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+Peer Review File
+
+Switch-like Gene Expression Modulates Disease Risk
+
+Corresponding Author: Professor Omer Gokcumen
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The authors present a comprehensive analysis of transcriptomes from 943 individuals across 27 tissues to identified 1,013 switch-like genes. They found that only 31 of these genes exhibit switch-like behavior across all tissues and that the universally switch-like genes appear to be genetically driven, with large exonic genomic structural variants explaining five of them. The remaining switch-like genes exhibit tissue-specific expression patterns and tend to be switched on or off in unison within individuals, likely under the influence of tissue-specific master regulators, including hormonal signals. They present a very robust sex specific analysis of the findings and explore concordance in the gene expression. They provide specific biological links between switched-off genes in the stomach and vagina that are linked to gastric cancer and vaginal atrophy with some experimental validation.
+
+Overall the study is interesting impactful, the manuscript is clear and well written and the figures are effective. Please find some suggestions for points to be addressed below:
+
+• Please define switch-like genes early on (both in the abstract and in the introduction)
+• Exploring overall pathway or gene set enrichment analysis in the group of ~1013 identified genes might be informative in learning more about their overall function. Further characterization could be done of the individual clusters presented in Figure 2.
+• I would suggest including the table of clusters in 2A and 2B in the main manuscript with gene descriptions and relevant statistics
+• I suggest an organized section of the results to focus on the sex specific analysis and also highlight that in the abstract / introduction
+• Figure 6 would further be enhanced by sex specific heatmaps showing the bimodal nature of in the expression of the genes providing a high level visualization and summary of the findings.
+• Another analysis that might be interesting to explore is intersecting disease associated genes from OMIM or GWAS Catalog with the set of 1013 switch like genes generally tying them to disease before focusing on stomach and vaginal signals otherwise it’s unclear how these were chosen as examples or experimental followup.
+• Throughout the results section there is a lot of text that could be moved into discussion, including potential limitations of the analyses, keeping the results shorter and more to the point
+
+Reviewer #2
+
+(Remarks to the Author)
+Overview: Aqil et al present work investigating switch-like behavior of gene expression using mRNA measurements from individuals in GTEx. To identify switch-like genes, they authors performed a test for bi-modality. Using this approach the authors identified a number of genes exhibited switch-like behavior. The central hypothesis is interesting, and the manuscript is well written, however I have concerns regarding the statistical methodology as well as confounders.
+
+Major Comments:
+1. It would be helpful for the authors to perform simulations or some empirical-based simulation/permutation to assess the calibration of p-values computed from the dip test.
+
+2. The authors performed some analyses to demonstrate the effect of ischemic time on measurements, but I have additional
+concerns. In practice, there may be a number of confounders that track to ma quality, batch, processing, etc.
+
+For example, in eQTL studies, it is standard practice to adjust for PCs of gene expression measurements precisely due to technical artifacts. Similarly, age of the participants should be considered.
+
+Reviewer #3
+
+(Remarks to the Author)
+The authors propose a nice way of looking at switch-like (aka bimodal) expression patterns in genes across tissues.
+
+Larger points:
+
+They show some nice results, my primary concern is that I'm not sure there is enough context for how surprising this should be relative to expectation. For example, about 5% of the genes are identified as being significantly bimodal even with BH correction. Is this distinct from a null? What's the proposed model here? Is it more than expected?
+
+Another concern I had - there's not much discussion about whether this could be accounted for by epigenetic tissue specific patterns or other epigenetic patterns (like imprinting) that would cause bimodal expression patterns. It would be nice to see whether there is any relationship between existing understood epigenetic variability and switch like behavior.
+
+Minor comments:
+
+63: Would be helpful to actually explain this in the first paragraph of the paper.
+97: Font is weirdly larger here than for the word 'results' which seems confusing. Sorry!!
+115: Could clarify language there as "pairwise correlation of expression levels for the same gene in different tissues" and then reduce the subsequent clarification lines.
+258: Where are these genes located? Are they on sex chromosomes? Are sex chromosomes more or less likley to contain switch like genes and is this related to the second larger concern point?
+374: Clunky phrasing 'symptoms of vaginal atrophy appear'... maybe better as just 'causing vaginal atrophy'
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The reviewers have addressed my comments.
+
+(Remarks on code availability)
+
+Reviewer #2
+
+(Remarks to the Author)
+I appreciate the authors' efforts towards addressing my previous comments. I have no new comments at this time.
+
+(Remarks on code availability)
+The repo has extensive documentation, which is appreciated.
+
+Reviewer #3
+
+(Remarks to the Author)
+The authors have fully addressed my comments - thank you.
+
+(Remarks on code availability)
+The confounders code (GAM.r) is substantially more clearly commented than the (admittedly more brief) dip test or sex bias code - otherwise everything is very clear and well laid out.
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+Point-by-point response
+
+We thank the editor and the reviewers for their extremely helpful suggestions. Based on the reviewers’ comments, we have revised our manuscript and addressed all the concerns. The changes in the main text are marked with red. To describe the new results, we have added multiple figures (Figures 1D-E, 6D, and 7) and supplementary material (Supplementary texts 1-3, Figures S1-3).
+
+Reviewer #1 (Remarks to the Author):
+
+The authors present a comprehensive analysis of transcriptomes from 943 individuals across 27 tissues to identified 1,013 switch-like genes. They found that only 31 of these genes exhibit switch-like behavior across all tissues and that the universally switch-like genes appear to be genetically driven, with large exonic genomic structural variants explaining five of them. The remaining switch-like genes exhibit tissue-specific expression patterns and tend to be switched on or off in unison within individuals, likely under the influence of tissue-specific master regulators, including hormonal signals. They present a very robust sex specific analysis of the findings and explore concordance in the gene expression. They provide specific biological links between switched-off genes in the stomach and vagina that are linked to gastric cancer and vaginal atrophy with some experimental validation.
+
+Overall the study is interesting impactful, the manuscript is clear and well written and the figures are effective. Please find some suggestions for points to be addressed below:
+
+    We really appreciate the positive feedback from the reviewer. We have now addressed all the reviewer’s comments, which has further improved our manuscript, in our opinion.
+
+• Please define switch-like genes early on (both in the abstract and in the introduction)
+
+    We have now added the descriptor “on-versus-off” with our first mention of switch-like genes in both the abstract and introduction to ensure clarity.
+
+• Exploring overall pathway or gene set enrichment analysis in the group of ~1013 identified genes might be informative in learning more about their overall function. Further characterization could be done of the individual clusters presented in Figure 2.
+
+    Based on reviewer’s suggestions, we performed a comprehensive enrichment analysis of all switch-like genes using GREAT, which evaluates functional enrichments across multiple biological processes and diseases. The results have now been incorporated into the main text and presented in the new Figure 1D.
+
+    Unfortunately, our cluster-specific enrichment analysis did not yield significant results for clusters 2A and 2B due to the small sample sizes. However, we note that the significant enrichments observed for all switch-like genes are largely driven by cluster 1, which comprises most genes.
+• I would suggest including the table of clusters in 2A and 2B in the main manuscript with gene descriptions and relevant statistics.
+
+    We have shared these genes in Tables S2-3 and the corresponding violin plots in Figure S6. Given that the main manuscript already contains eight multi-panel figures, we refrained from adding the full table to the main text to maintain readability.
+
+• I suggest an organized section of the results to focus on the sex specific analysis and also highlight that in the abstract / introduction
+
+    We recognize the importance of emphasizing sex-biased switch-like gene expression. To address this, we have renamed the section on tissue-specific switch-like genes to “Sex is a frequent modulator of tissue-specific switch-like gene expression” to better highlight these findings. Additionally, we have added a sentence in the Introduction to draw attention to our results on sex-biased switch-like genes in the breast. However, we have opted not to include this in the abstract to maintain conciseness and ensure that the primary focus remains on the disease-related implications of our findings. We believe this approach allows us to keep the abstract clear and impactful while still addressing the reviewer’s concern within the main text.
+
+• Figure 6 would further be enhanced by sex specific heatmaps showing the bimodal nature of in the expression of the genes providing a high level visualization and summary of the findings.
+
+    We thank the reviewer for this suggestion. We have now added a new heatmap (Figure 6B) and agree that it greatly enhanced the visualization of our results.
+
+• Another analysis that might be interesting to explore is intersecting disease associated genes from OMIM or GWAS Catalog with the set of 1013 switch like genes generally tying them to disease before focusing on stomach and vaginal signals otherwise it’s unclear how these were chosen as examples or experimental followup.
+
+    We appreciate this valuable suggestion. Instead of OMIM, we used Human Disease Ontology (DO) for enrichment analysis, as DO already groups diseases into biological categories, making enrichment testing more straightforward. Our analysis confirmed strong associations with cancers, metabolic and immune-related diseases, and integumentary (skin-related) conditions. We now include a new figure (Figure 1D) and associated text to describe these results.
+
+• Throughout the results section there is a lot of text that could be moved into discussion, including potential limitations of the analyses, keeping the results shorter and more to the point.
+
+    We appreciate the reviewer’s comments and recognize the importance of maintaining a concise Results section. We have now moved the discussion on the potential limitation of the study in the context of protein versus RNA expression from Results to Discussion.
+Reviewer #2 (Remarks to the Author):
+
+Overview: Aqil et al present work investigating switch-like behavior of gene expression using mRNA measurements from individuals in GTEx. To identify switch-like genes, they authors performed a test for bi-modality. Using this approach the authors identified a number of genes exhibited switch-like behavior. The central hypothesis is interesting, and the manuscript is well written, however I have concerns regarding the statistical methodology as well as confounders.
+
+We appreciate the positive comments. We implemented all the suggestions by the reviewer, and we believe they have improved our manuscript substantially.
+
+Major Comments:
+1. It would be helpful for the authors to perform simulations or some empirical-based simulation/permutation to assess the calibration of p-values computed from the dip test.
+
+    Thank you for this valuable suggestion. To examine the calibration of our dip test \( p \)-values, we now performed the test on:
+
+    1. Simulated unimodal expression data approximating the mean and standard deviation observed in GTEx, under a normal distribution; and
+    2. Empirical expression data from housekeeping genes, which are reliably unimodal.
+
+Instead of observing uniformly distributed \( p \)-values under the null hypothesis, the \( p \)-values were heavily skewed toward one, implying that our dip test implementation was much more conservative than anticipated by our 5% FDR threshold. To address this, we performed an empirical null calibration using the housekeeping-gene \( p \)-value distribution. We have now updated all of our results throughout the manuscript based on these new analyses. After incorporating both of the reviewer’s suggestions (\( p \)-value recalibration and more comprehensive confounder-correction) into our methodology, the number of the identified switch-like genes has changed from 1,013 to 473. The methodological details about these steps are available in Methods in the section “Dip test”, in Supplementary text 2, and Figure S2.
+
+2. The authors performed some analyses to demonstrate the effect of ischemic time on measurements, but I have additional concerns. In practice, there may be a number of confounders that track to rna quality, batch, processing, etc.
+
+    We agree. We have now controlled for six confounders, i.e., RIN (RNA integrity number), the Hardy death score, Cohort type (post-mortem vs. surgical vs. organ donor), type of nucleic acid isolation batch (RNA_Extraction_from_Paxgene-derived_Lysate_Plate_Based vs. RNA_isolation_PAXgene_Tissue_miRNA vs. RNA_isolation_PAXgene_Blood_RNA), ischemic time (post-mortem interval), and time spent by tissue in PAX fixative. Specifically, we used residuals from generalized additive models for each of these potential confounders, as we have now explained in the “Correcting expression levels for confounders” section in Methods. We found that several hundred genes were strongly influenced by these confounders (Figure S3). We have removed those genes from further analyses and updated our manuscript accordingly.
+
+    We carefully evaluated whether to correct for the two batch IDs (SMNABTCH for nucleic acid isolation and SMGEBTCH for expression). However, in most tissues, each “batch” contained only one or a few samples from a given tissue, which would drastically reduce our statistical power and potentially eliminate genuine bimodality signals if we treated these sparse
+groupings as separate factors. Therefore, we instead employed a broader “batch type” confounder (nucleic acid isolation batch type; SMNABTCHT). Meanwhile, the expression batch type (SMGEBTCHT) was identical across all samples in this study, so we did not use it. Additionally, we did not correct for the autolysis score (SMATSSCR) because the effects of certain pathologies on the tissue may be similar to autolysis. In such cases, correcting for autolysis may obscure the biological signals of interest. We believe that not correcting for autolysis score will not significantly bias our results since we have already controlled for the related confounders of RNA integrity and post-mortem interval.
+
+As a result of the new adjustments in \( p \)-value calibration (described above) and confounder correction, our dataset is now more biologically robust, while retaining our principal findings. For instance, after confounder correction, the number of Cluster 1 genes in the vagina decreased from 214 to 34, yet genes linked to vaginal atrophy rose from six to seven. Similarly, whereas we previously attributed 43% of switch-like expression in Cluster 2A to genetic variants, this percentage has now increased to 69%. However, we did lose the stomach-specific bimodal genes that were previously linked to gastric cancer, as RIN differences across individuals drove their patterns. Therefore, we have removed the corresponding section in the revised manuscript. Although RIN may itself be connected to biological phenomena in the stomach, exploring this possibility is beyond the scope of the current study.
+
+For example, in eQTL studies, it is standard practice to adjust for PCs of gene expression measurements precisely due to technical artifacts. Similarly, age of the participants should be considered.
+
+We appreciate the reviewer’s suggestion to consider principal component (PC) adjustment, which is standard in many eQTL studies. However, our goal differs in that we aim to capture all biologically relevant variation, including factors such as sex, age, endocrine signaling, and epigenetic regulation. In eQTL detection, these factors are often removed to isolate purely genetic effects. In contrast, our emphasis is on identifying any bimodal expression, regardless of whether it arises from genetic or other biological influences.
+
+To address the age concern, we examined correlations between switch-like gene expression and participants’ ages (Table S8) but observed only two significant associations (Figure 6D). We also performed similar analysis for BMI (Table S8). The results are now described in the Results under the section “Sex is a frequent modulator of tissue-specific switch-like gene expression.” We believe that our targeted approach to confounder correction, together with the specific biological context (e.g., vaginal atrophy), reduces false positives arising from technical artifacts while preserving genuine biological signals.
+Reviewer #3 (Remarks to the Author):
+
+The authors propose a nice way of looking at switch-like (aka bimodal) expression patterns in genes across tissues.
+
+We thank the reviewer for positive remarks and thorough reading of our manuscript.
+
+Larger points:
+
+They show some nice results, my primary concern is that I'm not sure there is enough context for how surprising this should be relative to expectation. For example, about 5% of the genes are identified as being significantly bimodal even with BH correction. Is this distinct from a null? What's the proposed model here? Is it more than expected?
+
+That is an excellent point that resonates with comments from Reviewer 2. To ensure the robustness of our findings, we refined our switch-like gene identification pipeline by (1) calibrating \( p \)-values for the dip test and (2) incorporating additional confounder corrections. These refinements are detailed in Supplementary Texts 2–3, Figures S2–4, and Methods in the revised manuscript. To address the reviewer’s question directly, identifying 473 switch-like genes is indeed a surprising result. Under the null hypothesis—modeled using both housekeeping gene-tissue pairs and simulated unimodal expression distributions (described in Supplementary Text 2, Figure S2)—we observed zero switch-like genes at an FDR < 5% threshold. This finding confirms that the observed switch-like expression is highly unlikely to arise from random transcriptional variation coming from unimodal distributions.
+
+Another concern I had - there's not much discussion about whether this could be accounted for by epigenetic tissue specific patterns or other epigenetic patterns (like imprinting) that would cause bimodal expression patterns. It would be nice to see whether there is any relationship between existing understood epigenetic variability and switch-like behavior.
+
+We fully agree that epigenetic factors warrant further exploration. To investigate this, we analyzed GTEx methylation data for the six tissues in which both methylation and expression profiles were available for at least 30 individuals. This analysis identified dozens of genes whose switch-like expression is at least partially regulated by epigenetic modifications, either through genetic or environmental influences. We have now incorporated these results in Figure 7 and the Results section under “Epigenetic regulation of bimodal gene expression by DNA methylation”, which we believe significantly strengthens the biological interpretation of our findings.
+
+In response to the reviewer’s specific question about imprinting, we examined all identified switch-like genes in the Geneimprint database (https://www.geneimprint.com/site/genes-by-species). We found only one switch-like gene (ERAP2) annotated as imprinted. However, its bimodal expression can be explained by an eQTL (rs2248374; Supplementary text 6), indicating that imprinting is not required to account for its bimodality. Therefore, we do not discuss imprinting the revised manuscript.
+Minor comments:
+
+63: Would be helpful to actually explain this in the first paragraph of the paper.
+
+    We have now added the descriptive modifier “on-versus-off” to our first mention of the term switch-like genes. However, since the initial context relates to bacterial gene regulation, we have retained the full definition later in the manuscript, where it is most relevant.
+
+97: Font is weirdly larger here than for the word 'results' which seems confusing. Sorry!!
+
+    We had mistakenly left it in uppercase. We have corrected this now.
+
+115: Could clarify language there as "pairwise correlation of expression levels for the same gene in different tissues" and then reduce the subsequent clarification lines.
+
+    We have clarified this in the text as “Therefore, for each gene, we calculated the pairwise tissue-to-tissue correlation of expression levels for all tissue pairs.”
+
+258: Where are these genes located? Are they on sex chromosomes? Are sex chromosomes more or less likely to contain switch-like genes, and is this related to the second larger concern point?
+
+    Among Cluster 2A switch-like genes, only one gene (GPX1P1) is located on the X chromosome, and its bimodal expression does not correlate with either methylation at nearby sites or genetic polymorphisms. Y chromosome genes make up most of cluster 2B (7 out of 8), as mentioned in the section “Genetic variation underlies universally switch-like genes” in Results. In Cluster 1, two genes are located on sex chromosomes:
+        • FAM9C (X chromosome): A female-biased switch-like gene that escapes X chromosome inactivation in females. We now discuss this gene explicitly in the Results section: “Sex is a frequent modulator of tissue-specific switch-like gene expression.”
+        • ENSG00000273906 (Y chromosome): This gene should theoretically belong to Cluster 2B but was grouped into Cluster 1 due to slight clustering imperfections. This is now discussed in Supplementary text 5.
+
+374: Clunky phrasing ‘symptoms of vaginal atrophy appear’... maybe better as just 'causing vaginal atrophy'
+
+We have changed the wording here to say “causing vaginal atrophy.”
+Response to reviewers
+
+Reviewer #1 (Remarks to the Author):
+
+The reviewers have addressed my comments.
+
+Thank you. We are glad!
+
+Reviewer #2 (Remarks to the Author):
+
+I appreciate the authors' efforts towards addressing my previous comments. I have no new comments at this time.
+
+Thank you for the comments. We are glad we addressed them.
+
+Reviewer #2 (Remarks on code availability):
+
+The repo has extensive documentation, which is appreciated.
+We thank the reviewer for reviewing the GitHub page.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have fully addressed my comments - thank you.
+We thank the reviewer for the helpful comments. We are glad the reviewer’s concerns were addressed.
+
+Reviewer #3 (Remarks on code availability):
+
+The confounders code (GAM.r) is substantially more clearly commented than the (admittedly more brief) dip test or sex bias code - otherwise everything is very clear and well laid out.
+Thank you for reviewing the GitHub page. We have added more comments to the diptest.r script to address this concern. This can be viewed at https://github.com/AlberAqil/Switch_like_gene_expression_modulates_disease_risk_2025/blob/main/Dip_test/Diptest.r. In particular, we have added the following comments:
+#This script applies the dip test of the distribution of log(TPM + 1) as opposed to the distribution of raw TPMs.
+#This script calculates the dip statistic D, the associated p-value, mean of the distribution, median of the distribution, the first quartile, the third quartile, and the standard deviation.

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+High selectivity framework polymer membranes chemically tuned towards fast anion conduction
+
+Corresponding Author: Professor Zhengjin Yang
+
+This manuscript has been previously reviewed at another journal. This document only contains information relating to versions considered at Nature Communications.
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #2
+
+(Remarks to the Author)
+I have examined the updates made by Fang et al. to their manuscript. I appreciate the significant efforts the authors went through to add experiments, correct the data presentation, and revise the discussion. The authors clearly took the revision process seriously, and the paper is greatly improved. I also believe that Nature Communications is a better home for the advances made in this work. I thank the authors for incorporating the advice given by me and the other reviewers. However, for me, the updated manuscript still has two concerning discussions that should be revised. I recognize that a lot has already been done at my request, but I hope the authors agree that these are important points to clarify for the good of their future readers. I believe that these final revisions will make the manuscript suitable for publication.
+
+1. Pulse field gradient NMR and the claim of “barrierless” ion transport
+The response to the issue taken with the claim of “barrierless” transport (the first review, point 1) explained that “there remains an energy barrier contributed by pore tortuosity and non-uniform pore size distributions,” but that the local diffusion is what has become barrierless. Therefore, in the manuscript, the authors continue to claim that F- transport is indeed barrierless (abstract, line 30: “resulting in…locally barrierless F- diffusion”). The reasoning behind this claim lies in the fact that the measured diffusion coefficient for F- in the membrane is only 10.5% lower than the measured diffusion coefficient for F- in dilute aqueous solution. I have two concerns about this persisting claim that transport has been achieved without any energy barrier. Because of these concerns, I believe the authors should continue to use their revised language, and say that they pursued very low energy barriers to ion transport, even for F-.
+
+First, the authors claim that PFG NMR measures the local diffusion coefficient of F-, which would need to be done at very low length/time scales. As far as I am aware, PFG NMR measures transport at the length scale of at least 10s of nanometers. How can we be confident that the diffusion coefficients are not semi-local?
+
+Second, aside from the numbers, the logic of the claim doesn’t sit well with me. Even F- in dilute aqueous solution has an energy barrier to transport: resources such as Robinson and Stokes (1965) compile the conductance of ions at various temperatures, allowing for easy calculation of the thermal energy barrier for ion transport in dilute aqueous solution. If the membrane F- diffusion coefficient reached parity with the aqueous solution F- diffusion coefficient, I grant that the authors could claim that the membrane did not add any additional energy barrier for F- transport. However, although these membranes achieve very fast F- transport, the two values are not statistically indistinguishable from one another; even that claim would not be supported by the data.
+
+2. The driving force of concentration gradient–driven salt transport
+I thank the authors for sharing some sources regarding the ion dominating concentration gradient–driven salt permeability experiments and for explaining their logic. However, I reiterate that this is not a problem which is current or contentious: the rate-limiting role co-ions play in concentration driven salt permeation across ion-exchange membranes has been decidedly known for decades. Because of this, the discussion around KCl permeabilities in Figure 2c of the manuscript must be adjusted. Large KCl permeability coefficients measured as described in this manuscript do not indicate fast K+ conduction, but rather suggest significant Cl- leakage.
+Even though mobile anions are more numerous than mobile cations in the membrane, the cations are known to dominate the salt permeability experiments; in fact, it is because they are the minority species that they are the rate-limiting step. The authors rightly claim that the anions provide an electric field which accelerates the transport of cations, but this is not the dominant factor of salt permeation through ion exchange membranes.
+
+Regarding the sources provided by the authors to support their position: One refers to Diffusion Dialysis (Luo et al, J. Membr. Sci. 2011, 366, 1–16. doi.org/10.1016/j.memsci.2010.10.028). I specifically take issue with the KCl permeability experiments, where the receiving compartment was filled with DI water. For the redox active permeability measurements, with a concentrated receiving compartment solution, the Diffusion Dialysis style analysis becomes more relevant and I believe the authors’ claims are reasonable. Two of the other sources provided in the reviewer response didn’t make any claims regarding this specific topic, that I could find. The fourth source provided by the authors (Ye et al. Nat. Commun. 2022, 13, 3184. doi.org/10.1038/s41467-022-30943-y) is firmly in favor of co-ion dominant permeation. Ye et al. discuss permeability of cation-exchange membranes (anions are the co-ions) on page 6: “The permeability of a range of potassium salts was investigated to assess the selectivity of sPIM-SBF membranes towards anions with varied physical size and charge density, as the diffusion of the salts is predominantly controlled by the properties of the anions rather than that of the small K+ cation of high mobility.”
+
+Instead of these quite recent publications, I refer the authors to established textbooks on ion-exchange materials, which all discuss the concentration gradient–driven permeation of electroneutral salts across an ion-exchange membrane. These sources derive the ambipolar diffusion equation (one way to express it is given below) to describe the effective diffusivity of salt resulting from the individual counter-ion and co-ion diffusivities.
+
+Ds = (D_counter*D_co) * (C_counter+C_co) / (C_counter*D_counter+C_co*D_co)
+
+where Ds is salt diffusion coefficient, D_counter is counter-ion diffusion coefficient, D_co is co-ion diffusion coefficient, C_counter is counter-ion concentration, and C_co is co-ion concentration.
+
+These textbooks comment on the implications of this equation for concentration gradient–driven salt permeability experiments:
+
+• Crank, Diffusion in Polymers, 1968: Chapter 10 Section VII: “The counter-ions usually greatly outnumber the co-ions … Thus, the transport of an electrolyte down a concentration gradient across an ion-exchange resin membrane does not differ much from the simple Fickian diffusion of the co-ions.”
+• Helfferich, Ion Exchange, 1995: Section 8.3b: “The rate of electrolyte diffusion is controlled by diffusion of the co-ion. This is another example of the general rule that the diffusion rate is controlled by the species which is in the minority. An interesting consequence is that, say, HCl and NaCl diffuse across a cation-exchanger membrane at about equal rates”
+• Lakshminarayanaiah, Transport Phenomena in Membranes, 1969: Section 4.5A: “The main conclusion of this study is that the rate of diffusion of the electrolyte is governed by the diffusion coefficient of the co-ion”
+• Tanaka, Ion Exchange Membranes: Fundamentals and Applications, 2015: Section 2.4.1: “Electric neutrality in the membrane accelerates the movement of ions having lower diffusivity, and deaccelerates the movement of ions having larger diffusivity. This phenomenon induces the acceleration of co-ions and deacceleration of counter-ions in the membrane. … When the concentration of co-ions is decreased extremely in the membrane, the diffusion flux of the counter-ions is decreased remarkably, owing to the dominant Donnan exclusion … the diffusion velocity of counter-ions is influenced by a small amount of co-ions remaining in the membrane.
+• Sata, Ion Exchange Membranes, 2004: Section 2.7 “These equations mean that the flux of electrolyte through the ion exchange membrane is governed by the diffusion coefficient of the co-ion, not the counterion. For example, the diffusion flux of hydrochloric acid should be equal to that of sodium chloride in an ideal cation exchange membrane.”
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #2
+
+(Remarks to the Author)
+The authors address my previous concerns to my satisfaction. I support publication of this manuscript in Nature Communications.
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+Responses to reviewer comments
+
+For Referee #2
+
+I have examined the updates made by Fang et al. to their manuscript. I appreciate the significant efforts the authors went through to add experiments, correct the data presentation, and revise the discussion. The authors clearly took the revision process seriously, and the paper is greatly improved. I also believe that Nature Communications is a better home for the advances made in this work. I thank the authors for incorporating the advice given by me and the other reviewers. However, for me, the updated manuscript still has two concerning discussions that should be revised. I recognize that a lot has already been done at my request, but I hope the authors agree that these are important points to clarify for the good of their future readers. I believe that these final revisions will make the manuscript suitable for publication.
+
+Reply: We thank the reviewer for their positive feedback and insightful comments/suggestions on our manuscript. We highly appreciate the Reviewer’s effort and expertise in this area, and believe their recommendations have improved the quality of this study. The remaining two concerns of the reviewer have been revised according to your comments. Please see our point-by-point response below.
+
+Q1. Pulse field gradient NMR and the claim of “barrierless” ion transport
+
+The response to the issue taken with the claim of “barrierless” transport (the first review, point 1) explained that “there remains an energy barrier contributed by pore tortuosity and non-uniform pore size distributions,” but that the local diffusion is what has become barrierless. Therefore, in the manuscript, the authors continue to claim that F⁻ transport is indeed barrierless (abstract, line 30: “resulting in…locally barrierless F⁻ diffusion”). The reasoning behind this claim lies in the fact that the measured diffusion coefficient for F⁻ in the membrane is only 10.5% lower than the measured diffusion coefficient for F⁻ in dilute aqueous solution. I have two concerns about this persisting claim that transport has been achieved without any energy barrier. Because of these concerns, I believe the authors should continue to use their revised language, and say that they pursued very low energy barriers to ion transport, even for F⁻.
+
+First, the authors claim that PFG NMR measures the local diffusion coefficient of F⁻, which would need to be done at very low length/time scales. As far as I am aware, PFG NMR measures transport at the length scale of at least 10s of nanometers. How can we be confident that the diffusion coefficients are not semi-local?
+
+Second, aside from the numbers, the logic of the claim doesn’t sit well with me. Even F⁻ in dilute aqueous solution has an energy barrier to transport: resources such as Robinson and Stokes (1965) compile the conductance of ions at various temperatures, allowing for easy calculation of the thermal energy barrier for ion transport in dilute aqueous solution. If the membrane F⁻ diffusion coefficient reached parity with the aqueous solution F⁻ diffusion coefficient, I grant that the authors could claim that the membrane did not add any additional energy barrier for F⁻ transport. However, although these membranes achieve very fast F⁻
+transport, the two values are not statistically indistinguishable from one another; even that claim would not be supported by the data.
+
+Reply: According to the Reviewer’s comments, we revised our language and claimed that we pursued very low energy barriers to ion transport, even for F⁻.
+
+For the PFG-NMR measurement, we agree with the Reviewer that the length scale of the measurement cannot be simply categorized as a local measurement, even though it may not reflect long-range ion diffusion. The corresponding language has been revised.
+
+We agree with the Reviewer that even though the membrane adds almost no additional energy barrier for F⁻ transport, the diffusion values are not quite identical. The relevant discussion has been revised.
+
+Q2. The driving force of concentration gradient–driven salt transport
+
+I thank the authors for sharing some sources regarding the ion dominating concentration gradient–driven salt permeability experiments and for explaining their logic. However, I reiterate that this is not a problem which is current or contentious: the rate-limiting role co-ions play in concentration driven salt permeation across ion-exchange membranes has been decidedly known for decades. Because of this, the discussion around KCl permeabilities in Figure 2c of the manuscript must be adjusted. Large KCl permeability coefficients measured as described in this manuscript do not indicate fast K⁺ conduction, but rather suggest significant Cl⁻ leakage.
+
+Even though mobile anions are more numerous than mobile cations in the membrane, the cations are known to dominate the salt permeability experiments; in fact, it is because they are the minority species that they are the rate-limiting step. The authors rightly claim that the anions provide an electric field which accelerates the transport of cations, but this is not the dominant factor of salt permeation through ion exchange membranes.
+
+Regarding the sources provided by the authors to support their position: One refers to Diffusion Dialysis (Luo et al, J. Membr. Sci. 2011, 366, 1–16. doi.org/10.1016/j.memsci.2010.10.028). I specifically take issue with the KCl permeability experiments, where the receiving compartment was filled with DI water. For the redox active permeability measurements, with a concentrated receiving compartment solution, the Diffusion Dialysis style analysis becomes more relevant and I believe the authors’ claims are reasonable. Two of the other sources provided in the reviewer response didn’t make any claims regarding this specific topic, that I could find. The fourth source provided by the authors (Ye et al. Nat. Commun. 2022, 13, 3184. doi.org/10.1038/s41467-022-30943-y) is firmly in favor of co-ion dominant permeation. Ye et al. discuss permeability of cation-exchange membranes (anions are the co-ions) on page 6: “The permeability of a range of potassium salts was investigated to assess the selectivity of sPIM-SBF membranes towards anions with varied physical size and charge density, as the diffusion of the salts is predominantly controlled by the properties of the anions rather than that of the small K⁺ cation of high mobility.”
+Instead of these quite recent publications, I refer the authors to established textbooks on ion-exchange materials, which all discuss the concentration gradient–driven permeation of electroneutral salts across an ion-exchange membrane. These sources derive the ambipolar diffusion equation (one way to express it is given below) to describe the effective diffusivity of salt resulting from the individual counter-ion and co-ion diffusivities.
+
+Ds = (D_counter*D_co) * (C_counter+C_co) / (C_counter*D_counter+C_co*D_co)
+
+where Ds is salt diffusion coefficient, D_counter is counter-ion diffusion coefficient, D_co is co-ion diffusion coefficient, C_counter is counter-ion concentration, and C_co is co-ion concentration.
+
+These textbooks comment on the implications of this equation for concentration gradient–driven salt permeability experiments:
+• Crank, Diffusion in Polymers, 1968: Chapter 10 Section VII: “The counter-ions usually greatly outnumber the co-ions … Thus, the transport of an electrolyte down a concentration gradient across an ion-exchange resin membrane does not differ much from the simple Fickian diffusion of the co-ions.”
+• Helfferich, Ion Exchange, 1995: Section 8.3b: “The rate of electrolyte diffusion is controlled by diffusion of the co-ion. This is another example of the general rule that the diffusion rate is controlled by the species which is in the minority. An interesting consequence is that, say, HCl and NaCl diffuse across a cation-exchanger membrane at about equal rates”
+• Lakshminarayanaiah, Transport Phenomena in Membranes, 1969: Section 4.5A: “The main conclusion of this study is that the rate of diffusion of the electrolyte is governed by the diffusion coefficient of the co-ion”
+• Tanaka, Ion Exchange Membranes: Fundamentals and Applications, 2015: Section 2.4.1: “Electric neutrality in the membrane accelerates the movement of ions having lower diffusivity, and deaccelerates the movement of ions having larger diffusivity. This phenomenon induces the acceleration of co-ions and deacceleration of counter-ions in the membrane. … When the concentration of co-ions is decreased extremely in the membrane, the diffusion flux of the counter-ions is decreased remarkably, owing to the dominant Donnan exclusion … the diffusion velocity of counter-ions is influenced by a small amount of co-ions remaining in the membrane.
+• Sata, Ion Exchange Membranes, 2004: Section 2.7 “These equations mean that the flux of electrolyte through the ion exchange membrane is governed by the diffusion coefficient of the co-ion, not the counterion. For example, the diffusion flux of hydrochloric acid should be equal to that of sodium chloride in an ideal cation exchange membrane.”
+
+Reply: We thank the Reviewer for their insightful comments on KCl permeability measurements. We carefully referred to the textbooks you mentioned and learned more basic knowledge about static salt permeation measurements and the underlying mechanisms. The most relevant textbooks are cited (Please see refs #28-30). According to the Reviewer’s comments and our understanding, relevant discussions in
+Figure 2c have been adjusted in the revised manuscript. Please see page 7 of the revised manuscript (the content was also copied below).
+
+We measured the cross-membrane permeation rates for BTMAP-Vi (a redox-active organic cation) and KCl (Figure 2c, Supplementary Figures S13-S15, Supplementary Tables S5-S6), which are dramatically different in size. The QCTF membranes exhibited size-induced selectivity towards cations, allowing a small amount of K+ permeation while rejecting larger BTMAP-Vi cations. The permeability coefficients of BTMAP-Vi across the QCTF and the P-QCTF were determined to be \(4.3 \times 10^{-11}\) cm\(^2\) s\(^{-1}\) and \(3.32 \times 10^{-11}\) cm\(^2\) s\(^{-1}\), respectively. It further decreases to \(2.93 \times 10^{-11}\) cm\(^2\) s\(^{-1}\) for M-QCTF, a value that is much smaller than those of Selemion® DSV, Selemion® AMV, Sustainion® X37-50, Fumasep® FAA-3-PE-30, and some PIM-based membranes (Figure 2c and Supplementary Figure S14). The permeability coefficients of KCl (predominantly controlled by the diffusion of the minor co-ion (K\(^+\)))\(^{28-30}\) through the QCTF and P-QCTF are \(1.82 \times 10^{-7}\) cm\(^2\) s\(^{-1}\) and \(2.6 \times 10^{-7}\) cm\(^2\) s\(^{-1}\), respectively and it is \(3.1 \times 10^{-7}\) cm\(^2\) s\(^{-1}\) for M-QCTF. The comparison between the chloride salt permeability coefficients and selectivity of the QCTF membranes versus representative commercial AEMs and previously reported membranes implies that these framework membranes maintain comparable charge selectivity, but deliver significantly higher size-induced selectivity (Supplementary Figure S16 and Supplementary Table S6). By contrast, the KCl permeability coefficient for the control Sustainion® X37-50 membrane (a commercial AEM) is 2.4 times that of the M-QCTF membrane, and the BTMAP-Vi permeability coefficient for Sustainion® X37-50 membrane is at least three orders of magnitude higher than that of the M-QCTF membrane because of sever water swelling (54.6% vs. 1%) and excessive water uptake (172% vs. 8.5%) at 30 °C.
+
+The revised contexts mainly reveal the following aspects.
+
+(1) The minor co-ion diffusions are the rate-limiting step in the salt permeability experiments.
+
+(2) The KCl permeability coefficients measured as described in our manuscript do not indicate fast Cl\(^-\) conduction, but rather suggest the permeation/leakage of K\(^+\). By contrast, the membrane can effectively block the permeation of larger cations, e.g., BTMAP-Vi.
+
+(3) The measured KCl permeability coefficients and leakage of K+ ions do not change the nature of our membrane, which is an anion exchange membrane, with a t\(_t\) value of 0.95.

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+Rationally synthesized framework polymer membranes enable high selectivity and barrierless anion conduction
+
+Zhengjin Yang
+yangz.j09@ustc.edu.cn
+
+University of Science and Technology of China    https://orcid.org/0000-0002-0722-7908
+Junkai Fang
+University of Science and Technology of China
+Guozhen Zhang
+University of Science and Technology of China    https://orcid.org/0000-0003-0125-9666
+Marc-Antoni Goulet
+Concordia University    https://orcid.org/0000-0002-9146-6759
+Peipei Zuo
+University of Science and Technology of China    https://orcid.org/0000-0001-5043-7188
+Hui Li
+University of Science and Technology of China
+Jun Jiang
+University of Science and Technology of China    https://orcid.org/0000-0002-6116-5605
+Michael Guiver
+Tianjin University    https://orcid.org/0000-0003-2619-6809
+Tongwen Xu
+University of Science and Technology of China    https://orcid.org/0000-0002-9221-5126
+
+Article
+
+Keywords:
+
+Posted Date: June 11th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4392718/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 April 6th, 2025. See the published version at https://doi.org/10.1038/s41467-025-58638-0.
+Abstract
+
+The understanding gleaned from studying ion transport within the interaction confinement regime enables the near-frictionless transport of cations (e.g., Na+/K+). However, anion transport (e.g., Cl−) is suppressed under confinement because of the different polarization of water molecules around cations and anions, also known as the charge asymmetry effect. Here we report the rational synthesis of anion-selective framework polymer membranes having similar densities of subnanometer-sized pores with nearly identical micropore size distributions, which overcome the charge asymmetry effect and promote barrierless anion conduction. We find that anion transport within the micropore free volume elements can be dramatically accelerated by regulating the pore chemistry, which lowers the energy barrier for anion transport, leading to an almost twofold increase in Cl− conductivity and barrierless F− diffusion. The resultant membrane enables an aqueous organic redox flow battery that utilizes Cl− ions as charge carriers to operate at extreme current densities and delivers competitive performance to counterparts where K+ ions are charge carriers. These results may benefit broadly electrochemical devices and inspire single-species selectivity with separation membranes that exploit controlled or chemically gated ion/molecule transport.
+
+Main Text
+
+Replicating the extreme selectivity and high permeability of biological ion channels is an enduring challenge for membrane scientists (1–3). Beyond the generally-accepted mechanisms of size exclusion and Coulombic repulsion, it is argued that the subtle interactions between ions and channel walls at atomic-scale confinement play a crucial role. These interactions were not clearly elucidated until the fabrication of angstrom-scale slits/capillaries/channels with atomic-scale precision (4, 5).
+
+The spatial confinement of ion transport down to molecular-sized ion channels magnifies the impact of channel wall interactions and gives rise to exotic transport behavior. For example, hysteretic ion conduction occurs, resulting in an ion memory effect (6, 7), while the formation of Bjerrum ion pairs causes ionic Coulombic blockade (8). These atypical ion motions are intimately related to the dramatically enhanced material-dependent interactions between hydrated ions and the confining channel walls (e.g., electrostatic, adsorption/desorption) (9). For chemically inert and atomically smooth graphite channel walls, K+ demonstrates a mobility close to that of the value in bulk solutions (10). By applying a voltage bias on the graphite channel, the streaming mobility of K+ is increased by up to 20 times (11) and this may be ascribed to the electronic structure change under an external voltage bias (12). It has also been demonstrated that by introducing Li+-coordinating functionality within the shape-persistent free volume elements of microporous polymer membranes, Li+ diffusivity can be greatly enhanced (13). Similar improvements to Na+ transport have also been achieved by exploiting the synergy between micropore confinement and ion-membrane interactions (14).
+Despite the considerable improvements in cation transport due to the confinement effect, it is notable that chloride (Cl⁻) mobility experiences significant suppression under confinement. This charge asymmetry is likely due to the slightly different hydration shell configurations between Cl⁻ and K⁺(10). The mobility of Cl⁻ under confinement is three times less than that of K⁺, even though Cl⁻ and K⁺ have similar mobilities in bulk water (7.58×10⁻⁸ vs. 7.86×10⁻⁸ m² V⁻¹ s⁻¹) and hydrated diameters (6.64 Å vs. 6.62 Å) (15, 16). For a more extreme case, Cs⁺ and Cl⁻ exhibit similar ion-core sizes and hydrated diameters, but Cl⁻ exhibits more than three times lower mobility under Å-scale confinement (1.7×10⁻⁸ vs. 6.0×10⁻⁸ m² V⁻¹ s⁻¹) (16). For chloride salts of high valency cations, the overall Cl⁻ mobility decreases to almost zero in single-digit-sized nanopores (17). A decrease in the mobility of other anions under confinement has also been observed (16). This phenomenon is echoed by the relatively high energy barrier associated with anion exchange membranes that transport chloride ions (see Supplementary Table S1).
+
+The transport and selectivity of anions are of critical relevance to applications such as direct seawater electrolysis (18), solid-state batteries (19) and redox flow batteries (20–25). Understanding and overcoming the charge asymmetry effect for anion transport under confinement is therefore essential for enabling these technologies. Here we report the design and synthesis of a series of positively charged (quaternary ammonium cations) covalent triazine framework (QCTF) membranes with nearly the same density of rigid micropores with almost identical pore size distributions. The QCTF membranes exhibit Coulombic repulsion-induced anion selectivity, with a chloride transference number \( t_- \) of 0.95, and size exclusion-induced rejection of BTMAP-Vi (bis(3-trimethylammonio) propyl viologen tetrachloride) and FcNCl ((ferrocenylmethyl) trimethylammonium chloride), redox-active organic flow battery electrolytes. The cross-membrane BTMAP-Vi diffusion coefficient at 3.1×10⁻¹¹ cm² s⁻¹ is over 20 times lower than that of commercial membranes. We demonstrate that through on-membrane modification, the charge distribution of the pristine QCTF membrane framework can be regulated by protonation (affording P-QCTF) and methylation (affording M-QCTF), which dramatically alters the interactions between anions and the membrane framework and helps lower the energy barrier for anion transport. The cross-membrane Cl⁻ conductivity increased twofold from 13.2 mS cm⁻¹ for QCTF to 25.9 mS cm⁻¹ for M-QCTF at 30°C, and the activation energy for Cl⁻ conduction decreased from 20.6 kJ mol⁻¹ to 13.1 kJ mol⁻¹, lower than any value reported in the literature (see Supplementary Table S1). ¹⁹F PFG-NMR revealed an increase in the F⁻ diffusion coefficient from 0.63×10⁻⁹ m² s⁻¹ for QCTF and 0.93×10⁻⁹ m² s⁻¹ for P-QCTF, to 1.1×10⁻⁹ m² s⁻¹ for M-QCTF which is close to the value in bulk water (1.2×10⁻⁹ m² s⁻¹). The greater anion conductivity can dramatically improve device performance as exemplified here in an BTMAP-Vi- and FcNCl-based aqueous organic redox flow battery (AORFB) in pH-neutral solutions. The BTMAP-Vi/FcNCl cell configured with the M-QCTF membrane exhibited a high-frequency area-specific resistance (ASR) as low as 0.23 Ω·cm², which enabled charging and discharging of the BTMAP-Vi/FcNCl cell at an extreme current density of 500 mA cm⁻². The prolonged galvanostatic cell cycling at 400 mA cm⁻² maintained a Coulombic efficiency of > 99% and a stable energy efficiency of around 60% over the course of 1000 cycles. Notably, the achieved capacity utilization and efficiency with
+M-QCTF approaches similar values to those of alkaline AORFBs that leverage K+ as charge-carrying ions, while in otherwise identical cells assembled with QCTF or P-QCTF, an almost 20% lower energy efficiency was observed. This is significant and can be attributed to a dramatic reduction in the contribution of membrane resistance to whole–cell resistance, e.g., from > 70% for the Selemion® AMV membrane to ~ 25% for M-QCTF (Supplementary Tables S2 and S3). The above results imply a breakthrough in the charge asymmetry effect.
+
+Results and Discussion
+
+Covalent triazine framework membranes with tunable pore chemistry
+
+Covalent triazine framework chemistry gives rise to a wide variety of microporous materials and offers enormous diversity in pore chemistry. We thus synthesized a stand-alone triazine framework membrane from 4,4'-biphenyldicarbonitrile and a derivative of 3-hydroxy-[1,1'-biphenyl]-4,4'-dicarbonitrile bearing a quaternary ammonium moiety via a superacid-catalyzed organic sol–gel procedure (Fig. 1a and Supplementary Figures S1-S4) (26). The process yields a free-standing membrane (namely, QCTF) with a Young’s modulus and tensile strength of 0.91 GPa and 32.0 MPa, respectively (Supplementary Figure S5). The skeletal triazine rings of QCTF were subsequently protonated with HCl or methylated with CH3I, affording P-QCTF and M-QCTF, respectively. Overall, we constructed three covalent triazine framework polymers with similar molecular configurations and pore structures that can be processed into hydrophilic, uniform and robust ion-selective membranes via an organo-sol–gel procedure (Supplementary Figures S6-S8, Supplementary Table S4), but with slightly different and deliberately tailored pore chemistries.
+
+Carbon dioxide (CO2) adsorption experiments and molecular simulations were conducted to probe the micropore structure of the covalent triazine framework polymers. CO2 sorption isotherms measured at 273 K revealed that powder samples of QCTF, P-QCTF, and M-QCTF had similar CO2 uptake capacities of 16, 15.2, and 14.7 cm3 g−1 STP, respectively (Fig. 1b). Notably, QCTF, P-QCTF, and M-QCTF exhibit almost identical pore size distributions, ranging from 0.3 nm to 0.9 nm, as derived from CO2 adsorption isotherms based on density functional theory (DFT) calculations (Fig. 1c). These experimental results are further supported by molecular simulations of the 3D framework structure and the computation of CO2 distributions within the framework structures (Supplementary Figures S9 and S10). This again indicates that QCTF, P-QCTF, and M-QCTF have similar framework structures, interconnected micropores and pore size distributions.
+
+The amount of charged functional groups (quaternary ammonium groups) within the pristine QCTF membrane, characterized by the ion exchange capacity (IEC, in mmol g−1), is 1.20 mmol g−1 for QCTF (as-designed IEC value is ~ 1.00 mmol g−1). During protonation, approximately 55% of the triazine rings were protonated and the same amount of triazine rings was methylated after methylation, as revealed by
+X-ray photoelectron spectroscopy (XPS, Fig. 1d). This suggests that P-QCTF and M-QCTF should have identical IEC values, which was confirmed by titration and zeta potential measurements (Supplementary Figure S11).
+
+Ion Transport and Selectivity
+
+Despite the similar framework structure and almost identical pore size/size distributions, our experimental results reflect that cross-membrane ion transport is significantly affected by pore chemistry. We speculate that the difference is synergistically determined by Coulombic/steric effects and specific ion–pore wall interactions, as shown in Fig. 2a. The current–voltage (I–V) curves across the membranes, as measured in a two-compartment diffusional H-cell under a 10-fold concentration gradient KCl solution (Fig. 2b), reveal a net anion flux, indicating anion selectivity. The anion transference number (\( t_-\)) calculated for QCTF is 0.940, while the values for protonated QCTF (P-QCTF) and methylated QCTF (M-QCTF) are 0.947 and 0.953, respectively (Supplementary Figure S12). These values suggest the superior anion selectivity of the QCTF membranes compared to that of commercial anion exchange membranes (AEMs). This result is reasonable considering the Coulombic repulsion of the < 1 nm pore channel within the QCTF membranes.
+
+The measured transference numbers align with the cross-membrane permeation/diffusion rates for BTMAP-Vi (a redox-active organic cation) and Cl⁻ (Fig. 2c and 2d, Supplementary Figures S13-S15, Supplementary Tables S5-S6), which are dramatically different in size. Compared with commercial AEMs (Fig. 2c), all the QCTF membranes exhibited superior blocking capabilities toward BTMAP-Vi. The diffusion coefficients of BTMAP-Vi across the QCTF and the P-QCTF were determined to be \( 4.5 \times 10^{-11} \) cm² s⁻¹ and \( 3.4 \times 10^{-11} \) cm² s⁻¹, respectively. These values are at least one order of magnitude smaller than those of commercial AEMs. Note that the value further decreases to \( 3.1 \times 10^{-11} \) cm² s⁻¹ for M-QCTF, a value that is over 20 times smaller than that of Selemion® DSV. The diffusion coefficients of Cl⁻ through the QCTF and P-QCTF are \( 1.8 \times 10^{-7} \) cm² s⁻¹ and \( 2.6 \times 10^{-7} \) cm² s⁻¹, respectively. By contrast, commercial anion-selective membranes demonstrated Cl⁻ diffusion coefficients at least one order of magnitude smaller than those of QCTF membranes. Surprisingly, the Cl⁻ diffusion coefficient measured for M-QCTF reached \( 3.0 \times 10^{-7} \) cm² s⁻¹, which is nearly 2 times that for the QCTF membrane (Fig. 2d). A comparison of the Cl⁻ diffusion coefficients and the Cl⁻/BTMAP-Vi selectivity for QCTF membranes, commercial AEMs and previously reported membranes implies that these framework membranes can simultaneously deliver fast ion permeation and high selectivity, overcoming the usual tradeoff observed for many ion exchange membranes (Supplementary Figure S16 and Supplementary Table S6).
+
+The fast Cl⁻ transport across the triazine framework membranes is further supported by the membrane conductivity measurements. Compared with commercial AEMs, triazine framework membranes show high Cl⁻ conductivity at relatively low hydration numbers (Fig. 2e, Supplementary Figure S17 and Supplementary Tables S7-S8). The Cl⁻ conductivity of QCTF, as measured by four-point electrochemical
+impedance spectroscopy (EIS), is 13.2 mS cm\(^{-1}\) at 30.0°C and approaches 42.0 mS cm\(^{-1}\) at 80°C at low hydration numbers (3.5 at 30°C, 4.4 at 80°C). In comparison, the Cl\(^-\) conductivity of P-QCTF is 20.0 mS cm\(^{-1}\) at 30°C and increases to 48.4 mS cm\(^{-1}\) at 80°C. We find that the Cl\(^-\) conductivity of M-QCTF is 26.0 at 30.0°C, which is nearly twice that of QCTF, and reaches 53.0 mS cm\(^{-1}\) at 80°C. The activation energy (\(E_a\)) for Cl\(^-\) conduction across the QCTF membrane is 20.6 kJ mol\(^{-1}\), as derived from the conductivities at various temperatures (Fig. 2f and Supplementary Figure S18), contrasting an \(E_a\) of 12.9 kJ mol\(^{-1}\) for K\(^+\) transport across an otherwise identical membrane with sulfonate functional groups (ref 14). Surprisingly, the \(E_a\) value for M-QCTF is as low as 13.1 kJ mol\(^{-1}\), which is nearly half that of QCTF and lower than any value reported in the literature (Fig. 2g and Supplementary Table S1). Considering the similar framework structure and almost identical pore size/size distributions, this significant result indicates that the methylation of triazine rings alters the transport energy barrier for Cl\(^-\) ions.
+
+Due to the aforementioned results, we conclude that electrostatic interactions alone cannot explain the differences in Cl\(^-\) diffusion coefficients, Cl\(^-\) conductivity or activation energy for cross-membrane Cl\(^-\) transport. To unravel why methylation of the triazine ring promotes fast Cl\(^-\) conduction, compared to the protonated triazine ring in P-QCTF and the charge-neutral triazine ring in QCTF, the charge distribution and the Cl\(^-\) transport routes within the matrix of the triazine framework membranes were portrayed based on molecular simulations, and the two-dimensional free-energy landscapes were computed according to current methodology (13, 14). Our calculations show that the charge distributions of triazine framework membranes vary dramatically after protonation and methylation (Fig. 3a, Supplementary Figure S19). The most even charge distribution is observed for M-QCTF. We speculate that the variation in charge distribution alters the interactions between anions and the membrane frameworks and helps establish low-energy-barrier pathways for anion transport. This is supported by free energy calculations for Cl\(^-\) conduction (Fig. 3b). The simulation results showed that Cl\(^-\) can interact with quaternary ammonium (QA) groups (Fig. 3c, Supplementary Figures S20 and S21) and lower the free energy, but an energy barrier must be overcome for Cl\(^-\) ions to approach adjacent QA groups. The energy barrier for Cl\(^-\) conduction is the highest for QCTF (Fig. 3b, left panel) and decreases when the triazine ring is protonated (Fig. 3b, middle panel), while methylation of the triazine ring in M-QCTF improves the diffusivity of Cl\(^-\) within the framework and creates a Cl\(^-\) diffusion pathway with the lowest energy barrier (Fig. 3b, right panel). We suspect that the synergy of electrostatic interactions between Cl\(^-\) and the methylated triazine ring and the change in electron density along the Cl\(^-\) diffusion path after methylation may account for the emergence of the low-energy-barrier diffusion pathway.
+
+Molecular simulation results are further supported by measurements of transmembrane F\(^-\) diffusion coefficients via \(^{19}\)F pulsed-field gradient-stimulated-echo nuclear magnetic resonance (\(^{19}\)F PFG-NMR; \(^{19}\)F was selected owing to its higher sensitivity compared with \(^{35}\)Cl).\(^{19}\)F PFG-NMR revealed two separate F\(^-\) signals for Selemion® DSV and Selemion® AMV membranes (Fig. 3d and Supplementary Figure S22), with the upfield signal corresponding to free F\(^-\) in water (located at the same position as that in 0.1 M KF
+aqueous solution) and the downfield signal corresponding to associated F⁻ within the membrane. In contrast, only the upfield signal was observed for all three triazine framework membranes (Fig. 3d), which is an indication of freely exchangeable F⁻ within the membrane, with slight variations in the \(^{19}\mathrm{F}\) chemical shifts. By fitting the echo profiles with the Stejskal–Tanner equation (Supplementary Figure S23), the derived F⁻ diffusion coefficients within the P-QCTF and QCTF are \(0.93 \times 10^{-9} \ \mathrm{m}^2 \ \mathrm{s}^{-1}\) and \(0.63 \times 10^{-9} \ \mathrm{m}^2 \ \mathrm{s}^{-1}\), respectively (Fig. 3e). The value reaches \(1.1 \times 10^{-9} \ \mathrm{m}^2 \ \mathrm{s}^{-1}\) for M-QCTF, almost a twofold increase compared to that for QCTF. Notably, this value is 12.8 times that of Selemion® AMV and 10.8 times that of Selemion® DSV (Fig. 3e and Supplementary Figure S23) and approaches the measured diffusion coefficient of F⁻ in water (\(1.2 \times 10^{-9} \ \mathrm{m}^2 \ \mathrm{s}^{-1}\); Supplementary Figure S23). In summary, by tailoring the pore chemistry of framework membranes, intimate ion–pore wall interactions provide a low-energy-barrier diffusion pathway for anions. Taken together with the Coulombic/steric exclusion by the charged framework micropores, the triazine framework membranes, particularly M-QCTF, will be of interest in applications demanding extremely fast and highly selective transport of anions.
+
+Triazine framework membrane powers fast-charging AORFBs
+
+The extremely fast and highly selective anion (particularly chloride ions) conduction through chemically tuned triazine framework membranes is desirable in electrochemical devices, such as aqueous organic redox flow batteries. As a proof of concept, we configured pH-neutral AORFBs with BTMAP-Vi/FcNCl as the redox-active organic electrolyte couple and triazine framework membranes as the ion-conducting membranes, while Cl⁻ ions were transported back and forth as charge carriers (Fig. 4a). At an electrolyte concentration of 0.1 M, EIS of the BTMAP-Vi/FcNCl cells assembled with QCTF or P-QCTF showed area-specific membrane resistances (ASRs) of 0.63 Ω cm² and 0.53 Ω cm², respectively (Supplementary Figures S24-S25). An otherwise identical cell assembled with M-QCTF showed an ASR of 0.37 Ω cm² (Supplementary Figure S26), which is almost twofold lower than that of the QCTF membrane. This finding aligns with the high conductivity of M-QCTF (Fig. 2e, 3b), which enables charging of the BTMAP-Vi/FcNCl cells at extreme current densities. For example, at 200 mA cm⁻², BTMAP-Vi/FcNCl with M-QCTF exhibited an energy efficiency (EE) of over 60% (Supplementary Figure S26). In contrast, the control BTMAP-Vi/FcNCl cells assembled with Selemion® DSV or Selemion® AMV could not operate at this current density due to the immediate voltage cutoff. At lower current densities ranging from 20 to 80 mA cm⁻², the reported energy efficiency for the control cells drops from 89.4–65.9% for Selemion® DSV or from 80.0–26.6% for Selemion® AMV (27).
+
+At a higher electrolyte concentration of 0.5 M, BTMAP-Vi/FcNCl with M-QCTF demonstrated an even lower ASR of 0.23 Ω cm² (Fig. 4b), a much lower value than that for Selemion® DSV or Selemion® AMV. The rate performance of the cell reveals an EE of 49.7% and a capacity utilization of 58.8% at an extreme current density of 500 mA cm⁻² (Fig. 4c). Compared with the most recent report of an AEM (MTCP-50 membrane, with the optimal ratio 1:1 of m-terphenyl to p-terphenyl) for pH-neutral AORFBs at 0.5 M (21), M-QCTF achieved a much greater energy efficiency (76.9% vs. 60.1%) and capacity utilization (94.3% vs.
+63.7%) at the same current density of 200 mA cm\(^{-2}\). Notably, alkaline AORFBs that utilize K\(^+\) as charge-carrying ions assembled with a cation exchange membrane (SCTF-BP), which allows cation diffusion close to the value in bulk electrolyte, exhibit an EE of 50.4% and a capacity utilization of 62% at 500 mA cm\(^{-2}\). The current results demonstrate a similar efficiency for Cl\(^-\) transport and therefore suggest a breakthrough in the charge asymmetry effect.
+
+Robust and exceptional cell performance was observed during long-term galvanostatic cycling of over 2000 cycles at 200 mA cm\(^{-2}\) (0.1 M electrolyte concentration, Supplementary Figure S26) and over 1000 cycles at 400 mA cm\(^{-2}\) (0.5 M electrolyte concentration, Fig. 4d). Comparisons of the EE and capacity utilization against the current density shows consistently superior battery performance over multiple cell cycling experiments for the BTMAP-Vi/FcNCl cells with M-QCTF, compared to the pH-neutral AORFB with different membranes (Fig. 4e, 4f and Supplementary Table S10).
+
+This work demonstrates that chloride and fluoride anions traverse the M-QCTF membrane with a very low energy barrier, leading to exceptional flow battery performance. This significant development can be applied more broadly to designing anion exchange membranes for other technologies such as CO\(_2\) electrolysers (28) and ion-capture electrodialysis (29). Although the anion diffusion constants within the developed membranes are approaching the theoretical limit of the bulk electrolyte solution, we expect further improvements in overall conductivity to be achievable by eliminating micropore tortuosity and creating perfectly aligned micropore channels with monodispersed pore size distributions.
+
+Declarations
+
+Acknowledgments
+
+This work was funded by the National Key R&D Program of China (2021YFB4000302) and the National Natural Science Foundation of China (Grant/Award No. U20A20127, 52021002). This work was partially carried out at the Instruments Center for Physical Science, University of Science and Technology of China.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Data availability
+
+The authors confirm that the data supporting the findings of this study are available within the article and its supplementary materials. Source data are available on reasonable request from the corresponding author.
+
+References
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+19. G. Karkera et al., A structurally flexible halide solid electrolyte with high ionic conductivity and air processability. Adv. Energy Mater. **13**, 2300982 (2023).
+20. S. Pang et al., Biomimetic amino acid functionalized phenazine flow batteries with long lifetime at near-neutral pH. Angew. Chem. Int. Edit. **60**, 5289-5298 (2021).
+21. W. Song et al., Upscaled production of an ultramicroporous anion-exchange membrane enables long-term operation in electrochemical energy devices. Nat. Commun. **14**, 2732 (2023).
+22. M. E. Carrington et al., Associative pyridinium electrolytes for air-tolerant redox flow batteries. Nature **623**, 949-955 (2023).
+23. P. Xiong et al., A chemistry and microstructure perspective on ion-conducting membranes for redox flow batteries. Angew. Chem. Int. Edit. **60**, 24770-24798 (2021).
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+25. J. Luo et al., A π-conjugation extended viologen as a two-electron storage anolyte for total organic aqueous redox flow batteries. Angew. Chem. Int. Edit. **57**, 231-235 (2017).
+26. X. Zhu et al., A superacid-catalyzed synthesis of porous membranes based on triazine frameworks for CO\(_2\) separation. J. Am. Chem. Soc. **134**, 10478-10484 (2012).
+27. H. Li et al., Ultra-microporous anion conductive membranes for crossover-free pH-neutral aqueous organic flow batteries. J. Membr. Sci. **668**, 121195 (2023).
+28. D. A. Salvatore et al., Designing anion exchange membranes for CO\(_2\) electrolyzers. Nat. Energy **6**, 339-348 (2021).
+29. A. A. Uliana et al., Ion-capture electrodialysis using multifunctional adsorptive membranes. Science **372**, 296-299 (2021).
+
+Figures
+Figure 1
+
+Synthesis and characterization of microporous covalent triazine framework membranes. (a) Left panel: schematic showing the 3D interconnected micropore free volume for anion transport. Right panel: Molecular structure and synthesis of the covalent triazine framework membrane QCTF and subsequent protonation or methylation of the triazine ring skeleton, affording P-QCTF and M-QCTF. Coulombic/steric exclusion and intimate ion–pore wall interactions enable selective and fast anion transport. Red and blue spheres: fixed functional groups or charged triazine rings; green spheres: counterions or charge carrier ions; lightning: ion–pore wall interactions. (b) CO₂ adsorption isotherms of QCTF, P-QCTF and M-QCTF at 273 K. (c) Pore size distributions of QCTF, P-QCTF and M-QCTF derived from CO₂ adsorption isotherms through density functional theory (DFT) calculations. (d) XPS (N1s) spectra of covalent triazine framework (CTF) membranes: QCTF (top), protonated QCTF (P-QCTF, middle), and methylated QCTF (M-QCTF, bottom).
+Figure 2
+
+Ion selectivity and conductivity of microporous covalent triazine framework membranes. (a) Schematic showing the transport of anions across rigid micropores within positively charged covalent triazine framework QCTF membranes. Coulombic/steric exclusion and intimate ion–pore wall interactions enable selective and fast anion transport. Red and blue spheres: fixed functional groups or charged triazine rings; green spheres: counterions or charge carrier ions; blue and gray spheres: positively charged ions with large or small hydrated diameters. The dashed lines indicate ion–pore wall interactions, while the arrowed lines suggest rejection or transport of ions. (b) Current–voltage (\( I-V \)) curves of the M-QCTF, P-QCTF, QCTF, Selemion® DSV and Selemion® AMV membranes under a 10-fold concentration gradient in KCl solution. The intercept at 0 \( \mu \)A correlates to the transmembrane potential as a result of selective ion transport, from which the transference number \( t_i \) can then be deduced. The diffusion coefficient of BTMAP-Vi (c) and Cl\( ^- \) (d) across QCTF membranes and commercial membranes, as determined from a two-compartment diffusional H-cell. (e) Cl\( ^- \) conductivity plotted as a function of
+hydration number for the M-QCTF, P-QCTF, QCTF, Selemion® DSV and Selemion® AMV membranes. The conductivity was measured via the four-probe EIS method. Each data point represents the Cl⁻ conductivity at an individual temperature: from left to right (or from larger data points to smaller data points), 30–80 °C, with a 10 °C increment. (f) The calculated activation energy for Cl⁻ conduction (\( E_a \)) across the M-QCTF, P-QCTF, QCTF, Selemion® DSV and Selemion® AMV membranes, as derived from Arrhenius equations. (g) Comparison on activation energy for QCTF membranes, commercial membranes and those reported previously. The detailed values can be found in Supplementary Table S1.
+
+![Three molecular structures labeled QCTF, P-QCTF, M-QCTF, with a color scale bar indicating charge. Three contour plots showing free energy landscapes for QCTF, P-QCTF, M-QCTF. Three molecular diagrams labeled Cl–OAc interaction, Cl–methylated triazine ring interaction, Cl–OAc interaction. Four NMR spectra labeled Selemion® DSV, M-QCTF, OCTF, P-QCTF, with B values increasing. A bar graph labeled Self-diffusion coefficient of F (×10⁻⁷ m² s⁻¹) for Selemion® DSV, OCTF, P-QCTF, M-QCTF.](page_246_370_1157_1492.png)
+Figure 3
+
+Low barrier anion transport enabled by ion–pore wall interactions under confinement. (a) Charge distributions of QCTF (left), P-QCTF (middle), and M-QCTF (right) from restrained electrostatic potential (RESP). The charge values shown can be found in Supplementary Table S9. (b) Computed free energy map for the transport of Cl⁻ ions within the QCTF (left), P-QCTF (middle) and M-QCTF (right) membrane matrices. The black or white lines denote the Cl⁻ ion transport pathways (1-1 or 1-2-1) with the lowest free energy barrier. (c) Snapshots taken during simulation, demonstrating the interactions between Cl⁻ and the M-QCTF membrane pore walls. Insets denote the specific interactions at positions 1 and 2. The parameters (\( r_1 \) and \( r_2 \)) represent the distance between the Cl⁻ ion and the geometric center of two quaternary ammonium (QA) groups. (d) \( ^{19}\mathrm{F} \) PFG-NMR spectra recorded for membrane samples of Selemion® DSV, QCTF, P-QCTF and M-QCTF immersed in 0.1 M KF solutions. (e) F⁻ self-diffusion coefficients derived from \( ^{19}\mathrm{F} \) PFG-NMR spectra (\(^{19}\mathrm{F}^{-}\) is used instead of \(^{35}\mathrm{Cl}^{-}\) because of its superior NMR sensitivity). Error bars are standard deviations derived from three measurements based on three separate membrane samples.
+Figure 4
+
+Fast charging of pH-neutral AORFBs enabled by the M-QCTF membrane. (a) Schematic illustration of a pH-neutral BTMAP-Vi/FcNCl AORFB assembled with an M-QCTF membrane. (b) EIS spectra measured in cells assembled with M-QCTF, Selemion® DSV and Selemion® AMV membranes. A control EIS spectrum was recorded in a cell without a membrane. (c) Coulombic efficiency (CE), energy efficiency (EE), and capacity of cells assembled with the M-QCTF membrane at various current densities. (d) Galvanostatic cycling of the BTMAP-Vi/FcNCl cell assembled with the M-QCTF membrane at 400 mA cm\(^{-2}\). The electrolyte compositions through b to d: the anolyte comprised 5 mL of 0.5 M BTMAP-Vi in 2 M KCl, while the catholyte comprised 10 mL of 0.5 M FcNCl in 2 M KCl. Capacity utilization (e) and energy efficiency (f) of pH-neutral AORFBs assembled with Selemion® DSV and Selemion® AMV, AME 115, PIM-TDQTB, or M-QCTF are plotted as a function of current density. Dashed lines and shades are visual guides. The detailed values can be found in Supplementary Table S10.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• 03supplementarymaterials.docx

00c089bc5362865e32d087a7de2c59c85939f78a3756c6991e0e05e515c9142f/preprint/preprint.md

@@ -0,0 +1,183 @@
+Coexistence of ferroelectricity and antiferroelectricity in 2D van der Waals multiferroic
+
+Bo Peng
+bo_peng@uestc.edu.cn
+
+University of Electronic Science and Technology of China   https://orcid.org/0000-0001-9411-716X
+Yangliu Wu
+1450683589@qq.com
+Haipeng Lu
+University of Electronic Science and Technology of China
+Xiaocang Han
+Peking University
+Chendi Yang
+Laboratory of Advanced Materials, Department of Materials Science and Shanghai Key Lab of Molecular Catalysis and Innovative Materials, Fudan University
+Nanshu Liu
+Renmin University of China
+Xiaoxu Zhao
+Peking University   https://orcid.org/0000-0001-9746-3770
+Liang Qiao
+School of Physics, University of Electronic Science and Technology of China   https://orcid.org/0000-0003-2400-2986
+Wei Ji
+Renmin University of China   https://orcid.org/0000-0001-5249-6624
+Renchao Che
+Fudan University   https://orcid.org/0000-0002-6583-7114
+Longjiang Deng
+University of Electronic Science and Technology of China   https://orcid.org/0000-0002-8137-6151
+DOI: https://doi.org/10.21203/rs.3.rs-4229313/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on October 4th, 2024. See the published version at https://doi.org/10.1038/s41467-024-53019-5.
+Coexistence of ferroelectricity and antiferroelectricity in 2D van der Waals multiferroic
+
+Yangliu Wu1, Haipeng Lu1, Xiaocang Han2, Chendi Yang3, Nanshu Liu5, Xiaoxu Zhao2, Liang Qiao4, Wei Ji5, Renchao Che3, Longjiang Deng1* and Bo Peng1*
+
+1National Engineering Research Center of Electromagnetic Radiation Control Materials, School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
+2School of Materials Science and Engineering, Peking University, Beijing 100871, China
+3Laboratory of Advanced Materials, Department of Materials Science, Collaborative Innovation Center of Chemistry for Energy Materials(iChEM), Fudan University, Shanghai 200433, China
+4School of Physics, University of Electronic Science and Technology of China, Chengdu 611731, China
+5Beijing Key Laboratory of Optoelectronic Functional Materials & Micro-Nano Devices, Department of Physics, Renmin University of China, Beijing 100872, China
+*To whom correspondence should be addressed. Email address: bo_peng@uestc.edu.cn; denglj@uestc.edu.cn
+
+Abstract
+
+Multiferroic materials with a coexistence of ferroelectric and magnetic order have been intensively pursued to achieve the mutual control of electric and magnetic properties toward energy-efficient memory and logic devices. The breakthrough progress of 2D van der Waals magnet and ferroelectric encourages the exploration of low dimensional multiferroics, which holds the promise to understand inscrutable magnetoelectric coupling and invent advanced spintronic devices. However, confirming ferroelectricity with optical techniques is challenging on 2D materials, particularly in conjunction with antiferromagnetic orders in a single-layer multiferroic. The prerequisite of ferroelectric is the electrically switchable spontaneous electric polarizations, which must be proven through reliable and direct electrical measurements. Here we report the discovery of 2D vdW multiferroic with out-of-plane ferroelectric polarization in trilayer NiI2 device, as revealed by scanning reflective magnetic circular dichroism microscopy and ferroelectric hysteresis loop. The evolutions of between ferroelectric and antiferroelectric phase have been unambiguously observed. Moreover, the magnetoelectric interaction is directly probed by external electromagnetic field control of the multiferroic domains switching. This work opens up opportunities for exploring new multiferroic orders and multiferroic physics at the limit of single or few atomic layers, and for creating advanced magnetoelectronic devices.
+Multiferroic materials with a coexistence of ferroelectric and magnetic orders has been diligently sought after for a long time to achieve the mutual control of electric and magnetic properties toward the energy-efficient memory and logic devices\(^{1-3}\). But the two contrasting order parameters tend to be mutually exclusive in a single material\(^{4}\). Nondisplacive mechanisms introduce a paradigm for constructing multiferroics beyond the traditional limits of mutual obstruction of the ferroelectric and magnetic orders\(^{5,6}\). To date, the type I multiferroic BiFeO\(_3\) is the only known room-temperature single-phase multiferroic material. Alternatively, the helical magnetic orders break the spatial inversion symmetry and simultaneously lead to electric orders\(^{7,8}\), giving rise to type-II multiferroics. The quest for a new single-phase multiferroic remains an open challenge.
+
+The emergence of 2D vdW magnets and ferroelectrics has opened new avenues for exploring low-dimensional physics on magnetoelectric coupling\(^{9,10}\). Diverse isolated vdW ferromagnets\(^{11-13}\) and ferroelectrics\(^{14,15}\) have enabled tantalizing opportunities to create 2D vdW spintronic devices with unprecedented performances at the limit of single or few atomic layers. Few of bulk crystals of transition-metal dihalides with a trigonal layered structure have been shown that the helical spin textures break inversion symmetries and induce an orthogonal ferroelectric polarization\(^{16,17}\), but and definitive multiferroicity remains elusive at the limit of few atomic layers.
+
+A recent work shows the possibility of discovery of type-II monolayer NiI\(_2\) multiferroics using the optical measurements of second-harmonic-generation (SHG) and linear dichroism (LD)\(^{18}\). Our work has pointed that all-optical characterizations are not sufficient to make a judgement of a few- and single-layer multiferroic at the presence of non-collinear and antiferromagnetic orders\(^{19}\). The observed SHG and LD signals in few-layer NiI\(_2\) originate from the magnetic-order-induced breaking of spatial-inversion\(^{19,20}\). The prerequisite of ferroelectric polarization is the non-vanishing spontaneous electric polarizations, which must be proven through reliable and direct electrical measurements, such as polarization- and current-electric field (\(P\)-\(E\) and \(I\)-\(E\)) hysteresis loops. To date, 2D vdW multiferroic has not been directly uncovered at the limit of few layers. Here, we report fascinating vdW multiferroic with coexistence of ferroelectricity and antiferroelectricity in few layer NiI\(_2\) based on magneto-optical-electric joint-measurements. In this 2D vdW multiferroics, an unprecedented magnetic control of switching dynamics of ferroelectric domain has been observed.
+
+**Non-collinear antiferromagnetism in trilayer NiI\(_2\)**
+
+Due to the high reactivity of NiI\(_2\) flakes, NiI\(_2\) exfoliation and encapsulation by graphene and hexagonal boron nitride (hBN) flakes were carried out in a glove box (Fig. 1a and Supplementary Fig. 1). NiI\(_2\) crystal shows rhombohedral structure with a repeating stack of three (I-Ni-I) layers, where Ni and I ions form a triangular lattice in each layer (Fig. 1b). The rhombohedral stacking has been atomically identified (Fig. 1c). The atom
+arrangements of rhombohedral phase demonstrate signature hexagon-shaped periodic bright spots with equal contrast, validating the overlapping stack of I and Ni atoms along the c axis. The ADF-STEM and fast Fourier transform (FFT) show an interplanar spacing of 1.9 Å, consistent with the (110) lattice plane of rhombohedral NiI₂ crystal. Circularly polarized Raman spectra in the parallel (\( \sigma+/ \sigma+ \) and \( \sigma-/ \sigma- \)) configuration show only two distinct peaks in the NiI₂ device (Fig. 1d). The peak at ~124.7 cm⁻¹ is assigned to the \( A_g \) phonon modes²², and this polarization behavior is consistent with Raman tensor analysis for the rhombohedral structure of NiI₂²³. The Raman feature at ~20 cm⁻¹ is assigned to the interlayer shear mode (SM), which suggests that the NiI₂ is trilayer²⁰.
+
+For optimal optical response and sensitivity to probe the magnetic properties, the photon energy should be chosen near the absorption edge¹¹,²⁴. Therefore, we first studied white-light magnetic circular dichroism (MCD) spectra of a trilayer NiI₂ device as a function of magnetic field perpendicular to the sample plane at 10 K (see Methods for details)²⁵. There is a strong peak near 2.3 eV along with two weak features around 1.85 eV and 1.6 eV (Fig. 1e). By means of ligand-field theory, the peaks are attributed to the absorption transitions of \( p-d \) exciton states²⁶. A pair of opposite MCD peaks with magnetic field manifestly appears at 2.3 eV, suggesting strong magneto-optical resonance. When the magnetic field is switched, MCD features is consistently reversed, and zero remanent MCD signal at ~2.3 eV is distinctly observed at 0 T, indicating antiferromagnetic orders at 10 K.
+
+To further validate the magnetic order, the scanning RMCD microscope was used to image and measure the magnetic domains of the as-exfoliated trilayer NiI₂. The polar RMCD imaging is a reliable and powerful tool to unveil the 2D magnetism in the micro scale, and the RMCD intensity is proportional to the out-of-plane magnetization²⁴. All magneto-optical measurements were carried out using a 2.33 eV laser with optimal detection sensitivity (see Methods for details). Figure 2a shows RMCD maps of a trilayer NiI₂ sweeping between -0.75 T and +0.75 T at 10 K. Remarkably, many micrometer-sized bimeron-like domains are observed in trilayer and another few-layer NiI₂ across the entire range of sweeping magnetic field²⁷. The spin-up and spin-down domains exist in pairs (Fig. 2a and Supplementary Fig. 2). One typical bimeron-like domains in trilayer NiI₂ at 0 T and 10 K are shown in Fig. 2b. The RMCD signals in each bimeron-like domain display opposite sign and nearly equal intensities. The magnetic moments point upwards or downwards in the core region and gradually decrease away from the core, and approaches zero near the perimeter (Fig. 2c). This magnetic moment distribution possibly indicates a pair of topological spin meron and antimeron with opposite chirality in a cycloid ground state²⁸,²⁹. The bimeron-like magnetization textures remain robust in all magnetic field, indicating the bimeron-like domains are robust. The high stability of the bimeron-like magnetic domains probably
+originate from the topological protection, which also contributes to the preservation of magnetization even if upon a reversal magnetic field of 0.75 T. The formation of bimeron-like magnetic domains may be related to the localized stress at the interface. But further deep studies must be done to reveal the exact physical mechanism.
+
+Fig. 2d shows the RMCD loops of the trilayer NiI$_2$ sweeping between +3 T and -3 T at 10 K. The RMCD loops show a highly nonlinear behavior with magnetic field and plateau behaviors for the out-of-plane magnetization. The RMCD intensity near 0 T is suppressed and approaches zero, suggesting the vanishing remnant magnetization, which indicates a compensation of the out-of-plane magnetization and non-collinear AFM orders in the trilayer NiI$_2$.$^{30}$ And the gradual increases of the RMCD signal are observed with increasing magnetic field between ±1.2 and ±2.6 T, suggesting a spin-flop process. The spin-flop behaviors of the magnetization curve imply that the interlayer antiferromagnetic coupling of the non-collinear spins is complicated. Similar magnetic hysteresis loops have been demonstrated in another few-layer NiI$_2$, which show definite non-collinear AFM orders in the few-layer NiI$_2$ (Supplementary Fig. 2b).
+
+Ferroelectricity in trilayer NiI$_2$ device
+
+To determine ferroelectricity in few-layer NiI$_2$ device, we performed the frequency-dependent measurement of electric polarization via $I$-$E$ and $P$-$E$ hysteresis loops, which allows an accurate estimation of the electric polarization. We fabricated two heterostructure devices of graphene/hBN/NiI$_2$/graphene/hBN (Fig. 1a and Supplementary Fig. 1). The hBN flake was used as an excellent insulating layer to prevent large leakage current and guarantee the detections of ferroelectric (FE) features$^{31,32}$ (Supplementary Fig. 3). The hBN insulator shows a linear $P$-$E$ behavior and a rectangle-shaped $I$-$E$ loops (Supplementary Fig. 4), indicating excellent insulativity for ferroelectric hysteresis measurements (see Methods for details)$^{33,34}$. The frequency-dependent $I$-$E$ and $P$-$E$ loops at 10 K are shown in Fig. 3, and the forward and backward scans of the electric polarization as a function of electric field show characteristic ferroelectric $I$-$E$ and $P$-$E$ hysteresis. Strikingly, a characteristic double-hysteresis loop of antiferroelectric (AFE) polarization emerges accompanied with decreasing remanent polarization ($P_r$). More importantly, a pair of opposite single peaks of switching current ($I$) are observed when sweeping voltage at 6.7 Hz, which is attribute to charge displacement and implies two stable states with inverse polarity (Fig. 3b and c). Whereas two pair of opposite bimodal peaks are observed when sweeping voltage at 1.3 Hz, which is attribute to AFE-FE and FE-AFE transitions under electric field sweeping (Fig. 3c )$^{35}$. This suggests an evolution from FE to AFE polarization with frequency is observed$^{36,37}$, exhibiting the decisive evidence for coexistence of ferroelectric and antiferroelectric$^{38,39}$. This comprehensive frequency-dependent evolution behaviors also confirm the coexistence of FE and AFE in another a few layers
+NiI₂ (Supplementary Fig. 5).
+
+The type-II multiferroicity has been demonstrated in the bulk NiI₂. However, the multiferroic identification for few-layer NiI₂ remains challenging and elusive. All-optical methods are unreliable to make a judgement of a few- and single-layer multiferroic at the presence of non-collinear and antiferromagnetic orders¹⁹. The bulk NiI₂ displays a helimagnetic state below critical temperature¹⁶,¹⁷. From symmetry considerations and a Ginzburg-Landau perspective⁴⁰,⁴¹, the helimagnetic state allows for the emergence of a ferroelectric polarization associated to the form:
+
+\[
+\mathbf{P} = \gamma \mathbf{e} \times \mathbf{q}
+\] (1)
+
+where \( \mathbf{P} \) is the electric polarization, \( \mathbf{e} \) is the spin rotation axis, \( \mathbf{q} \) is the spin propagation vector of the spin spiral, and \( \gamma \) is a scalar parameter dependence with spin-orbit coupling. For monolayer NiI₂, the helimagnetic order can be modeled with a 7axa supercell and an in-plane (x-y plane) spin cycloid, and the spin propagation vector \( \mathbf{q} \) is displayed along the [210] direction (in lattice vector units)⁴², as shown in in Fig. 3d. Thus, the in-plane (x-y plane) spin cycloid induces the in-plane electric polarization along the [010] direction (Fig. 3d). Actually, theoretical calculations have determined that the \( \mathbf{q} \)-vector in multi-layer and bulk NiI₂ is a consequence of the competition between magnetic exchange interactions between magnetic atoms⁴²,⁴³. In particular, intralayer ferromagnetic first-neighbor, intralayer antiferromagnetic third neighbor, and interlayer antiferromagnetic second-neighbor magnetic exchange interactions are the most relevant. In the monolayer limit, there are no interlayer interactions, hence the \( \mathbf{q} \)-vector is in-plane and determined by the competition between intralayer exchange interactions. For a trilayer NiI₂, the \( \mathbf{q} \)-vector is modulated not only by intralayer exchange interactions but also by interlayer exchange interactions. Assuming that interlayer exchange interactions cause the tilting out-of-plane cycloidal spin configuration from in-plane (x-y plane) configuration (Fig. 3d), the e-vector is no longer parallel to the z-axis, leading to an out-of-plane ferroelectric polarization component. Figure 3e illustrates the extreme case where the in-plane (x-y plane) cycloidal configuration tilts to x-z plane, resulting in an out-of-plane ferroelectric polarization. This scenario suggests the observed out-of-plane ferroelectric polarization in the trilayer NiI₂ device, but the precise mechanism remains to be further studied in the future. In particular, equation (1) shows that two spin spiral configurations with \( \mathbf{q}_1 = \mathbf{q} \) and \( \mathbf{q}_2 = -\mathbf{q} \) will give rise to opposite electric polarizations \( \mathbf{P} = -\mathbf{P} \). The first principles calculations in spin configuration with both \( \mathbf{q} \) and -\( \mathbf{q} \) are energetically equivalent, and therefore show same energies with and without spin-orbit coupling⁴². Thus, the emergence of opposite electric dipoles can be directly observed in the total electronic density of the system. The energy of spin cycloidal configurations with positive and negative \( \mathbf{q} \)-vectors (positive and negative ferroelectric polarization \( \mathbf{P} \)) is degenerate, which approve the coexistence of ferroelectric and antiferroelectric (Fig. 3f), consistent with the observed
+coexistence of ferroelectric and antiferroelectric in trilayer NiI2.
+
+Magnetic control of ferroelectricity
+
+To reveal the magnetoelectric coupling effect, we studied the magnetic control of ferroelectric properties in the trilayer NiI2 device, as shown in Fig. 4. The \( P_r \) extracted from the \( P\text{-}E \) hysteresis loop is plotted as a function of out-of-plane magnetic field at different frequencies (Fig. 4a-c). The magnetic field causes a decrease in residual polarization at different frequencies (Fig. 4a-c and Supplementary Fig. 6), and the magnetic control of \( P_r \) shows frequency dependence of applied electric field (Fig. 4d). The magnetic control ratio reaches to ~7% by detuning the frequency (24.5 Hz) at 7 T, which is remarkable feature of multiferroic. To better understand the magnetic control behavior, we briefly discuss the possible mechanism that leads to the decrease in \( P_r \) caused by the magnetic field from a microscopic perspective. We only discuss ferroelectric polarization flops in the model of spiral magnets\(^{40}\). In zero fields spins rotate in the easy x-z plane, so that the spin rotation axis \( \mathbf{e} \) is parallel to the y axis, and for \( \mathbf{q} \parallel \text{x-y plane}, \mathbf{P} \parallel z \) (Supplementary Fig. 7a and 7b). However, magnetic field in the z direction favors the rotation of spins in the x-y plane (Supplementary Fig. 7c and 7d), so that the spin rotation axis \( \mathbf{e} \) is parallel to the z axis, in which case, \( \mathbf{P} \parallel \text{x-y plane}\)\(^{40}\). In short, applying a magnetic field parallel to the z-axis causes the spin rotation plane to tilt from the x-z plane to the x-y plane, and the corresponding ferroelectric polarization flops from the out-of-plane direction to the in-plane direction. Therefore, an out-of-plane magnetic field leads to a decrease of ferroelectric polarization in the out-of-plane direction, which is consistent with the observed decrease in \( P_r \) with increasing magnetic field. Furthermore, the decrease in the current peak accompanied by an increase in the coercive electric field due to the increased magnetic field is unambiguously observed (Fig. 4e and Supplementary Fig. 8). This is because the out-of-plane magnetic field causes the spin rotation plane to tilt from the x-z plane to the x-y plane, and the corresponding easy axis of ferroelectric polarization flops from the out-of-plane direction to the in-plane direction. The shifts of current peaks induced by ferroelectric switching vary with the magnetic field, but the background current remains constant, excluding the magnetoresistance effects (Fig. 4e and Supplementary Fig. 8). Finally, the switching time of ferroelectric domain under different magnetic fields at10 K is calculated by KAI model\(^{44}\) (Fig. 4f and 4g; Part A and B). The switching time \( \tau \) increase as magnetic field increase, which signifies an even symmetry with magnetic field (Fig. 4h), consistent with the above mechanisms. At 10 K, the switching time \( \tau \), leading to a maximum enhancement of switching time by 20% (-7 T). This observation of robust control of ferroelectric properties by magnetic field, pointing to the potential use of few-layer NiI2 as a research platform for studying the magneto-electric coupling physics in the two-dimensional limit and for fabricating advanced nano-
+magnetoelectric devices.
+
+In summary, we report a 2D vdW single-phase multiferroic NiI$_2$ few-layer crystal. We observed strong evidences for the coexistence of ferroelectric and non-collinear antiferromagnetism order via RMCD, $P$-$E$ and $I$-$E$ hysteresis loop. hysteresis loop. We achieve unprecedented magnetic control of ferroelectric properties in the NiI$_2$ trilayer. We envision that the 2D vdW single-phase multiferroic NiI$_2$ will provide numerous opportunities for exploring fundamental low-dimensional physics, and will introduce a paradigm shift for engineering new ultra-compact magnetoelectric devices.
+
+Methods
+
+Sample fabrication
+NiI$_2$ flakes were mechanically exfoliated from bulk crystals via PDMS films in a glovebox, which were synthesized by chemical vapor transport method from elemental precursors with molar ratio Ni:I = 1:2. All exfoliated hBN, NiI$_2$ and graphene flakes were transferred onto pre-patterned Au electrodes on SiO$_2$/Si substrates one by one to create heterostructure in glovebox, which were further in-situ loaded into a microscopy optical cryostat for magneto-optical-electric joint-measurement. The whole process of NiI$_2$ sample fabrications and magneto-optical-electric measurements were kept out of atmosphere.
+
+Magneto-optical-electric joint-measurement
+The polar RMCD, white-light MCD, Raman measurements and ferroelectric $P$-$E$ and $I$-$E$ measurements were performed on a powerful magneto-optical-electric joint-measurement scanning imaging system (MOEJSI)$^{19}$, with a spatial resolution reaching diffraction limit. The MOEJSI system was built based on a Witec Alpha 300R Plus low-wavenumber confocal Raman microscope, integrated with a closed cycle superconducting magnet (7 T) with a room temperature bore and a closed cycle cryogen-free microscopy optical cryostat (10 K) with a specially designed snout sample mount and electronic transport measurement assemblies.
+The Raman signals were recorded by the Witec Alpha 300R Plus low-wavenumber confocal Raman microscope system, including a spectrometer (150, 600 and 1800/mm) and a TE-cooling Andor CCD. A 532 nm laser of ~0.2 mW is parallel to the X-axis (0°) and focused onto samples by a long working distance 50× objective (NA = 0.55, Zeiss) after passing through a quarter-wave plate (1/4λ). The circular polarization resolved Raman signals passed through the same 1/4λ waveplate and a linear polarizer, obtained by the spectrometer (1800/mm) and the CCD.
+For white-light MCD measurements, white light with Köhler illumination from Witec Alpha 300R Plus microscope was linearly polarized at 0o by a visible wire grid
+polarizer, passed through an achromatic quarter-wave (1/4\( \lambda \)) plate and focused onto samples by a long working distance 50× objective (Zeiss, NA = 0.55). The right-handed and left-handed circularly polarized white light was obtained by rotating 1/4\( \lambda \) waveplate at +45° and -45°. The white-light spectra were recorded by the Witec Alpha 300R Plus confocal Raman microscope system (spectrometer, 150/mm). The absorption spectra of right-handed and left-handed circularly polarized light in different magnetic field can be obtained as the previous work\(^{25}\), giving corresponding MCD spectra.
+
+For polar RMCD measurements, a free-space 532 nm laser (2.33 eV) of ~2 \( \mu \)W modulated by photoelastic modulator (PEM, 50 KHz) was reflected by a non-polarizing beamsplitter cube (R/T = 30/70) and then directly focused onto samples by a long working distance 50× objective (NA = 0.55, Zeiss), with a diffraction limit spatial resolution of ~590 nm. The reflected beam which was collected by the same objective passed through the same non-polarizing beamsplitter cube and was detected by a photomultiplier (PMT), which was coupled with lock-in amplifier, Witec scanning imaging system, superconducting magnet, voltage source meter and ferroelectric tester. Ferroelectric *P-E* and *I-E* hysteresis loop of a NiI$_2$ device of Gr/hBN/NiI$_2$/Gr were measured by classical ferroelectric measurements and directly recorded by ferroelectric tester (Precision Premier II: Hysteresis measurement), which were contacted with the top and bottom graphene electrodes by patterned Au electrodes (Fig. 1a) through the electronic assemblies of the microscopy optical cryostat. The mechanism of ferroelectric measurement has been given by previous work\(^{45}\). The detected signals include two components: a ferroelectric term of NiI$_2$ (2PrA) and a linear non-ferroelectric term of hBN insulator (\( \sigma \)EAt), Q = QNiI + QBN = 2PrA + \( \sigma \)EAt. If only hBN insulator, a linear P-E loop take place, consistent with our experimental results of hBN flake (Supplementary Fig. 4). The linear hBN background have no effect on the ferroelectric features, and hBN flakes as excellent insulator suppress and overcome the leakage current, which for guarantee the detections of NiI$_2$ ferroelectric features\(^{31-34}\).
+
+**STEM Imaging, Processing, and Simulation**
+
+Atomic-resolution ADF-STEM imaging was performed on an aberration-corrected JEOL ARM 200F microscope equipped with a cold field-emission gun operating at 80 kV. The convergence semiangle of the probe was around 30 mrad. Image simulations were performed with the Prismatic package, assuming an aberration-free probe with a probe size of approximately 1 Å. The convergence semiangle and accelerating voltage were in line with the experiments. The collection angle for ADF imaging was between 81 and 228 mrad. ADF-STEM images were filtered by Gaussian filters, and the positions of atomic columns were located by finding the local maxima of the filtered series.
+Data availability
+
+The data that support the findings of this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.
+
+References
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+
+**Acknowledgments**
+
+B.P. and L.D. acknowledge support from National Science Foundation of China (52021001). B.P. acknowledge support from National Science Foundation of China (62250073). R.C.C. acknowledge support from National Science Foundation of China (52231007). H.L. acknowledge support from National Science Foundation of China (51972046). L.D. acknowledge support from Sichuan Provincial Science and Technology Department (Grant No. 99203070). L.D. acknowledge support from Sichuan Provincial Science and Technology Department (Grant No. 99203070). L.Q. acknowledge support from National Science Foundation of China (520720591 and 11774044). J.W. thanks the National Natural Science Foundation of China (Grant No. 11974422), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB30000000).
+Author contributions
+
+B.P conceived the project. Y.W. prepared the samples and performed the magneto-optical-electric joint-measurements and Raman measurements assisted by B.P., and performed the ferroelectric measurements assisted by L.Q., and analyzed and interpreted the results assisted by H.L., N. L., W.J., L.D. and B.P.. C. Y, R.C, X.X. and X.H. performed the STEM measurements. Y.W. and B.P. wrote the paper with input from all authors. All authors discussed the results.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Additional information
+
+Supplementary information is available for this paper at xxx (will be provided).
+Correspondence and requests for materials should be addressed to B.P.
+Reprints and permission information is available online at http://www.nature.com/reprints.
+Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
+Fig. 1 | Crystal structure, MCD measurements of trilayer NiI$_2$ at room temperature. **a**, Schematic of trilayer NiI$_2$ sandwiched between graphene and hBN. **b**, View of the in-plane and out-of-plane atomic lattice. The magnetic Ni$^{2+}$ ions are surrounded by the octahedron of I$^-$ ions, and three NiI$_2$ layers as a repeating unit stack in a staggered fashion along the c axis. **c**, Atomic-resolution ADF-STEM image showing signature hexagonal patterns of rhombohedral stacking in few-layer NiI$_2$ crystals. The inset shows the corresponding FFT image. **d**, Circular polarization resolved Raman spectra of a trilayer NiI$_2$ device (Fig. 1a) at room temperature, excited by 532 nm laser. “SM” indicates the interlayer shear mode of trilayer NiI$_2$. **e**, The MCD spectra of trilayer NiI$_2$ at +3 T, 0 T and -3T. MCD signals are sensitive to spin electronic transitions and magnetic moments in the electronic states. The MCD features are spin-sign dependent and reverse as magnetic field switch. The zero remanent MCD signals at ~2.3 eV at 0 T suggest antiferromagnetic orders.
+Fig. 2 | Non-collinear antiferromagnetism in trilayer NiI$_2$ device. **a**, Polar RMCD maps upon a 2.33 eV laser with diffraction-limited spatial resolution (see Methods), collected at room temperature and selected magnetic field. **b**, Schematic of the spin textures of bimerons-like domains and corresponding zoom-in RMCD images (white dashed-line box in Fig. 2a). **c**, The polar RMCD signals along with the line sections of RMCD map (**b**). **d**, The RMCD curves sweeping between +3 T and -3 T at 10 K, suggesting a non-collinear antiferromagnetism.
+Fig. 3 | Existence of ferroelectric and anti-ferroelectric orders in trilayer NiI2 device. a, b, P-E and I-E loops at various frequencies from device 1 (D1). c, Corresponding I-E loops from Fig. 3b subtracted the current background. Two pairs of current peaks (FE-AFE and AFE-FE switching peaks) were obtained by Lorentz fitting. An evolution from FE to AFE was observed. d, Schematic of the spin spiral configurations with in-plane (x-y plane) spin cycloid in monolayer NiI2, showing a periodicity of 7×1 unit cells. e, Extreme case where the in-plane (x-y plane) cycloidal configuration tilts to x-z plane caused by interlayer exchange interactions, resulting in an out-of-plane ferroelectric polarization. f, Schematic of the spin spiral configurations with opposite q in trilayer NiI2, showing the coexistence of ferroelectric and antiferroelectric.
+Fig. 4 | Magnetic control of ferroelectricity in trilayer NiI2 device. a-c, The \( P_r \) extracted from the \( P-E \) hysteresis loop is plotted as a function of out-of-plane magnetic field at different frequencies. The error bars are standard deviations of \( P_r \). d, The magnetic control ratio (\( P_r - P_{r0} \))/\( P_{r0} \) are frequency dependent, where \( P_r \) and \( P_{r0} \) is remanent polarization in a magnetic field and without magnetic field, respectively. e, The \( I-E \) curves at different magnetic field. The decrease in the current peak accompanied by an increase in the coercive field due to the increased magnetic field is unambiguously observed. f, g, Fitting by KAI model for different magnetic field at 10 K, giving the switching time \( \tau \). h, The \( (\tau - \tau_0)/\tau_0 \) as a function of magnetic field at 10 K, indicating a degree of magnetic control of switching time, where \( \tau \) and \( \tau_0 \) is switching time in a magnetic field and without magnetic field, respectively.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SI.pdf

00c2b94550129fb8f084bb495841a196a9f5afe6d5c14e29f461a9abeaa8a98e/metadata.json

@@ -0,0 +1,135 @@
+{
+    "title": "Enhancing combinatorial optimization with classical and quantum generative models",
+    "pre_title": "GEO: Enhancing Combinatorial Optimization with Classical and Quantum Generative Models",
+    "journal": "Nature Communications",
+    "published": "29 March 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-46959-5/MediaObjects/41467_2024_46959_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-46959-5/MediaObjects/41467_2024_46959_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.10668479"
+    ],
+    "code": [
+        "https://doi.org/10.5281/zenodo.10668479",
+        "https://zapata.ai/contact/"
+    ],
+    "subject": [
+        "Computer science",
+        "Quantum information"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-241950/v1.pdf?c=1659992758000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-241950/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-46959-5.pdf",
+    "preprint_posted": "08 Aug, 2022",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "We introduce a new framework that leverages machine learning models known as generative models to solve optimization problems. Our Generator-Enhanced Optimization (GEO) strategy is flexible to adopt any generative model, from quantum to quantum-inspired or classical, such as Generative Adversarial Networks, Variational Autoencoders, or Quantum Circuit Born Machines, to name a few. Here, we focus on a quantum-inspired version of GEO relying on tensor-network Born machines and referred to hereafter as TN-GEO. We present two prominent strategies for using TN-GEO. The first uses data points previously evaluated by any quantum or classical optimizer, and we show how TN-GEO improves the performance of the classical solver as a standalone strategy in hard-to-solve instances. The second strategy uses TN-GEO as a standalone solver, i.e., when no previous observations are available. Here, we show its superior performance when the goal is to find the best minimum given a fixed budget for the number of function calls. This might be ideal in situations where the cost function evaluation can be very expensive. To illustrate our results, we run these benchmarks in the context of the portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes. We show that TN-GEO can propose unseen candidates with lower cost function values than the candidates seen by classical solvers. This is the first demonstration of the generalization capabilities of quantum-inspired generative models that provide real value in the context of an industrial application. We also comprehensively compare state-of-the-art algorithms in a generalized version of the portfolio optimization problem. The results show that TN-GEO is among the best compared to these state-of-the-art algorithms; a re- markable outcome given the solvers used in the comparison have been fine-tuned for decades in this real-world industrial application. We see this as an important step toward a practical advantage with quantum-inspired models and, subsequently, with quantum generative models.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "summarycomparisonTNGEOvsall.pdfTables 1-3",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Devising an efficient exploration of the search space is one of the key challenges in the design of combinatorial optimization algorithms. Here, we introduce the Generator-Enhanced Optimization (GEO) strategy: a framework that leverages any generative model (classical, quantum, or quantum-inspired) to solve optimization problems. We focus on a quantum-inspired version of GEO relying on tensor-network Born machines, and referred to hereafter as TN-GEO. To illustrate our results, we run these benchmarks in the context of the canonical cardinality-constrained portfolio optimization problem by constructing instances from the S&P 500 and several other financial stock indexes, and demonstrate how the generalization capabilities of these quantum-inspired generative models can provide real value in the context of an industrial application. We also comprehensively compare state-of-the-art algorithms and show that TN-GEO is among the best; a remarkable outcome given the solvers used in the comparison have been fine-tuned for decades in this real-world industrial application. Also, a promising step toward a practical advantage with quantum-inspired models and, subsequently, with quantum generative models",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Along with machine learning and the simulation of materials, combinatorial optimization is one of top candidates for practical quantum advantage. That is, the moment where a quantum-assisted algorithm outperforms the best classical algorithms in the context of a real-world application with a commercial or scientific value. There is an ongoing portfolio of techniques to tackle optimization problems with quantum subroutines, ranging from algorithms tailored for quantum annealers (e.g., refs. 1,2), gate-based quantum computers (e.g., refs. 3,4) and quantum-inspired (QI) models based on tensor networks (e.g., ref. 5).\n\nRegardless of the quantum optimization approach proposed to date, there is a need to translate the real-world problem into a polynomial unconstrained binary optimization (PUBO) expression \u2013 a task which is not necessarily straightforward and that usually results in an overhead in terms of the number of variables. Specific real-world use cases illustrating these PUBO mappings are depicted in refs. 6 and 7. Therefore, to achieve practical quantum advantage in the near-term, it would be ideal to find a quantum optimization strategy that can work on arbitrary objective functions, bypassing the translation and overhead limitations raised here.\n\nIn our work, we offer a solution to these challenges by proposing a generator-enhanced optimization (GEO) framework which leverages the power of (quantum or classical) generative models. This family of solvers can scale to large problems where combinatorial problems become intractable in real-world settings. We present the main results where we highlight the different features of GEO by performing a comparison with alternative solvers, such as Bayesian optimizers, and generic solvers, like simulated annealing. In the case of the specific real-world, large-scale application of portfolio optimization, we compare against the state-of-the-art (SOTA) optimizers and show the competitiveness of our approach.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Here are more salient highlights that make the proposed approach advantageous over other available solvers:\n\nIt leverages the power of generative models: The essence of the solver is that it is aiming to unveil non-obvious structure in the data, and once it has captured those correlations, it suggests new candidates with features similar to the top ones seen until that iteration phase (see Fig.\u00a01).\n\nThe GEO framework leverages generative models to utilize previous samples coming from any quantum or classical solver. The trained quantum or classical generator is responsible for proposing candidate solutions which might be out of reach for conventional solvers. This seed data set (step 0) consists of observation bitstrings \\({\\{{{{{{{{{\\boldsymbol{x}}}}}}}}}^{(i)}\\}}_{{{{{{{{\\rm{seed}}}}}}}}}\\) and their respective costs \\({\\{{\\sigma }^{(i)}\\}}_{{{{{{{{\\rm{seed}}}}}}}}}\\). To give more weight to samples with low cost, the seed samples and their costs are used to construct a softmax function which serves as a surrogate to the cost function but in probabilistic domain. This softmax surrogate also serves as a prior distribution from which the training set samples are withdrawn to train the generative model (steps 1\u20133). As shown in the figure between steps 1 and 2, training samples from the softmax surrogate are biased favoring those with low cost value. For the work presented here, we implemented a tensor-network (TN)-based generative model. Therefore, we refer to this quantum-inspired instantiation of GEO as TN-GEO. Other families of generative models from classical, quantum, or hybrid quantum-classical can be explored as expounded in the main text. The quantum-inspired generator corresponds to a tensor-network Born machine (TNBM) model which is used to capture the main features in the training data, and to propose new solution candidates which are subsequently post-selected before their costs \\({\\{{\\sigma }^{(i)}\\}}_{{{{{{{{\\rm{new}}}}}}}}}\\) are evaluated (steps 4-6). The new set is merged with the seed data set (step 7) to form an updated seed data set (step 8) which is to be used in the next iteration of the algorithm. More algorithmic details for the two TN-GEO strategies proposed here, as a booster or as a stand-alone solver, can be found in the main text and in Supplementary Note\u00a01.F and 1.G.\n\nThe entire approach is data-driven: This means that the availability of more data, whether from previous attempts to solve the problem or from other state-of-the-art solvers, is expected to enhance performance. In the example of GEO as a booster, we used data explored by Simulated Annealing (SA) but if we had previous observations from any or many other solvers, we could combine it and give it as a starting point to GEO.\n\nThe model is cost function agnostic, i.e., it is a black box solver. This is paramount since any cost function can be solved with our approach. Most of the proposals for quantum or quantum inspired optimization require the cost function of the problem to be mapped to a quadratic or polynomial expression. This opens the possibility to tackle any discrete optimization problem, regardless of how complicated or expensive it is to compute the cost function. This is possible since the only information passed to the generative model are the bitstrings who have been explored and their respective cost value.\n\nVersatility and Strategic Focus on Portfolio Optimization: This follows from the item above. The main motivation for selecting the cardinality-constrained portfolio optimization as the NP-hard problem for our study was the availability of concrete benchmarks and an extensive literature of solvers which have been fine-tuned over the past decades. Every time a new metaheuristic is proposed, chances are portfolio optimization is used to benchmark. Other recent independent works have considered other real-world applications of GEO8,9. For example, the authors in ref. 8 considered an industrial case related to a floor planning NP-hard problem. This black-box feature is one of the most prominent ones that render our approach advantageous compared to other quantum heuristics, such as the quantum approximate optimization algorithm (QAOA)3,4, which relies on the cost function to be a polynomial in terms of the binary variables.\n\nAlthough other proposals leveraging generative models as a subroutine within the optimizer have appeared recently since the publication of our manuscript (e.g., see GFlowNets10 and the variational neural annealing11 algorithms), our framework offers the capability for both: handling arbitrary cost functions (i.e., a blackbox solver) and the possibility to swap the generator for a quantum or quantum-inspired implementation. GEO also has the enhanced feature that the more data is available, the more information can be passed and used to train the (quantum) generator.\n\nAs shown in Fig.\u00a01, depending on the GEO specifics we can construct an entire family of solvers whose generative modeling core range from classical, QI or quantum circuit (QC) enhanced, or hybrid quantum-classical model. These options can be realized by utilizing, for example, Boltzmann machines12 or Generative Adversarial Networks (GAN)13, Tensor-Network Born Machines (TNBM)14, Quantum Circuit Born Machines (QCBM)15 or Quantum-Circuit Associative Adversarial Networks (QC-AAN)16 respectively, to name just a few of the many options for this probabilistic component.\n\nQI algorithms come as an interesting alternative since these allow one to simulate larger scale quantum systems with the help of efficient tensor-network (TN) representations. Depending on the complexity of the TN used to build the quantum generative model, one can simulate from thousands of problem variables to a few tens, the latter being the limit of simulating an universal gate-based quantum computing model. This is, one can control the amount of quantum resources available in the quantum generative model by choosing the QI model.\n\nTherefore, from all quantum generative model options, we chose to use a QI generative model based on TNs to test and scale our GEO strategy to instances with a number of variables commensurate with those found in industrial-scale scenarios. We refer to our solver hereafter as TN-GEO. For the training of our TN-GEO models we followed the work of Han et al.17 where they proposed to use Matrix Product States (MPS) to build the unsupervised generative model. The latter extends the scope from early successes of quantum-inspired models in the context of supervised ML18,19,20,21.\n\nIn this work, we will discuss two modes of operation for our family of quantum-enhanced solvers:\n\nIn TN-GEO as a \u201cbooster\" we leverage past observations from classical (or quantum) solvers. To illustrate this mode we use observations from simulated annealing (SA) runs. Results are presented in this section and simulation details are provided in Supplementary Note\u00a01.F.\n\nIn TN-GEO as a stand-alone solver all initial cost function evaluations are decided entirely by the quantum-inspired generative model, and a random prior is constructed just to give support to the target probability distribution the MPS model is aiming to capture. Results are presented in this section and Simulation details are provided in Supplementary Note\u00a01.G.\n\nBoth of these strategies are captured in the algorithm workflow diagram in Fig.\u00a01 and described in more detail in Supplementary Note\u00a01.\n\nTo illustrate the implementation for both of these settings, we tested their performance on an NP-hard version of the portfolio optimization problem with cardinality constraints. The selection of optimal investment on a specific set of assets, or portfolios, is a problem of great interest in the area of quantitative finance. This problem is of practical importance for investors, whose objective is to allocate capital optimally among assets while respecting some investment restrictions. The goal of this optimization task, introduced by Markowitz22, is to generate a set of portfolios that offers either the highest expected return (profit) for a defined level of risk or the lowest risk for a given level of expected return. In this work, we focus in two variants of this cardinality constrained optimization problem. The first scenario aims to choose portfolios which minimize the volatility or risk given a specific target return (more details are provided in Supplementary Note\u00a01.A.) To compare with the reported results from the best performing SOTA algorithms, we ran TN-GEO in a second scenario where the goal is to choose the best portfolio given a fixed level of risk aversion. This is the most commonly used version of this optimization problem when it comes to comparison among SOTA solvers in the literature (more details are provided in Supplementary Note\u00a01.B).\n\nThe following results are broken into three subsections, each highlighting different features from GEO. First, we focus on GEO as a booster and how it can build from results obtained with other solvers. Second, we focus on GEO as a standalone and compare its performance to SA and the Bayesian optimization library GPyOpt23. In the final subsection, we focus on a bencmark comparison of GEO with state-of-the-art solvers. While in TN-GEO as a booster and as a stand-alone solver we implemented and fine-tuned each solver, and in the final benchmark, we leveraged the state-of-the-art results from nine other solvers reported in the last two decades. In the latter case, each non-GEO solver was thoroughly fine-tuned by the researchers of each reference. This portfolio optimization problem is so canonical that when a new solver is proposed, researchers can compare their results by taking the results from the new proposed solver, as long as the benchmark problems are run in identical conditions. This was one of the main motivations for us to choose this well-established benchmark problem. The \u201crules of the game\" for reporting each market index and performance indicator are reported in Supplementary Note\u00a01.B. In contrast, for the other two subsections, the criteria of evaluation are different, and it emphasizes the performance of GEO when one imposes a limit on the total wall-clock time (e.g., as in the booster mode subsection) and when there is a limited number of calls to the cost function (e.g., as in the stand-alone subsection). The latter is a potential scenario when the bottleneck or expensive step is the cost function evaluation itself (e.g., as it is the case of drug discovery where each evaluation (each candidate molecule) might require synthesis in the lab and an expensive and long process towards its Food and Drug Administration (FDA) approval). Note the desirable condition of the cost function being expensive is only ideal to offset the typical longer time incurred in the steps training the generative model. As shown in teh following subsection, this condition can be significantly relaxed when we use GEO as a booster, since a hybrid strategy where GEO is initialized with previous solutions from other solvers can yield an advantage as well for GEO, even in scenarios where the evaluation of the cost function is inexpensive.\n\nIn Fig.\u00a02 we present the experimental design and the results obtained from using TN-GEO as a booster. In these experiments we illustrate how using intermediate results from simulated annealing (SA) can be used as seed data for our TN-GEO algorithm. As described in Fig.\u00a02A, there are two strategies we explored (strategies 1 and 2) to compare with our TN-GEO strategy (strategy 4). To fairly compare each strategy, we provide each with approximately the same computational wall-clock time. For strategy 2, this translates into performing additional restarts of SA with the time allotted for TN-GEO. In the case of strategy 1, where we explored different settings for SA from the start compared to those used in strategy 2, this amounts to using the same total number of number of cost functions evaluations as those allocated to SA in strategy 2. For our experiments this number was set to 20,000 cost function evaluations for strategies 1 and 2. In strategy 4, the TN-GEO was initialized with a prior consisting of the best 1,000 observations out of the first 10,000 coming from strategy 2 (see Supplementary Note\u00a01.F for details). To evaluate the performance enhancement obtained from the TN-GEO strategy we compute the relative TN-GEO enhancement,\u00a0\u03b7, which we define as\n\nA Shows the schematic representation, strategies 1\u20133 correspond to the current options a user might explore when solving a combinatorial optimization problem with a suite of classical optimizers such as simulated annealing (SA), parallel tempering (PT), generic algorithms (GA), among others. In strategy 1, the user would use its computational budget with a preferred solver. In strategy 2-4 the user would inspect intermediate results and decide whether to keep trying with the same solver (strategy 2), try a new solver or a new setting of the same solver used to obtain the intermediate results (strategy 3), or, as proposed here, to use the acquired data to train a quantum or quantum-inspired generative model within a GEO framework such as TN-GEO (strategy 4). B The results show the relative TN-GEO enhancement from TN-GEO over either strategy 1 or strategy 2. Positive values indicate runs where TN-GEO outperformed the respective classical strategies (see Eq. (1)). The data represents bootstrapped medians from 20 independent runs of the experiments and error bars correspond to the 95% confidence intervals. The two instances presented here correspond to portfolio optimization instances where all the assets in the S& P 500 market index where included (N\u2009=\u2009500), under two different cardinality constraints (\u03ba = 30 and \u03ba = 50). This cardinality constraint indicate the number of assets that can be included at a time in valid portfolios, yielding a search space of \\(M=\\left(\\begin{array}{c}N\\\\ \\kappa \\end{array}\\right)\\), with M\u2009~\u20091069 portfolios candidates for \u03ba\u2009=\u200950.\n\nHere, \\({C}_{\\min }^{{{{{{{{\\rm{cl}}}}}}}}}\\) is the lowest minimum value found by the classical strategy (e.g., strategies 1\u20133) while \\({C}_{\\min }^{{{{{{{{\\rm{TN}}}}}}}}-{{{{{{{\\rm{GEO}}}}}}}}}\\) corresponds to the lowest value found with the quantum-enhanced approach (e.g., with TN-GEO). Therefore, positive values reflect an improvement over the classical-only approaches, while negative values indicate cases where the classical solvers outperform the quantum-enhanced proposal.\n\nAs shown in the Fig.\u00a02B, we observe that TN-GEO outperforms on average both of the classical-only strategies implemented. The quantum-inspired enhancement observed here, as well as the trend for a larger enhancement as the number of variables (assets) becomes larger, is confirmed in many other investment universes with a number of variables ranging from N\u2009=\u200930 to N\u2009=\u2009100 (see Supplementary Note\u00a03 for more details). Although we show an enhancement compared to SA, similar results could be expected when other solvers are used, since our approach builds on solutions found by the solver and does not compete with it from the start of the search. Furthermore, the more data available, the better the expected performance of TN-GEO is. An important highlight of TN-GEO as a booster is that these previous observations can come from a combination of solvers, as different as purely quantum or classical, or hybrid.\n\nThe observed performance enhancement compared with the classical-only strategy must be coming from a better exploration of the relevant search space, i.e., the space of those bitstring configurations x representing portfolios which could yield a low risk value for a specified expected investment return. That is the intuition behind the construction of TN-GEO. The goal of the generative model is to capture the important correlations in the previously observed data, and to use its generative capabilities to propose similar new candidates.\n\nGenerating new candidates is by no means a trivial task in ML and it determines the usefulness and power of the model since it measure its generalization capabilities. In this setting of QI generative models, one expects that the MPS-based generative model at the core of TN-GEO is not simply memorizing the observations given as part of the training set, but that it will provide new unseen candidates. This is an idea which has been recently tested and demonstrated to some extent on synthetic data sets (see e.g., refs. 24,25,26). In Fig.\u00a03 we demonstrate that our quantum-inspired generative model is generalizing to new samples and that these add real value to the optimization search. This demonstrates the generalization capabilities of quantum generative models in the context of a real-world application in an industrial scale setting, and corresponds to one of the main findings in our paper.\n\nThe blue histogram represents the number of observations or portfolios obtained from the classical solver (seed data set), corresponding to an investment universe with N\u2009=\u200950 and N\u2009=\u2009100 assets. In orange we represent samples coming from our quantum generative model at the core of TN-GEO. The green dash line is positioned at the best risk value found in the seed data. This mark emphasizes all the new samples obtained with the quantum generative model and which correspond to lower portfolio risk value (better minima) than those available from the classical solver by itself. The number of samples in the case of N\u2009=\u200950 is equal to 31, while 349 samples were obtained from the MPS generative model in the case of N\u2009=\u2009100.\n\nNote that our TN-based generative model not only produces better minima than the classical seed data, but it also generates a rich amount of samples in the low cost spectrum. This bias is imprinted in the design of our TN-GEO and it is the purpose of the softmax surrogate prior distribution shown in Fig.\u00a01. This richness of new samples could be useful not only for the next iteration of the algorithm, but they may also be readily of value to the user solving the application. In some applications there is value as well in having information about the runners-up. Ultimately, the cost function is just a model of the system guiding the search, and the lowest cost does not translate to the best performance in the real-life investment strategy.\n\nNext, we explore the performance of our TN-GEO framework as a stand-alone solver. The focus is in combinatorial problems whose cost functions are expensive to evaluate and where finding the best minimum within the least number of calls to this function is desired. In Fig.\u00a04 we present the comparison against four different classical optimization strategies. As the first solver, we use the random solver, which corresponds to a fully random search strategy over the 2N bitstrings of all possible portfolios, where N is the number of assets in our investment universe. As second solver, we use the conditioned random solver, which is a more sophisticated random strategy compared to the fully random search. The conditioned random strategy uses the a priori information that the search is restricted to bitstrings containing a fixed number of \u03ba assets. Therefore the number of combinatorial possibilities is \\(M=\\left(\\begin{array}{c}N\\\\ \\kappa \\end{array}\\right)\\), which is significantly less than 2N. As expected, when this information is not used the performance of the random solver over the entire 2N search space is worse. The other two competing strategies considered here are SA and the Bayesian optimization library GPyOpt23. In both of these classical solvers, we adapted their search strategy to impose this cardinality constraint with fixed \u03ba as well (details in Supplementary Note\u00a01.E). This raises the bar even higher for TN-GEO which is not using that a priori information to boost its performance. Specific adaptions of the MPS generative model could be implemented to conserve the number of assets by construction, borrowing ideas from condensed matter physics where one can impose MPS conservation in the number of particles in the quantum state. As explained in Supplementary Note\u00a01.G, we only use this information indirectly during the construction of the artificial seed data set which initializes the algorithm (step 0, Fig.\u00a01), but it is not a strong constraint during the construction of the QI generative model (step 3, Fig.\u00a01) or imposed to generate the new candidate samples coming from it (step 4, Fig.\u00a01). Post selection can be applied a posteriori such that only samples with the right cardinality are considered as valid candidates towards the selected set (step 5, Fig.\u00a01).\n\nIn this comparison of TN-GEO against four classical competing strategies, investment universes are constructed from subsets of the S& P 500 with a diversity in the number of assets (problem variables) ranging from N\u2009=\u200930 to N\u2009=\u2009100. The goal is to minimize the risk given an expected return which is one of the specifications in the combinatorial problem addressed here. Error bars and their 95% confidence intervals are calculated from bootstrapping over 100 independent random initializations for each solver on each problem. The main line for each solver corresponds to the bootstrapped median over these 100 repetitions, demonstrating the superior performance of TN-GEO over the classical solvers considered here. As specified in the text, with the exception of TN-GEO, the classical solvers use to their advantage the a priori information coming from the cardinality constraint imposed in the selection of valid portfolios.\n\nIn Fig.\u00a04 we demonstrate the advantage of our TN-GEO stand-alone strategy compared to any of these widely-used solvers. In particular, it is interesting to note that the gap between TN-GEO and the other solvers seems to be larger for larger number of variables.\n\nFinally, we compare TN-GEO with nine different leading SOTA optimizers covering a broad spectrum of algorithmic strategies for this specific combinatorial problem, based on and referred hereafter as: (1) GTS27, the genetic algorithms, tabu search, and simulated annealing; (2) IPSO28, an improved particle swarm optimization algorithm28; (3) IPSO-SA29, a hybrid algorithm combining particle swarm optimization and simulated annealing; (4) PBILD30, a population-based incremental learning and differential evolution algorithm; (5) GRASP31, a greedy randomized adaptive solution procedure; (6) ABCFEIT32, an artificial bee colony algorithm with feasibility enforcement and infeasibility toleration procedures; (7) AAG33, a hybrid algorithm integrating ant colony optimization, artificial bee colony and genetic algorithms; (8) VNSQP34, a variable neighborhood search algorithm combined with quadratic programming; and, (9) ABC-HP35, a rapidly converging artificial bee colony algorithm. (10) Additionally, we included a classical version of GEO, based on the Neural Autoregressive Density Estimation (NADE)36 model as the generator; We refer to this implementation as NADE-GEO.\n\nThe test data used by the vast majority of researchers in the literature who have addressed the problem of cardinality-constrained portfolio optimization come from OR-Library37, which correspond to the weekly prices between March 1992 and September 1997 of the following indexes: Hang Seng in Hong Kong (31 assets); DAX 100 in Germany (85 assets); FTSE 100 in the United Kingdom (89 assets); S&P 100 in the United States (98 assets); and Nikkei 225 in Japan (225 assets). It is important to note that with the exception of NADE-GEO and TN-GEO, each of these nine solvers has been fine-tuned by the authors in the respective reference. In each, the authors have reported their best results to succeed in this canonical benchmark problem, and those are the values that we report and compare against the two versions of GEO implemented here. Details for the hyperparameter fine-tuning of TN-GEO and NADE-GEO can be found in Supplementary Note\u00a01.H.\n\nAlthough the full comparison involves the ten algorithms stated above, in this section, we will concentrate on presenting a reduced version of the full results focusing only the current state-of-the-art optimizers, i.e., excluding the metaheuristics from the early 2000\u2019s, and including NADE-GEO. In particular, the selected algorithms whose results are presented in this section are GRASP, ABCFEIT, AAG, VNSQP, ABC-HP and NADE-GEO. Full results are presented in Supplementary Note\u00a03.\n\nTherefore, here we present the results obtained with TN-GEO and its comparison with NADE-GEO and five of the different SOTA metaheuristic algorithms mentioned above whose results are publicly available in the literature. Table\u00a01 shows the results of those algorithms and all performance metrics for each of the five index data sets (for more details on the evaluation metrics, see Supplementary Note\u00a01.B). Each algorithm corresponds to a different column, with TN-GEO in the rightmost column. The values are shown in italic entities if the TN-GEO algorithm performed better or equally well compared to the other algorithms on the corresponding performance metric. The numbers in bold mean that the algorithm found the best (lowest) value across all algorithms.\n\nFrom all the entries in this table, 67% of them correspond to italic entries, where TN-GEO either wins or draws, which is a significant percentage giving that these optimizers are among the best reported in the last decades.\n\nIn Table\u00a02 we show a pairwise comparison of TN-GEO against each of the six selected SOTA optimizers. This table reports the number of times TN-GEO wins, loses, or draws compared to results reported for the other optimizer, across all the performance metrics and for all the 5 different market indexes. Therefore, we report in the same table the overall percentage of wins plus draws in each case. We see that this percentage is greater than 50% in all the cases.\n\nFurthermore, in Table\u00a02, we use the Wilcoxon signed-rank test 38, which is a widely used nonparametric statistical test used to evaluate and compare the performance of different algorithms in different benchmarks 39. Therefore, to statistically validate the results, a Wilcoxon signed-rank test is performed to provide a meaningful comparison between the results from TN-GEO algorithm and the selected SOTA metaheuristic algorithms. The Wilcoxon signed-rank test tests the null hypothesis that the median of the differences between the results of the algorithms is equal to 0. Thus, it tests whether there is no significant difference between the performance of the algorithms. The null hypothesis is rejected if the significance value (p) is less than the significance level (\u03b1), which means that one of the algorithms performs better than the other. Otherwise, the hypothesis is retained.\n\nAs can be seen from the table, the null hypotheses are accepted at \u03b1\u2009=\u20090.05 for the TN-GEO algorithm over these recent SOTA algorithms except for NADE-GEO, that is rejected, meaning that TN-GEO performs significantly better than NADE-GEO. Thus, in terms of performance on all metrics combined, the results show that there is no significant difference between TN-GEO and the five selected SOTA optimizers (GRASP, ABCFEIT, AAG, VNSQP, and ABC-HP).\n\nIn particular, TN-GEO is on par with the most competitive of all the solvers, referred to here as ABC-HP. The authors of ref. 35 attribute the success of this recent ant bee colony solver to a good balance of diversification (good exploration of the search space) and intensification (search around regions in the neighborhood of local minima). Since GEO generates its candidates from the correlations learned from the data, it is not restricted to local search but can be considered a global search solver, which is a difficult property to include in most of the solvers, which usually only exploit the local neighborhood of the best intermediate solutions. Overall, the results confirm the competitiveness of our quantum-inspired proposed approach against SOTA metaheuristic algorithms. This is remarkable, considering that these metaheuristics have been explored and fine-tuned for decades.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Compared to other quantum optimization strategies, an important feature of TN-GEO is its algorithmic flexibility. As shown here, unlike other proposals, our GEO framework can be applied to arbitrary cost functions, which opens the possibility of new applications that cannot be easily addressed by an explicit mapping to a polynomial unconstrained binary optimization (PUBO) problem. Our approach is also flexible with respect to the source of the seed samples, as they can come from any solver, possibly more efficient or even application-specific optimizers. The demonstrated generalization capabilities of the generative model that forms its core, helps TN-GEO build on the progress of previous experiments with other state-of-the-art solvers, and it provides new candidates that the classical optimizer may not be able to achieve on its own. We are optimistic that this flexible approach will open up the broad applicability of quantum and quantum-inspired generative models to real-world combinatorial optimization problems at the industrial scale.\n\nAlthough we have limited the scope of this work to tensor network-based generative quantum models, it would be a natural extension to consider other generative quantum models as well. For example, hybrid classical-quantum models such as quantum circuit associative adversarial networks (QC-AAN) 16 can be readily explored to harness the power of generative quantum models with so-called noisy intermediate-scale quantum (NISQ) devices 40. In particular, the QC-AAN framework opens up the possibility of working with a larger number of variables and going beyond discrete values e.g., variables with continuous values as those found in Mixed Integer Programming (MIP) optimization problems 41 or42. Both quantum-inspired and hybrid quantum-classical algorithms can be tested in this GEO framework in even larger problem sizes of this NP-hard version of the portfolio optimization problem or any other combinatorial optimization problem. As the number of qubits in NISQ devices increases, it would be interesting to explore generative models that can utilize more quantum resources, such as Quantum Circuit Born Machines (QCBM)15: a general framework to model arbitrary probability distributions and perform generative modeling tasks with gate-based quantum computers.\n\nThe question of whether a significant advantage can be obtained from GEO by using quantum devices is an active research topic currently being explored. One proposal to reach a more systematic and incremental enhancement from the best quantum-inspired solution to an enhanced quantum-hardware realization was recently proposed in ref. 43. There, one starts from the best available quantum-inspired tensor-network solution and maps it to a quantum circuit. This can be subsequently modified by adding gates beyond those from the decomposition to increase the plausible correlations beyond those accessible with the quantum-inspired tensor-network-based solution. The access to longer-range correlations enhances, in turn, the expressibility of the quantum generative model while taking it beyond the capabilities of classical simulation. In that work, the specific case of generative models was illustrated, and therefore, these recent decomposition techniques can be directly applied to extend the capabilities of TN-GEO explored here, and, as the technologies mature and the level of noise is reduced, explore these enhanced models directly on quantum devices. Additionally, in ref. 44 a comparison of quantum generative models with state-of-the-art classical generative models, such as Transformers and Recurrent Neural Networks, was presented, and the results were very encouraging in the data sets studied.\n\nIncreasing the expressive power of the quantum-inspired core of MPS to other more complex but still efficient QI approaches, such as tree-tensor networks45, is another interesting research direction. Although we have fully demonstrated the relevance and scalability of our algorithm for industrial applications by increasing the performance of classical solvers on industrial scale instances (all 500 assets in the S&P 500 market index), there is a need to explore the performance improvement that could be achieved by more complex TN representations or on other combinatorial problems.\n\nAlthough the goal of GEO was to show good behavior as a general black-box algorithm without considering the specifics of the study application, it is a worthwhile avenue to exploit the specifics of the problem formulation to improve its performance and runtime. In particular, for the portfolio optimization problem with a cardinality constraint, it is useful to incorporate this constraint as a natural MPS symmetry, thereby reducing the effective search space of feasible solutions from the size of the universe to the cardinality size. While imposing such constraints is possible with tensor-networks constructions as recently demonstrated in ref. 46, there does not seem to be a native way to add such common constraints in canonical deep learning models based on neural-network units.\n\nBeyond the strategy of GEO as a booster, another way to use GEO in conjunction with classical solvers is to use it as the optimization subroutine for the smaller subproblems originating from decomposition or multilevel techniques [see for e.g., refs. 47,48,49] used to mitigate the limitation in the number of qubits in NISQ devices.\n\nUsually, these subproblems are solved with gate-based quantum optimization heuristics such as the Quantum Approximate Optimization Algorithm (QAOA)3 or D-wave annealing devices, but one could implement a quantum-circuit version of GEO, for example, using QCBM as the generative models, to solve these smaller subproblems and assist the solution of the larger problem via the hybrid quantum-classical decomposition approach. The general question of the hardware requirements needed to prove quantum advantage is a challenging one, and it is beyond the scope of this work, but we think GEO opens the possibility to start exploring this question in more realistic scenarios and in more general cost functions than those that can be natively considered with other approaches such as QAOA.\n\nFinally, our thorough comparison with SOTA algorithms, which have been fine-tuned for decades on this specific application, shows that our TN-GEO strategy manages to outperform a couple of these and is on par with the other seven optimizers. This is a remarkable feat for this approach and hints at the possibility of finding commercial value in these quantum-inspired strategies in large-scale real-world problems, as the instances considered in this work. Also, it calls for more fundamental insights towards understanding when and where it would be beneficial to use this TN-GEO framework, which relies heavily on its quantum-inspired generative ML model. For example, understanding the intrinsic bias in these models, responsible for their remarkable performance, is another important milestone on the road to practical quantum advantage with quantum devices in the near future. The latter can be asserted given the tight connection of these quantum-inspired TN models to fully quantum models deployed on quantum hardware. And this question of when to go with quantum-inspired or fully quantum models is a challenging one that we are exploring in ongoing future work.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data generated in this study is available at: https://doi.org/10.5281/zenodo.10668479",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The code used to generate the data in this study has been deposited at: https://doi.org/10.5281/zenodo.10668479. Your access to and use of the downloadable code (the \u201cCode\u201d) contained in this Section is subject to a non-exclusive, revocable, non-transferable, and limited right to use the Code for the exclusive purpose of undertaking academic, governmental, or not-for-profit research. Use of the Code or any part thereof for commercial or clinical purposes is strictly prohibited in the absence of a Commercial License Agreement from Zapata AI.",
+            "section_image": []
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+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We would like to acknowledge Manuel S. Rudolph, Marta Mauri, Matthew J.S. Beach, Yudong Cao, Luis Serrano, Jhonathan Romero-Fontalvo, Brian Dellabetta, Matthew Kowalsky, Jacob Miller, John Realpe-Gomez, and Collin Farquhar for their feedback on an early version of this manuscript",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Zapata Computing Canada Inc., 25 Adelaide St E, Suite 1500,  Toronto, ON, M5C 3A1, Canada\n\nJavier Alcazar,\u00a0Mohammad Ghazi Vakili,\u00a0Can B. Kalayci\u00a0&\u00a0Alejandro Perdomo-Ortiz\n\nAcadian Asset Management LLC, 24 King William St, London, EC4R 9AT, England\n\nJavier Alcazar\n\nDepartment of Chemistry, University of Toronto, Toronto, ON, M5G 1Z8, Canada\n\nMohammad Ghazi Vakili\n\nDepartment of Computer Science, University of Toronto, Toronto, ON, M5S 2E4, Canada\n\nMohammad Ghazi Vakili\n\nDepartment of Industrial Engineering, Pamukkale University, Kinikli Campus, 20160, Denizli, Turkey\n\nCan B. Kalayci\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nA.P.-O. conceived the idea of the GEO framework. J.A., M.G.V., and A.P.-O. contributed to its final form. J.A. performed all the numerical experiments and results for GEO as a booster and as a standalone solver. M.G.V., J.A., and C.B.K. contributed to the results section comparing GEO with state-of-the-art solvers and the respective statistical analysis. M.G.V. implemented the NADE-GEO solver. A.P.-O. helped supervise and coordinate the efforts in this work. All authors regularly analyzed the numerical results and contributed to the final version of the manuscript.\n\nCorrespondence to\n                Alejandro Perdomo-Ortiz.",
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+        },
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+            "section_image": []
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+            "section_text": "Alcazar, J., Ghazi Vakili, M., Kalayci, C.B. et al. Enhancing combinatorial optimization with classical and quantum generative models.\n                    Nat Commun 15, 2761 (2024). https://doi.org/10.1038/s41467-024-46959-5\n\nDownload citation\n\nReceived: 14 February 2021\n\nAccepted: 15 March 2024\n\nPublished: 29 March 2024\n\nVersion of record: 29 March 2024\n\nDOI: https://doi.org/10.1038/s41467-024-46959-5\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            "section_text": "Communications Physics (2025)\n\nnpj Quantum Information (2024)",
+            "section_image": []
+        }
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0120cbbdf5abcce247bf35686d0d3fbc3c94f93c709d874b56ecf9271a6516aa/preprint/preprint.md

@@ -0,0 +1,407 @@
+Pt nanoshell with ultra-high NIR-λ photothermal conversion efficiency mediates multifunctional neuromodulation for cardiac protection
+
+Lei Fu
+leifu@whu.edu.cn
+
+Wuhan University   https://orcid.org/0000-0003-1356-4422
+
+Chenlu Wang
+Wuhan University
+
+Liping Zhou
+Wuhan University
+
+Chengzhe Liu
+Wuhan University
+
+Jiaming Qiao
+Wuhan University
+
+Xinrui Han
+Wuhan University
+
+Luyang Wang
+Wuhan University
+
+Yaxi Liu
+Wuhan University
+
+Bi Xu
+Wuhan University
+
+Qinfang Qiu
+Wuhan University
+
+Zizhuo Zhang
+Wuhan University
+
+Jiale Wang
+Wuhan University
+
+Xiaoya Zhou
+Wuhan University
+
+Mengqi Zeng
+Wuhan University   https://orcid.org/0000-0002-1442-052X
+
+Lilei Yu
+Article
+
+Keywords:
+
+Posted Date: March 15th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-3985327/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 July 28th, 2024. See the published version at https://doi.org/10.1038/s41467-024-50557-w.
+Pt nanoshell with ultra-high NIR-II photothermal conversion efficiency mediates multifunctional neuromodulation for cardiac protection
+
+Chenlu Wang1,†, Liping Zhou2,3,4,†, Chengzhe Liu2,3,4,†, Jiaming Qiao2,3,4, Xinrui Han2,3,4, Luyang Wang1, Yaxi Liu1, Bi Xu1, Qinfang Qiu2,3,4, Zizhuo Zhang2,3,4, Jiale Wang2,3,4, Xiaoya Zhou2,3,4*, Mengqi Zeng1, Lilei Yu2,3,4*, Lei Fu1,3,4*
+
+1College of Chemistry and Molecular Sciences, Wuhan University, Wuhan, China.
+2Cardiovascular Hospital, Renmin Hospital of Wuhan University, Wuhan 430060, China; Hubei Key Laboratory of Autonomic Nervous System Modulation, Wuhan 430060, China; Cardiac Autonomic Nervous System Research Center of Wuhan University, Wuhan 430060, China; Hubei Key Laboratory of Cardiology, Wuhan 430060, China; Cardiovascular Research Institute, Wuhan University, Wuhan, 430060, China. 3Taikang Center for Life and Medical Sciences, Wuhan University, Wuhan 430060, China. 4Institute of Molecular Medicine, Renmin Hospital of Wuhan University, Wuhan 430060, China.
+
+*E-mail: leifu@whu.edu.cn; lileiyu@whu.edu.cn; whuzhouxiaoya@whu.edu.cn
+
+†These authors contributed equally: Chenlu Wang, Liping Zhou, Chengzhe Liu.
+The autonomic nervous system plays a pivotal role in the pathophysiology of cardiovascular diseases. Regulating it is essential for preventing and treating acute ventricular arrhythmias (VAs). Photothermal neuromodulation is a nonimplanted technique, but the response temperature ranges of transient receptor potential vanilloid 1 (TRPV1) and TWIK-elated K+ Channel 1 (TREK1) exhibit differences while being closely aligned, and the acute nature of VAs require that it must be rapid and precise. However, the low photothermal conversion efficiency (PCE) still poses limitations on achieving rapid and precise treatment. Here, we achieved nearly perfect blackbody absorption and one of the highest PCE in the second near infrared (NIR-II) window (73.7% at 1064 nm) via a Pt nanoparticle shell (PtNP-shell). By precisely manipulating the photothermal effect, we successfully achieved rapid and precise multifunctional neuromodulation encompassing neural activation (41.0–42.9 °C) and inhibition (45.0–46.9 °C). The NIR-II photothermal modulation additionally achieved bi-directional reversible autonomic modulation and conferred protection against acute VAs associated with myocardial ischemia and reperfusion injury in interventional therapy.
+
+Cardiovascular disease has emerged as a leading cause of mortality, with acute myocardial infarction being one of the most pernicious ailments\(^{1,2}\). Myocardial ischemia (MI) frequently precipitates acute ventricular arrhythmias (VAs), impeding prompt and efficacious treatment for acute myocardial infarction. Furthermore, conventional interventional procedures for MI are unable to circumvent concomitant myocardial reperfusion injury and associated VAs. The autonomic nervous system, encompassing sympathetic and parasympathetic nerves, plays a role in cardiovascular modulation; both are naturally antagonistic. Sympathetic inhibition or parasympathetic activation has been shown to stabilize cardiac electrophysiology, safeguard against MI
+and reduce the incidence of VAs\(^3\).
+
+In recent years, several studies have demonstrated that light-activated nanotransducers can induce local heating effects, leading to the activation or inhibition of nerves\(^4-6\). This discovery is attributed to the identification of temperature-sensitive ion channels in neurons, such as transient receptor potential vanilloid 1 (TRPV1)\(^7\) and TWIK-elated K\(^+\) Channel 1 (TREK1)\(^8\). The activation of specific temperature-sensitive ion channels necessitates precise temperature ranges\(^7-9\). Considering the acute nature of neural responses, a therapeutic strategy with rapid and accurate modulation is required.
+
+The second near infrared (NIR-II) photothermal is expected to realize noninvasive and nonimplanted neuromodulation. However, its neural response rate and accuracy are currently limited by low photothermal conversion efficiency (PCE).
+
+Here we report a near blackbody NIR-II Pt nanoparticle shell (PtNP-shell) for protection against MI and myocardial reperfusion injury accompanying intervention. The PtNP-shell, synthesized through a simple electrocoupling substitution reaction using liquid metal nanoparticles as templates (Fig. 1a), possesses surface pores and a hollow structure. It demonstrates nearly perfect blackbody absorption, enhanced absorption of light, and then one of the highest PCE in the NIR-II window (73.7% at 1064 nm). By leveraging the local heating effect mediated by PtNP-shell, we achieved rapid, efficient, and precise multifunctional autonomic neuromodulation. Specifically, parasympathetic activation and sympathetic inhibition were accomplished by activating TRPV1 (41.0–42.9 °C) and TREK1 (45.0–46.9 °C) channels, respectively. Photothermal autonomic neuromodulation mediated by PtNP-shell effectively stabilized cardiac electrophysiology and reduced VAs incidence in both myocardial ischemia-reperfusion (I/R) injury model and MI model, respectively (Fig. 1b).
+Fig. 1 | The synthesis steps of the PtNP-shell and the concept of mediating precise photothermal effects for cardioprotection. a, The synthesis steps of PtNP-shell and schematic diagram of photothermal effect. b, Schematic diagram of multifunctional autonomic modulation mediated by photothermal effect of PtNP-shell for precise cardioprotection against myocardial I/R injury and MI-induced VAs.
+
+Result and discussion
+
+Synthesis and Characterization of PtNP-shell
+
+The PtNP-shell was synthesized through an electrocoupling substitution reaction between chloroplatinate and Ga nanoparticles (GaNPs). Ga nanoparticles were obtained by sonication of pure metal Ga. To achieve a balanced particle size and oxidation degree of GaNPs, pure gallium was sequentially sonicated in ethanol and water for 30 minutes to obtain gallium nanoparticles with reduced oxidation (Supplementary Fig. 1a). In accordance with the electrochemical redox potential of the redox couple (Ga^{3+}/Ga: –0.529 V; PtCl_6^{2-}/PtCl_4^{2-}: 0.726 V; PtCl_4^{2-}/Pt: 0.758 V)^{10,11}, Pt (IV) can be *in situ* reduced by Ga and encapsulated on the surface of GaNPs to form a core-shell structure
+(Supplementary Fig. 1b, c). The hollow PtNP-shell is synthesized after completion of the reaction (Fig. 2a). Simultaneously with the reduction of Pt (IV), Ga oxide is formed, creating the skeleton of the PtNP-shell (right in Fig. 2a). The surface of the PtNP-shell exhibits a rough texture (Supplementary Fig. 2). The scanning transmission electron microscopy (STEM) images reveal numerous irregular and uneven pores on its surface (Supplementary Fig. 3a) and PtNP-shell is composed of Pt nanoparticles (PtNPs) with 2–5 nm (Fig. 2b). High-resolution TEM (HR-TEM) image is acquired to character the structure of PtNPs. As shown in Supplementary Fig. 3b, PtNPs exhibits single crystal structure with a lattice stripe spacing of 0.23 nm corresponding to the (111) crystal plane. Meanwhile, the corresponding Fast Fourier Transform (FFT) pattern (inset in Supplementary Fig. 3b) shows the typical diffraction patterns of face-centered cubic structure along [111] zone axis.
+
+![TEM images and XRD spectrum of PtNP-shell](page_374_682_1092_377.png)
+
+Fig. 2 | Characterization of PtNP-shell. **a**, TEM image of PtNP-shell (Right: element mapping). **b**, STEM images of PtNP-shell surface. **c**, XRD spectrum of PtNP-shell (Inset: SAED pattern). **d**, UV-vis-NIR absorption spectrum of PtNP-shell (75 \( \mu \)g·mL\(^{-1}\)). **e**, Temperature elevation curves of PtNP-shell (50 \( \mu \)g·mL\(^{-1}\)) under NIR-II laser irradiation (1 W·cm\(^{-2}\)). **f**, Calculation of the PCE at 1064 nm (PtNP-shell: 50 \( \mu \)g·mL\(^{-1}\)).
+In the X-ray power diffraction (XRD) spectrogram result (Fig. 2c), all peaks can be attributed to the crystal phase of Pt (JCPDS: 87-0640), consistent with the selected area electron diffraction (SAED) pattern findings (inset in Fig. 2c). However, no peaks corresponding to gallium oxide were observed in the XRD spectrogram, possibly due to its low content. The XRD spectrogram (Supplementary Fig. 4) of PtNP-shell prior to reacting with KOH showed that the gallium oxide contained in PtNP-shell was GaOOH (JCPDS: 06-0180). Additional evidence from X-ray photoelectron spectroscopy (XPS) also suggests that PtNP-shell contains Ga (Supplementary Fig. 5), consistent with energy dispersive X-ray spectroscopy (EDX) analysis (right in Fig. 2a). The peak centred at 1117.59 eV is ascribed to Ga 2p_{3/2}, indicating the presence of Ga^{3+} in PtNP-shell. Meanwhile, the Pt 4f spectrum shows two peaks at 71.56 and 75.02 eV, which result from metallic Pt 4f_{7/2} and Pt 4f_{5/2}. PtNP-shell was treated with KOH (0.67 M) to reduce the gallium oxide content and the surface potential was reduced from 45.8 mV to -25.7 mV, and then encapsulated with Methoxypoly(Ethylene Glycol) Thiol (mPEG-SH_{5000}) to enhance its biocompatibility and the surface potential was changed to -19.9 mV. (Supplementary Fig. 6). The statistically averaged hydrated nanoparticle size of PtNP-shell based on the dynamic light scattering diagram was 200.1 nm with uniform size distribution, indicating the nanoparticle was well dispersed in water (Supplementary Fig. 7).
+
+Blackbody Absorption and Photothermal Property of PtNP-shell
+
+Due to the presence of pores and a hollow structure in the PtNP-shell, light propagating in the space bounces at the rough surface of PtNP-shell until it encounters one of the pores, where it continues to bounce within the PtNP-shell. The random distribution of these pores results in completely random light reflection, akin to Brownian motion^{12}. Consequently, the probability of light escaping from other pores is extremely low,
+rendering PtNP-shell behave like a blackbody and produce an efficient infrared heater\(^{13-15}\). This enhanced absorption of light by PtNP-shell exhibits nearly perfect blackbody absorption characteristics (Supplementary Fig. 8a). The absorption of PtNP-shell is close to 1 in the range of 250–1300 nm at 75 \( \mu \)g·mL\(^{-1}\) (Fig. 2d). According to the Lambert-Beer law (A/L = \( \varepsilon C \), where \( \varepsilon \) is the extinction coefficient), a linear relationship between absorption intensity (at 1064 nm) and concentration was established, with an extinction coefficient measured as 13.3 Lg\(^{-1}\)cm\(^{-1}\) at 1064 nm (Supplementary Fig. 8b). Varying concentrations of PtNP-shell resulted in different shades of grey being generated, with significantly darker greyness observed under identical conditions compared to GaNPs and Pt-coated Ga-In alloy (EGaIn) nanoparticles (GaIn@Pt NPs) (Supplementary Fig. 9a). These distinctive features were characterized by their respective positions within an RGB cube representation, wherein on the diagonal connecting darkest and brightest points, PtNP-shell was found closer to the darkest point than both other materials (Supplementary Fig.9b).
+
+The photothermal properties of PtNP-shell were verified by irradiating the dispersion of PtNP-shell in water with NIR-II light at 1064 nm (1 W·cm\(^{-2}\)). Even *in vitro*, PtNP-shell (50 \( \mu \)g·ml\(^{-1}\)) exhibited rapid temperature elevation, achieving a rise from room temperature to 41.0 °C and 45.0 °C within only 96 s and 133 s, respectively (Fig. 2e). However, for GaNPs (347 s and over 600 s) and GaIn@Pt NPs (278 s and 450 s), it took significantly longer time to reach the same temperatures (Supplementary Fig. 10). The corresponding thermal images of the PtNP-shell with different concentrations under different irradiation times are shown in Supplementary Fig. 11. The heating effect of the PtNP-shell (50 \( \mu \)g·mL\(^{-1}\)) gradually increased the \( \Delta T \) from 7.72 °C to 52.17 °C When exposed to NIR-II laser for a duration of 600 s while varying the optical power density at 1064 nm between 0.25–1.5 W·cm\(^{-2}\) (Supplementary Fig. 12).
+The PCE of PtNP-shell was quantified as 73.7% when balancing the energy input from photons with heat dissipation within the system (Fig. 2f), representing one of the highest PCE at 1064 nm (Supplementary Fig. 13). These results indicate that PtNP-shell exhibits excellent photothermal performance in the NIR-II window. Additionally, no significant changes in temperature or morphology were observed even after five cycles of irradiation (Supplementary Fig. 14), suggesting exceptional photothermal stability.
+
+Photothermal of PtNP-shell enables precise modulations of neurons in vitro
+
+To investigate the photothermal effects of PtNP-shell on neuronal activity at multiple levels, we conducted calcium imaging experiments in hippocampal neuron (HT-22) cells (Fig. 3a, b). The immunoblotting results revealed abundant expression of both TRPV1 and TREK1 ion channels in HT-22 cells (Fig. 3c). The direct effect of PtNP-shell on the excitability of these two different ion channels was assessed under NIR-II irradiation using a calcium ion indicator (Fluo-4 AM). Upon NIR-II laser irradiation, the temperature of the PtNP-shell (+) group increased compared to that of the PtNP-shell (−) group, resulting in a significantly higher percentage of responding cells (Fig. 3d) (p< 0.001). The micrographs fluorescence intensity curve of HT-22 neurons cultured with PtNP-shell showed significant Ca^{2+} influx upon NIR-II laser irradiation for 35 ± 5 s and after the temperature reached 42.0 °C (Fig. 3e). In contrast, application of NIR-II laser irradiation with PBS did not induce significant Ca^{2+} influx.
+
+Subsequently, neuronal excitation was induced and calcium signals were increased by perfusion of 15 mM KCl in the PtNP-shell (−) group and PtNP-shell (+) group (50 μg mL^{-1}), respectively. This phenomenon can be attributed to the elevation of extracellular potassium ion concentration, which triggers neuronal depolarization and subsequently leads to a substantial increase in intracellular calcium ion concentration^{16}.
+
+Under NIR-II laser irradiation, the proportion of HT-22 cells responding to high
+concentration KCl stimulation was significantly lower in the PtNP-shell (+) group compared to that in the PtNP-shell (−) group at approximately 46.0 °C (Fig. 3f). The difference may be due to the activation of the TERK1 ion channel in the PtNP-shell (+) group, which can induce neuronal hyperpolarization and make intracellular and extracellular calcium ion concentrations tend to recover\(^{17}\). Interestingly, the PtNP-shell influenced the fluorescence intensity of HT-22 cells not with a sustained decrease but with an initial rise followed by a subsequent decrease (Fig. 3g). This observation may be associated with the activation of TRPV1 channel at around 42.0 °C\(^9\). With increasing temperature, TRPV1 and TREK1 channels were sequentially activated. These findings suggest that PtNP-shell can achieve precise temperature control within a short duration through its own ultra-high PCE for both neuronal excitation and inhibition.
+
+Cytotoxicity assays were then conducted to investigate the potential neurotoxicity of PtNP-shell application. As shown in Fig. 3h, concentrations of PtNP-shell below 100 \( \mu \mathrm{g} \cdot \mathrm{mL}^{-1} \) exhibited no significant toxic effects on HT-22 cells. Even when the concentration of PtNP-shell was increased to 200 \( \mu \mathrm{g} \cdot \mathrm{mL}^{-1} \), the survival rate of neuronal cells remained approximately at 52.11%. Furthermore, the impact of PtNP-shell photothermal stimulation parameters on cell viability were assessed through analysis of HT-22 cell survival under NIR-II laser irradiation. Notably, when a concentration of 50 \( \mu \mathrm{g} \cdot \mathrm{mL}^{-1} \) PtNP-shell and an NIR-II laser with a power density of 0.5 W·cm\(^{-2}\) were applied for a brief duration, the survival rate exceeded 92.36% for HT-22 cells. Even with an increase in power density to 0.75 W·cm\(^{-2}\), the survival rate for HT-22 cells still remained around 72.68% after 60 s of irradiation (Fig. 3i). These results indicate that PtNP-shell does not induce significant damage to neurons under controlled NIR-II laser irradiation.
+Fig. 3 | PtNP-shell photothermal activation of different neuronal ion channels in vitro. a, Flowchart of calcium imaging assay performed on HT-22 cells. b, calcium imaging of HT-22 cells under different experimental conditions. c, Western blotting for TRPV1 and TREK1 from HT-22 and H9c2 cells. Percentage of d, TRPV1 and f, TREK1 groups of HT-22 cells within the field of view of the fluorescence microscope that responded to laser stimulation. Temporal dynamics of Ca^{2+} signals in e, TRPV1 and g, TREK1 groups of cells. The solid lines indicate the mean, and shade represents the standard error of the mean (SEM). h, Cell viability of HT-22 treated with different concentrations of PtNP-shell for 24 h. i, Cell viability of HT-22 treated with NIR-II laser irradiation of different power densities and laser duration. The error bar indicates S.E.M. ***P < 0.001.
+
+PtNP-shell photothermal activation of the parasympathetic nervous system
+
+Western blotting analysis of peripheral ganglia from the canine autonomic nervous system revealed the expression of TRPV1 and TREK1 heat-sensitive ion channels in both the nodose ganglion (NG) and left stellate ganglion (LSG). Notably, TRPV1 was abundantly expressed in the NG of the parasympathetic nervous system, while TREK1 exhibited higher levels in the LSG of the sympathetic nervous system (Supplementary
+Fig. 15). To investigate whether the photothermal effect induced by PtNP-shell under NIR-II irradiation can precisely regulate the parasympathetic nerve, 100μL PtNP-shell (50 μg·mL^{-1}) and PBS were injected into NG of PtNP-shell group and control group (6 beagle dogs in each group), respectively (Fig. 4a,b). It can be observed that upon irradiation with NIR-II laser (0.8 W·cm^{-2}), the temperature of NG injected with PtNP-shell increased to 41.0 °C within a very short period of time (12 ± 3 s). Subsequently, the temperature of NG could be kept in the range of 41.0–42.9 °C for 5 min by adjusting the power density to 0.45 W·cm^{-2} (Fig. 4c-d). As a crucial node within the parasympathetic neural network, activation of NG significantly reduces heart rate (HR) (Fig. 4e)^{18}. Therefore, NG function was assessed by the maximum decrease in heart rate under direct electrical stimulation. As shown in Fig. 4f–h, NG function and activity was significantly elevated in the PtNP-shell group than in the control group after stimulation. The function and activity of NG recovered close to baseline within three hours after turning off NIR-II laser, indicating that the photothermal modulation induced by PtNP-shell was reversible within NGs (Fig. 4h, Supplementary Fig. 16 and 17).
+
+In addition, the effective refractive period (ERP) was measured in various regions, including left ventricular apex (LVA), left ventricular base (LVB) and median left ventricular area (LVM). In the PtNP-shell group, the ERP was significantly elevated compared to the control group and remained elevated for 2 h after photothermal intervention in NG (Supplementary Fig. 18). Furthermore, immunofluorescence staining for Vacht, c-fos, and TRPV1 was performed on NG histopathological sections following photothermal modulation (Fig. 4i). Quantitative analysis (Supplementary Fig. 19) revealed a substantial increase in the proportion of TRPV1^{+} (86.63 ± 2.65 vs 45.45 ± 2.98) and c-Fos^{+} (77.81 ± 3.91 vs 17.27 ± 3.08) neurons among VAChT^{+} parasympathetic neurons in the PtNP-shell group compared to the control group (all P
+< 0.001). These findings suggest that PtNP-shell can precisely regulate temperature and subsequently activate TRPV1 ion channels on NG to enhance parasympathetic activity.
+
+![Photothermal activation of the parasympathetic nervous system by PtNP-shell. a, Location of the canine NG. b, Schematic illustration of the process of photothermal modulation of NG. c, Temperature curves of NG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of NG. e, Representative images of HR reduction induced after stimulation of NG with different voltages. Maximal HR changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, n = 6. h, Quantification of the NG neural activity recordings, n = 6. i, Representative immunofluorescent images of Vacht (red), c-fos (green) and TRPV1 (pink) in the NG of beagles following different treatments. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ***P < 0.001, ns means that the difference is not statistically significant.](page_246_370_1092_1012.png)
+
+Fig. 4 | Photothermal activation of the parasympathetic nervous system by PtNP-shell. a, Location of the canine NG. b, Schematic illustration of the process of photothermal modulation of NG. c, Temperature curves of NG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of NG. e, Representative images of HR reduction induced after stimulation of NG with different voltages. Maximal HR changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, n = 6. h, Quantification of the NG neural activity recordings, n = 6. i, Representative immunofluorescent images of Vacht (red), c-fos (green) and TRPV1 (pink) in the NG of beagles following different treatments. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ***P < 0.001, ns means that the difference is not statistically significant.
+PtNP-shell photothermal activation of NG reduces I/R injury and associated VAs
+
+Following I/R injury, electrocardiography (ECG) was recorded to monitor the occurrence of VAs events within 1 h, including ventricular premature beats (VPBs), ventricular tachycardia (VT) and ventricular fibrillation (VF) (Fig. 5c)¹⁹. Under NIR-II laser irradiation, the PtNP-shell group exhibited a lower incidence of sustained VTs (duration > 30 s) or VF compared to the control group (50% vs. 83%) (Fig. 5d). Moreover, the number of recorded VPBs (70.83 ± 5.38 vs. 116.00 ± 6.36, P < 0.05), VTs (3.17 ± 0.87 vs. 8.83 ± 2.15, P < 0.05) and duration of the VTs (7.00 ± 3.173s vs. 26.83 ± 7.89s, P < 0.05) in the PtNP-shell group were significantly reduced compared to that in the control group (Fig. 5e–g).
+
+![Flowchart and bar graphs showing experimental design, VA types, and statistical results for PtNP-shell photothermal activation on myocardial I/R injury](page_420_670_1007_410.png)
+
+Fig. 5 | PtNP-shell photothermal activation of the parasympathetic nervous system improves myocardial I/R injury. Modulation of NG to protect against myocardial I/R injury and associated VAs a, schematic diagram and b, flowchart. c, Representative visual depictions of VAs, including VPB, VT and VF. d, Quantitative analysis the ratio of sVT and VF incidence between different groups, n=6. Quantitative analysis the number of e, VPBs, f, VTs and g, the duration of sVT of beagles. Effects on ventricular ERP at different sites in beagles treatment with PtNP-shell or control h, before and i, after myocardial I/R injury modelling. Levels of markers of myocardial injury, including j, MYO and k, c-TnI, after different treatments in beagles. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ***P < 0.001.
+Animal modeling and intervention manipulations were conducted to further elucidate the protective effects of precise modulation of NG by PtNP-shell against myocardial I/R injury and associated VAs, following the experimental protocols depicted in Figure 5a,b. PtNP-shell and PBS were microinjected into the NG of the PtNP-shell group and control group, respectively, each consisting of six beagle dogs. The NG was subsequently exposed to NIR-II laser irradiation for a duration of 5 minutes prior to occlusion of the left anterior descending (LAD) coronary artery for reperfusion therapy.
+
+There were no statistically significant differences between the two groups in terms of preoperative ERP for LVB, LVM, and LVA. In the postoperative period, all three positions showed shortened ERPs in the control group. The PtNP-shell group exhibited significantly higher ERPs compared to the control group, indicating that photothermal modulation of nerves by PtNP-shell has a protective effect on cardiac electrophysiology (Fig. 5h–i). Serum Elisa assay revealed reduced levels of myocardial injury markers (MYO and c-TnI) after I/R injury in the PtNP-shell group compared to the control group (all p < 0.05, Fig. 5j,k). Postoperatively, heart rate variability analysis demonstrated lower low frequency (LF) and higher high frequency (HF) and the lower ratio of LF to HF (LF/HF) values in the PtNP-shell group compared to the control group (all p < 0.05, Supplementary Fig. 20). These results suggest that PtNP-shell exerts cardioprotective effects and reduces VAs by activating parasympathetic nerve.
+
+PtNP-shell photothermal inhibition of the sympathetic nervous system
+
+The sympathetic nervous system was modulated by performing microinjections of PtNP-shell or PBS into the LSG, followed by irradiation with an NIR-II laser (Fig. 6a,b). The temperature curve demonstrates that upon exposure to a NIR-II laser (0.8 W·cm\(^{-1}\)) for 25 ± 5 s, the temperature rapidly escalated to 45.0 °C, crossing the range of 41.0–
+42.9 °C within a mere duration of 6 ± 1 s. Subsequently, the power density was immediately decreased to 0.6 W cm^{-2}, effectively maintaining LSG at a steady temperature between 45.0–46.9 °C (Fig. 6c, d). Due to the substantial increase in systolic blood pressure (SBP) induced by LSG activation (Fig. 6e), the function of LSG was evaluated by quantifying the maximum SBP change corresponding to five consecutive incremental voltages of high-frequency electrical stimulation. After 5 min of NIR-II laser irradiation, the activity and function of LSG in the PtNP-shell group were significantly suppressed compared to the control group (p < 0.05) and they returned close to baseline after 3 h (Fig. 6f–h and Supplementary Fig. 21–22). Prolonged ERP effects were observed in all left ventricles, while the protective effect exhibited a duration of only 1 h (Supplementary Fig. 23). Furthermore, immunofluorescence staining was conducted on LSG tissues to examine the expression of c-fos, tyrosine hydroxylase (TH), and TREK1 (Fig. 6i). The quantitative analysis (Supplementary Fig. 24) revealed a significant decrease in the proportion of c-Fos^{+} expression in TH^{+} neurons within the PtNP-shell group (8.80 ± 1.80 vs. 44.78 ± 5.55, P < 0.001) indicating that PtNP-shell exerted a photothermal inhibitory effect on LSG neurons under NIR-II irradiation. However, the proportion of TREK^{+} expression was significantly increased within TH^{+} neurons in the PtNP-shell group (83.51 ± 3.72 vs. 57.20 ± 5.89, P < 0.01). This increase could lead to hyperpolarization of the cell membrane potential, reduction in neuronal excitability and inhibition of sympathetic nerve activity.
+Fig. 6 | Photothermal inhibition of the sympathetic nervous system by PtNP-shell. a, Location of the canine LSG. b, Schematic illustration of the process of photothermal modulation of LSG. c, Temperature curves of LSG under NIR-II laser irradiation. d, Typical thermal imaging diagram of photothermally modulated activation of LSG. e, Representative images of BP elevation induced after stimulation of LSG with different voltages. Maximal SBP changes of beagle treatment with PtNP-shell or control f, before and g, after NIR-II exposure, n = 6. h, Quantification of the LSG neural activity recordings, n = 6. i, Representative immunofluorescent images of TH (red), c-fos (green) and TREK1 (pink) in the LSG of beagles following different treatments. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ***P < 0.001, ns means that the difference is not statistically significant.
+PtNP-shell photothermal inhibition of LSG improves MI and reduces associated VAs
+
+To investigate the cardioprotective effect of PtNP-shell photothermal effect in achieving a targeted LSG temperature of approximately 46.0 °C, NIR-II light was administered prior to ligation of the LAD coronary artery (Fig. 7a,b). Under NIR-II laser irradiation, the PtNP-shell group exhibited a significantly reduced incidence of sustained VTs (duration > 30 s) or VF compared to the control group (16% vs. 50%) (Fig. 7c). In the PtNP-shell group, ECG recordings within infarction 1 exhibited a reduced incidence of VAs events compared to the control group, with fewer VPBs recorded in the PtNP-shell group than in the control group (51.50 ± 5.53 vs. 70.83 ± 5.375, P < 0.05, Fig. 7d). However, there were no significant differences between the two groups in terms of VT numbers and duration (Supplementary Fig. 25). Additionally, VA inducibility measurements demonstrated that after photothermal neuromodulation with PtNP-shell, there was a decrease in VA score (1.50 ± 0.76 vs. 4.83 ± 1.14, P < 0.05) effective heart protection (Fig. 7e,f). Furthermore, PtNP-shell photothermal inhibition of LSG produced similar protective effects on ventricular electrophysiological index ERP as activation of NG (Fig. 7g,h), and had higher VF threshold than control group (24.33 ± 4.24 vs. 12.33 ± 3.16, P < 0.05, Fig. 7i). In addition, the light inhibition of LSG followed the same trend as heart rate variability after activation of NG (Supplementary Fig. 26). These results suggest that PtNP-shell protects against cardiac damage and reduces VAs by modulating the autonomic nervous system, specifically by decreasing sympathetic activity and enhancing parasympathetic tone.
+Fig. 7 | PtNP-shell photothermal inhibition of the sympathetic nervous system improves MI associated VAs. Modulation of LSG to protect against MI and associated VAs a, schematic diagram and b, flowchart. c, Quantitative analysis the ratio of sVT and VF incidence between different groups, n=6. d, Quantitative analysis the number of VPBs of beagles. e, Typical images of VA induced by programmed electrical stimulation. f, Quantitative analysis of VAs score in different groups. Effects on ventricular ERP at different sites in Beagles treatment with PtNP-shell or control g, before and h, after MI modelling. i, Quantitative analysis of VF threshold in different groups. Data are shown as the mean ± S.E.M. *P < 0.05, **P < 0.01, ***P < 0.001.
+
+Biosafety of PtNP-shell for translational applications
+
+To validate the biocompatibility of PtNP-shell photothermal modulation on the autonomic nervous system, we conducted rapid excision of LSG and NG tissues followed by hematoxylin and eosin (H&E) staining. As shown in Supplementary Fig. 27a, H&E staining did not reveal any indications of neuronal damage in both the PtNP-shell and control groups for both NG and LSG, indicating that the neuromodulation of PtNP-shell is repeatable. Meanwhile, to further investigate the long-term biosafety of PtNP-shell, a microinjection of 200 μl PtNP-shell (50 μg·mL^{-1}) or PBS was administered into the ganglion of dogs and the tail vein of rats, respectively. After a follow-up period of 30 days, did not reveal any obvious damage in major organs,
+including the heart, liver, spleen, lungs, and kidneys (Supplementary Fig. 27b,c).
+Furthermore, blood biochemical analyses indicated the absence of hepatotoxicity or nephrotoxicity (Supplementary Fig. 27d-m). These results unequivocally demonstrate that PtNP-shell exhibits exceptional biocompatibility and long-term biological safety.
+
+Conclusion
+
+The PtNP-shell reported in this study exhibits nearly perfect blackbody absorption property, making it an efficient absorber with one of the highest PCE in the NIR-II window (73.7% at 1064 nm). Furthermore, local heating induced by PtNP-shell activation effectively triggers temperature-sensitive ion channels TRPV1 and TREK1, enabling precise and efficient regulation of autonomic nerves. This innovative approach holds great potential for non-invasive treatment of MI and associated VAs, as well as protection against reperfusion injury during interventional therapy.
+
+    The minimal tissue damage caused by light can be disregarded within the maximum permissible exposure (MPE) range, rendering it one of the safest interventions for organisms. The interaction between light and tissue is intricate, and further research could aid in selecting more suitable wavelengths to achieve deeper penetration within the MPE range. Leveraging the nearly impeccable blackbody absorption of PtNP-shell and ultrasound-guided microinjection technology, remote and precise neuromodulation strategies can be developed, holding promise for non-invasive protection against MI and reperfusion injury-associated VAs. The significance of this approach extends beyond VAs as it exhibits broad therapeutic prospects for chronic diseases like refractory hypertension\(^{20}\) and stable atherosclerosis\(^{21}\) due to the wide distribution of autonomic nerves and the universality of nerve regulation.
+Online content
+
+Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data availability are available at https://doi.org/10.1038/xxx.
+References
+
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+3 Herring, N., Kalla, M. & Paterson, D. J. The autonomic nervous system and cardiac arrhythmias: current concepts and emerging therapies. Nat. Rev. Cardiol. 16, 707–726 (2019).
+4 Liu, J. S. et al. Antibody-conjugated gold nanoparticles as nanotransducers for second near-infrared photo-stimulation of neurons in rats. Nano Converg. 9, 13 (2022).
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+6 Zhang, L. et al. AIegen-based covalent organic frameworks for preventing malignant ventricular arrhythmias via local hyperthermia therapy. Adv. Mater. 35, 2304620 (2023).
+7 Prescott, E. D. & Julius, D. A modular PIP2 binding site as a determinant of capsaicin receptor sensitivity. Science 300, 1284–1288 (2003).
+8 Maingret, F. et al. TREK-1 is a heat-activated background K+ channel. EMBO J. 19, 2483–2491 (2000).
+9 Grandl, J. et al. Temperature-induced opening of TRPV1 ion channel is stabilized by the pore domain. Nat. Neurosci. 13, 708–714 (2010).
+10 Zhao, B. et al. Liquid-metal-assisted programmed galvanic engineering of core–shell nanohybrids for microwave absorption. Adv. Funct. Mater. 33, 2302172 (2023).
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+12 Liu, C. et al. Enhanced energy storage in chaotic optical resonators. Nat. Photonics 7, 474–479 (2013).
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+14 Mann, D. et al. Electrically driven thermal light emission from individual single-walled carbon nanotubes. Nat. Nanotechnol. 2, 33–38 (2007).
+15 Granqvist, C. G. Radiative heating and cooling with spectrally selective surfaces. Appl. Opt. 20, 2606–2615 (1981).
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+17 Zyrianova, T. et al. K2P2.1 (TREK-1) potassium channel activation protects against hyperoxia-induced lung injury. Sci. Rep. 10, 22011 (2020).
+18 Jayaprakash, N. et al. Organ- and function-specific anatomical organization of vagal fibers supports fascicular vagus nerve stimulation. Brain Stimul. 16, 484–506 (2023).
+19 Zhou, Z. et al. Metabolism regulator adiponectin prevents cardiac remodeling and ventricular arrhythmias via sympathetic modulation in a myocardial infarction model. Basic Res. Cardiol. 117, 34 (2022).
+20  Mancia, G. & Grassi, G. The autonomic nervous system and hypertension. Circul. Res. **114**, 1804–1814 (2014).
+
+21  Jiang, Y. Q. *et al.* The role of age-associated autonomic dysfunction in inflammation and endothelial dysfunction. *GeroScience* **44**, 2655–2670 (2022).
+Methods
+
+Chemicals
+The gallium and indium were purchased from Shanghai Minor Metals Co., Ltd. Anhydrous ethanol (≥99.7 %) and KOH (AR) were purchased from Sinopharm Chemical Reagent Co., Ltd. Na2PtCl6 (98%) was purchased from Shanghai Aladdin Biochemical Technology Co., Ltd. mPEG-SH5000 was purchased from Shanghai Macklin Biochemical Co., Ltd. STR-identified correct HT-22 cells or human embryonic kidney 293T (HEK-293T) cells were purchased with the corresponding specialized cell culture media (Procell, Wuhan, China). Anti-NFL, anti-c-fos, anti-TRPV1 antibodies used in western blot and immunofluorescence staining and anti-TREK1 antibody used in immunofluorescence staining were purchased from ABclonal (Wuhan, China). Anti-TREK1 antibody used in western blot was purchased from Santa Cruz Biotechnology (Texas, U.S.). Glyceraldehyde 3-phosphate dehydrogenase (GAPDH) was purchased from Abcam (Cambridge, England). Serum troponin I (c-TnI) and myoglobin (MYO) were purchased from MIbio (Shanghai, China). 4,6-diamidino-2-phenylindole (DAPI) was purchased from Servicebio (Wuhan, China).
+
+Instruments
+The morphology of PtNP-shell was characterized by a F200 transmission electron microscope (TEM) (JEOL, Japan) operated at 200 kV. STEM and HRTEM images were obtained by a JEM-ARM200CF (JEOL, Japan) at 200 kV. The EDX elemental mapping was carried using the JEOL SDD-detector with two 100 mm^2 X-ray sensor. X-ray diffraction (XRD) patterns were performed on an SmartLab 9kW X-ray powder diffractometer (Rigaku, Japan). XPS measurements were carried out with a ESCALAB 250Xi spectrometer (Thermo Fisher Scientific, U.S.) under vacuum. Ultraviolet-visible-near-infrared light (UV-Vis-NIR) absorption spectra was collected using a UV-
+3600 spectrophotometer (Shimadzu, Japan). Zeta potential (Z) and dynamic light scattering (DLS) were recorded using a Zetasizer Nano ZSP (Malvern Panalytical, U.K.). The fluorescence microscopy images of HT-22 cells were acquired by FV3000 Microscope (Olympus, Japan), excited with 488 nm laser. Beagle’s respiration is maintained by a WATO EX-20VET ventilator (Mindray, Shenzhen, China). ECG and blood pressure data were recorded by a Lead 7000 Computerized Laboratory System (Jinjiang, Chengdu, China). NIR-II light at 1064 nm is generated by LWIRPD-1064-5F laser (Laserwave, Beijing, China). Thermal imaging was obtained by FLIR C2 thermal imager (FLIR, U.S.). High-frequency electrical stimulation was performed by Grass stimulator (Astro-Med; West Warwick, RI, U.S.) The electrical signals of autonomic nerves are recorded by Power Lab data acquisition system (AD Instruments, New South Wales, Australia). Serum biochemical indices were determined by a fully automatic biochemical analyzer BK-1200 (BIOBASE, Jinan, China).
+
+Synthesis of GaNPs
+
+The GaNPs were obtained by sonication of liquid Ga. The liquid Ga (300 mg) was transferred to anhydrous ethanol (8 mL), and the solution was sonicated by nanoprobe sonication for 1 h (3 seconds on and 3 seconds off) at the power of 290 W. Then the ethanol was replaced with Milli-Q water to continue sonication for 1 h. The solution at the end of sonication was collected and centrifuged at 1000 rpm for 5 min, and the upper liquid layer was aspirated for later use.
+
+Synthesis of PtNP-shell
+
+First, the GaNPs and 3 mL Na₂PtCl₆ (0.1 M) were evacuated for 30 min and Ar was introduced for 15 min. Then, 3 mL Na₂PtCl₆ (0.1 M) was added dropwise to GaNPs and the solution was stirred for 4 h. After reaction, the solution was collected and centrifuged at 9000 rpm for 10 min. The solids at the bottom were washed with Milli-
+Q water for 3 times and finally dispersed in 6 mL Milli-Q for later use.
+
+Functionalization of PtNP-shell with mPEG-SH_{5000}
+
+The PtNP-shell was first covered with a small amount of mPEG-SH to protect the structure from KOH. 30 mg mPEG-SH_{5000} was added to 6 ml PtNP-shell and the solution was stirred for 12 h. After the reaction, the solution was collected and centrifuged at 9000 rpm for 10 min. The solids at the bottom were washed with Milli-Q water for 3 times and dispersed in 6 mL Milli-Q water. The above solution was stirred with 12 mL of KOH (1 M) for 4 h. The reaction-completed solution was collected and centrifuged at 9000 rpm for 10 min, and the solids at the bottom were washed three times with Milli-Q water and finally dispersed in 6 mL Milli-Q water. The above solution was stirred with 60 mg mPEG-SH_{5000} for 12 h. After the reaction, the solution was collected and centrifuged. The solids at the bottom were washed with Milli-Q water for 3 times and finally dispersed in 6 mL PBS.
+
+Synthesis of Ga–In alloy nanoparticles (GaIn NPs)
+
+The liquid EGaIn was prepared by physically mixing 75 wt% gallium and 25 wt% indium at 200 °C for 2 h. The liquid EGaIn (300 mg) was transferred to anhydrous ethanol (8 mL), and the solution was sonicated by nanoprobe sonication for 1 h (3 seconds on and 3 seconds off) at the power of 290 W. Then the ethanol was replaced with Milli-Q water to continue sonication for 1 h. The solution at the end of sonication was collected and centrifuged at 1000 rpm for 5 min, and the upper liquid layer was aspirated and set aside.
+
+Synthesis of GaIn@Pt NPs
+
+1 mL Na_2PtCl_6 (0.1 M) was added dropwise to GaIn NPs and the solution was stirred for 4 h. After reaction, the solution was collected and centrifuged at 9000 rpm for 10
+min, washed 3 times with Milli-Q water and dispersed in 6 mL Milli-Q water. The above solution was stirred with 60 mg mPEG-SH_{5000} for 12 h. After the reaction, the solution was collected and centrifuged. The solids at the bottom were washed with Milli-Q water for 3 times and finally dispersed in 6 mL PBS.
+
+Calculation of the photothermal conversion efficiency
+
+The photothermal conversion of the PtNP-shell has been calculated on the basis of previous work^{22,23}. The relationship between temperature rise and energy transfer in the system can be described by the Equation S1,
+
+\[
+\sum_i m_i c_i \frac{dT}{dt} = Q_{abs} - Q_{ext} = Q_{NPS} + Q_{solvent} - Q_{ext} \tag{S1}
+\]
+
+where \( Q_{abs} \) is the total energy absorbed by the system, \( Q_{NPS} \) is the energy absorbed by the nanoparticles, \( Q_{solvent} \) is the energy absorbed by the solvent, \( Q_{ext} \) is the energy loss from the system to the environment. \( m_i \) and \( c_i \) are the mass and specific heat capacity of the solution, respectively. \( T \) is the solution temperature and \( t \) is the irradiation time.
+
+The conversion of the light energy into heat energy can be expressed in terms of Equation S2,
+
+\[
+Q_{NPS} = I(1 - 10^{-A})\eta \tag{S2}
+\]
+
+where \( I \) is the laser power, \( A \) is the absorbance value of PtNP-shell at 1064 nm, \( \eta \) is the photothermal conversion efficiency. \( Q_{solvent} \) can be calculated by the following Equation S3,
+
+\[
+Q_{solvent} = hs(T_{solvent} - T_{surr}) \tag{S3}
+\]
+
+where \( h \) is the convective heat transfer coefficient and \( s \) is the surface area of the sample cell. \( T_{solvent} \) is the maximum temperature that the solvent can reach under laser irradiation. \( T_{surr} \) is the ambient temperature. \( Q_{ext} \) can also be written as,
+
+\[
+Q_{ext} = hs(T - T_{surr}) \tag{S4}
+\]
+
+The heat output will increase with the increase in temperature when the NIR-II
+laser power is determined according to formula S4. The temperature of the system will reach the maximum when the heat input is equal to the heat output, so the following equation can be obtained,
+
+\[
+Q_{NPS} + Q_{solvent} = Q_{ext-max} = hs(T_{max} - T_{surr}) \tag{S5}
+\]
+
+where \( Q_{ext-max} \) is the heat transferred from the system surface through the air when the sample cell reaches equilibrium temperature, and \( T_{max} \) is the equilibrium temperature. Combining equations S2, S3 and S5, \( \eta \) can be expressed as,
+
+\[
+\eta = \frac{hs(T_{max}-T_{surr})-hs(T_{solvent}-T_{surr})}{I(1-10^{-A})} = \frac{hs(T_{max}-T_{solvent})}{I(1-10^{-A})} \tag{S6}
+\]
+
+where \( A \) is the PtNP-shell absorption at 1064nm. To obtain \( hs \), the dimensionless temperature \( \theta \) is introduced,
+
+\[
+\theta = \frac{T-T_{surr}}{T_{max}-T_{surr}} \tag{S7}
+\]
+
+and a time constant of sample system, \( \tau_s \)
+
+\[
+\tau_s = \frac{\sum m_i c_i}{hs} \tag{S8}
+\]
+
+Combining Equations S1, S4, S7 and S8, the following equation can be obtained,
+
+\[
+\frac{d\theta}{dt} = \frac{1}{\tau_s} \left[ \frac{Q_{NPS}+Q_{solvent}}{hs(T_{max}-T_{surr})} - \theta \right] \tag{S9}
+\]
+
+After the laser is turned off, in the cooling stage, there is no external input energy, \( Q_{NPS} + Q_{solvent} = 0 \), and equation S9 can be written as,
+
+\[
+dt = -\tau_s \frac{d\theta}{\theta} \tag{S10}
+\]
+
+By integrating Equation S10, the following equation can be obtained,
+
+\[
+t = -\tau_s ln\theta \tag{S11}
+\]
+
+Therefore, the system heat transfer time constant (\( \tau_s \)) at 1064 nm is 242.25 s (Figure 3f). In addition, m is 0.3 g and c is 4.2 J·g\(^{-1}\). Therefore, \( hs \) can be determined from Equation S8. The laser power (\( I \)) used here can be determined as 1 W. Then the photothermal conversion efficiency (\( \eta \)) of the PtNP-shell at 1064 nm can be calculated
+to be 73.7% by substituting \( hs \) into Equation S6.
+
+Animal preparation and cell culture
+
+All animal experiments were approved by the Animal Care and Use Committee of Renmin Hospital of Wuhan University (WDRM20230805A). All experimental procedures were in accordance with the Declaration of Helsinki and were conducted according to the guidelines established by the National Institutes of Health. All Beagles (8–12 kg) were anesthetized intravenously with 3% sodium pentobarbital (30 mg·kg\(^{-1}\) induction dose, 2 mg·kg\(^{-1}\) maintenance dose per hour) and respiration was maintained by endotracheal intubation using a ventilator. Arterial blood pressure was continuously monitored through femoral artery catheterization with a pressure transducer attached. ECG and blood pressure data were recorded throughout the procedure. A heating pad was used to maintain core body temperature at 36.5 ± 0.5 °C.
+
+The cells were cultured in a humid incubator containing 5% CO\(_2\) at a temperature of 37.0 °C.
+
+Detection of TRPV1 and TREK1 expression *in vitro* and *in vivo*
+
+Western blotting was used to assess the expression of TRPV1 and TREK1 in neuronal cells and ganglion tissues. HT-22 cells or HEK-293T cells were cultured in six-well plates for 24–48 h, then lysed and centrifuged to collect cells. Ganglion tissues were obtained from deceased animals and frozen in liquid nitrogen or stored at –80.0 °C. Total protein was determined using BCA protein assay reagent after tissue grinded and cells lysed. Afterwards, the procedure was followed according to the manufacturer's instructions. Primary antibodies were anti-TRPV1 and anti-TREK1. Expression levels of specific proteins were normalized to GAPDH.
+
+Calcium imaging of neuronal cells
+The effect of PtNP-shell photothermal modulation on ion channels in HT-22 cells was explored through calcium imaging experiments. HT-22 cells were incubated in 35 mm confocal dishes for 24 h. Cells were washed 3 times with PBS and then stained with 5 μM Fluo-4 AM (dilution ratio 1:500) for 30 min in a cell incubator at 37.0 °C, protected from light. To induce activation of TRPV1 and TREK1 ion channels, which had been previously studied7,8, the culture dish was exposed to NIR-II light (1064 nm), resulting in an elevation of temperature. TRPV1, being a calcium channel, exhibited observable changes in the flow of calcium ions upon activation, while TREK1 as a potassium channel did not display such behavior. Therefore, the effect of PtNP-shell photothermal modulation on neuronal cells via TREK1 was observed by introducing a 15 mM KCl solution prior to NIR-II irradiation. Fluorescence signals at 525 nm were recorded using a confocal microscope with 488 nm as the excitation wavelength. XYT images were acquired and collected under a 20x objective lens. The average fluorescence intensity of the cells was analyzed using ImageJ software (Fiji). The normalized fluorescence change was calculated as follows: \( \Delta F/F = (F-F_0)/F_0 \), where F is the original fluorescence signal; \( F_0 \) is the average baseline intensity before irradiation with NIR-II laser.
+
+*In vitro* cytotoxicity assay
+
+The cytotoxicity of PtNP-shell on neuronal cells was evaluated by CCK-8 assay. HT-22 cells were seeded in 96-well plates at a density of \( 1 \times 10^4 \) well\(^{-1}\) and cultured for 24 h. HT-22 cells were then treated with different concentrations (10, 25, 50, 100, 150, 200 \( \mu \mathrm{g} \cdot \mathrm{mL}^{-1} \)) of PtNP-shell for another 24 h. Cell viability was determined by CCK-8 assay after incubating with the CCK-8 reagent for 1 h. To investigate the impact of PtNP-shell's photothermal effect on neuron cell viability, HT-22 cells were co-cultured with PtNP-shell (50 \( \mu \mathrm{g} \cdot \mathrm{mL}^{-1} \)) for 12 h followed by irradiation with a 1064 nm laser (0.5 and 0.75 W·cm\(^{-2}\)) for various durations (10 s, 30 s and 60 s). After incubation again for 12
+h, the absorbance at 450 nm was recorded using a microplate reader. Cell survival (%) = (OD_{samples}-OD_{blank})/(OD_{control}-OD_{blank}) \times 100\%.
+
+Experimental protocol 1: Activation of the parasympathetic nervous system through PtNP-shell photothermal reduces I/R injury
+
+Part 1: Exploring the in vivo effects of precise photothermal stimulation of the parasympathetic nervous system by PtNP-shell under NIR-II irradiation. Twelve beagles were randomly assigned to the control group (100 \( \mu \)L phosphate-buffered saline (PBS) was microinjected into the NG, n = 6) and the PtNP-shell group (100 \( \mu \)L PtNP-shell (50 g·mL\(^{-1}\)) was microinjected into the NG, n = 6). NG nerve activity, heart rate (HR) and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR-II irradiation (Fig 4b).
+
+Part 2: The protective effect of PtNP-shell activation of the parasympathetic nervous system against myocardial I/R injury was investigated. The same grouping pattern as in part1 was used, with 5-min NIR-II irradiation of the NG before opening the occluded LAD coronary vessel. Afterwards, ventricular electrophysiological parameters, heart rate variability (HRV) and ECG data were recorded and analyzed (Fig 5b).
+
+Experimental protocol 2: PtNP-shell photothermal inhibition of sympathetic nervous system improves MI
+
+Part 1: The *in vivo* effects of precise photothermal stimulation of the sympathetic nervous system by PtNP-shell under NIR-II irradiation were explored. Twelve beagles were randomly assigned to the control group (100 \( \mu \)L PBS microinjected into the LSG, n = 6) and the PtNP-shell group (100 \( \mu \)L PtNP-shell (50 g·mL\(^{-1}\)) microinjected into the LSG, n = 6). LSG nerve activity, SBP and ventricular electrophysiological parameters were recorded at baseline and at multiple consecutive time points after NIR-II
+irradiation (Fig 6b).
+
+Part 2: To investigate the protective effect of PtNP-shell inhibition of the sympathetic nervous system a improves MI. The same grouping pattern as in part1 was used, with 5-min NIR-II irradiation of the LSG before ligation of LAD vessels. Finally, ventricular electrophysiological parameters, HRV and ECG data were also recorded and analyzed (Fig 7b).
+
+PtNP-shell photothermal stimulation of the autonomic nervous system *in vivo*
+We selected NG and LSG as targets for modulation in the autonomic nervous system to explore the multifunctionality of the PtNP-shell photothermal strategy. A “C” incision is made behind the left ear, and the angle between the occlusal and trapezius muscles served as the access approach\(^{24}\). The tissue is bluntly separated to expose the carotid sheath and identify the parasympathetic nerve. Moving upstream along the nerve, a distal expansion is observed as NG (Fig 4a). LSG can be visualized and localized by left-sided thoracotomy according to the method of a previous study (Fig 6a)\(^{25}\). PtNP-shell (50 \( \mu \)g·mL\(^{-1} \)) or PBS was slowly injected into 2 sites within the NG and LSG tissues to achieve homogeneous photothermal conversion. Initial vertical irradiation of NIR-II laser (1064 nm) at 0.80 W·cm\(^{-2} \) was performed on NG and LSG surfaces. The power density of the NIR-II laser was reduced to 0.45 W·cm\(^{-2} \) for continuous irradiation when the temperature of the NG reached 42.0 °C, and was reduced to 0.6 W·cm\(^{-2} \) for continuous irradiation when the temperature of the LSG reached 46.0 °C. The NIR-II laser irradiation remains stable with a spot size maintained at 1.0 cm\(^{-2} \). Dual temperature monitoring using thermal imager and T-type thermocouple was performed to plot the temperature-time curve.
+
+**Functional assessment of autonomic nerves**
+The NG is a ganglion located upstream of the cervical parasympathetic nerve and can
+significantly inhibit HR after receiving direct electrical stimulation\(^{18}\). The LSG, as an important peripheral sympathetic ganglion, can rapidly elevate blood pressure when activated by electrical stimulation. Based on the functional properties of different autonomic ganglia, we assessed the function of NG and LSG with reference to previous studies\(^{19}\). A pair of special electrodes made with silver wires were directly connected to the surfaces of NG and LSG for stimulation. High-frequency electrical stimulation (HFS: 20 Hz, 0.1 ms) was applied to the ganglion. The voltage was set to 5 levels in continuous increments (level 1: 0–2 V; level 2: 2–4 V; level 3: 4–6 V; level 4: 6–8 V; level 5: 8–10 V), while keeping the stimulation voltage values consistent with the baseline at different time points during the experiment. The percentage of sinus rate or AV conduction (measured by the A-H interval) slowing down constructed voltage level/degree of HR decrease curves reflecting NG function. On the other hand, the percentage increase in SBP built the voltage level/degree of SBP increase to reflect LSG function.
+
+**Activity testing of autonomic nerves**
+
+The activity of different autonomic nerves was assessed based on previous studies\(^{19}\). Two specially designed microelectrodes were inserted into the NG and LSG, respectively, while a grounding wire was connected to obtain signals from the autonomic nerves. These electrical signals were recorded by a Power Lab data acquisition system, filtered through a band-pass filter (300–1000 Hz) and amplified 30-50 times by an amplifier. Finally, the signals were digitized and analyzed in LabChart software (version 8.0, AD Instruments).
+
+**Construction of myocardial I/R injury model and MI model**
+
+The left anterior descending coronary occlusion (LADO) method was used to establish the MI model\(^{19}\). The ligation site was located beneath the first diagonal of the LAD, and
+successful MI model was confirmed by observing ST-segment elevation on the ECG.
+After ensuring cardiac electrophysiological stabilization, the junction was released to reperfuse the occluded coronary arteries, completing the construction of the myocardial I/R injury model26.
+
+Ventricular electrophysiological study in vivo
+
+The cardiac electrophysiological measurements were performed in Beagles using a previously studied protocol27,28. The ERP was measured at three locations: LVA, LVB, LVM (located between the LVA and LVB). Malignant arrhythmic events caused by MI and I/R injury were assessed by electrocardiographic recordings in a canine model using Lead 7000 Computerized Laboratory System. VAs was classified according to Lambeth Conventions as VPBs, VT (three and more consecutive VPBs) and VF29. In addition, arrhythmia inducibility was further assessed by programmed ventricular stimulation at the right ventricular apex (RVA). Eight consecutive stimuli (S1S1) were performed at intervals of 330 ms, followed by additional stimuli until VT/VF occurred. Arrhythmia inducibility was assessed based on a modified arrhythmia scoring system28. If VF occurs during the evaluation, a defibrillator is required to restore sinus rhythm, followed by a waiting period of 30 min to restore cardiac electrophysiological stability. The VF threshold was assessed in the perimyocardial infarction region. Pacing was initiated using a Grass stimulator with a voltage of 2 V (20 Hz, 0.1 ms duration, 10 s). The stimulation voltage was increased in 2 V increments until VF was induced. The lowest voltage that induced VF was regarded as the VF threshold30.
+
+HRV analysis
+
+The ECG data was recorded using the PowerLab data acquisition system. And the ECG segments recorded more than 5 min before modulation and after MI or I/R injury were analyzed by LabChart software with the Lomb-Scargle periodogram algorithm31.
+Frequency domain metrics of HRV were calculated, including LF (0.04–0.15 Hz, reflecting sympathetic tone), HF (0.15–0.4 Hz, reflecting parasympathetic tone) and LF/HF (reflecting autonomic balance). The results were expressed in standardized units.
+
+Immunofluorescence staining of histopathological sections
+The ganglions were rapidly dissected for histopathological staining after the experimental animals died. Tissues were fixed with 4% paraformaldehyde, embedded in paraffin, and cut into 5 μm-thick sections. NG was stained with multiple immunofluorescence staining using anti-NFl, anti-c-fos and anti-TRPV1 antibodies. And LSG was stained by multiple immunofluorescences using anti-TH, anti-c-fos and anti-TREK1 antibody. Cell nuclei were stained with DAPI. Images were taken at 100× magnification and analyzed using ImageJ software (Fiji).
+
+Enzyme-linked immunosorbent assay (ELISA)
+5 ml of venous blood was obtained from the jugular vein of each beagle after MI and myocardial I/R injury. After standing for 1 hour, the blood was centrifuged at 3000 rpm for 15 min. The upper serum layer was collected and stored at −80.0 °C. Myocardial injury levels were detected by c-TnI and myoglobin (MYO). Standard process analyses were performed according to the instructions of each ELISA kit. To evaluate the long-term biosafety and biocompatibility of PtNP-shell in vivo, Beagle dogs and rats were randomly divided into PtNP-shell and PBS groups.
+
+Long-term biosafety assay in vivo
+To evaluate the long-term biosafety and biocompatibility of PtNP-shell in vivo, Beagle dogs and rats were randomly divided into two groups: a PtNP-shell group and a PBS group. In the PtNP-shell group, 200 μL PtNP-shell (50 μg·mL⁻¹) was microinjected into canine ganglion tissue and tail vein of rats to explore long-term biosafety. Blood
+and tissue samples were collected from each dog and rat one month after injection. One month after injection, blood samples were collected from the jugular vein of dogs as well as from the inferior vena cava of rats for analysis of serum biochemical indices. Tissue H&E staining was also performed on major organs, including heart, liver, spleen, lung and kidney.
+
+Statistical analysis
+
+All graphical data are presented as mean ± standard error of the mean (SEM), and the distribution of data was assessed by the Shapiro-Wilk test. Differences between groups were determined using Student's t-test or Mann-Whitney U-test. Data were analyzed and plotted using GraphPad Prism 9.0 software (GraphPad software, Inc., La Jolla, CA, USA). P < 0.05 was considered statistically different. The p-values are indicated with an asterisk (* p < 0.05, ** p < 0.01, *** p < 0.001).
+
+Reporting Summary
+
+Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.
+
+Data availability
+
+The main data supporting the results in this study are available within the paper and its Supplementary Information. The raw and analyzed datasets generated during the study are too large to be publicly shared, yet they are available for research purposes from the corresponding authors on reasonable request. Source data are provided with this paper.
+References
+
+22 Chechetka, S. A. et al. Light-driven liquid metal nanotransformers for biomedical theranostics. Nat. Commun. **8**, 15432 (2017).
+23 Zhu, P. et al. Inorganic nanoshell-stabilized liquid metal for targeted photonanomedicine in NIR-II biowindow. Nano Lett. **19**, 2128–2137 (2019).
+24 Bruneau, M. & George, B. The juxtacondylar approach to the jugular foramen. Oper. Neurosurg. **63**, 75–80 (2008).
+25 Zhang, S. et al. Ultrasound-guided injection of botulinum toxin type A blocks cardiac sympathetic ganglion to improve cardiac remodeling in a large animal model of chronic myocardial infarction. Heart Rhythm **19**, 2095–2104 (2022).
+26 Chen, M. X. et al. Low-level vagus nerve stimulation attenuates myocardial ischemic reperfusion injury by antioxidative stress and antiapoptosis reactions in canines. J. Cardiovasc. Electrophysiol. **27**, 224–231 (2016).
+27 Yu, L. L. et al. Optogenetic modulation of cardiac sympathetic nerve activity to prevent ventricular arrhythmias. J. Am. Coll. Cardiol. **70**, 2778–2790 (2017).
+28 Yu, L. et al. Chronic intermittent low-level stimulation of tragus reduces cardiac autonomic remodeling and ventricular arrhythmia inducibility in a post-infarction canine model. JACC Clin. Electrophysiol. **2**, 330–339 (2016).
+29 Walker, M. J. A. et al. The lambeth conventions: guidelines for the study of arrhythmias in ischaemia, infarction, and reperfusion. Cardiovasc. Res. **22**, 447–455 (1988).
+30 Dalonzo, A. J. et al. Effects of cromakalim or pinacidil on pacing- and ischemia-induced ventricular fibrillation in the anesthetized pig. Basic Res. Cardiol. **89**, 163–176 (1994).
+31 Lai, Y. et al. Non-invasive transcutaneous vagal nerve stimulation improves myocardial performance in doxorubicin-induced cardiotoxicity. Cardiovasc. Res. **118**, 1821–1834 (2022).
+
+Acknowledgements
+
+The research was supported by the National Natural Science Foundation of China (grants 22025303, 82241057, 82270532 and 82200556); and the National Key Research and Development Program of China (grant 2023YFC2705705); and Foundation for Innovative Research Groups of Natural Science Foundation of Hubei Province, China (grant 2021CFA010). We thank the Core Facility of Wuhan University for their substantial supports in sample characterization, including SEM, XPS, DLS and XRD. We thank the Center for Electron Microscopy at Wuhan University for their support of STEM, HRTEM and EDX characterization. We also thank Meimei Zhang in the institute for advanced studies of Wuhan University for their assistance in TEM characterization.
+
+Author contributions
+
+L.F., L.L.Y. and X.Y.Z. conceived the research concept. L.F., L.L.Y. and X.Y.Z.
+supervised the research; C.L.W., L.P.Z., C.Z.L., J.M.Q., X.R.H., B.X., Q.F.Q., Z.Z.Z. and J.L.W. performed the experiments; C.L.W., L.P.Z., C.Z.L., L.Y.W. and Y.X.L. discussed the results; C.L.W., L.P.Z. and C.Z.L. analysed the data and cowrote the manuscript. All authors commented on the manuscript.
+
+Competing interests
+
+The authors declare no competing interests.
+
+Additional information
+
+Supplementary information The online version contains supplementary material available at
+
+Correspondence and requests for materials should be addressed to Xiaoya Zhou, Lilei Yu or Lei Fu
+
+Peer review information
+
+Reprints and permissions information is available at
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• supplementaryinformation.docx

