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019a1322a4a18120bcf8546c95c7927691c4f4ceee9e4ba840a419b80a2ebe10/peer_review/images_list.json

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+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Simulation results when \\(P = 1\\) (UVMR). (A-B) Results of the causal effect estimation and type I error rate when the causal effect is zero. (C-D) Results of causal effect estimation and statistical power 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\\) .",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Simulation results of causal effect estimation when there is correlated and uncorrelated pleiotropy (MVMR). The number of IVs is 100, and the proportion of invalid IVs is \\(30\\%\\) . The number of populations is \\(E = 3\\) . Among total of eight exposures, two ( \\(X_{1}\\) and \\(X_{2}\\) ) are causal exposures (with a causal effect of 0.2), and the other six ( \\(X_{3}, \\ldots , X_{8}\\) ) are spurious exposures (with causal effect of 0).",
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Simulation results of the type I error rate for spurious exposures and statistical power for causal exposures when there is correlated and uncorrelated pleiotropy (MVMR). The number of IVs is 100, and the proportion of invalid IVs is \\(30\\%\\) . The number of populations is \\(E = 3\\) . Among total of eight exposures, two ( \\(X_{1}\\) and \\(X_{2}\\) ) are causal exposures (with a causal effect of 0.2), and the other six ( \\(X_{3},\\dots,X_{8}\\) ) are spurious exposures (with a causal effect of 0). This figure displays the type I error rates for \\(X_{1}\\) and \\(X_{2}\\) , the statistical power for \\(X_{3},\\dots,X_{8}\\) .",
+    "bbox": [
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+    "page_idx": 9
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Simulation results of the 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\\) .",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_6.jpg",
+    "caption": "Figure 6. Heterogeneity plot of the application results. The heterogeneity of MR estimations in each population using MVMR-IVW, MVMR-Egger, MVMR-Lasso and MVMR-Median, whereas MVMR-cML and MVMR-Horse cannot output MR estimations owing to the substantial memory consumption and computational time.",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_7.jpg",
+    "caption": "Figure 7. Forest plot of the application results. Causal effect estimations of 11 blood cells on disease-related outcomes via the MVMR-EILLS method.",
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+    "caption": "Figure S34. I2 for MR estimations in each population",
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+    "page_idx": 22
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+    "caption": "Figure S35. Forest plot for MR estimations in each population",
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+    "page_idx": 22
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Simulation results of the type I error rate for spurious exposures and statistical power for causal exposures when there is correlated and uncorrelated pleiotropy (MVMR). The number of IVs is 100, and the proportion of invalid IVs is \\(30\\%\\) . The number of populations is \\(E = 3\\) . Among total of eight exposures, two ( \\(X_{1}\\) and \\(X_{2}\\) ) are causal exposures (with a causal effect of 0.2), and the other six ( \\(X_{3},\\dots,X_{8}\\) ) are spurious exposures (with a causal effect of 0). This figure displays the type I error rates for \\(X_{1}\\) and \\(X_{2}\\) , the statistical power for \\(X_{3},\\dots,X_{8}\\) .",
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+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. Simulation results when \\(P = 1\\) (UVMR). (A-B) Results of the causal effect estimation and type I error rate when the causal effect is zero. (C-D) Results of causal effect estimation and statistical power 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\\) .",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_3.jpg",
+    "caption": "Figure 3. Simulation results of causal effect estimation when there is correlated and uncorrelated pleiotropy (MVMR). The number of IVs is 100, and the proportion of invalid IVs is \\(30\\%\\) . The number of populations is \\(E = 3\\) . Among total of eight exposures, two ( \\(X_{1}\\) and \\(X_{2}\\) ) are causal exposures (with a causal effect of 0.2), and the other six ( \\(X_{3}, \\ldots , X_{8}\\) ) are spurious exposures (with causal effect of 0).",
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+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Simulation results of the type I error rate for spurious exposures and statistical power for causal exposures when there is correlated and uncorrelated pleiotropy (MVMR). The number of IVs is 100, and the proportion of invalid IVs is \\(30\\%\\) . The number of populations is \\(E = 3\\) . Among total of eight exposures, two ( \\(X_{1}\\) and \\(X_{2}\\) ) are causal exposures (with a causal effect of 0.2), and the other six ( \\(X_{3},\\dots,X_{8}\\) ) are spurious exposures (with a causal effect of 0). This figure displays the type I error rates for \\(X_{1}\\) and \\(X_{2}\\) , the statistical power for \\(X_{3},\\dots,X_{8}\\) .",
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+    "type": "image",
+    "img_path": "images/Figure_5.jpg",
+    "caption": "Figure 5. Simulation results of the 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\\) .",
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+    "type": "image",
+    "img_path": "images/Figure_unknown_2.jpg",
+    "caption": "Figure S22. Causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , unbalanced pleiotropy",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_3.jpg",
+    "caption": "Figure S23. Type I error of causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , unbalanced pleiotropy",
+    "bbox": [],
+    "page_idx": 33
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_4.jpg",
+    "caption": "Figure S24. Causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , balanced pleiotropy",
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+    "page_idx": 33
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+    "type": "image",
+    "img_path": "images/Figure_unknown_5.jpg",
+    "caption": "Figure S25. Type I error of causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , balanced pleiotropy",
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+    "img_path": "images/Figure_unknown_6.jpg",
+    "caption": "Figure S26. Causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , unbalanced pleiotropy",
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+    "page_idx": 34
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+    "type": "image",
+    "img_path": "images/Figure_unknown_7.jpg",
+    "caption": "Figure S27. Statistical Power of causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , unbalanced pleiotropy",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_8.jpg",
+    "caption": "Figure S28. Causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , balanced pleiotropy",
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+    "caption": "Figure S4. Causal effects' estimation when \\(g = 100\\) , \\(E = 3\\) , \\(P = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.2",
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+  {
+    "type": "image",
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+    "caption": "Figure S5. Type I error of causal effects' estimation when \\(g = 100\\) , \\(E = 3\\) , \\(P = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.2",
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+    "caption": "Figure S6. Causal effects' estimation when \\(g = 100\\) , \\(E = 3\\) , \\(P = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.6",
+    "bbox": [
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+    "img_path": "images/Figure_unknown_12.jpg",
+    "caption": "Figure S7. Type I error of causal effects' estimation when \\(g = 100\\) , \\(E = 3\\) , \\(P = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.6",
+    "bbox": [
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+    "page_idx": 37
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_13.jpg",
+    "caption": "Figure S14. Causal effects' estimation when \\(g = 100\\) , \\(E = 3\\) , \\(P = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.2",
+    "bbox": [
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+  {
+    "type": "image",
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+    "caption": "Figure S15. Type I error of causal effects' estimation when \\(g = 100\\) , \\(E = 3\\) , \\(P = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.2",
+    "bbox": [
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+    "page_idx": 37
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_15.jpg",
+    "caption": "Figure S16. Causal effects' estimation when \\(g = 100\\) , \\(E = 3\\) , \\(P = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.6",
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+    "page_idx": 38
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_16.jpg",
+    "caption": "Figure S17. Type I error of causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , genetic correlations among different datasets is 0.6",
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+    "page_idx": 38
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_17.jpg",
+    "caption": "Figure S40. Causal effects' estimation when proportion of invalid IVs is \\(30\\%\\) , \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 8\\) , genetic correlation is 0.2",
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+    "page_idx": 38
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_18.jpg",
+    "caption": "Figure S41. Type I error/Power of causal effects' estimation when proportion of invalid IVs is \\(30\\%\\) , \\(g = 100\\) , \\(E = 3\\) , \\(P = 8\\) , genetic correlation is 0.2",
+    "bbox": [],
+    "page_idx": 39
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_19.jpg",
+    "caption": "Figure S42. Causal effects' estimation when proportion of invalid IVs is \\(30\\%\\) , \\(g = 100\\) , \\(E = 3\\) , \\(P = 8\\) , genetic correlation is 0.6",
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_20.jpg",
+    "caption": "Figure S44. Causal effects' estimation when proportion of invalid IVs is \\(30\\%\\) , \\(g = 100\\) , \\(E = 3\\) , \\(P = 8\\) , weak IVs",
+    "bbox": [
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_21.jpg",
+    "caption": "Figure S45. Type I error/Power of causal effects' estimation when proportion of invalid IVs is \\(30\\%\\) , \\(g = 100\\) , \\(E = 3\\) , \\(P = 8\\) , weak IVs",
+    "bbox": [
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+    "type": "image",
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+    "caption": "Figure S24. Causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , balanced pleiotropy",
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+    "type": "image",
+    "img_path": "images/Figure_unknown_23.jpg",
+    "caption": "Figure S25. Type I error of causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , balanced pleiotropy",
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+  },
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+    "type": "image",
+    "img_path": "images/Figure_unknown_24.jpg",
+    "caption": "Figure S28. Causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , balanced pleiotropy",
+    "bbox": [
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+    "page_idx": 43
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_25.jpg",
+    "caption": "Figure S29. Statistical Power of causal effects' estimation when \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 1\\) , proportion of invalid IVs is \\(30\\%\\) , balanced pleiotropy",
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+    "page_idx": 50
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+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_26.jpg",
+    "caption": "Figure S56. Causal effects' estimation when proportion of invalid IVs is \\(30\\%\\) , \\(\\mathbf{g} = 100\\) , \\(\\mathbf{E} = 3\\) , \\(\\mathbf{P} = 8\\) , balanced pleiotropy",
+    "bbox": [
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+    "page_idx": 50
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_27.jpg",
+    "caption": "Figure S57. Type I error/Power of causal effects' estimation when proportion of invalid IVs is \\(30\\%\\) , \\(g = 100\\) , \\(E = 3\\) , \\(P = 8\\) , balanced pleiotropy",
+    "bbox": [
+      [
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+        85,
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+      ]
+    ],
+    "page_idx": 51
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_4.jpg",
+    "caption": "Figure 4. Simulation results of the type I error rate for spurious exposures and statistical power for causal exposures when there is correlated and uncorrelated pleiotropy (MVMR). The number of IVs is 100, and the proportion of invalid IVs is \\(30\\%\\) . The number of populations is \\(E = 3\\) . Among total of eight exposures, two ( \\(X_{1}\\) and \\(X_{2}\\) ) are causal exposures (with a causal effect of 0.2), and the other six ( \\(X_{3},\\ldots ,X_{8}\\) ) are spurious exposures (with a causal effect of 0). This figure displays the type I error rates for \\(X_{1}\\) and \\(X_{2}\\) , the statistical power for \\(X_{3},\\ldots ,X_{8}\\) .",
+    "bbox": [
+      [
+        148,
+        85,
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+        537
+      ]
+    ],
+    "page_idx": 51
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "The first pathway: Mediation pathway Figure 1. The mediation pathway",
+    "bbox": [
+      [
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+        120,
+        836,
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+      ]
+    ],
+    "page_idx": 51
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_2.jpg",
+    "caption": "Figure 2. The confounding pathway",
+    "bbox": [
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+    ],
+    "page_idx": 52
+  }
+]

019a1322a4a18120bcf8546c95c7927691c4f4ceee9e4ba840a419b80a2ebe10/preprint/preprint.md

@@ -0,0 +1,378 @@
+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

01cfd239b63d0b5b3bd8fba2f46c4523116e4ea7471e771fa2f189c14b26428e/peer_review/images_list.json

@@ -0,0 +1,9 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_4.jpg",
+    "caption": "Supplementary Fig. 4 The relationship between length and resistance of PANi fibres with increasing lengths from 1 cm to 10 cm.",
+    "bbox": [],
+    "page_idx": 0
+  }
+]

01cfd239b63d0b5b3bd8fba2f46c4523116e4ea7471e771fa2f189c14b26428e/peer_review/peer_review.md

@@ -0,0 +1,233 @@
+Peer Review File
+
+Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors
+REVIEWER COMMENTS</B>
+
+Reviewer #1 (Remarks to the Author):
+
+The research work reported in the paper represents a significant breakthrough in flexible, polymer-based electronic applications, particularly, (1) improved electrical performance, (2) a pathway for high-volume production, and (3) high mechanical performance. The fibers developed could be used for many other applications for flexible, wearable electronics beyond the examples highlighted in the paper. The production approach shows the promise for future commercial applications. The mechanical properties (strength, modulus) of the fibers are in the very high range, demonstrating the potential for many demanding applications. The paper is very well written, with a clear presentation of the state-of-the-art status, motivations, approached, and mechanisms. The conclusions are reasonable and supported by data presented.
+
+Comment regarding equation for D_AB^O: What is its source? From literature or by data fitting? Variables in equation are defined but units should also be given.
+
+Minor edits: less one => less than one; larger than of conventional => larger than that of conventional
+
+Reviewer #2 (Remarks to the Author):
+
+Summary:
+
+The authors report a method to develop PANI fibers using a wet spinning approach with small diameters (< 5 um), good mechanical strength, and electrical properties amenable for use in e-textile applications. The reported method leveraged predoping with camphor sulfonic acid, and careful solvent choice of the coagulation bath. The authors demonstrate that choice of solvent dramatically impacts the surface morphology of the fibers, with NMP and DMF providing smooth and thin fibers with stability in air for four weeks. The authors then speculate that the use of a “good” solvent prevented quick solidification, and increased interfacial pressure during solvent exchange, and therefore allowed stretching of the fiber to reduce diameter and enhance morphology. The fibers showed good mechanical performance compared to other non-blended conjugated polymer-based fibers, which was attributed to the decrease in diameter and structural defects.
+
+The fibers were then used to create a microcapacitor, which was characterized by CV and GCD. The capacitance, power density, energy density, and stability, demonstrated reliable electrochemical performance. The charge storage capacity was determined and rivals that of other similar platforms. As
+such the fiber was used to make a solid-state OECT with a silver wire as the gate electrode, the fiber as the channel, and a PVA-H3PO4 gel, all wrapped in a polyurethane protective coating. The OECT was characterized and demonstrated low power consumption. The OECT was then demonstrated to respond to mechanical deformation through the pressure induced change in ion penetration. The favorable mechanical and electronic properties, as well as the scalability of these fibers will be of interest to the scientific community and warrants publication in Nature Communications. Please respond to the following:
+
+1) What exactly do the authors mean by “good” or “bad” solvent? Solution viscosity? The speed at which the PANI solidifies/coagulates, preventing slenderization? PANI solubility? 2nd virial coefficient (A2)? Diffusivity?
+
+2) Why do the differences in morphology when using a “good” or “bad” solvent lead to differences in stability?
+
+3) How reproducible and uniform are the properties of these fibers?
+
+4) For the fiber based OECT, an insulating PU was used to encapsulate the Ag wire, how does the capacitance of the PU compare with the double layer capacitance near the fiber/solid-state electrolyte interface? How is the gate voltage distributing from the gate to the channel?
+
+5) Can the authors make a table to compare the basic electrical properties of their OECT with previously reported fiber based OECTs
+
+Figures
+
+-When referring to the 5.4 km of UFPF, the text says Fig. 1e but should refer to Fig. 1g.
+
+-Clearly indicate that the panel next to Fig. 3e is a zoom in.
+
+-Add a legend to Fig. 2e to indicate the meaning of color
+
+-For Fig. 5e, considering the relative position between the Ag wire and PU layer, why will a change in friction alter the position of Ag inside the PU?
+
+Methods
+
+-What molecular weight of PANI powder was used?
+
+-Was there a particular choice behind using camphor sulfonic acid? Others have used AMPSA, sulfuric acid, HClO4, and NMP.
+
+-When referring to Raman “de-doping” peaks, explain what bonds you are looking at and give a citation.
+
+-How did you perform your Rheology?
+Point by point responses to the reviewer comments:
+
+Reviewer 1:
+
+1. Reviewer's Comment: The research work reported in the paper represents a significant breakthrough in flexible, polymer-based electronic applications, particularly, (1) improved electrical performance, (2) a pathway for high-volume production, and (3) high mechanical performance. The fibers developed could be used for many other applications for flexible, wearable electronics beyond the examples highlighted in the paper. The production approach shows the promise for future commercial applications. The mechanical properties (strength, modulus) of the fibers are in the very high range, demonstrating the potential for many demanding applications. The paper is very well written, with a clear presentation of the state-of-the-art status, motivations, approached, and mechanisms. The conclusions are reasonable and supported by data presented.
+
+Our response: We thank the reviewer for the positive comments.
+
+2. Reviewer's Comment regarding equation for \( D_{AB}^0 \): What is its source? From literature or by data fitting? Variables in equation are defined but units should also be given.
+
+Our response: We thank the reviewer for kind concern. The equation for \( D_{AB}^0 \) is derived from Ref. 25 (Smart Structures and Materials 2001: Electroactive Polymer Actuators and Devices. 4329, 59-71, 2001). We have also added the units of every variable (highlighted in Line 174-177).
+
+3. Reviewer's Comment: Minor edits: less one => less than one; larger than of conventional => larger than that of conventional.
+
+Our response: We thank the reviewer for critically reading our manuscript and pointing out our mistakes. We have corrected all the edits (highlighted in Line 34, 81 and 282).
+
+Reviewer 2:
+
+1. Reviewer's Comment: The authors report a method to develop PANI fibers using a wet spinning approach with small diameters (< 5 um), good mechanical strength, and electrical
+properties amenable for use in e-textile applications. The reported method leveraged pre-doping with camphor sulfonic acid, and careful solvent choice of the coagulation bath. The authors demonstrate that choice of solvent dramatically impacts the surface morphology of the fibers, with NMP and DMF providing smooth and thin fibers with stability in air for four weeks. The authors then speculate that the use of a “good” solvent prevented quick solidification, and increased interfacial pressure during solvent exchange, and therefore allowed stretching of the fiber to reduce diameter and enhance morphology. The fibers showed good mechanical performance compared to other non-blended conjugated polymer-based fibers, which was attributed to the decrease in diameter and structural defects.
+
+The fibers were then used to create a micro capacitor, which was characterized by CV and GCD. The capacitance, power density, energy density, and stability, demonstrated reliable electrochemical performance. The charge storage capacity was determined and rivals that of other similar platforms. As such the fiber was used to make a solid-state OECT with a silver wire as the gate electrode, the fiber as the channel, and a PVA-H3PO4 gel, all wrapped in a polyurethane protective coating. The OECT was characterized and demonstrated low power consumption. The OECT was then demonstrated to respond to mechanical deformation through the pressure induced change in ion penetration. The favorable mechanical and electronic properties, as well as the scalability of these fibers will be of interest to the scientific community and warrants publication in Nature Communications.
+
+Our response: We thank the reviewer for the positive comments.
+
+2. Reviewer’s Comment: What exactly do the authors mean by “good” or “bad” solvent? Solution viscosity? The speed at which the PANI solidifies/coagulates, preventing slenderization? PANI solubility? 2nd virial coefficient (A2)? Diffusivity?
+
+Our response: We thank the reviewer for the important comment. From the perspective of physical interpretation, “good” and “poor” solvents of PAni are determined by the intermolecular interactions between PAni chains and solvent molecules. In a good solvent, interactions between PAni chains solvent molecules are energetically favorable, and will
+cause PAni chains to expand and disperse well. In a poor solvent, PAni-PAni interactions are preferred and cause the PAni chains to disperse poor. Consequently, PAni molecules disperse good in good solvents, and disperse poor in poor solvents. We have added the discussions in the revised manuscript (highlighted in Line 137-140).
+
+3. Reviewer’s Comment: Why do the differences in morphology when using a “good” or “bad” solvent lead to differences in stability?
+Our response: We thank the reviewer for the crucial questions. The morphology does not directly determine the differences in stability. According to our SEM observations and X-ray diffraction analysis, the fibres produced in good solvents behaved higher degree of orientation and crystallization. The higher degree of crystallization protects the doping bonding in PAni chains from the attack of ambientes at the molecular level. As a result, the fibres produced in good solvents could show better stability in air. To avoid the misleading, we have rearranged the related discussions in the revised manuscript (highlighted in Line 145-150).
+
+4. Reviewer’s Comment: How reproducible and uniform are the properties of these fibers?
+Our response: We thank the reviewer for the kind comment. We discuss the uniformity of PAni fibres from the perspective of electrical and mechanical properties. In the case of electrical properties, because we used pre-doped PAni solutions as the raw dopes, the PAni fibres show uniform charge distribution throughout the fibre length. To confirm this point, we added a measurement to record the relationship between length and resistance. As shown in Supplementary Fig. 4, the value of resistance increases linearly with increasing length from 1 cm to 10 cm, demonstrating the favorable uniformity of electrical properties. In the case of mechanical properties, we provided the mechanical tensile tests of 5 fibres from 5 different batches, the results are shown in Response Tab. 1 for the information. The tensile strength and strain are generally stable, demonstrating the reliable uniformity of mechanical properties. We have added the discussions in the revised manuscript (highlighted in Line 111).
+![The relationship between length and resistance of PAni fibres with increasing lengths from 1 cm to 10 cm.](page_324_186_795_496.png)
+
+Supplementary Fig. 4 The relationship between length and resistance of PAni fibres with increasing lengths from 1 cm to 10 cm.
+
+<table>
+  <tr>
+    <th colspan="3">Response Tab. 1: The mechanical tests of PAni fibre from 5 batches</th>
+  </tr>
+  <tr>
+    <th>Batches</th>
+    <th>Tensile strength (MPa)</th>
+    <th>Strain (%)</th>
+  </tr>
+  <tr>
+    <td>Batch 1</td>
+    <td>1117.8</td>
+    <td>4.23</td>
+  </tr>
+  <tr>
+    <td>Batch 2</td>
+    <td>1073.2</td>
+    <td>3.03</td>
+  </tr>
+  <tr>
+    <td>Batch 3</td>
+    <td>1076.1</td>
+    <td>3.83</td>
+  </tr>
+  <tr>
+    <td>Batch 4</td>
+    <td>1127.8</td>
+    <td>4.13</td>
+  </tr>
+  <tr>
+    <td>Batch 5</td>
+    <td>1009.1</td>
+    <td>3.13</td>
+  </tr>
+</table>
+
+5. Reviewer’s Comment: For the fiber based OECT, an insulating PU was used to encapsulate the Ag wire, how does the capacitance of the PU compare with the double layer capacitance near the fiber/solid-state electrolyte interface? How is the gate voltage distributing from the gate to the channel?
+
+Our response: We thank the reviewer for the kind comments. We do not have the suitable devices at the micrometer scale to measure those parameters. However, PU is a dielectric layer which are difficult to be doped, so the capacitance of PU layer should be much smaller than that of fibre/electrolyte interface. From the gate to the channel, there are mainly three parts: the gate/electrolyte interface, gel electrolyte, and electrolyte/fibre interface. Among of them, the used gel electrolyte, PVA-H$_3$PO$_4$ gel, is almost insulating according to our
+electrical test (with a resistance beyond 10 M\( \Omega \) along with the gate bias direction). Thus, the gate bias is mainly divided into gate/electrolyte voltage and electrolyte/channel voltage. Kindly for your information, please refer to Ref. 54 (*IEEE Electron Device Lett.* 42, 46-49, *2020*). We have added the discussions in the revised manuscript (highlighted in **Line 275-277**).
+
+**6. Reviewer's Comment:** Can the authors make a table to compare the basic electrical properties of their OECT with previously reported fiber based OECTs?
+
+*Our response:* We thank the reviewer for the kind suggestions. We have added the table to compare the electrical properties of our device to other fibre-based OECTs in the revised manuscript (highlighted in **Line 287-288**).
+
+<table>
+  <tr>
+    <th colspan="5">Supplementary Tab. 1: The electrical properties in fibre-based OECTs</th>
+  </tr>
+  <tr>
+    <th>Ref No.</th>
+    <th>Channel</th>
+    <th>On/Off ratio</th>
+    <th>Drive (V)</th>
+    <th>\( g_m \) (\( \mu \)S)</th>
+  </tr>
+  <tr>
+    <td>This work</td>
+    <td>PAni</td>
+    <td>10<sup>3</sup></td>
+    <td>0.6</td>
+    <td>60</td>
+  </tr>
+  <tr>
+    <td>Ref. S1</td>
+    <td>PPy/PVA/PE</td>
+    <td>2.6\times10^2</td>
+    <td>3</td>
+    <td>/</td>
+  </tr>
+  <tr>
+    <td>Ref. S2</td>
+    <td>PPy</td>
+    <td>10<sup>4</sup></td>
+    <td>2</td>
+    <td>/</td>
+  </tr>
+  <tr>
+    <td>Ref. S3</td>
+    <td>CNT</td>
+    <td>10<sup>2</sup></td>
+    <td>1</td>
+    <td>1350</td>
+  </tr>
+  <tr>
+    <td>Ref. S4</td>
+    <td>PPy/Graphene</td>
+    <td>10<sup>2</sup></td>
+    <td>2</td>
+    <td>/</td>
+  </tr>
+  <tr>
+    <td>Ref. S5</td>
+    <td>PEDOT/PSS</td>
+    <td>10<sup>3</sup></td>
+    <td>1</td>
+    <td>1000</td>
+  </tr>
+</table>
+
+**7. Reviewer's Comment:** When referring to the 5.4 km of UFPF, the text says Fig. 1e but should refer to Fig. 1g.
+
+*Our response:* We have corrected it in the revised manuscript (highlighted in **Line 114**).
+
+**8. Reviewer's Comment:** Clearly indicate that the panel next to Fig. 3e is a zoom in.
+
+*Our response:* We thank the kind suggestions of the reviewer. We have added the label in **Fig. 3e** in the revised manuscript.
+
+**9. Reviewer's Comment:** Add a legend to Fig. 2e to indicate the meaning of color.
+
+*Our response:* We thank the reviewer for the kind suggestion. We have added the legend
+in the revised manuscript (highlighted in Line 130-132).
+
+10. Reviewer's Comment: For Fig. 5e, considering the relative position between the Ag wire and PU layer, why will a change in friction alter the position of Ag inside the PU?
+
+Our response: We thank the reviewer for the kind comment. Our OECT is a polymer-based soft device. The Ag gate is located in the upper PU layer, close to the friction action interface. It feels like we rub our skins using fingers. The action of friction will incur repeated horizontal movement of PU layer, which drives the movement of Ag gate, as illustrated in Fig. 5e. We have added the discussions in the revised manuscript (highlighted in Line 314-318).
+
+11. Reviewer's Comment: What molecular weight of PANI powder was used?
+
+Our response: The molecular weight of PAni used is 91.1106. We are not sure the value of average chain length. It was purchased from Aladdin, and the CAS number is 25233-30-1. We have added the information of chemicals in the revised manuscript (highlighted in Line 354).
+
+12. Reviewer's Comment: Was there a particular choice behind using camphor sulfonic acid? Others have used AMPSA, sulfuric acid, HClO4, and NMP.
+
+Our response: We thank the reviewer for the kind comment. The use of camphor sulfonic acid plays two roles: sulfonic groups enhance the dispersibility of PAni molecules and the proton improves the transport performance along PAni chains. Although we do not try other dopants due to the lack of storage in our lab, other dopants with above features could also work in principle.
+
+13. Reviewer's Comment: When referring to Raman "de-doping" peaks, explain what bonds you are looking at and give a citation.
+
+Our response: We thank the reviewer for the kind suggestion. We have added the explanations and some citations in the revised manuscript (highlighted in Line 154-155).
+
+14. Reviewer's Comment: How did you perform your Rheology?
+Our response: We thank the reviewer for the kind comment. The test of viscosity was conducted by the viscometer (NDJ-5S/9S/8S). We prepared a series of PAni gels by extruding PAni solutions in different solvents. Then, the probe of viscometer inserted into PAni gels after soaking in solvents, and the viscosity was recorded. To monitor the real state of gels as far as possible, we controlled the shear speed of probes at a very low value from 10 to 60 Rev. We have summarized and added the explanations in the revised manuscript (highlighted in Line 351-353).
+REVIEWERS’ COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The revised manuscript has addressed my concerns in my earlier review. I have no further comment.
+Point by point responses to the reviewer comments:
+
+Reviewer 1:
+
+1. Reviewer's Comment: The revised manuscript has addressed my concerns in my earlier review. I have no further comment.
+
+Our response: We thank the reviewer for the positive comments.

01cfd239b63d0b5b3bd8fba2f46c4523116e4ea7471e771fa2f189c14b26428e/preprint/preprint.md

@@ -0,0 +1,196 @@
+Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors
+
+Bo Fang
+Hong Kong Polytechnic University
+Jianmin Yan
+Hong Kong Polytechnic University
+Dan Chang
+Zhejiang University
+Jinli Piao
+Hong Kong Polytechnic University
+Kit Ming Ma
+Hong Kong Polytechnic University
+Qiao Du
+Hong Kong University of Science and Technology
+Ping Gao
+Hong Kong University of Science and Technology
+Yang Chai
+Hong Kong Polytechnic University   https://orcid.org/0000-0002-8943-0861
+Xiaoming Tao ( xiao-ming.tao@polyu.edu.hk )
+Hong Kong Polytechnic University   https://orcid.org/0000-0002-2406-0695
+
+Article
+
+Keywords:
+
+Posted Date: December 8th, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-1126903/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on April 19th, 2022. See the published version at https://doi.org/10.1038/s41467-022-29773-9.
+Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors
+
+Bo Fang1,2, Jianmin Yan1,3, Dan Chang4, Jinli Piao1,2, Kit Ming Ma1,2, Qiao Gu5, Ping Gao5, Yang Chai1,3*, Xiaoming Tao1,2*
+
+1Research Institute for Intelligent Wearable Systems, Hong Kong Polytechnic University, Hong Kong, 999077 China
+2Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong, 999077 China
+3Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, 999077 China
+4Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310027 China
+5Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Hong Kong, 999077 China
+
+Email: ychai@polyu.edu.hk; xiao-ming.tao@polyu.edu.hk
+
+The development of continuous conducting polymer fibres is essential for applications ranging from advanced fibrous devices to frontier fabric electronics. The use of continuous conducting polymer fibres requires a small diameter to maximize their electroactive surfaces, microstructural orientations, and mechanical strengths. However, regularly used wet spinning techniques have rarely achieved this goal due primarily to the insufficient slenderization of rapidly solidified conducting polymer molecules in poor solvents. Here we report a good solvent exchange strategy to wet spin the ultrafine polyaniline fibres at the large scale. The slow diffusion between good solvents distinctly decreases the viscosity of gel protofibers, which undergo an impressive drawing ratio. The continuously collected polyaniline fibres have a previously unattained diameter below 5 \( \mu \)m, high energy and charge storage capacities, and favorable mechanical performance. We demonstrated an ultrathin all-solid organic electrochemical transistor based
+on ultrafine polyaniline fibres, which substantially amplified microampere drain-source electrical signals with less one volt driving voltage and effectively operated as a tactile sensor detecting pressure and friction forces at different levels. The aggressive electronical and electrochemical merits of ultrafine polyaniline fibres and their great potentials to prepare on industrial scale offer new opportunities for high-performance soft electronics and large-area electronic textiles.
+
+The extended conjugated and easily doped \( \pi \)-system along the backbone enables conducting polymers to possess intriguing transport, optical, and electrochemical properties, which have rarely been found in conventional polymers and metal conductors\( ^{1-3} \). Processing conducting polymers into macroscopically fibrous materials makes it possible to translate their nano-object features to human-friendly products in a continuous manner. The combined merits, including but not limited to mechanical flexibility, intrinsic conductivity, and electrochemical activity, of conducting polymer fibres (CPFs) have introduced a new era of “electronic textiles”\( ^{4} \). For instance, highly conductive and electrochemically active poly(3-methylthiophene) fibres have been achieved by in situ electrochemical oxidation of monomers\( ^{5} \). Fast ion transport between CPFs and ionic liquids has given birth to long-term operation actuators, electrochromic windows, and numeric displays\( ^{6} \). In recent studies, the wet-spun poly (3,4-ethylene dioxythiophene) (PEDOT) fibres have been widely used in various frontier fields, such as flexible energy storage electrodes, implantable bioelectronics, and organic transistors\( ^{7,8} \).
+Unfortunately, due primarily to the large diameters, the performance and expectations of most achieved continuous CPFs have been limited by their insufficient electroactive surfaces and weak breaking strengths. Electrospinning and wet spinning are two mainstream strategies to produce continuous CPFs. In the case of electrospinning, the fairly rigid backbone due to the high aromaticity results into an insufficient elasticity of conducting polymer solutions, which fails to be solely electrospun into fine fibres\( ^{9} \). Although a two-fluid electrospinning technique has been proposed by coating a soluble and electrospinnable fluid on the conducting polymer cores, the complex procedures
+involving the addition and removal of second components defy the mass production of electrospun CPFs\(^{10,11}\). In the case of conventional wet spinning, conducting polymer dopes tend to occur a transient solidification in poor solvents, induced by the strong interactions of conducting polymer chains. The rapidly hardened gels suppress the post-stretching and slenderizing procedures, and cause the wet-spun CPFs to show a large diameter, generally beyond 10 \( \mu \)m\(^{12-14}\). The large diameters largely discount the mechanical properties and electrochemical activities of CPFs\(^{4,15}\). Thus, there is an urgent need to realize the mass production of ultrafine CPFs, which remains challenging. In this work, we report a good solvent exchange strategy in a modified wet spinning technique to prepare the ultrafine polyaniline (PAni) fibres (UFPFs) at the large scale. Beyond conventional wet spinning protocol, we replaced poor solvents by good solvents as the coagulation bath to decrease the viscosity of gel protofibres, which were subject to an ultrahigh drawing ratio and reduced to an ultrafine morphology. The obtained UFPGs own a small diameter below 5 \( \mu \)m, an unprecedented mechanical strength of 1080 \( \pm \) 71 MPa, a high area capacitance beyond 1008 mF cm\(^{-2}\), and an enormous charge storage capacity of 5.25\( \times \)10\(^4\) mC cm\(^{-2}\). Based on the structural and electrochemical merits of UFPGs, we demonstrated an ultrathin all-solid organic electrochemical transistor (OECT) with less one volt driving voltage, which substantially amplified drain-source electrical signals with a low power-consumption and responded to vertical pressure and horizontal friction forces at different levels. Our work opens an avenue to prepare continuous ultrafine CPFs and high-performance soft electronics.
+Fig. 1: Scalable production of UFPFs. a Schematic of the good solvent exchange strategy to prepare UFPFs in a modified wet spinning protocol. In the case of poor solvent exchange (light orange region, upper panel), PAni molecules are rapidly solidified into thick gels and protofibres with rough crystallized particles. In the case of good solvent exchange (light blue region, lower panel), the formed gels with low viscosity occur an impressive gel extension and are slenderized into ultrafine fibres. b Schematic of the modified wet spinning process. c Scanning electron microscope (SEM) image of the marked region in b, showing the sharp necking behavior of gel PAni fibres. The close observation to region 1 (d), region 2 (e), and region 3 (f) in the marked zone of c, illustrating the sharply necking process of PAni gels. g Photograph of a 5.4-kilometres-long UFPF collected in two hours. Scale bars: c 20 μm, d 2 μm, e 10 μm, g 150 mm.
+Results
+
+Preparation and characterization of UFPFs. In the modified one-step wet spinning process, we used good solvents as the coagulation bath to realize the mass production of UFPFs (Fig. 1a-b and Supplementary Fig. 1). After doping PAni power (emeraldine base) with camphor sulfonic acid (CSA) at a molar ratio of 2:1, we dispersed fully doped PAni into m-cresol as the raw spinning dopes (see the Methods section)\(^{16}\). Significantly, the direct use of doped PAni solutions as the dopes saves the trouble of conventional post-doping procedures, and further permits the uniform charge distribution throughout the fibre length\(^{17}\). A good solvent, dimethyl formamide (DMF), of PAni operated as the coagulation bath. A slow solvent exchange between m-cresol and DMF facilitated the formation of PAni gel protofibres with a quite low viscosity below 3000 cP. Subsequently, we observed a sharp decrease of diameter from ~0.1 mm to ~4.7 \( \mu \)m when stretching the gel fibres in bath (Fig. 1c-f), which, to our knowledge, is a record small value in the achieved wet-spun CPFs\(^{4}\). The ultrafine fibre shows a smooth surface (Fig. 1f and Supplementary Fig. 2) and highly crystallized microstructures (Supplementary Fig.3). Moreover, such an impressive drawing ratio enables a very high production efficiency of UFPFs beyond 40 meters per minute. For example, we prepared a 5.4-kilometres-long UFPF in two hours (Fig. 1e).
+Fig. 2: Mechanism and mechanical properties of UFPPFs. a SEM images of the PAni fibres produced in different solvating species. Specifically, the upper four panels showing the fibres prepared from poor solvents, and the lower two panels showing the fibres fabricated from good solvents. b Raman spectra of PAni fibres after placing in air for four weeks. c The diffusivity from PAni dispersions (in m-cresol) to various solvating species. d The viscosity of PAni gels formed in various solvating species. e Mechanics simulation results of extension behaviors of PAni gel fibres at different interfacial pressure. f Typical tensile stress-strain curves of UFPPFs. g Ashby plot comparing the mechanical strength of UFPPFs to previously reported CPFs. Scale bars in a: Water, Ethanol, EA, Acetone 20 μm (left) 10 μm (right); NMP 20 μm (left) 5 μm (right), DMF 20 μm (left) 2 μm (right).
+
+The sharp necking behaviors of gel protofibres are highly related to the use of good solvents as the coagulation bath. We recorded the evolution of surface morphologies of PAni fibres collected from different solvating species. As shown in Fig. 2a, the obtained fibres in poor solvating species, i.e., water, ethanol, ethyl acetate (EA), and acetone, generally present coarse surfaces and large diameters around 20 μm. By comparison,
+we clearly observed a necking phenomenon in both cases of good solvents, i.e., N-methyl-2-pyrrolidone (NMP) and DMF. Such necking effects promoted the finally produced fibres to behave ultrafine morphologies, which assists PAni fibres to behave better structure and performance stabilities due to the higher degree of orientation and crystallization (see the X-ray diffraction analysis in Supplementary Fig. 3). We used Raman spectra to evaluate their structural evolution after placing fibres in air for four weeks. As shown in Fig. 2b, we did not find obvious de-doping signals in Raman spectra of the PAni fibres from good solvents, whereas various de-doping peaks (1223 cm\(^{-1}\) and 1462 cm\(^{-1}\)) appeared in the cases of poor solvents.
+
+We speculate that this sharp necking phenomenon may be caused by two factors: diffusion difference and interfacial pressure. In the conventional wet spinning protocol, the diffusion from good solvents to poor solvents occurs quickly to solidify dope fluids into gel fibres\(^{18,19}\). The rapid diffusion could be aggravated in the system of conducting polymers due to the strong interactions of rigid chains. Thus, PAni molecules tend to bond into irregularly crystallized particles prior to undergoing extensive drawing, as present in the upper panels of Fig. 1a. In previous reports using poor solvents as coagulation bath, although CPFs with a smooth surface could be collected by enhanced shear flow and strong stretching\(^{12,14}\), diameters are unable to be decreased to the ideal level due to the insufficient stretching slenderization of solidified gels. In contrast, the diffusion from dope fluids to good solvents is quite slow. Such slow diffusion allows the formation of fibrous gels with a low viscosity and the following high drawing ratios. Note that most conventional polymers are incapable of gelling in good solvents due to the poor chain interactions\(^{20,21}\).
+
+We calculated the diffusivities between various solvents and measured the viscosity of corresponding formed gels to support our explanations. The diffusivity from A molecules to B molecules, \( D_{AB}^0 \), is determined by the equation
+
+\[
+\frac{D_{AB}^0 \mu_B}{T} = 8.52 \times 10^{-8} V_{pB}^{-1/3} \left[ 1.40 \left( \frac{V_{BB}}{V_{bA}} \right)^{1/3} + \frac{V_{BB}}{V_{bA}} \right]
+\]
+, where \( \mu_B \) is the solvent viscosity, T is the temperature, and \( V_b \) is the molar volume of solvent at its normal boiling temperature\(^{22}\). As displayed in Fig. 2c, the diffusivities from m-cresol to DMF (\(7.5\times10^{-6}~cm^2s^{-1}\)) and NMP (\(7.71\times10^{-6}~cm^2s^{-1}\)) are generally lower than that of poor solvents. Diffusion in bath further dominates the viscosity of protofibres. To monitor the viscosity of gel fibres in practical conditions, we conducted the viscometer tests at a low revolution (e.g., 10 Rev.). As summarized in Fig. 2d, the formed PAni gels in good solvents show a viscosity below 3000 cP, much lower than that of poor solvents (>4000 cP). The established solvating specie-diffusivity-viscosity formula accords well with our proposed explanations.
+
+Interfacial pressure during solvent exchange is another major factor relating to the necking behavior of PAni protofibres. In a two fluid system, the interfacial pressure between two kind of solvents is inclined to decrease with the improved solvent diffusion\(^{23}\). Based on the slow diffusion from m-cresol to good solvents (Fig. 2c), the interfacial pressure between gel fibres and coagulation bath is considerable, which further induces the necking of protofibres. To understand this, we conducted a mechanic simulation to the stretching behavior of gel fibres at different interfacial pressure (see the progressive results in Supplementary Fig.4 and Method section). According to the simulation results in Fig. 2e, the higher interfacial pressure drives gel fibres to occur the sharper necking and thinning effects at a given tensile stress. This probably explains the formation of UFPPFs in DMF bath.
+
+UFPPFs show impressive mechanical performance. Different from that of conventional polymer fibres, the typical linear strain-stress curves of UFPPFs demonstrate a brittle fracture behavior with a small tensile strain of 3.67±0.64% (Fig. 2f). It is reasonable if considering the rigid backbone of PAni chains, which likely gather and condense into fragile fibrous assemblies after undergoing strong shear flow in spinning microtubes. According to classical Griffith theory on brittle fracture, fibres’ strength generally improves with the decrease of diameter due to the depressed structural defects\(^{24}\). We compared the mechanical performance of UFPPFs with previously reported CPFs.
+Fig. 3: Energy and charge storage capacities of UFPFs. a Schematic of a micro capacitor constructed using two UFPF electrodes on a substrate. b Cyclic voltammetry curves with the increasing scan rates from 10 to 20, 50, 80 and 100 mV s^{-1}. c Galvanostatic charge/discharge curves at various current densities increasing from 0.32 to 0.63, 1.59 and 3.18 mA cm^{-2}. d The area capacitance of UFPFs comparing to previous reported electrodes. e Cycle galvanostatic charge/discharge curves during 120 cycles between 0 and 0.6 V at 1.59 mA cm^{-2}. f. The relationship between current and voltage at a slow rate of 10 mV s^{-1}. g The charge storage capacity of UFPFs comparing to other charge storage materials.
+
+Derived from the strain-stress curves, we concluded that UFPFs have a modulus of 29.89±5.6% GPa, and a strength of 1080±71 MPa, at least one order of magnitude higher than that of CPFs with larger diameters (Fig. 2g), mainly including PEDOT fibres (<450 MPa)^{7,25-29} and PAni fibres (<400 MPa)^{30-33}.
+
+Energy and charge storage capacities. Ultrafine morphology optimizes the
+electroactive surfaces, which enables UFPFs to exhibit superb energy and charge storage capacities. To evaluate the electrochemical activity of UFPFs, we constructed a micro capacitor using polyvinyl alcohol (PVA)-H3PO4 gel electrolyte and two UFPF electrodes (Fig. 3a). The electrochemical properties were checked by cyclic voltammetry (CV) and galvanostatic charge-discharge (GCD) measurements. At different scan rates, the nearly rectangular shape of CV curves and instantaneous current response to voltage reversal at each end potential suggest the good electrochemical activity of UFPFs34 (Fig. 3b). The nearly triangular shape of GCD curves at different current densities illustrates the formation of efficient electric double layers and charge propagation across the UFPF electrodes35 (Fig. 3c). According to the GCD results, we determined the electrochemical properties of UFPFs. Among of them, the area capacitance, \( C_A \), is between 1008 and 1666 mF cm\(^{-2}\) at the current densities between 0.32 and 3.18 mA cm\(^{-2}\), outperforming previously reported thick CPFs29 and other electrodes, such as carbon nanomaterials3434,36, metal oxides37 and conducting polymers38-41, and approaching to that of PAni nanowires42 (Fig. 3d). The volumetric capacitance, power density and energy density reach 83.8 F cm\(^{-3}\), 0.96 W cm\(^{-3}\) and 4.19 mWh cm\(^{-3}\), respectively (Supplementary Fig. 5). In lifetime tests of UFPF-based capacitor, both the potential and capacitance continued without significant decrease for 120 charge/discharge cycles at a low current density of 1.59 mA cm\(^{-2}\), indicating the reliable electrochemical performance stability of UFPFs (Fig. 3e).
+
+We were able to confirm the amount of transported charge per unit area to UFPF during the charge/discharge cycle. The charge during a triangular wave potential between -0.9 V and 1.0 V (water window, see the Supplementary Fig. 6) was calculated by integrating the measured current with respect to the time of period at a low scan rate of 10 mV s\(^{-1}\) (Fig. 3f)6. We determined that the charge storage capacity of UFPF was 5.25×10\(^{4}\) mC cm\(^{-2}\), a value at least two orders of magnitude higher than that of noble metals43, carbon bulk44 - 46 and previously reported conducting polymers47 (Fig. 3g). This value decreases slightly to 2.015×10\(^{4}\) mC cm\(^{-2}\) at a tenfold scan rate of 100 mV s\(^{-1}\) (Supplementary Fig. 7).
+Fig. 4: Demonstration and characterization of all-solid organic electrochemical transistor based on UFPFs. a Schematic of the all-solid OECT composed of three polymer layers, one silver wire as the gate electrode, and one UFPF as the drain-source channel. b Cross-section SEM image and schematic of OECT. The yellow break lines direct the charge flow along the fibre chains (green solid lines). c Transmittance of the OECT in the region of visible light. A typical output curve (d), transfer curve (e), and power consumption in operation (f) of OECT. Scale bars: b 20 μm.
+
+Structure and performance of all-solid OECT. Benefitting from the favorable energy and charge storage performance of UFPFs, we demonstrated a high-performance all-solid OECT. OECT amplifies drain-source current intensities at low operating voltages by ion penetration into the organic mixed ionic-electronic conductors, i.e., conducting
+polymers^{48,49}. This process is controlled by the gate bias, and, to date, has generally conducted in aqueous electrolytes. To preclude the interference of external environment, we promoted the working conditions of OECT from aqueous environments to all-solid state by using gel electrolytes as the ion matrix. As shown in Fig. 4a-b, our OECT is mainly constructed by three polymer layers. The upper layer is the cured polyurethane (PU) working as the dielectric coating and also protecting the device from the invasion of external action^{50}. A fibrous silver gate electrode with a diameter of 7 \( \mu \)m is fixed in PU. Since UFPFs have demonstrated reliable electrochemical activities in PVA-H$_3$PO$_4$ gel, we used PVA-H$_3$PO$_4$ gel as the middle layer to inject ions to or uptake ions from the drain-source channel materials. A UFPF right below the silver gate is fused in the ion gel, and operates as the channel material. The bottom layer is also pure PU acting as the supporter of the whole device. Due to the remarkable flexibility and transparency of PVA and PU, the all-solid OECT is very soft, and shows a transmittance beyond 80 % in the region of visible light (Fig. 4c), and a small thickness below 300 \( \mu \)m.
+
+Despite the long channel length (~0.48 cm), much larger than of conventional micrometer-scale device, the all-solid OECT showed favorable amplification performance with a high on-off current ratio (>10$^3$, Fig. 4e) at low voltages (<1 V, Fig. 4d). The relatively fair transconductance (g$_{m}$, < 60 \( \mu \)S) is probably ascribed to the small cross-sectional area, which dramatically magnifies the resistance of fibrillar channel. Note that the all-solid OECT is an energy saving device with extremely low power consumptions. For example, at a given drain-source voltage of 0.6 V, the consumed power is below 18 \( \mu \)W (Fig. 4f).
+Fig. 5: Electrical response of the all-solid OECT to mechanical deformations. a Schematic of the mechanism explaining the response to the action of external pressure. b Relative drain-source change (\( \Delta I_{DS}/I_{DS0} \)) and sensitivity as a function of pressure. c Response time of the all-solid OECT when pressing (rising edge) and releasing (falling part) under the instantaneous pressure of 17.8 KPa. d Cyclic response at three different pressure levels (0.92, 6.8, and 22.2 KPa). e, Schematic of the working principle of the response to friction. f Cyclic response at three different frictions (1.84, 4.69, and 5.55 KPa). g An enlarged curve of the marked part in (f). h Cyclic response at different friction speeds from 4, 6, 8, 10, 15, to 20 mm s\(^{-1}\).
+
+We proved that the all-solid OECT functioned to amplify small electrical signals in gel environments and respond to mechanical deformation as a tactile sensor. As illustrated in Fig. 5a, the applied vertical pressure on the surface of the all-solid OECT adjusted the ion penetration due to the improved gate-source electric field and the redistribution of intrinsic capacitance\(^{51}\). At a \( V_G \) of -0.1 V and a \( V_D \) of 0.35 V, we observed a stable increase of drain-source current, \( I_{DS} \), with the increasing pressure, up to a 92% amplification from 0 to 40 KPa (Fig. 5b). The sensitivity is at the level of 0.01-0.1 KPa\(^{-1}\) in this process (dark cyan dots in Fig. 5b). As shown in Fig. 5c, the average rising time and falling time under instantaneous pressure of 17.8 KPa is ~536 ms and ~698 ms,
+respectively. Such integrated parameters facilitated the all-solid OECT to respond to different pressure levels from 0.92 to 22.2 KPa (Fig. 5d). In addition to the response to pressure at the vertical direction, the all-solid OECT also reacted to friction at the horizontal direction (Fig. 5e and Supplementary Fig. 8). The forward and backward friction of a load on the surface changed the real-time distance between silver gate and UFPF channel repeatedly, thus producing a bimodal response curve (Fig. 5g). Note that, to enable the enlargement of \( I_{DS} \) with the increasing gate-channel distance under the repeated friction, we applied a positive \( V_G \) of 0.1 V at a \( V_D \) of 0.55 V. The all-solid OECT responded stably to friction at different magnitudes (Fig. 5f, from 1.84 to 5.55 KPa) and different speeds (Fig. 5h, from 4 to 20 mm s\(^{-1}\)) during our cyclic tests. For example, \( I_{DS} \) increased ~86% at 5.55 KPa.
+
+Discussion
+The past decades have witnessed great achievements in preparing high-performance CPFs, which made a vast difference to the rapid development of advanced electronics. However, due to the limitations of both technology and strategy, it is still difficult to produce ultrafine CPFs at the large scale. We proposed a good solvents strategy in a modified wet spinning technology. With a principle of diffusion-controlled slow gelation of protofibres, the new system successfully downsized the diameter of PAni fibres to below 5 \( \mu \)m, a value smaller than that of most previous work. Furthermore, the ultrafine morphology with highly improved electroactive surfaces promotes UFPFs to behave superb electrochemical activities and mechanical performance. It is of great importance to realize the mass production of ultrafine CPFs. We constructed an all-solid OECT to employ the impressive energy and charge storage capacities of UFPFs. A handful of fibres are robust enough to satisfy the operation as the tactile sensor. In view of the ability to produce on the industrial scale, UFPFs are promised to be extended to large-area electronics, such as textile-scale numeric displays, soft electrochromic windows, and wearable energy harvesting systems.
+Methods
+
+Characterizations. All the SEM images were collected on a tungsten thermionic emission SEM system (the Tescan VEGA3). XRD spectra were obtained from XRD system (Rigaku SmartLab) equipped with 9 kW rotating anode X-ray source (\( \lambda \sim 1.54\text{\AA} \)) coupling with high-quality semiconductor detector that supports 0D, 1D or 2D x-ray diffraction measurement. Raman spectra were recorded from Renishaw Micro-Raman Spectroscopy system fully integrated with confocal microscope spectrometer and a 785 nm laser source. Mechanical tests were conducted on an advanced rheometric expansion system at the Hong Kong University of Science and Technology. All the electrochemical tests were processed on an electrochemical workstation (VersaSTAT3). The measurements of OECT were conducted on probe station (Micromanipulator) with Keithley 4200A-SCS parameter analyzer.
+
+The fabrication of UFPFs. PAni power (emeraldine base, purchased from Sigma-Aldrich) was mixed with CSA at a molar ratio of 2:1. After being milled for 15 minutes, the uniform doped PAni was dispersed in m-cresol (after degassing) at a concentration of 0.05 g mL\(^{-1}\). The dispersions were used as spinning dopes after blending in air for 8 hours, and extruded through a PEEK microtube with an inner diameter of 100 \( \mu \)m at a rate of 1mL min\(^{-1}\). Coagulation bath was chosen according to the experimental requirements. PAni fibres were directly drawn out from bath and collected on a graphite roller continuously.
+
+Numerical method. The experimental result is verified by numerical method using commercial software ANSYS. The simulation is performed using workbench 18.0. In the simplified computational model, a geometric model of gel tube is developed, in which the ratio of diameter to length is chosen as 1:18, and the mechanical properties, density, Young’s modulus and Poisson’s ratio are selected as 300kg/m3, 1000Pa and 0.01, respectively. For the boundary conditions, one end of the gel model set as fixed support, and another end applies extend displacement to mimic the stretching effect in the actual situation. Meanwhile, the corresponding pressure is applied on the outer surface of the gel model to account for the function of the impressive interfacial pressure on the surface of gel fibres. To ensure the convergence of the result, a grid independence test is conducted by refining mesh size sequentially, and the finite element mesh with 162641 nodes and 37128 hexahedral elements are adopted finally.
+
+The fabrication of micro capacitor. Micro capacitor composed of two UFPF electrodes and the
+gel electrolyte was constructed on a glass substrate. To prepare the gel electrolyte, PVA power was dispersed into deionized water at a mass ratio of 9:1. PVA was dissolved after being heated for 5 hours at 85 °C. Then phosphoric acid was added at a mass ratio of 1:10 with deionized water. The mixture cooled at room temperature and were ready for use. Two UFPPFs were placed in parallel on the glass slide. The transparent PVA-H3PO4 gel was dropped between UFPPFs. Two cooper wires connected to the UPPFs with silver paste worked as the conductor lines. After condensing for 10 minutes at 40 °C, the whole device was subject to electrochemical tests.
+
+The fabrication of all-solid OECT. The OECT was built from three layers: two PU layers and one ion gel layer. PU dispersion in DMF was casted on a PVDF substrate. After being treated in oven at 60 °C, a thin and transparent layer of pure PU was obtained. One drop of PVA-H3PO4 gel electrolyte was added on the surface of solidified PU. An UFPPF was immersed into gel. After been dried at 45 °C for 15 minutes, a UFPPF channel locked in PVA-H3PO4 gel was obtained. Afterwards, another drop of PU was added and a silver wire operation as the gate electrode was putted in PU at the liquid state. After being dried at 60 °C, an all-solid OECT was prepared. Note that all the three electrodes were connected to cooper electrodes for following measurements.
+
+Data availability
+
+The data that support the findings of this study are available from the corresponding author upon reasonable request. Correspondence and requests for materials should be addressed to Y.C. and X.T.
+
+Acknowledgements
+
+This work is supported by the Research Grants Council of Hong Kong (No. 15201419 ), Hong Kong Polytechnic University Postdoctoral Fellowship and Endowed Professorship Fund (No. 847A).
+
+Author contributions
+
+X. T. supervised this study. B. F. designed and conducted the main experiments. J. Y., Y. C. and B. F. constructed and characterized the transistor. D. C. helped to build the wet spinning equipment and discussed the results. J. P. did the mechanic simulations. K. M. M. helped to draw a part of schematics. Q. G. and P. G. helped to conduct the mechanical tests. B.F., X. T. and Y. C. wrote the manuscript.
+
+Competing interests
+
+The authors declare no competing interests.
+
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementaryinformation1130.pdf

01cfd239b63d0b5b3bd8fba2f46c4523116e4ea7471e771fa2f189c14b26428e/preprint/supplementaries/Supplementaryinformation1130/Supplementaryinformation1130.md

@@ -0,0 +1,33 @@
+Supplementary information for
+
+Scalable production of ultrafine polyaniline fibres for tactile organic electrochemical transistors
+
+Bo Fang1,2, Jianmin Yan1,3, Dan Chang4, Jinli Piao1,2, Kit Ming Ma1,2, Qiao Gu5, Ping Gao5, Yang Chai1,3* Xiaoming Tao1,2*
+
+1Research Institute for Intelligent Wearable Systems, Hong Kong Polytechnic University, Hong Kong, 999077 China
+2Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong, 999077 China
+3Department of Applied Physics, Hong Kong Polytechnic University, Hong Kong, 999077 China
+4Department of Polymer Science and Engineering, Zhejiang University, Hangzhou, 310027 China
+5Department of Chemical and Biological Engineering, The Hong Kong University of Science and Technology, Hong Kong, 999077 China
+
+Email: ychai@polyu.edu.hk; xiao-ming.tao@polyu.edu.hk
+Supplementary Fig. 1 | Photograph of continuous collecting of ultrafine polyaniline fibres (UFPFs) in dimethyl formamide (DMF) bath. A clear slenderization occurs along the fibre length.
+
+![Photograph of continuous collecting of ultrafine polyaniline fibres (UFPFs) in dimethyl formamide (DMF) bath.](page_246_180_957_232.png)
+Supplementary Fig. 2 | SEM images showing the surface and cross-section of UFPFs at different magnitudes.
+Supplementary Fig. 3 | X-ray diffraction spectra of ultrafine PAni fibres collected from DMF bath (orange curve) and rough PAni fibres collected from acetone bath (olive curve). Comparing to the rough fibres, the ultrafine PAni fibres exhibit rich crystalline peaks along the 12-1, 11-3 and 322 panels, suggesting the highly crystallized microstructures of UFPFs.
+
+![X-ray diffraction spectra of ultrafine PAni fibres collected from DMF bath (orange curve) and rough PAni fibres collected from acetone bath (olive curve)](page_374_186_700_500.png)
+Supplementary Fig. 4 | Mechanics simulation to the progressive extension behaviors of PAni gel protofibres at different interfacial pressures increasing from 0 (a), 100 Pa (b), 200 Pa (c) to 300 Pa (d). Obviously, the necking phenomena tend to occur at the higher interfacial pressures.
+Supplementary Fig. 5 | Volumetric capacitance, power and energy density of UFPFs. At the current densities between 127.4 and 1273.8 mA cm\(^{-3}\), the volumetric capacitance is calculated to be between 83.8 and 50.7 F cm\(^{-3}\), the power densities between 0.1 and 0.96 W cm\(^{-3}\), and energy densities between 2.53 and 4.19 mWh cm\(^{-3}\).
+Supplementary Fig. 6 | The identification of water window in UFPF-based micro capacitor. The water oxidation and reduction potentials, indicated by the steep increase of current densities in CV curve, define the water window of micro capacitor. The water window is located between -0.9 and 1 V in UFPF-based micro capacitor.
+
+![CV curve showing the water window region](page_246_312_1017_563.png)
+Supplementary Fig. 7 | The voltage-current relationship at a scan rate of 100 mV s^{-1}. Deriving from this curve, the area charge storage capacity and volumetric capacity is 2.015\times10^4\ \mathrm{mC}\ \mathrm{cm}^{-2} and 8.07\times10^4\ \mathrm{mC}\ \mathrm{cm}^{-3}, respectively.
+
+![Voltage-current relationship at a scan rate of 100 mV s^{-1}](page_312_232_823_627.png)
+Supplementary Fig. 8 | The device measuring the friction response of organic electrochemical transistor (OECT). The device is mainly composed of three parts: the upper holder directing the movement of friction analyzer (light red), an UFPF-based OECT right below the friction sensor connecting to a friction analyzer through optical fibres, and a XYZ-stage controlling the position of OECT. The working principle of friction analyze system referees to Zhang’s work¹.
+
+Reference
+
+1. Zhang, Z. F., Tao, X. M., Zhang, H. P. & Zhu, B. Soft fiber optic sensors for precision measurement of shear stress and pressure. IEEE Sens. J. **13**, 1478-1482 (2013).

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+    "caption": "Supplementary Fig. 2 | SEM images showing the surface and cross-section of UPFFs at different magnitudes.",
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+    "caption": "Supplementary Fig. 5 | Volumetric capacitance, power and energy density of UFPFs. At the current densities between 127.4 and 1273.8 mA cm<sup>-3</sup>, the volumetric capacitance is calculated to be between 83.8 and 50.7 F cm<sup>-3</sup>, the power densities between 0.1 and 0.96 W cm<sup>-3</sup>, and energy densities between 2.53 and 4.19 mWh cm<sup>-3</sup>.",
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_6.jpg",
+    "caption": "Supplementary Fig. 6 | The identification of water window in UFPF-based micro capacitor. The water oxidation and reduction potentials, indicated by the steep increase of current densities in CV curve, define the water window of micro capacitor. The water window is located between -0.9 and 1 V in UFPF-based micro capacitor.",
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+    "img_path": "images/Supplementary_Figure_7.jpg",
+    "caption": "Supplementary Fig. 7 | The voltage-current relationship at a scan rate of 100 mV \\(\\mathbf{s}^{-1}\\) . Deriving from this curve, the area charge storage capacity and volumetric capacity is \\(2.015 \\times 10^{4} \\mathrm{mC cm}^{-2}\\) and \\(8.07 \\times 10^{4} \\mathrm{mC cm}^{-3}\\) , respectively.",
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0207534b48d5dc7f202715e97467615fe845cf6d2005bff553f5b155b496fd65/peer_review/images_list.json

@@ -0,0 +1,30 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_1.jpg",
+    "caption": "Figure 1: (a-c) Illustrating the conceptual implementation of road fragmentation in ORCHIDEE-SPITFIRE. (a) Fragments are conceived of as circles whereby edge effects on fuel moisture, wind infiltration and human ignition (v1-3) are defined by the 'edge depth' through which there is a gradient from fragment edge to interior. This is shown in the transect at the bottom, where each gradient decreases/increases towards the fragment interior and values for the edge depth shown. (b) The ratio of the total 'edge area' (blue shading) versus the 'non-edge area' (green) is defined by the edge depth and the surface area of the individual patch, which depends on fragmentation extent and so the number of patches per grid cell. This surface area also limits the maximum size of any individual non-extreme fire. (c) (top) Fragmentation extent is proxied by road length to generate average circular patch area and radius ('average edge distance'), determining the size and number of fragment patches in a grid cell. (bottom) The result of these conceptual implementations alters a given variable (var1-3) in direct proportion to the edge area entailed by a-c. See Fig. S1 and S2 for greater detail on how these implementations affect the sequence of processes represented in the model. (d) Simplified schematic diagram describing the combined vegetation and fire modules of ORCHIDEE-SPITFIRE, and the relation of the AED-defined fragmentation scheme devised here, to fire-relevant variables in the model. Adapted from Supplementary Figure in ref.(Bowring et al., 2022). See Model Description text (Methods) and Supplementary Text S11 for details on model functioning.",
+    "bbox": [],
+    "page_idx": 8
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Figure S3: (a) The variation of grid cell-mean average edge distance with grid cell total road length, for a grid cell of \\(2500 \\mathrm{~km}^2\\) , calculated on the basis of the methodology used herein (the transformation of road length into perimeters of iso-radial circles. (b) Variation of the human ignition function originally implemented in ORCHIDEE-SPITFIRE (black line) by increasing levels of road fragmentation, as estimated here by a decreasing value of the average edge distance of vegetation fragments. As AED decreases (when there is more fragmentation), human ignition potential increases through a direct probabilistic multiplier given by the ratio of fragment edge area to fragment surface area (see Methods and Supplementary Text S5).",
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+  },
+  {
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+    "img_path": "images/Figure_unknown_1.jpg",
+    "caption": "Figure S4: (a) Histogram of fragment size (Ha) as calculated here, counted over grid cells with linear y-axis. (b) Histogram of both fragment size and maximum fire sizes from refs ((García et al., 2022; Laurent et al., 2018; Mouillot et al., 2023; Oom et al., 2016)) found in each grid cell over 2001-2020. Note the log y-axis scale, and that counts of small fires are far higher than counts of small fragments. (b) An extension of (a) and (b), this plot shows that fragment patch sizes (red bars) as estimated here are much larger than observed maximum, minimum and mean fire patch sizes (other colours), meaning physically-constrained fire size limitation can only occur in a small minority of cases (area C in the Figure): Frequency counts of (red bars) number of grid cells in bins of fragment patch size (Ha)). Blue/purple bars show the count of maximum observed fire patch sizes (the maximum size of each",
+    "bbox": [],
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0207534b48d5dc7f202715e97467615fe845cf6d2005bff553f5b155b496fd65/preprint/preprint.md

