]]<|/det|>
+In this work, we developed a three- dimensional (3D) nanostructured electrocatalyst consisting of two- dimensional (2D) NiO/Ni heterostructure nanosheets supported single- atom Pt attached on one- dimensional (1D) Ag nanowires (Ag NWs) conductive network (PtSA- NiO/Ni). Density functional theory (DFT) calculations reveal that the dual active sites consisting of metallic Ni sites and O vacancies modified NiO sites near the interfaces of NiO/Ni heterostructure in PtSA- NiO/Ni show the preferred adsorption affinity toward OH\* and H\*, respectively, which efficiently facilitates water adsorption and reaching a barrier- free water dissociation step with a lower energy barrier of 0.11 eV in Volmer step (step (i)) for PtSA- NiO/Ni in the alkaline condition compared with that of PtSA- NiO (0.34 eV) and PtSA- NiO (1.27 eV) catalysts. Additionally, anchoring Pt single atoms at the interfaces of NiO/Ni heterostructure induces more free electrons on Pt sites due to the elevated occupation of the Pt 5d orbital at Fermi level and the more suitable H binding energy ( \(\Delta G_{\mathrm{H}^*}\) , 0.07 eV) than that of Pt atoms at the NiO ( \(\Delta G_{\mathrm{H}^*}\) , 0.93 eV) and Ni ( \(\Delta G_{\mathrm{H}^*}\) , 0.26 eV), which efficiently promotes the H\* conversion and H2 desorption, thus accelerating overall alkaline HER. (step (ii)). Furthermore, the Ag NWs supported 3D morphology provides abundant active sites and accessible channels for charge transfer and mass transport. As a result, the fabricated PtSA- NiO/Ni catalyst exhibits outstanding HER activity with a quite lower overpotential of 26 mV at 10 mA cm- 2 in 1 M KOH. The mass activity of PtSA- NiO/Ni is 20.6 A mg- 1 Pt at the overpotential of 100 mV, which is 41 times greater than that of the commercial Pt/C catalyst, significantly outperforming the reported catalysts. This work provides a new design principle toward single- atom catalyst systems for efficient alkaline HER.  
+
+<|ref|>sub_title<|/ref|><|det|>[[149, 770, 225, 787]]<|/det|>
+## Results  
+
+<|ref|>text<|/ref|><|det|>[[148, 801, 852, 876]]<|/det|>
+Synthesis and characterization of PtSA- NiO/Ni catalyst. The fabrication process of PtSA- NiO/Ni on Ag NWs is illustrated in Figure 1. In brief, the synthesized Ag NWs by a typical hydrothermal method<sup>34</sup> were first loaded on the flexible cloth to form a
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[145, 90, 852, 390]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 400, 851, 472]]<|/det|>
+<center>Figure 1. Schematic illustration of synthesis and water splitting mechanism of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (a) The synthesis process of Pt single atom anchored NiO/Ni heterostructure nanosheets on Ag nanowires network. (b) The mechanism of \(\mathrm{Pt_{SA} - NiO / Ni}\) network as an efficient catalyst towards large-scale water electrolysis in alkaline media. </center>  
+
+<|ref|>text<|/ref|><|det|>[[147, 486, 852, 896]]<|/det|>
+conductive network. Then Ni/NiO composite is attached to the Ag network by the facile electrodeposition process. \(^{35}\) In detail, the Ag NWs network loaded cloth is immersed in nickel acetate aqueous solution followed by an electrochemical process with - 3.0 V versus SCE (saturated calomel electrode) for 200 s (Figure S1), forming the uniformly distributed nanosheets on the Ag network (Figure S2). Transmission electron microscopy (TEM, Figure S3a- b) images, high- resolution TEM (HRTEM, Figure S3c) image, fast Fourier transform (FFT, Figure S3d), and elements mapping (Figure S4) images clearly show that the metallic Ni nanoparticles uniformly embed in amorphous NiO nanosheets. Besides, the X- ray diffraction (XRD, Figure S5) pattern shows that only metallic Ni signal without the peaks of NiO can be detected, and X- ray photoelectron spectroscopy (XPS, Figure S6) spectra suggest both metallic Ni and Ni oxide exists in Ni/NiO sample, further confirming the composition of metallic Ni on amorphous NiO. Interestingly, the deposited composition can be facilely controlled by performing various voltage in the nickel acetate aqueous solution. \(^{35}\) Specifically, as above discussion, a high voltage of - 3 V versus SCE will generate the Ni/NiO
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 853, 526]]<|/det|>
+composite on Ag NWs (NiO/Ni), whereas a lower voltage of - 1 V versus SCE could prepare the amorphous NiO on Ag NWs (NiO, Figure S7- 9). Besides, the pure metallic Ni on Ag network (Ni, Figure S10- 13) was fabricated by a traditional electrodeposition method with 1.2 V for 200 s in a mix solution containing 0.10 M NiCl2 and 0.09 M \(\mathrm{H}_3\mathrm{BO}_3\) . Afterward, the single- atom Pt immobilized NiO/Ni (PtSA- NiO/Ni) is obtained by sequentially electroreduction process with cyclic voltammetry in 1 M KOH solution containing low- concentration Pt metallic salts. Abundant voids and O vacancy defects at the surface- exposed interfaces of NiO/Ni heterostructure induced by crystal- lattice dislocation and phase transition<sup>36-38</sup> will provide efficient sites for trapping Pt single atom. The water dissociation of Volmer step in alkaline media is expected to be accelerated by O vacancies modified NiO near the interfaces interacted strongly with OH and metallic Ni interacted with H for H- OH bond destabilization (step (i)). Apture from the Volmer step, NiO/Ni heterostructure supported single- atom Pt sites could show more suitable H binding ability for the conversion and deabsorption of dissociated H (step (ii)), further accelerating overall HER kinetics of PtSA- NiO/Ni in an alkaline condition.  
+
+<|ref|>text<|/ref|><|det|>[[147, 534, 853, 914]]<|/det|>
+The phase evolution of samples is investigated by XRD pattern as shown in Figure 2a, in which no Pt characteristic peaks are detected, implying the absence of Pt cluster and particles in PtSA- NiO/Ni. The scanning electron microscopy (SEM, Figure 2b- c) images show the well- distributed and open 3D nanosheets morphology for PtSA- NiO/Ni. Compared with the original NiO/Ni (Figure S2), the exposed PtSA- NiO/Ni nanosheets morphology on Ag NWs should be attributed to the \(\mathrm{H}_2\) - assisted delamination effect during Pt electro- reduction process in alkaline condition,<sup>21,34</sup> which will provide more sites for Pt atoms immobilization and improve the HER performance. The scanning transmission electron microscopy (STEM, Figure S14) images suggest that the exfoliated nanosheets consist of few NiO/Ni layers for PtSA- NiO/Ni. The high- angle annular dark- field STEM (HAADF- STEM, Figure 2d) image displays bright spots along with the interfaces of NiO/Ni heterostructure, corresponding to heavy constituent atoms species, which efficiently confirms the immobilization of atomically dispersed Pt atoms in the NiO/Ni nanosheets. The magnified HAADF- STEM image (Figure 2e)
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[150, 91, 845, 575]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 585, 852, 714]]<|/det|>
+<center>Figure 2. Structural characterization of the fabricated \(\mathrm{Pt_{SA} - NiO / Ni}\) catalyst. (a) XRD patterns of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{NiO / Ni}\) , and Ag NWs. (b-c) SEM images of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (d) HAADF-STEM image of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (e-f) Magnified HAADF-STEM image of \(\mathrm{Pt_{SA} - NiO / Ni} \mathrm{and} \mathrm{g}\) the corresponding DFT simulated image, showing the atomically dispersed Pt atoms at Ni position (circles in (e)). (h) HRTEM images of \(\mathrm{Pt_{SA} - NiO / Ni}\) and the insert in (h) shows the related FFT image of \(\mathrm{Pt_{SA} - NiO / Ni}\) . (i-j) Dark-field TEM images of \(\mathrm{Pt_{SA} - NiO / Ni}\) with different magnifications and (k-n) the mapping of the corresponding elements. </center>  
+
+<|ref|>text<|/ref|><|det|>[[147, 729, 852, 915]]<|/det|>
+suggests that the single Pt atoms are exactly immobilized at the interfaces of the NiO/Ni heterostructure. Based on these findings, a STEM simulation was performed to explore the atomic environment of Pt atom via the DFT- optimized structure (Figure 2f- g), and the simulated result suggests that the Pt atoms are fixed at the Ni positions by binding with O atom and Ni atoms near the interfaces of the NiO/Ni heterostructure. Further, the high- resolution TEM (HRTEM) shows one distinct lattice fringes of 0.18 nm, matching well with metallic (200) crystallographic planes (Figure 2h). The
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 853, 386]]<|/det|>
+selected- area electron diffraction pattern (inset in Figure 2h) shows four distinct rings: the red ring corresponds to the metallic Ni (200) plane, \(^{39}\) and the yellow rings with a highly diffused halo are assigned to the amorphous NiO phase. \(^{35,40}\) These results further confirm the formation of single- atom Pt anchored NiO/Ni composition, and the interfacial coupling of Pt single atom with NiO/Ni does not change the phase structure of NiO/Ni. Moreover, the elemental mapping (Figure 2i- n and Figure S15) shows that Pt atoms are uniformly dispersed throughout NiO/Ni nanosheets. Besides, as a comparison, Pt<sub>SA</sub>- NiO and Pt<sub>SA</sub>- Ni were fabricated under the same conditions as Pt<sub>SA</sub>- NiO/Ni but replacing NiO/Ni with NiO and Ni, respectively. The corresponding HAADF- STEM images (Figure S16) confirm the atomically dispersed Pt in the NiO and metallic Ni phase.  
+
+<|ref|>text<|/ref|><|det|>[[147, 393, 853, 914]]<|/det|>
+The electronic state evolution of the single Pt atoms in NiO/Ni, NiO, and Ni supports is explored by XPS as shown in Figure 3a. The Pt \(4f\) spectrums of Pt<sub>SA</sub>- NiO/Ni, Pt<sub>SA</sub>- NiO, and Pt<sub>SA</sub>- Ni are close to Pt<sup>0</sup> but show some positive shift with different extents compared with Pt foil, confirming the electrochemical reduction of PtCl<sub>6</sub><sup>2- </sup>and the electronic interaction by charge transfer from Pt sites to the supports (NiO/Ni, NiO, and Ni). \(^{41}\) Specifically, the Pt<sub>SA</sub>- NiO shows the largest positive shift in Pt \(4f\) spectrum, suggesting the maximum electron loss of Pt species. \(^{42,43}\) Besides, the fitting curve of Pt XPS spectrums display Pt(IV) species in the samples, which derives from the adsorbed PtCl<sub>6</sub><sup>2- </sup>ions on the surface of the sample. \(^{44,45}\) Further, the electronic state of Pt atoms in NiO/Ni, NiO, and Ni supports are further verified by performing X- ray absorption fine structure measurements. As shown in Figure 3b, the evolutions of Pt \(L_{3}\) - edge X- ray absorption near edge structure (XANES) spectra with different supports are distinguished, in which the intensity of white- line peaks corresponds to the transfer of the Pt \(2p_{3/2}\) core- electron to \(5d\) states, and thus is used as an indicator of Pt \(5d\) - band occupancy. \(^{46,47}\) The overall white- line intensity gradually decreases as the change of support from NiO, NiO/Ni to metallic Ni, corresponding to the increase of \(5d\) occupancy of Pt. Hence, higher \(5d\) occupancy indicates the less charge loss of the single- atom Pt after coordinating with the supports, which is consistent with the results of XPS analysis in Figure 3a.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[147, 85, 850, 433]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 437, 851, 530]]<|/det|>
+<center>Figure 3. Electronic state and atomic structure characterization. (a) Pt \(4f\) spectra, (b) XANES spectra, and (c) calculated Pt oxidation states derived from \(\Delta\) XANES spectra of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) , and Pt foil is given as a reference. (d) Corresponding FT-EXAFS curves of Figure 3b. (e) EXAFS fitting curve of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) \(R\) -space. (f) EXAFS wavelet transform plots of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , and Pt foil. </center>  
+
+<|ref|>text<|/ref|><|det|>[[147, 543, 852, 897]]<|/det|>
+To quantitate the electronic state structural information, the white- line peak evolution of Pt can be clearly described by the differential XANES spectra ( \(\Delta\) XANES, Figure S17) by subtracting the spectra from that of Pt foil. The valence state of Pt can be quantitatively examined by the integration of the white- line peak in \(\Delta\) XANES spectra. As shown in Figure 3c, the average valence state of Pt increase from \(+0.29\) , \(+0.73\) , to \(+1.23\) for the \(\mathrm{Pt_{SA} - Ni}\) , \(\mathrm{Pt_{SA} - NiO / Ni}\) , and \(\mathrm{Pt_{SA} - NiO}\) catalysts, respectively. The evolution of the atomic coordination configuration of Pt was further revealed by extended X- ray absorption fine structure spectroscopy (EXAFS, Figure 3d), in which the typical Pt- Pt contribution peak of Pt foil at about \(2.7 \mathring{\mathrm{A}}\) is absent for the fabricated \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) catalysts, strongly confirming the single Pt atoms dispersion. Further, the first- shell EXAFS fitting of \(\mathrm{Pt_{SA} - NiO / Ni}\) sample (Figure 3e and Table S1) gives a coordination number (CN) of 1.3 for Pt- O contribution and 5.8 for Pt- Ni contribution. For \(\mathrm{Pt_{SA} - NiO}\) , the fitting results of EXAFS spectra suggested CN about
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 853, 527]]<|/det|>
+2.4 for Pt-O contributions and 2.1 for \(CN\) for Pt-Ni contributions. Whereas Pt-Ni contribution with 4.9 for \(CN\) and no Pt-O contributions are found in the fitting of \(\mathrm{Pt_{SA}}\) - Ni EXAFS spectra. Combining the DFT-optimized structure (Figure S18), the Pt atoms are mainly immobilized at the interfacial Ni positions by coordinating with one O atom and 5 Ni atoms in \(\mathrm{Pt_{SA}}\) - NiO/Ni, which is consistent with the conclusion of HAADF-STEM analysis (Figure 2d-g). To more precisely clarify the atomic dispersion and coordination conditions of Pt, the wavelet transform (WT) analysis was carried out due to its more efficient resolution ability in \(K\) spaces and radial distance, \(^{48,49}\) in which the atoms at similar coordination conditions and distances could be discriminated. \(^{50,51}\) As shown in Figure 3f, \(\mathrm{Pt_{SA}}\) - NiO/Ni displays a different intensity maximum with \(\mathrm{Pt_{SA}}\) - NiO and \(\mathrm{Pt_{SA}}\) - Ni, and especially, the intensity maximum at 7.6 \(\mathrm{\AA^{-1}}\) for \(\mathrm{Pt_{SA}}\) - NiO/Ni is lower than that of \(\mathrm{Pt_{SA}}\) - NiO (8.5 \(\mathrm{\AA^{-1}}\) ), but high than that of \(\mathrm{Pt_{SA}}\) - Ni (7.4 \(\mathrm{\AA^{-1}}\) ), further confirming the interfacial coordination conditions for Pt atoms immobilized in NiO/Ni. Besides, the intensity maximum at 11.5 \(\mathrm{\AA^{-1}}\) corresponding to Pt-Pt coordination is absent in the fabricated catalysts; further confirming the successful loading of single Pt atoms in Ni, NiO/Ni, and NiO supports.  
+
+<|ref|>text<|/ref|><|det|>[[147, 543, 853, 896]]<|/det|>
+Theoretical investigations. Based on the above structure analysis, theoretical investigations were performed to disclose the influences of the evolved coordinate configurations of the Pt atom on the electronic structure and catalytic activity of the catalysts. According to the HAADF- STEM and EXAFS measurements, the models for \(\mathrm{Pt_{SA}}\) - NiO/Ni were shown in Figure 4a. Based on the calculated charge density distributions, an increased charge density area along the interface of NiO/Ni heterostructure was induced (Figure S19a- b). After coupling Pt single atom with NiO/Ni heterostructure, an electronic structure redistribution at the interfaces of the heterostructure is caused due to the different electronegativity of atoms (3.44 for O atom, 1.91 for Ni, and 2.28 for Pt). Especially, charge delocalizing from Pt to the bonded O atom and charge localizing from adjacent Ni atoms to Pt are displayed. Consequently, a locally enhanced electric field with a half- moon shape area around the Pt site was generated (Figure S19c- d), which is more intensive than that of \(\mathrm{Pt_{SA}}\) - NiO
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[147, 83, 850, 434]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[147, 438, 851, 565]]<|/det|>
+<center>Figure 4. Theoretical investigations. Computational models and localized electric field distribution of (a) \(\mathrm{Pt_{SA} - NiO / Ni}\) , (b) \(\mathrm{Pt_{SA} - NiO}\) and (c) \(\mathrm{Pt_{SA} - Ni}\) . (d) Calculated PDOS of \(\mathrm{NiO / Ni}\) and \(\mathrm{Pt_{SA} - NiO / Ni}\) , with aligned Fermi level. (e) Calculated Pt 5d band of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) . (f) The orbital alignment of the surficial sites for \(\mathrm{Pt_{SA} - NiO / Ni}\) binding with \(\mathrm{H_2O}\) molecule. (g) Calculated OH-binding energies \((\Delta E_{\mathrm{OH}})\) and H-binding energies \((\Delta E_{\mathrm{H}})\) for Ni, pure NiO, and O vacancies modified NiO surface. (h) Calculated energy barriers of water dissociation kinetic and (i) adsorption free energies of \(\mathrm{H^*}\) on the surface of the \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , and \(\mathrm{Pt_{SA} - Ni}\) catalysts, respectively. </center>  
+
+<|ref|>text<|/ref|><|det|>[[147, 580, 852, 905]]<|/det|>
+(Figure 4b) and \(\mathrm{Pt_{SA} - Ni}\) (Figure 4c), suggesting Pt single atom coupled with NiO/Ni heterostructure could possess the more free electrons to promote the adsorbed H conversion and \(\mathrm{H}_2\) evolution. \(^{22,44}\) Moreover, the projected density of states (PDOS, Figure 4d, and Figure S20) of the single- atom Pt immobilized NiO/Ni heterostructure shows higher occupation than that of the pure NiO/Ni near the Fermi level, suggesting a promoted electron transfer and higher conductivity of \(\mathrm{Pt_{SA} - NiO / Ni}\) . The contrast between the PDOS of NiO/Ni and \(\mathrm{Pt_{SA} - NiO / Ni}\) reveals that the increased DOS of the \(\mathrm{Pt_{SA} - NiO / Ni}\) near the Fermi level mainly derives from the contribution of Pt \(d\) orbitals (Figure 4d). These results suggest that the NiO/Ni heterostructure coupled single- atom Pt can effectively enhance the total \(d\) - electron domination of the catalyst near the Fermi level, which will benefit the activation of \(\mathrm{H}_2\mathrm{O}\) and lead to energetically catalytic activity. \(^{21,52}\) Moreover, the \(d\) - band features of the Pt atom in NiO/Ni, NiO and Ni
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 853, 358]]<|/det|>
+coordinated configurations are investigated. The wider \(5d\) band and higher density near the Fermi level for NiO/Ni supported Pt atom than that of \(\mathrm{Pt_{SA} - NiO}\) and \(\mathrm{Pt_{SA} - Ni}\) ((Figure 4e and Figure S21) suggest that the NiO/Ni coupled Pt atom can induce more free electrons near Pt sites than \(\mathrm{Pt_{SA} - NiO}\) and \(\mathrm{Pt_{SA} - Ni}\) , which is more favorable for the H reactants adsorption and transfer. Besides, the Pt- \(5d\) band of \(\mathrm{Pt_{SA} - NiO / Ni}\) also shows a substantially broad range for overlapping with H- \(1s\) and \(\mathrm{H_2O - 2p\pi}\) orbitals (Figure 4f). Therefore, the Pt- site could play a protecting role for stabilizing the Ni valence state and a distributive role by binding OH and H species to low the deactivation of absorption sites in case of over- binding of intermediates on the active sites for NiO/Ni heterostructure coupled single- atom Pt. \(^{53}\)  
+
+<|ref|>text<|/ref|><|det|>[[147, 366, 853, 916]]<|/det|>
+Based on the above finding, we further explore the reaction barrier of the fabricated catalysts for \(\mathrm{H_2O}\) splitting in alkaline conditions, consisting of the dissociation of \(\mathrm{H_2O}\) molecule of Volmer step and the subsequent conversion of H to \(\mathrm{H_2}\) , which mainly depends on how OH and H bond to the active sites on the surface of the catalysts. \(^{54}\) We found that both H and OH bind weakly to the pure NiO surface. While metallic Ni surface shows a preference for stabilizing H, and O vacancies modified NiO facilitates the adsorption of OH species (Figure 4g and Figure S22). For NiO/Ni composition, the O vacancies on the interfaces of the NiO/Ni heterostructure (Figure S23) are induced by the crystal- lattice dislocation and phase transition. \(^{36,37,55}\) As an integration, NiO/Ni coupled single- atom Pt catalyst demonstrates the strongest \(\mathrm{H_2O}\) adsorption ability (Figure S24) and largest energy release of - 0.24 eV for water dissociation in Volmer step (Figure 4h). Moreover, \(\mathrm{Pt_{SA} - NiO / Ni}\) hybrid catalyst only need the minimum energy barriers (0.11 eV) for the dissociation of \(\mathrm{H_2O}\) into OH and H under the assistance of NiO/Ni interfaces (Figure S25), confirming the critical role of surface- exposed NiO/Ni interfaces for the \(\mathrm{H_2O}\) dissociation of Volmer step in alkaline media. In the subsequent step, the NiO/Ni supported single- atom Pt sites at the NiO/Ni interfaces act as the proton- acceptor for the recombination of the dissociated proton (H\*) and \(\mathrm{H_2}\) evolution due to its near- zero H binding energy (0.07 eV, Figure 4i and Figure S26) and strong electron supply capacity deriving from locally enhanced charge distribution (Figure 4a) and the higher occupation of Pt \(5d\) band near Fermi lever
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 88, 850, 136]]<|/det|>
+(Figure 4e). Consequently, the overall steps of \(\mathrm{Pt_{SA} - NiO/Ni}\) hybrid catalyst for HER in alkaline media are significantly accelerated.  
+
+<|ref|>text<|/ref|><|det|>[[147, 150, 852, 900]]<|/det|>
+Electrocatalytic alkaline HER performances. Based on the structural characterizations and theoretical investigations, the Pt single- atom catalyst coupled with NiO/Ni heterostructure possesses the best intrinsic HER activity in alkaline media among the fabricated catalysts. Thus, the electrocatalytic activities of \(\mathrm{Pt_{SA} - NiO/Ni}\) for alkaline HER was measured in \(1\mathrm{M}\) KOH solution. As a comparison, the HER performance of \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , NiO/Ni, and \(20\%\) Pt/C were also tested under the same conditions. As shown in Figure 5a, the \(\mathrm{Pt_{SA} - NiO/Ni}\) shows the highest HER performance among all catalysts, and only needs a quite low overpotential of 26 and 85 mV to achieve the current density of 10 and \(100\mathrm{mAcm}^{- 2}\) , respectively, significantly superior to the \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , NiO/Ni and the Pt/C catalyst (Figure 5b). Moreover, the mass activity of \(\mathrm{Pt_{SA} - NiO/Ni}\) normalized to the loaded Pt mass (1.14 wt%, inductively coupled plasma- mass spectrometry) at an overpotential of \(100\mathrm{mV}\) is 20.6 \(\mathrm{Amg^{- 1}}\) , which is 2.4, 2.3, and 41.2 times greater than that of \(\mathrm{Pt_{SA} - NiO}\) (8.5 \(\mathrm{Amg^{- 1}}\) ), \(\mathrm{Pt_{SA} - Ni}\) (9.0 \(\mathrm{Amg^{- 1}}\) ) and the commercial Pt/C catalyst (0.5 \(\mathrm{Amg^{- 1}}\) ), respectively. These results suggest that single Pt atoms coupled with NiO/Ni can extremely maximize the alkaline HER activity of Pt- based catalysts, leading to a significant reduction in cost. Additionally, the \(\mathrm{Pt_{SA} - NiO/Ni}\) exhibits a smaller Tafel slope of \(27.07\mathrm{mVdec^{- 1}}\) than \(\mathrm{Pt_{SA} - NiO}\) (37.54 mV dec \(^{- 1}\) ), \(\mathrm{Pt_{SA} - Ni}\) (37.32 mV dec \(^{- 1}\) ), NiO/Ni (58.67 mV dec \(^{- 1}\) ), and Pt/C catalyst (41.69 mV dec \(^{- 1}\) ), which suggests a typical Volmer- Tafel mechanism for alkaline HER and implies that the rate- determining step of \(\mathrm{Pt_{SA} - NiO/Ni}\) is the \(\mathrm{H_2}\) desorption (Tafel step) rather than the \(\mathrm{H_2O}\) dissociation (Volmer step). \(^{56,57}\) Besides, \(\mathrm{Pt_{SA} - NiO/Ni}\) catalyst exhibits a 2.0 and, 2.4- fold enhancement in the double- layer capacitance \((C_{\mathrm{dl}})\) over \(\mathrm{Pt_{SA} - NiO}\) and \(\mathrm{Pt_{SA} - Ni}\) (Figure S27), respectively, suggesting the favorable nanostructure with more sites for Pt atoms immobilization and HER. Furthermore, the charge transfer resistance \((R_{\mathrm{ct}})\) of \(\mathrm{Pt_{SA} - NiO/Ni}\) (0.61 ohm, Figure 5e) is extremely low than that of \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , and NiO/Ni catalysts, which mainly originates from the introduction of Ag NWs and enhanced electronic structure of single
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 90, 400, 107]]<|/det|>
+Pt atoms coupled with NiO/Ni.  
+
+<|ref|>text<|/ref|><|det|>[[147, 117, 853, 470]]<|/det|>
+For real applications, HER catalyzing stability is another essential factor. As present in Figure 5f, the \(\mathrm{Pt_{SA} - NiO / Ni}\) shows high durability in the alkaline electrolyte with negligible loss in HER performance for 5000 cycles or 30 hours. The characterizations of \(\mathrm{Pt_{SA} - NiO / Ni}\) after the stability test, including HAADF- STEM image, elements mapping, and double- layer capacitance (Figure S28- 30), suggest the negligible structure changes and single- atom dispersion for \(\mathrm{Pt_{SA} - NiO / Ni}\) after long- term alkaline HER. Moreover, the turnover frequencies (TOFs) per Pt atom site are analyzed, and the TOFs of \(\mathrm{Pt_{SA} - NiO / Ni}\) (5.71 \(\mathrm{H_2 s^{- 1}}\) ) is 2.02, 1.99, and 38.06 times higher than that of \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , and \(\mathrm{Pt / C}\) catalyst, respectively (Figure 5g). To our knowledge, the electrocatalytic HER performances of our \(\mathrm{Pt_{SA} - NiO / Ni}\) catalyst in the alkaline media are almost optimal among the reported SACs, and are comparable with the performances of catalysts in acid media (Figure 5h and Table S2), confirming the advance by the constructing single- Pt sites in NiO/Ni hybrid system.  
+
+<|ref|>image<|/ref|><|det|>[[150, 477, 856, 857]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[148, 863, 850, 899]]<|/det|>
+<center>Figure 5. Electrocatalytic alkaline HER performances of the catalysts in 1 M KOH electrolyte. (a) HER polarization curves of \(\mathrm{Pt_{SA} - NiO / Ni}\) , \(\mathrm{Pt_{SA} - NiO}\) , \(\mathrm{Pt_{SA} - Ni}\) , NiO/Ni, and \(\mathrm{Pt / C}\) . (b) The comparison </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 85, 851, 195]]<|/det|>
+of overpotentials required to achieve \(10\mathrm{mAcm}^{- 2}\) for various catalysts. (c) The mass activity of the Pt- based catalysts. (d) Corresponding Tafel slope originated from LSV curves. (e) EIS (Electrochemical Impedance Spectroscopy) Nyquist plots of the catalysts. (f) Stability test of \(\mathrm{Pt_{SA}}\) - NiO/Ni through cyclic potential scanning and chronoamperometry method (Inset in f). (g) TOFs plots of the Pt- based electrocatalysts. (h) Comparison of the HER activity for \(\mathrm{Pt_{SA}}\) - NiO/Ni with reported catalysts, originating from Table S2.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 215, 256, 233]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[147, 245, 852, 910]]<|/det|>
+In summary, we reported a novel single- atom Pt \(\mathrm{(Pt_{SA})}\) immobilized NiO/Ni heterostructure nanosheets on Ag NWs network nanocomposite by the facile electrodeposition strategy, which serves as an efficient electrocatalyst for vigorous hydrogen production in alkaline media. Theoretical calculations revealed that the Pt SACs coupled with NiO/Ni heterostructure could efficiently tailoring water dissociation energy for accelerating alkaline HER. In particular, the dual active sites consisting of metallic Ni sites and O vacancies modified NiO sites near the interfaces of NiO/Ni have the preferred adsorption affinity toward both \(\mathrm{OH^*}\) and \(\mathrm{H^*}\) , which facilitates water adsorption and reaches a barrier- free water dissociation step with the lowest energy barrier of \(0.11\mathrm{eV}\) in Volmer step (step (i)) for \(\mathrm{Pt_{SA}}\) - NiO/Ni compared with that of \(\mathrm{Pt_{SA}}\) - NiO (0.34 eV) and \(\mathrm{Pt_{SA}}\) - NiO (1.27 eV) catalysts. Besides, fixing Pt atoms at the NiO/Ni interfaces induce a higher occupation of the Pt \(5d\) band at the Fermi level and the more suitable H binding energy \((\Delta G_{\mathrm{H}^*}, 0.07\mathrm{eV})\) than that of Pt atoms at the NiO \((\Delta G_{\mathrm{H}^*}, 0.93\mathrm{eV})\) and Ni \((\Delta G_{\mathrm{H}^*}, 0.26\mathrm{eV})\) , which efficiently promotes the \(\mathrm{H^*}\) conversion and \(\mathrm{H}_2\) desorption, thus accelerating overall alkaline HER. The further enhancement of alkaline HER performance was achieved by introducing Ag NWs network into 2D \(\mathrm{Pt_{SA}}\) - NiO/Ni nanosheets to construct a seamlessly conductive 3D nanostructure. The unique nanostructural feature and highly conductive Ag NWs network provide abundant active sites and accessible channels for electron transfer and mass transport. Consequently, the 3D \(\mathrm{Pt_{SA}}\) - NiO/Ni catalyst shows outstanding HER performances in alkaline conditions with a quite low overpotential of \(26\mathrm{mV}\) at a current density of \(10\mathrm{mAcm}^{- 2}\) and extremely high mass activity of \(20.6\mathrm{Amg}^{- 1}\) Pt in \(1\mathrm{MKOH}\) , significantly outperforming the reported catalysts. This study opens an efficient avenue for the advance of single- atom catalysts by introducing a water dissociation kinetic-
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[148, 91, 353, 107]]<|/det|>
+oriented material system.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 140, 240, 159]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[147, 172, 852, 358]]<|/det|>
+Synthesis of Ag NWs. An oil bath method was used to synthesize Ag NWs according to our previous report. \(^{58}\) Specifically, a mix solution consisting of ethylene glycol, \(\mathrm{FeCl}_3\) (7.19 mM), \(\mathrm{AgNO}_3\) (0.051 M), and polyvinylpyrrolidone (0.012 M) was heat and maintained under an oil bath pan with \(110^{\circ}\mathrm{C}\) for 12 hours. After that, the generated precipitate was washed with acetone and alcohol to get the pure Ag NWs. Subsequently, the Ag NWs were uniformly dispersed on a flexible cloth fabric by spray coating technology to fabricate a conductive network.  
+
+<|ref|>text<|/ref|><|det|>[[147, 376, 852, 590]]<|/det|>
+Synthesis of NiO/Ni on Ag NWs. Ni/NiO is grown on Ag NWs network by a facile electrodeposition process in the aqueous electrolyte of \(20\mathrm{mM}\mathrm{C}_4\mathrm{H}_6\mathrm{NiO}_4\cdot 4\mathrm{H}_2\mathrm{O}\) according to the recent report. \(^{35}\) The electrodeposition process was performed by chronoamperometry method with - 3 V vs SCE for 200 s under a standard three- electrode system, in which graphite sheet acted as a counter electrode, SCE acted as a reference electrode, and the fabricated Ag NWs network loaded on the cloth was directly used as working electrode. The obtained samples were washed with deionized water and then dried at room temperature.  
+
+<|ref|>text<|/ref|><|det|>[[147, 608, 851, 709]]<|/det|>
+Synthesis of NiO on Ag NWs. NiO is grown on Ag NWs network by the electrodeposition process with - 1 V vs SCE for 600 s in an aqueous electrolyte of 20 mM \(\mathrm{C}_4\mathrm{H}_6\mathrm{NiO}_4\cdot 4\mathrm{H}_2\mathrm{O}\) . The obtained samples were washed with deionized water and then dried at room temperature.  
+
+<|ref|>text<|/ref|><|det|>[[147, 728, 852, 886]]<|/det|>
+Synthesis of Ni on Ag NWs. Metallic Ni is grown on Ag NWs network by the electrodeposition process in an aqueous solution consisting of \(0.10\mathrm{M}\mathrm{NiCl}_2\) , \(0.09\mathrm{M}\mathrm{H}_3\mathrm{BO}_3\) , and a solvent containing ethanol and deionized water with 2:5 in volume ratio. The electrodeposition process was performed by chronoamperometry with - 1.2 V vs SCE for 200 s. The obtained samples were washed with deionized water and then dried at room temperature.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 852, 275]]<|/det|>
+Synthesis of \(\mathbf{PtsA - NiO / Ni}\) on Ag NWs. \(\mathrm{PtsA - NiO / Ni}\) on Ag NWs was fabricated by the electrochemical reduction process in the three- electrode system, in which the fabricated \(\mathrm{NiO / Ni}\) on Ag NWs was performed as the working electrode, graphite sheet acted as a counter electrode, saturated calomel electrode acted as a reference electrode. The corresponding electrochemical process was carried out by multi- cycle cathode polarization in \(1\mathrm{M}\) KOH solution containing \(50\mu \mathrm{M}\mathrm{H}_2\mathrm{PtCl}_6\) with a scan rate of \(50\mathrm{mV}\) \(\mathrm{s}^{- 1}\) between 0 V and - 0.50 V versus reversible hydrogen electrode (RHE) for 200 cycles.  
+
+<|ref|>text<|/ref|><|det|>[[147, 292, 850, 367]]<|/det|>
+Synthesis of \(\mathbf{PtsA - NiO}\) on Ag NWs. \(\mathrm{PtsA - NiO}\) on Ag NWs were fabricated by multicycle cathode polarization in \(1\mathrm{M}\) KOH solution containing \(50\mu \mathrm{M}\mathrm{H}_2\mathrm{PtCl}_6\) with a scan rate of \(50\mathrm{mV}\mathrm{s}^{- 1}\) between 0 V and - 0.50 V versus RHE for 200 cycles.  
+
+<|ref|>text<|/ref|><|det|>[[147, 384, 850, 460]]<|/det|>
+Synthesis of \(\mathbf{PtsA - Ni}\) on Ag NWs. \(\mathrm{PtsA - Ni}\) on Ag NWs were fabricated by multicycle cathode polarization in \(1\mathrm{M}\) KOH solution containing \(50\mu \mathrm{M}\mathrm{H}_2\mathrm{PtCl}_6\) with a scan rate of \(50\mathrm{mV}\mathrm{s}^{- 1}\) between 0 V and - 0.50 V versus RHE for 200 cycles.  
+
+<|ref|>text<|/ref|><|det|>[[147, 477, 852, 775]]<|/det|>
+Characterizations. The morphology measurement of the synthesized catalysts was performed by SEM (GeminiSEM 300). HRTEM images, HAADF- STEM images, and STEM- EDX mapping images were obtained by a TEM coupled with an energy spectrum analyzer (JEOL JEM2100). The Pt contents in the catalysts were measured by inductively coupled plasma optical emission spectrometry (ICP- OES). The XPS spectra of elements were tested by a surface analysis system (ESCALAB250Xi). The phase and crystal information were obtained by Cu \(K\alpha\) radiation in an X- ray diffractometer (XRD, Bruker, D8 Advance Davinci). The EXAFS measurement of the \(\mathrm{PtsA - NiO / Ni}\) , \(\mathrm{PtsA - NiO}\) , and \(\mathrm{PtsA - NiO / Ni}\) at the Pt \(L_3\) - edge was performed at 1W1B station at the Beijing Synchrotron Radiation Facility (BSRF). Data analysis and fitting were performed with Athena and Artemis in the Demeter package.  
+
+<|ref|>text<|/ref|><|det|>[[147, 792, 850, 895]]<|/det|>
+Electrochemical measurements. All electrochemical measurements were finished by an electrochemical workstation (CHI 660E) with a three- electrode configuration, in which fabricated catalysts were directly employed as the working electrode, graphite sheet acted as a counter electrode, saturated calomel electrode acted as a reference
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[147, 88, 853, 303]]<|/det|>
+electrode. All the presented potential in this work was transferred to RHE according to an experimental method. \(^{59}\) LSV with \(95\%\) iR- corrections were tested under the potential range from 0.05 to - 0.5 V and the scan rate of \(5\mathrm{mV}\mathrm{s}^{- 1}\) . EIS was obtained by a frequency range from \(100\mathrm{k}\) to \(0.1\mathrm{Hz}\) with an overpotential of \(230\mathrm{mV}\) vs RHE. For the preparation of 3D Pt/C@Ni foam, \(5\mathrm{mg}20\mathrm{wt}\%\) Pt/C was dispersed in \(0.9\mathrm{mL}\) alcohol containing \(0.1\mathrm{mL}5\mathrm{wt}\%\) Nafion solution to form a homogeneous ink. Then, the obtained ink was coated on the Ni foam and dried in air to form a porous Pt/C@Ni foam electrode.  
+
+<|ref|>text<|/ref|><|det|>[[147, 320, 853, 897]]<|/det|>
+DFT theoretical calculations. All the structural optimizations, charge density difference analysis, Bader charge analysis, and energy calculations were carried out based on DFT as implemented in the Vienna Ab- initio Simulation Package (VASP). \(^{60 - }\) \(^{62}\) The projector- augmented- wave (PAW) method was implemented to calculate the interaction between the ionic cores and valence electrons. \(^{63,64}\) The Perdew- Burke- Ernzerhof approach of spin- polarized generalized gradient approximation (GGA- PBE) was used to describe the exchange- correlation energy. \(^{65}\) Calculations were performed with the cut- off plane- wave kinetic energy of \(500\mathrm{eV}\) , and \(8\times 4\times 1\) \(k\) - mesh grids were employed for the integration of the Brillouin zone. Electronic relaxation was undertaken to utilize the conjugate- gradient (CG) method \(^{66}\) with the total energy convergence criterion being \(10^{- 5}\mathrm{eV}\) . Geometry optimization was employed by the quasi- Newton algorithm \(^{67,68}\) until all the residual forces on unconstrained atoms less than \(0.01\mathrm{eV / \AA}\) . Climbing image nudge elastic band (CI- NEB) calculations \(^{69}\) were employed for finding transition barriers with the initial configuration of \(\mathrm{H}_2\mathrm{O}\) absorbed on the catalyst surface and final configuration of \(\mathrm{OH} + \mathrm{H}\) absorbed on the catalyst surface. To ensure the initial configuration correctly, an \(\mathrm{H}_2\mathrm{O}\) molecule was deposited on the catalyst surface and relaxed for calculating its local minimum total energy on different sites, and the last one is the initially stable configuration. The final configuration is also found by relaxing \(\mathrm{OH}\) and \(\mathrm{H}\) near the \(\mathrm{H}_2\mathrm{O}\) absorbed site of the initial configuration. Next, The equation for calculating adsorption enthalpy \(\Delta E_{\mathrm{H}^*}\) as the following:
+
+<--- Page Split --->
+<|ref|>equation<|/ref|><|det|>[[419, 88, 617, 117]]<|/det|>
+\[\Delta E_{\mathrm{H}^*}{=}E_{\mathrm{slab + H}}{-}E_{\mathrm{slab}}{-}\frac{1}{2} E_{\mathrm{H}_2}\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 125, 850, 174]]<|/det|>
+Where the \(E_{\mathrm{slab + H}}\) is the total enthalpy of H adsorbing on the catalysts, the enthalpy of the catalysts is \(E_{\mathrm{slab}}\) , and the \(\mathrm{H}_2\) enthalpy is \(E_{\mathrm{H}_2}\) .  
+
+<|ref|>text<|/ref|><|det|>[[147, 181, 850, 258]]<|/det|>
+The H and \(\mathrm{H}_2\mathrm{O}\) absorbing on the slabs were investigated by comparing the formation energy of different sites. The equation for calculating adsorption enthalpy \(\Delta E_{\mathrm{H}^*}\) as the following:  
+
+<|ref|>equation<|/ref|><|det|>[[419, 265, 617, 294]]<|/det|>
+\[\Delta E_{\mathrm{H}^*}{=}E_{\mathrm{slab + H}}{-}E_{\mathrm{slab}}{-}\frac{1}{2} E_{\mathrm{H}_2}\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 302, 850, 378]]<|/det|>
+Where the \(E_{\mathrm{slab + H}}\) is the total enthalpy of H adsorbing on the catalysts, enthalpy of the catalysts is \(E_{\mathrm{slab}}\) , the \(\mathrm{H}_2\) enthalpy is \(E_{\mathrm{H}_2}\) . As similar, the equation for calculating the \(\mathrm{H}_2\mathrm{O}\) adsorption enthalpy \(\Delta E_{\mathrm{H}_2\mathrm{O}^*}\) as the following:  
+
+<|ref|>equation<|/ref|><|det|>[[395, 386, 640, 407]]<|/det|>
+\[\Delta E_{\mathrm{H}_2\mathrm{O}^*}{=}E_{\mathrm{slab + H}_2\mathrm{O}^-}E_{\mathrm{slab}^-}E_{\mathrm{H}_2\mathrm{O}^*}\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 414, 567, 433]]<|/det|>
+The free energy of adsorbed H and \(\mathrm{H}_2\mathrm{O}\) as follows:  
+
+<|ref|>equation<|/ref|><|det|>[[400, 441, 639, 490]]<|/det|>
+\[\Delta G_{\mathrm{H}^*}{=}\Delta E_{\mathrm{H}^*}{+}\Delta E_{\mathrm{ZPE}}{-}T\Delta S\] \[\Delta G_{\mathrm{H}_2\mathrm{O}^*}{=}\Delta E_{\mathrm{H}_2\mathrm{O}^*}{+}\Delta E_{\mathrm{ZPE}}{-}T\Delta S\]  
+
+<|ref|>text<|/ref|><|det|>[[147, 495, 850, 571]]<|/det|>
+where \(\Delta E_{\mathrm{H}^*}\) represent the H adsorption energy and \(\Delta E_{\mathrm{H}_2\mathrm{O}^*}\) represent the \(\mathrm{H}_2\mathrm{O}\) adsorption energy, and \(\Delta E_{\mathrm{ZPE}}\) represents the difference related to the zero- point energy between the gas phase and the adsorbed state.  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 599, 309, 616]]<|/det|>
+## Acknowledgments  
+
+<|ref|>text<|/ref|><|det|>[[147, 625, 852, 728]]<|/det|>
+This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 52070006, 11804012), the Scientific and Technological Development Project of the Beijing Education Committee (No. KZ201710005009), and the Beijing Municipal Education Commission (Grant No. KM201910005009).  
+
+<|ref|>sub_title<|/ref|><|det|>[[148, 752, 330, 769]]<|/det|>
+## Notes and references  
+
+<|ref|>text<|/ref|><|det|>[[147, 774, 852, 905]]<|/det|>
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+
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+
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+nanosheets with enhanced supercapacitive performance. RSC Adv. 4, 3181 (2014).41 Ye, S. et al. Highly stable single Pt atomic sites anchored on aniline-stacked graphene for hydrogen evolution reaction. Energy Environ. Sci. 12, 1000- 1007 (2019).42 Hunt, S. T. et al. Activating earth- abundant electrocatalysts for efficient, low- cost hydrogen evolution/oxidation: sub- monolayer platinum coatings on titanium tungsten carbide nanoparticles. Energy Environ. Sci. 9, 3290- 3301 (2016).43 Huang, X. et al. High- performance transition metal- doped \(\mathrm{Pt_3Ni}\) octahedra for oxygen reduction reaction. Science 348, 1230- 1234 (2015).44 Zhou, K. et al. Seamlessly conductive \(\mathrm{Co(OH)_2}\) tailored atomically dispersed Pt electrocatalyst in hierarchical nanostructure for efficient hydrogen evolution reaction. Energy Environ. Sci. 13, 3082- 3092 (2020).45 Romanchenko, A. et al. X- ray photoelectron spectroscopy (XPS) study of the products formed on sulfide minerals upon the interaction with aqueous platinum (IV) chloride complexes. Minerals 8, 578 (2018).46 Cai, W. et al. Platinum- trimer decorated cobalt- palladium core- shell nanocatalyst with promising performance for oxygen reduction reaction. Nat. Commun. 10, 440 (2019).47 Cheng, N. et al. Platinum single- atom and cluster catalysis of the hydrogen evolution reaction. Nat. Commun. 7, 13638 (2016).48 Fei, H. et al. Atomic cobalt on nitrogen- doped graphene for hydrogen generation. Nat. Commun. 6, 8668 (2015).49 Kwak, J. et al. Coordinatively unsaturated \(\mathrm{Al^{3 + }}\) centers as binding sites for Active catalyst phases of platinum on \(\mathrm{Al_2O_3}\) . Science 325, 1670- 1673 (2009).50 Savinelli, R et al. Wavelet transform EXAFS analysis of mono- and dimolybdate model compounds and a Mo/HZSM- 5 dehydroaromatization catalyst. Phys. Chem. Chem. Phys. 12, 5660- 5667 (2010).51 Funke, H. et al. Wavelet analysis of extended x- ray absorption fine structure data. Phys. Rev. B 71, 9 (2005).52 Fang, S. et al. Uncovering near- free platinum single- atom dynamics during
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[140, 88, 853, 916]]<|/det|>
+electrochemical hydrogen evolution reaction. Nat. Commun. 11, 1029, (2020).53 Yin, J. et al. Iridium single atoms coupling with oxygen vacancies boosts oxygen evolution reaction in acid media. J. Amer. Chem. Soc. 142, 43 (2020).54 Dinh, C. T. et al. Multi-site electrocatalysts for hydrogen evolution in neutral media by destabilization of water molecules. Nat. Energy 4, 107- 114(2019).55 Wang, Y. et al. Selectively anchoring Pt single atoms at hetero- interfaces of \(\gamma\) - \(\mathrm{Al}_2\mathrm{O}_3 / \mathrm{NiS}\) to promote hydrogen evolution reaction. J. Mater. Chem. A 6, 11783- 11789 (2018).56 Shi, Y. et al. Recent advances in transition metal phosphide nanomaterials: Synthesis and applications in hydrogen evolution reaction. Chem. Soc. Rev., 45, 1529- 1541 (2016).57 Huang, J. et al. Boosting the hydrogen transfer during volmer reaction at oxides/metal nanocomposites for efficient alkaline hydrogen evolution. ACS Energy Lett. 4, 12, 3002- 3010 (2019).58 Zhou, K. L. et al. Highly stable transparent conductive electrodes based on silver- platinum alloy- walled hollow nanowires for optoelectronic devices. ACS Appl. Mater. Interfaces 10, 36128- 36135 (2018).59 Fang, S. et al. Uncovering near- free platinum single- atom dynamics during electrochemical hydrogen evolution reaction. Nat. Commun. 11, 1029 (2020).60 Kresse, G. G. et al. Efficiency of ab- initio total energy calculations for metals and semiconductors using a plane- wave basis set. Comput. Mater. Sci. 6, 15 (1996).61 Kresse, G. G. et al. Efficient iterative schemes for ab initio total- energy calculations using a plane- wave basis set. Phys. Rev. B 54, 11169 (1996).62 Kresse, G. G. et al. Ab initio molecular- dynamics simulation of the liquid- metal- amorphous- semiconductor transition in germanium. Phys. Rev. B 49, 14251 (1994).63 Blöchl, P. et al. Projector augmented- wave method. Phys. Rev. B 50, 17953 (1994).64 Kresse, G. G. et al. From ultrasoft pseudopotentials to the projector augmented- wave method. Phys. Rev. B 59, 1758 (1999).65 Perdew, J. P. et al. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865 (1996).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[145, 88, 852, 333]]<|/det|>
+66 Payne, M. C. et al. Iterative minimization techniques for ab initio total- energy calculations: molecular dynamics and conjugate gradients. Rev. Mod. Phys. 64, 1045 (1992).67 Methfessel, M. et al. High- precision sampling for Brillouin- zone integration in metals. Phys. Rev. B 40, 3616 (1989).68 Pulay, P. Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett. 73, 393- 398 (1980).69 Henkelman, G. et al. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113, 9901- 9904 (2000).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 43, 143, 68]]<|/det|>
+## Figures  
+
+<|ref|>image<|/ref|><|det|>[[39, 100, 960, 530]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 555, 115, 574]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 596, 955, 685]]<|/det|>
+Schematic illustration of synthesis and water splitting mechanism of PtSA- NiO/ Ni. (a) The synthesis process of Pt single atom anchored NiO/ Ni heterostructure nanosheets on Ag nanowires network. (b) The mechanism of PtSA- NiO/ Ni network as an efficient catalyst towards large- scale water electrolysis in alkaline media.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[45, 42, 950, 737]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 755, 117, 774]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 794, 953, 931]]<|/det|>
+Structural characterization of the fabricated PtSA- NiO/Ni catalyst. (a) XRD patterns of PtSA- NiO/Ni, NiO/Ni, and Ag NWs. (b- c) SEM images of PtSA- NiO/Ni. (d) HAADF- STEM image of PtSA- NiO/Ni. (e- f) Magnified HAADF- STEM image of PtSA- NiO/Ni and (g) the corresponding DFT simulated image, showing the atomically dispersed Pt atoms at Ni position (circles in (e)). (h) HRTEM images of PtSA- NiO/Ni and the insert in (h) shows the related FFT image of PtSA- NiO/Ni. (i- j) Dark- field TEM images of PtSA- NiO/Ni with different magnifications and (k- n) the mapping of the corresponding elements.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[42, 42, 960, 545]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 560, 117, 580]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 602, 958, 712]]<|/det|>
+Electronic state and atomic structure characterization. (a) Pt 4f spectra, (b) XANES spectra, and (c) calculated Pt oxidation states derived from \(\Delta\) XANES spectra of PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni, and Pt foil is given as a reference. (d) Corresponding FT- EXAFS curves of Figure 3b. (e) EXAFS fitting curve of PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni R- space. (f) EXAFS wavelet transform plots of PtSA- NiO/Ni, PtSA- NiO, PtSA- Ni, and Pt foil.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[42, 40, 950, 545]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 560, 118, 579]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 601, 949, 760]]<|/det|>
+Theoretical investigations. Computational models and localized electric field distribution of (a) PtSAniO/Ni, (b) PtSA- NiO and (c) PtSA- Ni. (d) Calculated PDOS of NiO/Ni and PtSA- NiO/Ni, with aligned Fermi level. (e) Calculated Pt 5d band of PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni. (f) The orbital alignment of the surficial sites for PtSA- NiO/Ni binding with H2O molecule. (g) Calculated OH- binding energies (ΔEOH) and H- binding energies (ΔEH) for Ni, pure NiO, and O vacancies modified NiO surface. (h) Calculated energy barriers of water dissociation kinetic and (i) adsorption free energies of H\* on the surface of the PtSA- NiO/Ni, PtSA- NiO, and PtSA- Ni catalysts, respectively.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[44, 44, 951, 580]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 597, 120, 616]]<|/det|>
+<center>Figure 5 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 639, 951, 796]]<|/det|>
+Electrocatalytic alkaline HER performances of the catalysts in 1 M KOH electrolyte. (a) HER polarization curves of PtSA- NiO/Ni, PtSA- NiO, PtSA- Ni, NiO/Ni, and Pt/C. (b) The comparison of overpotentials required to achieve 10 mA cm- 2 for various catalysts. (c) The mass activity of the Pt- based catalysts. (d) Corresponding Tafel slope originated from LSV curves. (e) EIS (Electrochemical Impedance Spectroscopy) Nyquist plots of the catalysts. (f) Stability test of PtSA- NiO/Ni through cyclic potential scanning and chronoamperometry method (Inset in f). (g) TOFs plots of the Pt- based electrocatalysts. (h) Comparison of the HER activity for PtSA- NiO/Ni with reported catalysts, originating from Table S2.  
+
+<|ref|>sub_title<|/ref|><|det|>[[45, 819, 310, 846]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[45, 870, 764, 890]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 908, 330, 926]]<|/det|>
+- Supportinginformation.docx
+
+<--- Page Split --->

preprint/preprint__5fc2f276e635038fe4225ff26f4f6b284549bce2f6a07cb7b01f86ea2ec20969/images_list.json

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+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1 | Structural model of the adamantane-type cluster in the amorphous compound \\([(PhSn)_4S_6]\\) (A) and its simplified representations. a, Full cluster structure. b, Simplified representation with organic groups reduced to short grey sticks and the (nonbonded) \\(\\{Sn_4\\}\\) motif highlighted by a tetrahedron. c, Even more simplified representation by the inner tetrahedral \\(\\{Sn_4\\}\\) motif only.",
+    "footnote": [],
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+    "page_idx": 2
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2 | Schematic illustration of the 'crystalline sponge'1,2 method versus the 'π-trap' approach. The approaches are shown on the examples of the organic compound guaiazulene, \\(\\mathrm{C_{15}H_{18}}\\) ,1,2 represented by a light brown tetrahedron, and [(PhSn)4Se] (A), represented by its inner tetrahedral {Sn4} motif (see Fig. 1c). a, The 'crystal sponge' method applied to smaller-size organic compounds. b, The 'π-trap' approach leading to crystalline compounds accommodating organotetrel chalcogenide cluster molecules.",
+    "footnote": [],
+    "bbox": [
+      [
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+    ],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3 | Schematic representation of the preparation procedure for a single-crystalline cocrystals of \\(\\mathbf{C}_{60}\\) and [(PhSn)4S6] (A). a, Photograph of microcrystalline \\(\\mathrm{C}_{60}\\) (as purchased) and structure model of the \\(\\mathrm{C}_{60}\\) molecule. b, Photograph of the amorphous powder of pure compound A and simplified structure model of the [(PhSn)4S6] cluster molecule (see Fig. 1b). c, Layering of the two solutions comprising the starting materials and diffusion into one another. d, View of the crystal structure of [(PhSn)4S6]2·[C60]·(C7H8)1.2·[C4H8O]1.2 (1) viewed along the crystallographic \\(a\\) axis, with cluster pairs visible between the fullerene spheres. e, Light-microscopic image of single-crystals of compound 1 with scalebar.",
+    "footnote": [],
+    "bbox": [
+      [
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+        426
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4 | Details of the crystal structures of co-crystals 1, 2, and 3. a, Packing scheme of compound 1, viewed along the crystallographic \\(c\\) axis. b, Packing scheme of compound 2, viewed along the crystallographic \\(b\\) axis. c, Packing scheme of compound 3, viewed along the crystallographic \\(b\\) axis. d, Pair of [(PhSn)4S6] clusters in the crystal structure of 1 interacting with surrounding \\(C_{60}\\) molecules; for clarity, the phenyl groups are depicted in grey and green for the two distinct [(PhSn)4S6] molecules within the pair, respectively (disorder position shown in semitransparent mode). e, The cluster pair in 1 viewed along the Sn-Sn axis. f, Pair of [(PhSi)4S6] clusters in the crystal structure of C, for comparison; for clarity, the phenyl groups are depicted in grey and green for the two distinct [(PhSi)4S6] molecules within the pair, respectively. g, The cluster pair in C viewed along the Sn-Sn axis, for comparison.",
+    "footnote": [],
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+    ],
+    "page_idx": 7
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5 | UV-visible spectra of parent compounds and co-crystals 1, 2 and 3. The spectra were recorded on samples of [(PhSn)4S6] and [(PhSn)4Se6] as amorphous powders and in solution, of \\(\\mathrm{C}_{60}\\) as polycrystalline powder and in toluene, and on single-crystals of 1, 2 and 3.",
+    "footnote": [],
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+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6 | Electronic structures of the compounds calculated within DFT-PBE. a, Electronic band structure for calculated compound 1. b, Electronic band structure for calculated compound 2. c, Electronic band structure for calculated compound 3. d, Visualization of the top of the valence band (lhs), being strongly localized at the S atoms, similarly to the LUMO of A. e, Visualization of the bottom of the conduction band (rhs) of 1, resembling the HOMO of A. f, Density of states and partial density of states for compound 1; the partial density of states are shown in different colors for different atoms. g, Visualization of the squared wavefunctions associated to the mid gap electronic states in 1, localized at C60. Isosurfaces are drawn at \\(0.001 \\text{e}^{-} \\text{\\AA}^{-3}\\) .",
+    "footnote": [],
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preprint/preprint__5fc2f276e635038fe4225ff26f4f6b284549bce2f6a07cb7b01f86ea2ec20969/preprint__5fc2f276e635038fe4225ff26f4f6b284549bce2f6a07cb7b01f86ea2ec20969.mmd

@@ -0,0 +1,261 @@
+
+# The 'π-Trap' as an Unrestricted Crystal Sponge for Inherently Amorphous Cluster Compounds  
+
+Stefanie Dehnen  
+
+stefanie.dehnen@kit.edu  
+
+Karlsruhe Institute of Technology https://orcid.org/0000- 0002- 1325- 9228  
+
+Yaofeng Wang  
+
+Karlsruhe Institute of Technology  
+
+Niklas Rinn  
+
+Karlsruhe Institute of Technology  
+
+Kevin Eberheim  
+
+Justus Liebig University  
+
+Ferdinand Ziese  
+
+Justus Liebig University  
+
+Jan Christmann  
+
+Karlsruhe Institute of Technology  
+
+Simone Sanna  
+
+Justus Liebig University  
+
+Physical Sciences - Article  
+
+Keywords: π- π interactions, unrestricted crystal sponge, amorphous compounds, cluster molecules, C60  
+
+Posted Date: February 24th, 2025  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 5953585/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 August 25th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 62928- y.
+
+<--- Page Split --->
+
+# The "π-Trap' as an Unrestricted Crystal Sponge for Inherently Amorphous Cluster Compounds  
+
+Yaofeng Wang \(^{1}\) , Niklas Rinn \(^{1}\) , Kevin Eberheim \(^{2}\) , Ferdinand Ziese \(^{2}\) , Jan Christmann \(^{1}\) , Simone Sanna \(^{2}\) , and Stefanie Dehnen \(^{1,*}\)  
+
+(1) Karlsruhe Institute of Technology, Institute of Nanotechnology. Kaiserstrasse 12, 76131 Karlsruhe, Germany  
+
+(2) Institut für Theoretische Physik and Center for Materials Research (LaMa), Justus-Liebig-Universität Gießen, 35392 Gießen, Germany  
+
+## Abstract  
+
+Single crystal diffraction is one of the most common and powerful tools for structural elucidation in science. However, obtaining single crystals of adequate size and quality is not always trivial, with some chemicals inherently resisting all attempts. The 'crystalline sponge' method has attracted a lot of attention for crystallizing otherwise intrinsically amorphous compounds inside a metal organic framework (MOF). \(^{1 - 4}\) However, its application is limited by the size and stability of the pores within the networks. In this study, we propose a novel 'unrestricted crystalline sponge' method, which we denominate as the 'π- trap'. It makes use of π- π interactions between C₆₀ and nm- sized molecules that by themselves do not form crystalline compounds. Using this technique, we successfully crystallized adamantane- like organic- inorganic hybrid clusters, which exhibit extreme nonlinear optical properties only within the amorphous habitus, and resist any attempt for crystallization. As the clusters' low tendency to order in the long range was successfully overcome by the strong C₆₀···cluster interactions in the 'π- trap', we were able to precisely determine their molecular structures. As we could show by optical spectroscopy and quantum chemical calculations, both the clusters and C₆₀ behave like being dissolved in the other component, including the formation of cluster pairs previously proposed by theoretical studies and low- angle scattering experiments on amorphous samples. We propose that the described method is applicable to all kinds of amorphous compounds that allow for π- π interactions, without the size restrictions facing the 'crystalline sponge' method, especially when considering the usage of larger fullerenes.  
+
+Keywords: π- π interactions, unrestricted crystal sponge, amorphous compounds, cluster molecules, C₆₀
+
+<--- Page Split --->
+
+## Introduction  
+
+Single- crystal X- ray diffraction (SCXRD) analysis provides the most precise method for determining the structures of natural and synthetic molecules, making it an indispensable tool for chemists. Naturally, it requires the samples to be obtained in single crystalline form. However, many compounds are intrinsically amorphous, and therefore their structures cannot be subjected to SCXRD analysis. In 2010, Fujita and co- workers introduced a method in which porous coordination networks are used as 'crystalline sponges' that absorb target molecules from solution and orient them in a uniform fashion within the crystalline network, which enabled the determination of their molecular structures at atomic resolution by SCXRD. \(^{1 - 4}\) While this method does not require the crystallization of the target compound by itself, it requires that the networks' pores have a suitable size and stability to accommodate the guest molecules. Therefore, this technique has been mostly applied to smaller molecules, like 2,6- diisopropylaniline, guaiazulene, santonin, or chain- like molecules, such as miyakosyne, which comfortably fit into the pores. Larger guests, like fullerene molecules, could be included too, yet in this case, no crystal data were obtained. \(^{3}\) To the best of our knowledge, the method has so far been used mostly for (bio- )organic molecules or organometallic complexes. In contrast, methods to precisely determine the molecular structures of amorphous compounds that are comprised of (polyhedral) inorganic cluster molecules, have remained elusive to date.  
+
+Recently, adamantane- type organic- inorganic hybrid clusters with a general composition of \([(R\mathrm{Sn})_4\mathrm{E}_6]\) ( \(\mathrm{R} =\) organic substituent, \(\mathrm{E} = \mathrm{S}\) , Se), such as \([(PhSn)_4S_6]\) (A, Fig. 1) or \([(PhSn)_4Se_6]\) (B), have attracted significant attention due to their (extreme) nonlinear optical (NLO) properties. \(^{5,6}\) Particularly noteworthy is the phenomenon of continuous- wave infrared laser- induced directional white light generation (WLG). This has been demonstrated to work exclusively for rigorously amorphous \([(R\mathrm{Sn})_4\mathrm{E}_6]\) compounds containing electron- rich organic substituents like phenyl (Ph), styryl (Sty) or cyclopentadienyl (Cp), although the physical mechanism behind this phenomenon is still largely ununderstood. \(^{7,8}\) The structural conformations of the corresponding \([(R\mathrm{Sn})_4\mathrm{E}_6]\) cluster molecules have been suggested by theoretical studies, also in combination with X- ray and neutron scattering experiments, but could never be verified or supported crystallographically—as the amorphous habitus is intrinsic to those materials. \(^{9 - 11}\) Notably, related clusters, such as \([(MeSn)_4S_6]^5\) or \([(PhSi)_4S_6]\) (C), \(^{5}\) form crystalline solids and show strong second harmonic generation (SHG) instead of WLG.  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1 | Structural model of the adamantane-type cluster in the amorphous compound \([(PhSn)_4S_6]\) (A) and its simplified representations. a, Full cluster structure. b, Simplified representation with organic groups reduced to short grey sticks and the (nonbonded) \(\{Sn_4\}\) motif highlighted by a tetrahedron. c, Even more simplified representation by the inner tetrahedral \(\{Sn_4\}\) motif only. </center>
+
+<--- Page Split --->
+
+To date, it is still unclear why the amorphous habitus is required for the WLG phenomenon, and is has also not been clarified until today which parameters control that some of these highly related cluster compounds crystallize while other ones remain rigorously amorphous. There have been suggestions for answering the latter question based on theoretical studies of cluster pair models, which suggested more pronounced (directed) substituent-substituent interactions for compounds featuring smaller cluster cores (e.g., \(\{\mathrm{Si}_4\mathrm{S}_6\}\) ), whereas for clusters with larger cores (e.g., \(\{\mathrm{Sn}_4\mathrm{S}_6\}\) ), one observes a dominance of (rather isotropic) interactions of the polyhedral cluster cores.12 Combined scattering and reverse Monte- Carlo studies revealed information about cluster assemblies, and also suggested significant statistical distortions of the cluster cores, with an increased tendency for larger (and softer) cores.13 However, a crystallographic proof of all of those hypotheses has still been elusive. Experimental and theoretical physicists have been trying to find answers to the former question since the first observation of the WLG phenomenon, for which a full picture of the amorphous compounds' characteristics—including the essentially inaccessible structural data—is critical.14  
+
+We therefore aimed at identifying a tool for obtaining this data to get knowledge of and possibly confirm the reasons for an amorphous versus crystalline habitus. This would lay the foundation for eventually finding an explanation for the physical phenomenon in the near future and altogether ultimately allow to design and control the compounds' habitus and habitus- dependent properties. A rather obvious idea was to apply Fujita's 'crystalline sponge method'.1,2 However, as indicated by the Fujita group in their seminal work, the applicability of the technique is limited by the maximum cross- section of pores in crystalline sponge, which is typically below \(1\mathrm{nm}\) in the materials applied to this technique. MOFs with larger pores exist,15 but they tend to collapse during the process. Unsuccessful attempts with polyhedral \(\{\mathrm{RSn}_4\mathrm{E}_6\}\) molecules confirmed that their sizes, with outer diameters of \(\sim 1 - 1.5\mathrm{nm}\) , prohibit the application of this approach. So, for obtaining precise structural data of cluster molecules that form intrinsically amorphous powders, another methodology is needed.  
+
+Here, we report about the introduction of the \(\pi\) - trap' as an 'unrestricted crystalline sponge' method, which makes use of the co- crystallization of cluster molecules with commercially available fullerene \(\mathrm{C}_{60}\) as a simple, cheap and sustainable means of solving the problem (Fig. 2). The electronic structure of the fullerene molecules enables \(\pi\) - \(\pi\) interactions between their surface and aromatic organic substituents on the clusters, and their size and spherical shape allows for comfortably co- crystallizing with larger, polyhedral cluster compounds. While co- crystals with \(\mathrm{C}_{60}\) were previously shown to form with clusters that also crystallize by themselves, like Chevrel- type superatomic clusters,16- 18 we demonstrate this technique for the first time on the example of amorphous \(\{\mathrm{PhSn}_4\mathrm{E}_6\}\) clusters, the crystal structures of which are otherwise inaccessible. Specifically performed quantum- chemical calculations reveal how the crystal formation affects the atomic and electronic structure of the \(\{\mathrm{PhSn}_4\mathrm{E}_6\}\) clusters. We give perspectives to the expansion of the method to other amorphous- cluster- fullerene combinations. The method finally allowed to compare the structural data with previous theoretical predictions,12 and to rationalize and verify the computations.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 | Schematic illustration of the 'crystalline sponge'1,2 method versus the 'π-trap' approach. The approaches are shown on the examples of the organic compound guaiazulene, \(\mathrm{C_{15}H_{18}}\) ,1,2 represented by a light brown tetrahedron, and [(PhSn)4Se] (A), represented by its inner tetrahedral {Sn4} motif (see Fig. 1c). a, The 'crystal sponge' method applied to smaller-size organic compounds. b, The 'π-trap' approach leading to crystalline compounds accommodating organotetrel chalcogenide cluster molecules. </center>  
+
+## Results and Discussion  
+
+Syntheses and crystal structures. Two intrinsically amorphous adamantane- type cluster compounds, [(PhSn)4Se] (A) and [(PhSn)4Se] (B), were used for our proof- of- principle study to demonstrate the success of the 'π- trap' approach. As schematically depicted in Figure 3a- c, the crystallization process with \(\mathrm{C_{60}}\) involves layering a solution of the cluster compound in THF with a solution of the fullerene in toluene. Slow diffusion of the solutions into each other resulted in the formation of red single crystals at the solution interface after one week (see Supplementary Figure 1). SCXRD analyses of the single- crystals that were obtained from mixtures involving A, unveiled two different products to form simultaneously in the same batch. They feature different ratios of [(PhSn)4Se] and \(\mathrm{C_{60}}\) and also different amounts of crystal solvent molecules ( \(\mathrm{C_{7}H_{8} =}\) toluene or \(\mathrm{C_{4}H_{8}O = THF}\) ) per formula unit, [(PhSn)4Se]2- (C60)- (C7H8)1,2- (C4H8O)1,2 (1, Fig. 3d- e) and [(PhSn)4Se]2- (C60)1,5- (C7H8) (2). After adjusting the \(\mathrm{C_{60}}\) :A ratio, we were able to obtain both 1 or 2 selectively. Mixtures involving B yielded exclusively [(PhSn)4Se] (C60)- (C7H8)- (C4H8O)0,5 (3). Notably, these are the first crystal structures involving notoriously amorphous inorganic clusters compounds in general, and this specific type of amorphous clusters in particular, the mere synthesis and chemical characterization of which was reported as early as in 1987 in the case of A.19 More crystal photographs as well as different views and further details of the crystal structures of the three compounds are provided below and in Supplementary Figures 2- 15.
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3 | Schematic representation of the preparation procedure for a single-crystalline cocrystals of \(\mathbf{C}_{60}\) and [(PhSn)4S6] (A). a, Photograph of microcrystalline \(\mathrm{C}_{60}\) (as purchased) and structure model of the \(\mathrm{C}_{60}\) molecule. b, Photograph of the amorphous powder of pure compound A and simplified structure model of the [(PhSn)4S6] cluster molecule (see Fig. 1b). c, Layering of the two solutions comprising the starting materials and diffusion into one another. d, View of the crystal structure of [(PhSn)4S6]2·[C60]·(C7H8)1.2·[C4H8O]1.2 (1) viewed along the crystallographic \(a\) axis, with cluster pairs visible between the fullerene spheres. e, Light-microscopic image of single-crystals of compound 1 with scalebar. </center>  
+
+Figure 4 illustrates the crystal structures of the three co- crystals. The structures show several unique and informative features, which we outline in what follows. A view of the packing schemes in a selected crystallographic direction (see Fig. 4a- c) highlights that all compounds, 1, 2, and 3, comprise pairs of clusters embedded in an environment of \(\mathrm{C}_{60}\) molecules—albeit in very different, and very complex packing patterns. We observe relatively short distances between the centroids of the hexagonal faces of \(\mathrm{C}_{60}\) and the clusters' phenyl groups, down to \(3.897 \mathring{\mathrm{A}}\) in compound 1 (Fig. 4a), \(3.109 \mathring{\mathrm{A}}\) in 2, and \(3.250 \mathring{\mathrm{A}}\) in 3. This supports our assumption that the crystal lattice is stabilized by face- to- face \(\pi\) - \(\pi\) or C- H- \(\pi\) interactions. Moreover, the shortest distances between chalcogenide atoms (S or Se) and the hexagonal faces of neighboring \(\mathrm{C}_{60}\) molecules are \(3.528 \mathring{\mathrm{A}}\) for 1, \(3.566 \mathring{\mathrm{A}}\) for 2, and \(3.710 \mathring{\mathrm{A}}\) for 3, indicating another type of secondary interaction.  
+
+A close- up of the crystal structure of 1 (Fig. 4d) emphasizes the intense \(\pi\) - \(\pi\) interactions between the two types of molecules and, importantly, also within the cluster pairs. When viewed along the Sn- Sn axis, the phenyl groups within the pairs are arranged in staggered positions (Fig. 4e), which allows for a more intense (dominant) interaction of the cluster cores (6.228 \(\mathring{\mathrm{A}}\) from center to center) as compared to those between the substituents—as predicted by computational studies of various cluster pairs as minimal model for the interaction. \(^{12}\) In compound 1 the shortest distance between the centroids of adjacent phenyl groups is measured at \(5.568 \mathring{\mathrm{A}}\) . For comparison, in the analogue crystalline compound [(PhSi)4S6] (C), \(^{5}\) the staggered arrangement is different, resulting in a shorter distance of \(4.847 \mathring{\mathrm{A}}\) between adjacent phenyl groups, while the cluster cores are much more distant
+
+<--- Page Split --->
+
+(7.058 Å, Fig. 4f and Suppl. Fig. 10)—again in excellent agreement with the computations: these indicated stronger substituent–substituent interactions and weaker core–core interactions for the PhSi/S system than for the PhSn/S system (and vice versa). \(^{12}\) The core center-to-center distances between the [(PhSn)4E6] clusters in the other pairs are similarly small, 6.284 Å and 6.409 Å (compound 2), and 6.498 Å (compound 3) (see Suppl. Figs. 11, 12, 15). As suggested, the predominance of the relatively isotropic core-core interactions in PhSn/S-based clusters surpasses the directional interactions involving the substituents, which is perfectly reflected by the new crystal data, in which the pairs are retained also in the presence of C60. This finally rationalizes and explains why Sn-based compounds exhibit a distinctly lower tendency for order as a single compound in the solid state compared to their crystalline PhSi/S-based counterparts.  
+
+As another contrast to the ordered situation within crystalline [(PhSi)4S6] (C), \(^{5}\) the phenyl groups in compounds 1, 2 and 3 show a tendency for disorder (see Fig. 4d- e). This can be explained by the Sn- C bonds being naturally longer than Si- C bonds (2.103(14) – 2.126(19) Å for the former versus 1.8540(15) – 1.8562(15) Å for the latter, see Suppl. Table 2), which decreases the interaction barrier between the hydrogen atoms of the substituents and the S or Se atoms of the cluster for the heavier homologues. The overall higher flexibility of the phenyl groups obviously weakens their (directed) interaction and thus hampers crystallization. Both cluster cores observed herein, {Sn4S6} in 1 and 2 and {Sn4Se6} in 3, exhibit a notable tendency for molecular distortions. This is particularly obvious in compound 2, with S- Sn- S angles ranging from 107.84 to 116.03° (Suppl. Table 2). This range is notably greater than the reported range of S- Si- S angles in [(PhSi)4S6] (C; 111.29 to 113.27°), \(^{5}\) indicating a higher degree of distortion within the Sn/S cluster core than in the Si/S core of the lighter homologue. We suspect that these distortions reflect a certain degree of dynamic behavior, even under crystallization conditions, which refers to increased motion of the atoms as another argument for prohibiting crystallization as a sole compound.
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4 | Details of the crystal structures of co-crystals 1, 2, and 3. a, Packing scheme of compound 1, viewed along the crystallographic \(c\) axis. b, Packing scheme of compound 2, viewed along the crystallographic \(b\) axis. c, Packing scheme of compound 3, viewed along the crystallographic \(b\) axis. d, Pair of [(PhSn)4S6] clusters in the crystal structure of 1 interacting with surrounding \(C_{60}\) molecules; for clarity, the phenyl groups are depicted in grey and green for the two distinct [(PhSn)4S6] molecules within the pair, respectively (disorder position shown in semitransparent mode). e, The cluster pair in 1 viewed along the Sn-Sn axis. f, Pair of [(PhSi)4S6] clusters in the crystal structure of C, for comparison; for clarity, the phenyl groups are depicted in grey and green for the two distinct [(PhSi)4S6] molecules within the pair, respectively. g, The cluster pair in C viewed along the Sn-Sn axis, for comparison. </center>  
+
+So far, we can summarize that we were able to obtain the first crystallographic structural data from clusters of the [(RT)4E6] family that do not crystallize by themselves. Moreover, these data, as compared to those of the crystalline homologue [(PhSi)4S6] (C), served to confirm a theoretical prediction made on the basis of computed pair structures of different clusters in regards of their
+
+<--- Page Split --->
+
+preference of arranging in ordered structures (crystals) or rather assembling without any long- range periodicity (amorphous powders).<sup>12</sup>  
+
+It is worth noting that during the preparation of this manuscript, a similar method known as the 'crystalline mate' was showcased in a parallel work,<sup>20</sup> but this method was designed for smaller organic molecules only, making it inappropriate for cluster materials. It also required the preparation and provision of specific molecules instead of using commercially available fullerene. Our work was rather inspired by the co- crystallization of fullerene and [(RCo)6Es] clusters reported recently by the Nuckolls group.<sup>16- 18</sup> However, while the Co/E clusters do also crystallize without \(\mathrm{C}_{60}\) , this is not the case for the clusters we address in our approach, where addition of \(\mathrm{C}_{60}\) is the only means of growing crystals comprising those species. As shown by the quoted work though, such co- crystals can achieve new properties through this step. The mere color change upon combination of the colorless (cluster) powder with the black ( \(\mathrm{C}_{60}\) ) powder to form red crystals also suggests the combination of properties in the case of compounds 1 - 3. The nature of this combination remained to be explored though.  
+
+We therefore investigated whether the intense non- covalent interactions that lead the molecules into an ordered arrangement have an effect on the geometric and electronic structures of the clusters of interest, or whether the latter still behave like the pure substances—especially regarding their macroscopic properties (note that this question does not address WLG, as this requires the amorphous habitus, see above). The visual impression of the crystals, being neither black like \(\mathrm{C}_{60}\) nor colorless like [(PhSn)4E6] (E = S, Se), but red, could be caused by a mere physical mixture ('blend') of both components, but they may also result from electronic interactions. While the latter would be very interesting in terms of new semiconducting materials, the first is the primary goal we have in this work, as we aim to get the most reliable and unaffected structural data from this unique class of materials, which requires that they undergo the weakest interaction possible, just enough to order. For judging about this, we investigated optical absorption properties and performed concomitant quantum chemical calculations (DFT and TDDFT) of the crystalline blends.  
+
+Optical absorption properties. For being able to comment on the optical absorption properties of co- crystals 1, 2, and 3, we recorded UV- visible spectra of the pure (amorphous) parent compounds in the solid state and in solution, of \(\mathrm{C}_{60}\) in the solid state and in solution, and of the single- crystals of 1, 2, and 3. The spectra are displayed in Figure 5.  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5 | UV-visible spectra of parent compounds and co-crystals 1, 2 and 3. The spectra were recorded on samples of [(PhSn)4S6] and [(PhSn)4Se6] as amorphous powders and in solution, of \(\mathrm{C}_{60}\) as polycrystalline powder and in toluene, and on single-crystals of 1, 2 and 3. </center>
+
+<--- Page Split --->
+
+The UV- visible spectra of the co- crystals 1, 2, and 3 show an onset of absorption at around \(700\mathrm{nm}\) , slightly red- shifted for compound 3, followed by 2 and 1. We assume that the difference between the Sn/Se- based composition of 3 and the Sn/S- based compositions of 1 is not dominant here, but the ratio between the number of \([(PhSn)_4E_6]\) cluster units \((\mathrm{E} = \mathrm{S},\mathrm{Se})\) and \(\mathrm{C}_{60}\) molecules in the cocrystal. In the most red- shifted compound 3, this ratio is 1:1. In compound 2, the corresponding ratio is 2:1.5, and 1, it is 2:1. This is in agreement with the fact that a spectral feature around 600 nm agrees with the maximum at \(601\mathrm{nm}\mathrm{C}_{60}\) in toluene solution. So, for the onset of absorption, we see similar spectroscopic signatures of 1 – 3 that are controlled by the behavior of \(\mathrm{C}_{60}\) – notably not in the solid, but in solution phase. The more intense absorption that is observed for all cocrystals below \(500\mathrm{nm}\) mostly reflects the absorption characteristics of the pure clusters, for which the solid- state and solution spectra do not differ significantly.  
+
+We conclude that in the co- crystal, the two components are widely independent regarding their electronic properties, hence, they behave like a physical mixture ('ordered solid solution'). This would corroborate the fact that the structural data we obtained for the previously amorphous cluster compounds are those that are inherent to these molecules without great impact from the co- crystal. However, to confirm our working thesis, we performed quantum chemical calculations of the electronic structure of the co- crystals.  
+
+First- principles calculations of the electronic properties of the co- crystals. Crystals of the compounds 1, 2 and 3 have been modeled from first principles. Lattice type and lattice parameters as calculated within DFT- PBE are reported in Supplementary Table 3. The calculated lattice parameters are in very good agreement with the measured values and confirm the experimentally determined structure; upon crystallization into compounds 1, 2, and 3, the cluster cores of A and B are only slightly compressed according to the DFT studies (see Supplementary Table 4). The formation of the co- crystals leads to the band structures of 1, 2 and 3 as shown in Figure 6a – 6c, which perfectly reflect the mixing of the two compounds. The band structures of all compounds are very flat as typical for molecular crystals, indicating a minor intermolecular interaction. All compounds are moreover semi- conductors, as indicated by an energy gap of about \(1.5\mathrm{eV}\) that separates the top of the valence band from the unoccupied states. Notably, this is significantly smaller than the HOMO- LUMO gap of the parent clusters \([(PhSn)_4S_6]\) A and \([(PhSn)_4Se_6]\) B cluster, calculated by DFT to be \(3.199\mathrm{eV}\) and \(2.726\mathrm{eV}\) . Yet, the original HOMO- LUMO gap can be recognized in the band structure of 1, 2, and 3, as we show in the following on the example of 1. Indeed, the spatial localization of the electronic states of the valence band top at \(- 0.3\mathrm{eV}\) and of the bottom of the second conduction band at about \(2.7\mathrm{eV}\) in Figure 6a closely resembles the orbital nature of the HOMO and LUMO of A; this is in full agreement with the experimental spectrum, in which the signature of the parent clusters can also be identified in smaller wavelength regions. As illustrated in Supplementary Figure 16, the HOMO is rather localized at the S atoms, while the LUMO is less localized at the S atoms and extended to the substituents. The energetic separation of the electronic states represented in Figure 6d and 6e is \(2.96\mathrm{eV}\) , close to the HOMO- LUMO separation in A, which further confirms their origin. Thus, the group of localized states that appears within the energy of the HOMO and LUMO of the parent molecules, is more correctly interpreted as a group of localized mid- gap states than as the valence band bottom or conduction band top. In order to explore the origin of these states, we project the density of states (DOS) of 1, 2, and 3 onto the different atomic species, see in Figure 6f. The DOS clearly shows that the localized states have their origin in the carbon atoms of the \(\mathrm{C}_{60}\) molecules. The wavefunctions associated with these states are indeed localized at the fullerene cages, as shown in Figure 6g.
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Figure 6 | Electronic structures of the compounds calculated within DFT-PBE. a, Electronic band structure for calculated compound 1. b, Electronic band structure for calculated compound 2. c, Electronic band structure for calculated compound 3. d, Visualization of the top of the valence band (lhs), being strongly localized at the S atoms, similarly to the LUMO of A. e, Visualization of the bottom of the conduction band (rhs) of 1, resembling the HOMO of A. f, Density of states and partial density of states for compound 1; the partial density of states are shown in different colors for different atoms. g, Visualization of the squared wavefunctions associated to the mid gap electronic states in 1, localized at C60. Isosurfaces are drawn at \(0.001 \text{e}^{-} \text{\AA}^{-3}\) . </center>  
+
+Summarizing, upon crystallization the HOMO and LUMO of the [(PhSn)4Se] and [(PhSn)4Se6] cluster build the conduction and valence band. The fullerene related states lay in between and lead to the top of the conduction band, the bottom of the valence band and mid- gap states. All C60- related states are highly localized and almost completely dispersionless. The band structure of 1, 2 and 3 thus corresponds to that of the parent compounds, overlaid but not substantially altered by the C60 states. The calculated absorbance of the crystals 1, 2, and 3 is shown in Supplementary Figure 18. The spectra substantially resemble the absorption of [(PhSn)4Se] and [(PhSn)4Se6], with an additional signature related to electronic transition involving the C60 states (marked by an arrow in the figure). According to the measured data, the onset of the optical absorption is at \(700 - 710 \text{nm}\) for the compounds 2 and 1, and somewhat redshifted for 3, due to the smaller bandgap of B in comparison with A. Interestingly, the C60 signatures show a larger scattering than in the measured data, suggesting that the interaction of C60 with the clusters is slightly overestimated in the atomistic models.  
+
+## Conclusion  
+
+Overall, through our 'π- trap' approach as an 'unrestricted crystal sponge' method, we demonstrate for the first time that inherently amorphous adamantane- like cluster can be trapped in a crystal structure by the π- π interaction tendency of C60, which we showcased for the important white- light-
+
+<--- Page Split --->
+
+emitting compounds \([(PhSn)_4S_6]\) and \([(PhSn)_4Se_6]\) . The structural data obtained through this novel method confirmed the initial hypotheses regarding the structural features of these clusters, providing critical evidence of the diverse molecular interactions within these systems. This way, we revealed that the \(\pi - \pi\) interaction help to overcome distortions of the clusters and the predominance of core- core interactions of Sn- based clusters which were previously identified as reasons for such clusters to remain inevitably amorphous. By a combined experimental and theoretical study, we also demonstrated that the co- crystals are more than a mere source of structural information, but exhibit a combination of the electronic properties of the two underlaying components. This enhanced understanding of the structural and interactive properties of the amorphous clusters contributes to the ability to predict, design, and control their features, paving the way for future advancements in the targeted development of these compounds. This innovative strategy is being currently extended to other fullerenes and their combinations with various clusters, and holds promising potential for crystallizing other amorphous materials in the future.  
+
+## References  
+
+1. Inokuma, Y., Arai, T. & Fujita, M. Networked molecular cages as crystalline sponges for fullerenes and other guests. Nat. Chem. 2, 780–783 (2010).  
+2. Inokuma, Y. et al. X-ray analysis on the nanogram to microgram scale using porous complexes. Nature 495, 461–466 (2013).  
+3. Inokuma, Y., Yoshioka, S., Ariyoshi, J., Arai, T. & Fujita, M. Preparation and guest-uptake protocol for a porous complex useful for ‘crystal-free’ crystallography. Nat. Protoc. 9, 246–252 (2014).  
+4. Zigon, N., Duplan, V., Wada, N., & Fujita, M. Crystalline Sponge Method: X-ray Structure Analysis of Small Molecules by Post-Orientation within Porous Crystals—Principle and Proof-of-Concept Studies. Angew. Chem. Int. Ed. 60, 25204–25222 (2021).  
+5. Rosemann, N. W. et al. A highly efficient directional molecular white-light emitter driven by a continuous-wave laser diode. Science 352, 1301–1304 (2016).  
+6. Rosemann, N. W., EuBner, J. P., Dornsiepen, E., Chatterjee, S. & Dehnen, S. Organotetrel Chalcogenide Clusters: Between Strong Second-Harmonic and White-Light Continuum Generation. J. Am. Chem. Soc. 138, 16224–16227 (2016).  
+7. Dornsiepen, E., Dobener, F., Chatterjee, S. & Dehnen, S. Controlling the White-Light Generation of [(RSn)4E6]: Effects of Substituent and Chalcogenide Variation. Angew. Chem. Int. Ed. 58, 17041–17046 (2019).  
+8. Wang, J., Rojas-Leon, I., Rinn, N., Guggolz, L., Ziese, F., Sanna, S., Rosemann, N. W. & Dehnen, S. Strain-Induced Structural Rearrangement Towards a White-Light-Emitting Adamantane-Type Cluster Dimer. Angew. Chem. Int. Ed. 63, e202411752 (2024).  
+9. Stellhorn, J. R. et al. Local Cluster Distortions in Amorphous Organotin Sulfide Compounds and Their Influence on the Nonlinear Optical Properties. Adv. Opt. Mater. 11, 2201932 (2023).  
+10. Stellhorn, J. R. et al. Local Structure of Amorphous Organotin Sulfide Clusters by Low-Energy X-Ray Absorption Fine Structure. Phys. Status Solidi B 259, 2200088 (2022).  
+11. Klee, B. D. et al. Structure Determination of a New Molecular White-Light Source. Phys. Status Solidi B 255, 1800083 (2018).  
+12. Hanau, K. et al. Towards Understanding the Reactivity and Optical Properties of Organosilicon Sulfide Clusters. Angew. Chem. Int. Ed. 60, 1176–1186 (2021).  
+13. Klee, B. D. et al. Structure Determination of a New Molecular White-Light Source. Phys. Status Solidi B 255, 1800083 (2018).  
+14. Dehnen, S. et al. Amorphous Molecular Materials for Directed Supercontinuum Generation. ChemPhotoChem 5, 1033–1041 (2021).  
+15. Silva, P., Vilela, S. M. F., Tomé, J. P. C. & Almeida Paz, F. A. Multifunctional metal–organic frameworks: from academia to industrial applications. Chem. Soc. Rev. 44, 6774–6803 (2015).
+
+<--- Page Split --->
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+16. Roy, X. et al. Nanoscale Atoms in Solid-State Chemistry. Science 341, 157–160 (2013).  
+17. Lee, C.-H. et al. Ferromagnetic Ordering in Superatomic Solids. J. Am. Chem. Soc. 136, 16926–16931 (2014).  
+18. Doud, E. A. et al. Superatoms in materials science. Nat. Rev. Mater. 5, 371–387 (2020).  
+19. Berwe, H. & Haas, A. Thiastannacyclohexane (R₂SnS₃) und -adamantane (RSn)₄S₆ Synthesen, Eigenschaften und Strukturen. Chem. Ber. 120, 1175–1182 (1987).  
+20. Song, J.-G. et al. Crystalline mate for structure elucidation of organic molecules. Chem 10, 924–937 (2024).  
+
+## Acknowledgements  
+
+This work is supported by the German Research Foundation (DFG) through the research group FOR2824 (Grant No. 398143140). Calculations for this research were conducted on the Lichtenberg high performance computer of the TU Darmstadt and at the Höchstleistungrechenzentrum Stuttgart (HLRS). The authors furthermore acknowledge the computational resources provided by the HPC Core Facility and the HRZ of the Justus- Liebig- Universität Gießen. Y. W. thanks Dr. Zhou Wu and Katrin Beuthet (Karlsruhe Institute of Technology, Institute of Nanotechnology) for their help with the SC- XRD measurements.  
+
+## Author Contributions  
+
+J. C. synthesized the compounds [(PhSn)₄E₆] (E = S and Se) compounds. Y. W. conceived and performed the cocrystallization experiments, collected single-crystal X-ray crystallographic data, solved and refined the structures. K. E. and F. Z. performed the calculations and analysis with support from S. S. The manuscript was written through contributions of all authors, and all authors reviewed the manuscript. All authors have given approval to the final version of the manuscript.  
+
+## Additional information  
+
+The authors declare no competing interests.  
+
+Supplementary information and chemical compound information accompany this paper at www.nature.com/naturechemistry.  
+
+Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/.  
+
+Correspondence and requests for materials should be addressed to S. D.:  
+
+Stefanie Dehnen: Institute of Nanotechnology, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany, email: stefanie.dehnen@kit.edu  
+
+## Methods  
+
+General experimental methods: All solvents were dried by standard methods and were commercially obtained. All reaction and sample preparations were carried out under inert atmospheres using standard Schlenk techniques or in an argon- filled glovebox. [(PhSn)₄S₆] and [(PhSn)₄Se₆] were prepared according to literature procedures.⁷ C₆₀ (98%, Sigma- Aldrich Chemie GmbH, US) was used as received.  
+
+Synthesis of [(PhSn)₄S₆]₂·(C₆₀)·(C₇H₈)₁.₂·[(C₄H₈O)₁.₂ (1): [(PhSn)₄S₆] (9.7mg, 0.010 mmol) and C₆₀ (5 mg, 0.006 mmol) were dissolved in THF (3 mL) and toluene (3 mL), respectively, and filtered through 0.8μm PTFE filters. The solution of C₆₀ was slowly layered on the top of the [(PhSn)₄S₆] solution. The vial was placed in a freezer at - 19°C for one week, after which the formation of red cuboid 1 single crystals of 1 could be observed.  
+
+Synthesis of [(PhSn)₄S₆]₂·(C₆₀)₁.₅·(C₇H₈) (2): [(PhSn)₄S₆] (9.7mg, 0.010 mmol) and C₆₀ (14.0 mg, 0.019 mmol) were dissolved in THF (3 mL) and toluene (5 mL), respectively, and filtered through 0.8μm PTFE filters. The solution of C₆₀ was slowly layered on the top of the [(PhSn)₄S₆] solution.
+
+<--- Page Split --->
+
+The vial was placed in a freezer at \(- 19^{\circ}\mathrm{C}\) for one week, after which the formation of red cuboid single crystals of 2 could be observed.  
+
+Synthesis of [(PhSn)4Se6]·(C60)·(C7H8)·(C4H8O)0.5 (3): Compound 3 was obtained using procedures similar to those for 1- 2toluene: [(PhSn)4Se6] (0.010 mmol) and C60 (0.010 mmol) were dissolved in THF (3 mL) and toluene (3 mL), respectively, and filtered through \(0.8\mu \mathrm{m}\) PTFE filters. The solution of the fullerene was slowly layered on top of the tin cluster solution, and the vessel was placed in a freezer at \(- 19^{\circ}\mathrm{C}\) . After one week, a black amorphous precipitate could be observed in the purple solution. After filtration through \(0.8\mu \mathrm{m}\) PTFE filters, the purple filtrate was transferred into an \(8\mathrm{mL}\) vial, and the solvent was evaporated slowly at room temperature for one more week. Red single crystals formed on the walls of the vial.  
+
+Single crystal X- ray diffraction: The data for the X- ray structural analyses was collected at \(\mathrm{T} =\) 150.0 or \(180\mathrm{K}\) on a STOE STADI VARII diffractometer with \(\mathrm{Ga / K\alpha}\) radiation \((\lambda = 1.34143\mathrm{\AA})\) for all compounds. Data collection, integration, scaling (ABSPACK) and absorption correction were performed in X- area. The structures were solved using SHELXT from SHELXL- 2018/136, and refined by full matrix least- squares methods against \(\mathrm{F}^2\) with the SHELXL program.21 Olex2 was used for viewing and to prepare CIF files.22 Refinement was performed with anisotropic temperature factors for all non- hydrogen atoms. Hydrogen atoms were calculated on idealized positions. Figures were created with Diamond. Owing to heavy disorder of the atoms of the solvent (toluene and THF) molecules of compound 1, these were retracted by applying a solvent mask in Olex2 in order to get an optimal model of the cluster and \(\mathrm{C}_{60}\) molecules. The retracted electron density correlates to 0.6 equivalents of toluene and 0.6 equivalents of THF in the asymmetric unit.  
+
+Optical absorption spectroscopy: UV- visible spectra of 1, 2, and 3 single crystals, as well as \(\mathrm{C}_{60}\) , [(PhSn)4Se6], and [(PhSn)4Se6] powders, were measured in absorbance mode using a Varian Cary 5000 UV/VIS/NIR spectrometer from Agilent, equipped with a Praying Mantis accessory for solid- state samples. Additionally, \(\mathrm{C}_{60}\) in toluene solution was measured in absorbance mode using the same Varian Cary 5000 UV/VIS/NIR spectrometer.  
+
+Quantum chemical studies: Isolated molecular clusters as well as related crystals are modeled within Density Functional Theory (DFT) and periodic boundary conditions. Thereby, we employed the Vienna ab initio simulation package23,24 to evaluate the structural, electronic, and optical properties of the investigated compounds. Molecular clusters in the gas phase were modeled within the molecule- in- a- box approach. Cubic boxes with a volume of \(51179.6\mathrm{\AA}^3\) , explicitly designed to decouple periodic images of the clusters, were employed. Crystalline solids were modeled within their unit cell. The atomic positions were optimized until the Hellmann- Feynman forces acting on each atom are lower than \(0.001\mathrm{eV}\cdot \mathrm{\AA}^{- 1}\) .25 The ion- electron interaction was described by projected augmented wave pseudopotentials,26,27 implementing the PBE formulation28,29 of the generalized gradient approximation.30 The vdW DFT- D3 method with Becke- Johnson damping31,32 was applied in all calculations to account for dispersion forces, as (semi)local exchange- correlation (XC) functionals do not properly describe the long- range van der Waals (vdW) interactions. Plane waves up to a cutoff of \(600\mathrm{eV}\) were used as the basis for the expansion of electron wave functions. Due to the large cell size, gamma- point calculations were performed. The imaginary part of the frequency- dependent dielectric tensor \(\epsilon_{\alpha \beta}^{i}\) , \(\alpha ,\beta = x,y,z\) , was calculated as the sum over empty states at each point of the first Brillouin zone.33 The real part of the dielectric tensor \(\epsilon^{\prime}\) was obtained by Kramers- Kronig transformations. The absorbance coefficient \(k(\omega)\) was calculated from the dielectric function as  
+
+\[k_{j}(\omega) = \frac{1}{\sqrt{2}}\sqrt{\left(\epsilon_{jj}^{r}(\omega)\right)^{2} + \left(\epsilon_{jj}^{i}(\omega)\right)^{2} - \epsilon_{jj}^{r}(\omega))}\]
+
+<--- Page Split --->
+
+where \(\epsilon^{T}(\omega)\) and \(\epsilon^{i}(\omega)\) are the real part and the imaginary part of the dielectric tensor, respectively.  
+
+## Data availability  
+
+The structures of compounds \(\mathbf{1} - \mathbf{3}\) were determined by single- crystal X- ray diffraction. Crystallographic data for the structure reported in this Article have been deposited at the Cambridge Crystallographic Data Centre, under deposition numbers CCDC- 2419991 (1). CCDC- 2419992 (2), and CCDC- 2419993 (3). A copy of the data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/.  
+
+The Cartesian coordinates of all optimized structures and the respective SCF energies are summarized in the supplementary document "optimized- structures.txt". The files comprise all necessary data for reproducing the values. All non- default parameters for the computational studies are given in the Supplementary Information together with the corresponding references of the used methods.  
+
+## Code availability  
+
+The Vienna Ab initio Simulation Package (VASP) is a computer program for atomic scale materials modelling from first principles (see also Refs [23] and [24]). The copyright- protected software is property of the VASP Software GmbH and available at https://www.vasp.at upon license purchase from the VASP Software GmbH or from an official reseller. The VASP version 6.4.2 and the official PAW potentials (see also Refs. [26] and [27]) are employed for the calculations presented in this work.  
+
+## References for the methods section  
+
+21. Silen, W., Machen, T. & Forte, J. Acid-base balance in amphibian gastric mucosa. Am. J. Physiol.-Leg. Content 229, 721–730 (1975).  
+22. Duggleby, R. G. & Kaplan, H. Competitive labeling method for the determination of the chemical properties of solitary functional groups in proteins. Biochemistry 14, 5168–5175 (1975).  
+23. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).  
+24. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).  
+25. Feynman, R. P. Forces in Molecules. Phys. Rev. 56, 340–343 (1939).  
+26. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).  
+27. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).  
+28. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865–3868 (1996).  
+29. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 78, 1396–1396 (1997).  
+30. Perdew, J. P. et al. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671–6687 (1992).  
+31. Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).  
+32. Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).  
+33. Gajdoš, M., Hummer, K., Kresse, G., Furthmüller, J. & Bechstedt, F. Linear optical properties in the projector-augmented wave methodology. Phys. Rev. B 73, 045112 (2006).
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+1PhSnSC601checkcif.pdf 
+2PhSnSC601.5checkcif.pdf 
+3PhSnSeC60.pdf 
+PiTrapSISD.pdf
+
+<--- Page Split --->

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+<|ref|>title<|/ref|><|det|>[[44, 106, 909, 177]]<|/det|>
+# The 'π-Trap' as an Unrestricted Crystal Sponge for Inherently Amorphous Cluster Compounds  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 196, 214]]<|/det|>
+Stefanie Dehnen  
+
+<|ref|>text<|/ref|><|det|>[[55, 222, 312, 240]]<|/det|>
+stefanie.dehnen@kit.edu  
+
+<|ref|>text<|/ref|><|det|>[[44, 268, 704, 288]]<|/det|>
+Karlsruhe Institute of Technology https://orcid.org/0000- 0002- 1325- 9228  
+
+<|ref|>text<|/ref|><|det|>[[44, 293, 198, 312]]<|/det|>
+Yaofeng Wang  
+
+<|ref|>text<|/ref|><|det|>[[55, 316, 345, 334]]<|/det|>
+Karlsruhe Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 340, 198, 358]]<|/det|>
+Niklas Rinn  
+
+<|ref|>text<|/ref|><|det|>[[55, 363, 345, 381]]<|/det|>
+Karlsruhe Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 386, 182, 404]]<|/det|>
+Kevin Eberheim  
+
+<|ref|>text<|/ref|><|det|>[[55, 409, 264, 427]]<|/det|>
+Justus Liebig University  
+
+<|ref|>text<|/ref|><|det|>[[44, 433, 186, 451]]<|/det|>
+Ferdinand Ziese  
+
+<|ref|>text<|/ref|><|det|>[[55, 456, 264, 474]]<|/det|>
+Justus Liebig University  
+
+<|ref|>text<|/ref|><|det|>[[44, 480, 198, 497]]<|/det|>
+Jan Christmann  
+
+<|ref|>text<|/ref|><|det|>[[55, 502, 345, 520]]<|/det|>
+Karlsruhe Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 526, 172, 544]]<|/det|>
+Simone Sanna  
+
+<|ref|>text<|/ref|><|det|>[[55, 549, 264, 567]]<|/det|>
+Justus Liebig University  
+
+<|ref|>text<|/ref|><|det|>[[44, 608, 275, 627]]<|/det|>
+Physical Sciences - Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 646, 945, 667]]<|/det|>
+Keywords: π- π interactions, unrestricted crystal sponge, amorphous compounds, cluster molecules, C60  
+
+<|ref|>text<|/ref|><|det|>[[44, 684, 337, 703]]<|/det|>
+Posted Date: February 24th, 2025  
+
+<|ref|>text<|/ref|><|det|>[[44, 722, 475, 741]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 5953585/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 758, 914, 801]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 819, 535, 839]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 875, 936, 918]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on August 25th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 62928- y.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[102, 60, 894, 105]]<|/det|>
+# The "π-Trap' as an Unrestricted Crystal Sponge for Inherently Amorphous Cluster Compounds  
+
+<|ref|>text<|/ref|><|det|>[[100, 118, 895, 153]]<|/det|>
+Yaofeng Wang \(^{1}\) , Niklas Rinn \(^{1}\) , Kevin Eberheim \(^{2}\) , Ferdinand Ziese \(^{2}\) , Jan Christmann \(^{1}\) , Simone Sanna \(^{2}\) , and Stefanie Dehnen \(^{1,*}\)  
+
+<|ref|>text<|/ref|><|det|>[[100, 164, 894, 201]]<|/det|>
+(1) Karlsruhe Institute of Technology, Institute of Nanotechnology. Kaiserstrasse 12, 76131 Karlsruhe, Germany  
+
+<|ref|>text<|/ref|><|det|>[[100, 210, 894, 246]]<|/det|>
+(2) Institut für Theoretische Physik and Center for Materials Research (LaMa), Justus-Liebig-Universität Gießen, 35392 Gießen, Germany  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 287, 180, 302]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[100, 306, 896, 656]]<|/det|>
+Single crystal diffraction is one of the most common and powerful tools for structural elucidation in science. However, obtaining single crystals of adequate size and quality is not always trivial, with some chemicals inherently resisting all attempts. The 'crystalline sponge' method has attracted a lot of attention for crystallizing otherwise intrinsically amorphous compounds inside a metal organic framework (MOF). \(^{1 - 4}\) However, its application is limited by the size and stability of the pores within the networks. In this study, we propose a novel 'unrestricted crystalline sponge' method, which we denominate as the 'π- trap'. It makes use of π- π interactions between C₆₀ and nm- sized molecules that by themselves do not form crystalline compounds. Using this technique, we successfully crystallized adamantane- like organic- inorganic hybrid clusters, which exhibit extreme nonlinear optical properties only within the amorphous habitus, and resist any attempt for crystallization. As the clusters' low tendency to order in the long range was successfully overcome by the strong C₆₀···cluster interactions in the 'π- trap', we were able to precisely determine their molecular structures. As we could show by optical spectroscopy and quantum chemical calculations, both the clusters and C₆₀ behave like being dissolved in the other component, including the formation of cluster pairs previously proposed by theoretical studies and low- angle scattering experiments on amorphous samples. We propose that the described method is applicable to all kinds of amorphous compounds that allow for π- π interactions, without the size restrictions facing the 'crystalline sponge' method, especially when considering the usage of larger fullerenes.  
+
+<|ref|>text<|/ref|><|det|>[[100, 675, 900, 708]]<|/det|>
+Keywords: π- π interactions, unrestricted crystal sponge, amorphous compounds, cluster molecules, C₆₀
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[101, 60, 214, 75]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[101, 77, 897, 375]]<|/det|>
+Single- crystal X- ray diffraction (SCXRD) analysis provides the most precise method for determining the structures of natural and synthetic molecules, making it an indispensable tool for chemists. Naturally, it requires the samples to be obtained in single crystalline form. However, many compounds are intrinsically amorphous, and therefore their structures cannot be subjected to SCXRD analysis. In 2010, Fujita and co- workers introduced a method in which porous coordination networks are used as 'crystalline sponges' that absorb target molecules from solution and orient them in a uniform fashion within the crystalline network, which enabled the determination of their molecular structures at atomic resolution by SCXRD. \(^{1 - 4}\) While this method does not require the crystallization of the target compound by itself, it requires that the networks' pores have a suitable size and stability to accommodate the guest molecules. Therefore, this technique has been mostly applied to smaller molecules, like 2,6- diisopropylaniline, guaiazulene, santonin, or chain- like molecules, such as miyakosyne, which comfortably fit into the pores. Larger guests, like fullerene molecules, could be included too, yet in this case, no crystal data were obtained. \(^{3}\) To the best of our knowledge, the method has so far been used mostly for (bio- )organic molecules or organometallic complexes. In contrast, methods to precisely determine the molecular structures of amorphous compounds that are comprised of (polyhedral) inorganic cluster molecules, have remained elusive to date.  
+
+<|ref|>text<|/ref|><|det|>[[101, 376, 897, 605]]<|/det|>
+Recently, adamantane- type organic- inorganic hybrid clusters with a general composition of \([(R\mathrm{Sn})_4\mathrm{E}_6]\) ( \(\mathrm{R} =\) organic substituent, \(\mathrm{E} = \mathrm{S}\) , Se), such as \([(PhSn)_4S_6]\) (A, Fig. 1) or \([(PhSn)_4Se_6]\) (B), have attracted significant attention due to their (extreme) nonlinear optical (NLO) properties. \(^{5,6}\) Particularly noteworthy is the phenomenon of continuous- wave infrared laser- induced directional white light generation (WLG). This has been demonstrated to work exclusively for rigorously amorphous \([(R\mathrm{Sn})_4\mathrm{E}_6]\) compounds containing electron- rich organic substituents like phenyl (Ph), styryl (Sty) or cyclopentadienyl (Cp), although the physical mechanism behind this phenomenon is still largely ununderstood. \(^{7,8}\) The structural conformations of the corresponding \([(R\mathrm{Sn})_4\mathrm{E}_6]\) cluster molecules have been suggested by theoretical studies, also in combination with X- ray and neutron scattering experiments, but could never be verified or supported crystallographically—as the amorphous habitus is intrinsic to those materials. \(^{9 - 11}\) Notably, related clusters, such as \([(MeSn)_4S_6]^5\) or \([(PhSi)_4S_6]\) (C), \(^{5}\) form crystalline solids and show strong second harmonic generation (SHG) instead of WLG.  
+
+<|ref|>image<|/ref|><|det|>[[120, 608, 875, 838]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[101, 843, 897, 931]]<|/det|>
+<center>Figure 1 | Structural model of the adamantane-type cluster in the amorphous compound \([(PhSn)_4S_6]\) (A) and its simplified representations. a, Full cluster structure. b, Simplified representation with organic groups reduced to short grey sticks and the (nonbonded) \(\{Sn_4\}\) motif highlighted by a tetrahedron. c, Even more simplified representation by the inner tetrahedral \(\{Sn_4\}\) motif only. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[101, 58, 896, 305]]<|/det|>
+To date, it is still unclear why the amorphous habitus is required for the WLG phenomenon, and is has also not been clarified until today which parameters control that some of these highly related cluster compounds crystallize while other ones remain rigorously amorphous. There have been suggestions for answering the latter question based on theoretical studies of cluster pair models, which suggested more pronounced (directed) substituent-substituent interactions for compounds featuring smaller cluster cores (e.g., \(\{\mathrm{Si}_4\mathrm{S}_6\}\) ), whereas for clusters with larger cores (e.g., \(\{\mathrm{Sn}_4\mathrm{S}_6\}\) ), one observes a dominance of (rather isotropic) interactions of the polyhedral cluster cores.12 Combined scattering and reverse Monte- Carlo studies revealed information about cluster assemblies, and also suggested significant statistical distortions of the cluster cores, with an increased tendency for larger (and softer) cores.13 However, a crystallographic proof of all of those hypotheses has still been elusive. Experimental and theoretical physicists have been trying to find answers to the former question since the first observation of the WLG phenomenon, for which a full picture of the amorphous compounds' characteristics—including the essentially inaccessible structural data—is critical.14  
+
+<|ref|>text<|/ref|><|det|>[[101, 305, 897, 515]]<|/det|>
+We therefore aimed at identifying a tool for obtaining this data to get knowledge of and possibly confirm the reasons for an amorphous versus crystalline habitus. This would lay the foundation for eventually finding an explanation for the physical phenomenon in the near future and altogether ultimately allow to design and control the compounds' habitus and habitus- dependent properties. A rather obvious idea was to apply Fujita's 'crystalline sponge method'.1,2 However, as indicated by the Fujita group in their seminal work, the applicability of the technique is limited by the maximum cross- section of pores in crystalline sponge, which is typically below \(1\mathrm{nm}\) in the materials applied to this technique. MOFs with larger pores exist,15 but they tend to collapse during the process. Unsuccessful attempts with polyhedral \(\{\mathrm{RSn}_4\mathrm{E}_6\}\) molecules confirmed that their sizes, with outer diameters of \(\sim 1 - 1.5\mathrm{nm}\) , prohibit the application of this approach. So, for obtaining precise structural data of cluster molecules that form intrinsically amorphous powders, another methodology is needed.  
+
+<|ref|>text<|/ref|><|det|>[[101, 516, 897, 763]]<|/det|>
+Here, we report about the introduction of the \(\pi\) - trap' as an 'unrestricted crystalline sponge' method, which makes use of the co- crystallization of cluster molecules with commercially available fullerene \(\mathrm{C}_{60}\) as a simple, cheap and sustainable means of solving the problem (Fig. 2). The electronic structure of the fullerene molecules enables \(\pi\) - \(\pi\) interactions between their surface and aromatic organic substituents on the clusters, and their size and spherical shape allows for comfortably co- crystallizing with larger, polyhedral cluster compounds. While co- crystals with \(\mathrm{C}_{60}\) were previously shown to form with clusters that also crystallize by themselves, like Chevrel- type superatomic clusters,16- 18 we demonstrate this technique for the first time on the example of amorphous \(\{\mathrm{PhSn}_4\mathrm{E}_6\}\) clusters, the crystal structures of which are otherwise inaccessible. Specifically performed quantum- chemical calculations reveal how the crystal formation affects the atomic and electronic structure of the \(\{\mathrm{PhSn}_4\mathrm{E}_6\}\) clusters. We give perspectives to the expansion of the method to other amorphous- cluster- fullerene combinations. The method finally allowed to compare the structural data with previous theoretical predictions,12 and to rationalize and verify the computations.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[103, 100, 900, 448]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[100, 451, 896, 558]]<|/det|>
+<center>Figure 2 | Schematic illustration of the 'crystalline sponge'1,2 method versus the 'π-trap' approach. The approaches are shown on the examples of the organic compound guaiazulene, \(\mathrm{C_{15}H_{18}}\) ,1,2 represented by a light brown tetrahedron, and [(PhSn)4Se] (A), represented by its inner tetrahedral {Sn4} motif (see Fig. 1c). a, The 'crystal sponge' method applied to smaller-size organic compounds. b, The 'π-trap' approach leading to crystalline compounds accommodating organotetrel chalcogenide cluster molecules. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 577, 301, 593]]<|/det|>
+## Results and Discussion  
+
+<|ref|>text<|/ref|><|det|>[[100, 594, 897, 893]]<|/det|>
+Syntheses and crystal structures. Two intrinsically amorphous adamantane- type cluster compounds, [(PhSn)4Se] (A) and [(PhSn)4Se] (B), were used for our proof- of- principle study to demonstrate the success of the 'π- trap' approach. As schematically depicted in Figure 3a- c, the crystallization process with \(\mathrm{C_{60}}\) involves layering a solution of the cluster compound in THF with a solution of the fullerene in toluene. Slow diffusion of the solutions into each other resulted in the formation of red single crystals at the solution interface after one week (see Supplementary Figure 1). SCXRD analyses of the single- crystals that were obtained from mixtures involving A, unveiled two different products to form simultaneously in the same batch. They feature different ratios of [(PhSn)4Se] and \(\mathrm{C_{60}}\) and also different amounts of crystal solvent molecules ( \(\mathrm{C_{7}H_{8} =}\) toluene or \(\mathrm{C_{4}H_{8}O = THF}\) ) per formula unit, [(PhSn)4Se]2- (C60)- (C7H8)1,2- (C4H8O)1,2 (1, Fig. 3d- e) and [(PhSn)4Se]2- (C60)1,5- (C7H8) (2). After adjusting the \(\mathrm{C_{60}}\) :A ratio, we were able to obtain both 1 or 2 selectively. Mixtures involving B yielded exclusively [(PhSn)4Se] (C60)- (C7H8)- (C4H8O)0,5 (3). Notably, these are the first crystal structures involving notoriously amorphous inorganic clusters compounds in general, and this specific type of amorphous clusters in particular, the mere synthesis and chemical characterization of which was reported as early as in 1987 in the case of A.19 More crystal photographs as well as different views and further details of the crystal structures of the three compounds are provided below and in Supplementary Figures 2- 15.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[100, 58, 895, 426]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[100, 433, 896, 574]]<|/det|>
+<center>Figure 3 | Schematic representation of the preparation procedure for a single-crystalline cocrystals of \(\mathbf{C}_{60}\) and [(PhSn)4S6] (A). a, Photograph of microcrystalline \(\mathrm{C}_{60}\) (as purchased) and structure model of the \(\mathrm{C}_{60}\) molecule. b, Photograph of the amorphous powder of pure compound A and simplified structure model of the [(PhSn)4S6] cluster molecule (see Fig. 1b). c, Layering of the two solutions comprising the starting materials and diffusion into one another. d, View of the crystal structure of [(PhSn)4S6]2·[C60]·(C7H8)1.2·[C4H8O]1.2 (1) viewed along the crystallographic \(a\) axis, with cluster pairs visible between the fullerene spheres. e, Light-microscopic image of single-crystals of compound 1 with scalebar. </center>  
+
+<|ref|>text<|/ref|><|det|>[[100, 592, 896, 768]]<|/det|>
+Figure 4 illustrates the crystal structures of the three co- crystals. The structures show several unique and informative features, which we outline in what follows. A view of the packing schemes in a selected crystallographic direction (see Fig. 4a- c) highlights that all compounds, 1, 2, and 3, comprise pairs of clusters embedded in an environment of \(\mathrm{C}_{60}\) molecules—albeit in very different, and very complex packing patterns. We observe relatively short distances between the centroids of the hexagonal faces of \(\mathrm{C}_{60}\) and the clusters' phenyl groups, down to \(3.897 \mathring{\mathrm{A}}\) in compound 1 (Fig. 4a), \(3.109 \mathring{\mathrm{A}}\) in 2, and \(3.250 \mathring{\mathrm{A}}\) in 3. This supports our assumption that the crystal lattice is stabilized by face- to- face \(\pi\) - \(\pi\) or C- H- \(\pi\) interactions. Moreover, the shortest distances between chalcogenide atoms (S or Se) and the hexagonal faces of neighboring \(\mathrm{C}_{60}\) molecules are \(3.528 \mathring{\mathrm{A}}\) for 1, \(3.566 \mathring{\mathrm{A}}\) for 2, and \(3.710 \mathring{\mathrm{A}}\) for 3, indicating another type of secondary interaction.  
+
+<|ref|>text<|/ref|><|det|>[[100, 770, 896, 927]]<|/det|>
+A close- up of the crystal structure of 1 (Fig. 4d) emphasizes the intense \(\pi\) - \(\pi\) interactions between the two types of molecules and, importantly, also within the cluster pairs. When viewed along the Sn- Sn axis, the phenyl groups within the pairs are arranged in staggered positions (Fig. 4e), which allows for a more intense (dominant) interaction of the cluster cores (6.228 \(\mathring{\mathrm{A}}\) from center to center) as compared to those between the substituents—as predicted by computational studies of various cluster pairs as minimal model for the interaction. \(^{12}\) In compound 1 the shortest distance between the centroids of adjacent phenyl groups is measured at \(5.568 \mathring{\mathrm{A}}\) . For comparison, in the analogue crystalline compound [(PhSi)4S6] (C), \(^{5}\) the staggered arrangement is different, resulting in a shorter distance of \(4.847 \mathring{\mathrm{A}}\) between adjacent phenyl groups, while the cluster cores are much more distant
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[100, 58, 896, 234]]<|/det|>
+(7.058 Å, Fig. 4f and Suppl. Fig. 10)—again in excellent agreement with the computations: these indicated stronger substituent–substituent interactions and weaker core–core interactions for the PhSi/S system than for the PhSn/S system (and vice versa). \(^{12}\) The core center-to-center distances between the [(PhSn)4E6] clusters in the other pairs are similarly small, 6.284 Å and 6.409 Å (compound 2), and 6.498 Å (compound 3) (see Suppl. Figs. 11, 12, 15). As suggested, the predominance of the relatively isotropic core-core interactions in PhSn/S-based clusters surpasses the directional interactions involving the substituents, which is perfectly reflected by the new crystal data, in which the pairs are retained also in the presence of C60. This finally rationalizes and explains why Sn-based compounds exhibit a distinctly lower tendency for order as a single compound in the solid state compared to their crystalline PhSi/S-based counterparts.  
+
+<|ref|>text<|/ref|><|det|>[[100, 234, 896, 480]]<|/det|>
+As another contrast to the ordered situation within crystalline [(PhSi)4S6] (C), \(^{5}\) the phenyl groups in compounds 1, 2 and 3 show a tendency for disorder (see Fig. 4d- e). This can be explained by the Sn- C bonds being naturally longer than Si- C bonds (2.103(14) – 2.126(19) Å for the former versus 1.8540(15) – 1.8562(15) Å for the latter, see Suppl. Table 2), which decreases the interaction barrier between the hydrogen atoms of the substituents and the S or Se atoms of the cluster for the heavier homologues. The overall higher flexibility of the phenyl groups obviously weakens their (directed) interaction and thus hampers crystallization. Both cluster cores observed herein, {Sn4S6} in 1 and 2 and {Sn4Se6} in 3, exhibit a notable tendency for molecular distortions. This is particularly obvious in compound 2, with S- Sn- S angles ranging from 107.84 to 116.03° (Suppl. Table 2). This range is notably greater than the reported range of S- Si- S angles in [(PhSi)4S6] (C; 111.29 to 113.27°), \(^{5}\) indicating a higher degree of distortion within the Sn/S cluster core than in the Si/S core of the lighter homologue. We suspect that these distortions reflect a certain degree of dynamic behavior, even under crystallization conditions, which refers to increased motion of the atoms as another argument for prohibiting crystallization as a sole compound.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[95, 55, 900, 625]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[100, 639, 898, 816]]<|/det|>
+<center>Figure 4 | Details of the crystal structures of co-crystals 1, 2, and 3. a, Packing scheme of compound 1, viewed along the crystallographic \(c\) axis. b, Packing scheme of compound 2, viewed along the crystallographic \(b\) axis. c, Packing scheme of compound 3, viewed along the crystallographic \(b\) axis. d, Pair of [(PhSn)4S6] clusters in the crystal structure of 1 interacting with surrounding \(C_{60}\) molecules; for clarity, the phenyl groups are depicted in grey and green for the two distinct [(PhSn)4S6] molecules within the pair, respectively (disorder position shown in semitransparent mode). e, The cluster pair in 1 viewed along the Sn-Sn axis. f, Pair of [(PhSi)4S6] clusters in the crystal structure of C, for comparison; for clarity, the phenyl groups are depicted in grey and green for the two distinct [(PhSi)4S6] molecules within the pair, respectively. g, The cluster pair in C viewed along the Sn-Sn axis, for comparison. </center>  
+
+<|ref|>text<|/ref|><|det|>[[102, 835, 896, 906]]<|/det|>
+So far, we can summarize that we were able to obtain the first crystallographic structural data from clusters of the [(RT)4E6] family that do not crystallize by themselves. Moreover, these data, as compared to those of the crystalline homologue [(PhSi)4S6] (C), served to confirm a theoretical prediction made on the basis of computed pair structures of different clusters in regards of their
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[101, 59, 895, 94]]<|/det|>
+preference of arranging in ordered structures (crystals) or rather assembling without any long- range periodicity (amorphous powders).<sup>12</sup>  
+
+<|ref|>text<|/ref|><|det|>[[101, 95, 896, 306]]<|/det|>
+It is worth noting that during the preparation of this manuscript, a similar method known as the 'crystalline mate' was showcased in a parallel work,<sup>20</sup> but this method was designed for smaller organic molecules only, making it inappropriate for cluster materials. It also required the preparation and provision of specific molecules instead of using commercially available fullerene. Our work was rather inspired by the co- crystallization of fullerene and [(RCo)6Es] clusters reported recently by the Nuckolls group.<sup>16- 18</sup> However, while the Co/E clusters do also crystallize without \(\mathrm{C}_{60}\) , this is not the case for the clusters we address in our approach, where addition of \(\mathrm{C}_{60}\) is the only means of growing crystals comprising those species. As shown by the quoted work though, such co- crystals can achieve new properties through this step. The mere color change upon combination of the colorless (cluster) powder with the black ( \(\mathrm{C}_{60}\) ) powder to form red crystals also suggests the combination of properties in the case of compounds 1 - 3. The nature of this combination remained to be explored though.  
+
+<|ref|>text<|/ref|><|det|>[[101, 307, 896, 517]]<|/det|>
+We therefore investigated whether the intense non- covalent interactions that lead the molecules into an ordered arrangement have an effect on the geometric and electronic structures of the clusters of interest, or whether the latter still behave like the pure substances—especially regarding their macroscopic properties (note that this question does not address WLG, as this requires the amorphous habitus, see above). The visual impression of the crystals, being neither black like \(\mathrm{C}_{60}\) nor colorless like [(PhSn)4E6] (E = S, Se), but red, could be caused by a mere physical mixture ('blend') of both components, but they may also result from electronic interactions. While the latter would be very interesting in terms of new semiconducting materials, the first is the primary goal we have in this work, as we aim to get the most reliable and unaffected structural data from this unique class of materials, which requires that they undergo the weakest interaction possible, just enough to order. For judging about this, we investigated optical absorption properties and performed concomitant quantum chemical calculations (DFT and TDDFT) of the crystalline blends.  
+
+<|ref|>text<|/ref|><|det|>[[101, 535, 896, 605]]<|/det|>
+Optical absorption properties. For being able to comment on the optical absorption properties of co- crystals 1, 2, and 3, we recorded UV- visible spectra of the pure (amorphous) parent compounds in the solid state and in solution, of \(\mathrm{C}_{60}\) in the solid state and in solution, and of the single- crystals of 1, 2, and 3. The spectra are displayed in Figure 5.  
+
+<|ref|>image<|/ref|><|det|>[[228, 618, 767, 871]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[101, 880, 896, 933]]<|/det|>
+<center>Figure 5 | UV-visible spectra of parent compounds and co-crystals 1, 2 and 3. The spectra were recorded on samples of [(PhSn)4S6] and [(PhSn)4Se6] as amorphous powders and in solution, of \(\mathrm{C}_{60}\) as polycrystalline powder and in toluene, and on single-crystals of 1, 2 and 3. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[101, 76, 896, 271]]<|/det|>
+The UV- visible spectra of the co- crystals 1, 2, and 3 show an onset of absorption at around \(700\mathrm{nm}\) , slightly red- shifted for compound 3, followed by 2 and 1. We assume that the difference between the Sn/Se- based composition of 3 and the Sn/S- based compositions of 1 is not dominant here, but the ratio between the number of \([(PhSn)_4E_6]\) cluster units \((\mathrm{E} = \mathrm{S},\mathrm{Se})\) and \(\mathrm{C}_{60}\) molecules in the cocrystal. In the most red- shifted compound 3, this ratio is 1:1. In compound 2, the corresponding ratio is 2:1.5, and 1, it is 2:1. This is in agreement with the fact that a spectral feature around 600 nm agrees with the maximum at \(601\mathrm{nm}\mathrm{C}_{60}\) in toluene solution. So, for the onset of absorption, we see similar spectroscopic signatures of 1 – 3 that are controlled by the behavior of \(\mathrm{C}_{60}\) – notably not in the solid, but in solution phase. The more intense absorption that is observed for all cocrystals below \(500\mathrm{nm}\) mostly reflects the absorption characteristics of the pure clusters, for which the solid- state and solution spectra do not differ significantly.  
+
+<|ref|>text<|/ref|><|det|>[[101, 272, 896, 376]]<|/det|>
+We conclude that in the co- crystal, the two components are widely independent regarding their electronic properties, hence, they behave like a physical mixture ('ordered solid solution'). This would corroborate the fact that the structural data we obtained for the previously amorphous cluster compounds are those that are inherent to these molecules without great impact from the co- crystal. However, to confirm our working thesis, we performed quantum chemical calculations of the electronic structure of the co- crystals.  
+
+<|ref|>text<|/ref|><|det|>[[100, 394, 898, 887]]<|/det|>
+First- principles calculations of the electronic properties of the co- crystals. Crystals of the compounds 1, 2 and 3 have been modeled from first principles. Lattice type and lattice parameters as calculated within DFT- PBE are reported in Supplementary Table 3. The calculated lattice parameters are in very good agreement with the measured values and confirm the experimentally determined structure; upon crystallization into compounds 1, 2, and 3, the cluster cores of A and B are only slightly compressed according to the DFT studies (see Supplementary Table 4). The formation of the co- crystals leads to the band structures of 1, 2 and 3 as shown in Figure 6a – 6c, which perfectly reflect the mixing of the two compounds. The band structures of all compounds are very flat as typical for molecular crystals, indicating a minor intermolecular interaction. All compounds are moreover semi- conductors, as indicated by an energy gap of about \(1.5\mathrm{eV}\) that separates the top of the valence band from the unoccupied states. Notably, this is significantly smaller than the HOMO- LUMO gap of the parent clusters \([(PhSn)_4S_6]\) A and \([(PhSn)_4Se_6]\) B cluster, calculated by DFT to be \(3.199\mathrm{eV}\) and \(2.726\mathrm{eV}\) . Yet, the original HOMO- LUMO gap can be recognized in the band structure of 1, 2, and 3, as we show in the following on the example of 1. Indeed, the spatial localization of the electronic states of the valence band top at \(- 0.3\mathrm{eV}\) and of the bottom of the second conduction band at about \(2.7\mathrm{eV}\) in Figure 6a closely resembles the orbital nature of the HOMO and LUMO of A; this is in full agreement with the experimental spectrum, in which the signature of the parent clusters can also be identified in smaller wavelength regions. As illustrated in Supplementary Figure 16, the HOMO is rather localized at the S atoms, while the LUMO is less localized at the S atoms and extended to the substituents. The energetic separation of the electronic states represented in Figure 6d and 6e is \(2.96\mathrm{eV}\) , close to the HOMO- LUMO separation in A, which further confirms their origin. Thus, the group of localized states that appears within the energy of the HOMO and LUMO of the parent molecules, is more correctly interpreted as a group of localized mid- gap states than as the valence band bottom or conduction band top. In order to explore the origin of these states, we project the density of states (DOS) of 1, 2, and 3 onto the different atomic species, see in Figure 6f. The DOS clearly shows that the localized states have their origin in the carbon atoms of the \(\mathrm{C}_{60}\) molecules. The wavefunctions associated with these states are indeed localized at the fullerene cages, as shown in Figure 6g.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[98, 55, 899, 440]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[100, 445, 896, 586]]<|/det|>
+<center>Figure 6 | Electronic structures of the compounds calculated within DFT-PBE. a, Electronic band structure for calculated compound 1. b, Electronic band structure for calculated compound 2. c, Electronic band structure for calculated compound 3. d, Visualization of the top of the valence band (lhs), being strongly localized at the S atoms, similarly to the LUMO of A. e, Visualization of the bottom of the conduction band (rhs) of 1, resembling the HOMO of A. f, Density of states and partial density of states for compound 1; the partial density of states are shown in different colors for different atoms. g, Visualization of the squared wavefunctions associated to the mid gap electronic states in 1, localized at C60. Isosurfaces are drawn at \(0.001 \text{e}^{-} \text{\AA}^{-3}\) . </center>  
+
+<|ref|>text<|/ref|><|det|>[[101, 604, 896, 833]]<|/det|>
+Summarizing, upon crystallization the HOMO and LUMO of the [(PhSn)4Se] and [(PhSn)4Se6] cluster build the conduction and valence band. The fullerene related states lay in between and lead to the top of the conduction band, the bottom of the valence band and mid- gap states. All C60- related states are highly localized and almost completely dispersionless. The band structure of 1, 2 and 3 thus corresponds to that of the parent compounds, overlaid but not substantially altered by the C60 states. The calculated absorbance of the crystals 1, 2, and 3 is shown in Supplementary Figure 18. The spectra substantially resemble the absorption of [(PhSn)4Se] and [(PhSn)4Se6], with an additional signature related to electronic transition involving the C60 states (marked by an arrow in the figure). According to the measured data, the onset of the optical absorption is at \(700 - 710 \text{nm}\) for the compounds 2 and 1, and somewhat redshifted for 3, due to the smaller bandgap of B in comparison with A. Interestingly, the C60 signatures show a larger scattering than in the measured data, suggesting that the interaction of C60 with the clusters is slightly overestimated in the atomistic models.  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 854, 200, 869]]<|/det|>
+## Conclusion  
+
+<|ref|>text<|/ref|><|det|>[[102, 871, 895, 923]]<|/det|>
+Overall, through our 'π- trap' approach as an 'unrestricted crystal sponge' method, we demonstrate for the first time that inherently amorphous adamantane- like cluster can be trapped in a crystal structure by the π- π interaction tendency of C60, which we showcased for the important white- light-
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[102, 59, 897, 287]]<|/det|>
+emitting compounds \([(PhSn)_4S_6]\) and \([(PhSn)_4Se_6]\) . The structural data obtained through this novel method confirmed the initial hypotheses regarding the structural features of these clusters, providing critical evidence of the diverse molecular interactions within these systems. This way, we revealed that the \(\pi - \pi\) interaction help to overcome distortions of the clusters and the predominance of core- core interactions of Sn- based clusters which were previously identified as reasons for such clusters to remain inevitably amorphous. By a combined experimental and theoretical study, we also demonstrated that the co- crystals are more than a mere source of structural information, but exhibit a combination of the electronic properties of the two underlaying components. This enhanced understanding of the structural and interactive properties of the amorphous clusters contributes to the ability to predict, design, and control their features, paving the way for future advancements in the targeted development of these compounds. This innovative strategy is being currently extended to other fullerenes and their combinations with various clusters, and holds promising potential for crystallizing other amorphous materials in the future.  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 306, 198, 322]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[100, 346, 897, 928]]<|/det|>
+1. Inokuma, Y., Arai, T. & Fujita, M. Networked molecular cages as crystalline sponges for fullerenes and other guests. Nat. Chem. 2, 780–783 (2010).  
+2. Inokuma, Y. et al. X-ray analysis on the nanogram to microgram scale using porous complexes. Nature 495, 461–466 (2013).  
+3. Inokuma, Y., Yoshioka, S., Ariyoshi, J., Arai, T. & Fujita, M. Preparation and guest-uptake protocol for a porous complex useful for ‘crystal-free’ crystallography. Nat. Protoc. 9, 246–252 (2014).  
+4. Zigon, N., Duplan, V., Wada, N., & Fujita, M. Crystalline Sponge Method: X-ray Structure Analysis of Small Molecules by Post-Orientation within Porous Crystals—Principle and Proof-of-Concept Studies. Angew. Chem. Int. Ed. 60, 25204–25222 (2021).  
+5. Rosemann, N. W. et al. A highly efficient directional molecular white-light emitter driven by a continuous-wave laser diode. Science 352, 1301–1304 (2016).  
+6. Rosemann, N. W., EuBner, J. P., Dornsiepen, E., Chatterjee, S. & Dehnen, S. Organotetrel Chalcogenide Clusters: Between Strong Second-Harmonic and White-Light Continuum Generation. J. Am. Chem. Soc. 138, 16224–16227 (2016).  
+7. Dornsiepen, E., Dobener, F., Chatterjee, S. & Dehnen, S. Controlling the White-Light Generation of [(RSn)4E6]: Effects of Substituent and Chalcogenide Variation. Angew. Chem. Int. Ed. 58, 17041–17046 (2019).  
+8. Wang, J., Rojas-Leon, I., Rinn, N., Guggolz, L., Ziese, F., Sanna, S., Rosemann, N. W. & Dehnen, S. Strain-Induced Structural Rearrangement Towards a White-Light-Emitting Adamantane-Type Cluster Dimer. Angew. Chem. Int. Ed. 63, e202411752 (2024).  
+9. Stellhorn, J. R. et al. Local Cluster Distortions in Amorphous Organotin Sulfide Compounds and Their Influence on the Nonlinear Optical Properties. Adv. Opt. Mater. 11, 2201932 (2023).  
+10. Stellhorn, J. R. et al. Local Structure of Amorphous Organotin Sulfide Clusters by Low-Energy X-Ray Absorption Fine Structure. Phys. Status Solidi B 259, 2200088 (2022).  
+11. Klee, B. D. et al. Structure Determination of a New Molecular White-Light Source. Phys. Status Solidi B 255, 1800083 (2018).  
+12. Hanau, K. et al. Towards Understanding the Reactivity and Optical Properties of Organosilicon Sulfide Clusters. Angew. Chem. Int. Ed. 60, 1176–1186 (2021).  
+13. Klee, B. D. et al. Structure Determination of a New Molecular White-Light Source. Phys. Status Solidi B 255, 1800083 (2018).  
+14. Dehnen, S. et al. Amorphous Molecular Materials for Directed Supercontinuum Generation. ChemPhotoChem 5, 1033–1041 (2021).  
+15. Silva, P., Vilela, S. M. F., Tomé, J. P. C. & Almeida Paz, F. A. Multifunctional metal–organic frameworks: from academia to industrial applications. Chem. Soc. Rev. 44, 6774–6803 (2015).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[101, 59, 895, 193]]<|/det|>
+16. Roy, X. et al. Nanoscale Atoms in Solid-State Chemistry. Science 341, 157–160 (2013).  
+17. Lee, C.-H. et al. Ferromagnetic Ordering in Superatomic Solids. J. Am. Chem. Soc. 136, 16926–16931 (2014).  
+18. Doud, E. A. et al. Superatoms in materials science. Nat. Rev. Mater. 5, 371–387 (2020).  
+19. Berwe, H. & Haas, A. Thiastannacyclohexane (R₂SnS₃) und -adamantane (RSn)₄S₆ Synthesen, Eigenschaften und Strukturen. Chem. Ber. 120, 1175–1182 (1987).  
+20. Song, J.-G. et al. Crystalline mate for structure elucidation of organic molecules. Chem 10, 924–937 (2024).  
+
+<|ref|>sub_title<|/ref|><|det|>[[103, 218, 270, 233]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[102, 234, 896, 350]]<|/det|>
+This work is supported by the German Research Foundation (DFG) through the research group FOR2824 (Grant No. 398143140). Calculations for this research were conducted on the Lichtenberg high performance computer of the TU Darmstadt and at the Höchstleistungrechenzentrum Stuttgart (HLRS). The authors furthermore acknowledge the computational resources provided by the HPC Core Facility and the HRZ of the Justus- Liebig- Universität Gießen. Y. W. thanks Dr. Zhou Wu and Katrin Beuthet (Karlsruhe Institute of Technology, Institute of Nanotechnology) for their help with the SC- XRD measurements.  
+
+<|ref|>sub_title<|/ref|><|det|>[[103, 365, 293, 381]]<|/det|>
+## Author Contributions  
+
+<|ref|>text<|/ref|><|det|>[[102, 381, 896, 465]]<|/det|>
+J. C. synthesized the compounds [(PhSn)₄E₆] (E = S and Se) compounds. Y. W. conceived and performed the cocrystallization experiments, collected single-crystal X-ray crystallographic data, solved and refined the structures. K. E. and F. Z. performed the calculations and analysis with support from S. S. The manuscript was written through contributions of all authors, and all authors reviewed the manuscript. All authors have given approval to the final version of the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[103, 480, 304, 496]]<|/det|>
+## Additional information  
+
+<|ref|>text<|/ref|><|det|>[[103, 497, 456, 513]]<|/det|>
+The authors declare no competing interests.  
+
+<|ref|>text<|/ref|><|det|>[[102, 513, 896, 546]]<|/det|>
+Supplementary information and chemical compound information accompany this paper at www.nature.com/naturechemistry.  
+
+<|ref|>text<|/ref|><|det|>[[102, 546, 896, 579]]<|/det|>
+Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/.  
+
+<|ref|>text<|/ref|><|det|>[[102, 579, 690, 595]]<|/det|>
+Correspondence and requests for materials should be addressed to S. D.:  
+
+<|ref|>text<|/ref|><|det|>[[102, 595, 895, 628]]<|/det|>
+Stefanie Dehnen: Institute of Nanotechnology, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany, email: stefanie.dehnen@kit.edu  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 644, 180, 660]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[102, 676, 896, 758]]<|/det|>
+General experimental methods: All solvents were dried by standard methods and were commercially obtained. All reaction and sample preparations were carried out under inert atmospheres using standard Schlenk techniques or in an argon- filled glovebox. [(PhSn)₄S₆] and [(PhSn)₄Se₆] were prepared according to literature procedures.⁷ C₆₀ (98%, Sigma- Aldrich Chemie GmbH, US) was used as received.  
+
+<|ref|>text<|/ref|><|det|>[[101, 774, 896, 857]]<|/det|>
+Synthesis of [(PhSn)₄S₆]₂·(C₆₀)·(C₇H₈)₁.₂·[(C₄H₈O)₁.₂ (1): [(PhSn)₄S₆] (9.7mg, 0.010 mmol) and C₆₀ (5 mg, 0.006 mmol) were dissolved in THF (3 mL) and toluene (3 mL), respectively, and filtered through 0.8μm PTFE filters. The solution of C₆₀ was slowly layered on the top of the [(PhSn)₄S₆] solution. The vial was placed in a freezer at - 19°C for one week, after which the formation of red cuboid 1 single crystals of 1 could be observed.  
+
+<|ref|>text<|/ref|><|det|>[[101, 872, 895, 922]]<|/det|>
+Synthesis of [(PhSn)₄S₆]₂·(C₆₀)₁.₅·(C₇H₈) (2): [(PhSn)₄S₆] (9.7mg, 0.010 mmol) and C₆₀ (14.0 mg, 0.019 mmol) were dissolved in THF (3 mL) and toluene (5 mL), respectively, and filtered through 0.8μm PTFE filters. The solution of C₆₀ was slowly layered on the top of the [(PhSn)₄S₆] solution.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[100, 59, 895, 92]]<|/det|>
+The vial was placed in a freezer at \(- 19^{\circ}\mathrm{C}\) for one week, after which the formation of red cuboid single crystals of 2 could be observed.  
+
+<|ref|>text<|/ref|><|det|>[[100, 107, 896, 240]]<|/det|>
+Synthesis of [(PhSn)4Se6]·(C60)·(C7H8)·(C4H8O)0.5 (3): Compound 3 was obtained using procedures similar to those for 1- 2toluene: [(PhSn)4Se6] (0.010 mmol) and C60 (0.010 mmol) were dissolved in THF (3 mL) and toluene (3 mL), respectively, and filtered through \(0.8\mu \mathrm{m}\) PTFE filters. The solution of the fullerene was slowly layered on top of the tin cluster solution, and the vessel was placed in a freezer at \(- 19^{\circ}\mathrm{C}\) . After one week, a black amorphous precipitate could be observed in the purple solution. After filtration through \(0.8\mu \mathrm{m}\) PTFE filters, the purple filtrate was transferred into an \(8\mathrm{mL}\) vial, and the solvent was evaporated slowly at room temperature for one more week. Red single crystals formed on the walls of the vial.  
+
+<|ref|>text<|/ref|><|det|>[[100, 255, 896, 438]]<|/det|>
+Single crystal X- ray diffraction: The data for the X- ray structural analyses was collected at \(\mathrm{T} =\) 150.0 or \(180\mathrm{K}\) on a STOE STADI VARII diffractometer with \(\mathrm{Ga / K\alpha}\) radiation \((\lambda = 1.34143\mathrm{\AA})\) for all compounds. Data collection, integration, scaling (ABSPACK) and absorption correction were performed in X- area. The structures were solved using SHELXT from SHELXL- 2018/136, and refined by full matrix least- squares methods against \(\mathrm{F}^2\) with the SHELXL program.21 Olex2 was used for viewing and to prepare CIF files.22 Refinement was performed with anisotropic temperature factors for all non- hydrogen atoms. Hydrogen atoms were calculated on idealized positions. Figures were created with Diamond. Owing to heavy disorder of the atoms of the solvent (toluene and THF) molecules of compound 1, these were retracted by applying a solvent mask in Olex2 in order to get an optimal model of the cluster and \(\mathrm{C}_{60}\) molecules. The retracted electron density correlates to 0.6 equivalents of toluene and 0.6 equivalents of THF in the asymmetric unit.  
+
+<|ref|>text<|/ref|><|det|>[[100, 452, 896, 535]]<|/det|>
+Optical absorption spectroscopy: UV- visible spectra of 1, 2, and 3 single crystals, as well as \(\mathrm{C}_{60}\) , [(PhSn)4Se6], and [(PhSn)4Se6] powders, were measured in absorbance mode using a Varian Cary 5000 UV/VIS/NIR spectrometer from Agilent, equipped with a Praying Mantis accessory for solid- state samples. Additionally, \(\mathrm{C}_{60}\) in toluene solution was measured in absorbance mode using the same Varian Cary 5000 UV/VIS/NIR spectrometer.  
+
+<|ref|>text<|/ref|><|det|>[[100, 550, 896, 848]]<|/det|>
+Quantum chemical studies: Isolated molecular clusters as well as related crystals are modeled within Density Functional Theory (DFT) and periodic boundary conditions. Thereby, we employed the Vienna ab initio simulation package23,24 to evaluate the structural, electronic, and optical properties of the investigated compounds. Molecular clusters in the gas phase were modeled within the molecule- in- a- box approach. Cubic boxes with a volume of \(51179.6\mathrm{\AA}^3\) , explicitly designed to decouple periodic images of the clusters, were employed. Crystalline solids were modeled within their unit cell. The atomic positions were optimized until the Hellmann- Feynman forces acting on each atom are lower than \(0.001\mathrm{eV}\cdot \mathrm{\AA}^{- 1}\) .25 The ion- electron interaction was described by projected augmented wave pseudopotentials,26,27 implementing the PBE formulation28,29 of the generalized gradient approximation.30 The vdW DFT- D3 method with Becke- Johnson damping31,32 was applied in all calculations to account for dispersion forces, as (semi)local exchange- correlation (XC) functionals do not properly describe the long- range van der Waals (vdW) interactions. Plane waves up to a cutoff of \(600\mathrm{eV}\) were used as the basis for the expansion of electron wave functions. Due to the large cell size, gamma- point calculations were performed. The imaginary part of the frequency- dependent dielectric tensor \(\epsilon_{\alpha \beta}^{i}\) , \(\alpha ,\beta = x,y,z\) , was calculated as the sum over empty states at each point of the first Brillouin zone.33 The real part of the dielectric tensor \(\epsilon^{\prime}\) was obtained by Kramers- Kronig transformations. The absorbance coefficient \(k(\omega)\) was calculated from the dielectric function as  
+
+<|ref|>equation<|/ref|><|det|>[[291, 864, 702, 906]]<|/det|>
+\[k_{j}(\omega) = \frac{1}{\sqrt{2}}\sqrt{\left(\epsilon_{jj}^{r}(\omega)\right)^{2} + \left(\epsilon_{jj}^{i}(\omega)\right)^{2} - \epsilon_{jj}^{r}(\omega))}\]
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[100, 60, 900, 78]]<|/det|>
+where \(\epsilon^{T}(\omega)\) and \(\epsilon^{i}(\omega)\) are the real part and the imaginary part of the dielectric tensor, respectively.  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 95, 248, 110]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[102, 111, 896, 192]]<|/det|>
+The structures of compounds \(\mathbf{1} - \mathbf{3}\) were determined by single- crystal X- ray diffraction. Crystallographic data for the structure reported in this Article have been deposited at the Cambridge Crystallographic Data Centre, under deposition numbers CCDC- 2419991 (1). CCDC- 2419992 (2), and CCDC- 2419993 (3). A copy of the data can be obtained free of charge via https://www.ccdc.cam.ac.uk/structures/.  
+
+<|ref|>text<|/ref|><|det|>[[102, 192, 896, 272]]<|/det|>
+The Cartesian coordinates of all optimized structures and the respective SCF energies are summarized in the supplementary document "optimized- structures.txt". The files comprise all necessary data for reproducing the values. All non- default parameters for the computational studies are given in the Supplementary Information together with the corresponding references of the used methods.  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 290, 250, 305]]<|/det|>
+## Code availability  
+
+<|ref|>text<|/ref|><|det|>[[102, 306, 896, 404]]<|/det|>
+The Vienna Ab initio Simulation Package (VASP) is a computer program for atomic scale materials modelling from first principles (see also Refs [23] and [24]). The copyright- protected software is property of the VASP Software GmbH and available at https://www.vasp.at upon license purchase from the VASP Software GmbH or from an official reseller. The VASP version 6.4.2 and the official PAW potentials (see also Refs. [26] and [27]) are employed for the calculations presented in this work.  
+
+<|ref|>sub_title<|/ref|><|det|>[[102, 432, 403, 448]]<|/det|>
+## References for the methods section  
+
+<|ref|>text<|/ref|><|det|>[[100, 448, 897, 875]]<|/det|>
+21. Silen, W., Machen, T. & Forte, J. Acid-base balance in amphibian gastric mucosa. Am. J. Physiol.-Leg. Content 229, 721–730 (1975).  
+22. Duggleby, R. G. & Kaplan, H. Competitive labeling method for the determination of the chemical properties of solitary functional groups in proteins. Biochemistry 14, 5168–5175 (1975).  
+23. Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).  
+24. Kresse, G. & Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 6, 15–50 (1996).  
+25. Feynman, R. P. Forces in Molecules. Phys. Rev. 56, 340–343 (1939).  
+26. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).  
+27. Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).  
+28. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 77, 3865–3868 (1996).  
+29. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett. 78, 1396–1396 (1997).  
+30. Perdew, J. P. et al. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 6671–6687 (1992).  
+31. Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).  
+32. Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).  
+33. Gajdoš, M., Hummer, K., Kresse, G., Furthmüller, J. & Bechstedt, F. Linear optical properties in the projector-augmented wave methodology. Phys. Rev. B 73, 045112 (2006).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[42, 43, 312, 71]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[42, 93, 768, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 323, 230]]<|/det|>
+1PhSnSC601checkcif.pdf 
+2PhSnSC601.5checkcif.pdf 
+3PhSnSeC60.pdf 
+PiTrapSISD.pdf
+
+<--- Page Split --->