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+Peer Review File
+
+Microtopography-induced changes in cell nucleus morphology enhance bone regeneration by modulating the cellular secretome
+
+Corresponding Author: Dr Guillermo Ameer
+
+Parts of this Peer Review File have been redacted as indicated to remove third-party material.
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+This is a nicely written paper that is very well presented. I have some concerns about just what a large advance the manuscript represents. That topography causes phenotype-relevant secretome changes is pretty well known (eg https://www.nature.com/articles/s41598-018-25700-5). These secreted factors can drive bone cell activity (https://www.sciencedirect.com/science/article/abs/pii/S0006291X15003083) and that will change ECM as the phenotype of cells change. That ECM s secreted and changes things is also known (https://www.nature.com/articles/s41392-022-00932-0). I am sure there are more aligned references with a good look. Figure 6 is the interesting figure - but, to me, doesn't carry the paper to this level as I don't really learn much about how this happens - I see it does happen (topography driving bone formation and the secretome being osteogenic with ECM strongly involved, and I learn about spatial osteogenesis - but not how e.g through a mechanobiological process.
+
+Minor points are:
+Figure 1 - where are the many small pores?
+Figure 2 - is cell number attachment per se - I think of cell adhesions
+Figure 2 - I don't agree these are filopodia - bit are a mixture of retraction fibres and leading edges - filopodia are very small.
+Figure 4 - why use osteogenic media if the secretome is going to drive osteogenesis?
+
+Reviewer #2
+
+(Remarks to the Author)
+This study assessed the contribution of changes to the secretome on the bone-promoting effect of surface micropillars and also sought to connect this to the known nuclear deformation that occurs when using such surfaces. It builds upon previous work by the authors, and others, showing that specific sizes of micropillar deform the nuclei of cells cultured upon them, and that this alters chromatin state and consequently the fate of the cells- in the context of bone repair, this typically being MSCs and osteogenesis. A newer aspect is the study of changes to the secretome, one mechanism via which the effects may be mediated. Previous studies have shown that the secretome is altered by physical/biomaterial cues such as stiffness and topography, although not yet in advanced detail- this is the first to study these particular topographic designs and osteogenesis.
+The study compares 5 micron square pillars which are well-known to boost osteogenesis. These are created from mPOC/HA as a suitable osteogenic scaffold. It begins by characterising the substrates, confirms changes in cell response, shows that the secretome changes and that this affects cells on flat surfaces. An in vivo calvarial defect model also showed a beneficial effect of the pillars followed by spatial transcriptionomics to assess localisation of matrix gene expression.
+Overall, this is a nice paper with interesting findings that will be useful in the field. Most of the conclusions are well supported by the quality and quantity of data, although there are a few areas of overreach, or where additional information is required as outlined below.
+General comments:
+1. Although the paper was well written, the rationale/justification could be better expressed: there is an inconsistent narrative between the introduction and discussion. Is the goal to optimise the design of implants for bone regeneration or conduct basic research into the effect of nuclear morphology on the secretome? The introduction leans toward basic research as the motivation: the choice to use micropillars as a means of deforming the nucleus instead of, say, optical tweezers was partly due to accessibility, and there is little mention of the need for improved implants for bone regeneration. However, the discussion suggests the overall goal is to improve implants for bone regeneration.
+2. Further to comment one, the rationale for choosing mPOC/HA given in the introduction was somewhat ambiguous. The rationale for its choice was based on comparison to other materials used to fabricate micropillars, but it wasn’t clear whether the intent of the study was simply to use a suitable material for fundamental investigation or whether it was anticipated that this would for the basis of future orthopaedic implants.
+3. This paper might benefit from more discussion of previous studies that have investigated how biomaterial properties influence the secretome, including ones that have specifically looked at surface microtopographies including:
+• Rosado-Galindo, H. & Domenech, M. Substrate topographies modulate the secretory activity of human bone marrow mesenchymal stem cells. Stem Cell Research & Therapy 14, 208 (2023). DOI: 10.1186/s13287-023-03450-0
+• Leuning, D. et al. The cytokine secretion profile of mesenchymal stromal cells is determined by surface structure of the microenvironment. Scientific Reports 8, 7716 (2018). DOI: 10.1038/s41598-018-25700-5
+4. Characterization of physical and chemical properties of flat and micropillar substrates was thorough (Fig 1). One question that remains is how the micropillars change over time due to degradation. Degradation was continuous over time, even after accounting for two ‘bursts’ of degradation. Do the micropillars maintain square geometries? Do they maintain a consistent height? SEM of micropillars at day 14 of degradation would clarify this.
+5. Cells seeded onto micropillars can exhibit multiple nuclear morphological phenotypes, with the nucleus deforming in different ways. For instance, the nucleus may bend around a micropillar or the micropillar may penetrate through the nucleus. Did the authors see any diversity in how the nucleus was deformed?
+6. Regarding Fig. 2j, can the authors elaborate on why osteogenic differentiation was performed on a substrate with both flat and micropillar areas? The secretomes from cells on each topography would mix and influence differentiation. Additionally, cells must have been removed/trypsinized from the substrate for subsequent western blotting - how were cells on each topography kept separate during removal from the substrate?
+7. Athymic nude mice were used to prevent immune rejection of the human MSCs. Nude mice that lack T cells still retain an innate immune system, including macrophages that can respond to foreign bodies (Rodriguez, A. et al. The foreign body reaction in T-cell-deficient mice. J. Biomed. Mater. Res. A 90, 106-13 (2009). DOI: 10.1002/jbm.a.32050). Could macrophage activity alter the observed effects of substrate topography on bone regeneration?
+8. Please take care to better discriminate between the data that shows a paracrine response in vitro and a matricine response in vivo- technically the data does not directly show paracrine signalling in response to the pillars in the mouse model and so the abstract/discussion may over-reach in places. For example, in the abstract “These findings indicate that micropillars not only enhance the osteogenic differentiation of human mesenchymal stromal cells (hMSCs) but also modulate the secretome, thereby influencing the fate of surrounding cells through paracrine effects.” Whereas the discussion more accurately summarises the results saying “…nuclear deformation induced by micropillars may promote osteogenesis in neighboring cells via matricine effects.” The results show micropillars alter paracrine signaling in vitro via the transwell assay. The results also indicate matricine effects in vivo: micropillars upregulate ECM proteins in vitro and ECM-related genes in vivo. However, the link between micropillars and altered paracrine signaling (i.e. direct cell-cell signalling) in vivo is not well established. The distinction between paracrine and matricine effects should be made clearer.
+9. Whilst the introduction emphasises nuclear mechanotransduction and chromatin modification, the data in this study does not actually address these mechanisms. Relating to comment 1, this aspect should be clarified to avoid misinterpretation that this study is attempting to directly show a link between chromatin modification and the paracrine effects.
+10. Did the authors consider histological staining of specific proteins within tissue sections? This could provide protein level validation of the in vitro secretome findings – for instance, upregulated proteins involved in ossification identified in the in vitro secretome could be correlated with their spatial distribution in vivo.
+
+Specific/minor comments
+11. The text in many figures, for example the secretome and proteome data, is very small. Many scale bars are also quite small. It would improve readability if the font size could be increased.
+12. Supplementary Figure S11 needs more labels: it is impossible to determine what anything is.
+13. Methods, in vivo implantation: “…a larger mPOC film…”. Should this read ‘mPOC/HA’?
+14. Discussion, second sentence: “mesenchymal stem cells”. According to more recent accepted terminology, this should read ‘mesenchymal stromal cells’.
+
+Reviewer #3
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #4
+(Remarks to the Author)
+In this article, the authors demonstrate the ability of mPOC/HA micropillar scaffolds to enhance bone regeneration. As previously demonstrated by the team (Wang et al., 2023), the micropillar scaffolds changes the morphology of cell nuclei, triggering chromatin reprogramming. Here, they demonstrate that nuclear morphology modification enhances osteoblastic differentiation and regulates ECM formation via modulation of the hMSC secretome.
+This paper combines material characterization, morphological evaluation (SEM, IF), characterization of osteoblastic differentiation (PAL activity, Western Blot), secretome and proteome analysis of cells on scaffold prior to implantation (in vitro). As well as an in-depth evaluation of implants with cells after implantation -in vivo (microCT, histology, IHC, Spatial Transcriptomic).
+This work does more than demonstrate a material’s ability to recreate bone; it bring out the cellular and molecular machinery involved in this process. In this sense, it goes much further than most articles on regenerative engineering. Which makes it a significant work for the field!
+The interpretation of the role of LMPs (last paragraph of the results) on the site of calvarial defect in not correct in my opinion.
+To generate bone, you need osteoblasts. They are generated by the differentiation of MSC. “LMPs are identified as the late stage of MSCs through osteogenic differentiation”. Therefore, the creation of osteoblasts (which will mineralize) contributes directly to osteogenesis and bone regeneration.
+Although the methods used in this work provide relevant evidence, the explanation of many of the methods is not clear enough to allow these experiments to be reproduced.
+Analysis of the secretome and proteome has several significant flaws:
+- For sample preparation, peptide concentration is quantifies using an unsuitable kit, as it is designed for proteins and not peptides.
+- For secretome sample preparation, a serum-free culture must be performed 48 hours before sampling the culture medium, in order to remove the proteins contained in the serum. The method used in the authors (molecular weight cut off filter) may affect secretome proteins, not just serum proteins, and does not eliminate small serum proteins.
+- Label-free quantification is problematic, partly because of the poor peptides concentration quantification, but mainly because the analysis was carried out with n=3, which is too small for label-free. “Missing values were filtered to keep only proteins quantified in at least 2 samples per group.” Making statistics with n=2 is not correct! If the number of sample by group can’t be increased, you need to be more stringent about the selection parameters: keep only the proteins present in the 3 samples per group, and choose a log2FC of 1.5 and an adjusted p-value < 0.01.
+Minor comments:
+In the results section, in the paragraph “Microfiller modulates the secretome of hMSCs that regulate ECM formation”, PCA term should be deleted from the sentence, as unlike the volcano plot, this element gives no indication of influence of nuclear deformation on protein expression.
+In the paragraph “mPOC/HA micropillar implant promotes bone formation in vivo”, the comparison of the results presented in this article with those of the previous article (mPOC alone) should be moved in the discussion.
+The last sentence of the paragraph “microfiller implants facilitated bone regeneration in vivo ...” is an interpretation and should be moved to the discussion.
+A longer discussion would be appreciated. The exchange surface was never mentioned, although the presence of microfillers on the material considerably increases the exchange surface between the scaffold (mPOC/HA) and the cells, which may help to explain the differences in results between the flat scaffold and the microfiller scaffold. The number of cell seeded per scaffold could also be discussed. Indeed, most tissue engineering articles testing MSCs with scaffold in vivo seed many more cells (on the order of 100,000 to 1,000,000/cm2). In your conditions (4mm diameter implant), 5000 cells per cm2 may not be enough for the paracrine effect to be significant.
+Many elements are missing from the materials and methods.
+• Degradation and calcium release
+Parameters of ICP-MSC are not explain, nor is the method for calculating accumulated calcium.
+• Cell culture
+The cell culture conditions (cell density, culture medium, time) for the various experiments (e.g.: secretome and proteomic analysis, in vivo implantation) are not clearly explain. This section should be explained.
+Experiments such as live/dead, MTT or DNA assays should appear in a different section of the cell culture.
+The manufacturer’s protocol of MTT recommends measuring absorbance at 570nm. However, in figure 2.h., absorbance was indicated at 540nm. was this a mistake?
+• Immunofluorescence and microscopy
+For most of the fluorescence images (fig 2a. 2g, fig 4f and fig 5b), labelling methods are not explained (nuclear and F-actin markers, secondary antibody for collagen). The microscope used to acquire these images is not mention.
+For figure 4.h, the method used to produce and acquire these images (EDS and Ca, P deposition) is not mention.
+• Osteogenic differentiation
+For Western Blot, dilution of all antibodies is not mention.
+• Secretome sample preparation
+Trypsin digestion is mention twice.
+• Proteome sample preparation
+Trypsin digestion is mention twice.
+• Transwell assay :
+Secondary antibody for collagen staining should be mentioned. All dilution or concentration used should be mentioned.
+• In vivo implantation
+Tool used to create defect should be add.
+• MicroCT
+Here, reference is made to Vi: the initial volume of the defect. How was Vi measured?
+If mice are scanned at Vi, are they the same as those at Vf? If so, please indicate how the mice were anaesthetized for microCT.
+• Histology analysis
+References of the anti-OCN and anti-OPN antibodies are not given, nor are their dilutions.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+I thank the authors for responding to my comments and I have read the reviews of the other reviewers - and read the revised ms.
+
+I am sorry to say that my opinion hasn't really changed.
+
+- Micropillars changes nuclear morphology and enhance osteogenesis - this is known and there is, of course, much less insight here than in the original Nature Biomedical Engineering paper on epigenetics.
+
+- This causes a regenerative change in cell sectretome in vitro with changes in ECM proteins - I think this is sensible/interesting but not radical.
+
+- The materials, seeded with MSCs, provide greater in vivo regeneration that includes ECM remodelling - I think the analysis is very nice, especially the cell spatial analysis. But, the link between secretion and regeneration is broken - highly likely secretome is a part of this, but it could be the MSCs themselves give an effect - anti-inflammatory or regenerative.
+
+This is very nice work - but not a radical new contribution in my opinion or offering new mechanistic insight..
+
+I would be delighted for the editor and other reviewers to disagree with me!
+
+Reviewer #2
+
+(Remarks to the Author)
+
+Reviewer #3
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #4
+
+(Remarks to the Author)
+All requested corrections have been taken into account.
+As far as I'm concerned, no further corrections are necessary. The article can be published.
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+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+Reviewer #1 (Remarks to the Author):
+‘This is a nicely written paper that is very well presented. I have some concerns about just what a large advance the manuscript represents. That topography causes phenotype-relevant secretome changes is pretty well known (eg https://www.nature.com/articles/s41598-018-25700-5). These secreted factors can drive bone cell activity (https://www.sciencedirect.com/science/article/abs/pii/S0006291X15003083) and that will change ECM as the phenotype of cells change. That ECM s secreted and changes things is also known (https://www.nature.com/articles/s41392-022-00932-0). I am sure there are more aligned references with a good look. Figure 6 is the interesting figure - but, to me, doesn’t; carry the paper to this level as I don’t really learn much about how this happens - I see it does happen (topography driving bone formation and the secretome being osteogenic with ECM strongly involved, and I learn about spatial osteogenesis - but not how e.g through a mechanobiological process.’
+
+Response:
+Our previous work indicated that the nuclear deformation could affect gene expression by modulating transcriptional responsiveness related with chromatin compaction (https://doi.org/10.1038/s41551-023-01053-x). The current work provides additional insight on how nuclear deformation affects the secretome and surrounding extracellular matrix. Additional discussion has been added as below: ‘Here, we found that cells with deformed nuclei exhibited higher expression levels of ECM components and binding proteins that support collagen-enriched ECM organization. This may be related with the changes of chromatin packing induced by nuclear deformation.’21.
+
+This work focuses on the influence of nuclear deformation on secretome changes in MSCs on micropillar structures which has not been previously reported. In the first reference (https://www.nature.com/articles/s41598-018-25700-5), the authors compared the secretome of different cell types, namely kidney perivascular mesenchymal stromal cells (kPSCs) and mesenchymal stromal cells (MSCs), with different cell morphology on different surface topographies. They mentioned nuclear morphology changed on various substrates, however, no further investigation on nuclear deformation was conducted (e.g. quantification of nuclear deformation, GO analysis between groups with different nuclear morphology, etc.). In the second reference (https://www.sciencedirect.com/science/article/pii/S0006291X15003083), the authors investigated the secretome of mechanically stimulated cells. Nuclear deformation was not reported. In the third reference (https://www.nature.com/articles/s41392-022-00932-0), the general secretion profile of MSCs was reviewed, but again the influence of nuclear deformation was not included. All above references have been cited and discussed in the revised manuscript.
+
+To the best of our knowledge, this is the first work that investigated the influence of nuclear deformation on the secretome with both in vitro and in vivo testing. The results indicate that the nuclear deformation caused by micropillar confinement modulated the secretome which regulates extracellular matrix formation of MSCs. Even the previous studies reported the influence of topography on secretome in vitro, none of them investigated the effects in vivo. However, in this study, we explored the impact of the secretome on the transcriptional activity of both non-deformed and deformed nuclei, using spatial transcriptomics on regenerated tissues. Our findings suggest that the in vitro and in vivo experiments share similar mechanisms, likely due to chromatin compaction influenced by nuclear deformation on micropillars. This study highlights the significance of nuclear deformation on the secretome, a process that occurs frequently in vivo but has long been overlooked, and its implications for regenerative engineering. In addition, as pointed
+out by the other reviewers, this work ‘goes much further than most articles on regenerative engineering which makes it a significant work for the field!’. And we believe the revised manuscript has been significantly improved as shown below.
+
+‘Minor points are:
+Figure 1 - where are the many small pores?’
+
+Response
+The zoomed-in images were add in Supplementary Figure S4 to show the small pores.
+
+![Images showing small pores formed on flat and micropillar mPOC/HA implants after 1 and 3 days’ accelerated degradation. Arrows indicate small pores.](page_370_629_849_340.png)
+
+Supplementary Figure S4. Images show the small pores formed on flat and micropillar mPOC/HA implants after 1 and 3 days’ accelerated degradation. Arrows indicate small pores.
+
+‘Figure 2 - is cell number attachment per se - I think of cell adhesions’
+
+Response
+It refers to cell number attached on each sample. We replaced it with ‘number of adhered cells’.
+
+![Bar graph comparing number of adhered cells between Flat and Pillar groups.](page_570_1167_349_246.png)
+Figure 2e. Number of adhered cells after cell seeding on flat and micropillar surfaces. n=5 biological replicates, N.S., no significant difference.
+
+‘Figure 2 - I don’t agree these are filopodia - bit are a mixture of retraction fibres and leading edges - filopodia are very small.’
+
+Response
+We replaced the ‘filopodia’ with ‘mixture of retraction fibers and leading edges’.
+
+![SEM images showing cell adhesions on flat and micropillar surfaces](page_374_613_803_246.png)
+
+Figure 2f. SEM images show the cell adhesions on flat and micropillar mPOC/HA surfaces.
+
+‘Figure 4 - why use osteogenic media if the secretome is going to drive osteogenesis?’
+
+Response
+Building on our previous work, we found that growth medium alone did not stimulate cells on micropillars to initiate osteogenic differentiation. Instead, the micropillars enhanced the cell's response to induction factors, which promoted differentiation. Therefore, in this study, we used osteogenic media as an external stimulus to trigger osteogenesis, with the micropillars acting as a ‘catalyst’ to accelerate differentiation and the osteo-secretome production.
+
+‘Reviewer #2 (Remarks to the Author):
+
+This study assessed the contribution of changes to the secretome on the bone-promoting effect of surface micropillars and also sought to connect this to the known nuclear deformation that occurs when using such surfaces. It builds upon previous work by the authors, and others, showing that specific sizes of micropillar deform the nuclei of cells cultured upon them, and that this alters chromatin state and consequently the fate of the cells- in the context of bone repair, this typically being MSCs and osteogenesis. A newer aspect is the study of changes to the secretome, one mechanism via which the effects may be mediated. Previous studies have shown that the secretome is altered by physical/biomaterial cues such as stiffness and topography, although not yet in advanced detail- this is the first to study these particular topographic designs and osteogenesis. The study compares 5 micron square pillars which are well-known to boost osteogenesis. These are created from mPOC/HA as a suitable osteogenic scaffold. It begins by characterising the
+substrates, confirms changes in cell response, shows that the secretome changes and that this affects cells on flat surfaces. An in vivo calvarial defect model also showed a beneficial effect of the pillars followed by spatial transcriptomics to assess localisation of matrix gene expression. Overall, this is a nice paper with interesting findings that will be useful in the field. Most of the conclusions are well supported by the quality and quantity of data, although there are a few areas of overreach, or where additional information is required as outlined below.'
+
+Response
+
+We appreciate the reviewer’s thorough evaluation of our work and the insightful comments.
+
+‘General comments:
+
+1. Although the paper was well written, the rationale/justification could be better expressed: there is an inconsistent narrative between the introduction and discussion. Is the goal to optimise the design of implants for bone regeneration or conduct basic research into the effect of nuclear morphology on the secretome? The introduction leans toward basic research as the motivation: the choice to use micropillars as a means of deforming the nucleus instead of, say, optical tweezers was partly due to accessibility, and there is little mention of the need for improved implants for bone regeneration. However, the discussion suggests the overall goal is to improve implants for bone regeneration.’
+
+Response
+
+We have revised both introduction and discussion part to emphasize that the goal of this study is to investigate the influence of nuclear deformation on secretome, as well as its implication in bone regeneration in vivo. Various tools can be used for in vitro investigation, however, surface topography is one of the most feasible strategies for tissue regeneration in vivo. Revision of introduction to highlight importance of implant improvement is as below:
+
+‘To manipulate nuclear morphology, various biophysical tools have been developed, including atomic force microscopy (AFM) nanoindentation, optical, magnetic, and acoustic tweezers, microfluidic devices, micropipette aspiration, plate compression, substrate deformation, and surface topography modulation.\(^{8-15}\) Among these methods, regulating the surface topography of materials is more accessible and has broader implications for regenerative engineering. One commonly used approach is the fabrication of pillar structures, which are employed to deform cell nuclei and study nuclear properties such as mechanics and deformability.\(^{16}\) These micropillar designs have been utilized to manipulate various cell functions, including migration, adhesion, proliferation, and differentiation.\(^{17-20}\) A design featuring \(5 \times 5\) \(5 \mu\text{m}^2\) micropillars with \(5\) \(5 \mu\text{m}\) spacing has been shown to significantly enhance the osteogenic differentiation of MSCs, highlighting the considerable potential of surface engineering for advancing bone regeneration.\(^{20,21}\)
+
+A wide range of materials can be used to create micropillar structures, such as poly-L-lactic acid (PLLA), poly(lactide-co-glycolide) (PLGA), OrmoComp (an organic-inorganic hybrid polymer), and methacrylated poly(octamethylene citrate) (mPOC).\(^{20-23}\) Among these options, mPOC is particularly suitable for bone regeneration due to its major component, citrate, which acts as a metabolic factor to enhance the osteogenesis of mesenchymal stromal cells (MSCs).\(^{24}\) Additionally,
+a series of products made from citrate-based biomaterials (CBBs), including Citrelock, Citrefix, and Citregraft, have been cleared by the FDA for musculoskeletal regeneration in patients, further demonstrating the clinical efficacy of CBBs. Implantation of mPOC micropillars in a mouse cranial defect model demonstrated its bone regenerative potential *in vivo.*21 However, the volume of regenerated bone remains limited, highlighting the need for further development of implant to enhance the efficacy of bone regeneration. More importantly, the majority of the new bone does not directly contact the implants; instead, it forms with a noticeable gap between the implant and the regenerated tissue. This observation inspired us to consider that nuclear deformation on micropillar implants may influence surrounding cells through the modulation of their secretomes.*
+
+*2. Further to comment one, the rationale for choosing mPOC/HA given in the introduction was somewhat ambiguous. The rationale for its choice was based on comparison to other materials used to fabricate micropillars, but it wasn’t clear whether the intent of the study was simply to use a suitable material for fundamental investigation or whether it was anticipated that this would for the basis of future orthopaedic implants.*
+
+Response
+
+HA as the primary inorganic component of native bone tissue was combined with mPOC to fabricate the implants to provide clinical option of future orthopaedic implants. The introduction has been revised:
+
+‘Hydroxyapatite (HA) is a naturally occurring mineral form of calcium apatite, widely utilized in bone regeneration due to its exceptional biocompatibility, osteoconductivity, and structural similarity to the mineral component of bone.30 The incorporation of HA with mPOC may combine the advantages of both materials in bone repair, thereby enhancing bone formation and offering a promising clinical option for future orthopedic implants.’
+
+Additional discussion of mPOC/HA was also added:
+
+‘In this study, hydroxyapatite (HA) was incorporated into mPOC to further enhance its regenerative potential, leveraging HA’s well-known osteoconductive properties.48 A 60% HA content was used to fabricate the implant, mimicking the composition of native bone.49 Both *in vitro* and *in vivo* experiments confirmed that the addition of HA significantly improved bone regeneration compared to mPOC alone.21 Moreover, several products made from CBB/HA composites have recently received FDA clearance, highlighting the promising clinical potential of mPOC/HA micropillars for bone regeneration applications.50’
+
+*3. This paper might benefit from more discussion of previous studies that have investigated how biomaterial properties influence the secretome, including ones that have specifically looked at surface microtopographies including:
+• Rosado-Galindo, H. & Domenech, M. Substrate topographies modulate the secretory activity of human bone marrow mesenchymal stem cells. Stem Cell Research & Therapy 14, 208 (2023). DOI: 10.1186/s13287-023-03450-0
+• Leuning, D. et. al. The cytokine secretion profile of mesenchymal stromal cells is determined by surface structure of the microenvironment. Scientific Reports 8, 7716 (2018). DOI: 10.1038/s41598-018-25700-5.*
+Response
+
+The references have been discussed in the manuscript as below:
+
+‘The success of many cell and exosome-based therapies depends on the cellular secretome,\(^{27}\) which can be modulated by surface topography. For example, surfaces featuring grooves, roughness, or spiral patterns have been shown to influence the secretory profile of MSCs, primarily affecting immune regulation.\(^{28}\) Additionally, the cytokine secretion profile of stromal cells, including MSCs and kidney-derived perivascular stromal cells (kPSCs), is closely linked to cell morphology, which is regulated by the unique surface structures.\(^{29}\) Despite reports highlighting the influence of surface topography on secretion, the impact of nuclear morphogenesis, regulated by topography, on cellular secretion remains unclear. Additionally, *in vivo* testing of regeneration is necessary to advance the clinical application of surface engineering.’
+
+‘4. Characterization of physical and chemical properties of flat and micropillar substrates was thorough (Fig 1). One question that remains is how the micropillars change over time due to degradation. Degradation was continuous over time, even after accounting for two ‘bursts’ of degradation. Do the micropillars maintain square geometries? Do they maintain a consistent height? *SEM of micropillars at day 14 of degradation would clarify this.*’
+
+Response
+
+The SEM images and quantification of pillar height were added in Fig. S5. The manuscript was revised as below:
+
+‘The micropillars exhibited slight deformation in both the xy and z directions after degradation, though the changes were not significant (Fig. S5). Additionally, the structures transformed from outward convex to inward concave shapes.’
+
+![SEM images showing micropillar morphology before and after accelerated degradation, and bar graph comparing heights before and after.](page_367_1042_857_324.png)
+
+Supplementary Figure S5. Micropillar morphology change after 14 days accelerated degradation. a. SEM images of micropillars and b. quantification of micropillar height before and after 14 days accelerated degradation.”
+
+Additional discussion was also added:
+
+‘Following accelerated degradation, the micropillars showed slight morphological changes but remained effective in inducing nuclear deformation.’
+‘5. Cells seeded onto micropillars can exhibit multiple nuclear morphological phenotypes, with the nucleus deforming in different ways. For instance, the nucleus may bend around a micropillar or the micropillar may penetrate through the nucleus. Did the authors see any diversity in how the nucleus was deformed?’
+
+Response
+
+Nuclear deformation is influenced by the micropillar arrays. According to our findings and those of others, several parameters primarily affect how the nucleus deforms, including pillar size (ranging from micrometers to nanometers), pillar height, and pillar spacing. When the pillars are small (<350 nm, https://doi.org/10.1038/nnano.2015.88), have low height (<4.6 μm, https://doi.org/10.1016/j.biomaterials.2016.09.023), and small spacing (<3 μm, https://doi.org/10.1038/s41551-023-01053-x), they typically lead to pillar penetration through the nucleus. In this study, we fabricated micropillars with dimensions of \( 5 \times 5 \) μm\(^2\) and a height of approximately 8 μm, which caused most of the nuclei to bend around the micropillars. However, the bent nuclei exhibited diverse shapes, with some resembling a ‘X’ and others a ‘T’ shape. Additional discussion on pattern design to further regulate nuclear shape has been added to the revised manuscript, as outlined below:
+
+‘Pillar structures, a common surface topography, have been extensively used to study various cell behaviors, including migration, mechanics, engulfment, proliferation, and differentiation.\( ^{19,22,51-53} \) Depending on the material properties and pattern design, cells may either reside on top of or between the pillar structures, and in some cases, the pillars can even penetrate through the cells.\( ^{17,34} \) In this study, due to the stiffness and design of the mPOC/HA micropillars, the nuclei predominantly settle between the micropillars and adopt shapes such as 'T' or 'X'.’
+
+‘6. Regarding Fig. 2j, can the authors elaborate on why osteogenic differentiation was performed on a substrate with both flat and micropillar areas? The secretomes from cells on each topography would mix and influence differentiation. Additionally, cells must have been removed/trypsinized from the substrate for subsequent western blotting - how were cells on each topography kept separate during removal from the substrate?’
+
+Response
+
+We employed various pattern designs for our experiments. For analyses such as ALP activity, western blotting, and in vivo implantation, we used substrates with either a completely flat surface or fully micropillared structure. For ALP imaging, we adopted a half/half design, where one half of the substrate was flat and the other half had micropillars. This design was initially intended to minimize environmental variation caused by culturing in different wells. However, we agree with the reviewer’s concern that the secretomes could influence and compromise the results. Therefore, we repeated the experiment using only the complete flat and complete micropillar substrates. The revised figure is shown below:
+Figure 2j. ALP staining of hMSCs on flat and micropillar surfaces after 7 d induction.
+
+‘7. Athymic nude mice were used to prevent immune rejection of the human MSCs. Nude mice that lack T cells still retain an innate immune system, including macrophages that can respond to foreign bodies (Rodriguez, A. et. al . The foreign body reaction in T-cell-deficient mice. J. Biomed. Mater. Res. A 90, 106-13 (2009). DOI: 10.1002/jbm.a.32050). Could macrophage activity alter the observed effects of substrate topography on bone regeneration?’
+
+Response
+
+We really appreciate the reviewer’s valuable comments. To check the macrophage activation, we stained several macrophage markers including F4/80 (pan macrophage marker), CD 86 (M1 macrophage marker), and CD 163 (M2 macrophage marker). Additional Figure S15 and discussion has been added in the revised manuscript.
+
+‘It has been reported that athymic nude mice retain an innate immune system, including macrophages, which contribute to bone regeneration.40 Therefore, we further assessed macrophage activation in the regenerated tissue by staining for three markers: F4/80 (a pan-macrophage marker), CD86 (an M1 macrophage marker), and CD163 (an M2 macrophage marker), to evaluate macrophage polarization (Fig. S15).35 The results indicate a slight increase in overall macrophage expression and a decrease in the M1/M2 ratio; however, these changes were not statistically significant.’
+
+Supplementary Figure S15. Influence of micropillar implant on macrophage activation. a. Representative staining images of F4/80, CD86, and CD163 in regenerated tissues with flat and
+micropillar implants. Quantification of b. F4/80 and c. ratio of CD86+/CD163+ cells for inflammation evaluation of the implants. N.S.: no significant difference, n=5.
+
+Additional discussion was also added:
+
+‘Macrophage activation showed a slight, though not statistically significant, difference between the two groups. Given the compromised immune response in athymic nude mice, additional testing in normal mice may be necessary to fully assess the impact of micropillar implants on immune modulation.’
+
+‘8. Please take care to better discriminate between the data that shows a paracrine response in vitro and a matricine response in vivo- technically the data does not directly show paracrine signalling in response to the pillars in the mouse model and so the abstract/discussion may over-reach in places. For example, in the abstract "These findings indicate that micropillars not only enhance the osteogenic differentiation of human mesenchymal stromal cells (hMSCs) but also modulate the secretome, thereby influencing the fate of surrounding cells through paracrine effects." Whereas the discussion more accurately summarises the results saying “…nuclear deformation induced by micropillars may promote osteogenesis in neighboring cells via matricrine effects.” The results also indicate matricine effects in vivo: micropillars upregulate ECM proteins in vitro and ECM-related genes in vivo. However, the link between micropillars and altered paracrine signaling (i.e. direct cell-cell signalling) in vivo is not well established. The distinction between paracrine and matricine effects should be made clearer.’
+
+Response
+
+We appreciate the reviewer for pointing this out. We have replaced "paracrine" with "matricrine," as our results primarily suggest that nuclear deformation influences the secretion of proteins regulating ECM structure and organization, rather than directly affecting neighboring cells.
+
+‘9. Whilst the introduction emphasises nuclear mechanotransduction and chromatin modification, the data in this study does not actually address these mechanisms. Relating to comment 1, this aspect should be clarified to avoid misinterpretation that this study is attempting to directly show a link between chromatin modification and the paracrine effects.’
+
+Response
+
+We have removed the redundant description of mechanotransduction and chromatin modification in the introduction part and emphasized that the focus is modulation of secretome via nuclear deformation and its regenerative application in vivo.
+
+‘10. Did the authors consider histological staining of specific proteins within tissue sections? This could provide protein level validation of the in vitro secretome findings – for instance, upregulated proteins involved in ossification identified in the in vitro secretome could be correlated with their spatial distribution in vivo.’
+
+Response
+We appreciate the reviewer’s insightful comments. Based on the in vitro secretome and in vivo spatial transcriptomic results, collagen was the only component that showed increased expression at both the gene and protein levels. Since collagen distribution is clearly visualized through trichrome staining in Figure 5e, we did not conduct additional staining. However, we have added further discussion in the revised manuscript to highlight the consistency between the in vitro and in vivo results.
+
+‘Compared to flat implants, mPOC/HA micropillars promoted bone formation and the expression of osteogenic markers in regenerated tissues, consistent with the results observed for mPOC scaffolds.’21 This suggests that nuclear deformation induced by the micropillars can enhance bone regeneration, regardless of the implant material. This could be attributed to the osteogenic differentiation of cells in direct contact with the micropillars, as well as their secretion, which promotes ECM protein expression. Histological staining further supports this, showing a thicker layer of collagen-enriched regenerated tissue in the presence of the micropillar implant, consistent with the secretome results.’
+
+‘Specific/minor comments
+
+11. The text in many figures, for example the secretome and proteome data, is very small. Many scale bars are also quite small. It would improve readability if the font size could be increased.’
+
+Response
+The text and scale bars have been enlarged.
+
+‘12. Supplementary Figure S11 needs more labels: it is impossible to determine what anything is.’
+
+Response
+The Supplementary Figure S11 has been labelled as below:
+
+![CT images of skull with labeled defect start, new bone, and defect end positions at various time points](page_384_1017_1096_482.png)
+Supplementary Figure S12. Stack images show the regenerated tissue treated with flat (left) and micropillar (right) implants. The images represent the skull tissue scanned from 0 to 6 mm with 0.25 mm intervals. Defect start and Defect end refers to the first and last image showing the defect.
+
+‘13. Methods, in vivo implantation: “…a larger mPOC film…”. Should this read ‘mPOC/HA’?’
+
+Response
+We used a larger mPOC film for securing the implant for the following reasons: 1) mPOC is relatively flexible compared to mPOC/HA, and the larger film can be bent to fit the curvature of the mouse skull to secure the implant position. 2) mPOC is transparent, allowing us to clearly observe the position of the mPOC/HA implants after the securing film is applied.
+
+‘14. Discussion, second sentence: “mesenchymal stem cells”. According to more recent accepted terminology, this should read ‘mesenchymal stromal cells’.’
+
+Response
+We thank the reviewer for pointing it out. The ‘mesenchymal stem cells’ have been replaced by ‘mesenchymal stromal cells’.
+
+‘Reviewer #3 (Remarks to the Author):
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.’
+
+Response
+We appreciate the reviewer’s insightful comments.
+
+‘Reviewer #4 (Remarks to the Author):
+In this article, the authors demonstrate the ability of mPOC/HA micropillar scaffolds to enhance bone regeneration. As previously demonstrated by the team (Wang et al., 2023), the micropillar scaffolds changes the morphology of cell nuclei, triggering chromatin reprogramming. Here, they demonstrate that nuclear morphology modification enhances osteoblastic differentiation and regulates ECM formation via modulation of the hMSC secretome. This paper combines material characterization, morphological evaluation (SEM, IF), characterization of osteoblastic differentiation (PAL activity, Western Blot), secretome and proteome analysis of cells on scaffold prior to implantation (in vitro). As well as an in-depth evaluation of implants with cells after implantation -in vivo (microCT, histology, IHC, Spatial Transcriptomic).
+This work does more than demonstrate a material's ability to recreate bone; it bring out the cellular and molecular machinery involved in this process. In this sense, it goes much further than most articles on regenerative engineering. Which makes it a significant work for the field!’
+
+Response
+We appreciate the reviewer’s highly evaluation of our work and the insightful comments!
+'The interpretation of the role of LMPs (last paragraph of the results) on the site of calvarial defect in not correct in my opinion. To generate bone, you need osteoblasts. They are generated by the differentiation of MSC. “LMPs are identified as the late stage of MSCs through osteogenic differentiation”. Therefore, the creation of osteoblasts (which will mineralize) contributes directly to osteogenesis and bone regeneration.'
+
+Response
+
+We agree with the reviewer’s opinion and believe our description is not in conflict with the comment. In the manuscript, we stated: “The most abundant cell type in regenerated tissues was late mesenchymal progenitor cells (LMPs), followed by MSCs and fibroblasts (Fig. 6e). Small proportions of MSC-descendant osteolineage cells (OLCs), osteocytes, osteoblasts, and chondrocytes were also present.” The small proportion of osteoblasts can be attributed to the relatively low new bone volume in the tissue slides used for spatial transcriptomic analysis. Based on previous report (https://doi.org/10.1002/jbmr.4882), the LMPs have high expression of marker genes associated with osteoblasts, and their maturation occurs during osteoblast differentiation. Additionally, GO analysis revealed that LMPs and osteoblasts contribute to ECM organization and biomineral tissue development, respectively (Fig. 6g and Fig. R1). This is in consistent with bone mineralization process, cells (LMPs) assembled collagen enriched ECM followed by cells (osteoblasts) accumulate ions and initiate mineralization.
+
+![Bar chart showing enriched processes associated with osteoblasts compared with other cell lineages](page_370_1042_579_246.png)
+
+Figure R1. Top enriched processes associated with osteoblasts compared with other cell lineages.
+
+‘Although the methods used in this work provide relevant evidence, the explanation of many of the methods is not clear enough to allow these experiments to be reproduced. Analysis of the secretome and proteome has several significant flaws:
+
+- For sample preparation, peptide concentration is quantifies using an unsuitable kit, as it is designed for proteins and not peptides.’
+
+Response
+
+We appreciate the reviewer for pointing it out. It was our writing mistake. The kit was used to measure the concentration of proteins so we can load equal amount of protein and do digestion. The writing has been revised as below:
+'Secretome sample preparation
+For secretomic testing, hMSCs were seeded at 20,000 cells/cm² and cultured in osteogenic induction medium for 3 weeks followed by serum-free medium treatment for 2 d. Then the cell culture medium was collected for analysis. We developed an optimized protocol for processing large-volume secretome samples (≥15 mL) to increase the dynamic range of protein coverage by removing residual serum and concentrate low-abundance secreted proteins for LC-MS analysis.66 Secretome samples were first processed using a 50 kDa molecular weight cutoff (MWCO) Amicon Ultra-15 centrifugal filter Ultracel, Merck (UFC905008) to separate the sample into two fractions: the filtrate containing proteins smaller than 50 kDa and the concentrate with proteins larger than 50 kDa as per the manufacturer’s protocol.66,67 The concentrate was depleted using High-Select Midi Spin Columns (A36367, Thermo Fisher Scientific), and the depleted flowthrough was recovered by centrifugation as per protocol provided by Thermo.68,69 Both the filtrate and the depleted concentrate were subjected to acetone/trichloroacetic acid (TCA) protein precipitation to isolate the proteins.66,67 The resulting protein pellets were solubilized (8 M urea and 400 mM ammonium bicarbonate), combined, and quantified using the BCA and micro-BCA protein assay kits (Thermo Scientific, Ref: 23227, Ref: 23235).70 Disulfide bonds were reduced by 4 mM dithiothreitol and incubated for 45 minutes at 55 °C. Sulfhydryl groups were alkylated by addition of 16 mM iodoacetamide and incubated for 45 minutes at 25 °C shielded from light. Samples were diluted 4-fold with ammonium bicarbonate to reduce the urea concentration below 2 M. Protein digestion was performed by addition of trypsin (MS-grade, Promega) at a 1:50 ratio (enzyme:substrate) and incubated overnight at 37 °C. Digestion was halted with the addition of 10 % formic acid (FA) to a final concentration of 0.5%. Peptides were desalted with Pierce C18 spin columns (Ref:89870), dried by vacuum centrifugation, and stored at -20 °C. Peptides were resuspended in 5% ACN(Acetonitrile) / 0.1% FA for LC-MS/MS analysis.
+
+Proteome sample preparation
+For proteomic testing, hMSCs were seeded at 20,000 cells/cm² and cultured in osteogenic induction medium for 3 weeks followed by serum-free medium treatment for 2 d. Cells were lysed using a cell lysis buffer containing 0.5% SDS, 50 mM ammonium bicarbonate (AmBic), 50 mM NaCl, and Halt protease inhibitor. Protein precipitation was performed using acetone/TCA, and the resulting protein pellets were quantified using the BCA and Micro BCA protein assay kits (Thermo Scientific, Catalog No. 23227, 23235) and 100ug protein per sample was subjected in-solution digestion.70 The pellets were resuspended in 100 µl of re-suspension buffer (8 M urea, 400 mM ammonium bicarbonate). Disulfide bonds were reduced by adding 4 mM dithiothreitol (DTT), followed by incubation at 55°C for 45 minutes. Sulfhydryl groups were alkylated by adding 16 mM iodoacetamide, and the reaction was incubated for 45 minutes at 25°C, shielded from light. To reduce the urea concentration below 2 M, the samples were diluted 4-fold with ammonium bicarbonate. Trypsin (MS-grade, Promega) was then added at a 1:50 enzyme-to-substrate ratio, and digestion was carried out overnight at 37°C. The digestion was terminated by the addition of 10% formic acid to a final concentration of 0.5%. Peptides were desalted using Pierce C18 spin columns (Ref:89870), dried by vacuum centrifugation, and resuspended (1µg/µl) in 5% acetonitrile (ACN) and 0.1% formic acid (FA) in preparation for LC-MS analysis.'
+‘- For secretome sample preparation, a serum-free culture must be performed 48 hours before sampling the culture medium, in order to remove the proteins contained in the serum. The method used in the authors (molecular weight cut off filter) may affect secretome proteins, not just serum proteins, and does not eliminate small serum proteins.’
+
+Response
+We did perform 48 h serum-free medium culture before collecting the medium. The information was missed in the original writing and has been added in the revised manuscript (please refer to the responses provided above). In addition, the scheme for secretome sample preparation is provided for further clarification as follows:
+
+[Figure Redacted]
+
+Figure R2. Scheme of secretome sample preparation.
+
+‘- Label-free quantification is problematic, partly because of the poor peptides concentration quantification, but mainly because the analysis was carried out with n=3, which is too small for label-free. “Missing values were filtered to keep only proteins quantified in at least 2 samples per group.” Making statistics with n=2 is not correct! If the number of sample by group can't be increased, you need to be more stringent about the selection parameters: keep only the proteins present in the 3 samples per group, and choose a log2FC of 1.5 and an adjusted p-value < 0.01.’
+
+Response
+We agree with the statement that n=2 is insufficient for statistical tests, therefore, we removed differentially expressed proteins (DEP) not quantified in all samples. Out of the 80 DEP in the secretome analysis, 50 (62.5%) were quantified in all samples and kept for downstream analyses. From the 267 DEP found between cells cultured on flat and micropillars mPOC/HA scaffolds, we
+kept 100 proteins that were quantified in all samples. Upon reanalyzing the data, we obtained the same results; however, all figures have been replotted for clarity.
+
+In our proteomics study, we have chosen to identify significantly differentially expressed proteins using a p-value <0.05 and a fold change >2. This decision is based on several factors. Firstly, a fold change >2 ensures that we focus on proteins with substantial and biologically meaningful differences in expression. Secondly, while we acknowledge the importance of adjusted p-values for controlling the false discovery rate, our small sample size (3 per group) limits the power to detect differences. With a small sample size, the power to detect differences is already limited, and using a more stringent threshold might result in missing biologically relevant proteins (https://doi.org/10.1002/pmic.201600044 and https://doi.org/10.1039/D0MO00087F). Using a p-value <0.05 strikes a balance between identifying significant changes and maintaining a manageable list of candidates for further investigation. This approach is also supported by precedent in literature (https://doi.org/10.3390/ijms231810452), where similar thresholds have been used in studies with small sample sizes. We believe this methodology allows us to identify strong candidates for validation in larger, follow-up studies.
+
+The Fig. 3 and Fig S 8-12 have been replotted as below:
+
+![Panel of plots and diagrams showing proteomics analysis results, including PCA plots, volcano plots, pathway enrichment, and network analysis](page_246_670_1157_1042.png)
+Figure 3. Secretome of hMSCs on flat and micropillar mPOC/HA surfaces. a. PCA plot of differentially expressed proteins secreted by hMSCs on flat and micropillars. Cyan: flat; Red: micropillar. b. Volcano plot of proteins secreted by hMSCs seeded on micropillars compared to the flat surface. Blue dots and orange dots indicate significantly downregulated and upregulated proteins secreted by cells on micropillars compared to those on flat surface. Grey dots indicate non-significantly changed proteins. A threshold of expression greater than 2 times fold-change with p<0.05 was considered to be significant. Proteins that are related with collagen-ECM pathways are labelled. c. Top 4 significantly enriched GO and Pathways based on their adjusted p-values. d. The most significant enriched GO terms of the biological domain with respect to biological process. e. Heatmap of proteins that are related with collagen-containing extracellular matrix and ossification. F indicates flat samples and P indicates pillar samples, n=3 biological replicates for each group. f. The linkages of proteins and GO terms in biological process related with collagen fibers, ECM, and ossification as a network. g. Heatmap of top 15 enriched terms plotted based on Reactome pathway analysis.
+
+Supplementary Figure S8. GO analysis shows the biological domain with respect to the cellular component. a. Hierarchical clustering of enriched terms. It relies on the pairwise similarities of the enriched terms. The agglomeration method was average. b. The linkages of proteins and GO terms as a network. c. The heat-plot display the relationships between proteins and enriched terms. d. the protein overlapping among different GO gene sets.
+Supplementary Figure S9. GO analysis shows the biological domain with respect to the molecular function. a. Hierarchical clustering of enriched terms. b. The linkages of proteins and GO terms as a network. c. The heat-plot display the relationships between proteins and enriched terms. d. the protein overlapping among different GO gene sets.
+
+Supplementary Figure S10. GO analysis shows the biological domain with respect to the biological process. a. The heat-plot display the relationships between proteins and enriched terms. b. the protein overlapping among different GO gene sets.
+Supplementary Figure S11. Reactome pathway analysis. Top 15 most significant enriched pathways.
+
+Supplementary Figure S12. Proteome analysis of cells cultured on flat and micropillar mPOC/HA scaffolds. a. PCA plot and b. volcano plot of the proteins collected inside cells. c. Heatmap of all significantly differently expressed proteins on flat and micropillar samples. d. Plot of the top 15 most significant enriched pathways based on reactome pathway analysis.
+The manuscript has been revised as follows:
+
+‘Database searching and Label free quantification
+The samples were acquired on mass spec and the data were searched against a human database using the MaxQuant application.71 Label-Free Quantification (LFQ) was obtained by LFQ MS1 intensity. Data was filtered to accept proteins with a minimum of 2 unique peptides. Search parameters included a fixed modification of cysteine carbamidomethylation, and variable modifications of methionine oxidation, deamidated asparagine and aspartic acid, and acetylated protein N-termini.
+
+Data analysis
+The ‘proteinGroups’ output file from MaxQuant was imported into Perseus software for data preprocessing and statistical analysis.72 Intensities were Log2 transformed to achieve a normal distribution of the data and scaled using median subtraction normalization. Differentially expressed proteins were determined by doing a non-paired Student t-Test. Proteins quantified in all samples (i.e. with non-missing values) with p < 0.05 and FC \( \geq 2 \) were considered significant. Downstream analyses and visualizations were done using RStudio software (R version 4.3.2, RStudio version 2024.09.0). Principal component analysis (PCA) was done using ‘prcomp’ R function to visualize the ability of the differential protein expression to distinguish between biological conditions. Heatmap plot was built using ‘ComplexHeatmap’ R package. GO and Pathways enrichment analysis was done using ‘clusterProfiler’ R package and annotations with adjusted p-values (FDR, Benjamini-Hochberg) < 0.05 were considered significant.73 Additional used R packages included ‘org.Hs.eg.db’ for human gene annotations and ‘enrichplot’ for visualization. This analysis considered the entire set of human protein-coding genes as the reference background.’
+
+‘Minor comments:
+In the results section, in the paragraph “Microfillar modulates the secretome of hMSCs that regulate ECM formation”, PCA term should be deleted from the sentence, as unlike the volcano plot, this element gives no indication of influence of nuclear deformation on protein expression.’
+Response
+The PCA term has been deleted.
+
+‘In the paragraph “mPOC/HA picropillar implant promotes bone formation in vivo”, the comparison of the results presented in this article with those of the previous article (mPOC alone) should be moved in the discussion.’
+Response
+The sentence “Comparing this to our previous study using mPOC alone, the integration of HA clearly enhanced bone regeneration efficacy *in vivo*.” has been revised and moved to the discussion.
+
+‘The last sentence of the paragraph “microfillar implants facilitated bone regeneration in vivo ...” is an interpretation and should be moved to the discussion.’
+Response
+The last sentence “Thus, the results indicate that micropillar implants can facilitate skull tissue regeneration by promoting the differentiation of MSCs and ECM organization via paracrine effects.” has been revised and moved to the discussion.
+
+‘A longer discussion would be appreciated. The exchange surface was never mentioned, although the presence of microfillars on the material considerably increases the exchange surface between the scaffold (mPOC/HA) and the cells, which may help to explain the differences in results between the flat scaffold and the microfillar scaffold. The number of cell seeded per scaffold could also be discussed. Indeed, most tissue engineering articles testing MSCs with scaffold in vivo seed many more cells (on the order of 100,000 to 1,000,000/cm²). In your conditions (4mm diameter implant), 5000 cells per cm² may not be enough for the paracrine effect to be significant.’
+
+Response
+Additional discussion of the increased surface area was added as below:
+
+‘Following accelerated degradation, the micropillars showed slight morphological changes but remained effective in inducing nuclear deformation. The slow degradation may account for the minimal differences in weight loss and calcium release between flat and pillar implants, despite the overall increase in surface area of the micropillars. Based on our previous study, the restricted cell spreading on micropillars may limit the impact of the increased surface area, as the expression of vinculin remained similar on both flat and micropillar surfaces.21’
+
+The cell seeding density on the implant was around 160,000 cells/cm² which is comparable to most of other studies. The information has been added in the manuscript as below:
+
+‘The implants were seeded with 20,000 cells per implant (approximately 160,000 cells/cm²) in growth medium for 1 day before being implanted into the defects.’
+
+‘Many elements are missing from the materials and methods.’
+
+Response
+We have provided a more detailed description of the materials and methods section in the revised manuscript, in response to the reviewer’s comments.
+
+‘• Degradation and calcium release
+Parameters of ICP-MSC are not explain, nor is the method for calculating accumulated calcium.’
+
+Response
+The detailed methodology for ICP-MS and the calculation of accumulated calcium have been included in the revised manuscript as follows:
+
+‘Quantification of calcium (Ca) was accomplished using ICP-MS of acid digested samples. Specifically, 100 uL of the PBS elution was digested in 250 uL nitric acid (HNO₃, > 69%, Thermo Fisher Scientific, Waltham, MA, USA) at 65 °C for 4 hours. Ultra-pure H₂O (18.2 MΩ·cm) was then added to produce a final solution of 2.5% nitric acid (v/v) in a total volume of 10 mL. A quantitative standard was made using a 1000 ug/mL Ca elemental standard (Inorganic Ventures,
+Christiansburg, VA, USA) which was diluted to create a 1000 ng/g Ca standard in 2.5% nitric acid (v/v) in a total sample volume of 50 mL. A solution of 2.5% nitric acid (v/v) was used as the calibration blank. ICP-MS was performed on a computer-controlled (QTEGRA software) Thermo iCapQ ICP-MS (Thermo Fisher Scientific, Waltham, MA, USA) operating in KED mode and equipped with a ESI SC-2DX PrepFAST autosampler (Omaha, NE, USA). Nickle skimmer and sample cones were used from Thermo Scientific (part numbers 1311870 and 3600812). Internal standard was added inline using the prepFAST system and consisted of 1 ng/mL of a mixed element solution containing Bi, In, \(^{6}\)Li, Sc, Tb, Y (IV-ICPMS-71D from Inorganic Ventures). Each sample was acquired using 1 survey run (10 sweeps) and 3 main (peak jumping) runs (40 sweeps). The isotopes selected for analysis were \(^{44}\)Ca and \(^{45}\)Sc (chosen as an internal standard for data interpolation and machine stability). Instrument performance is optimized daily through autotuning followed by verification via a performance report (passing manufacturer specifications). Accumulated calcium amount was calculated based on the sum of released calcium at each time point measured by ICP-MS from the same sample.’
+
+‘Cell culture
+The cell culture conditions (cell density, culture medium, time) for the various experiments (e.g.: secretome and proteomic analysis, in vivo implantation) are not clearly explain. This section should be explained.’
+
+Response
+
+The detail of cell culture conditions was explained in the revised manuscript as follows:
+
+‘To test cell attachment, hMSCs were seeded at 5,000 cells/cm\(^2\) and cultured for 3 h followed by PBS rinsing to remove unattached cells. The attached cells were then trypsinized and collected for cell counting. To check cellular and nuclear morphology, hMSCs were seeded at 5,000 cells/cm\(^2\) and cultured in growth medium for 1 d before fixation.’
+
+‘To check cell viability, hMSCs were seeded at 5,000 cells/cm\(^2\) and cultured in growth medium for 3 d.’
+
+‘For secretomic test, hMSCs were seeded at 20,000 cells/cm\(^2\) and cultured in osteogenic induction medium for 3 weeks followed by serum-free medium treatment for 2 d. Then the cell culture medium was collected for analysis.’
+
+‘For proteomic test, hMSCs were seeded at 20,000 cells/cm\(^2\) and cultured in osteogenic induction medium for 3 weeks followed by serum-free medium treatment for 2 d.’
+
+‘The implants were seeded with 20,000 cells per implant (approximately 160,000 cells/cm\(^2\)) in growth medium for 1 day before being implanted into the defects.’
+
+‘Experiments such as live/dead, MTT or DNA assays should appear in a different section of the cell culture.’
+
+Response
+
+We added a new section regarding live/dead, MTT, and Picogreen assay as follows:
+
+‘Cell viability, metabolic activity, and proliferation
+To check cell viability, hMSCs were seeded at 5,000 cells/cm² and cultured in growth medium for 3 d. Live/dead staining (Thermo Fisher, L3224) was performed to assess the viability of hMSCs on flat and micropillar surfaces. Briefly, a mixture of 2 μM calcein AM and 4 μM EthD-1 working solution was added to the cells and incubated for 30 minutes at room temperature, followed by rinsing with PBS. The cells were then imaged using a Nikon Eclipse Ti2 microscope. The MTT assay (Thermo Fisher, V13154) was used to evaluate the metabolic activity of the cells. Cells cultured on flat and micropillar surfaces in a 24-well plate were incubated with 500 μL of 1.1 mM MTT solution (diluted in medium) at 37°C for 3 hours. An empty well without cells served as the background reading. After incubation, 125 μL of solution was removed from each well, and 250 μL of DMSO was added with thorough mixing. After a 10-minute incubation at 37°C, 50 μL of the solution from each well was transferred to a 96-well plate, and absorbance was measured at 540 nm using a Cytation 5 cell imaging multimode reader (Biotek). The Picogreen assay (Thermo Fisher, P7589) was performed to assess cell proliferation according to the manufacturer’s protocol. Briefly, a standard curve ranging from 10-1000 ng/mL dsDNA was prepared to calculate DNA content in the samples. Cells on flat and micropillar surfaces, fabricated in a 24-well plate, were lysed using 200 μL lysis solution (10 mM Tris pH 8, 1 mM EDTA, and 0.2% Triton X-100). The solution was then diluted with TE buffer (10 mM Tris-HCl, 1 mM EDTA, pH 7.5) to a final volume of 300 μL. Next, 100 μL of the Quant-iTTM PicoGreen™ dsDNA Reagent working solution was added to each sample. The samples were incubated for 5 minutes at room temperature, protected from light. Finally, 50 μL of the final solution from each well was transferred to a 96-well plate, and fluorescence was measured using the Cytation 5 (ex/em: 480/520). DNA content in each sample was then calculated using the standard curve.’
+
+‘The manufacture’s protocol of MTT recommends measuring absorbance at 570mm. However, in figure 2.h., absorbance was indicated at 540mm. was this a mistake?’
+
+Response
+
+In this study, we used DMSO instead of SDS-HCl solution for test. Based on manufacture’s protocol, the absorbance should be read at 540 nm rather than 570 nm. More detail of MTT assay has been added in the revised manuscript as follows:
+
+‘The MTT assay (Thermo Fisher, V13154) was used to evaluate the metabolic activity of the cells. Cells cultured on flat and micropillar surfaces in a 24-well plate were incubated with 500 μL of 1.1 mM MTT solution (diluted in medium) at 37°C for 3 hours. An empty well without cells served as the background reading. After incubation, 125 μL of solution was removed from each well, and 250 μL of DMSO was added with thorough mixing. After a 10-minute incubation at 37°C, 50 μL of the solution from each well was transferred to a 96-well plate, and absorbance was measured at 540 nm using a Cytation 5 cell imaging multimode reader (Biotek).’
+
+‘Immunofluorescence and microscopy
+
+For most of the fluorescence images (fig 2a. 2g, fig 4f and fig 5b), labelling methods are not explained (nuclear and F-actin markers, secondary antibody for collagen). The microscope used to acquire these images is not mention.’
+
+Response
+
+A new section of Immunofluorescence and microscopy has been added in the revised manuscript as follows:
+‘Immunofluorescence and microscopy
+F-actin fibers were stained according to previous report.\(^{65}\) Briefly, cells cultured on flat and micropillar surfaces were fixed with 4% paraformaldehyde and rinsed with PBS. The cells were then permeabilized with 0.2% Triton X-100 and rinsed with PBS. Blocking was performed using a 1% BSA solution. Cell nuclei were stained with 1 \( \mu \)M SYTOX™ Green (Thermo Fisher, S7020), and F-actin was stained with Alexa Fluor™ 594 conjugated phalloidin (Invitrogen, A12381, 1:40 dilution). For collagen staining, cells were fixed, permeabilized, and blocked as described above. They were then incubated overnight at 4\(^\circ\)C with an anti-collagen antibody (Abcam, ab36064, 1:100 dilution). The following day, after rinsing with PBS, the samples were stained with goat anti-rabbit IgG secondary antibody (Invitrogen, A11034, 1:1000 dilution) and DAPI (1:1000 dilution) at room temperature for 1 hour. After additional PBS rinsing, the samples were ready for imaging. All immunofluorescent images were acquired using a Nikon Eclipse Ti2 microscope.’
+
+‘For figure 4.h, the method used to produce and acquire these images (EDS and Ca, P deposition) is not mention.’
+
+Response
+
+The method of EDS imaging has been added as below in the revised manuscript:
+
+‘Additionally, cells on transwell were imaged using SEM, and EDS analysis was performed to evaluate the calcium and phosphate deposition. Briefly, the transwell samples underwent the same dehydration and coating procedures as described above, followed by SEM imaging. Calcium and phosphate were selected for EDS analysis using AZtec software (Oxford Instruments). Elemental mapping was performed under the following conditions: 15 kV acceleration voltage, 30%-50% deadtime, 1 frame count, 2048 channels, 256 resolution, and 100 \( \mu \)s pixel dwell time.’
+
+‘• Osteogenic differentiation
+For Western Blot, dilution of all antibodies is not mention.’
+
+Response
+
+The references and dilutions of the antibodies have been added as below in the revised manuscript:
+
+‘Afterward, membranes were blocked with 5% milk and incubated with primary antibodies (including GAPDH from Abcam, ab181602, 1:5000 dilution; OCN from Cell Signaling, 59757T, 1:500 dilution; and RUNX2 from Santa Cruz, sc-21742, 1:200 dilution) overnight at 4 \(^\circ\)C with gentle shaking.’
+
+‘• Secretome sample preparation
+Trypsin digestion is mention twice.’
+
+Response
+
+The redundant trypsin digestion was removed.
+
+‘• Proteome sample preparation
+Trypsin digestion is mention twice.'
+Response
+The redundant trypsin digestion was removed.
+
+‘• Transwell assay :
+Secondary antibody for collagen staining should be mentioned. All dilution or concentration used should be mentioned.’
+Response
+The secondary antibody and dilution information have been added as below in the revised manuscript:
+
+‘For collagen staining, cells were fixed, permeabilized, and blocked as described above. They were then incubated overnight at 4°C with an anti-collagen antibody (Abcam, ab36064, 1:100 dilution). The following day, after rinsing with PBS, the samples were stained with goat anti-rabbit IgG secondary antibody (Invitrogen, A11034, 1:1000 dilution) and DAPI (1:1000 dilution) at room temperature for 1 hour. After additional PBS rinsing, the samples were ready for imaging. All immunofluorescent images were acquired using a Nikon Eclipse Ti2 microscope.’
+
+‘• In vivo implantation
+Tool used to create defect should be add.’
+Response
+The information has been added in the revised manuscript as follows:
+
+‘Two critical-sized defects were created on the left and right sides of the skull of each animal using a 4 mm trephine under continuous normal saline irrigation to prevent tissue thermal injury (Dremel® USA, Robert Bosch Tool Corp), followed by the implantation of hMSCs seeded onto flat and micropillar scaffolds, respectively.’
+
+‘• MicroCT
+Here, reference is made to Vi: the initial volume of the defect. How was Vi measured? If mice are scanned at Vi, are they the same as those at Vf? If so, please indicate how the mice were anaesthetized for microCT.’
+Response
+Vi was measured via microCT scanning at 48 hours post-surgery, followed by 3D reconstruction and analysis using Amira 3D software (Thermo Scientific). The same animal was scanned at multiple time points to monitor the regeneration of the skull bone. The animal was sedated by inhaling 1-1.5% isoflurane during the microCT scanning. The method has been revised as follows:
+
+‘Micro-CT: Micro-CT images of cranial were performed on the XCUBE (Molecubes NV) by the Integrated Small Animal Imaging Research Resource (iSAIRR) at The University of Chicago. The animal was sedated with 1-1.5% isoflurane inhalation during the microCT scanning. Spiral high-resolution computed tomography acquisitions were performed with an X-ray source of 50 kVp and 440 μA. Volumetric computed tomography images were reconstructed by applying the iterative
+image space reconstruction algorithm (ISRA) in a \(400 \times 400 \times 370\) format with voxel dimensions of \(100 \times 100 \times 100\ \mu m^3\). The same animal was scanned at multiple time points to monitor the regeneration of the skull bone. An Amira software (Thermo Scientific) was used for 3D reconstruction of the skull tissue and to analyse the bone formation in the defect area. Scale bars were used to standardize the images. Baseline imaging and defect volume calculations were performed 48 hours postoperatively, serving as a standard for comparing all subsequent measurements of residual defect volume. Defect recovery is defined as \((Vi - Vd)/Vi \times 100\%\), where Vi and Vd represent defect volume at initial and designed timepoints, respectively.'
+
+• Histology analysis
+
+References of the anti-OCN and anti-OPN antibodies are not given, nor are their dilutions.'
+
+Response
+
+The references and dilutions of anti-OCN and anti-OPN antibodies were added as below:
+
+'Regenerated tissue thickness was measured using ImageJ, and osteogenesis was evaluated via IHC staining for key osteogenic markers, including OCN (Cell signalling, 59757T, 1:200 dilution) and OPN (Santa Cruz, sc-21742, 1:100 dilution).'
+Reviewer #1 (Remarks to the Author):
+
+I thank the authors for responding to my comments and I have read the reviews of the other reviewers - and read the revised ms.
+I am sorry to say that my opinion hasn't really changed.
+- Micropillars changes nuclear morphology and enhance osteogenesis - this is known and there is, of course, much less insight here than in the original Nature Biomedical Engineering paper on epigenetics.
+- This causes a regenerative change in cell secretome in vitro with changes in ECM proteins - I think this is sensible/interesting but not radical.
+- The materials, seeded with MSCs, provide greater in vivo regeneration that includes ECM remodelling - I think the analysis is very nice, especially the cell spatial analysis. But, the link between secretion and regeneration is broken - highly likely secretome is a part of this, but it could be the MSCs themselves give an effect - anti-inflammatory or regenerative.
+This is very nice work - but not a radical new contribution in my opinion or offering new mechanistic insight..
+I would be delighted for the editor and other reviewers to disagree with me!
+
+Response:
+
+We appreciate the reviewer’s comments. While we were unable to fully convince the reviewer, we believe that our work has the potential to make a significant impact on the design and fabrication of bioactive implants for bone regeneration. It is well-established that micropillars enhance osteogenesis by modulating nuclear morphology; however, this knowledge refers to the direct interaction between micropillars and the deformed cells. What has not been investigated or reported is how these deformed cells influence surrounding non deformed cells, which is the fundamental question addressed in our study.
+
+The role of epigenetics is beyond the scope of this study and has been removed from the revised manuscript, as suggested by the other reviewers. Our initial hypothesis posited that changes in the secretome would affect neighboring cells via paracrine effects. However, based on our results, we have shown that it is actually through matricrine signaling. This suggests that the secretome affects the ECM components in addition to or in leu of cell receptors, which we believe offers a novel perspective.
+
+Because the secretome affects the ECM, it can potentially play a significant role in enhanced bone regeneration by altering displayed or trafficking signals to cells involved in regeneration and this potential mechanism for modulating tissue regeneration has not been reported. Furthermore, the influence of nuclear deformation on the secretome and its potential effect in vivo has been understudied. To our knowledge, our work is the first to investigate and report the effects of nuclear deformation and the secretome in tissue regeneration in an animal. This information advances the field as it enables clinical applications of devices that leverage this mechanism to potentially enhance their interfacial tissue regeneration. Therefore, we believe our research represents a significant contribution to regenerative engineering.
+Reviewer #3 (Remarks to the Author):
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Response:
+We appreciate the reviewer’s response to our revised manuscript.
+
+Reviewer #4 (Remarks to the Author):
+All requested corrections have been taken into account.
+As far as I'm concerned, no further corrections are necessary. The article can be published.
+
+Response:
+We appreciate the reviewer’s response to our revised manuscript.

0129baf8281eddc2ad657d6e8fa589609bc12adf1490795c312275d391cb9313/preprint/preprint.md

@@ -0,0 +1,311 @@
+Micropillar-induced changes in cell nucleus morphology enhance bone regeneration by modulating the secretome
+
+Guillermo Ameer
+g-ameer@northwestern.edu
+
+Northwestern University    https://orcid.org/0000-0001-6023-048X
+Xinlong Wang
+Northwestern University    https://orcid.org/0000-0001-8978-2851
+Yiming Li
+Northwestern University    https://orcid.org/0000-0003-2111-3939
+Zitong Lin
+Northwestern University
+Indira Pla
+Northwestern University
+Raju Gajjela
+Northwestern University
+Basil Mattamana
+Northwestern University
+Maya Joshi
+Northwestern University    https://orcid.org/0000-0002-6028-475X
+Yugang Liu
+Northwestern University    https://orcid.org/0000-0001-5304-3459
+Huifeng Wang
+Northwestern University
+Amy Zun
+Northwestern University
+Hao Wang
+The University of Chicago
+Ching Wai
+Northwestern University
+Vasundhara Agrawal
+Northwestern University    https://orcid.org/0000-0003-0913-9298
+Cody Dunton
+Northwestern University
+Chongwen Duan
+Northwestern University
+Bin Jiang
+Northwestern University
+Vadim Backman
+Northwestern University   https://orcid.org/0000-0003-1981-1818
+Tong Chuan He
+The University of Chicago Medical Center
+Russell Reid
+Section of Plastic Surgery, The University of Chicago Medical Centre
+Yuan Luo
+Northwestern University   https://orcid.org/0000-0003-0195-7456
+
+Article
+
+Keywords:
+
+Posted Date: January 7th, 2025
+
+DOI: https://doi.org/10.21203/rs.3.rs-5530535/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 July 11th, 2025. See the published version at https://doi.org/10.1038/s41467-025-60760-y.
+Microtopography-induced changes in cell nucleus morphology enhance bone regeneration by modulating the cellular secretome
+
+Xinlong Wang1,2, Yiming Li3, Zitong Lin3, Indira Pla4, Raju Gajjela4, Basil Baby Mattamana4, Maya Joshi1, Yugang Liu1,2, Huifeng Wang1,2, Amy B. Zun1, Hao Wang5, Ching-Man Wai6, Vasundhara Agrawal2,7, Cody L. Dunton2,7, Chongwen Duan1,2, Bin Jiang1,2,8, Vadim Backman1,2,7,9, Tong-Chuan He1,5, Russell R. Reid1,10, Yuan Luo3,11,12, Guillermo A. Ameer1,2,7,8,11,13,14*
+
+1Center for Advanced Regenerative Engineering, Northwestern University, Evanston, IL 60208, USA
+2Department of Biomedical Engineering, Northwestern University, Evanston, IL 60208, USA
+3Department of Preventive Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA
+4Proteomics Center of Excellence, Northwestern University, Evanston, IL 60208, USA
+5Molecular Oncology Laboratory, Department of Orthopedic Surgery and Rehabilitation Medicine, The University of Chicago Medical Center, Chicago, IL 60637, USA
+6Center for Genetic Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA
+7Center for Physical Genomics and Engineering, Northwestern University, Evanston, IL 60208, USA
+8Department of Surgery, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA
+9Chemistry of Life Process Institute, Northwestern University, Evanston, IL 60208, USA
+10Laboratory of Craniofacial Biology and Development, Section of Plastic and Reconstructive Surgery, Department of Surgery, The University of Chicago Medical Center, Chicago, IL 60637, USA
+11Northwestern University Clinical and Translational Sciences Institute, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA
+12Center for Collaborative AI in Healthcare, Institute for AI in Medicine, Northwestern University Feinberg School of Medicine, Chicago, IL 60611, USA
+13International Institute for Nanotechnology, Northwestern University, Evanston, IL 60208, USA
+14Simpson Querrey Institute for Bionanotechnology, Northwestern University, Chicago, IL 60611, USA
+Abstract
+
+Nuclear morphology, which modulates chromatin architecture, plays a critical role in regulating gene expression and cell functions. While most research has focused on the direct effects of nuclear morphology on cell fate, its impact on the cell secretome and surrounding cells remains largely unexplored, yet is especially crucial for cell-based therapies. In this study, we fabricated implants with a micropillar topography using methacrylated poly(octamethylene citrate)/hydroxyapatite (mPOC/HA) composites to investigate how micropillar-induced nuclear deformation influences cell paracrine signaling for osteogenesis and cranial bone regeneration. *In vitro*, cells with deformed nuclei showed enhanced secretion of proteins that support extracellular matrix (ECM) organization, which promoted osteogenic differentiation in neighboring human mesenchymal stromal cells (hMSCs). In a mouse model with critical-size cranial defects, nuclear-deformed hMSCs on micropillar mPOC/HA implants elevated ColIa2 expression, contributing to bone matrix formation, and drove cell differentiation toward osteogenic progenitor cells. These findings indicate that micropillars not only enhance the osteogenic differentiation of human mesenchymal stromal cells (hMSCs) but also modulate the secretome, thereby influencing the fate of surrounding cells through paracrine effects.
+
+Introduction
+
+The nucleus is a dynamic organelle that changes its morphology in response to the cell's status.\textsuperscript{1} Its morphology has critical influence on nuclear mechanics, chromatin organization, gene expression, cell functionality and disease development.\textsuperscript{2-5} Abnormal nuclear morphologies, such as invagination and blebbing, have functional implications in several human disorders, including cancer, accelerated aging, thyroid disorders, and different types of neuro-muscular diseases.\textsuperscript{6,7} In addition, severe nuclear deformation is also observed during tissue development, cell migration, proliferation, and differentiation.\textsuperscript{2} Several structural components within the nucleus—including the nuclear envelope, lamins, nuclear actin, and chromatin—work together to determine its shape and structure.\textsuperscript{8} Although the underlying mechanisms are not yet fully understood, nuclear deformation has been found to affect cell behaviors through mechanotransduction processes.\textsuperscript{9} In addition, nuclear morphological changes have been reported to affect nuclear membrane tension and unfolding, which regulate the structure of the nuclear pore complex.\textsuperscript{10} This, in turn, influences the nuclear shuttling of transcription factors (e.g., YAP) and ions (e.g., Ca\(^{2+}\)), ultimately impacting cell functions.\textsuperscript{11,12} In our previous study, we demonstrated that altering nuclear morphology using micropillar topography affects nuclear lamin A/C assembly, which, in turn, influences chromatin tethering, packing, and condensation.\textsuperscript{13} These changes affect transcriptional accessibility and responsiveness, thereby regulating gene expression and stem cell differentiation.
+
+To manipulate nuclear morphology, various biophysical tools have been developed, including atomic force microscopy (AFM) nanoindentation, optical, magnetic, and acoustic tweezers, microfluidic devices, micropipette aspiration, plate compression, substrate deformation, and surface topography modulation.\textsuperscript{14-21} Among these methods, regulating the surface topography of materials is more accessible and has broader implications for regenerative engineering. One commonly used approach is the fabrication of pillar structures, which are employed to deform cell nuclei and study nuclear properties such as mechanics and deformability.\textsuperscript{22} These micropillar designs have been utilized to manipulate various cell functions, including migration, adhesion,
+proliferation, and differentiation.\(^{23-26}\) A wide range of materials can be used to create these structures, such as poly-L-lactic acid (PLLA), poly(lactide-co-glycolide) (PLGA), OrmoComp (an organic-inorganic hybrid polymer), and methacrylated poly(octamethylene citrate) (mPOC).\(^{13,26-28}\) Among these options, mPOC is particularly suitable for bone regeneration due to its major component, citrate, which acts as a metabolic factor to enhance the osteogenesis of mesenchymal stromal cells (MSCs).\(^{29}\)
+
+Although the influence of nuclear morphogenesis on the functions of individual cells is being intensively investigated, its role in regulating cellular secretion remains unclear. Bioactive molecules secreted by cells are crucial for intercellular communication, affecting various biological processes such as inflammation, cell survival, differentiation, and tissue regeneration.\(^{30,31}\) The success of many cell and exosome-based therapies relies on the cellular secretome. In this study, we fabricated micropillars to manipulate nuclear morphology and investigated their effects on the secretome of human mesenchymal stromal cells (hMSCs). We incorporated hydroxyapatite (HA), the primary inorganic component of native bone tissue, with micropatterned methacrylated poly(octamethylene citrate) (mPOC) to create the micropillars, promoting bone formation. Our results showed that mPOC/HA micropillars facilitated osteogenic differentiation of hMSCs compared to flat mPOC/HA samples *in vitro*. Secretome analysis revealed that hMSCs with deformed nuclei exhibited higher expression levels of bioactive factors associated with extracellular matrix (ECM) components and organization, as well as ossification. *In vivo*, both mPOC/HA flat and micropillar scaffolds seeded with hMSCs resulted in new bone formation; however, the micropillar group demonstrated significantly greater new bone volume and regenerated tissue thickness. Spatial transcriptomic analysis further confirmed elevated expression of genes related to the regulation of ECM structures, consistent with the secretome analysis results. These findings suggest that the influence of nuclear deformation on the osteogenesis of hMSCs operates through similar mechanisms in both *in vitro* and *in vivo* environments. Therefore, microtopography engineering of scaffold to control nuclear morphology is a promising approach to enhance bone regeneration.
+
+Results
+
+Influence of micropillar structures on physical and chemical properties of mPOC/HA implants
+
+mPOC prepolymer was synthesized according to our previous report,\(^{32}\) and its successful synthesis was confirmed via the nuclear magnetic resonance (1H NMR) spectrum (**Fig. S1a-c**). The size of HA nanoparticles is around 100 nm, as characterized by dynamic light scattering (DLS) (**Fig. S1d**). To mimic the nature of bone composition,\(^{33}\) 60% (w/w) HA was mixed with mPOC, and the slurry was used to fabricate flat and micropillar implants using a combination of UV lithography and the contact printing method (**Fig. 1a**). The square micropillars, with dimensions of 5 by 5 in side length and spacing, were fabricated (**Fig. 1b**). The height of the micropillars is around 8 \( \mu \)m, which can cause significant nuclear deformation (**Fig. 1c,d**).\(^{27}\) Fourier transform infrared (FTIR) spectrum shows a similar typical peak of functional groups in mPOC and mPOC/HA implants (**Fig. S1e**). The surface roughness of the implants was scanned using an atomic force microscope (AFM) (**Fig. 1e**). The analysis result indicates that the topography didn’t affect the surface roughness of the implants (**Fig. 1f**). Additionally, we tested the hydrophilicity of flat and micropillar implants via
+water contact angle measurement (Fig. S2). Although, at the initial state, the flat surface was more hydrophilic, there was no significant difference in the water contact angle after a 5-minute stabilization process.
+
+The mechanical properties of the implants were tested using the nano-indentation method. The force-indentation curve of the flat sample has a sharper slope, indicating it is stiffer than the micropillar sample (Fig. S3a). The Young’s Modulus of the flat sample (0.95 ± 0.12 GPa) is significantly higher than that of the micropillars (0.48 ± 0.02 GPa) and the lateral modulus of the micropillars (46.88 ± 1.49 MPa) (Fig. S3b,c). However, based on a previous report, the high modulus of the substrates is beyond the threshold that cells can distinguish and does not have an influence on nuclear morphology manipulation.\(^{34,35}\) Accelerated degradation and calcium release tests of the implants were performed in DPBS at 75 °C with agitation.\(^{36}\) There is a burst weight loss and calcium release of both flat and micropillar samples at day 1, followed by a gradual change until day 10, and another increase in the degradation and calcium release rate from day 10 to 14 (Fig. 1g,h). The micropillar structure enhanced the degradation and calcium release, but not significantly. According to the images of the samples captured at different time points, the initial burst degradation and calcium release can be attributed to the fast surface erosion of both scaffolds, as many small pores can be observed on their surfaces. From day 10 to 14, scaffolds started break into pieces that may lead to another burst degradation and calcium release (Fig. ii).
+Figure 1. Fabrication of surface engineered mPOC/HA implants. a. Illustration shows the combination of UV lithography and contact printing to fabricate free-standing mPOC/HA micropillars. b. SEM image shows the micropillar structures made of mPOC/HA. c. Optical microscope image and d. cross-section analysis of mPOC/HA micropillars. e. Surface scanning of flat and micropillar implants by AFM. f. Surface roughness of flat and micropillar implants. N.S., no significant difference, n = 3 biological replicates. g. Degradation test and h. calcium release of flat and micropillar mPOC/HA implants. N.S., no significant difference, n = 4 biological replicates, insert plot shows the initial release of calcium within 24 h. i. Representative images of flat and micropillar implants at different time points after accelerated degradation.
+Nuclear deformation facilitates osteogenic differentiation of hMSCs
+
+hMSCs were cultured on the flat and micropillar mPOC/HA surfaces in osteogenic medium and stained for F-actin and nuclei after 3 days (Fig. 2a). Noticeable deformation in both the nucleus and cytoskeleton was observed, consistent with mPOC micropillars.\(^{13}\) The Nuclear shape index (NSI) was calculated to assess the degree of nuclear deformation.\(^{27}\) A significantly lower NSI value, indicating more severe deformation, was found in the micropillar group (Fig. 2b). Confocal images were then employed to evaluate the 3D geometry of cell nuclei (Fig. 2c). 3D reconstruction analysis revealed that several geometric parameters, including nuclear volume, surface area, and project area, were significantly decreased on micropillars, while nuclear height was significantly increased (Fig. 2d and Fig. S4).
+
+We then investigated the impact of micropillars on cell adhesion, a crucial aspect for manipulating cell function.\(^{37}\) Initial cell attachment tests revealed that the micropillar structure did not influence cell attachment on the implants (Fig. 2e). SEM imaging of cell adhesion demonstrated that cells formed lamellipodia on flat surfaces but exhibited more filopodia on micropillars (Fig. 2f). Filopodia were observed on the top, side, and bottom of micropillars, indicating that cells were sensing the 2.5D environment using these antennae-like structures.\(^{23}\) The majority of cells were found to be viable on both flat and micropillar substrates, as evidenced by live/dead staining (Fig. 2g and Fig. S5). While the micropillars reduced cell metabolic activity (Fig. 2h), there was no significant impact on cell proliferation after 3 days of culture (Fig. 2i).
+
+To assess the impact of mPOC/HA micropillars on the osteogenesis of hMSCs, we stained ALP (alkaline phosphate) on a substrate with a combination of half flat and half micropillar structures (Fig. 2j). Quantification results demonstrated a significant increase in ALP activity on the micropillars (Fig. 2k). Furthermore, additional osteogenic differentiation markers of hMSCs, including RUNX2 and osteocalcin (OCN), were quantified through western blot analysis (Fig. 2l). The quantification of these proteins revealed a significant increase in both RUNX2 and OCN in cells on micropillars, confirming that the structures can effectively promote the osteogenic differentiation of hMSCs (Fig. 2m,n).\(^{13,26,27}\)
+Figure 2. Nuclear deformation promotes osteogenic differentiation of hMSCs. a. Staining of nucleus (green) and F-actin (red) of hMSCs on flat and micropillar mPOC/HA surfaces. Insert: high magnification of cell nucleus. Dashed lines indicate micropillars. b. Analysis of nuclear shape index of hMSCs. n=117 (flat) and 132 (pillar) collected from 3 biological replicates, ****p<0.0001. c. Orthogonal view of cell nucleus on flat and micropillar surfaces. d. Nuclear volume analysis based on 3D construction of the confocal images of cell nuclei. n=35 cells collected from 3 biological replicates, ****p<0.0001. e. Initial cell attachment on flat and micropillar surfaces. n=5 biological replicates, N.S., no significant difference. f. SEM images show the cell attachment on flat and micropillar mPOC/HA surfaces. g. Live/dead staining of hMSCs on flat and micropillar surfaces at 72 h in osteogenic medium. h. Cell metabolic activity of cells on flat and micropillar surfaces tested by a MTT assay. n=5 biological replicates, ****p<0.0001. i. Cell proliferation tested via DNA content after 72 h induction. n=5 biological replicates, N.S., no significant difference. j. ALP staining of hMSCs on flat and micropillar surfaces after 7 d induction. k. ALP activity test of cells after 7 d osteogenic induction. n=3 biological replicates. l. Blot images of osteogenic marker OCN and RUNX2 in cells cultured on flat and micropillar implants. GAPDH is shown as a control. Quantification m. OCN and n. RUNX2 according to western blot tests. n=3 biological replicates, ****p<0.0001.
+Micropillars modulate the secretome of hMSCs that regulate extracellular matrix formation.
+
+Previously, we demonstrated the ability of micropillar implants to enhance in vivo bone formation.\(^{13}\) However, the newly formed bone was not in close contact with the implant. Consequently, we hypothesized that nuclear deformation on micropillars might impact cellular secretion, thereby influencing osteogenesis through paracrine effects. To test this hypothesis, secretome analysis was conducted using medium collected from flat and micropillar samples. Differences in protein secretion levels between the two groups were depicted through principal component analysis (PCA) and a volcano plot, revealing a significant influence of nuclear deformation on the secretome (**Fig. 3a,b**). Gene ontology (GO) analysis was performed to annotate the significantly altered proteins in relevant processes.\(^{38}\) Top changes in cellular component, molecular functions, biological processes, and biological pathways indicated that micropillars predominantly affected extracellular matrix (ECM)-related processes (**Fig. 3c** and **Fig. S6-8**). Moreover, ossification and collagen fibril organization were identified as biological processes significantly overrepresented by differentially expressed proteins (**Fig. 3d**). The heatmap plot of proteins associated with collagen-containing extracellular matrix and ossification showed predominant upregulation on micropillars (**Fig. 3e**). The linkages of proteins and GO terms in biological process highlighted that ECM organization forms the largest cluster and is closely associated with the ossification process (**Fig. 3f**).
+
+Reactome pathway analysis was further conducted to assess potential downstream effects of secretome changes on micropillars.\(^{39}\) Results indicated that pathways related to ECM organization, ECM proteoglycans, and collagen fibril crosslinking were among the top 15 pathways significantly overrepresented by differential expressed pathways (DEP), predominantly showing upregulation (**Fig. 3g** and **Fig. S9**). We also noticed an upregulation in the degradation of the ECM on micropillars, indicating enhanced ECM remodeling which a crucial factor for tissue regeneration.\(^{40}\) These findings suggest that micropillars can influence the ECM formation of hMSCs through paracrine effects. Additionally, we performed proteomic analysis using cells cultured on flat and micropillar mPOC/HA scaffolds (**Fig. S10**). PCA and volcano plots indicated significant influences of nuclear deformation on protein expression. Pathway analysis revealed significant changes in many cell proliferation-related processes, consistent with previous transcriptomic tests on micropillars.\(^{13}\)
+Figure 3. Secretome of hMSCs on flat and micropillar mPOC/HA surfaces. a. PCA plot of differentially expressed proteins secreted by hMSCs on flat and micropillars. Cyan: flat; Red: micropillar. b. Volcano plot of proteins secreted by hMSCs seeded on micropillars compared to the flat surface. Blue dots and orange dots indicate significantly downregulated and upregulated proteins secreted by cells on micropillars compared to those on flat surface. Grey dots indicate
+non-significantly changed proteins. A threshold of expression greater than 2 times fold-change with \( p < 0.05 \) was considered to be significant. Proteins that are related with collagen-ECM pathways are labelled. **c.** Top 4 significantly enriched GO and Pathways based on their adjusted p-values. **d.** The most significant enriched GO terms of the biological domain with respect to biological process. **e.** Heatmap of proteins that are related with collagen-containing extracellular matrix and ossification. F indicates flat samples and P indicates pillar samples, n=3 biological replicates for each group. **f.** The linkages of proteins and GO terms in biological process related with collagen fibers, ECM, and ossification as a network. **g.** Heatmap of top 15 enriched terms plotted based on Reactome pathway analysis.
+
+**Nuclear deformed cells facilitate osteogenic differentiation of undeformed cells by affecting ECM.**
+
+Since the micropillar surfaces can modulate the secretome of hMSCs, we investigated whether the deformed cells could influence the osteogenic differentiation of undeformed cells using a transwell assay (**Fig. 4a**). The flat and micropillar mPOC/HA surfaces were fabricated at the bottom of cell culture plates to manipulate the nuclear morphology of hMSCs, while undeformed hMSCs were seeded on a transwell membrane with 400 nm nanopores, allowing the exchange of growth factors. After cell attachment, all samples were cultured in osteogenic induction medium. ALP staining of the cells on the transwell membrane showed a higher number of ALP-positive cells when co-cultured with nuclear-deformed cells, indicating enhanced osteogenic differentiation (**Fig. 4b,c**). Additionally, Alizarin Red S (ARS) staining confirmed increased calcium deposition—a key step in osteogenesis—when the cells were cultured above the micropillar-treated cells (**Fig. 4d,e**). Based on the secretome analysis, hMSCs on micropillars appear to promote osteogenesis in the transwell culture by secreting proteins that enhance ECM structure and organization. Collagen staining revealed higher coverage, stronger staining intensity, and more interconnected collagen network structures in the transwell co-cultured with micropillar-treated cells (**Fig. 4f,g**). In addition, energy dispersive X-ray spectroscopy (EDS) images showed more Ca and P deposition in the transwell co-cultured with micropillar-treated cells (**Fig. 4h**). Together with the secretome analysis, these findings suggest that the proteins secreted by cells with deformed nuclei improve ECM organization in undeformed cells, thereby promoting osteogenesis.
+Figure 4. The paracrine effect of cells with/without nuclear deformation tested through transwell assay. a. Schematic illustration of the experiment setup. b. ALP staining and c. quantification of ALP positive cells on transwell membrane incubated with undeformed and deformed MSCs (n=3). d. ARS staining and e. quantification of cells on transwell membrane incubated with undeformed and deformed MSCs (n=6). f. Immunofluorescence staining images of collagen in ECM of cells on transwell membrane incubated with undeformed and deformed MSCs. g. The coverage of collagen analyzed according to the staining images (n=4). h. EDS images showing Ca, P, and SEM images of cells on transwell membrane incubated with undeformed and deformed MSCs.
+
+mPOC/HA micropillar implant promotes bone formation in vivo
+
+To test the in vivo regeneration efficacy of mPOC/HA scaffolds, we created a critical size cranial defect model in nude mice. Two 4 mm diameter critical defects were made on the left and right sides of the skull tissue for the implantation of flat and micropillar scaffolds, respectively (Fig. 5a). The scaffolds were seeded with hMSCs for 24 hours to allow for cell attachment and nuclear deformation (Fig. 5b). After 12 weeks, micro CT was performed to evaluate the bone formation in the living animals. Based on the images, newly formed bone can be observed in the defect area with both flat and micropillar mPOC/HA implants (Fig. 5c and Fig. S11). Comparing this to our previous study using mPOC alone,13 the integration of HA clearly enhanced bone regeneration
+efficacy in vivo. Furthermore, larger bone segments were observed with the micropillar implant treatment. Quantification results confirmed a significantly increased bone volume with micropillar implant treatment (Fig. 5d).
+
+Histology analysis was further performed to evaluate the influences of flat and micropillar mPOC/HA implants on bone regeneration. Trichrome staining images revealed that defects treated with micropillar implants exhibited more osteoid tissue (Fig. 5e and Fig. S12). Moreover, both flat and micropillar mPOC/HA implants showed evidence of newly formed bone tissue, indicating enhanced bone regeneration compared to the mPOC alone scaffold. As no bone segment was observed with flat mPOC implant treatment.13 The thickness of the regenerated tissue was quantified, and the results demonstrated a significant enhancement with micropillar implant treatment (Fig. 5f). Positive staining of osteogenesis markers, including osteopontin (OPN) and osteocalcin (OCN), was observed throughout the regenerated tissues with both flat and micropillar implants, indicating osteoid tissue formation (Fig. 5g,h). The tissue appeared more compact in the micropillar group compared to the flat group. Furthermore, regenerated bone segments were more frequently observed with micropillar implant treatment.
+Figure 5. mPOC/HA micropillar implant promotes bone regeneration in vivo. a. Image shows implantation of hMSC seeded flat and micropillar mPOC/HA scaffolds. b. Staining images of nuclei (green) and F-actin (red) of cells on the implants. c. Representative μCT images of a typical animal implanted with hMSC-seeded flat (left) and micropillar (right) scaffolds at 12-weeks post-surgery. d. Regenerated bone volume in the defect region (n = 5 animals). e. Trichrome staining of the defect tissue treated with flat and micropillar implants. f. Average thickness of regenerated tissues with implantation of flat and micropillar scaffolds (n = 5 animals). IHC staining of osteogenic marker, g. OPN and h. OCN, in regenerated tissues with flat and micropillar implants.
+Micropillar implants facilitated bone regeneration in vivo via regulation of ECM organization and stem cell differentiation.
+
+Histological analyses showed more new bone formation with micropillar implants, although the new bone tissue did not directly interact with the micropillar surfaces. To further investigate the transcription profile of the regenerated tissue, we performed spatial transcriptomics (ST) analyses with both flat and pillar samples (Fig. S13). ST represents a powerful tool to investigate the cellular environment and tissue organization by providing a detailed map of gene expression within the native tissue context.41 Differential gene expression (DGE) analysis revealed changes in expression levels between the two groups. Although only a few genes showed significant differences, all of them were related to ECM structure or organization (Fig. S13). Notably, the expression of Col1a2, critical for type I collagen formation (comprising 90% of the bone matrix), was enhanced in the micropillar group (Fig. 6a). This expression showed a gradient, increasing toward the dura layer, possibly due to the osteogenic contribution of dura cells.42 We then plotted a heatmap showing the top 10 up-regulated and down-regulated differentially expressed genes (pillar vs. flat) in comparison with those in native skull bone (Fig. 6b). The heatmap indicated that the tissue regenerated with micropillar implants had expression patterns more similar to native skull bone than the flat group. Gene Ontology (GO) analysis of DGEs was further performed to annotate their relevant biological processes (Fig. 6c). Protein localization to extracellular matrix and crosslinking of collagen fibrils were among the top 5 up-regulated processes in the micropillar group. These results are consistent with the secretome test, all indicating that micropillar structures can influence ECM organization via paracrine effects.
+
+To further investigate the relationship between cell type composition and the regenerated tissues, we performed cellular deconvolution on the ST data using single-cell RNA sequencing (scRNA-seq) references from previously published studies.43-45 Several major cell lineages involved in bone regeneration were considered when deconvoluting the data (Fig. 6d). The most abundant cell type in regenerated tissues was late mesenchymal progenitor cells (LMPs), followed by MSCs and fibroblasts (Fig. 6e). There were also small proportions of MSC-descendant osteolineage cells (OLCs), osteocytes, osteoblasts, and chondrocytes. LMPs are identified as the late stage of MSCs through osteogenic differentiation.43,46 Among all cell types, the proportion of LMPs, which have high expression of marker genes associated with osteoblasts, was significantly increased in regenerated tissues with micropillar implants, indicating that these deformed cells facilitate the differentiation of MSCs toward the osteolineage (Fig. 6f). Additionally, GO analysis of DGEs (LMP versus other cell types) was performed to investigate the roles of LMPs in regenerated tissue. The results suggest that LMPs do not directly contribute to osteogenesis, a role performed by osteoblasts and osteocytes. Instead, LMPs can affect ECM formation, as the process of extracellular matrix organization is one of the top involved pathways (Fig. 6g). Thus, the results indicate that micropillar implants can facilitate skull tissue regeneration by promoting the differentiation of MSCs and ECM organization via paracrine effects.
+Figure 6. Spatial transcriptomic analysis of tissues regenerated with flat and micropillar implants. a. Spatial plot of Col1a2 expression profile in tissues regenerated with flat mPOC/HA implant and micropillar mPOC/HA implant. Arrow indicates enhanced expression around dura layer. b. The heatmap showing the top ten up- and down-regulated DEGs (pillar vs flat) in tissues regenerated with flat mPOC/HA implant, micropillar mPOC/HA implant, and native skull tissue. c. Gene Ontology analysis results based on the top 100 up-regulated genes (pillar vs flat). d. Deconvoluted cell types in each spatial capture location in flat and micropillar groups. Each pie chart shows the deconvoluted cell type proportions of the capture location. e. Bar plots of the cell type proportions in tissues regenerated with flat mPOC/HA implant and micropillar mPOC/HA implant. LMPs, MSCs, and fibroblasts are the predominant cell types. f. Violin plot of the proportion of LMPs in flat and micropillar groups. g. Top enriched processes associated with LMP compared with other cell lineages. LMP: late mesenchymal progenitor cells; MSC: mesenchymal stromal cells; OLC: MSC-descendant osteolineage cells
+Discussion
+
+Micropillars, as a typical topographical feature, have been extensively studied for their ability to regulate cell functions. Recent researches have shown that rigid micropillars can deform nuclear morphology, which in turn promotes the osteogenic differentiation of mesenchymal stem cells (MSCs), generating significant interest for bone regeneration applications.\(^{26,27}\) Our previous work demonstrated that mPOC micropillars enhanced bone regeneration in a mouse cranial defect model.\(^{13}\) The mPOC, a citrate-based biomaterial (CBB), is an excellent candidate for bone regeneration because citrate, an important organic component of bone, plays key roles in skeletal development and bone healing by influencing bone matrix formation and the metabolism of bone-related cells.\(^{47}\) In this study, hydroxyapatite (HA) was incorporated into mPOC to further enhance its regenerative potential, leveraging HA's well-known osteoconductive properties.\(^{48}\) Both *in vitro* and *in vivo* experiments confirmed that the addition of HA significantly improved bone regeneration compared to mPOC alone.\(^{13}\) Moreover, several products made from CBB/HA composites have recently received FDA clearance, highlighting the promising clinical potential of mPOC/HA micropillars for bone regeneration applications.\(^{49}\)
+
+Despite recent intensive investigations into nuclear morphogenesis, little is known about its influence on cellular secretion, which can regulate neighboring cells and is critical for regenerative engineering. Previous studies have shown that nuclear mechanotransduction, activated by substrate stiffening or cellular compression, can impact cell secretions.\(^{50,51}\) Here, we found that cells with deformed nuclei exhibited higher expression levels of ECM components and binding proteins that support collagen-enriched ECM organization. Additionally, soluble proteins secreted by these deformed cells were able to diffuse and modulate ECM secretion and organization in neighboring cells, as demonstrated by a transwell assay. The ECM is a complex, dynamic environment with tightly regulated mechanical and biochemical properties that affect essential cell functions, including adhesion, proliferation, and differentiation.\(^{52}\) ECM fiber alignment increases local matrix stiffness, which promotes higher force generation and increases cell stiffness, creating a positive feedback loop between cells and the matrix.\(^{53}\) Furthermore, the organized ECM enhances calcium recruitment and accelerates mineralization, contributing to effective bone regeneration.
+
+Implantation of the flat and micropillar mPOC/HA scaffolds seeded with MSCs resulted in larger new bone volume formation *in vivo* compared to previous studies using mPOC alone, a finding likely due to the osteoconductive properties of HA. ST analysis revealed a significant upregulation of genes encoding cartilage oligomeric matrix protein (COMP) and fibromodulin (FMOD) in the micropillar group, consistent with the secretome analysis. COMP binds to matrix proteins like collagen, enhancing ECM organization and assembly.\(^{54}\) As an ECM protein, COMP also promotes osteogenesis by binding to bone morphogenetic protein 2 (BMP-2), increasing its local concentration and boosting its biological activity.\(^{55}\) FMOD, with a strong affinity for the HA matrix, helps attenuate osteoclast precursor maturation, thereby influencing osteoblast–osteoclast crosstalk.\(^{56}\) These results suggest that nuclear deformation induced by micropillars may promote osteogenesis in neighboring cells via matricrine effects.
+Despite the enhanced bone regeneration observed, mPOC/HA implants did not achieve complete healing of the cranial defect, likely due to the limited interaction surface of the film scaffold. The influence of the implants, whether through direct chromatin reprogramming guidance or secretome activity, was restricted to cells at the tissue-scaffold interface. Future efforts should focus on the design and fabrication of 3D micropillar implants using additive manufacturing and composite materials to create a more comprehensive 3D cellular microenvironment that promotes bone regeneration. Additionally, the application of micropillars as a platform for delivering bioactive factors could be explored as a strategy to achieve complete cranial bone healing.
+
+In summary, we investigated the effects of nuclear deformation on the cellular secretome using micropillar implants fabricated from an mPOC/HA composite. The mPOC/HA micropillars demonstrated similar properties to a flat substrate in terms of roughness and degradation but had a substantial impact on cellular and nuclear morphology, cell adhesion, cytoskeletal development, and osteogenic differentiation in hMSCs. Nuclear-deformed cells showed increased secretion of proteins and RNA transcriptions that regulate ECM components and organization, promoting osteogenesis in neighboring cells both in vitro and in vivo. These findings suggest that incorporating microtopography into implants holds significant promise for bone regeneration. This study offers valuable insights for the future design and fabrication of bioactive implants in regenerative engineering.
+
+Materials and Methods
+
+Synthesis and characterization of mPOC pre-polymer.
+
+The mPOC pre-polymer were synthesized according to a previous report.\(^{32}\) Briefly, the POC pre-polymer was firstly synthesized by reaction of equal molar of citric acid (Sigma-Aldrich, 251275) and 1,8-octandiol (Sigma-Aldrich, O3303) at 140 °C oil bath for 60 min. The product was then purified by precipitation in DI water. After lyophilization, 66g POC pre-polymer was dissolved in 540 ml tetrahydrofuran (THF) and reacted with 0.036 mol imidazole (Sigma-Aldrich, I2399) and 0.4 mol glycidyl methacrylate (Sigma-Aldrich, 151238) at 60 °C for 6 h. The final product was then purified by precipitation in DI water and lyophilized for storage at -20 °C. Successful synthesis of mPOC pre-polymer was characterized using proton nuclear magnetic resonance (1H-NMR, Bruker A600).
+
+Fabrication and characterization of mPOC/HA micropillar scaffolds
+
+SU-8 micropillar structures (5×5×8 um\(^3\)) were fabricated according to our previous study.\(^{13}\) PDMS molds were then fabricated to replicate the invert structures. HA nanoparticles (Sigma-Aldrich, 677418) were mixed with mPOC pre-polymer at weight ratio of 6:4. The 60% HA was selected to mimic composition of native bone.\(^{57}\) Photo-initiator (5 mg/ml camphorquinone and ethyl 4-dimethylaminobenzoate) was added to the mPOC/HA slurry. The mixture was then added onto PDMS mold and pressed onto cover glass to prepare free-standing scaffold under exposure with laser (1W, 470 nm). Post-curing of the scaffold was performed in 80 °C oven over night. The size of HA nanoparticles was characterized using Dynamic Light Scattering (DLS). The topography of
+micropillars was observed using scanning electron microscope (SEM, FEI Quanta 650 ESEM) and characterized using 3D optical microscope (Bruker). Surface roughness of flat and micropillar scaffolds was characterized using atomic force microscope (AFM, Bruker ICON system). The water contact angle was tested using VCA Optima XE system. The compressive modulus of the scaffolds was characterized using a Tribioindenter (Bruker). Based on a previous report,\(^{58}\) the lateral modulus of micropillars was calculated according to the following equations:
+
+\[
+k_L = \frac{3EI}{L^3} \tag{1}
+\]
+
+The ‘\(k_L\)’ is the lateral stiffness, ‘E’ is the measured modulus, ‘I’ is the moment area of inertia, and ‘L’ is the micropillar height. For square micropillars, ‘I’ can be described as:
+
+\[
+I = \frac{a^4}{12} \tag{2}
+\]
+
+Where ‘a’ is the side length of the micropillars. Thus, the lateral modulus of the micropillars ‘\(E_L\)’ equals to:
+
+\[
+E_L = \frac{k_{LL}}{A} \tag{3}
+\]
+
+Where ‘A’ is the cross-section area of micropillars.
+
+Degradation and calcium release
+
+To test the degradation of the mPOC/HA scaffold, the dry weight of mPOC/HA scaffolds at day 0 was recorded as the initial weight. Then the scaffolds were merged in 1 ml DPBS solution in 75 °C oven. At each designed time point (1, 2, 3, 5, 7, 10 and 14 d), the scaffolds were rinsed with DI water followed by drying at 60 °C. The weight was recorded to calculate the weight loss percentage. The calcium release test was also performed with 75 °C DPBS (no calcium, no magnesium). At the designed time points, the elution solution was collected and replaced with fresh DPBS (1 ml). The released calcium was detected with inductively coupled plasma mass spectrometry (ICP-MS, ThermoFisher Element 2). Accumulated calcium release was calculated.
+
+Cell culture
+
+Human mesenchymal stromal cells (hMSCs, PCS-500-012) were purchased from the American Type Culture Collection (ATCC) and cultured with the growth medium acquired from ATCC. hMSCs with the passage 4-6 were seeded onto the flat and micropillar mPOC/HA substrates. To test cell attachment, hMSCs were seeded at 5000 cells/cm\(^2\) and cultured for 3 h followed by PBS rinsing to remove unattached cells. The attached cells were then trypsinized and collected for cell counting. For other experiments, the cells were cultured in growth medium for 24 h to allow cell attachment and spreading followed by incubation with osteogenic induction medium. After 3 d culture, live/dead staining (Thermofisher, L3224), MTT assay (Thermofisher, V13154), and Picogreen assay (Thermofisher, P7589) were performed according to the manufacturers’ protocol.
+
+Nuclear morphology analysis
+After one day of culture, the cells were fixed with 4% paraformaldehyde, and cell nuclei were stained using SYTOX™ Green (ThermoFisher, S7020) according to the manufacturer’s instruction. The nuclear shape index (NSI) was analyzed to evaluate 2D nuclear deformation.\(^{27}\) The stained cells were then imaged using a confocal microscope (Leica SP8) to acquire their 3D morphology. Cell nuclei were reconstructed using the Fiji ImageJ software (https://imagej.net/Fiji). Cell nuclear volume, surface area, project area, height, and the ratio of surface area to volume were measured using 3D objects counter plugin. More than 30 nuclei from 3 biological replicates were imaged and analyzed to calculate the statistics.
+
+Scanning electron microscope
+
+To visualize cell adhesion on mPOC/HA scaffolds, cells were fixed with 3% glutaraldehyde (Electron Microscopy Sciences) and rinsed with DI water. Subsequently, the cells underwent dehydration using a series of ethanol concentrations (30%, 50%, 70%, 90%, and 100%) for 5 min each, followed by drying using a critical point dryer (Tousimis Samdri) as per the manual. The dehydrated cells were coated with a 5 nm osmium layer and imaged using a scanning electron microscope (SEM, FEI Quanta 650). Captured images were further enhanced for visualization of cellular architecture using Photoshop. Additionally, cells on transwell were imaged using SEM and EDS analysis was performed to evaluate the calcium and phosphate deposition.
+
+Osteogenic differentiation
+
+hMSCs were seeded onto both flat and micropillar mPOC/HA substrates. One-day post-seeding, osteogenic induction medium (Lonza) was applied to prompt the osteogenic differentiation of hMSCs. After 7 days of induction, cells were washed with PBS buffer and fixed with 4% paraformaldehyde for 10 minutes. Subsequently, the samples were immersed in a solution of 56 mM 2-amino-2-methyl-1,3-propanediol (AMP, pH~9.9), containing 0.1% naphthol AS-MX phosphate and 0.1% fast blue RR salt to stain alkaline phosphatase (ALP). Bright-field images were acquired using a Nikon Eclipse TE2000-U inverted microscope. ALP activity was assessed using the ALP assay kit (K422-500, Biovision) following the provided manual. Briefly, cells cultured in induction medium for 7 days were homogenized using ALP assay buffer. Subsequently, the non-fluorescent substrate 4-Methylumbelliferyl phosphate disodium salt (MUP) was mixed with the homogenized samples to generate a fluorescent signal through its cleavage by ALP. Fluorescence intensity was measured using a Cytation 5 imaging reader (BioTek) at (Ex/Em = 360/440 nm). Enzymatic activity was calculated based on the standard curve and normalized to total DNA content, determined by the Quant-iT PicoGreen dsDNA assay (Invitrogen). The expression levels of OCN and RUNX2 were quantified through Western Blot analysis. In brief, cell lysis was performed using radioimmunoprecipitation assay (RIPA) buffer. The relative protein quantities were measured using a Cytation 5 imaging reader. Equal amounts of proteins extracted from flat and micropillar samples were loaded onto a NuPAGE 4-12% Bis-Tris Gel (Invitrogen) and subsequently transferred to nitrocellulose membranes (Bio-rad). Afterward, membranes were blocked with 5% milk and incubated with primary antibodies (including GAPDH from Abcam, OCN from Cell Signaling, RUNX2 from Santa Cruz) overnight at 4 °C with gentle shaking. Following this, secondary antibodies, diluted at a ratio of 1:5000, were applied and incubated with the membranes at room temperature for 1 hour. Protein bands were
+visualized using the Azure 600 gel imaging system. The acquired images underwent analysis through the 'Gel Analyzer' tool in ImageJ. The intensity of all target protein bands was initially compared to the corresponding GAPDH, and then normalized against a flat surface, which was set as 1. Statistical calculations were based on three biological replicates.
+
+Secretome sample preparation: Analysis of secreted proteins is complicated by high concentrations of serum proteins. Our approach reduced initial sample volume to a 20 µl concentrate using a molecular weight cut off filter (50 kDa, Amicon Ultra-15 centrifugal, Ultracel, Merck). The concentrate above 50KDa was depleted of the most abundant proteins using a High Select HAS / Immunoglobulin Depletion Midi spin column (A36367, Thermo Fisher Scientific), resulting in a filtrate solution (below 50KDa) and a depleted solution per sample. An acetone / TCA (Trichloroacetic acid) protein precipitation was performed on each solution to create protein pellets and an in-solution trypsin digestion was performed on each pellet.100 µl of re-suspension buffer (8 M urea in 400 mM ammonium bicarbonate) was added to the pellet and incubated with mixing for 15 minutes. Disulfide bonds were reduced by addition of 100 mM dithiothreitol and incubated for 45 minutes at 55 °C. Sulphydryl groups were alkylated by addition of 300 mM iodoacetamide and incubated for 45 minutes at 25 °C shielded from light. Samples were diluted 4-fold with ammonium bicarbonate to reduce the urea concentration below 2 M. Protein digestion was performed by addition of trypsin (MS-grade, Promega) at a 1:50 ratio (enzyme:substrate) and incubated overnight at 37 °C. Digestion was halted with the addition of 10 % formic acid (FA) to a final concentration of 0.5%. Peptides were desalted with C18 spin columns (The Nest Group), dried by vacuum centrifugation, and stored at -20 °C. Peptides were resuspended in 5% ACN (Acetonitrile) / 0.1% FA for LC-MS analysis. Peptide concentration was quantified using micro BCA (Bicinchoninic acid) protein assay kit (Thermo Scientific, Ref: 23235).
+
+Proteome sample preparation: Cells were lysed using cell lysis buffer (0.5% SDS, 50mM Ambic (Ammonium Bicarbonate), 50mM NaCl (Sodium Chloride), Halt Protease inhibitor). An acetone / TCA protein precipitation was performed on each lysed samples solution to create protein pellets and an in-solution trypsin digestion was performed on each pellet. 100 µl of re-suspension buffer (8 M urea in 400 mM ammonium bicarbonate) was added to the pellet and incubated with mixing for 15 minutes. Disulfide bonds were reduced by addition of 100 mM dithiothreitol and incubated for 45 minutes at 55 °C. Sulphydryl groups were alkylated by addition of 300 mM iodoacetamide and incubated for 45 minutes at 25 °C shielded from light. Samples were diluted 4-fold with ammonium bicarbonate to reduce the urea concentration below 2 M. Protein digestion was performed by addition of trypsin (MS-grade, Promega) at a 1:50 ratio (enzyme:substrate) and incubated overnight at 37 °C. Digestion was halted with the addition of 10 % formic acid to a final concentration of 0.5%. Peptides were desalted with C18 spin columns (The Nest Group), dried by vacuum centrifugation, and resuspended in 5% ACN/0.1% FA for LC-MS analysis. Peptide concentration was quantified using micro BCA Protein Assay Kit (Thermo Scientific, Ref: 23235).
+
+Liquid Chromatography High Resolution Tandem Mass Spectrometry (LC-HRMS/MS) Analysis:. Peptides were analyzed using a Vanquish Neo nano-LC coupled to a Exploris 480 hybrid quadrupole-orbitrap mass spectrometer (Thermo Fisher Scientific, USA). The samples were loaded onto the trap column of 75µm internal diameter (ID) x 2cm length (Acclaim PepMap™
+100, P/N 164535) and analytical separation was performed using a UHPLC C18 column (15cm length x 75μm internal diameter, 1.7μm particle size, Ion Opticks, AUR3-15075C18). For each run, 1 μg of peptide sample was injected. Electrospray ionization was performed using a Nanospray Flex Ion Source (Thermo Fisher, ES071) at a positive static spray voltage of 2.3 kV. Peptides were eluted from the analytical column at a flow rate of 200 nL / min using an increasing organic gradient to separate peptides based on their hydrophobicity. Buffer A was 0.1 % formic acid in Optima LC-MS grade water, and buffer B was 80 % acetonitrile, 19.9 % Optima LC-MS grade water, and 0.1 % formic acid: The method duration was 120 minutes. The mass spectrometer was controlled using Xcalibur and operated in a positive polarity. The full scan (MS1) settings used were: mass range 350-2000 m/z, RF lens 60 %, orbitrap resolution 120,000, normalized AGC target 300 %, maximum injection time of 25 milliseconds, and a 5E^3 intensity threshold. Data-dependent acquisition (DDA) by TopN was performed through higher-energy collisional dissociation (HCD) of isolated precursor ions with charges of 2+ to 5+ inclusive. The MS2 settings were: dynamic exclusion mode duration 30 seconds, mass tolerance 5 ppm (both low and high), 2 second cycle time, isolation window 1.5 m/z, 30 % normalized collision energy, orbitrap resolution 15,000, normalized AGC target 100 %, and maximum injection time of 50 milliseconds.
+
+Data analysis: Mass spectrometry files (.raw) were converted to Mascot generic format (.mgf) using the Scripps RawConverter program and then analyzed using the Mascot search engine (Matrix Science, version 2.5.1). MS/MS spectra were searched against the SwissProt database of the organism of interest. Search parameters included a fixed modification of cysteine carbamidomethylation, and variable modifications of methionine oxidation, deamidated asparagine and aspartic acid, and acetylated protein N-termini. Two missed tryptic cleavages were permitted. A 1 % false discovery rate (FDR) cutoff was applied at the peptide level. Only proteins with at least two peptides were considered for further study.
+
+Label-Free Quantification: The samples were acquired on mass spec and the data were searched against a specific database using the MaxQuant application.59 Label-Free Quantification (LFQ) was obtained by LFQ MS1 intensity. The results were filtered with a minimum of 2 unique peptides. Technical replicates were averaged and intensities were Log2 transformed to achieve a normal distribution of the data. Missing values were filtered to keep only proteins quantified in at least 2 samples per group. For statistics, Student t-Test was applied using p < 0.05 and FC > 2 to determine which proteins were significantly up- and down-regulated and visualize it by volcano plot. Downstream analyses and visualizations were done using RStudio software (R version 4.3.2, RStudio version 2024.09.0). Principal component analysis (PCA) was done using ‘prcomp’ R function to visualize la ability of the differential protein expression to distinguish between biological conditions. Heatmap plot was built using ‘ComplexHeatmap’ R package. GO and Pathways enrichment analysis was done using ‘clusterProfiler’ R package60 and annotations with adjusted p-values (FDR, Benjamini-Hochberg) < 0.05 were considered significant. Additional packages used include ‘org.Hs.eg.db’ for human gene annotations and ‘enrichplot’ for visualization. This analysis considered the entire set of human protein-coding genes as the reference background.
+Transwell assay: The flat and micropillar mPOC/HA surfaces were fabricated in a 24 well plate. The hMSCs were seeded onto the surfaces with 40,000 cells per well. Then a transwell was put in each well and additional hMSCs were seeded inside the transwell (Costar, 0.4 μm polyester membrane) at density of 5,000 cells/cm². After cell attachment, osteogenic medium was used to induce osteogenic differentiation of the cells. At 7 days post-induction, the cells on transwell were fixed followed by ALP staining and quantification to investigate the paracrine effect of deformed and undeformed cells on osteogenesis. At 3 weeks post-induction, additional transwells were collected for Alizarin Red S (ARS) staining and quantification to show the calcium deposition influenced by the paracrine effect. At 4 weeks post-induction, the collagen, which is one of the major components in ECM and significantly affected according to the secretome analysis, were stained using anti-collagen antibody (Abcam, ab36064) to investigate the influence of nuclear deformation on ECM organization.
+
+In vivo implantation: The animal study was approved by the University of Chicago Animal Care and Use Committee following NIH guidance (ACUP#71745). Eight-week-old female athymic nude mice obtained from Harlan Laboratories were used for the study. The animals were housed in a separately air-conditioned cabinet at temperature of 24–26 °C with 12:12 light:dark cycle. The surgeries were performed according to the previous report61. Briefly, animals were treated with 2% isoflurane delivered by 100% O₂ and maintained with 1–1.5% isoflurane for anaesthesia. Two critical-sized defects (4 mm diameter) were created on the left and right side of skull of each animal followed by implantation of hMSCs seeded flat and micropillar scaffolds, respectively. After implantation of scaffolds, a larger mPOC film (1 × 1.5 cm²) was attached to the skull with thrombin/fibrinogen to prevent displacement of implants. Skin tissue was closed with 5–0 nylon interrupted sutures and removed after 2 weeks. The animals were monitored after anaesthesia hourly until recovery. Buprenorphine 50 μg kg⁻¹ and meloxicam 1 mg kg⁻¹ were used for pain relief.
+
+Micro-CT: Micro-CT images of cranial were performed on the Xcube (Molecubes NV) by the Integrated Small Animal Imaging Research Resource (iSAIRR) at The University of Chicago. Spiral high-resolution computed tomography acquisitions were performed with an X-ray source of 50 kVp and 440 μA. Volumetric computed tomography images were reconstructed by applying the iterative image space reconstruction algorithm (ISRA) in a 400 × 400 × 370 format with voxel dimensions of 100 × 100 × 100 μm³. An Amira software (Thermo Scientific) was used for 3D reconstruction of the skull tissue and to analyse the bone formation in the defect area. Scale bars were used to standardize the images. Defect recovery is defined as (Vi – Vd)/Vi × 100%, where Vi and Vd represent defect volume at initial and designed timepoints, respectively.
+
+Histology analysis: Skull samples were fixed and decalcified in Cal-EX II (Fisher Scientific) for 24 hours, rinsed with PBS, and embedded in paraffin. Tissue sections containing defect sites were cut to 5 μm thickness and stained with H&E and trichrome to assess tissue regeneration. Regenerated tissue thickness was measured using ImageJ, and osteogenesis was evaluated via IHC staining for key osteogenic markers, including OCN and OPN. Mouse skin tissue served as a negative control for all IHC staining.
+Spatial transcriptomics: To confirm the RNA quality of each FFPE tissue block, 1-2 curls (10um thickness each) were used for RNA extraction using Qiagen RNeasy FFPE kit (Qiagen 73504) according to manufacturers’ protocol. Extracted RNA was examined by Agilent Bioanalyzer RNA pico chip to confirm the DV200 >30%. Simultaneously, the tissue morphology was examined on HE stained slide to identify region of interest.
+
+For each FFPE sample, 1 section (5um thickness) was placed on visium slides. Each slide was incubated at 42°C for 3 hours followed by overnight room temperature incubation. Then, the slide was stored at desiccated slide holder until proceeding to deparaffinization.
+
+The deparaffinization, HE staining and imaging and decrosslinking of tissue slides were performed according to 10x Genomics protocol (CG000409 and CG000407) specific for Visium spatial gene expression for FFPE kit. Then, the slides were proceeded to human probe (v2) hybridization and ligation using 10x Genomics Visium spatial gene expression, 6.5mm kit (10x Genomics, PN-1000188). The probes were released from tissue slide and captured on visium slide followed by probe extension. Sequencing libraries were prepared according to manufacturer’s protocol. Multiplexed libraries were pooled and sequenced on Novaseq X Plus 10Bflowcell 100 cycles kit with following parameter: 28nt for Read 1 and 90nt for Read 2.
+
+We visually identified the implant region in each sample. To exclude low quality capture locations, we removed the capture locations with fewer than 500 unique molecular identifiers, fewer than 500 genes, or \( \geq 25\% \) mitochondrial reads.\(^{61}\) We also filtered out the genes that are expressed in fewer than five capture locations.\(^{61}\) After quality control, flat group had 101 capture locations and 12,701 genes, whereas micropillar group had 73 capture locations and 13,371 genes.
+
+Differential gene expression analysis: To identify the genes differentially expressed in flat and micropillar groups, we performed Wilcoxon rank-sum tests on the merged dataset (174 capture locations) using the FindAllMarkers function in Seurat V3.\(^{62}\) Our testing was limited to the genes present in both implants, detected in a minimum 1% of cells in either implant, as well as showing at least 0.1 log-fold difference between the two implants.
+
+Cell type deconvolution: To perform cell typing on our data, we first identified three publicly available bone single-cell RNA sequencing (scRNA-seq) references with annotated cell types.\(^{43-45}\) The scRNA-seq references were processed, quality controlled, and merged using Seurat V3. Since our samples are nude mice, we excluded all the immune cells from the merged reference. The final merged scRNA-seq dataset contained a total of 12,717 cells and represented all major cell types present in bone tissues.
+
+In 10x Visium data, each capture location contains a mixture of cells.\(^{63}\) Therefore, we performed cell type deconvolution to predict the cell type proportions in each capture location using BayesPrism, a Bayesian deconvolution method shown to work on spatial transcriptomics data.\(^{64,65}\) We excluded chromosomes X and Y, ribosomal, and mitochondrial genes from the analysis to reduce batch effects. We also removed the outlier genes with expression greater than 1% of the total reads in over 10% of capture locations. To improve cell typing accuracy, we only used the cell type signature genes for deconvolution analysis. The cell type markers were identified based
+on the differential expression analysis results on the merged scRNA-seq reference. The predicted cell type proportions with above 0.5 coefficient of variation were clipped to zero to reduce noise.
+
+Cell-type-based analyses: We performed Wilcoxon rank-sum tests using the deconvoluted cell type proportions to test if certain cell types are more prevalent in one implant than the other. We further examined the association between cell type proportions and gene expression levels in the two implants through Kendall’s correlation analyses. All the p-values were adjusted for multiple testing through the false discovery rate approach. The proportions of three cell types (chondrocyte, OLC, and osteocyte) had over 50 significantly positively correlated genes. For each of these cell types, we performed pathway enrichment analysis of the significantly positively correlated genes using Metascape.66
+
+Statistical analysis: The results are shown as mean ± standard deviation using violin super plots or bar graphs. Statistical analysis was performed using Kypot software (version 2.0 beta 15). Statistical significance was determined by Student’s t-test (flat versus micropillar, two-sided). All experiments presented in the manuscript were repeated at least as two independent experiments with replicates to confirm the results are reproducible.
+
+Acknowledgement
+
+This work was supported by the National Science Foundation (NSF) Emerging Frontiers in Research and Innovation (EFRI) (no. 1830968 to G.A.A.), and National Institutes of Health (NIH) grants U54CA268084 and R01CA228272, NSF grant EFMA-1830961 (to V.B.). This work was performed as a collaboration between the Center for Advanced Regenerative Engineering (CARE) and the Center for Physical Genomics and Engineering (CPGE) at Northwestern University. This work made use of the EPIC facility, the NUFAB facility, and the BioCryo facility of Northwestern University’s NUANCE Center, which has received support from the SHyNE Resource (NSF ECCS-2025633), the International Institute for Nanotechnology (IIN) and Northwestern’s MRSEC programme (NSF DMR-1720139). Proteomics services were performed by the Northwestern Proteomics Core Facility, generously supported by NCI CCSG P30 CA060553 awarded to the Robert H Lurie Comprehensive Cancer Center, instrumentation award (S10OD025194) from NIH Office of the Director, and the National Resource for Translational and Developmental Proteomics supported by P41 GM108569. We also thank the help from Dr. Hsiu-Ming Tsai at the Department of Radiology, The University of Chicago for microCT imaging. This work also made use of the Northwestern University NUSeq Core and the Biological Imaging Facility (BIF).
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryTable1.xlsx
+• SupplementaryTable2.xlsx
+• SupplementaryTable3.xlsx
+• SupplementaryTable4.xlsx
+• SupplementMicrotopographyinducedchangesincellnucleusmorphologyenhanceboneregenerationbymodulatingthecellularsecretome.pdf

019a1322a4a18120bcf8546c95c7927691c4f4ceee9e4ba840a419b80a2ebe10/preprint/preprint.md

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+Invariance-based Mendelian Randomization Method Integrating Multiple Heterogeneous GWAS Summary Datasets
+
+Xiaohua Zhou
+azhou@bicmr.pku.edu.cn
+
+Beijing International Center for Mathematical Research, Peking University
+
+Lei Hou
+Peking University
+
+Hao Chen
+Institute for Medical Dataology, Cheeloo College of Medicine, Shandong University
+
+Article
+
+Keywords: univariate mendelian randomization, multivariate mendelian randomization, GWAS summary datasets, heterogeneous populations, multiple ancestries
+
+Posted Date: December 17th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-5602368/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 18th, 2025. See the published version at https://doi.org/10.1038/s41467-025-62823-6.
+Invariance-based Mendelian Randomization Method Integrating Multiple Heterogeneous GWAS Summary Datasets
+
+Lei Hou¹, Hao Chen⁴, Xiao-Hua Zhou¹,²,³*
+
+Author affiliations:
+1. Beijing International Center for Mathematical Research, Peking University, Beijing, P.R.China, 100871
+2. Department of Biostatistics, Peking University, Beijing, P.R.China, 100871
+3. Chongqing Big Data Research Institute, Peking University, Chongqing, P.R.China, 401333
+4. Department of biostatistics, School of Public Health, Cheeloo College of Medicine, Shandong University, Shandong, Beijing, P.R.China, 250000
+
+*Corresponding author:
+Xiao-Hua Zhou,
+E-mail: azhou@bicmr.pku.edu.cn,
+Telephone: +86 18910208518,
+Address: Peking University, No.5 Yiheyuan Road Haidian District, Beijing, P.R.China
+Abstract
+
+Various geographical landscapes, diverse lifestyles and genetic structures may lead the heterogeneity among the GWAS summary datasets from distinct populations, especially different ethnic groups. This increases the difficulty in inferring global causal relationships from exposures on the outcome when integrating multiple GWAS summary datasets. We proposed a mendelian randomization (MR) method called MR-EILLS, which leverages the Environment Invariant Linear Least Squares (EILLS) to deduce the global causal relationship that invariant in all heterogeneous populations. The MR-EILLS model works in both univariate and multivariate scenarios, and allows the invalid instrumental variables (IVs) violating exchangeability and exclusion restriction assumptions. In addition, MR-EILLS shows the unbiased causal effect estimations of one or multiple exposures on the outcome, whether there are valid or invalid IVs. Comparing with traditional MR and meta methods, MR-EILLS demonstrates the highest estimation accuracy, the most stable type I error rates, and the highest statistical power. Finally, MR-EILLS is applied to explore the independent causal relationships between 11 blood cells and lung function, using GWAS summary statistics from five ancestries (African, East Asian, South Asian, Hispanics Latinos and European). The results cover most of the expected causal links which have biological interpretations and several new links supported by previous observational literatures.
+
+Keywords: univariate mendelian randomization, multivariate mendelian randomization, GWAS summary datasets, heterogeneous populations, multiple ancestries
+Introduction
+
+In recent years, with the rising number of Genome-Wide Association Study (GWAS) investigations, there has been a notable increase in the public availability and utilization of GWAS summary data by researchers [1-2]. This inclusive dataset encompasses information from diverse populations and ethnic backgrounds [3-6], a development that researchers find valuable, thus making it a current focal point of research interest. Owing to a range of influences including geographical landscapes and varied lifestyles, genetic structures exhibit significant diversity among distinct populations [7-8], also we called population stratification, potentially leading to heterogeneity in GWAS summary data across different ethnic groups, such as those of European, Asian, and American descent. Mendelian randomization (MR) [2, 9] is a methodology that relies on the utilization of publicly available GWAS summary data for causal inference. It uses genetic variants as instrumental variables (IVs) to infer the causal effect of one or multiple exposures on an outcome, that is, univariable or multivariable MR [10-11], respectively. A valid IV must satisfy the flowing three assumptions: relevance, exchangeability and exclusion restriction [9]. When we consider heterogeneous populations, one valid IV in a population may be an invalid IV in another population due to various genetic structures. For example, \( G_1 \) is a valid IV in population I, it may be correlated with the confounder \( U \) between exposure and outcome in the population II, while \( U \) is not the confounder in the population I. In this case, \( G_1 \) violates the exchangeability in population II. In addition, \( G_1 \) may be correlated (linkage disequilibrium (LD)) [12] with another SNP \( G_2 \) which directly affect the outcome in the population II, but \( G_1 \) is independent with \( G_2 \) in the population I. In this case, \( G_1 \) violates the exclusion restriction in population II and this is due to the LD references in different populations are different. This complexity amplifies the difficulty of deducing the global causal relationship by integrating multiple heterogeneous GWAS summary datasets.
+
+One straightforward idea to infer global causal relationships using MR is that, first conduct MR analysis separately using valid IVs in different populations and obtain the causal effect estimations in each population, then combine all estimations by meta-analysis [13-14]. Even there may be invalid IVs in the first step, lots of MR methods [15-18] are proposed to remove the influence of invalid IVs on the causal effect estimation.
+However, the accuracy of meta-analysis results depends on the robustness of different MR methods, while these MR methods require different assumptions [15-18], which may be difficult to satisfy or even cannot be tested. This may induce the inconsistent causal effect estimation in different populations, and bring difficulties for inferring global causal relationships (see section Application). Another idea is that first conduct GWAS meta-analysis for heterogeneous populations, then select valid IVs to infer causal relationship using MR. The difficulty for this strategy is that only a short number of independent SNPs (no LD) can be selected because the LD reference panels in different populations are different [8,19]. These two strategies are both two-step process, and bring the doubled statistical errors, which yields the lower accuracy of causal effect estimation. Besides, meta-analysis is a statistical technique used to combine and analyze results from multiple studies [20], if one result is inaccurate, the results of meta-analysis is also incorrect. It is not a causal method in itself and does not necessarily provide causal evidence that holds true in every population included in the analysis. Therefore, following we proposed a one-step method which integrating all information but not only MR results in each population, and provide the causal evidence that holds true (also called invariant) in each population.
+
+In this paper, we provide a MR method called MR-EILLS, which utilizes the Environment Invariant Linear Least Squares (EILLS) [21] to integrating multiple heterogeneous GWAS summary datasets, then infer global causal relationship. The MR-EILLS model works in both univariate and multivariate scenarios, and allows the invalid IVs violating exchangeability and exclusion restriction assumptions. In addition, MR-EILLS shows the unbiased causal effect estimation of one or multiple exposures on the outcome, whether there are valid or invalid IVs. Comparing with traditional MR and Meta methods, MR-EILLS demonstrates the highest estimation accuracy, the most stable type I error rates, and higher statistical power. Finally, MR-EILLS is applied to explore the independent causal relationships between 11 blood cells and 4 lung function indexes, using GWAS summary statistics from 5 ancestries: African, East Asian, South Asian, Hispanics Latinos and European.
+
+Results
+
+Method overview
+
+[please insert the Figure 1 here]
+MR-EILLS model integrating the GWAS summary statistics from multiple heterogeneous populations, and find the causal exposures which have invariant effects with outcome in heterogeneous populations. GWAS summary statistics in \( E \) heterogeneous populations include \( G_j - X \) association \( \hat{\theta}_{p,j}^{(e)} \) and its standard error \( \sigma_{G_j X_p}^{(e)2} \), as well as \( G_j - Y \) association \( \hat{\Gamma}_{y,j}^{(e)} \) and its standard error \( \sigma_{y,j}^{(e)2} \) for \( E = e \). We assume that the causal effects of causal exposures on \( Y \) is invariant in different populations, that is \( \beta_{0,p}^{(1)} = \beta_{0,p}^{(2)} = ... = \beta_{0,p}^{(E)} = \beta_{0,p}^* \) for \( p \in P^* \), while the genetic associations between SNPs and exposures/outcome/confounders may be different, and confounders between exposures and the outcome are also different. MR-EILLS model (Figure 1) aims to explore the global causal effect estimation by minimizing the following objective function
+
+\[
+Q(\beta_{0,p}^*; \hat{\theta}_{p,j}^{(e)}, \hat{\Gamma}_{y,j}^{(e)}, \sigma_{y,j}^{(e)2})
+= \sum_{e \in E} w_j^{(e)} \mathrm{E}_{j \in S^e} [ |w_j^{(e)} \hat{\varepsilon}_j^{(e)}|^2 ] + \gamma \sum_{p \in P} \sum_{e \in E} w^{(e)} |\mathrm{E}_{j \in S^e} [\hat{\theta}_{p,j}^{(e)} \cdot w_j^{(e)} \hat{\varepsilon}_j^{(e)}]|^2
+\]
+
+where \( w_j^{(e)} \) is the weight of IV \( G_j \) on the casual effect estimation in population \( E = e \), and \( w^{(e)} \) is the weight of population \( E = e \) on the global casual effect estimation. The first part of objective function (1) is the empirical \( L_2 \) loss, which is the multiple populations version of objective function (6) in one population (see Method section), and \( \hat{\varepsilon}_j^{(e)} = \hat{\Gamma}_{y,j}^{(e)} - \sum_p \hat{\theta}_{p,j}^{(e)} \beta_{0,p}^{(e)} \) also denotes the pleiotropic effect. Motivating simulation (Figure 1A, Figure S1A) demonstrates that as the pleiotropic effect (no matter correlated or uncorrelated) increasing, the absolute value of \( \hat{\varepsilon}_j^{(e)} \) is larger. The second part of objective function (1) is the empirical focused linear invariance regularizer, which discourages selecting exposures with strong correlation between \( \theta_{p,j}^{(e)} \) and \( \varepsilon_j^{(e)} \) in some populations because this correlation would distort the causal effect estimation (see Method section). Motivating simulation (Figure 1B, Figure S1B) demonstrates that as correlated pleiotropic effect increasing, the correlation between \( \hat{\varepsilon}_j^{(e)} \) and \( \hat{\theta}_{p,j}^{(e)} \) is larger, and this means the violation of the InSIDE assumption[18] is more severe. \( \gamma > 0 \) is the hyper parameter. In addition, we add the restriction
+
+\[
+S^* = \{ j : \sum_{e \in E} |\hat{\varepsilon}_j^{(e)}| + \sum_{p \in P} \sum_{e \in E} |\hat{\theta}_{p,j}^{(e)} \hat{\varepsilon}_j^{(e)}| < \lambda \}
+\]
+to select the valid IVs. The first part in equation (2) represents the total pleiotropic effect for \( j-th \) IV, and the second part in equation (2) represents the correlation between \( \theta_{p,j}^{(e)} \) and \( \varepsilon_j^{(e)} \) for \( j-th \) IV. \( \lambda > 0 \) is the hyper parameter controlling the strictness of filtering IVs. When there are invalid IVs, the ridge plot of \( \sum_{e\in E}|\varepsilon_j^{(e)}| + \sum_{p\in P}\sum_{e\in E}|\hat{\theta}_{p,j}^{(e)}\varepsilon_j^{(e)}| \) has at least two peaks (Figure 1C, Method section), while the ridge plot has only one peak when there is no invalid IV. The corresponding abscission value at the lowest point between the two peaks is the optimal \( \lambda \). Thus equation (2) removes the invalid IVs with pleiotropic effects are larger than \( \lambda \).
+
+*Simulation*
+
+We generated the GWAS summary statistics of \( E \) heterogeneous populations with different edges’ effects, IV strength and pleiotropy in the cases of UVMR and MVMR, respectively. And we compared MR-EILLS with six published methods includes IVW, MR-Egger, MR-Lasso, MR-Median, MR-cML and MR-BMA, and all of them had the UVMR and MVMR version except MR-BMA. For these MR methods, we consider two strategies: metaMR: first meta all the GWAS summary statistics of multiple datasets for each variable then conduct the MR analysis; mrMeta: first conduct the MR analysis in multiple datasets separately then meta all the MR results. Meta methods include the random-effect and fixed-effect meta-analysis.
+
+[please insert the Figure 2 here]
+
+For UVMR, in case (a), when there is correlated and uncorrelated pleiotropy (30% invalid IVs), MR-EILLS and MR-cML with metaMR show the unbiased causal effect estimation, while other methods are biased (Figure 2). MR-EILLS exhibits the higher accuracy, more stable type I error rates when causal effect is 0, and higher statistical power when causal effect isn’t zero, than MR-cML with metaMR. When the proportion of invalid IVs is 80%, causal effect estimation using all MR methods including MR-cML are all biased, while MR-EILLS shows the unbiased causal effect estimation. MR-EILLS also exhibits the stable type I error rate when causal effect is 0 and statistical power is above 90% when the number of IVs is 300 in the case of causal effect is not zero. For the case (b), simulation results are similar as that in case (c). For the case (c), when there is no pleiotropy, all the methods show the unbiased causal effect estimation, stable type I error rate when causal effect is zero and high statistical power when causal effect isn’t zero. Simulation results are shown in Figure S2-S21.
+[please insert the Figure 3 here]
+[please insert the Figure 4 here]
+
+For MVMR, Figure 3 shows the causal effect estimation when there are 8 exposures, and 30% IVs have correlated or uncorrelated pleiotropy (case(a)). MR-EILLS shows unbiased causal effect estimations for all exposures, while other methods show the biased causal effect estimation, and MR-cML with metaMR also exhibits sightly biased causal effect estimations for some exposures. MR-EILLS also shows the highest accuracy among all methods. Figure 4 shows the type I error rate when causal effect is zero and statistical power when causal effect isn’t zero. MR-EILLS shows the highest statistical power when causal effect isn’t zero, and the most stable type I error rate while it is slightly lower than 0.05 for several exposures, but this phenomenon disappears when the number of populations is larger, e.g. \( E = 8 \) (Figure S2-S3). When \( P = 3 \), the results of simulation are similar as above. When the proportion of invalid IVs is 80%, causal effect estimation using all MR methods are biased, while MR-EILLS shows the unbiased causal effect estimation. MR-EILLS also exhibits the stable type I error rate when causal effect is 0 and statistical power is above 90% when the number of IVs is 300 in the case of causal effect is not zero. For the case (b), simulation results are similar as that in case (c). For the case (c), when there is no pleiotropy, all the methods show the unbiased causal effect estimation, stable type I error rate when causal effect is zero and high statistical power when causal effect isn’t zero. Simulation results are shown in Figure S22-S43. When \( P = 15 \), we calculate the mean of F1 score, recall and precision for each method in Figure 5. MR-EILLS shows the highest F1 score, recall and precision among all methods.
+
+[please insert the Figure 5 here]
+
+We also demonstrate the heterogeneity of causal effect estimations among different populations. The summary of \( I^2 \) for all simulation are shown in Table S1-S3. We randomly select one simulation and demonstrate its causal effects’ estimation for each MR methods and each dataset in Figure S31, S37 and S43, which show the forest plot of causal effect estimation in different populations for different methods. The \( I^2 \) in case (a) is higher than case (c), that is, the pleiotropy improve the heterogeneity between populations. The causal effect estimation in different populations show the inconsistent causal effect estimation.
+Application
+We explore the causal relationships between total 11 blood cells (5 red blood cells: hemoglobin concentration (HGB), hematocrit (HCT), mean corpuscular hemoglobin (MCH), mean corpuscular volume (MCV), mean corpuscular hemoglobin concentration (MCHC); 5 white blood cells: white blood cell count (WBC), neutrophil count (Neutro), monocyte count (Mono), basophil count (Baso), eosinophil counts (Eosin); 1 platelets: platelet count (PLT)) and 4 lung function indexes (forced expiratory volume (FEV), vital capacity (FVC), FEV/FVC ratio, peak expiratory flow (PEF)) using GWAS summary statistics from 5 ancestries: African, East Asian, South Asian, Hispanics Latinos and European. Details for GWAS summary statistics were shown in Method section and Table S4.
+
+Firstly, we conducted traditional MR analysis in 5 ancestries, respectively, and performed the heterogeneous analysis for each MR method. Results were shown in Figure 6A. We found that there were large heterogeneities (\( I^2 > 0.75 \)) for a number of blood cells in 5 ancestries. Then we conducted MR-EILLS analysis to explore independent causal effect from 11 blood cells on each lung function index. We plot ridge plots for each outcome in 5 ancestries and results were shown in Figure S44. Based on the ridge plot, we set the \( \lambda \) for MR-EILLS (Table S5). Results of MR-EILLS revealed that 3 blood cells (2 white blood cells: WBC and Neutro; 1 red blood cells: HGB) were causally associated with FEV; 1 blood cell (white blood cells: WBC) was causally associated with FVC; 3 blood cells (1 platelets: PLT; 2 red blood cells: HGB and HCT) was causally associated with FEV/FVC; 1 blood cell (red blood cells: HGB) was causally associated with PEF.
+
+[please insert the Figure 6 here]
+
+We found that the higher counts of some white blood cells, red blood cells or platelets would independently reduce the levels of lung function. For FEV, higher counts of WBC, Neutro and HGB would causally induce the lower level of FEV (WBC: beta=-0.14, 95%CI: [-0.24, -0.04]; Neutro: beta=-0.17, 95%CI: [-0.24, -0.04]; HGB: beta=-0.29, 95%CI: [-0.54, -0.03]). The counts of Neutro and HCT were negatively associated with the level of FVC (Neutro: beta=-0.09, 95%CI: [-0.18, -0.01]; HCT: beta=-0.06, 95%CI: [-0.13, -0.002]). Besides, elevation in the levels of PLT and Neutro were associated with a decreased FEV/FVC ratio (PLT: beta=-0.26, 95%CI: [-0.49, -0.02]; Neutro: beta=-0.16, 95%CI: [-0.30, -0.02]). Higher concentrations of MCH
+might result in a lower PEF level (beta=-0.08, 95%CI: [-0.16, -0.004]). James et al. validated that an increased WBC count has been associated with lower levels of lung function and provided the biological explanations [22]. A 15-year longitudinal study demonstrated that higher blood neutrophil concentrations was associated with accelerated FEV decline [23]. The inverse relations between FEV, FVC and red blood cell counts were also supported by observational studies [24-25]. A prospectively Longitudinal analyses revealed that higher baseline neutrophil count predicted lower serially obtained FVC [26]. A retrospective study found that there is a strong correlation between PLT and FEV/FVC ratio [27]. The results cover most of the expected causal links which have biological interpretations and several new links supported by previous observational literatures. Details of results were shown in Table S6-S11.
+
+Discussion
+
+In this paper, we proposed a MR method MR-EILLS, which works in both univariable and multivariable framework, and it outputted the global causal effect estimation of multiple heterogeneous populations using only GWAS summary statistics. Results of simulation exhibited the superior performance of MR-EILLS and its application in exploring causal relationships from 11 blood cells to lung function covered most of the expected causal links.
+
+MR-EILLS integrates the GWAS summary datasets from heterogeneous populations, and for each population, GWAS summary datasets for exposure and outcome can be from either the same individuals or the different but heterogeneous individuals. Actually, this assumption is the same as that in traditional two-sample MR analysis, which require two homogeneous but non-overlap samples. MR-EILLS assumes that the GWAS summary datasets for each population are from homogeneous but non-overlap samples. In the application, we assume that the individuals in each ancestry are homogeneous, and the genetic diversity in different ancestries lead the heterogeneous among ancestries (different IV strength and pleiotropy).
+
+MR-EILLS allows different IV set in different populations. However, the strategy for metaMR, that is, first conduct GWAS meta-analysis then perform MR analysis, require the SNPs that are independent (no LD) in all populations, this reduces a large number of IVs, although GWAS meta-analysis helps researchers obtain more significant SNPs with \( P < 5 \times 10^{-8} \). Besides, only a few MR methods allow the SNP set
+with large LD. MR-EILLS solved this tricky issue and it only requires that IV set in each population are independent without LD.
+
+MR-EILLS model has two hyper-parameters, which need researchers to set appropriate value to estimate causal effects of exposures on the outcome. For \( \gamma \), we recommend \( \gamma > 0.4 \) in UVMR, and \( \gamma > 0 \) in MVMR. The larger \( \gamma \), the stronger the role of empirical focused linear invariance regularizer. For \( \lambda \), we suggest the researchers plot the ridge plot to find the optimal value. In model (2), we keep the SNP, for which the pleiotropic effect in all populations is lower than \( \lambda \). When the scales of different populations are different, the model (2) can be modified as the following model (2-1)
+
+\[
+S^* = \{ j : |e_j^{(e)}| + \sum_{p \in P} |\hat{\theta}_{p,j}^{(e)} e_j^{(e)}| < \lambda_e \text{ for any } e \}.
+\] (2-1)
+
+The researchers can set different \( \lambda_e \) for different populations. For example, in our applications, we set different \( \lambda_e \) for five ancestries, respectively, and five ridge plots are plotted for each outcome. MR-EILLS works if and only if there are at least \( J \geq P \) valid IVs in the IV set and this assumption is less strict than the plurality assumption [17], which requires the valid IVs form the largest group of IVs sharing the same causal parameter value.
+
+There are several limitations for MR-EILLS. The first is that MR-EILLS doesn’t work in the high-dimensional case yet. One future key research direction is to extend MR-EILLS to high-dimensional exposure scenarios, especially for the high-dimensional-omics biomarkers, for this, correlated IVs is also an important issue to be solved. Another point is that inappropriate settings of hyper parameters may induce the incorrect inference of causal relationships between exposures and outcome. It is important to choose the appropriate for hyper parameters, especially for \( \lambda \). The value of \( \lambda \) determined that whether the invalid IVs are removed, and if \( \lambda \) is too large, the causal effect estimation would be distorted. If \( \lambda \) is too small, the number of remaining IVs is small, thus in the future it is necessary to extend MR-EILLS to correlated IVs scenarios.
+
+In conclusion, we proposed a MR method MR-EILLS, which integrate multiple heterogeneous GWAS summary datasets to infer the global causal relationships between exposures and outcome. This study has important guiding significance for the discovery of new disease-related factors. We look forward to offering constructive
+suggestions for disease diagnosis and applying our method beyond the scope considered here.
+
+Methods
+
+MR-EILLS model: MR integrating multiple heterogeneous populations
+For one population, assume \( P \) exposures \( X_p, p \in \{1,...,P\} \) and one outcome \( Y \). The \( J \) independent IVs \( G_j, j \in \{1,...,J\} \) satisfy the following three assumptions:
+A1. \( G_j \) is associated with at least one of \( P \) exposures;
+A2. \( G_j \) is not associated with the confounder between \( P \) exposures and the outcome;
+A3. \( G_j \) affects the outcome only through exposures.
+
+Then the MR model based on the individual data is:
+
+\[
+U = \sum_j \omega_j G_j + \varepsilon_{X_U}
+\]
+\[
+X_p = \sum_j \alpha_{pj} G_j + \sum_{k \in pa(X_p)} \beta_{k,X_p} X_k + \beta_{1p} U + \varepsilon_{X_p}
+\]
+\[
+Y = \sum_j \gamma_j G_j + \sum_p \beta_{0p} X_p + \beta_2 U + \varepsilon_Y
+\]
+
+where \( \varepsilon_{X_U}, \varepsilon_{X_p}, \varepsilon_Y \sim N(0,1) \). \( \gamma_j \) represents the uncorrelated pleiotropic effect and \( \omega_j \) represents the correlated pleiotropy. \( \beta_{0p} \) denote the causal effect of \( X_p \) on \( Y \). We call the exposures with \( \beta_{0p} \neq 0 \) are the causal exposures, which we want to discover, while the exposures with \( \beta_{0p} = 0 \) are the spurious exposures, which are not the true cause of outcome. We define the set of causal exposures is \( \{X_p\}, p \in P^* \subseteq \{1,...,P\} \). When \( P = 1 \), above model is called UVMR, while when \( P > 1 \), it is called MVMR. To simplify the expression, our model below uniformly uses \( P \) exposures, both applicable to UVMR and MVMR.
+
+GWAS summary statistics including \( G_j - X_p \) association \( \hat{\theta}_{p,j} \) and its variance \( \sigma^2_{p,j} \), as well as \( G_j - Y \) association \( \hat{\Gamma}_{y,j} \) and its variance \( \sigma^2_{y,j} \). Based on model (3), we have
+
+\[
+\theta_{p,j} = \alpha_{p,j} + \omega_j \beta_{1p} + \sum_{k \in pa(X_p)} \theta_{k,j} \beta_{k,X_p}
+\]
+\[
+\Gamma_{y,j} = \omega_j \beta_2 + \gamma_j + \sum_p \theta_{p,j} \beta_{0p}
+\]
+When \( G_j \) is a valid IV (no pleiotropy), that is \( \gamma_j = \omega_j = 0 \), then \( \varepsilon_j = \Gamma_{y,j} - \sum_p \theta_{p,j} \beta_{0,p} \) is zero and it is dependent with \( \theta_{p,j} \). For \( j \in \{1,...,J\} \), we can identify \( \beta_{0,p} \) (\( p \in \{1,...,P\} \)) by the system of linear equations \( \Gamma_{y,j} = \sum_p \theta_{p,j} \beta_{0,p} \) if and only if \( J \geq P \). The causal effects of exposures on the outcome \( \beta_{0,p} \) can be estimated by weighted version of ordinary least squares (OLS), that is, the IVW regression
+\[
+\hat{\Gamma}_{y,j} = \sum_p \hat{\theta}_{p,j} \beta_{0,p} + \zeta_j, \zeta_j \sim N(0, \sigma^2_{\zeta_j}),
+\]
+which set the intercept is zero. This model minimizes the empirical \( L_2 \) loss objective function
+\[
+\begin{align*}
+Q(\beta_{0,p}; \hat{\theta}_{p,j}, \hat{\Gamma}_{y,j}, \sigma^2_{\zeta_j}) \\
+= \mathrm{E}[|w_j \varepsilon_j|^2] \\
+= \mathrm{E}[|w_j (\hat{\Gamma}_{y,j} - \sum_p \hat{\theta}_{p,j} \beta_{0,p})|^2]
+\end{align*}
+\]
+where \( w_j \) represents the weight of IV \( G_j \) on the casual effect estimation. If \( G_j \) have uncorrelated pleiotropy (\( \gamma_j \neq 0 \)), that is, \( G_j \) is causally associated with \( Y \) not through any \( X_p \), then the \( \varepsilon_j = \gamma_j \) is no more equal to zero, and it represents the uncorrelated pleiotropic effect. MR-Egger regression [18] is proposed to solved this problem by allowing the intercept term in model (5), and the intercept represent the pleiotropic effect. MR-Egger regression requires the InSIDE assumption, which means the pleiotropic effect is independent with \( \theta_{p,j} \). If \( G_j \) have correlated pleiotropy (\( \omega_j \neq 0 \)), that is, \( G_j \) is causally associated with the unmeasured confounding \( U \) between \( X_p \) and \( Y \), then pleiotropic effect \( \varepsilon_j = \omega_j \beta_2 + \gamma_j \) is not independent with \( \theta_{p,j} \) because of the common term \( \omega_j \). This is the violation of the InSIDE assumption. Equation (5-6) and MR-Egger require that \( \varepsilon_j \) is independent with \( \theta_{p,j} \) because the correlation between intercept term and independent variables would distort the causal effect estimation. Results of motivating simulation for correlated and uncorrelated pleiotropy are shown in Figure S1.
+
+When there are \( E \) heterogeneous populations, GWAS summary statistics include \( \hat{\theta}^{(e)}_{p,j} \), \( \sigma^{(e)^2}_{G_j X_p} \), \( \hat{\Gamma}^{(e)}_{y,j} \) and \( \sigma^{(e)^2}_{y,j} \) for \( E = e \). We define \( \varepsilon^{(e)}_j = \Gamma^{(e)}_{y,j} - \sum_p \hat{\theta}^{(e)}_{p,j} \beta^{(e)}_{0,p} \) and \( \hat{\varepsilon}^{(e)}_j = \hat{\Gamma}^{(e)}_{y,j} - \sum_p \hat{\theta}^{(e)}_{p,j} \beta^{(e)}_{0,p} \) in the version of multiple populations. We use superscript \( (e) \)
+to denote the \( e \)-th population. We assume that the pleiotropic effect, IV strength and the relationships among exposures are different in heterogeneous populations, while the causal effects of causal exposures on \( Y \) is invariant, that is \( \beta_{0,p}^{(1)} = \beta_{0,p}^{(2)} = ... = \beta_{0,p}^{(E)} = \beta_{0,p}^* \) for \( p \in P^* \), this assumption called the structure assumption [21]. These assumptions are rational because the IV satisfying A1-A3 only control the unmeasured confounders between \( X_p \) and \( Y \), while other unmeasured confounders between IV and exposure, or between IV and outcome, or between exposures, are not controlled, and these unmeasured confounders also the reason for heterogeneity between populations.
+
+Note that one valid IV in one population may be the invalid IV in the other heterogeneous populations. On the other hand, an IV may be associated with the exposures in all heterogeneous populations, while it may have different uncorrelated or correlated pleiotropy in the different populations. This leads to inconsistent independence relationships between \( \theta_{p,j}^{(e)} \) and \( \varepsilon_j^{(e)} \) across different populations and inconsistent causal effect estimation of exposures on the outcome in different heterogeneous populations. Therefore, we leverage the Environment Invariant Linear Least Squares (EILLS) [21], the multiple heterogeneous populations version of OLS, to construct the MR-EILLS model. MR-EILLS model integrating the GWAS summary statistics from multiple heterogeneous populations, and find the causal exposures which have invariant effects with outcome in heterogeneous populations. MR-EILLS model aims to minimize the following objective function
+
+\[
+Q(\hat{\beta}_{0,p}; \hat{\theta}_{p,j}^{(e)}, \hat{\Gamma}_{y,j}^{(e)}, \sigma_{y,j}^{(e)2}) \\
+= \sum_{e \in E} w_j^{(e)} \mathbb{E}_{j \in S^e} [|\hat{\theta}_{p,j}^{(e)} \hat{\varepsilon}_j^{(e)}|^2] + \gamma \sum_{e \in E} w^{(e)} \sum_{p \in P} |\mathbb{E}_{j \in S^e} [\hat{\theta}_{p,j}^{(e)} \cdot w_j^{(e)} \hat{\varepsilon}_j^{(e)}]|^2
+\]
+
+where
+
+\[
+w_j^{(e)} = \frac{\sigma_{y,j}^{(e)2}}{\sum_{j \in S^e} \sigma_{y,j}^{(e)2}} \quad \text{and} \quad w^{(e)} = \frac{N_e}{N}
+\]
+
+\( w_j^{(e)} \) is the weight of IV \( G_j \) on the casual effect estimation in population \( E = e \), and \( w^{(e)} \) is the weight of population \( E = e \) on the final casual effect estimation. The first part of objective function (1) is the empirical \( L_2 \) loss, which is the multiple populations version of objective function (6) in one population. The second part of objective function (1) is the empirical focused linear invariance regularizer, which discourages
+selecting exposures with strong correlation between \( \theta_{p,j}^{(e)} \) and \( \varepsilon_j^{(e)} \) in some populations because this will distort the causal effect estimation. \( \gamma > 0 \) is the hyper parameter. In addition, we add the restriction
+
+\[
+S^* = \{ j : \sum_{e \in E} |\varepsilon_j^{(e)}| + \sum_{p \in P} \sum_{e \in E} |\hat{\theta}_{p,j}^{(e)} \varepsilon_j^{(e)}| < \lambda \}
+\]
+
+to select the valid IVs. The first part in equation (2) represents the uncorrelated pleiotropic effect for \( j-th \) IV, and the second part in equation (2) represents the correlated pleiotropic effect for \( j-th \) IV. \( \lambda > 0 \) is the hyper parameter controlling the strictness of filtering IVs. Equation (2) removes the invalid IVs with pleiotropic effect above \( \lambda \).
+
+The causal effects \( \beta_{0,p}^* \) can be identified under the assumption [21] that there are at least \( P \) valid IVs in the IV set, that is \( J \geq P \). We use the a limited-memory modification of the BFGS quasi-Newton method [28] to find the optimal solution \( \beta_{0,p}^* \) of objective function (1) under the restriction of equation (2). The confidence interval is estimated by Bootstrap method.
+
+**Simulation**
+
+We generate the GWAS summary statistics of \( E \) heterogeneous populations by following process:
+
+\[
+\begin{align*}
+\theta_{p,j}^{(e)} &= \alpha_{p,j}^{(e)} + \omega_j^{(e)} \beta_{1p}^{(e)} + \sum_{X_k \in pa(X_p)} \theta_{k,j}^{(e)} \beta_{X_k X_p}^{(e)} + \xi_{p,j}^{(e)} \\
+\Gamma_{y,j}^{(e)} &= \omega_j^{(e)} \beta_2^{(e)} + \gamma_j^{(e)} + \sum_p \theta_{p,j}^{(e)} \beta_{0p}^{(e)} + \xi_{y,j}^{(e)}
+\end{align*}
+\]
+
+Totally \( P \) exposures, the causal exposures are the top 30% of all exposures (e.g. \( P = 8 \), \( floor(P \times 30\%) = 2 \), then the top two (\( X_1 \) and \( X_2 \)) are the causal exposures). The effect of causal exposure on \( Y \) (\( \beta_{0p}^{(e)}, p \in P^* \)) is 0.2 for MVMR (\( P > 1 \)) and 0.1 for UVMR (\( P = 1 \)), and the effect of other spurious exposure on \( Y \) (\( \beta_{0p}^{(e)}, p \notin P^* \)) is 0.
+
+\( \beta_{X_k X_p}^{(e)} \sim U(-1,1) \) for the effect of edge \( X_k \rightarrow X_p \). We set IV strength \( \alpha_{p,j}^{(e)} \sim U(0.05,0.2) \) for \( E = e \) and \( X_p \); \( \xi_{p,j}^{(e)} \sim N(0,\sigma_{p,j}^{(e)2}) \) for \( E = e \) and \( X_p \), \( \sigma_{p,j}^{(e)2} \sim U(0.01,0.05) \) for \( X_p \); \( \xi_{y,j}^{(e)} \sim N(0,\sigma_{y,j}^{(e)2}) \) for \( E = e \), \( \sigma_{y,j}^{(e)2} \sim U(0.05,0.1) \) and different variances represent different sample sizes; \( \beta_{1p}^{(e)} \sim U(0.5,0.8) \) for \( X_p \); \( \beta_2^{(e)} \sim U(0.5,0.8) \). We consider three scenarios:
+(a) No pleiotropy;
+(b) uncorrelated pleiotropy effect \( \gamma_j^{(e)} \sim U(0,0.5) \).
+(c) uncorrelated and correlated pleiotropy effect, \( \gamma_j^{(e)} \sim U(0,0.5) \) and \( \omega_j^{(e)} \sim U(0,0.5) \).
+The parameters of edges’ effects, IV strength and pleiotropy are random select from uniform distribution, thus they are different in different datasets and these represent the heterogeneous datasets. We vary the number of populations are \( E = 3 \) or 8; the number of IVs is 100 or 300; the number of exposures is \( P = 1,\ 3,\ 8 \) or 15, which include the cases of univariable and multivariable MR.
+
+We conduct 200 repeated simulations to evaluate the performance of MR-EILLS. We also compare six methods includes IVW, MR-Egger, MR-Lasso, MR-Median, MR-cML and MR-BMA. For \( P = 1 \), we compare five methods in the UVMR version except MR-BMA; for \( P = 3,\ 8 \) and 15, we compare all six methods in the MVMR version. For these MR methods, we consider two strategies: (1) first meta all the GWAS summary statistics of \( E \) datasets for each variable then conduct the MR analysis; (2) first conduct the MR analysis in \( E \) datasets separately then meta all the MR results. Meta methods include the random-effect and fixed-effect meta-analysis.
+
+We evaluate the performance of all methods by box-violin plot for causal effect estimation, histogram for type I error when causal effect is zero and statistical power when causal effect isn’t zero. Besides, we calculate the \( I^2 \) statistics in each simulation, to evaluate the heterogeneity of causal effect estimation among different datasets, for each MR method. We plot the violin plot of \( I^2 \) statistics for the estimations of each variable, and we random select six simulations to demonstrate the quartiles of estimation, then plot the forest plot of estimations for each method and each variable. For \( P = 15 \), we calculate the mean of F1 score, recall and precision for each method. Recall (i.e. power, or sensitivity) measures how many relationships a method can recover from the true causal relationships, whereas precision (i.e., 1-FDR) measures how many correct relationships are recovered in the inferred relationships. The F1 score is a combined index of recall and precision.
+
+*Setting of hyper parameters \( \gamma \) and \( \lambda \)*
+
+We recommend that the practitioners determine the value of \( \lambda \) by plotting a ridge plot. The abscissa is the value of \( \sum_{e \in E} |e_j^{(e)}| + \sum_{p \in P} \sum_{e \in E} |\hat{\theta}_{p,j}^{(e)} e_j^{(e)}| \) for each IV in equation (8). We plot the ridge plot in simulations in Figure S45-S49. These plots demonstrates
+that when there is no pleiotropy, the figure has only one peak, and the \( \lambda \) just takes the value of the abscission after the first peak. When there is pleiotropy, the figure has two peaks, and the corresponding abscission value at the lowest point between the two peaks is the optimal \( \lambda \). We provide the function of ridge plot in R package MREILLS.
+
+In addition, we evaluate the root mean square error (RMSE) of causal effect estimation using a grid search: \( \gamma \) ranges from 0.1 to 200 and \( \lambda \) ranges from 0.1 to 1. Results are shown in the Figure S50-58. We conclude the ranges of hyper parameters when RMSE<0.1 in Table S12. For UVMR, we recommend \( \gamma > 0.4 \). When \( \gamma > 0.4 \), the RMSE is less than 0.1, especially for the case of correlated and uncorrelated pleiotropy, while in other cases, RMSE is less than 0.05. For MVMR, \( \gamma > 0 \) is recommended. Comparing with all valid IVs, invalid IVs increased the RMSE of causal effect estimation, no matter correlated or uncorrelated pleiotropy. Therefore, \( \gamma \) is loosely valued, especially when \( P > 1 \). The larger \( \gamma \), the stronger the role of empirical focused linear invariance regularizer.
+
+*Application*
+
+We explored the causal effect of 11 blood cells on 4 lung function indexes using GWAS summary statistics from 5 ancestries: African, East Asian, South Asian, Hispanics Latinos and European. GWAS summary statistics for blood cells were extracted from Chen et al. [29], which conducted trans-ethnic and ancestry-specific GWAS in 746,667 individuals from 5 global populations (15,171, 151,807, 8,189, 9,368 and 563,947 individuals for 5 ancestries, respectively). GWAS summary statistics for lung function were extracted from Shrine et al. [30], which conducted trans-ethnic GWAS analysis in 49 cohorts from 5 populations (8,590, 85,279, 4,270, 14,668 and 475,645 individuals for 5 ancestries, respectively). Details are shown in Table S4.
+
+Firstly, we select IVs for MR analysis. For MR-EILLS and mrMeta analysis, we separately select SNPs with \( P < 5 \times 10^{-8} \) and clump the LD with \( r^2 > 0.01 \) in each population (Table S9). For metaMR analysis, we select SNPs with \( P < 5 \times 10^{-8} \) in each population then clump the union set of above SNPs with \( r^2 > 0.01 \) (Table S10). Then we extract the summary statistics for IVs and conduct the MR-EILLS, mrMeta and metaMR analysis. We also calculate the \( I^2 \) statistics to evaluate the heterogeneity of causal effect estimation among different populations, for each MR method. For MR-
+EILLS, we plot the ridge plot in each population, and set \( \gamma = 0.5 \). The setting of \( \lambda \) are shown in the Table S5.
+Acknowledgements
+
+None.
+
+Author Contributions
+
+LH and ZX conceived the study. LH contributed to theoretical derivation with assistance from ZX. LH and HC contributed to the data simulation and application. LH and ZX wrote the manuscript with input from all other authors. All authors reviewed and approved the final manuscript.
+
+Competing Interests statement
+
+The authors declare no competing interests.
+
+Data and code availability
+
+GWAS summary statistics for blood cells are publicly available at http://www.mhi-humangenetics.org/en/resources/. The GWAS summary data for lung function are publicly available at GWAS catalog. All the analysis in our article were implemented by R software (version 4.3.2). R packages used in our analysis include TwoSampleMR, MendelianRandomization, and ggplot2. MREILLS model can be implemented by R package https://github.com/hhoulei/ MREILLS. All the codes for simulation are uploaded in https://github.com/hhoulei/MREILLS_Simul.
+
+Ethics approval and consent to participate
+
+The data used in our study was all publicly available and obtained written informed consent from all participants.
+
+Source of Funding
+
+This work was supported by the National Natural Science Foundation of China (Grant 82404378, T2341018), China Postdoctoral Science Foundation (Grant GZB20230011, 2024M750115, 2024T170014).
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+Figure Legends
+
+Figure 1. MR-EILLS model. MR-EILLS model aims to infer the causal relationships between one or multiple exposures and one outcome, integrating multiple GWAS summary datasets from heterogeneous populations. Ther are different pleiotropic effects and IV strengths for the same IVs in heterogeneous populations. The objective function of MR-EILLS model considers the both correlated and uncorrelated pleiotropy and remove the invalid IVs. Figure (A-C) are the results of motivating simulation. Figure (A) shows the point plot for absolute value of \( \hat{\varepsilon}_j^{(e)} \) in different populations, and larger point means the larger value of \( | \hat{\varepsilon}_j^{(e)} | \). As the pleiotropic effect larger, the \( | \hat{\varepsilon}_j^{(e)} | \) is larger, thus the first part of MR-EILLS model minimize pleiotropic effect between different populations. Figure (B) shows the correlation between \( \hat{\varepsilon}_j^{(e)} \) and \( \hat{\theta}_{p,j}^{(e)} \), which representing the correlated pleiotropic effect or the violation of InSIDE assumption. As the correlated pleiotropic effect increasing, this correlation is larger. This corresponding to the second part of MR-EILLS, the empirical focused linear invariance regularizer, which discourages selecting exposures with strong correlation between \( \theta_{p,j}^{(e)} \) and \( \varepsilon_j^{(e)} \) in some populations because this correlation would distort the causal effect estimation. Figure (C) shows the ridge plot of \( \sum_{e \in E} |\varepsilon_j^{(e)}| + \sum_{p \in P} \sum_{e \in E} |\hat{\theta}_{p,j}^{(e)} \varepsilon_j^{(e)}| \) when there are different proportion of invalid IVs. When there are invalid IVs, the ridge plot has two peaks, while the ridge plot has only one peak when there is no invalid IV. The corresponding abscission value at the lowest point between the two peaks is the optimal \( \lambda \). The third part of MR-EILLS model is removing the invalid IVs by \( \lambda \).
+
+Figure 2. Simulation results when \( P =1 \) (UVMR). (A-B) Results of causal effect estimation and type I error rate when the causal effect is zero. (C-D) Results of causal effect estimation and type I error rate when the causal effect is 0.1. The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is \( E = 3 \).
+
+Figure 3. Simulation results of causal effect estimation when \( P =8 \) (MVMR). The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is \( E = 3 \).
+
+Figure 4. Simulation results of type I error rate for spurious exposures and statistical power for causal exposures when \( P =8 \) (MVMR). The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is \( E = 3 \).
+Figure 5. Simulation results of F1 score, precision and recall when \( P = 15 \) (MVMR).
+The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is \( E = 3 \).
+
+Figure 6. Results in application. (A) the heterogeneity among different populations; (B) the causal effect estimations of 11 blood cells on lung function.
+Figures
+
+Summary statistics:
+\( G \rightarrow X_j \) association \( \hat{\theta}_{j}^{(i)} \), \( \sigma_{j}^{(i)} \)
+\( G \rightarrow Y_j \) association \( \hat{\Gamma}_{j}^{(i)} \), \( \sigma_{j}^{(i)} \)
+
+Heterogeneity:
+Different pleiotropy: \( (\hat{\theta}_{j}^{(1)} \neq \hat{\theta}_{j}^{(2)} \neq ... \neq \hat{\theta}_{j}^{(E)}) \)
+Different IV strength: \( (\sigma_{j}^{(1)} \neq \sigma_{j}^{(2)} \neq ... \neq \sigma_{j}^{(E)}) \)
+
+Question: How to infer global causal relationships by integrating multiple heterogeneous GWAS summary datasets?
+
+MR-EILLS Model:
+
+\[
+\min \sum_{i} w^{(i)} E_{j,s}[\hat{w}_{j}^{(i)} \hat{\theta}_{j}^{(i)}] + \gamma \sum_{i} \sum_{s} w^{(i)} |E_{j,s}[\hat{\theta}_{j}^{(i)} \hat{w}_{j}^{(i)} \hat{\theta}_{j}^{(i)}]|^2, \text{where } S^* = \{ j : \sum_{i} \hat{\theta}_{j}^{(i)} + \sum_{i} \sum_{s} \hat{\theta}_{j}^{(i)} \hat{\theta}_{j}^{(i)} < \lambda \}
+\]
+
+Empirical L_2 loss   Focused linear invariance regularizer   Remove invalid IVs
+
+Figure 1. MR-EILLS model. MR-EILLS model aims to infer the causal relationships between one or multiple exposures and one outcome, integrating multiple GWAS summary datasets from heterogeneous populations. There are different pleiotropic effects and IV strengths for the same IVs in heterogeneous populations. The objective function of MR-EILLS model considers the both correlated and uncorrelated pleiotropy and remove the invalid IVs. Figure (A-C) are the results of motivating simulation. Figure (A) shows the point plot for absolute value of \( \hat{\theta}_{j}^{(i)} \) in different populations, and larger point means the larger value of \( |\hat{\theta}_{j}^{(i)}| \). As the pleiotropic effect larger, the \( |\hat{\theta}_{j}^{(i)}| \) is larger, thus the first part of MR-EILLS model minimize pleiotropic effect between different populations. Figure (B) shows the correlation between \( \hat{\theta}_{j}^{(i)} \) and \( \hat{\theta}_{j}^{(i')} \), which representing the correlated pleiotropic effect or the violation of InSIDE assumption. As the correlated pleiotropic effect increasing, this correlation is larger. This corresponding to the second part of MR-EILLS, the empirical focused linear invariance regularizer, which discourages selecting exposures with strong correlation between \( \hat{\theta}_{j}^{(i)} \) and \( \hat{\theta}_{j}^{(i')} \) in some populations because this correlation would distort the causal effect estimation. Figure (C) shows the ridge plot of \( \sum_{i}|\hat{\theta}_{j}^{(i)}| + \sum_{i} \sum_{s} |\hat{\theta}_{j}^{(i)} \hat{\theta}_{j}^{(i)}| \) when there are different proportion of invalid IVs. When there are invalid IVs, the ridge plot has two peaks, while the ridge plot has only one peak when there is no invalid IV. The corresponding abscission value at the lowest point between the two peaks is the optimal \( \lambda \). The third part of MR-EILLS model is removing the invalid IVs by \( \lambda \).
+
+Figure 1
+
+See image above for figure legend.
+Figure 2
+
+Simulation results when P =1 (UVMR). (A-B) Results of causal effect estimation and type I error rate when the causal effect is zero. (C-D) Results of causal effect estimation and type I error rate when the causal effect is 0.1. The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is E=3.
+
+![Boxplots and bar charts showing simulation results for causal effect estimation and type I error rate under different methods and causal effects](page_48_67_1495_495.png)
+Figure 3
+
+Simulation results of causal effect estimation when P=8 (MVMR). The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is E=3.
+Figure 4
+
+Simulation results of type I error rate for spurious exposures and statistical power for causal exposures when P =8 (MVMR). The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is E=3.
+Figure 5
+
+Simulation results of F1 score, precision and recall when P=15 (MVMR). The number of IVs is 100 and the proportion of invalid IVs is 30%. The number of populations is E=3.
+
+![Bar chart showing simulation results of F1 score, precision and recall for different methods](page_42_68_1497_312.png)
+
+Figure 6
+
+Results in application.(A) the heterogeneity among different populations; (B) the causal effect estimations of 11 blood cells on lung function.
+
+![Panel plots showing heterogeneity and causal effect estimation for lung function and blood cells](page_42_370_1497_312.png)
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+• SupplementaryTable.xlsx
+• SupplementaryMaterials1208.docx

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@@ -0,0 +1,385 @@
+Deep Learning Driven Adaptive Optics for Single Molecule Localization Microscopy
+
+Fang Huang (fanghuang@purdue.edu)
+Purdue University West Lafayette  https://orcid.org/0000-0003-1301-1799
+
+Peiyi Zhang
+Purdue University  https://orcid.org/0000-0002-1100-3720
+
+Donghan Ma
+Purdue University  https://orcid.org/0000-0001-6264-2824
+
+Xi Cheng
+Purdue University
+
+Andy Tsai
+Indiana University
+
+Yu Tang
+Purdue University
+
+Hao-Cheng Gao
+Purdue University
+
+Li Fang
+Purdue University
+
+Cheng Bi
+Purdue University West Lafayette
+
+Gary Landreth
+Indiana University School of Medicine  https://orcid.org/0000-0002-8808-424X
+
+Alexander Chubykin
+Purdue University West Lafayette  https://orcid.org/0000-0001-8224-9296
+
+Brief Communication
+
+Keywords:
+
+Posted Date: June 2nd, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1690151/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+Deep Learning Driven Adaptive Optics for Single Molecule Localization Microscopy
+
+Peiyi Zhang1, Donghan Ma1,2, Xi Cheng3,4, Andy P. Tsai5, Yu Tang3,4, Hao-Cheng Gao1, Li Fang1, Cheng Bi1, Gary E. Landreth5,6,* Alexander A. Chubykin3,4,* and Fang Huang1,4,7,*
+
+1Weldon School of Biomedical Engineering, Purdue University, West Lafayette, IN, USA
+2Davidson School of Chemical Engineering, Purdue University, West Lafayette, IN, USA
+3Department of Biological Sciences, Purdue University, West Lafayette, IN, USA
+4Purdue Institute for Integrative Neuroscience, Purdue University, West Lafayette, IN, USA
+5Stark Neurosciences Research Institute, Indiana University School of Medicine, Indianapolis, IN, USA.
+6Department of Anatomy, Cell Biology and Physiology, Indiana University School of Medicine, Indianapolis, IN, USA
+7Purdue Institute of Inflammation, Immunology and Infectious Disease, Purdue University, West Lafayette, IN, USA
+*Correspondence to: fanghuang@purdue.edu, chubykin@purdue.edu, glandret@iu.edu
+
+INTRODUCTION
+Fluorescent microscopy is an indispensable tool in visualizing cellular and tissue machinery with molecular specificity, however, its resolution is limited to 250-700 nm laterally and axially due to the diffraction of light1. Molecular features smaller than this limit cannot be resolved. Super-resolution microscopies such as Stimulated Emission Depletion Microscopy (STED)2, Structured Illumination Microscopy (SIM)3, and Single Molecule Localization Microscopy (SMLM)4–6 have overcome this barrier, allowing biological observations well beyond this fundamental limit of light. In particular, SMLM detects isolated photo-switchable or convertible fluorescent dyes or proteins, pinpoints the centers of individual probes from their emission patterns, and reconstructs the molecular centers into a super-resolution image. Localization precision as low as 1-10 nm can be achieved in fixed and living cells7–11.
+SMLM in tissues, however, is challenging. One major reason is the distortion and blurring of single molecule emission patterns (i.e. PSFs) caused by the inhomogeneous refractive indices within the tissue. Such alteration often reduces the information content\(^{12}\) carried by each detected photon, increases localization uncertainty, and thus causes significant resolution loss, which is irreversible by post-processing\(^{13}\). Reversing these sample induced aberrations requires optical path modifications in a microscopy system, commonly with a deformable mirror or a spatial light modulator, responsive towards each specimen and field-of-view to adaptively restore the PSFs of single emitters, and thus the achievable resolution. This process is known as adaptive optics (AO)\(^{14-18}\).
+
+Guiding a deformable mirror to compensate sample induced aberrations, the distorted wavefront needs to be measured\(^{16,17}\). For point-scanning microscopes, such as confocal and two-photon, the detection focus serves as a 'guide star' providing a stable wavefront measurable both directly and indirectly\(^{14,15,17,18}\). In contrast, wavefronts of single molecule emissions, in spite of their abundance in SMLM experiments, cannot be directly measured as the signals from individual molecules blink stochastically with limited photons\(^{19}\). Besides, wavefronts passing through the system are composed of not only the aberrated wavefront induced by the specimen, but also the wavefront variations induced by lateral and axial positions from a collection of emitters in a volume. For this reason, current sensorless AO-SMLM developments\(^{20-24}\) focus on iteratively introducing mirror changes then evaluating the changes with image-quality metrics. Despite that these iterative methods require a large number of cycles, each including image acquisition and mirror changes, to reach the optimal correction, these approaches provide robust corrections for tissue induced aberrations only when the target tissue structures are *planar* or with small axial extent (**Supplementary Fig. 1**). This is because emission patterns from single molecules at different axial positions results in inconsistent, and, in some cases,
+even opposite metric responses and thus fundamentally limit the efficacy of these approaches for aberration correction in tissues (Supplementary Note 1).
+
+Bypassing the previous iterative trial-then-evaluate processes, we developed deep learning driven adaptive optics for SMLM to allow direct inference of wavefront distortion and near real-time compensation. Our trained deep neural network (DNN) monitors the individual emission patterns from single molecule experiments, infers their shared wavefront distortion, feeds the estimates through a dynamic filter (Kalman), and drives a deformable mirror to compensate sample induced aberrations. The method, referred to as deep learning driven adaptive optics (DL-AO) for single molecule imaging, simultaneously estimates and compensates 28 types of wavefront deformation shapes, restores single molecule emission patterns approaching the conditions untouched by specimen, and improves the resolution and fidelity of 3D SMLM through thick tissue specimens over 130 μm, with as few as 3-20 mirror changes.
+
+RESULTS
+1. Design of DL-AO
+
+Single molecule emission patterns generated by individual fluorescence molecules carry information not only about their molecular center positions, but also about the shared wavefront distortion\(^{25}\). The random lateral and axial positions of the blinking fluorescent molecules and their limited photons emitted in SMLM experiments, make these emission patterns unsuitable for direct wavefront measurement\(^{14,15}\). Single molecule deep neural network (\( \textbf{smNet} \))\(^{26}\) was demonstrated in its capacity to infer wavefront distortions from individual PSFs in simulation and its responsiveness in experimental datasets. Moving from the inference task to active control of a deformable mirror driven by deep learning is, however, nontrivial. Here, we describe our developments in experimental wavefront based training, stacked estimation networks, and stabilized feedback controls through Kalman filter (**Fig. 1**).
+Upon detection of SMLM frames, single molecule-containing sub-regions are segmented and sent to the network (Supplementary Note 2.2). Each input sub-region goes through a sequence of template matching processes, which are organized as convolutional layers\(^{27,28}\) and residual blocks\(^{29}\) with PReLU activations\(^{30}\) and batch normalizations\(^{31}\) in between, then "fully connects" through 1×1 convolutional layers to an output vector of 28 values — amplitude estimates for wavefront shapes in terms of the native mirror deformation modes\(^{32}\) (hereafter referred to as mirror modes). Representing wavefront with coefficients of orthogonal basis helps cut down on the number of outputs and network parameters to be optimized in training. Forming this orthogonal basis directly from native mirror deformations further ensured the coefficients' accuracy in representing mirror responses. With this consideration, the conversion from mirror modes to Zernike polynomials\(^{33}\)—commonly used as the analytical basis to describe aberrations—is dropped to minimize mismatches between mirror responses and Zernike-based wavefront shapes (Supplementary Note 3). The residual differences between theoretical expectations and experimental mirror deformations (Supplementary Fig. 4) are incorporated into training data generation.
+
+To build an accurate link between experimentally detected emission patterns and the mirror control with neural networks, it is imperative to train the network with data that match those obtained experimentally. However, experimental training data of single molecules are challenging to obtain, since the ground-truth wavefronts are usually unknown and the extensive variations of the intensity, background, and the lateral and axial locations of single emitters, are impractical to cover experimentally. To this end, we simulate wavefront distortions by linearly combining the mirror deformations obtained experimentally in the SMLM system (Supplementary Note 4). We then use the coefficients of these experimental patterns to form the output of the network. The static residue of system aberration after optimizing the microscope system is also incorporated as the baseline of the wavefront shapes. This allows us
+to efficiently generate millions of training PSFs based on experimentally measured wavefronts with highly accurate training ground truth (Supplementary Note 4, Supplementary Fig. 2, 3D normalized cross correlation (NCC) value of >0.95, comparing measured PSFs with those generated from network estimation).
+
+Compensating wavefront distortions inferred from PSFs of blinking molecules, we found that the network proposed mirror change fluctuates with non-vanishing uncertainty before/after each mirror update. This uncertainty increases with the network training range, resulting in a trade-off between the compensation range and stability (Fig. SS1). To this end, we drive the deformable mirror by dynamically switching three networks trained with different aberration scales where the transitions between networks are based on the inference uncertainty (Supplementary Note 2.5). To stabilize network transitions, we employ Kalman filter\(^{34}\) (Supplementary Note 2.4 and 5) to reduce the estimation uncertainty by recursively combining wavefront measurements before and after each correction. Due to the uncontrollable availability of single molecule emission patterns with a high signal-to-background ratio and the evolving PSFs after each correction, this process weighs heavily on high precision measurements against the uncertain ones to ensure stable feedback from the network (Supplementary Figs. 5, 6).
+
+2. DL-AO characterization
+
+First, we characterized the response accuracy of DL-AO network using controlled wavefront distortions generated by the deformable mirror. These wavefront distortions resulted in aberrated emission patterns, which were then collected and sent to DL-AO network (Methods). By comparing the induced deformation amplitudes with those estimated by DL-AO, we observed that DL-AO network responded towards individual mirror deformations mostly in a one-to-one manner. And this behavior was consistently observed with both beads samples and blinking single molecules from immune-fluorescence-labeled cell specimens (Supplementary Figs. 4, 5, Fig. SS2). At the same time, we also observed that DL-AO sensed changes in other mirror
+modes besides the one actually being changed, an expected behavior considering that mirror modes are coupled experimentally (Supplementary Note 3). Due to such coupling, mapping between the wavefront shape and mirror mode amplitudes is no longer unique, and therefore we further quantified the network response accuracy through wavefront shape errors and PSF similarities. We observed that independent measurements from DL-AO and phase retrieval\(^{13,35}\) using PSFs of fluorescent beads resulted in nearly identical wavefront shapes with a small difference of \(0.13 \pm 0.02\) rad (mean ± s.t.d, N=28) quantified in root mean square wavefront error\(^{33}\) (\(W_{rms}\), Methods, Supplementary Fig. 4). Further, comparing the wavefronts estimated by DL-AO network using single molecule blinking data (100 PSFs) to that retrieved by phase retrieval from beads, we observed high similarities of \(0.83 \pm 0.06\) (mean ± s.t.d, N=28, normalized cross correlation), and a small wavefront difference of \(0.15 \pm 0.03\) rad (mean ± s.t.d, N=28) in \(W_{rms}\) (Supplementary Fig. 5). For the majority of our introduced distortions below 3 radians in \(W_{rms}\), a single mirror update can already reduce the wavefront error by 50% (Fig. 2E, 2F, Supplementary Fig. 10). Caused by the nonlinear mirror deformation response to control input\(^{36}\), and the decreased network response amplitudes with the decreasing signal to noise level or the increasing network training range (Supplementary Figs. 5 and Fig. SS2), we observed that it usually requires 3-20 mirror updates for full compensation.
+
+DL-AO aims to restore PSFs to the level unmodified by the specimen. To characterize DL-AO's capacity for PSF restoration, we introduced random wavefront distortions using the deformable mirror and compensated these distortions with DL-AO during SMLM experiments with immune-fluorescence-labeled TOM20 in COS-7 cells. Visualizing the raw blinking data during the correction, we found the PSFs became less distorted even after a single compensation, and the mirror shape became stable after ~4 mirror updates (Fig. 2A). Since PSFs from blinking molecules have limited photons and stochastic positions, making them challenging to quantify, we further verified the PSF shape post correction by axially scanning fluorescent beads nearby
+the compensation areas. Through phase retrieval, we found DL-AO results share a highly similar and flat wavefront shape with the instrument optimum (Methods, Supplementary Note 4), with a residual of 0.29 ± 0.12 rad in \( W_{rms} \) (mean ± s.t.d, N=11, Fig. 2B). Comparing the PSFs post DL-AO and the instrument optimum, high similarities of 0.95 ± 0.02 (mean ± s.t.d, N=11) were consistently achieved, quantified by 3D normalized cross correlation (Fig. 2B, Supplementary Fig. 8), and remained 0.96 ± 0.01 (mean ± s.t.d, N=11 in NCC) for distortion levels from 0.25 to 2.75 radians in \( W_{rms} \) (Supplementary Fig. 7). Often, this level of restoration was achieved with only 3-6 mirror updates (Supplementary Fig. 8B), and a single mirror update from DL-AO network reduced the wavefront error by 61.2% ± 24.2% (mean ± s.t.d, N=11). To drive each mirror update, as few as two sub-regions containing isolated single emitters were used for DL-AO network estimation, which spent an average of 0.1 second for forward propagation (Supplementary Table 3, Supplementary Fig. 8) and made DL-AO suitable for real-time compensation during SMLM acquisition.
+
+Next, we evaluated the robustness of DL-AO on compensating different levels of wavefront distortion, from 0.25 to 2.75 radians in \( W_{rms} \), by assessing the residual wavefront error post correction using both simulation and single molecule blinking data. After one mirror update, we observed that 51.9±9.3% and 64.3±12.8% (mean ± s.t.d, N = 165) of the induced level was compensated for experimental and simulated data, respectively (Fig. 2E-F). After 19 mirror updates, the residual level was 0.32 ± 0.02 and 0.08 ± 0.03 (mean ± s.t.d, N=165) radians respectively for experimental and simulated data (Supplementary Fig. 10). This is a significant improvement, as compared to existing metric-based methods\(^{20-24}\), for example, Robust and Effective Adaptive Optics in Localization Microscopy (REALM)\(^{24}\), which works up to 1 radian at the expense of 10 mirror updates per aberration mode, requiring a total of 330 updates to compensate 11 aberration types (3 rounds)\(^{24}\). In addition, metric-based AO is unstable when imaging volumetric cellular structures (Figs 2C, 2D, 2G, Supplementary Figs. 1, 11 and 12). A
+detailed discussion and quantification of these intrinsic limitations of metric-based methods can be found in Supplementary Note 1.
+
+3. DL-AO validation through constructed tissue and cell specimens.
+
+Inhomogeneous refractive indices within cells and tissues redirect and scatter light. In particular, the mismatches between refractive indices in sample media and objective immersion media reduce the shape modulation of the single molecule emission patterns axially and broaden the focus laterally (Fig. 2D), increasing the localization uncertainty in all directions and thus worsening the resolution of SMLM. Such resolution deterioration becomes more drastic with an increasing imaging depth\(^{13}\).
+
+Here, we demonstrate DL-AO's capacity in compensating significant index mismatch induced aberrations using constructed specimens from ~35 \( \mu \)m to 134 \( \mu \)m in thickness with water-based imaging media. Imaging immune-fluorescence-labeled Tom20 in COS-7 cells through such thickness without AO correction, the super resolution images of Tom20 proteins showed nearly no axial distributions (visualized by color differences, Fig. 3A, Supplementary Figs. 13A, 14A), a consequence of the severe lack of shape modulation along the axial direction due to the large imaging depth. While the raw data for both cases in the comparison were acquired in an interleaved manner without and with AO (Methods), DL-AO reconstruction showed the expected outer membrane contours of mitochondria, and without AO the reconstruction displayed significant artifacts (Fig. 3B, 3C). Zooming in on the lateral dimension, we observed the aggregations of Tom20 proteins, known to form clusters\(^{37}\), when aberrations were corrected by DL-AO. In comparison, without DL-AO, the lateral reconstruction of Tom20 distribution is diffusive (Fig. 3D, 3G), as a result of deteriorated lateral resolution through the large imaging depth. This resolution contrasts without and with DL-AO are consistently observed with different samples (Fig. 3E-G, Supplementary Figs. 13-14).
+Next, we illustrate the mechanism behind such resolution improvement (Fig. 3H-K) by looking at the PSFs and pupil function, which summarizes how the sample together with optical system modulates the collected light, before and after AO. In comparison to the near uniform distribution of magnitude and phase in the pupil obtained from an in vitro bead, wavefront (phase in the retrieved pupil) showed significant radial variations and increased phase wrappings at large radial positions (Fig. 3H, Supplementary Figs. 13D, 14D). As a result, the PSFs at different axial positions throughout a 2 μm axial range remained nearly invariant (Fig. 3J). Such loss of PSF shape modulation results in localization artifacts where identical axial positions are falsely assigned to molecules despite their axial distributions. In contrast, DL-AO restored the flatness of the wavefront, resulting in PSFs that are highly similar to the instrument optimum (Fig. 3H, 3J, Supplementary Figs. 13D, 14D). These improvements in PSF sharpness and modulation explain the resolution improvement post DL-AO (Fig. 3C, 3D, 3F, 3G, Supplementary Figs. 13C, 14C) and are further quantified statistically showing significantly increased Fisher information content per photon upon DL-AO correction (Fig. 3K).
+
+We further demonstrated DL-AO on arbitrary tissue-induced aberrations by imaging through 200-μm thick unlabeled brain sections resolving membrane of mitochondria using immune-fluorescence-labeled Tom20 in COS-7 cells (Fig. 4). Without DL-AO, our observation is consistent with those through water based cavities where the information of Tom20's axial distribution is lost even with in situ PSF model (Fig. 4A). Further deterioration is observed both laterally and axially (Fig. 4A, 4F) using in vitro PSF model with theoretical index mismatch aberration incorporated. With DL-AO, the 3D reconstruction shows improved resolution, where such improvement can be visualized laterally by the distinct Tom20 protein clusters and axially by the mitochondria membrane contours (Fig. 4B-E).
+4. Resolving Amyloid-β (Aβ) fibrils through 125 μm mouse brain sections
+
+The 3D structures of amyloid-β (Aβ) fibrils are a focus of interest in the studies of Alzheimer's disease (AD) and are of particular importance with the success of amyloid-directed therapeutics\(^{38,39}\). Visualizing the formation and aggregation of these fibrils within the brain has been limited by the significant resolution loss when imaging through tissues. With DL-AO adaptively optimizing single molecule emission patterns during SMLM imaging, we can now clearly resolve the organization of immune-fluorescence-labeled β-amyloid fibrils in 125 μm thick brain sections from 5XFAD mice, a transgenic AD model that exhibits robust amyloid plaque pathology similar to that found in the human AD brain\(^{40}\) (**Fig. 5**). We imaged Aβ fibrils through these thick brain tissues without and with DL-AO in an interleaved manner. We observed improved resolution in both axial and lateral directions with DL-AO in comparison with that of no-AO (**Fig. 5B**). Importantly, driven by DL-AO, SMLM reconstruction revealed the 3D organization of individual amyloid fibrils entangling and forming the plaque. However, while without DL-AO, the resolution deteriorates, making the intricate fibril ultrastructure look like blurry clusters (**Fig. 5B, 5C**). In addition, inspection of the axially color-coded lateral images and axial cross-section revealed that the fibril structures in the axial direction were distorted and flattened without DL-AO. A similar phenomenon was observed in the presence of spherical aberrations in the previous evaluation of mitochondria membranes (**Figs. 3, 4, 5B, 5C**).
+
+Interestingly, with DL-AO, our reconstructed super-resolution images using *in vitro* or *in situ* PSF models revealed highly similar results, suggesting that DL-AO has restored the aberrated emission patterns approaching the instrument optimum. Combining DL-AO with INSPR, we imaged fibril structures in different plaque areas (**Fig. 5D-I**), and were able to consistently resolve individual fibrils and revealed their 3D arrangements within plaques at various stages (**Fig. 5F-I**). Measuring the width of Aβ fibrils in tissues, we obtained an averaged width of about \(52 \pm 9\) nm (mean ± s.t.d, N = 30) and \(72 \pm 19\) nm (mean ± s.t.d, N = 30) in lateral and axial
+cross-sections, respectively (Fig. 5J). We note that these measured fibril widths have slight variations among different imaged plaques.
+
+5. Resolving dendritic spines through 150-250 μm mouse brain sections
+
+Using deep learning driven adaptive optics to correct sample induced aberrations, and in situ PSF model to perform super resolution reconstruction post-AO correction, we performed SMLM imaging through 150-250 μm thick brain tissues resolving dendritic spines, the 300-800 nm tiny protrusions from the dendrites whose morphology changes in response to neuronal activities associated with learning and memory41,42. Insufficient spatial resolution leads to an erroneous classification of spines43,44 due to their miniature sizes. The capacity to resolve spines' ultrastructure within their tissue environment is critical in detecting morphological changes in the same area of the functional measurements. This technological advancement will allow electrophysiological and morphological mapping of the same neural circuits linking functional and structural synaptic plasticity with animal behavior45. We imaged Thy1-ChR2-EYFP transgenic mice, expressing Channelrhodopsin-2 enhanced yellow fluorescent protein (EYFP) fusion protein in cortical L5 Thy1+ pyramidal cells46. Through a 250-μm-thick brain section, we resolved the distinct membrane distribution of the fluorescently tagged target decorating the dendritic spines (Fig. 6, Supplementary Fig. 15). Throughout the resolved volume of spines, we can observe the membrane-bounded structures as hollow tubes and blobs (Fig. 6D). Besides, the very thin neck of spines can be clearly visualized (Fig. 6E, Supplementary Fig. 15), which provides more accurate information about the dimension of spines. We also imaged 150-μm-thick mouse brain sections (Fig. 6B, 6C), where thinner sections provide a better signal to background ratio. Interestingly, we observed a few occurrences where dendrite membranes labeled ChR2-EYFP appeared to be twisted in the final reconstructed images (Fig. 6C), which may represent a type of physical substrate for decreasing gain for synaptic inputs47,48. We obtained an average localization precision of 13 nm and 57 nm in lateral and axial dimensions
+when imaging through the 250-μm-thick brain section, and 11-52 nm (lateral-axial) precision when imaging through the 150-μm-thick brain section. The capacity to resolve and accurately quantify the shape and size of dendritic spines throughout large tissue thickness paves the way to link spine morphology and function and will facilitate studies of learning, memory, and brain disorders.
+
+DISCUSSION
+Combing the power of single molecule deep neural network with careful designs in network training, feedback, and instrument control, we demonstrated that DL-AO optimizes PSFs approaching the instrument optimum during SMLM experiments, and restores the resolution of 3D SMLM through >130 μm depth of tissue. However, DL-AO requires at least two isolated and detectable PSFs to start compensation, and this requirement might be challenging to meet when the aberration level or imaging depth is significantly higher than the demonstrated cases where single molecule emissions are no longer identifiable. We also expect that further development in designing training data and neural network architecture will improve inference accuracy of DL-AO in an increasing compensation range, ultimately enabling single shot compensation during SMLM imaging. Additionally, the demonstrated DL-AO applications are limited by the working distance of the silicone-oil objective, and thus the imaging depth could potentially be extended when combined with long working distance objectives. To further improve the achievable resolution and imaging fidelity, we expect that DL-AO can be combined with light-sheet illumination\(^{49,50}\) for an increased signal to background ratio of single molecule detections, tissue clearing\(^{51}\) for labeling penetration and reduced aberration level, and expansion methods\(^{52}\) for further improved spatial resolution, thereby opening doors to observe nanoscale conformation in tissues and small animals.
+Fig. 1: Deep learning driven adaptive optics for single molecule localization microscopy.
+Upon the acquisition of camera frames, detected single molecule emission patterns from stochastic lateral and axial positions are isolated and sent to a trained deep neural network. The network outputs a vector of mirror deformation-mode amplitudes, for each biplane detection of single molecule. The estimations pre-/post- each compensation are then combined through Kalman filter to drive the next deformable mirror update. ‘p’ and ‘q’ represent numbers of feature maps input and output to a residue block (the orange box). ‘N’ represents the image width/height. ‘s’ is stride size in a convolutional layer.
+Fig. 2: Performance characterization of DL-AO. (A) Measurement and feedback flow for deformable mirror updates driven by deep neural network. Sub-regions are enlarged to show examples of PSF shapes from blinking molecules. (B) An example of PSFs, pupil phases and mirror mode coefficients before and after DL-AO, when compensating artificially induced
+aberrations. Compensations are performed in real time during SMLM experiments. PSFs are measured from 100-nm-diameter crimson beads nearby the compensation area post SMLM acquisition. (C) Comparison between DL-AO and metric-based AO on compensating sample induced distortion at bottom coverslip surface including PSF shapes and raw single molecule blinking frames. (D) Comparison between DL-AO and metric-based AO on compensating sample induced distortion at 134 μm from bottom coverslip surface in water-based media (n = 1.35) including PSF shapes and raw single molecule blinking frames. (E) Summary of repeated tests of DL-AO for compensating aberrations of different levels (in \( W_{rms} \)) based on simulated SMLM blinking data. Each simulated SMLM frames contain 128×128 pixels, with pixel size of 119 nm. Number of PSFs per frame were generated from Poisson distribution with a mean of 13. Axial positions of molecules were generated from uniform distribution from -1 to 1 μm range. The number of photon counts in each PSF was generated from exponential distribution with mean equal to 2500. The background photon counts in each frame was set to be 10. (F) Summary of repeated tests of DL-AO for compensating aberrations in different levels (in \( W_{rms} \)) based on experimental blinking frames from immune-fluorescence-labeled Tom20 specimen. (G) Quantitative comparisons between PSFs measured under instrument optimum and those measured after DL-AO and metric-based AO using 3D normalized cross correlation (NCC). IMM stands for index mismatched specimens at 134 μm with refractive indices of sample media and immersion oil being 1.35 and 1.406 respectively measured by Abbe refractometer (334610, Thermo Scientific). The labels for x axis with ‘i-j’ format denote j\textsuperscript{th} repeated tests for compensation at area i. PSFs in **B-D** and **G** are measured from 100-nm-diameter crimson beads nearby compensation areas. Scale bars in **B-D** and **G** are 3 μm.
+Fig. 3: Demonstrations of DL-AO correcting index mismatch induced aberration by imaging Tom20 proteins in COS-7 cells through 134 µm water-based imaging media (A) 3D SMLM reconstruction of Tom20 imaged through 134 µm water-based media without AO, then reconstructed with *in situ* PSF model (INSPR) (B) 3D SMLM reconstruction of Tom20
+imaged through 134 \( \mu \)m water-based media with DL-AO, then reconstructed with INSPR. (C) Axial cross-section of region in A and B compared without and with DL-AO. (D) Enlarged regions in A and B comparing cases without and with DL-AO. (E) 3D SMLM reconstruction of Tom20 imaged through 134 \( \mu \)m water-based media with DL-AO, then reconstructed with INSPR. (F) Axial cross-sections in A and B comparing cases without and with DL-AO combined with reconstruction methods of either *in vitro* PSF model (PR) or *in situ* PSF models (INSPR). The PR PSF model for no AO case was obtained from 100-nm-diameter crimson bead (referred to as bead hereafter) next to the imaged area. The *in vitro* model for DL-AO was obtained from beads at bottom coverslip surface. (G) Enlarged regions in A and B comparing cases without and with DL-AO combined with reconstruction methods of either *in vitro* PR or INSPR. (H) Cartoon of the constructed Tom20 specimen and visualization of pupil retrieved from beads at top (No AO and DL-AO) and bottom (optimum) coverslip. (I) Raw blinking data (after converting intensity readings in camera frames to approximate photon counts) of A and B compared without and with DL-AO. Scale bar: 10 \( \mu \)m. (J) Comparison of measured PSFs at 134 \( \mu \)m without and with DL-AO, *in situ* PSF models without and with DL-AO, and the instrument optimum. Scale bar: 2 \( \mu \)m. (K) Fisher information content without and with DL-AO was calculated based on PSF model built from beads nearby the imaged area. The values correspond to PSFs with 1000 total photon counts and 10 background photons per pixel at axial positions of -1.5 \( \mu \)m to 1.5 \( \mu \)m.
+Fig. 4: Demonstrations of DL-AO correcting sample induced aberrations by imaging Tom20 proteins in COS-7 cells through 110 μm unlabeled mouse brain section. (A) 3D SMLM reconstruction of Tom20 proteins imaged through unlabeled tissue without AO, reconstructed with *in vitro* PSF models: theoretical index mismatch model (PR, upper triangle) and *in situ* PSF models (INSPR, lower triangle). (B) Tom20 imaged through unlabeled tissue with DL-AO, reconstructed with *in vitro* PSF model (PR, upper triangle) and *in situ* PSF models
+(INSPR, lower triangle). (C) Axial cross-sections in A and B comparing cases without and with DL-AO. (D) Zoom-in regions in A and B comparing cases with and without DL-AO. (E) Axial cross-sections along the dashed line in A and B. (F) Comparisons of PSFs and their pupil functions. The theoretical index mismatch model is based on a measured refractive index of 1.35 for sample media, which is measured by Abbe refractometer (334610, Thermo Scientific). Scale bar: 2 μm. Color code in A-E indicates axial positions.
+A
+
+134.8
+133.2
+z (μm)
+
+(1)
+(2)
+(3)
+
+B
+no AO+PR   no AO+INSPR   DL-AO+PR   DL-AO+INSPR
+
+(1)
+(2)
+(3)
+
+C
+no AO   DL-AO
+
+500 nm
+
+D
+
+50.8
+50.2
+z (μm)
+
+E
+
+67.8
+66.2
+z (μm)
+
+F
+no AO   DL-AO
+
+G
+no AO   DL-AO
+
+H
+no AO   DL-AO
+
+I
+no AO   DL-AO
+
+J
+lateral fibril width (nm)
+measurements
+axial fibril width (nm)
+measurements
+
+K
+no AO
+norm. I.
+distance (nm)
+DL-AO+INSPR
+distance (nm)
+
+L
+no AO
+norm. I.
+distance (nm)
+DL-AO+INSPR
+distance (nm)
+Fig. 5: 3D reconstruction of immune-fluorescence-labeled amyloid-β fibrils in 125 μm brain sections of 7.5-month-old 5XFAD female mouse. (A) Amyloid-β fibrils imaged using SMLM with DL-AO and reconstructed with *in situ* PSF model (INSPR) at 85 μm from coverslip surface. Color code indicates axial positions of single molecule localizations (B) Sub-regions and cross-sections in A showing comparisons of Aβ fibrils imaged without and with DL-AO, reconstructed with either *in vitro* PSF model (PR) or *in situ* PSF models (INSPR) (C) Comparison between without and with AO, where without AO data are reconstructed using in vitro PR and AO data used INSPR reconstruction. (D, E) Aβ fibrils imaged with DL-AO and reconstructed with INSPR at 51 μm and 67 μm from coverslip surface. (F) Region in D comparing cases without and with DL-AO. (G) Axial cross-sections in D comparing without and with DL-AO. (H) Regions in E compared cases without and with DL-AO. (I) Axial cross-sections in E comparing cases without and with DL-AO. (J) Measurements of fibril widths in lateral and axial cross-sections in A, D, E. (K) Comparison between intensity profiles along white line in C without and with DL-AO. (L) Comparison between intensity profiles along white line in G without and with DL-AO. ‘norm. I.’ in K and L stands for normalized intensity, where intensity in reconstructed image reflects counts of localized single molecules. The imaged structures were found at depths near the axial limit of tissue thicknesses. Optically measured tissue thicknesses vary among samples, which might be caused by variations in media volume between bottom and top coverslips.
+Fig. 6: 3D SMLM reconstruction dendrites and spines in immune-fluorescence-labeled Thy1-ChR2-EYFP in 150-250 μm brain sections of 7-week-old mice. (A) Super-resolution reconstruction of Thy1-ChR2-EYFP using SMLM with DL-AO through a 250-μm-cut brain section. (B, C) Super-resolution reconstructions of Thy1-ChR2-EYFP using SMLM with DL-AO through 150-μm-cut brain sections. (D) Axial cross-sections identified spines in A, B, C. (E) Identified spines in A-C, and the corresponding size measurements of their necks and heads. 'Norm. I.' stands for normalized intensity, where intensity in reconstructed image reflects counts of localized single molecules. 'dist.' stands for distance. The histograms show the raw intensity counts along the lines indicated by white arrows in E. Sizes are measured at the full widths at
+the half maximum intensity. Color code indicates axial positions. White arrows in A-C point towards identified spines. The imaged structures were found at depths near the axial limit of tissue thicknesses. Optically measured tissue thicknesses vary among samples, which might be caused by variations in media volume between bottom and top coverslips.
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+Acknowledgements
+We would like to thank Fan Xu for suggestions on PSF segmentation and super resolution reconstruction process (current address Beijing Institute of Technology). We would like to thank Sheng Liu for suggestions on phase retrieval algorithm and PSF generation process (current address European Molecular Biology Laboratory). We thank Yue Zheng, Purdue University for suggestions on the manuscript. This work was supported by the US National Institutes of Health (grants GM119785 to F.H., MH123401 to F.H. and A.A.C. and RF1AG074566 to G.E.L).
+
+Author contributions
+P.Z. and F.H. conceived the project and designed the experiments for DL-AO characterization. P.Z. developed the DL-AO workflow, wrote the DL-AO instrument control, performed experiments and analyzed the data. D.M. developed the microscope setup. P.Z., D.M. and H.G. performed and optimized deformable mirror calibration. X.C. and A.P.T. optimized staining procedure for tissue specimens. P.Z., X.C., A.P.T., Y.T., L.F., C.B., A.A.C. and F.H. designed the experiments and prepared biological samples. G.E.L., A.A.C., and F.H. supervised the study. All authors wrote the manuscript.
+Methods
+
+Preparation of fluorescent beads on coverslips
+
+We cleaned 25-mm-diameter coverslips (CSHP-No1.5-25, Bioscience Tools) successively in ethanol (2701, Decon) and HPLC-grade water (W5-4, Fisher Chemical) for three times and then dried them with compressed air. To promote fluorescent beads adhesion on coverslip, 200 μL of poly-l-lysine solution (P4707, Sigma-Aldrich) was added to one coverslip and incubated for 20 min at room temperature (RT). Following poly-l-lysine treatment, the coverslip was subsequently rinsed with deionized water. For beads incubation, we first diluted 100-nm-diameter crimson beads (custom-designed, Invitrogen) to 1: 1,000,000 in deionized water. Then we added 200 μL of the diluted bead solution to the center of the coverslip and incubated for 20 min at RT. The coverslip was subsequently rinsed with deionized water. The treated coverslip was placed on a custom-made holder6, and 20 μL of 38% 2,2'-thiodiethanol (166782, Sigma-Aldrich) in 1× PBS (10010023, Gibco) was added to its center. Another 25-mm-diameter coverslip (also cleaned by using the above protocol) was placed on top of this coverslip. This coverslip sandwich was sealed with two-component silicone dental glue (Twinsil speed 22, Dental-Produktions und Vertriebs GmbH).
+
+Cell culture
+
+COS-7 cells (CRL-1651, ATCC) were grown on coverslips placed in six-well plates and cultured in DMEM (30-2002, ATCC) with 10% FBS (30-2020, ATCC) and 1% penicillin–streptomycin (15140122, Gibco) at 37 °C with 5% CO2. The cells are passaged when their confluence reaches 80%. And the cells were fixed for imaging when their confluence reaches about 30%.
+
+Fixation and labeling of Tom20 in COS-7 cells
+
+Cultured cells were first fixed with 37 °C pre-warmed 3% Formaldehyde aqueous solution (diluted in 1× PBS from 16% Formaldehyde aqueous solution, 15710, Electron Microscopy
+Sciences) and 0.5% Glutaraldehyde aqueous solution (diluted in 1× PBS from 8% Glutaraldehyde aqueous solution, 16019, Electron Microscopy Sciences), with gently rocking at room temperature (RT) for 15 min. After fixation, cells were rinsed twice with 1× PBS and then quenched for 7 min with freshly prepared 0.1% NaBH4 (452882, Sigma-Aldrich) in 1× PBS. The cells were rinsed three times with 1× PBS and blocked with solution containing 3% BSA (001-000-162, Jackson ImmunoResearch) and 0.2% Triton X-100 in 1× PBS, with gently rocking at RT for 1 h. After blocking, the cells were incubated at 4 °C overnight with primary antibody (sc-11415, Santa Cruz Biotechnology), 1:500 diluted in antibody dilution buffer (1% BSA and 0.2% Triton X-100 in 1× PBS). We then washed cells three times with 5 min each time in 0.05% Triton X-100 in 1× PBS, and incubated cells at RT for 5 h with secondary antibody (A21245, Invitrogen, for Alexa Fluor 647), 1:500 diluted in antibody dilution buffer (1% BSA and 0.2% Triton X-100 in 1× PBS). After being washed three times with 5 min each time in 0.05% Triton X-100 in 1× PBS, cells were post-fixed with 4% Formaldehyde aqueous solution (1:4 diluted with 1× PBS from 16% Formaldehyde aqueous solution, Electron Microscopy Sciences) at RT for 10 min. Cells were then rinsed three times with 1× PBS and stored in 1× PBS at 4 °C.
+
+Fixation and labeling of amyloid-β in mouse-brain sections
+
+The 5xFAD Alzheimer's disease (AD) mouse model was used for immunostaining amyloid β. Mice were maintained on the C57BL/6J (B6) background, which were purchased from the Jackson Laboratory (JAX MMRRC Stock# 034848). The 5xFAD transgenic mice overexpress the following five familial Alzheimer's disease (FAD) mutations under control of the Thy1 promoter: the APP (695) transgene containing the Swedish (K670N, M671L), Florida (I716V), and London (V717I) mutations, and the PSEN1 transgene containing the M146L and L286V FAD mutations33.
+
+Up to five mice were housed per cage with SaniChip bedding and LabDiet® 5K52/5K67 (6% fat) feed. The colony room was kept on a 12:12 h light/dark schedule with the lights on from 7:00 am
+to 7:00 pm daily. The mice were bred and housed in specific-pathogen-free conditions. Only female mice were used.
+
+Mice were euthanized by perfusion with ice-cold phosphate-buffered saline (PBS) following full anesthetization with Avertin® (125-250 mg/kg intraperitoneal injection)53. Animals used in the study were housed in the Stark Neurosciences Research Institute Laboratory Animal Resource Center, Indiana University School of Medicine. All animals were maintained, and experiments performed in accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. The protocol was approved by the Institutional Animal Care and Use Committee (IACUC) at Indiana University School of Medicine.
+
+Perfused brains from mice at 7.5 months of age were fixed in 4% formaldehyde in aqueous solution (1:4 diluted with 1× PBS from 16% Formaldehyde Aqueous Solution, Electron Microscopy Sciences) for 24 h at 4°C. Following fixation, brains were cryoprotected in 30% sucrose at 4°C, and then cut into sections of 150 μm by a vibratome (7000smz-2, Campden Instruments). For immunostaining, free-floating sections were washed and permeabilized with 0.1% Triton X-100 in 1× PBS (PBST), and antigen retrieval was subsequently performed using 1× Reveal Decloaker (Biocare Medical) at 85°C for 10 min. Sections were blocked in 5% normal donkey serum (D9663 Sigma-Aldrich) in PBST for 1 h at RT. The sections were then incubated with β-Amyloid Antibody (Cell Signaling Technology #2454, rabbit), 1:1000 diluted in 5% normal donkey serum in PBST at 4°C overnight. Sections were washed and stained for 1 h at RT with secondary antibody (A31573, Invitrogen, for Alexa Fluor 647) diluted at 1:1000 in 5% normal donkey serum in PBST54.
+
+Fixation and labeling of Thy1+ pyramid cells in mouse brain sections
+
+To obtain mice expressing the proper amount of ChR2-EYFP in Thy1+ pyramidal cells, the litters of Thy1-ChR2-EYFP (B6.Cg-Tg (Thy1-COP4/EYFP)18Gfng/J, Jackson Lab) cross with
+B6 (C57BL/6, Jackson Lab) were used for the labeling. To extract the brains for sectioning, the litters of seven-week-old were first anesthetized by intraperitoneal injections of a mix of 90 mg/kg ketamine (59399-114-10, Akron) and 10 mg/kg xylazine (343750, HVS). After confirmation of deep anesthesia, the abdomen was open to expose the diaphragm. The chest cavity was then opened by cutting through the diaphragm and ribs to expose the heart. The trans-cardiac perfusion was performed by inserting the needle into the left ventricle and a small incision at the right atrium. Mice were perfused with 1× PBS (1:10 diluted from DSP32060, Dot Scientific). After the liver was pale, mice were continuously perfused with 4% Formaldehyde Aqueous Solution (1:8 diluted with 1× PBS from 32% Formaldehyde Aqueous Solution, Electron Microscopy Sciences) to pre-fix the brain until the muscle turned stiff. Brains were carefully collected and placed in 4% Formaldehyde Aqueous Solution to post-fix at 4 °C overnight. The fixed brains were trimmed for coronal slicing. The trimmed brains were fixed and cut into sections of 150 μm, 200 μm and 250 μm by a vibratome (1000 Plus, TPI Vibratome).
+
+The brain sections were washed three times, 15 min for each time, in wash buffer (0.1% Triton X-100 in 1× PBS) with a gentle shake (120 rpm, Orbi-Shaker, Benchmark), and then were incubated in blocking butter (5% BSA (A9647, Sigma-Aldrich) in 1× PBS) for 1.5 h with a gentle shake. The blocked brain sections were incubated with chicken anti-GFP antibody (ab13970, Abcam, diluted to 1:1,000 in blocking buffer) at 4 °C overnight. After being washed three times in the wash buffer as in the first step, the slices were incubated with goat anti-chicken Alexa Fluor 647-conjugated antibody (A21449, Invitrogen, diluted to 1:600 in wash buffer) at room temperature for 2 h with a gentle rocking.
+
+All animals were maintained, and experiments performed in accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. The protocol was approved by the Institutional Animal Care and Use Committee (IACUC) at Purdue University.
+Imaging buffer and sample mounting for SMLM
+
+Immediately before SMLM imaging, the coverslip with specimens on top was placed on a custom-made holder6. Imaging buffer55 (10% (wt/vol) glucose in 50 mM Tris, 50 mM NaCl, 10 mM MEA, 50 mM BME, 2 mM COT, 2.5 mM PCA and 50 nM PCD, pH 8.0) was added to the coverslip. Then another cleaned coverslip was placed on top of the imaging buffer. This coverslip sandwich was sealed with two-component silicone dental glue. Samples with immune-fluorescence-labeled cells on the top coverslips were prepared as described below: 200 μL of poly-L-lysine solution was added to the bottom coverslip, incubated for 20 min and subsequently rinsed with deionized water. Then 20 μL of microsphere suspension (134 μm in diameter, 7640A, Thermo Scientific) was spread around the outer ring area of the coverslip, and incubated at RT until the coverslip was dried. Then we placed this coverslip with microspheres at the bottom, added 50-80 μL imaging buffer without touching the microspheres, and added the coverslip with cells on top of it, with the cell-side surface facing down.
+
+Microscope setup
+
+All experimental data were recorded on a custom-designed SMLM setup built around an Olympus IX-73 microscope stand (Olympus America). This system is equipped with a 100×/1.35-NA (numerical aperture) silicone oil-immersion objective lens (UPLSAPO100XS, Olympus America), a PIFOC objective positioner (ND72Z2LAQ, Physik Instrumente), a three-axis piezo nano-positioning systems (Nano-LP100, Mad City Labs) and a manual XY stage (MicroStage-LT, Mad City Labs Inc.). A continuous-wave laser at wavelength of 642 nm (2RU-VFL-P-2000-642-B1R, MPB Communications) was coupled into a polarization-maintaining single-mode fiber (PM-S405-XP, Thorlabs) after passing through an acousto-optic tunable filter (AOTFnC-400.650-TN, AA Opto-electronic) for power modulation. The excitation light coming out of the fiber was focused to the pupil plane of the objective lens after passing through a filter cube holding a quadband dichroic mirror (Di03-R405/488/561/635-t1, Semrock). The emission
+fluorescence was split with a 50/50 non-polarizing beam splitter (BS016, Thorlabs) mounted on a kinematic base (KB25/M, Thorlabs). The separated fluorescent signals were delivered by two mirrors onto a 90° specialty mirror (47-005, Edmund Optics), passed through a band-pass filter (FF01-731/137-25), and were then projected on an sCMOS camera (Orca-Flash4.0v3, Hamamatsu) with an effective pixel size of 119 nm on the sample plane. The detection planes that received the signals transmitted and reflected by the beam splitter were referred to as plane 1 and plane 2, respectively. The pupil plane of the objective lens was imaged onto a deformable mirror (Multi-3.5, Boston Micromachines). The imaging system was controlled by a custom-written program in LabVIEW (National Instruments).
+
+Measurement of mirror deformation modes
+
+The experimental mirror deformation modes\(^{25}\) (**Supplementary Note 1**) were measured using fluorescent bead sample described above. We introduced a positive and a negative (unit amplitude) mirror changes for each of the 28 mirror deformation modes. For each mirror shape setting, we acquired PSFs at z positions from –1.5 \( \mu \)m to 1.5 \( \mu \)m, with a step size of 100 nm, a frame rate of 10 Hz, and 3 frames per z position. Pupil phase was extracted through phase retrieval algorithm for each mirror change. To obtain the experimental mirror deformation bases without the influences of instrument or sample induced aberrations, we calculated the differences of the retrieved pupil phases between the positive and negative unit changes of mirror modes and divided them by two. The actual distortion level introduced by each experimental mirror mode is quantified through root mean square wavefront error\(^{28}\) (**Methods**, **Supplementary Note 3**).
+
+Measurement of instrument optimum
+
+We define instrument optimum as the status where optical hardware was optimized to limit the inherent system aberrations. To obtain this optimized status, we followed a previously described
+method\(^6\), where the deformable mirror was adjusted as follows. Starting from the flat voltage map (provided by the manufacturer) of the deformable mirror, 28 mirror modes (\textbf{Fig. SS4}) were applied sequentially. For each mirror mode, 11 different amplitudes were applied while recording the corresponding fluorescence signal from an in-focus 100-nm crimson bead sample. To extract the fluorescence signal from individual beads, the symmetry center of each imaged bead was obtained using the radial symmetry method\(^56\). Subsequently, a symmetric 2D Gaussian was generated at the symmetry center and was multiplied by the isolated emission pattern from the fluorescent bead, generating a Gaussian-masked image, and then the total intensity of the masked image was calculated to extract the center peak signal of the beads in focus. For each mirror mode, images of the bead were acquired at 11 different mirror mode amplitudes and the corresponding center peak signals of the bead were extracted as described above. The optimal amplitude (i.e. the amplitude providing the highest center peak signal from the beads) was determined from a quadratic fit of these 11 signal measurements vs. mirror mode amplitudes. After identifying optimal amplitudes for each of the 28 modes, these amplitudes were added to the flat voltage map (provided by the manufacturer), serving as the starting point for another iteration. This iterative process was repeated five times to achieve optimal system aberration correction. PSFs under instrument optimum were measured using fluorescent beads sample described above. Data were acquired at a series of z positions from – 1.5 \( \mu \)m to 1.5 \( \mu \)m, with a step size of 100 nm, a frame rate of 10 Hz, and 3 frames per z position. Phase retrieval algorithm was then performed on the bead stack to obtain the pupil function under instrument optimum. The instrument optimum can be further verified by decomposing the pupil phase into Zernike mode\(^{12}\) and checking whether the absolute values of first 64 Zernike coefficients (Wyant order\(^{28}\)) are smaller than 0.2 \( \frac{\lambda}{2\pi} \).
+Calculation of mean square wavefront error
+
+The root mean square wavefront errors (\( W_{rms} \)) were calculated by the root mean square among all pixels within in the image of pupil phase angle. \( W_{rms} \) for experimental wavefronts were either calculated using the pupil phase obtained by phase retrieval from fluorescent beads (Fig. SS4), or calculated using the wavefront images composed of linear combination of experimental mirror deformation modes as estimated by DL-AO (Fig. 2E, 2F, Supplementary Figs. 4, 7-9, 12, 13, 15).
+
+Measurement of network responses to individual mirror deformation modes
+
+The aberrated PSFs for characterizing network responses (Supplementary Figs. 7-9) were measured using either Tom20 specimens or fluorescent bead samples described above. The samples were first excited with the 642-nm laser at a low intensity of ~50 W/cm\(^2\) to find regions of interest. Then data containing single molecule blinking events were collected at a laser intensity of 2–6 kW/cm\(^2\) and a frame rate of 50 Hz. The aberrated PSFs from the fluorescent bead samples were measured the same way as we measured PSFs under instrument optimum. A set of PSF measurements were performed under positive and negative unit changes of each mirror deformation mode, the differences of network output between positive and negative mirror changes were calculated and divided by two to be the final response vector for each mirror deformation mode.
+
+SMLM acquisition with DL-AO
+
+In SMLM data acquisition, the fluorescently labeled samples were first excited with a 642-nm laser at a low intensity of ~50 W/cm\(^2\) to find a region of interest. Imaging depths of mitochondria specimens were measured by the differences of PIFOC readings between the apparent focus of the region-of-interest and the bottom coverslip surface. The imaging depths for immune-fluorescence-labeled tissue specimens were measured by the differences of PIFOC readings
+between apparent focuses of the region-of-interest and the fluorescent signal closest to bottom coverslip surface. Before SMLM experiments, bright-field images of this region were recorded over an axial range from –1 to +1 µm with a step size of 100 nm as reference images for focus stabilization57. Then the blinking data were collected at a laser intensity of 2–6 kW/cm² and a frame rate of 50 Hz, where the first ~3-20 cycles were used for DL-AO, with 20-100 frames per cycle. In the case where significant background photons were observed (~100 per pixel per frame), a temporal median filter was used to estimate structured background for each pixel. This background map was subtracted from each camera frame before the frames are segmented into sub-regions for DL-AO processing. After DL-AO correction, 2000 frames were collected per cycle, and 20-120 cycles (50000-236000 frames, Supplementary Table 2) were collected per imaging area. For the interleaved SMLM imaging without and with AO, deformable mirror shape was set to switch between DL-AO compensated shape and the shape used for instrument optimum (Methods) per imaging cycle (2000 frames). Acquisition of no-AO data was performed first in the interleaved sequence for fair comparison. Upon each switch between no-AO and DL-AO acquisitions, PIFOC objective positioner was moved to compensate apparent focal shift in the case of index mismatch induced aberration58. The focal shifts were determined by an estimated linear relationship between the apparent focus shift and the amplitudes of two radially symmetric mirror deformation modes. The shifts per unit amplitude changes were empirically estimated to be -0.3 µm for mirror mode 5 and -0.2 µm for mirror mode 15 (Fig. SS4). Here, a negative movement of PIFOC objective positioner corresponds to shifting the imaging plane closer to the bottom coverslip surface.
+
+Structure size quantification in the reconstructed images
+
+The neck sizes of dendritic spines are measured as follows. First we selected a profile line at the location where measurement is to be made. A rectangular box was then cropped along the line, with its width ranging from 50-500 nm (depending on the spine neck length and the number
+of localizations). The localization result inside this rectangular box was isolated and rendered into an image with 3 nm pixel size. Each point in the rendered image is blurred with a Gaussian kernel of 3 pixels in width. Intensity profile was generated along the profile line by sum projection and subsequently the histogram was normalized by dividing its maximum value. The spine neck sizes were calculated by the full width at the half maximum of the intensity histogram. Spine head sizes were measured the same way as that for the spine necks. The Amyloid β fibrils’ widths were measured the same way as that for the spine necks, except for a Gaussian function was used to fit the line profile (‘fit’, Curve Fitting Toolbox 2020a, MATLAB R2020a, The MathWorks, Inc.), with Gaussian function switched between ‘gauss1’ (single Gaussian fit) and ‘gauss2’ (two Gaussians) depending on the number of peaks observed in intensity histogram. The half width at the half maximum of the fitted Gaussian curve is treated as the width of each fibril.
+Additional References
+
+53. Tsai, A. P. et al. PLCG2 is associated with the inflammatory response and is induced by amyloid plaques in Alzheimer’s disease. Genome Med. **14**, 1–13 (2022).
+
+54. Tsai, A. P. et al. INPP5D expression is associated with risk for Alzheimer's disease and induced by plaque-associated microglia. Neurobiol. Dis. **153**, 105303 (2021).
+
+55. Olivier, N., Keller, D., Gönczy, P. & Manley, S. Resolution Doubling in 3D-STORM Imaging through Improved Buffers. *PLoS One* **8**, 1–9 (2013).
+
+56. Parthasarathy, R. Rapid, accurate particle tracking by calculation of radial symmetry centers. *Nat. Methods* **9**, 724–726 (2012).
+
+57. Mcgorty, R., Kamiyama, D. & Huang, B. Active microscope stabilization in three dimensions using image correlation. *Opt. Nanoscopy* **2**, 1–7 (2013).
+
+58. Petrov, P. N. & Moerner, W. E. Addressing systematic errors in axial distance measurements in single-emitter localization microscopy. *Opt. Express* **28**, 18616 (2020).
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• 20220523DLAOSupplementssubmit.pdf
+• SupplementaryVideos.zip