@@ -0,0 +1,452 @@
+Human land fragmentation drives tropical forest fires but dampens global burned area
+
+Simon Bowring
+simon_bowring@hotmail.com
+
+Laboratoire des Sciences du Climat et de l’Environnement (LSCE), https://orcid.org/0000-0002-0041-0937
+Wei Li
+Tsinghua University https://orcid.org/0000-0003-2543-2558
+Florent Mouillot
+CEFE, Université de Montpellier
+Thais Rosan
+Faculty of Environment, Science and Economy, University of Exeter https://orcid.org/0000-0003-0155-1739
+Philippe Ciais
+Laboratoire des Sciences du Climat et de l'Environnement https://orcid.org/0000-0001-8560-4943
+
+Article
+
+Keywords:
+
+Posted Date: October 3rd, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-3337266/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 24th, 2024. See the published version at https://doi.org/10.1038/s41467-024-53460-6.
+Human land fragmentation drives tropical forest fires but dampens global burned area
+
+1,2Simon P.K. Bowring*, 3Wei Li, 4Florent Mouillot, 5Thais M. Rosan, 1Philippe Ciais.
+
+1 Laboratoire des Sciences du Climat et de l’Environnement (LSCE), IPSL-CEA-CNRS-UVSQ, Université Paris-Saclay, Gif-sur-Yvette, France.
+2 Laboratoire de Géologie, Département de Géosciences, Ecole normale supérieure (ENS), 24 rue Lhomond, 75231 Paris Cedex 05, France
+3 Department of Earth System Science, Ministry of Education Key Laboratory for Earth System Modeling, Institute for Global Change Studies, Tsinghua University, Beijing, China.
+4 UMR 5175 CEFE, Université de Montpellier, CNRS, IRD, 1919 Route de Mende, 34293 Montpellier, France
+5 Faculty of Environment, Science and Economy, University of Exeter, Exeter, United Kingdom
+
+*Corresponding author: simon.bowring@lsce.ipsl.fr
+
+Abstract
+Landscape fragmentation has been correlated with either increases or decreases in burned area (BA), but their causal mechanisms remain elusive. Here, road density, a fragmentation proxy, is implemented in a CMIP6 coupled land-fire model, enabling dynamic representation of bottom-up processes affecting fragment edges. Over 2000-2013, fragmentation altered BA by >10% in 16% of burned [0.5°] grid-cells and caused gross changes of -6.5% to +5.5% in global BA. Model output mimicked the global satellite-observed negative relationship between fragmentation and BA, although some regional BA decreases were matched by fire intensity increases. In recently-deforested tropical areas, however, fragmentation drove significant, observationally-consistent increases in BA (~1/4 of Brazilian, Indonesian total BA). Fragmentation BA’s relationship with population density is negative globally-averaged, but hump-shaped and largely positive in tropical and temperate forests. We suggest fragmentation could ‘tip’ toward net BA-amplification with future tropical forest degradation and fire-activity, providing policymakers a first quantification of fragmentation-fire risks.
+
+Introduction
+
+Human land use change (LUC) affects a third of the terrestrial surface1, and the fragmentation of natural land2 results in large-scale biodiversity loss3,4, habitat degradation5, changes to the surface energy balance6–10 and biogeochemical cycling11, leading to around one-third of global carbon (C) emissions12,13. LUC is forecast to increase substantially by 2100, with expansions in agricultural and settlement area across all future climate-SSP scenarios of +12-83%14 and +54-111%15, respectively forecast over a 2015 baseline. Concurrently, C emissions and attendant increases in global temperatures will perturb atmospheric and hydrologic circulations, combining to increase the future frequency and severity of fire events16–21, the global area prone to frequent fire (+ ~30%)22, and population-exposure to their immense socioeconomic cost23. Context-specific studies have demonstrated both negative and positive interactions of LUC with fire probability without determining their drivers18,24–27. Yet to date, no mechanistic representation of the link between the two has been developed. This restricts the capacity of a sustainable economic and infrastructural policy to consider the implications of LUC and fragmentation28 for fire risk, and hampers understanding and forecasting of fire behaviour, the role of human in altering prehistoric fire regimes29.
+
+Fire and LUC interact via weather and vegetation through landscape fragmentation, the natural or man-made spatial discontinuity of vegetation due to ecological and economic transitions such as roads, breaks in topography and parent material, disease outbreaks, and fire itself30. The fragment concept conceives of isolated vegetation patches, each with an interior and an ‘edge’ that is subject to a diverse range of
+‘edge effects’ due to contact with a non-vegetated space. The ‘edge limit’ represents the point where the thinning of interior vegetation is at a maximum, whereas the ‘edge area’ represents the area between fragment limit and interior that is subject to a gradient of ‘edge effects’ such as soil and fuel drying. This conception of fragmentation has been deployed for studying edge impacts on ecology, land use dynamics and spatial planning\(^{31-35}\); and more recently for a host of ecosystem properties, including air temperature \(^{36}\), soil moisture, microclimate \(^{9,37-42}\), vegetation growth\(^{7}\) and phenology\(^{43}\). Fragmentation today is predominantly driven by large-scale investment in LUC and access infrastructure (i.e. roads)\(^{1,44-46}\)-the latter the direct cause of many of the LUC effects described\(^{28,47,48}\).
+
+Fragmentation is difficult to measure empirically because: (1) Its definition is normative; what is fragmented and what makes it fragmented vary according to contextual lens\(^{49}\). (2) It isn’t readily amenable to numerical reduction. Fragments have different sizes, shapes and properties\(^{50,51}\). (3) Different climate-vegetation and shape-size pairings may have different fire responses to fragmentation.
+
+Extant empirical studies suggest that fragmentation tends to decrease landscape-scale BA in grassland-savannahs \(^{52,53}\), and increase it in forest ecosystems\(^{24,53,54}\), however these are limited in scope, scale and number. Empirical studies of fire- fragmentation effects are scarce\(^{24}\) primarily because measurement is an exercise in the counterfactual, asking: *what would fire outcomes be if fragmentation was/wasn’t here given that it isn’t/is here?* Addressing this under controlled unfragmented plot-scale conditions is possible, but would likely require removing key processes e.g., potential dependency of human ignitions on degree of fragmentation. Finally, fragmentation’s impact on fire takes one away from BA aggregated at annualised scales towards individual fire phenomena, with potentially opposing interpretations: Fragmentation may produce smaller/bigger individual fires while causing higher/lower annual BA.
+
+Land surface modelling is a powerful tool in this context for handling future emissions-based climate scenarios, sensitivity experiments, the integration of fragmentation-fire feedbacks and experimentation with worlds where fragmentation does and doesn’t affect fire. This enables isolation of these effects in a way that is effectively impossible at *in situ* scales and conditions. Here, we represent fire-fragmentation dynamics in the global land surface model ORCHIDEE-MICT-SPITFIRE\(^{55-57}\), a commonly-used and fire-enabled\(^{63,64}\) terrestrial branch of the [CMIP6] IPSL earth system model. ORCHIDEE-MICT-SPITFIRE (hereafter ORCHIDEE) integrates dynamic vegetation/fuel with climate, ignitions and fire physics\(^{65-67}\) and is a participant in the Global Fire Model Intercomparison Project (FireMIP \(^{68-70}\)).
+
+Conceptual Treatment of Fragmentation
+
+Model representation of fragmentation-fire must overcome three problems. First, fragments occupy a vast array of morphologies which cannot be represented explicitly at the sub-grid scales required by existing model resolutions. Second, although lack of an extant fragmentation metric might be overcome through a proxy, this proxy must be continuous and operable at sub-grid scale. Third, the edge-interior characterisation of fragments requires that gradients exist between these two states, raising the problem of how to represent such gradients given patch shape-size heterogeneity, for which predictive relationships with fire do not exist.
+
+In order of the problems outlined above, we proxy fragmentation as follows: First, fragmentation extent is proxied through road density. This is the only available satellite-derived data available that might capture fragmentation-fire effects, and simplifies analysis because roads are a fixed infrastructural feature in the medium term: Their existence is a state that changes far less than the patch interiors which they demarcate. Dirt, local, state and national summed roads are conceived of as defining the edges of fragments, because LUC and subsequent fragments require overland access, and hence the construction of roads (fragment boundaries). Roads may act as a physical barrier to fire spread, imposing limitations on individual fire size and aggregate BA\(^{71-73}\), yet simultaneously expose vegetation to increased human contact, edge effects and potential fire\(^{74-77}\). Second, vegetation patches arising from fragmentation are reduced to a single shape and size in a grid cell, given that the sub-grid scale is definitionally an average value. Third, this uniform patch shape is assumed to be circular, such that all patches in a grid can be
+reduced to an average size that is defined by total road length. This enables conversion of empirical data to probabilistic representation of fires through ‘edge effects’ as a function of the patch radius, facilitating a ‘bottom-up’ approach to representing fragmentation-fire phenomena (Fig. S1).
+
+![Log-scale global map of grid cell mean 'average edge distance' (AED, m), as used as model input in this study and interpretable as the average Euclidian distance from an average patch edge to its interior and calculated as described (Methods, Fig. S1) to remove the urban proportion of road area. System diagram of fragmentation-fire relations implemented within the ORCHIDEE model structure, where fragmentation is affecting fire size, spread, number and propensity/rate of spread (ROS)/intensity, with counteracting effects with respect to BA. Green boxes denote where AED impinges on individual fire variables (blue boxes), given modulating factors (orange) that result in emergent grid-scale fire tendencies (red). Arrows denote positive (red) and negative (blue) relationships. FDI=Fire Danger Index; ECO2=Fire CO2 emissions.](page_184_370_1080_654.png)
+
+Figure 1: (a) Log-scale global map of grid cell mean “average edge distance” (AED, m), as used as model input in this study and interpretable as the average Euclidian distance from an average patch edge to its interior and calculated as described (Methods, Fig. S1) to remove the urban proportion of road area. (b) System diagram of fragmentation-fire relations implemented within the ORCHIDEE model structure, where fragmentation is affecting fire size, spread, number and propensity/rate of spread (ROS)/intensity, with counteracting effects with respect to BA. Green boxes denote where AED impinges on individual fire variables (blue boxes), given modulating factors (orange) that result in emergent grid-scale fire tendencies (red). Arrows denote positive (red) and negative (blue) relationships. FDI=Fire Danger Index; ECO2=Fire CO2 emissions.
+
+We calculate satellite-estimated per-grid cell total road length (RL) globally from ref.46 and convert this to a number of circles (“fragment patches”) of equal area per grid-cell, whose summed circumferences satisfy both RL and grid area (Fig. S1, Methods). Patch radii provide the average Euclidean distance from patch interior to edge, or average edge distance (AED, Fig. 1a). This enables reduction of patch edge-interior gradients to a single distance, as used in other studies31, greatly simplifying conversion of observational edge effect data to model-relevant code. To calculate AED from RL, we removed the urban component (Methods) of RL for each grid cell44,45, given large fires don’t occur in urban areas (Methods). Remaining RL was doubled to account for miscellaneous vegetation breaks and because the original road dataset exhibits a significant low bias (Methods, Table 1))78–80.
+
+AED then defines the relationships between land surface variables and fire phenomena (Fig. 1b, Methods, Table 1). As fragmentation increases and AED decreases: (1) Individual fire size is restricted by patch size unless threshold conditions for crown fire spread and fuel bulk density limitation in forests and grasslands81, respectively, are surpassed. This was implemented because recent statistical evidence
+suggests that road density (m km\(^{-2}\)) is the strongest predictor for decreases in annual BA at global scale\(^{71}\). (2) Vegetation is more exposed to human contact and hence ignitions-potential through machinery, smoking, trash burning, etc., proportionately increasing human ignition probability\(^{66,82}\) (*Methods*). (3) Fuel moisture and threshold fuel ignition moisture at the patch edge decreases due to edge drying\(^{37-41}\), increasing fire risk and propagation potential; (4) Wind infiltration and hence speed at patch edges increases of forests only\(^{81}\) due to decreased surface roughness\(^{83,84}\) (*Methods*, Table 1). Thus, fragmentation potentially decouples fire rate of spread and fire intensity from BA (Figs.1,S2, *Methods*). We stress that this study does not seek to account for land *use* impacts of fragmentation (e.g. deforestation, plantation), but the impact of the fragment edge *in isolation*.
+
+Global-scale ORCHIDEE fire simulations were conducted at 0.5° grid-resolution over 2000-2013 with all fragmentation functions activated, in addition to a ‘control’ (‘CTRL’) simulation, with fragmentation deactivated (*Methods*). A separate suite of ten sensitivity simulations, in which fragmentation was arbitrarily varied globally for all grid cells at decreasing two-fold increments of AED of 10000 m, 5000m … ~39m (AED\(_{F2}\)) were performed to study the incremental effects of fragmentation-doubling on burned area at global and biome scale. These simulations were run from 2001-2003, straddling weak or neutral El Niño/La Niña years to dampen their signal.
+
+![World maps showing gross fractional increase and decrease in simulated mean annual BA, and regression plots and frequency counts related to fire size and fragmentation](page_184_624_1080_480.png)
+
+Figure 2: (a,b): Gross fractional increase (a) and decrease (b) in simulated mean annual BA (\(f(\Delta BA_{Frag})\)) versus a control simulation without fragmentation (log-scale). Grid cells where the absolute change in area burned < 0.2% of a grid cell (~5km\(^2\) yr\(^{-1}\)) were masked out. Aggregate annual increases and decreases in BA (Ha yr\(^{-1}\)) due to fragmentation are included in million hectares (Mha). (c) Regression of logit link-transformed monthly mean BA against the square root of RD (m km\(^{-2}\)). *Dashed black line*: Observation-based regression model between BA and road density from ref. (Haas et al., 2022 71). *Grey line*: all simulated grid cells. **Blue line and circles**: only the simulated grids where fragmentation explicitly decreases mean fire size, plotted against the original road density data used in Haas et al. **Red line and circles**: same but plotted against the road density used in our simulations where the urban fraction of roads is removed. (d) Frequency counts of grid cells across bins of mean fragmented vegetation patch size (Ha) aggregated from the global AED map in Fig. 1a (red bars), with observed maximum (blue/purple), mean (green) and minimum (orange) observed fire patch size frequencies averaged from 2001-2020 for each grid cell, across the observed range of fire patch size using data from refs (85–88). The overlap between maximum obs. fire size (blue) and fragment size (red) is shaded purple to highlight their statistical overlap. This Figure facilitates interpretation of the fire size range and grid cell quantity affected (C,B) or unaffected (A,D) by fragmentation (see Fig. 2c).
+
+Results
+Global scale fire-fragmentation
+
+Global time-averaged change in BA due to fragmentation with respect to the CTRL simulation (BA_{frag}-BA_{CTRL} = \Delta BA_{frag}) caused both gross BA decreases and increases, depending upon the region considered. The global sum of gross (\Delta BA_{frag}^{-}) decreases amounted to -30 MHa yr^{-1} and the sum of gross increases (\Delta BA_{frag}^{+}) were +25.6 MHa yr^{-1}, equivalent to -6.5% and +5.5% of 2001-2019 averaged satellite-observed BA^{89}, respectively (Fig. 2a,b). Fragmentation altered mean annual BA by more than ±10% in 17%, and by more than 25% in 7%, of burned grid cells, respectively. Generally, in areas with high levels of both fragmentation (Fig.1a) and population density (Fig. 2a,b), simulated fire activity saw the largest significant proportionate BA decreases, e.g. north-west Europe, California and northeast-USA . Conversely, significant increases in BA and combustion are simulated in areas with low to moderate fragmentation and population densities (Fig. S3, S4), e.g., Indonesia, eastern Brazil and the north Mediterranean.
+
+We evaluated the statistical relationship between BA and road density (RD) emerging from our simulations, to compare with the satellite-observation-based global logit-transformed relationship of \( (BA) = -0.05 * (RD) - 6.5 \) (dashed black line) in ref. (71) (Fig. 2c). While the overall simulated regression models closely replicate the observed slopes and intercept, the R^2 coefficient is low when (i) considering all grid cells (black line, Spearman’s rho (\rho)=0.07, R^2=0.05, p<0.001), but it is improved in (ii) grid cells where road-fragmentation actively decreases individual fire sizes, using the same RD as employed in ref. 71 (blue line, \rho=-0.46, R^2=0.21, p<0.001), and (iii) same as (ii) but RD has urban roads removed, as applied in these simulations (red line, \rho=-0.66, R^2 = 0.41, p<0.001).
+
+The low R^2 in (i) is due to: First, ORCHIDEE-SPITFIRE simulates large numbers of very small fires that aggregate to low levels of annual BA (bottom-left grey dots in Fig. 2c). Where realistic, these are generally not picked up by existing satellite (MODIS) BA retrieval/processing mechanisms^{90}. Second, removal of urban roads in the AED calculation (Methods) was not performed in [71], whose regression may reflect factors that correlate with RD that would strengthen its correlation coefficient (e.g. fire suppression in urban areas, large fire-retardant surface areas, population density). Third, counts of small patch sizes calculated by the model are about two orders of magnitude lower than counts of observed mean fire sizes, meaning that fragmentation extent can only feasibly constrain fire size in a limited number of grid cells (Fig. 2d).
+
+The probability of patch size constraining fire size is high for medium-large fire sizes (area C in Fig 2d), but low for small fires, because small patch size counts are about two orders of magnitude lower than those of small fire size counts (areas A vs. B, Fig.2d). As a result, fragmentation by roads cannot on average directly decrease fire size over a broad swath of areas where fires occur (Areas A and D, Fig. 2d). This exposes the limits of fragmentation as a physical constraint to fire size, although there may be other nonphysical constraints that we exclude. The red line in Fig. 2c therefore represents the areas B and C of Fig. 2d, giving the ‘effective’ fragmentation-fire relation with respect to model output.
+
+Regional scale and population fragmentation impacts
+
+General patterns in regional \Delta BA_{frag} are discernible in Fig. 2a,b, but precision evaluation requires an observational dataset that removes and adds fragmentation while holding population density, vegetation and climate constant –which is implausible. However, we can compare observed and modelled fire activity in areas over which large-scale increases in fragmentation have occurred during the period for which global satellite observations of fire are available (post-2000). This coincides with the ‘boom’ years of globalisation^{91,92}, in which lowered regulatory power and multinational corporate demand^{93} incentivised large-scale supply of cheap commodities for global markets^{94}. Large swathes of the largely-tropical global South^{1}, most notably in Indonesia and Brazil^{95,96}, were given over to clearing, selective logging and plantation/mining establishment over the last two decades^{97,98} that were associated with systematic increases in fire activity^{47,99–101}, and provides a ‘before-after’ comparison of fire behaviour with fragmentation. Fig. 3a plots f(\Delta BA_{frag}) in northern S. America, overlaid with data from ref.^{102} that
+identified where the running mean of BA and a fragmentation proxy experienced significant [+/-] trends over 2003-2018. That study suggested Amazon rainforest-interior BA rose with fragmentation, but either fell or was unresponsive to fragmentation increases in the cerrado. Model output replicates the same dynamic, where large \( \Delta BA_{frag}^+ \) values follow the Trans-Amazonian highway\(^{103}\) into the Amazon rainforest interior (Figs. 3a, S7), while the cerrado region tends to experience decreasing BA with fragmentation. Fig. 3a’s model-data comparison is not entirely commensurate as ref.\(^{105}\) identify temporal trends in fragmentation and *total* BA to approximate if and where they are correlated, whereas our fragmentation input is static and outputs only changes in the fragmentation component of BA. Thus, in cerrado areas that are subject to large climate-driven interannual variation in drought and fire extent, aggregate BA trends may subsume fragmentation BA effects. The inverse may be the case in the wet Amazon, where fragmentation can dominate fire causation\(^{54,104}\). Large simulated \( \Delta BA_{frag}^+ \) in the deep interior Amazon where ref.\(^{102}\) find no significant trends (no data points) reflect large fractional increases in simulated fire over a miniscule baseline -fires not visible to MODIS sensor detection.
+
+In Fig. 3b, we compared grid cells where average simulated BA increased in Indonesia and Malaysia, against satellite-based grids where BA increased between 2000-2019 over a 1982-1999 baseline\(^{105,106}\). We overlaid these with grid cells that experienced significant deforestation\(^{107}\) and tree plantation inception\(^{108}\) since 2000 (Fig. 3a, S5,S6). In Borneo/Kalimantan and Sumatra, where the majority of recent fragmentation and fire activity has occurred, the results from our fragmentation-fire model agreed with 58% of grid cells that experienced an observed increased of BA, of which 67% were areas of known significant deforestation and/or plantation establishment. This broadly agrees with ref.\(^{109}\), which found that human activity had amplified (but may not dominate) drought-related fires in Sumatra and Kalimantan since 1960. The model failed to reproduce large fire anomalies in southern Borneo/Kalimantan resulting from drained peatland-vegetation burning\(^{110,111}\), which is expected since this version of ORCHIDEE does not represent peat or soil burning.
+
+Simulated average gross \( \Delta BA_{frag}^+ \) values in the Amazon and Indonesia are equivalent to ~ 27% and 24% of observed average annual BA\(^{112}\), respectively, suggesting fragmentation is a significant driver of fire activity in tropical regions, *describing the linkage between initial deforestation and dry season severity*\(^{113}\) to promote fires that would otherwise not have spread.
+Figure 3: (a) Simulated fractional changes in BA due to fragmentation in northern S. America (\( f(\Delta BAFrag.) \), colour-bar), overlaid with BA and fragmentation-proxy trend data from Rosan et al. (2022)\(^{102}\), which were
+aggregated for Brazil’s Amazonian (circular points) and Cerrado regions (triangles), as comparison. Where both BA and fragmentation increased (+BA/+frag) over 2003-2018, points are coloured red and [(+BA/-frag)=orange; (-BA/+frag)=light blue; (-BA/-frag)=dark blue]. Note the comparison is not entirely commensurate (see text). Simulated gross BA changes due to fragmentation over the Figure region are shown inset. (b) Comparing \( f(\Delta B_{A_{frag}}) \) with observed (FireCCI) BA anomalies from a 1982-1999 baseline, over areas of known large-scale fragmentation in Indonesia and Malaysia, during the period for which satellite-based fire data are available (post-2000). Simulation-observation agreement (yellow-red) and observation-only fire anomaly grid cells (green-blue) are shaded darker along a gradient of increasing observed fire anomaly (Methods). Dots correspond to areas of significant deforestation activity(ref) and/or plantation establishment (ref) since the year 2000 (black, green), or preceding it (pink). Dot size is proportional to deforestation severity where applicable. The dotted grid highlights Borneo and Sumatra, where recent regional fragmentation is concentrated. (c) Binned frequency density scatter of fractional mean changes in BA per grid cell due to fragmentation relative to the Control (\( f(\Delta B_{A_{frag}}) \), y-axis) where this was >±1%, against the logarithm of population density (x-axis) of that grid cell, plotted globally across five biome types. A generalised additive model (GAM, black line) is included for interpretation. Asterisk(*) mark the PopD level at which \( f(\Delta B_{A_{frag}}) \) is maximum in tropical and temperate biomes (~0.5 and ~50 individuals km\(^{-2}\), respectively).
+
+How fire behaviour in different biomes may respond to fragmentation as population density (PopD) levels change provides insight into fire regime evolution with increasing human landscape encroachment. The per-grid relationship of \( f(\Delta B_{A_{frag}}) \) with population density for each global biome, as well as the generalised additive model (GAM) trend for each is shown in Fig. 3b. Tropical forests simulated a clear increase in BA at low population levels (max \( \Delta B_{A_{frag}} \) at a population density of ~0.5 individuals per km\(^{-2}\), (* in Fig. 3c)), and is the only biome where a fragmentation-related decrease in BA is less important than an increase. Temperate forest fragmentation drives a decrease in BA above low to moderate PopD and increases BA at moderately high PopD of 50 individuals km\(^{-2}\). Boreal forests appear relatively unaffected by changes in population, although this may reflect a low statistical spread of population density\(^{114}\). Temperate grasslands fragmentation correlated with increased BA at low population densities, and decreased dramatically at high levels, presumably because of fragmentation limitations to fire spread.
+
+Susceptibility of CO\(_2\) emissions and burned area to fragmentation
+
+Globally, the impact of fragmentation on fire C-emissions is similar to that of BA, with a net reduction of -1% (-0.02 PgC yr\(^{-1}\)) of global emissions. Conversely, the spatially disaggregated fragmentation-emission impact on specific biomes (Fig. S4) suggests that its relative effect in tropical, temperate and boreal forests is largely positive, despite being negative globally. This is highlighted in Figure 4a, which shows large areas of the world overlain by forest biomes in which the direction of change of C-emissions due to fragmentation is decoupled from that of BA. This is particularly true of boreal (per ref.\(^{77}\)) and to a lesser extent, tropical forests. This implies that fragmentation can reduce total BA while increasing the emissions-intensity of fires that do burn. This is relevant to observed increases in global fire intensity over the last twenty years\(^{115}\).
+
+Ten global sensitivity simulations were run, in which the AED across grid cells is synthetically varied globally at 9 factor-of-two values (F2) of AED from 10000m to 39m (AED\(_{F2}\), see Methods). We compared the fractional change in BA of grid cells *between each sequential* level of applied fragmentation (\( f(\Delta B_{A_{AF2}}) \)) as a measure of biome-scale fire sensitivity to fragmentation. BA declined everywhere as fragmentation increased when averaged over all AED\(_{F2}\) levels (Fig. S9), however BA decreases were lowest in tropical and boreal forest regions of the world (Figs. 4b, S9). We aggregated grid cell \( f(\Delta B_{A_{AF2}}) \) to a biome-scale average for each simulation to study how BA was altered by fragmentation as it increased. Fragmentation doubling caused biome-specific BA decreases \( f(\Delta B_{A_{AF2}}) \) of -7.5% (Tropical forest); -15% (Temperate forest); -19% (Boreal forest); -30% (C3 grasslands); -22% (C4 grasslands). On average, BA decreased monotonically for almost all biomes (Fig. S9, S10).
+
+Simulated BA begins to decrease at different AED levels for different biomes (Fig. S9), implying differential biome-average fire sensitivities to land fragmentation. For example, to reach the same fractional decrease in BA (-5%) due to fragmentation, an average tropical forest grid cell requires an
+additional road length of 2.5 km km\(^{-2}\) (~6000 km grid\(^{-1}\)), highlighting the higher resistance of the tropical biome to fragmentation-associated BA reductions (Fig. 4b).
+
+![Time-averaged map showing where fragmentation relative to the control simulation without fragmentation leads to coupled (increasing or decreasing in the same direction) changes in BA (\( \Delta B_{AFrag} \), Ha yr\(^{-1} \)) and fire CO\(_2\) emissions intensity (\( \Delta ECO2_{Frag} \), gC m\(^{-2} \) yr\(^{-1} \)), shown in light colours, or decoupled changes (one increasing, the other decreasing), in dark colours. Blue depicts areas where \( \Delta B_{AFrag} \) is negative, and red where it is positive. (b) Global spatial sensitivity of fire to hypothetical fragmentation levels: AED\(_F2\) simulation ensemble-averaged spatial distribution of fragmentation-doubling effects on fire burned area (unitless colour scale). All grid cells show a mean decrease in BA over the 9 simulations, but because of differential direction of change between simulations, we show in dark colours those grid cells where the average AED\(_F2\) impact is most likely to increase BA (highest fire susceptibility) and in light colours where it is most likely to decrease BA.](page_186_370_1077_312.png)
+
+Figure 4: (a) Time-averaged map showing where fragmentation relative to the control simulation without fragmentation leads to coupled (increasing or decreasing in the same direction) changes in BA (\( \Delta B_{AFrag} \), Ha yr\(^{-1} \)) and fire CO\(_2\) emissions intensity (\( \Delta ECO2_{Frag} \), gC m\(^{-2} \) yr\(^{-1} \)), shown in light colours, or decoupled changes (one increasing, the other decreasing), in dark colours. Blue depicts areas where \( \Delta B_{AFrag} \) is negative, and red where it is positive. (b) Global spatial sensitivity of fire to hypothetical fragmentation levels: AED\(_F2\) simulation ensemble-averaged spatial distribution of fragmentation-doubling effects on fire burned area (unitless colour scale). All grid cells show a mean decrease in BA over the 9 simulations, but because of differential direction of change between simulations, we show in dark colours those grid cells where the average AED\(_F2\) impact is most likely to increase BA (highest fire susceptibility) and in light colours where it is most likely to decrease BA.
+
+Discussion and Conclusion
+
+By generating a parsimonious representation for land fragmentation based on observed road density, we enable the simple representation of its impacts on fire probability and behaviour in a land surface model. This reproduces observed relationships between land fragmentation and fire probability, at globally-aggregated and regional scales. We show that fragmentation has globally-significant impacts on BA, and may be a principal driver of fire activity regionally. Our grid-average approximation of vegetation fragment size as a directly-proportional barrier to fire spread appears sufficient to reproduce the relationship of BA decreasing with road density in observations, but also highlights that this physical constraint to size remains limited by the observed fire size distribution (Fig. 2d), and may be most effective at dampening larger fires. Conversely, model output reproduced large increases in BA in tropical regions where deforestation and plantation expansion are rampant, .
+
+Broadly, our results mirror what is known anecdotally, but provides explanatory quantification and future projection potential for these small-scale or statistical relationships at global scale. This allows: (1) Identifying how and which edge effects may increase fire behaviour in specific locations/biomes, facilitating remediating action; (2) Dynamic forecasting of how projected changes in fragmentation/RD may impact fire behaviour in the future; (3) A first step towards policy assessment of fire risk and social welfare when considering fragmentation-relevant policy directives (e.g. Fig. S8). The methodology applied here also provides a route for large-scale modelling of other fragmentation effects in earth, ecological\(^{117,104,116,117}\) and epidemiological sciences\(^{118,119}\).
+
+We believe that our fire model representation would be improved by discriminating between road-types, although the empirical impact of these on edge effects is for now largely unknown. Further, our results suggest that fragmentation’s effect size on BA, where non-zero, varies hugely across space and time, and may only be a reflection of pre-existing model bias where modelled BA is otherwise low. Because the AED input map is static, year-by-year interpretation of output is problematic, and provides impetus for the production of higher resolution and better-identified gridded RL timeseries maps. This data shortcoming explains why we aggregate all output to simulation period average, interpretable as the probabilistic change in BA due to ~2014 road density, which we believe reasonably retains fragmentation-fire effects given a short simulation timespan. The model appears to fail in areas of very
+high soil moisture such as southern Kalimantan and the Pantanal (Fig.3a,b respectively), and peat fires/drainage should be included in future model iterations.
+
+Climate warming, population density and LUC will increase in the future, with socioeconomic effects of greatest magnitude forecast in the tropics120. Fragmentation largely increases fire in the tropics, meaning it may become a major driver of burned area there in the future, and suggests fragmentation could eventually ‘tip’ towards a global net-positive BA phenomenon with future tropical forest degradation and fire-activity, in a potential feedback loop. This may place greater burden on countries in these regions to balance economic policy with the environmental and welfare consequences of fire risk those policies may entail.
+
+Methods
+
+Model Description
+
+ORCHIDEE-MICT is a global-scale, grid-resolution model generally employed at 0.5 to 2 degrees, with boreal and permafrost -specific adaptations for high latitude biomes that affect soil, vegetation, hydrological and thermal processes specific to those latitudes. These process representations are particularly important in the context of this study for the modelling of future fire-vegetation-hydrological interactions. The model is carbon-based, in that it ultimately denominates earth system dynamics through their impacts on the C cycle, by which energy, soil, water and climate drive fluxes of C through the system via vegetation and associated biological and ecological processes. Thus, photosynthetic C is fixed by 11 plant functional types (PFTs), doing so differentially as each PFT is subject to specific primary production, senescence and C dynamics. The spatial distinction between PFTs can either be forced through an input vegetation map, defining the fractions of each grid cell covered by each PFT, or through the dynamic global vegetation model in ORCHIDEE, which predicts PFT type and allocation according to the biophysical suitability of each PFT to primarily climatic input variables. Fixed C is then allocated to foliage, fruit, roots, above/below -ground sapwood, heartwood and C reserves, that upon death or senescence are shunted to two reactivity-differentiated litter pools. ORCHIDEE-MICT is hard-coded with an adaptation of the SPITFIRE fire module 63,66,121,122, which divides the aboveground vegetation components described above and apportions them to potential fuel type categories differentiated by their potential time to oxidation. Fire ignitions are controlled by a positive linear function of lightning flash density and a positive logistic function of human population density to represent human ignitions. Vegetation flammability is determined by fuel and climatic conditions (Nesterov Index and Fire Danger Index). The area burned in an individual fire event is determined by the rate of fire spread and fire duration, as influenced by vegetation flammability. Fire CO₂ emissions depend on vegetation biomass, fire intensity and duration.
+
+Fragmentation Representation
+
+The average edge distance (AED) per grid (\( AED_G \)) given per-grid road length sum (\( RL_G \)) was solved analytically and is given by the following:
+
+\[
+AED_G = (2 * Area_G * f(Cont))/ \Sigma(RL_G)) \tag{1}
+\]
+
+Where \( Area_G \) is the grid area in m², and \( f(Cont) \) the fraction of each grid cell area taken up by the continental landmass. The gridded RL dataset in Meijer et al. (2018) gives a global road length estimate that is about 50% lower than that estimated by the World Road Statistics database (~30 million km), and about 300% lower than the estimate provided by the CIA World Factbook. Furthermore, a recent report 78 showed that the Global Roads Inventory Project (GRIP) database consistently and strongly under-predicted the existence of small roads, leading to large low biases against manually-observed road data in the report’s two case study sites in the Congo and Canada. The primary reason hypothesised for these mismatches, which are acknowledged in the 46 paper, is the under-representation of unofficial
+and unpaved roads in their source database. GRIP was shown to under-represent total manually-measured road length in a grid cell by a factor of over 8 in one area (Fig. 19 of78). For this reason, in Eq. 1, which generates the AED map used as input to ORCHIDEE, we make the assumption that the gridded road length data underrepresent actual road length by a factor of 2, which implies a total global road length roughly in between the WRS and CIA estimates. Further, as river and stream length as well as large topographic discontinuities can reasonably be expected to act as fire breaks in most circumstances, and given that these are excluded from the input data, we take these to be potentially integrated into the factorial AED map. We acknowledge that multiplying RL uniformly by a single factor masks the likely spatial distribution of bias inherent to the GRIP database, however given that the source bias has not been assessed or quantified, we retain this spatial uniformity assumption for simplicity in this study.
+
+In order to modulate the effects of fire by fragmentation, ORCHIDEE must first be fed a gridded input map containing the AED data. This is derived from46, which gives global gridded road length in m km\(^{-2}\) at 5 arc-minute (~8km) resolution for a single time period (~2017), downloaded from (https://zenodo.org/record/6420961, accessed 20/11/2022), converted to netcdf format and regridded to this study’s simulation resolution of 0.5° (~50km) using the conservative interpolation function in the Climate Data Operator (CDO) package123. The raw data were provided in five classes of road type: highway, primary, secondary, tertiary and local. Although we can reasonably expect each of these road classes to represent different scales of fragmentation, each conferring differential effects in their relation with fire phenomena, the paucity of empirical data on what these might be, coupled with the range of impacts that may, as mentioned be contradictory, mean that for the moment we take all road classes to be equal in effect, and as such sum them to a single road length density (RL) variable. Equation 1 is then applied to the dataset to generate a global gridded map of the average circular patch radius associated with each grid cell (\(AED_G\)).
+
+Next, we assume that spatially extensive fires do not occur on land that can be considered ‘urban’. This assumption is made on the basis that urban areas are characterised by very low fuel densities (compared to, say, a pine forest), large areas of concrete, asphalt and steel, which do not burn easily, and high population densities that strongly increase the probability of successful human fire suppression. Because road density in urban areas is very high, this assumption should also require that the urban proportion of road density in each grid cell is removed from the original RL data, and a corresponding AED map generated. To do so, we download the output data from [ref:45] which gives the urban area fraction (UAF) of grid cells at global 0.125° resolution, and projects this variable globally to 2100 under the Shared Socioeconomic Pathways (SSP) scenario suite: (https://dataverse.harvard.edu/dataverse/geospatial_human_dimensions_data, accessed January 12, 2023). We then plotted a simple linear regression between the 2018 UAF data and the original RL, giving a relationship between the fraction of urban area in a grid cell and the road density of that grid cell (RL=((2.68*10^4)*UAF)+292; R^2=0.43), where 2.68*10^4=is the regression coefficient (\(\alpha_{UAF}\), Table 1).
+
+The RL data were split into categories of urban fraction, whereby each grid cell was allocated to one of twelve UAF bins, corresponding to [0-1, 1-5, 5-10, 10-20, 20-30...90-100 percent] and the equation was used to estimate the implied RD at the numerical midpoint of each bin. Thus, on the basis of the RL/UAF regression, a road length per unit UAF was allocated to each of the UAF-based classes, multiplied by the actual UAF of each grid cell given its UAF, and the resulting ‘excess’ road length subtracted from the original RL data, to give an ‘effective’ road density and AED value. The resulting AED ‘fragmentation’ map can be compared to the original, and shows that in removing the impact of urban area roads on the representation of fragmentation, the world’s most fragmented landscapes are no longer found in north-west Europe but in the north-eastern United States and e.g. Bangladesh. This is likely indicative of extensive non-urban infrastructural sprawl in the former, and a symptom of uniformly high population density and low to medium intensity and highly-extensive agricultural land use in the latter, meaning that roads criss-cross large parts of the country (see Fig. 1a). We chose to use UAF bins and calculate the RD at their midpoint instead of direct application of the regression equation because the latter’s scatter is substantial, with binning more closely approximating the statistical value envelope.
+Description of Fire-Fragmentation Dynamics
+
+Fire size: In ORCHIDEE, total burned area per timestep is given by the product of average individual fire size in a given grid cell, and fire number. Because it has been shown in an anecdotal number of studies\(^{53}\) that for forests, fragmentation leads to decreases in fire size, and at the same time, ref.\(^{(7)}\) showed that the single strongest negative determinant of burned area at global scale is road density, we first approach fragmentation representation by decreasing the potential size of an individual fire as fragmentation increases. This is done first by assuming that the maximum individual fire size is a multiple (\(n_{pat}\)) of a grid cel’s AED-determined mean patch area. This is because fragmentation may delimit the boundaries of fire spread in many circumstances, the circular AED-derived patch area is itself only an average, and large variations in patch size will be the reality, with some patches much larger than others. In addition, it lends a lower degree of restriction of fragmentation on fire size, allowing for the real-world possibility that fires can spread beyond the borders of the original vegetated patch. \(n_{pat}\) allows for future refinement of model representation when empirical relations between sub-grid-scale fragment size distribution and propensity for spread become known. In the absence of such data, we set \(n_{pat}(forest)=1\) and \(n_{pat}(grass)=1.25\) (Table 1). We reason this because the observed individual fire size distribution is highly skewed towards small fires when compared to the fragment sizes defined by AED (see Fig. 2d), and because statistical treatment of observations suggests road fragmentation is a strong determinant of lower aggregate BA\(^{71}\). Without any empirical data to work with, a multiplier of unity appeared the most reasonable choice. We shunted grassland fire size limitation by AED by 25% above unity due to the relative ease of ignition of fine fuels in grasslands that may both more easily ignite and be carried over road barriers by wind.
+
+Fire Spread Thresholds: To introduce added realism and further reduce the restrictiveness of the fragmentation representation, the AED-denominated limit on individual fire size is only applied when separate conditions are met for forests and grasslands. For forests, if the simulated fire intensity and flame height exceed canopy base height, which is the pre-existing condition for canopy scorch in the original version of SPITFIRE \(^{63}\), and the condition for crown fire spread in an upcoming version (Bowring et al., in prep.) then no size limitation is imposed:
+
+\[
+\text{FST}_{\text{TREE}} = \text{True .IF. : SH > (H}_{\text{TREE}}-(\text{H}_{\text{TREE}}*\text{CL}_{\text{TREE}}))
+\] (2)
+
+Where FST\(_{\text{TREE}}\) is the fire spread threshold (Table 1), SH is the mean fire scorch height, H\(_{\text{TREE}}\) the mean tree height, CL\(_{\text{TREE}}\) the mean crown length. This is done to account for the possibility that high-intensity forest fires can’t ‘jump’ over roads through crown spread, particularly if meteorological conditions for doing so are favourable. When this condition is met, fire spread and fire size are calculated as in the original SPITFIRE formulation. Second, over grasslands, ref.\(^{(81)}\) found that a critical threshold limiting fire spread (FST\(_{\text{GRASS}}\)), and hence fire patch size, exists in grasslands, which results from grassland fuel connectivity as given by area-specific fuel mass (tons Ha\(^{-1}\)). They showed that if this 2.4 tons Ha\(^{-1}\) grass wet mass threshold is reached, even fuel at 100% moisture was able to burn. Thus, individual fire size limitation due to fragmentation on ORCHIDEE grasslands applies only to instances where the simulated grass fuel mass is below this biomass threshold, and are otherwise allowed to spread freely, as in the original SPITFIRE formulation:
+
+\[
+f_{\text{Grass}_{\text{WW}}} = \Sigma(F_{1hr}+F_{10hr}+F_{100hr}+F_{1000hr}+F_{Live})*(1/0.45)
+\] (3)
+
+\[
+\text{FST}_{\text{GRASS}} = \text{True .IF. } f_{\text{Grass}_{\text{WW}}}>2.5\ \text{tHa}^{-1}
+\] (4)
+
+Where fGrass\(_{\text{WW}}\) is the summed weight of grass and grass fuel, F\(_{nhr}\) refers to the different ‘hour’ fuel classes in ORCHIDEE, F\(_{Live}\) is live grass and (1/0.45) is the conversion of dry biomass to wet weight. Note that this ensures that the fragmentation model is able to account for the likely increases in extreme fire weather projected by future scenarios of climatic change. In a hot and dry season, a combination of
+fuel availability, low fuel moisture and high heat will enable an ignited fire to reach fire high reaction intensities, allowing high fuel consumption and flame heights to exceed those of the canopy and permit crown fire spread between forested patches. Likewise, fuel-limited grassland fires will, in dry seasons preceded by high pre-fire-season grass growth rates, spread when the medium of connectivity (fuel) is sufficient. Conversely, if there is insufficient fuel (i.e., prolonged drought), fire will not be able to spread between patches.
+
+Human Ignitions: Because the characterisation of fragmentation applied here is definitionally anthropogenic, it follows logically that an increment increase in road length in a given area exposes that length to human contact. Human contact in turn increases the risk of human ignitions, either through intentional (e.g., arson) or unintentional action (e.g., discarded cigarette butts, machinery, power lines, sunlit beer bottles, etc). In ORCHIDEE, human ignitions are controlled as a non-linear increasing then decreasing function of human population density, to reflect the fact that ignitions are more probable, and suppression less likely, when population density is low but not extremely sparse, such that the number of human ignitions (\( IG_H \), Ha\(^{-1}\)d\(^{-1}\)) is given by:
+
+\[
+IG_H = PopD * k(PopD) * a(Nd)/10000 \tag{5}
+\]
+
+\[
+k(PopD) = 30 * e^{-0.5*\sqrt{PopD}} \tag{6}
+\]
+
+Where \( PopD \) is population density and \( a(Nd) \) an observationally-estimated parameter representing ignitions per person per day, set at 0.01\(^{63,66}\).
+
+Here, we assume that an increase in fragmentation causes an increase in the probability of ignitions in direct proportion to the ratio of edge area: patch area, assuming conservatively that the human interaction with an edge can be characterised by a 1m edge depth (ED\(_{humig}\), i.e. a 1m increment into the radius of the assumed circle). This 1m edge depth assumption is equivalent to the depth from the patch edge (i.e., road) which is potentially subject to increased fire ignitions due to human contact (potentially resulting in fires through arson, cigarettes, machinery, etc). The 1m edge is assumed and low, because although human effects on ignition may be occur deeper into a patch, the time averaged edge depth that they do so along the length of fragment edges is likely small, so we hold this parameter at unity.
+
+This transforms the perimeter from a length to an area, allowing us to probabilistically modulate the ignition function directly by the area represented by the total fragmentation edge area present in the grid. We then adjust the human fire ignition function (\( IG_H \)) in SPITFIRE\(^{66}\) by the product of the number of patches that fit into a grid's area (\( Area_G \)) and the cumulative fractional grid area of the ignition surface as defined by the assumed 1m ignition edge depth to arrive at a fragmentation-affected ignition function (\( IG_{HFrag} \)), as illustrated in Fig. 1d.:
+
+\[
+IG_{HFrag} = IG_H + (((Area_G/(\pi * AED^2))) * ((2\pi * AED * 1)/Area_G))/10000) \tag{7}
+\]
+
+Thus, an AED of 20m yields a potentially increased ignition surface amounting to ~10% of a grid cell. This probability is scaled to the ignitions person\(^{-1}\)km\(^2\)\(d^{-1}\) as a constant (/10000), and results in significantly increased ignitions at low and high population density when fragmentation is high, which decreases exponentially as fragmentation decreases (AED increases). This is clearest at high population densities, where the suppression effect of high population is counteracted by fragmentation (Fig 1d).
+
+Fuel Wetness: Landscape fragmentation studies across many forested biomes have found that soil temperature and moisture was significantly higher and lower, respectively, at forest patch edge than in the patch interior\(^{37-41}\), with subsequent impacts on fuel moisture and fire ignition and spread probabilities. We represent this by simply using the relative areas of patch area and edge area to define the proportion of a grid cell made subject to edge drying. Thus, we calculate the ratio of the edge area to patch area (the edge-to-patch ratio, EPR), and assuming conservatively that the ‘edge-to-interior’
+gradient through which temperature and soil effects are significant can be defined as the 15m from the edge inwards (this is the distance to which edge-interior soil moisture and temperature gradient in the above studies falls to approximately zero). This is then the area subject to increased drying and higher temperatures owing to fragmentation:
+
+\[
+EPR = ((\pi * AED^2) - (\pi * (AED - 10)^2))/(\pi * AED^2)
+\] (8)
+
+In ORCHIDEE-SPITFIRE, each fuel class in each grid cell is allocated a simulated fuel moisture content (\(Wet_{FC}\)). In addition, there is a moisture threshold for each fuel class above which fuel consumption by fire no longer occurs (\(Thresh_{FC_{1,2}}\)), where the subscripts refer to the 1hr and 10hr fuel classes subjected to edge drying. The 100hr fuel class is not affected in this scheme, as we assume that the diameter of 100hr fuel is sufficiently high to preclude edge drying from affecting its sensitivity to ignition. Here, both the calculated wetness and the ignition threshold were used to proxy edge fuel drying, and are both lowered by the product of the fractional edge-to interior moisture gradient with \(EPR\).
+
+\[
+Wet_{FC} = Wet_{FC} - ((0.25/2) * Wet_{FC} * EPR)
+\] (9)
+
+\[
+Thresh_{FC_{1,2}} = Thresh_{FC_{1,2}} - ((0.25/2) * Thresh_{FC_{1,2}} * EPR)
+\] (10)
+
+Whereby 0.25 is the approximate 25% fractional soil moisture gradient difference between edge and interior (0-20m) found across the field studies cited above. Since we take the edge depth (\(ED_{Moisture}\)) to be 20m, and assume a linear moisture gradient from 0-20m, half of the maximum gradient is taken as the average decrease in soil moisture owing to fragmentation over the length of the edge, and total grid fuel wetness is then affected by the fractional area occupied by this edge.
+
+Wind Speed and Rate of Spread: Increasing fragmentation results in an increasing proportion of the landscape subject to a perimeter through which wind can travel with relatively less interruption. In other words, there is less of a barrier to wind at the patch edge and local surface roughness is lower, wind speeds are higher, and a larger proportion of the landscape is subject to these higher winds as fragmentation increases (e.g., 9). We treat this in ORCHIDEE by reducing the pre-existing model wind speed reduction factors at atmospheric versus ground level by an analytically-resolved factor derived from the implicit amount of fragment edge derived from AED. Specifically, we reduce the pre-existing reduction in windspeed due forest coverage in ORCHIDEE by the grid-areal proportion given by an assumed 16m mean edge depth (\(ED_{WIND}\)). Effective \(ED_{WIND}\) is actually 4m, since at any time in any patch, we assume the wind can only come from a single direction so that \(ED_{WIND}\) is divided by 4 in model implementation. We then reduce the fixed forest wind reduction factor (\(WRF = 0.4\)) in SPITFIRE proportional to the areal coverage of the fragment perimeter given by effective \(ED_{WIND}\).
+
+\[
+f_{EDGE} = Area_{patch}/Area_{edge}
+\] (11)
+
+\[
+WRF = WRF - ED_{WIND}
+\] (12)
+
+Increases in windspeed due to fragmentation in turn affects the fire ROS in areas that are considered substantially fragmented, leading in principle to increased BA within the patch area and (with the increase in fuel combustibility as a function of dryness and Fire Danger Index), potentially greater \emph{area-specific} total combustion, fire intensity, and C emissions, potentially decoupling BA from ECO2 (Fig.1b). The fragmentation-wind relation was not applied to grasslands, because, firstly, wind has been shown to not increase grassland ROS and BA 81, and secondly, because the relative exposure differential of grass height and ground height compared to forest areas was assessed to be minimal.
+Simulation Protocol
+The resulting model was spun up for 40 years to allow for vegetation to reach a quasi-equilibrium biomass state. This was done by forcing the model with the vegetation, climate and atmospheric CO_2 of 1901-1910, looped over that period of time, then looped again for 40 years over 1990-2000 forcing data, to bring the model to an equilibrium consistent with the near-present day. Principal and ‘control’ simulations were run over the period 2000-2013. Vegetation was imposed and not predicted using ORCHIDE’s dynamic global vegetation model to reduce uncertainties associated with its output. Climate forcing data for all runs came from the CRU-NCEP v8 dataset ^{124}, and vegetation imposed on the model from the ESA-LUH2 suite of projections with 13 plant functional types^{14}.
+
+A number of additional output variables were also implemented to ease assessment of the effects of fragmentation on fire behaviour. Thus, a ‘counterfactual’ burned area variable, giving the burned area that would have been simulated without the fragmentation code, is written to history along with fragmentation-affected burned area, to enable tracking of fragmentation’s effects. Likewise, differential burned area between the fire size and human ignitions fragmentation functions, assuming they are both activated, allows the user to track the relative burned area if either only the human ignitions or fire size -fragmentation flags were activated. This could not be done across all fragmentation-fire adaptations because of a necessarily large duplication of code and simulation runtime inefficiencies that would result.
+
+Sensitivity Analysis
+
+We created synthetic maps of factor-two levels of homogenous global AED levels to assess the global change in burned area for each biome type (tropical, temperate, boreal) resulting from a factor-2 change in fragmentation level. AED (not road density, which would cause differential AED because of grid area heterogeneity) was homogenised globally at 2-factor levels [of AED_{F2} =39.0625, 78.125, 156.25, 312.5, 625, 1250, 2500, 5000, 10000, 20000 metres], permitting analysis of the biome-scale effects of fragmentation on fire independent of historical fragmentation trajectory, by calculating the global average change in burned area for each homogenised AED bin and biome. The model was run over a three-year period (2001-2003 inclusive) for each RD_{F2} leve. This period was chosen because it incorporates a mixture of moderate El Niño and La Niña years, to limit its signal in simulated fire behaviour to be averaged out in annualised postprocessing. We initially maintained the existing global population distribution for the simulated years to gauge whether population density may cause a change in sign of sensitivity, and hence warrant further factorial analysis. Sensitivity was evaluated as the fractional change in BA (\Delta fBA_{F2}) per grid cell due to a two-fold increase in fragmentation (halving of AED):
+
+\[
+\Delta fBA_{F2} = ((BAAED_{F2[1/2]}) - (BAAED_{F2[1]}))/ (BAAED_{F2[1]})_{GRID}
+\]
+
+Where \( BAAED_{AED_{1/2}} \) is the burned area at an AED of half the value of \( BAAED_{F2[1]} \). For each of the ten sensitivity simulations, biomes were assigned to each grid cell by identifying the PFT in each grid that contributed the maximum amount of simulated fire CO_2 emissions within that grid cell. This was done to identify the actual vegetation that burned in a grid cell, and hence the fire-relevant vegetation type, as opposed to using the maximum value between vegetation fractions of each PFT assigned to a grid cell, given that within a grid, certain vegetation types may have a fractionally higher propensity to burning than their areal coverage. At global scale, the individual PFTs were then aggregated to tropical, temperate, boreal, C3 and C4 grassland/ savannah bins. BA in ORCHIDEE-SPITFIRE is not PFT-disaggregated. However, CO_2 emissions from burning are. This gives a reasonable proxy of what vegetation is burning in a grid cell. Each grid cell was assigned a PFT identity according to that PFT which produced the highest fire CO_2 emissions over the course of each sensitivity simulation; global biome-specific masks were then created by aggregating boreal tropical and temperate forest types, and \( \Delta fBA_{F2} \) calculated for biome.
+
+Analysis
+RD was recently estimated in a statistical generalised linear modelling study to be a strong negative predictor for BA globally\(^{71}\). We evaluated the statistical relationship between BA and road density that emerges from our simulations to compare with the same regression performed by ref.\(^{(7)}\). We transform these two variables by taking the square root of road density and the applying the logit-link function to monthly burned area. The latter requires reducing a variable (burned area) to a probabilistic value, which in this case means a conversion to fraction of grid cell area (\(p\)). The logit function is then given by:
+
+\[
+Logit(BA) = Ln \left( \frac{p}{1 - p} \right)
+\] (14)
+
+To estimate fragmentation-fire behaviour at biome scale, we found the maximum PFT-type that burned the most in carbon terms over the simulation period in each grid cell, by iteratively searching out the maximum value of time-aggregated CO\(_2\) emissions per PFT in each grid. This was done because burned area in SPITFIRE is not output in PFT-specific fractions, while CO\(_2\) emissions are, and informs us of what biome fire activity is most prevalent over time in each grid cell, such that these grid cells are collectively used to characterise global biome (PFT) -scale fire behaviour. All tropical, temperate and boreal PFTs were bundled into single biome bins to simplify explanation and analysis. Fig. 4a was produced by assigning Boolean numeric values to simulation average changes in BA and ECO2, then combining these to assign coupled/decoupled direction-of-change.
+
+Data
+
+UAF was obtained from ref.\(^{(44)}\). Fire size data used in Fig. 3c is sourced from FRYv2.0\(^{87}\), updated from FRYv1.0\(^{88}\) with single ignition point polygons delineation from re.\(^{(86)}\), based on pixel information MCD64A1 and FireCCI51, as recently used in ref.\(^{(85)}\). Long-term BA data for South-east Asia from\(^{105,106}\) was obtained from https://climate.esa.int/es/odp/#/project/fire (accessed 05/06/2023), while deforestation and pre-and post 2000 average tree plantation grid data were obtained from refs.\(^{(107,108)}\). Fragmentation and fire data for Brazil in Fig. 3a were provided by ref.\(^{(102)}\) and upscaled using CDO’s conservative remapping function from 10km to 0.5 degree grid resolution. All other datasets above were interpolated bilinearly in CDO to 0.5 degree resolution. Postprocessing was performed using NCL, Panoply, CDO and R, with R maps created including the following packages: ncf4, ggplot2, raster, maptools, rgdal, rgeos, maps, ggpubr, sp, geosphere, rColorBrewer, ggmap, lattice, dplyr, tidyr, plyr.
+<table>
+  <tr>
+    <th>Variable</th>
+    <th>Value</th>
+    <th>Description</th>
+    <th>Rationale</th>
+  </tr>
+  <tr>
+    <td>a<sub>UAF</sub></td>
+    <td>2.68*10<sup>4</sup></td>
+    <td>Urban area RL removal regression coefficient (RL/Urban Area Fraction).</td>
+    <td>High RL urban areas unlikely to have significant BA removed to isolate 'fragmentation' versus 'urban' effect.</td>
+  </tr>
+  <tr>
+    <td>n<sub>pat_forest</sub></td>
+    <td>1</td>
+    <td>Parameter multiplier allowing individual forest fire size to exceed patch size by this factor, otherwise limited by it.</td>
+    <td>No data to suggest that this size can or cannot be exceeded given patch size unless extreme/crown fire</td>
+  </tr>
+  <tr>
+    <td>n<sub>pat_grass</sub></td>
+    <td>1.25</td>
+    <td>Parameter multiplier allowing individual grass fire size to exceed patch size by this factor, otherwise limited by it.</td>
+    <td>Value over unity based on assumption that some proportion of fragmented grasslands may allow spread beyond patch due to proportion of fine fuel</td>
+  </tr>
+  <tr>
+    <td>FST<sub>TREE</sub></td>
+    <td>conditional, empirically derived</td>
+    <td>Tree fire spread threshold, a flame height, tree height, canopy width dependent 'crown fire' condition</td>
+    <td>Allows fire to spread beyond patch size when fuel dryness, wind speed and allow flame height to exceed canopy</td>
+  </tr>
+  <tr>
+    <td>FST<sub>GRASS</sub></td>
+    <td>conditional, empirical</td>
+    <td>Grass fire spread threshold, based on areal fuel density</td>
+    <td>Allows fire to spread beyond patch size when fuel density exceeds threshold.</td>
+  </tr>
+  <tr>
+    <td>ED<sub>wind</sub></td>
+    <td>16m</td>
+    <td>Edge depth through which wind infiltration is altered by fragment edge</td>
+    <td>Assumes wind comes from a 1 direction in a given patch, patch average edge depth is approx. to 4m (1/4) in a given fire.</td>
+  </tr>
+  <tr>
+    <td>ED<sub>Moisture</sub></td>
+    <td>20m</td>
+    <td>Edge depth through which fuel moisture affected by fragment edge</td>
+    <td>Empirically-derived (Methods), assumes linear gradient of drying, and fuel drying itself is scaled quadratically downward with fuel type to reflect radial thickness of model fuel classes.</td>
+  </tr>
+  <tr>
+    <td>ED<sub>humig.</sub></td>
+    <td>1m</td>
+    <td>Average depth through which human activities there affect ignition probability</td>
+    <td>This is assumed because although effects may be deeper, the time averaged edge depth along fragment edges is likely small.</td>
+  </tr>
+</table>
+
+Table 1: Key components of the fragmentation module, their value, description and rationale. See Methods for detailed description and calibration of each parameter.
+
+Competing Interests
+The authors declare no competing interests.
+
+Data Availability
+The data presented in this study are available on request from the corresponding author.
+
+Code Availability
+The version of ORCHIDEE-MICT-SPITFIRE developed here is published (DOI: ) and can be downloaded at the request of the corresponding author.
+
+Acknowledgements
+SPKB was funded by research project FirEUrisk, a European Union Horizon 2020 research and innovation program under Grant Agreement No. 101003890.
+
+References
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• MSSupplement.pdf

0207534b48d5dc7f202715e97467615fe845cf6d2005bff553f5b155b496fd65/preprint/supplementaries/MSSupplement/MSSupplement.md

@@ -0,0 +1,23 @@
+Supplementary Figures
+
+![Schematic of the fragmentation concept in this study. Road Length (RL) is calculated to circles of equal area satisfying both RL (sum of grid cell circle perimeters) and grid cell area; their radius gives the per-grid average edge distance (AED, Eq.1). Comparison of two 'grid cells' (Vegetated Area 'A', 'B') of differing road densities and fragmentation, whereby more RL means more fragmentation and a smaller AED. Smaller AED → increased %(landscape) exposed to potential human ignitions (proportional to edge length), a larger area exposed to edge drying effects, higher wind speeds and smaller individual fire sizes. AED in each grid cell modulates SPITFIRE’s pre-existing human ignition function, itself a f(population density).](page_246_370_1057_495.png)
+
+Figure S1: Schematic of the fragmentation concept in this study. Road Length (RL) is calculated to circles of equal area satisfying both RL (sum of grid cell circle perimeters) and grid cell area; their radius gives the per-grid average edge distance (AED, Eq.1). Comparison of two 'grid cells' (Vegetated Area 'A', 'B') of differing road densities and fragmentation, whereby more RL means more fragmentation and a smaller AED. Smaller AED → increased %(landscape) exposed to potential human ignitions (proportional to edge length), a larger area exposed to edge drying effects, higher wind speeds and smaller individual fire sizes. AED in each grid cell modulates SPITFIRE’s pre-existing human ignition function, itself a f(population density).
+Figure S2: Simplified schematic diagram describing the combined vegetation and fire modules of ORCHIDEE-SPITFIRE, and the relation of the AED-defined fragmentation scheme devised here, to fire-relevant variables in the model. Companion figure to Figure 1b in the Main Text. Adapted from Bowring et al. (2022), SI.
+Figure S3: (a-c) Mean annual fractional changes in simulated grid cell burned area due to fragmentation representation in (a) western Eurasia, (b) southern SE Asia, (c) northern South America. Gross increases, decreases and net burned area values (Ha yr\(^{-1}\)) over the displayed area are shown inset in each panel.
+Figure S4: Annual mean fractional fire CO$_2$ emission differential relative to the control simulation for each biome type.
+Figure S5: Post-2000 mean tree plantation age derived from Du et al. (2022) and upscaled to 0.5 degree resolution, used in Fig. 3.
+
+![Post-2000 mean tree plantation age map](page_184_120_1080_496.png)
+
+Figure S6: Post-2000 deforestation mask derived from Curtis et al. (2018) and upscaled to 0.5 degree resolution, used in Fig. 3.
+
+![Post-2000 deforestation mask map](page_184_728_1080_496.png)
+Figure S7: Comparing fragmentation-associated simulated increases in fire activity \( f(\Delta B A_{Frag.}) \) with observed (FireCCI) BA anomalies from a 1982-1999 baseline, over northern South America during the period for which satellite-based fire data are available (post-2000). Simulation-observation agreement (yellow-red) and observation-only fire anomaly grid cells (green-blue) are shaded darker along a gradient of increasing observed fire anomaly (Methods). Dots correspond to areas of significant deforestation activity(ref) and/or plantation establishment (ref) since the year 2000 (black, green), or preceding it (pink). Dot size is proportional to deforestation severity where applicable.
+Figure S8: The additional burned area per per-capita road length (Ha yr\(^{-1}\) km\(^{-2}\) person\(^{-1}\)), which shows the amount of additional burned area per additional person or km of road laid, in each grid cell, per year.
+
+![World map showing additional burned area per per-capita road length](page_153_120_1142_496.png)
+
+![Line graph showing biome-mean dBa fragmentation versus AED, with lines for Trop, Temp, Bor, C3, and C4, and annotations for mean dBa per AED_{ij} and additional fragmentation needed for equivalent BA decrease](page_153_670_1142_496.png)
+Figure S9: The average change in fractional BA of each biome for each AED_{F2} level, where change is calculated in the direction of increasing fragmentation. Averages across all AED levels are printed inset. Highlighted is the large difference in fragmentation extent required to produce the same BA decrease between tropical forest and C3 grassland biomes.
+Figure S10: Per-grid cell fractional changes in BA due to globally equal doubling of fragmentation extent in the AED\(_{F2}\) simulation suite, whereby the BA change denotes that change in BA from the preceding AED\(_{F2}\) level (e.g. the change BA due to the change in global AED from 10000m to 5000m).

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022065845b0149dd1bde836e14da3448f70c4603767a53533c6448baf134c8c3/peer_review/images_list.json

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022065845b0149dd1bde836e14da3448f70c4603767a53533c6448baf134c8c3/peer_review/peer_review.md

@@ -0,0 +1,474 @@
+Peer Review File
+
+Crowding results from optimal integration of visual targets with contextual information
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This is an outstanding manuscript. The authors propose a novel and fascinating connection between crowding and serial dependence, two extensively studied areas of perception and cognition. They thoroughly test their idea psychophysically and with modeling. The results support the hypothesis and this will stimulate a lot of future research. I know this hypothesis will be provocative in the field, and not everyone will agree (it’s a fairly contentious field), but this is a strength; the manuscript is exceptionally well balanced and approaches the issues in a most constructive way. The crowding field has been somewhat stagnant for years, and the authors’ novel connection is much needed inspiration for researchers to pursue new directions. I expect this paper will motivate a great flurry of new experiments. I have a few minor suggestions below, but these are just requested clarifications, nothing major. Given the broad connections this manuscript makes across fields and the novelty of the idea and results, the manuscript certainly merits publication in Nature Comms.
+
+Minor points:
+
+Flanker Similarity and the (unmentioned) Diagnostic criteria for crowding. There’s a nod to these diagnostic criteria (eg, Whitney & Levi, 2011) but not a direct statement. The critical spacing one is key of course (p. 6)—and the model does a great job predicting that—but it’s not the only one. Another key characteristic directly addressed in the MS is similarity. This is relevant here bc the prior literature had little explanation for why “similarity” matters in the way that it does (eg similarity modulates crowding and dissimilarity releases crowding). The authors’ idea of a connection between serial dependence and crowding, and their model, is very powerful and important in part bc it provides that “why”. In future work it will be interesting to test if other diagnostic criteria like inner-outer flanker asymmetry, upper lower visual field diff, etc also hold. This isn’t necessary here but readers may wonder and the authors could prompt that question and help motivate the important follow up research.
+
+P2, “tasks like or face recognition” delete “or” and perhaps add a reference here. Maybe Farzin et al 2009 (for faces) or the cited reviews (if this is a generic statement about objects).
+
+P3, “qualitatively and qualitatively”. Perhaps one of these was intended to be “quantitatively”?
+
+Fig 1b. Using red outline and blue outline around the respective panels (or at least red and blue color somehow in those two panels) would help readers follow the correspondence between all the Figs; red always indicates high reliability target. Might as well start using that rule in fig 1b.
+
+P.4. “…Formally the modeling section” should be “formally in the…”
+
+P5. “….With difference between…” should have “the” or an “s” after “difference”
+
+Fig 2, abscissa. Add clarification that this axis is “difference” in orientation. It’s not absolute orientation, right?
+
+Fig 2. Where would isolated (single) targets be on this graph?
+
+P.11. Is the “signature” of the “signature function” the derivative-of-Gaussian shape in the SD literature? If so, perhaps mention that or explain what is meant by “signature”
+
+P 12. The first sentence of the “causal inference model” section. That first sentence is too difficult to parse or understand. Not just because the word “form” probably isn’t intended. Rephrasing could help a lot.
+P12. "...the weight assigned of is the..." Rephrase, please.
+
+Aside from these very minor points, this is an excellent manuscript.
+
+Reviewer #2 (Remarks to the Author):
+
+This is a fascinating manuscript, with novel findings that present a new perspective on a widely studied phenomenon. The authors examine visual crowding, the disruptive effect of clutter on object recognition. A large body of research has depicted this effect as the ‘fundamental bottleneck on object recognition’ in peripheral vision especially. As a result, we know a great deal about the way this process affects object recognition and the potential mechanisms. What is much less clear is why crowding occurs in the first place. This manuscript presents an interesting answer to this question by considering its usefulness.
+
+The broad approach here is to compare crowding with properties of ‘serial dependence’, the effect whereby judgements of a stimulus are influenced by the presentation of other stimuli in prior trials. With this comparison, the authors ask whether crowding can be considered to be an efficient/optimal process, rather than reflecting a disruptive bottleneck. Several predictions are made in this case, all of which are ultimately argued to be supported by the data. The authors ask observers to judge the orientation of shapes made from an outline of dots. They first observe greater biases and higher response scatter with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. Second, they note that response scatter is greatest when the orientation of the flankers is close to the target, with a decrease as dissimilarity decreases (that is, performance improves as crowding increases, showing its efficiency). Finally, the pattern of biases follows the mean orientation of flankers rather than an independent combination, which is used to justify a higher-level model. The manuscript is well written and engaging, and presents a provocative view of a widely studied process. If the findings here are true then this presents an important aspect of our understanding. I do have a number of issues with the manuscript as it stands, however.
+
+1. The pattern of response scatter
+
+The main issue concerns the second finding – that response scatter is greatest (i.e. performance is worst) when the orientation of the flankers is most similar to the target. This finding is a key aspect of the proposal that crowding is efficient/optimal, since errors decrease as the strength of crowding increases. If true however, this finding is inconsistent with a large literature on the effect of target-flanker similarity in crowding. More typically, crowding is greatest when target and flanker elements are most similar to one another, decreasing as their dissimilarity increases (the opposite of the current observation). This has been found for a range of stimulus properties including contrast polarity, color, spatial frequency, and direction (Kooi, Toet, Tripathy, & Levi, 1994; Chung, Levi, & Legge, 2001; Gheri, Morgan, & Solomon, 2007), and in particular for orientation judgements (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellemberg, 1997), similar to those used in the present study. In those latter studies, flankers that share similar orientations to the target induce the most crowing, with less crowding as the orientation of the flankers rotates away. Given that a major premise of the current study rests on the opposite finding, this discrepancy needs explanation and/or further exploration. The authors do in fact cite some of these studies to begin the manuscript, describing the patterns above, but the discrepancy with the current results is subsequently ignored. How can this discrepancy be explained, and how does this fit with the central arguments regarding the efficiency/optimality of crowding?
+
+There seem to me at least two possibilities to explain the discrepancy. One is that the authors have not fully measured the range of possible target-flanker differences in orientation. Targets are
+presented at either 35 or 55 degrees rotation, with flankers that differ from these values by up to ±45 degrees. Response scatter peaks at the highest values measured (±45 degrees). It is however possible then that these values may drop again as the differences further increase, up to their maximum of 90 degrees from the target orientation. It is typically these 90 degree values that are compared in order to show target-flanker similarity effects (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellemberg, 1997), and I suspect that if the measurements continued here that performance would drop again. Indeed – patterns of this nature have been reported in a prior study (Solomon, Felisberti, & Morgan, 2004). There, orientation sensitivity is high when flankers are similarly oriented to the target, drops for orientations up to ±45 degrees, and then increases again as the rotation continues to 90 degrees. The same may be true of the present stimuli if a larger range of orientations were tested. Would that not alter the interpretations regarding the efficiency of this process?
+
+A second possibility is the eccentricity – the authors present their stimuli 26 degrees from fixation. Prior observations of target-flanker similarity have tended to use lower eccentricities. Given that some properties of crowding change with eccentricity, e.g. the response biases (Mareschal, Morgan, & Solomon, 2010) and of course the well-known effects of spatial extent (Bouma, 1970), it could be that the present results are something that only arises in the far periphery. Were this the case, however, the question remains – why is efficiency evident in the present results and not these other studies?
+
+To summarize, the results regarding response scatter appear to follow the opposite pattern to a range of well-established and replicated findings in the literature. The premise of the paper rests heavily on this observation. The authors need to demonstrate that this pattern is reliable by extending the range of their measurements in some way and/or by addressing this discrepancy with prior results. If the current results show efficiency, what does that say about all of these other results? If crowding is only efficient in these limited circumstances, is it really efficient?
+
+2. The lack of an unflanked baseline
+
+Part of the issue of interpretation with the above response scatter data also relates to the lack of an unflanked baseline. Typically, performance with flankers is used to measure crowding, with an unflanked baseline (with an isolated element) used to measure uncrowded performance. The authors here take their baseline using flanked performance, using flankers with orientations at the extremes of their range (p14). Given the odd pattern of response scatter (as above), this assumption is problematic. If unflanked performance is more like the values with a flanker difference of 0 degrees, then performance would go from largely unaffected with the 0 degree flankers to impaired with the ±45 degree flankers, rather than from improved with the 0 degree flankers to unaffected with the ±45 degree flankers, as the authors argue. Does that not change the interpretation of the results and their efficiency/optimality substantially?
+
+3. The distinction with ‘low-level’ pooling models of crowding
+
+The authors contrast their findings with ‘low level pooling models’, which do not seem to me to be at odds with the present results. This distinction begins in the abstract (e.g. on line 2), where low level models are contrasted with their ‘alternative hypothesis’, and continues throughout, e.g. on p15 of the discussion, where it is argued that pooling models cannot explaining the effects of flanker orientation. Later on however, the authors describe their model as a pooling process (p17). The mechanism proposed for their model, with large receptive fields in areas like V4 (p16), also sounds very similar to ideas raised in various pooling models. For instance, processes of ‘population pooling’ have attributed the crowding of orientation signals to pooling within receptive fields in area V2 or V4 (van den Berg, Roerdink, & Cornelissen, 2010; Harrison & Bex, 2015). Similar arguments are also made by ‘high dimensional’ pooling models (Rosenholtz, Yu, & Keshvari, 2019). In fact, patterns of bias that are very similar to those in Figure 2A of this manuscript have been reported previously and accounted for via pooling processes (Greenwood & Parsons, 2020). In this latter case, the model accounts for target-flanker similarity effects via variations in the weights applied to the flankers. I don’t see why this is
+inconsistent with the variations shown in the current study.
+
+The authors distinguish between two possible models, both of which seem like pooling models to me. One is a ‘low level’ version in which the interactions happen independently between each flanker and the target, linked with a feedforward local process. The other involves a broader integration in which the flankers have a combined influence on the target, linked with recurrent feedback interactions. The latter does not seem wholly distinct from the operation of the most recent population pooling models (Harrison & Bex, 2015; Greenwood & Parsons, 2020) described above however. In those cases, the flankers affect the target through their combination within a single population response. My feeling is that the results of Experiment 2 in the present study would be entirely consistent with these models – when flanker orientations vary independently, their combined population response would have a shifted mean that would tend to alter the subsequent judgements related to the target. If so, then I do not think these results are inconsistent with pooling, nor do they provide clear evidence for feedback. This is not to take away from the novelty of these findings, however – I agree that the results provide clear evidence that the flankers do not interact independently with the target. The distinction between the two models presented here is certainly interesting, but their physiological basis is clearly overstated.
+
+4. Effects of target reliability
+
+The first result reported in the manuscript is that biases are greater and response scatter higher with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. This effect is attributed to reliability, and explained via a Bayesian framework. Its relation to similar results with alternative explanations is unexplored, however. Most notably, crowding is strongest with flankers of high luminance contrast (Chung, Levi, & Legge, 2001; Pelli, Palomares, & Majaj, 2004). Lowering the target contrast can also increase crowding (Felisberti, Solomon, & Morgan, 2005). Assimilative biases related to orientation judgements are also increased when noise is added to stimuli (Mareschal, Morgan, & Solomon, 2010). Can all of these effects be understood via reliability? It seems to me there is an alternative explanation that crowding is determined by the strength of the target signal, relative to the strength of the flanker signal(s). Could these effects, including those of the present study, be understood as signal strength rather than reliability per se?
+
+5. The relation to serial dependence
+
+Much is made of the similarities between serial dependence and crowding, which I agree is a fascinating link to make. The arguments for efficiency in this context also sound to me like arguments made more broadly in vision for the principles of redundancy reduction (Atteave, 1954), including for processes like adaptation (Clifford, 2002) and surround suppression (Rao & Ballard, 1999). Could the similarities here in fact indicate a broader link in the form of a “canonical computation” across all of visual perception? I wonder if the strong link to serial dependence is a little short-sighted in this sense.
+
+5. The neural basis of crowding
+
+The idea of crowding relating to higher cortical areas like V4 is attributed to Pelli & Tillman (p2), but this idea derives from earlier work (Motter & Simoni, 2007; Motter, 2009). Others have also linked crowding with receptive field sizes in areas like V2 (He, Wang, & Fang, 2019).
+
+6. Stimulus details
+
+Was the rotation of flankers taken from the target orientation on each trial, such that the ±45 degree range differed in terms of absolute orientations for the 35 and 55 degree targets?
+Additionally, can we be sure that the judgements made by observers concern the orientation of these stimuli, rather than another property? Given the dotted nature of the stimuli used in the present task, perhaps observers are not judging orientation, but rather another property like the position of the outermost dots in the elements. This could allow a kind of relative position or Vernier judgement. Prior studies have tended to use line elements or Gabors in this context – if true, could this explain the difference with the studies of target-flanker similarity described above?
+
+References
+
+Andriessen, J. J., & Bouma, H. (1976). Eccentric vision: Adverse interactions between line segments. Vision Research, 16(1), 71-78.
+Attnave, F. (1954). Some informational aspects of visual perception. Psychological Review, 61(3), 183-193.
+Bouma, H. (1970). Interaction effects in parafoveal letter recognition. Nature, 226, 177-178.
+Chung, S. T. L., Levi, D. M., & Legge, G. E. (2001). Spatial-frequency and contrast properties of crowding. Vision Research, 41, 1833-1850.
+Clifford, C. W. G. (2002). Perceptual adaptation: Motion parallels orientation. Trends in Cognitive Sciences, 6(3), 136-143.
+Felisberti, F. M., Solomon, J. A., & Morgan, M. J. (2005). The role of target salience in crowding. Perception, 34(7), 823-833.
+Gheri, C., Morgan, M. J., & Solomon, J. A. (2007). The relationship between search efficiency and crowding. Perception, 36(12), 1779-1787.
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117(14), 8196-8202.
+Harrison, W. J., & Bex, P. J. (2015). A Unifying Model of Orientation Crowding in Peripheral Vision. Current Biology, 25(24), 3213-3219.
+He, D., Wang, Y., & Fang, F. (2019). The critical role of V2 population receptive fields in visual orientation crowding. Current Biology, 29(13), 2229-2236. e2223.
+Kooi, F. L., Toet, A., Tripathy, S. P., & Levi, D. M. (1994). The effect of similarity and duration on spatial interaction in peripheral vision. Spatial Vision, 8(2), 255-279.
+Mareschal, I., Morgan, M. J., & Solomon, J. A. (2010). Cortical distance determines whether flankers cause crowding or the tilt illusion. Journal of Vision, 10(8):13, 1-14.
+Motter, B. C. (2009). Central V4 Receptive Fields Are Scaled by the V1 Cortical Magnification and Correspond to a Constant-Sized Sampling of the V1 Surface. Journal of Neuroscience, 29(18), 5749-5757.
+Motter, B. C., & Simon, D. A. (2007). The roles of cortical image separation and size in active visual search performance. Journal of Vision, 7(2(6)), 1-15.
+Pelli, D. G., Palomares, M., & Majaj, N. J. (2004). Crowding is unlike ordinary masking: Distinguishing feature integration from detection. Journal of Vision, 4(12), 1136-1169.
+Rao, R. P. N., & Ballard, D. H. (1999). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1), 79-87.
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19(7), 1-25.
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+van den Berg, R., Roerdink, J. B. T. M., & Cornelissen, F. W. (2010). A Neurophysiologically Plausible Population Code Model for Feature Integration Explains Visual Crowding. PLoS Computational Biology, 6(1), e1000646.
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14(9), 2057-2068.
+Reviewer #3 (Remarks to the Author):
+
+Cicchini and colleagues put forward the hypothesis that crowding is results from Bayes-optimal integration of visual targets with spatial context. The authors identify four features of their empirical data that are consistent with Bayes-optimal integration: (1) Crowding is strongest for reliable flankers and unreliable targets, (2) Crowding depends on flanker-target similarity (here orientation), (3) precision of orientation judgments increases with increasing flanker-target similarity, and (4) Crowding depends on similarity of targets to average flanker orientation, not individual flanker orientations. The authors present two ideal observer models (a Bayesian ideal observer, and a causal inference model), which can reproduce the above features of the empirical data.
+
+While I find the hypothesis that crowding results from optimal integration intriguing, I am somewhat reserved when it comes to the evidence provided in the current study. I am also not convinced that the behavioral benefits described here can be ascribed to crowding rather than ensemble perception. Please find my detailed points below.
+
+1. The ideal observer models only provide adequate fits when equipped with scaling parameters that account for “sub-optimal” behavior. The required scaling is not negligible, rescaling the optimal integration weights by ~40 to 50%. Therefore, it is not clear whether the observers’ behavior is at all optimal, beyond resembling some qualitative features of the data. The authors could make a much stronger case when quantitatively accounting for the sub-optimal behavior. For instance, how strong would regression to the mean of orientation judgments need to be (put forward by the authors as an explanation of sub-optimality) in order to match this scaling? Is this consistent with the empirical data?
+
+2. Related to point 1, it is not clear in how far the empirical features are exclusively accounted for by Bayes-optimal integration versus other forms of (non-optimal) integration. As the authors note in their discussion feature 1 (orientation uncertainty) could be captured by obligatory integration models. Feature 2 (flanker-target similarity) could be explained by interference between similarly tuned, and therefore more strongly interconnected neural populations. For feature 4 (global vs local context), it seems that one could develop an alternative optimal observer that integrates local instead of global context. That is, I do not understand which optimality consideration would strictly dictate global versus local integration.
+I believe most of these concerns of whether the behavioral features really arise from optimal integration could be mitigated by improving point 1 above, i.e. providing a more detailed quantitative explanation of behavior, rather than absorbing a considerable mismatch between predictions and data into one or two unexplained “sub-optimality” parameters.
+
+3. It is not clear whether the behavioral benefits examined in this experiment are due to crowding or ensemble perception. While these appear to be at least partially distinct phenomena, they can co-occur (“Reexamining the possible benefits of visual crowding: dissociating crowding from ensemble percepts” Bulakowski et al., 2011). Cicchini et al. test the influence of target-distractor distance, and demonstrate that bias depends on distance, as expected for a crowding effect. However, I would contest that increasing flanker-target distance also alters the ensemble, and can therefore also impact ensemble perception. Perhaps one way to address this issue would be to test whether or not similar integration effects occur for more foveally presented stimuli, i.e. in the absence of crowding (albeit under matched conditions of visual uncertainty). If they do, the current observations would perhaps be better explained as resulting from ensemble perception, while crowding merely co-occurs in the current setup.
+
+Minor comments:
+
+Figure 5B. Minimum scatter appears to occur at 0 deg, while the ideal observer models predict the
+minimum to occur at 15 degrees. I am curious whether the authors have any explanation/speculation of why the bias and variance data diverge in this aspect.
+
+In their introduction the authors state “Crowding impacts on many important daily tasks, such as face recognition and reading [...]” I would be curious how the authors reconcile this view that crowding appears to negatively impact perception in real world scenarios (“daily tasks”) with their optimal integration theory.
+GENERAL
+
+We thank the editor and particularly the reviewers for their time and very helpful advice. We have taken all the suggestions on board, definitely resulting in an improved manuscript. We trust it is now acceptable for publication.
+
+We have marked the changes in blue on the revised manuscript.
+
+David Burr
+
+For the authors
+
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This is an outstanding manuscript. The authors propose a novel and fascinating connection between crowding and serial dependence, two extensively studied areas of perception and cognition. They thoroughly test their idea psychophysically and with modeling. The results support the hypothesis and this will stimulate a lot of future research. I know this hypothesis will be provocative in the field, and not everyone will agree (it’s a fairly contentious field), but this is a strength; the manuscript is exceptionally well balanced and approaches the issues in a most constructive way. The crowding field has been somewhat stagnant for years, and the authors’ novel connection is much needed inspiration for researchers to pursue new directions. I expect this paper will motivate a great flurry of new experiments. I have a few minor suggestions below, but these are just requested clarifications, nothing major. Given the broad connections this manuscript makes across fields and the novelty of the idea and results, the manuscript certainly merits publication in Nature Comms.
+
+We thank the reviewer for their kind words, and agree that the findings will be contentious, but hopefully stimulate useful research.
+
+Minor points:
+
+Flanker Similarity and the (unmentioned) Diagnostic criteria for crowding. There’s a nod to these diagnostic criteria (eg, Whitney & Levi, 2011) but not a direct statement. The critical spacing one is key of course (p. 6)—and the model does a great job predicting that—but it’s not the only one. Another key characteristic directly addressed in the MS is similarity. This is relevant here bc the prior literature had little explanation for why “similarity” matters in the way that it does (eg similarity modulates crowding and dissimilarity releases crowding). The authors’ idea of a connection between serial dependence and crowding, and their model, is very powerful and important in part bc it provides that “why”. In future work it will be interesting to test if other diagnostic criteria like inner-outer flanker asymmetry, upper lower visual field diff, etc also hold. This isn’t necessary here but readers may wonder and the authors could prompt that question and help motivate the important follow up research.
+
+Thanks for this important suggestion. We now mention the diagnosis criteria more clearly in introduction, and pick it up again in discussion.
+
+P2, “tasks like or face recognition” delete “or” and perhaps add a reference here. Maybe Farzin et al 2009 (for faces) or the cited reviews (if this is a generic statement about objects).
+
+P3, “qualitatively and qualitatively”. Perhaps one of these was intended to be “quantitatively”?
+
+Fig 1b. Using red outline and blue outline around the respective panels (or at least red and blue color somehow in those two panels) would help readers follow the correspondence between all the Figs; red always indicates high reliability target. Might as well start using that rule in fig 1b.
+
+Excellent idea
+
+P.4. “…Formally the modeling section” should be “formally in the…”
+
+P5. “…With difference between…” should have “the” or an “s” after “difference”
+
+Fig 2, abscissa. Add clarification that this axis is “difference” in orientation. It’s not absolute orientation, right?
+
+Fig 2. Where would isolated (single) targets be on this graph?
+Unfortunately we did not measure the effects without flankers.
+
+P.11. Is the “signature” of the “signature function” the derivative-of-Gaussian shape in the SD literature? If so, perhaps mention that or explain what is meant by “signature”
+
+P 12. The first sentence of the “causal inference model” section. That first sentence is too difficult to parse or understand. Not just because the word “form” probably isn’t intended. Rephrasing could help a lot.
+
+P12. "...the weight assigned of is the..."Rephrase, please.
+
+Aside from these very minor points, this is an excellent manuscript.
+
+Thank you very much, all the minor points have all been dealt with.
+
+Reviewer #2 (Remarks to the Author):
+
+This is a fascinating manuscript, with novel findings that present a new perspective on a widely studied phenomenon. The authors examine visual crowding, the disruptive effect of clutter on object recognition. A large body of research has depicted this effect as the ‘fundamental bottleneck on object recognition’ in peripheral vision especially. As a result, we know a great deal about the way this process affects object recognition and the potential mechanisms. What is much less clear is why crowding occurs in the first place. This manuscript presents an interesting answer to this question by considering its usefulness.
+
+Thank you for the kind words. Thank you also for the very detailed help you have given, providing useful references and encouraging us to make clearer our ideas.
+
+The broad approach here is to compare crowding with properties of ‘serial dependence’, the effect whereby judgements of a stimulus are influenced by the presentation of other stimuli in prior trials. With this comparison, the authors ask whether crowding can be considered to be an efficient/optimal process, rather than reflecting a disruptive bottleneck. Several predictions are made in this case, all of which are ultimately argued to be supported by the data. The authors ask observers to judge the orientation of shapes made from an outline of dots. They first observe greater biases and higher response scatter with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. Second, they note that response scatter is greatest when the orientation of the flankers is close to the target, with a decrease as dissimilarity decreases (that is, performance improves as crowding increases, showing its efficiency). Finally, the pattern of biases follows the mean orientation of flankers rather than an independent combination, which is used to justify a higher-level model. The manuscript is well written and engaging, and presents a provocative view of a widely studied process. If the findings here are true then this presents an important aspect of our understanding. I do have a number of issues with the manuscript as it stands, however.
+
+1. The pattern of response scatter
+
+The main issue concerns the second finding – that response scatter is greatest (i.e. performance is worst) when the orientation of the flankers is most similar to the target. This finding is a key aspect of the proposal that crowding is efficient/optimal, since errors decrease as the strength of crowding increases. It true however, this finding is inconsistent with a large literature on the effect of target-flanker similarity in crowding. More typically, crowding is greatest when target and flanker elements are most similar to one another, decreasing as their dissimilarity increases (the opposite of the current observation). This has been found for a range of stimulus properties including contrast polarity, color, spatial frequency, and direction (Kooi, Toet, Tripathy, & Levi, 1994; Chung, Levi, & Legge, 2001; Gheri, Morgan, & Solomon, 2007), and in particular for orientation judgements (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellenberg, 1997), similar to those used in the present study. In those latter studies, flankers that share similar orientations to the target induce the most crowding, with less crowding as the orientation of the flankers rotates away. Given that a major premise of the current study rests on the opposite finding, this discrepancy needs explanation and/or further exploration. The authors do in fact cite some of these studies to begin the manuscript, describing the patterns above, but the discrepancy with the current results is subsequently ignored. How can this discrepancy be explained, and how does this fit with the central arguments regarding the efficiency/optimality of crowding?
+
+This important comment shows that we need to do a better job explaining our results and ideas. Firstly, we assume that the first sentence was a typo – response scatter is least (precision greatest) when orientations coincide (where crowding is greatest). That may seem counter-intuitive, but it depends on how you measure crowding. Typically it is percent correct, or perhaps contrast sensitivity. We are saying that RMS Errors (which comprise both accuracy and precision) are reduced, because although average accuracy decreases (strong bias), the increased precision more than offsets the bias, resulting in lower RMSE (radial distance in Fig 2C). However, other performance measures need not necessarily improve. For example, simple measures of accuracy (whether the reproduction was near veridical) would be low when the bias is high, as the orientation
+judgement would seldom be “correct”; improved precision would not increase accuracy, and possibly decrease it, all responses become more tightly grouped around the incorrect bias. The only paper to measure separately bias and precision that we know of is Solomon, Felisberti and Morgan (JoV 2004: thanks for the pointer), and they report results very similar to ours (their Figure 4A). Also their data indicate a reduction in RMS Error (although they did not describe their results that way), shown in this figure below derived from their data. We have tried to make the explanations clearer in the results and discussion sections, and have added a brief paragraph discussing the apparent paradox.
+
+![RMSE calculated from Figure 4A of Solomon et al., 2004](page_312_670_823_393.png)
+
+Figure 1: RMSE calculated from Figure 4A of Solomon et al., 2004
+
+There seem to me at least two possibilities to explain the discrepancy. One is that the authors have not fully measured the range of possible target-flanker differences in orientation. Targets are presented at either 35 or 55 degrees rotation, with flankers that differ from these values by up to ±45 degrees. Response scatter peaks at the highest values measured (±45 degrees). It is however possible then that these values may drop again as the differences further increase, up to their maximum of 90 degrees from the target orientation. It is typically these 90 degree values that are compared in order to show target-flanker similarity effects (Andriessen & Bouma, 1976; Wilkinson, Wilson, & Ellemberg, 1997), and I suspect that if the measurements continued here that performance would drop again. Indeed – patterns of this nature have been reported in a prior study (Solomon, Felisberti, & Morgan, 2004). There, orientation sensitivity is high when flankers are similarly oriented to the target, drops for orientations up to ±45 degrees, and then increases again as the rotation continues to 90 degrees. The same may be true of the present stimuli if a larger range of orientations were tested. Would that not alter the interpretations regarding the efficiency of this process?
+
+See above response for the explanation of apparent discrepancy. It is interesting that precision (but not bias) improved for 90° flankers in Solomon et al. Unfortunately we did not measure out that far. However, it would not change our story, as we are interested in the range where the flankers cause crowding by biasing results; in that range there is a clear trade-off between accuracy and precision for both our and their data. Our data show maximum bias at a lower orientation than theirs (about 20° compared with their 45°), so it did not seem necessary to measure beyond 45°.
+
+A second possibility is the eccentricity – the authors present their stimuli 26 degrees from fixation. Prior observations of target-flanker similarity have tended to use lower eccentricities. Given that some properties of crowding change with eccentricity, e.g. the response biases (Mareschal, Morgan, & Solomon, 2010) and of course the well-known effects of spatial extent (Bouma, 1970), it could be that the present results are something that only arises in the far periphery. Were this the case, however, the question remains – why is efficiency evident in the present results and not these other studies?
+
+It is true that we used a large eccentricity, to maximize the effects, but our results agree with the only other study where efficiency can be calculated (Solomon et al. above figure), who worked at the much lower eccentricity of 3.7° (now mentioned).
+
+To summarize, the results regarding response scatter appear to follow the opposite pattern to a range of well-established and replicated findings in the literature. The premise of the paper rests heavily on this observation. The authors need to demonstrate that this pattern is reliable by extending the range of their measurements in some way and/or by addressing this discrepancy with prior results. If the current results show efficiency, what does that say about all of these other results? If crowding is only efficient in these limited circumstances, is it really efficient?
+We hope the above comments address this seeming paradox to the reviewer’s satisfaction.
+
+2. The lack of an unflanked baseline
+
+Part of the issue of interpretation with the above response scatter data also relates to the lack of an unflanked baseline. Typically, performance with flankers is used to measure crowding, with an unflanked baseline (with an isolated element) used to measure uncrowded performance. The authors here take their baseline using flanked performance, using flankers with orientations at the extremes of their range (p14). Given the odd pattern of response scatter (as above), this assumption is problematic. If unflanked performance is more like the values with a flanker difference of 0 degrees, then performance would go from largely unaffected with the 0 degree flankers to impaired with the ±45 degree flankers, rather than from improved with the 0 degree flankers to unaffected with the ±45 degree flankers, as the authors argue. Does that not change the interpretation of the results and their efficiency/optimality substantially?
+
+Unfortunately we did not measure a baseline. We did not think this is a major problem, but in retrospect it would have been useful to do so.
+
+3. The distinction with ‘low-level’ pooling models of crowding
+
+The authors contrast their findings with ‘low level pooling models’, which do not seem to me to be at odds with the present results. This distinction begins in the abstract (e.g. on line 2), where low level models are contrasted with their ‘alternative hypothesis’, and continues throughout, e.g. on p15 of the discussion, where it is argued that pooling models cannot explaining the effects of flanker orientation. Later on however, the authors describe their model as a pooling process (p17). The mechanism proposed for their model, with large receptive fields in areas like V4 (p16), also sounds very similar to ideas raised in various pooling models. For instance, processes of ‘population pooling’ have attributed the crowding of orientation signals to pooling within receptive fields in area V2 or V4 (van den Berg, Roerdink, & Cornelissen, 2010; Harrison & Bex, 2015). Similar arguments are also made by ‘high dimensional’ pooling models (Rosenholtz, Yu, & Keshvari, 2019). In fact, patterns of bias that are very similar to those in Figure 2A of this manuscript have been reported previously and accounted for via pooling processes (Greenwood & Parsons, 2020). In this latter case, the model accounts for target-flanker similarity effects via variations in the weights applied to the flankers. I don’t see why this is inconsistent with the variations shown in the current study.
+
+The authors distinguish between two possible models, both of which seem like pooling models to me. One is a ‘low level’ version in which the interactions happen independently between each flanker and the target, linked with a feedforward local process. The other involves a broader integration in which the flankers have a combined influence on the target, linked with recurrent feedback interactions. The latter does not seem wholly distinct from the operation of the most recent population pooling models (Harrison & Bex, 2015; Greenwood & Parsons, 2020) described above however. In those cases, the flankers affect the target through their combination within a single population response. My feeling is that the results of Experiment 2 in the present study would be entirely consistent with these models – when flanker orientations vary independently, their combined population response would have a shifted mean that would tend to alter the subsequent judgements related to the target.
+If so, then I do not think these results are inconsistent with pooling, nor do they provide clear evidence for feedback. This is not to take away from the novelty of these findings, however – I agree that the results provide clear evidence that the flankers do not interact independently with the target. The distinction between the two models presented here is certainly interesting, but their physiological basis is clearly overstated.
+
+Indeed most models of crowding since Morgan’s Nature paper involve some sort of obligatory pooling. The two novelty of what we propose are that the pooling is “intelligent”, occurring when it leads to improved efficiency (measured by RMS Error); and that it is relatable to serial dependence, allowing cross-fertilization of the two fields. No previous model that we are aware of predicts this. Certainly there are elements in common, especially with our preferred model involving compulsory (unintelligent) pooling of signals; but the key difference is that this integrated information is not to final output but is combined intelligently with the more local signal. We have tried to make that clearer in the text.
+
+4. Effects of target reliability
+
+The first result reported in the manuscript is that biases are greater and response scatter higher with “low reliability” near-circular target stimuli that are more difficult to judge, compared with “high reliability” elliptical targets. This effect is attributed to reliability, and explained via a Bayesian framework. Its relation to similar results with alternative explanations is unexplored, however. Most notably, crowding is strongest with flankers of high luminance contrast (Chung, Levi, & Legge, 2001; Pelli, Palomares, & Majaj, 2004). Lowering the target contrast can also increase crowding (Felisberti, Solomon, & Morgan, 2005). Assimilative biases related to orientation judgements are also increased when noise is added to stimuli (Mareschal, Morgan, & Solomon, 2010). Can all of these effects be understood via reliability? It seems to me there is an alternative explanation that crowding is determined by the strength of the target signal, relative to the strength of the
+flanker signal(s). Could these effects, including those of the present study, be understood as signal strength rather than reliability per se?
+
+This is a good point, and we have now added those references. Technically, reliability is the inverse of the variance of the underlying noise distribution. Variance will certainly be affected by contrast and by noise in the way suggested (these have been the standard techniques of manipulating reliability in the multi-sensory literature), so yes, signal strength will increase reliability. However, given that our modelling is quantitatively based on reliability of flanker and target, we prefer to remain within that framework.
+
+It is also interesting to note that the stimuli we employ (ellipses defined by dots), on the other hand allow manipulating reliability while keeping more basic parameters (contrast, visibility etc) as matched as possible. This suggests that the framework we chose could be a more general one and could encompass those special cases reported in the literature
+
+5. The relation to serial dependence
+
+Much is made of the similarities between serial dependence and crowding, which I agree is a fascinating link to make. The arguments for efficiency in this context also sound to me like arguments made more broadly in vision for the principles of redundancy reduction (Attneave, 1954), including for processes like adaptation (Clifford, 2002) and surround suppression (Rao & Ballard, 1999). Could the similarities here in fact indicate a broader link in the form of a “canonical computation” across all of visual perception? I wonder if the strong link to serial dependence is a little short-sighted in this sense.
+
+This is a great idea, but we feel it goes beyond this paper. We would prefer to link crowding to a specific and well studied phenomenon, like serial dependence, rather than trying to push our claims too far at this stage. But we expect that the idea of canonical calculation will prove to be correct.
+
+5. The neural basis of crowding
+
+The idea of crowding relating to higher cortical areas like V4 is attributed to Pelli & Tillman (p2), but this idea derives from earlier work (Motter & Simoni, 2007; Motter, 2009). Others have also linked crowding with receptive field sizes in areas like V2 (He, Wang, & Fang, 2019).
+
+Thanks for this feedback, we now have acknowledged these earlier scholars.
+
+6. Stimulus details
+
+Was the rotation of flankers taken from the target orientation on each trial, such that the ±45 degree range differed in terms of absolute orientations for the 35 and 55 degree targets?
+
+Yes it was.
+
+Additionally, can we be sure that the judgements made by observers concern the orientation of these stimuli, rather than another property? Given the dotted nature of the stimuli used in the present task, perhaps observers are not judging orientation, but rather another property like the position of the outermost dots in the elements. This could allow a kind of relative position or Vernier judgement. Prior studies have tended to use line elements or Gabor’s in this context – if true, could this explain the difference with the studies of target-flanker similarity described above?
+
+If we understand correctly the reviewer is asking us to consider the possibility that observers are not judging orientation of the main axis of the ellipse but rather the relative position of the outermost dot of the target object. This quantity could provide a rough proxy for orientation in that when the target exceeds (i.e. it is more to the right) the flankers likely the target is more horizontal (and vice versa if more inmost). If this was the case however in the “rounded target – slim flankers” the target would not exceed the flankers in this metric and reports should lean towards vertical. Conversely in the “slim target – rounded flanker”, condition. These two predictions however are not met as there are no substantial biases.
+Another possibility is that observers were judging the relative orientation (or position) of the two outmost dots of each stimulus. This would enable for instance judging the absolute orientation of the object (whereas previous hypothesis only would inform on relative orientation respect to the flanker). However, this mechanism cannot account for the clear difference of precision between the two types of stimuli.
+References
+
+Andriessen, J. J., & Bouma, H. (1976). Eccentric vision: Adverse interactions between line segments. Vision Research, 16(1), 71-78.
+
+Attenave, F. (1954). Some informational aspects of visual perception. Psychological Review, 61(3), 183-193.
+
+Bouma, H. (1970). Interaction effects in parafoveal letter recognition. Nature, 226, 177-178.
+
+Chung, S. T. L., Levi, D. M., & Legge, G. E. (2001). Spatial-frequency and contrast properties of crowding. Vision Research, 41, 1833-1850.
+
+Clifford, C. W. G. (2002). Perceptual adaptation: Motion parallels orientation. Trends in Cognitive Sciences, 6(3), 136-143.
+
+Felisberti, F. M., Solomon, J. A., & Morgan, M. J. (2005). The role of target salience in crowding. Perception, 34(7), 823-833.
+
+Gheri, C., Morgan, M. J., & Solomon, J. A. (2007). The relationship between search efficiency and crowding. Perception, 36(12), 1779-1787.
+
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117(14), 8196-8202.
+
+Harrison, W. J., & Bex, P. J. (2015). A Unifying Model of Orientation Crowding in Peripheral Vision. Current Biology, 25(24), 3213-3219.
+
+He, D., Wang, Y., & Fang, F. (2019). The critical role of V2 population receptive fields in visual orientation crowding. Current Biology, 29(13), 2229-2236.e2223.
+
+Kool, F. L., Toet, A., Tripathy, S. P., & Levi, D. M. (1994). The effect of similarity and duration on spatial interaction in peripheral vision. Spatial Vision, 8(2), 255-279.
+
+Mareschal, I., Morgan, M. J., & Solomon, J. A. (2010). Cortical distance determines whether flankers cause crowding or the tilt illusion. Journal of Vision, 10(8):13, 1-14.
+
+Motter, B. C. (2009). Central V4 Receptive Fields Are Scaled by the V1 Cortical Magnification and Correspond to a Constant-Sized Sampling of the V1 Surface. Journal of Neuroscience, 29(18), 5749-5757.
+
+Motter, B. C., & Simoni, D. A. (2007). The roles of cortical image separation and size in active visual search performance. Journal of Vision, 7(2)(6), 1-15.
+
+Pelli, D. G., Palomares, M., & Majaj, N. J. (2004). Crowding is unlike ordinary masking: Distinguishing feature integration from detection. Journal of Vision, 4(12), 1136-1169.
+
+Rao, R. P. N., & Ballard, D. H. (1999). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience, 2(1), 79-87.
+
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19(7), 1-25.
+
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+
+van den Berg, R., Roerdink, J. B. T. M., & Cornelissen, F. W. (2010). A Neurophysiologically Plausible Population Code Model for Feature Integration Explains Visual Crowding. PLoS Computational Biology, 6(1), e1000646.
+
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14(9), 2057-2068.
+
+Reviewer #3 (Remarks to the Author):
+
+Cicchini and colleagues put forward the hypothesis that crowding is results from Bayes-optimal integration of visual targets with spatial context. The authors identify four features of their empirical data that are consistent with Bayes-optimal integration: (1) Crowding is strongest for reliable flankers and unreliable targets, (2) Crowding depends on flanker-target similarity (here orientation), (3) precision of orientation judgments increases with increasing flanker-target similarity, and (4) Crowding depends on similarity of targets to average flanker orientation, not individual flanker orientations. The authors present two ideal observer models (a Bayesian ideal observer, and a causal inference model), which can reproduce the above features of the empirical data.
+
+While I find the hypothesis that crowding results from optimal integration intriguing, I am somewhat reserved when it comes to the evidence provided in the current study. I am also not convinced that the behavioral benefits described here can be ascribed to crowding rather than ensemble perception. Please find my detailed points below.
+
+1. The ideal observer models only provide adequate fits when equipped with scaling parameters that account for "sub-optimal" behavior. The required scaling is not negligible, rescaling the optimal integration weights by ~40 to 50%. Therefore, it is not clear whether the observers' behavior is at all optimal, beyond resembling some qualitative features of the data. The authors could make a much stronger case when quantitatively accounting for the sub-optimal behavior. For instance, how strong would regression to the mean of orientation judgments need to be (put forward by the authors as an explanation of sub-optimality) in order to match this scaling? Is this consistent with the empirical data?
+Thanks for this important suggestion. We were trying to keep our models as simple as possible to be more accessible to the reader, but the calculation proposed is quite simple. Regression to the mean compresses the output by about 30%, which accounts for much of the underestimation. We now need a scaling factor of only 0.7 to fit the data. The main features of the models is that the same models that fit well serial dependence capture the DoG pattern of results (to a scaling factor), but we agree it is more impressive when the scaling factor is close to unity.
+
+2. Related to point 1, it is not clear in how far the empirical features are exclusively accounted for by Bayes-optimal integration versus other forms of (non-optimal) integration. As the authors note in their discussion feature 1 (orientation uncertainty) could be captured by obligatory integration models. Feature 2 (flanker-target similarity) could be explained by interference between similarly tuned, and therefore more strongly interconnected neural populations. For feature 4 (global vs local context), it seems that one could develop an alternative optimal observer that integrates local instead of global context. That is, I do not understand which optimality consideration would strictly dictate global versus local integration.
+I believe most of these concerns of whether the behavioral features really arise from optimal integration could be mitigated by improving point 1 above, i.e. providing a more detailed quantitative explanation of behavior, rather than absorbing a considerable mismatch between predictions and data into one or two unexplained “sub-optimality” parameters.
+
+We trust that the improved absolute fit goes some way towards addressing the referee’s concerns. We do of course accept that mechanisms of the type suggested could be involved, such as interconnections between similarly tuned neural populations (which we now mention, pointing out they are not consistent with the second experiment). However, we believe that our models put considerable constraints on how these mechanisms act. We also believe that it is constructive to relate crowding to serial dependence, which is currently being studied intensely, prompting cross-fertilization of ideas and discussions between the two important fields of research.
+
+3. It is not clear whether the behavioral benefits examined in this experiment are due to crowding or ensemble perception. While these appear to be at least partially distinct phenomena, they can co-occur (“Reexamining the possible benefits of visual crowding: dissociating crowding from ensemble percepts” Bulakowski et al., 2011). Cicchini et al. test the influence of target-distractor distance, and demonstrate that bias depends on distance, as expected for a crowding effect. However, I would contest that increasing flanker-target distance also alters the ensemble, and can therefore also impact ensemble perception. Perhaps one way to address this issue would be to test whether or not similar integration effects occur for more foveally presented stimuli, i.e. in the absence of crowding (albeit under matched conditions of visual uncertainty). If they do, the current observations would perhaps be better explained as resulting from ensemble perception, while crowding merely co-occurs in the current setup.
+
+Thanks for pointing us to this interesting paper, of which we were unaware. It is interesting that ensemble perception and crowding follow partially different rules, opening the way for interesting experiments. In our experiment we only measured crowding (judging orientation of a single target, rather than the average). It would certainly be interesting to do the converse (ensemble judgements) to see if the two phenomena followed similar rules. If they do not, it would be further proof that the two are at least partially different phenomena. This is of course a large new study (which the second author may pursue for his PhD), but we do now mention ensemble perception, and cite the important study mentioned. Thank you
+
+Minor comments:
+
+Figure 5B. Minimum scatter appears to occur at 0 deg, while the ideal observer models predict the minimum to occur at 15 degrees. I am curious whether the authors have any explanation/speculation of why the bias and variance data diverge in this aspect.
+
+Indeed, the prediction was off. However, we had previous calculated variance of the aggregate participant together, so different individual biases added artificially to the variance. We now remove the individual biases from the calculation of scatter (essentially calculating variance separately for each participant and averaging), and the result is far closer to the predicted 15° (see new figure 5B). We explain this procedure in the methods.
+
+In their introduction the authors state “Crowding impacts on many important daily tasks, such as face recognition and reading […]” I would be curious how the authors reconcile this view that crowding appears to negatively impact perception in real world scenarios (“daily tasks”) with their optimal integration theory.
+
+This is a very good point, thank you. Perhaps it goes a bit beyond the scope of this study, but we now add a paragraph discussing how optimizing for one aspect (minimal RMS Errors) may lead to sub-optimal behaviour of others (such as face recognition), as occurs in other forms of Bayesian optimization.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have thoroughly addressed all of the reviewer concerns, and the manuscript is acceptable for publication.
+
+Reviewer #2 (Remarks to the Author):
+
+As in the first submission, this is a fascinating manuscript, with novel findings that present a new perspective on the widely studied phenomenon of crowding. The revisions have done much to clarify the contributions of this work and the nature of the associated analyses. My major issue was previously with the findings regarding response scatter and their relation to prior work, which is now addressed to some extent in the revised manuscript. Many of the other issues have also been resolved. However, there remains one major issue in particular that has been completely ignored in the revisions, along with some minor issues. It is clear to me that this paper presents a novel and useful viewpoint to the literature, but it is especially important that these claims be supported by evidence. At the moment it is still not clear to me that this is the case.
+
+1. The lack of an unflanked baseline
+
+The major shortcoming with the revised manuscript is the lack of an unflanked performance baseline – the authors seek to measure crowding (recognition of a target when surrounded by flankers) but never measure performance in the absence of crowding (a target without flankers). This issue was raised in the first submission, to which the authors responded that it “would have been useful”, but this shortcoming was neither measured nor is its absence acknowledged in the revised manuscript. This absence leads to problematic assumptions about the data, a potentially problematic implementation within the models, and problematic statements about the nature of crowding.
+
+The authors assert at many points that “crowding improves overall performance” (p6), and that they observe “improved perceptual performance” (p16), “a reduction in response scatter [and] total RMS error” (p16), “to improve performance” (p17) and “improved performance” (p20). However, without the measurement of an unflanked baseline where crowding is absent (i.e. measurement of orientation perception for an isolated target without flankers), it is not clear what this improvement is relative to.
+
+In the absence of this measurement, the authors have assumed that the most extreme values of target-flanker difference that were tested correspond to the performance baseline. As noted in my first review, this is not at all clear. Prior studies have shown that the reduction in crowding with increased dissimilarity between target and flankers does not often return performance to the unflanked baseline. This can be seen for instance in the cited studies on orientation judgements (Wilkinson, Wilson, & Ellemberg, 1997; Solomon, Felisberti, & Morgan, 2004) – a target surrounded by orthogonal flankers is not recognized as well as a target presented on its own. In the data of Wilkinson et al, for instance, the threshold elevations (from unflanked) can remain as high as 2.5 times the unflanked baseline, even with dissimilar flanker elements. It is not possible to assume that crowding is absent so long as the flankers remain present, in other words.
+
+If the authors were able to demonstrate that the response scatter with similar flankers (near the middle of Figure 2b) is indeed better than unflanked performance, this would be a convincing demonstration that the presence of crowding improves performance relative to its absence (with a target in isolation). Otherwise, what we are looking at is an improvement in performance when crowding is strong vs. when it is reduced. A far more problematic outcome would be that that the unflanked baseline may in fact yield very low values of response scatter, which would correspond more closely to the values with similar flankers (near the middle). In this case, all of the performance
+with flankers would in fact be a decrement/impairment, rather than an improvement. In other words, the apparent benefits of crowding that are described here would simply be a case of the authors arbitrarily relabelling “up” as “down”. Without these measurements, we can never know. The question of optimality is never truly addressed until we do.
+
+This is not simply a quibble about stimulus details – it it is a key aspect of the measurements being performed here. Without these measurements, the way in which performance with these circumstances is unclear, as reflected in the lack of a meaningful performance comparison in the statements quoted above (i.e. is it that crowding improves performance relative to uncrowded performance, or simply that strong crowding is better than reduced crowding?).
+
+These assumptions regarding performance also carry through to the modelling. On p15 the authors use the extreme points of the dataset as a baseline to estimate optimal sensory reliability. This in turn carries through to key operations of the model (equation 12). If the unflanked reliability is in fact lower than this point, can crowding truly be said to be optimal? Precision (when calculated as in this study) is certainly better when crowded biases are strongest (with small target-flanker differences) compared to when they are reduced, but the authors cannot say whether this is optimal compared to the absence of crowding altogether.
+
+2. Assumptions in the model and optimality
+
+Much has been improved in the discussion of how these findings relate to prior reports of impaired performance in tasks like letter and face recognition (p19). It seems to me however that a key aspect of this discrepancy relates to the assumptions of the model. The text on p11 states that “ideal responses...can be expressed as a linear weighted combination of [the] target and flankers...”. But this is surely suboptimal when the task is to judge the orientation of the target and to ignore the flankers (as in prior studies on letter/face recognition etc). The updated description of the causal inference model makes this assumption more explicit where it is stated (p13) that “…an optimal blend [assumes] that the two curves originate from the same cause” (with a similar comment on p14). With this assumption in place, I could see how these interactions are optimal, and indeed given the structural regularities of the visual scene (that similar orientations, colors, etc are likely to be found together) this is perhaps a sensible assumption for the most part, as exploited by texture/statistical models of peripheral vision and crowding (Freeman & Simoncelli, 2011; Rosenholtz, Yu, & Keshvari, 2019). But it is problematic in tasks where the observer must recognize the target, ignoring the flankers. Although performance may then be optimal given this assumption, it is clearly not optimal given the task being required of observers in (most) crowding paradigms. In these cases, where the task is clearly very different (identify the target face amongst flankers, for instance), is there not therefore an over-application of this principle and thus a suboptimality? I suspect that this again relates back to the lack of an unflanked baseline in the authors’ measurements, and the missing perspective that arises from this.
+
+3. The findings regarding response scatter
+
+The pattern of results obtained with response scatter are much more clear now. However, the authors now describe the discrepancy between the current and previous studies as being due to their separate measurement of bias and precision (p18). The work of Solomon, Felisberti, and Morgan (2004) is cited in this context as ‘the only study to our knowledge’ to have similarly measured bias and precision. A range of other studies have used this approach however, some of which report patterns that do not quite fit with that observed here, to my eye. For instance, Glen and Dakin (2013) report sensitivity and biases for orientation crowding, while Greenwood and Parsons (2020) measured crowded biases and precision/thresholds for color and motion. The patterns there do not quite match those of the current study, with the least precision arising when flankers are most similar to the target, though it could indeed be the case that on the whole the combination of bias and precision leads to a pattern of response scatter similar to that of the current work.
+4. Relation to pooling models
+
+The discussion of the relationship to pooling models is much improved in the introduction and modelling sections. But there is still a statement in the discussion (p16) that the findings are ‘difficult to reconcile’ with pooling models. On the contrary, effects of target-flanker similarity are simulated by pooling models both in Greenwood and Parsons (2020) and in the context of texture pooling models (Rosenholtz, Yu, & Keshvari, 2019). Again, these approaches do not seem so dissimilar to that employed in the current study.
+
+5. Missing references
+
+At points the authors make reference to prior literature without citing the studies being referred to, particularly in the new additions to the manuscript. This occurs on p2 ("Crowding is stronger in the upper than the lower visual field, and for radial than for tangential flankers") and p16 ("the myriad of experiments showing that similarities in shape...cause maximum crowding"). It is particularly unclear to me what studies the latter refers to.
+
+6. Biases
+
+It would help the clarity of the manuscript to have the direction of biases explained somewhere, e.g. on p6 to explain that the errors in Figure 2 follow the orientation of the flankers, and that they presumably go in the opposite direction with some separations in Figure 3.
+
+References
+
+Freeman, J., & Simoncelli, E. P. (2011). Metamers of the ventral stream. Nature Neuroscience, 14, 1195-1201.
+Glen, J. C., & Dakin, S. C. (2013). Orientation-crowding within contours. Journal of Vision, 13, 1-11.
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117, 8196-8202.
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19, 1-25.
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14, 2057-2068.
+
+Reviewer #3 (Remarks to the Author):
+
+I am still not entirely sure whether Nature Communications is the best outlet, as the study puts forward an intriguing idea, but leaves open many questions that would require more data. However, I agree with the authors and fellow reviewers that this is an interesting research direction.
+
+I appreciate the authors’ attempt to minimize the scaling factor, by quantitatively accounting for known suboptimalities due to the oblique bias. I am still not entirely convinced that we are dealing with optimal integration, or whether part of the required scaling is due to suboptimal integration, which would limit the authors’ claim of crowding resulting from optimal integration. If not done in the current manuscript, this will be an important point for future studies.
+
+I realize that I have been somewhat unclear about my previous point about crowding vs ensemble
+perception. My main question was whether the spatial integration observed in the current experiments could perhaps be more general than just occurring for peripheral targets surrounded by flankers (i.e., the conditions under which crowding occurs). For instance, would a similar bias occur for very noisy *foveal* target stimuli surrounded by flankers, in the absence of crowding. That is, would observers generally rely on a weighted average of an ensemble, when visual information about the target is very poor. In the current experiments, crowding might increase the uncertainty/reliability of the target, which might prompt observers to integrate information of the spatial context. In this case, optimal integration would be the *consequence* of crowding, not the *cause* of crowding. If I understand the authors correctly, they claim that optimal integration is the cause of the crowding phenomenon. I would appreciate if the authors could clarify this point.
+
+I also concur Reviewer #2 that an unflanked baseline (or orthogonal flankers) would help to clarify whether maximally similar flankers indeed enhance performance (better than baseline), or whether they are least detrimental (equal or worse performance than baseline).
+Please find enclosed the response to the reviewers and the novel submission with all changes flagged in blue.
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have thoroughly addressed all of the reviewer concerns, and the manuscript is acceptable for publication.
+
+Reviewer #2 (Remarks to the Author):
+
+As in the first submission, this is a fascinating manuscript, with novel findings that present a new perspective on the widely studied phenomenon of crowding. The revisions have done much to clarify the contributions of this work and the nature of the associated analyses. My major issue was previously with the findings regarding response scatter and their relation to prior work, which is now addressed to some extent in the revised manuscript. Many of the other issues have also been resolved. However, there remains one major issue in particular that has been completely ignored in the revisions, along with some minor issues. It is clear to me that this paper presents a novel and useful viewpoint to the literature, but it is especially important that these claims be supported by evidence. At the moment it is still not clear to me that this is the case.
+
+1. The lack of an unflanked baseline
+
+The major shortcoming with the revised manuscript is the lack of an unflanked performance baseline – the authors seek to measure crowding (recognition of a target when surrounded by flankers) but never measure performance in the absence of crowding (a target without flankers). This issue was raised in the first submission, to which the authors responded that it “would have been useful”, but this shortcoming was neither measured nor is its absence acknowledged in the revised manuscript. This absence leads to problematic assumptions about the data, a potentially problematic implementation within the models, and problematic statements about the nature of crowding.
+
+We have now measured baselines for the rounded targets condition (the main one, that leads to the strongest effects). We also measure with orthogonal flankers. The results are shown in Figure 2 as hollow squares/diamonds. The two thresholds are similar to each other, and worse than all the other flanker conditions. We hope this is sufficient for publication now.
+
+The authors assert at many points that “crowding improves overall performance” (p6), and that they observe “improved perceptual performance” (p16), “a reduction in response scatter [and] total RMS error” (p16), “to improve performance” (p17) and “improved performance” (p20). However, without the measurement of an unflanked baseline where crowding is absent (i.e. measurement of
+orientation perception for an isolated target without flankers), it is not clear what this improvement is relative to.
+
+In the absence of this measurement, the authors have assumed that the most extreme values of target-flanker difference that were tested correspond to the performance baseline. As noted in my first review, this is not at all clear. Prior studies have shown that the reduction in crowding with increased dissimilarity between target and flankers does not often return performance to the unflanked baseline. This can be seen for instance in the cited studies on orientation judgements (Wilkinson, Wilson, & Ellemburg, 1997; Solomon, Felisberti, & Morgan, 2004) – a target surrounded by orthogonal flankers is not recognized as well as a target presented on its own. In the data of Wilkinson et al, for instance, the threshold elevations (from unflanked) can remain as high as 2.5 times the unflanked baseline, even with dissimilar flanker elements. It is not possible to assume that crowding is absent so long as the flankers remain present, in other words.
+
+If the authors were able to demonstrate that the response scatter with similar flankers (near the middle of Figure 2b) is indeed better than unflanked performance, this would be a convincing demonstration that the presence of crowding improves performance relative to its absence (with a target in isolation). Otherwise, what we are looking at is an improvement in performance when crowding is strong vs. when it is reduced. A far more problematic outcome would be that that the unflanked baseline may in fact yield very low values of response scatter, which would correspond more closely to the values with similar flankers (near the middle). In this case, all of the performance with flankers would in fact be a decrement/impairment, rather than an improvement. In other words, the apparent benefits of crowding that are described here would simply be a case of the authors arbitrarily relabelling “up��� as “down”. Without these measurements, we can never know. The question of optimality is never truly addressed until we do.
+
+This is not simply a quibble about stimulus details – it it is a key aspect of the measurements being performed here. Without these measurements, the way in which performance with these circumstances is unclear, as reflected in the lack of a meaningful performance comparison in the statements quoted above (i.e. is it that crowding improves performance relative to uncrowded performance, or simply that strong crowding is better than reduced crowding?).
+
+These assumptions regarding performance also carry through to the modelling. On p15 the authors use the extreme points of the dataset as a baseline to estimate optimal sensory reliability. This in turn carries through to key operations of the model (equation 12). If the unflanked reliability is in fact lower than this point, can crowding truly be said to be optimal? Precision (when calculated as in this study) is certainly better when crowded biases are strongest (with small target-flanker differences) compared to when they are reduced, but the authors cannot say whether this is optimal compared to the absence of crowding altogether.
+
+We accept your arguments, thank you, and have added the baseline to the main condition. We agree that this strengthens the manuscript.
+2. Assumptions in the model and optimality
+
+Much has been improved in the discussion of how these findings relate to prior reports of impaired performance in tasks like letter and face recognition (p19). It seems to me however that a key aspect of this discrepancy relates to the assumptions of the model. The text on p11 states that “ideal responses...can be expressed as a linear weighted combination of [the] target and flankers...”. But this is surely suboptimal when the task is to judge the orientation of the target and to ignore the flankers (as in prior studies on letter/face recognition etc). The updated description of the causal inference model makes this assumption more explicit where it is stated (p13) that “…an optimal blend [assumes] that the two curves originate from the same cause” (with a similar comment on p14). With this assumption in place, I could see how these interactions are optimal, and indeed given the structural regularities of the visual scene (that similar orientations, colors, etc are likely to be found together) this is perhaps a sensible assumption for the most part, as exploited by texture/statistical models of peripheral vision and crowding (Freeman & Simoncelli, 2011; Rosenholtz, Yu, & Keshvari, 2019). But it is problematic in tasks where the observer must recognize the target, ignoring the flankers. Although performance may then be optimal given this assumption, it is clearly not optimal given the task being required of observers in (most) crowding paradigms. In these cases, where the task is clearly very different (identify the target face amongst flankers, for instance), is there not therefore an over-application of this principle and thus a suboptimality? I suspect that this again relates back to the lack of an unflanked baseline in the authors’ measurements, and the missing perspective that arises from this.
+
+We now stress that optimization of basic features while optimal strictly speaking, may still impact negatively in higher recognition processes. Indeed it is not uncommon that optimal processes lead to illusions such as the ventriloquist effect and the hollow face illusion
+
+3. The findings regarding response scatter
+
+The pattern of results obtained with response scatter are much more clear now. However, the authors now describe the discrepancy between the current and previous studies as being due to their separate measurement of bias and precision (p18). The work of Solomon, Felisberti, and Morgan (2004) is cited in this context as ‘the only study to our knowledge’ to have similarly measured bias and precision. A range of other studies have used this approach however, some of which report patterns that do not quite fit with that observed here, to my eye. For instance, Glen and Dakin (2013) report sensitivity and biases for orientation crowding, while Greenwood and Parsons (2020) measured crowded biases and precision/thresholds for color and motion. The patterns there do not quite match those of the current study, with the least precision arising when flankers are most similar to the target, though it could indeed be the case that on the whole the combination of bias and precision leads to a pattern of response scatter similar to that of the current work.
+
+Thank you, we were not aware of these studies. We now reference them and point out the differences in results (possibly due to differences in the experimental techniques). But we also take the opportunity to add a penultimate paragraph mentioning that our results may not generalize
+beyond orientation, encouraging experiments along these lines for other features such as motion and color. Thank you for prompting this caveat.
+
+4. Relation to pooling models
+
+The discussion of the relationship to pooling models is much improved in the introduction and modelling sections. But there is still a statement in the discussion (p16) that the findings are ‘difficult to reconcile’ with pooling models. On the contrary, effects of target-flanker similarity are simulated by pooling models both in Greenwood and Parsons (2020) and in the context of texture pooling models (Rosenholtz, Yu, & Keshvari, 2019). Again, these approaches do not seem so dissimilar to that employed in the current study.
+
+Thank you. We have toned down our claims of novelty, but do still want to stress the major difference, of flexible pooling.
+
+5. Missing references
+
+At points the authors make reference to prior literature without citing the studies being referred to, particularly in the new additions to the manuscript. This occurs on p2 (“Crowding is stronger in the upper than the lower visual field, and for radial than for tangential flankers”) and p16 (“the myriad of experiments showing that similarities in shape...cause maximum crowding”). It is particularly unclear to me what studies the latter refers to.
+
+Thank you we now added relevant references
+
+6. Biases
+
+It would help the clarity of the manuscript to have the direction of biases explained somewhere, e.g. on p6 to explain that the errors in Figure 2 follow the orientation of the flankers, and that they presumably go in the opposite direction with some separations in Figure 3.
+
+Thank you we now do.
+
+References
+
+Freeman, J., & Simoncelli, E. P. (2011). Metamers of the ventral stream. Nature Neuroscience, 14, 1195-1201.
+
+Glen, J. C., & Dakin, S. C. (2013). Orientation-crowding within contours. Journal of Vision, 13, 1-11.
+Greenwood, J. A., & Parsons, M. J. (2020). Dissociable effects of visual crowding on the perception of color and motion. Proceedings of the National Academy of Sciences of the United States of America, 117, 8196-8202.
+
+Rosenholtz, R., Yu, D., & Keshvari, S. (2019). Challenges to pooling models of crowding: Implications for visual mechanisms. Journal of Vision, 19, 1-25.
+
+Solomon, J. A., Felisberti, F. M., & Morgan, M. J. (2004). Crowding and the tilt illusion: Toward a unified account. Journal of Vision, 4, 500-508.
+
+Wilkinson, F., Wilson, H. R., & Ellemberg, D. (1997). Lateral interactions in peripherally viewed texture arrays. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 14, 2057-2068.
+
+Reviewer #3 (Remarks to the Author):
+
+I am still not entirely sure whether Nature Communications is the best outlet, as the study puts forward an intriguing idea, but leaves open many questions that would require more data. However, I agree with the authors and fellow reviewers that this is an interesting research direction.
+
+I appreciate the authors’ attempt to minimize the scaling factor, by quantitatively accounting for known suboptimalities due to the oblique bias. I am still not entirely convinced that we are dealing with optimal integration, or whether part of the required scaling is due to suboptimal integration, which would limit the authors’ claim of crowding resulting from optimal integration. If not done in the current manuscript, this will be an important point for future studies.
+
+I realize that I have been somewhat unclear about my previous point about crowding vs ensemble perception. My main question was whether the spatial integration observed in the current experiments could perhaps be more general than just occurring for peripheral targets surrounded by flankers (i.e., the conditions under which crowding occurs). For instance, would a similar bias occur for very noisy foveal target stimuli surrounded by flankers, in the absence of crowding. That is, would observers generally rely on a weighted average of an ensemble, when visual information about the target is very poor. In the current experiments, crowding might increase the uncertainty/reliability of the target, which might prompt observers to integrate information of the spatial context. In this case, optimal integration would be the consequence of crowding, not the cause of crowding. If I understand the authors correctly, they claim that optimal integration is the cause of the crowding phenomenon. I would appreciate if the authors could clarify this point.
+
+We thank the referee for making their point more clear. It is certainly a good point, which we are not able to address at this stage (other than showing in Figure 3 that the assimilative effects disappear at large separations). We do now mention that this is an open question meriting further research (in the penultimate paragraph).
+I also concur Reviewer #2 that an unflanked baseline (or orthogonal flankers) would help to clarify whether maximally similar flankers indeed enhance performance (better than baseline), or whether they are least detrimental (equal or worse performance than baseline).
+
+We too were convinced, and did the extra measurements (open symbols in Figure 2).
+REVIEWERS’ COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have responded comprehensively to issues raised in the previous rounds of submission, and my major issues with the manuscript are resolved. The new baseline measurements (with an additional condition including orthogonally-oriented flankers) are a convincing addition, providing a clear reference for the arguments that crowding can improve the precision of the shape judgements measured by the authors.
+
+As I have said in earlier rounds, this is a fascinating manuscript whose findings present a new perspective on a widely studied phenomenon. I do not agree with everything that is said, but the authors have sufficiently qualified their statements to the extent that the ideas are fully available for the reader to decide. I am sure this will inspire a great deal of future research.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have addressed the remaining issues. I have no further comments.