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@@ -0,0 +1,92 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Conceptual schematic of silicon-organic electro-optic tunable metasurfaces. A beam of light is incident on the metasurface, which consists of silicon nano-bars. The light is coupled into the slot mode inside the metasurface, which is sensitive to any refractive index perturbation in the slot. The OEO material is coated on top of the metasurface and fills the slot waveguide between the silicon nano-bars. The organic molecule inside the slot is aligned with the DC/RF field generated by the electrodes. When the RF bias voltage is applied on the electrodes, the electro-optic (Pockels) effect will generate refractive index modulation. As a result, the intensity of the reflected beam will be modulated accordingly.",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 The advantage of slot mode resonance in organic electro-optic modulators. a. The schematic view (top left), top view (bottom left) and cross-section (right) of the device that supports the slot mode. In the schematic view the OEO material is plotted transparent to show the slot structure underneath. The slots are formed in the device layer of the silicon-on-insulator (SOI) substrate which is covered by the OEO material HLD. To show the essence of the problem, only the slot is considered as the active region. The dashed rectangles in schematic view represent the top view across the device layer and the cross section of a period cell. b. The poling field profile when the left and right silicon rail have bias voltages \\(\\mathrm{V(V > 0)}\\) and 0, respectively. c-e. Normalized electric field profiles for three optical modes that could couple to \\(E_{x}\\) incident light. c. the slot mode. d. the guided mode in the silicon bar. e. the guided mode in the OEO material. f-h. the tuning performance of the three optical modes. Figures f,g, and h match with the field profile in figures c,d, and e, respectively. The inset in h is a zoom-in spectrum between \\(1649\\mathrm{nm}\\) and \\(1652.5\\mathrm{nm}\\) .",
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+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 The electro-optic free-space modulator. a-b. The cross-section and top view of the experimentally fabricated device. c-g. The step-by-step zoom-out image of the device and setup. c-f are the scanning electron microscopy(SEM) images. The scale bars are \\(500~\\mathrm{nm}\\) , \\(3~\\mu \\mathrm{m}\\) , \\(50~\\mu \\mathrm{m}\\) , and \\(1~\\mathrm{mm}\\) , respectively. g is the optical image of the device. Multiple devices are fabricated within a chip, and they are wire-bonded to the printed circuit board for parallel testing.",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Slot mode resonance characterization. a-d The simulated (a,c) and experimentally measured (b,d) reflection spectra when sweeping different sets of perturbation parameters. a-b. Sweep the periodicity of the notches. All curves have the same notch size \\(l = 160 \\mathrm{nm}\\) , \\(d = 80 \\mathrm{nm}\\) . Blue: \\(p = 720 \\mathrm{nm}\\) . Orange: \\(p = 740 \\mathrm{nm}\\) . Green: \\(p = 760 \\mathrm{nm}\\) . The resonance shifts due to periodicity changes are labelled in experiment and simulation curves. c-d. Sweep the notch sizes. All curves have the same notch periodicity \\(p = 740 \\mathrm{nm}\\) . Red: \\(l = 200 \\mathrm{nm}\\) , \\(d = 120 \\mathrm{nm}\\) . Purple: \\(l = 160 \\mathrm{nm}\\) , \\(d = 80 \\mathrm{nm}\\) . Brown: \\(l = 150 \\mathrm{nm}\\) , \\(d = 50 \\mathrm{nm}\\) . Pink: \\(l = 140 \\mathrm{nm}\\) , \\(d = 25 \\mathrm{nm}\\) . The quality factor of the resonances are labelled for experimental and simulated plots.",
+    "footnote": [],
+    "bbox": [
+      [
+        140,
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+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 DC tuning characteristics. a-c. Reflection spectra of three different devices under DC tuning. The applied biases are denoted in the legend. d. The reflection spectra of the device in b with bias voltages ranging from -11V to 11V. e. The maximum modulation ratio \\((\\Delta R / R = (R_{max} - R_{min}) / R_{V = 0})\\) for each wavelength in device shown in c. The inset depicts the absolute reflection as the DC bias voltage is swept from -12V to 12V for a fixed wavelength of incident light of 1486 nm. The absolute reflection changes over 10%.",
+    "footnote": [],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Fig. 6 AC tuning characteristics and circuit model scheme. a. The experimental and modeled AC response of the active device. Blue curve: the experimental normalized modulation depth. The cutoff bandwidth is at 3MHz. Green curve: the model prediction of the modulation depth. Insets: the example modulation signal(Orange) and the fitting sine wave (Red) in the time domain. The frequencies of the modulation signal are 80kHz (top left) and 4MHz (bottom right), respectively. b. The circuit model of the device. \\(V\\) : the voltage source. \\(R_{s}\\) : the source resistance. \\(C_{load}\\) : external stray capacitance outside the device. \\(C_{SOI}\\) : the capacitance due to the use of SOI wafer. \\(R_{Au}\\) : the resistance of the gold strip on top of the silicon nano-bar. \\(R_{Si}\\) : the resistance of the silicon nano-bar. \\(C_{Poly}\\) : the OEO material capacitance. \\(R_{Poly}\\) : the OEO material resistance.",
+    "footnote": [],
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+]

preprint/preprint__5fc5b1da05c4aed7e84ec30dba34d1d0027c21b0f93f20947370e74945964f1a/preprint__5fc5b1da05c4aed7e84ec30dba34d1d0027c21b0f93f20947370e74945964f1a.mmd

@@ -0,0 +1,278 @@
+
+# Low-voltage dynamic light manipulation with silicon-organic slot metasurfaces  
+
+Tianzhe Zheng  California Institute of Technology  
+
+Yiran Gu  California Institute of Technology  
+
+Hyounghan Kwon  California Institute of Technology  
+
+Gregory Roberts  California Institute of Technology  
+
+Andrei Faraon  
+
+faraon@caltech.edu  
+
+California Institute of Technology https://orcid.org/0000- 0002- 8141- 391X  
+
+## Article  
+
+Keywords: Metasurfaces, organic electro-optic material, slot waveguide  
+
+Posted Date: May 31st, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3001703/v1  
+
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+Additional Declarations: Yes there is potential Competing Interest. T.Z, Y.G, H.K. and A.F. have filed for a patent application based on the results of this paper.  
+
+Version of Record: A version of this preprint was published at Nature Communications on February 20th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 45544- 0.
+
+<--- Page Split --->
+
+# Low-voltage dynamic light manipulation with silicon-organic slot metasurfaces  
+
+Tianzhe Zheng, \(^{1, *}\) Yiran Gu, \(^{2, *}\) Hyounghan Kwon, \(^{1,3, \dagger}\) Gregory Roberts, \(^{1}\) and Andrei Faraon \(^{1,3, \ddagger}\)  
+
+\(^{1}T. J.\) Watson Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA \(^{2}\) Department of applied physics and material science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA \(^{3}\) Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
+
+<--- Page Split --->
+
+Abstract. Active metasurfaces provide the opportunity for fast spatio- temporal control of light. Among various tuning methods, organic electro- optic materials provide some unique advantages due to their fast speed and large nonlinearity, along with the possibility of using fabrication techniques based on infiltration. In this letter, we report a silicon- organic platform where organic electro- optic material is infiltrated into the narrow gaps of slot- mode metasurfaces with high quality factors. The mode confinement into the slot enables the placement of metallic electrodes in close proximity, thus enabling tunability at lower voltages. We demonstrate a tuning sensitivity of \(0.16\mathrm{nm / V}\) at telecommunication wavelength. These results provide a path towards tunable silicon- organic hybrid metasurfaces at CMOS- level voltages.  
+
+Keywords. Metasurfaces, organic electro- optic material, slot waveguide  
+
+## INTRODUCTION  
+
+Relying on sub- wavelength nanostructures, metasurfaces have been shown as promising candidates for replacing conventional free- space optical components by arbitrarily manipulating the amplitude, phase, and polarization of optical wavefronts in certain applications[1- 3]. In recent years, the scope of their applications has been expanded towards complete spatiotemporal control through the introduction of active metasurfaces. These developments open up exciting new possibilities for dynamic holography[4], faster spatial light modulators[5], and fast optical beam steering for LiDAR[6]. Large efforts have been channeled into various modulation mechanisms. Microelectromechanical and nanoelectromechanical systems (MEMS and NEMS)[7- 10] have the advantages of low- cost and CMOS- compatibility, but the speed is limited up to MHz. Phase- change materials[11- 13] have fast, drastic, and non- volatile refractive index change, but lack continuous refractive index tuning and have a limited number of cycles constraining applicability to reconfigurable devices. Thermal- optic effects can induce relatively large refractive index changes[14, 15], but the speed is inherently limited and the on- chip thermal management can be challenging. The co- integration of transparent conductive oxide and metallic plasmonic structures [5, 6] has been demonstrated in epsilon- near- zero (ENZ) regime to control the wavefront of reflected light, but the low reflection amplitude induced by the optical loss of the materials and the epsilon near zero regime is unavoidable.  
+
+In modern photonics, a multitude of technologies for tunable optics and frequency conversion[16, 17] are realized with nonlinear materials that have low loss and a strong \(\chi^{(2)}\) effect, such as lithium
+
+<--- Page Split --->
+
+niobate[18, 19], aluminum nitride[20], and organic electro-optic (OEO) materials[21]. Their ultrafast responses make it possible to use RF or millimeter- wave control[22]. Developments in computational chemistry have also led to artificially engineered organic molecules that have record- high nonlinear coefficients with long- term and high- temperature stability [23, 24]. However, their potential in modifying free- space light has been relatively unexplored until recently. Several OEO material- hybrid designs have demonstrated improved tunability of metasurfaces [25–27]. Utilizing dielectric resonant structures and RF- compatible coplanar waveguides, a free- space silicon- organic modulator has recently accomplished GHz modulation speed [28]. However, all demonstrations to date require high operating voltages \(\pm 60V\) , due to low resonance tuning capability(frequency shift / voltage) which hinders their integration with electronic chips. In this work, we propose combining high- Q metasurfaces based on slot- mode resonances with the unique nano- fabrication techniques enabled by OEO materials which drastically reduces the operating voltage. The low voltage is mainly achieved from the ability to place the electrodes in close proximity to each other while hosting high- Q modes in between and the large overlap of the optical and RF fields in OEO materials. In the following sections, we first provide the design concepts and considerations for achieving a reduced operating voltage. Next, we numerically demonstrate the advantage of a particular selected mode compared to other supported modes in the structure. Finally, we experimentally realize our concepts and characterize the performance of the electro- optic metasurface.  
+
+## RESULTS  
+
+The reported device and its operation scheme are depicted in Fig. 1. Light polarized along \(x\) \((E_{x})\) is incident onto the device along \(- z\) direction, and then couples into the slot mode hosted in between the silicon nano- bars. Gold electrodes are placed on top of the nano- bars and doped silicon is used to maximize the voltage drop across the slot filled with OEO material. The active OEO material regions have nonlinear coefficients \(r_{33}\) with each two adjacent slots exhibiting opposite signs of nonlinear coefficients due to the poling field direction. When the operating signal is applied, the active layer induces a spatially varied refractive index change  
+
+\[\Delta n(t) = -\frac{1}{2} n_{mat}^{3}r_{33}E_{AC}(t) \quad (1)\]
+
+<--- Page Split --->
+
+where \(E_{AC}\) is the local electric field in the OEO material. Notice that due to the geometry of the electrodes, the signal electric fields \(E_{AC}(t)\) also have opposite directions in adjacent gaps, as shown in Fig. 1. Therefore, the overall response from any two adjacent slots is the same. Besides the operating voltage or the field in slots, the perturbation strength to the optical mode also depends on the overlap factor \(\Gamma\) between the electric field profile and the optical mode profile (see supplementary section 2). Based on cavity perturbation theory [29], the shift of the resonant frequency can then be expressed as  
+
+\[\Delta \omega = -\frac{\Delta n_{avg}}{n_{mat}}\omega \Gamma \quad (2)\]  
+
+where \(\begin{array}{r}{\Delta n_{a v g} = - \frac{1}{2} n_{m a t}^{3}r_{33}\frac{V_{D C}}{w_{g}}} \end{array}\) denotes the refractive index change upon applying a constant field of \(\frac{V_{D C}}{w_{g}}\) across the gap.  
+
+By examining Equation 2, we can gain valuable insights into two distinct methods for reducing the voltage of the device: reducing the distance between electrodes and increasing the overlap factor. However, introducing closer metallic electrodes leads to inevitable losses, thus reducing the quality factors and limiting the sensitivity to refractive index changes. Therefore, transmitting electric fields through conductive dielectrics is preferred. In our reported device, doped silicon acts as the electrodes with gap width \((w_{g})\) down to \(100\mathrm{nm}\) . At the same time, this gap between the silicon nano- bars will host slot modes[30], whose demonstrated high overlap with the OEO material has been utilized in many integrated silicon- organic modulators[31- 33]. However, the slot waveguide is intrinsically decoupled from the free- space light due to momentum unmatching. To enable coupling with normally incident light, we create periodic notches along every slot [34, 35]. The notch periodicity and the notch size dominantly determine the resonance wavelength and the coupling strength of the slot resonance, respectively. As a result, both the quality factor and the resonant wavelength could be judiciously engineered (see supplementary sections 1- 2). Although a similar structure has been proposed for sensing[36], the design strategy and target applications here are completely different.  
+
+To show the advantage of the slot modes while shrinking the distance between electrodes down to \(100\mathrm{nm}\) , it is worth discussing the possible optical modes in such a structure. The detailed schematic view, top view, and cross- section view of the example device are shown in Fig. 2a, where three different colors (gray, blue, green) indicate different materials (silicon, silica, OEO material or HLD). In the numerical simulations shown in Fig. 2b- h, HLD has a refractive index of
+
+<--- Page Split --->
+
+1.85[24]. Fig. 2b shows the poling field profile upon applying a DC bias across the electrodes. The \(x - z\) cross-section is cut at the center of a notch pair shown as dashed rectangle in the schematic view of Fig. 2a. Neglecting any interface effect[37], we can treat the relative amplitude of \(r_{33}\) at each spatial point as following this pictured poling field profile. The geometry of the electrodes results in a high \(E_{x}\) field along the slot and a rapid field decay above and below the slot. Therefore, to simplify the simulation, we assume that only the OEO material inside the slot is nonlinearly active. The structure will host various optical modes, many of which have a significant \(E_{x}\) field component such that it could strongly overlap with the incident \(E_{x}\) beam. Fig. 2c- e show three cross- sectional optical mode profiles (Mode I, II, III) originating from different parts of the device. The cross- sections are cut at the same \(y\) position as in Fig. 2b. Mode I is the slot mode, which has the field highly confined inside the slot, as discussed above, even upon applying the notch perturbation. Mode II is the bounded state guided within the slab. Notice that besides the slot mode, periodic notches also unlock the free- space radiation for this guided mode in the slab [38]. Mode III is a guided mode in OEO material, which has also been reported in [26]. Unlike the other optical modes, the field in slot mode is well aligned with the poling field and thus has the highest overlap factor \(\Gamma\) . As a result, under the same bias voltage, the slot mode has the largest resonance shift, as demonstrated through the simulation results in Fig. 2g- i. With the same amount of index change in the active region, Mode I, II, and III have resonance shifts of 2.73 nm, 0.29 nm, and 0.46 nm, respectively. A more accurate model estimates the overlap factor by considering the orientation of the nonlinearity[26] (see supplementary material section 2). The calculated \(\Gamma\) based on this model for modes I, II, and III are 0.156, 0.017, and 0.015, respectively. The slot mode shows an order of magnitude higher \(\Gamma\) , compared to the others. Therefore, the slot mode is crucial for low- voltage modulation in silicon- organic metasurfaces.  
+
+We experimentally realize the concept discussed above, using a silicon- on- insulator (SOI) wafer. The device's cross- section, top view, and voltage setting are schematically illustrated in Fig. 3a- b. The detailed device parameters are shown in supplementary material section 6. The nanostructures are fabricated with conventional nanofabrication techniques (see Methods section for details on the fabrication procedure). The step- by- step zoom- out scanning electron microscopy(SEM) images (prior to spin- coating of OEO material) are shown in Fig. 3c- f. Doped silicon nano- bars have a resistance of \(1 \sim 10\Omega \cdot cm\) , and \(\sim 100\) - nm wide gold strips along the nano- bars are added to further reduce the voltage drop across the silicon. In Fig. 3c, the gold strips are deliberately aligned at the center of the silicon rail so that only minimal absorption is introduced (See supplementary section
+
+<--- Page Split --->
+
+2 and Fig. S3). Fig. 3e shows an \(80 \times 100 \mu m^2\) device. Multiple devices are fabricated on a chip as shown in Fig. 3f for increasing the tolerance of the fabrication errors and testing multiple geometric parameters. After the coating of the OEO material, the device is wire bonded to a customized printed circuit board for poling and operating, shown in Fig. 3g.  
+
+To experimentally verify the relationship between resonant optical characteristics of the slot modes and the geometry of the device, we have fabricated several devices having different design parameters and compared their measured optical properties with corresponding numerical calculations (see Methods, Supplementary Section 5, and Fig. S6 for details in optical measurement setup). Fig. 4 shows the calculated and measured spectra of the slot mode resonances with different geometries. We characterize the slot resonances by varying the notch period and notch size in Fig. 4a- b and Fig. 4c- d, respectively. In Fig. 4a- b, we observe that a 20- nm increment in notch periodicity leads to \(\sim 21.6 \mathrm{nm}\) and \(22.2 \mathrm{nm}\) average redshift of the resonance in simulation and experiment, respectively. Also, with respect to the resonant wavelengths, the resonance amplitudes, and the spectral shapes of the resonance, the measured spectra in Fig. 4c show good agreement with the calculated spectra in Fig. 4d. In particular, the quality factor increases with the decrease of the resonance amplitude. This trade- off is mainly due to the decreasing radiation rate to the top port (to \(+z\) direction), which results in the under- coupling between the slot mode and the illuminated light from the top [15]. Specifically, the amplitude of the resonance is determined by the ratio of the mode coupling rate between the input light and the slot mode to the sum of other undesired decay rates [39]. The undesired decays include absorption in the gold layer, scattering from the rough sidewalls or finite edge of the chips, and radiation to the oxide layer or the silicon substrate. As the absorption in the gold layer and the radiation to the silicon substrate is nearly inevitable in the proposed planar structures, the trade- off between the resonance amplitude and the quality factors is inevitable especially when the coupling rate decreases. The proposed devices in Fig. 4e can achieve modulation amplitude over \(10\%\) and Q- factor over 1000 in the experiment even with the absorption in the gold.  
+
+Operation results under DC bias are shown in Fig. 5. Fig. 5a- c show the results from 3 different devices under maximum bias voltages before any dielectric breakdown. The variation in the breakdown voltages results from the quality of the OEO material preparation and fabrication quality. The maximum absolute frequency shift of \(5.5 \mathrm{nm}\) is achieved under \(\pm 17V\) in Fig. 5a, and the spectral shift per unit external DC bias is \(S_{abs} = \Delta \lambda /\Delta V = 0.161nm / V\) , which is \(\sim 1.6 \times\) higher than that of the previously reported tunable free- space optical modulators [28]. Using Eqs. 1 and
+
+<--- Page Split --->
+
+2, \(r_{33}\) in- device is calculated at \(45.7\mathrm{pm / V}\) at \(1495\mathrm{nm}\) . The relatively low nonlinear coefficient compared to what we expected[24] is partly due to the surface state of highly doped silicon used as the electrode [40] and the small width of the slot[37]. In Fig. 5b and c, \(2.3\mathrm{nm}\) and \(2.6\mathrm{nm}\) resonance shifts are observed with \(\pm 11\mathrm{V}\) and \(\pm 12\mathrm{V}\) bias voltages, respectively. Figures 5b and c show high Q- factors over 1000. The increase in Q- factor also improves the normalized modulation figure- of- merit \((S_{n} = \Delta \lambda /(FWHM\cdot \Delta V)\) [41]. In our best- performing device shown in Fig.5b, \(S_{n}\) is \(0.09\mathrm{V}\) , which is an order of magnitude higher than other reported devices [41]. The reflection spectra are plotted in Fig. 5d as a function of different bias voltages. The spectra clearly show the bidirectional linear relationship between the bias voltage and the resonance shift, confirming that the spectral shift results from the electro- optic effect [26]. In Fig. 5e, the relative modulation ratio, \(\Delta R / R\) , from the device in Fig. 5c is plotted. The maximum modulation ratio is over \(40\%\) . It is worth noting that the asymmetry of the modulation is due to the Fano shape of the resonance [42]. The inset in Fig. 5e, shows the reflection intensity as a function of the bias voltage when the input light wavelength is \(1486.5\mathrm{nm}\) . From \(-12\mathrm{V}\) to \(+12\mathrm{V}\) , the reflection amplitude is gradually increasing.  
+
+The AC modulation characteristic is tested with the devices in Fig. 5a and plotted in Fig. 6a. A sine wave with peak- to- peak value, \(V_{pp}\) , of \(20\mathrm{V}\) is applied into the device while the wavelength of the incident light is set at \(1490\mathrm{nm}\) where the device achieves the highest modulation depth. The sine wave frequency is swept from \(50\mathrm{kHz}\) to \(5.8\mathrm{MHz}\) . The cutoff 3dB bandwidth is at \(3\mathrm{MHz}\) . The insets in Fig. 6a show the normalized modulation signal when driving with frequency \(f = 80kHz\) and \(f = 2.8MHz\) , respectively. To investigate the AC response, we use a simplified model to predict the AC response shown in Fig. 6b. The model collectively considers the contributing factors to the response speed within and outside the devices. In the devices, we model the nanobars as a resistance including the contribution from the gold strip \(R_{Au}\) and the silicon nano- bar \(R_{Si}\) (see supplementary note 4). The slot is modeled as the parallel connected resistance \(R_{OEO}\) and capacitance \(C_{OEO}\) . Outside the devices, we assume that the major electrical components are the stray capacitance in the circuits, which are split into the capacitance due to the SOI wafer [43] \(C_{SOI}\) and other factors \(C_{load}\) . The parameters in the model are determined by both the geometry of the devices and the AC response of similar devices with different substrates or electrode layouts (See supplementary material section 4). The AC response from the prediction of the model is shown as the green line in Fig. 6a, which agrees with the experimental result. Based on the model estimation, the capacitance from the silicon- organic platform and the stray capacitance along the whole circuits
+
+<--- Page Split --->
+
+are the main factors preventing the speed increase. The capacitance from the SOI wafer could be solved by advanced CMOS technology used in integrated electro-optic modulators [44]. Judicious material and structural engineering of these circuits have already achieved gigahertz operation of electro-optic modulators [28, 45- 47]. As a result, there is no fundamental limit in increasing the operation speed up to GHz in our platform.  
+
+## DISCUSSION  
+
+In this work, we propose a silicon- organic metasurface for free- space modulation with reduced operation voltage less than \(\pm 17V\) . We experimentally observed the resonance with quality factor \(330 - 1310\) and up to \(\sim 5.5\mathrm{nm}\) shift with nonlinear coefficient \(r_{33} = 45.7\mathrm{pm / V}\) at \(1495\mathrm{nm}\) . The proposed slot mode combines the advantages of a short distance between two electrodes and a large overlap with the OEO material, achieving a tuning sensitivity \(S_{abs} = 0.161nm / V\) , which shows an improvement with a factor of 1.6 in sensitivity compared to the state- of- art [28, 41]. Finally, the metasurface has up to \(3MHz\) bandwidth. The use of the slot mode is not limited to electro- optic systems. The proposed design approach can be applied to any system where sensitivity to perturbations in low- index media is critical. For example, in NEMS systems, the slot mode resonance could potentially improve sensitivity to the mechanical movement, compared to conventional guided mode resonances [8].  
+
+The currently demonstrated sensitivity is limited by the quality factor and the nonlinear coefficient \(r_{33}\) . The quality factor could be improved by using smaller notches or a refined fabrication process. The relatively low nonlinear coefficient is primarily due to the surface state of highly doped silicon as the electrode [40] and the small width of the slot[37]. Barrier layer protection[48] has the potential to increase the nonlinear coefficient \(r_{33}\) by 4- 5 times [49]. Judicious doping level adjustments and the microwave coplanar waveguide design could enable GHz speed operation[28, 32]. Therefore, with the increase of electro- optic coefficient and operation bandwidth, our platform is a potential solution for GHz free- space modulation at the CMOS level voltage.  
+
+This study primarily focuses on structures which are periodic in both \(x\) and \(y\) dimensions. However, it is not a necessary condition for preserving the slot mode. As a mode propagating along the \(y\) direction, the slot mode doesn't necessitate periodic conditions in \(x\) direction [50]. By varying the geometry of the slots, individual slot modulation could be potentially achieved. In the \(y\) - dimension, by introducing high contrast index variations or photonic crystal mirrors, the footprint
+
+<--- Page Split --->
+
+of the resonant device could be reduced considerably [51, 52]. Furthermore, the proposed devices expect to achieve phase modulation if the overcoupling condition is satisfied by the out- of- plane asymmetry in nanostructures [9] or a bottom mirror [5, 6].  
+
+In summary, this report presents a low- voltage amplitude modulator using a silicon- organic platform. The slot mode metasurface has the potential to enable high- speed and low- voltage optical switching, sensing, and tuning, for numerous applications such as LiFi, Lidar, spatial light modulators, and quantum optical communication.  
+
+## ACKNOWLEDGEMENT  
+
+We thank NLM Photonics for the HLD OEO material and for consulting on the preparation and poling process of the HLD. The device nanofabrication was performed at the Kavli Nanoscience Institute at Caltech. This work was supported by the Caltech Sensing to Intelligence program.  
+
+## METHODS  
+
+## Fabrication and poling methods  
+
+The device is fabricated from an SOI (silicon on insulator) wafer, which consists of \(300~\mathrm{nm}\) device p- doped silicon \((1 - 10\Omega \cdot cm)\) , \(300~\mathrm{nm}\) BOX (buffered silicon oxide), and \(500\mu m\) silicon substrate. The detailed fabrication workflow is shown in supplementary materials section 5. The device requires two sequential nanofabrication steps for the silicon rails and metallic strip. Both E- beam lithography steps utilize ZEP- 520A (Zion Corporation) as the resist, \(100\mathrm{kV}\) electron beam (EBPG- 5200, Raith GmbH) to expose, and ZED- N50 (Zion Corporation) as the developer. After the first E- beam lithography, we use the resist as the soft mask and the pattern is transferred to silicon by ICP- RIE etching (PlasmaLab System 100, Oxford Instrument). Next, the resist is removed by Remover PG. The second E- beam lithography writes the liftoff mask for the electrodes, following which \(5\mathrm{nm}\) Ti and \(60\mathrm{nm}\) Au are deposited sequentially using an E- beam evaporator (Kurt J. Lesker E- beam evaporator). Liftoff is then performed in Remover PG. Finally, a layer of OEO material (HLD, NLM Photonics) is spin- coated on top of the device, followed by a 3- hr solvent removal in a vacuum oven at \(65^{\circ}\mathrm{C}\) . The detailed workflow is shown in supplementary material section 5.
+
+<--- Page Split --->
+
+Poling of the HLD material is performed by heating the device under the nitrogen environment while applying a poling voltage. This voltage creates a poling field around \(100V / \mu m\) across the slot. The heating process consists of a \(6^{\circ}C / s\) temperature ramping, 5 to 10 minutes of holding at \(95^{\circ}\) , and rapid cooling.  
+
+## Simulation methods  
+
+The simulations in Fig. 2 and Fig. S3 use COMSOL Multiphysics software. The periodic condition is applied in both x and y directions. Refractive indexes of the silicon, silicon oxide, and OEO material are assumed to be 3.52, 1.44, and 1.85. Fig. 4a,c are simulated with FDTD (Lumerical) with periodic boundary conditions applied in x and y.  
+
+## Measurement  
+
+The measurements were conducted using the experimental setup depicted in Fig. S5. The light source utilized was a tunable external- cavity diode laser (Toptica CTL- 1550). A fiber collimator (Thorlabs, F260FC- 1550) was employed to collimate the beam. A beam splitter is placed in front of the collimator to split a small amount of power for the reference InGaAs detector (Thorlabs, PDA10CS). The polarized state of the incident light was set to TE polarization using a linear polarizer. Then the light goes through a beam splitter and only half of the power is used.  
+
+A \(\times 20\) infinity- corrected objective lens (Mitutoyo, M Plan Apo NIR) and a tube lens with a focal length of \(200\mathrm{mm}\) were used to image the sample at the object plane, with the tube lens and the mounting stage of the sample adjusted to ensure normal incidence. An iris (Thorlabs, ID25) was inserted at the image plane to select a region of interest with a diameter of \(45\mu m\) in the object plane. The spatially filtered light was either focused onto another InGaAs detector for the measurement of the spectra or imaged on an InGaAs SWIR camera (Goodrich, SU320HX- 1.7RT) using relay optics. The reflection signals were obtained by dividing the signal from the sample by the signal from the sources. It should be noted that due to different input polarization states, the incident power onto the sample varied at different wavelengths. Thus, the signals were further normalized by the signals from the gold.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Conceptual schematic of silicon-organic electro-optic tunable metasurfaces. A beam of light is incident on the metasurface, which consists of silicon nano-bars. The light is coupled into the slot mode inside the metasurface, which is sensitive to any refractive index perturbation in the slot. The OEO material is coated on top of the metasurface and fills the slot waveguide between the silicon nano-bars. The organic molecule inside the slot is aligned with the DC/RF field generated by the electrodes. When the RF bias voltage is applied on the electrodes, the electro-optic (Pockels) effect will generate refractive index modulation. As a result, the intensity of the reflected beam will be modulated accordingly. </center>  
+
+## AUTHOR CONTRIBUTIONS  
+
+H.K., T.Z. and A.F. conceived the project. A.F. supervised the project. H.K and T.Z. designed the structures. T.Z. and Y.G. fabricated devices, performed simulations and measurements, and analyzed data. T.Z. designed and prepared the printed circuit boards. G.R. provided feedback on the design of the structures. T.Z. wrote the manuscript. All authors discussed the results and commented on the manuscript.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 The advantage of slot mode resonance in organic electro-optic modulators. a. The schematic view (top left), top view (bottom left) and cross-section (right) of the device that supports the slot mode. In the schematic view the OEO material is plotted transparent to show the slot structure underneath. The slots are formed in the device layer of the silicon-on-insulator (SOI) substrate which is covered by the OEO material HLD. To show the essence of the problem, only the slot is considered as the active region. The dashed rectangles in schematic view represent the top view across the device layer and the cross section of a period cell. b. The poling field profile when the left and right silicon rail have bias voltages \(\mathrm{V(V > 0)}\) and 0, respectively. c-e. Normalized electric field profiles for three optical modes that could couple to \(E_{x}\) incident light. c. the slot mode. d. the guided mode in the silicon bar. e. the guided mode in the OEO material. f-h. the tuning performance of the three optical modes. Figures f,g, and h match with the field profile in figures c,d, and e, respectively. The inset in h is a zoom-in spectrum between \(1649\mathrm{nm}\) and \(1652.5\mathrm{nm}\) . </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 The electro-optic free-space modulator. a-b. The cross-section and top view of the experimentally fabricated device. c-g. The step-by-step zoom-out image of the device and setup. c-f are the scanning electron microscopy(SEM) images. The scale bars are \(500~\mathrm{nm}\) , \(3~\mu \mathrm{m}\) , \(50~\mu \mathrm{m}\) , and \(1~\mathrm{mm}\) , respectively. g is the optical image of the device. Multiple devices are fabricated within a chip, and they are wire-bonded to the printed circuit board for parallel testing. </center>  
+
+[1] A. Arbabi and A. Faraon, Nature Photonics 17, 16 (2023).  
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+[2] J. Scheuer, ACS Photonics 7, 1323 (2020).
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 Slot mode resonance characterization. a-d The simulated (a,c) and experimentally measured (b,d) reflection spectra when sweeping different sets of perturbation parameters. a-b. Sweep the periodicity of the notches. All curves have the same notch size \(l = 160 \mathrm{nm}\) , \(d = 80 \mathrm{nm}\) . Blue: \(p = 720 \mathrm{nm}\) . Orange: \(p = 740 \mathrm{nm}\) . Green: \(p = 760 \mathrm{nm}\) . The resonance shifts due to periodicity changes are labelled in experiment and simulation curves. c-d. Sweep the notch sizes. All curves have the same notch periodicity \(p = 740 \mathrm{nm}\) . Red: \(l = 200 \mathrm{nm}\) , \(d = 120 \mathrm{nm}\) . Purple: \(l = 160 \mathrm{nm}\) , \(d = 80 \mathrm{nm}\) . Brown: \(l = 150 \mathrm{nm}\) , \(d = 50 \mathrm{nm}\) . Pink: \(l = 140 \mathrm{nm}\) , \(d = 25 \mathrm{nm}\) . The quality factor of the resonances are labelled for experimental and simulated plots. </center>  
+
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+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 DC tuning characteristics. a-c. Reflection spectra of three different devices under DC tuning. The applied biases are denoted in the legend. d. The reflection spectra of the device in b with bias voltages ranging from -11V to 11V. e. The maximum modulation ratio \((\Delta R / R = (R_{max} - R_{min}) / R_{V = 0})\) for each wavelength in device shown in c. The inset depicts the absolute reflection as the DC bias voltage is swept from -12V to 12V for a fixed wavelength of incident light of 1486 nm. The absolute reflection changes over 10%. </center>  
+
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+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Fig. 6 AC tuning characteristics and circuit model scheme. a. The experimental and modeled AC response of the active device. Blue curve: the experimental normalized modulation depth. The cutoff bandwidth is at 3MHz. Green curve: the model prediction of the modulation depth. Insets: the example modulation signal(Orange) and the fitting sine wave (Red) in the time domain. The frequencies of the modulation signal are 80kHz (top left) and 4MHz (bottom right), respectively. b. The circuit model of the device. \(V\) : the voltage source. \(R_{s}\) : the source resistance. \(C_{load}\) : external stray capacitance outside the device. \(C_{SOI}\) : the capacitance due to the use of SOI wafer. \(R_{Au}\) : the resistance of the gold strip on top of the silicon nano-bar. \(R_{Si}\) : the resistance of the silicon nano-bar. \(C_{Poly}\) : the OEO material capacitance. \(R_{Poly}\) : the OEO material resistance. </center>  
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+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- Lowvoltagedynamiclightmanipulationwithsiliconorganicslotmetasurfaceassuppl.pdf
+
+<--- Page Split --->

preprint/preprint__5fc5b1da05c4aed7e84ec30dba34d1d0027c21b0f93f20947370e74945964f1a/preprint__5fc5b1da05c4aed7e84ec30dba34d1d0027c21b0f93f20947370e74945964f1a_det.mmd

@@ -0,0 +1,374 @@
+<|ref|>title<|/ref|><|det|>[[44, 108, 823, 175]]<|/det|>
+# Low-voltage dynamic light manipulation with silicon-organic slot metasurfaces  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 348, 238]]<|/det|>
+Tianzhe Zheng  California Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 244, 348, 285]]<|/det|>
+Yiran Gu  California Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 291, 348, 331]]<|/det|>
+Hyounghan Kwon  California Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 337, 348, 377]]<|/det|>
+Gregory Roberts  California Institute of Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 383, 168, 400]]<|/det|>
+Andrei Faraon  
+
+<|ref|>text<|/ref|><|det|>[[54, 409, 258, 426]]<|/det|>
+faraon@caltech.edu  
+
+<|ref|>text<|/ref|><|det|>[[54, 453, 705, 473]]<|/det|>
+California Institute of Technology https://orcid.org/0000- 0002- 8141- 391X  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 515, 102, 533]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 553, 660, 573]]<|/det|>
+Keywords: Metasurfaces, organic electro-optic material, slot waveguide  
+
+<|ref|>text<|/ref|><|det|>[[44, 591, 296, 610]]<|/det|>
+Posted Date: May 31st, 2023  
+
+<|ref|>text<|/ref|><|det|>[[44, 629, 475, 648]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 3001703/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 666, 911, 708]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[44, 727, 933, 770]]<|/det|>
+Additional Declarations: Yes there is potential Competing Interest. T.Z, Y.G, H.K. and A.F. have filed for a patent application based on the results of this paper.  
+
+<|ref|>text<|/ref|><|det|>[[42, 805, 945, 848]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on February 20th, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 45544- 0.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[170, 85, 824, 140]]<|/det|>
+# Low-voltage dynamic light manipulation with silicon-organic slot metasurfaces  
+
+<|ref|>text<|/ref|><|det|>[[115, 161, 880, 182]]<|/det|>
+Tianzhe Zheng, \(^{1, *}\) Yiran Gu, \(^{2, *}\) Hyounghan Kwon, \(^{1,3, \dagger}\) Gregory Roberts, \(^{1}\) and Andrei Faraon \(^{1,3, \ddagger}\)  
+
+<|ref|>text<|/ref|><|det|>[[149, 194, 848, 346]]<|/det|>
+\(^{1}T. J.\) Watson Laboratory of Applied Physics and Kavli Nanoscience Institute, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA \(^{2}\) Department of applied physics and material science, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA \(^{3}\) Department of Electrical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 882, 319]]<|/det|>
+Abstract. Active metasurfaces provide the opportunity for fast spatio- temporal control of light. Among various tuning methods, organic electro- optic materials provide some unique advantages due to their fast speed and large nonlinearity, along with the possibility of using fabrication techniques based on infiltration. In this letter, we report a silicon- organic platform where organic electro- optic material is infiltrated into the narrow gaps of slot- mode metasurfaces with high quality factors. The mode confinement into the slot enables the placement of metallic electrodes in close proximity, thus enabling tunability at lower voltages. We demonstrate a tuning sensitivity of \(0.16\mathrm{nm / V}\) at telecommunication wavelength. These results provide a path towards tunable silicon- organic hybrid metasurfaces at CMOS- level voltages.  
+
+<|ref|>text<|/ref|><|det|>[[139, 327, 707, 346]]<|/det|>
+Keywords. Metasurfaces, organic electro- optic material, slot waveguide  
+
+<|ref|>sub_title<|/ref|><|det|>[[139, 390, 283, 408]]<|/det|>
+## INTRODUCTION  
+
+<|ref|>text<|/ref|><|det|>[[113, 434, 882, 877]]<|/det|>
+Relying on sub- wavelength nanostructures, metasurfaces have been shown as promising candidates for replacing conventional free- space optical components by arbitrarily manipulating the amplitude, phase, and polarization of optical wavefronts in certain applications[1- 3]. In recent years, the scope of their applications has been expanded towards complete spatiotemporal control through the introduction of active metasurfaces. These developments open up exciting new possibilities for dynamic holography[4], faster spatial light modulators[5], and fast optical beam steering for LiDAR[6]. Large efforts have been channeled into various modulation mechanisms. Microelectromechanical and nanoelectromechanical systems (MEMS and NEMS)[7- 10] have the advantages of low- cost and CMOS- compatibility, but the speed is limited up to MHz. Phase- change materials[11- 13] have fast, drastic, and non- volatile refractive index change, but lack continuous refractive index tuning and have a limited number of cycles constraining applicability to reconfigurable devices. Thermal- optic effects can induce relatively large refractive index changes[14, 15], but the speed is inherently limited and the on- chip thermal management can be challenging. The co- integration of transparent conductive oxide and metallic plasmonic structures [5, 6] has been demonstrated in epsilon- near- zero (ENZ) regime to control the wavefront of reflected light, but the low reflection amplitude induced by the optical loss of the materials and the epsilon near zero regime is unavoidable.  
+
+<|ref|>text<|/ref|><|det|>[[115, 885, 880, 932]]<|/det|>
+In modern photonics, a multitude of technologies for tunable optics and frequency conversion[16, 17] are realized with nonlinear materials that have low loss and a strong \(\chi^{(2)}\) effect, such as lithium
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 85, 882, 558]]<|/det|>
+niobate[18, 19], aluminum nitride[20], and organic electro-optic (OEO) materials[21]. Their ultrafast responses make it possible to use RF or millimeter- wave control[22]. Developments in computational chemistry have also led to artificially engineered organic molecules that have record- high nonlinear coefficients with long- term and high- temperature stability [23, 24]. However, their potential in modifying free- space light has been relatively unexplored until recently. Several OEO material- hybrid designs have demonstrated improved tunability of metasurfaces [25–27]. Utilizing dielectric resonant structures and RF- compatible coplanar waveguides, a free- space silicon- organic modulator has recently accomplished GHz modulation speed [28]. However, all demonstrations to date require high operating voltages \(\pm 60V\) , due to low resonance tuning capability(frequency shift / voltage) which hinders their integration with electronic chips. In this work, we propose combining high- Q metasurfaces based on slot- mode resonances with the unique nano- fabrication techniques enabled by OEO materials which drastically reduces the operating voltage. The low voltage is mainly achieved from the ability to place the electrodes in close proximity to each other while hosting high- Q modes in between and the large overlap of the optical and RF fields in OEO materials. In the following sections, we first provide the design concepts and considerations for achieving a reduced operating voltage. Next, we numerically demonstrate the advantage of a particular selected mode compared to other supported modes in the structure. Finally, we experimentally realize our concepts and characterize the performance of the electro- optic metasurface.  
+
+<|ref|>sub_title<|/ref|><|det|>[[139, 648, 222, 664]]<|/det|>
+## RESULTS  
+
+<|ref|>text<|/ref|><|det|>[[113, 698, 882, 876]]<|/det|>
+The reported device and its operation scheme are depicted in Fig. 1. Light polarized along \(x\) \((E_{x})\) is incident onto the device along \(- z\) direction, and then couples into the slot mode hosted in between the silicon nano- bars. Gold electrodes are placed on top of the nano- bars and doped silicon is used to maximize the voltage drop across the slot filled with OEO material. The active OEO material regions have nonlinear coefficients \(r_{33}\) with each two adjacent slots exhibiting opposite signs of nonlinear coefficients due to the poling field direction. When the operating signal is applied, the active layer induces a spatially varied refractive index change  
+
+<|ref|>equation<|/ref|><|det|>[[389, 896, 877, 930]]<|/det|>
+\[\Delta n(t) = -\frac{1}{2} n_{mat}^{3}r_{33}E_{AC}(t) \quad (1)\]
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 85, 882, 266]]<|/det|>
+where \(E_{AC}\) is the local electric field in the OEO material. Notice that due to the geometry of the electrodes, the signal electric fields \(E_{AC}(t)\) also have opposite directions in adjacent gaps, as shown in Fig. 1. Therefore, the overall response from any two adjacent slots is the same. Besides the operating voltage or the field in slots, the perturbation strength to the optical mode also depends on the overlap factor \(\Gamma\) between the electric field profile and the optical mode profile (see supplementary section 2). Based on cavity perturbation theory [29], the shift of the resonant frequency can then be expressed as  
+
+<|ref|>equation<|/ref|><|det|>[[425, 285, 877, 325]]<|/det|>
+\[\Delta \omega = -\frac{\Delta n_{avg}}{n_{mat}}\omega \Gamma \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 343, 880, 396]]<|/det|>
+where \(\begin{array}{r}{\Delta n_{a v g} = - \frac{1}{2} n_{m a t}^{3}r_{33}\frac{V_{D C}}{w_{g}}} \end{array}\) denotes the refractive index change upon applying a constant field of \(\frac{V_{D C}}{w_{g}}\) across the gap.  
+
+<|ref|>text<|/ref|><|det|>[[113, 404, 882, 794]]<|/det|>
+By examining Equation 2, we can gain valuable insights into two distinct methods for reducing the voltage of the device: reducing the distance between electrodes and increasing the overlap factor. However, introducing closer metallic electrodes leads to inevitable losses, thus reducing the quality factors and limiting the sensitivity to refractive index changes. Therefore, transmitting electric fields through conductive dielectrics is preferred. In our reported device, doped silicon acts as the electrodes with gap width \((w_{g})\) down to \(100\mathrm{nm}\) . At the same time, this gap between the silicon nano- bars will host slot modes[30], whose demonstrated high overlap with the OEO material has been utilized in many integrated silicon- organic modulators[31- 33]. However, the slot waveguide is intrinsically decoupled from the free- space light due to momentum unmatching. To enable coupling with normally incident light, we create periodic notches along every slot [34, 35]. The notch periodicity and the notch size dominantly determine the resonance wavelength and the coupling strength of the slot resonance, respectively. As a result, both the quality factor and the resonant wavelength could be judiciously engineered (see supplementary sections 1- 2). Although a similar structure has been proposed for sensing[36], the design strategy and target applications here are completely different.  
+
+<|ref|>text<|/ref|><|det|>[[113, 806, 882, 931]]<|/det|>
+To show the advantage of the slot modes while shrinking the distance between electrodes down to \(100\mathrm{nm}\) , it is worth discussing the possible optical modes in such a structure. The detailed schematic view, top view, and cross- section view of the example device are shown in Fig. 2a, where three different colors (gray, blue, green) indicate different materials (silicon, silica, OEO material or HLD). In the numerical simulations shown in Fig. 2b- h, HLD has a refractive index of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 80, 883, 691]]<|/det|>
+1.85[24]. Fig. 2b shows the poling field profile upon applying a DC bias across the electrodes. The \(x - z\) cross-section is cut at the center of a notch pair shown as dashed rectangle in the schematic view of Fig. 2a. Neglecting any interface effect[37], we can treat the relative amplitude of \(r_{33}\) at each spatial point as following this pictured poling field profile. The geometry of the electrodes results in a high \(E_{x}\) field along the slot and a rapid field decay above and below the slot. Therefore, to simplify the simulation, we assume that only the OEO material inside the slot is nonlinearly active. The structure will host various optical modes, many of which have a significant \(E_{x}\) field component such that it could strongly overlap with the incident \(E_{x}\) beam. Fig. 2c- e show three cross- sectional optical mode profiles (Mode I, II, III) originating from different parts of the device. The cross- sections are cut at the same \(y\) position as in Fig. 2b. Mode I is the slot mode, which has the field highly confined inside the slot, as discussed above, even upon applying the notch perturbation. Mode II is the bounded state guided within the slab. Notice that besides the slot mode, periodic notches also unlock the free- space radiation for this guided mode in the slab [38]. Mode III is a guided mode in OEO material, which has also been reported in [26]. Unlike the other optical modes, the field in slot mode is well aligned with the poling field and thus has the highest overlap factor \(\Gamma\) . As a result, under the same bias voltage, the slot mode has the largest resonance shift, as demonstrated through the simulation results in Fig. 2g- i. With the same amount of index change in the active region, Mode I, II, and III have resonance shifts of 2.73 nm, 0.29 nm, and 0.46 nm, respectively. A more accurate model estimates the overlap factor by considering the orientation of the nonlinearity[26] (see supplementary material section 2). The calculated \(\Gamma\) based on this model for modes I, II, and III are 0.156, 0.017, and 0.015, respectively. The slot mode shows an order of magnitude higher \(\Gamma\) , compared to the others. Therefore, the slot mode is crucial for low- voltage modulation in silicon- organic metasurfaces.  
+
+<|ref|>text<|/ref|><|det|>[[113, 700, 883, 931]]<|/det|>
+We experimentally realize the concept discussed above, using a silicon- on- insulator (SOI) wafer. The device's cross- section, top view, and voltage setting are schematically illustrated in Fig. 3a- b. The detailed device parameters are shown in supplementary material section 6. The nanostructures are fabricated with conventional nanofabrication techniques (see Methods section for details on the fabrication procedure). The step- by- step zoom- out scanning electron microscopy(SEM) images (prior to spin- coating of OEO material) are shown in Fig. 3c- f. Doped silicon nano- bars have a resistance of \(1 \sim 10\Omega \cdot cm\) , and \(\sim 100\) - nm wide gold strips along the nano- bars are added to further reduce the voltage drop across the silicon. In Fig. 3c, the gold strips are deliberately aligned at the center of the silicon rail so that only minimal absorption is introduced (See supplementary section
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 87, 881, 188]]<|/det|>
+2 and Fig. S3). Fig. 3e shows an \(80 \times 100 \mu m^2\) device. Multiple devices are fabricated on a chip as shown in Fig. 3f for increasing the tolerance of the fabrication errors and testing multiple geometric parameters. After the coating of the OEO material, the device is wire bonded to a customized printed circuit board for poling and operating, shown in Fig. 3g.  
+
+<|ref|>text<|/ref|><|det|>[[113, 196, 882, 774]]<|/det|>
+To experimentally verify the relationship between resonant optical characteristics of the slot modes and the geometry of the device, we have fabricated several devices having different design parameters and compared their measured optical properties with corresponding numerical calculations (see Methods, Supplementary Section 5, and Fig. S6 for details in optical measurement setup). Fig. 4 shows the calculated and measured spectra of the slot mode resonances with different geometries. We characterize the slot resonances by varying the notch period and notch size in Fig. 4a- b and Fig. 4c- d, respectively. In Fig. 4a- b, we observe that a 20- nm increment in notch periodicity leads to \(\sim 21.6 \mathrm{nm}\) and \(22.2 \mathrm{nm}\) average redshift of the resonance in simulation and experiment, respectively. Also, with respect to the resonant wavelengths, the resonance amplitudes, and the spectral shapes of the resonance, the measured spectra in Fig. 4c show good agreement with the calculated spectra in Fig. 4d. In particular, the quality factor increases with the decrease of the resonance amplitude. This trade- off is mainly due to the decreasing radiation rate to the top port (to \(+z\) direction), which results in the under- coupling between the slot mode and the illuminated light from the top [15]. Specifically, the amplitude of the resonance is determined by the ratio of the mode coupling rate between the input light and the slot mode to the sum of other undesired decay rates [39]. The undesired decays include absorption in the gold layer, scattering from the rough sidewalls or finite edge of the chips, and radiation to the oxide layer or the silicon substrate. As the absorption in the gold layer and the radiation to the silicon substrate is nearly inevitable in the proposed planar structures, the trade- off between the resonance amplitude and the quality factors is inevitable especially when the coupling rate decreases. The proposed devices in Fig. 4e can achieve modulation amplitude over \(10\%\) and Q- factor over 1000 in the experiment even with the absorption in the gold.  
+
+<|ref|>text<|/ref|><|det|>[[114, 780, 882, 932]]<|/det|>
+Operation results under DC bias are shown in Fig. 5. Fig. 5a- c show the results from 3 different devices under maximum bias voltages before any dielectric breakdown. The variation in the breakdown voltages results from the quality of the OEO material preparation and fabrication quality. The maximum absolute frequency shift of \(5.5 \mathrm{nm}\) is achieved under \(\pm 17V\) in Fig. 5a, and the spectral shift per unit external DC bias is \(S_{abs} = \Delta \lambda /\Delta V = 0.161nm / V\) , which is \(\sim 1.6 \times\) higher than that of the previously reported tunable free- space optical modulators [28]. Using Eqs. 1 and
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 85, 882, 477]]<|/det|>
+2, \(r_{33}\) in- device is calculated at \(45.7\mathrm{pm / V}\) at \(1495\mathrm{nm}\) . The relatively low nonlinear coefficient compared to what we expected[24] is partly due to the surface state of highly doped silicon used as the electrode [40] and the small width of the slot[37]. In Fig. 5b and c, \(2.3\mathrm{nm}\) and \(2.6\mathrm{nm}\) resonance shifts are observed with \(\pm 11\mathrm{V}\) and \(\pm 12\mathrm{V}\) bias voltages, respectively. Figures 5b and c show high Q- factors over 1000. The increase in Q- factor also improves the normalized modulation figure- of- merit \((S_{n} = \Delta \lambda /(FWHM\cdot \Delta V)\) [41]. In our best- performing device shown in Fig.5b, \(S_{n}\) is \(0.09\mathrm{V}\) , which is an order of magnitude higher than other reported devices [41]. The reflection spectra are plotted in Fig. 5d as a function of different bias voltages. The spectra clearly show the bidirectional linear relationship between the bias voltage and the resonance shift, confirming that the spectral shift results from the electro- optic effect [26]. In Fig. 5e, the relative modulation ratio, \(\Delta R / R\) , from the device in Fig. 5c is plotted. The maximum modulation ratio is over \(40\%\) . It is worth noting that the asymmetry of the modulation is due to the Fano shape of the resonance [42]. The inset in Fig. 5e, shows the reflection intensity as a function of the bias voltage when the input light wavelength is \(1486.5\mathrm{nm}\) . From \(-12\mathrm{V}\) to \(+12\mathrm{V}\) , the reflection amplitude is gradually increasing.  
+
+<|ref|>text<|/ref|><|det|>[[112, 488, 882, 933]]<|/det|>
+The AC modulation characteristic is tested with the devices in Fig. 5a and plotted in Fig. 6a. A sine wave with peak- to- peak value, \(V_{pp}\) , of \(20\mathrm{V}\) is applied into the device while the wavelength of the incident light is set at \(1490\mathrm{nm}\) where the device achieves the highest modulation depth. The sine wave frequency is swept from \(50\mathrm{kHz}\) to \(5.8\mathrm{MHz}\) . The cutoff 3dB bandwidth is at \(3\mathrm{MHz}\) . The insets in Fig. 6a show the normalized modulation signal when driving with frequency \(f = 80kHz\) and \(f = 2.8MHz\) , respectively. To investigate the AC response, we use a simplified model to predict the AC response shown in Fig. 6b. The model collectively considers the contributing factors to the response speed within and outside the devices. In the devices, we model the nanobars as a resistance including the contribution from the gold strip \(R_{Au}\) and the silicon nano- bar \(R_{Si}\) (see supplementary note 4). The slot is modeled as the parallel connected resistance \(R_{OEO}\) and capacitance \(C_{OEO}\) . Outside the devices, we assume that the major electrical components are the stray capacitance in the circuits, which are split into the capacitance due to the SOI wafer [43] \(C_{SOI}\) and other factors \(C_{load}\) . The parameters in the model are determined by both the geometry of the devices and the AC response of similar devices with different substrates or electrode layouts (See supplementary material section 4). The AC response from the prediction of the model is shown as the green line in Fig. 6a, which agrees with the experimental result. Based on the model estimation, the capacitance from the silicon- organic platform and the stray capacitance along the whole circuits
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 87, 882, 213]]<|/det|>
+are the main factors preventing the speed increase. The capacitance from the SOI wafer could be solved by advanced CMOS technology used in integrated electro-optic modulators [44]. Judicious material and structural engineering of these circuits have already achieved gigahertz operation of electro-optic modulators [28, 45- 47]. As a result, there is no fundamental limit in increasing the operation speed up to GHz in our platform.  
+
+<|ref|>sub_title<|/ref|><|det|>[[139, 257, 251, 275]]<|/det|>
+## DISCUSSION  
+
+<|ref|>text<|/ref|><|det|>[[113, 301, 882, 586]]<|/det|>
+In this work, we propose a silicon- organic metasurface for free- space modulation with reduced operation voltage less than \(\pm 17V\) . We experimentally observed the resonance with quality factor \(330 - 1310\) and up to \(\sim 5.5\mathrm{nm}\) shift with nonlinear coefficient \(r_{33} = 45.7\mathrm{pm / V}\) at \(1495\mathrm{nm}\) . The proposed slot mode combines the advantages of a short distance between two electrodes and a large overlap with the OEO material, achieving a tuning sensitivity \(S_{abs} = 0.161nm / V\) , which shows an improvement with a factor of 1.6 in sensitivity compared to the state- of- art [28, 41]. Finally, the metasurface has up to \(3MHz\) bandwidth. The use of the slot mode is not limited to electro- optic systems. The proposed design approach can be applied to any system where sensitivity to perturbations in low- index media is critical. For example, in NEMS systems, the slot mode resonance could potentially improve sensitivity to the mechanical movement, compared to conventional guided mode resonances [8].  
+
+<|ref|>text<|/ref|><|det|>[[113, 593, 882, 799]]<|/det|>
+The currently demonstrated sensitivity is limited by the quality factor and the nonlinear coefficient \(r_{33}\) . The quality factor could be improved by using smaller notches or a refined fabrication process. The relatively low nonlinear coefficient is primarily due to the surface state of highly doped silicon as the electrode [40] and the small width of the slot[37]. Barrier layer protection[48] has the potential to increase the nonlinear coefficient \(r_{33}\) by 4- 5 times [49]. Judicious doping level adjustments and the microwave coplanar waveguide design could enable GHz speed operation[28, 32]. Therefore, with the increase of electro- optic coefficient and operation bandwidth, our platform is a potential solution for GHz free- space modulation at the CMOS level voltage.  
+
+<|ref|>text<|/ref|><|det|>[[113, 806, 882, 931]]<|/det|>
+This study primarily focuses on structures which are periodic in both \(x\) and \(y\) dimensions. However, it is not a necessary condition for preserving the slot mode. As a mode propagating along the \(y\) direction, the slot mode doesn't necessitate periodic conditions in \(x\) direction [50]. By varying the geometry of the slots, individual slot modulation could be potentially achieved. In the \(y\) - dimension, by introducing high contrast index variations or photonic crystal mirrors, the footprint
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 87, 880, 160]]<|/det|>
+of the resonant device could be reduced considerably [51, 52]. Furthermore, the proposed devices expect to achieve phase modulation if the overcoupling condition is satisfied by the out- of- plane asymmetry in nanostructures [9] or a bottom mirror [5, 6].  
+
+<|ref|>text<|/ref|><|det|>[[114, 169, 881, 267]]<|/det|>
+In summary, this report presents a low- voltage amplitude modulator using a silicon- organic platform. The slot mode metasurface has the potential to enable high- speed and low- voltage optical switching, sensing, and tuning, for numerous applications such as LiFi, Lidar, spatial light modulators, and quantum optical communication.  
+
+<|ref|>sub_title<|/ref|><|det|>[[140, 313, 339, 330]]<|/det|>
+## ACKNOWLEDGEMENT  
+
+<|ref|>text<|/ref|><|det|>[[114, 358, 881, 430]]<|/det|>
+We thank NLM Photonics for the HLD OEO material and for consulting on the preparation and poling process of the HLD. The device nanofabrication was performed at the Kavli Nanoscience Institute at Caltech. This work was supported by the Caltech Sensing to Intelligence program.  
+
+<|ref|>sub_title<|/ref|><|det|>[[140, 477, 233, 494]]<|/det|>
+## METHODS  
+
+<|ref|>sub_title<|/ref|><|det|>[[140, 524, 384, 542]]<|/det|>
+## Fabrication and poling methods  
+
+<|ref|>text<|/ref|><|det|>[[113, 567, 882, 931]]<|/det|>
+The device is fabricated from an SOI (silicon on insulator) wafer, which consists of \(300~\mathrm{nm}\) device p- doped silicon \((1 - 10\Omega \cdot cm)\) , \(300~\mathrm{nm}\) BOX (buffered silicon oxide), and \(500\mu m\) silicon substrate. The detailed fabrication workflow is shown in supplementary materials section 5. The device requires two sequential nanofabrication steps for the silicon rails and metallic strip. Both E- beam lithography steps utilize ZEP- 520A (Zion Corporation) as the resist, \(100\mathrm{kV}\) electron beam (EBPG- 5200, Raith GmbH) to expose, and ZED- N50 (Zion Corporation) as the developer. After the first E- beam lithography, we use the resist as the soft mask and the pattern is transferred to silicon by ICP- RIE etching (PlasmaLab System 100, Oxford Instrument). Next, the resist is removed by Remover PG. The second E- beam lithography writes the liftoff mask for the electrodes, following which \(5\mathrm{nm}\) Ti and \(60\mathrm{nm}\) Au are deposited sequentially using an E- beam evaporator (Kurt J. Lesker E- beam evaporator). Liftoff is then performed in Remover PG. Finally, a layer of OEO material (HLD, NLM Photonics) is spin- coated on top of the device, followed by a 3- hr solvent removal in a vacuum oven at \(65^{\circ}\mathrm{C}\) . The detailed workflow is shown in supplementary material section 5.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 87, 881, 187]]<|/det|>
+Poling of the HLD material is performed by heating the device under the nitrogen environment while applying a poling voltage. This voltage creates a poling field around \(100V / \mu m\) across the slot. The heating process consists of a \(6^{\circ}C / s\) temperature ramping, 5 to 10 minutes of holding at \(95^{\circ}\) , and rapid cooling.  
+
+<|ref|>sub_title<|/ref|><|det|>[[139, 252, 294, 269]]<|/det|>
+## Simulation methods  
+
+<|ref|>text<|/ref|><|det|>[[114, 298, 882, 399]]<|/det|>
+The simulations in Fig. 2 and Fig. S3 use COMSOL Multiphysics software. The periodic condition is applied in both x and y directions. Refractive indexes of the silicon, silicon oxide, and OEO material are assumed to be 3.52, 1.44, and 1.85. Fig. 4a,c are simulated with FDTD (Lumerical) with periodic boundary conditions applied in x and y.  
+
+<|ref|>sub_title<|/ref|><|det|>[[139, 464, 247, 480]]<|/det|>
+## Measurement  
+
+<|ref|>text<|/ref|><|det|>[[114, 510, 882, 664]]<|/det|>
+The measurements were conducted using the experimental setup depicted in Fig. S5. The light source utilized was a tunable external- cavity diode laser (Toptica CTL- 1550). A fiber collimator (Thorlabs, F260FC- 1550) was employed to collimate the beam. A beam splitter is placed in front of the collimator to split a small amount of power for the reference InGaAs detector (Thorlabs, PDA10CS). The polarized state of the incident light was set to TE polarization using a linear polarizer. Then the light goes through a beam splitter and only half of the power is used.  
+
+<|ref|>text<|/ref|><|det|>[[114, 673, 882, 932]]<|/det|>
+A \(\times 20\) infinity- corrected objective lens (Mitutoyo, M Plan Apo NIR) and a tube lens with a focal length of \(200\mathrm{mm}\) were used to image the sample at the object plane, with the tube lens and the mounting stage of the sample adjusted to ensure normal incidence. An iris (Thorlabs, ID25) was inserted at the image plane to select a region of interest with a diameter of \(45\mu m\) in the object plane. The spatially filtered light was either focused onto another InGaAs detector for the measurement of the spectra or imaged on an InGaAs SWIR camera (Goodrich, SU320HX- 1.7RT) using relay optics. The reflection signals were obtained by dividing the signal from the sample by the signal from the sources. It should be noted that due to different input polarization states, the incident power onto the sample varied at different wavelengths. Thus, the signals were further normalized by the signals from the gold.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[111, 98, 860, 512]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 539, 880, 668]]<|/det|>
+<center>Fig. 1 Conceptual schematic of silicon-organic electro-optic tunable metasurfaces. A beam of light is incident on the metasurface, which consists of silicon nano-bars. The light is coupled into the slot mode inside the metasurface, which is sensitive to any refractive index perturbation in the slot. The OEO material is coated on top of the metasurface and fills the slot waveguide between the silicon nano-bars. The organic molecule inside the slot is aligned with the DC/RF field generated by the electrodes. When the RF bias voltage is applied on the electrodes, the electro-optic (Pockels) effect will generate refractive index modulation. As a result, the intensity of the reflected beam will be modulated accordingly. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[140, 740, 375, 757]]<|/det|>
+## AUTHOR CONTRIBUTIONS  
+
+<|ref|>text<|/ref|><|det|>[[113, 805, 882, 932]]<|/det|>
+H.K., T.Z. and A.F. conceived the project. A.F. supervised the project. H.K and T.Z. designed the structures. T.Z. and Y.G. fabricated devices, performed simulations and measurements, and analyzed data. T.Z. designed and prepared the printed circuit boards. G.R. provided feedback on the design of the structures. T.Z. wrote the manuscript. All authors discussed the results and commented on the manuscript.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[130, 88, 857, 720]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 728, 881, 927]]<|/det|>
+<center>Fig. 2 The advantage of slot mode resonance in organic electro-optic modulators. a. The schematic view (top left), top view (bottom left) and cross-section (right) of the device that supports the slot mode. In the schematic view the OEO material is plotted transparent to show the slot structure underneath. The slots are formed in the device layer of the silicon-on-insulator (SOI) substrate which is covered by the OEO material HLD. To show the essence of the problem, only the slot is considered as the active region. The dashed rectangles in schematic view represent the top view across the device layer and the cross section of a period cell. b. The poling field profile when the left and right silicon rail have bias voltages \(\mathrm{V(V > 0)}\) and 0, respectively. c-e. Normalized electric field profiles for three optical modes that could couple to \(E_{x}\) incident light. c. the slot mode. d. the guided mode in the silicon bar. e. the guided mode in the OEO material. f-h. the tuning performance of the three optical modes. Figures f,g, and h match with the field profile in figures c,d, and e, respectively. The inset in h is a zoom-in spectrum between \(1649\mathrm{nm}\) and \(1652.5\mathrm{nm}\) . </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 88, 841, 680]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 701, 879, 793]]<|/det|>
+<center>Fig. 3 The electro-optic free-space modulator. a-b. The cross-section and top view of the experimentally fabricated device. c-g. The step-by-step zoom-out image of the device and setup. c-f are the scanning electron microscopy(SEM) images. The scale bars are \(500~\mathrm{nm}\) , \(3~\mu \mathrm{m}\) , \(50~\mu \mathrm{m}\) , and \(1~\mathrm{mm}\) , respectively. g is the optical image of the device. Multiple devices are fabricated within a chip, and they are wire-bonded to the printed circuit board for parallel testing. </center>  
+
+<|ref|>text<|/ref|><|det|>[[123, 885, 570, 903]]<|/det|>
+[1] A. Arbabi and A. Faraon, Nature Photonics 17, 16 (2023).  
+
+<|ref|>text<|/ref|><|det|>[[123, 913, 460, 930]]<|/det|>
+[2] J. Scheuer, ACS Photonics 7, 1323 (2020).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[140, 100, 816, 560]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 585, 880, 732]]<|/det|>
+<center>Fig. 4 Slot mode resonance characterization. a-d The simulated (a,c) and experimentally measured (b,d) reflection spectra when sweeping different sets of perturbation parameters. a-b. Sweep the periodicity of the notches. All curves have the same notch size \(l = 160 \mathrm{nm}\) , \(d = 80 \mathrm{nm}\) . Blue: \(p = 720 \mathrm{nm}\) . Orange: \(p = 740 \mathrm{nm}\) . Green: \(p = 760 \mathrm{nm}\) . The resonance shifts due to periodicity changes are labelled in experiment and simulation curves. c-d. Sweep the notch sizes. All curves have the same notch periodicity \(p = 740 \mathrm{nm}\) . Red: \(l = 200 \mathrm{nm}\) , \(d = 120 \mathrm{nm}\) . Purple: \(l = 160 \mathrm{nm}\) , \(d = 80 \mathrm{nm}\) . Brown: \(l = 150 \mathrm{nm}\) , \(d = 50 \mathrm{nm}\) . Pink: \(l = 140 \mathrm{nm}\) , \(d = 25 \mathrm{nm}\) . The quality factor of the resonances are labelled for experimental and simulated plots. </center>  
+
+<|ref|>text<|/ref|><|det|>[[120, 774, 881, 933]]<|/det|>
+[3] S. M. Kamali, E. Arbabi, A. Arbabi, and A. Faraon, Nanophotonics 7, 1041 (2018). [4] J. Li, Y. Chen, Y. Hu, H. Duan, and N. Liu, ACS nano 14, 7892 (2020). [5] G. K. Shirmanesh, R. Sokhoyan, P. C. Wu, and H. A. Atwater, ACS nano 14, 6912 (2020). [6] J. Park, B. G. Jeong, S. I. Kim, D. Lee, J. Kim, C. Shin, C. B. Lee, T. Otsuka, J. Kyoung, S. Kim, et al., Nature nanotechnology 16, 69 (2021). [7] A. L. Holsteen, A. F. Cihan, and M. L. Brongersma, Science 365, 257 (2019).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[118, 85, 870, 682]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 693, 880, 802]]<|/det|>
+<center>Fig. 5 DC tuning characteristics. a-c. Reflection spectra of three different devices under DC tuning. The applied biases are denoted in the legend. d. The reflection spectra of the device in b with bias voltages ranging from -11V to 11V. e. The maximum modulation ratio \((\Delta R / R = (R_{max} - R_{min}) / R_{V = 0})\) for each wavelength in device shown in c. The inset depicts the absolute reflection as the DC bias voltage is swept from -12V to 12V for a fixed wavelength of incident light of 1486 nm. The absolute reflection changes over 10%. </center>  
+
+<|ref|>text<|/ref|><|det|>[[118, 830, 634, 849]]<|/det|>
+[8] H. Kwon, T. Zheng, and A. Faraon, Nano Letters 21, 2817 (2021).  
+
+<|ref|>text<|/ref|><|det|>[[120, 857, 685, 876]]<|/det|>
+[9] H. Kwon, T. Zheng, and A. Faraon, Nature communications 13, 1 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[113, 885, 880, 930]]<|/det|>
+[10] A. Karvounis, B. Gholipour, K. F. MacDonald, and N. I. Zheludev, Advanced Materials 31, 1804801 (2019).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 880, 320]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 332, 875, 496]]<|/det|>
+<center>Fig. 6 AC tuning characteristics and circuit model scheme. a. The experimental and modeled AC response of the active device. Blue curve: the experimental normalized modulation depth. The cutoff bandwidth is at 3MHz. Green curve: the model prediction of the modulation depth. Insets: the example modulation signal(Orange) and the fitting sine wave (Red) in the time domain. The frequencies of the modulation signal are 80kHz (top left) and 4MHz (bottom right), respectively. b. The circuit model of the device. \(V\) : the voltage source. \(R_{s}\) : the source resistance. \(C_{load}\) : external stray capacitance outside the device. \(C_{SOI}\) : the capacitance due to the use of SOI wafer. \(R_{Au}\) : the resistance of the gold strip on top of the silicon nano-bar. \(R_{Si}\) : the resistance of the silicon nano-bar. \(C_{Poly}\) : the OEO material capacitance. \(R_{Poly}\) : the OEO material resistance. </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 528, 880, 568]]<|/det|>
+[11] Z. Fang, R. Chen, J. Zheng, A. I. Khan, K. M. Neilson, S. J. Geiger, D. M. Callahan, M. G. Moebius, A. Saxena, M. E. Chen, et al., Nature Nanotechnology 17, 842 (2022).  
+
+<|ref|>text<|/ref|><|det|>[[113, 584, 880, 630]]<|/det|>
+[12] Y. Zhang, C. Fowler, J. Liang, B. Azhar, M. Y. Shalaginov, S. Deckoff-Jones, S. An, J. B. Chou, C. M. Roberts, V. Liberman, et al., Nature Nanotechnology 16, 661 (2021).  
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+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 42, 311, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 92, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[58, 129, 805, 151]]<|/det|>
+- Lowvoltagedynamiclightmanipulationwithsiliconorganicslotmetasurfaceassuppl.pdf
+
+<--- Page Split --->

preprint/preprint__5fd9725d0ea93e8fd59ab5ffb773154f0a4d443324c2c4f58f1274b4801590df/images_list.json

@@ -0,0 +1,227 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. 3D visualization of macrophages allows insight into membrane structure and phosphatidylinositol dynamics during macropinocytosis. a) Isosurfaces show the plasma membrane of a live cell that is actively macropinocytosis. Region \\(68 \\times 72 \\times 25 \\mu m\\) (x, y, z). b) SEM image of a macrophage acutely stimulated with CSF-1 shows high-resolution fixed cells. Scale bar is 10 \\(\\mu m\\) . c) Volumetric intensities show specific local fluorescence (left->right) volumetric membrane (green), dual volumetric membrane and mSc-AktPH, volumetric mSc-AktPH (magenta). Volumetric renderings provide a method to visualize the transient fluorescent intensities throughout the volume of the cell. Region is \\(68 \\times 72 \\times 25 \\mu m\\) . d) Combinations of visualization techniques such as Isosurface (left) displayed alongside orthogonal planes (right) further clarify how each plane is chosen to show internal intensities. Region of \\(29 \\times 30 \\times 19 \\mu m\\) . e) Mesh rendering of the mNG-membrane probe along with volumetric mSc-AktPH provides a representation of the plasma membrane structure as well as underlying fluorescence. The white arrows indicate the post closure recruitment of mSc-AktPH. Region \\(13 \\times 14 \\times 7 \\mu m\\) . Different rendering methods provide insight into cellular characteristics such as structure, depth, and fluorescent intensity and provide a foundation for visualizing localization of mSc-AktPH to the constantly changing plasma membrane during macropinocytosis.",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        87,
+        880,
+        630
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Early PI3K activity leads to amplification of \\(\\mathsf{PIP}_3 / \\mathsf{PIP}_2\\) in developing ruffles, macropinosome formation, and post closure recruitment. a) Top view of an mNG-mem isosurface rendering provides depth for 3D visualization of ruffle extension. Dual-color volumetric intensity display comparing the recruitment of mSc-AktPH to early and expanding ruffles as well as sealed macropinosomes (Region 21x19um). b) Intensity line-scan of the volumetric mNG-Mem and mSc-AktPH shows their relative intensities for extending membrane ruffles, as well as recruitment around a sealed macropinosome. c) Side view of the isosurface mesh plasma membrane and volumetric mSc-AktPH (Magenta Hot color scale) from a shows that the early stages of ruffle development is filled with mSc-AktPH and the resulting macropinosome (white arrow) receives a final intense mSc-AktPH recruitment around the formed macropinosome at the bottom of the ruffle. Region of 21x19x15um.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        88,
+        878,
+        740
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. PI3K activity is required for membrane sealing and separation from PM/internalization of a complete macropinosome but not membrane ruffling a) Isosurface rendering of mNG-mem for an untreated macrophage during a successful macropinocytosis event where the sheet curls back toward the membrane for fusion/sealing. Region 12x13x10 μm b) Volumetric rendering of Sc-AktPH of the untreated cell shows the increase of PI3K activity in the ruffle that creates a macropinosome. 12x13x10 μm c) Mesh and orthogonal planes of mNG-mem show the internal membrane organization of the ruffle and resulting macropinosome. 12x13x10 μm d) Isosurface rendering of an LY294002 treated macrophage provides depth to the attempted closure of a macropinocytic cup. Region 10x12x10 μm. e) Volumetric intensity rendering of Sc-AktPH for an LY294002-treated macrophage shows the diffuse distribution of AktPH and minimal PI3K activity. The cytosolic intensities were co-scaled for the untreated and treated macrophage. Region 10x12x10 μm f) XY-plane for the mNG-mem probe of an LY294002-treated cell during a failed macropinocytosis event. In the surface view, the ruffle appeared to form a macropinosome; however, when overlaid with the plane view is became clear that it failed to fully form into a macropinosome. The ruffle quickly reduced in size and became undistinguishable within the cytosol, while never receiving the post closure increase of PI3K activity. Region 10x12x10 μm.",
+    "footnote": [],
+    "bbox": [
+      [
+        120,
+        88,
+        875,
+        712
+      ]
+    ],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Macropinosomes form via PI3K-primed ruffle fusion. a) Dual volumetric intensities of mNG-mem and mSc-AktPH show the intensity of each probe as the rufles and macropinosomes form. The montage shows the earliest stage of the ruffle that extends vertically and forms macropinosomes along the length near the base of the primary ruffle as a result of smaller mSc-AktPH-rich extensions colliding. The white arrow points at the macropinosome forming region further emphasized in the isosurface. Region 9x12x13 um. b) Isosurface rendering of mNG-membrane shows the structure of the extending ruffle and the continued sheet extension after the macropinosomes formed. The white arrow emphasizes the small pocket that closes to form one of the macropinosomes. Region 9x12x13 μm. c) Mesh surface rendering of mNG-mem and volumetric mSc-AktPH shows the internalized macropinosome with the increased localization of mSc-AktPH at the bottom of the ruffle. Region 11x9x12 μm.",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        90,
+        875,
+        500
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Phosphatidylinositol localization and chaotic ruffling underlie macropinocytosis in complex membrane structures. a) Single time point, full cell surface rendering of chaotic macropinocytosis event. The red box correlates to the same frame in c-d. b) SEM images of a BMDM showing similar highly active ruffling regions c) Isosurface montage shows the chaotic orientation of membrane structure. Region 27x22x16 \\(\\mu \\mathrm{m}\\) , 25° tilt. d) Volumetric AktPH (Magenta-Hot) provides a more detailed emphasis on the AktPH activity within the membrane ruffles and highlights the macropinosomes that have formed. Region 27x22x16 \\(\\mu \\mathrm{m}\\) with a 25° tilted view. e) Mesh Surface with AktPH (Magenta Hot) shows the AktPH activity as the ruffle develops as well as the increased recruitment around formed macropinosomes at the base of the event.",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        87,
+        881,
+        628
+      ]
+    ],
+    "page_idx": 16
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. Growth factor starvation and stimulation results in the formation of large circular dorsal ruffles that corrals \\(\\mathsf{PIP}_3 / \\mathsf{PIP}_2\\) . Macrophages were starved of CSF-1 for \\(24~\\mathrm{h}\\) , imaged for 5 minutes as a baseline, and imaging restarted 1 min after stimulation with \\(50~\\mathrm{ng}\\cdot \\mathrm{mL}^{-1}\\) CSF-1. Four-frame montages provide a visual display of the large dorsal ruffle that acts as a diffusional barrier that restricts \\(\\mathsf{PIP}_3 / \\mathsf{PIP}_2\\) to the inside of the ruffle as it is cleared from the surface. This barrier is likely acting as a signal amplification mechanism stimulating the production of many macropinosomes. a) Isosurface rendering provides crisp surface directionality, b) Surface mesh and volumetric AktPH (magenta-hot), show the restricted probe as the membrane converges c) Volumetric Intensity of both mNG-Membrane and mSc-AktPH show the intensity locations of the membrane ruffle and the restricted AktPH. \\(49\\times 60\\mu \\mathrm{m}\\) d) Bright field images showing multiple cells responding to stimulation with similar dorsal membrane clearing.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        90,
+        880,
+        555
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. LPS stimulation increases membrane ruffling and macropinocytosis. Macrophages were pretreated with \\(100\\mathrm{ng}\\cdot \\mathrm{ml}^{-1}\\) LPS for \\(24\\mathrm{h}\\) prior to imaging. a) Surface rendering of mNG-Mem on an LPS stimulated macrophage provides a surface level understanding of the membrane, exploration, ruffling, and PM structure. b) Dual-color volumetric intensity projections of mNG-Mem and mSc-AktPH for an LPS stimulated cell provided the intensity activity during increased macrophage activity and shows the highly AktPH rich regions of membrane ruffling. Region \\(68\\times 77\\times 21\\mu \\mathrm{m}\\) c) Untreated macrophage losurface showing visibly less exploratory behavior. d) Dual-color volumetric intensity rendering of the untreated macrophage gives insight on the AktPH activity inside of the cell during macropinocytosis and allows for the quantitative comparison of macropinosomes formed between the stimulated and unstimulated cells. Region \\(68\\times 77\\times 21\\mu \\mathrm{m}\\) e) Box plot showing the difference in macropinocytic activity between untreated and LPS treated macrophages. All macropinosomes greater than \\(1\\mu \\mathrm{m}\\) were manually counted using a z-projection MIP in Fiji and were distinguished by the post closure spike in mSc-AktPH intensity.",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
+        80,
+        874,
+        675
+      ]
+    ],
+    "page_idx": 18
+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_1.jpg",
+    "caption": "Supplementary Figure 1 - Constitutive macropinocytosis and the importance of reducing the dimensionality of data. a) Orthoplane (left) and isosurface (right) views of mNG-Membrane show the subsurface macropinosome and the complex structure of the full surface. b) Orthoplane montage of mNG-membrane depicting constitutive planar view of macropinocytosis where two sheets extend from the cell membrane, circularize, and connect to form a macropinosome. c) Isosurface view of mNG-Membrane showing the three spatial dimensions of the ruffle clearly depicting the multiple membrane sheets involved in the macropinocytic event. The red box shows the corresponding montage frames for panel a.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        88,
+        881,
+        470
+      ]
+    ],
+    "page_idx": 19
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
+    "footnote": [],
+    "bbox": [
+      [
+        42,
+        90,
+        955,
+        744
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2",
+    "footnote": [],
+    "bbox": [
+      [
+        45,
+        44,
+        900,
+        787
+      ]
+    ],
+    "page_idx": 25
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3",
+    "footnote": [],
+    "bbox": [
+      [
+        48,
+        152,
+        930,
+        896
+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4",
+    "footnote": [],
+    "bbox": [
+      [
+        57,
+        384,
+        941,
+        878
+      ]
+    ],
+    "page_idx": 27
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5",
+    "footnote": [],
+    "bbox": [
+      [
+        42,
+        270,
+        955,
+        920
+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6",
+    "footnote": [],
+    "bbox": [
+      [
+        44,
+        226,
+        951,
+        780
+      ]
+    ],
+    "page_idx": 29
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7",
+    "footnote": [],
+    "bbox": [
+      [
+        52,
+        150,
+        944,
+        870
+      ]
+    ],
+    "page_idx": 30
+  }
+]

preprint/preprint__5fd9725d0ea93e8fd59ab5ffb773154f0a4d443324c2c4f58f1274b4801590df/preprint__5fd9725d0ea93e8fd59ab5ffb773154f0a4d443324c2c4f58f1274b4801590df.mmd