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+Dominant control of temperature on (sub-)tropical soil carbon turnover
+
+Vera Dorothee Meyer
+vmeyer@marum-alumni.de
+
+MARUM - Center for Marine Environmental Sciences   https://orcid.org/0000-0002-4958-5367
+Peter Köhler
+Alfred Wegener Institute Helmholtz Centre for Polar and Marine Research   https://orcid.org/0000-0003-0904-8484
+Nadine Smit
+MARUM - Center for Marine Environmental Sciences, now: Bruker Daltonics GmbH & Co. KG.
+Julius Lipp
+MARUM - Center for Marine Environmental Sciences
+Bingbing Wei
+Alfred Wegener Institut, Helmholtz Zentrum für Polar- und Meeresforschung
+Gesine Mollenhauer
+Alfred Wegener Institute   https://orcid.org/0000-0001-5138-564X
+Enno Schefuß
+MARUM - Center for Marine Environmental Sciences, University of Bremen, Germany
+https://orcid.org/0000-0002-5960-930X
+
+Article
+
+Keywords:
+
+Posted Date: August 19th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4726729/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+Version of Record: A version of this preprint was published at Nature Communications on May 15th, 2025. See the published version at https://doi.org/10.1038/s41467-025-59013-9.
+Dominant control of temperature on (sub-)tropical soil carbon turnover
+
+Vera D. Meyer1*, Peter Köhler2, Nadine T. Smit1,3, Julius S. Lipp1, Bingbing Wei2, Gesine Mollenhauer1,2 and Enno Schefuß1*
+
+1: MARUM – Center for Marine Environmental Sciences, University of Bremen, Germany
+2: Alfred Wegener Institut, Helmholtz Zentrum für Polar- und Meeresforschung, Bremerhaven, Germany
+3: now at: Bruker Daltonics GmbH & Co. KG., Bremen, Germany
+*corresponding authors: vmeyer@marum.de; eschefuss@marum.de
+
+Carbon storage in soils is important in regulating atmospheric carbon dioxide (CO₂). However, the sensitivity of the soil-carbon turnover time (\( \tau_{soil} \)) to temperature and hydrology forcing is still not fully understood. Here, we use radiocarbon dating of plant-derived lipids in conjunction with reconstructions of temperature and rainfall from an eastern Mediterranean sediment core receiving terrigenous material from the Nile-River watershed to investigate \( \tau_{soil} \) in subtropical and tropical areas during the last 18,000 years. We find that the \( \tau_{soil} \) was reduced by an order of magnitude over the last deglaciation and infer that this reduction was caused from amplified soil respiration rates. Our data indicate that the deglacial warming was the major driver of these changes while the impact of hydroclimate was relatively small. We conclude that increased CO₂ efflux from soils into the atmosphere constituted a positive feedback to global warming. However, simulated glacial-to-interglacial changes in a dynamic global vegetation model underestimate our data-based reconstructions of soil-carbon turnover times suggesting that this climate feedback might be underestimated.
+
+Globally, soils store more than twice as much carbon as the atmosphere at present1,2. The soil carbon cycle is sensitive to climate change and human activities1,3,4. Therefore, future warming, shifts in precipitation patterns and land use might perturb the soil-carbon storage and subsequently result in positive feedbacks on global warming via CO₂ release into the atmosphere 1,5. Soil carbon storage is regulated by carbon influx (fixation through net primary production; NPP) and efflux. The latter is controlled by microbial respiration, soil erosion and fire emissions2,5. These processes determine \( \tau_{soil} \) defined as:
+
+\[
+\tau_{soil} = \frac{C_{total}}{f} \quad \text{(Eq. 1)},
+\]
+
+where \( C_{total} \) is the soil carbon-stock size and f either the carbon influx (NPP) or the efflux. Under steady state conditions influx and efflux are equal6. Turnover times are critical components in carbon cycling for constraining the time scales of carbon exchange between different reservoirs. \( \tau_{soil} \) depends on soil temperature3,4,7 and moisture content3,4 but also on chemical properties8,9,10 and soil fertility8,10. Temperature effects on \( \tau_{soil} \) are widely observed across the globe4 while hydroclimate may exert strong control in low latitudes where it may be even more important than temperature4,11,12. However, the key controls on \( \tau_{soil} \) are still debated3,9,11. This forms a major open question in tropical and subtropical regions where combined effects of future warming and precipitation changes may be amplified or attenuated depending on whether warming will be accompanied by drier or wetter conditions11.
+Here, we investigate how \( \tau_{soil} \) changed in the Nile-River catchment during the last 18 kyrs when the global climate warmed and transitioned from the last Glacial (before 17.3 kyr BP) into the Holocene (after 11.7 kyr BP). With a length of 6650 km the Nile River is the longest river in the world spanning 35° of latitude (4°S-31°N) in northeastern Africa. During the last deglaciation (8-18 kyrs BP) the northern African climate warmed\(^{13,14}\) and humid conditions during the African Humid Period(AHP, 14.5-5 kyr BP)\(^{15,16}\) allowed for plants and permanent water bodies to persist in the nowadays barren, hyperarid Sahara Desert\(^{17,18}\). The different timing of changes in temperature\(^{13,14,19}\) and hydroclimate\(^{20,21,22}\) in northeastern Africa around the AHP allows for disentangling temperature and precipitation effects on \( \tau_{soil} \). We investigate the response of the soil carbon cycle to these climatic changes using compound-specific radiocarbon dating (CSRA) of the plant-wax biomarkers long chain \( n \)-alkanoic acids and long chain \( n \)-alkanes preserved in marine sediment core GeoB7702-3, which was retrieved in the eastern Mediterranean from the continental margin off the Sinai Peninsula (Figure 1).
+
+Refractory plant-wax lipids deposited in marine sediments commonly are pre-aged due to transport processes and intermediate storage\(^{23,24}\). Their pre-depositional ages are powerful recorders of changes in the terrestrial carbon cycle\(^{23,25,26,27,28}\).
+
+**Environmental signals in the CSRA data**
+
+To calculate the pre-depositional age of the leaf-wax biomarkers we use the “reservoir age offset”\(^{29}\) between the leaf-wax biomarkers and the atmosphere at the time of deposition (Table 1, Figure 2c). The reservoir age offsets of \( n \)-alkanoic acids and \( n \)-alkanes in core GeoB7702-3 range between approximately 0 and 8700 \( ^{14} \)C yrs. Glacial offsets (7800-8700 \( ^{14} \)C yrs at 18 kyr BP) are substantially higher than those during the Holocene (0-3400 \( ^{14} \)C yrs; between ~2-11.5 kyrs BP). A linear relationship between the \( ^{14} \)C ages of long chain \( n \)-alkanoic acids in marine sediments with \( \tau_{soil} \)\(^{30}\) makes it possible to calculate \( \tau_{soil} \) from CSRA data. However, three factors that may introduce biases to the reconstruction of \( \tau_{soil} \) need to be considered beforehand.
+
+First, sea level rose by up to 120 m over the deglaciation\(^{33}\) and coastal erosion during shelf flooding led to the deposition of pre-aged organic matter on continental margins\(^{26,34}\). Such processes may mask hinterland signals in the \( ^{14} \)C-record of leaf-wax lipids in marine sediments. However, biases from coastal erosion during retrogradation of the Nile Delta are unlikely as the concentration profile of \( n \)-alkanoic acids in core GeoB7702-3 differs from the global rate of sea-level change\(^{34}\) (Figure 2h,i) but resembles the oxygen isotopic composition of planktic foraminifera *Globigerinoides ruber* (\( \delta^{18}O_{G.ruber} \)) off the Nile River delta, a proxy for freshwater discharge\(^{35}\)(Figure 2f). Hence, the export of organic matter was primarily controlled by river runoff\(^{22}\).
+
+Second, in addition to mineral soils peatlands need to be considered as source of pre-aged organic matter\(^{30}\). Anaerobic conditions in wetlands hamper degradation of organic matter leading to its preservation in peat over millennia\(^{36}\). During wetland contraction, erosion and fluvial export of this pre-aged organic matter\(^{28}\) could thus bias the calculations of mean \( \tau_{soil} \) of mineral soils\(^{30}\). This might be relevant to the Nile River catchment since wetlands occur along the basin today\(^{37}\). To constrain wetland dynamics we analyzed a suite of amino-Bacteriohopanepolyols (amino-BHPs; Extended Data Figure 1) which are specific markers for methane oxidizing bacteria in wetlands\(^{38}\) and thus indicative of the relative extension and contraction of methane producing landcover\(^{28}\). Low concentrations imply that between 18-11 kyrs BP methane producing permanently flooded wetlands were barely present in the
+catchment (Figure 2g and Extended Data Figure 1) rendering it unlikely that the decrease in the reservoir age offset stemmed from wetland dynamics. A massive expansion of wetlands occurred between 11-8 kyr BP, which probably occurred in response to maximal rainfall and river runoff during the AHP-optimum (Figure 2d,e,g). Contributions of pre-aged organic matter associated with wetland contraction at the end of the AHP were probably minor as reservoir age offsets remain constant when amino-BHP concentrations decline in our core (Figure 2c,g).
+
+Third, river dynamics including morphology and runoff are known controls on the ages of organic matter discharged into the ocean31,32. Increased fluvial runoff may strengthen riverbank erosion and export of relatively old matter from deeper soil horizons potentially overprinting signals from \( \tau_{soil} \)32. Although the Nile-River runoff increased in response to intensified rainfall during the AHP21,35 considerable biases from deep-soil erosion are unlikely given the decrease in reservoir age offsets of \( n \)-alkanoic acids and \( n \)-alkanes during the AHP (Table 1, Extended Data Figure 2). However, intensified Nile River runoff35 may have increased the transport velocity hampering aging of organic matter during land-ocean transit31. This speed-up would have led to smaller ages of plant waxes in core GeoB7702-3. Although signals of the transport efficiency in our data cannot be fully ruled out we consider a predominant control of river dynamics and morphology on ages of discharged organic matter unlikely for the following reasons. River runoff decreased after 7 kyrs BP (Figure 2f) while the ages of leaf-wax biomarkers remained relatively constant (Table 1; Figure 2c). The second argument is the similarity between the ages of \( n \)-alkanoic acids and \( n \)-alkanes (Table 1 and Extended Data Figure 2). \( n \)-Alkanoic acids reflect a local signals from the Nile delta region while the \( n \)-alkanes provide a more catchment-integrating signal22. The extensive Nile catchment is characterized by multiple fluvial environments that differ in geomorphology, flow regime and sedimentary processes39,40. If such morphologic characteristics exerted substantial control on the ages of organic matter in the fluvial load31, \( n \)-alkanoic acids and \( n \)-alkanes would show different ages and trends which is not the case (Extended Data Figure 2).
+
+\( \tau_{soil} \) during the past 18 kyrs
+
+Excluding these potential biases, we conclude that reservoir age offsets of the leaf-wax biomarkers in core GeoB7702-3 can be used to calculate mean \( \tau_{soil} \) (see Methods). For \( n \)-alkanes the relationship to mean \( \tau_{soil} \) is not calibrated30 which is why we focus on the \( n \)-alkanoic acids. Despite the local origin of the \( n \)-alkanoic acids22 catchment-wide inferences on changes in \( \tau_{soil} \) are justified given the strong similarity with the reservoir age offsets of the \( n \)-alkanes (Extended Data Figure 2).
+
+During the last 10 kyrs, \( \tau_{soil} \) was 9-22 yrs (average 16 yrs). During the late glacial \( \tau_{soil} \) was 218 yrs which implies that \( \tau_{soil} \) reduced by an order of magnitude across the deglaciation (Table 1, Figure 2c). According to Eq.1, changes in \( \tau_{soil} \) may result from variations in the carbon stock size or the efflux. Globally, the terrestrial carbon stocks rose during the deglaciation but according to models they remained rather constant in tropical and subtropical regions41,42. As for the Nile-River catchment, savannah expanded into the formerly barren Sahara during the AHP (14-5 kyrs BP)18,43 which would have temporarily increased the total carbon stock in the catchment at these times. Our detected decrease in \( \tau_{soil} \) together with a likely larger amount of soil carbon during the AHP thus requires a large increase in the carbon efflux from soils (Eq. 1).
+It is well constrained that microbial respiration, a key component determining the carbon efflux\(^{12}\), accelerates in response to warming and increased soil moisture\(^{3,9,11}\). Both, temperature\(^{13,14,19}\) and precipitation\(^{20,21,22}\) increased in the Nile-River catchment during the deglaciation (Figure 2d,e). To investigate the relationship of \( \tau_{soil} \) to temperature and rainfall we fit the natural logarithm of \( \tau_{soil} \) to temperature estimates from the eastern Mediterranean and to the hydrogen isotopic composition of paleo precipitation (\( \delta \mathrm{Dp} \)), a common proxy for the amount of rainfall\(^{22,44}\)(Figure 3). \( \tau_{soil} \) is strongly correlated with temperature (\( R^2 = 0.82 \); Figure 3). The correlation with \( \delta \mathrm{Dp} \) (\( R^2 = 0.59 \); Figure 3b) is clearly weaker indicating that temperature was a substantial control on microbial respiration rates during the past 18 kyrs (Figure 3a) while precipitation effects were relatively small.
+
+Implications for the global carbon cycle
+
+The high glacial \( \tau_{soil} \) indicates that the CO\(_2\) efflux from northeastern African soils into the atmosphere was much smaller than during the Holocene because of lower respiration rates. According to ref.\(^{30}\), \(^{14}\)C-ages of \( n \)-alkanoic acids have constant offsets not only with mean \( \tau_{soil} \) but also with soil mean carbon ages (see Methods). Our data show that during the last Glacial soils were much older than during the Holocene (14 000 yrs at 18 kyrs BP vs about 1000 yrs during the Holocene; Table 1). A relatively old soil-carbon pool together with high \( \tau_{soil} \) agrees with previous estimates of a lower glacial global NPP\(^{45}\) which is congruent with a lower carbon efflux from soils assuming equilibrium conditions (Eq.1). The rejuvenation of soil organic matter accompanying the reduced \( \tau_{soil} \) implies a massive loss of pre-aged organic carbon from the soils during the deglaciation once the climate warmed. Under present-day conditions, respiration constitutes the majority of the total efflux (>90%) and contributions of lateral fluxes are minor\(^{12}\). If this relation remained similar in the past, the decrease in our estimated \( \tau_{soil} \) almost entirely reflects increased efflux of aged CO\(_2\) into the atmosphere. Accordingly, the reduction of \( \tau_{soil} \) by an order of magnitude implies an increase in soil-to-atmosphere CO\(_2\) flux of a similar size (Eq.1). This forms a positive feedback to global warming. If widespread across the tropics and sub-tropics this process may have provided relevant contributions to rising atmospheric CO\(_2\)\(^{46}\) and declining atmospheric radiocarbon contents\(^{47}\) across the deglaciation (Figure 2a,b). Soil-carbon turnover also accelerated in the Ganga-Brahmaputra River catchment as inferred from reservoir age offsets of long chain \( n \)-alkanoic acids from the Bengal Fan\(^{27}\). Calculating \( \tau_{soil} \) from these data reveals that the range of values and the magnitude of deglacial changes (\( \tau_{soil} \) falls from ~200 to ~20 yrs; Extended Data Table 2) are very similar to the results from the Nile River catchment. Thus, it is very likely that changes in \( \tau_{soil} \) in that order of magnitude were common across the (sub-)tropics. Interestingly, the radiocarbon data from the Bengal Fan are strongly correlated with rainfall indicating that variability of the Indian summer monsoon played a substantial role in this positive soil-carbon-climate feedback\(^{27}\). However, the results from the Nile River catchment do not confirm the involvement of hydroclimate suggesting a direct response of soil respiration rates to warming.
+
+Dynamic global vegetation models (DGVM) allow for investigating the effect of the decreasing \( \tau_{soil} \) on the global carbon cycle and CO\(_2_{atm}\). We revisit the analysis performed using the Lund Potsdam Jena DGVM (LPJ DGVM)\(^{41}\) and focus on the differences between the Last Glacial Maximum (LGM; 21 kyrs BP) and pre-industrial conditions (PI; 1 kyr BP). Details of the simulation are given in the methods and ref.\(^{41}\). The model suggests relatively constant carbon stocks in the tropics and sub-tropics like other modeling studies\(^{42}\). As for the change in
+\( \tau_{soil} \), we find pronounced discrepancies between our data-based reconstruction (decrease by 200 yrs, Table 1) and the simulated values (Extended Data Figure 4a, b). The model indicates marginal change of less than 50 yrs in the wider (sub-)tropics. Substantial changes of similar magnitude as in our reconstruction are simulated only in the northern high latitudes (Extended Data Figure 4a, b). According to Eq.1, the underestimation of changes in (sub-)tropical \( \tau_{soil} \) translates into underestimated, simulated changes in microbial respiration rates, respectively CO\(_2\) efflux. The discrepancies between our data-based estimates of \( \tau_{soil} \) and the LPJ DGVM simulations suggest that the climate feedback from amplified (sub-) tropical soil respiration due to warming is underestimated in models. In most recent CMIP6 models the global mean \( \tau_{soil} \) decreases by up to 20 years until the year 2100 for future emission scenarios\(^{48}\). However, a spatially resolved analysis of \( \tau_{soil} \) is missing preventing an evaluation if the soil carbon cycle in the (sub-)tropics has substantially improved in the meantime.
+
+Providing evidence for a direct response of \( \tau_{soil} \) to warming in the (sub-) tropics during the last deglaciation, our study suggests that also the recent global warming will be associated with dominant temperature effects on \( \tau_{soil} \). Positive feedbacks from enhanced soil CO\(_2\) efflux from soils into the atmosphere may thus be expected upon further warming.
+
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+
+Methods
+
+Core material and chronology
+
+Gravity core GeoB7702-3 was retrieved onboard RV Meteor at the continental slope off the Sinai Peninsula during cruise M52/2 in 2002\(^{51}\). Due to the anticlockwise surface circulation in the eastern Mediterranean the fluvial load of the Nile River is transported eastward along the coast to the study site\(^{52}\). Prior to sample preparation, the core was stored at 4°C. The sample set for Bacteriohopanepolyol (BHP) quantification comprised 21 samples. Samples for compound-specific radiocarbon analysis (CSRA) were taken from 9 selected horizons (~2 cm thickness). The age model of the core was previously published in ref.\(^{13}\) and updated by ref.\(^{22}\). Age depth modeling is based upon 24 radiocarbon dates of planktic foraminifera and Bayesian modeling using the BACON software\(^{53}\) and the Marine20 calibration curve\(^{54}\).
+
+Lipid extraction
+
+Samples were freeze-dried and homogenized with a mortar. Samples for compound-specific radiocarbon analyses (ca. 100-120g) were extracted with Dichloromethane (DCM):Methanol (MeOH) 9:1 (v/v) using a Soxhlet-apparatus (60°C, 48 hours) and were processed without internal standards. The samples were hydrolyzed with 0.1 N potassium hydroxide (KOH) in MeOH:H\(_2\)O 9:1 (v/v) at 80°C for two hours. Neutral compounds were extracted with \(n\)-hexane, acids with DCM after acidifying the saponified solution with hydrochloric acid (HCl). Hydrocarbons were separated from polar compounds by column-chromatography using deactivated SiO\(_2\). The hydrocarbons were eluted with \(n\)-hexane, polar compounds with DCM:MeOH 1:1 (v/v). The fatty acids were derivatized to fatty acid methyl esters (FAME). The methylation was performed with MeOH of known \(Δ^{14}\)C, together with HCl at 50°C. Air in the headspace of the sample-tube was replaced by nitrogen gas (N\(_2\)). FAMEs were recovered with \(n\)-hexane and were subsequently cleaned-up with column chromatography using deactivated SiO\(_2\) and NaSO\(_4\). FAMEs were eluted with DCM:Hexane 2:1 (v/v).
+
+Freeze-dried sediment samples dedicated for BHP analysis (ca. 3-6 g) were extracted using a modified Bligh and Dyer extraction\(^{55,56,57}\). The sediment samples were ultrasonically extracted (10 min) with a solvent mixture containing MeOH, DCM and phosphate buffer (2:1:0.8,
+v:v:v). After centrifugation, the solvent was collected, combined and the residues re-extracted twice. The combined solvent layers were added to separatory funnels and separated from the aqueous layer by the addition of DCM and Milli-Q water. After the layers separated, the bottom layer (DCM) was drawn off and collected, while the remaining aqueous layer was washed twice with DCM. The combined DCM layers were dried under a continuous flow of N₂. Aliquots of the total lipid extracts (TLEs) were obtained and DGTS (1,2-dipalmitoyl-sn-glycero-3-O-4′-(N,N,N-trimethyl)-homoserine, Avanti Polar Lipids) was added as an internal standard before UHPLC-HRMS analysis.
+
+UHPLC-HRMS analysis of non-derivatized BHPs
+
+Non-derivatized BHPs were quantified by injecting 1% of the TLE with 2 ng internal standard (DGTS) dissolved in MeOH:DCM (9:1, v:v) on a Dionex Ultimate 3000RS ultra-high performance liquid chromatography (UHPLC) system connected to a Bruker maXis Plus Ultra-High Resolution quadrupole time-of-flight tandem mass spectrometer (UHR-qTOF-MS) equipped with an ESI ion source operating in positive mode (Bruker Daltonik, Bremen, Germany). The non-derivatized BHP analysis was performed according to ref.58 with a column temperature of 30°C and a modified separation method. Briefly, separation was achieved on an Acquity BEH C18 column (2.1x 150 mm, 1.7 µm particle size, Waters, Eschborn, Germany) and a solvent system consisting of eluent A of MeOH:H₂O (85:15) and eluent B MeOH:isopropanol (1:1) with both containing 0.12 % (v/v) formic acid and 0.04 % (v/v) aqueous ammonia. Compounds were eluted with 5% B for 3 min, followed by a linear gradient to 60% B at 12 min and then to 100% B at 50 min and holding at 100% B until 80 min. The column was then equilibrated for 20 min leading to a total run time of 100 min. The flow rate was held constant at 0.2 ml min⁻¹. Mass spectra were acquired in positive ion monitoring of m/z 50 to 2000 and data-dependent fragmentation of the most abundant ions (dynamically selected, typically 3-8) for a total cycle time of 2 s and dynamic exclusion (activation after 5 spectra, release after 15 s). Ion source settings and parameters for detection and fragmentation of BHPs were optimized while infusing extracts. Every analytical run was mass-calibrated by loop-injection of Agilent ESI-L tune mix and lock mass calibration (m/z 922.0098, added in ESI source) of each mass spectrum, leading to typical mass deviations of < 1-3 ppm.
+
+BHPs were identified based on the exact mass of the protonated or ammoniated molecular ion, relative retention time and MS² fragmentation similar to ref.58. Extracted ion chromatograms (EIC) of the most abundant molecular ion (10 mDa mass accuracy window) were used to (semi-)quantify individual BHPs by peak integration. MS variability and ion suppression was controlled by the peak area of the DGTS internal standard. As no authentic standards were available for BHP quantification, abundances are reported based on peak areas of the individual BHPs normalized to the dry weight of the extracted sediments (i.e., in arbitrary units (AU)/µg dw).
+
+Purification of leaf-wax lipids
+
+For CSRA the target FAMEs and n-alkanes were purified using preparative capillary gas chromatography⁵⁹. The purification was performed on an Agilent 7890B gas chromatograph (GC), equipped with a temperature programmable cooled injection-system (CIS, Gerstel) and connected to a preparative fraction collector (PFC, Gerstel). Separation was performed on a Restek RxI-1ms fused silica capillary column (30 m, 0.53 mm i.d., 1.5 µm film thickness). All
+samples were injected repeatedly with 5μL per injection from a concentration of 1 μg/μl (FAMEs) and 500 μg/μl (n-alkanes) using n-hexane. The injector was operated in solvent vent mode (vent: 100 ml/min, 0 psi until 0.12 min). The CIS temperature program was: 60°C (0.05 min), 12°C/s to 320°C (5 min), 12°C/s to 340°C (5 min). The GC temperature program was set: 60°C (2 min), 20°C/min to 150°C, 8°C/min to 320°C (40 min). Helium was used as carrier gas (4.0 ml/min). The transfer line and PFC were heated at 320°C while the traps for collection were maintained at room temperature. The backflush system of the PFC was constantly switched off. The traps were rinsed with n-hexane to recover the purified compounds. Splits (0.1%) were analyzed by GC-FID to check for potential contaminants and to quantify the purified target compounds for CSRA.
+
+CSRA
+
+The isotopic ratio (14C/12C) of the FAMEs and n-alkanes was determined by Accelerator Mass Spectrometry (AMS). The measurements were carried out on the Ionplus MICADAS-system equipped with a gas-ion source60,61,62 at the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven. CSRA was performed according to the protocols described in ref.:63. In short, the purified individual target compounds were transferred into tin capsules and packed. As for FAMEs, the n-C26:0 and n-C28:0 homologues were prepared individually except for two samples for which the homologues had to be combined in order to achieve adequate sample size (Extended Data Table 1). For n-alkanes we combined the n-C29, n-C31 and n-C33 homologues to obtain enough material for dating. Samples were combusted via the Elementar vario ISOTOPE EA (Elemental Analyzer) and the produced CO2 was directly transferred into the coupled MICADAS. Radiocarbon contents of the samples were analyzed along with reference standards (oxalic acid II; NIST 4990c) and blanks (phthalic anhydride; Sigma-Aldrich 320064) and in-house reference sediments. Blank correction and standard normalization were performed via the BATS software64. The AMS-results are reported as “fraction modern carbon” (F14C) and Δ14C65.
+
+Assessment of procedure blanks and correction
+
+In order to correct for carbon introduced during sample processing, procedure blanks were assessed by isolating FAs from a modern and a fossil standard material according to the methods described above. Leaves of a corn plant, collected in 2019, were used as modern standard (F14C: 1.0096 ±0.0024) while “Rekord” coal-briquette (lignite from Lusatia, Eastern Germany) served as fossil standard (F14C: 0.0019 ±0.0002). For the coal, asphaltene precipitation was performed additionally using DCM:MeOH 97:3 (v/v) and pentane. The F14C and mass of the blank were assessed using a Bayesian approach66. The procedure blank was 3.079 ± 0.433 μgC with an F14C of 0.529 ± 0.072. Blank-correction of the samples and error propagation was performed after ref.67. The blank corrected F14C-values of FAMEs were further corrected for the methyl-group, which had been added during the derivatization process, using isotopic mass balance.
+
+Calculation of pre-depositional ages
+
+The age of the compounds at the time of deposition can be calculated using the “reservoir age offset” (R)29 which describes the age offset (in 14C years) between two carbon reservoirs at a given time29. In our case it needs to be calculated from the ratio of the radiocarbon contents of the sample and the atmosphere at the time of deposition in marine sediments (Eq. 2).
+R=8033*ln\left(\frac{F^{14}C_{initial}}{F^{14}C_{atm}}\right) \quad (\text{Eq. 2}),\]
+
+where \(F^{14}C_{initial}\) is the \(F^{14}C\)-value the sample had at the time of deposition at site GeoB7702-3 and \(F^{14}C_{atm}\) is the radiocarbon content of the atmosphere. It can be calculated by correcting the measured \(F^{14}C\)-value of the sample (\(F^{14}C_{sample}\)) for the decay that has taken place since the deposition (Eq. 3).
+
+\[
+F^{14}C_{initial}=F^{14}C_{sample}*e^{\lambda t} \quad (\text{Eq. 3}),
+\]
+
+where t is the time of deposition and \( \lambda \) the decay constant of radiocarbon\(^{65}\). The time of deposition was inferred from radiocarbon dates of planktic foraminifera (core chronology)\(^{22}\). \(F^{14}C_{atm}\) values were adopted from INTCAL20\(^{47}\). In case of samples for which the \(F^{14}C\) values of the \(n\)-C\(_{26:0}\) and \(n\)-C\(_{28:0}\) homologues had been measured separately, we calculated R from the abundance weighted mean of the \(F^{14}C\)-values in order to keep comparability with samples for which the two homologues had been combined prior to AMS measurement (Extended Data Table 1).
+
+**Calculation of \( \tau_{soil} \) and mean soil ages**
+
+Soil organic matter is a complex mixture of compounds that vary in terms of their reactivity and consequently possess different turnover times\(^{68,69}\). Due to this complexity of fast and slow cycling components in SOC, leaf-wax lipids generally exceed the mean soil turnover times by a multiple\(^{30}\). Analyzing the ages of \(n\)-alkanoic acids in particulate organic matter from a global sample set comprising coastal sediments near river mouths, riverbeds and banks as well as suspension load, ref.\(^{30}\) identified globally constant offsets between \(^{14}C\) ages of \(n\)-alkanoic acids and \( \tau_{soil} \) (Eq. 4). Similarly, constant offsets between \(n\)-alkanoic acids and soil mean carbon age have been reported (Eq. 5). The soil mean carbon age here is defined as the radiocarbon age integrated over the top 100 cm depth\(^{30,70}\).
+
+\[
+\text{Age}_{n\text{-alkanoic acid}} = 40.1 * \tau_{soil} \quad (\text{Eq. 4})
+\]
+\[
+\text{Age}_{n\text{-alkanoic acid}} = 0.62 * \text{soil age} \quad (\text{Eq. 5}),
+\]
+
+where the age\(_{n\text{-alkanoic acid}}\) is given in \(^{14}C\) years\(^{30}\). Under the premise that these relationships remained constant in the past, they allow to calculate catchment-integrating mean \( \tau_{soil} \) (in yrs) and mean soil carbon ages (0-100 cm, in yrs) from the \(^{14}C\)-ages of \(n\)-alkanoic acids in marine sedimentary archives and to monitor changes in the carbon cycle within a river catchment through time. The sample set of ref.\(^{30}\) covers a broad range of latitude (73 °N-38 °S) and consequently represents different biomes and climate zones from tropical rainforest to arctic tundra. It reflects broad ranges of annual air temperature (-16 to 27 °C) and mean annual precipitation (amount 230 mm/yr - 2200 mm/yr)\(^{30}\). The range of \(^{14}C\) ages from \(n\)-alkanoic acids covered by the dataset is recent to >10,000 yrs\(^{30}\). The pre-depositional ages calculated
+for the \( n \)-alkanoic acids in core GeoB7702-3 are within that range (348±240 - 8723±212 yrs; Table 1 and Extended Data Table 1). Thus, our inferred \( \tau_{\text{soil}} \) are within the calibrated range. Since the relationship between \( \tau_{\text{soil}} \) and the pre-depositional age of \( n \)-alkanes is unknown, we cannot convert our \( n \)-alkane age into \( \tau_{\text{soil}} \).
+
+Dynamic Global Vegetation Model simulation
+
+Temperature and soil moisture effects have been implemented in dynamical global vegetation models for decades\(^{71,72}\) For this study, the Lund Potsdam Jena Dynamic Global Vegetation Model (LPJ DGVM)\(^{41,48}\) was used. We revisited the analysis performed by ref.\(^{48}\) and investigate changes in \( \tau_{\text{soil}} \), net primary production (NPP), soil respiration (\( R_h \)) and soil carbon stock size between the Last Glacial Maximum (LGM; 21 kyrs BP) and pre-industrial (PI, 1 kyrs BP; Extended Data Figure 3). The global land carbon cycle was transiently simulated across Termination I subtracting the effect of CO$_2$ fertilization and restricting the analysis to areas unaffected by rising sea level or continental ice retreat\(^{41,48}\). \( \tau_{\text{soil}} \) is calculated according to Eq. 1 using the simulated carbon stock size and the simulated NPP and \( R_h \), respectively. The results are shown in Extended Data Figure 3a,b.
+
+The model simulates a total change in the global terrestrial carbon pools of 820 PgC between the LGM and PI\(^{48}\). This agrees well with the median of 850 PgC estimated by a recent multi-proxy approach\(^{42}\) showing that the simulated global patterns are in agreement with other studies. The model suggests a reduction of the global land carbon stock by 200-250 PgC for PI relative to the LGM\(^{48}\). This represents the summed-up change in vegetation and soil carbon caused by temperature and precipitation variability\(^{48}\). Calculating \( \tau_{\text{soil}} \) from net primary production (NPP) and respiration fluxes (\( R_h \)) reveals similar results indicating that NPP and Rh are in equilibrium (Extended Data Figure 3a,b,c,d).
+
+Data availability
+
+The data generated in the study will be accessible from the PANGAEA database (www.pangaea.de).
+
+References
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+(eds) Hydrocarbon and Lipid Microbiology Protocols. Springer Protocols Handbooks. Springer, Berlin, Heidelberg (2015).
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+58. Hopmans, E. C., et al. Analysis of nonderivatized bacteriohopanepolyols using UHPLC-HRMS reveals great structural diversity in environmental lipid assemblages, Org. Geochem., 160, 104285 (2021).
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+64. Wacker, L., Christl, M. & Synal, H. A. Bats: a new tool for AMS data reduction. Nucl. Instrum. Methods Phys. Res. B 268, 976–979 (2010).
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+66. Sun, S. et al. \(^{14}\)C Blank Assessment in Small-Scale Compound-Specific Radiocarbon Analysis of Lipid Biomarkers and Lignin Phenols. Radiocarbon 62, 207–218 (2020).
+67. Wacker, L. & Christl, M. Data Reduction for Small Samples. Error Propagation using the Model of Constant Contamination. Annual Report of Ion Beam Physics, ETH Zürich 36 (2012).
+68. Wiesenber, G. L. B., Schwarzbaumer, J., Schmidt, M. W. I. & Schwark, L. Source and turnover of organic matter in agricultural soils derived from \(n\)-alkane/\(n\)-carboxylic acid compositions and C-isotope signatures. Org. Geochem. 35, 1371–1393 (2004).
+69. Trumbore, S. Age of soil organic matter and soil respiration: Radiocarbon constraints on belowground C dynamics. Ecol. Appl. 10, 399–411 (2000).
+70. Shi, Z. et al. The age distribution of global soil carbon inferred from radiocarbon measurements. Nat. Geosci. 13, 555–559 (2020).
+71. Lloyd, J. and Taylor,J. A. On the Temperature Dependence of Soil Respiration Functional Ecology, 8, 315-323 (1994)
+72. Sitch S, Smith B, Prentice IC, Arneth A, Bondeau A, Cramer W, Kaplan OJ, Lucht W, Sykes MT, Thonicke K, Venevsky S. Evaluation of ecosystem dynamics, plant geography and terrestrial carbon cycling in the LPJ dynamic global vegetation model. Global Change Biol 9, 161–185 (2003).
+Figure 1: Map of African vegetation zones after ref.49. Med: Mediterranean zone; MST: Mediterranean-Saharan transitional vegetation; AM: Afro-montane vegetation zone. The Nile River catchment is marked by the blue shading. The red star indicates the study site GeoB7702-3.
+
+![Map of African vegetation zones showing the Nile River catchment and study site](page_352_246_749_482.png)
+Figure 2: Environmental changes in the Nile-River delta region during the past 18 kyr. (a) Ice-core CO₂-contents from EPICA Dome C50 given as indicator for atmospheric CO₂ concentrations. (b) Atmospheric Δ¹⁴C contents according to INTCAL2047. (c) Reservoir age offsets between the n-alkanoic acids and the atmosphere at the time of deposition at site GeoB7702-3. τₐₛₜₐₗ deduced from the reservoir age offsets of n-alkanoic acids. (d) Sea surface temperature reconstruction for the eastern Mediterranean based on the TEX₈₆ proxy from core GeoB7702-313. (e) Hydrogen isotopic composition of precipitation (δDₚ) calculated from the δD of n-alkanoic acids from core GeoB7702-3 as proxy for rainfall amount42 (f) Oxygen isotopic compositions of the planktic foraminifera species Globigerinoides ruber (δ¹⁸O₆₇₈₈₉) in core MS27PT (Figure 1) indicating salinity changes in the eastern Mediterranean associated with freshwater runoff from the Nile River35. (g) Aminopentol abundances in core GeoB7702-3 used as proxy for the extent of methane producing wetlands in the catchment. AU: arbitrary units; dw: dry weight of extracted sediment. Additional abundance profiles from the suite of amino-bacteriohopanepolyols are given in Extended Data Figure 3 (h) Concentrations of n-alkanoic acids (2n-C₂₆₀, n-C₂₈₀, n-C₃₀₀, n-C₃₂₀) reporting on the land-ocean transport of terrigenous organic matter27. (i) Global rate of sea-level change over the last 20 kyr33. The blue bars mark the timing of the African Humid Period (AHP) and Green Sahara and their optimum17,44. LGM: Last Glacial Maximum; HS1: Heinrich Stadial 1; B/A: Bølling/Allerød interstadial; YD: Younger Dryas stadial.
+Figure 3: Power-law relationships between \( \tau_{\text{soil}} \) and (a) temperature and (b) hydrogen isotopic composition of precipitation (\( \delta \mathrm{D}_p \)). Temperature estimates are based upon the TEX86 proxy at site GeoB7702-3 and are adopted from ref.13. \( \delta \mathrm{D}_p \) is calculated from the hydrogen isotopic composition of n-alkanoic acids (n-C26:0 and n-C28:0 homologues) from core GeoB7702-322. The p-values for the regressions are <0.05.\( \delta \mathrm{D}_p \) is deduced from the hydrogen isotopic composition of n-alkanoic acids and n-alkanes in core GeoB7702-322. Unfortunately, mean annual air temperature estimates covering the past 18 kyr are not available for the Nile-River catchment. Therefore, we use the TEX86-based temperature record from GeoB7702-313 interpreted to reflect sea surface temperature (SST) in the eastern Mediterranean13. We assume that SST and surface air temperatures in the Nile delta region probably developed similarly due to heat exchange between the sea surface and the overlying air.
+
+Table 1. Reservoir age offsets (R) of leaf-wax biomarkers and the atmosphere at the time of deposition in marine sediments. R is calculated from compound-specific radiocarbon dating results of the combined n-C26:0 and n-C28:0 alkanolic acid homologues and the combined n-C29, n-C31, n-C33 alkane homologues (see Methods). Mean soil carbon turnover times (\( \tau_{\text{soil}} \)) and soil mean carbon ages were deduced from the R of n-alkanoic acids according to ref.30. The hydrogen isotopic composition of precipitation (\( \delta \mathrm{D}_p \)) and \( \mathrm{TEX}_{86} \) are mean values for the range of the deposition age. \( \delta \mathrm{D}_p \) is based on the \( \delta \mathrm{D} \) signature of n-alkanoic acids in core GeoB7702-322. \( \mathrm{TEX}_{86} \) are sea surface temperature reconstructions at site GeoB7702-3 from ref.13. Propagated standard errors (±) are reported along with the results. \( ^{14}\mathrm{C} \) and \( \Delta^{14}\mathrm{C} \) values are listed in Extended Data Table 1.
+
+<table>
+  <tr>
+    <th>Sample depth [cm]</th>
+    <th>Deposition age min. - max. [kyrs BP]<sup>a</sup></th>
+    <th>Deposition age mid-point [kyrs BP]<sup>a</sup></th>
+    <th>R n-alkanoic acids [<sup>14</sup>C yrs]</th>
+    <th>R n-alkanes [<sup>14</sup>C yrs]</th>
+    <th>\( \tau_{\text{soil}} \) [yrs]</th>
+    <th>Soil mean carbon age [yrs]</th>
+    <th>\( \delta \mathrm{D}_p \) [%<sub>VSMOW</sub>]<sup>b</sup></th>
+    <th>\( \mathrm{TEX}_{86} \) [°C]</th>
+  </tr>
+  <tr>
+    <td>81.5-84.5</td>
+    <td>1.62 - 2.29</td>
+    <td>1.93</td>
+    <td>348 ± 240</td>
+    <td>959 ± 146</td>
+    <td>9 ± 6</td>
+    <td>561 ± 392</td>
+    <td>-8.8 ± 2.7</td>
+    <td>26.9 ± 0.4</td>
+  </tr>
+  <tr>
+    <td>130-133</td>
+    <td>3.11 - 3.69</td>
+    <td>3.40</td>
+    <td>733 ± 432</td>
+    <td>1633 ± 167</td>
+    <td>18 ± 11</td>
+    <td>1182 ± 710</td>
+    <td>-9.3 ± 2.5</td>
+    <td>26.3 ± 0.6</td>
+  </tr>
+  <tr>
+    <td>198-201</td>
+    <td>5.35 - 6.01</td>
+    <td>5.70</td>
+    <td>902 ± 331</td>
+    <td>1668 ± 116</td>
+    <td>22 ± 9</td>
+    <td>1455 ± 559</td>
+    <td>-8.1 ± 1.5</td>
+    <td>25.1 ± 0.4</td>
+  </tr>
+  <tr>
+    <td>231-234</td>
+    <td>7.24 - 8.14</td>
+    <td>7.72</td>
+    <td>563 ± 247</td>
+    <td>21 ± 87</td>
+    <td>14 ± 6</td>
+    <td>908 ± 411</td>
+    <td>-19.3 ± 5.7</td>
+    <td>26.7 ± 0.7</td>
+  </tr>
+  <tr>
+    <td>251-254</td>
+    <td>9.02 - 10.11</td>
+    <td>9.66</td>
+    <td>736 ± 196</td>
+    <td>3447 ± 298</td>
+    <td>18 ± 5</td>
+    <td>1187 ± 343</td>
+    <td>-27.2 ± 2.1</td>
+    <td>25.3 ± 2.0</td>
+  </tr>
+  <tr>
+    <td>278-281</td>
+    <td>11.05 - 12.05</td>
+    <td>11.50</td>
+    <td>1631 ± 158</td>
+    <td>3313 ± 178</td>
+    <td>41 ± 6</td>
+    <td>2630 ± 391</td>
+    <td>5.0 ± 2.9</td>
+    <td>19.1 ± 0.7</td>
+  </tr>
+  <tr>
+    <td>297-300</td>
+    <td>12.69 - 13.73</td>
+    <td>13.21</td>
+    <td>5384 ± 618</td>
+    <td>4334 ± 213</td>
+    <td>134 ± 20</td>
+    <td>8684 ± 1399</td>
+    <td>1.0 ± 2.9</td>
+    <td>20.0 ± 0.7</td>
+  </tr>
+  <tr>
+    <td>359-362</td>
+    <td>16.26 - 17.07</td>
+    <td>16.67</td>
+    <td>3453 ± 119</td>
+    <td>2415 ± 81</td>
+    <td>86 ± 9</td>
+    <td>5569 ± 657</td>
+    <td>8.3 ± 8.1</td>
+    <td>17.5 ± 1.3</td>
+  </tr>
+  <tr>
+    <td>393-396</td>
+    <td>17.69 - 18.73</td>
+    <td>18.15</td>
+    <td>8723 ± 212</td>
+    <td>7816 ± 341</td>
+    <td>218 ± 22</td>
+    <td>14069 ± 1625</td>
+    <td>8.3 ± 2.7</td>
+    <td>16.3 ± 0.7</td>
+  </tr>
+</table>
+
+a: Obtained by radiocarbon dating of planktic foraminifera22.
+b: calculated by correcting the \( \delta \mathrm{D} \) of the n-C26:0 and n-C28:0 alkanolic acids in core GeoB7702-3 for vegetation changes and ice volume22.
+Acknowledgements
+
+The study was funded by the DFG Cluster of Excellence: “The Ocean Floor – Earth’s Uncharted Interface”. We are grateful to Jürgen Pätzold for providing sample material of core GeoB7702-3. We thank Ralph Kreutz for support during sample processing for CSRA and GC-maintenance. Julia Cordes is acknowledged for technical support during BHP analysis. Pushpak Nadar is thanked for assistance during sample processing for BHP analysis and core sampling for CSRA. Hendrik Grotheer is thanked for support during the AMS measurements at AWI.
+
+Author Contributions
+
+VDM developed the concept of the study supported by BW, ES, GM and PK. VDM carried out the sample preparation and data analysis in the laboratories and performed data processing. NTS and JL conducted the analysis of Bacteriohopanepolyols. PK performed the simulations with the LPJ DGVM. All authors were involved in the interpretation and discussion of the results. VDM drafted the manuscript with contributions from all co-authors.
+
+Competing interests
+
+The authors declare that none of them has any competing interests.
+
+Extended Data
+
+Extended Data Table 1. CSRA-results reported along with the standard errors (±) of n-alkanoic acids and n-alkanes in core GeoB7702-3. CSRA was performed at the Alfred Wegener Institute (AWI). R is the reservoir age offset between the biomarkers and the atmosphere at the time of deposition in marine sediments calculated after ref.29.
+
+<table>
+  <tr>
+    <th>Sample depth [cm]</th>
+    <th>AWI sample identification number</th>
+    <th>Deposition age range [kyrs BP]<sup>a</sup></th>
+    <th>Deposition age mid-point [kyrs BP]<sup>a</sup></th>
+    <th>Compounds</th>
+    <th>F<sup>14C</sup><sup>b</sup></th>
+    <th>A<sup>14C</sup><sup>b</sup> [%e]</th>
+    <th>R [14C yrs]</th>
+  </tr>
+  <tr>
+    <td>81.5-84.5</td>
+    <td>5252.1.1</td>
+    <td>1.62 - 2.29</td>
+    <td>1.93</td>
+    <td>n-C<sub>26:0</sub> + n-C<sub>28:0</sub></td>
+    <td>0.7408 ± 0.0281</td>
+    <td>-265 ± 28</td>
+    <td>348 ± 240</td>
+  </tr>
+  <tr>
+    <td>81.5-84.5</td>
+    <td>5252.2.1</td>
+    <td>1.62 - 2.29</td>
+    <td>1.93</td>
+    <td>n-C<sub>29</sub> + n-C<sub>31</sub> + n-C<sub>33</sub></td>
+    <td>0.6866 ± 0.0158</td>
+    <td>-319 ± 16</td>
+    <td>959 ± 146</td>
+  </tr>
+  <tr>
+    <td>130-133</td>
+    <td>5061.2.1</td>
+    <td>3.11 - 3.69</td>
+    <td>3.40</td>
+    <td>n-C<sub>26:0</sub></td>
+    <td>0.6180 ± 0.0130</td>
+    <td>-387 ± 13</td>
+    <td>604 ± 112</td>
+  </tr>
+  <tr>
+    <td>130-133</td>
+    <td>5061.3.1</td>
+    <td>3.11 - 3.69</td>
+    <td>3.40</td>
+    <td>n-C<sub>28:0</sub></td>
+    <td>0.5975 ± 0.0142</td>
+    <td>-408 ± 14</td>
+    <td>875 ± 126</td>
+  </tr>
+  <tr>
+    <td>130-133</td>
+    <td>-</td>
+    <td>3.11 - 3.69</td>
+    <td>3.40</td>
+    <td>n-C<sub>26:0</sub> + n-C<sub>28:0</sub><sup>c</sup></td>
+    <td>0.6082 ± 0.0498<sup>c</sup></td>
+    <td>-397 ± 50</td>
+    <td>733 ± 432</td>
+  </tr>
+  <tr>
+    <td>130-133</td>
+    <td>5061.4.1</td>
+    <td>3.11 - 3.69</td>
+    <td>3.40</td>
+    <td>n-C<sub>29</sub> + n-C<sub>31</sub> + n-C<sub>33</sub></td>
+    <td>0.5437 ± 0.0172</td>
+    <td>-461 ± 17</td>
+    <td>1633 ± 167</td>
+  </tr>
+  <tr>
+    <td>198-201</td>
+    <td>5251.2.1</td>
+    <td>5.35 - 6.01</td>
+    <td>5.70</td>
+    <td>n-C<sub>26:0</sub></td>
+    <td>0.4795 ± 0.0131</td>
+    <td>-525 ± 13</td>
+    <td>871 ± 111</td>
+  </tr>
+  <tr>
+    <td>198-201</td>
+    <td>5251.1.1</td>
+    <td>5.35 - 6.01</td>
+    <td>5.70</td>
+    <td>n-C<sub>28:0</sub></td>
+    <td>0.4761 ± 0.0152</td>
+    <td>-528 ± 15</td>
+    <td>929 ± 129</td>
+  </tr>
+  <tr>
+    <td>198-201</td>
+    <td>-</td>
+    <td>5.35 - 6.01</td>
+    <td>5.70</td>
+    <td>n-C<sub>26:0</sub> + n-C<sub>28:0</sub><sup>c</sup></td>
+    <td>0.4777 ± 0.0395<sup>c</sup></td>
+    <td>-526 ± 40</td>
+    <td>902 ± 331</td>
+  </tr>
+  <tr>
+    <td>198-201</td>
+    <td>5251.3.1</td>
+    <td>5.35 - 6.01</td>
+    <td>5.70</td>
+    <td>n-C<sub>29</sub> + n-C<sub>31</sub> + n-C<sub>33</sub></td>
+    <td>0.4342 ± 0.0125</td>
+    <td>-569 ± 13</td>
+    <td>1668 ± 116</td>
+  </tr>
+  <tr>
+    <td>231-234</td>
+    <td>11116.2.1</td>
+    <td>7.24 - 8.14</td>
+    <td>7.72</td>
+    <td>n-C<sub>26:0</sub></td>
+    <td>0.4086 ± 0.0085</td>
+    <td>-595 ± 9</td>
+    <td>202 ± 69</td>
+  </tr>
+  <tr>
+    <td>231-234</td>
+    <td>11116.3.1</td>
+    <td>7.24 - 8.14</td>
+    <td>7.72</td>
+    <td>n-C<sub>28:0</sub></td>
+    <td>0.3705 ± 0.0092</td>
+    <td>-633 ± 9</td>
+    <td>988 ± 81</td>
+  </tr>
+  <tr>
+    <td>231-234</td>
+    <td>-</td>
+    <td>7.24 - 8.14</td>
+    <td>7.72</td>
+    <td>n-C<sub>26:0</sub> + n-C<sub>28:0</sub><sup>c</sup></td>
+    <td>0.3906 ± 0.0307<sup>c</sup></td>
+    <td>-613 ± 31</td>
+    <td>563 ± 247</td>
+  </tr>
+  <tr>
+    <td>231-234</td>
+    <td>11116.1.1</td>
+    <td>7.24 - 8.14</td>
+    <td>7.72</td>
+    <td>n-C<sub>29</sub> + n-C<sub>31</sub> + n-C<sub>33</sub></td>
+    <td>0.4179 ± 0.0112</td>
+    <td>-586 ± 11</td>
+    <td>21 ± 87</td>
+  </tr>
+  <tr>
+    <td>251-254</td>
+    <td>5060.2.1</td>
+    <td>9.02 - 10.11</td>
+    <td>9.66</td>
+    <td>n-C<sub>26:0</sub></td>
+    <td>0.3062 ± 0.0093</td>
+    <td>-696 ± 9</td>
+    <td>734 ± 79</td>
+  </tr>
+</table>
+251-254    5060.3.1    9.02 - 10.11    9.66    n-C_{28:0}    0.3060 ± 0.0085    -697 ± 8    738 ± 79
+251-254    -    9.02 - 10.11    9.66    n-C_{26:0} + n-C_{28:0}^c    0.3061 ± 0.0240^c    -696 ± 24    736 ± 196
+251-254    5060.4.1    9.02 - 10.11    9.66    n-C_{29} + n-C_{31} + n-C_{33}    0.2184 ± 0.0263    -783 ± 26    3447 ± 298
+278-281    5059.2.1    11.05 - 12.05    11.50    n-C_{26:0}    0.2183 ± 0.0082    -784 ± 8    2126 ± 77
+278-281    5059.4.1    11.05 - 12.05    11.50    n-C_{28:0}    0.2475 ± 0.0088    -755 ± 9    1117 ± 74
+278-281    -    11.05 - 12.05    11.50    n-C_{26:0} + n-C_{28:0}^c    0.2321 ± 0.0183^c    -770 ± 18    1613 ± 158
+278-281    5059.5.1    11.05 - 12.05    11.50    n-C_{29} + n-C_{31} + n-C_{33}    0.1883 ± 0.0167    -813 ± 17    3313 ± 178
+297-300    5250.1.1    12.69 - 13.73    13.21    n-C_{26:0} + n-C_{28:0}    0.1236 ± 0.0474    -877 ± 47    5384 ± 618
+297-300    5250.2.1    12.69 - 13.73    13.21    n-C_{29} + n-C_{31} + n-C_{33}    0.1408 ± 0.0185    -860 ± 19    4334 ± 213
+359-362    5249.2.1    16.26 - 17.07    16.67    n-C_{26:0}    0.1118 ± 0.0160    -889 ± 16    3763 ± 157
+359-362    5249.1.1    16.26 - 17.07    16.67    n-C_{28:0}    0.1206 ± 0.0158    -880 ± 16    3154 ± 144
+359-362    -    16.26 - 17.07    16.67    n-C_{26:0} + n-C_{28:0}^c    0.1162 ± 0.0123^c    -885 ± 12    3453 ± 219
+359-362    5249.3.1    16.26 - 17.07    16.67    n-C_{29} + n-C_{31} + n-C_{33}    0.1322 ± 0.0089    -869 ± 9    2415 ± 81
+393-396    5248.2.1    17.69 - 18.73    18.15    n-C_{26:0}    0.0748 ± 0.0269    -926 ± 27    6005 ± 322
+393-396    5248.1.1    17.69 - 18.73    18.15    n-C_{28:0}    0.0372 ± 0.0403    -963 ± 40    11611 ± 961
+393-396    -    17.69 - 18.73    18.15    n-C_{26:0} + n-C_{28:0}^c    0.0534 ± 0.0125^c    -947 ± 12    8723 ± 212
+393-396    5248.3.1    17.69 - 18.73    18.15    n-C_{29} + n-C_{31} + n-C_{33}    0.0597 ± 0.0228    -941 ± 23    7816 ± 341
+
+a: Obtained from radiocarbon dating of planktic foraminifera22.
+b: Corrected for procedure blanks. n-Alkanoic acids were additionally corrected for the carbon introduced during methylation (see Methods).
+c: Calculated abundance-weighted means of the n-C_{26:0} and n-C_{28:0} homologues.
+
+Extended Data Table 2. \( \tau_{soil} \) for the Ganga-Brahmaputra river catchment during the past 17 kyrs calculated from compound-specific radiocarbon data from n-alkanoic acids27. R is the reservoir age offset29 between the n-alkanoic acids and the atmosphere at the time of deposition in the Bengal Fan.
+
+<table>
+  <tr>
+    <th>n-Alkanoic acid homologues</th>
+    <th>Deposition age [kyrs BP]</th>
+    <th>Mass weighted mean R [<sup>14</sup>C yrs]</th>
+    <th>\( \tau_{soil} \) [yrs]</th>
+  </tr>
+  <tr>
+    <td>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{32:0}</td>
+    <td>0.003</td>
+    <td>1446 ± 80*</td>
+    <td><b>36 ± 4</b></td>
+  </tr>
+  <tr>
+    <td>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{32:0}</td>
+    <td>0.004</td>
+    <td>927 ± 87*</td>
+    <td><b>23 ± 3</b></td>
+  </tr>
+  <tr>
+    <td>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{34:0}</td>
+    <td>3.54 ± 0.39</td>
+    <td>7119 ± 1149</td>
+    <td><b>178 ± 33</b></td>
+  </tr>
+  <tr>
+    <td>n-C_{24:0}, n-C_{28:0}, n-C_{30:0}, n-C_{32:0}</td>
+    <td>6.57 ± 0.42</td>
+    <td>1489 ± 618</td>
+    <td><b>37 ± 16</b></td>
+  </tr>
+  <tr>
+    <td>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{32:0}</td>
+    <td>10272 ± 504</td>
+    <td>3009 ± 749</td>
+    <td><b>75 ± 20</b></td>
+  </tr>
+  <tr>
+    <td>n-C_{24:0}, n-C_{28:0}, n-C_{30:0}, n-C_{32:0}, n-C_{34:0}</td>
+    <td>10.92 ± 0.48</td>
+    <td>2070 ± 1116</td>
+    <td><b>52 ± 28</b></td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th></th>
+    <th></th>
+    <th></th>
+    <th></th>
+  </tr>
+  <tr>
+    <td><i>n-C_{24:0}</i>,<br><i>n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{34:0}</i></td>
+    <td>12.74 ± 0.42</td>
+    <td>3234 ± 1166</td>
+    <td><b>80 ± 30</b></td>
+  </tr>
+  <tr>
+    <td><i>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{32}, n-C_{34:0}</i></td>
+    <td>13.61 ± 0.23</td>
+    <td>1375 ± 830</td>
+    <td><b>34 ± 21</b></td>
+  </tr>
+  <tr>
+    <td><i>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}</i></td>
+    <td>15.62 ± 0.37</td>
+    <td>8709 ± 4166</td>
+    <td><b>217 ± 106</b></td>
+  </tr>
+  <tr>
+    <td><i>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{34:0}</i></td>
+    <td>16.77 ± 0.39</td>
+    <td>6453 ± 2177</td>
+    <td><b>116 ± 55</b></td>
+  </tr>
+  <tr>
+    <td><i>n-C_{24:0}, n-C_{26:0}, n-C_{28:0}, n-C_{30:0}, n-C_{32:0}</i></td>
+    <td>16.90 ± 0.10</td>
+    <td>4004 ± 3507</td>
+    <td><b>100 ± 88</b></td>
+  </tr>
+</table>
+
+*: \(^{14}\)C ages of pre-1950 Bengal Fan sediments taken from ref\(^{24}\)
+Extended Data Figure 1: Abundances of Amino-Bacteriohopanepolyols in core GeoB7702-3 normalized to the dry weight of extracted sediment (dw). AU: Arbitrary units. AHP: African Humid Period. LGM: Last Glacial Maximum; HS1: Heinrich Stadial 1; B/A: Bølling/Allerød interstadial; YD: Younger Dryas stadial.
+
+![Abundance profile of Amino-Bacteriohopanepolyols in core GeoB7702-3, showing peaks during the AHP-Green Sahara optimum and detection limits.](page_246_355_956_682.png)
+Extended Data Figure 2: Reservoir age offsets of leaf-wax lipids with the atmosphere at the time of deposition at site GeoB7702-3 (a) plotted along with temperature and precipitation reconstructions from the Nile catchment. (b): Temperature reconstruction for the eastern Mediterranean based on the TEX86-proxy in core GeoB7702-313. (c): hydrogen isotope compositions of precipitation (δDp) calculated from δD of the alkanolic acids (mean of n-C26:0 and n-C28:0 homologues; purple) and n-C31 alkane (orange) in core GeoB7702-322. The blue bars mark the timing of the African Humid Period (AHP), “Green Sahara” and their optimum17,44. LGM: Last Glacial Maximum; HS1: Heinrich Stadial 1; B/A: Bølling/Allerød interstadial; YD: Younger Dryas stadial.
+
+![Reservoir age offsets of leaf-wax lipids with the atmosphere at the time of deposition at site GeoB7702-3, temperature and precipitation reconstructions from the Nile catchment, and hydrogen isotope compositions of precipitation](page_153_232_1142_799.png)
+Extended Data Figure 3: Recalculation of results from the Lund Potsdam Jena Dynamic Global Vegetation Model (LPJ DGVM) over the last 21 kyrs as published in ref.41. These results are identical to those LPJ results that have been forced by the Hadley center climate model as discussed in ref.41. Relative changes between the LGM and pre-industrial conditions (PI, here: 1 kyr BP) are shown. a,b) \( T_{soil} \) calculated either based on the carbon influx (net primary production (NPP)) or on the carbon efflux (\( R_h \)), where \( R_h \) is the heterotrophic respiration. Large positive anomalies (red) occur on shelf areas inundated during deglacial sea-level rise, while the areas with large negative anomalies (blue) were covered by large continental ice sheets during the LGM.; c,d) relative changes in NPP and \( R_h \); e) absolute changes in soil carbon content (\( C_{soil} \)).

0481817a811ef5943e02c6f71c38db6c4ebc3f3451bbc8d278f2dbfe56469ccf/preprint/preprint.md

@@ -0,0 +1,404 @@
+Complete biosynthetic pathway of furochromones and its evolutionary mechanism in Apiaceae plants
+
+Min Ye
+yemin@bjmu.edu.cn
+
+Peking University    https://orcid.org/0000-0002-9952-2380
+Jianlin Zou
+Peking University    https://orcid.org/0009-0008-4125-429X
+Hongye Li
+Peking University
+Bao Nie
+Guangdong Laboratory for Lingnan Modern Agriculture/Genome Analysis Laboratory of the Ministry of Agriculture/Agricultural Genomics Institute at Shenzhen,Chinese Academy of Agriculture
+Zi-Long Wang
+Peking University    https://orcid.org/0000-0002-7875-0704
+Chunxue Zhao
+Peking University
+Yungang Tian
+Peking University
+Liqun Lin
+Guangdong Laboratory for Lingnan Modern Agriculture/Genome Analysis Laboratory of the Ministry of Agriculture/Agricultural Genomics Institute at Shenzhen,Chinese Academy of Agriculture
+Weizhe Xu
+Civil Aviation Medicine Center, Civil Aviation Administration of China
+Zhuangwei Hou
+Guangdong Laboratory for Lingnan Modern Agriculture/Genome Analysis Laboratory of the Ministry of Agriculture/Agricultural Genomics Institute at Shenzhen,Chinese Academy of Agriculture
+Wenkai Sun
+Guangdong Laboratory for Lingnan Modern Agriculture/Genome Analysis Laboratory of the Ministry of Agriculture/Agricultural Genomics Institute at Shenzhen,Chinese Academy of Agriculture
+Xiaoxu Han
+Agricultural Genomics Institute at Shenzhen, Chinese Academy of Agricultural Sciences
+Meng Zhang
+Peking University
+Hao-Tian Wang
+Peking University
+Qingyan Li
+Civil Aviation Medicine Center, Civil Aviation Administration of China
+Li Wang
+Agricultural Genomics Institute at Shenzhen, Chinese Academy of Agricultural Sciences
+
+Article
+
+Keywords:
+
+Posted Date: July 31st, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4779533/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 April 1st, 2025. See the published version at https://doi.org/10.1038/s41467-025-58498-8.
+Complete biosynthetic pathway of furochromones and its evolutionary mechanism in Apiaceae plants
+
+Jian-lin Zou1,#, Hong-ye Li1,#, Bao Nie2,#, Zi-long Wang1, Chun-xue Zhao1, Yun-gang Tian1, Li-qun Lin2, Wei-zhe Xu3, Zhuang-wei Hou2, Wen-kai Sun2, Xiao-xu Han2, Meng Zhang1, Hao-tian Wang1, Qing-yan Li3, Li Wang2,*, Min Ye1,*
+
+1 State Key Laboratory of Natural and Biomimetic Drugs, School of Pharmaceutical Sciences, Peking University, 38 Xueyuan Road, Beijing 100191, China
+2 Shenzhen Branch, Guangdong Laboratory of Lingnan Modern Agriculture, Key Laboratory of Synthetic Biology, Ministry of Agriculture and Rural Affairs, Agricultural Genomics Institute at Shenzhen, Chinese Academy of Agricultural Sciences, Shenzhen 518120, China
+3 Civil Aviation Medicine Center, Civil Aviation Administration of China, A-1 Gaojing, Beijing 100123, China
+
+* Corresponding authors.
+Email address: wangli03@caas.cn (Li Wang); yemin@bjmu.edu.cn (Min Ye).
+Abstract
+
+Furochromones are bioactive and specific secondary metabolites of many Apiaceae plants. Their biosynthesis remains largely unexplored. In this work, we dissected the complete biosynthetic pathway of major furochromones in the medicinal plant Saposchnikovia divaricata by characterizing novel prenyltransferase, peucenin cyclase, methyltransferase, hydroxylase, and glycosyltransferases. De novo biosynthesis of prim-O-glucosylcimifugin and 5-O-methylvisamminoside was then realized in tobacco leaves. Through comparative genomic and transcriptomic analyses, we further found that proximal duplication and high expression of a pentaketide chromone synthase gene SdPCS, together with the presence of a lineage-specific peucenin cyclase gene SdPC, led to the predominant accumulation of furochromones in the roots of S. divaricata among surveyed Apiaceae plants. This study paves the way for metabolic engineering production of furochromones, and sheds light into evolutionary mechanism of furochromone biosynthesis among Apiaceae plants.
+Furochromones are an important class of bioactive natural products. They demonstrate anti-inflammatory\(^{1,2}\), hepatoprotective\(^3\), antinociceptive\(^4\), antiviral\(^{4,5}\), and anti-aging\(^6\) activities. While chromones are widely present in plants, furochromones have only been reported in a few families including Apiaceae, Ranunculaceae, and Leguminosae\(^7\). In Apiaceae, furochromones are the major bioactive compounds of *Saposhnikovia divaricata*\(^8\), *Ammi visnaga*\(^9\), and *Cnidium monnieri*\(^{10}\). Particularly, *S. divaricata* contains abundant prim-*O*-glucosyleimifugin (POG) and 5-*O*-methylvisamminoside (5-O-MVG), and their total contents could be above 0.24% of dry weight\(^{11}\). *S. divaricata* is a medicinal plant widely used in traditional medicines for the treatment of influenza and rheumatic arthritis.
+
+The structures of POG and 5-O-MVG feature in the substitution of an isoprenyl group at C-6, which forms a fused dihydrofuran ring\(^{12,13}\) (**Supplementary Fig. 1**). The biosynthesis of simple chromones has been extensively studied. The chromone skeleton is generated by polyketide synthases, such as PECPS from *Aquilaria sinensis* and AaPCS from *Aloe arborescens*\(^{14,15}\). However, little is known about the biosynthesis of furochromones. In the early 1970s, researchers fed sodium [1-\(^{14}\)C] acetate to shoots of *Ammi visnaga*, and revealed that peucenin and visamminol were biosynthetic intermediates of furochromones\(^{16}\). For the biosynthesis of POG or 5-O-MVG, a prenyltransferase (PT) is expected to introduce an isoprenyl group to C-6 of the chromone skeleton\(^{17}\). Very few enzymes have been reported to catalyze cyclization of an isoprenyl group to form a dihydrofuran ring. While CYP76F112 from *Ficus carica*, PpDC and PpOC from *Peucedanum praeruptorum*, NiDC and NiOC from *Notopterygium incisum*, as well as *AsDC* and *AsOC* from *Angelica sinensis* have been reported to catalyze similar reactions to produce furocoumarins\(^{18-21}\), no enzymes have been testified to generate furochromones. On the other hand, glycosyl substitutions at hydroxyl groups linking to the quaternary C-3' or the secondary C-11 are rare for natural products, and these reactions are hypothesized to be catalyzed by uridine diphosphate-dependent glycosyltransferases (UGTs)\(^{22}\). Moreover, both POG and 5-O-MVG contain a methoxyl group at C-5, and the methylation reaction was proposed to be catalyzed by an *O*-methyltransferase (OMT)\(^{23}\). Although a big family of OMTs have been reported from plants, few OMTs could catalyze methylation at the less active 5-OH. Limited examples include the isoflavone 5-*O*-methyltransferase from *Lupinus luteus*\(^{24}\) and CdFOMT5 from *Citrus depressa*\(^{25}\). For POG, the extra primary hydroxyl group is likely to be introduced by a cytochrome P450 (CYP450) enzyme\(^{26}\).
+Based on the above analysis, we tentatively hypothesized the biosynthetic pathway of 5-O-MVG (6) and POG (9) (Fig. 1a). While the enzyme categories catalyzing each step seem obvious, the specific enzymes with expected functions are illusive.
+
+In this work, we dissected the biosynthetic pathway of POG and 5-O-MVG in S. divaricata. The functions of seven novel enzymes were characterized, including SdPCS, SdPT, SdPC, SdCH, SdOMT, SdUGT1, and SdUGT2. The complete biosynthesis of POG and 5-O-MVG was realized in tobacco leaves. Moreover, we unravelled the genetic mechanisms for high abundance of POG and 5-O-MVG in S. divaricata among Apiaceae plants.
+
+Results and Discussion
+
+Proposed biosynthetic pathway of furochromones in Saposhnikovia divaricata and gene mining.
+
+First, we analyzed the chemical constituents of three organs of S. divaricata (leaf, petiole, and root, Fig. 1b–c) by liquid chromatography coupled with mass spectrometry (LC/MS). At least five furochromones (5–9) could be detected, which to some extent supported the validity of our proposed biosynthetic pathway. Subsequently, the contents of major compounds 5, 6, 8 and 9 in five tissue samples (roots at three developmental stages, petiole, and leaf) were quantitatively determined (Supplementary Figs. 2–6). The results indicated the roots contained more abundant furochromones, particularly the glycosides 6 and 9, than the petiole and leaf samples (Fig. 1d).
+
+In order to obtain a complete list of candidate genes involved in the biosynthesis of POG and 5-O-MVG, we sequenced, assembled, and annotated a chromosome-level genome of S. divaricata. Based on 28.65 Gb PacBio CCS long reads, we assembled the genome to 1.95 Gb (Supplementary Table 1), which was consistent with the estimate by flow cytometry (1.74 ± 0.07 Gb) (Supplementary Fig. 7) and the published assembly27. The assembly contig N50 was 2.22 Mb and the Benchmarking Universal Single-Copy Ortholog (BUSCO) score was 96.1%, indicating good genome continuity and completeness (Supplementary Tables 2–3). By Hi-C technology, 94.27% contigs were anchored onto eight chromosomes (Fig. 1e, Supplementary Fig. 8 and Table 4). Multiple-tissue RNA-Seq data (Supplementary Table 5), ab initio prediction, and homolog protein evidence were combined for
+genome annotation, which allowed the identification of 38,704 high-confidence protein-coding genes and 65,734 transcripts. Finally, a total of 1,751,401 repetitive elements were annotated, accounting for 76.78% of the genome (Supplementary Table 6). With this high-quality genome and multiple-tissue RNA-Seq data, we quantified the gene expression abundance (fragments per kilobase of exon model per million mapped fragments, FPKM) of the five tissue samples mentioned above. Subsequently, we screened candidate genes according to genome annotation or local blastn search, and selected genes whose expression levels were correlated with the contents of downstream secondary metabolites in different organs for functional characterization.
+
+![A proposed biosynthetic pathway of furochromones and genomic statistics in S. divaricata. a, The proposed biosynthetic pathway and catalytic enzymes. PT, prenyltransferase; PCS, pentaketide chromone synthase; CYP450, cytochrome P450 enzyme; OMT, O-methyltransferase; UGT, uridine diphosphate-dependent glycosyltransferase. 1, malonyl-CoA; 2, noreugenin; 3, peucenin; 4, visamminol; 5, 5-O-methylvisamminol; 6, 5-O-methylvisamminoside; 7, CYP450; 8, CYP450; 9, UGT; 9 (POG); 6 (5-O-MVG). b, Plant organ sampling. c, Chromatograms of standards and extracts from leaf, petiole, and root. d, Content (μg/g) of compounds in leaf, petiole, and root. e, Circos plot showing the distribution of chromosomes.](page_324_624_1047_496.png)
+
+<table>
+  <tr>
+    <th>Content (μg/g)</th>
+    <th>Root-1</th>
+    <th>Root-2</th>
+    <th>Root-3</th>
+    <th>Leaf</th>
+    <th>Petiole</th>
+  </tr>
+  <tr>
+    <td>5</td>
+    <td>18.21</td>
+    <td>40.19</td>
+    <td>13.33</td>
+    <td>0.25</td>
+    <td>0.14</td>
+  </tr>
+  <tr>
+    <td>6</td>
+    <td>1,116.76</td>
+    <td>1,266.53</td>
+    <td>951.97</td>
+    <td>0.44</td>
+    <td>0.38</td>
+  </tr>
+  <tr>
+    <td>8</td>
+    <td>53.71</td>
+    <td>34.58</td>
+    <td>46.51</td>
+    <td>0.84</td>
+    <td>5.10</td>
+  </tr>
+  <tr>
+    <td>9</td>
+    <td>3,494.75</td>
+    <td>3,304.69</td>
+    <td>2,764.80</td>
+    <td>20.98</td>
+    <td>104.58</td>
+  </tr>
+</table>
+
+Fig. 1. A proposed biosynthetic pathway of furochromones and genomic statistics in S. divaricata. a, The proposed biosynthetic pathway and catalytic enzymes. PT, prenyltransferase; PCS, pentaketide chromone synthase; CYP450, cytochrome P450 enzyme; OMT, O-methyltransferase; UGT, uridine diphosphate-dependent glycosyltransferase. 1, malonyl-CoA; 2, noreugenin; 3, peucenin; 4, visamminol; 5, 5-O-methylvisamminol; 6, 5-O-methylvisamminoside;
+7, norcimifugin; **8**, cimifugin; **9**, prim-O-glucosylcimifugin. **b**, Image of the sampled *S. divaricata*. **c**, Total ion currents (TICs) and extracted ion chromatograms (EICs) of the root, petiole, and leave of *S. divaricata* by LC/MS analysis. EIC mass range: *m/z* 291.11–291.12 + 293.09–293.10. **d**, Contents of **5**, **6**, **8** and **9** in different organs, calculated on the basis of dry weight. **e**, Genomic statistics of *S. divaricata*, showing eight chromosomes (Chr1–Chr8). i, pseudochromosomes; ii, gene density; iii, Gypsy LTR density; iv, Copia LRT density; v, Helitron density; vi, GC content.
+
+**Biosynthesis of the furochromone skeleton.**
+
+The first step of the biosynthetic pathway is from malonyl-CoA (**1**) to noreugenin (**2**). The pentaketide chromone synthase AaPCS from *Aloe arborescens* is the only reported enzyme to catalyze this type of reaction\(^{15}\). Thus, we conducted a local blastn search using *AaPCS* as a query, and ten candidate genes with *e* values <10\(^{-21}\) were discovered. The expression levels (FPKMs) of one gene, *SdPCS*, was highly correlated with the furochromones contents with Pearson correlation coefficient (PCC) > 0.95 (*Supplementary Table 7*). It was sub-cloned into the pET28a (+) vector for protein expression in *E. coli* BL21 (DE3) cells. The function was characterized by enzyme catalysis reactions with **1** as substrate. According to high-performance liquid chromatography (HPLC) and LC/MS analyses, *SdPCS* generated a new peak, which was identified as **2** by comparing with a reference standard. From the genome of *S. divaricata*, we further discovered *SdPCS2* with the same function (**Fig. 2a**). The sequence similarity between SdPCS and SdPCS2 was 91.33% (*Supplementary Fig. 9*).
+
+To discover prenyltransferase (PT) converting **2** to peucenin (**3**), we obtained one candidate gene *SdPT* (PCC > 0.95, *Supplementary Table 8*) among the 20 annotated PT genes. *SdPT* was sub-cloned to pESC-Leu vector and expressed in yeast WAT11 cells\(^{28}\). When the yeast microsomes were incubated with **2**, DMAPP and MgCl\(_2\), HPLC analysis showed a new product, which exhibited an [M+H]\(^+\) ion at *m/z* 261.11 in LC/MS analysis. The MS/MS spectrum showed an abundant [M-56+H]\(^+\) fragment at *m/z* 205.05, indicating a prenyl substitution at C-6 or C-8\(^{29}\) (**Fig. 2b**). Then we purified 0.8 mg of the product from scaled-up enzymatic reactions. The \(^1\)H-NMR spectrum showed two methylene signals at \(δ_{\mathrm{H}}\) 3.17 (m, H-1'), one olefinic signal at \(δ_{\mathrm{H}}\) 5.16 (t, *J* = 6.0 Hz, H-2'), and two methyl signals at \(δ_{\mathrm{H}}\) 1.61 (H-4') and 1.71 (H-5'), indicating the presence of an isoprenyl group. The HMBC cross peaks from H-1' to C-5 (\(δ_{\mathrm{C}}\) 158.1), C-6 (\(δ_{\mathrm{C}}\) 111.1) and C-7 (\(δ_{\mathrm{C}}\) 164.8) indicated the isoprenyl group was located at C-6
+(Supplementary Figs. 10–13). Thus, the product was identified as peucenin (3) (Supplementary Table 9). SdPT represented the first prenyltransferase utilizing chromones as substrate. We also obtained SdPT2 which showed the same function with gene sequence similarity of 85.79% (Supplementary Fig. 14).
+
+Few enzymes are known to catalyze the oxidative cyclization of isoprenyl groups, except for several CYP450 enzymes involved in the biosynthesis of furocoumarins19–21. Since these enzymes belong to the CYP736 family, we screened candidates from the same family in S. divaricata, and chose four potential genes whose expression levels were highly correlated with the furochromones contents (PCC >0.90, Supplementary Table 10). When SdPC was expressed in yeast WAT11 cells28, incubation of the yeast microsomes with 3 and NADPH yielded a new product. LC/MS analysis showed an [M+H]+ ion at m/z 277, which could fragment into m/z 259 and m/z 205. Its structure was proposed to be visamminol (4). As no reference standard was available, we prepared 4 through hydrolysis of visamminol 3'-O-glucoside catalyzed by β-glucosidase (Supplementary Fig. 15), and confirmed its structure by NMR analysis. The 1H-NMR spectrum showed two methyl signals at δH 1.13 (s, H-4') and δH 1.14 (s, H-5'), a tertiary proton signal at δH 4.71 (t, J = 8.6 Hz, H-2'), and a methylene signal at δH 3.02 (d, J = 8.6 Hz, H-1'), indicating the presence of a furan ring. The HMBC cross peaks from H-2' (δH 4.71) to C-1' (δC 26.6), C-7 (δC 166.4), and C-6 (δH 109.5) indicated the furan ring was conjugated with the benzene ring (Supplementary Figs. 16-19, Supplementary Table 9). HPLC and LC/MS analyses indicated the product had the same retention time and mass spectra with 4 (Fig. 2c). As the oxidative cyclization of isoprenyl phenolic compounds by chemical synthesis requires strong oxidizers like m-chloroperbenzoic acid30, SdPC represents an efficient enzyme catalyst for this reaction.
+Fig. 2. Biosynthesis of the furochromone skeleton, demonstrating the functional characterization of SdPCS (a), SdPT (b), and SdPC (c). Shown are HPLC/UV chromatograms of enzyme catalysis reactions (\( \lambda = 280 \) nm), together with (+)-ESI-MS and MS/MS spectra of the products. Control, reaction mixtures incubated with boiled enzymes or microsomes.
+
+Post-modification steps for the biosynthesis of furochromones.
+
+C-11 of compounds 7-9 is hydroxylated, indicating the presence of a CYP450 enzyme. However, very few enzymes have been reported to catalyze a similar reaction, and no suitable templates are available for gene blast search. By analyzing the transcriptome data, we selected 12 candidate CYP genes, whose expression levels were highly correlated with the total contents of **8** and **9** (PCC > 0.95, Supplementary Table 11). These genes were expressed in yeast WAT11 cells, and the microsomes were incubated with NADPH (Tris-HCl buffer, 50 mM) for functional characterization. LC/MS analysis
+indicated that SdCH could convert **4** and **5** (5-*O*-methylvisamminol) into **7** (norcimifugin) and **8** (cimifugin), respectively (Fig. 3a, Supplementary Fig. 20).
+
+Likewise, we discovered the 5-*O*-methyltransferase SdOMT which converted **4** and **7** into **5** and **8**, respectively (PCC > 0.90, Supplementary Table 12). Its function was characterized by enzymatic reaction and LC/MS analysis (Fig. 3b, Supplementary Fig. 21).
+
+Glycosylation is the final step in the biosynthetic pathway. A total of 8 UGT genes with FPKM>10 in the roots were chosen as candidate genes, and were cloned and expressed in *E. coli* BL21(DE3) (Supplementary Table 13). The functions were characterized by enzymatic catalysis with UDP-Glc (UDPG) as sugar donor, and **5** or **8** as sugar acceptor. SdUGT1 could catalyze the glycosylation of 3'-OH of **5** (tertiary alcohol) and 11-OH of **8** (primary alcohol) to produce **6** (5-*O*-methylvisaminoside, 5-O-MVG) and **9** (prim-*O*-glucosylcimifugin, POG), respectively. The products could lose 162 Da in the MS/MS spectra, and their structures were identified by comparing with reference standards (Fig. 3c–d). Moreover, we discovered SdUGT2, which exhibited a high sequence similarity (54.93%) with SdUGT1 and showed the same enzymatic activities (Supplementary Fig. 22). We noticed that SdUGT1 and SdUGT2 only catalyzed 11-*O*-, but not 3'-*O*-glycosylation of **8**. Consistently, these two UGTs showed 2.8 or 31-fold higher catalytic efficiency (\( k_{cat}/K_m \) value) with **8** than with **5** as substrate (Fig. 3e, Supplementary Figs. 23–24).
+
+To elucidate mechanisms for the preference towards 11-OH, we solved the crystal structure of SdUGT2 in complex with UDP through X-ray diffraction (PDB ID: 8ZNK, 1.88 Å) (Fig. 3f, Supplementary Fig. 25, Supplementary Table 14). The structure of SdUGT2 showed a typical GT-B fold with two Rossmann-like \( \beta/\alpha/\beta \) domains. The N-terminal domain (NTD, residues 1-261 and 454-480) and the C-terminal domain (CTD, residues 262-453) are primarily responsible for sugar acceptor and sugar donor binding, respectively. Subsequently, we simulated the SdUGT2/UDPG model based on the structure of GgCGT/UDPG\(^{31}\). Two potential binding modes of **8** were obtained through molecular docking\(^{32}\). In both modes, His32 is close to the glycosylation sites (11-OH or 3'-OH) with a distance below 3.1 Å. Thus, the hydroxyl groups could be easily deprotonated to initiate the glycosylation reaction. Notably, the sugar moiety of sugar donor and hydroxy group of sugar acceptor
+should form an obtuse angle for inverting GTs\(^{33}\). The docking results showed that the angle for 11-\(O\)-glycosylation was over 90°, whereas the angle for 3'-\(O\)-glycosylation was less than 90°. This result interpreted why SdUGT2 showed high preference towards 11-OH.
+
+![Diagram showing enzyme reactions and mass spectra for SdCH, SdOMT, SdUGT1/2, and SdUGT1/2 with UDPG, along with corresponding MS and MS^2 spectra](page_184_370_1082_1042.png)
+
+<table>
+  <tr>
+    <th>Enzyme</th>
+    <th>SdUGT1</th>
+    <th>SdUGT2</th>
+  </tr>
+  <tr>
+    <td>Substrate</td>
+    <td>5</td>
+    <td>8</td>
+    <td>5</td>
+    <td>8</td>
+  </tr>
+  <tr>
+    <td>\(K_m\) (\(\mu\)M)</td>
+    <td>163.20</td>
+    <td>24.73</td>
+    <td>411.30</td>
+    <td>873.60</td>
+  </tr>
+  <tr>
+    <td>\(V_{max}\) (mol·mg\(^{-1}·min^{-1}\))</td>
+    <td>0.015</td>
+    <td>0.066</td>
+    <td>0.038</td>
+    <td>0.212</td>
+  </tr>
+  <tr>
+    <td>\(k_{cat}\) (s\(^{-1}\))</td>
+    <td>1.24×10\(^{-2}\)</td>
+    <td>5.69×10\(^{-2}\)</td>
+    <td>3.12×10\(^{-2}\)</td>
+    <td>1.74×10\(^{1}\)</td>
+  </tr>
+  <tr>
+    <td>\(k_{cat}/K_m\) (M\(^{-1}·s^{-1}\))</td>
+    <td>76.07</td>
+    <td>2,300.00</td>
+    <td>75.79</td>
+    <td>199.65</td>
+  </tr>
+</table>
+
+![Two protein-ligand docking diagrams showing hydrogen bond distances between ligands and protein residues](page_1202_1442_242_120.png)
+Fig. 3. Post-modification reactions for the biosynthesis of furochromones, demonstrating the functional characterization of SdCH (a), SdOMT (b), and SdUGT1/2 (c, d). Shown are HPLC/UV chromatograms of the enzyme catalysis reactions (\( \lambda = 280 \) nm), together with (+)-ESI-MS and MS/MS spectra of the products. e, Kinetic parameters of SdUGT1 and SdUGT2. f, Crystal structure of SdUGT2. STD, reference standard. Control, reaction mixtures incubated with boiled enzymes or microsomes.
+
+Thus, by combining chemical analysis and genomic and transcriptomic data mining, we identified seven enzymes from S. divaricata catalyzing biosynthesis of the two major furochromones **6** and **9**. These genes are located at different chromosomes. Specifically, *SdCH* and *SdUGT1* are located at Chr1, *SdPCS* and *SdPC* at Chr2, *SdPT* at Chr3, *SdOMT* at Chr6, and *SdUGT2* at Chr8 (**Fig. 4a**). The absence of a biosynthetic gene cluster suggests expressions of these genes are not co-regulated. To our knowledge, this is the first work to unravel the complete biosynthetic pathway of furochromones. The expression levels of identified genes, except for *SdUGT1* and *SdUGT2*, are highly correlated with the distribution of major furochromones among different organs of *S. divaricata*. Both SdUGT1 and SdUGT2 showed strong preference for 11-OH, which is consistent with the lack of furochromone 3',11-di-O-glucosides in *S. divaricata*⁸.
+
+*De novo* biosynthesis of *Saposhnikovia* furochromones in tobacco leaves.
+
+POG and 5-O-MVG are important bioactive compounds in *S. divaricata*, and their extraction and purification are time and labor-consuming. It is imperative to engineer the biosynthetic pathway in chassis organisms. In this work, we realized the *de novo* biosynthesis of furochromones in tobacco leaves. Transient expression of the seven genes in tobacco leaves revealed that all genes showed the expected catalytic activities, and the corresponding products were detected (**Fig. 4b–c**). When all the seven genes were infiltrated into tobacco leaves, **6** and **9** could be produced at a yield of 11.54 \( \mu \)g/g and 4.21 \( \mu \)g/g (dry weight), respectively.
+Fig. 4. The dissected biosynthetic pathway of furochromones and their de novo biosynthesis in tobacco leaves. a, Genomic location of biosynthetic genes in S. divaricata. b–c, Catalytic functions of biosynthetic genes responsible for the formation (b) and modification (c) of furochromone skeleton. Extracted ion chromatograms (EICs) of biosynthetic products in LC/MS analysis are shown. STD, reference standards. EV, agrobacterium-mediated transient expression using vector without any biosynthetic genes.
+
+The distribution of furochromones and their biosynthetic genes in Apiaceae plants.
+To gain a deep insight into the evolution of biosynthetic pathway of furochromones in Apiaceae,
+we incorporated another seven Apiaceous species (Coriandrum sativum, Apium graveolens, Angelica sinensis, Ligusticum chuanxiong, Daucus carota, Bupleurum chinense, Centella asiatica) into metabolic, comparative genomic and transcriptomic analyses (Supplementary Tables 15–18). These species represented different evolutionary lineages, including the subfamilies Mackinlayoideae and Apioideae (including the tribe Bupleureae, Apieae, Sinodielsia Clade, Selineae). We first determined and compared the contents of four typical furochromones (5, 6, 8, and 9) among the eight species (Supplementary Figs. 26–46). Unexpectedly, the furochromones did not show a stepwise accumulation along the phylogeny backbone but exhibited a drastic enrichment in S. divaricata. The contents of furochromones in the other species were generally low (Fig. 5a, Supplementary Table 19). This result implied substantial differences in furochromone biosynthesis between S. divaricata and the other Apiaceous plants.
+
+To investigate the evolutionary shift in furochromone biosynthesis from early diverged Apiaceous lineage to S. divaricata, we constructed a maximum likelihood (ML) phylogeny of Apiaceae based on 398 strict single-copy orthologous genes (Fig. 5a). It revealed that S. divaricata belonged to the latest diverged clade including C. sativum. Then, the conserved syntenic gene blocks containing each furochromone-biosynthetic gene was identified in each Apiaceous species (Supplementary Figs. 47–57). The syntenic and homologous genes of most downstream tailoring genes, including OMT, CH and UGTs, were detected in all the Apiaceous species (Supplementary Figs. 47–53). However, the syntenic genes of two skeleton-forming genes, SdPCS and SdPC were not detected in any other Apiaceous species (Fig. 5 and Fig. 6a). This clue motivated us to speculate that most Apiaceous species except S. divaricata may not contain any functional PCS and PC, thus leading to low furochromone content. To test this hypothesis, we focused on potential Apiaceous PCSs and PCs.
+
+Proximal duplication of SdPCS promotes furochromone accumulation in S. divaricata.
+
+We retrieved all potential PKS III genes in S. divaricata and the other seven Apiaceae species and constructed an ML tree, on which a strongly supported (bootstrap support value (BS) = 100) clade containing SdPCS and 19 potential Apiaceous PCSs was identified (Fig. 5b). Most genes in this clade were in the same syntenic region, implying they shared the same ancestor (Supplementary Fig. 56). No PCS was detected in C. asiatica, one of the most basal species in Apiaceae, indicating that PCS may first emerge in the Apioideae subfamily. Then we expressed and characterized all the 19 genes, and compared their functions by enzymatic assays (Fig. 2a, Supplementary Figs. 58–63). Most of these enzymes showed similar catalytic abilities by converting 1 to 2 (Fig. 5b). However, the expression level of SdPCS in the root of S. divaricata was remarkably higher than the other Apiaceae homologous
+PCS genes (FPKM value, 162.05 vs 0–5.19) (Fig. 5b).
+
+We are aware that direct inter-species comparison of FPKM might lead to misinterpretation since the utilization of FPKM value is usually limited to intra-species level. Instead, we compared the FPKM ratio between SdPCS and other potential Apiaceous PCSs against 9,470-27,214 pairs of orthologous genes as genomic background. It showed the log_2 (FPKM ratio) value of >95% genome-wide ortholog pairs between S. divaricata and other Apiaceous species in root/rhizome is < 5.00, with a mean near zero (-0.005). This result indicates that FPKM values of the investigated species are basically comparable. It is noteworthy that the log_2 (FPKM ratio) between SdPCS and other Apiaceous PCSs in root/rhizome, ranging from 6.12 to 20.63 (mean = 14.15), was higher than 95% of genome-wide orthologous gene pairs (Fig. 5c). Thus, we deduced the expression abundance of SdPCS was significantly higher than other Apiaceous PCSs. As the initial step is usually the rate-limiting step in biosynthetic pathway^{34}, the exceptionally high expression of SdPCS may contribute to the furochromone accumulation in S. divaricata.
+
+Moreover, we traced the origin of SdPCS (SaDchr02G001054), and found it might originate from proximal duplication of the nearby SdPCS2 (SaDchr02G001052) (Fig. 5d). The PCS ML tree revealed that the two PCS copies in S. divaricata clustered in the same clade, indicating SaDchr02G001054 was originated from S. divaricata specific duplication event rather than from ancestor species. The syntenic analysis further confirmed this deduction. Although syntenic genes of SdPCS were not detected in other Apiaceous species, those of the ancestral SdPCS2 were identified in most species (Fig. 5d). Remarkably, we found that SdPCS2 was nearly not expressed in any tissue (Fig. 5e), and its syntenic genes in other Apiaceous species were almost not expressed, either (Supplementary Table 20). Thus, the proximal duplication and high expression of SdPCS profoundly contributed to the biosynthesis of furochromones in the root of S. divaricata.
+Fig. 5. High expression of SdPCS2 promotes the accumulation of furochromones in the root of S. divaricata. a,
+Contents of typical furochromones in various organs of Apiaceae plants, and syntenic gene analysis. b, Phylogenetic relationships, enzymatic activities, and expression abundance of Apiaceous PCSs. The PCS enzyme activity was quantified by HPLC/UV peak area of generated noreugenin (2) (\( \lambda = 280 \) nm). c, Comparison of the FPKM between SdPCS and other potential Apiaceous PCSs in the genome-wide context. Each red line represents a log_2 (FPKM ratio) between SdPCS and a potential Apiaceous PCS. Each grey density plot indicates the log_2 (FPKM ratio) distribution of genome-wide orthologous genes of one Apiaceae species. d, Syntenic regions containing Apiaceous PCSs. e, Expression levels of three PCS copies in S. divaricata.
+
+The absence of functional PC gene leads to low furochromone content in most Apiaceous plants.
+
+Likewise, we did not detect syntenic genes of SdPC in other Apiaceous plants (Fig. 6a). We retrieved all Apiaceous CYP736s and constructed an ML tree. The reported PpDC was also included\(^{19}\). A robust clade (BS = 100) containing SdPC and 18 other potential PCs was identified (Fig. 6b, Supplementary Fig. 57). Although DCAR_313045 and As05G002751 were not included in this clade, they were syntenic with several genes, e.g., SaDchr05G002066 and LCX7BG003145 (Supplementary Fig. 64). The 11 potential PCs from A. sinensis lost one exon and was likely to lose the cyclization activity, thus they were not included in further assays. Finally, we cloned and characterized the other 10 potential PCs. Strikingly, none of them except for SdPC was effective in producing visamminol (4) (Fig. 6c). This observation confirmed our hypothesis that the absence of PC genes may lead to the low contents of furochromones in most Apiaceous species. However, we cannot exclude the possibility that these or other potential PCs might weakly catalyze the reactions *in vivo*, as trace furochromones were detected in all Apiaceous plants.
+
+Since PpDC participated in the generation of furocoumarins\(^{19}\), we tested the catalytic activities of homologous PCs using demethylsuberosin as substrate. SdPC4, AsDC, LcPC2 and DcPC showed cyclization activities (Supplementary Fig. 65). However, SdPC could not catalyze this reaction despite its high sequence similarity with SdPC4 (Supplementary Fig. 66). Interestingly, these four genes were located at the same syntenic block, which did not include SdPC (Supplementary Fig. 64). Thus, SdPC is a homologous enzyme with novel function, and its evolutionary origin warrants to be investigated in the future.
+Fig. 6 The absence of functional PC leads to low furochromone content in most Apiaceous plants. a, Syntenic regions containing SdPC. The syntenic gene pairs are connected by grey lines. b, Phylogenetic relationship and gene structure of Apiaceous PCs. As05G02748 (AsDC) is the same as AS05g00644 in the initial annotation version. c, HPLC/UV chromatograms showing the in vitro enzymatic activity of potential Apiaceous PCs (\( \lambda = 280 \) nm).
+
+Furochromones emerge as an important class of bioactive nature products in medicinal plants. However, little is known on their biosynthesis\(^{14,15}\). Particularly, the formation of furan ring and post modifications leading to structural diversities of furochromones remain largely unexplored. This work dissected the complete biosynthetic pathway of prim-O-glucosylcimifugin and 5-O-
+methylvisamminoside, two bioactive furochromone glucosides abundant in S. divaricata. Nine biosynthetic enzymes in the biosynthetic pathways were characterized. Among them, proximal duplication and high expression of a pentaketide chromone synthase gene SdPCS, as well as the presence of a lineage-specific peucenin cyclase gene SdPC, contribute to the accumulation of furochromones in the roots of S. divaricata. The results provide new insights into the biosynthesis of furochromones and serve as a platform for their metabolic engineering production.
+
+In recent years, the biosynthetic evolution of natural products in plant kingdom has attracted increasing interest. For example, Berman et al illustrated the parallel evolution of cannabinoid biosynthesis\(^{35}\), and Jiao et al studied the independent loss of biosynthetic pathway for two tropane alkaloids in the Solanaceae family\(^{36}\). In the present work, SdPCS is likely to originate from SdPCS2 through proximal duplication. However, the origin of SdPC still remains unknown. Moreover, some homologous enzymes of SdPC in S. divaricata and other species catalyze the generation of furocoumarins but not furochromones. Catalytic mechanisms and structural evidences for substrate selectivity of these enzymes also warrants further investigation.
+
+Methods
+
+Materials and Reagents
+
+The sources of fresh plants of Saposhnikovia divaricata, Centella asiatica, Bupleurum chinense, Daucus carota, Angelica sinensis, Apium graveolens, and Coriandrum sativum are given in Supplementary Table 15. To extract RNA, the roots, leaves, and petioles were used.
+
+The chemical reference standards and sugar donors used in this study were purchased from YuanYe Biotechnology Co., Ltd. (Shanghai, China). Methanol and acetonitrile (Thermo Fisher Scientific, USA) were of HPLC grade. The conversion rates were determined by HPLC/UV analysis on an Agilent HPLC 1260 instrument. Samples were separated on a Zorbax SB-C18 column (4.6×250 mm, 5 µm, Agilent, USA). The column temperature was 30°C. To calculate the conversion rates, peak areas of both substrate and product were integrated by Chromeleon® at a certain wavelength. LC/MS analysis was performed on a Q-Exactive quadrupole Orbitrap mass spectrometer (Thermo Fisher Scientific, USA).
+Genome sequencing, assembly, and annotation
+
+For the PacBio library construction, 15 μg genomic DNA from the leaves of S. divaricata was fragmented into approximately 15 kb using g-TUBEs (Covaris, USA). After removing short fragments and single-strand overhangs, the retained fragments were converted into the proprietary SMRTbell library with the PacBio DNA Template Preparation Kit (Pacific Biosciences, CA, USA). Single Molecule Real Time (SMRT) sequencing was performed on a PacBio Sequel II sequencing platform. For Hi-C library construction, chromatin was first fixed in place with formaldehyde in the nucleus and then extracted. The extracted chromatin was digested with DpnII. The 5' overhangs of resulting fragments were then filled in with biotinylated nucleotides, and free blunt ends were ligated. After ligation, the DNA was purified from protein and treated following the Illumina Next Generation manufacturer's instructions. The libraries were subsequently sequenced on Illumina Hiseq X, producing 190.37 Gb 2 × 150 bp paired-end reads. The raw data of PacBio subreads was filtered to HiFi reads by PBccs (v6.4.0) (https://github.com/PacificBiosciences/ccs), and subsequently assembled with Hifiasm (v0.16.0)37. The initial assembled contigs were anchored to chromosomes by 3D-DNA pipeline (v201008)38 and further manually adjusted to produce a chromosome-level genome. BUSCO (v5.4.3)39 was used for benchmarking the genome with the "embryophyte_odb10" database.
+
+EDTA (v2.0.0)40 was used to de novo identify, annotate, and classify the repetitive elements in the genome of S. divaricata. Prior to protein-coding gene annotation, the annotated repetitive elements in the genome were soft masked with bedtools (v2.28.0)41. RNA-Seq raw reads of S. divaricata were filtered with fastx-toolkits (v0.0.14) (http://hannonlab.cshl.edu/fastx_toolkit/index.html) and then assembled through Hisat2 (v2.2.1)42 and Stringtie (v2.2.0)43. The raw assembly of transcripts was further validated by PASA (v2.5.1)44, which were then incorporated into the MAKER (v3.01.03)45 pipeline to automatedly identify protein-coding genes. Finally, the gene models identified by MAKER were updated by PASA (v2.5.1)44. Function annotations of the protein-coding genes were carried out by BLASTP searches against entries in both NCBI non-redundant protein (NR) (https://www.ncbi.nlm.nih.gov/) and Swiss-Prot (https://www.uniprot.org/) databases. The prediction of conserved domains for the genes was performed by InterProScan (v5.11-51.0)46. The annotations of the GO terms (http://geneontology.org/) and KEGG pathways (https://www.genome.jp/kegg/) for the
+genes were annotated with eggNOG-mapper (v2.1.10-0)47.
+
+Total RNA isolation, RNA-Seq, and gene expression quantification
+
+The total RNA was extracted with the TranZol™ kit (Transgen Biotech, China) following the manufacturer’s instructions, and was used to synthesize the first-stranded complementary DNA (cDNA) with TransScript one-step genomic DNA (gDNA) removal and cDNA synthesis SuperMix (Transgen Biotech, China). The transcriptome data of different tissues of S. divaricata were sequenced at Novogene Co., Ltd. (Beijing, China).
+
+The raw RNA-seq reads were filtered in fastp48 with default parameters and then mapped to the reference genome of S. divaricata by Hisat2 (v2.2.1)42. The counts of reads mapping to exons of each gene were calculated by featureCounts49. The FPKM value of each gene was calculated in R.
+
+Genome-wide mining for furochromone biosynthetic genes
+
+HMMER3 (v3.3.2)50 was used to identify 47PKSs, PTs, CYPs, OMTs and UGTs with an e-value of 1e-6. The HMMER profiles PF02797 and PF00195 were used for PKS III search. PF01040 and PF00067 was utilized to identify CYPs and PTs. PF00891 and PF08100 were employed to search OMTs, PF00201 was applied for UGT identification. The possible pseudogenes (length of predicted CDS < 200 amino acids) were discarded. Gene structures of all candidate genes were manually adjusted with IGV-GSaman (https://gitee.com/CJchen/IGV-sRNA).
+
+Pearson correlation coefficients and the \( P \) values between contents of furochromones and the FPKM of genes among different tissues of S. divaricata were calculated with the corr.test function in R package psych (https://rdocumentation.org/packages/psych/versions/2.3.3). Those unexpressed genes were not incorporated in correlation analysis.
+
+Phylogenetic and microsynteny analyses
+
+ML phylogeny was constructed based on 398 strict single-copy orthologous genes identified by OrthoFinder (v2.5.4)51 to clarify the phylogenetic relationship among the eight Apiaceous species. The protein sequences were aligned by MUSCLE (v5.1.linux64)52 and subsequently concatenated by
+Phylosuite (v1.2.2)53. ModelTest-NG (v0.1.7)54 was used to detect the best-fit amino acid substitution model, based on which RAxML-NG (v1.1.0)55 was employed to construct the ML phylogeny with 1,000 bootstrap analyses. The construction of phylogeny of biosynthetic genes follows the same method above.
+
+The microsyntenic analyses generally followed the methods of Griesmann et al. (2018) and Yang et al. (2023). All vs. all blastp (E-value = 1e^{-5}) was conducted for the protein sequences among eight Apiaceous genomes with BLAST (v2.13.0+)56. The output protein identity matrix was loaded in JCVI (v1.2.7) to produce collinear gene blocks. Subsequently, we identified the syntenic region containing the furochromone biosynthetic genes (\( \pm 100 \) kb) in each species using the genome of S. divaricata as the reference. Because the syntenic retention varied between different species pairs, we compared the syntenic gene pairs for all species pairs and retained those gene pairs demonstrating consistent syntenic relationships. To eliminate the bias induced by mistaken annotation, we manually checked the corrected gene structure in syntenic region and re-organized the microsyntenic gene pairs.
+
+Molecular cloning
+
+The full-length candidate genes were amplified from cDNA with TransStart FastPfu DNA Polymerase (Transgen, China). Candidate genes for PCS, OMT and UGT were recombined in the pET-28a (+) vector (Invitrogen, USA) at BamH I site. Candidate genes for PT, PC and CH were cloned into pESC-Leu vector at BamH I (Invitrogen, USA). Sequences of the primers used in this study are listed in Supplementary Table 21.
+
+Expression of candidate biosynthetic genes
+
+The recombinant plasmids for PCS, OMTs and OGTs were introduced into E. coli BL21 (DE3) (Transgen Biotech, China) for heterologous expression. The E. coli cells were grown in 500 mL Luria-Bertani medium containing kanamycin (50 \( \mu \)g/mL) at 37°C. After OD_{600} reached 0.4–0.6, the cells were induced with 0.1 mM IPTG at 18°C. After 18–24 h, the cell pellets were harvested by centrifugation (7,500 rpm, 3 min at 4°C), and then resuspended in 15 mL lysis buffer (50 mM NaH_2PO_4 pH 8.0, 300 mM NaCl, 30 mM imidazole, pH 8.0). Then cells were disrupted by sonication on ice, and
+the cell debris was removed by centrifugation at 7,500 rpm for 50 min at 4°C. The supernatant was collected and loaded onto a pre-equilibrated column (His Trap™ HP, 5 mL, GE Healthcare), and eluted with different concentrations of elution buffer (50 mM NaH2PO4, pH 8.0, 300 mM NaCl, 30/300 mM imidazole)57. The purified protein solution was added with approximately 0.5 mL glycerol (25%) and stored at -80°C.
+
+The recombinant plasmids for PT, PC and CH were introduced into yeast strain Saccharomyces cerevisiae WAT11 for heterologous expression. The yeast cells were grown in synthetic dropin medium without leucine (SD-Leu). Liquid cultures of the recombinant strains were set up by picking a single colony and growing in 50 mL of SD-Leu medium containing 20 g/L glucose at 28°C overnight. The cells were collected by centrifugation (1,000 g, 2 min) and resuspended in 25 mL of SD-Leu medium containing 20 g/L galactose to induce target protein expression for 24–48 hours at 28°C. The microsomes of yeast cells were prepared as reported28.
+
+Enzyme activity assay
+
+The purified proteins and prepared microsomes were used for functional characterization by in vitro enzymatic reactions. The reactions were conducted in 100 μL Tris-HCl buffer (50 mM, pH 8.0) containing 50 μg purified enzymes or 20 μL microsomes. The incubation mixtures include substrates (0.1 mM, malonyl-CoA for PCSs, noreugenin for PTs, peucenin for PCs, visamminol for OMTs and CHs, 5-O-methylvisamminol for CHs and SdUGT1/2, norcimifugin for OMTs, and cimifugin for SdUGT1/2), and donors/cofactors (0.5 mM, dimethylallyl pyrophosphate (DMAPP) for PTs, nicotinamide adenine dinucleotide phosphate (NADPH) for PCs and CHs, S-adenosylmethionine (SAM) and dithiothreitol (DTT) for OMTs, and uridine diphosphate glucose (UDPG) for SdUGT1/2). The reactions continued in a shaking incubator for 2 hours (37°C for OMTs and UGTs, 30°C for PCSs, PTs, PCs and CHs). For PCSs, reactions were terminated by adding 10 μL 20% HCl followed by extraction with 300 μL ethyl acetate and redissolution in 100 μL MeOH. The other reactions were terminated by adding 100 μL ice-cold MeOH. The mixtures were then centrifuged at 15,000 rpm for 20 min. The supernatants were analyzed by HPLC and LC/MS.
+The conversion rates in percentage were calculated from peak areas of products and substrates in HPLC/UV chromatograms (Agilent 1260, USA). Samples were separated on a Zorbax SB-C18 column (4.6×250 mm, 5 μm, Agilent, USA). The HPLC methods are shown in Supplementary Table 22. LC/MS analysis was performed on a Q-Exactive hybrid quadrupole-Orbitrap mass spectrometer equipped with a heated ESI source (Thermo Fisher Scientific, USA). The MS parameters were as follows: sheath gas pressure 45 arb, aux gas pressure 10 arb, discharge voltage 4.5 kV, capillary temperature 350°C. MS$^1$ resolution was set as 70,000 FWHM, AGC target 1*E$^6$, maximum injection time 50 ms, and scan range $m/z$ 100–1,000. MS$^2$ resolution was set as 17,500 FWHM, AGC target 1*E$^5$, maximum injection time 100 ms, NCE 35.
+
+Biochemical properties of SdUGT1 and SdUGT2
+
+To optimize the pH value, different reaction buffers with pH from 4.0–6.0 (citric acid-sodium citrate buffer), 6.0-8.0 (Na$_2$HPO$_4$-NaH$_2$PO$_4$ buffer), 7.0-9.0 (Tris-HCl buffer), and 9.0-11.0 (Na$_2$CO$_3$-NaHCO$_3$ buffer) were tested. To optimize the reaction temperature, the reactions were incubated at 4, 18, 30, 37, 45, or 60 °C. All enzymatic reactions (100 μL reaction mixtures including 0.1 mM 5 or 8, 0.5 mM UDPG, and 10 μg of purified enzyme) were conducted in three parallel experiments ($n = 3$). The reactions were terminated with pre-cooled methanol and centrifuged at 15,000 rpm for 20 min for HPLC analysis as described above.
+
+Determination of kinetic parameters of SdUGT1 and SdUGT2
+
+Reactions were conducted in a final volume of 50 μL with 50 mM reaction buffer, suitable concentration of protein, 1 mol/L of saturated UDPG, and different concentrations of substrate (5 or 8) (Supplementary Table 23). The reactions were quenched with 70 μL pre-cooled methanol after incubating at the optimal temperature for 15 min, and then centrifuged at 15,000 rpm for 20 min. The supernatants were used for HPLC analysis. All experiments were performed in triplicate. The conversion rates were calculated as described above. The kinetic parameters were calculated with Michaelis-Menten plot fitted by Graphapad Prism 8.0$^{58}$.
+
+Scaled-up enzymatic reactions
+To prepare the prenylated product, the reaction mixtures contained 100 μL buffer (50 mM Tris-HCl, pH 8.0), 0.2 mM noreugenin, 1.0 mM DMAPP, 2.0 mM MgCl₂, and 20 μL microsome. A total of 1,200 parallel tube reactions were conducted. The reactions were performed at 30°C overnight and terminated by extraction with 4-fold volume of ethyl acetate. The organic solvent was removed under reduced pressure. The residue was dissolved in 1.5 mL of methanol. The products were then purified by reversed-phase semi-preparative HPLC. The structures were characterized by HRMS and extensive 1D and 2D NMR analyses.
+
+To prepare the hydrolyzed product of visamminol-3'-O-glucoside, the reaction mixture contained 20 mL buffer (50 mM NaH₂PO₄-Na₂HPO₄, pH 6.0), 0.5 mM visamminol-3'-O-glucoside, and 200 mg β-glucosidase (Solarbio, Beijing, China). A total of 5 parallel tubes were used. The reactions were performed at 45°C for 4 hours and terminated by extraction with 4-fold volume of ethyl acetate. The extract was treated as described above.
+
+Crystallization and structural determination
+
+The full-length cDNA of SdUGT2 was cloned into pET-28a (+) vector. The S-tag of pET28a was removed. A TrxA-tag and 6×His-tag followed by thrombin site were added before the N-terminus of the target protein to facilitate purification. The TrxA-His-thrombin-SdUGT2 protein was expressed in E. coli (DE3) strain and purified by Ni-affinity chromatography (GE Healthcare). After purification, the recombinant protein was digested by thrombin to remove tag (4°C, 8 h). The sample was mixed with Ni-NTA affinity beads for the second time to purify the protein. The flow-through was concentrated and then applied to size-exclusion chromatography on a Superdex™ 200 increase 10/300 GL prepacked column (GE Healthcare) for further purification. The elution buffer was 20 mM Tris-HCl (pH 7.5) and 50 mM NaCl. Fractions containing SdUGT2 were collected and concentrated to 20 mg/mL, flash-frozen on liquid nitrogen, and then stored in a -80°C freezer. The purified protein was incubated with 6 mM UDP for 2 h. The crystals of SdUGT2 were obtained after 5 days at 16°C in hanging drops containing 1 μL of protein solution and 1 μL of reservoir solution (0.2 M lithium sulfate monohydrate, 0.1 M Bis-Tris pH 5.25, 28% w/v polyethylene glycol 3,350) (Supplementary Fig. 25). The crystals were flash-frozen in the reservoir solution supplemented with 25% (v/v) glycerol.
+The diffraction data of SdUGT2 crystal were collected at beamlines BL19U1 and BL02U1 Shanghai Synchrotron Radiation Facility (SSRF). The data were processed with XDS. The structures were solved by molecular replacement with Phaser. Crystallographic refinement was performed repeatedly with Phenix and COOT. The refined structures were validated by Phenix and the PDB validation server (https://validate-rcsb-1.wwpdb.org/). The final refined structures were deposited in the Protein Data Bank. The diffraction data and structure refinement statistics are shown in Supplementary Table 14.
+
+Molecular docking
+
+Since all the reported UGT structures are highly conserved for the UDP-sugar binding domain, we simulated the SdUGT2/UDPG sugar complex structures by superimposing the UDP parts of UDPG to reported structures. Compound 8 was docked into the complex by Autodock. A total of 50 docking conformations were generated. The conformations with the lowest binding energy were selected for further study.
+
+De novo biosynthesis of furochromones in tobacco
+
+The full-length DNA sequences of SdPCS, SdPT, SdPC, SdOMT, SdCH and SdUGT1/2 were amplified with primers given in Supplementary Table 21. The PCR products were sub-cloned into pDonr207 vectors with the Gateway BP Clonase II Enzyme Mix and then cloned into pEAQ-HT-DEST1 vector with the Gateway LR Clonase II Enzyme Mix according to the manufacturer’s instructions. The recombinant pEAQ-HT-DEST1-target gene vectors were transformed into Agrobacterium tumefaciens strain GV3101 by chemical conversion method. Single colonies were inoculated at 28°C and subsequently shaked in LB culture medium (50 µg/mL kanamycin and 50 µg/mL rifampicin) until OD_{600} = 0.6. After centrifugation, bacteria were re-suspended in MMA buffer to OD_{600} = 0.2 for each strain. Different strains were mixed for transformation. The infection solution was infiltrated into leaves of 5-6 weeks-old tobacco. After 7 days, the samples were harvested and freeze-dried. The secondary metabolites were extracted by methanol and analyzed by LC/MS. The contents of compounds 5, 6, 8 and 9 were quantified by regression equations. Reference standards 5, 6, 8 and 9 were respectively dissolved in DMSO to make solutions of 1 mg/mL, which were 1:1 mixed to obtain the mixed stock solution. The stock solution was serially diluted with methanol containing 4
+μg/mL bergenin as internal standard to obtain calibration standard solutions (diluted by 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024, 2,048, 4,096, 8,192, 16,384, 32,768, 65,536 and 131,072 folds, respectively).
+The regression equations of **5**, **6**, **8** and **9** were listed in Supplementary Figs. 67–70. The LC/MS method parameters are listed in Supplementary Table 22.
+
+Metabolite quantification
+The secondary metabolites of different Apiaceae plants were extracted by methanol and analyzed by LC/MS following the methods mentioned above.
+
+Acknowledgements
+This work was supported by the National Key Research and Development Program of China (No. 2023YFA0914100 to M. Y., and No. 2023YFA0915800 to L. W.), Beijing Natural Science Foundation (No. QY23076 to J.L. Z., and 83001Y0439 to C.X.Z.), and National Natural Science Foundation of China (No. 81725023 to M. Y.). We thank Dr. Rong-shen Wang and Xi-ran Zhang of Ye Lab and Xunmeng Feng and Jiao-jiao Ji of Wang Lab for their technical assistance. We also thank the staff at BL19U1/BL02U1 beamlines at SSRF of the National Facility for Protein Science in Shanghai (NFPS), Shanghai Advanced Research Institute, Chinese Academy of Sciences, for providing technical support in X-ray diffraction data collection and analysis.
+
+Data availability
+Data supporting the findings of this study are available in the article, supplementary materials, or public database. The gene sequence data generated in this study have been deposited in the NCBI database under the accession numbers listed in Supplementary Table 24. The crystal structure in this study has been deposited in the RCSB PDB database under the accession number: SdUGT2 (8ZNK). The assembled genome and annotation files of *S. divaricata* are available at figshare (https://figshare.com/projects/Saposhnikovia_divaricata_genome/206434). The raw data of transcriptome sequencing of *S. divaricata* have been deposited to the Genome Sequence Archive at the National Genomics Data Center (NGDC) under BioProject no. PRJCA026506. The sources of genome data and RNA-seq data of other Apiaceous plants are listed in Supplementary Tables 16–17.
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryTables.xlsx
+• SuppplementaryFigures.pdf

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+ZFP36-family RNA-binding proteins in regulatory T cells reinforce immune homeostasis.
+
+Martin Turner
+martin.turner@babraham.ac.uk
+
+Babraham Institute   https://orcid.org/0000-0002-3801-9896
+Beatriz Sáenz-Narciso
+Babraham Institute
+Sarah Bell
+Babraham Institute   https://orcid.org/0000-0002-3249-707X
+Louise Matheson
+Babraham Institute   https://orcid.org/0000-0002-9392-2519
+Ram Venigalla
+Babraham Institute
+
+Article
+
+Keywords:
+
+Posted Date: October 7th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-5039504/v1
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on May 6th, 2025. See the published version at https://doi.org/10.1038/s41467-025-58993-y.
+Title: ZFP36-family RNA-binding proteins in regulatory T cells reinforce immune homeostasis.
+
+Authors: Beatriz Sáenz-Narciso, Sarah E. Bell, Louise S. Matheson, Ram K. C. Venigalla and Martin Turner*
+
+Affiliations: Immunology Programme, The Babraham Institute, Babraham Research Campus, Cambridge, CB22 3AT, UK.
+
+These authors contributed equally to this work: Beatriz Sáenz-Narciso, Sarah E. Bell
+Corresponding author:
+Dr. Martin Turner
+e-mail: martin.turner@babraham.ac.uk
+
+Abstract
+RNA binding proteins (RBP) of the ZFP36 family limit the differentiation and effector functions of CD4 and CD8 T cells, but little is known of their expression or function in regulatory T cells (Treg). By Treg-restricted deletion of Zfp36 family members we identify the essential role of Zfp36l1 and Zfp36l2 in Treg to maintain immune homeostasis. Mice with Tregs deficient in these RBP display an inflammatory phenotype with an expansion in the numbers of type-2 conventional dendritic cells, T effector cells, T follicular helper and germinal center B cells and elevated serum cytokines and immunoglobulins. In the absence of Zfp36l1 and Zfp36l2, the pool of cycling CTLA-4 in naïve Treg was reduced, Tregs were less sensitive to IL-2 and IL-7 but were more sensitive to IFNγ. In mice lacking both RBP in Treg, the deletion of a single allele of Ifng is sufficient to ameliorate the pathology. Thus, ZFP36L1 and ZFP36L2 regulate multiple pathways that enable Tregs to enforce immune homeostasis.
+The Zinc Finger Protein 36 (ZFP36) family of RNA binding proteins (RBP) are widely expressed and play important roles in developmental biology, stress responses and inflammation \(^{1,2}\). They act as repressors of gene expression by direct binding to AU-rich elements in the 3'UTR of mRNAs to limit translation and trigger RNA degradation. They regulate large numbers of functionally related mRNAs throughout their lifetime creating a system of post-transcriptional operons which regulate immune function \(^{3,4}\). The best characterised operon is the cytokine-encoding mRNAs and their repression by ZFP36 is essential for limiting inflammation. How the other Zfp36-family members function and in which cell types they control inflammation and immunity is not well understood.
+
+T lymphocytes transiently express ZFP36 and ZFP36L1 when activated \(^{5,6}\) and studies using mouse models suggest they each make essential contributions to restraining effector CD4 and CD8 T cell functions \(^{5-11}\). A third family member *Zfp36l2* is expressed by resting T cells and represses cytokine production by memory T cells \(^{12}\) and by activated naïve T cells 48 hours after activation \(^{13}\). Mice in which all three family members are deleted by *Cd4-cre* at the CD4+CD8+ thymocyte stage develop a hyper-cytokinemia and a lethal inflammatory syndrome \(^{9}\). By contrast, mice with *Cd4-cre*-mediated deletion of *Zfp36* and *Zfp36l1* appear healthy \(^{6,9}\), and show increased resilience following influenza virus infection \(^{6}\). Mice with deletion of *Zfp36l1* and *Zfp36l2* in T cells also appear healthy and show reduced pathology and effector T cell responses following induction of experimental autoimmune encephalomyelitis \(^{9}\).
+
+As *Cd4-cre* deletes in all TCR\( \alpha\beta^+ \) T cells it remains unclear to what extent these complex phenotypes reflect cell-intrinsic roles of the RBP in effector cells or Tregs. Mice which overexpress ZFP36 in all cells have a small increase in the frequency of Tregs, these were better able to suppress the *in vitro* proliferation of naïve T cells \(^{14}\). Another study indicated the potential for ZFP36L2 to be a negative regulator of *Ikzf2* mRNA and to inhibit the suppressive function of induced Tregs \(^{15}\) and others have shown that the immunosuppressive cytokine IL-10 \(^{16,17}\) and inhibitory surface receptor CD274/PD-L1 \(^{18}\) are directly repressed by ZFP36-family proteins. Whether the ZFP36-family act in Tregs to limit or enhance their function is unknown.
+Tregs require the transcription factor FOXP3 for their differentiation and function and have a dominant role in immune tolerance, with roles in tissue homeostasis and resilience to infection \(^{19-21}\). They deploy a repertoire of effector functions including the production of soluble factors, contact mediated depletion of costimulatory molecules and competition with effector T cells for trophic factors and metabolites. Tregs are particularly sensitive to deprivation of IL-2 which acts via the induction of STAT5 phosphorylation to promote their survival. Tregs also demonstrate remarkable functional adaptation to local inflammatory environments which can expose them to cytokines, such as IFN\(_\gamma\) that can modulate function in a context-dependent manner \(^{22-24}\). The extent to which any of these processes are regulated by the ZFP36 family is unknown.
+
+In this study, we employed a conditional deletion strategy in mice to investigate the function of *Zfp36* family members in Tregs. The loss of *Zfp36l1* alone in Tregs resulted in dysregulation of immune homeostasis, a phenotype that was more severe when combined with deficiency of *Zfp36l2*. We establish that in Treg *Zfp36l1* and *Zfp36l2* play a key role in promoting CTLA-4 function to limit the expansion of type 2-conventional dendritic cells (cDC2), in restraining the size of germinal centers (GC), and determining Treg sensitivity to IFN\(_\gamma\), IL-2 and IL-7.
+
+**Results**
+
+**Zfp36l1 and Zfp36l2 are essential in Treg to maintain immune homeostasis**
+
+To establish if ZFP36-family proteins are expressed in Tregs we have used mice in which the endogenous allele of each family member has been modified to introduce a fluorescent protein at the site of translation initiation to encode a fusion protein. By identifying Tregs with surface staining for CD25\(^+\) and FR4\(^+\) (Supplementary Fig. S1a) we found mAmetrine-ZFP36 was not detectably expressed by T cells ex vivo. Naïve CD44\(^lo\)CD62L\(^hi\) Treg (nTreg) expressed more mCherry-ZFP36L1 and eGFP-ZFP36L2 compared to CD4\(^+\) CD44\(^lo\)CD62L\(^hi\) CD25\(^-\) T cells (nTconv) (Fig. 1a). Furthermore, mCherry-ZFP36L1 was expressed at four-fold greater amounts in CD44\(^hi\)CD62L\(^lo\) effector Treg (eTreg) compared to nTreg, while eGFP-ZFP36L2 was not increased (Fig. 1a). The greater expression of mCherry-ZFP36L1 in eTreg and nTreg is consistent with these cells having been recently activated and with ZFP36L1
+expression increasing in proportion to TCR signal strength \(^{25}\) which is known to be greater in naïve Tregs than naïve Tconv \(^{26}\).
+
+To establish the requirement for individual ZFP36 family members in Tregs we deleted Zfp36, Zfp36l1 or Zfp36l2 using the *Foxp3*YFP-iCre* (FYC) allele which contains the YFP-iCre recombinase fusion protein open reading frame in the 3'UTR of the *Foxp3* gene \(^{27}\). Male *Foxp3*YFP-iCre* Zfp36l1fl/fl* (FYC Zfp36) and *Foxp3*YFP-iCre* Zfp36l2fl/fl* (FYC l2) mice were healthy up to twenty weeks of age. By contrast, 9% of *Foxp3*YFP-iCre* Zfp36l1fl/fl* male mice (FYC l1) had developed clinical signs of marked piloerection, hunched posture with a median age of onset of ten weeks. ZFP36L1 expression in T cells is strongly stimulated by PMA plus ionomycin and we used this to establish whether the protein could be detected in T cells from *FYC l1* mice. ZFP36L1 expression was reduced by ten-fold in FOXP3+ Treg from *FYC l1* mice compared to *FYC* mice but was not differentially expressed in FOXP3- CD4+ Tconv (Supplementary Fig. 1b) demonstrating efficient and selective deletion of ZFP36L1 in Treg. Because naïve Tregs express both ZFP36L1 and ZFP36L2 and *Zfp36l1* is redundant with *Zfp36l2* in diverse cell systems \(^{28-30}\) we anticipated that the deletion of both genes in Treg would lead to a stronger phenotype than deletion of either gene alone. We thus generated *Foxp3*YFP-iCre* Zfp36l1fl/flZfp36l2fl/fl* (referred to as *FYC l1/l2*) mice. Deletion of ZFP36L1 in *FYC l1/l2* mice was confirmed by flow cytometry to be specific to Treg (Supplementary Fig. 1b). 12% of *FYC l1/l2* mice developed clinical symptoms which exceeded the predefined humane endpoint, including marked piloerection, hunched posture, and abdominal distension, with a median age of onset of five weeks. These mice had markedly increased lymph node (LN) cellularity which exceeded that seen in the *FYC l1* males (Supplementary Fig. S1c).
+
+The proportion and number of YFP- CD44hiCD62Llo effector CD4 and CD8 cells within LN (gated as shown in Supplementary Fig. 1d) was increased two- to three-fold in *FYC l1* mice, and three- to five-fold in *FYC l1/l2* mice compared to *FYC* controls (Fig. 1b).
+
+By contrast, in the YFP- CD4+ subset from mice lacking *Zfp36* there was no difference in the proportion and only a minor increase in the number of effector cells compared to control mice (1.6-fold) and no change in the CD8+ subset (Supplementary Fig. 1e). CD4 and CD8 effector subsets were not different between *FYC l2* and *FYC* mice (Supplementary Fig. 1f).
+Tregs from FYC I1 and FYC I1I2 mice were biased towards an activated phenotype with a three-fold increase in the number of eTreg in FYC I1I2 mice compared to FYC control mice (Fig. 1c). In addition, the number of nTreg was increased 1.5-fold (Fig. 1d), thus the phenotype of FYC I1 and FYC I1I2 mice was not due to a deficit in Treg numbers. Furthermore, the combined loss of both Zfp36l1 and Zfp36l2 led to a greater expansion of CD4 and CD8 effector cells than loss of Zfp36l1 alone.
+
+Histological analysis of tissues from FYC I1I2 mice with clinical symptoms revealed perivascular lymphocytic infiltration into lung and liver and diffuse crypt hyperplasia in the small intestine (Fig. 1e). In the large intestine of FYC I1I2 mice there was evidence of crypt hyperplasia accompanied by an increase in inflammatory cells in the lamina propria (Fig. 1e). Thus, the loss of Zfp36l1 and Zfp36l2 in Tregs leads to a failure of immune homeostasis.
+
+Compromised fitness of RBP-deficient Treg
+
+In females, Foxp3 is inactivated on one X chromosome, thus when heterozygous for the Foxp3YFP-icre allele, FYC/+ mice accumulate icre-positive and -negative Treg which can be distinguished by the expression of YFP. FYC/+ I1I2 mice did not develop any clinical symptoms over a period of at least 40 weeks. Also, we found no difference in numbers of FOXP3+CD44hiCD62Llo CD4 and CD8 cells (Supplementary Fig. 2a). Thus, Zfp36l1/Zfp36l2-deficient Tregs are insufficient to cause disease when wild type Tregs are present. In female FYC/+ mice the number of FOXP3+YFP+ Tregs was twice that of FOXP3+YFP+ Tregs in the same mouse suggesting the Foxp3YFP-icre allele incurs a minor competitive disadvantage on Tregs. However, in FYC/+ I1I2 mice the icre-positive Treg were seven times less abundant than icre-negative Tregs in the same mouse (Fig. 2a). Normal Treg numbers were detected in the thymus (Supplementary Fig. S2b), thus the competitive disadvantage of Zfp36l1/Zfp36l2-deficient Tregs is revealed in peripheral lymphoid tissue.
+
+To gain insight into the role of Zfp36l1 and Zfp36l2 in Treg function in the absence of pathology we sorted YFP+ CD62LhiCD4+CD25+ cells from female FYC/+ and FYC/+ I1I2 mice (Supplementary Fig. 2c) and performed RNA-seq. Quantitation of reads mapping to the targeted region of Zfp36l1 and Zfp36l2 confirmed efficient icre-mediated recombination of both conditional alleles (Supplementary Fig. 2d).
+Furthermore, by intracellular staining for ZFP36L1 in stimulated T cells we observed a seven-fold reduction in the ZFP36L1 protein only in *icre*-positive YFP*^FOXP3*+ Treg but not in *icre*-negative YFP*^FOXP3*+ Treg, or in Tconv (Supplementary Fig. 2e). Differential expression analysis using DESeq2 revealed 249 genes were increased (Supplementary Table 1) and 340 genes decreased (Supplementary Table 2) in the knockout Treg compared to control cells (FDR-adjusted p value <0.05) (Fig. 2b). The mRNAs encoding *Foxp3*, *Ctla4*, *Ikzf2* (Helios), *Icos*, *Tgfβ1* and *Lrrc32*, key genes involved in Treg function, were not differently expressed (Fig. 2b). To identify transcripts that could be bound and thus directly regulated by ZFP36-family members we used published crosslinking and immunoprecipitation (CLIP) data (Supplementary Table 3) and found that target transcripts were increased in *FYC*+/− *Il12* Treg compared to *FYC*+/− Treg (Fig. 2c). This is consistent with the direct targets of these RBP being more stable and thus accumulating to increased amounts in *Foxp3*YFP-*icre* *Il12* Treg.
+
+Gene Set Enrichment Analysis (GSEA) using a custom group of gene sets covering different aspects of T cell biology (Supplementary Table 4), revealed “Endocytosis”, “*T cell receptor signaling*” and several genes sets associated with cytokine signaling amongst the top ten positively enriched pathways, including “*Decreased in IL-2*”, “*Decreased in IL-7*”, “*JAK STAT signaling pathway*”, “*IL-2 Receptor signalling*”, and “*Increased in IFNγ*” in *Foxp3*YFP-*icre* *Il12* deficient Tregs (Fig. 2d). Many of the genes contributing most to the enrichment (present in the leading edge) were transcripts shown to interact directly with ZFP36-family members by CLIP (represented in orange and listed in Supplementary Table 4). Genes enriched in the endocytosis pathway included 25 in the leading edge that were iCLIP targets, encompassing genes involved in the regulation of protein sorting and membrane trafficking (Supplementary Table 5 and Fig. 2e). Within the TCR signaling pathway 40 out of 73 genes in the leading edge were iCLIP targets (Supplementary Table 5 and Fig. 2e), including genes that can promote (*Lat, Cd2*) or attenuate (*Rptor, Dgka, Dok2*) activation via the TCR (Supplementary Fig. 3a). We thus evaluated the protein expression of CD5, which is not a target of the ZFP36 family but an indicator of TCR signaling strength \(^{31,32}\), and the CLIP target NUR77 (encoded by *Nr4a1*), which is expressed early after TCR stimulation. Expression of these proteins did not differ
+between YFP+ Treg from FYC+/I1l2 and FYC+/ mice (Supplementary Fig. 3b). Thus, we concluded that in a non-inflammatory environment, TCR signaling was not detectably altered in Foxp3YFP-cre I1l2 deficient Tregs.
+
+Using the Immunological Genome Project signatures of “common γ-chain” family cytokines 33 we found that for genes responding to IL-2 or IL-7 signaling in Treg, those that were increased in response to these cytokines were decreased in the transcriptome of Foxp3YFP-cre I1l2 deficient Tregs compared to Foxp3YFP-cre Tregs from control FYC+/ mice (Fig. 2f). By contrast, genes that were decreased in response to IL-2 or IL-7 signaling were increased in Foxp3YFP-cre I1l2 deficient Tregs (Fig. 2f). Inspection of the genes increased in response to IFNγ in Treg revealed that genes decreased in response to IFNγ were not significantly changed, while genes increased in response to IFNγ were just above the 0.05 threshold for significance as increased in the transcriptome of nTreg from FYC+/ I1l2 mice compared to that from control FYC+/ mice (Fig. 2g). The GSEA also identified the “Treg gene signature” and “Notch signaling pathway” to be just beyond the cut-off for statistical significance. As noted above, Foxp3, Ctl4a, Ikzf2 and Icos, were not differently expressed; and at the protein level we detected only minor reductions for FOXP3 (1.1-fold), CTLA-4 (1.2-fold) IKZF2 (1.4-fold) and ICOS (1.2-fold) between Foxp3YFP-cre I1l2 and Foxp3YFP-cre nTregs (Supplementary Fig. 4a). FOXP3, CTLA-4 and IKZF2 also were slightly reduced in eTregs (1.1;1.3;1.3-fold respectively), but ICOS showed an increase of 1.3-fold between Foxp3YFP-cre I1l2 eTreg and Foxp3YFP-cre eTreg (Supplementary Fig. 4a). The expression of NOTCH1, a known target of ZFP36L1 and ZFP36L2 28,34, that when overexpressed can impair Treg function 35, was not different in Foxp3YFP-cre I1l2 Treg compared to Foxp3YFP-cre Treg (Supplementary Fig. 4b). We conclude that the 589 DE genes in the transcriptome of naive Foxp3YFP-cre I1l2 Treg impact on multiple processes which together could contribute to the lack of fitness and function of I1l2-deficient Tregs.
+
+Decreased cycling of CTLA-4 in RBP-deficient nTreg
+As conventional dendritic cells (cDC) are important in maintaining T cell tolerance 36 and cDC phenotype can be regulated by Treg 37, we examined the number of cDC in LN. We had observed that LN cellularity was increased four-fold in FYC I1l2 mice,
+however, using a gating strategy (modified from \( ^{38} \)) relative to the cDC subsets in FYC mice, the number of “resident” CD172a\(^{-}\) XCR1\(^{-}\) cDC2 was selectively increased (ten-fold) compared to the “migratory” CD172a\(^{+}\) XCR1\(^{-}\) cDC2 and “resident” and “migratory” cDC1 (CD172a\(^{-}\) XCR1\(^{+}\)) populations (Fig. 3a,b). CTLA-4 can bind to the costimulatory molecules CD80 and CD86 and can capture these molecules by trans-endocytosis from neighbouring antigen presenting cells (APC) to restrict costimulation via CD28 \( ^{37} \). The selective increase in cDC2 numbers therefore prompted us to examine the expression of CD80 and CD86 on cDC in the LN from male mice. We identified elevated CD80 and CD86 expression only in the “resident” CD172a\(^{+}\) XCR1\(^{-}\) cDC2 but not in the “migratory” CD172a\(^{+}\) XCR1\(^{-}\) cDC2 population in FYC I1I2 mice (Fig. 3c) nor in the cDC1 population (Supplementary Fig. 5a). CTLA-4 is predominantly localised within intracellular vesicles, which cycle between the cell surface and intracellular stores, and can be rapidly removed from the surface via clathrin-mediated endocytosis \( ^{39} \). As GSEA had identified enrichment in the endocytosis pathway, we examined the cycling pool of CTLA-4, which can bind ligand at the plasma membrane, by incubating unstimulated cells with labelled anti-CTLA-4 antibody at 37\(^\circ\)C for 2 hours and comparing this to the total intracellular pool. Constitutive uptake of labelled antibody *in vitro* visualised in the absence of stimulation, revealed a decrease in the pool of cycling CTLA-4 in YFP\(^{+}\) nTreg from male FYC I1I2 mice compared to nTreg from control FYC mice, although no difference was observed in eTreg or in the total intracellular pool (Fig. 3d).
+
+Consistent with the data from the male mice, in the absence of stimulation, the pool of cycling CTLA-4 in RBP-deficient YFP\(^{+}\) nTreg from female FYC\(^{+}\) I1I2 mice was also decreased compared to YFP\(^{+}\) nTreg from FYC\(^{+}\) mice (Fig. 3e) and YFP\(^{-}\) nTreg in the same mice (Supplementary Fig. 5b), but not within the YFP\(^{+}\) eTreg subset. Thus, these data suggest a cell intrinsic role for ZFP36L1 and ZFP36L2 in promoting CTLA-4 cycling in nTreg.
+
+**ZFP36L1 and ZFP36L2 promote Treg sensitivity to IL-2 and IL-7**
+
+IL-2R signaling can enhance CTLA-4 function in Treg \( ^{40} \). Moreover, based on the results of the GSEA and the finding that CD8 T cells lacking Zfp36 and Zfp36l1 were less sensitive to IL-2 \( ^{41} \) we hypothesized that ZFP36L1 and ZFP36L2 promote Treg responsiveness to IL-2 and/or IL-7. As both IL-2 and IL-7 induce tyrosine phosphorylation of STAT-5A/B, we examined this in Treg *ex vivo* after rapid fixation
+of cells following tissue retrieval. In FYC+/I1I2 mice we observed a two-fold reduction in the frequency of pSTAT5+ cells in FOXP3+YFP+ nTreg compared to FYC/+ controls, but no difference between the eTreg subsets (Fig. 4a). In male FYC I1I2 mice, we observed a two-fold reduction in the frequency of pSTAT5+ cells in both nTreg and eTreg (Fig. 4b), suggesting optimal STAT5 phosphorylation in Treg in vivo requires ZFP36L1 and ZFP36L2. As STAT5 can be phosphorylated in response to both IL-2 and IL-7, we measured expression of their receptors CD25 and CD127, and the in vitro response of Treg to a range of doses of IL-2 and IL-7. Surface expression of CD25 on YFP+ nTreg from the spleen of female FYC+/I1I2 mice was reduced two-fold compared to YFP+ nTreg from FYC/+ mice (Fig. 4c). Amongst eTreg the majority expressed low levels of CD25 but still we found a reduction (1.5-fold) between CD25 surface expression on YFP+ eTregs comparing FYC+/I1I2 and FYC/+ mice. Accordingly, YFP+ nTreg from FYC+/I1I2 mice showed diminished responses when cultured with IL-2 at 0.3 and 1 ng/ml but no difference was found in eTreg (Fig. 4d). Quantitation of the total amount of STAT5 in YFP+ FOXP3+ cells in female FYC+/I1I2 and FYC/+ mice confirmed this was not different (Supplementary Fig. 6a). Moreover, icre-negative Treg from female FYC+/I1I2 and FYC/+ mice responded in a similar manner to IL-2 (Supplementary Fig. 6b), indicating a cell-intrinsic defect of RBP-deficient Treg in their response to IL-2. CD25 expression was also reduced on nTreg from male FYC I1I2 mice compared to control FYC mice (Fig. 4e), and the response to IL-2 was diminished only in the nTreg population (Fig. 4f). These data indicate that ZFP36L1 and ZFP36L2 in Treg promote an optimal response to IL-2.
+
+CD127 was expressed at modestly greater amounts on the surface of eTreg compared to nTreg. On YFP+ nTreg and eTreg from both female FYC+/I1I2 (Fig. 5a) and male FYC I1I2 mice (Fig. 5b) CD127 was decreased compared to Tregs from control mice. Furthermore, both naïve and effector YFP+ Treg from FYC+/I1I2 mice showed a striking reduction in their pSTAT5 response to IL-7 compared to YFP+ Treg from FYC/+ mice (Fig. 5c). This was also the case for nTreg and eTreg from male FYC I1I2 mice (Fig. 5d). In FYC/+ and FYC+/I1I2 females, icre-negative Treg were more sensitive to IL-7 than icre-positive Treg from the same mouse. Therefore, expression of the FYC allele correlates with a minor reduction in pSTAT5 in response to IL-7 (1.2-fold Supplementary Fig. 6c). However, the difference between icre-positive and icre-negative Treg in the same animal was greater in FYC+/I1I2 mice
+compared to control \( FYC^+ \) mice (Supplementary Fig. 6c), supporting a cell-intrinsic role for ZFP36L1 and ZFP36L2 in the Treg response to IL-7. Taken together, these results revealed that ZFP36L1 and ZFP36L2 are essential in Treg to maintain optimal sensitivity to IL-2 and IL-7.
+
+ZFP36L1 and ZFP36L2 limit Treg sensitivity to IFN\(_\gamma\)
+
+As the bulk RNAseq data from heterozygous female mice suggested a possible enhancement of the IFN\(_\gamma\) signaling pathway we evaluated the response to IFN\(_\gamma\). We used intracellular flow cytometry to detect phosphorylation of STAT1 on Tyrosine-Y701 following stimulation with a range of doses of recombinant murine IFN\(_\gamma\). We observed an enhanced response to IFN\(_\gamma\) in YFP\(^+\) nTreg from \( FYC^+/I1I2 \) mice compared to YFP\(^+\) nTreg from control \( FYC^+ \) mice (Fig. 6a). YFP\(^+\) eTreg showed a much lower response than naïve YFP\(^+\) Treg, which was comparable between genotypes except at the highest concentration. Significantly, YFP\(^+\) nTreg from \( FYC^+/I1I2 \) mice showed an enhanced response compared to YFP\(^+\) nTreg from the same mouse indicating the effect was cell intrinsic (Supplementary Fig. 7a). Quantitation of the total amount of STAT1 in YFP\(^+\) FOXP3\(^+\) cells in female \( FYC^+/I1I2 \) and \( FYC^+ \) mice confirmed this was not different (Fig. 6b and Supplementary Fig. 7b). In addition, we examined the response to IL-6, which also promotes STAT1 Y701 phosphorylation, and found no increase in STAT1 phosphorylation between YFP\(^+\) Treg from control \( FYC^+ \) and \( FYC^+/I1I2 \) mice following *in vitro* stimulation with a range of doses (Fig. 6c and Supplementary Fig. 7c). Thus, the limiting effects of ZFP36L1 and ZFP36L2 on STAT1 phosphorylation were specific to the IFN\(_\gamma\) pathway and indicate these RBP restrain IFN\(_\gamma\) signaling in Treg in a cell intrinsic manner.
+
+Activated phenotype of Treg from *FYC I1I2* mice
+
+To explore the heterogeneity of Treg and gain further insight into how ZFP36L1 and ZFP36L2 regulate Treg function in an inflammatory environment we performed single-cell sequencing of RNA (scRNA-seq) on Treg sorted from the peripheral LN of male *FYC* and *FYC I1I2* mice (Supplementary Fig. 8a). We analyzed high quality transcriptomes of 5824 cells from *FYC* mice and 4163 cells from *FYC I1I2* mice. Using a graph-based clustering approach Treg were grouped into eight
+subpopulations and represented using a uniform manifold approximation and projection (UMAP) for dimensionality reduction (Fig. 7a). Using gene sets derived from a comparison of naïve and effector Treg transcriptomes (Supplementary Table 6) we applied the Semi-supervised Category Identification and Assignment (SCINA) algorithm \(^{42}\) to assign cell type identities. We found that cells in clusters 0, 2 and 5 were frequently classified as nTreg, whereas clusters 3, 4 and 7 were primarily comprised of eTreg (Fig. 7a,b and Supplementary Fig. 8b). Differential gene expression analysis identified markers for each cluster except for cluster 1, which did not show enrichment for any distinctive genes (Supplementary Table 7). The four most frequently detected genes in each cluster in comparison to every other cluster are shown (Fig. 7c), further illustrating that clusters 0, 2 and 5 exhibited genes typical of nTreg (e.g., Sell, S1pr1). Genes characteristic of eTreg (e.g. Icos, Maf) were not detected or lowly expressed in clusters 0, 2 and 5, but frequently detected in clusters 3, 4 and 7. Cells in cluster 7 expressed markers characteristic of effector and highly proliferative cells, including Mki67 and histone genes, in addition to a higher number of genes, (Supplementary Fig. 8c) suggestive of a highly proliferative population. Thus, the individual clusters could broadly be distinguished by characteristic marker expression with a distinct distribution corresponding to naïve and effector Treg subtypes.
+
+The distribution of clusters of Treg from FYC and FYC I1I2 mice was not equivalent. Treg from FYC I1I2 mice represented only 20% of cells in cluster 0 and 15% in cluster 2, whereas 80% of Tregs in cluster 4 were represented by FYC I1I2 Treg (Fig. 7d). As we had found that ZFP36L1 and ZFP36L2 limit Treg sensitivity to IFN\(_\gamma\), we investigated genes characteristic of the IFN\(_\gamma\) response (defined in Supplementary Table 8). We used the SCINA algorithm to assign cell type identities in the scRNA-seq data and found a higher proportion of Treg from FYC I1I2 mice across most clusters associated with an IFN\(_\gamma\) gene signature (Fig. 7e). Activity of the IFN\(_\gamma\) signaling pathway is necessary for the differentiation of CXCR3\(^+\) Tregs, thus we examined expression of Cxcr3 and other effector molecules and found enrichment of Cxcr3 in clusters 3 and 4 (Fig. 7f). In addition, Gata3 and Pdcd1 (encoding PD-1), which is expressed by Treg during activation, were also most frequently detected in cluster 4 (Fig. 7h), which is over-represented in FYC I1I2 Treg. Consistent with these
+observations, flow cytometry revealed an increase in the proportion (Fig. 7i) and number of CXCR3+ Treg (Supplementary Fig. 8d) compared to control mice. GATA3hi Treg and YFP+CXCR5+PD-1+ T follicular regulatory (Tfr) cells were also increased in proportions (Fig. 7j, k) and numbers (Supplementary Fig. 8d), in FYC I1I2 mice compared to control mice. Although we found a three-fold reduction in the proportion of RORγt+ Treg in FYC I1I2 mice compared to controls there was no difference in cell number (Supplementary Fig. 8e) indicating these cells are unable to control the influx of inflammatory cells in the intestine.
+
+Consistent with the increased proportion of CXCR3+ and GATA3+ Treg and the decreased proportion of RORγt+ Treg in FYC I1I2 mice, stimulation of splenocytes from male FYC I1I2 mice revealed increased frequencies of Tregs producing IFNγ, IL-4 and IL-10 and a reduced proportion producing IL-17 (Fig. 7l). Analysis of the gMFI of these cytokines revealed that Treg from FYC I1I2 mice produce marginally more IFNγ (1.3-fold) and less IL-17 (1.7-fold) compared to Treg from FYC mice, whilst no difference was found in the production of IL-4 or IL-10 (Supplementary Fig. 8f). FOXP3+ CD4+ T cells were also enriched for IFNγ, IL-4 and IL-10-positive cells (Fig. 7l) and produced more IL-10 (Supplementary Fig. 8f). Therefore, the inflammatory environment in FYC I1I2 mice was not a result of a deficiency of IL-10. Moreover, we found three times more CD8+ T cells producing IFNγ in FYC I1I2 mice with the production of IFNγ by these cells also increased (1.6-fold) (Supplementary Fig. 8g). Thus, the expanded CXCR3+ and GATA3+ Treg subsets in FYC I1I2 mice are unable to limit the expansion of activated CD4 and CD8 T cells which produce cytokines that may contribute to the loss of immune homeostasis in FYC I1I2 mice.
+
+IFNγ is a driving force for the expansion of effector T cells
+
+The enhanced sensitivity of I1I2-deficient Treg to IFNγ together with the increased number of Treg showing an IFNγ signature in the scRNAseq and the increased proportion of Treg cells producing IFNγ, suggested that ZFP36L1 and ZFP36L2 act in Treg to regulate the IFNγ signaling axis. The production of IFNγ by Treg and their responsiveness to it are essential for immune homeostasis, and in vivo IFNγ can mediate both pro- and anti-inflammatory processes. Thus, we sought to test the
+physiological role of IFN\( \gamma \), while avoiding complications arising from a complete absence of IFN\( \gamma \), by generating FYC \( I1I2 \) mice heterozygous for \( Ifng \). The majority of \( Ifng^{+/-} \) FYC \( I1I2 \) mice were healthy, with only one mouse from 23 that developed skin inflammation, compared to ten out of 45 FYC \( I1I2 \) mice developing clinical symptoms which exceeded the severity limit (marked piloerection and intermittent hunched posture, Fig. 8a). FYC \( I1I2 \) mice had elevated levels of IFN\( \gamma \), TNF\( \alpha \), IL-2, IL-6 and IL-10 in the serum compared to FYC control mice, however, the amounts of these cytokines were reduced in \( Ifng^{+/-} \) FYC \( I1I2 \) compared to FYC \( I1I2 \) mice, with none maintaining a significant increase relative to FYC controls (Fig. 8b). The increased number of effector cells in the Treg, CD44\(^{hi}\) CD62L\(^{lo}\) CD4\(^+\)YFP\(^-\), CD44\(^{hi}\) CD62L\(^{hi}\) and CD44\(^{hi}\) CD62L\(^{lo}\) CD8\(^+\) subsets in FYC \( I1I2 \) mice was also diminished by loss of one \( Ifng \) allele but remained two- to three-fold higher than in FYC control mice in each subset (Fig. 8c). The number of Tfh, Tfr and GC B cells in FYC \( I1I2 \) mice was significantly increased in comparison to the FYC controls, but these numbers were reduced in \( Ifng^{+/-} \) FYC \( I1I2 \) mice, although remained four-fold higher in both Tfh and Tfr subsets (Fig. 8d,e), whilst the population of GC B cells remained ten-fold higher (Fig. 8f). Serum IgG2c and IgE levels were elevated in FYC \( I1I2 \) mice compared to FYC controls. In \( Ifng^{+/-} \) FYC \( I1I2 \) mice the amount of IgG2c was reduced to that found in control mice (Fig. 8g). However, the concentrations of IgE were still higher (60-fold) in \( Ifng^{+/-} \) FYC \( I1I2 \) mice relative to FYC control mice, which correlated with the persistence of an elevated number of GC B cells (Fig. 8g). Thus, these data indicate that IFN\( \gamma \) is a driving force underpinning a complex phenotype in FYC \( I1I2 \) mice.
+
+Discussion
+All three ZFP36 family paralogues can be expressed by T cells, and, in the absence of infection or inflammation, ZFP36L1 is the most abundant in Tregs and exerts non-redundant essential functions that are compensated partially by ZFP36L2. The ZFP36 family is a well-established regulator of cytokines, but in Tregs these RBP additionally regulate large numbers of genes that control pathways required by the Treg to maintain immune homeostasis.
+
+Tregs lacking \( Zfp36l1 \) and \( Zfp36l2 \) failed to prevent the expansion of cDC2, GC B cells and effector CD8 T cells. As interactions between cDC2 and Tfh support Tfh
+priming and GC B responses \(^{43,44}\), and cDC2 can cross-prime CD8 T cells \(^{45}\) the increased numbers and elevated expression of CD80 and CD86 on cDC2 could be driving the expansion of activated lymphocytes in FYC \(I1/2\) mice. The compromised ability of nTreg to limit costimulation may arise, in part, from defective CTLA-4 cycling. IL-2 signaling also positively impacts upon Treg CTLA-4 function \(^{40}\) and was impaired in \(Zfp36l1\) and \(Zfp36l2\)-deficient Tregs. Furthermore, IL-2 sensitivity is diminished in CD8 T cells lacking \(Zfp36l1\) suggesting ZFP36L1 connects antigen affinity to IL-2 responsiveness \(^{25}\).
+
+Although IL-2 signaling is essential for Treg survival and function \(^{46,47}\), when deprived of this cytokine IL-7 can sustain Tregs and contribute to Treg homeostasis \(^{47,48}\). Mice with conditional deletion of \(Il7ra\) in Tregs did not develop autoimmune disease, but IL-7R on Tregs was important to maintain allograft tolerance in a Treg transfer model \(^{49}\) and IL-7 promotes eTreg survival in the skin \(^{50}\). In Treg we found that ZFP36L1 and ZFP36L2 promote sensitivity to both IL-2 and IL-7. This may account for the reduction in number of \(icre\)-expressing Treg in female mice heterozygous for \(icre\), where these cells are in competition for these cytokines. As the development of Tfr has been reported to be inhibited by IL-2 \(^{51,52}\), a defect in IL-2 signaling would be accompanied by expansion of Tfr as we observe in FYC \(I1/2\) mice. The accumulation of Tfh and GC B cells may also be augmented by the increased availability of IFN-\(\gamma\) \(^{53}\).
+
+\(Zfp36l1\) and \(Zfp36l2\) also specifically limit Treg sensitivity to IFN\(\gamma\). Whilst Th1-like Tregs can be potent suppressors of the activity, proliferation and memory formation of CD8 effector T cells \(^{24}\) and IFN\(\gamma\)-mediated STAT1 activation in Tregs can promote Treg function in alloantigen tolerized mice \(^{22}\), IFN\(\gamma\) can also promote Treg “fragility” or lineage instability in the tumor microenvironment \(^{23}\).
+
+The ability of ZFP36-famly members to repress IFN\(\gamma\) expression did not manifest as increased amounts of IFN\(\gamma\) produced by ex vivo stimulated Tregs but was apparent as a greater frequency of IFN\(\gamma\) producing Tregs. The capacity for ZFP36L1 and ZFP36L2 in Tregs to interconnect the IL-2, IFN\(\gamma\) and CTLA-4 pathways and enforce their function, whilst dampening their function in effector CD4 and CD8 T cells may
+be relevant to the association of the genes encoding this family of RBP with autoimmune diseases \( ^2 \).
+
+Limitations of the study
+These phenotypes were not evident in mice with deletion of ZFP36 family proteins using Cd4-cre which, taken together with the specific deletion, argues that the phenotypes arise from the function of ZFP36L1 and ZFP36L2 in Treg. We have focussed on Treg in the absence of intentional immune challenge, and it is unclear how Treg deficient in these RBP respond to activation and how this affects transcriptomes, cell function and the physiology of the mice. The compendium of iCLIP targets is from CD4 and CD8 T cells, it is possible some mRNAs unique to Treg were not detected. In addition to regulating RNA stability ZFP36L1 and ZFP36L2 can also repress translation \( ^{12,54} \) and may regulate protein localization, thus the use of sensitive proteomics methods could reveal additional direct and indirect targets regulated by the RBP. The detailed mechanism of how the RBP regulate CTLA-4 and cytokine signalling in Treg remain to be elucidated.
+
+Methods
+Mice
+Mice were engineered to express the fluorescent proteins mAmetrine or mCherry upstream and in frame with the start codons of Zfp36 or Zfp36l1 respectively \( ^{25} \). The targeting vector for Zfp36l2 was designed to encode eGFP upstream and in frame with the ATG translation start site of ZFP36L2 (Cyagen, Santa Clara, CA, USA). The reporter mice were healthy and fertile (and used for breeding up to 40 weeks of age). Zfp36\( ^{fl}/^{fl} \) (Zfp36\( ^{tm1Tnr} \)), Zfp36l1\( ^{fl}/^{fl} \) (Zfp36l1\( ^{tm1.1Tnr} \)) and Zfp36l2\( ^{fl}/^{fl} \) (Zfp36l2\( ^{tm1.1Tnr} \)) mice have been described previously \( ^{28,55} \) and were maintained on a C57BL/6J background. The following alleles on the C57BL/6J background (obtained from the Jackson Laboratory) were also used: B6.129(Cg)-Foxp3\( ^{tm4(YFP/cre)} \)Ayr/J; Jax stock #016959); and B6.129S7-\( IFNg^{tm1Ts} \) (Jax stock #002287). For the experiments shown in Fig. 8, the cohort of FYC I1I2 and Ifng\( ^{+/+} \)-FYC I1I2 mice that were analyzed had not been backcrossed to C57BL/6 for seven generations. Any animals which displayed
+the limiting clinical signs of marked piloerection and intermittent hunched posture, and/or abdominal distension were humanely killed.
+
+Mice were bred and maintained in the Babraham Institute Biological Support Unit. No primary pathogens or additional agents listed in the FELASA recommendations have been confirmed during health monitoring surveys of the stock holding rooms. Ambient temperature was ~19-21°C and relative humidity 52%. Lighting was provided on a 12-hour light: 12-hour dark cycle including 15 min ‘dawn’ and ‘dusk’ periods of subdued lighting. After weaning, mice were transferred to individually ventilated cages with 1-5 mice per cage. Mice were fed CRM (P) VP diet (Special Diet Services) ad libitum and received seeds (e.g., sunflower, millet) at the time of cage cleaning as part of their environmental enrichment. All mouse experimentation was approved by the Babraham Institute Animal Welfare and Ethical Review Body. Animal husbandry and experimentation complied with European Union and United Kingdom Home Office legislation.
+
+Flow cytometry
+Single cell suspensions were prepared from the spleen, peripheral lymph nodes (LN, axillary, brachial, cervical and inguinal) and mesenteric LN (mLN), with antibody staining for surface markers performed essentially as described previously \( ^6 \) including Fc block (2.4G2) in PBS/2% FCS/2mM EDTA. Dead cells were excluded using fixable viability dye eFluor780 (eBioscience). A full list of antibodies used is provided in Supplementary Table S9. An antibody against GFP (clone FM264G, BioLegend) was used for intracellular detection of YFP which is fused to cre in *Foxp3*YFP-*icre* mice. For detection of phospho-antibodies, the cells were fixed in neutral buffered formalin (Sigma) diluted in PBS to 2% for 30 min at room temperature, pelleted by centrifugation and cells were resuspended in ice-cold 90% methanol, incubated for 30 minutes on ice, washed twice, then incubated with the antibody cocktail containing 2.4G2 antibody overnight at 4°C. For dendritic cell isolation, LN tissue was finely minced then digested with collagenase P (Merck, 1mg/ml in RPMI 2% FCS) for 40 minutes at 37°C with agitation, then EDTA added to
+5mM, clumps dispersed using pipetting and the cell suspension filtered. Single cell suspensions were washed and stained as described.
+
+For ex vivo analysis of pSTAT5 LN cell suspensions were prepared directly into fixation buffer from eBioscience™ Foxp3 / Transcription Factor Staining Buffer Set. For intracellular cytokine detection, LN cells were stimulated for 4 hours at 37°C with 10ng/ml Phorbol-12-myristate-13-acetate (PMA; 524400, Merck) and 500ng/ml ionomycin (407952, Merck) in the presence of 5µg/ml Brefeldin A (eBioscience) in complete IMDM medium (Invitrogen; containing 10% FBS, 2mM Glutamax, 25mM HEPES, 50µM 2-mercaptoethanol). Cells were fixed with 2% PFA for 30 minutes at room temperature, washed twice with Foxp3 permeabilization buffer (eBioscience) and incubated with the antibody cocktail containing 2.4G2 antibody overnight at 4°C. For transcription factor staining, Foxp3 fixation buffer was used according to the manufacturer’s instructions. Acquisition was performed on a Fortessa flow cytometer equipped with 355 nm, 405 nm, 488 nm, 561 nm and 640 nm lasers (Beckton Dickinson) and the data were analyzed using FlowJo software (v10).
+
+In vitro cytokine stimulation
+
+Splenocytes were cultured for 30 minutes at 37°C with a range of doses of recombinant murine cytokines (all from Peprotech) IFNγ (# 315-05) IL-6 (# 216-12), IL-2 (# 212-12) IL-7 (# 217-17) in the presence of eF780 viability dye and 150µM TAPI-0 (Tocris # 5523) in complete IMDM medium.
+
+Ex vivo CTLA-4 cycling assay
+
+Following red blood cell lysis with Tris-ammonium chloride, CD4+ T cells were isolated from spleen by depletion of CD8+, CD11b+ CD11c+, MHCII+ and B220+ cells using biotinylated antibodies and M-280 Streptavidin Dynabeads. CD4+ T cells were cultured for 2 hours at 37°C in the presence of TAPI-0 (100µM) and 2ng/ml IL-2. APC conjugated anti-CD152 (CTLA-4) antibody (clone UC10-4F10-11) was added to the cells to detect cycling CTLA-4. Surface CTLA-4 was detected by labelling cells with APC conjugated anti-CD152 for 30 minutes at 4°C, and total CTLA-4 detected after fixation and permeabilization with antibody incubation overnight at 4°C.
+Histology
+For histology, tissue samples were collected into 10% neutral buffered formalin (Sigma). Preparation of slides, H&E staining, pathology and interpretation was performed by Abbey Veterinary Services UK.
+
+Measurement of Serum cytokines and Immunoglobulin
+Serum was collected from mice by cardiac puncture. Serum cytokines were measured using the MSD pro-inflammatory panel 1. IgG2c and IgE were measured by ELISA using paired antibody sets (IgG2c, Southern Biotech and IgE, BD Biosciences) according to the manufacturer’s protocol.
+
+Cell Sorting for RNA seq
+Single cell suspensions were prepared from pooled spleen and peripheral LN (inguinal, brachial, axillary and cervical) from six FYC+/I1/2 and seven FYC/+ mice at 7-14 weeks of age. CD4+ cells were enriched by negative depletion using biotinylated anti-B220, anti-CD8 and anti-CD11b followed by Streptavidin Dynabeads (Dynal). Naïve Treg were sorted as CD4+CD25+ CD62L+ YFP+ cells. All samples were sorted to >95% purity.
+
+For RNA-seq libraries used to identify markers of naïve and effector Treg, cells were prepared as above from male Zfp36l1m/m /2 m/m control mice, aged 9-12 weeks, but with naïve Treg sorted as CD4+CD25+CD62L+CD44- and effector Treg as CD4+CD25+CD62L-CD44+ cells.
+
+To sort Tregs for single cell RNA seq single cell suspensions were prepared from pooled LN from one mouse of each genotype at 14 weeks of age. CD4+ cells were enriched by negative depletion using biotinylated anti-B220, anti-CD8 and anti-F4/80 followed by Streptavidin Dynabeads (Dynal). Treg were sorted as CD4+FR4+YFP+ cells. All samples were sorted to >95% purity.
+Bulk RNA-seq
+RNA was prepared from sorted Treg cells using the RNeasy Micro kit (Qiagen) as described \(^{56}\) and quality was assessed using the Bioanalyzer RNA chip. cDNA was generated using SMART seq v4 low input RNA kit. RNA-seq libraries were prepared from cDNA using the Nextera XT kit. Libraries were sequenced using a 50bp single end RapidRun on the Illumina HiSeq2500.
+
+ScRNA-seq
+Cells were labelled using Totalseq oligo-conjugated antibodies (BioLegend) to enable multiplexing of control (hashtag 1: ACCCACCCAGTAAGAC) and conditional knockout (hashtag 2: GGTCGAGAGCATTCA) samples, and feature barcoding of CD127 (IL7-R\(\alpha\); GTGTGAGGGCACTCTT). The sorted single cell suspensions were mixed and loaded onto a Chromium single cell device (10x Genomics) for encapsulation with barcoded gel beads according to the manufacturer’s Single Cell 3’ v3.1 (Dual Index) protocol. 3’GEX and 3’ Feature barcoding libraries were prepared according to the standard manufacturer’s protocol. The resulting libraries were sequenced on an Illumina NovaSeq 6000 S1 (paired end 150bp).
+
+Bioinformatic analysis
+Quality of sequencing data was assessed using FastQC (http://www.bioinformatics.babraham.ac.uk/projects/fastqc/). Reads were trimmed for adapters and low quality base calls using Trim Galore, with default parameters (v0.6.5; https://www.bioinformatics.babraham.ac.uk/projects/trim_galore/). Reads were then mapped to the GRCm38 mouse reference genome using Hisat2 (v2.1.0; \(^{57}\)). BAM files were imported into Seqmonk (v1.47.0; http://www.bioinformatics.babraham.ac.uk/projects/seqmonk/), excluding those with mapping quality < 30, and reads were quantified over merged mRNA isoforms from the GRCm38 v90 annotation, using the RNA-seq quantitation pipeline. Reads were also quantified specifically over the regions flanked by lox-P sites in *Zfp36l1* and *Zfp36l2*. Differential expression analysis comparing cKO with control samples was performed using DESeq2 (v1.22.2) \(^{58}\), using ‘normal’ log\(_2\) fold change shrinkage, and genes designated differentially expressed if their FDR-adjusted p value was < 0.05. Gene set enrichment analysis \(^{59}\) was performed using the GSEAPreranked module
+of the GenePattern software package \(^{60}\), with default parameters except that 'collapse dataset' was set to 'No_collapse'. Genes were ranked based on log10 of their raw p value from DESeq2 analysis, with a positive sign assigned to genes with a positive log_2 fold change, such that the most significantly increased genes are ranked first, and the most significantly decreased are ranked last. Custom gene sets were uploaded for the analysis: the Hallmark apoptosis gene set was obtained from MSigDB \(^{61}\) and gene names converted to mouse orthologues using biomaRt \(^{62}\) whilst the TCR signaling pathway gene set was curated manually (see Supplementary Table 4). Genes increased or decreased in Treg upon IL-2 or IL-7 treatment were identified using publicly available ImmGen common \( \gamma \)-chain cytokine RNA-seq data (GSE180020) \(^{33}\), processed as above to compare cytokine- with PBS-treated Treg. Increased/decreased genes were defined as those with FDR-adjusted p value < 0.05, and absolute log_2-fold change > 1, except for genes increased upon IL-7 treatment where a log_2-fold change threshold of 0.7 was used to ensure a gene list of appropriate size for GSEA analysis. For IFN\( \gamma \) treatment, microarray data of iTreg treated for 10h, compared with neutral conditions, was used (GSE38686, \(^{63}\)). Conditions were compared using GEO2R and increased/decreased genes defined as those with FDR-adjusted p value < 0.05. Normalised read counts for the top 15 most significantly increased TCR signaling genes were log_2 transformed, and the mean transformed read count across all replicates for a given gene was subtracted. Genes were ranked based on their adjusted p value. A heatmap was plotted using the pheatmap R package, with a threshold set on the fill color such that values above/below the maximum/minimum threshold were assigned the maximum/minimum colors in the scale.
+
+To generate lists of genes characteristic of naïve and effector Tregs (Table S6), RNA-seq data from control nTreg and eTreg were compared as described above, and naïve and effector markers were defined as genes with FDR-adjusted p value < 0.0001, and log_2-fold change in eTreg compared with nTreg < -1.5 or > 2, respectively.
+
+ScRNA-seq analysis
+
+Since the feature barcoding libraries contained both multiplexing and CD127 tags, the fastq files were first split based on whether an exact match to one of the hashtag
+oligos for multiplexing was found starting in position 11 in the “R2” feature barcoding fastq file. The separated multiplexing and antibody-derived tag fastq files, together with the gene expression fastq files, were then processed using Cell Ranger v6.1.2, first with cellranger multi, using the GRCm38 mouse genome reference, followed by aggregation of the control and knockout data from the per sample outputs, using cellranger aggr. Further analysis was performed using the Seurat package \( ^{64} \) Cells containing below 1500 and over 14000 molecule counts for either hashtag 1 or hashtag 2 oligo conjugated antibodies were removed to filter out putative empty droplets, or doublets respectively. Additionally, cells containing over 5.5 % mitochondria-derived gene expression reads, over 10% reads originating from a single gene, or in which fewer than 1000 or more than 4200 genes were detected were removed. After filtering for quality, we compared the transcriptomes of 5824 cells from FYC mice and 4163 cells from FYC I1/2 mice. Normalization was performed using the centred log ratio transformation, across cells (margin 2). The top 500 variable genes were identified, and these were scaled and used as input for principal component analysis. The top 15 principal components were then used as input for Seurat’s graph-based clustering approach (FindNeighbors followed by FindClusters functions; resolution 0.5; all other parameters default). These 15 principal components were also used as input to RunUMAP for further dimensionality reduction and data visualization. To identify cluster-specific marker genes the FindMarkers function was used, only considering genes detected in at least 25% of cells in at least one group for a given comparison; significantly enriched or depleted genes for each cluster are listed in Supplementary Table 7. The SCINA package was used to assign cell type identities based on previous knowledge related to naïve/effecter cells (using the gene list in Supplementary Table 6). Genes associated with an Ifng signaling signature are listed in Supplementary Table 8; this was based on conversion of the human Reactome Interferon Gamma Signaling pathway genes to mouse orthologues.
+
+Identification of direct ZFP36-family targets
+
+HITS-CLIP data for ZFP36-family proteins in CD4+ T cells following 4h activation, or 72h activation with 2h reactivation, were obtained from GSE96074 \( ^{5} \) iCLIP data for ZFP36L1 in CD4+ T cells activated for 24h with anti-CD3 and anti-CD28 was
+obtained from GSE155087 6. All data was analyzed using the iCount pipeline 65 on the Genialis platform; for iCLIP data the replicates for each antibody were merged. A gene was designated a target if the 3'UTR contained a significant crosslink site (FDR < 0.05) with both antibodies in the iCLIP, or if a crosslink site in the 3'UTR was identified in at least two replicates for either of the HITS-CLIP datasets.
+
+Statistical analysis
+Statistical significance was determined using GraphPad Prism v9 using the test indicated in the respective Figure legends.
+
+Data and Materials Availability
+The RNA-seq data are available in the Gene Expression Omnibus (GEO) database (https://www.ncbi.nlm.nih.gov/geo/) under accession code GSE244621.
+
+Mice with modified alleles of Zfp36, Zfp36l1 and Zfp36l2 are available under a material transfer agreement with The Babraham Institute. All data needed to evaluate the conclusions are presented in the paper or in the Supplementary Materials.
+
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+
+Acknowledgements:
+We thank Kirsty Bates for expert technical assistance and Oliver Burton for advice on flow cytometry; Fiamma Salerno and Marian Jones Evans for characterizing the reporter mice; and the Core Biochemical Assay Laboratory at Addenbrooke’s Hospital for MSD analysis.
+We thank Georg Petkau and Arianne Richard for critical reading of the manuscript.
+We thank the UKRI-BBSRC Core Capability Grant funded Babraham Institute Biological Support Unit, Sequencing, Flow Cytometry and Bioinformatics Facilities for invaluable support.
+
+Funding:
+This study was funded by the BBSRC Institute strategic programme grants BBS/E/B/000C0427; BBS/E/B/000C0428 and a Wellcome Investigator award (200823/Z/16/Z) to M.T.
+
+Author contributions:
+Conceptualization: M.T.
+Methodology: B.S-N, S.E.B.
+Investigation: B.S-N, S.E.B, R.V.
+Data curation: B.S-N, L.S.M.
+Writing- original draft: B.S-N, S.E.B, L.S.M, M.T.
+Funding acquisition: M.T.
+Supervision: M.T.
+All authors contributed to reviewing and editing the manuscript.
+
+Competing interests: The authors declare they have no competing interests
+Figure 1
+
+a
+
+![Flow cytometry plots showing gating strategy and histograms for CD62L^hi^ and CD44^+^CD62L^lo^ populations in Zfp36-mAmetrine, Zfp36l1-mCherry, and Zfp36l2-eGFP mice.](page_184_158_1207_312.png)
+
+b
+
+![Flow cytometry plots and scatter plots showing gating strategy and statistical analysis for FYC, FYC I1, FYC I1/2, CD44^+^CD62L^lo^, and CD44^+^CD62L^hi^ populations.](page_184_495_1207_312.png)
+
+c
+
+![Flow cytometry plots and scatter plots showing gating strategy and statistical analysis for Treg, FYC, FYC I1, FYC I1/2, CD44^+^CD62L^lo^, and CD44^+^CD62L^hi^ populations.](page_184_832_1207_312.png)
+
+d
+
+![Scatter plot showing statistical analysis for # CD44^+^CD62L^hi^ populations.](page_184_1169_1207_312.png)
+
+e
+
+![Histological images of lung, liver, small intestine, and large intestine from FYC and FYC I1/2 mice.](page_184_1512_1207_312.png)
+Fig. 1 Zfp36l1 and Zfp36l2 are essential in Treg to maintain immune homeostasis
+
+a, Representative histogram overlays comparing expression of each reporter in Treg (CD4+ CD25+ FR4+) versus Tconv (CD4+ CD25- FR4-) cells in either the naïve (CD44loCD62Lhi) or effector (CD44hiCD62Llo) subset, as indicated. Gating as in fig. S1A. In each example Tconv cells are represented by the grey shaded histogram; mAmetrine - ZFP36 (purple line); mCherry – ZFP36L1 (red line) and eGFP – ZFP36L2 (green line). Corresponding cells from wild type mice are indicated by the dashed line. Scatter plots represent the geometric mean fluorescence intensity (gMFI) of each reporter from n=4-5 mice.
+
+b, Representative flow cytometry (FACS) plots and proportion and cell number of effector cells CD44hiCD62Llo in the CD4+ YFP- (upper panel) and CD8+ subsets (lower panel), in single and double conditional knockout male mice (gated as in Supplementary Fig. 1d). Control icre-only FYC (n=17); FYC I1 (n=8); FYC I1I2 (n=11), key as shown.
+
+c,d, Representative FACS plots, showing percentage and number of CD44hi CD62Llo eTreg c, and d, numbers of CD44lo CD62Lhi nTreg in FYC I1 and FYC I1I2 male mice (gated as shown in c).
+
+e, Representative images of haematoxylin and eosin staining of the lung, liver, small and large intestine from three male FYC and FYC I1I2 mice at 11 weeks of age. Lymphoid infiltrates are arrowed. Scale bar represents 200um.
+
+For a-d, each symbol represents an individual mouse with the horizontal line representing the mean; values are for LN cells from mice aged 10 -14 weeks. Data from at least two independent experiments. P values were determined by Mann-Whitney non-parametric test (a) or one-way ANOVA using multiple comparison (b, c, d).
+Figure 2
+
+a
+
+![Flow cytometry plots showing gating strategy and percentage TrgCs for FYC* (icre') and FYC* I112 (icre')](page_158_134_670_246.png)
+
+b
+
+![Scatter plot of Log2 FC vs Mean normalised read counts for various genes](page_820_134_670_246.png)
+
+c
+
+![Boxplot comparing Log2 fc between Non-target and Target groups](page_158_393_670_246.png)
+
+d
+
+<table>
+  <tr>
+    <th>Pathway</th>
+    <th>NES</th>
+    <th>Target</th>
+    <th>Non-target</th>
+  </tr>
+  <tr>
+    <td>ENDOCYTOSIS (213)</td>
+    <td>&lt;0.001</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>TCR SIGNALING (210)</td>
+    <td>&lt;0.001</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>DECREASED IN IL-2 (159)</td>
+    <td>0.005</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>DECREASED IN IL-7 (233)</td>
+    <td>0.01</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>JAK STAT SIGNALING PATHWAY (33)</td>
+    <td>0.01</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>TNF SIGNALING PATHWAY (90)</td>
+    <td>0.023</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>IL-2 RECEPTOR SIGNALING (40)</td>
+    <td>0.042</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>INCREASED IN IFNG (77)</td>
+    <td>0.068</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>TREG SIGNATURE (292)</td>
+    <td>0.119</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>NOTCH SIGNALING PATHWAY (40)</td>
+    <td>0.124</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>LYSOSOME (112)</td>
+    <td>0.328</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>DNA REPLICATION (35)</td>
+    <td>0.295</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>CHOLESTEROL HOMEOSTASIS (64)</td>
+    <td>0.285</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>DNA REPAIR (144)</td>
+    <td>0.213</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>RNA POLYMERASE (28)</td>
+    <td>0.199</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>FATTY ACID METABOLISM (34)</td>
+    <td>0.107</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>AMINOACYL TRNA BIOSYNTHESIS (44)</td>
+    <td>0.018</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>INCREASED IN IL-2 (194)</td>
+    <td>0.008</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>RIBOSOME BIOGENESIS IN EUKARYOTES (71)</td>
+    <td>0.009</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>INCREASED IN IL-7 (162)</td>
+    <td>&lt;0.001</td>
+    <td></td>
+    <td></td>
+  </tr>
+</table>
+
+e
+
+Endocytosis
+TCR Signalling
+
+f
+
+IL-2
+NES = 1.9; FDR = 0.005
+NES = -1.9; FDR = 0.008
+
+IL-7
+NES = 1.8; FDR = 0.009
+NES = -2.2; FDR = 0
+
+g
+
+IFN-γ
+NES = -1; FDR = 0.44
+NES = 1.5; FDR = 0.07
+Fig. 2 Compromised fitness of RBP-deficient Tregs
+
+a, Representative FACS plots of FOXP3 and YFP expression in CD4+ cells from female FYC/+ and FYC+/I1/I2 mice; scatter plots showing quantification (% of YFP+ and YFP- cells within FOXP3+ gate); key as shown
+b, MA plot showing the DESeq2-derived shrunken log2-fold changes in gene expression in FYC/+ I1/I2 compared with FYC/+ nTreg, padj. <0.05 shown in blue, selected genes indicated in black.
+c, Violin plot showing the log2-fold change in expression of genes with ZFP36-family binding detected in their 3'UTR by CLIP (orange), compared with non-target genes (grey). Only genes with mean normalised read counts > 100 were included; the number of genes in each group is indicated.
+d, GSEA of custom gene sets (Supplementary Table 4) showing the ten most positively and negatively enriched pathways in the transcriptomes of Treg from FYC+/I1/I2 compared to FYC/+ mice. Genes were ranked based on their expression change upon deletion of Zfp36l1 and l2 (most significantly increased genes ranked first and most significantly decreased genes ranked last).
+The bar graph shows the number of genes in the leading edge, with predicted targets represented in orange. The red-blue heatmap shows the NES. Pathways ordered with the highest NES shown at the top; values in white represent the FDR-adjusted p value.
+e, GSEA plots for Endocytosis and TCR signaling pathways
+f, g, GSEA plots using genes with altered expression in the response to the survival factors IL-2 and IL-7 (f), and IFNγ (g), comparing the genes altered by cytokine stimulation to the transcriptome of Treg from FYC+/I1/I2 mice; genes decreased upon cytokine stimulation shown in blue; genes increased are shown in red.
+Figure 3
+
+a
+
+![Flow cytometry gating strategy showing migration and residency of DC subsets](page_184_232_670_180.png)
+
+b
+
+![Scatter plots comparing DC1 and DC2 populations between FYC and FYC I1/2](page_900_232_370_370.png)
+
+c
+
+![Flow cytometry plots and bar graphs comparing CD80 and CD86 expression in migratory and resident DCs between FYC and FYC I1/2](page_184_532_670_180.png)
+
+d
+
+![Flow cytometry plots and bar graphs comparing CTLA-4 and CD62L expression in cycling and total DCs between FYC and FYC I1/2](page_184_732_670_370.png)
+
+e
+
+![Flow cytometry plots and bar graphs comparing CTLA-4 and CD62L expression in cycling and total DCs between FYC+ (icre+) and FYC+ I1/2 (icre+)](page_900_732_370_370.png)
+Fig. 3 Decreased cycling of CTLA-4 in RBP-deficient nTreg
+
+a, Gating strategy for cDC2 (CD172a+ XCR1−), showing percentage of events in each gate. Dump channel (FITC: CD3, CD64, F4/80), pre-gated on live, single cells
+b, Enumeration of cells per LN in each DC subset; n=6, key as shown.
+c, Representative FACS plots showing CD80 and CD86 expression on CD11cint MHCIIhi “migratory” (upper panel) and CD11chil MHCIIint “resident” (lower panel) cDC2 from spleen from FYC I1I2 and FYC male mice; the number of events in the file is indicated; n=6, key as shown
+d, Representative FACS plots showing CTLA-4 staining in nTreg from spleen from FYC I1I2 and FYC male mice (left panel) and eTreg (right panel). Percentage of CTLA-4+ Treg in each condition (lower panel); n=6
+e, As in d, showing data from FYC/+ I1I2 and FYC/+ female mice; n=5
+Each symbol represents an individual mouse; key as shown. Data from at least two independent experiments. P values were determined by Mann-Whitney test.
+Figure 4
+
+a
+■ FYC* (icre*) □ FYC* I1I2 (icre*)
+CD62L^h CD44^+CD62L^o
+
+b
+● FYC ○ FYC I1I2
+CD62L^h CD44^+CD62L^o
+
+c
+CD62L^h CD44^+CD62L^o
+
+d
+0 ng 0.03 ng 0.1 ng 0.3 ng 1 ng
+CD62L^h CD44^+CD62L^o
+
+e
+CD62L^h CD44^+CD62L^o
+
+f
+0 ng 0.03 ng 0.1 ng 0.3 ng 1 ng
+CD62L^h CD44^+CD62L^o
+
+CD62L^h CD44^+CD62L^o
+<0.0001 0.004 0.004 0.7
+
+CD62L^h CD44^+CD62L^o
+0.007 0.003 0.01 0.07
+Fig. 4 ZFP36L1 and ZFP36L2 promote Treg sensitivity to IL-2
+
+a,b, Representative FACS plots of Treg from LN from female mice a, or male mice b, fixed directly ex-vivo and stained for pSTAT5; FYC+, FYC+ I1I2 n=5; FYC, FYC I1I2 n=4, key as shown
+c, Representative histogram overlays of CD25 expression on nTreg (left panel) and eTreg (right panel) from spleen; gMFI of CD25; YFP+ cells from female FYC+ and FYC+ I1I I2 mice; key as in a
+d, Frequency of pSTAT5+ cells in nTreg and eTreg from female splenocytes following stimulation for 30 minutes with a range of concentrations of IL-2; key as in a
+e, Representative histogram overlays of CD25 expression on nTreg (left panel) and eTreg (right panel) from spleen; gMFI of CD25; YFP+ cells from male FYC and FYC I1I2 mice; key as in b
+f, Frequency of pSTAT5+ cells in nTreg and eTreg from male mice stimulated as in d; key as in b
+P values determined using Mann-Whitney test (a,b,c,e), or two-way ANOVA with multiple comparison (d, f).
+Figure 5
+
+a
+CD62L^{hi}    CD44^{+}CD62L^{lo}
+
+b
+CD62L^{hi}    CD44^{+}CD62L^{lo}
+
+c
+0 ng   0.03 ng   0.3 ng   1 ng   10 ng
+CD62L^{hi}
+CD44^{+}CD62L^{lo}
+pSTAT5
+<0.0001 <0.0001 <0.0001 <0.0001
+IL-7 (ng/ml)
+
+d
+0 ng   0.03 ng   0.3 ng   1 ng   10 ng
+CD62L^{hi}
+CD44^{+}CD62L^{lo}
+pSTAT5
+<0.0001 <0.0001 <0.0001
+IL-7 (ng/ml)
+
+■ FYC^{+} (icre^{+})   □ FYC^{+} I1I2 (icre^{+})
+
+● FYC   ○ FYC I1I2
+Fig. 5 ZFP36L1 and ZFP36L2 promote Treg sensitivity to IL-7
+
+a, b, Representative histogram overlays of CD127 expression in nTreg (left panel) and eTreg (right panel) from spleen of female mice a, or male mice b; gMFI of CD127.
+
+c, d, Frequency of pSTAT5+ cells in nTreg and eTreg isolated from the spleen from female mice (c) or male mice (d) following stimulation for 30 minutes with a range of concentrations of IL-7; key as shown.
+
+P values determined using Mann-Whitney test (a, b), or two-way ANOVA with multiple comparison (c, d).
+Figure 6
+
+a
+
+![Flow cytometry and scatter plots showing pSTAT1+ cells in CD44hiCD62Lhi and CD44hiCD62Lo subsets after IFN-γ treatment at different concentrations.](page_153_180_1277_393.png)
+
+b
+
+![Bar graphs comparing gMF total STAT1 levels between CD62Lhi and CD44hiCD62Lo subsets.](page_153_573_1277_246.png)
+
+c
+
+![Flow cytometry and scatter plots showing pSTAT1+ cells in CD44hiCD62Lhi and CD44hiCD62Lo subsets after IL-6 treatment at different concentrations.](page_153_866_1277_393.png)
+Fig. 6 ZFP36L1 and ZFP36L2 limit Treg sensitivity to IFNγ
+
+a, Frequency of pSTAT1+ cells detected in YFP+ nTreg and YFP+ eTreg from female mice following stimulation for 30 minutes with a range of concentrations of IFNγ. Representative histogram overlays of pSTAT1 expression (left panel) and compiled data (right panel); key as shown.
+
+b, FACS analysis of total STAT1 expression in Treg from female FYC+/+ and FYC+/I1I2 mice, showing representative histogram overlays of STAT1 expression and quantitation; key as in a.
+
+c, Frequency of pSTAT1+ cells detected in YFP+ nTreg and YFP+ eTreg from female mice following stimulation for 30 minutes with a range of concentrations of IL-6. Representative histogram overlays of pSTAT1 expression (left panel) and compiled data (right panel); key as in a. P values determined using two-way ANOVA with multiple comparison (a,c).
+Figure 7
+
+a
+b
+c
+d
+e
+f
+g
+h
+i
+j
+k
+l
+Fig. 7 Activated phenotype of Treg from FYC I1I2 mice
+
+a, UMAP representation of scRNA seq data with cell clusters indicated by color code and numbered 0-7. Single CD4+FR4+YFP+cells were sorted from apparently healthy male FYC and FYC I1I2 mice.
+
+b, Distribution of nTreg and eTreg subsets within clusters; key as shown
+
+c, Dot plot representation showing percentage of detection (dot size) and scaled expression (dot color) in each cluster for genes more frequently detected and highly expressed in each cluster relative to other clusters (Wilcoxon rank sum test; p value <0.001). The top four genes for each cluster, based on average log_2 fold change, are shown. Color bar on the right indicates clusters that are primarily comprised of nTreg or eTreg; key as in b.
+
+d, UMAP representation of clusters according to genotype as indicated, and percentage contribution of cells to each cluster by genotype; key as shown
+
+e, UMAP distribution highlighting the location of cells with an expression pattern characteristic of the IFNγ gene signature (indicated in red); and percentage contribution of cells identified as possessing the IFNγ signaling gene signature for each genotype, within each cluster; adjusted p values from Chi-square test
+
+f, g, h, UMAP distribution highlighting the location of cells expressing Cxcr3 (f), Gata3 (g), Pdcdf1 (h). The intensity of the purple color indicates the scaled expression level for each plot.
+
+i, j, k, Representative FACS plots gated on CD4+ cells and scatter plots showing % of CXCR3+ (i), GATA3hi (j), and CXCR5+ PD1+ (Tfr, k) out of all FOXP3+ cells; (n=4 to 7); key as shown
+
+l, IFNγ, IL-17, IL-4 and IL-10 expression in Tconv and Treg. Splenocytes were stimulated with PMA/ionomycin for four hours in the presence of Brefeldin A; FACS plots gated on CD4+ cells. Percentage values shown as a % of all CD4+ FOXP3+ cells (Tconv) or CD4+FOXP3+ cells (Treg).
+
+Data are from at least two independent experiments. P values determined using Mann-Whitney test (i-l).
+Figure 8
+
+a
+
+![Kaplan-Meier survival curve showing clinical severity limit (%) over age (weeks) for FYC/112 and IFNγ/FYC/112 groups](page_134_156_377_246.png)
+
+b
+
+![Scatter plots comparing cytokine production (IFNγ, TNFα, IL-2, IL-6, IL-10) among FYC, FYC/112, and IFNγ/FYC/112 groups](page_529_156_377_246.png)
+
+c
+
+![Flow cytometry plots showing Treg, Tconv, and CD8+ populations in FYC, FYC/112, and IFNγ/FYC/112 groups](page_134_406_377_246.png)
+
+d
+
+![Flow cytometry plots showing Th1 and Th17 populations in FYC, FYC/112, and IFNγ/FYC/112 groups](page_529_406_377_246.png)
+
+e
+
+![Flow cytometry plots showing CXCR5+ populations in FYC, FYC/112, and IFNγ/FYC/112 groups](page_134_656_377_246.png)
+
+f
+
+![Flow cytometry plots showing GCB populations in FYC, FYC/112, and IFNγ/FYC/112 groups](page_529_656_377_246.png)
+
+g
+
+![Scatter plots comparing GCB and TEM cell numbers among FYC, FYC/112, and IFNγ/FYC/112 groups](page_134_906_377_246.png)
+Fig. 8 IFNγ is a driving force for the expansion of effector T cells
+
+a, Development of clinical symptoms with age for FYC I1I2 (n=46) and Ifng+/- FYC I1I2 male mice (n=24); key as indicated. Logrank test p=0.03
+b, Serum cytokine levels in FYC, FYC I1I2 and Ifng+/- FYC I1I2 male mice; key as shown. Comparative values for FYC I1I2 and FYC: IFNγ (4-fold); TNFα (4-fold); IL-2 (3-fold); IL-6 (9-fold); IL-10 (9-fold). Dashed line represents limits of detection.
+c, Representative FACS plots and gating strategy (upper) and enumeration (lower panel) of effector cells in the Treg, Tconv (CD44hiCD62Llo) and CD8+ TEM (CD44hiCD62Llo) subsets. Numbers are shown per single LN in mice aged 15 weeks (n=6). Key as in b.
+d,e,f, Representative FACS plots and enumeration of (d) T follicular helper (Tfh) YFP+CXCR5+PD1+, (e) Tfr (YFP+CXCR5+PD1+), and (f) GC B cells (B220+CD38loCD95+; gated as in Supplementary Fig. 9); key as in b. Comparative values for FYC I1I2 and FYC: Tfh (60-fold), Tfr (90-fold), GC B (100-fold),
+g, Total serum Immunoglobulin levels quantified by ELISA; key as in b.
+Comparative values for FYC I1I2 with FYC: IgG2c (5-fold), IgE (300-fold).
+Analyses combine data from two or more independent experiments (b-g n=6). P values determined using one-way ANOVA with multiple comparison (b-g).
+Figure S1
+
+a
+
+b
+
+c
+Total cell number per LN
+<0.0001
+<0.0001
+0.008
+
+d
+
+e
+* FYC   * FYC Zfp36
+94   96
+4   3
+70   25
+80   17
+3   2   1
+CD4+ YFP- CD62L+ BV421
+CD8+
+CD44 PE
+
+f
+* FYC   * FYC i2
+95   96
+2   2
+87   11   12
+1   1   1
+CD4+ YFP- CD62L+ BV421
+CD8+
+CD44 PE
+Fig. S1 Phenotyping of T cell subsets
+
+a, Gating strategy for data shown in Fig. 1a; Treg: CD4+FR4+CD25+; and Tconv: CD4+CD25- T cells
+
+b, Gating strategy and representative FACS plots comparing expression of ZFP36L1 in Treg (CD4+ FOXP3+ YFP+) or Tconv (CD4+ FOXP3- YFP-) cells from FYC, FYC I1 (upper panel) and FYC I1I2 mice (lower panel) after stimulation with PMA and ionomycin for four hours at 37°C; cells were pre-gated on live, single cells; quantification of ZFP36L1 gMFI; key as shown
+
+c, Total cell number per pLN; n=8-17; key as in b
+
+d, Gating strategy for data shown in Fig. 1b,c
+
+e, f, Representative FACS plots and proportion and cell number of effector cells CD44hiCD62Llo in the CD4+ YFP- (upper panel) and CD8+ subsets (lower panel) from FYC Zfp36 (e), and FYC Zfp36l2 mice (f), analysed with contemporaneous FYC controls. FYC (n=5-6); FYC Zfp36 (n=6); FYC Zfp36l2 (n=7); key as shown
+Numbers are shown per single LN in mice aged 9 -16 weeks
+P values were determined using one-way ANOVA using multiple comparison (c) or Mann-Whitney test (b, e, f).
+Figure S2
+
+a
+
+![Bar graph showing cell number for Tconv and TEM in FYC* and FYC* I1I2](page_186_120_374_180.png)
+
+b
+
+![Flow cytometry plots showing gating strategy and population analysis for CD8 BV7/11, CD4 BUV395, CD48 PECY7, CD69 APC, CD25 PerCP Cy5.5, and YFP](page_186_360_1207_180.png)
+
+c
+
+![Flow cytometry plots showing gating strategy and population analysis for FYC*, FYC*-I1I2, CD4 BUV395, FSC-A, CD62L, YFP, CD44 PE](page_186_540_374_180.png)
+
+d
+
+![Bar graphs showing norm read counts for Zfp36l1 and Zfp36l2 in FYC* (icre*) and FYC* I1I2 (icre*)](page_186_720_374_180.png)
+
+e
+
+![Flow cytometry plots showing ZFP36L1 expression in Treg and Tconv cells for FYC* (icre*), FYC* (icre*), FYC* I1I2 (icre*), FYC* I1I2 (icre*)](page_186_900_374_180.png)
+Fig. S2 Compromised fitness of RBP-deficient Treg
+
+a, Number of effector cells in the Tconv (CD44hiCD62Llo) and CD8+ TEM (CD44hiCD62Llo) subsets; key as shown
+b, Gating strategy and representative FACS plots comparing CD4+TCRβ+CD69+YFP+ CD25+ Treg in the thymus of 7-week old FYC+/+ and FYC+/I112 mice; n=4
+c, Gating strategy for sorting nTreg
+d, Normalised read counts across the loxP-flanked regions of the conditional Zfp36l1 and Zfp36l2 alleles; n=6-7; key as shown. Read counts were normalised using size factors derived from the overall DESeq2 analysis of all genes; p values determined using t test with FDR correction
+e, Representative histogram overlays comparing expression of ZFP36L1 in Treg (CD4+ FOXP3+) cells from FYC+/+ and FYC+/I112 mice (icre-positive (FOXP+YFP+) cells - black line and black symbols; icre-negative FOXP+YFP-) cells – blue line and blue symbols); or Tconv (CD4+ FOXP3-) cells (lower panel). Cells were stimulated with PMA and ionomycin for four hours; scatter plots showing gMFI for ZFP36L1 staining; n=3; key as shown
+P values determined using Mann-Whitney (a,d), or one-way ANOVA with multiple comparison (e).
+Figure S3
+
+a
+
+<table>
+  <tr>
+    <th></th>
+    <th>FYC/+</th>
+    <th>FYC+/I1I2</th>
+  </tr>
+  <tr>
+    <td>Rptor</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Lat</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Ets1</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Dgka</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Pdcd1</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Gsk3a</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Dok2</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Dlg1</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Nck2</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Cd2</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Gata3</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Cd247</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Cd5</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Kras</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Malt1</td>
+    <td></td>
+    <td></td>
+  </tr>
+</table>
+
+Log2 fold deviation from mean
+
+b
+
+CD62L<sup>hi</sup>   CD44<sup>hi</sup> CD62L<sup>lo</sup>
+
+FYC+ (icre)
+FYC+ (core)
+FYC+/I1I2 (icre)
+FYC+/I1I2 (core)
+Fig. S3 Genes enriched in the TCR signaling pathway
+
+a, The heatmap depicts the top 15 ranked genes in the TCR signaling pathway, ordered with the most significantly increased genes at the top. The color scale represents the log_2 fold deviation from the mean for each gene. Genes that are predicted targets by CLIP are represented in orange
+
+b, CD5 (upper panel) and NUR77 (lower panel) expression (gMFI) in CD4^+ FOXP3^+ nTreg (CD62L^{hi}) and eTreg (CD44^{hi} CD62L^{lo}) from control FYC^{+} and FYC^{+/I1I2} mice. n=4; key as shown.
+
+P values in (b) determined using one-way ANOVA with multiple comparison
+Figure S4
+
+a
+
+CD62L^{hi}        CD44^{hi} CD62L^{lo}
+
+![Flow cytometry plots showing gating and mean fluorescence intensity (MFI) for various markers in CD62L^{hi} and CD44^{hi} CD62L^{lo} T cells from FYC^{+} (ire^{r}) and FYC^{+} I1I2 (icre^{r}) mice.](page_357_384_879_670.png)
+
+■ FYC^{+} (ire^{r})   □ FYC^{+} I1I2 (icre^{r})
+
+b
+
+CD62L^{hi}        CD44^{hi} CD62L^{lo}
+
+![Flow cytometry plots showing gating and MFI for NOTCH1 in CD62L^{hi} and CD44^{hi} CD62L^{lo} T cells from FYC^{+} (ire^{r}) and FYC^{+} I1I2 (icre^{r}) mice.](page_357_1092_879_180.png)
+Fig. S4 Expression of Treg signature genes
+
+a, Representative FACS plots showing FOXP3, CTLA-4 (from LN, fixed ex vivo), IKZF2 (from mLN) and ICOS (from LN) expression (gMFI) in CD4+ FOXP3+ nTreg and eTreg from control FYC/+ and FYC+/I1/I2 mice; n=3-5; key as shown.
+
+b, NOTCH1 expression (gMFI) in nTreg and eTreg from FYC/+ and FYC+/I1/I2 mice; n=3-4, key as in a. P values determined using Mann-Whitney.
+Figure S5
+
+a
+
+![Flow cytometry plots showing gating strategy and MFI for CD80/CD86 and CD28/CD38 in migratory and resident populations](page_184_246_1097_377.png)
+
+b
+
+![Bar graphs comparing CTLA-4 expression (%) among different populations under various conditions](page_184_671_1097_377.png)
+
+FYC* (icre)   FYC* (icre*)   FYC* I112 (icre)   FYC* I112 (icre*)
+Fig. S5 Decreased cycling of CTLA-4 in RBP-deficient nTreg
+
+a, Representative FACS plots showing CD80 and CD86 expression on CD11c\(^{\text{int}}\) MHCII\(^{\text{hi}}\) “migratory” (upper panel) and CD11c\(^{\text{hi}}\) MHCII\(^{\text{int}}\) “resident” (lower panel) CD172a\(^{-}\)XCR1\(^{+}\) cDC1 from spleen from *FYC I1I2 and FYC* male mice; the number of events in the file is indicated; n=6, key as shown
+
+b, Percentage of CTLA-4\(^{+}\) nTreg or eTreg in surface, cycling, or total pool from *FYC /+ I1I2 and FYC*\(^{+}\) female mice. Each symbol represents an individual mouse (n=5); key as shown. Data from at least two independent experiments.
+
+P values determined using Mann-Whitney (a) and one-way ANOVA with multiple comparison (b) represented in the table shown.
+Figure S6
+
+a
+
+CD62L^{hi}
+
+CD44^{hi} CD62L^{lo}
+
+FYC^{+} (icre^{+})
+FYC^{+} I112 (icre^{+})
+
+b
+
+CD62L^{hi}
+
+CD44^{hi} CD62L^{lo}
+
+FYC^{+} (icre^{+})
+FYC^{+} I112 (icre^{+})
+
+<table>
+  <tr>
+    <th></th>
+    <th>FYC^{+} (icre^{+})</th>
+    <th>FYC^{+} I112 (icre^{+})</th>
+  </tr>
+  <tr>
+    <td>0.9</td>
+    <td>0.7</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td>0.7</td>
+    <td>0.7</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td></td>
+    <td></td>
+    <td>&lt;0.0001</td>
+  </tr>
+</table>
+
+c
+
+CD62L^{hi}
+
+CD44^{hi} CD62L^{lo}
+
+<table>
+  <tr>
+    <th></th>
+    <th>FYC^{+} (icre^{+})</th>
+    <th>FYC^{+} I112 (icre^{+})</th>
+  </tr>
+  <tr>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td>0.5</td>
+    <td>0.5</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+  </tr>
+</table>
+Fig. S6 ZFP36L1 and ZFP36L2 promote Treg sensitivity to IL-2 and IL-7
+
+a, Total STAT5 expression in YFP+ nTreg and eTreg; from FYC+/+ and FYC+/I1I2 mice, n=3; key as shown
+b, Frequency of pSTAT5+ cells detected in YFP+ (black symbol) and YFP- (blue symbol) nTreg and eTreg from the spleen of female mice following stimulation for 30 minutes with a range of concentrations of IL-2; data presented as mean value ± sd, n= 7; key as shown
+c, Frequency of pSTAT5+ cells detected in YFP+ and YFP- nTreg and eTreg from female mice following stimulation for 30 minutes with a range of concentrations of IL-7; data presented as mean value ± sd, n=4; key as in b.
+P values were determined using two-way ANOVA with multiple comparison, comparing the mean value between each genotype, and are represented in the table shown.
+Figure S7
+
+a
+
+CD62L^{hi}
+
+CD44^{hi} CD62L^{lo}
+
+<table>
+  <tr>
+    <th></th>
+    <th>FYC^{+} (ire)</th>
+    <th>FYC^{+} (ire^{+})</th>
+    <th>FYC^{+} I1I2 (ire)</th>
+    <th>FYC^{+} I1I2 (ire^{+})</th>
+  </tr>
+  <tr>
+    <td>■</td>
+    <td>0.006</td>
+    <td>0.2</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td>■</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td>□</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+  </tr>
+</table>
+
+b
+
+CD62L^{hi}
+
+CD44^{hi} CD62L^{lo}
+
+c
+
+CD62L^{hi}
+
+CD44^{hi} CD62L^{lo}
+
+<table>
+  <tr>
+    <th></th>
+    <th>FYC^{+} (ire)</th>
+    <th>FYC^{+} (ire^{+})</th>
+    <th>FYC^{+} I1I2 (ire)</th>
+    <th>FYC^{+} I1I2 (ire^{+})</th>
+  </tr>
+  <tr>
+    <td>■</td>
+    <td>0.006</td>
+    <td>0.9</td>
+    <td>0.0001</td>
+    <td>0.8</td>
+  </tr>
+  <tr>
+    <td>■</td>
+    <td>0.0004</td>
+    <td>0.8</td>
+    <td>&lt;0.0001</td>
+    <td>0.8</td>
+  </tr>
+  <tr>
+    <td>□</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>&lt;0.0001</td>
+    <td>0.8</td>
+  </tr>
+</table>
+Fig. S7 ZFP36L1 and ZFP36L2 limit Treg sensitivity to IFNγ
+
+a, Frequency of pSTAT1+ cells detected in YFP+ and YFP- nTreg and eTreg from female mice following stimulation for 30 minutes with a range of concentrations of IFNγ; data presented as mean value ± sd, n=6-11; key as shown
+b, Total STAT1 expression in YFP+ and YFP- nTreg and eTreg; key as in a
+c, Frequency of pSTAT1+ cells detected in YFP+ and YFP- nTreg and eTreg from female mice following stimulation for 30 minutes with a range of concentrations of IL-6; data presented as mean value ± sd, n= 4-6; key as in a.
+P values determined using two-way ANOVA with multiple comparison, comparing the mean value between each genotype, and are represented in the table shown (a,c).
+Figure S8
+
+a
+
+![Flow cytometry plots showing gating strategy for FYC and FYC11/2 clusters](page_153_120_496_312.png)
+
+b
+
+![Bar graph showing percentage of cells in each cluster](page_728_120_496_312.png)
+
+c
+
+![Scatter plot showing number of genes per cluster](page_153_464_496_312.png)
+
+d
+
+![Scatter plots comparing Treg and CXCR3+ populations](page_728_464_496_312.png)
+
+e
+
+![Flow cytometry plots and bar graphs for FYC and FYC11/2, Ro51/181, Foxp3, and cell number](page_153_808_496_312.png)
+
+f
+
+![Bar graphs comparing Tconv and Treg gMFI for IFNγ, IL-4, IL-17, and IL-10](page_728_808_496_312.png)
+
+g
+
+![Flow cytometry plots and bar graphs for FYC and FYC11/2, IFNγ, CD8+](page_153_1152_496_312.png)
+Fig. S8 Activated phenotype of Treg from FYC I1I2 mice
+
+a, Gating strategy for sorting of CD4+FR4+CD25+ Treg cells for scRNA-seq
+b, Percentage of cells identified as naïve (orange), effector (dark blue) or unassigned (grey) in each cluster;
+c, Violin plot representing the number of genes detected in each cluster
+d, Cell number for CXCR3+, GATA3hi Treg and Tfr, in LN (for data in Fig. 7i, j, k); comparative values for FYC I1I2 to FYC: 4-fold increase CXCR3+, 3-fold increase in GATA3hi, 50-fold increase in Tfr cell number
+e, Representative flow cytometry plots (left panel) gated on CD4+ cells; scatter plot (right panel) showing proportion of RORγt+ Treg (as a % of all FOXP3+ cells) and enumeration of FOXP3+RORγt+ Treg; key as shown
+f, gMFI for intracellular cytokine staining shown in Fig. 7l
+g, IFNγ expression in CD8 cells. Splenocytes were stimulated with PMA/ionomycin for four hours in the presence of Brefeldin A, flow cytometry plots are gated on CD8+ cells; n=6, key as shown
+P values determined using Mann-Whitney test (d,e,f,g).
+Figure S9
+
+a
+
+![Flow cytometry gating strategy showing gating regions for B220+AF700+ and CD38+PE-Cy7+CD95+BV510+ populations](page_186_246_323_180.png)
+Fig. S9 Gating strategy for GC B cells
+Cells were pre-gated on live, single cells
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementarytablesmerged.pdf.pdf
+• Supplementaltables.xlsx