022065845b0149dd1bde836e14da3448f70c4603767a53533c6448baf134c8c3/preprint/preprint.md

@@ -0,0 +1,319 @@
+Crowding results from optimal integration of visual targets with contextual information
+
+Guido Marco Cicchini
+Consiglio Nazionale delle Ricerche   https://orcid.org/0000-0002-3303-0420
+
+Giovanni D'Errico
+CNR Neuroscience Institute   https://orcid.org/0000-0002-0491-581X
+
+David Burr (dave@in.cnr.it)
+University of Florence   https://orcid.org/0000-0003-1541-8832
+
+Article
+
+Keywords:
+
+Posted Date: March 1st, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-1296243/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on September 30th, 2022. See the published version at https://doi.org/10.1038/s41467-022-33508-1.
+Crowding results from optimal integration of visual targets with contextual information
+
+Guido Marco Cicchini¹, Giovanni D’Errico¹ and David C. Burr¹,²
+
+1. Institute of Neuroscience, CNR, via Moruzzi, 1 , 56124 – Pisa (ITALY)
+2. Department of Neurosciences, Psychology, Drug Research and Child Health, University of Florence, viale Pieraccini, 6 – 50139 Firenze (ITALY)
+
+ABSTRACT
+
+Crowding is the inability to recognize peripheral objects in clutter, usually considered a fundamental low-level bottleneck to object recognition. Here we advance and test an alternative hypothesis, that crowding, like “serial dependence”, results from optimizing strategies that exploit redundancies in natural scenes. This notion leads to several testable predictions: (1) crowding should be greatest for unreliable targets and reliable flankers; (2) crowding-induced biases should be maximal when target and flankers have similar orientations, falling off for differences around 20°; (3) flanker interference should be associated with higher precision in orientation judgements, leading to lower overall error rate; (4) effects should be maximal when the orientation of the target is near that of the average of the flankers, rather than to that of individual flankers. All these effects were verified, and well simulated with ideal-observer models that maximize performance. The results suggest that while crowding can impact strongly on object recognition, it is best understood not as a processing bottleneck, but as a consequence of efficient exploitation of the spatial redundancies of the natural world.
+INTRODUCTION
+
+Crowding is the inability to recognize and identify objects in clutter, despite their being clearly visible, and recognizable when presented in isolation¹ (see examples in Figure 1A). It is particularly elevated in the periphery, scaling linearly with eccentricity, such that the minimal spacing between targets and flanking elements for uncrowded vision is equal to about half the eccentricity (Bouma’s law² ). Crowding impacts on many important daily tasks, such as face recognition and reading (for reviews see³,⁴,⁵ ), to the extent it has been considered a major bottleneck to object recognition.
+
+Most popular current models of crowding involve some form of compulsory pooling (or substitution) of targets with flankers. For example, Parkes and colleagues⁶ showed that while the orientation of a single line cannot be determined when embedded in flankers, it does influence the perceived orientation of the ensemble: hence it is merged with the flankers, rather than suppressed. This is reinforced by several studies showing that the targets can take on characteristics of the flanker stimuli⁷-⁹. Pelli and Tillmann³ suggest that the compulsory integration occurs in higher cortical areas, such as V4, which have large receptive fields, appropriately sized to account for Bouma’s law (see also ¹⁰).
+
+However, compulsory integration does not explain all the known facts about crowding. For example, flankers that are similar in size, colour or orientation cause more crowding than dissimilar ones¹¹-¹³. More difficult to explain are the recent demonstrations of Herzog and colleagues¹⁴ of “uncrowding”, where the addition of extra flanking stimuli around the flankers can reduce drastically their crowding effect, particularly if the extra flankers group with the original flankers to form coherent objects. These data do not fit easily with compulsory integration, even with appropriate linear filtering, which could in principle account for other effects, such as orientation or size selectivity.
+
+Crowding has been studied for decades, and usually considered to be a defect in the system, “an essential bottleneck to object perception”¹⁵. Certainly, it impacts heavily on object recognition in tasks like or face recognition: but is it possible that it may reflect processes that are in principle advantageous to perception? Perception is strongly affected by contextual information, particularly temporal context, where recent and longer term perceptual history has been shown to exert a major influence on current perception¹⁶-¹⁹. While the role of context and experience has been appreciated for some time²⁰,²¹, it has
+become particularly topical in recent years within the framework of Bayesian analysis. This approach has revealed an interesting phenomenon termed “serial dependence”, where the appearance of many important attributes of a stimulus (including orientation, numerosity, facial identity, beauty etc) are biased towards previously viewed stimuli\(^{17,18,22,23}\). Counterintuitively, these consistent biases in perception have been shown to reflect an efficient perceptual strategy, exploiting temporal redundancies in natural viewing to reduce overall reproduction errors, despite the biases\(^{24,17,25}\).
+
+Could crowding also be a consequence of efficient integration processes that exploit spatial (rather than temporal) redundancies to improve performance? We investigate this possibility by studying crowding with a similar paradigm used for serial dependence studies. If, like serial dependence, crowding is a by-product of efficient redundancy-reducing mechanisms, it should display several specific signature characteristics. One is that crowding-induced biases should be stronger for targets that are unreliably perceived, and for flankers that are reliably perceived. In addition, crowding should follow the signature pattern seen in serial dependence, highest when the orientations of target and flankers are similar, then steadily falling off. We verify these characteristics qualitatively and qualitatively, and show that crowding, while leading to biases, also improves overall performance. The results fit well with models simulating intelligent combination of signals from a small receptive field centred on the target with signals from a much larger integration region, following the same rules that govern serial dependence. On this view crowding should not be considered a defect, or bottleneck, in the system, but the unavoidable consequence of efficient exploitation of spatial redundancies of the natural world.
+Figure 1
+a) Crowding is a visual phenomenon where items that can be easily identified in isolation are not identifiable if surrounded by similar items. The P and hand symbol on the right are difficult to recognize, while fixating the central red dots.
+b) Stimuli employed in this experiment. Observers judged the orientation of a peripheral target (the central oval), which was flanked above and below by oval stimuli. Two conditions were tested: a rounded target with elongated flankers (Low reliability target, high reliability flankers, at left) or an elongated target with rounded ovals (at right). In the main condition the centre-to-centre distance of flankers and targets was 5.5 deg, and eccentricity 26 degrees, leading to a Bouma ratio of 0.21.
+
+RESULTS
+
+To test if visual crowding follows the rules of optimal integration, which well describe serial dependence^{18,25}, we measured crowding with an orientation reproduction task. Participants reproduced the orientation of oval stimuli, which were either elongated (aspect ratio 1: 2.8) or rounded (aspect 1: 1.4). Targets were presented 26° to the right of fixation, and vertically flanked by similar oval stimuli, elongated if the target was rounded, and vice versa (see Fig. 1B). The orientation of the target was either 35° or 55° (at random). The orientations of the two flankers were yoked together, and varied randomly over a range of ±45° from target orientation. The clear prediction from the efficient integration model^{24} (see Eqn 10) is that the effects of crowding will be far stronger for the rounded targets and elongated flankers than vice versa. The reasons are explained formally the modelling section, but the intuition is that the rounded stimuli have less reliable orientation signals and therefore benefit more from integration with contextual information, especially if it is reliable.
+
+Figure 2A shows the bias in target reproduction as a function of difference in flanker orientation. Clearly, the rounded targets show the strongest contextual effects of crowding,
+with peak biases varying by up to ±5.1°, compared with ±1.9° for the elongated targets. Furthermore, the pattern of bias follows closely that predicted and observed in serial dependence studies25, varying non-linearly with difference between target and flanker orientation, increasing to a maximum around ±20°, then decreasing. These data are well fit by derivative of gaussian functions (eqn. 15, light-coloured lines), commonly used in serial dependence studies18, and expected from a causal inference model (see modelling section26). The dark lines show the predictions of another Bayesian model (eqn. 10), which has also proven successful with serial dependence data17,25. While the models are detailed later, it is worth noting that they are almost entirely anchored by data, down to a simple scaling factor, suggesting that the data are consistent with ideal behaviour.
+
+![Three panels showing bias and scatter plots for flanker orientation effects](page_340_682_1067_312.png)
+
+Figure 2
+a) Average response bias (response minus target orientation) as a function of the orientation of two identical flankers. Low reliability (rounded) targets in blue, high reliability (elongated) in red. Error bars show ±1 SEM. Dark lines show predictions from an ideal-observer Bayesian model which scales the action of flankers according to their reliability and orientation difference (Eqn 10 of model section). Light blue and red curves show predictions for the causal inference model that doses flanker and target information according to their reliability and the probability of originating from a common cause (Eqn 15 of model section).
+b) Response scatter as a function of the orientation of two identical flankers, together with model predictions. Colour coding as in A.
+c) Response Scatter error plotted against bias errors for the two conditions. Dashed circles indicate regions with identical RMSE error (given by the Pythagorean sum of the two types of error). RMSE varies with orientation, and is least around 0°, when target and flankers coincide.
+
+Another important prediction is that the contextual effects should improve performance. Figure 2B plots reproduction scatter (root-variance of reproduction trials) as a function of orientation difference. As expected, at all orientation differences, these are lower for the elongated than the rounded targets. However, for both targets, particularly the rounded
+targets, the scatter decreased as the difference between target and flanker orientation decreased. Figure 2C plots scatter against bias, with points connected to follow the change in orientation. On this plot, total error (the Pythagorean sum of scatter and bias) is the radial distance from the origin. For the points with flanker orientation most distant from the target (near ±45°), the total error is around 15°. Between these extremes, total error falls off, despite the constant bias. When the flankers and targets have similar orientations, the error falls to around 11°, evidence that “crowding” improves overall performance.
+
+If the effects shown in Figure 2 represent visual crowding, they should depend on critical spacing between target and flankers, and follow Bouma’s law¹. We therefore measured the effects as a function of target-flanker spacing, for 5 participants. Figure 3 shows the data for the rounded targets with elongated flankers (which show the strongest effects). For the two smallest spacings (5.5 and 7.5 deg), bias showed the characteristic S-shaped dependency on the orientation of the flankers. For the larger spacings (11.0 and 16.6 deg), however, the effect was much reduced and even inverted at 11 deg. As before, the curves are fit by a derivative of gaussian function (eqn 18), which is the product of a linear regression (illustrated by dashed line in Figure 3A) and a gaussian. The best fitting slope of this regression is an estimate of the weight given to the flankers when judging orientation. Figure 3B plots the fitted weight as a function of target-flanker spacing (lower abscissa), with the upper abscissa showing the Bouma constant, the distance between target and flanker centres divided by the eccentricity (26 deg). The weight drops from 0.5 to 0 for Bouma constants between 0.3 and 0.4, broadly in line with the literature, suggesting that the effects observed here relate to crowding.
+Figure 3
+a) Response bias as function of flanker orientation for various target-flanker distances leading to four different Bouma ratios (distance between flanker and target centres divided by eccentricity. Data are fit with a derivative of gaussian function with free parameters (Eqn 18).
+b) Weight of the flankers (maximal slope of the curves in panel A) as a function of the Bouma ratio (colour-code as before). Error bars show ±1 SEM.
+
+The results so far show that integration is not obligatory, but depends on the reliability of both target and flankers, and on their orientation similarity. A remaining question is how the flankers integrate with the target: each separately, or after combination with each other. Figure 4 illustrates two possibilities (see also modelling section). One is feedforward model where the target integrates independently with low-level, high-resolution neural representations of each of the flankers. The other depicts integration with a broader representation including both flankers, potentially implemented through recurrent feedback.
+Figure 4
+a) Rationale of Experiment 2. Flankers could either act independently on the target (as illustrated by purple arrows in top left panel), or first pooled into a larger RF, which in turn biases the target (illustrated by the large yellow circle and arrow in bottom left panel).
+b) Predictions for the two hypotheses. If the flankers act independently, when one flanker is locked at +15° and the other free to vary, the pattern should be similar to that of the main experiment (centre close to 0°), but raised because of the action of the locked flanker (purple curve). If flankers are first integrated at a more global stage, maximal effect is expected when all the elements in the larger operator average 0°. Since one of the flankers is locked at +15°, this occurs when the other flanker is −15°, leading to a leftward shift of the curve of the main experiment (yellow curve)
+
+To distinguish between these two plausible possibilities, we measured target bias with the orientation of the two flankers varying independently. Specifically, one flanker (randomly top or bottom) was always oriented +15° from the target, while the other varied randomly over the range. The logic is that the gaussian function windowing the contextual effect should be centred where the orientations of target and context coincide. If the integration occurs directly between the target and individual flankers, then the maximum effects should occur when the variable flanker coincides with the target; on the other hand, if the integration is with a broader representation including both flankers, maximum integration should occur when the flanker mean is zero, which occurs when the variable flanker is −15°. These predictions are illustrated in Figure 4B: note that the individual flanker effect also predicts the curve to be higher at all flanker orientations, as the fixed flanker will exert a constant effect at all orientations of the variable flanker.
+
+![Diagram showing flanker action types and corresponding bias curves](page_186_120_1077_495.png)
+The results for the rounded targets with elongated flankers are shown figure 5A. The biases clearly follow the signature pattern, well fit by a derivative of gaussian function. The centre of the function is −12.1°, closer to the 15° predicted by integration with the average orientation of the flankers, than 0° predicted by the individual flanker model. The mean height of the function is 0.5°, close to that observed in the previous experiment (−0.9°), while the individual-flanker integration model predicts a constant average bias 4.7°. Figure 5B shows the scatter for this experiment, which was reduced over the region of bias, well described by an inverted Gaussian.
+
+![Three panels showing bias, response scatter, and histogram data for flanker orientation and center of DoG](page_362_682_1047_312.png)
+
+Figure 5.
+a) Biasing errors as function of a single flanker orientation, while the other flanker was locked at +15°. Colours and conventions as for Figure 2. Thick dark lines refer to the ideal observer model (Eqn 10), thick light blue lines to the causal inference model (Eqn 15). Thin dashed lines show best-fitting derivative of gaussian, with all parameters free to vary (Eqn 18).
+b) Response Scatter as a function of the variable flanker orientation. Conventions as in panel a.
+c) Histogram of the centres of the gaussian derivative for 1000 bootstrap fits.
+
+To test significance, we bootstrapped the data 1000 times (sampling with replacement) and measured the centre of the gaussian derivative on each iteration. The results plotted in the histogram of Figure 5C show that on only 16 out of 1000 iterations (1.6%) was the centre closer to 0° (individual flanker prediction) than to −15° (joint-flanker prediction). This leads to a likelihood ratio (Bayes factor) of 984/16 = 61.5, strong evidence in favour of the joint-flanker-integration model.
+MODELLING
+
+We propose two plausible models to explain the pattern of data. Both are motivated by principles of “optimal cue integration” commonly used in multi-sensory perception\(^{27,28}\), which predict optimal combination of information from multiple sources after appropriate weighting to minimize overall root-mean-square error. The first is based on an ideal-observer model successfully used to model serial dependence\(^{17}\), the second on a “causal-inference” model of multi-sensory integration\(^{26}\). Both models predict well the data.
+
+Ideal Observer
+
+Total RMS error (\(E\)) can be decomposed into bias (\(B\)) and precision (scatter standard deviation: \(S\)), whose squares sum to give total squared error:
+
+\[
+E = \sqrt{B^2 + S^2}
+\] [eq. 1]
+
+The ideal responses (\(R\)) in a pooling model can be expressed as a linear weighted combination of internal representation of target (\(T\)) and flankers (\(F_1\) and \(F_2\)), each weighted by \(w_1\) and \(w_2\).
+
+\[
+R = w_1 F_1 + w_2 F_2 + (1 - w_1 - w_2) T
+\] [eq. 2]
+
+As the two flankers of this study had the same aspect ratio they should be weighted equally, (\(w_1 = w_2 = w\)), so Eqn. 2 simplifies to:
+
+\[
+R = w F_1 + w F_2 + (1 - 2w) T
+\] [eq. 3]
+
+The mean of the responses (\(\mu_R\)) is a simple linear combination of the means of flankers and target (\(\mu_1, \mu_2\) and \(\mu_T\)).
+
+\[
+\mu_R = w \mu_1 + w \mu_2 + (1 - 2w) \mu_T = w(\mu_1 + \mu_2) + (1 - 2w) \mu_T
+\] [eq. 4]
+
+Bias is the difference between the mean estimated response (\(\mu_R\)) and real orientation, \(x_T\); \(B = \mu_R - x_T\). Using equation 4 and considering that the average target representation (\(\mu_T\)) should be unbiased and coincide with target (\(\mu_T = x_T\)) it follows that:
+
+\[
+B = \mu_R - x_T = w(\mu_1 + \mu_2) + \mu_T - 2w \mu_T - x_T = w(\mu_1 + \mu_2 - 2 \mu_T)
+\] [eq. 5]
+The term \( \mu_1 + \mu_2 - 2\mu_T \) can be rearranged as \( 2((\mu_1 + \mu_2)/2 - \mu_T) \) which is twice the distance between the average of the flanker representations, \((\mu_1 + \mu_2)/2\), and the target representation \( \mu_T \). For convenience we define:
+
+\[
+d = (\mu_1 + \mu_2)/2 - \mu_T \tag{eq. 6}
+\]
+
+so that Eqn. 5 becomes:
+
+\[
+B = w(\mu_1 + \mu_2 - 2\mu_T) = 2wd \tag{eq. 7}
+\]
+
+Variance of the linear combination of the flankers and target is itself a linear combination of the flanker and target variances (\( \sigma_F^2 \) and \( \sigma_T^2 \)) with the squared coefficients
+
+\[
+S^2 = w^2 \sigma_F^2 + w^2 \sigma_F^2 + (1-2w)^2 \sigma_T^2 \tag{eq. 8}
+\]
+
+From Eqn 1, 7 and 8 it follows that \( RMSE \) can be written as:
+
+\[
+E = 4w^2 d^2 + w^2 \sigma_F^2 + w^2 \sigma_F^2 + (1-2w)^2 \sigma_T^2 \\
+= 4w^2 d^2 + w^2 \sigma_F^2 + w^2 \sigma_F^2 + (1-4w+4w^2)\sigma_T^2 \tag{eq. 9}
+\]
+
+Since RMSE is a function of second order of \( w \), it is minimized when \( w = \frac{-b}{2a} \), so the optimal weight (\( w_{opt} \)) is obtained at:
+
+\[
+w_{opt} = -\frac{1}{2} \frac{-4\sigma_T^2}{4\sigma_T^2 + 2\sigma_F^2 + 4d^2} = \frac{\sigma_T^2}{2\sigma_T^2 + \sigma_F^2 + 2d^2} \tag{eq. 10}
+\]
+
+This equation has much in common with that of all Bayesian-like integrations used in multi-sensory research and serial dependence: the weight depends directly on *target* variance \( \sigma_T^2 \), so *targets* of low reliability (inverse variance) benefit more from integration, resulting in higher weighting to the *flankers*. Increase in flanker variance (\( \sigma_F^2 \)) has the opposite effect.
+
+The term \( 2d^2 \) is fundamental for the signature function, as the weight of the *flankers* will decrease with angular difference between target and average flanker orientation. This is reminiscent of serial dependence effects, and ensures that contextual cues are used only if they are plausibly similar to the target\(^{24,17,25}\). Importantly, the point that will ensure maximal weight of the flankers is when the target coincides with the average of the flankers (i.e. \( d^2 = 0 \)).
+Together the behaviour of Eqns 3 and 10 define the ideal observer behaviour. In order to accommodate suboptimal behaviour we introduce a scaling factor (\( \alpha \)) which multiplies \( w_{opt} \) and sets the actual weight of the flankers:
+
+\[
+R = \alpha w_{opt} F_1 + \alpha w_{opt} F_2 + (1 - 2\alpha w_{opt}) T
+\]
+
+[eq. 11]
+
+**Causal Inference Model**
+
+An alternative model prescribes that the optimal blend of information can be obtained behaving as if the sources of information originated form one cause times the probability that two sources of information originate from the same cause\(^{26}\). Within this framework the maximal interaction between cues occurs when the two sources coincide, where the weight assigned of is the well known result known in sensory integration literature\(^{27,28}\) (see also eq. 10):
+
+\[
+w_A^{max} = \frac{\sigma_B^2}{\sigma_A^2 + \sigma_B^2}
+\]
+
+[eq. 12]
+
+The probability of the two sources originating from a common cause can be calculated using Bayes’ Theorem as demonstrated in\(^{26}\). Assuming gaussian probability distribution functions (with centres at \( \mu_A \) and \( \mu_B \) and variances \( \sigma_A^2 \) and \( \sigma_B^2 \)), the solution is soluable analytically\(^{26}\):
+
+\[
+p(A,B|C=1) \propto \exp \left( -\frac{1}{2} \frac{(\mu_A-\mu_B)^2 \sigma_P^2 + (\mu_A-\mu_P)^2 \sigma_A^2 + (\mu_B-\mu_P)^2 \sigma_B^2}{\sigma_A^2 \sigma_B^2 + \sigma_A^2 \sigma_P^2 + \sigma_B^2 \sigma_P^2} \right)
+\]
+
+[eq. 13]
+
+This is function of the variances of the two sources (\( \sigma_A^2 \) and \( \sigma_B^2 \)), the centres of the representations (\( \mu_A \) and \( \mu_B \)) and their distance, and the a-prior likelihood of there being one cause (itself gaussian and characterized by mean and variance \( \mu_P \) and \( \sigma_P^2 \)). If no prior knowledge is available (\( \sigma_P^2 \to \infty \)) Eqn 13 simplifies to
+
+\[
+p(A,B|C=1) \propto \exp \left( -\frac{1}{2} \frac{(\mu_A-\mu_B)^2}{\sigma_A^2 + \sigma_B^2} \right)
+\]
+
+[eq. 14]
+
+This is a gaussian peaking when the distribution of the two cues coincide (\( \mu_A = \mu_B \)) and falling off with a space constant related to the sum of their variances (\( \sigma_A^2 + \sigma_B^2 \)).
+
+In the specific case of our experiment we can map the two sources of information to the flanker compound (a gaussian with centre at \( \mu_F = (\mu_1 + \mu_2)/2 \), variance \( \sigma_F^2/2 \)) and the
+target (assumed gaussian with centre \( \mu_T \), and variance \( \sigma_T^2 \). Putting together Eqns 12 and 14, the bias (difference between the response and the target) is given by:
+
+\[
+B = w_F^{max} p(F,T|C=1)(\mu_F - \mu_T) = \frac{\sigma_T^2}{\sigma_F^2 + \sigma_T^2} \exp \left( -\frac{1}{2} \frac{(\mu_F - \mu_T)^2}{\sigma_F^2 + \sigma_T^2} \right) (\mu_F - \mu_T) \tag{eq 15}
+\]
+
+Which is a derivative of gaussian as a function of flanker orientation \( \mu_F \)
+
+It also follows that response scatter is minimized only when the system considers a common cause likely (Eqn 14), predicting U-shaped (gaussian) plots of Figures 2B and 5B.
+
+Again, to allow for suboptimal behaviour we introduced two free parameters that regulate the amplitude of the dependency on the flankers (\( \beta \)) and the breadth of the region of interaction (\( \gamma \)) so that the bias is:
+
+\[
+B = \beta \frac{\sigma_T^2}{\sigma_F^2 + \sigma_T^2} \exp \left( -\frac{1}{2} \frac{(\mu_F - \mu_T)^2}{\gamma^2 (\sigma_F^2 + \sigma_T^2)} \right) (\mu_F - \mu_T) \tag{eq 16}
+\]
+
+Interestingly, comparable behaviour is obtained if, instead of constructing a system which multiplies probabilities as in\(^{26}\), one considers a system that measures the similarity between two distributions via their point-by-point product of the distributions and takes either the peak or area under the distribution.
+
+The product of gaussians is itself a gaussian, is centred at \( \left( \frac{\mu_B \sigma_A^2 + \mu_A \sigma_B^2}{\sigma_A^2 + \sigma_B^2} \right) \), has variance \( \left( \frac{\sigma_A^2 \sigma_B^2}{\sigma_A^2 + \sigma_B^2} \right) \) and peak at:
+
+\[
+\frac{1}{2 \pi \sigma_A \sigma_B} \exp \left( -\frac{(\mu_A - \mu_B)^2}{2(\sigma_A^2 + \sigma_B^2)} \right) \tag{eq. 17}
+\]
+
+So the peak embeds the same behaviour of Eqn. 14. It is easy to demonstrate that also the area under the curve follows the same gaussian dependency on the distance between cues as the area of a gaussian is equivalent to the peak (Eqn. 16) times the standard deviation of the curve (\( \sqrt{\frac{\sigma_A^2 \sigma_B^2}{\sigma_A^2 + \sigma_B^2}} \)) and a constant factor \( 1/\sqrt{2 \pi} \) all of which are constant once the distributions have known width and thus reduce to a scaling factor.
+
+Model Fitting
+
+The predictions of the two modelling approaches are overlayed on the data of Figures 2 and 5 with dark and light colours. To minimize degrees of freedom we derived the values of
+sensory reliability from the data of Figure 2b, assuming that the extreme points (±30° and ±45°) give baseline data, not influenced by flanker integration: this is 17.1 for rounded targets (blue symbols), and 11.7 for elongated targets (red symbols).
+
+We implemented the ideal observer model (Eqn. 11) with only a scaling constant (\( \alpha \)), which allows for sub-optimal behaviour. These fits are particularly good for the rounded targets (with largest effects), with \( R^2 \) of 0.97 and 0.74 (for bias and scatter), and 0.24 and 0.60 for elongated targets) and come about assuming \( \alpha = 0.57 \). One of the key features of the ideal observer model is that it reduces RMSE by leveraging on all available information. Thus it predicts the Global Integration of Figure 4, with centres of the Gaussian derivatives close to −15°. Besides capturing this key feature, the model also provides good quantitative fits to the data of Figure 5a with \( R^2 \) of 0.76 and average fits to those of Figure 5b 0.23 for bias and scatter respectively (\( \alpha=0.32 \)).
+
+We used the same reliability values from Figure 2b to implement the “optimal causality gating model”\(^{26}\), the derivative of gaussian function plotted with light colours in Figures 2 and 5. The sensory reliabilities fix both the maximal slope of the curve (see Eqn 12) and the width of the region of interaction (see Eqn 14). Assuming the same sensory precisions as above (17.1 and 11.7 for the two types of stimuli) maximal slopes should be 0.81 and 0.48 for the two conditions, larger than the real data. Also the widths (27.8 and 33.2) are larger than those predicted by Eqn 14 (19 and 16.8). For this reason we allowed two scaling factors, one enabling lower weighting of the context (\( \beta \)) and the other modulating the width (\( \gamma \)). Setting \( \beta=0.54 \) and \( \gamma=1.46 \) led to good fits with \( R^2 = 0.97 \) and 0.89 for the low reliability target (bias and scatter curves), and 0.67 and 0.79 for the high reliability target (\( \beta=0.26 \) and \( \gamma=1.97 \)). As with the other model, the prediction in Experiment 2 is for large pooling of all available cues, thus the prediction is that of a centre at −15°. This model also provides good fits for response bias (\( R^2=0.89 \)) and acceptable fits for response scatter (\( R^2=0.38, \beta=0.62 \) and \( \gamma=1.37 \)).
+DISCUSSION
+
+The results of this study suggest a novel interpretation of visual crowding: that it is a by-product of efficient Bayesian processes, which lead to improved perceptual performance, minimizing production error. We tested and validated several key predictions of this idea. Firstly, crowding, measured as flanker-induced orientation bias, was greatest when targets had the weakest orientation signals (least reliability) and flankers had the strongest signals, as predicted from most models of optimal cue combination\(^{27,28}\). The magnitude of the bias varied with the difference of target and flanker orientation, following the predicted non-linear pattern, increasing to a maximum of around \(15^\circ\), then falling off for larger orientation differences. Importantly, the interaction of the flankers and target was associated with a reduction in response scatter, which led to a reduction in total RMS error, an index of improved performance. Finally, the results suggest that the bias does not result from direct interactions with individual flankers, but from interaction with a representation of the average orientations of the two flankers. All these results were predicted by optimal feature combination principles, and quantitatively well modelled an ideal-observer model that minimizes reproduction errors.
+
+These results are clearly difficult to reconcile with standard models of obligatory integration\(^{6,29}\). Passive integration systems may be tweaked to explain the stronger effects for more elongated flankers (such as having more Fourier energy at that orientation), but cannot explain the fall off in crowding effects when the difference exceeds \(15^\circ\). Any basic integrator would necessarily combine orientation energy of all angles, not only similar angles. On the other hand, the flexible integrator models proposed here (Eqns 10 and 15) predict both the pattern and the magnitude of the results. Furthermore, the final experiment suggests that this intelligent orientation-dependent integration is unlikely to occur directly within a higher order cell itself, as the orientation-dependent integration function aligns with the average of two disparate flankers, rather than with each individual flanker. This suggests that the integration is between the target and a broad representation that includes both flankers. Mechanisms operating directly between target and individual flankers (such as the proposed “local association field”\(^{30}\)) are not consistent with the results of Figure 5, which shows that flankers are first combined with each other before exerting their effects on the target.
+Combination of target and a broad representation of both flankers could be implemented in several ways. One physiologically plausible mechanism would be feedback from mid-level areas, such as V4, which have large receptive fields, integrating over a wide area. These cells could contain information of both flankers (as well as the target), which could be fed back to low levels (eg V1) to integrate flexibly with finer representations of the target. Within this framework the fine-grain target information is not lost, but combined with broad contextual information in an optimal manner to improve performance. This is analogous to the process of serial dependence, where representations of perceptual history (often termed Bayesian priors) are generated at mid- to high-levels of analysis, but feed back onto fairly low processing levels\(^{31}\). Similar processes could evoke crowding, integrating over space rather than time.
+
+The predictions of the crowding behaviour derive from theoretical minimization of total RMS errors, explained in detail in the modelling section, but readily understood intuitively. There are two orthogonal sources of error, bias (average accuracy) and response scatter (precision), which combine by Pythagorean sum to yield total error. Thus although the contextual effects do lead to inaccuracies (biases), these are more than offset by the decrease in response scatter (Fig. 2C). Clearly, if the effects were to increase continuously with orientation, then the bias would become large, and offset the reduction in scatter, leading to increased error: integration is therefore efficient only over a limited range. Note that the efficiency-driven ideal model gives good fits simultaneous to both bias and scatter data with only one free parameter, a scaling factor. This comes out at around 0.57 for the main data and probably reflects other processes in orientation judgements that we did not control for, such as regression to the mean\(^{32,33}\).
+
+The current experiment shows that under conditions of crowding, information about the target is not necessarily lost. This is consistent with a good deal of previous evidence (see reference\(^{34}\) for review), including studies showing that it can affect the ensemble judgment\(^6\), can cause adaptation\(^{35}\) and that crowding induced biases may not affect grasping\(^{36}\). Even more dramatic are the demonstrations that increasing flanker length\(^{37}\) or adding additional flankers\(^{14}\) can decrease or eliminate crowding. Our study employed simple well controlled stimuli to allow quantitative prediction and measurement of crowding-effects, similar to the studies with serial dependence studies. Thus they do not readily relate
+to the clever uncrowding studies of Herzog and colleagues. However, it is not difficult to envisage extensions to the model incorporating grouping principles within the rules of integration, in the spirit of the general principles of our model: flexible, “intelligent” combination of signals, rather than a rigid integration via “rectify and sum” or similar rules\(^{10}\).
+
+In summary, the current study suggests that crowding may be analogous to serial dependence, pointing to similar function and mechanisms. As serial dependence has been shown to exploit temporal redundancies to maximize performance, crowding may also reflect similar exploitation of redundancies over space. It is worth noting that while the rules governing crowding are flexible, leading to improved performance, crowding remains completely obligatory: no effort of will or deployment of attention can allow us to resolve the crowded objects, or to ignore the contextual effects of the orientated flankers. Indeed, while our proposed pooling process is flexible and “intelligent”, it remains automatic, not subject to voluntary control. This is similar to many of the experience-driven perceptual illusions, such as the “hollow mask illusion”\(^{21}\): no effort of will can cause us to see the inside of a hollow mask as concave, we always see the convex face. However, while visual crowding remains an obligatory limitation to object recognition, we conclude that like the effects of temporal context and experience, it is best understood not as a defect or bottleneck of the system, but the consequence of efficient exploitation of spatial redundancies of the natural world.
+
+METHODS
+
+Participants
+
+Fifteen healthy participants with normal or corrected-to-normal vision were recruited (aged 18-55 years, mean age = 36, 7 females). Experimental procedures are in line with the declaration of Helsinki and approved by the local ethics committee (*Commissione per l’Etica della Ricerca*, University of Florence, 7 July 2020). Written informed consent was obtained from each participant, which included consent to process, preserve and publish the data in anonymous form.
+Stimuli
+
+The stimuli, illustrated in Fig. 1A, were generated with Psychtoolbox for MATLAB (R2016b; MathWorks). They comprised an oval-shaped visual target flanked by oval-shaped upper and lower visual flankers, displayed 26 deg eccentric from the fixation point, with the target close to the horizontal meridian (vertical position was slightly varied from trial to trial to avoid pre-allocation of attention to the target) and flankers 5.5 deg away from the target. Both target and flankers were sketches of oval shapes, defined by 12 dark grey dots (diameter 0.3 deg, 1.4 deg inter-dots distant, 16.8 deg perimeter), presented against a uniform grey background. The target was orientated either +35° or +55° (clockwise) from the vertical, and flanker orientation randomly chosen in steps of 5° from –45° to +45° with respect to the target orientation. The two flankers were 5.5 deg from target, leading to a Bouma ratio of 0.2. We manipulated the reliability of orientation information of target and flanker stimuli by using two different aspect ratios, 2.8 (axes 3.48 and 1.23 deg) and 1.4 (axes 3.19 and 2.28 deg), illustrated in Fig. 1A. The more elongated target was always associated with more rounded flankers, and vice versa. In each experimental session of the three experiments, the two target-flanker combinations were shown both kinds of stimuli in random order.
+
+Procedure
+
+Stimuli were displayed on a linearized 22” LCD monitor (resolution 1920 x 1080 pixels, refresh rate 60 Hz). Observers were positioned 57 cm from the monitor, in a quiet room with dim lighting, and maintained fixation on a small (0.35 deg) black central dot. After a random delay from the observer initiating the trial, the stimulus was displayed for 167 ms. Then a thin rotatable white bar (0.05 x 5 deg with a gaussian profile) was presented at the fixation point with random orientation, and observers matched its orientation to that of the target by mouse control. In the first two experiments, the orientation of the two flankers was yoked, while in the third, one flanker was always +15° (clockwise) while the other varied from -45° to +45°. In the second experiment, the target-flanker distance varied, being 5.5, 7.5, 11.0 and 16.6 deg, leading to Bouma ratios of 0.21, 0.27, 0.4, 0.6.
+
+Ten observers participated in the first experiment, five in the second, thirteen in the third. They contributed for a total of 10699 trials for the first experiment, 14377 for the second (spread across the four flanker-target distances) and 16574 for the last.
+Data analysis
+
+Responses occurred out from the range between 0.5 and 3 seconds after the stimulus offset were removed (for a total of 15.9% trials across the 3 experiments), as were responses with reproduction error greater than 35° (6.9% of trials).
+
+For each target and relative orientation of the flanker, we calculated the average constant error (bias, positive meaning clockwise) and scatter. We then averaged the values for the two targets. Bias functions were fitted by a derivative of gaussian function, which can be considered to be a gaussian of width s multiplied by a straight line of slope a [or w], which can be considered the weighting given to the flankers: 1 means the flankers are weighted equally to the target. Bias is given by:
+
+\[
+B = a \cdot (\theta - m) \exp \left( - \frac{(\theta - m)^2}{s^2} \right) + b
+\]
+
+[eq. 18]
+
+Where \( \theta \) is orientation difference, \( m \) the centre, and \( b \) the vertical offset of the function. \( a \), \( b \) and \( m \) were free to vary.
+
+Scatter (\( S \)) was defined as the average root variance in each condition. The variation with orientation a gaussian function in the form:
+
+\[
+S = a \cdot \exp \left( - \frac{(\theta - m)^2}{s^2} \right) + b
+\]
+
+[eq. 19]
+
+Where \( b \) is the baseline at high orientation differences and \( a \) is the amplitude of the Gaussian. As Bias and Scatter likely originate from the same process, we yoked the parameter \( s \) to best fit both curves.
+
+REFERENCES
+
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+8 Levi, D. M. & Carney, T. Crowding in peripheral vision: why bigger is better. Curr Biol 19, 1988-1993, doi:10.1016/j.cub.2009.09.056 (2009).
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+10 Freeman, J. & Simoncelli, E. P. Metamers of the ventral stream. Nat Neurosci 14, 1195-1201, doi:10.1038/nn.2889 (2011).
+11 Nazir, T. A. Effects of lateral masking and spatial precueing on gap-resolution in central and peripheral vision. Vision Res 32, 771-777, doi:10.1016/0042-6989(92)90192-I (1992).
+12 Kooi, F. L., Toet, A., Tripathy, S. P. & Levi, D. M. The effect of similarity and duration on spatial interaction in peripheral vision. Spat Vis 8, 255-279, doi:10.1163/156856894x00350 (1994).
+13 Kennedy, G. J. & Whitaker, D. The chromatic selectivity of visual crowding. J Vis 10, 15, doi:10.1167/10.6.15 (2010).
+14 Manassi, M., Sayim, B. & Herzog, M. H. When crowding of crowding leads to uncrowding. J Vis 13, 10, doi:10.1167/13.13.10 (2013).
+15 Levi, D. M. Crowding--an essential bottleneck for object recognition: a mini-review. Vision Res 48, 635-654, doi:10.1016/j.visres.2007.12.009 (2008).
+16 Chopin, A. & Mamassian, P. Predictive properties of visual adaptation. Curr Biol 22, 622-626, doi:10.1016/j.cub.2012.02.021 (2012).
+17 Cicchini, G. M., Anobile, G. & Burr, D. C. Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform. Proc Natl Acad Sci U S A 111, 7867-7872, doi:10.1073/pnas.1402785111 (2014).
+18 Fischer, J. & Whitney, D. Serial dependence in visual perception. Nat Neurosci 17, 738-743, doi:10.1038/nn.3689 (2014).
+19 Pasuccci, D. et al. Laws of concatenated perception: Vision goes for novelty, decisions for perseverance. PLoS Biol 17, e3000144, doi:10.1371/journal.pbio.3000144 (2019).
+20 Helmholtz, H. v. Handbuch der physiologischen Optik. (Voss, 1867).
+21 Gregory, R. L. Eye and brain; the psychology of seeing. (McGraw-Hill, 1966).
+22 Liberman, A., Fischer, J. & Whitney, D. Serial dependence in the perception of faces. Curr Biol 24, 2569-2574, doi:10.1016/j.cub.2014.09.025 (2014).
+23 Taubert, J., Van der Burg, E. & Alais, D. Love at second sight: Sequential dependence of facial attractiveness in an on-line dating paradigm. Sci Rep 6, 22740, doi:10.1038/srep22740 (2016).
+24 Burr, D. & Cicchini, G. M. Vision: efficient adaptive coding. Curr Biol 24, R1096-1098, doi:10.1016/j.cub.2014.10.002 (2014).
+25 Cicchini, G. M., Mikellidou, K. & Burr, D. C. The functional role of serial dependence. Proc Biol Sci 285, doi:10.1098/rspb.2018.1722 (2018).
+26 Kording, K. P. et al. Causal inference in multisensory perception. PLoS One 2, e943, doi:10.1371/journal.pone.0000943 (2007).
+27 Ernst, M. O. & Banks, M. S. Humans integrate visual and haptic information in a statistically optimal fashion. Nature 415, 429-433, doi:10.1038/415429a (2002).
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+29 Rosenholtz, R., Yu, D. & Keshvari, S. Challenges to pooling models of crowding: Implications for visual mechanisms. J Vis 19, 15, doi:10.1167/19.7.15 (2019).
+30 Field, D. J., Hayes, A. & Hess, R. F. Contour integration by the human visual system: evidence for a local "association field". Vision Res 33, 173-193, doi:10.1016/0042-6989(93)90156-q (1993).
+31 Cicchini, G. M., Benedetto, A. & Burr, D. C. Perceptual history propagates down to early levels of sensory analysis. Curr Biol 31, 1245-1250 e1242, doi:10.1016/j.cub.2020.12.004 (2021).
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+36 Bulakowski, P. F., Post, R. B. & Whitney, D. Visuomotor crowding: the resolution of grasping in cluttered scenes. Front Behav Neurosci 3, 49, doi:10.3389/neuro.08.049.2009 (2009).
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+Peer Review File
+
+Changes in limiting factors for forager population dynamics in Europe across the Last Glacial-Interglacial Transition
+
+Open Access This file is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. In the cases where the authors are anonymous, such as is the case for the reports of anonymous peer reviewers, author attribution should be to 'Anonymous Referee' followed by a clear attribution to the source work. The images or other third party material in this file are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+This study aims to identify the limiting climate factors of hunter-gatherer population density in Europe from the LGM to early Holocene, which is a tempting research question that, if answered convincingly, could provide clues in resilience and adaptation strategies of ancient human societies. The authors built statistical models (quantile Generalised Additive Models) of population density versus each of the 18 climate variables based on contemporary hunter-gatherer dataset, and hindcasted population density using paleoclimate outputs from a climate model. This workflow and statistical techniques are not new (e.g. Tallavaara et al. 2015 pnas), but selecting the factor that predicts the lowest population density across space and time, based on the concept of limiting factor, provides a fresh angle of view. However, I have some major concerns about the robustness of the analysis and significance of current results, as outlined below. Based on these, I cannot recommend its publication, at least not in its current form.
+
+Robustness of results:
+Mean temperature of the Warmest Month (MWM) is identified a major limiting factor during all critical periods (Fig. 4), but MWM is the variable that has the most severe non-analogy problem comparing present-day climate space and past climates (Fig. 2 and Supplementary material S2). Although mentioned at Lines 126-128, considering the strong relevance to the main findings, the risk of an unreliable extrapolation out of the range of data used to fit the statistical model is higher than acknowledged here.
+In addition, it is not clear to me why the authors chose 90th percentile of population density to do the hindcast. First, the results, in principle, would not be comparable to previous estimates in literature. Second, does the resulted limiting factors change dependent on the choice of the percentile? Although the general shape of the population density versus climate relationship looks similar across different percentiles for each individual climate factor (Lines 311-312), it is the relative magnitudes between all predicted densities by these factors that ultimately selects the limiting factor. Thus, it is not straightforward whether your results are sensitive to the choice of percentiles.
+Regarding the comparison between hindcasted population density and the archeological population proxy (Fig. 3), I would not say they are “in line with” each other (Lines 139-140). The black curve in Fig. 3 starts to increase already since 18 ka, which is relatively flat in the red curve; the red curve increases significantly during GI1 and GS1, whereas it is stale in the black curve.
+By the way, at Lines 101-103, why do you separate higher and lower predictive accuracy by a threshold of “explained deviances < 0.79”? According to Table 1, these predictors are all so close.
+
+About mechanism insights:
+From the results it is hard to infer mechanisms regarding how the identified limiting factor has constrained population density. This is limited by the fact that only temperature and precipitation and their variants were used as predictors, without direct information about productivity; whereas climate impacts population density via indirect effects on ecosystem attributes like NPP (e.g. Freeman et al. 2020, doi:10.1016/j.jas.2020.105168). Throughout the text the authors have tried to relate some of the factors to environmental productivity, but it was highly speculative. Let me take Lines 185-192 as an example. During 14.7ka to 11.7ka, the importance of ET decreases while importance of MWM and temperature seasonality increases. But all three variables are linked to NPP (and possibly other aspects of the ecosystem). From these changes one still cannot judge what process is taking effect in the end.
+Given this, why not use NPP as a predictor in the first place? Data availability for the hindcast should not be a problem since simulated NPP for the past 21,000 years are publicly accessible from some climate models already.
+
+Significance of the results in archaeological perspective:
+I commend the authors’ effort to put the (more of ecology-oriented) results into archaeological
+context, but currently it is still limited in qualitative descriptions scattered in the text. If the authors could achieve a more systematic compilation of archaeological records regarding how these societies have tackled with the limiting climate factors and find a consistency with your hindcasted results in space and time, it would add much merit to this study, with broader significance and impacts.
+
+Aside from the above concerns, the organization of Results and discussion needs to be improved. Adding sub-headings would help. Besides, descriptions of the results in the text should be more careful. Currently they are sometimes inconsistent with the table or figures. For example, at Lines 104-110, it says seasonal temperature variables are among the lowest explained deviance, which is not the case as listed in Table 1.
+
+A minor point is that the uncertainties/biases in the paleoclimate outputs of the CCSM3 climate model should be discussed.
+
+Code availability: though not mandatory, it is strongly encouraged to make the code readily available so as to enable reproduction of the results.
+
+Table 1: A conceptual confusion: MCM is not “extreme events”. Same for MWM, PDM, and PWM. Extreme events are events that occur with low frequency, not the regular seasonal maxima or minima.
+
+There are a few careless errors in the manuscript, for example:
+Line 266: “16 climatic predictors”: there are 18 climate variables in Table 1.
+Line 289: it says “We use a subsample of 159 hunter-gatherers populations...” in the Reporting summary, while here it says “127 populations”.
+Table 1: Acronym of “Precipitation of the Wettest Month” should be PWM, not PDM.
+Figure caption of Fig. 3: “Minimum temperature of the Coldest Month” should be “Mean…”, and “Maximum temperature of the Warmest Month” should be “Mean…”
+Figure caption of Supplementary material S1: it is not “the six most important environmental factors”. Please check carefully throughout the paper.
+
+Reviewer #2:
+Remarks to the Author:
+This is truly thought-provoking, highly interesting and novel contribution to the hunter-gatherer ecology. I very much like the approach of applying the analysis of ecological limiting factors, for the first time, to prehistoric hunter-gatherers. Below I have highlighted few issues that you could consider to revise to further improve the paper.
+
+Best regards,
+Miikka Tallavaara
+
+1.
+Given that many of the climate predictors are highly correlated (as you also write in the manuscript), they will convey partly the same information. This can potentially make it difficult to differentiate the importance between different climatic variables as limiting factors. I would suggest that you add some more justification for using large number correlated variables in the analysis. Or, alternatively, consider reducing the dimensionality of the data.
+
+2.
+Partly related to the item 1, you could provide justification for using univariate instead of multivariate approach. The effect of a predictor variable can change (sometimes dramatically) when controlled for the effects of other variables by adding them to the model. Therefore, you should explain why you rely on univariate approach, or, alternatively, try to add the best predictor candidates in the same model
+and see how the results would change.
+
+3.
+Binford’s data is notorious for spatial auto-correlation, especially because in particular areas, he has basically split closely living ecologically, demographically and culturally similar groups into smaller units even though one might consider many of those belonging to the same ethnic group. This can lead to inflated performance metrics in traditional cross-validation schemes. The idea of cross-validation is to test the model with data that the model has not seen before, so in the presence of spatial auto-correlation, test data can be “too” similar to training data. Therefore, your performance metrics are quite likely “too good” and I suggest that you could use some kind of spatial block cross-validation scheme, such as h-block cross validation. See, e.g.
+Salonen, J.S., et al, 2016. Calibrating aquatic microfossil proxies with regression-tree ensembles: Cross-validation with modern chronomid and diatom data. The Holocene 26, 1040–1048.
+https://doi.org/10.1177/0959683616632881
+https://quantpalaeo.wordpress.com/2013/12/15/h-block-cross-validation-of-transfer-functions/
+https://cran.r-project.org/web/packages/blockCV/vignettes/BlockCV_for_SDM.html
+
+4.
+Related to the above issue, on page 3 you write that no single environmental variable explained more than 81% of the population density variation among ethnographic foraging societies. It might be because of my ignorance of quantile regression, but I’m not sure if you can really say that quantile regression model can explain some percentage of the variation in a response variable. So clarify this and explain what the explained deviance is measuring in your quantile regressions, is it the goodness of fit of the 90th quantile or what?
+
+I’m also not sure if one can directly compare your performance metrics (explained deviance) to e.g. our metrics (R2) (Tallavaara et al. 2015). Besides, our R2 e.g. for multivariate GAM is clearly smaller (0.6), not marginally better, than any your values. After a lot of exploration with Binford’s data, I also think that it is really difficult to push the R2 of (multivariate) population density models well above 0.7 unless you really overfit the model.
+
+5.
+On page 5, you provide the modelled population size estimates for Europe, which seems to be pretty high. The LGM estimate is twice as large as our previous estimate (which has been argued to be way too large by some) despite we having larger geographical area. However, am I right that your estimates are actually maximum estimates based on the modelled 90th quantile? Whatever the case, this needs to be stated clearly in the text and in the relevant figure captions.
+
+6.
+I might have missed it somehow, but which of the many univariate models you are using when estimating the population size or average density (including figures 3 and 4a–e)? Or is it ensemble of all models? This is nevertheless important information and if it is missing, you should clearly provide the information in the text and also to relevant figure captions.
+
+7.
+Mean temperature of the warmest month seems to be one of the most important limiting factors of hunter-gatherer density in Europe (Table 1, Figure 4). It is therefore interesting that its impact on maximum hunter-gatherer density is negative between 22kyBP and 8kyBP (figure 5B). The figure 1 shows that between 10 and 15 C the 90th quantile of MWM is decreasing, because of couple of outlier points. These kind of “edge effects” are a known problem in GAMs and therefore there are different kinds of constrained GAMs available:
+https://www.researchgate.net/publication/271740857_Shape_constrained_additive_models
+https://arxiv.org/pdf/1812.07696.pdf
+It is nevertheless quite unrealistic to assume that increase of MWM would have had negative impact on forager density from the LGM to Mid Holocene and I therefore suggest that you either try to use more conservative smoothing parameter value to get rid of wiggles or switch to constrained GAM, although I dont know if there are quantile versions available for such techniques. The negative (but unrealistic) effect of MWM is at least one of the reasons why MWM appears to increase its importance as a limiting factor over time in Europe.
+
+8.
+On page 5, you describe your results so that during the LGM the northern limit of human range would have been in central France and southern Germany. However, my reading of figure 4 is that the whole of France would have been within the human range. You use one individual/100km2 as threshold for human occupancy, which is pretty high given that lowest densities in ethnographic data are 0.2–0.25 individuals/100km2. But even with your threshold, the occupied area seems to be clearly bigger than you describe in the text. Why this discrepancy? I would suggest that you bravely stand behind your results and describe them as they are :-)
+
+Reviewer #3:
+Remarks to the Author:
+The manuscript focuses on the relation between the environmental factors explored here and population density. One central assumption that is adopted in this paper is that for foragers, demographic and environmental changes correlate strongly. And that there are causal relations between different environmental variables and human responses through time and Space. They then focus on limiting environmental factor which are defined as the variable predicting the lowest population density at a given place and time and assume that one of these limiting factors, or a combination of several, limited the scarcest recourse, and in turn regulate population sizes and densities. They then identify the dominant climatic constraints for hunter-gatherer population densities and then hindcast their changing dynamics in Europe for the period between 20kyBP to 8kyBP. They detect spatiotemporal variations in these factors in relation to the assessed demographic data for human groups which suggests that European Upper Palaeolithic hunter-gatherers at various regions and periods needed to overcome very different adaptive challenges.
+
+The paper is overall well written and the introduction and Results and Discussion are detailed, and cite a lot of relevant and up to date sources. Moreover, the main caveats associated with their data sources and analyses are mentioned and discussed
+
+I would like to raise three issues which I think can be handled in the revised manuscript.
+
+One is that while I agree that environmental changes seem to have been the main driving force behind evident demographic patterns in the case of human populations and various other species, as the authors indicate, there are also adaptive capacities of humans to buffer and manage at least to some extent, environmental changes and corresponding resource fluctuations. The cited paper by Filho et al. 2021, documents how several African communities deferentially adapted to climate changes. If we assume that at least some of the human groups, during the Last Glacial Maximum and post-LGM period had similar adaptive capacities, it follows that their population sizes, densities an even settlement patterns, will not only reflect a ‘passive’ causal relationship with a specific climatic limiting factor, but also a unique human capacity to buffer and perhaps even overcome some limitation. Some examples include shelters, fire, and projectile technology. Moreover, one of the main mechanisms is mobility and mainly dispersals to refugia with better resources and climatic conditions.
+
+A second issue is the reliance on ethnographic data. The authors cite the article by Bird a& Coddig
+2021, about the Promise and peril of ecological and evolutionary modelling using cross-cultural datasets. While the authors of this paper claim that the promise outweighs the peril. It will be useful for the authors to mention in more details, the potential caveats of drawing the analogy between present day and Upper Palaeolithic hunter-gatherers, since various papers argued that the former are not really a good proxy for the latter.
+
+A third issue is that on page 6, Figure 3, they refer to the date of recolonization of Europe to be 17 kyBP. This is no longer regarded, on the basis of archaeological data, as being the date of onset of the process, as new results indicate that it started around 19 kyBP- see the paper by Maier et al. 2020: https://doi.org/10.1007/s41982-019-00045-1
+
+In sum, the paper is informative and balanced but the above-mentioned points are raised as the way some of the text is worded, it seems that the underlying approach is that human demography is not only affected by environmental shifts, and more specifically climatic changes, but is directly caused only by these. In which case, the assessmentof which specific limiting factor exerted the most impact on a given human populations at a given location and time is indeed informative and interesting. But it should be made clearer that the paper does not test the specific role of human cultural capacities, to buffer and even overcome some limiting factors. Moreover, the spatiotemporal variations are expected to be a reflection of the fact that indeed limiting factors varied and that hunter-gatherers needed to overcome different adaptive challenges, but they cannot shed light on how they actually adapted, or alternatively failed to adapt, to these changes.
+
+Minor comments
+Some of the figures need to be improved in terms of colors and legends.:
+
+Figure 1. What are the abscissa? It is not clear from the figure legend.
+
+Figure 3, Change color for Maximum temperature of the Warmest Month.
+
+Figure 4, side panel legend, should be Population density and not population size
+It is also difficult to understand the panels, what is the difference between each side and the colors are difficult to detect at this scale.
+
+Figure 5, is it assessing population size or population density?
+Final responses:
+
+R1c1: Mean temperature of the Warmest Month (MWM) is identified a major limiting factor during all critical periods (Fig. 4), but MWM is the variable that has the most severe non-analogy problem comparing present-day climate space and past climates (Fig. 2 and Supplementary material S2). Although mentioned at Lines 126-128, considering the strong relevance to the main findings, the risk of an unreliable extrapolation out of the range of data used to fit the statistical model is higher than acknowledged here.
+
+To acknowledge the points made by the reviewer regarding the non-analogy problem with the variable, Mean temperature of the Warmest Month, we remove this variable from the pool of factors used to assess population densities and limiting factors. We explain this in the text in L137-140 and L401-403. We do not consider that removing this variable is a significant problem for our analyses. We reason that our objective is not to determine how a specific variable determines population densities but on the possible processes (as we specify in Table 1) by which climate can determine population densities.
+
+R1c2: It is not clear why the authors chose 90th percentile of population density to do the hindcast. First, the results, in principle, would not be comparable to previous estimates in literature. Second, does the resulted limiting factors change dependent on the choice of the percentile? Although the general shape of the population density versus climate relationship looks similar across different percentiles for each individual climate factor (Lines 311-312), it is the relative magnitudes between all predicted densities by these factors that ultimately selects the limiting factor. Thus, it is not straightforward whether your results are sensitive to the choice of percentiles.
+
+The reviewer’s point regarding the need to justify why we chose the 90th percentile in our analyses is welcomed. We have done all the analyses using the 10th, 50Th, and 90th percentile in this revision. As we now clarify in the text (L62-63; L365-359; L407-412), our goal is not to quantify the population size on each evaluated grid but to indicate what are the potential climatic limiting factors and which could be the expected values (maxi-mum/average/minimum) given this climatic limit. Furthermore, our results and discussion focus on how observed deviations from these estimates can be used to generate hypotheses to how different societies have (or not) tackled these climatic limits, allowing them to have larger population sizes.
+
+R1c3: Regarding the comparison between hindcasted population density and the archaeological population proxy (Fig. 3), I would not say they are “in line with” each other (Lines 139-140). The black curve in Fig. 3 starts to increase already since 18 ka, which is relatively flat in the red curve; the red curve increases significantly during GI1 and GSI, whereas it is stale in the black curve.
+
+While we now acknowledge the nuanced description of the trends by the reviewer in the text (L172-176), we consider that a perfect match on the timing of events cannot be expected as these are variables representing trends at two different resolutions. Having
+said that, the archaeological population proxy and our population density estimates show a strong correlation (rho = -0.7) when aggregated at the same temporal resolution as the archaeological population proxy. We now make this point explicit in our text (L172-176).
+
+R1c4: By the way, at Lines 101-103, why do you separate higher and lower predictive accuracy by a threshold of “explained deviances < 0.79”? According to Table 1, these predictors are all so close.
+We do make this distinction anymore. Now we acknowledge that there are differences in the predictive accuracy between variables, but that accuracy amongst predictors is somewhat similar (L122-124).
+
+R1c5: From the results it is hard to infer mechanisms regarding how the identified limiting factor has constrained population density. This is limited by the fact that only temperature and precipitation and their variants were used as predictors, without direct information about productivity; whereas climate impacts population density via indirect effects on ecosystem attributes like NPP (e.g. Freeman et al. 2020, doi:10.1016/j.jas.2020.105168). Throughout the text the authors have tried to relate some of the factors to environmental productivity, but it was highly speculative. Let me take Lines 185-192 as an example. During 14.7ka to 11.7ka, the importance of ET decreases while importance of MWM and temperature seasonality increases. But all three variables are linked to NPP (and possibly other aspects of the ecosystem). From these changes one still cannot judge what process is taking effect in the end. Given this, why not use NPP as a predictor in the first place? Data availability for the hindcast should not be a problem since simulated NPP for the past 21,000 years are publicly accessible from some climate models already.
+To address the comment, we have done two things:
+First, we no use Net Primary Productivity (NPP) in our work as a predictor. Using the Miami model, we calculate this variable (Lieth, 1972, as described in Table 1). We use this modelling approach instead of other possible NPP products as we want to reduce the potential biases that could come from using environmental datasets from alternative sources. As we do this, NPP as a predictor shows that it is not a significant factor.
+Second, we now refer to Effective Temperature and Potential Evapotranspiration as factors determining energy availability in a broad context (Table 1). NPP relates only to a variable indicating the energy available to hunter-gatherers from primary producers.
+
+R1c6: I commend the authors’ effort to put the (more of ecology-oriented) results into archaeological context, but currently it is still limited in qualitative descriptions scattered in the text. If the authors could achieve a more systematic compilation of archaeological records regarding how these societies have tackled with the limiting climate factors and find a consistency with your hindcasted results in space and time, it would add much merit to this study, with broader significance and impacts.
+Thank you for this comment – naturally, we love to expand on this particular issue. We now provide an extended discussion of how the archaeological record explicitly links to the identified limiting factors and how different forager groups overcame these. We also provide additional references relating to pyrotechnology, shelter, energy capture, etc. (e.g., L223-226 and L262–271).
+
+R1c7: Aside from the above concerns, the organization of Results and discussion needs to be improved. Adding sub-headings would help. Besides, descriptions of the results in the text should be more careful. Currently they are sometimes inconsistent with the table or figures. For example, at Lines 104–110, it says seasonal temperature variables are among the lowest explained deviance, which is not the case as listed in Table 1.
+
+As suggested, we have added subheadings to the Results and discussion section to provide a clear outline of our study results and their implication and relevance. We have now addressed all inconsistencies between the tables, figures and text.
+
+R1c8: A minor point is that the uncertainties/biases in the paleoclimate outputs of the CCSM3 climate model should be discussed.
+
+We would like to evaluate and discuss how CCSM3 SynTrace paleoclimate simulations uncertainties propagate to our population density models and definition of limiting factors. However, the used downscaled and debiased paleoclimatic simulations do not contain uncertainty estimates, and this is a point we acknowledge in our manuscript methods (L394-397).
+
+R1c9: Code availability: though not mandatory, it is strongly encouraged to make the code readily available so as to enable reproduction of the results.
+
+We have now made the code and data used in this study available through a project GitHub site: https://github.com/AlejoOrdonez/PaleoPopDen. This is now part of the data availability statement.
+
+R1c10: Table 1: A conceptual confusion: MCM is not “extreme events”. Same for MWM, PDM, and PWM. Extreme events are events that occur with low frequency, not the regular seasonal maxima or minima.
+
+We have now renamed these as annual limits.
+
+R1c11: Line 266: “16 climatic predictors”: there are 18 climate variables in Table 1.
+
+We have now change these to the current number of predictors.
+
+R1c12: Line 289: it says “We use a subsample of 159 hunter-gatherers populations...” in the Reporting summary, while here it says “127 populations”.
+
+We have corrected this to there is consistency with the Reporting summary.
+
+R1c13: Table 1: Acronym of “Precipitation of the Wettest Month” should be PWM, not PDM.
+
+We have corrected this as suggested.
+R1c14: Figure caption of Fig. 3: “Minimum temperature of the Coldest Month” should be “Mean...”, and “Maximum temperature of the Warmest Month” should be “Mean...”
+We have changed the figure layout to include all used variables and ensure the titles and legend match Table 1
+
+R1c15: Figure caption of Supplementary material S1: it is not “the six most important environmental factors”.
+We have removed this figure as all regressions are now shown in the main text.
+
+R2c1. Given that many of the climate predictors are highly correlated (as you also write in the manuscript), they will convey partly the same information. This can potentially make it difficult to differentiate the importance between different climatic variables as limiting factors. I would suggest that you add some more justification for using large number correlated variables in the analysis. Or, alternatively, consider reducing the dimensionality of the data.
+While we acknowledge in our study that the level of correlation between predictors is high, this level of relationship amongst predictors allows us to “[justify] our grouping of individual variables within groups of possible explanatory mechanisms (as listed in Table 1)” (L69-74; L124-129; and L326-327). We also provide further justifications for this in our response to the reviewer’s flowing point.
+
+R2c2. Partly related to the item 1, you could provide justification for using univariate instead of multivariate approach. The effect of a predictor variable can change (sometimes dramatically) when controlled for the effects of other variables by adding them to the model. Therefore, you should explain why you rely on univariate approach, or, alternatively, try to add the best predictor candidates in the same model and see how the results would change.
+As we now explicitly state in our text, “we are not aiming at determining the best combination of variables to predict population density, but rather at determining the limiting effect of a given environmental driver” (L69-74). This perspective aligns with the core idea of limiting factors behind the current study.
+
+R2c3. Binford’s data is notorious for spatial auto-correlation, especially because in particular areas, he has basically split closely living ecologically, demographically and culturally similar groups into smaller units even though one might consider many of those belonging to the same ethnic group. This can lead to inflated performance metrics in traditional cross-validation schemes. The idea of cross-validation is to test the model with data that the model has not seen before, so in the presence of spatial auto-correlation, test data can be “too” similar to training data. Therefore, your performance metrics are quite likely “too good” and I suggest that you could use some kind of spatial block cross-validation scheme, such as h-block cross validation.
+As suggested, we have used an h-block cross-validation approach (L68; L377-383; L398-401) to determine, for each qGAM model, its’ performance and use these multiple models to control for model specification variability in our estimates of Population Density.
+
+R2c4. Related to the above issue, on page 3 you write that no single environmental variable explained more than 81% of the population density variation among ethnographic foraging societies. It might be because of my ignorance of quantile regression, but I’m not sure if you can really say that quantile regression model can explain some percentage of the variation in a response variable. So clarify this and explain what the explained deviance is measuring in your quantile regressions, is it the goodness of fit of the 90th quantile or what?
+You are right in your assessment that quantile GAMs cannot provide an estimate of the “percentage of the variation in a response variable” (i.e., R2). Our values here refer to the 50th percentile qGAM (or a traditional GAM), a point that was not clear in the original submission. For these, it is possible to determine an R2 value. This revision ensures that the point is explicitly made in the text (L374-377). In both the main text and the method section (L110-120; Table 1), we now also describe the model deviance!
+
+R2c5. I’m also not sure if one can directly compare your performance metrics (explained deviance) to e.g. our metrics (R2) (Tallavaara et al. 2015). Besides, our R2 e.g. for multivariate GAM is clearly smaller (0.6), not marginally better, than any your values. After a lot of exploration with Binford’s data, I also think that it is really difficult to push the R2 of (multivariate) population density models well above 0.7 unless you really overfit the model.
+We agree that a proper comparison between the performance of our models and those in other publications is not so straightforward. Therefore decided to omit this statement in the revised text.
+
+R2c6. On page 5, you provide the modelled population size estimates for Europe, which seems to be pretty high. The LGM estimate is twice as large as our previous estimate (which has been argued to be way too large by some) despite we having larger geographical area. However, am I right that your estimates are actually maximum estimates based on the modelled 90th quantile? Whatever the case, this needs to be stated clearly in the text and in the relevant figure captions.
+We are aware of this, and it is a result of us using the 90th percentile model when describing these trends – as accurately pointed out in the comments. This revision states that “Taken at face value, these figures are gross overestimations of actual sustained and demographically viable human land-use across this timeframe” (L169-170). Furthermore, we state in the text that our goal is NOT to predict population density but rather to show the limiting effects of climate on this important variable (L74-76). Therefore, it makes sense to consider maximum (90th-percentile), average (50th-percentile), and minimum (10th-percentile) values as descriptors of these possible
+limits. These are clarifications we also make when describing our population size/density estimates (L154-169; L177-180).
+
+R2c7. I might have missed it somehow, but which of the many univariate models you are using when estimating the population size or average density (including figures 3 and 4a–e)? Or is it ensemble of all models? This is nevertheless important information and if it is missing, you should clearly provide the information in the text and also to relevant figure captions.
+
+This information was only in the methods in the original submission (L386-397), and now it is part of the main text (L84-89) and the relevant legends.
+
+R2c8. Mean temperature of the warmest month seems to be one of the most important limiting factors of hunter-gatherer density in Europe (Table 1, Figure 4). It is therefore interesting that its impact on maximum hunter-gatherer density is negative between 22kyBP and 8kyBP (figure 5B). The figure 1 shows that between 10 and 15 C the 90th quantile of MWM is decreasing, because of couple of outlier points. These kind of “edge effects” are a known problem in GAMs and therefore there are different kinds of constrained GAMs available.
+It is nevertheless quite unrealistic to assume that increase of MWM would have had negative impact on forager density from the LGM to Mid Holocene and I therefore suggest that you either try to use more conservative smoothing parameter value to get rid of wiggles or switch to constrained GAM, although I dont know if there are quantile versions available for such techniques. The negative (but unrealistic) effect of MWM is at least one of the reasons why MWM appears to increase its importance as a limiting factor over time in Europe.
+
+Thanks for your point regarding the patterns in this variable. This is one of the points we have been discussing in our revision. Given the issues highlighted in this comment and the points raised by Reviewer-1 (the fact that there is a large non-analogy for this variable, especially in the late Pleistocene), we have decided to remove this variable from our analyses. As we discussed in R1C1, we do not consider this a significant problem for our work. Our reasoning is that because our focus is mainly on the “environmental mechanisms” by which climate imposes a limitation to population density (captured usually by two to three variables in our dataset) and not the effect of an individual variable.
+
+R2c9. On page 5, you describe your results so that during the LGM the northern limit of human range would have been in central France and southern Germany. However, my reading of figure 4 is that the whole of France would have been within the human range. You use one individual/100km2 as threshold for human occupancy, which is pretty high given that lowest densities in ethnographic data are 0.2–0.25 individuals/100km2. But even with your threshold, the occupied area seems to be clearly bigger than you describe in the text. Why this discrepancy? I would suggest that you bravely stand behind your results and describe them as they are.
+This text section is now modified (L188-192) to reflect a more detailed discussion of the observed pattern.
+
+R3c1. One is that while I agree that environmental changes seem to have been the main driving force behind evident demographic patterns in the case of human populations and various other species, as the authors indicate, there are also adaptive capacities of humans to buffer and manage at least to some extent, environmental changes and corresponding resource fluctuations. The cited paper by Filho et al. 2021, documents how several African communities deferentially adapted to climate changes. If we assume that at least some of the human groups, during the Last Glacial Maximum and post-LGM period had similar adaptive capacities, it follows that their population sizes, densities an even settlement patterns, will not only reflect a ‘passive’ causal relationship with a specific climatic limiting factor, but also a unique human capacity to buffer and perhaps even overcome some limitation. Some examples include shelters, fire, and projectile technology. Moreover, one of the main mechanisms is mobility and mainly dispersals to refugia with better resources and climatic conditions.
+
+The reviewer points to one of the main points we wanted to showcase with this study, but perhaps it was not clear – that climate sets a stage for human adaptation to “act” (L289-297). You could see this as climate determining a baseline “limit”, where human-populations active interaction with the environment, via behaviour and tools, would result in a deviation from this limit. This is a point we make explicit in our text (L293-297), indicating that deviations from our estimates can be used to signpost which populations had buffering strategies and generate hypotheses as to which could these strategies be.
+
+R3c2. A second issue is the reliance on ethnographic data. The authors cite the article by Bird a& Coddling 2021, about the Promise and peril of ecological and evolutionary modelling using cross-cultural datasets. While the authors of this paper claim that the promise outweighs the peril. It will be useful for the authors to mention in more details, the potential caveats of drawing the analogy between present day and Upper Palaeolithic hunter-gatherers, since various papers argued that the former are not really a good proxy for the latter.
+A paragraph on the inferential limits of the available ethnographic datasets has been added (L148-152). However, we do consider a very detailed discussion of these issues outside of the scope of this particular study, not least because it has been discussed directly in the recent literature, e.g.: Hamilton, M.J., Tallavaara, M., 2022. Statistical inference, scale and noise in comparative anthropology. Nature Ecology & Evolution 6, 122–122. https://doi.org/10.1038/s41559-021-01637-3
+
+R3c3. A third issue is that on page 6, Figure 3, they refer to the date of recolonization of Europe to be 17 kyBP. This is no longer regarded, on the basis of archaeological data, as being the date of onset of the process, as new results indicate that it started
+around 19 kyBP- see the paper by Maier et al.
+2020: https://doi.org/10.1007/s41982-019-00045-1
+
+This text section has been amended (L201-203) and the appropriate reference added.
+
+R3c4. In sum, the paper is informative and balanced but the above-mentioned points are raised as the way some of the text is worded, it seems that the underlying approach is that human demography is not only affected by environmental shifts, and more specifically climatic changes, but is directly caused only by these. In which case, the assessment of which specific limiting factor exerted the most impact on a given human populations at a given location and time is indeed informative and interesting. But it should be made clearer that the paper does not test the specific role of human cultural capacities, to buffer and even overcome some limiting factors. Moreover, the spatio-temporal variations are expected to be a reflection of the fact that indeed limiting factors varied and that hunter-gatherers needed to overcome different adaptive challenges, but they cannot shed light on how they actually adapted, or alternatively failed to adapt, to these changes.
+Thank you for the thoughtful summary of our ideas in our study. We have now added text to ensure the points the reviewer so correctly highlights are even more evident in the text. Notably, the ideas of environmental conditions as factors affecting and determining human demography in the evaluated period (L42-44) determine how technology or behaviour resulted in particular populations overcoming the limitations imposed by the rapid clitic changes of the late-Pleistocene (L74-78).
+
+R3c5. Some of the figures need to be improved in terms of colors and legends.: We have done a substation change in the figures color and legend to clarify their message, and fully explain what the objective of these is.
+
+R3c6. Figure 1. What are the abscissa? It is not clear from the figure legend.
+Figure 1 now show what is the variable in the Abscissa (the same as the title)
+
+R3c7. Figure 3, Change color for Maximum temperature of the Warmest Month.
+In figure-1, we have now plated all the used variables and used a colour scheme that facilitates the readability of the variables.
+
+R3c8. Figure 4, side panel legend, should be Population density and not population size. It is also difficult to understand the panels, what is the difference between each side and the colors are difficult to detect at this scale.
+Figure one has been redrawn, and the density and limiting factors maps have been speared to clarify and enhance the message of each plot.
+
+R3c9. Figure 5, is it assessing population size or population density?
+We now clarify that the top panel shows the changes in the evaluated period (21kyBP to 8kyBP) in the proportion of ice-free cells where a viable is considered the limiting
+factor (predicts the min population density). The bottom panel shows the estimated population density based on the average climatic condition across Europe for each evaluated variable.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+The authors have addressed my major comments by 1) removing the MWM variable in assessing the limiting climate factors so that the serious non-analogy problem can be bypassed; 2) testing NPP as a potential limiting factor in the analysis; and 3) extending the discussion regarding the significance of the results in archaeological perspective. Overall I’m satisfied with these revisions. But there are some points to be clarified in the revised manuscript:
+
+For the variable temperature seasonality, why are the values so large, ~2000 °C (Figure 1F and Figure 2F)? How is it calculated? And for precipitation seasonality, is it the standard deviation of the monthly precipitation?
+
+Table 1: why are the metrics substantially lower than that in the previous version? Is it because now you have used h-block cross validation to address spatial auto-correlation? Besides, why do the deviance explained and R^2 differ so much for some variables like PWM and TAP?
+
+Line 165: what is the threshold of population density to define an occupied grid cell?
+
+Figure 4: It would be more informative if you could overlay the localities of the archaeological sites that correspond to each time interval on the predicted population density maps. It can serve as a qualitative comparison. Besides, the current color legend looks weird – the ticks are not at the boundaries of each color segment.
+
+In addition, there are still quite a few careless errors and inconsistencies in the revised manuscript. Below are some examples.
+Line 110: “most of environmental variable produced models that explaining over 50% of the population density variation” – according to Table 1, the explanatory power of the variables are mostly below 50%.
+Line 230: “PET” here should be TAP?
+Line 234: “PET and TAP were the main limiting factors” – according to Fig. 6, it should be TS and TAP.
+Line 254-255: MWM is no longer used in the prediction.
+Table 1: “TSeson” and “PREC” – inconsistent with those in the text. And check the footnote of Table 1.
+Figure 1: The precipitation has been log-transformed, right? Need to specify it.
+Figure 3 lower panel: why Precip. Dryiest Month is higher than Precip. Wettest Month?
+Figure 5 caption: what is “F-J”?
+
+It is the authors’ job to closely check every sentence, figures and tables to avoid any inconsistency or contradiction!
+
+Reviewer #2:
+Remarks to the Author:
+Authors have successfully revised their manuscript. I have just one follow-up comment because authors might have misunderstood my earlier comment about models having one predictor at a time. My intention was not to suggest to add multiple predictors to achieve better predictive ability, but to take into account the fact that the effect of a predictor can change when one takes into account the effect(s) of other potential predictor(s).
+For example, ET and MCM both appear to be important limiting factors and also representing different kinds of limiting factors, ET relating to energy availability and MCM to annual limits. However, these variables are also highly correlated, which already indicates that it will be difficult to tell apart their
+individual effects. When you include both variables as predictors in the same model it actually turns out that the effect of ET is not statistically significant, response of population density to ET being more or less flat. Similarly, if you add e.g. NPP, ET and TS to the same model their effect (response shapes) are different from their effect when each is the only predictor in the model.
+
+To me, all this suggests that the real limiting effects of climate variables can be different from those you get when you include these variables separately as predictors. However, I don’t know how severe issue this truly is, but I would like to know your thoughts on that. If it really is an issue, one might use PCA to create uncorrelated climate variables and use these as predictors in the models.
+
+Best wishes,
+Miikka Tallavaara
+
+Reviewer #3:
+Remarks to the Author:
+I am fully satisfied with the revised version and with the revised manuscript and the changes.
+REVIEWER COMMENTS
+
+Reviewer #1
+
+R12Co. The authors have addressed my major comments by 1) removing the MWM variable in assessing the limiting climate factors so that the serious non-analogy problem can be bypassed; 2) testing NPP as a potential limiting factor in the analysis; and 3) extending the discussion regarding the significance of the results in archaeological perspective. Overall, I’m satisfied with these revisions. But there are some points to be clarified in the revised manuscript:
+We appreciate your assessment regarding our revision.
+
+R1C1. For the variable temperature seasonality, why are the values so large, ~2000 °C (Figure 1F and Figure 2F)? How is it calculated?
+Thanks for bringing this to our attention. Temperature Seasonality (TS) is estimated as the SD of mean annual temperatures X 100. For Clarity, we have now done two things. First, we now clarify that TS is measured as the SD of mean annual temperatures (so that values are in the same order of magnitude as other temperature variables). Second, we specify how (TS) is calculated in Table 1.
+
+R1C2. And for precipitation seasonality, is it the standard deviation of the monthly precipitation?
+As for TS, we now explain in table 1 how precipitation seasonality (PS) is estimated. In short, yes, it is calculated as the variation in monthly precipitation. However, instead of the SD in monthly precipitation, we use the Coefficient of Variation (CV) as this is the standard when estimating bioclimatic variables. We also clarify this in the “variable” and “units” columns of Table 1.
+
+R1C3. Table 1: why are the metrics substantially lower than that in the previous version? Is it because now you have used h-block cross validation to address spatial autocorrelation? Besides, why do the deviance explained and R^2 differ so much for some variables like PWM and TAP?
+Yes, the values are lower due to using an h-block cross-validation approach to define the random samples. Furthermore, two points explain the lower deviance-explained when compared to the R2 values. First, adding the variable does not add more explanatory power to the model compared to an intercept-only model (hence the low deviance explained and likely low unadjusted R2. Second, we can interpret the higher R2 as the models built on the training dataset can accurately describe the test dataset, which ensures the idea of model transferability. To ensure these points are clear, we add these points of clarification to table 1 legend.
+
+R1C4. Line 165: what is the threshold of population density to define an occupied grid cell?
+A cell was defined as occupied if our model predicted population densities above 0.2 individuals per 100km2 (the lowest densities in the ethnographic dataset). This point is added to the main text (L162-163) and the methods (L405-406).
+
+R1C5. Figure 4: It would be more informative if you could overlay the localities of the archaeological sites that correspond to each time interval on the predicted population density maps. It can serve as a qualitative comparison. Besides, the current color legend looks weird – the ticks are not at the boundaries of each color segment.
+We explored adding the localities of the archaeological sites to figure 4 but decided not to include these as these create an unnecessary layer of complexity for the figure. We also address the point raised by the reviewer regarding the figure colour legend.
+
+R1C6. Line 110: “most of environmental variable produced models that explaining over 50% of the population density variation” – according to Table 1, the explanatory power of the variables are mostly below 50%.
+We appreciate the reviewer catching this inconsistency coming from a legacy text from the first version. We now changed the sentence, so it does not specify a cut-off value (50%) but the range of mean deviance across the 1000 different models (L110).
+
+R1C7. Line 230: “PET” here should be TAP?
+We consider that here the variable to include is PET, as we are building from the idea of a relationship between productivity and Evapotranspiration. This is the case as the second point relates to energy availability, not climate variability. To further justify this link, we add a reference (L232).
+
+R1C8. Line 234: “PET and TAP were the main limiting factors” – according to Fig. 6, it should be TS and TAP.
+We appreciate the reviewer catching this inconsistency coming from a legacy text from the original submission. We now changed the sentence accordingly.
+
+R1C9. Line 254-255: MWM is no longer used in the prediction.
+We appreciate the reviewer catching this legacy text from the first submission. We have rephased this point (L256).
+
+R1C10. Table 1: “TSeson” and “PREC” – inconsistent with those in the text. And check the footnote of Table 1.
+The acronym was changed as suggested in the table for consistency with the text.
+
+R1C11. Figure 1: The precipitation has been log-transformed, right? Need to specify it.
+We have added this clarification to the corresponding axes in figure 1 and table 1.
+
+R1C12. Figure 3 lower panel: why Precip. Dryiest Month is higher than Precip. Wet-test Month?
+We appreciate the reviewer catching this inconsistency. This was a problem in the code calling the different variables after we removed the Temperature of the Warmest Month, which caused a mismatch between the names and the data plotted in the bottom panels of figure 3. The figure now has corrected this.
+
+R1C13. Figure 5 caption: what is “F-J”?
+We appreciate the reviewer catching this legacy text from the first submission. This text was removed.
+
+Reviewer #2.
+
+R2C1. Authors have successfully revised their manuscript. I have just one follow-up comment because authors might have misunderstood my earlier comment about models having one predictor at a time.
+My intention was not to suggest to add multiple predictors to achieve better predictive ability, but to take into account the fact that the effect of a predictor can change when one takes into account the effect(s) of other potential predictor(s).
+For example, ET and MCM both appear to be important limiting factors and also representing different kinds of limiting factors, ET relating to energy availability and MCM to annual limits. However, these variables are also highly correlated, which already indicates that it will be difficult to tell apart their individual effects. When you include both variables as predictors in the same model it actually turns out that the effect of ET is not statistically significant, response of population density to ET being more or less flat. Similarly, if you add e.g. NPP, ET and TS to the same model their effect (response shapes) are different from their effect when each is the only predictor in the model.
+To me, all this suggests that the real limiting effects of climate variables can be different from those you get when you include these variables separately as predictors.
+However, I don’t know how severe issue this truly is, but I would like to know your thoughts on that. If it really is an issue, one might use PCA to create uncorrelated climate variables and use these as predictors in the models.
+
+We thank the reviewer for his positive feedback on our revision and the clarification of his original point. As we now understand the reviewer’s point, the issue is that significant absolute effects from univariate models would not translate into relative effects determined by multivariate models.
+While we agree with the point, we consider that the multiple regression approach does not translate to the idea of limiting factors we are evaluating here. We argue that multiple regression coefficients indicate effects in the context of other variables (hence contingent on which variables are included or omitted in a model). Therefore, these determine how much each variable contributes to the change in population density. To define which variables set a lower boundary, we require a measure of absolute effects provided by univariate approaches. Focusing on the relative effects would not allow us
+to define limiting factors but which variable(s) contribute the most to changes in population density from the "regional" mean.
+Suppose we could build models for change in population density for each evaluated time bin. In that case, we could define the variable that contributes the most to population density at each time bin. Still, this is not a limiting factor but the variable that contributes the most to changes in population density form the regional average (i.e., the model intercept). Last, there is the issue of translating these relative effects into space, which our approach based on univariate models can do.
+Furthermore, while PCA, or other ordination approaches, could be used here to determine "groups of variables" and the variable most representative of such "group", we will still be looking at relative effects when using the two or three most important axes.
+There also be questions about how suitable it is to use the eigenvectors generated by the ordination under current conditions to "reorganize" past climatic surfaces where the correlations between variables change.
+In summary, we consider that using univariate models, while far from perfect, is a practical approach to assessing the absolute effects of each variable and comparing these between variables over time. Also, it allows us to link our models to a process. All these points are now made in the text (L72-80) and the methods (L364-368).
+
+Reviewer #3.
+I am fully satisfied with the revised version and with the revised manuscript and the changes.
+Thanks for your positive assessment.
+Reviewers’ Comments:
+
+Reviewer #1:
+Remarks to the Author:
+I’m satisfied with the revisions and have no further comments.
+
+Reviewer #2:
+Remarks to the Author:
+While I still slightly disagree with you about the effects of univariate vs multivariate models on the results, I’m happy to do so. It is good that you now explain in the manuscript your choices regarding the matter, so I’m fully satisfied with this revised manuscript.
+
+Best,
+Miikka Tallavaara
+REVIEWER COMMENTS
+
+Reviewer #2 (Remarks to the Author):
+
+While I still slightly disagree with you about the effects of univariate vs multivariate models on the results, I’m happy to do so. It is good that you now explain in the manuscript your choices regarding the matter, so I’m fully satisfied with this revised manuscript.
+
+We appreciate your assessment regarding our revision and your willingness to agree to disagree regarding the effects of univariate vs multivariate models on the results.