@@ -0,0 +1,322 @@
+
+# The structural dynamics of macrosinosome formation and PI3-kinase-mediated sealing revealed by lattice lightsheet microscopy  
+
+Shayne Quinn South Dakota School of Mines and Technology  
+
+Lu Huang South Dakota State University  
+
+Jason Kerkvliet South Dakota State University  
+
+Joel Swanson University of Michigan- Ann Arbor https://orcid.org/0000- 0003- 0900- 8212  
+
+Steve Smith South Dakota School of Mines and Technology  
+
+Adam Hoppe South Dakota State University https://orcid.org/0000- 0003- 4180- 0840  
+
+Robert Anderson South Dakota School of Mines and Technology  
+
+Natalie Thiex South Dakota State University Brandon Scott ( brandon.scott@sdfmt.edu ) South Dakota School of Mines and Technology https://orcid.org/0000- 0002- 1950- 0748  
+
+## Article  
+
+Keywords: microscopy, lattice lightsheet microscopy, phosphatidylinositol 3- kinase (PI3K)  
+
+Posted Date: December 28th, 2020  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 121499/v1  
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
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+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- 25187- 1.
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+# 1. 1. 1. 1. 1. 1. 1. 2. 2. 2. 2. 2. 2. 2.
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+1 The structural dynamics of macrokinosome formation and PI3- kinase- mediated sealing revealed by lattice lightsheet microscopy  
+
+5 Shayne E. Quinn \(^{1,2}\) , Lu Huang \(^{3,4}\) , Jason G. Kerkvliet \(^{4,5}\) , Joel A. Swanson \(^{6}\) , Steve Smith \(^{1,2}\) , Adam D. Hoppe \(^{4,5}\) , Robert B. Anderson \(^{1,2}\) , Natalie W. Thiex \(^{3,4*}\) Brandon L. Scott \(^{1,2*}\)  
+
+7 1 South Dakota School of Mines and Technology (South Dakota Mines), Nanoscience and Nanoengineering, Rapid 8 City, SD. 2 BioSNTR, South Dakota Mines, Rapid City, SD. 3 South Dakota State University (SDSU), Department of 9 Biology and Microbiology, Brookings, SD. 4 BioSNTR, SDSU, Brookings, SD. 5 SDSU, Department of Chemistry and 10 Biochemistry, Brookings, SD.6 University of Michigan, Department of Microbiology and Immunology, Ann Arbor, MI.  
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+11 \* Co- corresponding authors: natalie.thiex@sdtate.edu, brandon.scott@sdsmt.edu
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+## Abstract  
+
+Macropinosomes are formed by shaping actin- rich plasma membrane ruffles into large intracellular organelles in a phosphatidylinositol 3- kinase (PI3K)- coordinated manner. Here, we utilize lattice lightsheet microscopy and image visualization methods to map the three- dimensional structure and dynamics of macropinosome formation relative to PI3K activity. We show that multiple ruffling morphologies produce macropinosomes and that the majority form through non- specific collisions of adjacent PI3K- rich ruffles. By combining multiple volumetric representations of the plasma membrane structure and PI3K products, we show that PI3K activity begins early throughout the entire ruffle volume and continues to increase until peak activity concentrates at the base of the ruffle after the macropinosome closes. Additionally, areas of the plasma membrane rich in ruffling had increased PI3K activity and produced many macropinosomes of various sizes. Pharmacologic inhibition of PI3K activity had little effect on the rate and morphology of membrane ruffling, demonstrating that early production of 3'- phosphoinositides within ruffles plays a minor in regulating their morphology. However, 3'- phosphoinositides are critical for the fusogenic activity that seals ruffles into macropinosomes. Taken together these data indicate that local PI3K activity is amplified in ruffles and serves as a priming mechanism for closure and sealing of ruffles into macropinosomes.  
+
+## Introduction  
+
+Macropinocytosis, or "cell drinking," is a form of clathrin- independent endocytosis that results in the nonspecific uptake of large volumes of extracellular fluid and solutes. This central macrophage function enables immune surveillance, clearing of debris, and sampling of the local environment for the presence of pathogen- or damage- associated molecular patterns, cytokines, growth factors, nutrients, and other soluble cues<sup>1-6</sup>. Macropinosomes also serve as platforms to integrate this diverse information and to activate a variety of signaling pathways<sup>7-10</sup>. The major macrophage growth factor, colony- stimulating factor- 1 (CSF- 1), stimulates macropinocytosis and contributes to ligand- dependent modulation of CSF- 1 receptor signaling<sup>9</sup>. Additionally, cytokines such as CXCL12, and the bacterial cell wall component lipopolysaccharide (LPS) acutely stimulate macropinocytosis<sup>5,11,12</sup>.  
+
+Construction of a macropinosome proceeds through autonomous, ligand- independent plasma membrane extensions known as ruffles, which are driven by actin polymerization and require the phosphorylation and dephosphorylation of the different signaling phospholipids<sup>13,14</sup>. The closely related process of solid particle uptake known as phagocytosis has been hypothesized to use the shape of the particle as a template for the structure of the phagosome<sup>15,16</sup>. In contrast, the fusion of ruffles into macropinosomes do not have a structural framework to use as a template. This has resulted in various proposed closing mechanisms including a 'purse string' closure of circular dorsal ruffles<sup>13</sup>, closure at the distal tips of ruffles<sup>17</sup>, and more recently closure following actin tentpole crossing<sup>12</sup>. Regardless, these proposed mechanisms result in an organelle derived from the plasma membrane filled with the extracellular medium<sup>18</sup>. The production of 3' phosphoinositides by PI 3- kinase (PI3K) is required to generate isolated
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+patches of phosphatidylinositol 3,4,5,triphosphate (PIP3) on the plasma membrane \(^{3,19}\) , and the sequential breakdown of PIP3 into PI(3,4)P2 and ultimately PI is necessary for successful macrokinosome formation \(^{20}\) . Previous ratiometric imaging has shown that PIP3 concentration peaks after ruffle circularization \(^{21- 23}\) . Additionally, PI3K inhibitors, including LY294002, have demonstrated that PI3K activity is only required for macrokinosome closure, but not ruffling \(^{24}\) . This dynamic lipid microenvironment impacts the localization of downstream effector molecules driving actin polymerization and ruffle growth into macrokinosomes \(^{22}\) . However, it is only in protozoa, i.e., Dictyostelium, that the spatial signaling coordination in the 3D ruffle volume during macrokinocytosis has been well described \(^{19}\) ; it remains unclear how these events are spatially coordinated in metazoan cells \(^{25}\) . The precise membrane dynamics of macrokinocytosis and the spatial coordination of PI3K in forming ruffles remains unclear because of the low spatial and temporal resolution of previous microscopy approaches. Recently, high-resolution imaging of macrokinocytosis in macrophage-like cell lines indicates that the prior models of macrokinocytosis may need to be reconsidered \(^{12}\) .  
+
+Here, we employ the powerful three- dimensional (3D) imaging capabilities of lattice lightsheet microscopy \(^{26}\) (LLSM) and volumetric image analysis to create high- resolution movies of plasma membrane dynamics and PI3K activity during ruffling and macrokinocytosis. The images and movies we present advance our understanding of the spatial dynamics of membrane ruffling and the morphologies that lead to macrokinosomes, as well as the spatial distribution of PI3K activity during macrokinocytosis. Our results show that the majority of macrokinosomes form by non- specific collisions of adjacent PI3K- rich ruffles. We show that PI3K activity is present at the earliest stages of ruffle extensions and is highly localized to the bottom of ruffles after the membrane has closed into a macrokinosome. Finally, we modulate the rate of macrokinocytosis using stimulation and pharmacological inhibition to demonstrate that the ruffle morphology is unaffected, but PI3K activity is required to prime ruffle membranes for sealing into macrokinosomes.  
+
+## Results  
+
+## LLSM allows volumetric visualization of plasma membrane movements relative to PIP3 and PI(3,4)P2 distribution during macrokinocytosis  
+
+Our first objective was to capture the 3D structure of the plasma membrane relative to the PI3K activity during macrokinosome formation. LLSM imaging was performed on fetal liver macrophages (FLMs) stably expressing the fluorescent proteins mNeonGreen localized to the plasma membrane via the lipidation signal sequence from Lck (mNG- Mem) and mScarlet- I fused to the pleckstrin homology domain of Akt (mSc- AktPH). The AktPH probe recognizes PIP3 and PI(3,4)P2 with similar affinity and has been used extensively to characterize PI3K activity during macrokinocytosis \(^{8}\) . LLSM imaging of mNG- Mem allowed visualization of plasma membranes via isosurface renderings in the molecular visualization software, ChimeraX \(^{27}\) . These images were of sufficient resolution that the detailed structure of ruffles and forming macrokinosomes could be observed in living cells (Fig. 1a), similar to scanning electron microscopy imaging of bone marrow derived macrophages (Fig. 1b). To visualize the recruitment of mSc- AktPH relative to the membrane, we used volumetric intensity renderings that maintain the spatial distribution of the fluorescence probes throughout the cellular volume. As can be seen in the volume renderings, the
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+mNG- Mem probe persisted on newly formed intracellular vesicles derived from the plasma membrane. Moreover, we observed membrane movements throughout the entire formation and early trafficking of macrosinosomes, as well as the recruitment of mSc- AktPH to forming macrosinosomes (Fig. 1c, Supplementary Movie 1). Orthogonal plane slices (orthoplanes) in xy, yz, and xz (0.1 \(\mu \mathrm{m}\) thick) showed that mSc- AktPH was enriched in ruffles to varying degrees and intensely labeled circular structures found near the base and sides of ruffles (Fig. 1d, Supplementary Movie 2). Orthoplanes are effective for examining the 2D relationships between the fluorescent signals, but can also produce incomplete or distorted perspectives that are resolved by viewing the full volumetric data (Supplementary Figure 1); such as when a macrosinosome appears closed vs open. Additionally, it is difficult to perceive depth in the still frame volumetric renderings. To overcome this limitation, we implemented a mesh derived from the mNG- Mem isosurface with transparent faces that enables visualizing the underlying volumetric mSc- AktPH signals while maintaining the structural framing needed to resolve plasma membrane rearrangements (Fig. 1e). Together, these visualization techniques were applied to 122 macrosinosome formations and enable correlating the location and timing of PI3K activity to the membrane extension, curvature, and fusion of macrosinosomes with unprecedented spatial and temporal resolution.  
+
+## mSc-AktPH is recruited early during ruffle expansion and peaks at the base of ruffles after macrosinosome sealing.  
+
+In prior analysis of macropinocytosis using microscopy methods with low axial resolution, AktPH was recruited as ruffles transitioned into closed circular ruffles and nascent macrosinosomes<sup>8</sup>. Here, the enhanced z- axis resolution and detection sensitivity of LLSM enabled visualizing the dynamic recruitment of mSc- AktPH to ruffles as they began to protrude from the plasma membrane (Fig. 2a) until maturation where tubulation and fusion between adjacent macrosinosomes occurs (Supplementary Movie 3). As these early ruffles expanded laterally along the plasma membrane and protruded vertically from the cell surface, some ruffles continued to accumulate mSc- AktPH, whereas others lost mSc- AktPH and receded back into the cell suggesting different levels of PI3K activity in neighboring ruffles influences the outcome of a ruffling region (Fig. 2b). Ruffles that maintained mSc- AktPH throughout the ruffle volume continued to grow and formed macrosinosomes, which were accompanied by an intense transient recruitment of mSc- AktPH to the base of the ruffle around the nascent macrosinosome (Fig. 2c, Supplementary Movie 4). Given the early localization and amplification of PI3K signaling in ruffles that become macrosinosomes, we wondered if PI3K activity contributed to 3D ruffle dynamics.  
+
+## PI3K activity is required for macrosinosome sealing, but not ruffling or closure  
+
+To gain insight into the role of PI3K in regulating the morphological dynamics of macropinocytosis, we used the broad- spectrum PI3K inhibitor LY294002, which inhibits the closure phase of macropinocytosis in macrophages<sup>24</sup>. Non- treated control cells formed transient dorsal ruffles that recruited mSc- AktPH and closed into macrosinosomes, as seen by the surface rendering and intracellular void that is maintained in the plane view (Fig. 3a- c, Supplementary Movie 5). LY294002 treatment did not impact ruffle formation, but eliminated mSc- AktPH recruitment to membrane ruffles (Fig. 3d, e, Supplementary Movie 6). Furthermore, LY294002- treated cells frequently formed ruffles that appeared to close into a macrosinosome but retracted back to the plasma membrane and failed to maintain an intracellular
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+organelle (Fig. 3f). Taken together, these data suggest that PI3K activity is dispensable for ruffle formation and membrane collision but is required for membrane sealing to generate a macropinosome.  
+
+## PI3K activity primes ruffles for fusion to seal nascent macropinosomes  
+
+We next sought to categorize the macropinosome formation based on the way the membrane fused and the relative amount of PI3K activity. Based on the previously established models for macropinosome formation there would be distinguishing characteristics depending on the sealing method. Either we would find linear extensions where the distal tips would collide to circularize and seal, or there would be filopodia- like spikes that form, the membrane would fill in the space between before twisting to seal. Surprisingly, we found that approximately \(88\%\) of the quantified macropinosomes formed when the leading edge of extending ruffles collided along the sides of nearby membrane surface or ruffles that typically only involved a small portion of the second ruffle, so long as the ruffle area had elevated mSc- AtkPH (Fig. 4). The remaining \(12\%\) of events we observed were classified as tidal- wave like structures in which a mostly isolated planar ruffle extended from the cell surface where the entire ruffle was rich in mSc- AktPH, the ruffle gained curvature in a rolling fashion, and resulted in fusing with the plasma membrane(Supplementary Movie 5). However, given that the entire ruffle area was rich in mSc- AktPH, these types of formation follow the same underlying mechanism as collisions with adjacent membrane extensions. Frequently, a single ruffle area produced multiple macropinosomes and were the result of similar but smaller ruffle extensions that quickly fused near the base of larger ruffles (Fig. 4). Within the ruffle, forming macropinosomes recruited mSc- AktPH near the base of the ruffle as they transitioned into a spherical shape prior to detaching from the plasma membrane and moving independently (Fig. 4, Supplementary Movies 3,7). We hypothesized that regions with highly concentrated mSc- AktPH localization would correlate with increased macropinocytic activity. Indeed, this phenomenon was observed in four of the eleven constitutive cells (Fig. 5). These ruffling regions resulted in the formation of many macropinosomes through the intersection of multiple ruffles that were nearly indistinguishable from one another and only became apparent through the PI3K post closure activity (Fig. 5d,e). Therefore, the elevated PI3K activity created a microenvironment suited for the rapid fusion of PI3K- primed ruffles into macropinosomes of various sizes within short timeframes (Supplementary Movies 8,9). We speculated that other signaling that activates PI3K activity may stimulate distinct ruffling morphologies and rates of macropinocytosis.  
+
+## CSF-1 growth factor signaling promotes extensive circular ruffling and macropinocytosis  
+
+CSF- 1 is an essential macrophage growth factor that stimulates macropinocytosis at levels controlled by the concentration of the CSF- 1 signal<sup>9</sup>. Macrophages starved of CSF- 1 for 24 hrs and then acutely stimulated produced expansive circular ruffles that initiated from the distal cellular margins coincident with cellular spreading (Fig. 6). LLSM imaging revealed a circular ruffle that initiated at the edge of the cell with a height of approximately \(2 \mu m\) above the dorsal surface and constricted to a central location in a coordinated manner (Fig. 6a). A striking feature of this ruffle was the confinement of mSc- AktPH within the limiting edge of the ruffle. As the circular ruffle constricted toward the center of the cell, mSc- AktPH was highly concentrated within and was nearly undetectable in the rest of the cell (Fig. 6b, Supplementary Movie 10), and macropinosomes formed during the constriction process without additional membrane protrusions being generated. This is consistent with PI3K activity priming membranes for fusion through
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+a purse- string closure to generate macro pinosomes (Fig. 6c, Supplementary Movies 10,11). Thus, CSF- 1 initiated long range signaling and PI3K activation resulting in coordinated movements of the cytoskeleton throughout the cell.  
+
+## LPS stimulates regional ruffling and generates large numbers of macro pinosomes  
+
+The bacterial cell wall component lipopolysaccharide (LPS) activates PI3K through the Akt pathway<sup>28</sup>, and acutely stimulates macro pinocytosis<sup>3</sup>. Recently, LPS stimulation was used to characterize a novel formation mechanism involving actin tentacles supporting membrane veils which cross to create a macro pinosome<sup>12</sup>. When FLMs were exposed to LPS, regional patches of membrane ruffling were generated that migrated around the dorsal surface of the macrophage (Fig. 7a, Supplementary Movie 12) in a manner distinct from the dorsal surface ruffle generated by CSF- 1 stimulated cells (Fig. 6); however, this process was similar in appearance to constitutive macro pinocytosis (Fig. 7c, Supplementary Movie 13). The patches of ruffles in LPS cells generated many small ruffles, had elevated PI3K activity and were more efficient at forming macro pinosomes as compared to control (Fig 7d). Thus, the nature of macro pinosome formation is coordinated over different length scales with differing intensities depending on the nature of the activating stimulus. Regardless, PI3K activity delineates ruffles and regions of the plasma membrane where macro pinosomes form.  
+
+## Discussion & Conclusion  
+
+Here, we have utilized lattice light sheet microscopy to develop a new level understanding of the structural dynamics and PI3K signaling underpinning macro pinocytosis. Until recently, dynamic processes such as macro pinocytosis were characterized using optical techniques with poor axial resolution and elevated phototoxicity leading to subsampling the spatial and temporal dynamics and requiring inference from multiple methods such as scanning electron microscopy of fixed cells to address the formation mechanism of macro pinosomes. Lightsheet microscopy overcomes these obstacles and enables us to record, with sufficient spatial and temporal resolution, the complete evolution of membrane ruffles and the mechanism by which these ruffles form into macro pinosomes, while also measuring the redistribution of signaling molecules controlling these processes. We have shown that macro pinosomes form through several possible morphologies; however, in each case PI3K activity primes ruffles for fusion with adjacent primed membranes to form macro pinosomes. Indeed, in areas with elevated PI3K activity, either naturally or through external stimulation, there was an increased ruffle density that lead to an increased probability of primed ruffles colliding to form macro pinosomes. This model of macro pinosome formation relying on PI3K priming rather than a defined geometry also explains the variation in diameter that is a hallmark of macro pinosomes. The improved sensitivity of LLSM enabled detection of PI3K activity at the earliest stages of ruffle development that grows in curving ruffles and peaks around macro pinosomes post closure. Our data are consistent with a mechanism driven by the geometry of curving ruffles that confines PI3K, thereby amplifying the signal, which in turn activates yet unknown fusogenic protein(s) localized to the ruffle edges mediating sealing during membrane collisions. This conclusion is supported by the observations that inhibition of PI3K activity with LY29004 did not substantially alter membrane ruffling structure, curvature or collisions, but completely inhibited sealing; even when fully spherical morphologies were observed that then collapsed back into the cell surface.
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+The model suggested in this work contrasts with a recent report in LPS- activated RAW264.7 cells that described F- actin- rich filopodia- like "tentpoles" protruding from the surface that twisted to constrict veils of membrane that then became macropinosomes<sup>12</sup>. Using a membrane probe and the same microscope, we should have recapitulated the filapodial- like protrusions in the initial extension- phase that then would have a concave appearance connecting the tips. Only rarely when visualizing single slices of ruffling membrane, did we observe filapodial- like extensions connecting at the distal margins (Supplementary Figure 1b). However, the isosurface and volumetric renderings of the same macropinocytic events were not filapodial- like but were, in fact, multiple linear ruffle sheets that protruded from the cell surface and intersected to form a macropinosome (Supplementary Figure 1c). Additionally, these ruffles protruding from the cell were convex as they emerged and formed which fits a model where actin polymerization occurs throughout the ruffle driving the extension forward.  
+
+Taken together, our experiments indicate a mechanism for macropinosome formation requiring amplified PI3K signaling within ruffles that become macropinosomes and contributes primarily to priming membranes for sealing. The membrane probe and visualizations we have described set the foundation to enable rigorous testing of this mechanism using specific inhibitors of phosphatidylinositol- modifying enzymes and sensors that specifically bind to the various products to determine how each step is regulated during macropinocytosis.  
+
+## Methods and Materials  
+
+Plasmids. pCMV- VSV- G was a gift from Bob Weinberg (Addgene plasmid #8454; http://n2t.net/addgene:8454; RRID:Addgene_8454)<sup>29</sup>. psPAX2 was a gift from Didier Trono (Addgene plasmid #12260; http://n2t.net/ addgene:12260; RRID:Addgene_12260). pLJM1- EGFP was a gift from David Sabatini (Addgene plasmid #19319; http://n2t.net/addgene:19319; RRID:Addgene_19319)<sup>30</sup>. Lck- mScarlet- l was a gift from Dorus Gadella (Addgene plasmid #98821; http://n2t.net/addgene:98821; RRID:Addgene_98821)<sup>31</sup>.  
+
+Construction of the membrane and AktPH probes. The membrane probe was constructed by combining the membrane localization motif (MGCVCSSNPE) from Lck<sup>31</sup> in frame with mNeonGreen in the pLJM1 backbone containing the puromycin resistance gene. The mSc- AktPH probe was constructed by using mScarlet- l in frame with the pleckstrin homology domain from Akt in the pLJM1 backbone, modified to contain the blasticidin resistance gene. Sequences were codon optimized for expression in mouse cells, synthesized, and sequence verified by GenScript (Piscataway, NJ).  
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+Viral transduction. Sequence- verified plasmids containing genes encoding FP- chimeras, plus the packaging plasmids pVSV- G and psPAX2 were transfected into NIH 293T cells for packaging using linear 25 kDa polyethyleneimine (PEI) as a transfection reagent. NIH 293T- cell culture supernatant containing lentiviral particles was collected and added to FLM treated with cyclosporin A (10 \(\mu \mathrm{M}\) ) for two days. Transduced FLMs were selected with puromycin and blasticidin (10 \(\mu \mathrm{g} \cdot \mathrm{ml}^{- 1}\) each).  
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+Macrophage culture media. DMEM/F- 12 (Gibco) supplemented with 20% Heat- inactivated FBS (R&D Systems), 1% Penicillin/Streptomycin (Gibco), 50 ng·ml<sup>- 1</sup> mCSF- 1 (BioLegend), and 5 μg·ml<sup>- 1</sup> plasmacin (Invivogen) maintained at 37°C with 7.5% CO<sub>2</sub>.
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+PIP3 inhibition (LY294002). Coverslips were prepared as described previously and were moved to a well of media containing \(0.16\mu M\) LY294002 and allowed to incubate for 30 minutes at \(37^{\circ}C\) and \(7.5\% \mathrm{CO}_2\) prior to imaging. The coverslip was then transferred to the LLSM bath containing Imaging Media, \(1.7 \mathrm{mM}\) Glucose, and \(0.16 \mu M\) LY294002. The coverslip was explored using the LLS software and three cells were chosen per coverslip that provided the best visual representation of the population. Each cell was imaged under the same parameters as described above.  
+
+CSF- 1 stimulation. The coverslip was starved overnight in DMEM/F- 12 with \(10\%\) FBS and \(1\%\) pen/strep. After 24hrs the coverslip was moved to the LLS bath containing \(7mL\) L- 15 imaging media, and \(1.7mM\) Glucose. The coverslip was explored using the LLS software and three cell targets were chosen and imaged for a pre- stimulation comparison. Immediately after imaging the third cell, CSF- 1 was introduced at \(50 \mathrm{ng}\) \(\cdot \mathrm{mL}^{- 1}\) to the \(7 \mathrm{mL}\) bath. The third cell was once again imaged \(< 1 \mathrm{min}\) after stimulation and each additional cell was imaged in reverse order (Imaging order 1- 2- 3- 3- 2- 1).  
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+Lipopolysaccharide stimulation. FLMs were stimulated with \(100 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) Lipopolysaccharides from Salmonella enterica serotype enteritidis (Sigma) for \(24 \mathrm{h}\) in culture media before being transferred to imaging media containing \(100 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) for LLSM experiments.  
+
+Macrophage isolation. Fetal liver macrophage (FLM) cell cultures were generated as described previously<sup>32,33</sup>. Livers were isolated from gestational day 15- 19 mouse fetuses from C57BL/6J mice (The Jackson Laboratory, Bar Harbor, ME) in accordance with South Dakota State University Institutional Animal Use and Care Committee. Liver tissue was mechanically dissociated using sterile fine- pointed forceps and a single- cell suspension was created by passing the tissue through a \(1 \mathrm{ml}\) pipette tip<sup>32</sup>. Cells were plated on non- tissue culture treated dishes and kept in growth and differentiation medium containing the following: \(20\%\) heat- inactivated fetal bovine serum; \(30\%\) L- cell supernatant, a source of M- CSF<sup>34,35</sup>; and \(50\%\) Dulbecco's modified growth medium containing \(4.5 \mathrm{g} \cdot \mathrm{L}^{- 1}\) glucose, \(110 \mathrm{mg} \cdot \mathrm{L}^{- 1}\) sodium pyruvate, \(584 \mathrm{mg} \cdot \mathrm{L}^{- 1}\) L- glutamine, \(1 \mathrm{IU} \cdot \mathrm{mL}^{- 1}\) penicillin and \(100 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) streptomycin. FLM were cultured for at least 8 weeks prior to transduction and experiments.  
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+Cell Culturing and Coverslip Plating. FLMs were cultured in untreated T- 25 tissue culture flasks using the following culture media: DMEM F- 12 with \(20\%\) FBS, \(1\%\) penicillin/streptomycin, \(50 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) CSF- 1, and 5 \(\mathrm{ng} \cdot \mathrm{mL}^{- 1}\) plasmonic. The cell cultures were split at \(\sim 85\%\) confluence, first by washing the T- 25 flask with 3 mL of PBS (- Ca/- Mg) 2 times. The cells were then lifted from the T- 25 flask using 4 mL of \(4^{\circ}\mathrm{C}\) PBS (- Ca/- Mg, \(+0.98 \mathrm{mM}\) EDTA) with gentle pipet washing for approximately \(10 \mathrm{min}\) . The lifted cells were moved to a \(15 \mathrm{mL}\) centrifuge tube (1 mL of culturing media was added to \(15 \mathrm{mL}\) tube if cells took \(>10 \mathrm{min}\) to lift) and centrifuged at \(200 \times \mathrm{g}\) for 5min. While the cells were being spun down, the T- 25 flask was washed with PBS (- Ca/- Mg), filled with 5mL of culture media, and placed in the \(37^{\circ}\mathrm{C}\) incubator to reach appropriate culture conditions. Once the cells were finished being spun down, the supernatant was removed from the \(15 \mathrm{mL}\) tube and the cells were resuspended in \(1 \mathrm{mL}\) culturing media and counted. The counting was done by mixing \(10 \mu \mathrm{L}\) of suspended cells with \(10 \mu \mathrm{L}\) of trypan blue and placed on a glass slip to be counted using a countess. The FLMs were re- plated in the original T- 25 flask with \(\sim 6 - 7 \times 10^{5}\) cells. The cells were washed
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+every 2 days and given fresh media until reaching \(\sim 85\%\) confluence where they would then be split. Cell lines were kept for approximately 2 months before being replaced with early state frozen aliquots. Macrophages were prepared for LLS imaging \(24h\) prior to imaging using 5mm glass coverslips. The coverslips were soaked in \(90 - 100\%\) ethanol and flame cleaned using a butane flame. Approximately 5 flame cleaned coverslips were placed per well of a 12 well plate each containing \(1mL\) of culture media. Cells were added to each well during the cell culture process described above at \(\sim 3\times 10^{5}\) cells to each \(3.5cm^2\) (12- well plate) for imaging. The FLMs incubated on the flame cleaned glass coverslips in culturing media for \(24h\) prior to imaging. The coverslips were transferred to the LLSM bath that was filled with 7 mL of Leibovitz's L- 15 Media (supplemented with \(1.7mM\) glucose) at \(\sim 37^{\circ}C\) .  
+
+Lattice Light Sheet Microscopy Imaging. The LLSM is a replica of the design described by Chen et al. \(^{36}\) , built under license from HHMI. Volumetric image stacks were generated using dithered square virtual lattices (Outer NA 0.55, Inner NA 0.50, approximately \(30\mu m\) long) and stage scanning with \(0.5\mu m\) step sizes, resulting in \(254nm\) deskewed z- steps. Excitation laser powers used were \(18\mu W\) (488 nm) and \(22\mu W\) (561 nm), measured at the back aperture of the excitation objective. The emission filter cube (DFM1, Thorlabs) comprised a quadband notch filter NF03- 405/488/561/635 (Semrock), longpass dichroic mirror Di02- R561 (Semrock), shortpass filter 550SP (Omega) on the reflected path, and longpass filter BLP01- 561R (Semrock) on the transmitted path; the resulting fluorescence was imaged onto a pair of ORCA- Flash4.0 v2 sCMOS cameras (Hamamatsu). The camera on the reflected image path was mounted on a manual x- y- z translation stage (Newport 462- XYZ stage, Thorlabs), and the images were registered using \(0.1\mu m\) Fluoresbrite YG microspheres (Polysciences). The image capturing rates varied between 5- 10 seconds per volume using 8- 12 ms planar exposures depending on the brightness of the cell and imaging region.  
+
+Scanning Electron Microscopy. BMDM were plated onto \(13mm\) diameter, circular glass coverslips and cultured overnight in RPMI with \(10\%\) FBS (R10). To stimulate macropinocytosis, BMDM were incubated \(30min\) in phosphate- buffered saline (PBS), then \(15min\) in PBS containing \(10nM\) CSF- 1. Cells were fixed in \(2\%\) glutaraldehyde, \(0.1M\) caccodylate buffer, \(\mathsf{pH}7.4\) \(6.8\%\) sucrose, \(60min\) at \(37^{\circ}C\) Fixative was replaced with a second fixative consisting of \(1\%\) \(\mathrm{OsO_4}\) in \(0.1M\) caccodylate buffer, \(\mathsf{pH}7.4\) , for \(60min\) at \(23^{\circ}C\) . The second fixative was replaced with \(1\%\) tannic acid in caccodylate buffer, \(30min\) at \(4^{\circ}C\) , the rinsed with 3 changes of \(0.1M\) caccodylate buffer. Coverslips were transferred through successive changes of acetone- water mixtures, progressively increasing acetone concentrations to \(100\%\) before a final incubation in hydroxymethylsilazidane (HMDS, EM Sciences). HMDS was removed and coverslips were dried for 2 days. Coverslips were shadowed with gold and observed on a Amray 1900 field emission scanning electron microscope.  
+
+Deconvolution and Post Processing. The raw volumes acquired from the LLSM were deskewed, deconvolved and rotated to coverslip coordinates in \(\mathsf{LLSp}\mathsf{y}^{37}\) . We applied a fixed background subtraction based on an average dark current image, 10 iterations of Lucy- Richardson deconvolution with experimentally measured point spread functions for each excitation followed by rotation to coverslip coordinates, and cropping to the region of interest surrounding the volume for visualization. We optimized the illumination intensity such that less than \(10\%\) photobleaching occurred during the experiment. The fully processed data was opened as a volume map series in UCSF ChimeraX and utilized isosurface, mesh, 3D volumetric intensities, and orthogonal planes renderings to exam the data. The
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+surface and mesh options utilize a three- dimensional analog of an isoline called an isosurface that represents points in volume space as constant values which were used to display the membrane probe. The isosurface provides a defined surface for the membrane probe resulting in shadowing providing visual depth to the three- dimensional data. The mesh rendering offers a similar surface definition while also providing an option to include the internal fluorescent mSc- AktPH signal. We used a volumetric intensity projection to visually display the localization of mSc- AktPH throughout the cell. At each pixel, the most intense color value underlying the pixel along the line of sight is displayed (ChimeraX User Guide). The final technique used to display the LLSM data was through orthogonal planes. This generates 2D planes each \(0.128\mu m\) thick for the entire volume in xy, yz, and xz. Multiple methods were overlapped and shown side by side to effectively represent the data and labeled within each figure.  
+
+## Acknowledgments  
+
+Funding: Funding provided by the South Dakota Board of Regents through BioSNTR and the SDBOR FY20 collaborative research award "IMAGEN: Biomaterials in South Dakota". Additional funding provided by the National Science Foundation through research award CNS- 1626579 "MRI: Development of a Scalable High- Performance Computing System in Support of the Lattice Light- sheet Microscope for Real- time Three- dimensional Imaging of Living Cells". J.A.S. was supported by NIH grant R35 GM131720. B.L.S. is supported by the Chan Zuckerberg Initiative through the Imaging Scientist program.  
+
+Visualization: The data visualization and analyses were performed using UCSF ChimeraX, developed by the Resource for Biocomputing, Visualization, and Informatics at the University of California, San Francisco, with support from National Institutes of Health R01- GM129325 and the Office of Cyber Infrastructure and Computational Biology, National Institute of Allergy and Infectious Diseases.  
+
+LLSM: The Lattice Light Sheet Microscope referenced in this research was developed under license from Howard Hughes Medical Institute, Janelia Farms Research Campus ("Bessel Beam" patent applications 13/160,492 and 13/844,405).  
+
+Author Contributions: S.E.Q. acquired and analyzed LLSM data and co- wrote the manuscript. L.H generated FLM cell lines used in experiments. J.G.K. Designed plasmid constructs and generated FLM cell lines. J.A.S. Performed SEM experiments and edited the manuscript. S.S. provided supervision and edited the manuscript. A.D.H. co- wrote the manuscript. R.B.A. built the LLSM and analysis cluster and provided supervision. N.W.T. designed experiments and co- wrote the manuscript. B.L.S. designed and performed initial experiments, assisted with data analysis and co- wrote the manuscript.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1. 3D visualization of macrophages allows insight into membrane structure and phosphatidylinositol dynamics during macropinocytosis. a) Isosurfaces show the plasma membrane of a live cell that is actively macropinocytosis. Region \(68 \times 72 \times 25 \mu m\) (x, y, z). b) SEM image of a macrophage acutely stimulated with CSF-1 shows high-resolution fixed cells. Scale bar is 10 \(\mu m\) . c) Volumetric intensities show specific local fluorescence (left->right) volumetric membrane (green), dual volumetric membrane and mSc-AktPH, volumetric mSc-AktPH (magenta). Volumetric renderings provide a method to visualize the transient fluorescent intensities throughout the volume of the cell. Region is \(68 \times 72 \times 25 \mu m\) . d) Combinations of visualization techniques such as Isosurface (left) displayed alongside orthogonal planes (right) further clarify how each plane is chosen to show internal intensities. Region of \(29 \times 30 \times 19 \mu m\) . e) Mesh rendering of the mNG-membrane probe along with volumetric mSc-AktPH provides a representation of the plasma membrane structure as well as underlying fluorescence. The white arrows indicate the post closure recruitment of mSc-AktPH. Region \(13 \times 14 \times 7 \mu m\) . Different rendering methods provide insight into cellular characteristics such as structure, depth, and fluorescent intensity and provide a foundation for visualizing localization of mSc-AktPH to the constantly changing plasma membrane during macropinocytosis. </center>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. Early PI3K activity leads to amplification of \(\mathsf{PIP}_3 / \mathsf{PIP}_2\) in developing ruffles, macropinosome formation, and post closure recruitment. a) Top view of an mNG-mem isosurface rendering provides depth for 3D visualization of ruffle extension. Dual-color volumetric intensity display comparing the recruitment of mSc-AktPH to early and expanding ruffles as well as sealed macropinosomes (Region 21x19um). b) Intensity line-scan of the volumetric mNG-Mem and mSc-AktPH shows their relative intensities for extending membrane ruffles, as well as recruitment around a sealed macropinosome. c) Side view of the isosurface mesh plasma membrane and volumetric mSc-AktPH (Magenta Hot color scale) from a shows that the early stages of ruffle development is filled with mSc-AktPH and the resulting macropinosome (white arrow) receives a final intense mSc-AktPH recruitment around the formed macropinosome at the bottom of the ruffle. Region of 21x19x15um. </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. PI3K activity is required for membrane sealing and separation from PM/internalization of a complete macropinosome but not membrane ruffling a) Isosurface rendering of mNG-mem for an untreated macrophage during a successful macropinocytosis event where the sheet curls back toward the membrane for fusion/sealing. Region 12x13x10 μm b) Volumetric rendering of Sc-AktPH of the untreated cell shows the increase of PI3K activity in the ruffle that creates a macropinosome. 12x13x10 μm c) Mesh and orthogonal planes of mNG-mem show the internal membrane organization of the ruffle and resulting macropinosome. 12x13x10 μm d) Isosurface rendering of an LY294002 treated macrophage provides depth to the attempted closure of a macropinocytic cup. Region 10x12x10 μm. e) Volumetric intensity rendering of Sc-AktPH for an LY294002-treated macrophage shows the diffuse distribution of AktPH and minimal PI3K activity. The cytosolic intensities were co-scaled for the untreated and treated macrophage. Region 10x12x10 μm f) XY-plane for the mNG-mem probe of an LY294002-treated cell during a failed macropinocytosis event. In the surface view, the ruffle appeared to form a macropinosome; however, when overlaid with the plane view is became clear that it failed to fully form into a macropinosome. The ruffle quickly reduced in size and became undistinguishable within the cytosol, while never receiving the post closure increase of PI3K activity. Region 10x12x10 μm. </center>
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Macropinosomes form via PI3K-primed ruffle fusion. a) Dual volumetric intensities of mNG-mem and mSc-AktPH show the intensity of each probe as the rufles and macropinosomes form. The montage shows the earliest stage of the ruffle that extends vertically and forms macropinosomes along the length near the base of the primary ruffle as a result of smaller mSc-AktPH-rich extensions colliding. The white arrow points at the macropinosome forming region further emphasized in the isosurface. Region 9x12x13 um. b) Isosurface rendering of mNG-membrane shows the structure of the extending ruffle and the continued sheet extension after the macropinosomes formed. The white arrow emphasizes the small pocket that closes to form one of the macropinosomes. Region 9x12x13 μm. c) Mesh surface rendering of mNG-mem and volumetric mSc-AktPH shows the internalized macropinosome with the increased localization of mSc-AktPH at the bottom of the ruffle. Region 11x9x12 μm. </center>
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5. Phosphatidylinositol localization and chaotic ruffling underlie macropinocytosis in complex membrane structures. a) Single time point, full cell surface rendering of chaotic macropinocytosis event. The red box correlates to the same frame in c-d. b) SEM images of a BMDM showing similar highly active ruffling regions c) Isosurface montage shows the chaotic orientation of membrane structure. Region 27x22x16 \(\mu \mathrm{m}\) , 25° tilt. d) Volumetric AktPH (Magenta-Hot) provides a more detailed emphasis on the AktPH activity within the membrane ruffles and highlights the macropinosomes that have formed. Region 27x22x16 \(\mu \mathrm{m}\) with a 25° tilted view. e) Mesh Surface with AktPH (Magenta Hot) shows the AktPH activity as the ruffle develops as well as the increased recruitment around formed macropinosomes at the base of the event. </center>
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Figure 6. Growth factor starvation and stimulation results in the formation of large circular dorsal ruffles that corrals \(\mathsf{PIP}_3 / \mathsf{PIP}_2\) . Macrophages were starved of CSF-1 for \(24~\mathrm{h}\) , imaged for 5 minutes as a baseline, and imaging restarted 1 min after stimulation with \(50~\mathrm{ng}\cdot \mathrm{mL}^{-1}\) CSF-1. Four-frame montages provide a visual display of the large dorsal ruffle that acts as a diffusional barrier that restricts \(\mathsf{PIP}_3 / \mathsf{PIP}_2\) to the inside of the ruffle as it is cleared from the surface. This barrier is likely acting as a signal amplification mechanism stimulating the production of many macropinosomes. a) Isosurface rendering provides crisp surface directionality, b) Surface mesh and volumetric AktPH (magenta-hot), show the restricted probe as the membrane converges c) Volumetric Intensity of both mNG-Membrane and mSc-AktPH show the intensity locations of the membrane ruffle and the restricted AktPH. \(49\times 60\mu \mathrm{m}\) d) Bright field images showing multiple cells responding to stimulation with similar dorsal membrane clearing. </center>
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Figure 7. LPS stimulation increases membrane ruffling and macropinocytosis. Macrophages were pretreated with \(100\mathrm{ng}\cdot \mathrm{ml}^{-1}\) LPS for \(24\mathrm{h}\) prior to imaging. a) Surface rendering of mNG-Mem on an LPS stimulated macrophage provides a surface level understanding of the membrane, exploration, ruffling, and PM structure. b) Dual-color volumetric intensity projections of mNG-Mem and mSc-AktPH for an LPS stimulated cell provided the intensity activity during increased macrophage activity and shows the highly AktPH rich regions of membrane ruffling. Region \(68\times 77\times 21\mu \mathrm{m}\) c) Untreated macrophage losurface showing visibly less exploratory behavior. d) Dual-color volumetric intensity rendering of the untreated macrophage gives insight on the AktPH activity inside of the cell during macropinocytosis and allows for the quantitative comparison of macropinosomes formed between the stimulated and unstimulated cells. Region \(68\times 77\times 21\mu \mathrm{m}\) e) Box plot showing the difference in macropinocytic activity between untreated and LPS treated macrophages. All macropinosomes greater than \(1\mu \mathrm{m}\) were manually counted using a z-projection MIP in Fiji and were distinguished by the post closure spike in mSc-AktPH intensity. </center>
+
+<--- Page Split --->
+![](images/Supplementary_Figure_1.jpg)
+
+<center>Supplementary Figure 1 - Constitutive macropinocytosis and the importance of reducing the dimensionality of data. a) Orthoplane (left) and isosurface (right) views of mNG-Membrane show the subsurface macropinosome and the complex structure of the full surface. b) Orthoplane montage of mNG-membrane depicting constitutive planar view of macropinocytosis where two sheets extend from the cell membrane, circularize, and connect to form a macropinosome. c) Isosurface view of mNG-Membrane showing the three spatial dimensions of the ruffle clearly depicting the multiple membrane sheets involved in the macropinocytic event. The red box shows the corresponding montage frames for panel a. </center>  
+
+## Supplementary Movie Legends  
+
+Video 1. Corresponds to Fig. 1a, c. Isosurface and volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) provides different methods of visualizing the formation (surface) and trafficking of macropinosomes and mSc- AktPH accumulation (volume). Movie timestamps highlight the following events: AktPH enriched ruffle development (02:42), newly formed macropinosomes (06:29; 08:51; 10:58), and post closure AktPH recruitment (11:19). Frame rate of \(\sim 7s\) and each region is \(68 \times 72 \times 25 \mu m\) .  
+
+Video 2. Corresponds to Fig. 1d. Isosurface rendering in conjunction with orthogonal plans moved through a volume provide \(\sim 0.1 \mu m\) thick planes to help visualize the internal and surface activity of mNG- mem and mSc- AktPH including macropinosome closures (02:41; 05:15), membrane rich rruffles (00:00; 02:34; 05:08), previously formed internal macropinosomes (05:15 during scan), and mSc- Akt localization around a closed macropinosome (05:15 during scan). Framerate of \(\sim 7s\) and two subregions each \(29 \times 30 \times 19 \mu m\) .  
+
+Video 3. Corresponds to Fig. 2a. Isosurface and dual- volumetric intensity projection of mNG- mem and mSc- AktPH with a 25 degree tilt shows a variety of formation events. Several early formations occur prior to relaxation of the plasma membrane (01:58), followed by the development of another AktPH rich ruffle (02:48), membrane closure into a macropinosome (03:07 \(\rightarrow 3:13\) ), and finally post closure recruitment of AktPH (03:25). Several macropinosomes form that are indicated by the recruitment of AktPH post closure (3:57; 07:16) and subsequently trafficked toward one another to merge (4:53; 05:18; 05:30; 07:54). Frame rate of \(\sim 6.25s\) and region of \(21 \times 19 \times 15 \mu m\) .  
+
+Video 4. Corresponds to Fig. 2c. Mesh rendering of mNG- membrane and volumetric intensity projection of mSc- AktPH (Magenta- Hot) using a 90 degree tilt. The second play through contains a pause to emphasize the frame shown in Fig 2c and highlight the AktPH rich membrane rruffles (02:48) and the post closure recruitments (03:25; 03:57). Frame rate \(\sim 6.25s\) region of \(21 \times 19 \times 15 \mu m\) .  
+
+Video 5. Corresponds to Fig. 3a, b. Isosurface in conjunction with three volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) display a traditional formation in an untreated cell including the initial ruffle (00:00) that vertically extends and begins to form a tidal wave (01:31) back toward the surface of the cell, with membrane scission (03:24 \(\rightarrow 03:31\) ) and finally the post closure recruitment for the largest macropinosome (08:07). Frame rate of \(7s\) and Region of \(12 \times 13 \times 10 \mu m\) .  
+
+Video 6. Corresponds to Fig. 3d, e. Isosurface with three volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) on an LY294002 treated macrophage showing the initial ruffle with uniform AktPH throughout the cytosol and ruffle (00:00), attempted closure of the ruffle (00:30), continued compression of the attempted macropinosome (00:30 \(\rightarrow 02:27\) ), becoming un- trackable within the cytosol with no AktPH recruitment to the attempted macropinosome. (Tracking done manually using orthogonal planes) Frame rate of 6.15s and Region \(10 \times 12 \times 10 \mu m\) .
+
+<--- Page Split --->
+
+Video 7. Corresponds to Fig. 4a, b. Isosurface alongside three volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) shows the formation of macrosinosomes at the base of a larger ruffle. Membrane relaxes (00:56), small protrusions form with increased AktPH (01:17), two small ruffles, one in the back and one in the front mergers with the larger ruffle (01:32 -> 01:39) followed by post closure AktPH recruitment (01:53). Frame rate of 7s and region of 11x9x12 μm.  
+
+Video 8. Corresponds to Fig. 5c. Isosurface and dual- volumetric intensity projection of mNG- membrane and mSc- AktPH showing a smooth and relaxed membrane (00:00). A single macrosinosome forms (05:06) followed by a large increased in membrane activity (06:35) resulting in a significant number of macrosinosomes, indicated by the post closure AktPH recruitment, that turns into the chaotic membrane structure (06:35 -> 13:18). Frame rate of 8s and region size of 27x22x16 μm.  
+
+Video 9. Corresponds to Fig. 5e. Side view of mNG- membrane isosurface and mesh membrane with volumetric AktPH (Magenta Hot) shows the continued AktPH localization within the extending membrane structure (06:35). Utilizing the Magenta- Hot LUT regions displaying in white represent the increase in AktPH post macrosinosome closure signifying a formed macrosinosome (05:55; 06:59; 08:12; 11:50). Frame rate of 8s and region size of 27x22x16 μm.  
+
+Video 10. Corresponds to Fig. 6a, b, c. CSF- 1 starved macrophage displayed using mNG- membrane isosurface/mesh/volume and AktPH volumes as magenta- hot under the mesh and Magenta alongside the volume membrane. The macrophage was imaged 07:41 prior to stimulation and reimaged one minute after CSF- 1 stimulation (08:41) providing time to ensure instrument and imaging conditions had not changed. The starved cell ruffled and formed macrosinosomes similar to the conventional cells (00:06; 01:46; 03:26) and upon stimulation (08:41) a large circular dorsal ruffle forms corralling the AktPH to one concentrated spot in the cell (16:22). Frame rate of 6.25s and region size of 49x60 μm.  
+
+Video 11. Corresponds to Fig. 6d. The brightfield view starts promptly after stimulation showing the majority of macrophages performing the similar dorsal membrane clearing seen in the LLSM imaging.  
+
+Video 12. Corresponds to Fig. 7a, b. LPS Stimulation. Isosurface of mNG- Mem and dual- color volumetric intensity projects of mNG- Mem and mSc- AktPH showing the activity of an LPS treated cell. Initial imaging starts (00:00) with a cluster of membrane rich in AktPH that goes on to create many macrosinosomes as it expands toward the upper right region of the field of view. The activity changes directions toward the upper left region of the cell and proceeds to move counterclockwise (01:14), over the nucleus and back to the initial location ending at (04:42). Additional macrosinosomes are seen forming on the left region with the increased AktPH flare up post closure (04:42). Finally, several formations occur in the bottom right of the cell (05:05 - 08:18) many of which go on to merge with one another. Framerate of ~7s and Region of 68x77x21 μm.  
+
+Video 13. Corresponds to Fig. 7c, d. Non- treated control. Isosurface of mNG- Mem and dual- color volumetric intensity projects of mNG- Mem and mSc- AktPH showing the imaging of a nontreated cell (10:47). Two AktPH rich regions of membrane ruffling are seen in the bottom right of the cell (02:17) that form several small macrosinosomes, indicated by a spike in AktPH around the formed macrosinosome. The cell shows activity that is representative of the untreated experiments including macrosinosome formations, exploration, and overall membrane ruffling. Framerate of ~6.5s and Region of 68x77x21 μm.  
+
+## References  
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+
+<--- Page Split --->
+
+## Figures  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1 </center>  
+
+3D visualization of macrophages allows insight into membrane structure and phosphatidylinositol dynamics during macropinocytosis. a) Isosurfaces show the plasma membrane of a live cell that is actively macropinocytosis. Region \(68 \times 72 \times 25 \mu \mathrm{m}\) (x, y, z). b) SEM image of a macrophage acutely stimulated with CSF- 1 shows high- resolution fixed cells. Scale bar is \(10 \mu \mathrm{m}\). c) Volumetric intensities show specific local fluorescence (left- right) volumetric membrane (green), dual volumetric membrane and mSc- AktPH, volumetric mSc- AktPH (magenta). Volumetric renderings provide a method to visualize
+
+<--- Page Split --->
+
+the transient fluorescent intensities throughout the volume of the cell. Region is \(68 \times 72 \times 25 \mu m\) . d) Combinations of visualization techniques such as Isosurface (left) displayed alongside orthogonal planes (right) further clarify how each 360 plane is chosen to show internal intensities. Region of \(29 \times 30 \times 19 \mu m\) . e) Mesh rendering of the mNG- membrane probe along with volumetric mSc- AktPH provides a representation of the plasma membrane structure as well as underlying fluorescence. The white arrows indicate the post closure recruitment of mSc- AktPH. Region \(13 \times 14 \times 7 \mu m\) . Different rendering methods provide insight into cellular characteristics such as structure, depth, and fluorescent intensity and provide a foundation for visualizing localization of mSc- AktPH to the constantly changing plasma membrane during macropinocytosis.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2 </center>  
+
+Early PI3K activity leads to amplification of PIP3/PIP2 in developing ruffles, macropinosome formation, and post closure recruitment. a) Top view of an mNG- mem isosurface rendering provides depth for 3D visualization of ruffle extension. Dual- color volumetric intensity display comparing the recruitment of mSc- AktPH to early and expanding ruffles as well as sealed macropinosomes (Region 21x19um). b) Intensity line- scan of the volumetric mNG- Mem and mSc- AktPH shows their relative intensities for
+
+<--- Page Split --->
+
+extending membrane ruffles, as well as recruitment around a sealed macropinosome. c) Side view of the isosurface mesh plasma membrane and volumetric mSc-AktPH (Magenta Hot color scale) from a shows that the early stages of ruffle development is filled with mSc-AktPH and the resulting macropinosome (white arrow) receives a final intense mSc-AktPH recruitment around the formed macropinosome at the bottom of the ruffle. Region of 21x19x15um.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>
+
+<--- Page Split --->
+
+<p>PI3K activity is required for membrane sealing and separation from PM/internalization of a complete macropinosome but not membrane ruffling a) Isosurface rendering of mNG-mem for an untreated macrophage during a successful macropinocytosis event where the sheet curls back toward the membrane for fusion/sealing. Region 12x13x10 &mu;m b) Volumetric rendering of Sc-AktPH of the untreated cell shows the increase of PI3K activity in the ruffle that creates a macropinosome. 12x13x10 &mu;m c) Mesh and orthogonal planes of mNG-mem show the internal membrane organization of the ruffle and resulting macropinosome. 12x13x10 &mu;m d) Isosurface rendering of an LY294002 treated 3macrophage provides depth to the attempted closure of a macropinocytic cup. Region 10x12x10 &mu;m. e) Volumetric intensity rendering of Sc-AktPH for an LY294002-treated macrophage shows the diffuse distribution of AktPH and minimal PI3K activity. The cytosolic intensities were co-scaled for the untreated and treated macrophage. Region 10x12x10 &mu;m f) XY-plane for the mNG-mem probe of an LY294002-treated cell during a failed macropinocytosis event. In the surface view, the ruffle appeared to form a macropinosome; however, when overlaid with the plane view is became clear that it failed to fully form into a macropinosome. The ruffle quickly reduced in size and became undistinguishable within the cytosol, while never receiving the post closure increase of PI3K activity. Region 10x12x10 &mu;m.</p>  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4 </center>
+
+<--- Page Split --->
+
+Macropinosomes form via PI3K- primed ruffle fusion. a) Dual volumetric intensities of mNG- mem and mSc- AktPH show the intensity of each probe as the rufles and macropinosomes form. The montage shows the earliest stage of the ruffle that extends vertically and forms macropinosomes along the length near the base of the primary ruffle as a result of smaller mSc- AktPH- rich extensions colliding. The white arrow points at the macropinosome forming region further emphasized in the isosurface. Region \(9\times 12\times 13\) um. b) Isosurface rendering of mNG- membrane shows the structure of the extending ruffle and the continued sheet extension after the macropinosomes formed. The white arrow emphasizes the small pocket that closes to form one of the macropinosomes. Region \(9\times 12\times 13\) um. c) Mesh surface rendering of mNG- mem and volumetric mSc- AktPH shows the internalized macropinosome with the increased localization of mSc- AktPH at the bottom of the ruffle. Region \(11\times 9\times 12\) um.  
+
+![](images/Figure_5.jpg)
+
+<center>Figure 5 </center>
+
+<--- Page Split --->
+
+Phosphatidylinositol localization and chaotic ruffling underlie macropinocytosis in complex membrane structures. a) Single time point, full cell surface rendering of chaotic macropinocytosis event. The red box correlates to the same frame in c- d. b) SEM images of a BMDM showing similar highly active ruffling regions c) Isosurface montage shows the chaotic orientation of membrane structure. Region \(27 \times 22 \times 16 \mu \mathrm{m}\) , \(25^{\circ}\) tilt. d) Volumetric AktPH (Magenta- Hot) provides a more detailed emphasis on the AktPH activity within the membrane ruffles and highlights the macropinosomes that have formed. Region \(27 \times 22 \times 16 \mu \mathrm{m}\) with a \(25^{\circ}\) tilted view. e) Mesh Surface with AktPH (Magenta Hot) shows the AktPH activity as the ruffle develops as well as the increased recruitment around formed macropinosomes at the base of the event.  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6 </center>  
+
+Growth factor starvation and stimulation results in the formation of large circular dorsal ruffles that corrals PIP3/PIP2. Macrophages were starved of CSF- 1 for \(24 \mathrm{~h}\) , imaged for 5 minutes as a baseline, and imaging restarted 1 min after stimulation with \(50 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) CSF- 1. Four- frame montages provide a visual display of the large dorsal ruffle that acts as a diffusional barrier that restricts PIP3/PIP2 to the inside of the ruffle as it is cleared from the surface. This barrier is likely acting as a signal amplification
+
+<--- Page Split --->
+
+mechanism stimulating the production of many macrosinosomes. a) Isosurface rendering provides crisp surface directionality, b) Surface mesh and volumetric AktPH (magenta- hot), show the restricted probe as the membrane converges c) Volumetric Intensity of both mNG- Membrane and mSc- AktPH show the intensity locations of the membrane ruffle and the restricted AktPH. 49x60 μm d) Bright field images showing multiple cells responding to stimulation with similar dorsal membrane clearing.  
+
+![](images/Figure_7.jpg)
+
+<center>Figure 7 </center>
+
+<--- Page Split --->
+
+LPS stimulation increases membrane ruffling and macropinocytosis. Macrophages were pretreated with \(100 \mathrm{ng} \cdot \mathrm{ml} \cdot 1\) LPS for \(24 \mathrm{~h}\) prior to imaging. a) Surface rendering of mNG- Mem on an LPS stimulated macrophage provides a surface level understanding of the membrane, exploration, ruffling, and PM structure. b) Dual- color volumetric intensity projections of mNG- Mem and mSc- AktPH for an LPS stimulated cell provided the intensity activity during increased macrophage activity and shows the highly AktPH rich regions of membrane ruffling. Region \(68 \times 77 \times 21 \mu \mathrm{m}\) c) Untreated macrophage lisosurface showing visibly less exploratory behavior. d) Dual- color volumetric intensity rendering of the untreated macrophage gives insight on the AktPH activity inside of the cell during macropinocytosis and allows for the quantitative comparison of macropinosomes formed between the stimulated and unstimulated cells. Region \(68 \times 77 \times 21 \mu \mathrm{m}\) e) Box plot showing the difference in macropinocytic activity between untreated and LPS treated macrophages. All macropinosomes greater than \(1 \mu \mathrm{m}\) were manually counted using a z- projection MIP in Fiji and were distinguished by the post closure spike in mSc- AktPH intensity.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+- Vid1Fig1ACVolumeSurfaceTimeStamped.avi- Vid2Fig1DXPlaneScanTimeStamped.avi- Vid3Fig2ASurfVolTimeStamped.avi- Vid4Fig2CMeshVolTimeStampedWithPause.avi- Vid5Fig3CostitComparisonTimeStamped.avi- Vid6Fig3LYSurfVolSplitTimeStamped.avi- Vid7Fig4SurfSplitVolumesTimeStamped.avi- Vid8Fig5CDChaosSurfVolsTimeStamped.avi- Vid9Fig5CEChaosSurfMeshVolTimeStamped.avi- Vid10Fig6ABCCSFFullTimeStamped.avi- Vid11Fig6DCSFBrightField.avi- Vid12Fig7ABLPSClusterTimeStamped.avi- Vid13Fig7BLPSUntreatedComparisonTimeStamped.avi
+
+<--- Page Split --->

preprint/preprint__5fd9725d0ea93e8fd59ab5ffb773154f0a4d443324c2c4f58f1274b4801590df/preprint__5fd9725d0ea93e8fd59ab5ffb773154f0a4d443324c2c4f58f1274b4801590df_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 108, 952, 210]]<|/det|>
+# The structural dynamics of macrosinosome formation and PI3-kinase-mediated sealing revealed by lattice lightsheet microscopy  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 470, 272]]<|/det|>
+Shayne Quinn South Dakota School of Mines and Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 278, 319, 317]]<|/det|>
+Lu Huang South Dakota State University  
+
+<|ref|>text<|/ref|><|det|>[[44, 324, 319, 363]]<|/det|>
+Jason Kerkvliet South Dakota State University  
+
+<|ref|>text<|/ref|><|det|>[[44, 370, 700, 410]]<|/det|>
+Joel Swanson University of Michigan- Ann Arbor https://orcid.org/0000- 0003- 0900- 8212  
+
+<|ref|>text<|/ref|><|det|>[[44, 415, 470, 456]]<|/det|>
+Steve Smith South Dakota School of Mines and Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 462, 675, 503]]<|/det|>
+Adam Hoppe South Dakota State University https://orcid.org/0000- 0003- 4180- 0840  
+
+<|ref|>text<|/ref|><|det|>[[44, 509, 470, 549]]<|/det|>
+Robert Anderson South Dakota School of Mines and Technology  
+
+<|ref|>text<|/ref|><|det|>[[44, 555, 820, 642]]<|/det|>
+Natalie Thiex South Dakota State University Brandon Scott ( brandon.scott@sdfmt.edu ) South Dakota School of Mines and Technology https://orcid.org/0000- 0002- 1950- 0748  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 686, 102, 703]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 722, 816, 742]]<|/det|>
+Keywords: microscopy, lattice lightsheet microscopy, phosphatidylinositol 3- kinase (PI3K)  
+
+<|ref|>text<|/ref|><|det|>[[44, 760, 346, 779]]<|/det|>
+Posted Date: December 28th, 2020  
+
+<|ref|>text<|/ref|><|det|>[[44, 798, 463, 817]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 121499/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 835, 910, 877]]<|/det|>
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 913, 930, 955]]<|/det|>
+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- 25187- 1.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[0, 0, 997, 997]]<|/det|>
+# 1. 1. 1. 1. 1. 1. 1. 2. 2. 2. 2. 2. 2. 2.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[70, 90, 875, 134]]<|/det|>
+1 The structural dynamics of macrokinosome formation and PI3- kinase- mediated sealing revealed by lattice lightsheet microscopy  
+
+<|ref|>text<|/ref|><|det|>[[67, 207, 880, 245]]<|/det|>
+5 Shayne E. Quinn \(^{1,2}\) , Lu Huang \(^{3,4}\) , Jason G. Kerkvliet \(^{4,5}\) , Joel A. Swanson \(^{6}\) , Steve Smith \(^{1,2}\) , Adam D. Hoppe \(^{4,5}\) , Robert B. Anderson \(^{1,2}\) , Natalie W. Thiex \(^{3,4*}\) Brandon L. Scott \(^{1,2*}\)  
+
+<|ref|>text<|/ref|><|det|>[[66, 257, 884, 330]]<|/det|>
+7 1 South Dakota School of Mines and Technology (South Dakota Mines), Nanoscience and Nanoengineering, Rapid 8 City, SD. 2 BioSNTR, South Dakota Mines, Rapid City, SD. 3 South Dakota State University (SDSU), Department of 9 Biology and Microbiology, Brookings, SD. 4 BioSNTR, SDSU, Brookings, SD. 5 SDSU, Department of Chemistry and 10 Biochemistry, Brookings, SD.6 University of Michigan, Department of Microbiology and Immunology, Ann Arbor, MI.  
+
+<|ref|>text<|/ref|><|det|>[[66, 340, 725, 357]]<|/det|>
+11 \* Co- corresponding authors: natalie.thiex@sdtate.edu, brandon.scott@sdsmt.edu
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 93, 221, 115]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[112, 130, 884, 423]]<|/det|>
+Macropinosomes are formed by shaping actin- rich plasma membrane ruffles into large intracellular organelles in a phosphatidylinositol 3- kinase (PI3K)- coordinated manner. Here, we utilize lattice lightsheet microscopy and image visualization methods to map the three- dimensional structure and dynamics of macropinosome formation relative to PI3K activity. We show that multiple ruffling morphologies produce macropinosomes and that the majority form through non- specific collisions of adjacent PI3K- rich ruffles. By combining multiple volumetric representations of the plasma membrane structure and PI3K products, we show that PI3K activity begins early throughout the entire ruffle volume and continues to increase until peak activity concentrates at the base of the ruffle after the macropinosome closes. Additionally, areas of the plasma membrane rich in ruffling had increased PI3K activity and produced many macropinosomes of various sizes. Pharmacologic inhibition of PI3K activity had little effect on the rate and morphology of membrane ruffling, demonstrating that early production of 3'- phosphoinositides within ruffles plays a minor in regulating their morphology. However, 3'- phosphoinositides are critical for the fusogenic activity that seals ruffles into macropinosomes. Taken together these data indicate that local PI3K activity is amplified in ruffles and serves as a priming mechanism for closure and sealing of ruffles into macropinosomes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 467, 270, 490]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[112, 505, 884, 679]]<|/det|>
+Macropinocytosis, or "cell drinking," is a form of clathrin- independent endocytosis that results in the nonspecific uptake of large volumes of extracellular fluid and solutes. This central macrophage function enables immune surveillance, clearing of debris, and sampling of the local environment for the presence of pathogen- or damage- associated molecular patterns, cytokines, growth factors, nutrients, and other soluble cues<sup>1-6</sup>. Macropinosomes also serve as platforms to integrate this diverse information and to activate a variety of signaling pathways<sup>7-10</sup>. The major macrophage growth factor, colony- stimulating factor- 1 (CSF- 1), stimulates macropinocytosis and contributes to ligand- dependent modulation of CSF- 1 receptor signaling<sup>9</sup>. Additionally, cytokines such as CXCL12, and the bacterial cell wall component lipopolysaccharide (LPS) acutely stimulate macropinocytosis<sup>5,11,12</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[112, 697, 884, 892]]<|/det|>
+Construction of a macropinosome proceeds through autonomous, ligand- independent plasma membrane extensions known as ruffles, which are driven by actin polymerization and require the phosphorylation and dephosphorylation of the different signaling phospholipids<sup>13,14</sup>. The closely related process of solid particle uptake known as phagocytosis has been hypothesized to use the shape of the particle as a template for the structure of the phagosome<sup>15,16</sup>. In contrast, the fusion of ruffles into macropinosomes do not have a structural framework to use as a template. This has resulted in various proposed closing mechanisms including a 'purse string' closure of circular dorsal ruffles<sup>13</sup>, closure at the distal tips of ruffles<sup>17</sup>, and more recently closure following actin tentpole crossing<sup>12</sup>. Regardless, these proposed mechanisms result in an organelle derived from the plasma membrane filled with the extracellular medium<sup>18</sup>. The production of 3' phosphoinositides by PI 3- kinase (PI3K) is required to generate isolated
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 884, 341]]<|/det|>
+patches of phosphatidylinositol 3,4,5,triphosphate (PIP3) on the plasma membrane \(^{3,19}\) , and the sequential breakdown of PIP3 into PI(3,4)P2 and ultimately PI is necessary for successful macrokinosome formation \(^{20}\) . Previous ratiometric imaging has shown that PIP3 concentration peaks after ruffle circularization \(^{21- 23}\) . Additionally, PI3K inhibitors, including LY294002, have demonstrated that PI3K activity is only required for macrokinosome closure, but not ruffling \(^{24}\) . This dynamic lipid microenvironment impacts the localization of downstream effector molecules driving actin polymerization and ruffle growth into macrokinosomes \(^{22}\) . However, it is only in protozoa, i.e., Dictyostelium, that the spatial signaling coordination in the 3D ruffle volume during macrokinocytosis has been well described \(^{19}\) ; it remains unclear how these events are spatially coordinated in metazoan cells \(^{25}\) . The precise membrane dynamics of macrokinocytosis and the spatial coordination of PI3K in forming ruffles remains unclear because of the low spatial and temporal resolution of previous microscopy approaches. Recently, high-resolution imaging of macrokinocytosis in macrophage-like cell lines indicates that the prior models of macrokinocytosis may need to be reconsidered \(^{12}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 352, 884, 565]]<|/det|>
+Here, we employ the powerful three- dimensional (3D) imaging capabilities of lattice lightsheet microscopy \(^{26}\) (LLSM) and volumetric image analysis to create high- resolution movies of plasma membrane dynamics and PI3K activity during ruffling and macrokinocytosis. The images and movies we present advance our understanding of the spatial dynamics of membrane ruffling and the morphologies that lead to macrokinosomes, as well as the spatial distribution of PI3K activity during macrokinocytosis. Our results show that the majority of macrokinosomes form by non- specific collisions of adjacent PI3K- rich ruffles. We show that PI3K activity is present at the earliest stages of ruffle extensions and is highly localized to the bottom of ruffles after the membrane has closed into a macrokinosome. Finally, we modulate the rate of macrokinocytosis using stimulation and pharmacological inhibition to demonstrate that the ruffle morphology is unaffected, but PI3K activity is required to prime ruffle membranes for sealing into macrokinosomes.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 580, 196, 600]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[112, 616, 863, 653]]<|/det|>
+## LLSM allows volumetric visualization of plasma membrane movements relative to PIP3 and PI(3,4)P2 distribution during macrokinocytosis  
+
+<|ref|>text<|/ref|><|det|>[[112, 664, 884, 897]]<|/det|>
+Our first objective was to capture the 3D structure of the plasma membrane relative to the PI3K activity during macrokinosome formation. LLSM imaging was performed on fetal liver macrophages (FLMs) stably expressing the fluorescent proteins mNeonGreen localized to the plasma membrane via the lipidation signal sequence from Lck (mNG- Mem) and mScarlet- I fused to the pleckstrin homology domain of Akt (mSc- AktPH). The AktPH probe recognizes PIP3 and PI(3,4)P2 with similar affinity and has been used extensively to characterize PI3K activity during macrokinocytosis \(^{8}\) . LLSM imaging of mNG- Mem allowed visualization of plasma membranes via isosurface renderings in the molecular visualization software, ChimeraX \(^{27}\) . These images were of sufficient resolution that the detailed structure of ruffles and forming macrokinosomes could be observed in living cells (Fig. 1a), similar to scanning electron microscopy imaging of bone marrow derived macrophages (Fig. 1b). To visualize the recruitment of mSc- AktPH relative to the membrane, we used volumetric intensity renderings that maintain the spatial distribution of the fluorescence probes throughout the cellular volume. As can be seen in the volume renderings, the
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 884, 380]]<|/det|>
+mNG- Mem probe persisted on newly formed intracellular vesicles derived from the plasma membrane. Moreover, we observed membrane movements throughout the entire formation and early trafficking of macrosinosomes, as well as the recruitment of mSc- AktPH to forming macrosinosomes (Fig. 1c, Supplementary Movie 1). Orthogonal plane slices (orthoplanes) in xy, yz, and xz (0.1 \(\mu \mathrm{m}\) thick) showed that mSc- AktPH was enriched in ruffles to varying degrees and intensely labeled circular structures found near the base and sides of ruffles (Fig. 1d, Supplementary Movie 2). Orthoplanes are effective for examining the 2D relationships between the fluorescent signals, but can also produce incomplete or distorted perspectives that are resolved by viewing the full volumetric data (Supplementary Figure 1); such as when a macrosinosome appears closed vs open. Additionally, it is difficult to perceive depth in the still frame volumetric renderings. To overcome this limitation, we implemented a mesh derived from the mNG- Mem isosurface with transparent faces that enables visualizing the underlying volumetric mSc- AktPH signals while maintaining the structural framing needed to resolve plasma membrane rearrangements (Fig. 1e). Together, these visualization techniques were applied to 122 macrosinosome formations and enable correlating the location and timing of PI3K activity to the membrane extension, curvature, and fusion of macrosinosomes with unprecedented spatial and temporal resolution.  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 392, 787, 428]]<|/det|>
+## mSc-AktPH is recruited early during ruffle expansion and peaks at the base of ruffles after macrosinosome sealing.  
+
+<|ref|>text<|/ref|><|det|>[[112, 439, 884, 692]]<|/det|>
+In prior analysis of macropinocytosis using microscopy methods with low axial resolution, AktPH was recruited as ruffles transitioned into closed circular ruffles and nascent macrosinosomes<sup>8</sup>. Here, the enhanced z- axis resolution and detection sensitivity of LLSM enabled visualizing the dynamic recruitment of mSc- AktPH to ruffles as they began to protrude from the plasma membrane (Fig. 2a) until maturation where tubulation and fusion between adjacent macrosinosomes occurs (Supplementary Movie 3). As these early ruffles expanded laterally along the plasma membrane and protruded vertically from the cell surface, some ruffles continued to accumulate mSc- AktPH, whereas others lost mSc- AktPH and receded back into the cell suggesting different levels of PI3K activity in neighboring ruffles influences the outcome of a ruffling region (Fig. 2b). Ruffles that maintained mSc- AktPH throughout the ruffle volume continued to grow and formed macrosinosomes, which were accompanied by an intense transient recruitment of mSc- AktPH to the base of the ruffle around the nascent macrosinosome (Fig. 2c, Supplementary Movie 4). Given the early localization and amplification of PI3K signaling in ruffles that become macrosinosomes, we wondered if PI3K activity contributed to 3D ruffle dynamics.  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 704, 701, 721]]<|/det|>
+## PI3K activity is required for macrosinosome sealing, but not ruffling or closure  
+
+<|ref|>text<|/ref|><|det|>[[112, 733, 884, 888]]<|/det|>
+To gain insight into the role of PI3K in regulating the morphological dynamics of macropinocytosis, we used the broad- spectrum PI3K inhibitor LY294002, which inhibits the closure phase of macropinocytosis in macrophages<sup>24</sup>. Non- treated control cells formed transient dorsal ruffles that recruited mSc- AktPH and closed into macrosinosomes, as seen by the surface rendering and intracellular void that is maintained in the plane view (Fig. 3a- c, Supplementary Movie 5). LY294002 treatment did not impact ruffle formation, but eliminated mSc- AktPH recruitment to membrane ruffles (Fig. 3d, e, Supplementary Movie 6). Furthermore, LY294002- treated cells frequently formed ruffles that appeared to close into a macrosinosome but retracted back to the plasma membrane and failed to maintain an intracellular
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[115, 90, 883, 127]]<|/det|>
+organelle (Fig. 3f). Taken together, these data suggest that PI3K activity is dispensable for ruffle formation and membrane collision but is required for membrane sealing to generate a macropinosome.  
+
+<|ref|>sub_title<|/ref|><|det|>[[118, 140, 645, 156]]<|/det|>
+## PI3K activity primes ruffles for fusion to seal nascent macropinosomes  
+
+<|ref|>text<|/ref|><|det|>[[112, 168, 884, 673]]<|/det|>
+We next sought to categorize the macropinosome formation based on the way the membrane fused and the relative amount of PI3K activity. Based on the previously established models for macropinosome formation there would be distinguishing characteristics depending on the sealing method. Either we would find linear extensions where the distal tips would collide to circularize and seal, or there would be filopodia- like spikes that form, the membrane would fill in the space between before twisting to seal. Surprisingly, we found that approximately \(88\%\) of the quantified macropinosomes formed when the leading edge of extending ruffles collided along the sides of nearby membrane surface or ruffles that typically only involved a small portion of the second ruffle, so long as the ruffle area had elevated mSc- AtkPH (Fig. 4). The remaining \(12\%\) of events we observed were classified as tidal- wave like structures in which a mostly isolated planar ruffle extended from the cell surface where the entire ruffle was rich in mSc- AktPH, the ruffle gained curvature in a rolling fashion, and resulted in fusing with the plasma membrane(Supplementary Movie 5). However, given that the entire ruffle area was rich in mSc- AktPH, these types of formation follow the same underlying mechanism as collisions with adjacent membrane extensions. Frequently, a single ruffle area produced multiple macropinosomes and were the result of similar but smaller ruffle extensions that quickly fused near the base of larger ruffles (Fig. 4). Within the ruffle, forming macropinosomes recruited mSc- AktPH near the base of the ruffle as they transitioned into a spherical shape prior to detaching from the plasma membrane and moving independently (Fig. 4, Supplementary Movies 3,7). We hypothesized that regions with highly concentrated mSc- AktPH localization would correlate with increased macropinocytic activity. Indeed, this phenomenon was observed in four of the eleven constitutive cells (Fig. 5). These ruffling regions resulted in the formation of many macropinosomes through the intersection of multiple ruffles that were nearly indistinguishable from one another and only became apparent through the PI3K post closure activity (Fig. 5d,e). Therefore, the elevated PI3K activity created a microenvironment suited for the rapid fusion of PI3K- primed ruffles into macropinosomes of various sizes within short timeframes (Supplementary Movies 8,9). We speculated that other signaling that activates PI3K activity may stimulate distinct ruffling morphologies and rates of macropinocytosis.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 685, 771, 702]]<|/det|>
+## CSF-1 growth factor signaling promotes extensive circular ruffling and macropinocytosis  
+
+<|ref|>text<|/ref|><|det|>[[112, 714, 884, 908]]<|/det|>
+CSF- 1 is an essential macrophage growth factor that stimulates macropinocytosis at levels controlled by the concentration of the CSF- 1 signal<sup>9</sup>. Macrophages starved of CSF- 1 for 24 hrs and then acutely stimulated produced expansive circular ruffles that initiated from the distal cellular margins coincident with cellular spreading (Fig. 6). LLSM imaging revealed a circular ruffle that initiated at the edge of the cell with a height of approximately \(2 \mu m\) above the dorsal surface and constricted to a central location in a coordinated manner (Fig. 6a). A striking feature of this ruffle was the confinement of mSc- AktPH within the limiting edge of the ruffle. As the circular ruffle constricted toward the center of the cell, mSc- AktPH was highly concentrated within and was nearly undetectable in the rest of the cell (Fig. 6b, Supplementary Movie 10), and macropinosomes formed during the constriction process without additional membrane protrusions being generated. This is consistent with PI3K activity priming membranes for fusion through
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 90, 883, 146]]<|/det|>
+a purse- string closure to generate macro pinosomes (Fig. 6c, Supplementary Movies 10,11). Thus, CSF- 1 initiated long range signaling and PI3K activation resulting in coordinated movements of the cytoskeleton throughout the cell.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 159, 722, 177]]<|/det|>
+## LPS stimulates regional ruffling and generates large numbers of macro pinosomes  
+
+<|ref|>text<|/ref|><|det|>[[112, 187, 884, 420]]<|/det|>
+The bacterial cell wall component lipopolysaccharide (LPS) activates PI3K through the Akt pathway<sup>28</sup>, and acutely stimulates macro pinocytosis<sup>3</sup>. Recently, LPS stimulation was used to characterize a novel formation mechanism involving actin tentacles supporting membrane veils which cross to create a macro pinosome<sup>12</sup>. When FLMs were exposed to LPS, regional patches of membrane ruffling were generated that migrated around the dorsal surface of the macrophage (Fig. 7a, Supplementary Movie 12) in a manner distinct from the dorsal surface ruffle generated by CSF- 1 stimulated cells (Fig. 6); however, this process was similar in appearance to constitutive macro pinocytosis (Fig. 7c, Supplementary Movie 13). The patches of ruffles in LPS cells generated many small ruffles, had elevated PI3K activity and were more efficient at forming macro pinosomes as compared to control (Fig 7d). Thus, the nature of macro pinosome formation is coordinated over different length scales with differing intensities depending on the nature of the activating stimulus. Regardless, PI3K activity delineates ruffles and regions of the plasma membrane where macro pinosomes form.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 433, 412, 457]]<|/det|>
+## Discussion & Conclusion  
+
+<|ref|>text<|/ref|><|det|>[[112, 472, 884, 902]]<|/det|>
+Here, we have utilized lattice light sheet microscopy to develop a new level understanding of the structural dynamics and PI3K signaling underpinning macro pinocytosis. Until recently, dynamic processes such as macro pinocytosis were characterized using optical techniques with poor axial resolution and elevated phototoxicity leading to subsampling the spatial and temporal dynamics and requiring inference from multiple methods such as scanning electron microscopy of fixed cells to address the formation mechanism of macro pinosomes. Lightsheet microscopy overcomes these obstacles and enables us to record, with sufficient spatial and temporal resolution, the complete evolution of membrane ruffles and the mechanism by which these ruffles form into macro pinosomes, while also measuring the redistribution of signaling molecules controlling these processes. We have shown that macro pinosomes form through several possible morphologies; however, in each case PI3K activity primes ruffles for fusion with adjacent primed membranes to form macro pinosomes. Indeed, in areas with elevated PI3K activity, either naturally or through external stimulation, there was an increased ruffle density that lead to an increased probability of primed ruffles colliding to form macro pinosomes. This model of macro pinosome formation relying on PI3K priming rather than a defined geometry also explains the variation in diameter that is a hallmark of macro pinosomes. The improved sensitivity of LLSM enabled detection of PI3K activity at the earliest stages of ruffle development that grows in curving ruffles and peaks around macro pinosomes post closure. Our data are consistent with a mechanism driven by the geometry of curving ruffles that confines PI3K, thereby amplifying the signal, which in turn activates yet unknown fusogenic protein(s) localized to the ruffle edges mediating sealing during membrane collisions. This conclusion is supported by the observations that inhibition of PI3K activity with LY29004 did not substantially alter membrane ruffling structure, curvature or collisions, but completely inhibited sealing; even when fully spherical morphologies were observed that then collapsed back into the cell surface.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 884, 303]]<|/det|>
+The model suggested in this work contrasts with a recent report in LPS- activated RAW264.7 cells that described F- actin- rich filopodia- like "tentpoles" protruding from the surface that twisted to constrict veils of membrane that then became macropinosomes<sup>12</sup>. Using a membrane probe and the same microscope, we should have recapitulated the filapodial- like protrusions in the initial extension- phase that then would have a concave appearance connecting the tips. Only rarely when visualizing single slices of ruffling membrane, did we observe filapodial- like extensions connecting at the distal margins (Supplementary Figure 1b). However, the isosurface and volumetric renderings of the same macropinocytic events were not filapodial- like but were, in fact, multiple linear ruffle sheets that protruded from the cell surface and intersected to form a macropinosome (Supplementary Figure 1c). Additionally, these ruffles protruding from the cell were convex as they emerged and formed which fits a model where actin polymerization occurs throughout the ruffle driving the extension forward.  
+
+<|ref|>text<|/ref|><|det|>[[112, 314, 884, 430]]<|/det|>
+Taken together, our experiments indicate a mechanism for macropinosome formation requiring amplified PI3K signaling within ruffles that become macropinosomes and contributes primarily to priming membranes for sealing. The membrane probe and visualizations we have described set the foundation to enable rigorous testing of this mechanism using specific inhibitors of phosphatidylinositol- modifying enzymes and sensors that specifically bind to the various products to determine how each step is regulated during macropinocytosis.  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 443, 371, 464]]<|/det|>
+## Methods and Materials  
+
+<|ref|>text<|/ref|><|det|>[[112, 479, 884, 595]]<|/det|>
+Plasmids. pCMV- VSV- G was a gift from Bob Weinberg (Addgene plasmid #8454; http://n2t.net/addgene:8454; RRID:Addgene_8454)<sup>29</sup>. psPAX2 was a gift from Didier Trono (Addgene plasmid #12260; http://n2t.net/ addgene:12260; RRID:Addgene_12260). pLJM1- EGFP was a gift from David Sabatini (Addgene plasmid #19319; http://n2t.net/addgene:19319; RRID:Addgene_19319)<sup>30</sup>. Lck- mScarlet- l was a gift from Dorus Gadella (Addgene plasmid #98821; http://n2t.net/addgene:98821; RRID:Addgene_98821)<sup>31</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[112, 606, 883, 722]]<|/det|>
+Construction of the membrane and AktPH probes. The membrane probe was constructed by combining the membrane localization motif (MGCVCSSNPE) from Lck<sup>31</sup> in frame with mNeonGreen in the pLJM1 backbone containing the puromycin resistance gene. The mSc- AktPH probe was constructed by using mScarlet- l in frame with the pleckstrin homology domain from Akt in the pLJM1 backbone, modified to contain the blasticidin resistance gene. Sequences were codon optimized for expression in mouse cells, synthesized, and sequence verified by GenScript (Piscataway, NJ).  
+
+<|ref|>text<|/ref|><|det|>[[112, 733, 883, 828]]<|/det|>
+Viral transduction. Sequence- verified plasmids containing genes encoding FP- chimeras, plus the packaging plasmids pVSV- G and psPAX2 were transfected into NIH 293T cells for packaging using linear 25 kDa polyethyleneimine (PEI) as a transfection reagent. NIH 293T- cell culture supernatant containing lentiviral particles was collected and added to FLM treated with cyclosporin A (10 \(\mu \mathrm{M}\) ) for two days. Transduced FLMs were selected with puromycin and blasticidin (10 \(\mu \mathrm{g} \cdot \mathrm{ml}^{- 1}\) each).  
+
+<|ref|>text<|/ref|><|det|>[[112, 840, 883, 897]]<|/det|>
+Macrophage culture media. DMEM/F- 12 (Gibco) supplemented with 20% Heat- inactivated FBS (R&D Systems), 1% Penicillin/Streptomycin (Gibco), 50 ng·ml<sup>- 1</sup> mCSF- 1 (BioLegend), and 5 μg·ml<sup>- 1</sup> plasmacin (Invivogen) maintained at 37°C with 7.5% CO<sub>2</sub>.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 884, 203]]<|/det|>
+PIP3 inhibition (LY294002). Coverslips were prepared as described previously and were moved to a well of media containing \(0.16\mu M\) LY294002 and allowed to incubate for 30 minutes at \(37^{\circ}C\) and \(7.5\% \mathrm{CO}_2\) prior to imaging. The coverslip was then transferred to the LLSM bath containing Imaging Media, \(1.7 \mathrm{mM}\) Glucose, and \(0.16 \mu M\) LY294002. The coverslip was explored using the LLS software and three cells were chosen per coverslip that provided the best visual representation of the population. Each cell was imaged under the same parameters as described above.  
+
+<|ref|>text<|/ref|><|det|>[[112, 216, 884, 331]]<|/det|>
+CSF- 1 stimulation. The coverslip was starved overnight in DMEM/F- 12 with \(10\%\) FBS and \(1\%\) pen/strep. After 24hrs the coverslip was moved to the LLS bath containing \(7mL\) L- 15 imaging media, and \(1.7mM\) Glucose. The coverslip was explored using the LLS software and three cell targets were chosen and imaged for a pre- stimulation comparison. Immediately after imaging the third cell, CSF- 1 was introduced at \(50 \mathrm{ng}\) \(\cdot \mathrm{mL}^{- 1}\) to the \(7 \mathrm{mL}\) bath. The third cell was once again imaged \(< 1 \mathrm{min}\) after stimulation and each additional cell was imaged in reverse order (Imaging order 1- 2- 3- 3- 2- 1).  
+
+<|ref|>text<|/ref|><|det|>[[112, 344, 883, 400]]<|/det|>
+Lipopolysaccharide stimulation. FLMs were stimulated with \(100 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) Lipopolysaccharides from Salmonella enterica serotype enteritidis (Sigma) for \(24 \mathrm{h}\) in culture media before being transferred to imaging media containing \(100 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) for LLSM experiments.  
+
+<|ref|>text<|/ref|><|det|>[[112, 411, 884, 604]]<|/det|>
+Macrophage isolation. Fetal liver macrophage (FLM) cell cultures were generated as described previously<sup>32,33</sup>. Livers were isolated from gestational day 15- 19 mouse fetuses from C57BL/6J mice (The Jackson Laboratory, Bar Harbor, ME) in accordance with South Dakota State University Institutional Animal Use and Care Committee. Liver tissue was mechanically dissociated using sterile fine- pointed forceps and a single- cell suspension was created by passing the tissue through a \(1 \mathrm{ml}\) pipette tip<sup>32</sup>. Cells were plated on non- tissue culture treated dishes and kept in growth and differentiation medium containing the following: \(20\%\) heat- inactivated fetal bovine serum; \(30\%\) L- cell supernatant, a source of M- CSF<sup>34,35</sup>; and \(50\%\) Dulbecco's modified growth medium containing \(4.5 \mathrm{g} \cdot \mathrm{L}^{- 1}\) glucose, \(110 \mathrm{mg} \cdot \mathrm{L}^{- 1}\) sodium pyruvate, \(584 \mathrm{mg} \cdot \mathrm{L}^{- 1}\) L- glutamine, \(1 \mathrm{IU} \cdot \mathrm{mL}^{- 1}\) penicillin and \(100 \mu \mathrm{g} \cdot \mathrm{mL}^{- 1}\) streptomycin. FLM were cultured for at least 8 weeks prior to transduction and experiments.  
+
+<|ref|>text<|/ref|><|det|>[[112, 616, 884, 848]]<|/det|>
+Cell Culturing and Coverslip Plating. FLMs were cultured in untreated T- 25 tissue culture flasks using the following culture media: DMEM F- 12 with \(20\%\) FBS, \(1\%\) penicillin/streptomycin, \(50 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) CSF- 1, and 5 \(\mathrm{ng} \cdot \mathrm{mL}^{- 1}\) plasmonic. The cell cultures were split at \(\sim 85\%\) confluence, first by washing the T- 25 flask with 3 mL of PBS (- Ca/- Mg) 2 times. The cells were then lifted from the T- 25 flask using 4 mL of \(4^{\circ}\mathrm{C}\) PBS (- Ca/- Mg, \(+0.98 \mathrm{mM}\) EDTA) with gentle pipet washing for approximately \(10 \mathrm{min}\) . The lifted cells were moved to a \(15 \mathrm{mL}\) centrifuge tube (1 mL of culturing media was added to \(15 \mathrm{mL}\) tube if cells took \(>10 \mathrm{min}\) to lift) and centrifuged at \(200 \times \mathrm{g}\) for 5min. While the cells were being spun down, the T- 25 flask was washed with PBS (- Ca/- Mg), filled with 5mL of culture media, and placed in the \(37^{\circ}\mathrm{C}\) incubator to reach appropriate culture conditions. Once the cells were finished being spun down, the supernatant was removed from the \(15 \mathrm{mL}\) tube and the cells were resuspended in \(1 \mathrm{mL}\) culturing media and counted. The counting was done by mixing \(10 \mu \mathrm{L}\) of suspended cells with \(10 \mu \mathrm{L}\) of trypan blue and placed on a glass slip to be counted using a countess. The FLMs were re- plated in the original T- 25 flask with \(\sim 6 - 7 \times 10^{5}\) cells. The cells were washed
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 884, 265]]<|/det|>
+every 2 days and given fresh media until reaching \(\sim 85\%\) confluence where they would then be split. Cell lines were kept for approximately 2 months before being replaced with early state frozen aliquots. Macrophages were prepared for LLS imaging \(24h\) prior to imaging using 5mm glass coverslips. The coverslips were soaked in \(90 - 100\%\) ethanol and flame cleaned using a butane flame. Approximately 5 flame cleaned coverslips were placed per well of a 12 well plate each containing \(1mL\) of culture media. Cells were added to each well during the cell culture process described above at \(\sim 3\times 10^{5}\) cells to each \(3.5cm^2\) (12- well plate) for imaging. The FLMs incubated on the flame cleaned glass coverslips in culturing media for \(24h\) prior to imaging. The coverslips were transferred to the LLSM bath that was filled with 7 mL of Leibovitz's L- 15 Media (supplemented with \(1.7mM\) glucose) at \(\sim 37^{\circ}C\) .  
+
+<|ref|>text<|/ref|><|det|>[[111, 275, 884, 526]]<|/det|>
+Lattice Light Sheet Microscopy Imaging. The LLSM is a replica of the design described by Chen et al. \(^{36}\) , built under license from HHMI. Volumetric image stacks were generated using dithered square virtual lattices (Outer NA 0.55, Inner NA 0.50, approximately \(30\mu m\) long) and stage scanning with \(0.5\mu m\) step sizes, resulting in \(254nm\) deskewed z- steps. Excitation laser powers used were \(18\mu W\) (488 nm) and \(22\mu W\) (561 nm), measured at the back aperture of the excitation objective. The emission filter cube (DFM1, Thorlabs) comprised a quadband notch filter NF03- 405/488/561/635 (Semrock), longpass dichroic mirror Di02- R561 (Semrock), shortpass filter 550SP (Omega) on the reflected path, and longpass filter BLP01- 561R (Semrock) on the transmitted path; the resulting fluorescence was imaged onto a pair of ORCA- Flash4.0 v2 sCMOS cameras (Hamamatsu). The camera on the reflected image path was mounted on a manual x- y- z translation stage (Newport 462- XYZ stage, Thorlabs), and the images were registered using \(0.1\mu m\) Fluoresbrite YG microspheres (Polysciences). The image capturing rates varied between 5- 10 seconds per volume using 8- 12 ms planar exposures depending on the brightness of the cell and imaging region.  
+
+<|ref|>text<|/ref|><|det|>[[111, 528, 884, 740]]<|/det|>
+Scanning Electron Microscopy. BMDM were plated onto \(13mm\) diameter, circular glass coverslips and cultured overnight in RPMI with \(10\%\) FBS (R10). To stimulate macropinocytosis, BMDM were incubated \(30min\) in phosphate- buffered saline (PBS), then \(15min\) in PBS containing \(10nM\) CSF- 1. Cells were fixed in \(2\%\) glutaraldehyde, \(0.1M\) caccodylate buffer, \(\mathsf{pH}7.4\) \(6.8\%\) sucrose, \(60min\) at \(37^{\circ}C\) Fixative was replaced with a second fixative consisting of \(1\%\) \(\mathrm{OsO_4}\) in \(0.1M\) caccodylate buffer, \(\mathsf{pH}7.4\) , for \(60min\) at \(23^{\circ}C\) . The second fixative was replaced with \(1\%\) tannic acid in caccodylate buffer, \(30min\) at \(4^{\circ}C\) , the rinsed with 3 changes of \(0.1M\) caccodylate buffer. Coverslips were transferred through successive changes of acetone- water mixtures, progressively increasing acetone concentrations to \(100\%\) before a final incubation in hydroxymethylsilazidane (HMDS, EM Sciences). HMDS was removed and coverslips were dried for 2 days. Coverslips were shadowed with gold and observed on a Amray 1900 field emission scanning electron microscope.  
+
+<|ref|>text<|/ref|><|det|>[[111, 742, 884, 896]]<|/det|>
+Deconvolution and Post Processing. The raw volumes acquired from the LLSM were deskewed, deconvolved and rotated to coverslip coordinates in \(\mathsf{LLSp}\mathsf{y}^{37}\) . We applied a fixed background subtraction based on an average dark current image, 10 iterations of Lucy- Richardson deconvolution with experimentally measured point spread functions for each excitation followed by rotation to coverslip coordinates, and cropping to the region of interest surrounding the volume for visualization. We optimized the illumination intensity such that less than \(10\%\) photobleaching occurred during the experiment. The fully processed data was opened as a volume map series in UCSF ChimeraX and utilized isosurface, mesh, 3D volumetric intensities, and orthogonal planes renderings to exam the data. The
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 884, 282]]<|/det|>
+surface and mesh options utilize a three- dimensional analog of an isoline called an isosurface that represents points in volume space as constant values which were used to display the membrane probe. The isosurface provides a defined surface for the membrane probe resulting in shadowing providing visual depth to the three- dimensional data. The mesh rendering offers a similar surface definition while also providing an option to include the internal fluorescent mSc- AktPH signal. We used a volumetric intensity projection to visually display the localization of mSc- AktPH throughout the cell. At each pixel, the most intense color value underlying the pixel along the line of sight is displayed (ChimeraX User Guide). The final technique used to display the LLSM data was through orthogonal planes. This generates 2D planes each \(0.128\mu m\) thick for the entire volume in xy, yz, and xz. Multiple methods were overlapped and shown side by side to effectively represent the data and labeled within each figure.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 296, 256, 311]]<|/det|>
+## Acknowledgments  
+
+<|ref|>text<|/ref|><|det|>[[113, 314, 884, 418]]<|/det|>
+Funding: Funding provided by the South Dakota Board of Regents through BioSNTR and the SDBOR FY20 collaborative research award "IMAGEN: Biomaterials in South Dakota". Additional funding provided by the National Science Foundation through research award CNS- 1626579 "MRI: Development of a Scalable High- Performance Computing System in Support of the Lattice Light- sheet Microscope for Real- time Three- dimensional Imaging of Living Cells". J.A.S. was supported by NIH grant R35 GM131720. B.L.S. is supported by the Chan Zuckerberg Initiative through the Imaging Scientist program.  
+
+<|ref|>text<|/ref|><|det|>[[112, 430, 883, 500]]<|/det|>
+Visualization: The data visualization and analyses were performed using UCSF ChimeraX, developed by the Resource for Biocomputing, Visualization, and Informatics at the University of California, San Francisco, with support from National Institutes of Health R01- GM129325 and the Office of Cyber Infrastructure and Computational Biology, National Institute of Allergy and Infectious Diseases.  
+
+<|ref|>text<|/ref|><|det|>[[112, 512, 883, 565]]<|/det|>
+LLSM: The Lattice Light Sheet Microscope referenced in this research was developed under license from Howard Hughes Medical Institute, Janelia Farms Research Campus ("Bessel Beam" patent applications 13/160,492 and 13/844,405).  
+
+<|ref|>text<|/ref|><|det|>[[111, 577, 883, 682]]<|/det|>
+Author Contributions: S.E.Q. acquired and analyzed LLSM data and co- wrote the manuscript. L.H generated FLM cell lines used in experiments. J.G.K. Designed plasmid constructs and generated FLM cell lines. J.A.S. Performed SEM experiments and edited the manuscript. S.S. provided supervision and edited the manuscript. A.D.H. co- wrote the manuscript. R.B.A. built the LLSM and analysis cluster and provided supervision. N.W.T. designed experiments and co- wrote the manuscript. B.L.S. designed and performed initial experiments, assisted with data analysis and co- wrote the manuscript.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 87, 880, 630]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 630, 883, 770]]<|/det|>
+<center>Figure 1. 3D visualization of macrophages allows insight into membrane structure and phosphatidylinositol dynamics during macropinocytosis. a) Isosurfaces show the plasma membrane of a live cell that is actively macropinocytosis. Region \(68 \times 72 \times 25 \mu m\) (x, y, z). b) SEM image of a macrophage acutely stimulated with CSF-1 shows high-resolution fixed cells. Scale bar is 10 \(\mu m\) . c) Volumetric intensities show specific local fluorescence (left->right) volumetric membrane (green), dual volumetric membrane and mSc-AktPH, volumetric mSc-AktPH (magenta). Volumetric renderings provide a method to visualize the transient fluorescent intensities throughout the volume of the cell. Region is \(68 \times 72 \times 25 \mu m\) . d) Combinations of visualization techniques such as Isosurface (left) displayed alongside orthogonal planes (right) further clarify how each plane is chosen to show internal intensities. Region of \(29 \times 30 \times 19 \mu m\) . e) Mesh rendering of the mNG-membrane probe along with volumetric mSc-AktPH provides a representation of the plasma membrane structure as well as underlying fluorescence. The white arrows indicate the post closure recruitment of mSc-AktPH. Region \(13 \times 14 \times 7 \mu m\) . Different rendering methods provide insight into cellular characteristics such as structure, depth, and fluorescent intensity and provide a foundation for visualizing localization of mSc-AktPH to the constantly changing plasma membrane during macropinocytosis. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 88, 878, 740]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 744, 883, 833]]<|/det|>
+<center>Figure 2. Early PI3K activity leads to amplification of \(\mathsf{PIP}_3 / \mathsf{PIP}_2\) in developing ruffles, macropinosome formation, and post closure recruitment. a) Top view of an mNG-mem isosurface rendering provides depth for 3D visualization of ruffle extension. Dual-color volumetric intensity display comparing the recruitment of mSc-AktPH to early and expanding ruffles as well as sealed macropinosomes (Region 21x19um). b) Intensity line-scan of the volumetric mNG-Mem and mSc-AktPH shows their relative intensities for extending membrane ruffles, as well as recruitment around a sealed macropinosome. c) Side view of the isosurface mesh plasma membrane and volumetric mSc-AktPH (Magenta Hot color scale) from a shows that the early stages of ruffle development is filled with mSc-AktPH and the resulting macropinosome (white arrow) receives a final intense mSc-AktPH recruitment around the formed macropinosome at the bottom of the ruffle. Region of 21x19x15um. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 88, 875, 712]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 714, 883, 853]]<|/det|>
+<center>Figure 3. PI3K activity is required for membrane sealing and separation from PM/internalization of a complete macropinosome but not membrane ruffling a) Isosurface rendering of mNG-mem for an untreated macrophage during a successful macropinocytosis event where the sheet curls back toward the membrane for fusion/sealing. Region 12x13x10 μm b) Volumetric rendering of Sc-AktPH of the untreated cell shows the increase of PI3K activity in the ruffle that creates a macropinosome. 12x13x10 μm c) Mesh and orthogonal planes of mNG-mem show the internal membrane organization of the ruffle and resulting macropinosome. 12x13x10 μm d) Isosurface rendering of an LY294002 treated macrophage provides depth to the attempted closure of a macropinocytic cup. Region 10x12x10 μm. e) Volumetric intensity rendering of Sc-AktPH for an LY294002-treated macrophage shows the diffuse distribution of AktPH and minimal PI3K activity. The cytosolic intensities were co-scaled for the untreated and treated macrophage. Region 10x12x10 μm f) XY-plane for the mNG-mem probe of an LY294002-treated cell during a failed macropinocytosis event. In the surface view, the ruffle appeared to form a macropinosome; however, when overlaid with the plane view is became clear that it failed to fully form into a macropinosome. The ruffle quickly reduced in size and became undistinguishable within the cytosol, while never receiving the post closure increase of PI3K activity. Region 10x12x10 μm. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 90, 875, 500]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 504, 883, 606]]<|/det|>
+<center>Figure 4. Macropinosomes form via PI3K-primed ruffle fusion. a) Dual volumetric intensities of mNG-mem and mSc-AktPH show the intensity of each probe as the rufles and macropinosomes form. The montage shows the earliest stage of the ruffle that extends vertically and forms macropinosomes along the length near the base of the primary ruffle as a result of smaller mSc-AktPH-rich extensions colliding. The white arrow points at the macropinosome forming region further emphasized in the isosurface. Region 9x12x13 um. b) Isosurface rendering of mNG-membrane shows the structure of the extending ruffle and the continued sheet extension after the macropinosomes formed. The white arrow emphasizes the small pocket that closes to form one of the macropinosomes. Region 9x12x13 μm. c) Mesh surface rendering of mNG-mem and volumetric mSc-AktPH shows the internalized macropinosome with the increased localization of mSc-AktPH at the bottom of the ruffle. Region 11x9x12 μm. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[113, 87, 881, 628]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 630, 882, 707]]<|/det|>
+<center>Figure 5. Phosphatidylinositol localization and chaotic ruffling underlie macropinocytosis in complex membrane structures. a) Single time point, full cell surface rendering of chaotic macropinocytosis event. The red box correlates to the same frame in c-d. b) SEM images of a BMDM showing similar highly active ruffling regions c) Isosurface montage shows the chaotic orientation of membrane structure. Region 27x22x16 \(\mu \mathrm{m}\) , 25° tilt. d) Volumetric AktPH (Magenta-Hot) provides a more detailed emphasis on the AktPH activity within the membrane ruffles and highlights the macropinosomes that have formed. Region 27x22x16 \(\mu \mathrm{m}\) with a 25° tilted view. e) Mesh Surface with AktPH (Magenta Hot) shows the AktPH activity as the ruffle develops as well as the increased recruitment around formed macropinosomes at the base of the event. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 880, 555]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 556, 882, 655]]<|/det|>
+<center>Figure 6. Growth factor starvation and stimulation results in the formation of large circular dorsal ruffles that corrals \(\mathsf{PIP}_3 / \mathsf{PIP}_2\) . Macrophages were starved of CSF-1 for \(24~\mathrm{h}\) , imaged for 5 minutes as a baseline, and imaging restarted 1 min after stimulation with \(50~\mathrm{ng}\cdot \mathrm{mL}^{-1}\) CSF-1. Four-frame montages provide a visual display of the large dorsal ruffle that acts as a diffusional barrier that restricts \(\mathsf{PIP}_3 / \mathsf{PIP}_2\) to the inside of the ruffle as it is cleared from the surface. This barrier is likely acting as a signal amplification mechanism stimulating the production of many macropinosomes. a) Isosurface rendering provides crisp surface directionality, b) Surface mesh and volumetric AktPH (magenta-hot), show the restricted probe as the membrane converges c) Volumetric Intensity of both mNG-Membrane and mSc-AktPH show the intensity locations of the membrane ruffle and the restricted AktPH. \(49\times 60\mu \mathrm{m}\) d) Bright field images showing multiple cells responding to stimulation with similar dorsal membrane clearing. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[123, 80, 874, 675]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 679, 883, 792]]<|/det|>
+<center>Figure 7. LPS stimulation increases membrane ruffling and macropinocytosis. Macrophages were pretreated with \(100\mathrm{ng}\cdot \mathrm{ml}^{-1}\) LPS for \(24\mathrm{h}\) prior to imaging. a) Surface rendering of mNG-Mem on an LPS stimulated macrophage provides a surface level understanding of the membrane, exploration, ruffling, and PM structure. b) Dual-color volumetric intensity projections of mNG-Mem and mSc-AktPH for an LPS stimulated cell provided the intensity activity during increased macrophage activity and shows the highly AktPH rich regions of membrane ruffling. Region \(68\times 77\times 21\mu \mathrm{m}\) c) Untreated macrophage losurface showing visibly less exploratory behavior. d) Dual-color volumetric intensity rendering of the untreated macrophage gives insight on the AktPH activity inside of the cell during macropinocytosis and allows for the quantitative comparison of macropinosomes formed between the stimulated and unstimulated cells. Region \(68\times 77\times 21\mu \mathrm{m}\) e) Box plot showing the difference in macropinocytic activity between untreated and LPS treated macrophages. All macropinosomes greater than \(1\mu \mathrm{m}\) were manually counted using a z-projection MIP in Fiji and were distinguished by the post closure spike in mSc-AktPH intensity. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 88, 881, 470]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 471, 882, 546]]<|/det|>
+<center>Supplementary Figure 1 - Constitutive macropinocytosis and the importance of reducing the dimensionality of data. a) Orthoplane (left) and isosurface (right) views of mNG-Membrane show the subsurface macropinosome and the complex structure of the full surface. b) Orthoplane montage of mNG-membrane depicting constitutive planar view of macropinocytosis where two sheets extend from the cell membrane, circularize, and connect to form a macropinosome. c) Isosurface view of mNG-Membrane showing the three spatial dimensions of the ruffle clearly depicting the multiple membrane sheets involved in the macropinocytic event. The red box shows the corresponding montage frames for panel a. </center>  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 572, 410, 590]]<|/det|>
+## Supplementary Movie Legends  
+
+<|ref|>text<|/ref|><|det|>[[115, 592, 882, 641]]<|/det|>
+Video 1. Corresponds to Fig. 1a, c. Isosurface and volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) provides different methods of visualizing the formation (surface) and trafficking of macropinosomes and mSc- AktPH accumulation (volume). Movie timestamps highlight the following events: AktPH enriched ruffle development (02:42), newly formed macropinosomes (06:29; 08:51; 10:58), and post closure AktPH recruitment (11:19). Frame rate of \(\sim 7s\) and each region is \(68 \times 72 \times 25 \mu m\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 641, 882, 690]]<|/det|>
+Video 2. Corresponds to Fig. 1d. Isosurface rendering in conjunction with orthogonal plans moved through a volume provide \(\sim 0.1 \mu m\) thick planes to help visualize the internal and surface activity of mNG- mem and mSc- AktPH including macropinosome closures (02:41; 05:15), membrane rich rruffles (00:00; 02:34; 05:08), previously formed internal macropinosomes (05:15 during scan), and mSc- Akt localization around a closed macropinosome (05:15 during scan). Framerate of \(\sim 7s\) and two subregions each \(29 \times 30 \times 19 \mu m\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 690, 882, 751]]<|/det|>
+Video 3. Corresponds to Fig. 2a. Isosurface and dual- volumetric intensity projection of mNG- mem and mSc- AktPH with a 25 degree tilt shows a variety of formation events. Several early formations occur prior to relaxation of the plasma membrane (01:58), followed by the development of another AktPH rich ruffle (02:48), membrane closure into a macropinosome (03:07 \(\rightarrow 3:13\) ), and finally post closure recruitment of AktPH (03:25). Several macropinosomes form that are indicated by the recruitment of AktPH post closure (3:57; 07:16) and subsequently trafficked toward one another to merge (4:53; 05:18; 05:30; 07:54). Frame rate of \(\sim 6.25s\) and region of \(21 \times 19 \times 15 \mu m\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 751, 882, 787]]<|/det|>
+Video 4. Corresponds to Fig. 2c. Mesh rendering of mNG- membrane and volumetric intensity projection of mSc- AktPH (Magenta- Hot) using a 90 degree tilt. The second play through contains a pause to emphasize the frame shown in Fig 2c and highlight the AktPH rich membrane rruffles (02:48) and the post closure recruitments (03:25; 03:57). Frame rate \(\sim 6.25s\) region of \(21 \times 19 \times 15 \mu m\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 787, 882, 836]]<|/det|>
+Video 5. Corresponds to Fig. 3a, b. Isosurface in conjunction with three volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) display a traditional formation in an untreated cell including the initial ruffle (00:00) that vertically extends and begins to form a tidal wave (01:31) back toward the surface of the cell, with membrane scission (03:24 \(\rightarrow 03:31\) ) and finally the post closure recruitment for the largest macropinosome (08:07). Frame rate of \(7s\) and Region of \(12 \times 13 \times 10 \mu m\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 837, 882, 886]]<|/det|>
+Video 6. Corresponds to Fig. 3d, e. Isosurface with three volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) on an LY294002 treated macrophage showing the initial ruffle with uniform AktPH throughout the cytosol and ruffle (00:00), attempted closure of the ruffle (00:30), continued compression of the attempted macropinosome (00:30 \(\rightarrow 02:27\) ), becoming un- trackable within the cytosol with no AktPH recruitment to the attempted macropinosome. (Tracking done manually using orthogonal planes) Frame rate of 6.15s and Region \(10 \times 12 \times 10 \mu m\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 90, 883, 140]]<|/det|>
+Video 7. Corresponds to Fig. 4a, b. Isosurface alongside three volumetric intensity renderings (Green mNG- Mem; Magenta mSc- AktPH) shows the formation of macrosinosomes at the base of a larger ruffle. Membrane relaxes (00:56), small protrusions form with increased AktPH (01:17), two small ruffles, one in the back and one in the front mergers with the larger ruffle (01:32 -> 01:39) followed by post closure AktPH recruitment (01:53). Frame rate of 7s and region of 11x9x12 μm.  
+
+<|ref|>text<|/ref|><|det|>[[111, 140, 883, 190]]<|/det|>
+Video 8. Corresponds to Fig. 5c. Isosurface and dual- volumetric intensity projection of mNG- membrane and mSc- AktPH showing a smooth and relaxed membrane (00:00). A single macrosinosome forms (05:06) followed by a large increased in membrane activity (06:35) resulting in a significant number of macrosinosomes, indicated by the post closure AktPH recruitment, that turns into the chaotic membrane structure (06:35 -> 13:18). Frame rate of 8s and region size of 27x22x16 μm.  
+
+<|ref|>text<|/ref|><|det|>[[111, 190, 883, 239]]<|/det|>
+Video 9. Corresponds to Fig. 5e. Side view of mNG- membrane isosurface and mesh membrane with volumetric AktPH (Magenta Hot) shows the continued AktPH localization within the extending membrane structure (06:35). Utilizing the Magenta- Hot LUT regions displaying in white represent the increase in AktPH post macrosinosome closure signifying a formed macrosinosome (05:55; 06:59; 08:12; 11:50). Frame rate of 8s and region size of 27x22x16 μm.  
+
+<|ref|>text<|/ref|><|det|>[[111, 239, 883, 300]]<|/det|>
+Video 10. Corresponds to Fig. 6a, b, c. CSF- 1 starved macrophage displayed using mNG- membrane isosurface/mesh/volume and AktPH volumes as magenta- hot under the mesh and Magenta alongside the volume membrane. The macrophage was imaged 07:41 prior to stimulation and reimaged one minute after CSF- 1 stimulation (08:41) providing time to ensure instrument and imaging conditions had not changed. The starved cell ruffled and formed macrosinosomes similar to the conventional cells (00:06; 01:46; 03:26) and upon stimulation (08:41) a large circular dorsal ruffle forms corralling the AktPH to one concentrated spot in the cell (16:22). Frame rate of 6.25s and region size of 49x60 μm.  
+
+<|ref|>text<|/ref|><|det|>[[111, 300, 883, 325]]<|/det|>
+Video 11. Corresponds to Fig. 6d. The brightfield view starts promptly after stimulation showing the majority of macrophages performing the similar dorsal membrane clearing seen in the LLSM imaging.  
+
+<|ref|>text<|/ref|><|det|>[[111, 325, 883, 398]]<|/det|>
+Video 12. Corresponds to Fig. 7a, b. LPS Stimulation. Isosurface of mNG- Mem and dual- color volumetric intensity projects of mNG- Mem and mSc- AktPH showing the activity of an LPS treated cell. Initial imaging starts (00:00) with a cluster of membrane rich in AktPH that goes on to create many macrosinosomes as it expands toward the upper right region of the field of view. The activity changes directions toward the upper left region of the cell and proceeds to move counterclockwise (01:14), over the nucleus and back to the initial location ending at (04:42). Additional macrosinosomes are seen forming on the left region with the increased AktPH flare up post closure (04:42). Finally, several formations occur in the bottom right of the cell (05:05 - 08:18) many of which go on to merge with one another. Framerate of ~7s and Region of 68x77x21 μm.  
+
+<|ref|>text<|/ref|><|det|>[[111, 398, 883, 460]]<|/det|>
+Video 13. Corresponds to Fig. 7c, d. Non- treated control. Isosurface of mNG- Mem and dual- color volumetric intensity projects of mNG- Mem and mSc- AktPH showing the imaging of a nontreated cell (10:47). Two AktPH rich regions of membrane ruffling are seen in the bottom right of the cell (02:17) that form several small macrosinosomes, indicated by a spike in AktPH around the formed macrosinosome. The cell shows activity that is representative of the untreated experiments including macrosinosome formations, exploration, and overall membrane ruffling. Framerate of ~6.5s and Region of 68x77x21 μm.  
+
+<|ref|>sub_title<|/ref|><|det|>[[111, 480, 238, 500]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[111, 506, 884, 860]]<|/det|>
+1 Freeman, S. A. et al. Lipid- gated monovalent ion fluxes regulate endocytic traffic and support immune surveillance. Science 367, 301- 305, doi:10.1126/science.aaw9544 (2020).  
+2 Bohdanowicz, M. & Grinstein, S. Role of phospholipids in endocytosis, phagocytosis, and macropinocytosis. Physiol Rev 93, 69- 106, doi:10.1152/physrev.00002.2012 (2013).  
+3 Doodnath, S. A., Grinstein, S. & Maxson, M. E. Constitutive and stimulated macropinocytosis in macrophages: roles in immunity and in the pathogenesis of atherosclerosis. Philos Trans R Soc Lond B Biol Sci 374, 20180147, doi:10.1098/rstb.2018.0147 (2019).  
+4 Kerr, M. C. & Teasdale, R. D. Defining macropinocytosis. Traffic 10, 364- 371, doi:10.1111/j.1600- 0854.2009.00878. x (2009).  
+5 Redka, D. S., Gutschow, M., Grinstein, S. & Canton, J. Differential ability of proinflammatory and anti- inflammatory macrophages to perform macropinocytosis. Mol Biol Cell 29, 53- 65, doi:10.1091/mbc.E17- 06- 0419 (2018).  
+6 Egami, Y., Taguchi, T., Maekawa, M., Arai, H. & Araki, N. Small GTPases and phosphoinositides in the regulatory mechanisms of macropinosome formation and maturation. Front Physiol 5, 374, doi:10.3389/fphys.2014.00374 (2014).  
+7 Swanson, J. A. & Yoshida, S. Macropinosomes as units of signal transduction. Philos Trans R Soc Lond B Biol Sci 374, 20180157, doi:10.1098/rstb.2018.0157 (2019).  
+8 Yoshida, S. et al. Differential signaling during macropinocytosis in response to M- CSF and PMA in macrophages. Front Physiol 6, 8, doi:10.3389/fphys.2015.00008 (2015).  
+9 Lou, J., Low- Nam, S. T., Kerkvliet, J. G. & Hoppe, A. D. Delivery of CSF- 1R to the lumen of macropinosomes promotes its destruction in macrophages. J Cell Sci 127, 5228- 5239, doi:10.1242/jcs.154393 (2014).  
+10 Bloomfield, G. & Kay, R. R. Uses and abuses of macropinocytosis. J Cell Sci 129, 2697- 2705, doi:10.1242/jcs.176149 (2016).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[55, 90, 886, 893]]<|/det|>
+516 11 Pacitto, R., Gaeta, I., Swanson, J. A. & Yoshida, S. CXCL12- induced macropinocytosis modulates two distinct 517 pathways to activate mTORC1 in macrophages. J Leukoc Biol 101, 683- 692, doi:10.1189/jlb.2A0316- 141RR 518 (2017). 519 12 Condon, N. D. et al. Macropinosome formation by tent pole ruffling in macrophages. J Cell Biol 217, 3873- 520 3885, doi:10.1083/jcb.201804137 (2018). 521 13 Swanson, J. A. Shaping cups into phagosomes and macropinosomes. Nat Rev Mol Cell Biol 9, 639- 649, 522 doi:10.1038/nrm2447 (2008). 523 14 Bohdanowicz, M. et al. Phosphatidic acid is required for the constitutive ruffling and macropinocytosis of 524 phagocytes. Mol Biol Cell 24, 1700- 1712, S1701- 1707, doi:10.1091/mbc.E12- 11- 0789 (2013). 525 15 Botelho, R. J. et al. Localized biphasic changes in phosphatidylinositol- 4,5- bisphosphate at sites of 526 phagocytosis. Journal of Cell Biology 151, 1353- 1367, doi:DOI 10.1083/jcb.151.7.1353 (2000). 527 16 Freeman, S. A. & Grinstein, S. Phagocytosis: receptors, signal integration, and the cytoskeleton. Immunol 528 Rev 262, 193- 215, doi:10.1111/imr.12212 (2014). 529 17 Swanson, J. A. & King, J. S. The breadth of macropinocytosis research. Philos Trans R Soc Lond B Biol Sci 374, 530 20180146, doi:10.1098/rstb.2018.0146 (2019). 531 18 King, J. S. & Kay, R. R. The origins and evolution of macropinocytosis. Philos Trans R Soc Lond B Biol Sci 374, 532 20180158, doi:10.1098/rstb.2018.0158 (2019). 533 19 Veltman, D. M. et al. A plasma membrane template for macropinocytic cups. Elife 5, 534 doi:10.7554/eLife.20085 (2016). 535 20 Maekawa, M. et al. Sequential breakdown of 3- phosphorylated phosphoinositides is essential for the 536 completion of macropinocytosis. Proc Natl Acad Sci U S A 111, E978- 987, doi:10.1073/pnas.1311029111 537 (2014). 538 21 Araki, N., Egami, Y., Watanabe, Y. & Hatae, T. Phosphoinositide metabolism during membrane ruffling and 539 macropinosome formation in EGF- stimulated A431 cells. Exp Cell Res 313, 1496- 1507, 540 doi:10.1016/j.yexcr.2007.02.012 (2007). 541 22 Yoshida, S., Hoppe, A. D., Araki, N. & Swanson, J. A. Sequential signaling in plasma- membrane domains 542 during macropinosome formation in macrophages. J Cell Sci 122, 3250- 3261, doi:10.1242/jcs.053207 543 (2009). 544 23 Welliver, T. P. & Swanson, J. A. A growth factor signaling cascade confined to circular ruffles in macrophages. 545 Biol Open 1, 754- 760, doi:10.1242/bio.20121784 (2012). 546 Araki, N., Johnson, M. T. & Swanson, J. A. A role for phosphoinositide 3- kinase in the completion of 547 macropinocytosis and phagocytosis by macrophages. J Cell Biol 135, 1249- 1260, 548 doi:10.1083/jcb.135.5.1249 (1996). 549 25 Buckley, C. M. & King, J. S. Drinking problems: mechanisms of macropinosome formation and maturation. 550 Febs Journal 284, 3778- 3790, doi:10.1111/febs.14115 (2017). 551 26 Gao, L., Shao, L., Chen, B. C. & Betzig, E. 3D live fluorescence imaging of cellular dynamics using Bessel beam 552 plane illumination microscopy. Nat Protoc 9, 1083- 1101, doi:10.1038/nprot.2014.087 (2014). 553 27 Goddard, T. D. et al. UCSF ChimeraX: Meeting modern challenges in visualization and analysis. Protein Sci 554 27, 14- 25, doi:10.1002/pro.3235 (2018). 555 28 Luyendyk, J. P. et al. Genetic analysis of the role of the PI3K- Akt pathway in lipopolysaccharide- induced 556 cytokine and tissue factor gene expression in monocytes/macrophages. J Immunol 180, 4218- 4226, doi:DOI 557 10.4049/jimmunol.180.6.4218 (2008). 558 29 Stewart, S. A. et al. Lentivirus- delivered stable gene silencing by RNAi in primary cells. RNA 9, 493- 501, 559 doi:10.1261/rna.2192803 (2003). 560 30 Sancak, Y. et al. The Rag GTPases bind raptor and mediate amino acid signaling to mTORC1. Science 320, 561 1496- 1501, doi:10.1126/science.1157535 (2008). 562 31 Chertkova, A. O. et al. Robust and Bright Genetically Encoded Fluorescent Markers for Highlighting 563 Structures and Compartments in Mammalian Cells. bioRxiv, 160374, doi:10.1101/160374 (2020). 564 32 Fejer, G. et al. Nontransformed, GM- CSF- dependent macrophage lines are a unique model to study tissue 565 macrophage functions. Proc Natl Acad Sci U S A 110, E2191- 2198, doi:10.1073/pnas.1302877110 (2013). 566 Lebedev M, S. P., Kerkvliet JG, Hoppe AD, Thiex N. Immortal fetal liver macrophages as a new model for 567 studying macrophage function. Molecular Biology of the Cell 27 (2016).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[57, 90, 884, 214]]<|/det|>
+568 34 Stanley, E. R., Cifone, M., Heard, P. M. & Defendi, V. Factors regulating macrophage production and growth: 569 identity of colony-stimulating factor and macrophage growth factor. J Exp Med 143, 631- 647, 570 doi:10.1084/jem.143.3.631 (1976). 571 35 Waheed, A. & Shadduck, R. K. Purification and properties of L cell-derived colony-stimulating factor. J Lab 572 Clin Med 94, 180- 193 (1979). 573 36 Chen, B. C. et al. Lattice light- sheet microscopy: imaging molecules to embryos at high spatiotemporal 574 resolution. Science 346, 1257998, doi:10.1126/science.1257998 (2014). 575 37 Lambert, T. & Shao, L. tlambert03/LLSpy: v0.4.8. doi:http://doi.org/10.5281/zenodo.3554482 (2019).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[45, 45, 143, 70]]<|/det|>
+## Figures  
+
+<|ref|>image<|/ref|><|det|>[[42, 90, 955, 744]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 765, 115, 785]]<|/det|>
+<center>Figure 1 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 807, 940, 942]]<|/det|>
+3D visualization of macrophages allows insight into membrane structure and phosphatidylinositol dynamics during macropinocytosis. a) Isosurfaces show the plasma membrane of a live cell that is actively macropinocytosis. Region \(68 \times 72 \times 25 \mu \mathrm{m}\) (x, y, z). b) SEM image of a macrophage acutely stimulated with CSF- 1 shows high- resolution fixed cells. Scale bar is \(10 \mu \mathrm{m}\). c) Volumetric intensities show specific local fluorescence (left- right) volumetric membrane (green), dual volumetric membrane and mSc- AktPH, volumetric mSc- AktPH (magenta). Volumetric renderings provide a method to visualize
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 45, 960, 247]]<|/det|>
+the transient fluorescent intensities throughout the volume of the cell. Region is \(68 \times 72 \times 25 \mu m\) . d) Combinations of visualization techniques such as Isosurface (left) displayed alongside orthogonal planes (right) further clarify how each 360 plane is chosen to show internal intensities. Region of \(29 \times 30 \times 19 \mu m\) . e) Mesh rendering of the mNG- membrane probe along with volumetric mSc- AktPH provides a representation of the plasma membrane structure as well as underlying fluorescence. The white arrows indicate the post closure recruitment of mSc- AktPH. Region \(13 \times 14 \times 7 \mu m\) . Different rendering methods provide insight into cellular characteristics such as structure, depth, and fluorescent intensity and provide a foundation for visualizing localization of mSc- AktPH to the constantly changing plasma membrane during macropinocytosis.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[45, 44, 900, 787]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 802, 118, 821]]<|/det|>
+<center>Figure 2 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 841, 936, 955]]<|/det|>
+Early PI3K activity leads to amplification of PIP3/PIP2 in developing ruffles, macropinosome formation, and post closure recruitment. a) Top view of an mNG- mem isosurface rendering provides depth for 3D visualization of ruffle extension. Dual- color volumetric intensity display comparing the recruitment of mSc- AktPH to early and expanding ruffles as well as sealed macropinosomes (Region 21x19um). b) Intensity line- scan of the volumetric mNG- Mem and mSc- AktPH shows their relative intensities for
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 46, 945, 156]]<|/det|>
+extending membrane ruffles, as well as recruitment around a sealed macropinosome. c) Side view of the isosurface mesh plasma membrane and volumetric mSc-AktPH (Magenta Hot color scale) from a shows that the early stages of ruffle development is filled with mSc-AktPH and the resulting macropinosome (white arrow) receives a final intense mSc-AktPH recruitment around the formed macropinosome at the bottom of the ruffle. Region of 21x19x15um.  
+
+<|ref|>image<|/ref|><|det|>[[48, 152, 930, 896]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 914, 116, 932]]<|/det|>
+<center>Figure 3 </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 45, 945, 384]]<|/det|>
+<p>PI3K activity is required for membrane sealing and separation from PM/internalization of a complete macropinosome but not membrane ruffling a) Isosurface rendering of mNG-mem for an untreated macrophage during a successful macropinocytosis event where the sheet curls back toward the membrane for fusion/sealing. Region 12x13x10 &mu;m b) Volumetric rendering of Sc-AktPH of the untreated cell shows the increase of PI3K activity in the ruffle that creates a macropinosome. 12x13x10 &mu;m c) Mesh and orthogonal planes of mNG-mem show the internal membrane organization of the ruffle and resulting macropinosome. 12x13x10 &mu;m d) Isosurface rendering of an LY294002 treated 3macrophage provides depth to the attempted closure of a macropinocytic cup. Region 10x12x10 &mu;m. e) Volumetric intensity rendering of Sc-AktPH for an LY294002-treated macrophage shows the diffuse distribution of AktPH and minimal PI3K activity. The cytosolic intensities were co-scaled for the untreated and treated macrophage. Region 10x12x10 &mu;m f) XY-plane for the mNG-mem probe of an LY294002-treated cell during a failed macropinocytosis event. In the surface view, the ruffle appeared to form a macropinosome; however, when overlaid with the plane view is became clear that it failed to fully form into a macropinosome. The ruffle quickly reduced in size and became undistinguishable within the cytosol, while never receiving the post closure increase of PI3K activity. Region 10x12x10 &mu;m.</p>  
+
+<|ref|>image<|/ref|><|det|>[[57, 384, 941, 878]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[43, 898, 117, 917]]<|/det|>
+<center>Figure 4 </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 45, 950, 270]]<|/det|>
+Macropinosomes form via PI3K- primed ruffle fusion. a) Dual volumetric intensities of mNG- mem and mSc- AktPH show the intensity of each probe as the rufles and macropinosomes form. The montage shows the earliest stage of the ruffle that extends vertically and forms macropinosomes along the length near the base of the primary ruffle as a result of smaller mSc- AktPH- rich extensions colliding. The white arrow points at the macropinosome forming region further emphasized in the isosurface. Region \(9\times 12\times 13\) um. b) Isosurface rendering of mNG- membrane shows the structure of the extending ruffle and the continued sheet extension after the macropinosomes formed. The white arrow emphasizes the small pocket that closes to form one of the macropinosomes. Region \(9\times 12\times 13\) um. c) Mesh surface rendering of mNG- mem and volumetric mSc- AktPH shows the internalized macropinosome with the increased localization of mSc- AktPH at the bottom of the ruffle. Region \(11\times 9\times 12\) um.  
+
+<|ref|>image<|/ref|><|det|>[[42, 270, 955, 920]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 939, 117, 956]]<|/det|>
+<center>Figure 5 </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 953, 225]]<|/det|>
+Phosphatidylinositol localization and chaotic ruffling underlie macropinocytosis in complex membrane structures. a) Single time point, full cell surface rendering of chaotic macropinocytosis event. The red box correlates to the same frame in c- d. b) SEM images of a BMDM showing similar highly active ruffling regions c) Isosurface montage shows the chaotic orientation of membrane structure. Region \(27 \times 22 \times 16 \mu \mathrm{m}\) , \(25^{\circ}\) tilt. d) Volumetric AktPH (Magenta- Hot) provides a more detailed emphasis on the AktPH activity within the membrane ruffles and highlights the macropinosomes that have formed. Region \(27 \times 22 \times 16 \mu \mathrm{m}\) with a \(25^{\circ}\) tilted view. e) Mesh Surface with AktPH (Magenta Hot) shows the AktPH activity as the ruffle develops as well as the increased recruitment around formed macropinosomes at the base of the event.  
+
+<|ref|>image<|/ref|><|det|>[[44, 226, 951, 780]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 802, 117, 821]]<|/det|>
+<center>Figure 6 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 843, 950, 955]]<|/det|>
+Growth factor starvation and stimulation results in the formation of large circular dorsal ruffles that corrals PIP3/PIP2. Macrophages were starved of CSF- 1 for \(24 \mathrm{~h}\) , imaged for 5 minutes as a baseline, and imaging restarted 1 min after stimulation with \(50 \mathrm{ng} \cdot \mathrm{mL}^{- 1}\) CSF- 1. Four- frame montages provide a visual display of the large dorsal ruffle that acts as a diffusional barrier that restricts PIP3/PIP2 to the inside of the ruffle as it is cleared from the surface. This barrier is likely acting as a signal amplification
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[41, 45, 950, 157]]<|/det|>
+mechanism stimulating the production of many macrosinosomes. a) Isosurface rendering provides crisp surface directionality, b) Surface mesh and volumetric AktPH (magenta- hot), show the restricted probe as the membrane converges c) Volumetric Intensity of both mNG- Membrane and mSc- AktPH show the intensity locations of the membrane ruffle and the restricted AktPH. 49x60 μm d) Bright field images showing multiple cells responding to stimulation with similar dorsal membrane clearing.  
+
+<|ref|>image<|/ref|><|det|>[[52, 150, 944, 870]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 884, 116, 903]]<|/det|>
+<center>Figure 7 </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[40, 44, 951, 316]]<|/det|>
+LPS stimulation increases membrane ruffling and macropinocytosis. Macrophages were pretreated with \(100 \mathrm{ng} \cdot \mathrm{ml} \cdot 1\) LPS for \(24 \mathrm{~h}\) prior to imaging. a) Surface rendering of mNG- Mem on an LPS stimulated macrophage provides a surface level understanding of the membrane, exploration, ruffling, and PM structure. b) Dual- color volumetric intensity projections of mNG- Mem and mSc- AktPH for an LPS stimulated cell provided the intensity activity during increased macrophage activity and shows the highly AktPH rich regions of membrane ruffling. Region \(68 \times 77 \times 21 \mu \mathrm{m}\) c) Untreated macrophage lisosurface showing visibly less exploratory behavior. d) Dual- color volumetric intensity rendering of the untreated macrophage gives insight on the AktPH activity inside of the cell during macropinocytosis and allows for the quantitative comparison of macropinosomes formed between the stimulated and unstimulated cells. Region \(68 \times 77 \times 21 \mu \mathrm{m}\) e) Box plot showing the difference in macropinocytic activity between untreated and LPS treated macrophages. All macropinosomes greater than \(1 \mu \mathrm{m}\) were manually counted using a z- projection MIP in Fiji and were distinguished by the post closure spike in mSc- AktPH intensity.  
+
+<|ref|>sub_title<|/ref|><|det|>[[43, 338, 311, 366]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 388, 765, 410]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[58, 425, 560, 767]]<|/det|>
+- Vid1Fig1ACVolumeSurfaceTimeStamped.avi- Vid2Fig1DXPlaneScanTimeStamped.avi- Vid3Fig2ASurfVolTimeStamped.avi- Vid4Fig2CMeshVolTimeStampedWithPause.avi- Vid5Fig3CostitComparisonTimeStamped.avi- Vid6Fig3LYSurfVolSplitTimeStamped.avi- Vid7Fig4SurfSplitVolumesTimeStamped.avi- Vid8Fig5CDChaosSurfVolsTimeStamped.avi- Vid9Fig5CEChaosSurfMeshVolTimeStamped.avi- Vid10Fig6ABCCSFFullTimeStamped.avi- Vid11Fig6DCSFBrightField.avi- Vid12Fig7ABLPSClusterTimeStamped.avi- Vid13Fig7BLPSUntreatedComparisonTimeStamped.avi
+
+<--- Page Split --->

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+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Time to ice-free conditions: Histograms of time from 2023 equivalent daily SIA minimum until the first ice-free day (top) or ice-free month (bottom), for the earliest (left) and latest (right) members of each model for all scenarios. For models that only had one ensemble member available, the same ensemble member is shown in the earliest and latest histograms. See Extended Data Table 1 for details on which models reach an ice-free day when and which models have only one ensemble member. The same is shown for the first ice-free month in Extended Data Table 2.",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        67,
+        900,
+        549
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Rapid transition from 2023 equivalent state to the first ice-free day: The simulated SIA daily minimum is shown in blue, simulated September monthly mean simulated SIA in cyan, and observed daily minimum SIA based on the CDR SIC data [17] is shown as black line [all in million km²]. Also shown are Rapid Ice Loss Events (RILEs) during September (shaded), defined based on the monthly SIE [24]. A vertical black dashed line indicates the year when the simulated daily SIA minimum was last at or above the 2023 observed daily SIA minimum of 3.39 million km², which is in turn is indicated with a horizontal black dashed line. Vertical dashed grey lines show when ice-free conditions are reached (first for daily, then for monthly, if there is only one both reach ice-free conditions for the first time in the same year). The grey dashed horizontal line shows the 1 million km² ice-free threshold. Extended Data Figure 1 shows that RILEs or near-RILES also occur during August. This illustrates that the transition to first daily ice-free conditions occurs during a RILE in the quick transition simulations.",
+    "footnote": [],
+    "bbox": [
+      [
+        150,
+        87,
+        856,
+        820
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Sea ice area on the way to first daily ice-free conditions: Seasonal cycle of daily SIA [in million \\(\\mathrm{km}^2\\) ] from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (3.39 million \\(\\mathrm{km}^2\\) , in dark blue), based on the CDR SIA [17] (shown in black) to the first year where the daily SIA reached ice-free conditions (bold line in pink; colors in between see legend). The intermediate years are colored as shown in the legend. The 2023 daily SIA minimum is shown as red dashed horizontal line and the 1 million \\(\\mathrm{km}^2\\) ice-free line is shown as grey dashed horizontal line. This shows that the SIA loss leading up to the first ice-free day is not limited to only the minimum SIA, but occurs throughout much of the year.",
+    "footnote": [],
+    "bbox": [
+      [
+        78,
+        115,
+        918,
+        556
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Atmospheric conditions on the way to the first daily ice-free conditions: For each quick transition simulation, we show the last year of the daily a) maximum surface air temperature and of the b) minimum and c) maximum sea level pressure, all north of \\(80^{\\circ}\\mathrm{N}\\) . A 5-day running mean was applied to all timeseries. On b) and c), bold lines highlight strong low and high pressure events, respectively, as discussed in the text. All cases are warm in winter, in association with extreme low (warm air intrusions) or high (blocking) pressure events. They are very warm in spring, and many become stormy in summer.",
+    "footnote": [],
+    "bbox": [
+      [
+        100,
+        230,
+        860,
+        690
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Extended_Data_Figure_2.jpg",
+    "caption": "Extended Data Fig. 2 Sea Ice Mass on the way to first daily ice-free conditions: As in Figure 3, but for the monthly mean total sea ice mass north of 66N [in million kg], from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend; same color coding as in Figure 3).",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 14
+  },
+  {
+    "type": "image",
+    "img_path": "images/Extended_Data_Figure_3.jpg",
+    "caption": "Extended Data Fig. 3 Surface air temperature on the way to first daily ice-free conditions: As in Figure 3, but for the daily average surface air temperature north of \\(80^{\\circ}\\mathrm{N}\\) , from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend, same color coding as in Figure 3). Black line is the pre-2023 average.",
+    "footnote": [],
+    "bbox": [
+      [
+        42,
+        155,
+        952,
+        711
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Extended_Data_Figure_4.jpg",
+    "caption": "Extended Data Fig. 4 Sea level pressure on the way to first daily ice-free conditions: As in Figure 3, but for the daily average sea level pressure north of \\(80^{\\circ}\\mathrm{N}\\) , from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend, same color coding as in Figure 3). Black line is the pre-2023 average. Only extreme events are coloured; the vertical thick grey line indicates the first ice-free day.",
+    "footnote": [],
+    "bbox": [
+      [
+        42,
+        160,
+        951,
+        710
+      ]
+    ],
+    "page_idx": 16
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "a) Warm air intrusion; EC-Earth3 r8i1p1f1 under SSP1-2.6, winter leading to first ice-free day (8 Feb)",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        101,
+        828,
+        343
+      ]
+    ],
+    "page_idx": 17
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "b) Blocked heatwave; EC-Earth3 r12i1p1f1 under SSP2-4.5, spring leading to first ice-free day (15 May)",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        368,
+        825,
+        602
+      ]
+    ],
+    "page_idx": 18
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "c) Series of storms; EC-Earth3 r12i1p1f1 under SSP2-4.5, one day before first ice-free day (13 Aug)",
+    "footnote": [],
+    "bbox": [
+      [
+        125,
+        633,
+        477,
+        867
+      ]
+    ],
+    "page_idx": 18
+  },
+  {
+    "type": "image",
+    "img_path": "images/Extended_Data_Figure_6.jpg",
+    "caption": "Extended Data Fig. 6 The fastest ice-loss simulation and its last storm: Sea level pressure, backtracking from the first ice-free day a storm crossing the Arctic for our fastest case, EC-Earth3 r4ilp1fl under SSP1-2.6.",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 18
+  }
+]

preprint/preprint__5fe2fc8e2502328f54eccd29a085f2221c4033f8258f867d265ea38390218380/preprint__5fe2fc8e2502328f54eccd29a085f2221c4033f8258f867d265ea38390218380.mmd