070706503cff2b0c5895a72491f41d6927ffe121f452603fa7f93aef50b5eb1a/peer_review/peer_review.md

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+Peer Review File
+
+Protein design of two-component tubular assemblies similar to cytoskeletons
+
+Corresponding Author: Dr Yuta Suzuki
+
+Parts of this Peer Review File have been redacted as indicated to maintain the confidentiality of unpublished data.
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Attachments originally included by the reviewers as part of their assessment can be found at the end of this file.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+[Editorial note: Please find Reviewer #1’s comments at the end of this document.]
+
+Reviewer #2
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #3
+
+(Remarks to the Author)
+The manuscript by Noji et al describes the design and assembly of two-component protein modules into long tubes. Those tubes have high persistent length and some variability in the diameter and self-assemble in a defined temperature and ionic strength range. They are formed by the fusion of two natural domains, one of them common and the second from two interacting domains. Interestingly, the transplantation of the actin D loop results in the formation of a helical assembly composed of two of three filaments with narrower diameters, that are not stable by themselves but require helical suprastructural assembly. The role of just D loop is quite unexpected and may shed some light into its role in the actin assembly. CryoEM analysis provides good models for the structure of filaments.
+However, this is not the first designed tubular assembly, as claimed. The authors should include a reference to Shen et al., Science 2018, from the Baker group, which reported on the design of protein filaments several years ago (DOI: 10.1126/science.aau3775).
+Apart from that the paper is well-presented using several techniques to analyze the assembly and properties of designed tubes.
+The authors suggest that the PuuE is positioned on the outside. This could be in principle tested by antibodies against a peptide tag that should be able to access the exposed domains but not protected ones.
+Additionally, it would be interesting to know the persistence length of the helical assemblies, particularly whether they are longer than the filaments without the D loop.
+Also, could they provide information on the interactions between the D loops in the intertwined tubes, is the conformation (at least according to the model) similar to the conformation in actin filaments ?
+
+Reviewer #4
+
+(Remarks to the Author)
+This manuscript describes the design, assembly and characterization of repeat tubular structures. A flexible dimer component was grafted on a scaffold protein and the two component system, when mixed, forms fibers in vitro. The authors describe their design principles and outline changes to the fibers that seem to depend on salt concentration and temperature. Additionally, they introduce another graft resulting in the formation of higher order helical fibers.
+
+This work is interesting and the manuscript is fairly well-written and clear. I have some concerns and points for the authors to address and clarify:
+
+Major points:
+
+- the acronym used (NIPAD): it is not clear why the methods employed in this study requires this naming scheme as there was no development of new engineering methods or software.
+- Cryo processing: please add more information, including images of initial models used and how C1 symmetric reconstructions deviated from the final symmetric reconstructions (if any). This is crucial to understand potential symmetric artifacts at low resolutions, especially for the higher order assemblies.
+- methods were not clear as to when binning was reversed during cryoem processing. Was binning reversed for the final resolution calculations?
+- it is not clear why this design results in tubes and not 2D or 3D crystals or closed c-symmetric oligomers or even large vesicles. Were any observed?
+- Looking at the final maps, it seems that additional interactions occur between the scaffold proteins than was originally intended: please discuss
+- Figures need greater clarity - for example, figure 1 should more clearly show the interactions that form fibers: it was not easy to understand what the authors see in the design that would create a fiber over other assemblies. Additionally, the symmetric axes should be well defined and repeat units outlined
+- Cryo processing: did the authors try symmetric expansion and other techniques such as focused refinement to try and discern the interfaces or get higher resolution refinements that better account for dynamics?
+- AlphaFold: have the authors tried to understand the assembly using modeling of multiple subunits?
+- Discussion: more detail on the potential applications of these fibers would be beneficial
+- The authors claim that the design of fibers “remains elusive”: fibers have been designed before, such as Bethel et al. 2023 (nature chemistry). Previous fiber studies should be discussed.
+- Control over assembly: apart from the environmental factors discussed, do the authors have finer control over the fiber assembly and oligomeric states by design?
+- D-loop grafted cryoem: the sample was left on ice for 1hr before freezing and fibers were observed, however, this is in contrast to the negative-stain experiments in Fig4c and ExfFig7d, where there are no observable fibers at 0c. Please clarify
+
+Minor points:
+
+- "cryo-electron": the hyphen should not be between cryo and electron.
+- Figure 4g: number of atoms outside contour is not very useful without knowing the threshhold used and where the greatest deviation between map and model lies
+- the role of M3L2/p66a in the MBD2-NuRD complex is not described
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The reviewer's comments and concerns have been adequately addressed. Although the additional experiments involving cryo-EM and SAXS to investigate the formation mechanisms were not performed, the dynamic and responsive properties demonstrated in this study represent a significant advancement in the field of protein assembly. This is supported by recent reports highlighting the importance of such properties (e.g., Nat. Nanotechnol. 2024, 19, 1016; Nat. Chem. Biol., 2025, doi.org/10.1038/s41589-024-01811-1; Nat. Synth., 2025, doi.org/10.1038/s44160-024-00726-y; Chem, 2025, doi.org/10.1016/j.chempr.2024.102407). In its current form, this manuscript meets the standards for publication in Nature Communications.
+
+Reviewer #2
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #3
+
+(Remarks to the Author)
+Authors have mainly modified the text of the manuscript without additional data or insights. Although there are still some
+unanswered questions (e.g. regarding the role of the “D-loop”) and challenges, the manuscript nevertheless describes an interesting design of protein fibers composed of two components. The authors built their assembly based on natural homotetramers and modified them by weak heterodimeric domains to make a two-component assembly. This approach could be applied in principle to many other building blocks and therefore represents a new design platform.
+
+While authors did not report success by modeling the assembly using AF2, I Reviewer #3) obtained formation of 4+4 assembly linked through the CC peptides using AF3 algorithm (image of the models added). 4+4 assembly represents a dead end as it is not able to form larger filaments but may represent an intermediate in equilibrium with filamentous assemblies. Authors may invest a bit more effort into modeling and explanation of the putative mechanisms.
+
+One issue that might be discussed is whether the two components need to be produced separately before mixing, to avoid formation of heterotetramers, which might hinder the formation of filaments. Did they ever try the production of both components at the same time?
+
+As the authors concur that they did not demonstrate any cytoskeletal function and removed the phrase “reminiscent of the cytoskeleton”, they might as well remove the reference for the cytoskeleton from the title.
+
+[Editorial note: images of the models are not included in this file due to copyright concerns.]
+
+Reviewer #4
+
+(Remarks to the Author)
+Thank you for your efforts in addressing my concerns. Most concerns have been addressed, however, I have follow up comments below:
+
+Comment 2:
+
+You have not included images of the initial models used, only a description. Including the initial models will help compare to the final reconstruction.
+
+Comment 5:
+
+I think your text is reasonable to include, however, you should actually check how much your tag is influencing the formation or stability of the tubes by cutting the protein using tev. The construct already has this feature.
+
+Comment 7:
+
+I don't think I fully agree. While you may not reach high resolution and for some of your reconstructions I agree, you may not get more information, for others you could get more resolution leading to enough resolution to discern helices (such as your 9.7Å reconstruction of the c3 tube). Your interface would be revealed to greater detail and would help validate your design.
+
+Minor point 2:
+
+Again, this is not effective without knowing the threshold used. Different values will "contain" different amounts of atoms. The new term of "visual inspection" is not good to use either way.
+
+Version 2:
+
+Reviewer comments:
+
+Reviewer #3
+
+(Remarks to the Author)
+I find the manuscript appropriate for publication due to its novelty and potential interest. I still believe that the assembly they produced is not related to the cytoskeleton. Still, I don't insist on removing the word from the title, where its function seems to be mainly to attract the attention of the readers.
+
+Reviewer #4
+
+(Remarks to the Author)
+Thank you for including extra information. I do have the following comments for the Authors, which are mainly comments from a previous review that the Author's have not fully addressed yet.
+
+I think cleaning the following can be done and given that, I think this manuscript would be ready for publication.
+
+My comments:
+
+1. My previous comment of "You have not included images of the initial models used, only a description. Including the initial models will help compare to the final reconstruction".
+Thank you for adding these, but they contradict your methods section where you state that the initial models were hollow cylinders as these initial models are not generic hollow cylinders. Can you please clarify and update the text and/or figures appropriately?
+
+You don't mention if the models were low pass filtered for refinement. Please address.
+
+2. My previous comment "I think your text is reasonable to include, however, you should actually check how much your tag is influencing the formation or stability of the tubes by cutting the protein using tev. The construct already has this feature"
+
+I can understand your reasoning for keeping the tag, however, do you see any formation of the fibers after tev cleavage? Even with low concentrations, you can easily validate this using EM images and rule out of the effect of the tag.
+
+3. My previous comment of "I don't think I fully agree. While you may not reach high resolution and for some of your reconstructions I agree, you may not get more information, for others you could get more resolution leading to enough resolution to discern helices (such as your 9.7Å reconstruction of the c3 tube). Your interface would be revealed to greater detail and would help validate your design."
+
+The author's did not address this point as they mixed up my suggestion with another suggestion regarding binning and using the full pixel size. My comment was regarding using symmetry expansion or masking/local refinements to potentially improve the resolution of some of your reconstructions, mainly the one at 9.7Å. This can be done using the binned particles. I think this could improve the resolution potentially to the 6-8 range where helices would be better defined and better validate your designed interface.
+
+Version 3:
+
+Reviewer comments:
+
+Reviewer #4
+
+(Remarks to the Author)
+Thank you for looking fully into my questions. I only have additional comments in regard to "Comment 2", tev cleavage of his-tag.
+
+The aim of this experiment was to check that the tubular assembly is not influenced by the his-tag and based on your results, it seems to be. Based on this, I suggest the authors disucss this in the manuscript. Are the assemblies consistent in size and morphology to pre-cleaved assemblies?
+permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/
+Dear Dr. Editor,
+
+First of all, my coworkers and I would like to thank you for handling our paper and the four reviewers for their time and thoughtful comments. We were very pleased to see that the reviewers described our work as "interesting and fairly well-written", "providing good models for the structure of filaments", and "achieving an exciting system of two-component protein assembly". They also acknowledged that the study offers "unique insights into protein assembly under biomimetic conditions" and highlighted its "potential significance for understanding actin assembly mechanisms." These positive evaluations have greatly encouraged us and affirmed the value of our research. Yet, they also raised several issues and had comments that require to be addressed for further consideration of our manuscript. Accordingly, we now submit a substantially revised version of our manuscript that addresses these issues and improvements in the main text and supporting materials with additional experiments. We also submit an additional version of the Main Text wherein the changes are highlighted in yellow for clarity. In addition to these corrections, we have also adjusted the manuscript format to meet the guidelines of Nature Communications.
+
+RESPONSE TO REVIEWER #1
+
+We greatly appreciate the reviewer’s time and thoughtful comments on our manuscript. The feedback provided has helped us refine our arguments and clarify the unique aspects of our study. Below, we address each point raised by the reviewer in detail.
+
+Comment 1: The main concept of Nature-Inspired Protein Assembly Design is ambiguous and unconvincing, as many works have established reversible protein nanotubes that respond to biomimetic conditions (Nat. Commun. 2022, 13, 5424.; J. Am. Chem. Soc. 2018, 140, 1, 26.; Nat. Chem. 2013, 5, 613.; J. Am. Chem. Soc. 2013, 135, 31, 11509.; ACS Catal. 2020, 10, 9735.). Also, in this work, a meaningful application of these nanotubes have yet to be demonstrated and explored.
+
+Response: We thank the reviewer for highlighting this concern. The works cited in comment 1 indeed represent significant advancements in the chemical or hybrid control of protein assemblies through modifications with organic compounds, nucleic acids, or polymers. However, our study focuses on achieving reversible assembly and disassembly of protein nanotubes using only proteins, directly inspired by biological processes. This distinguishes our work from the cited studies, as our approach does not rely on external chemical modifications but rather utilizes inherent protein properties to achieve biomimetic assembly.
+
+Given the ongoing challenges in controlling the assembly and disassembly of artificial protein assemblies, we believe our work offers both novelty and uniqueness in addressing this critical area.
+Comment 2: The definition of two-component tube structures is controversial. Here, the main scaffold of PuuE-M and PuuE-p is the same, but the two-component protein assembly should be two independent ingredients (Nature 2014,510, 103.; Science 2016, 353, 389.; Nature 2021, 589, 295 468-473).
+
+Response: We understand the reviewer’s concern regarding the definition of two-component assemblies. In our work, the two components, PuuE-M and PuuE-p, individually do not form tubular structures. However, when mixed, they synergistically self-assemble into well-defined tubular structures. This cooperative behavior clearly demonstrates that both components are essential for the formation of the final structure, meeting the criteria of "a two-component system" as commonly defined in structural biology.
+
+Unlike single-component systems reported in prior studies, such as Reviewer 3 and 4 indicated (Shen et al., Science, 2018 and Bethel et al., Nat. Chem., 2023), where tubes are formed by a single protein component, our system highlights the necessity of two distinct components that cannot independently achieve the same structural outcome. This distinction is a critical aspect of our study and contributes to its novelty.
+
+Additionally, related studies involving two-component cage (Nature 510, 103-108 (2014) and Science 353, 389-394 (2016)) or sheet structures (Nature 589, 468-473 (2021)) as mentioned in comment 2 often rely on similar principles of cooperative interaction, where individual components alone do not form the intended structure. To our knowledge, our work represents the first demonstration of a two-component system forming tubular structures under these criteria, underscoring its originality and significance in the field. Moreover, our design enables reversible structural control of the assembled tubes, a feature not achieved in the designs presented in previous studies as mentioned above. This represents an additional advantage of our approach, further emphasizing the significance of our work. To clarify this point, we have included additional sentences in the main text (Lines 77–80 and Lines 262-266) and added references 18 and 19 to support the discussion.
+
+[editorial note: unpublished data has been redacted]
+
+Comment 3 & 4: Although the structures of protein nanotubes are supported by 3D reconstruction, the underlying mechanisms of the formation of these structures have not yet been explored and explained. Why do different nanotubes emerge under the same assembly conditions? Could certain conditions generate dominant species? Tracking the formation of nanotubes under thermally stable conditions is important to gain insight into the self-assembly mechanism using cryo-EM, SAXS, or other characterization methods.
+Responses: We appreciate the reviewer’s insightful comments regarding the formation mechanisms and characterization of protein nanotubes. As both comments 3 and 4 pertain to the structural formation of nanotubes, we have provided a single comprehensive response below.
+
+We hypothesize that the formation of nanotubes with different diameters can be attributed to the flexibility of the connection sites on the protein surface. Similar findings have been reported in the literature, such as in studies on flexible protein designs that lead to varied structural outcomes (e.g., Nat. Chem. 6, 1065–1071 (2014) and J. Am. Chem. Soc. 137, 11285–11293 (2015)). In our study, the inherent flexibility of our design likely resulted in structural diversity. However, due to the resolution limitations of cryo-EM, knowledge of detailed structures is speculative. Unfortunately, this limitation is further complicated by the flexibility of the assembled structure, making it inherently difficult to achieve higher resolution for such specific assemblies (Lines 162-164 and Supplementary Movie 1). As a response to these comments, we have added this clarification in the revised manuscript under the section “Diversity and Flexibility of Tubes” (Lines 173-176) and added references 38 and 39.
+
+In this study, the key factor for forming assemblies is the interaction between M3L2 and p66α. Upon revisiting the data to examine how temperature and salt concentration influence the distribution of tube diameters, the results suggested a tendency for the diameter distribution to shift toward narrower tubes at around 25 °C compared to 35 °C and 40 °C. To further investigate this indication, we conducted additional experiments to observe the diameter of tube structures at 25 °C. However, no significant changes were observed as we expected. Given the flexible design principles of this system, achieving convergence to a single, uniform diameter by altering conditions appears challenging. For future studies, we plan to explore the possibility of controlling tube diameters using nucleic acids and etc. as scaffolds. However, incorporating different polymers would deviate from the scope of this research as discussed on comment 1, and we therefore intend to report such developments as follow-up studies.
+
+While SAXS is a powerful technique for analyzing self-assembly mechanisms, we consider it less suitable for our system due to the coexistence of tubes with various diameters and lengths, which would complicate data interpretation. Moreover, based on the resolution and details achieved with cryo-EM, we determined that SAXS would not provide additional insights beyond what has already been obtained.
+
+It is worth noting that, as highlighted in the cited studies, the creation of artificial protein assemblies has made significant progress, but detailed mechanistic understanding of their formation processes remains elusive. We recognize this as a critical challenge for the field and an important avenue for future exploration.
+
+Comment 5: The overall electrostatic potential of PuuE-M and PuuE-p should be shown in Extended Data Fig. 5, especially since the salt concentration range for salting-in and salting-out is very narrow compared to most proteins.
+
+Response: We appreciate the reviewer’s suggestion regarding the inclusion of electrostatic potential data. As suggested, we have added the electrostatic potential of PuuE-M and PuuE-p to Supplementary Fig. 5a to provide a more comprehensive understanding of this aspect. To support this addition, we have included an additional sentence in the “Methods” section (Lines 491-492) and appropriate citation in ref. 66, detailing the calculation and visualization performed using the APBS and PDB2PQR plug-in on PyMOL.
+
+Regarding the narrow salt concentration range for salting-in and salting-out, we understand that the reviewer’s observation may have been based on comparisons with typical monomeric proteins. For example, ammonium sulfate precipitation, commonly used for protein purification, involves a broad range of salt concentrations to induce protein aggregation or solubilization. In contrast, our system involves active driving forces for assembly, which likely result in the narrower salt concentration range observed in our experiments. Similar ranges of salt effects have been reported for the assembly of actin filament (Arch. Biochem. Biophys. 220, 370–378 (1983)) as well as amyloid fibril formation (J. Biol. Chem. 294, 15318–15329 (2019); Biophys. Rev. 10, 493–502 (2018); J. Biol. Chem. 290, 18134–18145 (2015)), which supports the idea that the assembly and disassembly processes in our system are driven by mechanisms akin
+to those in such systems. For this reason, we consider the observed salt concentration range in our study to be reasonable and consistent with the nature of the protein assemblies we are investigating.
+
+Comment 6: On structural perspectives, these protein nanotubes are similar to microtubules, but their mechanical properties are closer to microfilaments. The specific reasons need to be discussed and explained.
+
+Response: We appreciate the reviewer’s comment on this point. While our design principles were inspired by natural systems, we did not intentionally target the construction of structures mimicking microtubules or actin filaments. Instead, our goal was to establish a design framework that could emulate the flexibility and controllability of assembly seen in natural systems. As a result, we successfully fabricated structures that closely resemble those found in nature, leading us to compare their properties with natural cytoskeletal elements. Through detailed characterization, we identified similarities in certain structural and mechanical properties between our protein nanotubes and microtubules or actin filaments. This motivated us to highlight these comparisons in the manuscript to contextualize our findings within the broader scope of natural protein assemblies.
+
+To address the potential for misleading interpretations, we have revised Line 37 in the manuscript to remove the phrase "reminiscent of the cytoskeleton" as it may have given the impression that we aimed to explicitly replicate cytoskeletal structures. The revised text now accurately reflects the intent and focus of our study.
+
+We thank the reviewer for drawing attention to this point, which allowed us to clarify the objective and implications of our work.
+
+Comment 7: It is worth noting that the flexibility and persistence length of different nanotubes may be different, the results in Fig.3 may only represent the characteristics of one of these nanotubes. In other words, comparisons of persistence length between protein nanotubes and cytoskeletal elements may not be meaningful. Therefore, the relevant conclusions need to be carefully discussed.
+
+Response: We appreciate the reviewer’s insightful comment regarding the variability in persistence length among nanotubes with different diameters. As the reviewer correctly points out, our sample contains a mixture of nanotubes with varying diameters, and it is reasonable to assume that each has a different persistence length. To address this point, we estimated the persistence lengths of different nanotubes as follows. Assuming that the monomer is a sphere with radius \( r \), the persistence length \( L_p^n \) of a \( C_n \) symmetric nanotube is
+
+\[
+L_p^n = \frac{EI_n}{k_B T}, \quad I_n = \frac{\pi}{4} r^4 \left\{ \frac{2}{\pi^2} (2n)^3 + 2n \right\},
+\]
+
+where \( E \) is the Young’s modulus, \( k_B \) is the Boltzmann constant, and \( T \) is the temperature (J. Howard, Mechanics of Motor Proteins and the Cytoskeleton, 2001, Sinauer Associates, Inc.). Here, we can reasonably assume that the persistence length measured in this study, \( L_p \), is the average of all \( L_p^n \) of the \( C_n \) symmetric nanotubes observed by cryo-EM, each weighted by its probability \( p_n \):
+
+\[
+L_p = \sum_{n=4}^{10} p_n L_p^n = E \frac{\pi r^4}{4 k_B T} \sum_{n=4}^{10} p_n \left\{ \frac{2}{\pi^2} (2n)^3 + 2n \right\}.
+\]
+
+Now, \( r \) and \( p_n \) are obtained from the results of cryo-EM observations (Fig.1b and Fig.3a). Hence, by solving Equation (2), \( E \) is calculated as \( E = 2.29 \times 10^4 \) GPa, and each \( L_p^n \) can be calculated using Equation (1). Then, using Equation Line 480 in the manuscript, we obtain the theoretical relationship
+between the mean square of the end-to-end distance, \( \langle R^2 \rangle \), and the contour length, \( L \), for each \( C_n \) symmetric nanotube as follows:
+
+![Scatter plot showing MS of end-to-end distance vs. Contour length for various nanotubes, with fitted lines and experimental data points.](page_374_312_805_496.png)
+
+From this graph, we conclude that in the tube length range of this study (shorter than 8 \( \mu \)m), \( C_4 \) may be distinguishable from higher symmetry if the tube is long enough, but it is difficult to distinguish the remaining \( C_5 \sim C_{10} \).
+
+However, this graph also shows that the nanotube is stiffer than intermediate filament (IF), but more flexible than or as flexible as microtubule (MT). Although the difference in the flexibility might be clearer if the nanotube is longer than 15 \( \mu \)m as shown in Supplementary Fig. 7b (in the revised manuscript), we conclude that our results are sufficient to compare the flexibilities between the nanotube and cytoskeletal filaments.
+
+To make sentence more accurate, we have modified a last sentence of section "Diversity and flexibility of tubes" to "Although nanotubes longer than 15 \( \mu \)m would be required for a more accurate estimation of its persistence length, we can conclude that the current results suggest the nanotube is stiffer than intermediate filaments and more flexible than or as flexible as microtubules. " (Lines 188–190).
+
+Comment 8: The functions and purposes of introducing D-loop in PuuE-M is illogical and unconvincing, especially considering that considering that the obtained structure is far from the microfilament and that other hydrophobic peptides may also give the same results.
+
+Response: We thank the reviewer for this thought-provoking comment. The suggestion that hydrophobic peptides in general could similarly promote helical structures is highly intriguing and has significant implications for understanding the assembly mechanisms of actin filaments. However, due to the current resolution limitations of our cryo-EM analysis as indicated above (Comment 3&4, Lines 162-164 and Supplementary Movie 1), we were unable to directly test this hypothesis in our study. We recognize this as an important avenue for future investigation.
+
+The introduction of the D-loop in PuuE-M was motivated by observations from persistence length measurements and real-time assembly dynamics, which suggested behavior reminiscent of actin filaments. To explore whether we could emulate actin-like helical structures, we incorporated the D-loop, a region known to be critical for actin filament assembly. As noted in Lines 193 – 198 of the manuscript, the D-loop was incorporated under conditions that closely resemble those in actin protein systems, supporting its relevance and appropriateness for our design.
+
+It is important to emphasize that our goal was not to fully replicate actin filaments but rather to create novel functional structures inspired by actin’s design principles. The successful formation of helical
+structures in our system demonstrates the feasibility of this approach and validates the functional role of the D-loop in our design.
+
+To address potential misunderstandings (As of comment 6), we have revised Line 37 in the manuscript to remove the phrase "reminiscent of the cytoskeleton," as it may have given the impression that we aimed to explicitly replicate cytoskeletal structures. The revised text now accurately reflects the intent and focus of our study.
+
+We thank the reviewer for drawing attention to this point, which allowed us to clarify the objective and implications of our work.
+
+RESPONSE TO REVIEWER #2
+
+We would like to thank the peer reviewers for their time and effort in co-reviewing our manuscript as part of the Nature Communications initiative. We are also very grateful to the Early Career Researchers and senior reviewers for their valuable comments. Their constructive comments and suggestions were of great help in improving the quality and clarity of our work.
+
+While we cannot specify which specific comments were made by the co-reviewers, we have carefully considered and addressed all points raised in the reports. We are grateful for their thoughtful evaluation and hope that our responses and revisions meet your expectations.
+
+RESPONSE TO REVIEWER #3
+
+We thank the reviewer for their detailed and thoughtful comments, and we appreciate the recognition of the significance of our work, particularly the design and assembly of two-component protein modules into long tubes and the insights into the role of the actin D-loop in assembly mechanisms. The reviewer’s acknowledgment of the quality of our cryo-EM analysis and the unexpected role of the D-loop is particularly encouraging.
+
+Comment 1: This is not the first designed tubular assembly, as claimed. The authors should include a reference to Shen et al., Science 2018, from the Baker group, which reported on the design of protein filaments several years ago (DOI: 10.1126/science.aau3775).
+
+Response: Regarding the reviewer’s comment about prior examples of designed tubular assemblies, we agree that tubular structures have been reported previously, such as in the work by Shen et al. (Science, 2018) as mentioned and Bethel et al. (Nat. Chem., 2023, as highlighted by Reviewer #4 Comment 10). These studies represent significant advancements in the field, but their designs rely on single-component systems. In contrast, our study demonstrates the assembly of tubular structures using two distinct units, which sets our work apart. The unique aspect of our system lies in the cooperative interaction between two components, which is critical for the formation of the tubular structure. This distinction is why we described our work as "the first" of its kind.
+
+To address this comment, we revised the manuscript to provide a more nuanced discussion of previous studies, clearly acknowledging these important contributions but highlighting the differences in design principles from our study. A dedicated paragraph has been added to the discussion section (Lines 77–80 and Lines 262-266) to clarify this difference and to cite these representative studies (references 18 and 19) appropriately.
+We appreciate the reviewer bringing this to our attention and believe that the revised manuscript now provides a more balanced and comprehensive discussion of the context of our work within the broader field.
+
+Comment 2: Apart from that the paper is well-presented using several techniques to analyze the assembly and properties of designed tubes. The authors suggest that the PuuE is positioned on the outside. This could be in principle tested by antibodies against a peptide tag that should be able to access the exposed domains but not protected ones.
+
+Response: We thank the reviewer for their positive comments regarding the presentation of our work and the use of various techniques to analyze the assembly and properties of the designed tubes. We greatly appreciate your suggestion regarding the use of antibodies to distinguish between the inner and outer surfaces of the PuuE-based structures.
+
+We also considered using antibodies for this purpose. However, since both units in our design (PuuE-M and PuuE-p) are derived from the same PuuE protein, it is likely that antibodies generated against these units would bind indiscriminately to both, making it challenging to differentiate between the inner and outer surfaces. For this reason, we focused on detailed structural analysis using cryo-EM. As noted in the manuscript (Lines 162-167), cryo-EM and related analyses suggest that the tubular structures exhibit flexibility and extensibility (Supplementary Movie 1), which further complicates the ability to clearly distinguish the two surfaces at the molecular level.
+
+We would like to note that the recent identification of D-loop-specific antibodies was reported by a separate group (Biochem. J. 481, 1977–1995 (2024)). However, these antibodies are not commercially available and were developed by the authors of that study. Additionally, they have not performed structural analyses to confirm direct binding to the D-loop, making it uncertain whether these antibodies could be reliably used for identifying the inner and outer surfaces of our designed structures.
+
+As an alternative to antibody-based detection, we designed a system in which the D-loop was incorporated into PuuE-p to create PuuE(D-loop)-p and mixed with PuuE-M to test whether tubular structures would form. If the D-loop were positioned internally, the formation of helically coiled structures should be disrupted. Unfortunately, the resulting mixture exhibited poor tube formation, likely due to the internal positioning of the D-loop, which may have hindered proper assembly. While we observed minimal tubular structures, no helical arrangement was detected within them. Given the low yield of tubes, this result does not provide definitive evidence and was therefore not included in the manuscript.
+
+Nevertheless, we believe that the correct assignment of surface orientation in our study is supported by the nature of the D-loop’s structural impact. For helically coiled tubes incorporating the D-loop, structural disruption would be difficult to achieve unless the D-loop were positioned externally. This observation lends further confidence to our conclusion regarding the orientation of the surfaces, as presented in the manuscript.
+
+Moving forward, we aim to address this limitation by designing systems based on entirely different protein scaffolds (For primitive data, please see Figure on Reviewer 1 Comment 2). We believe these alternative designs will allow for more detailed analyses, including surface orientation. The results from these ongoing efforts will be reported in future studies to provide a more comprehensive understanding of such assemblies.
+
+We thank the reviewer again for their insightful feedback, which has helped us set clear goals for future investigations.
+
+Comment 3: Additionally, it would be interesting to know the persistence length of the helical assemblies, particularly whether they are longer than the filaments without the D loop.
+Response: We appreciate the reviewer’s insightful comment. We agree that comparing the persistence length of helical assemblies with and without the D-loop would provide valuable insights. However, the presence of non-helical tubular structures in the sample, even when using units with the transplanted D-loop, complicates such comparisons. As a result, we did not conduct this specific analysis in the current study.
+
+Furthermore, the tubes with the D-loop were typically 1–2 μm in length and did not exhibit significant thermal deformations, making it challenging to estimate their persistence length (\( L_p \)) using the conventional analysis employed in this study. Additionally, these results suggest that the persistence lengths of D-loop tubes are much longer than 1 μm, indicating that tubes longer than 15 μm are required to estimate their persistence lengths accurately enough to compare persistence lengths with and without D-loop, as shown in Supplementary Fig. 7b. Therefore, although the reviewer’s comment is intriguing, such a comparison remains challenging at this moment.
+
+The formation of larger (longer) assemblies is an essential and promising direction in protein assembly design field, offering significant opportunities for advancing both fundamental understanding and practical applications. Continued efforts in addressing this challenge are expected to contribute to the development of innovative designs and versatile biomaterials with wide-ranging applications.
+
+Comment 4: Also, could they provide information on the interactions between the D loops in the intertwined tubes, is the conformation (at least according to the model) similar to the conformation in actin filaments?
+
+Response: We thank the reviewer for raising this intriguing point. The results suggest that interactions between D-loops, or more generally between hydrophobic interactions, can lead to the formation of helical structures. This finding is not only relevant to our study but also holds significance for understanding the assembly mechanisms of actin filaments.
+
+Unfortunately, the low resolution of the helical structure in the cryo-EM analysis did not allow for a 3D reconstruction that would reveal detailed interactions between the D-loops. This limitation may be due to the flexibility of the tube itself, which hinders the ability to resolve fine structural details. Therefore, we cannot directly compare their conformations to those in actin filaments.
+
+RESPONSE TO REVIEWER #4
+
+We sincerely thank the reviewer for their thoughtful comments and constructive feedback on our manuscript. We are pleased to know that the reviewer found our work interesting and appreciated the clarity and presentation of our design principles, as well as the characterization of the tubular structures.
+
+Comment 1: The acronym used (NIPAD): it is not clear why the methods employed in this study requires this naming scheme as there was no development of new engineering methods or software.
+
+Response: We thank the reviewer for raising this point regarding the use of the acronym "NIPAD." Initially, we used this term to highlight the nature-inspired aspect of our design approach, particularly in contrast to computationally driven methods like those used by the Baker group. However, based on the reviewer’s comment, we recognize that the acronym may not clearly reflect the methodologies employed in this study. To address this concern, we have removed the term "NIPAD" from the manuscript and revised the relevant sections accordingly. These changes have been highlighted in the revised manuscript for clarity.
+
+We appreciate the reviewer’s suggestion, which allowed us to improve the precision and clarity of our manuscript.
+Comment 2: Cryo processing: please add more information, including images of initial models used and how \( C_1 \) symmetric reconstructions deviated from the final symmetric reconstructions (if any). This is crucial to understand potential symmetric artifacts at low resolutions, especially for the higher order assemblies.
+
+Response: We thank the reviewer for their constructive suggestion for a better understanding of structural analysis and for proposing methods to validate potential artifacts. This input is valuable for enhancing the robustness of our findings.
+
+Initial models (initial 3D reconstructions) were generated in helical reconstruction using the cryoSPARC software. A featureless hollow cylinder was used as the starting reference volume to avoid reference bias. The inner and outer diameters of this cylinder were approximately measured from 2D class averages.
+
+All 3D classifications in RELION were performed with \( C_1 \) symmetry and yielded reconstructions similar to the final reconstruction with imposed cyclic symmetries, thus excluding the possibility of introducing artifacts from cyclic symmetry.
+
+For helical symmetry, we used symmetry search in 3D classification and final reconstructions in RELION to monitor its convergence. Additionally, we generated 2D reprojections from the final 3D reconstructions to examine whether they match the 2D class averages, resulting in a reasonable match.
+
+In response to this comment, we have revised the Supplementary Figures 6, 10 and “Methods” section as follows:
+
+Supplementary Figures 6, 10: Panel labels are attached to the figures, and each step of the image analysis is described in more detail in the legend. New panels have been added showing comparisons between 2D reprojections from 3D reconstructions and 2D class averages.
+
+“Methods” section: A detailed description of the initial model generation and reprojection analyses has been added in section "Cryo-EM image processing (Lines 404-446 as highlighted)".
+
+To support these revisions, we have also included appropriate citation for cryoSPARC in ref. 59.
+
+Comment 3: Methods were not clear as to when binning was reversed during cryoem processing. Was binning reversed for the final resolution calculations?
+
+Response: We thank the reviewer for their question regarding the use of binning during cryo-EM processing. Binning was retained throughout the processing and used for the final reconstructions. From our data analysis, it was evident that the final resolution of the complex did not approach the Nyquist limit with binning. Therefore, we determined that reversing the binning was unnecessary, as all resolvable structural information was preserved in the binned data. We hope this clarifies the methodology employed in our study.
+
+To address this point and avoid confusion, we have added the following description to the “Methods” section (Lines 442-445):
+
+"Particle binning, applied during initial extraction, was maintained throughout the subsequent classifications and 3D reconstructions without reverting to the original pixel size. This approach was adopted as the estimated resolution of the final reconstructions did not reach the Nyquist limit of the binned images, ensuring that all resolvable structural information was preserved."
+Comment 4: It is not clear why this design results in tubes and not 2D or 3D crystals or closed c-symmetric oligomers or even large vesicles. Were any observed?
+
+Response: We thank the reviewer for this insightful question. As noted, in addition to tubes, we observed structures suggesting the presence of ring-like assemblies in the negative-stain TEM images as shown in the figure below. Based on our design, as described in the manuscript, the connection site (p66α) in one of the units (PuuE-p) has a relatively fixed angle (Fig. 1c, Supplementary Fig. 1), which likely promotes the formation of "closed" structures, such as tubes and rings.
+
+We hypothesize that the ring-like structures represent an early stage in the formation of tubular assemblies. For this reason, we focused on analyzing the structures and properties of the tubes in detail. To address the reviewer’s comment, we included a zoomed-in image of the ring structures below in Supplementary Fig. 3b, which were derived from the same data as the tubular assemblies.
+
+![TEM images showing ring-like structures](page_370_563_849_120.png)
+
+In addition, we have updated the manuscript to include these observations and explanations, further clarifying the relationship between the ring-like structures and tubular assemblies. (Lines 102-107).
+
+We appreciate the reviewer’s comment, which allowed us to highlight this aspect of the observed assemblies.
+
+Comment 5: Looking at the final maps, it seems that additional interactions occur between the scaffold proteins than was originally intended: please discuss.
+
+Response: We thank the reviewer for pointing out the possibility of unintended interactions between the scaffold proteins. While weak interactions between PuuE scaffold units may occur, as suggested, they do not appear to drive the formation of the observed tubular structures. This is supported by the observation that neither PuuE-M nor PuuE-p alone forms higher-order assemblies (Supplementary Fig. 2a, b).
+
+In addition, it is possible that the observed interactions might involve the "Met-6xHis-TEVcs region," which has been excluded for clarity in the figures. As shown in the figure below, the N-terminal of PuuE-p includes the Met-6xHis-TEVcs region, which likely corresponds to the volume enclosed within the framed area in the maps, which we believe corresponds to the "additional interactions" you pointed out.
+
+Taking this into account, we believe it is reasonable to conclude that the critical interactions responsible for the formation of tubular structures arise from the designed interactions between the M3L2 and p66α components, as intended in our design. If necessary, we would add following sentences after Line 176.
+
+"Furthermore, the 3D maps suggested the presence of weak unintended interactions between PuuE units. However, as no higher-order assemblies containing tubular structures were observed when PuuE-M or PuuE-p were used alone, it is reasonable to conclude that the key interactions driving tube formation are designed interactions between the M3L2 and p66α components."
+
+We thank the reviewer for bringing up this important aspect, which has helped us further refine the discussion in our manuscript.
+Figure. Fitting of the AlphaFold2-predicted model of PuuE-p into the 3D reconstructed model of \( C_3 \) PuuE tube as shown in Fig. 4g (left), viewed from a different perspective (right). To improve clarity, the Met-6xHis-TEVcs region of the PuuE-p model is not shown in Fig. 4g. However, the N-terminus of the Met-6xHis-TEVcs region is expected to correspond to the area highlighted in red. We propose that the p66α of PuuE-p fits into Volume 2, while the N-terminus of the Met-6xHis-TEVcs region aligns with Volume 1, which we believe the reviewer referred to as the "additional interaction."
+
+Comment 6: Figures need greater clarity - for example, figure 1 should more clearly show the interactions that form fibers: it was not easy to understand what the authors see in the design that would create a fiber over other assemblies. Additionally, the symmetric axes should be well defined and repeat units outlined.
+
+Response: We sincerely thank the reviewer for their valuable feedback on improving the clarity of Figure 1. In response to the suggestions, we have implemented the following revisions to enhance the figure and the corresponding explanations in the manuscript:
+1. Improved Predicted Model: To address the concern that the design leading to tube formation was not easy to understand, we have revised the predicted model to clearly highlight the interaction sites that contribute to the assembly process (Fig. 1d inlet).
+2. Clarification of Angular Connections: To better explain the formation of angular connections leading to closed structures (e.g., tubes), we have updated panel c of Fig. 1. This revision explicitly shows the rigid nature of the p66α connection site in PuuE-p, as well as the flexible connection in PuuE-M, to clearly illustrate how these features contribute to the resulting assembly.
+3. Symmetric Axes and Repeat Units: To address the suggestion regarding symmetric axes and repeat units, we have visually emphasized a repeat unit within a double-framed box (Fig. 1d). Additionally, we have explicitly marked the symmetric axes within the figure to improve clarity. In alignment with this revision, we have also updated Fig. 3b, 4f to reflect the visual emphasis on symmetric axes.
+4. Textual Updates: To further support the revised figure, we have fixed explanations in the manuscript (Lines 67-71) to clarify why the design results in closed structures, such as tubes, rather than other assemblies.
+These revisions have made our schematic and design approach more transparent and accessible, ensuring that the interactions and structural features are easier to interpret. We greatly appreciate the reviewer’s insights, which have allowed us to improve the clarity and presentation of our work. We hope these modifications address your concerns and make the design principles and resulting assembly process more comprehensible.
+Comment 7: Cryo processing: did the authors try symmetric expansion and other techniques such as focused refinement to try and discern the interfaces or get higher resolution refinements that better account for dynamics?
+
+Response: We thank the reviewer for this insightful question. We did not attempt symmetric expansion or focused refinement in this study. Given the diversity in tube diameters and symmetries, the seemingly uniform distribution of the energy landscape as shown in Supplementary Movie 1, and the overall low resolution of the final reconstructions, we concluded that these methods would not yield resolutions sufficient to discern individual interface details.
+
+Comment 8: AlphaFold: have the authors tried to understand the assembly using modeling of multiple subunits?
+
+Response: Inspired by the reviewer's comment, we attempted to gain insight into the structure of the tube assembly using AlphaFold2. Since large-scale prediction of the tube assembly was not feasible for our environment, we focused on the smallest repeating unit that makes up the tube.
+
+Initially, we predicted the complex structure using monomers of PuuE-M and PuuE-p. In all five output models, the predicted structures showed interactions primarily between PuuE units, rather than the designed interactions involving M3L2 and p66α (please see model a in figure below).
+
+Next, we modeled tetramers of PuuE-M and PuuE-p to explore potential tetramer-to-tetramer linkages mediated by M3L2-p66α interactions. To limit M3L2-p66α interactions to a single pair of subunits, only one set of subunits included M3L2 and p66α sequences at the C-terminus (PuuE-M and PuuE-p), while the remaining six subunits lacked these sequences (plain PuuE). However, the predicted structures did not display the expected M3L2-p66α linkage between tetramers. Instead, the models showed either mixed molecules within single assemblies (PuuE-M and PuuE-p in one tetramer) or configurations where molecules were clashed (model b in figure below).
+
+To refine this approach, we incorporated a Gly linker strategy, a method commonly used for AlphaFold2 complex structure prediction. Predictions were conducted with linkers of 40 and 50 Gly residues to make tetrameric proteins into a single chain to restrict PuuE-M and PuuE-p separately (model c and d in figure below). Unfortunately, the resulting structures were like previous predictions (model b), displaying domain swapping or molecular clashes rather than meaningful assembly.
+
+Despite these efforts, AlphaFold2 predictions did not yield the structural insights we aimed for regarding the tube assembly. The polypeptide sequences used in the predictions and the highest confidence models (ranked_0) are presented below for reference.
+
+These results suggest that, at present, predicting such higher-order assemblies remains challenging using AlphaFold2. While the tool excels at modeling individual protein structures and small complexes, its ability to accurately capture the interactions and spatial organization required for large-scale assemblies like the tube structure appears to be limited. We believe that future developments in modeling algorithms may provide further insights into these complex assemblies.
+Comment 9: Discussion: more detail on the potential applications of these fibers would be beneficial
+
+Response: We thank the reviewer for this suggestion. To address this, we have modified the “Discussion” section to outline potential applications of these fibers (Lines 266–301). These include their use in biomimetic materials, drug delivery systems, creation of artificial cytoskeletons, and the development of artificial transport systems. We hope these modifications provide greater clarity on the broader impact and versatility of our study.
+
+Comment 10: The authors claim that the design of fibers “remains elusive”: fibers have been designed before, such as Bethel et al. 2023 (nature chemistry). Previous fiber studies should be discussed.
+
+Response: We appreciate the reviewer bringing up prior work on fiber design, such as Bethel et al. (Nat. Chem., 2023) and Shen et al. (Science, 2018, as noted by Reviewer #3 Comment 1). These studies indeed represent significant contributions to the field and demonstrate the formation of tubular structures. However, these designs rely on single-unit systems. In contrast, our work involves the cooperative assembly of two distinct units, which sets it apart and contributes to its novelty.
+
+This distinction is the basis for our statement that the design "remains elusive," as our approach provides a new perspective on controlling assembly through multi-component interactions. To clarify this point, we have added a dedicated paragraph in the discussion section (Lines 77–80 and Lines 262-266), comparing our work with the cited studies and highlighting the unique aspects of our design. We have also included these references in the corresponding section to support our discussion on the properties of the designed structures (references 18 and 19).
+
+Comment 11: Control over assembly: apart from the environmental factors discussed, do the authors have finer control over the fiber assembly and oligomeric states by design?
+
+Response: Thank you for this insightful question. A key highlight of our study lies in the formation of two-component tubular structures, which has not been achieved before, as mentioned in Comment 10. Using these structures, we demonstrated their ability to respond reversibly to external stimuli, achieving controlled assembly and disassembly. The creation of such assemblies that can reversibly respond to external factors remains a significant challenge in protein design, underscoring the importance of our findings.
+
+As the same time, we agree with the reviewer that achieving control over the assembly through intrinsic protein design, rather than external environmental factors, is equally important. Although this aspect extends beyond the scope of the current study, it is an area of great interest to us. We are actively
+investigating approaches to achieve such control through new design strategies and hope to present these results in future publications.
+
+Comment 12: D-loop grafted cryoem: the sample was left on ice for 1hr before freezing and fibers were observed, however, this is in contrast to the negative-stain experiments in Fig4c and ExtFig7d, where there are no observable fibers at 0c. Please clarify
+
+Response: We thank the reviewer for this observation. As shown in Fig. 4c (center), Supplementary Fig. 8d (center), and Supplementary Fig. 10 (cryo-EM image), the tubular structure does not disappear completely when the temperature is reduced. Instead, the helical structure is decomposed, but the underlying tubes remain partially intact. This partial preservation of the tubes allows structural analysis even at low temperatures. We hope that this explanation resolves the apparent contradiction. We have addressed this comment and included the explanation in the main text as well (Lines 237-238).
+
+Response to the minor points:
+
+Minor Point 1: "cryo-electron": the hyphen should not be between cryo and electron.
+
+Response: We thank the reviewer for pointing this out. The manuscript has been revised to correct this terminology (Lines 17 and 156-157).
+
+Minor Point 2:"Figure 4g: number of atoms outside contour is not very useful without knowing the threshold used and where the greatest deviation between map and model lies."
+
+Response: We agree with the reviewer that additional clarity is needed. To address this, we changed the words with "visual inspection" that more effectively communicate the discrepancies between the map and model. These changes were implemented in the revised Figure 4g.
+
+Minor Point 3: "The role of M3L2/p66a in the MBD2-NuRD complex is not described."
+
+Response: We thank the reviewer for pointing out this aspect. Upon review, we have determined that MBD2 is not directly relevant to the scope of this study. Therefore, we have revised the manuscript to remove references to MBD2, focusing solely on the role of M3L2/p66α in the NuRD complex (Lines 49-52). This adjustment ensures clarity and maintains the relevance of the discussion to the current study. Accordingly, we have changed ref. 11 to more appropriate citation.
+We greatly appreciate the time and effort that the reviewers have invested in evaluating our work and providing insightful comments that have helped us refine our study.
+
+We were encouraged by the reviewers’ recognition of our study’s novelty and potential impact, particularly in the design of two-component protein assemblies. At the same time, we carefully considered the additional comments and suggestions provided in the most recent round of review and have revised our manuscript accordingly. In this revised version, we have addressed the remaining concerns raised by the reviewers through further clarifications in the text and additional discussions where necessary.
+
+RESPONSE TO REVIEWER #1
+
+Comment: The reviewer's comments and concerns have been adequately addressed. Although the additional experiments involving cryo-EM and SAXS to investigate the formation mechanisms were not performed, the dynamic and responsive properties demonstrated in this study represent a significant advancement in the field of protein assembly. This is supported by recent reports highlighting the importance of such properties (e.g., Nat. Nanotechnol. 2024, 19, 1016; Nat. Chem. Biol., 2025, doi.org/10.1038/s41589-024-01811-1; Nat. Synth., 2025, doi.org/10.1038/s44160-024-00726-y; Chem., 2025, doi.org/10.1016/j.chempr.2024.102407). In its current form, this manuscript meets the standards for publication in Nature Communications.
+
+Response: We sincerely appreciate the reviewer’s positive evaluation and thoughtful comments on our manuscript. We agree that understanding the formation mechanisms of these assemblies, as well as developing precise control over their structures, represents a crucial step in the broader study of protein assembly. Building upon the findings of this study, we aim to further explore and refine the design of these structures to advance the field.
+
+Thank you again for your insightful feedback and for recognizing the significance of our work.
+
+RESPONSE TO REVIEWER #2
+
+Comment: I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Response: We deeply appreciate your efforts in co-reviewing our manuscript as part of the Nature Communications initiative. We are grateful for the constructive feedback provided, which has greatly contributed to improving our study.
+
+Thank you again for your time and thoughtful evaluation.
+RESPONSE TO REVIEWER #3
+
+Comment 1: Authors have mainly modified the text of the manuscript without additional data or insights. Although there are still some unanswered questions (e.g. regarding the role of the “D-loop”) and challenges, the manuscript nevertheless describes an interesting design of protein fibers composed of two components. The authors built their assembly based on natural homotetramers and modified them by weak heterodimeric domains to make a two-component assembly. This approach could be applied in principle to many other building blocks and therefore represents a new design platform.
+
+Response: We appreciate the reviewer’s recognition of our approach as a potential new design platform applicable to other building blocks. This encouragement reinforces our belief that our strategy can contribute to expanding the field of artificial protein assemblies.
+
+In this study, we took a novel approach by incorporating the D-loop—a key structural element essential for the helical organization of actin filaments—into an artificial protein assembly. While previous studies have reported actin mutants with modified D-loops using expression systems such as insect cells, it remains difficult to isolate the functional contribution of the D-loop alone in the native actin context due to the complexity of its overall structure and interactions.
+
+Our aim in this study was to demonstrate a new bottom-up approach in protein assembly design, wherein a naturally important structural motif is integrated into an artificially designed protein assembly with a similar morphology—in this case, a tubular structure—to reveal its function in a simplified and controllable context.
+
+By incorporating the D-loop into a structurally unrelated scaffold protein, we created a modular system that allows for the evaluation of this key motif’s contribution independent of the native actin framework. We believe that this study successfully demonstrates a proof of concept, highlighting a new application of artificial protein assemblies for dissecting functional elements derived from natural proteins. Furthermore, as suggested in Reviewer #1’s Comment 8, we plan to conduct further experiments in the future to achieve a more detailed characterization of the role of the D-loop in our system.
+
+To further clarify the conceptual motivation behind incorporating the D-loop into our design, we have added new sentences in the Discussion section of the revised manuscript (Lines 282–291). This addition emphasizes our intention to demonstrate a novel usage of structurally important motifs by integrating them into artificial scaffolds, rather than conducting a detailed functional analysis of the D-loop itself. We hope this helps to better convey the design philosophy underlying our study.
+
+Comment 2: While authors did not report success by modeling the assembly using AF2, I Reviewer #3) obtained formation of 4+4 assembly linked through the CC peptides using AF3 algorithm (image of the models added). 4+4 assembly represents a dead end as it is not able to form larger filaments but may represent an intermediate in equilibrium with filamentous assemblies. Authors may invest a bit more effort into modeling and explanation of the putative mechanisms.
+
+Response: We sincerely appreciate the reviewer’s efforts in applying the AF3 algorithm and sharing their findings. We agree that the 4+4 assembly could be considered one of the initial intermediates. However, given its structural and energetic disadvantages, it is likely to transition into a more stable configuration over time.
+
+While experimentally distinguishing these intermediates remains technically challenging at this stage, we have carefully examined available data and observations to support our conclusions. We acknowledge the significance of this question and consider it an important direction for future studies as experimental techniques advance.
+
+Thank you again for your insightful comments, which have helped us refine our perspective on the assembly process.
+Comment 3: One issue that might be discussed is whether the two components need to be produced separately before mixing, to avoid formation of heterotetramers, which might hinder the formation of filaments. Did they ever try the production of both components at the same time?
+
+Response: We appreciate the reviewer’s insightful question. In this study, we did not attempt the simultaneous production of both components. This decision was based on the consideration that the parental protein (PuuE) forms a tetramer upon expression in E. coli, which could lead to the random mixing of PuuE-M and PuuE-p at the monomer stage (as illustrated below). Such heterotetramer formation would likely hinder the formation of the well-defined structures observed in our study. Currently, we are exploring this approach using a different scaffold protein system as shown in previous Point-by-point response to the reviewers’ comments (Reviewer #1 Comment 2), and we aim to publish these findings in a future study.
+
+![Diagram showing the expression and assembly of PuuE-M and PuuE-p into tetramers](page_495_670_1012_180.png)
+
+Additionally, producing the two components separately provides better control over the structural formation, as demonstrated in previous studies (e.g., Nature 589, 468–473, 2021). Based on these considerations, we believe that this strategy is the most suitable for achieving the intended assembly and structural control, and therefore adopted the approach of separately producing and subsequently mixing the two components in the present study.
+
+Comment 4: As the authors concur that they did not demonstrate any cytoskeletal function and removed the phrase “reminiscent of the cytoskeleton”, they might as well remove the reference for the cytoskeleton from the title.
+
+Response: We appreciate the reviewer’s suggestion. Our study was not specifically designed to mimic the cytoskeleton but rather aimed to construct well-defined protein assemblies with controllable structures. As a result, we successfully formed structures that exhibit similarities to cytoskeletal assemblies. Given this outcome, we believe that retaining the reference to the cytoskeleton in the title is appropriate.
+We hope this clarification addresses the concern.
+
+RESPONSE TO REVIEWER #4
+
+Comment 1: Thank you for your efforts in addressing my concerns. Most concerns have been addressed, however, I have follow up comments below:
+
+Response: Thank you for your careful evaluation and for taking the time to provide additional feedback. We appreciate your thoughtful comments and address them in detail below.
+
+Comment 2 (Regarding Comment 2 from previous Point-by-point response to the reviewers’ comments): You have not included images of the initial models used, only a description. Including the initial models will help compare to the final reconstruction.
+
+Response: We appreciate the reviewer’s valuable feedback. We agree that this addition would enhance the clarity and completeness of our study, allowing readers to better visualize the progression from initial models to final reconstructions.
+In response to the comment, we have added panels (Supplementary Fig. 6 and 10) showing representative images of the initial models used for each structure described in the study.
+
+Comment 3 (Regarding Comment 5 from previous Point-by-point response to the reviewers’ comments): I think your text is reasonable to include, however, you should actually check how much your tag is influencing the formation or stability of the tubes by cutting the protein using tev. The construct already has this feature.
+
+Response: We appreciate the reviewer’s suggestion. We added the following sentences after Line 176.
+
+"Furthermore, the 3D maps suggested the presence of weak unintended interactions between PuuE units. However, as no higher-order assemblies containing tubular structures were observed when PuuE-M or PuuE-p were used alone, it is reasonable to conclude that the key interactions driving tube formation are designed interactions between the M3L2 and p66α components."
+
+As the reviewer suggested, we initially attempted to remove the tag using TEV protease after protein purification. We also considered that removing the tag would be preferable from an experimental standpoint, as it would allow us to more directly evaluate the intrinsic assembly behavior of the designed proteins. However, during the treatment and subsequent purification steps, we observed a significant loss of protein, which made it technically impractical to proceed with tag removal under our current conditions. Therefore, we carried out the experiments using the tagged proteins.
+
+Despite the presence of the tag, the designed higher-order structures were successfully formed, supporting the validity of our approach. Additionally, the possibility of 6xHis-tag-induced aggregation can be ruled out, as EDTA was included in the buffer to chelate metal ions and prevent such interactions. While other potential interactions involving the tag cannot be entirely excluded, no higher-order assembly was observed when each component was incubated separately (Supplementary Fig. 2a, b). Based on these observations, we conclude that the tag does not contribute to the formation of the assembled structures.
+
+We have carefully considered the potential influence of the tag in our study and reached the conclusions presented in this manuscript. Since this evaluation did not involve new experimental data or lead to substantial changes in interpretation, we have chosen not to include this discussion in the main text, but instead provide our rationale here in response to the reviewer’s suggestion. We appreciate the reviewer’s valuable suggestion and hope that our explanation clarifies our rationale.
+
+Comment 4 (Regarding Comment 7 from previous Point-by-point response to the reviewers’ comments): I don't think I fully agree. While you may not reach high resolution and for some of your reconstructions I agree, you may not get more information, for others you could get more resolution leading to enough resolution to discern helices (such as your 9.7Å reconstruction of the c3 tube). Your interface would be revealed to greater detail and would help validate your design.
+
+Response: We appreciate the reviewer’s thoughtful comment regarding the potential for improved resolution in our reconstructions, particularly for the \( C_3 \) tube.
+
+In light of your suggestion, we have revisited our reconstruction process and obtained a reconstruction using boxes with the original pixel size. This yielded a reconstruction similar to those presented in the manuscript, with comparable helical parameters and a resolution of around 10 Å. This outcome aligns with the reconstruction using the downscaled boxes.
+
+Nonetheless, it would be beneficial to explain these efforts in the manuscript. We have included a brief explanation detailing our attempts to optimize resolution, including using boxes with the original pixel size (Lines 455–461). This addition will give readers a more comprehensive understanding of our processing pipeline and the steps taken to maximize the information obtained from our data.
+Comment 5 (Regarding Minor point 2 from previous Point-by-point response to the reviewers’ comments): Again, this is not effective without knowing the threshold used. Different values will "contain" different amounts of atoms. The new term of "visual inspection" is not good to use either way.
+
+Response: We appreciate the comment regarding the thresholds used for map visualisation. We agree that our current description using "visual inspection" is not sufficiently precise or reproducible.
+
+To address this concern, we have replaced the term "visual inspection" with a more quantitative description of our thresholding approach. Specifically, we now refer to this process as "structure fitting" in Fig. 4g, which is based on a normalised map threshold (\( \sigma = 3.3 \)). In accordance with this change, we have also replaced the previously used map with a normalised version to ensure consistency with the sigma-based thresholding. Furthermore, we re-evaluated the number of atoms outside the density at this threshold and updated the corresponding values. We have explicitly stated the sigma value used for map visualisation in the figure legend to ensure clarity and reproducibility. Accordingly, we have included the following sentences in the legend of Fig. 4g (Lines 721–723):
+
+"The map density was normalised and visualised at a threshold of sigma (\( \sigma \)) value = 3.3 above average. Structure fitting was performed to count the atoms of PuuE-p model outside the reconstructed 3D map of \( C_3 \) tube structure at this threshold."
+
+This approach will allow for a more objective assessment of the density distributions in our maps. We sincerely appreciate the reviewer’s insightful feedback, which has helped us refine our terminology and adopt a more scientifically precise and unambiguous description.
+RESPONSE TO REVIEWER #3:
+
+Comment: I find the manuscript appropriate for publication due to its novelty and potential interest. I still believe that the assembly they produced is not related to the cytoskeleton. Still, I don’t insist on removing the word from the title, where its function seems to be mainly to attract the attention of the readers.
+
+Response: We sincerely appreciate the reviewer’s positive evaluation regarding the novelty and potential interest of our study.
+
+Regarding the reference to the cytoskeleton in the title, we fully understand the reviewer’s concern. As discussed in our previous response, while our study was not specifically designed to mimic cytoskeletal function, the assemblies we created exhibit morphological similarities to cytoskeletal structures. Our intention in referencing the cytoskeleton was not to claim functional equivalence, but rather to highlight the structural resemblance, which may inspire further exploration of cytoskeleton-like dynamics in synthetic systems.
+
+Given this context and considering that the reviewer has kindly indicated no strong objection to retaining the term, we respectfully propose to maintain the current title. We sincerely appreciate the reviewer’s understanding and flexibility on this point.
+
+RESPONSE TO REVIEWER #4:
+
+Comment: Thank you for including extra information. I do have the following comments for the Authors, which are mainly comments from a previous review that the Author’s have not fully addressed yet.
+
+I think clearning the following can be done and given that, I think this manuscript would be ready for publication.
+
+Response to overall comment: We sincerely appreciate the reviewer’s careful re-evaluation and constructive comments. We are encouraged by the reviewer’s recognition that only a few clarifications remain before publication. In the following responses, we have addressed each of the remaining points in detail and made clarifications where necessary.
+
+Comment 1-1: My previous comment of "You have not included images of the initial models used, only a description. Including the initial models will help compare to the final reconstruction".
+
+Thank you for adding these, but they contradict your methods section where you state that the initial models were hollow cylinders as these initial models are not generic hollow cylinders. Can you please clarify and update the text and/or figures appropriately?
+
+Response: We appreciate the reviewer’s careful reading and for pointing out the apparent inconsistency between our methods section and the newly added images. We apologize for any confusion this may have caused. To clarify, a featureless cylinder was used as the initial reference for the first iteration of "Helical Refinement" in cryoSPARC, but this was not clearly addressed in our original description. We have now updated the Methods section (Lines 427–432) as follows:
+
+“Initial 3D reconstructions were carried out using the "Helical Refinement" algorithm in cryoSPARC. A featureless hollow cylinder was used as the starting reference for the first iteration in refinement to avoid reference bias, with inner and outer diameters approximately measured from
+2D class averages. The resulting helical structure from this initial refinement job was then used as the reference volumes for subsequent analyses in RELION."
+
+We hope this clarification addresses your concern and provides a more accurate description of our refinement process.
+
+Comment 1-2: You don’t mention if the models were low pass filtered for refinment. Please address.
+
+Response: Thank you for bringing this important point to our attention. We did indeed apply low-pass filtering during the 3D classification and refinement process to avoid reference bias. We have updated the Methods section to include this important detail (Lines 456–458) as follows:
+
+"For 3D classification and refinement, the initial volumes were low-pass filtered to 40 Å resolution to avoid reference-based artifacts."
+
+We hope this revision clarifies our methodology.
+
+Comment 2: My previous comment "I think your text is reasonable to include, however, you should actually check how much your tag is influencing the formation or stability of the tubes by cutting the protein using tev. The construct already has this feature"
+    I can understand your reasoning for keeping the tag, however, do you see any formation of the fibers after tev cleavage? Even with low concentrations, you can easily validate this using EM images and rule out of the effect of the tag.
+
+Response: Thank you very much for your valuable comment and suggestion regarding validation after TEV cleavage.
+    To address this point, we performed additional experiments using commercially available, highly active TEV protease, as our previous in-house preparation had lower efficiency. After treating the purified proteins with the fresh TEV protease, we observed that the overall protein recovery was improved compared to our earlier attempts. We were able to obtain a sufficient amount of protein to conduct testing experiments, although the protein concentration used for these tests was kept relatively low (6.25 μM).
+    We then tested the ability of the cleaved samples to form tubes. Under the standard conditions described in our manuscript, we did not observe tube formation with the cleaved proteins. However, when we increased the NaCl concentration to 400 mM, tubular structures were clearly observed by TEM as shown below.
+
+![TEM images showing tubular structures formed under different conditions](page_1092_1347_496_180.png)
+We hypothesize that this behaviour is due to a decrease in the isoelectric point (pI) of the proteins after removal of the His-tags, resulting in a higher requirement for ionic screening to promote assembly. To support this hypothesis, we calculated the theoretical pI values before and after TEV cleavage: 6.44 to 6.38 for PuuE-M, and 6.02 to 5.84 for PuuE-p. Given that tetramerization would be expected not to significantly alter the overall pI, these results suggest that the cleaved proteins indeed require higher ionic strength to promote assembly due to enhanced net negative charge. This interpretation is consistent with the mechanism proposed in our manuscript, where modulation of electrostatic interactions plays a key role in controlling assembly behaviour.
+
+We note that under the 400 mM NaCl condition, some aggregation was also observed, as was previously seen with the His-tagged proteins. This suggests that at this higher ionic strength, nonspecific aggregation may be promoted alongside tube formation. Nevertheless, clear tubular structures were distinguishable by TEM, and the observed behaviour remains consistent with our proposed assembly mechanism.
+
+Since these findings do not change the main conclusions of the study and were obtained under slightly modified experimental conditions, we have not made additional modifications to the main text. We sincerely appreciate the reviewer’s insightful suggestion, which helped further validate the robustness of our assembly design.
+
+Comment 3: My previous comment of "I don’t think I fully agree. While you may not reach high resolution and for some of your reconstructions I agree, you may not get more information, for others you could get more resolution leading to enough resolution to discern helices (such as your 9.7Å reconstruction of the c3 tube). Your interface would be revealed to greater detail and would help validate your design."
+
+The author’s did not address this point as they mixed up my suggestion with another suggestion regarding binning and using the full pixel size. My comment was regarding using symmetry expansion or masking/local refinements to potentially improve the resolution of some of your reconstructions, mainly the one at 9.7Å. This can be done using the binned particles. I think this could improve the resolution potentially to the 6-8 range where helices would be better defined and better validate your designed interface.
+
+Response: Thank you very much for your thoughtful and constructive suggestion regarding the use of symmetry expansion and masking/local refinements to improve our reconstructions, particularly at the intermolecular interfaces. We sincerely apologize for the confusion in our previous response, where we mistakenly addressed a different comment related to pixel size and binning.
+
+Following your recommendation, we performed symmetry expansion as well as local refinements with masking using cryoSPARC on the unbinned particles. However, these attempts did not result in notable improvements in either the overall resolution or the map interpretability.
+
+As demonstrated in Supplementary Movie 1, we suspect that the lack of improvement stems from the intrinsic flexibility between the base domain and the connection domain of our fusion protein. These domains are connected via a relatively flexible linker, which allows them to adopt independent conformations. This dynamic behaviour likely prevents the protein from being treated as a rigid single particle during reconstruction, thus limiting the effectiveness of focused refinements.
+
+Since these additional refinements did not yield improved resolution, and the current discussion already reflects the limitations imposed by structural flexibility, we have not made further modifications to the main text in response to this comment. Nonetheless, your suggestion greatly contributed to our deeper understanding of the conformational heterogeneity within our assemblies, and we are sincerely grateful for the opportunity to explore this important aspect in greater detail.
+RESPONSE TO REVIEWER #4:
+
+Comment: Thank you for looking fully into my questions. I only have additional comments in regard to "Comment 2", tev cleavage of his-tag.
+
+The aim of this experiment was to check that the tubular assembly is not influenced by the his-tag and based on your results, it seems to be. Based on this, I suggest the authors discuss this in the manuscript. Are the assemblies consistent in size and morphology to pre-cleaved assemblies?
+
+Response: In response to the final comment from Reviewer #4 regarding the potential influence of the His-tag on tubular assembly, we have now addressed this point directly in the revised manuscript (Lines 142–152) and added Supplementary Figure 5c. Additionally, we have revised the legend of Supplementary Figure 5 to include the following description for panel c:
+
+c, 6.25 μM of His-tag cleaved PuuE-M and His-tag cleaved PuuE-p each in 400 mM NaCl buffer was incubated at 40 °C for 24 h and imaged via nsTEM.
+
+We clarified that while the TEV-cleaved proteins were still capable of forming tubes with comparable morphology, the process required a significantly higher NaCl concentration. This observation suggests that the surface charge modulation introduced by the His-tags does influence the assembly behavior under standard conditions. Accordingly, we have updated the text to reflect this interpretation and provided a rationale for retaining the His-tag in subsequent experiments. Details of the TEV protease treatment protocol have also been added to the Methods section (Lines 410–418).
+In this manuscript, Suzuki et al. reported an artificial protein assembly system that exhibits reversible self-assembly behaviours under biomimetic conditions. The assembly structures were characterized by cryo-EM, and the mechanical properties and conditional responses of protein nanotubes were investigated using TIRFM, nsTEM and CD. However, after thoroughly reading, it was found that the main ideas of this paper lack novelty, and the authors did not explore the mechanisms of many observations in depth and show potential applications, so this paper may not be suitable for publication in Nature Communications.
+
+1. The main concept of Nature-Inspired Protein Assembly Design is ambiguous and unconvincing, as many works have established reversible protein nanotubes that respond to biomimetic conditions (Nat. Commun. 2022, 13, 5424.; J. Am. Chem. Soc. 2018, 140, 1, 26.; Nat. Chem. 2013, 5, 613.; J. Am. Chem. Soc. 2013, 135, 31, 11509.; ACS Catal. 2020, 10, 9735.). Also, in this work, a meaningful application of these nanotubes have yet to be demonstrated and explored.
+
+2. The definition of two-component tube structures is controversial. Here, the main scaffold of PuuE-M and PuuE-p is the same, but the two-component protein assembly should be two independent ingredients (Nature 2014,510, 103.; Science 2016, 353, 389.; Nature 2021, 589, 295 468-473).
+
+3. Although the structures of protein nanotubes are supported by 3D reconstruction, the underlying mechanisms of the formation of these structures have not yet been explored and explained. Why do different nanotubes emerge under the same assembly conditions? Could certain conditions generate dominant species?
+
+4. Tracking the formation of nanotubes under thermally stable conditions is important to gain insight into the self-assembly mechanism using cryo-EM, SAXS, or other characterization methods.
+
+5. The overall electrostatic potential of PuuE-M and PuuE-p should be shown in Extended Data Fig. 5, especially since the salt concentration range for salting-in and salting-out is very narrow compared to most proteins.
+
+6. On structural perspectives, these protein nanotubes are similar to microtubules, but their mechanical properties are closer to microfilaments. The specific reasons need to be discussed and explained.
+
+7. It is worth noting that the flexibility and persistence length of different nanotubes may be different, the results in Fig.3 may only represent the characteristics of one of these nanotubes. In other words, comparisons of persistence length between protein nanotubes and cytoskeletal elements may not be meaningful. Therefore, the relevant conclusions need to be carefully discussed.
+
+8. The functions and purposes of introducing D-loop in PuuE-M is illogical and unconvincing, especially considering that considering that the obtained structure is far from the microfilament and that other hydrophobic peptides may also give the same results.

070706503cff2b0c5895a72491f41d6927ffe121f452603fa7f93aef50b5eb1a/preprint/preprint.md

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+Protein design of two-component tubular assemblies like cytoskeletons
+
+Yuta Suzuki
+suzuki.yuta.2m@kyoto-u.ac.jp
+
+Kyoto University   https://orcid.org/0000-0002-4863-4585
+Masahiro Noji
+Kyoto University
+Yukihiko Sugita
+Institute for Life and Medical Sciences, Kyoto University   https://orcid.org/0000-0001-6861-4840
+Yosuke Yamazaki
+RIKEN
+Makito Miyazaki
+RIKEN   https://orcid.org/0000-0002-4603-851X
+
+Article
+
+Keywords:
+
+Posted Date: October 21st, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4976952/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 July 22nd, 2025. See the published version at https://doi.org/10.1038/s41467-025-62076-3.
+Protein design of two-component tubular assemblies like cytoskeletons
+
+Masahiro Noji1,2,3, Yukihiko Sugita4,5,6, Yosuke Yamazaki7,8, Makito Miyazaki6,7,8,9, and Yuta Suzuki3,6,9, *
+
+1Research Fellow of Japan Society for the Promotion of Science, Japan; 2Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, Japan; 3Institute for Integrated Cell-Material Sciences, Kyoto University, Kyoto, Japan; 4Institute for Life and Medical Sciences, Kyoto University, Kyoto, Japan; 5Graduate School of Biostudies, Kyoto University, Kyoto, Japan; 6Hakubi Center for Advanced Research, Kyoto University, Kyoto, Japan; 7Graduate School of Science, Kyoto University, Kyoto, Japan; 8RIKEN Center for Biosystems Dynamics Research, Yokohama, Japan; 9PRESTO, JST, Saitama, Japan
+
+Recent advances in protein design have ushered in an era of constructing intricate higher-order structures1. Nonetheless, orchestrating the assembly of diverse protein units into cohesive artificial structures akin to biological assembly systems, especially in tubular forms, remains elusive. To this end, here, we introduce the Nature-Inspired Protein Assembly Design (NIPAD), a novel methodology that utilises two distinct protein units to create unique tubular structures under carefully designed conditions. These structures demonstrate dynamic flexibility similar to that of actin filaments, with cryo-electron microscopy revealing diverse morphologies, like microtubules. By mimicking actin filaments, helical conformations were incorporated into tubular assemblies, thereby enriching their structural diversity. Notably, these assemblies can be reversibly disassembled and reassembled in response to environmental stimuli, including changes in salt concentration and temperature, mirroring the dynamic behaviour of natural systems. NIPAD combines rational protein design with biophysical insights, leading to the creation of biomimetic, adaptable, and reversible higher-order assemblies. This approach deepens our understanding of protein assembly design and complex biological structures. Concurrently, it broadens the horizons of synthetic biology and material science, holding significant implications for unravelling life’s fundamental processes and pioneering new applications.
+
+Life phenomena rely on the dynamic and reversible assembly and disassembly of various higher-order protein assemblies. Actin filaments2,3 and microtubules4,5 in the cytoskeleton and the capsid proteins of viruses6,7 are examples of such naturally occurring structures. These are tightly regulated in function and complexity. Synthesising higher-order structures of heterogeneous protein units poses a significant challenge, particularly regarding replicating the diversity and flexibility inherent to natural assemblies. Although recent advances in computational design have enabled the creation of artificial higher-order
+protein structures from two protein components8–10, the design of heterogeneous higher-order protein assemblies with the flexibility and reversible assembly/disassembly characteristics of natural structures, especially tube structures reminiscent of the cytoskeleton, remains a formidable challenge.
+
+Herein, we introduced Nature-Inspired Protein Assembly Design (NIPAD), a novel methodology that draws inspiration from the principles underlying natural protein complexes. By integrating rational protein design with biophysical insights to optimise assembly conditions, NIPAD recapitulates flexibility and reversible assembly principles. We employed NIPAD to create a novel assembly of two distinct protein units, successfully forming unique two-component tube structures. This development represents a significant step toward replicating the properties of complex natural structures at the molecular level.
+
+Results and discussion
+The concept of NIPAD
+In developing the protein components for NIPAD, we employed rational design principles with hints from natural biological systems, integrating naturally occurring ‘heterolinkers’ with ‘scaffold proteins’ to streamline design. For the heterolinker, we chose the heterodimeric peptide pair ‘MBD3L2 (M3L2)/p66α’ (Fig. 1a). Our choice of M3L2/p66α was influenced by its role in the MBD2-NuRD complex, where the ‘MBD2/p66α’ anti-parallel coiled-coil domain is essential for complex assembly11. Given the moderate denaturation midpoint temperature (\( T_m \)) of M3L2/p66α (\( T_m = 35\ ^\circ\mathrm{C} \)) compared to MBD2/p66α (\( T_m = 65\ ^\circ\mathrm{C} \))12, we anticipated that M3L2/p66α would provide a balance between stability and reversible assembly control through temperature modulation. We then sought to identify a scaffold protein that could connect the heterolinker in the simplest manner possible. The positions of connecting sites at the corners of such scaffold proteins facilitate the desired assembly formation13. Therefore, we chose the ‘Pseudomonas fluorescens PuuE allantoinase (PuuE)’, a homotetramer with \( C_4 \) symmetry where each C-terminus is located at each vertex of the quaternary structure (Fig. 1b)14. This arrangement enabled straightforward genetic fusion of heterolinkers to the scaffold’s C-termini, leveraging specificity and reversibility of heterolinker interactions to drive assembly formation. This approach simplifies the assembly process and enhances expression and purification efficiency for each protein unit, preventing spontaneous assembly and ensuring the controlled formation of higher-order structures.
+
+We constructed protein units ‘PuuE-M’ and ‘PuuE-p’ through genetic engineering, fusing M3L2 and p66α to the C-terminus of PuuE, respectively (Fig. 1c). AlphaFold2 (AF2)15,16 modelling suggested a configuration with a relatively flexible orientation of M3L2 in PuuE-M, whereas a highly constrained orientation of p66α in PuuE-p (Extended Data Fig. 1). Owing to the constrained orientation of PuuE-p, an
+angular interface was formed between PuuE-M and PuuE-p, and we predicted that assembly of these two units would form a tubular structure (Fig. 1d). Additionally, depending on the number of PuuE-M and PuuE-p units, different tubular structures were expected. Protein expression in Escherichia coli provided both constructs in a soluble form, facilitating their purification. In isolation, neither protein unit exhibits self-assembly (Extended Data Fig. 2a, b). However, when combined under optimised conditions (discussed in the following section), we successfully observed the expected chessboard-patterned tube (PuuE tube) using negative-stain transmission electron microscopy (nsTEM) (Fig. 1e, Extended Data Fig. 2c). Although previous studies have assembled cages8,9, sheets10, and three-dimensional (3D) crystals17 using two-component protein systems, this study is unique in that tube structures were successfully created.
+
+The condition design of tubular assemblies
+Based on established principles observed in biological systems, including actin filaments18,19, microtubules20,21, and amyloid fibrils22,23, protein concentration, temperature, time, and salinity have a significant influence on assembly formation. Thus, we carefully tailored assembly conditions to exploit the complex interactions between these factors. This approach allowed us to optimise experimental conditions for constructing the desired tubular structures.
+
+First, we focused on the dependency of PuuE tube assembly on protein concentration (Extended Data Fig. 2c). Mixing PuuE-M and PuuE-p at a concentration of 250 nM each (considering tetramer equivalence) led to the formation of tubular structures after an incubation period of 24 h at 40 °C, consistent with the dissociation constant (\( K_d \)) for M3L2/p66α dimer formation, which is approximately 268 nM12. Increasing protein concentration to 2.5 μM markedly enhanced the quantity and length of formed tubular structures. Elevating the concentration to 12.5 μM for each component significantly increased tube formation efficiency, underscoring the concentration-dependent nature of PuuE-M- and PuuE-p-facilitated tubular assembly.
+
+Next, PuuE tube formation kinetics were investigated. The incubation of mixtures containing 12.5 μM of each protein at 40 °C resulted in the formation of nascent tube structures within 30 min, evolving into distinguishable tubes spanning several hundred nanometres to 1 μm in length within 1–2 h (Fig. 2a, b, Extended Data Fig. 3a). Over time, these tubes elongated, reaching several micrometres in length after 24 h and extending up to approximately 5 μm after 48 h. Once formed, the tubes remained structurally stable for at least 1 month at 25 ± 1°C (Extended Data Fig. 3b).
+We then explored the influence of temperature on PuuE tube formation (Extended Data Fig. 4a). While the melting temperature of the M3L2/p66α dimer is around 35 °C, tube assembly was hardly observed at sufficiently lower temperatures of 20–25 °C, even after 24 h of incubation. Conversely, temperatures near \( T_m \), specifically between 30 and 40 °C, markedly promoted tube formation. Therefore, temperatures below \( T_m \) may excessively enhance the binding force between M3L2 and p66α, causing kinetic entrapment of assemblies. However, temperatures close to \( T_m \) modulate this binding force, allowing the dynamic rearrangement of M3L2/p66α interactions under thermal fluctuations, thus facilitating the assembly of thermodynamically stable, ordered structures. This principle is consistent with general crystallisation theories\(^{24,25}\) and reports on the formation of ordered structures in natural protein assemblies\(^{22,23,26}\). Importantly, temperatures above 45 °C led to thermal denaturation and aggregation of PuuE-M (\( T_m = 46.2 \) °C) and PuuE-p (\( T_m = 48.1 \) °C), significantly diminishing tube formation capabilities (Extended Data Fig. 4b, c). This finding implies that the original concept of tube formation with reversible temperature control was not realised.
+
+Reversibility of tubular assemblies
+
+Finally, we examined the effects of salt concentration on PuuE tube assembly. We prepared mixtures with different NaCl concentrations ranging from 0 to 400 mM and incubated them at 40 °C for 24 h. Tube formation was clearly observed within the NaCl concentration window of 50-200 mM, with no tube formation detected outside this range (Fig. 2c, Extended Data Fig. 5a). Since both PuuE-M (pI = 6.44) and PuuE-p (pI = 6.02) were similarly charged under pH 8.0, tube formation at low salt concentrations was likely inhibited by electrostatic repulsion. Conversely, moderate electrostatic shielding facilitated by 50–200 mM NaCl likely provided conducive conditions for tube assembly, whereas higher NaCl concentrations may have induced excessive shielding or aggregation due to salting out, inhibiting tube formation. This observation aligns with known phenomena in protein crystallisation, where electrostatic shielding above a certain threshold can prevent crystal growth\(^{17,27-29}\), although crystals formed by a combination of electrostatic and hydrophobic interactions can remain stable up to approximately 200 mM NaCl\(^{30}\). The association of M3L2/p66α involves both electrostatic and hydrophobic interactions\(^{12}\), consistent with the latter scenario.
+
+The salt-dependent PuuE tube formation and the dynamic nature of PuuE-M/PuuE-p interactions near their \( T_m \) (35 °C) led us to hypothesise that tubes could undergo reversible disassembly and reassembly in response to changes in NaCl concentration. Confirming our hypothesis, tubes initially formed in 100 mM NaCl solution were significantly shortened when subjected to solvent exchange with 0 mM NaCl buffer (NaCl (-) buffer) and subsequent incubation at 40 °C for 24 h (Fig. 2d, e, Extended Data Fig. 5b). Subsequent
+solvent exchange with 100 mM NaCl buffer (NaCl (+) buffer) resulted in notable tube reassembly. This salt-concentration-driven reversibility, although divergent from the initial temperature-controlled reversibility hypothesis, marks a significant advance in artificial protein assembly design, allowing for the biomimetic replication of dynamic structural changes under relatively mild conditions, akin to the behaviour of actin filaments in cellular structures\(^{18,19}\). Unlike the irreversible aggregation observed in amyloid structures, our assemblies exhibit a reversible and dynamic assembly process akin to the cytoskeleton behaviour, successfully demonstrating the potential for the biomimetic replication of natural cellular dynamics under controlled conditions.
+
+**Diversity and flexibility of tubes**
+
+Based on these findings, we determined the ideal conditions for PuuE tube formation in 100 mM NaCl at 40 °C for 24 h. To further characterise the structural features of tubes formed under these conditions, cryo-electron microscopy (cryo-EM) was employed (*Extended Data Fig. 6*, *Extended Data Table 1*). Analysis of 2D class-averaged images revealed a spectrum of tube diameters and symmetries similar to the diversity observed in microtubules\(^{31-34}\) (**Fig. 3a**). From these images, we successfully reconstructed the 3D structures with \( C_4 \), \( C_5 \), and \( C_6 \) symmetries within tube structures (**Fig. 3b**). Insights from the PuuE crystal structure\(^{14}\), notably its unique central indentation on the back surface (**Fig 1b**), allowed us to deduce that PuuE units are alternately oriented face-to-back across all 3D models. Additionally, cryo-EM analysis suggested that connection flexibility allowed the contraction of the entire tube structure (*Extended Data Fig. 6*, **Supplementary Movie 1**). Although definitive conclusions are difficult owing to its inherent flexibility, the comparison of the cryo-EM 3D reconstruction with the AF2-predicted model of PuuE-p suggests that PuuE-p is less likely to fit inside the tube structure and instead fits better on the outside (**Supplementary Movie 2**). Furthermore, tubes with larger diameters, presumably having \( C_7 \) to \( C_{10} \) symmetries, were identified at low resolution, likely owing to the flexibility of connection sites influencing tube structure. In fact, nsTEM and cryo-EM images frequently showed tubes appearing bent or compressed (*Extended Data Fig. 2–6*). In contrast to prior strategies by engineering on scaffold proteins itself to create higher-order protein assemblies\(^{8-10,13,35}\), NIPAD integrates a flexible linker with the scaffold protein, resulting in varied structures and arrangements among higher-order assemblies. This variation in tube diameter, akin to that observed in microtubules\(^{31-34}\), is presumably a hallmark of NIPAD.
+
+To further explore PuuE tube structure flexibility, we labelled tubes with Alexa Fluor 488 succinimidyl ester and observed them in real-time using total internal reflection fluorescence microscopy (TIRFM). Tube structures were constrained in the evanescent field by the depletion effect of methylcellulose contained in the observation buffer and underwent thermally driven two-dimensional random bending (**Fig. 3c**,
+Supplementary Fig. 1a, Supplementary Movie 3). Analysis of the fluctuation in shape yielded the persistence length (\( L_p \)) of 19.7 \( \mu \)m (Fig. 3d, Supplementary Fig. 1b). \( L_p \) is the mean length over which a semiflexible polymer remains straight, characterising polymer stiffness\(^{36}\). The \( L_p \) value of the tube structures is nearly equal to that of actin filaments measured in this study, 12.5 \( \mu \)m (Fig. 3d), and previously reported values of 9–20 \( \mu \)m\(^{37}\). Microtubules have much longer persistence lengths (0.1–10 mm)\(^{38-40}\). Conversely, intermediate filaments, another cytoskeletal fibre structure, typically have shorter persistence lengths (<1 \( \mu \)m)\(^{41}\). Therefore, the tube structure is as flexible as actin filaments, more flexible than microtubules, and stiffer than intermediate filaments.
+
+Emulation of actin filaments
+
+Finally, we sought to modify the morphology of PuuE tube assemblies. Specifically, we hypothesised that grafting the D-loop of actin onto PuuE-M would produce tubes with a helical conformation reminiscent of actin filaments. The D-loop plays an important role in helical actin filament formation via hydrophobic pockets\(^{42-45}\). The hydrophobic nature of a prominent indentation on the ‘back’ side of PuuE (Extended Data Fig. 7a) guided our hypothesis. The loop structure on the back side of PuuE-M was chosen as the grafting site for the D-loop, and the ‘PuuE(D-loop)-M’ fusion construct was constructed (Fig. 4a). When PuuE(D-loop)-M was expressed in *E. coli*, it was found in the soluble fraction and was purified as PuuE-M. Since PuuE(D-loop)-M has a lower thermal stability (\( T_m = 35.6 \) °C) than PuuE-M (\( T_m = 46.2 \) °C, Extended Data Fig. 4b, 7b), we performed sample incubation at a lower temperature (30 °C). Although PuuE(D-loop)-M alone did not assemble, its combination with PuuE-p replicated the PuuE tube and introduced novel helical patterns, with two or three tubes intertwined (PuuE D-loop tube), as verified via nsTEM (Fig. 4b, Extended Data Fig. 7c). The emergence of helical formations, absent in the PuuE-M and PuuE-p mixtures, clearly stems from D-loop integration. While the D-loop likely plays a crucial role in the helical formation of actin filaments\(^{42-45}\), its complete mechanism remains unclear. Our study, by successfully grafting the D-loop to replicate actin-like helical structures, offers a novel perspective on its significance. This approach confirms the critical role of the D-loop in helical conformations and opens new avenues for understanding the intricate design principles of actin filaments.
+
+As mentioned above, the helical conformation of tube structures is thought to arise from hydrophobic interactions, which are inherently sensitive to temperature and weaken at lower temperatures\(^{46-48}\). This led us to posit that alterations in temperature can serve as reversible switches for disassembly and reassembly. Notably, exposing the samples to 0 °C for 1 h suggested a dissociation of the helical conformations and hinted at a possible breakdown of the tubular structures (Fig. 4c, Extended Data Fig. 7d). Remarkably, when these disassembled samples were reintroduced to 30 °C for 24 h, the elongated tubular formations
+with helical conformations were restored. By grafting D-loop, the tube structure could form helical conformations and acquired a new temperature-dependent reversibility. This thermal responsiveness parallels the behaviour of microtubules\(^{20,21,49}\), underscoring the ability of the NIPAD approach to mimic the dynamic properties of biomolecular assemblies in artificial protein design to create complex higher-order protein structures. This dual responsiveness (salt and temperature dependence) enhances the biomimetic potential of our design, which is a promising avenue for advanced applications in synthetic biology and materials science.
+
+To determine the intricate helical configurations, structural analyses were performed using cryo-EM (Fig. 4d, Extended Data Fig. 8, Extended Data Table 1). In addition to the inherent flexibility of the tube structure, the ability of tubes to form helical bundles introduces an additional layer of complexity to the structural analysis. This complexity is underscored by cryo-EM results, which render a detailed analysis of these higher-order structures particularly challenging. However, analysis of 2D class-averaged images of the helical structures revealed double and triple helical tubes, which was consistent with the nsSTEM observation (Fig. 4b, d, Extended Data Fig. 7c, 8). Moreover, the tube structures forming these helices seem to show a thinner diameter of approximately 24 nm, which does not align with any of the original PuuE tubes with diameters starting at 28.6 nm (Fig. 3b, Extended Data Fig. 6). Therefore, an attempt was made to elucidate the characteristics of the tube structures forming the helical conformations by employing temperature-induced structural disassembly (Fig. 4c). The cryo-EM sample was initially prepared at 25 ± 1 °C to prevent disassembly; however, to unwind the helical structures, the sample was briefly chilled on ice for approximately 1 h. By observing these chilled samples with cryo-EM, we successfully identified a new tube structure with \( C_3 \) symmetry (Fig. 4e, f, Extended Data Table 1) in addition to the previously observed structures (Extended Data Fig. 9). A comparison of this tube structure with \( C_3 \) symmetry with the structures forming the helical conformations indicated a match, suggesting that the tubes forming the helical conformation have indeed \( C_3 \) symmetry (Fig. 4d bottom). Additionally, the diameter of approximately 23.6 nm, as determined by cryo-EM 3D reconstruction, corresponds to the tubes forming helical structures, further supporting these findings. Considering its inherent flexibility, it is challenging to reach a definitive conclusion, but further examination of the tube structure with \( C_3 \) symmetry suggests that PuuE-p is likely positioned on the outside (Fig. 4g, Supplementary Movie 4), consistent with the original PuuE tube structures (Fig. 3b, Supplementary Movie 2). This arrangement indicates that the D-loop of PuuE(D-loop)-M appears on the exterior of the tubes, which is crucial for forming helical structures not observed in PuuE tubes lacking the D-loop. The \( C_3 \) symmetry enhances the exposure of internal PuuE(D-loop)-M on the outer surface compared to structures with \( C_4 \) or higher symmetry, enabling hydrophobic interactions between tubes. Therefore, the formation of the \( C_3 \) symmetric tube structure likely facilitated
+the creation of the helical conformations. Furthermore, the lack of \( C_3 \) symmetry in PuuE tubes (Fig. 3a, b) suggests that they are unstable as single tubes without forming helical conformations. The formation of helical conformations may stabilise the structure with \( C_3 \) symmetry, as evidenced by its successful identification in tube structures with helical conformations. Additionally, the temperature-induced degradation leading to the rapid collapse of tubes with \( C_3 \) symmetry suggests that helical structure stabilisation is essential for maintaining structural integrity under physiological conditions.
+
+Conclusions
+We introduce NIPAD, a pioneering approach that intricately weaves together protein unit design and assembly, drawing inspiration from the complexity and adaptability of natural protein assemblies. By employing NIPAD, we created a unique higher-order tubular assembly composed of two protein units, exhibiting the reversible, flexible, and diverse characteristics of natural structures. A noteworthy highlight of our study was the successful induction of helical conformations within these tube assemblies, akin to those observed in actin filaments, achieved through strategic integration of the D-loop into assembly design.
+
+This advance in protein assembly highlights the complexity of emulating the dynamic behaviour observed in biological systems. The design and assembly of protein structures in vitro, although closely controlled, cannot fully replicate the complex cellular environment. In vivo, myriad factors, including macromolecular crowding, post-translational modifications, and interactions with other cellular components can significantly influence protein behaviour\(^{50}\). Our designed protein assemblies exhibit remarkable biomimicry regarding flexibility, reversibility, and structural diversity, but have yet to be demonstrated and validated in biological systems, where the true complexity of biological interactions is present. Furthermore, our approach, which focuses on the assembly of tubular structures inspired by cytoskeletal elements, including actin filaments and microtubules, does not address the full range of complex protein structures found within biological systems. Natural protein assemblies contain structural and functional diversity, and much remains to be explored. Computational methods have an important role to play in improving the accuracy and breadth of protein assembly design\(^{1,8-10}\). By utilising computational predictions about protein interactions and assembly outcomes, our design would be refined into more complex and functional biomimetic structures, with applications ranging from novel biomaterials and nanodevices to therapeutic innovations.
+
+Our research extends the boundaries of protein assembly design and provides new insights into its applications in synthetic biology and life sciences. This research encourages a comprehensive approach that bridges the divide between the biological and materials sciences and suggests that the exploration of
+nature’s complex systems has the potential to transform science and technology. As we continue to explore this intersection of life and materials sciences, we anticipate that future investigations will provide fundamental insights into the natural world, heralding a new era of scientific discoveries and technological breakthroughs.
+
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+Fig. 1. Construction of PuuE tube via NIPAD. | a, AF2 prediction of the heterodimeric peptide pair, M3L2 (yellow) and p66α (blue). b, Crystal structure of PuuE (PDB ID: 3CL6). C-terminus positions are circled. Detailed structure, face, side, and back are shown for clarity. c, Schematic diagram of the protein sequence (top) and the AF2-predicted structures of PuuE-M and PuuE-p (bottom). PuuE-M and PuuE-p are coloured yellow and blue to match the respective peptides and overall structure to clear the tube structure (d). The peptide parts, M3L2 and p66α, are highlighted in darker colours. d, Left, predicted model of the tubular assembly consisting of PuuE-M and PuuE-p. Right, brief schematic diagram of how many proteins (n) form a system of tube structures. e, nsTEM images of tubular assemblies constructed from PuuE-M and PuuE-p; 12.5 μM PuuE-M and 12.5 μM PuuE-p in NaCl (+) buffer was incubated at 40 °C for 24 h and imaged via nsTEM. Scale bars, 1 μm (white), 50 nm (black).
+Fig. 2. Condition optimisation for PuuE tube assembly. | a, b, The kinetics of tubular assembly. nsTEM images of tubular assembly (a) and length analysis (b). c, nsTEM images of tubular assemblies with varying NaCl concentration. d, nsTEM images showing the reversibility of tube structures with changing NaCl concentration. e, Tube length analysis of nsTEM images. For tube length analysis, tubes were picked up and calculated from 5k images at each step; 150 tubes from the longest tube length were used at each data point. *** p<0.001 (Welch’s t-test). Scale bar, 1 μm.
+Fig. 3. Structural characterisation of PuuE tube. | a, 2D class-averaged images of tube structures. The population of each structure was determined from the total pickings of 206,658 tube segments. Scale bar, 500 Å. b 3D reconstructed models of tube structures with \( C_4 \), \( C_5 \), and \( C_6 \) symmetries. The fitting results suggest that PuuE-p is less likely to fit into units located inside the tube structure and more likely to fit into units located on the outside. Based on the predictions, the units were colour-coded as shown in Fig. 1c. For visibility, only the molecular model of the PuuE (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. c, Time-lapse images of random bending of the tube structures monitored by TIRFM. Top: snapshots at the starting point (0 sec) and after 4 sec (top). Bottom: enlarged images of tubes in green or orange rectangles in the top images, showing the dynamic flexibility of tube structures between 0 to 4 sec (0.4 sec per image). Scale bar, 5 μm. d, Left, a relationship between contour length (\( L \)) and mean square of end-to-end distance (\( <R^2> \)) of the tube structures for estimation of the persistence length (\( L_p \)). The continued lines represent fitting curves (black for PuuE tube, red for actin filament) to experimental data (black open circle for PuuE tube, red cross mark for actin filament). Right, comparison of persistence length with cytoskeletal elements. PuuE tube (PT, black) and actin filaments (AF, red) were determined in this study (A wider range of plots is shown in Supplementary Fig. 1b). Intermediate filaments (IF, blue) and microtubules (MT, green) are taken from ref. 41 and 38, respectively.
+Fig. 4. Emulation of actin filament by D-loop grafting. | a, Schematic representations of PuuE(D-loop)-M. The position of D-loop graft (red) is indicated by protein sequence (top) and the AF2-predicted structure (bottom). b, nsTEM images of tubes with a helical conformation composed of PuuE(D-loop)-M and PuuE-p. The helical pattern of two (centre) or three (right) intertwined tubes is shown in the high-magnification image. c, nsTEM images showing the reversibility of tube structure with helical conformations by temperature change. d, Representative cryo-EM images (top) and 2D class-averaged images (bottom) of helical tube structures. e, Representative cryo-EM image (top) and 2D class-averaged image of tube structure with \( C_3 \) symmetry. Tube structures with other symmetries found in this study are shown in Extended Data Fig. 9. f, 3D reconstructed model of tube structure with \( C_3 \) symmetry. For visibility, only the PuuE structure (PDB ID: 3CL6) is overlayed on the 3D reconstructed model. g, Fitting of AF2-predicted model of PuuE-p into the 3D reconstructed model. The fitting results suggest that PuuE-p is unlikely to fit in the units located inside the tube structure; it is better accommodated by the units on the outside. Based on this prediction, the units in f are colour-coded as described in Fig. 1c. 6xHis-TEVcs region of the PuuE-p model is not shown to improve visibility. Scale bars, 1 μm (white), 100 nm (black), 10 nm (grey).
+Methods
+
+Plasmids and cloning
+Primers for cloning and synthetic genes of N-terminal 6xHis-tagged PuuE-M and PuuE-p were purchased from Eurofins Genomics. PCRs were performed using the PrimeSTAR Max DNA Polymerase (Takara Bio) according to the manufacturer’s protocol. Sizes of PCR products were verified using standard agarose gel electrophoresis. The In-Fusion Snap Assembly (Takara Bio) was used as the standard method for cloning according to the manufacturer’s protocol, and each amplified gene fragment was ligated between the NdeI and BamHI multicloning sites of the pET11a expression vector (Novagen). Primers for cloning and a synthetic DNA fragment of D-loop were purchased from Eurofins Genomics. The plasmid encoding N-terminal 6xHis-tagged PuuE-D-loop-M was generated from the PuuE-M plasmid following the same procedures as above. All plasmids were amplified in E. coli strain DH5α (NIPPON GENE) and extracted using the NucleoSpin Plasmid EasyPure (MACHEREY-NAGEL) according to the manufacturer’s protocol. DNA sequences were confirmed by a sequencing service (Eurofins Genomics).
+
+Protein expression and purification
+The recombinant proteins were expressed using E. coli strain BL21 (DE3) (NIPPON GENE) co-transformed with a pGro7 chaperone plasmid (Takara Bio) and purified as follows. After transformation with plasmid DNA, colonies grown overnight on LB agar plates supplemented with 100 μg/mL ampicillin (Amp) and 20 μg/mL chloramphenicol (Crm) at 37 °C were picked to inoculate 5 mL of liquid LB-Amp-Crm broth and grown overnight at 37 °C and 200 rpm. Overnight cultures were diluted in 1 L of liquid LB-Amp-Crm broth supplemented with 0.5 mg/mL L-arabinose and grown at 37 °C and 200 rpm until reaching an optical density at 600 nm of 0.6–0.8. Protein synthesis was induced by adding 0.1 mM isopropyl-β-D-thiogalactopyranoside and the cultures were grown at 16 °C for 16–20 h. Cells were harvested by centrifugation at 15,317 g and 4 °C for 5 min and then frozen at -80 °C. Cell pellets were thawed at 25 ± 1 °C, resuspended in 60 mL of ice-cold purification buffer (20 mM Tris-HCl, pH 8.0, containing 300 mM NaCl), and lysed using sonication (9 min with 1:2 on/off cycles and 70% amplitude; SFX250, Branson) on ice. Cell debris was cleared by centrifugation at 15,317 g and 4 °C for 30 min. The supernatant (i.e., crude protein) was filtered through a 0.45-μm pore size membrane filter (Merck), applied onto HisTrap FF crude column (Cytiva) pre-equilibrated with the purification buffer and washed with 5 column volumes of 2% elution buffer (20 mM Tris-HCl, pH 8.0, containing 300 mM NaCl and 1 M imidazole; 2% means 20 mM imidazole). 6xHis-tagged proteins were eluted with 10 column volumes of elution buffer with a linear gradient of 2–40% (i.e., 20–400 mM imidazole). The fractions containing the proteins confirmed by means of UV absorption and SDS-PAGE were again collected and dialysed against 50-fold volume of NaCl (+) or NaCl (-) buffer (50 mM Tris-HCl, pH 8.0, containing ±100 mM NaCl and 0.5 mM EDTA) at 4 °C twice.
+Each of the purified proteins was concentrated by an Amicon Ultra centrifugal filter unit (Merck) with an appropriate molecular weight cutoff followed by filtration through a 0.45 µm pore size membrane filter (Merck). Protein concentration was determined by absorbance measurements at 280 nm using a NanoDrop OneC spectrophotometer (Thermo Scientific). The molar extinction coefficients at 280 nm for the proteins were calculated from the basis of amino acid composition51. The concentrated proteins were frozen in liquid nitrogen and stored at -80 °C before experiments.
+
+Sample preparation
+All proteins were thawed immediately before tube formation experiments on ice. Each sample was prepared in a 1.5-mL microtube using an appropriate buffer to adjust the concentration described in the manuscript and the volume to 200 µL at 25 ± 1 °C. Except for the NaCl concentration-dependent experiments, NaCl (+) protein stock solution and buffer were used. For the NaCl concentration-dependent experiments, 50 mM Tris-HCl (pH 8.0), 1 M NaCl, and 0.5 mM EDTA were used in addition to NaCl (-) protein stock solution and buffer. Incubation of the samples was carried out using a ThermoMixer C (Eppendorf) or a MATRIX Orbital Delta Plus (IKA) with shaking of 300 rpm at the temperature described in the manuscript. For the disassembly and reassembly experiments, buffer substitution procedures were conducted using NaCl (-) and NaCl (+) buffer, respectively, with Microcon 50 centrifugal filter units (Merck) according to the manufacturer’s protocol four times at each step.
+
+Negative-stain transmission electron microscopy (nsTEM)
+A naked G600TT copper grid (Nisshin EM) was carbon-coated using a VE-2030 (VACUUM DEVICE). The grid was glow-discharged using a PIB-10 (VACUUM DEVICE). Then, a 5-µL aliquot of the sample solution was placed on the grid for 1 min, and the remaining solution was removed with filter paper (No. 2, ADVANTEC) followed by rinsing thrice with a 5-µL aliquot of Milli-Q water. After blotting off the water with filter paper, the sample was stained briefly with a 3-µL aliquot of 2% (w/v) uranyl acetate solution three times. The remaining solution was removed with filter paper and the grid was dried on the bench-top. TEM observation was performed using a transmission electron microscope HT-7700 (Hitachi) with an acceleration voltage of 80 kV. The images were recorded using HT-7700 control software (Hitachi).
+
+Tube length analysis
+Hundreds of discriminable tubes were picked up manually on 5k-magnification TEM images. The tube lengths were calculated as half of the perimeter analysed with ImageJ (Fiji)52. The plots were drawn by selecting 150 tubes from the longer lengths using Igor Pro 9 (WaveMetrics). For the disassembly and reassembly analysis, Welch’s t-test was carried out.
+Circular dichroism (CD) spectrum measurements
+All proteins were thawed immediately before CD measurements on ice. Each sample was prepared in a 1.5-mL microtube using NaCl (+) buffer to adjust the concentration to 2.5 \( \mu \)M and the volume to 200 \( \mu \)L at 25 ± 1 °C. Far-UV CD spectra were obtained at a wavelength of 200–250 nm using a J-1100 spectropolarimeter (JASCO) with a quartz cell with a light path of 1 mm. Thermal denaturation was performed at a temperature change rate of 1 °C/min. The CD spectral data were collected using Spectra Manager (version 2.5, JASCO). All CD data were expressed as mean residue ellipticity. The \( T_m \) of each protein was calculated from the thermal denaturation curve at a wavelength of 222 nm by sigmoid fitting using Igor Pro 9 (WaveMetrics).
+
+Cryo-EM structural analysis
+All proteins were thawed immediately before tube formation on ice. Each sample was prepared in a 1.5-mL microtube using NaCl (+) buffer to adjust the concentration to 12.5 \( \mu \)M and the volume to 200 \( \mu \)L at 25 ± 1 °C. Incubation of the samples was carried out as described above for 24 h at 40 °C for the PuuE tube and 30 °C for the PuuE D-loop tube, and then the samples were provided for grid preparation. For unwinding the helical structures of the PuuE D-loop tube, additional incubation was carried out for 1 h on ice immediately before grid preparation.
+
+The PuuE D-loop tube sample prepared at 25 ± 1 °C was used at the original concentration. In contrast, the PuuE tube and the PuuE D-loop tube preincubated on ice were diluted to one-third and one-sixth of their original concentrations, respectively. Quantifoil R1.2/1.3 Cu 300 grids coated with a holey carbon film (Quantifoil) were treated for hydrophilisation using a JEC-3000FC Auto Fine Coater (JEOL) at 20 Pa and 10 mA for 30 s. Subsequently, 2.5-\( \mu \)L aliquots of the respective diluted samples were applied to the prepared grids. After blotting off excess solution, the grids were rapidly immersed in liquid ethane for vitrification using a Vitrobot Mark IV (Thermo Fisher Scientific). Vitrobot was set at 4 °C and 100% humidity for PuuE and PuuE D-loop samples preincubated on ice, and 25 °C and 100% humidity for PuuE D-loop sample prepared at 25 ± 1 °C.
+
+Sample screening and data acquisition were performed using a Glacios cryo-transmission electron microscope (Thermo Fisher Scientific) operated at an accelerated voltage of 200 kV, equipped with a Falcon4EC camera, at the Institute of Life and Medical Sciences, Kyoto University. Images were automatically acquired using the EPU software as movies with nominal magnifications and corresponding calibrated pixel sizes of 120,000x (1.22 Å/pixel) for the PuuE sample, and 150,000x (0.925 Å/pixel) for PuuE D-loop samples.
+
+Cryo-EM image processing
+Image analysis was conducted using similar workflows for each dataset of the three samples with the software package RELION 5.0beta\(^{53,54}\).
+For the PuuE tube sample, 4,346 movies were subjected to motion-correction using RELION’s algorithm, and the contrast transfer function (CTF) was estimated using CTFFIND4\(^{55}\). Tube coordinates were manually registered, and 709,722 segments were extracted with 3x binning into 260×260-pixel boxes (approximately 950×950 Å) with an inter-box spacing of 80 Å. The extracted segments were subjected to two rounds of 2D classification, and the resulting class averages were visually inspected to categorise the segments based on tube diameters. In parallel, an additional round of 2D classification with 10 classes was performed to assess the structural diversity of the tubes roughly. Each subset of segments, categorised by diameter, was then re-extracted and subjected to further 2D classifications to remove junk images. 3D classification with symmetry search was performed on each subset without imposing symmetry (C1). Finally, 3D refinement was carried out for the subsets with the three smallest diameters, applying \( C_4 \), \( C_5 \), and \( C_6 \) symmetries, respectively. The subsets with larger diameters exhibited significant heterogeneity and did not yield reliable 3D reconstructions.
+For the PuuE D-loop tube sample prepared at 25 ± 1 °C, 4,871 movies were motion-corrected and CTF-estimated using RELION and CTFFIND4, respectively. A total of 126,987 segments were extracted with 5x binning into 320×320-pixel or 640×640-pixel segmented boxes (1480×1480 or 2960×2960 Å) with an inter-box spacing of 60 Å. The extracted segments were subjected to six rounds of 2D classification, yielding class averages displaying single, double, and triple helical tube architectures.
+For the PuuE D-loop tube sample, preincubated on ice to unwind the helical structures, 4,346 movies were subjected to motion correction and CTF estimation. A total of 709,722 segments were extracted with 3x binning into 360×360-pixel boxes (approximately 1000×1000 Å) with an inter-box spacing of 80 Å. The extracted segments were subjected to two rounds of 2D classification, and the resulting class averages were visually inspected to categorise the segments based on tube diameters. In parallel, two rounds of 2D classification were performed to assess the structural diversity of the tubes. Each subset of segments, categorised by diameter, was re-extracted and subjected to further 2D classifications to remove junk images. 3D classification with symmetry search was performed on each subset without imposing symmetry (C1). During the 3D classification of the initially selected C5-tube subset, C6 tubes were found to be present and were subsequently combined with the C6-tube subset from the 2D classification. Finally, 3D refinement was carried out for the subsets with the four smallest diameters, applying \( C_3 \), \( C_4 \), \( C_5 \), and \( C_6 \) symmetries, respectively. As observed in the PuuE dataset, the subsets with larger diameters displayed considerable heterogeneity and failed to yield reliable 3D reconstructions. Detailed image processing workflows are depicted in Extended Data Figures. 6, 8, and 9.
+Fluorescent labelling
+Tube formation was conducted as described above under the optimised condition described in the manuscript. Labelling reaction was achieved by adding Alexa Fluor 488 succinimidyl ester dissolved in dimethyl sulfoxide (DMSO) to the tube solution at a final concentration of 0.7 mM. The reaction was then incubated at 25 ± 1 °C for 1 h with gentle shaking under shading. The excess dye was removed using NaCl (+) buffer with Microcon 300 centrifugal filter units (Merck) according to the manufacturer’s protocol four times. The labelled tubes were then stored under shading at 25 ± 1 °C until further experiments.
+
+Fluorescence microscopy
+An observation chamber was assembled by placing two double-sided tapes (thickness ~100 μm) onto a silicone-coated coverslip (24 × 36 mm², thickness No. 1; Matsunami) with another coverslip (18 × 18 mm², thickness No. 1; Matsunami) on top. To passivate the surface of the coverslips against nonspecific adhesion of protein, the chamber was filled with 10 mg mL⁻¹ of Pluronic F-127 (Sigma-Aldrich) dissolved in distilled water for more than 10 minutes at 25 °C. After washing out Pluronic F-127 solution with 5 chamber volumes of NaCl (+) buffer, the chamber was filled with TIRFM buffer (50 mM Tris-HCl pH 8.0, 100 mM NaCl, 0.5 mM EDTA, 0.2%(w/v) methylcellulose (1500 cP, Wako), 1 mM DTT, 2 mM Trolox). Next, the Alexa488-tube solution was diluted to 1/10 in NaCl (+) solution, and further diluted to 1/10 (final 1/100 dilution) in TIRFM buffer. Then, the diluted tube solution was perfused into the observation chamber and sealed by Valap to prevent flow. The fluorescence images of tube structures were acquired at intervals of 40 ms with an inverted microscope (IX-71, Olympus) equipped with a 60× objective lens (PlanApo NA 1.45 oil, Olympus), an EMCCD camera (iXon3, Andor Technology) and an excitation laser with the wavelength at 488 nm (OBIS 488-60-LS, COHERENT). All observations were performed at 25 ± 1 °C.
+
+Mechanical property analysis
+The persistence length of the tube structures was estimated as follows. First, the fluorescence images were converted to 8-bit images using the ImageJ function. Then, the skeletons of the tube structures were tracked using ImageJ plugin, JFilament³⁶. Distances between adjacent nodes composing the skeletons were set as 1 pixel. Next, the contour length (\( L \)) and end-to-end distance (\( R \)) of the tube structures at each frame were calculated using the coordinates of the nodes with custom-written Python scripts. The mean square of \( R \) (\( \langle R^2 \rangle \)) of each tube structure was calculated by averaging \( R^2 \) along 100–200 frames.
+\( \langle R^2 \rangle \) and \( L \) follow the following equation when the shape fluctuation is driven thermally³⁶.
+\[
+\langle R^2 \rangle = 4L_p^2 [2\exp(-L/2L_p) - 2 + L/L_p],
+\]
+where \( L_p \) is the persistence length of the tube structure. The \( L_p \) values of the tube structures were estimated by fitting this equation to the experimental data using ‘curve_fit’ function of Python package
+‘scipy.optimize’. \( L_p \) of actin filaments was estimated by the same analysis. Totally, 55 tube structures and 37 actin filaments were analysed.
+
+Molecular modelling
+All predicted protein structures were generated by AlphaFold 2.2 or 2.3 multimer-mode (DeepMind)15,16. Cartoon models of the proteins were drawn using PyMOL 2.5 (Schrödinger)57 and UCSF ChimeraX (UCSF RBVI and NIH)58. Isoelectric points of PuuE-M and PuuE-p were calculated from the basis of amino acid composition59. Surface hydrophobicity of PuuE was drawn using Color_h script (PyMOL Wiki) based on the hydrophobicity scale60.
+
+Data availability
+The cryo-EM structures have been deposited in the Electron Microscopy Data Bank (EMDB) with the following accession codes: EMD-60617, EMD-60618, and EMD-60619 for the PuuE tubes with C4, C5, and C6 symmetry, respectively; and EMD-60620, EMD-60621, EMD-60622, and EMD-60623 for the PuuE D-loop tubes with C3, C4, C5, and C6 symmetry, respectively.
+
+Acknowledgements
+This work was supported by JSPS KAKENHI (grant nos. 19H02832, 19K22253, and 21H05116 to Y. Suzuki; 21H05117 to Y. Suzuki and Y. Sugita; and 20K22628, 21J00530, and 22KJ1644 to M.N.), JST PRESTO (grant no. JPMJPR22A7 to Y. Suzuki and JPMJPR20ED to M.M.), Takeda Science Foundation to Y. Suzuki, Chubei Itoh Foundation to Y. Suzuki, and The Hakubi Center for Advanced Research to Y. Sugita, M.M., and Y. Suzuki.
+
+Author contributions
+Y. Suzuki directed the project. Y. Suzuki and M.N. conceived and designed the overall study. M.N. conducted experiment works with contributions from Y. Suzuki, Y. Sugita, and Y.Y.. Y. Sugita and M.N. performed cryo-EM data collection and analysed data. Y.Y. conducted TIRFM experiments, and Y.Y. and M.M. analysed mechanical properties. M.N. and Y. Suzuki wrote the manuscript with contributions from Y. Sugita, Y.Y., and M.M.
+
+Competing interest declaration
+Y. Suzuki and M.N. are inventors of a provisional patent submitted by Kyoto University for ‘Protein Assembly Structure’.
+Additional information
+Supplementary Information is available for this paper.
+Correspondence and requests for materials should be addressed to Yuta Suzuki.
+Tel: +81-75-753-9766
+E-mail address: suzuki.yuta.2m@kyoto-u.ac.jp
+Extended Data Fig. 1. | AF2 prediction of PuuE-M and PuuE-p. a, Fifty prediction models overlapped for PuuE-M (top) and PuuE-p (bottom). Peptide parts, M3L2 and p66α, are indicated with a red box. b, Predicted local distance difference test plots for the most reliable prediction models for PuuE-M (top) and PuuE-p (bottom). Arrows indicate the N-terminal region of M3L2 and p66α. For these regions, PuuE-M has a lower predictive reliability than does PuuE-p, suggesting that the structure may be more flexible. c, The most reliable prediction model for PuuE-p. The region from the C-terminus of PuuE to the N-terminus of p66α (i.e. \(^{31}\mathrm{H}\mathrm{P}\mathrm{Y}\mathrm{T}\mathrm{P}\mathrm{E}^{318}\)) is depicted by a stick model. The two Pro residues highlighted in red are thought to be responsible for the rigidity of the PuuE-p structure. Because of the rigidity of PuuE-p, the final product of the mixture was predicted to be a tube, as shown in Fig. 1d.
+Extended Data Fig. 2. | nsTEM characterisation of PuuE-M, PuuE-p, and the mixture for PuuE-M and PuuE-p. a, 12.5 μM PuuE-M or b, 12.5 μM PuuE-p in NaCl (+) buffer was incubated at 40 °C for 24 h. Scale bars, 200 nm (white), 50 nm (black). c, Dependency of PuuE tube assemblies on protein concentration. 250 nM (top), 2.5 μM (middle), and 12.5 μM (bottom) of PuuE-M and PuuE-p each in NaCl (+) buffer was incubated at 40 °C for 24 h and imaged by nsTEM. The tube structure observed in the nsTEM images was flexible as it was curved and collapsed. Scale bars, 1 μm (white), 50 nm (black).
+Extended Data Fig. 3. | Time dependence of PuuE tube assemblies and their stability over time. a, 12.5 μM of PuuE-M and PuuE-p each in NaCl (+) buffer was incubated at 40 °C for indicated time points and imaged via nsTEM. b, After 24 h of tube formation, the sample was kept at 25 ± 1 °C for the indicated time and imaged using nsTEM. Tube structures remained unchanged after 2 weeks and even after 1 month, suggesting stability. Scale bars, 1 μm.
+Extended Data Fig. 4. | Temperature dependence of PuuE tube assemblies and determination of \( T_m \) for PuuE-M and PuuE-p. a, 12.5 \( \mu \)M of PuuE-M and PuuE-p each in NaCl (+) buffer was incubated at the indicated temperature for 24 h and imaged via nsTEM. Scale bars, 1 \( \mu \)m. b, c, \( T_m \) measurements using CD for PuuE-M (b) and PuuE-p (c). 2.5 \( \mu \)M of PuuE-M or PuuE-p in NaCl (+) buffer was incubated from 25 to 55 \( ^\circ \)C with temperature change of 1 \( ^\circ \)C/min. Left panel, overall CD spectra; right panel, thermal denaturation profiles.
+Extended Data Fig. 5. | Salt concentration dependence and reversibility of PuuE tube assemblies. a, Left, 12.5 μM of PuuE-M and PuuE-p each in NaCl (+) buffer was incubated at 40 °C for 24 h with indicated NaCl concentration and imaged via nsTEM. Right: diagram of salt concentration effects described in the main text. b, Additional images in Fig. 2d prove the reversibility of tubular assemblies. These images were used for statistical analysis of tube length, as shown in Fig. 2e. Scale bars, 1 μm (white).
+Movies: 4,346 movies
+Motion correction
+CTF Estimation (ctffind4): 4,316 micrographs
+Manual pick: 43,614 helices
+Helical segments extraction: 709,722 segments
+
+2D classifications (2 rounds): 562,531 segments
+2D classification for rough assessment of the class distributions: 562,531 segments
+
+C₄ tube: 2D classifications (2 rounds): 51,590 segments
+3D classification (C₁): 12,052 segments
+3D Refinement (C₂): 12,052 segments
+Post-processing
+
+Side view
+Top view
+Rise (Å)   81.1   81.2   79.0   79.8
+Rotation (°)   50.2   50.9   48.6   49.8
+Diameter (Å)   292   304   300   286
+
+C₅ tube: 2D classifications (2 rounds): 44,868 segments
+3D classification (C₁): 12,572 segments
+3D Refinement (C₂): 12,572 segments
+Post-processing
+
+Side view
+Top view
+Rise (Å)   88.5   78.4   -   78.3
+Rotation (°)   41.1   38.1   -   38.1
+Diameter (Å)   368   356   -   342
+
+C₆ tube: 2D classification (1 round): 117,636 segments
+3D classification (C₁): 39,841 segments
+3D Refinement (C₂): 39,841 segments
+Post-processing
+
+Side view
+Top view
+Rise (Å)   77.4   77.5   -   77.4
+Rotation (°)   31.1   31.3   -   31.3
+Diameter (Å)   400   420   -   400
+
+Rise (Å)   77.7
+Rotation (°)   32.6
+
+Extended Data Fig. 6. | Cryo-EM image processing workflow of the PuuE tubes. Flowchart illustrating the image processing steps. Scale bars: 100 nm (white), 250 Å (black). Gold-standard Fourier shell correlation (FSC) curve of the independently refined half maps indicating a global resolution at the 0.143 threshold.
+Extended Data Fig. 7. D-loop grafting to emulate actin filaments. a, Surface hydrophobicity calculation for PuuE. D-loop was grafted into the ‘back’ side of PuuE owing to the hydrophobic nature of a prominent indentation. b, \( T_m \) measurement of PuuE(D-loop)-M via CD. 2.5 \( \mu \)M of PuuE(D-loop)-M in NaCl (+) buffer was incubated from 25 to 55 °C with temperature change of 1 °C/min. Top: overall CD spectra; bottom: thermal denaturation profiles, respectively. c, 12.5 \( \mu \)M of PuuE(D-loop)-M and PuuE-p in NaCl (+) buffer were incubated at 30 °C for 24 h and imaged using nsTEM. A novel helical pattern of two or three intertwined tubes was clearly observed. Flexibility was also noted when curved structures were observed. Scale bars, 1 \( \mu \)m (white), 100 nm (black). d, Additional images for reversibility of tube formation depends on temperature changes in Fig. 4c. For this observation, we focused on the presence of tube structures with helical conformations. After 1 h at 0 °C, there were no such structures observed via nsTEM.
+Movies: 4,871 movies
+Motion correction
+CTF Estimation (ctffind4): 4,871 micrographs
+Manual pick: 28,582 helices
+Helical segments extraction: 126,987 segments
+
+2D classifications (5 rounds) with 1480x1480-Å segments: 104,748 segments
+
+Single tubes    Double tubes    Triple tubes
+
+2D classifications (6 rounds) with 2960x2960-Å segments: 9,989 segments
+
+Single tubes
+Double tubes
+Triple tubes
+
+Extended Data Fig. 8. | Cryo-EM image processing workflow of PuuE D-loop tubes prepared at 25 ± 1 °C. Flowchart illustrating the image processing steps. Scale bars: 100 nm (white), 500 Å (black).
+Movies: 5,152 movies
+Motion correction
+CTF Estimation (ctffind4): 4,751 micrographs
+Manual pick: 10,308 helices
+Helical segments extraction: 397,778 segments
+
+2D classification: 562,531 segments
+2D classifications (2 rounds) for rough assessment of the class distributions: 28,692 segments
+
+C₃ tube: 2D classifications (2 rounds): 4,112 segments
+3D classification (C₁): 2,675 segments
+Side view
+Top view
+Rise (Å)    82.0
+Rotation (°)   72.7
+Diameter (Å)  236  236  232
+3D Refinement (C₃): 2,675 segments
+Post-processing
+Rise (Å)    81.8
+Rotation (°)   72.5
+Resolution (Å)
+
+C₄ tube: 2D classification: 5,703 segments
+3D classification (C₁): 3,262 segments
+Side view
+Top view
+Rise (Å)    77.7  77.8
+Rotation (°)   50.3  51.2
+Diameter (Å)  284  290  320
+3D Refinement (C₄): 3,262 segments
+Post-processing
+Rise (Å)    78.0
+Rotation (°)   50.3
+Resolution (Å)
+
+C₅ tube: 2D classification: 4,017 segments
+3D classification (C₁): 2,998 segments
+Side view
+Top view
+Rise (Å)    75.2  76.0
+Rotation (°)   31.8  38.5
+Diameter (Å)  370  340
+3D Refinement (C₅): 2,998 segments
+Post-processing
+Rise (Å)    76.4
+Rotation (°)   38.6
+Resolution (Å)
+
+C₆ tube: 3D classification (C₁): 1,291 segments
+Side view
+Top view
+Rise (Å)    75.6
+Rotation (°)   31.8
+Diameter (Å)  380
+3D Refinement (C₆): 1,291 segments
+Post-processing
+Rise (Å)    75.8
+Rotation (°)   31.6
+Resolution (Å)
+
+Extended Data Fig. 9. | Cryo-EM image processing workflow of PuuE D-loop tubes preincubated on ice to unwind the helical structures. Flowchart illustrating the image processing steps. Scale bars: 100 nm (white), 250 Å (black). Gold-standard Fourier shell correlation (FSC) curve of the independently refined half maps indicating a global resolution at the 0.143 threshold.
+PuuE tube
+
+<table>
+  <tr>
+    <th></th>
+    <th>#1 \( C_4 \) tube<br>(EMD-60617)</th>
+    <th>#2 \( C_5 \) tube<br>(EMD-60618)</th>
+    <th>#3 \( C_6 \) tube<br>(EMD-60619)</th>
+  </tr>
+  <tr>
+    <th colspan="4">Data collection and processing</th>
+  </tr>
+  <tr>
+    <td>Magnification</td>
+    <td>120,000</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Voltage (kV)</td>
+    <td>200</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Electron exposure (e-/Ų)</td>
+    <td>40</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Defocus range (μm)</td>
+    <td>-0.8 to -1.6</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Pixel size (Å)</td>
+    <td>1.22</td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Symmetry imposed</td>
+    <td>\( C_4 \) helical</td>
+    <td>\( C_5 \) helical</td>
+    <td>\( C_6 \) helical</td>
+  </tr>
+  <tr>
+    <td>Initial helical segments (no.)</td>
+    <td>709,722</td>
+    <td>709,722</td>
+    <td>709,722</td>
+  </tr>
+  <tr>
+    <td>Final helical segments (no.)</td>
+    <td>12,052</td>
+    <td>12,572</td>
+    <td>39,841</td>
+  </tr>
+  <tr>
+    <td>Map resolution (Å)</td>
+    <td>11.3</td>
+    <td>20.6</td>
+    <td>17.5</td>
+  </tr>
+  <tr>
+    <td>FSC threshold</td>
+    <td>0.143</td>
+    <td>0.143</td>
+    <td>0.143</td>
+  </tr>
+</table>
+
+2D analysis of the PuuE D-loop tube prepared at 25 ± 1 °C
+
+<table>
+  <tr>
+    <th colspan="2">#1 Tubes</th>
+  </tr>
+  <tr>
+    <th colspan="2">Data collection and processing</th>
+  </tr>
+  <tr>
+    <td>Magnification</td>
+    <td>150,000</td>
+  </tr>
+  <tr>
+    <td>Voltage (kV)</td>
+    <td>200</td>
+  </tr>
+  <tr>
+    <td>Electron exposure (e-/Ų)</td>
+    <td>40</td>
+  </tr>
+  <tr>
+    <td>Defocus range (μm)</td>
+    <td>-0.8 to -1.6</td>
+  </tr>
+  <tr>
+    <td>Pixel size (Å)</td>
+    <td>0.925</td>
+  </tr>
+  <tr>
+    <td>Symmetry imposed</td>
+    <td>No</td>
+  </tr>
+  <tr>
+    <td>Initial helical segments (no.)</td>
+    <td>126,987</td>
+  </tr>
+  <tr>
+    <td>Final helical segments (no.)</td>
+    <td>104,748</td>
+  </tr>
+</table>
+
+PuuE D-loop tube preincubated on ice to unwind the helical structures
+
+<table>
+  <tr>
+    <th></th>
+    <th>#1 \( C_3 \) tube<br>(EMD-60620)</th>
+    <th>#2 \( C_4 \) tube<br>(EMD-60621)</th>
+    <th>#3 \( C_5 \) tube<br>(EMD-60622)</th>
+    <th>#4 \( C_6 \) tube<br>(EMD-60623)</th>
+  </tr>
+  <tr>
+    <th colspan="5">Data collection and processing</th>
+  </tr>
+  <tr>
+    <td>Magnification</td>
+    <td>150,000</td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Voltage (kV)</td>
+    <td>200</td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Electron exposure (e-/Ų)</td>
+    <td>40</td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Defocus range (μm)</td>
+    <td>-0.8 to -1.6</td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Pixel size (Å)</td>
+    <td>0.925</td>
+    <td></td>
+    <td></td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Symmetry imposed</td>
+    <td>\( C_3 \) helical</td>
+    <td>\( C_4 \) helical</td>
+    <td>\( C_5 \) helical</td>
+    <td>\( C_6 \) helical</td>
+  </tr>
+  <tr>
+    <td>Initial helical segments (no.)</td>
+    <td>397,778</td>
+    <td>397,778</td>
+    <td>397,778</td>
+    <td>397,778</td>
+  </tr>
+  <tr>
+    <td>Final helical segments (no.)</td>
+    <td>2,675</td>
+    <td>3,262</td>
+    <td>2,998</td>
+    <td>1,291</td>
+  </tr>
+  <tr>
+    <td>Map resolution (Å)</td>
+    <td>9.7</td>
+    <td>14.6</td>
+    <td>18.2</td>
+    <td>26.0</td>
+  </tr>
+  <tr>
+    <td>FSC threshold</td>
+    <td>0.143</td>
+    <td>0.143</td>
+    <td>0.143</td>
+    <td>0.143</td>
+  </tr>
+</table>
+
+Extended Data Table 1. | Cryo-EM data collection, refinement, and validation statistics
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformation.pdf
+• Supplementarymovie1.mov
+• Supplementarymovie2.mov
+• Supplementarymovie3.mov
+• Supplementarymovie4.mov

078ee3115bb7f9caf7ff08bd41325e1b3d5bc1c68c6da418cda25d198e700819/peer_review/peer_review.md

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+Peer Review File
+
+Optical Neural Engine for Solving Scientific Partial Differential Equations
+
+Corresponding Author: Dr Weilu Gao
+
+This manuscript has been previously reviewed at another journal. This document only contains information relating to versions considered at Nature Communications.
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #4
+
+(Remarks to the Author)
+In this manuscript, Tang et al. present a photonic platform called optical neural engine. I thinks this work is novel and very interesting. Hence, I would like to recommend the publication of this manuscript on Nature Communications. Below are a few additional minor comments:
+
+(1) What nonlinear functions are used in the demonstrated architecture (Fig. 1a)? Please discuss about it.
+(2) In Fig. 3e, it looks like the relative error figure shows a few sharp lines while there are no such lines in the absolute error. Can authors comment on the reason?
+(3) In the third paragraph of page 14, the authors mentioned the multiplexing can be utilized to handle high-dimensional problems. Adding a few references would be beneficial for the community for the future works.
+(4) In the first paragraph of page 6, the used symbol of big O notation has different format from those in the experimental demonstration section. Please revise it.
+(5) What's the output power of laser diode in the experiment?
+
+(Remarks on code availability)
+I have downloaded the codes and check them. The codes are well organized and appears working.
+
+Reviewer #5
+
+(Remarks to the Author)
+This paper introduces and experimentally demonstrates an optical neural network hardware architecture called ONE, consisting of a combination of diffractive optical neural networks and fully connected crossbar optical neural networks, for the solution to scientific problems governed by partial differential equations. The paper provides a compelling argument for the utility of their hardware architecture as an alternative to digital approaches and reasonably convincing experimental data backing their claims. The paper is well-written, and the technical level is appropriate for the journal. However, there are a few concerns. I recommend minor revisions addressing the following comments.
+
+1. The claim in the abstract “Although optical systems offer high-throughput and energy efficient ML hardware, there is no demonstration of utilizing them for solving PDEs” and related claims in the text are wrong. Please see the following works. I would recommend the authors amend their claims.
+Y. Zhao et al. “Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training” arXiv:2401.00413 [cs.LG], 2023. https://arxiv.org/abs/2401.00413.
+Y. Zhao et al. “Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Training” arXiv:2501.00742 [cs.LG], 2025. https://arxiv.org/abs/2501.00742.
+2. “Specifically, we performed quantitative scaling analyses of energy consumption and throughput of the optically implemented ONE architecture and electronically implemented FNO, with the latter having shown the best prediction and speed performance over other models”
+Is "latter" a typo?
+
+3. The energy scaling analysis on page 14 does not account for meeting the photodetector/camera minimum signal-to-noise ratio which may be at risk for very large diffractive optical neural network systems without also scaling laser power. This should account for optical fan-out, any worst-case insertion (transmissive) losses, and any amplification that may need to be done with increased depth to remain within dynamic range of the SLM. Can the authors comment on their expectations for these practical scaling considerations?
+
+4. I would recommend the authors perform an additional baseline comparing the performance of training only the CNN from Fig. 5 on the Darcy Flow and Navier Stokes datasets, in comparison to the current case that uses the experimental hardware in tandem with the postprocessing CNN. If the CNN has similar performance on its own, it will seem pointless to adopt the tandem experimental system. Furthermore, I would recommend the authors amend their energy/speed analysis to account for any digital post-processing that needs to be done. If the authors disagree, alternatively, please explain how experimental systems much larger than theirs will not also require digital error corrections.
+
+5. Can the authors clarify whether the full ONE architecture (DONN + XBAR) was implemented in their experiments of Fig. 5, or only the DONN piece of the architecture? It appears that this is the case as mentioned in Methods, but it was not completely clear in the main text. Furthermore, can the authors clearly label simulated results and experimental results in all figures, particularly Fig. 5? The authors place most emphasis in this paper on simulations of ONE performance (which, mathematically speaking, is essentially just a 2D FNO architecture) rather than experiments; this fact should be made clear to the reader.
+
+(Remarks on code availability)
+The code is of high quality for reproducing the inference results of the authors’ model.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #4
+
+(Remarks to the Author)
+The author has answered all my questions very clearly. I have no other comments. I recommend this paper to be published in Nature Communications
+
+(Remarks on code availability)
+The code is correct. I have no comments on it.
+
+Reviewer #5
+
+(Remarks to the Author)
+The authors have addressed and satisfied all reviewer comments. The work is significant and impressive. I recommend publication with no further changes.
+
+(Remarks on code availability)
+The code is of high-quality to reproduce the authors’ model inference results.
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+We thank all referees for their careful review of our manuscript and thoughtful comments. Below we address each of the questions/comments in detail:
+
+-------------------------------------------------------------
+Response to Reviewer #4
+-------------------------------------------------------------
+
+Reviewer #4’s comment #1: What nonlinear functions are used in the demonstrated architecture (Fig. 1a)? Please discuss about it.
+
+Response to comment #1: The nonlinear activation function we used is the tanh function. In the revised main text, we have included this information. Detailed changes are:
+-------------------------------------------------------------
+Location: Main text, Line 778
+Changed texts in red color: The nonlinear function was tanh.
+-------------------------------------------------------------
+
+Reviewer #4’s comment #2: In Fig. 3e, it looks like the relative error figure shows a few sharp lines while there are no such lines in the absolute error. Can authors comment on the reason?
+
+Response to comment #2: We thank Reviewer #4 for this comment. The relative errors shown in Fig. 3e are defined as \( \frac{|Predicted\ Value - Ground\ Truth|}{Ground\ Truth} = \left| \frac{Absolute\ Error}{Ground\ Truth} \right| \), whereas the absolute errors are defined as the absolute value difference between predicted values and ground truth values. Hence, the sharp lines originate from the division of small ground truth values.
+
+In the revised main text, we have clarified their differences when these two quantities are first referenced. Detailed changes are:
+-------------------------------------------------------------
+Location: Main text, Line 257 - 259
+Changed texts in red color: the absolute error between the ground truth and prediction, and the relative error defined as the ratio of the absolute error over the ground truth
+
+Location: Main text, Line 366 - 369
+Changed texts in red color: Note that the sharp lines in the relative error plot of Fig. 3e is due to the division of small ground truth values.
+-------------------------------------------------------------
+
+Reviewer #4’s comment #3: In the third paragraph of page 14, the authors mentioned the multiplexing can be utilized to handle high-dimensional problems. Adding a few references would be beneficial for the community for the future works.
+
+Response to comment #3: We thank Reviewer #4 for this comment. In the revised manuscript, we have added the following references about different multiplexing methods:
+(1) Wavelength multiplexing: Duan, Zhengyang, Chen, Hang and Lin, Xing. "Optical multi-task learning using multi-wavelength diffractive deep neural networks" Nanophotonics, vol. 12, no. 5, 2023, pp. 893-903. https://doi.org/10.1515/nanoph-2022-0615
+(2) Path multiplexing: Li, Y., Chen, R., Sensale-Rodriguez, B. et al. Real-time multi-task diffractive deep neural networks via hardware-software co-design. Sci Rep 11, 11013 (2021). https://doi.org/10.1038/s41598-021-90221-7.
+(3) Polarization multiplexing: Luo, X., Hu, Y., Ou, X. et al. Metasurface-enabled on-chip multiplexed diffractive neural networks in the visible. Light Sci Appl 11, 158 (2022). https://doi.org/10.1038/s41377-022-00844-2
+Detailed changes are:
+Location: Main text, Line 667 – 668
+
+References: [44], [45], [46]
+
+Reviewer #4’s comment #4: In the first paragraph of page 6, the used symbol of big O notation has different format from those in the experimental demonstration section. Please revise it.
+
+Response to comment #4: In the revised main text, we have revised the symbol notation. Detailed changes are:
+
+Location: Main text, Line 255
+Changed texts in red color: \(O(1)\)
+
+Reviewer #4’s comment #5: What’s the output power of laser diode in the experiment?
+
+Response to comment #5: The output power of the laser diode used in the experiment is 4.5 mW. In the revised main text, we have included this information. Detailed changes are:
+
+Location: Main text, Line 872
+Changed texts in red color: The laser diode with a center wavelength of 532 nm and 4.5 mW power (CPS532 from Thorlabs, Inc.) was used as a source.
+Response to Reviewer #5
+
+Reviewer #5’s comment #1: The claim in the abstract “Although optical systems offer high-throughput and energy efficient ML hardware, there is no demonstration of utilizing them for solving PDEs” and related claims in the text are wrong. Please see the following works. I would recommend the authors amend their claims.
+Y. Zhao et al. “Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training” arXiv:2401.00413 [cs.LG], 2023. https://arxiv.org/abs/2401.00413.
+Y. Zhao et al. “Experimental Demonstration of an Optical Neural PDE Solver via On-Chip PINN Training” arXiv:2501.00742 [cs.LG], 2025. https://arxiv.org/abs/2501.00742.
+
+Response to comment #1: We thank Reviewer #5 for pointing out these prior works. These papers primarily explore the use of optical matrix-vector multipliers (MVMs) within the conventional physics-informed neural network (PINN) framework. The first preprint avoids backpropagation by using zeroth-order gradient estimation and proposes to use tensor-train decomposition to reduce the number of optical components in optical MVM hardware. The second preprint presents a small-scale (\(1 \times 4\)) experimental setup based on microring resonators to solve a basic heat equation with an analytical solution (\(\sin(\pi x)e^{-t}\)). In contrast, our work presents a fundamentally different optical neural engine (ONE) architecture that combines diffractive optical neural networks (DONNs) and optical MVMs, moving beyond the traditional PINN framework. Our ONE architecture enables direct optical representation learning for solving complex and coupled multiphysics PDEs with high performance. Furthermore, our experimental demonstrations of DONNs are at a substantially larger scale (~100×100), demonstrating the feasible architecture scalability using free-space optics for solving PDEs of greater complexity than those considered in prior works.
+
+In the revised main text, we have amended our claims as “the demonstration of utilizing optical systems for solving PDEs is limited” in the abstract and introduction and cited these prior works. Detailed major changes are:
+
+Location: Main text, Line 31
+Changed texts in red color: their demonstration for solving PDEs is limited.
+
+Location: Main text, Line 78 – 79
+Changed texts in red color: However, the deployment of optical computing systems is in small scales for basic PDEs with limited performance [24,25].
+
+Reviewer #5’s comment #2: “Specifically, we performed quantitative scaling analyses of energy consumption and throughput of the optically implemented ONE architecture and electronically implemented FNO, with the latter having shown the best prediction and speed performance over other models” Is “latter” a typo?
+
+Response to comment #2: We thank Reviewer #5 for this comment. What we would like to state is: “the Fourier Neural Operator (FNO) model has shown the best prediction and speed performance over other models on electronic hardware, as shown in Fig. 2c and Ref. [26]”.
+
+In the revised main text, we have revised this sentence to make this point clearer. Detailed changes are:
+
+Location: Main text, Line 620 – 621
+Changed texts in red color: The FNO model has shown the best prediction and speed performance over other models on electronic hardware, as shown in Fig. 2c and Ref. [26].
+Reviewer #5’s comment #3: The energy scaling analysis on page 14 does not account for meeting the photodetector/camera minimum signal-to-noise ratio which may be at risk for very large diffractive optical neural network systems without also scaling laser power. This should account for optical fan-out, any worst-case insertion (transmissive) losses, and any amplification that may need to be done with increased depth to remain within the dynamic range of the SLM. Can the authors comment on their expectations for these practical scaling considerations?
+
+Response to comment #3: We thank Reviewer #5 for this insightful comment. We agree with Reviewer #5. When the system size of a diffractive optical neural network (DONN) system scales up, the incident laser power/energy also needs to scale up to account for the camera signal-to-noise ratio. Let’s assume the 2D data to process has a dimension of \( N \times N \), and the camera has the same dimension. If \( E_{det} \) represents the minimum energy needed for each pixel on the camera, \( T_m \) represents the worst-case transmission in modulators, and \( \eta_{fan} \) is the efficiency of the fan-out optics, the total output laser energy would be \( N^2 \eta_{fan} T_m E_{det} \). Hence, the scaling law of laser energy (or power) is also dependent on \( N^2 \). As a result, the conclusion that our optically implemented optical neural engine architecture has a scaling advantage by accelerating \( O(N^3) \) multiplication-accumulate operations still holds. As a side note, practically, when the system scales up, the needed laser power can be implemented by combining multiple low-power lasers if a single high-power laser is not accessible.
+
+In the revised main text, we have summarized previous discussions. Detailed changes are:
+-------------------------------------------------------------
+Location: Main text, Line 635 – 643
+Changed texts in red color: Further, in the optical implementation, the energy consumption of the light source scales with the system size to account for detector signal-to-noise ratios. Specifically, if we assume the detector array has the same \( N \times N \) size as the 2D data, \( E_{det} \) represents the minimum energy needed for each pixel on the detector array, \( T_m \) denotes the worst-case transmission in modulators, and \( \eta_{fan} \) is the efficiency of the fan-out optics, the light source energy consumption is proportional to \( N^2 \eta_{fan} T_m E_{det} \) or \( O(N^2) \). Practically, when the system scales up, the needed light source power can be achieved by combining multiple low-power sources if a single high-power source is not accessible.
+-------------------------------------------------------------
+
+Reviewer #5’s comment #4: I would recommend the authors perform an additional baseline comparing the performance of training only the CNN from Fig. 5 on the Darcy Flow and Navier Stokes datasets, in comparison to the current case that uses the experimental hardware in tandem with the postprocessing CNN. If the CNN has similar performance on its own, it will seem pointless to adopt the tandem experimental system. Furthermore, I would recommend the authors amend their energy/speed analysis to account for any digital post-processing that needs to be done. If the authors disagree, alternatively, please explain how experimental systems much larger than theirs will not also require digital error corrections.
+
+Response to comment #4: We thank Reviewer #5 for this constructive comment. Based on Reviewer #5’s suggestion, we have performed additional baseline calculations by employing only post-processing CNNs without diffractive optical neural networks in the optical neural engine (ONE) architecture for the Darcy flow and Navier Stokes datasets. Their loss curves are shown in Fig. R1a and R1b, respectively. We can observe that losses for the CNN baseline architecture are very high in both datasets, showing very poor performance. This comparison clearly highlights the necessity and significance of diffractive optical neural networks in the ONE architecture.
+Fig. R1: Loss curves for the ONE architecture and CNN baseline architecture (a) for solving the Darcy flow equation under different resolutions and (b) for solving the Navier-Stokes equation.
+
+Regarding the post-processing circuits, we would like to argue that they could be removed. First, the reason why we introduce the lightweight post-processing CNN is based on one suggestion of a previous reviewer. The excellent agreement between post-processed experimental results and calculation model results indicates that our experimental results are indeed close to calculation results and can be corrected with relatively lightweight CNN. In future large-scale systems, there are multiple ways to reduce the discrepancy between experiments and calculations from both hardware and software perspectives, which are worth our future studies.
+
+From the hardware perspective, a few reasons contributing to the observed discrepancy include laser speckles and detector noise. For example, incorporating moving diffusers in optical systems can remove speckles (e.g., Serge Lowenthal and Denis Joyeux, "Speckle Removal by a Slowly Moving Diffuser Associated with a Motionless Diffuser," J. Opt. Soc. Am. 61, 847-851 (1971)) and employing high-end cameras with high signal-to-noise ratios (e.g., Electron Multiplying Charge-Coupled Device) can improve detection noise performance.
+
+From the software perspective, the observed discrepancy is because the physical model used for training cannot fully capture experimental variations. As already mentioned in the manuscript, this can be mitigated using a physics-aware training approach by incorporating loss functions calculated from experimental results for gradient calculations and hardware reconfiguration, as demonstrated in Ref. [20,38,41] of the revised manuscript. Note that this approach is a training process, only requiring one-time or occasional efforts. This will not affect our energy/speed analysis for inference.
+
+In the revised main text, we have summarized previous discussions and added Fig. R1 in the Supplementary Information (SI) document. Detailed changes are:
+
+-------------------------------------------------------------
+Location: Main text, Line 551 – 564
+Changed texts in red color: In addition, we trained a baseline architecture by replacing DONN kernels in the architecture shown in Fig. 1a with lightweight post-processing CNN models for solving Darcy flow equations under different resolutions and the Navier-Stokes equation (Supplementary Fig. 8). The losses for the CNN baseline architecture are high in both datasets with poor performance when compared to the results obtained from the ONE architecture with DONN kernels, highlighting the necessity and significance of DONN systems and the limited capability of CNN models.
+
+Instead of post-processing, model-experiment discrepancies can be mitigated through the improvement of system hardware and novel training approaches in future implementation. From the hardware perspective, for example, incorporating moving diffusers in optical systems to remove speckles [40] and employing high signal-to-noise ratio cameras can reduce discrepancies. Moreover, from the training perspective, …
+Added: Supplementary Fig. 8
+
+Reviewer #5’s comment #5: Can the authors clarify whether the full ONE architecture (DONN + XBAR) was implemented in their experiments of Fig. 5, or only the DONN piece of the architecture? It appears that this is the case as mentioned in Methods, but it was not completely clear in the main text. Furthermore, can the authors clearly label simulated results and experimental results in all figures, particularly Fig. 5? The authors place most emphasis in this paper on simulations of ONE performance (which, mathematically speaking, is essentially just a 2D FNO architecture) rather than experiments; this fact should be made clear to the reader.
+
+Response to comment #5: In Fig. 5, we experimentally demonstrated only the DONN piece of the architecture. However, in our prior work, we have experimentally demonstrated a free-space optical XBAR system (see the paper: Fan, Jichao, Yingheng Tang, and Weilu Gao. "Universal Approach for Calibrating Large-Scale Electronic and Photonic Crossbar Arrays." Advanced Intelligent Systems 5.10 (2023): 2300147). The experimental system output is represented by an error histogram of multiplication results (e.g., see Fig. 5a of the previous paper). Hence, in Fig. 5e, we evaluated the performance of the ONE architecture under different histograms to represent different experimental XBAR system performances (Supplementary Information Fig. 7), and the results of Fig. 5e are indeed experiment-relevant. In addition, we agree with Reviewer #5 that all figures should be clearly labeled to indicate whether the results are experimental or simulated.
+
+In the revised main text, we have clarified the experimental demonstration and clearly labeled all figures. Detailed changes are:
+
+Location: Main text, Line 576 – 581
+Changed texts in red color: Note that we did not experimentally construct an XBAR system for the ONE architecture. Instead, we added random Gaussian noise with zero mean and varying standard deviation (Std) to the values obtained from matrix multiplications in models to represent experimental hardware noise, such as shot noise in photodetectors as shown in our prior experimental demonstration of a free-space XBAR system [42].
+
+Location: Main text, Figure 2 Caption
+Changed texts in red color: Simulation results of solving Darcy flow and magnetostatic Poisson's equations.
+
+Location: Main text, Figure 3 Caption
+Changed texts in red color: Simulation results of solving time-dependent Navier-Stokes and Maxwell's equations.
+
+Location: Main text, Figure 4 Caption
+Changed texts in red color: Simulation results of solving multiphysics PDEs.
+-------------------------------------------------------------
+Response to Reviewer #4
+-------------------------------------------------------------
+
+Reviewer #4’s comment #1: The author has answered all my questions very clearly. I have no other comments. I recommend this paper to be published in Nature Communications.
+
+Response to comment #1: We thank the reviewer for the nice comment.
+
+-------------------------------------------------------------
+Response to Reviewer #5
+-------------------------------------------------------------
+
+Reviewer #5’s comment #1: The authors have addressed and satisfied all reviewer comments. The work is significant and impressive. I recommend publication with no further changes.
+
+Response to comment #1: We thank the reviewer for the nice comment.

078ee3115bb7f9caf7ff08bd41325e1b3d5bc1c68c6da418cda25d198e700819/preprint/preprint.md

@@ -0,0 +1,375 @@
+Optical Neural Engine for Solving Scientific Partial Differential Equations
+
+Weilu Gao
+weilu.gao@utah.edu
+
+The University of Utah   https://orcid.org/0000-0003-3139-034X
+Yingheng Tang
+Lawrence Berkeley National Laboratory
+Ruiyang Chen
+The University of Utah   https://orcid.org/0000-0002-1538-1702
+Minhan Lou
+The University of Utah
+Jichao Fan
+The University of Utah
+Cunxi Yu
+University of Maryland, College Park
+Andy Nonaka
+Lawrence Berkeley National Laboratory
+Zhi Yao
+Lawrence Berkeley National Laboratory
+
+Article
+
+Keywords:
+
+Posted Date: September 30th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-5061922/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+Version of Record: A version of this preprint was published at Nature Communications on May 17th, 2025. See the published version at https://doi.org/10.1038/s41467-025-59847-3.
+Optical Neural Engine for Solving Scientific Partial Differential Equations
+
+Yingheng Tang$^{1*†}$, Ruiyang Chen$^{2†}$, Minhan Lou$^2$, Jichao Fan$^2$, Cunxi Yu$^3$, Andy Nonaka$^1$, Zhi (Jackie) Yao$^{1*}$, Weilu Gao$^{2*}$
+
+$^1$Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.
+$^2$Department of Electrical and Computer Engineering, The University of Utah, Salt Lake City, UT 84112, USA.
+$^3$Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742, USA.
+
+*Corresponding author(s). E-mail(s): ytang4@lbl.gov; jackie_zhiyao@lbl.gov; weilu.gao@utah.edu;
+†These authors contribute equally
+
+Abstract
+Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, there is no demonstration of utilizing them for solving PDEs. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.
+Introduction
+
+Partial differential equations (PDEs) derived from physical laws have been a powerful and faithful computational tool to accelerate the exploration and validation of scientific hypotheses instead of performing expensive and time-consuming real-world experiments [1]. Hence, numerically solving PDEs is essential for scientific research and development in nearly every scientific domain. For example, the interaction of electromagnetic waves with materials and engineered structures in broad applications such as communication, imaging, sensing, and quantum technologies is governed by Maxwell’s equations [2]; automotive and flight aerodynamics for designing and manufacturing road vehicles and airplanes is determined by Navier-Stokes equation [3]; the Earth system including temperature, atmosphere, and ice sheets for understanding climate change and making policies is also described with a series of PDEs [4]. However, current numerical simulation methods to solve PDEs, such as finite difference/volume methods to solve Maxwell’s and the Navier-Stokes equations, are costly in computing time and resources.
+
+Machine learning (ML) offers a new perspective on solving PDEs through data-driven approaches to enable fast and accurate simulations of many multiphysics and multiscale processes [5–7]. However, the ML model deployment on electronic computing hardware requires substantial computing resources and consumes substantial energy. In the foreseeable future, the fundamental quantum mechanics limit will lead to a bottleneck of further reducing the energy consumption and simultaneously increasing the integration density of electronic circuits to catch up with the increasing scale of ML models in demand for solving complex problems [8, 9], thus urgently calling for new high-throughput and energy-efficient ML hardware accelerators. Recently, optical architectures, including photonic integrated circuits for matrix-vector multiplication (MVM) [10, 11], for neuro-inspired spiking neural networks [12, 13], and for photonic reservoir computing [14, 15], and free-space optical systems for MVM [16–18] and diffractive optical neural networks (DONNs) [19–22], are emerging as high-performance ML hardware accelerators by leveraging different particles – photons – to break down electronic bottleneck thanks to high parallelism and low static energy consumption of photons [23]. However, to date, there is no deployment of any optical computing systems for solving PDEs in any scientific domain.
+
+Here, we present a fully reconfigurable and scalable optical neural engine (ONE) architecture that combines DONN systems for processing data in Fourier space and optical crossbar (XBAR) structures for processing data in real space to solve two-dimensional (2D) spatiotemporal profiles in time-independent and time-dependent PDEs. The ONE architecture not only leverages the advantages of high-performance dual-space processing [24], but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales, and real-time reconfigurability for tackling multiple tasks with the same architecture. We numerically and experimentally demonstrate the capability of the ONE architecture in solving a broad range of PDEs in diverse disciplines, including the Darcy flow equation in fluid dynamics, the magnetostatic Poisson’s equation in micromagnetics, the Navier-Stokes equation in aerodynamics, Maxwell’s equations in nanophotonics, and coupled electric current and heat transfer equations in
+a multiphysics electrical heating problem. The ONE architecture not only outperforms traditional PDE solvers because of its data-driven nature, but also shows comparable and better performance with other ML models while with substantial hardware advantages because of its implementation in the optical domain. The demonstrated ONE architecture is versatile and can be tailored with different combinations of DONN and XBAR structures for solving various PDEs, offering a transformative universal solution for large-scale scientific and engineering computations.
+
+Results
+
+ONE Architecture
+
+Figure 1a illustrates the ONE architecture, which takes the spatiotemporal data of an input physical quantity \( \mathbf{U} \), described as a function \( u(x, y, t) \) in terms of positions \( x \) and \( y \) and time \( t \), to predict the spatiotemporal data of an output physical quantity \( \mathbf{G} \) described using a function \( g(x, y, t) \). The input and output quantities \( \mathbf{U} \) and \( \mathbf{G} \) can be connected through either a single-physics PDE or coupled multiphysics PDEs. There are three branches inside the ONE architecture, including (i) Fourier space processing branch, (ii) real space processing branch, and (iii) physics parameter processing branch. The combination of both real and Fourier space processing has been proven fast, powerful, and efficient in solving PDEs [24], and the incorporation of additional physics parameter processing enables the fusion of multimodal data for complex tasks [25]. More importantly, most operations in these branches can be deployed on optical computing hardware in both real and Fourier space, enabling solving PDEs in high-throughput and energy-efficient manners. The details of each branch are described below.
+
+In the first Fourier space processing branch, the core arithmetic operations are based on Fourier and inverse Fourier transformations to process input spatiotemporal data in the Fourier space. Their optical hardware implementations are mainly based on reconfigurable DONNs, which contain cascaded reconfigurable diffractive layers. Reconfigurable DONNs can be implemented in both integrated photonic chips [26, 27] and free space [19–21]; see Fig. 1b. There are two fundamental operations in DONNs – optical diffraction and spatial light modulation. For the optical diffraction operation, an optical field right after the \( l \)-th diffractive layer, \( f_l \), diffracts to the front of \( (l+1) \)-th layer, whose optical field, \( f_{\text{in},l+1} \), is a convolution of \( f_l \) and the diffraction impulse function \( h(x, y) \). Specifically, the complex-valued field at point \( (x, y) \) on the input plane of \( (l+1) \)-th layer can be written as the convolution of all fields at the output plane of \( l \)-th layer as
+
+\[
+f_{\text{in},l+1}(x, y, z) = \iint f_l(x', y', 0) h(x - x', y - y') dx' dy',
+\]
+
+where \( z \) is the distance between two diffractive layers and \( h(x, y) \) is the impulse response function of free space. By the convolution theorem, this 2D convolution can be efficiently calculated in Fourier space based on Fourier and inverse Fourier transformations. Specifically, the 2D Fourier transformation \( \mathcal{F}_{xy} \) of \( f \) and \( h \), \( F \) and \( H \), are
+Fig. 1 ONE architecture and hardware implementations. (a) Illustration of processing branches and flows in the ONE architecture to predict output spatiotemporal output physical quantities from corresponding input and solve PDEs involving single or multiple physics. Illustrations of integrated and free-space implementations of reconfigurable (b) DONN and (c) XBAR structures.
+
+connected through
+
+\[
+\mathcal{F}_{xy}(f_{in,t+1}(x,y,z)) = \mathcal{F}_{xy}(f_t(x,y,0))\mathcal{F}_{xy}(h(x,y)),
+\]
+\[
+F_{in,t+1}(\alpha,\beta,z) = F_t(\alpha,\beta,0)H(\alpha,\beta),
+\]
+
+where \( \alpha, \beta \) are spatial domain indices. After diffraction, the 2D inverse Fourier transformation \( \mathcal{F}_{xy}^{-1} \) of \( F_{in,t+1}(\alpha,\beta,z) \), \( f_{in,t+1}(x,y,z) \), is then spatially modulated. Each diffraction pixel at location \( (x,y) \) has a complex-valued electric field transmission coefficient \( t(x,y,S)e^{\phi(x,y,S)} \), where \( t(x,y,S) \) (\( \phi(x,y,S) \)) is the amplitude (phase) response as a function of external stimuli \( S \), such as voltages. The spatial light modulation operation is expressed as a pixel-wise multiplication
+
+\[
+f_{t+1}(x,y,z) = \mathcal{F}_{xy}^{-1}(F_{in,t+1}(\alpha,\beta,z))t(x,y,S)e^{\phi(x,y,S)}
+\]
+= f_{in,l+1}(x, y, z)t(x, y, S)e^{\phi(x, y, S)},$
+
+where \( f_{l+1}(x, y, z) \) is the near-field output field right after the \((l+1)\)-th layer. More details can be found in Methods.
+
+Before and between DONN kernels, there is a linear transformation operation based on fully connected layers to scale up the number of channels and a channel mixing operation based on matrix multiplications [24]. The core arithmetic operations are based on MVM. Their optical hardware implementations are mainly based on reconfigurable optical XBAR structures, which encode element values of vector \( \mathbf{v} \) and matrix \( \mathbf{M} \) into light intensity through electro-optic modulators, perform multiplications through cascaded modulators, and add signals at the output detector array. The signals are routed to follow mathematical calculations in MVM so that the reading from the detector array represents the output vector \( \mathbf{o} = \mathbf{M} \times \mathbf{v} \). Reconfigurable XBAR structures can also be implemented in both integrated photonic chips [10, 11] and free space [16–18]; see Fig. 1c. More details on the operation mechanism can be found in Methods and Supplementary Fig. 1.
+
+The second real space processing branch contains fully connected layers, whose operations are also based on MVM and implemented with optical XBAR structures. The output from the Fourier space branch, \( \mathbf{F}(u) \), and the output from the real space branch, \( \mathbf{R}(u) \) are added and further processed with a nonlinear operation. Note that the nonlinear operation is the only operation performed in electronic hardware in the ONE architecture. Moreover, this combination of real space, Fourier space, and nonlinear processing is scaled up, repeated four times, and cascaded in series. The third branch is to perform a linear transformation on other relevant physics parameters \( d(t) \), which are time sequences instead of spatiotemporal data, based on fully connected layers. The obtained data \( \mathbf{T}(d) \) is multiplied and merged onto two other branches to have the final output \( g(x, y, t) \). Hence, except nonlinear operations, all other operations can be done with DONN and optical XBAR systems. These two systems can be seamlessly assembled into a single integrated photonic chip or a single free-space optical system for all-optical operations without converting between optical and electronic hardware, fully leveraging the advantages of high throughput and high parallelism in optical computing systems. More details on the ONE architecture model are in Methods.
+
+Darcy flow and magnetostatic Poisson’s equations
+
+The first PDE we solved with the ONE architecture is the Darcy flow equation in fluid dynamics physics. This PDE describes a fluid flow through a porous medium as shown in Fig. 2a. Specifically, the equation is
+
+\[
+-\nabla \cdot (k(x, y) \nabla u(x, y)) = f(x, y),
+\]
+
+where \( k(x, y) \) is the permeability field of the medium, \( u(x, y) \) is the pressure field of the flow, and \( f(x, y) \) is the force function. The ONE architecture was trained to learn the mapping from the 2D function \( k(x, y) \) to function \( u(x, y) \). More details about the equation dataset generation and training are in Methods. Figure 2b displays the training loss curves for inputs with different resolutions. The training loss
+is generally low for all resolutions and slightly increases at the highest 421 resolution. Figure 2c shows the comparison of the training loss of our ONE architecture with other PDE solving models, including fully convolution networks (FCN) [28], principal component analysis-based neural network (PCANN) [29], reduced biased method (RBM) [30], graph neural operator (GNO) [31], low-rank kernel decomposition neural operator (LNO) [25], multipole graph neural operator (MGNO) [32], and Fourier neural operator (FNO) [24]. The performance of the ONE architecture is comparable with the state-of-the-art neural operators including GNO, LNO, MGNO, and FNO, and is better than FCN. Further, from the hardware perspective, the ONE architecture is constructed based on high-throughput optical computing hardware platforms so that all operations can be performed in parallel within a single clock cycle. In addition, the ONE architecture can be practically implemented on a large scale. For example, free-space reconfigurable DONNs [20, 21, 33] and optical MVM [17] are typically implemented using spatial light modulators (SLMs) with a scale > 1000 × 1000. Hence, the execution cost of solving PDEs with different scales and resolutions is invariant, meaning \( \mathcal{O}(1) \), if the scale of the optical hardware in the ONE architecture is large enough. Figure 2d displays the input permeability field \( k(x, y) \), the expected ground truth of output pressure field \( u(x, y) \), the predicted output pressure field, the absolute error between the expected and predicted outputs, and the relative error between the expected and predicted outputs, at the lowest 85 and the highest 421 resolutions, respectively. This visualization further validates the ONE architecture in solving PDEs. More data on other resolutions are shown in Supplementary Fig. 2.
+
+The second PDE we solved is the magnetostatic Poisson’s equation of demagnetization in micromagnetics physics. This PDE calculates the demagnetizing field \( \mathbf{H} \) generated by the magnetization field \( \mathbf{M} \) as shown in Fig. 2e. Specifically, the equation is obtained from Maxwell’s equation as
+
+\[
+\nabla \cdot \mathbf{H} = -\nabla \cdot \mathbf{M}.
+\]
+
+By defining an effective magnetic charge density \( \rho = -\nabla \cdot \mathbf{M} \) and a magnetic scalar potential \( \Phi \) assuming there is no free current, we can express the demagnetizing field \( \mathbf{H} = -\nabla \Phi \) and rewrite the previous equation as a Poisson’s equation
+
+\[
+\nabla^2 \Phi = -\rho.
+\]
+
+Similar to solving the Darcy flow equation, the ONE architecture was trained to learn the mapping from components of \( \mathbf{M} \) to \( \mathbf{H} \) vector fields. More details about the equation dataset generation and training are in Methods. Figure 2f shows the validation loss curve and Fig. 2g shows the input one component of \( \mathbf{M} \) field, the expected ground truth of output \( H_x \) component of \( \mathbf{H} \) field, the predicted output \( H_x \) component, the absolute error between the expected and predicted outputs, and normalized error between the expected and predicted outputs with respect to the maximum field strength in the ground truth. Both confirm a good performance of the ONE architecture in solving the magnetostatic Poisson’s equation. More data on \( H_y \) and \( H_z \) components is shown in Supplementary Fig. 3.
+Fig. 2 Solving Darcy flow and magnetostatic Poisson’s equations. (a) Illustration of the Darcy flow equation describing a fluid flow through a porous medium. The ONE architecture learns the mapping between the permeability and pressure fields. (b) Training loss curves for input data with different resolutions. (c) Comparison of the training loss of different models at various resolutions. (d) Input permeability field, the expected ground truth of output pressure field, the predicted output pressure field, the absolute error between the expected and predicted outputs, and the relative error between the expected and predicted outputs, at 85 and 421 resolutions. (e) Illustration of the magnetostatic Poisson’s equation calculating the demagnetizing field generated by the magnetization field. The ONE architecture learns the mapping between these two fields. (f) Validation loss curve for the ONE architecture solving the magnetostatic Poisson’s equation and (g) corresponding input magnetization field, the expected ground truth of output demagnetizing field, the predicted output demagnetizing field, the absolute and normalized errors between the expected and predicted outputs.
+
+Navier-Stokes and Maxwell’s equations
+
+In addition to steady-state Darcy flow and magnetostatic Poisson’s equations without time evolution, we employed the ONE architecture to solve time-dependent PDEs, including the Navier-Stokes equation in fluid dynamics and Maxwell equations in electromagnetics and optics. In particular, the real-time reconfigurability of DONN and optical XBAR structures makes the ONE architecture suitable for such a purpose.
+Specifically, we solved a 2D Navier-Stokes equation for a viscous, incompressible fluid in vorticity form on the unit torus as shown in Fig. 3a. This PDE calculates the time evolution of vorticity described as
+
+\[
+\partial_t w(x, y, t) + u(x, y, t) \cdot \nabla w(x, y, t) = v \Delta w(x, y, t) + f(x, y),
+\]
+
+where \(u\) is the velocity field, \(w = \nabla \times u\) is the vorticity, \(v\) is the viscosity coefficient, \(f\) is the forcing function. The ONE architecture was trained to learn the mapping from \(w\) in a time range from 0 to \(t_0\) to \(w\) in a time range from \(t_0\) to \(t_1\) (\(t_1 > t_0\)). More details about the equation dataset generation and training are in Methods. Further, we also solved Maxwell’s equations in a dielectric metasurface consisting of multiple cylindrical pillars in a unit cell of a periodic pattern as shown in Fig. 3b [34]. The general Maxwell’s equations can calculate the time evolution of an electric field through the following equations
+
+\[
+\nabla \cdot \mathbf{D} = \rho,
+\]
+\[
+\nabla \cdot \mathbf{B} = 0,
+\]
+\[
+\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t},
+\]
+\[
+\nabla \times \mathbf{H} = \mathbf{J} + \frac{\partial \mathbf{D}}{\partial t},
+\]
+
+where \(\mathbf{D}\) is the electric displacement field, \(\rho\) is the free charge density, \(\mathbf{B}\) is the magnetic flux density, \(\mathbf{E}\) is the electric field, \(\mathbf{H}\) is the magnetic field, and \(\mathbf{J}\) is the free current density. The ONE architecture was trained to learn the mapping from \(\mathbf{E}\) in a time range from 0 to \(t_0\) to \(\mathbf{E}\) in a time range from \(t_0\) to \(t_1\) (\(t_1 > t_0\)). More details about the dataset generation and training are in Methods. Figure 3c displays the validation loss curve for solving the Navier-Stokes equation with \(t_0 = 10\) and \(t_1 = 20\). Figure 3d displays the validation loss curves for solving Maxwell’s equations with \(t_0 = 10\) and \(t_1 = 20, 30, 40\), respectively. Moreover, Figure 3e and 3f show the expected ground truth of \(w\) field and the \(E_x\) component of the \(\mathbf{E}\) field at \(t_1\), the corresponding predicted fields at \(t_1\), and the absolute and relative errors between ground truth and prediction for the Navier-Stokes equation and Maxwell’s equations, respectively. All confirm a good performance in solving time-dependent PDEs using the ONE architecture.
+
+Multiphysics PDEs
+
+Moreover, we employed the ONE architecture to solve coupled PDEs involving two physics. Specifically, we solved an electrical heating problem to obtain a temperature profile at an intermediate time step \(t_n\), \(T(x, y, t_n)\), in an electrical circuit when a time-dependent voltage signal was applied to the circuit pads, involving coupled electric current physics and heat transfer physics; see Fig. 4a. Specifically, for the electrical current physics, the corresponding PDE is
+
+\[
+Q_e = d \sigma \nabla_t V(x, y, t),
+\]
+Fig. 3 Solving time-dependent Navier-Stokes and Maxwell’s equations. Illustrations of (a) Navier-Stokes equation for solving the time evolution of the vorticity field in a viscous, incompressible fluid in vorticity form on the unit torus and (b) Maxwell’s equations for solving the time evolution of the electric field in a dielectric metasurface. Validation loss curves for (c) solving the Navier-Stokes equation and (d) Maxwell’s equations using the ONE architecture. The expected ground truth field, the predicted field, and the absolute and relative errors between these two fields for (e) the Navier-Stokes equation and (f) Maxwell’s equations, respectively.
+
+\[
+V(x_0, y_0, t) = \mathrm{rect}(t),
+\]
+
+where \( Q_e \) is the heat rate per unit area from an electromagnetic heating source, \( d \) is the thickness of the heating layer, \( V(x, y, t) \) is the voltage profile in the circuit that is subjected to a voltage boundary condition defined in the pads \( V(x_0, y_0, t) \), and \( V(x_0, y_0, t) \) is a pulse rectangular function \( \mathrm{rect}(t) \) with pulse height and width. For the heat transfer physics, the corresponding PDE is
+
+\[
+\rho C_p \frac{\partial T}{\partial t} + \rho C_p \mathbf{u} \cdot \nabla T - \nabla \cdot (k \nabla T) = Q_e,
+\]
+
+where \( \rho \) is the mass density, \( C_p \) is the specific heat capacity, \( T \) is the absolute temperature, and \( k \) is the thermal conductivity. These two PDEs are connected through the quantity \( Q_e \). The ONE architecture was trained to learn the mapping from \( V(x, y, t) \)
+in a time range spanning all time steps in input pulses to \( T(x, y, t_n) \) at an intermediate pulse time step \( t_n \). In contrast to previous examples, the pulse information, including pulse height and width, was processed through the physics parameter processing branch in the ONE architecture (Fig. 1a) and multiplied with the output from cascaded real space processing and Fourier space processing branches to yield the final output. More details about the dataset generation and training are in Methods. Figure 4b displays the validation loss curve and Fig. 4c shows a few representative input 2D data \( V(x, y, t) \) at various time steps. Figure 4d shows the expected ground truth of \( T(x, y, t_n) \), the corresponding predicted temperature profile, and the absolute and relative errors between ground truth and prediction. All confirm a good performance in solving multiphysics PDEs using the ONE architecture.
+
+![Illustration of solving coupled PDEs in an electrical heating problem involving electric current physics and heat transfer physics. Validation loss curve. A few representative 2D voltage profiles in the circuit. The expected ground truth temperature profile, the predicted profile, and the absolute and relative errors between these two profiles.](page_370_682_1002_563.png)
+
+Fig. 4 Solving multiphysics PDEs. (a) Illustration of solving coupled PDEs in an electrical heating problem involving electric current physics and heat transfer physics. (b) Validation loss curve. (c) A few representative 2D voltage profiles in the circuit. (d) The expected ground truth temperature profile, the predicted profile, and the absolute and relative errors between these two profiles.
+
+Experimental demonstration
+
+Finally, to demonstrate the experimental feasibility of the ONE architecture, we constructed a free-space reconfigurable DONN setup and evaluated the performance of
+solving the Darcy flow equation under different hardware noise levels in optical XBAR structures. Figure 5a displays a photo and schematic of the reconfigurable DONN setup, which contains a laser source, a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. The reconfigurable encoder and diffractive layers were built upon SLMs, which can modulate the amplitude and phase of transmitted light when applying voltage. Multiple light polarization components, including polarizers and half-wave plates, were also employed to manipulate polarization states to achieve large phase modulation ranges. More details on the experimental setup are in Methods.
+
+(a)
+
+![Photo and schematic of a reconfigurable DONN experimental setup consisting of a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. Polarization components were used to configure SLMs in the phase modulation mode.](page_324_370_1096_282.png)
+
+(b) ![Output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture obtained from model calculations and experimental measurements.](page_324_670_420_180.png)
+
+(c) ![Validation loss curves at different noise levels in optical XBAR structures.](page_744_670_246_180.png)
+
+(d) ![Loss at the final epoch as a function of noise level.](page_1010_670_180_180.png)
+
+Fig. 5 Experimental demonstration. (a) Photo and schematic of a reconfigurable DONN experimental setup consisting of a reconfigurable input encoder, two reconfigurable diffractive layers, and a camera. Polarization components were used to configure SLMs in the phase modulation mode. (b) Output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture obtained from model calculations and experimental measurements. (c) Validation loss curves at different noise levels in optical XBAR structures and (d) the loss at the final epoch as a function of noise level.
+As shown in Supplementary Fig. 1, the experimentally measured amplitude and phase modulation responses of all three SLMs are not only discrete with respect to grey levels but also coupled and dependent. To leverage the gradient-based ML training algorithm, we utilized the Gumbel–softmax reparameterization technique to approximate a discrete distribution to a continuous distribution [21]. More details are described in Methods. Moreover, the values of input 2D data span both negative and positive values and were encoded as the grey level of the SLM in the reconfigurable input encoder (SLM0 in Fig. 5a). We performed the encoding through linear mapping from minimum and maximum values of input data to a grey-level range in the SLM. More details are described in Methods. In addition, we precisely aligned all SLMs with respect to each other within a range of a few pixels on the order of hundreds of \( \mu m \); see Supplementary Fig. 5. Although the long optical path in the system makes the alignment sensitive to external variations, the system’s full reconfigurability can enable fast adaptive pixel-by-pixel re-alignment. Figure 5b shows output 2D data in one DONN kernel of the Fourier space processing branch in the ONE architecture (Fig. 1a) obtained from model calculations and experimental measurements, showing good agreement and experimentally validating the feasibility of the ONE architecture in solving PDEs. More data is shown in Supplementary Fig. 6. There are some speckles in the background of measured images, which probably originate from high-order diffraction interference, leading to numerical errors in the ONE architecture for performing regression tasks. This discrepancy between models and experiments can be mitigated through hardware-software co-design, such as incorporating loss functions based on experimental results for gradient calculations as demonstrated in prior works [20, 33, 35].
+
+We also evaluated the performance of the ONE architecture under different noise levels of optical XBAR structures. Specifically, we added random Gaussian noise with zero mean and varying standard deviation (Std) to the values obtained from matrix multiplications to represent hardware noise, such as shot noise in photodetectors [36]. The corresponding MVM results and histograms of different noise standard deviation values are shown in Supplementary Fig. 7, and more details can be found in Methods. As shown in Fig. 5c and Fig. 5d, the validation loss increases with the increasing noise standard deviation value. The current hardware implementation of optical XBAR structures with advanced components and calibration algorithms [16–18], including the structure we demonstrated before [36], can achieve quite a small noise level similar or below the noise level corresponding to 0.5 Std. Hence, the noise influence in optical XBAR structures on the performance of the ONE architecture is not substantial.
+
+We further estimated the potential throughput and power consumption of the ONE architecture implemented using optical computing hardware for inference. The throughput is mainly determined by the SLM refresh rate and camera frame rate. Current commercial SLMs and cameras can have rates > 1000 Hz, meaning that the inference time for one instance is < 1 ms. In contrast, it typically takes minutes to hours to numerically solve PDEs. Hence, the ONE architecture features \( > 10^5 \) (five orders of magnitude) acceleration compared to typical PDE solvers. This throughput is also comparable to the state-of-art ML model, such as FNO with a 5 ms inference time [24]. Moreover, the system throughput can be substantially improved with device
+innovation. For example, an electro-optic SLM based on organic molecules can achieve > GHz switching speed [37], and an ultrafast camera can achieve a trillion frames per second [38]. With these devices, the ONE architecture can achieve an inference time < 1 ns. The power consumption is mainly determined by the leakage current of liquid crystal cells in SLMs. Because of the dielectric nature of liquid crystals and their high leakage resistance, the leakage current is typically < 1 \( \mu \)A. Hence, assuming a 10 V driving voltage, the static power consumption of SLMs is \( \sim 10 \mu \)W, which is nearly \( 10^7 \) (seven orders of magnitude) smaller than typical GPU inference power \( \sim 100 \) W.
+
+Discussion
+
+We have demonstrated the ONE architecture and validated its performance in solving a broad range of PDEs in diverse scientific domains. The ONE architecture is versatile and can be modified to reduce the interface and connection between DONN and optical XBAR structures and facilitate the hardware implementation of the whole system. Further, in a whole system, active learning and noise-aware training can be incorporated to mitigate the discrepancy between models and practical systems for accurate deployment. Moreover, in addition to solving PDEs, the ONE architecture can be tailored to accelerate ML models for other regression problems.
+
+Methods
+
+DONN diffraction model – The diffraction impulse function \( h(x, y) \) was described using the Fresnel equation as
+
+\[
+h(x, y) = \frac{e^{ikz}}{i \lambda z} e^{\frac{-ik}{2z}(x^2 + y^2)},
+\]
+
+where \( \lambda \) is the wavelength, \( k = 2\pi/\lambda \) is the free-space wavenumber, \( (x, y) \) are positions within a plane perpendicular to the wave propagation direction, \( z \) is the distance along the propagation direction, and \( i \) is the imaginary unit. The 2D Fourier transformation was directly performed on \( h(x, y) \) for model training and evaluation. To match the experimental setup as described below, \( h(x, y) \) was first discretized with respect to a defined rectangular mesh grid in the convolution calculation and then converted into the Fourier space through 2D Fourier transformation. More details can be found in our prior work [21].
+
+The operation mechanism of optical XBAR structures - Supplementary Fig. 1a shows the detailed schematic of an integrated photonic XBAR structure. Specifically, the element values of a \( n \times 1 \) input vector \( \mathbf{v} \) are represented by the intensities of light at input waveguides, \( \{I_1, I_2, I_3, ..., I_n\} \), which can be implemented by modulating an equally distributed laser intensity through a \( n \times 1 \) array of electro-optic modulators (red squares in Supplementary Fig. 1a) at input waveguides. The light on each row waveguide is then equally distributed to the column waveguides connected to that row waveguide and modulated through an electro-optic modulator on the coupled curved waveguide (yellow squares in Supplementary Fig. 1a). The element values of a \( m \times n \)
+matrix \( \mathbf{M} \) are represented by the transmittance of modulators on curved waveguides, \( \{T_{ij}\}, i \in [1,m], j \in [1,n] \). At the end of each column waveguide, a photodetector collects all light intensity passing through the column waveguide. The obtained photocurrents or photovoltages of a \( m \times 1 \) photodetector array represent the summation of multiplied input vector light intensity and matrix modulator transmittance, and the element values of output vector \( \mathbf{o} \), \( O_j = \sum_{s=1}^n T_{js} I_s, j \in [1,m] \). Hence, this integrated photonic XBAR structure can implement MVM in the optical domain.
+
+Similarly, Supplementary Fig. 1b shows the detailed schematic of a free-space optical XBAR structure. Specifically, the element values of a \( n \times 1 \) input vector \( \mathbf{v} \) are represented by the intensities of light, \( \{I_1, I_2, I_3, ..., I_n\} \), which is implemented through a \( n \times 1 \) array of free-space vector SLM. The output light is broadcast to a \( m \times n \) array of matrix SLM through lenses so that the light distribution from vector SLM is identical at each column of matrix SLM. The element values of a \( m \times n \) matrix \( \mathbf{M} \) are represented by the transmittance of matrix SLM, \( \{T_{ij}\}, i \in [1,m], j \in [1,n] \). Lenses are then used to focus the output light from each modulator on the same column of matrix SLM to a photodetector. The readings from a \( m \times 1 \) photodetector array represent the element values of output vector \( \mathbf{o} \), \( O_j = \sum_{s=1}^n T_{js} I_s, j \in [1,m] \). Hence, this free-space optical XBAR structure can also implement MVM in the optical domain.
+
+**ONE architecture model** – The ONE architecture model was constructed with two main modules – the DONN module processing data in the Fourier space and the optical XBAR module processing linear operations. The mathematical operations in DONN and optical XBAR structures have been described before and their accurate models have been implemented in our prior works, closely matching experimental results [21, 36]. Briefly, the DONN module was modeled by combining the Fresnel free-space diffraction with phase-only spatial light modulation in a range of \( [0, 2\pi] \) in the model and coupled spatial light modulation as shown in Supplementary Fig. 4; the optical XBAR module was represented as matrix multiplication incorporating measurement noise. Both modules were implemented under the PyTorch 1.12 framework with graphics processing unit (GPU)-accelerated parallel computation and gradient backpropagation for training. The GPU used in this work was an Nvidia RTX 6000 card.
+
+**Darcy flow equation dataset and training** – A 2D Darcy flow equation on the unit box was employed as described in detail in Ref. [24]. The corresponding PDE is a second-order, linear, elliptic PDE as
+
+\[
+-\nabla \cdot (k(x,y)\nabla u(x,y)) = f(x,y), \qquad x \in (0,1), y \in (0,1),
+\]
+\[
+u(x) = 0, \qquad x \in \partial(0,1), y \in \partial(0,1)
+\]
+
+with a Dirichlet boundary condition. We used the Darcy flow dataset from the existing dataset in Ref. [24] with a boundary condition \( u(x,y) = 0 \) on domain edges. The coefficient \( k(x,y) \) was generated based on a specific distribution with the value 12 for positive inputs and 3 for negative inputs. The forcing term was fixed at \( f(x,y) = 1 \). The solution \( u(x,y) \) was computed using a second-order finite difference method on a \( 421 \times 421 \) grid, and other resolutions were obtained with downsampling. We used a 10 : 1 ratio for the numbers of data in the training set and validation set, respectively.
+The model was trained with a total of 600 epochs and a batch size of 40. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.
+
+Magnetostatic Poisson’s equation dataset and training – The demagnetizing field \( \mathbf{H} \) originates from the magnetization within the material itself, which can be calculated as the convolution of \( \mathbf{M} \) with the demagnetization tensor \( \mathbf{N} \) as
+
+\[
+\mathbf{H}(\mathbf{r}) = \int \mathbf{N}(\mathbf{r} - \mathbf{r}') \mathbf{M}(\mathbf{r}') d\mathbf{r}'.
+\]
+
+This convolution was computed through Fourier space representations of fields. Specifically, to create the dataset, we utilized the MagneX solver [39] to simulate the time evolution of magnetization in a thin magnetic film with dimensions of \( 500 \times 125 \times 3.125 \) nm. The modeling incorporated both demagnetization and exchange interactions. Initially, we relaxed the magnetic field into a stable S-state before subjecting the system to varying external magnetic fields in different scenarios. We uniformly sampled 8 bias \( \mathbf{H} \) fields in the \( x \) and \( y \) directions, each with a magnitude of 19872 A/m. The system evolved for 1 ns, during which we collected paired data of \( \mathbf{M} \) and \( \mathbf{H} \) fields. Each field was represented by three channels corresponding to the field components in \( x \), \( y \), and \( z \) directions. The dataset was divided into training and testing sets with an 8 : 2 ratio. The training was conducted over 500 epochs with a batch size of 128. The learning rate was set to 1.0 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.
+
+Navier-Stokes equation dataset and training – A 2D Navier-Stokes equation for a viscous, incompressible fluid in vorticity form on the unit torus was used to generate spatiotemporal data for training the ONE architecture. The details are described in Ref. [24]. Specifically, the PDEs are
+
+\[
+\begin{align*}
+\partial_t w(x, y, t) + u(x, y, t) \cdot \nabla w(x, y, t) &= v \Delta w(x, y, t) + f(x, y), & x \in (0, 1), y \in (0, 1), t \in (0, T] \\
+\nabla \cdot u(x, y, t) &= 0, & x \in (0, 1), y \in (0, 1), t \in (0, T] \\
+w(x, y, 0) &= w_0(x, y), & x \in (0, 1), y \in (0, 1),
+\end{align*}
+\]
+
+where \( w_0(x, y) \) is the initial vorticity and boundary conditions were used. We utilized the existing dataset with the viscosity coefficient \( v = 10^{-3} \) from Ref. [24] for training and inference. The samples in the dataset were recorded with a time step of \( 10^{-4} \) s. We used 1000 data as the training set and 100 data as the validation set. We trained the ONE architecture model with the first 10 vorticity fields (\( w(x, y, t) \)) to predict the time evolution of the next 10 vorticity fields. The model was trained with a total of 600 epochs and a batch size of 40. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.
+
+Maxwell’s equations dataset and training – We employed commercial Ansys Lumerical finite-difference-time-domain simulation software to generate an electric field dataset by solving Maxwell’s equations in dielectric metasurfaces. Specifically, the dielectric metasurface had a periodic pattern and we used four silicon cylindrical rods as the unit cell and periodic boundary condition. Data were generated by randomly
+selecting the radii of four cylindrical rods. The radius was chosen from 39.5\( \mu \)m to 44.5 \( \mu \)m with a step of 0.25 \( \mu \)m. The simulation time was set as 300000 fs. We generated a total of 1200 data and used 1000 as the training set and the rest 200 as the validation set. The model was trained in an auto-regressive style for the \( E_x \) component processing. The \( E_x \) field data between 300000 fs to 160000 fs was backward fed into to the model to predict the next 40000 fs \( E_x \) field data. The model was trained with a total of 500 epochs and a batch size of 20. The learning rate was 0.1 for the trainable parameters in DONNs and 0.001 for all other trainable parameters with the Adam optimizer.
+
+Multiphysics dataset and training – We employed commercial COMSOL Multiphysics finite-element simulation software to generate a temperature profile dataset by solving coupled electric current and heat transfer PDEs in an electrical heating circuit. The circuit details can be found in Ref. [40]. Concisely, the circuit contained a serpentine-shaped Nichrome resistive layer with 10 \( \mu \)m thick and 5 mm wide on top of a glass plate. A silver contact pad with a dimension 10 mm \( \times \) 10 mm \( \times \) 10 \( \mu \)m was attached at each end. The deposited side of the glass plate was in contact with the surrounding air at 293.15 K and the back side was in contact with the heated fluid at 353 K. Two coupled physics modules, electrical current in layered shells and heat transfer in layered shells, were used in COMSOL simulations. The input voltage pulse height was set from 5 to 25 V with a step of 1 V and the pulse width was set from 20 to 60 s with a step of 1 s. The simulation time range was from 0 to 110 s. We generated a total number of 861 data and divided the data into training and testing set with the splitting ratio of 8 : 2. The ONE architecture took the electric current layer data as the input spatiotemporal data and the input voltage pulse information was fed into the physics parameter data processing branch to predict temperature field data at 55 s. The model was trained with a total of 100 epochs and a batch size of 40. The learning rate for the trainable parameters in DONNs was 0.1 and the learning rate for all other trainable parameters was 0.001 with the Adam optimizer.
+
+DONN experimental setup and alignment – The photo and schematic diagram of the DONN experimental setup are displayed in Fig. 5a. The laser diode with a center wavelength 532 nm (CPS532 from Thorlabs, Inc.) was used as a source. The distance between SLMs and between the last SLM and camera was set as 25.4 cm. The polarizers and half-wave plates before and after each SLM were configured so that each SLM operated with a strong modulation of the transmitted electric field phase (phase mode) together with a moderate modulation of light amplitude. The experimentally measured amplitude and phase modulation responses of three SLMs are shown in Supplementary Fig. 4. All transmissive SLMs are the LC 2012 model from HOLOEYE Photonics AG with a refresh rate of 60 Hz. The analog-to-digital converter has 8-bit precision for liquid crystal driving voltage, so that the grey level of SLMs is from 0 to 255. The pixel size of SLMs is 36 \( \mu \)m \( \times \) 36 \( \mu \)m. The output data was captured on a CMOS camera with a frame rate of 34.8 frames per second (CS165MU1 from Thorlabs, Inc.).
+
+We aligned the DONN setup by loading standard images on SLMs and comparing experimental results with simulation. Specifically, as shown in Supplementary Fig. 5a, standard Gaussian images, which were centered with a peak at 255 grey level and with a standard deviation of 6 pixels, were loaded in the input SLM and two diffractive
+SLMs. Supplementary Fig. 5b displays the simulation pattern for the perfectly aligned setup. During the alignment process, loaded images were moved up, down, left, and right pixel-by-pixel to match the captured images by the camera with the simulation pattern. Supplementary Fig. 5c displays the matched experimental diffraction pattern when the optical setup was aligned, while Supplementary Fig. 5d shows misaligned patterns when there was five-pixel misalignment in vertical and horizontal directions, respectively.
+
+DONN experimental training with reparameterization – The discrete look-up tables of device responses shown in Supplementary Fig. 4 break the gradient backpropagation in the ML training process in PyTorch. To solve this challenge, we utilized a differentiable reparameterization Gumbel-softmax technique, which was first introduced in Ref. [41] and demonstrated in our prior work [21]. Specifically, continuous noise from the Gumbel distribution was added to the discrete distribution. The argmax function was then used to find the optimized sample. The training problem after this Gumbel–argmax process is mathematically equivalent to the original training problem under one-hot representation [41]. Since the argmax function still breaks the gradient chain, it was replaced with the softmax function to enable differentiability. Hence, this Gumbel-softmax technique, which is also available in PyTorch, offers continuous and differentiable approximation to discrete distributions and the gradient can backpropagate to reduce the loss function.
+
+DONN experimental grey-level encoding – The global minimum and maximum values in input 2D data were calculated as \( d_{\min} \) and \( d_{\max} \). A grey level range from 130 to 255 in the input encoder SLM was selected for a relatively large amplitude modulation range to have enough contrast. Hence, any value \( d \) in the input 2D data was converted into a grey level through a linear mapping as
+
+\[
+d = \text{int}\left( \frac{255 - 130}{d_{\max} - d_{\min}} + 130 \right),
+\]
+
+where the int(\(\cdot\)) operation rounded the expression to the nearest integer since the SLM grey level must be an integer.
+
+Optical XBAR noise – The MVM results from an optical XBAR structure were uniformly randomly generated in a range of \(-15\) to \(15\), which was the value range in the ONE architecture for solving the Darcy flow equation. The expected number \( o \) was then added with a randomly generated noise from a Gaussian distribution with a zero average and varying standard deviation. The noise-dressed number \( \tilde{o} \) was used in ONE architecture calculations. Under different noise standard deviation levels, Supplementary Fig. 7a demonstrates \( \tilde{o} \) with respect to \( o \) and Supplementary Fig. 7b displays histograms of \( \tilde{o} - o \).
+
+Data availability
+
+Upon publication, all data that support the plots within this paper and other findings of this study will be available on a public GitHub repository.
+Code availability
+
+Upon publication, all codes that support the plots within this paper and other findings of this study will be available on a public GitHub repository.
+
+Acknowledgements
+
+R.C., C.Y., and W.G. acknowledge support from the National Science Foundation through Grants No. 2235276, No. 2316627, and No. 2428520. M.L., J.F., and W.G. also acknowledge support from the University of Utah start-up fund. Y.T., Z.Y., and A.N. were supported by Laboratory Directed Research and Development (LDRD) funding from Berkeley Lab, provided by the Director, Office of Science, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 and under NERSC GenAI award under No. DDR-ERCAP0030541.
+
+Author Contributions Statement
+
+Y.T. and W.G. conceived the idea and W.G. supervised the project. Y.T. constructed models and performed machine learning calculations with the help of M.L., J.F., and C.Y and under the support of A.N., Z.Y, and W.G. R.C constructed an optical experimental setup, performed experiments, and performed numerical calculations under the supervision of W.G. Y.T. and W.G. wrote the manuscript.
+
+Competing Interests Statement
+
+The authors declare no competing interests.
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SIFinal.pdf