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+Changes in limiting factors for forager population dynamics in Europe across the Last Glacial-Interglacial Transition
+
+Alejandro Ordonez ( alejandro.ordonez@bio.au.dk )
+Aarhus University
+Felix Riede
+Aarhus University
+
+Article
+
+Keywords:
+
+Posted Date: December 22nd, 2021
+
+DOI: https://doi.org/10.21203/rs.3.rs-1173690/v1
+
+License: This work is licensed under a Creative Commons Attribution 4.0 International License.
+Read Full License
+
+Version of Record: A version of this preprint was published at Nature Communications on September 6th, 2022. See the published version at https://doi.org/10.1038/s41467-022-32750-x.
+Changes in limiting factors for forager population dynamics in Europe across the Last Glacial-Interglacial Transition
+
+Alejandro Ordonez1,2,4 & Felix Riede1,3
+
+1, Center for Biodiversity Dynamics in a Changing World, Aarhus University
+2, Department of Biology, Aarhus University
+3, Department of Archaeology and Heritage Studies, Aarhus University
+4, Center for Sustainable Landscapes under Global Change, Aarhus University
+
+Abstract
+
+Population dynamics set the framework for human genetic and cultural evolution. For foragers, demographic and environmental changes correlate strongly, although the causal relations between different environmental variables and human responses through time and space likely varied. Building on the notion of limiting factors, namely that the scarcest resource regulates population size, we present a statistical approach to identify the dominant climatic constraints for hunter-gatherer population densities and then hindcast their changing dynamics in Europe for the period between 20kyBP to 8kyBP. Limiting factors shifted from temperature-related variables during the Pleistocene to a regional mosaic of limiting factors in the Holocene. This spatiotemporal variation suggests that hunter-gatherers needed to overcome very different adaptive challenges in different parts of Europe, and that these challenges vary over time. The signatures of these changing adaptations may be visible archaeologically. In addition, the spatial disaggregation of limiting factors from the Pleistocene to the Holocene coincides with and may partly explain the diversification of the cultural geography at this time.
+
+Introduction
+
+As the link between exogenous environmental factors and organismal physiology, demography is vital for understanding evolution, including cultural evolution ¹. The relevance of past demography for understanding culture change in prehistory specifically has long been recognised ²,³. Demographic conditions impinge on cultural transmission ⁴⁻⁶ but are also clearly implicated in the boom-and-bust patterns of population fluctuations – including periodic
+extirpations – suggested to have characterised the demographic histories of prehistoric foragers and incipient farmers in many regions 7–10. Numerous recent studies have focused on the drivers of population expansion to explain the pattern and timing of human colonisation using a variety of ecological comparative approaches 11,12 (but see ref. 13 for a discussion of points of concern of such approaches ). Yet, as foragers have a high intrinsic growth rate, population increase is, in the absence of cultural or environmental constraints, the default demographic trajectory. Evidently, however, past populations did not grow substantially, making it particularly germane to understand the factors that curtailed population growth 14,15. The approach adopted here builds on the central theorem that population sizes would always be regulated by the scarcest resource: the limiting factor 16.
+
+Foragers of the recent past persisted in a wide variety of environments, from the frigid Arctic to tropical rainforests. Each environment offered particular opportunities but also posed particular challenges. While several earlier studies have pointed at temperature or seasonality as key drivers of forager demography at global or continental scales 17,18, the specific factors that would have capped or even depressed population size are likely to have varied in both space and time. Only in understanding these limiting factors can we begin to conduct targeted investigations of how specific forager populations may have overcome them via either population-specific genetic adaptations or the sort of ‘extra-somatic adaptions’19 that are so characteristic of human culture.
+
+In this study, we focus specifically on forager palaeodemography in Europe from the Last Glacial Maximum (Greenland Stadial 2, GS2) to 8000 years before present (BP), a climatically volatile period also known as the Last Glacial-Interglacial Transition 20. Previous studies have identified broad patterns of population growth and expansion using different methods commonly used in ecological analyses 12,21–23. Correlations between temperature and overall population density have been identified, suggesting overall increases in energy availability as the key driver of the increase in human population size following the end of GS2 17. However, regional population collapses have been suggested to have occurred asynchronously and in different places 9,24. This raises the question of which specific limiting factors acted on forager populations and how these limiting factors varied over space and time.
+
+Like many related studies, we begin with the global ethnographic hunter-gatherer dataset originally assembled by Binford and now digitally available 25,26. We couple this to a suite of quantile Generalised Additive Models (qGAMs) to describe changes in maximum (90-
+percentile) population density as a univariate function of environmental variables related to the effect of temperature and precipitation on available energy, annual variability, and productivity. We then use the downscaled centennial average-conditions of each predictor derived from a transient climatic simulation (CCSM3 SynTrace-21 \(^{27}\)) and the best performing univariate qGAM models to hindcast hunter-gatherer population densities between 20ky to 8kyBP. We define the limiting environmental factor as the variable predicting the lowest population density at a given place and time. This approach allows us to query the spatial dynamics of forager limiting factors across the Last Glacial-Interglacial Transition and derive specific hypotheses as to which selection pressures acted most strongly on different forager communities in Late Pleistocene and Early Holocene Europe.
+
+Our analysis demonstrates that the dynamics on limiting factors for forager population densities showed marked differences in space and time. Temperature-related variables were the main limiting factors during the Pleistocene, whereas the Early Holocene was characterised by a regional mosaic of limiting factors. Furthermore, our model reveals geographic differences in the limiting factors between Fennoscandia, Southern, Central, and Eastern Europe. The spatiotemporal variation in limiting factors suggests that hunter-gatherers needed to overcome very different adaptive challenges in different parts of Europe across this period of climatic and environmental change.
+
+Results and discussion
+
+The relation between the environmental factors explored here and population density assessed using qGAMs (Fig. 1) was negative for temperature seasonality, positive for effective temperature, winter/fall temperature, and unimodal for the warmest temperature. Seasonal, monthly, and extreme precipitation, and topographic heterogeneity showed an overall flat trend (supplementary figure S1), yet these also differed from a mean model as determined by the high deviance explained (Table 1).
+
+No single environmental variable explained more than 81% of the population density variation among ethnographic foraging societies (Table 1). However, the performance of more complex multivariate models using machine learning approaches \(^{12}\) or Structural Equation Models \(^{11}\) that combine three or more variables perform only marginally better. The five environmental variables with the highest predictive accuracies (based on the deviance explained; Table 1) were Temperature of the Coldest Month; Temperature Seasonality; Winter Mean Temperature;
+Effective Temperature and Mean Annual Temperature. These variables display high collinearity (Pearson correlations range between 0.83 and 0.96), suggesting that temperature overall best captures the effect of temperature minima and energy availability in relation to forager demography. Two of the variables (Temperature of the Coldest Month and Winter Mean Temperature) represent the effect of extreme cold conditions (= winter mortality) on demographic trends and/or ecological performance \(^{28,29}\). The other two (Mean Annual Temperature, Effective Temperature, Temperature Seasonality) relate to overall energy availability \(^{28}\). These factors are linked to higher environmental productivity and are expected to increase available resources, leading to higher population densities, as already suggested by a plethora of earlier studies \(^{30-32}\). Other variables related to environmental productivity have lower predictive accuracy (explained deviances < 0.79, see Table 1) and lower collinearity with other variables related to energy availability.
+
+Most seasonal temperature and precipitation variables showed some of the lowest explained deviances (Table 1), indicating that seasonal climatology most likely did not impose a direct limit on past forager populations densities in Late Pleistocene/Early Holocene Europe (contra \(^{18}\)). Topographic complexity, a variable shown to influence population density in other studies \(^{11}\), showed only above-average predictive accuracy (Table 1). Like seasonal temperature and precipitation, the topographic complexity effect on population density may be indirect and mediated by variables describing available resources or climate extremes.
+
+Besides the well-known limitations of using foragers of the recent past for reconstructing prehistoric social and demographic conditions \(^{13}\), the issue of model truncation and non-analogy of climatic conditions present themselves as major potential caveats. Climatic non-analogy here refers to the problem of projecting models beyond the domain for which they have been calibrated \(^{33-35}\). Model truncation refers to the incomplete characterisation of hunter-gatherer populations' total climate space \(^{36-38}\) and has been a long noted limitation of ethnographic analogies for prehistoric foragers \(^{39}\). However, it has also been shown that the dataset assembled by Binford is not critically biased in terms of forager niche space \(^{25}\). Likewise, we do not see either truncation or severe non-analogy in a temporal context, as the climate space observed at different moments during the 21-to-8kyBP period show broad overlaps with the climate space used to develop our qGAMs (Fig. 2; supplementary figure S2). This means that our models are not unduly extrapolating into environmental regions where there is no clear indication of how population density changes as a function of evaluated
+climatic variables. By the same token, it is necessary to highlight that the distributions of some paleoclimatic conditions – including all those with the highest predictive values in our models – are skewed towards the lower end of contemporary values. This is especially pronounced for the Pleistocene and variables such as maximum temperatures (Fig. 2), affecting our inference power on changes in population densities at these extremes.
+
+Our models indicate that the estimated human population size in Europe was the lowest at 22kyBP (~294,000 individuals) and largest at 8kyBP (~706,000 individuals). Also, based on our model, we show that at the warmest point of the Greenland Interstadial 1 (~14.7kyBP; GI1), Europe’s human population size estimated by our model was ~617,000 individuals; a number that decreased to ~607,000 individuals at the coldest point of the Greenland Stadial 1 (~11.7kyBP; GS1). Overall occupied area (number of inhabited cells) was 62.4% of the region at the end of the GS2 (~22kyBP). This number increased to ~98.8% during GI 1, decreased to ~97.7% during the GS 1, and reached the highest point (~99.8%) by the mid-Holocene (~8kyBP). Taken at face value, these values are gross overestimation of actual sustained forager land-use at this time. Forager land-use was evidently extensive, including largely empty spaces \(^{40}\). By the same token, these numbers are in line with archaeologically derived trends of overall population growth and expansion during this time (red lines; Fig. 3A).
+
+During the evaluated period, the mean population density in the inhabited area varied between 2.6 and 6.2 persons per 100 km\(^2\) (GS2 = 2.7 p/100 km\(^2\); GI1 = 5.25 p/100 km\(^2\); GS1 = 5.17p/100 km\(^2\); mHol = 6p/100 km\(^2\); Fig. 3A). Although the temporal patterns in average population density derived from our limiting-factor analysis are similar to those of core area estimates by Bocquet-Appel, et al. \(^{21}\) (blue areas, Fig. 3A), these do not match numerically due to our focus on maximum population densities. Moreover, our population density estimates are consistent with those suggested by Tallavaara, et al. \(^{12}\), and more recently Kavanagh, et al. \(^{11}\).
+
+The estimated pattern of human population density (Fig. 3) indicates a population expansion starting almost 3ky after the ice sheet began to recede from its maximum extent 22kaBP. Evaluating the spatially explicit predictions of our model, we find that at the end of the GS2, hunter-gatherer societies in Europe extended as far north as central France, southern Germany and southern parts of modern-day Ukraine (Fig. 4A), a pattern that is consistent with archaeological evidence for the recolonisation of Europe \(^{41-44}\). Our models also suggest that by the end of the GS2, a relatively large proportion of the European continent may have been at least sporadically inhabited (~62%; Fig. 4A-B), with the Mediterranean region up to the north
+of the Alps showing population densities up to 12 individuals/100 km². This restricted occurrence pattern is supported by the archaeological record \(^{40}\). Furthermore, our model indicates a persistent southwest-northeast gradient of decreasing population densities in this southern region, with the most populated areas occurring in the Iberian Peninsula and the Mediterranean region (**Fig. 4A-B**). From this point, the recolonisation of the continent began at ~17kyBP (**Fig. 3**), reaching almost all the way to Scandinavia by the start of GI1 (~14.7kyBP, **Fig. 4c**). Earlier archaeological \(^{45,46}\) and modelling studies \(^{22}\) have already suggested that this colonisation was rapid but also that it proceeded in several steps where both climate and landforms served as barriers to expansion\(^{47}\). Our results expand on this discussion by highlighting that different climate variables limited human dispersal for a given location and that these limits changed over time.
+
+Using our limiting-factor approach, we improve our understanding of demographic mechanisms in Late Pleistocene and Early Holocene European hunter-gatherer societies by highlighting the spatiotemporal changes in the main factor restricting population density (**Fig. 4F-T; and Fig. 5**). Our modelled population density estimates can be linked to regional or local narratives or empirical tests of changes in occurrences and population sizes (e.g., refs. \(^{25,48}\)). The changes in limiting factors suggested in our models can be divided into three periods. The first period spans from the termination of GS2 to the onset of interstadial warming at around 15kyBP. During this period, energy availability measured as effective temperature (ET) was the main factor limiting population density across most of the continent (~50% of cells; **Fig. 5A**). Mean temperature of the warmest month (MWM) was also a strong limiting factor (~30% of cells; **Fig. 5**). However, limitations imposed by winter temperatures, could be also considered as likely limiting factors based on estimates of average conditions at a continental scale (**Fig. 5B**). The range of experienced temperature conditions, represented by ET, can thus be seen as the major limiting factor shaping human population density in Europe between GS2 and the initiation of warming associated with GI1 (**Fig. 5A**). With temperature related variables as the overwhelming limiting factor during this period (**Fig. 5B**), it is likely that the emergence of sophisticated sewing techniques and pyrotechnology \(^{49}\) facilitated the persistence and even moderate expansion of populations at this time.
+
+The second period covers the rapid warming (GI1) as well as cooling (GS1) events between 14.7kyBP to 11.7kyBP. During this period, the importance of ET steadily decreased, and mean temperature of the warmest month (~27% of cells) and temperature seasonality (~23% of cells)
+became the main factors limiting population density (Fig. 5A). The decrease of ET as a limiting factor indicates that during this period of rapid change, it was not temperature but energy availability (due to the link between MWM and productivity) what determined human population density in Europe (Fig. 5B). Our models suggest that overall population densities increased (Fig. 3), although a temporary reduction associated with GS1 cooling is also clear.
+
+The last period encompasses the Early Holocene from its onset at 11.7ky to 8kyBP. Here, temperature of the warmest month increased in importance as the main limiting factor (~50% of cells; Fig. 5A), while the effect of ET became marginal (Fig. 5B). Also, temperature seasonality became a critical limiting factor in many regions (Fig. 4I, J). These patterns indicate a complete shift from experienced temperature conditions to available resources as the main limiting factor of European forager population densities during the Holocene. Such a shift is interesting as the Early Holocene also witnessed a significant reorganisation of forager socio-ecological systems towards more varied use of resources and more pronounced territoriality focused on spatial circumscribed and regionally available resources, and a widespread shift from immediate-return to delayed-return economies. This also aligns with the idea that decreasing territory sizes and more marked boundary formation directly relate to the spatiotemporal dynamics of resource availability \(^{50}\).
+
+The regional disaggregation of patterns in limiting factors shows strong differences between Fennoscandia, Southern, Central, and Eastern Europe (Fig. 4F-J). These patterns are persistent over time, with regional shifts linked to the main feature of temperature change. In Fennoscandia and the British Isles, effective temperature was the main limiting factor for most of the Late Pleistocene. This changed after the onset of the Holocene when seasonal temperatures and precipitation became the dominant limiting factor. In Eastern and Western Europe, effective temperature was the main limiting factor at the end of the GS2 but were replaced by Winter temperature and MWM at the onset of the GI1. During the GS1 and the early Holocene, the main limiting factors where MWM and TS. In southern Europe and especially in the Mediterranean, MWM was the main limiting factor throughout most of the GS2, after which precipitation became the dominant limiting factor.
+
+Our analyses show that the main limiting factors that limited forager population densities across the Last Glacial-Interglacial Transition in Europe changed markedly over time (Fig. 5) and space (Fig. 4F-J). We can now return to the archaeological record with these insights, searching for material culture proxies that may have allowed these past communities to
+overcome these particular limiting factors \(^{51-53}\). While these may have related to water availability (= containers) in the Mediterranean, they are predicted to relate to temperature (= clothing or pyrotechnology) in higher latitudes. Where such technologies are absent in the archaeological record, we can also begin to think about population vulnerability to climatic factors at regional levels. Especially in higher latitudes, population fluctuations may have been pronounced at the sub-centennial scale, to the point of local population extirpations \(^{9,54}\).
+
+Finally, the marked shift in limiting factors at the onset of the Holocene may be indicative of a greater focus on resource access at a regional scale. The spatiotemporal dynamics of resource availability have a direct impact on land-use, mobility, territoriality, and the formation of information networks in foragers \(^{50,55}\). In the Holocene, regional cultural signatures became more pronounced and borders between different cultural zones more strongly articulated. This itself may be seen as a response to the fundamental shift in limiting factors we have identified in our models.
+
+Seeking correlations between environmental variables and past human population densities is not a new endeavour. Following recent calls for more theoretically-informed rather than mere statistical explorations of this relationship \(^{13}\), we highlight that while the environment can be said to strongly constrain forager lifeways, precisely which aspects of the environment do so at any one place and time vary. Our approach offers a robust way to infer the hierarchy of limiting factors and hence provide a spatiotemporal hypothesis for major selection pressures acting on forager populations in the past.
+
+Independent palaeodemographic estimates broadly support our models, but many questions remain. Climate models, for instance, only indirectly capture the interaction of human population dynamics with changes in biodiversity and ecosystem compositions. In addition, the match between modelled population densities and the field-validated presence of Late Pleistocene/Early Holocene populations is not equally robust everywhere. These deviations may stimulate targeted field-testing with the aim of assessing whether and why population densities periodically fell short of or exceeded modelled values. In conjunction with legacy data derived from archives and the literature, such fieldwork can also shed light on the specific strategies these past foragers employed to mitigate the risks posed by specific limiting factors.
+
+Small-scale societies have a variety of adaptive options at their disposal (see ref.\(^{56}\)), most of which can be captured through archaeological proxies \(^{57-59}\). Our limiting factor model here
+serves as an explicit spatiotemporal hypothesis of which risk mitigation measures should be in use at which time and place. The successful identification of these would throw significant new light on the resilience and adaptation – or lack of it – during this climatically and environmentally tumultuous time. Finally, the marked shifts in dominant limiting factors identified in our models map into the results of Late Pleistocene/Early Holocene Earth System tipping points recently discussed by ref. 60. It is likely that, just like analogues anthropogenic warming in the present, these periods of rapid and substantive climatic change would have created challenges for contemporaneous forager populations. In an effort to align archaeological perspectives on climate change with the quandaries of our time (cf. 61 ), future research would be well-advised to focus on such periods of major systemic transitions.
+
+Methods
+
+Models of hunter-gatherers’ population density
+
+We use ethnographic data on terrestrially adapted mobile hunter-gatherers and their climatic space 25 to construct a series of statistical models that predict hunter-gatherer population density based on one of 16 climatic predictors (see Table 1 for rezoning and source). While there are important caveats 13, this approach builds on multiple ethnographic studies showing a link between climate on the one hand and hunter-gatherer diet, mobility, and demography on the other 55,62-66. This statistical connection is the basis of recent studies focused on building complex multivariate models of population dynamics 11,12,67. A benefit of our statistical approach is that it overcomes some significant limitations, such as lack of quantitative population size data based on the archaeological record itself or genetic data, each associated with their own limitations (as reviewed in refs. 2,12).
+
+We omitted four observation classes in the original ethnographic dataset in defining the association between hunter-gatherer population density and climatic predictors. First, we removed observations associated with food producers. Second, sedentary populations or those that reside at a single location for >1 year. Third, populations using aquatic resources (>30% of their dietary protein comes from aquatic environments, as defined in 68,69). Forth, we excluded all observations related to horse-riding populations. The filters employed here correspond to those used by Tallavaara, et al. 12 to maximise the match between ethnographic data and the current knowledge of the highly mobile and overwhelmingly terrestrially oriented lifestyles of Late Pleistocene/early Holocene hunter-gatherers in Europe. The implemented
+filters are less restrictive than those used by other studies that have sought to reconstruct forager population dynamics during this time \(^{70}\) and thus allow for a relatively large degree of behavioural variation. This is important given that increasing evidence of marine and lacustrine resource use is emerging for at least certain times and regions in Late Pleistocene Europe \(^{71-73}\), and that a marked diversification characterises the resource base of early Holocene foragers. Finally, these filters remove any population using external supplements to their hunter-gatherer lifestyle, resulting in a database including information on 127 populations.
+
+We used climate data on historical averages (1970-2000) for 19-climate variables (Table 1) to build our ethnography-based population density models. These were obtained from the Worldclim version 2.1 \(^{74}\) at a 10-ArcMin resolution. Importantly, we used Worldclim data instead of climatic variables directly available from the ethnographic dataset to ensure comparability between climatic variables not in the database (i.e., seasonal means). Equally importantly, this approach prevents any estimation biases due to differences between the data used to define climate-density relations and paleoclimatic surfaces (*see the section estimating human populations density across the Pleistocene-Holocene transition below*) used to estimate population density changes and limiting factors over time.
+
+Initially, we model how population densities of hunter-gatherer communities change along current environmental gradients using Quantile Generalised Additive Models (qGAMS). Modelling such dynamics using qGAMs offers a transparent way to determine the non-linear changes in different percentiles of a response variable (= population densities) to one or multiple environmental variables. This approach is commonly used in the ecological literature to determine the likelihood of occurrence or abundance of a given species under a particular environmental regime \(^{75-79}\) but has never before been applied to human palaeodemography. In contrast to previous studies evaluating past human population density changes, we do not consider the synergies between multiple climatic variables when describing the relation between population densities and climate. Instead, we focus on the individual effects of evaluated variables on the top 90-percentile of population densities to identify the most pronounced limiting factor that acted on palaeodemographic growth. The tendencies in population densities as a function of environmental variables were consistent for different percentiles (see supplementary figures S1).
+
+The population density derived from the ethnographic data followed a log-normal distribution, so these were log-transformed for subsequent analyses, and a gaussian response distribution
+was used in our qGAMs models. Annual, monthly, and seasonal precipitation variables were similarly transformed. The ability of each of the evaluated variables to predict hunter-gatherer population densities was determined using the mean deviance explained (1 - (Residual Deviance/Null Deviance)). These were calculated both for the whole dataset, and using a 1000-fold cross-validation approach (70% random sample for calibration and 30% for validation). All models and prediction accuracy estimates were implemented in R (version 3.6; \(^{80}\)) using the mgcv (version 1.8.24; \(^{81}\)) and qgam (version 1.3.2; \(^{82}\)) packages.
+
+Estimating human populations density across the Pleistocene-Holocene transition
+
+The monthly average temperature and annual precipitation values for Europe for the 21ky to 8kyBP period come from the CCSM3 SynTrace paleoclimate simulations \(^{83}\). These were bias-corrected and downscaled to 0.5° × 0.5° following the methods described by Lorenz, et al. \(^{84}\). The paleoclimatic simulation data used here was originally generated to evaluate changes in European and North American fossil pollen data and vegetation novelty since the Last Glacial Maximum \(^{27}\). Source climate surfaces were aggregated to centennial means from the original decadal averages of monthly values.
+
+Past hunter-gatherer population densities were then predicted for every 30ArcMin cell above sea level. For visualization we also show the areas covered by glaciers using the glacier extent shapefiles derived by PaleoMIST \(^{85}\). To generate 90% percentile population density estimates for each variable/century combination, only those qGAM models parametrised using the ethnographic data and current climatic conditions with cross-validated deviances above 70% were projected into past climatic conditions. As our objective was to establish the climatic variable that imposed the strongest constraints on hunter-gatherer population density at any one time, we determined the variable estimating the lowest 90%-percentile population density for a given cell at each evaluated time-period to be the limiting factor (the scarcest resource that would then limit population size cf. \(^{16}\)). For each evaluated time-period, we summarised the proportion of the available land area (i.e., land area not covered by ice) where each of the assessed variables was determined to be the limiting factor.
+
+We calculated the changes in the percentage of inhabited land area in Europe during the evaluated period by estimating the proportion of the inhabited area, here defined as the region where population densities were above 1 individual per 100km\(^2\). To calculate human-population size in Europe during every century, we multiplied the predicted population density
+in each cell by the land area of the corresponding cell to arrive at per cell population size. We then and summed these values to arrive at the total population size for each century.
+
+Uncertainties in population density, size, occupied area, and limiting factor estimates were determined using a cross-validation approach, where model fitting was iterated 1000 times using a random sample (70%) of the ethnographic and climate data at each time step. Each model was used to hindcast populations densities, estimate the percentage of inhabited land area and human population size, and define the relevant limiting factor. Uncertainty in continental-scale estimates of population densities, occupied area and population size was determined using 95% confidence intervals. The variable selected as the limiting factor in most cross-validation folds was selected as the limiting factor.
+
+Validation of population density estimates
+
+To assess the validity of our population density estimations, we use the International Union for Quaternary Science (INQUA) Radiocarbon Palaeolithic Europe Database v28 86. Changes in the density of records are a useful continental-scale proxy-measurement of prehistoric population size changes and are increasingly used to describe prehistoric human population dynamics trends 87-92. We extracted proxy dates (based on \(^{14}\mathrm{C}\) dates) from the INQUA Radiocarbon Palaeolithic Europe Database, aggregating these to the closest 1000 years. Our goal is to determine the match between our qGAM derived populations densities and prehistoric population occupation derived from the frequencies of radiocarbon dates between 20kaBP and 10kaBP as done by Tallavaara, et al. 12. This approach allowed validating our hindcasted estimates of absolute prehistoric population density since our model is not archaeologically informed, avoiding any possible circularity between model development and validation.
+
+We also used site-based estimates of population density as derived using the Cologne Protocol by Schmidt, et al. 23. We focus on estimates of extended interconnected socio-economic areas (Core Areas) for five unequal time bands between 25kaBP and 11.7KaBP. Although ultimately also based on Binford 25, these estimates present independently derived spatially implicit estimates of population density for the Late Palaeolithic in Europe.
+
+Data availability
+The ‘Binford’ ethnographic database \( ^{25} \) is available from the Database of Places, Language, Culture, and Environment (D-PLACE; https://d-place.org/about). Current and Late Quaternary environmental datasets are publicly available from the associated references. International Union for Quaternary Science (INQUA) Radiocarbon Palaeolithic Europe Database v28 is available from https://pandoradata.earth/am/dataset/radiocarbon-palaeolithic-europe-database-v28. Contemporary climate databases are available form the WorldClim project (https://www.worldclim.org), and late-Pleistocene climate sources are available at https://doi.org/10.6084/m9.figshare.c.4673120.v2.
+
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+Acknowledgements
+
+AO was supported by the AUFF Starting Grant (AUFF-F-2018-7-8). FR’s contribution is part of CLIOARCH, an ERC Consolidator Grant project that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 817564).
+Author contributions
+
+AO: Conceptualization; Methodology; Formal analysis; Resources; writing – original draft, writing – review & editing; Visualization.
+
+FR: Conceptualization; Methodology; writing – original draft, writing – review & editing.
+Table 1. Variables used to generate ethnographic based models of the effect of climate on hunter-gatherer population density and summary of cross-validated deviance explained for the evaluated variables. Estimates correspond to those of a 1000-fold cross-validation approach (1000 samples of 70% training and 30% testing observations) or the full dataset
+
+<table>
+  <tr>
+    <th>Variable name</th>
+    <th>Acronym</th>
+    <th>Units</th>
+    <th>How does the variable determine population density?</th>
+    <th>Cross-validated Deviance explained. Mean [95% CI]</th>
+    <th>Full-dataset Deviance explained</th>
+  </tr>
+  <tr>
+    <td>Effective Temperature *</td>
+    <td>ET</td>
+    <td>C</td>
+    <td>Energy availability</td>
+    <td>0.774<br>[0.8 - 0.826]</td>
+    <td>0.792</td>
+  </tr>
+  <tr>
+    <td>Potential Evapotranspiration**</td>
+    <td>PET</td>
+    <td>mm/yr</td>
+    <td>Energy availability</td>
+    <td>0.751<br>[0.8 - 0.81]</td>
+    <td>0.774</td>
+  </tr>
+  <tr>
+    <td>Mean Annual Temperature</td>
+    <td>MAT</td>
+    <td>C</td>
+    <td>Energy availability</td>
+    <td>0.733<br>[0.7 - 0.777]</td>
+    <td>0.757</td>
+  </tr>
+  <tr>
+    <td>Mean temperature of the Coldest Month</td>
+    <td>MCM</td>
+    <td>C</td>
+    <td>Extreme Events</td>
+    <td>0.798<br>[0.8 - 0.839]</td>
+    <td>0.812</td>
+  </tr>
+  <tr>
+    <td>Mean temperature of the Warmest Month</td>
+    <td>MWM</td>
+    <td>C</td>
+    <td>Extreme Events</td>
+    <td>0.705<br>[0.7 - 0.762]</td>
+    <td>0.737</td>
+  </tr>
+  <tr>
+    <td>Temperature Seasonality</td>
+    <td>TSeason</td>
+    <td>C</td>
+    <td>Annual Variability</td>
+    <td>0.777<br>[0.8 - 0.839]</td>
+    <td>0.811</td>
+  </tr>
+  <tr>
+    <td>Spring Mean Temperature</td>
+    <td>SpMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.789<br>[0.8 - 0.828]</td>
+    <td>0.804</td>
+  </tr>
+  <tr>
+    <td>Summer Mean Temperature</td>
+    <td>SmMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.773<br>[0.8 - 0.817]</td>
+    <td>0.786</td>
+  </tr>
+  <tr>
+    <td>Fall Mean Temperature</td>
+    <td>FMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.725<br>[0.7 - 0.786]</td>
+    <td>0.750</td>
+  </tr>
+  <tr>
+    <td>Winter Mean Temperature</td>
+    <td>WMT</td>
+    <td>C</td>
+    <td>Seasonal trends</td>
+    <td>0.765<br>[0.8 - 0.808]</td>
+    <td>0.782</td>
+  </tr>
+  <tr>
+    <td>Annual precipitation</td>
+    <td>PREC</td>
+    <td>mm/yr</td>
+    <td>Energy availability</td>
+    <td>0.701<br>[0.7 - 0.757]</td>
+    <td>0.712</td>
+  </tr>
+  <tr>
+    <td>Precipitation of the Driest Month</td>
+    <td>PDM</td>
+    <td>mm/month</td>
+    <td>Extreme Events</td>
+    <td>0.746<br>[0.7 - 0.793]</td>
+    <td>0.760</td>
+  </tr>
+  <tr>
+    <td>Precipitation of the Wettest Month</td>
+    <td>PDM</td>
+    <td>mm/month</td>
+    <td>Extreme Events</td>
+    <td>0.77<br>[0.8 - 0.804]</td>
+    <td>0.784</td>
+  </tr>
+  <tr>
+    <td>Precipitation Seasonality</td>
+    <td>PSeson</td>
+    <td>mm/month</td>
+    <td>Annual Variability</td>
+    <td>0.737<br>[0.7 - 0.772]</td>
+    <td>0.748</td>
+  </tr>
+  <tr>
+    <td>Spring Precipitation</td>
+    <td>SpPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.773<br>[0.8 - 0.814]</td>
+    <td>0.788</td>
+  </tr>
+  <tr>
+    <td>Summer Precipitation</td>
+    <td>SmPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.753<br>[0.8 - 0.8]</td>
+    <td>0.779</td>
+  </tr>
+  <tr>
+    <td>Fall Precipitation</td>
+    <td>FPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.7<br>[0.7 - 0.772]</td>
+    <td>0.711</td>
+  </tr>
+  <tr>
+    <td>Winter Precipitation</td>
+    <td>TPREC</td>
+    <td>mm/month</td>
+    <td>Seasonal trends</td>
+    <td>0.774<br>[0.8 - 0.826]</td>
+    <td>0.792</td>
+  </tr>
+  <tr>
+    <td>Topographic Ruggedness Index ***</td>
+    <td></td>
+    <td>m</td>
+    <td>Habitat Heterogeneity</td>
+    <td>0.751<br>[0.8 - 0.81]</td>
+    <td>0.774</td>
+  </tr>
+</table>
+
+* Calculated following \(^{25}\)
+** Calculated following on \(^{93}\).
+*** Calculated following \(^{94}\).
+Figure 1. Quantile Generalised Additive Models (qGAM) describing the relation between environmental factors and population density for 10-percentiles (dashed lines), 50-percentiles (solid lines), and 90-percentiles (doted lines). Here, only the six most limiting factors during the 22kaBP to 8kaBP are presented. Full explorations of evaluated variables presented in Supplementary material S1.
+Figure 2. Convergence between current climatic conditions (hashed density plots) and paleoclimatic conditions at four different periods (coloured density plots). Paleoclimatic periods are Greenland Stadial 2, Greenland Interstadial 1, Greenland Stadial 1, and Holocene. As in Figure 1, only the six most limiting factors during the 22kaBP to 8kaBP are presented. Full explorations of evaluated variables presented in Supplementary material S2.
+Figure 3. Contrast between Europe wide mean population density (top panel), and trends in key environmental variables (bottom). Estimated average population density for all Europe based on a randomization approach (top panel) are compared to archaeological population proxy based on number of calibrated radiocarbon dates for Europe between 21 and 11kyBP based on \(^{12}\) summaries of the Radiocarbon Palaeolithic Europe Database v28 \(^{86}\) (red), and core area (cf. \(^{23}\) population density mean and upper/lower estimates based on the Cologne Protocol (blue). On the bottom panel, plotted variables are: Effective temperature, Minimum temperature of the Coldest Month, and Maximum temperature of the Warmest Month.
+Figure 4. Estimated human population density and range (areas where population density > 1 individual per 100km^2) (A-E) and factors limiting population density (F-J) across Europe for selected times during the 22ky to 8kyBP period. (A, F) Greenland Stadial 2; (B, G) Greenland Interstadial 1; (C, H) Greenland Stadial 1 warming terminations (D, I) Holocene initiation; (E, J) Mid-Holocene. Areas in grey scale represent the glacier extent as derived by PaleoMIST 85.
+Figure 5. Proportion of the ice-free area of Europe where each variable was estimated to be the factor limiting population density (A); and estimated population size based on the mean environmental conditions for each century (B). In both panels, only the six variables with the highest percentages of cells where the variable is the limiting factor are presented.
+Supplementary material S1 Quantile Generalised Additive Models (qGAM) describing the relation between the six most important environmental factors explored and population density for 10-percentiles (dashed lines), 50-percentiles (solid lines), and 90-percentiles (doted lines). Title acronyms as in Table 1.
+Supplementary material S2. Overlap between current climatic conditions (hashed density plots) used for model building and paleoclimatic databases (coloured density plots) used to hindcast human population density for all 19-climatic variables used. Title acronyms as in Table 1.

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+Reference-free and cost-effective automated cell type annotation with GPT-4 in single-cell RNA-seq analysis
+
+Zhicheng Ji
+zhicheng.ji@duke.edu
+
+Duke University   https://orcid.org/0000-0002-9457-4704
+Wenpin Hou
+Columbia University   https://orcid.org/0000-0003-0972-2192
+
+Brief Communication
+
+Keywords:
+
+Posted Date: May 2nd, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-2824971/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 Methods on March 25th, 2024. See the published version at https://doi.org/10.1038/s41592-024-02235-4.
+Reference-free and cost-effective automated cell type annotation with GPT-4 in single-cell RNA-seq analysis
+
+Wenpin Hou1,† and Zhicheng Ji2,†
+
+1Department of Biostatistics, The Mailman School of Public Health, Columbia University, New York City, NY, USA
+2Department of Biostatistics and Bioinformatics, Duke University School of Medicine, Durham, NC, USA.
+†Corresponding author. E-mail: wh2526@cumc.columbia.edu; zhicheng.ji@duke.edu
+
+ABSTRACT
+
+Cell type annotation is an essential step in single-cell RNA-seq analysis. However, it is a time-consuming process that often requires expertise in collecting canonical marker genes and manually annotating cell types. Automated cell type annotation methods typically require the acquisition of high-quality reference datasets and the development of additional pipelines. We demonstrate that GPT-4, a highly potent large language model, can automatically and accurately annotate cell types by utilizing marker gene information generated from standard single-cell RNA-seq analysis pipelines. Evaluated across hundreds of tissue types and cell types, GPT-4 generates cell type annotations exhibiting strong concordance with manual annotations, and has the potential to considerably reduce the effort and expertise needed in cell type annotation.
+
+Main
+
+In single-cell RNA-sequencing (scRNA-seq) analysis1–2, cell type annotation is a fundamental step to elucidate cell population heterogeneity and understand the diverse functions of different cell populations within complex tissues. Standard single-cell analysis software, such as Seurat3 and Scanpy4, routinely employ manual cell type annotation. These software tools assign single cells into clusters by cell clustering and conduct differential analysis to identify differentially expressed genes across cell clusters. Subsequently, a human expert compares canonical cell type markers with differential gene information to assign a cell type annotation to each cell cluster. This manual annotation approach requires prior knowledge of canonical cell type markers in the given tissues and is often laborious and time-consuming. Although several automated cell type annotation methods have been developed5–13, manual cell type annotation using marker gene information remains widely used in scRNA-seq analysis14–28.
+
+Generative Pre-trained Transformers (GPT), including GPT-3, ChatGPT, and GPT-4, are large language models trained on massive amounts of data and capable of generating human-like text based on user-provided contexts. Recent studies have demonstrated the competitive performance of GPT models in answering biomedical questions29–32. Thus, we hypothesize that GPT-4, one of the most advanced GPT models, has the ability to accurately identify cell types using marker gene information. GPT-4 will potentially transform the manual cell type annotation process into a semi-automated procedure, with optional help from human experts to fine-tune GPT-4-generated annotations (Figure 1a). Compared to other automated cell type annotation methods that require building additional pipelines and collecting high-quality reference datasets, GPT-4 offers cost-efficiency and seamless integration into existing single-cell analysis pipelines, such as Seurat3 and Scanpy4. The vast amount of training data enables GPT-4 to be applied across a wide variety of tissues and cell types, overcoming the limitations of other automated cell type annotation methods restricted to specific reference datasets. Additionally, the chatbot-like nature of GPT-4 allows users to easily adjust annotation granularity and provide feedback for iterative answer improvement (Figure 1a-b)31.
+
+To validate the hypothesis, we systematically assessed GPT-4’s cell type annotation performance across five datasets, hundreds of tissue types and cell types, and in both human and mouse (Figure 2a). Computationally identified differential genes in four scRNA-seq datasets (Azimuth by HuBMAP22, Human Cell Atlas (HCA)17, Human Cell Landscape (HCL)19, and Mouse Cell Atlas (MCA)18), and canonical marker genes identified through literature search in one dataset (literature)17, were used as inputs to GPT-4. Cell type annotation for HCL and MCA was performed and evaluated once by aggregating all tissues, similar to the original studies. In other studies, cell type annotation was performed and evaluated within each tissue. GPT-4 was queried using prompts similar to Figure 1b, and its cell type annotations were compared to those provided by the original studies. The comparison results were classified as “fully match” if GPT-4 and manual annotations refer to the same cell type, “partially match” if the two annotations refer to similar but distinct cell types (e.g., monocyte and macrophage), and “mismatch” if the two annotations refer to different cell types (e.g., T cell and macrophage). If the granularity of the manual annotation
+exceeded GPT-4 annotation, GPT-4 was asked to give more specific annotations (Figure 1b). Figure 2b shows an example of evaluating GPT-4 cell type annotations in a human prostate tissue literature search dataset. Supplementary Table 1 contains all cell type annotations generated manually or by GPT-4 across different tissue types and datasets, as well as agreement between manual and GPT-4 annotations.
+
+The performance of cell type annotation can be affected by the number of top differential genes used as reference. So we first assessed whether the number of top differential genes would affect the performance of GPT-4 cell type annotation. To facilitate comparison, we assigned agreement scores of 1, 0.5, and 0 to cases of “fully match”, “partially match”, and “mismatch” respectively, and calculated the average scores across cell types within a tissue or dataset. The comparison was only performed in HCA, HCL, and MCA datasets, as full lists of differential genes were available. Figure 2c shows that GPT-4 has the best agreement with human annotation when using the top 10 differential genes, and using more differential genes may reduce agreement. A plausible explanation is that human experts may only rely on a small number of top differential genes if they already provide a clear cell type annotation. In subsequent analyses, we used GPT-4 cell type annotation with the top 10 differential genes for HCA, HCL, and MCA datasets.
+
+In almost all studies and tissues, GPT-4 annotations fully or partially match manual annotations for at least 75% of cell types (Figure 2d), demonstrating GPT-4’s ability to generate cell type annotations comparable to those of human experts. The agreement is highest for marker genes identified through literature search, with GPT-4 annotations fully matching manual annotations for approximately 75% of cell types. The agreement decreases in marker genes identified by differential analysis, which may be attributable to a lower proportion of canonical marker genes being identified as top differential genes. We then grouped cell types into major cell categories according to the manual cell type annotations (Figure 2e, Supplementary Table 1). The agreement between GPT-4 and manual annotations is highest among cell categories that are more homogeneous (e.g., erythroid cells and adipocytes), and lowest among cell categories that are more heterogeneous (e.g., stromal cells).
+
+The low agreement between GPT-4 and manual annotations in some cell types does not necessarily imply that GPT-4 annotation is incorrect. For instance, cell types classified as stromal cells include fibroblasts and osteoblasts, which express type I collagen genes, as well as chondrocytes, which express type II collagen genes. For cells manually annotated as stromal cells, GPT-4 assigns cell type annotations with higher granularity (e.g., fibroblasts, osteoblasts, and chondrocytes), resulting in partial matches and a lower agreement. For cell types manually annotated as stromal cells, the type I collagen genes appear in the differential gene lists in 80% of cases annotated as fibroblast or osteoblast by GPT-4 and in 0% of cases annotated as chondrocyte by GPT-4 (Figure 2f). This agrees with prior knowledge and the pattern observed in cell types manually annotated as chondrocyte, fibroblast, and osteoblast (Figure 2f), suggesting that GPT-4 provides more accurate cell type annotations than manual annotations for stromal cells.
+
+We further tested the performance of GPT-4 when dealing with more complicated situations in real data analysis (Figure 1c). We first tested GPT-4’s ability to identify a cell cluster representing a mixture of cell types, which may occur when a cluster contains a large number of doublets or has low-resolution cell clustering. We generated simulated datasets by combining canonical markers from two distinct cell types in half of the instances and using canonical markers from a single cell type in the other half (Methods). GPT-4 discriminated between single and mixed cell types with an average accuracy of 94% (Figure 2g). We then tested GPT-4’s ability to identify new cell types with marker genes not documented by existing literature. We created simulation datasets using randomly selected genes as cell type markers in half of the cases and canonical markers from a single cell type in the other half (Methods). GPT-4 is able to differentiate known and unknown cell types with an average accuracy of 100% (Figure 2h). We also tested the reproducibility of GPT-4 annotations leveraging results in previous simulation studies (Methods). On average, GPT-4 generated identical annotations for the same cell type markers in 91.2% of cases (Figure 2i), showing a high level of reproducibility. In conclusion, GPT-4 exhibits robust performance across various scenarios encountered in real data analysis.
+
+In conclusion, our findings demonstrate a high level of agreement between cell type annotations generated by GPT-4 and by human experts. Remarkably, GPT-4 exhibits higher accuracy in annotating specific cell types. GPT-4 can be employed as a dependable tool for automated cell type annotation of single-cell RNA-seq data, substantially reducing the time and effort required for manual annotation.
+
+Methods
+
+Dataset collection
+For the HuBMAP Azimuth project, manually annotated cell types and their marker genes were downloaded from the Azimuth website (https://azimuth.hubmapconsortium.org/). Azimuth provides cell type annotations for each tissue at different granularity levels. We selected the level of granularity with the fewest number of cell types, provided that there were more than 10 cell types within that level.
+
+For HCA17, HCL19, and MCA18, manually annotated cell types and corresponding differential gene lists were downloaded directly from the original studies. Lists of marker genes through literature search and the corresponding cell types were
+downloaded from the HCA study\(^{17}\), and only cell types with at least 5 marker genes were used.
+
+Gene set preparation and GPT-4 prompts
+Before using GPT-4 to identify cell types, one needs to first prepare a list of top differential genes for each cell cluster. For example, one can use the following R code to extract gene lists of top 10 differential genes obtained from the standard Seurat pipeline. In the extracted results, each row is a list of differential genes for one cell cluster, separated by ','.
+
+# d is the differential gene table generated by Seurat ordered by p-values
+cat(tapply(d$gene,list(d$cluster),function(i) paste0(i[1:10],collapse=',')),sep='\n')
+
+The gene lists used in this study were prepared using customized code.
+
+GPT-4 was accessed by visiting the ChatGPT website (https://chat.openai.com/). The “Mar 23” version of GPT-4 was used for this study. The following words were pasted on top of the differential gene lists and used as the initial prompt for GPT-4. The word “prostate” in the following prompt was replaced with the appropriate tissue names when annotating cell types for each tissue.
+
+Identify cell types of human prostate cells using the following markers.
+Identify one cell type for each row. Only provide the cell type name.
+
+GPT-4 returned a list of cell type names for each query. The following prompt was used to increase the granularity of cell type annotations when needed.
+
+Be more specific
+
+To annotate cell clusters that could be a mixture of multiple cell types, the following words are added to the prompt.
+
+Some could be a mixture of multiple cell types.
+
+To annotate cell clusters that cannot be characterized by known cell type markers and are potentially new cell types, the following words are added to the prompt
+
+Some could be unknown cell types.
+
+Finally, the following prompt can be used to convert the list of cell type annotations generated by GPT-4 into R code that directly creates a vector of cell type names in R.
+
+Use "'','" to concatenate all results into a single sentence.
+Put "c('\" in front of the sentence and "\')" after the sentence
+
+Simulation studies and reproducibility
+To generate simulation datasets of mixed cell types, we used the canonical cell type markers through literature search of human breast cells. In each simulation iteration, ten mixed cell types were generated. The marker genes for each mixed cell type were created by combining the marker gene lists of two randomly selected cell types. Additionally, we incorporated the original cell type markers of ten randomly chosen cell types as negative controls of single cell types. This entire simulation process was repeated five times. Subsequently, GPT-4 was queried using these simulated marker gene lists, and its performance in differentiating between mixed and single cell types was assessed.
+
+To generate simulation datasets of unknown cell types, we compiled a list of all human genes using the Bioconductor org.Hs.eg.db package\(^{33}\). In each simulation iteration, ten simulated unknown cell types were generated. The marker genes for each unknown cell type were produced by combining ten randomly selected human genes. Additionally, we included the literature-based cell type markers of ten randomly chosen human breast cell types as negative controls of known cell types, similar to the previous simulation study. This entire simulation process was repeated five times. Subsequently, GPT-4 was queried using these simulated marker gene lists, and its performance in distinguishing between known and unknown cell types was assessed.
+
+We assessed the reproducibility of GPT-4 responses by leveraging the repeated querying of GPT-4 with identical marker gene lists of the same negative control cell types in both simulation studies. For each cell type, reproducibility is defined as the proportion of instances in which GPT-4 generates the most prevalent cell type annotation. For instance, in the case of vascular endothelial cells, GPT-4 produces "endothelial cells" 8 times and "blood vascular endothelial cells" once. Consequently, the most prevalent cell type annotation is "endothelial cells," and the reproducibility is calculated as \( \frac{8}{9} = 0.89 \).
+Acknowledgments
+Z.J. was supported by the National Institutes of Health under Award Number 1U54AG075936-01. The manuscript was polished by GPT-4.
+
+Author contributions
+All authors conceived the study, conducted the analysis, and wrote the manuscript.
+
+Competing interests
+All authors declare no competing interests.
+a
+
+single-cell RNA-seq (scRNA-seq) datasets
+standard processing pipeline (e.g., Seurat or Scanpy)
+cell clusters and differential genes
+human expert manual annotation
+canonical marker collection
+manual annotation
+GPT-4 automated annotation
+GPT-4 automated annotation
+Optional:
+fine tuning by human expert
+other automated cell type annotation software
+reference data collection
+building and running pipelines
+
+<table>
+  <tr>
+    <th>requires strong biology expertise</th>
+    <th>no biology expertise required</th>
+    <th>no biology expertise required</th>
+  </tr>
+  <tr>
+    <td>no coding expertise required</td>
+    <td>no coding expertise required</td>
+    <td>requires medium coding expertise</td>
+  </tr>
+  <tr>
+    <td>reference scRNA-seq not needed</td>
+    <td>reference scRNA-seq not needed</td>
+    <td>may need to collect reference scRNA-seq</td>
+  </tr>
+  <tr>
+    <td>significant effort required</td>
+    <td>minimum effort required</td>
+    <td>moderate effort required</td>
+  </tr>
+  <tr>
+    <td>fits into existing pipeline</td>
+    <td>fits into existing pipeline</td>
+    <td>standalone pipeline</td>
+  </tr>
+  <tr>
+    <td>tissue type not restricted</td>
+    <td>tissue type not restricted</td>
+    <td>tissue types restricted to reference data</td>
+  </tr>
+  <tr>
+    <td>allows adjusting granularity</td>
+    <td>allows adjusting granularity</td>
+    <td>single granularity level</td>
+  </tr>
+</table>
+
+b
+Identify cell types of human prostate cells using the following markers. Identify one cell type for each row. Only provide the cell type name.
+
+CR2, CD24, FAS, CXCR3, CD1c
+KLK3, KRT8, KLK2, MSMB, ACPP, KLK1, KLK4
+MMRN1, FLT4, RELN, CCL21, PROX1, LYVE1
+TPSAB1, FCER1A, TPSB2, KIT, CD69, HDC
+ACTA2, MYO1B, ACTA2, ANPEP, DES, MCAM, PDGFBR, CSPG4
+
+1. Dendritic cells
+2. Luminal epithelial cells
+3. Lymphatic endothelial cells
+4. Mast cells
+5. Pericytes
+
+Be more specific
+
+1. Myeloid Dendritic cells (mDCs)
+2. Prostate Secretory Luminal Epithelial cells
+3. Prostate Lymphatic Endothelial cells
+4. Prostate Tissue-resident Mast cells
+5. Prostate Vascular Pericytes
+
+c
+Identify cell types of human prostate cells using the following markers. Identify one cell type for each row. Only provide the cell type name. Some could be a mixture of multiple cell types. Some could be unknown cell types.
+
+KLK3, KRT8, KLK2, MSMB, ACPP, KLK1, KLK4
+MMRN1, FLT4, RELN, CCL21, PROX1, LYVE1
+CD88, IL7RC, CD3D, CD3E, COSL, ACTA2, MYO1B, ACTA2, ANPEP, PDGFBR, CSPG4
+DIX4A3BLOC05B5T19REMTND1P30LLOC160579682,YAGLN2ZNF698,ZNP677COILP1
+
+1. Prostate epithelial cells
+2. Lymphatic endothelial cells
+3. T-cell and smooth muscle cell mixture
+4. Unknown cell type
+
+Figure 1. a, Diagram comparing cell type annotations by human experts, GPT-4, and other automated methods. b, An example showing GPT-4 prompts and answers for annotating human prostate cells with increasing granularity. c, An example showing GPT-4 prompts and answers for annotating single cell types (first two cell types), mixed cell types (third cell type), and new cell types (fourth cell type).
+<table>
+  <tr>
+    <th>Dataset</th>
+    <th>Species</th>
+    <th>Number of tissues</th>
+    <th>Number of cell types</th>
+    <th>Gene list source</th>
+  </tr>
+  <tr>
+    <td>Azimuth</td>
+    <td>Human</td>
+    <td>11</td>
+    <td>276</td>
+    <td>Differential analysis</td>
+  </tr>
+  <tr>
+    <td>Human Cell Atlas (HCA)</td>
+    <td>Human</td>
+    <td>7</td>
+    <td>72</td>
+    <td>Differential analysis</td>
+  </tr>
+  <tr>
+    <td>Human Cell Landscape (HCL)</td>
+    <td>Human</td>
+    <td>60*</td>
+    <td>101</td>
+    <td>Differential analysis</td>
+  </tr>
+  <tr>
+    <td>literature (from HCA)</td>
+    <td>Human</td>
+    <td>7</td>
+    <td>30</td>
+    <td>Literature search</td>
+  </tr>
+  <tr>
+    <td>Mouse Cell Atlas (MCA)</td>
+    <td>Mouse</td>
+    <td>51*</td>
+    <td>65</td>
+    <td>Differential analysis</td>
+  </tr>
+</table>
+
+* Cell type annotations were done by aggregating across tissues in the original studies
+
+<table>
+  <tr>
+    <th>Manual annotation</th>
+    <th>GPT-4 answer</th>
+    <th>Agreement</th>
+  </tr>
+  <tr>
+    <td>Adipocyte</td>
+    <td>Adipocytes</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>B cell_memory</td>
+    <td>B cells</td>
+    <td>Partial</td>
+  </tr>
+  <tr>
+    <td>Fibroblast</td>
+    <td>Fibroblasts</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Luminal Epithelial</td>
+    <td>Luminal epithelial cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Lymphatic Endothelial</td>
+    <td>Lymphatic endothelial</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Macrophage</td>
+    <td>Macrophages</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Mast Cell</td>
+    <td>Mast cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Pericyte</td>
+    <td>Pericytes</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Smooth Muscle</td>
+    <td>Smooth muscle cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>T cell</td>
+    <td>T cells</td>
+    <td>Full</td>
+  </tr>
+  <tr>
+    <td>Vascular Endothelial</td>
+    <td>Endothelial cells</td>
+    <td>Partial</td>
+  </tr>
+</table>
+
+![A violin plot showing proportions of cell types across different datasets and tissues](page_184_613_495_312.png)
+
+![A bar chart showing agreement levels between manual and GPT-4 annotations](page_1012_613_495_312.png)
+
+Figure 2. Evaluation of cell type annotation by GPT-4. **a**, Datasets included in this study **b**, Agreement between original and GPT-4 annotations in identifying cell types of human prostate cells. **c**, Averaged agreement score (y-axis) and the number of top differential genes (x-axis) in HCA, HCL, and MCA datasets. **d**, Proportion of cell types with different levels of agreement in each study and tissue. Averaged agreement scores are shown as black dots. **e**, Proportion of cell types with different levels of agreement in each cell category. Averaged agreement scores are shown as black dots. **f**, Proportion of cell types that include type I collagen gene in the differential gene lists. The cell types are either classified as stromal cells by manual annotations and fibroblast, osteoblast, or chondrocyte by GPT-4 annotations, or classified as fibroblast, osteoblast, or chondrocyte by manual annotations. **g**, Proportion of cases where GPT-4 correctly identifies mixed and single cell types. Each dot represents one round of simulation. **h**, Proportion of cases where GPT-4 correctly identifies known and unknown cell types. Each dot represents one round of simulation. **i**, Reproducibility of GPT-4 annotations. Each dot represents one cell type.
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+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• supptable1.csv

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+    "img_path": "images/Figure_5.jpg",
+    "caption": "Response Figure 5: A, Surface plasmon resonance (SPR) indicated binding of So(d18:1) to the HIF2a. B, Surface plasmon resonance (SPR) indicated no binding of So(d18:1) to the mutant HIF2a.",
+    "bbox": [],
+    "page_idx": 15
+  }
+]

02624773f6e6ce56158b53f0fcddcdef4027c464f514126d8dae690687431871/peer_review/peer_review.md