@@ -0,0 +1,341 @@
+
+# There is a 7% risk that the first ice-free day in the Arctic Ocean could occur before 2030  
+
+Céline Heuzé  
+
+celine.heuze@gu.se  
+
+University of Gothenburg https://orcid.org/0000- 0002- 8850- 5868  Alexandra Jahn  University of Colorado Boulder https://orcid.org/0000- 0002- 6580- 2579  
+
+## Article  
+
+Keywords: Arctic, sea ice, first ice- free day, CMIP6  
+
+Posted Date: July 26th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4783304/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 3rd, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 54508- 3.
+
+<--- Page Split --->
+
+# There is a \(7\%\) risk that the first ice-free day in the Arctic Ocean could occur before 2030  
+
+Céline Heuzel \(^{1*}\) and Alexandra Jahn \(^{2*}\)  
+
+\(^{1*}\) Department of Earth Sciences, University of Gothenburg, Box 460, 405 30, Göteborg, Sweden.  
+
+\(^{2*}\) Department of Atmospheric and Oceanic Sciences and Institute of Arctic and Alpine Research, University of Colorado at Boulder, Boulder, CO, USA.  
+
+\*Corresponding author(s). E- mail(s): celine.heuze@gu.se; alexandra.jahn@colorado.edu; †These authors contributed equally to this work.  
+
+## Abstract  
+
+The observed Arctic sea ice decline is predicted to continue until 'ice- free' conditions are reached in the September monthly mean (sea ice area \(< 1\) million \(\mathrm{km^2}\) ), which is likely to occur by 2050. Aside from being a symbol of ongoing anthropogenic climate change, an ice- free Arctic Ocean will have far- reaching consequences, from the local food web and global climate system to economics and geopolitics. So far all ice- free projection studies have been focused on monthly- mean ice- free conditions. However, the first time we will observe a sea ice area \(< 1\) million \(\mathrm{km^2}\) will be in the daily satellite data. Using daily output from multiple CMIP6 models, we here provide the first projections of when we could see the first ice- free day in the Arctic Ocean. We find that there is a large range of the projected first ice- free day, ranging from 3 years compared to a 2023- equivalent model state (daily sea ice area minimum equal or larger than 3.39 million \(\mathrm{km^2}\) ) to no ice- free day before the end of the simulation in 2100, depending on the model and forcing scenario used. Using a storyline approach, we here focus on the nine CMIP6 simulations where the first ice- free day occurs within 3- 6 years, i.e. potentially before 2030, to understand what could cause such a rapid transition to first ice- free conditions. We find that these early ice- free days all occur during a rapid ice loss event, and are associated with winter and spring warming. During the final year, all simulations with early ice- free days are exceptionally warm, with storms further aiding the break- up of sea ice until ice- free conditions are reached.  
+
+Keywords: Arctic, sea ice, first ice- free day, CMIP6  
+
+## 1 Introduction  
+
+The observed decline of the Arctic sea ice cover [1] is expected to continue in the future [2]. The potential of an ice- free Arctic Ocean is one of the most striking examples of the ongoing anthropogenic climate change, with a visible transition from a white Arctic Ocean to a predominantly blue Arctic Ocean during the summer [3]. Apart from this symbolic change, an ice- free Arctic Ocean is expected to have cascading effects on the rest of the climate system. It would notably enhance the warming of the upper ocean, accelerating sea ice loss year round [4] and therefore further accelerating climate change [5], and could also induce more extreme events at mid- latitudes [6]. A further reduction of the summer sea ice cover will also negatively impact the already- stressed Arctic ecosystem, from the emblematic polar bear to the crucial zooplankton [7, 8].  
+
+Current projections from climate models suggest that the first monthly mean September sea ice area (SIA) at or below 1 million \(\mathrm{km^2}\) (commonly used as the ice- free threshold [9- 12]) could occur by 2050 [2], but predictions of an ice- free Arctic have large uncertainties, due to model biases and internal variability [12- 14]. However, before the September monthly mean reaches the ice- free threshold, we will see ice- free days with a SIA of 1 million \(\mathrm{km^2}\) or less [12]. Given that multi- model projections of the first ice- free day are so far lacking, when such first ice- free days could occur is currently unknown. To fill this gap, we here present the first projection of daily ice- free conditions, based on daily CMIP6 [15, 16] sea ice concentration data.
+
+<--- Page Split --->
+
+We here focus on predictions of ice- free conditions relative to a 2023- equivalent model state with a daily SIA minimum equal or larger than the 3.39 million \(\mathrm{km^2}\) that were observed in 2023 [17], to illustrate how long it could take to transition from a SIA similar to the one observed in 2023 to the first day with a daily SIA of 1 million \(\mathrm{km^2}\) or less (see the Methods section 4 for details on the exact definition of the 2023 equivalent conditions). In section 2.1 we use 13 different CMIP6 models that performed best over the historical period (see Methods, section 4) with a total of 132 ensemble members to provide probabilistic predictions of first daily ice- free conditions, and show how much earlier they occur than monthly first ice- free predictions. In section 2.2, we then focus on understanding the evolution of the simulations that reach ice- free conditions the fastest from their 2023 equivalent states, following a storyline approach [18]. By focusing on these 'quick transition' simulations, which make up \(7\%\) of the analyzed simulations, we are not suggesting that ice- free conditions will be reached this quickly. Instead, we provide insights into what may lead to such rare but high- impact events.  
+
+## 2 Results  
+
+### 2.1 Timing of the first ice-free day  
+
+The earliest ice- free day occurs 3 years after 2023- equivalent conditions, based on the 13 analyzed CMIP6 models (under SSP1- 2.6, Fig. 1a and Table 1). Another two models show the earliest ice- free day within 4 years (also under SSP1- 2.6), and another 6 ensemble members go ice- free within 5- 6 years (under SSP1- 2.6 to SSP3- 7.0). Overall there are 34 ensemble members from four different models reaching the first ice- free day within 10 years, amounting to \(25\%\) of the assessed simulations (under SSP1- 2.6 through SSP5- 8.5, Extended Data Table 1). However, there are also ensemble members from the analyzed CMIP6 models that do not reach any ice- free day before the end of the 21st century simulations (under SSP1- 1.9 to SSP3- 7.0, Fig. 1a and b and Extended Data Table 1). Given the large range between the fastest and slowest ensemble members from each model, the first ice- free day is not exclusively the result of a specific climate- change forcing but internal variability has a large influence. This agrees with findings for the first ice- free month [2, 12, 14].  
+
+In terms of the forcing impact, we find that SSP5- 8.5 has the most models 7 to 10 years away from their first ice- free day, SSP3- 7.0 11 to 20 years away, while SSP1- 2.6 has a majority of models never becoming ice- free (Fig. 1a). The split is even more clear when considering the slowest ensemble member (Fig. 1b) of each model: SSP2- 4.5, 3- 7.0 and 5- 8.5 all have a majority of models with their slowest ensemble member 21 to 30 years away from an ice- free day, while SSP1- 1.9 and 2.6 both have a majority of models where the slowest ensemble member never becomes ice- free. The time between the slowest and earliest ensemble member is therefore often lower than 10 years (Extended Data Table 1), because the low emission simulations often agree on not being ice- free, whereas the stronger forced simulations agree on being ice- free somewhat soon. Overall, the stronger the forcing, the shorter the time between the fastest and slowest ensemble member reaching the first ice- free day, i.e. the more consistent the ice- free prediction (Extended Data Table 1).  
+
+The first ice- free day obviously comes before the first ice- free month, but the distance between the two varies strongly between the simulations (Fig. 1c and d). The warmest SSP5- 8.5 predicts an ice- free month between 7 to 50 years after the 2023 equivalent year; the second warmest SSP3- 7.0, 6 to 50 years after; and the third warmest SSP2- 4.5, 7 to 50 years after. At the other end of the warming range, both SSP1s have a majority of models that do not have an ice- free month before the end of the simulations in 2100, even if they have an ice- free day. This means that a reduction in warming to the level of the SSP1s may not prevent the internal- variability induced first ice- free day, but can potentially prevent an ice- free month in the lower emission scenarios. In general, we find that the ensemble member with the earliest ice- free day is also the one with the earliest ice- free month, although there can be up to 20 years delay even in the warmest simulations (compare Extended Data Table 2 to Extended Data Table 1).  
+
+### 2.2 Storylines: From 2023 equivalent conditions to the first ice-free day in 3-6 years  
+
+To illustrate how we could potentially transition from a seasonal daily SIA minimum comparable to what was observed in 2023 to the first daily ice- free conditions within just a few years, we will now focus on the simulations that do so in 3- 6 years - referred to in the following as 'quick transition simulations'. This includes nine simulations, one simulation that reaches ice- free conditions within 3 years, two that take 4 years, two that take 5 years, and four that take 6 years, spanning four different climate models (ACCESS- CM2, CanESM5, EC- Earth3, and MPI- ESM1- 2- LR, see Table 1). Note that for all of the models that have quick transition members, there are other members that take much longer to reach first daily ice- free conditions under the same forcing (with a maximum offset of 42 years, Extended Data Table 1), as internal variability in Arctic sea ice is large [19- 21]. Thus, it is not that these four models are fast to lose their SIA;
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Time to ice-free conditions: Histograms of time from 2023 equivalent daily SIA minimum until the first ice-free day (top) or ice-free month (bottom), for the earliest (left) and latest (right) members of each model for all scenarios. For models that only had one ensemble member available, the same ensemble member is shown in the earliest and latest histograms. See Extended Data Table 1 for details on which models reach an ice-free day when and which models have only one ensemble member. The same is shown for the first ice-free month in Extended Data Table 2. </center>  
+
+it is the specific evolution of the internal climate variability that leads to these ensemble members reaching daily ice- free conditions within 3- 6 years after the last 2023 equivalent SIA daily minimum.  
+
+#### 2.2.1 Multiyear SIA transition to the first ice-free day  
+
+By definition, all the quick transition simulations have a very rapid transition from a 2023 equivalent daily minimum SIA to daily ice- free conditions (Figure 2). Notably, all quick transition simulations meet the criteria for a Rapid Ice Loss Event (RILE) [22- 25] during September, with all of them reaching daily ice- free conditions during a RILE period, defined as an at least 4- year period where the trend in the 5- year running mean sea ice extent (SIE) is larger than \(- 0.3\) million \(\mathrm{km^2}\) per year [24] (see the shading in Figure 2). In addition, all of them show a RILE or near RILE (if relaxing the RILE threshold from \(- 0.3\) to \(- 0.299\) million \(\mathrm{km^2}\) per year) in August during the transition period from the 2023 equivalent conditions to the first ice- free day (Extended Data Figure 1). RILEs have been found in all CMIP6 models and all months of the year [25], and as their name implies, describe a rapid loss of sea ice, which exceeds even the September SIA loss observed in the early 21st century [25]. While the exact drivers of RILEs are still under investigation, both atmospheric and oceanic drivers have been suggested as being important [24]. The atmosphere was found to be especially important in driving RILEs once the sea ice cover is already primarily limited to the deep Arctic Ocean basin [24], as is the case during the summer on the way to the first ice- free day.  
+
+The rapid transition to a first early ice- free day, however, does not just occur in the summer, but also includes a reduction of the sea ice cover during the autumn, winter, and spring (Figure 3). While this is clear from the SIA alone in most of the quick transition models (Figure 3), the EC- Earth3 simulations do not
+
+<--- Page Split --->
+
+
+<table><tr><td>Model<br>&amp;amp; member &amp;amp; SSP</td><td>Time to first ice-free day</td><td>Warming by that year</td><td>First ice-free day</td><td>Ice-free period</td></tr><tr><td>ACCESS-CM2</td><td>6 years</td><td>1.7℃</td><td>Aug-11</td><td>53 days</td></tr><tr><td>r6ilp1f1 SSP3-7.0</td><td></td><td></td><td></td><td></td></tr><tr><td>ACCESS-CM2</td><td>4 years</td><td>1.5℃</td><td>Sep-09</td><td>12 days</td></tr><tr><td>r7ilp1f1 SSP1-2.6</td><td></td><td></td><td></td><td></td></tr><tr><td>CanESM5</td><td>4 years</td><td>2.3℃</td><td>Aug-20</td><td>25 days</td></tr><tr><td>r8ilp1f1 SSP1-2.6</td><td>6 years</td><td>2.5℃</td><td>Aug-15</td><td>42 days</td></tr><tr><td>EC-Earth3</td><td>3 years</td><td>1.7℃</td><td>Aug-26</td><td>25 days</td></tr><tr><td>r4ilp1f1 SSP1-2.6</td><td>5 years</td><td>1.6℃</td><td>Aug-29</td><td>17 days</td></tr><tr><td>EC-Earth3</td><td>5 years</td><td>1.5℃</td><td>Aug-14</td><td>32 days</td></tr><tr><td>r12ilp1f1 SSP2-4.5</td><td></td><td></td><td></td><td></td></tr><tr><td>MPI-ESM1-2-LR</td><td>6 years</td><td>1.7℃</td><td>Sep-03</td><td>11 days</td></tr><tr><td>r38ilp1f1 SSP3-7.0</td><td></td><td></td><td></td><td></td></tr><tr><td>MPI-ESM1-2-LR</td><td>6 years</td><td>1.5℃</td><td>Aug-27</td><td>23 days</td></tr><tr><td>r43ilp1f1 SSP2-4.5</td><td></td><td></td><td></td><td></td></tr></table>
+
+Table 1 Characteristics of the nine quick transition simulations: Showing the time from 2023 equivalent conditions to the first ice-free day, the degree of global warming for the year of the first ice-free day compared to pre-industrial period (5-year running mean, see Methods section 4), the date of that first ice-free day, and the duration of that first ice-free period (in days).
+
+119 show a notable change in the wintertime SIA. But when taking into account the sea ice thickness as well,120 and thus looking at the total sea ice mass (Extended Data Figure 2), it is clear that in all models we see a121 clear decrease in the total Arctic sea ice mass year-around. This means that reduced sea ice thickness in the122 wintertime occurs in all models soon (within 1 or 2 years) after they had a SIA minimum at or above the123 2023 conditions, even when it is not apparent in the wintertime SIA. As discussed in the next section, this124 reduction in sea ice is linked to warm winters and springs (Extended Data Figure 3), as well as a delayed125 freeze up in the autumn [26] (Figure 3).
+
+126 Once the first ice-free day is reached, the Arctic does not remain ice-free for one day only. The ice-free127 period lasts between 11 and 53 days in the 9 quick transition simulations, with an average duration of 27days (Table 1). The ice-free duration is set primarily by the day the first ice-free conditions occur, with the128 simulations that show ice-free conditions earliest showing the longest duration. Specifically, we find that the129 first ice-free day for the quick transition simulations ranges between Aug 11 to Sept 09 (days 223 to 252),130 with an average of Aug 26 (day 236). The first ice-free day occurs in September for ACCESS r7ilp1f1 and131 MPI-ESM1-2-LR r38ilp1f1, which also have the shortest ice-free duration (12 and 11 days, respectively).
+
+132 Notably, in the year with the first ice-free day in the quick transition simulations, the 2023 daily SIA133 minimum value of 3.39 million km2 is reached at the latest by day July 31st (day 212) (see Figure 3)-42days earlier than the observed 2023 daily minimum on Sept 11 (day 254, according to the Climate Data134 Record (CDR) derived SIA [17]). Thus, if in the future the observed SIA crosses the 3.39 million km2 SIA135 in July, this could be a warning sign that an ice-free day may occur later in the summer.
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Rapid transition from 2023 equivalent state to the first ice-free day: The simulated SIA daily minimum is shown in blue, simulated September monthly mean simulated SIA in cyan, and observed daily minimum SIA based on the CDR SIC data [17] is shown as black line [all in million km²]. Also shown are Rapid Ice Loss Events (RILEs) during September (shaded), defined based on the monthly SIE [24]. A vertical black dashed line indicates the year when the simulated daily SIA minimum was last at or above the 2023 observed daily SIA minimum of 3.39 million km², which is in turn is indicated with a horizontal black dashed line. Vertical dashed grey lines show when ice-free conditions are reached (first for daily, then for monthly, if there is only one both reach ice-free conditions for the first time in the same year). The grey dashed horizontal line shows the 1 million km² ice-free threshold. Extended Data Figure 1 shows that RILEs or near-RILES also occur during August. This illustrates that the transition to first daily ice-free conditions occurs during a RILE in the quick transition simulations. </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Sea ice area on the way to first daily ice-free conditions: Seasonal cycle of daily SIA [in million \(\mathrm{km}^2\) ] from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (3.39 million \(\mathrm{km}^2\) , in dark blue), based on the CDR SIA [17] (shown in black) to the first year where the daily SIA reached ice-free conditions (bold line in pink; colors in between see legend). The intermediate years are colored as shown in the legend. The 2023 daily SIA minimum is shown as red dashed horizontal line and the 1 million \(\mathrm{km}^2\) ice-free line is shown as grey dashed horizontal line. This shows that the SIA loss leading up to the first ice-free day is not limited to only the minimum SIA, but occurs throughout much of the year. </center>
+
+<--- Page Split --->
+
+### 2.2.2 Final-year triggers: Winter warm air intrusions, spring blocking, and summer storms  
+
+For all quick transition simulations, the sea ice is pre- conditioned for an ice- free day: Most years leading to the year of the first ice- free day have a delayed atmospheric cooling in autumn and warm spells all the way to December (Extended Data Figure 3), consistent with the delayed and reduced sea ice formation described above. A series of events in the last winter, spring, and summer finish weakening the ice both dynamically and thermodynamically, leading to that first ice- free day.  
+
+For all cases, the last winter is warm (Figure 4a and Extended Data Figure 3). North of \(80^{\circ}\mathrm{N}\) , maximum air temperatures exceed the "spring" transition temperature \(- 20^{\circ}\mathrm{C}\) [27] all winter long, most often in association with strong high pressures (Figure 4b and c, and Extended Data Figure 4), but also sometimes in association with strong low pressures, i.e. due to a warm air intrusion (Extended Data Figure 5a). The warmth and high pressure persist into the spring for all nine simulations, with two different patterns: A year where the spring warming is shifted up to one month early (see e.g. the case that becomes ice- free fastest, EC- Earth3 r4ilp1fl, Extended Data Figure 3), or a year that is not extreme but is more stable, has fewer cold spells than usual (see e.g. CanESM5 r9ilp1fl, Extended Data Figure 3). Heatwaves with maximum temperatures exceeding \(0^{\circ}\mathrm{C}\) are common (Fig. 4), lasting for several days because the warm air is blocked over the central Arctic by a high pressure system (Extended Data Figure 5b).  
+
+The last summer is warm to very warm for all quick transition simulations, with temperatures that can exceed \(10^{\circ}\mathrm{C}\) from day 151 (late May, Figure 4). The atmospheric pressure becomes less stable, and in six out of nine simulations (CanESM5 r8ilp1fl, all three EC- Earth3 and both MPI- ESM1- 2- LR), storms cross through the Arctic, especially so in the last month or even last days before the first ice- free day (Figure 4). EC- Earth3 r4ilp1fl, which has an ice- free day only 3 years after 2023 conditions, has one extensive storm shooting from the Kara Sea region to the Canada basin in 5 days, culminating in the earliest simulated first ice- free day (Extended Data Figure 6). In most of the quick transition simulations, such as EC- Earth3 r12ilp1fl (Extended Data Figure 5c), instead several weak storm systems simultaneously stress the sea ice at various locations across the Arctic in the days leading up to the first ice- free day.  
+
+The warm atmospheric conditions triggering the first ice- free day are predicted to become increasingly common in a warmer world [28]. As the Arctic warms, heatwaves at any season become more likely [29], as do warm air intrusions and storms [30]. But it is not too late to avoid an ice- free day: For all quick transition cases, the first ice- free day occurs on years at or above the \(1.5^{\circ}\mathrm{C}\) of global warming compared to pre- industrial level set as a target to not exceed by the Paris Agreement [31] (Table 1). This agrees with prior work on the first monthly ice- free Arctic, which also found that ice- free conditions may be avoided if global warming stayed below the Paris Agreement target of less than \(1.5^{\circ}\mathrm{C}\) [32- 34].
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 Atmospheric conditions on the way to the first daily ice-free conditions: For each quick transition simulation, we show the last year of the daily a) maximum surface air temperature and of the b) minimum and c) maximum sea level pressure, all north of \(80^{\circ}\mathrm{N}\) . A 5-day running mean was applied to all timeseries. On b) and c), bold lines highlight strong low and high pressure events, respectively, as discussed in the text. All cases are warm in winter, in association with extreme low (warm air intrusions) or high (blocking) pressure events. They are very warm in spring, and many become stormy in summer. </center>
+
+<--- Page Split --->
+
+## 3 Discussion and Conclusions  
+
+We showed that based on CMIP6 models, the earliest ice- free day in the Arctic occurs within 3 years from 2023 equivalent conditions, with a \(7\%\) probability of an ice- free day within 6 years. The highest probability of the first ice- free day occurring lies within 7- 20 years (Figure 1). Note that all of these projections start from the last time the daily SIA minimum is above or equal to 3.39 million \(\mathrm{km^2}\) . That could be in 2023, if all future daily SIA minima are below 3.39 million \(\mathrm{km^2}\) . But the countdown to ice- free could also start from a future year, if the observed daily SIA minimum in years after 2023 is above 3.39 million \(\mathrm{km^2}\) .  
+
+While 7- 20 years beyond 2023 equivalent conditions represents the most likely range during which the first ice- free day is projected to occur, there is a large prediction uncertainty of the first ice- free day, associated with all three sources of climate prediction uncertainties [35]. The scenario uncertainty introduced by the unknown future emissions is two- fold. First, there is a distinct difference between the lowest SSP1- 1.9 scenario, which shows no early ice- free day (earliest projection is 13 years), and the other SSPs (SSP1- 2.6 to SSP5- 8.5), which all have members with ice- free days within a decade. The finding that early ice- free days occur under SSP1- 2.6 to SSP5- 8.5 without any influence of the strength of the forcing scenario agrees with prior work on the timing of the first ice- free month in the Arctic [2, 36]. SSP1- 1.9 has not generally been used in many studies of an ice- free Arctic. However, as SSP1- 1.9 tends to stay around \(1.5^{\circ}\mathrm{C}\) by 2100 [37], the possibility to avoid ice- free conditions under this scenario matches with studies that found that for a global warming below the \(1.5^{\circ}\mathrm{C}\) Paris target [31] a monthly mean ice- free Arctic may be avoidable [32- 34]. The second effect of the scenario uncertainty is that the stronger the forcing, the narrower the internal variability prediction uncertainty, ranging from 26 years for SSP5- 8.5 to more than 60 years for SSP1- 1.9 and SSP1- 2.6. A similarly large internal variability uncertainty has also been found for projections of the first ice- free month [14, 38]. This highlights that internal variability uncertainty affects all projections of an ice- free Arctic, be it monthly or daily, limiting the prediction accuracy to a range of at least two decades, if not more. In addition, despite performing model selection based on the historical SIA simulation, model differences further add to the prediction uncertainty, as also seen for monthly ice- free projections [13].  
+
+To understand the rare but high- impact possibility of a rapid loss of SIA to 1 million \(\mathrm{km^2}\) from 2023 equivalent conditions, we investigated the storylines of the nine fastest cases, which reached ice- free conditions within 3- 6 years. Most of the first ice- free days occurs in August, and the first ice- free period lasted between 11 and 53 days. What they all had in common was that the first ice- free day occurred during a RILE (Figure 2). What is noteworthy is that for all quick transition cases the 2023 equivalent year occurs after a period of little or no trend in the daily and monthly SIA over the previous 10- 15 years, with previously lower SIA than the the 2023 equivalent. This is not dis- similar to the observed SIA evolution in the 15 years prior to 2023 (see Figure 2). Furthermore, in an investigation of RILE events in CMIP6 models, it has been shown that the probability of a RILE increases by \(20\%\) compared to the overall RILE probability after a 10- year stable period in the SIE [25]. These results suggest that if a RILE were to occur in the near future, it could potentially bring us a first ice- free day relatively quickly.  
+
+The primary trigger of the rapid transition to the first ice- free day within 3- 6 years that we identified was a warm atmosphere in the previous autumns/winters, leading to a loss of sea ice mass year- round (Extended Data Figure 2). The last year had "spring" daily mean temperatures already in January, thanks to heatwaves/blockings and/or warm air intrusions (Figure 4). In addition, we frequently found storms going across the Arctic in the days leading up to the first ice- free day. All these events are projected to increase in frequency as the Arctic warms [29], making the first ice- free day increasingly more likely. The good news is, for all storyline cases, the first ice- free day occurs in years with a 5- year running mean global temperature at or above \(1.5^{\circ}\mathrm{C}\) compared to pre- industrial level (Table 1). This means that if we could keep warming below the Paris Agreement target of \(1.5^{\circ}\mathrm{C}\) of global warming [31], ice- free days could potentially still be avoided.  
+
+## 4 Methods  
+
+### 4.1 Data and Definitions  
+
+We analyzed simulations from all models that participated in the Climate Model Intercomparison Project phase 6 (CMIP6, [15]) that had daily sea ice on the ocean ("siconc") or atmosphere grids ("siconca") available on any of the Earth System Grid Federation (ESGF) portals in late May 2024, as well as files that had been previously downloaded onto the Levante server of the German Climate Computing Center (DKRZ). We also obtained their grid cell area ("areacello" and "areacella", respectively). All available ensemble members were used. We used the historical scenario for our model selection (see next subsection), and the Shared Socioeconomic Pathways SSP1- 1.9, SSP1- 2.6, SSP2- 4.5, SSP3- 7.0 and SSP5- 8.5 [16] for our ice- free projections. For the subset of cases that we investigated further in section 2.2, we also used their daily surface air temperature ("tas"), daily sea level pressure ("psl"), and their monthly sea ice mass ("simass") (monthly due to the unavailability of daily simass in some of these models).
+
+<--- Page Split --->
+
+The SIA, SIE and sea ice mass (SIMASS) were calculated north of \(30^{\circ}\mathrm{N}\) , on the model's native grid. SIA was defined as the sum over all grid cells n of the sea ice concentration multiplied by the grid cell area:  
+
+\[SIA = \sum_{n}\mathrm{sicone(n)}\times \mathrm{areacello(n)}. \quad (1)\]  
+
+SIE was defined as the sum of the grid cell area for all grid cells m where the sea ice concentration was larger than 0.15:  
+
+\[SIE = \sum_{m}\mathrm{areacello(m)}. \quad (2)\]  
+
+As recommended in previous studies (see review in [12]), we conducted our analyses using only SIA, with the exception of the RILE analysis.  
+
+The first ice- free year was defined as the first year where daily or monthly SIA is lower than or equal to 1 million \(\mathrm{km}^2\) .  
+
+RILEs were defined based on the September monthly SIE, following [24], which means that a RILE is defined as "a period of at least 4 years for which the trend in the 5- year running mean minimum SIE is lower than \(- 0.3\) million \(\mathrm{km}^2\) /year".  
+
+The warming of the models compared to pre- industrial was computed by using the daily surface air temperature for the first 50 years of the pre- industrial control simulation (on ensemble member rli1p1fl); taking the area- weighted global temperature, averaged over these 50 years; and subtracting it from the area- weighted global temperature averaged 2 year prior to the first year with an ice- free day until 2 years after that first year (i.e., over a 5 year period).  
+
+All analysis using daily data was performed on a no- leap 365 day calendar, and models that produced output on a standard calendar with leap years had their Feb 29th data dropped. Models that used a 360 day calendar (specifically UKESM1- 0- LL and HadGEM3- GC31- LL) were not included in the analysis, as their results can not be directly compared with models with 365 days when analyzing the timing of daily ice- free conditions.  
+
+### 4.2 Model selection  
+
+Due to the large model spread in simulations of Arctic sea ice evolution [2], we used two SIA based criteria to select the models that performed best over years 2000- 2014 in the historical CMIP6 simulations.  
+
+The first criterion used here was that the simulated September monthly mean falls within the satellite- derived SIA in September over 2000- 2014, plus/minus the average standard deviation of the 2000- 2014 average September SIA in models with more than 6 members \((\pm 0.45\) million \(\mathrm{km}^2\) ). To account for observational uncertainty, we used the monthly SIA calculated from daily NOAA/NSIDC CDR SIC data, version 4 [17], using the CDR as upper bound and the NASA Team [39] as lower bound (both with pole hole filled from the [17] dataset). For September, the 2000- 2014 mean difference between the two is \(- 1.48\) million \(\mathrm{km}^2\) . This criteria means that we exclude models that have a mean state over the last 15 years of the historical simulations that is too high or low compared to observations.  
+
+The second criterion used here was that the day of the minimum daily SIA from the simulations between 2000 and 2014 falls within the observational range of day 238 (August 26) to day 272 (Sept 29), plus/minus 5 days (the average standard deviation of the sea ice minimum day over 2000- 2014 from the models with more than 6 members). We chose this second criterion to ensure that models simulate the daily minimum at a time comparable to observations, since the focus of this study is on the first ice- free day.  
+
+For both criteria, if any ensemble member from a model fell within the observational ranges, the criterion was considered to be met. Both criteria had to be met for a model to be retained. Applying these two criteria reduced the number of models from 30 to 13 models. The models retained are listed and cited in Supplementary Table S1.  
+
+### 4.3 Detection of the '2023 equivalent year'  
+
+In order to assess the storyline of how soon the Arctic Ocean could be ice- free (1 million \(\mathrm{km}^2\) or less of SIA remaining), we start our analysis from the last year the daily SIA minimum was equal to or larger than the observed 2023 daily SIA minimum before a simulation reaches daily ice- free conditions for the first time. The observed 2023 daily SIA minimum was 3.39 million \(\mathrm{km}^2\) , based on the daily SIA calculated from the pole- hole filled daily NOAA/NSIDC CDR SIC data, version 4 [17].  
+
+Some ensemble members from the selected models had to be discarded because their 2023 equivalent pre- dated the beginning of the scenario simulations, as their daily SIA minimum was below 3.39 million \(\mathrm{km}^2\) at the beginning of the scenario simulations, but their historical simulation could not be obtained (broken link, corrupted data, not turning up on any of the portals).
+
+<--- Page Split --->
+
+Acknowledgements. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP6. We thank the Sea Ice Model Intercomparison Project (SIMIP) for requesting daily sea ice output for CMIP6. We thank the climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data and providing access, and the multiple funding agencies who support CMIP6 and ESGF. CH acknowledges the data access and computing supported provided by the Deutsches Klimarechenzentrum (DKRZ) fourth High Performance Computer System for Earth System Research (HLRE- 4) "Levante". AJ acknowledges the data access and computing support provided by the NCAR CMIP Analysis Platform (doi:10.5065/D60R9MSP) as well as the high- performance computing support from Derecho (doi:10.5065/qx9a- pg09) provided by NSF NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation.  
+
+## Declarations  
+
+- Funding: C. Heuzé's contribution was supported by Swedish National Research Council Starting Grant award 2018-03859 and Swedish National Space Agency award 2022-00149. A. Jahn's contribution was supported by NSF-CAREER award 1847398.  
+
+- Competing interests: The authors declare no competing interests.  
+
+- Ethics approval and consent to participate: Not applicable  
+
+- Consent for publication: Not applicable  
+
+- Data availability: The CMIP6 data is freely available on the Earth System Grid Federation (ESGF, https://esgf-node.llnl.gov/search/cmip6/, https://esgf-metagrid.cloud.dkrz.de/search, https://esgf-node.ipsl.upmc.fr/projects/cmip6-ipsl/ and https://esgf-ui.ceda.ac.uk/cog/search/cmip6-ceda/). The derived daily SIE and SIA data will be archived in a freely accessible repository upon acceptance of the manuscript and the link to the data will be added here before publication.  
+
+- Materials availability: Not applicable  
+
+- Code availability: Not applicable  
+
+- Author contribution: CH and AJ jointly and with equal contributions conceptualized the article, obtained and analyzed data, produced figures and wrote the article.  
+
+## References  
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+
+<--- Page Split --->
+![](images/Extended_Data_Figure_2.jpg)
+  
+
+Extended Data Fig. 1 RILE events on the way to the first ice- free day: The monthly mean SIA from each quick transition simulation for all months of the year is shown in blue shading [in million \(\mathrm{km^2}\) ], with RILE events in a given month overlaid in red. RILE events in each month of the year are defined based on monthly mean SIE [24], as described in the Methods section 4. When slightly relaxing the RILE criteria from a trend of \(- 0.3\) million \(\mathrm{km^2}\) per year to \(- 0.299\) million \(\mathrm{km^2}\) per year, additional RILE events show up for some simulations (shown in pink). Vertical dashed grey lines indicate the year of the first ice- free day and first ice- free month. When only one grey line is shown then the first ice- free day and month occur in the same year. The vertical dashed black line shows the 2023 equivalent year. This figure shows that all quick transition members have a RILE or near RILE in August and September during the transition from the 2023 equivalent year to the first ice- free day, with some simulations also showing RILES in additional months.
+
+<--- Page Split --->
+![](images/Extended_Data_Figure_3.jpg)
+
+<center>Extended Data Fig. 2 Sea Ice Mass on the way to first daily ice-free conditions: As in Figure 3, but for the monthly mean total sea ice mass north of 66N [in million kg], from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend; same color coding as in Figure 3). </center>
+
+<--- Page Split --->
+![](images/Extended_Data_Figure_4.jpg)
+
+<center>Extended Data Fig. 3 Surface air temperature on the way to first daily ice-free conditions: As in Figure 3, but for the daily average surface air temperature north of \(80^{\circ}\mathrm{N}\) , from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend, same color coding as in Figure 3). Black line is the pre-2023 average. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_0.jpg)
+
+<center>Extended Data Fig. 4 Sea level pressure on the way to first daily ice-free conditions: As in Figure 3, but for the daily average sea level pressure north of \(80^{\circ}\mathrm{N}\) , from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend, same color coding as in Figure 3). Black line is the pre-2023 average. Only extreme events are coloured; the vertical thick grey line indicates the first ice-free day. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_1.jpg)
+
+<center>a) Warm air intrusion; EC-Earth3 r8i1p1f1 under SSP1-2.6, winter leading to first ice-free day (8 Feb) </center>  
+
+![](images/Figure_unknown_2.jpg)
+
+<center>b) Blocked heatwave; EC-Earth3 r12i1p1f1 under SSP2-4.5, spring leading to first ice-free day (15 May) </center>  
+
+![](images/Extended_Data_Figure_6.jpg)
+
+<center>c) Series of storms; EC-Earth3 r12i1p1f1 under SSP2-4.5, one day before first ice-free day (13 Aug) </center>  
+
+![PLACEHOLDER_18_3]
+  
+
+Extended Data Fig. 5 Atmospheric events leading to an ice- free day: Sea level pressure (left) and when relevant, surface air temperature (right) on exemplary days of the last year before the model had its first ice- free day illustrating a) a warm air intrusion; b) a blocking pattern coinciding with a heatwave; and c) a series of a least four storms.
+
+<--- Page Split --->
+![PLACEHOLDER_19_0]
+
+<center>Extended Data Fig. 6 The fastest ice-loss simulation and its last storm: Sea level pressure, backtracking from the first ice-free day a storm crossing the Arctic for our fastest case, EC-Earth3 r4ilp1fl under SSP1-2.6. </center>
+
+<--- Page Split --->
+
+<table><tr><td>Model</td><td>SSP1-1.9</td><td>SSP1-2.6</td><td>SSP2-4.5</td><td>SSP3-7.0</td><td>SSP5-8.5</td></tr><tr><td>ACCESS-CM2</td><td>-</td><td>r1ilplf 4<br/>r6ilplf 23</td><td>r1ilplf 9<br/>r4ilplf 20</td><td>r6ilplf 6<br/>r3ilplf 21</td><td>r9ilplf 8<br/>r4ilplf 22</td></tr><tr><td>BCC-CSM2-MR</td><td>-</td><td>r1ilplf 54</td><td>r1ilplf 20</td><td>-</td><td>r1ilplf 28</td></tr><tr><td>CanESM5</td><td>r4ilplf 18<br/>r5ilplf 34</td><td>r8ilplf 4<br/>r1ilp2f 28</td><td>r8ilplf 8<br/>r5ilp2f 27</td><td>r7ilplf 9<br/>r5ilp2f 22</td><td>r5ilp2f 9<br/>r10ilp2f 21</td></tr><tr><td>CNRM-CM6-1-HR</td><td>-</td><td>r1ilp2f &gt;70</td><td>-</td><td>-</td><td>r1ilp2f 10</td></tr><tr><td>EC-Earth3</td><td>r4ilplf 18</td><td>r4ilplf 3<br/>r1ilplf 7</td><td>r12ilp1f 5<br/>r16ilp1f 21</td><td>-</td><td>-</td></tr><tr><td>EC-Earth3-Veg-LR</td><td>r3ilplf 13<br/>r2ilplf &gt;70</td><td>r1ilplf 11<br/>r2ilplf 17</td><td>r1ilplf &gt;70</td><td>-</td><td>-</td></tr><tr><td>IPSL-CM5A2-INCA</td><td>-</td><td>r1ilplf &gt;70</td><td>-</td><td>r1ilplf 18</td><td>-</td></tr><tr><td>MIROC6</td><td>r1ilplf 52</td><td>r3ilplf 20<br/>r1ilplf 35</td><td>r1ilplf 22<br/>r3ilplf 39</td><td>r2ilplf 15<br/>r3ilplf 27</td><td>r3ilplf 23<br/>r1ilplf 27</td></tr><tr><td>MIROC-ES2H</td><td>r1ilp4f2 &gt;70</td><td>r1ilp4f2 &gt;70</td><td>r3ilp4f2 16<br/>r2ilp4f2 33</td><td>r1ilp4f2 23</td><td>r1ilp4f2 17<br/>r2ilp4f2 25</td></tr><tr><td>MIROC-ES2L</td><td>r1ilp1f2 24<br/>r10ilp1f2 59</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MPI-ESM-1-2-HAM</td><td>-</td><td>-</td><td>-</td><td>r2ilp1f 13<br/>r1ilp1f 19</td><td>-</td></tr><tr><td>MPI-ESM1-2-LR</td><td>r4ilplf 36<br/>r50ilp1f1 &gt;70</td><td>r5ilp1f 12<br/>r48ilp1f1 &gt;70</td><td>r43ilp1f 6<br/>r18ilp1f 46</td><td>r38ilp1f 6<br/>r1ilp1f 48</td><td>r7ilp1f 9<br/>r44ilp1f 35</td></tr><tr><td>NorESM2-LM</td><td>-</td><td>r1ilplf &gt;70</td><td>r2ilplf 24<br/>r3ilp1f 36</td><td>r1ilplf 38<br/>r3ilp1f &gt;70</td><td>r1ilp1f 23</td></tr></table>
+
+**Extended Data Table 1** Time to the first ice-free day: For each selected CMIP6 model and for each scenario, the ensemble members with the earliest (top) and latest (bottom) ice-free day, and years until that ice free day. Only one value is shown if the model had only one ensemble member available. If the entry is &gt;70 years, this means that the simulation did not reach ice-free conditions before the end of the 21st century simulations. 
+
+<table><tr><td>Model</td><td>SSP1-1.9</td><td>SSP1-2.6</td><td>SSP2-4.5</td><td>SSP3-7.0</td><td>SSP5-8.5</td></tr><tr><td>ACCESS-CM2</td><td>-</td><td>r9ilplf 7<br/>r10ilp1f 26</td><td>r2ilplf 10<br/>r4ilplf 20</td><td>r6ilplf 6<br/>r4ilplf 22</td><td>r9ilplf 8<br/>r4ilplf 22</td></tr><tr><td>BCC-CSM2-MR</td><td>-</td><td>r1ilplf 54</td><td>r1ilplf 21</td><td>-</td><td>r1ilplf 31</td></tr><tr><td>CanESM5</td><td>r4ilplf 18<br/>r5ilplf 34</td><td>r9ilplf 6<br/>r1ilp2f 32</td><td>r8ilplf 8<br/>r5ilp2f 28</td><td>r7ilplf 11<br/>r10ilp1f 29</td><td>r6ilplf 11<br/>r1ilp1f 22</td></tr><tr><td>CNRM-CM6-1-HR</td><td>-</td><td>r1ilplf &gt;70</td><td>-</td><td>-</td><td>r1ilplf 10</td></tr><tr><td>EC-Earth3</td><td>r4ilplf 27<br/>r4ilplf 27</td><td>r1ilplf 8<br/>r8ilplf 26</td><td>r10ilp1f 7<br/>r16ilp1f 22</td><td>-</td><td>-</td></tr><tr><td>EC-Earth3-Veg-LR</td><td>r3ilplf 18<br/>r2ilplf &gt;70</td><td>r2ilplf 39<br/>r1ilplf 42</td><td>r1ilplf &gt;70</td><td>-</td><td>-</td></tr><tr><td>IPSL-CM5A2-INCA</td><td>-</td><td>r1ilplf &gt;70</td><td>-</td><td>r1ilplf 18</td><td>-</td></tr><tr><td>MIROC6</td><td>r1ilplf &gt;70</td><td>r2ilplf 25<br/>r3ilplf 48</td><td>r1ilplf 23<br/>r3ilplf 42</td><td>r2ilplf 15<br/>r3ilplf 27</td><td>r3ilplf 24<br/>r2ilplf 29</td></tr><tr><td>MIROC-ES2H</td><td>r1ilp4f2 &gt;70</td><td>r1ilp4f2 &gt;70</td><td>r3ilp4f2 16<br/>r1ilp4f2 34</td><td>r1ilp4f2 23</td><td>r1ilp4f2 17<br/>r2ilp4f2 25</td></tr><tr><td>MIROC-ES2L</td><td>r1ilp1f2 28<br/>r3ilp1f2 &gt;70</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MPI-ESM-1-2-HAM</td><td>-</td><td>-</td><td>-</td><td>r2ilplf 13<br/>r1ilplf 20</td><td>-</td></tr><tr><td>MPI-ESM1-2-LR</td><td>r48ilp1f 48<br/>r50ilp1f1 &gt;70</td><td>r34ilp1f 21<br/>r9ilp1f 1&gt;70</td><td>r26ilp1f 15<br/>r18ilp1f 46</td><td>r38ilp1f 7<br/>r1ilp1f 48</td><td>r7ilp1f 9<br/>r42ilp1f 40</td></tr><tr><td>NorESM2-LM</td><td>-</td><td>r1ilplf &gt;70</td><td>r1ilplf 32<br/>r2ilplf 42</td><td>r1ilplf 41<br/>r3ilplf &gt;70</td><td>r1ilplf 24</td></tr></table>
+
+**Extended Data Table 2** Time the first ice-free month: Same as Extended Data Table 1 but for the first ice-free month.
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+HeuzeJahnsupplementary.pdf
+
+<--- Page Split --->

preprint/preprint__5fe2fc8e2502328f54eccd29a085f2221c4033f8258f867d265ea38390218380/preprint__5fe2fc8e2502328f54eccd29a085f2221c4033f8258f867d265ea38390218380_det.mmd

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+<|ref|>title<|/ref|><|det|>[[43, 106, 888, 175]]<|/det|>
+# There is a 7% risk that the first ice-free day in the Arctic Ocean could occur before 2030  
+
+<|ref|>text<|/ref|><|det|>[[44, 195, 158, 214]]<|/det|>
+Céline Heuzé  
+
+<|ref|>text<|/ref|><|det|>[[53, 223, 256, 241]]<|/det|>
+celine.heuze@gu.se  
+
+<|ref|>text<|/ref|><|det|>[[45, 268, 680, 335]]<|/det|>
+University of Gothenburg https://orcid.org/0000- 0002- 8850- 5868  Alexandra Jahn  University of Colorado Boulder https://orcid.org/0000- 0002- 6580- 2579  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 375, 103, 393]]<|/det|>
+## Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 412, 476, 432]]<|/det|>
+Keywords: Arctic, sea ice, first ice- free day, CMIP6  
+
+<|ref|>text<|/ref|><|det|>[[44, 451, 295, 470]]<|/det|>
+Posted Date: July 26th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 489, 475, 509]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4783304/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 526, 914, 570]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License.  Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 587, 534, 607]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 643, 950, 687]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on December 3rd, 2024. See the published version at https://doi.org/10.1038/s41467- 024- 54508- 3.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[96, 136, 884, 187]]<|/det|>
+# There is a \(7\%\) risk that the first ice-free day in the Arctic Ocean could occur before 2030  
+
+<|ref|>text<|/ref|><|det|>[[343, 208, 681, 226]]<|/det|>
+Céline Heuzel \(^{1*}\) and Alexandra Jahn \(^{2*}\)  
+
+<|ref|>text<|/ref|><|det|>[[160, 234, 864, 265]]<|/det|>
+\(^{1*}\) Department of Earth Sciences, University of Gothenburg, Box 460, 405 30, Göteborg, Sweden.  
+
+<|ref|>text<|/ref|><|det|>[[160, 266, 864, 300]]<|/det|>
+\(^{2*}\) Department of Atmospheric and Oceanic Sciences and Institute of Arctic and Alpine Research, University of Colorado at Boulder, Boulder, CO, USA.  
+
+<|ref|>text<|/ref|><|det|>[[160, 327, 864, 360]]<|/det|>
+\*Corresponding author(s). E- mail(s): celine.heuze@gu.se; alexandra.jahn@colorado.edu; †These authors contributed equally to this work.  
+
+<|ref|>sub_title<|/ref|><|det|>[[478, 386, 546, 400]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[160, 402, 864, 613]]<|/det|>
+The observed Arctic sea ice decline is predicted to continue until 'ice- free' conditions are reached in the September monthly mean (sea ice area \(< 1\) million \(\mathrm{km^2}\) ), which is likely to occur by 2050. Aside from being a symbol of ongoing anthropogenic climate change, an ice- free Arctic Ocean will have far- reaching consequences, from the local food web and global climate system to economics and geopolitics. So far all ice- free projection studies have been focused on monthly- mean ice- free conditions. However, the first time we will observe a sea ice area \(< 1\) million \(\mathrm{km^2}\) will be in the daily satellite data. Using daily output from multiple CMIP6 models, we here provide the first projections of when we could see the first ice- free day in the Arctic Ocean. We find that there is a large range of the projected first ice- free day, ranging from 3 years compared to a 2023- equivalent model state (daily sea ice area minimum equal or larger than 3.39 million \(\mathrm{km^2}\) ) to no ice- free day before the end of the simulation in 2100, depending on the model and forcing scenario used. Using a storyline approach, we here focus on the nine CMIP6 simulations where the first ice- free day occurs within 3- 6 years, i.e. potentially before 2030, to understand what could cause such a rapid transition to first ice- free conditions. We find that these early ice- free days all occur during a rapid ice loss event, and are associated with winter and spring warming. During the final year, all simulations with early ice- free days are exceptionally warm, with storms further aiding the break- up of sea ice until ice- free conditions are reached.  
+
+<|ref|>text<|/ref|><|det|>[[160, 623, 495, 636]]<|/det|>
+Keywords: Arctic, sea ice, first ice- free day, CMIP6  
+
+<|ref|>sub_title<|/ref|><|det|>[[96, 680, 298, 699]]<|/det|>
+## 1 Introduction  
+
+<|ref|>text<|/ref|><|det|>[[96, 708, 905, 824]]<|/det|>
+The observed decline of the Arctic sea ice cover [1] is expected to continue in the future [2]. The potential of an ice- free Arctic Ocean is one of the most striking examples of the ongoing anthropogenic climate change, with a visible transition from a white Arctic Ocean to a predominantly blue Arctic Ocean during the summer [3]. Apart from this symbolic change, an ice- free Arctic Ocean is expected to have cascading effects on the rest of the climate system. It would notably enhance the warming of the upper ocean, accelerating sea ice loss year round [4] and therefore further accelerating climate change [5], and could also induce more extreme events at mid- latitudes [6]. A further reduction of the summer sea ice cover will also negatively impact the already- stressed Arctic ecosystem, from the emblematic polar bear to the crucial zooplankton [7, 8].  
+
+<|ref|>text<|/ref|><|det|>[[96, 824, 905, 923]]<|/det|>
+Current projections from climate models suggest that the first monthly mean September sea ice area (SIA) at or below 1 million \(\mathrm{km^2}\) (commonly used as the ice- free threshold [9- 12]) could occur by 2050 [2], but predictions of an ice- free Arctic have large uncertainties, due to model biases and internal variability [12- 14]. However, before the September monthly mean reaches the ice- free threshold, we will see ice- free days with a SIA of 1 million \(\mathrm{km^2}\) or less [12]. Given that multi- model projections of the first ice- free day are so far lacking, when such first ice- free days could occur is currently unknown. To fill this gap, we here present the first projection of daily ice- free conditions, based on daily CMIP6 [15, 16] sea ice concentration data.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[66, 66, 876, 239]]<|/det|>
+We here focus on predictions of ice- free conditions relative to a 2023- equivalent model state with a daily SIA minimum equal or larger than the 3.39 million \(\mathrm{km^2}\) that were observed in 2023 [17], to illustrate how long it could take to transition from a SIA similar to the one observed in 2023 to the first day with a daily SIA of 1 million \(\mathrm{km^2}\) or less (see the Methods section 4 for details on the exact definition of the 2023 equivalent conditions). In section 2.1 we use 13 different CMIP6 models that performed best over the historical period (see Methods, section 4) with a total of 132 ensemble members to provide probabilistic predictions of first daily ice- free conditions, and show how much earlier they occur than monthly first ice- free predictions. In section 2.2, we then focus on understanding the evolution of the simulations that reach ice- free conditions the fastest from their 2023 equivalent states, following a storyline approach [18]. By focusing on these 'quick transition' simulations, which make up \(7\%\) of the analyzed simulations, we are not suggesting that ice- free conditions will be reached this quickly. Instead, we provide insights into what may lead to such rare but high- impact events.  
+
+<|ref|>sub_title<|/ref|><|det|>[[68, 254, 209, 272]]<|/det|>
+## 2 Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[68, 282, 439, 299]]<|/det|>
+### 2.1 Timing of the first ice-free day  
+
+<|ref|>text<|/ref|><|det|>[[68, 305, 876, 460]]<|/det|>
+The earliest ice- free day occurs 3 years after 2023- equivalent conditions, based on the 13 analyzed CMIP6 models (under SSP1- 2.6, Fig. 1a and Table 1). Another two models show the earliest ice- free day within 4 years (also under SSP1- 2.6), and another 6 ensemble members go ice- free within 5- 6 years (under SSP1- 2.6 to SSP3- 7.0). Overall there are 34 ensemble members from four different models reaching the first ice- free day within 10 years, amounting to \(25\%\) of the assessed simulations (under SSP1- 2.6 through SSP5- 8.5, Extended Data Table 1). However, there are also ensemble members from the analyzed CMIP6 models that do not reach any ice- free day before the end of the 21st century simulations (under SSP1- 1.9 to SSP3- 7.0, Fig. 1a and b and Extended Data Table 1). Given the large range between the fastest and slowest ensemble members from each model, the first ice- free day is not exclusively the result of a specific climate- change forcing but internal variability has a large influence. This agrees with findings for the first ice- free month [2, 12, 14].  
+
+<|ref|>text<|/ref|><|det|>[[68, 460, 876, 604]]<|/det|>
+In terms of the forcing impact, we find that SSP5- 8.5 has the most models 7 to 10 years away from their first ice- free day, SSP3- 7.0 11 to 20 years away, while SSP1- 2.6 has a majority of models never becoming ice- free (Fig. 1a). The split is even more clear when considering the slowest ensemble member (Fig. 1b) of each model: SSP2- 4.5, 3- 7.0 and 5- 8.5 all have a majority of models with their slowest ensemble member 21 to 30 years away from an ice- free day, while SSP1- 1.9 and 2.6 both have a majority of models where the slowest ensemble member never becomes ice- free. The time between the slowest and earliest ensemble member is therefore often lower than 10 years (Extended Data Table 1), because the low emission simulations often agree on not being ice- free, whereas the stronger forced simulations agree on being ice- free somewhat soon. Overall, the stronger the forcing, the shorter the time between the fastest and slowest ensemble member reaching the first ice- free day, i.e. the more consistent the ice- free prediction (Extended Data Table 1).  
+
+<|ref|>text<|/ref|><|det|>[[68, 604, 876, 747]]<|/det|>
+The first ice- free day obviously comes before the first ice- free month, but the distance between the two varies strongly between the simulations (Fig. 1c and d). The warmest SSP5- 8.5 predicts an ice- free month between 7 to 50 years after the 2023 equivalent year; the second warmest SSP3- 7.0, 6 to 50 years after; and the third warmest SSP2- 4.5, 7 to 50 years after. At the other end of the warming range, both SSP1s have a majority of models that do not have an ice- free month before the end of the simulations in 2100, even if they have an ice- free day. This means that a reduction in warming to the level of the SSP1s may not prevent the internal- variability induced first ice- free day, but can potentially prevent an ice- free month in the lower emission scenarios. In general, we find that the ensemble member with the earliest ice- free day is also the one with the earliest ice- free month, although there can be up to 20 years delay even in the warmest simulations (compare Extended Data Table 2 to Extended Data Table 1).  
+
+<|ref|>sub_title<|/ref|><|det|>[[68, 761, 866, 795]]<|/det|>
+### 2.2 Storylines: From 2023 equivalent conditions to the first ice-free day in 3-6 years  
+
+<|ref|>text<|/ref|><|det|>[[68, 801, 876, 930]]<|/det|>
+To illustrate how we could potentially transition from a seasonal daily SIA minimum comparable to what was observed in 2023 to the first daily ice- free conditions within just a few years, we will now focus on the simulations that do so in 3- 6 years - referred to in the following as 'quick transition simulations'. This includes nine simulations, one simulation that reaches ice- free conditions within 3 years, two that take 4 years, two that take 5 years, and four that take 6 years, spanning four different climate models (ACCESS- CM2, CanESM5, EC- Earth3, and MPI- ESM1- 2- LR, see Table 1). Note that for all of the models that have quick transition members, there are other members that take much longer to reach first daily ice- free conditions under the same forcing (with a maximum offset of 42 years, Extended Data Table 1), as internal variability in Arctic sea ice is large [19- 21]. Thus, it is not that these four models are fast to lose their SIA;
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 67, 900, 549]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[120, 564, 905, 622]]<|/det|>
+<center>Fig. 1 Time to ice-free conditions: Histograms of time from 2023 equivalent daily SIA minimum until the first ice-free day (top) or ice-free month (bottom), for the earliest (left) and latest (right) members of each model for all scenarios. For models that only had one ensemble member available, the same ensemble member is shown in the earliest and latest histograms. See Extended Data Table 1 for details on which models reach an ice-free day when and which models have only one ensemble member. The same is shown for the first ice-free month in Extended Data Table 2. </center>  
+
+<|ref|>text<|/ref|><|det|>[[98, 636, 904, 666]]<|/det|>
+it is the specific evolution of the internal climate variability that leads to these ensemble members reaching daily ice- free conditions within 3- 6 years after the last 2023 equivalent SIA daily minimum.  
+
+<|ref|>title<|/ref|><|det|>[[120, 678, 626, 694]]<|/det|>
+#### 2.2.1 Multiyear SIA transition to the first ice-free day  
+
+<|ref|>text<|/ref|><|det|>[[120, 700, 905, 886]]<|/det|>
+By definition, all the quick transition simulations have a very rapid transition from a 2023 equivalent daily minimum SIA to daily ice- free conditions (Figure 2). Notably, all quick transition simulations meet the criteria for a Rapid Ice Loss Event (RILE) [22- 25] during September, with all of them reaching daily ice- free conditions during a RILE period, defined as an at least 4- year period where the trend in the 5- year running mean sea ice extent (SIE) is larger than \(- 0.3\) million \(\mathrm{km^2}\) per year [24] (see the shading in Figure 2). In addition, all of them show a RILE or near RILE (if relaxing the RILE threshold from \(- 0.3\) to \(- 0.299\) million \(\mathrm{km^2}\) per year) in August during the transition period from the 2023 equivalent conditions to the first ice- free day (Extended Data Figure 1). RILEs have been found in all CMIP6 models and all months of the year [25], and as their name implies, describe a rapid loss of sea ice, which exceeds even the September SIA loss observed in the early 21st century [25]. While the exact drivers of RILEs are still under investigation, both atmospheric and oceanic drivers have been suggested as being important [24]. The atmosphere was found to be especially important in driving RILEs once the sea ice cover is already primarily limited to the deep Arctic Ocean basin [24], as is the case during the summer on the way to the first ice- free day.  
+
+<|ref|>text<|/ref|><|det|>[[120, 886, 904, 928]]<|/det|>
+The rapid transition to a first early ice- free day, however, does not just occur in the summer, but also includes a reduction of the sea ice cover during the autumn, winter, and spring (Figure 3). While this is clear from the SIA alone in most of the quick transition models (Figure 3), the EC- Earth3 simulations do not
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[210, 64, 758, 297]]<|/det|>
+
+<table><tr><td>Model<br>&amp;amp; member &amp;amp; SSP</td><td>Time to first ice-free day</td><td>Warming by that year</td><td>First ice-free day</td><td>Ice-free period</td></tr><tr><td>ACCESS-CM2</td><td>6 years</td><td>1.7℃</td><td>Aug-11</td><td>53 days</td></tr><tr><td>r6ilp1f1 SSP3-7.0</td><td></td><td></td><td></td><td></td></tr><tr><td>ACCESS-CM2</td><td>4 years</td><td>1.5℃</td><td>Sep-09</td><td>12 days</td></tr><tr><td>r7ilp1f1 SSP1-2.6</td><td></td><td></td><td></td><td></td></tr><tr><td>CanESM5</td><td>4 years</td><td>2.3℃</td><td>Aug-20</td><td>25 days</td></tr><tr><td>r8ilp1f1 SSP1-2.6</td><td>6 years</td><td>2.5℃</td><td>Aug-15</td><td>42 days</td></tr><tr><td>EC-Earth3</td><td>3 years</td><td>1.7℃</td><td>Aug-26</td><td>25 days</td></tr><tr><td>r4ilp1f1 SSP1-2.6</td><td>5 years</td><td>1.6℃</td><td>Aug-29</td><td>17 days</td></tr><tr><td>EC-Earth3</td><td>5 years</td><td>1.5℃</td><td>Aug-14</td><td>32 days</td></tr><tr><td>r12ilp1f1 SSP2-4.5</td><td></td><td></td><td></td><td></td></tr><tr><td>MPI-ESM1-2-LR</td><td>6 years</td><td>1.7℃</td><td>Sep-03</td><td>11 days</td></tr><tr><td>r38ilp1f1 SSP3-7.0</td><td></td><td></td><td></td><td></td></tr><tr><td>MPI-ESM1-2-LR</td><td>6 years</td><td>1.5℃</td><td>Aug-27</td><td>23 days</td></tr><tr><td>r43ilp1f1 SSP2-4.5</td><td></td><td></td><td></td><td></td></tr></table>
+
+<|ref|>table_caption<|/ref|><|det|>[[210, 306, 757, 360]]<|/det|>
+Table 1 Characteristics of the nine quick transition simulations: Showing the time from 2023 equivalent conditions to the first ice-free day, the degree of global warming for the year of the first ice-free day compared to pre-industrial period (5-year running mean, see Methods section 4), the date of that first ice-free day, and the duration of that first ice-free period (in days).
+
+<|ref|>text<|/ref|><|det|>[[61, 389, 877, 488]]<|/det|>
+119 show a notable change in the wintertime SIA. But when taking into account the sea ice thickness as well,120 and thus looking at the total sea ice mass (Extended Data Figure 2), it is clear that in all models we see a121 clear decrease in the total Arctic sea ice mass year-around. This means that reduced sea ice thickness in the122 wintertime occurs in all models soon (within 1 or 2 years) after they had a SIA minimum at or above the123 2023 conditions, even when it is not apparent in the wintertime SIA. As discussed in the next section, this124 reduction in sea ice is linked to warm winters and springs (Extended Data Figure 3), as well as a delayed125 freeze up in the autumn [26] (Figure 3).
+
+<|ref|>text<|/ref|><|det|>[[61, 490, 877, 587]]<|/det|>
+126 Once the first ice-free day is reached, the Arctic does not remain ice-free for one day only. The ice-free127 period lasts between 11 and 53 days in the 9 quick transition simulations, with an average duration of 27days (Table 1). The ice-free duration is set primarily by the day the first ice-free conditions occur, with the128 simulations that show ice-free conditions earliest showing the longest duration. Specifically, we find that the129 first ice-free day for the quick transition simulations ranges between Aug 11 to Sept 09 (days 223 to 252),130 with an average of Aug 26 (day 236). The first ice-free day occurs in September for ACCESS r7ilp1f1 and131 MPI-ESM1-2-LR r38ilp1f1, which also have the shortest ice-free duration (12 and 11 days, respectively).
+
+<|ref|>text<|/ref|><|det|>[[61, 590, 877, 658]]<|/det|>
+132 Notably, in the year with the first ice-free day in the quick transition simulations, the 2023 daily SIA133 minimum value of 3.39 million km2 is reached at the latest by day July 31st (day 212) (see Figure 3)-42days earlier than the observed 2023 daily minimum on Sept 11 (day 254, according to the Climate Data134 Record (CDR) derived SIA [17]). Thus, if in the future the observed SIA crosses the 3.39 million km2 SIA135 in July, this could be a warning sign that an ice-free day may occur later in the summer.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[150, 87, 856, 820]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[120, 824, 905, 925]]<|/det|>
+<center>Fig. 2 Rapid transition from 2023 equivalent state to the first ice-free day: The simulated SIA daily minimum is shown in blue, simulated September monthly mean simulated SIA in cyan, and observed daily minimum SIA based on the CDR SIC data [17] is shown as black line [all in million km²]. Also shown are Rapid Ice Loss Events (RILEs) during September (shaded), defined based on the monthly SIE [24]. A vertical black dashed line indicates the year when the simulated daily SIA minimum was last at or above the 2023 observed daily SIA minimum of 3.39 million km², which is in turn is indicated with a horizontal black dashed line. Vertical dashed grey lines show when ice-free conditions are reached (first for daily, then for monthly, if there is only one both reach ice-free conditions for the first time in the same year). The grey dashed horizontal line shows the 1 million km² ice-free threshold. Extended Data Figure 1 shows that RILEs or near-RILES also occur during August. This illustrates that the transition to first daily ice-free conditions occurs during a RILE in the quick transition simulations. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[78, 115, 918, 556]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[68, 560, 930, 629]]<|/det|>
+<center>Fig. 3 Sea ice area on the way to first daily ice-free conditions: Seasonal cycle of daily SIA [in million \(\mathrm{km}^2\) ] from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (3.39 million \(\mathrm{km}^2\) , in dark blue), based on the CDR SIA [17] (shown in black) to the first year where the daily SIA reached ice-free conditions (bold line in pink; colors in between see legend). The intermediate years are colored as shown in the legend. The 2023 daily SIA minimum is shown as red dashed horizontal line and the 1 million \(\mathrm{km}^2\) ice-free line is shown as grey dashed horizontal line. This shows that the SIA loss leading up to the first ice-free day is not limited to only the minimum SIA, but occurs throughout much of the year. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[120, 65, 895, 96]]<|/det|>
+### 2.2.2 Final-year triggers: Winter warm air intrusions, spring blocking, and summer storms  
+
+<|ref|>text<|/ref|><|det|>[[120, 102, 905, 174]]<|/det|>
+For all quick transition simulations, the sea ice is pre- conditioned for an ice- free day: Most years leading to the year of the first ice- free day have a delayed atmospheric cooling in autumn and warm spells all the way to December (Extended Data Figure 3), consistent with the delayed and reduced sea ice formation described above. A series of events in the last winter, spring, and summer finish weakening the ice both dynamically and thermodynamically, leading to that first ice- free day.  
+
+<|ref|>text<|/ref|><|det|>[[120, 175, 905, 319]]<|/det|>
+For all cases, the last winter is warm (Figure 4a and Extended Data Figure 3). North of \(80^{\circ}\mathrm{N}\) , maximum air temperatures exceed the "spring" transition temperature \(- 20^{\circ}\mathrm{C}\) [27] all winter long, most often in association with strong high pressures (Figure 4b and c, and Extended Data Figure 4), but also sometimes in association with strong low pressures, i.e. due to a warm air intrusion (Extended Data Figure 5a). The warmth and high pressure persist into the spring for all nine simulations, with two different patterns: A year where the spring warming is shifted up to one month early (see e.g. the case that becomes ice- free fastest, EC- Earth3 r4ilp1fl, Extended Data Figure 3), or a year that is not extreme but is more stable, has fewer cold spells than usual (see e.g. CanESM5 r9ilp1fl, Extended Data Figure 3). Heatwaves with maximum temperatures exceeding \(0^{\circ}\mathrm{C}\) are common (Fig. 4), lasting for several days because the warm air is blocked over the central Arctic by a high pressure system (Extended Data Figure 5b).  
+
+<|ref|>text<|/ref|><|det|>[[120, 319, 905, 445]]<|/det|>
+The last summer is warm to very warm for all quick transition simulations, with temperatures that can exceed \(10^{\circ}\mathrm{C}\) from day 151 (late May, Figure 4). The atmospheric pressure becomes less stable, and in six out of nine simulations (CanESM5 r8ilp1fl, all three EC- Earth3 and both MPI- ESM1- 2- LR), storms cross through the Arctic, especially so in the last month or even last days before the first ice- free day (Figure 4). EC- Earth3 r4ilp1fl, which has an ice- free day only 3 years after 2023 conditions, has one extensive storm shooting from the Kara Sea region to the Canada basin in 5 days, culminating in the earliest simulated first ice- free day (Extended Data Figure 6). In most of the quick transition simulations, such as EC- Earth3 r12ilp1fl (Extended Data Figure 5c), instead several weak storm systems simultaneously stress the sea ice at various locations across the Arctic in the days leading up to the first ice- free day.  
+
+<|ref|>text<|/ref|><|det|>[[120, 445, 905, 546]]<|/det|>
+The warm atmospheric conditions triggering the first ice- free day are predicted to become increasingly common in a warmer world [28]. As the Arctic warms, heatwaves at any season become more likely [29], as do warm air intrusions and storms [30]. But it is not too late to avoid an ice- free day: For all quick transition cases, the first ice- free day occurs on years at or above the \(1.5^{\circ}\mathrm{C}\) of global warming compared to pre- industrial level set as a target to not exceed by the Paris Agreement [31] (Table 1). This agrees with prior work on the first monthly ice- free Arctic, which also found that ice- free conditions may be avoided if global warming stayed below the Paris Agreement target of less than \(1.5^{\circ}\mathrm{C}\) [32- 34].
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[100, 230, 860, 690]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[92, 715, 877, 775]]<|/det|>
+<center>Fig. 4 Atmospheric conditions on the way to the first daily ice-free conditions: For each quick transition simulation, we show the last year of the daily a) maximum surface air temperature and of the b) minimum and c) maximum sea level pressure, all north of \(80^{\circ}\mathrm{N}\) . A 5-day running mean was applied to all timeseries. On b) and c), bold lines highlight strong low and high pressure events, respectively, as discussed in the text. All cases are warm in winter, in association with extreme low (warm air intrusions) or high (blocking) pressure events. They are very warm in spring, and many become stormy in summer. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[120, 61, 475, 81]]<|/det|>
+## 3 Discussion and Conclusions  
+
+<|ref|>text<|/ref|><|det|>[[120, 90, 905, 176]]<|/det|>
+We showed that based on CMIP6 models, the earliest ice- free day in the Arctic occurs within 3 years from 2023 equivalent conditions, with a \(7\%\) probability of an ice- free day within 6 years. The highest probability of the first ice- free day occurring lies within 7- 20 years (Figure 1). Note that all of these projections start from the last time the daily SIA minimum is above or equal to 3.39 million \(\mathrm{km^2}\) . That could be in 2023, if all future daily SIA minima are below 3.39 million \(\mathrm{km^2}\) . But the countdown to ice- free could also start from a future year, if the observed daily SIA minimum in years after 2023 is above 3.39 million \(\mathrm{km^2}\) .  
+
+<|ref|>text<|/ref|><|det|>[[120, 177, 905, 433]]<|/det|>
+While 7- 20 years beyond 2023 equivalent conditions represents the most likely range during which the first ice- free day is projected to occur, there is a large prediction uncertainty of the first ice- free day, associated with all three sources of climate prediction uncertainties [35]. The scenario uncertainty introduced by the unknown future emissions is two- fold. First, there is a distinct difference between the lowest SSP1- 1.9 scenario, which shows no early ice- free day (earliest projection is 13 years), and the other SSPs (SSP1- 2.6 to SSP5- 8.5), which all have members with ice- free days within a decade. The finding that early ice- free days occur under SSP1- 2.6 to SSP5- 8.5 without any influence of the strength of the forcing scenario agrees with prior work on the timing of the first ice- free month in the Arctic [2, 36]. SSP1- 1.9 has not generally been used in many studies of an ice- free Arctic. However, as SSP1- 1.9 tends to stay around \(1.5^{\circ}\mathrm{C}\) by 2100 [37], the possibility to avoid ice- free conditions under this scenario matches with studies that found that for a global warming below the \(1.5^{\circ}\mathrm{C}\) Paris target [31] a monthly mean ice- free Arctic may be avoidable [32- 34]. The second effect of the scenario uncertainty is that the stronger the forcing, the narrower the internal variability prediction uncertainty, ranging from 26 years for SSP5- 8.5 to more than 60 years for SSP1- 1.9 and SSP1- 2.6. A similarly large internal variability uncertainty has also been found for projections of the first ice- free month [14, 38]. This highlights that internal variability uncertainty affects all projections of an ice- free Arctic, be it monthly or daily, limiting the prediction accuracy to a range of at least two decades, if not more. In addition, despite performing model selection based on the historical SIA simulation, model differences further add to the prediction uncertainty, as also seen for monthly ice- free projections [13].  
+
+<|ref|>text<|/ref|><|det|>[[120, 433, 905, 590]]<|/det|>
+To understand the rare but high- impact possibility of a rapid loss of SIA to 1 million \(\mathrm{km^2}\) from 2023 equivalent conditions, we investigated the storylines of the nine fastest cases, which reached ice- free conditions within 3- 6 years. Most of the first ice- free days occurs in August, and the first ice- free period lasted between 11 and 53 days. What they all had in common was that the first ice- free day occurred during a RILE (Figure 2). What is noteworthy is that for all quick transition cases the 2023 equivalent year occurs after a period of little or no trend in the daily and monthly SIA over the previous 10- 15 years, with previously lower SIA than the the 2023 equivalent. This is not dis- similar to the observed SIA evolution in the 15 years prior to 2023 (see Figure 2). Furthermore, in an investigation of RILE events in CMIP6 models, it has been shown that the probability of a RILE increases by \(20\%\) compared to the overall RILE probability after a 10- year stable period in the SIE [25]. These results suggest that if a RILE were to occur in the near future, it could potentially bring us a first ice- free day relatively quickly.  
+
+<|ref|>text<|/ref|><|det|>[[120, 590, 905, 718]]<|/det|>
+The primary trigger of the rapid transition to the first ice- free day within 3- 6 years that we identified was a warm atmosphere in the previous autumns/winters, leading to a loss of sea ice mass year- round (Extended Data Figure 2). The last year had "spring" daily mean temperatures already in January, thanks to heatwaves/blockings and/or warm air intrusions (Figure 4). In addition, we frequently found storms going across the Arctic in the days leading up to the first ice- free day. All these events are projected to increase in frequency as the Arctic warms [29], making the first ice- free day increasingly more likely. The good news is, for all storyline cases, the first ice- free day occurs in years with a 5- year running mean global temperature at or above \(1.5^{\circ}\mathrm{C}\) compared to pre- industrial level (Table 1). This means that if we could keep warming below the Paris Agreement target of \(1.5^{\circ}\mathrm{C}\) of global warming [31], ice- free days could potentially still be avoided.  
+
+<|ref|>sub_title<|/ref|><|det|>[[120, 733, 254, 750]]<|/det|>
+## 4 Methods  
+
+<|ref|>sub_title<|/ref|><|det|>[[120, 762, 369, 779]]<|/det|>
+### 4.1 Data and Definitions  
+
+<|ref|>text<|/ref|><|det|>[[120, 786, 905, 928]]<|/det|>
+We analyzed simulations from all models that participated in the Climate Model Intercomparison Project phase 6 (CMIP6, [15]) that had daily sea ice on the ocean ("siconc") or atmosphere grids ("siconca") available on any of the Earth System Grid Federation (ESGF) portals in late May 2024, as well as files that had been previously downloaded onto the Levante server of the German Climate Computing Center (DKRZ). We also obtained their grid cell area ("areacello" and "areacella", respectively). All available ensemble members were used. We used the historical scenario for our model selection (see next subsection), and the Shared Socioeconomic Pathways SSP1- 1.9, SSP1- 2.6, SSP2- 4.5, SSP3- 7.0 and SSP5- 8.5 [16] for our ice- free projections. For the subset of cases that we investigated further in section 2.2, we also used their daily surface air temperature ("tas"), daily sea level pressure ("psl"), and their monthly sea ice mass ("simass") (monthly due to the unavailability of daily simass in some of these models).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[60, 66, 875, 95]]<|/det|>
+The SIA, SIE and sea ice mass (SIMASS) were calculated north of \(30^{\circ}\mathrm{N}\) , on the model's native grid. SIA was defined as the sum over all grid cells n of the sea ice concentration multiplied by the grid cell area:  
+
+<|ref|>equation<|/ref|><|det|>[[352, 107, 874, 139]]<|/det|>
+\[SIA = \sum_{n}\mathrm{sicone(n)}\times \mathrm{areacello(n)}. \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[60, 150, 875, 179]]<|/det|>
+SIE was defined as the sum of the grid cell area for all grid cells m where the sea ice concentration was larger than 0.15:  
+
+<|ref|>equation<|/ref|><|det|>[[393, 177, 874, 207]]<|/det|>
+\[SIE = \sum_{m}\mathrm{areacello(m)}. \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[60, 207, 875, 237]]<|/det|>
+As recommended in previous studies (see review in [12]), we conducted our analyses using only SIA, with the exception of the RILE analysis.  
+
+<|ref|>text<|/ref|><|det|>[[60, 237, 875, 265]]<|/det|>
+The first ice- free year was defined as the first year where daily or monthly SIA is lower than or equal to 1 million \(\mathrm{km}^2\) .  
+
+<|ref|>text<|/ref|><|det|>[[60, 265, 875, 308]]<|/det|>
+RILEs were defined based on the September monthly SIE, following [24], which means that a RILE is defined as "a period of at least 4 years for which the trend in the 5- year running mean minimum SIE is lower than \(- 0.3\) million \(\mathrm{km}^2\) /year".  
+
+<|ref|>text<|/ref|><|det|>[[90, 308, 875, 380]]<|/det|>
+The warming of the models compared to pre- industrial was computed by using the daily surface air temperature for the first 50 years of the pre- industrial control simulation (on ensemble member rli1p1fl); taking the area- weighted global temperature, averaged over these 50 years; and subtracting it from the area- weighted global temperature averaged 2 year prior to the first year with an ice- free day until 2 years after that first year (i.e., over a 5 year period).  
+
+<|ref|>text<|/ref|><|det|>[[90, 380, 875, 450]]<|/det|>
+All analysis using daily data was performed on a no- leap 365 day calendar, and models that produced output on a standard calendar with leap years had their Feb 29th data dropped. Models that used a 360 day calendar (specifically UKESM1- 0- LL and HadGEM3- GC31- LL) were not included in the analysis, as their results can not be directly compared with models with 365 days when analyzing the timing of daily ice- free conditions.  
+
+<|ref|>sub_title<|/ref|><|det|>[[92, 465, 290, 481]]<|/det|>
+### 4.2 Model selection  
+
+<|ref|>text<|/ref|><|det|>[[90, 488, 875, 515]]<|/det|>
+Due to the large model spread in simulations of Arctic sea ice evolution [2], we used two SIA based criteria to select the models that performed best over years 2000- 2014 in the historical CMIP6 simulations.  
+
+<|ref|>text<|/ref|><|det|>[[90, 515, 875, 630]]<|/det|>
+The first criterion used here was that the simulated September monthly mean falls within the satellite- derived SIA in September over 2000- 2014, plus/minus the average standard deviation of the 2000- 2014 average September SIA in models with more than 6 members \((\pm 0.45\) million \(\mathrm{km}^2\) ). To account for observational uncertainty, we used the monthly SIA calculated from daily NOAA/NSIDC CDR SIC data, version 4 [17], using the CDR as upper bound and the NASA Team [39] as lower bound (both with pole hole filled from the [17] dataset). For September, the 2000- 2014 mean difference between the two is \(- 1.48\) million \(\mathrm{km}^2\) . This criteria means that we exclude models that have a mean state over the last 15 years of the historical simulations that is too high or low compared to observations.  
+
+<|ref|>text<|/ref|><|det|>[[90, 630, 875, 701]]<|/det|>
+The second criterion used here was that the day of the minimum daily SIA from the simulations between 2000 and 2014 falls within the observational range of day 238 (August 26) to day 272 (Sept 29), plus/minus 5 days (the average standard deviation of the sea ice minimum day over 2000- 2014 from the models with more than 6 members). We chose this second criterion to ensure that models simulate the daily minimum at a time comparable to observations, since the focus of this study is on the first ice- free day.  
+
+<|ref|>text<|/ref|><|det|>[[90, 701, 875, 757]]<|/det|>
+For both criteria, if any ensemble member from a model fell within the observational ranges, the criterion was considered to be met. Both criteria had to be met for a model to be retained. Applying these two criteria reduced the number of models from 30 to 13 models. The models retained are listed and cited in Supplementary Table S1.  
+
+<|ref|>sub_title<|/ref|><|det|>[[90, 773, 518, 790]]<|/det|>
+### 4.3 Detection of the '2023 equivalent year'  
+
+<|ref|>text<|/ref|><|det|>[[90, 796, 875, 868]]<|/det|>
+In order to assess the storyline of how soon the Arctic Ocean could be ice- free (1 million \(\mathrm{km}^2\) or less of SIA remaining), we start our analysis from the last year the daily SIA minimum was equal to or larger than the observed 2023 daily SIA minimum before a simulation reaches daily ice- free conditions for the first time. The observed 2023 daily SIA minimum was 3.39 million \(\mathrm{km}^2\) , based on the daily SIA calculated from the pole- hole filled daily NOAA/NSIDC CDR SIC data, version 4 [17].  
+
+<|ref|>text<|/ref|><|det|>[[90, 869, 875, 926]]<|/det|>
+Some ensemble members from the selected models had to be discarded because their 2023 equivalent pre- dated the beginning of the scenario simulations, as their daily SIA minimum was below 3.39 million \(\mathrm{km}^2\) at the beginning of the scenario simulations, but their historical simulation could not be obtained (broken link, corrupted data, not turning up on any of the portals).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[90, 66, 905, 224]]<|/det|>
+Acknowledgements. We acknowledge the World Climate Research Programme, which, through its Working Group on Coupled Modelling, coordinated and promoted CMIP6. We thank the Sea Ice Model Intercomparison Project (SIMIP) for requesting daily sea ice output for CMIP6. We thank the climate modeling groups for producing and making available their model output, the Earth System Grid Federation (ESGF) for archiving the data and providing access, and the multiple funding agencies who support CMIP6 and ESGF. CH acknowledges the data access and computing supported provided by the Deutsches Klimarechenzentrum (DKRZ) fourth High Performance Computer System for Earth System Research (HLRE- 4) "Levante". AJ acknowledges the data access and computing support provided by the NCAR CMIP Analysis Platform (doi:10.5065/D60R9MSP) as well as the high- performance computing support from Derecho (doi:10.5065/qx9a- pg09) provided by NSF NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation.  
+
+<|ref|>sub_title<|/ref|><|det|>[[120, 237, 271, 255]]<|/det|>
+## Declarations  
+
+<|ref|>text<|/ref|><|det|>[[120, 265, 905, 310]]<|/det|>
+- Funding: C. Heuzé's contribution was supported by Swedish National Research Council Starting Grant award 2018-03859 and Swedish National Space Agency award 2022-00149. A. Jahn's contribution was supported by NSF-CAREER award 1847398.  
+
+<|ref|>text<|/ref|><|det|>[[120, 310, 619, 324]]<|/det|>
+- Competing interests: The authors declare no competing interests.  
+
+<|ref|>text<|/ref|><|det|>[[120, 325, 571, 338]]<|/det|>
+- Ethics approval and consent to participate: Not applicable  
+
+<|ref|>text<|/ref|><|det|>[[120, 339, 430, 352]]<|/det|>
+- Consent for publication: Not applicable  
+
+<|ref|>text<|/ref|><|det|>[[120, 353, 905, 425]]<|/det|>
+- Data availability: The CMIP6 data is freely available on the Earth System Grid Federation (ESGF, https://esgf-node.llnl.gov/search/cmip6/, https://esgf-metagrid.cloud.dkrz.de/search, https://esgf-node.ipsl.upmc.fr/projects/cmip6-ipsl/ and https://esgf-ui.ceda.ac.uk/cog/search/cmip6-ceda/). The derived daily SIE and SIA data will be archived in a freely accessible repository upon acceptance of the manuscript and the link to the data will be added here before publication.  
+
+<|ref|>text<|/ref|><|det|>[[120, 425, 415, 438]]<|/det|>
+- Materials availability: Not applicable  
+
+<|ref|>text<|/ref|><|det|>[[120, 439, 380, 452]]<|/det|>
+- Code availability: Not applicable  
+
+<|ref|>text<|/ref|><|det|>[[120, 453, 905, 481]]<|/det|>
+- Author contribution: CH and AJ jointly and with equal contributions conceptualized the article, obtained and analyzed data, produced figures and wrote the article.  
+
+<|ref|>sub_title<|/ref|><|det|>[[120, 503, 250, 521]]<|/det|>
+## References  
+
+<|ref|>text<|/ref|><|det|>[[120, 530, 905, 560]]<|/det|>
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+
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+
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+
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+<--- Page Split --->
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+
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+
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+[38] Wyburn- Powell, C. & Jahn, A. Large- scale climate modes drive low- frequency regional Arctic sea ice variability. J. Clim. (2024).  
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+[39] Cavalieri, D., Gloersen, P. & Campbell, W. Determination of sea ice parameters with the Nimbus 7 SMMR. J. Geophys. Res. 89, 5355- 5369 (1984).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[145, 80, 808, 820]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[92, 828, 878, 931]]<|/det|>
+Extended Data Fig. 1 RILE events on the way to the first ice- free day: The monthly mean SIA from each quick transition simulation for all months of the year is shown in blue shading [in million \(\mathrm{km^2}\) ], with RILE events in a given month overlaid in red. RILE events in each month of the year are defined based on monthly mean SIE [24], as described in the Methods section 4. When slightly relaxing the RILE criteria from a trend of \(- 0.3\) million \(\mathrm{km^2}\) per year to \(- 0.299\) million \(\mathrm{km^2}\) per year, additional RILE events show up for some simulations (shown in pink). Vertical dashed grey lines indicate the year of the first ice- free day and first ice- free month. When only one grey line is shown then the first ice- free day and month occur in the same year. The vertical dashed black line shows the 2023 equivalent year. This figure shows that all quick transition members have a RILE or near RILE in August and September during the transition from the 2023 equivalent year to the first ice- free day, with some simulations also showing RILES in additional months.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[80, 113, 915, 555]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[45, 558, 950, 594]]<|/det|>
+<center>Extended Data Fig. 2 Sea Ice Mass on the way to first daily ice-free conditions: As in Figure 3, but for the monthly mean total sea ice mass north of 66N [in million kg], from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend; same color coding as in Figure 3). </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[42, 155, 952, 711]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[45, 729, 952, 777]]<|/det|>
+<center>Extended Data Fig. 3 Surface air temperature on the way to first daily ice-free conditions: As in Figure 3, but for the daily average surface air temperature north of \(80^{\circ}\mathrm{N}\) , from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend, same color coding as in Figure 3). Black line is the pre-2023 average. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[42, 160, 951, 710]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[45, 727, 953, 775]]<|/det|>
+<center>Extended Data Fig. 4 Sea level pressure on the way to first daily ice-free conditions: As in Figure 3, but for the daily average sea level pressure north of \(80^{\circ}\mathrm{N}\) , from the last year the daily SIA minimum was above to or equal to the 2023 daily SIA minimum (in dark blue) to the first year where the daily SIA goes ice-free (bold line in pink, see legend, same color coding as in Figure 3). Black line is the pre-2023 average. Only extreme events are coloured; the vertical thick grey line indicates the first ice-free day. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[125, 101, 828, 343]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[140, 87, 805, 101]]<|/det|>
+<center>a) Warm air intrusion; EC-Earth3 r8i1p1f1 under SSP1-2.6, winter leading to first ice-free day (8 Feb) </center>  
+
+<|ref|>image<|/ref|><|det|>[[125, 368, 825, 602]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[140, 348, 813, 363]]<|/det|>
+<center>b) Blocked heatwave; EC-Earth3 r12i1p1f1 under SSP2-4.5, spring leading to first ice-free day (15 May) </center>  
+
+<|ref|>image<|/ref|><|det|>[[125, 633, 477, 867]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[145, 610, 800, 625]]<|/det|>
+<center>c) Series of storms; EC-Earth3 r12i1p1f1 under SSP2-4.5, one day before first ice-free day (13 Aug) </center>  
+
+<|ref|>image<|/ref|><|det|>[[531, 700, 785, 802]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[92, 876, 877, 912]]<|/det|>
+Extended Data Fig. 5 Atmospheric events leading to an ice- free day: Sea level pressure (left) and when relevant, surface air temperature (right) on exemplary days of the last year before the model had its first ice- free day illustrating a) a warm air intrusion; b) a blocking pattern coinciding with a heatwave; and c) a series of a least four storms.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[150, 110, 861, 853]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[120, 861, 904, 886]]<|/det|>
+<center>Extended Data Fig. 6 The fastest ice-loss simulation and its last storm: Sea level pressure, backtracking from the first ice-free day a storm crossing the Arctic for our fastest case, EC-Earth3 r4ilp1fl under SSP1-2.6. </center>
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[108, 95, 860, 410]]<|/det|>
+<table><tr><td>Model</td><td>SSP1-1.9</td><td>SSP1-2.6</td><td>SSP2-4.5</td><td>SSP3-7.0</td><td>SSP5-8.5</td></tr><tr><td>ACCESS-CM2</td><td>-</td><td>r1ilplf 4<br/>r6ilplf 23</td><td>r1ilplf 9<br/>r4ilplf 20</td><td>r6ilplf 6<br/>r3ilplf 21</td><td>r9ilplf 8<br/>r4ilplf 22</td></tr><tr><td>BCC-CSM2-MR</td><td>-</td><td>r1ilplf 54</td><td>r1ilplf 20</td><td>-</td><td>r1ilplf 28</td></tr><tr><td>CanESM5</td><td>r4ilplf 18<br/>r5ilplf 34</td><td>r8ilplf 4<br/>r1ilp2f 28</td><td>r8ilplf 8<br/>r5ilp2f 27</td><td>r7ilplf 9<br/>r5ilp2f 22</td><td>r5ilp2f 9<br/>r10ilp2f 21</td></tr><tr><td>CNRM-CM6-1-HR</td><td>-</td><td>r1ilp2f &gt;70</td><td>-</td><td>-</td><td>r1ilp2f 10</td></tr><tr><td>EC-Earth3</td><td>r4ilplf 18</td><td>r4ilplf 3<br/>r1ilplf 7</td><td>r12ilp1f 5<br/>r16ilp1f 21</td><td>-</td><td>-</td></tr><tr><td>EC-Earth3-Veg-LR</td><td>r3ilplf 13<br/>r2ilplf &gt;70</td><td>r1ilplf 11<br/>r2ilplf 17</td><td>r1ilplf &gt;70</td><td>-</td><td>-</td></tr><tr><td>IPSL-CM5A2-INCA</td><td>-</td><td>r1ilplf &gt;70</td><td>-</td><td>r1ilplf 18</td><td>-</td></tr><tr><td>MIROC6</td><td>r1ilplf 52</td><td>r3ilplf 20<br/>r1ilplf 35</td><td>r1ilplf 22<br/>r3ilplf 39</td><td>r2ilplf 15<br/>r3ilplf 27</td><td>r3ilplf 23<br/>r1ilplf 27</td></tr><tr><td>MIROC-ES2H</td><td>r1ilp4f2 &gt;70</td><td>r1ilp4f2 &gt;70</td><td>r3ilp4f2 16<br/>r2ilp4f2 33</td><td>r1ilp4f2 23</td><td>r1ilp4f2 17<br/>r2ilp4f2 25</td></tr><tr><td>MIROC-ES2L</td><td>r1ilp1f2 24<br/>r10ilp1f2 59</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MPI-ESM-1-2-HAM</td><td>-</td><td>-</td><td>-</td><td>r2ilp1f 13<br/>r1ilp1f 19</td><td>-</td></tr><tr><td>MPI-ESM1-2-LR</td><td>r4ilplf 36<br/>r50ilp1f1 &gt;70</td><td>r5ilp1f 12<br/>r48ilp1f1 &gt;70</td><td>r43ilp1f 6<br/>r18ilp1f 46</td><td>r38ilp1f 6<br/>r1ilp1f 48</td><td>r7ilp1f 9<br/>r44ilp1f 35</td></tr><tr><td>NorESM2-LM</td><td>-</td><td>r1ilplf &gt;70</td><td>r2ilplf 24<br/>r3ilp1f 36</td><td>r1ilplf 38<br/>r3ilp1f &gt;70</td><td>r1ilp1f 23</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[108, 419, 857, 465]]<|/det|>
+**Extended Data Table 1** Time to the first ice-free day: For each selected CMIP6 model and for each scenario, the ensemble members with the earliest (top) and latest (bottom) ice-free day, and years until that ice free day. Only one value is shown if the model had only one ensemble member available. If the entry is &gt;70 years, this means that the simulation did not reach ice-free conditions before the end of the 21st century simulations. 
+
+<|ref|>table<|/ref|><|det|>[[108, 544, 860, 862]]<|/det|>
+<table><tr><td>Model</td><td>SSP1-1.9</td><td>SSP1-2.6</td><td>SSP2-4.5</td><td>SSP3-7.0</td><td>SSP5-8.5</td></tr><tr><td>ACCESS-CM2</td><td>-</td><td>r9ilplf 7<br/>r10ilp1f 26</td><td>r2ilplf 10<br/>r4ilplf 20</td><td>r6ilplf 6<br/>r4ilplf 22</td><td>r9ilplf 8<br/>r4ilplf 22</td></tr><tr><td>BCC-CSM2-MR</td><td>-</td><td>r1ilplf 54</td><td>r1ilplf 21</td><td>-</td><td>r1ilplf 31</td></tr><tr><td>CanESM5</td><td>r4ilplf 18<br/>r5ilplf 34</td><td>r9ilplf 6<br/>r1ilp2f 32</td><td>r8ilplf 8<br/>r5ilp2f 28</td><td>r7ilplf 11<br/>r10ilp1f 29</td><td>r6ilplf 11<br/>r1ilp1f 22</td></tr><tr><td>CNRM-CM6-1-HR</td><td>-</td><td>r1ilplf &gt;70</td><td>-</td><td>-</td><td>r1ilplf 10</td></tr><tr><td>EC-Earth3</td><td>r4ilplf 27<br/>r4ilplf 27</td><td>r1ilplf 8<br/>r8ilplf 26</td><td>r10ilp1f 7<br/>r16ilp1f 22</td><td>-</td><td>-</td></tr><tr><td>EC-Earth3-Veg-LR</td><td>r3ilplf 18<br/>r2ilplf &gt;70</td><td>r2ilplf 39<br/>r1ilplf 42</td><td>r1ilplf &gt;70</td><td>-</td><td>-</td></tr><tr><td>IPSL-CM5A2-INCA</td><td>-</td><td>r1ilplf &gt;70</td><td>-</td><td>r1ilplf 18</td><td>-</td></tr><tr><td>MIROC6</td><td>r1ilplf &gt;70</td><td>r2ilplf 25<br/>r3ilplf 48</td><td>r1ilplf 23<br/>r3ilplf 42</td><td>r2ilplf 15<br/>r3ilplf 27</td><td>r3ilplf 24<br/>r2ilplf 29</td></tr><tr><td>MIROC-ES2H</td><td>r1ilp4f2 &gt;70</td><td>r1ilp4f2 &gt;70</td><td>r3ilp4f2 16<br/>r1ilp4f2 34</td><td>r1ilp4f2 23</td><td>r1ilp4f2 17<br/>r2ilp4f2 25</td></tr><tr><td>MIROC-ES2L</td><td>r1ilp1f2 28<br/>r3ilp1f2 &gt;70</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>MPI-ESM-1-2-HAM</td><td>-</td><td>-</td><td>-</td><td>r2ilplf 13<br/>r1ilplf 20</td><td>-</td></tr><tr><td>MPI-ESM1-2-LR</td><td>r48ilp1f 48<br/>r50ilp1f1 &gt;70</td><td>r34ilp1f 21<br/>r9ilp1f 1&gt;70</td><td>r26ilp1f 15<br/>r18ilp1f 46</td><td>r38ilp1f 7<br/>r1ilp1f 48</td><td>r7ilp1f 9<br/>r42ilp1f 40</td></tr><tr><td>NorESM2-LM</td><td>-</td><td>r1ilplf &gt;70</td><td>r1ilplf 32<br/>r2ilplf 42</td><td>r1ilplf 41<br/>r3ilplf &gt;70</td><td>r1ilplf 24</td></tr></table>
+
+<|ref|>text<|/ref|><|det|>[[108, 871, 857, 895]]<|/det|>
+**Extended Data Table 2** Time the first ice-free month: Same as Extended Data Table 1 but for the first ice-free month.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[43, 42, 312, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[43, 92, 768, 112]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 130, 348, 150]]<|/det|>
+HeuzeJahnsupplementary.pdf
+
+<--- Page Split --->

preprint/preprint__5fee14beff17ca1093e89044a7ea4de75436c82ca0f97f3bc6cb86357cd8945d/images_list.json

@@ -0,0 +1,47 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "FIG. 1. (a) ColabFold sends a FASTA input sequence to a MMseqs2 server searching two databases UniRef100 and a database of environmental sequences with three profile-search iterations each. The second database is searched using a sequence-profile generated from the UniRef100 search as input. The server generates two MSAs in A3M format containing all detected sequences. (b1) For single structure predictions we filter both A3Ms using a diversity aware filter and return this to be provided as the MSA input feature to the AlphaFold2 models. (b2) For complex prediction we pair the top hits within the same species to resolve the inter-complex contacts and additionally add two unpaired MSAs (same to b1) to guide the structure prediction. (c) To help researchers judge the prediction quality we visualize MSA depth and diversity and show the AlphaFold2 confidence measures (pLDDT and PAE).",
+    "footnote": [],
+    "bbox": [
+      [
+        515,
+        222,
+        960,
+        543
+      ]
+    ],
+    "page_idx": 1
+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_2.jpg",
+    "caption": "FIG. 2. (a) Structure prediction comparison of AlphaFold2 (yellow), AlphaFold-Colab (green) and ColabFold with BFD/MGnify (blue) and with the ColabFoldDB (magenta) using predictions of 96 domains of 69 CASP14 targets. The 28 domains from the 20 free-modeling (FM) targets are shown first. FM targets were used to optimize MMseqs2 search parameters. Each target was evaluated for each individual domain (in total 96 domains). (b) MSA generation time for each CASP14 FM target sorted by protein length (same colors as before). FM target T1064 shown separately to improve readability. (c) Comparison of ColabFold complex predictions with unpaired (red) and unpaired+paired (blue) MSA-pairing modes, the databases BFD/MGnify (left of line) and ColabFoldDB (right). See Supplementary Fig. 2 for comparison to paired-only mode.",
+    "footnote": [],
+    "bbox": [
+      [
+        55,
+        81,
+        951,
+        480
+      ]
+    ],
+    "page_idx": 2
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "FIG. 3. Anecdotal examples showcasing the capabilities of advanced ColabFold features. (a) Setting the homo-oligomer setting to 6, allows modeling of the homo-6-mer structure of 4-Oxalocrotonate Tautomerase. Colored by chain (top), pLDDT (predicted Local Distance Difference Test, bottom). The inter PAE (Predicted Aligned Error) between chains is very low indicating a confident prediction. (b) Providing three different proteins with 2:1:2 homo-oligomer setting allows modeling a hetero-complex with mismatching symmetries of the D-methionine transport system.",
+    "footnote": [],
+    "bbox": [
+      [
+        525,
+        90,
+        940,
+        430
+      ]
+    ],
+    "page_idx": 3
+  }
+]

preprint/preprint__5fee14beff17ca1093e89044a7ea4de75436c82ca0f97f3bc6cb86357cd8945d/preprint__5fee14beff17ca1093e89044a7ea4de75436c82ca0f97f3bc6cb86357cd8945d.mmd

@@ -0,0 +1,211 @@
+
+# ColabFold - Making protein folding accessible to all  
+
+Milot Mirdita ( milot.mirdita@mpibpc.mpg.de )  
+
+Max Planck Institute for Biophysical Chemistry https://orcid.org/0000- 0001- 8637- 6719  
+
+Konstantin Schütze  
+
+Seoul National University https://orcid.org/0000- 0002- 3957- 412X  
+
+Yoshitaka Moriwaki  
+
+The University of Tokyo https://orcid.org/0000- 0003- 0448- 9790  
+
+Lim Heo  
+
+Michigan State University  
+
+Sergey Ovchinnikov  
+
+Harvard University https://orcid.org/0000- 0003- 2774- 2744  
+
+Martin Steinegger  
+
+Seoul National University  
+
+## Brief Communication  
+
+Keywords: ColabFold, protein folding, environmental databases  
+
+Posted Date: November 12th, 2021  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1032816/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 Methods on May 30th, 2022. See the published version at https://doi.org/10.1038/s41592- 022- 01488- 1.
+
+<--- Page Split --->
+
+# ColabFold - Making protein folding accessible to all  
+
+Milot Mirdita, \(^{1, *}\) Konstantin Schütze, \(^{2}\) Yoshitaka Moriwaki, \(^{3, 4}\) Lim Heo, \(^{5}\) Sergey Ovchinnikov, \(^{6, 7, *}\) and Martin Steinegger \(^{2, 8, *}\)  
+
+ColabFold offers accelerated protein structure and complex predictions by combining the fast homology search of MMseqs2 with AlphaFold2 or RoseTTAFold. ColabFold's \(20 - 30x\) faster search and optimized model use allows predicting thousands of proteins per day on a server with one GPU. Coupled with Google Colaboratory, ColabFold becomes a free and accessible platform for protein folding. ColabFold is open- source software available at github.com/sokrypton/ColabFold. Its novel environmental databases are available at colabfold.mmseqs.com Contact: milot.mirdita@mpibpc.mpg.de, so@fas.harvard.edu, martin.steinegger@snu.ac.kr  
+
+1 Predicting the three- dimensional structure of a protein from its sequence alone remains an unsolved problem. However, by exploiting the information in multiple sequence alignments (MSAs) of related proteins as raw input features for end- to- end training, AlphaFold2 [1] was able to predict the 3D atomic coordinates of folded protein structures at an median GDT- TS of \(92.4\%\) in the latest CASP14 [2] competition. The accuracy of many of the predicted structures was within the error margin of experimental structure determination methods. Many ideas of AlphaFold2 were independently reproduced and implemented in RoseTTAFold [3]. Additionally to single chain predictions, RoseTTAFold was shown to model protein complexes. Evans et al. [3] also announced a refined version of AlphaFold2 for complex prediction. Thus, two highly accurate open- source prediction methods are now publicly available.  
+
+In order to leverage the power of these methods researchers require powerful compute- capabilities. First, to build diverse MSAs, large collections of protein sequences from public reference [4] and environmental [1, 5] databases are searched using the most sensitive homology detection methods HMMer [6] and HHblits [7]. Due to the large database sizes these searches can take up to hours for a single protein, while requiring over two terabyte of storage space alone. Second, to execute the deep neural networks GPUs with a large amount of GPU RAM are required even for relatively common protein sizes of \(\sim 1000\) residues. Though, for these the MSA generation dominates the overall run- time (Supplementary Fig. 1).  
+
+To enable researchers without these resources to use AlphaFold2 independent solutions based on Google Colaboratory were developed. Colaboratory is a proprietary version of Jupyter Notebook hosted by Google. It is accessible for free to logged- in users and includes access to powerful GPUs. Tunyasuvunakool et al. [8] developed an AlphaFold2 Jupyter Notebook for Google Colaboratory (referred to as AlphaFoldColab), where the input MSA is built by searching with HMMer against a clustered UniProt and an eight- fold reduced environmental databases. Resulting in less accurate predictions, while still requiring long search times.  
+
+![](images/Figure_1.jpg)
+
+<center>FIG. 1. (a) ColabFold sends a FASTA input sequence to a MMseqs2 server searching two databases UniRef100 and a database of environmental sequences with three profile-search iterations each. The second database is searched using a sequence-profile generated from the UniRef100 search as input. The server generates two MSAs in A3M format containing all detected sequences. (b1) For single structure predictions we filter both A3Ms using a diversity aware filter and return this to be provided as the MSA input feature to the AlphaFold2 models. (b2) For complex prediction we pair the top hits within the same species to resolve the inter-complex contacts and additionally add two unpaired MSAs (same to b1) to guide the structure prediction. (c) To help researchers judge the prediction quality we visualize MSA depth and diversity and show the AlphaFold2 confidence measures (pLDDT and PAE). </center>  
+
+Here, we present ColabFold, a fast and easy to use software for protein structure and homo- and heteromer complex prediction, for use as a Jupyter Notebook inside Google Colaboratory, on researchers' local computers as a notebook or through a command line interface. ColabFold speed- ups the prediction by replacing the AlphaFold2's input feature generation stage with a fast MMseqs2 [9, 10] search. It additionally implements speed- ups for predictions of multiple structures by avoiding recompilation and adding early stop criteria. We show that ColabFold outperforms AlphaFold- Colab and matches AlphaFold2 on CASP14 targets while being 20- 30 times faster. ColabFold can compute a proteome (excluding proteins \(>1000\) residues) in 41 hours on a consumer GPU.
+
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+![](images/Supplementary_Figure_2.jpg)
+
+<center>FIG. 2. (a) Structure prediction comparison of AlphaFold2 (yellow), AlphaFold-Colab (green) and ColabFold with BFD/MGnify (blue) and with the ColabFoldDB (magenta) using predictions of 96 domains of 69 CASP14 targets. The 28 domains from the 20 free-modeling (FM) targets are shown first. FM targets were used to optimize MMseqs2 search parameters. Each target was evaluated for each individual domain (in total 96 domains). (b) MSA generation time for each CASP14 FM target sorted by protein length (same colors as before). FM target T1064 shown separately to improve readability. (c) Comparison of ColabFold complex predictions with unpaired (red) and unpaired+paired (blue) MSA-pairing modes, the databases BFD/MGnify (left of line) and ColabFoldDB (right). See Supplementary Fig. 2 for comparison to paired-only mode. </center>  
+
+52 ColabFold (Fig. 1) consists of three parts: (1) An MMseqs2 hased homology search server to build diverse MSAs and to find templates. The server efficiently aligns input sequence(s) against the UniRef100, the PDB70 and an environmental sequence set. (2) A Python library that communicates with the MMseqs2 search server, prepares the input features for (single or complex) structure inference, and visualizes of results. This library also implements a command line interface. (3) Jupyter notebooks for basic, advanced and batch use (Methods "ColabFold notebooks") using the Python library.  
+
+In ColabFold we replace the sensitive search methods HMMer and HHblits by MMseqs2. We optimized the MSA generation by MMseqs2 to have the following three properties: (1) MSA generation should be fast. (2) The MSA has to capture diversity well and (3) it has to be small enough to run on GPUs with limited RAM. Reducing the memory requirement is especially helpful in Google Colaboratory where the provided GPU is selected from a pool with widely differing capabilities. While (1) is achieved through the fast MMseqs2 prefilter for (2 and 3) we developed a search workflow to maximize sensitivity (Methods "MSA generation") and a new filter that  
+
+73 samples the sequence space evenly (Methods "New diversity 74 aware filter" and Supplementary Fig. 3). Prediction quality highly depends on the input MSA. However, often only a few \((\sim 30)\) sufficiently diverse sequences are enough to produce 75 high quality predictions [1].  
+
+Additionally, we combined the BFD and MGnify databases that are used in AlphaFold2 by HHblits and HMMer respectively into a combined redundancy reduced version we refer to as BFD/MGnify (Methods "Reducing size of BFD/MGnify"). The environmental search database presented an opportunity to improve structure predictions of non- bacterial sequences, as e.g., eukaryotic protein diversity is not well represented in the BFD and MGnify databases. Limitations in assembly and gene calling due to complex intron/exon structures result in under representation in reference databases. We therefore extended the BFD/MGnify with additional metagenomic protein catalogues containing eukaryotic proteins [11, 12, 13], phage catalogues [14, 15] and an updated version of MetaClust [16]. We refer to this database as ColabFoldDB (Methods "ColabFoldDB"). In Supplementary Fig. 4 we show that the ColabFoldDB in comparison to the BFD/MGnify produces more
+
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+
+diverse MSAs for PFAM [17] domains with \(< 30\) members.  
+
+To compare the accuracy of predicted structures we compared AlphaFold2 (default settings with templates), AlphaFold- Colab (no templates), and ColabFold (no templates) with the BFD/MGnify and ColabFoldDB on TM- scores for all targets from the CASP14 competition (Fig. 2a), split by free modeling (FM) targets on the left and the remaining ones on the right. We show this split as we used the FM- targets for optimization of search workflow parameters.  
+
+The mean TM- scores for the FM targets are 0.826, 0.818, 0.79 and 0.744 for ColabFold (BFD/MGnify), ColabFold (ColabFoldDB), AlphaFold2 and the AlphaFold- Colab, respectively. Over all CASP14 targets the TM- scores are 0.88, 0.877 and 0.88 for the former three respectively. For AlphaFold- Colab we measured TM- scores only for FM targets as it cannot be used stand- alone.  
+
+ColabFold could not predict T1084 well as MMseqs2 suppresses all databases hits as false positives due to its amino acid composition filter and masking procedure. If these filters are deactivated T1084 can be predicted with an TM- score of 0.872 (Supplementary Fig. 5).  
+
+ColabFold is on average 5x faster for single predictions than AlphaFold2 and AlphaFold- Colab, when taking both MSA generation (Fig. 2b) and model inference into account.  
+
+AlphaFold2 itself has no capabilities to model complexes. However, we found that by combining two sequences with a glycine linker [18] it could often successfully model complexes. Shortly afterwards, Baek [19] found that incrementing the model- internal residue index - the method that was used in RoseTTAFold - could also be used in AlphaFold2.  
+
+For high quality predictions it was shown that sequences should be provided in paired- form to AlphaFold2 [20]. We implemented a similar pairing procedure (Methods "MSA pairing for complex prediction") and show the complex prediction capabilities of ColabFold in Fig. 2c. We achieve high accuracy in complex prediction in two datasets from Ovchinnikov et al. [21] and the CASP14 protein complex targets with two unique sequences (Methods "Complex Benchmark" for benchmark details). We note though that the structures from [21] were already public and were likely used as individual chains during the training of AlphaFold2.  
+
+Fig. 3 shows two examples of ColabFold's complex prediction capabilities: (a) shows a homo- six- mer and (b) shows a D- methionine transport system composed of three different proteins. For single structure prediction AlphaFold2 provides a pLDDT measure to indicate the prediction quality. A high pLDDT does not necessarily indicate a correct complex prediction, though the inter- complex predicted alignment error (PAE) helps to rank complexes. We visualize plots of PAE and complex conformation to help users judge the prediction quality of a complex. An example for heteromer complex prediction is shown in Supplementary Fig. 6 with its PAE plot. Furthermore, ColabFold complexes were successfully used to aid the cryo- EM structure determination of the 120 MDa human nucleopore complex [22].  
+
+In ColabFold we expose many internal parameters of AlphaFold2 to aid users to model difficult targets, such as the recycle count (default 3). It controls the number of times the  
+
+![](images/Figure_3.jpg)
+
+<center>FIG. 3. Anecdotal examples showcasing the capabilities of advanced ColabFold features. (a) Setting the homo-oligomer setting to 6, allows modeling of the homo-6-mer structure of 4-Oxalocrotonate Tautomerase. Colored by chain (top), pLDDT (predicted Local Distance Difference Test, bottom). The inter PAE (Predicted Aligned Error) between chains is very low indicating a confident prediction. (b) Providing three different proteins with 2:1:2 homo-oligomer setting allows modeling a hetero-complex with mismatching symmetries of the D-methionine transport system. </center>  
+
+prediction is repeatedly feed through the model. For difficult targets as well as for designed proteins without known homologs additional recycling iterations can result in a high quality prediction (Supplementary Fig. 7).  
+
+To meet the demand for high throughput structure prediction we introduced several features in ColabFold. (1) MSA generation can be executed in batch- mode independently from model batch- inference. (2) We compile only two of the five AlphaFold2 models and reuse weights. (3) We provide a batch execution mode, that avoids recompilation for sequences of similar length. (4) We implement early stop criteria, to avoid running additional recycles or models if a sufficiently accurate structure was already found. All together, we show that the proteome of 1762 proteins shorter than 1000 aa of the archaeon Methanocaldococcus jannaschii can be predicted in 40h on one Nvidia RTX 3090 (Methods "Proteome Benchmark").  
+
+ColabFold builds beyond the initial offerings of AlphaFold2 by improving its sequence search, providing tools for modeling homo- and heteromer complexes, exposing advanced functionality, expanding the environmental databases and performing structure prediction in batch within a minute.  
+
+In summary, ColabFold makes high quality protein structure prediction accessible and additionally provides novel features to explore the full potential of AlphaFold2 and RoseTTAFold.
+
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+
+## REFERENCES  
+
+[1] Jumper, J. et al. Nature 596, 583- 589 (2021).  [2] Kryshtafovych, A. et al. Proteins 1- 11 (2021).  [3] Evans, R. et al. bioRxiv 2021.10.04.463034 (2021).  [4] UniProt Consortium. Nucleic Acids Res. 47, D506- D515 (2019).  [5] Mitchell, A. L. et al. Nucleic Acids Res. 48, D570- D578 (2020).  [6] Eddy, S. R. PLoS Comput. Biol. 7, e1002195 (2011).  [7] Steinegger, M. et al. BMC Bioinform. 20, 473 (2019).  [8] Tunyasuvunakool, K. et al. Nature 596, 590- 596 (2021).  [9] Steinegger, M. & Söding, J. Nat. Biotechnol. 35, 1026- 1028 (2017).  [10] Mirdita, M. et al. Bioinformatics 35, 2856- 2858 (2019).  [11] Levy Karin, E. et al. Microbiome 8, 48 (2020).  [12] Delmont, T. O. et al. bioRxiv 2020.10.15.341214 (2020).  [13] Alexander, H. et al. bioRxiv 2021.07.25.453713 (2021).  [14] Nayfach, S. et al. Nat. Microbiol. 6, 960- 970 (2021).  [15] Camarillo- Guerrero, L. F. et al. Cell 184, 1098- 1109. e9 (2021).  [16] Steinegger, M. & Söding, J. Nat. Commun. 9, 2542 (2018).  [17] Mistry, J. et al. Nucleic Acids Res. 49 (2021).  [18] Moriwaki, Y. AlphaFold2 can also predict heterocomplexes, all you have to do is input the two sequences you want to predict and connect them with a long linker. https://twitter.com/Ag_smith/status/1417063635000598528 (2021).  [19] Baek, M. Adding a big enough number for "residue_index" feature is enough to model hetero- complex using AlphaFold (green&cyan: crystal structure / magenta: predicted model w/ residue_index modification). https://twitter.com/minkbaek/status/1417538291709071362 (2021).  [20] Bryant, P. et al. bioRxiv 2021.09.15.460468 (2021).  [21] Ovchinnikov, S. et al. eLife 3, e02030 (2014).  [22] Mosalaganti, S. et al. bioRxiv 2021.10.26.465776 (2021).  
+
+## AUTHOR CONTRIBUTION  
+
+205 M.M., K.S., S.O. and M.S. performed research and programming, M.M., S.O. and M.S. jointly designed the research and 206 wrotethe manuscript. Y.M. provided the initial methodology 207 for hetero- complex modeling and created an installer for use 208 on local servers. L.H. provided initial benchmarking.  
+
+## COMPETING INTERESTS  
+
+210 The authors declare no competing interests.  
+
+## ACKNOWLEDGEMENTS  
+
+177 We thank Johannes Söding for providing computational resources. John Jumper and Tim Green for answering questions regarding AF2. Minkyung Baek for the complex residue trick. 180 Do- Yoon Kim for creating the ColabFold logo. Enzo Guerrero- 181 Araya and Jakub Kaczmarzyk for providing bug fixes. Alon 182 Markovich and Julia Varga for notifying us about MSA quality 183 issues. Harriet Alexander for providing the TOPAZ proteins 184 as a single file to download. We thank all users for using ColabFold and reporting issues. 185 This work used the Scientific Compute Cluster at GWDG, 187 the joint data center of Max Planck Society for the 188 Advancement of Science (MPG) and University of Göttingen. Milot Mirdita acknowledges the BMBF Comp- 190 LifeSci project horizontal4meta. Martin Steinegger acknowledges support from the National Research Foundation of 192 Korea grant [2019R1A6A1A10073437, 2020M3A9G7103933, 193 2021R1C1C102065]; New Faculty Startup Fund and the 194 Creative- Pioneering Researchers Program through Seoul National University. Yoshitaka Moriwaki acknowledges support 195 from Platform Project for Supporting Drug Discovery and Life 196 Science Research (Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS)) from AMED under Grant Number JP21am0101107. For this project, Sergey 200 Ovchinnikov was supported by the National Science Foundation under Grant No. MCB2032259. Any opinions, findings, 202 and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect 204 the views of the National Science Foundation.
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+211 ColabFold notebooks ColabFold has four main Jupyter notebooks [23]: AlphaFold2_mmseqs2 for basic use that supports protein structure prediction using (1) MSAs generated by MMseqs2, (2) custom MSA upload, (3) using template information, (4) relaxing the predicted structures using amber force fields [24], and (5) monomer complex prediction. AlphaFold2_advanced for advanced users additionally supports (6) MSA generation using HMMer (same as AlphaFold- Colab), (7) the sampling of diverse structures by iterating through a series of random seeds (num_samples), and (8) control of AlphaFold2 model internals, such as changing the number of recycles (max_recycle), number of ensembles (num_ensemble), and enabling the stochastic part of the models via the (is_training) option. AlphaFold2_batch for batch prediction of multiple sequences or MSAs. The batch notebook saves time by avoiding recompilation of the AlphaFold2 models ("Avoid recompiling during batch computation") for each individual input sequence. RoseTTAFold for basic use of RoseTTAFold that supports protein structure prediction using (1) MSAs generated by MMseqs2, (2) custom MSAs and (4) sidechain prediction using SCWRL4 [25].  
+
+232 ColabFold command line interface We initially focused on making ColabFold as widely available as possible through our Notebooks running in Google Colaboratory. To meet the demand for a version that runs on local users' machines, we released "LocalColabFold". LocalColabFold can take command line arguments to specify an input FASTA file, an output directory, and various options to tweak structure predictions. LocalColabFold runs on wide range of operating systems, such as Windows 10 or later (using Windows Subsystem for Linux 2), macOS, and Linux. The structure inference and energy minimization are accelerated if a CUDA 11.1 or later compatible GPU is present. LocalColabFold is available as free open- source software at github.com/YoshitakaMo/ localcolabfold.  
+
+Specifically for running large numbers of protein complexes or structure predictions e.g., for an entire proteome (Methods "Proteome benchmark"), we provide the colabfold_batch command line tool through the colabfold python package. It can be installed with pip install colabfold, followed by pip install - U "jax[uda]" - f https://storage.googleapis.com/jax-releases/jax_releases.html. It can be used as colabfold_batch input_file_or_directory output_directory, supporting FASTA, A3M and CSV files as input.  
+
+256 MSA generation by MMseqs2 ColabFold sends the query sequence to a MMseqs2 server [12]. It searches the sequence(s) with three iterations against the consensus sequences of the UniRef30, a clustered version of the UniRef100 [26]. We accept hits with an E- value of lower than 0.1. For each hit, we realign its respective UniRef100 cluster member using the pro- . 262 file generated by the last iterative search, filter them (Methods "New diversity aware filter") and add these to the MSA. This 264 expanding search results in a speed up of \(\sim 10x\) as only 29.3 265 million cluster consensus sequence are searched instead of all 266 277.5 million UniRef100 sequences. Additionally, it has the  
+
+267 advantages to be more sensitive since the cluster consensus 268 sequences are used. We use the UniRef30 sequence- profile to 269 perform an iterative search against the BFD/MGnify or Co- 270 labFoldDB using the same parameters, filters and expansion 271 strategy. 272 New diversity aware filter To limit the number of hits 273 in the final MSA we use the HHblits diversity filtering 274 algorithm [8] implemented in MMseqs2 in multiple stages: 275 (1) During UniRef cluster expansion, we filter each individual 276 UniRef30 cluster before adding the cluster members to the 277 MSA, such that no cluster- pair has a higher maximum 278 sequence identity than \(95\%\) (max- seq- id 0.95. (2) After 279 realignment enable only the - qsc 0.8 threshold and disable 280 all other thresholds (- - qid 0 - diff 0 - max- seq- id 281 1.0). Additionally, the qsc filtering is only used if least 100 282 hits were found (- - filter- min- enable 100). (3) During 283 MSA construction we filter again with the following pa- 284 rameters: - - filter- min- enable 1000 - diff 3000 - qid 285 0.0,0.2,0.4,0.6,0.8,1.0 - qsc 0 - max- seq- id 0.95. 286 Here, we extended the HHblits filtering algorithm to filter 287 within a given sequence identity bucket, such that it cannot 288 eliminate redundancy across filter buckets. Our filter keeps 289 the 3000 most diverse sequences in the identity buckets 290 [0.0- 0.2], [0.2- 0.4], [0.4- 0.6], [0.6- 0.8] and [0.8- 1.0]. In buckets 291 containing less than 1000 hits we disable the filtering. 292 New MMseqs2 pre- computed index to support ex- 293 panding cluster members MMseqs2 was initially built to 294 perform fast many- against- many sequence searches. Mirdita 295 et al. [11] improved it to also support fast single- against- 296 many searches. This type of search requires the database 297 to be index and stored in memory. mmseqs createindex in- 298 dexes the sequences and stores all time- consuming- to- compute 299 data structures used for MMseqs2 searches to disk. We load 300 the index into the operating systems cache using vmtouch 301 (github.com/hoytech/vmtouch) to allow calls to the different 302 MMseqs2 modules become near- overhead free. We extended 303 the index to store, in addition to the already present cluster 304 consensus sequences, all member sequences and the pairwise 305 alignments of the cluster representatives to the cluster mem- 306 bers. With these resident in cache, we eliminate the overhead 307 of the remaining module calls. 308 Reducing size of BFD/MGnify To keep all required se- 309 quences and data structures in memory we needed to reduce 310 the size of the environmental databases BFD and MGnify, as 311 both databases together would have required \(\sim 517\) GB RAM 312 for headers and sequences alone. 313 BFD is a clustered protein database consisting of \(\sim 2.2\) 314 billion proteins organized in 64 million clusters. MGnify 315 (2019_05) contains \(\sim 300\) million environmental proteins. We 316 merged both databases by searching the MGnify sequences 317 against the BFD cluster representative sequences using MM- 318 seqs2. Each MGnify sequence with a sequence identity of 319 \(>30\%\) and a local alignment that covers at least \(90\%\) of its 320 length is assigned to the respective BFD cluster. All unassigned sequences are clustered at \(30\%\) sequence identity and 321 \(90\%\) coverage (- - min- seq- id 0.3 - c 0.3 - - cov- mode 1 - s 322 3) and merged with the BFD clusters, resulting in 182 million 323 clusters. In order to reduce the size of the database we fil
+
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+325 tered each cluster keeping only the 10 most diverse sequences 326 using (mmeqs filterresult - - diff 10). This reduced the 327 total number of sequences from 2.5 billion to 513 million, thus 328 requiring only 84 GB RAM for headers and sequences.  
+
+329 ColabFoldDB We built ColabFoldDB by expanding the 330 BFD/MGnify with metagenomic sequences from various environments. To update the database, we searched the proteins from the SMAG (eukaryotes) [14], MetaEuk (eukaryotes) [13], TOPAZ (eukaryotes) [15], MGV (DNA viruses) [16], 334 GPD (bacteriophages) [17] and updated version of MetaClust 335 [17] against the BFD/MGnify centroids using MMseqs2 and 336 assigned each sequence to the respective cluster if they have 337 a \(30\%\) sequence identity at a \(90\%\) sequence overlap \((- \mathrm{c}0.9\) 338 - cov- mode 1 - min- seq- id 0.3). All remaining sequences 339 were clustered using MMseqs2 cluster - c 0.9 - cov- mode 340 1 - min- seq- id 0.3 and appended to the database. We re- 341 move redundancy per cluster by keeping the most 10 diverse 342 sequences using (mmeqs filterresult - - diff 10). The fi- 343 nal database consists of 209,335,865 million representative se- 344 quences and 738,695,580 members. See "Data availability" for 345 input files. We extracted the MMseqs2 search workflow used 346 in the server ("MSA generation by MMseqs2") into a stan- 347 dalone script colabfold_search.sh and provide it together 348 with the databases.  
+
+349 Template information AlphaFold2 searches with HHsearch 350 through a clustered version of the PDB (PDB70 [8]) to find 351 the 20 top ranked templates. In order to save time, we use 352 MMseqs2 [10] to search against the PDB70 cluster represen- 353 tatives as a prefiltering step to find candidate templates. This 354 search is also done as part of the MMseqs2 API call on our 355 server. Only the top 20 target templates according to E- value 356 are then aligned by HHsearch. The accepted templates are 357 given to AlphaFold2 as input features. This alignment step is 358 done in the ColabFold client and therefore requires the subset 359 of the PDB70 containing the respective HMMs. The PDB70 360 subset and the PDB mmCIF files are fetched from our server. 361 For benchmarking, no templates are given to ColabFold.  
+
+362 Custom MSAs ColabFold allows researchers to upload their 363 own MSAs. Any kind of alignment tool can be used to gener- 364 ate the MSA. The uploaded MSA can be provided in aligned 365 FASTA, A3M, STOCKHOLM or Clustal format. We con- 366 vert the respective MSA format into A3M format using the 367 reformat.pl script from the HH- suite [8].  
+
+368 Modeling of protein- protein complexes Baek et al. [3] 369 show that RoseTTAFold is able to model complexes, despite 370 being trained only on single chains. This is done by provid- 371 ing a paired alignment and modifying the residue index. The 372 residue index is used as an input to the models to compute 373 positional embeddings. In AlphaFold2, we find the same to be 374 true, although surprisingly the paired alignment is often not 375 needed (Fig. 2c). AlphaFold2 uses relative positional encod- 376 ing with a cap at \(|i - j|\geq 32\) . Meaning, any pair of residues 377 separated by 32 or more are given the same relative positional 378 encoding. By offsetting the residue index between two proteins 379 to be \(>32\) , AlphaFold2 treats them as separate poly- peptide 380 chains. ColabFold integrates this for modeling complexes.  
+
+381 For homo-oligomeric complexes (Fig. 3a), the MSA is 382 copied multiple times for each component. Interestingly, it  
+
+383 was found that providing a separate MSA copy (padding by 384 gap characters to extend to other copies) to work significantly 385 better than concatenating left- to- right.  
+
+386 For hetero- oligomeric complexes (Fig. 3b), a separate MSA 387 is generated for each component. The MSA is paired according 388 to the chosen pair_mode ("MSA pairing for complex predic- 389 tion"). Since pLDDT is only useful for assessing local struc- 390 ture confidence, we use the fine- tuned model parameters to 391 return the PAE for each prediction. As illustrated in Sup- 392 plermentary Fig. 6, the inter- PAE (predicted aligned error) 393 or the predicted TM- score (derived from PAE) can be used to 394 rank and assess the confidence of the predicted protein- protein 395 interaction.  
+
+396 MSA pairing for complex prediction A paired MSA helps 397 AlphaFold2 to predict complexes more accurately only if or- 398 thologous genes are paired with each other. We followed a 399 similar strategy as Bryant et al. [21] to pair sequences accord- 400 ing to their taxonomic identifier. For the pairing we search 401 each distinct sequence of a complex against the UniRef100 402 using the same procedure as described in "MSA generation". 403 We return only hits that cover all complex proteins within one 404 species and pair only the best hit (smallest e- value) with an 405 alignment that covers the query to at least \(50\%\) . The pairing 406 is implemented in the new MMseqs2 module pairaln.  
+
+407 For prokaryotic protein prediction, we additionally imple- 408 mented the protocol described in [3] to pair sequences based 409 on their distances in the genome as predicted from the UniProt 410 accession numbers.  
+
+411 Taxonomic labels for MSA pairing To pair MSAs for com- 412 plex prediction, we retrieve for each found UniRef100 member 413 sequence the taxonomic identifier from the NCBI taxonomy 414 [27]. The taxonomic labels are extracted from the lowest com- 415 mon ancestor field ("common taxon ID") of each UniRef100 416 sequence from the uniref100. xml (2021_03) file.  
+
+417 Complex benchmark We compare predictions of five 418 CASP14 complex targets (H1045, H1046, H1047, H1065, 419 H1072) and 32 targets from Ovchinnikov et al. [22] to their 420 native structures using MM- align [28] and extract TM- scores. 421 We used colabfold_batch with BFD/MGnify and Colab- 422 FoldDB to predict structures in three different modes: (1) 423 without MSA pairing, (2) with MSA pairing as described in 424 "MSA pairing for complex prediction" and (3) with MSA pair- 425 ing and also adding unpaired sequences. Models are ranked 426 by pTMscore predicted by AlphaFold2.  
+
+427 Avoid recompiling AlphaFold2 models The AlphaFold2 428 models are compiled using JAX [29] to optimize the model 429 for specific MSA or template input sizes. When no templates 430 are provided, we compile once and, during inference, replace 431 the weights from the other models, using the configuration 432 of model 5. This saves 7 minutes of compile time. When 433 templates are enabled, model 1 is compiled and weights from 434 model 2 are used, model 3 is compiled and weights from models 435 4 and 5 are used. This saves 5 minutes of compile time. If 436 the user changes the sequence or settings, without changing 437 the length or number of sequences in the MSA, the compiled 438 models are reused without triggering recompilation.
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+439 Avoid recompiling during batch computation In order to avoid AlphaFold2 model recompilation for every protein 441 AlphaFold2 provides a function to add padding to the input 442 MSA and templates called make_fixed_size. However, this is 443 not exposed in AlphaFold2. We used the function in our batch 444 notebook as well as in our command line tool colabfold_batch, 445 in order to maximize GPU utilization and minimize the need 446 of model recompilation. We sort the input queries by sequence 447 length and process them in ascending order. We pad the input 448 features by 10% (by default). All sequences that lie within the 449 query length and an additional 10% margin do not require to 450 be recompiled, resulting in a large speed up for short proteins.  
+
+451 Speed- up of predictions through early stop AlphaFold2 452 computes five models. We noted that for prediction of high 453 certainty ( \(>85\) pLDDT), all five models would often produce 454 structures of very similar confidence. In order to speed up 455 the computation we added a parameter to colabfold_batch 456 to define an early stop criterion that halts additional model 457 inferences if a given pLDDT or pTMscore threshold is reached.  
+
+458 Recycle count AlphaFold2 improves the predicted protein 459 structure by recycling (by default) 3 times, meaning the pre- 460 diction is fed multiple times through the model. We exposed 461 the recycle count as a customizable parameter as additional 462 recycles can often improve a model at the cost of a longer run- 463 time. We also implemented an option to specify a tolerance 464 threshold to stop early. For some designed proteins without 465 known homologous sequences, this helped to fold the final pro- 466 tein (Supplementary Fig. 7).  
+
+467 Sampling of diverse structures To reduce memory requirements, only a subset of the MSA is used as input to the model. 468 Alphafold2, depending on model configuration, subsamples 470 the MSA to a maximum of 512 cluster centers and 1024 "extra" 471 sequences. Changing the random seed can result in different 472 cluster centers and thus different structure predictions. Colab- 473 Fold provides an option to iterate through a series of random 474 seeds, resulting in structure diversity. Further structure di- 475 versity can be generated by using the original or fine- tuned 476 (use_ptm) model parameters and/or enabling (is_training) 477 to activate the stochastic (dropout) part of model. Enabling 478 the latter, can be used to sample an ensemble of models for 479 the uncertain parts of the structure prediction.  
+
+480 Proteome benchmark We predict the proteome of the ar- 481 chaeon M. jannaschii. Of the 1787 proteins we exclude the 482 25 proteins longer than 1000 residues, leaving 1762 proteins of 483 268 aa average length. We search in 58 min using 100 threads 484 on a system with 2x64-core AMD EPYC 7742 CPUs and 2TB 485 RAM using colabfold_search.sh against the ColabFoldDB 486 ("ColabFoldDB"), though we reduce the sensitivity to the con- 487 siderably faster - s 6 setting. We then predict the structures 488 on a single Nvidia RTX 3090 with 28 GB RAM in 39.6 h using 489 only MSAs (no templates). For each query we stop early if 490 any model reaches a pLDDT of at least 85. We extrapolate 491 the runtime for no- early- stopping by multiplying the runtime 492 of model 3 for each protein to five models, yielding an overall 493 speedup of factor 2.8. We observe a high structural agree- 494 ment with an median TM- Score of 0.986 and mean TM- score 495 of 0.953 when comparing the best predictions of ColabFold 496 and AlphaFold2 with TMalign [30].  
+
+497 Benchmark with CASP14 targets We compare the 498 AlphaFold- Colab and the AlphaFold2 (commit b88f8da) 499 against ColabFold (commit 2b49880, Fig.2) using all 500 CASP14 [2] targets. ColabFold uses UniRef30 (2021_03) [31] 501 and the BFD/Mgnify or ColabFoldDB. AlphaFold- Colab uses 502 the UniRef90 (2021_03), MGnify (2019_05) and the small 503 BFD. AlphaFold2 uses the full_dbs preset with and de- 504 fault databases downloaded with the download_all_data.sh 505 script. The 69 targets contain 96 domains, among these are 506 20 FM- targets with 28 domains. We compared the predictions 507 against the experimental structures using TMalign [30].  
+
+508 Measuring time for CASP14 and complex targets All 509 ColabFold and AlphaFold2 benchmarks were executed on sys- 510 tems with 2x16 core Intel Gold 6242 CPUs with 192 GB RAM 511 and 4x Nvidia Quadro RTX5000 GPUs. Only one GPU was 512 used in each individual run.  
+
+513 ColabFold was executed using colabfold_batch. The MM- 514 seqs2 server which computes MSAs for ColabFold has 2x14 515 core Intel E5- 2680v4 CPUs and 768 GB RAM. Each gener- 516 ated MSA was processed by a single CPU- core. Runtimes 517 were computed from server logs.  
+
+518 Runtimes for AlphaFold2 were extracted from the features 519 entry of generated timings.json file. Where indicated with 520 multicore, AlphaFold2 was used with the default 8 CPU cores 521 for HMMer and 4 CPU cores for HHblits to process one query. 522 For a fair comparison, AlphaFold2 was modified to allow HM- 523 Mer and HHblits to access one CPU core.  
+
+524 AlphaFold- Colab was executed in the browser using a 525 Google Colab Pro account. Times for homology search were 526 taken from the notebook output cell "Search against genetic 527 databases" cell. The JackHMMer search uses 8 threads.  
+
+528 Lightweight 2D structure renderer For visualization, we 529 developed a matplotlib [32] compatible module for displaying 530 the 3D ribbon diagram of a protein structure or complex. The 531 ribbon can be colored by residue index (N to C terminus) 532 or by a predicted confidence metric (such as pLDDT). For 533 complexes, each protein can be colored by chain ID. Instead 534 of using a 3D renderer, we instead use a 2D line plotting based 535 technique. The lines that make up the ribbon are plotted in 536 the order in which they appear along the z- axis. Furthermore, 537 we add shade to the lines according to the z- axis. This creates 538 the illusion of a 3D rendered graphic. The advantage over a 539 3D renderer is that the images are very lightweight, can be 540 used in animations and saved as vector graphics for lossless 541 inclusion in documents.  
+
+## CODE AVAILABILITY  
+
+542 ColabFold is free open- source software (MIT) and avail- 543 able at github.com/sokrypton/ColabFold. A locally in- 544 stallable version is available at github.com/YoshitakaMo/ 545 localcolabfold. The ColabFold development version shown 546 in this manuscript is available at github.com/konstin/ 547 ColabFold. The ColabFold server components are free 548 open- source software (GPLv3) and available at github.com/ 549 soedinglab/mmseqs2- app. MMseqs2 is free open- source soft- 550 ware (GPLv3) and available at mmseqs.com.
+
+<--- Page Split --->
+
+## DATA AVAILABILITY  
+
+Data AVAILABILITY 551 ColabFold databases are freely (CC- BY- NC- SA 4.0) available 552 at colabfold.mmseqs.com. 553 Input databases used for building ColabFold databases: 554 UniRef30: uniclust.mmseqs.com 555 BFD: bfd.mmseqs.com 556 MGNify: ftp.ebi.ac.uk/pub/databases/metagenomics/ 557 peptide_database/2019_05 558 PDB70: wwwuser.gwdg.de/\\~compbiol/data/hhsuite/ 559 databases/hhsuite_dbs 560 MetaEuk: wwwuser.gwdg.de/\\~compbiol/metaueuk/2019_11/ 561 MetaEuk_preds_Tara_vs_euk_profiles_unigs.fas.gz 562 SMAG: www.genoscope.cns.fr/tara/localdata/data/ 563 SMAGs- v1/SMAGs_v1_concat.faa.tar.gz 564 TOPAZ: osf.io/gm564 565 MGV: portal.nersc.gov/MGV/MGV_v1.0_2021_07_08/mgv_ 566 proteins.faa 567 GPD: ftp.ebi.ac.uk/pub/databases/metagenomics/ 568 genome_sets/gut_phage_database/GPD_proteome.faa  
+
+Further datasets used for benchmarking ColabFold: 570 PFAM (Pfam- A.seed.gz & Pfam- A.full.gz): 571 ftp.ebi.ac.uk/pub/databases/Pfam/releases/Pfam34.0 572 Methanocadococcus jannaschii proteome: 573 uniprot.org/proteomes/UP000000805  
+
+## REFERENCES  
+
+REFERENCES[23] Kluyver, T. et al. Jupyter notebooks - a publishing format for reproducible computesteinegger2018ational workflows. In Positioning and Power in Academic Publishing: Players, Agents and Agendas, 87- 90 (IOS Press, 2016).[24] Eastman, P. et al. PLoS Comput. Biol. 13, 1- 17 (2017).[25] Krivov, G. G. et al. Proteins 77, 778795 (2009).[26] Suzek, B. E. et al. Bioinformatics 31, 926- 932 (2015).[27] Federhen, S. Nucleic Acids Res. 40, D136- D143 (2012).[28] Mukherjee, S. & Zhang, Y. Nucleic Acids Res. 37, e83- e83 (2009).[29] Bradbury, J. et al. JAX: composable transformations of Python+NumPy programs (2018).[30] Zhang, Y. & Skolnick, J. Nucleic Acids Res. 33, 2302- 2309 (2005).[31] Mirdita, M. et al. Nucleic Acids Res. 45, D170- D176 (2017).[32] Hunter, J. D. Comput. Sci. Eng. 9, 90- 95 (2007).
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+colabfoldssupplement.pdf  MirditaCodeFlat.pdf  MirditaEPCFlat.pdf
+
+<--- Page Split --->