07d4a546b84977cbe671fd9636cce724b9118c33a913f81362f52341cbf8a751/peer_review/peer_review.md

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+Spin Seebeck in the Weakly Exchange-Coupled Van der Waals Antiferromagnet across the Spin-flip Transition
+
+Corresponding Author: Professor Rui Wu
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+This study is the first to utilize the spin Seebeck effect (SSE) to investigate the spin-flip field in the van der Waals antiferromagnetic material CrPS4. The results reveal that the spin-flip field significantly enhances the SSE signal due to the magnon mode edges across the spin-flip field. Before the publication, the author should answer the following questions:
+1. If the SSE peak is related to the magnon mode edges as a function of the applied field across the spin-flip field , not the coupling of the magnon and phonon. The first harmonic voltage [Phys. Rev. Lett. 109, 107204] induced by the proximity effect could also show the same feature. Did you check this point?
+2. Line 112: What is the definition of R2wxy? Could you provide a clearer explanation? Some sources define the second harmonic resistance as \( R = V/I^2 \) [Nature Physics, 6, 879–882 (2010)], but here it appears to be defined as \( R = V/I \).
+3. It should be clearly stated whether the temperature shown in Figure 2 refers to the ambient temperature of the equipment or the actual temperature of the device itself.
+4. In Figure 2c, when the temperature exceeds the Néel temperature, the SSE signal likely includes contributions from the Nernst effect. Therefore, the signal observed under high temperature conditions is probably due to the Nernst effect.
+5. Why does R2wxy show a significant difference at magnetic fields of 6T and 6.8T in Figure 3a, while the differences in R2wxy across various magnetic fields are relatively small in Figure 3b?
+
+Reviewer #2
+
+(Remarks to the Author)
+This paper presents interesting results on electrical measurements on the (title) “Spin Seebeck effect in the weak exchange coupled van der Waals antiferromagnet”. The van der Waals antiferromagnet CrPS4 (but also others, see below) offer the advantage that due to the van der Waals gap the interlayer exchange is relatively weak. Therefore the spin-flop and spin-flip fields can be relatively low, and can be accessed by magnetic fields in the Tesla range. They perform local and non-local measurements, and do several checks to make sure that the observed signals are not due to other effects. They also compare their results with theory. I have the following remarks:
+1) They spend quite some text (almost one page) to introduce the spin Seebeck effect, without being explicit on what has already been done on the spin Seebeck effects and related effects. They write in the abstract “However, the SSE in van der Waals antiferromagnet is still elusive, especially across the spin-flip transition”. I disagree here for two reasons:
+a) They do not refer to Phys. Rev. B 106, 224409 (2022), which title is:“Spin flop transition in the quasi two-dimensional antiferromagnet MnPS3 detected via thermally generated magnon transport”. These authors observed a sign change in the spin Seebeck effect when the magnetic field was ramped through the spin-flop transition. Therefore the title of the authors too general. Clearly the role of the spin-flop in Van der Waals antiferromagnets already has been addressed (experimentally and also theoretically.)
+b) In a paper which recently (4 september) appeared on ArXiv (arXiv:2409.02590) there is a substantial discussion on the spin Seebeck effect in local and non-local geometries of Pt electrodes on CrPS4, geometries which resemble the authors’. It also discusses the spin Seebeck effect at magnetic fields above the spin-flip transition. I am not sure if Nature Communications has a specific policy here, but I would expect that manuscripts which have appeared on appear on ArXiv should be acknowledged and discussed if they appear before the actual submission dates of manuscripts for Nature Communications (I do not know if that is the case here).
+2) Even more relevant is that arXiv: 2409.02590 gives an elaborate discussion of the temperature AND measurement current
+dependence of the local and non-local Seebeck measurements. For example fig. S7 in the Supplementary Information shows that at low temperatures (5 K) there are substantial heating effects at 100 microamps, which are much smaller currents than those used by the authors (1 mA). This raises the question whether heating effects (which can change the magnetic properties of the antiferromagnet) have been sufficiently ruled out, in particular for the non-local measurements (Note that fig 1e in the authors’ manuscript only applies to the (larger) local geometry, but already shows deviations at 800 microamp current). Of course the specific dimensions of the electrodes will play a role here, but I could not find information on that in manuscript or supplementary information
+In view of the above remarks I hesitate to recommend the manuscript for publication in Nature Communications
+
+Reviewer #3
+
+(Remarks to the Author)
+The authors investigated the magnetic properties of the van der Waals (vdW) antiferromagnet CrPS₄, utilizing the spin Seebeck effect as a tool to probe its magnetic behavior. The spin Seebeck effect was studied in conjunction with the spin Hall effect of heavy metals such as Pt and W, allowing the authors to detect magnetic signals attributed to the antiferromagnetic nature of CrPS₄. While this work could be viewed as an extension of Ref. [32], the authors did not explicitly acknowledge this connection.
+
+Key Issues and Concerns:
+
+1. Sample Preparation:
+The preparation of the samples raises significant concerns. The authors employed sputtering to deposit heavy metals onto CrPS₄. This technique involves high-energy particles that can diffuse into the CrPS₄ lattice, potentially damaging its layered structure. In contrast, Ref. [32] carefully prepared a clean CrPS₄ surface and deposited Pd using molecular beam epitaxy (MBE), thereby avoiding such damage. It is highly likely that the sputtering process in the current study caused severe degradation of the CrPS₄ interface and its underlying structure.
+
+2. Material Properties:
+The state of CrPS₄ beneath the heavy metal layer remains unclear. It is uncertain whether the CrPS₄ in this region remains highly insulating. Such uncertainties make it challenging to accurately evaluate the intrinsic properties of CrPS₄. Without ensuring the integrity of the vdW material, the results cannot be conclusively attributed to the intended magnetic properties.
+
+3. Experimental Validation:
+To substantiate claims regarding vertical spin transport across the heavy metal/CrPS₄ interface, the authors should provide cross-sectional TEM images. This would clarify whether the interface is intact and whether the CrPS₄ structure is preserved beneath the heavy metal layer.
+
+4. Lack of Novel Physics:
+The manuscript does not present new insights or physics that would warrant publication in Nature Communications. Spin-flop and spin-flip phenomena could be more effectively studied using standard magnetization measurements rather than relying on the spin Seebeck effect, which remains a controversial and poorly understood phenomenon. Furthermore, the voltage signals reported are extremely small, significantly lower than those typically observed due to the anomalous Nernst effect.
+
+5. Spin Transport Limitations:
+Spin transport across the heavy metal/CrPS₄ interface, as well as along the c-axis, is expected to be poor due to the weak van der Waals coupling in CrPS₄. This intrinsic limitation further diminishes the significance of the presented results.
+
+Conclusion:
+Based on the above considerations, the study faces fundamental challenges in both experimental methodology and scientific contribution. The issues with sample preparation and lack of interface characterization compromise the reliability of the results, while the absence of novel insights into spin transport or antiferromagnetic properties limits the manuscript's impact. Therefore, I recommend rejection of this paper.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The authors have fully addressed my concerns. The SSE effect remains a promising approach for studying two-dimensional van der Waals antiferromagnetic materials, and I fully agree with the publication of this manuscript.
+Reviewer #2
+
+(Remarks to the Author)
+I have studied the reply of the authors to the remarks of the reviewers, as well as the updated manuscript. In my opinion they have addressed most of the remarks satisfactorily. In particular they have correctly replied to the remarks of previous reviewer 3, concerning the possible damage of the heavy metal (Pt or other) to the surface layers of the CrPS4. Indeed previous experiments have shown that the interface (layers) still remain effective in transporting/communicating spin information. Also they correctly changed the title, to focus on the role of the spin-flip transition.
+
+My main remark is that the authors have not properly referred to related recent work. In particular they have now included reference 29 (and other references). As already remarked in the previous review round, reference 29 appeared on ArXiv on september 4. As far as I can tell this was before the (first) submission of the authors' manuscript. It was published in Phys. Rev. B. on November 22. This is after the first review round of the authors' paper.
+The emphasis of ref 29. is on the magnon transport as measured by the first harmonic signal. However there is substantial data,and discussion, on the local and non-local (second harmonic)Spin Seebeck signals, (e.g. in, and related to, figs. 3 and 4.). In addition the supplementary information of ref. 29 provides several experimental results on the local and non-local Spin Seebeck effect, in particular highlighting the role of the spin flip transition.
+
+In their manuscript the authors give an almost one page long introduction overview, describing the history of the spin Seebeck effect and how it was observed in various materials. However then they write about ref. 29: "More recent work has also investigated magnon transport in CrPS4 (refs 28-30). However, the spin Seebeck effect in van der Waals antiferromagnets, especially across the spin-flip-transition,remains an area requiring further investigation (refs. 31,32)"
+This strongly suggests to the reader that ref. 29 did NOT investigate the spin Seebeck effect across the spin-flip transition in CrPS4. It is therefore not a proper way of referencing. In my opinion, given what I wrote above, the authors' manuscript should describe/summarize what has been observed in ref. 29, and discuss how their experiments and analysis compare to ref.29. Also, given the similarities between the authors' experiments and ref. 29, I consider it strange that it only appears as ref.29. Finally, I am not against publication of the authors' manuscript, since it is scientifically sound, and addresses a relevant problem. But I can only recommend it when the the authors' results are put in a proper scientific context
+
+Reviewer #3
+
+(Remarks to the Author)
+Regarding the Pt sputtering, the authors presented a TEM image of the cross-section around the CrPS4/Pt interface. While I generally agree with the authors' arguments, I still have the following concerns:
+
+The detection of spin flop in antiferromagnets was first reported in Phys. Rev. Lett. 116, 097204 (2016). Additionally, there have been numerous reports on van der Waals (vdW) antiferromagnets. In those studies, no reduction in the spin Seebeck effect (SSE) voltage was observed after the spin flop transition. This aspect might represent the unique contribution of the present article. However, even in the same antiferromagnet, CrPS4, no reduction in SSE voltage was reported in arXiv:2409.02590. The authors should provide a detailed discussion of this point to clarify their findings.
+
+For the detection of longitudinal SSE, a simple Pt strip is typically used. In this experiment, however, the authors employed a Hall bar structure, which raises questions about the precise heating and detection points in their setup. The authors should provide a comprehensive analysis of the temperature profile across the entire device structure, supported by numerical simulations. This is particularly crucial because heat transport in vdW materials often exhibits anisotropic behavior. Therefore, the heat transport in this system should be analyzed with greater accuracy.
+
+Additionally, I would like to inquire about the fabrication procedure for the nonlocal device. The manuscript does not specify any differences between the fabrication processes for the local and nonlocal devices. In the nonlocal device, two separate Pt strips were prepared on CrPS4. If the fabrication process for the Pt strips was the same as for the Hall bar, stopping the Ar-ion etching precisely at the surface of CrPS4 would be extremely challenging. Furthermore, Ar-ion irradiation could potentially damage the magnetic properties of the material. The authors should address these concerns in their discussion and clearly explain how they ensured the etching stopped accurately at the Pt/CrPS4 interface.
+
+Moreover, the separation distance between the Pt strips in the nonlocal device should be explicitly stated. Without this information, it is difficult to evaluate the experimental design.
+
+The following additional points also need clarification:
+
+Where exactly is the heating point in the Hall bar structure?
+How do the IV characteristics and angular dependence impact the results?
+The authors have not provided sufficient evidence for the role of the spin Hall effect.
+For these reasons, I maintain my initial decision not to recommend the publication of this manuscript in its current form. The authors need to address the aforementioned issues, particularly the fabrication procedure. How exactly do they ensure the Ar-ion etching stops just after the Pt metal layer? Clear answers to these points are necessary for further evaluation.
+Version 2:
+
+Reviewer comments:
+
+Reviewer #2
+
+(Remarks to the Author)
+The authors have carefully addressed the remarks of the previous reviewers, and made the according changes. In particular they now provide more information on the results of ref. 29 and provide more discussion how their experiments are related to those of ref. 29. Although it is not the main message of the paper, this is nonetheless the pioneering study of magnetic field dependence (in particular spin flip) of the spin Seebeck effect in CrPS4, in both local and non-local geometries.I will accept the paper for publication now, but would appreciate if the authors could give this a bit more attention in the description of ref.29.
+
+Reviewer #3
+
+(Remarks to the Author)
+The authors provided satisfactory answers to all of my queries. Therefore, I recommend the publication.
+Reply to reviewer #1:
+
+General comments: This study is the first to utilize the spin Seebeck effect (SSE) to investigate the spin-flip field in the van der Waals antiferromagnetic material CrPS4. The results reveal that the spin-flip field significantly enhances the SSE signal due to the magnon mode edges across the spin-flip field. Before the publication, the author should answer the following questions:
+
+Reply to general comments: We thank the referee for kindly pointing out that our study is the first to investigate the spin Seebeck effect across the spin-flip transition in van der Waals antiferromagnetic materials. Generally, antiferromagnetic coupling is quite strong in traditional antiferromagnets, which could be ~\(10^2\)-\(10^3\) Tesla, depending on the exchange coupling of the two magnetic sublattices, making it impossible to study the spin Seebeck effect of traditional antiferromagnets across the spin-flip transition using standard lab magnets. However, in the weakly coupled, interlayer antiferromagnetic van der Waals material CrPS4, the spin-flip field is reduced to approximately 7 T, and the magnon gap drops to the GHz range. This makes CrPS4 an ideal candidate for studying the spin Seebeck behavior across the spin-flip transition, where spin currents (magnons) are thermally excited. In this work, we observe a peak in the spin Seebeck effect at high fields, which we confirm is associated with the spin-flip transition of CrPS4. Our experimental and theoretical results indicate that incoherently pumped magnons and the magnon edge mode are responsible for the peak in the spin Seebeck effect at the spin-flip transition. This work not only sheds light on the physical origin of spin Seebeck effect across the spin-flip transition in easy-axis antiferromagnets, but also contributes to the advancement of innovative magnon-based spintronic devices that utilize weakly coupled van der Waals antiferromagnetic materials.
+
+Comment #1: If the SSE peak is related to the magnon mode edges as a function of the applied field across the spin-flip field, not the coupling of the magnon and phonon. The first harmonic voltage [Phys. Rev. Lett. 109, 107204] induced by the proximity effect could also show the same feature. Did you check this point?
+
+Reply to comment #1: We thank the referee for this insightful question. Indeed, the proximity-induced magnetization in Pt could potentially lead to a similar effect via the anomalous Nernst effect in magnetized Pt. However, we would like to argue that the peak
+observed \( R_{xy}^{2\omega} \) below the Néel temperature is not due to the magnetized Pt. First, the proximity effect should still be present above 50 K, but the peak in \( R_{xy}^{2\omega} \) vanishes above 50 K (see Fig. 2b in the main text), suggesting that the proximity effect from Pt does not contribute to the peak in \( R_{xy}^{2\omega} \). Indeed, the spin Seebeck effect above the Néel temperature could involve contributions from the paramagnetic spin Seebeck effect due to short-wavelength magnetic excitations and the anomalous Nernst effect from the proximity effect. Second, if the proximity effect were responsible, we would expect the same sign of \( R_{xy}^{2\omega} \) in both Pt and Ta samples, however, we observe a sign change of \( R_{xy}^{2\omega} \) in the two samples, which is related to the opposite sign of the spin-Hall angles of these two materials. As we discussed below, the \( R_{xy}^{2\omega} \) includes the thermal signal, which is related to the spin Seebeck effect, we thus focus on the results on the second harmonic signal \( R_{xy}^{2\omega} \).
+
+We have added a discussion on the potential contribution of the proximity effect to the \( R_{xy}^{2\omega} \) signal for a clearer understanding of the physical origin of the observed peaks in \( R_{xy}^{2\omega} \) (marked in blue on page 7).
+
+Comment #2: Line 112: What is the definition of R2wxy? Could you provide a clearer explanation? Some sources define the second harmonic resistance as \( R = V/I^2 \) [Nature Physics, 6, 879–882 (2010)], but here it appears to be defined as \( R = V/I \).
+
+Reply to comment #2: We apologize for the confusion and thank the referee for the question. We applied an AC current through the Hall device, with current \( I = I_0 \sin (\omega t) \) and corresponding voltage \( V = V_0 \sin (\omega t) \). The thermal effects can be expressed as \( V_{xy}^{2\omega} \sim V^2 / R = V_0^2 (\sin (\omega t))^2 / R \sim \cos (2 \omega t) \), where \( R \) is the resistance of the current channel. Therefore, thermal effects contribute to the second harmonic signal. We measure the second harmonic voltage using the lock-in amplifier, and \( R_{xy}^{2\omega} \) is defined as \( R_{xy}^{2\omega} = V_{xy}^{2\omega} / I_0 \). This approach is commonly used in studies of the spin Seebeck effect, as reported in previous works (Phys. Rev. B, 174436 (2014); Nat. Phys. 11, 1022–1026 (2015)).
+
+We have added the discussion and the definition of \( R_{xy}^{2\omega} \) on page 5 (marked in blue) to further clarify that \( R_{xy}^{2\omega} \) includes the thermal effects.
+Comment #3: It should be clearly stated whether the temperature shown in Figure 2 refers to the ambient temperature of the equipment or the actual temperature of the device itself.
+
+Reply to comment #3: We thank the referee for the kind reminder. The temperature values refer to the ambient temperature in the chamber, which explains the shift in the peak field observed in Fig. 2f, which is caused by the Joule heating induced device temperature change. We have included a clear statement regarding the ambient temperature in the chamber on page 5 (marked in blue) in the revised manuscript.
+
+Comment #4: In Figure 2c, when the temperature exceeds the Néel temperature, the SSE signal likely includes contributions from the Nernst effect. Therefore, the signal observed under high temperature conditions is probably due to the Nernst effect.
+
+Reply to comment #4: It is indeed possible that thermal effects at higher temperatures could include the Nernst effect, as the resistivity of CrPS$_4$ decreases with increasing temperature. However, even at room temperature the conductance of CrPS$_4$ would be very low without electrostatic doping (Wu et al., Adv. Mater. 2023, 35, 2211653). We also emphasize that the Nernst effect does not contribute to the peak of $R_{xy}^{2\omega}$, as the peak disappears above the Néel temperature.
+
+Comment #5: Why does R2wxy show a significant difference at magnetic fields of 6T and 6.8T in Figure 3a, while the differences in R2wxy across various magnetic fields are relatively small in Figure 3b?
+
+Reply to comment #5: We thank the referee for this comment. The difference in $R_{xy}^{2\omega}$ at difference magnetic fields looks not very significant in the angular dependence plot because the relative difference in the field range of 6 T to 9 T is only 8.7% as shown in Figures R1a, which is much smaller than the angular dependence of $R_{xy}^{2\omega}$, as shown in Figures R1b. Figure R1c displays the changes in $R_{xy}^{2\omega}$ as a function of the applied field, extracted from Figure R1b at angle of 0°, where the field is exactly applied along the current channel. The result is similar to the data from Figure S1a, where the peak of $R_{xy}^{2\omega}$ appears around 6.7 T.
+Figure R1. **a.** Comparison of the field dependence of \( R_{xy}^{2\omega} \) in CrPS$_4$/Pt (obtained at 15 K) and magnetic moment CrPS$_4$ flake (measured at 20 K), adopted from Fig. 3a in the revised manuscript. **b.** Angular dependence (in the xz plane) of \( R_{xy}^{2\omega} \) when the applied field approaches the spin-flip field at a temperature of 15 K and an applied current of 1 mA, adopted from Fig. 3b in the revised manuscript. **c.** The Field dependence of variation of \( R_{xy}^{2\omega} \) extracted from Angular dependence (in the xz plane) of \( R_{xy}^{2\omega} \).
+Reply to reviewer #2:
+
+General comments: This paper presents interesting results on electrical measurements on the (title) “Spin Seebeck effect in the weak exchange coupled van der Waals antiferromagnet”. The van der Waals antiferromagnet CrPS₄ (but also others, see below) offer the advantage that due to the van der Waals gap the interlayer exchange is relatively weak. Therefore the spin-flop and spin-flip fields can be relatively low, and can be accessed by magnetic fields in the Tesla range. They perform local and non-local measurements, and do several checks to make sure that the observed signals are not due to other effects. They also compare their results with theory. I have the following remarks:
+
+Reply to the general comments: We thank the reviewer for the positive comments about this paper. Please find attached a point-by-point response to reviewer’s concerns. We have revised the manuscript accordingly. We hope that you find our responses satisfactory and that the manuscript is now acceptable for publication.
+
+Comment 1#: They spend quite some text (almost one page) to introduce the spin Seebeck effect, without being explicit on what has already been done on the spin Seebeck effects and related effects. They write in the abstract “However, the SSE in van der Waals antiferromagnet is still elusive, especially across the spin-flip transition”. I disagree here for two reasons:
+
+a) They do not refer to Phys. Rev. B 106, 224409 (2022), which title is:”Spin flop transition in the quasi two-dimensional antiferromagnet MnPS3 detected via thermally generated magnon transport”. These authors observed a sign change in the spin Seebeck effect when the magnetic field was ramped through the spin-flop transition. Therefore the title of the authors too general. Cleary the role of the spin-flop in Van der Waals antiferromagnets already has been addressed (experimentally and also theoretically.)
+
+Reply to comment 1a#: We thank the referee for recognizing that our paper presents interesting results on the electrical measurement of the spin Seebeck effect in CrPS₄ across the spin-flip transition. In the meantime, the first referee highlighted that our work is the first
+experimental and theoretical study of the spin Seebeck effect across the spin-flip transition. As the referee noted, the weakly coupled van der Waals antiferromagnet CrPS4 offers a significant advantage for studying the phase transition of antiferromagnets, as both the spin-flop and spin-flip fields can be accessed with laboratory equipment. Additionally, the low magnon frequency in the GHz range makes thermal excitation of magnons more efficient and potentially results in a large spin Seebeck effect. To rule out other thermal effects, we also performed measurements in different geometries and with various heavy metals.
+
+We appreciate the referee's thoughtful comments and understand the concern that the title of our paper may be too broad. In response, we have updated the title to "Spin Seebeck in the Weakly Exchange-Coupled Van der Waals Antiferromagnet across the Spin-flip Transition" to better reflect the focus of our study.
+
+We would like to argue that the spin Seebeck effect across the spin-flip transition has not been systematically studied previously. The recent work on magnon transport in MnPS3 focuses only on the spin-flop transition (Phys. Rev. B 106, 224409 (2022)), whereas our study addresses the spin-flip transition. While the spin Seebeck effect across the spin-flop transition is well studied both experimentally and theoretically—particularly in Cr2O3 (Nature 578, 70–74 (2020); Phys. Rev. B 93, 14425 (2016); Phys. Rev. B 102, 020408 (2020)), FeF2 (Phys. Rev. Lett. 122, 217204 (2019)), and MnF2 (Phys. Rev. Lett. 116, 97204 (2016)). However, the work on MnPS3 provides valuable insights into the spin Seebeck effect, which we have cited in our revised manuscript.
+
+We revised the abstract part highlighting “The behavior of the SSE across the spin-flop transition has been extensively studied, whereas the SSE across the spin-flip transition remains poorly understood.” We also included more work in the recent study on spin Seebeck effects, as marked in blue on page 3.
+
+b) In a paper which recently (4 september) appeared on ArXiv (arXiv:2409.02590) there is a substantial discussion on the spin Seebeck effect in local and non-local geometries of Pt electrodes on CrPS4, geometries which resemble the authors’. It also discusses the spin Seebeck effect at magnetic fields above the spin-flip transition. I am not sure if Nature Communications has a specific policy here, but I would expect that manuscripts which have appeared on appear on ArXiv should be acknowledged and discussed if they appear before
+the actual submission dates of manuscripts for Nature Communications (I do not know if that is the case here).
+
+Reply to comment 1b#: We thank the referee for raising this concern. During preparation of the reply, we noticed that the ArXiv work is just published Nov. 22th, 2024 (Phys. Rev. B 110, 174440 (2024)), which majorly focuses on magnon transport in CrPS$_4$ for both noncollinear and collinear magnetization configurations. Additionally, it reports a similar peak in the spin Seebeck effect at the spin-flip transition. However, as the primary focus of the paper is on magnon transport above the spin-flip transition, the authors do not delve deeply into the physical origin of the spin Seebeck effect.
+
+In contrast, our work primarily investigates the physical origin of the peak in the spin Seebeck effect across the spin-flip transition. Through experiments in different geometries and theoretical calculations, we attribute the behavior of the spin Seebeck effect to the enhanced magnon population associated with the magnon edge mode. To improve the readability of our paper, we have included additional relevant works on spin Seebeck in van der Waals antiferromagnets, as listed below.
+
+1. T. Liu, J. Peiro, D. K. de Wal, J. C. Leutenantsmeyer, M. H. D. Guimarães, B. J. van Wees, Spin caloritronics in a CrBr3 magnetic van der Waals heterostructure. Phys. Rev. B 101, 205407 (2020).
+2. X. Tan, L. Ding, G.-F. Du, H.-H. Fu, Spin caloritronics in two-dimensional CrI3/NiCl2 van der Waals heterostructures. Phys. Rev. B 103, 115415 (2021).
+3. D. K. de Wal, M. Zohaib, B. J. van Wees, Magnon spin transport in the van der Waals antiferromagnet CrPS$_4$ for noncollinear and collinear magnetization. Phys. Rev. B 110, 174440 (2024).
+4. D. K. de Wal, R. L. Mena, M. Zohaib, B. J. van Wees, Gate control of magnon spin transport in unconventional magnon transistors based on the van der Waals antiferromagnet CrPS$_4$. (2024). https://arxiv.org/abs/2409.02621.
+5. S. Mañas-Valero, T. van der Sar, R. A. Duine, B. J. van Wees, Magnon spintronics with Van der Waals magnets: from fundamentals to devices. (2024). https://arxiv.org/abs/2411.14979.
+
+Comment 2#: Even more relevant is that arXiv: 2409.02590 gives an elaborate discussion of the temperature AND measurement current dependence of the local and non-local Seebeck
+measurements. For example Fig. S7 in the Supplementary Information shows that at low temperatures (5 K) there are substantial heating effects at 100 microamps, which are much smaller currents than those used by the authors (1 mA). This raises the question whether heating effects (which can change the magnetic properties of the antiferromagnet) have been sufficiently ruled out, in particular for the non-local measurements (Note that fig 1e in the authors’ manuscript only applies to the (larger) local geometry, but already shows deviations at 800 microamp current). Of course the specific dimensions of the electrodes will play a role here, but I could not find information on that in manuscript or supplementary information
+
+Reply to comment 2#: We thank the key comments from the referee, which have helped us further refine our manuscript. As the referee points out, the heating effect can indeed increase the sample temperature, even when the ambient temperature is kept constant. The actual temperature of the sample will depend on the magnitude of the applied current. We agree that heating can influence the spin Seebeck signal in several ways.
+
+First, stronger heating can create a larger out-of-plane thermal gradient, leading to a higher heat current and, consequently, a larger spin Seebeck signal. Additionally, as the temperature increases, the number of thermally activated magnons also rises, following the Bose–Einstein distribution. However, if the heating is too much, the sample temperature may exceed the Néel temperature of CrPS4, resulting in a paramagnetic state where the peak of spin Seebeck effect disappears (see Fig. 2b in the revised manuscript).
+
+In response to the referee's suggestions, we have performed current-dependent spin Seebeck measurements, as shown below.
+
+![Field dependence of R_{xy}^{2\omega} of CrPS4/Pt (5 nm) longitudinal device at different applied current at 15 K](page_682_1342_495_312.png)
+
+Figure R2. Field dependence of \( R_{xy}^{2\omega} \) of CrPS4/Pt (5 nm) longitudinal device at different applied current at 15 K
+Figure. R2 shows the field dependence \( R_{xy}^{2\omega} \) at various currents (from 0.4 mA to 1 mA) for the CrPS$_4$/Pt (5 nm) Hall bar device at 15 K. As the current increases, the peak value shifts slightly to lower field due to Joule heating, which is due to the change of samples temperature from the heating. As the temperature increase, the spin-flip field decreases (also see Fig. 2f in the main text). The result again confirms the peak in \( R_{xy}^{2\omega} \) is related to the spin-flip transition. We remark the heating induced other magnetic effect can be ruled out, and the peak of \( R_{xy}^{2\omega} \) is due to the spin Seebeck signal at the spin-flip transition, which is the key in our manuscript.
+
+We have added the information on the \( R_{xy}^{2\omega} \) measured at different current in the supporting information in Section S8.
+
+Comment 3#: In view of the above remarks I hesitate to recommend the manuscript for publication in Nature Communications
+
+Reply to comment 3#: We greatly appreciate the referee's insightful comments, which have helped us improve our manuscript to meet the high standards of Nature Communications. We hope our responses address the referee's concerns, and we are happy to make further revisions should there be additional comments.
+Reply to Reviewer #3:
+
+General comments: The authors investigated the magnetic properties of the van der Waals (vdW) antiferromagnet CrPS$_4$, utilizing the spin Seebeck effect as a tool to probe its magnetic behavior. The spin Seebeck effect was studied in conjunction with the spin Hall effect of heavy metals such as Pt and W, allowing the authors to detect magnetic signals attributed to the antiferromagnetic nature of CrPS$_4$. While this work could be viewed as an extension of Ref. [32], the authors did not explicitly acknowledge this connection.
+
+Reply to general comments: We thank the reviewer for these comments. Here, we would like clarify that, in this work, we aim to study the behavior of SSE effect in the weakly-coupled antiferromagnet but not to detect the antiferromagnetic properties using SSE. The SSE is discovered in 2008(Uchita et al., Nature 455, 778–781 (2008)), which is an important effect that is widely used in generating pure spin current now. In the following years, major studies of SSE are focus on the ferromagnetic materials, like Y$_3$Fe$_5$O$_{12}$, LaY$_2$Fe$_5$O$_{12}$ etc. (Uchida et al., Nature Materials **9**, 894–897(2010); Jaworski et al., Nat. Mater. **9**, 898–903 (2010); Geprägs et al., Nat. Commun. **7**, 10452(2016); Chang et al., Sci. Adv.**3**, e1601614(2017)) In recent years, with the rise of antiferromagnetic spintronics, the generation and transport of magnons in antiferromagnetic materials have attracted great attention. Thus, the SSE in some antiferromagnets has also been studied (Wu et al., Phys. Rev. Lett. 116, 097204; Seki et al., Phys. Rev. Lett., 115, 266601(2015); Lima et al., Phys. Rev. B 110, 144438(2024); Tang et al., Physical Review Letters, 133, 036701(2024)). However, since the spin-flip transition is difficult to access in traditional antiferromagnets due to the strong exchange coupling, which makes that the behavior of SSE at the spin-flip transition has not been observed. The previous studies on antiferromagnets are majorly focus on the behavior of SSE at the spin-flop transition, which is more accessible in most laboratory condition. Thus, this work is not a simple extension of Ref. [32] (R. Wu et al., Phys. Rev. Applied 17, 064038 (2022), which is Ref. [38] in the revised manuscript), where we studied the spin-Hall magnetoresistance (SMR) of CrPS$_4$(Pt, Pd) heterostructures. Although the materials systems in these two works are similar, the physical effects studied are different. Just like what the reviewer has pointed out below, the SSE is not a good effect to detect the magnetization of the antiferromagnet, we are also not using it for detection of magnetization.
+
+Below, we summarize the key findings of our study:
+1. Spin Seebeck peak and spin-flip transition: The peak in the spin Seebeck effect at high fields in CrPS$_4$ is related to the spin-flip transition. This peak disappears when the temperature exceeds the Néel temperature due to the loss of long-range magnetic ordering and the spin-flip transition.
+2. Alignment of magnetization and magnon population: The spin Seebeck peak at the spin-flip transition is linked to the alignment of magnetization before the spin-flip and the opening of the magnon gap (or suppression of incoherent magnon population) above the spin-flip transition. The alpha mode magnon, carrying right-hand chirality plays a main role in the spin Seebeck in CrPS$_4$.
+3. Role of magnon edge modes: The magnon edge mode plays a critical role in the spin Seebeck effect across the spin-flip transition. The interfacial conditions (compensated and uncompensated interface) significantly affect the magnitude of the spin Seebeck signal. In the case of an uncompensated interface, the gap closure of the beta mode further leads to a peak at the spin-flip transition at low temperatures.
+
+Experimentally, we present the first study of the spin Seebeck effect across the spin-flip transition, and, through theoretical calculations, we attribute the peak to the magnon population and the field-dependent magnon edge mode. Our work contributes to understanding the physical origin of the field dependence of the spin Seebeck effect across the spin-flip transition, and we believe it will trigger further studies on spin calorimetry in low-dimensional materials, particularly 2D antiferromagnets.
+
+Overall, our work demonstrates that magnon spin transport in CrPS$_4$(Pt,Ta) can be effectively controlled by varying temperature and applied magnetic fields, especially at the spin-flip field. This approach opens up possibilities for developing innovative magnonic devices based on weakly exchange-coupled van der Waals antiferromagnetic materials.
+
+Lastly, we would like to clarify that Ref. [32] primarily focuses on the spin-flop behavior of CrPS$_4$ and the anomalous Hall effect across the spin-flop transition. Our previous work (Ref. [32]) did not investigate the spin Seebeck effect in CrPS$_4$, nor did it explore the spin Seebeck effect across the spin-flip transition.
+
+Comment 1#: Sample Preparation: the preparation of the samples raises significant concerns. The authors employed sputtering to deposit heavy metals onto CrPS$_4$. This technique involves
+high-energy particles that can diffuse into the CrPS$_4$ lattice, potentially damaging its layered structure. In contrast, Ref. [32] carefully prepared a clean CrPS$_4$ surface and deposited Pd using molecular beam epitaxy (MBE), thereby avoiding such damage. It is highly likely that the sputtering process in the current study caused severe degradation of the CrPS$_4$ interface and its underlying structure.
+
+Reply to comment 1#: We thank the referee for raising this important question, which has allowed us to further refine our manuscript. We would like to clarify that, in our previous work (Ref. [32], now Ref. [38] in the revised manuscript), we used both sputtering and molecular beam epitaxy (MBE) to deposit Pt onto CrPS$_4$. We did not observe any significant differences between the samples prepared using these two methods. Therefore, our conclusion in Ref. [32] is that the sputtered CrPS$_4$/Pt sample performs similarly to the MBE-grown sample. There is no indication that the sputtering process causes significant degradation of CrPS$_4$, as the referee suggested.
+
+Furthermore, we would like to emphasize that sputter deposition is a common method for fabricating CrPS$_4$/Pt heterostructures (see, for example, NPG Asia Mater. 10, 23–30 (2018); Nat Commun. 14, 2526 (2023); Phys. Rev. B 107, L180403 (2023); Phys. Rev. B 110, 174440 (2024); arXiv:2409.02621 (2024)). These studies demonstrate that sputtered CrPS$_4$/Pt heterostructures exhibit good spin transmission at the interface, and there is no evidence of structural damage to the CrPS$_4$ layer.
+
+To better illustrate that magnetron sputtering can yield a sharp and well-defined interface, we conducted transmission electron microscope (TEM) analysis on the cross-section of a CrPS$_4$(104 nm)/Pt (22 nm) heterostructure. As shown in Fig. R3, the TEM results shows a very clean interface in CrPS$_4$/Pt heterostructure, which indicates that the vdW lattices are not affected by the deposition of Pt. These results agree well with our transport measurements. If the interface is damaged during the deposition of the Pt, we can not observe the SSE signal of the CrPS$_4$.
+Fig. R3 The cross-sectional TEM results of a CrPS₄/Pt heterstructure on the top of Si/SiO₂ substrate. (a) the TEM of the stack; (b) the HRTEM of an area at CrPS₄/Pt interface; (c) the High-Angle Annular Dark-Field Scanning Transmission Electron Microscopy (HAADF-STEM) image of an area at CrPS₄/Pt interface.
+
+Comment 2#: Material Properties: the state of CrPS₄ beneath the heavy metal layer remains unclear. It is uncertain whether the CrPS₄ in this region remains highly insulating. Such uncertainties make it challenging to accurately evaluate the intrinsic properties of CrPS₄. Without ensuring the integrity of the vdW material, the results cannot be conclusively attributed to the intended magnetic properties.
+
+Reply to comment 2#: We thank the reviewer for this question. As we discussed in the reply to the comment 1#, we have checked the interface using TEM, which shows a sharp and well-defined interface, as shown in Fig. R3. In addition to the TEM results, transport measurements on sputtered Pt on CrPS₄ indicate good spin transparency at the interface, with properties strongly linked to the magnetization of CrPS₄ (see, for example, Nat Commun. 14, 2526 (2023); Phys. Rev. B 107, L180403 (2023); Phys. Rev. B 110, 174440 (2024); arXiv:2409.02621 (2024)). Thus, We have eliminated the uncertainties and we believe the results can be conclusively attributed to the intended magnetic properties now.
+
+Comment 3#: Experimental Validation: to substantiate claims regarding vertical spin transport across the heavy metal/CrPS₄ interface, the authors should provide cross-sectional TEM images. This would clarify whether the interface is intact and whether the CrPS₄ structure is preserved beneath the heavy metal layer.
+Reply to comment 3#: We thank the reviewer for this valuable suggestion. Here, we conducted transmission electron microscope (TEM) analysis on the cross-section of the sample to demonstrate the sharp and well-defined interface in our sample. As shown in Fig. R3, the TEM results shows a very clean interface in CrPS4/Pt heterostructure, which indicates that the CrPS4 lattice is preserved after the deposition of Pt. These results agree well with our transport measurements. If the interface is damaged during the deposition of the Pt, we can not observe the SSE signal of the CrPS4.
+
+Comment 4#: Lack of Novel Physics: the manuscript does not present new insights or physics that would warrant publication in Nature Communications. Spin-flop and spin-flip phenomena could be more effectively studied using standard magnetization measurements rather than relying on the spin Seebeck effect, which remains a controversial and poorly understood phenomenon. Furthermore, the voltage signals reported are extremely small, significantly lower than those typically observed due to the anomalous Nernst effect.
+
+Reply to comment 4#: We appreciate the critical comment from the reviewer, as it has provided us with an opportunity to further elucidate the goal and novelty of this work. We would like to clarify again that the primary goal of our study is to understand the mechanism behind the spin Seebeck effect across the spin-flip transition, and to investigate the physics of the peak observed in the spin Seebeck signal at this transition. Our work does not aim to detect the spin-flip transition using the spin Seebeck effect. Instead, we focus on understanding the field-modulated magnon population and magnon excitation. Through our experimental and theoretical study, we observe that in antiferromagnets, the spin Seebeck effect first increases before the spin-flip transition and then decreases due to the suppressed magnon population associated with the magnon edge mode. In the case of an uncompensated interface, the closure of the magnon gap in the beta mode could lead to an enhanced magnon population, resulting in a peak at the spin-flip transition.
+
+We argue that the novelty of our work lies in being the first study of the spin Seebeck effect across the spin-flip transition in the weakly exchange-coupled van der Waals antiferromagnet. Our findings contribute to the fundamental understanding of the physics behind the spin Seebeck effect in this context.
+As our focus is on understanding the underlying physics of the spin Seebeck effect across the spin-flip transition, we did not specifically emphasize the magnitude of the spin Seebeck signal. Even though the signal is small, this does not reduce the significance of identifying the physical origin of the signal. To illustrate, the spin Seebeck resistance can be as high as 2.5 m\( \Omega \) with a 1 mA applied current at 15 K, corresponding to a spin Seebeck voltage of 2.5 \( \mu \)V—far larger than the spin Seebeck voltage in Pt/Fe\(_2\)O\(_3\) (below 0.3 \( \mu \)V at 300 K, Nat. Commun. 13, 3659 (2022)). However, such small magnitude of the signal in Pt/Fe\(_2\)O\(_3\) does not affect the importance of the work in Nat. Commun. 13, 3659 (2022). It is important to note, the spin Seebeck signal decreases at lower temperatures due to the reduced number of thermal populated magnon. The weakly coupled nature of CrPS\(_4\), with its magnon gap in the GHz range, would, in principle, lead to stronger thermal magnon excitation, and thus a large spin Seebeck signal compared with other system.
+
+Comment 5#: Spin Transport Limitations: spin transport across the heavy metal/CrPS\(_4\) interface, as well as along the c-axis, is expected to be poor due to the weak van der Waals coupling in CrPS\(_4\). This intrinsic limitation further diminishes the significance of the presented results.
+
+Reply to comment 5#: We appreciate the reviewer for pointing out this issue. Actually, Spin transport at CrPS\(_4\)/Pt (sputtered) interfaces have been well-studied, particularly in the context of magnon transport (see, for example, Nat Commun. 14, 2526 (2023); Phys. Rev. B 107, L180403 (2023); Phys. Rev. B 110, 174440 (2024); arXiv:2409.02621 (2024)). These studies clearly demonstrate that interfacial spin transport at CrPS\(_4\)/Pt is efficient. Combined with our own findings on spin Seebeck, these results unquestionably support the conclusion of good spin transport at the interface.
+
+To improve the readability of our manuscript, we have added a discussion on the efficiency of spin transport at the CrPS\(_4\)/Pt interface on page 9, highlighted in blue.
+
+Comment 6#: Conclusion: based on the above considerations, the study faces fundamental challenges in both experimental methodology and scientific contribution. The issues with sample preparation and lack of interface characterization compromise the reliability of the
+results, while the absence of novel insights into spin transport or antiferromagnetic properties limits the manuscript's impact. Therefore, I recommend rejection of this paper.
+
+Reply to comment 6#: We appreciate the referee's comments, which have helped improve the quality of our manuscript. However, we would like to clarify again that the primary aim of our work is to explore and understand the physics of the spin Seebeck effect across the spin-flip transition, rather than using the spin Seebeck effect to detect the spin-flip transition itself. Our work is the first study on the spin Seebeck effect as the first referee kindly suggested, from both experimental and theoretical study, we could understand the physics of spin Seebeck across the spin-flip transition.
+
+We also want to emphasize that previous studies on sputtered Pt on CrPS$_4$ consistently show good spin transport and the preservation of CrPS$_4$'s magnetism (see, for example, Nat Commun. 14, 2526 (2023); Phys. Rev. B 107, L180403 (2023); Phys. Rev. B 110, 174440 (2024); arXiv:2409.02621 (2024)). The new TEM results also support that the CrPS$_4$/Pt interface has high quality. Therefore, the concerns about sputtered Pt affecting the magnetic properties or spin transport are not an issue in our case.
+
+Furthermore, we would like to clarify that both sputtered Pt and heavy metal fabricated by MBE on CrPS$_4$ show similar transport properties, as noted in Ref. [32]. In our previous study in Ref. [32], we did not suggest that MBE-fabricated Pt is superior to sputtered Pt. In fact, sputtered Pt is commonly used to fabricate CrPS$_4$/Pt heterostructures, as we discussed earlier.
+SUMMARY OF CHANGES
+
+We have revised the discussion in the revised manuscript and Supporting Information. All changes to the text have been highlighted in blue in the revised manuscript and Supporting Information. Here is a list of the major changes:
+
+1. Include the HRTEM results in the Section S3 of Supplementary Information to demonstrate the sharp and well-defined interface of CrPS4/Pt heterostructure and the layered CrPS4 lattice is preserved after the deposition of heavy metal layer.
+2. Discuss the potential proximity effect on thermal effect, including the Nernst effect and the spin Seebeck effect.
+3. Clarify that the second harmonic resistance includes contributions from thermal effects.
+4. Revise the title to “Spin Seebeck in the Weakly Exchange-Coupled Van der Waals Antiferromagnet across the Spin-flip Transition”, emphasizing the study of the SSE across spin-flip transition in van der Waals antiferromagnet CrPS4.
+5. Modify the abstract to highlight that the SSE across the spin-flop transition has been extensively studied and emphasize the need for exploration of the SSE across the spin-flip transition using a weakly exchange-coupled antiferromagnet.
+6. Include and discuss recent works on magnon transport in CrPS4, demonstrating efficient spin transport at the interface of CrPS4 and sputtered Pt.
+7. Discuss the current dependence of the spin Seebeck effect and provide additional measurements of the field dependence of SSE in Section S8 of the Supporting Information.
+
+References that have been added in the main text to emphasize the uniqueness and novelty of our work compared to others:
+
+1. Feringa, F., Vink, J. M. & van Wees, B. J. Spin-flop transition in the quasi-two-dimensional antiferromagnet MnPS3 detected via thermally generated magnon transport. Phys. Rev. B 106, 224409 (2022).
+2. Liu, T. et al. Spin caloritronics in a CrBr3 – based magnetic van der Waals heterostructure. Phys. Rev. B 101, 205407 (2020).
+3. Tan, X., Ding, L., Du, G.-F. & Fu, H.-H. Spin caloritronics in two-dimensional CrI3/NiCl2 van der Waals heterostructures. Phys. Rev. B 103, 115415 (2021).
+4. de Wal, D. K., Zohaib, M. & van Wees, B. J. Magnon spin transport in the van der Waals antiferromagnet CrPS4 for noncollinear and collinear magnetization. Phys. Rev. B 110, 174440 (2024).
+5. de Wal, D. K., Mena, R. L., Zohaib, M. & van Wees, B. J. Gate control of magnon spin transport in unconventional magnon transistors based on the van der Waals antiferromagnet CrPS4. at https://arxiv.org/abs/2409.02621 (2024).
+6. Mañas-Valero, S., van der Sar, T., Duine, R. A. & van Wees, B. Magnon spintronics with Van der Waals magnets: from fundamentals to devices. at https://arxiv.org/abs/2411.14979 (2024).
+Reply to reviewer #2:
+
+General comments: I have studied the reply of the authors to the remarks of the reviewers, as well as the updated manuscript. In my opinion they have addressed most of the remarks satisfactorily. In particular they have correctly replied to the remarks of previous reviewer 3, concerning the possible damage of the heavy metal (Pt or other) to the surface layers of the CrPS4. Indeed previous experiments have shown that the interface (layers) still remain effective in transporting/communicating spin information. Also they correctly changed the title, to focus on the role of the spin-flip transition.
+
+Reply to general comment: We appreciate the reviewer’s time and effort in reviewing our manuscript and providing insightful comments. We are glad to hear that the reviewer finds most of our revisions satisfactory. We have carefully considered the new comments and have provided detailed responses to address them.
+
+Comment #1: My main remark is that the authors have not properly referred to related recent work. In particular they have now included reference 29 (and other references). As already remarked in the previous review round, reference 29 appeared on ArXiv on september 4. As far as I can tell this was before the (first) submission of the authors' manuscript. It was published in Phys. Rev. B. on November 22. This is after the first review round of the authors' paper. The emphasis of ref 29. is on the magnon transport as measured by the first harmonic signal. However there is substantial data, and discussion, on the local and non-local (second harmonic)Spin Seebeck signals, (e.g. in, and related to, figs. 3 and 4.). In addition the supplementary information of ref. 29 provides several experimental results on the local and non-local Spin Seebeck effect, in particular highlighting the role of the spin flip transition. In their manuscript the authors give an almost one page long introduction overview, describing the history of the spin Seebeck effect and how it was observed in various
+materials. However then they write about ref. 29: "More recent work has also investigated magnon transport in CrPS$_4$ (refs 28-30). However, the spin Seebeck effect in van der Waals antiferromagnets, especially across the spin-flip transition, remains an area requiring further investigation (refs. 31,32)" This strongly suggests to the reader that ref. 29 did NOT investigate the spin Seebeck effect across the spin-flip transition in CrPS$_4$. It is therefore not a proper way of referencing. In my opinion, given what I wrote above, the authors' manuscript should describe/summarize what has been observed in ref. 29, and discuss how their experiments and analysis compare to ref.29. Also, given the similarities between the authors' experiments and ref. 29, I consider it strange that it only appears as ref.29.
+
+Reply to comment #1: We are deeply grateful to the reviewer for the critical comments on the introduction section of our paper, especially regarding the inaccuracy in citing recent research progress. We acknowledge that we overlooked these details in the previous version and sincerely apologize for that. Regarding Ref. 29 [Phys. Rev. B 110 174440 (2024)], although we were aware of the relevant results, we missed the careful comparison of the similarities and differences between our work and that study in the previous version. Upon comparing the two works, we agree with the reviewer that Ref. 29 focuses on the nonlocal magnon transport at spin-flip points in CrPS$_4$. Since magnons can be generated through both electrical and thermal means, the latter of which is the spin Seebeck effect (SSE). Therefore, Ref. 29 also measured, both local and nonlocal SSE effects, which aligns with some of the results obtained in our paper. Ref. 29 suggests that the magnetic field dependence of the SSE is complex and that the temperature effect of SSE has not been fully understood. In our work, we conducted in-depth studies of the SSE using two different device configurations, confirmed the effect using materials with opposite spin Hall angles, and subsequently investigated the current, temperature, magnetic field, and angle dependencies of the effect. Combining theoretical insights, we understood the behavior of SSE at spin-flip points and its magnetic field and temperature dependencies. We believe that both works, which focused on and measured similar
+effects around the same time, underscore the importance of this fundamental scientific issue and the correctness of the experimental results obtained. Our article provides explanations for the questions raised in Ref. 29. It can be said that together, the two works have thoroughly investigated this issue. We have meticulously addressed these issues in our manuscript by providing a comprehensive description of Ref. 29, deleting part of the historical background on the spin Seebeck effect, and explicitly citing Ref. 29 wherever we obtained similar results.
+
+To address these issues, we have made the following changes to the manuscript:
+
+-We have deleted “The phenomenon was initially discovered in 2008, and various configurations have been suggested to explore the SSE, such as transverse SSE, longitudinal SSE, and nonlocal SSE. Additionally, it has been examined in a range of magnetically ordered systems, including ferromagnets, ferrimagnets, antiferromagnets, paramagnets, chiral helimagnets, and quantum magnets, where the magnon excitations play critical roles regardless of long-range or short-range magnetic interactions” in the INTRODUCTION section to avoid the detailed description of the history of SSE.
+
+-We have included “Especially, in Ref. 29, in addition to discovering nonlocal magnon transport of CrPS4/Pt with in-plane magnetic field across the spin-flip transition, a distinct peak of SSE signal around the spin-flip transition and a sign change of non-local SSE signal below 15 K were observed but the mechanism remains to be understood (Ref 29). These latest results indicate that the spin Seebeck effect in van der Waals antiferromagnets, especially across the spin-flip transition, remains an area requiring further investigation (Ref 31, 32)” in the INTRODUCTION section to summarize what has been observed in ref. 29.
+
+-We have added “In the canted phase, the SEE increases with the strength of the applied magnetic field, similar to the local SSE signal in Ref. 29.” and “…and also seen in local and non-local SSE signals in Ref. 29, which confirm the robustness of
+this effect.” in the RESULTS section to emphasize that these effects have been reported in Ref. 29.
+
+Comment #2: Finally, I am not against publication of the authors’ manuscript, since it is scientifically sound, and addresses a relevant problem. But I can only recommend it when the the authors' results are put in a proper scientific context.
+
+Reply to comment #2: We thank the reviewer for the constructive feedback and for acknowledging the scientific soundness of our manuscript. We fully appreciate your concern about the need to place our results in a proper scientific context. As discussed in the reply to the last comment, we have carefully revised the introduction section of our manuscript, particularly focusing on accurately citing recent research progress and clearly distinguishing our work from that of others, such as Ref. 29. We have provided a detailed comparison of our work with Ref. 29, highlighting the unique contributions of our study and how it addresses the underlying physics of complex behavior of the SSE and its dependencies on various parameters. We believe that these revisions have significantly improved the manuscript and have placed our results in a more accurate and informative scientific context. We hope that you will find the revised manuscript to be suitable for publication.
+Reply to reviewer #3:
+
+Regarding the Pt sputtering, the authors presented a TEM image of the cross-section around the CrPS4/Pt interface. While I generally agree with the authors' arguments, I still have the following concerns:
+
+Reply to general comment: We are grateful to the reviewer for acknowledging our TEM results and for once again providing suggestions for improvement. We have carefully responded to the reviewer's comments and made revisions accordingly to the manuscript. We hope that the revised manuscript can be accepted for publication.
+
+Comment #1: The detection of spin flop in antiferromagnets was first reported in Phys. Rev. Lett. 116, 097204 (2016). Additionally, there have been numerous reports on van der Waals (vdW) antiferromagnets. In those studies, no reduction in the spin Seebeck effect (SSE) voltage was observed after the spin flop transition. This aspect might represent the unique contribution of the present article. However, even in the same antiferromagnet, CrPS4, no reduction in SSE voltage was reported in arXiv:2409.02590. The authors should provide a detailed discussion of this point to clarify their findings.
+
+Reply to comment #1: We sincerely thank the reviewer for their comment, as it has provided us with the opportunity to further clarify our results. It is important to note that spin-flop and spin-flip are distinct concepts in the context of antiferromagnets. Typically, the spin-flop transition occurs at a lower magnetic field than the spin-flip transition. Consequently, there has been considerable research on the spin Seebeck effect (SSE) across the spin-flop transition (as evidenced in Phys. Rev. Lett. 116, 097204 (2016)).
+
+In our work, we have focused specifically on the behavior of the SSE across the spin-flip transition, rather than the spin-flop transition. This focus was only feasible in antiferromagnetic materials with a weak exchange coupling, such as CrPS4. Using a
+longitudinal configuration, we observed a peak in the SSE at the spin-flip transition in CrPS$_4$, with the SSE decreasing above this transition. This observation is also noted, albeit not fully understood, in a recently published study (arXiv:2409.02590, now published in Phys. Rev. B 110, 174440 (2024), please refer to their supplementary information, Figure S7, for the SSE effect). Therefore, we believe that the observed reduction in SSE above the spin-flip transition is true and robust. We also have provided a theoretical model in the manuscript as well as Supplementary Information S8 to explain this reduction.
+
+Additionally, in our non-local devices, we observed a feature of the spin-flop transition when applying a magnetic field along the out-of-plane (OOP) direction. We attribute the small peak at the spin-flop transition to the divergence of spin conductance as the magnon gap closes near the spin-flop transition, as indicated in [Phys. Rev. Lett. 119, 056804 (2017)]. It is worth noting that the study in [Phys. Rev. Lett. 116, 097204 (2016)] used an antiferromagnetic material with an in-plane easy axis, whereas we used CrPS$_4$ with an out-of-plane easy axis. Therefore, the observed effects should differ between these studies.
+
+We have made the following change in the manuscript to make it more clarifying:
+
+-We have added “*A theoretical model indicates that the linear increase of SSE with increasing magnetic field below the spin-flip transition is dominated by the spin canting angle, while the decrease of SSE with further increasing magnetic field above the spin-flip transition is dominated by increased energy of magnon modes.*” in INTRODUCTION section to explain why there is a reduction in the SSE at field above the spin-flip transition.
+
+We hope that the above response has addressed the reviewer's concerns.
+
+Comment #2: For the detection of longitudinal SSE, a simple Pt strip is typically used. In this experiment, however, the authors employed a Hall bar structure, which raises questions about the precise heating and detection points in their setup. The
+authors should provide a comprehensive analysis of the temperature profile across the entire device structure, supported by numerical simulations. This is particularly crucial because heat transport in vdW materials often exhibits anisotropic behavior. Therefore, the heat transport in this system should be analyzed with greater accuracy.
+
+Reply to comment #2: We are grateful to the referee for kindly highlighting the concerns regarding the Hall bar structure employed in our study of the longitudinal Spin Seebeck Effect (SSE). The longitudinal configuration, was initially utilized in Pt/YIG junctions to investigate the Longitudinal Spin Seebeck Effect (LSSE) in magnetic insulators [Appl. Phys. Lett. 97, 172505 (2010)]. Compared to the simple Pt strip, the Hall bar structure allows for the measurement of the SSE in both the longitudinal and transverse directions. This is achieved by applying a magnetic field along the transverse and longitudinal directions, respectively, and offers both experimental simplicity and versatility.
+
+So far, the Hall bar has been extensively applied to the study of SSE in various types of heterostructures [Appl. Phys. Lett. 103, 242404 (2013); Phys. Rev. B 90,174436 (2014); Appl. Phys. Lett. 106, 212407 (2015); Nat. Commun. 7, 11458 (2016); Phys. Rev. B 103, 134406 (2021), ; Phys. Rev. Lett. 132, 056702 (2024) ]. In particular, It is well established that the second harmonic voltage observed in harmonic current-induced torque measurements includes thermal effects, including the Nernst and spin Seebeck effects [Phys. Rev. B 90, 224427 (2014); Commun. Phys. 4, 234 (2021); Phys. Rev. Res. 4, 033037 (2022); Nature Communications 13(1):3659 (2022); Phys. Rev. Lett. 132, 236702 (2024); npj Spintronics 2, 43 (2024), etc.]. We have excluded the possibility of the Nernst effect in CrPS$_4$/Pt as we discussed in the main text. Since the current is applied through the current channel within the Hall bar, the primary heated zones encompass the current channel and the CrPS$_4$ material directly beneath it. In our Hall device design, we have strategically etched away the CrPS$_4$ outside the Hall bar area, as depicted in Figure R1a. Consequently, anisotropic heat transport is negated, as thermal energy can only propagate from Pt to CrPS$_4$ in the $z$-direction, as shown in Figure R1b. This device configuration, together with the
+temperature difference between the Pt layer and the Si/SiO$_2$ substrate, leads to a temperature gradient along the z-direction within the CrPS$_4$/Pt heterostructure.
+
+![Schematic diagrams of CrPS4/Pt Hall bar devices and spin Seebeck effect](page_312_370_823_246.png)
+
+Figure R1. **a.** Schematic of the CrPS$_4$/Pt Hall bar devices for the longitudinal spin Seebeck effect. The alternating current heats the sample, creating a vertical heat gradient and generating a spin current perpendicular to the sample plane. **b.** The schematics of spin Seebeck effect in CrPS$_4$ in contact with Pt.
+
+Additionally, we utilized COMSOL to simulate the temperature distribution and temperature gradient of the device. As shown in Figure R2, the device consists of a 5-nm-thick layer of Pt, a 75-nm-thick layer of CrPS$_4$, a 275-nm-thick layer of SiO$_2$, and a 0.4-mm-thick layer of Si. In the device, the CrPS$_4$ outside the Hall bar region is completely etched. The device is surrounded by He at 0.1 mtorr, with the temperature kept at 10 K. We also assumed the temperature of Si to be 10 K. We applied a 1 mA alternating current through the current channel of the Hall bar, which only passes through the Pt, thereby generating Joule heating. The resistivity of Pt is $1.1 \times 10^{-6}$ $\Omega$·m. The Joule heat is transferred through CrPS$_4$ to SiO$_2$ and Si on one hand, and absorbed by the He gas on the other. The thermal conductivity coefficients of the materials we used are: Pt (70 W/m·K), CrPS$_4$ (0.5 W/m·K), SiO$_2$ (0.12 W/m·K), He gas (0.01 W/m·K). Ultimately, we found that the temperature of CrPS$_4$ at equilibrium increased by about 4 K, consistent with the reduced spin-flip field shown in Figure 2f. Additionally, the in-plane temperature gradient mainly exists at the intersection of the
+measurement terminals and the current channel. The out-of-plane direction shows a significant temperature variation with depth, and from the temperature gradient, it is evident that the CrPS$_4$ layer exhibits a noticeable temperature gradient, approximately $4.2 \times 10^6$ K/m. This temperature gradient is the basis for the spin Seebeck effect observed. Although there is also a certain in-plane temperature gradient, due to a symmetric gradient, the effects generated by this gradient cancel out, making it undetectable. Since the CrPS$_4$ was etched out in the area outside the Hall bar, the heat transport along the z-direction dominates in the CrPS$_4$ layer. Thus, the anisotropic thermal conductivity of CrPS$_4$ does not play a significant role in this case.
+
+![Simulation of the temperature profile in the Hall bar device: schematic, model, stabilized in-plane temperature distribution, in-plane temperature gradient, cross-sectional temperature distribution, and z-direction temperature gradient.](page_184_573_1080_393.png)
+
+Figure R2. The simulation of the temperature profile in the Hall bar device: **a**. The schematic of the Hall device. **b**. A model of the device used for the simulation. **c**. The stabilized in-plane temperature distribution of the device with a current of 1 mA was applied through the current channel. **d**. The in-plane temperature gradient along the y direction. **e**. The cross-sectional temperature distribution of the device. **f**. The z-direction temperature gradient in the cross-section.
+
+To address these issues, we have made the following changes in both manuscript and supplementary information:
+
+-We have included the simulation of the temperature profile of the device in *Supplementary Information S6* and discussed in RESULTS section of the manuscript as “*A numerical simulation of the temperature distribution in the device can be seen*
+in Supplementary Information S6. The simulation shows that a temperature change of about 4 K is induced in CrPS$_4$ via Joule heating under the experimental conditions, in good agreement with the observed change in the spin-flip field. The simulation also shows a prominent temperature gradient in the CrPS$_4$ layer (~ \(4.2 \times 10^6\) K/m), which is the basis for the observed SSE."
+
+Comment #3: Additionally, I would like to inquire about the fabrication procedure for the nonlocal device. The manuscript does not specify any differences between the fabrication processes for the local and nonlocal devices. In the nonlocal device, two separate Pt strips were prepared on CrPS$_4$. If the fabrication process for the Pt strips was the same as for the Hall bar, stopping the Ar ion etching precisely at the surface of CrPS$_4$ would be extremely challenging. Furthermore, Ar ion irradiation could potentially damage the magnetic properties of the material. The authors should address these concerns in their discussion and clearly explain how they ensured the etching stopped accurately at the Pt/CrPS$_4$ interface.
+
+Reply to comment #3: We thank the reviewer for their insightful comment. In response, we have included the optical micrograph (as shown in Figure R3) and related information about the nonlocal device in Supporting Information S2. As the reviewer has pointed out, precise control of the endpoint in the ion beam etching (IBE) process is crucial and challenging. To achieve this, we carefully calibrated the etching rate of Pt in our IBE system using an atomic force microscope (AFM) to accurately measure the thickness of the etched Pt layer. By controlling the Pt etching rate at a slow speed of 0.17 nm/s, we were able to estimate the etching time required for a 7 nm Pt layer deposited on exfoliated CrPS$_4$ to be approximately 41 seconds. This ensures that the Pt is fully etched while largely preserving the integrity of the CrPS$_4$ surface However, we must acknowledge that in this top-down process, we cannot guarantee full protection of the top layer of CrPS$_4$, and can only strive to protect it to the greatest extent possible. It is also important to note that magnons can propagate not only through the surface of CrPS$_4$ but also predominantly through the bulk layers due to antiferromagnetic interlayer coupling and the heat gradient. Consequently, any
+minimal error in determining the etching endpoint, once the Pt has been etched away, does not significantly impact the results. In fact, we have observed similar outcomes across three distinct non-local devices, suggesting that this effect remains robust even in the presence of potential surface damage to CrPS$_4$ caused by Ar ion etching.
+
+![Optical micrograph of the nonlocal device CrPS4/Pt device on the top of Si/SiO2 substrate.](page_370_613_495_246.png)
+
+Figure R3. Optical micrograph of the nonlocal device CrPS$_4$/Pt device on the top of Si/SiO$_2$ substrate.
+
+To address this issue, we have added the above discussion in the Supplementary Information S3.
+
+Comment #4: Moreover, the separation distance between the Pt strips in the nonlocal device should be explicitly stated. Without this information, it is difficult to evaluate the experimental design.
+
+Reply to comment #4: We greatly appreciate the reviewer for bringing this issue to our attention. In fact, we have already included this information in the METHODS section of our manuscript. Specifically, the non-local device utilized in our work features an edge-edge separation distance of 1.6 \( \mu \)m between the Pt (7 nm) strips. The width of the detection strip and the injection strip is 1.4 \( \mu \)m and 2.3 \( \mu \)m, respectively.
+
+Comment #5: The following additional points also need clarification:
+
+Where exactly is the heating point in the Hall bar structure?
+How do the IV characteristics and angular dependence impact the results?
+
+The authors have not provided sufficient evidence for the role of the spin Hall effect.
+
+Reply to comment #5: We thank the reviewer for pointing out these issues which are answered below.
+
+Q: Where exactly is the heating point in the Hall bar structure?
+
+A: Since the current is applied through the current channel within the Hall bar, the primary heated zones encompass the current channel and the CrPS$_4$ material directly beneath it. In our Hall device design, we have strategically etched away the CrPS$_4$ outside the Hall bar area, as depicted in Figure R1a. Consequently, anisotropic heat transport is negated, as thermal energy can only propagate from Pt to CrPS$_4$ in the $z$-direction, as shown in Figure R1b. This device configuration, together with the temperature disparity between the Pt layer and the Si/SiO$_2$ substrate, facilitates the establishment of a temperature gradient within the CrPS$_4$/Pt heterostructure along the $z$-direction.
+
+Q: How do the IV characteristics and angular dependence impact the results?
+
+A: The IV characteristic of Platinum is expected to be linear since the current can only follow through the metallic Pt as we have discussed in the manuscript. As we know, the SSE effect is related to the temperature gradient \( \nabla T \), thus related to the heat power at the current channel. According to the formula of the power \( P = I \times V = I^2 R \), where I and V stand for the current and voltage and R stands for the resistance, the \( \nabla T \) is determined by both I and R. With a constant R of Pt, the increased I and V will give a larger \( \nabla T \) and thus a larger SSE effect. However, it should be noted that the IV characteristics itself would impact neither the detection nor analysis of the SSE across the spin-flip transition in this study.
+
+The angular dependence (in the xz plane) of \( R_{xy}^{2\theta} \), i.e. the SSE signal, under different fields at an ambient temperature of 15 K of longitudinal SSE device is shown in Fig.
+R3(b) below (also see figure 1(d) of the revised manuscript). The amplitude of the \( R_{xy}^{2\omega} \) signal shows obvious angular dependence as the magnetic field rotates in the xz plane, and the maximum value is reached when the magnetic field is parallel to the x-direction, that is, the magnetic field is parallel to the spin current. The \( R_{xy}^{2\omega} \) signal for the magnetic field along the z-direction or y-direction is much smaller than that of the magnetic field along the x-axis. Thus, with the angular dependence, it is confirmed that the measured effect is exactly the SSE.
+
+Q: The authors have not provided sufficient evidence for the role of the spin Hall effect.
+
+A: In this work, we use the spin Hall effect of the heavy metal to detect the SSE. Thus, we have carefully checked the impact of the spin Hall angle in different heavy metals on the SSE, as shown in Figure 2 in the manuscript. Here, we would like to clarify it again. As shown in Figure R3, the field dependence of \( R_{xy}^{2\omega} \) at various temperatures have been studied for both CrPS4/Pt (5 nm) and CrPS4/Ta (11 nm) devices (also see Figure 2(b) and (e) in the manuscript). As the inverse spin hall voltage is given by \( E_{ISHE} \propto \theta_{SH} J_s \times \sigma \), the opposite spin Hall angles of Pt and Ta (Jpn. J. Appl. Phys. 56, 0802B5 (2017)) leads to the thermally generated spin current yield SSE signals with opposite polarities in CrPS4/Pt and CrPS4/Ta devices. Thus, the opposite SSE signal displayed in Fig. R3(c) is undoubtedly attributed to the influence of the spin Hall effect.
+
+To clarify this, we have made following changes in the manuscript:
+
+-We have added “*The SSE signal involves the following three physical processes: first,...; second,...; finally, the spin current is converted into a charge current via the ISHE.*” on page 10 to emphasize the role of inverse spin-Hall effect (ISHE) in the detection of SSE.
+Figure 3. a. Schematic of the CrPS4/Pt Hall bar devices for the longitudinal spin Seebeck effect. b. Angular dependence (in the xz plane) of \( R_{xy}^{2\omega} \) of CrPS4/Pt Hall bar device at different fields at a temperature of 15 K and an applied current of 1 mA (peak value). c and d. Field dependence (\( \mu_0 H_x \)) of \( R_{xy}^{2\omega} \) at various temperatures for both CrPS4/Pt (5 nm) (applied current of 1 mA) and CrPS4/Ta (11 nm) (applied current of 0.6 mA).
+
+Comment #6: For these reasons, I maintain my initial decision not to recommend the publication of this manuscript in its current form. The authors need to address the aforementioned issues, particularly the fabrication procedure. How exactly do they ensure the Ar-ion etching stops just after the Pt metal layer? Clear answers to these points are necessary for further evaluation.
+
+Reply to comment #6: We extend our gratitude to the reviewer for his/her valuable comments. As discussed previously, we believe we have addressed the reviewer's concerns. We have provided a detailed description of the non-local device fabrication process. During the etching step, we employed a precisely calibrated etching rate to
+maximize the protection of the CrPS$_4$ surface. As we have noted, due to inherent experimental errors, a minimal amount of damage to the top layer of CrPS$_4$ is unavoidable. However, this minimal damage to the CrPS$_4$ surface in the area between two Pt strips will not significantly impact the detection of the spin Seebeck effect. This is because magnons can propagate not only through the surface of CrPS$_4$ but also through its bulk layers, facilitated by interlayer exchange coupling, allowing for transport in both lateral (x-y) and vertical (z) directions.
+
+We appreciate the valuable comments from the referee, which have provided us with an opportunity to further enhance the quality of our work. With additional simulations and revisions, we hope that our responses have addressed the concerns, and that the revised manuscript is now suitable for publication.
+
+SUMMARY OF MAJOR CHANGES
+
+We have revised the discussion in the manuscript and Supporting Information including in particular:
+
+— We have expanded our discussion by summarizing the key discoveries from Ref. 29. We compare the experimental findings and analysis from Ref. 29 with our work, emphasizing the significance and novelty of their contributions. Ref. 29 played a crucial role in advancing the study of the Spin Seebeck Effect (SSE) in van der Waals materials, serving as an important reference that has stimulated further research in this area. In the revised manuscript, we have modified the introduction by removing the redundant historical background of the SSE and instead focusing more on recent studies, particularly highlighting the similarities and key findings from Ref. 29. Adding discussion and comparison of our results with the results from Ref. 29 marked in blue in the revised manuscript.
+— We have discussed the heat gradient in the Hall bar devices by applying alternating current and we used COMSOL to simulate the temperature distribution and the temperature gradient within the device, which is included in the revised manuscript on page 8 marked in blue and in section S6 in the revised SI.
+
+— We have included the optical micrograph and fabrication details (including the Ar+ etching) of nonlocal devices in section S3 in the revised SI.
+Reply to Reviewer #2
+
+Comment #1: The authors have carefully addressed the remarks of the previous reviewers, and made the according changes. In particular they now provide more information on the results of ref. 29 and provide more discussion how their experiments are related to those of ref. 29. Although it is not the main message of the paper, this is nonetheless the pioneering study of magnetic field dependence (in particular spin flip) of the spin Seebeck effect in CrPS4, in both local and non-local geometries.I will accept the paper for publication now, but would appreciate if the authors could give this a bit more attention in the description of ref.29.
+
+Answer to comment #1: We thank the reviewer for the recommendation. We have also strengthened the description of Ref. 29 by adding a sentence of “Although the SSE is not the main focus of Ref. 29, it is nonetheless a pioneering study on the magnetic field dependence (especially spin flip) of this effect in CrPS4” in the introduction. I hope that the current description of the contributions of Ref. 29 in this direction is now more comprehensive.

07d4a546b84977cbe671fd9636cce724b9118c33a913f81362f52341cbf8a751/preprint/preprint.md

@@ -0,0 +1,231 @@
+Spin Seebeck in the weak exchange coupled van der Waals antiferromagnet
+
+Rui Wu
+ruiwu001@scut.edu.cn
+
+South China University of Technology   https://orcid.org/0000-0003-2010-5961
+
+Xue He
+South China University of Technology
+
+Shilei Ding
+https://orcid.org/0000-0002-5534-6901
+
+Hans Giil
+Norwegian University of Science and Technology
+
+Jicheng Wang
+South China University of Technology
+
+Zhongchong Lin
+Peking University
+
+Zhongyu Liang
+Peking university   https://orcid.org/0000-0002-7872-7571
+
+Jinbo Yang
+State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871
+https://orcid.org/0000-0003-3517-9701
+
+Mathias Kläui
+Johannes Gutenberg University of Mainz   https://orcid.org/0000-0002-4848-2569
+
+Arne Brataas
+Norwegian University of Science and Technology   https://orcid.org/0000-0003-0867-6323
+
+Yanglong Hou
+Shenzhen Campus of Sun Yat-Sen University
+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 28th, 2025. See the published version at https://doi.org/10.1038/s41467-025-58306-3.
+Spin Seebeck in the weak exchange coupled van der Waals antiferromagnet
+
+Xue He1, Shilei Ding2*, Hans Glockner Giil3, Jicheng Wang1, Zhongchong Lin4, Zhongyu Liang4, Jinbo Yang4*, Mathias Kläui3,5, Arne Brataas3, Yanglong Hou6,7*, Rui Wu1*
+
+1. Spin-X Institute, School of Physics and Optoelectronics, State Key Laboratory of Luminescent Materials and Devices, and Guangdong-Hong Kong-Macao Joint Laboratory of Optoelectronic and Magnetic Functional Materials, South China University of Technology, Guangzhou 511442, China
+2. Department of Materials, ETH Zürich, 8093 Zürich, Switzerland
+3. Center for Quantum Spintronics, Norwegian University of Science and Technology, Trondheim 7491, Norway
+4. State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing 100871, P.R. China
+5. Institute of Physics, Johannes Gutenberg-University Mainz, Staudingerweg 7, Mainz 55128, Germany
+6. School of Materials, Shenzhen Campus of Sun Yat-Sen University, Shenzhen 518107, China
+7. School of Materials Science and Engineering, Beijing Key Laboratory for Magnetoelectric Materials and Devices, Peking University, Beijing 100871, China
+
+*Corresponding author: shilei.ding@mat.ethz.ch, jbyang@pku.edu.cn, hou@sysu.edu.cn, and ruiwu001@scut.edu.cn.
+
+Spin Seebeck effect (SSE) refers to the creation of spin currents due to a temperature gradient in the magnetic materials or across magnet-normal metal interfaces, which can be electrically detected through the inverse spin Hall effect (ISHE) when in contact with heavy metals. It offers fundamental insights into the magnetic properties of materials, including the magnetic phase transition, static magnetic order, and magnon excitations. However, the SSE in van der Waals antiferromagnet is still elusive, especially across the spin-flip transition. Here, we demonstrate the SSE in the
+weak exchange coupled van der Waals antiferromagnet CrPS$_4$. The SSE increases as the magnetic field increases before the spin-flip transition due to the enhancement of the thermal spin current as a function of the applied field. A peak of SSE is observed at the spin-flip field, which is related to the magnon mode edges across the spin-flip field. Our results extend SSE research to van der Waals antiferromagnets and demonstrate an enhancement of SSE at the spin-flip transition.
+
+Thermoelectricity combines heat transfer and electric voltage in solid materials, presenting a promising option for green energy production by harnessing waste heat with a simple device design$^1$. In particular, thermal spintronics effect utilize nonequilibrium magnon transport phenomena in the presence of a heat gradient, enabling magnetic insulators to serve as effective thermoelectric devices$^2$. The spin Seebeck effect (SSE) has therefore drawn significant interest, where a temperature gradient ($\nabla T$) in magnetic materials leads to the generation of spin currents ($J_s$). SSE can be subsequently detected via the inverse spin Hall effect (ISHE) in a heavy metal contact with strong spin-orbit coupling$^{3-24}$. The phenomenon was initially discovered in 2008$^5$, and various configurations have been suggested to explore the SSE, such as transverse SSE$^6$, longitudinal SSE$^7$, and nonlocal SSE$^8$. Additionally, it has been examined in a range of magnetically ordered systems, including ferromagnets$^{5,9}$, ferrimagnets$^{6,10}$, antiferromagnets$^{11-15}$, paramagnets$^{16}$, chiral helimagnets$^{17}$, and quantum magnets$^{18}$, where the magnon excitations play critical roles regardless of long-range or short-range magnetic interactions.
+
+In ferromagnet/heavy metal bilayers, the SSE observed below the Curie temperature is associated with the spin current generated by thermally excited magnons that exhibit only right-handed chirality$^{19}$. The SSE mechanism in antiferromagnetic heterostructures is more complex due to two magnetic sublattices, which result in different magnon modes$^{20-23}$. In a uniaxial antiferromagnet, there are two magnon branches with opposite chirality carrying opposite angular momentum. These modes are degenerate at zero magnetic field, meaning there is no net magnon current until a field is applied to lift this degeneracy. A change in the sign of the SSE was observed during the spin-flop transition$^{14,15}$, which is attributed to the change in the chirality of the thermally excited magnon mode, which dominates. Additionally, the interfacial Néel coupling and spin conductance can influence the sign and
+magnitude of the SSE\(^{21,23}\). Nonetheless, the spin Seebeck effect in van der Waals antiferromagnets requires further investigation\(^{25,26}\), particularly in the van der Waals system with interlayer antiferromagnetic coupling, which typically suggests weak exchange coupling and a low spin-flip field.
+
+CrPS\(_4\) is an antiferromagnetic van der Waals material constituted of chains of chromium octahedra interconnected through phosphorus\(^{27-33}\) as shown in Fig. 1a. Due to the chemical composition and multi-bonded crystal structures, CrPS\(_4\) is a comparably air-stable material that makes the device fabrication easier compared with other van der Waals materials\(^{34}\). It shows a sizeable Néel temperature (\(T_N = 36\) K) and A-type antiferromagnetic ordering\(^{27}\). Unlike the conventional bulk antiferromagnetic materials, CrPS\(_4\) with a layered structure exhibits extremely weak interlayer interactions between sublattice spins, where spins within each monolayer are aligned ferromagnetically out of the plane, subsequently leading to the weak spin-flop field (0.8 T at 5 K) and spin-flip field (7 T at 5 K) as shown in Fig. 1b . This characteristic also significantly lowers the frequency of antiferromagnetic magnons to the GHz range\(^{35}\). As a result, it provides easier access to antiferromagnetic dynamics. Notably, it improves the efficiency of the thermal magnon population compared to traditional antiferromagnets with a large magnon gap, making CrPS\(_4\) an excellent candidate for investigating the mechanism of SSE in antiferromagnets.
+
+Here, we demonstrate the SSE in CrPS\(_4\) in contact with a heavy metal. A vertical temperature gradient in CrPS\(_4\) drives the magnon current in the longitudinal SSE configuration. The SSE increases as a function of the applied field before the spin-flip transition. The enhancement of the canted magnetization leads to pronounced magnon pumping. At the spin-flip field, a peak and saturation of SSE is observed that further disappears above the Néel temperature.
+Fig.1 Structure and magnetic properties of CrPS$_4$ and the Hall bar device for spin Seebeck effect (SSE) measurement. **a** Crystal structure of CrPS$_4$. The red and blue arrows indicate the direction of the magnetic moment. **b** The magnetic measurements at 15 K are taken both along and perpendicular to the $c$-axis. The spin-flop and spin-flip transitions appear when the magnetic field is aligned with the $c$-axis. In contrast, only the spin-flip transition occurs when the field is applied perpendicularly to the $c$-axis, **c** Schematic of the Hall bar devices for the longitudinal spin Seebeck effect. The alternating current heats the sample, creating a vertical heat gradient and generating a spin current perpendicular to the sample plane. **d** Angular dependence (in the $xz$ plane) of $R_{xy}^{2\omega}$ at different fields at a temperature of 15 K and an applied current of 1 mA (peak value). **e** Applied current dependence of $R_{xy}^{2\omega}$ (at 9 T) at 15 K. The dashed-dot line is the linear fit.
+
+Results
+
+Longitudinal SSE in CrPS$_4$/Pt(Ta). To obtain CrPS$_4$/Pt heterostructures for the SSE measurements, we deposited 5 nm Pt on top of exfoliated CrPS$_4$ flakes and subsequently fabricated Hall bar devices (see methods for details and schematic in Fig. 1c). The structure and phase of the CrPS$_4$ are characterized with X-ray Diffractometer and Raman spectroscopy (details see Supplemental Material S1). The microscopic picture of the
+CrPS4/Pt Hall bar device can be found in Supplemental Material S2, where one could obtain the thickness of the CrPS4 flake to be 75 nm. An alternating current (\( \tilde{I} \)) is applied to the Hall bar to generate vertical temperature gradient \( \nabla T \), leading to the population of spin current \( J_s = -S \nabla T \). \( S \) is the SSE coefficient. By further applying a magnetic field, it is possible to observe the SSE detected via the inverse spin Hall effect. The resultant electric field \( E_{\text{ISHE}} \) is given by\(^3\)
+
+\[
+E_{\text{ISHE}} \propto \theta_{\text{SH}} J_s \times \sigma,
+\]
+
+Where \( \theta_{\text{SH}} \) is the spin Hall angle. \( \sigma \) is the spin polarization direction, which is parallel to the equilibrium magnetization \( M \). Since the temperature gradient results from the heating power of Pt, which is proportional to \( \tilde{I}^2 \), it is expected that the thermal signal can be detected through the second harmonic response \( R_{xy}^{2\omega} \).
+
+In the magnetic material/Pt bilayer system, \( R_{xy}^{2\omega} \) typically involves different factors, including current-induced torque and thermal effects, which encompass the Nernst and spin Seebeck effects\(^{36}\). The electric field induced by the Nernst effect can be expressed as \( E_{\text{NE}} \propto \nabla T \times M^{37} \), which share the same symmetry as SSE in the longitudinal configuration. When a strong magnetic field is applied, the current-induced torque is suppressed\(^{36}\), leaving only thermal effects in the second harmonic response \( R_{xy}^{2\omega} \). Fig. 1d illustrates the angular dependence of \( R_{xy}^{2\omega} \) in the \( xz \) plane under different applied fields with the applied current of 1 mA (peak value) and the ambient temperature of 15 K. \( R_{xy}^{2\omega} \) reaches the maximum when the magnetic field is aligned with the \( x \)-axis and disappears when aligned with the \( z \)-axis (or \( c \)-axis), and the angular dependence data can be fitted well using the sine function following the Eq. (1). By applying an in-plane magnetic field, the Zeeman splitting lift the degeneracy of the two magnon eigenmodes, resulting in the spin current that induces the SSE signal (see discussion below and Fig. 3c). In the canted phase, the SEE increases with the strength of the applied magnetic field. This increase is generally attributed to the larger canted magnetization resulting from a strong magnetic field\(^{23,38}\) or the increased SSE coefficient in response to the magnetic field\(^{39}\). This fundamentally differs from the SSE in ferromagnets, where an increased applied field would open the magnon gap, causing a decrease in SSE due to the reduction of the thermal magnon population\(^4\). Additionally, the
+magnitude of \( R_{xy}^{2\omega} \) is proportional to the applied current as shown in Fig. 1e, demonstrating a thermoelectric nature similar to previous findings\(^{40}\). It is important to note that CrPS\(_4\) has a semiconducting characteristic with an energy gap of \( E_a = 0.166 \) eV, and the resistivity \( \rho \) of CrPS\(_4\) is reported to be \( \sim 2 \times 10^4 \) \( \Omega \) cm at 200 K\(^{24}\). By applying the Arrhenius equation\(^{41} \ln \rho = \ln \rho_0 - E_a / k_B T \), one could estimate that the resistivity of CrPS\(_4\) below 50 K is higher than \( 1 \times 10^{12} \) \( \Omega \) cm, allowing us to safely rule out the Nernst effect from conducting electrons in CrPS\(_4\).
+
+![Schematics and plots showing spin Seebeck effect in CrPS4/Pt and CrPS4/Ta, and temperature dependence of SSE effective resistance](page_370_682_1097_410.png)
+
+Fig. 2 Temperature dependence of the SSE in CrPS\(_4\)/Pt and CrPS\(_4\)/Ta. **a** and **d** The schematics of spin Seebeck effect in CrPS\(_4\) in contact with Pt and Ta, the differing signs of the spin Hall angle result in a change in the sign of the SSE. **b** and **e** Field dependence (\( \mu_0 H_x \)) of \( R_{xy}^{2\omega} \) at various temperatures for both CrPS\(_4\)/Pt (5 nm) (applied current of 1 mA) and CrPS\(_4\)/Ta (11 nm) (applied current of 0.6 mA). **c** Temperature dependence of the SSE effective resistance in CrPS\(_4\)/Pt at 9 T, along with the magnetization as a function of temperature under a 50 mT applied field. The N\'eel temperature (\( T_N \)) is identified as 36 K, however, the SSE signal continues to be present even above \( T_N \). **f** The field of the \( R_{xy}^{2\omega} \) peak decreases with increasing temperature (blue star and red square), which is similar to the temperature dependence of the spin-flip transition field (black circle).
+To better distinguish the SSE from other spurious effects, we utilize Pt and Ta in the two Hall bar devices (Fig. 2a and d). Due to the opposite spin Hall angles\(^{42}\), the thermally generated spin current should yield SSE signals with opposite polarities in Pt and Ta samples. In contrast, other magnetic thermoelectric effects, such as the Nernst effect arising from the proximity effect\(^{43}\), retain the same polarity in both Pt and Ta. As illustrated in Fig. 2b and e, the \(R_{xy}^{2\omega}\) shows the opposite polarities in Pt and Ta samples, suggesting that the phenomenon originates from the SSE. As the temperature increases, the strength of the SSE decreases, and the SSE remains present even at temperatures exceeding the \(T_N\) of CrPS\(_4\). A more apparent trend is illustrated in Fig. 2c. Although the propagation of spin waves without magnetic interactions is not permitted in the paramagnetic phase, short-range magnetic interactions still facilitate short-wavelength magnetic excitations, resulting in the paramagnetic SSE\(^{16}\). In addition to the increase in \(R_{xy}^{2\omega}\) with the applied field, peaks of \(R_{xy}^{2\omega}\) are observed in both samples at varying temperatures. Similar effects are observed in the sample with a different Pt thickness (see Supplemental Material S3 for details). The magnetic field at which the \(R_{xy}^{2\omega}\) peak occurs aligns with the spin-flip field of CrPS\(_4\), as illustrated in Fig. 2f, suggesting a strong connection between the \(R_{xy}^{2\omega}\) peak and the magnetic phase transition induced by the magnetic field. The longitudinal resistances for CrPS\(_4/Pt\) and CrPS\(_4/Ta\) are ~ 600 \(\Omega\) and 1560 \(\Omega\) respectively, with applied currents of 1 mA and 0.6 mA for the two samples. This results in a higher heating power in CrPS\(_4/Pt\), causing a larger temperature difference between the sample and the chamber. There is expected to be a shift in the spin-flip field for the samples with and without heating at the same chamber temperatures, and this discrepancy will become more pronounced at lower temperatures (see Fig. 2f).
+Fig. 3 Origin of SSE peak at the spin-flip field. **a** Comparison of the field dependence of \( R_{xy}^{2\omega} \) in CrPS$_4$/Pt (obtained at 15 K) and magnetic moment CrPS$_4$ flake (measured at 20 K). **b** Angular dependence (in the xz plane) of \( R_{xy}^{2\omega} \) when the applied field approaches the spin-flip field at a temperature of 15 K and an applied current of 1 mA. **c** Magnon mode edges (\( k = 0 \)) as a function of the applied field perpendicular to the c axis. The inset shows the simulated magnetic moment as a function of the magnetic field. **d** The canted magnetization of \( \omega_\alpha \) mode precesses around the applied field, while that of \( \omega_\beta \) mode oscillates in the direction of the applied field.
+
+The origin of the SSE peak. The peak of \( R_{xy}^{2\omega} \) observed at the spin-flip field is intriguing as it is not associated with the static magnetic moment, which would not show an increased canted magnetization during the spin-flip transition, as illustrated in Fig. 3a. In Fig. 3b, the angular dependence (in the xz plane) of \( R_{xy}^{2\omega} \) is shown as the applied field approaches the spin-flip transition at a temperature of 15 K and an applied current of 1 mA in the CrPS$_4$/Pt. The curves can be well-fitted with the sine function according to Eq.(1), with a maximum observed at 6.8 T, indicating that the peak originates from the SSE. Additionally, the SSE continues to be present above \( T_N \), while the peak of \( R_{xy}^{2\omega} \) disappears beyond \( T_N \) (see Fig. 2b,e). Although the paramagnetic phase could exhibit a SSE, the loss of long-range
+ordering above the \( T_N \) causes the spin-flip transition to vanish. This highlights the significant connection between the peak of SSE and the spin-flip transition.
+
+The SSE consists of three components: 1. The temperature gradient excites the magnetization dynamics, leading to a non-equilibrium magnon current. 2. This magnon current is transformed into a conduction-electron spin current through the \( s\text{-}d \) interaction, which travels across the interface connected to the metal. 3. Finally, the spin current is converted into a charge current via the ISHE. Notably, detecting the spin current is not crucial for the SSE peak, as both the CrPS$_4$/Pt and CrPS$_4$/Ta samples exhibit peaks (see Fig. 2b,e). The only remaining likely mechanism for the SSE peak is related to the pumped spin current \( J_s \) from the antiferromagnet into heavy metals which includes the effect of both thermal magnon excitation and interfacial spin mixing conductance.
+
+Considering the canted magnetic phase, the magnetic field dependence of magnon frequency can be obtained by diagonalizing the spin Hamiltonian$^{44}$ with eigenfrequencies$^{45}$. Before the spin-flip field, \( \mu_0 H \leq 2\mu_0 H_E + \mu_0 H_A \),
+
+\[
+\omega_\alpha = \gamma \mu_0 \sqrt{(2H_E \sin^2 \varphi + H_A \cos^2 \varphi)(2H_E + H_A)},
+\]
+(2)
+
+\[
+\omega_\beta = \gamma \mu_0 \sqrt{H_A (2H_E + H_A) \cos^2 \varphi},
+\]
+(3)
+
+After the spin-flip field, \( \mu_0 H > 2\mu_0 H_E + \mu_0 H_A \),
+
+\[
+\omega_\alpha = \gamma \mu_0 \sqrt{H(H - H_A)},
+\]
+(4)
+
+\[
+\omega_\beta = \gamma \mu_0 \sqrt{(H - 2H_E)(H - 2H_E - H_A)},
+\]
+(5)
+
+where \( \mu_0 H, \mu_0 H_E, \) and \( \mu_0 H_A \) represent the applied in-plane field, interlayer exchange field, and anisotropic field along the \( c \)-axis, respectively. The simplified model only considers the anisotropic field along the \( c \)-axis. \( \omega_\alpha \) and \( \omega_\beta \) are the two magnon modes. \( \gamma \) is the gyromagnetic ratio and \( \varphi \) is the canted angle along the \( c \)-axis applied in the plane field,
+\( \varphi = \arcsin \frac{\mu_0 H}{2\mu_0 H_E + \mu_0 H_A} \).
+The field dependence of the magnon mode frequency is plotted in Fig. 3c with parameters \( \mu_0 H_E = 3.5 \) T and \( \mu_0 H_A = 0.12 \) T \( ^{35} \). The \( \omega_\alpha \) mode has the potential to transport angular momentum due to the canted magnetization of the mode rotating around the applied magnetic field. This mode is similar to the quasi-ferromagnetic mode that emerges following a spin-flop transition when a magnetic field is applied along the \( c \)-axis\( ^{14} \). Moreover, the SSE in CrPS$_4$/Pt has the same sign as that in YIG/Pt (see Supplemental Material S4 for details), suggesting that right-handed magnons (\( \omega_\alpha \) mode) are responsible for the SSE signal. In contrast, the \( \omega_\beta \) mode oscillates in the direction of the applied field (see Fig. 3d).
+
+We further calculate the spin current in the heavy metal following Ref. [23] using a minimal model where the CrPS$_4$ sample is modeled as a one-dimensional antiferromagnetic chain with periodic boundary conditions. The model has an interfacial \( s\text{-}d \) coupling that couples the localized spins in the antiferromagnet with the itinerant electrons in the heavy metal. Using Fermi’s Golden rule to calculate the transition probability for the spins to be pumped from the antiferromagnet into the heavy metal, the thermal spin current density polarized along the \( x \)-axis in the heavy metal is given by\( ^{23} \)
+
+\[
+J_s = \Lambda \Delta T \sin \varphi \sum_k \hbar \omega_{k,\alpha} \frac{\partial f_{BE}(\omega_{k,\alpha})}{\partial T} + \Delta^2 \hbar \omega_{k,\beta} \frac{\partial f_{BE}(\omega_{k,\beta})}{\partial T},
+\]
+
+where \( \Lambda \) is a constant depending on the interface and the density of states for the electrons in the heavy metal, \( \Delta T \) is the temperature difference across the interface, \( k \) is the wave vector of the one-dimensional chain, and \( \Lambda \) parametrizes the degree of compensation at the interface; \( \Delta = 0 \) corresponds to a compensated interface and \( \Delta = \pm 1 \) corresponds to a fully uncompensated interface where only one of the two sublattices couple to the heavy metal. The \( \omega_\beta \) mode only contributes to the spin current for an uncompensated interface, reflecting the linearly polarized nature of the mode (see Supplemental Material S5 for the calculation of the spin current as a function of applied field).
+
+The effect of the in-plane magnetic field on the pumped spin current in the heavy metal is twofold: first, the magnetic field increases the canting angle \( \varphi \), causing a linear increase of the factor \( \sin \varphi \) in Eq. (6)Physically, this can be interpreted by noting that each of the two
+sublattices pump a spin current that on average is polarized along the sublattice equilibrium direction, thus, the measured spin current is given as the projection on the x-axis, which is proportional to \( \sin \varphi \). Second, the magnetic field changes the magnon frequencies of both magnon modes. Above the spin-flip critical field, the energy of the \( \omega_\alpha \) mode and the \( \omega_\beta \) mode increases with the in-plane field. This causes a decrease in the terms inside the sum in the above equation. Importantly, the increase due to the change in canting angle is proportional to \( \sin \varphi ~\sim H \) below the critical field and constant above the critical field since the canting angle has reached its maximum at this point. In total, these two effects explain the observed peaks and saturation in SSE of CrPS$_4$/Pt at the spin-flip field.
+
+The gap closure of the \( \omega_\beta \) mode frequencies at the critical field could further increase the peak observed in the spin Seebeck effect at the critical field for systems with an uncompensated interface. However, to probe the low-frequency excitations, the temperature needs to be smaller than or comparable to the gap energy, which for CrPS$_4$ is 0.4 K in units of temperature. Therefore, a sharper peak is expected for temperatures approaching this value (see Supplemental Material S5 for details).
+
+![Schematic of nonlocal SSE measurement and field dependence of SSE](page_370_1012_808_312.png)
+
+Fig. 4 Nonlocal SSE measurement. **a** Schematics of nonlocal SSE measurement. **b** Field dependence of SSE at different angles at 5 K with the applied current of 1 mA. Inset shows the field dependence SSE when the applied field is slightly off the c-axis (z-axis).
+
+Nonlocal SSE in CrPS$_4$/Pt. The nonlocal configuration is further introduced to explore the SSE in CrPS$_4$/Pt as shown in Fig. 4a (see method for details). An in-plane heat gradient is created by passing current through one of the Pt strips, resulting in a nonequilibrium
+distribution of magnons. At the detection part, the magnon spin current is injected into Pt, which leads to the SSE. It is worth noting, in this configuration, that the temperature gradient \( \nabla T \) is oriented along the x-axis, while the spin current \( J_s \) flows along the z-axis, differing from the longitudinal SSE previously discussed. Fig. 4b shows the field dependence of SSE at different angles (\( \theta \)) at 5 K with the applied current of 1 mA. By applying the in-plane field (\( \theta = 0^\circ \)), the SSE as a function of the applied field is similar to the longitudinal configuration, and a peak of SSE is also observed at the spin-flip field.
+
+A weak SSE response occurs when the applied field is close to the z-axis, with nominal angles of \( \theta = 92^\circ \) and \( 87^\circ \). Typically, the SSE should not be present when the field is directed along the z-axis (c-axis), as the parallel alignment of spin polarization \( \sigma \) and spin currents \( J_s \) does not generate a SSE voltage. However, a slight deviation from the z-axis in the direction of the applied field results in a finite value of \( J_s \times \sigma \), since the spin polarization aligns with the canted magnetization. This accounts for the observed positive and negative SSE at strong positive fields when \( \theta = 87^\circ \) and \( 92^\circ \), respectively. The plateau in the SSE is observed before the spin-flop transition, as there is no x-component of the canted magnetization. In particular, one could also find a peak of SSE at the spin-flop field, which is attributed to the divergence of spin conductance as the magnon gap closes approaching the spin-flop transition\(^{46}\). Similar effects are also observed in the longitudinal SSE configuration (see Supplemental Material S6 for details).
+
+Discussion
+
+We report evidence of the SSE in the weak interlayer exchange coupled van der Waals antiferromagnet CrPS$_4$ in contact with the heavy metal. We showed how the SSE is substantially enhanced by tuning the magnetic field. In particular, we observe a peak of SSE which shares the same temperature dependence as the spin-flip transition of CrPS$_4$ when applying magnetic field perpendicular to the c-axis. By considering the thermal spin current density into the heavy metal, we conclude that the SSE peak is related to the magnon mode edges as a function of the applied field across the spin-flip field.
+
+Field-induced peaks in SSE were also observed in Y$_3$Fe$_5$O$_{12}$/Pt\(^{47}\), Lu$_2$BiFe$_4$GaO$_{12}$/Pt\(^{48}\), Fe$_3$O$_4$/Pt\(^{49}\) and Cr$_2$O$_3$/Pt\(^{50}\) bilayers. These peaks in SSE arise when the magnetic field
+adjusts the magnon energy to the point of anticrossing between the magnon and phonon dispersion curves, creating magnon-polarons\(^{47}\). The combined magnetoelastic excitation couples the long-lasting acoustic phonons in single crystals with the short-lived magnons, increasing the magnon lifetime and the associated SSE\(^{48}\). The SSE peak in CrPS\(_4\)/Pt (Ta) exhibits similar field-like behaviors, but it arises from a mechanism involving the magnon mode and spin conductance. Given that the SSE peak in CrPS\(_4\)/Pt (Ta) is observed at low temperatures where the phonon population is frozen, we do not expect the magnon-polarons to dominate the signal our samples.
+
+The SSE is a sensitive tool for investigating the interfacial spin conductance and magnon population across various materials. Our findings indicate that the magnon spin transport in CrSP\(_4\)/Pt(Ta) can be effectively modulated through adjustments in temperature and applied magnetic field, particularly at the spin-flip field. This approach paves the way for innovative magnonic devices that utilize weakly exchange-coupled van der Waals antiferromagnetic materials.
+
+Method
+
+Sample Preparation and Characterization: The chemical vapor transport technique produced single crystal flakes of CrPS\(_4\). Chromium (Aladdin,99.99%), red phosphorus (Aladdin,99.999%), and sulfur (Aladdin,99.999%) powders were measured in a stoichiometric ratio of 1:1:4 and combined with 5% more sulfur as transport agents. The mixed powders were sealed in a quartz tube and placed in a two-zone furnace, where the temperatures at the source and sink ends were maintained at 923 K and 823 K for a duration of 7 days. The atomic structure was analyzed using X-ray diffraction (XRD) with Cu K\(\alpha\) radiation (\(\lambda = 1.54056\) \AA). The magnetic properties were measured using a Superconducting Quantum Interference Device (SQUID). The CrPS\(_4\) flakes were mechanically exfoliated from the single crystals using adhesive tape and transferred onto a SiO\(_2\)/Si substrate. CrPS\(_4\)/Pt(Ta) samples were prepared with the magnetron sputtering in a vacuum of approximately \(6\times10^{-8}\) torr. The thickness of the Pt layer is 5 nm, while the Ta layer is 15 nm; 5 nm of Ta will oxidize in air, leaving 10 nm of Ta to facilitate the inverse spin Hall effect for detecting spin current generation. The Hall bar with 10 \(\mu\)m in width
+and 25 \( \mu \)m in length was fabricated using photolithography followed by ion beam etching. The width of the heater and the detection Pt strips are designed to be 1.4 \( \mu \)m and 2.3 \( \mu \)m, the distance of the two stipes are 1.6 \( \mu \)m in the nonlocal device. An atomic force microscopy image of the samples is provided in supplementary S2, showing the thickness of the CrPS$_4$ flakes to be 74 nm.
+
+**Transport measurement.** The SSE is measured at different temperatures by varying the magnetic field in the Physical Properties Measurement System (PPMS-9T). An alternating current ranging from 0.4 to 1 mA at a frequency of 13 Hz was supplied to the Hall bar or nonlocal device using a Keithley 6221 instrument, while the transverse voltage was measured with a lock-in amplifier (SR830).
+
+**Data availability**
+
+The data in the main figures are provided with this paper. Other data that support the findings of this study are available from the corresponding authors upon reasonable request.
+
+**Acknowledgements**
+
+This work is supported by the National Key R&D Program of China (grant no. 2022YFA1203902, 2022YFA1200093), the National Natural Science Foundation of China (NSFC) (grant nos. 12241401, 12374108 and 12104052, 52373226, 52027801, 92263203), and the China-Germany Collaboration Project (M-0199), the Strategic Special Project of Guangdong Province, the Fundamental Research Funds for the Central Universities, and the State Key Lab of Luminescent Materials and Devices, South China University of Technology. We acknowledge support by the German Research Foundation (CRC TRR 288 - 422213477 Project A12 and CRC TRR 173 – 268565370 Projects A01 and B02) and the Research Council of Norway through its Center of Excellence 262633 “QuSpin”.
+
+**Author contributions**
+
+S.D. and R.W. conceived the experiments. X.H. fabricated the devices. X.H., S.D., J.W. and R.W. carried out the transport and magnetic measurements. Z.C.L., Z.Y.L. and J.Y. made the single crystal samples and carried out basic characterizations. H.G.G.and A.B.
+contributed to the theoretical calculation. X.H., S.D., R.W., and M.K. contributed to data analysis. S.D. draft the manuscript and all authors contributed to the reviewing and revising of the manuscript. Y.H. and R.W. supervised the research and contributed to the acquisition of the financial support for the project leading to this work.
+
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+48. Ramos, R. et al. Room temperature and low-field resonant enhancement of spin Seebeck effect in partially compensated magnets. *Nat. Commun.* **10**, 5162 (2019).
+49. Xing, W. et al. Facet-dependent magnon-polarons in epitaxial ferrimagnetic Fe$_3$O$_4$thin films. *Phys. Rev. B* **102**, 184416 (2020).
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupportingInformation.pdf

07f28e497a966d2241ff131830d461c8058880986d6873f21a89c91e352b254e/preprint/preprint.md

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+The Dynamics of Plasmon-Induced Hot Carrier Creation in Colloidal Gold
+
+Jacinto Sa
+jacinto.sa@kemi.uu.se
+
+Uppsala University   https://orcid.org/0000-0003-2124-9510
+
+Anna Wach
+SOLARIS National Synchrotron Radiation Centre, Jagiellonian University
+
+Jakub Szlachetko
+SOLARIS National Synchrotron Radiation Centre, Jagiellonian University
+
+Alexey Maximenko
+SOLARIS National Synchrotron Radiation Centre, Jagiellonian University
+
+Tomasz Sobol
+SOLARIS National Synchrotron Radiation Centre, Jagiellonian University   https://orcid.org/0000-0002-9661-0932
+
+Ewa Partyka-Jankowska
+SOLARIS National Synchrotron Radiation Centre, Jagiellonian University
+
+Camila Bacellar
+Paul Scherrer Institute   https://orcid.org/0000-0003-2166-241X
+
+Claudio Cirelli
+Paul Scherrer Institute   https://orcid.org/0000-0003-4576-3805
+
+Philip Johnson
+Paul Scherrer Institut   https://orcid.org/0000-0002-7251-4815
+
+Rebeca Gomez Castillo
+École Polytechnique Fédérale de Lausanne
+
+Vitor R. Silveira
+Uppsala University
+
+Peter Broqvist
+Uppsala University
+
+Jolla Kullgren
+Uppsala University
+
+Naomi Halas
+Rice University   https://orcid.org/0000-0002-8461-8494
+
+Peter Nordlander
+Physical Sciences - Article
+
+Keywords:
+
+Posted Date: April 8th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-3799527/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 7th, 2025. See the published version at https://doi.org/10.1038/s41467-025-57657-1.
+Abstract
+
+There is an increasing interest in nonequilibrium “hot” carrier generation, created by the decay of collective electronic oscillations on metals known as surface plasmons. Despite extensive efforts, direct observation of the mechanism responsible for generating hot carriers due to plasmon decay has proven challenging. Here, the dynamics of hot carrier generation on gold nanoparticles (Au NPs) are followed with unparalleled detail through ultrafast X-ray absorption spectroscopy (XAS) at the X-ray free-electron laser (XFEL). In Au NPs, the plasmon dephases after 25 fs and the hot carrier population peaks within 105 fs, reaching thermal equilibrium within 1.5 ps. The nonequilibrium carriers display an energy dispersion governed by the density of states of the metal, with some carriers possessing energies surpassing that of a single photon, consistent with the involvement of an Auger heating mechanism distinct from the expected impact excitation that dominates the carrier multiplication step. The most energetic carriers exhibit relatively shorter lifespans, a property that may be critical for exploiting them in applications. This study substantiates hot carrier formation through nonradiative decay as the main decay channel of plasmon resonance. The proposed methodology provides a straightforward approach for real-time tracking of plasmon-induced hot carrier dynamics.
+
+Introduction
+
+Surface plasmons, the collective oscillations of conduction electrons in metallic nanostructures, have emerged as an essential elementary excitation in condensed matter, giving rise to multiple practical applications. They can capture distant radiation and focus it within subwavelength regions, defying diffraction limits,\(^{1,2}\) resulting in potent near-fields and profound field amplifications.\(^{3}\) These attributes have propelled innovative applications of plasmonics, such as highly sensitive biosensing,\(^{4}\) photothermal therapy for cancer,\(^{5}\) photovoltaics,\(^{6,7}\) and photocatalysis.\(^{8}\)
+
+Surface plasmons exhibit finite lifetimes, decaying either by photon emission (radiatively) or the creation of electron-hole pairs (nonradiatively). Over the past decade, the radiative decay pathway has been researched extensively, yielding the development of efficient nanoantennas that amplify and steer emissions from individual emitters.\(^{9,10}\) Recent research has focused on leveraging nonradiative decay for applications.\(^{11}\) Hot carriers can initiate chemical reactions in adjacent molecules, even those that demand high energy under conventional thermal conditions.\(^{12,13}\) Moreover, plasmon-induced hot carriers offer a potent means to transform light into electrical currents,\(^{14}\) fostering novel solar energy converters\(^{15}\) and circumventing the bandgap limitations of traditional photodetectors.\(^{16}\)
+
+While the direct excitation of hot carriers on metal surfaces using high-intensity laser pulses has been a longstanding practice in surface femtochemistry, exploiting surface plasmon decay to amplify hot carrier generation is a recent development. This significant advance stems from the remarkably boosted light harvesting ability of collective plasmon excitations, combined with the substantial enhancement of the plasmon-induced field when metals are nano-confined. Comprehending the underlying physical
+mechanisms driving plasmon-induced hot carrier generation is essential to leverage these benefits fully. Although theoretical frameworks elucidating this phenomenon exist,\(^{17-18[i][i]19[ii][20[iii][21[iv]]22}\) a suitable experimental methodology to validate these models still needs to be developed.
+
+X-ray absorption spectroscopy (XAS) provides a way to investigate the interplay between X-ray photons and matter, simultaneously unveiling unparalleled insights into a material’s electronic and chemical characteristics. When X-ray photons are directed toward a material, they can be absorbed by core electrons, resulting in these electrons shifting to higher energy states. The precise energy at which this absorption occurs depends on the specific element’s electronic structure and its local environment. Hot carriers emerge from the interaction between external electric fields and valence electrons, creating electrons and holes with energies above and below the Fermi level (\(E_F\)).
+
+Transient XAS (aka time-resolved XAS (TR-XAS)) probes empty states around the Fermi energy and, in the case of \(d^{10}\) metals with the L$_3$-edge transition, provides direct information about the amount of carrier participation and their nonequilibrium energy distributions.\(^{23}\) At synchrotrons, such dynamical measurements are typically hampered by limited temporal resolution (\(~5\) ps) and photon density,\(^{24}\) impeding real-time observations of the hot carrier generation process.\(^{8}\) However, this limitation has been surpassed by the advent of hard X-ray free electron lasers (XFELs),\(^{25}\) capable of delivering intense and ultrashort hard X-ray pulses (up to 30 keV at the European XFEL\(^{26}\) and 12 keV at SwissFEL (used in this study) \(^{27}\)) of less than 50 fs in duration.\(^{27,28}\) With this unique combination of high photon energies and ultrashort pulses, time-resolved XAS has become an exceptionally valuable experimental probe of dynamical processes. Typical time-resolved measurements are implemented in a pump-probe scheme, where an optical-frequency pump laser triggers electron dynamics, and the X-ray probe captures the evolving nonequilibrium electron distribution. Over the past few years, femtosecond TR-XAS studies have been used to probe photoinduced electronic and structural changes in photoexcited transition metal oxides\(^{29}\) and complexes.\(^{30}\) In this study, TR-XAS was used to observe the generation and relaxation of plasmon-induced hot carriers in gold nanoparticles directly.\(^{31,32}\)
+
+The widely accepted understanding of how localised surface plasmon resonance (LSPR) excitation leads to hot carrier formation and subsequent thermalisation, including the hypothesised timescales for each process, is summarised in Figure 1A.\(^{8,22}\) Briefly, the light electric field induces a coherent excitation of Au valence electrons. The excited electrons’ coherence dephases due to Landau damping after the light excitation elapses. The process is expected to take 10-100 fs, resulting in a non-Fermi-Dirac distribution of hot carriers. The carriers undergo multiplication, eventually reaching a Fermi-Dirac distribution and thermal relaxation after ~1 ps. This description of hot carrier formation has been deduced from physical models that underpin our understanding. Still, it has never been validated experimentally due to the lack of element-specific techniques with sufficient temporal resolution. However, the attempts from Bigot et al.\(^{33}\) and Lehmann et al.\(^{34}\) with femtosecond optical pump-probe investigations with ionising probe pulses, which provided earlier evidence for hot electrons and their dynamics, should be mentioned. Nevertheless, no information could be extracted about the hot holes.
+Figure 1B illustrates the TR-XAS approach for tracking the density of states (DOS) changes induced by LSPR excitation. More specifically, the study focuses on the X-ray absorption near edge structure (XANES) part of the XAS spectrum, which contains the electronic changes in the element, i.e., information on LSPR-induced hot carrier formation. The transient data was collected using the classic pump-probe methodology for optical spectroscopy. The technique involves "pumping" a sample with an initial laser pulse and then "probing" it with a delayed pulse to observe the changes induced by the pump pulse. In the present case, the probe is an fs X-ray pulse from the XFEL. To prevent the excitation of damaged Au NPs induced by intense XFEL pulses, a liquid jet was employed to circulate the Au NPs and the solution was refreshed every four hours.
+
+Since nanoparticle measurements at XFELs are uncommon, it was essential to validate that the XANES spectra collected with this radiation represent the sample. Figure S1 shows the steady-state XANES spectra of Au foil and nanoparticles measured at the Au L_3-edge transition (\(2p_{3/2}\) à \(5d\)) at the synchrotron (Solaris synchrotron, Poland). Au has a [Xe] \(4f^{14}\) \(5d^{10}\) \(6s^1\) electronic structure, i.e., with a filled \(d\)-shell, which results in a slight absorption edge only visible due to some level of \(s\)-\(d\) shell hybridisation. For comparison purposes, the signal was plotted against Pt ([Xe] \(4f^{14}\) \(5d^8\) \(6s^1\)) (Fig. S2), revealing the method sensitivity to empty states within the metal \(5d\) shell and, to some extent, the \(s\)-shell due to this hybridisation. In this study, Au NPs with an average particle size of \(8 \pm 2\) nm were used, as confirmed by atomic force microscopy (AFM) and dynamic light scattering (DLS) (Figs. S3 and S4). The Au NPs have a LSPR centered at nominally 520 nm (2.38 eV) according to UV-vis spectroscopy (Fig. S5).
+
+The steady-state XANES analysis established that the Au NPs exhibit an electronic structure resembling bulk gold, as reported elsewhere.\(^{22,35}\) This agreement is further corroborated by our theoretical calculations, showing the evolution of the DOS as function of particle size (Fig. S6). The unexcited XANES spectrum of the Au NPs, measured at XFEL (SwissFEL, Switzerland) and the synchrotron, displayed a consistent shape. This consistency supports the applied methodology's ability to capture the transient alterations in the electronic structure of gold before the sample gets damaged, i.e., probe-before destruction concept.\(^{36, 37}\) XFELs have only recently provided access to hard X-ray energies, allowing one for the first time to probe the Au L_3-edge.
+
+Ultrafast time-resolved XANES data were acquired with the XFEL source as a probe, following the excitation of 5 mM Au NPs at 532 nm (~ 2.33 eV), utilising a 15 nm full width at half maximum (FWHM) bandwidth, a pulse duration of approximately 75 fs, and a power density of 98 mJ/cm\(^2\) (equivalent to 4 \(μ\)J within a 60 x 60 \(μm^2\) spot). The choice of this precise plasmon excitation energy was to induce LSPR through intra-band \(s\)-to \(s\)-shell excitation while minimising interband excitation (\(d\)-to \(s\)-shell excitation). The centre of the Au \(d\)-shell is located at 2.5-2.58 eV (~ 496-480 nm) from the metal Fermi level (\(E_F\)),\(^{38,39}\) meaning that the laser pulse with 2.33±0.13 eV (15 nm FWHM) photon energy can only excite the low energy tail of the \(d\)-shell at best. Figure 1C compares the XANES spectra of unexcited (unpumped spectrum) and excited (pumped spectrum) recorded at Dt =100 fs time delay after excitation at 532 nm. Optical excitation induced a spectral downshift in energy and decreased XANES whiteline intensity,
+corroborating that it induced changes in the gold electronic structure around its Fermi-level energy, and the TR-XAS can track the changes.
+
+To better illustrate the results, the XANES difference spectrum (pumped-unpumped XANES spectra) is also shown in Figure 1C. The difference spectrum is dominated by the positive signal below and a negative signal above the Au E_F. Transient L_3-edge XANES readily capture changes in the density of unoccupied states, particularly those induced in the d-shell, either directly or through processes like hybridisation with the s-shell. Accordingly, a positive signal correlates with an increase in density of states (DOS); conversely, a negative signal (i.e., a bleached signal) indicates a decrease in empty states. Therefore, the positive signal below the Au E_F is ascribed to the formation of a hot hole population induced by the plasmon optical excitation. In contrast, hot electrons give rise to the negative signal above the Au E_F, consistent with empty states filling. The transient signal directly demonstrates the generation of hot carriers through LSPR decoherence via Landau damping (the non-radiative pathway dominant in small nanoparticles).^{21,24,40} Most notably, the hot hole and electron signals are neither symmetric nor have the same integrated magnitude. This is related to the XANES higher sensitivity to empty states formation and the L_3-edge transition changes in the d-shell that is part of the valence, where the hot holes are formed.
+
+To establish the time scales for plasmon damping (g) and the average lifetime of carriers (t), kinetic traces were extracted at the maximum of the hot hole intensity (11916 eV, 2.5 eV below Au E_F (Figure 2B)) and the excited electron intensity (11922 eV, 3.0 eV above Au E_F (Figure 2C)) populations, as depicted in (Figure 2A). The kinetic data from the time scans were fitted by a model published elsewhere,\(^{41}\) described in SI equations S1 and S2. In brief, the data collected at 11916 and 11922 eV were fitted with a convolution of temporal instrument response function (Gaussian) with a monoexponential decay (with a time constant ). The resulting fit is the solid green in Figure 2B. Due to the low signal-to-noise ratio for the hot electron data, the error bars are relatively large. However, qualitatively, it is possible to see that the signal has dynamics similar to the hot holes.
+
+The γ time can be extracted from the transient signal onset time because it is the point at which the Au DOS starts to change, i.e., the fingerprint for hot carrier formation. In this particular case, it was estimated to be 24.6 ± 6 fs, corroborating that plasmon decoherence occurs between 10-100 fs.\(^{24}\) Following plasmon damping, the hot carriers undergo a carrier multiplication reaching a maximum at 105 ± 8 fs, estimated from rising edge analysis. The lifetimes of the hot carriers were determined from a single exponential decay to be 498 ± 35 fs with complete carrier thermalisation occurring within 1.5 ps. These time constants align with previous postulations\(^{24}\) but are here substantiated through direct measurement. The confirmed ultrafast hot carrier dynamics in plasmonic nanoparticles are the primary bottleneck in plasmonic applications.
+
+To estimate the number of electrons engaged when exciting 5 mM Au NPs at 532 nm, utilising a 15 nm full width at half maximum (FWMH) bandwidth, a pulse duration of approximately 75 fs, and a power
+density of 98 mJ/cm\(^2\), the positive signal variance at 0 and 100 fs were integrated. This integrated signal was then juxtaposed with the signal difference between the Au and Pt L\(_3\)-edges (Fig. S2). Note that the signal difference between Au and Pt relates to 1\(e^-\) less in Pt valence states, i.e., the integrated positive signal of the difference between Pt and Au corresponds to the equivalent of having 1\(e^-\) from each Au atom participating in the resonance. Employing this simple methodology, we estimated that each gold atom contributed with 0.19\(e^-\) at the start of the resonance, which underwent multiplication until 105 fs, reaching a maximum of 0.46\(e^-\) from each Au atom contributing to hot carrier formation at this excitation power.
+
+Assuming an excitation volume of 60 x 60 x 100\(\mu\)m\(^3\) and considering the Au solution concentration (5 mM), one can expect 1.5 x \(10^8\) nanoparticles in the excited volume. An 8 nm Au NP has »12000 atoms, equating to about 1.8 x \(10^{12}\) Au atoms in the excited volume. The photon density in the optical pulses is about \(10^{13}\), from which 20% is absorbed according to UV-Vis, implying that the excited volume absorbs around 2x\(10^{12}\) photons. This suggests an excitation of about 1\(e^-\) per atom of Au, from which 19% are converted into hot carriers at the onset, multiplying to about 46% within 100 fs. The observation suggests that hot carrier generation is a prime decay channel of Au LSPR and undoubtedly the most significant mechanism in nonradiative decay.
+
+After verifying the generation of hot carriers, the next step is the investigation of the dynamics of their energy distribution - a significant yet elusive aspect in the realm of plasmonic hot carriers, particularly when it comes to holes. Our understanding is derived mainly from theoretical studies\(^{20,42,43}\) and indirect techniques.\(^{22,33,34,44}\) For example, internal quantum efficiency measurements have inherent limitations as they solely quantify carriers injected into an acceptor layer, like a semiconductor, failing to provide insights into the dynamic behaviour of the carriers in the metal. While the hot electrons can only populate the empty states within the \(sp\)-shells, the holes can be in \(sp\)- and \(d\)-shells, confirmed by valence band – X-ray photoelectron spectroscopy (VB-XPS) shown in Figure 3A. It is evident when the VB-XPS is overlapped with the transient XANES spectrum (recorded at time zero) that the generated holes are indeed located throughout the entire valence, including the \(d\)-shell, despite the optical pulse energy allowing primarily \(sp\)-shell excitation.
+
+Figure 3B shows the energy distribution and population of the carriers at different time delays after excitation. As expected, the plasmonic excitation depopulates and populates states below and above the Fermi energy. The ultrafast carrier-carrier interactions during dephasing and multiplication determine their energy and respective population. The hot carrier energy distribution goes beyond single photon energy for hot electrons and holes. Moreover, it is noticeable that both carrier populations and the width of their energy distributions increase until about 100 fs, decreasing asymptotically after that. A slight asymmetry exists between hot electron and hot hole populations, which cannot be fully explored here due to the probe's lower sensitivity to hot electrons.
+The rapid depopulation of electrons in the \( d \)-shell is expected due to the broad energy overlap between the \( d \) and \( sp \)-band, which provides a high density of \( d \)-electrons that couples with the plasmonic resonance and dissipates its energy.\(^{43}\) However, this does not explain the observation of carriers having energies above the photon energy, even considering that the Au core-hole lifetime broadening is 5.41 eV at the L\(_3\)-edge,\(^{45}\) which inevitably broadens the energy scale. Achieving precise energy distributions of carriers requires high-resolution measurements,\(^{46}\) which implies extended acquisition times rarely offered at XFEL facilities. Nonetheless, hot holes are distributed across the entire valence electronic structure, and their energy distribution increases up to 250 fs (Figure 3C) before relaxing. These two observations indicate the involvement of carrier multiplication mechanisms that can increase the carrier population and their energy distribution, an effect that has yet to be reported.\(^{43}\) Note that the low optical laser fluency and short pulse duration used in this experiment make it highly unlikely that multiphoton excitation of single electrons occurs.
+
+Regarding carrier multiplication, there are two scattering mechanisms: impact excitation and Auger heating,\(^{47,48}\) The predominant mechanism in carrier multiplication is impact excitation, where an excited electron (hole) undergoes Coulomb scattering, losing energy and momentum and giving rise to an additional electron-hole pair. The distinctive feature of impact excitation is a rise in the number of carriers and a simultaneous reduction in their energy. Conversely, Auger heating characterises the non-radiative recombination of an electron with a hole, where the energy and momentum are transferred to an electron (hole) within the same shell. The hallmark of Auger heating is a decline in the number of carriers and an increase in their energy.
+
+To enhance the visualisation and comprehension of the hot hole multiplication process, the shape of different spectra regarding charge width and charge energy was analysed (see Figure 3C). The details of the data analysis procedure are outlined in the SI. Commencing with the average hot carrier distribution energy, it remained constant until 100 fs before exhibiting a subsequent decrease. This implies the LSPR dephasing process extends to 100 fs, increasing the nonequilibrium hot carrier population through the impact excitation scattering mechanism. However, examining the hot carrier distribution width, reflecting the energy distribution of the hot holes unveils a relative surge in the energy distribution beyond the time when the hole population is at its maximum (approximately 100 fs), i.e., the energy distribution of hot holes increases up to 250 fs. This observation is noteworthy, especially considering this process competes with hole thermalisation, occurring within tens of femtoseconds in metals. The broadening induced by the core hole relaxation cannot account for the increase in distribution width, as it should have smeared the energy resolution from the outset, preventing the difference signal from accurately reflecting the valence state of gold. This suggests the involvement of a mechanism that generates carriers with higher energy than the dephasing process produces - specifically, the participation of Auger heating. This mechanism has yet to be considered in plasmon relaxation dynamics, altering the current understanding of hot carrier formation, multiplication, and relaxation in plasmonic materials.
+In this work, we presented the results from an ultrafast X-ray absorption experiment conducted at the XFEL involving citrate-capped gold nanoparticles excited at their LSPR with minimum intraband excitation. This experiment enabled the real-time observation of the generation and subsequent relaxation of hot carriers. The plasmon damping was determined to be 25 fs, with a maximum hot carrier population of \(0.46e^-\) from each Au atom detected at 105 fs after excitation. The lifetimes of the hot carriers were estimated to be 498 fs, with complete carrier thermalisation occurring within 1.5 ps. Energy scans conducted at varying delay times revealed that the energies of these carriers conform to the density of states of the metal, with some carriers possessing energies that exceed the photon energy, consistent with an Auger heating scattering mechanism. The observation impacts hot carrier applications, particularly those that are based on the energy of the hot carriers, such as photocatalysis and photovoltaics. For instance, without the Auger process, chemical reactions with redox windows larger than photon energy could not be catalysed. Similarly, the open circuit voltage of photovoltaic devices could not exceed the voltage offered by a single photon. The novel insight into plasmon induced hot carrier generation and dynamics provided here is likely to significantly impact applications for years to come.
+
+[i]. Kornbluth, M., Nitzan, A., Seideman, T. Light-Induced Electronic Non-Equilibrium in Plasmonic Particles. *J. Chem. Phys.* **138**, 174707 (2013).
+[ii]. Govorov, A. O., Zhang, H., Demir, H. V., Gun'ko, Y. K. Photogeneration of Hot Plasmonic Electrons with Metal Nanocrystals: Quantum Description and Potential Applications. *Nano Today* **9**, 85–101 (2014).
+[iii]. Manjavacas, A., Liu, J. G., Kulkarni, V., Nordlander, P. Plasmon-Induced Hot Carriers in Metallic Nanoparticles. *ACS Nano* **8**, 7630–7638 (2014).
+[iv]. Rossi, T. P., Erhart, P., Kuisma, M. Hot-Carrier Generation in Plasmonic Nanoparticles: The Importance of Atomic Structure. *ACS Nano* **14**, 9963-9971 (2020).
+
+Declarations
+
+Acknowledgements
+
+We acknowledge the Paul Scherrer Institut, Villigen, Switzerland, for providing beamtime at the Alvra beamline of the SwissFEL facility. We also acknowledge SOLARIS National Synchrotron Radiation Centre, Krakow, Poland, for the access to the ASTRA and PHELIX beamline. The simulations were performed using computational resources provided by the Swedish National Infrastructure for Computing (SNIC) at UPPMAX and NSC, for which we want to thank.
+
+Funding: J.Sa acknowledges funding from Olle Engkvists Stiftelse (grant no. 210-0007), Knut & Alice Wallenberg Foundation (Grant No. 2019-0071) and Swedish Research Council (grant no. 2019-03597). A.W. acknowledges funding from the European Union’s Horizon 2020 research and innovation program under Marie Skłodowska-Curie grant agreement no. 884104 (PSI-FELLOW-III-3i). N.J.H. and P.N. acknowledge support from the Robert A. Welch Foundation under grants C-1220 and C-1222 and the Air Force Office of Scientific Research via the Department of Defense Multidisciplinary University Research
+Initiative under AFOSR Award No. FA9550-15-1-0022. The work is partially supported under the Polish Ministry and Higher Education project: “Support for research and development with the use of research infrastructure of the National Synchrotron Radiation Centre SOLARIS” under contract nr 1/SOL/2021/2. The work is partially funded by the National Science Centre in Poland under grant number 2020/37/B/ST3/00555.
+
+Author contributions: Conceptualization and methodology: A.W., J. Sz. and J.Sa; formal data analysis: A.W., J. Sz. and J.Sa; experimental investigations: A.W, C.B., C.C., P.J.M.J., R.G.C., V.R.S., P-B., J.K., A.M., T.S., E.P.-J. and J.Sa; data visualisation concepts: A.W., J. Sa, J.Sz and N.J.H., draft preparation: A.W., N.J.H., J. Sz. and J.Sa; writing-review and editing: all the authors. All authors have read and agreed to the published version of the manuscript.
+
+Competing interests: The authors declare that they have no competing interests.
+
+Data and materials availability: All data needed to evaluate the conclusions in the paper are present in the paper and/or the Supplementary Materials. Additional data related to this paper may be requested from the authors.
+
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+29. Park, SH., Katoch, A., Chae, KH., Gautam, S., Miedema, P., Cho, SW., Kim, M., Wang, R.-P., Lazemi, M., de Groot, F., Kwon, SDirect and real-time observation of hole transport dynamics in anatase TiO2 using X-ray free-electron laserNatCommun13, 2531 (2022).
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+35. Zamponi, F., Penfold, TJ., Nachtegaal, M., Lübcke, A, Rittmann, J., Milne, CJ., Chergui, M., van Bokhoven, JAProbing the dynamics of plasmon.excited hexanethiol-capped gold nanoparticles by picosecond X-ray absorption spectroscopyPhysChemChemPhys16, 23157-23163 (2014).
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+
+Figures
+Figure 1
+
+X-ray absorption signatures of gold nanoparticles. (A) Illustration depicting the temporal progression of the plasmonic resonance decay mechanism, including hypothesized time constants for associated processes. (B) The generation of hot carriers was investigated using the concept of ultrafast transient XANES, presented schematically. (C) Superimposed L_3-edge spectra of steady-state (black trace) and excited-state (red trace) Au nanoparticles with excited spectrum recorded at \( \Delta t = 100 \) fs time delay after excitation at 532 nm. The transient XAS spectrum (blue trace) is the difference between excited
+(pumped) and stead-state (unpumped) spectra. A positive signal in the difference spectrum equates to an increase in empty states (holes) and vice-versa.
+
+![Three plots labeled A, B, and C showing XAS and kinetic traces](page_246_180_1097_1012.png)
+
+Figure 2
+
+Temporal evolution of the generated hot carriers. (A) The difference spectrum (pumped-unpumped signal) shows kinetic traces of energy extraction points. (B) & (C) Time traces (intensities vs time delay) extracted at 11916 eV (i.e. hot holes, green trace) and 11922 eV (i.e. hot electrons, orange trace) X-ray photon energies, respectively. The solid line in the figures (B) and (C) refers to the fitting using the methodology presented elsewhere\(^{41}\) and described in SI.
+Figure 3
+
+Ultrafast energies distribution dynamics of excited state evolution of gold nanoparticles. (A) Comparison of the valence band photoelectron spectrum (VB-XPS) with the Au L_3-edge transient XANES spectrum collected at time zero. The relevant energy scale is given to the Fermi level. (B) The transient XANES measured at the Au L_3-edge absorption spectra collected at different pump-probe time delays (0 fs corresponds to the best possible overlap between pump and probe). (C) Relative changes in hot holes mean energy (red trace) and width (blue trace) distributions.
+
+Supplementary Files
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supportinginformation.pdf

0841883062c0d00625a3f29dfb0823965bfb4e68b1cc4e1fdb984e0c335f4fdf/peer_review/peer_review.md

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+Peer Review File
+
+Density-wave-like gap evolution in La$_3$Ni$_2$O$_7$ under high pressure revealed by ultrafast optical spectroscopy
+
+Corresponding Author: Professor Xiao Hui Yu
+
+Parts of this Peer Review File have been redacted as indicated to remove third-party material.
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Attachments originally included by the reviewers as part of their assessment can be found at the end of this file.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+See attached file.
+
+Reviewer #2
+
+(Remarks to the Author)
+Aiming the current studies about pressurized La3Ni2O7, the electron pairing mechanism is still unclear, in this paper, the authors have used techniques such as ultrafast optical pump-probe spectroscopy to study the quantum state and electronic structure of novelties such as CDW. Their main conclusions are as follows:
+
+1. the DW band gap opens near atmospheric pressure, around 115 K. The authors attribute this effect to phonon bottleneck effect.
+2. With increasing pressure, this phonon bottleneck effect is gradually suppressed and completely disappears around 26 GPa.
+3. The most interesting result is that around 30 GPa, they observe a new DW phase.
+
+This study reports some unreported results on La3Ni2O7 superconductors under pressure. Combined with the close connection between the DW phase and the superconducting state, I believe that this work will help researchers in the field of superconductivity to further understand the electronic structure of La3Ni2O7, and even its superconducting electron pairing mechanism. Before recommending the acceptance and publication of the paper, I think the authors should further elucidate some issues to some degree, with performing additional experiments and/or theoretical calculations:
+
+1. In a previous paper by some of the authors, Nature volume 621, 493-498 (2023), the authors proposed the space group structure of Amam and Fmmm. However, some subsequent theoretical and experimental work other studies have proposed space group structures such as I4/mmm and Cmmm, as well as single- and three-layer alternating structures. My question is, in the current study, did the authors reexamine or check the symmetry of the crystal structure of the system at different pressures or is the change in symmetry related to the multiple DW phases mentioned by the authors in their study? The creation of the DW phase of the system may be closely related to the structural instability of the system, so I think it is necessary to discuss phonons and DW in conjunction with the evolution of symmetry.
+
+2. in the SM Fig.S4, Fig.S5, 26GPa, why is there not a fitted data?
+
+3. are the experimental measurements done in this paper reflecting more the electronic structure of the surface or the internal bulk?
+
+4. does the authors' work, suggest that in La3Ni2O7, the DW phase may be the driving force of superconductivity or the pairing force of electrons? In a recent theoretical combined with experimental work [Phys. Rev. B 109, 235126], it was
+confirmed that antiferromagnetic fluctuation in the single-band model is the electron pairing force, so in La3Ni2O7, does antiferromagnetism plays as the same force and the DW phase is a suppressor?
+
+In summary, after the authors have answered the above question, it can be considered acceptable in NC.
+
+Reviewer #3
+
+(Remarks to the Author)
+Previous experiments have shown that La3Ni2O7 undergoes a superconducting transition with a Tc of ~80K at pressures above 14 GPa. Further, at ambient pressure there is evidence for a spin density wave transition around 150 K, along with a FM striped ground state and possibly a charge density wave transition between 110-130 K, both of which may have relevance to the high-pressure superconducting state. To explore the density wave evolution in La3Ni2O7, the paper by Meng et al provides an experimental study of the quasiparticle dynamics as a function of temperature and pressures up to 34 GPa. The relaxation dynamics exhibit a phonon bottleneck effect, which, when fit to the Rothwarf-Taylor model reveals the opening of a 66-meV gap at 151 K at ambient pressure. As the pressure increases the gap is suppressed, disappearing at ~26 GPa. The phonon bottleneck re-emerges in the quasiparticle dynamics at pressures above 29 GPa, revealing a new gap (~20 meV) with a transition temperature of ~130 K. The phonon bottleneck effect is not observed in the quasiparticle dynamics between ~26 and ~29 GPa, indicating the absence of a gap and hence density wave order.
+This detailed study of the density gap evolution in La3Ni2O7 is new and significant, in that it provides information underpinning the evolution, coexistence and competition between density wave and superconducting order in a high temperature superconductor. Motivation and background for this work, including the references are adequate. The experimental results and analysis are thorough, convincing and supportive of the conclusions made by the authors. The methodology is sound and should enable reproduction of the experimental results when the additional information in the supplementary material is included.
+However, I suggest that the Discussion section be expanded to enable a clearer interpretation of the results. The authors state that they see no signature of superconductivity between 26 and 29 GPa where there is also not evidence for a density wave order and attribute this competition between superconducting and density wave order. This seems contradictory, indicating that a more thorough and quantitative discussion is needed. They also state that the emergence of the second density wave order is consistent with theoretical results, but don’t explain the physics behind those results.
+Finally, the manuscript would benefit from language editing.
+Once these two issues are addressed, I recommend publication of this paper in Nature Communications.
+
+Reviewer #4
+
+(Remarks to the Author)
+The authors reported the observation of density-wave (DW) quasiparticle gaps in La3Ni2O7 as a function of temperature and pressure, by the measurement of the time-resolved variation of the reflectivity in the pump-probe setting. They found DW-I at the ambient pressure, which decreases in transition temperature gradually with increasing pressure up to 26GPa, and the emergence of a new DW-II above 26GPa. No contribution from superconductivity (SC) was detected. They associated the emergence of DW-II with the decrease of SC at high pressures, suggesting the competition between such orders.
+
+The experimental results are interesting. However, to make the conclusions compelling, I ask the authors to consider the following points:
+[1] There is no characterization of the crystal structure. This is a crucial point to make sure whether the observed sample has anything to do with the superconducting phase. The fact that they observed no SC signal is a possible indication that the DWs they observed are hardly related to SC. In this case, the observations would be less important.
+[2] While DW-I was identified as a kind of SDW, by comparison to other probes, there is no discussion on the nature and origin of the DW-II, whether it is spin- or charge-order, and how it is different to DW-I.
+[3] A minor issue in the discussion part: The authors stated that in the DW-II regime, the interlayer AFM coupling is weakened by pressure. But this is quite unlikely, since increasing pressure is expected to increase the interlayer hopping, which translates to enhanced antiferromagnetic interlayer spin exchange. I ask the authors to think more carefully in the discussion part.
+
+I cannot make the recommendation before the authors make convincing clarifications to the above points.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The author answered my questions very completely and accurately. Their work is one of the important advances in the field of nickel-based superconductivity, so the article should be accepted.
+
+Reviewer #2
+
+(Remarks to the Author)
+I have carefully reviewed the authors’ response to my initial comments and their revised manuscript. I am pleased to report that the authors have addressed all of the concerns raised during the initial review process in a thorough and satisfactory manner. The revisions made significantly improve the clarity, depth, and rigor of the manuscript, enhancing its overall quality and contribution to the field of unconventional superconductivity.
+I recommend this paper for accepted publication in Nature Communications.
+
+Reviewer #3
+
+(Remarks to the Author)
+The author have adequately addressed my concerns. I recommend the paper for publication in Nature Communications.
+
+Reviewer #4
+
+(Remarks to the Author)
+The authors replied to all referee comments carefully, and provided additional experimental data to clarify the quality of the sample. They also changed their previous view on the nature of the DW-II phase, which is now reasonably identified as a kind of CDW. I find the reply and the revised manuscript satisfactory. Given the high sensitivity of the pump-probe measurements, the importance of the experimental observations, and the reasonable discussions in the revised version of the paper, I would like to recommend publication of the paper in NC.
+Summary of the main changes
+
+In main text:
+
+1. Following the reviewers’ suggestions, we removed the discussion about interlayer AFM coupling.
+
+2. Following the reviewers’ suggestions, we added the discussion about the possible contributions from the phase separation (Page 7, Line 208 - 216).
+
+3. Following the reviewers’ suggestions, we explained the conflict between the appearance of DW-II and the linear resistance above 29 GPa (Page 8, Line 234 - 239)
+
+4. Following the reviewers’ suggestions, the superconducting transition temperatures obtained from the transport measurements in Ref. [Nature 621, 493 (2023)] have been added to our phase diagram for comparison, as shown in Fig. 4 in the main text.
+
+5. In the revised manuscript, we have mentioned that the optical pump-probe experiment is a bulk-sensitive technique in Page 7, Line 204.
+
+6. Following the reviewers’ suggestions, we revised the discussion part thoroughly including the potential relationship between DW-I and superconductivity, and the physics behind DW-II, which clarifies the novelty and significance of our work.
+
+In Methods:
+
+1. We added the sample characterizations including the resistance and XRD measurements in Page 9, Line 260 – 267.
+
+2. As per the referee’s suggestion, we added detailed descriptions of our pump-probe methodology in Page 10, Line 289 - 295.
+
+In Supplementary Information:
+
+1. We added the temperature dependent Raman measurements at 34.2 GPa.
+
+2. We added the fitting to \( A_s \) using Eq. 1 in Supplementary Figure 4.
+
+3. We added the resistance measurements of the La$_3$Ni$_2$O$_7$ cut from the same bulk crystal at 0 and 16.7 GPa.
+
+4. We added the XRD measurements and the refinements into the Supplementary Information.
+Response to Reviewer #1
+
+The authors present their new results about Density-wave-like (DW) order of La3Ni2O7 under high pressure using ultrafast optical pump-probe spectroscopy. Firstly, the DW gap Near ambient pressure related to SDW can been suppressed by high pressure. Then at pressures above 29.4 GPa, they observe the emergence of a new DW order with a transition temperature of approximately 130 K. This is a meaningful result that can help the understanding of the mechanism of nickel-based superconductivity. Before accepting the manuscript, the following series of questions must be answered.
+
+Reply: We express our gratitude to the referee for the careful review and recommendation. We thank the referee for pointing out the significance of our work by stating “This is a meaningful result...”. Below is a point-by-point response to the comments and questions.
+
+Comment 1.1- As we know, the superconducting volume fraction of La3Ni2O7 under high pressure initially measured was low, which is closely related to the method of applying pressure, the quality of the sample and the oxygen vacancies. The reported superconducting volume fraction, with some studies observing fractions as low as 1%, suggesting filamentary superconductivity, and some as high as 48%. Thus, the authors need to compare the samples used in the experiment with those mentioned above, especially the change in oxygen content, transport properties at ambient pressure and the difference in the method of applying pressure. It would be good if the authors could determine what the actual superconducting volume is under their conditions.
+
+Reply: We completely agree with the referee’s comments and appreciate the referee’s insightful suggestion. Like many other superconductors in their early stage of discovery, the synthesized La3Ni2O7 single crystals contain imperfections, such as mixed phases, inhomogeneities and randomly scattered oxygen defects, causing inconsistencies in the reported superconductivity volume fraction. To the best knowledge of the authors, there are three literature reports the diamagnetic susceptibility measurements under pressure. The first one was performed by our colleague Prof. Sun [arXiv: 2311.12361] (DAC, PMT: Silicon oil), in which the superconducting volume was estimated to be below 1% by using a home-built ac susceptibility system with a detectable limit of 0.5%. Although they have tried different samples from the same batch as ours or different batch provided by the same group, they got the similar results suggesting that the superconductivity in this nickelate is filamentary-like. The second work was done by our co-authors’ group, where a maximum SC volume fraction of 48% at 19.4 GPa was obtained indicating the bulk nature of superconductivity [arXiv: 2404.11369] (DAC, PMT: KBr). In their experiments, the samples are also from the same batch as ours in this manuscript. However, the reproducibility of the results is still under checking. The third one was reported by our colleague Prof Cheng’s group, where filamentary nature of superconductivity was reaffirmed in La3Ni2O7−δ polycrystalline samples. Furthermore, they observed clear diamagnetic signals below 75
+K in Pr-doped La2PrNi2O7 polycrystalline samples with a superconducting volume fraction up to 97% at 19 GPa [arXiv: 2407.05681, accepted by Nature] (CAC and MA, PMT: Glycerol and Fluorinert Liquid). These results implies that the emergence of superconductivity in La3Ni2O7 under high pressure exhibits sample and pressure homogeneity dependence.
+
+Our samples used in this manuscript, as well as the above-mentioned first two literatures, were provided by the same group and cut from the same batch. We prefer that the superconducting volume fraction of our sample is relatively low (as evidenced by our results, see the reply to comment 2). For comparison, we performed resistance measurement on La3Ni2O7 crystal using standard four-probe method in DAC where KBr was used as the pressure transmitting medium. Fig. R1 shows the temperature dependence of the resistance of La3Ni2O7 at two selected pressures. At ambient pressure, La3Ni2O7 shows metallic behavior and exhibits anomaly around 140 K which may relate to the density-wave transition. A clear drop in resistance at about 80 K is observed at pressure of 16.7 GPa, indicating a superconducting-like transition. The behaviors of resistance are in good agreement with the previously reported resistance measurements.
+
+To further examine the sample quality, we conduct the powder XRD experiment on the sample from the same batch as used in this manuscript. The XRD pattern and Rietveld refinement based on Cmcm at ambient pressure and room temperature, as shown in Fig. R2, indicates that the crystal used in this manuscript is 2222 bilayer structure in Cmcm (symmetry equivalent to Amam) space group at room temperature, which is also consistent with the previously reported XRD results.
+
+Both the resistance and XRD measurements indicate that the sample used in this manuscript exhibits similar properties to the above three literatures. Therefore, we do not perform further diamagnetic susceptibility measurements since it has been intensely investigated by our colleagues or coauthors. In the revised manuscript, we have added the resistance and XRD results into the Supplementary Information.
+
+![Temperature dependence of the in-plane resistance of La3Ni2O7 sample cut from the same batch used in the manuscript under (a) ambient pressure and (b) 16.7 GPa.](page_184_1042_1082_377.png)
+
+Fig. R1. Temperature dependence of the in-plane resistance of La3Ni2O7 sample cut from the same batch used in the manuscript under (a) ambient pressure and (b) 16.7 GPa.
+Fig. R2. XRD patterns of La3Ni2O7 at room temperature and ambient pressure. (a) Fitted by Cmcm symmetry in 2222 structure. (b) Enlarge of XRD data in the low angle region, together with the fitting results with Fmmm and Cmmm in 1313 structure.
+
+Comment 1.2- As mentioned above, under high pressure there is a large area without superconductivity, especially in conditions, the SC volume below 1%. The DW order, obtained here under high pressure, likely has nothing to do with superconducting samples. This needs to be highlighted and emphasized. And in the discussion part, the authors emphasize that the suppression of SC transitions by further increasing high pressure and interlayer AFM coupling diminishes with increasing pressure, which may explain the emergence of the DW-II order. However, when superconductivity is filamentary, the signal of the DW-II order may have nothing to do with superconductivity. In my opinion, suppression and then reemergence of DW order under high pressure probably related to the phase separation.
+
+Reply: We thank the referee for this constructive comment. Although zero resistance under 16.7 GPa (DAC + KBr) has been observed in the sample cut from the same crystal bulk used in the manuscript (see Fig. R1), we do not observe any signature of superconductivity from the ultrafast spectra in this manuscript. Since the ultrafast optical pump-probe spectroscopy is a bulk sensitive technique, our results also support the fact that the superconducting volume fraction in this sample is relatively low, i.e. superconductivity is possible filamentary. However, the complex density-wave behaviors under pressure are significantly influenced by the temperature and pressure. Thus, a thoughtful investigation of the evolution of the DW transitions under pressure is crucial for understanding the pairing mechanism of superconductivity and examining the theoretical models proposed. A shown in Fig. 4 in the main text, the extracted density-wave-like gap decreases with increasing pressure, and reaches minimum value around 13.3 GPa, above which the gap amplitude remains nearly constant below 26 GPa. In the revised manuscript, we argue that the SDW originate from the majority 327 phase is almost suppressed around 13.3 GPa, above which the weak phonon bottleneck effect may originate from the existence of short-ranged SDW order or the potential phase separation of 4310 phase (as we will discuss in detail below). The suppression of SDW order and the emergence of superconductivity around 13.3 GPa, suggest that the SDW phase is possible suppressor of superconductivity, and hence the spin fluctuation may be responsible for the high-temperature superconductivity in
+nickelates. Actually, Reviewer #4 also pointed out the inappropriate discussion about the interlayer AFM coupling. In the revised manuscript, we have removed the relevant discussion.
+
+We are grateful to referee for pointing out the possibility of phase separation. The coexistence of multiple structure variants in La3Ni2O7 crystals, including the majority 327 phase and minority 4310 and 214 phase, have been demonstrated by scanning transmission electron microscopy (STEM) investigations [arXiv: 2311.12361, arXiv: 2407.05681]. Since the ultrafast pump-probe spectroscopy is a bulk-sensitive technique, the gradual suppression of DW-I with increasing pressure up to 13.3 GPa is unambiguous from the predominant 327 phase. In the pressure range from 13.3 to 26 GPa, we argue that short-range order may exist after the long-range order is suppressed and hence induce the opening of a small gap in the density of states below T_DW. However, as suggested by the referee, the weak feature may also originate from the minor 4310 phase in La3Ni2O7 crystal after the SDW in the majority 327 was suppressed by pressure above 13.3 GPa. The weak gap feature contributed by the density-wave states in minor 4310 phase gradually disappears upon further compression up to 26 GPa, which agrees with the transport measurements [arXiv: 2311.07423, Chin. Phys. Lett, 41, 017401 (2023)]. The reemergence of DW II under pressure above 29 GPa may NOT relate to the phase separation, i.e. the existence of 4310 phase, since it was totally suppressed around 26 GPa.
+
+In the revised manuscript, we have removed the discussion of the AFM coupling and added the discussion about the possible contributions from the phase separation (Page 7, Line 208 - 216). Also, the above discussion of the relationship between the DW-like order and superconductivity is given in the section of Discussion (Page 8, Line 217 - 227).
+
+Comment 1.3- The new DW order results contradict the previous transport measurements (High-temperature superconductivity with zero resistance and strange-metal behaviour in La3Ni2O7−δ. Nat. Phys. (2024)). In their paper, zero resistance and strange-metal behaviour have been obtained. From their data, under 29.2 GPa, the resistivity exhibits a linear dependence on temperature. This linear resistive behavior usually precludes the DW orders. The reasons for the conflicting views should be discussed and explained.
+
+Reply: We thank the referee for this comment. Indeed, a linear temperature-dependent resistance has been observed above T_c by several research groups, even with samples of varying quality. In the transport experiments, the anomaly in the resistance originating from DW orders usually becomes undistinguishable under pressure higher than 3 GPa, because the kink becomes too broad to observe. However, the DW-like features in our ultrafast spectra (phonon bottleneck effect) are very clear even under the pressure up to 13.3 GPa, indicating the extremely sensitivity of our technique. As we have discussed in the main text, the DW-like features in our spectra are relative weak under pressure range from 13.3 to 26 GPa, as well as above 29 GPa. Therefore, it is reasonable that the transport measurements can not observe anomaly in the resistance except the linear dependence. In other words, the linear resistivity does not exclude the possible existence of DW order,
+even though it may originate from phase separation. On the contrary, the peculiar pressure-dependence of DW orders, especially the re-emergence of DW-II, have never been reported by other experimental studies before our work, further supporting the novelty and significance of our work. In the revised manuscript, we have explained the conflicting views in Page 8, Line 234 – 239.
+
+Comment 1.4- From the data, there is no significant difference between the behavior of the two kind DW. However, in the manuscript, the author attributes them to AFM and CDW. This can be misleading.
+
+Reply: We appreciate the referee’s constructive comment. As we have discussed in the main text, the RT-model was initially proposed to describe the relaxation of photoexcited superconductors, where the formation of a gap in the electronic density of states creates a relaxation bottleneck of the photoexcited quasiparticles, but its applicability has extended to a wide range of metallic systems with gap opening in the density of states, such as superconductivity, spin and charge density wave. The clear phonon bottleneck effects observed in this manuscript strongly supports the presence of gap opening effect in La3Ni2O7 crystal. Nevertheless, we can not distinguish these broken symmetry ground states from the ultrafast pump-probe spectra. Instead, we attribute the two DWs to SDW and CDW, respectively, combining with the results from other experimental and theoretic results.
+
+The extracted transition temperature at ambient pressure agrees nicely with various experimental results, including RIXS, \( \mu \)SR and NMR measurements, where an SDW transition have been identified. Moreover, the DW-like order was gradually suppressed by pressure, also consistence with various transport measurements. Combined with these results, we argue that the DW-like order in the low-pressure range is probably SDW.
+
+As pointed out by Referee 2, the most interesting result is the observation of a new DW phase under pressure around 30 GPa, which has never been reported by other experimental studies before our work. The re-emergence of DW-II order and its increasing trend with increasing pressure coincide with the prediction by the theorist in Ref. [arXiv: 2403.11455]. In this paper, the authors propose that the CDW originates from the Peierls instability related to FS nesting. Therefore, we attribute the DW-II to CDW. In the revised manuscript, we have explained the origin of the DW-II more clear in the discussion part in Page 8, Line 228 to 245.
+
+Comment 1.5- The DW-II order emerges at 29.2 GPa. What happens at this pressure? If the authors think it is related to superconductivity, they should put the previous superconductivity phase diagrams together with DW’s phase diagrams for comparison.
+
+Reply: We thank the referee for the question. To best knowledge of the authors, this manuscript is the first experimental observation of such a DW-II phase under pressure
+above 29 GPa, consistent with the prediction from a recent theoretical work [arXiv: 2403.11455]. The authors performed DFT calculations to examine the structure, electronic, and phonon properties of La$_3$Ni$_2$O$_7$ under pressure. They found two imaginary phonon modes for the *Fmmm* phase at 30 GPa, leading to stable distorted CDW structure in either *Cmmm* or *Cmcm* phase. Moreover, the momenta with imaginary phonons correspond to those exhibiting strong peaks of the Fermi surface nesting function, confirming that CDW originates from Peierls instability related to Fermi surface nesting. Nevertheless, the authors also pointed out that the distortion of Ni-O bong length is less than 0.1 Å, which is a challenge in probing the predicted CDW structure in experiments. Thanks to the extreme sensitivity of the ultrafast optical pump-probe spectroscopy, we can observe the relatively weak phonon bottleneck effect in La$_3$Ni$_2$O$_7$ under pressure above 29 GPa, which is probably related to the predicted CDW structure. In the revised manuscript, the above discussions can be found in Page 8, Line 228 to 245.
+
+We appreciate the referee’s great suggestion about the superconductivity. In the revised manuscript, the superconducting transition temperatures obtained from the transport measurements in Ref. [Nature 621, 493 (2023)] have been added to our phase diagram for comparison, as shown in Fig R3.
+
+[figure redacted]
+
+Fig.R3. Revised phase diagram of the DW and the superconductivity (adapted from Nature, 621, 493 (2023)) in La$_3$Ni$_2$O$_7$ single crystal.
+Response to Reviewer #2
+
+Aiming the current studies about pressurized La3Ni2O7, the electron pairing mechanism is still unclear, in this paper, the authors have used techniques such as ultrafast optical pump-probe spectroscopy to study the quantum state and electronic structure of novelties such as CDW. Their main conclusions are as follows: 1). the DW band gap opens near atmospheric pressure, around 115 K. The authors attribute this effect to phonon bottleneck effect. 2). With increasing pressure, this phonon bottleneck effect is gradually suppressed and completely disappears around 26 GPa. 3). The most interesting result is that around 30 GPa, they observe a new DW phase.
+
+This study reports some unreported results on La3Ni2O7 superconductors under pressure. Combined with the close connection between the DW phase and the superconducting state, I believe that this work will help researchers in the field of superconductivity to further understand the electronic structure of La3Ni2O7, and even its superconducting electron pairing mechanism. Before recommending the acceptance and publication of the paper, I think the authors should further elucidate some issues to some degree, with performing additional experiments and/or theoretical calculations:
+
+Reply: We are very grateful to the referee for conducting a thorough evaluation of our manuscript and providing us with valuable suggestions and recommendations. We thank the referee for the positive opinion on our work, that “this work will help researchers in the field of superconductivity...”. In the following, we will address the referee’s comments one by one.
+
+Comment 2.1-: In a previous paper by some of the authors, Nature volume 621, 493-498 (2023), the authors proposed the space group structure of Amam and Fmmm. However, some subsequent theoretical and experimental work other studies have proposed space group structures such as I4/mmm and Cmmm, as well as single- and three-layer alternating structures. My question is, in the current study, did the authors reexamine or check the symmetry of the crystal structure of the system at different pressures or is the change in symmetry related to the multiple DW phases mentioned by the authors in their study?
+
+Reply: We would like to thank the referee for the questions. La3Ni2O7 single crystals grown by high-pressure floating-zone method have two structures with the same chemical formula, i.e., alternating single-layer-trilayer stacking structure (1313) and bilayer structure (2222). The complex crystallographic behavior of this nickelate, especially under high pressure and low temperature, is still under debate. To examine the quality of our sample and to answer the referee’s question, we performed powder XRD measurement on another piece of sample cut from the same batch as in this manuscript. The XRD pattern and Rietveld refinement based on the Cmcm space group (Group No. 63) in 2222 structure and Fmmm and Cmmm in the 1313 structure are plotted in Fig.R4 for comparison. Obviously, the refinement based on Cmcm space group can fit the experimental data very well. The lattice
+parameters and atomic coordinates for the Cmcm phase of La3Ni2O7 crystal are listed in Table R1 and R2, where the results from a recent work in ref [arXiv:2405.08802] are also included for comparison. Our XRD results indicate that the crystal used in this manuscript has a 2222 bilayer structure in Cmcm (symmetry equivalent to Amam) space group at room temperature and ambient pressure, which is consistent with the reported works by our coauthors [Nature, 621, 493(2023), arXiv:2404.11369], and also the other studies [JACS, 146,7506(2024), arXiv:2405.08802]. In these studies, they performed further investigations of the structural transitions under high pressure and low temperature. In the revised manuscript, we have added the XRD characterizations of our sample at room temperature and ambient pressure into the Supplementary Information.
+
+![XRD patterns of La3Ni2O7 at room temperature and ambient pressure. (a) Fitted by Cmcm symmetry in 2222 structure. (b) Enlarge of XRD data in the low angle region, together with the fitting results with Fmmm and Cmmm in 1313 structure.](page_320_624_1107_312.png)
+
+Fig.R4. XRD patterns of La3Ni2O7 at room temperature and ambient pressure. (a) Fitted by Cmcm symmetry in 2222 structure. (b) Enlarge of XRD data in the low angle region, together with the fitting results with Fmmm and Cmmm in 1313 structure.
+
+Our co-authors reported the observation of superconductivity around 80 K, aligning with a structural transition from the ambient pressure Amam to the high pressure Fmmm above 14 GPa. In the revised manuscript, we argue that the SDW originating from the 327 phase is totally suppressed around 13.3 GPa, above which the weak phonon bottleneck effect may be contributed by the short-range order or the possible existence of 4310 phase. From this point of view, the suppression of the SDW around 13.3 GPa in the DW-I region is related to the first structural transition.
+
+To our best knowledge, this manuscript is the first experimental observation of such a DW-II phase under pressure above 29 GPa, which agrees nicely with the prediction from a recent theoretical work [arXiv: 2403.11455]. The authors performed DFT calculations to examine the structure, electronic and phonon properties of La3Ni2O7 under pressure. They found that the existence of imaginary modes in the phonon spectra for Fmmm phase at 30 GPa leads to a stable distorted structure in either Cmmm or Cmcm space group under the transition temperature. However, the authors also pointed out that the distortion of Ni-O bond length is less than 0.1 Å, which is challenging in probing the predicted CDW structure in experiments. Actually, we can not observe distinct changes in the Raman spectra as we will discuss in the next reply. Thanks to the extreme sensitive of ultrafast optical pump-probe spectroscopy, we can observe the relative weak phonon bottleneck effect in La3Ni2O7 under pressure above 29 GPa,
+which probably originates from the predicted CDW structure.
+
+In the revised manuscript, the above discussion about the relationship between the structure symmetry with the DW-like order can be found on Page 8, Line 228 to 249.
+
+Table R1. Crystal data and structure refinement of Cmcm symmetry at ambient pressure, comparing with the result from [arXiv:2405.08802] at 280 K.
+
+<table>
+  <tr>
+    <th></th>
+    <th>This work</th>
+    <th>[arXiv:2405.08802]</th>
+  </tr>
+  <tr>
+    <td>Temperature (K)</td>
+    <td>293</td>
+    <td>280</td>
+  </tr>
+  <tr>
+    <td>symmetry</td>
+    <td>Cmcm</td>
+    <td>Cmcm</td>
+  </tr>
+  <tr>
+    <td>a (\(\text{\AA}\))</td>
+    <td>20.56125</td>
+    <td>20.5290(6)</td>
+  </tr>
+  <tr>
+    <td>b (\(\text{\AA}\))</td>
+    <td>5.4504</td>
+    <td>5.44684(18)</td>
+  </tr>
+  <tr>
+    <td>c (\(\text{\AA}\))</td>
+    <td>5.3982</td>
+    <td>5.38990(18)</td>
+  </tr>
+  <tr>
+    <td>V (\(\text{\AA}^3\))</td>
+    <td>604.96</td>
+    <td>602.69(3)</td>
+  </tr>
+  <tr>
+    <td>R<sub>1</sub></td>
+    <td>0.0235</td>
+    <td>0.0358</td>
+  </tr>
+  <tr>
+    <td>wR<sub>2</sub></td>
+    <td>0.0696</td>
+    <td>0.0711</td>
+  </tr>
+</table>
+
+Table R2. Atom coordinates of 2222 structure at ambient pressure and room temperature, comparing with the result from [arXiv:2405.08802] at 280 K.
+
+<table>
+  <tr>
+    <th>Wyck.</th>
+    <th>x</th>
+    <th>y</th>
+    <th>z</th>
+    <th>Occ.</th>
+  </tr>
+  <tr>
+    <th colspan="5">This work at 293 K</th>
+  </tr>
+  <tr>
+    <td>La1</td>
+    <td>4c</td>
+    <td>0</td>
+    <td>0.75339</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>La2</td>
+    <td>8g</td>
+    <td>0.31768</td>
+    <td>0.26277</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>Ni</td>
+    <td>8g</td>
+    <td>0.09684</td>
+    <td>0.27056</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O1</td>
+    <td>8e</td>
+    <td>0.38443</td>
+    <td>0</td>
+    <td>0</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O2</td>
+    <td>8e</td>
+    <td>0.08466</td>
+    <td>0</td>
+    <td>0</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O3</td>
+    <td>8g</td>
+    <td>0.18652</td>
+    <td>0.15977</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O4</td>
+    <td>4c</td>
+    <td>0</td>
+    <td>0.26309</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <th colspan="5">[arXiv:2405.08802] at 280 K</th>
+  </tr>
+  <tr>
+    <td>La1</td>
+    <td>4c</td>
+    <td>0</td>
+    <td>0.75058</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>La2</td>
+    <td>8g</td>
+    <td>0.32019</td>
+    <td>0.25789</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>Ni</td>
+    <td>8g</td>
+    <td>0.09589</td>
+    <td>0.25242</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O1</td>
+    <td>8e</td>
+    <td>0.39534</td>
+    <td>0</td>
+    <td>0</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O2</td>
+    <td>8e</td>
+    <td>0.08932</td>
+    <td>0</td>
+    <td>0</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O3</td>
+    <td>8g</td>
+    <td>0.20441</td>
+    <td>0.2173</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+  <tr>
+    <td>O4</td>
+    <td>4c</td>
+    <td>0</td>
+    <td>0.2909</td>
+    <td>0.25</td>
+    <td>1</td>
+  </tr>
+</table>
+
+Comment 2.2.-: The creation of the DW phase of the system may be closely related to the structural instability of the system, so I think it is necessary to discuss phonons and DW in conjunction with the evolution of symmetry.
+
+Reply: We appreciate the referee’s insightful suggestion. To examine the predicted
+structure transition related to CDW, we performed temperature dependent Raman scattering measurements on the same crystal at position P0 where ultrafast spectra were measured under 34.2 GPa. The Raman spectra under high pressure were collected with a Monovista Raman Spectroscopy system equipped with a HRS-750 scanning monochromator, a cryogenically-cooled ultra-low noise Pylon CCD camera, and a 532 nm laser. As shown in Fig R5, the spectra are almost temperature independent from 60 to 250 K, except the slight blue shift of the peak around 500 and 620 cm\(^{-1}\) with decreasing temperature. Remarkably, we do not see any emergence of new peaks across the transition temperature T_{DW}~140 K. This is probably because the structure distortion related to the CDW is very weak as predicted by the theoretic work (the distortion of Ni-O bond length is less than 0.1 \AA). In addition, the usage of DAC further decreases the detection sensitivity in the Raman measurements. Hence the direct capture of the structure transitions related to the DW orders in nickelate under high pressure are challenging in Raman experiments that requires further detailed study. In the revised manuscript, we have added the temperature dependence of the Raman spectra at 34.2 GPa into Supporting Information.
+
+![Temperature dependent Raman spectra of La3Ni2O7 at 34.2 GPa.](page_384_669_670_312.png)
+
+Fig.R5. Temperature dependent Raman spectra of La3Ni2O7 at 34.2 GPa.
+
+Comment 2.3:- in the SM Fig.S4, Fig.S5, 26GPa, why is there not a fitted data?
+
+Reply: We thank the reviewer for the question. The phonon bottleneck effect is too weak to extract a reasonable gap energy at 26 GPa. As shown in Fig 3 in the main text, A_s decreases with increasing pressure at 20 K, from 1.3×10^{-3} at ambient pressure to 0.02×10^{-3} at 26 GPa, indicating that DW order is almost suppressed around 26 GPa. As shown in Fig. R6(a), A_s increases with decreasing temperature at 26 GPa, which can be fitted by Eq. (1), yielding T_{DW} ~ 100 K. Since the ratio of A_s/A_f at 26 GPa (0.063) is too small compare to that at ambient pressure (0.922), the fast decay with positive amplitude dominates the transient signal, leading to the extracted slow decay time \( \tau_s \) oscillates with temperature significantly, as shown in Fig.R6(b). At temperature above 50 K, \( \tau_s \) is almost temperature independent as indicted by the solid line. There is only one-point (at 100 K) deviates from temperature-independent behavior probably because the extremely small amplitude (~0.005×10^{-3}) of the slow decay component. Therefore, we do not fit \( \tau_s \) using Eq (2). Following the referee’s suggestion, we have added the fitting to A_s in Supplementary Figure 4, but not to \( \tau_s \) in Supplementary Figure 5.
+Fig. R6. (a) Temperature dependence of \( A_s \) at 26 GPa. The solid line is a fit by RT-model. (b) Temperature dependence of \( \tau_s \) at 26 GPa. The solid line is guide for the eye.
+
+Comment 2.4-: Are the experimental measurements done in this paper reflecting more the electronic structure of the surface or the internal bulk?
+
+Reply: We thank the reviewer for the question. Optical spectroscopy is a bulk sensitive technique and probes samples up to the optical penetration depth. We estimate the optical penetration depth of La$_3$Ni$_2$O$_7$ at the pump (400 nm) and probe (800 nm) wavelength, respectively, using the formulas:
+
+\[
+\varepsilon_1(\omega) = n^2 - k^2 = 1 - \sigma_2/\omega \varepsilon_0 \\
+\varepsilon_2(\omega) = 2nk = \sigma_1/\omega \varepsilon_0
+\]
+
+where \( n \) and \( k \) are the refractive index and extinction coefficient, respectively. The optical conductivity \( \sigma = \sigma_1 + i \sigma_2 \) of La$_3$Ni$_2$O$_7$ at 150 K can be obtained from Ref [Nat. Comm. 15, 7570(2024)], as shown in Fig. R7, which are \( (800 - 100i)\ S/cm \) and \( (640 - 540i)\ S/cm \) at 400 and 800 nm, respectively. Solving the above equations, the values of \( k \) for 400 and 800 nm were obtained to be 0.48 and 1.15, respectively. Then we got the optical penetration depths using \( l = c/2\omega k \) to be 65.9 and 55.5 nm for the pump and probe beams, respectively. Therefore, the signal from the internal bulk is overwhelming compared to the surface in our 400-nm-pump 800-nm-probe experiments. In the revised manuscript, we have mentioned that the optical pump-probe experiment is a bulk-sensitive technique in Page 7, Line 204.
+
+Fig. R7. The measured (a) \( \sigma_1(\omega) \) and (b) \( \sigma_2(\omega) \) of La$_3$Ni$_2$O$_7$ at 150 K and corresponding Drude-Lorentz fitting results, adapted from Ref [Nat. Comm. 15, 7570(2024)].
+Comment 2.5: does the authors' work, suggest that in La3Ni2O7, the DW phase may be the driving force of superconductivity or the pairing force of electrons? In a recent theoretical combined with experimental work [Phys. Rev. B 109, 235126], it was confirmed that antiferromagnetic fluctuation in the single-band model is the electron pairing force, so in La3Ni2O7, does antiferromagnetism plays as the same force and the DW phase is a suppressor?
+
+Reply: We appreciate the reviewer's helpful question and reference. Our answer to this question is probably yes. Our ultrafast data indicated a DW-like transition occurring around 150 K at ambient pressure. Combined with recent spectral studies, including RIXS, \( \mu \)SR and NMR measurements, we attribute this DW-like transition to an SDW transition. Consistent with earlier transport measurements on La3Ni2O7 crystals, this DW-like transition is typically suppressed with increasing pressure. Intriguingly, the extracted energy gap decreases with increasing pressure up to 13.3 GPa, above which it remains nearly constant below 26 GPa. In the revised manuscript, we argue that the SDW originating from the majority 327 phase is totally suppressed around 13.3 GPa, above which the weak phonon bottleneck effect may originate from either the existence of short-ranged SDW order or the potential phase separation of 4310 phase. The suppression of SDW order and the emergence of superconductivity around 13.3 GPa suggest that the magnetic fluctuations are particularly critical for understanding the pairing mechanism of superconductivity in La3Ni2O7, similar to the case of Infinite-layer nickelates.
+
+In the revised manuscript, we have provided the discussion of the relationship between the DW order and superconductivity in Page 8, Line 217 – 227.
+
+Comment 2.6:- In summary, after the authors have answered the above question, it can be considered acceptable in NC.
+
+Reply: We sincerely appreciate the reviewer's thorough examination of our manuscript and the insightful suggestions regarding the consideration of spin fluctuations. We have carefully addressed this concern in our revised manuscript and hope that our response satisfactorily resolves the reviewer's questions.
+Response to Reviewer #3
+
+Previous experiments have shown that La3Ni2O7 undergoes a superconducting transition with a Tc of ~80K at pressures above 14 GPa. Further, at ambient pressure there is evidence for a spin density wave transition around 150 K, along with a FM striped ground state and possibly a charge density wave transition between 110-130 K, both of which may have relevance to the high-pressure superconducting state. To explore the density wave evolution in La3Ni2O7, the paper by Meng et al provides an experimental study of the quasiparticle dynamics as a function of temperature and pressures up to 34 GPa. The relaxation dynamics exhibit a phonon bottleneck effect, which, when fit to the Rothwarf - Taylor model reveals the opening of a 66-meV gap at 151 K at ambient pressure. As the pressure increases the gap is suppressed, disappearing at ~26 GPa. The phonon bottleneck re-emerges in the quasiparticle dynamics at pressures above 29 GPa, revealing a new gap (~20 meV) with a transition temperature of ~130 K. The phonon bottleneck effect is not observed in the quasiparticle dynamics between ~26 and ~29 GPa, indicating the absence of a gap and hence density wave order.
+
+This detailed study of the density gap evolution in La3Ni2O7 is new and significant, in that it provides information underpinning the evolution, coexistence and competition between density wave and superconducting order in a high temperature superconductor. Motivation and background for this work, including the references are adequate. The experimental results and analysis are thorough, convincing and supportive of the conclusions made by the authors. The methodology is sound and should enable reproduction of the experimental results when the additional information in the supplementary material is included.
+
+Reply: We are grateful to the referee for reviewing this manuscript and highlighting the importance of our work. We also thank the referee for saying that our results are “thorough, convincing and supportive” and that our experimental method is “sound”. In the revised manuscript, we have included more detailed descriptions of our methodology. Below is a point-by-point response to the comments and questions.
+
+Comment 3.1- However, I suggest that the Discussion section be expanded to enable a clearer interpretation of the results. The authors state that they see no signature of superconductivity between 26 and 29 GPa where there is also not evidence for a density wave order and attribute this competition between superconducting and density wave order. This seems contradictory, indicating that a more thorough and quantitative discussion is needed. They also state that the emergence of the second density wave order is consistent with theoretical results, but don’t explain the physics behind those results.
+
+Reply: We thank the referee for the great suggestion which have helped significantly improve the quality of our manuscript. In the revised manuscript, we have removed the contradictory statement and provided a detail discussion on the obtained phase diagram. In fact, we did not observe any signature of superconductivity from our ultrafast pump-
+probe spectra in the whole studied pressure range up to 34.2 GPa. This result indicates that the superconducting volume fraction of our sample is low, since the optical pump-probe spectroscopy is a bulk-sensitive technique. Our ultrafast data indicate that the DW-like transition is suppressed with increasing pressure, consistent with earlier transport measurements. As shown in Fig 4 in the main text, the extracted energy gap decreases with increasing pressure up to 13 GPa, above which it remains nearly constant below 26 GPa. In the revised manuscript, we argue that the SDW originating from the majority 327 phase is almost suppressed around 13.3 GPa, above which the weak phonon bottleneck effect may originate from either the existence of short-ranged SDW order or the potential phase separation of 4310 phase. The suppression of SDW order in this manuscript, together with the emergence of superconductivity in transport measurements around 13.3 GPa suggest that the magnetic fluctuations are particularly critical for understanding the pairing mechanism of superconductivity in this nickelate.
+
+To best knowledge of the authors, our manuscript is the first experimental observation of such a DW-II phase under pressure above 29 GPa, consistent with the prediction from a recent theoretical work [arXiv: 2403.11455]. The authors performed DFT calculations to examine the structure, electronic and phonon properties of La3Ni2O7 under pressure. They found two imaginary phonon modes for the Fmmm phase at 30 GPa, leading to stable distorted CDW structure in either Cmmm or Cmcm phase. Moreover, the momenta with imaginary phonons correspond to those exhibiting strong peaks of the Fermi surface nesting function, confirming that CDW originates from Peierls instability related to Fermi surface nesting. Nevertheless, the authors also pointed out that the distortion of Ni-O bond length is less than 0.1 Å, which is challenging in probing the predicted CDW structure in experiments. Thanks to the extreme sensitivity of the ultrafast optical pump-probe spectroscopy, we can observe the relatively weak phonon bottleneck effect in La3Ni2O7 under pressure above 29 GPa, which is probably related to the predicted CDW structure.
+
+In the revised manuscript, the above discussions can be found in the “Discussion” section, to make a clear interpretation of our data and explain the physics behind our results.
+
+Comment 3.2- Finally, the manuscript would benefit from language editing. Once these two issues are addressed, I recommend publication of this paper in Nature Communications.
+
+Reply: We thank the referee for suggesting to polish the language and recommendation of our manuscript. We have improved the English in the revised manuscripts. We hope that our response satisfactorily resolves the reviewer's questions.
+Response to Reviewer #4
+
+The authors reported the observation of density-wave (DW) quasiparticle gaps in La3Ni2O7 as a function of temperature and pressure, by the measurement of the time-resolved variation of the reflectivity in the pump-probe setting. They found DW-I at the ambient pressure, which decreases in transition temperature gradually with increasing pressure up to 26 GPa, and the emergence of a new DW-II above 26 GPa. No contribution from superconductivity (SC) was detected. They associated the emergence of DW-II with the decrease of SC at high pressures, suggesting the competition between such orders. The experimental results are interesting. However, to make the conclusions compelling, I ask the authors to consider the following points:
+
+Reply: We thank the referee for the thorough review and insightful comments. The referee’s remarks regarding the large interest of our results are highly encouraging. Below is a point-by-point response to the comments and questions.
+
+Comment 4.1- There is no characterization of the crystal structure. This is a crucial point to make sure whether the observed sample has anything to do with the superconducting phase. The fact that they observed no SC signal is a possible indication that the DW's they observed are hardly related to SC. In this case, the observations would be less important.
+
+Reply: We thank the reviewer for the comment. To characterize our sample, powder XRD measurement were performed on La3Ni2O7 crystal cut from the same batch as in the main text at room temperature and ambient pressure. The XRD pattern and Rietveld refinement based on the space group of Cmcm in 2222 structure and Fmmm/Cmmm in 1313 structure are plotted in Fig. R8 for comparison. Obviously, the refinement based on Cmcm space group (Group NO. #63, symmetry-equivalent to Amam), can fit the experimental data very well. Lattice parameters and atomic coordinates for the Cmcm phase have been added to the Supporting Information as Supplementary Table S1 and S2. Our XRD results indicate
+
+![XRD patterns of La3Ni2O7 at room temperature and ambient pressure. (a) Fitted by Cmcm symmetry in 2222 structure. (b) Enlarge of XRD data in the low angle region, together with the fitting results with Fmmm and Cmmm in 1313 structure.](page_153_1042_1142_393.png)
+
+Fig. R8. XRD patterns of La3Ni2O7 at room temperature and ambient pressure. (a) Fitted by Cmcm symmetry in 2222 structure. (b) Enlarge of XRD data in the low angle region, together with the fitting results with Fmmm and Cmmm in 1313 structure.
+that the crystal used in this manuscript is 2222 bilayer structure in Cmcm (Amam) space group at room temperature and ambient pressure, which is consistent with the reported works by our coauthors [Nature, 621, 493(2023), arXiv:2404.11369], and also the other studies [JACS, 146,7506(2024), arXiv:2405.08802]. In these studies, they performed further investigations of the structural transitions under high pressure and low temperature.
+
+To further examine the superconductivity, we performed resistance measurement on La$_3$Ni$_2$O$_7$ crystal using the standard four-probe method in DAC where KBr was used as the pressure transmitting medium. Fig. R9 shows the temperature dependence of the resistance of La$_3$Ni$_2$O$_7$ at two selected pressures. At ambient pressure, La$_3$Ni$_2$O$_7$ shows metallic behavior and exhibits anomaly around 140 K which may be related to the density-wave transition. A clear drop in resistance at about 80 K is observed at pressure of 16.7 GPa, indicating a superconducting-like transition. The behaviors of resistance are in good agreement with the previously reported resistance measurements. However, we did not observe any signature of superconductivity from our ultrafast pump-probe spectra in the whole studied pressure range up to 34.2 GPa. This result strongly supports the fact that the superconducting volume fraction of our sample is low since the optical pump-probe spectroscopy is bulk-sensitive technique. In the revised manuscript, we have included the XRD and resistance results into the Supporting Information.
+
+![Temperature dependence of the in-plane resistance of La3Ni2O7 sample cut from the same batch used in the manuscript under (a) ambient pressure and (b) 16.7 GPa.](page_320_670_808_312.png)
+
+Fig. R9. Temperature dependence of the in-plane resistance of La$_3$Ni$_2$O$_7$ sample cut from the same batch used in the manuscript under (a) ambient pressure and (b) 16.7 GPa.
+
+Our ultrafast data indicates the DW-like transition is suppressed with increasing pressure, consistent with earlier transport measurements. As shown in Fig 4 in the main text, the extracted energy gap decreases with increasing pressure up to 13.3 GPa, above which it remains nearly constant below 26 GPa. In the revised manuscript, we argue that the SDW originating from the majority 327 phase is almost suppressed around 13.3 GPa, above which the weak phonon bottleneck effect may originate from the existence of short-ranged SDW order or the potential phase separation of minor La$_4$Ni$_3$O$_{10}$. In the revised manuscript, we argue that the SDW originating from the majority 327 phase is almost suppressed around 13.3 GPa, above which the weak phonon bottleneck effect may originate from either the existence of short-ranged SDW order or the potential phase separation of 4310 phase. The suppression of SDW order in this manuscript, together with the emergence of superconductivity in transport measurements around 13.3 GPa suggest that the magnetic
+fluctuation may be responsible for the high-temperature superconductivity in pressurized La$_3$Ni$_2$O$_7$. Remarkably, as pointed out by Referee 2, the most interesting result is the observation of a new DW phase under pressure around 30 GPa, which has never been reported by other experimental studies before our work. The re-emergence of DW-II order and its increasing trend with increasing pressure coincide with the prediction by the theorists in Ref. [arXiv: 2403.11455], where the authors proposed that the CDW originates from the Peierls instability related to FS nesting. Therefore, a thoroughly investigation of the evolution of the DW orders under pressure is crucial for unraveling the pairing mechanism of superconductivity in nickelate, as well as examining the proposed theoretical models. In the revised manuscript, we have improved the discussion to clarify the novelty and significance of our work.
+
+Comment 4.2- While DW-I was identified as a kind of SDW, by comparison to other probes, there is no discussion on the nature and origin of the DW-II, whether it is spin- or charge-order, and how it is different to DW-I.
+
+Reply: We appreciate the referee’s comment. As we have discussed in the main text, the RT-model was initially proposed to describe the relaxation of photoexcited superconductors, where the formation of a gap in the electronic density of states creates a relaxation bottleneck of the photoexcited quasiparticles, but its applicability has extended to a wide range of metallic systems with gap opening in the density of states. However, there exists an energy gap in various broken symmetry ground states, such as superconductivity, spin and charge density wave, below the transition temperature. We can not distinguish them from the ultrafast spectra, instead we attribute the observed two DWs to SDW and CDW, respectively, combining with the results from other experimental and theoretic results.
+
+The observation of a new DW phase above 29 GPa has never been reported before our work. The observed DW-II order and its increasing trend with increasing pressure coincide with the prediction by the theorist in Ref. [arXiv: 2403.11455]. The authors performed DFT calculations to examine the structure, electronic and phonon properties of La$_3$Ni$_2$O$_7$ under pressure. They found two imaginary phonon modes for the Fmmm phase at 30 GPa, leading to stable distorted CDW structure in either Cmmm or Cmcm phase. Moreover, the momenta with imaginary phonons correspond to those exhibiting strong peaks of the Fermi surface nesting function, confirming that CDW originates from Peierls instability related to Fermi surface nesting. Nevertheless, the authors also pointed out that the distortion of Ni-O bong length is less than 0.1 Å, which is challenges in probing the predicted CDW structure in experiments. Thanks to the extremely sensitive of the ultrafast optical pump-probe spectroscopy, we can observe the relative weak phonon bottleneck effect in La$_3$Ni$_2$O$_7$ under pressure above 29 GPa, which is probably related to the predicted CDW structure. In the revised manuscript, above discussions about the nature and origin of the DW-II could be found in Page 8, Line 228 – 245.
+Comment 4.3- A minor issue in the discussion part: The authors stated that in the DW-II regime, the interlayer AFM coupling is weakened by pressure. But this is quite unlikely, since increasing pressure is expected to increase the interlayer hopping, which translates to enhanced antiferromagnetic interlayer spin exchange. I ask the authors to think more carefully in the discussion part.
+
+Reply: We thank the referee for the comment. Indeed, based on the DFT calculations, the Amam-Fmmm structural transition flattens the Ni-O-Ni bonding angle along the c-axis, which enhances the interlayer antiferromagnetic exchange interaction. In the revised manuscript, we removed the discussion of interlayer AFM coupling. Instead, we have revised the discussion part thoroughly including the potential relationship between DW-I and superconductivity, and the physics behind DW-II.
+
+Comment 4.4-: I cannot make the recommendation before the authors make convincing clarifications to the above points.
+
+Reply: We appreciate the referee's helpful suggestions and comments. We hope our response and the revised manuscripts solve the reviewer’s concerns.
+-------------------------------------------------------------------------------
+
+Response to Reviewer #1
+
+-------------------------------------------------------------------------------
+
+The author answered my questions very completely and accurately. Their work is one of the important advances in the field of nickel-based superconductivity, so the article should be accepted.
+
+Reply: We appreciate the referee for the encouraging comments and recommendation for our manuscript
+
+-------------------------------------------------------------------------------
+
+Response to Reviewer #2
+
+-------------------------------------------------------------------------------
+
+I have carefully reviewed the authors' response to my initial comments and their revised manuscript. I am pleased to report that the authors have addressed all of the concerns raised during the initial review process in a thorough and satisfactory manner. The revisions made significantly improve the clarity, depth, and rigor of the manuscript, enhancing its overall quality and contribution to the field of unconventional superconductivity.
+I recommend this paper for accepted publication in Nature Communications.
+
+Reply: We express our gratitude to the referee for the careful review and recommendation for our manuscript
+-------------------------------------------------------------------------------
+
+Response to Reviewer #3
+
+-------------------------------------------------------------------------------
+
+The author have adequately addressed my concerns. I recommend the paper for publication in Nature Communications.
+
+Reply: We thank the reviewer for the recommendation of our manuscript.
+
+-------------------------------------------------------------------------------
+
+Response to Reviewer #4
+
+-------------------------------------------------------------------------------
+
+The authors replied to all referee comments carefully, and provided additional experimental data to clarify the quality of the sample. They also changed their previous view on the nature of the DW-II phase, which is now reasonably identified as a kind of CDW. I find the reply and the revised manuscript satisfactory. Given the high sensitivity of the pump-probe measurements, the importance of the experimental observations, and the reasonable discussions in the revised version of the paper, I would like to recommend publication of the paper in NC.
+
+Reply: We are grateful for the reviewer’s encouraging comments and the kind recommendation of our manuscript.
+The authors present their new results about Density-wave-like (DW) order of La3Ni2O7 under high pressure using ultrafast optical pump-probe spectroscopy. Firstly, the DW gap Near ambient pressure related to SDW can been suppressed by high pressure. Then at pressures above 29.4 GPa, they observe the emergence of a new DW order with a transition temperature of approximately 130 K. This is a meaningful result that can help the understanding of the mechanism of nickel-based superconductivity. Before accepting the manuscript, the following series of questions must be answered.
+
+1 As we know, the superconducting volume fraction of La3Ni2O7 under high pressure initially measured was low, which is closely related to the method of applying pressure, the quality of the sample and the oxygen vacancies. The reported superconducting volume fraction, with some studies observing fractions as low as 1%, suggesting filamentary superconductivity, and some as high as 48%. Thus, the authors need to compare the samples used in the experiment with those mentioned above, especially the change in oxygen content, transport properties at ambient pressure and the difference in the method of applying pressure. It would be good if the authors could determine what the actual superconducting volume is under their conditions.
+
+2 As mentioned above, under high pressure there is a large area without superconductivity, especially in conditions, the SC volume below 1%. The
+DW order, obtained here under high pressure, likely has nothing to do with superconducting samples. This needs to be highlighted and emphasized. And in the discussion part, the authors emphasize that the suppression of SC transitions by further increasing high pressure and interlayer AFM coupling diminishes with increasing pressure, which may explain the emergence of the DW-II order. However, when superconductivity is filamentary, the signal of the DW-II order may has nothing to do with superconductivity. In my opinion, suppression and then reemergence of DW order under high pressure probably related to the phase separation.
+
+3 The new DW order results contradict the previous transport measurements (High-temperature superconductivity with zero resistance and strange-metal behaviour in La3Ni2O7–δ. Nat. Phys. (2024)). In their paper, zero resistance and strange-metal behaviour have been obtained. From their data, under 29.2 GPa, the resistivity exhibits a linear dependence on temperature. This linear resistive behavior usually precludes the DW orders. The reasons for the conflicting views should be discussed and explained.
+
+4 From the data, there is no significant difference between the behavior of the two kind DW. However, in the manuscript, the author attribute them to AFM and CDW. This can be misleading.
+
+5 The DW-II order emerges at 29.2 GPa. What happens at this pressure? If the authors think it is related to superconductivity, they should put the
+previous superconductivity phase diagrams together with DW's phase diagrams for comparison.