@@ -0,0 +1,386 @@
+Peer Review File
+
+Sphingosine d18:1 Promotes Nonalcoholic Steatohepatitis by Inhibiting Macrophage HIF-2α
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+This first section of this manuscript describes the identification of a specific lipid (sphingosine [So]18:1) whose plasma levels are associated with NASH progression (in humans and mouse models). The second section is a series of mechanistic studies aimed at understanding how So18:1 promotes NASH progression. The conclusion is that So18:1 promotes NLRP3 activation in macrophages through affecting Hif2a levels/activity. There are many aspects of this data set that are interesting and that have the potential to be an important contribution to the field, but I think key additional control experiments are required to support the conclusions.
+
+The data presented in Figure 1 and Supp Figure 1 on the identification of So18:1 is fairly compelling and sets up the subsequent mechanistic work well. However, the subsequent mechanistic studies fall short of proving the thesis of the manuscript. The major concern (across many of the studies) is the nature of the vehicle used when administering So18:1. It is not explicitly stated what this is, but in my opinion the authors should be using the other lipids they ID from the metabolomics, but that are not associated with NASH progression. Only by doing this can they be sure that the effects they see across many of the experiments (Figure 2, Figure 3, Figure 6) are due to specific effects of So18:1. Such evidence would provide a far more compelling argument that So18:1 is a specific driver of NASH progression.
+
+The HIF2a KO and overexpression studies in Figure 3 and 4 are also quite convincing, but how this phenotype is related to So18:1 is not clear. For example, the authors do not provide evidence that the expression of Hif2a is decreased in macrophages from So18:1 treated mice or NASH mouse models. Finally, the suggestion that the So18:1 and Hif2a effects are driven through NLRP3 inflammasome activation are overstated, particularly in vivo.
+
+My specific comments are also outlined below.
+
+Line 32, sphingomyelins are the predominant sphingolipid, please add to your statement.
+
+For the heat maps in Figure 1 it should be stated what the values are, are these z-scores, concentrations, something else, it is not known from the figure or legend. I would personally move the data in Sup Figure 1D, 1E and 1J into the main text, this is important and strong evidence.
+Line 70. I think this is a one-sided interpretation. One could equally postulate that because the liver So18:1 levels decrease over the course of the CDAA-HFD, and that liver enzymes also increase over this time, perhaps the increased plasma levels are the result of hepatocyte damage and release into the circulation. I’m not saying this is the case, but a more balanced interpretation may be warranted.
+
+There is a lack of description of how the sub-class of disease progression (e.g. the data in Supp 1B) data is obtained. Is this a re-classification of the NASH group, I assume so, but please be more descriptive in the text. Also, I would like to see the concentration data (i.e. that shown in Supp Figure 1D) for the other Sa and So species that you show in the heat map. They all look to change to a very similar extent. Also, I would re-format the data in Supp Figure 1B/C to look like Supp Figure 1E. Collectively, these changes will make it easier for the reader to see that while a number of sphingolipids changes in NASH, only So18:1 actually increases during disease progression.
+
+Line 83. The conclusion is not convincing based on the data. Indeed, from a statistical point of view, they are not different. The conclusion should be tempered.
+
+Line 88. ‘accepted’ is rather an odd phrasing. Perhaps just say mice ‘were injected with’.
+
+The data in Figure 2 seem reasonably robust, but I have a number of issues that I think should be addressed. (i) what is the nature of the vehicle? It does not say in the methods what this is; indeed, the methods only state that the So treated group were injected with So everyday, while there is no mention of the vehicle treated group. So, are these mice not being injected at all? If they are, what are they receiving? (ii) Relatedly, I’d very much like to see other lipids that the authors identified in the data in Figure 1 being used as controls – i.e. use lipids that are not associated with NASH progression. This would present a far stronger case that So18:1 has specific effects. (iii) You need to perform the metabolomics to show that your injections are increasing the plasma concentrations of So18:1, and also to what extent, they may be increased to levels far beyond what you see endogenously. Ideally, you want your So18:1 injections to increase plasma So18:1 within pathological levels. (iii) What is happening to lipid levels in the liver following these injections? Collectively, I think several additional experiments are required to convincingly show that So18:1 specifically has the claimed effects.
+
+Figure 3A,B. n numbers are very low, this is obviously from a single experiment. I would like to see a greater sample number used. Additionally, my comments above about the vehicle control apply here also. So, I would like to see the authors using the other So and Sa species they identify as being increased in NASH, but not increasing during disease progression, to show that the specific pro-inflammatory/immune recruitment effects they see are specifically due to So18:1.
+
+Figure 3E-I. Same comment as above, repeat with other lipids to show the effect is specific to So18:1.
+Line 149 seems to be the first mention of the GAN diet. Please define.
+
+Line 148-149. You are not testing this. You are only determining if Hif2a contributes to NASH. You don’t present any evidence that the deletion of Hif2a exacerbates NASH due to inflammasome activation. To support such a claim you should at least show that various inflammasome components, within macrophages, are increased in the Hif2a KO model – yes, il-1b is up a bit but so are lots of other inflammatory markers and this measure is just in a whole liver homogenate, not isolated cells. While inflammatory pathways are activated in Hif2a KO cells, figure 3E shows a large reduction in several markers of M2 macrophages, this is also likely to be a major reason for the potentiated inflammation in the Hif2a KO model – i.e. you are altering the balance of pro/anti-inflammatory macrophages. Furthermore, while you show that So18:1 decreases Hif2a in vitro, you do not show that either So18:1 administration in vivo or the CDAA-HFD diet reduced Hif2a in macrophages in vivo. Nor do you show that blocking NLRP3 inflammasome activity can reverse the effects described in Figure 4.
+
+Line 221, I’m again concerned that a solvent is not the most appropriate control. Your whole thesis is that So18:1, and not other closely related lipids, promote NASH progression. Therefore, the best control would be the other related lipids. If you could show that So16:1 and some of the Sn lipids do not have the same effects as So18:1, this would present a far more compelling argument that So18:1 has specific properties not shared by other related lipid species.
+
+Your central argument is that So18:1 decrease Hif2a protein levels (e.g. figure 2F). Yet looking at the input controls for your IP experiment in Figure 6C, it does not appear to do so. What is the reason for this apparent discrepancy?
+
+Line 229. You somewhat establish this in vitro (see my previous comments about appropriate lipid controls), you do not provide evidence that (a) hif2a is reduced in vivo, either in response to So18:1 or in the NASH model, (b) you don’t demonstrate that the effects of manipulating Hif2a expression (KO/over-expression) on NASH are via effects on NLRP3.
+
+Reviewer #2 (Remarks to the Author):
+
+In the current study, Xia et al. reported the association between plasma sphingosine d18:1 [So(d18:1)] levels and the severity of NASH. They also found that So(d18:1) aggravated the NASH phenotype in mice. Regarding the mechanism, they studied the effects of So(d18:1)-promoted activation of the NLRP3 inflammasome by inhibiting HIF-2a activity in macrophages. They found that So(d18:1) directly bound
+with HIF-2a and inhibited the interaction of HIF-2a and ARNT. This study integrates clinical patient data and animal experiments. In general, this study provides a novel serological indicator for NASH diagnosis and novel targets for NASH treatment. However, there are several critical issues that should be addressed.
+
+1. So(d18:1) increased ALT and AST levels in CADD-HFD-fed mice. Did So(d18:1) directly promote hepatocyte injury during NASH?
+
+2. The possibility that So(d18:1) directly acts on other liver cell types should be discussed.
+
+3. Did So(d18:1) treatment change ceramide and S1P levels in macrophage?
+
+4. In Line 116, the author mentioned So(d18:1) promoted macrophage activation. To support this statement, did So(d18:1) upregulate inflammatory gene expression from the RNA-seq data?
+
+5. Could macrophage-specific HIF-2a overexpression confront the effects of So(d18:1) on NASH in vivo? This is important because So(d18:1) may also act on other cell types, and this experiment could demonstrate the central role of macrophages in this process.
+
+6. Regarding to “HIF-2α plasmid with two proven missense mutations in the pocket which disabled other molecules to bind with HIF-2α”, the mutations need to be described in detail and the related literature should be cited.
+
+7. The direct binding of So(d18:1) with HIF-2a is an important mechanism of this study. However, the authors only provide docking model to predict the direct binding, which is not enough. The evidence of direct binding of So(d18:1) with HIF-2a should be provided (such as SPR or ITC). It will be helpful if the disturbed binding of HIF-2a with mutated HIF-2a is also proven by experiments.
+
+8. From the input of Figure 6C, So(d18:1) did not influence the protein level of HIF-2a. Was HIF-2a exogenous overexpressed in this experiment? If so, this should be clearly described in Figure legends or in method section.
+
+9. Regarding Figure 6F, the figure shows that when HIF-2a was overexpressed, So(d18:1) increased luciferase activity. However, the authors describe the data as “similar to the fluorescence values of the empty plasmid” in line 251. In addition, in the same paragraph, there seems to be 4 groups of treatment in Figure 6F, however, the authors only showed 2 groups. Pleased check this result.
+
+Minor
+
+1. Figure legend of Fig. 2, “Il1b in J, statistical analysis was performed using two tailed Mann-Whitney U-tests”. Il1b is in panel K not J.
+
+2. For the western blot of HIF-2a, why there are two bands in Figure 3F and one band in Figure 6C?
+Reviewer #3 (Remarks to the Author):
+
+In this study, Jialin Xia et al. found that sphingosine d18:1 (So(d18:1)) is elevated in the plasma of NASH patients as well as in the plasma of mice subjected to a NASH mouse model. Authors claim that this So(d18:1) elevation results in liver inflammation and fibrosis and that the pro-fibrotic and pro-inflammatory potential of sphingosine d18:1 rely on its ability to block HIF2a and HIFbeta heterodimerization and therefore HIF2 activity. Along this line authors clearly show that macrophage HIF2 inactivation leads to liver inflammation and fibrosis. These data are interesting but the following comments should be addressed.
+
+1.- In Figure 3F, authors should run in parallel samples of BMDMs obtained from LysM-HIF2aLSL/LSL and HIF2aLysM mice in order to confirm that the two bands shown in the western blot correspond to HIF2a.
+
+2.- Authors should show whether gene expression of Arginase 1, VEGF-a, Spint, Depdc7 and IL-10 are elevated in LysMHIF2aLSL/LSL BMDMs or reduced in LysMHIF2a deficient BMDMs.
+
+3.- Authors show that So(d18:1) blunted HIF2a activity in BMDMs. But is this also in So(d18:1)-treated mice? Authors should try to perform liver immunostaining using antibodies against HIF2 (or HIF2 target genes) in costaining with macrophage markers in order to evaluate whether macrophage HIF2 expression/activity is really reduced in macrophages of So(d18:1)-treated mice in vivo. Or alternatively assess this point in macrophages isolated from the liver of control and So(d18:1)-treated mice. If these experiments reveals a partial decline of HIF2a, authors might assess whether macrophage-HIF2 heterozygous mice also results in increased liver inflammation and fibrosis.
+
+4.- Authors should further assess whether So(d18:1) inhibits specifically HIF2 activity but not HIF1a. Along this line - in Figure 6C - authors should assess whether HIF1a and ARNT heterodimerization is affected by So(d18:1)?. Moreover, in Figure 6B, authors should assess the effect of So(d18:1) on the luciferase activity driven by a pBIND-HIF1a construct.
+
+5.- In page 8, authors mentioned ‘We administered So(d18:1) intraperitoneally to mice for 1 week, results showed that So(d18:1) increased the proportion of liver macrophages among all immune cells (Figure S3C, 3A-C)”. However it is not clear whether Figure S3C refers to HFD-fed mice or So(d18:1)-treated mice. Authors should clarify this point.
+6.- Authors use a GAN diet to assess liver inflammation and fibrosis in macrophages HIF2a-deficient mice. Why authors not use CDAA-HFD diet as in other experiments presented in this study?. Moreover in figure S3A, authors used HFHFD diet. Authors should clarify why they used these different diets.
+
+7.- In Figure 3A, control group correspond to CDAA-HFD-fed mice?
+Response to Reviewers’ Comments
+
+Reviewer #1 (Remarks to the Author):
+
+This first section of this manuscript describes the identification of a specific lipid (sphingosine [So]18:1) whose plasma levels are associated with NASH progression (in humans and mouse models). The second section is a series of mechanistic studies aimed at understanding how So18:1 promotes NASH progression. The conclusion is that So18:1 promotes NLRP3 activation in macrophages through affecting Hif2a levels/activity. There are many aspects of this data set that are interesting and that have the potential to be an important contribution to the field, but I think key additional control experiments are required to support the conclusions.
+
+Response: We appreciate the comments from reviewer #1 on our manuscript. We believe that all concerns raised by the reviewer can be addressed by additional rigorous experimentation and more detailed discussions. We have added the following experiments:
+1) regarding the control for So18:1 administration, we added So(d16:1) as control to the animal experiment in Figures 2, and So(d16:1), So(d20:1) and So(d18:1) as control to the cell experiments in Figure 3 and Figure 6 to illustrate the specific effects of So(d18:1).
+2) We used flow cytometry to detect the decrease of HIF-2a in liver macrophage in vivo under So(d18:1) treatment and in the NASH model. We have increased the sample size for flow cytometry analysis of liver macrophages in Figures 3A and 3B.
+3) We conducted metabolomics studies to detect the plasma concentration of So(d18:1) in mice treated with vehicle and So(d18:1). Besides, we conducted lipidomics testing to determine what changes have occurred in the lipid levels in the liver after the treatment.
+
+The data presented in Figure 1 and Supp Figure 1 on the identification of So18:1 is fairly compelling and sets up the subsequent mechanistic work well. However, the subsequent mechanistic studies fall short of proving the thesis of the manuscript. The major concern (across many of the studies) is the nature of the vehicle used when administering So18:1. It is not explicitly stated what this is, but in my opinion the authors should be using the other lipids they ID from the metabolomics, but that are not associated with NASH progression. Only by doing this can they be sure that the effects they see across many of the experiments (Figure 2, Figure 3, Figure 6) are due to specific effects of So18:1. Such evidence would provide a far more compelling argument that So18:1 is a specific driver of NASH progression.
+
+Response:
+We thank the reviewer believe that our data have the potential to be an important contribution to the field. In this original revision, we mainly used 0.5% CMC-Na
+solution as solvent to make a suspension of So(d18:1) for the administration. We agree with the reviewer that using another lipid from the metabolomics as a control can better highlight the unique role of So(d18:1). We have found that So(d16:1), So(d20:1) and Sa(18:1) changed in the NASH patients’ serum, but their concentrations were not increased as NASH progression (Fig1D, SupFig1C). So we used So(d16:1), So(d20:1) and Sa(d18:1) as control to the cell experiments and used So (d16:1) as control to the animal expriments in Figure 2, 3, and 6 to illustrate the specific effects of So(d18:1). We found only So18:1 promotes macrophages secreting inflammation factors through affecting HIF-2a levels/activity and promotes the progression of NASH, which reinforced the specific role of So(d18:1) in NASH progression.
+
+The HIF2a KO and overexpression studies in Figure 3 and 4 are also quite convincing, but how this phenotype is related to So18:1 is not clear. For example, the authors do not provide evidence that the expression of Hif2a is decreased in macrophages from So18:1 treated mice or NASH mouse models. Finally, the suggestion that the So18:1 and Hif2a effects are driven through NLRP3 inflammasome activation are overstated, particularly in vivo.
+
+Response:
+We used flow cytometry to detect the expression of HIF-2a in macrophages in So(d18:1) treated mice or NASH mouse models. Data shows that the expression of Hif2a decreased in macrophages after So(d18:1) administration or NASH mouse models. The data and figures were added in the article now (Figure 3G and Supplementary Figure 3E). And as to NLRP3 activation, we agree that there will be other machnisms that could affect NASH progression too. Thus, we revised the statement that the So(d18:1) and Hif2a effects are driven only by NLRP3 inflammasome activation in the article.
+
+My specific comments are also outlined below.
+
+1. Line 32, sphingomyelins are the predominant sphingolipid, please add to your statement.
+For the heat maps in Figure 1 it should be stated what the values are, are these z-scores, concentrations, something else, it is not known from the figure or legend. I would personally move the data in Sup Figure 1D, 1E and 1J into the main text, this is important and strong evidence.
+
+Response:
+We’ve added Sphingomyelin as the main sphingolipids, and explained what the mean value of the heat map is in the figure legend of Figure 1. And we have moved the data Sup Figures 1D, 1E, and 1J into the main text in Figure 1E, 1F, 1G.
+
+2. Line 70. I think this is a one-sided interpretation. One could equally postulate that because the liver So18:1 levels decrease over the course of the CDAA-HFD, and that
+liver enzymes also increase over this time, perhaps the increased plasma levels are the result of hepatocyte damage and release into the circulation. I’m not saying this is the case, but a more balanced interpretation may be warranted.
+
+Response:
+    We agree with the reviewer that the statement in line 70 is a one-sided interpretation. We changed the statement (now Line 121) and discussed the reason for the increase of sphingosine in plasma in discussion. In Supplementary figures, we tested the whole liver So(d18:1) content during the NASH model processing (SupFig 1C), and it showed a downward trend within the first two weeks, but no further change in the coming 6 weeks. We agreed that the increased plasma levels may be the result of hepatocyte damage and release into the circulation. Besides, according to existing articles, So(d18:1) is also present in feces (PMID: 32610095), so we infer that the increased So(d18:1) may originate from the intestine, too. These origins of So(d18:1) may exit together.
+
+3. There is a lack of description of how the sub-class of disease progression (e.g. the data in Supp 1B) data is obtained. Is this a re-classification of the NASH group, I assume so, but please be more descriptive in the text. Also, I would like to see the concentration data (i.e. that shown in Supp Figure 1D) for the other Sa and So species that you show in the heat map. They all look to change to a very similar extent. Also, I would re-format the data in Supp Figure 1B/C to look like Supp Figure 1E. Collectively, these changes will make it easier for the reader to see that while a number of sphingolipids changes in NASH, only So18:1 actually increases during disease progression.
+
+Response:
+    Yes, we used the NAS scores of the liver pathological slices to classify the disease progression. We added the description of the subgroup in the method (NAS scoring section) and the figure legend of Supplementary Figure 1. As for the heatmap, we used the intensity of response of each sphingolipids to make that figure. Although they all increased in NASH patients, So(d18:1) is the most significant one. And as for Supp Figure 1B/C (now supplementary Figure 1E-1I), we already redrown them to match the format of Supp Figure 1E (now Figure 1F), indicating that only So(d18:1) truly increases during disease progression.
+
+4. Line 83. The conclusion is not convincing based on the data. Indeed, from a statistical point of view, they are not different. The conclusion should be tempered.
+
+Response:
+    We corrected and tempered the statement on line 83 (now line 132).
+
+5. Line 88. ‘accepted’ is rather an odd phrasing. Perhaps just say mice ‘were injected with’.
+Response:
+    We have changed 'accepted' to 'injected'.
+
+6. The data in Figure 2 seem reasonably robust, but I have a number of issues that I think should be addressed. (i) what is the nature of the vehicle? It does not say in the methods what this is; indeed, the methods only state that the So treated group were injected with So everyday, while there is no mention of the vehicle treated group. So, are these mice not being injected at all? If they are, what are they receiving? (ii) Relatedly, I’d very much like to see other lipids that the authors identified in the data in Figure 1 being used as controls – i.e. use lipids that are not associated with NASH progression. This would present a far stronger case that So18:1 has specific effects. (iii) You need to perform the metabolomics to show that your injections are increasing the plasma concentrations of So18:1, and also to what extent, they may be increased to levels far beyond what you see endogenously. Ideally, you want your So18:1 injections to increase plasma So18:1 within pathological levels. (iii) What is happening to lipid levels in the liver following these injections? Collectively, I think several additional experiments are required to convincingly show that So18:1 specifically has the claimed effects.
+
+Response:
+    (i) In this paper we mainly used 0.5% CMC-Na as the solvent. Control group was injected with the solvent every day. We have added this description in the method.
+    (ii) In Fig1D, we found that So(d16:1) increased in NASH patients serum, but they didn’t show any future accumulation with the disease progression (SupFig 1H-I). In order to verify the unique function of So(d18:1), we chose So(d16:1) as a control lipid to administrate the NASH mice. As the figures showed in Fig2 and SupFig2, So(d16:1) injection didn’t exacerbate NASH in mice.
+    (iii) We conducted metabolomics studies to detect whether So18:1 injection increases plasma concentration within the pathological range as expected. Data is showed in SupFig 2A.
+    (iii) After injection of vehicles and So(d18:1), we conducted lipidomics testing to determine what changes have occurred in the lipid levels in the liver (Response Figure 1).
+Response Figure 1: A, PLS-DA analysis of sphingolipids in liver of CDAA-HFD mice treated with vehicle or So(d18:1). B, VIP score plot of the difference sphingolipids between the two groups.
+
+7. Figure 3A,B. n numbers are very low, this is obviously from a single experiment. I would like to see a greater sample number used. Additionally, my comments above about the vehicle control apply here also. So, I would like to see the authors using the other So and Sa species they identify as being increased in NASH, but not increasing during disease progression, to show that the specific pro-inflammatory/immune recruitment effects they see are specifically due to So18:1.
+
+Response:
+    We have increased the sample size for flow cytometry analysis of liver macrophages in Figures 3A and B. And we supplied So(d16:1) as control in this experiment.
+
+8. Figure 3E-I. Same comment as above, repeat with other lipids to show the effect is specific to So18:1.
+
+Response:
+    We have supplemented other So and Sa species (So(d16:1), So(d20:1), Sa(d18:1)) in Figure 3E-I as controls (now figure 3E, supplementary figure 3G, 3H). As these So and Sa species (So(d16:1), So(d20:1), Sa(d18:1)) didn’t influence the HIF-2a downstream genes and the protein level of IL-1β and IL-18, we didn’t detect their influence on HIF-2a and caspase-1 protein further.
+
+9. Line 149 seems to be the first mention of the GAN diet. Please define.
+
+Response:
+    GAN diet is Gubra Amylin NASH (GAN) diet, which is a high fat, high cholesterol, and high fructose feed (40% fat powered, 20% fructose, and 2% cholesterol), is fed to mice for more than 24 weeks (generally, steatosis begins at 16 weeks, NASH forms at 24 weeks, and fibrosis is induced at 26-32 weeks). We have added the definition of
+GAN diet on Line 149 (now it is Line 213).
+
+10. Line 148-149. You are not testing this. You are only determining if Hif2a contributes to NASH. You don’t present any evidence that the deletion of Hif2a exacerbates NASH due to inflammasome activation. To support such a claim you should at least show that various inflammasome components, within macrophages, are increased in the Hif2a KO model – yes, il-1b is up a bit but so are lots of other inflammatory markers and this measure is just in a whole liver homogenate, not isolated cells. While inflammatory pathways are activated in Hif2a KO cells, figure 3E shows a large reduction in several markers of M2 macrophages, this is also likely to be a major reason for the potentiated inflammation in the Hif2a KO model – i.e. you are altering the balance of pro/anti-inflammatory macrophages. Furthermore, while you show that So18:1 decreases Hif2a in vitro, you do not show that either So18:1 administration in vivo or the CDAA-HFD diet reduced Hif2a in macrophages in vivo. Nor do you show that blocking NLRP3 inflammasome activity can reverse the effects described in Figure 4.
+
+Response:
+We changed the description of lines 148 to 149 (now line 212) as “To investigate whether HIF-2α in macrophages can influence NASH disease progression”. Our previous work has demonstrated that the absence of HIF-2a leads to the activation of macrophage inflammasomes (PMID: 34433035), and many other reports have also found that the activation of NLRP3 inflammasomes is an important mechanism for the occurrence and development of NASH. We detected the levels of IL-1β and IL-18 in macrophages of HIF2aΔLysm, which is consistent with our previous report (PMID: 34433035), indicating an increase in IL-1β levels in macrophages of HIF2a KO. However, we also agree that NLRP3 inflammasome activation induced by reduced HIF-2a may be only one of the mechanisms by which HIF-2a deficiency leads to NASH. We would therefore modify the state of the conclusions and add discussions.
+As to whether So(d18:1) also reduces HIF-2a in vivo, we added flow cytometry analysis of liver macrophages to verify (Fig 3G, SupFig 3E). Data shows that HIF-2a also reduced in liver macrophages.
+
+![Bar graphs showing quantification of IL-1β and IL-18 secretion from Hif2αfl/fl and Hif2αΔLysm BMDMs transfected with two independent Nlrp3-](page_1016_1342_377_246.png)
+
+Response Figure 2: A-B, Quantification of IL-1β (A) and IL-18 (B) secretion from Hif2αfl/fl and Hif2αΔLysm BMDMs that were transfected with two independent Nlrp3-
+targeting siRNAs or a nontargeting siRNA after treatment with LPS and nigericin (n = 6). C, Representative immunoblot analysis of caspase-1 and IL-1β from Hif2αnull and Hif2αΔLysm BMDMs that were stimulated with LPS and nigericin (n = 3).
+
+11. Line 221, I’m again concerned that a solvent is not the most appropriate control. Your whole thesis is that So18:1, and not other closely related lipids, promote NASH progression. Therefore, the best control would be the other related lipids. If you could show that So16:1 and some of the Sn lipids do not have the same effects as So18:1, this would present a far more compelling argument that So18:1 has specific properties not shared by other related lipid species.
+
+Response:
+    We have added other sphingolipids (So(d16:1), So(d20:1), Sa(d18:1)) as controls to repeat the HIF-2α Luciferase assay for transcriptional activity test.
+
+12. Your central argument is that So18:1 decrease Hif2a protein levels (e.g. figure 2F). Yet looking at the input controls for your IP experiment in Figure 6C, it does not appear to do so. What is the reason for this apparent discrepancy?
+
+Response:
+    Because the Hif2a protein in Input (now Figure 6D) is exogenously overexpression. We transfected the HIF2a overexpression plasmid ( oxygen stable HIF-2α triple mutant (HIF-2αTM) plasmid) into the cells, so that there is stable and large amount of HIF2a present in the cell, which avoids the influence of HIF2a degradation on the experiment, and also amplifies the effect and makes the inhibition of HIF-2α binding with ARNT more obvious. However, in Figure 3F, HIF2a is endogenous and unstable. So(d18:1) inhibit the binding of HIF-2α to ARNT, which impedes HIF-2α entry into the nucleus for transcriptional regulation. HIF-2α that remains in the cytoplasm is very easily hydrolysed and therefore protein levels are reduced.
+
+13. Line 229. You somewhat establish this in vitro (see my previous comments about appropriate lipid controls), you do not provide evidence that (a) hif2a is reduced in vivo, either in response to So18:1 or in the NASH model, (b) you don’t demonstrate that the effects of manipulating Hif2a expression (KO/over-expression) on NASH are via effects on NLRP3.
+
+Response:
+    (a) We used flow cytometry to detect the decrease of hif2a in vivo, whether for So18:1 or in the NASH model (Fig3G, S3E). (b) Yes, we agree that NLRP3 may not the only pathway which lead Hif2a KO to NASH. We have therefore modified the state about NLRP3 inflammation in the conclusion and discussion. We mainly focused on the impact of macrophage hif2a KO/overexpression on the progression on NASH in this paper.
+Reviewer #2 (Remarks to the Author):
+
+In the current study, Xia et al. reported the association between plasma sphingosine d18:1 [So(d18:1)] levels and the severity of NASH. They also found that So(d18:1) aggravated the NASH phenotype in mice. Regarding the mechanism, they studied the effects of So(d18:1)-promoted activation of the NLRP3 inflammasome by inhibiting HIF-2a activity in macrophages. They found that So(d18:1) directly bound with HIF-2a and inhibited the interaction of HIF-2a and ARNT. This study integrates clinical patient data and animal experiments. In general, this study provides a novel serological indicator for NASH diagnosis and novel targets for NASH treatment. However, there are several critical issues that should be addressed.
+
+Response: We appreciate the comments from reviewer #2 on our manuscript. We believe that all concerns raised by the reviewer can be addressed by additional rigorous experimentation and more detailed discussions. We have added the following experiments: We used LysM-HIF-2aLSL/LSL mouse experiments to test whether macrophage specific HIF-2a overexpression can counteract the effect of So(d18:1) on NASH in vivo. And we treated primary hepatocytes and LX-2 cell with So(d18:1) in vitro. Moreover, we conducted SPR experiments to verify the evidence of direct binding of So(d18:1) with HIF-2a. Besides, we have detected the level of ceramide and S1P levels after treatment of So(d18:1) on macrophages and analyzed the inflammatory gene expression from the RNA-seq data.
+
+1. So(d18:1) increased ALT and AST levels in CADD-HFD-fed mice. Did So(d18:1) directly promote hepatocyte injury during NASH?
+
+Response:
+    We used 20 \( \mu \)M So(d18:1) to stimulate the primary hepatocytes directly and found that So(d18:1) didn’t have a brutal ability to damage hepatocytes (SupFig 3I).
+
+2. The possibility that So(d18:1) directly acts on other liver cell types should be discussed.
+
+Response:
+    We used 20 \( \mu \)M So(d18:1) to stimulate the primary hepatocytes and LX-2 cells, which are derived from human hepatic stellate cells, directly and found that So(d18:1) didn’t have a brutal ability to damage hepatocytes (SupFig 3I), neither induced fibrosis in LX-2 cells (SupFig 3J). So(d18:1) may still have possibility directly on other liver cell types, such as endothelial cells, bile duct cells, T cells, B cells, dendritic cells, and so on. However, macrophage-specific HIF-2a overexpression confronted the effects of So(d18:1) largely (Figure 5), which could demonstrate the central role of macrophages in this process. We have added these into discussion.
+3. Did So(d18:1) treatment change ceramide and S1P levels in macrophage?
+
+Response:
+    So(d18:1) treatment didn’t change the level of ceramide, while increased the concentration of S1P significantly in macrophages (Response Figure 3A-B). Besides, So(d18:1) treatment increased the concentration of So(d18:1) in macrophages as expected (Response Figure 3C). Furthermore, when we used a S1P synthesis inhibitor SKI178 to avoid the change of S1P totally, So(d18:1) treatment still inhibits transcriptional regulation function of HIF-2a significantly (Response Figure 3D). These results suggest that the function of treatment of So(d18:1) on macrophages mainly comes from So(d18:1) itself rather than the S1P or ceramide.
+
+![Bar graphs showing ceramide, S1P, and So(d18:1) concentrations in macrophages at different time points, and HIF-2α luciferase activity assays](page_346_563_1092_496.png)
+
+Response Figure 3: A-C, The concentration of total ceramide, S1P, So(d18:1) in macrophages after treatment of So(d18:1) at different time point. D, HRE-based luciferase assay in HEK293T transfected with HIF-2a, followed by treatment of PT-2385, So(d18:1) and So(d18:1) with S1P synthesis inhibitor SKI178.
+
+4. In Line 116, the author mentioned So(d18:1) promoted macrophage activation. To support this statement, did So(d18:1) upregulate inflammatory gene expression from the RNA-seq data?
+
+Response:
+We analyzed the expression of inflammatory genes in RNA seq data and found that So(d18:1) didn’t upregulate inflammatory gene expression of macrophages from the RNA-seq data. The result suggests that so (d18:1) didn’t directly affect transcription of inflammation factors. BP pathway enrichment revealed So(d18:1) inhibits HIF-2α-regulated signalling pathway (Figure 3C). So (d18:1) inhibits HIF2a downstream genes M2 macrophages marker genes, Arg1, Vegf, and so on, which may induce macrophages transition to an inflammatory state. On the other hand, So(d18:1) promotes synthesis and secretion of inflammatory factors but not transcription of inflammatory factors through HIF2a which promotes macrophage fatty acid oxidation, thereby promoting the second signal of inflammasomes (PMID: 34433035).
+
+![RNA-seq data scatter plot showing transcripts per million (Tpm) of inflammatory genes from the RNA-seq data.](page_370_670_698_312.png)
+
+Response Figure 4: transcripts per million (Tpm) of inflammatory genes from the RNA-seq data.
+
+5. Could macrophage-specific HIF-2a overexpression confront the effects of So(d18:1) on NASH in vivo? This is important because So(d18:1) may also act on other cell types, and this experiment could demonstrate the central role of macrophages in this process.
+
+Response:
+We used LysMHif2aLSL/LSL mouse experiments to test whether macrophage specific HIF-2a overexpression can counteract the effect of So(d18:1) on NASH in vivo in Fig5 and SupFig5. Specifically, the mice were divided into four groups: Hif2a+/+, Hif2a+/+ + So(d18:1), LysMHif2aLSL/LSL and LysMHif2aLSL/LSL+So(d18:1), all fed with CDAA-HFD. The level of ALT, AST, the lobular inflammation score, the fibrosis area of HE and sirus staning and the inflammation and fibrosis genes, all showed that macrophage-specific HIF-2a overexpression confronted the effects of So(d18:1) on NASH in vivo.
+
+6. Regarding to “HIF-2α plasmid with two proven missense mutations in the pocket which disabled other molecules to bind with HIF-2α”, the mutations need to be described in detail and the related literature should be cited.
+
+Response:
+We cited relevant literature in these part. The Missense mutations are S304M and G323E, which disabled the binding of other molecules, such as 1,3-diaminopropane and PT2385, with HIF-2a (PMID: 31708445; PMID: 27595394; PMID: 27595393).
+7. The direct binding of So(d18:1) with HIF-2a is an important mechanism of this study. However, the authors only provide docking model to predict the direct binding, which is not enough. The evidence of direct binding of So(d18:1) with HIF-2a should be provided (such as SPR or ITC). It will be helpful if the disturbed binding of HIF-2a with mutated HIF-2a is also proven by experiments.
+
+Response:
+We conducted SPR experiments to verify the binding of So (d18:1) with HIF-2a. The result showed that So(d18:1) had a direct binding with HIF-2a and \( K_D \) (binding affinity) values were determined as 19.51 \( \mu \)M (Response Figure 5A). We also conduct SPR experimen to detect the binding of So(d18:1) with mutated HIF-2a （Response Figure 5B). The result showed that So(d18:1) had no binding with mutated HIF-2a which indicated that the S304M and G323E mutation of HIF-2a disturbed the binding of So(d18:1) with HIF-2a.
+
+![Surface plasmon resonance (SPR) indicated binding of So(d18:1) to the HIF2a. Surface plasmon resonance (SPR) indicated no binding of So(d18:1) to the mutant HIF2a.](page_324_670_1097_324.png)
+
+Response Figure 5: A, Surface plasmon resonance (SPR) indicated binding of So(d18:1) to the HIF2a. B, Surface plasmon resonance (SPR) indicated no binding of So(d18:1) to the mutant HIF2a.
+
+8. From the input of Figure 6C, So(d18:1) did not influence the protein level of HIF-2a. Was HIF-2a exogenous overexpressed in this experiment? If so, this should be clearly described in Figure legends or in method section.
+
+Response:
+We clearly described that HIF-2a is exogenous overexpression in the Figure legends of Figure 6C (now Figure 6D).
+
+9. Regarding Figure 6F, the figure shows that when HIF-2a was overexpressed, So(d18:1) increased luciferase activity. However, the authors describe the data as “similar to the fluorescence values of the empty plasmid” in line 251. In addition, in the same paragraph, there seems to be 4 groups of treatment in Figure 6F, however, the authors only showed 2 groups. Pleased check this result.
+
+Response: In Figure 6F (now Figure 6G), The Y axis of this figure represents the ratio
+of fluorescence values between overexpressing plasmids to empty plasmids. In the control group, due to the inhibition of cpt1a by overexpressed HIF-2a, the fluorescence value of HIF-2a overexpression plasmid group was lower than that of the empty plasmid group, so their ratio was close to 0.5; When administered with So(d18:1), the effect of overexpressed HIF-2a was inhibited by So(d18:1). Therefore, the fluorescence value of the overexpressed plasmid group is approximately equal to the fluorescence of the empty plasmid group, so their ratio is close to 1. As the Y axis of this figure represents the ratio of two groups, so the figure only showed 2 groups rather than 4 groups.
+
+Minor
+1. Figure legend of Fig. 2, “II1b in J, statistical analysis was performed using two tailed Mann-Whitney U-tests”. II1b is in panel K not J.
+
+Response:
+    We have changed J to K.
+
+2. For the western blot of HIF-2a, why there are two bands in Figure 3F and one band in Figure 6C?
+
+Response:
+    Figure 3F showes endogenous HIF-2α protein, which is more delicate and can be influenced by post-translational modifications, post-translational cleavage and relative charge. Figure 6C (now Figure 6D) shows exogenous HIF-2α protein derived from the overexpression plasmid, oxygen-stable HIF-2α triple mutant (HIF-2αTM) plasmid, which is more stable and hard to be degrade.
+
+Reviewer #3 (Remarks to the Author):
+
+In this study, Jialin Xia et al. found that sphingosine d18:1 (So(d18:1)) is elevated in the plasma of NASH patients as well as in the plasma of mice subjected to a NASH mouse model. Authors claim that this So(d18:1) elevation results in liver inflammation and fibrosis and that the pro-fibrotic and pro-inflammatory potential of sphingosine d18:1 rely on its ability to block HIF2a and HIFbeta heterodimerization and therefore HIF2 activity. Along this line authors clearly show that macrophage HIF2 inactivation leads to liver inflammation and fibrosis. These data are interesting but the following comments should be addressed.
+
+Response: We appreciate the comments from reviewer #3 on our manuscript. We believe that all concerns raised by the reviewer can be addressed by additional rigorous experimentation and more detailed discussions. We have added the following experiments: We run in parallel samples of BMDMs obtained from LysMHIF2aLSL/LSL and HIF2aΔLysM mice to confirm that the two bands shown in the western blot correspond to HIF2a. And we detected gene expression of Arginase 1, VEGF-a, Spint,
+Depdc7 and IL-10 in LysMHif2aLSL/LSL BMDMs. Moreover, we performance flow cytometry to detect the HIF2a levels in liver macrophages. Besides, we used luciferase assay to illustrate that So(d18:1) inhibits specifically HIF2a activity but not HIF1a. We evaluated whether HIF1a and ARNT heterodimerization are affected by So(d18:1) by co-IP and pBIND-HIF1a construct.
+
+1.- In Figure 3F, authors should run in parallel samples of BMDMs obtained from LysM-HIF2aLSL/LSL and HIF2aLysM mice in order to confirm that the two bands shown in the western blot correspond to HIF2a.
+
+Response: We run in parallel samples of BMDMs obtained from LysMHIF2aLSL/LSL and HIF2aΔLysM mice to confirm that the two bands shown in the western blot correspond to HIF2a.
+
+![Representative immunoblot analysis of HIF-2α of BMDMs from stimulated with vehicle and So(d18:1) isolated from wild-type mice and BMDMs isolated from LysMHif2aLSL/LSL and Hif2aΔLysM BMDMs.](page_495_613_495_120.png)
+
+Response Figure 6: representative immunoblot analysis of HIF-2α of BMDMs from stimulated with vehicle and So(d18:1) isolated from wild-type mice and BMDMs isolated from LysMHif2aLSL/LSL and Hif2aΔLysM BMDMs.
+
+2.- Authors should show whether gene expression of Arginase 1, VEGF-a, Spint, Depdc7 and IL-10 are elevated in LysMHIF2aLSL/LSL BMDMs or reduced in LysMHIF2a deficient BMDMs.
+
+Response:
+The gene expression of Arginase 1, VEGF-a, Spint, Depdc7 and IL-10 were elevated in LysMHif2aLSL/LSL BMDMs. They all increased because of Hif2a overexpression.
+
+![Relative mRNA levels of Hif2a and its downstream target genes in Hif2a+/+ or LysMHif2aLSL/LSL BMDMs.](page_495_1097_495_246.png)
+
+Response Figure 7: Relative mRNA levels of Hif2a and its downstream target genes in Hif2a+/+ or LysMHif2aLSL/LSL BMDMs.
+
+3.- Authors show that So(d18:1) blunted HIF2a activity in BMDMs. But is this also in
+So(d18:1)-treated mice? Authors should try to perform liver immunostaining using antibodies against HIF2 (or HIF2 target genes) in costaining with macrophage markers in order to evaluate whether macrophage HIF2 expression/activity is really reduced in macrophages of So(d18:1)-treated mice in vivo. Or alternatively assess this point in macrophages isolated from the liver of control and So(d18:1)-treated mice. If these experiments reveals a partial decline of HIF2a, authors might assess whether macrophage-HIF2 heterozygous mice also results in increased liver inflammation and fibrosis.
+
+Response:
+We performance flow cytometry to detect the HIF2a levels in liver macrophages (Fig 3G and SupFig 3E). These suggested that macrophage HIF2 expression/activity is really reduced in macrophages of So(d18:1)-treated or CDAA-HFD fed mice in vivo. As HIF2a^{LysM} mice have a partial decline of HIF2a in BMDMs (Response Figure 6), so we used the HIF2a^{LysM} mice to detected the liver inflammation and fibrosis (Figure 4).
+
+4.- Authors should further assess whether So(d18:1) inhibits specifically HIF2 activity but not HIF1a. Along this line - in Figure 6C - authors should assess whether HIF1a and ARNT heterodimerization is affected by So(d18:1)?. Moreover, in Figure 6B, authors should assess the effect of So(d18:1) on the luciferase activity driven by a pBIND-HIF1a construct.
+
+Response:
+We used luciferase assay to illustrate that So(d18:1) inhibits specifically HIF2a activity but not HIF1a (Fig 6B). We evaluated whether HIF1a and ARNT heterodimerization are affected by So(d18:1) by co-IP (Fig 6E) and pBIND-HIF1a construct (Response Figure 8).
+
+![Schematic and experimental representation of TAY-cyclo or So(d18:1) mediated HIF-1a-ARNT interaction by pG5GAL4 luciferase assay followed by pBINDHIF-1a and pACT-ARNT transfection of HEK293T cells (n = 6).](page_1012_1347_377_181.png)
+
+Response Figure 8: Schematic and experimental representation of TAY-cyclo or So(d18:1) mediated HIF-1a-ARNT interaction by pG5GAL4 luciferase assay followed by pBINDHIF-1a and pACT-ARNT transfection of HEK293T cells (n = 6).
+
+5.- In page 8, authors mentioned ‘We administered So(d18:1) intraperitoneally to mice for 1 week, results showed that So(d18:1) increased the proportion of liver macrophages among all immune cells (Figure S3C, 3A-C)”. However it is not clear whether Figure S3C refers to HFD-fed mice or So(d18:1)-treated mice. Authors should clarify this
+point.
+
+Response:
+    Figure S3C is the gating strategy of liver macrophages from chow diet mice treated with vehicle. Figure3A-B showed the flow cytometric and statistical analysis of chow-diet fed mice treated with control, So(d16:1) and So(d18:1). We have clarified this point in the Figure legend of Figure S3C and Figure3A-B, as well as in the text of Line 169-172 in page 9.
+
+6.- Authors use a GAN diet to assess liver inflammation and fibrosis in macrophages HIF2a-deficient mice. Why authors not use CDAA-HFD diet as in other experiments presented in this study?. Moreover in figure S3A, authors used HFHFD diet. Authors should clarify why they used these different diets.
+
+Response:
+    CDAA-HFD food induced NASH inflammation and fibrosis are more severe. Since we found in Fig1 that So (d18:1) may be more closely related to inflammation and fibrosis compared to fat accumulation, we chose CDAA-HFD to highlight the phenotypic changes of inflammation and fibrosis. GAN diet has a longer processing time and is more in line with the disease development process of NASH in humans. Therefore, we chose this model to observe whether the impact of HIF-2a on NASH disease progression only affects inflammation and fibrosis, without affecting fat accumulation. But now, to further emphasise that macrophage-specific HIF-2a overexpression can resist NASH, we switched to a more intense CDAA-HFD.
+
+7.- In Figure 3A, control group correspond to CDAA-HFD-fed mice?
+
+Response:
+    In Figure 3A, the control group correspond to chow-diet fed mice. We have added the descriptions in the figure legend of Figure 3A.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have done an excellent job of addressing my comments. They have added in the essential controls that I felt were necessary to more fully understand the specificity of So(18:1). The new data clearly show that indeed So18:1 has specific effects not shared by related lipids, thus supporting the main conclusion of the manuscript. They have also added essentially all the new pieces of data/experiments I suggested and made various textual changes, all of which strengthens the manuscript.
+
+There remain a few odd phrases in the manuscript, for example line 407 describing the potential of So18:1 to causes cell death directly – “brutal ability”. The authors may wish to carefully check through the manuscript for other textual/grammatical issues. In the main the language is fine, just a few minor things could be corrected.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have addressed my concerns.
+
+Reviewer #3 (Remarks to the Author):
+
+Authors have addressed most of my comments. However, regarding my original comment #3, authors should demonstrate more convincingly that So(d18:1) reduces HIF2a expression in macrophages in vivo. Moreover, I am including a minor comment related to my original comments #1.
+
+Regarding my original comment #1.
+
+In the figure legend of the figure shown in the response letter, BMDMs isolated from LysMHif2αLSL/LSL and Hif2αΔLysM were treated with vehicle?, is this correct? If so, this should be included in the figure legend. Moreover, this figure might be included in the Supplementary information section.
+Regarding my original comment #3.
+
+In Figure 3G and S3E, authors have assessed HIF2a expression by flow cytometry in macrophages isolated from So(d18:1)-treated or CDAA-HFD fed mice in vivo.
+
+However, authors should include - as positive and negative control - BMDMs isolated from LysMHif2αLSL/LSL and Hif2αΔLysM mice to confirm that signal detected by flow cytometry really corresponds to mouse HIF2a.
+
+Alternatively, authors could use western blot instead of flow cytometry.
+
+On the other hand, Figure legend 3G should be corrected to ‘Flow cytometric and statistical analysis of HIF-2a in liver macrophages…..’ instead of ‘Flow cytometric and statistical analysis of HIF-1a in liver macrophages…..’
+
+Finally, in the Figure legend S3E, 'chow dier' should be corrected to 'chow diet'.
+REVIEWER COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have done an excellent job of addressing my comments. They have added in the essential controls that I felt were necessary to more fully understand the specificity of So(18:1). The new data clearly show that indeed So18:1 has specific effects not shared by related lipids, thus supporting the main conclusion of the manuscript. They have also added essentially all the new pieces of data/experiments I suggested and made various textual changes, all of which strengthens the manuscript.
+
+There remain a few odd phrases in the manuscript, for example line 407 describing the potential of So18:1 to causes cell death directly – “brutal ability”. The authors may wish to carefully check through the manuscript for other textual/grammatical issues. In the main the language is fine, just a few minor things could be corrected.
+Response:
+    We have changed the “brutal ability” to “didn’t directly promote hepatocyte death”. We have carefully check through the manuscript for other textual/grammatical issues and corrected a few minor things.
+
+Reviewer #2 (Remarks to the Author):
+
+The authors have addressed my concerns.
+
+Reviewer #3 (Remarks to the Author):
+
+Authors have addressed most of my comments. However, regarding my original comment #3, authors should demonstrate more convincingly that So(d18:1) reduces HIF2a expression in macrophages in vivo. Moreover, I am including a minor comment related to my original comments #1.
+
+Regarding my original comment #1.
+
+In the figure legend of the figure shown in the response letter, BMDMs isolated from LysMHif2αLSL/LSL and Hif2αΔLysM were treated with vehicle?, is this correct? If so, this should be included in the figure legend. Moreover, this figure might be included in the Supplementary information section.
+Response:
+    Yes, BMDMs isolated from LysMHif2α^{LSL/LSL} and Hif2α^{ΔLysM} were treated with vehicle. We have included this in the figure legend of . And we have included the figure in the Supplementary information section.
+
+Regarding my original comment #3.
+In Figure 3G and S3E, authors have assessed HIF2a expression by flow cytometry in macrophages isolated from So(d18:1)-treated or CDAA-HFD fed mice in vivo. However, authors should include - as positive and negative control - BMDMs isolated from LysMHif2αLSL/LSL and Hif2αΔLysM mice to confirm that signal detected by flow cytometry really corresponds to mouse HIF2a.
+Alternatively, authors could use western blot instead of flow cytometry.
+
+Response:
+    We have included BMDMs isolated from LysMHif2αLSL/LSL and Hif2αΔLysM mice as positive and negative control to confirm that signal detected by flow cytometry really corresponds to mouse HIF2a.
+
+On the other hand, Figure legend 3G should be corrected to ‘Flow cytometric and statistical analysis of HIF-2a in liver macrophages…….’ instead of ‘Flow cytometric and statistical analysis of HIF-1a in liver macrophages…….’
+
+Response:
+    We have corrected the Figure legend 3G as “Flow cytometric and statistical analysis of HIF-2a in liver macrophages”.
+
+Finally, in the Figure legend S3E, 'chow dier' should be corrected to 'chow diet'.
+
+Response:
+    We have corrected the Figure legend S3E 'chow dier' to 'chow diet'.
+REVIEWERS' COMMENTS
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have satisfactorily addressed my final concerns.

02624773f6e6ce56158b53f0fcddcdef4027c464f514126d8dae690687431871/preprint/preprint.md

@@ -0,0 +1,413 @@
+Sphingosine d18:1 Promotes Nonalcoholic Steatohepatitis by Inhibiting Macrophage HIF-2α
+
+Changtao Jiang
+jiangchangtao@bjmu.edu.cn
+
+Department of Physiology and Pathophysiology, School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University   https://orcid.org/0000-0002-5206-2372
+
+Jialin Xia
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Hong Chen
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Xiaoxiao Wang
+Peking University People’s Hospital
+
+Weixuan Chen
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Jun Lin
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Feng Xu
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Qixing Nie
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Chuan Ye
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Bitao Zhong
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Min Zhao
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Chuyu Yun
+School of Basic Medical Sciences, Peking University
+
+Guangyi Zeng
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Sen Yan
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+
+Xuemei Wang
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+Lulu Sun
+School of Basic Medical Sciences, Center for Reproductive Medicine, Peking University
+Feng Liu
+Peking University People’s Hospital
+Huiying Rao
+Peking University People’s Hospital
+Yanli Pang
+Center for Reproductive Medicine, Department of Obstetrics and Gynecology, Peking University Third Hospital   https://orcid.org/0000-0003-1967-2416
+
+Article
+
+Keywords: NASH, macrophage, HIF-2α, sphingosine
+
+Posted Date: July 11th, 2023
+
+DOI: https://doi.org/10.21203/rs.3.rs-3092076/v1
+
+License: © This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License
+
+Additional Declarations: There is NO Competing Interest.
+
+Version of Record: A version of this preprint was published at Nature Communications on June 4th, 2024. See the published version at https://doi.org/10.1038/s41467-024-48954-2.
+Sphingosine d18:1 Promotes Nonalcoholic Steatohepatitis by Inhibiting Macrophage HIF-2α
+
+Jialin Xia1,2,3,7, Hong Chen1,4,7, Xiaoxiao Wang6,7, Weixuan Chen4, Jun Lin1,2,3, Feng Xu1,2,3, Qixing Nie1,2,3, Chuan Ye1,2,3, Bitao Zhong1, Min Zhao4, Chuyu Yun4, Guangyi Zeng1,2,3, Sen Yan4, Xuemei Wang1,2,3, Lulu Sun5, Feng Liu6, Huiying Rao6,*, Changtao Jiang1,2,3,* and Yanli Pang1,4,*
+
+1Department of Physiology and Pathophysiology, School of Basic Medical Sciences, Center for Reproductive Medicine, Third Hospital, Peking University, Beijing, China
+
+2Center of Basic Medical Research, Institute of Medical Innovation and Research, Peking University Third Hospital, Beijing, China.
+
+3Center for Obesity and Metabolic Disease Research, School of Basic Medical Sciences, Peking University, Beijing, China.
+
+4State Key Laboratory of Female Fertility Promote, Center for Reproductive Medicine, Department of Obstetrics and Gynecology, Peking University Third Hospital, Beijing, China.
+
+5Department of Endocrinology and Metabolism, Peking University Third Hospital, Beijing, China.
+
+6Peking University People’s Hospital, Peking University Hepatology Institute, Beijing Key Laboratory of Hepatitis C and Immunotherapy for Liver Diseases, Beijing International Cooperation Base for Science and Technology on NAFLD Diagnosis, Beijing, China.
+
+7These authors contribute equally.
+
+*Correspondence: yanlipang@bjmu.edu.cn (Yanli Pang), jiangchangtao@bjmu.edu.cn (Changtao Jiang), raohuiying@pkuph.edu.cn (Huiying Rao)
+Conflict of interest
+
+The authors declare no conflicts of interest that pertain to this work.
+
+Financial support
+
+This work was supported by the National Natural Science Foundation of China (No. 82130022, 31925021, 82022028, 82288102, 91857115, 81921001, and 92149306), and the National Key Research of Development Program of China (no. 2018YFA0800700 and 2022YFA0806400).
+
+Author contributions
+
+Y.P, C.J. and J.X. conceptualized and designed the study. J.X, H.C., X.W., F.X., Q.N., C.Y., B.Z., M.Z., CY.Y., G.Z., S.Y. and F.L. performed the experiments and analyzed the data. Y.P., C.J. and H.R supervised the study. J.X. and H.C. wrote the manuscript with input from all authors. J.L., XM.W. and L.S. revised the manuscript. J.X, H.C. and X.W. contributed equally to this work. All authors edited the manuscript and approved the final manuscript.
+Abstract
+
+Non-alcoholic steatohepatitis (NASH) is a severe type of the non-alcoholic fatty liver disease (NAFLD). NASH is a growing global health concern due to its increasing morbidity, lack of well-defined biomarkers and lack of clinically effective treatments. Using metabolomic analysis, the most significantly changed active lipid sphingosine d18:1 [So(d18:1)] was selected from NASH patients. So(d18:1) inhibits macrophage HIF-2α as a direct inhibitor and promotes the activation of NLRP3 inflammasome. Macrophage-specific HIF-2α knockout and overexpression mice verified the effect of HIF-2α on NASH progression. Importantly, the HIF-2α stabilizer FG-4592 alleviated liver inflammation and fibrosis in NASH, which indicated that macrophage HIF-2α was a potential drug target for NASH treatment. Overall, this study confirms that So(d18:1) promotes NASH and clarifies that So(d18:1) inhibits the transcriptional activity of HIF-2α in liver macrophages by suppressing the interaction of HIF-2α with ARNT, suggesting that macrophage HIF-2α may be a new target for the treatment of NASH.
+
+Key words
+
+NASH, macrophage, HIF-2α, sphingosine
+
+Introduction
+
+With lifestyle changes, nonalcoholic fatty liver disease (NAFLD) has become a major chronic disease in contemporary society[1]. NAFLD is a chronic metabolic disease characterized by excessive accumulation of fat in hepatocytes. NAFLD can be divided into simple fatty liver (NAFL) and nonalcoholic steatohepatitis (NASH)[2].
+Chronic liver injury in NASH significantly increases the risk of end-stage liver diseases (such as cirrhosis and liver cancer). However, there is no effective drug for NASH in clinical practice[3]. Therefore, clarifying the key molecular mechanism of the occurrence and development of NASH will help to develop new strategies for anti-NASH treatment.
+
+The classical theory of NASH pathogenesis is that NASH is caused by the excessive accumulation of lipids in hepatocytes. Then, extreme oxidative stress and inflammation further induce hepatocyte death and the development of inflammation and fibrosis[4]. Sphingolipids are lipids with high biological activity and are one of the main factors affecting the progression of NASH. Sphingolipids mainly include ceramide and sphingosine-1-phosphate (S1P), and sphingosine is an intermediate product between them[5]. Previous studies have found changes in ceramide and S1P levels in NASH patients[6]. However, they both failed to act as sensitive biomarkers to guide disease diagnosis in NASH because of their widespread variation in many other early-stage NAFLD patients. Sphingosine has not only been found to vary in NAFL[7, 8] but has even been found to be useful as a biomarker to predict cirrhosis[9].
+
+Here, we found that So(d18:1) increases significantly in patients with NASH by metabolomics profiling analysis. So(d18:1) promotes liver inflammation and fibrosis in the NASH model. RNA-seq data revealed that So(d18:1) inhibits HIF-2α expression. Macrophage-specific knockout or overexpression of HIF-2α has been used to clarify the role of macrophage HIF-2α in NASH development. Mechanistically, So(d18:1) inhibits macrophage HIF-2α by inhibiting its combination with ARNT and then
+promotes the excessive activation of the macrophage NLRP3 inflammasome, increasing the secretion of inflammatory factors. Notably, we found that the pharmacological activation of macrophage HIF-2\( \alpha \) by FG-4592, a HIF prolyl hydroxylase inhibitor that is approved for the treatment of anaemia in China, had preventive effects on NASH in mice. This work suggests that macrophage HIF-2\( \alpha \) is a novel target for the treatment of NASH.
+
+Results
+
+1. Disturbances in sphingolipid metabolism in NASH patients
+
+In the Chinese patient population, we employed a metabolomics screen of NASH patients and healthy volunteers (Table S1). The results showed that the changes in the sphingolipid pathway are the most concentrated, significant and dramatic compared to other lipids that are considered to change routinely (Figure 1A). After that we further examined the whole sphingolipidome using targeted metabolomics (Figure 1B). Principal component analysis (PCA) showed a clear separation between the healthy volunteers and NASH patients (Figure 1C). The VIP score indicated a significant increase in the levels of several sphingolipids, especially So(d18:1) (Figure 1D).
+
+We fed the mice with CDAA-HFD for 8 weeks to establish NASH mice model. Serum So(d18:1) concentrations was assayed in NASH model mice, and the trend of increasing serum So(d18:1) concentrations in mice was exactly the same as the trend of increasing ALT and AST levels (Figure S1H-J). In human cohort, So(d18:1) accumulated largely in serum of NASH patients (Figure S1D) and increased as the
+disease progresses (Figure S1E). Moreover, the concentration of So(d18:1) was positively correlated with serum ALT, AST levels and Fibrosacn index (Figure 1E-1G). These results suggested that So(d18:1) concentrations may be closely related to NASH progression. However, So(d18:1) relative concentration in whole liver tissue didn’t show any change between healthy and NASH mice (Figure S1K), that suggests the origin of So(d18:1) may not from hepatocytes.
+
+In our sphingolipidome results, the upstream and downstream metabolites of sphingosine, ceramide and S1P, were also altered in content. In our previous study, we had found that ceramide was enriched in NASH patients similarly[6]. But ceramides did not increase more with disease progression (Figure S1A). S1p and the other type of sphingosines also failed to show any growth trends during the progression of NASH (Figure S1B-C). These results further demonstrated the unique indicative role of So(d18:1) in the progression of NASH.
+
+Hepatic steatosis and lobular inflammation are two important features of the NASH. We analysed the relationship between So(d18:1) levels and these two aspects. There was no significant increase in the So(d18:1) level as hepatic steatosis progressed (Figure S1F). However, the So(d18:1) concentration gradually increased with the aggravation of lobular inflammation (Figure S1G), suggesting that the function of So(d18:1) may be related to lobular inflammation.
+
+2. So(d18:1) aggravates inflammation and fibrosis in NASH
+
+To test whether So(d18:1) is involved in the progression of NASH, CDAA-HFD-fed mice accepted a simultaneous intraperitoneal injection of So(d18:1). There was no
+significant difference in the liver weight or body weight between the two groups of mice (Figure 2A-B and S2A). The levels of ALT and AST in the serum of mice injected with So(d18:1) were significantly higher than those in control mice (Figure 2C-D), which suggests that So(d18:1) exacerbated liver damage in mice. While there were no differences in liver triglyceride (TG), serum TG and serum non-esterified fatty acid (NEFA) levels, there was also no difference in liver and serum cholesterol (CE) levels (Figure S2B-F). For a clearer image of the liver damage in mice, we made pathological sections and performed H&E staining and Sirius red staining. The pathological sections showed that So(d18:1) treatment increased the fibrosis, lobular inflammation and NASs but did not affect the histology score of hepatic steatosis (Figures 2E–2J). Consistently, the mRNA expression of inflammation genes and fibrosis genes was significantly upregulated in the liver of the So(d18:1) group compared with that of the vehicle group (Figure 2K-L), while the lipid metabolism genes were mostly not different between the two groups (Figure S2G). Collectively, these results suggest that So(d18:1) can exacerbate lobular inflammation and fibrosis in the livers of NASH mice.
+
+3. So(d18:1) inhibits HIF-2α transcription function in liver macrophages
+
+So(d18:1) can exacerbate lobular inflammation in the liver of NASH, suggesting that it alters the immune status of the liver, so we focused on immune cells for in-depth study. To confirm the changes of various immune cells during the development of NASH, a set of public single-cell RNA-sequencing data from the livers of NASH mice was located and analysed[10]. The results showed an increase of all kinds of immune cells in the livers of NASH mice. However, the largest proportion of these cells were
+macrophages and monocytes. Importantly, they were recruited to the livers much earlier than other immune cells (Figure S3A-B). We therefore wanted to see whether So(d18:1) would also cause changes in macrophage proportion. We administered So(d18:1) intraperitoneally to mice for 1 week, results showed that So(d18:1) increased the proportion of liver macrophages among all immune cells (Figure S3C, 3A-B).
+
+To search for the mechanisms by which So(d18:1) promotes macrophages activation, we treated mouse bone-marrow derived macrophages (BMDM) with So(d18:1) or control vehicle under inflammatory stimulation and performed RNA sequencing to explore the changed genes pathways. GO:BP pathway enrichment showed that hypoxia-related pathways were changed significantly between the control and So(d18:1) groups (Figure 3C). There are two transcription factors that play a major role in the hypoxia-related signalling pathway, HIF-1\( \alpha \) and HIF-2\( \alpha \). We further targeted the signalling pathways regulated by these two transcription factors for enrichment analysis. BP pathway enrichment revealed transcriptional changes in the HIF-2\( \alpha \)-regulated signalling pathway (Figure 3D), while HIF-1\( \alpha \) signalling pathway was not changed (Figure S3D).
+
+To validate the RNA-seq results, we treated mouse BMDMs with So(d18:1). The results showed that the transcription levels of the *Hif2a* gene were not changed, but its downstream genes *Arg1*, *Vegf*, *Spint*, *Depdc7* and *Il10* decreased after So(d18:1) treatment (Figure 3E). We also detected *Hif1a* and its downstream genes and their expression levels were unchanged (Figure S3E). As for the protein levels of HIF-2\( \alpha \), the results showed that So(d18:1) treatment could significantly inhibit the protein
+expression of HIF-2α (Figure 3F).
+
+Intrahepatic macrophages IL-1β and IL-18 secretion due to NLRP3 inflammasome activation is an important mechanism that promotes the progression of NASH[11]. Our previous study also found that macrophage HIF-2α could suppress NLRP3 inflammasome activation by inhibiting CPT1A[12]. Results showed that So(d18:1) administration could increase NLRP3 inflammasome assembly therefore increase Caspase-1 cleavage, while HIF-2α overexpression could quell the stimulation caused by So(d18:1) (Figure 3G). IL-1β and IL-18 secretion levels also confirmed that So(d18:1) promoted NLRP3 inflammasome activation, but not in HIF-2α overexpressing macrophages (Figure 3H-I).
+
+This may be the cellular mechanism by which So(d18:1) activates macrophages to promote hepatic inflammation in NASH. And the above mechanism was regulated by HIF-2α.
+
+4. Macrophage-specific HIF-2α deletion aggravates inflammation and fibrosis in NASH
+
+To investigate whether HIF-2α-mediated activation of the NLRP3 inflammasome can influence NASH disease progression, we fed Hif2afl/fl and Hif2aALysm mice a GAN diet for 24 weeks to compare the severity of inflammation and fibrosis in the liver. There was no significant difference in body weight between the two groups of mice (Figure S4A). Liver weight and the ratio of liver weight to body weight were significantly increased in Hif2aALysm mice compared with Hif2afl/fl mice (Figures 4A–B). Moreover, the levels of ALT and AST in the serum of Hif2aALysm mice were
+significantly higher than those in \( Hif2a^{fl/fl} \) mice, suggesting that knockdown of \( Hif2a \) exacerbates the disease symptoms of NASH (Figure 4C-D). Next, we examined the changes in lipids in the liver tissue and plasma of the two groups of mice. The results revealed that the concentrations of serum TG, CE, and NEFAs and hepatic TG and CE were not significantly different between \( Hif2a^{fl/fl} \) mice and \( Hif2a^{\Delta Lysm} \) mice (Figure S4C-F). This result suggests that knockdown of macrophage \( Hif2a \) does not affect total lipid metabolism or consequently exacerbate lipid accumulation in the liver.
+
+To further determine the changes in the levels of inflammation and fibrosis within the mouse liver to determine the progression of NASH, pathological sections were made from the livers of the two groups of mice to observe the extent of liver injury in the mice (Figure 4E). The degree of hepatic steatosis was consistent between the two groups of mice (Figure 4G), and there was no significant difference in the ballooning score (Figure 4I). However, mice in the \( Hif2a^{\Delta Lysm} \) group had more foci of inflammation in the liver, with a large number of mononuclear macrophages diffusely distributed and a significantly higher inflammation score in the liver lobules than in the \( Hif2a^{fl/fl} \) group (Figure 4H). The sections were also stained with Sirius red (Figure 4E), and the fibrosis area was quantified to show that the \( Hif2a^{\Delta Lysm} \) group had a significantly greater fibrosis area than that of the \( Hif2a^{fl/fl} \) group (Figure 4F). These results demonstrate that macrophage \( Hif2a \) knockdown can indeed significantly exacerbate NASH symptoms and promote inflammatory activation and fibrosis formation.
+
+Consistently, the mRNA expression of inflammation genes and fibrosis genes was significantly upregulated in the livers of \( Hif2a^{\Delta Lysm} \) mice compared with that of \( Hif2a^{fl/fl} \)
+mice (Figure 4K-L), while the lipid metabolism genes were not different between the two groups (Figure S4G). Collectively, these data showed that genetic disruption of macrophage-specific HIF-2α accelerated hepatic inflammation and fibrosis but did not affect hepatic steatosis.
+
+5. Macrophage-specific HIF-2α overexpression alleviated inflammation and fibrosis in NASH
+
+To further verify the role of macrophage HIF-2α overexpression in NASH, Hif2a+/+ and LysMHif2aLSL/LSL mice were fed a GAN diet for 24 weeks. There was no significant difference in body weight between the two groups of mice (Figure S5A). The liver weight and the ratio of liver weight to body weight tended to decrease in LysMHif2aLSL/LSL mice compared with Hif2a+/+ mice (Figures 5A–B). The levels of ALT and AST in the serum were significantly lower in LysMHif2aLSL/LSL mice than in Hif2a+/+ mice (Figures 5C–5D), suggesting that Hif2a overexpression can protect the liver and reduce liver injury. We also measured TG, total CE and NEFA levels in the liver and plasma to investigate whether macrophage-specific Hif2a overexpression could reduce fat accumulation in the liver, but there were no differences between the two groups in any of these parameters (Figure S5B-F).
+
+The liver tissues of Hif2a+/+ and LysMHif2aLSL/LSL mice were also paraffin sectioned and stained with H&E and Sirius red. The H&E staining results showed that there was no significant difference in the steatosis scores between the two groups (Figure 5G). However, the LysMHif2aLSL/LSL group mice had fewer inflammatory foci in the liver, so their hepatic lobular inflammation scores were significantly lower than those of the
+Hif2α+/+ group mice (Figure 5H), their hepatocyte ballooning scores were also significantly lower (Figure 5I), and the final calculated NAS of the LysMHi2αLSL/LSL group mice was significantly lower than that of the Hif2α+/+ group mice (Figure 5J). We next examined Sirius red-stained sections, and it was evident that intrahepatic fibrosis production was reduced in the LysMHi2αLSL/LSL group of mice (Figure 5E-F). The above results suggest that macrophage Hif2α overexpression may inhibit macrophage activation and thus stellate cell activation, reducing fibrogenesis and protecting the liver from damage during NASH.
+
+Consistently, the mRNA expression of inflammation-related genes and fibrosis-related genes was significantly downregulated in the livers of LysMHi2αLSL/LSL mice compared with Hif2α+/+ mice (Figure 5K-L), while the lipid metabolism-related genes were not different between the two groups (Figure S5G). Collectively, these data showed that macrophage-specific HIF-2α overexpression ameliorated hepatic inflammation and fibrosis but did not affect hepatic steatosis.
+
+6. So(d18:1) reduces the transcriptional activity of HIF-2α
+
+In previous results, we have verified that So(d18:1) could promote NLRP3 inflammasome activation in macrophages and identified HIF-2α as a key transcription factor by which So(d18:1) alters the inflammatory state of macrophages. Therefore, how does the increased So(d18:1) in NASH patients affect HIF-2α protein function in macrophages? We conducted a more in-depth mechanistic study to address this question. First, to determine whether So(d18:1) could inhibit HIF-2α transcriptional activity, we constructed a HIF response element (HRE)-based luciferase reporter assay and treated
+the cells with control solvent, So(d18:1) and HIF-2α-specific inhibitor PT2385 as positive control. Fluorescein detection showed that So(d18:1) could significantly inhibit the transcriptional activity of HIF-2α (Figure 6A). The transcriptional action of HIF-2α requires binding to the ARNT subunit. Thus, we utilized a mammalian two-hybrid system that could further verified that So(d18:1) repressed the transcriptional function of HIF-2α by inhibiting the binding of ARNT (Figure 6B). In addition, coimmunoprecipitation was performed to determine that So(d18:1) directly disrupted the direct binding of HIF-2α to ARNT (Figure 6C).
+
+HIF-2α has a hydrophobic pocket PAS-B domain to bind with ARNT[13]. Structural prediction by docking revealed some potential for So(d18:1) to fill into this hydrophobic pocket (Figure 6D). So, we constructed a HIF-2α plasmid with two proven missense mutations in the pocket which disabled other molecules to bind with HIF-2α. Luciferase reporter system was performed, and the results showed that So(d18:1) could normally inhibit the binding of wild-type HIF-2α to ARNT but not that of mutant HIF-2α to ARNT (Figure 6E). From these results, we learned that So(d18:1) may fill into the hydrophobic pocket of HIF-2α and thereby inhibit the binding of HIF-2α to ARNT, which impedes HIF-2α entry into the nucleus for transcriptional regulation. HIF-2α that remains in the cytoplasm is very easily hydrolysed and therefore protein levels are reduced. This finding also explained why So(d18:1) can only change the protein expression level of HIF-2α but not the mRNA expression level.
+
+HIF-2α regulates metabolism reprogramming by binding to the rHRE region on the Cpt1a promoter[12]. We therefore transfected a luciferase reporter gene plasmid
+containing a Cpt1a rHRE region with a HIF-2α plasmid or empty plasmid into cells, treated with control solvent or So(d18:1) and observed the fluorescence activity ratio. The results showed that in the vehicle group, the fluorescence values of HIF-2α™-transfected cells were lower than those with empty plasmid, indicating that overexpression of HIF-2α inhibited the transcription of Cpt1a rHRE-linked luciferase. In contrast, the overexpression of HIF-2α in the So(d18:1) group did not affect the transcription of Cpt1a rHRE-linked luciferase, as it was unable to bind to ARNT and localize to the rHRE region in the nucleus, so the fluorescence values of HIF-2α™ plasmid-transfected cells were similar to the fluorescence values of the empty plasmid group (Figure 6F).
+
+The above results suggest that So(d18:1) could inhibits the binding of HIF-2α to ARNT, thus promoting NLRP3 inflammasome activation and promotes NASH disease progression. These results also suggest to us the possibility that lipids bind directly to transcription factors and regulate their functions, showing us new mechanisms by which lipids influence cellular metabolism.
+
+7. Stabilization of HIF-2α expression in macrophages significantly alleviated inflammation and fibrosis in NASH
+
+We further investigated the therapeutic effect of the specific HIF-2α agonist FG-4592 in treating NASH. SPF mice were given a CDAA-HFD diet for 8 weeks and were administered vehicle or FG-4592 (25 mg/kg) by intraperitoneal injection. At the end of the treatment, there was no significant difference in body weight between the two groups of mice (Figure S6A), but there was a significant reduction in liver weight
+(Figure 7A), as well as a significant reduction in the calculated liver weight/body weight ratio (Figure 7B). Measurement of the blood levels of ALT and AST showed significant decreases in both transaminase levels suggestive of liver injury (Figure 7C-D). To assess whether FG-4592 could improve intrahepatic fat accumulation, we also measured intrahepatic TG (Figure S6B) and blood TG levels (Figure S6C), neither of which showed a significant change. Total intrahepatic CE (Figure S6D) and total plasma CE levels (Figure S6E) were also tested, and there was no significant improvement in either of these results. With respect to NEFAs in the blood, there was also no improvement after FG-4592 injection (Figure S6F). The above results suggest that although FG-4592 may improve liver injury, it does not improve lipid accumulation in the liver.
+
+To further observe liver injury in mice, we made paraffin sections of liver tissue from both groups and stained them with H&E and Sirius red. In the H&E-stained sections, we observed that the degree of steatosis in the livers of the two groups of mice was the same, and therefore, there was no difference in the steatosis score (Figure 7G). However, there were significantly fewer foci of inflammation than in the vehicle group, and therefore, the score of the lobular inflammation was lower than that of the vehicle group (Figure 7H). The final calculation of the NASs also showed that FG-4592 injection reduced the symptoms of NASH in mice (Figure 7J). In Sirius red-stained sections, fibrosis was significantly reduced in the FG-4592-injected group, and this result could be better visualized by counting the fibrosis area proportion (Figure 7E-F).
+
+After FG-4592 injection, inflammation-related genes were significantly
+downregulated in the mouse liver (Figure 7K). Additionally, genes related to fibrosis were significantly reduced (Figure 7L). However, genes related to fatty acid uptake and de novo synthesis were slightly changed, with only the expression level of Fasn being reduced (Figure S6G).
+
+In conclusion, FG-4592 injection can reduce liver fibrosis and improve NASH symptoms by reducing intrahepatic inflammation.
+
+Discussion
+
+Chronic liver injury caused by NASH can significantly increase the risk of end-stage liver diseases. However, there is currently no effective drug to treat NASH in the clinic. Here, we found that the abundance of So(d18:1) in patients with NASH was significantly increased through metabolomics analysis. So(d18:1) significantly aggravated hepatic lobular inflammation and fibrosis in the livers of NASH model mice. Mechanistically, So(d18:1) inhibits macrophage HIF-2α binding with ARNT, thus promoting overactivation of the macrophage NLRP3 inflammasome and increasing the secretion of inflammatory factors. This mechanism reveals that macrophage HIF-2α may be a new target for the treatment of NASH. Based on this finding, we tried to use the HIF-2α stabilizer FG-4592 to improve NASH, and the results showed that FG-4592 alleviated inflammation and fibrosis in NASH.
+
+Liver steatosis is an early event of NASH. A large amount of lipid accumulation in hepatocytes leads to excessive oxidative stress in hepatocytes, which further induces hepatocyte death, thereby activating inflammation and fibrosis in hepatic lobules[4]. In NASH patients, we have seen several significant changes in sphingolipids, such as Cer
+(d18:1/16:0), Cer (d18:1/14:0), Cer (d18:1/20:0), Cer (d18:1/22:0), Cer (d18:1/18:0) and Cer (d18:1/18:0). Their abundances significantly increased in the serum of NASH patients. Our previous work found that the excessive accumulation of nicotine in the intestine can promote the secretion of intestinal ceramide by upregulating the phosphorylation level of SMPD3, thus promoting the progression of NAFLD to NASH[6]. In addition, knocking out alkaline ceramidase 3 (Acer3), which is upregulated in NASH, increases liver Cer (d18:1/18:0) in mice fed a Western diet, reduces oxidative stress and reduces the severity of NASH[14]. S1P released from apoptotic hepatocytes damaged by lipids induces the expression of Trem2 in liver macrophages through S1PR, thereby limiting the occurrence and development of chronic inflammation in NAFLD[15]. These studies suggest that sphingolipid metabolism may play an important role in the pathogenesis of NAFLD. However, none of changes in these sphingolipids perfectly fit the trend of NASH disease exacerbation and indicate the severity of NASH. But So(d18:1) closely related to the disease progression of NASH and was completely consistent with the trends of the changes in the ALT and AST levels representing liver injury. Thus, So(d18:1) is a better indicator of the progression of NASH.
+
+In addition, although sphingosine has not been deeply discussed in previous studies, some studies have found sphingosine in metabolomics[7, 8], and they have even found that So(d18:1) in stool can be used as a biomarker to predict cirrhosis[9]. However, So(d18:1) is usually regarded just as an intermediate product of metabolism between ceramide and S1P, and in-depth mechanistic and functional research is lacking. In this study, we found that So(d18:1) can exist stably in cells at a certain concentration and
+will not be rapidly converted into ceramide or S1P. Our results showed that So(d18:1) can not only promote overactivation of the NLRP3 inflammasome in BMDMs but can also aggravate liver inflammation and fibrosis and promote the progression of NASH in animals.
+
+Regarding the origin of the increased circulating So(d18:1) in NASH patients, we examined the amount of So(d18:1) in the whole liver tissue of NASH-modelled mice and found that the rise in total So(d18:1) in liver tissue was not significant, so we inferred that the increased circulating So(d18:1) was not produced by the liver. The metabolism of ceramide is also known to occur in the gut and adipose tissue, so we will subsequently examine the levels of So(d18:1) in the gut and adipose tissue of NASH-modelled mice at different time points to further investigate the source of the increased circulating So(d18:1). There are also results showed that increased levels of So(d18:1) in the faeces of NASH-cirrhotic patients, which may serve as one of the biomarkers for predicting NASH-cirrhosis[16]. This also suggests that the role of microbiota in sphingolipid metabolism should not be underestimated.
+
+HIF is a heterodimer made up of an oxygen-sensitive \( \alpha \) subunit and a constitutively expressed \( \beta \) subunit (ARNT). Under normoxic conditions, HIF-\( \alpha \) is rapidly hydroxylated and degraded by prolyl hydroxylase (PHD). In contrast, under hypoxia, the activity of prolyl hydroxylase was inhibited, and the HIF protein was stable. HIF-2\( \alpha \) accumulates and translocates to the nucleus and combines with ARNT to form an active transcription factor complex[17]. In NASH, HIF-1\( \alpha \) in macrophages induced by palmitic acid damages autophagic flux and increases IL-1\( \beta \) production, aggravating
+liver injury induced by an MCD diet[18]. Digoxin inhibits the transcription of the HIF-1a pathway by directly binding to pyruvate kinase M2, thus changing the chromatin structure and reducing NASH[19]. However, the role of HIF-2α in macrophages in the progression of NASH is still unclear. In this article we have validated the role of HIF-2α in NASH progression using mice with macrophage-specific knockdown or overexpression of HIF-2α. Identified that HIF-2α as a potential target for intervention in NASH.
+
+Rosalistat (FG-4592) is a mature small-molecule drug that is mainly used to treat chronic kidney disease and anaemia, but its role in metabolic diseases has not yet entered clinical trials. In our previous studies, FG-4592 injection was used to improve insulin resistance[20]. In this study, FG-4592 injection significantly reduced the levels of ALT and AST in the livers of mice, suggesting that the degree of liver injury was reduced. In addition, the expression of genes related to inflammation and fibrosis also decreased. The above results showed that FG-4592 injection can reduce the incidence of NASH. However, many articles have also clarified that the overexpression of HIF-2α in liver cells plays a worsening role in insulin resistance and fatty liver[21, 22]. Continuous activation of hepatocyte HIF-2α can damage the transcription of fatty acid β-oxidation-related genes, leading to fat accumulation in the liver[22, 23]. Hepatocyte HIF-2α stimulated the production of histidine-rich glycoprotein (HRGP) to activate macrophages to polarize to the M1 type, thus causing liver damage. In our study, the administration of FG-4592 can block the response ability of proinflammatory macrophages, thus playing a protective role. After FG-4592 reaches the liver, it may
+indeed lead to the accumulation of lipids in the liver, but it also ensures that hepatocytes damaged by lipotoxicity will not cause further macrophage inflammation. Therefore, from the overall animal experimental data, the administration of FG-4592 still protects the liver from damage in NASH disease. In addition, FG-4592 can also act on other targets, such as adipose tissue HIF-2\( \alpha \), and promote the production of erythropoietin\(^{[24, 25]}\), which will delay or even improve the disease in many chronic metabolic diseases. Of course, we are also actively seeking ways to improve FG-4592 drug delivery methods, such as using liposome encapsulation to minimize the side effects induced by FG-4592 activation of hepatocyte HIF-2\( \alpha \).
+
+In summary, our study found that the active sphingolipid So(d18:1) has good indicating ability in patients with NASH and that it can bind to HIF-2\( \alpha \) to promote the activation of the NLRP3 inflammasome in macrophages and aggravate liver inflammation and fibrosis in NASH model mice. Macrophage-specific knockout or overexpression of HIF-2\( \alpha \) showed that macrophage HIF-2\( \alpha \) can reduce liver injury and can reduce intrahepatic inflammation and fibrosis. These results not only provide us with a possibility that So(d18:1), a long-chain lipid, binding transcription factor to regulate cellular immune metabolism, but also suggest that the proinflammatory function of So(d18:1) in NASH cannot be ignored. Finally, we used FG-4592 to improve inflammation and fibrosis in NASH. This study provides new targets and potential therapeutic strategies for NASH.
+
+**Conclusions**
+
+Starting from the metabolomics of NASH patients, this study identified So(d18:1),
+which could activate the liver macrophage inflammasome, and found that it could inhibit the binding of the transcription factor HIF-2α with ARNT. We clarified the role of HIF-2α in the development of NASH and explored the role of FG-4592, a stabilizer of HIF-2α, in combating NASH disease progression. The results suggest that HIF-2α is a possible new therapeutic target for the treatment of NASH.
+
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+Figure
+
+![Clustering heatmap of metabolic pathway (A), targeted metabonomic detection of sphingolipids (B), PLS-DA analysis of sphingolipids in serum of patients (C), VIP scores plot (D), scatter plots showing correlations between So(d18:1) concentration and ALT (E), AST (F), Fibroscan (G)](page_124_153_1207_1642.png)
+
+Figure 1 Metabolomic analysis revealed changes of sphingosine in NASH patients
+
+Metabolic analysis of serum samples collected from NASH patients (n=20) and healthy control (n=20). A, clustering heatmap of metabolic pathway. B, targeted metabonomic detection of sphingolipids. C, PLS-DA analysis of sphingolipids in serum of patients.
+D, VIP score plot of the difference sphingolipids between the two groups. E-G, correlative analysis of So(d18:1) concentration in serum with ALT (E), AST (F) and Fibroscan index (G). Correlations between variables were assessed by linear regression analysis. Linear correction index R square and P values were calculated. Data are the means ± s.e.m. One-way ANOVA with Tukey’s post hoc test.
+Figure 2 Sphingosine 18:1 aggravates NASH.
+
+CDAA-HFD-fed mice were treated with vehicle or sphingosine 18:1 for 8 weeks (n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver sections. The circles marked the inflammation foci. n=3 mice per group, 3 images per
+mouse. Scale bar is 100 μm. F, the percentage of fibrosis area. G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means ± s.e.m. A-D, F, J-L, statistical analysis was performed using two-tailed Student’s t-tests; G-I, *Il1b* in J, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Figure 3 So(d18:1) inhibits HIF-2α transcription function in liver macrophages.
+
+A and B, flow cytometry representative chart representative showing that macrophages increased after So(d18:1) treatment. (n=3). C, GO:BP pathway enrichment showing the transcriptional level changes of some immune-related pathways. (n=4). D, Epas1 targets enrichment. E, relative mRNA levels of Hif2a and its downstream target genes in macrophages treated with vehicle or different concentration of So(d18:1). (n=6). F, assessment of HIF-2α protein level of BMDMs stimulated with vehicle and So(d18:1). (n=3). G, representative immunoblot analysis of pro-caspase-1 and caspase-1 from
+Hif2α+/+ and LysMHif2αLSL/LSL BMDMs that were treated with So(d18:1) or not under NLRP3 inflammasome stimulation. (n=3). H and I, protein level of IL-1β (H), IL-18 (I) from Hif2α+/+ and LysMHif2αLSL/LS BMDMs treated with So(d18:1) or not under NLRP3 inflammasome stimulation. (n=6).
+
+Data are the means ± s.e.m. B, H, I, statistical analysis was performed using two-tailed Student’s t-tests; E, statistical analysis was performed using Kruskal-Wallis test with Dunn’s test.
+Figure 4 HIF-2α KO in macrophages accelerated inflammation and fibrosis in NASH mice.
+
+Eight-week-old male Hif2afl/fl and Hif2αLysm mice were administered a GAN diet for 24 weeks (SPF, n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver sections. The circles marked the inflammation foci. n=3 mice
+per group, 3 images per mouse. Scale bar is 100 μm. F, the percentage of fibrosis area.
+
+G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means ± s.e.m. A-D, F, K-L, statistical analysis was performed using two-tailed Student’s t-tests; G-J, *Col2a1* in L, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Figure 5 HIF-2α overexpression in macrophages ameliorated inflammation and fibrosis in NASH mice
+Eight-week-old male Hif2α+/+ and LysMHif2αLSL/LSL mice were administered a GAN diet for 24 weeks (SPF, n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver sections. The circles marked the inflammation foci. n=3 mice per group, 3 images per mouse. Scale bar is 100 μm. F, the percentage of fibrosis area. G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means ± s.e.m. A-D, F, J-L, statistical analysis was performed using two-tailed Student’s t-tests; G-I, Ccl2 in K, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Figure 6 So(d18:1) suppress the binding of HIF-2α and ARNT
+A, PT2385 and So(d18:1) could inhibit HIF-2α transcription ability. (n=6). B, schematic diagram of mammalian two-hybrid system. PT2385 and So(d18:1) could inhibit HIF-2α to bind to ARNT. (n=6). C, Co-immunoprecipitation for ARNT and HIF-2α in HEK293T cells treated with control solvent, So(d18:1) or PT2385, PT2385 and So(d18:1) could inhibit HIF-2α to bind to ARNT. D, molecule docking prediction of So(d18:1) binding sites in HIF-2α PAS-B domain. E, schematic diagram of site missense mutation experiment. PT2385 and So(d18:1) could inhibit normal HIF-2α transcription ability but not HIF-2α with missense mutations. (n=6). F, Cpt1a promoter rHRE constructs plasmid were co-transfected with HIF-2αTM followed by control
+solvent or So(d18:1) treatment. So(d18:1) could inhibit HIF-2α binding ability to rHRE. (n=3).
+
+Data are the means ± s.e.m. A, statistical analysis was performed using One-way ANOVA with Tukey’s post hoc test. B, E, statistical analysis was performed using Kruskal-Wallis test with Dunn’s test. F, statistical analysis was performed using Mann-Whitney U test.
+Figure 7 FG-4592 significantly mitigates CDAA-HFD diet induced NASH
+
+CDAA-HFD-fed mice were treated with vehicle or FG-4592 for 8 weeks (n=6 mice/group). A, liver weights. B, ratios of liver mass to body mass. C, serum ALT. D, serum AST. E, representative H&E (up), and Sirius Red (down) staining of liver
+sections. The circles marked the inflammation foci. n=3 mice per group, 3 images per mouse. Scale bar is 100 \( \mu \)m. F, the percentage of fibrosis area. G-J, Histology scores of hepatic steatosis (G), lobular inflammation (H), ballooning (I), and NAFLD activity (J). K-L, relative mRNA levels of genes related to hepatic inflammation (K) and fibrosis (L).
+
+Data are the means \( \pm \) s.e.m. A-D, F, K-L, statistical analysis was performed using two-tailed Student’s t-tests; G-J, *Il1b* in K, *Timp1* and *Col5a2* in L, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Materials and Methods
+
+Human participants
+
+The clinical patient cohorts of this study were collected from Peking University People’s Hospital. With the approval of the Ethics Committee of Peking University People’s Hospital (Ethics Review Approval No.: 2021PHB124-001), all volunteers who participated in the study signed a written informed consent form.
+
+The inclusion criteria were as follows: NASH disease diagnosis was in accordance with the Guidelines of Prevention and Treatment of Non-Alcoholic Fatty Liver Disease: a 2018 Update prepared by the National Workshop on Fatty Liver and Alcoholic Liver Disease, Chinese Society of Hepatology, Chinese Medical Association; Fatty Liver Experts Committee, Chinese Medical Doctor Association. The diagnosis requires the patient to have histological evidence of diffuse hepatocyte steatosis, intrahepatic inflammation and fibrosis, and persistent serum ALT and GGT increases. Patients with alcoholic liver disease, type 3 hepatitis C virus infection, autoimmune hepatitis, hepatolenticular degeneration and drug-induced liver disease were excluded. A FibroScan liver elasticity test was performed to support the diagnosis. All patients were newly diagnosed with NASH and did not receive relevant treatment. Healthy volunteers were also recruited from Peking University People’s Hospital. They were required to have normal serum ALT and GGT levels. FibroScan indicated that their liver elasticity was normal. Their age, sex and BMI were matched to those of NASH patients.
+
+Animals
+
+C57BL/6J wild-type mice were purchased from the Department of Laboratory
+Animal Science, Peking University Health Science Center. *Hif2α*^fl/fl*, *Hif2α*^ΔLysm*, *Hif2α*^+/+* and LysMHif2α^LSL/LSL* mice were purchased from Jackson Lab.
+
+Mice were randomly divided into different groups and raised in cages under standard SPF laboratory conditions with free access to water and feed. The temperature was maintained at 21-24 °C, and the humidity was maintained at 40-70%. The light was on from 08:00 to 20:00. The animal use licence number was SYXK (Beijing) 2011-0039. All animal experiments complied with the rules for the use of experimental animals, treatment and euthanasia approved by Peking University Health Science Center (permit: LA2020481).
+
+A normal chow diet (NCD) was purchased from Beijing Keaoxieli Feed Co., Ltd., in which fat supplies 20% of calories for energy. The GAN diet (D09100310) was purchased from Research Diets, USA, in which fat provides 40% of calories for energy (including palm oil), fructose provides 20% of calories for energy, and 2% cholesterol is added. Mice were fed the GAN diet for 24 weeks to create the NASH model. The CDAA-HFD (A06071302) was purchased from Research Diets, USA, in which fat supplies 60% of calories for energy, and the diet contains 0.1% methionine and does not contain any added choline. Mice were fed the CDAA-HFD for 8 weeks to create the NASH model.
+
+For the So(d18:1) intraperitoneal injection experiment, 6-week-old male mice were randomly fed the CDAA-HFD for 8 weeks with So(d18:1) (10 mg/kg body weight) injected intraperitoneally every day. For the FG-4592 intraperitoneal injection experiment, 6-week-old male mice were randomly fed the CDAA-HFD for 8 weeks
+with FG-4592 (25 mg/kg body weight) injected intraperitoneally every day.
+
+Cell lines
+
+The HEK293T cell line used in this study was purchased from the National Collection of Authenticated Cell Cultures.
+
+Primary mouse bone marrow-derived macrophage culture
+
+Bone marrow-derived macrophages were isolated from the bone marrow of C57BL/6J wild-type mice, macrophage-specific knockout HIF-2α mice (\(Hif2a^{\Delta Lysm}\)) and macrophage-specific overexpressing HIF-2α mice (LysMHif2a^{LSL/LSL}).
+
+BMDMs were prepared as previously described[26]. The bone marrow collected from the femur and tibia of mice was inoculated on sterile petri dishes and cultured in RPMI 1640 containing 10% FBS, 100 units/ml penicillin, 100 mg/ml streptomycin and 10 ng/ml macrophage colony stimulating factor (M-CSF) for 5-6 days. When activating the NLRP3 inflammasome, BMDMs were incubated with LPS (500 ng/ml, 4 hours) and then were treated with nigericin (6.7 μM, 1 hour).
+
+Separation of liver nonparenchymal cells
+
+As mentioned earlier[27], primary hepatic macrophages were isolated from male mice by injecting type IV collagenase into the liver. Mice were anaesthetized with isoflurane and perfused through the portal vein. Krebs buffer was used to remove blood from the liver. Then, Krebs buffer supplemented with type IV collagenase was used for digestion. After digestion, the liver was collected and rinsed with RPMI 1640. The digested liver cell suspension was passed through a 70-μm cell filter (BD). The samples were centrifuged at \(50 \times g\) for 3 minutes, and the supernatant was retained. The cells
+were centrifuged at 1200 rpm for 10 minutes again to precipitate the nonparenchymal cells from the supernatant.
+
+Flow cytometry
+
+Isolated liver nonparenchymal cells were washed in PBS buffer containing 10% FBS, and red cells were removed. The cells were stained with specific antibodies (7AAD BD, APC/cy7 anti-CD45 BioLegend, PE anti-CD11b BioLegend, APC anti-F4/80 BioLegend) at 4 °C for 30 minutes protected from light, washed with cold PBS 3 times, and analysed by flow cytometry using FACS SORP flow cytometry (BD). The data were analysed using FlowJo software (TreeStar).
+
+Dual-luciferase reporter assay
+
+Cells were seeded into a 48-well plate at a density of \(2 \times 10^4\) per well. The luciferase constructs for the HIF response element (HRE) and the oxygen-stable HIF-2α triple mutant (HIF-2αTM) plasmid were previously described[20, 28]. To explore the effect of So(d18:1) on the transcriptional regulatory activity of HIF-2α, HIF-2αTM plasmid, p2.1 HRE-Luc plasmid and Renilla positive control plasmid mixed with Lipo8000 transfection reagent were added to each well cells.
+
+For the Mammalian Two-Hybrid System, pG5 luciferase vector was cotransfected with pBIND-HIF-2a and pACT-ARNT into cells using the protocol described in the CheckMate™ Mammalian Two-Hybrid System (Promega)[29].
+
+For the mutant assay, HIF-2αTM plasmid and mHIF-2a G324E+S305M plasmid were used. For the *Cpt1a* rHRE binding assay, the pGL3 basic vector (Promega) was cloned with the presumed rHRE1 region in the *Cpt1a* promoter upstream of the firefly
+luciferase gene as the reporter plasmid. The reporter plasmid, HIF-2α™ plasmid or corresponding control empty vector were transfected into HEK293T cells together. The luciferase assay was performed as previously described.
+
+The cells were treated with control vehicle, 2 μM HIF-2α-specific inhibitor PT2385 and 2 μM So(d18:1) for 24 h, the supernatant was discarded, and the samples were gently rinsed with PBS buffer. Next, 100 μL of PLB lysis solution was added to the cells, and they were incubated at room temperature for 10 minutes. Ten microlitres of the cell lysate was added to a white flat-bottomed 96-well plate, and the following procedure was used in the multifunction microplate reader (Tecan): 40 μL of luciferase substrate was added, the fluorescence value was detected, and 40 μL of stop liquid was added. Finally, the ratio of the two fluorescence values was calculated.
+
+Mass spectrometry
+
+Targeted lipidomics was performed according to a previous study with minor modifications[30]. Liver tissue (20 mg) was added to 80 μL of water and homogenized for 1 minute. Then, 400 μL of chloroform and methanol (v/v, 2:1) was added, and the samples were vortexed for 10 minutes and centrifuged at 4 °C and 12,000 rpm for 10 minutes. The lower layer was transferred into a new 1.5-ml tube and dried by a SpeedVac. Subsequently, 100 μL of cold methanol and isopropanol (v/v, 4:1) was added, and the tubes were vortexed for 10 minutes and centrifuged at 4 °C and 18,000 rpm for 10 minutes. The supernatant was transferred to a vial for MS detection. For plasma (100 μL), 400 μL of chloroform and methanol (v/v, 2:1) was added, and the remaining processes were the same as for liver tissue. A Waters UPLC BEH C18 column (2.1 mm
+(inner diameter) × 100 mm (length), 1.7 μm (particle dimension)) was used for separation. The mobile phase consisted of water (containing 5 mM ammonium acetate and 0.1% formic acid; phase A) and isopropanol:acetonitrile (1:1, v/v, containing 5 mM ammonium acetate and 0.1% formic acid; phase B) at a flow rate of 0.4 ml/min and a column temperature of 40 °C, with an injection volume of 2 μL. The UPLC and MS parameters used were chosen according to a previous study[30].
+
+For the quantification of ceramides, S1P and sphingosine, 25 μl of plasma or 20 mg of liver tissue was homogenized with 400 μl of chloroform and methanol (v/v, 2:1) containing 5 μM sphingosine-d7 d18:1 and 25 μM ceramide-d7 d18:1/15:0 (Avanti Polar Lipids) as the internal standards. The mixture was oscillated immediately and then centrifuged at 13,000 rpm for 20 min. The lower phase was dried using a SpeedVac. The sediment was dissolved in 100 μl of isopropanol and acetonitrile (v/v, 1:1) and analysed using the Waters Acquity UPLC coupled with the AB SCIEX QTRAP 5500 system using a Waters UPLC CSH C18 column (3.5 μm, 2.1 × 100 mm). The UPLC and MS parameters used were chosen according to a previous study[31]. The lipid metabolites were quantified using MultiQuant 2.1 (AB SCIEX).
+
+NAS scoring
+
+The NAS, also known as the NAFLD activity score (NAS), is calculated as the sum of three histological components, that is, steatosis (0-3), ballooning (0-2) and lobular inflammation (0-3). Patients with NAS \( \geq 5 \) were considered definite NASH, patients with scores of 3 or 4 were considered borderline NASH, and patients with scores of less than 3 were diagnosed as NAFL.
+Enzyme-linked immunosorbent assay (ELISA)
+
+The levels of IL-1β (Abclonal, RK00006) and IL-18 (Abclonal, RK00104) were measured by ELISA kits according to the manufacturer’s instructions. In short, the standard or sample was added to the antibody-coated plate and incubated at 37 °C for 120 minutes. Bio-coupled antibody solution, avidin HRP solution and TMB substrate solution were added to the microporous plate in turn. The absorbance at 450 nm was measured within 15 minutes after adding the termination solution.
+
+Western blot and immunoprecipitation
+
+Whole cell lysates were prepared with RIPA buffer. The cell homogenate was incubated on ice in RIPA buffer for 15-20 minutes and then centrifuged at 10,000 rpm at 4 °C for 10 minutes. The supernatant was transferred into a new tube and mixed with 5× loading buffer. The mixture was boiled for 10 minutes.
+
+For co-IP, Protein A/G PLUS agarose beads (Santa Cruz) were placed in the cell lysate supernatant. The samples were incubated upside down overnight at 4 °C. TBST buffer was used to wash 3 times. Then, 50 μl of 2× loading buffer was added to the beads and boiled for 10 minutes.
+
+Each well containing 50 μg of protein lysate was separated by SDS–PAGE, transferred to a nitrocellulose membrane, and immunoblotted at 4 °C overnight. The antibodies were anti-caspase-1 (AdipoGen, AG-20B-0042), anti-HIF-2α (Novus, NB100-132), anti-ARNT (Santa Cruz, sc-17811), anti-GAPDH (CST, #5174) and anti-β-Actin (Abclonal, AC038). All primary antibodies were used at a dilution of 1:2000. The HRP-coupled secondary antibodies used were anti-rabbit (Abclonal, AS014) and
+anti-mouse (Abclonal, AS003) secondary antibodies at a dilution of 1:2000, and immunoblotting was carried out using a chemical imaging system (ChemiDoc, Bio-Rad).
+
+RT-qPCR analysis
+
+Liver tissues were flash-frozen in liquid nitrogen and stored at -80 °C.
+
+Total RNA from frozen liver tissues was extracted using TRIzol reagent (Invitrogen). cDNA was synthesized from 2 µg of total RNA using 5× All-In-One RT MasterMix (Abm). A list of quantitative PCR (qPCR) primer sequences is provided in Supplementary Table 2. The relative amount of each mRNA was compared to the corresponding gene and normalized, and the results are expressed as fold changes relative to the control group.
+
+RNA sequencing and analysis
+
+Library preparation and transcriptome sequencing were conducted by GENEWIZ LLC. The Illumina HiSeq platform was used for sequencing. For the data analysis, we first evaluated the quality of the sequence data by fastqc v0.11.9, and the sequence quality was considered to be good for subsequent analysis. Trim-galore v0.6.7 was used for adapter trimming and low-quality reads. Clean read mapping was conducted by Hisat2 v2.2.1, and we used mm10 as the mouse reference genome. After that, gene expression was quantified by featureCounts v2.0.1. All downstream analyses were performed in R v4.2.1. We used the edgeR v3.38.4 R package for differential expression analysis. We set the cut-off of differentially expressed genes as follows: p value of 0.05 and absolute value of fold change of 1.5. Gene Ontology (GO) enrichment analysis and
+transcription factor enrichment analysis were conducted by the clusterProfiler v4.4.4 R package. We used the ARCHS4 transcription factor coexpression database from the Enrichr library as the database for transcription factor enrichment analysis. The record GSE228548 has been submitted to GEO database.
+
+Single-cell RNA sequencing analysis
+
+We downloaded the count matrix of the GSE166504 dataset from the GEO database and analysed it using R. This is a single-cell transcriptome dataset of livers where mice were fed a chow diet, a HFHFD diet for 15 weeks, and a HFHFD diet for 30 weeks. We clustered these cells by mRNA expression level using the Seurat package, and then we annotated these cell clusters using the SingleR package.
+
+Statistics analysis
+
+This study used GraphPad Prism software v.9.0. and SPSS software v.27.0 for analysis and statistics. The experimental results of this study are presented as the mean ± standard error of the mean (SEM). First, the Kolmogorov-Smirnov statistical method was used to detect the normality of all data. If the data conformed to a normal distribution, Student’s t test was used to compare two groups, one-way ANOVA was used for three or more groups, and Tukey’s post-test was used for statistical analysis. If the data did not conform to a normal distribution, a nonparametric test was used. Mann-Whitney’s statistical method was used for analysis between two groups, and the Kruskal-Wallis and Dunn’s time tests were used for statistical analysis of three or more groups.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• Supplementary.pdf