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+<|ref|>title<|/ref|><|det|>[[44, 106, 940, 144]]<|/det|>
+# ColabFold - Making protein folding accessible to all  
+
+<|ref|>text<|/ref|><|det|>[[44, 161, 480, 183]]<|/det|>
+Milot Mirdita ( milot.mirdita@mpibpc.mpg.de )  
+
+<|ref|>text<|/ref|><|det|>[[50, 184, 820, 204]]<|/det|>
+Max Planck Institute for Biophysical Chemistry https://orcid.org/0000- 0001- 8637- 6719  
+
+<|ref|>text<|/ref|><|det|>[[44, 209, 218, 226]]<|/det|>
+Konstantin Schütze  
+
+<|ref|>text<|/ref|><|det|>[[50, 230, 635, 250]]<|/det|>
+Seoul National University https://orcid.org/0000- 0002- 3957- 412X  
+
+<|ref|>text<|/ref|><|det|>[[44, 255, 218, 273]]<|/det|>
+Yoshitaka Moriwaki  
+
+<|ref|>text<|/ref|><|det|>[[50, 277, 620, 296]]<|/det|>
+The University of Tokyo https://orcid.org/0000- 0003- 0448- 9790  
+
+<|ref|>text<|/ref|><|det|>[[44, 302, 120, 319]]<|/det|>
+Lim Heo  
+
+<|ref|>text<|/ref|><|det|>[[50, 323, 280, 342]]<|/det|>
+Michigan State University  
+
+<|ref|>text<|/ref|><|det|>[[44, 348, 218, 366]]<|/det|>
+Sergey Ovchinnikov  
+
+<|ref|>text<|/ref|><|det|>[[50, 370, 574, 389]]<|/det|>
+Harvard University https://orcid.org/0000- 0003- 2774- 2744  
+
+<|ref|>text<|/ref|><|det|>[[44, 394, 201, 412]]<|/det|>
+Martin Steinegger  
+
+<|ref|>text<|/ref|><|det|>[[52, 416, 275, 434]]<|/det|>
+Seoul National University  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 475, 230, 495]]<|/det|>
+## Brief Communication  
+
+<|ref|>text<|/ref|><|det|>[[44, 513, 592, 534]]<|/det|>
+Keywords: ColabFold, protein folding, environmental databases  
+
+<|ref|>text<|/ref|><|det|>[[44, 552, 345, 571]]<|/det|>
+Posted Date: November 12th, 2021  
+
+<|ref|>text<|/ref|><|det|>[[44, 590, 474, 610]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 1032816/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 627, 909, 671]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 705, 958, 749]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Methods on May 30th, 2022. See the published version at https://doi.org/10.1038/s41592- 022- 01488- 1.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[207, 76, 806, 99]]<|/det|>
+# ColabFold - Making protein folding accessible to all  
+
+<|ref|>text<|/ref|><|det|>[[55, 109, 958, 130]]<|/det|>
+Milot Mirdita, \(^{1, *}\) Konstantin Schütze, \(^{2}\) Yoshitaka Moriwaki, \(^{3, 4}\) Lim Heo, \(^{5}\) Sergey Ovchinnikov, \(^{6, 7, *}\) and Martin Steinegger \(^{2, 8, *}\)  
+
+<|ref|>text<|/ref|><|det|>[[55, 137, 960, 207]]<|/det|>
+ColabFold offers accelerated protein structure and complex predictions by combining the fast homology search of MMseqs2 with AlphaFold2 or RoseTTAFold. ColabFold's \(20 - 30x\) faster search and optimized model use allows predicting thousands of proteins per day on a server with one GPU. Coupled with Google Colaboratory, ColabFold becomes a free and accessible platform for protein folding. ColabFold is open- source software available at github.com/sokrypton/ColabFold. Its novel environmental databases are available at colabfold.mmseqs.com Contact: milot.mirdita@mpibpc.mpg.de, so@fas.harvard.edu, martin.steinegger@snu.ac.kr  
+
+<|ref|>text<|/ref|><|det|>[[42, 222, 494, 440]]<|/det|>
+1 Predicting the three- dimensional structure of a protein from its sequence alone remains an unsolved problem. However, by exploiting the information in multiple sequence alignments (MSAs) of related proteins as raw input features for end- to- end training, AlphaFold2 [1] was able to predict the 3D atomic coordinates of folded protein structures at an median GDT- TS of \(92.4\%\) in the latest CASP14 [2] competition. The accuracy of many of the predicted structures was within the error margin of experimental structure determination methods. Many ideas of AlphaFold2 were independently reproduced and implemented in RoseTTAFold [3]. Additionally to single chain predictions, RoseTTAFold was shown to model protein complexes. Evans et al. [3] also announced a refined version of AlphaFold2 for complex prediction. Thus, two highly accurate open- source prediction methods are now publicly available.  
+
+<|ref|>text<|/ref|><|det|>[[42, 440, 493, 610]]<|/det|>
+In order to leverage the power of these methods researchers require powerful compute- capabilities. First, to build diverse MSAs, large collections of protein sequences from public reference [4] and environmental [1, 5] databases are searched using the most sensitive homology detection methods HMMer [6] and HHblits [7]. Due to the large database sizes these searches can take up to hours for a single protein, while requiring over two terabyte of storage space alone. Second, to execute the deep neural networks GPUs with a large amount of GPU RAM are required even for relatively common protein sizes of \(\sim 1000\) residues. Though, for these the MSA generation dominates the overall run- time (Supplementary Fig. 1).  
+
+<|ref|>text<|/ref|><|det|>[[42, 610, 492, 771]]<|/det|>
+To enable researchers without these resources to use AlphaFold2 independent solutions based on Google Colaboratory were developed. Colaboratory is a proprietary version of Jupyter Notebook hosted by Google. It is accessible for free to logged- in users and includes access to powerful GPUs. Tunyasuvunakool et al. [8] developed an AlphaFold2 Jupyter Notebook for Google Colaboratory (referred to as AlphaFoldColab), where the input MSA is built by searching with HMMer against a clustered UniProt and an eight- fold reduced environmental databases. Resulting in less accurate predictions, while still requiring long search times.  
+
+<|ref|>image<|/ref|><|det|>[[515, 222, 960, 543]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[515, 550, 960, 735]]<|/det|>
+<center>FIG. 1. (a) ColabFold sends a FASTA input sequence to a MMseqs2 server searching two databases UniRef100 and a database of environmental sequences with three profile-search iterations each. The second database is searched using a sequence-profile generated from the UniRef100 search as input. The server generates two MSAs in A3M format containing all detected sequences. (b1) For single structure predictions we filter both A3Ms using a diversity aware filter and return this to be provided as the MSA input feature to the AlphaFold2 models. (b2) For complex prediction we pair the top hits within the same species to resolve the inter-complex contacts and additionally add two unpaired MSAs (same to b1) to guide the structure prediction. (c) To help researchers judge the prediction quality we visualize MSA depth and diversity and show the AlphaFold2 confidence measures (pLDDT and PAE). </center>  
+
+<|ref|>text<|/ref|><|det|>[[512, 742, 959, 933]]<|/det|>
+Here, we present ColabFold, a fast and easy to use software for protein structure and homo- and heteromer complex prediction, for use as a Jupyter Notebook inside Google Colaboratory, on researchers' local computers as a notebook or through a command line interface. ColabFold speed- ups the prediction by replacing the AlphaFold2's input feature generation stage with a fast MMseqs2 [9, 10] search. It additionally implements speed- ups for predictions of multiple structures by avoiding recompilation and adding early stop criteria. We show that ColabFold outperforms AlphaFold- Colab and matches AlphaFold2 on CASP14 targets while being 20- 30 times faster. ColabFold can compute a proteome (excluding proteins \(>1000\) residues) in 41 hours on a consumer GPU.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[55, 81, 951, 480]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[52, 495, 960, 590]]<|/det|>
+<center>FIG. 2. (a) Structure prediction comparison of AlphaFold2 (yellow), AlphaFold-Colab (green) and ColabFold with BFD/MGnify (blue) and with the ColabFoldDB (magenta) using predictions of 96 domains of 69 CASP14 targets. The 28 domains from the 20 free-modeling (FM) targets are shown first. FM targets were used to optimize MMseqs2 search parameters. Each target was evaluated for each individual domain (in total 96 domains). (b) MSA generation time for each CASP14 FM target sorted by protein length (same colors as before). FM target T1064 shown separately to improve readability. (c) Comparison of ColabFold complex predictions with unpaired (red) and unpaired+paired (blue) MSA-pairing modes, the databases BFD/MGnify (left of line) and ColabFoldDB (right). See Supplementary Fig. 2 for comparison to paired-only mode. </center>  
+
+<|ref|>text<|/ref|><|det|>[[40, 613, 494, 760]]<|/det|>
+52 ColabFold (Fig. 1) consists of three parts: (1) An MMseqs2 hased homology search server to build diverse MSAs and to find templates. The server efficiently aligns input sequence(s) against the UniRef100, the PDB70 and an environmental sequence set. (2) A Python library that communicates with the MMseqs2 search server, prepares the input features for (single or complex) structure inference, and visualizes of results. This library also implements a command line interface. (3) Jupyter notebooks for basic, advanced and batch use (Methods "ColabFold notebooks") using the Python library.  
+
+<|ref|>text<|/ref|><|det|>[[39, 760, 493, 920]]<|/det|>
+In ColabFold we replace the sensitive search methods HMMer and HHblits by MMseqs2. We optimized the MSA generation by MMseqs2 to have the following three properties: (1) MSA generation should be fast. (2) The MSA has to capture diversity well and (3) it has to be small enough to run on GPUs with limited RAM. Reducing the memory requirement is especially helpful in Google Colaboratory where the provided GPU is selected from a pool with widely differing capabilities. While (1) is achieved through the fast MMseqs2 prefilter for (2 and 3) we developed a search workflow to maximize sensitivity (Methods "MSA generation") and a new filter that  
+
+<|ref|>text<|/ref|><|det|>[[503, 614, 958, 689]]<|/det|>
+73 samples the sequence space evenly (Methods "New diversity 74 aware filter" and Supplementary Fig. 3). Prediction quality highly depends on the input MSA. However, often only a few \((\sim 30)\) sufficiently diverse sequences are enough to produce 75 high quality predictions [1].  
+
+<|ref|>text<|/ref|><|det|>[[502, 689, 958, 920]]<|/det|>
+Additionally, we combined the BFD and MGnify databases that are used in AlphaFold2 by HHblits and HMMer respectively into a combined redundancy reduced version we refer to as BFD/MGnify (Methods "Reducing size of BFD/MGnify"). The environmental search database presented an opportunity to improve structure predictions of non- bacterial sequences, as e.g., eukaryotic protein diversity is not well represented in the BFD and MGnify databases. Limitations in assembly and gene calling due to complex intron/exon structures result in under representation in reference databases. We therefore extended the BFD/MGnify with additional metagenomic protein catalogues containing eukaryotic proteins [11, 12, 13], phage catalogues [14, 15] and an updated version of MetaClust [16]. We refer to this database as ColabFoldDB (Methods "ColabFoldDB"). In Supplementary Fig. 4 we show that the ColabFoldDB in comparison to the BFD/MGnify produces more
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[37, 81, 472, 96]]<|/det|>
+diverse MSAs for PFAM [17] domains with \(< 30\) members.  
+
+<|ref|>text<|/ref|><|det|>[[37, 97, 491, 212]]<|/det|>
+To compare the accuracy of predicted structures we compared AlphaFold2 (default settings with templates), AlphaFold- Colab (no templates), and ColabFold (no templates) with the BFD/MGnify and ColabFoldDB on TM- scores for all targets from the CASP14 competition (Fig. 2a), split by free modeling (FM) targets on the left and the remaining ones on the right. We show this split as we used the FM- targets for optimization of search workflow parameters.  
+
+<|ref|>text<|/ref|><|det|>[[36, 212, 490, 313]]<|/det|>
+The mean TM- scores for the FM targets are 0.826, 0.818, 0.79 and 0.744 for ColabFold (BFD/MGnify), ColabFold (ColabFoldDB), AlphaFold2 and the AlphaFold- Colab, respectively. Over all CASP14 targets the TM- scores are 0.88, 0.877 and 0.88 for the former three respectively. For AlphaFold- Colab we measured TM- scores only for FM targets as it cannot be used stand- alone.  
+
+<|ref|>text<|/ref|><|det|>[[36, 313, 490, 386]]<|/det|>
+ColabFold could not predict T1084 well as MMseqs2 suppresses all databases hits as false positives due to its amino acid composition filter and masking procedure. If these filters are deactivated T1084 can be predicted with an TM- score of 0.872 (Supplementary Fig. 5).  
+
+<|ref|>text<|/ref|><|det|>[[36, 386, 490, 430]]<|/det|>
+ColabFold is on average 5x faster for single predictions than AlphaFold2 and AlphaFold- Colab, when taking both MSA generation (Fig. 2b) and model inference into account.  
+
+<|ref|>text<|/ref|><|det|>[[36, 430, 490, 515]]<|/det|>
+AlphaFold2 itself has no capabilities to model complexes. However, we found that by combining two sequences with a glycine linker [18] it could often successfully model complexes. Shortly afterwards, Baek [19] found that incrementing the model- internal residue index - the method that was used in RoseTTAFold - could also be used in AlphaFold2.  
+
+<|ref|>text<|/ref|><|det|>[[36, 515, 490, 675]]<|/det|>
+For high quality predictions it was shown that sequences should be provided in paired- form to AlphaFold2 [20]. We implemented a similar pairing procedure (Methods "MSA pairing for complex prediction") and show the complex prediction capabilities of ColabFold in Fig. 2c. We achieve high accuracy in complex prediction in two datasets from Ovchinnikov et al. [21] and the CASP14 protein complex targets with two unique sequences (Methods "Complex Benchmark" for benchmark details). We note though that the structures from [21] were already public and were likely used as individual chains during the training of AlphaFold2.  
+
+<|ref|>text<|/ref|><|det|>[[36, 676, 490, 877]]<|/det|>
+Fig. 3 shows two examples of ColabFold's complex prediction capabilities: (a) shows a homo- six- mer and (b) shows a D- methionine transport system composed of three different proteins. For single structure prediction AlphaFold2 provides a pLDDT measure to indicate the prediction quality. A high pLDDT does not necessarily indicate a correct complex prediction, though the inter- complex predicted alignment error (PAE) helps to rank complexes. We visualize plots of PAE and complex conformation to help users judge the prediction quality of a complex. An example for heteromer complex prediction is shown in Supplementary Fig. 6 with its PAE plot. Furthermore, ColabFold complexes were successfully used to aid the cryo- EM structure determination of the 120 MDa human nucleopore complex [22].  
+
+<|ref|>text<|/ref|><|det|>[[36, 878, 490, 921]]<|/det|>
+In ColabFold we expose many internal parameters of AlphaFold2 to aid users to model difficult targets, such as the recycle count (default 3). It controls the number of times the  
+
+<|ref|>image<|/ref|><|det|>[[525, 90, 940, 430]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[522, 439, 960, 559]]<|/det|>
+<center>FIG. 3. Anecdotal examples showcasing the capabilities of advanced ColabFold features. (a) Setting the homo-oligomer setting to 6, allows modeling of the homo-6-mer structure of 4-Oxalocrotonate Tautomerase. Colored by chain (top), pLDDT (predicted Local Distance Difference Test, bottom). The inter PAE (Predicted Aligned Error) between chains is very low indicating a confident prediction. (b) Providing three different proteins with 2:1:2 homo-oligomer setting allows modeling a hetero-complex with mismatching symmetries of the D-methionine transport system. </center>  
+
+<|ref|>text<|/ref|><|det|>[[505, 567, 960, 624]]<|/det|>
+prediction is repeatedly feed through the model. For difficult targets as well as for designed proteins without known homologs additional recycling iterations can result in a high quality prediction (Supplementary Fig. 7).  
+
+<|ref|>text<|/ref|><|det|>[[505, 624, 960, 799]]<|/det|>
+To meet the demand for high throughput structure prediction we introduced several features in ColabFold. (1) MSA generation can be executed in batch- mode independently from model batch- inference. (2) We compile only two of the five AlphaFold2 models and reuse weights. (3) We provide a batch execution mode, that avoids recompilation for sequences of similar length. (4) We implement early stop criteria, to avoid running additional recycles or models if a sufficiently accurate structure was already found. All together, we show that the proteome of 1762 proteins shorter than 1000 aa of the archaeon Methanocaldococcus jannaschii can be predicted in 40h on one Nvidia RTX 3090 (Methods "Proteome Benchmark").  
+
+<|ref|>text<|/ref|><|det|>[[505, 799, 960, 870]]<|/det|>
+ColabFold builds beyond the initial offerings of AlphaFold2 by improving its sequence search, providing tools for modeling homo- and heteromer complexes, exposing advanced functionality, expanding the environmental databases and performing structure prediction in batch within a minute.  
+
+<|ref|>text<|/ref|><|det|>[[505, 870, 960, 928]]<|/det|>
+In summary, ColabFold makes high quality protein structure prediction accessible and additionally provides novel features to explore the full potential of AlphaFold2 and RoseTTAFold.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[214, 82, 333, 95]]<|/det|>
+## REFERENCES  
+
+<|ref|>text<|/ref|><|det|>[[62, 111, 480, 430]]<|/det|>
+[1] Jumper, J. et al. Nature 596, 583- 589 (2021).  [2] Kryshtafovych, A. et al. Proteins 1- 11 (2021).  [3] Evans, R. et al. bioRxiv 2021.10.04.463034 (2021).  [4] UniProt Consortium. Nucleic Acids Res. 47, D506- D515 (2019).  [5] Mitchell, A. L. et al. Nucleic Acids Res. 48, D570- D578 (2020).  [6] Eddy, S. R. PLoS Comput. Biol. 7, e1002195 (2011).  [7] Steinegger, M. et al. BMC Bioinform. 20, 473 (2019).  [8] Tunyasuvunakool, K. et al. Nature 596, 590- 596 (2021).  [9] Steinegger, M. & Söding, J. Nat. Biotechnol. 35, 1026- 1028 (2017).  [10] Mirdita, M. et al. Bioinformatics 35, 2856- 2858 (2019).  [11] Levy Karin, E. et al. Microbiome 8, 48 (2020).  [12] Delmont, T. O. et al. bioRxiv 2020.10.15.341214 (2020).  [13] Alexander, H. et al. bioRxiv 2021.07.25.453713 (2021).  [14] Nayfach, S. et al. Nat. Microbiol. 6, 960- 970 (2021).  [15] Camarillo- Guerrero, L. F. et al. Cell 184, 1098- 1109. e9 (2021).  [16] Steinegger, M. & Söding, J. Nat. Commun. 9, 2542 (2018).  [17] Mistry, J. et al. Nucleic Acids Res. 49 (2021).  [18] Moriwaki, Y. AlphaFold2 can also predict heterocomplexes, all you have to do is input the two sequences you want to predict and connect them with a long linker. https://twitter.com/Ag_smith/status/1417063635000598528 (2021).  [19] Baek, M. Adding a big enough number for "residue_index" feature is enough to model hetero- complex using AlphaFold (green&cyan: crystal structure / magenta: predicted model w/ residue_index modification). https://twitter.com/minkbaek/status/1417538291709071362 (2021).  [20] Bryant, P. et al. bioRxiv 2021.09.15.460468 (2021).  [21] Ovchinnikov, S. et al. eLife 3, e02030 (2014).  [22] Mosalaganti, S. et al. bioRxiv 2021.10.26.465776 (2021).  
+
+<|ref|>sub_title<|/ref|><|det|>[[627, 82, 852, 95]]<|/det|>
+## AUTHOR CONTRIBUTION  
+
+<|ref|>text<|/ref|><|det|>[[503, 101, 960, 173]]<|/det|>
+205 M.M., K.S., S.O. and M.S. performed research and programming, M.M., S.O. and M.S. jointly designed the research and 206 wrotethe manuscript. Y.M. provided the initial methodology 207 for hetero- complex modeling and created an installer for use 208 on local servers. L.H. provided initial benchmarking.  
+
+<|ref|>sub_title<|/ref|><|det|>[[631, 189, 848, 202]]<|/det|>
+## COMPETING INTERESTS  
+
+<|ref|>text<|/ref|><|det|>[[503, 209, 852, 222]]<|/det|>
+210 The authors declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[172, 519, 378, 532]]<|/det|>
+## ACKNOWLEDGEMENTS  
+
+<|ref|>text<|/ref|><|det|>[[35, 538, 494, 944]]<|/det|>
+177 We thank Johannes Söding for providing computational resources. John Jumper and Tim Green for answering questions regarding AF2. Minkyung Baek for the complex residue trick. 180 Do- Yoon Kim for creating the ColabFold logo. Enzo Guerrero- 181 Araya and Jakub Kaczmarzyk for providing bug fixes. Alon 182 Markovich and Julia Varga for notifying us about MSA quality 183 issues. Harriet Alexander for providing the TOPAZ proteins 184 as a single file to download. We thank all users for using ColabFold and reporting issues. 185 This work used the Scientific Compute Cluster at GWDG, 187 the joint data center of Max Planck Society for the 188 Advancement of Science (MPG) and University of Göttingen. Milot Mirdita acknowledges the BMBF Comp- 190 LifeSci project horizontal4meta. Martin Steinegger acknowledges support from the National Research Foundation of 192 Korea grant [2019R1A6A1A10073437, 2020M3A9G7103933, 193 2021R1C1C102065]; New Faculty Startup Fund and the 194 Creative- Pioneering Researchers Program through Seoul National University. Yoshitaka Moriwaki acknowledges support 195 from Platform Project for Supporting Drug Discovery and Life 196 Science Research (Basis for Supporting Innovative Drug Discovery and Life Science Research (BINDS)) from AMED under Grant Number JP21am0101107. For this project, Sergey 200 Ovchinnikov was supported by the National Science Foundation under Grant No. MCB2032259. Any opinions, findings, 202 and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect 204 the views of the National Science Foundation.
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+211 ColabFold notebooks ColabFold has four main Jupyter notebooks [23]: AlphaFold2_mmseqs2 for basic use that supports protein structure prediction using (1) MSAs generated by MMseqs2, (2) custom MSA upload, (3) using template information, (4) relaxing the predicted structures using amber force fields [24], and (5) monomer complex prediction. AlphaFold2_advanced for advanced users additionally supports (6) MSA generation using HMMer (same as AlphaFold- Colab), (7) the sampling of diverse structures by iterating through a series of random seeds (num_samples), and (8) control of AlphaFold2 model internals, such as changing the number of recycles (max_recycle), number of ensembles (num_ensemble), and enabling the stochastic part of the models via the (is_training) option. AlphaFold2_batch for batch prediction of multiple sequences or MSAs. The batch notebook saves time by avoiding recompilation of the AlphaFold2 models ("Avoid recompiling during batch computation") for each individual input sequence. RoseTTAFold for basic use of RoseTTAFold that supports protein structure prediction using (1) MSAs generated by MMseqs2, (2) custom MSAs and (4) sidechain prediction using SCWRL4 [25].  
+
+<|ref|>text<|/ref|><|det|>[[35, 420, 493, 620]]<|/det|>
+232 ColabFold command line interface We initially focused on making ColabFold as widely available as possible through our Notebooks running in Google Colaboratory. To meet the demand for a version that runs on local users' machines, we released "LocalColabFold". LocalColabFold can take command line arguments to specify an input FASTA file, an output directory, and various options to tweak structure predictions. LocalColabFold runs on wide range of operating systems, such as Windows 10 or later (using Windows Subsystem for Linux 2), macOS, and Linux. The structure inference and energy minimization are accelerated if a CUDA 11.1 or later compatible GPU is present. LocalColabFold is available as free open- source software at github.com/YoshitakaMo/ localcolabfold.  
+
+<|ref|>text<|/ref|><|det|>[[35, 620, 493, 765]]<|/det|>
+Specifically for running large numbers of protein complexes or structure predictions e.g., for an entire proteome (Methods "Proteome benchmark"), we provide the colabfold_batch command line tool through the colabfold python package. It can be installed with pip install colabfold, followed by pip install - U "jax[uda]" - f https://storage.googleapis.com/jax-releases/jax_releases.html. It can be used as colabfold_batch input_file_or_directory output_directory, supporting FASTA, A3M and CSV files as input.  
+
+<|ref|>text<|/ref|><|det|>[[35, 766, 493, 925]]<|/det|>
+256 MSA generation by MMseqs2 ColabFold sends the query sequence to a MMseqs2 server [12]. It searches the sequence(s) with three iterations against the consensus sequences of the UniRef30, a clustered version of the UniRef100 [26]. We accept hits with an E- value of lower than 0.1. For each hit, we realign its respective UniRef100 cluster member using the pro- . 262 file generated by the last iterative search, filter them (Methods "New diversity aware filter") and add these to the MSA. This 264 expanding search results in a speed up of \(\sim 10x\) as only 29.3 265 million cluster consensus sequence are searched instead of all 266 277.5 million UniRef100 sequences. Additionally, it has the  
+
+<|ref|>text<|/ref|><|det|>[[500, 85, 960, 666]]<|/det|>
+267 advantages to be more sensitive since the cluster consensus 268 sequences are used. We use the UniRef30 sequence- profile to 269 perform an iterative search against the BFD/MGnify or Co- 270 labFoldDB using the same parameters, filters and expansion 271 strategy. 272 New diversity aware filter To limit the number of hits 273 in the final MSA we use the HHblits diversity filtering 274 algorithm [8] implemented in MMseqs2 in multiple stages: 275 (1) During UniRef cluster expansion, we filter each individual 276 UniRef30 cluster before adding the cluster members to the 277 MSA, such that no cluster- pair has a higher maximum 278 sequence identity than \(95\%\) (max- seq- id 0.95. (2) After 279 realignment enable only the - qsc 0.8 threshold and disable 280 all other thresholds (- - qid 0 - diff 0 - max- seq- id 281 1.0). Additionally, the qsc filtering is only used if least 100 282 hits were found (- - filter- min- enable 100). (3) During 283 MSA construction we filter again with the following pa- 284 rameters: - - filter- min- enable 1000 - diff 3000 - qid 285 0.0,0.2,0.4,0.6,0.8,1.0 - qsc 0 - max- seq- id 0.95. 286 Here, we extended the HHblits filtering algorithm to filter 287 within a given sequence identity bucket, such that it cannot 288 eliminate redundancy across filter buckets. Our filter keeps 289 the 3000 most diverse sequences in the identity buckets 290 [0.0- 0.2], [0.2- 0.4], [0.4- 0.6], [0.6- 0.8] and [0.8- 1.0]. In buckets 291 containing less than 1000 hits we disable the filtering. 292 New MMseqs2 pre- computed index to support ex- 293 panding cluster members MMseqs2 was initially built to 294 perform fast many- against- many sequence searches. Mirdita 295 et al. [11] improved it to also support fast single- against- 296 many searches. This type of search requires the database 297 to be index and stored in memory. mmseqs createindex in- 298 dexes the sequences and stores all time- consuming- to- compute 299 data structures used for MMseqs2 searches to disk. We load 300 the index into the operating systems cache using vmtouch 301 (github.com/hoytech/vmtouch) to allow calls to the different 302 MMseqs2 modules become near- overhead free. We extended 303 the index to store, in addition to the already present cluster 304 consensus sequences, all member sequences and the pairwise 305 alignments of the cluster representatives to the cluster mem- 306 bers. With these resident in cache, we eliminate the overhead 307 of the remaining module calls. 308 Reducing size of BFD/MGnify To keep all required se- 309 quences and data structures in memory we needed to reduce 310 the size of the environmental databases BFD and MGnify, as 311 both databases together would have required \(\sim 517\) GB RAM 312 for headers and sequences alone. 313 BFD is a clustered protein database consisting of \(\sim 2.2\) 314 billion proteins organized in 64 million clusters. MGnify 315 (2019_05) contains \(\sim 300\) million environmental proteins. We 316 merged both databases by searching the MGnify sequences 317 against the BFD cluster representative sequences using MM- 318 seqs2. Each MGnify sequence with a sequence identity of 319 \(>30\%\) and a local alignment that covers at least \(90\%\) of its 320 length is assigned to the respective BFD cluster. All unassigned sequences are clustered at \(30\%\) sequence identity and 321 \(90\%\) coverage (- - min- seq- id 0.3 - c 0.3 - - cov- mode 1 - s 322 3) and merged with the BFD clusters, resulting in 182 million 323 clusters. In order to reduce the size of the database we fil
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[35, 81, 494, 140]]<|/det|>
+325 tered each cluster keeping only the 10 most diverse sequences 326 using (mmeqs filterresult - - diff 10). This reduced the 327 total number of sequences from 2.5 billion to 513 million, thus 328 requiring only 84 GB RAM for headers and sequences.  
+
+<|ref|>text<|/ref|><|det|>[[35, 140, 494, 427]]<|/det|>
+329 ColabFoldDB We built ColabFoldDB by expanding the 330 BFD/MGnify with metagenomic sequences from various environments. To update the database, we searched the proteins from the SMAG (eukaryotes) [14], MetaEuk (eukaryotes) [13], TOPAZ (eukaryotes) [15], MGV (DNA viruses) [16], 334 GPD (bacteriophages) [17] and updated version of MetaClust 335 [17] against the BFD/MGnify centroids using MMseqs2 and 336 assigned each sequence to the respective cluster if they have 337 a \(30\%\) sequence identity at a \(90\%\) sequence overlap \((- \mathrm{c}0.9\) 338 - cov- mode 1 - min- seq- id 0.3). All remaining sequences 339 were clustered using MMseqs2 cluster - c 0.9 - cov- mode 340 1 - min- seq- id 0.3 and appended to the database. We re- 341 move redundancy per cluster by keeping the most 10 diverse 342 sequences using (mmeqs filterresult - - diff 10). The fi- 343 nal database consists of 209,335,865 million representative se- 344 quences and 738,695,580 members. See "Data availability" for 345 input files. We extracted the MMseqs2 search workflow used 346 in the server ("MSA generation by MMseqs2") into a stan- 347 dalone script colabfold_search.sh and provide it together 348 with the databases.  
+
+<|ref|>text<|/ref|><|det|>[[35, 428, 494, 616]]<|/det|>
+349 Template information AlphaFold2 searches with HHsearch 350 through a clustered version of the PDB (PDB70 [8]) to find 351 the 20 top ranked templates. In order to save time, we use 352 MMseqs2 [10] to search against the PDB70 cluster represen- 353 tatives as a prefiltering step to find candidate templates. This 354 search is also done as part of the MMseqs2 API call on our 355 server. Only the top 20 target templates according to E- value 356 are then aligned by HHsearch. The accepted templates are 357 given to AlphaFold2 as input features. This alignment step is 358 done in the ColabFold client and therefore requires the subset 359 of the PDB70 containing the respective HMMs. The PDB70 360 subset and the PDB mmCIF files are fetched from our server. 361 For benchmarking, no templates are given to ColabFold.  
+
+<|ref|>text<|/ref|><|det|>[[35, 616, 494, 702]]<|/det|>
+362 Custom MSAs ColabFold allows researchers to upload their 363 own MSAs. Any kind of alignment tool can be used to gener- 364 ate the MSA. The uploaded MSA can be provided in aligned 365 FASTA, A3M, STOCKHOLM or Clustal format. We con- 366 vert the respective MSA format into A3M format using the 367 reformat.pl script from the HH- suite [8].  
+
+<|ref|>text<|/ref|><|det|>[[35, 703, 494, 890]]<|/det|>
+368 Modeling of protein- protein complexes Baek et al. [3] 369 show that RoseTTAFold is able to model complexes, despite 370 being trained only on single chains. This is done by provid- 371 ing a paired alignment and modifying the residue index. The 372 residue index is used as an input to the models to compute 373 positional embeddings. In AlphaFold2, we find the same to be 374 true, although surprisingly the paired alignment is often not 375 needed (Fig. 2c). AlphaFold2 uses relative positional encod- 376 ing with a cap at \(|i - j|\geq 32\) . Meaning, any pair of residues 377 separated by 32 or more are given the same relative positional 378 encoding. By offsetting the residue index between two proteins 379 to be \(>32\) , AlphaFold2 treats them as separate poly- peptide 380 chains. ColabFold integrates this for modeling complexes.  
+
+<|ref|>text<|/ref|><|det|>[[35, 890, 494, 920]]<|/det|>
+381 For homo-oligomeric complexes (Fig. 3a), the MSA is 382 copied multiple times for each component. Interestingly, it  
+
+<|ref|>text<|/ref|><|det|>[[500, 81, 960, 123]]<|/det|>
+383 was found that providing a separate MSA copy (padding by 384 gap characters to extend to other copies) to work significantly 385 better than concatenating left- to- right.  
+
+<|ref|>text<|/ref|><|det|>[[500, 124, 960, 270]]<|/det|>
+386 For hetero- oligomeric complexes (Fig. 3b), a separate MSA 387 is generated for each component. The MSA is paired according 388 to the chosen pair_mode ("MSA pairing for complex predic- 389 tion"). Since pLDDT is only useful for assessing local struc- 390 ture confidence, we use the fine- tuned model parameters to 391 return the PAE for each prediction. As illustrated in Sup- 392 plermentary Fig. 6, the inter- PAE (predicted aligned error) 393 or the predicted TM- score (derived from PAE) can be used to 394 rank and assess the confidence of the predicted protein- protein 395 interaction.  
+
+<|ref|>text<|/ref|><|det|>[[500, 270, 960, 428]]<|/det|>
+396 MSA pairing for complex prediction A paired MSA helps 397 AlphaFold2 to predict complexes more accurately only if or- 398 thologous genes are paired with each other. We followed a 399 similar strategy as Bryant et al. [21] to pair sequences accord- 400 ing to their taxonomic identifier. For the pairing we search 401 each distinct sequence of a complex against the UniRef100 402 using the same procedure as described in "MSA generation". 403 We return only hits that cover all complex proteins within one 404 species and pair only the best hit (smallest e- value) with an 405 alignment that covers the query to at least \(50\%\) . The pairing 406 is implemented in the new MMseqs2 module pairaln.  
+
+<|ref|>text<|/ref|><|det|>[[500, 428, 960, 484]]<|/det|>
+407 For prokaryotic protein prediction, we additionally imple- 408 mented the protocol described in [3] to pair sequences based 409 on their distances in the genome as predicted from the UniProt 410 accession numbers.  
+
+<|ref|>text<|/ref|><|det|>[[500, 485, 960, 572]]<|/det|>
+411 Taxonomic labels for MSA pairing To pair MSAs for com- 412 plex prediction, we retrieve for each found UniRef100 member 413 sequence the taxonomic identifier from the NCBI taxonomy 414 [27]. The taxonomic labels are extracted from the lowest com- 415 mon ancestor field ("common taxon ID") of each UniRef100 416 sequence from the uniref100. xml (2021_03) file.  
+
+<|ref|>text<|/ref|><|det|>[[500, 573, 960, 718]]<|/det|>
+417 Complex benchmark We compare predictions of five 418 CASP14 complex targets (H1045, H1046, H1047, H1065, 419 H1072) and 32 targets from Ovchinnikov et al. [22] to their 420 native structures using MM- align [28] and extract TM- scores. 421 We used colabfold_batch with BFD/MGnify and Colab- 422 FoldDB to predict structures in three different modes: (1) 423 without MSA pairing, (2) with MSA pairing as described in 424 "MSA pairing for complex prediction" and (3) with MSA pair- 425 ing and also adding unpaired sequences. Models are ranked 426 by pTMscore predicted by AlphaFold2.  
+
+<|ref|>text<|/ref|><|det|>[[500, 718, 960, 890]]<|/det|>
+427 Avoid recompiling AlphaFold2 models The AlphaFold2 428 models are compiled using JAX [29] to optimize the model 429 for specific MSA or template input sizes. When no templates 430 are provided, we compile once and, during inference, replace 431 the weights from the other models, using the configuration 432 of model 5. This saves 7 minutes of compile time. When 433 templates are enabled, model 1 is compiled and weights from 434 model 2 are used, model 3 is compiled and weights from models 435 4 and 5 are used. This saves 5 minutes of compile time. If 436 the user changes the sequence or settings, without changing 437 the length or number of sequences in the MSA, the compiled 438 models are reused without triggering recompilation.
+
+<--- Page Split --->
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+439 Avoid recompiling during batch computation In order to avoid AlphaFold2 model recompilation for every protein 441 AlphaFold2 provides a function to add padding to the input 442 MSA and templates called make_fixed_size. However, this is 443 not exposed in AlphaFold2. We used the function in our batch 444 notebook as well as in our command line tool colabfold_batch, 445 in order to maximize GPU utilization and minimize the need 446 of model recompilation. We sort the input queries by sequence 447 length and process them in ascending order. We pad the input 448 features by 10% (by default). All sequences that lie within the 449 query length and an additional 10% margin do not require to 450 be recompiled, resulting in a large speed up for short proteins.  
+
+<|ref|>text<|/ref|><|det|>[[35, 252, 494, 360]]<|/det|>
+451 Speed- up of predictions through early stop AlphaFold2 452 computes five models. We noted that for prediction of high 453 certainty ( \(>85\) pLDDT), all five models would often produce 454 structures of very similar confidence. In order to speed up 455 the computation we added a parameter to colabfold_batch 456 to define an early stop criterion that halts additional model 457 inferences if a given pLDDT or pTMscore threshold is reached.  
+
+<|ref|>text<|/ref|><|det|>[[35, 360, 494, 486]]<|/det|>
+458 Recycle count AlphaFold2 improves the predicted protein 459 structure by recycling (by default) 3 times, meaning the pre- 460 diction is fed multiple times through the model. We exposed 461 the recycle count as a customizable parameter as additional 462 recycles can often improve a model at the cost of a longer run- 463 time. We also implemented an option to specify a tolerance 464 threshold to stop early. For some designed proteins without 465 known homologous sequences, this helped to fold the final pro- 466 tein (Supplementary Fig. 7).  
+
+<|ref|>text<|/ref|><|det|>[[35, 486, 494, 673]]<|/det|>
+467 Sampling of diverse structures To reduce memory requirements, only a subset of the MSA is used as input to the model. 468 Alphafold2, depending on model configuration, subsamples 470 the MSA to a maximum of 512 cluster centers and 1024 "extra" 471 sequences. Changing the random seed can result in different 472 cluster centers and thus different structure predictions. Colab- 473 Fold provides an option to iterate through a series of random 474 seeds, resulting in structure diversity. Further structure di- 475 versity can be generated by using the original or fine- tuned 476 (use_ptm) model parameters and/or enabling (is_training) 477 to activate the stochastic (dropout) part of model. Enabling 478 the latter, can be used to sample an ensemble of models for 479 the uncertain parts of the structure prediction.  
+
+<|ref|>text<|/ref|><|det|>[[35, 675, 494, 920]]<|/det|>
+480 Proteome benchmark We predict the proteome of the ar- 481 chaeon M. jannaschii. Of the 1787 proteins we exclude the 482 25 proteins longer than 1000 residues, leaving 1762 proteins of 483 268 aa average length. We search in 58 min using 100 threads 484 on a system with 2x64-core AMD EPYC 7742 CPUs and 2TB 485 RAM using colabfold_search.sh against the ColabFoldDB 486 ("ColabFoldDB"), though we reduce the sensitivity to the con- 487 siderably faster - s 6 setting. We then predict the structures 488 on a single Nvidia RTX 3090 with 28 GB RAM in 39.6 h using 489 only MSAs (no templates). For each query we stop early if 490 any model reaches a pLDDT of at least 85. We extrapolate 491 the runtime for no- early- stopping by multiplying the runtime 492 of model 3 for each protein to five models, yielding an overall 493 speedup of factor 2.8. We observe a high structural agree- 494 ment with an median TM- Score of 0.986 and mean TM- score 495 of 0.953 when comparing the best predictions of ColabFold 496 and AlphaFold2 with TMalign [30].  
+
+<|ref|>text<|/ref|><|det|>[[500, 81, 960, 242]]<|/det|>
+497 Benchmark with CASP14 targets We compare the 498 AlphaFold- Colab and the AlphaFold2 (commit b88f8da) 499 against ColabFold (commit 2b49880, Fig.2) using all 500 CASP14 [2] targets. ColabFold uses UniRef30 (2021_03) [31] 501 and the BFD/Mgnify or ColabFoldDB. AlphaFold- Colab uses 502 the UniRef90 (2021_03), MGnify (2019_05) and the small 503 BFD. AlphaFold2 uses the full_dbs preset with and de- 504 fault databases downloaded with the download_all_data.sh 505 script. The 69 targets contain 96 domains, among these are 506 20 FM- targets with 28 domains. We compared the predictions 507 against the experimental structures using TMalign [30].  
+
+<|ref|>text<|/ref|><|det|>[[500, 242, 960, 344]]<|/det|>
+508 Measuring time for CASP14 and complex targets All 509 ColabFold and AlphaFold2 benchmarks were executed on sys- 510 tems with 2x16 core Intel Gold 6242 CPUs with 192 GB RAM 511 and 4x Nvidia Quadro RTX5000 GPUs. Only one GPU was 512 used in each individual run.  
+
+<|ref|>text<|/ref|><|det|>[[500, 345, 960, 386]]<|/det|>
+513 ColabFold was executed using colabfold_batch. The MM- 514 seqs2 server which computes MSAs for ColabFold has 2x14 515 core Intel E5- 2680v4 CPUs and 768 GB RAM. Each gener- 516 ated MSA was processed by a single CPU- core. Runtimes 517 were computed from server logs.  
+
+<|ref|>text<|/ref|><|det|>[[500, 386, 960, 472]]<|/det|>
+518 Runtimes for AlphaFold2 were extracted from the features 519 entry of generated timings.json file. Where indicated with 520 multicore, AlphaFold2 was used with the default 8 CPU cores 521 for HMMer and 4 CPU cores for HHblits to process one query. 522 For a fair comparison, AlphaFold2 was modified to allow HM- 523 Mer and HHblits to access one CPU core.  
+
+<|ref|>text<|/ref|><|det|>[[500, 473, 960, 530]]<|/det|>
+524 AlphaFold- Colab was executed in the browser using a 525 Google Colab Pro account. Times for homology search were 526 taken from the notebook output cell "Search against genetic 527 databases" cell. The JackHMMer search uses 8 threads.  
+
+<|ref|>text<|/ref|><|det|>[[500, 530, 960, 732]]<|/det|>
+528 Lightweight 2D structure renderer For visualization, we 529 developed a matplotlib [32] compatible module for displaying 530 the 3D ribbon diagram of a protein structure or complex. The 531 ribbon can be colored by residue index (N to C terminus) 532 or by a predicted confidence metric (such as pLDDT). For 533 complexes, each protein can be colored by chain ID. Instead 534 of using a 3D renderer, we instead use a 2D line plotting based 535 technique. The lines that make up the ribbon are plotted in 536 the order in which they appear along the z- axis. Furthermore, 537 we add shade to the lines according to the z- axis. This creates 538 the illusion of a 3D rendered graphic. The advantage over a 539 3D renderer is that the images are very lightweight, can be 540 used in animations and saved as vector graphics for lossless 541 inclusion in documents.  
+
+<|ref|>sub_title<|/ref|><|det|>[[648, 769, 830, 783]]<|/det|>
+## CODE AVAILABILITY  
+
+<|ref|>text<|/ref|><|det|>[[500, 802, 960, 932]]<|/det|>
+542 ColabFold is free open- source software (MIT) and avail- 543 able at github.com/sokrypton/ColabFold. A locally in- 544 stallable version is available at github.com/YoshitakaMo/ 545 localcolabfold. The ColabFold development version shown 546 in this manuscript is available at github.com/konstin/ 547 ColabFold. The ColabFold server components are free 548 open- source software (GPLv3) and available at github.com/ 549 soedinglab/mmseqs2- app. MMseqs2 is free open- source soft- 550 ware (GPLv3) and available at mmseqs.com.
+
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+## DATA AVAILABILITY  
+
+<|ref|>text<|/ref|><|det|>[[33, 113, 496, 377]]<|/det|>
+Data AVAILABILITY 551 ColabFold databases are freely (CC- BY- NC- SA 4.0) available 552 at colabfold.mmseqs.com. 553 Input databases used for building ColabFold databases: 554 UniRef30: uniclust.mmseqs.com 555 BFD: bfd.mmseqs.com 556 MGNify: ftp.ebi.ac.uk/pub/databases/metagenomics/ 557 peptide_database/2019_05 558 PDB70: wwwuser.gwdg.de/\\~compbiol/data/hhsuite/ 559 databases/hhsuite_dbs 560 MetaEuk: wwwuser.gwdg.de/\\~compbiol/metaueuk/2019_11/ 561 MetaEuk_preds_Tara_vs_euk_profiles_unigs.fas.gz 562 SMAG: www.genoscope.cns.fr/tara/localdata/data/ 563 SMAGs- v1/SMAGs_v1_concat.faa.tar.gz 564 TOPAZ: osf.io/gm564 565 MGV: portal.nersc.gov/MGV/MGV_v1.0_2021_07_08/mgv_ 566 proteins.faa 567 GPD: ftp.ebi.ac.uk/pub/databases/metagenomics/ 568 genome_sets/gut_phage_database/GPD_proteome.faa  
+
+<|ref|>text<|/ref|><|det|>[[522, 81, 951, 155]]<|/det|>
+Further datasets used for benchmarking ColabFold: 570 PFAM (Pfam- A.seed.gz & Pfam- A.full.gz): 571 ftp.ebi.ac.uk/pub/databases/Pfam/releases/Pfam34.0 572 Methanocadococcus jannaschii proteome: 573 uniprot.org/proteomes/UP000000805  
+
+<|ref|>sub_title<|/ref|><|det|>[[681, 180, 800, 195]]<|/det|>
+## REFERENCES  
+
+<|ref|>text<|/ref|><|det|>[[524, 211, 961, 375]]<|/det|>
+REFERENCES[23] Kluyver, T. et al. Jupyter notebooks - a publishing format for reproducible computesteinegger2018ational workflows. In Positioning and Power in Academic Publishing: Players, Agents and Agendas, 87- 90 (IOS Press, 2016).[24] Eastman, P. et al. PLoS Comput. Biol. 13, 1- 17 (2017).[25] Krivov, G. G. et al. Proteins 77, 778795 (2009).[26] Suzek, B. E. et al. Bioinformatics 31, 926- 932 (2015).[27] Federhen, S. Nucleic Acids Res. 40, D136- D143 (2012).[28] Mukherjee, S. & Zhang, Y. Nucleic Acids Res. 37, e83- e83 (2009).[29] Bradbury, J. et al. JAX: composable transformations of Python+NumPy programs (2018).[30] Zhang, Y. & Skolnick, J. Nucleic Acids Res. 33, 2302- 2309 (2005).[31] Mirdita, M. et al. Nucleic Acids Res. 45, D170- D176 (2017).[32] Hunter, J. D. Comput. Sci. Eng. 9, 90- 95 (2007).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 43, 311, 70]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 93, 765, 113]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 131, 304, 203]]<|/det|>
+colabfoldssupplement.pdf  MirditaCodeFlat.pdf  MirditaEPCFlat.pdf
+
+<--- Page Split --->

preprint/preprint__5feffe5f1c13034029fc275ecedfe86f7025cefbf654f8388e079a0a04529991/images_list.json

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+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Enthalpy and Gibbs Free Energy differences, Electronic Density of States, and Electron Localised Function (ELF) of carbon in solid, metallic hydrogen. a) Enthalpy of solution (eV/atom) as a function of number of removed hydrogens from static relaxation (blue) and NPT-ensemble molecular dynamics (orange) b) Electronic density of states from a typical BOMD snapshot, showing the characteristic free electron form with a pseudogap at the Fermi Energy. c) Phonon density of states from DFPT of a structure from a relaxed \\(\\mathrm{CH_{124}}\\) MD snapshot (blue), compared with pure \\(I_{41} / a m d\\) hydrogen (orange). d-f) Electron Localization Function (ELF) surrounding a single carbon atom, including cross-sections of planes A and B. The octahedral arrangement of the high ELF values indicates the presence of six covalent-type bonds per carbon.",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 Radial Function Distribution, Mean Square Displacement, and Cumulative Number of Bonds per Carbon from BOMD in NPT ensemble.",
+    "footnote": [],
+    "bbox": [
+      [
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+    ],
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+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 Radial Function Distribution, Cumulative Number of Bonds per Carbon, and Novel Hydrocarbons and representative snapshots from liquid simulations. a) Displays the RDF of the carbon-hydrogen pairs in metallic hydrogen with one carbon (blue line), two carbons (orange line), three carbons (green line), one oxygen and a CO pair (red line), indicating a smearing of the first peak from \\(1.0\\mathrm{\\AA}\\) to \\(1.3\\mathrm{\\AA}\\) . In the \\(\\sim 10^{2}\\) atom simulations (main figure), structure extends throughout the supercell, however the \\(\\sim 10^{3}\\) atom simulations (inset) indicates a suppression of these structural peaks in CH separation at greater distances. b) Shows the CDF (number of CH neighbours per carbon) at \\(1.3\\mathrm{\\AA}\\) , revealing values of approximately 6, 4, 3.3, and 4 respectively. The short-range order is nearly identical in both system sizes (solid lines: \\(\\sim 10^{2}\\) atoms, dashed lines \\(\\sim 10^{3}\\) atoms) c-d) equivalent RDF and CDF for OH pairs, showing well-defined and long-lived bonding. These values suggest the formation of new organic compounds, as depicted in e-i): Snapshots from molecular dynamics showcasing novel chemical species in liquid metallic hydrogen, including e) \\(\\mathrm{CH}_6\\) , f) \\(\\mathrm{C_2H_8}\\) , g) \\(\\mathrm{C_3H_{10}}\\) , h) \\(\\mathrm{CH_4OH}\\) and i) \\(\\mathrm{OH}_3\\) , with schematic molecular bonding shown below.",
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preprint/preprint__5feffe5f1c13034029fc275ecedfe86f7025cefbf654f8388e079a0a04529991/preprint__5feffe5f1c13034029fc275ecedfe86f7025cefbf654f8388e079a0a04529991.mmd

@@ -0,0 +1,349 @@
+
+# Organic compounds in metallic hydrogen  
+
+Graeme Ackland  g.jackland@ed.ac.uk  
+
+University of Edinburgh https://orcid.org/0000- 0002- 1205- 7675  
+
+Jakkapat Seeyangnok  
+
+Centre for Science at Extreme Conditions, School of Physics and Astronomy, University of Edinburgh  
+
+Udomsilp Pinsook  
+
+Department of Physics, Faculty of Science, Chulalongkorn University  
+
+Physical Sciences - Article  
+
+Keywords: atomic hydrogen, organic compounds, hydrocarbon, solubility.  
+
+Posted Date: August 8th, 2024  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 4618413/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 29th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 63552- 6.
+
+<--- Page Split --->
+
+# Organic compounds in metallic hydrogen.  
+
+Jakkapat Seeyangnok \(^{1,2}\) , Udomsilp Pinsook \(^{2}\) , Graeme John Ackland \(^{1}\)  
+
+\(^{1}\) Centre for Science at Extreme Conditions, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom.  
+
+\(^{2}\) Department of Physics, Faculty of Science, Chulalongkorn University, 254 Phaya Thai Rd, Bangkok, 10330, Thailand.  
+
+Contributing authors: jakkapatjtp@gmail.com; udomsilp.p@chula.ac.th; gjackland@ed.ac.uk;  
+
+## Abstract  
+
+Metallic hydrogen[1] is the most common condensed material in the universe, comprising the centre of gas giant planets[2- 4] However, experimental studies are extremely challenging[5- 8], and most of our understanding of this material has been led by theory. Chemistry in this environment has not been probed experimentally, so here we examine hydrocarbon chemistry in metallic hydrogen using density functional theory calculations[9, 10]. We find that carbon and oxygen react with metallic hydrogen to produce an entirely new type of hydrocarbon chemistry based on sixfold coordinated carbon with organic- style molecules \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) , \(\mathrm{C_3H_{10}}\) \(\mathrm{OH_3}\) and \(\mathrm{CH_4OH}\) . These are charged molecules stabilised by the metallic environment. Their associated electric fields are screened, giving oscillation in the surrounding electron and proton densities. In view of the excess hydrogen we refer to them as hypermethane, hyperethane etc. The relationship to traditional chemistry is that the metallic background acts as an electron donor and stabilizes negatively charged ions. This enables the formation of six covalent bonds per carbon atom, or three per oxygen atom. This demonstrates that organic chemistry may take place in very different environments from those found on earth, and may be common throughout the universe.  
+
+Keywords: atomic hydrogen, organic compounds, hydrocarbon, solubility.
+
+<--- Page Split --->
+
+## 1 Introduction  
+
+Metallic hydrogen is believed to be the most common condensed phase of matter in the universe, comprising the cores of gas- giant planets, and giving rise to their enormous magnetic fields. However, it is exceptionally challenging to make metallic hydrogen on earth. Consequently, most of our understanding of this material comes from theory.  
+
+Modern planetary models depict layers separated by the weight of elements, e.g. gas giants feature an outer molecular hydrogen and helium envelope and a core of metallic hydrogen depleted of helium in[4, 11- 13] which is predicted to be insoluble below its own metallization conditions [14- 21]. Understanding of material properties allows us to infer the composition and structure of exoplanets from their mass- radius relation[2, 3, 14, 22- 26]. Chemical bonding is different at high pressure. For example, on earth, the major components of the mantle exhibit sixfold coordinated silicon[27- 31], in contrast to the fourfold \(\mathrm{sp}^3\) bonding found in normal conditions. The unconventional formation of sixfold coordinated silicon is well described by density functional theory calculations as being enabled by the electrons donated from the Mg ions, and stabilised at pressure thanks to the increased density[32- 38]. If chemistry can change so radically just few thousand kilometres beneath our feet, how different might it be elsewhere in the solar system?  
+
+While helium in hydrogen, and high pressure hydrogen- rich metals are very well studied, particularly with potential applications to superconductivity, less attention has been paid to the issue of solubility of heavier elements in metallic hydrogen, and the implications different chemical bonding within giant planets[21, 39- 41].  
+
+Theoretical study of metallic hydrogen began in 1935, when Wigner and Huntington [1] used free electron theory to estimate the density of metallic hydrogen, obtaining a value remarkably close to current estimates. This implied that hydrogen molecules would transition into atomic metallic hydrogen when subjected to sufficiently high pressure - unfortunately their estimate of 25GPa was more than an order of magnitude too low. In 1968, Ashcroft made a remarkable prediction that metallic hydrogen would be a room temperature superconductor. Predictions of the crystal structure of metallic hydrogen came even later[9, 42- 44], through ab initio random- structure exploration. Theoretical assessments [9, 42, 45- 49] indicate that at low temperature hydrogen remains molecular to about 500GPa. Surprisingly, the first atomic and metallic phase is now believed to be a complex, open structure, rather than the dense- packed structures assumed by Wigner, Huntington and Ashcroft. This type of open structure is typical of the high pressure Group I electric materials, having \(I4_{1} / amd\) symmetry, isostructural with cesium IV[50- 53]. 500GPa is at the limit of current experiments which have seen signs of bandgap closure and reflectivity.[5- 7]. This \(I4_{1} / amd\) structure persists until 2.5 TPa, beyond which more densely packed structures are favoured[42, 54]. Fluid metallic hydrogen has been detected at much lower pressures, but higher temperatures, in both static and dynamic compression[8, 55], and calculation[24, 56- 58].  
+
+In experiments[59], synthesis of solid metallic hydrogen has been claimed at pressures exceeding 420 GPa using infrared absorption measurements [5], and at an even higher pressure of 495 GPa as evidenced by reflectivity measurements [6]. Liquid metallic hydrogen has been reported at much lower pressures both in experiment [8, 55, 60] and simulation[56, 57, 61, 62].
+
+<--- Page Split --->
+
+Carbon is particularly important, being the fourth most abundant element and the building block of organic chemistry. The solubility of hydrocarbons in metallic hydrogen remains the preserve of theorists. Studies on giant planets suggest that hydrocarbons likely exist within the middle layer of their structure [63- 65]. Methane \(\mathrm{(CH_4)}\) has been identified as the most abundant hydrocarbon at pressures of up to several hundred GPa and forms hydrogen- rich compounds with \(\mathrm{H_2}\) up to 160GPa[66, 67]. At higher pressures, simulations suggested that methane decomposes into hydrogen and diamond [41, 63, 64]. Due to its density, the latter subsequently gravitationally sinks deeper into the planet in a phenomenon known as diamond rain.[63, 64, 68- 74]. This predicted demixing contrasts with the observation of high pressure reaction between diamond and hydrogen[75] - an issue which has caused significant practical challenges to synthesizing metallic hydrogen in diamond anvil cells[59].  
+
+One challenge for theory is the richness of hydrocarbon chemistry. The demonstration that methane is unstable to decomposition does not preclude other stable hydrocarbons. Moreover, given the high temperatures and excess of hydrogen over carbon in gas giant planets, even a low solubility limit could result in much of the carbon remaining in solution in the metallic hydrogen layers.  
+
+Here, we use density functional theory calculations to consider what form of carbon will exist in a metallic hydrogen environment. We start by examining the free energy in the well- characterized case of solid solution carbon in crystalline \(\mathrm{I4_1 / amd}\) metallic hydrogen. Then we demonstrate the equivalence of the molecular dynamics approach as a reliable estimator of thermodynamic properties, and apply molecular dynamics to investigate the planetary- relevant fluid metallic hydrogen.  
+
+We predict the existence of a new hydrocarbon chemistry, based around a basic sixfold coordination of carbon and threefold coordination of oxygen. For example we observe \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) , \(\mathrm{C_3H_{10}}\) , \(\mathrm{OH_3}\) and \(\mathrm{CH_4OH}\) .  
+
+## 2 Results and Discussion  
+
+### 2.1 Solid solubility of carbon in \(\mathrm{I4_1 / amd}\) metallic hydrogen  
+
+The solid solubility of carbon in metallic hydrogen can be calculated using the Gibbs free energies (Eqn. 1). Hydrogen exhibits strong nuclear quantum effects, so our calculation includes the zero- point energy of the system, as well as the enthalpy, configurational entropy, and vibrational entropy.  
+
+\[G(P,T) = H(P,T) + U_{ZPE} + TS_{con} + TS_{vib} \quad (1)\]  
+
+Initially we consider a single carbon solute in hydrogen. This is more complicated than standard solid solubility calculation[76- 78] because carbon is significantly larger than hydrogen, so substituting one carbon atom for a single hydrogen is not the most stable arrangement. We tried removing clusters of up to eight hydrogens and found that the most stable arrangement involves removing five hydrogens (Table 1, Fig. 1. ) As a check, particularly of anharmonic effects, we also calculated the free energy from the phonon density of states derived from the velocity autocorrelation function of a molecular dynamics calculation. The results are is very good agreement for carbon,
+
+<--- Page Split --->
+
+
+Table 1 Thermodynamic properties for the solid solution at 300K and 500GPa As-calculated enthalpy \(H\) (eV/atom), entropy \(TS\) (eV/atom), zero-point energy \(U_{ZPE}\) (eV/atom), configurational entropy (eV/atom), Gibbs free energy (eV/atom), and the free energy of solution (eV) for different arrangements. Calculated energies are relative to the fully ionised atomic states, hence the high degree of precision required. \(H_{MD}\) represents the ensemble average enthalpy obtained from NPT molecular dynamics at 500GPa, while \(H_{static}\) is derived from static optimization. Entropy \(TS\) is the summation of both vibrational and configurational entropy ( \(S_{vib} + S_{conf.}\) ). \(U_{ZPE}\) and \(S_{vib}\) were calculated using the phonon density of states. The upper two sections are per atom, the lower section refers to solution compared to an unmixed reference state, quoted in units of eV per carbon atom   
+
+<table><tr><td>Supercell</td><td>HMD</td><td>Hstatic</td><td>TS (MD)</td><td>UZPE (MD)</td><td>G (MD)</td></tr><tr><td>CH126</td><td>-10.7925±0.0006</td><td>-10.91109</td><td>0.00988</td><td>0.32588</td><td>-10.4764±0.0006</td></tr><tr><td>CH125</td><td>-10.8024 ±0.0010</td><td>-10.92137</td><td>0.00950</td><td>0.32125</td><td>-10.4906±0.0010</td></tr><tr><td>CH124</td><td>-10.8139±0.0007</td><td>-10.93038</td><td>0.00875</td><td>0.32154</td><td>-10.5011±0.0007</td></tr><tr><td>CH123</td><td>-10.8176±0.0010</td><td>-10.93814</td><td>0.01094</td><td>0.31637</td><td>-10.5122±0.0010</td></tr><tr><td>C (diamond)</td><td>-144.0846±0.0016</td><td>-144.35980</td><td>0.00414</td><td>0.27343</td><td>-143.8153±0.0016</td></tr><tr><td>H (I4amd)</td><td>-9.7593±0.0004</td><td>-9.87520</td><td>0.00488</td><td>0.33264</td><td>-9.4316±0.0004</td></tr><tr><td>Supercell</td><td></td><td>Hstatic</td><td>TS (DFPT)</td><td>UZPE (DFPT)</td><td></td></tr><tr><td>CH124</td><td></td><td>-10.93038</td><td>0.00611</td><td>0.29304</td><td></td></tr><tr><td>C (diamond)</td><td></td><td>-144.35980</td><td>0.00404</td><td>0.27565</td><td></td></tr><tr><td>H (I4amd)</td><td></td><td>-9.87520</td><td>0.00358</td><td>0.29202</td><td></td></tr><tr><td>Supercell</td><td>ΔHMD</td><td>ΔHstatic</td><td>-TΔS (MD)</td><td>ΔUZPE (MD)</td><td>gsol-MD</td></tr><tr><td>CH126</td><td>3.12±0.13</td><td>2.9264</td><td>-0.63543</td><td>-0.79825</td><td>1.69±0.13</td></tr><tr><td>CH125</td><td>2.90±0.18</td><td>2.66684</td><td>-0.58265</td><td>-1.37589</td><td>0.94±0.18</td></tr><tr><td>CH124</td><td>2.51±0.14</td><td>2.58685</td><td>-0.48408</td><td>-1.32760</td><td>0.69±0.14</td></tr><tr><td>CH123</td><td>3.10±0.17</td><td>2.68081</td><td>-0.75218</td><td>-1.95750</td><td>0.39±0.17</td></tr></table>  
+
+and reasonably good for hydrogen: this is expected from the different anharmonicity in the two systems.  
+
+From both MD and static enthalpy, it shows that classical enthalpy prefers pure substances to the mixture with positive values \(\Delta H_{\mathrm{MD}}\) and \(\Delta H_{\mathrm{Static}}\) . On the other hand, the entropy and zero- point energy[79- 81], favour the mixture, with negative values in both \(- T\Delta S\) and \(\Delta U_{ZPE}\) (see Table 1 and Figure 1a).  
+
+For a single substitutional carbon, the lowest free energy has an impurity formation energy of \(\Delta g = 0.39\pm 0.17\mathrm{eV}\) , which implies a solid solubility in the parts per million range at room temperature. If more than five hydrogens are removed from the starting configuration, a vacancy defect is created which diffuses through the lattice.  
+
+Strikingly, we always observe an octahedral arrangement of six neighbouring hydrogens, forming \(\mathrm{CH_6}\) . The overall electronic density of states (Fig.1) is uninformative, being dominated by characteristic free- electron form, with the hydrogen atoms arranged in a way to produce a pseudogap at the Fermi energy, similar to isostructural Cs- IV [51, 82]. However, the electron localization function (ELF) around the carbon (Figure 1d- f) shows that electrons are localized between the hydrogens and carbon in \(\mathrm{CH_6}\) , but not between hydrogen pairs. This suggests that carbon has reacted to form a \(\mathrm{CH_6}\) molecule with six covalent CH bonds, which we call hypermethane.  
+
+The phonon calculations show that pure hydrogen exhibits the expected two- peaked acoustic and optical branches of \(I4_{1} / \mathrm{amd}\) . The \(\mathrm{CH_{124}}\) supercell retains smeared- out versions of these modes, and the heavier carbon reduces the frequency of the acoustic modes in the supercell. Strikingly, the \(\mathrm{CH_6}\) molecule has a well- defined
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Enthalpy and Gibbs Free Energy differences, Electronic Density of States, and Electron Localised Function (ELF) of carbon in solid, metallic hydrogen. a) Enthalpy of solution (eV/atom) as a function of number of removed hydrogens from static relaxation (blue) and NPT-ensemble molecular dynamics (orange) b) Electronic density of states from a typical BOMD snapshot, showing the characteristic free electron form with a pseudogap at the Fermi Energy. c) Phonon density of states from DFPT of a structure from a relaxed \(\mathrm{CH_{124}}\) MD snapshot (blue), compared with pure \(I_{41} / a m d\) hydrogen (orange). d-f) Electron Localization Function (ELF) surrounding a single carbon atom, including cross-sections of planes A and B. The octahedral arrangement of the high ELF values indicates the presence of six covalent-type bonds per carbon. </center>  
+
+vibrational mode at \(3163 \mathrm{cm}^{- 1}\) a higher frequency than anything in the pure metallic hydrogen (Figure 1c). This mode results from the in- phase vibration of the six hydrogen of \(\mathrm{CH_6}\) . Other modes involving asymmetric CH stretches are mixed with the highest frequency \(\mathrm{I4_1 / amd}\) modes.  
+
+The solid solution gives us an indication that, like silicon on earth, carbon will go from fourfold to sixfold coordination in giant planets. However, the positive heat of solution suggests that temperatures well above the melting point would be needed for significant solubility. We investigate this further in the next section.  
+
+### 2.2 Organic compounds in liquid metallic hydrogen  
+
+To further investigate this hypermethane, we simulated a \(\mathrm{CH_6 + H_{118}}\) supercell in the NPT ensemble at \(500 \mathrm{GPa}\) . The radial distribution function (RDF), as shown Figure 2(a), indicates that at \(300 \mathrm{K}\) , we have well- defined H- H peaks representing the \(\mathrm{I4_1 / amd}\) crystal. In the cases of \(600 \mathrm{K}\) and \(900 \mathrm{K}\) , the structure melted as expected[10], indicated by the smoothness of the RDFs in Figure 2a). The mean square displacement (MSD) confirms melting, with a stable MSD at \(300 \mathrm{K}\) and a linear increase for \(600 \mathrm{K}\) and \(900 \mathrm{K}\) , as shown in Figure 2(b).
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 Radial Function Distribution, Mean Square Displacement, and Cumulative Number of Bonds per Carbon from BOMD in NPT ensemble. </center>  
+
+a) The radial distribution function of the \(\mathrm{CH_6 + H_{118}}\) BOMD simulations under the NPT ensemble at varying temperatures, and 500GPa. The blue solid line denotes the presence of structural peaks in \(\mathrm{CH_6 + H_{118}}\) , while the orange and green solid lines signify the disappearance of these peaks due to system melting. b) Mean square displacement (MSD) of \(\mathrm{CH_6 + H_{118}}\) is examined, with the MSD depicting the crystal structure of \(\mathrm{CH_6 + H_{118}}\) with a finite MSD at 300K, represented by the blue solid line. Conversely, cases of melting at 600K and 900K exhibit increased MSD. c) The radial distribution function illustrates the distribution of carbon-hydrogen pairs. The first peak of the CH-pair radial distribution function experiences smearing from 1.0 Å to 1.3 Å. d) Cumulative number of bonds (CH bonds per carbon) is evaluated, indicating the count of hydrogens surrounding each carbon atom.  
+
+In all cases, the carbon- hydrogen RDF (Figure 2c), has a strong peak between 1.0Å and 1.3Å. Even in melted conditions, we observe hydrocarbon \(\mathrm{CH_6}\) molecules, as shown in Figure 2(d), where the cumulative number of bonds in the first peak of the RDF being six. These results suggest the existence of the hypermethane \(\mathrm{CH_6}\) molecule above the melting line of metallic hydrogen at 500 GPa.  
+
+### 2.3 Other hypermolecules: \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) , \(\mathrm{C_3H_{10}}\) , \(\mathrm{H_3O}\) and \(\mathrm{CH_4OH}\)  
+
+We now investigate whether more complex organic molecules can form in liquid metallic hydrogen, using NVT molecular dynamics at around 500GPa and 600K. We investigate five cases, adding a single carbon or oxygen atom, \(\mathrm{C_2}\) dimer, \(\mathrm{C_3}\) trimer and CO molecule to liquid metallic hydrogen. In each case, an exothermic reaction took place with the metallic hydrogen to produce a well- defined, stable hypermolecule with OH and CH bondlengths oscillating in the range 1.0 Å to 1.3 Å.  
+
+We identify these molecules as being hypervalent and hydrogen- rich \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) \(\mathrm{C_3H_{10}}\) , \(\mathrm{H_3O}\) and \(\mathrm{CH_4OH}\) . These correspond to sixfold valence for carbon and trivalent oxygen, with CC and CO double bonds (Figure 3). We note that this mimics the high
+
+<--- Page Split --->
+
+pressure behaviour of the equivalent second row elements: hexavalent Silicon[32] and trivalent Sulphur[83].  
+
+Figure 3 shows the CH and OH radial and cumulative distribution functions for the hypermolecules we investigated, with the sharp first peak in RDF defining the covalent bond, and the plateau in CDF showing the coordination. All hypermolecules remain stable throughout the 10ps simulation. The covalent bonding is further evidenced by ELF analysis. The negative charge on these hypermolecules is evidenced from molecular orbital considerations and the observation of screening with Friedel oscillations.  
+
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 Radial Function Distribution, Cumulative Number of Bonds per Carbon, and Novel Hydrocarbons and representative snapshots from liquid simulations. a) Displays the RDF of the carbon-hydrogen pairs in metallic hydrogen with one carbon (blue line), two carbons (orange line), three carbons (green line), one oxygen and a CO pair (red line), indicating a smearing of the first peak from \(1.0\mathrm{\AA}\) to \(1.3\mathrm{\AA}\) . In the \(\sim 10^{2}\) atom simulations (main figure), structure extends throughout the supercell, however the \(\sim 10^{3}\) atom simulations (inset) indicates a suppression of these structural peaks in CH separation at greater distances. b) Shows the CDF (number of CH neighbours per carbon) at \(1.3\mathrm{\AA}\) , revealing values of approximately 6, 4, 3.3, and 4 respectively. The short-range order is nearly identical in both system sizes (solid lines: \(\sim 10^{2}\) atoms, dashed lines \(\sim 10^{3}\) atoms) c-d) equivalent RDF and CDF for OH pairs, showing well-defined and long-lived bonding. These values suggest the formation of new organic compounds, as depicted in e-i): Snapshots from molecular dynamics showcasing novel chemical species in liquid metallic hydrogen, including e) \(\mathrm{CH}_6\) , f) \(\mathrm{C_2H_8}\) , g) \(\mathrm{C_3H_{10}}\) , h) \(\mathrm{CH_4OH}\) and i) \(\mathrm{OH}_3\) , with schematic molecular bonding shown below. </center>  
+
+We can understand the chemistry of these hypermolecules by considering that, in a metallic environment, extra electrons are readily available to stabilise charged molecules. The local electronic structure of the molecule shows a similar situation to the hypermethane solid solubility, with electrons in covalent type bonds. The hypermolecules carry a formal negative charge from the excess of electrons, e.g. \(\mathrm{CH}_6\) has 14 electrons and a total nuclear charge of only 12. This charge will be screened by the surrounding liquid. The simple case of a charge in a metal gives slowly decaying Friedel oscillations[84, 85] in the electrostatic potential. Fluid metallic hydrogen is a
+
+<--- Page Split --->
+
+more complicated case because both protons and electrons play a role in the screening. Our large simulations with around 1000 atoms for \(\mathrm{CH}_6\) shows that there are Friedel oscillations in the proton density extending to seven distinctive peaks.  
+
+## 3 Methods  
+
+Calculations were performed using density functional theory (DFT) [86, 87] implemented in both Quantum Espresso (QE) [88, 89] and Born- Oppenheimer molecular dynamics (BOMD) implemented in the CAMbridge Serial Total Energy Package (CASTEP) [90].  
+
+Using the Broyden- Fletcher- Goldfarb- Shanno algorithm (BFGS) method [91- 93], the four- atom conventional \(I4_{1} / amd\) structure of atomic metallic hydrogen and the diamond (for carbon) were fully optimized at 500GPa, using a force convergence criterion of \(10^{- 5} \mathrm{eV / \AA}\) and a very dense Monkhorst- Pack grid k mesh. We used the exchange- correlation functional of Perdew- Burke- Ernzerhof (GGA- PBE) [94]. The Born- Oppenheimer molecular dynamics (BOMD), time step was 0.5 fs with velocity- Verlet integration[95]. The isothermal- isobaric ensemble (NPT) [96] was implemented, employing the Parrinello- Rahman barostat[97]. Additionally, a thermostat was set at 300 K, and Berendsen thermostat [98]. Solubility calculations, both static relaxation ( \(a = 4.84 \mathrm{\AA}\) and \(c = 6.23 \mathrm{\AA}\) ) and NPT molecular dynamics, were based on a \(4 \times 4 \times 2\) supercell (128 hydrogens) of the four- atom conventional \(I4_{1} / amd\) structure, with carbon substituted for some hydrogens.  
+
+For the BOMD calculations in the melt, our long simulations were run with boxes containing \(\mathrm{CH}_{124}\) (blue line), \(\mathrm{C}_2\mathrm{H}_{120}\) (orange line), and \(\mathrm{C}_3\mathrm{H}_{276}\) (green line), \(\mathrm{COH}_{124}\) (red line) and \(\mathrm{H}_3\mathrm{O}\) (purple line) respectively, as shown in Figure 3. The \(\mathrm{CH}_6\) \(\mathrm{C}_2\mathrm{H}_{10}\) \(\mathrm{CH}_4\mathrm{OH}\) and \(\mathrm{OH}_3\) molecule simulations were initiated using a \(4\times 4\times 2\) supercell with four hydrogens removed for each insert oxygen or carbon. For \(\mathrm{C}_3\mathrm{H}_8\) , a \(6\times 6\times 2\) supercell (288 hydrogens) with lattice constants \(a = 7.25\mathrm{Å}\) and \(c = 6.23\mathrm{\AA}\) was used. The simulations of melted samples used the NVT ensemble. In the carbon BOMD- NPT simulation, we used a \(3\times 3\times 3\) supercell of the two- atom primitive cell of diamond with the same parameters as the other cases. All of our BOMD simulations were performed up to 20,000 steps and checked for convergence of potential energy. In no case did the hypermolecules dissociate.  
+
+For lattice dynamics, we analyzed the phonon spectrum of the diamond structure and the four- atom conventional \(I4_{1} / amd\) structure of atomic metallic hydrogen under a pressure of 500 GPa using Quantum ESPRESSO (QE). Structural optimization was conducted using the BFGS method [91, 92], fully relaxing crystal structures with a force convergence criterion of \(1.0^{- 5} \mathrm{eV / \AA}\) . The Monkhorst- Pack grid k mesh [99] employed a dense grid, with Marzari- Vanderbilt- DeVita- Payne cold smearing of 0.02 Ry applied to the Fermi surface [100]. As with CASTEP, the PBE[94], exchange correlation energy functional was implemented, and we used optimized norm- conserving Vanderbilt pseudopotentials [101, 102]. The lattice dynamics was performed using QE based on density functional perturbation theory (DFPT) [103]. The electronic density of states of \(\mathrm{CH}_{124}\) and \(\mathrm{H}_{128}\) were computed with the optimized structures from the final step of the BOMD simulations.
+
+<--- Page Split --->
+
+We find the solubility limit from equating the Gibbs free energy in the mixture with that in the pure substances \(\mathrm{I4_{1} / amd}\) hydrogen and diamond carbon at 500GPa[104].  
+
+\[G_{xy}(P,T) + k_BT\left[c\ln c + (1 - c)\ln (1 - c)\right] = xG_H(P,T) + yG_C(P,T) \quad (2)\]  
+
+Where \(c = y / (x + y)\) is the carbon concentration and \(y = 1 - x\) is the atomic fraction of C.  
+
+For the liquid simulations we use the NVT ensemble at density and system- sizes equivalent to the \(\mathrm{I4_{1} / amd}\) . We compare these with larger simulations of around 1,000 atoms which previous work [56] has shown sufficient to converge the RDF of metallic liquid hydrogen.  
+
+Our initial analysis is based on partial RDFs of CH and OH separations, as shown in (a) of Figure 3. This shows that simulations of around one hundred or one thousand atoms gives the same hypermolecule formation, both number of bonds and bondlength Figure 3(b). We observe liquid structure peaks which extend beyond the small unit cell size, however, within a thousand- atom simulation, this oscillating structure has decayed away exponentially (Figure 3a). Therefore, we are confident that the results from our hundred- atom simulations give a good description of the hypermolecules.  
+
+## 4 Discussion and Conclusions  
+
+In this study, we used density functional theory calculation to predict the existence of hyperorganic molecules such as \(\mathrm{CH_{8}}\) , \(\mathrm{C_{2}H_{8}}\) , \(\mathrm{C_{3}H_{10}}\) , \(\mathrm{OH_{3}}\) and \(\mathrm{CH_{4}OH}\) in metallic hydrogen.  
+
+The chemical bonding can be understood in terms of standard covalent chemistry, with hypervalent carbon/oxygen forming single bonds to H, and double bonds between heavier elements. This means that these hyperorganic molecules are negatively charged: the charges are screened by the surrounding metallic hydrogen and we show that this causes an oscillating charge density wave around the molecules.  
+
+Regarding consequences for astronomy, exact details will vary from planet to planet, depending on its history. We note that the temperatures considered here are considerably lower than in the cores of Jupiter and Saturn, but well about the equivalent blackbody temperature of these planets[105].  
+
+The positive heat of solution for carbon suggests that carbon will condense and fall as diamond rain, again depending on the gravitational field as well as the chemistry. However, under the conditions expected in gas giants with metallic hydrogen cores this solubility limit is more than parts per thousand, close to or above the expected primordial carbon- hydrogen ratio. Therefore, we anticipate that in many gas giant planets a significant proportion of the carbon will remain in solution in metallic hydrogen.  
+
+Terrestrial synthesis of these molecules is challenging but within the reach of current methodology. Liquid metallic hydrogen forms at lower pressures than its solid counterpart, in both static and dynamic compression [8, 55, 106]. So creation of hypermolecules is plausible, but detection is more difficult. Our \(\mathrm{CH_{6}}\) calculation suggests that the molecules will have distinctive vibrational modes beyond the atomic hydrogen frequencies, but measuring these in such an extreme, metallic environment will be challenging
+
+<--- Page Split --->
+
+Since all our simulations produces long- lived hypermolecules, it seems certain that more complex molecules will also be stable. Thus it appears that the metallic hydrogen environment, the most common state of condensed matter in the universe, is capable of supporting its own rich organic chemistry.  
+
+Acknowledgements. This research project is supported by the Second Century Fund (C2F), Chulalongkorn University. GJA acknowledges funding from the ERC project Hecate. This work used the Cirrus UK National Tier- 2 HPC Service at EPCC (http://www.cirrus.ac.uk) funded by the University of Edinburgh and EPSRC (EP/P020267/1). This also work used the ARCHER2 UK National Supercomputing Service (https://www.archer2.ac.uk) as part of the UKCP collaboration. We acknowledge the supporting computing infrastructure provided by NSTDA, CU, CUAASC, NSRF via PMUB [B05F650021, B37G660013] (Thailand). URL:www.e- science.in.th. We thank David Ceperley and Jeffrey M. McMahon for their valuable suggestions on DFT(QE)- related issues for studying metallic hydrogen. We thank Miriam Pena- Alvarez and Stewart McWilliams for comment and proofreading.  
+
+## Data availability statement  
+
+The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.  
+
+## Conflict of interest  
+
+The authors have no conflicts of interest to declare. All co- authors have seen and agree with the contents of the manuscript and there is no financial interest to report. We certify that the submission is original work and is not under review at any other publication.  
+
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+[100] Marzari, N., Vanderbilt, D., De Vita, A., Payne, M.: Thermal contraction and disordering of the al (110) surface. Physical review letters 82(16), 3296 (1999)  
+
+[101] Hamann, D.: Optimized norm- conserving vanderbilt pseudopotentials. Physical Review B 88(8), 085117 (2013)  
+
+[102] Schlipf, M., Gygi, F.: Optimization algorithm for the generation of oncv pseudopotentials. Computer Physics Communications 196, 36- 44 (2015)  
+
+[103] Baroni, S., De Gironcoli, S., Dal Corso, A., Giannozzi, P.: Phonons and related crystal properties from density- functional perturbation theory. Reviews of modern Physics 73(2), 515 (2001)  
+
+[104] Clark, S., Ackland, G., Crain, J.: Theoretical stability limit of diamond at ultrahigh pressure. Physical Review B 52(21), 15035 (1995)  
+
+[105] Wallace, J.M., Hobbs, P.V.: Atmospheric Science: An Introductory Survey, 2nd edn. Elsevier, Amsterdam (2006)  
+
+[106] Zaghoo, M., Husband, R.J., Silvera, I.F.: Striking isotope effect on the metallization phase lines of liquid hydrogen and deuterium. Physical Review B 98(10), 104102 (2018)
+
+<--- Page Split --->

preprint/preprint__5feffe5f1c13034029fc275ecedfe86f7025cefbf654f8388e079a0a04529991/preprint__5feffe5f1c13034029fc275ecedfe86f7025cefbf654f8388e079a0a04529991_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 107, 759, 144]]<|/det|>
+# Organic compounds in metallic hydrogen  
+
+<|ref|>text<|/ref|><|det|>[[44, 161, 256, 208]]<|/det|>
+Graeme Ackland  g.jackland@ed.ac.uk  
+
+<|ref|>text<|/ref|><|det|>[[50, 234, 620, 255]]<|/det|>
+University of Edinburgh https://orcid.org/0000- 0002- 1205- 7675  
+
+<|ref|>text<|/ref|><|det|>[[44, 260, 240, 278]]<|/det|>
+Jakkapat Seeyangnok  
+
+<|ref|>text<|/ref|><|det|>[[44, 281, 927, 301]]<|/det|>
+Centre for Science at Extreme Conditions, School of Physics and Astronomy, University of Edinburgh  
+
+<|ref|>text<|/ref|><|det|>[[44, 306, 206, 324]]<|/det|>
+Udomsilp Pinsook  
+
+<|ref|>text<|/ref|><|det|>[[52, 327, 650, 348]]<|/det|>
+Department of Physics, Faculty of Science, Chulalongkorn University  
+
+<|ref|>text<|/ref|><|det|>[[44, 387, 275, 407]]<|/det|>
+Physical Sciences - Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 425, 675, 446]]<|/det|>
+Keywords: atomic hydrogen, organic compounds, hydrocarbon, solubility.  
+
+<|ref|>text<|/ref|><|det|>[[44, 463, 310, 483]]<|/det|>
+Posted Date: August 8th, 2024  
+
+<|ref|>text<|/ref|><|det|>[[44, 501, 474, 521]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 4618413/v1  
+
+<|ref|>text<|/ref|><|det|>[[42, 538, 915, 581]]<|/det|>
+License: © © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 599, 535, 620]]<|/det|>
+Additional Declarations: There is NO Competing Interest.  
+
+<|ref|>text<|/ref|><|det|>[[42, 655, 920, 699]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on September 29th, 2025. See the published version at https://doi.org/10.1038/s41467- 025- 63552- 6.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[234, 157, 718, 180]]<|/det|>
+# Organic compounds in metallic hydrogen.  
+
+<|ref|>text<|/ref|><|det|>[[280, 202, 674, 236]]<|/det|>
+Jakkapat Seeyangnok \(^{1,2}\) , Udomsilp Pinsook \(^{2}\) , Graeme John Ackland \(^{1}\)  
+
+<|ref|>text<|/ref|><|det|>[[196, 245, 761, 290]]<|/det|>
+\(^{1}\) Centre for Science at Extreme Conditions, School of Physics and Astronomy, University of Edinburgh, Edinburgh, EH9 3FD, Scotland, United Kingdom.  
+
+<|ref|>text<|/ref|><|det|>[[195, 292, 761, 325]]<|/det|>
+\(^{2}\) Department of Physics, Faculty of Science, Chulalongkorn University, 254 Phaya Thai Rd, Bangkok, 10330, Thailand.  
+
+<|ref|>text<|/ref|><|det|>[[191, 353, 764, 386]]<|/det|>
+Contributing authors: jakkapatjtp@gmail.com; udomsilp.p@chula.ac.th; gjackland@ed.ac.uk;  
+
+<|ref|>sub_title<|/ref|><|det|>[[444, 412, 512, 425]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[206, 429, 750, 652]]<|/det|>
+Metallic hydrogen[1] is the most common condensed material in the universe, comprising the centre of gas giant planets[2- 4] However, experimental studies are extremely challenging[5- 8], and most of our understanding of this material has been led by theory. Chemistry in this environment has not been probed experimentally, so here we examine hydrocarbon chemistry in metallic hydrogen using density functional theory calculations[9, 10]. We find that carbon and oxygen react with metallic hydrogen to produce an entirely new type of hydrocarbon chemistry based on sixfold coordinated carbon with organic- style molecules \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) , \(\mathrm{C_3H_{10}}\) \(\mathrm{OH_3}\) and \(\mathrm{CH_4OH}\) . These are charged molecules stabilised by the metallic environment. Their associated electric fields are screened, giving oscillation in the surrounding electron and proton densities. In view of the excess hydrogen we refer to them as hypermethane, hyperethane etc. The relationship to traditional chemistry is that the metallic background acts as an electron donor and stabilizes negatively charged ions. This enables the formation of six covalent bonds per carbon atom, or three per oxygen atom. This demonstrates that organic chemistry may take place in very different environments from those found on earth, and may be common throughout the universe.  
+
+<|ref|>text<|/ref|><|det|>[[206, 662, 674, 675]]<|/det|>
+Keywords: atomic hydrogen, organic compounds, hydrocarbon, solubility.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[208, 83, 384, 101]]<|/det|>
+## 1 Introduction  
+
+<|ref|>text<|/ref|><|det|>[[207, 111, 832, 169]]<|/det|>
+Metallic hydrogen is believed to be the most common condensed phase of matter in the universe, comprising the cores of gas- giant planets, and giving rise to their enormous magnetic fields. However, it is exceptionally challenging to make metallic hydrogen on earth. Consequently, most of our understanding of this material comes from theory.  
+
+<|ref|>text<|/ref|><|det|>[[207, 170, 832, 352]]<|/det|>
+Modern planetary models depict layers separated by the weight of elements, e.g. gas giants feature an outer molecular hydrogen and helium envelope and a core of metallic hydrogen depleted of helium in[4, 11- 13] which is predicted to be insoluble below its own metallization conditions [14- 21]. Understanding of material properties allows us to infer the composition and structure of exoplanets from their mass- radius relation[2, 3, 14, 22- 26]. Chemical bonding is different at high pressure. For example, on earth, the major components of the mantle exhibit sixfold coordinated silicon[27- 31], in contrast to the fourfold \(\mathrm{sp}^3\) bonding found in normal conditions. The unconventional formation of sixfold coordinated silicon is well described by density functional theory calculations as being enabled by the electrons donated from the Mg ions, and stabilised at pressure thanks to the increased density[32- 38]. If chemistry can change so radically just few thousand kilometres beneath our feet, how different might it be elsewhere in the solar system?  
+
+<|ref|>text<|/ref|><|det|>[[207, 354, 832, 410]]<|/det|>
+While helium in hydrogen, and high pressure hydrogen- rich metals are very well studied, particularly with potential applications to superconductivity, less attention has been paid to the issue of solubility of heavier elements in metallic hydrogen, and the implications different chemical bonding within giant planets[21, 39- 41].  
+
+<|ref|>text<|/ref|><|det|>[[207, 411, 832, 667]]<|/det|>
+Theoretical study of metallic hydrogen began in 1935, when Wigner and Huntington [1] used free electron theory to estimate the density of metallic hydrogen, obtaining a value remarkably close to current estimates. This implied that hydrogen molecules would transition into atomic metallic hydrogen when subjected to sufficiently high pressure - unfortunately their estimate of 25GPa was more than an order of magnitude too low. In 1968, Ashcroft made a remarkable prediction that metallic hydrogen would be a room temperature superconductor. Predictions of the crystal structure of metallic hydrogen came even later[9, 42- 44], through ab initio random- structure exploration. Theoretical assessments [9, 42, 45- 49] indicate that at low temperature hydrogen remains molecular to about 500GPa. Surprisingly, the first atomic and metallic phase is now believed to be a complex, open structure, rather than the dense- packed structures assumed by Wigner, Huntington and Ashcroft. This type of open structure is typical of the high pressure Group I electric materials, having \(I4_{1} / amd\) symmetry, isostructural with cesium IV[50- 53]. 500GPa is at the limit of current experiments which have seen signs of bandgap closure and reflectivity.[5- 7]. This \(I4_{1} / amd\) structure persists until 2.5 TPa, beyond which more densely packed structures are favoured[42, 54]. Fluid metallic hydrogen has been detected at much lower pressures, but higher temperatures, in both static and dynamic compression[8, 55], and calculation[24, 56- 58].  
+
+<|ref|>text<|/ref|><|det|>[[207, 668, 832, 739]]<|/det|>
+In experiments[59], synthesis of solid metallic hydrogen has been claimed at pressures exceeding 420 GPa using infrared absorption measurements [5], and at an even higher pressure of 495 GPa as evidenced by reflectivity measurements [6]. Liquid metallic hydrogen has been reported at much lower pressures both in experiment [8, 55, 60] and simulation[56, 57, 61, 62].
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 87, 790, 258]]<|/det|>
+Carbon is particularly important, being the fourth most abundant element and the building block of organic chemistry. The solubility of hydrocarbons in metallic hydrogen remains the preserve of theorists. Studies on giant planets suggest that hydrocarbons likely exist within the middle layer of their structure [63- 65]. Methane \(\mathrm{(CH_4)}\) has been identified as the most abundant hydrocarbon at pressures of up to several hundred GPa and forms hydrogen- rich compounds with \(\mathrm{H_2}\) up to 160GPa[66, 67]. At higher pressures, simulations suggested that methane decomposes into hydrogen and diamond [41, 63, 64]. Due to its density, the latter subsequently gravitationally sinks deeper into the planet in a phenomenon known as diamond rain.[63, 64, 68- 74]. This predicted demixing contrasts with the observation of high pressure reaction between diamond and hydrogen[75] - an issue which has caused significant practical challenges to synthesizing metallic hydrogen in diamond anvil cells[59].  
+
+<|ref|>text<|/ref|><|det|>[[165, 258, 790, 329]]<|/det|>
+One challenge for theory is the richness of hydrocarbon chemistry. The demonstration that methane is unstable to decomposition does not preclude other stable hydrocarbons. Moreover, given the high temperatures and excess of hydrogen over carbon in gas giant planets, even a low solubility limit could result in much of the carbon remaining in solution in the metallic hydrogen layers.  
+
+<|ref|>text<|/ref|><|det|>[[165, 329, 790, 415]]<|/det|>
+Here, we use density functional theory calculations to consider what form of carbon will exist in a metallic hydrogen environment. We start by examining the free energy in the well- characterized case of solid solution carbon in crystalline \(\mathrm{I4_1 / amd}\) metallic hydrogen. Then we demonstrate the equivalence of the molecular dynamics approach as a reliable estimator of thermodynamic properties, and apply molecular dynamics to investigate the planetary- relevant fluid metallic hydrogen.  
+
+<|ref|>text<|/ref|><|det|>[[165, 415, 790, 458]]<|/det|>
+We predict the existence of a new hydrocarbon chemistry, based around a basic sixfold coordination of carbon and threefold coordination of oxygen. For example we observe \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) , \(\mathrm{C_3H_{10}}\) , \(\mathrm{OH_3}\) and \(\mathrm{CH_4OH}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 472, 466, 491]]<|/det|>
+## 2 Results and Discussion  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 501, 755, 519]]<|/det|>
+### 2.1 Solid solubility of carbon in \(\mathrm{I4_1 / amd}\) metallic hydrogen  
+
+<|ref|>text<|/ref|><|det|>[[165, 525, 790, 582]]<|/det|>
+The solid solubility of carbon in metallic hydrogen can be calculated using the Gibbs free energies (Eqn. 1). Hydrogen exhibits strong nuclear quantum effects, so our calculation includes the zero- point energy of the system, as well as the enthalpy, configurational entropy, and vibrational entropy.  
+
+<|ref|>equation<|/ref|><|det|>[[312, 595, 788, 611]]<|/det|>
+\[G(P,T) = H(P,T) + U_{ZPE} + TS_{con} + TS_{vib} \quad (1)\]  
+
+<|ref|>text<|/ref|><|det|>[[165, 624, 790, 739]]<|/det|>
+Initially we consider a single carbon solute in hydrogen. This is more complicated than standard solid solubility calculation[76- 78] because carbon is significantly larger than hydrogen, so substituting one carbon atom for a single hydrogen is not the most stable arrangement. We tried removing clusters of up to eight hydrogens and found that the most stable arrangement involves removing five hydrogens (Table 1, Fig. 1. ) As a check, particularly of anharmonic effects, we also calculated the free energy from the phonon density of states derived from the velocity autocorrelation function of a molecular dynamics calculation. The results are is very good agreement for carbon,
+
+<--- Page Split --->
+<|ref|>table<|/ref|><|det|>[[205, 83, 870, 270]]<|/det|>
+<|ref|>table_caption<|/ref|><|det|>[[205, 270, 868, 373]]<|/det|>
+Table 1 Thermodynamic properties for the solid solution at 300K and 500GPa As-calculated enthalpy \(H\) (eV/atom), entropy \(TS\) (eV/atom), zero-point energy \(U_{ZPE}\) (eV/atom), configurational entropy (eV/atom), Gibbs free energy (eV/atom), and the free energy of solution (eV) for different arrangements. Calculated energies are relative to the fully ionised atomic states, hence the high degree of precision required. \(H_{MD}\) represents the ensemble average enthalpy obtained from NPT molecular dynamics at 500GPa, while \(H_{static}\) is derived from static optimization. Entropy \(TS\) is the summation of both vibrational and configurational entropy ( \(S_{vib} + S_{conf.}\) ). \(U_{ZPE}\) and \(S_{vib}\) were calculated using the phonon density of states. The upper two sections are per atom, the lower section refers to solution compared to an unmixed reference state, quoted in units of eV per carbon atom   
+
+<table><tr><td>Supercell</td><td>HMD</td><td>Hstatic</td><td>TS (MD)</td><td>UZPE (MD)</td><td>G (MD)</td></tr><tr><td>CH126</td><td>-10.7925±0.0006</td><td>-10.91109</td><td>0.00988</td><td>0.32588</td><td>-10.4764±0.0006</td></tr><tr><td>CH125</td><td>-10.8024 ±0.0010</td><td>-10.92137</td><td>0.00950</td><td>0.32125</td><td>-10.4906±0.0010</td></tr><tr><td>CH124</td><td>-10.8139±0.0007</td><td>-10.93038</td><td>0.00875</td><td>0.32154</td><td>-10.5011±0.0007</td></tr><tr><td>CH123</td><td>-10.8176±0.0010</td><td>-10.93814</td><td>0.01094</td><td>0.31637</td><td>-10.5122±0.0010</td></tr><tr><td>C (diamond)</td><td>-144.0846±0.0016</td><td>-144.35980</td><td>0.00414</td><td>0.27343</td><td>-143.8153±0.0016</td></tr><tr><td>H (I4amd)</td><td>-9.7593±0.0004</td><td>-9.87520</td><td>0.00488</td><td>0.33264</td><td>-9.4316±0.0004</td></tr><tr><td>Supercell</td><td></td><td>Hstatic</td><td>TS (DFPT)</td><td>UZPE (DFPT)</td><td></td></tr><tr><td>CH124</td><td></td><td>-10.93038</td><td>0.00611</td><td>0.29304</td><td></td></tr><tr><td>C (diamond)</td><td></td><td>-144.35980</td><td>0.00404</td><td>0.27565</td><td></td></tr><tr><td>H (I4amd)</td><td></td><td>-9.87520</td><td>0.00358</td><td>0.29202</td><td></td></tr><tr><td>Supercell</td><td>ΔHMD</td><td>ΔHstatic</td><td>-TΔS (MD)</td><td>ΔUZPE (MD)</td><td>gsol-MD</td></tr><tr><td>CH126</td><td>3.12±0.13</td><td>2.9264</td><td>-0.63543</td><td>-0.79825</td><td>1.69±0.13</td></tr><tr><td>CH125</td><td>2.90±0.18</td><td>2.66684</td><td>-0.58265</td><td>-1.37589</td><td>0.94±0.18</td></tr><tr><td>CH124</td><td>2.51±0.14</td><td>2.58685</td><td>-0.48408</td><td>-1.32760</td><td>0.69±0.14</td></tr><tr><td>CH123</td><td>3.10±0.17</td><td>2.68081</td><td>-0.75218</td><td>-1.95750</td><td>0.39±0.17</td></tr></table>  
+
+<|ref|>text<|/ref|><|det|>[[205, 397, 830, 425]]<|/det|>
+and reasonably good for hydrogen: this is expected from the different anharmonicity in the two systems.  
+
+<|ref|>text<|/ref|><|det|>[[205, 426, 830, 483]]<|/det|>
+From both MD and static enthalpy, it shows that classical enthalpy prefers pure substances to the mixture with positive values \(\Delta H_{\mathrm{MD}}\) and \(\Delta H_{\mathrm{Static}}\) . On the other hand, the entropy and zero- point energy[79- 81], favour the mixture, with negative values in both \(- T\Delta S\) and \(\Delta U_{ZPE}\) (see Table 1 and Figure 1a).  
+
+<|ref|>text<|/ref|><|det|>[[205, 484, 830, 541]]<|/det|>
+For a single substitutional carbon, the lowest free energy has an impurity formation energy of \(\Delta g = 0.39\pm 0.17\mathrm{eV}\) , which implies a solid solubility in the parts per million range at room temperature. If more than five hydrogens are removed from the starting configuration, a vacancy defect is created which diffuses through the lattice.  
+
+<|ref|>text<|/ref|><|det|>[[205, 542, 830, 654]]<|/det|>
+Strikingly, we always observe an octahedral arrangement of six neighbouring hydrogens, forming \(\mathrm{CH_6}\) . The overall electronic density of states (Fig.1) is uninformative, being dominated by characteristic free- electron form, with the hydrogen atoms arranged in a way to produce a pseudogap at the Fermi energy, similar to isostructural Cs- IV [51, 82]. However, the electron localization function (ELF) around the carbon (Figure 1d- f) shows that electrons are localized between the hydrogens and carbon in \(\mathrm{CH_6}\) , but not between hydrogen pairs. This suggests that carbon has reacted to form a \(\mathrm{CH_6}\) molecule with six covalent CH bonds, which we call hypermethane.  
+
+<|ref|>text<|/ref|><|det|>[[205, 655, 830, 712]]<|/det|>
+The phonon calculations show that pure hydrogen exhibits the expected two- peaked acoustic and optical branches of \(I4_{1} / \mathrm{amd}\) . The \(\mathrm{CH_{124}}\) supercell retains smeared- out versions of these modes, and the heavier carbon reduces the frequency of the acoustic modes in the supercell. Strikingly, the \(\mathrm{CH_6}\) molecule has a well- defined
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[172, 85, 785, 325]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[164, 345, 790, 449]]<|/det|>
+<center>Fig. 1 Enthalpy and Gibbs Free Energy differences, Electronic Density of States, and Electron Localised Function (ELF) of carbon in solid, metallic hydrogen. a) Enthalpy of solution (eV/atom) as a function of number of removed hydrogens from static relaxation (blue) and NPT-ensemble molecular dynamics (orange) b) Electronic density of states from a typical BOMD snapshot, showing the characteristic free electron form with a pseudogap at the Fermi Energy. c) Phonon density of states from DFPT of a structure from a relaxed \(\mathrm{CH_{124}}\) MD snapshot (blue), compared with pure \(I_{41} / a m d\) hydrogen (orange). d-f) Electron Localization Function (ELF) surrounding a single carbon atom, including cross-sections of planes A and B. The octahedral arrangement of the high ELF values indicates the presence of six covalent-type bonds per carbon. </center>  
+
+<|ref|>text<|/ref|><|det|>[[165, 465, 790, 523]]<|/det|>
+vibrational mode at \(3163 \mathrm{cm}^{- 1}\) a higher frequency than anything in the pure metallic hydrogen (Figure 1c). This mode results from the in- phase vibration of the six hydrogen of \(\mathrm{CH_6}\) . Other modes involving asymmetric CH stretches are mixed with the highest frequency \(\mathrm{I4_1 / amd}\) modes.  
+
+<|ref|>text<|/ref|><|det|>[[165, 524, 790, 581]]<|/det|>
+The solid solution gives us an indication that, like silicon on earth, carbon will go from fourfold to sixfold coordination in giant planets. However, the positive heat of solution suggests that temperatures well above the melting point would be needed for significant solubility. We investigate this further in the next section.  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 595, 677, 613]]<|/det|>
+### 2.2 Organic compounds in liquid metallic hydrogen  
+
+<|ref|>text<|/ref|><|det|>[[165, 618, 790, 718]]<|/det|>
+To further investigate this hypermethane, we simulated a \(\mathrm{CH_6 + H_{118}}\) supercell in the NPT ensemble at \(500 \mathrm{GPa}\) . The radial distribution function (RDF), as shown Figure 2(a), indicates that at \(300 \mathrm{K}\) , we have well- defined H- H peaks representing the \(\mathrm{I4_1 / amd}\) crystal. In the cases of \(600 \mathrm{K}\) and \(900 \mathrm{K}\) , the structure melted as expected[10], indicated by the smoothness of the RDFs in Figure 2a). The mean square displacement (MSD) confirms melting, with a stable MSD at \(300 \mathrm{K}\) and a linear increase for \(600 \mathrm{K}\) and \(900 \mathrm{K}\) , as shown in Figure 2(b).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[281, 88, 750, 333]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[206, 341, 830, 364]]<|/det|>
+<center>Fig. 2 Radial Function Distribution, Mean Square Displacement, and Cumulative Number of Bonds per Carbon from BOMD in NPT ensemble. </center>  
+
+<|ref|>text<|/ref|><|det|>[[207, 363, 831, 466]]<|/det|>
+a) The radial distribution function of the \(\mathrm{CH_6 + H_{118}}\) BOMD simulations under the NPT ensemble at varying temperatures, and 500GPa. The blue solid line denotes the presence of structural peaks in \(\mathrm{CH_6 + H_{118}}\) , while the orange and green solid lines signify the disappearance of these peaks due to system melting. b) Mean square displacement (MSD) of \(\mathrm{CH_6 + H_{118}}\) is examined, with the MSD depicting the crystal structure of \(\mathrm{CH_6 + H_{118}}\) with a finite MSD at 300K, represented by the blue solid line. Conversely, cases of melting at 600K and 900K exhibit increased MSD. c) The radial distribution function illustrates the distribution of carbon-hydrogen pairs. The first peak of the CH-pair radial distribution function experiences smearing from 1.0 Å to 1.3 Å. d) Cumulative number of bonds (CH bonds per carbon) is evaluated, indicating the count of hydrogens surrounding each carbon atom.  
+
+<|ref|>text<|/ref|><|det|>[[207, 483, 831, 555]]<|/det|>
+In all cases, the carbon- hydrogen RDF (Figure 2c), has a strong peak between 1.0Å and 1.3Å. Even in melted conditions, we observe hydrocarbon \(\mathrm{CH_6}\) molecules, as shown in Figure 2(d), where the cumulative number of bonds in the first peak of the RDF being six. These results suggest the existence of the hypermethane \(\mathrm{CH_6}\) molecule above the melting line of metallic hydrogen at 500 GPa.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 568, 831, 587]]<|/det|>
+### 2.3 Other hypermolecules: \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) , \(\mathrm{C_3H_{10}}\) , \(\mathrm{H_3O}\) and \(\mathrm{CH_4OH}\)  
+
+<|ref|>text<|/ref|><|det|>[[207, 592, 831, 679]]<|/det|>
+We now investigate whether more complex organic molecules can form in liquid metallic hydrogen, using NVT molecular dynamics at around 500GPa and 600K. We investigate five cases, adding a single carbon or oxygen atom, \(\mathrm{C_2}\) dimer, \(\mathrm{C_3}\) trimer and CO molecule to liquid metallic hydrogen. In each case, an exothermic reaction took place with the metallic hydrogen to produce a well- defined, stable hypermolecule with OH and CH bondlengths oscillating in the range 1.0 Å to 1.3 Å.  
+
+<|ref|>text<|/ref|><|det|>[[207, 679, 831, 722]]<|/det|>
+We identify these molecules as being hypervalent and hydrogen- rich \(\mathrm{CH_6}\) , \(\mathrm{C_2H_8}\) \(\mathrm{C_3H_{10}}\) , \(\mathrm{H_3O}\) and \(\mathrm{CH_4OH}\) . These correspond to sixfold valence for carbon and trivalent oxygen, with CC and CO double bonds (Figure 3). We note that this mimics the high
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[165, 87, 790, 115]]<|/det|>
+pressure behaviour of the equivalent second row elements: hexavalent Silicon[32] and trivalent Sulphur[83].  
+
+<|ref|>text<|/ref|><|det|>[[165, 115, 790, 214]]<|/det|>
+Figure 3 shows the CH and OH radial and cumulative distribution functions for the hypermolecules we investigated, with the sharp first peak in RDF defining the covalent bond, and the plateau in CDF showing the coordination. All hypermolecules remain stable throughout the 10ps simulation. The covalent bonding is further evidenced by ELF analysis. The negative charge on these hypermolecules is evidenced from molecular orbital considerations and the observation of screening with Friedel oscillations.  
+
+<|ref|>image<|/ref|><|det|>[[168, 234, 787, 435]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[164, 453, 790, 602]]<|/det|>
+<center>Fig. 3 Radial Function Distribution, Cumulative Number of Bonds per Carbon, and Novel Hydrocarbons and representative snapshots from liquid simulations. a) Displays the RDF of the carbon-hydrogen pairs in metallic hydrogen with one carbon (blue line), two carbons (orange line), three carbons (green line), one oxygen and a CO pair (red line), indicating a smearing of the first peak from \(1.0\mathrm{\AA}\) to \(1.3\mathrm{\AA}\) . In the \(\sim 10^{2}\) atom simulations (main figure), structure extends throughout the supercell, however the \(\sim 10^{3}\) atom simulations (inset) indicates a suppression of these structural peaks in CH separation at greater distances. b) Shows the CDF (number of CH neighbours per carbon) at \(1.3\mathrm{\AA}\) , revealing values of approximately 6, 4, 3.3, and 4 respectively. The short-range order is nearly identical in both system sizes (solid lines: \(\sim 10^{2}\) atoms, dashed lines \(\sim 10^{3}\) atoms) c-d) equivalent RDF and CDF for OH pairs, showing well-defined and long-lived bonding. These values suggest the formation of new organic compounds, as depicted in e-i): Snapshots from molecular dynamics showcasing novel chemical species in liquid metallic hydrogen, including e) \(\mathrm{CH}_6\) , f) \(\mathrm{C_2H_8}\) , g) \(\mathrm{C_3H_{10}}\) , h) \(\mathrm{CH_4OH}\) and i) \(\mathrm{OH}_3\) , with schematic molecular bonding shown below. </center>  
+
+<|ref|>text<|/ref|><|det|>[[165, 625, 790, 740]]<|/det|>
+We can understand the chemistry of these hypermolecules by considering that, in a metallic environment, extra electrons are readily available to stabilise charged molecules. The local electronic structure of the molecule shows a similar situation to the hypermethane solid solubility, with electrons in covalent type bonds. The hypermolecules carry a formal negative charge from the excess of electrons, e.g. \(\mathrm{CH}_6\) has 14 electrons and a total nuclear charge of only 12. This charge will be screened by the surrounding liquid. The simple case of a charge in a metal gives slowly decaying Friedel oscillations[84, 85] in the electrostatic potential. Fluid metallic hydrogen is a
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[207, 87, 832, 130]]<|/det|>
+more complicated case because both protons and electrons play a role in the screening. Our large simulations with around 1000 atoms for \(\mathrm{CH}_6\) shows that there are Friedel oscillations in the proton density extending to seven distinctive peaks.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 145, 339, 163]]<|/det|>
+## 3 Methods  
+
+<|ref|>text<|/ref|><|det|>[[207, 173, 832, 231]]<|/det|>
+Calculations were performed using density functional theory (DFT) [86, 87] implemented in both Quantum Espresso (QE) [88, 89] and Born- Oppenheimer molecular dynamics (BOMD) implemented in the CAMbridge Serial Total Energy Package (CASTEP) [90].  
+
+<|ref|>text<|/ref|><|det|>[[207, 231, 832, 400]]<|/det|>
+Using the Broyden- Fletcher- Goldfarb- Shanno algorithm (BFGS) method [91- 93], the four- atom conventional \(I4_{1} / amd\) structure of atomic metallic hydrogen and the diamond (for carbon) were fully optimized at 500GPa, using a force convergence criterion of \(10^{- 5} \mathrm{eV / \AA}\) and a very dense Monkhorst- Pack grid k mesh. We used the exchange- correlation functional of Perdew- Burke- Ernzerhof (GGA- PBE) [94]. The Born- Oppenheimer molecular dynamics (BOMD), time step was 0.5 fs with velocity- Verlet integration[95]. The isothermal- isobaric ensemble (NPT) [96] was implemented, employing the Parrinello- Rahman barostat[97]. Additionally, a thermostat was set at 300 K, and Berendsen thermostat [98]. Solubility calculations, both static relaxation ( \(a = 4.84 \mathrm{\AA}\) and \(c = 6.23 \mathrm{\AA}\) ) and NPT molecular dynamics, were based on a \(4 \times 4 \times 2\) supercell (128 hydrogens) of the four- atom conventional \(I4_{1} / amd\) structure, with carbon substituted for some hydrogens.  
+
+<|ref|>text<|/ref|><|det|>[[207, 401, 832, 556]]<|/det|>
+For the BOMD calculations in the melt, our long simulations were run with boxes containing \(\mathrm{CH}_{124}\) (blue line), \(\mathrm{C}_2\mathrm{H}_{120}\) (orange line), and \(\mathrm{C}_3\mathrm{H}_{276}\) (green line), \(\mathrm{COH}_{124}\) (red line) and \(\mathrm{H}_3\mathrm{O}\) (purple line) respectively, as shown in Figure 3. The \(\mathrm{CH}_6\) \(\mathrm{C}_2\mathrm{H}_{10}\) \(\mathrm{CH}_4\mathrm{OH}\) and \(\mathrm{OH}_3\) molecule simulations were initiated using a \(4\times 4\times 2\) supercell with four hydrogens removed for each insert oxygen or carbon. For \(\mathrm{C}_3\mathrm{H}_8\) , a \(6\times 6\times 2\) supercell (288 hydrogens) with lattice constants \(a = 7.25\mathrm{Å}\) and \(c = 6.23\mathrm{\AA}\) was used. The simulations of melted samples used the NVT ensemble. In the carbon BOMD- NPT simulation, we used a \(3\times 3\times 3\) supercell of the two- atom primitive cell of diamond with the same parameters as the other cases. All of our BOMD simulations were performed up to 20,000 steps and checked for convergence of potential energy. In no case did the hypermolecules dissociate.  
+
+<|ref|>text<|/ref|><|det|>[[207, 557, 832, 728]]<|/det|>
+For lattice dynamics, we analyzed the phonon spectrum of the diamond structure and the four- atom conventional \(I4_{1} / amd\) structure of atomic metallic hydrogen under a pressure of 500 GPa using Quantum ESPRESSO (QE). Structural optimization was conducted using the BFGS method [91, 92], fully relaxing crystal structures with a force convergence criterion of \(1.0^{- 5} \mathrm{eV / \AA}\) . The Monkhorst- Pack grid k mesh [99] employed a dense grid, with Marzari- Vanderbilt- DeVita- Payne cold smearing of 0.02 Ry applied to the Fermi surface [100]. As with CASTEP, the PBE[94], exchange correlation energy functional was implemented, and we used optimized norm- conserving Vanderbilt pseudopotentials [101, 102]. The lattice dynamics was performed using QE based on density functional perturbation theory (DFPT) [103]. The electronic density of states of \(\mathrm{CH}_{124}\) and \(\mathrm{H}_{128}\) were computed with the optimized structures from the final step of the BOMD simulations.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[164, 86, 790, 116]]<|/det|>
+We find the solubility limit from equating the Gibbs free energy in the mixture with that in the pure substances \(\mathrm{I4_{1} / amd}\) hydrogen and diamond carbon at 500GPa[104].  
+
+<|ref|>equation<|/ref|><|det|>[[223, 127, 788, 145]]<|/det|>
+\[G_{xy}(P,T) + k_BT\left[c\ln c + (1 - c)\ln (1 - c)\right] = xG_H(P,T) + yG_C(P,T) \quad (2)\]  
+
+<|ref|>text<|/ref|><|det|>[[164, 156, 790, 185]]<|/det|>
+Where \(c = y / (x + y)\) is the carbon concentration and \(y = 1 - x\) is the atomic fraction of C.  
+
+<|ref|>text<|/ref|><|det|>[[165, 185, 790, 242]]<|/det|>
+For the liquid simulations we use the NVT ensemble at density and system- sizes equivalent to the \(\mathrm{I4_{1} / amd}\) . We compare these with larger simulations of around 1,000 atoms which previous work [56] has shown sufficient to converge the RDF of metallic liquid hydrogen.  
+
+<|ref|>text<|/ref|><|det|>[[165, 242, 790, 343]]<|/det|>
+Our initial analysis is based on partial RDFs of CH and OH separations, as shown in (a) of Figure 3. This shows that simulations of around one hundred or one thousand atoms gives the same hypermolecule formation, both number of bonds and bondlength Figure 3(b). We observe liquid structure peaks which extend beyond the small unit cell size, however, within a thousand- atom simulation, this oscillating structure has decayed away exponentially (Figure 3a). Therefore, we are confident that the results from our hundred- atom simulations give a good description of the hypermolecules.  
+
+<|ref|>sub_title<|/ref|><|det|>[[165, 355, 520, 374]]<|/det|>
+## 4 Discussion and Conclusions  
+
+<|ref|>text<|/ref|><|det|>[[165, 384, 790, 427]]<|/det|>
+In this study, we used density functional theory calculation to predict the existence of hyperorganic molecules such as \(\mathrm{CH_{8}}\) , \(\mathrm{C_{2}H_{8}}\) , \(\mathrm{C_{3}H_{10}}\) , \(\mathrm{OH_{3}}\) and \(\mathrm{CH_{4}OH}\) in metallic hydrogen.  
+
+<|ref|>text<|/ref|><|det|>[[165, 428, 790, 499]]<|/det|>
+The chemical bonding can be understood in terms of standard covalent chemistry, with hypervalent carbon/oxygen forming single bonds to H, and double bonds between heavier elements. This means that these hyperorganic molecules are negatively charged: the charges are screened by the surrounding metallic hydrogen and we show that this causes an oscillating charge density wave around the molecules.  
+
+<|ref|>text<|/ref|><|det|>[[165, 499, 790, 555]]<|/det|>
+Regarding consequences for astronomy, exact details will vary from planet to planet, depending on its history. We note that the temperatures considered here are considerably lower than in the cores of Jupiter and Saturn, but well about the equivalent blackbody temperature of these planets[105].  
+
+<|ref|>text<|/ref|><|det|>[[165, 556, 790, 642]]<|/det|>
+The positive heat of solution for carbon suggests that carbon will condense and fall as diamond rain, again depending on the gravitational field as well as the chemistry. However, under the conditions expected in gas giants with metallic hydrogen cores this solubility limit is more than parts per thousand, close to or above the expected primordial carbon- hydrogen ratio. Therefore, we anticipate that in many gas giant planets a significant proportion of the carbon will remain in solution in metallic hydrogen.  
+
+<|ref|>text<|/ref|><|det|>[[165, 643, 790, 740]]<|/det|>
+Terrestrial synthesis of these molecules is challenging but within the reach of current methodology. Liquid metallic hydrogen forms at lower pressures than its solid counterpart, in both static and dynamic compression [8, 55, 106]. So creation of hypermolecules is plausible, but detection is more difficult. Our \(\mathrm{CH_{6}}\) calculation suggests that the molecules will have distinctive vibrational modes beyond the atomic hydrogen frequencies, but measuring these in such an extreme, metallic environment will be challenging
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[207, 87, 831, 144]]<|/det|>
+Since all our simulations produces long- lived hypermolecules, it seems certain that more complex molecules will also be stable. Thus it appears that the metallic hydrogen environment, the most common state of condensed matter in the universe, is capable of supporting its own rich organic chemistry.  
+
+<|ref|>text<|/ref|><|det|>[[207, 150, 832, 308]]<|/det|>
+Acknowledgements. This research project is supported by the Second Century Fund (C2F), Chulalongkorn University. GJA acknowledges funding from the ERC project Hecate. This work used the Cirrus UK National Tier- 2 HPC Service at EPCC (http://www.cirrus.ac.uk) funded by the University of Edinburgh and EPSRC (EP/P020267/1). This also work used the ARCHER2 UK National Supercomputing Service (https://www.archer2.ac.uk) as part of the UKCP collaboration. We acknowledge the supporting computing infrastructure provided by NSTDA, CU, CUAASC, NSRF via PMUB [B05F650021, B37G660013] (Thailand). URL:www.e- science.in.th. We thank David Ceperley and Jeffrey M. McMahon for their valuable suggestions on DFT(QE)- related issues for studying metallic hydrogen. We thank Miriam Pena- Alvarez and Stewart McWilliams for comment and proofreading.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 321, 530, 340]]<|/det|>
+## Data availability statement  
+
+<|ref|>text<|/ref|><|det|>[[207, 349, 831, 406]]<|/det|>
+The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 420, 430, 439]]<|/det|>
+## Conflict of interest  
+
+<|ref|>text<|/ref|><|det|>[[207, 449, 831, 506]]<|/det|>
+The authors have no conflicts of interest to declare. All co- authors have seen and agree with the contents of the manuscript and there is no financial interest to report. We certify that the submission is original work and is not under review at any other publication.  
+
+<|ref|>sub_title<|/ref|><|det|>[[207, 519, 334, 538]]<|/det|>
+## References  
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+of Chemical Physics 160(19) (2024)  
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+
+<--- Page Split --->

preprint/preprint__601f685f5ff3d3c7aeccd00337f1e979e1cb7d35e2fc47084b324e63a27dfe8f/images_list.json