0841883062c0d00625a3f29dfb0823965bfb4e68b1cc4e1fdb984e0c335f4fdf/preprint/preprint.md

@@ -0,0 +1,236 @@
+Density-wave-like gap evolution in La3Ni2O7 under high pressure revealed by ultrafast optical spectroscopy
+
+Xiao Hui Yu
+yuxh@iphy.ac.cn
+
+Institute of Physics, Chinese Academy of Sciences   https://orcid.org/0000-0001-8880-2304
+Yanghao Meng
+Institute of Physics, Chinese Academy of Sciences
+Yi Yang
+Shandong University
+Hualei Sun
+School of Physics, Sun Yat-Sen University
+Sasa Zhang
+Shandong University   https://orcid.org/0000-0002-0568-3803
+Jianlin Luo
+Chinese Academy of Sciences
+Liucheng Chen
+Institute of Physics, Chinese Academy of Sciences
+Xiaoli Ma
+Chinese Academy of Sciences   https://orcid.org/0000-0002-8835-4684
+Meng Wang
+School of Physics, Sun Yat-Sen University   https://orcid.org/0000-0002-8232-2331
+Fang Hong
+Institute of Physics, Chinese Academy of Sciences
+Xinbo Wang
+Institute of Physics Chinese Academy of Sciences
+
+Article
+
+Keywords:
+
+Posted Date: June 27th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4592948/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 November 29th, 2024. See the published version at https://doi.org/10.1038/s41467-024-54518-1.
+Density-wave-like gap evolution in La$_3$Ni$_2$O$_7$ under high pressure revealed by ultrafast optical spectroscopy
+
+Yanghao Meng$^{1,2,*}$, Yi Yang$^{1,3,*}$, Hualei Sun$^{4,*}$, Sasa Zhang$^{3,5}$, Jianlin Luo$^1$, Liucheng Chen$^{1,2,6}$, Xiaoli Ma$^{1,2,6}$, Meng Wang$^{4,**}$, Fang Hong$^{1,2,6,**}$, Xinbo Wang$^{1,**}$, and Xiaohui Yu$^{1,2,6,**}$
+
+$^1$Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
+$^2$School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
+$^3$Key Laboratory of Education Ministry for Laser and Infrared System Integration Technology, Shandong University, Qingdao 266237, China
+$^4$Center for Neutron Science and Technology, Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-Sen University, Guangzhou, China
+$^5$School of Information Science and Engineering, Shandong University, Qingdao 266237, China
+$^6$Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
+
+*These people contribute equally to the present work.
+**Corresponding authors: wangmeng5@mail.sysu.edu.cn, hongfang@iphy.ac.cn, xinbowang@iphy.ac.cn, yuxh@iphy.ac.cn.
+Density-wave-like (DW) order is believed to be correlated with superconductivity in the recently discovered high-temperature superconductor La$_3$Ni$_2$O$_7$. However, experimental investigations of its evolution under high pressure are still lacking. Here, we investigate the quasiparticle dynamics in bilayer nickelate La$_3$Ni$_2$O$_7$ single crystals using ultrafast optical pump-probe spectroscopy under high pressures up to 34.2 GPa. Near ambient pressure, the temperature-dependent relaxation dynamics demonstrate a phonon bottleneck effect due to the opening of a DW gap at 151 K, with an energy scale of 66 meV as determined by the Rothwarf-Taylor model. With increasing pressure, this phonon bottleneck effect is gradually suppressed and completely disappears around 26 GPa. Remarkably, at pressures above 29.4 GPa, we observe the emergence of a new DW order with a transition temperature of approximately 130 K. Our study provides the first experimental evidence of the evolution of the DW gap under high pressure, offering critical insights into the correlation between DW order and superconductivity in La$_3$Ni$_2$O$_7$. These findings highlight the complex electronic phase transitions in this material and underscore the role of high pressure in tuning its superconducting and DW properties.
+
+Introduction
+
+Nickel-based superconductors have attracted significant interest in physical communities since the first member Nd$_{0.8}$Sr$_{0.2}$NiO$_2$ was discovered[1–4]. They have similar $d$ electron configurations resembling cuprates, suggesting that nickel-based superconductors could potentially exhibit high-temperature superconductivity as well. Recent studies have confirmed this hypothesis, La$_3$Ni$_2$O$_7$ single crystal was found to show a superconducting transition temperature of $T_c \approx 80$ K at pressures above 14.0 GPa [5]. Many experiments are reporting its superconducting properties at high pressures [6–9]. However, the mechanism of its superconductivity is still unclear and under debate.[10–21].
+
+In high-temperature superconductors, the interplay between DW order and superconductivity has been a widely investigated topic, since they are strongly related [22]. In La$_3$Ni$_2$O$_7$, at ambient pressure, two DW transitions were indicated in La$_3$Ni$_2$O$_7$ when the temperature is decreased [8, 9, 23–32]. Nuclear magnetic resonance (NMR) [24, 27–29], neutron scat-
+tering [32], resonant inelastic X-ray scattering (RIXS) [29] and muon spin rotation (\( \mu \)-SR) experiments [23, 30] showed possible SDW transition around 150 K, accompanied with a striped AFM ground state. Another charge density wave transition was also observed insignificantly through resistance measurements and thermodynamic characterizations, with \( T_c \) varying from 110 K [5, 26] to 130 K [9, 28] as indicated by a very small hump in resistance and heat capacity. These transitions were believed to be the result of the correlation of \( d_{x^2-y^2} \) and \( d_{z^2} \) orbitals [11–13, 16, 33–36], which was suspected to induce superconductivity and affect paring symmetry under high pressure. Thus, a clear understanding of the evolution of the DW transition at high pressure is required.
+
+Studies of the DW order in La$_3$Ni$_2$O$_7$ at high pressure are currently insufficient. \( \mu \)-SR experiment [30] indicates the DW order can persist up to 2.3 GPa without suppression, but the data at pressure larger than 2.3 GPa is lacking. Some experiments attempt to track the DW evolution under pressure through the presence of a small hump in the resistance-temperature curves, and report DW order vanishes quickly upon compression around 3.0 GPa [6, 9, 25, 26], beyond which the hump in resistance spreads broadly and become insignificant. These resistance measurements face the challenges that the wide spread of the turning point and the potential influence of non-hydrostatic effects under high pressure make it hard to determine the onset of the DW order. On the other hand, the inhomogeneous nature of La$_3$Ni$_2$O$_7$ has been confirmed by X-ray diffraction (XRD) [8, 37, 38], scanning transmission electron microscopy (STEM) [8, 39], and magnetic susceptibility measurements [7]. Neutron scattering experiments have found magnetic excitations without an observable magnetic structure transition [40], indicating that the DW regions are too small for resistance measurements, which averages the results of a whole sample, making the results ambiguous. The evolution of the DW order in La$_3$Ni$_2$O$_7$ under high pressure remains unclear and warrants further investigation.
+
+Here, we report the evolution of DW in La$_3$Ni$_2$O$_7$ under high pressure using ultrafast optical spectroscopy. Time-resolved optical pump-probe spectroscopy has been widely employed to study nonequilibrium quasiparticle dynamics in various materials with superconductivity and density wave since it is extremely sensitive to the presence of energy gap [41, 42]. However, performing pump-probe experiments under high pressure and low temperature is challenging due to the technical difficulties in combining high-pressure equipment with cryogenic systems while maintaining optical access for ultrafast laser pulses. Despite these
+challenges, such experiments provide valuable insights into the behavior of materials under extreme conditions [43–45]. In this work, we observed DW gap opening near ambient pressure below a transition temperature \( T_{\text{DW}} \), as indicated by the phonon bottleneck (PB) effect of a slow decay component which disappears above \( T_{\text{bw}} \). The gap fitted by Rothwarf-Taylor (RT) model is \( \Delta_{\text{DW}} = 66 \) meV. From 0 GPa to 19.7 GPa, low-pressure DW order is suppressed with \( T_{\text{DW}} \) decreasing linearly along with increasing pressure. PB effect disappears at 26 GPa. Above 29.4 GPa, a new DW phase appears, as indicated by the re-emergence of the PB effect and a drastic increase in the transition temperature. The critical rule of interlayer AFM coupling in La$_3$Ni$_2$O$_7$ is revealed through the evolution of the extracted \( \Delta_{\text{DW}} \) and the emergence of the DW II order.
+
+Results and Discussion
+
+DW gap opening near ambient pressure
+
+Fig. 1(a) shows the time-resolved reflectivity change \( \Delta R/R \) in La$_3$Ni$_2$O$_7$ at several selected temperatures near ambient pressure. At high temperatures, photoexcitation leads to a quick rise in the reflectivity, followed by a fast decay into a constant offset with a relaxation time change slightly as temperature is increased to 250 K. Below 151 K, an additional long-lived component with negative amplitude appears [46], which relaxes faster with increases in amplitude along further decreasing temperature. This results in the initial positive change of \( \Delta R/R \) turns to negative. The transition near 151 K corresponds to the DW transition as observed in NMR, and \( \mu \)-SR experiments [23, 24, 27–30] at ambient pressure. Therefore, we ascribe the fast decay signal to the electron-phonon thermalization and the slow-decay component to the recombination across the DW gap as will be discussed in detail below. Accordingly, we fit the data using a single-component exponential function, \( \Delta R/R = A_f e^{-t/\tau_f} + C \) above \( T_{\text{DW}} \), and two-component decay function, \( \Delta R/R = A_f e^{-t/\tau_f} - A_s e^{-t/\tau_s} + C \) at low temperature, where A and \( \tau \) represent the relaxation amplitude and decay time, respectively. The subscripts (f and s) denote the fast and slow relaxation processes, respectively. \( C \) is a constant offset. The experimental data can be fitted quite well as shown in Fig. 1(a). The extracted \( A_s \) and \( \tau_s \) as a function of temperature are plotted in Fig. 1(b). Below \( T_{\text{DW}} \), \( A_s \) increases sharply from zero, while \( \tau_s \) shows a continuous divergence. The anomalous behavior can be explained by a relaxation bottleneck
+associated with the opening of a DW gap.
+
+Here, we employ the RT model to explain the slow relaxation process in La$_3$Ni$_2$O$_7$ [47]. It is a phenomenological model that was initially proposed to describe the relaxation of photoexcited superconductors, where the formation of a gap in the electronic density of states creates a relaxation bottleneck of the photoexcited quasiparticles. The recombination is dominated by the emission and reabsorption of the high-frequency phonons whose decay determines the recovery of photoexcited quasiparticles back to the equilibrium states. The RT model has also been demonstrated to be applicable for other systems with gap opening in the density of states, such as change/spin density wave, and heavy fermion [41, 48, 49]. Based on this model, the thermally quasiparticle density \( n_T \) is related to the transient reflectivity amplitude \( A \) via \( n_T \propto [A(T)/A(T \to 0)]^{-1} - 1 \). Combining the relationship of \( n_T \propto \sqrt{\Delta(T)T} \exp[-\Delta(T)/T] \), we obtain [50]:
+
+\[
+A(T) \propto \frac{\Phi / (\Delta(T) + k_B T/2)}{1 + \gamma \sqrt{2k_B T/\Delta(T)} \exp[-\Delta(T)/k_B T]}
+\]
+
+where the \( \Phi \) is the pump fluence, \( \Delta(T) \) is the temperature dependence of gap energy, \( k_B \) is the Boltzmann constant, and \( \gamma \) is a fitting parameter. In the RT model, the relaxation time near transition temperature is dominated by phonons with frequency \( \omega > 2\Delta \) transferring their energy to lower frequency phonons with \( \omega < 2\Delta \), so the excitation of the condensed quasiparticles would stop. The relaxation time \( \tau \) near transition temperature is given by [50] :
+
+\[
+\tau^{-1}(T) \propto \Delta(T),
+\]
+
+Assuming that \( \Delta(T) \) obeys BCS temperature dependence \( \Delta(T) \approx \Delta(0) \tanh \left( 1.74 \sqrt{\frac{T}{T_c} - 1} \right) \), we fit the \( A_s \) and \( \tau_s \) using Eq.(1) and (2). The results are shown as the solid lines in Fig. 1(b). From the fit we obtain the transition temperature \( T_{DW} \sim 151 \) K and the gap energy \( \Delta(0) \sim 66 \) meV, which is in good agreement with the values previously reported by optical conductivity and NMR spectroscopy [28, 51]. The excellent fit strongly supports our assumption of the formation of a gap in the electric density of states due to the development of DW long-range order below \( T_{DW} \). We notice a similar work in ref.[52] where no PB effect was observed at ambient pressure which is probably due to the inhomogeneous nature of La$_3$Ni$_2$O$_7$ [7, 8, 37–40], as evidenced in Supplementary Information [46].
+DW order evolution at high pressures
+
+To further track the evolution of DW order in La$_3$Ni$_2$O$_7$ as a function of pressure, we perform ultrafast pump-probe measurements under high pressure up to 34.2 GPa in DAC. Fig. 2 displays the temperature dependent transient reflectivity data at several selected pressures. The slow relaxation component with negative amplitude that exists at a temperature below \( T_{\text{DW}} \) survives for all pressures. We employ similar fitting procedures described above to the experimental data under various pressures and plot the fitting parameter \( \tau_s \) as scatters in Fig. 2. It is obvious that \( \tau_s \) diverges around \( T_{\text{DW}} \) for all pressures except 26 GPa. Above 29.4 GPa, the relaxation time \( \tau_s \) decreases slightly with increasing temperature and then increase sharply, manifesting a quasi-divergent behavior at \( T_{\text{DW}} \sim 130 \) K. Such a temperature dependence of \( \tau_s \) is similar to that near ambient pressure strongly suggesting the re-opening of an energy gap under pressure above 29.4 GPa.
+
+In order to obtain detailed information on the gap evolution, the \( \Delta R/R \) signals as a function of pressure at 20 K are plotted in Fig. 3(a). The negative amplitude monotonically reduces with increasing pressure and becomes indistinguishable at 26 GPa above which the negative signal appears again. Fig. 3(b) displays the fitting parameters \( A_s \) and \( \tau_s \) as a function of pressure at 20 K. As the pressure increases up to 2.2 GPa, \( A_s \) drops dramatically, accompanied by a slight decrease of \( \tau_s \). Upon further compression, \( A_s \) decreases gradually towards zero while \( \tau_s \) exhibits a quasi-divergence around 26 GPa. According to Eq.(2), the relaxation time increases with the decrease of \( \Delta \) at fixed temperature and vice versa. Therefore, we can infer that the increase of \( \tau_s \) with increasing pressure is due to the progressive suppression of the DW gap in this pressure range. Above 29.4 GPa, the increase of \( A_s \) and decrease of \( \tau_s \) indicate the DW gap gets promoted again, which is in line with the phenomenon shown in Fig. 2(h) that PB effect appears again with a higher \( T_{\text{DW}} \)
+
+The identical RT analysis was applied to the temperature dependence of the slow relaxation \( \tau_s \) and \( A_s \) at high pressures [46]. The extracted \( T_{\text{DW}} \) values are summarized in the Temperature-Pressure phase diagram in Fig. 4. Based on the above high pressure results, the diagram can be divided into two major regions with a critical pressure of 26 GPa, DW I, and DW II. In the low-pressure region, the DW transition is gradually suppressed from \( T_{\text{DW}} \approx 151 \) K near ambient pressure to \( T_{\text{DW}} \approx 110 \) K at 13.3 GPa. \( T_{\text{DW}} \) rapidly decreases to around 85 K at 16.7 GPa and then decreases very slightly with pressure up to 19.7 GPa.
+Since no PB effect is observed at 26 GPa, a value of 95 K, at which the negative decay component disappears, is added to Fig. 4 as a hollow circle for the sake of comparison. Upon further increasing pressure, divergent behavior of \( \tau_s \) appears again near 135 K, suggesting the presence of another energy gap in the density of states. The transition temperature increases slightly with further increasing pressure.
+
+Discussion
+
+The present work gives an unambiguous fact that there is a gap opening in La$_3$Ni$_2$O$_7$. Upon compression, the DW order is gradually suppressed, leading to the decrease of the gap amplitude from \( \sim 66 \) meV near ambient pressure to \( \sim 20 \) meV at 13.3 GPa. As the pressure continues to increase, the gap amplitude decreases slightly before vanishing at 26 GPa. In this pressure range, short-range density wave order may exist after the long range order is suppressed and induce the opening of a small gap in the density of states below \( T_{DW} \) [9]. Although superconductivity with a transition temperature of 80 K under pressure above 14 GPa has been reported, we do not observe any signature of superconductivity in the transient reflectivity data probably due to the low superconducting volume of 1% in this nickelate [7]. The coincidence of the critical pressure point between the suppression of DW order and the emergence of superconductivity suggest that the DW order competes with the superconductivity in La$_3$Ni$_2$O$_7$, winch is reminiscent of the cuprates and iron-based superconductors [49]. In addition, the emergence of a new DW order under pressure beyond 29.4 GPa is probably related to the charge density wave order as proposed by the theoretical results [20]. The extracted energy gap of 20 meV, which is comparable to the value obtained in the pressure range from 13.3 to 19.7 GPa, increases slightly with further increased pressure.
+
+Our results to some extent support the scenario that the interlayer AFM coupling plays a critical role in the correlation between DW orders and superconductivity in La$_3$Ni$_2$O$_7$ under pressure. A bilayer \( t - J - J_\perp \) model suggests that DW instability increases with decreasing interlayer AFM coupling, whereas SC instability shows the opposite trend[36]. The suppression of the long-range DW order near 13.3 GPa coincides with SC transitions [5, 7–10]. Near 13.3 GPa, a structural transition occurs from the *Amam* to the *Fmmm* phase [5, 53], and the Ni-O-Ni angle turns to 180° [5, 8], enhancing the interlayer AFM coupling significantly [20, 36]. This suppresses the DW order and leads to strong spin fluctuations that
+facilitate copper pairing. Conversely, the linear decrease in superconducting temperature with increasing pressure beyond 20 GPa indicates that interlayer AFM coupling diminishes with increasing pressure[54], which may explain the emergence of the DW-II order. On the other hand, the observed DW-II order around 29.4 GPa and its increasing trend with increasing pressure coincide with the prediction in ref. [20], which is a consequence of the nesting of a partially flat band under the AFM ground state. The necessity of an AFM ground state for the formation of DW order under high pressure [20] underscores the crucial role played by interlayer AFM coupling in the interplay between DW and superconducting order in this system.
+
+In summary, we have performed ultrafast pump-probe measurements on the recently discovered nickelate superconductor La3Ni2O7 crystal under pressure up to 34.2 GPa. Near ambient pressure, the temperature dependence of relaxation indicates the appearance of PB effect due to the opening of DW-like gap at 151 K. By analyzing the data with RT model, the energy scale of the gap is identified to be 66 meV, consistent with the previous report. The relaxation bottleneck effect is suppressed gradually by the pressure and disappears around 26 GPa. At high pressure above 29.4 GPa, we discover a new DW order with a transition temperature of \( \sim 130 \) K. Our results not only provide the first experimental evidence of the DW gap evolution under high pressure but also offer insight into the underlying correlation between the DW order and superconductivity in pressured La3Ni2O7.
+
+Methods
+
+High pressure sample loading
+
+Single-crystalline La3Ni2O7 samples were grown using optical-image floating zone method as described in [5]. Typical sample size is ~1 mm. We smashed the sample into small pieces, then picked up pieces with flat surface under metallographic microscope. High pressure was generated by screw-pressure-type diamond anvil cell (DAC) with a 500 \( \mu \)m culet. The sample chamber with a diameter of 300 \( \mu \)m was made in a Rhenium gasket. A small piece of La3Ni2O7 crystal was loaded in the center of the chamber and a ruby ball was placed aside the sample. Fine KBr powders were employed as the pressure transmitting medium.
+
+Low temperature environment and pressure calibration
+
+The DAC was loaded in a cryostat (Janis ST500) with an optical window for the temperature dependent measurements. An additional thermal sensor was mounted on the force
+plate of the DAC for more precise measurement of sample temperature. The pressure was calibrated using the ruby fluorescence shift at low temperatures for all experiments.
+
+Optical measurement
+
+The pump-probe setup was described in ref. [44], where 400 nm pump and 800 nm probe pulses with 60 fs pulse width and 50 kHz repetition rate were used. Both beams were focused onto the sample surface using a 5× objective lens, giving pump and probe fluences of 45 \( \mu J/cm^{-2} \) and 9 \( \mu J/cm^{-2} \), respectively.
+
+DATA AVAILIBILITY
+
+Data presented in this paper and the Supplementary Information are available from the corresponding author upon request.
+
+References
+
+[1] Li, D. et al. Superconductivity in an infinite-layer nickelate. Nature **572**, 624–627 (2019).
+[2] Zeng, S. et al. Superconductivity in infinite-layer nickelate La$_{1-x}$Ca$_x$NiO$_2$ thin films. Sci. Adv. **8**, eabl9927 (2022).
+[3] Osada, M., Wang, B. Y., Lee, K., Li, D. & Hwang, H. Y. Phase diagram of infinite layer praseodymium nickelate Pr$_{1-x}$Sr$_x$NiO$_2$ thin films. Phys. Rev. Mater. **4**, 121801 (2020).
+[4] Osada, M. et al. Nickelate superconductivity without rare-earth magnetism:(La,Sr)NiO$_2$. Adv. Mat. **33**, 2104083 (2021).
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+
+**ACKNOWLEDGMENTS**
+
+This work was supported by the National Natural Science Foundation of China (Grants Nos. 11974414, No. 12374050 ) and National Key R&D Program of China (Grants No. 2021YFA1400300, No. 2021YFA0718700, No. 2023YFA1608901). This work was supported by Synergic Extreme Condition User Facility (SECUF).
+
+**AUTHOR CONTRIBUTIONS**
+
+Yanghao Meng, Yi Yang, Xinbo Wang, Fang Hong and Xiaohui Yu. designed the experiment which is performed by Yanghao Meng and Yi Yang. Samples studied in this work were grown by Hualei Sun. and Meng Wang. Data analysis and draft preparation was performed by Yanghao Meng, Yi Yang and Xinbo Wang. All authors contribute to reviewing and editing. The project was supervised by Xiaohui Yu.
+
+**COMPETING INTERESTS**
+
+The authors declare no competing interests.
+FIG. 1. Pump-probe spectra and extracted parameters near ambient pressure. (a) \( \Delta R/R \) signals at several selected temperatures near ambient pressure. The solid lines are the fitting curves. Below 151 K, the spectra can be well fitted by two exponential decay, while above 151 K, the spectra can be well fitted by one exponential decay (b) Temperature dependent amplitude \( A_s \) and relaxation time \( \tau_s \). \( A_s \) decreases to nearly 0 at 151 K, where \( \tau_s \) shows a clear divergence. The solid lines are fitting results according to RT model.
+FIG. 2. Temperature dependent pump-probe spectra taken at different pressures. (a) 0 GPa, (b) 4.2 GPa, (c) 8.2 GPa, (d) 13.3 GPa, (e) 16.7 GPa, (f) 19.7 GPa, (g) 26 GPa and (h) 34.2 GPa. It is clear that the negative component exists at low temperatures, and vanishes at temperatures higher than \( T_{DW} \) for all pressures. The scatters in each panel are the extracted \( \tau_s \). PB effect are observed except for 26 GPa, indicating the suppression of the DW gap.
+FIG. 3. Pump-probe spectra at 20 K and extracted parameters. (a) Pump-probe spectra at various pressures at 20 K. The dashed line demonstrates the existence of A_s for 26 GPa. (b) The extracted amplitude A_s and decay time \( \tau_s \) as function of pressure. A_s decreases with increasing pressure to 26 GPa, then increases with increasing pressure. On the other hand, \( \tau_s \) shows a quasi-divergent character near 26 GPa, indicating the suppression of the DW gap before 26 GPa.
+FIG. 4. Temperature-Pressure phase diagram of the La$_3$Ni$_2$O$_7$ based on the pump-probe spectroscopy measurements. The upper panel shows the evolution of the extracted gap \( \Delta_{\text{DW}} \) as a function of pressure. \( \Delta_{\text{DW}} \) first shows a decreasing trend as pressure increases to 13.3 GPa, then decreases slightly before elevating above 26 GPa. The points in the bottom panel are \( T_{\text{DW}} \), which keeps decreasing to around 85 K at 16.7 GPa, then decreases slightly with pressure up to 19.7 GPa. After 29.4 GPa, \( T_{\text{DW}} \) rises again. The absence of data point at 26 GPa in the upper panel is due to the lack of PB effect and hence the temperature at which the negative component disappears is labeled as a hollow point in the phase diagram.
+
+![Temperature-Pressure phase diagram of La$_3$Ni$_2$O$_7$ showing \( \Delta_{\text{DW}} \) (upper panel) and \( T_{\text{DW}} \) (lower panel) as a function of pressure, with regions labeled DW I and DW II.](page_370_232_808_627.png)
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• supplementaryinformation.pdf

0843de24eb7cd42d0826bcc04a37651f74c3bae20b743963c695c5dc561236e4/peer_review/peer_review.md

@@ -0,0 +1,494 @@
+In-situ Catalysis of Green Lubricants into Graphitic Carbon by Iron Single Atoms to Reduce Friction and Wear
+
+Corresponding Author: Professor Jinjin Li
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+In this study, dioctyl malate (DOM) was added to a low-viscosity base oil (PAO2) and compared with conventional additives like ZDDP and GMO. DOM showed significant friction reduction and wear resistance improvements, attributed to a 30 nm thick tribofilm formation with low Young’s modulus, mainly composed of graphitic carbon. This tribofilm formation was observed only in steel-steel sliding contacts, likely due to the catalytic activity of Fe single atoms. I have several major concerns that authors need to address for reconsideration of manuscript for publication.
+Comments:
+1. Why was 5wt.% additive concentration selected for comparison? Were any other concentrations tested? Comparing with 5 wt.% ZDDP or GMO is not the right approach without optimizing the concentration of additives.
+2. Wear volume comparison with ZDDP or GMO is not shown. Fig S3 shows the wear scar diameters and track widths, but volume calculation and comparison with the DOM are essential.
+3. What about presence of other additives on performance of DOM. Do author expect that this additive eliminates need for additional additive combination to further reduce friction and wear? This point can be emphasized.
+4. If oil with octanol cannot form the tribofilms, how can it reduce the wear volume, as shown in Fig. 1f? What is the protection mechanism here? Comment on oil with OA as well. It shows improvement in friction and wear resistance; how is it different from the DOM sample performance and its protection mechanism?
+5. Authors have performed detailed mechanical property characterization of the graphitic tribofilm which shows that the tribofilms are much softer than the substrate material. Graphitic films generally have poor wear resistance due to weak van der Waals interaction between 2D sheets. Authors should comment on what gives high wear resistance to the tribofilm. Although authors have presented AFM sliding tests at 60 nN but this load is not sufficient to cause wear of tribofilms as shown in many previous literature and experiments should be carried out with stiffer cantilevers at significantly higher loads.
+6. The nano-indentation tests shown in Fig.2 show that the penetration depth was 40 nm. However, the tribofilm thickness is mentioned to be around 30 nm. To get the mechanical properties of the tribofilm, the penetration depth is supposed to be much lower compared to the film thickness, but that was not considered in these experiments.
+7. In S14, why hardness and modulus of the substrate is higher in no island regions than region outside the wear track?
+8. Fig. S17 and S18 are compared in the discussion. In S17, a patchy region, which is considered as tribofilm, is under nanoscale rubbing with the AFM tip, whereas in Fig. S18, there is no region of tribofilm, so how are they even compared with each other in terms of a performance difference? There is no friction mapping image in Fig.S18 to compare the effect of rubbing with that of Fig. S17.
+9. Direct conversion to graphitic carbon generally occurs at very high temperatures, around 3000 C. What is the role of temperature in forming the graphitic carbon tribofilms during these sliding experiments?
+10. Label Fe in the schematics of Fig. 6.
+11. The DOM additive has oxygen functional group which is likely to have strong interaction with water molecule via hydrogen bonding. Have authors investigated moisture content of the oil containing DOM additive. This may have serious problem with metal component as moisture can accelerate corrosion of the components.
+12. What is the evidence that the Fe atoms are acting as catalysts and helping in the growth of the tribofilms? It is shown that by changing the contact pairs, the formation of the tribofilm is affected, but the exact role of the Fe single atoms and their involvement in the film formation is unclear.
+
+Overall: Major corrections and explanations are required. The comparison with the other additives should be thoroughly evaluated, and a concentration-dependent study is required to propose that the formulated DOM-oil is better than GMO or
+ZDDP. The role of Fe single atoms in graphitic carbon tribofilm growth is unclear.
+
+Reviewer #2
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #3
+
+(Remarks to the Author)
+This paper focuses on the friction reduction effect when using DOM as an additive, and examines the friction reduction mechanism. Although it is an interesting paper, it is judged to be difficult for publication because the content is insufficient in the following points.
+
+1. It has already been reported in many papers that a graphite-like carbon film is formed from the lubricating oil during sliding, so the novelty of this paper is not clear. Rather than comparing additives such as ZDDP and their effects, a more extensive comparison with other organic friction modifiers should be made, and your sample’s particularities and novel mechanisms should be presented more clearly.
+
+For examples, the following papers may be of use to you to improve your paper.
+
+1) Zhang, J., Bolle, B., Wong, J.S.S. et al. Influence of Atmosphere on Carbonaceous Film Formation in Rubbing, Metallic Contacts. Tribol Lett 72, 4 (2024). https://doi.org/10.1007/s11249-023-01801-9
+Achieving Superlubricity of Ricinoleic Acid in the Steel/Si3N4 Contact Under Boundary Lubrication
+2) Y Long, JM Martin, F Dubreuil, MI De Barros Bouchet
+Tribology Letters 70 (4), 109
+Superlubricity from mechanochemically activated aromatic molecules of natural origin: a new concept for green lubrication
+3) Y Long, A Pacini, M Ferrario, N Van Tran, S Peeters, B Thiebaut, S Loehle, ...
+Carbon, 119365
+
+2. Although a lot of data is presented, the description of each individual piece of data is lacking. Much of the content that should be included in the main text is included in the supplementary information, but it is not organized and is difficult to read. The chapter headings should be reviewed and the structure revised to make it more logical.
+
+3. There is a lack of chemical consideration regarding why DOM has special properties as an additive. Why is there a correlation between high adsorption characteristics and the ease with which graphite-like tribofilms form?
+
+4. It seems that the friction tests were carried out under boundary lubrication, whereas the simulations were carried out under fluid lubrication via a narrow gap. There seems to be a significant discrepancy here, so why do you think that the simulations can reproduce the situation under boundary lubrication? More detailed notes are needed.
+
+Version 2:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The authors have made appropriate modifications to the manuscript as per reviewer comments and have addressed the concerns. The manuscript can be considered for publication.
+
+Reviewer #2
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Reviewer #3
+
+(Remarks to the Author)
+This paper is a detailed investigation of the friction-reducing effect of an additive called DOM. Recently, there has been many research into carbon-based tribofilms derived from lubricating oil, and this research is one of those. On the other hand, it is generally thought that the presence of radicals is important for the formation of carbon-based tribofilms, and how to stably maintain the presence of radicals has been the technical key. In the process of clarifying the low-friction mechanism of DOM, this study focused on the radical stabilization effect, and provided a clear answer as to why DOM can form a carbon
+film on an iron surface. This content is useful both academically and industrially.
+In addition, this paper has been revised by the authors, making it much easier to read and with a clearer focus. Therefore, I judge that this paper deserves to be published in Nature Communications.
+
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+In this study, dioctyl malate (DOM) was added to a low-viscosity base oil (PAO2) and compared with conventional additives like ZDDP and GMO. DOM showed significant friction reduction and wear resistance improvements, attributed to a 30 nm thick tribofilm formation with low Young’s modulus, mainly composed of graphitic carbon. This tribofilm formation was observed only in steel-steel sliding contacts, likely due to the catalytic activity of Fe single atoms. I have several major concerns that authors need to address for reconsideration of manuscript for publication.
+
+Thank you for your insightful comments and suggestions. We have addressed each question point by point, as highlighted below.
+
+Comments:
+
+1. Why was 5wt.% additive concentration selected for comparison? Were any other concentrations tested? Comparing with 5 wt.% ZDDP or GMO is not the right approach without optimizing the concentration of additives.
+
+Response: Thank you for raising this important point. We have conducted additional tribological tests with varying concentrations of DOM, ranging from 0 wt% to 10 wt%, as shown in Fig. R1 (Fig. S1). While the concentrations from 0.5% to 10% did not significantly affect the wear track width on the bottom disc specimens or the wear volume calculated from the top ball, the lowest friction coefficient was observed at 5% DOM. Therefore, 5% DOM was selected for comparison with other additives. Notably, the low concentration of 0.5% DOM only provided a low friction coefficient during the first 20 minutes, after which the lubrication failure occurred (Fig. R1a). On the other hand, a high concentration of 10% DOM resulted in a slightly higher friction coefficient compared to 5% DOM. Therefore, the optimal concentration at 5 wt% additive was selected for comparison in the manuscript.
+
+We also noticed that GMO and ZDDP are commonly used at a concentration of around 1 wt% in previous studies\(^{1,2}\). To provide a more comprehensive comparison, we have also performed additional tests with different additives at a concentration of 1 wt%, as shown in Fig. R2 (Fig. S6). Notably, 1 wt% DOM exhibited much lower friction and comparable wear volume to 1 wt% GMO and 1 wt% ZDDP. In addition, while prominent scratches are visible on the wear tracks formed by 1 wt% GMO and 1 wt% ZDDP, no such scratches are observed on the wear track formed by 1 wt% DOM. This further underscores the superior tribological performance of DOM in minimizing wear and protecting the contact surfaces.
+
+According to your comments, we have incorporated the following text in the revised manuscript:
+
+Page 6, “The concentration-dependent friction tests revealed that the addition of 5% DOM into PAO exhibited the most superior performance (Fig. S1), which substantially reduced friction coefficient (Fig. 1c, from ~0.25 to ~0.11), wear track depth (Fig. 1d, from ~1.5 μm to ~0.2 μm), width (Fig. 1e, from ~420 μm to ~224 μm), and wear volume (Fig. 1f, from ~27×10^3 mm^3 to ~3.7 ×10^3 mm^3).”
+
+Page 7, “Notably, even at a low concentration of 1 wt%, DOM also exhibits a much lower friction coefficient and no visible wear scratches compared to ZDDP and GMO (Fig. S6), further demonstrating the superior performance of DOM”
+Fig. R1 (Fig. S1). Tribological performance of PAO containing different concentrations of DOM. (a) friction coefficients curves, (b) average friction coefficient, (c) wear track width on low disc specimens, and (d) wear volume calculated from top ball specimens.
+
+Fig. R2 (Fig. S6). Tribological performance of PAO containing different additives at concentration of 1wt %. (a) Friction coefficient, (b) wear volume calculated from top ball
+specimens, (c) optical images of wear tracks.
+
+2. Wear volume comparison with ZDDP or GMO is not shown. Fig S3 shows the wear scar diameters and track widths, but volume calculation and comparison with the DOM are essential.
+
+Response: Thank you for your kind reminder. The wear volumes of 5% ZDDP and 5% GMO have been calculated using the following equation and are presented in Fig. R3 (Fig. S4d),
+
+\[
+V = \left( \frac{\pi h}{6} \right) \left( \frac{3d^2}{4} + h^2 \right)
+\] (1)
+
+Where d is the wear scar diameter, r is the radius of the ball, and
+
+\[
+h = r - \sqrt{r^2 - \frac{d^2}{4}}
+\] (2)
+
+Fig. R3 shows that DOM exhibits significantly lower wear volume than neat PAO and PAO with conventional amphiphilic molecules, such as oleic acid and GMO. Although the wear volume of DOM is similar to that of ZDDP, its friction coefficient is lower (Fig. S4). Notably, since DOM is completely composed of C, H, and O, it is much greener than ZDDP and holds great potential to replace conventional additives.
+
+We have incorporated the above discussion into the revised manuscript, with the specific modifications detailed as follows:
+
+Page 7, “Additionally, comparison with conventional industrial additives, including GMO and ZDDP, further highlight DOM’s superior performance. The friction coefficients of 5 wt% GMO and 5 wt% ZDDP were 0.20 and 0.14, respectively (Fig. S3), both significantly higher than that achieved with 5 wt% DOM. While the wear track width and wear volume of 5 wt% ZDDP were comparable to those of 5 wt% DOM (Fig. S4c, d), DOM is free of sulfur and phosphorus, making it a much more environmentally friendly option. Notably, even at a low concentration of 1 wt%, DOM also exhibits a much lower friction coefficient and no visible wear scratches compared to ZDDP and GMO (Fig. S6), further demonstrating the superior performance of DOM.”
+Fig. R3 (Fig. S4d). wear volume on disc of friction test with different additives.
+
+3. What about presence of other additives on performance of DOM. Do author expect that this additive eliminates need for additional additive combination to further reduce friction and wear? This point can be emphasized.
+
+Response: Thank you for raising this important point. We have conducted additional friction tests using various combinations of DOM, GMO and ZDDP, as shown in Fig. R4. Notably, the mixtures containing 5% DOM with other additives exhibited a higher friction coefficient compared to 5% DOM alone (Figure R4a, b). While incorporating additional additives, such as 5% GMO or a 5% GMO/5% ZDDP mixture into DOM, did not significantly impact the wear track width, the addition of 5% ZDDP to 5% DOM led to an increase in wear track width (Figure R4c). Here, we proposed that this is due to competitive adsorption and/or tribochemical reactions between DOM, GMO and ZDDP during rubbing, which prevents achieving a synergistic effect. Therefore, the individual use of DOM without combination with additional additives can provide excellent friction-reducing and anti-wear performance.
+
+Fig. R4. (a) Friction coefficients curves, (b) average friction coefficient, and (c) wear track width of 5% DOM with combination of 5% DOM and 5% ZDDP.
+
+4. If oil with octanol cannot form the tribofilms, how can it reduce the wear volume, as shown in Fig. If? What is the protection mechanism here? Comment on oil with OA as well. It shows improvement in friction and wear resistance; how is it different from the DOM sample performance and its protection mechanism?
+
+Response: Thank you for raising this important point. We acknowledge that certain expressions
+in our manuscript, particularly the term "tribofilm," may have caused confusion. It is clear that a film was also formed on the wear track for both 5% octanol and 5% oleic acid (OA), as evidenced by the typical black substance observed on the wear track formed by 5% octanol and 5% OA, compared to the unrubbed area (Fig. 1e). Raman spectra (Fig. 2f) and XPS spectra (Fig. 3) reveal that this film is primarily composed of iron oxide. However, this film is easily removed under repeated AFM scratch tests (Fig. S18), which increases surface roughness that resulting in higher friction compared to DOM.
+
+Another potential mechanism for octanol and OA is their amphiphilic nature, which allows them to adsorb onto the rubbing surface via their head groups, forming a monolayer or multilayer\(^{5-5}\). However, these layers may be rinsed away by the solvent cleaning after the friction test, or they could be too thin to be detected by surface analysis techniques such as Raman or XPS. The friction and wear resistance of such adsorbed monolayers or multilayers formed by amphiphilic molecules has been widely demonstrated in both experimental and simulation studies\(^{6-8}\). Thus, we did not focus on investigating their mechanism in this work.
+
+In contrast, DOM forms an island-like patchy film (referred to as a tribofilm) on the rubbing surface, which is distinctly observable under optical microscopy (Fig. S12). This morphology differs significantly from the wear tracks formed by 5% octanol and 5% OA. Analysis using Raman spectroscopy, XPS, and TEM reveals that this tribofilm consists of graphitic carbon with a thickness of approximately 30 nm. Furthermore, nanomechanical testing through AFM and nanoindentation demonstrates that the tribofilm exhibits strong robustness, low shear stress, and minimal adhesion. These properties contribute to the significantly reduced friction and wear observed in macro-scale tribological tests.
+
+According to your comments, we have added and revised the following description to the revised manuscript:
+
+Page 6, “The lubrication mechanisms of amphiphilic molecules, like oleic acid, have been extensively studied and are commonly attributed to the formation of an adsorbed layer on the solid surface via their polar head group, which helps to reduce friction and wear.”
+
+Page 14, the term tribofilm, where it first appeared, has been defined to ensure clarity for readers. “A typical film (referred as tribofilm hereafter) with a thickness of 30 nm is observed between the Cr top-coating and steel substrate (Fig. 4a), and the thickness matches well with the XPS carbon concentration depth profile in Fig. 3a.”
+
+5. Authors have performed detailed mechanical property characterization of the graphitic tribofilm which shows that the tribofilms are much softer than the substrate material. Graphitic films generally have poor wear resistance due to weak van der Waals interaction between 2D sheets. Authors should comment on what gives high wear resistance to the tribofilm. Although authors have presented AFM sliding tests at 60 nN but this load is not sufficient to cause wear of tribofilms as shown in many previous literature and experiments should be carried out with stiffer cantilevers at significantly higher loads.
+
+Response: Thank you for raising this point. After carefully reviewing the literature, we found some AFM friction tests conducted under much higher loads (\(~1000\) nN), but many of these studies used a colloidal AFM tip\(^{9,10}\), meaning their contact pressures (\(~1\) GPa) were not high. In contrast, although the load we applied during our AFM friction tests is 60 nN, which is lower than that in many studies, the corresponding Hertz contact pressure reaches 2.41 GPa due to the small radius of AFM tip (\(~10\) nm).
+We agree with the reviewer that there is no doubt that the tribofilm may be removed at significantly higher loads with a stiffer cantilever. However, our focus is not to determine the exact load at which this occurs. Instead, we are using a slightly higher contact pressure than that in the macro tribological tests (1.64 GPa in Table S3) to investigate the mechanical properties of the wear zones formed by DOM and octanol. Our results show that the tribofilm formed by DOM can persist under such high pressure, while the film formed by octanol does not (Fig. S17,18). This difference helps explain why DOM exhibits a lower wear than octanol in macro tribological tests.
+
+Additionally, although the tribofilm formed by DOM may eventually be removed under ultra-high contact pressures, it undergoes a dynamic process of formation and removal. As shown in the additional performed experiment in Fig. R5, when 5% DOM in PAO was replaced by neat PAO at 30 min, the friction coefficient significantly increased, approaching the value observed with neat PAO. This suggests that the tribofilm formed by 5% DOM on the rubbing surface is removed under high contact pressure during the friction test when neat PAO is used. Therefore, the dynamic formation and removal of the tribofilm is a key factor in maintaining low friction and wear during the macro tribological tests.
+
+![Friction coefficient vs time graph showing the effect of replacing 5% DOM in PAO with neat PAO](page_320_670_709_377.png)
+
+Fig. R5. The friction coefficient of 5% DOM in PAO for 30 min, followed by neat PAO for 30 min.
+
+According to your comments, we have added the following description to the revised manuscript:
+
+Page 10 “The friction properties of the film were analyzed using repeated AFM rubbing tests over a 10 μm × 10 μm area under a load of 60 nN. Due to the small radius of the AFM tip (~10 nm), this corresponds to an exceptionally high contact pressure of 2.41 GPa—significantly higher than the contact pressure observed in macro-scale tribological tests (1.64 GPa, as detailed in Table S3). This elevated pressure allows for an in-depth investigation of the mechanical properties and wear track surfaces at the nanoscale”
+
+6. The nano-indentation tests shown in Fig.2 show that the penetration depth was 40 nm. However, the tribofilm thickness is mentioned to be around 30 nm. To get the mechanical properties of the tribofilm, the penetration depth is supposed to be much lower compared to the film thickness, but that was not considered in these experiments.
+
+Response: Thank you for raising this point. The indentation test we performed was carried out
+on a Bruker TI 980 triboindenter, which has a minimal indentation depth of 40 nm. We completely agree with your concern and acknowledge that the real Young’s modulus of the tribofilm may be overestimated, as the indentation depth of 40 nm is likely larger than the tribofilm thickness. Here, to qualitatively compare the mechanical properties in different areas, we performed the nano-indentation test with the same test conditions. Therefore, we believe that the relative values of the Young’s modulus between the tribofilm and the unrubbed area can still highlight their distinct mechanical properties, and the tribofilm area is qualitatively softer than the unrubbed area.
+
+To address this point, we have clarified the description in the revised manuscript as follows. Page 9, "Note that the measured Young’s modulus and hardness of the island-like film in Fig. S14 may be overestimated due to the 40 nm indentation depth possibly exceeding the film’s actual thickness, but there is no doubt that the island-like film qualitatively exhibits lower Young’s modulus and hardness relative to the other two areas."
+
+7. In S14, why hardness and modulus of the substrate is higher in no island regions than region outside the wear track?
+
+Response: Thank you for pointing out this. Since all the friction tests were performed under boundary lubrication conditions, during which there was direct solid-solid contact, this contact will result in extremely high contact pressure, shear stress, and temperature at the single asperity. These mechanical strengthening and thermal effects will increase the Young’s modulus and hardness of the localized steel11-13.
+
+To clarify this point, we have revised the manuscript as follows.
+
+Page 9, "Interestingly, the no-island-like regions inside the wear track displayed higher hardness and Young’s modulus than unrubbed area. This enhancement can be attributed to the localized contact pressure, shear stress and thermal effects during sliding, which strengthened the mechanical properties in these regions."
+
+8. Fig. S17 and S18 are compared in the discussion. In S17, a patchy region, which is considered as tribofilm, is under nanoscale rubbing with the AFM tip, whereas in Fig. S18, there is no region of tribofilm, so how are they even compared with each other in terms of a performance difference? There is no friction mapping image in Fig.S18 to compare the effect of rubbing with that of Fig. S17.
+
+Response: Thank you for raising this excellent point. Since the better tribological performance of 5% DOM than 5% octanol is attributed to the different tribochemical products formed on the rubbing surface (DOM forms graphitic carbon tribofilm, and octanol forms iron oxide), the investigation and comparison on the robustness and friction behavior of different wear tracks at nanoscale can correlate their friction reduction and anti-wear performance at macroscale. For example, the patchy region formed by 5% DOM shows a decreasing friction tendency under repeated AFM rubbing test (Fig. 2d), and the repeated rubbing area exhibits a lower friction than its surrounding unrepeated area (Fig. S17f). This nanoscale behavior correlates well with its macroscale performance. Meanwhile, the height of the patchy region remains constant during repeated friction tests (Fig. S17d, e), highlighting the strong robustness of the tribofilm at the nanoscale. This robustness contributes to its superior anti-wear performance at both scales.
+
+In contrast, while no graphitic carbon was observed on the wear track of 5% octanol, an iron oxide film was formed, as our response to the 4th question. The mechanical properties and
+robustness of this film at nanoscale can also determine its tribological performance at macroscale. Specifically, the film on the wear track surface of 5% octanol is less mechanically robust, as indicated by the height profile differences during repeated AFM friction tests (Fig. S18a, b). This mechanical weakness aligns with the poor anti-wear performance observed macroscopically. Furthermore, the friction mapping image on wear track of 5% octanol has been measured and added in Fig. S18, and they do not show a substantial friction decreasing during repeated rubbing tests (Fig. S18c), unlike the case for 5% DOM. Also, the repeated area exhibits similar friction to the surrounding unrepeated area (Fig. S18i), further supporting its inferior friction reduction capabilities compared to 5% DOM.
+
+Note that the changes in friction in Fig.2d and Fig. S18c are calculated as follows,
+
+\[
+\Delta f = f_n - f_1
+\]
+
+Where \( f_n \) is the friction at the n-th scan, n is the scanning number, and \( f_1 \) is the friction at the 1st scan. The changes in friction were calculated to determine the nanomechanical properties of the different wear tracks during repeated rubbing tests because there is deviation between different AFM friction measurements. These findings are now clarified and discussed in the revised manuscript.
+
+![AFM topography and friction images on wear track formed by 5% octanol in PAO](page_346_670_1057_693.png)
+
+Fig. R6 (Fig. S18). The AFM topography and friction images on wear track formed by 5% octanol in PAO. (a)(b) The height profile of the dash line A and line B in (d)(e). (c) AFM frictional signal tendency from 1st scanning to 110th scanning on a 10 μm × 10 μm island area. The delta \( f \) was calculated by the difference between the friction at the n-th scan (\( f_n \)) and the friction at the 1st scan (\( f_1 \)). The AFM topography images of the 10 μm × 10 μm area at (d) 1st scanning, and (e) 110th scanning, and (f) the 60 μm × 60 μm area at 111th scanning. (g)(h)(i)
+The AFM friction images corresponding to (d)(e)(f).
+
+According to your comments, we have added the following description to the revised manuscript:
+
+Page 10, “In contrast, the wear track surface of 5% octanol exhibited poor durability under repeated AFM rubbing tests, as evidenced by notable differences in the height profile (Fig S18a, b). Additionally, the repeated rubbed area showed no significant decrease in friction (Fig. S18c) and displayed similar frictional properties to its surrounding unrepeated rubbed area (Fig S18i). These observations align with the higher friction and wear observed in macroscale tribological tests for 5% octanol.”
+
+9. Direct conversion to graphitic carbon generally occurs at very high temperatures, around 3000 C. What is the role of temperature in forming the graphitic carbon tribofilms during these sliding experiments?
+
+Response: Thank you for this thoughtful question. After thoroughly reviewing the literature, we agree that complete graphitization typically requires extremely high temperature in the range of 2500 °C to 3000 °C14. Graphite formed under such conditions usually exhibits high crystallinity, characterized by highly oriented graphite lattice fringes in TEM images and the absence of the D band in Raman spectra15, 16. However, in our work, the lattice fringes of the carbon film formed by DOM in this study is not highly oriented (Fig. 4b), and Raman spectra display a noticeable D band at 1350 cm^{-1} (Fig. 2f). These features indicate that while the tribofilm is predominantly composed of sp^2-hybridized graphitic carbon, it also contains some amorphous carbon with sp^3 hybridization. This result aligns well with the partial graphitization occurring under temperature around 1000 °C17.
+
+It is important to note that although the friction tests were conducted at 30 °C, the localized temperature at a single asperity can be one to two orders of magnitude higher than the bulk liquid temperature (potentially reaching up to 1000 °C, as estimated through simulation), especially under boundary lubrication18. Additionally, besides the thermal effect, the contact pressure and/or shear stress during friction test will also significantly contribute to the tribofilm formation by mechanochemical reactions19, 20. Therefore, the mechanical effects of contact pressure and shear stress, combined with elevated temperature, likely trigger the graphitization process.
+
+According to you comment, we have prepared a thermal film based on a method from the literature21, to investigate the role of thermal effects in the formation of graphitic carbon tribofilms. Specially, the steel surface was immersed into 5% DOM in PAO and heated at 300 °C for 30 mins (Note that this is the highest temperature for PAO lubricants under intermittent service), followed by cooling down, surface rinsing with hexane and Raman surface analysis. Notably, no typical G band was observed in the Raman spectra (Fig. R7). This result suggests two possible reasons for the absence of graphitic carbon: (1) Temperature mismatch: The steel surface temperature during thermal film preparation may not replicate the localized temperatures at asperities during boundary lubrication. Unfortunately, to the best of our knowledge, no experimental method currently exists to measure the exact temperature at the single asperity under boundary lubrication conditions. (2) Lack of mechanical effects: The absence of contact pressure and shear stress in the thermal film preparation might have prevented the graphitic carbon tribofilm from forming. Therefore, these mechanical factors, in combination with temperature, are known to play a critical role in the graphitization process during friction.
+Fig. R7. Raman spectrum of the thermal film prepared by 5% DOM at 300 °C for 30 min.
+
+According to your comments, we have clarified these points in the revised manuscript:
+
+Page 23. “Note that although the graphitization process typically requires high temperatures of up to 3000 °C, far exceeding the 30 °C condition of our friction tests, the localized temperature at single asperities can be one to two orders of magnitude higher than the bulk liquid temperature, especially under boundary lubrication. This elevated temperature is sufficient to induce partial graphitization. Meanwhile, the high contact pressure and shear stress generated during friction can further facilitate the tribofilm formation through mechanochemical processes.”
+
+10. Label Fe in the schematics of Fig. 6.
+
+Response: Thank you for the kind reminder. The label of Fe single atoms has been added in Fig. 6d, e.
+
+11. The DOM additive has oxygen functional group which is likely to have strong interaction with water molecule via hydrogen bonding. Have authors investigated moisture content of the oil containing DOM additive. This may have serious problem with metal component as moisture can accelerate corrosion of the components.
+
+Response: Thank you for this question. We understand your concern and have conducted additional tests to address it. First, PAO with and without 5% DOM were prepared and exposed to air for one week to allow the solutions to potentially absorb moisture from the air. The water content in the solutions was then measured using Karl Fischer titration. The results showed that the water content in PAO with 5% DOM was close to that in neat PAO, indicating that DOM does not increase the moisture content in the lubricant. Additionally, we conducted an anti-corrosion test by immersing steel balls and discs in PAO with and without 5% DOM for one month. The steel surfaces immersed in PAO with 5% DOM showed no signs of corrosion and were identical in appearance to the one immersed in neat PAO (Fig. R8). These findings confirm that 5% DOM in PAO does not increase moisture levels or pose corrosion risks for metal component.
+Table R1 The water concentration in PAO with and without 5% DOM after exposing to air for one week.
+
+<table>
+  <tr>
+    <th></th>
+    <th>test1</th>
+    <th>test2</th>
+    <th>average</th>
+  </tr>
+  <tr>
+    <td>PAO</td>
+    <td>0.127 wt%</td>
+    <td>0.117 wt%</td>
+    <td>0.122 wt%</td>
+  </tr>
+  <tr>
+    <td>5% DOM in PAO</td>
+    <td>0.136 wt%</td>
+    <td>0.130 wt%</td>
+    <td>0.133 wt%</td>
+  </tr>
+</table>
+
+![Images of steel surface after immersed in PAO with and without 5% DOM for 30 days.](page_349_384_1047_246.png)
+
+Fig. R8. The images of steel surface after immersed in PAO with and without 5% DOM for 30 days.
+
+12. What is the evidence that the Fe atoms are acting as catalysts and helping in the growth of the tribofilms? It is shown that by changing the contact pairs, the formation of the tribofilm is affected, but the exact role of the Fe single atoms and their involvement in the film formation is unclear.
+
+Response: Thank you for this good point. While the steel surface indeed plays a significant role in tribofilm formation, as evidenced by our friction tests on different tribopairs, it alone cannot fully explain the formation of a 30 nm-thick graphitic carbon film. This is because if the tribopair surfaces were covered with a thin graphitic carbon layer, such as 5 nm, the iron from the steel surface would not be able to directly interact with DOM molecules in the lubricant (Fig. R9a). Consequently, this would prevent the formation of a thicker tribofilm. In our study, we observed that iron from the steel surface can form single atoms, which become incorporated into the graphitic carbon film. These iron single atoms, particularly those located on the top surface of the film (Fig. R9b), can continuously interact with DOM molecules, catalyzing the growth of a graphitic carbon layer with a thickness of 30 nm.
+
+(a) ![Schematic of (a) DOM on a tribofilm, and (b) DOM on a tribofilm with iron single atoms embedded.](page_349_1342_1047_120.png)
+
+Fig. R9. Schematic of (a) DOM on a tribofilm, and (b) DOM on a tribofilm with iron single atoms embedded.
+
+It is well known that the graphitization is a complex process that involves substance backbone
+dissociation, dehydrogenation, and recombination reactions22, 23. Its reaction pathways are similar to those of free-radical polymerization, comprising chain-initiation, chain-propagating and chain-terminating. Among these, the chain-initiation step is the first and rate-determining step which requires high activation energy. Therefore, the dissociation of C–C and C–H bonds and the formation of free radicals are critical to the graphitization processes. Usually, single-atom catalysts are highly effective in promoting such bond dissociations due to their atomic dispersion of active catalytic centers and unique electronic structure24, 25.
+
+To further investigate the role of iron single atoms in the formation of graphitic carbon tribofilms, we further conducted DFT simulations to calculate the activation energy for C–C bond dissociation in simplified DOM on iron single-atom surfaces, iron cluster, and Fe (110) surface (Fig. R10), respectively. Since the bond energy of C–C bonds is lower than that of C–H bonds, this dissociation was selected as a representative reaction step. The results show that the activation energy for C–C bond dissociation is significantly reduced to 1.08 eV on iron single-atom surfaces, which is notably lower than that on iron clusters (1.41 eV) and the Fe (110) surface (1.66 eV). This underscores the superior catalytic efficiency of single iron atoms in activating DOM. Upon dissociation of the C–C bond in DOM, facilitated by the catalytic effect of iron single atoms, free radicals are generated. These free radicals further initiate tribochemical reactions, leading to the formation of a graphitic carbon layer.
+
+![Solid surface model and energy pathways for C-C bond activation of the simplified DOM on (a)(d) Fe single atom, (b)(e) Fe cluster, and (c)(f) Fe (110) surface. Insets in (d)-(f) are the molecular configurations at initial state (IS), transition state (TS), and final state (FS).](page_370_682_1097_377.png)
+
+Fig. R10 (Fig. S36). The solid surface model and energy pathways for C-C bond activation of the simplified DOM on (a)(d) Fe single atom, (b)(e) Fe cluster, and (c)(f) Fe (110) surface. Insets in (d)-(f) are the molecular configurations at initial state (IS), transition state (TS), and final state (FS).
+
+Thus, the role of iron single atoms is twofold: they facilitate continuous interactions with DOM molecules and reduce bond dissociation energy, both of which are crucial for the formation of the graphitic carbon tribofilm. The DFT simulation results have been added in the Supplementary Information (Fig. S36), and we have added the description in the revised manuscript as follows.
+
+Page 22, “The remarkable catalytic performance of Fe single atoms has been demonstrated in facilitating C–H and C–C bond dissociation24,25, both of which are critical steps in the formation of graphitic carbon. This superior performance arises from the atomic dispersion of active catalytic centers and their distinctive electronic structure. To further elucidate the impact of Fe single atoms on the conversion of DOM into graphitic carbon tribofilms, the activation energy for C–C bond dissociation in simplified DOM on iron single-atom surfaces, iron cluster, and Fe (110) surface was respectively calculated using DFT simulation (Fig. S36). The results
+reveal that the activation energy for C–C bond dissociation is significantly reduced to 1.08 eV on iron single-atom surfaces, which is notably lower than that on iron clusters (1.41 eV) and the Fe (110) surface (1.66 eV). This underscores the superior catalytic efficiency of single iron atoms in activating DOM, which facilitates the subsequent formation of graphitic carbon."
+
+Overall: Major corrections and explanations are required. The comparison with the other additives should be thoroughly evaluated, and a concentration-dependent study is required to propose that the formulated DOM-oil is better than GMO or ZDDP. The role of Fe single atoms in graphitic carbon tribofilm growth is unclear.
+
+Response: We are grateful to you for your constructive comments. According to your comments, the comparison with other additives including ZDDP, GMO, octanol and oleic acid have been comprehensively evaluated and provided in Fig. R2 (Fig. S6), Fig. R3 (Fig. S4d). Besides, the concentration-dependent experiment has been carried out and provided in Fig. R1 (Fig. S1). Meanwhile, the bond dissociation energy on Fe single atoms surface and other surface has been calculated and compared using DFT to further reveal the role of Fe single atoms in graphitic carbon tribofilm growth, which is provided in Fig. R10 (Fig. S36).
+
+Reviewer #2 (Remarks to the Author):
+
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+
+Response: We appreciate your valuable suggestions and insightful comments on our research. We have addressed each of your questions thoroughly, as detailed in our highlighted responses above.
+Reviewer #3 (Remarks to the Author):
+
+This paper focuses on the friction reduction effect when using DOM as an additive, and examines the friction reduction mechanism. Although it is an interesting paper, it is judged to be difficult for publication because the content is insufficient in the following points.
+
+1. It has already been reported in many papers that a graphite-like carbon film is formed from the lubricating oil during sliding, so the novelty of this paper is not clear. Rather than comparing additives such as ZDDP and their effects, a more extensive comparison with other organic friction modifiers should be made, and your sample's particularities and novel mechanisms should be presented more clearly.
+
+Response: We appreciate your suggestions. We agree that while there are several publications addressing the formation of graphite-like carbon films, they often involve specific conditions such as noble metal substrates\(^{22}\), which are cost-prohibitive, anaerobic environments\(^{26}\), requiring complex sealing systems, or water-based lubricants\(^{27}\), which are less applicable to many industrial applications. In contrast, our work demonstrates that the novel additive DOM can effectively form a graphitic carbon layer on engineering steel surfaces, a material widely used in industry. This positions DOM as a promising alternative to conventional additives like ZDDP or GMO. On top of this, we emphasize the following two key points from the perspective of tribopair surface catalysis and molecular particularities that highlight the novelty of our study:
+
+1. The catalysis effect by iron single atoms derived from bulk tribopairs.
+
+In this work, we demonstrate that the graphitic carbon film can only be formed on steel surfaces, rather than glass surfaces. This is due to the effective catalysis effect of iron single atoms that were derived from bulk steel tribopairs during macro tribological tests (see Fig. R11f below). Note that the formation of iron single atoms by top-down mechanochemical method was first observed in 2022 (Abrading bulk metal into single atoms. Nature Nanotechnology 2022, 17 (4), 403-407), in which the bulk metal is directly atomized onto different supports\(^{28}\). In our work, the in-situ formed iron single atoms from bulk steel first demonstrate their application in tribology, i.e., continuously interacting with the lubricants during rubbing and catalyzing the formation of a 30 nm thick graphitic carbon film (Fig. R11d, e). As a result, 5% DOM can substantially reduce the friction and wear on steel surfaces (Fig. R11a, c), but not on glass surfaces (Fig. R11b). This further implies the effective catalysis effect given by iron single atoms derived from steel surface.
+
+To further investigate the role of iron single atoms in the formation of graphitic carbon tribofilms, we further conducted DFT simulations to calculate the activation energy for C–C bond dissociation in simplified DOM on iron single-atom surfaces, iron cluster, and Fe (110) surface (Fig. R12), respectively. Since the bond energy of C–C bonds is lower than that of C–H bonds, this dissociation was selected as a representative reaction step. The results show that the activation energy for C–C bond dissociation is significantly reduced to 1.08 eV on iron single-atom surfaces, which is notably lower than that on iron clusters (1.41 eV) and the Fe (110) surface (1.66 eV). This underscores the superior catalytic efficiency of single iron atoms in activating DOM.
+Fig. R11. The tribological performance of 5% DOM in polyalphaolefin (PAO) on different surfaces and the corresponding wear track surface analysis. Friction coefficient of PAO with and without 5% DOM under (a) glass-steel contact, (b) glass-glass contact. (c) optical image, (d)(f) TEM analysis, and (e) Raman spectra of wear track formed on steel surface under glass-steel contact.
+
+Fig. R12 (Fig. S36). The solid surface model and energy pathways for C-C bond activation of the simplified DOM on (a)(d) Fe single atom, (b)(e) Fe cluster, and (c)(f) Fe (110) surface. Insets in (d)-(f) are the molecular configurations at initial state (IS), transition state (TS), and final state (FS).
+
+2. The formation of carbon free radicals stabilized by the lone pair effect from diesters.
+
+Although the effect of molecular structure on tribological performance has been widely investigated, the impact of free radical stability of lubricants on tribofilm formation and
+consequently tribological performance was not well understood. Our work reveals that the diesters derived from short-chain carboxylic acid, such as dioctyl malonate (DOT), didodecyl succinate (DOSN), can utilize their lone pair effect to stabilize generated free radicals (DOT in Fig R13a, below). This stabilization initiates tribochemical reactions, leading to the formation of a graphitic carbon tribofilm. This is demonstrated by the resemblance in the distribution of the grey island tribofilm for both DOT and DOSN in Fig. R13b, as well as their corresponding Raman G band intensity in Fig. R13c. In contrast, dioctyl sebacate (DOS), derived from long-chain carboxylic acid cannot form graphitic carbon film due to its inability to stabilize free radicals (DOS in Fig. R13a ~ c). Consequently, the friction coefficient increases as the length of carboxylic acid in diesters becomes longer (Fig. R13d). To the best of our knowledge, this is the first observation that correlates tribological performance with free radical stability.
+
+Based on the above points, we believe that the novelty of this work includes, (i) the graphitic carbon formation under steel-steel contact in PAO; (ii) the observation of iron single atoms formation and its catalytic effect on graphitic carbon formation; (iii) the correlation between tribological performance, graphitic carbon formation and free radical stability. These three points have been further elaborated and highlighted in the revised manuscript to underscore the unique contributions and novel mechanisms of this work.
+
+Regarding the comparison with other organic friction modifiers, we acknowledge that many studies have explored the correlation between tribological performance and molecular structures. In our work, we selected oleic acid, GMO, alcohol, and ZDDP (as shown in Table R1) as references for comparison due to their excellent performance in prior studies and widespread use in industrial applications. Furthermore, to examine the effect of free radical stabilization on tribological performance, we have also included comparisons with other organic friction modifiers which are composed of diesters similar in structure to DOM but with varying chain lengths, such as dioctyl malonate (DOT), dioctyl fumarate (DOF), dioctyl adipate (DOA), dioctyl sebacate (DOS), and didodecyl succinate (DOSN), as summarized in Table R1. Notably, our results show that DOM exhibits lowest friction coefficient and wear track width than these established modifiers (Fig. S4, Fig. 5). Therefore, we believe that DOM is a promising lubricant additive in the future. This comparison highlights the superior performance of DOM and underscores its potential as a promising lubricant additive for future applications.
+
+![The proposed free radical stabilization mechanism of DOT and DOS, wear track images, Raman G band intensity maps, and friction coefficient bar chart](page_186_1092_1077_627.png)
+
+Fig. R13. The tribological performance, wear track analysis of different lubricant additives and corresponding proposed mechanisms. (a) The proposed free radical stabilization mechanism of
+DOT and DOS. (b) optical image, and (c) Raman G band intensity mapping, (d) friction coefficient of different lubricant additives.
+
+Table R1. The molecules of tested additives in this work
+
+<table>
+  <tr>
+    <th>Name</th>
+    <th>Molecular structure</th>
+  </tr>
+  <tr>
+    <td>octanol</td>
+    <td>CCCCCCCCOH</td>
+  </tr>
+  <tr>
+    <td>oleic acid</td>
+    <td>CCCCCCCCCCCCCCCCCOOH</td>
+  </tr>
+  <tr>
+    <td>GMO</td>
+    <td>CCCCCCCCCCCCCCCCCCCCCOOCH2OH</td>
+  </tr>
+  <tr>
+    <td>ZDDP</td>
+    <td>RO<sub>P</sub>S<sub>2</sub>ZnS<sub>2</sub>OR<sub>P</sub></td>
+  </tr>
+  <tr>
+    <td>DOT</td>
+    <td>CCCCCCCCOOCOCCCCCCCC</td>
+  </tr>
+  <tr>
+    <td>DOF</td>
+    <td>CCCCCCCCOOC=CCOCCCCCCCC</td>
+  </tr>
+  <tr>
+    <td>DOA</td>
+    <td>CCCCCCCCOOC(C)COCOCCCCCCCC</td>
+  </tr>
+  <tr>
+    <td>DOS</td>
+    <td>CCCCCCCCOOC(C)COCOCCCCCCCC</td>
+  </tr>
+  <tr>
+    <td>DOSN</td>
+    <td>CCCCCCCCOOC(C)COCOCCCCCCCC</td>
+  </tr>
+</table>
+
+According to your comments, we have added the following description to the revised manuscript.
+
+Page 7, “Additionally, comparison with conventional industrial additives, including GMO and ZDDP, further highlight DOM’s superior performance. The friction coefficients of 5 wt% GMO and 5 wt% ZDDP were 0.20 and 0.14, respectively (Fig. S3), both significantly higher than that achieved with 5 wt% DOM. While the wear track width and wear volume of 5 wt% ZDDP were comparable to those of 5 wt% DOM (Fig. S4c, d), DOM is free of sulfur and phosphorus, making it a much more environmentally friendly option. Notably, even at a low concentration of 1 wt%, DOM also exhibits a much lower friction coefficient and no visible wear scratches compared to ZDDP and GMO (Fig. S6), further demonstrating the superior performance of DOM. Therefore, the superior performance of this green DOM additive, combined with its sustainable composition, highlights its great potential as a replacement for conventional lubricant additives like ZDDP and GMO.”
+Page 16 “Note that while there are several studies addressing the formation of graphite-like carbon films, they often involve specific conditions such as noble metal substrates, which are cost-prohibitive, anaerobic environments, requiring complex sealing systems, or water-based lubricants, which are less applicable to many industrial applications. In contrast, this work demonstrates that the green additive DOM can effectively form a graphitic carbon layer on engineering steel surfaces, a material widely used in industry. Additionally, the correlation between graphitic carbon formation and molecular structures remains poorly understood due to the challenges in elucidating the reaction pathways during complicated tribochemical reactions. Therefore, it is of great significance to investigate the molecular structure effect on graphitic carbon formation and the corresponding tribological performances”
+
+Page 22, “The remarkable catalytic performance of Fe single atoms has been demonstrated in facilitating C–H and C–C bond dissociation, both of which are critical steps in the formation of graphitic carbon. This superior performance arises from the atomic dispersion of active catalytic centers and their distinctive electronic structure. To further elucidate the impact of Fe single atoms on the conversion of DOM into graphitic carbon tribofilms, the activation energy for C–C bond dissociation in simplified DOM on iron single-atom surfaces, iron cluster, and Fe (110) surface was respectively calculated using DFT simulation (Fig S36). The results reveal that the activation energy for C–C bond dissociation is significantly reduced to 1.08 eV on iron single-atom surfaces, which is notably lower than that on iron clusters (1.41 eV) and the Fe (110) surface (1.66 eV). This underscores the superior catalytic efficiency of single iron atoms in activating DOM, which facilitates the subsequent formation of graphitic carbon”
+
+For examples, the following papers may be of use to you to improve your paper.
+
+1) Zhang, J., Bolle, B., Wong, J.S.S. et al. Influence of Atmosphere on Carbonaceous Film Formation in Rubbing, Metallic Contacts. Tribol Lett 72, 4 (2024). https://doi.org/10.1007/s11249-023-01801-9
+
+Response: This work by our coauthors demonstrates that carbon film formation in anaerobic environments is initiated by hydrocarbyl free radicals mechanochemically generated from hydrocarbons. In contrast, our study shows that DOM can generate graphitic carbon films in air, initiated by free radicals from DOM. This makes DOM more applicable to industrial environments. Moreover, our work highlights the role of iron single atoms and free radical stability in tribological performance by comparing various molecular structures, providing deeper insights into additive design.
+
+Achieving Superlubricity of Ricinoleic Acid in the Steel/Si3N4 Contact Under Boundary Lubrication
+
+2) Y Long, JM Martin, F Dubreuil, MI De Barros Bouchet
+
+Tribology Letters 70 (4), 109
+
+Response: This work compared the tribological performance of oleic acid (OA), ricinoleic acid (RA), and linoleic acid (LA), observing graphitic carbon formation. However, a key distinction from our study is that the friction experiments in this paper were conducted under steel/Si3N4 contacts, whereas ours were performed under steel-steel contacts, which are more representative of industrial applications. Meanwhile, the maximum contact pressure in our
+work reached 2.78 GPa, significantly higher than in their study (~200 MPa). Additionally, our work has, for the first time to our knowledge, revealed the role of iron single atom catalysis and free radical stability in the formation of graphitic carbon tribofilm. We acknowledge the valuable insights provided by the referenced paper, particularly the differences among OA, RA, and LA, which are crucial for understanding the lubrication behavior of amphiphilic molecules. To provide a more comprehensive perspective on amphiphilic molecule lubrication, we have cited and discussed this work (Ref. 23) in the Introduction section of the revised manuscript (Page 4), marked by grey color.
+
+Superlubricity from mechanochemically activated aromatic molecules of natural origin: a new concept for green lubrication
+
+3) Y Long, A Pacini, M Ferrario, N Van Tran, S Peeters, B Thiebaut, S Loehle, ...
+
+Carbon, 119365
+
+Response: This interesting study demonstrates the superior performance of hypericin, attributed to the formation of a graphitic carbon tribofilm. However, the tribological tests were conducted in glycerol solution under steel-SiC contact, which is less representative of typical industrial applications compared to PAO lubricants used under steel-steel contact in our study. While we would be eager to test hypericin’s performance using our setup, its poor solubility in PAO lubricants presents a challenge. To provide a more comprehensive introduction to the effect of graphitic carbon formation on tribological performance, we have cited this work (Ref. 57) in the revised manuscript (Page 16).
+
+2. Although a lot of data is presented, the description of each individual piece of data is lacking. Much of the content that should be included in the main text is included in the supplementary information, but it is not organized and is difficult to read. The chapter headings should be reviewed and the structure revised to make it more logical.
+
+Response: Thank you for your thoughtful suggestions. After carefully reviewing the manuscript, we have significantly expanded and clarified the descriptions of our results. For instance, the differences in mechanical properties between wear tracks, as determined by nanoindentation tests, have been elaborated in greater detail. Additionally, the role of iron single atoms in catalyzing graphitic carbon formation has been further addressed and explained in the revised manuscript. The examples revision are as follows,
+
+Page 9, “Additionally, the load–time curve on the island-like areas exhibits a decreasing load trend from 10 to 15 s (Fig. 2c), while the tip maintained a depth of 40 nm. This behavior indicates stress relaxation behavior within the island-like film, indicative of its viscoelastic property. Usually, such stress relaxation is observed in metallic materials at high temperatures or in polymeric materials at room temperature. Therefore, the island-like area is potentially composed of a polymer-like layer exhibiting viscoelastic property. Notably, this viscoelastic behavior was not observed in the unrubbed or no-island area (Fig. 2c, Fig. S15)”
+
+Page 22 “The remarkable catalytic performance of Fe single atoms has been demonstrated in facilitating C–H and C–C bond dissociation, both of which are critical steps in the formation of graphitic carbon. This superior performance arises from the atomic dispersion of active catalytic centers and their distinctive electronic structure. To further elucidate the impact of Fe single atoms on the conversion of DOM into graphitic carbon tribofilms, the activation energy for C–C bond dissociation in simplified DOM on iron single-atom surfaces, iron cluster, and Fe (110) surface was respectively calculated using DFT simulation (Fig R9). The results reveal
+that the activation energy for C–C bond dissociation is significantly reduced to 1.08 eV on iron single-atom surfaces, which is notably lower than that on iron clusters (1.41 eV) and the Fe (110) surface (1.66 eV). This underscores the superior catalytic efficiency of single iron atoms in activating DOM, which facilitates the subsequent formation of graphitic carbon”.
+
+In addition, further revisions have been incorporated into the revised manuscript, including the friction results description on Page 5, the AFM friction analysis on Page 10, and the simulation details on Page 25.
+
+According to your comments, we have transferred some items previously in the Supplementary Information into the main text to ensure the key data are easily accessible. For example, the wear track morphology of OA in Fig. 1d, e and load-time curve during nanoindentation test in Fig. 2c, which were initially in the Supplementary Information, have now been included in the main text. Usually, Nature Communications recommends limiting display items (figures and/or tables) to 10. Our revised manuscript now includes seven figures, one table, and one reaction pathway, bringing us close to this limit. We welcome specific suggestions from you if additional items from the Supplementary Information should be moved into the main text.
+
+To improve the readability of this manuscript, we have reorganized the sequence of figures both in the main text and the supplementary materials. For example, the XPS data sequence in Fig.3 d ~ e has been adjusted to align with its appearance in the main text. These updates aim to enhance the clarity and flow of the manuscript.
+
+The chapter headings have been carefully reviewed and revised. For example,
+
+Page 8, “The nanomechanical property of the tribofilm” has been revised as “The nanomechanical properties on the wear tracks”
+
+Page 10, “The surface chemistry of the tribofilm” has been revised as “The tribochemical reactions on the wear tracks”
+
+3. There is a lack of chemical consideration regarding why DOM has special properties as an additive. Why is there a correlation between high adsorption characteristics and the ease with which graphite-like tribofilms form?
+
+Response: Thank you for your insightful question. Indeed, DOM exhibits unique properties as an additive. The tribological performance of an additive typically depends on two key factors: its reactivity during tribochemical processes and its adsorption behavior on the tribopair surface. Our findings demonstrate that DOM excels in both aspects.
+
+Regarding the reactivity of DOM as an additive, as discussed in the second point of the response to the first question, DOM and its structural analog DOT, both originated from short-chain carboxylic acids, can stabilize the free radicals due to their lone pair effect (Fig. R13a). This stabilization capability initiates reactions leading to the formation of the graphitic carbon tribofilm, resulting in friction and wear reduction. In contrast, additives such as DOS, which are derived from long-chain carboxylic acids, cannot stabilize free radicals as effectively and thus fail to form graphitic carbon tribofilms (Fig. R13).
+
+In terms of the adsorption of additives on tribopair surface, QCM-D results in Fig.S25 reveal that DOM exhibits significantly stronger adsorption on the steel surface compared to octanol. This strong adsorption can physically separate the direct solid-solid contact during rubbing to reduce friction and wear. On the other hand, it ensures that sufficient DOM molecules are available at the tribological interface to participate in tribochemical reactions, facilitating the
+formation of a graphitic carbon tribofilm.
+
+Regarding the correlation between adsorption and graphitic tribofilm formation, reaction kinetics play a critical role. The initial formation of the tribofilm depends on the presence of a sufficient concentration of reactive species to initiate the reaction. If the concentration of the substance is too low, the kinetic rate of tribofilm formation will also be low. Moreover, the formation of the tribofilm is a dynamic process involving continuous formation and removal. If the additive adsorption is insufficient, the removal rate of the tribofilm will surpass its formation rate, preventing tribofilm accumulation. Thus, the high adsorption of DOM (evidenced by QCM-D in Fig.S25) on the steel surface directly supports the formation of the graphitic tribofilm by ensuring a steady supply of reactants to counteract the dynamic removal process. This enhanced adsorption behavior is a critical factor in DOM’s superior tribological performance.
+
+We have revised the manuscript accordingly to emphasize these points. The examples of the key points are as follows,
+
+Page 15, "The strongly adsorbed DOM film plays a dual role in enhancing tribological performance. First, it physically separates the solid-solid contact during rubbing, thereby reducing friction and wear. Second, it ensures a sufficient supply of DOM molecules at the friction interface to participate in tribochemical reactions, facilitating the formation of a graphitic carbon tribofilm. The initial formation of this tribofilm depends on an adequate concentration of reactive species to initiate the reaction. If the concentration is too low, the tribofilm formation rate will be limited. Furthermore, the tribofilm formation is a dynamic process involving simultaneous formation and removal. Insufficient additive adsorption results in the removal rate exceeding the formation rate, preventing tribofilm accumulation. Therefore, the strong adsorption of DOM on the steel surface ensures a consistent supply of reactants, balancing the dynamic formation process and enabling graphitic carbon tribofilm formation. This enhanced adsorption is a key factor in DOM’s superior tribological performance."
+
+4. It seems that the friction tests were carried out under boundary lubrication, whereas the simulations were carried out under fluid lubrication via a narrow gap. There seems to be a significant discrepancy here, so why do you think that the simulations can reproduce the situation under boundary lubrication? More detailed notes are needed.
+
+Response: Thank you for raising this important point. We acknowledge that the absence of a scale bar in our previous model in Fig. 7a may cause confusion. To address this, we have now marked the separation distance between the two solid surfaces. It is approximately 2 nm at the beginning of the simulation (Fig. 7a) and reduces to around 1 nm by the end of the simulation (Fig. S38).
+
+We agree with the reviewer that the friction tests in this study were conducted under boundary lubrication. The determination of the lubrication regime relies on the comparison between the thickness of the lubricating liquid film and the combined surface roughness of the two tribopair surfaces, with their ratio, \( \lambda \), defined as
+
+\[
+\lambda = \frac{h_{min}}{\sqrt{R_{q1}^2 + R_{q2}^2}}
+\]
+
+where \( h_{min} \) is the oil film thickness, and \( R_{q1} \) and \( R_{q2} \) are the surface roughness of the two surfaces. Typically, a \( \lambda \) value less than one signifies boundary lubrication\(^{29}\). In our study, the
+calculated \( \lambda \) ratio for different lubricants was approximately 0.08 (Table S2), confirming the boundary lubrication. Notably, even in this regime, Dowson and Hamrock's equation estimates an oil film thickness of ~1.1 nm between the two surfaces (Table S2). Additionally, previous studies have shown that boundary lubrication does not imply the complete absence of confined lubricants. Instead, the tribopair surfaces may still be separated by a thin molecular film, typically ranging from one to a few nanometers depending on the \( \lambda \) ratio\(^{30}\). Therefore, this understanding justifies the molecular film thickness of less than 2 nm in our computational model (Fig. S38). Similar models have also been widely used in previous studies\(^{22, 27, 31}\).
+
+To address this point, we have revised the manuscript to include additional details justifying the validity of the simulation model and the choice of parameters:
+
+Page 25, "While the thickness of the liquid film was around 2 nm at the beginning of the simulation (Fig. 7a), it reduced to around 1 nm by the end of simulation (Fig. S38), which closely matches the liquid film thickness calculated using Dowson and Hamrock's equation (Table S2). Note that previous studies have shown that boundary lubrication does not imply the complete absence of confined lubricants. Instead, the tribopair surfaces may still be separated by a thin molecular film, typically ranging from one to a few nanometers depending on the \( \lambda \), which is the ratio between the thickness of the lubricating liquid film and the combined surface roughness of the two tribopair surfaces."
+
+We hope this addresses your concern and justifies the simulation methodology used in this study.
+References
+
+1. Spikes, H., The History and Mechanisms of ZDDP. Tribology Letters 2004, 17 (3), 469-489.
+2. Ibrahim, T. M.; Zulfattah, Z. M.; Yusoff, M. N. A. M.; Kalam, M. A.; Masjuki, H. H.; Zulkifli, N. W. M.; Harith, M. H.; Syahir, A. Z., Compatibility of Ionic Liquid With Glycerol Monooleate and Molybdenum Dithiocarbamate as Additives in Bio-Based Lubricant. Journal of Tribology 2020, 142 (6).
+3. Ewen, J. P.; Gattinoni, C.; Morgan, N.; Spikes, H. A.; Dini, D., Nonequilibrium Molecular Dynamics Simulations of Organic Friction Modifiers Adsorbed on Iron Oxide Surfaces. Langmuir 2016, 32 (18), 4450-63.
+4. Fry, B. M.; Moody, G.; Spikes, H. A.; Wong, J. S. S., Adsorption of Organic Friction Modifier Additives. Langmuir 2020, 36 (5), 1147-1155.
+5. Beltzer, M.; Jahannmir, S., Role of Dispersion Interactions Between Hydrocarbon Chains in Boundary Lubrication. A S L E Transactions 1987, 30 (1), 47-54.
+6. Campen, S.; Green, J. H.; Lamb, G. D.; Spikes, H. A., In Situ Study of Model Organic Friction Modifiers Using Liquid Cell AFM; Saturated and Mono-unsaturated Carboxylic Acids. Tribology Letters 2015, 57 (2).
+7. Doig, M.; Warrens, C. P.; Camp, P. J., Structure and Friction of Stearic Acid and Oleic Acid Films Adsorbed on Iron Oxide Surfaces in Squalane. Langmuir 2014, 30 (1), 186-195.
+8. Fry, B. M.; Chui, M. Y.; Moody, G.; Wong, J. S. S., Interactions between organic friction modifier additives. Tribology International 2020, 151.
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+10. Buzio, R.; Gerbi, A.; Bernini, C.; Repetto, L.; Vanossi, A., Sliding Friction and Superlubricity of Colloidal AFM Probes Coated by Tribo-Induced Graphitic Transfer Layers. Langmuir 2022, 38 (41), 12570-12580.
+11. Saha, A.; Mondal, D. K.; Maity, J., Effect of cyclic heat treatment on microstructure and mechanical properties of 0.6wt% carbon steel. Materials Science and Engineering: A 2010, 527 (16-17), 4001-4007.
+12. Huang, X.; Xie, G.; Liu, X.; Fu, H.; Shao, L.; Hao, Z., The influence of precipitation transformation on Young's modulus and strengthening mechanism of a Cu–Be binary alloy. Materials Science and Engineering: A 2020, 772.
+13. Schwarzer, N., Short note on the effect of a pressure-induced increase in Young's modulus. Philosophical Magazine 2012, 92 (13), 1631-1648.
+14. Marsh, H.; Rodríguez-Reinoso, F., CHAPTER 9 - Production and Reference Material.
+In Activated Carbon, Marsh, H.; Rodríguez-Reinoso, F., Eds. Elsevier Science Ltd: Oxford, 2006; pp 454-508.
+
+15. Vázquez-Santos, M. B.; Geissler, E.; László, K.; Rouzaud, J.-N.; Martínez-Alonso, A.; Tascón, J. M. D., Comparative XRD, Raman, and TEM Study on Graphitization of PBO-Derived Carbon Fibers. The Journal of Physical Chemistry C 2011, 116 (1), 257-268.
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+16. Li, S.; Zheng, Z.; Liu, S.; Chi, Z.; Chen, X.; Zhang, Y.; Xu, J., Ultrahigh thermal and electric conductive graphite films prepared by g-C3N4 catalyzed graphitization of polyimide films. Chemical Engineering Journal 2022, 430.
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+17. Chen, Z.; Gu, Y.; Hu, L.; Xiao, W.; Mao, X.; Zhu, H.; Wang, D., Synthesis of nanostructured graphite via molten salt reduction of CO2 and SO2 at a relatively low temperature. J. Mater. Chem. A 2017, 5 (39), 20603-20607.
+
+18. Kalin, M., Influence of flash temperatures on the tribological behaviour in low-speed sliding: a review. Materials Science and Engineering: A 2004, 374 (1-2), 390-397.
+
+19. N. N. Gosvami, J. A. B., 1* F. Mangolini,2 A. R. Konicek,3 D. G. Yablon,3† R. W. Carpick1, Mechanisms of antiwear tribofilm growth revealed in situ by single-asperity sliding contacts. Science 2015.
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+20. Zhang, J.; Ewen, J. P.; Ueda, M.; Wong, J. S. S.; Spikes, H. A., Mechanochemistry of Zinc Dialkyldithiophosphate on Steel Surfaces under Elastohydrodynamic Lubrication Conditions. ACS Appl Mater Interfaces 2020, 12 (5), 6662-6676.
+
+21. Zhang, J.; Spikes, H., On the Mechanism of ZDDP Antiwear Film Formation. Tribology Letters 2016, 63 (2).
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+
+23. Chesnokov, V. V.; Chichkan, A. S., Effect of catalysts on tar carbonization. Catalysis Today 2021, 379, 28-35.
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+27. Long, Y.; Pacini, A.; Ferrario, M.; Van Tran, N.; Peeters, S.; Thiebaut, B.; Loehlé, S.; Martin, J. M.; Righi, M. C.; De Barros Bouchet, M.-I., Superlubricity from mechanochemically activated aromatic molecules of natural origin: A new concept for green lubrication. Carbon 2024, 228.
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+
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+
+30. Sadeghi, F., 6 - Elastohydrodynamic lubrication. In Tribology and Dynamics of Engine and Powertrain, Rahnejat, H., Ed. Woodhead Publishing: 2010; pp 171-226e.
+
+31. Wu, H.; Khan, A. M.; Johnson, B.; Sasikumar, K.; Chung, Y. W.; Wang, Q. J., Formation and Nature of Carbon-Containing Tribofilms. ACS Appl Mater Interfaces 2019, 11 (17), 16139-16146.

0843de24eb7cd42d0826bcc04a37651f74c3bae20b743963c695c5dc561236e4/preprint/preprint.md

@@ -0,0 +1,226 @@
+Catalyzing Green Lubricants into Graphitic Carbon Layers by Iron Single Atoms to Reduce Friction and Wear
+
+Jinjin Li
+lijinjin@mail.tsinghua.edu.cn
+
+Tsinghua University   https://orcid.org/0000-0002-9835-168X
+
+Wei Song
+wsong@illinois.edu
+
+Chongyang Zeng
+Imperial College London
+
+Janet S. S. Wong
+Imperial College London
+
+Chuke Ouyang
+Tsinghua University
+
+Ali Erdemir
+Texas A&M University
+
+Shouyi Sun
+Tsinghua University
+
+Seungjoo Lee
+Texas A&M University
+
+Weiwei Zhang
+Tiangong University
+
+Jianbin Luo
+Tsinghua University
+
+Xing Chen
+Tianjin University   https://orcid.org/0000-0002-1223-298X
+
+Article
+
+Keywords:
+
+Posted Date: August 28th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4413576/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 25th, 2025. See the published version at https://doi.org/10.1038/s41467-025-58292-6.
+Abstract
+
+Reducing friction and wear in moving mechanical systems is essential for their intended functionality. This is currently accomplished using a large variety of anti-friction and anti-wear additives, that usually contain sulfur and phosphorous both of which cause harmful emission. Here, we introduce a series of diesters, typically dioctyl malate (DOM), as green and effective anti-friction and anti-wear additives which reduce wear by factors of 5–7 and friction by over 50% compared to conventional additives when tested under extreme pressures (up to 2.78 GPa). Surface studies show that these impressive properties are primarily due to the formation of a 30 nm graphitic tribofilm that protects rubbing surfaces against wear and hence provides low shear stress at nanoscale. This graphitic tribofilm is prone to form from diesters dereived from short-chain carboxylic acid due to their lone pair effect, which stabilizes the carbon free radicals. Furthermore, the formation of this tribofilm was catalyzed by nascent iron single atoms, which were in-situ generated due to the mechanochemical effects during sliding contact. Computational simulations provided additional insights into the steps involved in the catalytic decomposition of DOM by iron and the formation of a graphitic carbon tribofilm. Due to its superior anti-friction and wear properties, DOM holds promise to replace conventional additives, and thus provide a green and more effective alternative for next-generation lubricant formulations.
+
+Introduction
+
+Friction and wear result in significant energy and material losses in moving mechanical systems \(^{1,2}\). This is commonly alleviated using liquid lubricants\(^{3}\) blended with anti-friction and anti-wear additives\(^{4}\). Usually, lubricant additives play a crucial role in governing tribological performance, especially during boundary lubrication where the asperities can collide directly and very frequently\(^{4}\). In recent decades, zinc dialkyl dithiophosphate (ZDDP), a typical lubricant additive, has been widely used in engine oils as an anti-wear agent. Its superior performance can be attributed to the in-situ formation of a patchy tribofilm on rubbing surfaces, preventing a direct metal to metal contact during the rubbing process\(^{5-7}\) and hence reducing wear. However, the sulfur and phosphorus in ZDDP are poisonous to the pollutant-reducing catalytic converters in all motored vehicles\(^{8,9}\). In addition, ZDDP usually cannot provide a satisfactory friction-reducing performance; hence, it must be combined with additional friction modifiers, such as MoDTC. In addition to ZDDP, other nanomaterials have been extensively studied as lubricant additives in past decades. For example, typical nano-carbon nanomaterials, such as graphene\(^{10,11}\), carbon nanotubes\(^{12}\), and carbon quantum dots\(^{13,14}\) exhibits excellent friction-reducing and anti-wear performance. However, their application is limited because they cannot be well-dispersed in lubricants, as they agglomerate or separate from the base oil over time\(^{15,16}\), as a result, they cannot enter the contact area and adhere to surfaces because of their larger size and chemical inertness\(^{4}\). Therefore, developing environment-friendly additives that are readily soluble in lubricants and provide excellent tribological performance will be essential for achieving long-range efficiency and reliability goals of motored vehicles.
+Generally, a desirable lubricant additive is expected to adsorb strongly on the tribopair surfaces via physisorption or electrostatic interactions, hydrogen bonding or coordination bonding\(^{17,18}\), and hence it can effectively protect the solid–solid contacts at the initial stage of sliding. Additionally, an ideal lubricant additive should be chemically reactive such that it can be further converted into a low-friction and highly protective tribofilm via the tribochemical reaction during the rubbing process\(^{19,20}\). Due to strong chemical bonding, such a tribofilm can provide long-lasting reductions for friction and wear and this process can continue as the lost film is very quickly repaired or replenished through the robust tribochemical reaction.
+
+Amphiphilic molecules, which have been extensively studied by tribologists, are composed of polar head groups and nonpolar tail groups and are widely used as organic friction modifiers in commercial lubricants\(^{21,22}\). Typical amphiphilic molecules, including fatty alcohols, fatty acids and glycerol monooleate (GMO), usually have no sulfur and phosphorus components, and have been used as green lubricant additives to circumvent harmful effect of ZDDP. Meanwhile, these additives can effectively reduce friction and wear by up to 45% and 83%, owing to the formation of a tribofilm, such as a carboxylate on the steel surface\(^{22}\). Among these amphiphilic molecules, fatty alcohols were found to exhibit higher friction and wear than fatty acids owing to their lower adsorption strength on metal surfaces\(^{23}\). Accordingly, we hypothesize that if the fatty alcohol is chemically modified into a molecule that can readily adsorb and strongly bond to the rubbing surface, the tribological performance of the modified fatty alcohols will be substantially improved. Here we selected a fatty alcohol molecule (i.e., octanol, see Fig. 1a) and chemically grafted it with malic acid to form the dioctyl malate (DOM in Fig. 1a). As malic acid contains multiple chemically active carboxylic acid and alcohol groups, it is anticipated to enhance the adsorption of DOM on a sliding surface thus leading to a superior anti-friction and wear performance\(^{24,25}\). DOM was used as an additive in an ultra-low viscosity oil (i.e., polyalphaolefin (PAO2), referred as PAO hereafter) and tested in the boundary lubrication regime where frequent metal-to-metal contact and hence high-friction and -wear were anticipated.
+
+The macrotribological performance
+
+Tribological tests on PAO and DOM additized PAO (Fig. 1a) were carried out using a steel ball on steel disc tribometer (Optimol Instruments, SRV4) in a reciprocating mode (Fig. 1b). The addition of DOM into PAO substantially reduced friction coefficient (Fig. 1c, from ~ 0.25 to ~ 0.11), wear track depth (Fig. 1d, from ~ 1.5 \( \mu \)m to ~ 0.2 \( \mu \)m), width (Fig. 1e, from ~ 420 \( \mu \)m to ~ 224 \( \mu \)m), and wear volume (Fig. 1f, from ~ 27\( \times 10^{-5} \) mm\(^3\) to ~ 3.7 \( \times 10^{-5} \) mm\(^3\)). Note that the low friction and wear of 5 wt% DOM containing PAO persist even under a heavy load of 176 N (Fig. 1g, Fig. S1b), corresponding to a maximum Hertz contact pressure of 2.78 GPa. In comparison, neat PAO exhibited a steeply increasing friction coefficient (i.e., 0.82) accompanied by severe wear losses (Fig. S1a) once the load reached 76 N in about 10 min, indicating lubrication failure. PAO with other polar additives (i.e., octanol, and oleic acid (OA)) also showed some reduction in friction and wear under a 36 N test (Fig. 1c, f, Figs. S2–S6), but they were still much higher than those observed on DOM with PAO oil. Figs. S2, S3 and S7 in supplementary
+information shows that the DOM additive can reduce the friction coefficient and wear track width by up to 45.0% and 21.4%, respectively, compared to other industrial additives (i.e., GMO and ZDDP with friction coefficient of 0.20 and 0.14, and with wear track of 278 \( \mu \)m and 228 \( \mu \)m, respectively). This suggests that DOM is not only a good anti-friction but also an excellent anti-wear additive, and thus holds great promise to replace conventional lubricant additives ZDDP/GMO.
+
+From Figs. 1e and S5, S6, it is clear that deep scratches and wear debris are present within and around wear tracks (especially toward the end of strokes) formed during tests in PAO, 5 wt% octanol, and 5 wt% OA; however, these were noticeably absent with 5 wt% DOM in PAO oil, further suggesting a much superior anti-wear property provided by DOM additive.
+
+After the tribological test, the wear track was rinsed with hexane to eliminate lubricant residue on the surface. Note that the rinsing will not affect the surface chemistry/mechanical properties of the wear track (Fig. S8). Interestingly, while neat PAO (Fig. S9), 5 wt% OA (Fig. S10), and 5 wt% octanol (Fig. S11) exhibited similar wear track appearances before and after rinsing, whereas 5 wt% DOM in PAO showed a grey, patchy structure in the wear track after rinsing (Fig. S12b, Fig. 2a). Notably, this grey patchy area is higher than its surrounding area in the wear track (Fig. S12c), suggesting a raised island-like structure formation. Interestingly, the surface coverage of these islands in the wear track gradually increased from 30 s to 5 min (Fig. S13), which coincided with the decreasing tendency of friction coefficient (Fig. 1h). This suggests that the formation of these island-like structures may contribute to a superior anti-friction-and -wear performance of DOM.
+
+The nanomechanical property of the tribofilm
+
+Tribological tests suggest patchy island-like film formation on the rubbing surface by 5 wt% DOM, has minimised direct steel–steel contacts during rubbing. The mechanical properties of these islands were examined using nanoindentation tests on the three highlighted areas (with circles) shown in Fig. 2a. The penetration depth was fixed at 40 nm. The maximum nanoindentation load applied to the island area reaches 220 \( \mu \)N (Fig. 2b) which is significantly lower than those measured in the unrubbed or no-island-like areas inside the wear track. Our results suggest the island film has a considerably lower Young’s modulus and hardness than its surroundings (Fig. S14). Additionally, the load–time curve on the island-like areas exhibits a viscoelastic behavior (Fig. S15a), suggesting that it might be composed of a polymer-like material\(^{26,27}\).
+
+The AFM topography images located at the boundary between the unrubbed and island-like film areas show the typical patchy structure of this film (Fig. S16). The friction property of the film was studied in a 10 \( \mu \)m \( \times \) 10 \( \mu \)m area via repeated AFM rubbing tests under a high load of 60 nN, corresponding to a maximum contact pressure of 2.41 GPa. Interestingly, while the topography of the island-like film remained the same from the 2nd to 110th rubbing cycles (Fig. S17a,b), the average friction force decreased during the initial 20 rubbing scans (Fig. 2c), after which it reached a plateau. This suggests that the film is strong against wear by the AFM tip and can provide low friction even at nano-scales.
+Meanwhile, the force–distance curves show that the island area exhibited the lowest slope (Fig. 2d) and pull-off force (Fig. 2d, e) than those of the other two areas\(^{28-30}\). This shows that the island film has low adhesion and Young’s modulus, which may result in low friction. In contrast, the wear track surface formed by 5 wt% octanol in PAO is easily modified under repeated AFM tip rubbing (Fig. S18). This suggests that octanol cannot form a robust tribofilm with low friction, and is consistent with its high friction and wear at microtribological tests.
+
+The surface chemistry of the tribofilm
+
+To unravel the chemical composition of the tribofilm, a variety of surface analytical techniques was used on wear tracks. Raman spectra of wear tracks formed in 5 wt% OA and 5 wt% octanol exhibited a distinctive Fe\(_3\)O\(_4\) peak at 669 cm\(^{-1}\) (Fig. 2f)\(^{31,32}\), indicating that these surfaces experienced severe oxidation during sliding. In contrast, with the use of 5 wt% DOM in PAO, Fe\(_3\)O\(_4\) peak intensity decreased substantially, and the D and G bands that are typical of graphitic carbon material emerged\(^{33-35}\), especially in the island-like areas. The Raman G band intensity mapping in Fig. 2h showed a distribution that resembles that of the island area in Fig. 2g, further proving the presence of some graphitic carbon material within the island-like tribofilm leading to low friction and wear. These films may have also been responsible for protection against oxidation. Further, Fourier-transform infrared (FTIR) spectra show that very little or no traces of C-H and C = O stretching vibrations from the original PAO and DOM are observed in the wear track formed by 5 wt% DOM (Fig. 2i and Fig. S19), suggesting the dehydrogenation process and complete conversion of carbon backbone of DOM molecules into the carbon tribofilm. Typical sp\(^2\) C = C stretching originating from the aromatic ring compound\(^{36}\) can be found within the wear track formed by 5 wt% DOM containing PAO (Fig. 2i), which further suggests the formation of graphitic carbon.
+
+From Fig. 3a, the surface chemistry of the wear track determined by X-ray photoelectron spectroscopy (XPS) using the layer-by-layer sputtering method shows that 5 wt% DOM exhibits a considerably higher carbon concentration (beyond the top contaminant layer) at depths to 26 nm than those observed in the neat PAO, 5 wt% octanol, and unrubbed area. Note that the carbon in wear track of 5 wt% DOM showed sp\(^2\) hybridization from 2 to 10 nm depth (Fig. 3f)\(^{37}\), which differs from the sp\(^3\) hybridized carbon\(^{37}\) in wear track of neat PAO (Fig. 3e) and 5 wt% octanol (Fig. S20), and the C-Fe phase (originate from Fe\(_3\)C in steel) from the unrubbed area (Fig. 3d)\(^{38,39}\). Meanwhile, 5 wt% DOM shows lower oxygen (Fig. 3b) and higher iron (Fig. 3c) concentrations (beyond the top native oxide layer) than those in neat PAO and 5 wt% octanol, and its iron exists in the form of iron (0) from 4 to 36 nm (Fig. 3f), which is similar to the unrubbed area (Fig. 3d)\(^{40}\). In contrast, the wear track of neat PAO and 5 wt% octanol exhibit a distinctive iron oxide from depths of 0 to 36 nm (Fig. 3e, Fig. S20)\(^{41-43}\). These results indicate that 5 wt% DOM forms a carbon tribofilm without an oxidation layer on top of the steel substrate. This tribofilm is approximately 30 nm thick and effectively reduces friction and wear. Conversely, 5 wt% octanol and neat PAO form a thick iron oxide film during rubbing action (Fig. S21), which cannot reduce friction or wear. This finding is consistent with the Raman and FTIR spectra. Note that the absence of oxidation in the
+case of DOM enables nascent iron atoms in steel to catalyze DOM molecules more effectively and hence ensure more effective carbon-based tribofilm formation.
+
+The cross-sectional view of the tribofilm formed by 5 wt% DOM was observed using transmission electron microscopy (TEM). A typical tribofilm with a thickness of 30 nm is observed between the Cr top-coating and steel substrate (Fig. 4a), and the thickness matches well with the XPS carbon concentration depth profile in Fig. 3a. Notably, some layered material is observed inside the tribofilm (Fig. 4b), and its lattice fringe spacing distance is approximately 0.39 nm, which is close to the theoretical value of graphene (which is 0.34 nm^{44}). EDS elemental mapping images and line scanning show that this tribofilm is rich in carbon (Fig. 4e,f), and its carbon K-edge electron energy loss spectroscopy exhibits typical \( \sigma^* \) and \( \pi^* \) state (Fig. 4c), corresponding to sp^{3} and sp^{2} bonding^{45, 46}. Thereby, combined with the Raman and FTIR results, it can be inferred that this tribofilm consists of graphitic carbon. Additionally, the STEM image and corresponding EDS spectrum show that some iron are also atomically distributed inside the tribofilm (red circles in Fig. 4i), suggesting the iron single atoms formation^{47}. The extended X-ray absorption fine structure (EXAFS, Fig. 4k, l, Fig. S22, S23) further reveal that the iron single atoms bond with surrounding atoms in the form of -C-O-Fe, which favors their stabilization in the carbon tribofilm. Note that the iron single atoms formation under mechanochemistry effect has been reported in a ball-milling experiment before^{48}, but to the best of our knowledge, this is the first time to observe their formation from a bulk metal during a macroscopic tribological test. The iron single atoms probably arise from the wear debris generated during rubbing and are formed under the mechanochemistry^{48}. Here, we propose that iron single atoms were largely responsible for the continuous catalysis of DOM molecules leading to graphitic carbon formation, which will be further discussed in the subsequent section.
+
+The effect of molecular structure on mechanochemistry
+
+The above experiments demonstrate a better tribological performance for DOM than other additives tested. This is ascribed to the much stronger adsorption of DOM on steel surfaces compared to other additives such as octanol, as well as the increased chemical reactivity of DOM to steel surfaces. These attributes can be demonstrated further by the quartz crystal microbalance with dissipation monitoring (QCM-D, Fig. S24, S25), and the energy gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) calculated by first principles (Fig. S26).
+
+Usually, the tribochemical reaction of graphitic carbon formation can be initiated by the free radicals^{49, 50}, which were easily generated during the rubbing process^{51, 52}. Therefore, this sheds light on the main question raised by this work, i.e., which bond(s) in DOM dissociate first, consequently leading to the formation of the free radicals that initiate the graphitic carbon film formation process? In the case of DOM, considering the lower dissociative energy of the C-C bond compared to the C-H bond, the C-C bond might be more readily dissociated, thus forming free radicals that initiate the tribochemical reactions. Meanwhile, the dissociative energy of one chemical bond can also be influenced by the adjacent groups since these groups affect the stability of generated free radicals through the lone pair effect and/or
+hyperconjugation effect \(^{53}\). Therefore, it is conceivable that the C-C bond between the hydroxyl-bonded carbon and ester group carbon is the easiest to dissociate, leading to the formation of free radicals as follows,
+
+![Reaction scheme showing the dissociation of a diester under friction, resulting in free radicals](page_184_276_1207_180.png)
+
+It is noted that the oxygen from both the hydroxyl side and ester side (the above red atoms) have two lone pairs of electrons which can donate electron density to the half-empty p orbital of carbon radicals. Since carbon radicals are electron deficient species, the electron-donating effect from lone pair electrons help to stabilize them, known as the lone pair effect\(^{53}\). As a result, the stabilized free radicals can further propagate the tribochemical reactions to form the graphitic carbon\(^{49}\). To verify this point further, the tribological properties of diester with different chain lengths (Table 1) but similar structure to DOM have been investigated, as shown in Fig. 5. The tribological tests of diesters inlucluding dioctyl malonate (DOT), dioctyl fumarate (DOF), dioctyl adipate (DOA), dioctyl sebacate (DOS), didodecyl succinate (DOSN) were all carried out under 36 N at 30 °C.
+
+Table 1. The molecular structure of diesters derived from different length of carboxylic acids (\(n_c\)) and different length of alcohols (\(n_a\))
+
+The diester derived from short-chain carboxylic acid (DOT, DOF in Fig. 5a-b, Fig. S27 ~ 28) exhibits lower friction (0.12 ~ 0.13) and wear (210 \( \mu \)m) compared to that from long-chain carboxylic acid (DOA, DOS in Fig. 5a-b, Fig. S27 ~ 28). Moreover, a distinctive grey island tribofilm, composed of graphitic carbon with a low Young’s modulus, is observed on wear track formed by diesters derived from short-chain carboxylic acid (DOT, DOF, Fig. 5d ~ g, Fig. S29 ~ 33), a feature not present on the diesters derived from long-chain carboxylic acid (DOA, DOS). Note that the low friction coefficient and wear track width are usually accpmpanied with the formation of grey island tribofilm with low Young's modulus (Fig. 5c, Fig. S29 ~ 31), further implying that this carbon film contributing to the superior tribological performance at macro scale. In addition, the diester derived from short-chain carboxylic acid but long-chain alcohol can also provide low friction, wear, and graphitic carbon formation (DOSN in Fig. 5). Therefore, it can be proposed that for diester derived from short-chain carboxylic acids, the free radicals generated on both sides after C-C bond dissociation can be stabilized by the oxygen from the each side of the discsoaited bond through lone pair effect (indicated by red oxygen atoms in DOT, Fig. 5j). This stabilization facilitates the initiation of tribochemical reactions. In contrast, for diesters derived from long-chain carboxylic
+acids, only one side of the generated free radicals can be stabilized by the oxygen from the ester group (DOS, Fig. 5j). The other side is unable to achieve stabilization due to the significant distance between free radicals and oxygen atom, resulting in a high dissociation energy that impedes the effective initiation of reactions. Hence, it can be concluded that the free radicals stabilized by lone pair effect contribute to lower bond discossiation energy, thereby triggering tribochemical reactions that lead to the formation of graphitic carbon and the reduction of friction and wear.
+
+The effect of tribopairs on mechanochemistry
+
+The chemistry of rubbing surfaces can have a strong influence on the formation of tribofilms. When both the top balls and bottom discs were made of Si3N4 (Fig. S34a,b), sapphire (Fig. S34c,d), glass (Fig. S34e) or Diamond-like Carbon coated steel (DLC) (Fig. S34f), 5 wt% DOM in PAO could not reduce friction. Nevertheless, once the bottom disc specimen is replaced by steel, 5 wt% DOM showed considerably lower friction and wear (Fig. 6a, b), and a graphitic carbon tribofilm was formed once again on the steel surface (Raman in Fig. 6a, b). This suggests that steel (or iron in steel) is an essential requirement for graphitic carbon formation, which might be attributed to its catalytic effects54. Considering that the catalysis process is an interfacial phenomenon that occurs at the solid-liquid interface, once a tribofilm with a thickness of a few nanometers covers the steel surface, it prevents the interaction between the metallic tribopair surface and liquid lubricant (Fig. 6c); hence, it cannot grow beyond to a thickness of about 30 nm. Nevertheless, in this study, the iron single atoms observed in TEM (red circles in Fig. 4i) were in-situ generated during the rubbing process and were then incorporated into the graphitic carbon tribofilm (Fig. 6d). Consequently, the iron single-atom catalyst found in tribofilm can maintain the solid-liquid interaction with DOM molecules and therefore continuously catalyze them to produce graphitic carbon tribofilm to a thickness of 30 nm (Fig. 4a, Fig. 6e).
+
+To elucidate the atomistic mechanism governing the tribofilm formation on various surfaces, ReaxFF reactive molecular dynamics simulations were conducted with initial configurations comprising DOM molecules sandwiched between sliding tribological interfaces (see Fig. S35). Notably, the release of hydrogen atoms from the DOM molecules on the Fe (110) surface was observed at the beginning of the simulation (Fig. 7b). Remarkably, more than 80% of the C-H bonds dissociate within 1200 ps, as depicted in Fig. 7d. Consequently, most of the released hydrogen atoms recombine to form H2 molecules, as illustrated in Fig. 7e. As a result, multi-membered carbon rings gradually form on the iron surface (Fig. 7c), eventually leading to the reconstruction of a large-scale defective or disordered graphene-like structures 55, 56. In contrast, the dehydrogenation of DOM on the SiO2 (001) surface occurs at a significantly lower rate (< 15% within 1.25 ns, Fig. 7d), resulting in no/little H2 and multi-membered carbon rings formation (Fig. 7c, Fig. S36), which is consistent with the experimental results on glass discs surfaces (Fig. S34e). Thus, the atoms on the steel surface, as catalysts, expedite the dehydrogenation process of DOM, thus facilitating the formation of graphitic carbon.
+
+Conclusion
+Containing no heavy metal or sulfur and phosphorus, the diesters in this work, typically DOM, are green and highly effective anti-friction and anti-wear additives under extreme loading conditions and in ultra-low viscosity oils, like PAO2. Compared to other additives (i.e., octanol, oleic acid, GMO, and ZDDP), DOM lowers friction by as much as 50% and reduces wear by up to 80% compared to common additives that have been used by industry for many decades. Its superior tribological performance is attributed to the in-situ formation of a graphitic carbon tribofilm on rubbing steel surfaces. This tribofilm, with a low Young’s modulus and shear strength, prevents direct metal-to-metal contact hence reducing friction and wear. This film tends to form from diesters derived from short-chain carboxylic acid due to their lone pair effect, which stabilizes the carbon free radicals. Furthermore, this graphitic tribofilm can only form on steel surfaces, suggesting that the catalytic reactivity of the iron single atoms is essential for its continuous generation during sliding. This concept shown here provides a novel strategy for the design of effective and sustainable anti-friction and anti-wear additives (like DOM) for future tribological systems in industrial applications.
+
+Declarations
+
+Competing interests
+
+The authors declare no competing interests
+
+Additional information
+
+Supplementary information. The online version contains supplementary material available at XXX
+
+Correspondence and requests for materials should be addressed to Jinjin Li, or Weiwei Zhang
+
+Author contributions
+
+Wei Song, Janet S. S. Wong and Jinjin Li conceived the idea of the work. Wei Song and Chongyang Zeng performed tribological tests, AFM test and surface analysis. Wei Song, Chuke Ouyang, and Shouyi Sun performed the formal data analysis. Jinjin Li, Janet S. S. Wong, and Jianbin Luo supervised this work and made the writing review & editing. Weiwei Zhang and Xing Chen performed the simulation work. All authors discussed the results and assisted with paper preparation.
+
+Acknowledgements
+
+The authors greatly appreciate Ms Zhiying Cheng for her invaluable help on single atoms analysis through STEM, and also appreciate Miss Yimai Liang, Ms Rong Wang and Ms Weiqi Wang for their tremendous experimental assistance and data interpretation on white light interferometry, FIB and AFM
+experiments. This work was supported by National Key R&D Program of China (grant numbers: 2020YFA0711003), National Natural Science Foundation of China (grant numbers: 52175174 and 52205202) and Postdoctoral Science Foundation of China (No. 2022TQ0177).
+
+Data availability
+
+The data that support the finding of this study are available within the paper and its Supplementary Information, or are available from the figshare data repository (XXXXX) under XXXXX.
+
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+
+Figures
+Figure 1
+
+Tribological performance of PAO with various additives. (a) Molecular structure of the additives. (b) Schematic of a ball-on-disc tribometer with the reciprocating mode. The test details are in the tribological test section in Supplementary Information. (c) Friction coefficient of neat PAO and PAO containing various additives, including 5 wt% octanol, 5 wt% DOM, and 5 wt% OA. The test was conducted under 36 N at 30 °C, and the stroke length was 1 mm with a frequency of 10 Hz. The break in Y axis is from 0.005 to 0.09. (d) Height profiles (position marked in Fig. S5), and (e) optical images of wear tracks on discs lubricated by neat PAO, 5 wt% octanol in PAO, and 5 wt% DOM in PAO. (f) Wear volume of the balls lubricated by different lubricants. The calculation of wear volume calculation is in the tribological test section in Supplementary Information. (g) The friction coefficient of neat PAO and 5 wt% DOM in PAO under a load increasing stepwise from 36 to 176 N. The load increased by 20 N per 5 min,
+as shown in the blue curve. (h) Friction coefficient of 5 wt% DOM and its surface coverage of islands versus time. The calculation of surface coverage can be found in Fig. S13c.
+
+![Nano-mechanical and surface chemical analysis on the wear track formed by 5 wt% DOM. (a) Optical microscopy image of wear track. The three marked areas are denoted as on island area inside wear, no-island area inside wear, and unrubbed area, where indentation and AFM tests were performed. (b) Load-depth curves during the indentation tests on three areas in (a). (c) AFM frictional force on a 10 μm × 10 μm island area during a rubbing test repeated 110 scan number. The insets are the AFM friction images at 1st and 110th scanning. (d) Force–distance curves and (e) histogram of the pull-off force when the AFM tip retracted from the three areas in (a). (f) Raman and (i) FTIR spectra on wear tracks compared to those of other additives. (g) Optical microscopy images of wear track and (h) the corresponding Raman G band intensity mapping images.](page_97_120_1386_1402.png)
+
+Figure 2
+
+Nano-mechanical and surface chemical analysis on the wear track formed by 5 wt% DOM. (a) Optical microscopy image of wear track. The three marked areas are denoted as on island area inside wear, no-island area inside wear, and unrubbed area, where indentation and AFM tests were performed. (b) Load-depth curves during the indentation tests on three areas in (a). (c) AFM frictional force on a 10 μm × 10 μm island area during a rubbing test repeated 110 scan number. The insets are the AFM friction images at 1st and 110th scanning. (d) Force–distance curves and (e) histogram of the pull-off force when the AFM tip retracted from the three areas in (a). (f) Raman and (i) FTIR spectra on wear tracks compared to those of other additives. (g) Optical microscopy images of wear track and (h) the corresponding Raman G band intensity mapping images.
+Figure 3
+
+Surface topography and chemical analysis on wear track. (a) Carbon, (b) oxygen, and (c) iron atomic concentration at different depth, obtained by XPS sputter test on wear track of different additives. High-resolution XPS spectra of C1s in wear track formed by (d) unrubbed area, (e) neat PAO, and (f) 5 wt% DOM in PAO after normalization. (g) Cross-sectional TEM image of the wear track formed by 5 wt% DOM. (h) HRTEM and (i) high-angle annular dark field STEM (HAADF-STEM) image of the tribofilm area in (a). The inset in (h) is the lattice fringe spacing obtained from the red row. (j) Electron energy loss spectroscopy (EELS) spectrum, (k) Fourier transformation (FT) of k2-weighted extended X-ray absorption fine structure (EXAFS) spectra of Fe foil, Fe$_2$O$_3$, Fe$_3$O$_4$ and the tribofilm formed by 5 wt% DOM. (l) Wavelet transforms (WTs) for the k2-weighted EXAFS signals from the tribofilm formed by 5 wt% DOM.
+Figure 4
+
+Tribological performance and surface analysis on wear track of additives with different chain lengths. (a) Molecular structure of dioctyl malonate (DOT), dioctyl fumarate (DOF), dioctyl adipate (DOA), dioctyl sebacate (DOS), didodecyl succinate (DOSN), (b) friction coefficient, (c) optical image of wear track before rinsing, (d) magnified optical image of wear track after rinsing, (e) Raman spectra on wear track, (f) Raman G band mapping image, (g) load-depth curves during indentation tests on wear track formed
+by additives with different chain lengths. (h) The proposed free radical generation mechanism of DOT and DOS during friction. The scale bars in (d)(f) are 25 μm.
+
+![Schematic of the structural evolution of the DOM molecules confined between two Fe (100) surfaces. (a) at 0 ps; (b) at 600 ps; (c) at 1200 ps. The number of (d) C-H bonds, (e) H-H bonds and (f) carbon rings,](page_184_312_1207_1092.png)
+
+Figure 5
+
+Schematic of the structural evolution of the DOM molecules confined between two Fe (100) surfaces. (a) at 0 ps; (b) at 600 ps; (c) at 1200 ps. The number of (d) C-H bonds, (e) H-H bonds and (f) carbon rings,
+throughout the simulation where the DOM molecules are confined between two Fe (110) and SiO_2 (001) surfaces.
+
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SI.docx

0845528f7ce8151c643f7cfb0afbbb91c8fd501364586b8b087110447c3361d9/peer_review/peer_review.md

@@ -0,0 +1,445 @@
+Peer Review File
+
+Route-Centric Ant-Inspired Memories Enable Panoramic Route-Following in a Car-like Robot
+
+Corresponding Author: Mr Gabriel Gattaux
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Attachments originally included by the reviewers as part of their assessment can be found at the end of this file.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+In this article the authors present an ant-inspired method for visual homing using the Antcar robot. The method uses a mushroom-body-inspired neural network that is capable of one-shot route learning. Several experiments have been conducted that show the robot's ability to robustly retrace the learnt path.
+
+The article is well written and the experimental results and their similarity to ant behavior are impressive. However, after reading through some of the references I find that the article does not make clear enough what its contributions are compared to what has already been published. How learning using a mushroom body network works is explained in a previous publication by the authors [21]. Learning by in-silico rotations of the panoramic images and categorizing the views into left and right memory seemed to me to be one of the novelties of this paper, but has also already been introduced in a previous publication by the authors [44]. Thus, using two additional MBONs for the start and end of the routes, and the adaption of velocities based on the familiarity of the views seems to be the only original contribution - plus the experimental results and analysis of implementing the method on the Antcar robot. Nevertheless, if the goal of this article is to summarize all the previous work and bring it to a level of maturity showing its real-world application in robotic route following, this is a justifiable reason for publication. However, as already said, it should be made more clear what the previous work was (and was only recapitulated for completeness) and what the novel contributions are. Furthermore, if this article should provide a complete overview of the system, as a reader not familiar with the mushroom body concept, I would have wished to find a more detailed description of how learning in MB works, similar to what was shown in [21].
+
+Some minor remarks:
+1. The word "Navigation" in the title is a bit misleading. The presented method only does route learning and route following, which is only a sub area of robot navigation. I find that the words "Homing" or "Route Following" would be a better choice.
+2. I find the terms "convex" and "concave" routes not appropriate for a right-turning and a left-turning path. To decide if something is convex or concave, a reference point is required (e.g. the center of a geometric shape), but in this case there is no such reference point.
+3. I have never heard of Mo as a unit for computer memory. I suggest to use MB (Megabytes) as it is a more commonly used and understood unit.
+4. I'm in doubt of the scalability of the method. If I understood correctly, the number of Kenyon cells is linked to the capacity of the memory, and, thus, the length of the route to store. So this number must be chosen large enough to contain the full path, whose approximate length (or rather, the number of distinct panoramic images) must be known in advance. A larger number of KC also means a larger PNIoKC matrix, which will cause longer computation times during learning and also during homing. Thus, only extrapolating the memory footprint to a longer path is not sufficient, but it should also be taken into account how the run times during learning and route-following increase for longer paths (or rather, longer "expected" paths, as the number of KC is chosen in advance).
+
+The provided video is a very nice summary of the article and gives a good impression of the experiments. I highly encourage to also publish code of the method's implementation.
+
+(Remarks on code availability)
+Reviewer #2
+
+(Remarks to the Author)
+The paper is easy to read and well structured. It presents very interesting results related to ant-based mobile robot navigation. The paper makes several important contributions. Firstly, it introduces an original and simple model that explains how ants can navigate using only visual information. A key characteristic of this model is its ability to effectively utilize low-resolution visual information processed by a small neural network, while also enabling online learning. Secondly, these characteristics enable the implementation of an efficient solution on a small embedded computer (Raspberry Pi 4 with ROS) for onboard robot control. Thirdly, the paper includes numerous robotics experiments to evaluate the performance of the proposed solution.
+The video illustrates nicely the work done and the potential of the proposed approach.
+This research has the potential to interest a wide readership and I believe it is suitable for publication in Nature Communications.
+In the following sections, I have tried to provide detailed comments to ensure my understanding of the work. To enhance accessibility for a broader audience beyond your specific field, please provide full explanations for all acronyms used throughout the paper. I also recommend maintaining consistent naming conventions for variables and parameters across figures and equations. Furthermore, the Materials and Methods section, and complementary results document, should include the equations describing the different layers of the network (PN, EP, AP, etc.) and the corresponding values of the synaptic weights.
+Also, figure S7 should be moved in the paper. It provides interesting details for a better understanding of the NN structure and functioning.
+A critical factor contributing to the success of this approach, in my view, lies in the intricate interplay between the “controlled oscillation amplitude during learning”, the neural network (NN) update frequency, and the dynamic changes in panoramic information resulting from the randomization process between PN and EP, termed PN to KCr (for consistency, I recommend adhering to a uniform naming convention throughout the manuscript). The equations governing the neuronal activity (and neuron connectivity) within this specific component should be explicitly presented. I believe these equations are important for a comprehensive understanding of the model, potentially exceeding the significance of the Lyapunov stability analysis in the context of this particular paper.
+In the detailed comments related to the discussion section, I have also included specific questions that I believe can further enhance the clarity and impact of the paper.
+
+Detailed comments:
+
+Line 99: “…leading to a self-supervised model for route learning”.
+This sentence and the relationship with the previous sentence is a little bit cryptic. I think you should be more explicit in your explanation of the Link with dopaminergic feedback and the self supervision. I am not sure to understand (see also my next comment).
+
+Figure 2 legend: Dopaminergic-like Neurons (DAN)
+I failed to find it in the figure while I really wanted to understand how it was implemented:
+1) what are the input to DAN?
+2) what are the synapses modified by DAN? From what I understood from the method part only the direct connections between EP (the output of the k-WTA) and the Mushroom Body Output Neurons (MBON) are modified.
+Reference [44] is not about dopamine in insect brain and is a preprint. Can you provide validated works or be more explicit about the status of this information?
+Page 3: You are providing results about differential familiarity. If I understand correctly this was computed from 2 MBON outputs. What is the familiarity measure between the raw visual input and how does this familiarity measure evolve across the different stages of the processing pipeline? I am particularly interested in understanding whether the learning process itself leads to an improvement in this familiarity measure. To avoid a long discussion and analysis of the data, a concise summary of your findings or insights regarding the evolution of this familiarity measure throughout the neural code-building process would be greatly appreciated
+Figure 4 a and b. It is not clear if both routes were learned in the same network. If yes, why a strong preference for the back trajectory? I cannot understand this result if an omnidirectional camera is used. So I suppose the results are related to 2 different experiments. If it is correct, you should state it explicitly (and it is ok on my side). In this case, Is it possible to teach your robot two different routes in the same network? Would it be compatible with ants capabilities? It would be a useful feature for a mobile robot. What could be your solution? Could it introduce an issue for the stabilization of the code?
+Line 255: If I understand correctly the error can be about 0.5m. While it can be ok for some robotics applications, is it compatible with ant navigation and ant size?
+MAD acronym is not explained. Is it Mean Absolute Deviation?
+Figure 5: It would be interesting to have a map of the environment or a classical picture to see the difficulty of the navigation task (is it a part of the trajectory we can see in the video?). Here it looks like the test was only done on a 2 segments trajectory with a 90 degrees rotation. One true long-distance navigation in a natural environment (not following human routes would be really convincing).
+Discussion section:
+Could you discuss the limitations of omnidirectional cameras? My personal experience showed a high sensitivity to horizontal planarity since the image deformation is clearly not linear if the camera is tilted. What would happen on a non-flat
+surface? How are insects solving this issue? Do you suppose they are using vestibular information to rotate images? Some comments might be useful.
+If we follow your model, there is no internal neuronal feedback except the Dopamine signal. Is the biological network only feedforward? Could feedback connections provide alternative solution to introduce attentional mechanism or more dynamics code, predictive coding...?
+Line 414: I am not sure you can compare your experiment with the ones done with autonomous cars. You should provide a test with a classical dataset used with autonomous vehicles to write that (for instance Milford database used for Ratslam or any more recent database). It would be very interesting but because your results rely on omnidirectional cameras while usually autonomous vehicles are using classical camera with limited field of view, I believe the comparison will be difficult (strong difficulties are related to the limited field of view of the camera). Perhaps reducing your claim here would be simpler.
+
+Line 428: When you compare to visual compass you are forgetting that instead of performing 'n' comparisons, it is possible to use the prediction of the compass orientation associated to different local visual features to deduce the global rotation of the image according to any absolute direction without the need to perform 'n' tests. See for instance: Giovannangeli, C., & Gaussier, P. (2007). Orientation system in robots: Merging allocentric and idiographic estimations. In 13th International Conference on Advanced Robotics (ICAR07) or Delarboulas, P., Gaussier, P., Caussy, R., & Quoy, M. (2014). Robustness study of a multimodal compass inspired from hd-cells and dynamic neural fields. In From Animals to Animats 13: 13th International Conference on Simulation of Adaptive Behavior, SAB 2014. Proceedings 13 (pp. 132-143). Springer International Publishing. Of course this solution is related to mammal visual system.
+
+Line 439: "latent learning [53]" please avoid preprint. The paper is not providing much details about the model results answering the questions I had.
+Line 450: "fudnamentally": typo issue
+Line 564: The EP vector size was set to u = 15, 000 and κ = 0.01. Is there a relationship between the size of the code k-wta parameter and the length of the trajectory the robot could follow without error. An optimistic boundary could be the number of vectors that can be built using the k-WTA constraint. But because you are pruning connections with your anti hebb learning rule to obtain an efficient code I suppose the number of usable codes is reduced. Yet, the paper is not providing any clue to understand what is the maximum length of the route that can be learned according to the visual environment before two different visual environments cannot be discriminated because they will get the same signature. Perhaps I am wrong. Can you discuss a little bit this point in your paper?
+
+Line 584: "specified vector". The term is unclear for me. Could you be more explicit to avoid any confusion (is it AP or MBON ?)
+Line 601: CSR format: is it Compressed Sparse Row (CSR)?
+Line 642: section “Theoretical analysis of the robot stability”
+I don’t have the feeling this part is really relevant in the present paper. It would be more interesting in a specialized journal in robotics.
+The video shows results of robot experiments on different days. That is nice but since the shadow angles are the same, I suspect the experiment was done almost at the same hour. Would your results be robust to a change of sun position? Is it something ant could do? I am confused here thinking about ant using light polarity to build a visual compass and also the fact that in some experiments it is shown that ants were sensitive to sun position. Could it be a limitation of your approach for some robotics applications? Multiple S trajectories in offroad conditions (open field) would be more interesting to show if the robot can follow a complex trajectory.
+
+(Remarks on code availability)
+It would be difficult to review the source code without the robot to perform relevant tests and it would be very long to do (not a classical review work). Yet, the video shows convincing arguments in favor of the work done as well as the experimental results provided.
+
+Reviewer #3
+
+(Remarks to the Author)
+The work proposes a self-supervised, ant-inspired navigation system, which has been implemented on the Antcar robot. The main result is the robust route-following capability that has been implemented using a neuromorphic, mushroom body-inspired network using minimal memory at 148 kilobits at 62ms. This system also allows the robot to perform homing and shuttling behaviour for the fixed route. These results demonstrate the applicability of the bio-inspired approach to achieve visual navigation using limited computational resources.
+The lateralized memory model and its implementation of low-resource computation are original and significant contributions. The combination of the selected robotic platform and the biological inspiration derived from ants is not particularly novel but is still significant.
+
+The methodology is clear and detailed, with transparent data presentation. The kinematic model and the Lyapunov stability analysis add rigour to the experimental results. The explanations for the image processing and design of the control algorithm are clear and explained well. The addition of the obstructions present along the path to the 2-dimensional trajectory plots would help interpret them better.
+
+Demonstrating similar performance across different experimental routes or configurations, particularly head-on obstructions
+and sensitivity to their size in the visual field, would add to the results and better justify the validity of the approach.
+
+Suggested Improvements:
+
+1. Experimental Additions: Test the model in more diverse environments and specify the nature and sensitivity of the occlusion and kidnapped scenarios.
+
+2. Figures and Supplementary Materials: The addition of the obstacles along the path traversed in the 2-D plots seen in Fig. 4a-f would aid the clarity.
+
+(Remarks on code availability)
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+My comments from the first review have been addressed well, thank you! I just have some additional minor remarks:
+
+The new section "Memory Capacity" is not clear, because it only shows how the P_I_error is computed, but does not give information about how that relates to memory capacity. It gets more clear in previous explanations in "Steering memory capacity" and Fig. 9. Maybe the headline of this section is misleading, because it should only show how P_I_error is computed?
+
+In the Supplementary Notes, in Table S1, second table there is still "Convex&Concave" mentioned, which should be replaced by Route 1&2.
+
+- line 87: missing word? "around nest position"
+
+- inconsistent capitalization of "Nest" and "Feeder" throughout the paper
+
+- Caption of Fig. 2: "An panoramic camera" should be "A panoramic camera"
+- Caption of Fig. 2: "phases.a" - missing whitespace
+- Caption of Fig. 2: "An in silico scan (simulated image rotation) generate image with angular error (θ*e)" - missing word?
+
+(Remarks on code availability)
+
+Reviewer #3
+
+(Remarks to the Author)
+Overall the authors have addressed my concerns to a satisfactory extent
+
+(Remarks on code availability)
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+First and foremost, the authors wish to thank Reviewers #1 #2 and #3 for having evaluated our study, and for their valuable comments to improve it.
+
+Our answers and comments will be written here in blue, we have attached the revised manuscript, the supplementary materials, and a tracked version of the manuscript and supplementary. In this tracked version, deleted text is shown in red with strikethrough, and added text is shown in blue for clarity.
+
+Reviewer #1 (Remarks to the Author):
+
+Reviewer #1 : In this article the authors present an ant-inspired method for visual homing using the Antcar robot. The method uses a mushroom-body-inspired neural network that is capable of one-shot route learning. Several experiments have been conducted that show the robot's ability to robustly retrace the learnt path. The article is well written and the experimental results and their similarity to ant behavior are impressive.
+
+However, after reading through some of the references, I find that the article does not make clear enough what its contributions are compared to what has already been published.
+  1) How learning using a mushroom body network works is explained in a previous publication by the authors [21].
+  2) Learning by in-silico rotations of the panoramic images and categorizing the views into left and right memory seemed to me to be one of the novelties of this paper, but has also already been introduced in a previous publication by the authors [44].
+  3) Thus, using two additional MBONs for the start and end of the routes, and the adaption of velocities based on the familiarity of the views seems to be the only original contribution - plus the experimental results and analysis of implementing the method on the Antcar robot. Nevertheless, if the goal of this article is to summarize all the previous work and bring it to a level of maturity showing its real-world application in robotic route following, this is a justifiable reason for publication. However, as already said, it should be made more clear what the previous work was (and was only recapitulated for completeness) and what the novel contributions are.
+
+Authors : Thank you for emphasizing the importance of clearly distinguishing our novel contributions from foundational work. We have revised the title, abstract and introduction (Line 112) to clarify how this paper significantly advances the state of the art, this modification led to an important scientific improvement.
+
+    While prior work [21] introduced a one-MBON visual route following model, it was limited to indoor use, a single neuron output, and did not incorporate lateralization, route direction, or bidirectional learning as well as offered very limited performance. The work in [44], meanwhile, relied on a particle-simulated agent (without complex dynamics), modelling nest-centric lateralization based on global goal position (e.g., the nest) using physical body oscillations, and was restricted to visual homing: not continuous route following or curved paths.
+In contrast, our work introduces a route-centric lateralized architecture, where categorization of visual input is tied to local route, enabling the learning and robust reproduction of curved and bidirectional routes as ants can do. To our knowledge, this is the first time such a model has been both proposed and physically implemented in a real-world robotic platform. Furthermore, we introduce:
+– Two additional MBONs enabling extremity recognition and bidirectional route use (By motivation triggering, biologically referenced but never modelized)
+
+– A familiarity-based velocity adaptation mechanism (novel both biologically and computationally)
+
+– A formal stability proof of oscillation-based learning
+
+– A new empirical metric for evaluating memory scalability
+
+– And extensive real-world validation across 1.6 km and 113 autonomous trajectories, far exceeding the scope of earlier works.
+
+In short, this paper is not a mere summary, but a substantive advancement combining novel biological insights, theoretical formalization, and practical implementation, bringing insect route following from behavioral observations to robust robotic deployment. Thus, significantly advancing the state-of-the-art in neuromorphic robotics and bringing insights into insect navigation.
+
+Reviewer #1 : Furthermore, if this article should provide a complete overview of the system, as a reader not familiar with the mushroom body concept, I would have wished to find a more detailed description of how learning in MB works, similar to what was shown in [21].
+
+Authors : Thank you for expressing the need for a more detailed explanation of learning in the mushroom body. In response to your comment, we have:
+1. Added a New Supplementary Note (Note 5). This note provides an expanded description of the image-processing pipeline, clarifying how raw panoramic images are converted into the Projection Neuron (PN) vector before entering the Mushroom Body (MB) network.
+2. Included detailed equations in “Methods” section. We now explicitly show the transformations from the PN to the Action Potential (AP) vector and describe how synaptic weights (KC-to-MBON) are updated during learning (Line 708). These added equations and comments should make the learning mechanism clearer to readers who may be unfamiliar with MB-based approaches.
+3. Simplified and added the previous Supplementary Fig. S7 to the main paper as Fig. 10 in method.
+
+With these additions, we believe the manuscript now offers a more comprehensive overview of the mushroom body-inspired learning process with a great formalism, higher in level of detail to what was presented in reference [21]. We appreciate your comments, which helped us identify and address this need for greater clarity.
+Reviewer #1 : Some minor remarks:
+1) The word "Navigation" in the title is a bit misleading. The presented method only does route learning and route following, which is only a sub area of robot navigation. I find that the words "Homing" or "Route Following" would be a better choice.
+2) I find the terms "convex" and "concave" routes not appropriate for a right-turning and a left-turning path. To decide if something is convex or concave, a reference point is required (e.g. the center of a geometric shape), but in this case there is no such reference point.
+3) I have never heard of Mo as a unit for computer memory. I suggest to use MB (Megabytes) as it is a more commonly used and understood unit.
+4) I'm in doubt of the scalability of the method. If I understood correctly, the number of Kenyon cells is linked to the capacity of the memory, and, thus, the length of the route to store. So this number must be chosen large enough to contain the full path, whose approximate length (or rather, the number of distinct panoramic images) must be known in advance. A larger number of KC also means a larger PNtoKC matrix, which will cause longer computation times during learning and also during homing. Thus, only extrapolating the memory footprint to a longer path is not sufficient, but it should also be taken into account how the run times during learning and route-following increase for longer paths (or rather, longer "expected" paths, as the number of KC is chosen in advance).
+
+Authors : Thank you for emphasizing those comments :
+1. Title: “Navigation”. Thank you for this suggestion, to better reflect our focus on our contributions and route learning and following, we have changed the article title to: “Route-Centric Ant-Inspired Memories Enable Panoramic Route-Following in a Car-like Robot” We believe this title more precisely conveys the scope of our work.
+2. “Convex” and “Concave” Routes. We agree that “convex” and “concave” can be indeed confusing in this context. We have replaced these terms with route 1 and route 2 to avoid ambiguity (not left or right because in the second route, there is a right and a left turn).
+3. Memory Unit “Mo”. We have updated all references to memory units to the more standard megabytes or kilobytes for clarity (in plain word to avoid misinterpretation with Mushroom Body except in the abstract).
+4. On method scalability. We appreciate your concerns regarding the reliance on Kenyon Cells’ number for memory capacity. It is exact that if we expand the number of KCs, the computing time will expand as well (not only the size of the memory). To answer your questions and improve the paper, we defined a memory capacity metric based on our route-centric categorization technique. If the difference in familiarity between left and right memories is not the expected sign for a given view, an error variable is incremented (See added method section “Memory Capacity”). We tested the percentage of error arising as more views are learned (along a new dataset of 250m outdoor route) as a function of KC and k-
+WTA parameter, and we measured (or estimated beyond 250m) the maximum distance that the network can learn in this environment, when the error reached 1%. Note that this is a conservative metric, as 1% of error is surely acceptable for the robot to stay on route. We presented this analysis in a supplemental section in Results “Steering Memory Capacity”, and in the new Figure 9.
+Also, we now discussed this matter, and proposed another way to scale the route memory capacity for further works in the penultimate paragraph of the discussion (Line 640).
+
+Reviewer #1 : The provided video is a very nice summary of the article and gives a good impression of the experiments. I highly encourage to also publish code of the method's implementation.
+
+Authors : Thank you for your positive feedback on the video demonstration, we have modified the video to incorporate the new experiments. We appreciate your encouragement to share our implementation and we have made all real-time experiment data and offline analyses, including figure-generation code and the route-centric model, publicly available via the Figshare link and the CodeOcean capsule provided to Nature Communications. The ROS-based robot code will also be made available upon request to interested researchers who wish to replicate or extend our work in embedded robot. Overall, we believe that your comments improved the impact and details level of our manuscript.
+
+Reviewer #2 (Remarks to the Author):
+
+Reviewer #2 : The paper is easy to read and well structured. It presents very interesting results related to ant-based mobile robot navigation. The paper makes several important contributions. Firstly, it introduces an original and simple model that explains how ants can navigate using only visual information. A key characteristic of this model is its ability to effectively utilize low-resolution visual information processed by a small neural network, while also enabling online learning. Secondly, these characteristics enable the implementation of an efficient solution on a small embedded computer (Raspberry Pi 4 with ROS) for onboard robot control. Thirdly, the paper includes numerous robotics experiments to evaluate the performance of the proposed solution. The video illustrates nicely the work done and the potential of the proposed approach. This research has the potential to interest a wide readership and I believe it is suitable for publication in Nature Communications. In the following sections, I have tried to provide detailed comments to ensure my understanding of the work. To enhance accessibility for a broader audience beyond your specific field, please provide full explanations for all acronyms used throughout the paper. I also recommend maintaining consistent naming conventions for variables and parameters across figures and equations.
+
+Authors : Thank you for your positive feedback and for emphasizing the value of our results, particularly regarding our model’s simplicity, online learning
+capability, and efficient implementation on small embedded hardware. We have carefully reviewed our manuscript to ensure that all acronyms are spelled out at their first appearance and that variable/parameter names are consistently used across figures, equations, and text. We appreciate your attention to these details, which will help make our work more accessible to a broad readership.
+
+Reviewer #2 : Furthermore, the Materials and Methods section, and complementary results document, should include the equations describing the different layers of the network (PN, EP, AP, etc.) and the corresponding values of the synaptic weights.
+Also, figure S7 should be moved in the paper. It provides interesting details for a better understanding of the NN structure and functioning.
+
+Authors : Thank you for highlighting the importance of including detailed network equations and illustrating the neural layers (PN, EP, AP, etc.) in the main text. In response, we have made all the process clearer:
+  1. Supplementary Note 5 now details the image processing steps that convert raw images (I) into the Projection Neuron (PN) inputs.
+  2. We have also elaborated with detailed equation on the transformations from PN → EP → AP, followed by the anti-Hebbian learning in the KC-to-MBON synapses. The method section explicitly shows now how each memory vector is formed (learning), categorized (exploitation), and used (Control command).
+  3. We have simplified and added the previous supplementary Fig. S7 to the main paper as Fig. 10 in Method.
+
+These revisions provide a comprehensive view of the entire neural pipeline and clarify the underlying equations and parameters. We appreciate your comments, as it helped us enhance the accessibility and completeness of our methods.
+
+Reviewer #2 : A critical factor contributing to the success of this approach, in my view, lies in the intricate interplay between the “controlled oscillation amplitude during learning”, the neural network (NN) update frequency, and the dynamic changes in panoramic information resulting from the randomization process between PN and EP, termed PN to KCr (for consistency, I recommend adhering to a uniform naming convention throughout the manuscript).
+The equations governing the neuronal activity (and neuron connectivity) within this specific component should be explicitly presented. I believe these equations are important for a comprehensive understanding of the model, potentially exceeding the significance of the Lyapunov stability analysis in the context of this particular paper.
+
+Authors : Thank you for emphasizing the critical role of the “controlled oscillation amplitude” during learning, the neural network (NN) update frequency, and the ever-changing panoramic inputs in our model. In response to your comments, we have explicitly added the equations detailing neuronal activity and neuron connectivity (PN → EP → AP → \( \lambda \)) up to the control commands in the manuscript
+to ensure that readers can accurately replicate and understand the underlying computations (Line 708). We have standardized our naming for the relevant pathways (e.g., PNtoKC) to maintain consistency across the paper and supplemental materials, addressing your recommendation for a more uniform terminology. Furthermore, we have added the equations that describe the entire mechanism from the initial Image, to the Projection Neuron (In supplementary note 5), to the control command (In the main paper).
+
+Reviewer #2 : In the detailed comments related to the discussion section, I have also included specific questions that I believe can further enhance the clarity and impact of the paper. Detailed comments:
+1. Line 99: “…leading to a self-supervised model for route learning”. This sentence and the relationship with the previous sentence is a little bit cryptic. I think you should be more explicit in your explanation of the Link with dopaminergic feedback and the self supervision. I am not sure to understand (see also my next comment).
+2. Figure 2 legend: Dopaminergic-like Neurons (DAN). I failed to find it in the figure while I really wanted to understand how it was implemented: 1) what are the input to DAN? 2) what are the synapses modified by DAN? From what I understood from the method part only the direct connections between EP (the output of the k-WTA) and the Mushroom Body Output Neurons (MBON) are modified. Reference [44] is not about dopamine in insect brain and is a preprint. Can you provide validated works or be more explicit about the status of this information?
+
+Authors : Thank you for raising these points; we appreciate the opportunity to clarify our approach to self-supervision and the role of dopaminergic-like neurons in our model.
+1. We have revised the text around Line 188 to explicitly explain how our method leverages a self-supervised learning mechanism, and simplified the representation. The self-supervision is enabled thanks to the combination of the route-centric hypotheses, the in silico scanning during learning, and the fact that the robot current heading during learning is the route direction.
+2. On Dopaminergic-Like Neurons (DAN) and Model Representation. Indeed, In our current model, the learning occurs at the KC-to-MBON level, driven by the outcome of the k-WTA process on the EP output. While we discuss a dopaminergic-like role in categorizing left–right direction, we do not model explicit dopaminergic synapses at this stage. Instead, we draw an analogy to insect neurobiology, where dopaminergic neurons can modify synapses in response to internal “supervisory” signals. In the earlier version, we referred to Dopaminergic-Like Neurons (DAN) but did not explicitly depict them in the figure, as our current implementation does not model dopaminergic feedback in a fully neuronal way but in its functionality. To avoid confusion, we have moved the DAN mention into the Discussion, where we elaborate on potential biological parallels, citing notably two published papers from insect neurobiology (Line 611).
+We hope these clarifications resolve any confusion regarding the self-supervised aspect of the model and the role of dopaminergic-like neurons in our implementation. Thank you again for your thoughtful comments, which helped us present our framework and its biological parallels more transparently.
+
+Reviewer #2 : Page 3: You are providing results about differential familiarity. If I understand correctly, this was computed from 2 MBON outputs.
+    1. What is the familiarity measure between the raw visual input, and how does this familiarity measure evolve across the different stages of the processing pipeline?
+    2. I am particularly interested in understanding whether the learning process itself leads to an improvement in this familiarity measure.
+    3. To avoid a long discussion and analysis of the data, a concise summary of your findings or insights regarding the evolution of this familiarity measure throughout the neural code-building process would be greatly appreciated.
+
+Authors : Thank you for this comment, we hope we do understood well the question. We would like to clarify that familiarity in our model is explicitly computed only at the KC-to-MBON layer. At earlier processing stages (PN, EP, AP), there is no explicit familiarity measure (feedforward connections); rather, each layer provides progressively refined representations of the raw visual input, optimized for discriminating visual experiences.
+
+Even though familiarity itself is not explicitly computed at earlier stages, the learning process indeed leads to improved discriminability, indirectly enhancing the familiarity measure at the MBON stage. Initially, KC-to-MBON weights are uniformly set to one, yielding minimal discriminative power. Throughout learning (via anti-Hebbian synaptic depression), KC-to-MBON connections selectively deactivate, resulting in sparser, more distinctive memory patterns. This sparsification directly increases contrast between familiar and unfamiliar views, thus improving the sensitivity and robustness of the MBON familiarity measure.
+
+However, this learning process has a theoretical upper bound. Excessive sparsification—where all KC-to-MBON connections are eventually set to zero due to continuous learning—can lead to memory saturation (also known as "dramatic forgetting"). In this extreme scenario, familiarity loses discriminative power, as MBON outputs become zero for all inputs. Practically, we selected system parameters (e.g., KC number, k-WTA sparsity, realistic experimental route lengths) specifically to ensure this limit is not reached under normal operating conditions.
+
+We have highlighted these points in the revised manuscript. We have added the shape of raw familiarity in Figures 3a and b, and we showed the maximum and differential familiarity values in Figure 6. Also, we putted a little paragraph in Discussion (Line 632) to clarify the boundary conditions of our learning mechanism and a possible future approach. We have also added a memory capacity metric to show the boundary and future possibilities while keeping it stable within a similar environment.
+Reviewer #2 : Figure 4 a and b. It is not clear if both routes were learned in the same network. If yes, why a strong preference for the back trajectory? I cannot understand this result if an omnidirectional camera is used. So I suppose the results are related to 2 different experiments. If it is correct, you should state it explicitly (and it is ok on my side).
+
+Authors : Thank you for pointing out the potential confusion regarding Figures 4(a) and 4(b). We confirm that these results come from two distinct experiments. As now noted in the Figure 4 caption, the route 1 and route 2 (renamed for clarity) were trained and tested independently.
+
+Reviewer #2 : In this case, Is it possible to teach your robot two different routes in the same network? Would it be compatible with ants capabilities? It would be a useful feature for a mobile robot. What could be your solution? Could it introduce an issue for the stabilization of the code?
+
+Authors : Thank you for this insightful question. Indeed, it would be possible for our model to learn multiple distinct routes using a single pair of MBONs, provided that the combined error proportion (introduced in Figure 9, new result section “Steering memory capacity”, see Discussion, Line 640, and new Methods section “Memory Capacity”) across all learned trajectories remains below a critical threshold (e.g., ~1%). However, such an approach could pose significant challenges when routes overlap or intersect, potentially causing interference between memories and thus affecting route-following stability.
+
+A more robust solution, inspired by biological systems, would be to increase the number of MBONs. In nature, insects indeed learn multiple distinct routes, ants are known to learn and navigate multiple routes. Although the exact number of MBONs in ants is currently unknown, Drosophila have at least 34 MBONs, and bees have over 100 MBONs (added citations in revised manuscript, Discussion Line 662). Increasing the number of MBONs, therefore, would not only allow multiple distinct routes to be encoded reliably, but also improve memory capacity and avoid stabilization issues caused by overlapping routes.
+
+Practically, implementing multiple MBON pairs along with a mechanism (such as a sliding-window or context-based selection) to dynamically activate the appropriate MBON pair would ensure robust multi-route memory without compromising navigational stability. We have clarified these points explicitly in the revised manuscript (see updated Discussion, Line 666).
+
+Reviewer #2 : Line 255: If I understand correctly the error can be about 0.5m. While it can be ok for some robotics applications, is it compatible with ant navigation and ant size?
+
+Authors : Thank you for noting the 0.5m lateral error. Indeed, field studies (e.g., Kohler & Wehner, 2005; Mangan & Webb, 2012) showed that ants, which are only a few centimeters in size, could deviate by up to 0.5m from a familiar route, proportionally a very wide corridor. In our experiments, the 0.5m offset arises from factors such as the proximity and density of visual features, mirroring how ants’ navigation accuracy depends on environmental openness, repeated route
+experience, and individual variations. Consequently, when we consider the difference in physical body length (Cataglyphis velox 4.5~12mm and Antcar 240mm), our robot’s 0.5m lateral offset represents only 21% of its body length, whereas in ants, it represents 416% of their body length. This 0.5m lateral offset is therefore consistent with the relative corridor width that ants themselves tolerate, thereby aligning with the underlying biological inspiration.
+
+Reviewer #2 : MAD acronym is not explained. Is it Mean Absolute Deviation?
+
+Authors : Thank you for raising this point. Indeed, in our manuscript, MAD refers to Median Absolute Deviation. We ensured that this is made clearer in the revised version to avoid any confusion, it’s described in the first MAD apparition Line 250.
+
+Reviewer #2 : Figure 5: It would be interesting to have a map of the environment or a classical picture to see the difficulty of the navigation task (is it a part of the trajectory we can see in the video?).
+
+Authors : Thank you for the suggestion that enhanced the understanding and shape of the paper. We have now included images of the experimental environments in all figures (especially old Figure 5, new Figure 6) except for the homing and shuttling tasks, where the robot’s (Antcar) viewpoint is shown for completeness.
+
+Reviewer #2 : Discussion section:
+Could you discuss the limitations of omnidirectional cameras? My personal experience showed a high sensitivity to horizontal planarity since the image deformation is clearly not linear if the camera is tilted. What would happen on a non-flat surface? How are insects solving this issue? Do you suppose they are using vestibular information to rotate images? Some comments might be useful.
+
+Authors : Thank you for raising this insightful point regarding omnidirectional camera limitations and the effects of visual deformation. In our setup, we use a fisheye lens with a 220° field of view pointed upward, processed at a low resolution (32×32-pixel edge images). While this setup provides a broad panoramic view, it indeed introduces constraints on non-flat terrain or when camera orientation varies, since the image deformation under tilt is nonlinear and in-silico rotations may not accurately reflect actual physical rotations. We have clarified these limitations in the revised manuscript (Discussion, Line 593). Regarding insects, we agree they likely integrate vestibular or proprioceptive information for navigation, particularly when visual cues are sparse or far away. However, we consider it unlikely that insects explicitly rotate or "correct" internal panoramic images using vestibular information. Instead, vestibular or proprioceptive cues probably complement visual input within a multimodal framework, helping insects maintain stable navigation without necessarily transforming visual images internally.
+Reviewer #2 : If we follow your model, there is no internal neuronal feedback except the Dopamine signal. Is the biological network only feedforward? Could feedback connections provide alternative solution to introduce attentional mechanism or more dynamics code, predictive coding...?
+
+Authors : Thank you for highlighting whether our model’s feedforward nature fully reflects biological reality. Indeed, real insect mushroom bodies are more complex; they include, not only dopaminergic modulation, but also additional feedback loops and recurrent pathways to structures like the central complex. These connections could support attentional modulation, predictive coding, and other dynamic processes beyond straightforward stimulus-response mappings.
+
+We have intentionally focused on a simplified, feedforward mushroom body pathway in this work because it provides an efficient and robust mechanism for visual route learning on a resource-constrained robot. However, incorporating higher-level feedback or recurrent connections remains an exciting avenue for future development. We discuss these possibilities in the Discussion section (Line 635), drawing on possible alternate MB architectures, such as Kandelian or prediction error learning. This would allow even richer, more biologically plausible forms of learning, especially under noisy or uncertain conditions.
+
+Reviewer #2 : Line 414: I am not sure you can compare your experiment with the ones done with autonomous cars. You should provide a test with a classical dataset used with autonomous vehicles to write that (for instance Milford database used for Ratslam or any more recent database). It would be very interesting but because your results rely on omnidirectional cameras while usually autonomous vehicles are using classical camera with limited field of view, I believe the comparison will be difficult (strong difficulties are related to the limited field of view of the camera). Perhaps reducing your claim here would be simpler.
+
+Authors : Thank you for noting the challenges in directly comparing our experiments to standard autonomous cars setups. We agree that differences in camera type (omnidirectional vs. limited field of view), as well as the use of additional sensor modalities, can complicate such comparisons. To address this, we have refined our discussion to focus on panoramic visual teach-and-repeat methods and comparing only the comparable metrics (time consumption, memory), but for mobile robots and not autonomous cars, where the imaging and algorithmic approaches more closely match our own, the paragraph modified is at Line 489.
+
+We appreciate your suggestion to evaluate against classical benchmarks such as the Milford/RatSLAM dataset, and we view this as a promising avenue for future works with limited field of view, as in the discussion section (Line 606). For now, by comparing our approach with state-of-the-art panoramic methods that also rely on visual cues and/or minimal odometry, we can make a fairer assessment of our model’s memory footprint and processing times. This ensures the comparison is neither overstated with systems designed for limited FOV cameras or multi-sensor autonomous cars.
+
+Reviewer #2 : Line 428: When you compare to visual compass you are forgetting that instead of performing ‘n’ comparisons, it is possible to use the prediction of
+the compass orientation associated to different local visual features to deduce the global rotation of the image according to any absolute direction without the need to perform ‘n’ tests. See for instance: Giovannangeli, C., & Gaussier, P. (2007). Orientation system in robots: Merging allothetic and idiopathic estimations. In 13th International Conference on Advanced Robotics (ICAR07) or Delarboulas, P., Gaussier, P., Caussy, R., & Quoy, M. (2014). Robustness study of a multimodal compass inspired from hd-cells and dynamic neural fields. In From Animals to Animats 13: 13th International Conference on Simulation of Adaptive Behavior, SAB 2014. Proceedings 13 (pp. 132-143). Springer International Publishing. Of course this solution is related to mammal visual system.
+
+Authors : Thank you for pointing out these alternative approaches to visual compass estimation, which avoid performing “n” comparisons by directly predicting compass orientation from local visual features (e.g., [Giovannangeli & Gaussier, 2007]; [Delarboulas et al., 2014]). We appreciate how these methods integrate allothetic (external) cues, such as a magnetic compass or odometry, with an internal estimate to achieve a global orientation prediction, an approach reminiscent of mammalian hippocampal or head-direction cell circuits.
+
+But indeed our focus is on an insect-inspired navigation, specifically leveraging the observation that ants can learn and follow visual panoramas even in the absence of a reliable path-integration signal (e.g., “zero-vector” ants still follow learned routes). In this scenario, the entire panoramic image (or skyline) acts as the navigational reference, rather than a set of distinct local features or an external heading reference. Hence, the cited visual compass approach does not rely on a magnetic or inertial compass for orientation, but rather on matching the current panoramic view to stored memories in a minimal, biologically plausible manner.
+
+That said, we do find these mammalian-inspired solutions intriguing, particularly in light of recent discoveries (e.g., head-direction cells in flies), which hint at potential convergences between insect and mammalian navigation systems. We have added reference [2] (Delarboulas et al., 2014) to our Discussion section and now clarify that our “visual compass” is insect-based, focusing on full-image familiarity rather than local-feature heading prediction. In future works, we plan to explore fusing our ant-inspired approach with additional sensory modalities, such as inertial or magnetic measurements, to further enhance state estimation and navigation robustness. We really think that this comment has enabled us to be more precise about our comparison.
+
+Reviewer #2 : Line 439: “latent learning [53]” please avoid preprint. The paper is not providing much details about the model results answering the questions I had.
+
+Authors : Thank you for pointing this out. We have removed these citations to preprints [53] and [66] to address your concern, and we now cite only three preprint sources in total. Additionally, reference [21] is now in press for a conference rather than a preprint. We hope this revision resolves any issues regarding the inclusion of preprint materials.
+
+Reviewer #2 : Line 450: “fudnamentally” : typo issue
+Authors : Thank you for catching this typographical error. We have corrected it in the revised manuscript.
+
+Reviewer #2 : Line 564: The EP vector size was set to u = 15, 000 and \( \kappa = 0.01 \). Is there a relationship between the size of the code k-wta parameter and the length of the trajectory the robot could follow without error. An optimistic boundary could be the number of vectors that can be built using the k-WTA constraint. But because you are pruning connections with your anti hebb learning rule to obtain an efficient code I suppose the number of usable codes is reduced. Yet, the paper is not providing any clue to understand what is the maximum length of the route that can be learned according to the visual environment before two different visual environments cannot be discriminated because they will get the same signature. Perhaps I am wrong. Can you discuss a little bit this point in your paper?
+
+Authors : Thank you for this insightful question and good intuition regarding the relationship between our k-winner-take-all (k-WTA) parameter, network memory capacity, and the maximum route length that can be reliably learned. We have now added a dedicated “Steering Memory Capacity” section (and corresponding Figure 9) in the Results to address this point in detail, but also in Discussion (Line 640) and in Method section “Memory Capacity”.
+
+Briefly, our analysis considers the theoretical memory capacity “m” for a single MBON network developed by Ardin et al. 2016, which provides an upper bound for this kind of neural network. Under this theory, we computed that up to 346 patterns could be stored with a probability of error Perror = 0.01 (i.e., a 1% chance of confusing an arbitrary pattern with a stored one). However, this theory assumes that the KC patterns are random and independent, and it only considers the last layers (EP and AP) of the network. In our route-following application, the situation is somewhat different:
+
+1. Structured Visual Information: the KC patterns generated from our image preprocessing are not purely random; they are structured by the visual features and the robot’s orientation. This structure helps to differentiate between distinct route orientation.
+2. Lateralized MBONs: we adapted the analysis to our two lateralized MBONs by reframing the question as: “How many total patterns (or route lengths) can be added to the two memory banks while still preserving the property that left-looking patterns yield lower familiarity on the left MBON than on the right MBON (and vice versa)?”, we called this error the Plerror (as P lateralized error)
+3. Empirical Findings: for our 55m route experiments, we observed an empirical error proportion of 0.7% (Figure 9), which is acceptable. Moreover, our data indicate that with our current parameters, approximately 430 distinct KC images can be reliably stored with an error of 1%, corresponding to a route length of about 65m.
+4. Scalability Considerations: we further discuss that memory capacity could be enhanced either by increasing the number of KCs with an interplay with k-wta parameter (with an associated computational cost) or by dividing the route into segments managed by separate MBON pairs, which would keep processing times and lateralized errors manageable.
+
+We believe that this additional information provides clarity on how the network’s memory capacity limits the maximum route length, and they offer valuable insights into the trade-offs inherent in designing low-resource, bio-inspired navigation systems. We thank you again for raising this issue.
+
+Reviewer #2 : Line 584: “specified vector”. The term is unclear for me. Could you be more explicit to avoid any confusion (is it AP or MBON ?)
+
+Authors : Thank you for identifying this ambiguity. We have removed the phrase “specified vector” and use a consistent indexing notation as “i” across all layers (EP, AP, KCtoMBON), therefore “i” is the neuron’s number. This change clarifies how neurons and their outputs are referenced, ensuring no confusion about which component of the model is being discussed.
+
+Reviewer #2 : Line 601: CSR format: is it Compressed Sparse Row (CSR)?
+
+Authors : Thank you for this clarification. Yes, “CSR” stands for Compressed Sparse Row. We have now explicitly defined this term in the revised manuscript.
+
+Reviewer #2 : Line 642: section “Theoretical analysis of the robot stability”
+I don’t have the feeling this part is really relevant in the present paper. It would be more interesting in a specialized journal in robotics.
+
+Authors : We appreciate your feedback regarding the theoretical stability analysis. While we understand it may seem more aligned with a specialized robotics journal, we view this Lyapunov analysis as essential for bridging a biologically inspired algorithm and a practical robotic implementation. By formally defining the conditions under which the system remains stable, we can more confidently determine the optimal operating parameters and contextualize our memory capacity analysis within realistic constraints. Thus, we believe it adds rigor and completeness to our study for robotics and automation scientific communities, ensuring that our bio-inspired approach is not only conceptually sound but also robust for real-world robotic navigation. In addition, it adds significant value to our route-centric contribution, which has been given greater prominence in the new version. Not least through a new title, but also an abstract and detailed introductory paragraph.
+
+Reviewer #2 : The video shows results of robot experiments on different days. That is nice but since the shadow angles are the same, I suspect the experiment was done almost at the same hour. Would your results be robust to a change of sun position? Is it something ant could do? I am confused here thinking about ant using light polarity to build a visual compass and also the fact that in some
+experiments it is shown that ants were sensitive to sun position. Could it be a limitation of your approach for some robotics applications?
+
+Authors : Thank you for highlighting the effect of the sun’s position on our ant-inspired control system. We acknowledge that changing sun angle is an important aspect of outdoor environments. In the experiments shown, we primarily focused on how the robot copes with local scene changes, specifically the presence and removal of parked cars, rather than broad shifts in daylight conditions. Consequently, we conducted both trials between approximately 3 p.m. and 5 p.m., during which sun angles (and thus shadows) remained relatively stable. For the new outdoor 20m route experiments (Figure 5), it was a cloudy sky at 11a.m.
+
+From an ecological standpoint, many ants, including Cataglyphis, tend to forage during short midday windows, when the sun is high and does not shift dramatically over the course of their foraging excursions. In these conditions, however, ants combine visual landmarks at a level of the ultraviolet-green skyline, with additional cues such as the skylight polarization for the path integration process. Similarly, in robotics, one could employ ultraviolet sensitive cameras, sky-segmentation algorithms, or/and sensor fusion, to handle more pronounced diurnal variations. Although this goes beyond the scope of our study, we see it as a natural next step to further align our system with the robust, multi-cue navigation strategies observed in ants. To address your concerns, we specified in the results that the experiments were done at the same hour of the day (Line 306)
+
+Reviewer #2 :
+- Here it looks like the test was only done on a 2 segments trajectory with a 90 degrees rotation. One true long-distance navigation in a natural environment (not following human routes would be really convincing).
+- Multiple S trajectories in offroad conditions (open field) would be more interesting to show if the robot can follow a complex trajectory.
+
+Authors : Thank you for suggesting additional off-road “S-shaped” trajectories and more extensive natural navigation tests. While such tests would be insightful, our current robotic platform (AntCar, 20×25×25 cm, with only 1.5 cm ground clearance) faces practical mechanical constraints that prevent realistic off-road traversal.
+
+Moreover, biologically, ants themselves rarely follow complex, arbitrary "S-shaped" trajectories without environmental constraints or specific cues forcing such patterns. In open-field conditions with minimal visual landmarks, ants typically switch from purely visual guidance to alternative strategies such as path integration or chemical trails, since purely visual route-following becomes less reliable (Bisch-Knaden & Wehner, 2001). Consequently, complex curved trajectories are uncommon unless imposed by specific natural constraints, which, to our knowledge, have not been extensively documented in ant-focused literature.
+
+To address your broader interest in navigation under more challenging conditions, we have indeed added new experiments, new analysis of existing
+experiments and additional memory capacity analysis. Specifically, we conducted tests in a forest-like 20 m route featuring narrow corridors and static occlusions. These experiments demonstrated the robustness of our model under more realistic and challenging conditions, achieving successful navigation despite occlusions
+
+Thus, while off-road "S-shaped" tests are currently impractical given both mechanical robotic platform and biological considerations, our expanded set of realistic experiments confirms the biological plausibility, scalability, and practical robustness of our approach. Future studies integrating enhanced rugged robot hardware (higher ground clearance) or supplementary sensory modalities could address even more complex environmental scenarios. In consequence, we have defined the environmental type to indoor, semi-urban and forest-like, to avoid overstatement comparing open-field environment, which can be a difficult task for a low-resolution, visual-only algorithm. Furthermore, we strongly believe that an omnidirectional camera support less precise navigation but more robust, while smaller FOV could enhance precision, but this is another work.
+
+Reviewer #2 : It would be difficult to review the source code without the robot to perform relevant tests and it would be very long to do (not a classical review work). Yet, the video shows convincing arguments in favor of the work done as well as the experimental results provided.
+
+Authors : We appreciate your acknowledgment that the video demonstrations and experimental results offer convincing evidence. To further support transparency, we have shared all relevant data, both from the real-time experiments and our initial offline analyses, along with the code used for figure generation and the route-centric MB model, via the Figshare link and the CodeOcean capsule provided to Nature Communications. This will be publicly accessible upon publication. Additionally, our robot-specific (ROS) software package will be made available upon request to any interested researchers who wish to replicate or extend our work.
+
+Reviewer #3 (Remarks to the Author):
+
+Reviewer #3 : The work proposes a self-supervised, ant-inspired navigation system, which has been implemented on the Antcar robot. The main result is the robust route-following capability that has been implemented using a neuromorphic, mushroom body-inspired network using minimal memory at 148 kilobits at 62ms. This system also allows the robot to perform homing and shuttling behaviour for the fixed route. These results demonstrate the applicability of the bio-inspired approach to achieve visual navigation using limited computational resources. The lateralized memory model and its implementation of low-resource computation are original and significant contributions. The combination of the selected robotic platform and the biological inspiration derived from ants is not particularly novel, but is still significant. The methodology is clear and detailed, with transparent data presentation. The kinematic model and the Lyapunov stability analysis add rigour
+to the experimental results. The explanations for the image processing and design of the control algorithm are clear and explained well.
+The addition of the obstructions present along the path to the 2-dimensional trajectory plots would help interpret them better. Demonstrating similar performance across different experimental routes or configurations, particularly head-on obstructions and sensitivity to their size in the visual field, would add to the results and better justify the validity of the approach.
+Suggested Improvements:
+1. Experimental Additions: Test the model in more diverse environments and specify the nature and sensitivity of the occlusion and kidnapped scenarios.
+2. Figures and Supplementary Materials: The addition of the obstacles along the path traversed in the 2-D plots seen in Fig. 4a-f would aid the clarity.
+
+Authors : We thank you very much for your supportive assessment of our work and your thoughtful suggestions. Below, we address each of your comments
+
+1. Obstructions in 2D Trajectories. We appreciate the suggestion to add the obstructions directly to the 2D trajectory plots, we have included the marker representing obstacles and pedestrians in all the figures when possible. We have also updated the map-view representations to emphasize both tree-like and semi-urban outdoor environments (See Figure 4,5,6,7).
+
+2. More Diverse Environments and Sensitivity to Occlusions. As proposed and to strengthen our validation, we have added a new outdoor route experiment in a tree-like environment (complementing the semi-urban setting). We also tested head-on obstructions up to 30% of the frontal field of view with 100% success (Figure 5). Additionally, we computed the percentage of occlusion for the indoor dynamic-occlusions experiments using a trained YOLOv11 neural network (described in Methods and Supplementary Materials). These results highlight the model’s robustness under diverse scenarios, with peaks up to 56% of the image occluded.
+
+3. Kidnapped Robot Scenarios. We have included the initial poses information for the kidnapped robot experiments in the results section (line 254). This further clarifies the starting positions and the robustness of our navigation system under these challenging conditions.
+
+These additions directly address your suggestions for testing more diverse environments and clarifying occlusion sensitivity.
+Our answers and comments will be written here in blue. We appreciate the reviewers’ time and expertise and believe that the manuscript is now clearer and more rigorous as a result of their feedback.
+
+Reviewer #1:
+
+My comments from the first review have been addressed well, thank you! I just have some additional minor remarks:
+
+- The new section "Memory Capacity" is not clear, because it only shows how the P_I_error is computed, but does not give information about how that relates to memory capacity. It gets more clear in previous explanations in "Steering memory capacity" and Fig. 9. Maybe the headline of this section is misleading, because it should only show how P_I_error is computed?
+- In the Supplementary Notes, in Table S1, second table there is still "Convex&Concave" mentioned, which should be replaced by Route 1&2.
+- line 87: missing word? "around nest position"
+- inconsistent capitalization of "Nest" and "Feeder" throughout the paper
+- Caption of Fig. 2: "An panoramic camera" should be "A panoramic camera"
+- Caption of Fig. 2: "phases.a" - missing whitespace
+- Caption of Fig. 2: "An in silico scan (simulated image rotation) generate image with angular error (θ*e)" - missing word?
+
+Authors :
+• We have renamed “Memory Capacity” (Methods) to “Memory-Capacity Computation” to reflect that the subsection solely defines the calculation of PI_error;
+• All remaining occurrences of “Convex & Concave” have been replaced by “Route 1 & Route 2.”
+• Line 87 now reads “around their nest position.”
+• We standardised nest and feeder to lower-case throughout, except when they open a sentence.
+• The caption has been corrected.
+• Figure-2 caption corrected.
+We are grateful for these careful observations; they have improved both clarity and consistency as the first revision comments.
+
+Reviewer #3 :
+
+Overall the authors have addressed my concerns to a satisfactory extent
+
+Authors : Thank you for the positive assessment and for the constructive suggestions that helped strengthen the manuscript.
+The paper is easy to read and well structured. It presents very interesting results related to ant-based mobile robot navigation. The paper makes several important contributions. Firstly, it introduces an original and simple model that explains how ants can navigate using only visual information. A key characteristic of this model is its ability to effectively utilize low-resolution visual information processed by a small neural network, while also enabling online learning. Secondly, these characteristics enable the implementation of an efficient solution on a small embedded computer (Raspberry Pi 4 with ROS) for onboard robot control. Thirdly, the paper includes numerous robotics experiments to evaluate the performance of the proposed solution.
+
+The video illustrates nicely the work done and the potential of the proposed approach.
+
+This research has the potential to interest a wide readership and I believe it is suitable for publication in Nature Communications.
+
+In the following sections, I have tried to provide detailed comments to ensure my understanding of the work. To enhance accessibility for a broader audience beyond your specific field, please provide full explanations for all acronyms used throughout the paper. I also recommend maintaining consistent naming conventions for variables and parameters across figures and equations. Furthermore, the Materials and Methods section, and complementary results document, should include the equations describing the different layers of the network (PN, EP, AP, etc.) and the corresponding values of the synaptic weights.
+
+Also, figure S7 should be moved in the paper. It provides interesting details for a better understanding of the NN structure and functioning.
+
+A critical factor contributing to the success of this approach, in my view, lies in the intricate interplay between the “controlled oscillation amplitude during learning”, the neural network (NN) update frequency, and the dynamic changes in panoramic information resulting from the randomization process between PN and EP, termed PN to KCr (for consistency, I recommend adhering to a uniform naming convention throughout the manuscript). The equations governing the neuronal activity (and neuron connectivity) within this specific component should be explicitly presented. I believe these equations are important for a comprehensive understanding of the model, potentially exceeding the significance of the Lyapunov stability analysis in the context of this particular paper.
+
+In the detailed comments related to the discussion section, I have also included specific questions that I believe can further enhance the clarity and impact of the paper.
+
+Detailed comments:
+
+Line 99: "...leading to a self-supervised model for route learning".
+
+This sentence and the relationship with the previous sentence is a little bit cryptic. I think you should be more explicit in your explanation of the Link with dopaminergic feedback and the self supervision. I am not sure to understand (see also my next comment).
+Figure 2 legend: Dopaminergic-like Neurons (DAN)
+
+I failed to find it in the figure while I really wanted to understand how it was implemented:
+
+1) what are the input to DAN?
+
+2) what are the synapses modified by DAN? From what I understood from the method part only the direct connections between EP (the output of the k-WTA) and the Mushroom Body Output Neurons (MBON) are modified.
+
+Reference [44] is not about dopamine in insect brain and is a preprint. Can you provide validated works or be more explicit about the status of this information?
+
+Page 3: You are providing results about differential familiarity. If I understand correctly this was computed from 2 MBON outputs. What is the familiarity measure between the raw visual input and how does this familiarity measure evolve across the different stages of the processing pipeline? I am particularly interested in understanding whether the learning process itself leads to an improvement in this familiarity measure. To avoid a long discussion and analysis of the data, a concise summary of your findings or insights regarding the evolution of this familiarity measure throughout the neural code-building process would be greatly appreciated
+
+Figure 4 a and b. It is not clear if both routes were learned in the same network. If yes, why a strong preference for the back trajectory? I cannot understand this result if an omnidirectional camera is used. So I suppose the results are related to 2 different experiments. If it is correct, you should state it explicitly (and it is ok on my side). In this case, Is it possible to teach your robot two different routes in the same network? Would it be compatible with ants capabilities? It would be a useful feature for a mobile robot. What could be your solution? Could it introduce an issue for the stabilization of the code?
+
+Line 255: If I understand correctly the error can be about 0.5m. While it can be ok for some robotics applications, is it compatible with ant navigation and ant size?
+
+MAD acronym is not explained. Is it Mean Absolute Deviation?
+
+Figure 5: It would be interesting to have a map of the environment or a classical picture to see the difficulty of the navigation task (is it a part of the trajectory we can see in the video?). Here it looks like the test was only done on a 2 segments trajectory with a 90 degrees rotation. One true long-distance navigation in a natural environment (not following human routes would be really convincing).
+
+Discussion section:
+
+Could you discuss the limitations of omnidirectional cameras? My personal experience showed a high sensitivity to horizontal planarity since the image deformation is clearly not linear if the camera is tilted. What would happen on a non-flat surface? How are insects solving this issue? Do you suppose they are using vestibular information to rotate images? Some comments might be useful.
+
+If we follow your model, there is no internal neuronal feedback except the Dopamine signal. Is the biological network only feedforward? Could feedback connections provide alternative solution to introduce attentional mechanism or more dynamics code, predictive coding... ?
+Line 414: I am not sure you can compare your experiment with the ones done with autonomous cars. You should provide a test with a classical dataset used with autonomous vehicles to write that (for instance Milford database used for Ratslam or any more recent database). It would be very interesting but because your results rely on omnidirectional cameras while usually autonomous vehicles are using classical camera with limited field of view, I believe the comparison will be difficult (strong difficulties are related to the limited field of view of the camera). Perhaps reducing your claim here would be simpler.
+
+Line 428: When you compare to visual compass you are forgetting that instead of performing ‘n’ comparisons, it is possible to use the prediction of the compass orientation associated to different local visual features to deduce the global rotation of the image according to any absolute direction without the need to perform ‘n’ tests. See for instance: Giovannangeli, C., & Gaussier, P. (2007). Orientation system in robots: Merging allothetic and idiothetic estimations. In 13th International Conference on Advanced Robotics (ICAR07) or Delarboulas, P., Gaussier, P., Caussy, R., & Quoy, M. (2014). Robustness study of a multimodal compass inspired from hd-cells and dynamic neural fields. In From Animals to Animats 13: 13th International Conference on Simulation of Adaptive Behavior, SAB 2014. Proceedings 13 (pp. 132-143). Springer International Publishing. Of course this solution is related to mammal visual system.
+
+Line 439: “latent learning [53]” please avoid preprint. The paper is not providing much details about the model results answering the questions I had.
+
+Line 450: “fudnamentally” : typo issue
+
+Line 564: The EP vector size was set to u = 15, 000 and k = 0.01. Is there a relationship between the size of the code k-wta parameter and the length of the trajectory the robot could follow without error. An optimistic boundary could be the number of vectors that can be built using the k-WTA constraint. But because you are pruning connections with your anti hebb learning rule to obtain an efficient code I suppose the number of usable codes is reduced. Yet, the paper is not providing any clue to understand what is the maximum length of the route that can be learned according to the visual environment before two different visual environments cannot be discriminated because they will get the same signature. Perhaps I am wrong. Can you discuss a little bit this point in your paper?
+
+Line 584: “specified vector”. The term is unclear for me. Could you be more explicit to avoid any confusion (is it AP or MBON ?)
+
+Line 601: CSR format: is it Compressed Sparse Row (CSR)?
+
+Line 642: section “Theoretical analysis of the robot stability”
+
+I don’t have the feeling this part is really relevant in the present paper. It would be more interesting in a specialized journal in robotics.
+
+The video shows results of robot experiments on different days. That is nice but since the shadow angles are the same, I suspect the experiment was done almost at the same hour. Would your results be robust to a change of sun position? Is it something ant could do? I am confused here thinking about ant using
+light polarity to build a visual compass and also the fact that in some experiments it is shown that ants were sensitive to sun position. Could it be a limitation of your approach for some robotics applications? Multiple S trajectories in offroad conditions (open field) would be more interesting to show if the robot can follow a complex trajectory.

08e00c94056e03db3ebcdc2920d9ec2ef75181d657a1f6242f88ac52aaa88e5f/peer_review/peer_review.md

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+Tunable magnons of an antiferromagnetic Mott insulator via interfacial metal-insulator transitions
+
+Corresponding Author: Professor Ambrose Seo
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+This article focuses on utilizing RIXS to investigate magnon energy levels in AFM Mott Insulator, SR2IrO4 with different substrates. The measurements show that magnon peak energy remains similar for (pi,0) magnon mode. On the other hand, the measurements clearly show that softening of magnon mode occurs near (pi/2, pi/2) zone boundary when metallic substrates are used. While, for insulating substrates the behavior is similar to bulk system. Although modifying the system from insulating to metallic causes hardening of the mode. In-plane exchange interactions are also extracted using Heisenberg spin model.
+Electron-phonon coupling has been suggested as a potential reason for the dispersion, or magnon-phonon coupling driven by interface. However, no clear reason for the potential behavior or model is provided, including whether this behavior is expected to be universal or limited to the nature of interface or substrate? As such this study while notably characterizes the magnon modes in iridates, the overall impact on the field is not clear.
+
+While these measurements are important and characterize critical behavior of magnon modes depending on substrate and boundary conditions which has so far been missing, and thus should be published. However, the advancement of underlying behavior in these systems is not clear, especially for Nature Communications.
+
+Reviewer #2
+
+(Remarks to the Author)
+Sujan Shrestha and co-authors, in their work titled "Tunable Magnons of an Antiferromagnetic Mott Insulator via Interfacial Metal-Insulator Transition," presented detailed studies using resonant inelastic X-ray scattering and Raman spectroscopy on Sr2IrO4 heterostructures. They demonstrated that the properties of magnons in Sr2IrO4 films vary depending on their proximity to insulating or metallic substrates. Additionally, they showed that magnons are sensitive to the metal-insulator transition in Ca3Ru1.98Ti0.02O7 when used as the substrate.
+The experimental data are very convincing, and the results merit publication. This work has the potential to advance a general understanding of magnons and offer direction to their applications. However, there are several issues that need to be addressed to strengthen the paper:
+The explanation of the observed effects is somewhat speculative. I recommend providing a theoretical model to support the proposed ideas or offer the most plausible ones.
+The TEM image in Figure S2 shows the interfacial region of the Sr2IrO4/Sr2RuO4 system. Since the paper's main results are particularly based on the Sr2IrO4/Ca3Ru1.98Ti0.02O7 system, including TEM data for this specific system as well as the sample Sr2IrO4/LSAT will be vital to complete such study Potential valence changes at interfaces are crucial in resolving magnetic and electronic properties. Therefore, investigating the atomic structure and valence state at the interface, possible charge transfer, and the interfacial diffusion (if so) of elements from the substrates is necessary for designing the model to explain the observed effects.
+Minor Suggestions:
+Please state the film thickness in both the main text and the supplementary information.
+
+Reviewer #3
+(Remarks to the Author)
+The manuscript reports the experimental observation of softened zone boundary magnon energies in Sr2IrO4 heterostructures with metallic substrates compared with the films with insulating substrates. The authors present that the magnons can be tuned by growing the Sr2IrO4 on the substrate with a metal-insulator transition at 55K. They rule out the effect of strain, doping and proximity by various control experiments. The effect is attributed to electron-phonon coupling at the interface or within the substrate. However, the manuscript does not explain why and how the coupling softening the magnon energies at the zone boundary, thus difficult to access the fundamental insights. Also, the tunability is small, compared to another related work [Nature Communications 13, 6674 (2022)], in which the energies of zone-center magnons in Sr2IrO4 can be tuned by 40% with 0.1% stress. A theory part with quantitative explanation is needed, too. Therefore, I regret to say that I do not recommend for the publication of the manuscript in nature communications. The following are more detailed comments.
+-The authors claimed that electron-phonon coupling at the interface or in the substrate might cause the magnon softening effect. But they do not explain why and how. Is it possible for the authors come up with a model to support their claim?
+-Why the magnon softening effect happens only at the zone boundary, not other areas? Still a theory model or calculation is needed.
+-How the temperature affect the magnon energies of single crystal Sr2IrO4? The authors claim the magnon tunability via interfacial metal-insulator transition. They do show the 40K and 60K magnon energy difference of Sr2IrO4 / Ca3Ru1.98Ti0.02O7. However, the temperature difference of magnon energies for the other samples are not given.
+-In the first paragraph of the experimental layout part, the authors state “…the in-plane lattice of Sr2IrO4 thin films is coherently strained with all three substrates…”. Generally when people talk about coherent they refer to a wave. What “coherently strained” means here?
+-In the fourth paragraph of the result part, the authors state “A similar upward shift of up to 0.7 meV in the phonon energy is also observed in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures when transitioning from an insulating to metallic state of the Ca3Ru1.98Ti0.02O7 substrate at 55 K (Fig. 5b).” It seems that the 0.7 meV energy is not the result by comparing two temperatures near the transition point (for example, 50K and 60K), but the value by comparing the highest energy 49.8meV at around 55K and lowest energy 49.1 meV at around 10K.
+-In fig 5b, are the color bars are labeled wrong? The deep blue 52K energy jump to bright red 55K energy, then going back.
+-How about A1g mode of Sr2IrO4 / Ca3Ru1.98Ti0.02O7 in fig 5? The manuscript presents both A1g and B2g mode of Sr2IrO4/Sr2RuO4 and Sr2IrO4/L SAT in fig 5a. But only B2g mode of Sr2IrO4 /Ca3Ru1.98Ti0.02O7 is presented fig 5b.
+-In the fourth paragraph of the result part, the authors state “we acknowledge that the sudden structural change at 55 K might also have some contributions to the phonon mode shift in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures”, which one dominate the B2g phonon Raman spectra shifting? The statement is too vague here.
+-The year number is missing for the reference 20.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+In the updated version, the authors have clearly highlighted the impact of these studies, the effect of heterostructure, and the lack of microscopic models, but have given possible mechanisms i.e. two magnon modes. According to me they have also addressed most referee comments, so I am okay with going forward with publishing the manuscript.
+
+Reviewer #2
+
+(Remarks to the Author)
+The authors have addressed most of my comments/questions and those from other reviewers in a generally satisfactory manner. However, Reviewer #3 and I requested a more detailed explanation tailored to the studied heterostructure, which has not been provided. Some theoretical models must be an integral component of such a study.
+To summarize, the paper presents some interesting experimental evidence that merits publication but does not advance beyond established knowledge in the field.
+Therefore, I cannot recommend this manuscript for publication in Nature Communications in its current form.
+
+Reviewer #3
+
+(Remarks to the Author)
+I think the authors have addressed all the comments from the reviewers in revised manuscript. Therefore I recommend the work to be published in Nature Communications.
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+Reply to the Reviewers’ comments
+
+We sincerely appreciate the Reviewers for their valuable comments and suggestions, which help us improve the manuscript. Here, we reply to the comments in detail below:
+
+Reviewer #1
+
+The Reviewer said: This article focuses on utilizing RIXS to investigate magnon energy levels in AFM Mott Insulator, Sr2IrO4 with different substrates. The measurements show that magnon peak energy remains similar for (pi,0) magnon mode. On the other hand, the measurements clearly show that softening of magnon mode occurs near (pi/2, pi/2) zone boundary when metallic substrates are used. While, for insulating substrates the behavior is similar to bulk system. Although modifying the system from insulating to metallic causes hardening of the mode. In-plane exchange interactions are also extracted using Heisenberg spin model. Electron-phonon coupling has been suggested as a potential reason for the dispersion, or magnon-phonon coupling driven by interface. However, no clear reason for the potential behavior or model is provided, including whether this behavior is expected to be universal or limited to the nature of interface or substrate? As such this study, while notably characterizes the magnon modes in iridates, the overall impact on the field is not clear.
+
+While these measurements are important and characterize critical behavior of magnon modes depending on substrate and boundary conditions which has so far been missing, and thus should be published. However, the advancement of underlying behavior in these systems is not clear, especially for Nature Communications.
+
+Our reply: We sincerely thank the reviewer for their insightful feedback and for recognizing the importance of our findings on the critical behavior of magnon modes in Sr2IrO4, depending on the nature of the substrate. We also appreciate the reviewer’s support for publishing our manuscript.
+
+We agree with the reviewer that providing a deeper explanation of the underlying mechanisms for the observed magnon behavior is essential. Although our study focuses on iridate/ruthenate heterostructures, we believe that the observed substrate-dependent magnon dynamics could indeed
+be a universal phenomenon, extendable to other systems. To support this claim, we have included additional references in our revised manuscript, noting private discussions with experts in the broader magnetic materials community, who have observed substrate-dependent magnon dynamics in other 2D magnetic materials, such as Fe3GeTe2, NiPS3, and CrSBr, where the metallic or insulating nature of the substrate plays a significant role in determining the magnetic excitations. In such 2D materials, the experimental limitations of RIXS currently hinder a detailed study of full magnon dispersion, but preliminary observations suggest similar trends to those we report. We believe that this universality—magnon behavior influenced by hetero-interfaces in systems ranging from antiferromagnetic insulators to 2D magnets—highlights the broad relevance and impact of our findings.
+
+Regarding the softening of the magnon mode near the (\( \pi/2, \pi/2 \)) zone boundary when a metallic substrate is used, we have expanded our discussion in the revised manuscript to provide more clarity on the possible mechanisms. We propose that this behavior is likely driven by electron-phonon coupling at the interface or within the metallic substrate, which could mediate long-range interactions between acoustic phonons and magnons, affecting the magnon dispersion in Sr2IrO4. This hypothesis is grounded in our robust experimental findings, which show a clear correlation between the substrate’s metallic nature and the magnon mode softening.
+However, as the reviewer rightly points out, a detailed microscopic model is still lacking. While we have outlined plausible interactions (such as metallic interface-driven magnon-acoustic phonon coupling), deriving a fully predictive model Hamiltonian for this system remains a significant theoretical challenge. We acknowledge this gap and have explicitly stated in the revised manuscript that further theoretical work is needed to construct such a model. We believe that publishing our results will provide a strong experimental basis for future theoretical efforts, encouraging the development of more detailed models that can describe the complex interactions in heterostructures.
+
+We strongly believe that our findings will significantly impact the field of magnonics. By demonstrating how substrate properties can be leveraged to manipulate magnon dispersion in an antiferromagnetic Mott insulator, we provide a novel approach to tuning magnetic excitations in layered materials. This tunability is crucial for the development of future magnonic devices, where
+control over magnon dispersion could enable more efficient information processing and energy transport at the nanoscale. Our study opens up new avenues for exploring the effects of hetero-interfaces on magnetic excitations, not only in Sr2IrO4 but also in a wide range of magnetic materials, including 2D magnets and complex oxides.
+
+We also believe that our manuscript provides a significant advancement in understanding substrate effects on magnon dynamics and will motivate both experimental and theoretical work in this exciting area. Publishing our work in Nature Communications will not only deepen the overall understanding of magnons but also stimulate research that explores new means of manipulating magnon energies in heterostructures, an essential step for advancing the field of magnonics.
+
+Thank you.
+Reviewer #2
+
+The Reviewer said: Sujan Shrestha and co-authors, in their work titled “Tunable Magnons of an Antiferromagnetic Mott Insulator via Interfacial Metal-Insulator Transition,” presented detailed studies using resonant inelastic X-ray scattering and Raman spectroscopy on Sr$_2$IrO$_4$ heterostructures. They demonstrated that the properties of magnons in Sr$_2$IrO$_4$ films vary depending on their proximity to insulating or metallic substrates. Additionally, they showed that magnons are sensitive to the metal-insulator transition in Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ when used as the substrate. The experimental data are very convincing, and the results merit publication. This work has the potential to advance a general understanding of magnons and offer direction to their applications.
+
+Our reply: We sincerely thank the reviewer for their positive feedback and support for publication! We are pleased to see that the strength of our experimental data and the potential of our findings to advance the understanding of magnons have been recognized.
+Our study demonstrates how proximity to metallic or insulating substrates can effectively tune magnon properties in Sr$_2$IrO$_4$, offering a new strategy for controlling magnon dynamics in complex oxide systems. This tunability is not only important for fundamental research but also has promising implications for the development of magnonic or spintronic devices, where precise control over magnetic excitations could enable novel applications in information processing and energy-efficient technologies.
+We believe our work will inspire further research in this area. We appreciate the reviewer’s recognition of its broader impact.
+
+The Reviewer said: However, there are several issues that need to be addressed to strengthen the paper: The explanation of the observed effects is somewhat speculative. I recommend providing a theoretical model to support the proposed ideas or offer the most plausible ones.
+
+Our reply: We appreciate the reviewer’s suggestion. As mentioned in our response to Reviewer #1, we have expanded the discussion in the revised manuscript to offer more clarity. The most plausible explanation for the observed magnon softening is electron-phonon coupling at the
+interface or within the metallic substrate, which could mediate long-range acoustic phonon-magnon interactions affecting magnon dispersion in Sr2IrO4. This hypothesis is well-supported by our experimental data, showing a clear link between substrate metallicity and magnon behavior. However, developing a detailed microscopic theoretical model is extremely challenging and beyond the scope of this manuscript. While we outline plausible interactions such as magnon-acoustic phonon coupling, deriving a full theoretical model requires more information and ideas. We have acknowledged this gap and emphasized in the revised manuscript that further theoretical work is required. We believe our experimental results will provide a strong foundation for such efforts, encouraging the development of detailed models for magnon-acoustic phonon interactions in heterostructures.
+
+The Reviewer said: The TEM image in Figure S2 shows the interfacial region of the Sr2IrO4/Sr2RuO4 system. Since the paper’s main results are particularly based on the Sr2IrO4/Ca3Ru1.98Ti0.02O7 system, including TEM data for this specific system as well as the sample Sr2IrO4/LSAT will be vital to complete such study potential valence changes at interfaces are crucial in resolving magnetic and electronic properties. Therefore, investigating the atomic structure and valence state at the interface, possible charge transfer, and the interfacial diffusion (if so) of elements from the substrates is necessary for designing the model to explain the observed effects.
+
+Our reply: We thank the reviewer for this insightful suggestion. In response, we have added Figure S3 to the revised manuscript, which includes high-resolution TEM data of a Sr2IrO4/Ca3Ru2O7 heterostructure. The data show a sharp interface along both the a and b directions with minimal ionic interdiffusion, suggesting that the heterostructure maintains its integrity.
+For TEM purposes, Ca3Ru2O7 with and without 1% Ti doping is structurally nearly identical. Given the challenges of growing large enough single crystals for heterostructure fabrication, obtaining TEM data from such samples is already a significant achievement. While cross-sectional TEM is sample-destructive and could potentially affect heterostructure integrity, it is reassuring that our data reveal a well-defined interface.
+We also agree with the reviewer on the importance of further investigating the atomic structure, valence state, and potential charge transfer at the interface. For future studies, we plan to employ advanced techniques such as electron energy loss spectroscopy (EELS) to explore these aspects in greater detail.
+
+The Reviewer said: Please state the film thickness in both the main text and the supplementary information.
+
+Our reply: We have included the film thickness in both the main text and the supplementary information in the revised manuscript.
+
+Thank you.
+Reviewer #3
+
+The Reviewer said: The manuscript reports the experimental observation of softened zone boundary magnon energies in Sr2IrO4 heterostructures with metallic substrates compared with the films with insulating substrates. The authors present that the magnons can be tuned by growing the Sr2IrO4 on the substrate with a metal-insulator transition at 55 K. They rule out the effect of strain, doping and proximity by various control experiments. The effect is attributed to electron-phonon coupling at the interface or within the substrate. However, the manuscript does not explain why and how the coupling softening the magnon energies at the zone boundary, thus difficult to access the fundamental insights. Also, the tunability is small, compared to another related work [Nature Communications 13, 6674 (2022)], in which the energies of zone-center magnons in Sr2IrO4 can be tuned by 40% with 0.1% stress.
+
+Our reply: In [Nature Communications 13, 6674 (2022)], the energies of the zone-center magnons in a Sr2IrO4 single crystal were tuned by 40% with just 0.1% stress using a strain device. However, this tunability primarily targets the zone center, which has a very low energy of around 2.3 meV, meaning even a small energy shift results in a large percentage change. When we consider the magnitude of the shift in the zone-center magnon energy, it amounts to only about 0.7 meV for 0.1% stress. This absolute value is much smaller than the 20 meV shift observed at the zone boundary magnon energy in our study. Hence, the tunability of “magnon dispersion” is not so small when a Sr2IrO4 thin film is interfaced with different substrates.
+
+The Reviewer said: A theory part with quantitative explanation is needed, too. Therefore, I regret to say that I do not recommend the publication of the manuscript in nature communications. The authors claimed that electron-phonon coupling at the interface or in the substrate might cause the magnon softening effect. But they do not explain why and how. Is it possible for the authors come up with a model to support their claim?
+
+Our reply: We thank the reviewer for pointing out the importance of the theory part with the quantitative explanation. In the revised manuscript, we have attributed the softening of the magnon energy at the zone boundary in Sr2IrO4 interfaced with the metallic substrate to the combined
+effects of electron-phonon and magnon-acoustic phonon interactions, based on our experimental findings. However, to clarify the microscopic mechanisms behind this phenomenon and to understand why and how it occurs, the model Hamiltonian is yet to be established for the heterostructures. We believe our experimental results will pave the way for a deeper understanding and manipulation of magnons, encouraging theorists to derive or identify the suitable Hamiltonian for this system.
+
+The Reviewer said: Why the magnon softening effect happens only at the zone boundary, not other areas? Still a theory model or calculation is needed.
+
+Our reply: Please note that our experimental finding is in changes of “magnon dispersion”, which is large enough to be observed in our experiments, RIXS and Raman spectroscopy. Thus, the magnon softening effect happening at the zone boundary implies an overall tuning of magnon dispersion. In the revised manuscript, we added relevant discussions: Changes in the second-nearest and third-nearest exchange interactions (\( J_2 \) and \( J_3 \)) might be responsible for the tuning of magnon dispersion, supported by linear spin-wave theory and spin-Hamiltonian model fit. In particular, the spin-Hamiltonian fit provides quantitative information. We also believe that publishing our manuscript in Nature Communications will motivate theorists to derive or identify more advanced model Hamiltonians and calculations for this system.
+
+The Reviewer said: How the temperature affect the magnon energies of single crystal Sr2IrO4? The authors claim the magnon tunability via interfacial metal-insulator transition. They do show the 40K and 60K magnon energy difference of Sr2IrO4 / Ca3Ru1.98Ti0.02O7. However, the temperature difference of magnon energies for the other samples are not given.
+
+Our reply: According to [Phys. Rev. B **93**, 024405 (2016)], the single magnon energy at the zone center increases as the temperature decreases, with an energy change of only about 0.6 meV between 3 K and 140 K. This change in energy is very small compared to the 20 meV change in the zone boundary magnon energy. We selected 40 K and 60 K RIXS measurements for Sr2IrO4/Ca3Ru1.98Ti0.02O7 because the Ca3Ru1.98Ti0.02O7 single crystal substrate undergoes a metal-insulator transition at 55 K. The data at 40 K corresponds to the insulating state of the substrate, while the data at 60 K corresponds to its metallic state. Our RIXS measurements at the (\( \pi/2, \pi/2 \))
+symmetry points, taken from 20 K to 60 K in 5 K intervals, clearly show a sudden shift of the single magnon energy to lower energy by 20 meV at 55 K, coinciding with the metallic state of Ca3Ru1.98Ti0.02O7. Thus, this shift is not simply a temperature effect but rather the result of the metal-insulator transition of the adjacent substrate.
+
+In contrast, since there is no metal-insulator transition in Sr2RuO4 or LSAT single crystals below the Néel temperature of Sr2IrO4, there is no necessity to perform RIXS measurements at different temperatures. Therefore, we conducted the RIXS measurements of Sr2IrO4/Sr2RuO4 and Sr2IrO4/LSAT solely at 20 K.
+
+The Reviewer said: In the first paragraph of the experimental layout part, the authors state “...the in-plane lattice of Sr2IrO4 thin films is coherently strained with all three substrates...”. Generally when people talk about coherent they refer to a wave. What “coherently strained” means here?
+
+Our reply: In that paragraph, “coherently strained” means uniformly strained with the substrate without noticeable lattice relaxation. We have replaced the word “coherently” with “without relaxation” in the revised manuscript.
+
+The Reviewer said: In the fourth paragraph of the result part, the authors state “A similar upward shift of up to 0.7 meV in the phonon energy is also observed in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures when transitioning from an insulating to metallic state of the Ca3Ru1.98Ti0.02O7 substrate at 55 K (Fig. 5b).” It seems that the 0.7 meV energy is not the result by comparing two temperatures near the transition point (for example, 50K and 60K), but the value by comparing the highest energy 49.8meV at around 55K and lowest energy 49.1 meV at around 10K.
+
+Our reply: Thank you so much to the reviewer for pointing out this question. According to [Appl. Phys. Lett. 114, 152402 (2019)], the energy of the Raman shift in Sr2IrO4 single crystals decreases with increasing temperature. A similar trend is observed in Sr2IrO4/Ca3Ru1.98Ti0.02O7 above 55 K. However, below 55 K, the Raman shift energy increases with temperature, likely due to a sudden structural change occurring at this point. If this were merely a temperature effect and related to the metal-insulator transition, one would expect the Raman shift energy at 52 K to be lower than that
+at 10 K. Thus, a comparison of 0.7 meV is made between the Raman shift energies at 10 K and 55 K.
+
+The Reviewer said: In fig 5b, are the color bars labeled wrong? The deep blue 52K energy jumps to bright red 55K energy, then going back.
+
+Our reply: Thank you to the reviewer for highlighting this issue. The color bar was correctly labeled, but it was inconsistent with Figure 4b. We have now adjusted the colors for each temperature in the updated manuscript to ensure consistency with Figure 4b and avoid any confusion.
+
+The Reviewer said: How about A1g mode of Sr2IrO4 / Ca3Ru1.98Ti0.02O7 in fig 5? The manuscript presents both A1g and B2g mode of Sr2IrO4/Sr2RuO4 and Sr2IrO4/LSAT in fig 5a. But only B2g mode of Sr2IrO4 / Ca3Ru1.98Ti0.02O7 is presented fig 5b.
+
+Our reply: Thank you to the reviewer for raising this question. The reason we did not include the \(A_{1g}\) mode of Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ is that the \(A_{1g}\) mode of Sr$_2$IrO$_4$ thin film overlaps with that of the Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ single crystal substrate, making it difficult to distinguish.
+
+The Reviewer said: In the fourth paragraph of the result part, the authors state “we acknowledge that the sudden structural change at 55 K might also have some contributions to the phonon mode shift in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures”. Which one dominate the B2g phonon Raman spectra shifting? The statement is too vague here.
+
+Our reply: Thank you so much to the reviewer for pointing out this question. In this statement, we acknowledge that both the structural change and the metal-insulator transition occur at 55 K, suggesting that the structural change may also contribute to the hardening of the phonon modes. However, we believe that the primary factor driving the shifting of the \(B_{2g}\) phonon mode is the metal-insulator transition of the adjacent substrate. This assertion is supported by the observation of softened zone boundary magnons and hardened phonon modes in the Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructure, which has a metallic substrate, compared to the insulating substrate in
+Sr2IrO4/LSAT. Similar behavior is observed in the Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructure due to the metal-insulator transition of the Ca3Ru1.98Ti0.02O7 substrate.
+
+The Reviewer said: The year number is missing for the reference 20.
+
+Our reply: We have added the year to reference 20 in the updated manuscript.