02624773f6e6ce56158b53f0fcddcdef4027c464f514126d8dae690687431871/preprint/supplementaries/Supplementary/Supplementary.md

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+Sphingosine d18:1 Promotes Nonalcoholic Steatohepatitis by Inhibiting Macrophage HIF-2α
+
+Jialin Xia1,2,3,7, Hong Chen1,4,7, Xiaoxiao Wang6,7, Weixuan Chen4, Jun Lin1,2,3, Feng Xu1,2,3, Qixing Nie1,2,3, Chuan Ye1,2,3, Bitao Zhong1, Min Zhao4, Chuyu Yun4, Guangyi Zeng1,2,3, Sen Yan4, Xuemei Wang1,2,3, Lulu Sun5, Feng Liu6, Huiying Rao6,*; Changtao Jiang1,2,3,* and Yanli Pang1,4,*
+Supplementary Figures
+
+A-C, levels of ceramides (A), S1P (B) and other types of sphingosine (C) in the serum of patients in different NAFLD stages. D, E, serum So(d18:1) concentration in healthy volunteers (D) and different stages of NASH patients (E). F, G, serum So(d18:1) concentration of patients in different steatosis stages (F) and different lobular inflammation stages (G). H-J, serum ALT (H), AST (I) and serum concentration of So(d18:1) (J) in different time point of NASH modeling mice. K, liver So(d18:1) relative concentration fold changes.
+
+Data are the means ± s.e.m., G, statistical analysis was performed using two-tailed Student’s t-tests; D, F, statistical analysis were performed using two-tailed Mann-Whitney U-tests. B, E, H, J statistical analysis were performed using One-way ANOVA
+with Tukey’s post hoc test. A, C, I, K statistical analysis were performed using Kruskal-Wallis test with Dunn’s test.
+Supplementary Figure 2 So(d18:1) could not influence the lipid metabolism in NASH progression
+
+CDAA-HFD-fed mice were treated with vehicle or sphingosine 18:1 for 8 weeks (n=6 mice/group). A, body weights. B, hepatic TG. C, serum TG. D, hepatic CE. E, serum CE. F, serum NEFA. G, relative mRNA levels of genes related to lipid metabolism.
+
+Data are the means ± s.e.m. A-C, E-G, statistical analysis was performed using two-tailed Student’s t-tests; D, Cd36 in G, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Supplementary Figure 3 So(d18:1) inhibits HIF-2α transcription function in liver macrophages
+
+A and B, analyze of non-parenchymal cells subcluster single-cell RNA-sequencing data from mice fed with chow diet or HFHFD diet for 15 weeks or 30 weeks. Cell clustering changed through NASH progression (A), and macrophages and monocytes increased largely (B). (n=6). C, gating strategy of liver macrophages which were characterized as live CD45+F4/80+CD11b+. D, Hif1a targets enrichment had no change after So(d18:1) treatment. (n=4). E, relative mRNA levels of Hif1a and its downstream target genes in macrophages treated with vehicle or So(d18:1). (n=6).
+Data are the means ± s.e.m. B, E, statistical analysis was performed using One-way ANOVA with Tukey’s post hoc test.
+Supplementary Figure 4 HIF-2α KO in macrophages didn’t affect lipid metabolism in liver.
+
+Eight-week-old male *Hif2a*fl/fl and *Hif2a*ΔLysm mice were administered a GAN diet for 24 weeks (SPF, n=6 mice/group). A, body weights. B, hepatic TG. C, serum TG. D, hepatic CE. E, serum CE. F, serum NEFA. G, relative mRNA levels of genes related to lipid metabolism.
+
+Data are the means ± s.e.m. A-G, statistical analysis was performed using two-tailed Student’s t-tests.
+Supplementary Figure 5 HIF-2α overexpression in macrophages didn’t affect lipid metabolism
+
+Eight-week-old male *Hif2a*+/+ and LysMHif2αLSL/LSL mice were administered a GAN diet for 24 weeks (SPF, n=6 mice/group). A, body weights. B, hepatic TG. C, serum TG. D, hepatic CE. E, serum CE. F, serum NEFA. G, relative mRNA levels of genes related to lipid metabolism.
+
+Data are the means ± s.e.m. A-G, statistical analysis was performed using two-tailed Student’s t-tests. *Scd1* in G, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Supplementary Figure 6 FG-4592 didn’t affect lipid metabolism
+
+CDAA-HFD-fed mice were treated with vehicle or FG-4592 for 8 weeks (n=6 mice/group). A, body weights. B, hepatic TG. C, serum TG. D, hepatic CE. E, serum CE. F, serum NEFA. G, relative mRNA levels of genes related to lipid metabolism.
+
+Data are the means ± s.e.m. A-C, F-G, statistical analysis was performed using two-tailed Student’s t-tests. D-E, Scd1 in G, statistical analysis was performed using two-tailed Mann-Whitney U-tests.
+Supplementary Table 1
+
+<table>
+  <tr>
+    <th></th>
+    <th>Healthy volunteer</th>
+    <th>NASH patient</th>
+    <th>p value</th>
+  </tr>
+  <tr>
+    <td>Female sex (%)</td>
+    <td>50</td>
+    <td>50</td>
+    <td></td>
+  </tr>
+  <tr>
+    <td>Age (y)</td>
+    <td>45.63 ± 14.97</td>
+    <td>43.00 ± 14.53</td>
+    <td>0.6184</td>
+  </tr>
+  <tr>
+    <td>BMI (kg/m2)</td>
+    <td>21.68 ± 1.94</td>
+    <td>27.88 ± 5.22</td>
+    <td>0.0001</td>
+  </tr>
+  <tr>
+    <td>TG (mmol/L)</td>
+    <td>0.98 ± 0.36</td>
+    <td>1.66 ± 0.59</td>
+    <td>0.0004</td>
+  </tr>
+  <tr>
+    <td>TC (mmo/L)</td>
+    <td>4.91 ± 1.06</td>
+    <td>5.07 ± 1.19</td>
+    <td>0.6849</td>
+  </tr>
+  <tr>
+    <td>ALT (U/L)</td>
+    <td>16.44 ± 5.92</td>
+    <td>106.63 ± 56.80</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td>GGT (U/L)</td>
+    <td>22.31 ± 11.38</td>
+    <td>91.44 ± 79.70</td>
+    <td>0.0018</td>
+  </tr>
+  <tr>
+    <td>AST (U/L)</td>
+    <td>21.06 ± 5.30</td>
+    <td>66.38 ± 20.34</td>
+    <td>&lt;0.0001</td>
+  </tr>
+  <tr>
+    <td>Fibroscan (CAP)</td>
+    <td>182.87 ± 43.89</td>
+    <td>277.31 ± 73.58</td>
+    <td>&lt;0.0001</td>
+  </tr>
+</table>
+
+This table shows the general information of healthy volunteers and NASH patients. There ages and gender are totally matched.
+<table>
+  <tr>
+    <th>Genes</th>
+    <th>Primer sequences</th>
+  </tr>
+  <tr>
+    <td>Hif2a Fwd</td>
+    <td>5′- CTGAGGAAGGAGAAATCCCGT-3′</td>
+  </tr>
+  <tr>
+    <td>Hif2a Rev</td>
+    <td>5′- TGTGTCCGAAGGAAGCTGATG-3′</td>
+  </tr>
+  <tr>
+    <td>Arg1 Fwd</td>
+    <td>5′-AAGAATGGGAAGAGTCAGTGTTGG-3′</td>
+  </tr>
+  <tr>
+    <td>Arg1 Rev</td>
+    <td>5′-GGGAGTGTGTGATGTCAGTGTTG-3′</td>
+  </tr>
+  <tr>
+    <td>VEGF Fwd</td>
+    <td>5′- GGAGATCCTTTCGAGGAGCACCTT-3′</td>
+  </tr>
+  <tr>
+    <td>VEGF Rev</td>
+    <td>5′- GGCAGATTTAGCAGCAGATAAAGAA -3′</td>
+  </tr>
+  <tr>
+    <td>Spiint Fwd</td>
+    <td>5′-GTCGGCGTATGGCTCCTT -3′</td>
+  </tr>
+  <tr>
+    <td>Spiint Rev</td>
+    <td>5′-GCTTCCGGTGTCGCCAGCACCAA-3′</td>
+  </tr>
+  <tr>
+    <td>Depdc7 Fwd</td>
+    <td>5′-AGCAGAGCTCCTGGTAAAATGG-3′</td>
+  </tr>
+  <tr>
+    <td>Depdc7 Rev</td>
+    <td>5′-AGCCGTCTAAACTCCTCCCT-3′</td>
+  </tr>
+  <tr>
+    <td>Il10 Fwd</td>
+    <td>5′-ACCTGCTCCACTGCCTTGCT-3′</td>
+  </tr>
+  <tr>
+    <td>Il10 Rev</td>
+    <td>5′-GGTTGCACAAGCCTTATCGGA-3′</td>
+  </tr>
+  <tr>
+    <td>Tnfa Fwd</td>
+    <td>5′-AGGGTCTGGGCCATAGAACT-3′</td>
+  </tr>
+  <tr>
+    <td>Tnfa Rev</td>
+    <td>5′-CCACCACGCTCTTCTGTCTAC-3′</td>
+  </tr>
+  <tr>
+    <td>Il1b Fwd</td>
+    <td>5′-AAGAGCTTCAGGCAGGCAGTATCA-3′</td>
+  </tr>
+  <tr>
+    <td>Il1b Rev</td>
+    <td>5′-TGCAGCTGTCTAGGAACGTCA-3′</td>
+  </tr>
+  <tr>
+    <td>Il6 Fwd</td>
+    <td>5′-TAGTCCTTCCTACCCCAATTTCC-3′</td>
+  </tr>
+  <tr>
+    <td>Il6 Rev</td>
+    <td>5′-TTGGTCCTTAGCCACTCCTTC-3′</td>
+  </tr>
+  <tr>
+    <td>Ccl2 Fwd</td>
+    <td>5′-TTAAAAACCTGGATCGGAACCAA-3′</td>
+  </tr>
+  <tr>
+    <td>Ccl2 Rev</td>
+    <td>5′-GCATTAGCTTCAGATTTCAGGGT-3′</td>
+  </tr>
+  <tr>
+    <td>F4/80 Fwd</td>
+    <td>5′-GGATGTACAGATGGGGGATG-3′</td>
+  </tr>
+  <tr>
+    <td>F4/80 Rev</td>
+    <td>5′-CATAGCTGGGCAAGTGGTA-3′</td>
+  </tr>
+  <tr>
+    <td>Tgfb Fwd</td>
+    <td>5′-GTCACTGGAGTTGTACGGCA-3′</td>
+  </tr>
+  <tr>
+    <td>Tgfb Rev</td>
+    <td>5′-GGGCTGATCCCGTTGATTTTC-3′</td>
+  </tr>
+  <tr>
+    <td>Sma Fwd</td>
+    <td>5′-CCAGCCATCTTTTCATTGGGATG-3′</td>
+  </tr>
+  <tr>
+    <td>Sma Rev</td>
+    <td>5′-TACCCCCTGACAGGACGTTG-3′</td>
+  </tr>
+  <tr>
+    <td>Timp1 Fwd</td>
+    <td>5′-CCTTTGCACTCTCTGGCATCT-3′</td>
+  </tr>
+  <tr>
+    <td>Timp1 Rev</td>
+    <td>5′-CTCGTTTGATTTCTTGGGGAAC-3′</td>
+  </tr>
+  <tr>
+    <td>Col1al Fwd</td>
+    <td>5′-TAGGCCATTGTGTATGCAGC-3′</td>
+  </tr>
+  <tr>
+    <td>Col1al Rev</td>
+    <td>5′-ACATGTTTCAGCTTTGTGGACC-3′</td>
+  </tr>
+  <tr>
+    <td>Col2a1 Fwd</td>
+    <td>5′-TGAGGTCTGGGTAAAGGCAA-3′</td>
+  </tr>
+</table>
+<table>
+  <tr>
+    <th>Gene</th>
+    <th>Oligo sequence</th>
+  </tr>
+  <tr>
+    <td>Col2a1 Rev</td>
+    <td>5′-GTATGAGGTCACCGTCCAGG-3′</td>
+  </tr>
+  <tr>
+    <td>Col3a1 Fwd</td>
+    <td>5′-TAGGACTGACCAAGGTGGCT-3′</td>
+  </tr>
+  <tr>
+    <td>Col3a1 Rev</td>
+    <td>5′-GGAACCTGGTTTCTTCTTCACC-3′</td>
+  </tr>
+  <tr>
+    <td>Col4a1 Fwd</td>
+    <td>5′-CACATTTTCCACAGCCAGAG-3′</td>
+  </tr>
+  <tr>
+    <td>Col4a1 Rev</td>
+    <td>5′-GTCTGGCTTCTGCTGCTCTT-3′</td>
+  </tr>
+  <tr>
+    <td>Col4a2 Fwd</td>
+    <td>5′- GCCCTGTAGTCCTGGGAATC -3′</td>
+  </tr>
+  <tr>
+    <td>Col4a2 Rev</td>
+    <td>5′- CCAGTGCTACCCCGGAGAAA -3′</td>
+  </tr>
+  <tr>
+    <td>Col5a2 Fwd</td>
+    <td>5′- CATGGAGAAGGTTTCCAATG -3′</td>
+  </tr>
+  <tr>
+    <td>Col5a2 Rev</td>
+    <td>5′- AAAGCCCAGGAACAAGAGAA -3′</td>
+  </tr>
+  <tr>
+    <td>Cd36 Fwd</td>
+    <td>5′-AGATGACGTGGCAAAGAACAG-3′</td>
+  </tr>
+  <tr>
+    <td>Cd36 Rev</td>
+    <td>5′-CCTTGGCTAGATAACGAACCTCTG-3′</td>
+  </tr>
+  <tr>
+    <td>Srebp1c Fwd</td>
+    <td>5′-GGAGCCATGGATTGCACATT-3′</td>
+  </tr>
+  <tr>
+    <td>Srebp1c Rev</td>
+    <td>5′-GCTTCCAGAGAGGGAGGCCAG-3′</td>
+  </tr>
+  <tr>
+    <td>Acaca Fwd</td>
+    <td>5′-ATGGGCGGAATGGTCTCTTTTC-3′</td>
+  </tr>
+  <tr>
+    <td>Acaca Rev</td>
+    <td>5′-TGGGGACCTTGTCTTTCATCAT-3′</td>
+  </tr>
+  <tr>
+    <td>Fasn Fwd</td>
+    <td>5′-GGAGGTGGGTGATAGCCGGTAT-3′</td>
+  </tr>
+  <tr>
+    <td>Fasn Rev</td>
+    <td>5′-TGGGTAATCCATAGAGCCCCAG- 3′</td>
+  </tr>
+  <tr>
+    <td>Scd1 Fwd</td>
+    <td>5′-TTCTTGCGATAACACTCTGGTGCG-3′</td>
+  </tr>
+  <tr>
+    <td>Scd1 Rev</td>
+    <td>5′-CGGGATTGAATGTTCTTGTTCGT-3′</td>
+  </tr>
+  <tr>
+    <td>β-Actin Fwd</td>
+    <td>5′-GGCTGTATTCCCCTCCATCG-3′</td>
+  </tr>
+  <tr>
+    <td>β-Actin Rev</td>
+    <td>5���-CCAGTTGGTAACAATGCCATGT-3′</td>
+  </tr>
+</table>

02624773f6e6ce56158b53f0fcddcdef4027c464f514126d8dae690687431871/preprint/supplementaries/Supplementary/images_list.json

@@ -0,0 +1,51 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_1.jpg",
+    "caption": "Supplementary Figure 1 Serum concentration of sphingolipid in NASH patients",
+    "bbox": [
+      [
+        150,
+        110,
+        827,
+        625
+      ]
+    ],
+    "page_idx": 1
+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_2.jpg",
+    "caption": "Supplementary Figure 2 So(d18:1) could not influence the lipid metabolism in NASH progression",
+    "bbox": [
+      [
+        150,
+        93,
+        840,
+        393
+      ]
+    ],
+    "page_idx": 3
+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_4.jpg",
+    "caption": "Supplementary Figure 4 HIF-2α KO in macrophages didn't affect lipid metabolism in liver.",
+    "bbox": [],
+    "page_idx": 4
+  },
+  {
+    "type": "image",
+    "img_path": "images/Supplementary_Figure_5.jpg",
+    "caption": "Supplementary Figure 5 HIF-2α overexpression in macrophages didn't affect lipid metabolism",
+    "bbox": [
+      [
+        145,
+        87,
+        830,
+        410
+      ]
+    ],
+    "page_idx": 6
+  }
+]

027b827c3b80c86306a8c299d162b6cb2bb24a38c0ffa3c834d579a1e6c6338c/peer_review/images_list.json

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+[]

027b827c3b80c86306a8c299d162b6cb2bb24a38c0ffa3c834d579a1e6c6338c/peer_review/peer_review.md

@@ -0,0 +1,282 @@
+Peer Review File
+
+Toll-like receptor mediated inflammation directs B cells towards protective antiviral extrafollicular responses
+
+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):
+
+This manuscript by Lam and Baumgarth investigates the signals that control the generation of the EF versus GC B cell response following infection or vaccination. This is a question of high import given that early control of infection can determine the extent of pathology and severity of illness. The authors reveal a regulatory role of TLR mediated signals in determining the fate decision of activated B cells, with a sustained innate signal promoting differentiation along the EF pathway resulting in early production of antibody capable of promoting clearance. The study includes a careful timecourse of EF versus GC cell and the source of virus-specific antibody. This is an important study that significantly extends our understanding of B cell differentiation. Overall the conclusions are well supported although at times conclusions are based on results that do not appear to be significant (detailed below).
+
+Major comments:
+1. One would expect an increase in HA-specific B cells in Fig 3e given the substantial increase in GC cells in the vaccinated animals, but this seems not to be the case. Could the authors comment on the specificity of these new GC cells?
+2. What percentage of cells fall into the positive quadrant in non vaccinated mice (Fig. 3d)? As there is no increase in HA-sp B cells from d3 to d7, without a control, can one be certain these are in fact HA specific cells being analyzed?
+3. The data in SF2 appear to be total and not HA-specific. Without that, it is difficult to draw conclusions about the HA response.
+4. In SF3, there is a trend towards increased EF in TLR7KO mice. The low number of animals and variability in the TLR7 KO mice make achieving significance challenging. If the two types of EF cells are pooled for analysis, does the picture become clearer?
+5. In Fig 4b, did the DKO serum provide any protection? Was a control serum transfer experiment performed?
+6. The data in SF5 are challenging for comparison between conditions as there are limited times when the same dose is used in combination versus individual stimulations. Nonetheless, one can compare the 1ug/ml anti-IgM and 1ug/ml LPS in this way. When doing so it is hard to see the how the combination strongly supported viability (SF5a) or proliferation (SF5b) compared to the LPS alone as is stated. They appear similar.
+7. Are the reductions in Ki67+ cells in SF7 significant? If not this limits the conclusion that can be drawn in lines 247-49.
+8. In lines 264-65 authors should state trend as it does not appear to significantly increase. For many of the animals there is a very modest increase and one TKO has a major decrease. Thus conclusions should be drawn with care.
+9. Additional discussion of the TLR ligand independent requirement for TLR pathway in B cell activation would be welcome.
+
+Minor comments
+1. Line 81: believe meant vesicular not vaccinia
+2. Line 127: add virus after influenza
+3. Line 197: EFR-derived serum is a bit unclear, suggest “serum from d10 animals wherein antibody is predominantly EFR derived” if this is what is meant
+4. Line 211: the chimera to which the authors are referring should be noted prior to BMC
+5. Line 370: induce for indue
+6. The authors are asked to increase axis labels and percentage values in flow plot font size where possible as many are quite hard to read.
+7. Consider keeping nomenclature similar- “fold difference” axis label Fig 6e
+Reviewer #2 (Remarks to the Author):
+
+The paper by Lam et al explores the mechanisms underlying the formation of extrafollicular plasmablasts (EFRs) and short term humoral memory toward influenza. The authors provide support for a correlation between the formation of EFRs and protective properties of serum at early time points after antigen challenge. Using a series of KO models the authors determine that a key component for the formation of EFRs is Toll like receptor signaling that they find stimulate IRF4 transcription in the activated B-cell. They conclude that inflammatory signals impact the fate of activated B-cells to generate efficient short term response to antigen.
+
+This is in many regards an interesting report representing an impressive amount of work in different model systems. The large number of models and experimental setups explored does, however, become a liability as parts of the data are of limited quality. The authors base many of their conclusions on data collected from few animals creating a challenge in interpretation of the results. This problem is aggravated by that substantial portions of the data are presented as relative controls, in some cases wt, and other cases as compared to non-stimulated cells. It is difficult to fully delineate how this normalization was made. Furthermore, the authors does at times ignore significant differences in their data when they and put forward differences that are not indicated as significant. This creates a challenge to read and validate the data in a proper manner making it difficult to fully appreciate the reported findings and to understand the relevance of the findings.
+
+Specific comments.
+1: The authors should go over their data and decide what parts that are conclusive and where there is a need to repeat the experiments, alternatively take some data out of the paper or rephrase their conclusions. This is a general problem throughout the report and my list below in mainly to exemplify the problem rather than to provide a complete list of concerns.
+- Figure 1, no indication of # of animals or experiments.
+- Figure 1c-e, no significances indicated, hence not possible to support the authors conclusion on row 148 that the response peak at day 9.
+- Figure 2 c-e, no stats indicated. There would appear to be as much HA+GC as HA+EF cells at day 6.
+- The only stats indicated in figure 3b are infection day 10 and 3 days postimmunization. This is not an optimal or relevant comparison. Why have the authors used day 7 data to analyze EF and 10 for GC?
+- In S3a, significant increase in GC is not mentioned. Many data points so spread out that phenotypes well can be lost.
+- In s3b, is there really not any significant difference in EFs in the TLR7 KO?
+- In figure 4b, the TKO display a significant reduction in CD138+EFs that is ignored.
+- In row 204 the authors claim that there is no significant difference between wt and Tko serum in figure 4c. However, the graph shows clear differences day 7 and 8.
+- Row 246 the authors claim that fewer DK and TK cells express Ki67, however, no statistical analysis has been performed in figure S7.
+- Row 261, the authors claim that pMtor is increased in TLR signaling deficient cells. However, stat analysis only shown for 0 and 100 Ig concentrations within each one of the genotypes. Hence, I cannot see proper validation of KO vs wt.
+- Row 264, the authors claim that TLR signaling led to enhanced surface IgD expression, however, figure 9a does not show any statistical significances.
+- Row 331 the authors claim that Ag+LPS boosted mice had the highest anti influenza serum levels but in panel 8f, there is no significant difference between Ag boosted and Ag LPS boosted animals.
+
+Minor comments:
+- Figure legend for fig 2 contains ref to panels I, j, k not in the figure.
+- Row 162-165 talks about smaller GCs. Should this be fewer cells as the size of the GC hardly is investigated?
+- 3b GC cells compared to infection day 10 and EF cells day 7.
+- Row 214 talks about larger ERFs, correct?
+- Are the significance values in figure S8c really correct?
+Reviewer #3 (Remarks to the Author):
+
+In this manuscript the authors show that Influenza infection induces rapid early antibody response that is driven by signals from the toll-like receptors (TLRs). This response appears to be protective as seen by serum transfer experiments and inclusion of TLR signals also increases early antibody response during immunization with Influenza antigens. This study is interesting and important in terms of understanding signals regulating early antibody response against viruses and will be important in thinking about vaccine design for Influenza virus. However, the manuscript is presented in manner that makes it difficult understand the relevance and contribution of extrafollicular response. It is known that TLR signals can affect both early B cell responses and germinal center (GC) B cell responses. The main interesting point of this study is the specific effects of TLR signals on extra follicular (EF) response during infection and immunization. But the lack of clarity on what is considered EF response, whether EF response is protective or pathogenic makes it difficult to understand the specific role of EF response. Similarly, it is also not clear which effects of TLR signals are specific to EF B cells and not GC B cells. Details on EF response as well as additional clarification of the data and figures is necessary to appreciate the importance of EF response during Influenza infection and for publication of the manuscript.
+
+Main comments:
+
+It is not described anywhere in the manuscript what the authors consider to be extra follicular response and whether it is the timing or response, location or the markers on the cells that define this type of response. Similarly, many of the figures are based on using CD24 to delineate both GC and EF B cells and again it is not stated anywhere why this strategy was chosen as CD24 is not a marker normally used to delineate GC cells. More details are needed with regards to these.
+
+Strategy for gating of extrafollicular B cells, extrafollicular plasma blasts and germinal center B cells should be explained at least in the first figure on the figure legends and the results section. Similarly in Figure 2 gating strategy for gating on Influenza HA – specific B cells is unclear and there is very little details given in the text or figure legends. Figure2 legend has multiple errors including mislabeling of the figure legends.
+
+GC B cell data on Figure 1 and 2 or at least just one of the figures should be confirmed with other GC markers apart from CD24 such as PNA or FAS or GL7.
+
+Influenza infection induces early antibody responses in the lungs and recent studies have shown the importance of antigen localization and B cell responses in the lungs (Allie SR et. al 2019 Nature Immunology, Oh EJ Science Immunology 2021) and part of this could also be driven by EF response. It is not clear why the authors decided to investigate only EF response in the mediastinal lymph nodes and not in the lungs which could be more relevant for intranasal infection. Authors could include findings from the lungs or discuss the rationale for only looking at the lymph nodes.
+
+In Figure 4a, the data show that loss of TLR signals lead to specific changes in EF cells but the bone marrow chimera data in Figure 5 b shows that the DKO and TKO chimeras show reduction in both EF and GC responses indicating B cell specific TLR signals have effects on both populations. Similarly, the BCR are responses data are from total B cells showing that changes in TLR signals alters the response of all B cells. Could the authors clarify based on these data how they are concluding that TLR signals specifically effect EF cells? How does the changes in BCR dynamics in all B cells in the knockout condition only lead to effects only on EF cells?
+
+The authors conclude that repeated LPS stimulation polarizes the cells to EF fate, but the data are from time points where you see mostly EF cells and not GC cells, therefore effect is only seen on EF cells. Can the authors look at later time points when GC response are optimal and show that repeated LPS does not have any effect on GC cells?
+
+Could the authors discuss how repeated LPS immunization leads to protective response, is it due to changes in amount of antibody, affinity of antibody or cytokines that might be present in the serum?
+Overall, the exact contribution of the EF response during infection is not clear. If EF responses are protective, they should induce viral clearance at early time points? Therefore, in supplementary Fig4a should the viral titre not be higher in the chimeric knockout mice also since they are not able to induce optimal EFR response? If EFR response does not affect viral clearance could the authors discuss how it could be leading to protection ? Similarly, In page 9 it is stated “Thus B cell-intrinsic TLR signaling supports early EFR formation, while additional B cell extrinsic signal further drives EFR generation in a manner that correlates with pathogen burden. How is early EFR response protective and later EFR response pathogenic? Could the authors clarify this and discuss this further as this would be important in thinking of vaccine design?
+
+The data on repeated LPS immunization inducing EFR response are very interesting. Do the authors think this is specific to LPS or inclusion of other TLR ligands such as TLR9 or TLR7 ligands also lead to this feature? The Influenza virus incorporates ssRNA therefore could this be due to stimulation of both TLR4 and TLR7? Additional discussion on this would be useful.
+Point-by-point response to reviewer’s comments
+
+We thank the reviewers and editors for the thoughtful and constructive comments provided to our manuscript. As we outline below, we have considered and addressed each of the comments provided. This included removal of some data from the supplemental data that lacked statistical power, the strengthening of key findings with additional experimental data and the provision of additional data that demonstrate the induction of protective extrafollicular-derived antibodies against lethal influenza challenge in wild type mice but not those deficient in TLR signaling. Furthermore, we have altered a number of figures and the accompanying text to enhance clarity as requested by the reviewers. We feel that these changes have significantly strengthened the manuscript on both the technical and conceptual aspects of the data. Responses to comments are outlined in blue.
+
+Reviewer #1 (Remarks to the Author):
+
+This manuscript by Lam and Baumgarth investigates the signals that control the generation of the EF versus GC B cell response following infection or vaccination. This is a question of high import given that early control of infection can determine the extent of pathology and severity of illness. The authors reveal a regulatory role of TLR mediated signals in determining the fate decision of activated B cells, with a sustained innate signal promoting differentiation along the EF pathway resulting in early production of antibody capable of promoting clearance. The study includes a careful timecourse of EF versus GC cell and the source of virus-specific antibody. This is an important study that significantly extends our understanding of B cell differentiation. Overall the conclusions are well supported although at times conclusions are based on results that do not appear to be significant (detailed below).
+
+Major comments:
+1. One would expect an increase in HA-specific B cells in Fig 3e given the substantial increase in GC cells in the vaccinated animals, but this seems not to be the case. Could the authors comment on the specificity of these new GC cells?
+We thank the reviewer for this question. In response we have reanalyzed the data that now show a significant increase in HA-specific B cells between day 0 and day 3, with further increases on day 10 post infection (Fig. 3c-d). Furthermore, we now also demonstrate that HA - binding B cells are enriched for a GC phenotype over an EF phenotype (Fig 3e). The number of HA-specific cells captured with our HA-baits is likely smaller than the total number of HA-specific cells present in the population, as not all HA-specific cells can retain binding to the HA-protein. This is a well known limitation of antigen-specific B cell staining for non-transgenic B cells. In addition, as HA is one of 10 influenza proteins encoded by the virus, other GC cells are directed especially against the nuclear protein and the neuraminidase.
+
+2. What percentage of cells fall into the positive quadrant in non vaccinated mice (Fig. 3d)? As there is no increase in HA-sp B cells from d3 to d7, without a control, can one be certain these are in fact HA specific cells being analyzed?
+We thank the reviewer for this question. In response we have made changes to the HA data in Fig. 3c-e, as also outlined above. We are now showing representative flow plots of HA staining on B cells (c), quantifying total HA B cells per timepoint (d), and showing the phenotype (EF vs
+GC) of HA B cells per time point (e) post-immunization. We hope this clarifies the identity of the cells in question.
+
+3. The data in SF2 appear to be total and not HA-specific. Without that, it is difficult to draw conclusions about the HA response.
+We thank the reviewer for this comment. SF2 does not attempt to specifically address antigen-specific responses. Rather, it supplements Fig. 3’s immunization data by showing how EFRs do not respond to greater antigen levels alone, while overall GC sizes do increase upon increased antigen exposure. To clarify and simplify this message, we have incorporated SF2 into subfigures of Fig. 3 as Fig. 3b, which immediate follows the quantification of GC and EF responses in the immunization of original dosage. Although not identifying antigen-specific cells the data very clearly demonstrate the antigen-dose dependent nature of the GC but not the EF response, further supporting our claims that antigen alone does not drive EF responses.
+
+4. In SF3, there is a trend towards increased EF in TLR7KO mice. The low number of animals and variability in the TLR7 KO mice make achieving significance challenging. If the two types of EF cells are pooled for analysis, does the picture become clearer?
+This question by the reviewer is much appreciated. We did find statistical significance for TLR7 KO EFRs, but the displayed p-value was lost during editing, we apologize for the oversight. The CD138+ EFs (which are NOT significant) are a subset of the total EF PBs, not a separate population, and therefore are already included in the EF PB population. Text has been added to improve clarification for former SF3 (now SF2) on these populations at Line 188: However, infection of mice lacking TLR3, TLR4, or TLR7 did not result in significant decreases in total EF PBs, nor EF PBs that were CD138+, compared to their WT controls (Suppl. Fig. 3b). In fact, there was a slight but significant increase in EFRs of TLR7 KOs. Thus, individual cytokines or innate signaling receptors appeared either not necessary or redundant for EFR development and, in the case of TLR7, may even contribute towards negative regulation.
+
+5. In Fig 4b, did the DKO serum provide any protection? Was a control serum transfer experiment performed?
+We thank the reviewer for this question. Control experiments from naïve animal serum transfer of all strains (WT, DKO, TKO) have been added to the revised Fig. 4b as per the reviewer’s suggestion. The data demonstrate that serum from naïve mice, independent of their genotype, could not provide immune protection against a lethal influenza irus challenge.
+
+6. The data in SF5 are challenging for comparison between conditions as there are limited times when the same dose is used in combination versus individual stimulations. Nonetheless, one can compare the 1ug/ml anti-IgM and 1ug/ml LPS in this way. When doing so it is hard to see the how the combination strongly supported viability (SF5a) or proliferation (SF5b) compared to the LPS alone as is stated. They appear similar.
+We thank the reviewer for this comment. In response we have removed some of the data in SF5 and now only compare the most relevant groups, as suggested by the reviewer. The data now clearly demonstrate that 1) TLR signaling has a significantly stronger effect on B cell viability than BCR stimulation at the given doses. However, there is still a small and significant additive effect using both and 2) both TLR and BCR signaling have sizable, additive effects on proliferation and IRF4 upregulation. Clarification has also been added to the relevant text.
+7. Are the reductions in Ki67+ cells in SF7 significant? If not this limits the conclusion that can be drawn in lines 247-49.
+We thank the reviewer for this comment. After consideration of the importance of demonstrating a difference in Ki67+ cell frequencies, we have decided to remove this particular supplemental data and the associated text. While we are confident that additional sample size would yield significant differences, due to time constraints we opted to omit their repeat. Furthermore, we like to point out that we already demonstrated a relation between TLR signaling and increased proliferation in the in vitro B cell activation data and LPS-boosted immunization data, where we measured Ki67 among HA-specific B cells, providing models that are B cell intrinsic and both intrinsic/extrinsic.
+
+8. In lines 264-65 authors should state trend as it does not appear to significantly increase. For many of the animals there is a very modest increase and one TKO has a major decrease. Thus conclusions should be drawn with care.
+We thank the reviewer for this comment have decided to remove the supplemental figure in question. While we are confident that additional sample size would yield significant differences in IgD expression in vivo and support the significant differences found in vitro, it is an observation that is not central to understanding the mechanisms of EF fate decisions explored in this manuscript.
+9. Additional discussion of the TLR ligand independent requirement for TLR pathway in B cell activation would be welcome.
+We thank the reviewer for the suggestion. In response we have provided additional discussion on the topic of TLR-ligand-independent requirement of optimal BCR activation, stating on line 370 of the amended text: “Evidence of enhanced TLR9-MyD88-BCR complexing in activated B cell-like lymphoma cells suggests that TLRs may provide a platform for downstream TLR targets to become activated through the BCR and its effector pathway (Phelan et al., 2018)”. Consequentially, this would make activation of the integrated TLR pathway as the most crucial source of BCR-mediated IRF4.”
+
+Minor comments
+1. Line 81: believe meant vesicular not vaccinia
+This error has been corrected.
+
+2. Line 127: add virus after influenza
+This error has been corrected.
+
+3. Line 197: EFR-derived serum is a bit unclear, suggest “serum from d10 animals wherein antibody is predominantly EFR derived” if this is what is meant
+This edit has been made, we thank the reviewer for this suggestion.
+
+4. Line 211: the chimera to which the authors are referring should be noted prior to BMC
+This error has been corrected.
+
+5. Line 370: induce for indue
+The error has been corrected.
+6. The authors are asked to increase axis labels and percentage values in flow plot font size where possible as many are quite hard to read.
+Axes and labels have been increased where needed, we thank the reviewer for this suggestion.
+
+7. Consider keeping nomenclature similar- “fold difference” axis label Fig 6e
+The axis label has been changed, we thank the reviewer for this suggestion.
+
+Reviewer #2 (Remarks to the Author):
+
+The paper by Lam et al explores the mechanisms underlying the formation of extrafollicular plasmablasts (EFRs) and short term humoral memory toward influenza. The authors provide support for a correlation between the formation of EFRs and protective properties of serum at early time points after antigen challenge. Using a series of KO models the authors determine that a key component for the formation of EFRs is Toll like receptor signaling that they find stimulate IRF4 transcription in the activated B-cell. They conclude that inflammatory signals impact the fate of activated B-cells to generate efficient short term response to antigen.
+
+This is in many regards an interesting report representing an impressive amount of work in different model systems. The large number of models and experimental setups explored does, however, become a liability as parts of the data are of limited quality. The authors base many of their conclusions on data collected from few animals creating a challenge in interpretation of the results. This problem is aggravated by that substantial portions of the data are presented as relative controls, in some cases wt, and other cases as compared to non-stimulated cells. It is difficult to fully delineate how this normalization was made. Furthermore, the authors does at times ignore significant differences in their data when they and put forward differences that are not indicated as significant. This creates a challenge to read and validate the data in a proper manner making it difficult to fully appreciate the reported findings and to understand the relevance of the findings.
+
+Specific comments.
+1. The authors should go over their data and decide what parts that are conclusive and where there is a need to repeat the experiments, alternatively take some data out of the paper or rephrase their conclusions. This is a general problem throughout the report and my list below in mainly to exemplify the problem rather than to provide a complete list of concerns.
+We thank the reviewer for these suggestions and have taken specific steps to clarify data representation and conclusions drawn, some in response also to comments from reviewer #1. We now explicitely describe fold-differences to WT controls in figure legends and text for appropriate data. Data lacking significance have been removed (chimera HA-specific Ki67 and IgD expression) or repeated (immunization with LPS boosting experiments in Figs. 7 and 8). The results have strengthened and further confirmed our initial conclusions.
+
+2. Figure 1, no indication of # of animals or experiments.
+We apologize for this oversight. The number of animals and experiments conducted have now been added to the legend for Figure 1.
+3. Figure 1c-e, no significances indicated, hence not possible to support the authors conclusion on row 148 that the response peak at day 9.
+We thank the reviewer for this comment and have conducted statistical analysis using one-way ANOVAs on each time course measurement (Fig. 1c-e). Significance has now been indicated at the amended Fig. 1 and the corresponding text has been clarified.
+
+4. Figure 2 c-e, no stats indicated. There would appear to be as much HA+GC as HA+EF cells at day 6.
+One-way ANOVAs were conducted on each time course measurement (Fig. 2c-e) and significance has now been indicated in the amended Figure. The observation by the reviewer that HA+GC and HA+EF cell frequencies are similar was likely based on the fact that we had used y-axes of different scales to indicate small changes in the GC populations. As the most important comparision here is between GC and EF responses and to avoid that potential confusion, we have now adjusted both y-axes for Figs. 2d and 2e to be the same.
+
+5. The only stats indicated in figure 3b are infection day 10 and 3 days postimmunization. This is not an optimal or relevant comparison. Why have the authors used day 7 data to analyze EF and 10 for GC?
+We thank the reviewer for this comment. We had included the data simply to indicate the large differences between these responses, but agree with the reviewer that this is hard to justify. Therefore, we have made several changes to Figure 3 to better articulate that GC responses are the dominant B cell fate during immunization and that EF responses are minimal. As the reviewer has suggested, we have removed the infection timepoint comparisons and focused solely on characterizing the immunization response. Fig. 3a now quantifies EF and GC responses, while data from SF2 has been incorporated as Fig. 3b to show that increasing antigen dose does not increase or rescue total EF responses, while it does increase overall GC responses in an antigen dose-dependent manner. Furthermore, Figs. 3c-e have been reconfigured to better show EF vs GC fate of HA-specific B cells, showing their expansion after immunization in Fig. 3c - d, and characterizing their phenotype (EF vs GC) in Fig. 3e. We believe this amended figure more clearly demonstrates that immunization s.c. favors GC responses and provides contrast to primary infection’s early bias towards EF responses.
+
+6. In S3a, significant increase in GC is not mentioned. Many data points so spread out that phenotypes well can be lost.
+We thank the reviewer for this comment. We have now added text to the manuscript to mention the significant increase in GC responses in mice lacking TNFa signaling at line 183.
+We acknowledge the reviewer’s concern that some data points are spread out in some of the many groups of gene-targeted mice we screened (we only show the most pertinent ones we tested in the paper), we are confident that each of the genotypes tested failed to show measurable reductions in EFRs at the chosen timepoint, thus that these genes/signaling pathways are no critical for early EFR formation after influenza virus infection. The data were always obtained by simultaneously testing the various KO mice against age and sex-matched congenic strains of C57BL/6 mice and for numerous of these comparisons we performed ELISA for virus-specific serum antibodies. Because these ELISA data failed to show any significant differences, and because day 7 is a rather early timepoint to measure antibody levels, we are not showing this additional data in the manuscript.
+
+7. In s3b, is there really not any significant difference in EFs in the TLR7 KO?
+We apologize for the omission, also remarked by reviewer #1. Indeed, we did find statistical significance for TLR7 KO EFRs, but the displayed p-value was lost during editing, we apologize for the oversight. The CD138+ EFs (which are NOT significant) are a subset of the total EF PBs, not a separate population, and therefore are already included in the EF PB population. Text has been added to improve clarification for former SF3 (now SF2) on these populations at Line 188: However, infection of mice lacking TLR3, TLR4, or TLR7 did not result in significant decreases in total EF PBs, nor EF PBs that were CD138+, compared to their WT controls (Suppl. Fig. 3b). In fact, there was a slight but significant increase in EFRs of TLR7 KOs. Thus, individual cytokines or innate signaling receptors appeared either not necessary or redundant for EFR development and, in the case of TLR7, may even contribute towards negative regulation.
+
+8. In figure 4b, the TKO display a significant reduction in CD138+EFs that is ignored.
+We thank the reviewer for this comment. In response we now added to the amened manuscript that there was a significant reduction in TKO CD138+ EFs (Fig. 4a) at line 206: Surprisingly, infection of another TLR-null model, through deletion of genes for TLR2^{37}, TLR4^{38} and a missense mutation of Unc93b^{39} (TKO), showed EFRs similar to WT controls (**Fig. 4a**) along with nominal passive protective capacity (**Fig. 4c**), despite slight reductions in CD138+ EF PBs at 7 dpi (**Fig. 4a**).
+
+9. In row 204 the authors claim that there is no significant difference between wt and Tko serum in figure 4c. However, the graph shows clear differences day 7 and 8.
+We thank the reviewer for this comment and have now changed the wording of the results section for Fig. 4c to specifically address the outcome of TKO serum transfer in these protection experiments on Line 205: “Surprisingly, infection of another TLR-null model, through deletion of genes for TLR2^{37}, TLR4^{38} and a missense mutation of Unc93b^{39} (TKO), showed EFRs similar to WT controls (**Fig. 4a**) along with nominal passive protective capacity (**Fig. 4c**), despite slight reductions in CD138+ EF PBs at 7 dpi (**Fig. 4a**).”
+
+10. Row 246 the authors claim that fewer DK and TK cells express Ki67, however, no statistical analysis has been performed in figure S7.
+We thank the reviewer for this comment also made by reviewer #1. As outlined above, we decided to remove the supplemental figure and associated text, as we have shown this to be the case in other parts of the manuscript.
+
+11. Row 261, the authors claim that pMtor is increased in TLR signaling deficient cells. However, stat analysis only shown for 0 and 100 lg concentrations within each one of the genotypes. Hence, I cannot see proper validation of KO vs wt.
+We apologize for this oversight. In the revised manuscript we have now added the statistical analysis comparing each treatment from each KO to their respective WT treatment control, indicated by stars above each individual treatment condition. The associated text has been clarified/changed as well to better reflect the data.
+
+12. Row 264, the authors claim that TLR signaling led to enhanced surface IgD expression, however, figure 9a does not show any statistical significances.
+We thank the reviewer for this comment. As also remarked in response to reviewer #1, we have decided to remove the supplemental figure in question. While we are confident that additional sample size would yield significant differences in IgD expression *in vivo* and support the
+significant differences found in vitro, it is a supplemental observation that does not specifically address the question of the mechanisms of EF fate decisions explored in this manuscript.
+
+13. Row 331 the authors claim that Ag+LPS boosted mice had the highest anti influenza serum levels but in panel 8f, there is no significant difference between Ag boosted and Ag LPS boosted animals.
+We thank the reviewer for this comment. In response we have conducted additional experiments and added the data to the figure. The data now clearly demonstrate significant differences between Ag+LPS and Antigen only (Fig. 8f) both when expressed as relative units total flu-specific IgG (left panel) and when showing normalized data to the average “Antigen Only” IgG levels from each experiment, then expressed as fold-change. The data demonstrate the significant increases in antigen-specific, serum IgG when LPS boosting occurs in both absolute and relative terms, explaining the enhanced passive protective capacity of the sera from these mice, shown in Fig. 8g-h.
+
+Minor comments:
+1. Figure legend for fig 2 contains ref to panels l, j, k not in the figure.
+This error has been corrected, we apologize for the oversight.
+
+2. Row 162-165 talks about smaller GCs. Should this be fewer cells as the size of the GC hardly is investigated?
+This error has been corrected.
+
+3. 3b GC cells compared to infection day 10 and EF cells day 7.
+We believe we have addressed this above (Major Comment #5) and made the appropriate changes to the figure in question (Fig. 3).
+
+4. Row 214 talks about larger ERFs, correct?
+The text has been clarified to address the reviewers comment.
+
+5. Are the significance values in figure S8c really correct?
+We thank the reviewer for this question. The significances shown in (former) SF8c are from one-way ANOVAs of each strain to demonstrate that different anti-IgM treatment concentrations were actually causing changes in the measured protein’s phosphorylation signature. With the changes made from the reviewer’s previous comment on the figure, the effect on p38 in TLR-null B cells has been clarified.
+
+Reviewer #3 (Remarks to the Author):
+
+In this manuscript the authors show that Influenza infection induces rapid early antibody response that is driven by signals from the toll-like receptors (TLRs). This response appears to be protective as seen by serum transfer experiments and inclusion of TLR signals also increases early antibody response during immunization with Influenza antigens. This study is interesting and important in terms of understanding signals regulating early antibody response against viruses and will be important in thinking about vaccine design for Influenza virus. However, the manuscript is presented in manner that makes it difficult understand the relevance and contribution of extrafollicular response. It is known that TLR signals can affect both early B
+cell responses and germinal center (GC) B cell responses. The main interesting point of this study is the specific effects of TLR signals on extra follicular (EF) response during infection and immunization. But the lack of clarity on what is considered EF response, whether EF response is protective or pathogenic makes it difficult to understand the specific role of EF response. Similarly, it is also not clear which effects of TLR signals are specific to EF B cells and not GC B cells. Details on EF response as well as additional clarification of the data and figures is necessary to appreciate the importance of EF response during Influenza infection and for publication of the manuscript.
+
+Main comments:
+
+1. It is not described anywhere in the manuscript what the authors consider to be extra follicular response and whether it is the timing or response, location or the markers on the cells that define this type of response. Similarly, many of the figures are based on using CD24 to delineate both GC and EF B cells and again it is not stated anywhere why this strategy was chosen as CD24 is not a marker normally used to delineate GC cells. More details are needed with regards to these.
+We thank the reviewer for this comment. In response we have added additional details to the description of EFRs in the introduction of the amended manuscript at Line 59: “Instead, early antibodies are produced from short-lived plasmablasts of the extrafollicular response (EFR), which develop and localize within the medulla and interfollicular regions2 of the respiratory tract-draining mediastinal lymph nodes (medLN) shortly after infection and before GC formation3.” Furthermore, on Line 67: “EFRs thus appear physiologically distinct from GCs and can generate protective, germline-encoded, antigen-specific ASCs from the restrictive repertoire of inbred mice.”
+We and others previously demonstrated that CD24 staining can delineate B cell subsets. Specifically, that CD45R+/PNA+ cells identified as GC B cells had high CD24 expression and additionally co-stained as GL7+ and Fas+ (Shinall et al., 2000, JI; Baumgarth, 2004, Methods Cell Biol.; Elsner et al. 2015 PloSPathog). Nonetheless, to more clearly delineate our gating strategy we have updated Fig. 1 with added labels and we show the expression of GL7 and relatively high IRF8 on CD24hi gated GC and expression of CD138 and high IRF4, in EF PB, respectively.
+
+2. Strategy for gating of extrafollicular B cells, extrafollicular plasma blasts and germinal center B cells should be explained at least in the first figure on the figure legends and the results section. Similarly in Figure 2 gating strategy for gating on Influenza HA – specific B cells is unclear and there is very little details given in the text or figure legends. Figure 2 legend has multiple errors including mislabeling of the figure legends.
+We thank the reviewer for this comment. In response we have made multiple changes to the relevant text in the results section and figure legends to Figs 1 and 2 to clarify gating strategy. Furthemore, labels were added to Fig. 1 to aid the identification of target cell populations. We hope that these changes are clarifying identification of each cell subset.
+
+3. GC B cell data on Figure 1 and 2 or at least just one of the figures should be confirmed with other GC markers apart from CD24 such as PNA or FAS or GL7.
+We thank the reviewer for this suggestion. CD24/CD38 gating for GCs is now confirmed by GL7 staining in Figure 1 along with IRF8 expression level as outlined in response to the previous comment. In addition, we refer to our previous publications that identify this gating strategy as
+appropriate as these cells are PNA+ FAS+ and GL7+ (Elsner et al, 2015 PloSPathog), the latter now added to the Figure.
+
+4. Influenza infection induces early antibody responses in the lungs and recent studies have shown the importance of antigen localization and B cell responses in the lungs (Allie SR et. al 2019 Nature Immunology, Oh EJ Science Immunology 2021) and part of this could also be driven by EF response. It is not clear why the authors decided to investigate only EF response in the mediastinal lymph nodes and not in the lungs which could be more relevant for intranasal infection. Authors could include findings from the lungs or discuss the rationale for only looking at the lymph nodes.
+We thank the reviewer for this comment. In response, we have now added to the text at the beginning of the results section that “Influenza-specific ASCs can be found predominantly in the medLN within 7 days after primary infection but are not found in the lungs until 14 dpi3, well after virus clearance. This indicated that medLN EFRs are the main source of the early antigen-specific antibody response and were thus investigated.”
+
+5. In Figure 4a, the data show that loss of TLR signals lead to specific changes in EF cells but the bone marrow chimera data in Figure 5 b shows that the DKO and TKO chimeras show reduction in both EF and GC responses indicating B cell specific TLR signals have effects on both populations. Similarly, the BCR are responses data are from total B cells showing that changes in TLR signals alters the response of all B cells. Could the authors clarify based on these data how they are concluding that TLR signals specifically effect EF cells? How does the changes in BCR dynamics in all B cells in the knockout condition only lead to effects only on EF cells?
+We thank the reviewer for this comment and acknowledge the observations made about differences in phenotypes between the knockout models, with the TLR-null bone-marrow chimera data and in vitro data showing a universal effect on B cell activation, suggesting an effect on both EF and GC, while the global TLR knockout in vivo data demonstrated a more specific effect on EF responses. Firstly, the global knockout and chimera infection data demonstrate that there is a bona-fide B cell-intrinsic effect through TLRs on the EF response, not that it is exclusive to the EF response. We have ensured the text reflects this conclusion carefully as well. However, this does indicate that the GC response can be rescued if non-B cells also lack TLR signaling. As the focus of this paper is on the EF response, we did not explore the mechanisms by which GC responses are rescued in a global TLR-null context, but have provided a possible explanation in the discussion at Line 361: “As TLR signaling in DCs leads to increased Th1 polarization50, perhaps a total ablation of TLR signaling may polarize more CD4 T cells towards a Tfh phenotype, compensating for the GC B cell-intrinsic defect in TLR-mediated activation”.
+
+6. The authors conclude that repeated LPS stimulation polarizes the cells to EF fate, but the data are from time points where you see mostly EF cells and not GC cells, therefore effect is only seen on EF cells. Can the authors look at later time points when GC response are optimal and show that repeated LPS does not have any effect on GC cells?
+We thank the reviewer for this question. Additional data has been added (Suppl. Fig. 8) that shows GCs were not affected by the LPS-boosting regimen. Thus, demonstrating no detrimental effect on the development of GC responses. Text addressing these data have been added as well.
+7. Could the authors discuss how repeated LPS immunization leads to protective response, is it due to changes in amount of antibody, affinity of antibody or cytokines that might be present in the serum?
+Additional discussion on how repeated LPS boosting leads to more protection has been included as per the reviewer’s request at Line 398: “As the data suggest, this may be due to an overall increase in anti-influenza antibodies with functional protective capacity under continuous TLR-activating conditions (Fig. 7f) but could also be due to differences in antibody quality, i.e differences in repertoire that target unique or a higher number of epitopes. As TLR activation provides B cells with increased IRF4 expression, this allows for clones with relatively weaker BCR interactions to partake in antibody secretion by reaching the required IRF4 threshold.”
+
+8. Overall, the exact contribution of the EF response during infection is not clear. If EF responses are protective, they should induce viral clearance at early time points? Therefore, in supplementary Fig4a should the viral titre not be higher in the chimeric knockout mice also since they are not able to induce optimal EFR response? If EFR response does not affect viral clearance could the authors discuss how it could be leading to protection? Similarly, in page 9 it is stated “Thus B cell-intrinsic TLR signaling supports early EFR formation, while additional B cell extrinsic signal further drives EFR generation in a manner that correlates with pathogen burden. How is early EFR response protective and later EFR response pathogenic? Could the authors clarify this and discuss this further as this would be important in thinking of vaccine design?
+We thank the reviewer for these pertinent questions. The follow text has been added to address the reviewer’s questions on the contributions of EFRs towards virus clearance at Line 70:
+“Addressing how these distinct B cell activation outcomes contribute to humoral immunity against acute respiratory tract virus infections, where rapid induction of immunity is a key determinant of survival, is pertinent for our understanding of the pathogenesis of these infections and the role of B cell immunity. While CD8 T cells are credited the most in clearance of influenza during primary infection, they alone cannot prevent mortality5 and may collaterally target non-infected antigen-presenting cells6. Additionally, lack of B cells lead to a ~50 fold increase in virus titers by day 10 post-infection7 demonstrating the potential importance of early antibody generation against influenza. This has important implications for vaccine design, as vaccines are generally considered only successful if inducing GC-derived, long-lived plasma cells and memory B cells. However, vaccinations during the ongoing COVID-19 pandemic or during seasonal influenza virus infections are likely more effective if they can induce immune protection more quickly, i. e. through EFRs.”
+
+As for addressing if EFRs are protective vs pathogenic, we demonstrate here that EFRs during influenza are protective when MyD88/TRIF signaling is replete and that this protective effect is lost when MyD88/TRIF is absent, but upstream TLR ablation does not lead to this defect. Differences in virus clearance between global TLR-null mice and B cell-specific, TLR-null chimeras demonstrate the contribution of TLR signaling in both manners, with TLR-null chimeras having replete TLR signaling in non-B cells that allows for optimal innate and T cell responses leading to nominal virus clearance (Suppl. Fig. 3a), despite disruptions in both B cell responses (Fig. 5b).
+
+9. The data on repeated LPS immunization inducing EFR response are very interesting. Do the authors think this is specific to LPS or inclusion of other TLR ligands such as TLR9 or TLR7
+ligands also lead to this feature? The Influenza virus incorporates ssRNA therefore could this be due to stimulation of both TLR4 and TLR7? Additional discussion on this would be useful.
+We thank the reviewer for this comment and have addressed questions regarding specific TLR activation with the following text at Line 408: “Whether the type of TLR agonist, i.e. one which activates MyD88 or TRIF exclusively, would differentially affect EFR dynamics is unclear. As stated previously, using TLR4 (MyD88 and TRIF) and TLR7 (MyD88 only) adjuvant made no difference in early antibody responses after immunization compared to either alone15.
+Additionally, TLR9 activation by CpG enhanced titers but worsened the quality of antigen-specific antibody responses due to a lack of GC-mediated affinity maturation to the hallmark antigen hapten19. Affinity for hapten increases over time as GCs mature and affinity maturation takes place54, indicating that clones with low avidity interactions with hapten may be ‘pulled’ into differentiation through activation of TLRs, thus lowering the overall avidity of the response. Given the PAMPs present in influenza virus, characterization of TLR/BCR synergy upon virus recognition and uptake by B cells, and how this may contribute towards plasmablast formation, would be of interest. Yet increases in serum antibody affinities over time were not observed following infection with vesicular stomatitis virus8,9 and high affinity, germline-encoded antibodies to hemagglutinin were induced early after influenza inoculation4.”
+REVIEWERS' COMMENTS
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have addressed the concerns raised.
+
+I note a few edits that are needed.
+1. Line 333 and "=" mark
+2. Line 399 "in in"
+3. Line 407 Was the or meant to be an and?
+
+Reviewer #2 (Remarks to the Author):
+
+The paper is now of acceptable quality and the general story holds up. I do, however, believe that the authors should be more careful in future submissions as it is not reasonable that reviewers should act as proofreaders of submitted reports.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have addressed all of my concerns from the previous review , including adding new data related to markers for GC cells and clarification of phenotype and function of extra follicular cells. Additional comments in the discussion about the role of TLR signaling are also adequate.
+Point-by-point response to reviewer’s comments:
+We’d like to thank all the reviewers for their comments that improved this manuscript’s message and data robustness/fidelity. It is much appreciated.
+
+Reviewer #1 (Remarks to the Author):
+
+The authors have addressed the concerns raised.
+We thank the reviewer for their helpful feedback in making this a stronger manuscript.
+
+I note a few edits that are needed.
+1. Line 333 and "=" mark
+The error has been corrected, apologies for the oversight.
+
+2. Line 399 "in in"
+This error has been corrected, apologies for the oversight.
+
+3. Line 407 Was the or meant to be an and?
+This error has been corrected, apologies for the oversight.
+
+Reviewer #2 (Remarks to the Author):
+
+The paper is now of acceptable quality and the general story holds up. I do, however, believe that the authors should be more careful in future submissions as it is not reasonable that reviewers should act as proofreaders of submitted reports.
+We thank the reviewer for their helpful feedback, apologize for the original manuscript appeared insufficiently edited/proofread.
+
+Reviewer #3 (Remarks to the Author):
+
+The authors have addressed all of my concerns from the previous review, including adding new data related to markers for GC cells and clarification of phenotype and function of extra follicular cells. Additional comments in the discussion about the role of TLR signaling are also adequate.
+We thank the reviewer for their helpful feedback in making this a stronger manuscript.

027b827c3b80c86306a8c299d162b6cb2bb24a38c0ffa3c834d579a1e6c6338c/preprint/preprint.md