@@ -0,0 +1,70 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Bayesian networks (BNs). a) Schematic of basic building block of a BN comprising of a parent node, A, a child node, B, and an edge connecting the two. Each node represents an event, and the connection represents how two events are mutually dependent. The dependence is provided in a conditional probability table (CPT), which contains the conditional probability or likelihood values, i.e., \\(P(B / A)\\) and \\(P(B / A^c)\\) , where \\(A^c\\) is the complement of the event. Knowing the probability of occurrence for the event A, i.e., \\(P(A)\\) , the marginal probability of occurrence of the event B, i.e., \\(P(B)\\) can be evaluated using Bayes' theorem. b) Acceleration of 2-node BN in (a) using three stochastic bit (s-bit) generators and one \\(2 \\times 1\\) multiplexer (MUX) circuit. c) Examples of BN architecture that represent real-life situations from ecology to forecasting and drug discovery highlighting its usefulness in decision making.",
+    "footnote": [],
+    "bbox": [
+      [
+        205,
+        356,
+        710,
+        777
+      ]
+    ],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. 2D memtransistors. a) 3D schematic and b) optical image of a representative 2D memtransistor based on monolayer MoS2, which are locally back-gated using a stack comprising of atomic layer deposition (ALD) grown \\(50 \\mathrm{nm} \\mathrm{Al}_2\\mathrm{O}_3\\) on sputter deposited \\(40 / 30 \\mathrm{nm} \\mathrm{Pt} / \\mathrm{TiN}\\) . All back-gate islands were placed on a commercially purchased \\(\\mathrm{SiO}_2 / \\mathrm{p}^{++}\\) -Si substrate. c) Transfer characteristics, i.e., source-to-drain current \\((I_{\\mathrm{DS}})\\) versus local back-gate voltage \\((V_{\\mathrm{BG}})\\) measured using source-to-drain bias, \\(V_{\\mathrm{DS}} = 1 \\mathrm{V}\\) , in linear and logarithmic scale for a representative MoS2 memtransistor with channel length, \\(L = 1 \\mu \\mathrm{m}\\) , and channel width, \\(W = 5 \\mu \\mathrm{m}\\) . d) Output characteristics, i.e., \\(I_{\\mathrm{DS}}\\) versus \\(V_{\\mathrm{DS}}\\) for different \\(V_{\\mathrm{BG}}\\) for the same MoS2 memtransistor. e) Post-programmed and f) post-erased transfer characteristics of a representative 2D memtransistor. g) Non-volatile retention for 4 representative post-programmed and post-erased conductance states \\((G_{\\mathrm{MT}})\\) for 100 seconds.",
+    "footnote": [],
+    "bbox": [
+      [
+        135,
+        112,
+        875,
+        384
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. 2D memtransistor based s-bit generator. a) Transfer characteristics of a representative 2D memtransistor, measured each time after the application of \\(V_{\\mathrm{P}} = -10\\) V and \\(V_{\\mathrm{E}} = 10\\) V each for \\(\\tau_{\\mathrm{s}} = 100\\) ms, for a total of 100 cycles. Distribution of b) post-programmed and c) post-erased conductance \\((G_{\\mathrm{MT}})\\) measured using \\(V_{BG} = 0\\) V. d) Circuit diagram and e) corresponding optical image for the proposed s-bit generator consisting of six memtransistors (MT1, MT2, MT3, MT1, MT2, MT3). f) Voltage waveforms applied to the nodes, N1, N2, i.e., \\(V_{N1}\\) , \\(V_{N2}\\) . During each clock cycle \\((\\tau_{\\mathrm{clk}})\\) , \\(V_{N1}\\) toggles between 0 V, 0 V, and \\(V_{DD} = 2\\) V and \\(V_{N2}\\) toggles between \\(V_{\\mathrm{P}} = -7\\) V, \\(V_{\\mathrm{E}} = 10\\) V, and \\(V_{\\mathrm{R}} = 1\\) V. Voltages applied to nodes, N3, and N4, i.e., \\(V_{N3}\\) , and \\(V_{N4}\\) are held constant at 1V and 0 V, respectively. g) Voltage readout at node, N5, i.e., \\(V_{N5}\\) . h) Distribution of \\(V_{N5}\\) over \\(200\\tau_{\\mathrm{clk}}\\) follows a random Gaussian distribution with mean, \\(\\mu_{VN5} = 0.37\\) V and standard deviation, \\(\\sigma_{VN5} = 0.05\\) V. i) Output, \\(V_{N6}\\) , of an inverting amplifier constructed using MT3 and MT4 as a function of the input, \\(V_{N5}\\) with a gain of \\(\\sim 8\\) . j) \\(V_{N6}\\) corresponding to \\(V_{N5}\\) shown in (g). k) Distribution of \\(V_{N6}\\) follows a random Gaussian distribution with mean, \\(\\mu_{VN6} = 0.74\\) V and an increased standard deviation of \\(\\sigma_{VN6} = 0.3\\) V. l) Output, \\(V_{N7}\\) , of a thresholding inverter constructed using MT5 and MT6 as a function of the input, \\(V_{N6}\\) for different inversion threshold, \\(V_{IT}\\) . m) \\(V_{N7}\\) corresponding to \\(V_{N6}\\) shown in (i) for different \\(V_{IT}\\) . n) Probability of obtaining '1' in the bit stream (p_s) as a function of \\(V_{IT}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        140,
+        92,
+        857,
+        707
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Hardware acceleration of BN. a) Circuit schematic for hardware acceleration of BN using three s-bit generator and one \\(2\\times 1\\) MUX. The MUX consists of one inverter and three 2-input NAND gates. b) Optical image and corresponding circuit configuration of a 2-input NAND gate comprising of 3 memtransistors, MT1 MT2, and MT3 connected in series with MT1 serving as the depletion load. c) Input waveforms, \\(V_{N3}\\) and \\(V_{N4}\\) , which are applied to the local back-gate terminals of MT2 and MT3 at nodes \\(N_{3}\\) and \\(N_{4}\\) , respectively, and the corresponding output waveform, \\(V_{N2}\\) , which is obtained at node \\(N_{2}\\) . d) Optical image and e) corresponding circuit configuration for hardware acceleration of a 2-node BN consisting of 3 s-bit generators and a \\(2\\times 1\\) MUX with a total of 29 memtransistors. The \\(V_{IT}\\) values for the s-bit generators for \\(X_{1}\\) and \\(X_{2}\\) can be pre-programmed using the CPT for the nodes A and B. f) Representative stochastic bit-streams for the random variables A, \\(X_{1}\\) , and \\(X_{2}\\) with \\(P(A) = 0.12\\) , \\(P(X_{1}) = P(B / A) = 0.26\\) , and \\(P(X_{2}) = P(B / A^{C}) = 0.36\\) . g) Correlation coefficient (CC) values between A, \\(X_{1}\\) , and \\(X_{2}\\) confirm mutual independence of the s-bit generator modules. h) Stochastic bit-streams obtained at the output node, B. The measured and expected values for \\(P(B)\\) are 0.56 and 0.54.",
+    "footnote": [],
+    "bbox": [
+      [
+        123,
+        95,
+        860,
+        580
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Extended Data Figure 3. Three examples of representative stochastic bit-streams for the random variables \\(A\\) , \\(X_{1}\\) , and \\(X_{2}\\) , correlation coefficient (CC) values between \\(A\\) , \\(X_{1}\\) , and \\(X_{2}\\) , and stochastic bit-streams obtained at the output node, \\(B\\) for the 2-node BN. The measured and expected values for \\(P(B)\\) are very similar confirming high precision hardware acceleration of BN.",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 23
+  }
+]

preprint/preprint__601f685f5ff3d3c7aeccd00337f1e979e1cb7d35e2fc47084b324e63a27dfe8f/preprint__601f685f5ff3d3c7aeccd00337f1e979e1cb7d35e2fc47084b324e63a27dfe8f.mmd

@@ -0,0 +1,275 @@
+
+# Hardware Acceleration of Bayesian Network based on Two-dimensional Memtransistors  
+
+Yikai Zheng  Pennsylvania State University  
+
+Harikrishnan Ravichandran  Pennsylvania State University  
+
+Thomas Schranghamer  Pennsylvania State University  
+
+Nicholas Trainor  Pennsylvania State University  
+
+Joan Redwing  Saptarshi Das ( \(\boxed{\text {sud70@psu.edu}}\) )  Pennsylvania State University  https://orcid.org/0000- 0002- 0188- 945X  
+
+Article  
+
+Keywords:  
+
+Posted Date: February 1st, 2022  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 1196768/v1  
+
+License: © \(\circledast\) 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 23rd, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 33053-x.
+
+<--- Page Split --->
+
+# Hardware Acceleration of Bayesian Network based on Two-dimensional  
+
+# Memtransistors  
+
+Yikai Zheng \(^{1}\) , Harikrishnan Ravichandran \(^{1}\) , Thomas F Schranghamer \(^{1}\) , Nicholas Trainor \(^{2,3}\) ,  
+
+Joan M Redwing \(^{2,3}\) , and Saptarshi Das \(^{2,3,4,5,*}\)  
+
+\(^{1}\) Engineering Science and Mechanics, Penn State University, University Park, PA 16802, USA \(^{2}\) Materials Science and Engineering, Penn State University, University Park, PA 16802, USA \(^{3}\) Materials Research Institute, Penn State University, University Park, PA 16802, USA \(^{4}\) Electrical Engineering and Computer Science, Penn State University, University Park, PA 16802, USA  
+
+Abstract: Long before Bayes proposed his landmark theorem on the probability of an event, based on prior knowledge of other events, natural intelligence has adopted Bayesian inference as a tool to ensure survival for almost all species. The fact that living beings must make critical decision for finding food, avoiding predators, and locating mates, based on information gathered by their sensory organs with limited sensitivity and under noisy surroundings, emphasizes the importance of probabilistic computing for evolutionary success. While the anatomy of neural hardware that accomplishes such task is far from being known, it is clear that stochastic computing is a fundamental aspect of natural intelligence, and Bayesian networks (BNs) are powerful mathematical constructs for the same. Interestingly, BNs also find widespread application in many real- world probabilistic problems including diagnostics, forecasting, computer vision, etc. While the concept of BN is well known, there are very limited hardware realizations of BN. CMOS [1, 2] based BNs
+
+<--- Page Split --->
+
+require massive hardware resources (thousands of transistors), whereas, memristor [3- 5] and spintronics [6- 8] based BNs necessitate hybrid design with CMOS peripherals limiting the area and energy efficiency [9]. Here, we circumvent these challenges by introducing a compact and low- power BN architecture embedded in memory based on 2D memtransistors.  
+
+## Introduction  
+
+Animals gather information from their surroundings with the help of their sensory organs and process the same using their brain to make decisions, which aid them to locate mates, find preys, and escape from predators. Better decision making leads to better survival, which naturally translates into the evolutionary success for the species. However, it is often very difficult for animals to gather accurate information either due to the limitations of their sensory organ or because of the information being obscured by noisy environment. For example, visual cues are unreliable source of information for freshwater fishes like the rainbow trout since these can be both misleading and manipulated by a predator. In contrast chemical cues released into the water from the epidermis of an injured fish are more reliable indicators of predatory events [10]. The decision to invoke an alarm responses, i.e. less swimming and more time to resume foraging, therefore, depends on how the brain of the rainbow trout processes the visual and the chemical cues based on their relative probability of success from prior experiences. While the neural basis of such computation is relatively unknown, the mathematical construct can be represented using a Bayesian network (BN) with theoretical foundation in Bayes' theorem.  
+
+BN is a probabilistic graphic network used to estimate and infer the probability of events, where events are interdependent on each other [11]. Fig. 1a shows the basic building block of a BN comprising of a parent node, \(A\) , a child node, \(B\) , and an edge connecting the two. Each node
+
+<--- Page Split --->
+
+represents an event, e.g., presence of chemical cue or \(A\) and presence of a predator or \(B\) , and the connection represents how two events are mutually dependent. The dependence is provided in a conditional probability table (CPT), which contains the conditional probability or likelihood values, i.e. \(P(B / A)\) and \(P(B / A^c)\) , where \(A^c\) is the complement of the event \(A\) . In the present example, these represents the likelihood of presence of a predator given that a chemical cue is present \((A)\) or absent \((A^c)\) , respectively. Knowing the probability of occurrence for the event \(A\) , i.e., \(P(A)\) , the marginal probability of occurrence of the event \(B\) , i.e. \(P(B)\) can be evaluated using Bayes' theorem following Eq. 1.  
+
+\[\begin{array}{l}{P(B) = P(B / A)P(A) + P(B / A^c)P(A^c) = P(B / A)P(A) + P(B / A^c)[1 - P(A)]}\\ {P(A) + P(A^c) = 1} \end{array} \quad (1a)\]  
+
+In a generic BN, a child node can have multiple parent nodes, and a parent node can have multiple children. For example, Extended Data Fig. 1a shows a BN where the child node, \(B\) is connected to \(n\) parent nodes, \(A_{1}, A_{2}, \ldots , A_{n}\) . Note that the CPT in this instance contains \(N = 2^n\) entries, which are the conditional probability or likelihood for the occurrence of the event \(B\) for all possible combinations of occurrence of the events \(A_{i}\) 's, \(i = 1,2, \ldots n\) . Similarly, Extended Data Fig. 1b shows a BN where the parent node, \(A\) is connected to \(m\) children, \(B_{1}, B_{2}, \ldots , B_{m}\) . In this case, there are \(m\) CPTs each with \(N = 2\) entries.  
+
+Note that the probability estimation for a child node with \(n\) parent require \(n2^n\) multiplications, \(n2^{n - 1}\) subtractions, and \(2^n - 1\) additions or a total of \(2^{n - 1}(3n + 2) - 1\) arithmetic operations. Needless to mention that the number of arithmetic operations increases as the number of nodes in the BN increases. This makes hardware acceleration of BN using conventional silicon complementary metal oxide semiconductor (CMOS) technology resources extensive since
+
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+
+arithmetic operations require circuits consisting of hundreds of transistors, which have large footprints and consume significant amount of energy. Furthermore, the von Neumann bottleneck necessitates storing of the CPT in the memory, which is physically separated from the arithmetic core and, therefore, requires frequent data shuttling between the two increasing the energy burden. In contrast, even the tiniest brains with very limited number of neurons can perform such apparently complex computational tasks with miniscule energy expenditure. The success of biological brains in implementing BN lie in the inherently stochastic nature of neural computation.  
+
+![](images/Figure_1.jpg)
+
+<center>Figure 1. Bayesian networks (BNs). a) Schematic of basic building block of a BN comprising of a parent node, A, a child node, B, and an edge connecting the two. Each node represents an event, and the connection represents how two events are mutually dependent. The dependence is provided in a conditional probability table (CPT), which contains the conditional probability or likelihood values, i.e., \(P(B / A)\) and \(P(B / A^c)\) , where \(A^c\) is the complement of the event. Knowing the probability of occurrence for the event A, i.e., \(P(A)\) , the marginal probability of occurrence of the event B, i.e., \(P(B)\) can be evaluated using Bayes' theorem. b) Acceleration of 2-node BN in (a) using three stochastic bit (s-bit) generators and one \(2 \times 1\) multiplexer (MUX) circuit. c) Examples of BN architecture that represent real-life situations from ecology to forecasting and drug discovery highlighting its usefulness in decision making. </center>
+
+<--- Page Split --->
+
+Drawing inspiration from biology, stochastic computing (SC) has been explored for the hardware acceleration of BN [12]. The key difference is that unlike classical computing where information in presented in the form of binary values (1's and 0's), SC encodes information using stochastic bits (s- bits) that are interpreted as probabilities that fall in the interval [0,1]. For instance, the bitstream, \(S = [10010100]\) encodes the value \(P(S) = 3 / 8\) , i.e., the probability of finding '1' in the bit- stream, \(S\) . An attractive feature of SC is that arithmetic operations to be performed using simple logic gates [13, 14]. For example, the 2- node BN in Fig. 1a can be realized using a multiplexer (MUX) circuit as shown in Fig. 1b. The output, \(B\) , of a MUX with two input variables, \(X_{1}, X_{2}\) , and a select line, \(A\) , is given by Eq. 2.  
+
+\[B = A X_{1} + A^{c}X_{2}\]  
+
+Instead of being digital variables, if \(X_{1}, X_{2}\) , and \(A\) represent stochastic variables with \(P(X_{1}), P(X_{2})\) , and \(P(A)\) being the probability of obtaining '1' in their respective bit- streams, then \(B\) also transforms into a random variable whose probability is given by Eq. 3.  
+
+\[P(B) = P(A)P(X_{1}) + P(A^{c})P(X_{2})\]  
+
+Note that, if \(P(X_{1}) = P(B / A)\) and \(P(X_{2}) = P(B / A^{C})\) , then Eq. 3 transforms into Eq. 1. Therefore, hardware acceleration of a child node with single parent can be accomplished by using 3 s- bit generators and a \(2 \times 1\) MUX. Interestingly, the MUX architecture can be scaled to accelerate any BN. For example, hardware acceleration of BN in Extended Data Fig. 1a can be achieved by using \(n\) s- bit generators to obtain the \(A_{i}\) 's, another \(N = 2^{n}\) s- bit generators to obtain the CPT, and one \(N \times 1\) MUX with \(n\) select lines as shown in Extended Data Fig. 1c. Similarly, Extended Data Fig. 1d shows the hardware architecture for the BN in Extended Data Fig. 1b consisting of 1 s- bit generator to obtain \(A\) , another \(2m\) s- bit generators to obtain the \(m\) CPTs, and \(m\) \(2 \times 1\) MUXs.
+
+<--- Page Split --->
+
+Note that BN architecture can be used to represent many real- life situations as shown in Fig. 1c. For example, in the case of the rainbow trout, the events \(A_{1}\) and \(A_{2}\) represent the presence of visual and chemical cues, respectively, which are independent of each other, the event \(B\) represents the presence of a predator, and the events \(C_{1}\) and \(C_{2}\) represent the decision taken by the rainbow trout to stop swimming and stop foraging, respectively, which are also independent of each other but depend on \(B\) . Similarly, in forecasting, the events \(A_{1}\) and \(A_{2}\) represent the probability of a day being cloudy and windy, respectively, the event \(B\) represent the probability of rain, and the events \(C_{1}\) and \(C_{2}\) may represent the decision to purchase an umbrella or drink coffee, respectively. Finally, a third example is derived from genetics and drug discovery, where the events \(A_{1}\) and \(A_{2}\) may represent the probability of expressing gene 1 and gene 2 when intervening with a specific drug, the event \(B\) represents the activation of a critical signaling pathway, and the events \(C_{1}\) and \(C_{2}\) represent production of specific hormones or antibodies. The above discussion exemplifies the usefulness of BNs in depicting causal relationship using acyclic graphs, which can subsequently be used to predict outcomes based on prior knowledge and likelihood. For example, to predict the relative effectiveness between drug- 1 and drug- 2 that influence expression for gene 1 and gene 2, respectively, the only experiments that one needs to do is to obtain respective prior, i.e., \(P(A_{1})\) and \(P(A_{2})\) . BN can then be used to obtain marginal likelihoods, i.e., \(P(C_{1})\) and/or \(P(C_{2})\) to assess the relative effectiveness of the two drugs.  
+
+The fundamental computing primitive for BN is a s- bit generator, which allows control of the output probability of obtaining ‘1’ in a given bit- stream. So far, probabilistic CMOS [15], field- programmable gate arrays (FPGA) [16- 18], memristors [3, 4], and spintronic devices [19- 22] have been successfully used for BN acceleration. However, CMOS and FPGA based BN architecture
+
+<--- Page Split --->
+
+require hundreds of transistors to generate s- bits due, which limits its area and energy efficiency [9]. In contrast, memristors offer inherent stochasticity in their switching dynamics, which can be exploited to obtain random bits. However, memristor- based BN architectures heavily rely on CMOS peripherals to translate random bits into s- bits and for subsequent logic operations using those s- bits. Recently, spintronic device such as magnetic random access memory (MRAM) [23] and magnetic tunnel junctions (MTJs) [24] have shown potential for BN acceleration since s- bits can be obtained by controlling the probability of spin- flip through externally driven current. However, temperature and supply voltage fluctuations can impact the spin- flip probability, which necessitates additional CMOS- based peripheral circuits to remove the bit- bias. In addition, spin- based devices still require CMOS- based logic circuits for BN acceleration.  
+
+In this work, we demonstrate hardware acceleration of BN using a monolithic memtransistor technology based on two- dimensional (2D) semiconductors such as monolayer \(\mathrm{MoS_2}\) . Memtransistors are three terminal devices with the gate terminal allowing non- volatile and analog programming of the conductance states, which can be readout by applying source- to- drain bias. Our main contributions in this work are 1) the design of an area and energy efficient s- bit generator circuit comprising of six memtransistors to achieve tunable probability of obtaining '1' in the bitstream in the range [0,1] and 2) integration of s- bit generators with 2D memtransistor based \(2 \times 1\) MUX that consists of three NAND gates and one as NOT gate for BN acceleration. In brief, we exploit the inherent stochasticity in the charge trapping and detrapping processes in the gate dielectric of the memtransistor as the source of randomness. Our in- memory compute approach based on 3- terminal 2D memtransistors not only overcomes the von Neumann limitations of
+
+<--- Page Split --->
+
+conventional digital CMOS, but also eliminates the need for peripherals, which is inescapable for emerging memristor- and spin- based 2- terminal stochastic devices for BN acceleration.  
+
+## Fabrication and characterization of 2D memtransistors  
+
+Fig. 2a- b, respectively, show the 3D schematic and optical image of a representative 2D memtransistor based on monolayer \(\mathrm{MoS}_2\) , which are locally back- gated using a stack comprising of atomic layer deposition (ALD) grown \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) on sputter deposited \(40 / 30 \mathrm{nm} \mathrm{Pt / TiN}\) . All back- gate islands were placed on a commercially purchased \(\mathrm{SiO}_2 / \mathrm{p}^{++}\) - Si substrate. As we will discuss later, the analog, non- volatile, and stochastic programming capability offered by the \(\mathrm{Al}_2\mathrm{O}_3 / \mathrm{Pt / TiN}\) gate stack is central to our BN architecture. The monolayer \(\mathrm{MoS}_2\) used in this work was grown using metal organic chemical vapor deposition (MOCVD) technique on sapphire substrate at \(950^{\circ}\mathrm{C}\) [25, 26]. Use of epitaxial substrate and elevated growth temperature ensure uniform and high quality 2D film, which is critical for the successful demonstration of our BN architecture that involves many 2D memtransistors. The monolayer \(\mathrm{MoS}_2\) film was transferred from the growth substrate to the \(\mathrm{SiO}_2 / \mathrm{p}^{++}\) - Si substrate with predefined islands of \(\mathrm{Al}_2\mathrm{O}_3 / \mathrm{Pt / TiN}\) for subsequent 2D memtransistor fabrication. Details on monolayer \(\mathrm{MoS}_2\) synthesis, film transfer, and fabrication of the local back- gate gate islands, \(\mathrm{MoS}_2\) memtransistors, and BN architecture can be found in the Methods section.  
+
+The film quality and device performance were assessed using optical and electrical measurements. Raman spectra (Extended Data Fig. 2a) obtained for a representative 2D memtransistor shows two characteristics monolayer \(\mathrm{MoS}_2\) peaks at \(383 \mathrm{cm}^{- 1}\) and \(404 \mathrm{cm}^{- 1}\) corresponding to the in- plane \(E_{2g}^1\) and out- of- plane \(A_{1g}\) modes, respectively, with the expected peak separation of \(\sim 20 \mathrm{cm}^{- 1}\) for
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2. 2D memtransistors. a) 3D schematic and b) optical image of a representative 2D memtransistor based on monolayer MoS2, which are locally back-gated using a stack comprising of atomic layer deposition (ALD) grown \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) on sputter deposited \(40 / 30 \mathrm{nm} \mathrm{Pt} / \mathrm{TiN}\) . All back-gate islands were placed on a commercially purchased \(\mathrm{SiO}_2 / \mathrm{p}^{++}\) -Si substrate. c) Transfer characteristics, i.e., source-to-drain current \((I_{\mathrm{DS}})\) versus local back-gate voltage \((V_{\mathrm{BG}})\) measured using source-to-drain bias, \(V_{\mathrm{DS}} = 1 \mathrm{V}\) , in linear and logarithmic scale for a representative MoS2 memtransistor with channel length, \(L = 1 \mu \mathrm{m}\) , and channel width, \(W = 5 \mu \mathrm{m}\) . d) Output characteristics, i.e., \(I_{\mathrm{DS}}\) versus \(V_{\mathrm{DS}}\) for different \(V_{\mathrm{BG}}\) for the same MoS2 memtransistor. e) Post-programmed and f) post-erased transfer characteristics of a representative 2D memtransistor. g) Non-volatile retention for 4 representative post-programmed and post-erased conductance states \((G_{\mathrm{MT}})\) for 100 seconds. </center>  
+
+monolayer MoS2 [27]. Similarly, the photoluminescence (PL) spectra (Extended Data Fig. 2b) shows peak at 1.83 eV corresponding to the direct bandgap of monolayer MoS2. The transfer characteristics, i.e. source to drain current \((I_{\mathrm{DS}})\) versus local back- gate voltage \((V_{\mathrm{BG}})\) measured using source- to- drain bias, \(V_{\mathrm{DS}} = 1 \mathrm{V}\) , in linear and logarithmic scale for a representative MoS2 memtransistor with channel length, \(L = 1 \mu \mathrm{m}\) , and channel width, \(W = 5 \mu \mathrm{m}\) is shown in Fig. 2c. As expected, n- type transport is observed in MoS2, which is attributed to the pinning of the metal Fermi level near the conduction band [28- 30]. Nevertheless, MoS2 memtransistor exhibits excellent electrostatic gate control with current on/off ratio \((r_{\mathrm{ON / OFF}}) > 10^5\) , subthreshold slope \((SS) < 400 \mathrm{mV / decade}\) averaged over 3 orders of magnitude change in \(I_{\mathrm{DS}}\) , minimal gate hysteresis when measured in air, and low gate leakage current. The threshold voltage \((V_{\mathrm{TH}})\) was found to be \(\sim 2.2 \mathrm{V}\) extracted at iso- current of \(10 \mathrm{nA / \mu m}\) and the electron field effect mobility \((\mu_{\mathrm{FE}})\) extracted
+
+<--- Page Split --->
+
+from the peak trans- conductance was found to be \(6 \mathrm{cm}^{2} / \mathrm{V} \cdot \mathrm{s}\) . Fig. 2d shows the output characteristics, i.e. \(I_{\mathrm{DS}}\) versus \(V_{\mathrm{DS}}\) for different \(V_{\mathrm{BG}}\) for the same \(\mathrm{MoS}_{2}\) memtransistor. The on current \((I_{\mathrm{ON}})\) reached as high as \(\sim 15 \mu \mathrm{A} / \mu \mathrm{m}\) for an inversion carrier density of \(\sim 1 \times 10^{12} / \mathrm{cm}^{2}\) at \(V_{\mathrm{DS}} = 5 \mathrm{V}\) . These results indicate reasonably good quality monolayer film growth using MOCVD, relatively damage- free film transfer, and clean memtransistor fabrication processes.  
+
+The post- programmed and post- erased transfer characteristics of a representative 2D memtransistor after being subjected to negative "Write" \((V_{P})\) and positive "Erase" \((V_{E})\) voltage pulses of different amplitudes applied to the local back- gate electrode, each for a duration of \(\tau_{P / E} = 100 \mathrm{ms}\) is shown in Fig. 2e. The negative and positive shift in the respective transfer characteristics can be ascribed to electron trapping and detrapping at and near the \(\mathrm{MoS}_{2} / \mathrm{Al}_{2} \mathrm{O}_{3}\) interface, respectively. The trapping and de- trapping processes were found to be non- volatile as shown in Fig. 2f for 4 representative post- programmed and post- erased conductance states \((G_{MT})\) , respectively, for 100 seconds. We also examined long- term memory retention for the 2D memtransistors and found that states remain indistinguishable even after 3 hrs. Memory retention is important to store the CPT and the memtransistors demonstrate adequate memory performance for the acceleration of BN using SC.  
+
+## Programming stochasticity in 2D memtransistor and design of s-bit generator  
+
+Design of hardware for high- quality random bit generation is central to the acceleration of BN. Here, we exploit the cycle- to- cycle variation in the post- programmed and post- erased conductance states \((G_{MT})\) of 2D memtransistor as the source of true randomness. Fig. 3a shows the transfer characteristics of a representative \(\mathrm{MoS}_{2}\) memtransistor, which is measured each time after applying
+
+<--- Page Split --->
+
+\(V_{P} = - 10 \mathrm{V}\) and \(V_{E} = 10 \mathrm{V}\) for \(\tau_{s} = 100 \mathrm{ms}\) , for a total of 100 cycles and Fig. 3b- c, respectively, show the histogram of post- programmed and post- erased \(G_{MT}\) extracted at \(V_{BG} = 0 \mathrm{V}\) . Clearly, \(G_{MT}\) follow Gaussian random distributions. To translate the stochastic conductance fluctuation into s- bits, we deploy a circuit consisting of six memtransistors ( \(MT1\) , \(MT2\) , \(MT3\) , \(MT4\) , \(MT5\) , and \(MT6\) ) as shown using the circuit diagram and the corresponding optical image in Fig. 3d- e, respectively. The voltage waveforms applied to the nodes, \(N1\) , \(N2\) , i.e., \(V_{N1}\) , \(V_{N2}\) , respectively, are shown in Fig. 3f. Note that during each clock cycle \((\tau_{clk})\) , \(V_{N1}\) switches between 0 V, 0 V, and 2 V and \(V_{N2}\) switches between \(V_{P} = - 7 \mathrm{V}\) , \(V_{E} = 10 \mathrm{V}\) , and \(V_{R} = 1 \mathrm{V}\) . Voltages applied to nodes, \(N3\) , and \(N4\) , i.e., \(V_{N3}\) , and \(V_{N4}\) are held constant at 1V and 0 V, respectively. This allows programming and reset of \(MT1\) during each \(\tau_{clk}\) . The voltage readout at node, \(N5\) , i.e., \(V_{N5}\) is shown in Fig. 3g, which exhibits stochastic fluctuation. Note that the series connection of memtransistors, \(MT1\) and \(MT2\) represents a voltage divider circuit, and hence \(V_{N5}\) is determined by their respective conductance values, i.e., \(G_{MT1}\) and \(G_{MT2}\) . Since \(G_{MT1}\) fluctuates from cycle- to- cycle owing to programming and reset voltages applied to its local back- gate terminal, i.e., \(N2\) , so does \(V_{N5}\) . In other words, the voltage divider translates conductance fluctuation into voltage fluctuation. Fig. 3h shows the histogram of \(V_{N5}\) , which, as expected, follows a random Gaussian distribution with mean, \(\mu_{VN5} = 0.37 \mathrm{V}\) and standard deviation, \(\sigma_{VN5} = 0.05 \mathrm{V}\) .  
+
+Next the Gaussian distribution is broadened by using an inverting amplifier constructed using \(MT3\) and \(MT4\) . Note that the local back- gate of \(MT3\) is shorted to its source at node, \(N_{6}\) . This ensures that \(MT3\) operates as a depletion mode (normally on) transistor or as a load resistor. Fig. 3i shows the output, \(V_{N6}\) , as a function of the input, \(V_{N5}\) . The slope of the curve is referred to as the gain of the amplifier, and higher the gain wider is the broadening of the Gaussian. We achieved a gain of
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3. 2D memtransistor based s-bit generator. a) Transfer characteristics of a representative 2D memtransistor, measured each time after the application of \(V_{\mathrm{P}} = -10\) V and \(V_{\mathrm{E}} = 10\) V each for \(\tau_{\mathrm{s}} = 100\) ms, for a total of 100 cycles. Distribution of b) post-programmed and c) post-erased conductance \((G_{\mathrm{MT}})\) measured using \(V_{BG} = 0\) V. d) Circuit diagram and e) corresponding optical image for the proposed s-bit generator consisting of six memtransistors (MT1, MT2, MT3, MT1, MT2, MT3). f) Voltage waveforms applied to the nodes, N1, N2, i.e., \(V_{N1}\) , \(V_{N2}\) . During each clock cycle \((\tau_{\mathrm{clk}})\) , \(V_{N1}\) toggles between 0 V, 0 V, and \(V_{DD} = 2\) V and \(V_{N2}\) toggles between \(V_{\mathrm{P}} = -7\) V, \(V_{\mathrm{E}} = 10\) V, and \(V_{\mathrm{R}} = 1\) V. Voltages applied to nodes, N3, and N4, i.e., \(V_{N3}\) , and \(V_{N4}\) are held constant at 1V and 0 V, respectively. g) Voltage readout at node, N5, i.e., \(V_{N5}\) . h) Distribution of \(V_{N5}\) over \(200\tau_{\mathrm{clk}}\) follows a random Gaussian distribution with mean, \(\mu_{VN5} = 0.37\) V and standard deviation, \(\sigma_{VN5} = 0.05\) V. i) Output, \(V_{N6}\) , of an inverting amplifier constructed using MT3 and MT4 as a function of the input, \(V_{N5}\) with a gain of \(\sim 8\) . j) \(V_{N6}\) corresponding to \(V_{N5}\) shown in (g). k) Distribution of \(V_{N6}\) follows a random Gaussian distribution with mean, \(\mu_{VN6} = 0.74\) V and an increased standard deviation of \(\sigma_{VN6} = 0.3\) V. l) Output, \(V_{N7}\) , of a thresholding inverter constructed using MT5 and MT6 as a function of the input, \(V_{N6}\) for different inversion threshold, \(V_{IT}\) . m) \(V_{N7}\) corresponding to \(V_{N6}\) shown in (i) for different \(V_{IT}\) . n) Probability of obtaining '1' in the bit stream (p_s) as a function of \(V_{IT}\) . </center>
+
+<--- Page Split --->
+
+\~8. The gain can be increased by cascading multiple amplifiers; however it adds area and energy overhead. Fig. 3j shows \(V_{N6}\) corresponding to \(V_{N5}\) obtained in Fig. 3g. Clearly, the histogram of \(V_{N6}\) shown in Fig. 3k exhibit a Gaussian distribution with mean, \(\mu_{V N6} = 0.74 \mathrm{V}\) and an increased standard deviation of \(\sigma_{V N6} = 0.3 \mathrm{V}\) .  
+
+Finally, to transform the analog fluctuations seen in \(V_{N6}\) into s- bits, a thresholding inverter with programmable inversion threshold, \(V_{\mathrm{IT}}\) , is constructed using \(M T5\) and \(M T6\) . Fig. 3l shows the output, \(V_{N7}\) , as a function of the input, \(V_{N6}\) for different \(V_{\mathrm{IT}}\) . Note that \(V_{\mathrm{IT}}\) is the magnitude of \(V_{N6}\) for which \(V_{N7}\) reaches \(V_{\mathrm{DD}} / 2\) , i.e. 1 V in the present case. The programmability of \(V_{\mathrm{IT}}\) is a critical feature that distinguishes 2D memtransistors based inverters from conventional CMOS- based inverters and allows us to seamlessly obtain the s- bits. Fig. 3m shows \(V_{N7}\) corresponding to \(V_{N6}\) obtained in Fig. 3j for different \(V_{\mathrm{IT}}\) and Fig. 3n shows the corresponding probability of obtaining '1' in the bit stream, i.e., \(p_{s}\) as a function of \(V_{\mathrm{IT}}\) . As expected, if \(V_{\mathrm{IT}}\) is too low, then almost all \(V_{N6}\) values translate into \(V_{N7} \approx 0 \mathrm{V}\) , which is reflected as near zero \(p_{s}\) . Similarly, if \(V_{\mathrm{IT}}\) is too high, then almost all \(V_{N6}\) values translate into \(V_{N7} \approx 2 \mathrm{V}\) leading to \(p_{s} = 1\) . Between these two extremes, \(p_{s}\) increases monotonically with \(V_{\mathrm{IT}}\) . This clearly shows that we are able to convert the cycle- to- cycle random conductance fluctuations in 2D memtransistor into s- bits with reconfigurable \(p_{s}\) that lie between [0,1] using the circuit based on 6 memtransistors. The average energy expenditure for s- bit generation \((E_{s - bit})\) was calculated using Eq. 3.  
+
+\[E_{s - bit} = \frac{1}{2} C_{G}\big[V_{\mathrm{P}}^{2} + V_{\mathrm{E}}^{2} + V_{D D}^{2}\big]; C_{G} = \frac{\epsilon_{0}\epsilon_{o x}W L}{t_{o x}} /t_{o x} \quad (3)\]  
+
+In Eq. 3, \(C_{G}\) is the gate capacitance, \(\epsilon_{0} = 8.85 \times 10^{- 12} \mathrm{F / m}\) is the vacuum permittivity, \(\epsilon_{ox} = 10\) , and \(t_{ox} = 50 \mathrm{nm}\) are, respectively, the relative permittivity and thickness of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) . We found that \(E_{s - bit} < 2 \mathrm{pJ / cycle}\) , which supports our claim on energy efficient s- bit generation. The active
+
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+
+footprint for the s- bit generator is \(\sim 30 \mu \mathrm{m}^2\) since each memtransistor has an active device area of \(\sim 5 \mu \mathrm{m}^2\) excluding the large contact pads used for probing. Since monolayer 2D materials offer aggressive dimensional scalability, it is possible to reduce the footprint of s- bit generators even further. Nevertheless the use of only 6 memtransistors is the key towards the realization of area and energy efficient s- bit generator circuit.  
+
+## 2D memtransistor based digital circuits and BN acceleration  
+
+As described earlier, stochastic multiplexers (MUXs) can be used for computing the marginal probability values at any BN node. Fig. 4a shows the circuit configuration of a \(2 \times 1 MUX\) , which consists of one inverter and three 2- input NAND gates. Fig. 4b show the optical image and corresponding circuit configuration of a 2- input NAND gate comprising of 3 memtransistors, \(MT1\) \(MT2\) , and \(MT3\) connected in series with \(MT1\) serving as the depletion load. The supply voltage, \(V_{DD} = 2 \mathrm{V}\) , is applied to the drain terminal of \(MT1\) at node \(N_{1}\) , whereas the source terminal of \(MT3\) , i.e., node \(N_{5}\) is kept grounded. Fig. 4c shows the input waveforms, \(V_{N3}\) and \(V_{N4}\) , which are applied to the local back- gate terminals of \(MT2\) and \(MT3\) at nodes \(N_{3}\) and \(N_{4}\) , respectively, and the corresponding output waveform, \(V_{N2}\) , which is obtained at node \(N_{2}\) . Clearly, the circuit operates as a NAND gate.  
+
+Fig. 4d- e, respectively, show the optical image and corresponding circuit configuration for hardware acceleration of a 2- node BN consisting of 3 s- bit generators and a \(2 \times 1 MUX\) with a total of 29 memtransistors. The \(V_{\mathrm{IT}}\) values for the s- bit generators for \(X_{1}\) and \(X_{2}\) can be pre- programmed using the CPT for the nodes \(A\) and \(B\) . Fig. 4f shows the representative stochastic bit- streams for the random variables \(A\) , \(X_{1}\) , and \(X_{2}\) with \(P(A) = 0.12\) , \(P(X_{1}) = P(B / A) = 0.26\) , and \(P(X_{2}) =\)
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4. Hardware acceleration of BN. a) Circuit schematic for hardware acceleration of BN using three s-bit generator and one \(2\times 1\) MUX. The MUX consists of one inverter and three 2-input NAND gates. b) Optical image and corresponding circuit configuration of a 2-input NAND gate comprising of 3 memtransistors, MT1 MT2, and MT3 connected in series with MT1 serving as the depletion load. c) Input waveforms, \(V_{N3}\) and \(V_{N4}\) , which are applied to the local back-gate terminals of MT2 and MT3 at nodes \(N_{3}\) and \(N_{4}\) , respectively, and the corresponding output waveform, \(V_{N2}\) , which is obtained at node \(N_{2}\) . d) Optical image and e) corresponding circuit configuration for hardware acceleration of a 2-node BN consisting of 3 s-bit generators and a \(2\times 1\) MUX with a total of 29 memtransistors. The \(V_{IT}\) values for the s-bit generators for \(X_{1}\) and \(X_{2}\) can be pre-programmed using the CPT for the nodes A and B. f) Representative stochastic bit-streams for the random variables A, \(X_{1}\) , and \(X_{2}\) with \(P(A) = 0.12\) , \(P(X_{1}) = P(B / A) = 0.26\) , and \(P(X_{2}) = P(B / A^{C}) = 0.36\) . g) Correlation coefficient (CC) values between A, \(X_{1}\) , and \(X_{2}\) confirm mutual independence of the s-bit generator modules. h) Stochastic bit-streams obtained at the output node, B. The measured and expected values for \(P(B)\) are 0.56 and 0.54. </center>  
+
+\(P(B / A^{C}) = 0.36\) . Note that accurate estimation of \(P(B)\) requires that the stochastic input variables to the MUX, i.e., \(A\) , \(X_{1}\) , \(X_{2}\) must be mutually independent. Fig. 4g shows the correlation coefficient (CC) between these three variables. The CC values were found to be close to zero, which confirm mutual independence of the s- bit generator modules. Fig. 4h shows the stochastic bit- streams
+
+<--- Page Split --->
+
+obtained at the output node, \(B\) . The measured and expected values for \(P(B)\) are 0.56 and 0.54. Extended Data Fig. 3 shows the results for three more sets of measurement. In all instances, we found that our 29 memtransistor module is able to accelerate a 2- node BN with relatively high accuracy. The average energy expenditure for the BN acceleration is miniscule \(\sim 1.2 \mathrm{nJ}\) , when 200 \(\tau_{clk}\) are used. Certainly, the energy expense can be reduced by reducing the length of the s- bit streams at the cost of reduced precision.  
+
+## Conclusion  
+
+In conclusion, we have exploited the cycle- to- cycle variability in the programmed conductance of 2D memtransistors and transcribed the same into s- bits with reconfigurable probability of obtaining '1' in the bit- stream using a circuit that comprises of only 6 memtransistors and by spending \(< 2 \mathrm{pJ}\) per clock- cycle. We subsequently combined the s- bit generator with 2D memtransistor based \(2 \times 1\) MUX to demonstrated hardware acceleration of BN. The BN architecture comprises of total 29 memtransistors and require \(\sim 1.2 \mathrm{nJ}\) energy for precise computation. Our demonstration of memtransistor based standalone in- memory compute fabric shows the potential for emerging 2D materials and devices.
+
+<--- Page Split --->
+
+## Methods  
+
+Fabrication of local back- gate islands: To define the back- gate island regions, the substrate 285 nm \(\mathrm{SiO_2}\) on \(\mathrm{p^{+ + }}\) - Si was spin coated with bilayer photoresist consisting of Lift- Off- Resist (LOR 5A) and Series Photoresist (SPR 3012) baked at \(185^{\circ}\mathrm{C}\) and \(95^{\circ}\mathrm{C}\) , respectively. The bilayer photoresist was then exposed to Heidelberg Maskless Aligner (MLA 150) to define the island and developed using MF CD26 microposit, followed by a de- ionized (DI) water rinse. The back gate electrode of \(20 / 50 \mathrm{nm} \mathrm{TiN / Pt}\) was deposited using reactive sputtering. The photoresist was removed using acetone and Photo Resist Stripper (PRS 3000) and cleaned using 2- propanol (IPA) and DI water. Atomic layer deposition (ALD) process was then implemented to grow \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) on the entire substrate including the island regions. To access the individual Pt back- gate electrodes etch patterns were defined using the same bilayer photoresist consisting of LOR 5A and SPR 3012. The bilayer photoresist was then exposed to MLA 150 and developed using MF CD26 microposit. \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) was subsequently dry etched using the \(\mathrm{BCI}_3\) chemistry at \(5^{\circ}\mathrm{C}\) for 20 seconds, which was repeated four times to minimize heating in the substrate. Next the photoresist was removed to give access to the individual Pt electrodes.  
+
+Large area monolayer \(\mathrm{MoS_2}\) film growth: Monolayer \(\mathrm{MoS_2}\) was deposited on epi- ready \(2^{\circ}\mathrm{c}\) - sapphire substrate by metalorganic chemical vapor deposition (MOCVD). An inductively heated graphite susceptor equipped with wafer rotation in a cold- wall horizontal reactor was used to achieve uniform monolayer deposition as previously described [31]. Molybdenum hexacarbonyl \(\mathrm{(Mo(CO)_6)}\) and hydrogen sulfide \(\mathrm{(H_2S)}\) were used as precursors. \(\mathrm{Mo(CO)_6}\) maintained at \(10^{\circ}\mathrm{C}\) and 650 Torr in a stainless- steel bubbler was used to deliver \(1.1 \times 10^{- 3} \mathrm{sccm}\) of the metal precursor for the growth, while 400 sccm of \(\mathrm{H_2S}\) was used for the process. \(\mathrm{MoS_2}\) deposition was carried out at
+
+<--- Page Split --->
+
+\(1000^{\circ}\mathrm{C}\) and 50 Torr in \(\mathrm{H}_{2}\) ambient, where monolayer growth was achieved in 18 min. The substrate was first heated to \(1000^{\circ}\mathrm{C}\) in \(\mathrm{H}_{2}\) and maintained for 10 min before the growth was initiated. After growth, the substrate was cooled in \(\mathrm{H}_{2}\mathrm{S}\) to \(300^{\circ}\mathrm{C}\) to inhibit decomposition of the \(\mathrm{MoS}_{2}\) films. More details can be found in our earlier work [26, 32, 33].  
+
+\(\mathrm{MoS}_{2}\) film transfer to local back- gate islands: To fabricate the 2D memtransistors, MOCVD grown monolayer \(\mathrm{MoS}_{2}\) film was transferred from the sapphire to \(\mathrm{SiO}_{2} / \mathrm{p}^{++}\) - Si substrate with local back- gate islands using PMMA (polymethyl- methacrylate) assisted wet transfer process. First, \(\mathrm{MoS}_{2}\) on sapphire substrate was spin coated with PMMA and then baked at \(180^{\circ}\mathrm{C}\) for \(90\mathrm{~s}\) . The corners of the spin- coated film were scratched using a razor blade and immersed inside 1 M NaOH solution kept at \(90^{\circ}\mathrm{C}\) . Capillary action causes the \(\mathrm{NaOH}\) to be drawn into the substrate/film interface, separating the PMMA/ \(\mathrm{MoS}_{2}\) film from the sapphire substrate. The separated film was rinsed multiple times inside a water bath and finally transferred onto the \(\mathrm{SiO}_{2} / \mathrm{p}^{++}\) - Si substrate with local back- gate islands and then baked at \(50^{\circ}\mathrm{C}\) and \(70^{\circ}\mathrm{C}\) for 10 min each to remove moisture and residual PMMA, ensuring a pristine interface.  
+
+Fabrication of 2D memtransistors: To define the channel regions for the memtransistors, the substrate was spin- coated with PMMA and baked at \(180^{\circ}\mathrm{C}\) for \(90\mathrm{~s}\) . The resist was then exposed to electron beam (e- beam) and developed using 1:1 mixture of 4- methyl- 2- pentanone (MIBK) and 2 propanol (IPA). The monolayer \(\mathrm{MoS}_{2}\) film was subsequently etched using sulfur hexafluoride (SF6) at \(5^{\circ}\mathrm{C}\) for \(30\mathrm{~s}\) . Next, the sample was rinsed in acetone and IPA to remove the e- beam resist. To define the source and drain contacts, sample is then spin coated with methyl methacrylate (MMA) followed by A3 PMMA. Then using e- beam lithography source and drain contacts are
+
+<--- Page Split --->
+
+patterned and developed by using 1:1 mixture of MIBK and IPA for 60s. 40 nm of Nickel (Ni) and 30 nm of Gold (Au) are deposited using e- beam evaporation. Finally, lift- off process is performed to remove the evaporated Ni/Au except from the source/drain patterns by immersing the sample in acetone for 30 min followed by IPA for another 30 mins. Each island contains one memtransistor to allow for individual gate control.  
+
+Monolithic Integration: To define the connections between the respective memtransistors the substrate was spin coated with MMA and PMMA, followed by the e- beam lithography and developing using 1:1 mixture of MIBK and IPA, and e- beam evaporation of 60 nm Au. Finally, the e- beam resist was rinsed away by lift- off process using acetone and IPA.  
+
+Electrical Characterization: Electrical characterization of the fabricated devices are performed using Lake Shore CRX- VF probe station under atmospheric condition using a Keysight B1500A parameter analyzer.  
+
+Data Availability: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.  
+
+Code Availability: The codes used for plotting the data are available from the corresponding authors on reasonable request.
+
+<--- Page Split --->
+
+## AUTHOR INFORMATION  
+
+## Corresponding Author  
+
+sud70@psu.edu, das.sapt@gmail.com  
+
+## Author Contributions  
+
+S.D conceived the idea and designed the experiments. Y.Z., H.R., and T. F. S. fabricated the memtransistors. Y.Z., H.R., and S.D performed the measurements, analyzed the data, discussed the results, and agreed on their implications. N. T. grew MOCVD MoS₂. All authors contributed to the preparation of the manuscript.  
+
+## Competing Interest  
+
+The authors declare no competing interests  
+
+## Acknowledgement  
+
+The work was supported by Army Research Office (ARO) through Contract Number W911NF1920338. Authors also acknowledge the materials support from the National Science Foundation (NSF) through the Pennsylvania State University 2D Crystal Consortium- Materials Innovation Platform (2DCCMIP) under NSF cooperative agreement DMR- 1539916.
+
+<--- Page Split --->
+
+## Reference  
+
+1. Smithson, S.C., et al., Efficient CMOS invertible logic using stochastic computing. IEEE Transactions on Circuits and Systems I: Regular Papers, 2019. 66(6): p. 2263-2274.  
+2. Ardakani, A., et al., VLSI implementation of deep neural network using integral stochastic computing. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2017. 25(10): p. 2688-2699.  
+3. Knag, P., W. Lu, and Z. Zhang, A native stochastic computing architecture enabled by memristors. IEEE Transactions on Nanotechnology, 2014. 13(2): p. 283-293.  
+4. Gaba, S., et al. Memristive devices for stochastic computing. in 2014 IEEE International Symposium on Circuits and Systems (ISCAS). 2014. IEEE.  
+5. Gaba, S., et al., Stochastic memristive devices for computing and neuromorphic applications. Nanoscale, 2013. 5(13): p. 5872-5878.  
+6. Venkatesan, R., et al. Spintastic: Spin-based stochastic logic for energy-efficient computing. in 2015 Design, Automation & Test in Europe Conference & Exhibition (DATE). 2015. IEEE.  
+7. Finocchio, G., et al., The promise of spintronics for unconventional computing. arXiv preprint arXiv:1910.07176, 2019.  
+8. Hu, J., et al., Spin-hall-effect-based stochastic number generator for parallel stochastic computing. IEEE Transactions on Electron Devices, 2019. 66(8): p. 3620-3627.  
+9. Yang, K., et al. 16.3 A 23Mb/s 23pJ/b fully synthesized true-random-number generator in 28nm and 65nm CMOS. in 2014 IEEE International Solid-State Circuits Conference Digest of Technical Papers (ISSCC). 2014. IEEE.  
+10. Brown, G.E. and R.J.F. Smith, Conspecific skin extracts elicit antipredator responses in juvenile rainbow trout (Oncorhynchus mykiss). Canadian Journal of Zoology, 1997. 75(11): p. 1916-1922.  
+11. Puga, J.L., M. Krzywinski, and N. Altman, Bayesian networks. Nature Methods, 2015. 12(9): p. 799-800.  
+12. Alaghi, A. and J.P. Hayes, Survey of stochastic computing. ACM Transactions on Embedded computing systems (TECS), 2013. 12(2s): p. 1-19.  
+13. Gaines, B.R. Stochastic computing. in Proceedings of the April 18-20, 1967, spring joint computer conference. 1967.  
+14. Poppelbaum, W., C. Afuso, and J. Esch. Stochastic computing elements and systems. in Proceedings of the November 14-16, 1967, fall joint computer conference. 1967.  
+15. Weijia, Z., G.W. Ling, and Y.K. Seng. PCMOS-based Hardware Implementation of Bayesian Network. in 2007 IEEE Conference on Electron Devices and Solid-State Circuits. 2007.  
+16. Cai, R., et al., VIBNN: Hardware Acceleration of Bayesian Neural Networks, in Proceedings of the Twenty-Third International Conference on Architectural Support for Programming Languages and Operating Systems. 2018, Association for Computing Machinery: Williamsburg, VA, USA. p. 476-488.  
+17. Kulesza, Z. and W. Tylman. Implementation Of Bayesian Network In FPGA Circuit. in Proceedings of the International Conference Mixed Design of Integrated Circuits and System, 2006. MIXDES 2006. 2006.  
+18. Zermani, S., et al. FPGA implementation of Bayesian network inference for an embedded diagnosis. in 2015 IEEE Conference on Prognostics and Health Management (PHM). 2015.  
+19. Debashis, P., et al., Hardware implementation of Bayesian network building blocks with stochastic spintronic devices. Scientific Reports, 2020. 10(1).  
+20. Faria, R., et al., Hardware Design for Autonomous Bayesian Networks. Frontiers in Computational Neuroscience, 2021. 15(14).
+
+<--- Page Split --->
+
+21. Shim, Y., et al., Stochastic Spin-Orbit Torque Devices as Elements for Bayesian Inference. Scientific Reports, 2017. 7(1): p. 14101.  
+22. Faria, R., K.Y. Camsari, and S. Datta, Implementing Bayesian networks with embedded stochastic MRAM. AIP Advances, 2018. 8(4): p. 045101.  
+23. Jaiswal, A., X. Fong, and K. Roy, Comprehensive scaling analysis of current induced switching in magnetic memories based on in-plane and perpendicular anisotropies. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2016. 6(2): p. 120-133.  
+24. Sengupta, A., et al., Magnetic tunnel junction mimics stochastic cortical spiking neurons. Scientific reports, 2016. 6(1): p. 1-8.  
+25. 2DCC. 2d-crystal-consortium. Available from: https://www.mri.psu.edu/2d-crystal-consortium/user-facilities/thin-films/list-thin-film-samples-available.  
+26. Sebastian, A., et al., Benchmarking monolayer MoS2 and WS2 field-effect transistors. Nature Communications, 2021. 12(1): p. 693.  
+27. Li, H., et al., From bulk to monolayer MoS2: evolution of Raman scattering. Advanced Functional Materials, 2012. 22(7): p. 1385-1390.  
+28. Das, S., et al., High performance multilayer MoS2 transistors with scandium contacts. Nano letters, 2013. 13(1): p. 100-105.  
+29. Schulman, D.S., A.J. Arnold, and S. Das, Contact engineering for 2D materials and devices. Chemical Society Reviews, 2018. 47(9): p. 3037-3058.  
+30. Chuang, S., et al., MoS2 p-type transistors and diodes enabled by high work function MoO x contacts. Nano letters, 2014. 14(3): p. 1337-1342.  
+31. Xuan, Y., et al., Multi-scale modeling of gas-phase reactions in metal-organic chemical vapor deposition growth of WSe2. Journal of Crystal Growth, 2019. 527.  
+32. Jayachandran, D., et al., A low-power biomimetic collision detector based on an in-memory molybdenum disulfide photodetector. Nature Electronics, 2020. 3(10): p. 646-655.  
+33. Dodda, A., et al., Stochastic resonance in MoS2 photodetector. Nature Communications, 2020. 11(1): p. 4406.
+
+<--- Page Split --->
+
+## Extended Data Figure 1  
+
+![](images/Figure_3.jpg)
+  
+
+Extended Data Figure 1. a) A BN where the child node, B is connected to n parent nodes, \(A_{1}\) , \(A_{2}\) , ..., \(A_{n}\) . b) A BN where the parent node, A is connected to m children, \(B_{1}\) , \(B_{2}\) , ..., \(B_{m}\) . c) Hardware acceleration of BN shown in (a) can be achieved by using n s- bit generators to obtain the \(A_{i}\) 's, another \(N = 2^{n}\) s- bit generators to obtain the CPT, and one \(N \times 1\) MUX with n select lines d) Hardware acceleration of BN shown in (b) can be achieved by using 1 s- bit generator to obtain A, another \(2m\) s- bit generators to obtain the m CPTs, and \(m \geq 1\) MUXs.  
+
+## Extended Data Figure 2  
+
+![PLACEHOLDER_23_1]
+  
+
+Extended Data Figure 2. a) Raman spectra obtained for a representative 2D memtransistor shows two characteristics monolayer MoS₂ peaks at 383 cm⁻¹ and 404 cm⁻¹ corresponding to the in- plane \(E_{2g}^{1}\) and out- of- plane \(A_{1g}\) modes, respectively, with the expected peak separation of \(\sim 20\) cm⁻¹. b) Photoluminescence (PL) spectra for a representative 2D memtransistor shows peak at 1.83 eV corresponding to the direct bandgap of monolayer MoS₂.
+
+<--- Page Split --->
+![PLACEHOLDER_24_0]
+
+<center>Extended Data Figure 3. Three examples of representative stochastic bit-streams for the random variables \(A\) , \(X_{1}\) , and \(X_{2}\) , correlation coefficient (CC) values between \(A\) , \(X_{1}\) , and \(X_{2}\) , and stochastic bit-streams obtained at the output node, \(B\) for the 2-node BN. The measured and expected values for \(P(B)\) are very similar confirming high precision hardware acceleration of BN. </center>
+
+<--- Page Split --->

preprint/preprint__601f685f5ff3d3c7aeccd00337f1e979e1cb7d35e2fc47084b324e63a27dfe8f/preprint__601f685f5ff3d3c7aeccd00337f1e979e1cb7d35e2fc47084b324e63a27dfe8f_det.mmd

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+<|ref|>title<|/ref|><|det|>[[44, 106, 930, 175]]<|/det|>
+# Hardware Acceleration of Bayesian Network based on Two-dimensional Memtransistors  
+
+<|ref|>text<|/ref|><|det|>[[44, 196, 315, 238]]<|/det|>
+Yikai Zheng  Pennsylvania State University  
+
+<|ref|>text<|/ref|><|det|>[[44, 243, 315, 284]]<|/det|>
+Harikrishnan Ravichandran  Pennsylvania State University  
+
+<|ref|>text<|/ref|><|det|>[[44, 290, 315, 331]]<|/det|>
+Thomas Schranghamer  Pennsylvania State University  
+
+<|ref|>text<|/ref|><|det|>[[44, 336, 315, 377]]<|/det|>
+Nicholas Trainor  Pennsylvania State University  
+
+<|ref|>text<|/ref|><|det|>[[44, 383, 672, 444]]<|/det|>
+Joan Redwing  Saptarshi Das ( \(\boxed{\text {sud70@psu.edu}}\) )  Pennsylvania State University  https://orcid.org/0000- 0002- 0188- 945X  
+
+<|ref|>text<|/ref|><|det|>[[44, 485, 102, 503]]<|/det|>
+Article  
+
+<|ref|>text<|/ref|><|det|>[[44, 523, 137, 541]]<|/det|>
+Keywords:  
+
+<|ref|>text<|/ref|><|det|>[[44, 561, 323, 580]]<|/det|>
+Posted Date: February 1st, 2022  
+
+<|ref|>text<|/ref|><|det|>[[44, 599, 475, 619]]<|/det|>
+DOI: https://doi.org/10.21203/rs.3.rs- 1196768/v1  
+
+<|ref|>text<|/ref|><|det|>[[44, 636, 910, 679]]<|/det|>
+License: © \(\circledast\) This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License  
+
+<|ref|>text<|/ref|><|det|>[[42, 715, 916, 758]]<|/det|>
+Version of Record: A version of this preprint was published at Nature Communications on September 23rd, 2022. See the published version at https://doi.org/10.1038/s41467- 022- 33053-x.
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[116, 90, 881, 115]]<|/det|>
+# Hardware Acceleration of Bayesian Network based on Two-dimensional  
+
+<|ref|>title<|/ref|><|det|>[[414, 138, 581, 160]]<|/det|>
+# Memtransistors  
+
+<|ref|>text<|/ref|><|det|>[[137, 180, 863, 202]]<|/det|>
+Yikai Zheng \(^{1}\) , Harikrishnan Ravichandran \(^{1}\) , Thomas F Schranghamer \(^{1}\) , Nicholas Trainor \(^{2,3}\) ,  
+
+<|ref|>text<|/ref|><|det|>[[319, 216, 676, 236]]<|/det|>
+Joan M Redwing \(^{2,3}\) , and Saptarshi Das \(^{2,3,4,5,*}\)  
+
+<|ref|>text<|/ref|><|det|>[[113, 251, 884, 410]]<|/det|>
+\(^{1}\) Engineering Science and Mechanics, Penn State University, University Park, PA 16802, USA \(^{2}\) Materials Science and Engineering, Penn State University, University Park, PA 16802, USA \(^{3}\) Materials Research Institute, Penn State University, University Park, PA 16802, USA \(^{4}\) Electrical Engineering and Computer Science, Penn State University, University Park, PA 16802, USA  
+
+<|ref|>text<|/ref|><|det|>[[113, 471, 886, 877]]<|/det|>
+Abstract: Long before Bayes proposed his landmark theorem on the probability of an event, based on prior knowledge of other events, natural intelligence has adopted Bayesian inference as a tool to ensure survival for almost all species. The fact that living beings must make critical decision for finding food, avoiding predators, and locating mates, based on information gathered by their sensory organs with limited sensitivity and under noisy surroundings, emphasizes the importance of probabilistic computing for evolutionary success. While the anatomy of neural hardware that accomplishes such task is far from being known, it is clear that stochastic computing is a fundamental aspect of natural intelligence, and Bayesian networks (BNs) are powerful mathematical constructs for the same. Interestingly, BNs also find widespread application in many real- world probabilistic problems including diagnostics, forecasting, computer vision, etc. While the concept of BN is well known, there are very limited hardware realizations of BN. CMOS [1, 2] based BNs
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 214]]<|/det|>
+require massive hardware resources (thousands of transistors), whereas, memristor [3- 5] and spintronics [6- 8] based BNs necessitate hybrid design with CMOS peripherals limiting the area and energy efficiency [9]. Here, we circumvent these challenges by introducing a compact and low- power BN architecture embedded in memory based on 2D memtransistors.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 258, 224, 276]]<|/det|>
+## Introduction  
+
+<|ref|>text<|/ref|><|det|>[[112, 290, 886, 767]]<|/det|>
+Animals gather information from their surroundings with the help of their sensory organs and process the same using their brain to make decisions, which aid them to locate mates, find preys, and escape from predators. Better decision making leads to better survival, which naturally translates into the evolutionary success for the species. However, it is often very difficult for animals to gather accurate information either due to the limitations of their sensory organ or because of the information being obscured by noisy environment. For example, visual cues are unreliable source of information for freshwater fishes like the rainbow trout since these can be both misleading and manipulated by a predator. In contrast chemical cues released into the water from the epidermis of an injured fish are more reliable indicators of predatory events [10]. The decision to invoke an alarm responses, i.e. less swimming and more time to resume foraging, therefore, depends on how the brain of the rainbow trout processes the visual and the chemical cues based on their relative probability of success from prior experiences. While the neural basis of such computation is relatively unknown, the mathematical construct can be represented using a Bayesian network (BN) with theoretical foundation in Bayes' theorem.  
+
+<|ref|>text<|/ref|><|det|>[[114, 814, 884, 904]]<|/det|>
+BN is a probabilistic graphic network used to estimate and infer the probability of events, where events are interdependent on each other [11]. Fig. 1a shows the basic building block of a BN comprising of a parent node, \(A\) , a child node, \(B\) , and an edge connecting the two. Each node
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 356]]<|/det|>
+represents an event, e.g., presence of chemical cue or \(A\) and presence of a predator or \(B\) , and the connection represents how two events are mutually dependent. The dependence is provided in a conditional probability table (CPT), which contains the conditional probability or likelihood values, i.e. \(P(B / A)\) and \(P(B / A^c)\) , where \(A^c\) is the complement of the event \(A\) . In the present example, these represents the likelihood of presence of a predator given that a chemical cue is present \((A)\) or absent \((A^c)\) , respectively. Knowing the probability of occurrence for the event \(A\) , i.e., \(P(A)\) , the marginal probability of occurrence of the event \(B\) , i.e. \(P(B)\) can be evaluated using Bayes' theorem following Eq. 1.  
+
+<|ref|>equation<|/ref|><|det|>[[112, 368, 880, 425]]<|/det|>
+\[\begin{array}{l}{P(B) = P(B / A)P(A) + P(B / A^c)P(A^c) = P(B / A)P(A) + P(B / A^c)[1 - P(A)]}\\ {P(A) + P(A^c) = 1} \end{array} \quad (1a)\]  
+
+<|ref|>text<|/ref|><|det|>[[112, 439, 886, 673]]<|/det|>
+In a generic BN, a child node can have multiple parent nodes, and a parent node can have multiple children. For example, Extended Data Fig. 1a shows a BN where the child node, \(B\) is connected to \(n\) parent nodes, \(A_{1}, A_{2}, \ldots , A_{n}\) . Note that the CPT in this instance contains \(N = 2^n\) entries, which are the conditional probability or likelihood for the occurrence of the event \(B\) for all possible combinations of occurrence of the events \(A_{i}\) 's, \(i = 1,2, \ldots n\) . Similarly, Extended Data Fig. 1b shows a BN where the parent node, \(A\) is connected to \(m\) children, \(B_{1}, B_{2}, \ldots , B_{m}\) . In this case, there are \(m\) CPTs each with \(N = 2\) entries.  
+
+<|ref|>text<|/ref|><|det|>[[112, 723, 886, 886]]<|/det|>
+Note that the probability estimation for a child node with \(n\) parent require \(n2^n\) multiplications, \(n2^{n - 1}\) subtractions, and \(2^n - 1\) additions or a total of \(2^{n - 1}(3n + 2) - 1\) arithmetic operations. Needless to mention that the number of arithmetic operations increases as the number of nodes in the BN increases. This makes hardware acceleration of BN using conventional silicon complementary metal oxide semiconductor (CMOS) technology resources extensive since
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 884, 319]]<|/det|>
+arithmetic operations require circuits consisting of hundreds of transistors, which have large footprints and consume significant amount of energy. Furthermore, the von Neumann bottleneck necessitates storing of the CPT in the memory, which is physically separated from the arithmetic core and, therefore, requires frequent data shuttling between the two increasing the energy burden. In contrast, even the tiniest brains with very limited number of neurons can perform such apparently complex computational tasks with miniscule energy expenditure. The success of biological brains in implementing BN lie in the inherently stochastic nature of neural computation.  
+
+<|ref|>image<|/ref|><|det|>[[205, 356, 710, 777]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[129, 782, 872, 893]]<|/det|>
+<center>Figure 1. Bayesian networks (BNs). a) Schematic of basic building block of a BN comprising of a parent node, A, a child node, B, and an edge connecting the two. Each node represents an event, and the connection represents how two events are mutually dependent. The dependence is provided in a conditional probability table (CPT), which contains the conditional probability or likelihood values, i.e., \(P(B / A)\) and \(P(B / A^c)\) , where \(A^c\) is the complement of the event. Knowing the probability of occurrence for the event A, i.e., \(P(A)\) , the marginal probability of occurrence of the event B, i.e., \(P(B)\) can be evaluated using Bayes' theorem. b) Acceleration of 2-node BN in (a) using three stochastic bit (s-bit) generators and one \(2 \times 1\) multiplexer (MUX) circuit. c) Examples of BN architecture that represent real-life situations from ecology to forecasting and drug discovery highlighting its usefulness in decision making. </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 884, 392]]<|/det|>
+Drawing inspiration from biology, stochastic computing (SC) has been explored for the hardware acceleration of BN [12]. The key difference is that unlike classical computing where information in presented in the form of binary values (1's and 0's), SC encodes information using stochastic bits (s- bits) that are interpreted as probabilities that fall in the interval [0,1]. For instance, the bitstream, \(S = [10010100]\) encodes the value \(P(S) = 3 / 8\) , i.e., the probability of finding '1' in the bit- stream, \(S\) . An attractive feature of SC is that arithmetic operations to be performed using simple logic gates [13, 14]. For example, the 2- node BN in Fig. 1a can be realized using a multiplexer (MUX) circuit as shown in Fig. 1b. The output, \(B\) , of a MUX with two input variables, \(X_{1}, X_{2}\) , and a select line, \(A\) , is given by Eq. 2.  
+
+<|ref|>equation<|/ref|><|det|>[[115, 404, 255, 425]]<|/det|>
+\[B = A X_{1} + A^{c}X_{2}\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 439, 883, 531]]<|/det|>
+Instead of being digital variables, if \(X_{1}, X_{2}\) , and \(A\) represent stochastic variables with \(P(X_{1}), P(X_{2})\) , and \(P(A)\) being the probability of obtaining '1' in their respective bit- streams, then \(B\) also transforms into a random variable whose probability is given by Eq. 3.  
+
+<|ref|>equation<|/ref|><|det|>[[115, 544, 400, 566]]<|/det|>
+\[P(B) = P(A)P(X_{1}) + P(A^{c})P(X_{2})\]  
+
+<|ref|>text<|/ref|><|det|>[[112, 580, 884, 886]]<|/det|>
+Note that, if \(P(X_{1}) = P(B / A)\) and \(P(X_{2}) = P(B / A^{C})\) , then Eq. 3 transforms into Eq. 1. Therefore, hardware acceleration of a child node with single parent can be accomplished by using 3 s- bit generators and a \(2 \times 1\) MUX. Interestingly, the MUX architecture can be scaled to accelerate any BN. For example, hardware acceleration of BN in Extended Data Fig. 1a can be achieved by using \(n\) s- bit generators to obtain the \(A_{i}\) 's, another \(N = 2^{n}\) s- bit generators to obtain the CPT, and one \(N \times 1\) MUX with \(n\) select lines as shown in Extended Data Fig. 1c. Similarly, Extended Data Fig. 1d shows the hardware architecture for the BN in Extended Data Fig. 1b consisting of 1 s- bit generator to obtain \(A\) , another \(2m\) s- bit generators to obtain the \(m\) CPTs, and \(m\) \(2 \times 1\) MUXs.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 81, 886, 716]]<|/det|>
+Note that BN architecture can be used to represent many real- life situations as shown in Fig. 1c. For example, in the case of the rainbow trout, the events \(A_{1}\) and \(A_{2}\) represent the presence of visual and chemical cues, respectively, which are independent of each other, the event \(B\) represents the presence of a predator, and the events \(C_{1}\) and \(C_{2}\) represent the decision taken by the rainbow trout to stop swimming and stop foraging, respectively, which are also independent of each other but depend on \(B\) . Similarly, in forecasting, the events \(A_{1}\) and \(A_{2}\) represent the probability of a day being cloudy and windy, respectively, the event \(B\) represent the probability of rain, and the events \(C_{1}\) and \(C_{2}\) may represent the decision to purchase an umbrella or drink coffee, respectively. Finally, a third example is derived from genetics and drug discovery, where the events \(A_{1}\) and \(A_{2}\) may represent the probability of expressing gene 1 and gene 2 when intervening with a specific drug, the event \(B\) represents the activation of a critical signaling pathway, and the events \(C_{1}\) and \(C_{2}\) represent production of specific hormones or antibodies. The above discussion exemplifies the usefulness of BNs in depicting causal relationship using acyclic graphs, which can subsequently be used to predict outcomes based on prior knowledge and likelihood. For example, to predict the relative effectiveness between drug- 1 and drug- 2 that influence expression for gene 1 and gene 2, respectively, the only experiments that one needs to do is to obtain respective prior, i.e., \(P(A_{1})\) and \(P(A_{2})\) . BN can then be used to obtain marginal likelihoods, i.e., \(P(C_{1})\) and/or \(P(C_{2})\) to assess the relative effectiveness of the two drugs.  
+
+<|ref|>text<|/ref|><|det|>[[113, 757, 884, 883]]<|/det|>
+The fundamental computing primitive for BN is a s- bit generator, which allows control of the output probability of obtaining ‘1’ in a given bit- stream. So far, probabilistic CMOS [15], field- programmable gate arrays (FPGA) [16- 18], memristors [3, 4], and spintronic devices [19- 22] have been successfully used for BN acceleration. However, CMOS and FPGA based BN architecture
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 87, 886, 424]]<|/det|>
+require hundreds of transistors to generate s- bits due, which limits its area and energy efficiency [9]. In contrast, memristors offer inherent stochasticity in their switching dynamics, which can be exploited to obtain random bits. However, memristor- based BN architectures heavily rely on CMOS peripherals to translate random bits into s- bits and for subsequent logic operations using those s- bits. Recently, spintronic device such as magnetic random access memory (MRAM) [23] and magnetic tunnel junctions (MTJs) [24] have shown potential for BN acceleration since s- bits can be obtained by controlling the probability of spin- flip through externally driven current. However, temperature and supply voltage fluctuations can impact the spin- flip probability, which necessitates additional CMOS- based peripheral circuits to remove the bit- bias. In addition, spin- based devices still require CMOS- based logic circuits for BN acceleration.  
+
+<|ref|>text<|/ref|><|det|>[[112, 471, 886, 842]]<|/det|>
+In this work, we demonstrate hardware acceleration of BN using a monolithic memtransistor technology based on two- dimensional (2D) semiconductors such as monolayer \(\mathrm{MoS_2}\) . Memtransistors are three terminal devices with the gate terminal allowing non- volatile and analog programming of the conductance states, which can be readout by applying source- to- drain bias. Our main contributions in this work are 1) the design of an area and energy efficient s- bit generator circuit comprising of six memtransistors to achieve tunable probability of obtaining '1' in the bitstream in the range [0,1] and 2) integration of s- bit generators with 2D memtransistor based \(2 \times 1\) MUX that consists of three NAND gates and one as NOT gate for BN acceleration. In brief, we exploit the inherent stochasticity in the charge trapping and detrapping processes in the gate dielectric of the memtransistor as the source of randomness. Our in- memory compute approach based on 3- terminal 2D memtransistors not only overcomes the von Neumann limitations of
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[114, 88, 883, 144]]<|/det|>
+conventional digital CMOS, but also eliminates the need for peripherals, which is inescapable for emerging memristor- and spin- based 2- terminal stochastic devices for BN acceleration.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 194, 580, 213]]<|/det|>
+## Fabrication and characterization of 2D memtransistors  
+
+<|ref|>text<|/ref|><|det|>[[112, 226, 886, 703]]<|/det|>
+Fig. 2a- b, respectively, show the 3D schematic and optical image of a representative 2D memtransistor based on monolayer \(\mathrm{MoS}_2\) , which are locally back- gated using a stack comprising of atomic layer deposition (ALD) grown \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) on sputter deposited \(40 / 30 \mathrm{nm} \mathrm{Pt / TiN}\) . All back- gate islands were placed on a commercially purchased \(\mathrm{SiO}_2 / \mathrm{p}^{++}\) - Si substrate. As we will discuss later, the analog, non- volatile, and stochastic programming capability offered by the \(\mathrm{Al}_2\mathrm{O}_3 / \mathrm{Pt / TiN}\) gate stack is central to our BN architecture. The monolayer \(\mathrm{MoS}_2\) used in this work was grown using metal organic chemical vapor deposition (MOCVD) technique on sapphire substrate at \(950^{\circ}\mathrm{C}\) [25, 26]. Use of epitaxial substrate and elevated growth temperature ensure uniform and high quality 2D film, which is critical for the successful demonstration of our BN architecture that involves many 2D memtransistors. The monolayer \(\mathrm{MoS}_2\) film was transferred from the growth substrate to the \(\mathrm{SiO}_2 / \mathrm{p}^{++}\) - Si substrate with predefined islands of \(\mathrm{Al}_2\mathrm{O}_3 / \mathrm{Pt / TiN}\) for subsequent 2D memtransistor fabrication. Details on monolayer \(\mathrm{MoS}_2\) synthesis, film transfer, and fabrication of the local back- gate gate islands, \(\mathrm{MoS}_2\) memtransistors, and BN architecture can be found in the Methods section.  
+
+<|ref|>text<|/ref|><|det|>[[113, 750, 884, 876]]<|/det|>
+The film quality and device performance were assessed using optical and electrical measurements. Raman spectra (Extended Data Fig. 2a) obtained for a representative 2D memtransistor shows two characteristics monolayer \(\mathrm{MoS}_2\) peaks at \(383 \mathrm{cm}^{- 1}\) and \(404 \mathrm{cm}^{- 1}\) corresponding to the in- plane \(E_{2g}^1\) and out- of- plane \(A_{1g}\) modes, respectively, with the expected peak separation of \(\sim 20 \mathrm{cm}^{- 1}\) for
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[135, 112, 875, 384]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[128, 388, 870, 496]]<|/det|>
+<center>Figure 2. 2D memtransistors. a) 3D schematic and b) optical image of a representative 2D memtransistor based on monolayer MoS2, which are locally back-gated using a stack comprising of atomic layer deposition (ALD) grown \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) on sputter deposited \(40 / 30 \mathrm{nm} \mathrm{Pt} / \mathrm{TiN}\) . All back-gate islands were placed on a commercially purchased \(\mathrm{SiO}_2 / \mathrm{p}^{++}\) -Si substrate. c) Transfer characteristics, i.e., source-to-drain current \((I_{\mathrm{DS}})\) versus local back-gate voltage \((V_{\mathrm{BG}})\) measured using source-to-drain bias, \(V_{\mathrm{DS}} = 1 \mathrm{V}\) , in linear and logarithmic scale for a representative MoS2 memtransistor with channel length, \(L = 1 \mu \mathrm{m}\) , and channel width, \(W = 5 \mu \mathrm{m}\) . d) Output characteristics, i.e., \(I_{\mathrm{DS}}\) versus \(V_{\mathrm{DS}}\) for different \(V_{\mathrm{BG}}\) for the same MoS2 memtransistor. e) Post-programmed and f) post-erased transfer characteristics of a representative 2D memtransistor. g) Non-volatile retention for 4 representative post-programmed and post-erased conductance states \((G_{\mathrm{MT}})\) for 100 seconds. </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 523, 885, 900]]<|/det|>
+monolayer MoS2 [27]. Similarly, the photoluminescence (PL) spectra (Extended Data Fig. 2b) shows peak at 1.83 eV corresponding to the direct bandgap of monolayer MoS2. The transfer characteristics, i.e. source to drain current \((I_{\mathrm{DS}})\) versus local back- gate voltage \((V_{\mathrm{BG}})\) measured using source- to- drain bias, \(V_{\mathrm{DS}} = 1 \mathrm{V}\) , in linear and logarithmic scale for a representative MoS2 memtransistor with channel length, \(L = 1 \mu \mathrm{m}\) , and channel width, \(W = 5 \mu \mathrm{m}\) is shown in Fig. 2c. As expected, n- type transport is observed in MoS2, which is attributed to the pinning of the metal Fermi level near the conduction band [28- 30]. Nevertheless, MoS2 memtransistor exhibits excellent electrostatic gate control with current on/off ratio \((r_{\mathrm{ON / OFF}}) > 10^5\) , subthreshold slope \((SS) < 400 \mathrm{mV / decade}\) averaged over 3 orders of magnitude change in \(I_{\mathrm{DS}}\) , minimal gate hysteresis when measured in air, and low gate leakage current. The threshold voltage \((V_{\mathrm{TH}})\) was found to be \(\sim 2.2 \mathrm{V}\) extracted at iso- current of \(10 \mathrm{nA / \mu m}\) and the electron field effect mobility \((\mu_{\mathrm{FE}})\) extracted
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 885, 251]]<|/det|>
+from the peak trans- conductance was found to be \(6 \mathrm{cm}^{2} / \mathrm{V} \cdot \mathrm{s}\) . Fig. 2d shows the output characteristics, i.e. \(I_{\mathrm{DS}}\) versus \(V_{\mathrm{DS}}\) for different \(V_{\mathrm{BG}}\) for the same \(\mathrm{MoS}_{2}\) memtransistor. The on current \((I_{\mathrm{ON}})\) reached as high as \(\sim 15 \mu \mathrm{A} / \mu \mathrm{m}\) for an inversion carrier density of \(\sim 1 \times 10^{12} / \mathrm{cm}^{2}\) at \(V_{\mathrm{DS}} = 5 \mathrm{V}\) . These results indicate reasonably good quality monolayer film growth using MOCVD, relatively damage- free film transfer, and clean memtransistor fabrication processes.  
+
+<|ref|>text<|/ref|><|det|>[[112, 300, 885, 672]]<|/det|>
+The post- programmed and post- erased transfer characteristics of a representative 2D memtransistor after being subjected to negative "Write" \((V_{P})\) and positive "Erase" \((V_{E})\) voltage pulses of different amplitudes applied to the local back- gate electrode, each for a duration of \(\tau_{P / E} = 100 \mathrm{ms}\) is shown in Fig. 2e. The negative and positive shift in the respective transfer characteristics can be ascribed to electron trapping and detrapping at and near the \(\mathrm{MoS}_{2} / \mathrm{Al}_{2} \mathrm{O}_{3}\) interface, respectively. The trapping and de- trapping processes were found to be non- volatile as shown in Fig. 2f for 4 representative post- programmed and post- erased conductance states \((G_{MT})\) , respectively, for 100 seconds. We also examined long- term memory retention for the 2D memtransistors and found that states remain indistinguishable even after 3 hrs. Memory retention is important to store the CPT and the memtransistors demonstrate adequate memory performance for the acceleration of BN using SC.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 722, 765, 743]]<|/det|>
+## Programming stochasticity in 2D memtransistor and design of s-bit generator  
+
+<|ref|>text<|/ref|><|det|>[[113, 756, 884, 882]]<|/det|>
+Design of hardware for high- quality random bit generation is central to the acceleration of BN. Here, we exploit the cycle- to- cycle variation in the post- programmed and post- erased conductance states \((G_{MT})\) of 2D memtransistor as the source of true randomness. Fig. 3a shows the transfer characteristics of a representative \(\mathrm{MoS}_{2}\) memtransistor, which is measured each time after applying
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 85, 886, 682]]<|/det|>
+\(V_{P} = - 10 \mathrm{V}\) and \(V_{E} = 10 \mathrm{V}\) for \(\tau_{s} = 100 \mathrm{ms}\) , for a total of 100 cycles and Fig. 3b- c, respectively, show the histogram of post- programmed and post- erased \(G_{MT}\) extracted at \(V_{BG} = 0 \mathrm{V}\) . Clearly, \(G_{MT}\) follow Gaussian random distributions. To translate the stochastic conductance fluctuation into s- bits, we deploy a circuit consisting of six memtransistors ( \(MT1\) , \(MT2\) , \(MT3\) , \(MT4\) , \(MT5\) , and \(MT6\) ) as shown using the circuit diagram and the corresponding optical image in Fig. 3d- e, respectively. The voltage waveforms applied to the nodes, \(N1\) , \(N2\) , i.e., \(V_{N1}\) , \(V_{N2}\) , respectively, are shown in Fig. 3f. Note that during each clock cycle \((\tau_{clk})\) , \(V_{N1}\) switches between 0 V, 0 V, and 2 V and \(V_{N2}\) switches between \(V_{P} = - 7 \mathrm{V}\) , \(V_{E} = 10 \mathrm{V}\) , and \(V_{R} = 1 \mathrm{V}\) . Voltages applied to nodes, \(N3\) , and \(N4\) , i.e., \(V_{N3}\) , and \(V_{N4}\) are held constant at 1V and 0 V, respectively. This allows programming and reset of \(MT1\) during each \(\tau_{clk}\) . The voltage readout at node, \(N5\) , i.e., \(V_{N5}\) is shown in Fig. 3g, which exhibits stochastic fluctuation. Note that the series connection of memtransistors, \(MT1\) and \(MT2\) represents a voltage divider circuit, and hence \(V_{N5}\) is determined by their respective conductance values, i.e., \(G_{MT1}\) and \(G_{MT2}\) . Since \(G_{MT1}\) fluctuates from cycle- to- cycle owing to programming and reset voltages applied to its local back- gate terminal, i.e., \(N2\) , so does \(V_{N5}\) . In other words, the voltage divider translates conductance fluctuation into voltage fluctuation. Fig. 3h shows the histogram of \(V_{N5}\) , which, as expected, follows a random Gaussian distribution with mean, \(\mu_{VN5} = 0.37 \mathrm{V}\) and standard deviation, \(\sigma_{VN5} = 0.05 \mathrm{V}\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 725, 886, 889]]<|/det|>
+Next the Gaussian distribution is broadened by using an inverting amplifier constructed using \(MT3\) and \(MT4\) . Note that the local back- gate of \(MT3\) is shorted to its source at node, \(N_{6}\) . This ensures that \(MT3\) operates as a depletion mode (normally on) transistor or as a load resistor. Fig. 3i shows the output, \(V_{N6}\) , as a function of the input, \(V_{N5}\) . The slope of the curve is referred to as the gain of the amplifier, and higher the gain wider is the broadening of the Gaussian. We achieved a gain of
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[140, 92, 857, 707]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[125, 708, 866, 883]]<|/det|>
+<center>Figure 3. 2D memtransistor based s-bit generator. a) Transfer characteristics of a representative 2D memtransistor, measured each time after the application of \(V_{\mathrm{P}} = -10\) V and \(V_{\mathrm{E}} = 10\) V each for \(\tau_{\mathrm{s}} = 100\) ms, for a total of 100 cycles. Distribution of b) post-programmed and c) post-erased conductance \((G_{\mathrm{MT}})\) measured using \(V_{BG} = 0\) V. d) Circuit diagram and e) corresponding optical image for the proposed s-bit generator consisting of six memtransistors (MT1, MT2, MT3, MT1, MT2, MT3). f) Voltage waveforms applied to the nodes, N1, N2, i.e., \(V_{N1}\) , \(V_{N2}\) . During each clock cycle \((\tau_{\mathrm{clk}})\) , \(V_{N1}\) toggles between 0 V, 0 V, and \(V_{DD} = 2\) V and \(V_{N2}\) toggles between \(V_{\mathrm{P}} = -7\) V, \(V_{\mathrm{E}} = 10\) V, and \(V_{\mathrm{R}} = 1\) V. Voltages applied to nodes, N3, and N4, i.e., \(V_{N3}\) , and \(V_{N4}\) are held constant at 1V and 0 V, respectively. g) Voltage readout at node, N5, i.e., \(V_{N5}\) . h) Distribution of \(V_{N5}\) over \(200\tau_{\mathrm{clk}}\) follows a random Gaussian distribution with mean, \(\mu_{VN5} = 0.37\) V and standard deviation, \(\sigma_{VN5} = 0.05\) V. i) Output, \(V_{N6}\) , of an inverting amplifier constructed using MT3 and MT4 as a function of the input, \(V_{N5}\) with a gain of \(\sim 8\) . j) \(V_{N6}\) corresponding to \(V_{N5}\) shown in (g). k) Distribution of \(V_{N6}\) follows a random Gaussian distribution with mean, \(\mu_{VN6} = 0.74\) V and an increased standard deviation of \(\sigma_{VN6} = 0.3\) V. l) Output, \(V_{N7}\) , of a thresholding inverter constructed using MT5 and MT6 as a function of the input, \(V_{N6}\) for different inversion threshold, \(V_{IT}\) . m) \(V_{N7}\) corresponding to \(V_{N6}\) shown in (i) for different \(V_{IT}\) . n) Probability of obtaining '1' in the bit stream (p_s) as a function of \(V_{IT}\) . </center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 886, 216]]<|/det|>
+\~8. The gain can be increased by cascading multiple amplifiers; however it adds area and energy overhead. Fig. 3j shows \(V_{N6}\) corresponding to \(V_{N5}\) obtained in Fig. 3g. Clearly, the histogram of \(V_{N6}\) shown in Fig. 3k exhibit a Gaussian distribution with mean, \(\mu_{V N6} = 0.74 \mathrm{V}\) and an increased standard deviation of \(\sigma_{V N6} = 0.3 \mathrm{V}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 264, 886, 750]]<|/det|>
+Finally, to transform the analog fluctuations seen in \(V_{N6}\) into s- bits, a thresholding inverter with programmable inversion threshold, \(V_{\mathrm{IT}}\) , is constructed using \(M T5\) and \(M T6\) . Fig. 3l shows the output, \(V_{N7}\) , as a function of the input, \(V_{N6}\) for different \(V_{\mathrm{IT}}\) . Note that \(V_{\mathrm{IT}}\) is the magnitude of \(V_{N6}\) for which \(V_{N7}\) reaches \(V_{\mathrm{DD}} / 2\) , i.e. 1 V in the present case. The programmability of \(V_{\mathrm{IT}}\) is a critical feature that distinguishes 2D memtransistors based inverters from conventional CMOS- based inverters and allows us to seamlessly obtain the s- bits. Fig. 3m shows \(V_{N7}\) corresponding to \(V_{N6}\) obtained in Fig. 3j for different \(V_{\mathrm{IT}}\) and Fig. 3n shows the corresponding probability of obtaining '1' in the bit stream, i.e., \(p_{s}\) as a function of \(V_{\mathrm{IT}}\) . As expected, if \(V_{\mathrm{IT}}\) is too low, then almost all \(V_{N6}\) values translate into \(V_{N7} \approx 0 \mathrm{V}\) , which is reflected as near zero \(p_{s}\) . Similarly, if \(V_{\mathrm{IT}}\) is too high, then almost all \(V_{N6}\) values translate into \(V_{N7} \approx 2 \mathrm{V}\) leading to \(p_{s} = 1\) . Between these two extremes, \(p_{s}\) increases monotonically with \(V_{\mathrm{IT}}\) . This clearly shows that we are able to convert the cycle- to- cycle random conductance fluctuations in 2D memtransistor into s- bits with reconfigurable \(p_{s}\) that lie between [0,1] using the circuit based on 6 memtransistors. The average energy expenditure for s- bit generation \((E_{s - bit})\) was calculated using Eq. 3.  
+
+<|ref|>equation<|/ref|><|det|>[[113, 760, 880, 794]]<|/det|>
+\[E_{s - bit} = \frac{1}{2} C_{G}\big[V_{\mathrm{P}}^{2} + V_{\mathrm{E}}^{2} + V_{D D}^{2}\big]; C_{G} = \frac{\epsilon_{0}\epsilon_{o x}W L}{t_{o x}} /t_{o x} \quad (3)\]  
+
+<|ref|>text<|/ref|><|det|>[[113, 806, 884, 899]]<|/det|>
+In Eq. 3, \(C_{G}\) is the gate capacitance, \(\epsilon_{0} = 8.85 \times 10^{- 12} \mathrm{F / m}\) is the vacuum permittivity, \(\epsilon_{ox} = 10\) , and \(t_{ox} = 50 \mathrm{nm}\) are, respectively, the relative permittivity and thickness of \(\mathrm{Al}_{2} \mathrm{O}_{3}\) . We found that \(E_{s - bit} < 2 \mathrm{pJ / cycle}\) , which supports our claim on energy efficient s- bit generation. The active
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 885, 249]]<|/det|>
+footprint for the s- bit generator is \(\sim 30 \mu \mathrm{m}^2\) since each memtransistor has an active device area of \(\sim 5 \mu \mathrm{m}^2\) excluding the large contact pads used for probing. Since monolayer 2D materials offer aggressive dimensional scalability, it is possible to reduce the footprint of s- bit generators even further. Nevertheless the use of only 6 memtransistors is the key towards the realization of area and energy efficient s- bit generator circuit.  
+
+<|ref|>sub_title<|/ref|><|det|>[[114, 298, 622, 318]]<|/det|>
+## 2D memtransistor based digital circuits and BN acceleration  
+
+<|ref|>text<|/ref|><|det|>[[112, 331, 886, 673]]<|/det|>
+As described earlier, stochastic multiplexers (MUXs) can be used for computing the marginal probability values at any BN node. Fig. 4a shows the circuit configuration of a \(2 \times 1 MUX\) , which consists of one inverter and three 2- input NAND gates. Fig. 4b show the optical image and corresponding circuit configuration of a 2- input NAND gate comprising of 3 memtransistors, \(MT1\) \(MT2\) , and \(MT3\) connected in series with \(MT1\) serving as the depletion load. The supply voltage, \(V_{DD} = 2 \mathrm{V}\) , is applied to the drain terminal of \(MT1\) at node \(N_{1}\) , whereas the source terminal of \(MT3\) , i.e., node \(N_{5}\) is kept grounded. Fig. 4c shows the input waveforms, \(V_{N3}\) and \(V_{N4}\) , which are applied to the local back- gate terminals of \(MT2\) and \(MT3\) at nodes \(N_{3}\) and \(N_{4}\) , respectively, and the corresponding output waveform, \(V_{N2}\) , which is obtained at node \(N_{2}\) . Clearly, the circuit operates as a NAND gate.  
+
+<|ref|>text<|/ref|><|det|>[[113, 722, 885, 886]]<|/det|>
+Fig. 4d- e, respectively, show the optical image and corresponding circuit configuration for hardware acceleration of a 2- node BN consisting of 3 s- bit generators and a \(2 \times 1 MUX\) with a total of 29 memtransistors. The \(V_{\mathrm{IT}}\) values for the s- bit generators for \(X_{1}\) and \(X_{2}\) can be pre- programmed using the CPT for the nodes \(A\) and \(B\) . Fig. 4f shows the representative stochastic bit- streams for the random variables \(A\) , \(X_{1}\) , and \(X_{2}\) with \(P(A) = 0.12\) , \(P(X_{1}) = P(B / A) = 0.26\) , and \(P(X_{2}) =\)
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[123, 95, 860, 580]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[125, 584, 872, 732]]<|/det|>
+<center>Figure 4. Hardware acceleration of BN. a) Circuit schematic for hardware acceleration of BN using three s-bit generator and one \(2\times 1\) MUX. The MUX consists of one inverter and three 2-input NAND gates. b) Optical image and corresponding circuit configuration of a 2-input NAND gate comprising of 3 memtransistors, MT1 MT2, and MT3 connected in series with MT1 serving as the depletion load. c) Input waveforms, \(V_{N3}\) and \(V_{N4}\) , which are applied to the local back-gate terminals of MT2 and MT3 at nodes \(N_{3}\) and \(N_{4}\) , respectively, and the corresponding output waveform, \(V_{N2}\) , which is obtained at node \(N_{2}\) . d) Optical image and e) corresponding circuit configuration for hardware acceleration of a 2-node BN consisting of 3 s-bit generators and a \(2\times 1\) MUX with a total of 29 memtransistors. The \(V_{IT}\) values for the s-bit generators for \(X_{1}\) and \(X_{2}\) can be pre-programmed using the CPT for the nodes A and B. f) Representative stochastic bit-streams for the random variables A, \(X_{1}\) , and \(X_{2}\) with \(P(A) = 0.12\) , \(P(X_{1}) = P(B / A) = 0.26\) , and \(P(X_{2}) = P(B / A^{C}) = 0.36\) . g) Correlation coefficient (CC) values between A, \(X_{1}\) , and \(X_{2}\) confirm mutual independence of the s-bit generator modules. h) Stochastic bit-streams obtained at the output node, B. The measured and expected values for \(P(B)\) are 0.56 and 0.54. </center>  
+
+<|ref|>text<|/ref|><|det|>[[113, 763, 884, 891]]<|/det|>
+\(P(B / A^{C}) = 0.36\) . Note that accurate estimation of \(P(B)\) requires that the stochastic input variables to the MUX, i.e., \(A\) , \(X_{1}\) , \(X_{2}\) must be mutually independent. Fig. 4g shows the correlation coefficient (CC) between these three variables. The CC values were found to be close to zero, which confirm mutual independence of the s- bit generator modules. Fig. 4h shows the stochastic bit- streams
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 284]]<|/det|>
+obtained at the output node, \(B\) . The measured and expected values for \(P(B)\) are 0.56 and 0.54. Extended Data Fig. 3 shows the results for three more sets of measurement. In all instances, we found that our 29 memtransistor module is able to accelerate a 2- node BN with relatively high accuracy. The average energy expenditure for the BN acceleration is miniscule \(\sim 1.2 \mathrm{nJ}\) , when 200 \(\tau_{clk}\) are used. Certainly, the energy expense can be reduced by reducing the length of the s- bit streams at the cost of reduced precision.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 335, 211, 352]]<|/det|>
+## Conclusion  
+
+<|ref|>text<|/ref|><|det|>[[113, 368, 886, 633]]<|/det|>
+In conclusion, we have exploited the cycle- to- cycle variability in the programmed conductance of 2D memtransistors and transcribed the same into s- bits with reconfigurable probability of obtaining '1' in the bit- stream using a circuit that comprises of only 6 memtransistors and by spending \(< 2 \mathrm{pJ}\) per clock- cycle. We subsequently combined the s- bit generator with 2D memtransistor based \(2 \times 1\) MUX to demonstrated hardware acceleration of BN. The BN architecture comprises of total 29 memtransistors and require \(\sim 1.2 \mathrm{nJ}\) energy for precise computation. Our demonstration of memtransistor based standalone in- memory compute fabric shows the potential for emerging 2D materials and devices.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 191, 108]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[112, 120, 886, 600]]<|/det|>
+Fabrication of local back- gate islands: To define the back- gate island regions, the substrate 285 nm \(\mathrm{SiO_2}\) on \(\mathrm{p^{+ + }}\) - Si was spin coated with bilayer photoresist consisting of Lift- Off- Resist (LOR 5A) and Series Photoresist (SPR 3012) baked at \(185^{\circ}\mathrm{C}\) and \(95^{\circ}\mathrm{C}\) , respectively. The bilayer photoresist was then exposed to Heidelberg Maskless Aligner (MLA 150) to define the island and developed using MF CD26 microposit, followed by a de- ionized (DI) water rinse. The back gate electrode of \(20 / 50 \mathrm{nm} \mathrm{TiN / Pt}\) was deposited using reactive sputtering. The photoresist was removed using acetone and Photo Resist Stripper (PRS 3000) and cleaned using 2- propanol (IPA) and DI water. Atomic layer deposition (ALD) process was then implemented to grow \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) on the entire substrate including the island regions. To access the individual Pt back- gate electrodes etch patterns were defined using the same bilayer photoresist consisting of LOR 5A and SPR 3012. The bilayer photoresist was then exposed to MLA 150 and developed using MF CD26 microposit. \(50 \mathrm{nm} \mathrm{Al}_2\mathrm{O}_3\) was subsequently dry etched using the \(\mathrm{BCI}_3\) chemistry at \(5^{\circ}\mathrm{C}\) for 20 seconds, which was repeated four times to minimize heating in the substrate. Next the photoresist was removed to give access to the individual Pt electrodes.  
+
+<|ref|>text<|/ref|><|det|>[[112, 646, 886, 877]]<|/det|>
+Large area monolayer \(\mathrm{MoS_2}\) film growth: Monolayer \(\mathrm{MoS_2}\) was deposited on epi- ready \(2^{\circ}\mathrm{c}\) - sapphire substrate by metalorganic chemical vapor deposition (MOCVD). An inductively heated graphite susceptor equipped with wafer rotation in a cold- wall horizontal reactor was used to achieve uniform monolayer deposition as previously described [31]. Molybdenum hexacarbonyl \(\mathrm{(Mo(CO)_6)}\) and hydrogen sulfide \(\mathrm{(H_2S)}\) were used as precursors. \(\mathrm{Mo(CO)_6}\) maintained at \(10^{\circ}\mathrm{C}\) and 650 Torr in a stainless- steel bubbler was used to deliver \(1.1 \times 10^{- 3} \mathrm{sccm}\) of the metal precursor for the growth, while 400 sccm of \(\mathrm{H_2S}\) was used for the process. \(\mathrm{MoS_2}\) deposition was carried out at
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 884, 221]]<|/det|>
+\(1000^{\circ}\mathrm{C}\) and 50 Torr in \(\mathrm{H}_{2}\) ambient, where monolayer growth was achieved in 18 min. The substrate was first heated to \(1000^{\circ}\mathrm{C}\) in \(\mathrm{H}_{2}\) and maintained for 10 min before the growth was initiated. After growth, the substrate was cooled in \(\mathrm{H}_{2}\mathrm{S}\) to \(300^{\circ}\mathrm{C}\) to inhibit decomposition of the \(\mathrm{MoS}_{2}\) films. More details can be found in our earlier work [26, 32, 33].  
+
+<|ref|>text<|/ref|><|det|>[[112, 269, 886, 604]]<|/det|>
+\(\mathrm{MoS}_{2}\) film transfer to local back- gate islands: To fabricate the 2D memtransistors, MOCVD grown monolayer \(\mathrm{MoS}_{2}\) film was transferred from the sapphire to \(\mathrm{SiO}_{2} / \mathrm{p}^{++}\) - Si substrate with local back- gate islands using PMMA (polymethyl- methacrylate) assisted wet transfer process. First, \(\mathrm{MoS}_{2}\) on sapphire substrate was spin coated with PMMA and then baked at \(180^{\circ}\mathrm{C}\) for \(90\mathrm{~s}\) . The corners of the spin- coated film were scratched using a razor blade and immersed inside 1 M NaOH solution kept at \(90^{\circ}\mathrm{C}\) . Capillary action causes the \(\mathrm{NaOH}\) to be drawn into the substrate/film interface, separating the PMMA/ \(\mathrm{MoS}_{2}\) film from the sapphire substrate. The separated film was rinsed multiple times inside a water bath and finally transferred onto the \(\mathrm{SiO}_{2} / \mathrm{p}^{++}\) - Si substrate with local back- gate islands and then baked at \(50^{\circ}\mathrm{C}\) and \(70^{\circ}\mathrm{C}\) for 10 min each to remove moisture and residual PMMA, ensuring a pristine interface.  
+
+<|ref|>text<|/ref|><|det|>[[112, 652, 886, 885]]<|/det|>
+Fabrication of 2D memtransistors: To define the channel regions for the memtransistors, the substrate was spin- coated with PMMA and baked at \(180^{\circ}\mathrm{C}\) for \(90\mathrm{~s}\) . The resist was then exposed to electron beam (e- beam) and developed using 1:1 mixture of 4- methyl- 2- pentanone (MIBK) and 2 propanol (IPA). The monolayer \(\mathrm{MoS}_{2}\) film was subsequently etched using sulfur hexafluoride (SF6) at \(5^{\circ}\mathrm{C}\) for \(30\mathrm{~s}\) . Next, the sample was rinsed in acetone and IPA to remove the e- beam resist. To define the source and drain contacts, sample is then spin coated with methyl methacrylate (MMA) followed by A3 PMMA. Then using e- beam lithography source and drain contacts are
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 87, 884, 249]]<|/det|>
+patterned and developed by using 1:1 mixture of MIBK and IPA for 60s. 40 nm of Nickel (Ni) and 30 nm of Gold (Au) are deposited using e- beam evaporation. Finally, lift- off process is performed to remove the evaporated Ni/Au except from the source/drain patterns by immersing the sample in acetone for 30 min followed by IPA for another 30 mins. Each island contains one memtransistor to allow for individual gate control.  
+
+<|ref|>text<|/ref|><|det|>[[113, 298, 884, 423]]<|/det|>
+Monolithic Integration: To define the connections between the respective memtransistors the substrate was spin coated with MMA and PMMA, followed by the e- beam lithography and developing using 1:1 mixture of MIBK and IPA, and e- beam evaporation of 60 nm Au. Finally, the e- beam resist was rinsed away by lift- off process using acetone and IPA.  
+
+<|ref|>text<|/ref|><|det|>[[113, 472, 884, 562]]<|/det|>
+Electrical Characterization: Electrical characterization of the fabricated devices are performed using Lake Shore CRX- VF probe station under atmospheric condition using a Keysight B1500A parameter analyzer.  
+
+<|ref|>text<|/ref|><|det|>[[113, 611, 883, 667]]<|/det|>
+Data Availability: The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.  
+
+<|ref|>text<|/ref|><|det|>[[113, 716, 883, 771]]<|/det|>
+Code Availability: The codes used for plotting the data are available from the corresponding authors on reasonable request.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 355, 108]]<|/det|>
+## AUTHOR INFORMATION  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 119, 310, 137]]<|/det|>
+## Corresponding Author  
+
+<|ref|>text<|/ref|><|det|>[[115, 154, 417, 172]]<|/det|>
+sud70@psu.edu, das.sapt@gmail.com  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 223, 301, 241]]<|/det|>
+## Author Contributions  
+
+<|ref|>text<|/ref|><|det|>[[113, 256, 884, 383]]<|/det|>
+S.D conceived the idea and designed the experiments. Y.Z., H.R., and T. F. S. fabricated the memtransistors. Y.Z., H.R., and S.D performed the measurements, analyzed the data, discussed the results, and agreed on their implications. N. T. grew MOCVD MoS₂. All authors contributed to the preparation of the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 426, 281, 445]]<|/det|>
+## Competing Interest  
+
+<|ref|>text<|/ref|><|det|>[[115, 461, 456, 480]]<|/det|>
+The authors declare no competing interests  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 530, 273, 548]]<|/det|>
+## Acknowledgement  
+
+<|ref|>text<|/ref|><|det|>[[113, 563, 884, 688]]<|/det|>
+The work was supported by Army Research Office (ARO) through Contract Number W911NF1920338. Authors also acknowledge the materials support from the National Science Foundation (NSF) through the Pennsylvania State University 2D Crystal Consortium- Materials Innovation Platform (2DCCMIP) under NSF cooperative agreement DMR- 1539916.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 202, 107]]<|/det|>
+## Reference  
+
+<|ref|>text<|/ref|><|det|>[[110, 120, 880, 890]]<|/det|>
+1. Smithson, S.C., et al., Efficient CMOS invertible logic using stochastic computing. IEEE Transactions on Circuits and Systems I: Regular Papers, 2019. 66(6): p. 2263-2274.  
+2. Ardakani, A., et al., VLSI implementation of deep neural network using integral stochastic computing. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 2017. 25(10): p. 2688-2699.  
+3. Knag, P., W. Lu, and Z. Zhang, A native stochastic computing architecture enabled by memristors. IEEE Transactions on Nanotechnology, 2014. 13(2): p. 283-293.  
+4. Gaba, S., et al. Memristive devices for stochastic computing. in 2014 IEEE International Symposium on Circuits and Systems (ISCAS). 2014. IEEE.  
+5. Gaba, S., et al., Stochastic memristive devices for computing and neuromorphic applications. Nanoscale, 2013. 5(13): p. 5872-5878.  
+6. Venkatesan, R., et al. Spintastic: Spin-based stochastic logic for energy-efficient computing. in 2015 Design, Automation & Test in Europe Conference & Exhibition (DATE). 2015. IEEE.  
+7. Finocchio, G., et al., The promise of spintronics for unconventional computing. arXiv preprint arXiv:1910.07176, 2019.  
+8. Hu, J., et al., Spin-hall-effect-based stochastic number generator for parallel stochastic computing. IEEE Transactions on Electron Devices, 2019. 66(8): p. 3620-3627.  
+9. Yang, K., et al. 16.3 A 23Mb/s 23pJ/b fully synthesized true-random-number generator in 28nm and 65nm CMOS. in 2014 IEEE International Solid-State Circuits Conference Digest of Technical Papers (ISSCC). 2014. IEEE.  
+10. Brown, G.E. and R.J.F. Smith, Conspecific skin extracts elicit antipredator responses in juvenile rainbow trout (Oncorhynchus mykiss). Canadian Journal of Zoology, 1997. 75(11): p. 1916-1922.  
+11. Puga, J.L., M. Krzywinski, and N. Altman, Bayesian networks. Nature Methods, 2015. 12(9): p. 799-800.  
+12. Alaghi, A. and J.P. Hayes, Survey of stochastic computing. ACM Transactions on Embedded computing systems (TECS), 2013. 12(2s): p. 1-19.  
+13. Gaines, B.R. Stochastic computing. in Proceedings of the April 18-20, 1967, spring joint computer conference. 1967.  
+14. Poppelbaum, W., C. Afuso, and J. Esch. Stochastic computing elements and systems. in Proceedings of the November 14-16, 1967, fall joint computer conference. 1967.  
+15. Weijia, Z., G.W. Ling, and Y.K. Seng. PCMOS-based Hardware Implementation of Bayesian Network. in 2007 IEEE Conference on Electron Devices and Solid-State Circuits. 2007.  
+16. Cai, R., et al., VIBNN: Hardware Acceleration of Bayesian Neural Networks, in Proceedings of the Twenty-Third International Conference on Architectural Support for Programming Languages and Operating Systems. 2018, Association for Computing Machinery: Williamsburg, VA, USA. p. 476-488.  
+17. Kulesza, Z. and W. Tylman. Implementation Of Bayesian Network In FPGA Circuit. in Proceedings of the International Conference Mixed Design of Integrated Circuits and System, 2006. MIXDES 2006. 2006.  
+18. Zermani, S., et al. FPGA implementation of Bayesian network inference for an embedded diagnosis. in 2015 IEEE Conference on Prognostics and Health Management (PHM). 2015.  
+19. Debashis, P., et al., Hardware implementation of Bayesian network building blocks with stochastic spintronic devices. Scientific Reports, 2020. 10(1).  
+20. Faria, R., et al., Hardware Design for Autonomous Bayesian Networks. Frontiers in Computational Neuroscience, 2021. 15(14).
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 90, 875, 551]]<|/det|>
+21. Shim, Y., et al., Stochastic Spin-Orbit Torque Devices as Elements for Bayesian Inference. Scientific Reports, 2017. 7(1): p. 14101.  
+22. Faria, R., K.Y. Camsari, and S. Datta, Implementing Bayesian networks with embedded stochastic MRAM. AIP Advances, 2018. 8(4): p. 045101.  
+23. Jaiswal, A., X. Fong, and K. Roy, Comprehensive scaling analysis of current induced switching in magnetic memories based on in-plane and perpendicular anisotropies. IEEE Journal on Emerging and Selected Topics in Circuits and Systems, 2016. 6(2): p. 120-133.  
+24. Sengupta, A., et al., Magnetic tunnel junction mimics stochastic cortical spiking neurons. Scientific reports, 2016. 6(1): p. 1-8.  
+25. 2DCC. 2d-crystal-consortium. Available from: https://www.mri.psu.edu/2d-crystal-consortium/user-facilities/thin-films/list-thin-film-samples-available.  
+26. Sebastian, A., et al., Benchmarking monolayer MoS2 and WS2 field-effect transistors. Nature Communications, 2021. 12(1): p. 693.  
+27. Li, H., et al., From bulk to monolayer MoS2: evolution of Raman scattering. Advanced Functional Materials, 2012. 22(7): p. 1385-1390.  
+28. Das, S., et al., High performance multilayer MoS2 transistors with scandium contacts. Nano letters, 2013. 13(1): p. 100-105.  
+29. Schulman, D.S., A.J. Arnold, and S. Das, Contact engineering for 2D materials and devices. Chemical Society Reviews, 2018. 47(9): p. 3037-3058.  
+30. Chuang, S., et al., MoS2 p-type transistors and diodes enabled by high work function MoO x contacts. Nano letters, 2014. 14(3): p. 1337-1342.  
+31. Xuan, Y., et al., Multi-scale modeling of gas-phase reactions in metal-organic chemical vapor deposition growth of WSe2. Journal of Crystal Growth, 2019. 527.  
+32. Jayachandran, D., et al., A low-power biomimetic collision detector based on an in-memory molybdenum disulfide photodetector. Nature Electronics, 2020. 3(10): p. 646-655.  
+33. Dodda, A., et al., Stochastic resonance in MoS2 photodetector. Nature Communications, 2020. 11(1): p. 4406.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[115, 90, 316, 108]]<|/det|>
+## Extended Data Figure 1  
+
+<|ref|>image<|/ref|><|det|>[[213, 130, 784, 442]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[126, 455, 867, 525]]<|/det|>
+Extended Data Figure 1. a) A BN where the child node, B is connected to n parent nodes, \(A_{1}\) , \(A_{2}\) , ..., \(A_{n}\) . b) A BN where the parent node, A is connected to m children, \(B_{1}\) , \(B_{2}\) , ..., \(B_{m}\) . c) Hardware acceleration of BN shown in (a) can be achieved by using n s- bit generators to obtain the \(A_{i}\) 's, another \(N = 2^{n}\) s- bit generators to obtain the CPT, and one \(N \times 1\) MUX with n select lines d) Hardware acceleration of BN shown in (b) can be achieved by using 1 s- bit generator to obtain A, another \(2m\) s- bit generators to obtain the m CPTs, and \(m \geq 1\) MUXs.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 572, 317, 590]]<|/det|>
+## Extended Data Figure 2  
+
+<|ref|>image<|/ref|><|det|>[[273, 603, 688, 777]]<|/det|>  
+
+<|ref|>text<|/ref|><|det|>[[130, 787, 870, 844]]<|/det|>
+Extended Data Figure 2. a) Raman spectra obtained for a representative 2D memtransistor shows two characteristics monolayer MoS₂ peaks at 383 cm⁻¹ and 404 cm⁻¹ corresponding to the in- plane \(E_{2g}^{1}\) and out- of- plane \(A_{1g}\) modes, respectively, with the expected peak separation of \(\sim 20\) cm⁻¹. b) Photoluminescence (PL) spectra for a representative 2D memtransistor shows peak at 1.83 eV corresponding to the direct bandgap of monolayer MoS₂.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 117, 875, 417]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[130, 424, 872, 479]]<|/det|>
+<center>Extended Data Figure 3. Three examples of representative stochastic bit-streams for the random variables \(A\) , \(X_{1}\) , and \(X_{2}\) , correlation coefficient (CC) values between \(A\) , \(X_{1}\) , and \(X_{2}\) , and stochastic bit-streams obtained at the output node, \(B\) for the 2-node BN. The measured and expected values for \(P(B)\) are very similar confirming high precision hardware acceleration of BN. </center>
+
+<--- Page Split --->

preprint/preprint__6031ed77ce1fb77f9ba9a18b15b24ca6cab721ccdb50048c438e03a2f459bc7b/images_list.json

@@ -0,0 +1,107 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Overview of the kinase active and inactive conformations and sequence features that distinguish TKs (Tyr Kinases) from STKs (Ser/Thr Kinases). (top) Illustrations of the active and inactive conformation of the activation loop for a representative TK, INSR. The active conformation is characterized by three main structural motifs – the N-terminal anchor, RD-pocket, and C-terminal anchor. In the inactive conformation, the C-terminal anchor of TKs remains intact while the rest of the activation loop is “folded up”, with the DFG+10 residue Y154 mimicking the binding mode of Tyr substrates. (bottom) Sequence logo visualization of key motifs in our MSA of kinase catalytic domains, where the vertical axes represent the raw residue frequency for STKs (blue) and TKs (orange) in our MSA, calculated separately. The residue numbering in this MSA is displayed on the horizontal axis. Only key motifs are displayed for clarity. The conserved triads “HRD”, “DFG”, and “APE” were used as reference points for a more general numbering scheme: for example, DFG+10 refers to residue 154 in our alignment (written as 154DFG+10 in the main text) and is located ten residues C-terminal from the DFG motif, and the Gly of DFG is located at position 144 in our MSA. Sequence logos were plotted using Logomaker<sup>40</sup>.",
+    "footnote": [],
+    "bbox": [
+      [
+        45,
+        100,
+        950,
+        610
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Choosing kinase targets (top) to analyze differences in the conformational landscapes of TKs and STKs. CDKs are STKs belonging to the “CMGC” group<sup>8</sup>, which are distantly related to TKs. BRAF, an STK from the “Tyrosine Kinase-Like” (TKL) group, is more closely related to TKs. INSR is a typical receptor TK, with active and inactive conformations that are representative of both cytoplasmic and receptor TKs. Icons are displayed to the left to mark the divergence of kinase-containing taxa (from top to bottom – H. sapiens<sup>8</sup> and porifera<sup>41</sup> (animals), choanoflagellates<sup>10</sup>, archaea and bacteria<sup>3</sup>). The Potentials of Mean Force (PMFs) shown on the right are artistic illustrations to help visualize the free-energy landscapes of TKs and TKs and STKs described previously<sup>15</sup> – while the barrier heights are unknown, the relative depths of the two basins at the end-states are accurately depicted. (bottom) The Potts DFG-out penalties of 90 human TKs (receptor and non-receptor families) and 58 STKs (41 TKL kinases and 21 CDKs) were estimated by threading over structural ensembles of the active and inactive (DFG-out) conformations (see Methods), showing a bias for human TKs (orange) towards inactive relative to STKs (blue).",
+    "footnote": [],
+    "bbox": [
+      [
+        241,
+        94,
+        748,
+        520
+      ]
+    ],
+    "page_idx": 10
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Potts statistical energy \\(\\Delta \\Delta T\\) s for the effects of mutations are consistent with corresponding \\(\\Delta \\Delta G_{reorg}\\) from FEP. (A) Results of scanning double and single mutations in the Potts model, plotted as a histogram of raw mutant \\(\\Delta T\\) s \\((\\Delta T_{mut} = \\Delta \\Delta T + \\Delta T_{wt})\\) for \\(>10^{4}\\) mutations from each kinase (see Methods). Mutations chosen for FEP simulations are marked with triangles and scored with vertical lines. (see Table S3 for a full list of mutations chosen for FEP). (B) Thermodynamic cycle (left) which we used to calculate each of the \\(54\\Delta \\Delta G\\) s in A. The vertical legs represent the alchemical transformations performed in FEP simulations in the active basin A and the inactive basin B, while the horizontal legs represent the physical free energy of reorganization between the two basins for wildtype (top) and mutant (bottom). (C) Plot of \\(\\Delta \\Delta T\\) calculated from the Potts model vs \\(\\Delta \\Delta G_{reorg}\\) for 54 mutations calculated from 108 FEP simulations in the active and inactive conformations (see Methods). \\(\\Delta \\Delta G_{reorg}\\) and \\(\\Delta \\Delta T\\) share a sign convention; positive values indicate a shift in conformational stability towards the active conformation, and negative values indicate a shift towards the inactive conformation.",
+    "footnote": [],
+    "bbox": [
+      [
+        80,
+        181,
+        880,
+        666
+      ]
+    ],
+    "page_idx": 12
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Mutating STK residues to those found in TKs destabilizes the active conformation relative to inactive. (A) Top: surface representation of wildtype CDK6 (PDB: 1XO2 chain B) in the active conformation (see Methods), with the N-terminal anchor highlighted. Peptides from TK (light green) and STK (dark green) holoenzymes are superimposed for reference – STK holoenzymes rely on interactions between peptides and the N-terminal anchor, in contrast to TKs which bind peptides further away. Bottom: van der Waals (vdW) space-filling models of the CDK6 wildtype (left) and mutant (right) N-terminal anchor residue \\(146_{\\mathrm{DFG + 2}}\\) and its interaction partner \\(120_{\\mathrm{HRD - 2}}\\) , showing the loss of favorable vdW contacts between the \\(\\mathrm{C}_{\\beta}\\) atom of \\(146_{\\mathrm{DFG + 2}}\\) and \\(\\mathrm{C}_{\\gamma}\\) of \\(120_{\\mathrm{HRD - 2}}\\) . Backbone hydrogen bonding patterns that define the \\(\\beta\\) -strands are shown with dashed lines. (B) Top: same as A but with the RD-pocket highlighted. As before, peptides from TK and STK co-crystal structures are superimposed for reference. Bottom: vdW space-filling models of residue \\(160_{\\mathrm{APE - 7}}\\) in the wildtype (left) and mutant structure (right), located in the activation loop C-terminus, which stabilizes the RD-pocket in STKs. Small aliphatic residues like V160APE-7 in CDK6 pack favorably against the HRD-Arg, while bulky sidechains, e.g., K160APE-7 (seen in TKs), decouple from the RD-pocket and flip “out” in our MD free-energy simulations to interact with solvent (or peptides in the TK holoenzyme only).",
+    "footnote": [],
+    "bbox": [
+      [
+        57,
+        160,
+        940,
+        600
+      ]
+    ],
+    "page_idx": 15
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Divergent features of the active \\(\\rightarrow\\) inactive conformational change for TKs vs STKs. Key residues are displayed with \\(\\alpha\\) -carbon spheres and “sticks” representation. (A) Active conformation of CDK6 (PDB: 1X02), an STK. In the active state the activation loop (dark blue) is extended and the C-terminal anchor is formed by a hydrogen bond between K126HRD+2 in the catalytic loop and T162APE-5 in the activation loop C-terminus. The activation loop C-terminus is also anchored in-place via the stacked residues 161APE-7 and 166APE-6. (B) Viewing the inactive DFG-out activation loop of CDK6 (PDB: 1G3N) – a large rotation about T162 can be seen which distorts the C-terminal anchor and breaks the contact between 161 and 166. (C) Viewing the active holoenzyme of INSR (PDB: 3BU3) with a peptide substrate bound to the active kinase in the C-lobe binding mode. (D) Viewing the inactive activation loop of INSR (PDB: 3ETA). Unphosphorylated Y154 in the activation loops of TKs (light blue) acts as a pseudo-substrate, forming the same interactions as the substrate phosphoacceptor in C. (E) Depiction of the active \\(\\leftrightarrow\\) inactive landscape suggested by the Potts model and structural observations, for STKs (solid line) and TKs (dashed). The barrier heights are unknown and were drawn for the sake of illustration, while the relative depths of the active and inactive free energy basins were drawn descriptively, based on estimates of \\(\\Delta G_{\\text{reorg}}\\) (see ref. 15) and \\(\\Delta \\Delta G_{\\text{reorg}}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        132,
+        95,
+        833,
+        620
+      ]
+    ],
+    "page_idx": 19
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. (continued from previous page)",
+    "footnote": [],
+    "bbox": [
+      [
+        128,
+        95,
+        870,
+        888
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. (continued from previous page)",
+    "footnote": [],
+    "bbox": [
+      [
+        128,
+        110,
+        880,
+        799
+      ]
+    ],
+    "page_idx": 28
+  }
+]

preprint/preprint__603ef0a9f08b3144aab5e4c8bcfcd0a27a21acb9266edd87d344cef28d26eac2/images_list.json