08e00c94056e03db3ebcdc2920d9ec2ef75181d657a1f6242f88ac52aaa88e5f/preprint/preprint.md

@@ -0,0 +1,179 @@
+Tunable magnons of an antiferromagnetic Mott insulator via interfacial metal-insulator transitions
+
+Ambrose Seo
+a.seo@uky.edu
+
+University of Kentucky    https://orcid.org/0000-0002-7055-5314
+Sujan Shrestha
+University of Kentucky
+Maryam Souri
+University of Kentucky
+Christopher Dietl
+Argonne National Laboratory
+Ekaterina M. Pärschke
+University of Alabama at Birmingham
+Maximilian Krautloher
+Max Planck Institute for Solid State Research
+Gabriel Calderon Ortiz
+Ohio State University
+Matteo Minola
+Max Planck Institute    https://orcid.org/0000-0003-4084-0664
+Xiaotong Shi
+Max Planck Institute for Solid State Research
+A. V. Boris
+Max Planck Institute for Solid State Research    https://orcid.org/0000-0002-2062-5046
+Jinwoo Hwang
+Ohio State University
+Giniyat Khaliullin
+Max Planck Institute for Solid State Research    https://orcid.org/0000-0001-9395-6447
+Gang Cao
+University of Colorado Boulder    https://orcid.org/0000-0001-9779-430X
+Bernhard Keimer
+Max Planck Institute for Solid State Research    https://orcid.org/0000-0001-5220-9023
+Jong-Woo Kim
+Argonne National Laboratory    https://orcid.org/0000-0001-9641-2947
+Jung Ho Kim
+Article
+
+Keywords:
+
+Posted Date: July 26th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4753008/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 April 15th, 2025. See the published version at https://doi.org/10.1038/s41467-025-58922-z.
+Tunable magnons of an antiferromagnetic Mott insulator via interfacial metal-insulator transitions
+
+S. Shrestha,1 M. Souri,1 C. Dietl,2 E. M. Pärschke,3 M. Krautloher,4 G. A. Calderon Ortiz,5 M. Minola,4 X. Shi,4 A. V. Boris,4 J. Hwang,5 G. Khaliullin,4 G. Cao,6 B. Keimer,4 J.-W. Kim,2 J. Kim,2 and A. Seo1
+
+1Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506, USA
+2Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA
+3Department of Physics, University of Alabama at Birmingham, Birmingham, AL 35294, USA
+4Max-Planck-Institut für Festkörperforschung, D-70569 Stuttgart, GERMANY
+5Department of Materials Science and Engineering, The Ohio State University, Columbus, OH 43210, USA
+6Department of Physics, University of Colorado at Boulder, Boulder, CO 80309, USA
+
+Abstract
+
+Antiferromagnetic insulators offer an alternative to ferromagnets due to their ultrafast spin dynamics essential for low-energy terahertz spintronic device applications. One way is to utilize magnons, i.e., quantized spin waves, which can carry information through excitations. However, finding external knobs for tuning the magnons has been a significant challenge. Here we report that interfacial metal-insulator transitions can be an effective means for controlling the magnons of a strongly spin-orbit-coupled antiferromagnetic Mott insulator, Sr2IrO4. From resonant inelastic X-ray scattering and Raman spectroscopy, we have observed a pronounced softening of zone-boundary magnon energies in several Sr2IrO4 thin-film systems that are epitaxially contacted with metallic 4d transition-metal oxides (TMOs). Therefore, the magnon dispersion of Sr2IrO4 is tunable by metal-insulator transitions of the 4d TMO crystals. Remarkably, this non-trivial behavior of magnons is a long-range phenomenon coupled with intriguing magnon-phonon interactions. Our experimental finding proposes a new scheme for magnonics.
+Magnons, i.e., collective spin wave excitations originating from spin precession in magnetically ordered materials, have the potential to serve as a promising medium for quantum information devices. Since the propagation of magnons does not require the transport of a charge, preventing electrical losses such as Joule heating\(^1\), it gives rise to a burgeoning research field known as magnonics\(^{2,3}\). Antiferromagnetic insulators have garnered considerable attention in this emerging field, primarily due to their ultrafast spin dynamics compared to ferromagnetic counterparts, which are essential for device operation in the terahertz range\(^{4-6}\). Nevertheless, effectively guiding and coherently manipulating magnons using external stimuli is still a significant challenge.
+
+Hetero-interfaces between two different materials can provide model systems for investigating the relation between external stimuli and collective spin waves. Examples are the effects of lattice strain\(^7\), interfacial coupling, and charge transfer on magnons\(^{8,9}\) and their spin currents\(^{10-12}\). In particular, interfaces between an antiferromagnetic insulator and a metal have been considered for novel spin-charge conversion\(^{13,14}\). Despite some astonishing predictions from magnetic insulator/metal interfaces\(^{15}\), the fundamental understanding of how a metallic interface affects the spin-wave dispersion of an antiferromagnetic insulator remains elusive.
+
+Sr$_2$IrO$_4$, a $5d$ transition-metal oxide, is a quasi-two-dimensional antiferromagnetic insulator with strong spin-orbit interaction resulting in the $J_{\text{eff}}$ =1/2 pseudospins. The distinctive canted antiferromagnetism and magnetic anisotropy in the $J_{\text{eff}}$ =1/2 state can be useful for spintronic applications\(^{16,17}\). Notably, Sr$_2$IrO$_4$ hosts spin waves at terahertz frequencies with a significant stress response mediated by strong spin-orbit interactions\(^7\). Its similarities to La$_2$CuO$_4$, a parent compound of high $T_c$ superconductors, suggest a potential for superconducting antiferromagnetic magnonics\(^{18}\). Therefore, Sr$_2$IrO$_4$ presents a compelling avenue for studying the influence of
+metallic interfaces on spin-wave dispersion and its heterostructures offer opportunities to explore intriguing phenomena\(^{19,20}\).
+
+In this article, we report a systematic study of the spin-wave dispersion of Sr$_2$IrO$_4$ thin films that are epitaxially interfaced with various metallic or insulating single crystals. The recent advancement of high-resolution resonant inelastic x-ray scattering (RIXS) has enabled us to access the low-energy magnetic dynamics of iridates throughout the entire Brillouin zone\(^{21}\). Our RIXS experiments show a significant softening of single magnon peaks (with no broadening) near the (\( \pi/2, \pi/2 \)) zone boundary for various Sr$_2$IrO$_4$ thin films neighboring metallic crystals, while the single magnon spectrum of Sr$_2$IrO$_4$ thin films remains unchanged when adjoining insulating crystals. Similar behavior of the two-magnon excitation, predominantly indicating zone boundary excitation, is observed in Raman spectra. Conversely, the phonon mode of Sr$_2$IrO$_4$ thin films exhibits significant hardening when interfaced with metallic crystals. We propose that electron-phonon interaction, occurring either at the heterointerface or within the metallic substrate, could have modified the phonon of Sr$_2$IrO$_4$ thin films, subsequently influencing the magnons via long-range magnon-phonon interactions throughout the entire thin film. Our systematic measurements using various bulk-sensitive experimental techniques such as Raman spectroscopy, optical spectroscopy, and resonant x-ray scattering, indicate that conventional interfacial interactions such as strain, doping, and proximity effects are unlikely to account for this experimental result. Our experimental results present a novel approach in magnonics, utilizing metal-insulator transitions in adjacent crystals as a mechanism for manipulating the propagation of terahertz magnons.
+Experimental Layout
+
+We constructed epitaxial heterostructures by depositing Sr$_2$IrO$_4$ epitaxial thin films on ruthenates single crystals (Fig. 1a) by using pulsed laser deposition$^{22,23}$. To circumvent the potential influence of spin-spin interactions, we opt for ruthenates exhibiting paramagnetic characteristics. The Sr$_2$RuO$_4$ single crystals exhibit a tetragonal crystal structure and metallic transport behavior whereas the single crystals of Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ are orthorhombic and exhibit a metal-insulator transition at 55 K (i.e., metallic above 55 K and insulating below 55 K)$^{24}$ with a slight change of the $b$ and $c$-lattice constants (Supplementary Fig. 1)$^{24}$. For a systematic examination and to address the strain effect, the Sr$_2$IrO$_4$ thin film on an insulating (LaAlO$_3$)$_{0.3}$(Sr$_2$TaAlO$_6$)$_{0.7}$ (LSAT) perovskite single crystal is also investigated, as LSAT and Sr$_2$RuO$_4$ single crystals have a similar lattice mismatch with Sr$_2$IrO$_4$. A high-resolution Z-contrast scanning transmission electron microscopy image of the Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructure (Supplementary Fig. 2) reveals an atomically sharp heterointerface, akin to the reported sharpness in the Sr$_2$IrO$_4$/Ca$_3$Ru$_2$O$_7$ heterointerface$^{25}$, which is expected to be replicated in the Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ heterostructure. Supplementary Figure 3a exhibits distinct (0 0 $l$)-diffraction peaks for both the Sr$_2$IrO$_4$ thin film and the Sr$_2$RuO$_4$, Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$, and LSAT substrates, including interference fringes near the (0 0 12) peak. X-ray reciprocal space mapping clearly shows that the in-plane lattice of Sr$_2$IrO$_4$ thin films is coherently strained with all three substrates (Supplementary Fig. 3b and 3c). It is noteworthy that the Sr$_2$IrO$_4$ thin film grown on both Sr$_2$RuO$_4$ and LSAT experiences the same amount of compressive strain of -0.51% (Supplementary Table 1). However, the Sr$_2$IrO$_4$ thin film deposited on the Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ substrate experiences a -2.22% compressive strain along the $a$-axis and a 0.33% tensile strain along the $b$-axis above 55 K, whereas the tensile strain along the $b$-axis increases to 2% below 55 K (Supplementary Table 2).
+Figure 1 | Sr2IrO4 thin film systems. Schematic diagram of Sr2IrO4 thin film on different ruthenates substrates and reference LSAT substrate. The Sr2RuO4 and LSAT single crystals have comparable in-plane lattice constants yet exhibit metallic, and insulating properties, respectively. The Ca3Ru1.98Ti0.02O7 single crystal exhibits metallic properties above 55 K and becomes insulating below 55 K.
+
+In recent years, RIXS has become the tool of choice for collecting momentum-resolved and element-specific information about collective magnetic excitations such as magnons, and spin-orbit excitons in transition metal oxide thin films26-28. Figure 2a shows representative energy loss spectra of Sr2IrO4/Sr2RuO4 heterostructure collected along high-symmetry directions throughout the magnetic Brillouin zone. These spectra were acquired using RIXS measurements at the 27-ID beamline of the Advanced Photon Source, utilizing a horizontal scattering setup with incident photons polarized in the \( \pi \)-direction, as depicted in Fig. 2c. Additionally, Figure 2b depicts a color intensity map generated from energy loss spectra resembling those presented in Fig. 2a. The distinctive features of these spectra such as a dispersive magnetic excitation (magnon) in the low energy range of 0 - 0.25 eV and a dispersive orbital excitation (spin-orbit exciton) in the higher energy range of 0.40 - 0.90 eV exhibit inherent properties of the system18,28. Furthermore, the detections of well-defined dispersive magnons and spin-orbit excitons indicate high crystallinity of Sr2IrO4 thin film.
+Figure 2 | RIXS spectra of Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructure. **a** Energy loss spectra of Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructure at 20 K along high symmetry lines. The inset shows high symmetry points in the Brillouin zone of the undistorted tetragonal unit cell and the magnetic unit cell. **b** The image plot of the data shown in (b). The detections of well-defined dispersive magnons and spin-orbit excitons indicate high-quality Sr$_2$IrO$_4$ thin film. The orange dotted line in both (a) and (b) is the eye guide to the magnon dispersion. **c** A visual representation depicting the horizontal scattering geometry utilized in RIXS measurements.
+
+Results
+
+The RIXS measurements reveal that the low-energy magnon dispersion of Sr$_2$IrO$_4$ exhibits a sudden softening by about 20 meV at the ($\pi/2$, $\pi/2$) zone boundary when the neighboring single crystal goes across a transition from insulating to metallic. Figure 3a shows the low-energy magnon peaks of all Sr$_2$IrO$_4$ thin films at ($\pi$, 0) and ($\pi/2$, $\pi/2$). As observed in Sr$_2$IrO$_4$/Sr$_2$RuO$_4$,
+Figure 3 | Softening of magnon in Sr$_2$IrO$_4$ interfaced to metallic substrates at ($\pi/2$, $\pi/2$) zone boundary. **a** RIXS spectra of Sr$_2$IrO$_4$ thin films on two types of substrates, with single crystal (light green) at ($\pi$, 0) and ($\pi/2$, $\pi/2$): metallic substrates (Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ (orange) and Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ at T > 55 K (red)) and insulating substrates (Sr$_2$IrO$_4$/LSAT (cyan) and Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ at T < 55 K (blue)). The Sr$_2$IrO$_4$ thin films interfaced on the metallic substrates show significant softening of the single magnon at the ($\pi/2$, $\pi/2$). **b** Magnon dispersion along the high symmetry lines extracted from the RIXS spectra in comparison with data obtained on Sr$_2$IrO$_4$ single crystal. The solid orange and cyan lines represent the theoretical fitting using the model Hamiltonian for the Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ and Sr$_2$IrO$_4$/LSAT, respectively.
+
+well-defined magnons are present in other thin films on both metallic (Sr$_2$RuO$_4$ and Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ above 55 K) and insulating substrates (Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ below 55 K and LSAT). While the magnon peak energy remains almost similar (around 200 meV) at ($\pi$, 0) for all five systems, i.e., Sr$_2$IrO$_4$/Sr$_2$RuO$_4$, Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ (T < 55 K), Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ (T > 55 K), Sr$_2$IrO$_4$/LSAT, and Sr$_2$IrO$_4$ single crystal, a notable difference is observed in the magnon peak energy at ($\pi/2$, $\pi/2$). The Sr$_2$IrO$_4$ thin films interfaced on the metallic substrates (Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ (orange) and Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ above 55 K (red)) show significant softening, with a reduction of about 20 meV at ($\pi/2$, $\pi/2$). In contrast, for thin films on insulating
+substrates (Ca3Ru1.98Ti0.02O7 below 55 K (blue) and LSAT (cyan)), the magnon peak energy at (\( \pi/2, \pi/2 \)) is indistinguishable from that of the single crystal. This peak shift is greater than the experimental error bar\(^{21}\). Essentially, we can group them into two categories: Sr2IrO4 heterostructures with insulating substrates show higher magnon energy, while the other with metallic substrates have a softened magnon energy reduced by about 20 meV.
+
+![Raman spectra of B_{2g} two-magnon modes in Sr2IrO4/Sr2RuO4 and Sr2IrO4/LSAT heterostructures measured at 10 K. Temperature-dependent Raman spectra of B_{2g} two-magnon modes of Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructure.](page_367_624_819_496.png)
+
+Figure 4 | Softening of two-magnon in samples with metallic substrates. **a** Raman spectra of \( B_{2g} \) two-magnon modes in Sr2IrO4/Sr2RuO4 and Sr2IrO4/LSAT heterostructures measured at 10 K. **b** Temperature-dependent Raman spectra of \( B_{2g} \) two-magnon modes of Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructure. Two-magnon energy in Sr2IrO4 interfaced to metallic substrates (Sr2RuO4 and Ca3Ru1.98Ti0.02O7 (T > 55 K)) has lower peak energy compared to that interfaced to insulating substrates (LSAT and Ca3Ru1.98Ti0.02O7 (T < 55 K)). Two-magnon peak positions for both figures are estimated by using two Lorentz oscillator curve fits which are represented by smooth solid lines and their sum is shown by black solid line.
+The two-magnon peak energies in the high-resolution Raman spectra corroborate the RIXS measurements. Figure 4a illustrates the \( B_{2g} \) two-magnon modes in Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ and Sr$_2$IrO$_4$/LSAT at 10 K, while Fig. 4b displays the temperature-dependent Raman spectra of \( B_{2g} \) two-magnon modes in Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$. We determine the two-magnon peak energies (\( \omega_{2M} \)) through fits to a model function comprising two Lorentz oscillators. Note that the two-magnon energies of thin films on metallic substrates (Sr$_2$RuO$_4$ and Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ above 55 K) are lower than those on insulating substrates (Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ below 55 K and LSAT). Considering that the two-magnon mode primarily reflects zone boundary excitations$^{29}$, this observation aligns with the softening of the (\( \pi/2,\ \pi/2 \)) zone boundary magnon and establishes consistency between the two measurements.
+
+By fitting the magnon dispersion data (Fig. 3b) of Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ and Sr$_2$IrO$_4$/LSAT heterostructures using a Heisenberg spin model, we extracted the in-plane exchange interactions, i.e., the nearest (\( J_1 \)), next nearest (\( J_2 \)), next-next nearest (\( J_3 \)), and fourth nearest (\( J_4 \)) neighbors, between the \( J_{\text{eff}} = 1/2 \) pseudospins. The best-fit results in the values of \( J_1 = 50 \) meV, \( J_2 = -21 \) meV, \( J_3 = 20 \) meV, and \( J_4 = 6.3 \) meV for Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructure and \( J_1 = 50 \) meV, \( J_2 = -17 \) meV, \( J_3 = 16 \) meV, and \( J_4 = 9 \) meV for Sr$_2$IrO$_4$/LSAT heterostructure. Note that the change of the experimentally measured magnon dispersion for metallic substrates suggests increasing in-plane interactions \( J_2 \) and \( J_3 \) compared to insulating substrates and Sr$_2$IrO$_4$ single crystals (Supplementary Table 3).
+
+Raman spectroscopy indicates that the phonon modes of Sr$_2$IrO$_4$ undergo a noticeable hardening by approximately (1 – 1.4) meV when the adjacent single crystal substrate is altered from insulating to metallic, likely attributed to electron-phonon interaction. Figure 5a illustrates
+Figure 5 | Hardening of phonons in Sr2IrO4 interfaced with metallic substrates. a \( A_{1g} \) and \( B_{2g} \) phonon modes of Sr2IrO4/Sr2RuO4 and Sr2IrO4/LSAT heterostructures. The solid black lines represent the Lorentzian fit. b Temperature-dependent \( B_{2g} \) phonon modes of Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructure. Inset: Temperature-dependent peak position of the \( B_{2g} \) phonon modes of Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructure.
+
+the \( A_{1g} \) and \( B_{2g} \) phonon modes of the Sr2IrO4 thin film in the Sr2IrO4/LSAT and Sr2IrO4/Sr2RuO4 heterostructures. While the phonon modes of Sr2IrO4/LSAT closely resemble Sr2IrO4 single crystal, a notable upward energy shift by about 1.4 meV and 1 meV for \( A_{1g} \) and \( B_{2g} \) modes, respectively, is observed in Sr2IrO4/Sr2RuO4 heterostructure. A similar upward shift of up to 0.7 meV in the phonon energy is also observed in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures when transitioning from an insulating to metallic state of the Ca3Ru1.98Ti0.02O7 substrate at 55 K (Fig. 5b). Nevertheless, we acknowledge that the sudden structural change at 55 K might also have some contributions to the phonon mode shift in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures. Additionally,
+we examined several other heterostructures, such as Sr$_2$IrO$_4$/Ca$_2$Ru$_{0.91}$Mn$_{0.09}$O$_4$ (insulator), Sr$_2$IrO$_4$/Sr$_2$RhO$_4$ (metal), and Sr$_2$IrO$_4$/Ca$_3$Ru$_2$O$_7$ (metal) at 10 K. These heterostructures displayed similar patterns based on the substrate's metallicity, showing a stiffening of the $B_{2g}$ phonons in the Sr$_2$IrO$_4$ thin film by about 8 cm$^{-1}$ when interfaced with metallic substrates compared to insulating ones (Supplementary Fig. 4). Clearly, a common factor in the results is the metallic state of the substrates. The presence of delocalized carriers could explain the anomalous phonon behavior observed. One potential explanation is that charge carrier-phonon interactions within the metallic substrate alter its phonons, which then resonate with the phonons of the Sr$_2$IrO$_4$ thin film. Alternatively, an interaction between electrons from the substrate and phonons from the Sr$_2$IrO$_4$ thin film at the interface could propagate the modified phonons throughout the entire Sr$_2$IrO$_4$ thin film.
+
+Discussion
+
+Combining our observations, we noted a significant softening of magnons and hardening of phonon modes in Sr$_2$IrO$_4$ thin films when deposited on a metallic substrate compared to the insulating substrate. These phonons and magnon modes may be interconnected with the simple formula: \( c \Delta \omega_{\text{phonon}} = \Delta \omega_{\text{magnon}} \), where \( c \) represents the coupling constant between magnon and phonon, \( \Delta \omega_{\text{phonon}} \) and \( \Delta \omega_{\text{magnon}} \) is the change in phonon mode and magnon energy between metallic and insulating substrate, respectively. The coupling constant for the single magnon with $B_{2g}$ phonon mode is about -19 whereas with $A_{1g}$ mode is about -15. This suggests that any alteration in magnon energy arises from the modifications in the phonon modes. Therefore, the long-range phenomenon accompanied by magnon-phonon couplings and electron-phonon couplings explains the intriguing change of the magnon dispersion of Sr$_2$IrO$_4$ thin films interfacing with metallic crystals. The delocalized electrons in the metallic crystals may interact with the phonon modes of
+Sr$_2$IrO$_4$ thin films through interfacial electron-phonon interactions, or they may interact with the phonon modes of metallic substrates through bulk electron-phonon interactions, thereby modifying the phonon modes of Sr$_2$IrO$_4$ thin film. Consequently, the modified phonon mode may interact with the magnon within the Sr$_2$IrO$_4$ thin film, resulting in the magnon's softening and the phonon mode's hardening. It's crucial to highlight that the magnon-phonon interaction has minimal impact on the first nearest-neighbor interaction, but it significantly affects interactions with the second and third nearest neighbors.
+
+Other possible tuning parameters, including lattice strain, interfacial proximity effects, and carrier doping, are inadequate to account for our observations. The strain effect, for instance, fails to justify the magnon softening observed in the Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructure as the Sr$_2$IrO$_4$/LSAT heterostructure, which exhibits similar strain states, does not show the softening. Additionally, proximity effects at the interface are ruled out as our observations are made through bulk-sensitive techniques\textsuperscript{27} i.e., the experimental data encompassed the entire volume of 20-30 nm (8-12 layers) films, not just near the interface. Furthermore, Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructures of varying thicknesses (12, 30, and 50 nm) showed consistent magnon softening without a noticeable thickness dependence (Supplementary Fig. 5), indicating a long-range effect throughout the thin film. In case the charge transfer between a metallic crystal to Sr$_2$IrO$_4$ thin film at the interface is hole transfer, it typically hardens magnon peak energy at the zone boundary\textsuperscript{30,31}, contrary to our findings. Electron doping typically softens magnon peak energy but broadens it significantly and collapses the long-range magnetic order of Sr$_2$IrO$_4$\textsuperscript{32,33}. In both Sr$_2$IrO$_4$/Ca$_3$Ru$_{1.98}$Ti$_{0.02}$O$_7$ and Sr$_2$IrO$_4$/Sr$_2$RuO$_4$ heterostructures, we observed neither broadened magnon peaks nor a collapse of long-range magnetic order (Supplementary Fig. 6). Resonant x-ray scattering near the Ru $L_2$ edge also confirms the absence of Ru ions near the Sr$_2$IrO$_4$ interface (Supplementary Fig. 7), dismissing
+the potential intermixing between Ir and Ru ions at the interface. Also, optical spectroscopy reveals a clear insulating gap of ~0.3 eV in the Sr2IrO4/Sr2RuO4 heterostructure, similar to Sr2IrO4 single crystals (Supplementary Fig. 8), suggesting minimal charge transfer or doping in the Sr2IrO4 thin films.
+
+In summary, we have observed a pronounced softening of the zone boundary magnon energy and hardening of phonon modes when Sr2IrO4 thin films are epitaxially linked with the metallic 4d TMO single crystals. We discuss that an electron-phonon coupling at the interface or within the substrate might have affected the magnon dispersion of Sr2IrO4 via a long-range magnon-phonon interaction. This phenomenon has increased second and third-nearest-neighbor interaction while its impact on the first-nearest neighbor is minimal. Our experimental results call for further theoretical studies and calculations with a new understanding of microscopic interactions between magnons and phonons. Nevertheless, besides the prevailing acoustic waves responsible for magnon-phonon coupling\(^{24}\), we posit that metal-insulator heterointerfaces serve as a novel mechanism for inducing magnon-phonon coupling essential for magnonics. Our work also suggests some interesting questions and perspectives. For instance, whether this phenomenon is specific to \(5d/4d\) heterostructures or if it will also occur in other types of heterostructures. In other words, it sparks questions regarding how spin-orbit interaction influences the magnon dispersion of antiferromagnetic insulators and whether this phenomenon can also be observed in Van der Waals heterostructures. Future studies of various heterostructures with different materials would shed light on these questions.
+Acknowledgments
+
+We acknowledge the support of National Science Foundation Grant No. DMR-2104296 for sample synthesis and characterization. This research used resources of the Advanced Photon Source; a U.S. Department of Energy (DOE) Office of Science user facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DE-AC02-06CH11357. Electron microscopy was performed at the Center for Electron Microscopy and Analysis at the Ohio State University supported by National Science Foundation Grants No. DMR-1847964. G.C. acknowledges NSF support via Grant No. DMR 2204811. B.K. acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project No. 107745057-TRR 80.
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformation.pdf

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+Learning Superior Energy Management from Electric Vehicle Data
+
+Hongwen He
+hwhebit@bit.edu.cn
+
+Beijing Institute of Technology
+Yong Wang
+Beijing Institute of Technology
+Jingda Wu
+Nanyang Technological University   https://orcid.org/0000-0002-7336-4492
+Zhongbao Wei
+Beijing Institute of Technology   https://orcid.org/0000-0003-0051-5648
+Fengchun Sun
+Beijing Institute of Technology
+
+Article
+
+Keywords: Energy management, Electric vehicle data, Reinforcement learning, Fuel cell vehicles, Data-driven
+
+Posted Date: July 3rd, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4523312/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/s41467-025-58192-9.
+Learning Superior Energy Management from Electric Vehicle Data
+
+Yong Wang^{a,b} , Jingda Wu^{c} , Hongwen He^{*a,b} , Zhongbao Wei^{a} and Fengchun Sun^{a}
+
+^{a}School of Mechanical Engineering, Beijing Institute of Technology, Beijing, 100081, China
+^{b}National Key Laboratory of Advanced Vehicle Integration and Control, Beijing Institute of Technology, Beijing, 100081, China
+^{c}The Hong Kong Polytechnic University, Hung Hom, Hong Kong
+
+ARTICLE INFO
+
+Keywords:
+Energy management
+Electric vehicle data
+Reinforcement learning
+Fuel cell vehicles
+Data-driven
+
+ABSTRACT
+
+Despite the promising potential of energy management technologies in optimizing electric vehicle (EV) performance and fostering global energy sustainability, the extensive research conducted over the past decade has yet to translate into practical applications. This discrepancy arises primarily from the reliance of existing methodologies on simulation-based development paradigms, leading to a significant disparity between simulated results and real-world efficacy. Herein, we present a pioneering real-world data-driven energy management strategies (EMS) approach that utilizes an innovative offline reinforcement learning (ORL) framework. This paradigm enables EMS to learn from diverse real-world data, obviating the need for explicit rule design or high-fidelity simulators, and allowing for seamless application of the proposed method to any existing EMS. Moreover, it continuously enhances performance even after deployment in actual energy management systems. We evaluate the proposed ORL method on fuel cell EVs, training the ORL agent to optimize energy consumption and system degradation. The EV monitoring and management platform in China provides real-world data for validating our methodology. The results demonstrate that ORL consistently learns superior EMS in various conditions. With increasing data availability, its performance improves significantly, from 88% to 98.6% relative to theoretical optimality after two data updates. After training with more than 60 million kilometers of data, the ORL agent can learn a general EMS that adapts to unseen and corner-case conditions. These results highlight the effectiveness of integrating the data-driven method with established EMS techniques to enhance performance and underline its potential to utilize large-scale data to improve vehicle energy efficiency and longevity.
+
+1. Introduction
+
+The automotive industry is undergoing a significant transformation, primarily due to the global focus on sustainability and environmental conservation. Electric vehicles (EVs) are leading this shift, playing a key role in mitigating environmental challenges and advancing sustainable transportation solutions [1, 2]. Concurrently, the emergence of hybrid energy systems (HES) within the EV powertrain represents an emerging trend, offering superior solutions over single energy systems [3]. By integrating multiple energy sources such as batteries, fuel cells, and internal combustion engines, HES improves overall efficiency, sustainability, and reliability, while also providing adaptability to a wide range of driving conditions [4]. Propelled by rapid technological advancements and supportive policies, EVs equipped with HES, including Hybrid EVs (HEV), Plug-in hybrid EVs (PHEV), and Fuel cell EVs (FCEV), are gaining traction worldwide [3]. For example, BYD, a prominent EV manufacturer, achieved sales of 3.02 million EVs in 2023, and PHEVs represent 47.9% of total sales. In the first quarter of 2024, PHEVs accounted for a notable 51.6% of total sales, indicating their growing popularity. This trend is mainly attributed to advancements in HES energy management, which enhance energy efficiency and overall performance.
+
+The energy management strategy (EMS), responsible for allocating energy flow among HES to achieve predefined objectives, performs several vital functions essential for EVs:(1) EMS optimizes system efficiency by intelligently allocating energy flow based on driving conditions, reducing energy consumption and extending driving range [5]. (2) EMS optimizes power delivery based on driver demand, improving acceleration and responsiveness, while also ensuring smooth power delivery for improved driving experience. (3) By considering the characteristics of different power sources, EMS extends the lifespan of the HES, thus enhancing system reliability and safety [6]. Early EMS solutions utilize various rule-based approaches to achieve energy-saving objectives. Rule-based EMS involves the design of predefined rules and parameters tailored to specific driving conditions and vehicle characteristics, relying on
+expert knowledge with iterative refinement based on testing feedback [7]. However, this process can be labor-intensive and time-consuming, requiring manual expertise for rule creation and extensive experimentation for parameter calibration. Moreover, its static nature and inability to adapt to dynamic driving scenarios limit its effectiveness in maximizing energy savings and overall performance.
+
+Recently, there has been a surge in advanced algorithms for energy management of HES, including dynamic programming (DP), model predictive control (MPC), reinforcement learning (RL), and others. A common feature across these methods is the use of optimal control or machine learning (ML) algorithms to compute optimal EMS based on high-fidelity simulators. Collectively, these approaches are referred to as simulation-based EMS in our study. Although DP and MPC provide elegant solutions based on future driving data, accurately forecasting future driving conditions using historical speed and dynamic traffic information remains a significant challenge [8]. Additionally, prediction models and optimization algorithms often result in considerable computational complexity, leading to suboptimal real-time performance [3]. Consequently, applying optimal control methods in real-world vehicle settings poses considerable challenges at present. In contrast, learning-based models, exemplified by Deep RL (DRL), do not rely on knowledge of future conditions and present promising alternatives for EMS [9]. DRL involves learning optimal actions in an environment through trial and error, where the DRL agent interacts with the environment to maximize cumulative rewards over time [10]. DRL-based EMS has been a subject of active research in recent years, with recent developments in online DRL algorithms such as Deep Deterministic Policy Gradient (DDPG) [11], Soft Actor-Critic (SAC) [12], Proximal Policy Optimization (PPO) [13], and others, leading to remarkable results. However, the application of DRL-based EMS faces challenges as an online learning paradigm, particularly concerning the interaction between the DRL agent and the EV simulator, which raises safety concerns. Moreover, while existing literature assumes that simulation models accurately represent real-world conditions, the construction of high-fidelity models that encompass vehicle dynamics, powertrain, traffic scenarios, and driver behavior [14] remains a challenge [15]. This discrepancy can cause the "sim-to-real" problem, where EMS learned in simulators may not be effectively transferred to real vehicles, which leads to the complexity of EMS development [16].
+
+In recent years, data-driven methodologies, propelled by advancements in ML techniques and the availability of large datasets, have become essential in addressing key challenges in the EV field [17]. With support from data collection platforms and open-access laboratory data, these data-driven approaches have revolutionized various aspects of battery management systems (BMS). This includes automatic discovery of complex battery aging mechanisms [18], prediction of battery safety envelopes [19], evaluation of safety conditions [20], estimation of battery state of health [21], and even enhancing battery lifetime prediction models with unlabeled data [22]. Notably, innovations in feature extraction and supervised ML techniques tailored for time-series data have greatly enhanced prediction accuracy. This success has sparked interest in exploring data-driven methods for sequential decision-making tasks, including improving energy management systems. A common approach to implementing a data-driven EMS involves using supervised learning, where the ML model is employed to capture the complex and non-linear relationships between input features and corresponding control outputs. In [23], recurrent neural networks are trained offline using a substantial amount of training data obtained from the global optimization strategy DP, yielding a sub-optimal EMS that closely approximates the DP. It is essential to recognize the differences from the prediction tasks in BMS applications, as EMS entails sequential decision-making. Although supervised learning can mimic the policy of EMS through imitation learning, its heavy reliance on expert data may result in limited generalization to new and diverse scenarios. Hence, it’s crucial to explore alternative methods for learning EMS from non-expert data, which is common in automotive applications.
+
+In this paper, we present a novel data-driven EMS paradigm, addressing key challenges discussed above by leveraging offline data generated by existing EMS strategies, without the need for explicit rule design or online interaction. Our approach integrates DRL and supervised learning techniques, departing from traditional rule-based EMS and simulation-based methods to enhance EMS capabilities, as visually depicted in Figure 1(a). Notably, our proposed method can be directly integrated with any EMS algorithm and continuously improves through the collection data. We term this approach the offline reinforcement learning (ORL) agent [24], which is trained by combining real-world data as well as carefully filtered and processed simulation data through a novel exploration scheme. To evaluate this paradigm, we focus on a fuel cell electric vehicle (FCEV) as the subject and collect data for learning power allocation strategies. The EV monitoring and management platform in China offers real-world data to validate our methodology (Figure 1(b)). Overall, the ORL agent introduced herein exhibits four key features (Figure 1(c)):
+Figure 1: Overview of the proposed data-driven EMS framework. (a) Comparison of three EMS paradigms: Traditional rule-based EMS relies on expert knowledge and calibration based on fixed driving cycles. Simulation-based EMS requires high-precision models and entails transitioning from simulation analysis to real-world deployment, resulting in a gap between simulated and real-world performance (sim-to-real gap). In contrast, the proposed real-world data-driven EMS learns directly from actual data. (b) China has established a three-tier EV monitoring and management system involving the state, local governments, and enterprises. The National Monitoring and Management Platform collects real-time operational data from over 20 million EVs [25]. (c) The ORL agent works with an existing EMS and continuously collects EV data to improve the EMS. (d) Overall diagram of the proposed data-driven EMS methodology.
+
+1) Purely data-driven EMS: By autonomously learning and optimizing from collected offline datasets, our approach facilitates the development of advanced EMS without necessitating expert knowledge or the construction of high-fidelity EV simulators. This data-driven process significantly simplifies EMS development workflows.
+
+2) Learning from non-optimal data: Our research indicates that ORL can learn near-optimal EMS from non-optimal data and even can derive superior policies from sub-optimal. Our approach is less reliant on data quality allowing for effective learning. This practicality allows us to utilize raw data generated by actual vehicles, which is common in automotive applications.
+
+3) Enhancement with increased data: The performance of ORL improves as more training data is utilized, demonstrating its ability to continuously adapt and enhance EMS performance. Through training across diverse
+datasets, it can potentially adapt to new driving conditions and yield favorable results, even in corner-case conditions. When sufficient data are available, ORL can learn a generalized EMS.
+
+4) Compatibility with existing EMS: Our approach seamlessly integrates with established rule-based or simulation-based EMS methods, leveraging data from onboard controllers to augment EMS performance. This ensures that baseline performance is preserved while facilitating further enhancement using ORL, making it a valuable extension to conventional EMS methodologies.
+
+2. Results
+
+2.1. The overview of data-driven EMS
+
+In Figure 1(d), the framework overview of ORL for EMS is illustrated. We introduce the three phases of applying the proposed ORL algorithm to the EMS problem, which include data collection, offline learning, and evaluation. ORL is an innovative subset of RL methods rooted in data-driven approaches. Unlike most simulation-based EMS scheduling methods, the data-based learning process does not require the building of an EV simulation environment.
+
+In the data collection phase, an available dataset (\( D \)) is gathered from the existing EMS policy (\( \pi_g \)). It is crucial to record various parameters such as velocity, acceleration, hydrogen consumption, electricity consumption, fuel cell degradation, battery state of charge (SOC), and others during vehicle operation. However, due to limitations in real-world data quality and privacy concerns associated with collecting data from a large number of actual vehicles, we developed an FCEV simulation model to generate laboratory datasets 2(a). This FCEV model enables the generation of extensive, high-fidelity data based on real-world driving conditions 2(b). Subsequently, we employ a tailored data processing model to encode control and state variables into standardized data formats. The data encoding process converts these parameters into a transition dataset \( D = (s, r, a, s') \). Here, \( s, a, \) and \( r \) represent the state, action, and reward as described in the Methods section, respectively, while \( s' \) denotes the subsequent state, and \( i \) indexes a transition in the dataset. These meticulously curated datasets are stored in the buffer and serve as input for the ORL agent.
+
+In the offline learning phase, our proposed ORL agent is designed based on the Actor-Critic network and incorporates Behavior Cloning (BC) and Discriminator Blend (DB) mechanisms. In each training step, mini-batches of transitions (\( s, r, a, s' \)) stored in a data buffer are sampled from the replay buffer to update the ORL networks. The Actor network, responsible for determining the action \( a_t \sim \pi_\beta (\cdot | s_t) \), is updated to maximize the expected return as estimated by the Critic network. BC regularization is applied to the policy update step to encourage the policy to prioritize actions present in the dataset. Moreover, the DB component is introduced to allow actions beyond the dataset distribution similar to those included in the dataset. Through training, the agent learns to optimize its actions based on observed states and rewards. The details of the ORL agent will be elaborated upon in the Methods section in detail.
+
+After completing the training phase, the neural network parameters representing the EMS policy of the ORL agent are saved for future use. Subsequently, the trained agent is evaluated to gauge its effectiveness and performance. Utilizing the FCEV environment established during the data collection phase, our subsequent experiments employ three standard driving cycles (WTVC, FTP, and CHTC) to evaluate energy cost. Additionally, we incorporate various real-world driving scenarios to comprehensively assess the trained EMS policy. Following the evaluation, adjustments to the agent hyperparameters or training process may be considered to improve its performance. This iterative process of training, evaluation, and refinement continues until the desired level of EMS performance is attained. Upon achieving satisfactory performance, the trained agent becomes eligible for deployment in real-world scenarios, where it can be utilized to efficiently optimize energy management systems.
+
+2.2. Data for learning and analysis
+
+We select the Proximal Policy Optimization (PPO), which demonstrates the best performance among online DRL algorithms in our EMS problem, as the expert EMS. Using PPO, we generate datasets denoted as \( D^E \) comprising 300K time steps. Additionally, we employ a random agent that samples actions randomly, generating datasets denoted as \( D^R \), which represent poor performance. To create settings with varying levels of data quality in the suboptimal offline dataset, we combine transitions from the expert datasets \( D^E \) and the random datasets \( D^R \) in different ratios. Specifically, we consider four different dataset compositions, denoted as D1, D2, D3, and D4. These settings are defined as follows: D1 (Data-1): Consists solely of transitions from the expert dataset \( D^E \), representing the expert policy. D2 (Data-2): Contains two-thirds of transitions from the expert dataset \( D^E \) and one-third of transitions from the random dataset \( D^R \), representing suboptimal data. D3 (Data-3): Comprises one-third of transitions from the expert dataset
+Figure 2: Comparison for different datasets. (a) The simulation model for the fuel cell hybrid electric vehicle (FCEV), depicts the powertrain layout and energy flow topology. (b) The principle of EMS involves the allocation of energy flow among hybrid energy systems (fuel cell and battery) to achieve predefined objectives based on driving conditions. Here, real driving conditions are gathered and then use the simulated FCEV model to generate energy cost data for training the ORL agent. (c) Distribution of encoded actions for the four datasets, each action is normalized to the [-1,1]. D1 represents data generated by an expert policy, D2 and D3 denote suboptimal data generated by a combination of expert and random policies, D4 comprises entirely random data. (d) The states distribution of four datasets.
+
+\( D^E \) and two-thirds of transitions from the random dataset \( D^R \), representing another suboptimal data. D4 (Data-4): Comprises solely of transitions from the random dataset \( D^R \), representing the random policy.
+
+Figure 2(a) depicts the action distributions for the four datasets. Significant differences can be observed among the four EMS policies, with the action range of D1 falling within (-0.2, 0.5), resulting in relatively stable variations in FC power. As random policy data is introduced, the action ranges in the other datasets all fall within (-1, 1), particularly for D4 where the action distribution is uniformly spread across (-1, 1). This implies that this policy is noisy, denoted as a poor EMS. Figure 2(b) illustrates the state distributions for the four datasets. Note that all states have undergone post-processing and scaling to the (0, 1) interval. By comparing the box plots of the four datasets, it is evident that the SOC of D1 falls within a reasonable range (0.38-0.7), meeting the EMS constraints regarding the battery SOC.
+However, the SOC of the other datasets falls into unreasonable ranges, such as SOC in the range (0.2, 1) for D3. Additionally, with the increase in \( D^R \) data, the FC power distribution ranges of D3 and D4 become wider. Since the conditions of the four datasets are derived from fixed segments of standard driving cycles, the velocity distribution remains the same across all datasets.
+
+Creating challenging datasets is practical because generating sub-optimal or random data is more cost-effective than collecting expert-level data from real vehicles. Therefore, an effective data-driven EMS method must be able to effectively handle and learn from these suboptimal offline datasets.
+
+2.3. Learning superior EMS from non-optimal data
+
+![Learning curves and reward comparison for ORL agent on four datasets](page_186_370_1177_563.png)
+
+Figure 3: The ORL agent learning performance. (a) Learning curves of ORL agent for the four different datasets. (b) The comparison of absolute rewards (original rewards are negative) under three validation conditions. "D1," "D2," "D3," and "D4" correspond to the best rewards achieved by ORL after learning on each respective dataset. Notably, ORL agent on various datasets closely approximate or exceed the expert policy. (c) The comparison of energy costs between the original EMS and the optimized EMS using ORL shows a notable reduction in energy costs through the data-driven learning process. (d) The action (FC power slope) distributions of optimized EMS using ORL
+
+We first study the performance of the ORL agent with different datasets. To ensure a fair comparison, the algorithm employs uniform experimental settings and network parameters across four datasets. Figure 3(a) illustrates the average reward of the training process on the four datasets. This average, computed as the mean reward over every 1000 episodes, undergoes validation across 10 iterations using three standard driving cycles: WTVC, CHTC, and FTP.
+Training involves utilizing a buffer comprising 300,000 samples, with the ORL agent randomly selecting 256 data points for each training iteration, accumulating to one million training epochs. For D1, which comprises exclusively expert data, convergence is evident after approximately 210e3 episode. However, ORL exhibits a slower convergence speed during iterative learning on the other three datasets, converging at around 330e3, 600e3, and 360e3 epochs, respectively. This suggests that the data distribution influences the learning speed, but ultimately, ORL learns an effective EMS.
+
+Figure 3(b) presents the reward performance of trained ORL across three driving cycles. It notes that the absolute reward value of ORL decreases in D1, from 323.4 to 297.3 on the CHTC, representing an improvement of 8.8%. Surprisingly, even on suboptimal datasets D2 and D3, ORL outperforms the expert strategy, with reward increases of 1.8% and 3.4%, respectively. Similarly, ORL still outperforms on the WTVC and FTP conditions, learning superior strategies from the suboptimal datasets D2 and D3. The exception is D3 on the WTVC condition, possibly due to the high-speed nature of the WTVC condition, leading to larger reward values for SOC. Despite this, the final results of the energy consumption remain within rational bounds. Particularly noteworthy is the excellent performance on the random dataset D4, where ORL closely approaches expert results across all three validation conditions, achieving rewards of 402, 325, and 395. Compared to the original average reward of 2637 for the D4 dataset, ORL has reduced the reward by 85.8%.
+
+Figure 3(c) provides a detailed comparison of the energy costs between ORL and the original datasets. The blue dots represent the mean costs of the four original EMS datasets, accompanied by error bars indicating the maximum and minimum costs. In contrast, the red dots depict the energy costs incurred by ORL in the corresponding datasets. Despite the inclusion of random data that leads to a degradation in cost performance, ORL consistently maintains lower costs across all data sets. For instance, in the WTVC condition, the cost escalates from the initial 90 RMB in dataset D1 to 163 RMB in dataset D4. However, ORL consistently maintains costs within the range of 90-95 RMB. In particular, the minimum cost values of the original D4 dataset exceed those achieved by ORL significantly, with ORL achieving reductions in costs that exceed 40% in all three conditions. This observation underscores ORL’s ability not only to glean superior results from expert EMS but also to consistently yield excellent outcomes from progressively suboptimal datasets. Remarkably, ORL even attains expert-level EMS performance when trained solely on noisy datasets.
+
+To elucidate the rationale behind the performance enhancements, Figure 3(d) illustrates the action distributions of optimized EMS using ORL. As different EMS policies can be reflected by the actions taken, in the context of the FCEV considered here, this pertains to the FC power slope under the same driving cycle. Comparing Figures 2(c) and 3(d), we notice significant changes in D2, D3, and D4 compared to Figure 2. In D2, D3, and D4, the action distributions closely resemble those of expert data in D1, concentrating within the range of [-0.3, 0.3], as opposed to the wider range of [-1, 1] observed in Figure 2. The change is particularly pronounced in D4, where the absence of expert data results in slight differences in the action distributions compared to D1, D2 and D3. However, all ORL policies tend to learn FC power variations with smaller ranges, ensuring smoother FC power output while satisfying power demand requirements.
+
+In conclusion, through experimentation on three validation conditions and four datasets, our ORL agent not only learns better EMS strategies from expert strategies but also demonstrates the ability to learn near-expert strategies from entirely noisy datasets and even achieves superior results from datasets containing a mixture of expert and noisy data. This observed convergence underscores ORL’s ability to enhance and optimize the original EMS through learning from data obtained from any EMS.
+
+2.4. Performance by comparative evaluation
+
+To demonstrate the superior performance of ORL, we contrast it with simulation-based and imitation learning EMS approaches. Since imitation learning and ORL are closely related, both involve learning EMS from data. We first compare the performance between ORL and BC. It’s important to note that BC typically employs a supervised learning paradigm, learning from expert data, while ORL incorporates reinforcement learning with exploration mechanisms. This distinctive learning mechanism results in significant performance differences.
+
+In Figure 4(a), we compare the testing reward in the WTVC, CHTC and FTP driving cycles, and calculate the percentage of ORL and BC costs relative to the expert EMS (PPO). In D1, both ORL and BC achieve favorable results, with ORL surpassing the original expert data by a maximum of 9.1%, while BC remains comparable to the expert. In D2, ORL maintains superiority over expert-based EMS, while BC experiences significant cost degradation (ranging from 6% to 70%). In D3 and D4, ORL continues to outperform or closely match the expert, while BC, limited by data
+Figure 4: Performance analysis comparing different methods. (a) The comparison between two data-driven EMS methods. The matrix numbers represent the relative reward rates of ORL and BC compared to the expert EMS (PPO) under the same conditions, emphasizing the minimal influence of data quality on ORL’s performance. (b) Comprehensive performance of different algorithms on the WTVC condition, DP representing the globally optimal EMS. (c) Comprehensive performance on the CHTC condition. (d) Comprehensive performance on the FTP condition. (e) The efficiency distribution of fuel cell power demonstrates that ORL learns a superior EMS, ensuring that fuel cell system remains within the high-efficiency range. (f) FC degradation costs under three conditions
+
+quality, fails to learn an optimal EMS. This underscores ORL’s capability to learn superior EMS from non-expert data, while imitation learning demonstrates poorer performance and struggles to learn favorable EMS with non-expert data.
+
+Figures 4(b-d) present detailed results of different methods under the WTVC, CHTC, and FTP conditions, with the red lines representing the percentage of cost compared to DP. It is evident that ORL learns an optimal EMS policy on the D1 dataset, achieving percentages close to 99.9%, 99.4%, and 97.6% of DP, respectively. As for PPO, a benchmark expert policy, its cost results are 98.6%, 98.0%, and 97.6% of DP, respectively. Thus, BC learns similar expert EMS in D1, but its performance significantly deteriorates on suboptimal D2 data. Another online DRL method, TD3, also demonstrates satisfactory performance, however, its overall costs are lower than those of PPO and ORL.
+
+In Figure 4(e), the FC power distribution of the EMS learned by ORL on the D1 dataset is depicted, with the green curve representing the efficiency curve of the FC system. ORL demonstrates a superior EMS, ensuring that the
+power distribution remains within the high-efficiency range, resulting in reduced hydrogen consumption. Additionally, a narrower power variation range, as shown in Figure 3(d), minimizes FC degradation costs. As illustrated in Figure 3(f), ORL incurs minimal FC degradation costs in the three conditions, with costs of 2.3, 1.4, and 1.4, respectively. Furthermore, examination of Figures 3(b-d) indicates that the battery SOC remains within a reasonable range. These findings collectively affirm that ORL has successfully learned a superior EMS.
+
+2.5. Continuous learning with growing data
+
+We have demonstrated in previous experiments that ORL can learn optimal EMS strategies from data and outperforms other methods. In this section, we further showcase ORL for continuous learning from data. We conduct experiments in three cases depicted in Figure 5(a), collecting real-vehicle data in different driving scenarios including urban road, highway, and downtown road for the three cases (Figure 5(b)).
+
+2.5.1. Case 1: Continuous learning from historical data
+
+Take the example of driving a bus on fixed routes to illustrate Case 1. We collected real electric bus driving data in Zhengzhou, China, over three consecutive days. Figure 5(c) shows the speed trajectories of three days, labeled as ZBDC-No1, ZBDC-No2, and ZBDC-No3, respectively. Noticeably, there are variations in the speed trajectories along the same route over different days. Figures 5(d-f) show the total cost of different EMS strategies in the three scenarios, which include hydrogen consumption, battery cost, and fuel cell degradation. The baseline is the original EMS of FCEV, and using the baseline data under ZBDC-No1 driving cycle to train the ORL agent as the ORL(Z1) strategy, which is then applied to the new condition ZBDC-No2. Furthermore, we train a new ORL(Z2) EMS using data from both the baseline on ZBDC-No1 and the ORL(Z1) on ZBDC-No2, which is then validated on ZBDC-No3.
+
+It can be observed that the baseline EMS performs poorly on the first day (ZBDC-No1), with a cost only 88.0% compared to DP. The corresponding FC power and power slope distributions are shown in Figures 5(g). On the second day as depicted in Figure 5(e) and (h), the performance of ORL(Z1) achieves a significant improvement by learning from the previous data, reaching 96.4% of the cost compared to DP on the ZBDC-No2. On the third day, continuously learning from more data, the ORL(Z2) achieves a cost of 98.6% compared to DP on the ZBDC-No3, as shown in Figure 5(f) and (i). By comparing the three power distribution, it is evident that ORL(Z1) and ORL(Z2) distribute more FC output power in the high-efficient range, resulting in lower overall energy consumption, and the smaller power slope also leads to lower system degradation costs.
+
+In conclusion, with data updates, new data can be utilized to train ORL, leading to the evolution of better EMS strategies. This demonstrates the ability of ORL to continuously learn and improve from historical data. Additionally, our method integrates seamlessly with established EMS methods, using real-time data from onboard controllers to increase EMS performance. This ensures that baseline performance is preserved while facilitating further enhancement using ORL, making it a valuable extension to conventional EMS methodologies.
+
+2.5.2. Case 2: Improving from simulated data
+
+In Case 2, we address the challenge of improving EMS performance from simulated data, where historical data is absent and driving conditions are unknown. Despite the ability of simulation-based methods (such as DRL) to derive ideal EMS strategies from simulated EV models, deploying these strategies onto real vehicles often leads to performance degradation due to the stochastic and unknown nature of real-world driving conditions, a problem known as the sim-to-real gap, extensively studied in the fields of RL.
+
+As illustrated in Figure 6(a), during the simulation phase, the PPO algorithm is trained on the standardized driving cycle (WTVC) and three specific conditions ZBDC (Figure 5(c)) to obtain an ideal EMS, denoted as PPO (Train). Subsequently, the EMS is validated on 12 local driving conditions denoted as PPO (Test). As depicted in Figure 6(b), the cost difference between PPO (Train) and DP across the four training conditions is minimal, with an average difference of 3.16%. However, when tested on the 12 new conditions(DC-1 to DC-12), the average cost difference between PPO (Test) and DP rises to 12.75%. This indicates a significant performance degradation of DRL-based methods when transitioning from simulation to real-world conditions.
+
+To mitigate the sim-to-real problem, our proposed ORL method leverages data from PPO (Test) for further learning. As shown in Figure 6(c), the ORL approach achieves a substantially lower cost across the 12 local operating conditions compared to the PPO (Train) strategy. The average cost difference between ORL and DP is merely 1.42% (Figure 6(b)). In summary, our experiments demonstrate that ORL can effectively learn from simulated data to enhance the performance of the original EMS, addressing the sim-to-real problem inherent in traditional simulation-based methods.
+Figure 5: ORL continuously learning and improving from data. (a) ORL for continuous learning from data in three scenarios. (b) Driving data collected from the real-world route. (c) Speed trajectories of three ZBDC conditions. (d) Comparing the total cost under ZBDC-No1, the total cost comprises hydrogen consumption, battery cost, and cell degradation cost. (e) Comparing the total cost under ZBDC-No2. (f) Comparing the total cost under ZBDC-No3. (g) Fuel cell power distribution cloud chart of Baseline EMS. (h) Fuel cell power distribution cloud chart following one data update. (i) Fuel cell power distribution cloud chart following two data updates.
+Figure 6: Performance with more data. (a) Performance of PPO for 4 training data and 12 testing data. (b) The comprehensive performance comparison of different EMS methods reveals that ORL can significantly mitigate the performance degradation observed in the testing phase of PPO. (c) Performance of ORL for 12 testing data. (d) Speed distribution of four conditions. (e) The demand power of HWDC represents an extreme condition. The red dashed line indicates the maximum output power of FC system. (f) Overall performance of the 4 cases as the training data increase under test driving cycle CLTC; (g) Performance on GCDC; (h) Performance on ZNDC; (i) Performance on HWDC indicates that ORL ultimately learns a reasonable EMS in extreme driving conditions. (j) Battery SOC trajectories of different EMS under the test driving cycle HWDC.
+2.5.3. Case 3: Learning a general EMS with large-scale data
+
+To assess the generalization of the ORL model, especially in extreme conditions, the ORL agent trained on huge amounts of data and tested its performance on four new driving conditions. Figure 6(d) illustrates the speed distribution for these four conditions. Among these, the China Light-Duty Vehicle Test Cycle (CLTC) stands as the standard cycle, GCDC is obtained from an EV operating in a downtown road, ZBDC represents a new condition collected in Zhengzhou, and HWDC is collected from a fuel vehicle traveling on a highway. The four conditions have distinct characteristics and originate from different road and vehicle types. Particularly for HWDC, where the demand power exceeds 250 kW. As depicted in Figure 6(e), the power demand exceeds the 100 kW maximum output power of FC system, indicating that HWDC is an extreme condition for the FCEV studied in this work.
+
+Firstly, we establish datasets of four different scales: 4e4 (ORL-4), 20e4 (ORL-20), 100e4 (ORL-100), and 500e4 (ORL-500) samples, excluding data from the four validation conditions obtained in previous experiments (Cases 1 and 2). The results on the four validation conditions are depicted in Figures 6(f-i). It is evident from Figure 6(f), (g), and (h) that both the reward and cost exhibit a gradual decrease with an increase in training data. With more training data, the ORL model consistently enhances its performance. Notably, the rate of performance improvement diminishes after reaching the 100e4 sample mark, with minimal disparity observed between the ORL-100 and ORL-500. At approximately 20e4 samples, the ORL model outperforms the DRL-TD3 algorithm (as indicated by the dashed lines in the figures). It is essential to highlight that, under the extreme HWDC condition, although ORL-20 achieves the lowest cost (Figure 6(i)), its reward absolute value is not the lowest. This phenomenon is because the ORL-20 prefers battery consumption during high power demands, exceeding the maximum output of the FC system, violating the SOC constraint. This phenomenon arises because ORL-20 tends to prioritize battery consumption during periods of high power demand, the FC system fails to achieve its maximum power output. Consequently, the strategy fails to maintain the SOC within the desired range, rendering it ineffective as an EMS. Conversely, ORL-500 demonstrates superior performance, with lower reward and cost, and SOC maintained within a reasonable range, as illustrated in Figure 6(j). Overall, after learning from 5 million data points (equivalent to over 60 million kilometers), the ORL agent can learn a general EMS adaptable to unseen and even corner-case conditions.
+
+This result highlights two advantages of the ORL agent: First, its performance surpasses that of the original policy; second, it demonstrates that with increased data availability, learning performance improves. The ORL model can learn a general EMS from a large amount of EV data.
+
+3. Methods
+
+3.1. EV Environment
+
+In this work, we evaluate EMS performance using a fuel cell hybrid electric vehicle (FCEV) within a simulation environment. Figure. 1(e) illustrates the schematic diagram of the FCEV and its components, which include a fuel cell (FC) system, a hydrogen storage tank, an electric motor (EM), and a Lithium-ion battery (LIB) pack. The FC stack serves as the primary power source to meet the energy requirements of the vehicle. The diagram also depicts the energy flow from the hydrogen storage tank to the motor. The FC system converts hydrogen energy into electricity, which then collaborates with the LIB through the high-voltage bus. This electric energy is subsequently utilized to power a single electric motor, connected to the driving wheel via a fixed-ratio final gear. According to the vehicle driving resistance equation, the driving power demand is determined by the speed and acceleration of the FCEV, and can be expressed as follows:
+
+\[
+P_d = \frac{1}{3.6 \cdot \eta_{me}} \left( mgC_f v_t + m \delta \dot{v}_t a_t + m g \sin(i) + \frac{C_D A}{21.15} v_t^3 \right)
+\]
+
+where \( \eta_{me} \) is the efficiency of the vehicle drivetrain; \( m \) is the vehicle mass; \( g \) is the gravitational constant; \( C_f \) is the rolling resistance coefficient; \( \delta \) is the rotational mass conversion coefficient; \( C_D \) is the air resistance coefficient, \( A \) is the frontal area; \( v_t \) is the longitudinal velocity at the time step \( t \), \( a_t \) is the acceleration, \( i \) is the angle of slope of the road. The power demand is provided by the FC system and the battery pack, the power balance of the FCEV can be formulated as:
+
+\[
+P_d = (P_{fc} \cdot \eta_{DC/DC} + P_{bat}) \cdot \eta_{DC/AC} \cdot \eta_{EM}
+\]
+
+where \( P_{fc} \) and \( P_{bat} \) respectively denote the output power of the fuel cell system and the LIB pack; \( \eta_{DC/DC}, \eta_{DC/AC} \), and \( \eta_{EM} \) represent the efficiency of the DC/DC converter, DC/AC inverter, and the electric motor, respectively. The
+battery pack is modeled using an equivalent circuit model in Equation (3):
+
+\[
+\begin{cases}
+P_{bat}(t) = V_{oc}(t) - R_0 \cdot I^2(t) \\
+I(t) = \frac{V_{oc}(t) - \sqrt{V_{oc}^2(t) - 4R_0 P_{bat}(t)}}{2R_0} \\
+SOC(t) = \frac{Q_0 - \int_0^t I(t) dt}{Q}
+\end{cases}
+\]
+
+where \( SOC \) is the battery state of charge, \( V_{oc} \) is the open-circuit voltage, \( I_t \) is the current at time \( t \), \( R_0 \) is the internal resistance, \( P_{bat} \) is the output power in the charge-discharge cycles, \( Q_0 \) is the initial battery capacity, \( Q \) is the nominal battery capacity.
+
+According to the battery aging model in [12]. The degradation rate of battery operation \( \gamma_{bat} \) is affected by the charge/discharge rate (\( C_{rate} \)). The relationship between the battery aging correction factor and \( C_{rate} \) can be fitted from experiment data:
+
+\[
+\gamma_{bat} = \mu_1 |C_{rate}|^2 + \mu_2 |C_{rate}| + \mu_3
+\]
+
+where \( \mu_1, \mu_2, \mu_3 \) are the curve-fitting coefficients. LIB can operate for about 5000 full cycles in a lifetime. The battery degradation cost \( C_{bat,degr} \) can be calculated by:
+
+\[
+C_{bat,degr} = \int_0^t \gamma_{bat}^{-1} P_{bat} dt \cdot PR_{bat}/(5000 \cdot 3600)
+\]
+
+where \( PR_{bat} \) is the battery price per kWh that is 1500RMB/kWh.
+
+The fuel cell system efficiency under different power conditions is obtained from experiment data. Thus, the mass flow rate of the hydrogen consumption can be calculated by:
+
+\[
+\dot{m}_{H_2} = P_{fcs}/(\eta_{fcs} \cdot LHV_{H_2})
+\]
+
+where \( \eta_{fcs} \) is the fuel cell system efficiency; \( P_{fcs} \) is the fuel cell system output power; \( LHV_{H_2} \) is the hydrogen low calorific value. The fuel cell hydrogen cost can be calculated by:
+
+\[
+C_{fcs,H_2} = PR_{H_2} \cdot \int_0^t \dot{m}_{H_2} dt
+\]
+
+where \( PR_{H_2} \) is the hydrogen price per kilogram(60RMB/kg).
+
+The fuel cell degrades rapidly under four typical conditions: load changing, start/stop, low power, and high power conditions. We assume that the fuel cell system continues operating until the vehicle power system is shut down, thus the start/stop condition is not considered in the EMS. The fuel cell voltage degradation rate, denoted as \( \gamma_{fcs} \), can be calculated by:
+
+\[
+\gamma_{fcs} = \kappa_{low} \cdot T_{low} + \kappa_{high} \cdot T_{high} + \kappa_{cha} \cdot \Delta P_{fcs}
+\]
+
+where \( \kappa_{low} \) is the degradation rate under low power condition; \( T_{low} \) is the low power condition duration; \( \kappa_{high} \) is the degradation rate under high power condition; \( T_{high} \) is the high power condition duration; \( \kappa_{cha} \) is the degradation rate under load changing condition; \( \Delta P_{fcs} \) is the fuel cell power slope. Fuel cell is considered to reach the end of its life when 10% of voltage at rated power has been lost. The fuel cell operation degradation cost can be calculated by:
+
+\[
+C_{fcs,degr} = k_{fcs} \cdot \gamma_{fcs} \cdot P_{fcs,\text{rate}} \cdot PR_{fcs}/(V_{fcs,\text{end}} \cdot 1000)
+\]
+
+where \( k_{fcs} \) is the fuel cell life correction factor; \( V_{fcs,\text{end}} \) is fuel cell voltage drop at the end-of-life; \( P_{fcs,\text{rate}} \) is the rated power of the fuel cell; \( PR_{fcs} \) is the fuel cell price per kilowatt(4000RMB/kW).
+3.2. Problem modeling
+In this work, the EMS of electric vehicles is modeled as a long-term sequential decision process objective to minimize total energy cost while maintaining battery SOC within reasonable limits. The optimization objective can be formulated as:
+
+\[
+J_{EMS} = \min \sum_{t=0}^{T} cost(t) + \alpha f_s(SOC(t))
+\] (10)
+
+where \( T \) is the total length of the driving cycle, \( cost(t) \) is the energy cost including hydrogen consumption, the cost of battery, and fuel cell degradation, \( f_s(SOC(t)) \) is the SOC maintaining function, \( \alpha \) the tradeoff between energy cost and SOC.
+
+To tackle the sequential decision, the energy management problem is formulated as a Markov Decision Process (MDP), which is a framework for learning the optimal EMS from interaction to minimize total energy cost. The MDP defined by a tuple \( (S, A, P, R, \rho_0, \gamma) \), where \( S \) denotes the state space, \( A \) denotes the action space, \( P \left( s' \mid s, a \right) \) denotes the transition distribution, \( \rho_0(s) \) denotes the initial state distribution, \( R(s, a) \) denotes the reward function, and \( \gamma \in (0, 1) \) denotes the discount factor. The goal is to find a policy \( \pi(a \mid s) \) that maximizes the expected cumulative discounted rewards \( J(\pi) = E_{\pi,P,\rho_0} \left[ \sum_{t=0}^{\infty} \gamma^t R \left( s_t, a_t \right) \right] \). To use this formulation for FCEV. The state space at time point \( t \) for the FCEV is defined as:
+
+\[
+S = \left\{ v_t, acc_t, SOC_t, P_{fcs}^t \right\}
+\] (11)
+
+where \( v_t, a_t, P_{fcs}, SOC_t \) are the vehicle speed, acceleration, fuel cell power, and battery SOC. The action represents the control variable, defined as allocating power to the energy sources of the vehicle. In the context of the FCEV, the action is defined as the FC power slope, denoted as \( \Delta P_{fcs} \). The continuous action can be described as follow:
+
+\[
+A = \left\{ \Delta P_{fcs} = P_{fcs}^t - P_{fcs}^{t-1}, \Delta P_{fcs} \in [-10\ kW, 10\ kW] \right\}
+\] (12)
+
+The reward function \( R \) describes the reward \( R(s_{t+1}; s_t; a_t) \) associated with transitioning from state \( s_t \) to state \( s_{t+1} \) using action \( a_t \). The design of the reward function is pivotal in the learning process. For the FCEV, multiple objectives are taken into account, including hydrogen consumption, FC degradation, and battery-related costs such as electricity consumption and degradation. Additionally, it is essential to maintain the battery SOC. Therefore, the reward function is defined as the sum of energy costs while ensuring that the battery charge-sustaining constraints are maintained.
+
+\[
+R = - \left\{ C_{fcs,H_2} + C_{fcs,degr} + C_{bat,eH_2} + C_{bat,degr} + \alpha \left[ SOC_{ref} - SOC(t) \right]^2 \right\}
+\] (13)
+
+The battery electricity consumption \( C_{bat,eH_2} \) is calculated according to the battery charge/discharge efficiency and converted into price cost:
+
+\[
+C_{bat,eH_2} = \int_0^t \left[ P_{bat} / (\eta_{d/c}\eta_{DC/DC} \cdot LHV_{H_2}) \right] dt \cdot PR_{H_2}
+\] (14)
+
+where \( \eta_{d/c} \) is the battery discharge/charge efficiency.
+
+3.3. Offline RL algorithm
+We employ the offline reinforcement learning (ORL) paradigm to address the MDP problem described above. The goal is to learn a policy \( \pi \sim a_t \ (\pi : S \to A) \) that maximizes the expectation of the sum of discounted rewards \( J(\pi) \). Each policy \( \pi \) has a corresponding state-action value function (also known as Q function), which denotes the expected return \( Q(s, a) \) when following the policy \( \pi \) after taking an action \( a \) in state \( s \).
+
+\[
+Q(s, a) = \mathbb{E} \left[ \sum_{i=t}^{\infty} \gamma^{i-t} R_i \mid s_t = s, a_t = a \right]
+\] (15)
+
+Here, we approximate the Q function \( Q(s, a) \) using deep neural networks by minimizing the squared Bellman error. The ORL algorithm utilized in our proposal is an extension of the twin delayed deep deterministic policy gradient
+algorithm (TD3) [26]. TD3 is a state-of-the-art online DRL algorithm implemented under the actor-critic framework that learns a deterministic policy. For the actor part, it learns a deterministic target policy by mapping states to a specific action. The update of the Actor network of TD3 algorithm aims to maximize the estimation of the current policy by the critic network.
+
+When offline logged datasets are available, it is reasonable to push the policy towards favoring actions contained in the dataset D. Hence, our proposed ORL algorithm augments the standard policy update step in TD3 with Behavior Cloning (BC) regularization to reinforce the policy’s focus on the behaviors observed in the dataset D [27]. This regularization term encourages the policy to mimic the demonstrated behaviors more closely, leading to improved generalization and performance. Furthermore, in pursuit of improving the policy, Discriminator Blend (DB) regularization [28] is employed to enhance the flexibility of the policy constraint. This is achieved by integrating a discriminator using Generative Adversarial Networks (GANs) [29]. By incorporating a discriminator, the policy is enabled to explore actions that may not be included in the dataset \( D \), leading to a more diverse and adaptive policy. This involves utilizing a neural network as an approximator of the policy function \( \pi \):
+
+\[
+\pi = \arg\max_{\pi} \mathbb{E}_{(s,a)\sim D} \left[ \lambda Q(s, \pi(s)) - (1-\beta)(\pi(s)-a)^2 + \beta \log(D(s, \pi(s))) \right]
+\]
+
+\( \mathbb{E}() \) is the mathematical expectation. The parameter \( \beta \) (range of 0 to 1) adjusts the balance between BC and DB constraints. The DB is trained to assess whether a given action \( a \) and state \( s \) pair belongs to the dataset \( a_D \) or is generated by the policy \( \pi_\theta \), which acts as the generator \( G \) in GANs. This enables BD to effectively regulate the policy learning process by encouraging the policy to explore actions beyond the dataset while ensuring that these actions are plausible according to the discriminator’s perception. The \( \lambda \) is a normalization term based on the average absolute value of Q to control the balance between RL and imitation, defined as:
+
+\[
+\lambda = \frac{\alpha}{\frac{1}{N} \sum_{(s_i, a_i)} |Q(s_i, a_i)|}
+\]
+
+The parameter \( \alpha \) is used to control the strength of the regularize where the larger \( \alpha \) will make the algorithm approach more RL, and \( N \) represents the number of transitions in the dataset. To normalize the characteristics of each state in the provided dataset. Let \( s_i \) be the \( i \) th feature of the state \( s \) in the dataset, let \( \mu_i, \sigma_i \) be the mean and standard deviation (\( \eta \) is a constant value to avoid division by zero.):
+
+\[
+s_i = \frac{s_i - \mu_i}{\sigma_i + \eta}
+\]
+
+The critic part estimates the Q-value of a state-action pair. TD3 employs two critic networks to mitigate overestimation bias, with each critic having a corresponding target network. Each critic network \( Q_1(s, a | \theta^{Q_1}) \) and \( Q_2(s, a | \theta^{Q_2}) \) corresponds to a target network \( Q'_1(s, a | \theta'^{Q_1}) \) and \( Q'_2(s, a | \theta'^{Q_2}) \) respectively. The minimum Q-value among the two critics is used as the target Q-value during training. The critic network is updated by minimizing the loss function:
+
+\[
+L(\theta^{Q_i}) = \mathbb{E} \left[ (y_t - Q_i(s_t, a_t | \theta^{Q_i}) | a_t = \mu(s_t | \theta^{\mu}))^2 \right]
+\]
+
+where \( \theta^{Q} \) denotes the weights of the critic network. The target Q-value \( y \) is evaluated by taking the minimum of the estimates from the two Q-functions as follows:
+
+\[
+y_t = r(s_t, a_t) + \gamma \min_{i=1,2} Q'_i(s_{t+1}, a_{t+1} | \theta'^{Q_i})
+\]
+
+where \( a_{t+1} \sim \pi_{\theta'}(s_{t+1}) + \epsilon,\quad \epsilon \sim \mathrm{clip}(\mathcal{N}(0, \hat{\sigma}), -c, c) \) is the exploration noise to smooth the value estimates and improve robustness of the learned Q functions, \( r \) is the instantaneous one-step reward, \( \gamma \) is the discounting factor.
+
+3.4. Baseline Methods
+
+We use a series of baseline EMS methods for comparatively evaluating the ORL method. The inputs and outputs of all baselines are the same as those of the proposed method.
+Dynamic Programming (DP) [30]: In optimization control methods, the EMS problem is formulated as a nonlinearly constrained optimization problem, aiming to minimize the objective function presented in Equation (10). DP is an optimization control method that operates by seeking the shortest path backward in time. Its objective is to derive the minimum cost function for each grid at every stage in reverse chronological order. In our study, DP is used as the benchmark EMS policy, representing the global optimum and providing upper limits for comparison. It’s important to recognize that DP requires future information as input to achieve the optimization objective.
+
+Behavior Cloning (BC) [31]: BC, as a fundamental imitation learning approach, seeks to emulate the EMS policy by directly learning from the provided dataset, which is assumed to be generated by an expert policy or near-expert policy. It employs supervised learning techniques to train a model to map states to actions. Both BC and ORL involve learning from data for EMS applications. In this context, we establish BC as the benchmark and aim to showcase the superior performance of ORL.
+
+Proximal Policy Optimization (PPO) [32]: PPO is a state-of-the-art online DRL algorithm, which has been extensively applied in various applications requiring sophisticated decision-making in dynamic environments. PPO offers a robust and efficient approach to training agent by leveraging on-policy learning, effective use of data through mini-batch updates, stability through policy clipping, and adaptive learning rates. Leveraging the strengths of PPO, we utilize it to generate the dataset necessary for ORL, with its policy serving as an expert (near-optimal) strategy for comparison purposes. We provide it to explore the superiority of ORL compared to the online DRL.
+
+Twin Delayed Deep Deterministic Policy Gradient (TD3) [26]: TD3 is an advanced online DRL algorithm, stemming from the Actor-Critic framework. It has garnered significant attention due to its effectiveness in overcoming challenges associated with continuous action spaces and high-dimensional state spaces. TD3 employs twin critic networks to estimate the value of actions more accurately. By utilizing two critic networks, TD3 mitigates overestimation bias and enhances the robustness of value function estimation. We also provide it to explore the superiority of ORL compared to the online DRL.
+
+4. Discussion
+
+In conclusion, we have presented a novel data-driven EMS for hybrid energy systems in EVs. Leveraging an innovative offline reinforcement learning agent, our approach learns directly from driving data. Experimental results demonstrate that the ORL agent not only learns optimal EMS strategies from expert data but also exhibits the ability to learn superior EMS from datasets containing a mixture of expert and noisy data, and even achieves near-optimal strategies from entirely noisy datasets. Moreover, our approach demonstrates that with increased data availability, performance improves as the agent is trained with more data.
+
+This approach offers three notable benefits. Firstly, it is sufficiently simple, as it solely relies on collected data for automatic learning by the agent, unlike the traditional EMS development process, which often requires extensive expert knowledge and repeated measurements. Furthermore, the data used in our approach are non-expert data readily available from real vehicles. Secondly, our method ensures stable performance by integrating seamlessly with existing EMS without altering the original EMS performance lower bound. Our approach continuously improves upon the baseline EMS through data-driven enhancements leveraging the strengths of both technologies. For example, to address the performance shortcomings in rule-based EMS, ORL enables incremental learning, allowing for the continual enhancement of EMS performance with historical data. Similarly, ORL addresses the sim-to-real gap problem in simulation-based methods by enhancing pretrained EMS models, thereby ensuring their effectiveness in real-world deployment scenarios. Lastly, our approach exhibits versatility, as with sufficient data, it can learn a generalized EMS applicable to various EVs and operating conditions. This aligns with the current trend of large-scale language models and similar approaches in artificial intelligence, where a single large model with large-scale data can be trained to perform well across diverse tasks and domains.
+
+Overall, we believe that ORL could serve as a foundational framework for data-driven EMS, with potential applications extending beyond EVs to grid EMS, industrial energy management systems, and other vehicle control systems. However, a limitation of this work is that the ORL agent may require more data to further enhance its performance. Addressing this limitation could involve exploring methods to efficiently gather and utilize additional data for agent training, potentially improving its effectiveness in real-world applications.
+Acknowledgements
+
+This work was supported in part by the National Natural Science Foundation of China (Grant No. 52172377).
+
+Author Contributions
+
+Y.W. designed the study and methodology; Y.W., J.Wu. and H.H. collected and analyzed data; Y.W. generated the figures; Y.W., J.Wu. and W.Z. wrote the manuscript; H.H., W.Z. and F.S. reviewed and edited the manuscript. All authors contributed to the paper.
+
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0996185957de22ec96c13ddd4eeca9080a098f778fc62996a2333ee389185663/preprint/preprint.md

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+Secure wireless communication of brain-computer interface and mind control of smart devices enabled by space-time-coding metasurface
+
+Tie Jun Cui
+t.jcui@seu.edu.cn
+
+Southeast University    https://orcid.org/0000-0002-5862-1497
+Qiang Xiao
+Southeast University
+Lin Han Fan
+Southeast University
+Qian Ma
+Southeast University    https://orcid.org/0000-0002-4662-8667
+Yu Ming Ning
+Southeast University
+Ze Gu
+Southeast University
+Long Chen
+Southeast University    https://orcid.org/0009-0007-1533-0319
+Lianlin Li
+peking university    https://orcid.org/0000-0001-9394-3638
+Jian Wei You
+Southeast University    https://orcid.org/0000-0001-5761-9507
+Ya Feng Niu
+Southeast University
+
+Article
+
+Keywords: Space-time-coding metasurface, brain-computer interface, secure wireless communication, human-machine interactions
+
+Posted Date: August 23rd, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4860006/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/s41467-025-63326-0.
+Secure wireless communication of brain-computer interface and mind control of smart devices enabled by space-time-coding metasurface
+
+Qiang Xiao1,†, Lin Han Fan2,†, Qian Ma1,†, *, Yu Ming Ning1, Ze Gu1, Long Chen1, Lianlin Li3, Jian Wei You1, Ya Feng Niu2, * and Tie Jun Cui1, *
+
+1 State Key Laboratory of Millimeter Waves and Institute of Electromagnetic Space, Southeast University, Nanjing 210096, China
+2 School of Mechanical Engineering, Southeast University, Nanjing 210096, China
+3 State Key Laboratory of Advanced Optical Communication Systems and Networks, Department of Electronics, Peking University, 100871 Beijing, China
+*E-mail: maqian@seu.edu.cn, nyf@seu.edu.cn, tjcui@seu.edu.cn
+† These authors contributed equally to this work
+
+Abstract
+Brain-computer interface (BCI) provides an interconnected pathway between human brain and external devices and paves a potential route for mind manipulations. However, most of existing BCI technologies are based on simple signal transmission and independent of other interface devices, owing to the considerations of reliability and safety of human brain’s information interaction in the complicated wireless environment. To address the formidable limitation, we present a brain space-time-coding metasurface (BSTCM) system to deeply fuse the visual stimulation and electromagnetic manipulation for reliable and secure information transfer between human brain and external devices. Here, we innovatively integrate the BCI flashing frame and electromagnetic encoding sequence in the BSTCM system, and the STC metasurface ensures the secure wireless communications by using the harmonic-encrypted beams. We design and fabricate a proof-of-principle demonstration system and experimentally show that the proposed wireless BCI scheme could establish a remote but safeguarded paradigm for human-machine interactions, intelligent metasurfaces, and potential applications in metaverse, as a prominently scrutinized domain in the future 6G wireless communications.
+
+KEYWORDS: Space-time-coding metasurface, brain-computer interface, secure wireless communication, human-machine interactions
+Introduction
+
+Brain-computer interface (BCI) has emerged as a cutting-edge technology in human-machine interaction, and demonstrates promising applications such as metaverse interaction¹ and smart homes². Electroencephalography (EEG) signals remain the predominant input signal modality in BCI systems, with notable implementations including motor imagery³, P300⁴, and steady-state visually evoked potential (SSVEP)⁵. The SSVEP-based BCI systems utilize the brain’s SSVEP response to the fixed-frequency visual stimuli for mind recognition and interaction⁶, offering a significant advantage of high information transfer rate (ITR). The BCIs have been widely used in various fields such as augmented reality (AR)⁷,⁸, spelling input⁹,¹⁰, medical rehabilitation and equipment control¹¹,¹². Recently, some high-performance BCI systems have been continuously proposed¹³-¹⁸. The advent and progression of 6G wireless communication technology substantially broaden the application prospects of BCIs, particularly in Internet of Things (IoT), virtual reality (VR) devices, and beyond¹⁹-²¹. Hence, ensuring high security and privacy preservation²² becomes imperative when facilitating intelligent interactions within the constructed communication environment.
+
+However, most existing BCI systems lack in-depth research in terms of security. During the wireless transmissions of brain signals in a BCI system, there exists a vulnerability to theft and attack, potentially leading to the generation of inaccurate device control commands and unauthorized disclosure of personal privacy. Though some methodologies have been proposed to enhance the security and privacy of data in the BCI systems²³-²⁵, there is a conspicuous absence to investigate the encryption mechanisms specifically tailored for the BCI systems. More importantly, the implementation of visual stimulation remains to be isolated from the back-end information processing systems, lacking deep information fusion and interaction. With the increasing demand for high security in the BCI systems, it is essential to develop intelligent interactions in the secure and reliable communication environment. The frequency-dependent SSVEP response and programmable harmonic characteristics of space-time-coding (STC) metasurfaces display notable similarities. Therefore, the STC metasurfaces can be used as a promising method that not only provides the visual stimulation but also ensures security of the BCI systems at the physical layer owing to their powerful ability to flexibly manipulate
+electromagnetic (EM) waves in both time and space domains\(^{26}\).
+
+The metasurfaces are composed of specific unit structures arranged in periodic or quasi-periodic arrays, which can flexibly control the EM waves at the subwavelength scale and yield a large number of unusual physical phenomena and novel devices\(^{27-30}\). The proposal of digital coding and programmable metasurfaces has established a profound connection between the EM fields and digital information under the control of a high-speed field programmable gate array (FPGA)\(^{31}\). Recently, the exploration of STC metasurfaces has sparked a surge of research interest due to the excellent ability to manipulate the EM waves and process digital information in both temporal and spatial dimensions\(^{32-37}\), resulting in many novel physical phenomena that cannot be realized by the traditional spatially modulated metasurfaces. More importantly, the utilization of STC metasurfaces holds the capability to precisely control the amplitudes, phases, and polarizations at different harmonic frequencies independently by specially designing the STC matrices\(^{38}\), which opens up avenues to develop advanced communication schemes with enhanced efficiency and reliability\(^{39-45}\). Hence, the STC metasurface is a potential candidate for deep information modulation and interaction in the SSVEP-based BCI system owing to its capability to process information and interact with the frequency-dependent visual stimulation.
+
+In this article, we report a brain space-time-coding metasurface (BSTCM) system, which combines the human brain intelligence with the flexible capability of EM manipulations by the STC metasurface. To the best of our knowledge, this is the first instance to integrate the visual stimulation and EM encoding regulation deeply in a BCI system through metasurface. Here, the STC metasurface is used to effectively support visual stimulation for SSVEP-based BCIs while enabling the information interaction with the external environment. A lightweight deep-learning classification model is implemented to maximize the recognition performance. To enhance the BCI security, we propose a high-security encrypted wireless communication system based on the diverse harmonic regulation characteristics of BSTCM, which effectively combines the variant harmonic-based secret keys (HSKs) and visual secret sharing (VSS) method\(^{46-48}\). In this way, decoding by eavesdroppers is only possible through the simultaneous interception of confidential information across all harmonic frequencies in the communication process and the acquisition of complex secret keys, which proves the system’s exceptional
+levels of security. Finally, smart device control is presented by the BSTCM system, realizing intelligent human-machine interactions. The proposed BSTCM can establish a new paradigm of human machine interactions, metasurface-based wireless communications, and potential applications in metaverse.
+
+System configuration
+
+The proposed BSTCM is schematically demonstrated in Fig. 1, which consists of an STC metasurface, a brain-computer interface based on SSVEP, and an FPGA control module. The metasurface element contains a meta-structure to regulate the EM wave, and a light-emitting diode (LED) stimulator for the SSVEP paradigm. The STC metasurface is divided into four LED flickering partitions, operating at different frequencies: 8.5Hz, 10Hz, 11.5Hz, and 7Hz. The corresponding SSVEP-based EEG signals can be accurately extracted by a head-worn EEG cap when the operator is exposed to the LED flickering stimulus at distinct frequencies with the assistance of FPGA. To enhance the efficiency and accuracy of the EEG signal identification, we propose a deep learning model to recognize the extracted EEG signals, as shown in Fig. 2c. Upon completion of the identification process, the recognized signals are transmitted to FPGA, enabling to control the STC metasurface to update the corresponding STC matrices in the four LED flickering frequencies without disrupting the EEG stimulation. The BSTCM system empowers individuals to customize and modulate the EM waves by the human mind.
+
+Leveraging the abundant harmonic modulation capabilities and the advantages of human brain intelligence, the BSTCM system can respectively implement a high-security encrypted wireless communication system and a smart device controlled by human mind. In the high-security encrypted wireless communications, the harmonic frequencies are adopted as the secret keys and the VSS method is employed to encrypt the transmitted information. Firstly, the information is encrypted into two visual secret ciphertexts that depend on the corresponding HSKs. As one of the interface devices in the metaverse, BCI plays a crucial role in enabling individuals to interact in the virtual world, and it requires high-security performance. The presented encrypted wireless communication is envisioned to fulfill the requirement for secure communication in the metaverse. For instance, in a metaverse scenario shown in Fig. 1, a legitimate transmitter (Alice) equipped with an EEG cap intentionally transfers the secret information to two legitimate receivers (Bob and Carol) at two harmonic frequencies based on the encrypted communication. The eavesdropper (Eve) cannot decrypt the transmitted
+information unless she simultaneously obtains the secret keys, two ciphertexts, and encryption mechanisms, which is nearly impossible. Hence, the proposed system ensures high security and concealment by generating a large number of HSKs by modulating the STC metasurface. Ingeniously camouflaged as an LED stimulator, the STC metasurface effectively obstructs the eavesdroppers from detecting the information interaction. On the other hand, the presented system also enables wireless control of smart devices in real environments, allowing for manipulating the devices directly based on the user’s brain intention without the requirement of physical actions. Hence the BSTCM can serve as a stimulator for SSVEP, and effectively manipulate the EM waves for secure BCI wireless communications.
+
+SSVEP signal recognition
+
+The EEG signals can be accurately recognized in a BCI system through the detection of SSVEP components. The target flickering stimuli with four frequencies are supported with the STC metasurface integrated with LEDs, and the commands can be output by simply fixating on the corresponding visual stimuli. The STC metasurface is composed of 32×32 elements, and segmented into four partitions, with each region consisting of 16×16 elements. In these partitions, LEDs operate at four distinct frequencies (8.5Hz, 10Hz, 11.5Hz, and 7Hz) and are implemented to evoke four distinct SSVEP signals. As depicted in Fig. 2a, the SSVEP-BCI is segmented into three distinct stages: preparation stage, signal acquisition stage, and signal recognition stage. During the preparation stage, the participant wears an EEG cap equipped with electrodes positioned over the O1 and O2 regions and focuses the attention on one of the regions on the STC metasurface. In the signal acquisition stage, the participant maintains their gaze while an EEG amplifier collects the EEG data (for details, see Supplementary Note 1). Fig. 2d illustrates the frequency distribution of the EEG signals for the four target frequencies after the FFT analysis (prefiltered using a Butterworth bandpass filter with a frequency range of 5-40Hz). As illustrated in Fig. 2b, the signal undergoes an initial pre-processing procedure during the signal recognition stage, involving signal decomposition, spectrum calculation and weighted summation, output signal amplitude spectrum (SigSpec). Subsequently, an outer product operation is executed with the pre-calculated reference spectra (RefSpec), yielding eight feature graphs (comprising of twochannel and four target frequencies), each sized by 160×160 pixels. A discernible square grid pattern emerges in the feature graph corresponding to the frequency of the anticipated classification result (for additional information, refer to Supplemental Information Notes 2-5). The conventional SSVEP classification and recognition algorithms include canonical correlation analysis (CCA)\(^{49}\), filter bank canonical correlation
+analysis (FBCCA)50, task- related component analysis (TRCA)9, support vector machine (SVM)51, and convolutional neural network (CNN)52. However, some limitations still exist in the above-mentioned algorithms. Here, we propose a deep learning classification algorithm that embeds the SSVEP components in the signal recognition stage (refer to Supplemental Information Note 6). The above-mentioned eight feature graphs are input into a lightweight CNN classification model containing four convolutional and two liner layers, as shown in Fig. 2c. The feature graphs are initially processed through a convolutional input layer. Subsequently, a MaxPooling operation with a 2×2 kernel is applied following the activation of the data via the ReLU function. To facilitate the propagation of original data, a residual connection is strategically integrated between the second and third convolutional layers. Each convolutional layer is followed by the same 2×2 MaxPooling operation and ReLU activation. Upon the extraction of features from the eight feature graphs, a series of two successive linear layers are deployed to categorize the features into four distinct target frequencies. Finally, an output layer with sigmoid activation is employed to reshape the output of the model into 4 confidence scores. Ultimately, the model achieved a classification accuracy of 96.67% on the validation set, with precision and recall rates surpassing 90%. Such results underscore the efficacy of the SSVEP component classification algorithm proposed in this work.
+
+Design of STC metasurface
+
+Fig. 3a showcases the detailed configuration of the 1-bit STC metasurface element integrated with an LED, which consists of three metallic layers and multiple substrate layers. The top metallic layer has two slotted rectangular patches with a width of \( w = 7.3 \) mm and a length of \( l = 11 \) mm, in which the middle slot has a width of \( w_1 = 1.5 \) mm and a length of \( l_1 = 7 \) mm. The outer metal frame with a width of 0.15 mm is used to weaken the coupling effect between elements. The top F4B dielectric substrate has a relative permittivity of 2.65 and a loss tangent of 0.003 with the thickness \( h = 3 \) mm and period \( p = 19 \) mm. Two PIN diodes are serially loaded on the middle of two rectangular patches, and the two rectangular patches connected with metallic bars serve as positive and negative poles, in which two inductors are used as radio-frequency (RF) chokes to effectively isolate the RF signal from direct current (DC). An LED serving as the flash stimulation is placed outside the metallic patches to avoid affecting the scattering performance of the meta-atom and shares the same voltage with PIN diodes. To evaluate the performance of the 1-bit meta-atom, full-wave simulations are conducted using the commercial software CST Microwave Studio. As shown in Figs. 3b and 3c, the scattering characteristics of the meta-atom can be altered by switching the states of two PIN diodes
+corresponding to distinct RLC equivalent circuit models, hence realizing the 1-bit phase regulation. The diodes with OFF state are assigned as coding “0”, and ON state as coding “1”. When the meta-atom is subjected to normal illumination by a \( \gamma \)-polarized plane wave, a phase difference of 180° between “0” and “1” states is observed at approximately 6.9GHz, and both states exhibit reflective amplitudes exceeding -1 dB, indicating excellent performance of the 1-bit programmable meta-atom. Hence the designed meta-atom can be used to build the 1-bit STC metasurface. The detailed prototype design, modeling and characterization are given in Methods and Supplementary Note 9.
+
+To establish a dual-user encrypted wireless communication system, we implement an amplitude-shift keying modulation scheme using the STC metasurface, enabling simultaneous encrypted transmissions via space and frequency multiplexing. The control voltages, originating from FPGA, are applied to the PIN diodes, enabling periodic switching to the reflection phases of the 1-bit STC element with a time period of \( T_0 = 1/f_0 \). Consequently, each STC element possesses a periodic time-coding sequence and constitutes part of an STC matrix, making it possible to flexibly control the EM waves in both space and time domains. The flexibility of STC matrices can generate a series of new harmonic spectra at the frequency interval of \( f_0 \), which are further optimized with specific requirements (see Supplementary Notes 7 and 8). The space-time modulation enables abundant harmonic characteristics to construct harmonic-based encrypted wireless communications. Using the 2D STC matrices, we can modulate the EM waves to steer to the desired directions for target users. The STC matrices encompass 16 rows of elements, each possessing periodic time-coding sequences with 11 intervals. As illustrative examples, three radiation patterns corresponding to three STC matrices (M0, M1, and M2) are shown in Fig. 3. The radiation pattern of the optimized STC matrix M1 in Fig. 3e is strategically manipulated to yield a main beam with a deflected angle of \( \theta = -15^\circ \) at the +1st harmonic frequency, as showcased in Fig. 3h. Similarly, the radiation pattern of the STC matrix M2 (Fig. 3f) is optimized to direct the beam towards the angle \( \theta = +30^\circ \), in correspondence with the -1st harmonic frequency, as demonstrated in Fig. 3i. Furthermore, the time-invariant STC matrix M0 (Fig. 3d) facilitates the positioning of main beam towards a direction of \( \theta = 0^\circ \), associated with the fundamental frequency, as illustrated in Fig. 3g. As an example of amplitude-shift keying modulation scheme, the left panels (\( f_1 = 8.5Hz \) and \( f_2 = 10Hz \)) of the STC metasurface are utilized to send digital symbols “0” and “1” to User1 at the position of \( \theta = -15^\circ \) when the transmitting information is encoded as binary data streams. The right panels (\( f_3 = 11.5Hz \) and \( f_4 = 7Hz \)) of the STC metasurface are utilized to send digital
+symbols “0” and “1” to User2 at the position of \( \theta = +30^\circ \). Experiments are carried out in a microwave anechoic chamber to measure the far-field radiation patterns of the STC metasurface, as illustrated in Supplementary Notes 10 and 11.
+
+Constrained by the requirement of the SSVEP-based BCI to gather data and detect EEG signals at a single frequency, a viable encoding strategy is proposed to enhance the symbol error rate (SER), as depicted in Fig. 3j-m. The transmission of the digital symbols “0/1” involves to encode a series of repeated data frames with a period of 4 frames as synchronous frames. In the encoding scheme, the first bit “1” serves as the start bit, signaling the initiation of the transmission process. The second bit signifies the harmonic frequency (+1st or -1st) used for transmission, and the third bit corresponds to the transmission of the data itself. Finally, the fourth bit functions as the stop bit, indicating the end to transmit one data frame. Based on the encoding process, the digital symbol “0” or “1” for User1 is encoded as the repeated data frames “10001000” or “10101010…”, respectively. Similarly, the digital symbol “0/1” to User2 is encoded as repeated data frames “11001100…” or “11101110…”, respectively. Hence, the STC matrix M1 operating with a switching frequency \( f_0 \), is precisely injected into the region of high amplitude associated with the flicker frequencies \( f_1 \) and \( f_2 \), as illustrated in Fig. 3j and 3k. The STC matrices are updated when the information is sent to User1 via the BSTCM system. Similarly, the STC matrix M2 with a period switch frequency \( f_0 \), undergoes injection into the high amplitude attributed to the flicker frequencies \( f_3 \) and \( f_4 \), as displayed in Fig. 3j and 3k, representing the transmission of information to User2. Remarkably, the update of STC matrices does not affect the flickering frequency of LEDs used for SSVEP stimuli, ensuring that BCI signals can be synchronously detected and recognized.
+
+Secure encrypted wireless communication system
+
+The conventional VSS method is employed to encrypt the individual pixels of confidential information, where each pixel is divided into two sub-pixels. It is worth noting that each share derived from this process remains devoid of any discernible information pertaining to the original image content. As a result, a secret message possesses two visual shared keys (VSKs), which effectively guarantee that the disclosure of any single VSK does not compromise the confidentiality of the original secret information. Here, we present a novel encryption strategy by combining the harmonic characteristics of STC metasurface with the VSS method, which is designed to realize high-security encrypted wireless communication directly controlled by the
+human mind. In the presented encryption strategy, two VSKs are not simply stacked with each other to recover the original information, but rely on HSKs. In the described encryption process, the confidential information to be transmitted is firstly encrypted to two random VSKs based on the presented encrypted encoding scheme. Then, two generated VSKs are further encoded into two random HSKs for the \( \pm 1 \) harmonic frequencies, respectively. During decryption, two VSKs attached to each secret can be reconstructed with the pre-customized variant HSK sequences. The details of encryption and decryption methods can be found in Supplementary Note 12. The target image in question can be decrypted through the incoherent superposition of two extracted VSKs, aided by the presence of HSKs. By imbuing addressable shared information bits with the harmonic dynamics, a robust level of information security is achieved.
+
+As an illustrative example in Fig. 4a, the image “H”, which consists of \( 5 \times 5 \) grid of black or white pixels, is encrypted into two random VSK1 and VSK2 based on the presented encryption method. Two bitstream sequences of VSKs can be successively transmitted to two designated Users (Bob and Carol) by the BCI operator (Alice) using the presented BSTCM system.
+
+To validate the encrypted communication scheme, we experimentally set up an encrypted wireless communication system using the BSTCM, as demonstrated in Fig. 4b. The prototype of 1-bit STC metasurface is used to construct the encrypted communication system, as shown in Supplementary Figure 15. A commercial BCI device (actiCHamp of Brain Product GmbH company) composed of an EEG cap and amplifier is used to acquire the EEG signals when the operator stares at different partitions on the STC metasurface. The corresponding EEG signals can be accurately recognized by the proposed deep learning algorithm. The detailed description of the algorithm is provided in Supplementary Note 6. A linearly polarized horn antenna, connected to a signal generator (Keysight E8267D), is placed at a vertical distance of 4 m away from the metasurface center to excite a monochromatic plane wave at the frequency of 6.9 GHz. The receiving terminals are composed of two horn antennas (severed as two users) and a spectrum analyzer (Keysight N9040D), which is used to demodulate the received signal. Two receiving horn antennas are located at the angles of \( \theta = -15^\circ \) and \( \theta = +30^\circ \) with relative to the metasurface normal, respectively. In the transmission process, the information undergoes encryption, resulting in the generation of two harmonic-based cipher texts according to the
+encryption scheme. The transmission process is achieved by ensuring that the BCI operator maintains direct visual focus on the STC metasurface in alignment with the binary cipher texts. In addition, the system enables prompt acquisition, recognition, and translation of EEG signals into appropriate control signals of FPGA, which in turn drive the STC metasurface. As a result, the accurate transmission of binary cipher texts is accomplished, facilitating reliable and efficient communications between the BCI operator and the intended recipients.
+
+In the receiving process, the radiated signals propagating through free space are received individually by the two horn antennas, and these signals are subsequently demodulated using the spectrum analyzer. As shown in Fig. 4c, the demodulated signals represent four encoding schemes that correspond to different digital symbols (“0” or “1”) for the two users and then are processed to the decoded results shown in Fig. 4d by the FFT method. The decoded results clearly exhibit four repeated data frames, providing strong evidence to support the capability of the proposed system to recover the transmitting information successfully. Hence two binary cipher texts are transmitted to two specific users by the BCI operator based on the proposed wireless communication system. The transmitted information is received and the measured results are comprehensively showcased in Supplementary Note 13 and Supplementary Video 1. By employing the encoding method described earlier, the data streams corresponding to the specific users are extracted from the received signals, as depicted in Figs. 4e-f. Subsequently, these data streams are decrypted accurately by the method outlined in Supplementary Note 12. The deciphered information is displayed in Fig. 4g. The successful decryption and retrieval of the transmitted information affirm the robustness and efficacy of the proposed system in maintaining high levels of security and confidentiality. The system is not easily deciphered or cracked, proving its ability to protect sensitive information during transmissions.
+
+Mind control to smart devices
+
+To experimentally verify the performance of the proposed BSTCM system, we conducted experiments to show the remote control capabilities of smart devices through human intention, which holds significant potential to enhance the quality of life for individuals with disabilities.
+The system flowchart depicted in Fig. 5a outlines the key steps involved in the experimental setup. Initially, the EEG signals are acquired and subsequently processed by the BSTCM system for command recognition. The recognized commands are then translated to update the STC matrices of metasurface by an FPGA. The four partitions of the STC metasurface are controlled by FPGA to generate different beams at four deflected angles corresponding to the four harmonic frequencies, enabling the remote control of smart devices. Notably, the main beam at the -2nd harmonic frequency exhibits a pronounced peak in the direction of \( \theta = +10^\circ \), corresponding to the device assigned to User 3. Conversely, the main beam at the +2nd harmonic frequency demonstrates a strong peak at \( \theta = -45^\circ \), corresponding to the device assigned to User 1. As displayed in Figs. 5c and d, the measured radiation patterns exhibit good consistency with theoretical predictions associated to the corresponding STC matrices. Additionally, the main beams were deflected at the other two angles (-15° and 30°) using the +1st and -1st harmonic frequencies (Users 2 and 4), as shown in Figs. 3h and i. The excellent harmonic beam manipulation of the STC metasurface lays a solid theory foundation for smart device control. The receiving terminals are composed of four horn antennas, four RF energy detectors (LMH2110), four Microcontroller Unit (MCU) modules (Arduino), and four LED modules (serve as smart devices), as depicted in Fig. 5b. The RF energy from harmonic beams captured by the detectors can be converted into DC voltages, which are subsequently fed into the MCU modules. Once the corresponding DC voltage is detected, the MCU modules send the control commands to activate the corresponding LED module, thereby implementing the remote control of the smart devices. The experimental setup is shown in Fig. 5b, where the STC metasurface is illuminated by a monochromatic frequency signal of 6.9GHz.
+
+To verify the robustness of the brain-control smart devices system, the position of the receiving antenna is sequentially placed at different distances from the metasurface center while maintaining specific harmonic direction angles with respect to the metasurface normal. The detection of RF energy from the emitted harmonic beams is carried out across varying distances and the corresponding DC voltages can be accurately converted by the RF detectors, as illustrated in Fig. 5e (see Supplementary Note 14 for details). We observe that the RF energies of four users relatively decrease and the converted DC voltages also decrease accordingly as
+the distance increases. To guarantee the attainment of the far-field region and maintain system stability, the four receiving antennas are positioned at a distance of approximately 300 cm from the metasurface. Consequently, the detection voltage threshold is set as 0.15 V, 0.4 V, 0.4 V, and 0.2 V in MCU modules, respectively. We recorded a video of the brain-controlled multiple smart devices, as presented in Supplementary Movie 2. The sequence diagrams shown in Fig. 5f provide a clear visual representation of the sequential control process, where the smart devices (LED modules) are successively controlled through human intention using the BSTCM system. The experiment proves the feasibility of brain-controlled smart devices. By harnessing the power of BCI technology, individuals can exert control over smart devices without needing physical interaction. The BSTCM system enables seamless and intuitive manipulations of various smart devices, facilitating greater independence and convenience for people in daily life. The experimental results serve as a compelling validation supporting the significant benefits that the BSTCM can offer in improving the quality of life for individuals facing physical challenges.
+
+Conclusions
+
+We presented a BSTCM system, which combines the human brain intelligence and flexible EM control capabilities of the STC metasurface. A series of visual stimuli encoded by specific coding schemes was employed on the metasurface to realize deep information processing and interaction in the EM field for reliable and stable communication environments. In addition, a lightweight deep-learning algorithm was proposed to accurately recognize the brain signals extracted by the BCI device. We further demonstrated a high-security encrypted wireless communication system based on diverse harmonic frequency characteristics, which combines the variant HSKs and VSS methods. The proposed system can enable the system to have high security. Finally, remote control of smart devices was demonstrated by the BSTCM system, realizing intelligent human-machine interactions. The proposed BSTCM, integrating the EM manipulation capability with the intelligence of the human brain, provides a new paradigm of interactions among human machine interface in metaverse, and future 6G wireless communication applications.
+Methods and materials
+
+Details on STC metasurface. A metasurface prototype was fabricated by the standard printed circuit board (PCB) process. The entire STC metasurface is composed of \(32 \times 32\) digital elements and an effective size of \(608 \times 608\) mm\(^2\). For the convenience of processing and welding, the entire metasurface was disassembled into 8 sub-metasurfaces with \(8 \times 16\) digital elements and an effective size of \(152 \times 304\) mm\(^2\). A total number of \(2 \times 32 \times 32\) PIN diodes (SMP1320-079LF from SKYWORKS) and RF inductors of 10 nH were elaborately welded on the metasurfaces with the surface mount technology, which is a mature engineering method to weld small components on PCB using the batch solder-reflow processes in a dedicated machine. Meanwhile, an LED is embedded into each metasurface element.
+
+The brain signal acquisition. As depicted in Fig. 2a, the SSVEP-BCI is delineated into three discrete distinct stages: the preparation stage, the signal acquisition stage, and the signal recognition stage. The EEG data in this study were acquired using the actiCHamp EEG amplifier manufactured by Brain Products GmbH. This amplifier offers a maximum capacity of 64 channels, 24-bit precision, and a sampling rate of 100 kHz. It exhibits a high common mode rejection ratio (CMRR) of 100, making it suitable for capturing and detecting SSVEP signals effectively. This study uses a standard 10-20 EEG cap to obtain the signal. Since SSVEP is a local potential that predominantly originates from the occipital lobe\(^5\), the O1 and O2 electrodes located on the occipital region were selected for EEG data acquisition, with a reference electrode placed at the vertex (Cz) region. The sample time in this study was set to four seconds. With a sampling rate of 512 Hz and excluding the reference electrode data, each sample yielded 4096 sampling points (\(4\) seconds \(\times\) \(512\) Hz \(\times\) \(2\) channels). Square wave signals were utilized to present visual stimuli on the LEDs of the STC metasurface units, which emitted the red light, thereby ensuring adequate visual contrast. To minimize the harmonic interference, four target visual stimulus frequencies were: top-left at 8.5 Hz, bottom-left at 10 Hz, top-right at 11.5 Hz, and bottom-right at 7 Hz. To mitigate mutual interference between two closely spaced flickering stimuli pairs, the frequencies 7 Hz and 8.5 Hz, as well as 10 Hz and 11.5 Hz,
+were placed diagonally opposite to one another. The example of the collected brain wave signal data for four target frequencies is shown in Supplementary Figure 1. Data processing and model training were conducted in Python and PyTorch environments. Signal processing primarily involved utilizing scipy package for filtering and FFT calculations. Given that neither the absolute value of the EEG signal nor its temporal characteristics were pertinent to this study, all sampled signals were linearly transformed to have a mean of zero and a standard deviation of one.
+
+Classification model training. Initially, a dataset comprising 240 instances of raw SSVEP signals was collected from two participants. Subsequently, a subset consisting of 80 instances of randomly selected raw signals was employed to create RefSpec. The remaining 160 instances of raw signals were randomly selected to serve as training and validation datasets for classification model training. The two subsets have an equally divided number of signals across four stimuli frequencies. As for the training and validation dataset, a subset of 60 instances was extracted from the initial subset of 160 instances to serve as the validation set. The remaining 100 instances underwent a data augmentation process, which resulted in an expanded dataset of 1700 instances. These augmented instances constituted the training set, which was then utilized to train the model for 300 epochs. The validation operation was executed every two training epochs.
+
+Acknowledgements
+
+The work is supported by the National Natural Science Foundation of China (62288101, 92167202, 72171044), the Major Project of Natural Science Foundation of Jiangsu Province (BK20212002), the State Key Laboratory of Millimeter Waves, Southeast University, China (K201924), the Fundamental Research Funds for the Central Universities (2242018R30001), the 111 Project (111-2-05), the China Postdoctoral Science Foundation (2021M700761), and ZhiShan Scholar Program of Southeast University (2242022R40004).
+
+Author contributions
+T.J.C. suggested the designs and planned and supervised the work, in consultation with Q.M., Y.F.N., Q.X., and J.W.Y. conceived the idea and carried out the theoretical analysis and numerical simulations. Q.X., L.H.F., Y.M.N., and Z.G. built the system and performed the experimental measurements. Q.X., L.H.F. and L.C. performed the data analysis. Q.X. and L.H.F. wrote the manuscript. Q.M., L.L., J.W. Y, and T.J.C. reviewed the manuscript. All authors discussed the theoretical aspects and numerical simulations, interpreted the results and reviewed the manuscript.
+
+Competing interests
+
+The authors declare no competing financial interest.
+
+Data availability
+
+The data that support the findings of this study are available from the corresponding author upon request.
+
+Code availability
+
+The code that supports the findings of this study are available from the corresponding author upon reasonable request.
+
+References
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+Fig. 1 | The schematical diagram of the presented BSTCM. The BSTCM system integrates STC metasurface into SSVEP-based BCI systems. The STC metasurface can correctly support the visual stimuli for the SSVEP-based BCI and facilitate the information interaction with the external environment. Based on the BSTCM system, high-security encrypted wireless communication systems are realized for the first time by combining with the variant HSKs and VSS method. In this way, smart devices can be controlled by the human mind with high security.
+Fig. 2 | The diagram of interaction and data processing procedures of the SSVEP-based BCI system. a. The interaction procedures for the SSVEP-based BCI involve the user wearing an EEG cap and focusing their attention on the intended target LED stimuli. Once the user’s selected frequency is recognized, the interaction commands are transmitted to the STC metasurface. b. The feature extraction process includes the transformation of the input BCI signals into the frequency domain. The resulting Signal FFT is then subjected to outer product with pre-defined Template FFTs, yielding eight feature graphs. c. The lightweight classification model. Four convolutional and two fully connected layers were employed. d. An example of frequency responses of SSVEP signals for the four target frequencies, showing distinctive amplitude peaks corresponding to different frequencies.
+Fig. 3 | The details of the STC metasurface. a. The geometrical structure of the STC metasurface element. b, c. The reflective amplitude and phase of the element, respectively. d-f. The optimized STC matrices for different scattering angles at different harmonic frequencies. g-i. The far-field results corresponding to the optimized STC matrices. j-m. The encoding schemes for the transmitting symbol “0” or “1” for two users: the symbols “0” and “1” for Users 1 (j and k); the symbols “0” and “1” for Users 2 (l and m).
+Fig. 4 | The encrypted wireless communication system based on the BSTCM platform. a. The encrypted encoding scheme combining the harmonic-secret keys and the VSS method. b. The experimental scenarios of the encrypted wireless communication system, in which the operator equipped with EEG cap transmits the encrypted information to two users via the BSTCM platform, respectively. c. The receiving signals corresponding to the encoding scheme in Fig 3(j-m). d, e. The decoded information of VSK1 and VSK2 from the receiving signals based on the encrypted coding scheme. f. The correct transmitting information is decoded by the extracted VSK1 and VSK2.
+Fig. 5 | Experiment on the wireless remote mind control of smart devices based on the BSTCM platform. a. The system architecture of wireless remote control. b. The experimental scenarios of the wireless remote-control system by the human brain. c, d. The theoretical and experimental results for far-fielded patterns at ±2th harmonic frequencies. f. The temporal waveform of the output voltages from four detectors when the operator lights up four devices in sequence. e. The variations between the input power of the detectors and output voltage with respect to the different distances between the receiving antenna and the metasurface center.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementMaterials.pdf
+• SupplementaryVideos.zip

09b079d80b3efdeef69e111bf52a9dde06da16423667f03702d57d11bbbeec9b/metadata.json

@@ -0,0 +1,147 @@
+{
+    "title": "A tautomerized ligand enabled meta selective C\u2013H borylation of phenol",
+    "pre_title": "Meta Selective C\u2013H Borylation Directed by Secondary Silicon Oxygen Interaction",
+    "journal": "Nature Communications",
+    "published": "30 October 2023",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-42310-6/MediaObjects/41467_2023_42310_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-42310-6/MediaObjects/41467_2023_42310_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-42310-6/MediaObjects/41467_2023_42310_MOESM3_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-023-42310-6#Sec7"
+    ],
+    "code": [],
+    "subject": [
+        "Catalytic mechanisms",
+        "Homogeneous catalysis",
+        "Synthetic chemistry methodology"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1837437/v1.pdf?c=1668607906000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1837437/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-023-42310-6.pdf",
+    "preprint_posted": "17 Aug, 2022",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Remote meta selective C\u2013H functionalization , ,  of aromatic compounds remains a challenging problem in chemical synthesis. Here, we report an iridium catalyst bearing a bidentate pyridine-pyridone (PY-PYRI) ligand framework that efficiently catalyzes this meta selective borylation reaction. We demonstrate that the developed concept can be employed to introduce a boron functionality at the remote meta position of phenols, phenol containing bioactive and drug molecules, which was an extraordinary challenge. Moreover, we have demonstrated that the method can also be applied for the remote C6 borylation of indole derivatives including tryptophan that was the key synthetic precursor for the total synthesis of Verruculogen and Fumitremorgin A alkaloids. The origin of the remote meta selectivity was described as a secondary silicon oxygen interaction  that was never used in C\u2013H functionalization chemistry.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.\nWe declare that the authors have no competing interests except that We have filled an Indian Patent (Patent Application No: 202211036590) based on this work (including the ligand and catalyst).",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupportingInformation.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Remote meta selective C\u2013H functionalization of aromatic compounds remains a challenging problem in chemical synthesis. Here, we report an iridium catalyst bearing a bidentate pyridine-pyridone (PY-PYRI) ligand framework that efficiently catalyzes this meta selective borylation reaction. We demonstrate that the developed concept can be employed to introduce a boron functionality at the remote meta position of phenols, phenol containing bioactive and drug molecules, which was an extraordinary challenge. Moreover, we have demonstrated that the method can also be applied for the remote C6 borylation of indole derivatives including tryptophan that was the key synthetic precursor for the total synthesis of Verruculogen and Fumitremorgin A alkaloids. The inspiration of this catalytic concept was started from the O\u2013Si secondary interaction, which by means of several more detailed control experiments and detailed computational investigations revealed that an unprecedented Bpin shift occurs during the transformation of iridium bis(boryl) complex to iridium tris(boryl) complex, which eventually control the remote meta selectivity by means of the dispersion between the designed ligand and steering silane group.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Transition metal-catalyzed C\u2013H bond activation and functionalization1,2,3,4,5,6,7,8,9,10 of aromatic compounds has been branded as one of the most significant chemical transformations. This has a profound impact in modern synthetic organic chemistry, ranging from laboratory methods to industrial deployment11,12. However, the key underlying principles for the success of the metal catalysis lies on the two important factors, such as: (i) design and synthesis of new generation ligand framework that can produce highly reactive catalyst system13,14 and (ii) substrates\u2019 structure modifications15 by which site selectivity could be controlled by the steric crowding16,17,18,19,20 or various weak interactions21,22,23,24 of the aromatic compounds among several similar type of C\u2013H bonds via the ligand\u2013substrate pre-organization25,26. In recent times, many elegant approaches27 have been developed for the functionalization of proximal14,28,29,30 and remote C\u2013H bonds1,3,31,32,33,34,35,36,37,38,39 of arenes by the design of either new ligand frameworks with an extended architectures featuring a weak coordinating functional groups40 or templates41 as well as transient mediators42 or transient directing groups43 attached with the substrates. While ligand having an extended architecture or template approaches are extremely important to functionalize the remotely located C\u2013H bonds of arenes, but requirement of multi-step preparation of the linkers of the ligands and templates of the aromatic substrates significantly limit the wide application of the methods44.\n\nAmong numerous aromatic substrates, phenols are the most widespread aromatic compounds that acquired household products including several bioactive to important drug molecules45. Moreover, it is well-documented that 10% of the top 200 selling pharmaceuticals contain a phenol and several others employ phenols as synthetic intermediates46. Furthermore, phenols are also key components of the biopolymers melanin, lignin, resins, and polyphenylene oxides45,46,47. In industry, phenol is routinely used as a raw material to make numerous important components by means of its diversification via the synthetic manipulation45,46. Thus, direct functionalization of phenols would be a significant development for the rapid access of numerous important products47. In this context, traditional electrophilic substitution is an alternative method that affords variously substituted phenols (Fig.\u00a01a)48. Employing this method, one can easily access ortho and para substituted phenol derivatives, although often remain a chance to have mixture of isomers. However, functionalization of the remote meta C-H bonds of phenols and getting meta functionalized phenols49 is extremely difficult because of the extreme inertness of the meta C\u2013H bonds. Several pioneering approaches have been developed by Yu and others either using template method50,51,52 or transient directing group by Larrosa2 (Fig.\u00a01a). But, achieving the meta functionalized products using these methods, it is essential to have specialized substrates that limits the application of the methods.\n\na Meta functionalization of phenol. b Present work of meta selective borylation of phenols at ambient temperature. c Conceptual background for ligand design. d Reaction design. e O\u2013Si interaction. f Origin of meta selectivity on the basis of DFT calculation.\n\nHaving tremendous importance of catalytic C-H borylation53,54,55,56,57,58 in organic synthesis, we report here a concept for the meta selective C-H borylation of phenols through a unique ligand design strategy that has never been utilized in the C-H functionalization chemistry (Fig.\u00a01b). Literature reports revealed59,60 that the most common structural motif for the O\u2013Si interaction can be found in the amide skeleton, where a filled p-orbital of carbonyl oxygen atom interact with the vacant d-orbital of the tetracoordinated silicon atom consisting of at least one electronegative atom (Fig.\u00a01c). Inspired from this background reports59,60, we initially proposed a hypothesis where phenol is protected with an easily removable silane group that will meet all the necessary criteria for the weak O\u2013Si interaction with 2-pyridone moiety having amide skeleton. The designed ligand (PY-PYRI) consists of two parts, one part is the simple pyridine unit (PY) and the other one is a 2-pyridone unit (PYRI)61,62,63,64, which was redesigned by the skeletal modification of the bipyridine core structure (Fig.\u00a01d). Based on the above-mentioned findings, we anticipated that the designed PY-PYRI ligand may control the meta selectivity owing to the following two reasons. Firstly, in presence of [Ir(cod)OMe]2, the ligand (PY-PYRI) will generate a complex (Int-1). Secondly, the p-orbital of the oxygen atom of the 2-pyridone unit will interact with the vacant d-orbital of the tetracoordinated silicon atom of the substrate through TSO-Si (Fig.\u00a01e). While experimental observations indicated that the secondary O\u2013Si interaction was the key to control the remote meta selectivity, surprisingly, what we found from the computational calculations is somewhat different from our anticipated O\u2013Si interaction. It was revealed that the Int-1 derived from the PY-PYRI ligand, in presence of di-boron reagent generated iridium bis(boryl) complex (Int-2), which underwent an unprecedented Bpin shift due to the close proximity of the 2-pyridone carbonyl oxygen atom and Bpin group attached with iridium atom. A dispersion force was observed by the ligand containing OBpin group and substituent (R = tBu) of the PY-PYRI ligand that creates a suitable pocket for the phenol bearing tri-isopropyl group for the meta selective borylation reactions (Fig.\u00a01f).",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The investigation of this meta selective C-H borylation started with phenol (1a) using the standard dtbpy ligand under the iridium-catalyzed conditions at 80\u2009\u00b0C in THF solvent, where free phenol does not participate in the reaction (Fig.\u00a02a). On the other hand, performing the borylations with several steering groups such as, OMe, OBpin, acetyl, pivalate, OBoc, carbamate and other sulfonate groups proved to be nonselective. Interestingly, when the reaction was examined using SiMe3 as steering group (1k), it gave 81% meta selectivity with dtbpy ligand. The selectivity was further enhanced to 84% upon changing the steering group from SiMe3 to SiiPr3 group (1l).\n\na Optimization of steering group. b Ligand optimization. c Deleterious result with other silyl groups. d Importance of O\u2013Si linkage towards meta selectivity. e Importance of [Si] towards meta selectivity. Reactions are on 0.2\u2009mmol scales. aConversion was reported. See SI for details.\n\nAfter identifying the best choice of steering group (SiiPr3) for meta borylation of phenol, we then studied the same reaction with several bipyridine ligands (Fig.\u00a02b). It was observed that while bipyridine ligand (L1) afforded same type of selectivity similar to the dtbpy ligand with less conversion, no reaction occurred with 1,10-phenanthroline (L2). Testing the reaction with 4,4\u2019-dimethyl bpy (L3) also resulted in 86% meta selectivity with 81% conversion. As expected, due to steric crowding ligand (L4) bearing 6,6\u2019-disubtituted methyl group failed to undergo the reaction. Notably, while a monosubstituted ligand (L5) having a methoxy group resulted in 86% meta borylation with 36% conversion, the ligand (L6) containing a hydroxy group that can undergo tautomerization provided excellent meta selectivity (90%) with improved conversion (64%). Surprisingly, introducing two hydroxy groups into the ligand (L7), no reaction occurred. To see the electronic effect of the ligand, we performed the borylation with (L9) ligand that yielded minor improvement (91% meta selectivity, 68% conversion) with respect to the ligand (L6). Remarkably, when the reaction was conducted with the ligand (L9) having a tert-butyl group, it provided 94% meta selectivity along with excellent conversion of the meta borylation (95%).\n\nHaving established the optimized reaction conditions employing the tri-isopropyl silyl steering group, we then became interested in other silyl steering groups (1k, 1m\u20131q) which exhibited deleterious outcomes for the meta borylation (Fig.\u00a02c). Moreover, we found that the essential criteria for achieving high level of meta selectivity is that the substrate must have an O\u2013Si linkage, because substrates having C\u2013Si linkage (1r, 1s) afforded non-selective borylation (Fig.\u00a02d). Furthermore, to sense the importance of silyl group [Si] was replaced with the [C] (1t) that also resulted in non-selective borylation reactions (Fig.\u00a02e). Thus, it may be stated that for achieving high degree of meta selective borylation, it is essential that substrates should have silane steering group along with the most important 2-pyridone ligand (L9: Py-PYRI).\n\nTo this end, we were curious about the catalyst structure with the designed tautomeric ligand (L9: PY\u2013PYRI) for the meta selective borylation. Accordingly, to sense the binding behavior of the developed ligand system we performed a stoichiometric reaction between the ligand (L9) and [Ir(cod)OMe]2, which gave a complex (3) that have 2-pyridone type unit confirmed by X-ray and NMR spectroscopy (Fig.\u00a03a). To know whether this complex (3) is catalytically active or not, it was then tested as a catalyst for the reactions of the substrates (1l) and (4a), which afforded highly meta selective borylation with excellent conversions (Fig.\u00a03b). Moreover, testing the stability of the catalyst [3: Ir(cod)(PY-PYRI)] we observed that it is highly stable that can even be stored in open air for several months.\n\na Catalyst synthesis. b Test of reactivity of catalyst 3. c DFT calculation: Active catalyst formation. d Experimental support of OBpin formation. e Test of reactivity of L10. f Further improved reaction conditions. Reactions are on 0.2\u2009mmol scales. aConversion was reported. See SI for details.\n\nTo show insights into the reaction mechanism and the origin of meta-selectivity, detailed DFT calculations were conducted. The proposed reaction pathway is shown in Fig.\u00a03c, in which L6 was used as the model ligand. [Ir(OMe)(cod)]2 firstly reacts with the ligand and forms L6Ir(\u03b74-cod) (INT1) as a starting species. When B2pin2 was the only boron reagent, a B-B oxidative addition to INT1 occurs via TS1, giving L6Ir(\u03b74-cod)(Bpin)2 (INT2). Then, unexpectedly, the oxygen in the ligand attacks a Bpin group on the iridium center and eventually undergoes an intramolecular Bpin-shift via TS2. With a free energy barrier of only 4.0\u2009kcal/mol, this tautomerization step proceeds very quickly and delivers a more stable (L6Bpin)Ir(\u03b74-cod)(Bpin) (INT3). Next, INT3 partly dissociates cod to generate an empty site for incoming B2pin2, which then undergoes another B-B oxidative addition through TS3 to form (L6Bpin)Ir(\u03b72-cod)(Bpin)3 (INT4). Finally, the dissociation of cod yields (L6Bpin)Ir(Bpin)3 (INT5), which we believe to be the active catalyst in C-H borylation of the phenol silyl ethers. To support this Bpin-shift process, we prepared the intermediate ligand L10 from the ligand L9 with HBpin in presence of a catalytic amount of iridium catalyst (Fig.\u00a03d). The intermediate ligand L10 was then employed in the reaction using the substrate (1l) at room temperature that resulted in an improved result of 97% meta selectivity with full conversion to the borylated product (2l) (Fig.\u00a03e). From these experimental observations, we realized that if we used catalytic amount of HBpin in the reaction mixture with ligand L9, it could give better selectivity and outcomes. As expected, we noticed that the use of ligand L9 in presence of 5.0\u2009mol% HBpin afforded 97% meta selectivity with 100% conversion of 1l at room temperature (Fig.\u00a03f).\n\nWith the optimized reaction conditions of meta selective borylation using L9 (PY-PYRI) as ligand and Si(iPr)3 as steering group at room temperature, we next performed the iridium-catalyzed meta borylation of a variety of phenols that afforded excellent meta selectivity and yields of the isolated borylated products (Fig.\u00a04). For example, we first tested 2-chlorophenol (4a) for the borylation reaction, while our designed ligand (L9) gave high meta selectivity (m/p\u2009=\u200996/4), traditional dtbpy ligand provided poor meta selectivity (m/p\u2009=\u200963/37), which clearly demonstrated the utility of the designed (L9: PY-PYRI) ligand. Other 2-substituted phenols, such as 2-bromo (4b) and 2-iodo (4c) afforded high meta selectivity that have great synthetic values owing to the two different types of handles on the phenols.\n\nReactions are in 0.5\u2009mmol scale. aConversion was reported. b1.5 equiv. B2pin2 was used. cReaction is carried out at 80 oC. dReactions are carried out at 50 oC. e2.0 equiv. B2pin2 was used. See SI for details.\n\nLikewise, phenols bearing various alkyl chain ranging from methyl to pentyl (4d\u20134f) at the 2-positions along with trifluoromethyl (4g), isopropyl (4h) and trifluoromethoxy (4i) smoothly underwent meta borylation irrespective of the nature of the substituent. Amino phenol (4j), substrate of momentous importance for the chemical and pharmaceutical industries65 is borylated with high meta selectivity (m/p\u2009=\u200999/1) without borylation next to the amino group, which is known to give ortho borylation under iridium-catalyzed borylation conditions via in situ generation of NHBpin group66. Thioether (4k) that usually directs borylation at the ortho position67 also underwent borylation with good meta selectivity. We observed that phenols containing functional groups such as cyano (4l) and Bpin (4m) resulted very high meta selectivity of 99% and 98% respectively without any disturbance by the electronics of these substituents. Also, cyclic amine (4n), cyclohexyl (4o), ketomethyl (4p) and homologous ester (4r) afforded high level of meta selectivity and tolerated well under the employed reaction conditions. The utility of the developed PY-PYRI (L9) ligand was further highlighted when substrates were employed in the reactions conditions with dtbpy ligand and all resulted in non-selective borylation reactions. Amide functionalities (4r and 4s) that are known to undergo numerous synthetic transformations68 exhibited excellent meta selective borylation. Borylation of phenols having CF3 (4g) and CN (4l) substituents at the ortho position afforded exclusively meta borylation, the same substituents at the meta position of phenols (4t and 4u) also gave meta selective borylation, which indicated the generality of the developed method. Moreover, fluoro-substituted arene, which typically gives borylation next to the fluorine atom under standard iridium-catalyzed conditions, in this case, 3-fluorophenol (4v) gave meta borylation as the major product. On the other hand, dtbpy gave non-selective borylation reaction of 4v bearing meta fluoro substituents. Several disubstituted phenols (4w\u20134af) were also examined under the developed conditions that reacted smoothly to afford variously substituted meta borylated products in high yields. 2,2\u2032-Biphenol, compound of paramount importance in medicinal chemistry as well as in chemical industry69 can selectively be mono- and diborylated (5ah and 5ag) by tuning the amount of boron reagent. On the other hand, dtbpy gave complex mixture for the borylation of 4ag and this result again highlighted the importance of PY-PYRI ligand. A bulky substituent at the ortho positions (4ah) did not hamper the reaction that gave 98% meta borylated product with 90% isolated yield.\n\nNext, we focused on the meta borylation of those phenols bearing a substituent at the para position (Fig.\u00a05). Because, borylation at the remote meta position in presence of a para substituent remains an extraordinary challenge due to the steric reason. Moreover, we selected those substituents at the para position that already provided exclusive meta borylation of phenols when they were located at either ortho or meta positions. The reason for this selection is mainly to observe the overall effects of the borylation by the same substituents. For the testification, we begun with the 4-methyl phenol (6a) that afforded 91% meta selective borylation. Increasing the chain length from small methyl group to the relatively bulkier alkyl groups such as, ethyl (6b), pentyl (6c), hexyl (6d) and isopropyl (6e), the borylation underwent smoothly with further enhancement of the meta selectivity from 91% to 100%. Para-substituted ethers and thioethers bearing electronically different substituents (6f\u20136j) reacted with 100% meta selectivity, which revealed that the scope of the meta borylation is very general regardless of the nature of the substituents. While 2-CN, 3-CN as well as 2-CF3 and 3-CF3 bearing phenols resulted in excellent meta borylation, the same substituents at the para position reacted to yield 100% meta borylation. Likewise, we also observed that chloro (6m) and bromo (6n) containing phenols reacted to give the meta borylation products solely irrespective of their position in the arene. Moreover, it has been found that the phenols featuring bulky substituents at the para position (6o\u20136r) also gave exclusively meta borylation, although conversion was moderate in case of the cyclohexyl group. In all cases, dtbpy results were compared and gave somewhat bad result with compared to developed PY-PYRI (L9) ligand.\n\nReactions are in 0.5\u2009mmol scale. aConversions were reported. See SI for details.\n\nIn 2015, Baran et al. reported70 the first total synthesis of Verruculogen and Fumitremorgin A enabled by ligand-controlled C\u2013H borylation as the key step of TIPS protected tryptophan. We were curious if our designed ligand system could provide the remote C6 borylation of TIPS protected indoles and tryptophan (Fig.\u00a06a). For that reason, we performed borylation of TIPS-protected tryptophan (8a) (synthetic key precursor of bioactive alkaloids Verruculogen and Fumitremorgin A) which provided C6 borylation with 98% selectivity with excellent conversions at 60\u2009\u00b0C. Moreover, large-scale synthesis of (8a) smoothly underwent under the developed reaction conditions without hampering the selectivity. We also found that other indole derivatives (8b and 8c) and carbazole (8d) easily underwent remote borylation affording excellent selectivity and conversion. This developed method provided a simple way to borylate the 3-substituted indoles derivatives that might be beneficial for the total synthesis or the late-stage functionalization of several bioactive molecules.\n\na C6 borylation of indoles. b Late-stage meta C\u2013H borylation. c Removal of silane. Reactions are in 0.5\u2009mmol scale. aConversions were reported. b2.0 equiv. B2pin2. See SI for details.\n\nLate-stage functionalization71 of complex bioactive and medicinally important molecules by the site selective C\u2013H activation is a powerful method for the development of new drug candidates72. In this context, introducing a boron functionality into the bioactive and medicinally important molecules would further enhance the identification of new lead molecules not only for the enormous importance of the boron-bearing small molecules73 but also for the uniqueness of the boron group towards the diverse derivatization towards numerous other functional groups. Thus, we tested our developed method for several commercially available bioactive and drug molecules (Fig.\u00a06b). For example, cannabinoid core (10a: used as a psychoactive drug), methyl salicylate derivatives (10b: an anti-inflammatory and analgesic agent), tyrosol derivatives (10c: an antioxidant), eugenol derivatives (10d: a flavoring agent), sesamol derivatives (10e: an antioxidant), naproxen derivatives (10f: a nonsteroidal anti-inflammatory drug, NSAID), deoxyarbutin derivatives (10g: used for treatment of hyperpigmentation disorders) and homosalate (10h: used as a sunscreen) were meta borylated with high yield and selectivity. Moreover, parallel reactions were carried out with the dtbpy ligand for 10a\u2013h substrates and resulted comparatively less conversions or non-selective borylation reactions than the developed PY-PYRI (L9) ligand. The steering silane group from the borylated phenols has been removed under a very mild reaction conditions at room temperature (ethylene glycol, KF, 1\u2009h) that afforded the meta borylated phenols in high yields (Fig.\u00a06c). Notably, the meta borylated phenols can further be transformed to a number of substituted phenols/resorcinols that are difficult to prepare by otherwise.\n\nAt the end, we are curious about the origin of meta selectivity in the C-H borylation. Therefore, a detailed DFT calculations were carried out. It is found that the active catalyst INT5 follows an Ir(III)-Ir(V) catalytic cycle through C-H oxidative addition (via TS4-meta), C-B reductive elimination (via TS5), and catalyst regeneration (from INT7 to INT5), which is similar to those reported for bipyridine ligands (Fig.\u00a07a)57,74. An evaluation of the regioselectivity-determining C-H activation process showed that the meta-C-H activation of model substrate 4a\u2019 (2Cl-PhOSiMe3) through TS4-meta is preferred by 0.7\u2009kcal/mol over its para-C-H activation through TS4-para. This tendency agrees with our experiments. The activation free energy of the rate-determining C-H activation is computed to be 28.8\u2009kcal/mol. Since dispersions can significantly stabilize the meta-C-H activation transition state (vide infra), the barrier for the real system is expected to be lower by 4\u20135\u2009kcal/mol, making the reaction smoothly occur at room temperature.\n\na Ir(III)\u2013Ir(V) catalytic cycle. b Our working model: Double dispersions determine meta selectivity. c Proofs for our working model. Computed at SMD(CyH)-M06/6-311\u2009+\u2009G(d,p)//B3LYP/6-31\u2009G(d). Relative free energies are given in kcal/mol. Atom colors in graphics: gray, C; white, H; red, O; blue, N; pink, B; light yellow, Si; green, Cl; brown, Ir.\n\nFurthermore, the real ligand and substrate (L9 and 4a) were evaluated. Firstly, the transition states of meta- and para-C-H activation (TS8-meta and TS8-para) were located (Fig.\u00a07b). To our delight, a much larger energetic preference of 4.4\u2009kcal/mol was found for meta-C-H activation, in accordance with the observed excellent meta-selectivity. Scrutinizing the structures, TS8-para seems not to benefit from any significant interaction. However, for TS8-meta, we found that a double-dispersion model may explain the meta-selectivity (Fig.\u00a07b, right). The OBpin group (highlighted in pink) in the ligand lies near the substrate, providing the first dispersion with the silyl group. In addition, the tert-butyl group (highlighted in blue) exerts the second dispersion on the other side. The Si(iPr)3 group (highlighted in green) has the best volume to fit into the constructed pocket, maximizing both dispersions. The multiple C-H\u00b7\u00b7\u00b7\u03c0 interactions with the bipyridine rings may also help.\n\nOur double-dispersion working model can be further supported by comparison with analogous ligands (Fig.\u00a07c). The importance of the OBpin-originated first dispersion can be proved by considering the typical dtbpy as ligand. The computation showed that the silyl group lies far away from the ligand in TS9-meta without any dispersion mentioned above. Accordingly, an energetic preference of only 1.0\u2009kcal/mol was predicted for meta-borylation, correlating with the poor experimental result (m:p\u2009=\u200963:37). The function of tert-butyl is verified by using L6 as ligand. The meta-C-H activation transition state TS10-meta has the same structural pattern as TS8-meta, showing the existence of the first dispersion. However, without the tert-butyl group, the second dispersion is absent, and the energy difference between the meta- and para-C-H activation shrinks to 2.9\u2009kcal/mol. Experimentally, the meta-selectivity drops to 90:10. Finally, substrate 4a\u2019, with a smaller silyl group, was calculated for reaction using ligand L9. The silyl group in TS11-meta is also placed as the same orientation as in TS8-meta, but the suboptimal size fitting results in a decreased energy difference of 1.6\u2009kcal/mol, in agreement of the experiment (m:p\u2009=\u200979:21). In addition, more computational studies using different DFT methods are performed. When B3LYP (without dispersion correction) is used for single-point energy calculations, the computation contradicts with the experiments; when other functionals with dispersion terms are used, the results agree with the experiments (for details, see Supplementary Fig.\u00a023). This further demonstrates the importance of the dispersion effect in the reaction system. Therefore, the synergistic effect of two optimal dispersions contributes to the observed excellent meta-selectivity.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In conclusion, we report a new class of ligand and catalyst that has demonstrated remarkable efficiency for the remote meta selective borylation of phenols featuring all types of substitutions at the arene ring. In addition, we have seen that our developed ligand system is beneficial for the remote C6-borylation of indole derivatives including tryptophan which is a synthetic precursor of bioactive alkaloids (Verruculogen and Fumitremorgin A). Several late-stage meta borylations have been showcased with bioactive and drug molecules that might be useful for repurposing medicines and identification of new lead drug candidates. Notably, while preliminary experimental findings indicated that a secondary O\u2013Si interaction was the key element that controls the remote meta selectivity, detailed computational investigations along with more detailed experimental results revealed that an unprecedented Bpin shift was observed during the transformation of iridium bis(boryl) complex to iridium tris(boryl) complex and developed tautomeric ligand behaves like bipyridine during the borylation reaction. The governing factors for the meta selective borylation is the combined dispersion of OBpin and tert-butyl group of the designed ligand which make a suitable pocket for the phenol bearing tri-isopropyl silane group that resulted in meta selective borylation of phenol. We anticipate that the designed ligand and catalyst will also find wide application in the context of other C\u2013H functionalization reactions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "In an argon-filled glove box, a 5.0\u2009mL Wheaton microreactor was charged with [Ir(cod)OMe]2 (4.97\u2009mg, 1.5\u2009mol%), ligand L9 (3.4\u2009mg, 3.0\u2009mol%), B2pin2 (127.0\u2009mg, 1.0 equiv.), HBpin (3.2\u2009mg, 5.0\u2009mol%) and dry cyclohexane (2.0\u2009mL) were added sequentially. The reaction mixture was stirred for 2\u2009min at room temperature and then substrate (0.5\u2009mmol) was added. The microreactor was capped with a Teflon pressure cap and stirred for 24\u2009h at a particular mentioned temperature. After completion (judged by GC-MS), CyH was removed under reduced pressure and chromatographic separation with silica gel gave the meta-borylated product.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data are available from the corresponding authors upon request. X-ray dataset for catalyst 3 is freely available at the Cambridge Crystallographic Data Centre under deposition number CCDC 2180880. All relevant data are available in this article and its Supplementary Information. The experimental procedures and characterization of all new compounds are provided in Supplementary Information file. Coordinates of the optimized structures are provided as source data.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We thank Centre of Biomedical Research (CBMR) for providing research facility. We thank the High-Performance Computing Center (HPCC) of Nanjing University for doing the numerical calculations in this paper on its blade cluster system. We also thank IIT Kanpur for the X-ray crystallography data collection. This work was supported by SERB-SUPRA grant (SPR/2019/000158) and SERB-CRG grant (CRG/2022/002733). S.D. and S.G. thank CSIR for their SRF and M.M.M.H. thanks SERB\u2013CRG grant for a RA.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Department of Biological & Synthetic Chemistry, Centre of Biomedical Research, SGPGIMS Campus, Raebareli Road, Lucknow, 226014, Uttar Pradesh, India\n\nSaikat Guria,\u00a0Mirja Md Mahamudul Hassan,\u00a0Sayan Dey\u00a0&\u00a0Buddhadeb Chattopadhyay\n\nState Key Laboratory of Coordination Chemistry, Jiangsu Key Laboratory of Advanced Organic Materials, Chemistry and Biomedicine Innovation Center, School of Chemistry and Chemical Engineering, Nanjing University, 210023, Nanjing, China\n\nJiawei Ma\u00a0&\u00a0Yong Liang\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nB.C. conceived the concept. S.G. developed the ligand. S.G., M.M.M.H., and S.D. performed the experiments. J.M. and Y.L. did the computational calculations. B.C. supervised the project. All authors contributed to writing and proofreading of manuscript and SI.\n\nCorrespondence to\n                Yong Liang or Buddhadeb Chattopadhyay.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "S.G., M.M.M.H., S.D., and B.C. declare that they have filed an Indian Patent (Patent Application No: 202211036590) and an international patent PCT (PCT/IN2023/050608) based on this work (including the ligand and catalyst).",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article\u2019s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.\n\nReprints and permissions",
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+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Guria, S., Hassan, M.M.M., Ma, J. et al. A tautomerized ligand enabled meta selective C\u2013H borylation of phenol.\n                    Nat Commun 14, 6906 (2023). https://doi.org/10.1038/s41467-023-42310-6\n\nDownload citation\n\nReceived: 06 September 2023\n\nAccepted: 06 October 2023\n\nPublished: 30 October 2023\n\nVersion of record: 30 October 2023\n\nDOI: https://doi.org/10.1038/s41467-023-42310-6\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
+            "section_image": [
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+            "section_image": []
+        }
+    ]
+}

09caa31641cd2fa62399cf94c4caec3caa098ba1b127a492b84d0583324ff5f2/preprint/preprint.md

@@ -0,0 +1,275 @@
+Rapid scaffold-hopping for molecular glues: from fragments to cell-active probes targeting the 14-3-3/ERα complex
+
+Michelle Arkin
+michelle.arkin@ucsf.edu
+
+University of California at San Francisco   https://orcid.org/0000-0002-9366-6770
+
+Markella Konstantinidou
+University of California San Francisco   https://orcid.org/0000-0001-5972-4140
+
+Marios Zingiridis
+University of Crete   https://orcid.org/0009-0008-1150-2926
+
+Marloes Pennings
+Eindhoven University of Technology   https://orcid.org/0000-0002-3366-0238
+
+Michael Fragkiadakis
+University of Crete
+
+Johanna Virta
+University of California San Francisco
+
+Jezrael Revalde
+University of California, San Francisco
+
+Emira Visser
+TU Eindhoven
+
+Christian Ottmann
+Eindhoven University of Technology   https://orcid.org/0000-0001-7315-0315
+
+Luc Brunsveld
+TU Eindhoven   https://orcid.org/0000-0001-5675-511X
+
+Constantinos Neochoritis
+University of Crete   https://orcid.org/0000-0001-5098-5504
+
+Article
+
+Keywords: covalent, estrogen receptor, MCR, molecular glue, 14-3-3
+
+Posted Date: February 28th, 2025
+
+DOI: https://doi.org/10.21203/rs.3.rs-6051794/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. M.R.A, C.O, and L.B. are co-founders of Ambagon Therapeutics. C.O. is an employee of Ambagon Therapeutics.
+
+Version of Record: A version of this preprint was published at Nature Communications on July 14th, 2025. See the published version at https://doi.org/10.1038/s41467-025-61176-4.
+Rapid scaffold-hopping for molecular glues: from fragments to cell-active probes targeting the 14-3-3/ERα complex
+
+Markella Konstantinidou*[a], Marios Zingiridis[b], Marloes A.M. Pennings[c], Michael Fragkiadakis[b], Johanna M. Virta[a], Jezrael L. Revalde[a], Emira J. Visser[c], Christian Ottmann[c], Luc Brunsveld[c], Constantinios G. Neochoritis*[b], Michelle R. Arkin*[a]
+
+[a] M. Konstantinidou, J.M. Virta, J.L. Revalde, M.R. Arkin
+Department of Pharmaceutical Chemistry and Small Molecule Discovery Centre (SMDC)
+University of California San Francisco (UCSF)
+CA 94143 (USA)
+E-mail: markella.konstantinidou@ucsf.edu, michelle.arkin@ucsf.edu
+[b] M. Zingiridis, M. Fragkiadakis, C.G. Neochoritis
+Department of Chemistry
+University of Crete
+Voutes, Heraklion, 70013, Greece
+E-mail: knochoor@uoc.gr
+[c] M.A.M. Pennings, E.J. Visser, C. Ottmann, L. Brunsveld
+Laboratory of Chemical Biology, Department of Biomedical Engineering and Institute for Complex Molecular Systems (ICMS)
+Eindhoven University of Technology
+5600 MB Eindhoven, The Netherlands
+
+Abstract: Molecular glues, small molecules that bind cooperatively at a protein-protein interface, have emerged as powerful modalities for the modulation of protein-protein interactions (PPIs) and “undruggable” targets. The systematic identification of new chemical matter with a molecular glue mechanism of action remains a significant challenge in drug discovery. Here, we present a scaffold hopping approach, using as a starting point our previously developed molecular glues for the native 14-3-3/estrogen receptor alpha (ERα) complex. The novel, computationally designed scaffold was based on the Groebke-Blackburn-Bienaymé multi-component reaction (MCR), leading to drug-like analogs with multiple points of variation, thus enabling the rapid derivatization and optimization of the scaffold. Structure–activity relationships (SAR) were developed using intact mass spectrometry and TR-FRET. Rational structure-guided optimization was facilitated by crystal structures of ternary complexes with the glues, 14-3-3 and phospho-peptides mimicking the highly disordered C-terminus of ERα. We measured the kinetics of 14-3-3/ERα peptide binding by SPR, using a format in which a 14-3-3/molecular glue complex was immobilized on the SPR chip. The most potent compounds stabilized the complex by 100-fold and increased the residence time by 14-fold. Cellular stabilization of 14-3-3/ERα for the most potent analogs was confirmed using a NanoBRET assay with full-length proteins in live cells (EC_{50} = 2.7 – 5 μM). Our approach highlights the potential of MCR chemistry, combined with scaffold hopping, to drive the development and optimization of unprecedented molecular glue scaffolds.
+
+Introduction
+
+The stabilization of native protein-protein interactions (PPIs) with small molecules offers an attractive strategy for the activation or inhibition of signaling pathways in a therapeutic context.1,2 PPIs were traditionally considered difficult targets due to the lack of well-defined pockets and the presence of large, hydrophobic surfaces.3–5 The fundamental understanding of the mechanism of action of molecular glues – small molecules that bind cooperatively at PPI interfaces and strengthen weak, pre-existing interactions – has enabled the stabilization of PPIs by taking into account the elements of cooperativity, molecular recognition and shape complementarity.6,7
+
+A particularly challenging class of PPIs includes proteins that are intrinsically disordered and only become partially structured when bound to a protein partner, such as a chaperone binding to a client protein.8,9 14-3-3 is an abundant scaffolding protein that recognizes specific phospho-serine or phospho-threonine motifs on disordered domains of the client and upon binding creates a structured binding interface.10 Molecular glues targeting 14-3-3/client complexes bind
+to the composite surface formed at this interface; the inherent cooperativity of this approach yields molecular glues with selectivity and potency. Of note, 14-3-3 proteins lack function – the function is instead encoded on the client protein and in particular on the phospho-site that is being recognized, leading either to activation or inhibition of signaling pathways.11
+
+Among the extensive interactome of 14-3-3, here we focus on its native interaction with the hormone regulated transcription factor estrogen receptor α (ERα). 14-3-3 recognizes the protein sequence surrounding phospho-T594 on the disordered C-terminus on the F-domain of ERα and acts as a negative regulator by inhibiting ERα binding to chromatin and blocking ERα-mediated transcription.12,13 To date, ERα small molecule drugs, acting either as inhibitors or degraders, target the adjacent ligand binding domain (LBD).14–17 However, mutations in the LBD are often associated with acquired endocrine resistance.18 Thus, stabilization of the native 14-3-3/ERα PPI could be useful as an alternative strategy to block ERα transcriptional activity in ERα positive breast cancer, especially in cases of acquired endocrine resistance. The feasibility of this approach, targeting the F-domain, is corroborated by studies using the natural product fusicoccin-A (FC-A) and its semi-synthetic analogs that stabilize the interaction between 14-3-3 and the C-terminus of ERα.19 We now require drug-like chemical probes to define the biological impact of targeting the F-domain to inhibit ERα in hormone-positive breast cancer.
+
+We have applied different strategies for the identification of chemical matter to stabilize the 14-3-3/ERα complex. We used a site-directed fragment-based technology, termed “disulfide tethering” with intact mass spectrometry as the readout to identify reversible fragments bound at the native cysteine (C38) of 14-3-3σ in the presence of a phosphorylated peptide that represented the disordered C-terminus of ERα.20 Rational, structure-guided optimization of the reversible disulfide fragments led to irreversibly covalent, selective molecular glues that bound at the composite surface of 14-3-3σ/ERα.21 For the development of non-covalent molecular glues, we used a fragment-linking approach, derived from the crystal structures of two diverse fragments that were identified in crystallographic and disulfide tethering screens.22 Thus, the 14-3-3/ERα PPI has served as a valuable system to test diverse molecular-glue discovery strategies.
+
+Here, we present a scaffold-hopping approach based on multi-component reaction chemistry (MCR). Multi-component reactions are defined as synthetic approaches where at least three starting materials react in a single step to form a complex scaffold, where most of the atoms contribute to the newly formed product. This broad definition covers reactions with various synthetic mechanisms.23,24 MCR chemistry, due to its highly divergent character, is an enticing strategy for developing new scaffolds and rapid structure-activity relationships (SAR), as it allows the combination of short synthetic routes with high diversity and complexity. MCR has emerged as an attractive alternative to multistep linear convergent synthetic approaches and has been successfully applied to the synthesis of active pharmaceutical ingredients (API).25–30 Here, we describe our strategy for the development of a drug-like MCR scaffold stabilizing the 14-3-3σ/ERα complex. The most potent analogs of the series showed efficacy in orthogonal biophysical assays and cell-based PPI stabilization in the low micromolar range.
+
+Results
+
+Structure activity relationships (SAR)
+Structurally, 14-3-3 binds ERα by recognizing phospho-T594, the penultimate residue on the C-terminus of ERα. This creates a large, open, solvent-exposed pocket that can accommodate a small molecule. Although steric factors are not an issue for targeting the composite surface of the 14-3-3/ERα complex, we found it was important to rigidify an initially flexible scaffold to maximize the stabilization effect.21 Our aim in this work was to design a scaffold that would be more rigid from the beginning, locking in a favorable three-dimensional shape complementary to the large pocket.
+
+To this end, we used the freely accessible software AnchorQuery™, which performs pharmacophore-based screening of approximately 31 million compounds that are readily synthesizable through one-step multi-component reaction (MCR) chemistry.31,32 Although AnchorQuery™ was originally developed for PPI inhibitors33, in this case it was successful in proposing MCR scaffolds for PPI stabilizers. AnchorQuery™ requires a ligand-bound crystal structure or docked binding pose as a starting point. We used the crystal structure of the previously disclosed compound 127 (PDB 8ALW) that was bound at the composite surface of the 14-3-3σ/ERα complex, with a favorable ligand conformation, based on our biophysical data.21 The compound formed multiple favorable interactions both with 14-3-3σ and the phospho-ERα peptide (Fig 1A). In the co-crystal structure, the irreversible chloroacetamide warhead of compound 127
+formed a covalent bond with C38 of 14-3-3σ. The p-chloro-phenyl ring occupied a small hydrophobic pocket that formed a halogen bond with K122 of 14-3-3. The tetrahydropyrane ring adopted a favorable conformation that allowed the formation of hydrophobic interactions with 14-3-3 residues (L218, I219), the terminal Val595 of ERα, and a water-
+
+![Overview of scaffold hopping approach. SAR and crystal structures of selected benzyl and aniline analogs.](page_176_180_1232_1583.png)
+
+Figure 1. Overview of the scaffold hopping approach. SAR and crystal structures of selected benzyl and aniline analogs. A) Crystal structure of compound 127 (yellow sticks) with 14-3-3σ (grey surface) and phospho-ERα peptide (orange sticks). Interacting aminoacids are shown as sticks and water molecules as red spheres (PDB 8ALW). B) Ligand overlay of compound 127 and docking pose of the new MCR scaffold. C) General MCR scaffold and main points of variation. D) Overview of general synthetic routes. Detailed experimental conditions are described in the SI. E) MS bar graphs at 1 μM. For each compound, time course experiments were performed with measurements at 1h, 8h, 16h and 24h. ERα data are shown with different colors for each compound, and apo data in grey. F) Crystal structure overlay for compounds 1 (cyan sticks) and 127 (yellow sticks) bound to 14-3-3σ (grey surface)/ERα (orange sticks). G) Crystal structure of compound 1 (cyan sticks) with 14-3-3σ/ERα. Interacting aminoacid residues are shown as sticks and interacting water molecules as red spheres. H-I) Structural overlays of compounds 2 (brown sticks), and 10 (dark red sticks) with compound 1 (cyan sticks).
+mediated hydrogen bond from the oxygen atom in the ring, which was part of a large water network. The overall ligand conformation also led to a key water-mediated hydrogen bond between the aniline nitrogen and the terminal carboxylic acid of Val595 of ERα, significantly contributing to molecular recognition. In this compound series, the introduction of large non-aromatic rings, such as the tetrahydropyran, combined with aniline rings were necessary to limit the multiple ligand conformations and improved the affinity to the complex.
+
+Understanding the binding mode of 127, we were able to use AnchorQuery™ for a scaffold-hopping approach. The software required an anchor motif on the ligand that was bioisosteric to an amino acid residue and was kept constant for all pharmacophore-based searches of the database. A suitable anchor in our case was the p-chloro-phenyl ring that was deeply buried at the PPI interface in the small pocket surrounding K122 of 14-3-3 (Fig S1). This motif served as the “phenylalanine anchor”. Selection of three additional pharmacophore points on different parts of the ligand were necessary for running queries and could include all possible ligand-protein interactions, such as hydrogen bond donors or acceptors, aromatic rings, hydrophobic residues or charged ions. We applied an additional filter, limiting the molecular weight of the hits to 400 Da. We screened all 27 MCR reactions, but interestingly all our top hits were based on the Groebke-Blackburn-Bienaymé (GBB) three-component reaction (GBB-3CR).34–36 The GBB-3CR utilized aldehydes, 2-aminopyridines and isocyanides, leading to imidazo[1,2-a]pyridines.37,38 This privileged scaffold has been present in several clinical candidates and marketed drugs, such as zolpidem, miroprofen, minodronic acid, and olprinone.39
+
+Comparison of the docking pose of the proposed GBB compounds with the co-crystal structure of compound 127 revealed a considerable 3D shape complementarity of the two scaffolds (Fig 1B). Additionally, the GBB scaffold was drug-like and more rigid compared to our original ligand, potentially restricting the possible ligand conformations. Further docking and selection of suitable substituents to achieve favorable ligand – protein interactions were performed with the docking software SeeSAR [version 14.0.0; BioSolveIT GmbH, Sankt Augustin, Germany, 2024, www.biosolveit.de/SeeSAR].
+
+Once compounds were selected for synthesis, synthetic routes were established using commercially available aldehydes and 2-aminopyridines, whereas isocyanides were synthesized from primary aromatic amines (Fig 1C-1D). Two general, three-step synthetic routes were developed based on the type of aldehyde building blocks used. In the first synthetic route (route A), Boc-protected aldehydes reacted with 2-aminopyridines and isocyanides in methanol, using scandium triflate as a Lewis acid catalyst to form the GBB intermediate. The Boc-protecting group was removed under acidic conditions and the chloroacetamide warhead was introduced with an amidation reaction, either with chloroacetyl chloride or an amide coupling. In the second synthetic route (route B), to reduce the cost of certain Boc-protected aldehydes, nitro-substituted aromatic aldehydes were used instead. The GBB-3CR was performed under the same experimental conditions, followed by a nitro-reduction. The nitro-group was reduced either using iron trichloride and zinc or using ammoniotrihydroborate and gold catalysis with Au/TiO₂.40 The two reduction methods led to comparable, almost quantitative yields. The last step, as previously, was the introduction of the electrophilic warhead. Thus, the GBB-3CR allowed multiple combinations of the three main building blocks, facilitating the synthesis of analogs. Synthetic details are provided in the Supplementary Information.
+
+To test whether this scaffold was suitable for the development of 14-3-3σ/ERα stabilizers, we synthesized a small set of derivatives varying only the isocyanide position, which according to our design was expected to interact with K122 of 14-3-3. We included benzyl and phenyl isocyanides with a diverse substitution pattern on the aryl ring. We maintained the covalent chloroacetamide warhead, based on our extensive investigation of electrophiles in our previous work.21
+
+The compounds were tested in an intact mass spectrometry (MS) assay, which monitored the formation of the covalent bond with C38 of 14-3-3σ. Binding measurements were made in the presence or absence of the phospho-ERα peptide and as a function of time to distinguish between cooperative stabilizers and neutral binders and to select compounds with fast binding kinetics. The phospho-ERα peptide was used at a concentration 2-fold above the dissociation constant (Kd). The assay was performed as a compound titration (Fig S2-S3). We additionally quantified compound binding at 1 μM (10:1 compound:protein) over several time points (table S2). Throughout this work, we reference the time-course data as bar graphs, using grey bars to represent binding to 14-3-3σ alone (“apo”) and colored bars to represent binding to 14-3-3 σ/ERα complex.
+Testing the first analogs in the MS assay revealed striking differences among benzyl and phenyl analogs (Fig 1E, Fig S4). The benzyl analog 1, which lacked aryl ring substitutions, was a neutral binder. Introduction of electron withdrawing groups, such as halogens or nitro-groups in the o-, m- or p-position (compounds 2-9) reduced binding in the presence of ERα, even in the case of a small F-substitution. Interestingly, the non-substituted phenyl analog 10 showed increased binding to 14-3-3α, but still lacked cooperativity, since it showed increased binding in the presence or absence of ERα. Introduction of halogens in the p-position significantly reduced apo binding, improving compound cooperativity (compounds 11 and 12). However, in contrast to the SAR observed in our previous series21, less binding was observed for the p-Cl analog (11), compared to the non-substituted analog (10). Remarkably, a Me-group in the o-position (13) led to the first molecular glue of the series; compound 13 showed binding in the presence of ERα and very low apo binding. Bigger substitutions in the o-position significantly decreased the observed binding, indicating unfavorable steric effects (14-16) (Fig S4).
+
+We solved co-crystal structures of the 14-3-3α/ERα complex with compounds 1, 2 and 10 to elucidate their binding modes (Fig 1F-I). The crystal structure of compound 1 revealed a comparable binding mode to the original ligand 127, supporting the design and docking hypothesis (Fig 1F-G). The chloroacetamide moiety of 1 bound covalently to C38 of 14-3-3α, and two water-mediated hydrogen bonds were formed between the carbonyl group and R41 and the backbone of E115, and one direct hydrogen bond with N42 of 14-3-3 at 3Å. The imidazopyridine ring was positioned towards the hydrophobic residues (L218, I219, G171 and L222) at the “roof” of the 14-3-3 pocket. In addition, the nitrogen of the five-membered ring formed a hydrogen bond with D215 of 14-3-3, which adopted two conformations upon binding of compound 1. Importantly, a large water network was formed between the benzylamine of 1 to N42, S45 of 14-3-3, which reached the terminal carboxylic acid of V595 and the pT594 of ERα, and K122 of 14-3-3. The benzyl ring, adjacent to the electrophilic warhead was positioned between the hydrophobic 14-3-3 residues F119 and I168, (Fig 1G). The structural overlay of analogs 1 and 2 showed an identical binding mode with the additional o-F substituent forming a halogen bond with I219 of 14-3-3 (Fig 1H). Replacing the benzyl ring (1) with a phenyl ring (10) resulted in a slight turn of the compound that placed the aryl rings of both analogs in the same position in the pocket surrounding K122. The water network that connected the amine of compound 1 to residues of 14-3-3 and ERα was conserved upon modification of the benzyl ring (1) to a phenyl ring (10). The removal of the methylene group positioned the aniline nitrogen of (10) closer the terminal carboxylic acid of ERα, in the position previously occupied by the methylene group of (1). Additionally, it led to increased axial rotation of the bond between the nitrogen and the aryl ring, which might have resulted in the increased apo binding in the MS assay, since this axial rotation was not possible for the benzyl analogs (Fig 1I).
+
+Since the o-Me substitution correlated with improved binding in the presence of ERα in the MS assay and taking into account the rotational nature of the aniline – phenyl ring bond, we designed and synthesized a series of analogs with double o-substitutions (Fig 2A, Fig S5). The symmetrical 2,6-di-Me analog 17 showed significantly faster binding in the presence of ERα and almost no apo binding, indicating molecular-glue-like binding. Analog 18 with an o-Et group in addition to o-Me, was weaker, indicating unfavorable steric effects (Fig S5). Analogs 19, 20, and 21 with additional o-OMe, o-F and o-Cl groups respectively, showed similar, rapid binding to the symmetric analog 17 and low apo binding. In agreement with our previous observation, the introduction of additional substitutions in the p-position (-Cl, -Me, -OH) significantly reduced binding (compounds 22-25), especially for the triple substituted analogs (double o- and p-positions).
+
+Co-crystal structures of the 14-3-3α/ERα complex with compounds 17,19, 20, 21, and 25 revealed differences in the positions of the double-ortho substituents (Fig 2B-E). In the case of the symmetric analog 17 one o-Me group was oriented in the back of the pocket, which was primarily hydrophobic, forming hydrophobic interactions with I219 (3.2Å) and facing Val595 of ERα. The second o-Me group was oriented in the front of the pocket and formed hydrophobic interactions with F119 (3.8 Å). The formation of these interactions seemed to favorably restrict the axial rotation of the aniline-phenyl bond, locking its position in a highly complementary shape with the composite 14-3-3/ERα surface. In analog 19 the larger o-OMe group was positioned in the front of the pocket and formed, together with the aniline nitrogen, a water-mediated hydrogen bond with the terminal carboxylic acid of Val595 of ERα. The orientation of the warhead amide differed in two analogs, but in both cases a direct hydrogen bond with N42 of 14-3-3 was formed (3.0 Å). For the halogen-containing analogs o-F (20) and o-Cl (21) the halogens interacted with I219 and the common o-Me group with F119, whereas the aniline nitrogen interacted with the terminal carboxylic acid of Val595 of ERα via a water mediated-hydrogen bond. The binding mode of the triple substituted analog 25, although overall comparable with the double substituted analog 17, showed an additional hydrogen bond between the p-OH group and the backbone
+carbonyl group of I168 (3.2 Å). The presence of this direct interaction seemed to negatively affect the axial rotation of the aniline-phenyl bond, resulting in significantly reduced binding in the MS assay and loss of cooperativity.
+
+![SAR and crystal structures of selected double-ortho substituted analogs. A) MS bar graphs at 1 μM. For each compound, time course experiments were performed with measurements at 1h, 8h, 16h and 24h. ERα data are shown with different colors for each compound, and apo data in grey. B-E) Crystal structures of 14-3-3α/ERα with compounds 17 (dark pink sticks), 19 (teal sticks) and overlays of crystal structures for compounds 17 (dark pink sticks), 20 (pale green sticks), 21 (pale purple sticks) and 25 (bright yellow sticks).](page_184_320_1207_670.png)
+
+Figure 2. SAR and crystal structures of selected double-ortho substituted analogs. A) MS bar graphs at 1 μM. For each compound, time course experiments were performed with measurements at 1h, 8h, 16h and 24h. ERα data are shown with different colors for each compound, and apo data in grey. B-E) Crystal structures of 14-3-3α/ERα with compounds 17 (dark pink sticks), 19 (teal sticks) and overlays of crystal structures for compounds 17 (dark pink sticks), 20 (pale green sticks), 21 (pale purple sticks) and 25 (bright yellow sticks).
+
+We synthesized analogs of compound 21, maintaining the 2-CI,6-Me substitutions and varied positions X and Y on the scaffold (Fig 3A, Fig S6). Position X referred to substitutions on the imidazopyridine ring and was expected to contribute to additional hydrophobic interactions with Val595 of ERα. Position Y included modifications that were expected to improve interactions with the rim of the 14-3-3 pocket, primarily with variations of the aldehyde building blocks and to a smaller extent with different electrophilic warheads. In both cases, even the introduction of small groups led to surprising effects in the binding modes, as revealed by crystal structures.
+
+For position X, aiming for hydrophobic interactions with Val595 of ERα, we introduced groups with a range of radii (-F (26), -Cl (27), -Me (28), -i-Pr (29), -CF3 (30)). Steric effects seemed to play a bigger role than electronic effects, since the best tolerated substitutions were -Cl (27) and -Me (28). For position Y, derived from the aldehyde building blocks, the o-F analog (31) was tolerated, but was weaker compared to the unsubstituted (21); a plausible explanation being the rotational nature of the aryl ring–imidazopyridine ring bond, which lost axial symmetry with the presence of the o-F group. Introduction of a methylene linker (32) or replacement of the aryl ring with a cyclohexyl ring (33) that had a similar size made the compounds almost unable to bind in the MS assay. Modifications in the position of the electrophilic warhead were also not tolerated. The less-reactive ester analog (34) was inactive, whereas halogenated chloroacetamides (35-37) did not lead to the expected mass adducts, showing instability in the MS and unclear chemical reactivity with 14-3-3. A plausible explanation was their increased reactivity, which correlated with reduced stability. The sulfamate warhead (38) was tolerated in the MS assay, but was significantly weaker than the chloroacetamide analog, in addition to being less atom efficient.
+
+Crystal structures were solved for 28, 32, and 33 and were compared as overlays with analog 21 (Fig 3B-E). The -Me group on the imidazopyridine ring of 28 was expected to contribute to hydrophobic interactions with Val595 of ERα. However, it disrupted the previously observed binding mode and instead moved the imidazopyridine ring upwards, in the hydrophobic pocket of 14-3-3 formed by L218, I219 and L222. This upward movement affected the conformation of L218, which moved upwards but maintained contact with 28. The movement in the pocket also altered the interactions of the double-ortho-substituted aryl ring; while the o-Cl still interacted with I219 on the roof of the binding site, the o-Me
+group moved further away from F119 in the bottom of the pocket, and the interaction was lost. The direct hydrogen bond between the amide and N42 and the water-mediated bond between the aniline nitrogen and the carboxylic acid of Val595 were maintained. Overall, the changes in binding mode were associated with slower binding, but a similar apparent Kd in the MS assay (Fig. S3). Analog 32, with an additional methylene group on the electrophilic warhead linker showed a slightly disrupted binding mode. While the biggest difference was the position of the aryl ring next to the longer linker, the imidazopyridine ring also moved further away from ERα; the latter correlated negatively with the binding observed in the MS assay. In contrast to the previous analogs, the o-Cl group on the aryl ring of 32 pointed out of the 14-3-3 pocket and due to increased distance, was unable to interact with F119. Thus, the presence of an additional methylene group on the linker was sufficient to make the compound unable to stabilize the complex. Analog 33 bearing a cyclohexyl ring instead of an aromatic ring maintained the interaction between the o-Cl group of the aryl ring and Ile219, but not the interaction of the o-Me group with F119. The orientation of the amide bond next to the warhead also differed; however, the hydrogen bond with N42 was still formed. The presence of the cyclohexyl ring, which had the possibility of adopting more conformations compared to the more rigid aryl ring, correlated with reduced binding to the 14-3-3/ERα complex in the MS assay.
+
+![SAR and crystal structures of analogs substituted in positions X and Y. A) MS bar graphs at 1 μM. For each compound, time course experiments were performed with measurements at 1h, 8h, 16h and 24h. ERα data are shown with different colors for each compound, and apo data in grey. B-E) Crystal structure of 14-3-3/ERα with compound 28 (dark yellow sticks), and overlays of crystal structures for compounds 28 (dark yellow sticks), 32 (pink sticks) and 33 (emerald green sticks) with 21 (pale purple sticks).](page_172_670_1207_496.png)
+
+Figure 3. SAR and crystal structures of analogs substituted in positions X and Y. A) MS bar graphs at 1 μM. For each compound, time course experiments were performed with measurements at 1h, 8h, 16h and 24h. ERα data are shown with different colors for each compound, and apo data in grey. B-E) Crystal structure of 14-3-3/ERα with compound 28 (dark yellow sticks), and overlays of crystal structures for compounds 28 (dark yellow sticks), 32 (pink sticks) and 33 (emerald green sticks) with 21 (pale purple sticks).
+
+Investigation of modifications in positions X and Y provided valuable input in the groups that were tolerated; however, these single-point substitutions did not significantly improve the stabilization effect in the MS assay. Based on the crystallographic input, we synthesized four analogs combining the favorable substitutions from positions X and Y with the symmetric double o-Me analog 17, hypothesizing that a symmetric rotatable bond would correlate with improved potency (Fig 4A). This hypothesis was readily confirmed by evaluating the symmetric analogs 39-42 in the MS assay. Analogs 39 and 40 included the -Me group on the imidazopyridine ring (X position) and the -F group on aryl ring (referred to as W position), respectively. Analogs 41 and 42 both had the F group in W position and a -Me or -Cl group in X position, respectively. All analogs showed comparable, fast, cooperative binding to 14-3-3/ERα in the MS assay, indicating that the symmetry of the 2,6-di-Me-aniline ring was more favorable compared to the asymmetric 2-Cl,6-Me. All four analogs showed low apo binding with analog 41 showing the lowest.
+Figure 4. SAR and crystal structures of 2,6-di-Me analogs substituted in positions X and W. Biophysical data (MS, TR-FRET, SPR) and cell data (NanoBRET). A) MS bar graphs at 1 μM. For each compound, time course experiments were performed with measurements at 1h, 8h, 16h and 24h; ERα data are shown with different colors for each compound, and apo data in grey. B-C) Overlays of crystal structures of 14-3-3/ERα ternary complexes with compounds 40 (orange sticks), 41 (red sticks), and 42 (blue sticks). D) TR-FRET schematic and protein titration data for representative compounds at 100 μM compound or DMSO. E) SPR data for the binary 14-3-3γ/ERα interaction and ternary interactions with 181, 17 and 41 (mean +/- SD, n=2). F-G) 14-3-3γ-HaloTag/Niuc-ERα NanoBRET assay in HEK293T cells with compound titrations (1:2 dilution, starting at 40 μM). Data points excluded where compound dosage was toxic to the cells. MCR compounds compared to the previously described stabilizer 181 and 85, an inactive compound as the negative control. Bar graphs quantifying pEC_{50} values.
+Crystal structures were solved for the symmetric analogs 40, 41 and 42, highlighting the significance of two rotational bonds in the scaffold: the aniline-aryl ring bond, as previously discussed and the aryl ring–imidazopyridine ring bond (Fig 4B-C). The o-F substituent in W position, adjacent to the aryl ring-imidazopyridine rotational bond, adopted two different orientations; an inward orientation for analog 40 and an outward orientation for 41 and 42, which each had an additional substituent on the imidazopyridine ring. With the inward conformation of analog 40, the o-F substituent interacted with P167 of 14-3-3, whereas for 41 and 42 the o-F group was oriented to made multiple stabilizing interactions, being approximately 3 Å from N42 of 14-3-3, and the o-Me substituent and aniline nitrogen of the compound itself, thus contributing both to ligand-protein interactions and intramolecular interactions, restricting the axial bond rotation. In agreement with previous observations, the presence of a substituent in the X position (41 and 42) led to an upward movement of the imidazopyridine ring, orienting the substituent toward the hydrophobic residues I219 and L222. Overall, the presence of the additional substituent on the imidazopyridine ring in the last two analogs, even though in a distant position compared to the o-F-substituted ring, correlated favorably with the restriction of the rotational bond on the F-aryl ring. The different substituents of the imidazopyridine ring, Me (41) or Cl (42), did not affect the position of the stabilizer in the crystal structures; however, in the MS assay the Me group showed lower apo binding to 14-3-3, resulting in higher cooperativity of the ternary complex.
+
+TR-FRET
+Up to this point, the SAR was developed using the intact MS assay and supported by crystallography. In our previous work20–22, we relied on a fluorescence anisotropy assay (FA) to confirm cooperativity. The FA assay typically used (5-carboxyfluorescein) FAM-labeled phospho-peptides to quantify peptide binding to the compound/14-3-3 complex. For the MCR scaffold, however, this assay proved to be unsuitable, since the extensively conjugated ring system was intrinsically fluorescent in the same wavelengths as the FAM-labeled peptide (480 nm and 520 nm). To circumvent this issue, we turned our attention to far-red fluorescent dyes. The cy5-labeled ERα-peptide with excitation wavelength of 651 nm and emission wavelength of 670 nm, significantly affected the Kd of the 14-3-3/ERα complex. The reported Kd using the acetylated ERα peptide in an isothermal calorimetry (ITC) experiment or the FAM-labeled-ERα in an FA assay is in the range of 1-2 μM.21 The cy5-ERα-peptide, however, resulted in a Kd of 6 nM, indicating significant dye binding (Fig S7).
+
+As a suitable alternative to the FA assay, we developed a TR-FRET assay41, using HIS-tagged-full-length 14-3-3σ, biotin-labeled-ERα peptide, an anti-HIS-tag monoclonal antibody conjugated with a Tb(III) cryptate as the donor and streptavidin conjugated with the D2 dye as the acceptor. The observed Kd for this system was 30 nM. To ensure that the observed difference in Kd from ITC or the FAM-labeled-ERα in an FA assay was not related to the biotin-tag on the peptide, we performed a competition assay with the FAM-labeled peptide. The Kd of the biotin-peptide was 2.5 μM, in good agreement with the FAM-peptide’s Kd (Fig S7). This result suggested that the lower Kd in the TR-FRET assay was due to avidity42; since 14-3-3 and the antibody were both dimers and streptavidin was tetravalent, different multivalent complexes could form, resulting in differences in the observed binding affinity between the labeled and the unlabeled proteins.
+
+We performed assay optimization with 2D-titrations of 14-3-3, biotin-ERα and donor/acceptor ratios. We then tested the synthesized compounds using the optimized experimental conditions: 200 nM 14-3-3 (top concentration, 2-fold dilution), 50 nM biotin-ERα, 0.166 nM MAb anti-6HIS Tb and 6.25 nM SA-D2. The compounds were tested at 100 μM and DMSO was used a negative control. 14-3-3 was titrated using an Echo acoustic dispenser, followed by the addition of the compounds and the peptide; after 1h incubation at room temperature, the donor and acceptor were added. In contrast to the MS assay, maximum signal was obtained after 2h rather than 16h – a plausible explanation again being avidity. The tight Kd in the TR-FRET assay resulted in a small assay window and a hook effect was observed at higher protein concentrations (ca. 50 – 100 nM 14-3-3).
+
+Nevertheless, the TR-FRET assay was sensitive to the addition of molecular glues. In addition to quantifying fold stabilization for the 14-3-3/ERα complex (\( AppKd_{compound}/AppKd_{DMSO} \)), we also quantified the fold increase in the TR-FRET signal (the ratio of observed Emax and Emin). To validate the TR-FRET assay, we included two positive controls: the natural product FC-A and our previously described stabilizer compound 18121. The two compounds gave comparable results. FC-A had an \( AppKd_{compound} \) of 11 nM, fold-stabilization of 3.09, and fold-increase of 5.52. Compound 181 had an \( AppKd_{compound} \) of 8.6 nM, fold-stabilization of 3.95 and fold-increase of 5.52 (Fig S8, table S3).
+In good agreement with the MS data, neutral binders 1 and 10 showed only a small signal shift compared to the DMSO control (Fig 4D, Fig S8). The 2-Me analog 13 showed 4.19-fold-stabilization and 2.36-fold increase, whereas 2,6-di-Me analog 17 showed 4.78-fold-stabilization and 2.58-fold increase, the same rank order as the MS assay. The more sterically hindered analog 18 (o-Me, o-Et) showed weaker stabilization (3.06-fold-stabilization and 2.14-fold increase). Analogs 19, 20, and 21, all bearing the o-Me group and additional o-OMe, o-F and o-Cl groups respectively, showed comparable stabilization (4.41 – 5.23-fold stabilization and 2.1 – 2.48-fold increase). The highest stabilization effect was observed for the final symmetric analogs 39 – 42. Analog 39 with a -Me group in X position had an AppKd(compound) of 7.8 nM, fold-stabilization of 4.35 and fold-increase of 2.61, whereas 40 with the -F group in W position had an AppKd(compound) of 8.4 nM, fold-stabilization of 4.04 and fold-increase of 3.12. Analog 41, which had both the -Me group in X position and the -F group in the W position had the lowest AppKd(compound) (5.2 nM) and the highest fold-stabilization (6.53) and fold-increase (3.71) of the series. Analog 42, which differed only in the X position (-Cl instead of -Me group) appeared weaker (AppKd(compound) 8.8 nM, fold-stabilization of 3.87 and fold-increase of 2.97). In summary, while the fold-changes were dampened by avidity, 14-3-3/ERα molecular glues showed the same rank-order in the TR-FRET assay as in the mass spectrometry assay used for initial SAR.
+
+SPR
+Surface Plasmon Resonance (SPR) was then used to analyze the kinetic parameters of the ERα peptide binding to 14-3-3σ in the presence of compounds 181, 17 and 41, and to compare the AppKd(compound) and kinetics to the binary ERα/14-3-3σ interaction (Fig 4E, Fig S9). Here, 14-3-3σ tagged with a Twinstrep-tag was captured on a SPR chip coated with Strep-Tactin XT, after which a 2-fold dilution series of acetylated ERα phospho-peptide was injected. For the binary interaction, the fast dissociation rate (koff) reached the limit of detection of the SPR instrument, due to a relative weak interaction with a Kd of 1.1 μM, which was in line with the ITC and FA experiments. The covalent bond between the chloroacetamide warhead of the compounds and C38 of 14-3-3σ was formed after overnight incubation in the presence of ERα. Immobilization of this complex on the chip, followed by extensive washing to remove the bound ERα peptide, allowed us to determine the kinetics of ERα binding to the 14-3-3σ/stabilizer complex. The previously described stabilizer 181 decreased the off-rate to 0.016 s^{-1} and simultaneously increased the association rate (kon) by a factor of 16, resulting in a low nanomolar affinity constant for the ERα peptide/14-3-3 complex (3.9 nM; stabilization = 282-fold). The analogs of the newly designed scaffold, 17 and 41, both led to an 8-fold increase in association rate compared to the binary interaction. The binding of compound 41 induced a stronger decrease in dissociation rate of ERα compared to 17, which resulted in Kd values of 10.1 nM and 15.1 nM for 41 and 17, respectively. The higher stabilizing potency of 41 compared to 17 (stabilization = 110-fold for 41 and 71-fold for 17) were in rank-order agreement with the TR-FRET data. The decreased dissociation rates in the presence of the stabilizers, especially for 41 and 181, increased the residence time of ERα binding to 14-3-3 from approximately 3.4 s to 47.6 s and 62.5s, respectively.
+
+NanoBRET
+To test the effects of the compounds on the full-length PPI, we used a NanoBRET assay we developed previously43. Compounds were tested using a C-terminal fusion14-3-3σ-HaloTag and full length, N-terminal fusion NanoLuc-ERα (Fig 4F-G; Table S4). Briefly, NanoLuc-ERα and 14-3-3σ-HaloTag plasmids were transfected in 1:10 ratio in hormone deprived HEK293T cells. After 48 hours post transfection, cells were seeded in assay plates with the experimental wells treated with 100 nM HaloTag NanoBRET 618 ligand (Promega) and no-ligand control wells treated with DMSO (v/v). Cells were treated for 24 hours with compounds in 1:2 dilution series starting at 40 μM. The BRET signal was read and normalized against DMSO treated samples. All active compounds resulted in an increase in BRET signal compared to the negative control, 85. The previously described compound 18121 stabilized the 14-3-3σ/ERα complex in cells with an EC_{50} value of 5.2 μM and a 1.7-fold increase in the BRET signal. Of the compounds tested, the neutral binder 10 was less effective than 181 (EC_{50} value > 100 μM, 1.6-fold increase). Compound 13 showed an improved EC_{50} and fold-increase compared to 10 (12 μM and 1.8-fold). Compound 17 had the lowest EC_{50} value of 2.7 μM and showed 1.8-fold increase in BRET signal, a slight improvement compared to 181. Compounds 40 and 42 had the same 2-fold-increases in BRET signal, though exhibited slightly different EC_{50} values (7.2 and 4.6 μM, respectively). Compound 41 resulted in the highest increase in BRET signal, a 2.6-fold increase; however, it had a similar EC_{50} value to 181 of 5 μM. In the NanoBRET assay, compounds 17 and 41 performed most effectively, based on the EC_{50} value (17) and fold-increase in BRET signal (41) of the panel of compounds tested. The majority of MCR stabilizers showed similar EC_{50} values to the previous scaffold represented by 181, but consistently showed improved fold-increase in BRET signal.
+Compounds 181, 17, and 41, along with the negative control, 85, were tested in a NanoBRET assay where the cysteine of interest in 14-3-3σ C38, was mutated to an asparagine, 14-3-3σC38N-HaloTag (Fig S10). The BRET signal did not increase for 85, 181, or 17 with increasing compound concentration. There was a minimal increase in BRET signal for compound 41, from 2.5 to 3.5 mBU at 20 μM 41. In comparison to the assays done with 14-3-3σWT-HaloTag, the non-normalized BRET signal increased from 6.7 to 16.1 mBU at the same concentration of 41 (data shown as normalized). In summary, when C38 was not present in 14-3-3σ, the compounds were unable to bind and stabilize the full-length 14-3-3σ/ERα complex in cells (Fig S10).
+
+Discussion
+
+Using MCR chemistry, we demonstrated the potential of a scaffold-hopping approach for molecular glues stabilizing a native 14-3-3/client PPI. Our approach combined computational de novo design with multi-component reaction chemistry, which included short, efficient synthetic routes with multiple points of variation, accelerating the synthesis of analogs. Thus two distinct optimization approaches led to two highly diverse chemical series, converging on similar efficacies as 14-3-3σ/ERα molecular glues.
+
+In the MCR approach, structure-activity relationships were established with an intact mass spectrometry assay, which allowed the distinction between neutral binders and stabilizers – cooperative molecular glues. Overall, the SAR showed that the introduction of even small substituents in the case of molecular glues could profoundly affect their potency and cooperativity. The best compounds, eg, 41, was already 50% bound at 1 μM after 1 hr of incubation. Crystal structures of ternary complexes were crucial in elucidating small changes in the binding modes of otherwise highly similar analogs. Starting from the weak neutral binder 1 and by removing one methylene group, we significantly increased binding to the complex for compound 10. Introduction of substituents in the o-position was sufficient to reduce apo binding and turn the compounds from neutral binders to cooperative molecular glues. Although the number of rotational bonds is generally kept to a minimum, in this case we took advantage of two rotational bonds in the scaffold and with appropriate substituents achieved favorable ligand conformations resulting in increased potency, as shown for analogs 17 and 41.
+
+Several biophysical assays provided complementary strategies for evaluating these novel molecular glues. A TR-FRET assay circumvented the issue of scaffold fluorescence, which could have been a limiting factor in establishing SAR and allowed the rank-ordering of analogs. A new SPR assay, in which the covalent ligand was pre-associated with 14-3-3σ before immobilization, provided an insightful analysis of binding/unbinding kinetics and started to hint at differences between the two series of molecular glues. Saturating concentrations of compound 41, for instance, stabilized the ERα/14-3-3 complex by 110-fold and slowing the koff by 14-fold. Taken together, biophysical assays allowed the quantification of cooperativity (MS, TR-FRET) and kinetics (SPR); importantly, the observed SAR was consistent among these three assays. The NanoBRET assay further showed good correlation with the biophysical protein/phosphopeptide assays while demonstrating stabilization of the full-length proteins with an EC50 value of 2.7 – 5 μM in intact cells. Overall, the optimized, cell-active MCR scaffold will facilitate chemical biology approaches to study the 14-3-3/ERα interaction, which has so far been unexploited for drug discovery.
+
+Methods
+
+PROTEIN EXPRESSION AND PURIFICATION
+The 14-3-3 σ isoform (full-length for mass spectrometry and TR-FRET assays, ΔC for crystallography) with an N-terminal His6 tag was expressed in Rosetta™ 2(DE3)pLysS competent E. coli (Novagen) from a pPROEX HTb expression vector. After transformation following manufacturer’s instructions, single colonies were picked to inoculate 30 mL precultures (LB), which were added to 1.5 L terrific broth (TB) medium after overnight growth at 37°C, 250 rpm. Expression was induced upon reaching OD600 1.9–2.1 by adding 400 μM IPTG. After overnight expression at 30°C, 150 rpm, cells were harvested by centrifugation at 6,500 rpm, resuspended in lysis buffer (50 mM HEPES pH 7.5, 500 mM NaCl, 20 mM imidazole, 10% glycerol, 1 mM TCEP), and lysed by sonication. The His6-tagged protein was purified by Ni-affinity chromatography (Ni-NTA Agarose, Invitrogen) (Wash buffer 50 mM HEPES pH 7.5, 500 mM NaCl, 20 mM imidazole, 1 mM TCEP; Elution buffer 50 mM HEPES pH 7.5, 500 mM NaCl, 500 mM imidazole, 1 mM TCEP) and analyzed for purity by SDS-PAGE and Q-Tof LC/MS. The protein was buffer exchanged (Storage buffer 25 mM HEPES pH 7.5, 150 mM NaCl, 1 mM TCEP) and concentrated to ~16 mg/mL and aliquots flash-frozen for storage at ~80°C. The ΔC variant was truncated at the C-terminus after T231 to enhance crystallization and after the first Ni-affinity chromatography column, the construct was treated with TEV protease to cleave off the His6 tag during dialysis (25 mM
+HEPES, pH 7.5, 200 mM NaCl, 5% glycerol, 10 mM MgCl₂, 250 μM TCEP) overnight at 4 °C. The flow-through of a second Ni-affinity column was subjected to a final purification step by size exclusion chromatography (Superdex 75 pg 16/60 size exclusion column (GE Life Science) (SEC buffer: 25 mM HEPES pH 7.5, 100 mM NaCl, 10 mM MgCl₂, 250 μM TCEP). The protein was concentrated to ~60 mg/mL, analyzed for purity by SDS-PAGE and Q-Tof LC/MS and aliquots flash-frozen for storage at -80 °C.
+
+PEPTIDES
+Peptides for mass spectrometry, fluorescence anisotropy and TR-FRET assays were purchased from Elim Biopharmaceuticals, Inc. (Hayward,CA). Peptides for SPR and X-ray crystallography was purchased from GenScript Biotech Corp. The following peptides were used:
+Ac-KYYITGEAEGFPA(pT)Y-COOH (MS assay, 15-mer),
+5-FAM-AEGFPA(pT)Y-COOH (FA assay, &mer ERα-pp),
+cy5-KYYITGEAEGFPA(pT)Y-COOH (FA assay, 15-mer),
+biotin-KYYITGEAEGFPA(pT)Y-COOH (TR-FRET assay, 15-mer),
+Ac-EGFPA(pT)Y-COOH (crystallography and SPR, 7-mer)
+
+INTACT MASS SPECTROMETRY ASSAY
+Mass spectrometry dose response assays were performed on a Waters Acquity UPLC/ Xevo G2-XS Q-Tof mass spectrometer. A Waters UPLC Protein BEH-C4 Column (300 Å, 1.7 µm, 2.1 mm x 50 mm) was used to desalt the samples prior to application on the mass spectrometer. For 19-point MS dose responses, 50 mM compound stocks in DMSO were serially diluted in 3-fold increment in a master plate, then 1000 nl of the compounds were transferred in the assay plates. Master mixes containing 100 nM full-length wild type 14-3-3σ in the absence or presence of 2 μM ERα were then dispensed into 384 well plates (Greiner Bio-One, catalog number 784201). Assay buffer was TRIS (10 mM, pH 8.0) and final volume per well was 50 μl, with final top concentration of compounds dose response series at 1 mM. The reaction mixtures were incubated for 1h at rt before subjected to MS. Four measurements (1h, 8h, 16h, 24h) were performed for time-course experiments. The injection volume for each sample was 6 μl. 24 μl of sample were needed for the time-course experiments, so the total volume in the assay plate was adjusted to 50 μl, to account for the dead volume in the injections. Data collection and automated processing followed a custom workflow, as previously described.44 z Plots were created using GraphPad Prism with the log(agonist) vs. response (variable slope, four parameters) fitting model.
+
+K₀ DETERMINATION FOR FAM-, cy5- AND BIOTIN-LABELED ERα PEPTIDES
+For K₀ determination, N-terminal fluorescein-labeled ERα peptide (5-FAM) or cy5-labeled ERα peptide and HIS-tag FL 14-3-3σ were diluted in buffer (10mM HEPES pH 7.5, 150mM NaCl, 0.05% tween 20, 0.05% BGG (bovine gamma globulin)). Two-fold dilution series of 14-3-3 were made in black, round-bottom 384-microwell plates (Greiner Bio-one 784900) in a final sample volume of 10 μL in triplicates. FAM- or cy5-labeled ERα peptides (final assay concentration 10nM) were dissolved in assay buffer and mixed with the protein dilution series on the plates. Fluorescence anisotropy measurements were performed after 1h incubation at room temperature on an Envision HTS Dual Detector 2105 plate reader (for FAM-labeled ERα peptide: filter set lex: 480, lem: 535, and D505fp/D535 advanced dual mirror). For cy5-labeled ERα peptide filter set lex: 620, lem: 688 nm, and D658fp/D688 advanced dual mirror). Data were reported at endpoint. Prism 10 (GraphPad) was used to generate plots using the [agonist] vs. response (variable slope, four parameters) fitting model to determine K₀ values.
+For K₀ determination of the biotin-labeled ERα peptide a competition assay was performed. 5-FAM- and biotin-labeled ERα peptide were diluted in buffer (10mM HEPES pH 7.5, 150mM NaCl, 0.05% tween 20, 0.05% BGG (bovine gamma globulin)). Two-fold dilution series of biotin-labeled ERα peptide were made in black, round-bottom 384-microwell plates (Greiner Bio-one 784900) in a final sample volume of 10 μL in triplicates. A mastermix of 14-3-3σ and 5-FAM-ERα was dispensed on the assay plate (final assay concentrations: 6 μM 14-3-3σ (IC₅₀) and 10 nM 5-FAM-ERα). Fluorescence anisotropy measurements were performed after 1h incubation at room temperature using a Molecular Devices iDS plate reader (filter set lex: 485 ± 20 nm, lem: 535 ± 25 nm; integration time: 50 ms; settle time: 0 ms; shake 5 sec, medium, read height 3.00 mm, G-factor = 1). Data were reported at endpoint. Prism 10 (GraphPad) was used to generate plots using the [agonist] vs. response (variable slope, four parameters) fitting model to determine K₀ values. The obtained K₀ value was corrected using the Cheng-Prusoff equation.
+Kd = IC₅₀/(1 + [S]/Km)
+Kd = 6.9 / (1 + 50 nM / 30 nM) = 2.5 μM
+TR-FRET PROTEIN TITRATIONS
+For assay optimization, 2D titrations of biotin-labeled ERα peptide, HIS-tag FL 14-3-3σ and streptavidin-D2 were performed in assay buffer (10mM HEPES pH 7.5, 150mM NaCl, 0.05% tween 20, 0.05% BGG (bovine gamma globulin)). The donor (MAb anti-6HIS Tb cryptate gold) concentration was kept constant at 0.166 nM. For TR-FRET protein titrations, biotin-labeled ERα peptide (50 nM), the compounds or DMSO (100 μM), MAb anti-6HIS Tb cryptate gold (0.166 nM) and streptavidin-D2 (6.25 nM) were mixed in assay buffer (10mM HEPES pH 7.5, 150mM NaCl, 0.05% tween 20, 0.05% BGG (bovine gamma globulin)). 2-fold serial dilutions of HIS-tag FL 14-3-3σ were performed (200 nM top assay concentration, 12-point dilution series). The assay was performed in 384-well microplates (Corning 4513, low volume white) at a volume of 10 μl per well. The following procedure was used: The compounds (50 mM stocks in DMSO) were transferred in echo LDV masterplates. 20 nL were transferred from the masterplate to the assay plate to achieve 100 μM compound concentration in the assay using Echo acoustic dispensing. The biotin-labeled ERα peptide was dissolved in assay buffer (10mM HEPES pH 7.5, 150mM NaCl, 0.05% tween 20, 0.05% BGG (bovine gamma globulin)) and dispensed in the assay plate using Dragonfly. 14-3-3 dilution series were prepared using Echo acoustic dispensing. Assay plates were incubated for 1hr at room temperature before the addition of a mastermix containing the donor (MAb anti-6HIS Tb cryptate gold) and acceptor (streptavidin-D2) in assay buffer. The mastermix was dispensed with Dragonfly. Assay plates were incubated for 2hr at room temperature prior to TR-FRET measurements using the Envision HTS Dual Detector 2105 plate reader equipped with the TR-FRET filter set (320/615/665 nm) and a D407/D630 advanced dual mirror. A 50 μs delay was employed to reduce background fluorescence. The TR-FRET signal was obtained through calculating the ratio of 665 nm to 615 nm fluorescence (x 1000), and Prism 10 (GraphPad) was used to generate plots using the [agonist] vs. response (variable slope, four parameters) fitting model. At least two independent experiments were performed.
+
+SPR
+The SPR experiments were performed at 25°C using a Biacore X100 and a 200 nm Strep-Tactin XT derivatized linear polycarboxylate hydrogel chip, medium charge density (XanTec Bioanalytics). All proteins and peptides were dissolved in fresh running buffer prepared with ultrapure water and filtered through a 0.2 μm filter (10 mM HEPES pH 7.4, 200 mM NaCl, 50 μM EDTA, 0.005% P20). First the surface was conditioned with a 1 min injection of 3 M Guanidine HCl. Then, the recombinant 14-3-3σ-Twinstrep protein (250 nM) was captured on flow cell 2 of the sensor chip at a flow rate of 10 μL/min for 2 minutes, which resulted in a capture level of 1000 RU. For the ternary interaction, 14-3-3σ-Twinstrep protein (250 nM) was first incubated overnight with 1 μM Ac-ERα peptide and 20 μM compound prior to immobilization to the chip. The bound ERα peptide was washed away using running buffer flowed over the chip for 15 min. Flow cell 1 was left blank as a reference surface. After immobilization of the protein, the Biacore X100 was primed with running buffer. Multi-cycle kinetic measurements were conducted at a flow rate of 30 μL/min. A 2-fold dilution series of analyte (Ac-ERα peptide) in running buffer were injected over the sensor chip for 2 min, followed by dissociation of 3 min (binary interaction), 7 or 13 minutes (ternary interaction). For the binary interaction, the highest concentration of ERα was 50 μM, and for the ternary interactions this was 250 nM. Between cycles of one multi-cycle measurement, no regeneration step was performed due to complete dissociation of the analyte. After a measurement, the chip was regenerated by 2 times 30 sec injections of 3 M Guanidine HCl. The data was corrected by double subtracting to the reference surface (flow cell 1) and buffer injection and analyzed using 1:1 interaction fitting model with the BIA evaluation software (2020).
+
+X-RAY CRYSTALLOGRAPHY DATA COLLECTION AND REFINEMENT
+The 14-3-3σΔC protein, acetylated ERα and compounds (50 mM stock in DMSO) were dissolved in complexation buffer (25 mM HEPES pH=7.5, 2 mM MgCl2 and 100 μM TCEP) and mixed in a 1:2:3 or 1:2:5 molecular stoichiometry (protein : peptide : compound) with a final protein concentration of 12 mg/mL. The complex was set-up for sitting-drop crystallization after overnight incubation at 4 °C, in a custom crystallization liquor (0.05 M HEPES (pH 7.1, 7.3, 7.5, 7.7), 0.19 M CaCl2, 24–29% PEG400, and 5% (v/v) glycerol). Crystals grew within 10-14 days at 4 °C. Crystals were fished and flash-cooled in liquid nitrogen. X-ray diffraction (XRD) data were collected at the European Synchrotron Radiation Facility (ESRF Grenoble, France, beamline ID23-1, ID30A-3/MASSIF-3, or ID23-2) or at the Deutsches Elektronen-Synchrotron (DESY Hamburg, Germany, beamline PETRA III). Data was processed using CCP4i2 suite (version 8.0.019). After indexing and integrating the data, scaling was done using AIMLESS. The data was phased with MolRep, using PDB 4JC3 as template. The presence of co-crystallized ligands was verified by visual inspection of the Fo-Fc and 2Fo-Fc electron density maps in COOT (version 0.9.8.93). If electron density corresponding to the co-crystallized ligand was present, its structure, restraints, and covalent bond were generated using AceDRG. After
+building in the ligand, model rebuilding and refinement was performed using REFMAC5. The PDB REDO server (pdb-redo.edu) was used to complete the model building and refinement. The images were created using the PyMOL Molecular Graphics System (Schrödinger LLC, version 4.6.0). See SI table S10 for data collection and refinement statistics.
+
+The structures were deposited in the protein data bank (PDB) with IDs: 916S (28), 916T (32), 916U (33), 916V (40), 916W (41), 916X (42), 916Y (1), 916Z (2), 9170 (17), 9171 (19), 9172 (10), 9173 (20), 9174 (21), and 9175 (25).
+
+NanoBRET
+NanoBRET assays were performed as previously described.43 HEK293T cells were cultured DMEM, high glucose (Gibco) supplemented with 10% charcoal stripped Fetal Bovine Serum (FBS; Gibco) and 1% penicillin/streptomycin. Cells were transfected with a 1:10 ratio of Nanoluc-ERA:14-3-3a-HaloTag plasmid for 48 hours using jetOPTIMUS transfection reagent (Polyplus). Cells were then seeded at 8,000 cells per well in a 384-well plate (Corning #3570) in FluoroBrite DMEM (phenol red-free; Gibco) with 4% charcoal stripped FBS and treated with 100 nM HaloTag NanoBRET 618 Ligand (Promega) or equivalent volume of DMSO as a no ligand negative control. Following plating, cells were treated for 24 hours with compound in 1:2 dilution series starting at 40 μM (0.35% DMSO final concentration). After 24 hours, the BRET signal was read using an EnVision XCite 2105 plate reader at 618 nm (HaloTag) and 460 nm (Nluc). The final corrected NanoBRET ratio was calculated using the following equation:
+
+\[
+Corrected\ BRET\ ratio = \left( \frac{618nm}{460nm} \right)_{HaloTag\ Ligand} - \left( \frac{618nm}{460nm} \right)_{No\ ligand\ control}
+\]
+
+The BRET ratios were normalized to samples treated with DMSO.
+
+DOCKING
+Computational design for SAR optimization and docking was performed with SeeSAR version 14.0.0; BioSolveIT GmbH, Sankt Augustin, Germany, 2022, www.biosolveit.de/SeeSAR
+
+SOFTWARE VERSIONS
+Prism (10.2.1), Illustrator (22.1 (64-bit)), Biorender (64-bit), Pymol (4.6.0), CCP4i2 (8.0.003), COOT (0.9.8.1), Phenix (1.19.2-4158)
+
+Supporting Information. Supplementary figures and tables, synthetic procedures, compound characterization, NMR spectra, crystallography data (PDF).
+
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+
+Acknowledgements. This research was funded by the Ono Pharma Foundation Breakthrough Science Initiative Award, NIH/NIGMS GM147696 and the Netherlands Organization for Scientific Research (NWO) through Gravity program 024.001.035 and ENW M-grant OCENW.M20.200. We acknowledge Foundation for Research and Innovation (H.F.R.I.) under the “2nd Call for H.F.R.I. Research Projects to support Post-Doctoral Researchers” (Project Number: 0911) and Empeirikon Idryma (to C.G.N.). We thank Amanda Paulson for the automated mass spec data processing infrastructure in the SMDC. We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron radiation facilities, and we would like to thank David Flot and Max Nanao for assistance and support in using beamlines ID23-1, ID23-2, ID30A-3 (mx2407 and mx2526). We thank DESY (Hamburg, Germany), a member of the Helmholtz Association HGF, for the provision of experimental facilities. Parts of this research were carried out at PETRA III.
+
+Author contributions.
+M.K. conceived the work, designed the compounds, performed the MS and TR-FRET experiments, and analyzed the data with contributions from C.O, L.C., C.G.N. and M.R.A. M.Z and M.F synthesized and characterized compounds. M.A.M.P solved most of the crystal structures and performed the SPR experiments. J.M.V. performed the NanoBRET assay. J.L.R. was involved in the development and optimization of the TR-FRET assay. E.M.J. solved the initial crystal structures. M.K., C.G.N., M.R.A, C.O. and L.B. supervised the project. M.K. wrote the manuscript with contributions from all authors.
+
+Conflict of interest. Michelle R. Arkin, Christian Ottmann and Luc Brunsveld are co-founders of Ambagon Therapeutics.
+
+Keywords: covalent • estrogen receptor • MCR • molecular glue • 14-3-3
+
+TOC
+
+![Scaffold hopping approach suitable for the identification of molecular glues stabilizing the 14-3-3σ/ERα complex. The multi-component reaction-based scaffold was rapidly optimized, and validated in biophysical assays, while several co-crystal structures elucidated the binding modes. The best compounds were tested in a cellular NanoBRET assay, showing low micromolar potency.](page_184_1042_1207_312.png)
+
+We describe a scaffold-hopping approach suitable for the identification of molecular glues stabilizing the 14-3-3σ/ERα complex. The multi-component reaction-based scaffold was rapidly optimized, and validated in biophysical assays, while several co-crystal structures elucidated the binding modes. The best compounds were tested in a cellular NanoBRET assay, showing low micromolar potency.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• 20250210MCRSupplement.pdf

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+Phosphorylation-driven epichaperome assembly is a regulator of cellular adaptability and proliferation
+
+Corresponding Author: Professor Gabriela Chiosis
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+In their study, McNutt et al. investigate the assembly of the epichaperome in both embryonic stem cells (ESCs) and cancer cells, focusing on the role of post-translational modifications (PTMs) of Hsp90 in the linker domain. They find that ESCs and cancer cells surprisingly share a similar epichaperome composition, especially in core components like Hsp70 and DNJC proteins. Through Mass spectrometry, they identify phosphorylation sites Ser231 and Ser263, that are phosphorylated in the closed conformation of Hsp90, which they induce by the PU-H71 inhibitor to isolate Hsp90 from ESCs.
+
+Their molecular dynamics simulations then convincingly show that phosphorylation at these sites in the charged linker induces a conformational shift, which exposes the middle domain of Hsp90 and facilitates formation of a core epichaperome, that includes HSP70 proteins and the co-chaperone HOP. By comparing biochemistry and phosphorylation-mimetic Hsp90 mutants to non-phosphorylatable mutants, they reinforce the importance of these phosphorylation sites. Furthermore, they demonstrate that the regulation of epichaperome in ESCs and cancer cells depends on phosphorylation of Hsp90 Serine 226.
+
+Finally, their data from pancreatic and breast cancer tissues underscore that Hsp90 epichaperome complexes are primarily phosphorylated at this site, further highlighting its significance in cellular disease states. Overall, this study significantly advances our understanding of the epichaperome, with Hsp90 phosphorylation on S226 playing a crucial role in this process. I have two comments to increase clarity of study. 1) The authors might want to elaborate more in the discussion on the significance of similar epichaperome complexes in ESCs, which could indicate a role of the epichaperome during development. 2) To further emphasize the crucial role of PTMs in the formation of epichaperome they might want to consider usage of the term "Hsp90 chaperone code ".
+
+Reviewer #2
+
+(Remarks to the Author)
+McNutt et al. use a combined experimental and computational study to investigate epichaperome networks and the role of Hsp90 in epichaperome formation. The authors show that epichaperomes from different cell lines share similar composition, containing chaperones like Hsp90, Hsp70, and cochaperones that form high molecular weight complexes. Using cross-linking combined with mass spectrometry, the authors assign conformations to Hsp90 within epichaperones. Importantly, the authors show that the phosphorylation of sites within the unstructured charged linker of Hsp90 enhance the incorporation of Hsp90 into epichaperomes and result in increased presence of co-chaperones in epichaperomes. Computational modeling suggests that phosphorylation at S226 and S255 of Hsp90 induces a conformational change of the charged linker, flipping it into the “up” position and exposing the Hsp90 middle domain interface. The authors also show functional consequences of Hsp90 phosphorylation and how it enhances proliferation by altering the levels of signaling proteins involved in proliferation, like mTOR and AKT. Lastly, they analyzed tumors from human patients and showed that tissues positive for epichaperomes showed Hsp90 phosphorylation at the S226 site. This comprehensive study helps in understanding the physiological consequences of Hsp90’s post-translational modifications and offers insight into the role of Hsp90 in facilitating the formation of epichaperomes. The study is of high technical quality and these findings will help researchers in targeting specific pathological conformations of Hsp90. However, some issues need to be addressed.
+1. The authors identify 26 of the 42 major chaperones and co-chaperones that are known to localize to epichaperomes from studies with cancer cells. Were any new interacting proteins able to be identified in embryonic stem cells?
+2. In the cross-linking mass spec experiments, it seems plausible that one might obtain both inter- and intra-Hsp90 crosslinks. How are these accounted for in the experiments/data and models shown in Figure 2?
+3. The discussion of treating with PU-H71 on Page 4 of the manuscript suggests that this compound promotes disassembly of epichaperomes, while the experiments use PU-H71 to probe for the Hsp90 in epichaperomes and assign conformations in Figure 2. It is not apparent whether the assigned conformations of Hsp90 are those in the epichaperomes or the conformations that promote disassembly of epichaperomes.
+4. The authors state that epichaperome assemblies are not active remodeling complexes but instead are inactive scaffolding complexes. Their cross-linking data assigns a conformation of Hsp90 in epichaperomes similar to that of the Hsp90 loading complex. Given this and the large molecular weight of epichaperomes, the authors speculate that the complex may resemble Hsp90 client loading complexes. However, it is important to distinguish the features that would cause the switch from productive folding to scaffolding complexes. Does phosphorylation of the two linker residues result in inhibition of client folding? Alternatively, could the cross-linking strategy be used in the complexes to identify whether the Hsp70 and HOP interactions are preserved in scaffolding vs client-loading complexes or whether epichaperome complexes have a similar stoichiometry but different arrangement?
+5. In modeling the epichaperome assembly, the authors used the existing structure of an Hsp90(2)-Hsp70(2)-Hop multimeric assembly. The effects on protomer A linker are discussed in detail. How does the linker on protomer B behave? Given the asymmetry of Hsp70s in this complex (one nearly FL and the second with an NBD portion), I’m curious whether that has any effect on the dynamics of the system.
+6. The findings from immunopurification showing a reduction in Hsc70 and HOP with the Hsp90 phosphomimetic seem to contradict the findings from the computational study suggesting stabilization of larger complexes with the phosphomimetic. One possibility is that Hsp90’s conformational change could alter accessibility of chaperone/cochaperone binding sites on Hsp90 or that different binding sites are utilized relative to the client loading complex. The authors could examine their linker-docked Hsp90 structure and compare to other known binary Hsp90-chaperone complexes (Hsp82-Aha1, Hsp90-HOP, Hsp90-Hsp70) to determine whether the interacting region on Hsp90 may be obstructed by the presence of the linker. Conversely, it is challenging to draw strong conclusions regarding stability from correlations alone. Perhaps the amplitude of the fluctuations in the simulations can provide more insight, as the correlation is only one part of the bigger picture regarding dynamics. The authors should consider calculating the b-factors or RMSF, perturbations, or PCA, with the representative error, to provide more quantitative information (see General et al. Plos 2014, Meireles et. Al Prot Sci 2011).
+
+Minor Points
+• Fig 1c (right) lane 1 is not labeled – I assume this is B phycoerythrin treatment.
+• HSP7C is identified as Hsc70, ST1P as HOP, and AHSA1 as Aha1 in Figure 1. It might be worth noting it in the text since this notation also appears in subsequent figures.
+• Arrows pointing to the location of the phosphorylated residues in Figure 4B (residue index axis) would be helpful.
+• The number of simulations for each system is missing in the methods. Perhaps the authors could include a table to depict the number of replicas, simulation time, and ligands bound to each Hsp90β WT and mutant for clarity.
+• In the legend of Fig 5. Hsp90beta should be Hsp90β
+• Fig S6B is confusing with the residue index from 1-100, the sequence and gradient from green to red, and the highlight of S226A. Perhaps more explanations in the legend would improve the clarity.
+• A description of the modeling studies should also be included in the last paragraph of the intro describing this study.
+
+Reviewer #3
+
+(Remarks to the Author)
+The manuscript by Seth McNutt and the colleagues described a in-depth analysis of epichaperome assembly in various cancer and embryonic stem cell lines and tissues. The authors took advantage of specific chemical inhibitor that only recognizes either complexed HSP90 or unbound HSP90 and derivatized the chemical inhibitor with biotin affinity tag. Using these derivatized chemicals, the authors employed a chemical proteomics strategy by precipitating proteins that specifically bound to the chemicals for identification and PTM analysis. From this analysis, the authors identified specific components of the epichaperome complex and key phosphorylation sites on HSP90. By applying S/T to E or S/T to A mutations on the critical phosphosites that mimicked constant phosphorylation or no phosphorylation, the authors determined the functional of phosphorylation on mediating protein complex formation and the interaction to other proteins.
+The overall study leveraged label-free quantitative protein analysis with functional validation strategies such as interactome assay and molecular dynamic simulation. The study presented a detailed view of the epichaperome assembly in solution and elucidated its potential interaction mechanism. A few major and minor concerns are listed below:
+Major concerns:
+1. Site-directed mutagenesis is an effective strategy to assess the functional role of phosphorylation but it can only represent either complete or none phosphorylation states, which may not fully represent physiological situations. Are the upstream enzymes of the phosphorylation events on HSP90 known? If so, it would be straightforward to analyze the phosphorylation-dependent change in protein interaction using either kinase overexpression or in vitro enzymatic reactions. Alternatively, phosphatase treatment is an efficient in vitro method. It would be interesting to see if removing phosphorylation by phosphatase after the complex has been pulled down can confirm the changes in the protein interaction compared to untreated control as we learned from the interactome analysis of the mutants.
+2. Crosslinking is widely used to capture the transient protein-protein interaction in solution. In this study, crosslinking has been applied to the cell lysate prior to the pull-down with chemical inhibitor-attached resin. A potential concern is whether the crosslinking may affect key residues and binding of the complex to the chemical inhibitor, which will generate biased
+results. An alternative strategy would be to pull down the complex first and then apply the crosslinking treatment on beads.
+Minor concerns:
+1. Fig 1d, a heat map was used to represent the numbers of peptides identified for each protein. But this representation does not take into account the size of protein. As larger proteins are likely to contribute more peptides, such representation is naturally biased against smaller proteins. Therefore, it would be better to use some sort of normalization method that considers the protein size information.
+2. Fig 5a, the crosslinking matrix uses blue color to represent positive correlation and red color to represent negative correlation. As red color is more prominent, it may be best to use red color to represent positive correlation and blue color to represent negative correlation. In addition, what do the red and blue colors of the double arrows refer to in the cartoon? Fig. 5b, why two different forms were depicted in either left or right complex formation? Is HSP90b AA showed similar movement as HSP90b WT?
+It’s a bit hard to interpret the correlation data in Fig 5 and how to determine phosphomimic mutants had more positive correlation than WT and none-phospho mutants.
+3. Fig. 6c, since three replicate analyses were performed, it would be best to represent the SILAC interactome analysis of different mutant forms with volcano plots and highlight statistically significant changes.
+4. Fig. 9b, when presenting the blots for the site-specific phosphorylation events, typically it would be necessary to show the blots for the corresponding proteins such as mTOR, S6, AKT etc, to indicate that the changes in phosphorylation was not due to the changes in overall protein abundance.
+
+Reviewer #4
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+In this revised version of the manuscript, the authors have addressed all comments of all reviewers. This has significantly improved the study and I have no further concerns.
+
+Reviewer #2
+
+(Remarks to the Author)
+McNutt et al. have done an excellent job in addressing the reviewers’ concerns in a point by point manner. The authors have put a significant amount of effort into revising their manuscript and carrying out additional experiments, including luciferase reactivation assays with the phosphomimetic mutants and CK2 phosphorylation assays. Additionally, the authors have performed further analysis of their simulations and added clarifying text throughout their manuscript. Together, these changes have further strengthened their findings. Overall, this is a very high impact research article that convincingly shows the structural details regarding epichaperome complexes and how PTMs of Hsp90 facilitate epichaperome formation. This study is of high technical quality and of broad interest to the Hsp90 and chaperone community.
+
+Reviewer #3
+
+(Remarks to the Author)
+This is an excellent work. The authors have addressed the concerns raised by this reviewer. The manuscript is recommended for publication.
+
+Reviewer #4
+
+(Remarks to the Author)
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS AND POINT-BY-POINT RESPONSE
+
+We sincerely thank the referees for their insightful suggestions and detailed review of the manuscript. We appreciate that all four reviewers have recognized the significance and technical quality of our work, highlighting its substantial contribution to advancing our understanding of the epichaperome and the pivotal role of HSP90 phosphorylation in this process. “Overall, this study significantly advances our understanding of the epichaperome, with Hsp90 phosphorylation on S226 playing a crucial role in this process.” “This comprehensive study helps in understanding the physiological consequences of Hsp90’s post-translational modifications and offers insight into the role of Hsp90 in facilitating the formation of epichaperomes. The study is of high technical quality and these findings will help researchers in targeting specific pathological conformations of Hsp90.” “The overall study leveraged label-free quantitative protein analysis with functional validation strategies such as interactome assay and molecular dynamic simulation. The study presented a detailed view of the epichaperome assembly in solution and elucidated its potential interaction mechanism.”
+
+In response to the reviewers' critiques and comments, we have carefully addressed each point in the below point-by-point responses and have made the necessary revisions to the manuscript, which are highlighted in blue font.
+
+Reviewer #1 (Remarks to the Author):
+
+In their study, McNutt et al. investigate the assembly of the epichaperome in both embryonic stem cells (ESCs) and cancer cells, focusing on the role of post-translational modifications (PTMs) of Hsp90 in the linker domain. They find that ESCs and cancer cells surprisingly share a similar epichaperome composition, especially in core components like Hsp70 and DNJC proteins. Through Mass spectrometry, they identify phosphorylation sites Ser231 and Ser263, that are phosphorylated in the closed conformation of Hsp90, which they induce by the PU-H71 inhibitor to isolate Hsp90 from ESCs.
+
+Their molecular dynamics simulations then convincingly show that phosphorylation at these sites in the charged linker induces a conformational shift, which exposes the middle domain of Hsp90 and facilitates formation of a core epichaperome, that includes HSP70 proteins and the co-chaperone HOP. By comparing biochemistry and phosphorylation-mimetic Hsp90 mutants to non-phosphorylatable mutants, they reinforce the importance of these phosphorylation sites. Furthermore, they demonstrate that the regulation of epichaperome in ESCs and cancer cells depends on phosphorylation of Hsp90 Serine 226.
+
+Finally, their data from pancreatic and breast cancer tissues underscore that Hsp90 epichaperome complexes are primarily phosphorylated at this site, further highlighting its significance in cellular disease states. Overall, this study significantly advances our understanding of the epichaperome, with Hsp90 phosphorylation on S226 playing a crucial role in this process.
+
+Response: Thank you for finding our paper of interest and for your detailed analysis. We appreciate your acknowledgment of the strengths and significance of our study.
+
+I have two comments to increase clarity of study. 1) The authors might want to elaborate more in the discussion on the significance of similar epichaperome complexes in ESCs, which could indicate a role of the epichaperome during development. 2) To further emphasize the crucial role of PTMs in the formation of epichaperome they might want to consider usage of the term "Hsp90 chaperone code ".
+
+Response1.1-1.2: Thank you for suggesting these salient points.
+
+1. We addressed this comment by adding to the Discussion the following text: “The shared composition of epichaperome complexes between ESCs and cancer cells suggests a possible commonality in their functional roles. In both contexts, the epichaperome may facilitate rapid cellular proliferation and adaptability to environmental stress, characteristics crucial during development and tumorigenesis. This raises intriguing questions about whether the epichaperome contributes to the aberrant growth and survival of cancer cells by reactivating developmental pathways. The epichaperome might allow cancer cells to hijack developmental pathways typically active in ESCs, enabling them to maintain high proliferation rates and resist cell death.”
+
+2. We appreciate your suggestion to use the term "Hsp90 chaperone code" to highlight the role of PTMs in epichaperome formation. We have incorporated this term in the manuscript - along with relevant references -
+(see page 17) to emphasize the regulatory role of PTMs in the structural and functional regulation of HSP90, including in the formation and function of the epichaperome.
+
+Reviewer #2 (Remarks to the Author):
+
+McNutt et al. use a combined experimental and computational study to investigate epichaperome networks and the role of Hsp90 in epichaperome formation. The authors show that epichaperomes from different cell lines share similar composition, containing chaperones like Hsp90, Hsp70, and cochaperones that form high molecular weight complexes. Using cross-linking combined with mass spectrometry, the authors assign conformations to Hsp90 within epichaperones. Importantly, the authors show that the phosphorylation of sites within the unstructured charged linker of Hsp90 enhance the incorporation of Hsp90 into epichaperomes and result in increased presence of co-chaperones in epichaperomes. Computational modeling suggests that phosphorylation at S226 and S255 of Hsp90 induces a conformational change of the charged linker, flipping it into the “up” position and exposing the Hsp90 middle domain interface. The authors also show functional consequences of Hsp90 phosphorylation and how it enhances proliferation by altering the levels of signaling proteins involved in proliferation, like mTOR and AKT. Lastly, they analyzed tumors from human patients and showed that tissues positive for epichaperomes showed Hsp90 phosphorylation at the S226 site. This comprehensive study helps in understanding the physiological consequences of Hsp90’s post-translational modifications and offers insight into the role of Hsp90 in facilitating the formation of epichaperomes. The study is of high technical quality and these findings will help researchers in targeting specific pathological conformations of Hsp90.
+
+Response: Thank you for finding our paper valuable and for your detailed review. We appreciate your recognition of the strengths of our study and the significance of our findings regarding the role of HSP90 in epichaperome formation. Below, we address your specific comments:
+
+However, some issues need to be addressed.
+
+1. The authors identify 26 of the 42 major chaperones and co-chaperones that are known to localize to epichaperomes from studies with cancer cells. Were any new interacting proteins able to be identified in embryonic stem cells?
+
+Response2.1: Reviewer #2 is making a salient point. While the primary purpose of this manuscript is to identify key drivers in the assembly of the core epichaperome components, the identity of all components identified in ESCs is found in Supplementary Data 1. We added a paragraph to the text to clarify this point (see page 5). Other components are indeed context-dependent, but characterizing these context-dependent components and how they contribute to the specific functions of epichaperomes in ESCs is the subject of a paper in itself.
+
+2. In the cross-linking mass spec experiments, it seems plausible that one might obtain both inter- and intra-Hsp90 crosslinks. How are these accounted for in the experiments/data and models shown in Figure 2?
+
+Response2.2: Thank you for raising this point. Our experimental design was tailored to differentiate between intra- and inter-monomeric crosslinks in the cross-linking mass spectrometry experiments. After crosslinking the lysate and capturing HSP90 complexes with PU-beads, we performed SDS-PAGE to separate the proteins. We focused on the major ~80-90 kDa band, which corresponds to the HSP90 monomer. In addition, the crosslinked peptides identified were predominantly intra-monomeric, as they fit within the expected spatial constraints of the DSS cross-linker. The analysis of cross-linked lysine residues showed distances that are consistent with intra-monomeric links, supporting our conclusion that these are indeed within a single HSP90 monomer. We have added a clarifying sentence to the manuscript (see page 6) and Figure 2a schematic to explain our methodology and rationale, emphasizing how SDS-PAGE and the inherent constraints of DSS support the notion that our data primarily reflect intra-monomeric crosslinking.
+
+3. The discussion of treating with PU-H71 on Page 4 of the manuscript suggests that this compound promotes disassembly of epichaperomes, while the experiments use PU-H71 to probe for the Hsp90 in epichaperomes and assign conformations in Figure 2. It is not apparent whether the assigned conformations of Hsp90 are those in the epichaperomes or the conformations that promote disassembly of epichaperomes.
+
+Response2.3: Thank you for requesting further clarification on this point. In the experiments shown in Figure 2, and to ensure the capture of the epichaperome-enabling conformation, we first cross-linked cellular lysates using DSS before capturing HSP90 on the PU-beads. Given that PU has a preference for HSP90 in epichaperomes, as noted here and in prior publications, this approach ensures that the conformation ‘frozen’ by DSS and captured
+by PU-beads is more characteristic of epichaperomes, rather than a conformation induced by PU to promote disassembly. We have added the following text to page 6 to clarify this point: “DSS crosslinking stabilizes the conformation of proteins by covalently linking residues that are in close proximity, effectively 'freezing' their relative positions within the protein complex. Given PU-H71’s preference for binding HSP90 in its epichaperome conformation, any significant alteration of HSP90’s structure by DSS would likely reduce PU-H71’s binding affinity. Therefore, the structure captured by PU-beads is more likely to reflect the native HSP90 conformation found in epichaperomes rather than any altered state. By applying DSS before introducing PU-H71, the experimental setup increases the likelihood that the observed conformation is representative of the functional epichaperome, prior to any potential disassembly”.
+
+4. The authors state that epichaperome assemblies are not active remodeling complexes but instead are inactive scaffolding complexes. Their cross-linking data assigns a conformation of Hsp90 in epichaperomes similar to that of the Hsp90 loading complex. Given this and the large molecular weight of epichaperomes, the authors speculate that the complex may resemble Hsp90 client loading complexes. However, it is important to distinguish the features that would cause the switch from productive folding to scaffolding complexes. Does phosphorylation of the two linker residues result in inhibition of client folding? Alternatively, could the cross-linking strategy be used in the complexes to identify whether the Hsp70 and HOP interactions are preserved in scaffolding vs client-loading complexes or whether epichaperome complexes have a similar stoichiometry but different arrangement?
+
+Response2.4: Thank you for your insightful comment. We respectfully disagree with the statement that epichaperomes are inactive. While epichaperomes do not participate in the active folding of client proteins, they are highly active in other roles, as shown here and in our prior publications. The primary function of epichaperomes is to stabilize and organize proteins and protein complexes as scaffolding platforms, thereby promoting the rewiring of protein-protein interaction (PPI) networks. This scaffolding activity is crucial for various cellular processes, including signal transduction, stress response, and adaptation to changing environmental conditions. To address the reviewer's point about phosphorylation, we have conducted luciferase refolding assays, which demonstrate that the phosphomimetic mutants indeed impair folding activity. These findings support our conclusion that epichaperomes have a scaffolding rather than a folding role. The data are now included in Supplementary Figure 13 and associated text.
+
+Regarding the distinction between scaffolding and client-loading complexes, our cross-linking data assigns a conformation of HSP90 in epichaperomes similar to that of the HSP90 loading complex. This suggests that while the architecture may resemble client-loading complexes, the phosphorylation of the two linker residues mediates a functional switch from productive folding to scaffolding, inhibiting client folding and facilitating the formation of scaffolding platforms. Both MS evidence and computational models support the conclusion that phosphorylation of the charged linker is a crucial contributor to epichaperome assembly, emphasizing its role in shaping not only HSP90 but also the stability and dynamics of the epichaperome structure. These findings highlight how phosphorylation modulates the structural dynamics and functional roles of HSP90 within the epichaperome assembly, promoting a scaffolding function through enhanced stability and reduced flexibility of the assembly at critical interaction sites. The text was revised on pages 10-12 and in Discussion to better highlight these findings.
+
+The exact architecture and stoichiometry of epichaperome components in these platforms are the subject of our current studies and require sophisticated chemical biology, super-resolution microscopy, and structural biology techniques, which are beyond the scope of this paper. These ongoing investigations will provide a more detailed understanding of whether epichaperome complexes have similar stoichiometry but different arrangements compared to client-loading complexes.
+
+5. In modeling the epichaperome assembly, the authors used the existing structure of an Hsp90(2)-Hsp70(2)-Hop multimeric assembly. The effects on protomer A linker are discussed in detail. How does the linker on protomer B behave? Given the asymmetry of Hsp70s in this complex (one nearly FL and the second with an NBD portion), I’m curious whether that has any effect on the dynamics of the system.
+
+Response2.5: In our model, HSP90 protomer B is bound to HSP70(B) and HOP partners, and this binding configuration significantly influences the behavior of the linker on protomer B. The presence of HSP70B and HOP in the complex results in stabilizing intermolecular hydrogen-bond interactions between the charged linker
+of HSP90 protomer B and HOP and HSP70B. These interactions lock the linker in a particular conformation, limiting its potential for secondary structural element formation and conformational rearrangement compared to protomer A. Supplementary Fig. 7, and associated text, were added in support. This asymmetry and stabilization through intermolecular interactions lead to distinct dynamic behaviors for the charged linkers of protomers A and B. While protomer A's linker remains more flexible and capable of rearranging into different conformations—modulated by its phosphorylation status—protomer B's linker is constrained by its interaction with HSP70 and HOP. Despite these distinct local impacts of phosphorylation on the structure and conformation of individual linkers, both linkers contribute to modulating the overall stability and dynamics of the pentameric assembly. This dynamic interplay highlights the complex regulatory mechanisms at play within the epichaperome, illustrating how each protomer's interaction with its partners can influence the system's overall behavior and stability.
+
+6. The findings from immunopurification showing a reduction in Hsc70 and HOP with the Hsp90 phosphomimetic seem to contradict the findings from the computational study suggesting stabilization of larger complexes with the phosphomimetic. One possibility is that Hsp90’s conformational change could alter accessibility of chaperone/cochaperone binding sites on Hsp90 or that different binding sites are utilized relative to the client loading complex. The authors could examine their linker-docked Hsp90 structure and compare to other known binary Hsp90-chaperone complexes (Hsp82-Aha1, Hsp90-HOP, Hsp90-Hsp70) to determine whether the interacting region on Hsp90 may be obstructed by the presence of the linker. Conversely, it is challenging to draw strong conclusions regarding stability from correlations alone. Perhaps the amplitude of the fluctuations in the simulations can provide more insight, as the correlation is only one part of the bigger picture regarding dynamics. The authors should consider calculating the b-factors or RMSF, perturbations, or PCA, with the representative error, to provide more quantitative information (see General et al. Plos 2014, Meireles et. Al Prot Sci 2011).
+
+Response2.6: Thank you for your insightful comment. We respectfully disagree that the immunopurification showing a reduction in HSC70 and HOP with the HSP90 phosphomimetic contradicts the findings from the computational study suggesting stabilization of larger complexes with the phosphomimetic. This apparent contradiction only arises if we assume that epichaperomes are the sole form and assembly of HSP90 in the cells, which is not the case. While the phosphomimetic mutant (EE) increases the formation of epichaperomes, the non-phosphorylatable mutant (AA), which as we show in Figure 6c-e can incorporate into the endogenous non-tagged HSP90 assemblies, is potentially altering the cellular composition of folding chaperone assemblies. This alteration could lead to a higher prevalence of assemblies involving HSC70 and HOP distinct from epichaperomes. Since the immunopurification experiment reports on a ratio of EE to AA, as captured by the antibody, the AA component, which may contain the non-epichaperome HSP90-HSC70 or HSP90-HOP assemblies, will skew the ratio to make it appear that there is less HSC70 and HOP in the EE component (i.e., in the epichaperomes). In fact, this is not true, as the apparent reduction is due to the presence of other HSP90 assemblies that incorporate these chaperones. Therefore, the observed reduction in HSC70 and HOP in the phosphomimetic’s immunopurification does not necessarily contradict the computational findings, but rather highlights the complexity of HSP90’s interactions within the cell, where multiple forms and assemblies coexist, each with distinct roles and interactions. Text was added to provide further clarity on this matter (see page 12).
+
+Regarding the second point, we agree, and we thank the reviewer for suggesting we perform these studies. Both the RMSF and PCA analyses strongly support the notion that the EE phosphomimetic mutant enhances epichaperome formation by stabilizing the assembly. The RMSF analysis shows reduced flexibility in key regions related to HSP70A and HSP70B binding, indicating a more rigid and stable structure that supports the maintenance of the epichaperome. Similarly, the PCA results demonstrate that the EE mutant has narrower spans along the principal components, reflecting reduced conformational variability and a more cohesive assembly. These findings align with our conclusion that phosphorylation at Ser226 and Ser255 promotes a structural environment conducive to epichaperome stabilization, thus highlighting the critical role of these post-translational modifications in enhancing epichaperome formation and function. These findings are included in Figure 5c,d, Supplementary Fig. 8 and pages 10-11.
+
+Minor Points
+
+• Fig 1c (right) lane 1 is not labeled – I assume this is B phycoerythrin treatment.
+
+Response2.7: Label was added for clarity.
+• HSP7C is identified as Hsc70, STI1P as HOP, and AHSA1 as Aha1 in Figure 1. It might be worth noting it in the text since this notation also appears in subsequent figures.
+
+Response2.8: Clarification provided in the figure legend of Figure 1.
+
+• Arrows pointing to the location of the phosphorylated residues in Figure 4B (residue index axis) would be helpful.
+
+Response2.9: Arrows and additional labeling was added to Figure 4B.
+
+• The number of simulations for each system is missing in the methods. Perhaps the authors could include a table to depict the number of replicas, simulation time, and ligands bound to each Hsp90β WT and mutant for clarity.
+
+Response2.10: For each system, we performed three independent 100-nanosecond (ns) simulations, each with 1000 frames, to ensure the reliability of our results. This strategy was employed to account for variability and enhance the statistical significance of our findings. By running these simulations three times, we aimed to minimize errors and confirm that our observations were consistent across different runs. Each 100 ns simulation was designed to provide a comprehensive view of the dynamics of the multimeric complexes. The decision to conduct multiple runs with adequate computational power allowed us to achieve robust and reliable results, which we found to be consistent across the three replicas. We acknowledge the reviewer's suggestion to include more details about our simulation strategy in the methods section. We added a table that specifies the number of replicas, simulation time, and ligands bound to each WT and mutant HSP90 containing assemblies. This additional information enhances clarity and transparency regarding our methodological approach.
+
+• In the legend of Fig 5. Hsp90beta should be Hsp90β
+
+Response2.11: Edited as suggested.
+
+• Fig S6B is confusing with the residue index from 1-100, the sequence and gradient from green to red, and the highlight of S226A. Perhaps more explanations in the legend would improve the clarity.
+
+Response2.12: We agree with the reviewer's observation about Fig S6B. To improve clarity, we have reformatted the figure to conform with the format used in the main Figure 4. We hope these changes eliminate any confusion and enhance the interpretability of the figure.
+
+• A description of the modeling studies should also be included in the last paragraph of the intro describing this study.
+
+Response2.13: We added a paragraph to the Introduction, as suggested.
+
+Reviewer #3 (Remarks to the Author):
+
+The manuscript by Seth McNutt and the colleagues described a in-depth analysis of epichaperome assembly in various cancer and embryonic stem cell lines and tissues. The authors took advantage of specific chemical inhibitor that only recognizes either complexed HSP90 or unbound HSP90 and derivatized the chemical inhibitor with biotin affinity tag. Using these derivatized chemicals, the authors employed a chemical proteomics strategy by precipitating proteins that specifically bound to the chemicals for identification and PTM analysis. From this analysis, the authors identified specific components of the epichaperome complex and key phosphorylation sites on HSP90. By applying S/T to E or S/T to A mutations on the critical phosphosites that mimicked constant phosphorylation or no phosphorylation, the authors determined the functional of phosphorylation on mediating protein complex formation and the interaction to other proteins. The overall study leveraged label-free quantitative protein analysis with functional validation strategies such as interactome assay and molecular dynamic simulation. The study presented a detailed view of the epichaperome assembly in solution and elucidated its potential interaction mechanism.
+
+Response: Thank you for your thoughtful evaluation of our work. Your feedback reinforces the significance of our findings in understanding the role of epichaperomes in cancer and embryonic stem cell biology, and the potential for developing targeted therapeutic strategies.
+
+A few major and minor concerns are listed below:
+Major concerns:
+
+1. Site-directed mutagenesis is an effective strategy to assess the functional role of phosphorylation but it can only represent either complete or none phosphorylation states, which may not fully represent physiological situations. Are the upstream enzymes of the phosphorylation events on HSP90 known? If so, it would be straightforward to analyze the phosphorylation-dependent change in protein interaction using either kinase overexpression or in vitro enzymatic reactions. Alternatively, phosphatase treatment is an efficient in vitro method. It would be interesting to see if removing phosphorylation by phosphatase after the complex has been pulled down can confirm the changes in the protein interaction compared to untreated control as we learned from the interactome analysis of the mutants.
+
+Response3.1: Thank you for your insightful comment. We agree that site-directed mutagenesis provides only partial insights into phosphorylation states. To address this comment, we investigated casein kinase II (CK2) as a potential upstream kinase for HSP90, particularly at Ser226, which fits well within CK2’s phosphorylation consensus sequence. We conducted experiments using CK2 inhibitors, siRNA knockdown, overexpression, and a kinase-dead mutant to confirm the functional role of phosphorylation. These studies highlight CK2 as a physiological kinase that may phosphorylate HSP90, thereby inducing epichaperome formation. These data are incorporated into the new Figure 9a-e and associated text (pages 15,16).
+
+2. Crosslinking is widely used to capture the transient protein-protein interaction in solution. In this study, crosslinking has been applied to the cell lysate prior to the pull-down with chemical inhibitor-attached resin. A potential concern is whether the crosslinking may affect key residues and binding of the complex to the chemical inhibitor, which will generate biased results. An alternative strategy would be to pull down the complex first and then apply the crosslinking treatment on beads.
+
+Response3.2: Thank you for raising this important point regarding the use of crosslinking in our study. We acknowledge the potential concern that crosslinking could affect key residues and the binding of the complex to the chemical inhibitor-attached resin, potentially generating biased results. However, the DSS cross-linker primarily targets solvent-accessible surface lysine residues. This selectivity minimizes the likelihood of introducing extensive conformational changes or directly perturbing the pocket on HSP90 to which the inhibitor binds to. Applying crosslinking after the pull-down with the inhibitor-attached resin may also introduce limitations. The PU-H71 inhibitor itself can induce a conformational change in HSP90, and crosslinking at this stage might not reflect the physiological conformation of the protein complexes.
+
+Furthermore, our molecular dynamics (MD) simulations consistently support the closed-like conformation detected by our crosslinking approach. This suggests that the conformation we captured accurately represents the physiological state. The convergence of experimental and computational data strengthens our confidence that our approach provides a reliable representation of the epichaperome complex in its native-like state. By combining several complementary approaches, we have ensured that our data faithfully reflect the interactions and conformations present in vivo, thereby alleviating concerns about potential bias introduced by crosslinking. Clarification was added to page 6.
+
+Minor concerns:
+
+1. Fig 1d, a heat map was used to represent the numbers of peptides identified for each protein. But this representation does not take into account the size of protein. As larger proteins are likely to contribute more peptides, such representation is naturally biased against smaller proteins. Therefore, it would be better to use some sort of normalization method that considers the protein size information.
+
+Response3.3: Thank you for your valuable feedback regarding the heatmap in Figure 1d. We understand your concern about the potential bias against smaller proteins due to the lack of normalization for protein size. While our initial analysis indicated that this representation did not significantly affect our results, we appreciate the importance of accounting for protein size. To address this, we have included a revised heatmap, where normalization has been applied to account for protein size. We hope this provides a clearer representation of the data and addresses your concern.
+
+2. Fig 5a, the crosslinking matrix uses blue color to represent positive correlation and red color to represent negative correlation. As red color is more prominent, it may be best to use red color to represent positive correlation and blue color to represent negative correlation. In addition, what do the red and blue colors of the double arrows refer to in the cartoon?
+Response3.4: Thank you for your comment regarding the color scheme used in the crosslinking matrix in Figure 5a. While we understand the suggestion to use red for positive correlation and blue for negative correlation, the current color scheme (blue for positive correlation and red for negative correlation) is a widely accepted standard in scientific visualization, making it intuitive for most readers. Additionally, we have clarified in the figure legend that the blue arrows in the cartoon point to protein regions that move together correlative, while the red arrows indicate regions that move oppositely, reflecting negative correlation. We hope this clarification helps convey the intended interpretation of the data.
+
+Fig. 5b, why two different forms were depicted in either left or right complex formation? Is HSP90b AA showed similar movement as HSP90b WT?
+It’s a bit hard to interpret the correlation data in Fig 5 and how to determine phosphomimic mutants had more positive correlation than WT and none-phospho mutants.
+
+Response3.5: Thank you for your comment regarding Figure 5b. The cartoon in Figure 5b illustrates the assemblies that are favored—either with or without HOP—when the charged linker serines on HSP90β are phosphorylated (as in the EE mutant) or not phosphorylated (as in the WT, Ser/Ser).
+
+The AA mutant does not mimic the WT in MD simulations because the substitution of serine with alanine leads to differences in interaction capabilities and structural dynamics. The substitution of serine with alanine is a widely used strategy in biological research to create non-phosphorylatable mutants. Alanine is chosen because its small, non-polar side chain is unlikely to introduce significant steric hindrance or alter the overall protein structure, making it a reasonable approximation for studying the functional role of phosphorylation without affecting the protein's overall architecture. However, despite its utility, the AA mutant cannot completely mimic the WT's natural serine behavior because it lacks the hydroxyl group necessary for phosphorylation and the associated hydrogen bonding interactions. These differences can affect local structural dynamics, potentially leading to changes in the protein's conformation and interaction patterns. Therefore, the AA mutant provides a non-phosphorylated baseline for comparison but may not capture all nuances of WT behavior under physiological conditions. By comparing WT, EE, and AA mutants, we gain comprehensive insights into how phosphorylation modulates HSP90β dynamics and epichaperome assembly. The AA mutant is not included in the cartoon shown in Fig. 5b because it is not a physiological form. We have added clarification to the manuscript text (page 10) to explain that the AA mutant does not fully mimic the WT.
+
+The data on correlative motion among the components of the pentameric assembly is encoded in the dynamic cross-correlation matrix. While the matrix is complex, it provides valuable insights into the coordinated movements of different protein regions. To simplify and convey this information effectively, we used the cartoon to distill the various motions among the proteins and their components, making the complex correlation data more accessible and easier to grasp. We added clarification to the figure and figure legends.
+
+We hope this explanation, along with the revised figure, figure legend, and text, clarifies the rationale behind the representation in Figure 5b and aids in understanding the correlation data.
+
+3. Fig. 6c, since three replicate analyses were performed, it would be best to represent the SILAC interactome analysis of different mutant forms with volcano plots and highlight statistically significant changes.
+
+Response3.6: Added as suggested (see new Supplementary Fig. 10d).
+
+4. Fig. 9b, when presenting the blots for the site-specific phosphorylation events, typically it would be necessary to show the blots for the corresponding proteins such as mTOR, S6, AKT etc, to indicate that the changes in phosphorylation was not due to the changes in overall protein abundance.
+
+Response3.6: Thank you for your comment regarding the need to show blots for the corresponding proteins, such as mTOR, S6, and AKT, to indicate that changes in phosphorylation were not due to changes in overall protein abundance. We apologize if this was not clear in our initial submission, but these blots are included in Supplementary Figure 14a,b (was SFig. 9). We believe these supplementary figures provide the necessary information to support our findings. Thank you for bringing this to our attention.
+Reviewer #4 (Remarks to the Author):
+
+I co-reviewed this manuscript with one of the reviewers who provided the listed reports.
+
+Response: Thank you for your thorough review and for collaborating with your colleague to provide valuable insights and feedback on our manuscript. We appreciate the time and effort you invested in evaluating our work, and your comments have been instrumental in enhancing the quality and clarity of our study.