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+Toll-like receptor mediated inflammation directs B cells towards protective antiviral extrafollicular responses
+
+Jonathan Lam
+University of California, Davis
+Nicole Baumgarth (nbaumga3@jhmi.edu)
+School of Veterinary Medicine, University of California, Davis
+
+Article
+
+Keywords:
+
+Posted Date: November 22nd, 2022
+
+DOI: https://doi.org/10.21203/rs.3.rs-2226474/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 5th, 2023.
+See the published version at https://doi.org/10.1038/s41467-023-39734-5.
+Toll-like receptor mediated inflammation directs B cells towards protective antiviral extrafollicular responses
+
+Jonathan H. Lam1,2 and Nicole Baumgarth1,2,3,4
+1Graduate Group in Immunology, 2Center for Immunology and Infectious Diseases, 3Dept. Pathology, Microbiology and Immunology, University of California Davis, Davis, USA
+
+Correspondence
+Nicole Baumgarth DVM PhD
+W. Harry Feinstone Dept. Molecular Microbiology and Immunology
+Johns Hopkins Bloomberg School of Public Health
+615 N Wolfe Street, E4135
+Baltimore, MD 21205
+(p) 410 614 2718
+nbaumga3@jhmi.edu
+Abstract
+
+Extrafollicular plasmablast responses (EFRs) are considered to generate antibodies of low affinity that offer little protection from infections. Paradoxically, high avidity antigen-B cell receptor engagement is thought to be the main driver of B cell differentiation, whether in EFRs or the slower-developing germinal centers (GCs). This study demonstrates that influenza infection rapidly induced EFRs generating protective antibodies in a B cell intrinsic and extrinsic Toll-like receptor (TLR)-dependent manner. B cell-intrinsic TLR signals supported antigen-stimulated B cell survival, clonal expansion, and the differentiation of B cells via induction of IRF4, the master regulator of B cell differentiation, through activation of NF-kB c-Rel. Provision of sustained TLR4 stimulation after immunization altered the fate of virus-specific B cells towards EFRs instead of GCs, accelerating rapid antibody production and improving their protective capacity over antigen/alum administration alone. Thus, inflammatory signals act as B cell fate-determinants for the rapid generation of protective, antiviral EF responses.
+Introduction
+
+Acute respiratory tract infections induce neutralizing antibody responses that are critical for long lasting protection. Germinal center (GC) responses are considered the most effective in generating protective antibodies, as antigen-specific GC B cells undergo extensive somatic hypermutation, resulting in long-lived antibody-secreting plasma cells (ASCs) that generate high-affinity, strongly neutralizing antibodies. However, after primary influenza virus infection, GCs appear relatively late, usually after viral contraction, and thus are unlikely to contribute towards virus clearance (Lam and Baumgarth, 2019). Instead, early antibodies are produced from extrafollicular plasmablast responses (EFRs) that develop in the respiratory tract-draining mediastinal lymph nodes (medLN) shortly after infection and before GC formation (Rothaeusler and Baumgarth, 2010). Early studies by Gerhard and colleagues demonstrated that influenza inoculations of BALB/c mice resulted in rapid production of early hemagglutinin (HA)-specific, neutralizing IgG antibodies that were protective and in repertoire distinct from those induced later in the response (Kavaler et al., 1990). This included unmutated IgG from B cells of the prototypic HA-specific C12 idiotype, which were excluded from GCs after intra-nasal (i.n.) influenza infection (Rothaeusler and Baumgarth, 2010). This indicates that protective, germline-encoded, antigen-specific ASCs can be generated from the restrictive repertoire of inbred mice via EFRs that are temporally distinct from GCs.
+
+Addressing how these distinct B cell activation outcomes contribute to humoral immunity against acute respiratory tract virus infections, where rapid induction of immunity is a key determinant of survival, is pertinent for our understanding of the pathogenesis of these infections and the role of B cell immunity. Additionally, it is important for vaccine design. Vaccines are generally considered only successful if inducing GC-derived, long-lived plasma cells and memory B cells. However, vaccinations during the ongoing COVID-19 pandemic or during seasonal influenza virus infections, are likely more effective if they can induce immune
+protection more quickly, i. e. through EFRs. The signals required for EFR induction, however, have not been resolved. Indeed, EFR induction has been considered of little consequence, as these responses are thought of as only short-lived and of low protective capacity.
+
+Yet, groundbreaking studies by the Hengartner’s group over two decades ago, demonstrated that antibody responses to vaccinia stomatitis virus showed a surprising lack of changes in virus-specific serum antibody affinities over the course of infection. Instead, they demonstrated that antibodies of relatively high affinity for their cognate antigen were generated both early and late after infection (Kalinke et al., 1996; Roost et al., 1995), suggesting that following a viral infection both EFR and GC-derived antibodies might generate antibody responses of overall high affinity. These data are consistent also with reports by the Brink lab, who demonstrated using the BCR-transgenic swHEL model, that strong BCR-affinity for antigen drove the rapid proliferation and differentiation of hen egg lysozyme (HEL)-specific B cells in EFRs, while lower affinity interactions induced stronger GC responses instead (Paus et al., 2006). Generation of EFRs from high-affinity B cells is consistent also with findings that strong BCR-signaling drives upregulation of interferon regulatory factor 4 (IRF4), a critical transcriptional regulator of plasma cell development (Ochiai et al., 2013). Such a model of affinity-based induction of proliferation and differentiation would be consistent with EFRs’ potential to generate high affinity antibodies.
+
+However, whether BCR-antigen interactions alone drive B cell fate decisions towards EFRs remains unknown. Furthermore, in contrast to studies indicating that highly functional antibodies emerge from EFRs, other work has shown that EFRs developing in the spleen following Salmonella thyphimurium and Ehrlichia infections generate large quantities of predominantly non-specific antibodies (Di Niro et al., 2015; Trivedi et al., 2019), in support of the idea that EFR are of little protective consequence. Together, these data seem to indicate that
+additional infection-induced signals shape EFRs. What these signals are, and how they might affect the functionality and protective capacity of EFR-derived antibodies, is unresolved.
+
+Work interrogating pattern recognition receptors (PPR) signaling after immunization has identified numerous effects on B cells and it is well appreciated that certain PAMPS can work as adjuvants to support vaccine responses. For example, RNA of sheep red blood cells stimulated RNA-sensing PPR mitochondrial antiviral signaling protein (MAVS) and TLR3 (Loetsch et al., 2017), that supported more robust B cell responses. Also, mice immunized with nanoparticles containing the TLR4 ligand 4'-monophosphoryl lipid A induced a more robust, antigen-specific ASC response compared to mice given antigen alone, while the combination of TLR4 and TLR7 agonists was reported to fate B cells towards early memory and germinal center responses, resulting in persistent antibody responses from bone marrow long-lived plasma cells, rather than rapid EFRs (Kasturi et al., 2011). B cell-intrinsic MyD88 signaling was shown also to increase proliferation and differentiation of plasma cells and induced expansion of Bcl6+ germinal center B cells to virus-like particles (Tian et al., 2018). And in Friend virus infection and after infection with influenza virus, B cell-intrinsic expression of TLR7 (but not TLR3) was shown to be required for germinal center formation (Browne, 2011; Heer et al., 2007). In contrast, stimulation with the TLR9 ligand CpG antagonized B cell antigen uptake and processing resulting in disruption of affinity maturation and a reduction in early-formed, antigen-specific plasma cells in the spleen, along with a reduction in long-term, antigen-specific serum IgG avidity (Akkaya et al., 2018).
+
+Observations of TLR integration with canonically distinct B cell activation pathways may play a role in the reported effects of TLR agonists on antibody responses, as TLR4 was shown to integrate with BCR signaling via the phosphorylation of syk (Schweighoffer et al., 2017), while the TLR adaptor MyD88 was shown to be critical for signaling via the B cell survival receptor TACI (He et al., 2010). Collectively, existing evidence suggests that TLR and/or MyD88-
+mediated signaling affects B cell responses, but how these signals integrate to regulate B cell responses remains incompletely resolved.
+
+Here we demonstrate that inflammatory signals induced by influenza infection, but not immunization with virus particles in alum, triggers the rapid generation of protective antibody responses via formation of EFRs in a TLR signaling-dependent manner. TLR- signaling fated B cells towards the EFR/plasma cell state after infection through the strong induction of IRF4 via activation of NFkB c-Rel. Similarly, sustained co-administration of LPS with virus/alum immunization rescued EFR induction after vaccination and improved antibody-mediated protection against lethal influenza challenge.
+
+Results
+
+The extrafollicular B cell response generates antigen-specific antibodies after intranasal influenza infection but not after peripheral immunization
+
+Intranasal infection of C57BL/6 mice resulted in the appearance of pre-GC/GC-like (GC) B cells (CD45Rhi/CD19hi/CD38lo/CD24hi) at 7 days post infection (dpi) that were also interferon regulatory factor 8 (IRF8) high, a transcription factor associated with GC polarization(Xu et al., 2015) (Fig. 1a, top). Early formed plasmablasts of the EFR (EF PBs) were identified as CD45Rlo/CD19+/CD38lo/CD24+ as well as IRF4-high, the latter associated with an ASC fate (Ochiai et al., 2013; Xu et al., 2015), with many also expressing CD138 (Fig. 1a, bottom), a canonical marker of ASCs. EF PBs and GC B cells both had lost surface IgD and most had lost IgM by 7 dpi (Fig. 1b), indicating a high level of class-switching. While B cell frequencies in the medLN remained relatively constant throughout the time course (Fig. 1c), drastic changes in EF and GC compartments took place. Relatively few GC B cells were found
+until after 9 dpi (Fig. 1d), while EF PBs were seen as early as 5 dpi, peaking at 9 dpi and contracting by 14 dpi (Fig. 1e).
+
+Only EF PBs, purified by flow cytometry, secreted pathogen-specific antibodies at 7 dpi, detected as influenza-bound total Ig and IgG2c by ELISPOT on cells (Fig. 2a), demonstrating that EF PBs contain the only functional, influenza-specific ASCs in the medLN at this timepoint. Additionally, use of two distinct fluorophore-labeled, recombinant hemagglutinin (HA) of A/PR8 identified HA-specific (HA) B cells (Fig. 2b) and their preferred participation in EF over GC B cell responses (Fig. 2c-e), with HA-bound B cells comprising as much as 15% of the EFR compartment at the early time points. The independence of EFR formation from GCs during influenza infection, suggested previously (Miyauchi et al., 2016), was confirmed with the presence of EF B cells in infected Mb-1-Cre Bcl6 f/f mice that are unable to form GCs (Suppl. Fig. 1). Thus, EFRs are responsible for the earliest antigen-specific antibody response to influenza infection and are independent of GCs.
+
+A different B cell response quality was seen after subcutaneous (s.c.) immunization with influenza virions in alum adjuvant. Compared to infection, immunizations yielded smaller GCs and little to no EFRs in draining LN at 3, 7 and 10 dpi (Fig. 3a, b). At the antigen-dose used, GCs were only 3-fold smaller but EFRs were at least 40-fold smaller and barely detectable after immunization (Fig. 3c). Consequently, fewer HA B cells were detected over the course of immunization compared to infection (Fig. 3d, e). The HA-specific B cells that were present expressed no CD138 and only a few expressed Ki67 (Fig. 3d, e), a marker of cell cycling. Increasing the virus antigen-dose for immunization increased GC B cell numbers but had no effect on the size of the EFR (Suppl. Fig. 2). We conclude that infection-induced signals are required for EFRs to influenza.
+To identify the influenza infection-induced signals that support EFRs, we first considered inflammatory cytokines that were previously identified as contributing towards B cell differentiation and ASC maintenance, as well as S100A9, a damage-associated molecular pattern protein produced by stressed and dying cells and released during influenza infection(Tsai et al., 2014). Among the cytokines tested, IL-1, Type I interferons (IFN), IL-6, and TNF\( \alpha \) are induced early after influenza infection (Coro et al., 2006; Hayden et al., 1998; Sanders et al., 2011) and support ASCs (Aversa et al., 1993; Chatziandreou et al., 2017; Jego et al., 2003). IL-12 and the effector cytokine it supports, IFN\( \gamma \), which is produced by T cells, NK cells, and ILC1, are known to support ASC maintenance (Dubois et al., 1998; Miyauchi et al., 2016). However, mice deficient in each of these soluble cytokines or their receptors showed EFRs similar to their wild type (WT) controls at 7 dpi (**Suppl. Fig 3a**). B cells are also importantly affected through innate signals received via Toll-like receptors (TLRs). Influenza pathogen-associated molecular patterns (PAMPs) activate endosomal TLR3(Le Goffic et al., 2007) and TLR7 (Diebold et al., 2004), while TLR4 has a role in infection-mediated pathology (Nhu et al., 2010). However, infection of mice lacking TLR3, TLR4, or TLR7 had no significant effects on the number of total EF PBs and CD138+ EF PBs compared to their WT controls (**Suppl. Fig. 3b**). Thus, individual cytokines or innate signaling receptors appeared either not necessary or redundant for EFR development.
+
+The potential for redundancy of inflammatory signals contributing to the regulation of EFRs was addressed with mice double- deficient for both TLR adaptors, TRIF (Yamamoto et al., 2003) and MyD88 (DKO), which also transduces IL-1 and IL-18 signaling (Adachi et al., 1998). Indeed, the DKO mice showed strongly reduced EFRs at 7 dpi (**Fig. 4a**). TRIF single knockouts had EFRs comparable to that of wild type. While MyD88 single knockouts EFRs were variably reduced on average, these differences did not reach statistical significance (**Fig. 4a**).
+Importantly, while EFR-derived serum from WT mice provided robust protection against a lethal influenza virus challenge after adoptive transfer, DKO serum provided substantially reduced passive protection (Fig. 4b). Surprisingly, infection of another TLR-null model, through deletion of genes for TLR2 (Takeuchi et al., 1999), TLR4 (Hoshino et al., 1999) and a missense mutation of Unc93b (Tabeta et al., 2006) (TKO), showed EFRs similar to WT controls (Fig. 4a) and had no significant reduction in serum passive protective capacity compared to controls (Fig. 4c), despite slight reductions in CD138+ EF PBs at 7 dpi (Fig. 4a). This indicated a divergence in EFR dynamics mediated by the method of TLR abrogation.
+
+To distinguish potential B cell extrinsic from intrinsic effects of TLR signaling on EFR induction, mixed bone marrow irradiation chimeras, in which only B cells lacked either MyD88 plus TRIF (DKO BMC) or all TLRs (TKO BMC), were infected with influenza and analyzed at 7 dpi (Fig. 5a). Both the DKO and the TKO BMCs showed reduced EF and GC responses compared to WT chimera controls (Fig. 5b). The data indicate the importance of B cell intrinsic MyD88/TRIF and TLR signaling in regulating B cell responses overall. The differences in EF responses between the BMC and the total TLR-null chimeras is likely due to their differences in virus clearance. While virus titers at 10 dpi were no different between control and TLR-null BMC (Suppl. Fig. 4a), global DKO and TKO mice showed higher viral loads compared to wild type (Suppl. Fig 4b). These higher virus titers correlated with significantly larger EFRs in TLR-null mice (Suppl. Fig. 4c). Thus, B cell-intrinsic TLR signaling support early EFR formation, while additional B cell-extrinsic inflammatory signals, further drive EFR generation in a manner that correlates with pathogen burden,
+
+B cell intrinsic TLRs support B cell proliferation and survival
+To assess the direct effects of TLR signaling on B cell dynamics, negatively enriched naïve, follicular B cells were cultured with graded doses of anti-IgM (Fab)₂ and LPS, BCR and TLR agonists, respectively. Anti-IgM plus LPS co-treatment modestly enhanced viability compared to LPS alone and strongly supported B cell proliferation, as indicated by increased Ki67 expression compared to either treatment alone (**Suppl. Fig. 5a, b**). Co-stimulation also strongly induced IRF4 and IRF8, critical transcriptional regulators of the B cell fate (**Suppl. Fig. 5c, d**), while anti-IgM enhanced (and LPS inhibited) induction of IL21R expression, a cytokine receptor required for the generation of ASCs (Ozaki et al., 2002) (**Suppl. Fig. 5e**). Taken together, intrinsic TLR stimulation enhanced BCR-induced B cell entry into the cell cycle, promoted cell survival, and along with BCR signaling, maintained expression of IL21R.
+
+Canonical TLR signaling is known to integrate with the BCR (Pone et al., 2012; Schweighoffer et al., 2017) and with TNF superfamily receptors (He et al., 2010), suggesting that TLR signaling-deficient B cells are altered not only in their response to TLR agonists, but also to signals induced via the BCR, or via co-stimulation through CD40 or BAFFR. Indeed, stimulation of naïve, follicular DKO and TKO B cells pulsed with anti-IgM(Fab)₂ for three hours, followed by incubation with CD40L and BAFF for 48 hours (**Fig. 5c**) showed reduced viability (**Fig. 5d top**) and a near inability to enter the cell cycle, as measured by Ki67 staining (**Fig. 5d, bottom**), compared to WT controls. MyD88 and TRIF single KO B cells showed reductions in survival (**Suppl. Fig. 6a**) and proliferation (**Suppl. Fig. 6b**) similar to each other with frequencies approximately half between those of WT and DKO B cells, indicating that TRIF, along with MyD88, support BCR-mediated activation signals in a non-redundant, additive manner. Similar results were obtained with BCR-stimulation alone (**Suppl. Fig 6c, d**), demonstrating participation of the TLR signaling axis in antigen-mediated activation. Consistent with these data, analysis of non-EF/GC B cells from influenza infected DKO and TKO B cell chimeras revealed significantly reduced expression of Ki67 ex vivo, compared to controls at 5
+dpi, when IRF4 is highest within this uncommitted population during infection (**Fig. 5e** and not shown). Among the few HA-specific B cells present in DKO and TKO chimeras at this timepoint fewer expressed Ki67 (**Suppl. Fig. 7**). Thus, lack of antigen mediated integrated TLR signaling significantly reduced B cell survival and cell cycle entry consistent with earlier reports (Schweighoffer et al., 2017).
+
+*Lack of functional TLR signaling leads to abnormal BCR complex dynamics and transcriptional control*
+
+BCR-mediated calcium flux, an immediate readout of BCR crosslinking, was comparable between WT, DKO or TKO B cells (**Suppl. Fig. 8a**), indicating that TLR-null B cells were not merely defective overall. Effector protein phosphorylation downstream of the BCR showed minor pre-treatment differences (**Suppl. Fig. 8b**), but activation of mitogenic pathway MAPK p38 (Khiem et al., 2008) and the pro-inflammatory NFκB1 (Liu et al., 1991) also were roughly similar following BCR stimulation for 30 min (**Suppl. Fig. 8c, d**). Somewhat surprisingly, Syk phosphorylation, a major activation node for several BCR-mediated signaling pathways (Kurosaki et al., 1994), and phosphorylation of the pro-growth regulator mTOR (Donahue and Fruman, 2007) were increased in TLR-signaling deficient B cells compared to WT (**Supp. Fig. 8e, f**). Together, these data indicate that TLR signaling defects have little effects on early induction of IgM-BCR mediated signal transduction pathways.
+
+In contrast, the absence of TLR signaling led to enhanced surface IgD expression in HA-specific B cells *in vivo* compared to controls (**Suppl. Fig. 9a**). Indeed, loss of surface IgD after anti-IgM plus BAFF/CD40L stimulation was strongly attenuated in DKO and TKO B cells relative to WT (**Suppl. Fig. 9b**). Along with the enhanced induction of cell death and the inability to proliferate to antigen-mediated activation, despite apparently normal early downstream BCR
+signal transduction, TLR-signaling deficient B cells resembled anergic B cells (Goodnow et al., 1988).
+
+IRF4 is upregulated proportionately to BCR signaling strength (Ochiai et al., 2013). Consistent with that, ex vivo analysis of EF plasmablasts showed their distinct higher expression of IRF4 and intermediate expression of IRF8 compared to non-EFR B cells (**Fig. 6a, left**). *While ex vivo* baseline levels of IRF4 in naïve B cells were similar between the strains (**Fig. 6b, left**), non-differentiated B cells from DKO and TKO chimeras expressed significantly less IRF4 and IRF8 than WT at 5 dpi (**Fig. 6a, right**), indicating defects in IRF4 upregulation just before nascent EFRs form. In vitro IgM-BCR stimulation increased IRF4 and IRF8 expression in B cells from WT mice in an anti-IgM dose-dependent manner in the presence of CD40L and BAFF (**Fig. 6b right, Fig. 6c**). Strikingly, B cells from DKO and TKO mice failed to upregulate IRF4 under these conditions (**Fig. 6b right, Fig. 6c**), while IRF8 expression remained similar in all strains (**Fig. 6b right, Fig. 6d**). The data thus indicate defective BCR-mediated IRF4 induction in the absence of TLRs.
+
+NF-kB c-Rel is known to promote IRF4 expression upon nuclear re-localization and is downstream of both BCR and TLR4 (Grumont and Gerondakis, 2000). Strong, BCR dose-dependent stimulation-induced reductions in cytoplasmic c-Rel, inferring translocation of c-Rel to the nucleus, were seen in WT but much less so in TLR-signaling deficient B cells by flow cytometry as early as 30 min post stimulation (**Fig. 6e, Suppl. Fig. 10a**). Consistent with that result, WT but not DKO nor TKO B cells showed significant accumulation of c-Rel in the nucleus 1h but not 2h after anti-IgM and LPS stimulation, as assessed by ELISA on isolated nuclear-fractions (**Suppl. Fig. 10b, c**, concomitant with significant increases in total c-Rel expression (**Suppl. Fig 10d**). However, this delayed normalization in BCR-induced c-Rel expression was short-lived, as sustained c-Rel expression, which is associated with initialization of the B cell differentiation program (Roy et al., 2019), remained drastically lower in B cells lacking TLR-
+signaling than in WT B cells 48h after anti-IgM pulse (**Fig. 6f**). Thus, even in the absence of deliberate addition of a TLR agonist, B cells require the presence of TLRs for proper activation of the c-Rel circuitry and for the long-term maintenance of c-Rel expression in response to antigen-mediated stimulation.
+
+*Reconstitution of EFRs during influenza immunization through LPS adjuvant*
+
+Since both B cell-intrinsic and -extrinsic TLR signals influenced EFR magnitude and kinetics, we tested whether LPS, a TLR4 agonist that initiates both MyD88 and TRIF signaling, could overcome the lack of EFRs induction after s.c. immunization with influenza virions in alum (**Fig. 3**). Indeed, C57BL/6 mice inoculated with influenza in alum plus LPS and provided with repeated LPS boosts thereafter (Ag+LPS; **Fig. 7a**), showed increased total B cells, GC B cells, and EF PBs compared to mice receiving influenza in alum alone (Ag Only) (**Fig. 7b**). Importantly, the number of HA-binding B cells were twice as high than in mice receiving antigen/alum alone (**Fig. 7c**), with several-fold increases of HA B cells in the EFR but not GC compartment (**Fig. 7c**). Thus, indicating that TLR activation not only increased expansion of antigen-specific B cells but preferentially shunted them towards an EFR fate. HA B cells from Ag+LPS mice were mostly positive for Ki67 and CD138, IRF4hi IRF8int., similar to EF PBs from influenza-infected mice (**Fig. 7d**, e). This level of EFR polarization was not seen in Ag Only mice (**Fig. 7d**, e). HA B cells from Ag+LPS immunized mice also showed improved survival compared to Ag Only mice (**Suppl. Fig. 11a**), consistent with results seen after infection, where HA-specific B cells from DKO and TKO mice showed much lower ratios of live/dead cells compared to those of WT mice (**Suppl. Fig. 11b**). Thus, sustained TLR-mediated inflammation in the presence of antigen leads to greater expansion of antigen-specific B cells and polarizes them towards the EFR fate.
+Recent reports suggest that increased antigen valency (Kato et al., 2020) and antigen availability (Glaros et al., 2021) bias B cells towards a plasmablast fate. Given the above results, we asked how B cell fate dynamics and EFR-derived antibody functionality is affected by repeated antigen exposure with or without TLR agonist provision. For that, all mice were primed with influenza and LPS to ensure equivalent initiation of LN activation (Denton et al., 2022), followed by two additional boosts with antigen alone (Ag Boosted), or antigen plus LPS (Ag+LPS Boosted) or LPS alone (LPS Boosted) as a control (**Fig. 8a**). Both Ag Boosted and Ag+LPS Boosted mice had similar frequencies of HA B cells in the draining LN (**Fig. 8b**), and similar frequencies Ki67+ cells (**Fig. 8c**). However, HA B cells from Ag Boosted mice significantly polarized towards a GC fate (**Fig. 8d**), while HA B cells from Ag+LPS Boosted mice polarized significantly towards EFRs (**Fig. 8e**), indicating that despite repeated antigen inoculations, continued TLR stimulation was required for B cell development towards an EFR fate.
+
+Ag+LPS Boosted mice had the highest levels of serum anti-influenza antibodies (**Fig. 8f**), demonstrating that increased EFRs correlated with enhanced antigen-specific antibody responses compared to a GC-biased response at 10 days post-prime. To determine whether the increased in IgG levels correlated with increased serum passive protective capacity, pooled serum from each boosted group was transferred to naïve animals, who were subsequently challenged with a lethal dose of influenza. Mice receiving Ag+LPS Boosted serum showed no mortality, in contrast to mice receiving Ag Boosted or LPS Boosted serum (**Fig. 8g**). Moreover, mice that received serum from Ag+LPS Boosted mice lost significantly less weight overall than mice receiving serum from Ag Boosted animals (**Fig. 8h**). Together, these data demonstrate that sustained TLR-mediated inflammation polarizes antigen-specific B cells towards the EFR, leading to faster and stronger increases in protective, antigen-specific serum antibodies.
+Discussion
+
+These studies demonstrate that TLR-mediated inflammatory signals direct antigen-specific B cells towards the formation of ASCs through EFRs and that EFR-derived antibodies induced after both influenza infection and following LPS-boosted immunization are functionally protective. Thus, EFRs triggered and supported by inflammatory stimuli can provide a high quality antibody response at a fraction of the time relative to GCs by taking a more direct route to becoming ASCs, forming actively secreting, hemagglutinin-specific plasmablasts during the first 7-14 days of influenza infection prior to formation of GCs.
+
+EFR development seems to be driven by specificities already present in the repertoire at the time of infection, including in a naïve repertoire (Kalinke et al., 1996; Paus et al., 2006; Roost et al., 1995). In support, high affinity interactions between the BCR and its cognate antigen can drive a B cell effector fate, while lower affinity interactions confers a predispositon for the GC (Paus et al., 2006). However, the presence of high avidity B cells alone unlikely explains B cell fate decisions, as we show here that GC formation dominated early B cell responses to influenza immunization, while EFR dominated responses after influenza infection in the same inbred mice. If antigen-BCR affinity alone drives polarization towards an ASC fate, then the presence of antigen alone, assuming optimal delivery, stability, etc., should have resulted in an appreciable expansion of the same high affinity clones into the EFR than we saw after infection. Together, the data presented here demonstrate the need for infection-induced inflammation as a critical addition that supports EFR development. Inflammation affected EFR induction in an intrinsic manner, as functional Toll-like receptor (TLR) signaling axes either through MyD88/TRIF or TLR2/4/Unc93b induced optimal activation of the NF-kB c-Rel:IRF4 pathway (Suppl. Fig 12, top), as well as in an extrinsic manner, where TLR-mediated inflammation drove expansion of antigen-specific B cells into the EFR over the GC (Suppl. Fig 12, bottom), perhaps through alterations of the LN stromal compartment (Denton et al., 2022).
+TLR stimulation leads to the activation of multiple gene programs, but a defect in NF-kB c-Rel nuclear localization and upregulation after BCR stimulation was specifically observed in DKO and TKO B cells, along with suboptimal survival and the inability to proliferate or induce IRF4 expression. Additionally, the TLR adaptor TRIF, which has not been shown previously to influence BCR-mediated activation, was demonstrated here to contribute equally and non-redundantly with MyD88 towards B cell survival and proliferation after anti-IgM treatment. The observed defect in IRF4 upregulation in TLR-null B cells is consistent with previous studies demonstrating the dependence of IRF4 induction on c-Rel nuclear translocation after both, TLR4 and BCR activation (Grumont and Gerondakis, 2000). Delayed normalization of BCR-mediated c-Rel localization in TLR-null B cells did occur two hours after initial stimulation. Given that c-Rel has multiple c-terminal phosphorylation sites (Harris et al., 2006), perhaps TLR components are required for an optimal phosphorylation signature in addition to release of c-Rel from IkBs. Indeed, it was observed that the regulatory activity of c-Rel carrying a truncated c-terminus was severely altered, despite functional dimerization, nuclear localization, and DNA binding (Carrasco et al., 1998). Therefore, ablation of a functional TLR axis may dictate the nuclear activity of c-Rel, while maintaining localization potential. Further work is needed to determine how TLRs affect phosphorylation of the c-terminal trans-activation domain of c-Rel and how specific gene regulation is altered in their absence. Additionally, while total c-Rel levels did increase after 48 hours in TLR-null B cells, they were still significantly below levels observed in respective WT controls at every concentration of anti-IgM treatment measured. Therefore, IRF4 and c-Rel expression correlate and reaching a certain threshold of c-Rel seems required for the optimal induction of IRF4 in B cells. Indeed, c-Rel dominates the NF-kB program of B cells after antigen-mediated activation (Roy et al., 2019), potentiating an activated clone for several rounds of proliferation and enabling access to genes associated with terminal differentiation into plasma cells.
+Vaccination with antigen in alum, whether used as a prime or a boost, led to an expansion of antigen-specific clones primarily within the GC compartment, generating protracted serum antibody responses that were less protective at early times after immunization compared to the EFR dominated responses generated via antigen plus TLR agonist boosting. This suggests that increasing antigen valency (Kato et al., 2020) and/or amounts (Glaros et al., 2021) alone have a limited capacity to direct B cells towards early plasmablast responses following vaccinations, in contrast to vaccines adjuvanted with TLR agonists. The question that remains to be resolved is whether a drive towards EFR comes at the cost of effective GC-induced humoral immunity. Indeed, a recent study noted that TLR activation can worsen the quality of antigen-specific antibody responses due to a lack of GC-mediated affinity maturation (Akkaya et al., 2018), measuring a hallmark anti-hapten antibody response, where antibody affinity for the hapten increases over time as GCs mature and affinity maturation takes place (Foote and Milstein, 1991). However, increases in serum antibody affinities over time were not observed following infection with vesicular stomatitis virus (Kalinke et al., 1996; Roost et al., 1995) and high affinity, germline-encoded antibodies to hemagglutinin were induced early after influenza inoculation (Kavaler et al., 1990). Thus, the level of EFR-derived antibody avidity is contextual and relies on the inherent specificities of the host’s pre-infection repertoire, while the initiation, kinetics, and magnitude of the EFR rely on TLR-mediated inflammatory signals. The data are consistent with findings that memory B cells upon reactivation preferentially form EFR rather than enter GCs, even during heterotypic responses (Wong et al., 2020). Given the predominance of inflammatory signals during acute infection, this allows for antigen-specific B cells to be shunted into EFR for rapid production of protective antibodies to infections. The data also provide a mechanistic explanation for the association of EFRs with severe COVID-19 infection (Woodruff et al., 2020), and increased EFR-derived auto-antibody production with chronic inflammation, where a positive feed-forward loop may induce antibody-mediated pathology, driving enhanced inflammation, and thus further supporting ongoing EFRs. Even
+when the host may carry a highly restricted BCR repertoire, TLR activation may allow for EFR-derived antibodies of low affinity to contribute towards protection, without which these antibodies’ respective B cell clones would not reach the threshold of differentiation, nor activation. We conclude that B cell response fates are critically regulated by the innate, inflammatory milieu during antigen encounter.
+
+METHODS
+
+Mice. Male and female 8- to 12-wk-old C57BL/6 (WT; CD45.2), B6.SJL-Ptprrca Pepcb/BoyJ (CD45.1), B cell–deficient (μMT) mice as well asTNFAR1/2 KO, IFN-gamma KO, IL-12 KO, CD19-Cre IFNAR KO, IL-1R KO, TLR3 KO, TLR4 KO, TLR7 KO were commercially obtained (The Jackson Laboratories). Breeding pairs of MyD88/TRIF DKO and TLR2/4/unc93b TKO mouse strains were gifts from Dr. Barton (UC Berkeley). Breeding pairs of S100A9 KO mice were a kind gift of Dr. Rafatellu (UC San Diego).
+
+Mixed bone marrow (BM) chimeras were generated by adoptively transferring 5x \(10^6\) total mixed BM cells from slgM-deficient (CD45.2, 75%) and either C57BL/6 (WT; CD45.2), MyD88/TRIF double knockout (CD45.2), or TLR4/TLR2/Unc93b triple knockout (CD45.2) BM (25%) into 5-6 week-old B6.SJL-Ptprrca Pepcb/BoyJ (CD45.1) mice, lethally irradiated by exposure to a gamma irradiation source 24 h prior to transfer. Chimeras were rested for at least 6 weeks before infection and analysis.
+
+Infections, and immunizations. Mice were anesthetized with isoflurane and infected intranasally with a sublethal dose (10 PFU/ml) of influenza A/Puerto Rico/8/34 (A/PR8) in 40 μl volumes in PBS. Virus was grown in hen eggs as previously outlined(Doucett et al., 2005) and each virus batch was titrated for its effect on mice prior to use. Specifically, sublethal infection doses were chosen that incurred no more than 20% weight loss. For immunizations, mice were
+inoculated subcutaneously with 1x10^7 PFU A/PR8 in a 50:50 alum to PBS mixture. For some experiments immunizations were supplemented with 3μg LPS, or mice were in addition boosted repeatedly with 1x10^6 PFU A/PR8 and 3μg LPS in PBS or PBS alone as indicated.
+
+Adoptive serum transfer for passive protection. Indicated strains of mice were infected with 10 PFU A/PR8. Blood from terminally anesthetized mice at 10 dpi was collected via cardiac puncture and spun down for serum separation. Serum from each strain was pooled and naïve C57BL/6 mice were subsequently injected i.v. with a mixture of 50μl pooled serum and 150μl 1x PBS. These mice were then inoculated i.n. with 100 PFU A/PR8 one day later and measured for weight loss.
+
+Magnetic B cell enrichment. Splenic B cells were treated with Fc Block (anti-mouse CD16/32, clone 2.4.G2) and were then enriched using a mixture of biotinylated Abs (anti-CD90.2 (30-H12), anti-CD4 (GK1.5), anti-CD8a (53-6.7), anti-Gr-1 (RB6-8C5), anti-CD11b (M1/70), anti-NK1.1 (PK136), anti-F4/80 (BM8), anti-CD5 (53-7.3), anti-CD9 (MZ3), anti-CD138 (281-2) and anti-biotin MicroBeads (Miltenyi Biotec). Nylon-filtered stained splenocytes were separated using autoMACS (Miltenyi Biotec). Purities of enriched mouse B cells were >98% as determined by subsequent FACS analysis.
+
+Flow cytometry and phospho-flow. Single-cell suspensions from mediastinal lymph nodes (medLN) were made and labeled for phenotyping as previously outlined(Doucett et al., 2005). Briefly, after Fc receptor block with anti-CD16/32 (5 mg/ml for 20 min on ice), cells were stained with the following antibody-fluorophore conjugates at temperatures and times according to manufacturer/provider: HA-PE and HA-APC oligomers (kindly provided by Dr. Frances Lund, UAB), BV786 anti-CD19 (1D3) (BD Bioscience), APC-eFluor780 anti-CD45R (RA3-6B2), PE-Dazzle 594 anti-CD38 (90) (both Thermo Fisher), BV711 anti-CD24 (M1/69), BV605 anti-CD138 (281-2) (both Biolegend), eFluor450 anti-GL-7 (GL7), PE or PE/Cy7 anti-IRF4 (3E4), PerCP-
+eFluor710 anti-IRF8 (V3GYWCH), eFluor450 anti-Ki67 (SolA15) (all Thermo Fisher), FITC anti-IgM (331, in-house), and BV650 anti-IgD (11-26c.2a) (Biolegend). For a non-B cell “dump”, the following antibodies on AlexaFluor 700 were used: anti-CD90.2, anti-CD4, anti-CD8a, anti-Gr-1, anti-CD11b, anti-NK1.1, anti-F4/80 (all Thermo Fisher). The Foxp3 Staining Buffer Set (Thermo Fisher) was used for fixation and permeabilization of cells for staining of transcription factors according to manufacturer’s protocol. For cytoplasmic only staining, Cytofix/cytoperm buffer set (BD Biosciences) was used according to manufacturer’s protocol. For phospho-flow, APC anti-p-Syk (moch1ct), PerCP-eFluor710 anti-p-p38 (4NIT4KK), PE/Cy7 anti-p-mTOR (MRRBY), and PE anti-p-p65 (B33B4WP) were stained according to manufacturer’s protocol (Thermo Fisher). B cells from 7 dpi medLN were sorted by flow cytometry for ELISPOT using pooled antibodies for dump channel, anti-CD19, anti-CD45R, anti-CD24, and anti-CD38. Purity of sorted cells was assessed immediately afterwards (>96%).
+
+In vitro B cell cultures. Magnetically enriched B cells were cultured at 5 x 10^6 cells/ml at 37 °C. Cells were incubated with anti-IgM (Fab)_2 and/or LPS in culture media at the indicated concentrations for 30 minutes, one, two, and three hours. Three-hour anti-IgM-pulsed B cells were washed twice with PBS, and then cultured in culture media containing 200 ng/mlCD40L (Peprotech) and 5 ng/ml BAFF (R&D Systems) in 96-well round-bottom plates for 48 hours at 5% CO_2. Subsequent flow cytometric analysis was done using Fixable Aqua, PE anti-c-Rel (1RELAH5) (both Thermo Fisher), BV786 anti-CD19, eFluor450 anti-Ki67, PE/Cy7 anti-IRF4, PerCP-eFluor710 anti-IRF8 and APC anti-IL-21R (4A9) (all eBioscience).
+
+ELISPOT. A/PR8-specific Ig-secreting cells were measured. Briefly, ELISPOT plates were coated with 500 HAU of purified A/PR8 overnight, then blocked for non-specific binding for 1 hour. Serial dilutions of FACS-sorted EF PBs and pooled non-EF B cells were incubated overnight at 37 °C. Ab-secreting cells (ASC) were revealed with goat anti-mouse IgM, IgG-biotin
+(Southern Biotech) followed by SA-HRP (Vector Laboratories) and 3-amino-9-ethylcarbazole (Sigma-Aldrich).
+
+Nuclear fraction ELISA. c-Rel nuclear localization was measured. Briefly, nuclear and cytoplasmic protein fractions were extracted from cultured, purified B cells using NE-PER Nuclear and Cytoplasmic Extraction (Thermo Fisher) according to manufacturer’s protocol. ELISA plates were coated at 4 \( \mu \)g/ml dilution of polyclonal anti-c-Rel (Thermo Fisher) overnight, then blocked for non-specific binding for 1 hour. Bound c-Rel was detected using 4 \( \mu \)g/ml monoclonal anti-c-Rel (1RELAH5). Binding was revealed by SA-HRP (Vector Laboratories).
+
+Viral-load rtPCR. Infected mice were euthanized and lung tissue was extracted and homogenized using Gentle Macs (Miltenyi) in 1 ml PBS. Tissue was pelleted and supernatant was aliquoted and frozen. Viral RNA was purified from aliquots using the QIAamp viral RNA mini-kit (Qiagen). Presence of influenza was detected through amplification of influenza M gene using rtPCR. Primers used were AM-151 (5'-CATGCAATGGCTAAAGACAAGACC-3') and AM-397 (5'-AAGTGCACCAGCAGAATAACTGAG-3') and primer/probe AM-245 (6FAM-5'-CTGCAGCGTAGAGCTTTGTCCAAAATG-3'-TAMRA). Reverse transcription and amplication were done using TaqPath Multiplex Master Mix (Thermo Fisher). Samples were quantified to a standard of A/PR8 virus stock.
+
+Calcium flux assay. To measure changes in cellular calcium concentrations, B cells were stained with 2\( \mu \)M cell-permeant Fluor-3 and 4\( \mu \)M FuraRed (both Thermo Fisher) according to manufacturer’s protocol and stimulated with 10 \( \mu \)g/ml anti-IgM(fab)\(_2\) fragments prior to analysis by flow cytometry. The ratio of the calcium-excitible (Fluor3) and calcium-quenched (FuraRed) dyes were calculated to determine free-intracellular concentrations.
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+Xu, H., Chaudhri, V.K., Wu, Z., Biliouris, K., Dienger-Stambaugh, K., Rochman, Y., and Singh, H. (2015). Regulation of bifurcating B cell trajectories by mutual antagonism between transcription factors IRF4 and IRF8. Nat Immunol 16, 1274-1281.
+
+Yamamoto, M., Sato, S., Hemmi, H., Hoshino, K., Kaisho, T., Sanjo, H., Takeuchi, O., Sugiyama, M., Okabe, M., Takeda, K., and Akira, S. (2003). Role of adaptor TRIF in the MyD88-independent toll-like receptor signaling pathway. Science 301, 640-643.
+
+Acknowledgements
+
+This work was supported by research grants from the NIH/NIAID, R01AI117890, R01AI085568 and U19AI109962 and an institutional NIH training grant from the NIH/NHLBI, T-32 HL007013.
+
+We thank Ms. Zheng Luo and Jacqueline Dieter for expert technical support, Drs. Gregory Barton (UC Berkeley) and Manuela Raffatellu (UC San Diego) for mice, and Dr. Frances Lund (UAB) for HA-baits. We further thank Tracy Rourke of the California National Primate Research Center (UC Davis) for technical assistance with flow cytometry and the UC Davis TRACS personnel for animal care and husbandry.
+
+Author Contributions. J.H.L. designed and conducted experiments, analyzed data, and wrote the manuscript. N.B. designed and supervised experiments, data analysis, and wrote the manuscript.
+
+Competing Interests. No competing interests are declared by either author.
+Figure 1. Primary influenza infection induces strong early EFRs prior to GC formation.
+
+Shown are flow cytometric analyses of mediastinal lymph nodes (medLN) from C57BL/6 mice infected with influenza A/PR8 intra-nasally (i. n.) at seven days post-infection (dpi). (a) Identification of extrafollicular plasmablasts (EF PBs) and pre-GC/GC B cells by flow cytometry. (b) IgM and IgD expression on EF PBs, pre-GC/GC B cells, and non-EF/non-GC B cells. (c-e) C57BL/6 mice were infected and medLN were collected on the days specified, measuring B cell frequencies of total cells (c), pre-GC/GC frequency of B cells (d), EF frequency of B cells (e).
+Figure 2. EFRs generate influenza-specific antibody-secreting cells. (a) Influenza-specific ELISPOTS of sorted EF PBs and pooled non-EF cells for total Ig (left) and IgG2c (right). (b) Flow plots of HA-specific B cells using double HA-tetramer staining. (c-e) Time course of HA-specific B cell subsets during influenza infection as in (c-e), measuring frequency of HA-specific clones (i), HA-specific pre-GC/GC clones (j), and HA-specific EF PBs (k). Graphs are representative of two experiments (n>/=3). Error bars represent 95% confidence interval (CI), statistical significance determined by unpaired Student’s t-test with Welch’s correction. **: p<0.01
+Figure 3. Subcutaneous immunization with influenza and alum does not elicit EFRs. (a-e) C57BL/6 mice were immunized s.c. with 1x \(10^7\) PFU influenza A/PR8 in alum and inguinal LNs were analyzed on days indicated. (a) Flow plots comparing immunization to infection EF and GC formation. (b) Kinetics of EF and pre-GC/GC B cells compared to infection. (c) Fold-difference of EF and GC responses compared to infection. (d) Flow plots comparing HA-specific B cell populations during immunization and infection. (e) Kinetics of total (left) and proliferating (right) HA-specific B cells compared to infection. Graphs are representative of two experiments (n=4). Error bars represent 95% CI, statistical significance determined by one-way ANOVA (b, e). ****: p<0.0001
+Figure 4. Optimal EFR kinetics and protective antibodies require MyD88 and TRIF.
+
+Knockout and WT mice were infected with 10 PFU A/PR8 and medLNs were collected at 7 days post-infection (dpi). (a) Fold-difference of B cell subsets in TLR-deficient versus WT mice at 7 dpi. (b-c) Sera from influenza-infected MyD88/TRIF-deficient (DKO) mice (b) or TLR2/4/unc93b-deficient (TKO) mice (c) at 10 dpi were transferred to C57BL/6 mice prior to infection with a lethal dose (100 PFU) of influenza A/PR8 the next day. Shown is % change in weight over the course of infection. Graphs are representative of two or more experiments (n>/=3 (a), n=10 (b,c)). Error bars represent 95% CI, statistical significance determined by one-way ANOVA (a) and unpaired Student’s t-test with Welch’s correction. *: p<0.05, **: p<0.01, ***: p<0.001, ****: p<0.0001 or indicated in subfigures.
+Figure 5. BCR-mediated survival and proliferation are defective in the absence of TLR signaling. (a) Mixed bone-marrow chimeras (BMC) established with irradiated CD45.1 C57BL/6 host mice reconstituted with μMT donor BM and BM from either DKO or TKO, then infected with 10 PFU A/PR8 6 weeks later. (b) Quantification of DKO and TKO BMC compared to WT BMC controls of B cell subsets at 7 dpi. (c) Pooled splenic and LN B cells from WT, DKO, or TKO B cells negatively enriched (>98% purity) were pulsed with graded levels of anti-IgM for 3 hours, then stimulated with CD40L and BAFF for 48 hours. (d) Quantification of cell viability (top) and cell proliferation (bottom). (e) Ki67+ non-EF/GC B cells in chimeras from 5 dpi. Graphs are representative of two experiments (n>/=4). Error bars represent 95% CI, statistical significance determined by one-way ANOVA and unpaired Student’s t-test with Welch’s correction. *: p<0.05, **: p<0.001, ****: p<0.0001.
+Figure 6. Lack of functional TLR signaling leads to altered BCR complex dynamics and failure to upregulate IRF4. (a) Representative flow plots showing IRF4 and IRF8 expression in infected mice, highlighting clustering of EF PBs (left). Fold-difference in IRF4 and IRF8 of non-EF/GC B cells from chimeras at 5 dpi (right). (b) Pre-enrichment baseline of IRF4 and IRF8 in B cells of each strain (left) and representative IRF4 versus IRF8 flow plots from cells stimulated with indicated anti-IgM concentrations (right). Colored numbers in plots correspond to each like-colored axis. (c-d) Fold-change compared to non-stimulated WT B cells in IRF4 (c) and IRF8 expression (d) after treatment outlined in Fig. 5c. (e) Fold-change in cytoplasmic c-Rel
+measured by flow cytometry after 30-minute anti-IgM or LPS treatment. (f) Fold-differences in total c-Rel expression after a 3h anti-IgM pulse and 48h culture in complete media only. Error bars represent 95% CI, statistical significance determined by one-way ANOVA and unpaired Student’s t-test with Welch’s correction. *: p<0.05 **: p<0.01 ***: p<0.001, ****: p<0.0001. Stars in (g,h) are Student’s t-test comparison to respective WT control.
+Figure 7. Sustained TLR-mediated inflammation generates strong EFRs in the draining LN after immunization. (a) Mice were immunized s.c. with or without influenza in alum and with or without LPS, then boosted with either LPS or PBS on days specified, followed by analysis of draining LN. (b) Counts of major B cell subsets. (c) Quantification of HA-specific B cell subsets as in (b). (d) Flow plots of HA-specific B cells from each regimen in terms of proliferation and plasma cell differentiation (left) and IRF4 vs IRF8 signature (right, HA-sp. highlighted in red). (e) Quantification of HA-specific EF PBs, proliferation, and relative expression of IRF4. Graphs are representative of two experiments (n>/=4). Error bars represent 95% CI. Statistical significance determined by one-way ANOVA and unpaired Student’s t-test with Welch’s correction. *: p<0.05, **: p<0.01 ***: p<0.001, ****: p<0.0001.
+Figure 8. Repeated antigen exposure alone biases antigen-specific B cells towards a GC fate, requires sustained LPS exposure to polarize towards an EF fate. (a) Mice were immunized s.c. with influenza and LPS in alum, then boosted with antigen alone or antigen with LPS and LPS alone on days specified, followed by analysis of draining LN. (b-e) Quantification of total HA B cells (b), Ki67+ HA B cells (c), HA GC B cells (d) and HA EF PBs (e). (f) Concentration of influenza-specific serum IgG at 10 days post-prime. (g,h) Serum from primed/boosted mice at 10 days post-prime was transferred to C57BL/6 mice prior to infection with a lethal dose (100 PFU) of influenza A/PR8 the next day. Shown is survival probability (g) and percent change in weight (h) by average (left) and individually (right) over the course of infection. Graphs are representative of two experiments (n>/=7, g, h n=10). Error bars represent 95% CI. Statistical significance determined by one-way ANOVA and unpaired Student’s t-test with Welch’s correction. *: p<0.05, **: p<0.01 ***: p<0.001, ****: p<0.0001.
+Supplementary Files
+
+This is a list of supplementary files associated with this preprint. Click to download.
+
+• SUPPLFIGSPluSTextFinal.pdf

027b827c3b80c86306a8c299d162b6cb2bb24a38c0ffa3c834d579a1e6c6338c/preprint/supplementaries/SUPPLFIGSPluSTextFinal/SUPPLFIGSPluSTextFinal.md

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+SUPPLEMENTAL INFORMATION
+
+Toll-like receptor mediated inflammation directs B cells towards protective antiviral extrafollicular responses
+
+Jonathan H. Lam1,2 and Nicole Baumgarth1,2,3,4
+1Graduate Group in Immunology, 2Center for Immunology and Infectious Diseases, 3Dept. Pathology, Microbiology and Immunology, University of California Davis, Davis, USA
+
+Supplemental Figures 1-12
+Supplemental Figure 1. EFR are not generated through GC reactions WT, Mb-1 Cre+ control, and Mb-1 Cre+ Bcl6 f/f mice were infected with 10 PFU A/PR8 and medLNs were analyzed at 10 dpi. (a) B cell frequency of total cells. (b) EF PB frequency of total B cells. (c) GC B cell frequency of total B cells. Error bars represent 95% CI, p-values determined by unpaired Student’s t-test with Welch’s correction. *: p<0.05, **: p<0.01.
+Supplemental Figure 2. Antigen-dose increases germinal centers but not plasmablast responses. Scatter plots indicate frequencies of B220+ CD38+ CD24hi germinal center B cells (left) and B220lo CD138hi plasmablasts in draining lymph nodes of BALB/c mice (n=4 per group) either infected intranasally with indicated PFU influenza A/PR8 (top) or immunized s.c. with indicated HAU sucrose-gradient purified influenza A/PR8 virion emulsified in Complete Freund’s adjuvant. Analysis was done on day 7 after infection/immunization. All data are frequencies of cells after gating for live, lymphocytes.
+Supplemental Figure 3. Lack of single cytokine or TLR pathway does not affect EFR to influenza. Knockout and WT mice were infected with 10 PFU A/PR8 and medLNs were collected at 7 days post-infection (dpi). Shown are fold-differences in major B cell subsets in C57BL/6 WT and indicated gene-targeted mice (a), as well as (b) single TLR-knockouts. Error bars represent 95% CI, p-values determined by unpaired Student’s t-test with Welch’s correction. P-values indicated on charts.
+Supplemental Figure 4. Passive protection with TKO serum and late-stage viral loads and EF responses. (a,b) Viral loads as analyzed by viral qRt-PCR on lung homogenates at 10 dpi of B cell-specific chimera (a) and global knockout (b) mice. c) Fold-differences of B cell subsets in DKO, TKO and WT mice at 7 dpi. Graphs are representative of two experiments (n>4). Error bars represent 95% CI. Statistical significance determined by one-way ANOVA and unpaired Student’s t-test with Welch’s correction. *: p<0.05 (or shown) **: p<0.01 ***: p<0.001, ****: p<0.0001. ***** p>1E-5.
+Supplemental Figure 5. BCR and TLR4 stimulation have additive effects on cell viability, proliferation, and activation phenotype. Pooled and enriched splenic and lymph node WT B cells were cultured with indicated graded concentrations anti-IgM 3h pulsed or graded, sustained concentrations of LPS and assessed for (a) cell viability, (b) proliferation, (c) IRF4 (d) IRF8, and (e) IL-21R expression. Graphs are representative of two experiments (n=4). Error bars represent 95% CI. Statistical significance determined by one-way ANOVA and unpaired Student’s t-test with Welch’s correction. *: p<0.05 **: p<0.01 ***: p<0.001, ****: p<0.0001.
+Supplemental Figure 6. MyD88 and TRIF non-redundantly regulate B cell viability and proliferation in response to BCR stimulus. Pooled splenic/LN WT, DKO, MyD88 KO, and TRIF KO B cells were negatively enriched (>98%) and pulsed with graded anti-IgM for 3 hours, then stimulated with CD40L and BAFF for 48 hours and assessed for (a) viability and (b) proliferation. (c,d) Cells as in (a) were pulsed with graded doses anti-IgM for 3 hours followed by incubation in complete medium only for 48h, then assessed for (c) cell viability and (d) proliferation. Error bars represent 95% CI. Statistical significance determined by one-way ANOVA and unpaired Student’s t-test with Welch’s correction. *: p<0.05 **: p<0.01 ***: p<0.001, ****: p<0.0001.
+Supplemental Figure 7. Antigen-specific B cells have greater proliferative capacity than TLR-signaling deficient B cells after influenza infection. Relative fold-change in HA-specific, Ki67+ B cells compared to WT controls in medLN of mice at 5 dpi with influenza A/PR8. Graph is representative of two experiments (n>/=5). Error bars represent 95% CI.
+
+![Bar graph showing fold difference in HA Ki67+ B cells between WT, DKO, and TKO groups](page_420_312_324_324.png)
+Supplemental Figure 8. TLR-signaling deficient B cells have nominal immediate activation and functional downstream effector protein activation. (a) Calcium flux of BCR-independent (iono) and BCR-mediated, anti-IgM(Fab)_2 activation in purified WT, DKO, and TKO
+B cells. (b,c) Pooled splenic/LN WT, DKO, TKO, MyD88 KO, and TRIF KO B cells were negatively enriched (>98%) and stimulated with graded indicated doses anti-IgM(Fab)_2 for 30 minutes, then assessed for phosphorylated, intracellular proteins. (b) Baseline fold-difference in phosphorylation between WT and knockout B cells. (c) Fold-changes in protein phosphorylation of target proteins relative to non-stimulated conditions for each strain. Graphs are representative of two experiments (n=6) except for (b) (n=3). Error bars represent 95% CI. Statistical significance determined by one-way ANOVA only. *: p<0.05 **: p<0.01 ***: p<0.001, ****: p<0.0001.
+Supplemental Figure 9. Early HA-specific B cells in DKO and TKO BMCs have an anergic phenotype early during influenza infection. (a,b) Relative expression of IgD in vivo at 5 dpi in HA-specific B cells from bone marrow chimeras (a) and in vitro after 48h anti-IgM pulse plus CD40L/BAFF treatment (b). Graphs are representative of two experiments (n>/=5). Error bars represent 95% CI. Statistical significance determined by one-way ANOVA only. *: p<0.05 **: p<0.01 ***: p<0.001.
+Supplemental Figure 10. Immediate activation of c-Rel after BCR stimulation is defective in TLR-signaling deficient B cells. (a) (b-c) Shown are the ratios of nuclear vs cytoplasmic c-Rel in WT, DKO, and TKO B cells as determined by ELISA on nuclear versus cytoplasmic protein extracts at 60 minutes (b) and 120 minutes (c) after anti-IgM or LPS stimulation. (d) Total c-Rel expression after 120-minute anti-IgM or LPS stimulation as assessed by flow cytometry. Error bars represent 95% CI. Statistical significance determined by one-way ANOVA (a, intra-strain comparisons in b-d) and unpaired Student’s t-test with Welch’s correction (b-d). *: p<0.05 **: p<0.01 ***: p<0.001, ****: p<0.0001.
+Supplemental Figure 11. HA-specific B cell survival is modulated by TLR signals. (a) Mice were immunized s.c. with or without influenza in alum and with or without LPS, then boosted with either LPS or PBS on days specified, followed by analysis of draining LN. The ratio of live versus dead HA-specific B cell populations were assessed for each treatment. (b) Analysis of live versus dead HA-specific B cells as in (a) but from infected mice, 7 dpi. Graphs are representative of two experiments (n>/=3). Error bars represent 95% CI, statistical significance determined by one-way ANOVA (p<0.01 for both a,b) and unpaired Student’s t-test with Welch’s correction (d,e). *: p<0.05 **: p<0.01.
+Supplemental Figure 12. Model of TLR-mediated induction of B cell differentiation and EFRs. (Top) With a functional TLR axis either through MyD88/TRIF or TLR2/4/unc93b, BCR stimulation leads to efficient c-Rel nuclear localization and sustained upregulation of IRF4. Without a functional TLR axis, BCR signaling leads to delayed c-Rel localization, lack of long-term c-Rel expression, and a lack of sustained IRF4 induction and upregulation. (Bottom) During infection or immunization, TLR agonism or an equivalent aggregate of inflammatory stimuli polarizes antigen-specific B cells towards EFR and away from the GC response when antigen is limiting or in excess, resulting in early and protective antigen-specific antibody generation.

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0297e09c8c2b5e744ded2ba5e84ab6868857ddbdce0ca65775323250f8a61cea/peer_review/peer_review.md

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

0297e09c8c2b5e744ded2ba5e84ab6868857ddbdce0ca65775323250f8a61cea/preprint/preprint.md

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

0297e09c8c2b5e744ded2ba5e84ab6868857ddbdce0ca65775323250f8a61cea/preprint/supplementaries/SupportingInformation100MB/SupportingInformation100MB.md

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+Deep learning shows declining groundwater levels in Germany until 2100 due to climate change (Supplementary Material)
+
+Wunsch, A., Liesch, T., Broda, S.
+
+Content Overview:
+
+• Table S1 lists all hydrographs including additional information such as identifiers and coordinates
+
+• Table S1 lists the accuracy of the models in the past as well as the optimized hyperparameters
+
+• Figures S1 to S118 show the evaluation graph for the test period (2012-2016), the performance under extreme climatic conditions and the SHAP summary plot for each site
+
+• Figures S119 to 236 show the long term groundwater simulation results for each individual climate projection consolidated in one plot.
+
+.
+
+List of Tables
+
+<table>
+  <tr>
+    <th>S1</th>
+    <th>List of all wells</th>
+    <th>8</th>
+  </tr>
+  <tr>
+    <th>S2</th>
+    <th>Model Errors and Hyperparameters</th>
+    <th>10</th>
+  </tr>
+</table>
+
+List of Figures
+
+<table>
+  <tr>
+    <th>S1</th>
+    <th>Evaluation of BB_27381010 Model</th>
+    <th>12</th>
+  </tr>
+  <tr>
+    <th>S2</th>
+    <th>Evaluation of BB_28390113 Model</th>
+    <th>13</th>
+  </tr>
+  <tr>
+    <th>S3</th>
+    <th>Evaluation of BB_29519030 Model</th>
+    <th>14</th>
+  </tr>
+  <tr>
+    <th>S4</th>
+    <th>Evaluation of BB_30400591 Model</th>
+    <th>15</th>
+  </tr>
+  <tr>
+    <th>S5</th>
+    <th>Evaluation of BB_31400780 Model</th>
+    <th>16</th>
+  </tr>
+  <tr>
+    <th>S6</th>
+    <th>Evaluation of BB_31491979 Model</th>
+    <th>17</th>
+  </tr>
+  <tr>
+    <th>S7</th>
+    <th>Evaluation of BB_32455305 Model</th>
+    <th>18</th>
+  </tr>
+  <tr>
+    <th>S8</th>
+    <th>Evaluation of BB_33437070 Model</th>
+    <th>19</th>
+  </tr>
+  <tr>
+    <th>S9</th>
+    <th>Evaluation of BB_33437090 Model</th>
+    <th>20</th>
+  </tr>
+  <tr>
+    <th>S10</th>
+    <th>Evaluation of BB_33437106 Model</th>
+    <th>21</th>
+  </tr>
+  <tr>
+    <th>S11</th>
+    <th>Evaluation of BB_33452451 Model</th>
+    <th>22</th>
+  </tr>
+  <tr>
+    <th>S12</th>
+    <th>Evaluation of BB_33470960 Model</th>
+    <th>23</th>
+  </tr>
+  <tr>
+    <th>S13</th>
+    <th>Evaluation of BB_34426110 Model</th>
+    <th>24</th>
+  </tr>
+  <tr>
+    <th>S14</th>
+    <th>Evaluation of BB_34522461 Model</th>
+    <th>25</th>
+  </tr>
+</table>
+S15  Evaluation of BB_37451908 Model ............................................. 26
+S16  Evaluation of BB_39441476 Model ............................................. 27
+S17  Evaluation of BB_39496056 Model ............................................. 28
+S18  Evaluation of BB_40500136 Model ............................................. 29
+S19  Evaluation of BB_42458092 Model ............................................. 30
+S20  Evaluation of BW_100-813-7 Model ........................................... 31
+S21  Evaluation of BW_103-763-0 Model ........................................... 32
+S22  Evaluation of BW_107-666-2 Model ........................................... 33
+S23  Evaluation of BW_110-619-8 Model ........................................... 34
+S24  Evaluation of BW_112-211-1 Model ........................................... 35
+S25  Evaluation of BW_124-068-9 Model ........................................... 36
+S26  Evaluation of BW_131-115-0 Model ........................................... 37
+S27  Evaluation of BW_145-772-0 Model ........................................... 38
+S28  Evaluation of BW_15-568-2 Model ............................................ 39
+S29  Evaluation of BW_16-706-8 Model ............................................ 40
+S30  Evaluation of BW_177-770-1 Model ........................................... 41
+S31  Evaluation of BW_194-069-9 Model ........................................... 42
+S32  Evaluation of BY_11119 Model .................................................. 43
+S33  Evaluation of BY_13126 Model .................................................. 44
+S34  Evaluation of BY_15120 Model .................................................. 45
+S35  Evaluation of BY_22008 Model .................................................. 46
+S36  Evaluation of BY_24153 Model .................................................. 47
+S37  Evaluation of BY_25155 Model .................................................. 48
+S38  Evaluation of BY_3108 Model ................................................... 49
+S39  Evaluation of BY_5158 Model ................................................... 50
+S40  Evaluation of BY_5162 Model ................................................... 51
+S41  Evaluation of BY_7126 Model ................................................... 52
+S42  Evaluation of BY_8252 Model ................................................... 53
+S43  Evaluation of BY_83614 Model .................................................. 54
+S44  Evaluation of BY_9275 Model ................................................... 55
+S45  Evaluation of HE_10319 Model .................................................. 56
+S46  Evaluation of HE_11781 Model .................................................. 57
+S47  Evaluation of HE_12117 Model .................................................. 58
+S48  Evaluation of HE_14293 Model .................................................. 59
+S49  Evaluation of HE_14297 Model .................................................. 60
+S50  Evaluation of HE_6253 Model ................................................... 61
+S51  Evaluation of HE_6645 Model ................................................... 62
+S52  Evaluation of HE_7824 Model ................................................... 63
+S53  Evaluation of MV_16450200 Model ............................................. 64
+S54  Evaluation of MV_17390002 Model ............................................. 65
+S55  Evaluation of NI_100000728 Model ............................................ 66
+S56  Evaluation of NI_100000842 Model ............................................ 67
+S57  Evaluation of NI_100000926 Model ............................................ 68
+S58  Evaluation of NI_129300060 Model ............................................ 69
+S59  Evaluation of NI_200000620 Model ............................................. 70
+S60  Evaluation of NI_200000788 Model ............................................. 71
+S61  Evaluation of NI_200001068 Model ............................................. 72
+S62  Evaluation of NI_200001722 Model ............................................. 73
+S63  Evaluation of NI_200002153 Model ............................................. 74
+S64  Evaluation of NI_40000175 Model ............................................... 75
+S65  Evaluation of NI_40000233 Model ............................................... 76
+S66  Evaluation of NI_400080190 Model ............................................. 77
+S67  Evaluation of NI_400081660 Model ............................................. 78
+S68  Evaluation of NI_40501911 Model ............................................... 79
+S69  Evaluation of NI_405160331 Model ............................................. 80
+S70  Evaluation of NI_500000592 Model ............................................. 81
+S71  Evaluation of NI_600041871 Model ............................................. 82
+S72  Evaluation of NI_9700020 Model ................................................ 83
+S73  Evaluation of NI_9700080 Model ................................................ 84
+S74  Evaluation of NI_9700159 Model ................................................ 85
+S75  Evaluation of NI_9840391 Model ................................................ 86
+S76  Evaluation of NI_9840901 Model ................................................ 87
+S77  Evaluation of NI_9853172 Model ................................................ 88
+S78  Evaluation of NW_100140142 Model ............................................ 89
+S79  Evaluation of NW_100140762 Model ............................................ 90
+S80  Evaluation of NW_110040028 Model ............................................ 91
+S81  Evaluation of NW_110040041 Model ............................................ 92
+S82  Evaluation of NW_110060143 Model ............................................ 93
+S83  Evaluation of NW_110240017 Model ............................................ 94
+S84  Evaluation of NW_129660176 Model ............................................ 95
+S85  Evaluation of NW_129660206 Model ............................................ 96
+S86  Evaluation of NW_60090169 Model ............................................... 97
+S87  Evaluation of NW_60240258 Model ............................................... 98
+S88  Evaluation of NW_80000186 Model ............................................... 99
+S89  Evaluation of NW_80300376 Model ............................................... 100
+S90  Evaluation of NW_91163705 Model ............................................... 101
+S91  Evaluation of NW_91174909 Model ............................................... 102
+S92  Evaluation of RP_2373131200 Model ........................................... 103
+S93  Evaluation of RP_2378140100 Model ........................................... 104
+S94  Evaluation of RP_2587150500 Model ........................................... 105
+S95  Evaluation of SH_10L53126001 Model .......................................... 106
+S96  Evaluation of SH_10L54010004 Model .......................................... 107
+S97  Evaluation of SH_10L55005005 Model .......................................... 108
+S98  Evaluation of SH_10L55538005 Model .......................................... 109
+S99  Evaluation of SH_10L56048003 Model .......................................... 110
+S100 Evaluation of SH_10L57066002 Model .......................................... 111
+S101 Evaluation of SH_10L62060004 Model .......................................... 112
+S102 Evaluation of SN_46440927 Model ............................................... 113
+S103 Evaluation of SN_46460564 Model .................................................. 114
+S104 Evaluation of SN_47500596 Model .................................................. 115
+S105 Evaluation of SN_48390509 Model .................................................. 116
+S106 Evaluation of SN_49430964 Model .................................................. 117
+S107 Evaluation of SN_49484004 Model .................................................. 118
+S108 Evaluation of SN_49531740 Model .................................................. 119
+S109 Evaluation of SN_52410759 Model .................................................. 120
+S110 Evaluation of ST_31340028 Model .................................................. 121
+S111 Evaluation of ST_33340002 Model .................................................. 122
+S112 Evaluation of ST_34376608 Model .................................................. 123
+S113 Evaluation of ST_36340007 Model .................................................. 124
+S114 Evaluation of ST_39320023 Model .................................................. 125
+S115 Evaluation of ST_40415442 Model .................................................. 126
+S116 Evaluation of ST_41300015 Model .................................................. 127
+S117 Evaluation of ST_43435116 Model .................................................. 128
+S118 Evaluation of ST_44339213 Model .................................................. 129
+S119 Projection Results BB_27381010 Model ............................................. 130
+S120 Projection Results BB_28390113 Model ............................................. 130
+S121 Projection Results BB_29519030 Model ............................................. 130
+S122 Projection Results BB_30400591 Model ............................................ 130
+S123 Projection Results BB_31400780 Model ............................................ 131
+S124 Projection Results BB_31491979 Model ............................................ 131
+S125 Projection Results BB_32455305 Model ............................................ 131
+S126 Projection Results BB_33437070 Model ............................................ 131
+S127 Projection Results BB_33437090 Model ............................................ 132
+S128 Projection Results BB_33437106 Model ............................................ 132
+S129 Projection Results BB_33452451 Model ............................................ 132
+S130 Projection Results BB_33470960 Model ............................................ 132
+S131 Projection Results BB_34426110 Model ............................................ 133
+S132 Projection Results BB_34522461 Model ............................................ 133
+S133 Projection Results BB_37451908 Model ............................................ 133
+S134 Projection Results BB_39441476 Model ............................................ 133
+S135 Projection Results BB_39496056 Model ............................................ 134
+S136 Projection Results BB_40500136 Model ............................................ 134
+S137 Projection Results BB_42458092 Model ............................................ 134
+S138 Projection Results BW_100-813-7 Model .......................................... 134
+S139 Projection Results BW_103-763-0 Model .......................................... 135
+S140 Projection Results BW_107-666-2 Model .......................................... 135
+S141 Projection Results BW_110-619-8 Model .......................................... 135
+S142 Projection Results BW_112-211-1 Model .......................................... 135
+S143 Projection Results BW_124-068-9 Model .......................................... 136
+S144 Projection Results BW_131-115-0 Model .......................................... 136
+S145 Projection Results BW_145-772-0 Model .......................................... 136
+S146 Projection Results BW_15-568-2 Model ........................................... 136
+S147 Projection Results BW_16-706-8 Model ............................................. 137
+S148 Projection Results BW_177-770-1 Model ............................................. 137
+S149 Projection Results BW_194-069-9 Model ............................................. 137
+S150 Projection Results BY_11119 Model .................................................. 137
+S151 Projection Results BY_13126 Model .................................................. 138
+S152 Projection Results BY_15120 Model .................................................. 138
+S153 Projection Results BY_22008 Model .................................................. 138
+S154 Projection Results BY_24153 Model .................................................. 138
+S155 Projection Results BY_25155 Model .................................................. 139
+S156 Projection Results BY_3108 Model .................................................... 139
+S157 Projection Results BY_5158 Model .................................................... 139
+S158 Projection Results BY_5162 Model .................................................... 139
+S159 Projection Results BY_7126 Model .................................................... 140
+S160 Projection Results BY_8252 Model .................................................... 140
+S161 Projection Results BY_83614 Model ................................................... 140
+S162 Projection Results BY_9275 Model .................................................... 140
+S163 Projection Results HE_10319 Model ................................................... 141
+S164 Projection Results HE_11781 Model ................................................... 141
+S165 Projection Results HE_12117 Model ................................................... 141
+S166 Projection Results HE_14293 Model ................................................... 141
+S167 Projection Results HE_14297 Model ................................................... 142
+S168 Projection Results HE_6253 Model .................................................... 142
+S169 Projection Results HE_6645 Model .................................................... 142
+S170 Projection Results HE_7824 Model .................................................... 142
+S171 Projection Results MV_16450200 Model ............................................. 143
+S172 Projection Results MV_17390002 Model .............................................. 143
+S173 Projection Results NI_100000728 Model ............................................. 143
+S174 Projection Results NI_100000842 Model ............................................. 143
+S175 Projection Results NI_100000926 Model ............................................. 144
+S176 Projection Results NI_129300060 Model ............................................. 144
+S177 Projection Results NI_200000620 Model ............................................. 144
+S178 Projection Results NI_200000788 Model ............................................. 144
+S179 Projection Results NI_200001068 Model ............................................. 145
+S180 Projection Results NI_200001722 Model ............................................. 145
+S181 Projection Results NI_200002153 Model ............................................. 145
+S182 Projection Results NI_40000175 Model ............................................... 145
+S183 Projection Results NI_40000233 Model ............................................... 146
+S184 Projection Results NI_400080190 Model ............................................. 146
+S185 Projection Results NI_400081660 Model ............................................. 146
+S186 Projection Results NI_40501911 Model ............................................... 146
+S187 Projection Results NI_405160331 Model ............................................. 147
+S188 Projection Results NI_500000592 Model ............................................. 147
+S189 Projection Results NI_600041871 Model ............................................. 147
+S190 Projection Results NI_9700020 Model ............................................... 147
+S191 Projection Results NL_9700080 Model ......................... 148
+S192 Projection Results NL_9700159 Model ......................... 148
+S193 Projection Results NL_9840391 Model ......................... 148
+S194 Projection Results NL_9840901 Model ......................... 148
+S195 Projection Results NL_9853172 Model ......................... 149
+S196 Projection Results NW_100140142 Model ..................... 149
+S197 Projection Results NW_100140762 Model ..................... 149
+S198 Projection Results NW_110040028 Model .................... 149
+S199 Projection Results NW_110040041 Model .................... 150
+S200 Projection Results NW_110060143 Model .................... 150
+S201 Projection Results NW_110240017 Model .................... 150
+S202 Projection Results NW_129660176 Model .................... 150
+S203 Projection Results NW_129660206 Model .................... 151
+S204 Projection Results NW_60090169 Model ..................... 151
+S205 Projection Results NW_60240258 Model ..................... 151
+S206 Projection Results NW_80000186 Model ..................... 151
+S207 Projection Results NW_80300376 Model ..................... 152
+S208 Projection Results NW_91163705 Model ..................... 152
+S209 Projection Results NW_91174909 Model ..................... 152
+S210 Projection Results RP_2373131200 Model .................. 152
+S211 Projection Results RP_2378140100 Model .................. 153
+S212 Projection Results RP_2587150500 Model .................. 153
+S213 Projection Results SH_10L53126001 Model .................. 153
+S214 Projection Results SH_10L54010004 Model .................. 153
+S215 Projection Results SH_10L55005005 Model .................. 154
+S216 Projection Results SH_10L55038005 Model .................. 154
+S217 Projection Results SH_10L56048003 Model .................. 154
+S218 Projection Results SH_10L57066002 Model .................. 154
+S219 Projection Results SH_10L62060004 Model .................. 155
+S220 Projection Results SN_46440927 Model ..................... 155
+S221 Projection Results SN_46460564 Model ..................... 155
+S222 Projection Results SN_47500596 Model ..................... 155
+S223 Projection Results SN_48390509 Model ..................... 156
+S224 Projection Results SN_49430964 Model ..................... 156
+S225 Projection Results SN_49484004 Model ..................... 156
+S226 Projection Results SN_49531740 Model ..................... 156
+S227 Projection Results SN_52410759 Model ..................... 157
+S228 Projection Results ST_31340028 Model ..................... 157
+S229 Projection Results ST_33340002 Model ..................... 157
+S230 Projection Results ST_34376608 Model ..................... 157
+S231 Projection Results ST_36340007 Model ..................... 158
+S232 Projection Results ST_39320023 Model ..................... 158
+S233 Projection Results ST_40415442 Model ..................... 158
+S234 Projection Results ST_41300015 Model ..................... 158
+S235 Projection Results ST_43435116 Model ............................................. 159
+S236 Projection Results ST_44339213 Model ............................................. 159
+Table S1: List of all wells included in the dataset. ID refers to the respective data web service.
+
+<table>
+  <tr>
+    <th>ID</th>
+    <th>Name</th>
+    <th>X_Coord (UTM 32N)</th>
+    <th>Y_Coord (UTM 32N)</th>
+    <th>Aquifer</th>
+    <th>Ground Type<sup>1</sup></th>
+    <th>Surf. [m asl]</th>
+    <th>GW [m]</th>
+  </tr>
+  <tr><td>BB_27381010</td><td>Lockstaedt OP</td><td>701838</td><td>5900152</td><td>p</td><td></td><td>49.7</td><td>1.32</td></tr>
+  <tr><td>BB_28390113</td><td>Beveringen OP</td><td>716212</td><td>5893813</td><td>p</td><td></td><td>69.7</td><td>0.45</td></tr>
+  <tr><td>BB_29519030</td><td>Schw.Krzg.Teichm.-Seelenb.str.</td><td>853218</td><td>5892330</td><td>p</td><td></td><td>6</td><td>2.63</td></tr>
+  <tr><td>BB_30400591</td><td>Stolpe, Birkenallee</td><td>731260</td><td>5874653</td><td>p</td><td></td><td>43.7</td><td>3.39</td></tr>
+  <tr><td>BB_31400780</td><td>Wusterhausen, Bahnhilne</td><td>732280</td><td>5863903</td><td>p</td><td></td><td>33.2</td><td>1.11</td></tr>
+  <tr><td>BB_31491979</td><td>Amalienhof-Falkenberg, KSP Nr. 6 GeDO</td><td>833480</td><td>5863149</td><td>p</td><td></td><td>1.7</td><td>0.48</td></tr>
+  <tr><td>BB_32455305</td><td>Hohenbruch, Weg n.Teeroften</td><td>781331</td><td>5857671</td><td>p</td><td></td><td>37.2</td><td>1.87</td></tr>
+  <tr><td>BB_33437070</td><td>Bredow, Siedlung Glien</td><td>768609</td><td>5836914</td><td>p</td><td></td><td>31.6</td><td>1.97</td></tr>
+  <tr><td>BB_33437090</td><td>Perwenitz, Luchstraße, OP</td><td>769303</td><td>5838525</td><td>p</td><td></td><td>32.35</td><td>1.67</td></tr>
+  <tr><td>BB_33437106</td><td>Nauen, gegenue.G.-Arco-Str. 148</td><td>764414</td><td>5838901</td><td>p</td><td></td><td>31.2</td><td>1.97</td></tr>
+  <tr><td>BB_33452451</td><td>Hennigsdorf,1.3km v.Trappen-A.</td><td>782655</td><td>5838050</td><td>p</td><td></td><td>32.15</td><td>0.93</td></tr>
+  <tr><td>BB_33470960</td><td>Lindow_Bernau</td><td>809679</td><td>5844936</td><td>p</td><td></td><td>66</td><td>1.39</td></tr>
+  <tr><td>BB_34426110</td><td>Bagow, Bollmannsruth</td><td>749731</td><td>5823802</td><td>p</td><td></td><td>31</td><td>2.31</td></tr>
+  <tr><td>BB_34522461</td><td>Sachsendorf, KSP Nr. 71</td><td>872109</td><td>5832083</td><td>p</td><td></td><td>12</td><td>2.64</td></tr>
+  <tr><td>BB_37451908</td><td>Juethendorf/Stro.Groben-Gr.Beu.</td><td>785736</td><td>5800205</td><td>p</td><td></td><td>35.98</td><td>1.58</td></tr>
+  <tr><td>BB_39441476</td><td>Felgentreu, ca. 2 km oestl.</td><td>777374</td><td>5779401</td><td>p</td><td></td><td>51.35</td><td>1.74</td></tr>
+  <tr><td>BB_39496056</td><td>Kuschkow</td><td>839963</td><td>5779849</td><td>p</td><td></td><td>46.23</td><td>1.83</td></tr>
+  <tr><td>BB_40500136</td><td>Byhlen</td><td>853890</td><td>5762850</td><td>p</td><td></td><td>54.5</td><td>2.36</td></tr>
+  <tr><td>BB_42458092</td><td>Mahdel</td><td>788491</td><td>5735916</td><td>p</td><td></td><td>79.97</td><td>1.65</td></tr>
+  <tr><td>BW_100-813-7</td><td>GIENGEN TAUBENTAL</td><td>590920</td><td>5388935</td><td>k</td><td></td><td>497.28</td><td>35.32</td></tr>
+  <tr><td>BW_103-763-0</td><td>Sonheimer Wirtschaule,STEINHEIM</td><td>578522</td><td>5391582</td><td>k</td><td></td><td>520.7</td><td>15.69</td></tr>
+  <tr><td>BW_107-666-2</td><td>GWM KB 3 A Weiler, Blaubeuren</td><td>557027</td><td>5360033</td><td>k</td><td></td><td>527.43</td><td>6.27</td></tr>
+  <tr><td>BW_110-619-8</td><td>GWM 7N SATTENBREUEN</td><td>546728</td><td>5320909</td><td>k</td><td></td><td>586.98</td><td>4.42</td></tr>
+  <tr><td>BW_112-211-1</td><td>3342 RASTATT-STW-KA</td><td>443158</td><td>5414341</td><td>p</td><td></td><td>112.51</td><td>1.32</td></tr>
+  <tr><td>BW_124-068-9</td><td>3492 A KENZINGEN 2</td><td>405812</td><td>5338896</td><td>p</td><td></td><td>173.46</td><td>3.42</td></tr>
+  <tr><td>BW_131-115-0</td><td>GWM 3709, Ohlsbach</td><td>424415</td><td>5364473</td><td>p</td><td></td><td>162.06</td><td>1.82</td></tr>
+  <tr><td>BW_145-772-0</td><td>GWM 13-79 ALLMISHOFEN</td><td>578383</td><td>5294371</td><td>p</td><td></td><td>670.87</td><td>5.43</td></tr>
+  <tr><td>BW_15-568-2</td><td>GWM 129 ALTHEIM</td><td>532967</td><td>5331483</td><td>p</td><td></td><td>535.79</td><td>4.47</td></tr>
+  <tr><td>BW_16-706-8</td><td>GWM B2 Staffeln, Niederstetten-Neuweiler</td><td>566991</td><td>5471838</td><td>p</td><td></td><td>325.56</td><td>12.78</td></tr>
+  <tr><td>BW_177-770-1</td><td>SBR 13, Altrach</td><td>581180</td><td>5309055</td><td>p</td><td></td><td>612.57</td><td>18.51</td></tr>
+  <tr><td>BW_194-069-9</td><td>GWM 8 A Merdingen</td><td>401903</td><td>5319041</td><td>p</td><td></td><td>194.26</td><td>3.76</td></tr>
+  <tr><td>BY_11119</td><td>BADANHAUSEN 8B</td><td>679209</td><td>5432380</td><td>p</td><td></td><td>366.43</td><td>1.62</td></tr>
+  <tr><td>BY_13126</td><td>EIBENHOFEN 758</td><td>620742</td><td>5296428</td><td>p</td><td></td><td>714.92</td><td>11.49</td></tr>
+  <tr><td>BY_15120</td><td>IHRLESTEIN TIEF K1</td><td>707357</td><td>5426437</td><td>k</td><td></td><td>480.03</td><td>94.03</td></tr>
+  <tr><td>BY_22008</td><td>PAFFENHAUSEN 82A</td><td>563680</td><td>5550758</td><td>p</td><td></td><td>179.7</td><td>2.91</td></tr>
+  <tr><td>BY_24153</td><td>SPENSHART Q3</td><td>705931</td><td>5516765</td><td>k</td><td></td><td>416.22</td><td>1.42</td></tr>
+  <tr><td>BY_25155</td><td>IGLING 957</td><td>635606</td><td>5326788</td><td>p</td><td></td><td>592.7</td><td>12.73</td></tr>
+  <tr><td>BY_3108</td><td>MEINHEIM 429</td><td>634866</td><td>5432872</td><td>p</td><td></td><td>413.05</td><td>2.33</td></tr>
+  <tr><td>BY_5158</td><td>NEUSES</td><td>657993</td><td>5557607</td><td>p</td><td></td><td>273.22</td><td>0.59</td></tr>
+  <tr><td>BY_5162</td><td>Leitenbach 2</td><td>634999</td><td>5533371</td><td>p</td><td></td><td>240.54</td><td>4.73</td></tr>
+  <tr><td>BY_7126</td><td>ARBIG 336A</td><td>799009</td><td>5401742</td><td>p</td><td></td><td>308.75</td><td>3.78</td></tr>
+  <tr><td>BY_8252</td><td>THIERHAUPTEN-S. D 36</td><td>640590</td><td>5371410</td><td>p</td><td></td><td>445.61</td><td>2.91</td></tr>
+  <tr><td>BY_83614</td><td>NBS-H_W KB 11_1</td><td>544375</td><td>5561463</td><td>f</td><td></td><td>233.42</td><td>37.16</td></tr>
+  <tr><td>BY_9275</td><td>GERLENHOFEN B3</td><td>576324</td><td>5355565</td><td>p</td><td></td><td>479.96</td><td>1.69</td></tr>
+  <tr><td>HE_10319</td><td>LETTGENBRUNN</td><td>532274</td><td>5555656</td><td>p</td><td></td><td>380.83</td><td>11.58</td></tr>
+  <tr><td>HE_11781</td><td>NAUHEIM</td><td>463126</td><td>5534254</td><td>p</td><td></td><td>89.03</td><td>1.12</td></tr>
+  <tr><td>HE_12117</td><td>DIEBURG</td><td>487910</td><td>5528018</td><td>p</td><td></td><td>142.12</td><td>2.76</td></tr>
+  <tr><td>HE_14293</td><td>KAILBACH</td><td>508261</td><td>5485664</td><td>p</td><td></td><td>354.5</td><td>8.56</td></tr>
+  <tr><td>HE_14297</td><td>SCHOELLENBACH</td><td>505323</td><td>5490972</td><td>p</td><td></td><td>294.52</td><td>5.26</td></tr>
+  <tr><td>HE_6253</td><td>NETRA</td><td>576396</td><td>5661004</td><td>p</td><td></td><td>312.7</td><td>8.86</td></tr>
+  <tr><td>HE_6645</td><td>KOMBACH</td><td>468878</td><td>5636195</td><td>p</td><td></td><td>259.71</td><td>8.23</td></tr>
+  <tr><td>HE_7824</td><td>LEIHGESTERN</td><td>476165</td><td>5597300</td><td>p</td><td></td><td>188.66</td><td>2.49</td></tr>
+  <tr><td>MV_16450200</td><td>Güttin</td><td>778860</td><td>6034537</td><td>p</td><td></td><td>11.34</td><td>4.22</td></tr>
+  <tr><td>MV_17390002</td><td>Klein Müritz</td><td>715409</td><td>6016858</td><td>p</td><td></td><td>3.8</td><td>1.97</td></tr>
+  <tr><td>NL_100000728</td><td>Ehra-Lessien I</td><td>622547</td><td>5824077</td><td>p</td><td></td><td>63.42</td><td>2.07</td></tr>
+  <tr><td>NL_100000842</td><td>Ehmen II</td><td>614668</td><td>5805451</td><td>f</td><td></td><td>76.5</td><td>1.62</td></tr>
+  <tr><td>NL_100000926</td><td>Sehlide</td><td>586584</td><td>5767546</td><td>f</td><td></td><td>117</td><td>1.82</td></tr>
+  <tr><td>NL_129300060</td><td>Rühren_RA 14 09</td><td>630065</td><td>5818918</td><td>p</td><td></td><td>57.68</td><td>0.94</td></tr>
+</table>
+
+<sup>1</sup> p: porous, f: fractured, k:kantig
+<table>
+  <tr>
+    <th>ID</th>
+    <th>Name</th>
+    <th>X_Coord (UTM 32N)</th>
+    <th>Y_Coord (UTM 32N)</th>
+    <th>Aquifer Type<sup>1</sup></th>
+    <th>Ground Surf. [m asl]</th>
+    <th>Depth to GW [m]</th>
+  </tr>
+  <tr><td>NL_200000620</td><td>Walsen</td><td>463773</td><td>5840294</td><td>p</td><td>37.22</td><td>2.18</td></tr>
+  <tr><td>NL_200000788</td><td>Wietzen</td><td>504336</td><td>5839574</td><td>p</td><td>64.54</td><td>1.97</td></tr>
+  <tr><td>NL_200001068</td><td>Rodewald MB I</td><td>534027</td><td>5835353</td><td>p</td><td>26.3</td><td>1.67</td></tr>
+  <tr><td>NL_200001722</td><td>Martfeld</td><td>503025</td><td>5858185</td><td>p</td><td>13.41</td><td>1.97</td></tr>
+  <tr><td>NL_200002153</td><td>Donstorf</td><td>470640</td><td>5835536</td><td>p</td><td>36.43</td><td>1.62</td></tr>
+  <tr><td>NL_40000175</td><td>Suttorf 261_7R</td><td>534210</td><td>5819061</td><td>p</td><td>40.92</td><td>3.14</td></tr>
+  <tr><td>NL_40000233</td><td>Fuhrberg-Ahrensnestgehege I</td><td>559587</td><td>5822985</td><td>p</td><td>41.75</td><td>2.25</td></tr>
+  <tr><td>NL_400080190</td><td>Wiepenkathen UE 19 FI</td><td>528647</td><td>5937096</td><td>p</td><td>4.3</td><td>0.80</td></tr>
+  <tr><td>NL_400081660</td><td>Huvenhoopsmoor UE 166</td><td>508134</td><td>5915473</td><td>p</td><td>8.1</td><td>2.66</td></tr>
+  <tr><td>NL_40501911</td><td>Wieste I</td><td>409615</td><td>5851908</td><td>p</td><td>31.63</td><td>4.20</td></tr>
+  <tr><td>NL_405160331</td><td>Klein Wohnste UE 33 FI</td><td>536583</td><td>5913023</td><td>p</td><td>36.7</td><td>2.17</td></tr>
+  <tr><td>NL_500000592</td><td>UWO 113 1 Uphusen</td><td>496767</td><td>5875283</td><td>p</td><td>6.83</td><td>2.10</td></tr>
+  <tr><td>NL_600041871</td><td>Wrestedt F1</td><td>606074</td><td>5862647</td><td>p</td><td>47.39</td><td>1.59</td></tr>
+  <tr><td>NL_9700020</td><td>Beverbruch 3_6</td><td>440656</td><td>5870819</td><td>p</td><td>15.59</td><td>0.31</td></tr>
+  <tr><td>NL_9700080</td><td>Feldkamp</td><td>449994</td><td>5801631</td><td>p</td><td>46.72</td><td>1.88</td></tr>
+  <tr><td>NL_9700159</td><td>Langwege</td><td>440052</td><td>5830351</td><td>p</td><td>29.01</td><td>1.59</td></tr>
+  <tr><td>NL_9840391</td><td>Tijcher Wilde I</td><td>388288</td><td>5932921</td><td>p</td><td>3.01</td><td>2.34</td></tr>
+  <tr><td>NL_9840901</td><td>Neermoor I</td><td>397042</td><td>5907998</td><td>p</td><td>0.83</td><td>1.41</td></tr>
+  <tr><td>NL_9853172</td><td>Südseegroßfehner Moor</td><td>419063</td><td>5902646</td><td>p</td><td>6.39</td><td>2.42</td></tr>
+  <tr><td>NW_100140142</td><td>WG 22 LEVKENSTAD</td><td>484414</td><td>5800070</td><td>p</td><td>53.34</td><td>2.25</td></tr>
+  <tr><td>NW_100140762</td><td>WG 70 TAPPENAU</td><td>492808</td><td>5802796</td><td>f</td><td>56.03</td><td>3.85</td></tr>
+  <tr><td>NW_110040028</td><td>IV-2 -LIENEN-</td><td>430293</td><td>5774838</td><td>p</td><td>73.43</td><td>1.24</td></tr>
+  <tr><td>NW_110040041</td><td>IV-4 -SCHWEGE-</td><td>425943</td><td>5768989</td><td>p</td><td>55.55</td><td>1.07</td></tr>
+  <tr><td>NW_110061413</td><td>VI-14 - HANDFORD -</td><td>412382</td><td>5760509</td><td>p</td><td>52.12</td><td>1.64</td></tr>
+  <tr><td>NW_110240017</td><td>AH-1 J WELBERGEN</td><td>381429</td><td>5784337</td><td>p</td><td>48.58</td><td>2.17</td></tr>
+  <tr><td>NW_129660176</td><td>Silbecke</td><td>428864</td><td>5666613</td><td>k</td><td>320.32</td><td>53.38</td></tr>
+  <tr><td>NW_129660206</td><td>Schönholthausen I</td><td>432093</td><td>5671301</td><td>k</td><td>324.93</td><td>47.89</td></tr>
+  <tr><td>NW_60090169</td><td>HS 67</td><td>383993</td><td>5725893</td><td>p</td><td>58.17</td><td>5.38</td></tr>
+  <tr><td>NW_60240258</td><td>AH-25 VREDEN GRMAST</td><td>350479</td><td>5764657</td><td>p</td><td>40.61</td><td>1.65</td></tr>
+  <tr><td>NW_80000186</td><td>OEDT Nr020</td><td>317961</td><td>5688134</td><td>p</td><td>37.64</td><td>5.64</td></tr>
+  <tr><td>NW_80300376</td><td>MÜHLHAUSEN Nr00-91</td><td>316792</td><td>5692404</td><td>p</td><td>32.21</td><td>2.03</td></tr>
+  <tr><td>NW_91163705</td><td>Pöppelsche Eikeloh</td><td>458197</td><td>5718515</td><td>k</td><td>109.91</td><td>11.26</td></tr>
+  <tr><td>NW_91174909</td><td>Brilon LederkeO1748</td><td>467638</td><td>5692896</td><td>k</td><td>446.53</td><td>15.72</td></tr>
+  <tr><td>RP_2373131200</td><td>1341 I Woerth am Rhein</td><td>432791</td><td>5431646</td><td>p</td><td>137.460007</td><td>2.00</td></tr>
+  <tr><td>RP_2378140100</td><td>1057 Boeblingen</td><td>445538</td><td>5460551</td><td>p</td><td>113.989998</td><td>1.08</td></tr>
+  <tr><td>RP_2587150500</td><td>6024 Westerburg, Wengenroth</td><td>428344</td><td>5600050</td><td>p</td><td>313.140015</td><td>4.62</td></tr>
+  <tr><td>SH_1053126001</td><td>4384 TRAMM_NORD_F1</td><td>606775</td><td>5937188</td><td>p</td><td>50.78</td><td>4.07</td></tr>
+  <tr><td>SH_1054010004</td><td>1386 WESTERBARGUM_II</td><td>496464</td><td>6061837</td><td>p</td><td>4.78</td><td>4.39</td></tr>
+  <tr><td>SH_1055005005</td><td>4522 RASTORFERMARKELS DORF</td><td>640373</td><td>6037388</td><td>p</td><td>9.8</td><td>1.27</td></tr>
+  <tr><td>SH_1055038005</td><td>4565 LANGENHAGEN_HELMSTEICH</td><td>615529</td><td>6009571</td><td>p</td><td>105.59</td><td>0.90</td></tr>
+  <tr><td>SH_1056048003</td><td>3587 TORNESCH_LIETHER_DAMM_F1</td><td>546919</td><td>5951632</td><td>p</td><td>13.34</td><td>3.68</td></tr>
+  <tr><td>SH_1057066002</td><td>6067 RASTORFER_BAHNHOF</td><td>584911</td><td>6013922</td><td>p</td><td>29.32</td><td>9.08</td></tr>
+  <tr><td>SH_1062060004</td><td>4712 REINBEK_SILKERFELD_F1</td><td>584999</td><td>5931988</td><td>p</td><td>22.78</td><td>9.03</td></tr>
+  <tr><td>SN_46400927</td><td>Bucha</td><td>781034</td><td>5700917</td><td>p</td><td>142.43</td><td>1.66</td></tr>
+  <tr><td>SN_46460564</td><td>Walda</td><td>813164</td><td>5695042</td><td>p</td><td>109.22</td><td>1.90</td></tr>
+  <tr><td>SN_47500596</td><td>Bischheim</td><td>851569</td><td>5688389</td><td>p</td><td>222.98</td><td>5.14</td></tr>
+  <tr><td>SN_48390509</td><td>Gatzen</td><td>727700</td><td>5668631</td><td>p</td><td>142.74</td><td>2.36</td></tr>
+  <tr><td>SN_49430964</td><td>Arras</td><td>773575</td><td>5663318</td><td>p</td><td>264.37</td><td>2.46</td></tr>
+  <tr><td>SN_49484004</td><td>Dresden, Königstraße</td><td>832311</td><td>5667461</td><td>p</td><td>112.25</td><td>7.13</td></tr>
+  <tr><td>SN_49531740</td><td>Schönbach</td><td>890527</td><td>5670891</td><td>p</td><td>386.83</td><td>7.12</td></tr>
+  <tr><td>SN_52410759</td><td>Muelsen-St-Niclas</td><td>752926</td><td>5625203</td><td>f</td><td>328.46</td><td>5.34</td></tr>
+  <tr><td>ST_31340028</td><td>Arendsee Süd</td><td>668011</td><td>5860747</td><td>p</td><td>32.5</td><td>2.13</td></tr>
+  <tr><td>ST_33340002</td><td>Altmersleben-Butterhorst</td><td>665806</td><td>5839436</td><td>p</td><td>29.66</td><td>1.20</td></tr>
+  <tr><td>ST_34376608</td><td>Charlottenhof</td><td>698014</td><td>5830461</td><td>p</td><td>32.42</td><td>1.43</td></tr>
+  <tr><td>ST_36340007</td><td>Satuelle</td><td>661910</td><td>5808099</td><td>p</td><td>55.5</td><td>1.14</td></tr>
+  <tr><td>ST_39320023</td><td>Hornhausen - Güte OP</td><td>647351</td><td>5767443</td><td>p</td><td>79.76</td><td>0.80</td></tr>
+  <tr><td>ST_40415442</td><td>Möllendorf</td><td>743052</td><td>5757819</td><td>p</td><td>103.14</td><td>2.63</td></tr>
+  <tr><td>ST_41300015</td><td>Ilsenburg</td><td>616332</td><td>5749114</td><td>f</td><td>221.55</td><td>6.00</td></tr>
+  <tr><td>ST_43435116</td><td>Axien</td><td>767008</td><td>5734326</td><td>p</td><td>74.63</td><td>2.54</td></tr>
+  <tr><td>ST_44339213</td><td>Lengefeld</td><td>657980</td><td>5708535</td><td>p</td><td>258.48</td><td>6.15</td></tr>
+</table>
+
+<sup>1</sup> p: porous; f: fractured; k: karstic
+Table S2: Model Errors in the past (2012-2016) and optimized Hyperparameters
+
+<table>
+  <tr>
+    <th>ID</th>
+    <th>NSE</th>
+    <th>R<sup>2</sup></th>
+    <th>RMSE</th>
+    <th>rRMSE</th>
+    <th>Bias</th>
+    <th>rBias</th>
+    <th>filters</th>
+    <th>dense size</th>
+    <th>seqlength</th>
+    <th>batchsize</th>
+  </tr>
+  <tr><td>BB_27381010</td><td>0.91</td><td>0.91</td><td>0.09</td><td>5.53</td><td>0</td><td>0.09</td><td>192</td><td>19</td><td>29</td><td>41</td></tr>
+  <tr><td>BB_28390113</td><td>0.81</td><td>0.88</td><td>0.12</td><td>9.86</td><td>0.08</td><td>6.34</td><td>114</td><td>224</td><td>28</td><td>36</td></tr>
+  <tr><td>BB_29519030</td><td>0.7</td><td>0.81</td><td>0.1</td><td>7.26</td><td>0.07</td><td>4.75</td><td>190</td><td>47</td><td>36</td><td>16</td></tr>
+  <tr><td>BB_30400591</td><td>0.91</td><td>0.91</td><td>0.09</td><td>4.17</td><td>0.02</td><td>0.71</td><td>149</td><td>29</td><td>51</td><td>40</td></tr>
+  <tr><td>BB_31400780</td><td>0.7</td><td>0.75</td><td>0.1</td><td>8.18</td><td>-0.04</td><td>-3.32</td><td>254</td><td>72</td><td>51</td><td>41</td></tr>
+  <tr><td>BB_31491979</td><td>0.88</td><td>0.89</td><td>0.08</td><td>7.75</td><td>0.03</td><td>3.02</td><td>145</td><td>3</td><td>52</td><td>16</td></tr>
+  <tr><td>BB_32455305</td><td>0.91</td><td>0.93</td><td>0.1</td><td>5.37</td><td>-0.01</td><td>-0.54</td><td>176</td><td>81</td><td>39</td><td>182</td></tr>
+  <tr><td>BB_33437070</td><td>0.85</td><td>0.92</td><td>0.08</td><td>5.78</td><td>-0.05</td><td>-3.91</td><td>222</td><td>34</td><td>50</td><td>157</td></tr>
+  <tr><td>BB_33437090</td><td>0.8</td><td>0.85</td><td>0.15</td><td>7.84</td><td>-0.06</td><td>-3.46</td><td>201</td><td>54</td><td>37</td><td>46</td></tr>
+  <tr><td>BB_33437106</td><td>0.79</td><td>0.89</td><td>0.15</td><td>8.76</td><td>-0.1</td><td>-5.71</td><td>243</td><td>24</td><td>51</td><td>154</td></tr>
+  <tr><td>BB_33452451</td><td>0.86</td><td>0.86</td><td>0.13</td><td>8.88</td><td>0.01</td><td>0.75</td><td>110</td><td>55</td><td>51</td><td>16</td></tr>
+  <tr><td>BB_33470960</td><td>0.75</td><td>0.78</td><td>0.13</td><td>7.69</td><td>-0.04</td><td>-2.02</td><td>192</td><td>256</td><td>34</td><td>16</td></tr>
+  <tr><td>BB_34426110</td><td>0.85</td><td>0.9</td><td>0.09</td><td>5.16</td><td>-0.05</td><td>-2.97</td><td>248</td><td>29</td><td>50</td><td>201</td></tr>
+  <tr><td>BB_34522461</td><td>0.86</td><td>0.84</td><td>0.11</td><td>6.76</td><td>-0.01</td><td>-0.81</td><td>185</td><td>20</td><td>51</td><td>50</td></tr>
+  <tr><td>BB_37451908</td><td>0.75</td><td>0.8</td><td>0.12</td><td>9.53</td><td>-0.03</td><td>-2.08</td><td>199</td><td>21</td><td>52</td><td>205</td></tr>
+  <tr><td>BB_39441476</td><td>0.72</td><td>0.75</td><td>0.14</td><td>8.7</td><td>-0.07</td><td>-4.46</td><td>226</td><td>100</td><td>51</td><td>55</td></tr>
+  <tr><td>BB_39460566</td><td>0.86</td><td>0.89</td><td>0.1</td><td>6.04</td><td>0.02</td><td>1.06</td><td>220</td><td>63</td><td>43</td><td>22</td></tr>
+  <tr><td>BB_40500136</td><td>0.82</td><td>0.82</td><td>0.08</td><td>5.4</td><td>0.01</td><td>0.38</td><td>29</td><td>81</td><td>51</td><td>16</td></tr>
+  <tr><td>BB_42458092</td><td>0.79</td><td>0.88</td><td>0.14</td><td>8.05</td><td>-0.05</td><td>-3.1</td><td>226</td><td>17</td><td>51</td><td>143</td></tr>
+  <tr><td>BW_100-813-7</td><td>0.82</td><td>0.85</td><td>1.32</td><td>6.55</td><td>-0.59</td><td>-2.95</td><td>104</td><td>153</td><td>29</td><td>18</td></tr>
+  <tr><td>BW_103-763-0</td><td>0.86</td><td>0.84</td><td>2.54</td><td>8.78</td><td>0.65</td><td>2.25</td><td>164</td><td>32</td><td>28</td><td>16</td></tr>
+  <tr><td>BW_107-666-2</td><td>0.78</td><td>0.82</td><td>0.92</td><td>8.48</td><td>-0.41</td><td>-3.79</td><td>251</td><td>45</td><td>33</td><td>21</td></tr>
+  <tr><td>BW_110-619-8</td><td>0.8</td><td>0.87</td><td>0.22</td><td>7.65</td><td>-0.12</td><td>-4.06</td><td>198</td><td>94</td><td>37</td><td>18</td></tr>
+  <tr><td>BW_112-211-1</td><td>0.84</td><td>0.8</td><td>0.12</td><td>7.66</td><td>0.01</td><td>0.9</td><td>101</td><td>13</td><td>50</td><td>39</td></tr>
+  <tr><td>BW_124-068-9</td><td>0.78</td><td>0.79</td><td>0.18</td><td>6.43</td><td>-0.04</td><td>-1.55</td><td>201</td><td>53</td><td>36</td><td>16</td></tr>
+  <tr><td>BW_131-115-0</td><td>0.77</td><td>0.77</td><td>0.27</td><td>8.92</td><td>-0.01</td><td>-0.23</td><td>138</td><td>64</td><td>29</td><td>26</td></tr>
+  <tr><td>BW_145-772-0</td><td>0.86</td><td>0.87</td><td>0.37</td><td>6.46</td><td>-0.1</td><td>-1.69</td><td>179</td><td>76</td><td>52</td><td>34</td></tr>
+  <tr><td>BW_15-568-2</td><td>0.77</td><td>0.83</td><td>0.1</td><td>7.39</td><td>-0.01</td><td>-0.78</td><td>199</td><td>56</td><td>26</td><td>24</td></tr>
+  <tr><td>BW_16-706-8</td><td>0.86</td><td>0.86</td><td>0.3</td><td>7.63</td><td>0.07</td><td>1.8</td><td>90</td><td>154</td><td>28</td><td>25</td></tr>
+  <tr><td>BW_177-770-1</td><td>0.88</td><td>0.87</td><td>0.14</td><td>5.78</td><td>0.05</td><td>2.22</td><td>180</td><td>23</td><td>37</td><td>16</td></tr>
+  <tr><td>BW_194-069-9</td><td>0.85</td><td>0.85</td><td>0.09</td><td>5.43</td><td>-0.02</td><td>-1.19</td><td>225</td><td>27</td><td>51</td><td>18</td></tr>
+  <tr><td>BY_11119</td><td>0.77</td><td>0.75</td><td>0.2</td><td>8.67</td><td>-0.04</td><td>-1.57</td><td>225</td><td>85</td><td>34</td><td>47</td></tr>
+  <tr><td>BY_13126</td><td>0.85</td><td>0.87</td><td>0.31</td><td>6.14</td><td>-0.05</td><td>-1.05</td><td>255</td><td>25</td><td>51</td><td>16</td></tr>
+  <tr><td>BY_15120</td><td>0.78</td><td>0.77</td><td>1.41</td><td>7.34</td><td>0.72</td><td>3.78</td><td>156</td><td>58</td><td>52</td><td>16</td></tr>
+  <tr><td>BY_22008</td><td>0.81</td><td>0.8</td><td>0.23</td><td>6.4</td><td>-0.06</td><td>-1.71</td><td>51</td><td>7</td><td>30</td><td>36</td></tr>
+  <tr><td>BY_24153</td><td>0.81</td><td>0.82</td><td>0.11</td><td>9.69</td><td>0.03</td><td>2.2</td><td>178</td><td>242</td><td>9</td><td>17</td></tr>
+  <tr><td>BY_25155</td><td>0.79</td><td>0.82</td><td>0.19</td><td>7.95</td><td>-0.04</td><td>-1.47</td><td>202</td><td>45</td><td>45</td><td>24</td></tr>
+  <tr><td>BY_3108</td><td>0.81</td><td>0.82</td><td>0.26</td><td>8.96</td><td>-0.09</td><td>-3.12</td><td>237</td><td>43</td><td>38</td><td>111</td></tr>
+  <tr><td>BY_5158</td><td>0.76</td><td>0.76</td><td>0.2</td><td>9.78</td><td>-0.02</td><td>-1.14</td><td>178</td><td>198</td><td>20</td><td>16</td></tr>
+  <tr><td>BY_5162</td><td>0.87</td><td>0.87</td><td>0.14</td><td>6.92</td><td>0.02</td><td>0.82</td><td>239</td><td>31</td><td>29</td><td>22</td></tr>
+  <tr><td>BY_7126</td><td>0.85</td><td>0.89</td><td>0.15</td><td>6.4</td><td>-0.04</td><td>-1.6</td><td>83</td><td>130</td><td>52</td><td>16</td></tr>
+  <tr><td>BY_8252</td><td>0.78</td><td>0.81</td><td>0.19</td><td>9.06</td><td>0.11</td><td>5.3</td><td>236</td><td>169</td><td>52</td><td>16</td></tr>
+  <tr><td>BY_83614</td><td>0.8</td><td>0.78</td><td>0.62</td><td>8.36</td><td>0.05</td><td>0.73</td><td>132</td><td>40</td><td>51</td><td>16</td></tr>
+  <tr><td>BY_9275</td><td>0.87</td><td>0.87</td><td>0.06</td><td>6.5</td><td>0.02</td><td>1.95</td><td>187</td><td>256</td><td>42</td><td>16</td></tr>
+  <tr><td>HE_10319</td><td>0.82</td><td>0.83</td><td>2.03</td><td>9.71</td><td>-0.62</td><td>-2.98</td><td>254</td><td>80</td><td>17</td><td>24</td></tr>
+  <tr><td>HE_11781</td><td>0.84</td><td>0.86</td><td>0.18</td><td>9.8</td><td>0.02</td><td>0.91</td><td>85</td><td>107</td><td>28</td><td>37</td></tr>
+  <tr><td>HE_12117</td><td>0.86</td><td>0.93</td><td>0.11</td><td>5.64</td><td>-0.08</td><td>-3.92</td><td>180</td><td>54</td><td>52</td><td>96</td></tr>
+  <tr><td>HE_14293</td><td>0.78</td><td>0.75</td><td>0.25</td><td>7.98</td><td>0.07</td><td>2.05</td><td>248</td><td>103</td><td>30</td><td>29</td></tr>
+  <tr><td>HE_14297</td><td>0.77</td><td>0.75</td><td>0.24</td><td>5.58</td><td>-0.06</td><td>-1.48</td><td>144</td><td>255</td><td>46</td><td>16</td></tr>
+  <tr><td>HE_6253</td><td>0.79</td><td>0.75</td><td>0.48</td><td>6.78</td><td>0.13</td><td>1.86</td><td>225</td><td>59</td><td>43</td><td>40</td></tr>
+  <tr><td>HE_6645</td><td>0.93</td><td>0.91</td><td>0.12</td><td>3.64</td><td>-0.02</td><td>-0.7</td><td>220</td><td>63</td><td>43</td><td>22</td></tr>
+  <tr><td>HE_7824</td><td>0.8</td><td>0.83</td><td>0.24</td><td>6.45</td><td>-0.12</td><td>-3.06</td><td>41</td><td>12</td><td>51</td><td>52</td></tr>
+  <tr><td>MV_16450200</td><td>0.84</td><td>0.81</td><td>0.19</td><td>9.88</td><td>-0.02</td><td>-0.82</td><td>104</td><td>16</td><td>46</td><td>19</td></tr>
+  <tr><td>MV_17390002</td><td>0.8</td><td>0.79</td><td>0.24</td><td>10.67</td><td>-0.02</td><td>-0.71</td><td>249</td><td>217</td><td>51</td><td>18</td></tr>
+  <tr><td>NJ_100000728</td><td>0.82</td><td>0.84</td><td>0.21</td><td>9.3</td><td>0.06</td><td>2.52</td><td>125</td><td>10</td><td>51</td><td>56</td></tr>
+  <tr><td>NJ_100000842</td><td>0.77</td><td>0.76</td><td>0.17</td><td>10.14</td><td>0.04</td><td>2.44</td><td>255</td><td>4</td><td>42</td><td>52</td></tr>
+  <tr><td>NJ_100000926</td><td>0.7</td><td>0.74</td><td>0.17</td><td>7.3</td><td>0.05</td><td>1.98</td><td>84</td><td>158</td><td>19</td><td>16</td></tr>
+  <tr><td>NJ_129300060</td><td>0.87</td><td>0.88</td><td>0.19</td><td>8.22</td><td>0.05</td><td>2.28</td><td>169</td><td>122</td><td>51</td><td>80</td></tr>
+</table>
+<table>
+  <tr>
+    <th>ID</th>
+    <th>NSE</th>
+    <th>R<sup>2</sup></th>
+    <th>RMSE</th>
+    <th>rRMSE</th>
+    <th>Bias</th>
+    <th>rBias</th>
+    <th>filters</th>
+    <th>dense</th>
+    <th>size</th>
+    <th>seqlength</th>
+    <th>batchsize</th>
+  </tr>
+  <tr><td>NL_200000620</td><td>0.82</td><td>0.87</td><td>0.22</td><td>8.24</td><td>0.14</td><td>5.39</td><td>197</td><td>93</td><td>52</td><td>46</td></tr>
+  <tr><td>NL_200000788</td><td>0.9</td><td>0.88</td><td>0.16</td><td>6.99</td><td>0.04</td><td>1.7</td><td>231</td><td>16</td><td>52</td><td>78</td></tr>
+  <tr><td>NL_200001068</td><td>0.83</td><td>0.83</td><td>0.13</td><td>8.19</td><td>0.04</td><td>2.63</td><td>218</td><td>70</td><td>50</td><td>76</td></tr>
+  <tr><td>NL_200001722</td><td>0.9</td><td>0.81</td><td>0.06</td><td>4.78</td><td>0</td><td>0.06</td><td>254</td><td>87</td><td>47</td><td>30</td></tr>
+  <tr><td>NL_200002153</td><td>0.76</td><td>0.85</td><td>0.19</td><td>9.86</td><td>0.13</td><td>6.41</td><td>144</td><td>248</td><td>12</td><td>156</td></tr>
+  <tr><td>NL_40000175</td><td>0.7</td><td>0.77</td><td>0.19</td><td>9.75</td><td>0.11</td><td>5.49</td><td>79</td><td>89</td><td>26</td><td>20</td></tr>
+  <tr><td>NL_40000233</td><td>0.88</td><td>0.88</td><td>0.09</td><td>4.99</td><td>0.05</td><td>2.53</td><td>238</td><td>100</td><td>39</td><td>19</td></tr>
+  <tr><td>NL_40000190</td><td>0.72</td><td>0.77</td><td>0.15</td><td>8.62</td><td>0.1</td><td>5.53</td><td>241</td><td>53</td><td>52</td><td>36</td></tr>
+  <tr><td>NL_400001660</td><td>0.75</td><td>0.76</td><td>0.15</td><td>9.63</td><td>0.06</td><td>4.24</td><td>138</td><td>224</td><td>11</td><td>157</td></tr>
+  <tr><td>NL_40501191</td><td>0.91</td><td>0.83</td><td>0.12</td><td>4.89</td><td>0.01</td><td>4.45</td><td>216</td><td>48</td><td>51</td><td>20</td></tr>
+  <tr><td>NL_405160331</td><td>0.8</td><td>0.83</td><td>0.21</td><td>7.75</td><td>0.12</td><td>4.59</td><td>197</td><td>27</td><td>50</td><td>26</td></tr>
+  <tr><td>NL_500000592</td><td>0.88</td><td>0.9</td><td>0.06</td><td>6.51</td><td>0.04</td><td>4.11</td><td>44</td><td>10</td><td>22</td><td>36</td></tr>
+  <tr><td>NL_600041871</td><td>0.79</td><td>0.8</td><td>0.12</td><td>7.59</td><td>-0.02</td><td>-1.5</td><td>217</td><td>97</td><td>42</td><td>18</td></tr>
+  <tr><td>NL_9700020</td><td>0.87</td><td>0.84</td><td>0.11</td><td>6.87</td><td>0.02</td><td>1.35</td><td>231</td><td>76</td><td>40</td><td>60</td></tr>
+  <tr><td>NL_9700080</td><td>0.84</td><td>0.84</td><td>0.21</td><td>8.03</td><td>0.11</td><td>4.07</td><td>195</td><td>31</td><td>23</td><td>29</td></tr>
+  <tr><td>NL_9700159</td><td>0.86</td><td>0.86</td><td>0.12</td><td>6.14</td><td>-0.01</td><td>-0.75</td><td>44</td><td>10</td><td>22</td><td>36</td></tr>
+  <tr><td>NL_9840391</td><td>0.9</td><td>0.89</td><td>0.08</td><td>6.58</td><td>0</td><td>0.38</td><td>217</td><td>246</td><td>19</td><td>21</td></tr>
+  <tr><td>NL_9840901</td><td>0.83</td><td>0.83</td><td>0.07</td><td>6.06</td><td>-0.01</td><td>-0.86</td><td>242</td><td>87</td><td>28</td><td>16</td></tr>
+  <tr><td>NL_9853172</td><td>0.87</td><td>0.89</td><td>0.1</td><td>7.73</td><td>0.02</td><td>1.53</td><td>203</td><td>52</td><td>13</td><td>63</td></tr>
+  <tr><td>NW_100140142</td><td>0.79</td><td>0.79</td><td>0.19</td><td>9.31</td><td>0.13</td><td>6.3</td><td>256</td><td>13</td><td>52</td><td>127</td></tr>
+  <tr><td>NW_100140762</td><td>0.83</td><td>0.81</td><td>0.16</td><td>7.1</td><td>0.02</td><td>1.05</td><td>205</td><td>51</td><td>36</td><td>49</td></tr>
+  <tr><td>NW_110040028</td><td>0.83</td><td>0.89</td><td>0.12</td><td>7.97</td><td>0.06</td><td>4.44</td><td>254</td><td>65</td><td>28</td><td>37</td></tr>
+  <tr><td>NW_110040041</td><td>0.86</td><td>0.87</td><td>0.12</td><td>7.08</td><td>0.03</td><td>1.95</td><td>149</td><td>98</td><td>25</td><td>16</td></tr>
+  <tr><td>NW_110060143</td><td>0.86</td><td>0.86</td><td>0.22</td><td>7.8</td><td>-0.01</td><td>-0.31</td><td>173</td><td>255</td><td>39</td><td>17</td></tr>
+  <tr><td>NW_110240017</td><td>0.84</td><td>0.83</td><td>0.11</td><td>5.47</td><td>0.03</td><td>1.33</td><td>223</td><td>58</td><td>42</td><td>27</td></tr>
+  <tr><td>NW_129660176</td><td>0.87</td><td>0.88</td><td>0.4</td><td>7.41</td><td>-0.29</td><td>-0.53</td><td>84</td><td>158</td><td>19</td><td>16</td></tr>
+  <tr><td>NW_129660206</td><td>0.81</td><td>0.8</td><td>1.45</td><td>6.95</td><td>0.28</td><td>1.34</td><td>34</td><td>132</td><td>52</td><td>16</td></tr>
+  <tr><td>NW_60090169</td><td>0.89</td><td>0.9</td><td>0.21</td><td>5.1</td><td>-0.03</td><td>-0.75</td><td>202</td><td>61</td><td>51</td><td>195</td></tr>
+  <tr><td>NW_60240258</td><td>0.77</td><td>0.81</td><td>0.15</td><td>7.85</td><td>0.07</td><td>3.46</td><td>205</td><td>51</td><td>36</td><td>49</td></tr>
+  <tr><td>NW_80000186</td><td>0.84</td><td>0.84</td><td>0.09</td><td>4.84</td><td>-0.01</td><td>-0.74</td><td>76</td><td>256</td><td>52</td><td>16</td></tr>
+  <tr><td>NW_80300376</td><td>0.83</td><td>0.83</td><td>0.1</td><td>5.47</td><td>0</td><td>0.23</td><td>241</td><td>204</td><td>16</td><td>16</td></tr>
+  <tr><td>NW_91163705</td><td>0.82</td><td>0.77</td><td>1.18</td><td>8.57</td><td>0.11</td><td>0.82</td><td>237</td><td>43</td><td>38</td><td>111</td></tr>
+  <tr><td>NW_91174909</td><td>0.82</td><td>0.81</td><td>0.44</td><td>5.29</td><td>0.12</td><td>1.46</td><td>189</td><td>195</td><td>12</td><td>57</td></tr>
+  <tr><td>RP_237311200</td><td>0.76</td><td>0.84</td><td>0.23</td><td>13.08</td><td>-0.13</td><td>-7.56</td><td>256</td><td>68</td><td>52</td><td>16</td></tr>
+  <tr><td>RP_2378140100</td><td>0.81</td><td>0.79</td><td>0.25</td><td>9.14</td><td>-0.04</td><td>-1.53</td><td>74</td><td>168</td><td>49</td><td>41</td></tr>
+  <tr><td>RP_2587150500</td><td>0.78</td><td>0.78</td><td>0.3</td><td>8.22</td><td>0.03</td><td>0.78</td><td>96</td><td>154</td><td>18</td><td>17</td></tr>
+  <tr><td>SH_1053126001</td><td>0.84</td><td>0.66</td><td>0.18</td><td>6.34</td><td>0</td><td>0.13</td><td>82</td><td>107</td><td>52</td><td>65</td></tr>
+  <tr><td>SH_1054010004</td><td>0.77</td><td>0.82</td><td>0.16</td><td>11.45</td><td>-0.06</td><td>-4.28</td><td>115</td><td>221</td><td>22</td><td>68</td></tr>
+  <tr><td>SH_1055005005</td><td>0.85</td><td>0.88</td><td>0.21</td><td>11.46</td><td>0.04</td><td>2.05</td><td>243</td><td>2</td><td>44</td><td>27</td></tr>
+  <tr><td>SH_1055308005</td><td>0.76</td><td>0.76</td><td>0.14</td><td>10.14</td><td>0.06</td><td>4.29</td><td>210</td><td>60</td><td>29</td><td>16</td></tr>
+  <tr><td>SH_1056048003</td><td>0.78</td><td>0.75</td><td>0.13</td><td>7.28</td><td>0</td><td>0.12</td><td>236</td><td>10</td><td>26</td><td>21</td></tr>
+  <tr><td>SH_1057060002</td><td>0.81</td><td>0.79</td><td>0.11</td><td>6.87</td><td>0.04</td><td>2.78</td><td>96</td><td>7</td><td>45</td><td>16</td></tr>
+  <tr><td>SH_1062060004</td><td>0.88</td><td>0.89</td><td>0.1</td><td>7.1</td><td>0</td><td>0.17</td><td>163</td><td>248</td><td>23</td><td>16</td></tr>
+  <tr><td>SN_46440927</td><td>0.85</td><td>0.85</td><td>0.25</td><td>6.74</td><td>0.03</td><td>0.78</td><td>227</td><td>24</td><td>52</td><td>16</td></tr>
+  <tr><td>SN_46460564</td><td>0.71</td><td>0.79</td><td>0.15</td><td>8.31</td><td>-0.08</td><td>-4.32</td><td>244</td><td>154</td><td>50</td><td>78</td></tr>
+  <tr><td>SN_47500596</td><td>0.74</td><td>0.77</td><td>0.19</td><td>7.91</td><td>-0.07</td><td>-2.71</td><td>187</td><td>30</td><td>52</td><td>48</td></tr>
+  <tr><td>SN_48390509</td><td>0.8</td><td>0.71</td><td>0.22</td><td>7.1</td><td>0.03</td><td>0.82</td><td>252</td><td>75</td><td>51</td><td>37</td></tr>
+  <tr><td>SN_49430964</td><td>0.75</td><td>0.74</td><td>0.49</td><td>9.07</td><td>-0.04</td><td>-0.68</td><td>238</td><td>16</td><td>40</td><td>93</td></tr>
+  <tr><td>SN_49484004</td><td>0.73</td><td>0.76</td><td>0.32</td><td>8.19</td><td>0.09</td><td>2.37</td><td>135</td><td>34</td><td>31</td><td>16</td></tr>
+  <tr><td>SN_49531740</td><td>0.71</td><td>0.71</td><td>0.28</td><td>8.16</td><td>0.01</td><td>0.15</td><td>220</td><td>31</td><td>52</td><td>96</td></tr>
+  <tr><td>SN_52410759</td><td>0.82</td><td>0.84</td><td>0.28</td><td>6.16</td><td>0.05</td><td>1.14</td><td>217</td><td>70</td><td>43</td><td>35</td></tr>
+  <tr><td>ST_31340028</td><td>0.85</td><td>0.86</td><td>0.12</td><td>6.63</td><td>0.08</td><td>4.22</td><td>243</td><td>115</td><td>51</td><td>22</td></tr>
+  <tr><td>ST_33340002</td><td>0.79</td><td>0.86</td><td>0.12</td><td>7.37</td><td>-0.06</td><td>-3.7</td><td>41</td><td>34</td><td>29</td><td>39</td></tr>
+  <tr><td>ST_34376608</td><td>0.84</td><td>0.85</td><td>0.09</td><td>7.32</td><td>0.02</td><td>1.84</td><td>106</td><td>174</td><td>16</td><td>17</td></tr>
+  <tr><td>ST_36340007</td><td>0.73</td><td>0.73</td><td>0.14</td><td>6.6</td><td>-0.03</td><td>-1.57</td><td>245</td><td>56</td><td>42</td><td>20</td></tr>
+  <tr><td>ST_39320023</td><td>0.78</td><td>0.81</td><td>0.11</td><td>6.29</td><td>-0.03</td><td>-1.7</td><td>245</td><td>27</td><td>26</td><td>51</td></tr>
+  <tr><td>ST_40415442</td><td>0.83</td><td>0.84</td><td>0.14</td><td>6.38</td><td>0.06</td><td>2.85</td><td>182</td><td>17</td><td>50</td><td>33</td></tr>
+  <tr><td>ST_41300015</td><td>0.81</td><td>0.87</td><td>0.47</td><td>8.35</td><td>-0.25</td><td>-4.43</td><td>180</td><td>32</td><td>23</td><td>20</td></tr>
+  <tr><td>ST_43435116</td><td>0.72</td><td>0.75</td><td>0.23</td><td>7.69</td><td>-0.06</td><td>-2.04</td><td>232</td><td>41</td><td>48</td><td>16</td></tr>
+  <tr><td>ST_44339213</td><td>0.8</td><td>0.83</td><td>0.18</td><td>6.11</td><td>0.02</td><td>0.62</td><td>47</td><td>45</td><td>30</td><td>21</td></tr>
+</table>
+Figure S1: Evaluation of BB_27381010 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S2: Evaluation of BB_28390113 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S3: Evaluation of BB_29519030 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S4: Evaluation of BB_30400591 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S5: Evaluation of BB_31400780 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S6: Evaluation of BB_31491979 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S7: Evaluation of BB_32455305 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S8: Evaluation of BB_33437070 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S9: Evaluation of BB_33437090 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S10: Evaluation of BB_33437106 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S11: Evaluation of BB_33452451 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S12: Evaluation of BB_33470960 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S13: Evaluation of BB_34426110 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S14: Evaluation of BB_34522461 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S15: Evaluation of BB_37451908 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S16: Evaluation of BB_39441476 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S17: Evaluation of BB_39496056 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S18: Evaluation of BB_40500136 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S19: Evaluation of BB_42458092 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S20: Evaluation of BW_100-813-7 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S21: Evaluation of BW_103-763-0 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S22: Evaluation of BW_107-666-2 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S23: Evaluation of BW_110-619-8 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S24: Evaluation of BW_112-211-1 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S25: Evaluation of BW_124-068-9 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S26: Evaluation of BW_131-115-0 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S27: Evaluation of BW_145-772-0 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S28: Evaluation of BW_15-568-2 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S29: Evaluation of BW_16-706-8 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S30: Evaluation of BW_177-770-1 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S31: Evaluation of BW_194-069-9 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S32: Evaluation of BY_11119 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S33: Evaluation of BY_13126 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S34: Evaluation of BY_15120 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S35: Evaluation of BY_22008 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S36: Evaluation of BY_24153 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S37: Evaluation of BY_25155 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S38: Evaluation of BY_3108 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S39: Evaluation of BY_5158 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S40: Evaluation of BY_5162 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S41: Evaluation of BY_7126 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S42: Evaluation of BY_8252 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S43: Evaluation of BY_83614 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S44: Evaluation of BY_9275 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S45: Evaluation of HE_10319 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S46: Evaluation of HE_11781 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S47: Evaluation of HE_12117 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S48: Evaluation of HE_14293 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S49: Evaluation of HE_14297 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S50: Evaluation of HE_6253 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S51: Evaluation of HE_6645 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S52: Evaluation of HE_7824 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S53: Evaluation of MV_16450200 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S54: Evaluation of MV_17390002 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S55: Evaluation of NI_100000728 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S56: Evaluation of NI_100000842 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S57: Evaluation of NI_100000926 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S58: Evaluation of NL129300060 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S59: Evaluation of NI_200000620 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S60: Evaluation of NI_200000788 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S61: Evaluation of NI_200001068 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S62: Evaluation of NI_200001722 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S63: Evaluation of NI_200002153 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S64: Evaluation of NI_40000175 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S65: Evaluation of NI_40000233 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S66: Evaluation of NI_400080190 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S67: Evaluation of NI_400081660 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S68: Evaluation of NI_40501911 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S69: Evaluation of NI_405160331 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S70: Evaluation of NI_500000592 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S71: Evaluation of NI_600041871 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S72: Evaluation of NI_9700020 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S73: Evaluation of NI_9700080 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S74: Evaluation of NI_9700159 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S75: Evaluation of NI_9840391 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S76: Evaluation of NI_9840901 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S77: Evaluation of NI_9853172 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S78: Evaluation of NW_100140142 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S79: Evaluation of NW_100140762 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S80: Evaluation of NW_110040028 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S81: Evaluation of NW_110040041 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S82: Evaluation of NW_110060143 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S83: Evaluation of NW_110240017 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S84: Evaluation of NW_129660176 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S85: Evaluation of NW_129660206 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S86: Evaluation of NW_60090169 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S87: Evaluation of NW_60240258 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S88: Evaluation of NW_80000186 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S89: Evaluation of NW_80300376 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S90: Evaluation of NW_91163705 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S91: Evaluation of NW_91174909 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S92: Evaluation of RP_2373131200 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S93: Evaluation of RP_2378140100 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S94: Evaluation of RP_2587150500 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S95: Evaluation of SH_10L53126001 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S96: Evaluation of SH_10L54010004 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S97: Evaluation of SH_10L55005005 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S98: Evaluation of SH_10L55038005 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S99: Evaluation of SH_10L56048003 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S100: Evaluation of SH_10L57066002 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S101: Evaluation of SH_10L62060004 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S102: Evaluation of SN_46440927 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S103: Evaluation of SN_46460564 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S104: Evaluation of SN_47500596 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S105: Evaluation of SN_48390509 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S106: Evaluation of SN_49430964 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S107: Evaluation of SN_49484004 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S108: Evaluation of SN_49531740 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S109: Evaluation of SN_52410759 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S110: Evaluation of ST_31340028 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S111: Evaluation of ST_33340002 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S112: Evaluation of ST_34376608 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S113: Evaluation of ST_36340007 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S114: Evaluation of ST_39320023 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S115: Evaluation of ST_40415442 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S116: Evaluation of ST_41300015 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S117: Evaluation of ST_43435116 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S118: Evaluation of ST_44339213 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)
+Figure S119: Projection Results BB_27381010 Model
+
+Figure S120: Projection Results BB_28390113 Model
+
+Figure S121: Projection Results BB_29519030 Model
+
+Figure S122: Projection Results BB_30400591 Model
+Figure S123: Projection Results BB_31400780 Model
+
+Figure S124: Projection Results BB_31491979 Model
+
+Figure S125: Projection Results BB_32455305 Model
+
+Figure S126: Projection Results BB_33437070 Model
+Figure S127: Projection Results BB_33437090 Model
+
+Figure S128: Projection Results BB_33437106 Model
+
+Figure S129: Projection Results BB_33452451 Model
+
+Figure S130: Projection Results BB_33470960 Model
+Figure S131: Projection Results BB_34426110 Model
+
+Figure S132: Projection Results BB_34522461 Model
+
+Figure S133: Projection Results BB_37451908 Model
+
+Figure S134: Projection Results BB_39441476 Model
+Figure S135: Projection Results BB_39496056 Model
+
+Figure S136: Projection Results BB_40500136 Model
+
+Figure S137: Projection Results BB_42458092 Model
+
+Figure S138: Projection Results BW_100-813-7 Model
+Figure S139: Projection Results BW_103-763-0 Model
+
+Figure S140: Projection Results BW_107-666-2 Model
+
+Figure S141: Projection Results BW_110-619-8 Model
+
+Figure S142: Projection Results BW_112-211-1 Model
+Figure S143: Projection Results BW_124-068-9 Model
+
+Figure S144: Projection Results BW_131-115-0 Model
+
+Figure S145: Projection Results BW_145-772-0 Model
+
+Figure S146: Projection Results BW_15-568-2 Model
+Figure S147: Projection Results BW_16-706-8 Model
+
+Figure S148: Projection Results BW_177-770-1 Model
+
+Figure S149: Projection Results BW_194-069-9 Model
+
+Figure S150: Projection Results BY_11119 Model
+Figure S151: Projection Results BY_13126 Model
+
+Figure S152: Projection Results BY_15120 Model
+
+Figure S153: Projection Results BY_22008 Model
+
+Figure S154: Projection Results BY_24153 Model
+Figure S155: Projection Results BY_25155 Model
+
+Figure S156: Projection Results BY_3108 Model
+
+Figure S157: Projection Results BY_5158 Model
+
+Figure S158: Projection Results BY_5162 Model
+Figure S159: Projection Results BY_7126 Model
+
+Figure S160: Projection Results BY_8252 Model
+
+Figure S161: Projection Results BY_83614 Model
+
+Figure S162: Projection Results BY_9275 Model
+Figure S163: Projection Results HE_10319 Model
+
+Figure S164: Projection Results HE_11781 Model
+
+Figure S165: Projection Results HE_12117 Model
+
+Figure S166: Projection Results HE_14293 Model
+Figure S167: Projection Results HE_14297 Model
+
+Figure S168: Projection Results HE_6253 Model
+
+Figure S169: Projection Results HE_6645 Model
+
+Figure S170: Projection Results HE_7824 Model
+Figure S171: Projection Results MV_16450200 Model
+
+Figure S172: Projection Results MV_17390002 Model
+
+Figure S173: Projection Results NL_100000728 Model
+
+Figure S174: Projection Results NL_100000842 Model
+Figure S175: Projection Results NL_100000926 Model
+
+Figure S176: Projection Results NL_129300060 Model
+
+Figure S177: Projection Results NL_200000620 Model
+
+Figure S178: Projection Results NL_200000788 Model
+Figure S179: Projection Results NL_200001068 Model
+
+Figure S180: Projection Results NL_200001722 Model
+
+Figure S181: Projection Results NL_200002153 Model
+
+Figure S182: Projection Results NI_40000175 Model
+Figure S183: Projection Results NL_40000233 Model
+
+Figure S184: Projection Results NL_400080190 Model
+
+Figure S185: Projection Results NL_400081660 Model
+
+Figure S186: Projection Results NL_40501911 Model
+Figure S187: Projection Results NL_405160331 Model
+
+Figure S188: Projection Results NL_500000592 Model
+
+Figure S189: Projection Results NL_600041871 Model
+
+Figure S190: Projection Results NL_9700020 Model
+Figure S191: Projection Results NI_9700080 Model
+
+Figure S192: Projection Results NI_9700159 Model
+
+Figure S193: Projection Results NI_9840391 Model
+
+Figure S194: Projection Results NI_9840901 Model
+Figure S195: Projection Results NI_9853172 Model
+
+Figure S196: Projection Results NW_100140142 Model
+
+Figure S197: Projection Results NW_100140762 Model
+
+Figure S198: Projection Results NW_110040028 Model
+Figure S199: Projection Results NW_110040041 Model
+
+Figure S200: Projection Results NW_110060143 Model
+
+Figure S201: Projection Results NW_110240017 Model
+
+Figure S202: Projection Results NW_129660176 Model
+Figure S203: Projection Results NW_129660206 Model
+
+Figure S204: Projection Results NW_60090169 Model
+
+Figure S205: Projection Results NW_60240258 Model
+
+Figure S206: Projection Results NW_80000186 Model
+Figure S207: Projection Results NW_80300376 Model
+
+Figure S208: Projection Results NW_91163705 Model
+
+Figure S209: Projection Results NW_91174909 Model
+
+Figure S210: Projection Results RP_2373131200 Model
+Figure S211: Projection Results RP_2378140100 Model
+
+Figure S212: Projection Results RP_2587150500 Model
+
+Figure S213: Projection Results SH_10L53126001 Model
+
+Figure S214: Projection Results SH_10L54010004 Model
+Figure S215: Projection Results SH_10L55005005 Model
+
+Figure S216: Projection Results SH_10L55038005 Model
+
+Figure S217: Projection Results SH_10L56048003 Model
+
+Figure S218: Projection Results SH_10L57066002 Model
+Figure S219: Projection Results SH_10L62060004 Model
+
+Figure S220: Projection Results SN_46440927 Model
+
+Figure S221: Projection Results SN_46460564 Model
+
+Figure S222: Projection Results SN_47500596 Model
+Figure S223: Projection Results SN_48390509 Model
+
+Figure S224: Projection Results SN_49430964 Model
+
+Figure S225: Projection Results SN_49484004 Model
+
+Figure S226: Projection Results SN_49531740 Model
+Figure S227: Projection Results SN_52410759 Model
+
+Figure S228: Projection Results ST_31340028 Model
+
+Figure S229: Projection Results ST_33340002 Model
+
+Figure S230: Projection Results ST_34376608 Model
+Figure S231: Projection Results ST_36340007 Model
+
+Figure S232: Projection Results ST_39320023 Model
+
+Figure S233: Projection Results ST_40415442 Model
+
+Figure S234: Projection Results ST_41300015 Model
+Figure S235: Projection Results ST_43435116 Model
+
+![Projection Results ST_43435116 Model](page_246_180_957_246.png)
+
+Figure S236: Projection Results ST_44339213 Model
+
+![Projection Results ST_44339213 Model](page_246_661_957_246.png)