@@ -0,0 +1,242 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Fig. 1 Feeding a \\(1\\%\\) protein diet with or without NAM supplementation on basic animal characteristics. a Experimental design. b Average food and liquid intake during day 7 to day 14 \\((n = 7\\) for \\(18\\%\\) \\(n = 5\\) for \\(1\\%\\) and \\(1\\% +\\) NAM). c Body weight change throughout experiment \\((n = 15)\\) d Final body weight and body length assessed on day 14 \\((n = 15)\\) . e Liver weight and liver weight/body weight ratio \\((n = 12\\) for \\(18\\%\\) \\(n = 10\\) for \\(1\\%\\) and \\(1\\% +\\) NAM). f Fasting glucose levels \\((n = 7\\) for \\(18\\%\\) \\(n = 8\\) for \\(1\\%\\) \\(n = 7\\) for \\(1\\% +\\) NAM). g Respiratory exchange ratio (RER) and energy expenditure \\((n = 7\\) for \\(18\\%\\) \\(n = 6\\) for \\(1\\%\\) \\(n = 7\\) for \\(1\\% +\\) NAM). \\(^{*}\\mathrm{p}< 0.05\\) \\(^{**}\\mathrm{p}< 0.01\\) \\(^{**}\\mathrm{p}< 0.001\\) ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \\(\\pm\\) S.E.M.",
+    "footnote": [],
+    "bbox": [
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+    "page_idx": 24
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Fig. 2 The effect of \\(1\\%\\) protein feeding with or without NAM supplementation on hepatic lipid accumulation. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Representative oil red o stain staining images of the liver (20X magnification). Fat droplet was stained in red, and nucleus was stained in purple. c Representative immunofluorescence images of the liver (40X magnification). BODYPY was used to stain fat droplet in green, and DAPI was used to counter stain nucleus in blue. d Quantification of fat vacuoles area (n=9). e Liver TG concentrations (n=6). f Serum TG concentrations (n=6). \\(^{*}\\mathrm{p}< 0.05\\) , \\(^{**}p< 0.01\\) , \\(^{***}p< 0.001\\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \\(\\pm\\) S.E.M. Scale bars are as indicated.",
+    "footnote": [],
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+    ],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Fig. 3 The effect of NAM supplementation on mitochondrial characteristics of 1% protein fed model. a Representative immunofluorescence images of mitochondrial (60X magnification). HSP60 was used to stain mitochondrial in red, and DAPI was used to counter stain nucleus in blue. b mtDNA copy number (n=6). c, d Western blots and quantification of HSP60 and TOM20 (n=3). e ATP levels (n=11 for 18% and 1%; n=7 for 1%+NAM). f, g Western blots and quantification of complex I, complex IV and complex V (n=3). h mRNA expression of \\(\\beta\\) -oxidation genes (n=6). i mRNA expression of lipid genesis genes (n=6). \\(^{*}\\mathrm{p}< 0.05\\) , \\(^{**}p< 0.01\\) , \\(^{***}p< 0.001\\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \\(\\pm\\) S.E.M. Scale bars are as indicated.",
+    "footnote": [],
+    "bbox": [
+      [
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+      ]
+    ],
+    "page_idx": 26
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Fig. 4 Hepatic metabolomic and lipidomic profiles under 18% protein diet, 1% protein diet, and 1% protein diet with NAM supplementation. a sPLS-DA and correlation circle plots of hepatic central carbon metabolism showing separation of 18% and 1% protein diet group (n=5). b sPLS-DA and correlation circle plots of hepatic central carbon metabolism showing separation of 1% protein diet and NAM treated group (n=5 for 1%; n=7 for 1%+NAM). c sPLS-DA and correlation circle plots of hepatic lipidomics showing separation of 18% and 1% protein diet group (n=6). d sPLS-DA and correlation circle plots of hepatic lipidomics showing separation of 1% protein diet and NAM treated group (n=6).",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Fig. 5 The effect of \\(1\\%\\) protein feeding with or without NAM supplementation on TRP-NAM pathway metabolites, SIRT1 and downstream targets, and autophagy levels. a Hepatic NAD+ levels and TRP-NAM pathway metabolites (n=6). b SIRT1 and PGC-1α western blots (n=3). c p65 and Acetyl-p65 western blots (n=3). d Autophagy markers LC3 western blots (n=3). e Quantification of protein levels in western blots. \\(^{*}p < 0.05\\) , \\(^{**}p < 0.01\\) , \\(^{***}p < 0.001\\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M.",
+    "footnote": [],
+    "bbox": [
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+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Fig. 6 The effect of SIRT1 modulators on basic animal characteristics. a Experiment design. b Body weight change throughout experiment (n=6). c Average food and liquid intake during day 7 to day 14 (n=6). d Final body weight, body length, and weight for length ratio assessed at day 14 (n=6). e Liver weight, liver weight to body weight ratio (n=6). \\*p < 0.05, \\*\\*p < 0.01, \\*\\*\\*p < 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M.",
+    "footnote": [],
+    "bbox": [
+      [
+        201,
+        92,
+        800,
+        380
+      ]
+    ],
+    "page_idx": 29
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Fig. 7 The effect of SIRT1 modulators on hepatic steatosis, mitochondrial characteristics, SIRT1 and its downstream targets. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Quantification of liver histology and TG levels (n=6). c mtDNA copy number (n=6). d ATP levels (n=6). e mRNA expression of \\(\\beta\\) -oxidation genes (n=6). f mRNA expression of lipid genesis genes (n=6). g SIRT1 and PGC-1 \\(\\alpha\\) western blots and quantification (n=3). \\(^{*}\\mathrm{p}< 0.05\\) , \\(^{**}p< 0.01\\) , \\(^{**}p<\\) 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \\(\\pm\\) S.E.M. Scale bars are as indicated.",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Fig. 8 Proposed model of the role of the TRP-NAM pathway in malnutrition-induced hepatic metabolic disturbances. In protein malnutrition, decreased TRP availability will decrease the kynurenine pathway activity, which is associated with NAD+ and NAM deficiency. This would disturb NAD+ salvage pathway, including SIRT1, influence its downstream target PGC-1α and autophagy, which affect mitochondrial quality and function. These changes lead to ATP depletion and lipid accumulation in the liver. We hypothesize that supplement with TRP-NAM modulator would influence NAD+ salvage pathway. This would thereby activate SIRT1, influence PGC-1α deacetylation and autophagy, which will have a positive effect on mitochondrial health, affect mitochondrial biogenesis and clearance of damaged mitochondrial, then improve ATP generation and reduce lipid accumulation in the liver.",
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+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1",
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+    "caption": "Figure 2",
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+    "caption": "Figure 3",
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+    "caption": "Figure 4",
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preprint/preprint__603ef0a9f08b3144aab5e4c8bcfcd0a27a21acb9266edd87d344cef28d26eac2/preprint__603ef0a9f08b3144aab5e4c8bcfcd0a27a21acb9266edd87d344cef28d26eac2.mmd

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+
+# The role of the tryptophan-nicotinamide pathway in a model of severe malnutrition induced liver dysfunction  
+
+Guanlan Hu University of Toronto/The Hospital for Sick Children  
+
+Catriona Ling University of Toronto/The Hospital for Sick Children  
+
+Lijun Chi The Hospital for Sick Children  
+
+Samuel Furse University of Cambridge https://orcid.org/0000- 0003- 4267- 2051  
+
+Albert Koulman University of Cambridge https://orcid.org/0000- 0001- 9998- 051X  
+
+Jonathan Swann Imperial College London/University of Southampton  
+
+Mehakpreet Thind University of Toronto/The Hospital for Sick Children  
+
+Dorothy Lee Hospital for Sick Children  
+
+Marjolein Calon The Hospital for Sick Children  
+
+Christian Versloot University Medical Center Groningen https://orcid.org/0000- 0002- 3991- 6652  
+
+Barbara Bakker University Medical Center Groningen  
+
+Gerard Gonzales Ghent University/The Hospital for Sick Children  
+
+Peter Kim Hospital for Sick Children, University of Toronto  
+
+Robert Bandsma ( \(\boxed{\bullet}\) robert.bandsma@sickkids.ca) The Hospital for Sick Children
+
+<--- Page Split --->
+
+**Keywords:** Severe Malnutrition, Metabolic Dysfunction, Hepatic Mitochondrial Turnover and Function
+
+**Posted Date**: November 19th, 2020
+
+**DOI**: https://doi.org/10.21203/rs.3.rs-104804/v1
+
+**License:** © This work is licensed under a Creative Commons Attribution 4.0 International License.Read Full License
+
+<--- Page Split --->
+
+# The role of the tryptophan-nicotinamide pathway in a model of severe malnutrition induced liver dysfunction  
+
+Guanlan Hu \(^{1,2}\) , Catriona Ling \(^{1,2}\) , Lijun Chi \(^{2}\) , Samuel Furs \(^{3}\) , Albert Koulman \(^{3}\) , Jonathan Swann \(^{4,5}\) , Mehakpreet K. Thind \(^{1,2}\) , Dorothy Lee \(^{2}\) , Marjolein Calon \(^{2}\) , Christian J. Versloot \(^{6}\) , Barbara M. Bakker \(^{6}\) , Gerard B. Gonzales \(^{2,7,8}\) , Peter K. Kim \(^{9,10}\) & Robert H.J. Bandma \(^{1,2,11,12}\) \*  
+
+1 Department of Nutritional Sciences, Faculty of Medicine, University of Toronto, Toronto, ON M5G 1A8, Canada  2 Translational Medicine Program, The Hospital for Sick Children, Toronto, ON M5G 0A4, Canada  3 Core Metabolomics and Lipidomics Laboratory, Wellcome Trust-Metabolic Research Laboratories, Institute of Metabolic Sciences, University of Cambridge, Cambridge, CB2 0QQ, United Kingdom  4 School of Human Development and Health, Faculty of Medicine, University of Southampton, SO16 6YD, United Kingdom  5 Department of Metabolism, Digestion and Reproduction, Faculty of Medicine, Imperial College London, SW7 2AZ, United Kingdom  6 Laboratory of Pediatrics, Center for Liver, Digestive, and Metabolic Diseases, University of Groningen, University Medical Center Groningen, Groningen, The Netherlands  7 Gastroenterology, Department of Pediatrics and Internal Medicine, Faculty of Medicine and Health Sciences, Ghent University, Ghent 9000, Belgium  8 VIB Inflammation Research Center, Zwijnaarde 9052, Belgium  9 Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada  10 Cell Biology Program, The Hospital for Sick Children, Toronto, ON M5G 0A4, Canada  11 Division of Gastroenterology, Hepatology, and Nutrition, The Hospital for Sick Children, Toronto, ON M5G 0A4, Canada 12 The Childhood Acute Illness & Nutrition Network (CHAIN), Blantyre, Malawi  \* Correspondence and requests for materials should be addressed to  Robert H.J. Bandma, Translational Medicine Program, The Hospital for Sick Children, Peter Gilgan Centre for Research and Learning, 686 Bay Street, Toronto, ON M5G 0A4, Canada. Tel.: +1 4168137654x9057; Fax: +1 4168134972 (R.H.J. Bandma).  E-mail address: robert.bandma@sickkids.ca (R.H.J. Bandma)
+
+<--- Page Split --->
+
+## Abstract  
+
+Mortality in children with severe malnutrition is strongly related to signs of metabolic dysfunction, such as hypoglycemia. Lower circulating tryptophan levels in children with severe malnutrition suggest a possible disturbance in the tryptophan- nicotinamide (TRP- NAM) pathway and subsequently NAD+ dependent metabolism regulator sirtuin1 (SIRT1). We report that severe malnutrition in weanling mice, induced by feeding a low protein diet, leads to an impaired TRP- NAM pathway and affects hepatic mitochondrial turnover and function. We demonstrate that stimulating the TRP- NAM pathway improves hepatic mitochondrial and overall metabolic function which is dependent on SIRT1. Activating SIRT1 is sufficient to induce improvement in metabolic functions. Our findings indicate that modulating the TRP- NAM pathway can partially improve liver metabolic function in severe malnutrition and could lead to the development of new interventions for children with severe malnutrition.
+
+<--- Page Split --->
+
+## 44 Introduction  
+
+Malnutrition contributes to nearly \(45\%\) of deaths among children under 5 years of age worldwide<sup>1</sup>. Malnourished children, especially those with severe malnutrition are at a substantially increased risk of mortality compared to well- nourished children<sup>2</sup>. The current treatment guidelines developed by the World Health Organization (WHO) for children with severe malnutrition are based on limited scientific evidence<sup>3</sup>. Thus, new evidence- based interventions are urgently needed.  
+
+The liver is a central organ that regulates nutrient metabolism. In severe malnutrition, hepatic metabolism has been found to be disturbed and is associated with hypoglycemia, hypoalbuminemia, and steatosis<sup>4- 6</sup>. Children with severe malnutrition have impaired hepatic glucose production, which increases the risk of hypoglycemia and is related to mortality<sup>5</sup>. We recently discovered in both patients and a rodent model of severe malnutrition, that hepatic mitochondrial function is impaired leading to reduced nutrient oxidation and adenosine triphosphate (ATP) depletion<sup>5,6</sup>. However, the pathophysiology of hepatic mitochondrial dysfunction in severe malnutrition remains poorly understood.  
+
+Children with severe malnutrition have been found to have significantly lower serum tryptophan levels<sup>7- 9</sup>. As an essential amino acid, tryptophan is crucial for growth and protein synthesis. It is also a precursor of nicotinamide adenine dinucleotide (NAD+) and nicotinamide adenine dinucleotide phosphate (NADP+), which are essential co- factors in metabolic and biosynthesis pathways. We have previously shown that higher excretion of \(N\) - methylnicotinamide, a urinary biomarker of NAD+ and nicotinamide availability, was associated with catch- up growth in stunted infants<sup>10</sup>. NAD+ is also a co- substrate for sirtuin1 (SIRT1), which is an important enzyme for mitochondrial health and biogenesis through activation of peroxisome proliferator- activated receptor- gamma coactivator- 1 alpha (PGC- 1α)<sup>11</sup>. SIRT1 has also been shown to regulate autophagy<sup>12- 14</sup>. There have been reports that targeting this pathway in non- alcoholic fatty liver disease (NAFLD) has beneficial effects on hepatic metabolism<sup>15- 18</sup>. The role of tryptophan nicotinamide (TRP- NAM) pathway in severe malnutrition- associated hepatic metabolic dysfunction remains unknown.
+
+<--- Page Split --->
+
+In this study we aimed to characterize the role of the TRP- NAM pathway in hepatic metabolic dysfunction in a mouse model of severe malnutrition. We demonstrate that the TRP- NAM pathway is affected in this model and that hepatic mitochondrial dysfunction is related to deficiencies in the TRP- NAM pathway. We demonstrate supplementing with NAM and related components of this pathway improve mitochondrial and overall hepatic metabolic dysfunction. We find that the effects of modulating the TRP- NAM pathway are mediated through SIRT1. These findings identify the importance of the TRP- NAM pathway and SIRT1 in malnutrition- associated hepatic metabolic dysfunction.  
+
+## Results  
+
+## Feeding a low protein diet leads to hepatic steatosis in young mice.  
+
+To develop a mouse model of severe malnutrition, we fed 3- weeks- old weanling male C57BL/6J mice a \(1\%\) protein isocaloric diet for two weeks (malnourished group) and compared it to the control group fed an \(18\%\) protein diet (control group) (Fig. 1a). Mice subjected to the \(1\%\) protein diet lost a significant amount of body weight (approximately \(20\%\) ) over two weeks and had a lower body length and weight for length ratio compared to the \(18\%\) protein- fed control group (Fig. 1b- d). The \(1\%\) protein- fed mice showed a lower liver weight and liver to body weight ratio compared to control (Fig. 1e). Lower glucose concentrations were also noted in the \(1\%\) protein- fed mice before and after fasting (Fig. 1f), consistent with reduced hepatic glucose production. The respiratory exchange ratio (RER) was lower during the dark phase and higher during the light phase in \(1\%\) protein- fed mice, indicating a loss of the day- night feeding cycle in this group. Energy expenditure was lower in \(1\%\) protein- fed mice compared to the \(18\%\) protein- fed control group (Fig. 1g).  
+
+Histological H&E staining and Oil Red O staining of the livers identified steatosis in the mice fed with \(1\%\) protein diet as evidenced by an increase in fat vacuoles and larger fat droplets compared to the mice fed with \(18\%\) protein diet (Fig 2a- b). The increase in lipid droplets in the liver of the \(1\%\) protein- fed mice was confirmed by immunofluorescence staining with BODIPY (Fig. 2c). Further quantification of histology slides showed consistency with these observations (Fig. 2d)
+
+<--- Page Split --->
+
+and was validated by measurement of liver triglyceride (TG) levels (Fig. 2e). Serum TGs were lower in the \(1\%\) protein- fed group, indicating steatosis is not linked to hypertriglyceridemia (Fig. 2f). Together, these results indicate that the \(1\%\) protein diet induces hepatic steatosis in mice similar to those observed in patients and rat model of severe malnutrition \(^{2,6}\) .  
+
+## NAM and TRP-NAM pathway modulators reduce the development of low protein diet-induced hepatic steatosis.  
+
+Examination for blood tryptophan levels showed the \(1\%\) protein diet mice to be lower than \(18\%\) protein diet control animals \((43.0\pm 5.0 \mu \mathrm{mol / L}\) and \(88.4\pm 13.2 \mu \mathrm{mol / L}\) respectively, \(\mathrm{p} = 0.0035\) ). To examine the role of a reduced tryptophan levels and possible nicotinamide (NAM) deficiency on liver health, the \(1\%\) protein- fed mice were supplemented with \(160 \mathrm{mg / kg}\) body weight NAM from day 7 to day 14 (Fig. 1a). NAM treatment did not alter the average body weight, body length, or food and liquid consumption in the \(1\%\) protein- fed group (Fig. 1b- d). The mice treated with NAM had no significant difference in liver weight, liver/body weight ratio, or fasting glucose levels compared to the untreated \(1\%\) protein diet- fed mice (Fig. 1e- f). RER and energy expenditure were not affected by NAM treatment (Fig. 1g). NAM treatment improved the hepatic steatosis compared to the \(1\%\) protein- fed mice, indicated by a reduction in the fat vacuoles area and a \(30\%\) reduction in liver TG levels compared to untreated animals (Fig. 2a- e). The NAM treatment had no effect on serum TG concentrations (Fig. 2f).  
+
+To determine whether the effect of NAM treatment was due to improvement of the NAD salvage pathway specifically, we treated the \(1\%\) protein- fed mice with nicotinamide riboside (NR) or tryptophan (TRP). Both NR and TRP act as NAD+ precursors in the NAD salvage pathway \(^{16}\) . The allocated interventions were given from day 7 to day 14 (Supplementary Fig. 1a). NR and TRP supplementation, similar to NAM treatment, did not recover body weight, body length or liver weight/body weight ratio compared to the untreated \(1\%\) protein- fed group (Supplementary Fig. 1b- e). Similar to the NAM treated malnourished mice, hepatic steatosis was reduced in the NR and TRP treated groups (Supplementary Fig. 2a- f). To determine whether the effects were specific to the TRP- NAM pathway, we also performed similar experiments in mice who received supplementation with methionine (MET), another essential amino acid like tryptophan. This
+
+<--- Page Split --->
+
+particular amino acid was chosen as MET has been shown to decrease hepatic steatosis in mice on ketogenic diets<sup>19</sup>, and diets completely devoid of MET and choline can induce hepatic steatosis<sup>20,21</sup>. Supplementation with methionine did not improve hepatic steatosis among the 1% protein- fed mice (Supplementary Fig. 2a- f). MET supplementation also did not recover body weight and body length, but increased liver weight and body weight ratio in comparison to the untreated 1% protein- fed mice alone (Supplementary Fig. 1b- d). Together, these results indicate that supplementation of different NAD+ precursors improve low protein- induced hepatic steatosis.  
+
+## NAM improves low protein diet-induced mitochondrial changes.  
+
+To further understand the mechanisms underlying the improved hepatic steatosis in response to NAM treatment, we next evaluated changes in hepatic mitochondrial characteristics in our model. We have previously shown that protein- deficient diet induces mitochondrial morphological and functional changes and reduces mitochondrial activity in rats under protein restricted diet<sup>6</sup>. In our mouse model, immunofluorescent staining of mitochondria in the liver showed that the mitochondria were enlarged and elongated but decreased in numbers in the 1% protein- fed mice compared to the 18% protein- fed control group (Fig. 3a). The loss of mitochondria was further confirmed by a significant decrease in the mitochondrial DNA (mtDNA) copy number (Fig. 3b). This feature improved after NAM, NR, and TRP treatment (Fig. 3b, Supplementary Fig. 2h). Mitochondrial abundance markers including TOM20 and HSP60 were both significantly lower in the 1% protein diet- fed mice compared to the control, but improved with NAM treatment (Fig. 3c,d). This suggests that NAM treatment can either reduce mitochondria degradation or increase its biogenesis in our model of severe malnutrition.  
+
+To examine mitochondrial fitness, we examined hepatic ATP levels, and levels of mitochondrial complex proteins. Further, we quantified the expression of genes in the \(\beta\) - oxidation and lipogenesis pathway. The livers of the 1% protein- fed malnourished mice had significantly lower hepatic ATP levels compared to the 18% protein- fed control group (Fig. 3e). NAM and other TRP- NAM pathway modulators significantly restored hepatic ATP levels (Fig. 3e, Supplementary Fig. 2i). Complex I, Complex IV, and Complex V protein levels were significantly lower in the 1% protein- fed group compared to the control group (Fig. 3f,g). Complex IV levels improved significantly
+
+<--- Page Split --->
+
+after NAM treatment, while no significant change was observed in levels of other complexes. Expression of the genes in the \(\beta\) - oxidation pathway was reduced in the livers of mice fed a \(1\%\) protein diet and were partially restored after NAM treatment, especially Acaa2 and Hadha (Fig. 3h). The expression of lipogenesis genes including Fasn and Acaca were decreased in mice fed a \(1\%\) protein diet (Fig. 3i). NAM supplementation did not influence the mRNA expression of lipogenesis genes (Fig. 3i). In summary, feeding mice a \(1\%\) protein diet altered the hepatic mitochondrial morphology, decreased mitochondrial number and mass, and affected markers of oxidative phosphorylation and \(\beta\) - oxidation. NAM treatment improved the \(1\%\) protein diet-induced mitochondrial changes associated with a recovery in ATP content.  
+
+## A low protein diet leads to changes in hepatic energy metabolism that improve with NAM treatment.  
+
+To better understand the overall liver metabolic change in mice fed with \(1\%\) protein diet and evaluate the effect of NAM supplementation, we performed quantitative analysis of liver central carbon metabolism metabolites<sup>22</sup>. The major metabolic profile differences between groups was highlighted by sparse- partial least squares- discriminant analysis (sPLS- DA)<sup>23</sup>. Variable importance in projection (VIP) scores were used to identify the most important metabolites for the clustering. Overall, the hepatic metabolic profiles of the \(1\%\) protein diet- fed malnourished group were clearly separated from those of the \(18\%\) protein diet- fed control group, and distinct from NAM treatment group (Fig. 4a- b). Among the metabolomic features, acetylglucosamine- 1P, glycerylaldehyde- 3P, malonyl- CoA, lactic acid, ATP, erythrose- 4P, UMP, UDP- glucose, glucose, pyruvic acid, and ADP- glucose mostly discriminated \(18\%\) protein diet from \(1\%\) protein diet groups, with variable importance in projection (VIP) score \(>1\) in both components 1 and 2 (Fig. 4a). To be more specific, the \(1\%\) protein- fed group showed significantly lower glucose, lactic acid, and pyruvic acid content compared to control (Supplementary Table 1)<sup>24</sup>. GMP and UMP concentrations decreased in the \(1\%\) protein diet- fed group, suggesting disturbed nucleotide metabolism including pyrimidine and purine synthesis. Malonyl- CoA levels also changed in the \(1\%\) protein- diet fed group, consistent with altered lipogenesis<sup>25,26</sup>. The overall results were also in line with an earlier report of impaired ATP production and decreased pyruvate uptake,
+
+<--- Page Split --->
+
+accompanied by altered tricarboxylic acid cycle (TCA) cycle intermediates in a rat model of malnutrition \(^{6}\) . Modulation of the TRP- NAM pathway altered hepatic metabolic profiles as observed by sPLS- DA (Fig. 4b and Supplementary Fig. 3a). NAM treatment shifted malonyl- CoA, UTP, ATP, Hs- CoA, UDP- Glucose, total fructose- bisP/glucose- 1,6- bisP, acetyl- CoA, AMP, and succinyl- CoA, which mostly differentiate them with \(1\%\) protein diet group (VIP score \(>1\) ). The concentration of ATP, malonyl- CoA, and acetyl- CoA in NAM treated group shifted towards the \(18\%\) protein diet- fed control group, which was related to the improved energy production and carbohydrate and lipid metabolism (Supplementary Table 1) \(^{27}\) .  
+
+To further explore the changes in lipid metabolism in our model and evaluate the effect of TRP- NAM modulation, we performed a lipidomic analyses. Overall, discriminating features were identified that clearly separate the \(18\%\) protein diet and \(1\%\) protein diet group, dominated by increased levels of triacylglycerols, diacylglycerols, and sterols (VIP score \(>1\) ) (Fig. 4c and Supplementary Table 2). Interestingly, hepatic phospholipid content was lower in the \(1\%\) group compared to the \(18\%\) group. The decreased PC/TG ratio and phosphatidylcholines to phosphatidylethanolamines ratio (PC/PE) in the \(1\%\) protein diet group might be linked to the altered energy metabolism and lipid droplet size and dynamics \(^{28,29}\) . Decreased PC/PE ratios have also been observed in NASH patients \(^{30,31}\) , potentially through mitochondrial respiratory chain dysfunction and disability to meet energy requirements \(^{32}\) . NAM treatment clearly separated this group from the \(1\%\) protein diet group and separation was primarily caused differences in phosphatidylcholines and diacylglycerols (VIP score \(>1\) ) (Fig. 4d and Supplementary Table 2). NR and TRP treatment groups were close to each other but clearly separate from MET treatment group, mostly highlighted by altered triacylglycerols and diacylglycerols (with VIP score \(>1\) ) (Supplementary Fig. 3b).  
+
+## NAM treatment affects NAD+ and the SIRT1 pathway in low protein-fed mice.  
+
+To determine whether NAM treatment directly affects the NAD salvage pathway, we measured the abundance of hepatic NAD+ and tryptophan pathway metabolites in the liver of these animals. NAD+ levels and many metabolites in the tryptophan pathway (such as kynurenine, kynurenine acid, serotonin) were decreased in the \(1\%\) protein- fed mice compared to the \(18\%\) protein- fed
+
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+control group (Fig. 5a). NAM treatment increased hepatic nicotinic acid concentrations, indicating NAM was bioavailable and affected the TRP- NAM pathway. However, we did not observe a significant effect of NAM treatment on \(\mathrm{NAD + }\) levels itself \(\mathrm{(p = 0.640)}\) , whereas NR treatment did significantly increase hepatic \(\mathrm{NAD + }\) levels (Supplementary Fig. 2j). This result is consistent with other studies that have reported that NR increased hepatic \(\mathrm{NAD + }\) levels \(^{33}\) . Another chronic NAM supplementation study showed that NAM did not boost \(\mathrm{NAD + }\) but enhanced the de- acetylation of SIRT1 targets \(^{18}\) .  
+
+Next, we investigated changes in the NAD dependent SIRT1 pathway. The protein levels of SIRT1 and its downstream target PGC- 1 \(\alpha\) were significantly decreased in the mice fed a \(1\%\) protein diet compared to the \(18\%\) protein- fed control group and levels of these proteins were significantly improved after NAM treatment, albeit not to the same level as the control group (Fig. 5b,e). The ratio of p65 to Ac- p65 significantly increased in the \(1\%\) protein- fed group compared to the control, which was improved after NAM treatment, indicating a change in SIRT1 deacetylation activity (Fig. 5c,e).  
+
+Since SIRT1 has been shown to influence autophagy and we previously showed an impairment in autophagy flux in livers of low protein- fed rodents \(^{6}\) , we next evaluated autophagy levels by measuring microtubule- associated protein 1A/1B- light chain 3 (LC3) LC3- I and LC3- II protein levels. Autophagy pathway marker of LC3- II/LC3- I ratio significantly decreased in the \(1\%\) protein- fed malnourished group compared to the \(18\%\) protein- fed control group, suggesting a decrease in autophagy activation (Fig. 5d,e). NAM treatment increased the LC3- II/LC3- I ratio, which suggests an increase in activation of macro- autophagy. Taken together, our results suggest that the TRP- NAM pathway is disturbed after feeding a \(1\%\) protein diet to mice and that it can be partially restored by NAM treatment. In turn, the improvement in the TRP- NAM pathway elevates SIRT1 which may be linked to the increase in PGC- 1 \(\alpha\) and activation of autophagy.  
+
+The effect of NAM on low protein diet- induced liver metabolic dysfunction is mediated through SIRT1.
+
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+To further test the whether the effect of NAM is SIRT1- dependent, we performed experiments using SIRT1 modulators in the \(1\%\) protein- fed mice with or without NAM supplementation (Fig. 6a). The SIRT1 activator, resveratrol (REV) \(^{34,35}\) , was used to investigate if SIRT1 activation was sufficient to demonstrate an improvement in the hepatic metabolic changes caused by \(1\%\) protein feeding. The SIRT1 inhibitor, selisistat (EX- 527) \(^{36,37}\) , was subsequently used in combination with NAM treatment to determine if the effect of NAM was dependent on the activation of SIRT1.  
+
+Intraperitoneal injection of REV did not change body weight, body length and liver weight compared to the vehicle control group (Fig. 6b- e). However, we observed a decrease in the degree of hepatic steatosis in the \(1\%\) protein- fed malnourished group treated with REV, with nearly 2 folds decrease in fat vacuole area and decreased liver TG levels compared to untreated \(1\%\) protein fed animals (Fig. 7a,b). mtDNA copy number and ATP levels significantly increased after REV treatment (Fig. 7c,d). Among the \(\beta\) - oxidation genes, we observed small but significant increases in Hadha and Acadm expression after REV treatment, without a significant change in expression of lipogenesis genes compared to vehicle treated group (Fig. 7e,f). When the \(1\%\) protein- fed malnourished mice were treated with both EX- 527 and NAM, the effects of NAM treatment on hepatic steatosis and mtDNA copy number were lost (Fig. 7a- c). SIRT1 protein level was upregulated after REV treatment (Fig. 7g). There was also a trend toward increased PGC- 1 \(\alpha\) protein levels in the REV treated group (p- value \(= 0.083\) ). EX- 527 with NAM treatment also did not affect SIRT1 and PGC- 1 \(\alpha\) levels compared to the \(1\%\) protein- fed malnourished group alone (Fig. 7g). These data indicate that the SIRT1 increase is sufficient to improve \(1\%\) protein diet- induced hepatic metabolic dysfunction and the effect of NAM treatment on hepatic metabolism is dependent on the elevation of SIRT1.  
+
+## Discussion  
+
+Our study indicates that feeding weanling mice a \(1\%\) protein diet leads to stunted growth, severe wasting, hepatic lipid accumulation and mitochondrial dysfunction that is associated with a reduction in activity in SIRT1, PGC- 1 \(\alpha\) and autophagy. We demonstrate that supplementing the TRP- NAM pathway is able to improve the metabolic phenotype and that this effect is dependent
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+on SIRT1. This is the first report on the role of the TRP- NAM pathway in a murine malnutrition model.  
+
+The hepatic metabolic changes induced by the protein deficient diet were consistent with our previous findings in a rat model of severe malnutrition showing liver steatosis and ATP depletion caused by mitochondrial dysfunction in a rat model of severe malnutrition<sup>11</sup>. The data are also consistent with limited reports in children with severe malnutrition that have found impaired mitochondrial function<sup>4,5</sup>. Interestingly, there is considerable overlap with features seen in patients with NAFLD, including changes in mitochondrial complexes, mitochondrial biogenesis, and hepatic lipid accumulation<sup>38- 40</sup>. The reduction in mitochondrial mass seen in our mouse model is different from previous observations in low protein fed rats, where an increase in mitochondrial mass was observed<sup>6</sup>. However, reduction in mtDNA in our low protein diet mouse model was consistent with another previous report in fetal and early postnatal malnourished rats fed a low casein diet<sup>41</sup>.  
+
+The reduction in mitochondrial mass and mtDNA in low protein- fed mice was associated with a reduction in PGC- 1α, a well- known regulator of cellular energy metabolism and activator of mitochondrial biogenesis<sup>42,43</sup>. PGC- 1α can co- activate transcription factors such as peroxisome proliferator- activated receptor (PPARα) and nuclear respiratory factors (NRF1 and NRF2) to regulate mitochondrial biogenesis and fatty acid oxidation<sup>44</sup>. Mice that are deficient in PGC- 1α have impaired energy metabolism that is related to a decrease in mitochondrial number and respiratory capacity<sup>45</sup>. This suggests that the reduction in mitochondrial mass is related to a decrease in mitochondrial biogenesis upon low protein feeding. The changes in mitochondrial morphology, mitochondrial complex content, and markers of mitochondrial function, such as ATP, also indicate that the mitochondria that are present in the liver after a period of low protein feeding are damaged and dysfunctional. Mitochondrial degradation is regulated through a selective autophagy process called mitophagy<sup>12</sup>, and our data suggests that autophagy activation is decreased during nutritional stress. This could contribute to a high relative content of damaged mitochondria that would normally have been degraded through mitophagy. NAM treatment increased PGC- 1α protein levels, mitochondrial mass and content of mitochondrial complexes, while activating the autophagy pathway, suggesting a rebalancing of mitochondrial biogenesis and mitophagy.
+
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+PGC- 1 \(\alpha\) and autophagy are both regulated by SIRT1. SIRT1 directly deacetylates PGC- 1 \(\alpha\) at multiple lysine sites and the induction pattern of SIRT1 protein correlates with the expression of PGC- 1 \(\alpha^{46}\) . In addition, SIRT1 regulate autophagy by acting on multiple autophagy effectors. These mechanisms include directly inducing autophagy by deacetylating autophagy- related genes (ATGs) and LC3, indirectly inhibiting the mTOR pathway by activation of AMPK, as well as modulating the expression of autophagy and mitophagy regulatory molecules (e.g. Rab7 and Bnip3) through deacetylation of Forkhead box O transcription factors (FOXOs) \(^{47,48}\) . SIRT1 levels were decreased in our low protein diet- fed mice. As SIRT1 activity is dependent on NAD availability, we propose that lower SIRT1 activity is associated with reduced levels of NAD and other metabolites in the TRP- NAM pathway in low protein diet- fed mice. Supplementing these protein deficient animals with NAM was found to rescue SIRT1 mediated activity. We propose that the reduction in NAD prevents the SIRT1 mediated activation of PGC- 1 \(\alpha\) and autophagy pathway. Our results are consistent with a clinical study reporting that increased malnutrition risk was associated with decreased SIRT1 expression \(^{49}\) . The decreased protein levels of SIRT1 found after low protein feeding could potentially be explained by diet- triggered cleavage of SIRT1 protein. For example, a high- fat diet has been shown to induce SIRT1 protein cleavage leading to metabolic dysfunction \(^{50}\) .  
+
+NAM was shown to increase SIRT1 levels. The effect was not specific to NAM, as NR and TRP demonstrated a similar effect. Other NAD+ precursors such as NR and TRP have demonstrated a similar effect in previous studies \(^{17,51,52}\) . We focused on NAM specifically for more in depth investigations because of its low cost and excellent safety profile. Treatment with NAM and other NAD+ precursors have shown beneficial effects in various metabolic dysfunction models, including fatty liver, obesity, metabolic syndrome, and diabetes \(^{18,53,54}\) . The beneficial effects in these studies have been related to an improved mitochondrial function, mediated by NAD+ dependent sirtuin activation \(^{17,51,52}\) . Our SIRT1 modulation experiments demonstrated that in our malnutrition model the effects of NAM were dependent on the presence of SIRT1 and that stimulating SIRT1 was sufficient to produce the beneficial effects on mitochondrial function. The results are consistent with studies in high fat- fed mice where resveratrol impacted mitochondrial function and prevented hepatic steatosis \(^{34}\) .
+
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+In our study, NAM treatment did not significantly restore NAD+ levels whereas NR did, however NAM improved SIRT1 and PGC- 1α levels. Some studies have shown that NAM has the ability to increase cellular and blood NAD+ content in different metabolic disorder models (e.g. NAFLD mice, hepatocytes with endoplasmic reticulum stress) \(^{55 - 58}\) . However, other studies have found no direct effect of NAM supplementation on NAD+ levels \(^{18,59}\) . If the extra NAD that is synthesized, is readily used for deacetylation, then you would not see a significant increase. These differences in findings might also be related to the duration and variation in the dose of NAM and the animal models used affecting NAM metabolism. For example, NAM can affect SIRT1 activity differently by acting as a non- competitive end- product inhibitor and as a NAD+ precursor \(^{60}\) . In addition, NAM clearance pathways through MNAM- mediated SIRT1 protein stabilization can also regulate hepatic nutrient metabolism \(^{61,62}\) .  
+
+In conclusion, this work provides evidence for the role of TRP- NAM pathway in liver metabolic dysfunction in a mouse model of severe malnutrition, mediated through changes in levels of SIRT1. This study improves our understanding of the cellular pathophysiology of severe malnutrition. The results of this project could lead to the development of new interventions that target the TRP- NAM pathway which could then be taken to clinical trials.  
+
+## Methods  
+
+Animals and diets. A breeding colony of C57BL/6 mice was obtained from Jackson Laboratories (Bar Harbor, ME, USA). Male mice at 3 weeks post- partum were weaned and housed socially in filtered cages at The Hospital for Sick Children, Toronto. Weanling male C57BL/6J mice were randomized into different groups fed with control diet (18% protein) or malnourished diet (1% protein) for a period of 2 weeks. Diets were purchased from ENVIGO (Madison, WI, USA), and the protein proportions contribute to diet calories were primarily adjusted by casein and corn starch. After 7 days, malnourished subgroups were treated with modulators of the TRP- NAM pathway until sacrifice on day 14. Nicotinamide, nicotinamide- riboside and tryptophan were given by drinking water in a dose of 160 mg/kg body weight/day, and methionine was included in diets at a concentration of 0.75 g/kg diet \(^{15,59,63}\) . Nicotinamide, nicotinamide- riboside and tryptophan
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+were provided by Sigma- Aldrich (St. Louis, MO, USA). In a subset of mice, after \(1\%\) protein diet for 7 days, intraperitoneal injections treated with either resveratrol (25 mg/kg/d) or EX- 527 (10 mg/kg/d) with NAM were given for 7 consecutive days until sacrifice \(^{36,37,64}\) . All groups were housed in a temperature- controlled environment (23 °C), 12 h light- dark cycle, and had ad libitum access to diet and water throughout the study. All animal experiments were approved by the Animal Care Committee of The Hospital for Sick Children, Toronto (Animal Use Protocol Number: 1000030900).  
+
+Physiological parameters. Body weight, food intake, and liquid intake were monitored from day 1 to day 14. At the end of the experimental protocol (on day 14 post weaning), mice were humanely euthanized and necropsied. Final body weight, body length, and liver weight were recorded. Blood was collected by cardiac puncture. Liver tissue was collected for histology or stored at \(- 80^{\circ}\mathrm{C}\) for later use in biochemical analyses. Glucose concentration was determined via tail snip at 0h, 4h, 8h, and 12h fasting in the day light cycle, using an automatic glucometer (Freestyle, Abbott, IL). Metabolic rate was assessed by indirect calorimetry using the Columbus Instruments (Oxymax Lab Animal Monitoring System: CLAMS, Columbus, OH) \(^{18}\) .  
+
+Histology. Fresh livers tissues were fixed in \(4\%\) paraformaldehyde (PFA) overnight at \(4^{\circ}\mathrm{C}\) and then embedded in either paraffin or optimum cutting temperature (OCT) compound. Liver paraffin sections (5 \(\mu \mathrm{m}\) ) were stained with hematoxylin and eosin (H&E) for morphology. Liver OCT sections were stained with Oil red O (10 \(\mu \mathrm{m}\) ) for lipid droplets. Slides were visualized under a light microscope and was measured using Panoramic Viewer version 1.15 software (3DHISTECH Ltd, Budapest, Hungary). For each slide, at least five pictures were captured. Quantification analysis of the images was conducted using ImageJ 1.52v and Python 3.7.2.  
+
+Immunofluorescence. OCT- embedded liver sections were cut into \(4\mu \mathrm{m}\) slices for immunofluorescent staining. A fluorinated boron- dipyrromethene (BODYPI) antibody was used to visualize fat droplets. An HSP60 antibody was used to visualize mitochondrial morphology. Nuclei were counterstained with DAPI. Slides were mounted with mounting medium (Vector Laboratories Inc., Burlington, Canada) and images were acquired on a Nikon Spinning Disk Confocal Microscope (Nikon Inc., NY, USA). Additional information can be found in the Supplementary Table 3.
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+Plasma tryptophan analysis. Plasma samples were mixed with equal volumes of internal standard (Norleucine). Samples were centrifuged at 14000 rpm for 5 minutes and subsequently measured on Biochrom \(30+\) Amino Acid Analyzer (Biochrom, Cambridge, UK).  
+
+Triglyceride analysis. Liver and serum TG concentrations were quantified by a commercially available kit (Randox, London, UK). Liver tissue lipids were extracted with methanol- chloroform, dried and dissolved for TG analysis. Values were also normalized to protein concentrations determined using a bicinchoninic acid assay (BCA) kit (Thermo Fisher Scientific, USA).  
+
+Western blotting. Western blot analysis was conducted to measure the protein levels. Liver tissue protein was extracted through sonication of tissue with extraction buffer and protease inhibitor cocktail (Sigma- Aldrich). The protein concentration was measured using pierce BCA kit (Thermo Fisher Scientific). Equal concentrations of the samples were electrophoresed through \(4\% - 12\%\) Bis Tris gel and transferred onto a polyvinylidene fluoride (PVDF) membrane. Membranes were probed with 1:1000 dilutions of anti HSP60 (Abcam, USA), TOM20 (Santa Cruz, USA), Complex I (Abcam, USA), Complex IV (Abcam, USA), Complex V (Abcam, USA), SIRT1 (Cell Signalling, USA), PGC- 1α (Abcam, USA), p65 (Abcam, USA), Ac- p65 (Abcam, USA), LC3B (Sigma, USA). \(\beta\) - actin (Sigma, USA) was used as a loading control in 1:1000 dilution. Then proteins were visualized using a pierce enhanced chemiluminescence (ECL) plus kit (Invitrogen, CA, USA). Western blot quantification was performed using Image Studio (LI- COR Biosciences). Additional information can be found in the Supplementary Table 3.  
+
+qPCR. Total RNA was isolated from frozen liver tissue using Direct- zol RNA MiniPrep Kit (ZYMO research Inc., Irvine, CA, USA). cDNA was synthesized by the Super Script VILO cDNA Synthesis Kit (Thermo Fisher Scientific, USA). 500 ng of liver total RNA were used for cDNA synthesis. Ribosomal protein 113a (Rpl13a) was used as reference gene. qPCR was performed on CFX384 Touch Real- Time PCR Detection System (Bio- Rad, CA, USA). For mtDNA copy number measurements, 500 ng of genomic DNA were used for each qPCR reaction and \(\beta\) - globin were used as reference \(^{65}\) . Additional information can be found in the Supplementary Table 4.  
+
+Metabolomic analysis. Targeted metabolomic profiling (pathway specific assays) was performed by The Metabolomics Innovation Centre (TMIC, Edmonton, AB Canada). The quantitation of central carbon metabolism metabolites in mouse liver was measured by ultraperformance liquid
+
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+chromatography- tandem mass spectrometry (UPLC- MS/MS). A Dionex 3400 UHPLC system coupled to a 4000 QTRAP mass spectrometer was used. The MS instrument was operated in the multiple- reaction monitoring (MRM) mode with negative- ion (- ) or positive- ion (+) detection, depending on which groups of metabolites were measured. Each liver tissue sample was frozen and placed into an Eppendorf tube. Water, at \(2\mu \mathrm{L}\) per mg tissue, was added and the samples were homogenized for 1 min twice at a shaking frequency of \(30\mathrm{Hz}\) , with the aid of two 4- mm metal balls, on a MM 400 mill mixer. After a short- time centrifuge, methanol, at \(8\mu \mathrm{L}\) per mg tissue, was added and the samples were homogenized again for 1 min twice using the same settings. The samples were then sonicated in an ice- water bath for 3 min, followed by centrifugal clarification at \(15,000\mathrm{rpm}\) and \(5^{\circ}\mathrm{C}\) in an Eppendorf 5424R centrifuge for \(20\mathrm{min}\) . The clear supernatants were collected to conduct quantitation of TCA cycle carboxylic acids, glucose and selected sugar phosphates, and other phosphate- containing metabolites and nucleotides by UPLC- MS/MS. Concentrations of the detected metabolites were calculated from their linear- regression calibration curves with internal calibration. Tryptophan pathway metabolites were also measured using a UPLC- MS based targeted method<sup>66</sup>.  
+
+Lipidomic analysis. Lipidomic analysis was performed at Core Metabolomics and Lipidomics Laboratory, Wellcome Trust- Metabolic Research Laboratories (University of Cambridge, Cambridge, UK). Liver samples were homogenised, lipids were extracted according to a published procedure, and data was acquired through Direct Infusion Mass Spectrometry (DI- MS)<sup>67</sup>. Briefly, liver sections ( \(30\mathrm{mg / each}\) ) were homogenised (Tissue homogeniser II, Qiagen) in a buffer of chaotropes (guanidinium chloride (6 M) and thiourea (1.5 M) in deionised water, \(500\mu \mathrm{L / sample}\) ). The liver homogenates ( \(30\mu \mathrm{L}\) ) were injected into a well (96w plate, Esslab Plate+TM, \(2.4\mathrm{mL / well}\) , glass- coated) followed by methanol spiked with internal standards ( \(150\mu \mathrm{L}\) ), water ( \(500\mu \mathrm{L}\) ) and DMT ( \(500\mu \mathrm{L}\) , dichloromethane, methanol and triethylammonium chloride, 3:1:0.005). Most of the aqueous solution was removed (96 channel pipette). A portion of the organic solution ( \(20\mu \mathrm{L}\) ) was transferred to a high throughput plate ( \(384\mathrm{w}\) , glass coated, Esslab Plate+TM) before being dried ( \(\mathrm{N}_2\) (g)). The dried films were re- dissolved (TBME, \(30\mu \mathrm{L / well}\) ) and diluted with a stock mixture of alcohols and ammonium acetate ( \(100\mu \mathrm{L / well}\) ; propan- 2- ol: methanol, 2:1; \(\mathrm{CH}_3\mathrm{COONH}_4\) \(7.5\mathrm{mM}\) ). The analytical plate was heat- sealed and run immediately. Lipid fraction isolates were profiled using a three- part method in DI- MS<sup>67</sup>. All samples were infused into an Exactive Orbitrap (Thermo, Hemel Hampstead, UK), using a TriVersa NanoMate (Advion, Ithaca
+
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+US). Samples (15 \(\mu \mathrm{L}\) ) were sprayed at 1.2 kV in the positive ion mode. The Exactive started acquiring data 20 s after sample aspiration began. The Exactive acquired data with a scan rate of 1 Hz (resulting in a mass resolution of 100,000 full width at half- maximum [fwhm] at 400 \(m / z\) ). The Automatic Gain Control was set to 3,000,000 and the maximum ion injection time to 50 ms. After 72 s of acquisition in positive mode the NanoMate and the Exactive switched over to negative ionization mode, decreasing the voltage to - 1.5 kV and the maximum ion injection time to 50 ms. The spray was maintained for another 66 s, after which the NanoMate and Exactive switched over to negative mode with in- source fragmentation (also known as collision- induced dissociation, CID; 70 eV) for a further 66 s. After this time, the spray was stopped and the tip discarded, before the analysis of the next sample began. The sample plate was kept at 15 \(^\circ \mathrm{C}\) throughout the acquisition. Samples were run in row order. The instrument was operated in full scan mode from \(m / z\) 150- 1200 Da (for singly charged species).  
+
+Statistical analysis. Statistical significance for the difference between two groups was calculated by using an unpaired two- tailed student's T- test. Statistical significance for the difference among more than two groups was calculated by using an ordinary one- way ANOVA followed by the Turkey's post hoc test<sup>68</sup>. The FDR and Bonferroni correction were applied to the metabolomic and lipidomic metabolites. Statistical analysis was performed with R software (version 3.5.2) and MetaBoAnalyst (version 4.0). Statistical significance was given as \(* \mathrm{p} < 0.05\) , \(** \mathrm{p} < 0.01\) , and \(*** \mathrm{p} < 0.001\) . The results are expressed as mean \(\pm\) standard error of mean (S.E.M.), unless otherwise indicated.  
+
+## Data availability  
+
+All relevant data of this study are available within the paper and its supplementary information files. All data that support this study are available from the corresponding authors upon reasonable request.
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+562 41. Park, K.S., et al. Fetal and early postnatal protein malnutrition cause long-term changes in rat liver and muscle mitochondria. The Journal of nutrition 133, 3085- 3090 (2003). 563 42. Wu, Z., et al. Mechanisms controlling mitochondrial biogenesis and respiration through the thermogenic coactivator PGC- 1. Cell 98, 115- 124 (1999). 565 43. Piccinin, E., Villani, G. & Moschetta, A. Metabolic aspects in NAFLD, NASH and hepatocellular carcinoma: the role of PGC1 coactivators. Nature Reviews Gastroenterology & Hepatology 16, 160- 174 (2019). 568 44. Scarpulla, R.C. Metabolic control of mitochondrial biogenesis through the PGC- 1 family regulatory network. Biochimica et Biophysica Acta (BBA)- Molecular Cell Research 1813, 1269- 1278 (2011). 572 45. Leone, T.C., et al. PGC- 1α deficiency causes multi- system energy metabolic derangements: muscle dysfunction, abnormal weight control and hepatic steatosis. PLoS biology 3(2005). 573 46. Rodgers, J.T., et al. Nutrient control of glucose homeostasis through a complex of PGC- 1α and SIRT1. Nature 434, 113- 118 (2005). 575 47. Lee, I.H., et al. A role for the NAD- dependent deacetylase Sirt1 in the regulation of autophagy. Proc Natl Acad Sci U S A 105, 3374- 3379 (2008). 578 48. Kitada, M., Ogura, Y. & Koya, D. Chapter 3 - Role of sirt1 as a regulator of autophagy. in Autophagy: Cancer, Other Pathologies, Inflammation, Immunity, Infection, and Aging (ed. Hayat, M.A.) 89- 100 (Academic Press, San Diego, 2016). 581 49. El Assar, M., et al. Better nutritional status is positively associated with mRNA expression of SIRT1 in community- dwelling older adults in the Toledo Study for Healthy Aging. J Nutr 148, 1408- 1414 (2018). 584 50. Chalkiadaki, A. & Guarente, L. High- fat diet triggers inflammation- induced cleavage of SIRT1 in adipose tissue to promote metabolic dysfunction. Cell metabolism 16, 180- 188 (2012). 587 51. Wang, S., et al. Nicotinamide riboside attenuates alcohol induced liver injuries via activation of SirT1/PGC- 1alpha/mitochondrial biosynthesis pathway. Redox Biol 17, 89- 98 (2018). 590 52. Ritze, Y., Bardos, G., Hubert, A., Bohle, M. & Bischoff, S.C. Effect of tryptophan supplementation on diet- induced non- alcoholic fatty liver disease in mice. Br J Nutr 112, 1- 7 (2014). 593 53. Morizono, S., et al. Nicotinamide, not N1 methylnicotinamide, ameliorates hepatic steatosis via NAD- depended sirtuin activation. Journal of Hepatology 68, S350- S351 (2018). 596 54. Mejia, S.Á., et al. Nicotinamide prevents sweet beverage- induced hepatic steatosis in rats by regulating the G6PD, NADPH/NADP+ and GSH/GSSG ratios and reducing oxidative and inflammatory stress. European journal of pharmacology 818, 499- 507 (2018). 599 55. Li, J., et al. Nicotinamide ameliorates palmitate- induced ER stress in hepatocytes via cAMP/PKA/CREB pathway- dependent Sirt1 upregulation. Biochimica et Biophysica Acta (BBA)- Molecular Cell Research 1853, 2929- 2936 (2015). 602 56. Majamaa, K., Rusanen, H., Remes, A.M., Pyhtinen, J. & Hassinen, I.E. Increase of blood NAD+ and attenuation of lactacidemia during nicotinamide treatment of a patient with the MELAS syndrome. Life sciences 58, 691- 699 (1996). 605 57. Williams, P.A., et al. Vitamin B3 modulates mitochondrial vulnerability and prevents glaucoma in aged mice. Science 355, 756- 760 (2017).
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+607 58. Liu, D., Gharavi, R., Pitta, M., Gleichmann, M. & Mattson, M.P. Nicotinamide prevents 608 NAD+ depletion and protects neurons against excitotoxicity and cerebral ischemia: NAD+ 609 consumption by SIRT1 may endanger energetically compromised neurons. 610 Neuromolecular Med 11, 28-42 (2009). 611 59. Sambeat, A., et al. Endogenous nicotinamide riboside metabolism protects against diet- 612 induced liver damage. Nat Commun 10, 4291 (2019). 613 60. Hwang, E.S. & Song, S.B. Nicotinamide is an inhibitor of SIRT1 in vitro, but can be a 614 stimulator in cells. Cell Mol Life Sci 74, 3347-3362 (2017). 615 61. Hong, S., et al. Nicotinamide N-methyltransferase regulates hepatic nutrient metabolism 616 through Sirt1 protein stabilization. Nature medicine 21, 887 (2015). 617 62. Canto, C., Menzies, K.J. & Auwers, J. NAD+ metabolism and the control of energy 618 homeostasis: a balancing act between mitochondria and the nucleus. Cell metabolism 22, 31-53 (2015). 619 63. Hashimoto, T., et al. ACE2 links amino acid malnutrition to microbial ecology and 620 intestinal inflammation. Nature 487, 477-481 (2012). 621 64. Ma, S., et al. SIRT1 activation by resveratrol alleviates cardiac dysfunction via 622 mitochondrial regulation in diabetic cardiomyopathy mice. Oxidative medicine and 623 cellular longevity 2017(2017). 624 65. Rooney, J.P., et al. PCR based determination of mitochondrial DNA copy number in 625 multiple species. in Mitochondrial Regulation 23-38 (Springer, 2015). 626 66. Whiley, L., et al. Ultrahigh-Performance liquid chromatography tandem mass 627 spectrometry with electrospray ionization quantification of tryptophan metabolites and 628 markers of gut health in serum and plasma - application to clinical and epidemiology 629 cohorts. Analytical chemistry 91, 5207-5216 (2019). 630 67. Furse, S., et al. A high-throughput platform for detailed lipidomic analysis of a range of 631 mouse and human tissues. Analytical and Bioanalytical Chemistry, 1-12 (2020). 632 68. Singh, R., et al. Autophagy regulates lipid metabolism. Nature 458, 1131 (2009).
+
+<--- Page Split --->
+
+## Acknowledgements  
+
+We thank The Metabolomics Innovation Centre for performing targeted metabolomic assays, thank Lucy Wang and Ainsley Su- Williams for performing the experiments, and thank Bijun Wen, Celine Bourdon, and Amber Farooqui for help with statistical analyzing methods and animal use protocol update. This research was supported by the Bill & Melinda Gates Foundation.  
+
+## Author contributions  
+
+R.H.J.B. and G.H. were primarily responsible for the study design. G.H. wrote the manuscript. G.H., C.L., L.C., S.F., J.S., M.K.T., D.L., M.C., C.J.V., and G.B.G. contributed to the conduction of lab experiments. G.H., L.C., S.F., and J.S. contributed to data analysis. P.K.K., A.K., and B.M.B. provided expertise, interpreted results, and commented on the manuscript. All authors contributed to editing of the manuscript. R.H.J.B. was responsible for the final content of the manuscript.  
+
+## Competing interests  
+
+All participants declare no competing interests.  
+
+## Additional information  
+
+Supplementary Information is available for this paper.  
+
+Correspondence and requests for materials should be addressed to R.H.J.B.
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Fig. 1 Feeding a \(1\%\) protein diet with or without NAM supplementation on basic animal characteristics. a Experimental design. b Average food and liquid intake during day 7 to day 14 \((n = 7\) for \(18\%\) \(n = 5\) for \(1\%\) and \(1\% +\) NAM). c Body weight change throughout experiment \((n = 15)\) d Final body weight and body length assessed on day 14 \((n = 15)\) . e Liver weight and liver weight/body weight ratio \((n = 12\) for \(18\%\) \(n = 10\) for \(1\%\) and \(1\% +\) NAM). f Fasting glucose levels \((n = 7\) for \(18\%\) \(n = 8\) for \(1\%\) \(n = 7\) for \(1\% +\) NAM). g Respiratory exchange ratio (RER) and energy expenditure \((n = 7\) for \(18\%\) \(n = 6\) for \(1\%\) \(n = 7\) for \(1\% +\) NAM). \(^{*}\mathrm{p}< 0.05\) \(^{**}\mathrm{p}< 0.01\) \(^{**}\mathrm{p}< 0.001\) ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. </center>
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Fig. 2 The effect of \(1\%\) protein feeding with or without NAM supplementation on hepatic lipid accumulation. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Representative oil red o stain staining images of the liver (20X magnification). Fat droplet was stained in red, and nucleus was stained in purple. c Representative immunofluorescence images of the liver (40X magnification). BODYPY was used to stain fat droplet in green, and DAPI was used to counter stain nucleus in blue. d Quantification of fat vacuoles area (n=9). e Liver TG concentrations (n=6). f Serum TG concentrations (n=6). \(^{*}\mathrm{p}< 0.05\) , \(^{**}p< 0.01\) , \(^{***}p< 0.001\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated. </center>
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Fig. 3 The effect of NAM supplementation on mitochondrial characteristics of 1% protein fed model. a Representative immunofluorescence images of mitochondrial (60X magnification). HSP60 was used to stain mitochondrial in red, and DAPI was used to counter stain nucleus in blue. b mtDNA copy number (n=6). c, d Western blots and quantification of HSP60 and TOM20 (n=3). e ATP levels (n=11 for 18% and 1%; n=7 for 1%+NAM). f, g Western blots and quantification of complex I, complex IV and complex V (n=3). h mRNA expression of \(\beta\) -oxidation genes (n=6). i mRNA expression of lipid genesis genes (n=6). \(^{*}\mathrm{p}< 0.05\) , \(^{**}p< 0.01\) , \(^{***}p< 0.001\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated. </center>
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Fig. 4 Hepatic metabolomic and lipidomic profiles under 18% protein diet, 1% protein diet, and 1% protein diet with NAM supplementation. a sPLS-DA and correlation circle plots of hepatic central carbon metabolism showing separation of 18% and 1% protein diet group (n=5). b sPLS-DA and correlation circle plots of hepatic central carbon metabolism showing separation of 1% protein diet and NAM treated group (n=5 for 1%; n=7 for 1%+NAM). c sPLS-DA and correlation circle plots of hepatic lipidomics showing separation of 18% and 1% protein diet group (n=6). d sPLS-DA and correlation circle plots of hepatic lipidomics showing separation of 1% protein diet and NAM treated group (n=6). </center>
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Fig. 5 The effect of \(1\%\) protein feeding with or without NAM supplementation on TRP-NAM pathway metabolites, SIRT1 and downstream targets, and autophagy levels. a Hepatic NAD+ levels and TRP-NAM pathway metabolites (n=6). b SIRT1 and PGC-1α western blots (n=3). c p65 and Acetyl-p65 western blots (n=3). d Autophagy markers LC3 western blots (n=3). e Quantification of protein levels in western blots. \(^{*}p < 0.05\) , \(^{**}p < 0.01\) , \(^{***}p < 0.001\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. </center>
+
+<--- Page Split --->
+![](images/Figure_6.jpg)
+
+<center>Fig. 6 The effect of SIRT1 modulators on basic animal characteristics. a Experiment design. b Body weight change throughout experiment (n=6). c Average food and liquid intake during day 7 to day 14 (n=6). d Final body weight, body length, and weight for length ratio assessed at day 14 (n=6). e Liver weight, liver weight to body weight ratio (n=6). \*p < 0.05, \*\*p < 0.01, \*\*\*p < 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. </center>
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Fig. 7 The effect of SIRT1 modulators on hepatic steatosis, mitochondrial characteristics, SIRT1 and its downstream targets. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Quantification of liver histology and TG levels (n=6). c mtDNA copy number (n=6). d ATP levels (n=6). e mRNA expression of \(\beta\) -oxidation genes (n=6). f mRNA expression of lipid genesis genes (n=6). g SIRT1 and PGC-1 \(\alpha\) western blots and quantification (n=3). \(^{*}\mathrm{p}< 0.05\) , \(^{**}p< 0.01\) , \(^{**}p<\) 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated. </center>
+
+<--- Page Split --->
+![](images/Figure_8.jpg)
+
+<center>Fig. 8 Proposed model of the role of the TRP-NAM pathway in malnutrition-induced hepatic metabolic disturbances. In protein malnutrition, decreased TRP availability will decrease the kynurenine pathway activity, which is associated with NAD+ and NAM deficiency. This would disturb NAD+ salvage pathway, including SIRT1, influence its downstream target PGC-1α and autophagy, which affect mitochondrial quality and function. These changes lead to ATP depletion and lipid accumulation in the liver. We hypothesize that supplement with TRP-NAM modulator would influence NAD+ salvage pathway. This would thereby activate SIRT1, influence PGC-1α deacetylation and autophagy, which will have a positive effect on mitochondrial health, affect mitochondrial biogenesis and clearance of damaged mitochondrial, then improve ATP generation and reduce lipid accumulation in the liver. </center>
+
+<--- Page Split --->
+
+## Figures 
+
+![](images/Figure_1.jpg)
+
+ 
+
+<center>Figure 1</center> 
+
+Feeding a 1% protein diet with or without NAM supplementation on basic animal characteristics. a Experimental design. b Average food and liquid intake during day 7 to day 14 (n=7 for 18%; n=5 for 1% and 1%+NAM). c Body weight change throughout experiment (n=15). d Final body weight and body
+
+<--- Page Split --->
+
+length assessed on day 14 (n=15). e Liver weight and liver weight/body weight ratio (n=12 for 18%; n=10 for 1% and 1%+NAM). f Fasting glucose levels (n=7 for 18%; n=8 for 1%; n=7 for 1%+NAM). g Respiratory exchange ratio (RER) and energy expenditure (n=7 for 18%; n=6 for 1%; n=7 for 1%+NAM). \*p < 0.05, \*\*p < 0.01, \*\*\*p < 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. 
+
+![](images/Figure_2.jpg)
+
+ 
+
+<center>Figure 2</center>
+
+<--- Page Split --->
+
+The effect of \(1\%\) protein feeding with or without NAM supplementation on hepatic lipid accumulation. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Representative oil red o stain staining images of the liver (20X magnification). Fat droplet was stained in red, and nucleus was stained in purple. c Representative immunofluorescence images of the liver (40X magnification). BODYPY was used to stain fat droplet in green, and DAPI was used to counter stain nucleus in blue. d Quantification of fat vacuoles area \((n = 9)\) . e Liver TG concentrations \((n = 6)\) . f Serum TG concentrations \((n = 6)\) . \(*p < 0.05\) , \(**p < 0.01\) , \(***p < 0.001\) , ns as not significant, one way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated.  
+
+![](images/Figure_3.jpg)
+
+<center>Figure 3 </center>  
+
+The effect of NAM supplementation on mitochondrial characteristics of \(1\%\) protein fed model. a Representative immunofluorescence images of mitochondrial (60X magnification). HSP60 was used to stain mitochondrial in red, and DAPI was used to counter stain nucleus in blue. b mtDNA copy number
+
+<--- Page Split --->
+
+(n=6). c, d Western blots and quantification of HSP60 and TOM20 (n=3). e ATP levels (n=11 for 18% and 1%; n=7 for 1%+NAM). f, g Western blots and quantification of complex I, complex IV and complex V (n=3). h mRNA expression of \(\beta\) -oxidation genes (n=6). i mRNA expression of lipid genesis genes (n=6). \*p < 0.05, \*\*p < 0.01, \*\*\*p < 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. Scale bars are as indicated.  
+
+![](images/Figure_4.jpg)
+
+<center>Figure 4 </center>  
+
+Hepatic metabolomic and lipidomic profiles under 18% protein diet, 1% protein diet, and 1% protein diet with NAM supplementation. a sPLS- DA and correlation circle plots of hepatic central carbon metabolism showing separation of 18% and 1% protein diet group (n=5). b sPLS- DA and correlation circle plots of hepatic central carbon metabolism showing separation of 1% protein diet and NAM treated group (n=5 for 1%; n=7 for 1%+NAM). c sPLS- DA and correlation circle plots of hepatic lipidomics showing separation of 18% and 1% protein diet group (n=6). d sPLS- DA and correlation circle plots of hepatic lipidomics showing separation of 1% protein diet and NAM treated group (n=6).
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5 </center>  
+
+The effect of \(1\%\) protein feeding with or without NAM supplementation on TRP- NAM pathway metabolites, SIRT1 and downstream targets, and autophagy levels. a Hepatic NAD+ levels and TRP- NAM pathway metabolites \((n = 6)\) . b SIRT1 and PGC- 1 \(\alpha\) western blots \((n = 3)\) . c p65 and Acetyl- p65 western blots \((n = 3)\) . d Autophagy markers LC3 western blots \((n = 3)\) . e Quantification of protein levels in western blots.
+
+<--- Page Split --->
+
+\(*p < 0.05\) , \(**p < 0.01\) , \(***p < 0.001\) , ns as not significant, one- way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M.  
+
+![](images/Figure_6.jpg)
+
+<center>Figure 6 </center>  
+
+The effect of SIRT1 modulators on basic animal characteristics. a Experiment design. b Body weight change throughout experiment \((n = 6)\) . c Average food and liquid intake during day 7 to day 14 \((n = 6)\) . d Final body weight, body length, and weight for length ratio assessed at day 14 \((n = 6)\) . e Liver weight, liver weight to body weight ratio \((n = 6)\) . \(*p < 0.05\) , \(**p < 0.01\) , \(***p < 0.001\) , ns as not significant, one- way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M.
+
+<--- Page Split --->
+![](images/Figure_7.jpg)
+
+<center>Figure 7 </center>  
+
+The effect of SIRT1 modulators on hepatic steatosis, mitochondrial characteristics, SIRT1 and its downstream targets. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Quantification of liver histology and TG levels \((n = 6)\) . c mtDNA copy number \((n = 6)\) . d ATP levels \((n = 6)\) . e mRNA expression of \(\beta\) - oxidation genes \((n = 6)\) . f mRNA expression of lipid genesis genes \((n = 6)\) . g SIRT1 and PGC- 1α western blots and quantification \((n = 3)\) . \(^{*}p < 0.05\) , \(^{**}p < 0.01\) , \(^{***}p < 0.001\) , ns as not significant, one- way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated.
+
+<--- Page Split --->
+![](images/Figure_8.jpg)
+
+<center>Figure 8 </center>  
+
+Proposed model of the role of the TRP- NAM pathway in malnutrition- induced hepatic metabolic disturbances. In protein malnutrition, decreased TRP availability will decrease the kynurenine pathway activity, which is associated with NAD+ and NAM deficiency. This would disturb NAD+ salvage pathway, including SIRT1, influence its downstream target PGC- 1α and autophagy, which affect mitochondrial quality and function. These changes lead to ATP depletion and lipid accumulation in the liver. We hypothesize that supplement with TRP- NAM modulator would influence NAD+ salvage pathway. This would thereby activate SIRT1, influence PGC- 1α deacetylation and autophagy, which will have a positive effect on mitochondrial health, affect mitochondrial biogenesis and clearance of damaged mitochondrial, then improve ATP generation and reduce lipid accumulation in the liver.  
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+Supplementary information.pdf
+
+<--- Page Split --->

preprint/preprint__603ef0a9f08b3144aab5e4c8bcfcd0a27a21acb9266edd87d344cef28d26eac2/preprint__603ef0a9f08b3144aab5e4c8bcfcd0a27a21acb9266edd87d344cef28d26eac2_det.mmd

@@ -0,0 +1,432 @@
+<|ref|>title<|/ref|><|det|>[[44, 106, 931, 208]]<|/det|>
+# The role of the tryptophan-nicotinamide pathway in a model of severe malnutrition induced liver dysfunction  
+
+<|ref|>text<|/ref|><|det|>[[44, 230, 505, 272]]<|/det|>
+Guanlan Hu University of Toronto/The Hospital for Sick Children  
+
+<|ref|>text<|/ref|><|det|>[[44, 277, 505, 318]]<|/det|>
+Catriona Ling University of Toronto/The Hospital for Sick Children  
+
+<|ref|>text<|/ref|><|det|>[[44, 324, 316, 364]]<|/det|>
+Lijun Chi The Hospital for Sick Children  
+
+<|ref|>text<|/ref|><|det|>[[44, 370, 622, 411]]<|/det|>
+Samuel Furse University of Cambridge https://orcid.org/0000- 0003- 4267- 2051  
+
+<|ref|>text<|/ref|><|det|>[[44, 416, 625, 457]]<|/det|>
+Albert Koulman University of Cambridge https://orcid.org/0000- 0001- 9998- 051X  
+
+<|ref|>text<|/ref|><|det|>[[44, 462, 510, 503]]<|/det|>
+Jonathan Swann Imperial College London/University of Southampton  
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+Mehakpreet Thind University of Toronto/The Hospital for Sick Children  
+
+<|ref|>text<|/ref|><|det|>[[44, 555, 279, 595]]<|/det|>
+Dorothy Lee Hospital for Sick Children  
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+<|ref|>text<|/ref|><|det|>[[44, 601, 316, 641]]<|/det|>
+Marjolein Calon The Hospital for Sick Children  
+
+<|ref|>text<|/ref|><|det|>[[44, 648, 728, 688]]<|/det|>
+Christian Versloot University Medical Center Groningen https://orcid.org/0000- 0002- 3991- 6652  
+
+<|ref|>text<|/ref|><|det|>[[44, 694, 371, 734]]<|/det|>
+Barbara Bakker University Medical Center Groningen  
+
+<|ref|>text<|/ref|><|det|>[[44, 740, 465, 780]]<|/det|>
+Gerard Gonzales Ghent University/The Hospital for Sick Children  
+
+<|ref|>text<|/ref|><|det|>[[44, 787, 501, 827]]<|/det|>
+Peter Kim Hospital for Sick Children, University of Toronto  
+
+<|ref|>text<|/ref|><|det|>[[44, 832, 500, 873]]<|/det|>
+Robert Bandsma ( \(\boxed{\bullet}\) robert.bandsma@sickkids.ca) The Hospital for Sick Children
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 912, 66]]<|/det|>
+**Keywords:** Severe Malnutrition, Metabolic Dysfunction, Hepatic Mitochondrial Turnover and Function
+
+<|ref|>text<|/ref|><|det|>[[42, 86, 348, 101]]<|/det|>
+**Posted Date**: November 19th, 2020
+
+<|ref|>text<|/ref|><|det|>[[42, 123, 464, 140]]<|/det|>
+**DOI**: https://doi.org/10.21203/rs.3.rs-104804/v1
+
+<|ref|>text<|/ref|><|det|>[[42, 161, 909, 201]]<|/det|>
+**License:** © This work is licensed under a Creative Commons Attribution 4.0 International License.Read Full License
+
+<--- Page Split --->
+<|ref|>title<|/ref|><|det|>[[95, 106, 857, 165]]<|/det|>
+# The role of the tryptophan-nicotinamide pathway in a model of severe malnutrition induced liver dysfunction  
+
+<|ref|>text<|/ref|><|det|>[[70, 186, 884, 250]]<|/det|>
+Guanlan Hu \(^{1,2}\) , Catriona Ling \(^{1,2}\) , Lijun Chi \(^{2}\) , Samuel Furs \(^{3}\) , Albert Koulman \(^{3}\) , Jonathan Swann \(^{4,5}\) , Mehakpreet K. Thind \(^{1,2}\) , Dorothy Lee \(^{2}\) , Marjolein Calon \(^{2}\) , Christian J. Versloot \(^{6}\) , Barbara M. Bakker \(^{6}\) , Gerard B. Gonzales \(^{2,7,8}\) , Peter K. Kim \(^{9,10}\) & Robert H.J. Bandma \(^{1,2,11,12}\) \*  
+
+<|ref|>text<|/ref|><|det|>[[67, 272, 888, 820]]<|/det|>
+1 Department of Nutritional Sciences, Faculty of Medicine, University of Toronto, Toronto, ON M5G 1A8, Canada  2 Translational Medicine Program, The Hospital for Sick Children, Toronto, ON M5G 0A4, Canada  3 Core Metabolomics and Lipidomics Laboratory, Wellcome Trust-Metabolic Research Laboratories, Institute of Metabolic Sciences, University of Cambridge, Cambridge, CB2 0QQ, United Kingdom  4 School of Human Development and Health, Faculty of Medicine, University of Southampton, SO16 6YD, United Kingdom  5 Department of Metabolism, Digestion and Reproduction, Faculty of Medicine, Imperial College London, SW7 2AZ, United Kingdom  6 Laboratory of Pediatrics, Center for Liver, Digestive, and Metabolic Diseases, University of Groningen, University Medical Center Groningen, Groningen, The Netherlands  7 Gastroenterology, Department of Pediatrics and Internal Medicine, Faculty of Medicine and Health Sciences, Ghent University, Ghent 9000, Belgium  8 VIB Inflammation Research Center, Zwijnaarde 9052, Belgium  9 Department of Biochemistry, University of Toronto, Toronto, ON M5S 1A8, Canada  10 Cell Biology Program, The Hospital for Sick Children, Toronto, ON M5G 0A4, Canada  11 Division of Gastroenterology, Hepatology, and Nutrition, The Hospital for Sick Children, Toronto, ON M5G 0A4, Canada 12 The Childhood Acute Illness & Nutrition Network (CHAIN), Blantyre, Malawi  \* Correspondence and requests for materials should be addressed to  Robert H.J. Bandma, Translational Medicine Program, The Hospital for Sick Children, Peter Gilgan Centre for Research and Learning, 686 Bay Street, Toronto, ON M5G 0A4, Canada. Tel.: +1 4168137654x9057; Fax: +1 4168134972 (R.H.J. Bandma).  E-mail address: robert.bandma@sickkids.ca (R.H.J. Bandma)
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[68, 93, 217, 115]]<|/det|>
+## Abstract  
+
+<|ref|>text<|/ref|><|det|>[[112, 139, 886, 420]]<|/det|>
+Mortality in children with severe malnutrition is strongly related to signs of metabolic dysfunction, such as hypoglycemia. Lower circulating tryptophan levels in children with severe malnutrition suggest a possible disturbance in the tryptophan- nicotinamide (TRP- NAM) pathway and subsequently NAD+ dependent metabolism regulator sirtuin1 (SIRT1). We report that severe malnutrition in weanling mice, induced by feeding a low protein diet, leads to an impaired TRP- NAM pathway and affects hepatic mitochondrial turnover and function. We demonstrate that stimulating the TRP- NAM pathway improves hepatic mitochondrial and overall metabolic function which is dependent on SIRT1. Activating SIRT1 is sufficient to induce improvement in metabolic functions. Our findings indicate that modulating the TRP- NAM pathway can partially improve liver metabolic function in severe malnutrition and could lead to the development of new interventions for children with severe malnutrition.
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[66, 92, 261, 115]]<|/det|>
+## 44 Introduction  
+
+<|ref|>text<|/ref|><|det|>[[66, 139, 886, 266]]<|/det|>
+Malnutrition contributes to nearly \(45\%\) of deaths among children under 5 years of age worldwide<sup>1</sup>. Malnourished children, especially those with severe malnutrition are at a substantially increased risk of mortality compared to well- nourished children<sup>2</sup>. The current treatment guidelines developed by the World Health Organization (WHO) for children with severe malnutrition are based on limited scientific evidence<sup>3</sup>. Thus, new evidence- based interventions are urgently needed.  
+
+<|ref|>text<|/ref|><|det|>[[66, 285, 886, 490]]<|/det|>
+The liver is a central organ that regulates nutrient metabolism. In severe malnutrition, hepatic metabolism has been found to be disturbed and is associated with hypoglycemia, hypoalbuminemia, and steatosis<sup>4- 6</sup>. Children with severe malnutrition have impaired hepatic glucose production, which increases the risk of hypoglycemia and is related to mortality<sup>5</sup>. We recently discovered in both patients and a rodent model of severe malnutrition, that hepatic mitochondrial function is impaired leading to reduced nutrient oxidation and adenosine triphosphate (ATP) depletion<sup>5,6</sup>. However, the pathophysiology of hepatic mitochondrial dysfunction in severe malnutrition remains poorly understood.  
+
+<|ref|>text<|/ref|><|det|>[[66, 508, 886, 846]]<|/det|>
+Children with severe malnutrition have been found to have significantly lower serum tryptophan levels<sup>7- 9</sup>. As an essential amino acid, tryptophan is crucial for growth and protein synthesis. It is also a precursor of nicotinamide adenine dinucleotide (NAD+) and nicotinamide adenine dinucleotide phosphate (NADP+), which are essential co- factors in metabolic and biosynthesis pathways. We have previously shown that higher excretion of \(N\) - methylnicotinamide, a urinary biomarker of NAD+ and nicotinamide availability, was associated with catch- up growth in stunted infants<sup>10</sup>. NAD+ is also a co- substrate for sirtuin1 (SIRT1), which is an important enzyme for mitochondrial health and biogenesis through activation of peroxisome proliferator- activated receptor- gamma coactivator- 1 alpha (PGC- 1α)<sup>11</sup>. SIRT1 has also been shown to regulate autophagy<sup>12- 14</sup>. There have been reports that targeting this pathway in non- alcoholic fatty liver disease (NAFLD) has beneficial effects on hepatic metabolism<sup>15- 18</sup>. The role of tryptophan nicotinamide (TRP- NAM) pathway in severe malnutrition- associated hepatic metabolic dysfunction remains unknown.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 293]]<|/det|>
+In this study we aimed to characterize the role of the TRP- NAM pathway in hepatic metabolic dysfunction in a mouse model of severe malnutrition. We demonstrate that the TRP- NAM pathway is affected in this model and that hepatic mitochondrial dysfunction is related to deficiencies in the TRP- NAM pathway. We demonstrate supplementing with NAM and related components of this pathway improve mitochondrial and overall hepatic metabolic dysfunction. We find that the effects of modulating the TRP- NAM pathway are mediated through SIRT1. These findings identify the importance of the TRP- NAM pathway and SIRT1 in malnutrition- associated hepatic metabolic dysfunction.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 358, 201, 379]]<|/det|>
+## Results  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 405, 671, 425]]<|/det|>
+## Feeding a low protein diet leads to hepatic steatosis in young mice.  
+
+<|ref|>text<|/ref|><|det|>[[112, 445, 886, 755]]<|/det|>
+To develop a mouse model of severe malnutrition, we fed 3- weeks- old weanling male C57BL/6J mice a \(1\%\) protein isocaloric diet for two weeks (malnourished group) and compared it to the control group fed an \(18\%\) protein diet (control group) (Fig. 1a). Mice subjected to the \(1\%\) protein diet lost a significant amount of body weight (approximately \(20\%\) ) over two weeks and had a lower body length and weight for length ratio compared to the \(18\%\) protein- fed control group (Fig. 1b- d). The \(1\%\) protein- fed mice showed a lower liver weight and liver to body weight ratio compared to control (Fig. 1e). Lower glucose concentrations were also noted in the \(1\%\) protein- fed mice before and after fasting (Fig. 1f), consistent with reduced hepatic glucose production. The respiratory exchange ratio (RER) was lower during the dark phase and higher during the light phase in \(1\%\) protein- fed mice, indicating a loss of the day- night feeding cycle in this group. Energy expenditure was lower in \(1\%\) protein- fed mice compared to the \(18\%\) protein- fed control group (Fig. 1g).  
+
+<|ref|>text<|/ref|><|det|>[[112, 775, 886, 900]]<|/det|>
+Histological H&E staining and Oil Red O staining of the livers identified steatosis in the mice fed with \(1\%\) protein diet as evidenced by an increase in fat vacuoles and larger fat droplets compared to the mice fed with \(18\%\) protein diet (Fig 2a- b). The increase in lipid droplets in the liver of the \(1\%\) protein- fed mice was confirmed by immunofluorescence staining with BODIPY (Fig. 2c). Further quantification of histology slides showed consistency with these observations (Fig. 2d)
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 886, 190]]<|/det|>
+and was validated by measurement of liver triglyceride (TG) levels (Fig. 2e). Serum TGs were lower in the \(1\%\) protein- fed group, indicating steatosis is not linked to hypertriglyceridemia (Fig. 2f). Together, these results indicate that the \(1\%\) protein diet induces hepatic steatosis in mice similar to those observed in patients and rat model of severe malnutrition \(^{2,6}\) .  
+
+<|ref|>sub_title<|/ref|><|det|>[[113, 252, 884, 297]]<|/det|>
+## NAM and TRP-NAM pathway modulators reduce the development of low protein diet-induced hepatic steatosis.  
+
+<|ref|>text<|/ref|><|det|>[[112, 316, 886, 626]]<|/det|>
+Examination for blood tryptophan levels showed the \(1\%\) protein diet mice to be lower than \(18\%\) protein diet control animals \((43.0\pm 5.0 \mu \mathrm{mol / L}\) and \(88.4\pm 13.2 \mu \mathrm{mol / L}\) respectively, \(\mathrm{p} = 0.0035\) ). To examine the role of a reduced tryptophan levels and possible nicotinamide (NAM) deficiency on liver health, the \(1\%\) protein- fed mice were supplemented with \(160 \mathrm{mg / kg}\) body weight NAM from day 7 to day 14 (Fig. 1a). NAM treatment did not alter the average body weight, body length, or food and liquid consumption in the \(1\%\) protein- fed group (Fig. 1b- d). The mice treated with NAM had no significant difference in liver weight, liver/body weight ratio, or fasting glucose levels compared to the untreated \(1\%\) protein diet- fed mice (Fig. 1e- f). RER and energy expenditure were not affected by NAM treatment (Fig. 1g). NAM treatment improved the hepatic steatosis compared to the \(1\%\) protein- fed mice, indicated by a reduction in the fat vacuoles area and a \(30\%\) reduction in liver TG levels compared to untreated animals (Fig. 2a- e). The NAM treatment had no effect on serum TG concentrations (Fig. 2f).  
+
+<|ref|>text<|/ref|><|det|>[[112, 646, 886, 903]]<|/det|>
+To determine whether the effect of NAM treatment was due to improvement of the NAD salvage pathway specifically, we treated the \(1\%\) protein- fed mice with nicotinamide riboside (NR) or tryptophan (TRP). Both NR and TRP act as NAD+ precursors in the NAD salvage pathway \(^{16}\) . The allocated interventions were given from day 7 to day 14 (Supplementary Fig. 1a). NR and TRP supplementation, similar to NAM treatment, did not recover body weight, body length or liver weight/body weight ratio compared to the untreated \(1\%\) protein- fed group (Supplementary Fig. 1b- e). Similar to the NAM treated malnourished mice, hepatic steatosis was reduced in the NR and TRP treated groups (Supplementary Fig. 2a- f). To determine whether the effects were specific to the TRP- NAM pathway, we also performed similar experiments in mice who received supplementation with methionine (MET), another essential amino acid like tryptophan. This
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 886, 269]]<|/det|>
+particular amino acid was chosen as MET has been shown to decrease hepatic steatosis in mice on ketogenic diets<sup>19</sup>, and diets completely devoid of MET and choline can induce hepatic steatosis<sup>20,21</sup>. Supplementation with methionine did not improve hepatic steatosis among the 1% protein- fed mice (Supplementary Fig. 2a- f). MET supplementation also did not recover body weight and body length, but increased liver weight and body weight ratio in comparison to the untreated 1% protein- fed mice alone (Supplementary Fig. 1b- d). Together, these results indicate that supplementation of different NAD+ precursors improve low protein- induced hepatic steatosis.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 330, 657, 350]]<|/det|>
+## NAM improves low protein diet-induced mitochondrial changes.  
+
+<|ref|>text<|/ref|><|det|>[[113, 370, 886, 704]]<|/det|>
+To further understand the mechanisms underlying the improved hepatic steatosis in response to NAM treatment, we next evaluated changes in hepatic mitochondrial characteristics in our model. We have previously shown that protein- deficient diet induces mitochondrial morphological and functional changes and reduces mitochondrial activity in rats under protein restricted diet<sup>6</sup>. In our mouse model, immunofluorescent staining of mitochondria in the liver showed that the mitochondria were enlarged and elongated but decreased in numbers in the 1% protein- fed mice compared to the 18% protein- fed control group (Fig. 3a). The loss of mitochondria was further confirmed by a significant decrease in the mitochondrial DNA (mtDNA) copy number (Fig. 3b). This feature improved after NAM, NR, and TRP treatment (Fig. 3b, Supplementary Fig. 2h). Mitochondrial abundance markers including TOM20 and HSP60 were both significantly lower in the 1% protein diet- fed mice compared to the control, but improved with NAM treatment (Fig. 3c,d). This suggests that NAM treatment can either reduce mitochondria degradation or increase its biogenesis in our model of severe malnutrition.  
+
+<|ref|>text<|/ref|><|det|>[[113, 724, 886, 903]]<|/det|>
+To examine mitochondrial fitness, we examined hepatic ATP levels, and levels of mitochondrial complex proteins. Further, we quantified the expression of genes in the \(\beta\) - oxidation and lipogenesis pathway. The livers of the 1% protein- fed malnourished mice had significantly lower hepatic ATP levels compared to the 18% protein- fed control group (Fig. 3e). NAM and other TRP- NAM pathway modulators significantly restored hepatic ATP levels (Fig. 3e, Supplementary Fig. 2i). Complex I, Complex IV, and Complex V protein levels were significantly lower in the 1% protein- fed group compared to the control group (Fig. 3f,g). Complex IV levels improved significantly
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 320]]<|/det|>
+after NAM treatment, while no significant change was observed in levels of other complexes. Expression of the genes in the \(\beta\) - oxidation pathway was reduced in the livers of mice fed a \(1\%\) protein diet and were partially restored after NAM treatment, especially Acaa2 and Hadha (Fig. 3h). The expression of lipogenesis genes including Fasn and Acaca were decreased in mice fed a \(1\%\) protein diet (Fig. 3i). NAM supplementation did not influence the mRNA expression of lipogenesis genes (Fig. 3i). In summary, feeding mice a \(1\%\) protein diet altered the hepatic mitochondrial morphology, decreased mitochondrial number and mass, and affected markers of oxidative phosphorylation and \(\beta\) - oxidation. NAM treatment improved the \(1\%\) protein diet-induced mitochondrial changes associated with a recovery in ATP content.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 381, 884, 428]]<|/det|>
+## A low protein diet leads to changes in hepatic energy metabolism that improve with NAM treatment.  
+
+<|ref|>text<|/ref|><|det|>[[112, 448, 886, 888]]<|/det|>
+To better understand the overall liver metabolic change in mice fed with \(1\%\) protein diet and evaluate the effect of NAM supplementation, we performed quantitative analysis of liver central carbon metabolism metabolites<sup>22</sup>. The major metabolic profile differences between groups was highlighted by sparse- partial least squares- discriminant analysis (sPLS- DA)<sup>23</sup>. Variable importance in projection (VIP) scores were used to identify the most important metabolites for the clustering. Overall, the hepatic metabolic profiles of the \(1\%\) protein diet- fed malnourished group were clearly separated from those of the \(18\%\) protein diet- fed control group, and distinct from NAM treatment group (Fig. 4a- b). Among the metabolomic features, acetylglucosamine- 1P, glycerylaldehyde- 3P, malonyl- CoA, lactic acid, ATP, erythrose- 4P, UMP, UDP- glucose, glucose, pyruvic acid, and ADP- glucose mostly discriminated \(18\%\) protein diet from \(1\%\) protein diet groups, with variable importance in projection (VIP) score \(>1\) in both components 1 and 2 (Fig. 4a). To be more specific, the \(1\%\) protein- fed group showed significantly lower glucose, lactic acid, and pyruvic acid content compared to control (Supplementary Table 1)<sup>24</sup>. GMP and UMP concentrations decreased in the \(1\%\) protein diet- fed group, suggesting disturbed nucleotide metabolism including pyrimidine and purine synthesis. Malonyl- CoA levels also changed in the \(1\%\) protein- diet fed group, consistent with altered lipogenesis<sup>25,26</sup>. The overall results were also in line with an earlier report of impaired ATP production and decreased pyruvate uptake,
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 294]]<|/det|>
+accompanied by altered tricarboxylic acid cycle (TCA) cycle intermediates in a rat model of malnutrition \(^{6}\) . Modulation of the TRP- NAM pathway altered hepatic metabolic profiles as observed by sPLS- DA (Fig. 4b and Supplementary Fig. 3a). NAM treatment shifted malonyl- CoA, UTP, ATP, Hs- CoA, UDP- Glucose, total fructose- bisP/glucose- 1,6- bisP, acetyl- CoA, AMP, and succinyl- CoA, which mostly differentiate them with \(1\%\) protein diet group (VIP score \(>1\) ). The concentration of ATP, malonyl- CoA, and acetyl- CoA in NAM treated group shifted towards the \(18\%\) protein diet- fed control group, which was related to the improved energy production and carbohydrate and lipid metabolism (Supplementary Table 1) \(^{27}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 313, 886, 701]]<|/det|>
+To further explore the changes in lipid metabolism in our model and evaluate the effect of TRP- NAM modulation, we performed a lipidomic analyses. Overall, discriminating features were identified that clearly separate the \(18\%\) protein diet and \(1\%\) protein diet group, dominated by increased levels of triacylglycerols, diacylglycerols, and sterols (VIP score \(>1\) ) (Fig. 4c and Supplementary Table 2). Interestingly, hepatic phospholipid content was lower in the \(1\%\) group compared to the \(18\%\) group. The decreased PC/TG ratio and phosphatidylcholines to phosphatidylethanolamines ratio (PC/PE) in the \(1\%\) protein diet group might be linked to the altered energy metabolism and lipid droplet size and dynamics \(^{28,29}\) . Decreased PC/PE ratios have also been observed in NASH patients \(^{30,31}\) , potentially through mitochondrial respiratory chain dysfunction and disability to meet energy requirements \(^{32}\) . NAM treatment clearly separated this group from the \(1\%\) protein diet group and separation was primarily caused differences in phosphatidylcholines and diacylglycerols (VIP score \(>1\) ) (Fig. 4d and Supplementary Table 2). NR and TRP treatment groups were close to each other but clearly separate from MET treatment group, mostly highlighted by altered triacylglycerols and diacylglycerols (with VIP score \(>1\) ) (Supplementary Fig. 3b).  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 763, 778, 784]]<|/det|>
+## NAM treatment affects NAD+ and the SIRT1 pathway in low protein-fed mice.  
+
+<|ref|>text<|/ref|><|det|>[[115, 804, 886, 902]]<|/det|>
+To determine whether NAM treatment directly affects the NAD salvage pathway, we measured the abundance of hepatic NAD+ and tryptophan pathway metabolites in the liver of these animals. NAD+ levels and many metabolites in the tryptophan pathway (such as kynurenine, kynurenine acid, serotonin) were decreased in the \(1\%\) protein- fed mice compared to the \(18\%\) protein- fed
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 268]]<|/det|>
+control group (Fig. 5a). NAM treatment increased hepatic nicotinic acid concentrations, indicating NAM was bioavailable and affected the TRP- NAM pathway. However, we did not observe a significant effect of NAM treatment on \(\mathrm{NAD + }\) levels itself \(\mathrm{(p = 0.640)}\) , whereas NR treatment did significantly increase hepatic \(\mathrm{NAD + }\) levels (Supplementary Fig. 2j). This result is consistent with other studies that have reported that NR increased hepatic \(\mathrm{NAD + }\) levels \(^{33}\) . Another chronic NAM supplementation study showed that NAM did not boost \(\mathrm{NAD + }\) but enhanced the de- acetylation of SIRT1 targets \(^{18}\) .  
+
+<|ref|>text<|/ref|><|det|>[[113, 287, 886, 466]]<|/det|>
+Next, we investigated changes in the NAD dependent SIRT1 pathway. The protein levels of SIRT1 and its downstream target PGC- 1 \(\alpha\) were significantly decreased in the mice fed a \(1\%\) protein diet compared to the \(18\%\) protein- fed control group and levels of these proteins were significantly improved after NAM treatment, albeit not to the same level as the control group (Fig. 5b,e). The ratio of p65 to Ac- p65 significantly increased in the \(1\%\) protein- fed group compared to the control, which was improved after NAM treatment, indicating a change in SIRT1 deacetylation activity (Fig. 5c,e).  
+
+<|ref|>text<|/ref|><|det|>[[112, 485, 886, 741]]<|/det|>
+Since SIRT1 has been shown to influence autophagy and we previously showed an impairment in autophagy flux in livers of low protein- fed rodents \(^{6}\) , we next evaluated autophagy levels by measuring microtubule- associated protein 1A/1B- light chain 3 (LC3) LC3- I and LC3- II protein levels. Autophagy pathway marker of LC3- II/LC3- I ratio significantly decreased in the \(1\%\) protein- fed malnourished group compared to the \(18\%\) protein- fed control group, suggesting a decrease in autophagy activation (Fig. 5d,e). NAM treatment increased the LC3- II/LC3- I ratio, which suggests an increase in activation of macro- autophagy. Taken together, our results suggest that the TRP- NAM pathway is disturbed after feeding a \(1\%\) protein diet to mice and that it can be partially restored by NAM treatment. In turn, the improvement in the TRP- NAM pathway elevates SIRT1 which may be linked to the increase in PGC- 1 \(\alpha\) and activation of autophagy.  
+
+<|ref|>text<|/ref|><|det|>[[113, 805, 884, 850]]<|/det|>
+The effect of NAM on low protein diet- induced liver metabolic dysfunction is mediated through SIRT1.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 241]]<|/det|>
+To further test the whether the effect of NAM is SIRT1- dependent, we performed experiments using SIRT1 modulators in the \(1\%\) protein- fed mice with or without NAM supplementation (Fig. 6a). The SIRT1 activator, resveratrol (REV) \(^{34,35}\) , was used to investigate if SIRT1 activation was sufficient to demonstrate an improvement in the hepatic metabolic changes caused by \(1\%\) protein feeding. The SIRT1 inhibitor, selisistat (EX- 527) \(^{36,37}\) , was subsequently used in combination with NAM treatment to determine if the effect of NAM was dependent on the activation of SIRT1.  
+
+<|ref|>text<|/ref|><|det|>[[112, 260, 886, 675]]<|/det|>
+Intraperitoneal injection of REV did not change body weight, body length and liver weight compared to the vehicle control group (Fig. 6b- e). However, we observed a decrease in the degree of hepatic steatosis in the \(1\%\) protein- fed malnourished group treated with REV, with nearly 2 folds decrease in fat vacuole area and decreased liver TG levels compared to untreated \(1\%\) protein fed animals (Fig. 7a,b). mtDNA copy number and ATP levels significantly increased after REV treatment (Fig. 7c,d). Among the \(\beta\) - oxidation genes, we observed small but significant increases in Hadha and Acadm expression after REV treatment, without a significant change in expression of lipogenesis genes compared to vehicle treated group (Fig. 7e,f). When the \(1\%\) protein- fed malnourished mice were treated with both EX- 527 and NAM, the effects of NAM treatment on hepatic steatosis and mtDNA copy number were lost (Fig. 7a- c). SIRT1 protein level was upregulated after REV treatment (Fig. 7g). There was also a trend toward increased PGC- 1 \(\alpha\) protein levels in the REV treated group (p- value \(= 0.083\) ). EX- 527 with NAM treatment also did not affect SIRT1 and PGC- 1 \(\alpha\) levels compared to the \(1\%\) protein- fed malnourished group alone (Fig. 7g). These data indicate that the SIRT1 increase is sufficient to improve \(1\%\) protein diet- induced hepatic metabolic dysfunction and the effect of NAM treatment on hepatic metabolism is dependent on the elevation of SIRT1.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 737, 237, 760]]<|/det|>
+## Discussion  
+
+<|ref|>text<|/ref|><|det|>[[115, 786, 886, 885]]<|/det|>
+Our study indicates that feeding weanling mice a \(1\%\) protein diet leads to stunted growth, severe wasting, hepatic lipid accumulation and mitochondrial dysfunction that is associated with a reduction in activity in SIRT1, PGC- 1 \(\alpha\) and autophagy. We demonstrate that supplementing the TRP- NAM pathway is able to improve the metabolic phenotype and that this effect is dependent
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 90, 884, 135]]<|/det|>
+on SIRT1. This is the first report on the role of the TRP- NAM pathway in a murine malnutrition model.  
+
+<|ref|>text<|/ref|><|det|>[[112, 156, 886, 440]]<|/det|>
+The hepatic metabolic changes induced by the protein deficient diet were consistent with our previous findings in a rat model of severe malnutrition showing liver steatosis and ATP depletion caused by mitochondrial dysfunction in a rat model of severe malnutrition<sup>11</sup>. The data are also consistent with limited reports in children with severe malnutrition that have found impaired mitochondrial function<sup>4,5</sup>. Interestingly, there is considerable overlap with features seen in patients with NAFLD, including changes in mitochondrial complexes, mitochondrial biogenesis, and hepatic lipid accumulation<sup>38- 40</sup>. The reduction in mitochondrial mass seen in our mouse model is different from previous observations in low protein fed rats, where an increase in mitochondrial mass was observed<sup>6</sup>. However, reduction in mtDNA in our low protein diet mouse model was consistent with another previous report in fetal and early postnatal malnourished rats fed a low casein diet<sup>41</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[112, 459, 886, 900]]<|/det|>
+The reduction in mitochondrial mass and mtDNA in low protein- fed mice was associated with a reduction in PGC- 1α, a well- known regulator of cellular energy metabolism and activator of mitochondrial biogenesis<sup>42,43</sup>. PGC- 1α can co- activate transcription factors such as peroxisome proliferator- activated receptor (PPARα) and nuclear respiratory factors (NRF1 and NRF2) to regulate mitochondrial biogenesis and fatty acid oxidation<sup>44</sup>. Mice that are deficient in PGC- 1α have impaired energy metabolism that is related to a decrease in mitochondrial number and respiratory capacity<sup>45</sup>. This suggests that the reduction in mitochondrial mass is related to a decrease in mitochondrial biogenesis upon low protein feeding. The changes in mitochondrial morphology, mitochondrial complex content, and markers of mitochondrial function, such as ATP, also indicate that the mitochondria that are present in the liver after a period of low protein feeding are damaged and dysfunctional. Mitochondrial degradation is regulated through a selective autophagy process called mitophagy<sup>12</sup>, and our data suggests that autophagy activation is decreased during nutritional stress. This could contribute to a high relative content of damaged mitochondria that would normally have been degraded through mitophagy. NAM treatment increased PGC- 1α protein levels, mitochondrial mass and content of mitochondrial complexes, while activating the autophagy pathway, suggesting a rebalancing of mitochondrial biogenesis and mitophagy.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 888, 530]]<|/det|>
+PGC- 1 \(\alpha\) and autophagy are both regulated by SIRT1. SIRT1 directly deacetylates PGC- 1 \(\alpha\) at multiple lysine sites and the induction pattern of SIRT1 protein correlates with the expression of PGC- 1 \(\alpha^{46}\) . In addition, SIRT1 regulate autophagy by acting on multiple autophagy effectors. These mechanisms include directly inducing autophagy by deacetylating autophagy- related genes (ATGs) and LC3, indirectly inhibiting the mTOR pathway by activation of AMPK, as well as modulating the expression of autophagy and mitophagy regulatory molecules (e.g. Rab7 and Bnip3) through deacetylation of Forkhead box O transcription factors (FOXOs) \(^{47,48}\) . SIRT1 levels were decreased in our low protein diet- fed mice. As SIRT1 activity is dependent on NAD availability, we propose that lower SIRT1 activity is associated with reduced levels of NAD and other metabolites in the TRP- NAM pathway in low protein diet- fed mice. Supplementing these protein deficient animals with NAM was found to rescue SIRT1 mediated activity. We propose that the reduction in NAD prevents the SIRT1 mediated activation of PGC- 1 \(\alpha\) and autophagy pathway. Our results are consistent with a clinical study reporting that increased malnutrition risk was associated with decreased SIRT1 expression \(^{49}\) . The decreased protein levels of SIRT1 found after low protein feeding could potentially be explained by diet- triggered cleavage of SIRT1 protein. For example, a high- fat diet has been shown to induce SIRT1 protein cleavage leading to metabolic dysfunction \(^{50}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 548, 886, 858]]<|/det|>
+NAM was shown to increase SIRT1 levels. The effect was not specific to NAM, as NR and TRP demonstrated a similar effect. Other NAD+ precursors such as NR and TRP have demonstrated a similar effect in previous studies \(^{17,51,52}\) . We focused on NAM specifically for more in depth investigations because of its low cost and excellent safety profile. Treatment with NAM and other NAD+ precursors have shown beneficial effects in various metabolic dysfunction models, including fatty liver, obesity, metabolic syndrome, and diabetes \(^{18,53,54}\) . The beneficial effects in these studies have been related to an improved mitochondrial function, mediated by NAD+ dependent sirtuin activation \(^{17,51,52}\) . Our SIRT1 modulation experiments demonstrated that in our malnutrition model the effects of NAM were dependent on the presence of SIRT1 and that stimulating SIRT1 was sufficient to produce the beneficial effects on mitochondrial function. The results are consistent with studies in high fat- fed mice where resveratrol impacted mitochondrial function and prevented hepatic steatosis \(^{34}\) .
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 373]]<|/det|>
+In our study, NAM treatment did not significantly restore NAD+ levels whereas NR did, however NAM improved SIRT1 and PGC- 1α levels. Some studies have shown that NAM has the ability to increase cellular and blood NAD+ content in different metabolic disorder models (e.g. NAFLD mice, hepatocytes with endoplasmic reticulum stress) \(^{55 - 58}\) . However, other studies have found no direct effect of NAM supplementation on NAD+ levels \(^{18,59}\) . If the extra NAD that is synthesized, is readily used for deacetylation, then you would not see a significant increase. These differences in findings might also be related to the duration and variation in the dose of NAM and the animal models used affecting NAM metabolism. For example, NAM can affect SIRT1 activity differently by acting as a non- competitive end- product inhibitor and as a NAD+ precursor \(^{60}\) . In addition, NAM clearance pathways through MNAM- mediated SIRT1 protein stabilization can also regulate hepatic nutrient metabolism \(^{61,62}\) .  
+
+<|ref|>text<|/ref|><|det|>[[115, 392, 888, 519]]<|/det|>
+In conclusion, this work provides evidence for the role of TRP- NAM pathway in liver metabolic dysfunction in a mouse model of severe malnutrition, mediated through changes in levels of SIRT1. This study improves our understanding of the cellular pathophysiology of severe malnutrition. The results of this project could lead to the development of new interventions that target the TRP- NAM pathway which could then be taken to clinical trials.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 583, 216, 604]]<|/det|>
+## Methods  
+
+<|ref|>text<|/ref|><|det|>[[112, 629, 886, 886]]<|/det|>
+Animals and diets. A breeding colony of C57BL/6 mice was obtained from Jackson Laboratories (Bar Harbor, ME, USA). Male mice at 3 weeks post- partum were weaned and housed socially in filtered cages at The Hospital for Sick Children, Toronto. Weanling male C57BL/6J mice were randomized into different groups fed with control diet (18% protein) or malnourished diet (1% protein) for a period of 2 weeks. Diets were purchased from ENVIGO (Madison, WI, USA), and the protein proportions contribute to diet calories were primarily adjusted by casein and corn starch. After 7 days, malnourished subgroups were treated with modulators of the TRP- NAM pathway until sacrifice on day 14. Nicotinamide, nicotinamide- riboside and tryptophan were given by drinking water in a dose of 160 mg/kg body weight/day, and methionine was included in diets at a concentration of 0.75 g/kg diet \(^{15,59,63}\) . Nicotinamide, nicotinamide- riboside and tryptophan
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 268]]<|/det|>
+were provided by Sigma- Aldrich (St. Louis, MO, USA). In a subset of mice, after \(1\%\) protein diet for 7 days, intraperitoneal injections treated with either resveratrol (25 mg/kg/d) or EX- 527 (10 mg/kg/d) with NAM were given for 7 consecutive days until sacrifice \(^{36,37,64}\) . All groups were housed in a temperature- controlled environment (23 °C), 12 h light- dark cycle, and had ad libitum access to diet and water throughout the study. All animal experiments were approved by the Animal Care Committee of The Hospital for Sick Children, Toronto (Animal Use Protocol Number: 1000030900).  
+
+<|ref|>text<|/ref|><|det|>[[112, 287, 886, 492]]<|/det|>
+Physiological parameters. Body weight, food intake, and liquid intake were monitored from day 1 to day 14. At the end of the experimental protocol (on day 14 post weaning), mice were humanely euthanized and necropsied. Final body weight, body length, and liver weight were recorded. Blood was collected by cardiac puncture. Liver tissue was collected for histology or stored at \(- 80^{\circ}\mathrm{C}\) for later use in biochemical analyses. Glucose concentration was determined via tail snip at 0h, 4h, 8h, and 12h fasting in the day light cycle, using an automatic glucometer (Freestyle, Abbott, IL). Metabolic rate was assessed by indirect calorimetry using the Columbus Instruments (Oxymax Lab Animal Monitoring System: CLAMS, Columbus, OH) \(^{18}\) .  
+
+<|ref|>text<|/ref|><|det|>[[112, 512, 886, 690]]<|/det|>
+Histology. Fresh livers tissues were fixed in \(4\%\) paraformaldehyde (PFA) overnight at \(4^{\circ}\mathrm{C}\) and then embedded in either paraffin or optimum cutting temperature (OCT) compound. Liver paraffin sections (5 \(\mu \mathrm{m}\) ) were stained with hematoxylin and eosin (H&E) for morphology. Liver OCT sections were stained with Oil red O (10 \(\mu \mathrm{m}\) ) for lipid droplets. Slides were visualized under a light microscope and was measured using Panoramic Viewer version 1.15 software (3DHISTECH Ltd, Budapest, Hungary). For each slide, at least five pictures were captured. Quantification analysis of the images was conducted using ImageJ 1.52v and Python 3.7.2.  
+
+<|ref|>text<|/ref|><|det|>[[112, 709, 886, 888]]<|/det|>
+Immunofluorescence. OCT- embedded liver sections were cut into \(4\mu \mathrm{m}\) slices for immunofluorescent staining. A fluorinated boron- dipyrromethene (BODYPI) antibody was used to visualize fat droplets. An HSP60 antibody was used to visualize mitochondrial morphology. Nuclei were counterstained with DAPI. Slides were mounted with mounting medium (Vector Laboratories Inc., Burlington, Canada) and images were acquired on a Nikon Spinning Disk Confocal Microscope (Nikon Inc., NY, USA). Additional information can be found in the Supplementary Table 3.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[113, 88, 886, 163]]<|/det|>
+Plasma tryptophan analysis. Plasma samples were mixed with equal volumes of internal standard (Norleucine). Samples were centrifuged at 14000 rpm for 5 minutes and subsequently measured on Biochrom \(30+\) Amino Acid Analyzer (Biochrom, Cambridge, UK).  
+
+<|ref|>text<|/ref|><|det|>[[113, 183, 886, 283]]<|/det|>
+Triglyceride analysis. Liver and serum TG concentrations were quantified by a commercially available kit (Randox, London, UK). Liver tissue lipids were extracted with methanol- chloroform, dried and dissolved for TG analysis. Values were also normalized to protein concentrations determined using a bicinchoninic acid assay (BCA) kit (Thermo Fisher Scientific, USA).  
+
+<|ref|>text<|/ref|><|det|>[[112, 303, 886, 610]]<|/det|>
+Western blotting. Western blot analysis was conducted to measure the protein levels. Liver tissue protein was extracted through sonication of tissue with extraction buffer and protease inhibitor cocktail (Sigma- Aldrich). The protein concentration was measured using pierce BCA kit (Thermo Fisher Scientific). Equal concentrations of the samples were electrophoresed through \(4\% - 12\%\) Bis Tris gel and transferred onto a polyvinylidene fluoride (PVDF) membrane. Membranes were probed with 1:1000 dilutions of anti HSP60 (Abcam, USA), TOM20 (Santa Cruz, USA), Complex I (Abcam, USA), Complex IV (Abcam, USA), Complex V (Abcam, USA), SIRT1 (Cell Signalling, USA), PGC- 1α (Abcam, USA), p65 (Abcam, USA), Ac- p65 (Abcam, USA), LC3B (Sigma, USA). \(\beta\) - actin (Sigma, USA) was used as a loading control in 1:1000 dilution. Then proteins were visualized using a pierce enhanced chemiluminescence (ECL) plus kit (Invitrogen, CA, USA). Western blot quantification was performed using Image Studio (LI- COR Biosciences). Additional information can be found in the Supplementary Table 3.  
+
+<|ref|>text<|/ref|><|det|>[[112, 631, 886, 809]]<|/det|>
+qPCR. Total RNA was isolated from frozen liver tissue using Direct- zol RNA MiniPrep Kit (ZYMO research Inc., Irvine, CA, USA). cDNA was synthesized by the Super Script VILO cDNA Synthesis Kit (Thermo Fisher Scientific, USA). 500 ng of liver total RNA were used for cDNA synthesis. Ribosomal protein 113a (Rpl13a) was used as reference gene. qPCR was performed on CFX384 Touch Real- Time PCR Detection System (Bio- Rad, CA, USA). For mtDNA copy number measurements, 500 ng of genomic DNA were used for each qPCR reaction and \(\beta\) - globin were used as reference \(^{65}\) . Additional information can be found in the Supplementary Table 4.  
+
+<|ref|>text<|/ref|><|det|>[[112, 830, 886, 902]]<|/det|>
+Metabolomic analysis. Targeted metabolomic profiling (pathway specific assays) was performed by The Metabolomics Innovation Centre (TMIC, Edmonton, AB Canada). The quantitation of central carbon metabolism metabolites in mouse liver was measured by ultraperformance liquid
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[111, 88, 886, 477]]<|/det|>
+chromatography- tandem mass spectrometry (UPLC- MS/MS). A Dionex 3400 UHPLC system coupled to a 4000 QTRAP mass spectrometer was used. The MS instrument was operated in the multiple- reaction monitoring (MRM) mode with negative- ion (- ) or positive- ion (+) detection, depending on which groups of metabolites were measured. Each liver tissue sample was frozen and placed into an Eppendorf tube. Water, at \(2\mu \mathrm{L}\) per mg tissue, was added and the samples were homogenized for 1 min twice at a shaking frequency of \(30\mathrm{Hz}\) , with the aid of two 4- mm metal balls, on a MM 400 mill mixer. After a short- time centrifuge, methanol, at \(8\mu \mathrm{L}\) per mg tissue, was added and the samples were homogenized again for 1 min twice using the same settings. The samples were then sonicated in an ice- water bath for 3 min, followed by centrifugal clarification at \(15,000\mathrm{rpm}\) and \(5^{\circ}\mathrm{C}\) in an Eppendorf 5424R centrifuge for \(20\mathrm{min}\) . The clear supernatants were collected to conduct quantitation of TCA cycle carboxylic acids, glucose and selected sugar phosphates, and other phosphate- containing metabolites and nucleotides by UPLC- MS/MS. Concentrations of the detected metabolites were calculated from their linear- regression calibration curves with internal calibration. Tryptophan pathway metabolites were also measured using a UPLC- MS based targeted method<sup>66</sup>.  
+
+<|ref|>text<|/ref|><|det|>[[112, 497, 888, 910]]<|/det|>
+Lipidomic analysis. Lipidomic analysis was performed at Core Metabolomics and Lipidomics Laboratory, Wellcome Trust- Metabolic Research Laboratories (University of Cambridge, Cambridge, UK). Liver samples were homogenised, lipids were extracted according to a published procedure, and data was acquired through Direct Infusion Mass Spectrometry (DI- MS)<sup>67</sup>. Briefly, liver sections ( \(30\mathrm{mg / each}\) ) were homogenised (Tissue homogeniser II, Qiagen) in a buffer of chaotropes (guanidinium chloride (6 M) and thiourea (1.5 M) in deionised water, \(500\mu \mathrm{L / sample}\) ). The liver homogenates ( \(30\mu \mathrm{L}\) ) were injected into a well (96w plate, Esslab Plate+TM, \(2.4\mathrm{mL / well}\) , glass- coated) followed by methanol spiked with internal standards ( \(150\mu \mathrm{L}\) ), water ( \(500\mu \mathrm{L}\) ) and DMT ( \(500\mu \mathrm{L}\) , dichloromethane, methanol and triethylammonium chloride, 3:1:0.005). Most of the aqueous solution was removed (96 channel pipette). A portion of the organic solution ( \(20\mu \mathrm{L}\) ) was transferred to a high throughput plate ( \(384\mathrm{w}\) , glass coated, Esslab Plate+TM) before being dried ( \(\mathrm{N}_2\) (g)). The dried films were re- dissolved (TBME, \(30\mu \mathrm{L / well}\) ) and diluted with a stock mixture of alcohols and ammonium acetate ( \(100\mu \mathrm{L / well}\) ; propan- 2- ol: methanol, 2:1; \(\mathrm{CH}_3\mathrm{COONH}_4\) \(7.5\mathrm{mM}\) ). The analytical plate was heat- sealed and run immediately. Lipid fraction isolates were profiled using a three- part method in DI- MS<sup>67</sup>. All samples were infused into an Exactive Orbitrap (Thermo, Hemel Hampstead, UK), using a TriVersa NanoMate (Advion, Ithaca
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[112, 88, 886, 400]]<|/det|>
+US). Samples (15 \(\mu \mathrm{L}\) ) were sprayed at 1.2 kV in the positive ion mode. The Exactive started acquiring data 20 s after sample aspiration began. The Exactive acquired data with a scan rate of 1 Hz (resulting in a mass resolution of 100,000 full width at half- maximum [fwhm] at 400 \(m / z\) ). The Automatic Gain Control was set to 3,000,000 and the maximum ion injection time to 50 ms. After 72 s of acquisition in positive mode the NanoMate and the Exactive switched over to negative ionization mode, decreasing the voltage to - 1.5 kV and the maximum ion injection time to 50 ms. The spray was maintained for another 66 s, after which the NanoMate and Exactive switched over to negative mode with in- source fragmentation (also known as collision- induced dissociation, CID; 70 eV) for a further 66 s. After this time, the spray was stopped and the tip discarded, before the analysis of the next sample began. The sample plate was kept at 15 \(^\circ \mathrm{C}\) throughout the acquisition. Samples were run in row order. The instrument was operated in full scan mode from \(m / z\) 150- 1200 Da (for singly charged species).  
+
+<|ref|>text<|/ref|><|det|>[[112, 418, 886, 620]]<|/det|>
+Statistical analysis. Statistical significance for the difference between two groups was calculated by using an unpaired two- tailed student's T- test. Statistical significance for the difference among more than two groups was calculated by using an ordinary one- way ANOVA followed by the Turkey's post hoc test<sup>68</sup>. The FDR and Bonferroni correction were applied to the metabolomic and lipidomic metabolites. Statistical analysis was performed with R software (version 3.5.2) and MetaBoAnalyst (version 4.0). Statistical significance was given as \(* \mathrm{p} < 0.05\) , \(** \mathrm{p} < 0.01\) , and \(*** \mathrm{p} < 0.001\) . The results are expressed as mean \(\pm\) standard error of mean (S.E.M.), unless otherwise indicated.  
+
+<|ref|>sub_title<|/ref|><|det|>[[115, 686, 304, 708]]<|/det|>
+## Data availability  
+
+<|ref|>text<|/ref|><|det|>[[112, 733, 885, 806]]<|/det|>
+All relevant data of this study are available within the paper and its supplementary information files. All data that support this study are available from the corresponding authors upon reasonable request.
+
+<--- Page Split --->
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+562 41. Park, K.S., et al. Fetal and early postnatal protein malnutrition cause long-term changes in rat liver and muscle mitochondria. The Journal of nutrition 133, 3085- 3090 (2003). 563 42. Wu, Z., et al. Mechanisms controlling mitochondrial biogenesis and respiration through the thermogenic coactivator PGC- 1. Cell 98, 115- 124 (1999). 565 43. Piccinin, E., Villani, G. & Moschetta, A. Metabolic aspects in NAFLD, NASH and hepatocellular carcinoma: the role of PGC1 coactivators. Nature Reviews Gastroenterology & Hepatology 16, 160- 174 (2019). 568 44. Scarpulla, R.C. Metabolic control of mitochondrial biogenesis through the PGC- 1 family regulatory network. Biochimica et Biophysica Acta (BBA)- Molecular Cell Research 1813, 1269- 1278 (2011). 572 45. Leone, T.C., et al. PGC- 1α deficiency causes multi- system energy metabolic derangements: muscle dysfunction, abnormal weight control and hepatic steatosis. PLoS biology 3(2005). 573 46. Rodgers, J.T., et al. Nutrient control of glucose homeostasis through a complex of PGC- 1α and SIRT1. Nature 434, 113- 118 (2005). 575 47. Lee, I.H., et al. A role for the NAD- dependent deacetylase Sirt1 in the regulation of autophagy. Proc Natl Acad Sci U S A 105, 3374- 3379 (2008). 578 48. Kitada, M., Ogura, Y. & Koya, D. Chapter 3 - Role of sirt1 as a regulator of autophagy. in Autophagy: Cancer, Other Pathologies, Inflammation, Immunity, Infection, and Aging (ed. Hayat, M.A.) 89- 100 (Academic Press, San Diego, 2016). 581 49. El Assar, M., et al. Better nutritional status is positively associated with mRNA expression of SIRT1 in community- dwelling older adults in the Toledo Study for Healthy Aging. J Nutr 148, 1408- 1414 (2018). 584 50. Chalkiadaki, A. & Guarente, L. High- fat diet triggers inflammation- induced cleavage of SIRT1 in adipose tissue to promote metabolic dysfunction. Cell metabolism 16, 180- 188 (2012). 587 51. Wang, S., et al. Nicotinamide riboside attenuates alcohol induced liver injuries via activation of SirT1/PGC- 1alpha/mitochondrial biosynthesis pathway. Redox Biol 17, 89- 98 (2018). 590 52. Ritze, Y., Bardos, G., Hubert, A., Bohle, M. & Bischoff, S.C. Effect of tryptophan supplementation on diet- induced non- alcoholic fatty liver disease in mice. Br J Nutr 112, 1- 7 (2014). 593 53. Morizono, S., et al. Nicotinamide, not N1 methylnicotinamide, ameliorates hepatic steatosis via NAD- depended sirtuin activation. Journal of Hepatology 68, S350- S351 (2018). 596 54. Mejia, S.Á., et al. Nicotinamide prevents sweet beverage- induced hepatic steatosis in rats by regulating the G6PD, NADPH/NADP+ and GSH/GSSG ratios and reducing oxidative and inflammatory stress. European journal of pharmacology 818, 499- 507 (2018). 599 55. Li, J., et al. Nicotinamide ameliorates palmitate- induced ER stress in hepatocytes via cAMP/PKA/CREB pathway- dependent Sirt1 upregulation. Biochimica et Biophysica Acta (BBA)- Molecular Cell Research 1853, 2929- 2936 (2015). 602 56. Majamaa, K., Rusanen, H., Remes, A.M., Pyhtinen, J. & Hassinen, I.E. Increase of blood NAD+ and attenuation of lactacidemia during nicotinamide treatment of a patient with the MELAS syndrome. Life sciences 58, 691- 699 (1996). 605 57. Williams, P.A., et al. Vitamin B3 modulates mitochondrial vulnerability and prevents glaucoma in aged mice. Science 355, 756- 760 (2017).
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+607 58. Liu, D., Gharavi, R., Pitta, M., Gleichmann, M. & Mattson, M.P. Nicotinamide prevents 608 NAD+ depletion and protects neurons against excitotoxicity and cerebral ischemia: NAD+ 609 consumption by SIRT1 may endanger energetically compromised neurons. 610 Neuromolecular Med 11, 28-42 (2009). 611 59. Sambeat, A., et al. Endogenous nicotinamide riboside metabolism protects against diet- 612 induced liver damage. Nat Commun 10, 4291 (2019). 613 60. Hwang, E.S. & Song, S.B. Nicotinamide is an inhibitor of SIRT1 in vitro, but can be a 614 stimulator in cells. Cell Mol Life Sci 74, 3347-3362 (2017). 615 61. Hong, S., et al. Nicotinamide N-methyltransferase regulates hepatic nutrient metabolism 616 through Sirt1 protein stabilization. Nature medicine 21, 887 (2015). 617 62. Canto, C., Menzies, K.J. & Auwers, J. NAD+ metabolism and the control of energy 618 homeostasis: a balancing act between mitochondria and the nucleus. Cell metabolism 22, 31-53 (2015). 619 63. Hashimoto, T., et al. ACE2 links amino acid malnutrition to microbial ecology and 620 intestinal inflammation. Nature 487, 477-481 (2012). 621 64. Ma, S., et al. SIRT1 activation by resveratrol alleviates cardiac dysfunction via 622 mitochondrial regulation in diabetic cardiomyopathy mice. Oxidative medicine and 623 cellular longevity 2017(2017). 624 65. Rooney, J.P., et al. PCR based determination of mitochondrial DNA copy number in 625 multiple species. in Mitochondrial Regulation 23-38 (Springer, 2015). 626 66. Whiley, L., et al. Ultrahigh-Performance liquid chromatography tandem mass 627 spectrometry with electrospray ionization quantification of tryptophan metabolites and 628 markers of gut health in serum and plasma - application to clinical and epidemiology 629 cohorts. Analytical chemistry 91, 5207-5216 (2019). 630 67. Furse, S., et al. A high-throughput platform for detailed lipidomic analysis of a range of 631 mouse and human tissues. Analytical and Bioanalytical Chemistry, 1-12 (2020). 632 68. Singh, R., et al. Autophagy regulates lipid metabolism. Nature 458, 1131 (2009).
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[68, 92, 336, 116]]<|/det|>
+## Acknowledgements  
+
+<|ref|>text<|/ref|><|det|>[[115, 140, 886, 240]]<|/det|>
+We thank The Metabolomics Innovation Centre for performing targeted metabolomic assays, thank Lucy Wang and Ainsley Su- Williams for performing the experiments, and thank Bijun Wen, Celine Bourdon, and Amber Farooqui for help with statistical analyzing methods and animal use protocol update. This research was supported by the Bill & Melinda Gates Foundation.  
+
+<|ref|>sub_title<|/ref|><|det|>[[68, 303, 357, 326]]<|/det|>
+## Author contributions  
+
+<|ref|>text<|/ref|><|det|>[[115, 350, 888, 475]]<|/det|>
+R.H.J.B. and G.H. were primarily responsible for the study design. G.H. wrote the manuscript. G.H., C.L., L.C., S.F., J.S., M.K.T., D.L., M.C., C.J.V., and G.B.G. contributed to the conduction of lab experiments. G.H., L.C., S.F., and J.S. contributed to data analysis. P.K.K., A.K., and B.M.B. provided expertise, interpreted results, and commented on the manuscript. All authors contributed to editing of the manuscript. R.H.J.B. was responsible for the final content of the manuscript.  
+
+<|ref|>sub_title<|/ref|><|det|>[[68, 541, 345, 564]]<|/det|>
+## Competing interests  
+
+<|ref|>text<|/ref|><|det|>[[115, 589, 489, 608]]<|/det|>
+All participants declare no competing interests.  
+
+<|ref|>sub_title<|/ref|><|det|>[[68, 671, 380, 696]]<|/det|>
+## Additional information  
+
+<|ref|>text<|/ref|><|det|>[[68, 720, 562, 740]]<|/det|>
+Supplementary Information is available for this paper.  
+
+<|ref|>text<|/ref|><|det|>[[68, 761, 718, 782]]<|/det|>
+Correspondence and requests for materials should be addressed to R.H.J.B.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[204, 88, 790, 644]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 661, 884, 819]]<|/det|>
+<center>Fig. 1 Feeding a \(1\%\) protein diet with or without NAM supplementation on basic animal characteristics. a Experimental design. b Average food and liquid intake during day 7 to day 14 \((n = 7\) for \(18\%\) \(n = 5\) for \(1\%\) and \(1\% +\) NAM). c Body weight change throughout experiment \((n = 15)\) d Final body weight and body length assessed on day 14 \((n = 15)\) . e Liver weight and liver weight/body weight ratio \((n = 12\) for \(18\%\) \(n = 10\) for \(1\%\) and \(1\% +\) NAM). f Fasting glucose levels \((n = 7\) for \(18\%\) \(n = 8\) for \(1\%\) \(n = 7\) for \(1\% +\) NAM). g Respiratory exchange ratio (RER) and energy expenditure \((n = 7\) for \(18\%\) \(n = 6\) for \(1\%\) \(n = 7\) for \(1\% +\) NAM). \(^{*}\mathrm{p}< 0.05\) \(^{**}\mathrm{p}< 0.01\) \(^{**}\mathrm{p}< 0.001\) ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[270, 90, 720, 530]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 550, 884, 724]]<|/det|>
+<center>Fig. 2 The effect of \(1\%\) protein feeding with or without NAM supplementation on hepatic lipid accumulation. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Representative oil red o stain staining images of the liver (20X magnification). Fat droplet was stained in red, and nucleus was stained in purple. c Representative immunofluorescence images of the liver (40X magnification). BODYPY was used to stain fat droplet in green, and DAPI was used to counter stain nucleus in blue. d Quantification of fat vacuoles area (n=9). e Liver TG concentrations (n=6). f Serum TG concentrations (n=6). \(^{*}\mathrm{p}< 0.05\) , \(^{**}p< 0.01\) , \(^{***}p< 0.001\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[115, 90, 886, 600]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 612, 886, 770]]<|/det|>
+<center>Fig. 3 The effect of NAM supplementation on mitochondrial characteristics of 1% protein fed model. a Representative immunofluorescence images of mitochondrial (60X magnification). HSP60 was used to stain mitochondrial in red, and DAPI was used to counter stain nucleus in blue. b mtDNA copy number (n=6). c, d Western blots and quantification of HSP60 and TOM20 (n=3). e ATP levels (n=11 for 18% and 1%; n=7 for 1%+NAM). f, g Western blots and quantification of complex I, complex IV and complex V (n=3). h mRNA expression of \(\beta\) -oxidation genes (n=6). i mRNA expression of lipid genesis genes (n=6). \(^{*}\mathrm{p}< 0.05\) , \(^{**}p< 0.01\) , \(^{***}p< 0.001\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[120, 90, 880, 380]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[115, 400, 884, 543]]<|/det|>
+<center>Fig. 4 Hepatic metabolomic and lipidomic profiles under 18% protein diet, 1% protein diet, and 1% protein diet with NAM supplementation. a sPLS-DA and correlation circle plots of hepatic central carbon metabolism showing separation of 18% and 1% protein diet group (n=5). b sPLS-DA and correlation circle plots of hepatic central carbon metabolism showing separation of 1% protein diet and NAM treated group (n=5 for 1%; n=7 for 1%+NAM). c sPLS-DA and correlation circle plots of hepatic lipidomics showing separation of 18% and 1% protein diet group (n=6). d sPLS-DA and correlation circle plots of hepatic lipidomics showing separation of 1% protein diet and NAM treated group (n=6). </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[201, 95, 800, 670]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 682, 884, 805]]<|/det|>
+<center>Fig. 5 The effect of \(1\%\) protein feeding with or without NAM supplementation on TRP-NAM pathway metabolites, SIRT1 and downstream targets, and autophagy levels. a Hepatic NAD+ levels and TRP-NAM pathway metabolites (n=6). b SIRT1 and PGC-1α western blots (n=3). c p65 and Acetyl-p65 western blots (n=3). d Autophagy markers LC3 western blots (n=3). e Quantification of protein levels in western blots. \(^{*}p < 0.05\) , \(^{**}p < 0.01\) , \(^{***}p < 0.001\) , ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[201, 92, 800, 380]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[113, 395, 884, 504]]<|/det|>
+<center>Fig. 6 The effect of SIRT1 modulators on basic animal characteristics. a Experiment design. b Body weight change throughout experiment (n=6). c Average food and liquid intake during day 7 to day 14 (n=6). d Final body weight, body length, and weight for length ratio assessed at day 14 (n=6). e Liver weight, liver weight to body weight ratio (n=6). \*p < 0.05, \*\*p < 0.01, \*\*\*p < 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[112, 90, 886, 465]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[112, 480, 886, 620]]<|/det|>
+<center>Fig. 7 The effect of SIRT1 modulators on hepatic steatosis, mitochondrial characteristics, SIRT1 and its downstream targets. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Quantification of liver histology and TG levels (n=6). c mtDNA copy number (n=6). d ATP levels (n=6). e mRNA expression of \(\beta\) -oxidation genes (n=6). f mRNA expression of lipid genesis genes (n=6). g SIRT1 and PGC-1 \(\alpha\) western blots and quantification (n=3). \(^{*}\mathrm{p}< 0.05\) , \(^{**}p< 0.01\) , \(^{**}p<\) 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated. </center>
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[201, 92, 795, 384]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[114, 400, 884, 575]]<|/det|>
+<center>Fig. 8 Proposed model of the role of the TRP-NAM pathway in malnutrition-induced hepatic metabolic disturbances. In protein malnutrition, decreased TRP availability will decrease the kynurenine pathway activity, which is associated with NAD+ and NAM deficiency. This would disturb NAD+ salvage pathway, including SIRT1, influence its downstream target PGC-1α and autophagy, which affect mitochondrial quality and function. These changes lead to ATP depletion and lipid accumulation in the liver. We hypothesize that supplement with TRP-NAM modulator would influence NAD+ salvage pathway. This would thereby activate SIRT1, influence PGC-1α deacetylation and autophagy, which will have a positive effect on mitochondrial health, affect mitochondrial biogenesis and clearance of damaged mitochondrial, then improve ATP generation and reduce lipid accumulation in the liver. </center>
+
+<--- Page Split --->
+<|ref|>sub_title<|/ref|><|det|>[[44, 43, 143, 68]]<|/det|>
+## Figures 
+
+<|ref|>image<|/ref|><|det|>[[52, 100, 816, 830]]<|/det|>
+ 
+
+<|ref|>image_caption<|/ref|><|det|>[[44, 852, 118, 870]]<|/det|>
+<center>Figure 1</center> 
+
+<|ref|>text<|/ref|><|det|>[[44, 894, 928, 958]]<|/det|>
+Feeding a 1% protein diet with or without NAM supplementation on basic animal characteristics. a Experimental design. b Average food and liquid intake during day 7 to day 14 (n=7 for 18%; n=5 for 1% and 1%+NAM). c Body weight change throughout experiment (n=15). d Final body weight and body
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[40, 45, 950, 156]]<|/det|>
+length assessed on day 14 (n=15). e Liver weight and liver weight/body weight ratio (n=12 for 18%; n=10 for 1% and 1%+NAM). f Fasting glucose levels (n=7 for 18%; n=8 for 1%; n=7 for 1%+NAM). g Respiratory exchange ratio (RER) and energy expenditure (n=7 for 18%; n=6 for 1%; n=7 for 1%+NAM). \*p < 0.05, \*\*p < 0.01, \*\*\*p < 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. 
+
+<|ref|>image<|/ref|><|det|>[[60, 171, 789, 875]]<|/det|>
+ 
+
+<|ref|>image_caption<|/ref|><|det|>[[42, 917, 123, 935]]<|/det|>
+<center>Figure 2</center>
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[38, 44, 950, 247]]<|/det|>
+The effect of \(1\%\) protein feeding with or without NAM supplementation on hepatic lipid accumulation. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Representative oil red o stain staining images of the liver (20X magnification). Fat droplet was stained in red, and nucleus was stained in purple. c Representative immunofluorescence images of the liver (40X magnification). BODYPY was used to stain fat droplet in green, and DAPI was used to counter stain nucleus in blue. d Quantification of fat vacuoles area \((n = 9)\) . e Liver TG concentrations \((n = 6)\) . f Serum TG concentrations \((n = 6)\) . \(*p < 0.05\) , \(**p < 0.01\) , \(***p < 0.001\) , ns as not significant, one way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated.  
+
+<|ref|>image<|/ref|><|det|>[[50, 255, 920, 825]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 840, 116, 860]]<|/det|>
+<center>Figure 3 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 883, 933, 949]]<|/det|>
+The effect of NAM supplementation on mitochondrial characteristics of \(1\%\) protein fed model. a Representative immunofluorescence images of mitochondrial (60X magnification). HSP60 was used to stain mitochondrial in red, and DAPI was used to counter stain nucleus in blue. b mtDNA copy number
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[42, 45, 950, 155]]<|/det|>
+(n=6). c, d Western blots and quantification of HSP60 and TOM20 (n=3). e ATP levels (n=11 for 18% and 1%; n=7 for 1%+NAM). f, g Western blots and quantification of complex I, complex IV and complex V (n=3). h mRNA expression of \(\beta\) -oxidation genes (n=6). i mRNA expression of lipid genesis genes (n=6). \*p < 0.05, \*\*p < 0.01, \*\*\*p < 0.001, ns as not significant, one-way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M. Scale bars are as indicated.  
+
+<|ref|>image<|/ref|><|det|>[[62, 170, 940, 504]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 531, 118, 550]]<|/det|>
+<center>Figure 4 </center>  
+
+<|ref|>text<|/ref|><|det|>[[41, 572, 940, 730]]<|/det|>
+Hepatic metabolomic and lipidomic profiles under 18% protein diet, 1% protein diet, and 1% protein diet with NAM supplementation. a sPLS- DA and correlation circle plots of hepatic central carbon metabolism showing separation of 18% and 1% protein diet group (n=5). b sPLS- DA and correlation circle plots of hepatic central carbon metabolism showing separation of 1% protein diet and NAM treated group (n=5 for 1%; n=7 for 1%+NAM). c sPLS- DA and correlation circle plots of hepatic lipidomics showing separation of 18% and 1% protein diet group (n=6). d sPLS- DA and correlation circle plots of hepatic lipidomics showing separation of 1% protein diet and NAM treated group (n=6).
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[60, 57, 800, 780]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[44, 802, 118, 820]]<|/det|>
+<center>Figure 5 </center>  
+
+<|ref|>text<|/ref|><|det|>[[42, 842, 950, 933]]<|/det|>
+The effect of \(1\%\) protein feeding with or without NAM supplementation on TRP- NAM pathway metabolites, SIRT1 and downstream targets, and autophagy levels. a Hepatic NAD+ levels and TRP- NAM pathway metabolites \((n = 6)\) . b SIRT1 and PGC- 1 \(\alpha\) western blots \((n = 3)\) . c p65 and Acetyl- p65 western blots \((n = 3)\) . d Autophagy markers LC3 western blots \((n = 3)\) . e Quantification of protein levels in western blots.
+
+<--- Page Split --->
+<|ref|>text<|/ref|><|det|>[[40, 45, 919, 88]]<|/det|>
+\(*p < 0.05\) , \(**p < 0.01\) , \(***p < 0.001\) , ns as not significant, one- way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M.  
+
+<|ref|>image<|/ref|><|det|>[[70, 108, 899, 504]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 536, 116, 555]]<|/det|>
+<center>Figure 6 </center>  
+
+<|ref|>text<|/ref|><|det|>[[40, 577, 944, 689]]<|/det|>
+The effect of SIRT1 modulators on basic animal characteristics. a Experiment design. b Body weight change throughout experiment \((n = 6)\) . c Average food and liquid intake during day 7 to day 14 \((n = 6)\) . d Final body weight, body length, and weight for length ratio assessed at day 14 \((n = 6)\) . e Liver weight, liver weight to body weight ratio \((n = 6)\) . \(*p < 0.05\) , \(**p < 0.01\) , \(***p < 0.001\) , ns as not significant, one- way ANOVA followed by Tukey's post hoc test. Data are shown as the mean ± S.E.M.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[62, 55, 930, 480]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 504, 116, 524]]<|/det|>
+<center>Figure 7 </center>  
+
+<|ref|>text<|/ref|><|det|>[[40, 546, 955, 704]]<|/det|>
+The effect of SIRT1 modulators on hepatic steatosis, mitochondrial characteristics, SIRT1 and its downstream targets. a Representative hematoxylin and eosin staining images of the liver (20X magnification). Cytoplasm was stained in red, and nucleus was stained in purple. b Quantification of liver histology and TG levels \((n = 6)\) . c mtDNA copy number \((n = 6)\) . d ATP levels \((n = 6)\) . e mRNA expression of \(\beta\) - oxidation genes \((n = 6)\) . f mRNA expression of lipid genesis genes \((n = 6)\) . g SIRT1 and PGC- 1α western blots and quantification \((n = 3)\) . \(^{*}p < 0.05\) , \(^{**}p < 0.01\) , \(^{***}p < 0.001\) , ns as not significant, one- way ANOVA followed by Tukey's post hoc test. Data are shown as the mean \(\pm\) S.E.M. Scale bars are as indicated.
+
+<--- Page Split --->
+<|ref|>image<|/ref|><|det|>[[65, 60, 927, 485]]<|/det|>
+<|ref|>image_caption<|/ref|><|det|>[[42, 519, 117, 538]]<|/det|>
+<center>Figure 8 </center>  
+
+<|ref|>text<|/ref|><|det|>[[40, 560, 951, 763]]<|/det|>
+Proposed model of the role of the TRP- NAM pathway in malnutrition- induced hepatic metabolic disturbances. In protein malnutrition, decreased TRP availability will decrease the kynurenine pathway activity, which is associated with NAD+ and NAM deficiency. This would disturb NAD+ salvage pathway, including SIRT1, influence its downstream target PGC- 1α and autophagy, which affect mitochondrial quality and function. These changes lead to ATP depletion and lipid accumulation in the liver. We hypothesize that supplement with TRP- NAM modulator would influence NAD+ salvage pathway. This would thereby activate SIRT1, influence PGC- 1α deacetylation and autophagy, which will have a positive effect on mitochondrial health, affect mitochondrial biogenesis and clearance of damaged mitochondrial, then improve ATP generation and reduce lipid accumulation in the liver.  
+
+<|ref|>sub_title<|/ref|><|det|>[[44, 785, 310, 812]]<|/det|>
+## Supplementary Files  
+
+<|ref|>text<|/ref|><|det|>[[44, 836, 764, 857]]<|/det|>
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+<|ref|>text<|/ref|><|det|>[[60, 875, 354, 894]]<|/det|>
+Supplementary information.pdf
+
+<--- Page Split --->

preprint/preprint__6045f1cc7053a878943843f76d2ebd452da890290222e5f1735908e055ec6649/images_list.json