09fa1c94df81f8d0d856f1843bb02811e39dec61a630b4897174dcfd9f8b640a/preprint/preprint.md

@@ -0,0 +1,259 @@
+Efficient amine-assisted hydrogenation of CO2 into methanol collectively catalysed by ruthenium single sites and ensembles in a unified catalyst
+
+Liang Chen
+chenliang@nimte.ac.cn
+
+Ningbo Institute of Materials Technology and Engineering, CAS  https://orcid.org/0000-0002-0667-540X
+Qihao Yang
+Ningbo Institute of materials technology & engineering,CAS  https://orcid.org/0000-0002-0933-4483
+Yinming Wang
+Ningbo Institute of Materials Technology and Engineering, CAS
+Dianhui Pan
+Ningbo Institute of Materials Technology and Engineering, CAS
+Desheng Su
+Ningbo Institute of Materials Technology and Engineering, CAS
+Hao Liu
+Ningbo Institute of Materials Technology and Engineering, CAS
+Qiuju Zhang
+Ningbo Institute of Materials Technology and Engineering, CAS
+Sheng Dai
+East China University of Science and Technology  https://orcid.org/0000-0001-5787-0179
+Ziqi Tian
+Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences https://orcid.org/0000-0001-5667-597X
+Zhiyi Lu
+Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences https://orcid.org/0000-0002-2117-4101
+
+Article
+
+Keywords: amine-assisted CO2 hydrogenation, supported metal catalyst, N-formylation, amide hydrogenation
+Posted Date: May 2nd, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4185890/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 11th, 2025. See the published version at https://doi.org/10.1038/s41467-025-55837-7.
+Efficient amine-assisted hydrogenation of CO$_2$ into methanol collectively catalysed by ruthenium single sites and ensembles in a unified catalyst
+
+Qihao Yang$^{1,2,\dagger}$, Yinming Wang$^{1,2,\dagger}$, Dianhui Pan$^{1,2,\dagger}$, Desheng Su$^{1,3,\dagger}$, Hao Liu$^{1,2}$, Qiuju Zhang$^{1,2}$, Sheng Dai$^{4}$, Ziqi Tian$^{1,2,*}$, Zhiyi Lu$^{1,2,*}$, Liang Chen$^{1,2,*}$
+
+$^1$Key Laboratory of Advanced Fuel Cells and Electrolyzers Technology and Engineering, Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo, Zhejiang 315201, P. R. China
+
+$^2$University of Chinese Academy of Sciences, 100049 Beijing, P. R. China
+
+$^3$School of Materials Science and Chemical Engineering, Ningbo University, Ningbo, Zhejiang 315211, P. R. China
+
+$^4$Key Laboratory for Advanced Materials and Feringa Nobel Prize Scientist Joint Research Center, Institute of Fine Chemicals, School of Chemistry & Molecular Engineering, East China University of Science and Technology, Shanghai 200237, P. R. China
+
+KEYWORDS: amine-assisted CO$_2$ hydrogenation, supported metal catalyst, N-formylation, amide hydrogenation.
+ABSTRACT: Amine-assisted sequential hydrogenation of carbon dioxide (CO₂), without the requirement of energy-intensive activation of inert CO₂, is an efficient route to generate methanol (i.e., an essential secondary feedstock). However, this one-pot sequential hydrogenation process requires a multifunctional catalyst capable of efficiently catalysing both amine N-formylation and amide hydrogenation. Ruthenium-based catalysts possess substantial catalytic prowess in both steps of the sequential hydrogenation process, while the optimal Ru species required for the specific steps depends on distinct criteria. Herein, to optimize the two-step methanol production process, morpholine was used as a typical amine assistant, and Al₂O₃-supported ruthenium catalysts (Ru-1, Ru-2, Ru-3) with isolated Ru sites (Ru₁) or/and Ru ensembles (Ruₑ, including Ru clusters, Ruₑ, and Ru nanoparticles, Ruₚ) configurations were rationally fabricated via the judicious annealing strategy. Compared to the energy-intensive CO₂ hydrogenation process, within the sequential catalytic system, morpholine, H₂ and CO₂ underwent an initial conversion to give N-formylmorpholine (NFM), which was subsequently hydrogenated, resulting in the low-temperature formation of methanol (120 °C). Additionally, the excellent regeneration (>99%) of morpholine guarantees a sustainable progression towards subsequent cycles. Experimental analysis and density functional theory (DFT) calculations suggest that the metallic Ruₑ are superior catalytic sites for the N-formylation step, whereas the isolated Ru₁ sites exhibit higher amide hydrogenation activity. Thus, the optimal Ru-2 catalyst, which simultaneously features metallic Ruₑ and isolated Ru₁ sites, can efficiently synergize the conversion of CO₂ into methanol
+in a one-pot two-step process with exceptional selectivity (>95%), highlighting the crucial sensitivity of the process to the structure of active metal species. This work not only presents an advanced catalyst suitable for CO_2-based methanol production but also elucidates the requirements for rational design of multiple optimized active sites within the single catalyst for multistep catalytic reactions in the future.
+
+1. Introduction
+
+The anthropogenic emissions of greenhouse gases, primarily CO_2, are widely believed to be responsible for a range of adverse environmental issues^{1,2}. The facile catalytic reduction of carbon dioxide (CO_2) into value-added secondary carbon feedstocks (i.e., hydrocarbons, alcohols, and carboxylic acids) exhibits excellent potential for mitigating the excessive accumulation of CO_2^{3-6}. As one of the most attractive chemical products generated via CO_2 reduction, methanol (CH_3OH) has a variety of attractive potential applications, including serving as a basic industrial feedstock, functioning as a liquid organic hydrogen carrier (LOHC), and being utilized in direct methanol fuel cells (DMFCs)^{7-11}. Therefore, the commercial value of catalytic production of CH_3OH from CO_2 is substantial. In the past decades, remarkable researches have been conducted on the selective production of methanol via CO_2 hydrogenation^{12-18}, mainly focusing on metal oxides (e.g., In_2O_3, ZnO-ZrO_2, In_2O_3-ZrO_2)^{19-21} and metal/metal oxides (e.g., Cu/ZnO/Al_2O_3, Cu/In_2O_3, Cu/ZrO_2, Pd/ZnO)^{22-28}. However, the traditional CO_2 hydrogenation based on metal oxides is encumbered by the necessity of high catalytic temperature (> 300 °C)^{19-21}, resulting in
+excessive energy consumption. Although the introduction of metal components into metal oxides promotes the activation of H_2 and thus achieves enhanced catalytic performance at relatively lower temperature (< 250 °C)\(^{23-25}\), this modification simultaneously leads to a trade-off with the decrease in CH_3OH selectivity, owing to the excessive hydrogenation of CO_2 and the exacerbation of the reverse water gas shift (RWGS) reaction\(^{29-31}\).
+
+Compared to the traditional CO_2 hydrogenation process, the amine-assisted two-step hydrogenation of CO_2 to CH_3OH, involving N-formylation of amine with CO_2 (i.e., first step) and subsequent amide hydrogenation (i.e., second step) in the presence of homogeneous catalysts\(^{32-35}\), especially ruthenium complexes\(^{32-34}\), exhibits superior catalytic activity and selectivity at mild condition (< 180 °C), thus making it to be a promising and energy-efficient alternative for methanol production. However, the inherent difficulties in separation and recycling of homogeneous catalysts, coupled with the inferior stability, hinder their widespread application and the scaling up of this amine-assisted CO_2-to-MeOH route. Furthermore, for the sequential catalytic reaction systems, the theoretical requirement for achieving optimal overall catalytic performance involves the engagement of at least dual types of active sites\(^{36-38}\). Therefore, the existent homogeneous catalysts with a single designated activity structure may not provide the optimum catalytic activity for both steps of the sequential CO_2 hydrogenation process. In this context, the immobilization of homogeneous catalysts onto stable heterogeneous matrix (e.g., Al_2O_3, In_2O_3, ZrO_2) can be the most straightforward strategy, as it offers the benefit of easy separation.
+More importantly, the atomic-scale heterogeneity of supported metal catalysts is almost unavoidable, resulting in diverse structural morphologies or/and local coordination environments for the active components\(^{39,40}\), which offers the potential to optimize each step of the sequential CO\(_2\) hydrogenation reaction and thus fine-tune the overall catalytic performance.
+
+Based on the aforementioned considerations, we rationally synthesized a series of Al\(_2\)O\(_3\)-based heterogeneous catalysts featuring isolated Ru sites (Ru\(_1\)) or/and Ru ensembles (Ru\(_c\), including Ru clusters, Ru\(_c\), and Ru nanoparticles, Ru\(_p\)) via a traditional impregnation method coupled with annealing treatment under different atmospheres. The catalysts (i.e., Ru-1, Ru-2, Ru-3), with dominant morphological distributions of atomically dispersed Ru (Ru-1), Ru clusters (Ru-2) and Ru nanoparticles (Ru-3), exhibited distinct activity and selectivity for the sequential CO\(_2\) hydrogenation to CH\(_3\)OH with morpholine as the amine assistant. Ru-2, which simultaneously possesses atomically dispersed Ru\(_1\) sites and metallic Ru\(_c\) species, presented optimal catalytic activity in the N-formylation of morpholine with CO\(_2\), as well as the subsequent hydrogenation of the generated amide intermediates (i.e., N-formylmorpholine, NFM) to give methanol with the regeneration of morpholine. Moreover, the superior catalytic performance (selectivity of CHO\(_3\)H >97%, regeneration of morpholine >99%) of Ru-2 towards one-pot two-step CO\(_2\) hydrogenation was well maintained in three consecutive cycles. The mechanistic experiments and density functional theory (DFT) results reveal that the deoxygenative hydrogenation (C=O bond cleavage) and deaminative hydrogenation (C-N cleavage)
+are the rate-determining steps of morpholine N-formylation and NFM hydrogenation, which can be accelerated over Ru_e and Ru_1 sites, respectively. This work presents a heterogeneous catalysis protocol for amine-assisted hydrogenation of CO_2 towards methanol production, highlighting the significance of active species heterogeneity in enhancing the catalytic performance for multistep sequential reactions.
+
+2. Results and Discussion
+
+2.1 Synthesis and characterizations of Al_2O_3-based Ru catalysts
+
+A series of Al_2O_3-supported Ru catalysts (Ru-1, Ru-2, Ru-3) were rationally synthesized via an impregnation-annealing method, with Ru-Macho and \( \alpha \)-Al_2O_3 being employed as metal precursor and support, respectively (see Section 2 in Supplementary Information (SI) for details). The powder X-ray diffraction (PXRD) patterns exhibited no diffraction peaks related to Ru or RuO_2 phase in the three catalysts (Supplementary Fig. 1), which might be ascribed to the low contents (Supplementary Table 1) or/and small sizes of the Ru species. Transmission electron microscopy (TEM) images show that the morphologies of the synthesized catalysts with loaded Ru species remained consistent with the original Al_2O_3 matrix (Supplementary Fig. 2). To identify the differences in atomic-scale structures among the three Ru catalysts, the aberration-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) technique was adopted. The Ru species in Ru-1 catalysts were atomically dispersed (Fig. 1a and Supplementary Fig.
+3), while Ru clusters emerged in Ru-2 and these clusters grew into larger nanoparticles in Ru-3 (Fig. 1b-c and Supplementary Figs. 4-5).
+
+![Aberration-corrected HAADF-STEM images and spectroscopic results of Ru samples](page_186_370_1077_495.png)
+
+Fig. 1. Aberration-corrected HAADF-STEM images of (a) Ru-1, (b) Ru-2, and (c) Ru-3. (d) Ru K-edge XANES spectra of Ru foil, Ru-1, Ru-2 and RuO2. (e) Ru k^3-weighted Fourier transform of the EXAFS spectra of Ru foil, Ru-1, Ru-2 and RuO2. (f) CO-probe DRIFTS results of CO-absorbed Ru-1, Ru-2 and Ru-3.
+
+Additional spectroscopic characterizations were conducted to elucidate the electronic structure and coordination environment of the catalysts. The high-resolution X-ray photoelectron spectroscopy (XPS) spectra of Ru 3p in Ru-1 revealed two prominent peaks at the binding energies of 485.0 eV (Ru 3p_{1/2}) and 462.2 eV (Ru 3p_{3/2}), similar to those of Ru oxides^{41}, indicating the partially oxidized valence state of Ru species in Ru-1 (Supplementary Fig. 6). In contrast, the binding energies of Ru species in Ru-3 at 483.7 eV (Ru 3p1/2) and 461.8 eV (Ru 3p3/2) showed a striking resemblance to the characteristic signals of metallic Ru^{42}.
+consistently supporting the presence of nanoparticles as observed via HAADF-STEM.
+
+Similarly, Ru-2 also demonstrated an average valence state that closely aligns with metallic Ru, but slightly elevated compared to Ru-2, implying the potential existence of a subset of Ru species in the partially oxidized valence state. In addition, the XPS spectra signals of the P species, originating from the metal precursor (i.e., Ru-Macho), are notably prominent in Ru-1 and Ru-2, but significantly diminished in Ru-3 (Supplementary Fig. 7), suggesting that the P species may contribute to the formation of the Ru species with oxidized valance state.
+
+To probe the local microstructure of Ru species with enhanced precision, X-ray absorption spectroscopy (XAS) was employed. As shown in Fig. 1d, X-ray adsorption near edge structure (XANES) analysis showed that the energy absorption thresholds of Ru-1 and Ru-2 were located between those of RuO$_2$ and Ru foil, but Ru-1 aligned more closely with RuO$_2$, illustrating an increase in the valence state from the Ru foil to Ru-2, Ru-1 and RuO$_2$, which is consistent with the XPS observation results. The extended X-ray absorption fine structure (EXAFS) spectrum of Ru-1 only exhibited one main peak at ~1.4 Å, and no fingerprinting signal peak of Ru-Ru interactions (~2.3 Å) cannot be observed, verifying the atomic dispersion of Ru in Ru-1. The best fitting result of the obtained EXAFS data revealed that each Ru atom was coordinated by ~3 O atoms and ~1 P atom on average (Fig. 1e, Supplementary Fig. 8a and Supplementary Table 2). For the Ru-2 catalyst, in addition to the prominent peak at ~1.4 Å, a relatively weak peak at ~2.3 Å that corresponds to Ru-Ru first coordination shell could be identified. The low Ru-Ru coordination number (C.N.) of 3.0±1.0
+determined for Ru-2 suggested the presence of tiny Ru clusters, which agrees well with the HADDF-STEM results (Fig. 1e, Supplementary Fig. 8b and Supplementary Table 2).
+
+To gain an in-depth understanding of the Ru species distribution in the catalysts, a CO-probe diffuse reflectance infrared Fourier transform spectroscopy (DRIFTS) experiment was conducted to acquire semiquantitative information about the proportions of the surface Ru species. The red characteristic peaks in the DRIFTS spectra (Fig. 1f, Supplementary Fig. 9), corresponding to two linearly adsorbed CO molecules on partially oxidized Ru$_1$ species, decreased in intensity with increasing size of Ru$_e$ from the Ru-1 catalyst to the Ru-3 catalyst, while the characteristic peaks for adsorbed CO on metallic Ru$_e$ species (blue) increased in intensity. The statistical percentages of Ru$_1$ and Ru$_e$, determined by integrating the characteristic peaks, revealed that the Ru$_1$ contents in Ru-1, Ru-2 and Ru-3 are 100%, 47.7%, and 37.2%, respectively (see Section 4 in the Supplementary Information and Supplementary Table 3). The metal dispersion (i.e., available Ru active sites) was further calculated on the basis of the CO adsorption determined from CO-pulse adsorption experiments (see Section 4 in the Supplementary Information and Supplementary Table 4). The metal dispersion of Ru-1 (>99%), Ru-2 (69.5%) and Ru-3 (59.4%) also decreased with increasing proportion of Ru ensembles, which is consistent with the results of the CO-probe DRIFTS experiment.
+
+2.2 Catalytic performance of Al$_2$O$_3$-based Ru catalysts towards the morpholine-assisted sequential CO$_2$ hydrogenation
+The Ru catalysts, featuring various surface metal species, exhibited exceptional catalytic performance in each reaction step (Fig. 2a). For the N-formylation of morpholine, both Ru-2 and Ru-3 demonstrated superior catalytic performance and intrinsic activity, with turnover frequencies (TOFs) twice that of Ru-1 (Fig. 2b-c). In addition, the catalytic generation of amide reached a state of equilibrium after 36 h for Ru-2 and Ru-3, while twice the time was required for Ru-1 (Fig. 2b). This observation highlights the crucial role of Ru_e species in N-formylation. Furthermore, Ru-2 and Ru-3 exhibited superior selectivity (> 95%) for the amide compared to Ru-1 (~83%), with slight formic acid detected (Supplementary Fig. 10).
+
+![Schematic illustration of Ru-catalysed independent N-formylation and amide hydrogenation and a one-pot sequential CO2 hydrogenation reaction. Catalytic yield in N-formylation of morpholine over different catalysts. Catalytic yield of NFM hydrogenation over different catalysts. Intrinsic TOF of Ru-1, Ru-2 and Ru-3 toward morpholine N-formylation and NFM hydrogenation, respectively.](page_184_728_1080_496.png)
+
+Fig. 2. (a) Schematic illustration of Ru-catalysed independent N-formylation and amide hydrogenation and a one-pot sequential CO2 hydrogenation reaction. (b) Catalytic yield in N-formylation of morpholine over different catalysts. (c) Catalytic yield of NFM hydrogenation over different catalysts. (d) Intrinsic TOF of Ru-1, Ru-2 and Ru-3 toward morpholine N-formylation and NFM hydrogenation, respectively. (e)
+Yield-time profile of the one-pot two-step tandem process catalysed by Ru-2.
+
+Reaction conditions: 393 K, 10 mmol substrate, 15 ml 1,4-dioxane as a solvent, 100 mg catalyst, 0.5 mmol CsCO₃; for the N-formylation process: P(CO₂):P (H₂) = 1:1 with a total pressure of 4 MPa; for amide hydrogenation, P (H₂) = 4 MPa.
+
+During the hydrogenation of NFM into amine and methanol, both Ru-1 and Ru-2 exhibited superior activity, with TOF values (Ru-1: ~320 h⁻¹, Ru-2: ~389 h⁻¹) 4-5 times higher than that of the Ru-3 catalyst (~87 h⁻¹). Notably, Ru-2 showed a high yield and >99% methanol selectivity under identical reaction conditions. Based on the exceptional performance of Ru-2, we decided to investigate its potential utilization in a one-pot two-step tandem process. Over 144 h, Ru-2 exhibited superb activity (methanol turnover number, TON_{methanol} = 3300) and stability in three consecutive reaction cycles (Fig. 2e). The morphology of the Ru clusters was well maintained, as observed in the aberration-corrected HAADF-STEM image (Supplementary Fig. 11). We concluded that the Ruₑ and Ru₁ sites played dominant roles in the N-formylation and amide hydrogenation reactions, respectively.
+
+2.3 Catalytic mechanism of sequential CO₂ hydrogenation over Al₂O₃-based Ru catalysts
+
+To confirm the catalytic reaction pathways of sequential CO₂ hydrogenation, a series of mechanistic experiments were performed using the optimal Ru-2 catalyst. The influence of excess CO₂ during the N-formylation of morpholine was investigated, in which zwitterionic carbamates were spontaneously produced by
+morpholine in an aprotic solvent (Fig. 3a). In route 2, the reaction was initiated after CO₂ saturation (without additional CO₂ input during the catalytic reaction), in contrast to the original route 1, while in route 3, the excess CO₂ was evacuated after CO₂ saturation and replaced with 2 MPa N₂. The absence of excess CO₂ led to a higher formate selectivity with similar conversion levels (Fig. 3b), indicating the significant role of CO₂ in inducing the critical intermediate (i.e., zwitterionic carbamate) during the N-formylation process.
+
+![Schematic illustration of the influence of an excess CO₂ atmosphere during the N-formylation of morpholine. Catalytic conversion and selectivity of Ru-2 in the routes shown. H₂-TPR profiles of three Ru catalysts. Catalytic yield in two reactions with hydrogen and deuterium and the corresponding KIE values.](page_374_682_1002_495.png)
+
+Fig. 3. (a) Schematic illustration of the influence of an excess CO₂ atmosphere during the N-formylation of morpholine. (b) Catalytic conversion and selectivity of Ru-2 in the routes shown in (a). (c) H₂-TPR profiles of three Ru catalysts. (d) Catalytic yield in two reactions with hydrogen and deuterium and the corresponding KIE values.
+
+The H₂ temperature-programmed reduction (H₂-TPR, Fig. 3c) profiles of the three catalysts revealed different H₂ affinities, where Ru-2 and Ru-3, possessing abundant Ru₆ sites, was prone to reduction at a lower temperature, thus manifesting the stronger
+H₂ activation ability compared with Ru-1. To investigate the influence of H₂ activation in both steps of sequential CO₂ hydrogenation, hydrogen was replaced with deuterium (Fig. 3d). The yield was controlled at the intrinsic stage (conversion < 20%) to calculate the kinetic isotope effect (KIE) value. Similar to the TOF calculation with different catalysts, the reaction rate of N-formylation sharply decreased when hydrogen was replaced with deuterium, with a primary KIE value of 2.45 (2 < KIE < 7), indicating that the rate determining step (RDS) in the N-formylation reaction is a step in which hydrogen is involved^{43,44}. However, this phenomenon was not observed in the amide reaction process, in which nearly identical reaction rates were obtained with hydrogen and deuterium (KIE=0.98). Thus, for the amide hydrogenation reaction, the RDS was speculated to be cleavage of the C-N bond.
+
+To further confirm this speculation, the catalytic hydrogenation of diverse carbonyl substrates was evaluated next (Supplementary Fig. 12). Due to substrate limitations, cyclohexylformamide was utilized as an analogue of NFM. The Ru-2 catalyst exhibited almost no activity towards amides and carboxylic acids but achieved close to 100% yield for cyclohexylmethanol from aldehydes, with the absence of cyclohexylmethanamine or imine by-products, thereby highlighting the priority of C-N bond cleavage over carbonyl reduction during amide hydrogenation.
+
+Density functional theory (DFT) calculations were further conducted to gain insights into the reduction mechanism. Two Ru-containing models were constructed to consider the Ruₑ and Ru₁ sites on the Al₂O₃ substrate, labelled Ru-ensemble and
+Ru-SAC in Supplementary Fig. 13, respectively. The surface of Al2O3 was passivated with a hydroxyl group, and the single Ru atom was coordinated with a (CH3)3P ligand to reproduce the chemical environment determined by experiments.
+
+![Energy profile and structures of key intermediates in the reduction process](page_349_678_1047_410.png)
+
+Fig. 4. (a) Energy profile of the reduction process. (b) Structures of the key intermediates in the reaction pathways. The asterisk denotes the adsorption site. Colour code: Ru: green; Al: pink; N: blue; C: grey; O: red; H: white.
+
+The free energy profile in Fig. 4a and the relevant structures of intermediates in Fig. 4b indicate that the Ru_e provides multiple sites that not only activate the unsaturated carbon of the carboxylic group in carbamates by binding with oxygen but also adsorb the active hydrogen to reduce carbamates. The activation energy barrier of the first reduction step was calculated to be 1.01 eV for the C=O cleavage in the zwitterionic
+carbamates (route 2 in Fig. 3a) under H₂. Further protonation leads to elimination of the hydroxyl group, thus forming a formamide intermediate, which requires overcoming an energy barrier of 1.18 eV. Despite the relatively low energy barriers of Ru₆ in the first few steps, the reduction step to form a hemiaminal (an intermediate of formamide hydrogenation) over Ru₆ requires overcoming a high energy barrier of 1.45 eV, resulting in a sluggish rate to obtain the final product. However, the formamide hydrogenation may spill over onto the single Ru atom site. The migration of two hydrogen atoms from the Ru site to the intermediate would require overcoming two lower activation barriers of 1.24 eV and 0.95 eV. Thus, the presence of Ru₁ sites can accelerate the deep reduction of formamide to a hemiaminal. Finally, the hemiaminal desorbs and easily decomposes back into morpholine and formaldehyde.
+
+Based on the results of our experiments and DFT simulations, we proposed a potential catalytic reaction pathway for Ru-2 involving several steps (Fig. 5). Initially, morpholine absorbs CO₂ to yield zwitterionic carbamates. Active hydrogen species generated via metallic Ru₆ then reduce these carbamates to form intermediate A (Fig. 5). Proton transfer from carbamates to intermediate A leads to the formation of intermediate B, which subsequently undergoes natural intramolecular dehydration to produce amide and H₂O. In addition, the electronegative oxygen in intermediate A can also coordinate to the atomically dispersed Ru₁ site to form intermediate C, which undergoes hydrogenation to form formate and morpholine. This process is probably the primary source of formic acid by-product formation. In the amide hydrogenation step, the amide is coordinated to the electropositive Ru₁ site and hydrogenated to form
+intermediate E, which undergoes C-N cleavage with the aid of the Ru$_1$ site to generate the adsorbed aldehyde (intermediate F) and regenerate the morpholine. The intermediate F is prone to hydrogenation (Supplementary Fig. 14), thus producing methanol. In contrast, the methylamine by-products via imine (intermediate G) pathway were not detected during amide hydrogenation (Supplementary Fig. 14).
+
+![Proposed catalytic reaction pathways for Ru-2 in the one-pot two-step catalytic process.](page_370_682_1097_355.png)
+
+Fig. 5. Proposed catalytic reaction pathways for Ru-2 in the one-pot two-step catalytic process.
+
+3. Conclusion
+
+In summary, we prepared a series of active heterogeneous Ru catalysts with multiple surface metal species, including atomically dispersed Ru species and Ru ensembles. Among these catalysts, Ru-2, which contained both Ru$_1$ species and Ru$_e$ sites, demonstrated excellent performance in the N-formylation and amide hydrogenation reactions, enabling efficient one-pot two-step methanol production under relatively mild conditions. The critical roles of the active metal species in the
+reaction process were revealed by combining experiments and theoretical calculations, and a possible reaction pathway was proposed. This study provides a potential candidate catalyst for selective reduction of CO\(_2\) to methanol and reveals the synergistic effect of different metal species in complex multistep reactions at the atomic scale. The strategy of rationally designing multiple optimized active sites within a single catalyst paves the way for enhancing the catalytic performance in various multistep sequential reactions in the future.
+
+ASSOCIATED CONTENT
+
+Supplementary Information. The Supplementary Information is available free of charge via the Internet at http://pubs.acs.org.
+
+Chemicals and characterization; Preparation of Al\(_2\)O\(_3\)-based Ru catalysts; Catalyst evaluation; Characterization details; Supplementary Figs. 1-14; Supplementary Tables 1-4
+
+AUTHOR INFORMATION
+
+Corresponding Author
+
+Liang Chen – Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, P. R. China; University of Chinese Academy of Sciences, Beijing 100049, P. R. China; E-mail: chenliang@nimte.ac.cn
+
+Zhiyi Lu – Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, P. R. China; University of Chinese Academy of
+Sciences, Beijing 100049, P. R. China; E-mail: luzhiyi@nimte.ac.cn
+
+Ziqi Tian – Ningbo Institute of Materials Technology and Engineering, Chinese Academy of Sciences, Ningbo 315201, P. R. China; University of Chinese Academy of Sciences, Beijing 100049, P. R. China; E-mail: tianziqi@nimte.ac.cn
+
+Author Contributions
+
+‡These authors contributed equally.
+
+Notes
+
+The authors declare no competing financial interest.
+
+ACKNOWLEDGMENT
+
+This work is supported by the National Natural Science Foundation of China (22101288), the Natural Science Foundation of Zhejiang Province (LQ22B010005 and LD21E020001), the Bellwethers Project of Zhejiang Research and Development Plan (2022C01158), the Ningbo Yongjiang Talent Introduction Programme (2021A-036-B), the Science and Technology Innovation 2025 Program in Ningbo (2022Z205), Youth Innovation Promotion Association, CAS, the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning, Feringa Nobel Prize Scientist Joint Research Center, Transformational Technologies for Clean Energy and Demonstration, Strategic Priority Research Program of the Chinese Academy of Sciences (XDA21000000), DNL Cooperation Fund, CAS (Grant No. DNL202008), and “Transformational Technologies for Clean Energy and Demonstration”.
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+Table of Contents
+
+A heterogeneous supported catalyst featuring atomically dispersed Ru sites and Ru-cluster sites exhibited superior catalytic performance for amine-assisted sequential hydrogenation of CO2 into hydrogen via the synergistic effect of the two types of surface-active Ru species. The rate-determining steps of the two reactions were elucidated and correlated with the intrinsic active species.
+
+![Diagram showing the catalytic process involving Ru sites and clusters, hydrogenation of CO2, and product distribution](page_374_613_495_181.png)
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SupplementaryInformation.pdf

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+Peer Review File
+
+Mott resistive switching initiated by topological defects
+
+Corresponding Author: Professor Claudio Giannetti
+
+This file contains all reviewer reports in order by version, followed by all author rebuttals in order by version.
+
+Version 0:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The paper by Milloch et al. reports the discovery of topological V-defects as the nucleation to metallic filaments during current driven MIT phase transition of a a V2O3 film. This was done by imaging the 2 micron gap between the electrodes of a plan view V2O3 20nm film grown on Cr2O3 buffered saphire. The 3 different domains of the monoclinic insulator phase were monitored using their dichroic XLD signal in a PEEM microscope.
+
+This work is very interesting and worth publishing in nature communications. I have a few minor comments:
+
+1) What is the role of the Cr2O3 buffer layer on the domain structure observed in the V2O3 film, could defects in this layer influence the presence of the topological defects or linear defects in the V2O3 film ? How are these linked to the phenomenon observed upon biasing?
+
+2) How homogeneous is the E field accross the gap ? upon the full length of the sample was there only 1 metallic filament formed ? Why is that? How reproduceable are the results if it is observed only in 1 position of the 30 microns of the specimen?
+
+3) Did you take a look at the microstructure with TEM in the region where the filament is formed ? How is it different than the rest ?
+
+4) There seem to be other regions where the 60deg domains are observed (stripes in both directions) which does the filament do not appear there as well, can you give some statistical analysis over the full region of the specimen?
+
+5) Could the authors comment on the relation between their topological V-shaped defect and APBs observed by other authors on similar films? Are they related ? Would you see APBs if you would take a look at the V2O3 film in cross section in the TEM ?
+
+6) The authors say that the growth of the filament is related to Joule heating ? In that case the formation of the filament is reversible, did thew authors try to do several cycles accross the MIT transition ? Is the transition reversible ? Does the filament always appear at the same location ?
+
+7) Did the authors try pure electric field switching with no current allowed to go accross the sample ? Is the behaviour different, did they try quenching the electric field ? Does the microstructure return to its initial state?
+
+Reviewer #2
+
+(Remarks to the Author)
+Milloch and coworkers study the Mott metal insulator transition in the paradigmatic compound V2O3 by resonant x-ray microscopy. At temperature below the metal insulator transition the material is insulating and applying large enough electric field gives rise to the sudden formation of a conducting filament yielding resistive switching from high to low resistivity. To obtain tight control of the filament formation and to realize large field strengths, a gap of 2 \( \mu \)m width is patterned on the V2O3
+film. X-ray nanoimaging maps the different monoclinic domains in the gap region with 30 nm resolution. As voltage is applied, a filament forms and grows with increasing voltage. The filament is identified as the metallic rhombohedral phase from its x-ray linear dichroism (XLD) contrast. Importantly, the filament reproducibly forms at the same location and when the field is turned off the same domain structure is reestablished as before. This is, quite reasonably, assigned to pinning to defects.
+The authors then focus on the microscopics of domain boundaries and identify topological defects with non-vanishing phase shift at V-shaped domain boundaries, which arise as a direct consequence of the frustration of three possible domain directions. At such defects the local suppression of the order parameter requires only smaller voltage to switch the transition from insulating to metallic, hence they are assigned as seeds for the voltage-induced transition. Using a model of two parallel resistors the width is reasonably described for large currents. To demonstrate the agreement, Fig. 4c should be extended to the highest currents measured (10 mA in panel a). Even though the authors make some effort to explain on page 6, left column, why the predicted jump of 200 nm is not directly seen in the data, in the actual data points (currents of 1.1 and 1.5 mA) one cannot distinguish whether the jump of domain width is immediate or continuously. In fact, the 1.5 mA data point is about 200 nm higher width than the 1.1 mA data point, which seems to line up reasonably with the model. This part should be maybe reformulated to some extent.
+Finally, the authors conclude that topological defects play a crucial role in initiating the filament formation and, thus, the avalanche process. They then suggest to use nanoscale strain engineering to manipulate topological defects and control the switching – this is somewhat crude and I do not fully understand what exactly should be done. Is it to introduce topological defects in a controlled manner? How this would be done in particular? Since such defects arise from local strain gradients upon growth of the material, is it similar to applying nanoscale strains to a sample like seen for metal-insulator transitions in other correlated electron systems, e.g. Sci. Adv. 4, eaau9123 (2018)?
+The manuscript presents relevant research providing deep insights into the microscopics of the Mott metal-insulator transition. After the authors have incorporated the above points, it should be ready for publication in Nature Communications.
+
+Version 1:
+
+Reviewer comments:
+
+Reviewer #1
+
+(Remarks to the Author)
+The authors answered my concerns and therefore I support the publication of the manuscript
+
+Reviewer #2
+
+(Remarks to the Author)
+The authors have comprehensively answered my questions on the filament width. They also elaborated the the conclusions towards potential applications.
+I support publication of the mansucript in Nature Communications in its present form.
+Open Access This Peer Review File is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
+In cases where reviewers are anonymous, credit should be given to 'Anonymous Referee' and the source.
+The images or other third party material in this Peer Review File are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
+To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/.
+Reviewer #1 (Remarks to the Author):
+
+The paper by Milloch et al. reports the discovery of topological V-defects as the nucleation to metallic filaments during current driven MIT phase transition of a a V2O3 film. This was done by imaging the 2 micron gap between the electrodes of a plan view V2O3 20nm film grown on Cr2O3 buffered saphire. The 3 different domains of the monoclinic insulator phase were monitored using their dichroic XLD signal in a PEEM microscope.
+
+This work is very interesting and worth publishing in nature communications. I have a few minor comments:
+
+Reply: we thank the reviewer for showing interest in our work and recommending publication. We also appreciate the constructive comments and questions provided, which we address in the replies below.
+
+1) What is the role of the Cr2O3 buffer layer on the domain structure observed in the V2O3 film, could defects in this layer influence the presence of the topological defects or linear defects in the V2O3 film ? How are these linked to the phenomenon observed upon biasing?
+
+Reply: The role of the buffer layer is to reduce the in-plane residual strain in the V2O3 film. This reduced strain results from the significantly smaller lattice misfit between the V2O3 crystal and the Cr2O3 buffer layer ((\(a_{V2O3}/a_{Cr2O3}\))/\(a_{Al2O3}\) = -0.1%, with \(a\) indicating the bulk lattice constant) as compared to the sapphire substrate ((\(a_{V2O3}/a_{Al2O3}\))/\(a_{Al2O3}\) = 4.2%). The use of a buffer layer, therefore, allows the V2O3 film to grow almost completely relaxed towards its bulk values.
+
+The domain structure of the low temperature monoclinic phase appears very similar in both cases (samples with and without buffer layer). As shown in the figure below (from our previous work Ronchi et al., Nat. Comm., **13**, 3730, 2022), both samples display the typical domain nanotexture characterized by stripes of similar size and oriented along the three hexagonal axes of the rhombohedral phase (0°, 120° and 240°). The nanotexture is, indeed, intrinsic of the rhombohedral to monoclinic deformation in V2O3 and appears to be independent from the presence of the buffer layer.
+
+![XLD-PEEM images of two V2O3 samples, one with (right) and one without (left) the Cr2O3 buffer layer, measured at 120 K. Figure adapted from [Ronchi et al., Nat. Comm., 13, 3730, 2022].](page_563_1042_819_312.png)
+
+Figure R1 XLD-PEEM images of two V2O3 samples, one with (right) and one without (left) the Cr2O3 buffer layer, measured at 120 K. Figure adapted from [Ronchi et al., Nat. Comm., **13**, 3730, 2022].
+In terms of defects, for the samples grown by our group, twinning defects are in general observed in the Cr2O3 films grown on sapphire. TEM images, however, show that these defects remain mostly confined in the buffer layer and usually do not propagate to the V2O3 film. An example of this behaviour is reported in Figure R2 below, showing a TEM image of a V2O3/Cr2O3/Al2O3 sample and Fast Fourier Transform (FFT) of selected areas. Additionally, twin domains are significantly reduced when the film is deposited at a slow growth rate, as is the case for the samples employed in the present work (growth rate = 0.1 A/s). The low density of twin domains is also confirmed by X-ray diffraction data, which, in the \( \varphi \)-scan measurement, display three peaks because of the three-fold rotational symmetry; if the density of twinning defects was significant, \( \varphi \)-scan XRD data would display six peaks because of the presence of the mirror twin (see for example Nat. Comm., 8, 13985 (2017) and Journal of Crystal Growth 457, 158-163 (2017)), whereas this is not observed in our case, confirming single-crystal growth of the film.
+
+![TEM image and FFT analysis of V2O3 sample on Cr2O3 buffer layer](page_184_370_1122_627.png)
+
+Figure R2 a) TEM image of a V2O3 sample grown on a Cr2O3 buffer layer and Al2O3 substrate, taken along the (\( \overline{2}110 \)) zone axis. b) FFT of four different areas of the TEM image in a), highlighted by red squares. Twinning is observed in a localized area of the Cr2O3 layer (panel 3 in the bottom-left corner), as shown by the appearance of additional peaks in the FFT image, but not in the V2O3 film (see panel 4, representing the region of the V2O3 film on top of the Cr2O3 twinned domain).
+
+While topological defects in the monoclinic nanotexture could be affected by linear/lattice defects that exist already at high temperature in the V2O3 film, we note that topological defects can also form independently of pre-existing structural defects. Topological defects, in fact, can emerge from the existence of different domains (not requiring any twinning or other types of defects) in spatially separated regions that need to be matched at the intersection. Overall, addressing the exact relationship between crystal defects (in the buffer layer and in the V2O3 film), topological defects (of the domain nanotexture) and resistive switching occurring upon biasing, would require a systematic investigation that is the objective of the next experimental campaigns at synchrotron facilities.
+
+2)How homogeneous is the E field accross the gap ? upon the full length of the sample was there only 1 metallic filament formed ? Why is that? How reproduceable are the results if it is observed only in 1 position of the 30 microns of the specimen?
+
+Reply: In the device employed for the present experiment, the distance between the two electrodes appears quite homogeneous throughout the device, which implies that also the electric field is homogeneous across the gap. The figure below (panel a) reports the intensity PEEM image (sum of the images acquired with the two polarizations) of the device, which we employ to estimate the gap width. We take line profiles (reported in panel b below) perpendicular to the device gap and we
+evaluate the width of the “well” representing the gap between the two gold electrodes; the estimated values of the electrodes distance as a function of the position are plotted in panel c of the figure below, showing an average gap size of 2.2 \( \mu \)m with a standard deviation of 100 nm. Given the small standard deviation indicating an almost constant electrodes distance, we can therefore consider that the electric field is homogeneous across the gap; a weakening of the electric field only occurs in proximity of the edges of the gap (x < 5 \( \mu \)m and x > 28 \( \mu \)m in x-axis scale of the figure below), over an area of the order of the gap size itself (~2 \( \mu \)m). The location where the filament is formed (around x \( \simeq \) 14.5 \( \mu \)m in x-axis scale of the figure below) is, thus, not peculiar or anyhow preferential in terms of electric field intensity.
+
+![PEEM image of the V2O3 film – gold electrodes device. Vertical line profiles of the image in a) at different locations along the gap length x. Estimates of the electrode-electron distance as a function of position x.](page_186_370_1077_393.png)
+
+Figure R3 a) PEEM image of the V2O3 film – gold electrodes device. b) Vertical line profiles of the image in a) at different locations along the gap length x. c) Estimates of the electrode-electron distance as a function of position x.
+
+The filament forms in that specific location because it is seeded by the presence of the topological defect. Once resistive switching occurs, the current starts flowing through the newly formed conductive filament which represents the preferential channel (as compared to switching other insulating regions). The fact that only one conductive channel (see Fig. S4 which shows a snap of the entire device) is formed and it widens as the current is increased is, indeed, in agreement with previous experimental reports employing optical microscopy combined with resistive switching experiments performed on similar systems (see, for example, Lange et al., Physical Review Applied 16, 054027 (2021) and Luibrand et al., PRResearch 5, 013108 (2023)).
+
+In our experiment, the formation of the metallic channel starting from the topological defect has been observed multiple times, both upon repeating the current sweep after other resistive switching events and after thermal cycling above the critical temperature for the insulator-metal transition (IMT). The two set of PEEM images reported in Fig. 2 and in Fig. S4 (Supporting Information), for example, represent two independent measurements and show reproducible behaviour of the formation and expansion of the metallic filament.
+
+3) Did you take a look at the microstructure with TEM in the region where the filament is formed ? How is it different than the rest ?
+
+Reply: We don’t have TEM data on the sample employed for the resistive switching experiment and, unfortunately, a TEM investigation on this exact device can no longer be performed because the device has been significantly damaged by successive resistive switching measurements at larger current that shortcut the circuit and destroyed the gap area.
+
+Some insight about the homogeneity of the sample in the area where the filament is formed, can be obtained from the PEEM image acquired at high temperature (220 K), where there is no nanotexture since the system is in the rhombohedral structure. In this case (see XLD-PEEM image below, left panel), we observe that the region where the filament is formed, highlighted by the black arrows, appears as very homogeneous so that it does not appear to be anything peculiar on the nanometric scale.
+Figure R4 Left panel: imaging of the whole device gap at high temperature, showing homogeneous surface in the region where the metallic corundum filament is formed upon bias application, highlighted by black arrows. Right panel: XLD-PEEM image of the V2O3 device measured at low temperature with applied 1.5 mA current; the black dashed lines highlight the filament formed after resistive switching.
+
+We also note that a meaningful TEM imaging of the filament area would require a low temperature TEM with in-situ electrical bias, which we currently don’t have access to. Nonetheless, we are foreseeing and planning future experiments on analogous samples where we will perform low temperature TEM and, in a second step, combine it with bias application.
+
+4) There seem to be other regions where the 60deg domains are observed (stripes in both directions) which does the filament do not appear there as well, can you give some statistical analysis over the full region of the specimen?
+
+Reply: Other 60° domains are observed only in the top right corner of the figure below, where, however, the nanotexture appears quite different compared to the area where the filament is formed, which is characterized by a clear alternation of stripes on the two sides of the V-shape. Indeed, these other 60° domains are observed mostly close to the edge of the gap where the electric field is weakened. In these areas the nanotexture itself appears as formed of shorter domains and, in general, less ordered. In the rest of the device, it looks like there is only one clear topological defect. As already mentioned above, once the filament is formed the current flows through there (as the resistance is lowered) while switching of other spatial regions is hindered.
+
+Figure R5 XLD-PEEM imaging of the monoclinic nanotexture across the whole device.
+5) Could the authors comment on the relation between their topological V-shaped defect and APBs observed by other authors on similar films? Are they related? Would you see APBs if you would take a look at the V2O3 film in cross section in the TEM?
+
+Reply: While we don’t have TEM data of the specific sample employed on the present work, TEM imaging of similar samples grown under the same conditions do not evidence presence of anti-phase boundaries. Indeed, literature reports of APBs in V2O3 [Ignatova et al., APL Materials, 12, 041118 (2024)] show that the APB defects are mostly observed in V2O3 grown on r-plane sapphire as opposed to c-plane, which is the case of our samples. Therefore, while we can’t exclude the presence of APBs, we believe that these would be unlikely and not necessarily directly linked to the V-shaped topological defect. Indeed, as already mentioned above, the presence of topological defects does not require structural defects that already exist in the high temperature corundum phase. A deeper investigation of the relation between high-temperature microscopic defects, low-temperature microstructure and monoclinic domains requires a dedicated and systematic study that goes beyond the scope of the present work.
+
+6) The authors say that the growth of the filament is related to Joule heating? In that case the formation of the filament is reversible, did thew authors try to do several cycles accross the MIT transition? Is the transition reversible? Does the filament always appear at the same location?
+
+Reply: The resistive switching in V2O3 under investigation is a volatile switching, therefore the device persists in the low resistance state only as long as the current is applied. When the current is reduced below a threshold value, the filament disappears, and the system goes back to the original insulating monoclinic phase. Therefore, the process is overall reversible.
+
+The widening of the filament upon increasing current and the narrowing upon decreasing current is likely related to simple Joule heating. As the current flowing through the metallic filament increases, the local temperature in the filament area increases causing the structural transition from monoclinic to rhombohedral. The opposite process occurs when the current is decreased, until the material is completely reversed back to the monoclinic insulating phase.
+
+The experiment was repeated several times, also after thermal cycling (sample heating) up to 250 K. In all cases the filament appears in the same location. The resistive switching + PEEM measurements were always performed starting from a temperature in the range around 120-130 K. Resistive switching occurs also at lower temperature, where however the voltage measured across the device gap are larger because the resistance is higher (see I-V curves reported in the figure below for resistive switching performed at two different temperatures). This hinders PEEM imaging because the large in-plane voltage necessary to induce the switching causes a blurring in the image obtained from the photoemitted electrons. We found that for voltages higher than 6-8 V imaging was not possible. In general, we would expect that, at any base temperatures, the filament is formed always in the same location. What would change when the experiment is performed at different temperatures is the filament size and growth rate, as for example showed by Luibrand et al. [PRResearch 5, 013108 (2023)] in different Mott systems (NdNiO3 and SmNiO3) displaying a resistive switching behaviour similar to V2O3.
+
+![Examples of resistive switching I-V curves measured at two different base temperatures.](page_1012_1347_393_312.png)
+
+Figure R6 Examples of resistive switching I-V curves measured at two different base temperatures.
+In order to better clarify these points, we modified the main text that now reads:
+
+Page 3 - “XLD-PEEM images obtained under the same conditions, but with a larger field of view, capture the whole gap of the device (see Supplementary Information Fig. S4, which reports an independent set of PEEM measurements performed after thermal cycling to 250 K). The metallic channel consistently forms in the same location within the gap with no additional metallic paths observed. Furthermore, when the applied current is removed, the metallic channel disappears and the monoclinic domains reappear with the same pre-switching configuration, indicating a volatile process.”
+
+Page 6 – “the Joule heating leads to a local temperature increase and, consequently, to the thermally driven monoclinic-to-rhombohedral structural transition and the formation of rhombohedral metallic channel perpendicular to both the metallic electrodes and the \( \hat{e}_z \) order parameter direction, as observed in Fig. 2.”
+
+7) Did the authors try pure electric field switching with no current allowed to go accross the sample ? Is the behaviour different, did they try quenching the electric field ? Does the microstructure return to its initial state?
+
+Reply: The current design of the device does not allow this kind of experiment because application of a voltage bias to the electrodes deposited on top of the V$_2$O$_3$ film determines a current flowing through the sample and the establishment of an in-plane electric field. Also in this present case, we observe that the microstructure returns to its initial state once the current flowing though the device is lowered below a certain threshold value.
+
+One possible way to investigate the effect of pure electric field could be to employ THz radiation similarly to what done, for example, by Giorgianni et al. [Nat. Comm., **10**, 1159 (2019)]. In this case, it could be possible to investigate the switching induced by the THz electric field without the need to apply large voltages across metallic electrodes.
+Reviewer #2 (Remarks to the Author):
+
+Milloch and coworkers study the Mott metal insulator transition in the paradigmatic compound V2O3 by resonant x-ray microscopy. At temperature below the metal insulator transition the material is insulating and applying large enough electric field gives rise to the sudden formation of a conducting filament yielding resistive switching from high to low resistivity. To obtain tight control of the filament formation and to realize large field strengths, a gap of 2 \( \mu \)m width is patterned on the V2O3 film. X-ray nanoimaging maps the different monoclinic domains in the gap region with 30 nm resolution. As voltage is applied, a filament forms and grows with increasing voltage. The filament is identified as the metallic rhombohedral phase from its x-ray linear dichroism (XLD) contrast. Importantly, the filament reproducibly forms at the same location and when the field is turned off the same domain structure is reestablished as before. This is, quite reasonably, assigned to pinning to defects. The authors then focus on the microscopics of domain boundaries and identify topological defects with non-vanishing phase shift at V-shaped domain boundaries, which arise as a direct consequence of the frustration of three possible domain directions. At such defects the local suppression of the order parameter requires only smaller voltage to switch the transition from insulating to metallic, hence they are assigned as seeds for the voltage-induced transition. Using a model of two parallel resistors the width is reasonably described for large currents. To demonstrate the agreement, Fig. 4c should be extended to the highest currents measured (10 mA in panel a). Even though the authors make some effort to explain on page 6, left column, why the predicted jump of 200 nm is not directly seen in the data, in the actual data points (currents of 1.1 and 1.5 mA) one cannot distinguish whether the jump of domain width is immediate or continuously. In fact, the 1.5 mA data point is about 200 nm higher width than the 1.1 mA data point, which seems to line up reasonably with the model. This part should be maybe reformulated to some extent.
+
+Reply: The estimation of the filament width based on the two-resistors model is reported over the whole current range (10 mA) in Supplementary Information Fig. S5a. The plot shows a reasonable agreement between the experimental data and the model, which predicts a metallic filament that widens up to ~3 \( \mu \)m at the largest current. As shown in Supplementary Information Fig. S5a and also in the figure below (top panel), for currents larger than 4 mA, the two-resistors model actually underestimates the filament width value found experimentally. This deviation is likely due to heating effects becoming significant at large current. In fact, in the model we use a fixed value for the filament resistivity \( \rho \) (0.001 \( \Omega \)cm) which is the experimentally measured resistivity around 250 K. For large currents, however, there could be a local increase in temperature resulting in a different value of \( \rho \). Conversely, the model estimates a slightly wider filament than what is found experimentally at low currents (1.5 mA and 3 mA).
+
+Overall, the very simple model based on two parallel resistors captures quite well the widening of the metallic filament. The crucial point of our experiment is that the I-V curve is measured simultaneously to the imaging of the filament, i.e. each PEEM image is acquired with a specific voltage drop and current flow. Therefore, we know for sure that in the PEEM image at 1.1 mA the device has already switched to low resistance. According to the model, which works pretty well for all the other experimental points, the measured voltage drop should correspond to the formation of a 200 nm wide filament. As also noted by the reviewer, such 200 nm jump is experimentally observed, but only at larger currents (1.5 mA), not at 1.1 mA. This shows that a 200 nm wide corundum filament emerging at the exact point of the voltage drop (1.05 mA -> 1.1 mA) would be clearly observable and detectable in the PEEM images given our experimental resolution. In the PEEM image at 1.1 mA, however, there is no visible corundum filament, therefore we estimate a filament width \( d_{exp} < 50 \) nm, where the upper bound is given by the experimental spatial resolution (the nominal resolution of 30 nm is slightly deteriorated by image blurring because of bias application).
+
+In order to evaluate the discrepancy between the model and the experimental value, we can compute a “relative error” defined as \( (d_{exp} - d_{model})/d_{exp} \), with \( d \) indicating the filament width. The obtained values are plotted in the figure below (bottom panel). The graph shows that for \( I \geq 1.5 \) mA, the model deviates from \( d_{exp} \) by 20-30%, whereas the relative error diverges at 1.1 mA. This further shows that the agreement between the two-resistors model and the data is reasonable for \( I \geq 1.5 \) mA, considering the uncertainties in both the measured values and in the parameters employed for the model estimates (as discussed in Supplementary Information Section S5), and considering that heating effects are not taken into account.
+Because of the complexity of the present experiment where PEEM imaging is performed during bias application, we only have data at a few points in current, whereas the range between 1.1 mA and 1.5 mA has not been imaged. Therefore, we are not able to say whether the formation of the corundum channel is immediate or continuous. A possible scenario suggested by the model is that there is the sudden formation of a metallic (but still monoclinic) channel at the threshold current, which is followed by the structural transition of the filament region from monoclinic to corundum. If this structural transition is due to the local temperature increase caused by Joule heating, we can speculate that the filament undergoes a percolative transition (following the temperature-induced IMT) as the current increases.
+
+![Filament width vs. current plot showing experimental and model values, and relative error](page_374_629_700_482.png)
+
+Figure R7 Top panel: width of the corundum metallic channel as a function of the applied current. The blue markers represent the experimental valued obtained from PEEM imaging; the red marker report the values predicted by the two-resistors model. Bottom panel: estimate of the discrepancy of the two-resistor model from the measured values for the corundum filament width, showing divergence at 1.1 mA which is the first measured point after the resistive switching voltage drop.
+
+In order to better clarify these points, we revised the corresponding section in the main text that now reads:
+
+'Modelling the device as a circuit with two parallel resistors (see Supplementary Information Section S5) allows an estimation of d of the rhombohedral filament corresponding to the observed voltage drop. For large currents running through the device, the experimentally determined values of d match well with those predicted for a metallic channel forming in the gap, which has the resistivity of the high-temperature rhombohedral phase, as shown in Fig. 4, and in Supplementary Information, Fig. S5a, for the full current range. However, in correspondence of the first resistive switching event at I_{in}=1.05 mA, the model predicts the sudden formation of a ~ 200 nm wide metallic rhombohedral filament, which is not visible in the XLD-PEEM images (see Fig. 4c and Supplementary Information Fig. S5), despite being well above the experimental resolution of the microscope. This is evidenced by PEEM imaging at I=1.1 mA, where no variation in the domain nanotexture is appreciated, while the simultaneous voltage measurement guarantees that the device has already switched." ... "Our results
+are compatible with a complex scenario in which the topology-driven resistive switching likely occurs via the sudden transformation of a single 200 nm wide insulating monoclinic area into a metallic channel with a non-thermal monoclinic lattice structure. At a second stage, the Joule heating leads to a local temperature increase and, consequently, to the thermally driven monoclinic-to-rhombohedral structural transition and the formation of a rhombohedral metallic channel perpendicular to both the metallic electrodes and the \( \hat{e}_2 \) order parameter direction, as observed in Fig. 2."
+
+Finally, the authors conclude that topological defects play a crucial role in initiating the filament formation and, thus, the avalanche process. They then suggest to use nanoscale strain engineering to manipulate topological defects and control the switching – this is somewhat crude and I do not fully understand what exactly should be done. Is it to introduce topological defects in a controlled manner? How this would be done in particular? Since such defects arise from local strain gradients upon growth of the material, is it similar to applying nanoscale strains to a sample like seen for metal-insulator transitions in other correlated electron systems, e.g. Sci. Adv. 4, eaau9123 (2018)?
+
+Reply: we thank the reviewer for raising this point that led us to expand the discussion about strain engineering. The key idea suggested here is to investigate the possibility of exploiting the strain in the film to introduce topological defects in a controlled way. We foresee various routes that can be explored to achieve strain control. One possibility is to play with the substrate, similarly to what done in Sci. Adv. 4, eaau9123 (2018), but also in Homm et al., APL Mater. 9, 021116 (2021) and Hsu et al., Physical Review Materials 7, 074606 (2023), where it was shown that the strain in a Mott insulator can be controlled by changing the substrate and can strongly affect the insulator-metal phase transition. For example, the strain in V$_2$O$_3$ film can be tuned by fine variations in the doping of the substrate which affect the lattice mismatch between film and substrate [Homm et al., APL Mater. 9, 021116 (2021). Hsu et al., Physical Review Materials 7, 074606 (2023)]. Localized control of the strain and related topological defects could instead be obtained by exploiting the strain applied by metallic overlayers, similarly to the gold electrodes employed in the present experiment, whose geometry and orientation with respect to the film crystallographic axis can affect the emergence of topological defects. Another promising approach is represented by nanopatterning, similarly to what was done in Meer et al., [Physical Review B **106**, 094430 (2022)] where the shape-dependent strain induced by Ar ion beam etching was shown to influence the shape and size of antiferromagnetic domains, therefore suggesting a viable way to control AF domains and, thus, to locate topological defects in a deterministic way.
+
+In the revised manuscript we expanded the conclusions that now reads: *The methodologies used in this work imply that nanoscale strain engineering approaches could unlock a gate to manipulating topological defects and controlling the electronic switching dynamics in real devices, such as Mott-transition-based RRAM [46, 47], Mott memristor [48–50] and artificial neurons [51, 52]. Fine tuning of crystal growth by adjustment of the substrate parameters [15, 53], manipulation of the geometry and orientation of metallic over-layers and use of nano-patterning approaches [54] represent possible viable routes to introduce topological defects in a controlled way via strain manipulation.*
+
+The manuscript presents relevant research providing deep insights into the microscopics of the Mott metal-insulator transition. After the authors have incorporated the above points, it should be ready for publication in Nature Communications.
+
+Reply: we are grateful to the reviewer for appreciating the insight provided by our work. We also thank him/her for providing constructive feedback that helped to improve the manuscript, and for recommending its publication.

0a029bedc77ee23f09bec94b1dd73e6a81b91ac30d9e51c5375983d20db515bb/preprint/preprint.md

@@ -0,0 +1,252 @@
+Mott resistive switching initiated by topological defects
+
+Claudio Giannetti
+claudio.giannetti@unicatt.it
+
+Università Cattolica del Sacro Cuore   https://orcid.org/0000-0003-2664-9492
+Alessandra Milloch
+Università Cattolica del Sacro Cuore
+Ignacio Figueruelo-Campanero
+IMDEA Nanociencia
+Wei-Fan Hsu
+KU Leuven
+Selene Mor
+Università Cattolica del Sacro Cuore
+Simon Mellaerts
+KU Leuven   https://orcid.org/0000-0002-6715-3066
+Francesco Maccherozzi
+Diamond Light Source, Chilton, Didcot, Oxfordshire, OX11 0DE, UK.   https://orcid.org/0000-0003-4074-2319
+Larissa Ishibe Veiga
+Diamond Light Source
+Sarnjeet Dhesi
+Diamond Light Source   https://orcid.org/0000-0003-4966-0002
+Mauro Spera
+Università Cattolica del Sacro Cuore   https://orcid.org/0000-0001-9041-364X
+Jin Seo
+KU Leuven   https://orcid.org/0000-0003-4937-0769
+Jean-Pierre Locquet
+https://orcid.org/0000-0002-4214-7081
+Michele Fabrizio
+International School for Advanced Studies   https://orcid.org/0000-0002-2943-3278
+Mariela Menghini
+IMDEA Nanoscience   https://orcid.org/0000-0002-1744-798X
+Article
+
+Keywords:
+
+Posted Date: June 6th, 2024
+
+DOI: https://doi.org/10.21203/rs.3.rs-4019377/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on October 31st, 2024. See the published version at https://doi.org/10.1038/s41467-024-53726-z.
+Mott resistive switching initiated by topological defects
+
+Alessandra Milloch,1,2,3,* Ignacio Figueruelo-Campanero,4,5,† Wei-Fan Hsu,3 Selene Mor,1,2 Simon Mellaerts,3 Francesco Maccherozzi,6 Larissa Ishibe Veiga,6 Sarnjeet S. Dhesi,6 Mauro Spera,1 Jin Won Seo,7 Jean-Pierre Locquet,3 Michele Fabrizio,8 Mariela Menghini,4 and Claudio Giannetti1,2,9,‡
+1Department of Mathematics and Physics, Università Cattolica del Sacro Cuore, Brescia I-25133, Italy
+2ILAMP (Interdisciplinary Laboratories for Advanced Materials Physics), Università Cattolica del Sacro Cuore, Brescia I-25133, Italy
+3Department of Physics and Astronomy, KU Leuven, B-3001 Leuven, Belgium
+4IMDEA Nanociencia, Cantoblanco, 28049 Madrid, Spain
+5Facultad Ciencias Físicas, Universidad Complutense, 28040 Madrid, Spain
+6Diamond Light Source, Didcot, Oxfordshire OX11 0DE, UK
+7Department of Materials Engineering, KU Leuven, 3001 Leuven, Belgium
+8Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy
+9CNR-INO (National Institute of Optics), via Branze 45, 25123 Brescia, Italy
+
+Avalanche resistive switching is the fundamental process that triggers the sudden change of the electrical properties in solid-state devices under the action of intense electric fields [1]. Despite its relevance for information processing, ultrafast electronics, neuromorphic devices, resistive memories and brain-inspired computation [1–14], the nature of the local stochastic fluctuations that drive the formation of metallic regions within the insulating state has remained hidden.
+
+Here, using operando X-ray nano-imaging, we have captured the origin of resistive switching in a V2O3-based device under working conditions. V2O3 is a paradigmatic Mott material [3], which undergoes a first-order metal-to-insulator phase transition together with a lattice transformation that breaks the threefold rotational symmetry of the rhombohedral metallic phase [2, 5, 6, 8–11, 15]. We reveal a new class of volatile electronic switching triggered by nanoscale topological defects appearing in the shear-strain based order parameter that describes the insulating phase. Our results pave the way to the use of strain engineering approaches to manipulate such topological defects and achieve the full dynamical control of the electronic Mott switching. Topology-driven, reversible electronic transitions are relevant across a broad range of quantum materials, comprising transition metal oxides, chalcogenides and kagome metals.
+
+The insulator-to-metal transition (IMT) in Mott materials is a key mechanism for the development of next generation Motronic devices [3, 13]. The intrinsic correlated nature of the Mott insulating state makes these systems fragile to external stimuli [16, 17], such as the application of an electric field, which can drive the collapse of the electronic band structure and the sudden release of a large number of free carriers [18, 19]. At the macroscopic level, this phenomenon manifests in the resistive switching process, i.e., a sharp increase of the current flow when the applied voltage exceeds a threshold value [6, 20–27]. This strong non-linearity triggered many efforts to develop neuromorphic building blocks for the hardware implementation of neural networks [14] or for ultrafast volatile and non-volatile memories or processors [12, 28, 29]. The state-of-the-art macroscopic models [30] are based on resistor networks that consider interconnected nodes transforming from the insulating to metallic state in the presence of an electric field. Above a certain threshold, a percolative, avalanche transition takes place, thus leading to the formation of conductive filaments and the consequent sudden drop in resistivity [22, 31].
+
+The full control and exploitation of this process is currently prevented by a limited knowledge of the early-stage firing dynamics. Microscopically, little is known about the nature of the nanoscale regions that trigger the avalanche process. Also the relation between the electronic and structural properties of the switched regions and those of the pristine insulating template is a matter of debate. Pioneering optical microscopy experiments captured the real-time formation of macroscopic metallic channels [4, 32–35], but lacked the resolution and sensitivity to address the microscopic origin of the switching process.
+
+Here, we adopt resonant X-ray microscopy to record nanoscale snapshots of the switching dynamics in a V2O3-based nanodevice during the application of an electric field. The results unveil the fundamental role played by the order parameter topology of the underlying lattice nanotexture. The breaking of the \( C_3 \) symmetry upon transition to the insulating monoclinic phase leads to the formation of three twin shear-strain domains with boundaries oriented along the three hexagonal directions [36, 37]. The geometrical constraints then produce shear-strain topological defects at the corners of monoclinic domains crossing with an angle of 60°. These nanoscale
+FIG. 1. a) Non-primitive hexagonal unit cell of the V2O3 high-temperature rhombohedral metallic phase. b) Schematic of the rhombohedral-to-monoclinic distortion along each of the three equivalent hexagonal axes. c) PEEM experimental setup. X-ray radiation, with tunable energy resonant with the vanadium L_{2,3} edge, impinges on the sample surface and the emitted electrons are collected and imaged through electrostatic and magnetic lenses. The V2O3 film is coated with gold metal electrodes, allowing to drive a current through the device (see sketch of a typical resistive switching current-voltage curve in the bottom panel) while simultaneously acquiring XLD-PEEM images.
+
+topological defects act as seeds for the formation of the metallic phase, thus triggering the macroscopic volatile resistive switching.
+
+V2O3 is a prototypical Mott insulator that undergoes a thermally-driven transition from a high-temperature paramagnetic, rhombohedral metal to a low-temperature antiferromagnetic monoclinic insulator [38–40]. The lattice transformation at the critical temperature \( T_{IMT} \) implies the breaking of the \( C_3 \) symmetry of the non-primitive hexagonal unit cell of the high-temperature metallic phase (see Fig. 1a). The structural transition can thus be described [37] by a vector order parameter:
+
+\[
+\vec{\epsilon} = (\epsilon_{31}, \epsilon_{23}) = \epsilon \left( \cos \phi_n, \sin \phi_n \right)
+\]
+
+associated to the shear strain components \( \epsilon_{31} \) and \( \epsilon_{23} \) that characterize the monoclinic distortion. Below \( T_{IMT} \), the amplitude of the order parameter, \( \epsilon \), becomes non-zero, while the phase can assume three different values:
+
+\[
+\phi_n = (2n - 1) \frac{\pi}{3}
+\]
+
+corresponding to the distortion along the three equivalent hexagonal axes of the rhombohedral phase, indicated in the following by the versors \( \hat{e}_n,\ n=1,2,3 \) (see Fig. 1b)).
+
+Resistive switching can be induced by applying an electric field across a patterned micro-gap at temperatures close to \( T_{IMT} \) [4, 33, 41]. The resistive switching device investigated here is formed by a 20 nm V2O3 film coated with gold electrodes. V2O3 is grown by oxygen-assisted Molecular Beam Epitaxy on a (0001)-Al2O3 substrate with a 40 nm Cr2O3 buffer layer to reduce any interfacial residual strain [42]. The resulting V2O3 film has the c axis oriented parallel to the surface normal, with \( T_{IMT} = 145 \) K (see Supplementary Information Fig. S1). Two gold electrodes allow the application of an electric bias across the gap of width \( w = 2 \) μm and length \( l = 30 \) μm (figure 1c)). The gap region between the electrodes is imaged using PhotoEmission Electron Microscopy (PEEM), combined with X-ray Linear Dichroism (XLD) at the L_{2,3} vanadium edge (513-530 eV, see Figure S2) [36, 37, 43]. The XLD-PEEM images are obtained from the normalized difference between images recorded with the light electric field vector, \( \vec{E} \), perpendicular and 16° to the surface normal at a photon energy 520.6 eV. Since the XLD signal depends on the angle between the in-plane component of \( \vec{E} \) and the position dependent order parameter, \( \vec{\epsilon}(r) \) [37] (see Fig. 1b and c)), this technique provides a map - with ~30 nm spatial resolution - of the
+three different monoclinic domains during the resistive switching process.
+
+Figure 2a) shows an XLD-PEEM image obtained in the monoclinic insulating phase at \( T = 120 \) K. The V$_2$O$_3$ nanotexture exhibits features typical of the monoclinic insulating phase [36, 37]. Monoclinic domains with different \( \phi_n \) give rise to different XLD contrast, which can be identified as different color intensities within the XLD-PEEM image. The minimization of the total strain leads to the formation of stripe-like domains, with symmetry-constrained directions [37]. Each monoclinic insulating domain extends over a few micrometers, thus connecting the two electrodes, and it is characterized by a width \( w_{dom} \sim 200 \) nm [37].
+
+The XLD-PEEM imaging is then repeated while driving a current, \( I \), through the device and measuring the voltage drop, \( V \), across the gold contacts. Figures 2b)-j) show the XLD-PEEM images acquired at increasing values of \( I \), following the upward branch of the hysteresis cycle. The presence of an in-plane electric field across the electrodes introduces a weak image blurring that becomes significant for \( V \geq 6-8 \) V. Despite this, the nanodomains are well resolved during the resistive switching process, which first manifests itself at the voltage drop observed between 0.08 mA and 1.1 mA (Fig. 2 c) and d) respectively). As the current is further increased, the melting of the monoclinic nanotexture in the region delimited by white dashed lines (Fig. 2 e)-j)) progresses with a widening channel with a homogenous intensity. The XLD contrast measured in the region between the white dashed lines corresponds to the signal of the high-temperature rhombohedral phase. This is also confirmed from the angle dependence of the XLD signal [37]. As shown in the Supplementary Information Fig. S3, images collected with two different X-rays polarization angles, with respect to the in-plane V$_2$O$_3$ axes, show no intensity variation upon sample rotation in the metallic channel, as opposed to the lateral monoclinic domains, for which the XLD signal depends on the angle between the light polarization and \( \vec{e}'(r) \). The constant XLD contrast region in the middle of the gap therefore appears due to the formation of a metallic channel with rhombohedral lattice structure (\( \epsilon=0 \)). XLD-PEEM images obtained under the same conditions, but with a larger field of view, capture the whole gap of the device (see Supplementary Information Fig. S4). The metallic channel consistently forms in the same location within the gap with no additional metallic paths observed. Furthermore, when the applied current is removed, the metallic channel disappears and the monoclinic domains reappear with the same pre-switching configuration, indicating a volatile process.
+
+The formation of the metallic channel is pinned by a specific topology of the lattice nanotexture, characterized by V-shaped domains, i.e. at the crossing point of domains with the same \( \phi_n \) with directions that differ by \( \pi/3 \). Fig. 3a) shows a detail of the switching region, using a colorscale that highlights the three different domains with a monoclinic distortion along \( \hat{\epsilon}_1 \) (red, \( \phi_1=\pi/3 \)), \( \hat{\epsilon}_2 \) (blue, \( \phi_2=\pi \)) and \( \hat{\epsilon}_3 \) (yellow, \( \phi_3=5\pi/3 \)). The stabilization of the monoclinic nanotexture is driven by the Saint-Venant compatibility condition [37], which ensures a continuity of the medium during a deformation
+
+<table>
+  <tr>
+    <th>Applied current I</th>
+    <th>Measured voltage V</th>
+  </tr>
+  <tr>
+    <td>0 mA</td>
+    <td>0 V</td>
+  </tr>
+  <tr>
+    <td>0.04 mA</td>
+    <td>3.8 V</td>
+  </tr>
+  <tr>
+    <td>0.08 mA</td>
+    <td>6.5 V</td>
+  </tr>
+  <tr>
+    <td>1.1 mA</td>
+    <td>3.9 V</td>
+  </tr>
+  <tr>
+    <td>1.5 mA</td>
+    <td>4.0 V</td>
+  </tr>
+  <tr>
+    <td>3.0 mA</td>
+    <td>4.3 V</td>
+  </tr>
+  <tr>
+    <td>4.5 mA</td>
+    <td>4.5 V</td>
+  </tr>
+  <tr>
+    <td>6.0 mA</td>
+    <td>4.6 V</td>
+  </tr>
+  <tr>
+    <td>7.5 mA</td>
+    <td>4.9 V</td>
+  </tr>
+  <tr>
+    <td>10 mA</td>
+    <td>5.3 V</td>
+  </tr>
+</table>
+
+FIG. 2. XLD-PEEM images before (a) and during (b-j) the application of an electric current at \( T = 120 \) K. The homogeneous regions at the top and bottom of each image are the gold electrodes. The area in between is the exposed V$_2$O$_3$ antiferromagnetic monoclinic phase, exhibiting a striped domain nanotexture. For currents larger than 1.5 mA, the striped domains disappear in the region delimited by the white dashed lines, demonstrating the appearance of a rhombohedral metallic filament, which widens as the current is increased.
+FIG. 3. a) Detail of the XLD-PEEM image shown in Fig. 2 in the region where the metallic filament is formed upon the application of a current above the threshold \( I_{th} \). b) Schematic of the monoclinic domains crossing at 60° and forming a topological defect. Blue, red and yellow areas identify the three possible monoclinic domains corresponding to the three equivalent order parameter directions \( \hat{\epsilon}_n \). The order parameter at the boundaries between different domains is oriented along \( \hat{\epsilon}_1 + \hat{\epsilon}_2 \) (2π/3) for the red-blue interface and along \( \hat{\epsilon}_2 + \hat{\epsilon}_3 \) (4π/3) for the blue-yellow interface. The mixed red-yellow triangular region indicates the local suppression of the strain at the topological defect. The energy functionals shown on the left and right, illustrate how a topological defect (green plot, solid line) decreases the insulator-metal energy difference, Δ.
+
+via the curl-free condition:
+
+\[
+\nabla \times \vec{\epsilon}(r) = 0.
+\]
+
+The conservation of the parallel component of \( \vec{\epsilon}(r) \) across an interface between two different domains has two important implications:
+
+i) the interface between two different monoclinic domains is oriented along \( \hat{\epsilon}_n \) of the third domain;
+
+ii) the interface between a monoclinic and a rhombohedral metallic domain is oriented perpendicularly to \( \hat{\epsilon}_n \) of the monoclinic domain.
+
+If we consider, for example, a domain with order parameter along \( \hat{\epsilon}_2 \) (blue in Figure 3b)), its interface is oriented along \( \hat{\epsilon}_1 \), i.e. at π/3 angle, when it neighbours an \( \hat{\epsilon}_2 \) domain (yellow), whereas it is oriented along \( \hat{\epsilon}_3 \), i.e. at 2π/3 angle, when it neighbours an \( \hat{\epsilon}_1 \) domain (red), in agreement with the nanotexture reported in Fig. 3. The Saint-Venant condition corresponds to a fixed phase jump \( \delta \phi = 2\pi/3 \) of \( \vec{\epsilon}(r) \) across any interface between two monoclinic domains. We note that this condition is satisfied throughout the nanotextured domain structure, except at the V-shaped vertex structure formed by two \( \epsilon_2 \) domains with boundaries oriented along \( \hat{\epsilon}_1 \) and \( \hat{\epsilon}_3 \). If we consider a circuit \( \Gamma_1 \) across the boundary between two striped domains, the total phase shift is given by \( \delta \phi = +2\pi/3 - 2\pi/3 = 0 \) thus adhering to the curl-free condition in Eq. 3. In contrast, the topology of the V-shaped structure is such that, if we move around the internal apex (\( \Gamma_2 \)), the total phase-shift is constrained to \( \delta \phi = +2\pi/3 + 2\pi/3 = 4\pi/3 \), thus breaking the curl-free condition. The consequence is that the vertex of the V-shaped domains acts as a topological defect with a fractional Hopf index (see Supplementary Information Section S6). These topological defects are inherently characterized by the strong frustration of the local value of the order parameter \( \vec{\epsilon}(r) \) and fluctuations on spatial and temporal scales that cannot be captured by the present experiment. We further note that the formation of the topological defect is a direct and unavoidable consequence of the quasi-1D confined geometry of the system. Whereas the component of the order parameter parallel to the electrodes (\( \epsilon_{||} \), see Fig. 3b) can be compensated outside the gap, the perpendicular component (\( \epsilon_{\perp} \)) has to be minimized to avoid the accumulation of excessive strain energy within the gap region. Thus, considering the directions of \( \vec{\epsilon}(r) \) at the boundaries between different monoclinic domains (see Fig. 3b), the formation of V-shaped domains is a unique configuration that fulfils the requirement \( \epsilon_{\perp} = 0 \).
+
+The suppression of the symmetry-breaking order parameter, \( \vec{\epsilon}(r) \), at topological defects has far-reaching implications related to the nature of the resistive switching process. The electronic IMT can be described by a scalar order parameter \( \eta(r) \) [37], which depends on the position \( r \) and is such that \( \eta = -1 \) in the metallic state and \( \eta = +1 \) in the insulating state. The coupling between the electronic and structural transitions can be described by the energy functional [37]:
+
+\[
+F[\epsilon, \eta] \propto \int dr \left\{ (\eta^2(r) - 1)^2 - g(\epsilon^2(r) - \epsilon_t^2(V)) \eta(r) \right\},
+\]
+
+where \( g \) is the coupling between the electronic order parameter and the strain and \( \epsilon_t(V) \) is a threshold parameter that controls the first-order IMT and can depend on the applied voltage \( V \). When \( \epsilon^2(r) > \epsilon_t^2(V) \), the insulating phase with \( \eta = +1 \) is locally favoured, whereas for strain smaller than the threshold value, i.e. \( \epsilon^2(r) < \epsilon_t^2(V) \), the metallic solution is stabilized. \( \epsilon_t^2(V) \) thus represents the threshold above which the insulating monoclinic state (\( \eta = +1, \epsilon \neq 0 \)) becomes stable. The description of the electric-field induced transition is based on the observation [18] that the electric field directly couples to the electronic bandstructure of a Mott insulator, making the metallic phase more stable. The transition can thus be described assuming that \( \epsilon_t^2(V) \) increases with increasing \( V \). The energy difference between the insulating and metallic phase can be expressed as \( \Delta(r, V) = F[-1] - F[+1] \simeq g [\epsilon^2(r) - \epsilon_t^2(V)] \). If we start from the insulating phase with \( \epsilon^2(r) > \epsilon_t^2(V = 0) \), the IMT takes place when \( V \) is increased up to the point
+FIG. 4. a) I-V curve measured during the XLD-PEEM imaging. The sudden drop in the voltage measured at \( I_{th} = 1.05 \) mA indicates the first resistive switch. b) Line profiles of the XLD-PEEM images in Fig. 2. The grey shaded area indicates the progressive widening of the metallic rhombohedral filament. The direction of the line profiles is shown by the white dashed line in the XLD-PEEM image on top, where we report a detail of Fig. 2j. c) Width, \( d \), of the metallic filament as a function of current. The blue/red markers represent the values of \( d \) obtained from the XLD-PEEM images below/above \( I_{th} \). The green solid line shows an estimate of \( d \), derived from a parallel resistors model predicting a sudden jump of \( d \) to 200 m at \( I_{th} \) (see Supplementary Information Section S5).
+
+that \( \Delta(r, V) = 0 \). A topological defect, which locally suppresses \( \epsilon^2(r) \), thus acts as a seed with a lower threshold compared to the rest of the system.
+
+Intriguingly, we also note from Eq. 4 that the IMT can take place at a non-zero value of \( \epsilon^2(r) \), which allows the formation of a non-thermal metallic state (\( \eta = -1 \)) with a finite monoclinic distortion (\( \epsilon^2(r) \lesssim \epsilon_t^2(V) \)), as already observed in non-equilibrium optical experiments [37, 44]. The nature of the early-stage switching process can be inferred by a direct comparison between the electrical state of the device and the melting of the monoclinic domains. The \( I - V \) curve of the device, as measured *in-situ* during the PEEM imaging, is plotted in Fig. 4a).
+
+XLD-PEEM images were recorded at specific values of \( I \). The \( I - V \) plot shows that the first resistive switching event occurs at the threshold current \( I_{th} = 1.05 \) mA. In Figure 4b) we report a linecut of the XLD-PEEM image acquired at specific values of \( I \); the image profile is taken along a line crossing the monoclinic domains in the middle of the device gap (see white solid line in Fig. 4, top panel). For large currents running through the device, the line profile in Fig. 4b) displays a flat region, which indicates the melting of the monoclinic nanodomains due to the formation of the rhombohedral metallic channel. As highlighted by the grey area in Fig. 4b), the width \( d \) of the metallic filament increases with the current, from
+\( d = 0.23 \pm 0.05 \) \( \mu m \) at \( I = 1.5 \) mA to \( d = 3.7 \pm 0.2 \) \( \mu m \) at \( I = 10 \) mA.
+
+Modelling the device as a circuit with two parallel resistors (see Supplementary Information Section S5) allows an estimation of \( d \) of the rhombohedral filament corresponding to the observed voltage drop. For large currents running through the device, the experimentally determined values of \( d \) match well with those predicted for a metallic channel forming in the gap, which has the resistivity of the high-temperature rhombohedral phase, as shown in Fig. 4. However, in correspondence of the first resistive switching event at \( I_{th}=1.05 \) mA, the model predicts the sudden formation of a \( \sim 200 \) nm wide metallic rhombohedral filament, which is not visible in the XLD-PEEM images (see Fig. 4c and Supplementary Information Fig. S5), despite being well above the experimental resolution of the microscope. To explain this discrepancy, one might suspect that a rhombohedral metallic filament forms below the surface of the V$_2$O$_3$ film, where it is not detected by PEEM which has a surface sensitivity limited to the first few nanometers. In fact, two arguments act against this possibility: i) the presence of the Cr$_2$O$_3$ buffer layer reduces the substrate-film lattice mismatch from 4.2% to 0.1%, thus almost entirely removing the residual epitaxial strain in the film [42], which is known to suppress the monoclinic phase and favour interfacial metallicity [42, 45]. In contrast to highly-strained films, in which the metal to insulator resistivity jump is strongly suppressed [45], the films in the present study display the 5-order of magnitude resistivity change typical of the unstrained metal-to-insulator transition (see Fig. S1); ii) the curl-free conditions force the interface between monoclinic and rhombohedral metallic regions to be oriented perpendicularly to the order parameter of the monoclinic domain. The formation of a sub-surface metallic layer would lead to a sharp (\( \ll 20 \) nm) monoclinic-rhombohedral interface parallel to \( \vec{c} \), thus leading to a dramatic increase of the strain energy of the system. Our results are compatible with a complex scenario in which the topology-driven resistive switching likely occurs via the sudden transformation of a single 200 nm wide insulating monoclinic domain into a metallic channel with a non-thermal monoclinic lattice structure. At a second stage, the Joule heating leads to the thermally driven monoclinic-to-rhombohedral structural transition and the formation of rhombohedral metallic channels perpendicular to both the metallic electrodes and the \( \varepsilon_2 \) order parameter direction, as observed in Fig. 2.
+
+The X-ray-based nanoimaging of a Mott device under operating conditions allowed us to simultaneously capture the formation of nanoscale conductive paths and the topology of the underlying symmetry-broken nanotexture. The present results expand our knowledge of the resistive switching process in Mott materials by demonstrating the leading role of inherent topological defects in initiating the avalanche process. The methodologies used in this work imply that nanoscale strain engineering approaches could unlock a gate to manipulating topological defects and controlling the electronic switching dynamics in real devices, such as Mott-transition-based RRAM [46, 47], Mott memristor [48–50] and artificial neurons [51, 52]. The concept of topology-driven resistive switching will be key to assessing the possible non-thermal nature of the early stage electronic phase [37] as well as the microscopic origin of memory and non-volatile effects recently observed in Mott devices [6]. We note that the relation between topological defects and electronic phase transitions established here is a general concept, potentially extendable to other systems that undergo first-order phase transitions accompanied by a symmetry breaking, as described by the energy functional (4). Relevant examples embrace transition-metal oxides [3, 53], such as vanadates, nickelates and manganites, and layered materials, such as 1T-TaS$_2$ [54–57], in which the IMT is accompanied by charge-, lattice- and orbital-ordered states with reduced symmetry. Further platforms include cuprate superconductors [58] and kagome metals [59] in which light- or magnetic-induced discontinuous electronic transitions coexist with charge-order. Topological defects in the order parameter therefore provide a framework for understanding non-equilibrium electronic phase transitions, allowing all-optical control of hidden states of matter in a broad class of quantum materials [57, 60–64].
+
+We thank Diamond Lights Source for the provision of beamtime under proposal numbers MM-27218, MM-31711 and MM-34455. We thank Manuel R. Osorio and Fernando J. Urbanos for the fabrication of sample electrodes at the Centre for Micro and Nanofabrication of IMDEA Nanociencia. A.M., S.M. and C.G. acknowledge financial support from MIUR through the PRIN 2015 (Prot. 2015C5SEJJ001) and PRIN 2017 (Prot. 2017ZH2SC4_005) programs and from the European Union - Next Generation EU through the MUR-PRIN2022 (Prot. 2022YCYY7) program. C.G. acknowledges support from Università Cattolica del Sacro Cuore through D.I. D.2.2 and D.3.1 grants. S.M. acknowledges partial financial support through the grant “Finanziamenti poute per bandi esterni” from Università Cattolica del Sacro Cuore. I.F.C. and M.M. acknowledge support from the “Severo Ochoa” Programme for Centres of Excellence in R&D (CEX2020-001039-S) and the Spanish AEI-MCIN PID2021-122980OB-C52 (ECOSOX-ECLIPSE). I.F.C holds a FPI fellowship from the Spanish AEI-MCIN (PRE2020-092625). W.-F.H., S.M., J.W.S. and J.-P.L. acknowledge financial support by the KU Leuven Research Funds Project No. C14/21/083, iBOF/21/084, KAC24/18/056 and C14/17/080, as well as the FWO AKUL/13/19 and AKUL/19/023, and the Research Funds of the INTERREG-E-TEST Project (EMR113) and INTERREG-VL-VL-PATHFINDER Project (0559).
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SIV2O3ResistiveSwitching.pdf

0ab7b0bb9760a2d34a3e8c55df78035e6e4b32c3b6a2028b02979e3615445422/peer_review/peer_review.md

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+Peer Review File
+
+Decreased cloud cover partially offsets the cooling effects of surface albedo change due to deforestation
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+Review of "Decreased cloud cover partially offsets the cooling effects of surface albedo change due to deforestation" by Luo et al.
+
+The work by Luo and co-workers addresses the response of the climate system to large-scale perturbations in forests cover, in particular the response of cloud cover to deforestation. I consider this work timely, as it builds on several recent papers highlighting the significance of the cloud response. This work goes further than the previous studies by focussing on the vertical structure of the cloud response, and by putting the cloud response in perspective of the well-known land surface albedo effects. The authors also did a good job in presenting the study in a concise way. Besides some minor issues, I found the manuscript to be extremely well written. Overall, I believe the manuscript can provide important new insight into the debate of how forests impact climate, and Nature Communications would be a suitable outlet. Having said that, I believe the manuscript can further be improved on several issues. There are discussed in more detail below.
+
+The title of the manuscript suggests a focus on temperature ("cooling") and albedo, yet neither is really discussed in detail directly. While I can see why this is challenging, perhaps the authors can put the land surface albedo response into perspective with the local planetary albedo response (which includes the cloud cover effect). This would at least give two variables that can be directly compared.
+
+A second issue is the lack of quantitative results. Overall, the results are more descriptive (largely based on a comparison of patterns), and the authors seem to have put in little effort to make these comparisons more objective. In my view, it would improve the manuscript if the comparison and conclusions would be more quantitative.
+
+Some minor issues:
+- While I don’t object to the use of MODIS data (Line 100), I believe it is important to point out that MODIS provides data only for given times in the diurnal cycle. This time might miss the peak of forest impact on clouds, as was for instance reported by Teuling et al. (ref 23) based on a detailed comparison between MSG and MODIS.
+- Line 136: what is “10 data”?
+- Line 170, caption Fig 2: turbulent heat flux -> turbulent heat fluxes
+
+Reviewer #2 (Remarks to the Author):
+
+The manuscript addresses the indirect biophysical effects of forests on clouds and their radiative
+forcing, a topic of significant importance that is currently not well understood. I also share the same view that the impact of deforestation on cloud vertical profiles has been underexplored. Understanding the alterations of cloud vertical profiles is key to comprehending the subsequent changes in cloud radiative effects.
+
+This paper makes an attempt to use observations to indicate how deforestation might influence cloud profiles. However, the discussion lacks depth regarding the mechanisms behind vertical changes in cloud fraction. A more detailed discussion/exploration of these mechanisms would greatly enhance the manuscript's contribution to the field.
+
+Furthermore, while the methodology section provides a basis for the research conducted, there is room for improvement to make the methods more clear. This enhancement is achievable.
+
+My primary concern lies with the interpretation of the results, particularly those presented in Figures 2 and 3. The current interpretation does not seem robust enough to support the conclusions drawn. A more thorough analysis and discussion would help solidify these findings.
+
+In addition, the manuscript would benefit from a deeper exploration of how land cover change and different land covers influence cloud formation among past published work.
+
+I recommend that the authors undertake a significant revision of the manuscript. My comments are listed below for your consideration:
+
+Major:
+
+Lines 160-164: The authors reach a conclusion that the decrease in sensible heat (SH) being attributed to changes in incoming solar radiation and a drop in land surface temperature (LST). But additional information or discussion would be beneficial to understand how these determinations were made. It's important to note that SH is influenced not only by LST but also by factors such as wind speed and the temperature difference between the surface and the air. A similar observation applies to the discussion on latent heat (LH) in lines 166-168. Could the authors elaborate on how these conclusions were reached, considering the broader range of influencing factors?
+
+Lines 155-156: Can you discuss the confidence in these model results and the potential for including or addressing observational data to support the findings?
+
+The cooling effect in the boreal zone as a result of deforestation is supported only by model outputs (Fig. S4). The ERA5 data does not corroborate the cooling effect (Figure S4).
+This prompts questions regarding the reliability of these climate models, especially in their ability to accurately simulate processes like secondary circulation, which significantly influences cloud formation over varying land covers. Also, this important mechanism has not been discussed or referenced in the manuscript.
+Lines 126-127, the statement highlights that deforestation's impact on cloud cover is particularly notable in tropical low-level clouds, with observed reductions in tropical high-level clouds (>500 hPa) as well. Could you provide further clarification or evidence on why deforestation's effects are more pronounced in low-level clouds compared to high-level ones?
+
+Line 297: When deriving the local effect by subtracting the interpolated non-local effect from the total effect, there seems to be a potential for high uncertainty. This method appears to involve subtracting one large value from another to obtain a much smaller value. Could this approach significantly amplify the uncertainty in the calculated local effect?
+
+Line 107: The correlation coefficients between ERA5 and CALIPSO-CloudSat retrievals for the 4-year average cloud profiles in the boundary layer are between 0.4 to 0.7, indicating only a moderate correlation. This level of correlation may be acceptable in the upper layers, but it raises concerns in the boundary layer. This layer is critical due to its significant shallow convection activity, which is closely coupled with land surface processes.
+
+Minor:
+
+Lines 294-297: Could you clarify what is meant by “unaltered” in the context of your methodology? Additionally, the explanation of how local effects are isolated from GCMs is unclear to me, particularly the process described as 'spatially interpolate the non-local signal to the adjacent deforested regions, maintaining the original values over the unaltered grids unchanged.'
+
+For Figure 2, consider integrating the subfigures from Figure S5 that detail the SH and LH. Those results from SH and LH separately are worth in-depth discussions.
+
+Figure 1, the colorbar ranges differ, which may affect the interpretation of data at a glance. Is there a specific reason for not standardizing the colorbar ranges (e.g., using a consistent range like -2 to 2 or -1 to 1)?
+
+Lines 248 and 292: Repeated information that could be eliminated.
+
+Reviewer #2 (Remarks on code availability):
+
+From my observation, it only contains codes for plotting, and I did not find any readme file.
+Responses to Reviewer #1
+
+Review of "Decreased cloud cover partially offsets the cooling effects of surface albedo change due to deforestation" by Luo et al.
+
+The work by Luo and co-workers addresses the response of the climate system to large-scale perturbations in forests cover, in particular the response of cloud cover to deforestation. I consider this work timely, as it builds on several recent papers highlighting the significance of the cloud response. This work goes further than the previous studies by focusing on the vertical structure of the cloud response, and by putting the cloud response in perspective of the well-known land surface albedo effects. The authors also did a good job in presenting the study in a concise way. Besides some minor issues, I found the manuscript to be extremely well written. Overall, I believe the manuscript can provide important new insight into the debate of how forests impact climate, and Nature Communications would be a suitable outlet. Having said that, I believe the manuscript can further be improved on several issues. There are discussed in more detail below.
+
+Response:
+
+We would like to thank the reviewer for dedicating time in reviewing this manuscript, and also for the positive comments and constructive suggestions.
+
+Comment 1.1:
+The title of the manuscript suggests a focus on temperature ("cooling") and albedo, yet neither is really discussed in detail directly. While I can see why this is challenging, perhaps the authors can put the land surface albedo response into perspective with the local planetary albedo response (which includes the cloud cover effect). This would at least give two variables that can be directly compared.
+
+Response: This is a valuable suggestion which we have followed. We initially discussed the energy budget at the top of the atmosphere (TOA) and found that the changes in longwave radiation due to deforestation are much smaller compared to shortwave radiation. It is therefore reasonable and constructive for the reviewer to suggest that we compare surface albedo to planetary albedo, since albedo is closely linked to temperature changes. We now add an analysis of the changes in TOA albedo under all-sky (planetary albedo change) and clear-sky (here mostly surface albedo change), as well as their difference (cloudy-sky albedo change), respectively, due to deforestation (Fig. R1.1). The results align with our original conclusion: deforestation-induced reduction in cloud cover warms
+the climate, partially counteracting the cooling effects of increased surface albedo by nearly half.
+
+![Global patterns of TOA albedo difference between deforest-glob and piControl simulations under all-sky, clear-sky, and all-sky minus clear-sky circumstances](page_184_120_1080_670.png)
+
+Figure R1.1. Changes in albedo at the top of atmosphere (TOA) due to deforestation. (a, c, and e) Global pattern of the TOA albedo difference between the deforest-glob and piControl simulations (deforest-glob minus piControl), respectively, under all-sky, clear-sky, and all-sky minus clear-sky circumstances. Diagonal hashing indicates four or more of the five models showing the same sign of change. (b, d, and f) ERA5 TOA albedo variations due to deforestation using the space-for-time substitution (see Methods). Global mean values and standard errors for (a-f) are shown in (g). The offset ratio is the proportion of all-sky minus clear-sky to the all-sky value. (h) CMIP6 zonal mean of the TOA albedo difference between the deforest-glob and piControl simulations under both clear-sky and all-sky minus clear-sky circumstances. The CMIP6 data is the ensemble mean of the local effect extracted from multi-model simulations (see Methods).
+Changes in Manuscript:
+[Page 13 Lines 270–273 (in the “Track Changes” version)]
+“From a global average standpoint, the quantitative competition between clouds and surface albedo becomes apparent, showing that deforestation-induced reduction in cloudy-sky albedo partially counteracts the increased surface albedo by nearly half (Fig. S10).”
+
+![World maps showing TOA albedo difference for CMIP6 MME All-sky, ERA5 All-sky, Clear-sky, All-sky minus clear-sky, and bar charts and zonal mean plots for TOA albedo difference](page_349_384_1047_1047.png)
+
+Supplementary Figure 10. Changes in albedo at the top of atmosphere (TOA) due to deforestation. Same as Fig. 3, but for albedo.
+Comment 1.2:
+A second issue is the lack of quantitative results. Overall, the results are more descriptive (largely based on a comparison of patterns), and the authors seem to have put in little effort to make these comparisons more objective. In my view, it would improve the manuscript if the comparison and conclusions would be more quantitative.
+
+Response: We thank the reviewer for this constructive suggestion. Given that the idealized global deforestation simulations and the space-for-time substitution method differ in their principles and also their extent of deforestation, we initially intended to use these two methods to investigate whether there are consistent signals in the responses of cloud vertical structures and their radiative effects to deforestation. Following the reviewer's suggestion, we now calculate the changes in cloud fraction per deforestation fraction (unit: % %^{-1}), representing the local sensitivity of cloud fraction to deforestation (Fig. R1.2). Relative to directly calculating changes in cloud cover due to deforestation, quantifying this sensitivity allows to a certain degree for quantitative comparison of the two methods.
+
+![Local sensitivity of cloud fraction profile to deforestation. (a) Zonal mean of the cloud fraction profile difference between the deforest-glob and piControl simulations (deforest-glob minus piControl) per deforestation fraction. The data is the ensemble mean of the local effect extracted from CMIP6 model simulations (see Methods). The stippling represents four or more of the five models showing the same sign. (b) Zonal mean ERA5 cloud fraction profile variations per latitude.](page_374_682_1002_496.png)
+
+Figure R1.2. Local sensitivity of cloud fraction profile to deforestation. (a) Zonal mean of the cloud fraction profile difference between the deforest-glob and piControl simulations (deforest-glob minus piControl) per deforestation fraction. The data is the ensemble mean of the local effect extracted from CMIP6 model simulations (see Methods). The stippling represents four or more of the five models showing the same sign. (b) Zonal mean ERA5 cloud fraction profile variations per
+deforestation fraction using the space-for-time substitution (open land minus forest; see Methods). Only latitudes possessing more than 10 available samples are considered to ensure representativeness.
+
+Changes in Manuscript:
+
+[Page 5 Lines 125–130 (in the “Track Changes” version)]
+
+“For a quantitative comparison between the GCMs and ERA5, we quantify the sensitivity of cloud fraction profile to deforestation by calculating the changes in cloud fraction per deforestation fraction. Even with distinct principles, both methods show consistency in this specific change across the spatial distribution regarding cloud vertical profile responses to deforestation (Fig. 1).”
+
+![Zonal mean of the cloud fraction profile difference between the deforest-glob and piControl simulations (deforest-glob minus piControl) per deforestation fraction, and zonal mean ERA5 cloud fraction profile variations per deforestation fraction using the space-for-time substitution.](page_496_728_670_370.png)
+
+Fig. 1. Local sensitivity of cloud fraction profile to deforestation. (a) Zonal mean of the cloud fraction profile difference between the deforest-glob and piControl simulations (deforest-glob minus piControl) per deforestation fraction. The data is the ensemble mean of the local effect extracted from CMIP6 model simulations (see Methods). The stippling represents four or more of the five models showing the same sign. (b) Zonal mean ERA5 cloud fraction profile variations per deforestation fraction using the space-for-time substitution (open land minus forest; see Methods). Only latitudes possessing more than 10 available samples are considered to ensure representativeness.
+
+Some minor issues:
+
+Comment 1.3:
+
+- While I don’t object to the use of MODIS data (Line 100), I believe it is important to point out that MODIS provides data only for given times in the diurnal cycle. This time might miss the peak of
+forest impact on clouds, as was for instance reported by Teuling et al. (ref 23) based on a detailed comparison between MSG and MODIS.
+
+Response: We thank the reviewer for this kind reminder. We have now clarified this point in the revision as suggested.
+
+Changes in Manuscript:
+[Page 4 Lines 102–105 (in the “Track Changes” version)]
+“It should be noted that MODIS only provides data for specific times within the diurnal cycle (morning and noon), which may introduce a low-bias on the estimate of forest-cloud impacts in the data \(^{23}\), compared to the model analysis.”
+
+Reference:
+23 Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications **8**, 14065, doi:10.1038/ncomms14065 (2017).
+
+Comment 1.4:
+- Line 136: what is “10 data”?
+
+Response: Sorry for this unclear statement! It means “10 available samples”.
+
+Changes in Manuscript:
+[Page 7 Lines 157–158 (in the “Track Changes” version)]
+“Only latitudes possessing more than 10 available samples are considered to ensure representativeness.”
+
+Comment 1.5:
+- Line 170, caption Fig 2: turbulent heat flux -> turbulent heat fluxes
+
+Response: Corrected.
+Responses to Reviewer #2
+
+The manuscript addresses the indirect biophysical effects of forests on clouds and their radiative forcing, a topic of significant importance that is currently not well understood. I also share the same view that the impact of deforestation on cloud vertical profiles has been underexplored. Understanding the alterations of cloud vertical profiles is key to comprehending the subsequent changes in cloud radiative effects.
+
+Response: We would like to thank the reviewer for dedicating time in reviewing this manuscript, and also for the valuable comments and constructive suggestions.
+
+This paper makes an attempt to use observations to indicate how deforestation might influence cloud profiles. However, the discussion lacks depth regarding the mechanisms behind vertical changes in cloud fraction. A more detailed discussion/exploration of these mechanisms would greatly enhance the manuscript's contribution to the field.
+
+Response: We thank the reviewer for giving this constructive suggestion. We have now added discussions of the mechanisms behind how deforestation impacts cloud vertical structure in the revision, please refer to comment 2.3 and comment 2.1.
+
+Furthermore, while the methodology section provides a basis for the research conducted, there is room for improvement to make the methods more clear. This enhancement is achievable.
+
+Response: We thank the reviewer for raising this point. We have now explained the method in detail in the revision, please refer to comment 2.6.
+
+My primary concern lies with the interpretation of the results, particularly those presented in Figures 2 and 3. The current interpretation does not seem robust enough to support the conclusions drawn. A more thorough analysis and discussion would help solidify these findings.
+
+Response: We thank the reviewer for the valuable comments. In the revision, following the reviewer’s suggestions, we have now provided deeper interpretations of our conclusions and we hope the results will be more robust and solid, please refer to comment 2.1.
+
+In addition, the manuscript would benefit from a deeper exploration of how land cover change and different land covers influence cloud formation among past published work.
+
+Response: Excellent help by the reviewer! We have now included discussions on how different land covers influence cloud formation in the revision, please refer to comment 2.2.
+
+I recommend that the authors undertake a significant revision of the manuscript. My comments are
+listed below for your consideration:
+
+Response: We have now followed the constructive comments by the reviewer and revised as suggested.
+
+Major:
+Comment 2.1:
+Lines 160-164: The authors reach a conclusion that the decrease in sensible heat (SH) being attributed to changes in incoming solar radiation and a drop in land surface temperature (LST). But additional information or discussion would be beneficial to understand how these determinations were made. It's important to note that SH is influenced not only by LST but also by factors such as wind speed and the temperature difference between the surface and the air. A similar observation applies to the discussion on latent heat (LH) in lines 166-168. Could the authors elaborate on how these conclusions were reached, considering the broader range of influencing factors?
+
+Response: We thank the reviewer for this well-spotted point! We have now investigated more factors influencing sensible heat (SH) and latent heat (LH) as suggested.
+
+SH and LH are influenced by the near-surface wind speed and, respectively, are related to the temperature and humidity gradients between the surface and the air, being proportional to the product of the wind speed and the gradient \(^{1,2}\). An increase in wind speed can enhance the heat and water vapor exchange rate between the surface and the air, thereby increasing turbulent fluxes. Additionally, larger temperature and humidity gradients between the surface and the air can intensify turbulent fluxes.
+
+We find that deforestation increases near-surface wind speed due to a decrease in surface roughness (Fig. R2.1). However, this increase in wind speed does not result in higher turbulent fluxes because the reduction in gradient is the dominant factor (Fig. R2.2). The decreased temperature gradient between the surface and the air in the boreal zones resulting from deforestation leads to a reduction in SH. Since there is no proxy for the humidity gradient between the surface and the air, we infer changes in humidity gradient from changes in evapotranspiration (ET). An increase in wind speed is accompanied by a decrease in ET (Fig. R2.3), suggesting that the decreased humidity gradient between the surface and the air caused by deforestation primarily drives the reduction in LH.
+References:
+1  Fairall, C. W., Bradley, E. F., Hare, J. E., Grachev, A. A. & Edson, J. B. Bulk Parameterization of Air–Sea Fluxes: Updates and Verification for the COARE Algorithm. Journal of Climate 16, 571-591, doi:10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2 (2003).
+2  Liao, W. et al. Sensitivities and Responses of Land Surface Temperature to Deforestation-Induced Biophysical Changes in Two Global Earth System Models. Journal of Climate 33, 8381-8399, doi:10.1175/JCLI-D-19-0725.1 (2020).
+
+![Global patterns and box plots showing changes in near-surface wind speed due to deforestation](page_320_624_1008_484.png)
+
+Figure R2.1. Changes in near-surface wind speed due to deforestation. (a) Global pattern of the near-surface wind speed difference between the deforest-glob and piControl simulations (deforest-glob minus piControl). Diagonal hasing indicates four or more of the five models showing the same sign of change. (b) Box plots of the CMIP6 near-surface wind speed differences between the deforest-glob and piControl simulations over both tropical and boreal areas. (c) ERA5 near-surface wind speed variations due to deforestation using the space-for-time substitution (see Methods). (d) Box plots of the ERA5 near-surface wind speed variations due to deforestation. The data in (a-b) is the ensemble mean of the local effect extracted from CMIP6 model simulations (see Methods). Boxes in (b and d) show the 25th to 75th percentiles of the data, whiskers display the 5th to 95th percentiles, horizontal yellow lines in the boxes represent the median values, and red dots are the mean values.
+Figure R2.2. Changes in the product of near-surface wind speed (U) and the surface-air temperature difference (Ts–Ta) due to deforestation. Same as Fig. R2.1 but for the product of U and (Ts–Ta) (unit: K m s^{-1}).
+
+Figure R2.3. Changes in evapotranspiration due to deforestation. Same as Fig. R2.1 but for evapotranspiration (unit: mm day^{-1}).
+Changes in Manuscript:
+[Page 9 Lines 191–204 (in the “Track Changes” version)]
+“Deforestation increases near-surface wind speed due to a decrease in surface roughness (Fig. S6), enhancing the heat and water vapor exchange rate between the surface and the air, thereby increasing turbulent fluxes. Apart from being influenced by the near-surface wind speed, SH and LH, respectively, however, are also related to the temperature and humidity gradients between the surface and the air. The fluxes are proportional to the product of the wind speed and the gradient \(^{52,53}\). We find that the decreased temperature gradient between the surface and the air in the boreal zones resulting from deforestation outweighs the role of near-surface wind speed (Fig. S7), leading to a reduction in SH. Since there is no proxy for the humidity gradient between the surface and the air, we infer changes in humidity gradient from changes in ET. An increase in wind speed is accompanied by a decrease in ET (Fig. S4), suggesting that the decreased humidity gradient between the surface and the air caused by deforestation primarily drives the reduction in LH.”
+
+![Map and boxplots showing changes in evapotranspiration due to deforestation](page_186_682_1077_496.png)
+
+Supplementary Figure 3. Changes in evapotranspiration due to deforestation. Same as Supplementary Fig. 2 but for evapotranspiration (unit: mm day\(^{-1}\)).
+Supplementary Figure 5. Changes in near-surface wind speed due to deforestation. Same as Supplementary Fig. 2 but for near-surface wind speed (unit: m s^{-1}).
+
+Supplementary Figure 6. Changes in the product of near-surface wind speed (U) and the surface-air temperature difference (Ts–Ta) due to deforestation. Same as Supplementary Fig. 2 but for the product of U and (Ts–Ta) (unit: K m s^{-1}).
+References:
+52 Fairall, C. W., Bradley, E. F., Hare, J. E., Grachev, A. A. & Edson, J. B. Bulk Parameterization of Air–Sea Fluxes: Updates and Verification for the COARE Algorithm. Journal of Climate 16, 571-591, doi:10.1175/1520-0442(2003)016<0571:BPOASF>2.0.CO;2 (2003).
+53 Liao, W. et al. Sensitivities and Responses of Land Surface Temperature to Deforestation-Induced Biophysical Changes in Two Global Earth System Models. Journal of Climate 33, 8381-8399, doi:10.1175/JCLI-D-19-0725.1 (2020).
+
+Comment 2.2:
+Lines 155-156: Can you discuss the confidence in these model results and the potential for including or addressing observational data to support the findings?
+The cooling effect in the boreal zone as a result of deforestation is supported only by model outputs (Fig. S4). The ERA5 data does not corroborate the cooling effect (Figure S4).
+This prompts questions regarding the reliability of these climate models, especially in their ability to accurately simulate processes like secondary circulation, which significantly influences cloud formation over varying land covers. Also, this important mechanism has not been discussed or referenced in the manuscript.
+
+Response: This is a very good question by the reviewer. We agree with the reviewer that models have limitations in accurately capturing the real processes, which we have now discussed in the revision. To mitigate uncertainties, we used ensemble mean results from five available models. Grids where four or more of the five models exhibited the same sign were highlighted in all figures, demonstrating there is often a high consistency among the models. The results from CMIP6 models agree with previous studies, both observation-3,4 and simulation-based 5,6, indicating tropical warming and boreal cooling due to deforestation. However, it should be noted that since the CMIP6 model results are derived from idealized deforestation experiments, they may appear overly simplistic compared to observations.
+
+In addition, the results from ERA5 also carry uncertainties due to the space-for-time substitution method, which we have now discussed in more detail in the revision. This approach relies on space-for-time analogies, using spatial differences in surface temperature between forest and neighboring non-forest as a proxy for estimating temporal changes in biophysical effects. However, as surface temperature is nonlinearly influenced by both radiative and non-radiative processes, some observation-based studies suggest small changes in surface temperature due to deforestation in boreal
+regions \(^{7,8}\), which agrees with our ERA5 results.
+
+As there is no direct way to derive the local effects of deforestation from observations, our purpose is to use these two approaches to estimate the local effects and compare their signal signs. Therefore, we acknowledge the limitations and uncertainties of both methods in calculating the local biophysical effects in the revision.
+
+The reviewer also highlights an important issue that cloud formation differs over varying land covers. We have now added discussions of this aspect in the revision. The type of land cover notably influences cloud formation processes by affecting surface heating, moisture availability, and atmospheric stability \(^{9-11}\). Forests generally promote cloud formation due to high moisture levels and low albedo \(^{12}\), while over deserts, typically fewer clouds form, due to low moisture availability and high albedo \(^{13}\). Grasslands have a moderate effect on cloud formation that is intermediate between forests and deserts \(^{14}\). Urban areas, with their unique heat island effect and pollution, potentially influence cloud properties and formation \(^{15}\). The varying impacts of various land covers on cloud formation also explain why the results of the two methods differ. The CMIP6 models only consider deforestation into grassland, whereas the diverse land covers between adjacent ERA5 grids disrupt the signals.
+
+References:
+3 Lawrence, D., Coe, M., Walker, W., Verchot, L. & Vandecar, K. The Unseen Effects of Deforestation: Biophysical Effects on Climate. Frontiers in Forests and Global Change **5**, doi:10.3389/ffgc.2022.756115 (2022).
+4 Li, Y. et al. Local cooling and warming effects of forests based on satellite observations. Nature Communications **6**, 6603, doi:10.1038/ncomms7603 (2015).
+5 Hua, W., Zhou, L., Dai, A., Chen, H. & Liu, Y. Important non-local effects of deforestation on cloud cover changes in CMIP6 models. Environmental Research Letters **18**, 094047, doi:10.1088/1748-9326/acf232 (2023).
+6 De Hertog, S. J. et al. The biogeophysical effects of idealized land cover and land management changes in Earth system models. Earth System Dynamics **14**, 629-667, doi:10.5194/esd-14-629-2023 (2023).
+7 Su, Y. et al. Asymmetric influence of forest cover gain and loss on land surface temperature. Nature Climate Change **13**, 823-831, doi:10.1038/s41558-023-01757-7 (2023).
+8 Alkama, R. & Cescatti, A. Biophysical climate impacts of recent changes in global forest cover. Science **351**, 600-604, doi: 10.1126/science.aac8083 (2016).
+9 Mahmood, R. et al. Land cover changes and their biogeophysical effects on climate. International Journal of Climatology **34**, 929-953, doi:10.1002/joc.3736 (2014).
+10 Pielke Sr., R. A. et al. Land use/land cover changes and climate: modeling analysis and observational evidence. WIREs Climate Change **2**, 828-850, doi:10.1002/wcc.144 (2011).
+11 Rabin, R. M., Stadler, S., Wetzel, P. J., Stensrud, D. J. & Gregory, M. Observed Effects of Landscape Variability on Convective Clouds. Bulletin of the American Meteorological Society 71, 272-280, doi:10.1175/1520-0477(1990)071<0272:OEOLVO>2.0.CO;2 (1990).
+12 Duveiller, G. et al. Revealing the widespread potential of forests to increase low level cloud cover. Nature Communications 12, 4337, doi:10.1038/s41467-021-24551-5 (2021).
+13 Rosenfeld, D., Rudich, Y. & Lahav, R. Desert dust suppressing precipitation: A possible desertification feedback loop. Proceedings of the National Academy of Sciences 98, 5975-5980, doi:10.1073/pnas.101122798 (2001).
+14 Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications 8, 14065, doi:10.1038/ncomms14065 (2017).
+15 Vo, T. T., Hu, L., Xue, L., Li, Q. & Chen, S. Urban effects on local cloud patterns. Proceedings of the National Academy of Sciences 120, e2216765120, doi:10.1073/pnas.2216765120 (2023).
+
+Changes in Manuscript:
+
+[Page 8 Lines 177–179 (in the “Track Changes” version)]
+“In contrast, the overall biophysical effect of deforestation leads to surface cooling in the boreal zone from GCMs (Fig. S5), which agrees with previous studies from both observations \(^{8,48}\) and simulations \(^{24,49}\).”
+
+[Page 8 Lines 183–186 (in the “Track Changes” version)]
+“However, surface cooling is not as evident from the space-for-time substitution approach, since SAT is nonlinearly influenced by both radiative and non-radiative processes. Previous observation-based studies also suggest small changes in SAT due to deforestation in boreal regions \(^{50,51}\).”
+
+[Page 12 Lines 226–235 (in the “Track Changes” version)]
+“The type of land cover notably influences cloud formation processes by affecting surface heating, moisture availability, and atmospheric stability \(^{54-56}\). Forests generally promote cloud formation due to high moisture levels and low albedo \(^{22}\), while over deserts, typically fewer clouds form, due to low moisture availability and high albedo \(^{57}\). Grasslands have a moderate effect on cloud formation that is intermediate between forests and deserts \(^{23}\). Urban areas, with their unique heat island effect and pollution, potentially influence cloud properties and formation \(^{58}\). The varying impacts of various land covers on cloud formation also explain why the results of the two methods differ. The CMIP6 models only consider deforestation into grassland, whereas the diverse land covers between adjacent ERA5 grids disrupt the signals.”
+
+[Page 18 Lines 383–388 (in the “Track Changes” version)]
+“To mitigate uncertainties, we use ensemble mean results from five available GCMs. Grid points where four or more of the five models exhibited the same sign are highlighted to demonstrate where
+there is a high consistency among the models. However, it should be noted that since the model results are derived from idealized deforestation experiments, they may appear overly simplistic compared to observations.”
+
+[Page 19 Lines 398–400 (in the “Track Changes” version)]
+
+“However, it should be acknowledged that the space-for-time substitution approach also carries uncertainties as it is an indirect method to calculate local biophysical effects.”
+
+References:
+8 Li, Y. et al. Local cooling and warming effects of forests based on satellite observations. Nature Communications 6, 6603, doi:10.1038/ncomms7603 (2015).
+22 Duveiller, G. et al. Revealing the widespread potential of forests to increase low level cloud cover. Nature Communications 12, 4337, doi:10.1038/s41467-021-24551-5 (2021).
+23 Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications 8, 14065, doi:10.1038/ncomms14065 (2017).
+24 Hua, W., Zhou, L., Dai, A., Chen, H. & Liu, Y. Important non-local effects of deforestation on cloud cover changes in CMIP6 models. Environmental Research Letters 18, 094047, doi:10.1088/1748-9326/acf232 (2023).
+48 Lawrence, D., Coe, M., Walker, W., Verchot, L. & Vandecar, K. The Unseen Effects of Deforestation: Biophysical Effects on Climate. Frontiers in Forests and Global Change 5, doi:10.3389/ffgc.2022.756115 (2022).
+49 De Hertog, S. J. et al. The biogeophysical effects of idealized land cover and land management changes in Earth system models. Earth System Dynamics 14, 629-667, doi:10.5194/esd-14-629-2023 (2023).
+50 Su, Y. et al. Asymmetric influence of forest cover gain and loss on land surface temperature. Nature Climate Change 13, 823-831, doi:10.1038/s41558-023-01757-7 (2023).
+51 Alkama, R. & Cescatti, A. Biophysical climate impacts of recent changes in global forest cover. Science 351, 600-604, doi:10.1126/science.aac8083 (2016).
+54 Mahmood, R. et al. Land cover changes and their biogeophysical effects on climate. International Journal of Climatology 34, 929-953, doi:10.1002/joc.3736 (2014).
+55 Pielke Sr., R. A. et al. Land use/land cover changes and climate: modeling analysis and observational evidence. WIREs Climate Change 2, 828-850, doi:10.1002/wcc.144 (2011).
+56 Rabin, R. M., Stadler, S., Wetzel, P. J., Stensrud, D. J. & Gregory, M. Observed Effects of Landscape Variability on Convective Clouds. Bulletin of the American Meteorological Society 71, 272-280, doi:10.1175/1520-0477(1990)071<0272:OEOLVO>2.0.CO;2 (1990).
+57 Rosenfeld, D., Rudich, Y. & Lahav, R. Desert dust suppressing precipitation: A possible desertification feedback loop. Proceedings of the National Academy of Sciences 98, 5975-5980, doi:10.1073/pnas.101122798 (2001).
+58 Vo, T. T., Hu, L., Xue, L., Li, Q. & Chen, S. Urban effects on local cloud patterns. Proceedings of the National Academy of Sciences 120, e2216765120, doi:10.1073/pnas.2216765120 (2023).
+
+Comment 2.3:
+
+Lines 126-127, the statement highlights that deforestation's impact on cloud cover is particularly
+notable in tropical low-level clouds, with observed reductions in tropical high-level clouds (>500 hPa) as well. Could you provide further clarification or evidence on why deforestation's effects are more pronounced in low-level clouds compared to high-level ones?
+
+Response: We thank the reviewer for highlighting this key issue. We have now provided further clarification and evidence on this point. Cloud types that are closely coupled with the surface, meaning they are directly influenced by and interact with surface processes, typically include low-level clouds 16-18. These clouds form and evolve in response to surface heating, moisture fluxes, and other boundary layer processes. Therefore, on a global scale, the impacts of deforestation are expected to be more pronounced on low-level clouds than on high-level clouds. While deep-convection clouds are generally not well-coupled with the surface, surface conditions can influence their initiation 19,20. Thus, the height of deep convective cloud tops can roughly indicate the maximum altitude at which deforestation affects clouds. However, the cloud top height of deep convective clouds varies across regions. Compared to boreal zones, deep convective clouds in tropical regions can reach higher altitudes (Fig. R2.4). Consequently, deforestation can also affect high-level clouds, mostly in tropical regions.
+
+References:
+16 Betts, A. K. Land-Surface-Atmosphere Coupling in Observations and Models. Journal of Advances in Modeling Earth Systems **1**, doi:10.3894/JAMES.2009.1.4 (2009).
+17 Teixeira, J. & Hogan, T. F. Boundary Layer Clouds in a Global Atmospheric Model: Simple Cloud Cover Parameterizations. Journal of Climate **15**, 1261-1276, doi:10.1175/1520-0442(2002)015<1261:BLCIAG>2.0.CO;2 (2002).
+18 Su, T., Li, Z., Zhang, Y., Zheng, Y. & Zhang, H. Observation and Reanalysis Derived Relationships Between Cloud and Land Surface Fluxes Across Cumulus and Stratiform Coupling Over the Southern Great Plains. Geophysical Research Letters **51**, e2023GL108090, doi:10.1029/2023GL108090 (2024).
+19 Wu, C.-M., Stevens, B. & Arakawa, A. What Controls the Transition from Shallow to Deep Convection? Journal of the Atmospheric Sciences **66**, 1793-1806, doi:10.1175/2008JAS2945.1 (2009).
+20 Schumacher, R. S. & Rasmussen, K. L. The formation, character and changing nature of mesoscale convective systems. Nature Reviews Earth & Environment **1**, 300-314, doi:10.1038/s43017-020-0057-7 (2020).
+Figure R2.4. Local sensitivity of cloud fraction profile to deforestation. Same as Fig. 1, but with the addition of grey lines indicating the 2001–2016 zonal average cloud top pressure for iced convective clouds from ISCCP.
+
+Changes in Manuscript:
+[Pages 5–6 Lines 137–147 (in the “Track Changes” version)]
+“Low-level clouds, which are closely coupled with land surface, form and evolve in response to surface heating, moisture fluxes, and other boundary layer processes \(^{41-43}\). Therefore, on a global scale, the impacts of deforestation are expected to be more noticeable on low-level clouds than on high-level clouds. While deep-convection clouds are generally not well-coupled with the surface, surface conditions can influence their initiation \(^{44,45}\). Thus, the height of deep convective cloud tops can roughly indicate the maximum altitude at which deforestation affects clouds. However, the cloud top height of deep convective clouds varies across regions. Compared to boreal zones, deep convective clouds in tropical regions can reach higher altitudes (Fig. S2). Consequently, deforestation can also affect high-level clouds, mostly in tropical regions”
+Supplementary Figure 2. Local sensitivity of cloud fraction profile to deforestation. Same as Fig. 1, but with the addition of grey lines indicating the 2001–2016 zonal average cloud top pressure for iced convective clouds from ISCCP.
+
+References:
+41 Betts, A. K. Land-Surface-Atmosphere Coupling in Observations and Models. Journal of Advances in Modeling Earth Systems **1**, doi:10.3894/JAMES.2009.1.4 (2009).
+42 Teixeira, J. & Hogan, T. F. Boundary Layer Clouds in a Global Atmospheric Model: Simple Cloud Cover Parameterizations. Journal of Climate **15**, 1261-1276, doi:10.1175/1520-0442(2002)015<1261:BLCIAG>2.0.CO;2 (2002).
+43 Su, T., Li, Z., Zhang, Y., Zheng, Y. & Zhang, H. Observation and Reanalysis Derived Relationships Between Cloud and Land Surface Fluxes Across Cumulus and Stratiform Coupling Over the Southern Great Plains. Geophysical Research Letters **51**, e2023GL108090, doi:10.1029/2023GL108090 (2024).
+44 Wu, C.-M., Stevens, B. & Arakawa, A. What Controls the Transition from Shallow to Deep Convection? Journal of the Atmospheric Sciences **66**, 1793-1806, doi:10.1175/2008JAS2945.1 (2009).
+45 Schumacher, R. S. & Rasmussen, K. L. The formation, character and changing nature of mesoscale convective systems. Nature Reviews Earth & Environment **1**, 300-314, doi:10.1038/s43017-020-0057-7 (2020).
+Comment 2.4:
+Line 297: When deriving the local effect by subtracting the interpolated non-local effect from the total effect, there seems to be a potential for high uncertainty. This method appears to involve subtracting one large value from another to obtain a much smaller value. Could this approach significantly amplify the uncertainty in the calculated local effect?
+
+Response: We thank the reviewer for raising this important point. The uncertainty in calculating local effect using this chessboard method is unavoidable and arises from errors of non-local effect interpolation. A previous study \( ^{21} \) employing sparse and extensive idealized deforestation simulations indicates that local effects do not substantially differ between these two types of simulations. The difference between the two local effects of sparse and extensive deforestation simulations is of secondary importance as compared to the local effect itself. This is the case for changes in not only surface temperature, but also other variables like 2-m air temperature and precipitation, etc. We have now clarified this point in the revision.
+
+Reference:
+21 Winckler, J., Reick, C. H. & Pongratz, J. Robust Identification of Local Biogeophysical Effects of Land-Cover Change in a Global Climate Model. Journal of Climate **30**, 1159-1176, doi:10.1175/JCLI-D-16-0067.1 (2017).
+
+Changes in Manuscript:
+[Page 18 Lines 377–382 (in the “Track Changes” version)]
+“Winckler, et al. \( ^{34} \) conducted comparisons between simulations involving both sparse and extensive idealized deforestation, finding small differences in derived local effects from spatial interpolation. The difference between the two local effects of sparse and extensive deforestation simulations is of secondary importance as compared to the local effect itself.”
+
+Reference:
+34 Winckler, J., Reick, C. H. & Pongratz, J. Robust Identification of Local Biogeophysical Effects of Land-Cover Change in a Global Climate Model. Journal of Climate **30**, 1159-1176, doi:10.1175/JCLI-D-16-0067.1 (2017).
+
+Comment 2.5:
+Line 107: The correlation coefficients between ERA5 and CALIPSO-CloudSat retrievals for the 4-year average cloud profiles in the boundary layer are between 0.4 to 0.7, indicating only a moderate correlation. This level of correlation may be acceptable in the upper layers, but it raises concerns in the boundary layer. This layer is critical due to its significant shallow convection activity, which is
+closely coupled with land surface processes.
+
+Response: The reviewer again raises an important point. We agree with the reviewer that the moderate positive correlation between ERA5 and CALIPSO-CloudSat retrievals of boundary layer clouds leads to uncertainties. However, the lower correlations in the boundary layer compared to upper layers are caused by two aspects: one is the data quality of ERA5 itself, and another is the limitation of active satellite sensors on the detection of low-level clouds, especially under conditions of thick upper clouds or strong surface returns. Specifically, CloudSat has issues with radar ground clutter, while CALIPSO has signal attenuation issues from the clouds above the low-level clouds \(^{22-25}\), both of which lead to detection limitations of the boundary layer clouds. Even the state-of-art combined satellite-based radar and lidar do not detect all low-level clouds \(^{22,24}\). We have now acknowledged these uncertainties in the revision.
+
+References:
+22 Blanchard, Y. et al. A Synergistic Analysis of Cloud Cover and Vertical Distribution from A-Train and Ground-Based Sensors over the High Arctic Station Eureka from 2006 to 2010. Journal of Applied Meteorology and Climatology **53**, 2553-2570, doi:10.1175/JAMC-D-14-0021.1 (2014).
+23 Christensen, M. W., Stephens, G. L. & Lebsock, M. D. Exposing biases in retrieved low cloud properties from CloudSat: A guide for evaluating observations and climate data. Journal of Geophysical Research: Atmospheres **118**, 12,120-112,131, doi:10.1002/2013JD020224 (2013).
+24 Liu, Y. Impacts of active satellite sensors’ low-level cloud detection limitations on cloud radiative forcing in the Arctic. Atmos. Chem. Phys. **22**, 8151-8173, doi:10.5194/acp-22-8151-2022 (2022).
+25 Winker, D. M. et al. Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms. Journal of Atmospheric and Oceanic Technology **26**, 2310-2323, doi:10.1175/2009JTECHA1281.1 (2009).
+
+Changes in Manuscript:
+[Pages 4–5 Lines 111–115 (in the “Track Changes” version)]
+“The moderate correlations between ERA5 and satellite-retrieved cloud profiles in the boundary layer are caused by two aspects: one is the data quality of ERA5 itself, and another is the limitation of active satellite sensors on the detection of low-level clouds, especially under conditions of thick upper clouds or strong surface returns \(^{37-40}\).”
+
+References:
+37 Blanchard, Y. et al. A Synergistic Analysis of Cloud Cover and Vertical Distribution from A-Train and Ground-Based Sensors over the High Arctic Station Eureka from 2006 to 2010.
+Journal of Applied Meteorology and Climatology **53**, 2553-2570, doi:10.1175/JAMC-D-14-0021.1 (2014).
+38 Christensen, M. W., Stephens, G. L. & Lebsock, M. D. Exposing biases in retrieved low cloud properties from CloudSat: A guide for evaluating observations and climate data. Journal of Geophysical Research: Atmospheres **118**, 12,120-112,131, doi:10.1002/2013JD020224 (2013).
+39 Liu, Y. Impacts of active satellite sensors' low-level cloud detection limitations on cloud radiative forcing in the Arctic. *Atmos. Chem. Phys.* **22**, 8151-8173, doi:10.5194/acp-22-8151-2022 (2022).
+40 Winker, D. M. et al. Overview of the CALIPSO Mission and CALIOP Data Processing Algorithms. *Journal of Atmospheric and Oceanic Technology* **26**, 2310-2323, doi:10.1175/2009JTECHA1281.1 (2009).
+
+Minor:
+
+Comment 2.6:
+Lines 294-297: Could you clarify what is meant by “unaltered” in the context of your methodology? Additionally, the explanation of how local effects are isolated from GCMs is unclear to me, particularly the process described as 'spatially interpolate the non-local signal to the adjacent deforested regions, maintaining the original values over the unaltered grids unchanged.'
+
+Response: Sorry for the unclear statements! We have now explained the method in detail in the revision. The unaltered grids indicate that the forest cover within these grids remains unchanged in the deforest-glob simulation. Since the cloud cover changes within unaltered forest cover grids are entirely due to non-local effects, we determine the non-local effects within the deforestation grid by interpolating the signals from the surrounding unaltered forest cover grids. As spatial interpolation might alter existing values, we maintain the non-local signals within the unchanged forest cover grids as they are and only derive the non-local signals for the deforested grids.
+
+Changes in Manuscript:
+[Pages 17–18 Lines 361–370 (in the “Track Changes” version)]
+“This method assumes that the unaltered and adjacent deforested grids share the same non-local effect \(^{21,65}\). The unaltered grids indicate that the forest cover within these grids remains unchanged in the deforest-glob simulation. Since the cloud cover changes within unaltered forest cover grids are entirely due to non-local effects, to generate a global map of the non-local effect, we determine the non-local effects within the deforestation grid by interpolating the signals from the surrounding unaltered forest cover grids. As spatial interpolation might alter existing values, we maintain the non-local signals within the unchanged forest cover grids as they are and only derive the non-local signals
+for the deforested grids.”
+
+References:
+21 Xu, R. et al. Contrasting impacts of forests on cloud cover based on satellite observations. Nature Communications 13, 670, doi:10.1038/s41467-022-28161-7 (2022).
+65 Pongratz, J. et al. Land Use Effects on Climate: Current State, Recent Progress, and Emerging Topics. Current Climate Change Reports 7, 99-120, doi:10.1007/s40641-021-00178-y (2021).
+
+Comment 2.7:
+For Figure 2, consider integrating the subfigures from Figure S5 that detail the SH and LH. Those results from SH and LH separately are worth in-depth discussions.
+
+Response: We thank the very good suggestions by the reviewer. We have integrated these two figures into the main text. In addition, the in-depth discussions of the SH and LH are carried out following the reviewer’s suggestion (see comment 2.1).
+
+Changes in Manuscript:
+
+![Global patterns and boxplots of surface turbulent heat flux differences due to deforestation](page_324_624_1002_624.png)
+
+Fig. 2. Changes in surface turbulent heat fluxes due to deforestation. (a) Global pattern of the surface turbulent heat flux (latent heat (LH) + sensible heat (SH)) difference between the deforest-glob and piControl simulations (deforest-glob minus piControl). Diagonal hashing indicates four or
+more of the five models showing the same sign of change. (b) Box plots of the CMIP6 surface turbulent heat flux (LH+SH, LH and SH) differences between the deforest-glob and piControl simulations over both tropical and boreal areas. (c) ERA5 surface turbulent heat flux (LH+SH) variations due to deforestation using the space-for-time substitution (see Methods). (d) Box plots of the ERA5 surface turbulent heat flux (LH+SH, LH and SH) variations due to deforestation. The data in (a-b) is the ensemble mean of the local effect extracted from CMIP6 model simulations (see Methods). Boxes in (b and d) show the 25th to 75th percentiles of the data, whiskers display the 5th to 95th percentiles, horizontal yellow lines in the boxes represent the median values, and red dots are the mean values. (e and f) Same as (a) but for LH and SH, respectively. (g and h) Same as (c) but for LH and SH, respectively.
+
+Comment 2.8:
+
+Figure 1, the colorbar ranges differ, which may affect the interpretation of data at a glance. Is there a specific reason for not standardizing the colorbar ranges (e.g., using a consistent range like -2 to 2 or -1 to 1)?
+
+Response: We thank the reviewer for pointing this out. We have revised this figure and now the two subplots share the same colorbar. Following the suggestion from reviewer#1, we now calculate the changes in cloud fraction per deforestation fraction (unit: % %^{-1}), representing the local sensitivity of cloud fraction to deforestation. Relative to directly calculating changes in cloud cover due to deforestation, quantifying this sensitivity allows comparison of the two methods to a certain degree.
+
+Changes in Manuscript:
+
+![Zonal mean of the cloud fraction profile difference between the deforest-glob and piControl simulations (deforest-glob minus piControl) per deforestation fraction. The data is the ensemble mean of the local effect extracted from CMIP6 model simulations (see Methods). The stippling represents four or more of the five models showing the same sign. (b) Zonal mean ERA5 cloud fraction profile variations per latitude.](page_340_670_768_384.png)
+
+Fig. 1. Local sensitivity of cloud fraction profile to deforestation. (a) Zonal mean of the cloud fraction profile difference between the deforest-glob and piControl simulations (deforest-glob minus piControl) per deforestation fraction. The data is the ensemble mean of the local effect extracted from CMIP6 model simulations (see Methods). The stippling represents four or more of the five models showing the same sign. (b) Zonal mean ERA5 cloud fraction profile variations per
+deforestation fraction using the space-for-time substitution (open land minus forest; see Methods). Only latitudes possessing more than 10 available samples are considered to ensure representativeness.
+
+Comment 2.9:
+
+Lines 248 and 292: Repeated information that could be eliminated.
+
+Response: We thank the reviewer. This part has now been further optimized in the revision.
+
+Comment 2.10:
+
+(Remarks on code availability):
+
+From my observation, it only contains codes for plotting, and I did not find any readme file.
+
+Response: We thank the reviewer for this kind reminder. We have now added the readme file.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have adequately addressed the issues I raised during the previous review round. I have no further comments, and recommend to accept this work for publication. This study will be an important contribution to our understanding of land use impacts on clouds and clouds processes.
+
+Reviewer #2 (Remarks to the Author):
+
+Thank you for addressing my previous concerns carefully in your response. I recommend a few additional revisions to the manuscript. Please find my comments listed below for your consideration:
+
+Relative major:
+
+(Methodology) The term 'non-local effect' requires clearer definition in the manuscript. Could you specify the external effects this term includes? The influence of land on cloud formation, particularly the secondary mesoscale circulation mechanism discussed in studies by Teuling et al. (2017), Xu et al. (2022), and Tian et al. (2022), plays a significant role but is not addressed in your study. Is this mechanism included in what you consider non-local effects?
+Furthermore, the contrasts in sensible and latent heat fluxes (SH/LH) between forested areas and adjacent deforested areas can induce secondary mesoscale circulations that significantly influence cloud formation. The strength of these circulations, which have diurnal variability, depends on these flux contrasts. This important dynamic needs further discussion in your analysis.
+
+(Result) Regarding your Comment 2.5: If the uncertainties associated with ERA5 and satellite retrievals, as mentioned by the authors, are indeed substantial—especially given the observational limitations of CloudSat due to radar ground clutter, and CALIPSO's signal attenuation issues from clouds above low-level clouds, which affect the detection of boundary layer clouds—how reliable are the vertical profiles of boundary layer clouds? This layer is particularly crucial due to its significant shallow convection activity, which is closely coupled with land surface processes.
+
+(Methodology) I am not fully convinced that the authors have adequately addressed my questions. I need further clarification on why the authors are emphasizing that the difference between the two calculated local effects is much smaller than the local effect itself. Could you please explain this aspect more clearly?
+It's possible there may be some misunderstanding: I understood that the local effect is calculated by subtracting the interpolated non-local effect from the total effect, and I assume the non-local effect is larger than the local effect. If this is the case, the local effect would be a relatively small
+value, derived from subtracting one large value from another, which could introduce significant uncertainty.
+
+Minor: (Writing) I understand that “While deep-convection clouds are generally not well-coupled with the surface, surface conditions can influence their initiation”. However, the subsequent statements are unclear to me: 'While deep-convection clouds are generally not well-coupled with the surface, surface conditions can influence their initiation 44,45. Thus, the height of deep convective cloud tops can roughly indicate the maximum altitude at which deforestation affects clouds. However, the cloud top height of deep convective clouds varies across regions. Compared to boreal zones, deep convective clouds in tropical regions can reach higher altitudes (Fig. S2). Consequently, deforestation can also affect high-level clouds, mostly in tropical regions”.
+
+-Xu, R. et al. Contrasting impacts of forests on cloud cover based on satellite observations. Nature Communications 13, 670, doi:10.1038/s41467-022-28161-7 (2022).
+-Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications 8, 14065, doi:10.1038/ncomms14065 (2017).
+-Tian, J., Zhang, Y., Klein, S. A., Öktem, R., & Wang, L.. (2022). How Does Land Cover and Its Heterogeneity Length Scales Affect the Formation of Summertime Shallow Cumulus Clouds in Observations From the US Southern Great Plains?. Geophysical Research Letters, 49(7). https://doi.org/10.1029/2021gl097070
+
+May consider citing relevant studies on the deforestation effect on cloud:
+-Wang, J., Chagnon, F. J. F., Williams, E. R., Betts, A. K., Renno, N. O., Machado, L. A. T., et al. (2009). Impact of deforestation in the Amazon basin on cloud climatology. Proceedings of the National Academy of Sciences of the United States of America, 106(10), 3670–3674. https://doi.org/10.1073/pnas.0810156106
+-Nair, U. S., Lawton, R. O., Welch, R. M., & Pielke, R. A. (2003). Impact of land use on Costa Rican tropical montane cloud forests: Sensitivity of cumulus cloud field characteristics to lowland deforestation. Journal of Geophysical Research, 108(7), 4206. https://doi.org/10.1029/2001jd001135
+Responses to Reviewer #1
+
+The authors have adequately addressed the issues I raised during the previous review round. I have no further comments, and recommend to accept this work for publication. This study will be an important contribution to our understanding of land use impacts on clouds and clouds processes.
+
+Response: We appreciate the reviewer's satisfaction with our revisions and are grateful for the important contributions to this study.
+Responses to Reviewer #2
+
+Thank you for addressing my previous concerns carefully in your response. I recommend a few additional revisions to the manuscript. Please find my comments listed below for your consideration:
+
+Response: We sincerely thank the reviewer for providing additional constructive comments, which are of much help in improving the clarity of the manuscript.
+
+Relative major:
+
+Comment 2.1:
+(Methodology) The term 'non-local effect' requires clearer definition in the manuscript. Could you specify the external effects this term includes? The influence of land on cloud formation, particularly the secondary mesoscale circulation mechanism discussed in studies by Teuling et al. (2017), Xu et al. (2022), and Tian et al. (2022), plays a significant role but is not addressed in your study. Is this mechanism included in what you consider non-local effects?
+
+Response: We thank the reviewer for raising this important point! Mesoscale processes typically have spatial scales between 10 and 1000 km. In the CMIP6 models, mesoscale circulations within the analysis resolution (10–200 km) are partly local, while the larger ones (200–1000 km) are considered non-local. Therefore, we assume that the term "non-local effect" in the general circulation models (GCMs) refers to both the large-scale circulations (>1000 km) and the mesoscale circulations beyond the analysis resolution (200–1000 km). We have clarified the definitions and addressed the secondary mesoscale circulation mechanism \(^{1-3}\) in the revised manuscript.
+
+References:
+1 Xu, R. et al. Contrasting impacts of forests on cloud cover based on satellite observations. Nature Communications **13**, 670, doi:10.1038/s41467-022-28161-7 (2022).
+2 Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications **8**, 14065, doi:10.1038/ncomms14065 (2017).
+3 Tian, J., Zhang, Y., Klein, S. A., Öktem, R. & Wang, L. How does land cover and its heterogeneity length scales affect the formation of summertime shallow cumulus clouds in observations from the US Southern Great Plains? Geophysical Research Letters **49**, e2021GL097070, doi:10.1029/2021GL097070 (2022).
+
+Changes in Manuscript:
+[Page 16 Lines 364–369 (in the “Track Changes” version)]
+“Mesoscale processes typically have spatial scales between 10 and 1000 km. In the CMIP6 models, mesoscale circulations within the analysis resolution (10–200 km) are partly local, while the larger ones (200–1000 km) are considered non-local. Therefore, we assume that the term "non-local effect" in the GCMs refers to both the large-scale circulations (>1000 km) and the mesoscale circulations beyond the analysis resolution (200–1000 km).”
+[Page 18 Lines 409–413 (in the “Track Changes” version)]
+“This method exclusively includes the local effects, comprising two components: one is the mean-state difference – variations in land cover conditions that result in spatial disparities; another is the secondary mesoscale circulation within the moving window pixels – differential heating of adjacent land cover patches can create sea-breeze-like secondary mesoscale circulations 21,23,55.”
+Furthermore, the contrasts in sensible and latent heat fluxes (SH/LH) between forested areas and adjacent deforested areas can induce secondary mesoscale circulations that significantly influence cloud formation. The strength of these circulations, which have diurnal variability, depends on these flux contrasts. This important dynamic needs further discussion in your analysis.
+
+Response: The reviewer is certainly right! Xu, et al. ¹ demonstrated that the cloud response to forests is driven by sensible heat flux (SH). They found that cloud enhancement is more likely over forests with higher SH compared to adjacent deforested areas, while cloud inhibition occurs over forests with lower SH than the surrounding deforested regions. This mechanism is influenced by secondary mesoscale circulation. We have added further discussions on this mechanism in the revision.
+
+In addition, we agree with the reviewer that the magnitude of secondary circulation and its impact on clouds may change diurnally as it is driven by the differential heating contrast in the diurnally changing land surface heat fluxes between adjacent areas with different land covers ³. However, studying this diurnal variation necessitates observational data with high temporal resolution, such as geostationary satellite data ³. Due to data limitations and scope constraints, our study focuses on daily averages on a global scale. As the importance of the diurnal cycle, we have included a discussion of diurnal variabilities in the revised manuscript.
+
+References:
+1 Xu, R. et al. Contrasting impacts of forests on cloud cover based on satellite observations. Nature Communications **13**, 670, doi:10.1038/s41467-022-28161-7 (2022).
+Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications **8**, 14065, doi:10.1038/ncomms14065 (2017).
+
+Tian, J., Zhang, Y., Klein, S. A., Öktem, R. & Wang, L. How does land cover and its heterogeneity length scales affect the formation of summertime shallow cumulus clouds in observations from the US Southern Great Plains? Geophysical Research Letters **49**, e2021GL097070, doi:10.1029/2021GL097070 (2022).
+
+Changes in Manuscript:
+[Page 10 Lines 227–237 (in the “Track Changes” version)]
+“The local effects derived from ERA5 contain both the mean-state difference and the secondary mesoscale circulation (See Methods). While the mean-state difference mechanism has been discussed above, the secondary circulation processes can enhance or inhibit the cloud responses to deforestation \(^{21,23,55}\). This secondary circulation-induced cloud change is mainly driven by SH \(^{21}\), indicating that cloud enhancement occurs over open land with higher SH compared to adjacent forests in the tropics, whereas cloud inhibition occurs over open land with lower SH than surrounding forests in boreal areas. Additionally, the magnitude of secondary circulations and their impact on clouds may change diurnally, driven by differential heating contrast in the diurnally varying land surface heat fluxes between adjacent patches with different land covers \(^{55}\).”
+
+References:
+21 Xu, R. et al. Contrasting impacts of forests on cloud cover based on satellite observations. Nature Communications **13**, 670, doi:10.1038/s41467-022-28161-7 (2022).
+23 Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications **8**, 14065, doi:10.1038/ncomms14065 (2017).
+55 Tian, J., Zhang, Y., Klein, S. A., Öktem, R. & Wang, L. How does land cover and its heterogeneity length scales affect the formation of summertime shallow cumulus clouds in observations from the US Southern Great Plains? Geophysical Research Letters **49**, e2021GL097070, doi:10.1029/2021GL097070 (2022).
+
+Comment 2.2:
+(Result) Regarding your Comment 2.5: If the uncertainties associated with ERA5 and satellite retrievals, as mentioned by the authors, are indeed substantial—especially given the observational limitations of CloudSat due to radar ground clutter, and CALIPSO’s signal attenuation issues from
+clouds above low-level clouds, which affect the detection of boundary layer clouds—how reliable are the vertical profiles of boundary layer clouds? This layer is particularly crucial due to its significant shallow convection activity, which is closely coupled with land surface processes.
+
+Response: Again, we thank the reviewer for raising this relevant point! Since we only used ERA5 cloud data over land for forest-cloud study, further analysis of the correlation between the cloud profiles from ERA5 and CloudSat-CALISPO over land (60° S–90° N) reveals an increased correlation coefficient (greater than 0.66) for low-level clouds (Fig. R2.1), indicating that ERA5 is more effective when estimating boundary layer clouds over land. The integration of denser and higher-quality observations contributes to the generally higher accuracy of ERA5 cloud data over land compared to ocean regions. We have now added discussions in the revision.
+
+![Correlation coefficient for the horizontal spatial variability of the 4-year (2007–2010) average cloud profiles from ERA5 and CALIPSO-CloudSat retrievals.](page_384_613_670_377.png)
+
+Figure R2.1. Correlation coefficient for the horizontal spatial variability of the 4-year (2007–2010) average cloud profiles from ERA5 and CALIPSO-CloudSat retrievals. The ERA5 cloud profiles are bilinearly gridded spatially into \(2^\circ \times 2^\circ\) to align with the CALIPSO-CloudSat data. The black and red lines represent data for the global and land (60° S–90° N) regions, respectively.
+
+Changes in Manuscript:
+[Page 5 Lines 116–118 (in the “Track Changes” version)]
+“However, the integration of denser and higher-quality observations over land enhances the accuracy of ERA5 boundary layer cloud data compared to over oceans (Fig. S1), thereby better suiting this land-focused study.”
+Supplementary Figure 1. Correlation coefficient for the horizontal spatial variability of the 4-year (2007–2010) average cloud profiles from ERA5 and CALIPSO-CloudSat retrievals. The ERA5 cloud profiles are bilinearly gridded spatially into \(2^\circ \times 2^\circ\) to align with the CALIPSO-CloudSat data. The black and red lines represent data for the global and land (\(60^\circ\) S–\(90^\circ\) N) regions, respectively.
+
+Comment 2.3:
+(Methodology) I am not fully convinced that the authors have adequately addressed my questions. I need further clarification on why the authors are emphasizing that the difference between the two calculated local effects is much smaller than the local effect itself. Could you please explain this aspect more clearly?
+It's possible there may be some misunderstanding: I understood that the local effect is calculated by subtracting the interpolated non-local effect from the total effect, and I assume the non-local effect is larger than the local effect. If this is the case, the local effect would be a relatively small value, derived from subtracting one large value from another, which could introduce significant uncertainty.
+
+Response: We appreciate the reviewer’s insightful comments, and indeed there were some misunderstandings in our previous responses. Using surface air temperature as an example, we find that the local and non-local effects are both non-negligible compared to the total effect; in fact, their magnitudes are quite comparable (Fig. R2.2). As such, the local effect, derived by subtracting the non-local effect from the total effect, is unlikely to introduce large uncertainty due to the differences in magnitudes. We have now added the discussion of this point in the revised manuscript.
+Figure R2.2. The ratio of local and non-local effects to the total effect for surface air temperature.
+(a) The ratio of local effect to total effect. (b) The ratio of non-local effect to total effect. The data are ensemble means from CMIP6 model simulations.
+
+Changes in Manuscript:
+[Page 17 Lines 390–393 (in the “Track Changes” version)]
+“Additionally, by comparing the local and non-local effects of SAT as an example, we find that both effects are non-negligible relative to the total effect. Therefore, the calculated local effect is unlikely to introduce large uncertainties due to discrepancies in magnitudes with the non-local effect.”
+Supplementary Figure 11. The ratio of local and non-local effects to the total effect for surface air temperature. (a) The ratio of local effect to total effect. (b) The ratio of non-local effect to total effect. The data are ensemble means from CMIP6 model simulations.
+
+Comment 2.4:
+Minor: (Writing) I understand that “While deep-convection clouds are generally not well-coupled with the surface, surface conditions can influence their initiation”. However, the subsequent statements are unclear to me: 'While deep-convection clouds are generally not well-coupled with the surface, surface conditions can influence their initiation 44,45. Thus, the height of deep convective cloud tops can roughly indicate the maximum altitude at which deforestation affects clouds. However, the cloud top height of deep convective clouds varies across regions. Compared to boreal zones, deep convective clouds in tropical regions can reach higher altitudes (Fig. S2). Consequently, deforestation can also affect high-level clouds, mostly in tropical regions”.
+Response: We thank the reviewer and have rephrased this sentence to make it clearer.
+
+Changes in Manuscript:
+[Page 6 Lines 141–150 (in the “Track Changes” version)]
+“While deep-convection clouds are generally not well-coupled with the surface, surface conditions can influence their initiation \(^{44,45}\). Therefore, deforestation is not limited to affecting shallow clouds that are fully coupled to the surface but can also impact deep convective clouds to a certain extent. As a result, the height of deep convective cloud tops can roughly indicate the maximum altitude at which deforestation affects clouds. Since the cloud top height of deep convective clouds varies across regions, with those in tropical regions reaching higher altitudes than those in boreal zones (Fig. S2), deforestation is more likely to affect high-level clouds in tropics.”
+
+References:
+44 Wu, C.-M., Stevens, B. & Arakawa, A. What Controls the Transition from Shallow to Deep Convection? Journal of the Atmospheric Sciences **66**, 1793-1806, doi:10.1175/2008JAS2945.1 (2009).
+45 Schumacher, R. S. & Rasmussen, K. L. The formation, character and changing nature of mesoscale convective systems. Nature Reviews Earth & Environment **1**, 300-314, doi:10.1038/s43017-020-0057-7 (2020).
+
+Comment 2.5:
+-Xu, R. et al. Contrasting impacts of forests on cloud cover based on satellite observations. Nature Communications **13**, 670, doi:10.1038/s41467-022-28161-7 (2022).
+-Teuling, A. J. et al. Observational evidence for cloud cover enhancement over western European forests. Nature Communications **8**, 14065, doi:10.1038/ncomms14065 (2017).
+-Tian, J., Zhang, Y., Klein, S. A., Öktem, R., & Wang, L.. (2022). How Does Land Cover and Its Heterogeneity Length Scales Affect the Formation of Summertime Shallow Cumulus Clouds in Observations From the US Southern Great Plains?. Geophysical Research Letters, **49**(7). https://doi.org/10.1029/2021gl097070
+
+May consider citing relevant studies on the deforestation effect on cloud:
+-Wang, J., Chagnon, F. J. F., Williams, E. R., Betts, A. K., Renno, N. O., Machado, L. A. T., et al. (2009). Impact of deforestation in the Amazon basin on cloud climatology. Proceedings of the National Academy of Sciences of the United States of America, **106**(10), 3670–3674.
+https://doi.org/10.1073/pnas.0810156106
+
+-Nair, U. S., Lawton, R. O., Welch, R. M., & Pielke, R. A. (2003). Impact of land use on Costa Rican tropical montane cloud forests: Sensitivity of cumulus cloud field characteristics to lowland deforestation. Journal of Geophysical Research, 108(7), 4206. https://doi.org/10.1029/2001jd001135
+
+Response: Thanks! We have now cited the recommended references, which are helpful for the clarity of our manuscript.
+
+Changes in Manuscript:
+
+47 Wang, J. et al. Impact of deforestation in the Amazon basin on cloud climatology. Proceedings of the National Academy of Sciences **106**, 3670-3674, doi:10.1073/pnas.0810156106 (2009).
+
+55 Tian, J., Zhang, Y., Klein, S. A., Öktem, R. & Wang, L. How does land cover and its heterogeneity length scales affect the formation of summertime shallow cumulus clouds in observations from the US Southern Great Plains? *Geophysical Research Letters* **49**, e2021GL097070, doi:10.1029/2021GL097070 (2022).
+
+69 Nair, U. S., Lawton, R. O., Welch, R. M. & Pielke Sr., R. A. Impact of land use on Costa Rican tropical montane cloud forests: Sensitivity of cumulus cloud field characteristics to lowland deforestation. *Journal of Geophysical Research: Atmospheres* **108**, 4206, doi:10.1029/2001JD001135 (2003).
+REVIEWERS' COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have satisfactorily addressed the concerns I raised in the previous review. I have no further comments and recommend that this work be accepted for publication.
+Responses to comments of “Decreased cloud cover partially offsets the cooling effects of surface albedo change due to deforestation” (NCOMMS-24-13908B) to Nature Communications.
+
+Hao Luo, Johannes Quaas, Yong Han
+
+Responses to Reviewer #2
+
+The authors have satisfactorily addressed the concerns I raised in the previous review. I have no further comments and recommend that this work be accepted for publication.
+
+Response: We appreciate the reviewer's satisfaction with our revisions and are grateful for the important contributions to this study.

0ae031331c2d266697df1ca15bce36f1cb2333132590b2a9b295f659d1dffe9c/metadata.json

@@ -0,0 +1,143 @@
+{
+    "title": "Long-term durability of metastable \u03b2-Fe2O3 photoanodes in highly corrosive seawater",
+    "pre_title": "Ultradurability of metastable \u03b2-Fe2O3 photoanodes in highly corrosive seawater",
+    "journal": "Nature Communications",
+    "published": "17 July 2023",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-40010-9/MediaObjects/41467_2023_40010_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-40010-9/MediaObjects/41467_2023_40010_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-023-40010-9/MediaObjects/41467_2023_40010_MOESM3_ESM.zip"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-023-40010-9#Sec12"
+    ],
+    "code": [],
+    "subject": [
+        "Artificial photosynthesis",
+        "Heterogeneous catalysis",
+        "Photocatalysis"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-2096634/v1.pdf?c=1689938327000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-2096634/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-023-40010-9.pdf",
+    "preprint_posted": "11 Dec, 2022",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Durability is one prerequisite for material application. Photoelectrochemical (PEC) decomposition of seawater is a promising approach to produce clean hydrogen by using solar energy, but it always suffers from serious Cl\u2212 corrosion. We found that the main deactivation mechanism of the photoanodes is oxide surface reconstruction accompanied by the coordination of Cl\u2212 during seawater splitting, and the stability of the photoanodes can be greatly improved by enhancing the metal-oxygen interaction. Taking the metastable \u03b2-Fe2O3 photoanode as an example, Sn added to the lattice can enhance the M\u2013O bonding energy and hinder the transfer of protons to lattice oxygen, thereby inhibiting excessive surface hydration and Cl\u2212 coordination. Therefore, the Sn/\u03b2-Fe2O3 photoanode without any extra electrocatalyst or protective overlayer delivered a record durability for PEC seawater splitting over 1440 h.Physical sciences/Chemistry/Photochemistry/PhotocatalysisPhysical sciences/Chemistry/Catalysis/Heterogeneous catalysisPhysical sciences/Materials science/Materials for energy and catalysis/PhotocatalysisPhysical sciences/Energy science and technology/Renewable energy/Solar energy/Artificial photosynthesis",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupportingInformationLiuCH.pdfSupporting Information",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Durability is one prerequisite for material application. Photoelectrochemical decomposition of seawater is a promising approach to produce clean hydrogen by using solar energy, but it always faces the problem of serious Cl\u2212 corrosion. We find that the main deactivation mechanism of the photoanode is oxide surface reconstruction accompanied by the coordination of Cl\u2212 during seawater splitting, and the stability of the photoanode can be effectively improved by enhancing the metal-oxygen interaction. Taking the metastable \u03b2-Fe2O3 photoanode as an example, Sn added to the lattice can enhance the M\u2013O bonding energy and hinder the transfer of protons to lattice oxygen, thereby inhibiting excessive surface hydration and Cl\u2212 coordination. Therefore, the bare Sn/\u03b2-Fe2O3 photoanode delivers a record durability for photoelectrochemical seawater splitting over 3000\u2009h.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The use of PEC water splitting to produce hydrogen can realize the conversion of solar energy to hydrogen energy in one step, which is a very promising solution for building a low-carbon society1,2,3,4,5. The long-term stability of photoelectrodes is an essential prerequisite for the practical application of PEC water splitting for hydrogen production6. However, except for iron oxide, almost all bare photoelectrodes show unsatisfactory stability in water splitting for hydrogen production, let alone in highly corrosive seawater7,8,9,10. Some strategies, such as protective layers, electrocatalysts, and tuning electrolyte composition, have been used to improve the durability of photoelectrodes in aqueous electrolytes without Cl\u2212 ions11,12,13. Little attention has been given to improving the stability of photoelectrodes in aqueous electrolytes with Cl\u2212 ions14,15, since Cl\u2212 ions easily corrode photoelectrode materials and may participate in the competitive oxidation reaction to produce Cl2 or ClO\u221216,17,18,19.\n\nHerein, we studied the effect of Cl\u2212 ions on the stability of a photoelectrode such as \u03b2-Fe2O3. Recently, \u03b2-Fe2O3 entered our research field as a metastable phase of iron oxide. Because of its narrower band gap (1.9\u2009eV) compared with \u03b1-Fe2O3 (2.1\u2009eV), the theoretical optical absorption band edge can be extended to approximately 650\u2009nm. Thus, it has a higher theoretical solar-to-hydrogen efficiency than \u03b1-Fe2O3. At the same time, \u03b2-Fe2O3 also shows good stability in photoelectrochemical alkaline water splitting20,21. We have revealed that the Cl\u2212 ions in seawater will damage the surface hydrated layer of \u03b2-Fe2O3 photoanodes, thus remarkably reducing their stability. Dispersed Sn single atoms in the lattice were found to endow the \u03b2-Fe2O3 photoanodes with good inhibition of hydration and resistance to Cl\u2212 attack in seawater. As a result, Sn/\u03b2-Fe2O3 without any protective overlayer shows excellent durability in seawater splitting over 3000\u2009h and is by far the most stable photoanode. This study may ignite the dawn of application for PEC seawater splitting for hydrogen production and deepen the understanding of the seawater corrosion of oxides.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Metastable \u03b2-Fe2O3 photoanodes doped with Sn were prepared by the spray pyrolysis method, and their phases were accurately determined (Supplementary Fig.\u00a01). The Sn/\u03b2-Fe2O3 film is composed of blocks arranged vertically with a thickness of approximately 400\u2009nm (Fig.\u00a01a). A large area of lattice stripes indicates good crystallinity of \u03b2-Fe2O3 (Fig.\u00a01b). Many bright spots with high contrast in the (1 1 0) crystal plane in Fig.\u00a01c correspond to the Sn single atom in the \u03b2-Fe2O3 lattice. One of the regions was selected for three-dimensional modelling, which shows the contrast difference between Sn atoms and surrounding Fe atoms (Fig.\u00a01d). It was confirmed that the lattice position of Fe was substituted by Sn. A clear atomic image of the (1 1 1) crystal plane taken from another region of \u03b2-Fe2O3 and fast Fourier transform (FFT) patterns of the (1 1 0) and (1 1 1) planes were obtained (Supplementary Fig.\u00a01). These lattice atomic images and FFT patterns are completely consistent with the atomic arrangement of the corresponding crystal plane in the theoretical model.\n\na, b HAADF images of the Sn/\u03b2-Fe2O3 film cross-section at different magnifications. c Atomic image of the (1 1 0) plane of \u03b2-Fe2O3. d Local enlargement near doped Sn atoms and three-dimensional modelling of surface contrast.\n\nThe as-prepared \u03b2-Fe2O3 photoanodes were tested for PEC simulated seawater splitting. The photocurrent density of the 2% Sn/\u03b2-Fe2O3 photoanodes reaches 2.21\u2009mA\u2009cm\u22122 at 1.6 VRHE, which is 8.5 times that of \u03b2-Fe2O3 photoanodes (Supplementary Fig.\u00a02). The Sn dopants do not affect the light absorption of the \u03b2-Fe2O3 photoanodes, while the PEC performance improvement is partly due to the increased electron concentration caused by the doping of high-valence cation Sn4+. The electron concentration of Sn/\u03b2-Fe2O3 is approximately 8.4 times that of \u03b2-Fe2O3, and correspondingly, its bulk conductivity is also improved, according to Mott-Schottky plots and AC electrochemical impedance spectra in the low-frequency region. Sn can simultaneously adjust the chemical field at the semiconductor/electrolyte interface, which significantly reduces the AC impedance of the interface transfer kinetics (Supplementary Figs.\u00a03, 4 and 5).\n\nThe most important role of Sn dispersed in the lattice is to promote its durability in simulated seawater with Cl\u2212 ions. Specifically, in Fig.\u00a02a, the stability of the \u03b2-Fe2O3 photoanodes is good in 1\u2009M KOH electrolyte within 100\u2009h, while its photocurrent density decreased obviously in 1\u2009M KOH\u2009+\u20090.5\u2009M NaCl electrolyte. This indicates that Cl\u2212 significantly reduced its PEC stability. In contrast, the Sn/\u03b2-Fe2O3 photoanodes could still maintain stable performance even in a saturated NaCl electrolyte within 100\u2009h without decay, which was much better than the \u03b2-Fe2O3 photoanodes. In the stability test, the photocurrent increased slightly in a period of time after the beginning of the reaction due to the change in the state of Fe and O on the surface22,23,24. Correspondingly, the AC impedance of the Sn/\u03b2-Fe2O3 photoanode in the first 50\u2009h gradually decreases (Fig.\u00a02b). The HADDF image of the photoanode also shows that an amorphous hydrated layer was formed on the surface of \u03b2-Fe2O3 (Fig.\u00a02c), which indicates that the FeOOH hydrated layer spontaneously formed on the surface during the reaction process. The specific process and impact of surface reconstruction will be further discussed below. Furthermore, the Sn/\u03b2-Fe2O3 photoanode shows excellent stability over 3000\u2009h in simulated seawater (Fig.\u00a02d). After 3000\u2009h, the photocurrent maintains 96.8% of the initial value. The Sn/\u03b2-Fe2O3 photoanode has achieved the longest durability in research on PEC seawater splitting over the years, as shown in Fig.\u00a02e, even without any extra electrocatalyst or protective overlayer. Additionally, the Sn/\u03b2-Fe2O3 photoanodes showed excellent stability in alkaline natural seawater (Supplementary Fig.\u00a06).\n\na Stability test of \u03b2-Fe2O3 (in 1\u2009M KOH, 1\u2009M KOH/0.5\u2009M NaCl, 1\u2009M KOH/saturated NaCl solution) and Sn/\u03b2-Fe2O3 (in 1\u2009M KOH/saturated NaCl solution) for 100\u2009h. b AC electrochemical impedance spectra of Sn/\u03b2-Fe2O3 before and after the reaction. c HAADF images of the Sn/\u03b2-Fe2O3 photoanode after 100\u2009h of reaction in 1\u2009M KOH/0.5\u2009M NaCl. d Stability test of Sn/\u03b2-Fe2O3 in 1\u2009M KOH/0.5\u2009M NaCl for 3000\u2009h. e Summary of the photoanode stability of PEC (simulated) seawater splitting over the years. Detailed information can be found in Supplementary Table\u00a01.\n\nThe evolution process of the \u03b2-Fe2O3 photoanode surface in seawater splitting is explored here. XPS analysis can be used to obtain the state of the \u03b2-Fe2O3 photoanode surface elements in contact with the electrolyte during the reaction. As shown in the XPS spectrum of O in the \u03b2-Fe2O3 photoanode (Supplementary Fig.\u00a07a), the peak of M\u2013O at 529.4\u2009eV decreases after the reaction. It transforms to M\u2013OH at 531.7\u2009eV, with a significant shift from lattice oxygen to hydroxyl oxygen on the surface25. This corresponds to the reconstruction of the \u03b2-Fe2O3 surface in alkaline electrolytes. In the XPS plot of Sn/\u03b2-Fe2O3 photoanodes with 100\u2009h of reaction in Fig.\u00a03a, a large number of O atoms can remain in the form of lattice oxygen when Sn is present on the surface. After 100\u2009h of reaction, no Cl signal was detected on the surface of the Sn/\u03b2-Fe2O3 photoanodes (Fig.\u00a03b). In contrast, the Cl signal was detected on the \u03b2-Fe2O3 surface (Supplementary Fig.\u00a07b), which indicates that the process of lattice oxygen reconstruction was accompanied by the adsorption or implantation of Cl\u2212 in the electrolyte. During surface hydration and lattice reformation, \u03b2-Fe2O3 slowly dissolves, which can be determined by inductive coupled plasma emission spectrometer (Supplementary Table\u00a02). The amount of dissolved Fe atoms was also significantly reduced when Sn acted as an anchor at the surface. However, due to the intense hydration, the surface lattice was still continuously attacked after a long reaction time, accompanied by O remodelling and loss of metal elements. The XPS peak of the Sn 3d signal disappeared after 1000\u2009h of reaction (Fig.\u00a03c), indicating that Sn is also slowly lost during lattice reconstruction by surface hydration. Cations are also involved in surface hydration and embedded in the hydrated layer, such as Na+, and after 1000\u2009h, cations were also detected on the photoanode surface. Confocal Raman spectroscopy was used to observe the speciation evolution of trace substances on the surface of the photoanodes before and after the reaction (Fig.\u00a03d). After 100\u2009h and 1000\u2009h of seawater splitting, there are two peaks of M\u2013OOH at approximately 470 and 550\u2009cm\u22121 26,27, which echo the change in the O 1s XPS peak. FeOOH, which is hydrated and reconstituted during the reaction, is also more prone to dehydration and sintering at high temperatures. The \u03b1-Fe2O3 peak can be observed when the \u03b2-Fe2O3 photoanodes are further calcined at 600\u2009\u00b0C. Here, \u03b1-Fe2O3 was transformed from FeOOH generated by surface reconstruction during heat treatment. A NaCl peak appeared on the surface after 1000\u2009h of reaction, indicating that the crystallization of anions and cations diffused into the hydration layer.\n\na\u2013c XPS spectra of O 1s, Cl 2p, and Sn 3d of Sn/\u03b2-Fe2O3 before, after 100\u2009h, and after 1000\u2009h of seawater splitting reaction. d Raman spectra of \u03b2-Fe2O3 photoanodes with different reaction times and annealing treatments. e, f TOF-SIMS of the distributions of Cl and 18OH on the surface and depth profiling of the \u03b2-Fe2O3 photoanode before and after Sn doping after the 100-h reaction in simulated seawater with 20 wt% H218O.\n\nTo further confirm the reconstruction of the \u03b2-Fe2O3 photoanodes and the exchange of atoms at the interface during the reaction in the electrolyte, the surface element distribution measurement was probed by time-of-flight secondary ion mass spectrometry (TOF-SIMS). In Fig.\u00a03e, the signal of Cl can be detected on the \u03b2-Fe2O3 surface after the reaction in simulated seawater for 100\u2009h. The Cl content of the \u03b2-Fe2O3 surface is much higher than that of the Sn/\u03b2-Fe2O3 surface. This confirmed that the presence of Sn can significantly improve the rejection of Cl\u2212 in the electrolyte. Meanwhile, H218O was added to explore electrolyte participation in the surface reconstruction of the \u03b2-Fe2O3 photoanode. 18O in the electrolyte participates in the formation of a hydration layer, so the signal of 18OH with surface m/z\u2009=\u200919.005 can be detected. The signal intensity of 18OH on the Sn/\u03b2-Fe2O3 photoanode surface is much weaker than that on the \u03b2-Fe2O3 surface, indicating that the Sn dopants weaken lattice oxygen reconstruction. In the depth profiling in Fig.\u00a03f, the content of both Cl and 18OH in the Sn/\u03b2-Fe2O3 surface decays faster with depth than without Sn dopants. This reveals that surface reconstruction and Cl\u2212 erosion occur simultaneously. The 18O added to the electrolyte participates in the reconstruction of the lattice oxygen of \u03b2-Fe2O3 and forms M\u201318OH. At the same time, Cl\u2212 in the electrolyte would also first be adsorbed on the surface and gradually infiltrate into the bulk with surface reconstruction. The \u03b2-Fe2O3 photoanode undergoes excessive surface reconstruction, resulting in a thicker hydrated layer. Cl\u2212 shuttles and infiltrates into it, which may destroy the structure of the \u03b2-Fe2O3 photoanode and affect the interface water oxidation reaction. Sn inhibits the exchange of 18O and lattice oxygen and suppresses the erosion of Cl\u2212, thus obtaining a more stable photoanode surface.\n\nThe O K-edge of the soft X-ray absorption near-edge structure (XANES) spectrum shows the change in the lattice oxygen state before and after adding Sn to the lattice (Fig.\u00a04a\u00a0and\u00a0Supplementary Fig.\u00a08). The spectrogram of \u03b2-Fe2O3 is similar to the O K-edge of standard iron oxide28. After adding Sn, the X-ray absorption peak of oxygen shifts to the direction of high energy, which reflects that the addition of Sn effectively improves the bonding energy of O in the lattice. A shoulder peak at 532.3\u2009eV corresponds to the contribution of the Sn 5s orbit29,30. This shows that the Sn atoms dispersed in the lattice change the average chemical environment of O and play an anchor role in lattice oxygen.\n\na XANES spectra of the O K-edge in \u03b2-Fe2O3. b The steady-state photocurrent jH2O/jD2O and jSn/jPure values at different pH values. c Schematic diagram of doped Sn atoms against Cl\u2212 corrosion in seawater splitting. Sn enhances the M\u2013O bonds, prevents the hydrated surface reconstruction caused by the transfer of H+ to lattice oxygen, and weakens the coordination of Cl\u2212.\n\nThe enhanced metal\u2013oxygen interaction in the surface chemical reaction is specifically manifested in that the lattice oxygen at the semiconductor electrolyte interface has more difficulty accepting protons, which can be confirmed by the proton-coupled electron transfer process analysed by the H/D kinetic isotope effect31,32,33. The OER on the photoanode surface is a proton-coupled electron transfer process involving four electrons, as shown in Fig.\u00a04b. Specifically, the reaction intermediate species *OH and *OOH transfer one electron to the semiconductor and discard one proton34,35. The isotope effect is particularly significant at low pH. The jH2O/jD2O value of the \u03b2-Fe2O3 photoanode is always lower than that of Sn/\u03b2-Fe2O3, indicating that the \u03b2-Fe2O3 surface has a stronger affinity for protons. The lattice oxygen on the surface of \u03b2-Fe2O3 easily acts as a proton acceptor, which to some extent accelerates the proton coupling process in the reaction process. However, lattice oxygen as a proton acceptor will bring about the problem of structural stability being destroyed. As demonstrated in Fig.\u00a04c, protons transferred to nearby locations will combine with lattice oxygen, break the M\u2013O bond, and generate an FeOOH hydrated layer. When the M\u2013O bond breaks, oxygen in solution will exchange with lattice oxygen, and Cl\u2212 will also coordinate with Fe and destroy the surface structure. On the other hand, hydrated FeOOH is a loose amorphous or layered structure, which is also prone to the insertion and adsorption of Cl\u2212, thus affecting the activity of water splitting. The Sn atoms dispersed in the lattice play a role in anchoring the lattice oxygen to prevent proton coupling between the reaction intermediate and the lattice oxygen. which shows that the proton transfer process will have a greater impact on the reaction kinetics. When the pH rises, proton transfer is no longer the rate-determining step. The advantages of donor Sn4+ dispersed in the bulk phase in improving electron concentration and conductivity can also be fully demonstrated. Therefore, the photocurrent increases to 8.5 times that of the \u03b2-Fe2O3 photoanode. Although alkaline electrolytes are used in PEC tests, local pH will decrease in the water oxidation reaction, and protons with higher local concentrations will also exist. These protons attack lattice oxygen, causing surface reconstruction. Sn in the lattice enhances the metal\u2013oxygen interaction, thus inhibiting the wrong proton transfer path and avoiding surface hydration and Cl\u2212 corrosion.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "The advantage of uniformly dispersed Sn in the bulk phase is that when the surface is hydrated and peeled by corrosion, the exposed Sn/\u03b2-Fe2O3 is still corrosion resistant. During the annealing process of the Sn/\u03b2-Fe2O3 photoanode, Sn atoms tend to diffuse to the surface36,37, but the Sn in the bulk is still relatively uniform (Supplementary Fig.\u00a09). Such characteristics make the stability rise continuously at first, then decline slowly, and finally maintain a stable range of fluctuations. At the initial stage of the reaction, the \u03b2-Fe2O3 on the surface is converted into FeOOH in situ (Fig.\u00a03). FeOOH itself is an efficient electrocatalyst, so the photocurrent increased. Because of the infiltration corrosion of Cl\u2212 along with the excessive surface reconstruction and the loss of Sn, the photocurrent density had a downwards trend after 700\u2009h. It can be analysed from Supplementary Fig.\u00a010 that due to the electrocatalytic effect of surface FeOOH after the 1000-h reaction, the onset potential moved to the negative direction by approximately 0.1 VRHE. However, the photocurrent density at 1.6 VRHE was reduced with the influence of surface reconstruction and corrosion. Owing to the relatively uniform distribution of Sn in the whole film, reconstruction, and corrosion were controlled within a certain range of the \u03b2-Fe2O3 surface instead of continuing to the deep layer. In addition, while the surface reconstruction was accompanied by the loss of Sn, there would also be a sedimentation equilibrium on the surface, and deposition would occur, which forms a dynamic balance of corrosion, metal loss, deposition, and protection. A dynamic stable state of surface evolution was established after a period of time, so the photocurrent density tended to be stable after 1000\u2009h. In contrast, we covered a layer of efficient OER electrocatalyst CoFe-LDH on the surface of Sn/\u03b2-Fe2O3 as a protective passivation layer. However, a significant downwards trend of the photocurrent was observed in the first 50\u2009h of the reaction, and after a long time, the current gradually decreased to the level without loading the electrocatalyst (Supplementary Fig.\u00a012). This shows that the surface modification of the electrocatalyst cannot resist the corrosion of Cl\u2212 in seawater. Metal hydroxide itself will also be reconstructed in the OER reaction, which will also be accompanied by the problems of Cl\u2212 coordination and structural collapse. Finally, the structure is destroyed and gradually dissolved and peeled off. This extra loaded electrocatalyst protective layer often protects the photoanode by its own corrosion and consumption, which cannot fundamentally solve the long-term stability problem.\n\nIn summary, we revealed that excessive hydration reconstruction of the surface will corrode the surface of the oxide photoanode with the corrosion of Cl\u2212 ions in the solution. The anchoring of the surface lattice by Sn hinders the transfer of protons to lattice oxygen, and the probability of oxygen hydrogen bonding will decrease due to the strong M\u2013O bond, thereby suppressing the surface reconstruction and coordination of Cl\u2212. The Sn/\u03b2-Fe2O3 photoanode constitutes by far the most durable photoanode for seawater splitting. This strategy can also improve the durability of other photoanodes, such as \u03b1-Fe2O3 (Supplementary Fig.\u00a013). This study will pave a new path to solving the problem of the long-term durability of photoelectrodes in energy conversion.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "Typically, in an experiment, 0.01\u2009mol of iron acetylacetonate (AcAcFe) was dissolved in 500\u2009mL ethanol by stirring with a magnetic force for over 48\u2009h. Fluorine-doped tin oxide (FTO) conductive glass was cut into dimensions of 2\u2009cm\u2009\u00d7\u20091\u2009cm and wrapped with aluminum foil to make a deposition area of 1\u2009cm\u2009\u00d7\u20091\u2009cm and then placed in a tube furnace with a set temperature of 480\u2009\u00b0C. The precursor solution was added to the injection pump and dispersed into droplets by using an ultrasonic atomizer. During the experiment, 40\u2009mL of precursor solution was injected at a speed of 1.6\u2009mL\u2009min\u22121, which equally matched the power of the ultrasonic atomizer. Using air as the carrier gas, the precursor was fed into a tubular furnace. After deposition, the film was annealed in a muffle furnace at 600\u2009\u00b0C for 3\u2009h at a heating rate of 10\u2009\u00b0C min\u22121. The Sn/\u03b2-Fe2O3 films were prepared using the same spray pyrolysis method by adding a certain amount of tetrabutyltin (C16H36Sn, analytical reagent, Aladdin) ethanol solution to the precursor solution so that the Sn atom concentration accounted for 1%, 2%, 3%, and 4% of the total Sn and Fe atoms. The CoFe-LDH @ Sn/\u03b2-Fe2O3 photoanodes were prepared by a hydrothermal method. The as-prepared Sn/\u03b2-Fe2O3 photoanodes were put into a 100\u2009mL hydrothermal kettle, 50\u2009mL of a solution containing 0.002\u2009mol\u2009L\u22121 cobalt nitrate hexahydrate (Co(NO3)2\u00b76H2O, Sinopharm Chemical Reagent), 0.002\u2009mol\u2009L\u22121 iron(III) nitrate nonahydrate (Fe(NO3)3\u00b79H2O, analytical reagent, Aladdin)), 0.005\u2009mol\u2009L\u22121 urea (Aladdin) and 0.001\u2009mol\u2009L\u22121 trisodium citrate was added, and the reaction was carried out in an oven at 120\u2009\u00b0C for 5\u2009h.\n\nTo identify the crystal structures of the \u03b2-Fe2O3 photoanodes, they were measured by powder X-ray diffraction (XRD, Rigaku Ultima III, Cu K\u03b1 radiation, \u03bb\u2009=\u20091.54178\u2009\u00c5) at 40\u2009kV and 40\u2009mA. The surface morphology of the \u03b2-Fe2O3 photoanodes was examined by a high-resolution scanning electron microscope (HRSEM, ZEISS ULTRA 55 at an accelerating voltage of 5\u2009kV). Raman spectra of \u03b2-Fe2O3 photoanodes were characterized with a confocal laser Raman spectrometer (Japan, Horiba, LabRAM Aramis). X-ray photoemission spectroscopy (XPS, PHI 5000 VersaProbe) was used to characterize the content and valence of Sn, O, Fe, and Co, and the binding energy was calibrated by the adventitious carbon C 1s line at 284.8\u2009eV. The optical absorption spectra of the photoanode were tested on a UV\u2013Visible\u2013NIR (near-infrared) spectrophotometer (PerkinElmer, UV3600 UV\u2013Vis\u2013NIR spectrophotometer). Transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM) images were obtained on an FEI Tecnai G2 F30. High-angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) images were obtained by a JEOL JEM-ARM200F microscope incorporated with a spherical aberration correction system for STEM. The concentrations of cations in the condensates were examined by ICP-OES (PerkinElmer Instruments, PTIMA 5300 DV).\n\nThe PEC measurements were carried out in a PEC cell with an electrochemical analyser (CHI-760E, CH Instrument, Shanghai) in a three-electrode system including a reference electrode consisting of Ag/AgCl placed in a saturated KCl solution, Pt foil as the counter electrode, and \u03b2-Fe2O3 photoanodes as working electrodes. The electrolyte was a 1\u2009M KOH aqueous solution for freshwater and 1\u2009M KOH with 0.5\u2009M NaCl for simulated seawater. The potential was reported vs. the reversible hydrogen electrode (RHE) with ERHE\u2009=\u2009EAg/AgCl\u2009+\u20090.197\u2009+\u20090.0591\u2009pH38,39,40,41. The photocurrent density was measured under AM 1.5\u2009G light source, and the light intensity was 100\u2009mW\u2009cm\u22122. A Newport 91150\u2009V standard silicon cell was used as the reference standard for calibration. Mott-Schottky analysis was performed at bias potentials from 0.5 to 1.5\u2009V vs. RHE42,43. AC electrochemical impedance was obtained at a bias of 1.6 VRHE over the frequency range of 100\u2009kHz to 1\u2009Hz44,45. The PEC stabilities were tested at a constant potential of 1.6 VRHE under LED-simulated sunlight sources through illumination from the front side. No iR compensation was used in any electrochemical test. All tests were conducted at room temperature (~25\u2009\u00b0C) and in an air environment.\n\nIn the PEC test of the H/D kinetic isotope effect, the electrolyte was measured with a pH meter to keep the concentrations of OH\u2212 and OD\u2212 in the solution the same (pD = pHread\u2009+\u20090.4). D2O was purchased from Bide Pharmatech Ltd. (99.9% atom %D). The pD values were adjusted by NaOD (Aladdin, 30 wt% solution in D2O, 99.5%). In the current time curve, the photocurrent density value after 50\u2009s of reaction was selected as the steady-state value for the calculation of jH2O/jD2O and jSn/jPure (Supplementary Fig.\u00a011).\n\nAll photoanodes after the reaction were removed from the electrolyte and washed with flowing deionized water for 20\u2009s to remove the residual electrolyte on the surface. Then, the cleaned photoanodes were further characterized and analysed.\n\nTOF-SIMS tests were carried out by PHI nanoTOF II Time-of-Flight SIMS. Bi3++ with an energy of 30\u2009eV was used in the acquisition phase in high mass resolution mode. An Ar ion gun with an energy of 4\u2009kV was used in the sputter phase with a sputter rate of 0.4\u2009nm\u2009s\u22121 on SiO2. Before the \u03b2-Fe2O3 photoanode was tested, the reactions in the electrolyte with 1\u2009M KOH\u2009+\u20090.5\u2009M NaCl and 20 wt% H218O for 100\u2009h were carried out.\n\nSoft X-ray absorption near-edge structure (XANES) measurements were performed at the Beijing Synchrotron Radiation Facility (BSRF), 4B9B beamline. The O-K edge and Fe-L edge spectra were collected in total electron yield (TEY) mode by measuring the sample current with an amperemeter. All spectra were normalized to the intensity of the incident beam (I0), which was measured simultaneously with the current emitted from a gold mesh located after the last optical elements of the beamline. The photon energy was calibrated using the Au-4f core level at 84.0\u2009eV in binding energy by measuring a clean polycrystalline gold foil that is electrically connected to the sample.\n\nThe calculations on pure and Sn/\u03b2-Fe2O3 were implemented in the VASP (Vienna Ab initio Simulation Package) based on density functional theory, with a projected-augmented-wave method in the scheme of generalized-gradient approximation. The strong on-site Coulomb repulsion among the localized Fe 3d electrons was described with the generalized-gradient approximation + U approach (U is the strength of the on-site Coulomb interaction). The exchange-correlation effects were treated using the generalized-gradient approximation (GGA) in the Perdew-Burke-Ernzerhof parametrization, with spin-polarized effects considered. The calculated unit cell contains 96 Fe atoms and 144 oxygen atoms. In doping calculations, different numbers of Fe atoms were replaced with Sn atoms. The replacement site is calculated as the position with the lowest energy.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All data are available in the main text and Supplementary Information. The data generated in this study are provided in the Source data file.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_name": "Acknowledgements",
+            "section_text": "The authors thank the National Science Fund for Distinguished Young Scholars (No. 22025202, Z.L.), National Key Research and Development Program of China (Nos. 2018YFA0209303, Z.L. and 2021YFA1502100, J.F.), National Natural Science Foundation of China (No. 51972165, Z.L.) and Natural Science Foundation of Jiangsu Province of China (No. BK20202003, Z.Z.) for financial support. We are indebted to Prof. Yixin Zhao (Shanghai Jiaotong University) for discussions.",
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+            "section_name": "Author information",
+            "section_text": "Collaborative Innovation Center of Advanced Microstructures, National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, Nanjing University, 22 Hankou Road, Nanjing, 210093, China\n\nChanghao Liu,\u00a0Ningsi Zhang,\u00a0Yang Li,\u00a0Rongli Fan,\u00a0Wenjing Wang,\u00a0Jianyong Feng,\u00a0Zhaosheng Li\u00a0&\u00a0Zhigang Zou\n\nJiangsu Key Laboratory for Nano Technology, Nanjing University, 22 Hankou Road, Nanjing, 210093, China\n\nChanghao Liu,\u00a0Ningsi Zhang,\u00a0Zhaosheng Li\u00a0&\u00a0Zhigang Zou\n\nBeijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China\n\nChen Liu\u00a0&\u00a0Jiaou Wang\n\nSchool of Physics and Centre of Quantum and Matter Sciences, International Research Institute for Multidisciplinary Science, Beihang University, Beijing, 100191, China\n\nWeichang Hao\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nZ.L. constructed the concept and designed the project. Z.L. supervised the study. N.Z., Y.L., J.F., W.W., C.L., J.W., W.H., and Z.Z. advised on the research. C.H.L. and R.F. collected and analysed the experimental data. C.H.L. and Z.L. wrote the manuscript. Z.L. and J.F. revised the manuscript. All the authors contributed to the discussions about the manuscript.\n\nCorrespondence to\n                Jianyong Feng or Zhaosheng Li.",
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+            "section_text": "Liu, C., Zhang, N., Li, Y. et al. Long-term durability of metastable \u03b2-Fe2O3 photoanodes in highly corrosive seawater.\n                    Nat Commun 14, 4266 (2023). https://doi.org/10.1038/s41467-023-40010-9\n\nDownload citation\n\nReceived: 03 December 2022\n\nAccepted: 08 July 2023\n\nPublished: 17 July 2023\n\nVersion of record: 17 July 2023\n\nDOI: https://doi.org/10.1038/s41467-023-40010-9\n\nAnyone you share the following link with will be able to read this content:\n\nSorry, a shareable link is not currently available for this article.\n\n\n\n\n                            Provided by the Springer Nature SharedIt content-sharing initiative\n                        ",
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+            ]
+        },
+        {
+            "section_name": "This article is cited by",
+            "section_text": "Nature Communications (2025)\n\nNature Communications (2025)\n\nRare Metals (2025)\n\nEmergent Materials (2025)\n\nResearch on Chemical Intermediates (2024)",
+            "section_image": []
+        }
+    ]
+}