@@ -0,0 +1,257 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1: (a) Schematic illustration of the local helicoidal order modulation in cholesterics, defining the director \\(\\mathbf{n}\\) , the helix axis \\(\\mathbf{m}\\) and the helix pitch \\(p_0\\) . The wavelength- and polarization-selective Bragg diffraction is illustrated for three different angles of incidence. Cross sections of cholesteric shells are drawn schematically for tangential (b) and normal (c) boundary conditions, in the latter case ignoring the topographical surface modulation found in the experiments. The density of the inner isotropic aqueous solution droplet is assumed lower than that of the LC, driving the droplet upwards in gravity and giving the shell a thin top and thick bottom.",
+    "footnote": [],
+    "bbox": [
+      [
+        160,
+        90,
+        835,
+        234
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2: Transmission POM images (from Supplementary Video 1) of a shell of the CLC base mixture stabilized by \\(86 - 87\\%\\) hydrolyzed PVA heated from room temperature to \\(T = 73.7^{\\circ}\\mathrm{C}\\) , where it is fully isotropic. The heating rate changes across three ranges: \\(5^{\\circ}\\mathrm{C / min}\\) for \\(T = 25 - 65^{\\circ}\\mathrm{C}\\) , \\(1^{\\circ}\\mathrm{C / min}\\) for \\(T = 65 - 69^{\\circ}\\mathrm{C}\\) , and \\(0.3^{\\circ}\\mathrm{C / min}\\) for \\(T = 69 - 74^{\\circ}\\mathrm{C}\\) . The shell is between crossed polarizers (orientations indicated in (a)) and the focus is at the equator of the shell in (a–d), then changing to the bottom surface in (e–h). Scale bar: \\(50\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        135,
+        87,
+        863,
+        352
+      ]
+    ],
+    "page_idx": 6
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3: (a-d) Transmission POM images (polarizer orientation indicated in (a)) of a CLC shell produced with a 6 wt.% HDDA mixture as it is heated from room temperature to to \\(52^{\\circ}\\mathrm{C}\\) . UV light is applied to the shell at \\(47.4^{\\circ}\\mathrm{C}\\) for 180 s, initiating polymerization. The heating rate was separated in four ranges: \\(5^{\\circ}\\mathrm{C / min}\\) for \\(25 - 45^{\\circ}\\mathrm{C}\\) , \\(0.3^{\\circ}\\mathrm{C / min}\\) for \\(45 - 47^{\\circ}\\mathrm{C}\\) , \\(0.1^{\\circ}\\mathrm{C / min}\\) for \\(47 - 48^{\\circ}\\mathrm{C}\\) , and \\(1^{\\circ}\\mathrm{C / min}\\) for \\(48 - 52^{\\circ}\\mathrm{C}\\) . The focus is at the equator of the shell in (a) and at the bottom surface in (b-d). Scale bar: \\(50\\mu \\mathrm{m}\\) . (e-j) SEM images of two gold-coated shells, with \\(9\\%\\) (e-g) and \\(10\\%\\) (h-j) HDDA, respectively. Both were polymerized at room temperature, yielding tangential boundary conditions for the former and normal for the latter. Images (e/h), (f/g) and (g/h), respectively, are obtained on the outer, inner and cross section surfaces of each shell. Scale bar on images (e,f) and (h,i) is \\(50\\mu \\mathrm{m}\\) , and on images (g/j) \\(10\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        95,
+        880,
+        545
+      ]
+    ],
+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4: (a-j) Reflection POM images of a CLC shell produced with 6 wt% HDDA mixture suspended in and surrounding isotropic PVA solutions (1.5 wt.%, 86–87% hydrolyzed) in glycerol (70 wt%) and water, as it is heated from room temperature until the shell turns isotropic. Temperature values are those reported by the hot stage, which are higher than at the sample because the experiment required the hot stage to be operated with open lid. The heating rate was separated in three ranges: \\(5^{\\circ}\\mathrm{C / min}\\) for \\(25.4 - 47.0^{\\circ}\\mathrm{C}\\) , \\(1^{\\circ}\\mathrm{C / min}\\) for \\(47.0 - 49.0^{\\circ}\\mathrm{C}\\) , and \\(0.3^{\\circ}\\mathrm{C / min}\\) for \\(49.0 - 61.0^{\\circ}\\mathrm{C}\\) . The focus is at the shell equator in (a-c) and at the top surface in (d-j). Scale bar: \\(50\\mu \\mathrm{m}\\) . (k-l) Reflection POM images of a polymerized and washed shell in air, made from the same CLC mixture and surrounding isotropic phases. The focus is at the shell equator in (k) and at the top surface in (l). Scale bar: \\(20\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        88,
+        882,
+        520
+      ]
+    ],
+    "page_idx": 11
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5: Polymerized, cleaned and dried FCD shells from a mixture with \\(9\\%\\) HDDA are dispersed in NOA160 binder that is photocured into a solid film. POM images in transmission mode are taken without analyzer (a) and between crossed polarizers (b), and reflection images between crossed polarizers are taken with two slightly different focus adjustments (c,d). Macroscopic photos (no polarizers, ambient illumination) of the film on a black background (left column) compared with a corresponding film with tangential-aligned shells (right column) are shown as function of viewing angle in (e)–(h). The large cyan spots in the left sample are due to a few polymerized CLC droplets dispersed together with the shells.",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        88,
+        880,
+        397
+      ]
+    ],
+    "page_idx": 13
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6: The equilibrium profiles (a1-e1) with tangential boundary conditions on the inner and outer surfaces with anchoring strength \\(\\omega = \\omega_{1} = \\omega_{2} = 0.1\\) , (a2-e2) with normal on the inner surface and tangential on the outer surface \\(\\omega = \\omega_{1} = \\omega_{2} = 0.01\\) , (a3-e3) with tangential on the inner surface and normal on the outer surface \\(\\omega = \\omega_{1} = \\omega_{2} = 0.01\\) , (a4-e4) with normal on the inner and outer surfaces \\(\\omega = \\omega_{1} = \\omega_{2} = 0.01\\) , at fixed temperature \\(t = -1.79\\) , \\(\\xi_{R} = 1 / 50\\) , \\(\\eta = 1\\) , \\(\\sigma = 10\\pi\\) , \\(c = 0.1\\) , \\(\\rho = 0.7\\) . (ai) Bottom of outer surface; (bi) top of outer surface; (ci) bottom of inner surface; (di) top of inner surface; (ei) Cross-section, \\(i = 1, \\dots , 4\\) . The colour bars label the biaxiality parameter \\(\\beta = 1 - 6 \\frac{\\left(t r \\mathbf{Q}^{3}\\right)^{2}}{\\left(t r \\mathbf{Q}^{2}\\right)^{3}}\\) in (a1-d1), \\(\\gamma_{1} = |\\mathbf{n} \\cdot \\mathbf{e}_{x}|\\) in (e1), and \\(\\gamma_{2} = |\\mathbf{n} \\cdot \\mathbf{e}_{\\xi}|\\) in (a2-e4), where \\(\\mathbf{e}_{\\xi}\\) is the unit \\(\\xi\\) -direction in the bispherical coordinate, in the Supplementary Information. The white lines in (a1-d1) label the director \\(\\mathbf{n}\\) , which is the eigenvector of \\(\\mathbf{Q}\\) with the largest eigenvalue.",
+    "footnote": [],
+    "bbox": [
+      [
+        115,
+        85,
+        886,
+        584
+      ]
+    ],
+    "page_idx": 18
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7: (a-h) Transmission POM images (polarizer orientations indicated in (a)) of a CLC shell produced with a 6 wt.% HDDA mixture and stabilized by 5 wt.% aqueous solution of PVA ( \\(M_{w} = 85 - 124 \\mathrm{kg / mol}\\) , \\(99\\% \\mathrm{hydrolyzed}\\) ) solution as it is heated from room temperature to \\(50^{\\circ}\\mathrm{C}\\) and then cooling to \\(25^{\\circ}\\mathrm{C}\\) . The temperature changing rate was separated in four ranges: \\(5^{\\circ}\\mathrm{C / min}\\) for \\(23.6 - 43^{\\circ}\\mathrm{C}\\) , \\(1^{\\circ}\\mathrm{C / min}\\) for \\(43 - 45^{\\circ}\\mathrm{C}\\) , \\(0.3^{\\circ}\\mathrm{C / min}\\) for \\(45 - 50^{\\circ}\\mathrm{C}\\) , and \\(3^{\\circ}\\mathrm{C / min}\\) for \\(50 - 25^{\\circ}\\mathrm{C}\\) . The focus is at equator of the shell in (a-b) and at the bottom surface in (c-h). Scale bar: \\(50\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        460,
+        883,
+        744
+      ]
+    ],
+    "page_idx": 23
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_8.jpg",
+    "caption": "Figure 8: Chemical structures of monomers used to prepare CLC mixtures.",
+    "footnote": [],
+    "bbox": [
+      [
+        137,
+        95,
+        866,
+        404
+      ]
+    ],
+    "page_idx": 28
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Figure S1: Shell production using a glass capillary microfluidic set-up. The production was done around \\(10^{\\circ}\\mathrm{C}\\) below the clearing temperature for each mixture. For mixtures with low HDDA content, the heating is important to reduce the effective viscosity. Scale bar: \\(200\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        250,
+        446,
+        738,
+        568
+      ]
+    ],
+    "page_idx": 38
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "Figure S2: An equilibrium profile on a symmetric shell with tangential boundary conditions on the inner and outer surfaces, at fixed temperature \\(t = -1.79\\) , \\(\\xi_{R} = 1 / 50\\) , \\(\\eta = 1\\) , \\(\\sigma = 10\\pi\\) , \\(\\omega_{1} = \\omega_{2} = 0.1\\) . (a) Bottom of outer surface; (b) top of outer surface; (c) bottom of inner surface; (d) top of inner surface; (e) cross-section. The colorbars label the \\(\\beta = 1 - 6 \\frac{\\left(t r \\mathbf{Q}^{3}\\right)^{2}}{\\left(t r \\mathbf{Q}^{2}\\right)^{3}}\\) in (a-d), \\(\\gamma_{1} = |\\mathbf{n} \\cdot \\mathbf{e}_{x}|\\) in (e). The white lines in (a-d) label the director \\(\\mathbf{n}\\) , which is the eigenvector of \\(\\mathbf{Q}\\) with the largest eigenvalue.",
+    "footnote": [],
+    "bbox": [
+      [
+        150,
+        198,
+        848,
+        333
+      ]
+    ],
+    "page_idx": 45
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "Figure S3: An equilibrium profile on a symmetric shell with hybrid boundary conditions - normal boundary conditions on the outer surface and tangential boundary conditions on the inner surface. The model parameters are \\(t = -1.79\\) , \\(\\xi_{R} = 1 / 50\\) , \\(\\eta = 1\\) , \\(\\sigma = 10\\pi\\) , \\(\\omega = \\omega_{1} = \\omega_{2} = 0.02\\) . The profile of \\(\\gamma_{2} = |\\mathbf{n} \\cdot \\mathbf{e}_{\\xi}|\\) where \\(\\mathbf{e}_{\\xi}\\) is the unit \\(\\xi\\) -direction in bispherical coordinate, on (a) the surface with \\(r = 1\\) , 0.9, 0.8, 0.7 (from left to right), and (b) cross-section.",
+    "footnote": [],
+    "bbox": [
+      [
+        158,
+        510,
+        828,
+        645
+      ]
+    ],
+    "page_idx": 45
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "Figure S4: (a) Differential scanning calorimetry (DSC) thermograms (first heating run, with a rate of \\(5^{\\circ}\\mathrm{C / min}\\) .) of the crystallized CLC base mixture, without HDDA. The indicated temperatures are onset melting and clearing temperatures. (b) DSC thermograms (second heating run, with a rate of \\(10^{\\circ}\\mathrm{C / min}\\) .) of CLC mixtures with different HDDA concentrations. The indicated temperatures are the onset temperatures for clearing in each mixture.",
+    "footnote": [],
+    "bbox": [
+      [
+        130,
+        586,
+        833,
+        799
+      ]
+    ],
+    "page_idx": 46
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "Figure S5: The effective shear viscosity (see text for comments on interpretation) of CLC mixtures as a function of \\(w_{HDDA}\\) , i.e., the mass percentage of HDDA in the CLC mixture, at room temperature.",
+    "footnote": [],
+    "bbox": [
+      [
+        315,
+        111,
+        646,
+        312
+      ]
+    ],
+    "page_idx": 47
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "Figure S6: Transmission POM images (polarizer orientation indicated in (a)) of a CLC shell produced with a 6 wt.% HDDA mixture and stabilized by our standard PVA solution as it is heated from room temperature to the isotropic state. The heating rate was separated in three ranges: \\(5^{\\circ}\\mathrm{C / min}\\) for \\(23.7 - 43^{\\circ}\\mathrm{C}\\) , \\(1^{\\circ}\\mathrm{C / min}\\) for \\(43 - 45^{\\circ}\\mathrm{C}\\) , and \\(0.3^{\\circ}\\mathrm{C / min}\\) for \\(45 - 50^{\\circ}\\mathrm{C}\\) . The focus is at the shell equator in (a-d) and at the bottom surface in (e-l). Scale bar: \\(50\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        133,
+        99,
+        864,
+        504
+      ]
+    ],
+    "page_idx": 48
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_6.jpg",
+    "caption": "Figure S7: Transmission POM images (polarizer orientation indicated in (b)) at room temperature of CLC shells produced with 10 wt. \\(\\%\\) (a) and 11 wt. \\(\\%\\) (b) HDDA mixtures, after annealing at room temperature. Scale bar: \\(50\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        312,
+        102,
+        684,
+        242
+      ]
+    ],
+    "page_idx": 49
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_7.jpg",
+    "caption": "Figure S8: Transmission POM images (polarizer orientation indicated in (a)) of a CLC shell produced with a 6 wt. \\(\\%\\) HDDA mixture stabilized by F-127 after annealing at room temperature. The texture at room temperature is shown in (a), while (b) shows the texture after placing the shell in a fridge at \\(5^{\\circ}\\mathrm{C}\\) overnight. Scale bar: \\(50\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        312,
+        658,
+        684,
+        799
+      ]
+    ],
+    "page_idx": 49
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_8.jpg",
+    "caption": "Figure S9: Transmission POM images (polarizer orientations indicated in (a)) of a CLC shell produced with a 0 wt.% HDDA mixture and stabilized by 1 wt.% aqueous solution of Pluronic F-127 block copolymer surfactant as inner and outer phase, as it is heated from room temperature to isotropic. The heating rate was separated in two ranges: \\(5^{\\circ}\\mathrm{C / min}\\) for \\(23.5 - 55^{\\circ}\\mathrm{C}\\) and \\(1^{\\circ}\\mathrm{C / min}\\) for \\(55 - 72^{\\circ}\\mathrm{C}\\) . The focus is at equator of the shell in (a-e) and at the bottom surface in (f-l). Scale bar: \\(50\\mu \\mathrm{m}\\) .",
+    "footnote": [],
+    "bbox": [
+      [
+        113,
+        92,
+        884,
+        533
+      ]
+    ],
+    "page_idx": 50
+  }
+]

preprint/preprint__6045f1cc7053a878943843f76d2ebd452da890290222e5f1735908e055ec6649/preprint__6045f1cc7053a878943843f76d2ebd452da890290222e5f1735908e055ec6649.mmd

@@ -0,0 +1,650 @@
+
+# Tunable templating of photonic microparticles via liquid crystal order-guided adsorption of amphiphilic polymers in emulsions  
+
+Jan Lagerwall ( \(\boxed{\pm}\) jan.lagerwall@lcsoftmatter.com) University of Luxembourg https://orcid.org/0000- 0001- 9753- 1147  
+
+Xu Ma University of Luxembourg  
+
+Yucen Han University of Strathclyde https://orcid.org/0000- 0001- 9436- 4224  
+
+Yan- Song Zhang University of Luxembourg  
+
+Yong Geng University of Luxembourg https://orcid.org/0000- 0001- 5299- 1596  
+
+Apala Majumdar University of Strathclyde  
+
+Article  
+
+Keywords:  
+
+Posted Date: August 7th, 2023  
+
+DOI: https://doi.org/10.21203/rs.3.rs- 3228865/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- 45674- 5.
+
+<--- Page Split --->
+
+# Tunable templating of photonic microparticles via liquid crystal order-guided adsorption of amphiphilic polymers in emulsions  
+
+Xu Ma, \(^{1}\) Yucen Han, \(^{1}\) Yan- Song Zhang, \(^{1}\) Yong Geng, \(^{1}\) Apala Majumdar, \(^{2}\) and Jan P.F. Lagerwall\*, \(^{1}\)  
+
+\(^{1}\) Experimental Soft Matter Physics group, Department of Physics and Materials Science, University of Luxembourg, L- 1511, Luxembourg \(^{2}\) Department of Mathematics and Statistics, University of Strathclyde, Glasgow, United Kingdom  
+
+E- mail: jan.lagerwall@lcsotfmatter.com  
+
+## Abstract  
+
+Multiple emulsions are usually stabilized by amphiphilic molecules that combine the chemical characteristics of the different phases in contact. When one phase is a liquid crystal (LC), the choice of stabilizer also determines its configuration, but conventional wisdom assumes that the orientational order of the LC has no impact on the stabilizer. Here we show that, for the case of amphiphilic polymer stabilizers, this impact can be considerable. The mode of interaction between stabilizer and LC changes if the latter is heated close to its isotropic state, initiating a feedback loop that reverberates on the LC in form of a complete structural rearrangement. We utilize this phenomenon to dynamically tune the configuration of cholesteric LC shells from one with radial helix and spherically symmetric Bragg diffraction to a focal conic domain configuration
+
+<--- Page Split --->
+
+with highly complex optics. Moreover, we template photonic microparticles from the LC shells by photopolymerizing them into solids, retaining any selected LC- derived structure. Our study places LC emulsions in a new light, calling for a reevaluation of the behavior of stabilizer molecules in contact with long- range ordered phases, while also enabling highly interesting photonic elements with application opportunities across vast fields.  
+
+## Introduction  
+
+Introduced only 16 years ago, \(^{1}\) liquid crystal shells—a double emulsion where a middle phase of hydrophobic liquid crystal (LC) forms a thin self- closing spherical layer that surrounds, and is surrounded by, isotropic aqueous solutions—have emerged into a prolific platform for conducting stimulating fundamental physics research \(^{2,3}\) as well as making innovative and broadly applicable photonic materials. \(^{4,5}\) The latter activities focus strongly on cholesteric LC (CLC), also called chiral nematic, shells that exhibit omnidirectional wavelength- and polarization- selective retroreflection, giving rise to intriguing colorful patterns. \(^{6 - 8}\) This highly useful phenomenon arises because CLCs self- organize with a helical modulation of period (pitch) \(p_{0}\) of the director \(\mathbf{n}\) (the average orientation of the LC- forming molecules, called mesogens) along an axis \(\mathbf{m}\) that is perpendicular to \(\mathbf{n}\) , see Fig. 1a.  
+
+Because LCs are birefringent with \(\mathbf{n}\) equal to the optic axis, the helical modulation leads to a periodic variation of the effective refractive index along \(\mathbf{m}\) that causes Bragg diffraction of light with wavelength \(\lambda = \bar{n}\cos \theta\) , where \(\bar{n}\) is the average refractive index in the CLC and \(\theta\) is the angle of incidence with respect to \(\mathbf{m}\) . The reflected light is circularly polarized with the same handedness as the helix. The fact that \(p_{0}\) can easily be tuned by varying the composition of the CLC mixture means that we can choose the retroreflection \((\theta = 0)\) wavelength at will. Finally, by using reactive mesogens (RMs), the shells can be turned solid and durable by photopolymerization once the CLC order has reached its equilibrium state. \(^{9 - 11}\) The resulting powerful photonic components have stimulated proposals for appli
+
+<--- Page Split --->
+![](images/Figure_1.jpg)
+
+<center>Figure 1: (a) Schematic illustration of the local helicoidal order modulation in cholesterics, defining the director \(\mathbf{n}\) , the helix axis \(\mathbf{m}\) and the helix pitch \(p_0\) . The wavelength- and polarization-selective Bragg diffraction is illustrated for three different angles of incidence. Cross sections of cholesteric shells are drawn schematically for tangential (b) and normal (c) boundary conditions, in the latter case ignoring the topographical surface modulation found in the experiments. The density of the inner isotropic aqueous solution droplet is assumed lower than that of the LC, driving the droplet upwards in gravity and giving the shell a thin top and thick bottom. </center>  
+
+cations across diverse fields, from invisibly encoding information onto surfaces \(^9\) to linking physical objects securely to their digital twins \(^{12}\) and thereby allow secure authentication and thwart counterfeiting, \(^{7,13,14}\) and from generating non- spectral colors using structural color only \(^{15}\) to providing human- invisible navigation support for robots and augmented reality devices. \(^{4}\)  
+
+The spherical symmetry giving rise to omnidirectional selective retroreflection is achieved by preparing the CLC shells such that \(\mathbf{m}\) is oriented radially. This is done by imposing boundary conditions that force \(\mathbf{n}\) to be in the plane of the CLC- water interfaces (tangential, also called planar, alignment), thereby promoting radial \(\mathbf{m}\) (since \(\mathbf{m} \perp \mathbf{n}\) ). The traditional way of achieving this is to stabilize the shells using a water soluble polymer such as polyvinylalcohol (PVA), which should not enter the LC and thus allow water in contact with the LC to promote tangential \(\mathbf{n}\) . If normal alignment ( \(\mathbf{n}\) perpendicular to the interface, for flat samples often called homeotropic alignment) is desired, ionic surfactants are often used. However, boundary conditions at an interface between an LC and an isotropic liquid solution are complex, with surprising variations reported. In fact, ionic surfactants can give both tangential and hybrid alignment if the surfactant concentration is kept low, \(^{16}\) and polymeric stabilizers
+
+<--- Page Split --->
+
+were recently found to change their aligning influence from tangential to normal as the shells are heated close to the LC- isotropic transition. \(^{17,18}\) Very recently we also demonstrated that the chemical nature of the mesogens has great impact on both shell stability and alignment. \(^{19}\)  
+
+In this work we make use of the temperature- dependent boundary conditions enabled by amphiphilic polymeric stabilizers to dynamically tune the configuration of CLC shells with \(p_0\) in the range for visible Bragg diffraction, from radial \(\mathbf{m}\) with omnidirectional Bragg diffraction \(^{6,15}\) at low temperature to a modulated polygonal texture with (imperfect) focal conic domain (FCD) configuration \(^{2,20,21}\) at elevated temperature, or vice versa. The highly regular packing of FCDs has been well studied in smectic- A (SmA) LCs, \(^{22 - 24}\) also on curved substrates, \(^{25 - 27}\) but SmA phases do not exhibit Bragg diffraction of visible light. Cholesteric FCDs are less studied, and CLC shells were investigated only with \(p_0\) much too long to give visible reflections. \(^{21}\) Moreover, the ease of our method in continuously tuning the configuration offers an unprecedented level of structural control. We propose a new model for explaining the tunability, for the first time considering the entropic impact of the LC orientational order on the conformational freedom of water- dissolved amphiphilic polymers used to stabilize LC shells. This leads to a feedback loop where the stabilizer influences the LC configuration, but the LC order also influences the stabilizer molecules' behavior, reverberating back to the LC in terms of boundary conditions that change with temperature.  
+
+Using short- pitch CLCs we obtain a self- assembled structure that is a topographically inverted analogue to the intricate polygonal texture on the cuticle of certain beetles, responsible for their spectacular reflective colors. \(^{28,29}\) The experimental results are complemented by a mathematical modeling and numerical simulation of cholesteric ordering in shells with different combinations of boundary conditions, reproducing the experimental findings. By using reactive mesogens we transform the LC shells into solid particles by photopolymerization at any temperature of our choice, preserving either the radial helix or the FCD configuration, exhibiting very different photonic functionality.
+
+<--- Page Split --->
+
+## Results  
+
+## Texture development on heating toward the clearing transition  
+
+To demonstrate the dynamic alignment tuning we first produce shells of a polymerizable CLC base mixture using a standard aqueous solution of PVA (86- 87% hydrolyzed; see Methods for further details) for the surrounding isotropic phases. After annealing until the shells are nearly defect- free, we heat them from room temperature to \(T_{N^{*}I}\approx 72.4^{\circ}\mathrm{C}\) (we use \(T_{N^{*}I}\) to indicate the onset on heating of the transition, which extends over a range of a few degrees since we are using multicomponent CLC mixtures). The process is monitored with polarizing optical microscope (POM) in transmission mode, as shown in full in Supplementary Video 1, representative snapshots focusing on a single shell shown in Fig. 2. The aqueous PVA solutions impose tangential alignment of the CLC shell at room temperature, as recognized by a texture (Fig. 2a) that is characteristic of tangential short- pitch CLC shells viewed in transmission. \(^{13,30}\) As the temperature is raised, the shell texture remains qualitatively unchanged up to \(T\approx 70^{\circ}\mathrm{C}\) , see Fig. 2b, the only significant change being a reduction in the number of interference rings which can be understood as a result of the decreasing birefringence upon heating. \(^{30}\)  
+
+However, at an alignment transition onset temperature \(T_{t} = 70.8^{\circ}\mathrm{C}\) a qualitative texture change is seen, with radial striations first appearing along the circumference, see panel (c). As the temperature is further raised to the vicinity of \(T_{N^{*}I}\) , multiple polygons appear, as recognized in Fig. 2d- f. In (d), a transient texture reminiscent of soliton- like structures reported for CLC shells with much longer pitch \(^{31}\) can be seen temporarily. This suggests \(^{20}\) that the initially tangential boundary conditions change to normal—at one or both interfaces—near the clearing transition. When the temperature reaches the window of clearing, about \(T = 72.4 - 73.7^{\circ}\mathrm{C}\) , the domains gradually disappear and the texture gets increasingly dark (g), until the shell can no longer be recognized between crossed polarizers because it is fully isotropic (Fig. 2h). Unfortunately, the shells break almost immediately when they are again
+
+<--- Page Split --->
+![](images/Figure_2.jpg)
+
+<center>Figure 2: Transmission POM images (from Supplementary Video 1) of a shell of the CLC base mixture stabilized by \(86 - 87\%\) hydrolyzed PVA heated from room temperature to \(T = 73.7^{\circ}\mathrm{C}\) , where it is fully isotropic. The heating rate changes across three ranges: \(5^{\circ}\mathrm{C / min}\) for \(T = 25 - 65^{\circ}\mathrm{C}\) , \(1^{\circ}\mathrm{C / min}\) for \(T = 65 - 69^{\circ}\mathrm{C}\) , and \(0.3^{\circ}\mathrm{C / min}\) for \(T = 69 - 74^{\circ}\mathrm{C}\) . The shell is between crossed polarizers (orientations indicated in (a)) and the focus is at the equator of the shell in (a–d), then changing to the bottom surface in (e–h). Scale bar: \(50\mu \mathrm{m}\) . </center>  
+
+cooled down to the cholesteric state (this is further discussed toward the end of the article). For the purpose of facilitating comparisons with the experiments to follow, we calculate a reduced temperature for the onset of the alignment transition, stating all measured temperature values in Kelvin, as \(T_{r} = \frac{T_{t} - T_{N^{*}t}}{T_{N^{*}t}} \approx \frac{343.8 - 345.3}{345.3} \approx - 0.0043\) .  
+
+## Tuning the mixture for optimized phase sequence and viscosity  
+
+The physical behavior of LC mixtures can be greatly modified by changing the composition or adding or removing certain components, the impact depending on the specific interactions between the mixed compounds. \(^{32}\) Adding a low molar mass flexible molecule like 1,6- hexanediol diacrylate (HDDA) disturbs ordering, hence it lowers both melting and clearing points, and it reduces the effective shear viscosity experienced during flow in a microfluidic device. Both effects are useful to us, because the effective shear viscosity of the basic CLC mixture has the rather high value of 1085 mPa s at room temperature, and its melting range
+
+<--- Page Split --->
+
+is near room temperature (Fig. S4a in the Supplementary Information). This requires us to heat all liquids and the glass capillary microfluidic device to successfully produce shells with this mixture, whereas HDDA- doped mixtures should allow processing at room temperature. The dual acrylate termination of HDDA ensures that it will become part of the final solid achieved by photopolymerization. \(^{33}\)  
+
+The expected reduction in \(T_{N^{*}I}\) is confirmed by DSC (Fig. S4b in the Supplementary Information), monotonically decreasing with increasing HDDA content from the original \(T_{N^{*}I} \approx 72.4^{\circ}\mathrm{C}\) of the CLC base mixture to \(T_{N^{*}I} \approx 29.4^{\circ}\mathrm{C}\) with \(11\%\) HDDA, yet with negligible impact on the CLC reflection color. With increasing HDDA concentration, the peak in the heat flow curve broadens, reflecting an expanding temperature range of the phase transition. The reduction in viscosity is also confirmed, see Fig. S5 in the Supplementary Information. We find an apparently exponential decrease as a function of HDDA mass fraction.  
+
+As a representative example of HDDA- doped CLC shells, we show textures of a shell with \(6\%\) HDDA surrounded by our standard PVA solutions in Supplementary Video 2, snapshots of which are shown in Fig. S6. Upon heating toward \(T_{N^{*}I}\) , the textural behavior is qualitatively identical to that seen in Fig. 2, but the significant difference is that all changes take place at much lower temperature. The alignment transition starts at \(T_{t} = 45.8^{\circ}\mathrm{C}\) and clearing starts at \(T_{N^{*}I} \approx 48.5^{\circ}\mathrm{C}\) , yielding a reduced temperature for the onset of the alignment transition \(T_{r} = \frac{T_{t} - T_{N^{*}I}}{T_{N^{*}I}} \approx \frac{318.8 - 321.5}{321.5} \approx - 0.0084\) . This is about twice the magnitude of when no HDDA was present in the CLC mixture.  
+
+The reduction in temperature of the textural change reflects the reduction in clearing temperature range shown in Fig. S4b. Because the clearing is near room temperature at \(10 - 11\%\) HDDA, annealed shells made with these mixtures exhibit an FCD texture already at room temperature, see Fig. S7 of the Supplementary Information.
+
+<--- Page Split --->
+
+## Polymerizing the shells at different temperatures to lock in different configurations  
+
+During the temperature- driven realignment process, UV light can be used to initiate and drive the polymerization reaction of LC monomers and HDDA at a selected temperature in order to preserve the CLC shell structure in any state we desire. To get a solid CLC shell with FCD configuration, we first anneal a shell made with the \(6\%\) HDDA mixture at room temperature until it exhibits a nearly defect- free tangential texture (Fig. 3a), and then heat it to \(47.4^{\circ}\mathrm{C}\) where it exhibits an FCD texture. We now apply UV light for 180 s to polymerize the shell, see Fig. 3b and Supplementary Video 3. If the tangential configuration is desired, the same UV irradiation procedure is carried out at room temperature directly after annealing. Following polymerization, even with temperature increasing past the clearing transition of the CLC precursor mixture, the shell retains the exact same texture as when polymerization occurred, see Fig.3c- d for the case of a shell polymerized in the FCD state.  
+
+The solid shells are washed by water and acetone following the procedure introduced by Geng et al. \(^{9}\) Because the polymerization induces shrinkage of the shell, it bulges out slightly at the thinnest point as it must still encapsulate the same volume of incompressible aqueous solution inside. The stress induced upon acetone swelling ruptures the bulge, leaving a single hole in each shell that allows complete removal of PVA from the shell inside, leaving a smooth surface of the polymerized CLC material.  
+
+The solid state of the polymerized shells allows us to conduct Scanning Electron Microscopy (SEM) imaging of the shells after coating them with a thin layer of gold, the results shown in Fig. 3e- j. These images provide a deeper understanding of the director field configuration in shells with different texture, as well as of the shell surface topography. In a shell polymerized during tangential alignment both the inner and outer surfaces are smooth, as shown in Fig. 3e- f. In the shell cross section in Fig. 3g, visible pitch lines parallel to the inner and outer surfaces are seen, arising where the director aligns perpendicular to the fracture surface, leading to protrusions and holes since covalent bonds are broken during
+
+<--- Page Split --->
+![](images/Figure_3.jpg)
+
+<center>Figure 3: (a-d) Transmission POM images (polarizer orientation indicated in (a)) of a CLC shell produced with a 6 wt.% HDDA mixture as it is heated from room temperature to to \(52^{\circ}\mathrm{C}\) . UV light is applied to the shell at \(47.4^{\circ}\mathrm{C}\) for 180 s, initiating polymerization. The heating rate was separated in four ranges: \(5^{\circ}\mathrm{C / min}\) for \(25 - 45^{\circ}\mathrm{C}\) , \(0.3^{\circ}\mathrm{C / min}\) for \(45 - 47^{\circ}\mathrm{C}\) , \(0.1^{\circ}\mathrm{C / min}\) for \(47 - 48^{\circ}\mathrm{C}\) , and \(1^{\circ}\mathrm{C / min}\) for \(48 - 52^{\circ}\mathrm{C}\) . The focus is at the equator of the shell in (a) and at the bottom surface in (b-d). Scale bar: \(50\mu \mathrm{m}\) . (e-j) SEM images of two gold-coated shells, with \(9\%\) (e-g) and \(10\%\) (h-j) HDDA, respectively. Both were polymerized at room temperature, yielding tangential boundary conditions for the former and normal for the latter. Images (e/h), (f/g) and (g/h), respectively, are obtained on the outer, inner and cross section surfaces of each shell. Scale bar on images (e,f) and (h,i) is \(50\mu \mathrm{m}\) , and on images (g/j) \(10\mu \mathrm{m}\) . </center>  
+
+the fracture. \(^{34}\) The orientation of these lines indicate a radial helix axis, normal to the shell boundaries, thus with tangential boundary conditions for the director. If the shell is instead polymerized under conditions of FCD formation, we recognize a regular array of protruding polygons with a recessed dot in the center on the outer surface, see Fig. 3h. On the inner
+
+<--- Page Split --->
+
+surface of the shell the polygons are replaced by a diamond lattice with a recessed dot at each vertex, as shown in Fig. 3i. The zoomed- in image of the cross section of this shell (Fig. 3j) reveals undulating pitch lines, as expected for a director field breaking up into FCDs.  
+
+## Reflection behavior during alignment change  
+
+The unique reflective properties of cholesteric LC shells showcase their tremendous potential for various applications. The properties are qualitatively very different for thin- and thick- topped shells. \(^{35}\) As our CLC mixtures are denser than the aqueous solutions used so far, we have a thin top, yielding comparatively weak external reflection and allowing light into the interior of the shell, where it experiences a sequence of internal selective reflections giving rise to a characteristic ring- shaped pattern. \(^{35}\) To instead emphasize the external reflections we need a thick- topped shell, hence we change both the inner and outer phases to a 1.5 wt.% solution of PVA (same type as before) in a mixture of 30 wt.% water and 70 wt.% glycerol to give it greater density than that of the CLC. The internal droplet then sinks down in gravity, yielding a thick- topped shell which gives strong reflection when we observe the shells from the top in the POM.  
+
+In Fig. 4a- j (snapshots from the Supplementary Video 4), we show the reflection behavior between crossed polarizers of such a thick- topped shell of a CLC mixture with 6 wt.% HDDA as we heat it from room temperature to \(59^{\circ}\mathrm{C}\) according to the hot stage, at which the shell is fully isotropic. This temperature reading for \(T_{N^{*}I}\) is higher than when the regular aqueous PVA solution is used, but this is most likely an artifact arising from the way the experiment is conducted. Here the shells are in a droplet of the PVA solution on a glass slide, without any cover glass, thus with a top interface to air. This means that water evaporates as the sample is heated, and if the hot stage lid is closed, the water condenses on the top glass, blurring the images. For this reason we work with open hot stage, which means that the reported temperatures are higher than the actual sample temperatures. An additional effect may be related to some fraction of HDDA dissolving into the glycerol- rich isotropic phases,
+
+<--- Page Split --->
+![](images/Figure_4.jpg)
+
+<center>Figure 4: (a-j) Reflection POM images of a CLC shell produced with 6 wt% HDDA mixture suspended in and surrounding isotropic PVA solutions (1.5 wt.%, 86–87% hydrolyzed) in glycerol (70 wt%) and water, as it is heated from room temperature until the shell turns isotropic. Temperature values are those reported by the hot stage, which are higher than at the sample because the experiment required the hot stage to be operated with open lid. The heating rate was separated in three ranges: \(5^{\circ}\mathrm{C / min}\) for \(25.4 - 47.0^{\circ}\mathrm{C}\) , \(1^{\circ}\mathrm{C / min}\) for \(47.0 - 49.0^{\circ}\mathrm{C}\) , and \(0.3^{\circ}\mathrm{C / min}\) for \(49.0 - 61.0^{\circ}\mathrm{C}\) . The focus is at the shell equator in (a-c) and at the top surface in (d-j). Scale bar: \(50\mu \mathrm{m}\) . (k-l) Reflection POM images of a polymerized and washed shell in air, made from the same CLC mixture and surrounding isotropic phases. The focus is at the shell equator in (k) and at the top surface in (l). Scale bar: \(20\mu \mathrm{m}\) . </center>  
+
+thereby reducing the HDDA content in the CLC phase and thus raising \(T_{N^{*}I}\) , see Fig. S4b.  
+
+The top interface to air is important for the reflection behavior at room temperature, because the lower refractive index of the bounding medium means that we get three types of reflections from the shell: \(^{36}\) a retroreflection spot with red color in the middle, a discontinuous ring of blue spots arising from cross communication directly between adjacent shells, and a discontinuous ring with slightly smaller radius of green spots arising from cross communi
+
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+cation mediated by a Total Internal Reflection event at the water- air interface. As the shell is heated, the reflection pattern remains quite constant up to \(47^{\circ}\mathrm{C}\) (b), but at \(49.3^{\circ}\mathrm{C}\) (c) we clearly see that the central spot as well as the cross communication spots get blurred. The alignment transition has started, and at \(49.5^{\circ}\mathrm{C}\) (d) we recognize the break- up into FCDs also in the retroreflection spot. As can be seen in Supplementary Video 4, the texture now becomes extremely sensitive to the focus, with even fine adjustments significantly changing the pattern. The cross communication remains active but the resulting pattern is almost impossible to distinguish if the focal plane is at the retroreflection from the shell top. Upon further heating the top reflection gradually expands into a flower- like arrangement which in one focal plane (e- f) is reminiscent of the appearance of the FCDs in the cuticle of the beetle Chrysina Gloriosa in dark field microscopy, \(^{28}\) but in a slightly different focal plane (g) shifts to a set of six radial reflection lines. Upon further heating, the reflection texture loses both regularity and intensity at \(52.4^{\circ}\mathrm{C}\) , indicating that the transition to isotropic phase has started. At \(53^{\circ}\mathrm{C}\) (i) the red reflection can hardly be recognized and at \(59^{\circ}\mathrm{C}\) (j) the isotropic state of the shell is confirmed by an entirely black image.  
+
+We also study a solid, washed and dried shell made from the same mixture, photopolymerized below the clearing point but after the transition to FCDs, using reflection POM, see Fig. 4k- l. The shell is surrounded by air during imaging. Because the washing leads to some shrinkage of the structure, and thus reduction of \(p_{0}\) , the reflection is now green- yellow rather than red. We find a quite regular reflection pattern also in the polymerized shell, with a character that depends sensitively on the focus, just like for the CLC precursor shell. Focusing on the equator (k) we see a green spiky pattern around the perimeter, while focus at the top (l) shows mainly yellow reflections from the boundaries and centers of the FCDs.  
+
+To make a first assessment of the usefulness of the FCD- templated solid particles, we disperse them in a photocurable transparent binder (NOA160 from Norland Optical Adhesives) with refractive index \(n = 1.6\) , which is similar to the average refractive index \(\bar{n}\) of the polymerized CLC. Taking care to avoid air bubbles, we distribute about 1000 shells of
+
+<--- Page Split --->
+![](images/Figure_5.jpg)
+
+<center>Figure 5: Polymerized, cleaned and dried FCD shells from a mixture with \(9\%\) HDDA are dispersed in NOA160 binder that is photocured into a solid film. POM images in transmission mode are taken without analyzer (a) and between crossed polarizers (b), and reflection images between crossed polarizers are taken with two slightly different focus adjustments (c,d). Macroscopic photos (no polarizers, ambient illumination) of the film on a black background (left column) compared with a corresponding film with tangential-aligned shells (right column) are shown as function of viewing angle in (e)–(h). The large cyan spots in the left sample are due to a few polymerized CLC droplets dispersed together with the shells. </center>  
+
+FCD type, and for reference a similar amount of shells of tangential type, made from the same CLC precursor mixture (containing \(9\%\) HDDA), in NOA160 spread over a square of about 1 cm by 1 cm area for each sample, and cure NOA160 into solid state. The resulting composites are shown in Fig. 5, panels a–d showing the microscopic appearance of the sample with FCD shells, while panels e–h show the macroscopic appearance of the sample with FCD shells (left) next to the sample with tangential shells (right), as a function of viewing angle under ambient light.  
+
+We note in the microscopic images that the near- field reflection behavior of the composite film is very different from corresponding films with tangential shells, \(^{4}\) with the same strong sensitivity to focal plane variations as the individual shells in air (Fig. 3k–l). The complex near- field reflections render the FCD shells exceptionally useful in tags for anticounterfeiting
+
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+and track- and- trace purposes, \(^{6,12}\) the ideal solution probably being to combine FCD and tangential shells in one tag. No cross communication can be seen but this is likely a result of the short pitch of the polymerized shells, yielding retroreflection of green light. The blueshift of the cross communication wavelengths \(^{36}\) then moves these patterns into the invisible UV region. Interestingly, the very different near- field behavior does not persist in the far field: the macroscopic appearance of the film with FCD shells is overall very similar to that with tangential shells (Fig. 5e- h). One beneficial difference is that the colored cross section from each shell is slightly larger with FCD shells than with tangential- aligned shells, hence we may expect stronger signals when these are used in markers for robotics and augmented reality. \(^{4}\) Similar to the cuticle of the beetle Chrysina Gloriosa, the apparent color under diffuse light is nearly independent of viewing angle, a very useful feature that is unusual for structural color. We are currently conducting a systematic and detailed study of the FCD shell optics, fine- tuning the procedure for obtaining regular FCD configurations. The results will be reported in a follow- up paper.  
+
+## CLC shells stabilized by the block copolymer surfactant Pluronic F-127  
+
+With nematic shells of the commonly used mesogen 5CB stabilized between aqueous solutions of 87- 89% hydrolyzed PVA, Durey et al. found an analogous alignment change to what we have described above, from tangential to radial director at the shell boundaries, in the extreme vicinity of the clearing transition. \(^{18}\) In that case, detection of the phenomenon required very slow heating. We noticed the same effect, with the same mesogen, over a much greater temperature range when replacing PVA with the non- ionic amphiphilic block copolymer Pluronic F- 127. \(^{17}\) Different from PVA, F- 127 is designed as a surfactant, comprising a central hydrophobic polypropylene oxide (PPO) block flanked by two hydrophilic polyethylene oxide (PEO) blocks. \(^{37,38}\) However, in terms of its impact on director config
+
+<--- Page Split --->
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+uration, F- 127 is significantly different from the ionic surfactants that are usually used to impose normal \(\mathbf{n}\) at a boundary of an LC to water. Such surfactants are expected to extend their single relatively long all- trans alkyl chain into the LC along a direction that on average is normal to the interface. F- 127, in contrast, cannot be expected to extend much into a liquid crystal phase, as its hydrophobic moiety is a highly flexible polymer block that would suffer a significant entropic penalty in terms of reduced conformational freedom if it were to be orientationally ordered by the LC. It is thus likely to rather adsorb onto the LC, without much penetration. The twin PEO blocks, which are expected to be fully hydrated and extend away from the LC, are also very different from the single small hydrophilic headgroup of ionic surfactants. Consequently, the impact of F- 127 on LC alignment is non- trivial to predict.  
+
+Given the previously observed alignment change over a broad temperature range, from tangential to normal upon heating and vice versa on cooling, \(^{17}\) we study the impact of F- 127 on our cholesteric shells. We replace PVA by Pluronic F- 127 (1 wt. \(\%\) ) in both inner and outer phases and we first prepare shells with the 6 wt \(\%\) HDDA mixture. To our surprise, the FCD texture now appears on the surface of the shells already at room temperature. Only after placing the shells in a fridge at \(5^{\circ}\mathrm{C}\) , they adopt tangential alignment, see Fig. S8 of the Supplementary Information. The clearing point is not affected by the change of stabilizer.  
+
+We then prepare shells of the CLC base mixture stabilized by the aqueous F- 127 solutions and now we find the full textural development from tangential at room temperature to FCDs as the shells are heated toward \(T_{N^{*}I}\) , as shown in Fig. S9 in the Supplementary Information and Supplementary Video 5. The response to heating is qualitatively similar to the shells of the same CLC mixture stabilized by PVA solution, but while the PVA- stabilized shells had to be heated to \(T_{t} \approx 71^{\circ}\mathrm{C}\) , about \(1.5^{\circ}\mathrm{C}\) below \(T_{N^{*}I}\) , to see the transition to FCDs (Fig. 2d- e), the F- 127- stabilized shells undergo this alignment transition already at \(T_{t} \approx 58^{\circ}\) , see Fig. S9c- e. The overall process is slower and extends over the much larger temperature range up to the clearing transition. With a clearing temperature of \(T_{N^{*}I} \approx 72^{\circ}\mathrm{C} \approx 345\mathrm{K}\)
+
+<--- Page Split --->
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+\((T_{N^{*}I}\) is not quite identical to that in the experiment with PVA as stabilizer, a consequence of slight variations in the CLC mixture composition, which is difficult to reproduce perfectly given the many components), we obtain \(T_{r} \approx \frac{331 - 345}{345} \approx - 0.041\) . The reduced temperature range of non- tangential alignment is thus 10- fold greater with F- 127 as stabilizer than when PVA is used, a significant expansion.  
+
+## Numerical Simulation Results  
+
+In what follows, we present numerically computed equilibrium profiles of CLC shells, which are results from the mathematical model defined in the Supplementary Information. The profiles are either local or global approximate minimisers of the free energy, (2) in the Supplementary Information subject to different combinations of tangential and normal boundary conditions. We work with a fixed low temperature, \(t = - 1.79\) , which is simply a temperature for which the CLC system prefers an ordered (chiral) nematic state to a disordered isotropic state, on energetic grounds. This temperature has not been matched to the experiments, and we speculate that the qualitative deductions are independent of \(t\) , provided \(t < 0\) . In our simulations, we use a fixed shell size, defined by \(\xi_{R} = \frac{1}{50}\) (see Supplementary Information for definition of \(\xi_{R}\) ). This is a material- dependent and geometry- dependent length scale, but corresponds to shells which are approximately 50 times larger than the nematic correlation lengths. This is a small shell size, perhaps of the order of 1 micron, whereas shells used in experiments are much larger. The choice of the relatively small shell size stems from the computational expense of using a smaller value of \(\xi_{R}\) (which would correspond to a larger shell size). However, our results do capture the tangential textures and FCDs qualitatively, as observed in the experimental snapshots in the preceding sections.  
+
+We consider symmetric and asymmetric shells separately, noting that only asymmetric shells are used in experiments. Symmetric shells can be easier for visualisation purposes, and some numerical results for symmetric shells are deferred to the Supplementary Information.
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+<--- Page Split --->
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+In Figure 6(a1- e1), we numerically compute a stable CLC configuration for an asymmetric shell, with approximately tangential boundary conditions on both the inner and outer surfaces. For the anchoring coefficients (see Supplementary Information for definition) we choose \(\omega_{1} = \omega_{2} = 0.1\) , but these are arbitrary choices which cannot be related to experimentally measurable quantities here. We speculate that this is moderately strong tangential anchoring. The biaxiality parameter is defined to be \(\beta = 1 - 6\frac{(\mathrm{tr}\mathbf{Q}^{3})^{2}}{|\mathbf{Q}|^{6}}\) where \(\mathbf{Q}\) is the LdG Q- tensor order parameter, such that \(0\leq \beta \leq 1\) , and \(\beta = 0\) if and only if \(\mathbf{Q}\) has a pair of degenerate eigenvalues i.e. is either uniaxial or isotropic. \(^{39}\) The maximal value, \(\beta = 1\) , occurs when \(\mathbf{Q}\) has one zero eigenvalue. We plot \(\beta\) on the inner and outer surfaces, and see that \(\beta = 0\) almost everywhere, except for near two point defects which are an essential topological consequence of the imposed tangential boundary conditions.  
+
+Consider Figure 6(e1), wherein we plot a scalar quantity, \(\gamma_{1} = |\mathbf{n}\cdot \mathbf{e}_{x}|\) on a shell cross- section in the \((y,z)\) - plane and \(\mathbf{n}\) is the director or the eigenvector of \(\mathbf{Q}\) with the largest positive eigenvalue. If \(\gamma_{1} = 1\) , then \(\mathbf{n}\) is along \(\pm \mathbf{e}_{x}\) and if \(\gamma_{1} = 0\) , then \(\mathbf{n}\) is in the \((y,z)\) - plane. We plot the contours of \(\gamma_{1}\) to track the pitch of the CLC i.e. \(\mathbf{n}\) rotates by \(\pi\) - radians between two red contours or between two blue contours. This plot of \(\gamma_{1}\) corresponds to a structure that gives rise to the low- temperature images in Figure 2a- c for which the boundary conditions are expected to be tangential on both shell surfaces. In Figure S2 in the Supplementary Information, the numerical computation is repeated on a tangential symmetric shell, and the circular twist contours of \(\gamma_{1}\) are reproduced, as in Figure 6(a1- e1).  
+
+In Figure 6(a2- e2), we consider a hybrid asymmetric shell, with normal boundary conditions on the inner surface and tangential boundary conditions on the outer surface. The anchoring coefficients are an order of magnitude smaller than the anchoring coefficients in Figure 6(a1- e1), and we only plot a scalar quantity, defined to be \(\gamma_{2} = |\mathbf{n}\cdot \mathbf{e}_{\xi}|\) , and \(\mathbf{e}_{\xi}\) is the radial unit- vector in the unit \(\xi\) - direction (refer to the bispherical coordinates in the Supplementary Information). For a symmetric shell, \(\mathbf{e}_{\xi}\) coincides with the radial unit- vector. On the inner surface, \(\gamma_{2}\) is approximately unity, consistent with the normal boundary con
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+![](images/Figure_6.jpg)
+
+<center>Figure 6: The equilibrium profiles (a1-e1) with tangential boundary conditions on the inner and outer surfaces with anchoring strength \(\omega = \omega_{1} = \omega_{2} = 0.1\) , (a2-e2) with normal on the inner surface and tangential on the outer surface \(\omega = \omega_{1} = \omega_{2} = 0.01\) , (a3-e3) with tangential on the inner surface and normal on the outer surface \(\omega = \omega_{1} = \omega_{2} = 0.01\) , (a4-e4) with normal on the inner and outer surfaces \(\omega = \omega_{1} = \omega_{2} = 0.01\) , at fixed temperature \(t = -1.79\) , \(\xi_{R} = 1 / 50\) , \(\eta = 1\) , \(\sigma = 10\pi\) , \(c = 0.1\) , \(\rho = 0.7\) . (ai) Bottom of outer surface; (bi) top of outer surface; (ci) bottom of inner surface; (di) top of inner surface; (ei) Cross-section, \(i = 1, \dots , 4\) . The colour bars label the biaxiality parameter \(\beta = 1 - 6 \frac{\left(t r \mathbf{Q}^{3}\right)^{2}}{\left(t r \mathbf{Q}^{2}\right)^{3}}\) in (a1-d1), \(\gamma_{1} = |\mathbf{n} \cdot \mathbf{e}_{x}|\) in (e1), and \(\gamma_{2} = |\mathbf{n} \cdot \mathbf{e}_{\xi}|\) in (a2-e4), where \(\mathbf{e}_{\xi}\) is the unit \(\xi\) -direction in the bispherical coordinate, in the Supplementary Information. The white lines in (a1-d1) label the director \(\mathbf{n}\) , which is the eigenvector of \(\mathbf{Q}\) with the largest eigenvalue. </center>  
+
+ditions which coerce \(\mathbf{n}\) to align with the normal to the shell surface. Similarly, \(\gamma_{2}\) almost vanishes on the outer surface, consistent with the tangential boundary conditions so that
+
+<--- Page Split --->
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+\(\mathbf{n}\) is approximately in the plane of the outer shell surface. Notably, the contours of \(\gamma_{2}\) are approximately polygonal on the inner spherical shell cross- sections, strongly reminiscent of the FCDs reported in Figures 2, S6 and other experimental figures of FCD shells. In fact, the FCDs in those figures may well correspond to hybrid shells, as used in the simulation, since the change of the boundary conditions from tangential to normal upon heating occurs at different threshold temperatures according to the study in. \(^{17}\) The numerical computation of the FCDs as stable equilibrium structures is perhaps the main theoretical result, since it requires a carefully designed non- trivial initial condition for the numerical solver. We essentially need to prescribe a regular lattice of discs that tessellate the shell surfaces, and prescribe the locations of the disc centers, to imitate the FCDs in experiments.  
+
+In Figure 6(a2- e2), the shell has normal boundary conditions on the inner surface and tangential boundary conditions on the outer surface. We see FCDs on the surface with normal boundary conditions, the inner surface. In Figure 6(a3- e3), we switch the boundary conditions to normal on the outer surface and tangential on the inner surface, for which FCDs are then observed on the outer surface. The contour plots of \(\gamma_{2}\) demonstrate how \(\mathbf{n}\) interpolates between the boundary conditions across the width of the shell. In Figure S3 in the Supplementary Information, we repeat the numerical computation on a tangential symmetric shell, and reproduce the FCD contours of \(\gamma_{2}\) , as in Figure 6(a3- e3). In Figure 6(a4- e4), we plot a numerically computed stable configuration inside an asymmetric CLC shell, with normal boundary conditions on the inner and outer shell surfaces. This yields FCDs on the inner and the outer surfaces.  
+
+To summarise, our numerical results suggest that the textures in Figures 6(a1- e1) and S2 are found for tangentially aligned shells, with relatively strong anchoring. This is consistent with the experimental observation of tangential textures for low temperatures. The FCDs are more common with normal boundary conditions in Fig. 6(a2- e4), which can be associated with relatively high temperatures as further discussed below. Our model has several limitations with respect to parameter choices and the absence of a mapping between the
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+model parameters and experimental variables, but nevertheless, the numerical simulations do capture the qualitative features of the structural transitions in CLC shells, as described in the preceding sections.  
+
+## Discussion  
+
+Our experiments clearly demonstrate that amphiphilic polymer- stabilized cholesteric LC shells in water—like non- chiral nematic shells<sup>17,18</sup>—will change their alignment from tangential to radial as their clearing point is approached. The realignment starts at much lower temperature for F- 127- than for PVA- stabilized shells. The key question is why this happens and which phenomena drive the alignment transition. For non- chiral shells we had previously proposed<sup>17</sup> that it may be related to the reduced anisotropy in interfacial tension<sup>40</sup> upon decreasing orientational order parameter \(S\) as the LC approaches its clearing point. We argued that the resulting weakened anchoring may render dominant the elastic energy due to the deformed director field in a tangential- aligned shell, thus promoting a change to normal alignment. However, this argument does not hold for the cholesteric shells, where the FCD arrangement clearly has a higher elastic energy cost than the tangential configuration, and the argument is also refuted by the observation by Durey et al.<sup>18</sup> that the same alignment transition happens for a flat 5CB film surrounded by PVA solution, where no elastic deformation is present.  
+
+Durey et al. instead suggested that the alignment change happens because the LC layer closest to the water transitions to isotropic at a temperature slightly lower than the clearing point of the bulk LC, hence the anchoring would then be determined by an interface between nematic and isotropic LC rather than an LC- water interface, and this would promote normal alignment. The reason for the lower clearing point in the interfacial layer was suggested to be PVA partially dissolving into the LC. However, liquid crystals are poor polymer solvents since their long- range orientational order imposes an entropic penalty in terms of reduced
+
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+orientational freedom. Samitsu et al. demonstrated that this entropy penalty leads to polymeric solutes in an LC to leave the ordered regimes and aggregate in disordered ones if a spatial variation of \(S\) is imposed. \(^{41}\) Considering this as well as the chemical incompatibility between 5CB and water soluble PVA, it seems unlikely that PVA can dissolve into nematic 5CB to an extent where it would decrease the phase transition temperatures. Moreover, the temperature range of the realignment process when using F- 127 as stabilizer appears too large for corresponding to (chiral) nematic- isotropic phase coexistence.  
+
+To find a more convincing explanation, we first consider the amphiphilicity of both stabilizing polymers to be a key factor. While F- 127 is amphiphilic by design, the PVA that is normally used for stabilizing LC shells is actually also somewhat amphiphilic. This is because PVA is synthesized by hydrolyzing polyvinylacetate (PVAc) which is insoluble in water. Since 11- 13% acetate pendants remain in the 87- 89% hydrolyzed PVA it can thus be considered amphiphilic, albeit with a random distribution of the alcohol and acetate pendants. We believe that PVA and F- 127 are both entirely in the aqueous phases when the shell is in a (chiral) nematic state, but the hydrophobic components tend to adsorb onto the LC while the hydrophilic parts reach away from it to be fully hydrated.  
+
+Next, we propose to consider an aspect that was never before considered regarding LC- aqueous phase interfaces, namely the impact of the LC orientational order on the behavior of the stabilizer molecules. Given the amphiphilic nature of the polymers studied here and their consequent preference for bringing the more hydrophobic sections in contact with the LC, we should consider what impact tangential and normal boundary conditions, respectively, have on the polymer fractions in direct contact with the LC. Since the polymers are nonaromatic, the greatest chemical compatibility would arise for normal alignment, bringing the aliphatic end chains of mesogens in contact with the polymers. If \(S\) is large, the resulting steric interactions between ordered mesogen end chains and hydrophobic parts of the stabilizer polymers would then reduce the conformational freedom for the latter. This would correspond to an entropy penalty that could lead to steric repulsion, just as for non- ionic
+
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+surfactants that approach each other close enough for steric interaction. With the stabilizer molecule being repelled from the LC, water molecules would be present together with the stabilizer in contact with the LC, which would then instead promote tangential alignment of the LC such that the aromatic cores capable of hydrogen bonding face the water and thus lower the free energy of the interface. \(^{19}\) This would thus explain the tangential alignment at low temperatures, where \(S\) is high, when PVA and F- 127 are used to stabilize the LC- water interface.  
+
+Upon heating, however, \(S\) is reduced, significantly so in the vicinity of the first- order transition to the isotropic state. \(^{42}\) If it reaches a sufficiently low value, the entropic cost of LC- imposed ordering of the more hydrophobic parts of the stabilizer molecules may be low enough that the enthalpic gain of having aliphatic mesogen end chains in contact with the hydrophobic polymer components becomes dominant. This means that normal alignment would be favorable, and this could then explain the heating- induced alignment transition. Since the PVA has only a rather small fraction of 11–13% of acetate groups, and since they additionally are randomly distributed along the overall PVA molecule, one should expect more water to be present at the LC boundary than when F- 127 is used, hence the transition only happens upon very strong reduction of \(S\) , explaining why we only see it rather close to the phase transition. If the LC mixture contains non- mesogenic HDDA, this may preferentially aggregate towards the interface, favoring interaction with the acetate pendants in the PVA, thus explaining the expanded reduced temperature range of the alignment temperature for HDDA- rich shells. With F- 127 as stabilizer, on the other hand, a full central block of the polymer is hydrophobic, and we can thus expect much less water in contact with the LC and stronger PPO- LC contact. In this case, even a minor reduction in \(S\) may be enough for the alignment change to be favorable, which would explain the much lower reduced temperature for the LC configuration to change and the greater temperature range of FCD texture, even without any HDDA in the LC mixture.  
+
+While this at present is only a conjecture that needs to be corroborated in future work,
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+preferably with dedicated computer simulations and possibly with neutron scattering using strategically deuterated molecules, we can immediately conduct one further experiment to put the conjecture to the test. Since our model relies on the stabilizer molecules having some non- hydrophilic parts which may interact directly with the LC and which are not hydrated, a switch to a stabilizer molecule that is fully hydrophilic and thus hydrated throughout ought to bring water into contact with the LC at all temperatures, regardless of \(S\) , and we should not expect any alignment change. To test this, we prepare shells of the \(6\%\) HDDA mixture using \(99\%\) hydrolyzed PVA (the highest hydrolysis degree that is commercially available), \(M_{w} = 85 - 124 \mathrm{kg / mol}\) , as stabilizer and study the alignment as a function of temperature, see Fig. 7 (snapshots from Supplementary Video 6). In line with our expectations, the shells now remain tangentially aligned at all temperatures, transitioning to isotropic without any trace of FCD configuration.  
+
+![](images/Figure_7.jpg)
+
+<center>Figure 7: (a-h) Transmission POM images (polarizer orientations indicated in (a)) of a CLC shell produced with a 6 wt.% HDDA mixture and stabilized by 5 wt.% aqueous solution of PVA ( \(M_{w} = 85 - 124 \mathrm{kg / mol}\) , \(99\% \mathrm{hydrolyzed}\) ) solution as it is heated from room temperature to \(50^{\circ}\mathrm{C}\) and then cooling to \(25^{\circ}\mathrm{C}\) . The temperature changing rate was separated in four ranges: \(5^{\circ}\mathrm{C / min}\) for \(23.6 - 43^{\circ}\mathrm{C}\) , \(1^{\circ}\mathrm{C / min}\) for \(43 - 45^{\circ}\mathrm{C}\) , \(0.3^{\circ}\mathrm{C / min}\) for \(45 - 50^{\circ}\mathrm{C}\) , and \(3^{\circ}\mathrm{C / min}\) for \(50 - 25^{\circ}\mathrm{C}\) . The focus is at equator of the shell in (a-b) and at the bottom surface in (c-h). Scale bar: \(50\mu \mathrm{m}\) . </center>
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+The last three panels of Fig. 7 show the texture of the shell on cooling back from isotropic. These images are interesting, first, because they reveal that the cholesteric phase forms with an entirely new texture, a highly irregular fan- shaped texture with randomly oriented inplane helix. \(^{43}\) The broad temperature range of isotropic—cholesteric phase coexistence in the multicomponent shell mixture used in this study means that the transition from isotropic to cholesteric nucleates in multiple small points in the bulk of the shell, away from the boundaries to the aqueous phases. In each nucleus the helix develops with \(\mathbf{m}\) in a random direction. Once nuclei meet, a system full of grain boundaries across which \(\mathbf{m}\) changes abruptly forms, which can rearrange in response to specific boundary conditions only very slowly. In Fig. 7h we see red Bragg diffraction, but the texture is still highly irregular. This emphasizes the importance of making the shells in the cholesteric state, as the shear flow and absence of phase boundaries promote the formation of a well- aligned state as defined by the boundary conditions.  
+
+Second, the very existence of these images reveals that the shells remain stable when using the \(99\substack{+ \%}\) hydrolyzed PVA as stabilizer. The reason that no corresponding images are included from the experiments with \(87–89\%\) hydrolyzed PVA is that the shells always break within seconds after cooling past the isotropic- cholesteric transition when using this stabilizer. Both PVA types thus function well as a stabilizer for shells produced in the cholesteric phase, but if the phase forms in an existing shell on cooling from isotropic, only the \(99\substack{+ \%}\) hydrolyzed PVA provides sufficient interface stabilization. Moreover, when comparing the transition with the two stabilizers (Supplementary Videos 6 and 7), we note that the nucleation of LC order takes place simultaneously across the entire shell in case of \(99\substack{+ \%}\) hydrolyzed PVA, and the birefringence then gradually increases everywhere as the coexistence between isotropic and cholesteric phase appears to be concentric, the cholesteric gradually replacing the isotropic. When using PVA with the lower degree of hydrolysis, in contrast, the cholesteric phase appears in localized patches, each with high birefringence from the start. This suggests that the phase coexistence is now lateral rather than concentric,
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+with islands of ordered phase nucleating and then growing in size, surrounded by a sea of isotropic phase. Such lateral phase separation was recently seen in case of lipids adsorbing onto nematic and smectic shells, \(^{44}\) driven by localized concentration of lipids as a result of the interaction with the LC phase. The amphiphilicity of the 87–89% hydrolyzed PVA may give rise to a similar type of phase separation in case of the short- pitch cholesteric phase seen here, but this time with the result that the shell stability is compromised.  
+
+In a first attempt to explain this observation we speculate that the acetate pendants in the incompletely hydrolyzed PVA, shunned by the water, may have been able to mix partially into the shell phase while it was in its isotropic state, as the absence of orientational order removes the entropic penalty arising when the solvent is ordered. As the transition to LC order takes place upon cooling, the isotropic regions which allow PVA inclusions would then be increasingly compressed by the growing LC regions that expel the polymer, leaving the ordered phase areas largely without stabilizer, thus with high interfacial tension that leads to shell breaking. Such compression of inclusions upon cooling a solvent from an isotropic to an LC state is well known, albeit in very different contexts. \(^{45 - 47}\) The rather high concentration of PVA (5%) may amplify this effect compared to studies using the more common 1%.  
+
+In both earlier studies of the alignment transition in non- chiral nematic shells, \(^{17,18}\) experiments revealed that the transition takes place on the shell outside at lower temperature than at the inside, yielding an intermediate temperature range of hybrid alignment, with normal- aligned outside and tangential inside. With the cholesteric shells, it is difficult to judge experimentally if such hybrid alignment persists, but the numerical simulations show that the textures to be expected on the shell outside are quite similar for hybrid and fully normal boundary conditions. It is thus reasonable to assume that the difference in temperature \(T_{t}\) of the anchoring transition between the in- and outside exists whether the LC is chiral or non- chiral, hence we end by discussing what could cause this difference.  
+
+In the framework of our newly proposed model, we consider that the opposite signs of curvature may be the reason. The positive curvature on the outside yields a convex
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+<--- Page Split --->
+
+interface, at which the mesogen alkyl chains in case of normal alignment have some more flexibility than at a flat interface. This would reduce the entropic penalty for a stabilizer polymer interacting with them, hence a transition to normal alignment might be expected at slightly higher bulk value of \(S\) than with a flat interface, thus at lower temperature. In contrast, the negative curvature of the shell inside causes a concave interface, in which the mesogen alkyl chains in case of normal alignment are slightly squeezed together. This would reduce their flexibility and thus enhance the entropic penalty for polymers interacting sterically with them, causing repulsion even at bulk values of \(S\) that are low enough for the outside to switch alignment, explaining the higher temperature at which the inside turns normal- aligned. Again, computer simulations of flexible amphiphilic polymers in an aqueous environment interacting with curved LC interfaces are needed to put this hypothesis to the test.  
+
+## Conclusions and Outlook  
+
+We have demonstrated that the recently discovered ability to dynamically tune the alignment of thermotropic liquid crystals in contact with aqueous phases, using an amphiphilic polymer as stabilizer, by heating them close to the clearing temperature works highly reliably for cholesteric phases exhibiting visible Bragg diffraction. This allows a controlled tuning from uniformly tangential (radial helix) to focal conic domain configuration, as demonstrated both experimentally and via numerical simulation. By mixing in an appropriate non- mesogenic reactive monomer to the liquid crystal, the temperatures of different alignments can be conveniently adjusted without affecting the optical properties. Moreover, since we use reactive monomers for the LC mixture, which is molded into a spherical shell form factor, we can easily make solid particles by photopolymerization, which carry over the photonic performance of the precursor LC state. When polymerizing in the focal conic state, intricate near- field selective reflection properties arise and the effective far- field reflection area per shell is in
+
+<--- Page Split --->
+
+creased, which may be of great value for anticounterfeiting purposes and for various photonic applications.  
+
+We propose an entirely new explanation to the origin of the temperature sensitivity of the LC configuration, which for the first time considers the impact of the nematic order on polymeric stabilizers adsorbing at the LC- water interface. When the stabilizing polymer is to some extent amphiphilic, as in the case of the polymeric surfactant F- 127 or with incompletely hydrolyzed PVA, interaction between the aliphatic chains of the LC molecules with the more hydrophobic polymer components is enthalpically favorable, but at high degree of orientational order in the LC it is entropically disfavored. For this reason, steric repulsion arises at low temperatures which leads to water being present at the LC boundary, thus leading to tangential alignment. As the temperature approaches the clearing point of the LC, however, the orientational order decreases sufficiently as to reduce the entropic penalty of close polymer- LC interaction, leading to the alignment transition. While a deeper investigation is required to test this hypothesis, the fact that LC shells stabilized by fully hydrolyzed PVA—which is fully hydrophilic—do not exhibit any alignment transition supports the model.  
+
+## Methods  
+
+The basic CLC phase used as middle phase for shell production was a mixture of (chemical structures shown in Fig. 8) 4'- hex- 5- enyloxy- biphenyl- 4- carbonitrile (6OCB- 1- ene, \(^{48}\) Synthon Chemicals), 1,4- bis- [4- (3- acryloyloxypropyloxy) benzoyloxy]- 2- methylbenzene (RM257, Wilshire Technologies), S5011 (chiral dopant, HCCH, China) and 2,2- Dimethoxy- 2- phenylacetophenone (photoinitiator Irg651, Sigma Aldrich) at mass ratios shown in the top row of Table 1. In order to reduce the clearing point and viscosity of the base mixture, varying amounts of 1,6- hexanediol diacrylate (HDDA, Sigma Aldrich) were added. All mixtures exhibit a nearly temperature- independent pitch yielding red retroreflection. The mixtures were
+
+<--- Page Split --->
+![](images/Figure_8.jpg)
+
+<center>Figure 8: Chemical structures of monomers used to prepare CLC mixtures. </center>  
+
+magnetically stirred in a closed vial in a water bath at \(60^{\circ}\mathrm{C}\) for around 5h. The thermal analysis of each mixture was carried out by differential scanning calorimetry (DSC, Mettler Toledo DSC823e, USA) as described in the Supplementary Information. The results are presented in Fig. S4. The viscosity of each mixture was measured by a RheoSense microVISC- m, USA viscometer with a flow rate of \(0.5~\mu \mathrm{L} / \mathrm{min}\) at \(23^{\circ}\mathrm{C}\) , as shown in Fig. S5.  
+
+Table 1: Compositions of CLC mixtures   
+
+<table><tr><td>HDDA (wt.%)</td><td>60CB-1-ene (wt.%)</td><td>RM257 (wt.%)</td><td>S5011 (wt.%)</td><td>Irg651 (wt.%)</td></tr><tr><td>0</td><td>50</td><td>46</td><td>2</td><td>2</td></tr><tr><td>3</td><td>50</td><td>43</td><td>2</td><td>2</td></tr><tr><td>6</td><td>50</td><td>40</td><td>2</td><td>2</td></tr><tr><td>9</td><td>50</td><td>37</td><td>2</td><td>2</td></tr><tr><td>10</td><td>50</td><td>36</td><td>2</td><td>2</td></tr><tr><td>11</td><td>50</td><td>35</td><td>2</td><td>2</td></tr></table>  
+
+A nested glass capillary based flow- focusing microfluidic device (see Fig. S1 in the Supplementary Information, which also contains a detailed account of the assembly process), based on a design originally introduced by Utada et al., \(^{49}\) was used for the shell production.
+
+<--- Page Split --->
+
+Our standard choice for isotropic inner and outer phases was a 5 wt% aqueous solution of polyvinylalcohol (PVA, \(M_{w} = 13 - 23 \mathrm{kg / mol}\) , 87 - 89% hydrolyzed, Sigma- Aldrich), flowed through the injection capillary and through the space between the cylindrical collection and the encasing square capillary as inner and outer phase, respectively. The high PVA concentration is to match the relatively high viscosity of our CLC base mixture. When other isotropic solutions were used this is noted in the main text. The CLC mixture was flowed through the space between the cylindrical injection and the square capillary. To decrease the viscosity and avoid crystallization of the middle phase, fluids and capillaries were heated if required by placing the microfluidic device on a hot stage (Linkam PE120), with the temperature set to about \(10^{\circ}\mathrm{C}\) below the clearing point of each mixture. An NX4- S3 (Integrated Design Tools, Inc.) high speed video camera mounted on a Nikon Eclipse TS100 inverted microscope was used to monitor the production process.  
+
+Shells were collected into a \(20 \mathrm{mL}\) vial and kept in an incubator for annealing around \(12 \mathrm{h}\) at the production temperature. Then, shells were either investigated optically at a POM or transferred into a petri dish and placed in a UV- curing chamber (Opsytec Dr. Gröbel Irradiation Chamber BSL- 01) for about 5 mins for UV polymerization, with the wavelengths 330- 450 nm and light intensity of \(200 \mathrm{mW / cm^2}\) at the sample plane. A handheld UV- LED system (30W IP66 Onforuled, China) was also used for photopolymerization while observing shells through a POM. After polymerization, solvent exchange and washing processes \(^{9}\) were performed to remove all the PVA left in- and outside of shells, leaving shells dispersed in acetone for further characterization or application.  
+
+A POM (Olympus BX51, Japan) equipped with an Olympus DP73 camera (Japan) was used for optical characterization. During these studies, unpolymerized shells were kept in petri dishes or in sealed rectangular glass capillaries ( \(0.3 \mathrm{mm} \times 3 \mathrm{mm}\) cross section, CM Scientific), and a Linkam T95- PE hotstage was used to control the temperature. Macroscopic optical still images of films with embedded polymerized shells were acquired with a Canon EOS 100D digital camera. SEM imaging was carried out with a JEOL JSM- 6010LA
+
+<--- Page Split --->
+
+(Akishima, Japan), operated in 15- 20 kV range. Samples were coated with gold ( \(\sim 3 \mathrm{nm}\) thickness) using a Quorum Q150R ES coater (Quorum Technologies Ltd, Laughton, East Sussex, England). For SEM imaging of shell cross- sections, a rotary Microtome (Leica RM2200) was used to cut polymerized shells that had been mounted in UV- cured glue (Norland Optical Adhesive, NOA160) by applying the glue directly onto dried shells on a glass slide and shine UV light. The microtome cutting step thickness was \(10 \mu \mathrm{m}\) .  
+
+## Data availability  
+
+All original data behind the results in this paper will be made available in a public repository at zenodo.org upon manuscript acceptance.  
+
+## Acknowledgement  
+
+This research was funded by the Luxembourg National Research Fund (FNR), grant references C20/MS/14771094 (ECLIPSE) and C21_MS_16325006 (BIOFLICS). For the purpose of open access, the authors have applied a Creative Commons Attribution 4.0 International (CC BY 4.0) license to any Author Accepted Manuscript version arising from this submission. AM is supported by the University of Strathclyde New Professors Fund, the Humboldt Foundation and a Leverhulme Research Project Grant RPG- 2021- 401. YH is supported by the Sir David Anderson Bequest Award at University of Strathclyde and a Leverhulme Research Project Grant.  
+
+## Author contributions  
+
+X.M. performed most experiments, some with the help of Y.G. and Y.- S.Z. Y.- S.Z. formulated the mixtures. Y.H. carried out the numerical simulations under guidance of A.M. J.P.F.L. supervised the study and wrote most of the paper with input from all authors.
+
+<--- Page Split --->
+
+## Competing interests  
+
+The authors declare no competing interests.  
+
+## References  
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+
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+(37) Alexandridis, P.; Holzwarth, J. F.; Hatton, T. A. Micellization of poly (ethylene oxide)-poly (propylene oxide)-poly (ethylene oxide) triblock copolymers in aqueous solutions: thermodynamics of copolymer association. Macromolecules 1994, 27, 2414–2425.  
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+(47) Petrov, P.; Terentjev, E. M. Formation of cellular solid in liquid crystal colloids. Langmuir 2001, 17, 2942–2949.
+
+<--- Page Split --->
+
+(48) Azuma, K.; Iwata, N.; Takano, Y.; Matsumoto, H.; Tokita, M. Uniaxial alignment of nematic liquid crystals filling vacant spaces in surface-treated nanofibre nonwoven. Liquid Crystals 2019, 46, 1241–1245.  
+
+(49) Utada, A. S.; Lorenceau, E.; Link, D. R.; Kaplan, P. D.; Stone, H. A.; Weitz, D. Monodisperse double emulsions generated from a microcapillary device. Science 2005, 308, 537–541.
+
+<--- Page Split --->
+
+Supplementary information for Tunable templating of photonic microparticles via liquid crystal order- guided adsorption of amphiphilic polymers in emulsions  
+
+by  
+
+Xu Ma, Yucen Han, Yan- Song Zhang, Yong Geng, Apala Majumdar and Jan P.F. Lagerwall
+
+<--- Page Split --->
+
+## Microfluidic device assembly and shell production  
+
+Two cylindrical borosilicate glass capillaries (inner and outer diameter 0.5 and \(1\mathrm{mm}\) , respectively, Science Products GmbH) were first tapered by a micropipette puller (P- 100, Sutter Instruments) and then cut using a Micro Forge (Narishige, MF- 900), creating orifices with inner diameters around 120 and \(210\mu \mathrm{m}\) for the injection and collection capillaries, respectively. The injection capillary was treated to give it a hydrophobic surface character by immersing it into a \(1\mathrm{wt}\%\) aqueous solution of octadecyldimethyl (3- trimethoxysilylpropyl) ammonium chloride (DMOAP, Sigma- Aldrich) for 5 mins. Afterward it was flushed by distilled water and then dried in an oven at \(80^{\circ}\mathrm{C}\) for about \(12\mathrm{h}\) . The injection and collection capillaries were inserted head to head into a \(2\mathrm{cm}\) long square cross section capillary with \(1\mathrm{mm}\) inner side length (CM Scientific).  
+
+![](images/Figure_unknown_0.jpg)
+
+<center>Figure S1: Shell production using a glass capillary microfluidic set-up. The production was done around \(10^{\circ}\mathrm{C}\) below the clearing temperature for each mixture. For mixtures with low HDDA content, the heating is important to reduce the effective viscosity. Scale bar: \(200\mu \mathrm{m}\) . </center>
+
+<--- Page Split --->
+
+Mathematical Modeling of Director Fields for Different Boundary Conditions  
+
+## The Free Energy  
+
+In the LdG framework, the ordering of a CLC sample is described by a macroscopic order parameter: the LdG \(\mathbf{Q}\) - tensor order parameter, which is a symmetric, traceless \(3\times 3\) matrix.1  
+
+\[\mathbf{Q} = \left( \begin{array}{ccc}q_{1} & q_{2} & q_{3}\\ q_{2} & q_{4} & q_{5}\\ q_{3} & q_{5} & -q_{1} - q_{4}. \end{array} \right) \quad (1)\]  
+
+The eigenvectors of the \(\mathbf{Q}\) - tensor model the preferred directions of averaged molecular alignment, and the eigenvalues are a measure of the degree of orientational order about the corresponding eigenvectors. The director, \(\mathbf{n}\) , is defined to be the eigenvector with the largest positive eigenvalue. A CLC phase is said to be isotropic if \(\mathbf{Q} = 0\) , uniaxial if the LdG \(\mathbf{Q}\) - tensor has a pair of equal non- zero eigenvalues and the director is the eigenvector with the non- degenerate eigenvalue, and the CLC phase is biaxial if the associated \(\mathbf{Q}\) - tensor has three distinct eigenvalues. The LdG theory is a variational theory and the equilibrium or physically observable configurations in experiments are modelled by local or global energy minimisers, subject to the imposed boundary conditions. Structural transitions and defects are often associated with biaxiality, and in what follows, we only focus on the director of the numerically computed energy minimisers, and track structural transitions in the director of the energy minimisers as a function of the imposed boundary conditions on the shell surfaces.
+
+<--- Page Split --->
+
+The LdG free energy for CLCs is given by 2  
+
+\[F(\mathbf{Q}) = \int_{\Omega}\frac{K_{0}}{2} (\nabla \cdot \mathbf{Q})^{2} + \frac{K_{1}}{2} |\nabla \times \mathbf{Q} + 2q_{0}\mathbf{Q}|^{2} + f_{b}(\mathbf{Q})dV, \quad (2)\]  
+
+where the bulk energy density is given by  
+
+\[f_{b}(\mathbf{Q}):= \frac{A}{2}\mathrm{tr}\mathbf{Q}^{2} - \frac{B}{3}\mathrm{tr}\mathbf{Q}^{3} + \frac{C}{4} (\mathrm{tr}\mathbf{Q}^{2})^{2}. \quad (3)\]  
+
+Here \(K_{0}\) and \(K_{1}\) are material- dependent elastic constants, usually associated with characteristic splay and twist deformations, and \(q_{0} = 2\pi /p_{0}\) . For an achiral nematic, \(q_{0} = 0\) . \(A\) is a temperature dependent constant, i.e., \(A = \alpha (T - T^{*})\) where \(\alpha\) is a positive material- dependent constant and \(T^{*}\) is a critical material- dependent temperature, \(B\) and \(C\) are positive material dependent constants. The minimisers of \(f_{b}\) dictate the nematic ordering in spatially homogeneous samples, and their dependence on the temperature. The minimisers of \(f_{b}\) are isotropic for high temperatures ( \(A > \frac{B^{2}}{27C}\) ) and the minimisers of \(f_{b}\) are ordered uniaxial states for low temperatures defined by \(A< 0\) . We note, \(|\cdot |\) is the matrix norm, so that  
+
+\[|\mathbf{Q}| = \sqrt{\mathrm{tr}\mathbf{Q}^{2}} = \sqrt{Q_{ij}Q_{ij}}. \quad (4)\]  
+
+Using summation notation, we have \(\nabla \cdot \mathbf{Q} = \partial_{\alpha}Q_{i\alpha}\) and \(\nabla \times \mathbf{Q} = \epsilon_{i,j,k}\partial_{j}Q_{k\beta}\) , where \(\epsilon_{i,j,k}\) is the Levi- Civita antisymmetric symbol, and \(i,j,k = 1,2,3\) . The equilibrium or the physically observable configurations are either local or global minimisers of (2) subject to the imposed boundary conditions.  
+
+Our domain is the spherical shell defined by, \(\Omega = B(\mathbf{0},R_{o})\backslash B(\mathbf{x}_{c},R_{i})\) , where \(B(\mathbf{x}_{c},R_{i})\subset\) \(B(\mathbf{0},R_{o})\) . The choice of \(\mathbf{x}_{c}\) differentiates between symmetric and asymmetric shells i.e. symmetric shells have \(\mathbf{x}_{c} = \mathbf{0}\) i.e. the origin in three dimensions, and \(R_{i}\) and \(R_{o}\) are the radii
+
+<--- Page Split --->
+
+of the inner and outer shells. We nondimensionalize the system using the following rescaling  
+
+\[\bar{\mathbf{x}} = \mathbf{x} / R_{o}, \bar{\mathbf{Q}} = \sqrt{\frac{27C^{2}}{2B^{2}}}\mathbf{Q}, \bar{\mathcal{F}} = \frac{27C^{3}}{2B^{4}R_{o}^{3}}\mathcal{F}. \quad (5)\]  
+
+Dropping all bars for convenience, the dimensionless LdG energy can be written as  
+
+\[\mathcal{F}(\mathbf{Q}) = \int_{\Omega}\left\{\frac{\xi_{R}^{2}}{2} ((\nabla \cdot \mathbf{Q})^{2} + \eta |\nabla \times \mathbf{Q} + 2\sigma \mathbf{Q}|^{2}) + \frac{t}{2}\mathrm{tr}\mathbf{Q}^{2} - \sqrt{6}\mathrm{tr}\mathbf{Q}^{3} + \frac{1}{2} (\mathrm{tr}\mathbf{Q}^{2})^{2}\right\} d\mathbf{x}. \quad (6)\]  
+
+The nondimensionalised domain, \(\Omega = B(\mathbf{0},1)\backslash B(\mathbf{x}_{c} / R_{o},\rho)\) , \(\rho_{c} = R_{i} / R_{o}\) , where \(\mathbf{x}_{c} / R_{o} = (0,0,c)\) , \(c\) and \(\rho\) satisfy \(c > \rho > 0\) and \(c + \rho < 1\) . If \(c = 0\) , we have a symmetric shell. The parameter \(t = \frac{27AC}{B^{2}}\) is the reduced temperature, \(\xi_{R} = \sqrt{\frac{27CL_{1}}{B^{2}R_{o}^{2}}}\) , \(\eta = \frac{K_{1}}{K_{0}}\) , is a measure of the elastic anisotropy and equal elastic constants correspond to \(\eta = 1\) ; the parameter \(\sigma = q_{0}R_{o}\) , where \(q_{0}\) has been defined above.  
+
+The inner and outer shells surfaces are denoted by \(\partial \Omega_{i}\) and \(\partial \Omega_{o}\) . We perform multiple numerical computations by imposing either tangential or normal boundary conditions on the inner and outer surfaces, or hybrid boundary conditions. For both surfaces, the boundary conditions are imposed by means of surface anchoring energies. There is considerable freedom in the choice of the surface energies and the anchoring coefficients, and our results are by no means comprehensive, but do serve as good numerical illustrations.  
+
+Normal boundary conditions require the director to be normal or orthogonal to the shell surface. Such anchoring can be imposed on either the inner or outer shell surfaces (or both) by means of the following surface energy \(^3\)  
+
+\[F_{s} = \frac{\omega}{2}\int_{\partial \Omega_{k}}|\mathbf{Q} - \mathbf{Q}^{\perp}|^{2}dA, k = i \text{or} o, \quad (7)\]  
+
+where \(\omega\) is the reduced anchoring strength and  
+
+\[\mathbf{Q}^{\perp} = s_{+}(\mathbf{v}\otimes \mathbf{v} - \frac{\mathbf{I}}{3}), \quad (8)\]
+
+<--- Page Split --->
+
+where \(\mathbf{v}\) is the surface normal of \(\partial \omega_{i}\) . If \(\omega\) is small, then the anchoring is weakly imposed, and if \(\omega\) is large, then the anchoring is strongly imposed. We work with fixed values of \(\omega\) , but in practice, \(\omega\) is dynamically tuned in experiments by varying temperature.  
+
+The tangential boundary conditions are enforced by the following surface energy,  
+
+\[F_{s} = \int_{\partial \Omega_{k}}\frac{\omega_{1}}{2} |\tilde{\mathbf{Q}} -\tilde{\mathbf{Q}} |^{2} + \frac{\omega_{2}}{2} (t r\tilde{\mathbf{Q}}^{2} - s_{+}^{2})^{2}d A, k = i o r o, \quad (9)\]  
+
+where  
+
+\[\tilde{\mathbf{Q}} = \mathbf{Q} + \frac{\mathbf{s}_{+}\mathbf{I}}{3}, \tilde{\mathbf{Q}}^{\parallel} = \mathbf{P}\tilde{\mathbf{Q}}\mathbf{P}, \mathbf{P} = \mathbf{I} - \mathbf{v}\otimes \mathbf{v}, \quad (10)\]  
+
+\(\tilde{\mathbf{Q}}^{\parallel}\) is the tangential projection of \(\mathbf{Q}\) on the shell surfaces, \(\mathbf{v}\) is the normal to the shell surface, \(\omega_{1}\) is the reduced anchoring strength that favors the tangential boundary conditions or favours the director, \(\mathbf{n}\) , to be tangent to the shell surfaces and \(\omega_{2}\) is an anchoring coefficient that enforces the preferred degree of orientational ordering on the shell surfaces.  
+
+## Numerical Method  
+
+We numerically model the domain \(\Omega\) using the bispherical coordinate system, \((\xi , \mu , \psi)\) , which is given by 4  
+
+\[x = \frac{a\sin\mu\cos\psi}{\cosh\xi - \cos\mu}, y = \frac{a\sin\mu\sin\psi}{\cosh\xi - \cos\mu}, z = \frac{a\sinh\xi}{\cosh\xi - \cos\mu} \quad (11)\]  
+
+where \((x, y, z)\) are Cartesian coordinates,  
+
+\[a = \frac{\sqrt{(1 - \rho^{2} - c^{2})^{2} - 4c^{2}\rho^{2}}}{2c}. \quad (12)\]
+
+<--- Page Split --->
+
+For fixed \(\xi\) , \((\mu , \psi)\) represent a spherical surface given by  
+
+\[x^{2} + y^{2} + (z - a \coth \xi)^{2} = \frac{a^{2}}{\sinh^{2} \xi}. \quad (13)\]  
+
+The shell surfaces, \(\partial \Omega_{i}\) and \(\partial \Omega_{o}\) , correspond to \(\xi_{i}\) and \(\xi_{o}\) , where  
+
+\[\xi_{o} = \sinh^{-1}(a), \xi_{i} = \sinh^{-1}(a / c). \quad (14)\]  
+
+Let \(\zeta = 2(\xi - \xi_{o}) / (\xi_{i} - \xi_{o}) - 1\) and the original domain is mapped to  
+
+\[\Omega = \{(\zeta , \mu , \psi)| - 1 \leq \zeta \leq 1, 0 \leq \mu \leq \pi , 0 \leq \psi \leq 2\pi \} . \quad (15)\]  
+
+We expand the tensor function \(\mathbf{Q}\) in terms of real spherical harmonics of \((\mu , \psi)\) and Legendre polynomials of \(\zeta\) ,  
+
+\[q_{i}(\zeta , \mu , \psi) = \sum_{l = 0}^{L - 1} \sum_{m = 1 - M}^{M - 1} \sum_{n = |m|}^{N - 1} A_{l m}^{(i)} Z_{l n m}(\zeta , \mu , \psi), \quad (16)\]  
+
+where \(N \geq M \geq L \geq 0\) specify the truncation limits of the expanded series, with  
+
+\[\begin{array}{l}{{Z_{l n m}(\zeta,\mu,\psi)=P^{l}(\zeta)Y_{n m}(\mu,\psi),}}\\ {{Y_{n m}=P_{n}^{|m|}(\cos\mu)X_{m}(\psi),}}\\ {{X_{m}(\psi)=\left\{\begin{array}{l l}{\cos m\psi,}&{\mathrm{if}~m\geq0,}\\ {\sin|m|\psi,}&{\mathrm{if}~m< 0.}\end{array}\right.}}\end{array} \quad (17)\]  
+
+and \(P_{n}^{m}(x) (m \geq 0)\) are the normalized associated Legendre polynomials. Using this series expansion, the LdG energy of \(q_{i}\) , \(i = 1, \dots , 5\) is a function for the \(5NML\) unknowns. Substituting (16) into the non- dimensionalized free energy (6) and surface energy (7) and/or (9), we obtain a free energy as a function of these unknown tensor order parameter elements,
+
+<--- Page Split --->
+
+\(A_{l m n}^{(i)}\) . The redefined free energy function is then minimized by using a standard optimization method, such as L- BFGS \(^5\) that treats the independent elements of tensor \(A_{l m n}^{(i)}\) as variables. Most of simulation results in this paper are obtained by taking \((N,L,M) = (64,32,64)\) .
+
+<--- Page Split --->
+
+## Numerical results on symmetric shells  
+
+All results from numerical simulation of asymmetric shells are shown in the main paper. Our numerical results for symmetric shells are shown in Figures S2 and S3.  
+
+![](images/Figure_unknown_1.jpg)
+
+<center>Figure S2: An equilibrium profile on a symmetric shell with tangential boundary conditions on the inner and outer surfaces, at fixed temperature \(t = -1.79\) , \(\xi_{R} = 1 / 50\) , \(\eta = 1\) , \(\sigma = 10\pi\) , \(\omega_{1} = \omega_{2} = 0.1\) . (a) Bottom of outer surface; (b) top of outer surface; (c) bottom of inner surface; (d) top of inner surface; (e) cross-section. The colorbars label the \(\beta = 1 - 6 \frac{\left(t r \mathbf{Q}^{3}\right)^{2}}{\left(t r \mathbf{Q}^{2}\right)^{3}}\) in (a-d), \(\gamma_{1} = |\mathbf{n} \cdot \mathbf{e}_{x}|\) in (e). The white lines in (a-d) label the director \(\mathbf{n}\) , which is the eigenvector of \(\mathbf{Q}\) with the largest eigenvalue. </center>  
+
+![](images/Figure_unknown_2.jpg)
+
+<center>Figure S3: An equilibrium profile on a symmetric shell with hybrid boundary conditions - normal boundary conditions on the outer surface and tangential boundary conditions on the inner surface. The model parameters are \(t = -1.79\) , \(\xi_{R} = 1 / 50\) , \(\eta = 1\) , \(\sigma = 10\pi\) , \(\omega = \omega_{1} = \omega_{2} = 0.02\) . The profile of \(\gamma_{2} = |\mathbf{n} \cdot \mathbf{e}_{\xi}|\) where \(\mathbf{e}_{\xi}\) is the unit \(\xi\) -direction in bispherical coordinate, on (a) the surface with \(r = 1\) , 0.9, 0.8, 0.7 (from left to right), and (b) cross-section. </center>
+
+<--- Page Split --->
+
+## Characterization of CLC mixtures as a function of HDDA addition  
+
+Samples of each of the seven CLC mixtures defined in Table 1 in the main paper were investigated with respect to their phase sequences by DSC. For each mixture containing HDDA, around 3 to \(10\mathrm{mg}\) was placed in a crimped DSC aluminum pan, rapidly cooled to \(- 40^{\circ}\mathrm{C}\) , and then a program with subsequent heating to \(90^{\circ}\mathrm{C}\) at \(5^{\circ}\mathrm{C / min}\) , cooling back to \(- 40^{\circ}\mathrm{C}\) at \(5^{\circ}\mathrm{C / min}\) and then reheating to \(90^{\circ}\mathrm{C}\) at \(10^{\circ}\mathrm{C / min}\) , was carried out under nitrogen environment. As shown in Fig. S4a, components of the CLC base mixture, without HDDA, crystallized during the first rapid cooling to \(- 40^{\circ}\mathrm{C}\) , in contrast to the case with HDDA- containing mixtures. The results are presented in Fig. S4.  
+
+Each mixture was also investigated with respect to its effective shear viscosity at \(23^{\circ}\mathrm{C}\) , using a microfluidic flow viscosimeter operating at a flow rate of \(0.5\mu \mathrm{L} / \mathrm{min}\) . Each sample had a volume of \(1\mathrm{mL}\) . Given that a nematic liquid crystal has five independent viscosity parameters, the read- out of the device must be interpreted with care. We do not wish to attribute the measured value to any of the actual liquid crystal viscosities, but rather consider  
+
+![](images/Figure_unknown_3.jpg)
+
+<center>Figure S4: (a) Differential scanning calorimetry (DSC) thermograms (first heating run, with a rate of \(5^{\circ}\mathrm{C / min}\) .) of the crystallized CLC base mixture, without HDDA. The indicated temperatures are onset melting and clearing temperatures. (b) DSC thermograms (second heating run, with a rate of \(10^{\circ}\mathrm{C / min}\) .) of CLC mixtures with different HDDA concentrations. The indicated temperatures are the onset temperatures for clearing in each mixture. </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_4.jpg)
+
+<center>Figure S5: The effective shear viscosity (see text for comments on interpretation) of CLC mixtures as a function of \(w_{HDDA}\) , i.e., the mass percentage of HDDA in the CLC mixture, at room temperature. </center>  
+
+it an abstract benchmark for comparing effective shear viscosities within the series of mixtures considered. Since the mixtures are subject to a similar shear flow during microfluidic shell production, we consider these data useful with respect to optimization of the mixtures for making shells. The results, shown in Fig. S5, suggest that this effective shear viscosity decays exponentially with increasing HDDA content.  
+
+## Shells of HDDA-doped CLC mixtures  
+
+Fig. S6 shows the transmission POM textures of a shell with \(6\%\) HDDA stabilized between inner and outer isotropic phases of the standard aqueous PVA solution, as it is heated from room temperature to about \(49^{\circ}\mathrm{C}\) , at which the CLC mixture is completely isotropic. We recognize the exact same qualitative texture development from tangential (a- d) to FCD configuration (e- k) as for the HDDA- free CLC shell stabilized with the same PVA solution in Fig. 2 in the main paper, but the temperatures of realignment are depressed just as the clearing temperature is depressed in this mixture compared to the base mixture. At the beginning, the CLC phase is tangentially aligned (Fig. S6a- d) but at at \(T_{t} = 45.8^{\circ}\mathrm{C}\) , a major rearrangement toward FCDs is seen near the bottom of the shell (Fig. S6e- l). The
+
+<--- Page Split --->
+![](images/Figure_unknown_5.jpg)
+
+<center>Figure S6: Transmission POM images (polarizer orientation indicated in (a)) of a CLC shell produced with a 6 wt.% HDDA mixture and stabilized by our standard PVA solution as it is heated from room temperature to the isotropic state. The heating rate was separated in three ranges: \(5^{\circ}\mathrm{C / min}\) for \(23.7 - 43^{\circ}\mathrm{C}\) , \(1^{\circ}\mathrm{C / min}\) for \(43 - 45^{\circ}\mathrm{C}\) , and \(0.3^{\circ}\mathrm{C / min}\) for \(45 - 50^{\circ}\mathrm{C}\) . The focus is at the shell equator in (a-d) and at the bottom surface in (e-l). Scale bar: \(50\mu \mathrm{m}\) . </center>  
+
+FCD texture persists and intensifies as the temperature increases, eventually filling the sphere surface at about \(47^{\circ}\mathrm{C}\) , see Fig. S6h-j. Clearing starts at \(T_{N^{*}I} \approx 48.5^{\circ}\mathrm{C}\) , with only the last traces of FCDs being visible at \(48.7^{\circ}\mathrm{C}\) (m) before the shell is fully isotropic at \(48.9^{\circ}\mathrm{C}\) (n).  
+
+If the HDDA content is increased to \(10\%\) or more, the FCD texture is present already at room temperature, as shown in Fig. S7.
+
+<--- Page Split --->
+![](images/Figure_unknown_6.jpg)
+
+<center>Figure S7: Transmission POM images (polarizer orientation indicated in (b)) at room temperature of CLC shells produced with 10 wt. \(\%\) (a) and 11 wt. \(\%\) (b) HDDA mixtures, after annealing at room temperature. Scale bar: \(50\mu \mathrm{m}\) . </center>  
+
+## F-127-stabilized CLC shells  
+
+When stabilizing a shell of the \(6\%\) HDDA CLC mixture by F- 127, the FCD configuration is found already at room temperature, as shown in Fig. S8a. By cooling the sample in a fridge to \(5^{\circ}\) , we see the reverse transition compared to what was studied in the rest of the paper, with the tangential texture developing out of the FCD texture as the shell is cooled far from the clearing point of the mixture,. see Fig. S8b.  
+
+If we instead use the base CLC mixture, without any HDDA, for shells stabilized by F- 127, the texture is tangential at room temperature and transforms to FCD configuration upon heating, as shown in Fig. S9. The behavior is qualitatively similar to the corresponding  
+
+![](images/Figure_unknown_7.jpg)
+
+<center>Figure S8: Transmission POM images (polarizer orientation indicated in (a)) of a CLC shell produced with a 6 wt. \(\%\) HDDA mixture stabilized by F-127 after annealing at room temperature. The texture at room temperature is shown in (a), while (b) shows the texture after placing the shell in a fridge at \(5^{\circ}\mathrm{C}\) overnight. Scale bar: \(50\mu \mathrm{m}\) . </center>
+
+<--- Page Split --->
+![](images/Figure_unknown_8.jpg)
+
+<center>Figure S9: Transmission POM images (polarizer orientations indicated in (a)) of a CLC shell produced with a 0 wt.% HDDA mixture and stabilized by 1 wt.% aqueous solution of Pluronic F-127 block copolymer surfactant as inner and outer phase, as it is heated from room temperature to isotropic. The heating rate was separated in two ranges: \(5^{\circ}\mathrm{C / min}\) for \(23.5 - 55^{\circ}\mathrm{C}\) and \(1^{\circ}\mathrm{C / min}\) for \(55 - 72^{\circ}\mathrm{C}\) . The focus is at equator of the shell in (a-e) and at the bottom surface in (f-l). Scale bar: \(50\mu \mathrm{m}\) . </center>  
+
+experiment with PVA stabilization in Fig. 2 in the main paper, but the onset temperature of the realignment (Fig. 2c) is much lower when F- 127 is used for stabilizing the shell.  
+
+## Video captions  
+
+- Video 1: Transmission POM video of CLC base mixture shells stabilized by 87-89% hydrolyzed PVA heated from room temperature to above clearing transition, and start of re-cooling. 8x sped up.
+
+<--- Page Split --->
+
+- Video 2: Transmission POM video of \(6\%\) HDDA mixture shells stabilized by \(87 - 89\%\) hydrolyzed PVA heated from room temperature to above clearing transition, and start of re-cooling. 8x sped up.  
+
+- Video 3: Transmission POM video of \(6\%\) HDDA mixture shells stabilized by \(87 - 89\%\) hydrolyzed PVA polymerized at different temperatures. 8x sped up.  
+
+- Video 4: Reflection POM video of \(6\%\) HDDA mixture shells stabilized by \(87 - 89\%\) hydrolyzed PVA with glycerol-rich isotropic phases heated from room temperature to above clearing transition, and start of re-cooling. 8x sped up.  
+
+- Video 5: Transmission POM video of CLC base mixture shells stabilized by F-127 heated from room temperature to above clearing transition, and start of re-cooling. 8x sped up.  
+
+- Video 6: Transmission POM video of \(6\%\) HDDA mixture shells stabilized by \(99 + \%\) hydrolyzed PVA heated from room temperature to above clearing transition, and re-cooling. 8x sped up.  
+
+- Video 7: Transmission POM video of \(6\%\) HDDA mixture shells stabilized by \(87 - 89\%\) hydrolyzed PVA cooled from isotropic until shell rupture. 8x sped up.
+
+<--- Page Split --->
+
+## TOC Graphic  
+
+![PLACEHOLDER_52_0]
+
+
+<--- Page Split --->
+
+## Supplementary Files  
+
+This is a list of supplementary files associated with this preprint. Click to download.  
+
+Video1. mp4 Video2. mp4 Video3. mp4 Video4. mp4 Video5. mp4 Video6. mp4 Video7. mp4
+
+<--- Page Split --->

preprint/preprint__604b85d4f8fe76bc76d3c59314ceae679b296161160d49138928f89c968f5183/images_list.json

@@ -0,0 +1,70 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1. Scheme to illustrate the relation between the bus voltage frequency dynamics in power grids and the Langevin model approach. The most frequent and important components of each grid level are shown for the sake of clarity. In general, overlaps between the levels of grid components are possible. (a) A power grid typically consists of various voltage levels from highest-voltage supergrid to low voltage local grid scales connected by electric tension transformers. The most prominent grid suppliers and consumers which are shown in the scheme, live on various time scales. Their dynamics can only be controlled and modelled by the deterministic drift \\(h(\\underline{x}(t),t)\\) if they live on a suitable slow time scale \\(\\tau_{\\mathrm{det}}\\) . Phenomena of the grid participants on shorter time scales \\(\\tau_{\\mathrm{fast}}\\) have to be captured by the diffusion \\(g(\\underline{x}(t),t)\\cdot \\overline{\\Gamma} (t)\\) in form of intrinsic stochastic dynamics. We assign the suitable time scales to the components with gray tiles for \\(\\tau_{\\mathrm{det}}\\) , orange tiles for \\(\\tau_{\\mathrm{fast}}\\) and mixed tiles for components that partially contribute in each manner. The assignment is only an approximation and serves for illustration purposes. (b.1) From a modeller's point of view the power grid in stable operation is located in the minimum of the potential \\(V(\\underline{x}) = - \\int h(\\underline{x}(t),t)\\mathrm{d}\\underline{x}\\)",
+    "footnote": [],
+    "bbox": [
+      [
+        110,
+        113,
+        614,
+        585
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. We give two examples of similar time series pairs (a,b) (similar in the second half) and (c,d) (similar over the whole range), but originate from pure B-tipping destabilization (a,c) or a combination of B-tipping and decreasing (b)/increasing (c) noise level. The analysis results, shown in the lower graphs, reveal the B-tipping candidates (a,c) by a drift slope estimate \\(\\hat{\\zeta}\\) approaching zero (blue with orange credibility bands (CBs)) and the decreasing/increasing noise counterparts (b,d) by decreasing/increasing noise level estimates \\(\\hat{\\sigma}\\) (red with green CBs) that match the true noise level (red dotted lines). In contrast to the BL-estimation results, the statistical leading indicators lag-one autocorrelation (AR1) \\(\\hat{\\rho}\\) and standard deviation (std) \\(\\bar{\\sigma}\\) show almost the same fingerprints, namely positive trends, in three different destabilization scenarios (a,c,d) and thus do not provide information about the ongoing dynamical processes. Furthermore, they are not applicable in example (b) due to a convex std \\(\\bar{\\sigma}\\) curve that cannot be interpreted unambiguously in terms of a leading indicator. For more details we refer to the main text.",
+    "footnote": [],
+    "bbox": [],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. The results of the BL-estimation applied to the four test sets in (a, d, g, j). The red, dotted vertical lines in (a-c, j-l) indicate the approximate times when N-tipping into a flickering regime and B-tipping take place, respectively. The example datasets are analysed with the BL-estimation in windows of 2000 points with a shift of 100 points per window. In the examples (d,g,j), the data of each window is linearly detrended to account for the non-stationary trends in the mean. (b, e, h, k) The drift slope estimates \\(\\hat{\\zeta}\\) with the \\(1\\%\\) to \\(99\\%\\) and the \\(16\\%\\) to \\(84\\%\\) CBs are compared to the ground truth indicated by the green solid lines. The shift in time is due to the rolling window approach and ascribing the estimates to the last point of each window. Ascribing them to the mid point of each window, makes them match the true values almost perfectly (cf. supplementary information \\(^{19}\\) , section S2, figure S2). For completeness the evolution of the control parameters is marked by the green dotted lines. The leading indicators \\(\\hat{\\zeta}\\) mirror correctly the unchanged dynamics in (b) as well as the stabilizing/destabilizing dynamics in (e, h) and (k) by constant, negative and positive trends, respectively. The BL-estimation results of the Markovian examples are qualitatively and quantitatively correct. As expected the drift slope estimates are biased in the case of correlated noise which is confirmed by comparison to the analytical values in (h, k). Note the broken axis in (k). In (b) at time \\(t = 1386.8\\) the N-tipping causes artificial drift slope peaks with the width of one rolling time window as indicated by the grey-shaded area. (c, f, i, l) The evolution of the noise level \\(\\sigma\\) is compared to the estimates \\(\\hat{\\sigma}\\) with the corresponding CBs. Apart from an expected time lag of the rolling window approach the original noise level is reconstructed in (c, f) and the first half of (i). In (i), the Markovian Langevin model assumptions become progressively less valid as the multiplicative coupling increases over time through \\(X_{\\mathrm{h,g}}^{\\mathrm{corr}}\\) , and consequently, a precise quantitative reconstruction of the noise evolution fails in the second half of (i). Nevertheless, the qualitative behaviour of the noise level is preserved over the whole time range. The noise level estimates in (l) tend to show an artificial increase in the vicinity of a bifurcation, because the Markov assumption does not hold.",
+    "footnote": [],
+    "bbox": [
+      [
+        100,
+        95,
+        904,
+        396
+      ]
+    ],
+    "page_idx": 5
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. BL-estimation results for the pre-outage and restoration bus voltage frequency time series \\(\\omega_{\\mathrm{P}}(t)\\) (a-c) and \\(\\omega_{\\mathrm{R}}(t)\\) (d-f). The time axes are aligned with the time stamps of the approved disturbance report. The end of the black-hatched interval falls together with the end of time series \\(\\omega_{\\mathrm{P}}(t)\\) . The shaded intervals follow a traffic light coloring from destabilizing to stabilizing. (a,d) The Gaussian kernel-detrended versions \\(\\delta [\\omega_{\\mathrm{P}}](t)\\) (kernel bandwidth \\(\\sigma = 5\\) ) and \\(\\delta [\\omega_{\\mathrm{R}}](t)\\) (bandwidth \\(\\sigma = 10.68\\mathrm{min}\\) ) are shown. They were used for the analysis. The insets in (d) show corrections (blue) of two artificial outliers (orange) (cf. section 7 and the supplementary material, section S7) which cause as expected a discontinuous bias of the BL-estimates over one window length (cf. grey lines in (e,f)). (b) The drift slope estimates \\(\\hat{\\zeta}\\) reveal mostly three different states over the pre-outage time interval. At the beginning of the red shaded interval at 15:40:09.00 o'clock the drift slope estimates \\(\\hat{\\zeta}\\) converge to a new slightly more stable state roughly around \\(\\hat{\\zeta} \\approx -4\\) , but with increased inter-window fluctuations. The state change could be triggered by a tree-to-line contact of the 500kV Keeler-Allston line that tripped in consequence at 15:42:03.139 o'clock, marked by the end of the first red interval and easily observable due to the strongly pronounced peak in the time series \\(\\delta [\\omega_{\\mathrm{P}}](t)\\) . If it is not directly caused by the tree-to-line contact, it still falls together with a dip in the original frequency time series (cf. supplementary material, section S5) at 15:40:09.00 o'clock which might indicate a sudden load increase in the system which favors tree-to-line faults. That suggests that the changing drift slope estimates \\(\\hat{\\zeta}\\) decode an important permanent state change of the pre-outage region roughly two minutes earlier than the officially defined triggering key event of the historic cascading failure. The second red area covers the interval in which the four McNary stations were lost. Thereafter, increasing frequency oscillations led to the NAWI segregation into four islands with heavy and wide-spread blackouts in the end of the time series. The loss of the McNary units is resembled by rapidly increasing drift slopes \\(\\hat{\\zeta}\\) reaching a new barely stable plateau. This observation is in good agreement with our theoretical considerations in Infobox 1, figure 1, in the sense that loss of a grid component can modify the potential landscape negatively. (c) The noise level estimates \\(\\hat{\\sigma}\\) change anti-correlated to the drift slopes \\(\\hat{\\zeta}\\) at the beginning of the first red interval which implies higher impact of fast scale phenomena in the grid, although the potential landscape was slightly more narrow than before. This hints to a strongly increasing impact of fast scale phenomena, since the more narrow potential cannot damp the noise level increase. The loss of the McNary units in the second red interval has no influence on the noise level which supports our model reasoning by similar arguments as before. (e) The first drift slope estimates \\(\\hat{\\zeta} > 0\\) are not trustworthy, since the windows incorporate pre-outage data. In particular, the estimates are sensitive to the dip and pronounced peak of the beginning outage at 15:48 o'clock. The drift slope suggests a barely stable grid over the orange shaded key restoration interval. We define it from re-synchronization of the last island at 18:47 o'clock until 21:42 o'clock when the full load of the system was restored. The indicated weak stability makes sense, since most of the grid components are only step-wise recovered during the marked interval, some of them even much later, i.e. over the next days until the 16th August 1996. After the load restoration, the system approaches steadily the physical pre-outage configuration. At 01:00 o'clock in the morning of 11th August 1996 the last customers were supplied with electric energy again which corresponds to the end of the green shaded period. The drift slope indicates a new stabilization plateau. (f) The first noise level estimates \\(\\hat{\\sigma}\\) are not trustworthy analogously to (e). Afterwards the noise level exhibits a negative transient with ongoing restoration of the grid which illustrates the steepening of the potential that traps the grid state in the potential valley's stable operation fixed point according to Infobox 1, figure 1 (b.1). For more detailed information we refer to the main text.",
+    "footnote": [],
+    "bbox": [
+      [
+        97,
+        80,
+        907,
+        335
+      ]
+    ],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. The computed noise level results \\(g(x)\\) are shown for the pitchfork model with linearly shifted control parameter from \\([- 28,5]\\) if the noise \\(g(x)\\) is matched to the data distribution in equation 11 of the time series in figure 3 (a). A smoothed version via a Gaussian kernel with bandwidth of \\(\\sigma_{\\mathrm{kernel}} = 325\\) points (i.e. \\(\\sigma_{\\mathrm{kernel}} = 21.6\\mathrm{a.u.})\\) is also shown and corresponds to the shaded red dotted line in the lower graph of figure 3 (b).",
+    "footnote": [],
+    "bbox": [
+      [
+        544,
+        87,
+        900,
+        290
+      ]
+    ],
+    "page_idx": 12
+  }
+]