0297e09c8c2b5e744ded2ba5e84ab6868857ddbdce0ca65775323250f8a61cea/preprint/supplementaries/SupportingInformation100MB/images_list.json

@@ -0,0 +1,3306 @@
+[
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_0.jpg",
+    "caption": "Figure S1: Evaluation of BB_27381010 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+  },
+  {
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+    "caption": "Figure S2: Evaluation of BB_28390113 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+    "caption": "Figure S3: Evaluation of BB_29519030 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+    "caption": "Figure S20: Evaluation of BW_100-813-7 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+  {
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+    "caption": "Figure S26: Evaluation of BW_131-115-0 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_26.jpg",
+    "caption": "Figure S27: Evaluation of BW_145-772-0 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_27.jpg",
+    "caption": "Figure S28: Evaluation of BW_15-568-2 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+  },
+  {
+    "type": "image",
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+    "caption": "Figure S29: Evaluation of BW_16-706-8 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+    "page_idx": 39
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_29.jpg",
+    "caption": "Figure S30: Evaluation of BW_177-770-1 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        848,
+        655
+      ]
+    ],
+    "page_idx": 40
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_30.jpg",
+    "caption": "Figure S31: Evaluation of BW_194-069-9 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        848,
+        654
+      ]
+    ],
+    "page_idx": 41
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_31.jpg",
+    "caption": "Figure S32: Evaluation of BY_11119 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        848,
+        654
+      ]
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+    "page_idx": 42
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_32.jpg",
+    "caption": "Figure S33: Evaluation of BY_13126 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        654
+      ]
+    ],
+    "page_idx": 43
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_33.jpg",
+    "caption": "Figure S34: Evaluation of BY_15120 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        655
+      ]
+    ],
+    "page_idx": 44
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_34.jpg",
+    "caption": "Figure S35: Evaluation of BY_22008 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        654
+      ]
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+    "page_idx": 45
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_35.jpg",
+    "caption": "Figure S36: Evaluation of BY_24153 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        653
+      ]
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+    "page_idx": 46
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_36.jpg",
+    "caption": "Figure S37: Evaluation of BY_25155 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        654
+      ]
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+    "page_idx": 47
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_37.jpg",
+    "caption": "Figure S38: Evaluation of BY_3108 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        654
+      ]
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+    "page_idx": 48
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_38.jpg",
+    "caption": "Figure S39: Evaluation of BY_5158 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        655
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+    "page_idx": 49
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_39.jpg",
+    "caption": "Figure S40: Evaluation of BY_5162 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        200,
+        848,
+        653
+      ]
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+    "page_idx": 50
+  },
+  {
+    "type": "image",
+    "img_path": "images/Figure_unknown_40.jpg",
+    "caption": "Figure S41: Evaluation of BY_7126 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+  {
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+    "caption": "Figure S100: Evaluation of SH_10L57066002 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+      ]
+    ],
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+  },
+  {
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+    "caption": "Figure S101: Evaluation of SH_10L62060004 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        847,
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+      ]
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+  },
+  {
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+    "caption": "Figure S102: Evaluation of SN_46440927 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+  },
+  {
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+    "caption": "Figure S103: Evaluation of SN_46460564 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        654
+      ]
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+    "page_idx": 113
+  },
+  {
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+    "caption": "Figure S104: Evaluation of SN_47500596 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
+      [
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+      ]
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+  },
+  {
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+    "caption": "Figure S105: Evaluation of SN_48390509 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+      ]
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+  },
+  {
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+    "caption": "Figure S106: Evaluation of SN_49430964 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        655
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+  },
+  {
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+    "caption": "Figure S107: Evaluation of SN_49484004 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+    "page_idx": 117
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+  {
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+    "caption": "Figure S108: Evaluation of SN_49531740 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+        653
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+  {
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+    "caption": "Figure S109: Evaluation of SN_52410759 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
+      [
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+        850,
+        655
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+    "page_idx": 119
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+  {
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+    "caption": "Figure S110: Evaluation of ST_31340028 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
+      [
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+        850,
+        655
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+    "page_idx": 120
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+    "caption": "Figure S111: Evaluation of ST_33340002 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+    "page_idx": 121
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+  {
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+    "caption": "Figure S112: Evaluation of ST_34376608 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+        655
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+    "page_idx": 122
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+  {
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+    "caption": "Figure S113: Evaluation of ST_36340007 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        654
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+    "page_idx": 123
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+  {
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+    "caption": "Figure S114: Evaluation of ST-39320023 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
+      [
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+        848,
+        655
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+    "page_idx": 124
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+    "caption": "Figure S115: Evaluation of ST_40415442 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        848,
+        653
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+    "page_idx": 125
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+  {
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+    "caption": "Figure S116: Evaluation of ST_41300015 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+        846,
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+    "page_idx": 126
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+    "caption": "Figure S117: Evaluation of ST_43435116 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
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+        848,
+        655
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+    "page_idx": 127
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+  {
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+    "caption": "Figure S118: Evaluation of ST_44339213 Model Performance in the past (upper), under extreme climate conditions (middle) and SHAP Summary plot (lower)",
+    "bbox": [
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+        848,
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+    "page_idx": 128
+  },
+  {
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+    "caption": "Figure S119: Projection Results BB_27381010 Model",
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+    "page_idx": 129
+  },
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+    "caption": "Figure S120: Projection Results BB_28390113 Model",
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+        404
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+    "page_idx": 129
+  },
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+    "caption": "Figure S121: Projection Results BB_29519030 Model",
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+    "page_idx": 129
+  },
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+    "page_idx": 129
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+    "caption": "Figure S123: Projection Results BB_31400780 Model",
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+    "page_idx": 130
+  },
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+    "caption": "Figure S124: Projection Results BB_31491979 Model",
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+    "caption": "Figure S126: Projection Results BB_33437070 Model",
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+    "caption": "Figure S127: Projection Results BB_33437090 Model",
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+    "page_idx": 131
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+    "caption": "Figure S128: Projection Results BB_33437106 Model",
+    "bbox": [
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+    "page_idx": 131
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+    "caption": "Figure S129: Projection Results BB_33452451 Model",
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+    "page_idx": 131
+  },
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+    "caption": "Figure S130: Projection Results BB_33470960 Model",
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+    "page_idx": 131
+  },
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+    "caption": "Figure S131: Projection Results BB_34426110 Model",
+    "bbox": [
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+    "page_idx": 132
+  },
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+    "caption": "Figure S132: Projection Results BB_34522461 Model",
+    "bbox": [
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+    "page_idx": 132
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+    "caption": "Figure S133: Projection Results BB_37451908 Model",
+    "bbox": [
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+    "page_idx": 132
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+    "caption": "Figure S134: Projection Results BB_39441476 Model",
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+    "page_idx": 132
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+    "caption": "Figure S135: Projection Results BB_39496056 Model",
+    "bbox": [
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+    "page_idx": 133
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+    "caption": "Figure S136: Projection Results BB_40500136 Model",
+    "bbox": [
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+    "page_idx": 133
+  },
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+    "caption": "Figure S137: Projection Results BB_42458092 Model",
+    "bbox": [
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+    "page_idx": 133
+  },
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+    "caption": "Figure S138: Projection Results BW_100-813-7 Model",
+    "bbox": [
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+    "page_idx": 133
+  },
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+    "caption": "Figure S139: Projection Results BW_103-763-0 Model",
+    "bbox": [
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+        228
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+    "page_idx": 134
+  },
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+    "caption": "Figure S140: Projection Results BW_107-666-2 Model",
+    "bbox": [
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+        406
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+    "page_idx": 134
+  },
+  {
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+    "caption": "Figure S141: Projection Results BW_110-619-8 Model",
+    "bbox": [
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+    "page_idx": 134
+  },
+  {
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+    "caption": "Figure S142: Projection Results BW_112-211-1 Model",
+    "bbox": [
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+    "page_idx": 134
+  },
+  {
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+    "caption": "Figure S143: Projection Results BW_124-068-9 Model",
+    "bbox": [
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+        228
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+    "page_idx": 135
+  },
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+    "caption": "Figure S144: Projection Results BW_131-115-0 Model",
+    "bbox": [
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+    "page_idx": 135
+  },
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+    "caption": "Figure S145: Projection Results BW_145-772-0 Model",
+    "bbox": [
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+    "page_idx": 135
+  },
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+    "caption": "Figure S146: Projection Results BW_15-568-2 Model",
+    "bbox": [
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+    "page_idx": 135
+  },
+  {
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+    "caption": "Figure S147: Projection Results BW_16-706-8 Model",
+    "bbox": [
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+    "page_idx": 136
+  },
+  {
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+    "caption": "Figure S148: Projection Results BW_177-770-1 Model",
+    "bbox": [
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+    "page_idx": 136
+  },
+  {
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+    "caption": "Figure S149: Projection Results BW_194-069-9 Model",
+    "bbox": [
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+    "page_idx": 136
+  },
+  {
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+    "caption": "Figure S150: Projection Results BY_11119 Model",
+    "bbox": [
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+    "page_idx": 136
+  },
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+    "caption": "Figure S151: Projection Results BY_13126 Model",
+    "bbox": [
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+    "page_idx": 137
+  },
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+    "caption": "Figure S152: Projection Results BY_15120 Model",
+    "bbox": [
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+        405
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+    "page_idx": 137
+  },
+  {
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+    "caption": "Figure S153: Projection Results BY_22008 Model",
+    "bbox": [
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+    "page_idx": 137
+  },
+  {
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+    "caption": "Figure S154: Projection Results BY_24153 Model",
+    "bbox": [
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+    "caption": "Figure S155: Projection Results BY_25155 Model",
+    "bbox": [
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+    "page_idx": 138
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+    "bbox": [
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+  {
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+    "bbox": [
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+        585
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+  },
+  {
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+    "bbox": [
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+  },
+  {
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+    "bbox": [
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+  {
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+        408
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+  {
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+    "bbox": [
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+    "page_idx": 139
+  },
+  {
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+    "caption": "Figure S162: Projection Results BY_9275 Model",
+    "bbox": [
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+    "page_idx": 139
+  },
+  {
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+    "caption": "Figure S163: Projection Results HE_10319 Model",
+    "bbox": [
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+    "page_idx": 140
+  },
+  {
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+    "caption": "Figure S164: Projection Results HE_11781 Model",
+    "bbox": [
+      [
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+  },
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+    "caption": "Figure S166: Projection Results HE_14293 Model",
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+  },
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+  },
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+    "bbox": [
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+        406
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+    "bbox": [
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+    "bbox": [
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+        228
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+    "caption": "Figure S232: Projection Results ST_39320023 Model",
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+    "caption": "Figure S233: Projection Results ST_40415442 Model",
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+    "caption": "Figure S234: Projection Results ST_41300015 Model",
+    "bbox": [
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+    "type": "image",
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+    "caption": "Figure S235: Projection Results ST_43435116 Model",
+    "bbox": [
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+    "type": "image",
+    "img_path": "images/Figure_unknown_235.jpg",
+    "caption": "Figure S236: Projection Results ST_44339213 Model",
+    "bbox": [
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3b4a323d4faa60d098f8ad3666a03cd4e164672a457b181247197da1ee488d27/metadata.json

@@ -0,0 +1,165 @@
+{
+    "title": "Use of a glycomics array to establish the anti-carbohydrate antibody repertoire in type 1 diabetes",
+    "pre_title": "The Anti-carbohydrate antibody repertoire in type 1 diabetes",
+    "journal": "Nature Communications",
+    "published": "01 November 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-34341-2/MediaObjects/41467_2022_34341_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-34341-2/MediaObjects/41467_2022_34341_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-34341-2/MediaObjects/41467_2022_34341_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-34341-2/MediaObjects/41467_2022_34341_MOESM4_ESM.xlsx"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-34341-2/MediaObjects/41467_2022_34341_MOESM5_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-34341-2/MediaObjects/41467_2022_34341_MOESM6_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.7143430",
+        "/articles/s41467-022-34341-2#Sec28"
+    ],
+    "code": [],
+    "subject": [
+        "Antibodies",
+        "Autoimmune diseases",
+        "Autoimmunity",
+        "High-throughput screening",
+        "Type 1 diabetes"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1490184/v1.pdf?c=1668105487000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1490184/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-34341-2.pdf",
+    "preprint_posted": "14 Apr, 2022",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Type 1 diabetes (T1D)  is an autoimmune disease, characterized by the presence of auto-antibodies to several protein and non-protein antigens. We report circulating levels of antibodies towards naturally occurring glycans using our customized glycan array and show that anti-carbohydrate antibodies (ACA) are associated with pathogenesis and progression to T1D. We compared circulatory levels of ACAs against 202 glycans in a cross-sectional cohort of T1D patients (n=278) and healthy controls (n=298), as well as in a longitudinal cohort (n=112). We identified 11 clusters of ACAs associated with glycan function class. Clusters enriched for aminoglycosides, blood group A and B antigens, glycolipids, ganglio-series, and O-linked glycans were associated with progression to T1D.  ACAs against the aminoglycoside commonly used for neonatal sepsis, gentamicin, and its related structures, G418 and sisomicin, were associated with islet autoimmunity. ACAs improved discrimination of T1D status of individuals over a model with only clinical variables. ACAs are potential biomarkers for T1D.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "Yes there is potential Competing Interest.\nJin-Xiong She is founder and CEO of Jinfiniti LLC. All other authors declare no conflict of interests",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "ACAT1DSuplMaterials4upload.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Type 1 diabetes (T1D) is an autoimmune disease, characterized by the presence of autoantibodies to protein and non-protein antigens. Here we report the identification of specific anti-carbohydrate antibodies (ACAs) that are associated with pathogenesis and progression to T1D. We compare circulatory levels of ACAs against 202 glycans in a cross-sectional cohort of T1D patients (n\u2009=\u2009278) and healthy controls (n\u2009=\u2009298), as well as in a longitudinal cohort (n\u2009=\u2009112). We identify 11 clusters of ACAs associated with glycan function class. Clusters enriched for aminoglycosides, blood group A and B antigens, glycolipids, ganglio-series, and O-linked glycans are associated with progression to T1D. ACAs against gentamicin and its related structures, G418 and sisomicin, are also associated with islet autoimmunity. ACAs improve discrimination of T1D status of individuals over a model with only clinical variables and are potential biomarkers for T1D.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The sugars within complex carbohydrates or glycans, are components of glycoproteins and glycolipids on the surface of all cell types including those of all microbes. Both bound and free glycans also originate from microbial flora, dietary sources, as well as normal metabolism of host glycoconjugates. Glyco-chemistry, encouraged by the diversity of the tumor glycome, has fueled research in identifying the immunological functions of these glycans in diseases such as cancers and autoimmune diseases1,2,3,4. Tumor cells have been found to incorporate non-human derived glycan modifications, such as N-glycolylneuraminic acid (NeuGc) onto glycoproteins5. Recognition of abnormal glycosylation in human diseases has raised interest in research for carbohydrate-based biomarkers and treatment of human diseases6,7,8. Using glycan microarrays, researchers have identified the presence of naturally occurring anti-carbohydrate antibodies (ACAs) in normal human serum9,10,11. Specific types of ACAs have been reported in human pathologic conditions such as cancer and auto-immune diseases7,8,12. The serum repertoire of ACAs to natural glycans are involved in the progression and pathogenesis of cancer and autoimmune diseases and have prognostic and diagnostic value for disease course and treatment outcome3,12,13. Presence of ACAs has been reported in rheumatoid arthritis1, inflammatory bowel diseases like Crohn\u2019s disease14,15, and multiple sclerosis16. An important feature of these anti-glycan antibodies is their levels persist during the life of an individual17 suggesting that these could serve as surrogate markers for T1D.\n\nType 1 diabetes (T1D) is characterized by immune-mediated destruction of the insulin-secreting \u03b2-cells of the pancreas. T1D comprises the majority of cases of diabetes seen in childhood, accounts for ~5\u201310% of all cases of diabetes mellitus in the USA, and perhaps accounts for an even higher percentage in those nations with lower rates of obesity18. A characteristic feature of T1D is the presence of auto-antibodies against antigens of pancreatic and non-pancreatic origin19,20. HLA genotyping and auto-antibodies to glutamate decarboxylase (GADA), islet cells (ICA), protein tyrosine phosphatase (IA-2A) and zinc transporter (ZnT8A) are used for diagnosis, prediction, and risk analysis of T1D21,22,23, and additional antigens are being discovered24. These auto-antibodies have been extensively utilized for identification and risk stratification in both T1D patients and their first-degree relatives25,26,27,28. Auto-antibodies to ganglioside GT3 and the glycolipid sulfatide have also been identified in T1D patients29.\n\nPast efforts to identify environmental triggers of islet autoimmunity have used regular follow-up to collect information on diet, viral, and bacterial infections, among other factors30,31,32. We reasoned those environmental agents which can trigger islet autoimmunity will result in generation of ACAs and may be identified through serologic detection of immunoglobulins recognizing carbohydrates in a high-throughput multiplex assay. This approach allows identification of exposures not collected in current cohort studies and can also identify exposures occurring during periods between the regular follow ups.\n\nHere we show that serum levels of ACAs correspond with functional glycan classes and that certain classes are strongly associated with islet autoimmunity and progression to T1D in high-risk individuals recruited in the Diabetes Autoimmunity Study in the Young (DAISY). Notably, ACAs targeting Micromonospora spp derived aminoglycosides were associated with progression to T1D, while ACAs targeting the Streptomyces spp derived aminoglycosides were not. This suggests an influence for environmental exposures in the differential prevalence of aminoglycoside targeting ACAs and risk of T1D progression. Finally, we show that a prediction model with both clinical variables and ACAs clusters is better able to discriminate T1D progressors vs non-progressors as compared to a clinical variable only model or a combined random forest model with both clinical variables and ACA.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Serum ACAs were profiled against 202 naturally occurring glycans using a bead-based suspension array developed in-house33 (Fig.\u00a01a). Details on the validation of the assay have been previously published, but we re-assessed the analytical parameters of the assay for select glycans in this study (Supplementary Figs.\u00a01\u20136). Based on their structure and functional roles in cellular localization and recognition, these glycans were divided into 22 major functional classes, including glycolipid antigens, blood group antigens, Lewis antigens, monosaccharides, chitin derivatives and many glycans that are expressed in algae and plants. A list of the glycans, their structures, and functional classes are provided in\u00a0Supplementary data. The participants profiled for ACAs were from the Phenome and Genome of Diabetic Autoimmunity study (PAGODA, Georgia, USA) and Diabetes Autoimmunity Study in the Young (DAISY, Denver, Colorado, USA). The ACA levels were profiled in 576 participants from the PAGODA study, which is a case-control study with limited clinical data (Table\u00a01). We measured ACA levels in the earliest serum sample available from 112 participants from the DAISY study, which is a cohort study with monitored from birth to development of T1D and contains an extensive clinically relevant data for progression to T1D (Table\u00a02).\n\na Overview of multiplex glycan suspension array platform and methodology. Briefly, diluted human serum is added to a mixture of fluorescent beads each linked to a different glycan structure to allow human anti-carbohydrated antibodies (ACAs) to bind to the immobilized glycans. A biotin-conjugated anti-human IgG antibody is added. Finally, streptavidin-conjugated phycoerythrin is added and the median fluorescence intensity is measured on a Luminex instrument. Created with BioRender.com. b Distribution of ACAs in the Diabetes Autoimmunity Study (DAISY) and Phenome and Genome of Diabetic Autoimmunity (PAGODA) shown as median fluorescence intensity dot plots. 5-nearest neighbor graphs were constructed based on cosine similarity and projected onto 2 dimensions using the UMAP algorithm for ACAs detected. Each color is arbitrarily chosen to represent a different cluster using the Louvain algorithm. c The PAGODA and DAISY k-nearest neighbors graphs were merged together. Edge weights unique to each graph were kept as is. For edges where both the PAGODA and DAISY graphs had weights, the product was subtracted from the sum of the two weights. The Louvain clustering algorithm was applied to identify glycan communities (arbitrary color for each cluster). Source data are provided as a Source Data file.\n\nAs found in previous studies29,34, varying levels of ACAs were detected in both the PAGODA and DAISY cohorts against several classes of glycans. Antibodies to monosaccharides (#5), blood group and Lewis antigens (#35, 36, 60, 128, 129,), isoglobo series (#155, 156), foreign antigens viz., \u03b1Gal antigens (#149,152), Forssmann antigens (#183,184) and aminoglycosides (#96-102) were detected at the highest abundance (Fig.\u00a01b and Supplementary Table\u00a01). This is in general agreement with previous ACA profiling studies35,36. Some individuals in the DAISY longitudinal study had multiple serum samples available from different time points, and we were able to see stability of ACA detection over time (Supplementary Fig.\u00a07).\n\nThe type and structure of glycans have an important function in glycoprotein structure and function inside the cells37, as well as in control of innate and adaptive immune responses38,39. Since many of the glycan structures we assessed had overlapping substructures and linkages which can be recognized by the same ACA, the ACA levels against these glycans have a degree of interdependence and cannot be individually analyzed. The ACA data from both clinical cohorts were individually subjected to community clustering40 to account for ACAs which recognize similar idiotypes (Fig.\u00a01b). We then combined all the individuals from each cohort to create a merged k-nearest neighbors (KNN) graph to identify closely related ACAs. Community clustering of the merged KNN graph led to identification of 11 major ACA clusters (Fig.\u00a01c). These clusters are mostly unique from each other with some correlation observed between Clusters 1 and 8 and among Clusters 2, 3, 5, and 10 (Supplementary Fig.\u00a08).\n\nThe ACA clusters were found to be enriched for functional glycan classes (Fig.\u00a02a). Cluster 1 was enriched for ACAs against mono-, di-, and tri-saccharides, and glycolipids. Cluster 2 was enriched for ACAs against blood group oligosaccharide analogues, chitin, ganglio-series analogues, globo-series and globo-series analogues, glucuronylated oligosaccharides, maltodextrins, and stage-specific embryonic antigens. Cluster 3 was enriched for ACAs against ganglio-series and O-linked glycans. ACAs against blood group H antigens were enriched in Cluster 4. ACAs against both blood group A and B antigens were enriched in Cluster 5. Cluster 6 is enriched for ACAs against lacto-series and plant oligosaccharides. Cluster 7 and 9 were not enriched for ACAs against any specific glycan class. Cluster 8 is enriched for ACAs against aminoglycoside antibiotics and glycolipids. Cluster 10 is enriched for ACAs against maltodextrins. Cluster 11 is enriched for ACAs against isoglobo-series and Lewis antigens.\n\na Bubble chart showing glycan classes enriched (lighter blue and larger bubble size) in each ACA cluster calculated using fisher\u2019s exact test. b Forest plot showing linear model for the first principal component of each glycan cluster against the clinical variables age at blood draw, presence of first degree relative with T1D, non-progression to T1D, progression to T1D, HLA risk, and sex in DAISY participants (n\u2009=\u2009112). Effect size (dots) and 95% confidence interval (bars) are presented. All p values were two sided and a p\u2009<\u20090.05 was considered significant (significant associations are displayed as red, while non-significant associations are displayed as black). Source data are provided as a Source Data file.\n\nWe assessed ACA cluster association with T1D phenotypes in the DAISY cohort since it is more clinically balanced than the PAGODA cohort (Tables\u00a01 and 2). All glycans belonging to individual ACA clusters were subjected to principal component analysis (PCA), and the first PC values from each cluster were then subjected to linear regression. Our linear regression models show that the first principal components of ACA clusters are associated with the development of auto-antibody and progression to T1D (Fig.\u00a02b). Higher levels of ACAs against glycans in cluster 7 were associated with increased age at blood draw. No ACA clusters were associated with first degree relative with T1D, HLA risk, or sex. Higher levels of ACAs in clusters 2, 5, and 7 are associated with progression to T1D, whereas lower levels of ACAs in clusters 1 and 8 (enriched for aminoglycosides) are associated with progression to T1D. Higher levels of ACAs against glycans in cluster 3 (enriched for ganglio-series and O-linked glycans) were associated with islet autoimmunity and T1D.\n\nWe performed univariate analysis on the glycan classes enriched in the islet autoimmunity and T1D associated clusters to discern substructure patterns. ACAs against the monosaccharides \u03b2GalNAc (#7) and \u03b1mannose (#16) were associated with progression to T1D (Supplementary Fig.\u00a09). These are both natural monosaccharides expressed in the human body41. In contrast, ACAs against foreign monosaccharides, such as \u03b1rhamnose (#5), and D-rhamnose (#72) were not associated with T1D. Additionally, the ACAs associated with progression are not the most abundant ACAs in circulation, which are \u03b1rhamnose (#5), \u03b1GlcNAc (#21), and \u03b2GlcNAc (#6)13,35.\n\nACAs against the disaccharides Gal\u03b21,4Glc\u03b2 (#15) and Gal\u03b21,4GalNAc\u03b2 (#17) were associated with progression to T1D (Supplementary Figure\u00a09). In contrast, ACAs against the disaccharides Gal\u03b21,3GlcNAc\u03b2 (#18) and Gal\u03b21,3GalNAc\u03b1 (#27) were not associated with islet autoimmunity or progression. This suggests that the \u03b21,4\u2009Gal linkage may be associated with T1D progression compared to the \u03b21,3\u2009Gal linkage.\n\nACAs against the trisaccharides Gal\u03b11,3Gal-\u03b21,4Glc\u03b2 (#21) and GlcNAc\u03b21,3Gal\u03b21,4Glc\u03b2 (#28) were associated with progression to T1D (Supplementary Fig.\u00a09). However, there are no consistent structural differences between these two glycans and the remaining four glycans in the trisaccharide group.\n\nOf the five blood group A antigens assessed, ACAs against two glycans (#125,127) were associated with both islet autoimmunity and T1D progression (Fig.\u00a03). Of the five blood group B antigens assessed, only ACAs against #131 were associated with islet autoimmunity and T1D progression.\n\nRadar charts showing \u2013log10(p value) with blue representing association with progression and red representing association with non-progressors. The gray shadowed area represents non-significances (p\u2009>\u20090.05). Shaded area in red shows significant associations with non-progressors status (red dots and shaded area). Blue dots and shaded area shows significant associations with progression to type 1 diabetes (progressors). BGB: blood group B antigen, GD3: ganglioside GD3, GD2: ganglioside GD2, Gc-Ac: N-Acetyl-Glycolylneuraminic acid, Gc: N-Glycolylneuraminic acid. Source data are provided as a Source Data file.\n\nACAs against the glycolipids Neu5Ac\u03b12,3Gal\u03b21,3GlcNAc\u03b2 (#22), Neu5Gc\u03b12,6Gal\u03b2 1,3GlcNAc\u03b2 (#25), and Neu5Gc\u03b12,6,Gal\u03b21,4Glc\u03b2 (#31) were associated with T1D progression. ACAs against the six remaining glycolipids were not associated with islet autoimmunity or T1D progression (Fig.\u00a03).\n\nACAs against ganglioseries have been reported to be enriched in new-onset T1D patients42,43. We found ACA against one of four GD3 antigens (#107) associated with islet autoimmunity and one of two GD2 antigens (#114) associated with both islet autoimmunity and T1D progression (Fig.\u00a03). ACAs against GM2 (#43, 69, 115) and GT3 antigens (#110, 111) were not associated with islet autoimmunity or T1D.\n\nACAs against the O-linked glycans GlcNAc\u03b2-O-Ser (#51) were associated with islet autoimmunity and T1D progression while those against Gal\u03b2,3GalNAc\u03b1-O-Ser (Gal-Tn-Antigen, #52) were associated with T1D progression (Fig.\u00a03).\n\nIn our ACA data, higher levels of ACA against gentamicin (#98), geneticin (#100), and sisomicin (#102) were detected in individuals persistently positive for islet autoantibodies compared to controls (Fig.\u00a04a). These three aminoglycosides are all derived from the Micromonospora spp44,45 and all three contain the carbohydrate garosamine46, suggesting that the ACAs may target garosamine. By comparison, the remaining four aminoglycosides (#96, #97, #99, #101) profiled are all derived from Streptomyces spp and lack the glycoside garosamine in their structure. The density distribution of the median fluorescence intensity for ACAs against gentamicin shows a bimodal distribution with 5.3% of individuals in the higher MFI peak (Supplementary Fig.\u00a010). This is similar to the rate of gentamicin administration for suspected neonatal sepsis47.\n\na Radar charts showing \u2013log10(p value) with blue representing association with progression (blue dots and shaded area) and red representing association with non-progressors (red dots and shaded area). The gray shadowed area represents non-significances (p\u2009>\u20090.05). Aminoglycoside structures drawn using ChemDraw version 19.1.0.8. b Boxplot of ACA levels against gentamicin for fucosyltransferase-2 (FUT2) (rs601338) genotypes G/G (N\u2009=\u200941), A/A (N\u2009=\u200939), and G/A (N\u2009=\u200984). Differences between the FUT2 genotype groups were evaluated by Tukey\u2019s test accounting for multiple testing with Benjamini-Hochberg method, horizontal lines on the box represent the 25th, 50th and 75th percentile, the whiskers represent maximum and minimum values of anti-gentamicin IgG values. All p values were two-sided and a p\u2009<\u20090.05 was considered significant. c Directed acyclic graph of report associations related to FUT2 and T1D51,52, FUT2 and neonatal sepsis48, prematurity and T1D58, prematurity and neonatal sepsis56, neonatal sepsis and gentamicin56, and our reports of FUT2 association with ACAs against gentamicin and of ACAs against gentamicin and T1D. Created with BioRender.com. spp.: species. Source data are provided as a Source Data file.\n\nPrevious groups have shown a potential association between the FUT2 genotype and neonatal sepsis risk48. In addition, the FUT2 locus is a well-documented autoimmune disease associated region49,50, including for T1D51,52. We assessed if the anti-aminoglycoside IgG level association with islet autoimmunity and T1D could be mediated by the FUT2 genotype. FUT2 non-secretors (A/A) have higher anti-gentamicin IgG levels than FUT2 secretors (G/G) on average (Fig.\u00a04b). We constructed a directed acyclic graph of the known associations between FUT2, neonatal sepsis, prematurity, and T1D, and included associations between anti-gentamicin IgG levels and FUT2 and anti-gentamicin IgG levels and T1D (red, Fig.\u00a04c).\n\nWe assessed if ACAs can improve discrimination of T1D status in the DAISY cohort using a binomial model with progressors and controls. The full model with all ACA clusters and clinical variables improved discrimination of T1D and control compared to a null model with only clinical variables (LRT p\u2009=\u20090.0056, Fig.\u00a05a). Based on permutation testing, the full model was a robust predictor of T1D status (q\u2009=\u20090.0291) compared to the 8 ACA cluster model (q\u2009=\u20090.2084) and the clinical variable only model (q\u2009=\u20090.9878). The glycan clusters account for 18.4% of variance of T1D status while all genetic components together, including sex, first degree relative with T1D status, and HLA risk account for 9.8% of variance in the DAISY cohort (Fig.\u00a05b). We assessed if enough ACAs have been profiled for maximal discrimination of T1D status by performing bootstrapping without resampling with increasing number of glycans and found that ACAs profiled against 50 glycans in the DAISY cohort was sufficient for T1D status discrimination with an AUC of 0.85 (Fig.\u00a05c). We compared our discrimination analysis to random forest, a well-established machine learning method that can account for data with high correlation structure. We found that a random forest model of 202 ACA features to discriminate control and progressors in the DAISY cohort is not significantly different from the null distribution based on permutation analysis (q\u2009=\u20090.063).\n\na Receiver-operator characteristic curve for three predictive models of T1D. A null model including sex, HLA risk, FDR, and draw age (black). A full model including all variables in the null model plus the first principal component from each of the 11 clusters of ACA (red). A partial model including all variables in the null model plus the first principal component from each of the 5 clusters of ACA significantly associated with progressors or non-progressors (blue). b The variance accounted for by each component of the full model from A. Partial correlation coefficient (R2) values from full model was plotted (black bars) against the variables (x-axis). c The area under the receiver-operator characteristic curve for a random number of glycans included in a ridge regression model with clinical variables from 1 to 200. AUC (dots, y-axis) values were plotted against number of glycans (x-axis), the dots represent mean AUC value while error bars represent 95% confidence intervals for the AUC values. Source data are provided as a Source Data file.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We present a large-scale profiling study of ACAs against 202 glycans in two T1D cohorts totaling 688 samples and individuals (Fig.\u00a01). Clusters enriched for mono-, di-, and tri- saccharides, aminoglycosides, blood group A and B antigens, and glycolipids were associated with progression to T1D. A recent T1D GWAS meta-analysis51 shows a potential association between T1D and the ABO genetic locus, although these findings vary with the ABO prevalence of the cohort studied40,53. Other studies have shown potential associations between autoimmune disease and ABO blood type40,54 albeit in smaller cohort sizes. Clusters enriched for ganglio-series and O-linked glycans were associated with both islet autoimmunity and progression to T1D (Fig.\u00a03).\n\nThe FUT2 genetic locus has been associated with T1D in T1D GWAS51,52 and with multiple other autoimmune diseases49,50. The ABO, FUT2 genetic, and ACA associations with T1D may be related to changes in the microbiome55. We showed the FUT2 genotype is associated with ACAs against aminoglycosides (Fig.\u00a04b).\n\nAminoglycoside exposure occurs for newborns suspected of neonatal sepsis56. The individuals are treated with gentamicin. Approximately 5\u201310% of the population is treated with gentamicin for suspected neonatal sepsis after birth47, which matches the proportion of individuals with higher ACA against gentamicin (5.3%). In addition, premature infants are at higher risk of developing neonatal sepsis57 and of developing type 1 diabetes58 (Fig.\u00a04C). Further research is required to discern the causal relationships between prematurity, altered microbiome, aminoglycoside exposure, and type 1 diabetes.\n\nCurrently, oligosaccharides (including mono-, di-, and tri-) and blood group antigens have not been associated with progression to T1D. Glycolipids and gangliosides have been associated with progression to T1D. We found that IgG antibodies against GM2 and GT3 were not associated with islet autoimmunity or T1D as previously reported42,43 (Fig.\u00a03, #69 and #110, respectively). Instead, our study identified the GD2 and GD3 gangliosides were associated with progression to T1D. The previous studies were limited by smaller sample sizes and less glycans to assess. Additionally, the previous studies used ELISA based assays whereas we applied a bead-based study. Thus, different epitopes could be exposed for these glycans. Different glycan densities can also affect antibody affinity and this can vary across assays and platforms59.\n\nWhile all four are gangliosides, GM2 is an a-series ganglioside, GD2 and GD3 are b-series gangliosides, GT3 is a c-series ganglioside. A-, b-, and c-series gangliosdies have 1, 2, and 3 sialic acid residues, respectively. Interestingly, a biochemical study of the glycolipids showed that GM3 makes up the majority (66.7%) of total gangliosides detected in the whole pancreas whereas an unspecified GM2 co-migrating glycolipid makes up the majority (74.2%) of total gangliosides detected in pancreatic islets60. The co-migrating glycolipid is likely GD2 since the number of sialic acid residues have a strong influence in glycolipid migration in both HPLC and HPTLC. This data suggests that GD2 ganglioside is expressed more in pancreatic islets and that ACAs against GD2 are associated with progression to T1D.\n\nWe developed a cluster-based analysis method for ACA profiling since many of the glycan structures tested are similar and the signals from ACA to these different glycans are likely dependent. However, since the idiotype targeted by the ACA were not known beforehand, we used an unsupervised clustering approach rather than using the known functional glycan classes. The unsupervised clusters were enriched for these glycan classes (Fig.\u00a02A), which further reassured us of this approach.\n\nACA profiling provides a method to identify environmental exposures associated with disease. It is advantageous over viral and microbial sequencing methods which only provide a snapshot at the time of sample collection. Instead, ACA profiling depends on the serologic memory of the environmental exposure.\n\nThe limitations of our study include a small cross-sectional study design with most serum samples collected after islet autoantibody seroconversion. In addition, only assays with known glycan binding proteins could be validated, while others were not. Hence, our findings require validation in a larger longitudinal cohort.\n\nIn summary, our data demonstrated that ACAs are associated with islet immunity and progression to T1D. The combination of ACA and cluster-based analysis accounts for more variance than clinical variables alone for the T1D phenotype (18.4% vs 9.8%). We found associations between FUT2 genotype, ACA against gentamicin, and islet autoimmunity, which suggests the potential influence of environmental agents in T1D pathogenesis that requires validation in a larger, longitudinal cohort.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The study was performed according to Declaration of Helsinki (1997), and approved by the institutional review boards at Augusta University, Augusta, GA and University of Colorado, Denver, CO. Written informed consent was obtained from all participants or their parents. The samples used in the study were obtained from participants of the Phenome and Genome of Diabetes Autoimmunity (PAGODA)61 and Diabetes Autoimmunity Study in the Young (DAISY) study62. PAGODA study is a cross-sectional design and contained controls (n\u2009=\u2009278) and T1D patients (n\u2009=\u2009298). 112 children at high risk for T1D from DAISY were followed for development of autoantibody or progression to T1D and they were divided into three comparison groups: progressors (n\u2009=\u200947), non-progressors (n\u2009=\u200935), and controls (n\u2009=\u200930). Progressors were children who progressed to type 1 diabetes (T1D). Non-progressors are children having at least two consecutive positive visits for islet autoantibodies by radiobinding assay (RBA), but did not develop T1D at their last follow-up. The control are individuals who are neither progressors nor non-progressors. The islet autoantibodies included insulin, GAD, IA-2 and ZnT8. The sex and age of the serum sample, as well as HLA-DQB1 genotypes for all participants were summarized in Tables\u00a01 and 2. Serum samples were collected in Tiger top tubes and processed and stored at \u221280\u2009\u00b0C within 45\u2009min of collection. Repeated freezer/thawing cycles were avoided for all samples.\n\nAccess to large quantities of diverse natural glycans remains a challenge in the field of glycobiology and the glycans published in ours and other similar studies represent those simple enough to be synthesized de novo63 or those able to be isolated from a natural source64. Thus, our set of 202 glycans represents the current capability of synthetic and purification chemistry in the field of glycobiology.\n\nAll the glycans with free amino-terminal were sourced from the Consortium for Functional Glycomics (CFG), the laboratory of Dr. Peng Wang at Georgia State University, and the laboratory of Dr. Richard D. Cummings at Harvard Medical School and the National Center for Functional Glycomics. Glycans with 3 or 4 carbon spacer63, glycans with bifunctional fluorescent tag, 2-amino(N-aminoethyl) benzamide (AEAB), and labelled glycans64 with a free amino group were conjugated to fluorescent dye encoded microspheres containing carboxyl (-COOH) groups (Luminex Corp., Austin, Tx, USA). Glycans (2.5\u2009ug) containing free-amino group were covalently linked to the beads by one-step method using 1-Ethyl-3-[3-dimethylaminopropyl] carbo-diimide hydrochloride (10\u2009mg/ml) in deionized water. Conjugation was carried out for 2\u2009h at room temperature with shaking. After conjugation, the beads were collected from unreacted glycans. All unreactive sites were blocked with human serum albumin (1%, w/v) prepared in phosphate buffer saline33.\n\nFor measurement of anti-glycan IgG, human serum samples were diluted 500-fold in 1% BSA in PBS. Briefly, 1000 microspheres for each glycan were added to each well and incubated with 10\u2009\u00b5L of diluted serum sample for 2\u2009h. After 2\u2009h, unbound reagents were removed by vacuum suction and the wells were washed with wash buffer (PBS containing 0.1% Tween-20). Detection was performed by adding biotinylated anti-human IgG (3\u2009\u00b5g/mL in 1% HSA/PBS Southern Biotech, AL, USA) to each well and the plates were incubated for 1\u2009h. After the incubation, the plates were washed and incubated with SAPE (3\u2009\u00b5g/mL in wash buffer) for 30\u2009min. The plates were washed and the beads resuspended in 60\u2009\u00b5L of wash buffer. The median fluorescent intensity (MFI) was captured on FlexMAP 3D reader (Millipore, Billerica, MA, USA) using xPONENT4.3 (v4.3, Luminex Corp, Tx, USA)with the following instrument settings: events/bead: 50, minimum events: 0, flow rate: 60\u2009\u00b5L/min, sample size: 50\u2009\u00b5L and doublet discriminator gate: 8000-13500. Raw data files from Luminex FM3D machine were processed using a software pipeline, which we have developed for quality control, visualization and normalization of raw Luminex data33. No glycan beads (3 bead regions) were included within each well to control for background noise. The average MFI for no glycan beads were then subtracted from the glycan beads to determine anti-glycan antibody positivity.\n\nPolymorphism rs601338, in FUT2 gene, was determined in DNA samples from the participants of PAGODA study using Taqman probe Assay ID C___2405292_10 (Applied Biosystems). The reaction mixture consisted of 2\u00d7 Genotyping master mix (cat#4371353, Applied Biosystems), 20\u2009ng of DNA, and probes, the cycling conditions recommended by the manufacturer.\n\nThe samples analyzed from the PAGODA study were cross-sectional with a random selection of type 1 diabetes patients and controls included. The main advantage of this study was to increase the sample size and therefore the power to detect ACA clusters. However, the baseline characteristics are quite different between cases and controls in this data set in terms of age, sex, HLA genotype, and FDR status. These confounders would affect the identification of biomarkers associated with type 1 diabetes.\n\nBy contrast, the DAISY cohort includes age and sex matched controls but includes a smaller number of individuals. This study is more ideal for identifying biomarkers associated with type 1 diabetes but is underpowered by itself for clustering ACAs. Hence, both studies were combined for ACA clustering, but only DAISY was used to identify ACA clusters associated with T1D.\n\nAll analyses were performed using the R Studio (v2022.07.1 Build 554.pro3) on R language and environment for statistical computing (R version 4.1.2; R Foundation for Statistical Computing; www.r-project.org) and SAS (version 9.4, SAS Institute, Cary, NC). All p values were two sided, a p value <0.05 was considered significant. For Tables\u00a01 and 2, continuous variables were compared using Kruskal\u2013Wallis tests; categorical variables were compared using \u03c72 tests. Linear regression was used to estimate mean anti-glycan antibody levels. Covariates included age, sex, HLA type, and FDR status. ROC curves were visualized using the \u201cpROC\u201d package. Partial r-squared was calculated from the \u201crsq\u201d package. Radar/spider plots were generated using the \u201cfmsb\u201d package.\n\nOur goal is to cluster ACAs into groups based on their profiles in our cohort. However, using the data as is for clustering is limited by the curse of dimensionality both in terms of the number of potential combinations of ACAs and becomes a difficult optimization problem. Thus, our first task is to identify a lower dimension graph of the data for clustering. We selected the K-nearest neighbors algorithm to construct a graph of the high dimensional data. The use of this algorithm to create a faithful topological representation is supported by extensive mathematical work described in the Uniform Manifold Approximation and Projection (UMAP) publication65.Reiminian geometry supports the use of different distance functions for each simplex and Nerve theorem supports that the Cech simplices constructed from the K-nearest neighbors algorithm give a representation of the topology. This is advantageous to matrix factorization based approaches, like PCA, which do not preserve local data structure. The nearest neighbors and minimum distance parameters of the algorithm were selected to balance the trade off between global and local structure preservation.\n\nOur second task is to identify clusters from this graph. While it is possible to cluster based on the UMAP embedding, the 2-dimensional embedding would lose information compared to the nearest neighbors graph since this step applies a force directed graph layout in order to give the two-dimensional representation. Cluster or community detection algorithms are often compared using different measures to determine the optimal algorithm for the specific use case. We used the louvain community detection method66, a greedy algorithm which optimizes the modularity parameter. This method is widely used to cluster single cell sequencing data as well, where there is much sparsity, similar to our ACA dataset.\n\nWe analyzed ACAs in community clusters rather than individual models for ACAs against each glycan since many of the glycans were in functionally similar classes with overlapping structure. Therefore, ACAs against related structures would not be statistically independent from one another. Network analysis provides a stronger approach to identify associations among the ACAs.\n\nThe K-nearest neighbor (KNN) graph for ACAs was constructed for each cohort. The k-nearest neighbor algorithm was implemented from the \u201cumap\u201d package with k\u2009=\u20095 and the cosine metric was used as the distance measure. The graph was then constructed as an igraph object. The KNN graphs for each cohort were then merged. The edge weights unique to each graph were kept as is. For edges where both the PAGODA and DAISY graphs had weights, the product was subtracted from the summation of the weights to calculate the new weight. The Louvain clustering algorithm as implemented in the \u201cigraph\u201d package was applied to identify glycan communities from the merged KNN graph.\n\nGlycan functional classes were provided from the Consortium for Functional Glycomics and Fisher\u2019s exact test was applied to identify glycan classes enriched in the ACA clusters.\n\nLinear regression was implemented with the \u201clm\u201d function in R using the model shown in Model 1.\n\nThe first principal component (FPC) was calculated for each ACA cluster to assign an ACA \u201clevel\u201d for each individual in the DAISY cohort. PCA was implemented using the \u201cPCAtools\u201d package. The ACA clusters were assessed for correlation along the FPC and the pairwise correlation were visualized using the \u201ccorrplot\u201d package. The Spearman correlation was assessed and the correlation heatmap was ordered using hierarchical clustering.\n\nModels to discriminate T1D status were constructed through a binomial model, implemented as a generalized linear model with a logit link function. The likelihood ratio test was applied to compare discrimination between the full (model 2) and null models (model 3).\n\nRandom forest was implemented through the \u201crandomForest\u201d package in R. We calculated the q-values of the calculated AUC values using a permutation test. Specifically, we shuffled the labels of the predictor class labels and trained a full linear model (all clinical variables and the first principal component of all ACA clusters) against these randomized predictors. We repeated this for 10000 iterations and calculated the AUC for each run to establish the null distribution of AUCs in this dataset. The q value was estimated as the one minus the percentile of the model AUC value against the null distribution.\n\nA ridge regression model as implemented in the \u201cglmnet\u201d package is applied with clinical variables and a set number of random glycans, with the number increasing from 1 to 200. Each number of random glycans was repeated for 1000 iterations. See the pseudocode below:\n\nSaturation analysis for T1D status discrimination\n\nInput: glycan1\u2026.glycanN\n\nOutput: AUC (T1D vs Control)\n\nFunction loop for 1, 10, 20 \u2026.200 number of glycans:\n\nCalculate AUC for binomial model (model 4) below\n\nDisease Status ~ Sex\u2009+\u2009First Degree Relative Status\u2009+\u2009HLA Risk\u2009+\u2009Age of Blood Draw\u2009+\u2009Random Glycan 1 \u2026\u2026 +Random number of Glycans \u2026\u2026\u2026\u2026\u2026. (4)\n\nRepeat 1000 times\n\nEnd function\n\nAll code used for data analysis and figure generation are accessible through the github repository (https://github.com/pmtran5884/Glycancc). The code was run on both a Windows 10 and macOS Big Sur 11.6 computer with two independent users. All packages and version numbers used are provided in the\u00a0supplementary information file.\n\nFurther information on research design is available in the\u00a0Nature Research Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The processed clinical and ACA data generated in this study have been deposited on Zenodo under accession https://doi.org/10.5281/zenodo.7143430.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by National Institute of Health (NIH)/ National Cancer Institute (NCI) grant 1 R21 CA199868 and U01CA221242 to J.X.S., P.G.W., R.D.C., and S.P., as well as the P41GM103694 and R24GM137763 to R.D.C. PMHT was supported by NIH/NIDDK fellowship (F30DK121461). Diabetes Autoimmunity Study in the Young (M.R., K.W., and F.D.) is supported by the National Institutes of Health (R01 DK032493 and P30 DK116073) and Helmsley Charitable Trust (G-1901-03687). The funding agencies have no role in data interpretation and publication of the results.",
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+            "section_name": "Author information",
+            "section_text": "Center for Biotechnology and Genomic Medicine, Medical College of Georgia, Augusta University, 1120 15th Street, Augusta, GA, 30912, USA\n\nPaul M. H. Tran,\u00a0Eileen Kim,\u00a0Katherine P. Richardson,\u00a0Lynn K. H. Tran,\u00a0Diane Hopkins,\u00a0Jin-Xiong She\u00a0&\u00a0Sharad Purohit\n\nDepartment of Internal Medicine, Yale School of Medicine, New Haven, CT, CT06510, USA\n\nPaul M. H. Tran\n\nBarbara Davis Center for Diabetes, University of Colorado Denver, Mail Stop A-140, 1775 Aurora Court, Aurora, CO, 80045, USA\n\nFran Dong,\u00a0Kathleen Waugh\u00a0&\u00a0Marian J. Rewers\n\nDepartment of Surgery, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, 02115, USA\n\nRichard D. Cummings\n\nSchool of Medicine, Southern University of Science and Technology, Shenzhen, 518055, Guangdong, China\n\nPeng George Wang\n\nDepartment of Obstetrics and Gynecology, Medical College of Georgia, Augusta University, 1120 15th Street, Augusta, GA, 30912, USA\n\nSharad Purohit\n\nDepartment of Undergraduate Health Professionals, College of Allied Health Sciences Augusta University, 1120 15th Street, Augusta, GA, 30912, USA\n\nSharad Purohit\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\nSearch author on:PubMed\u00a0Google Scholar\n\nP.M.H.T., S.P., J.X.S., P.G.W., and R.D.C. were involved with conception of the project. S.P. developed the glycan array and performed measurement of ACA in serum samples. J.X.S., R.D.C., and P.G.W. synthesized the glycan with linker. P.M.H.T., S.P., E.K., F.D., L.T., and K.P.R. were responsible for data analysis. J.X.S., D.H., K.W., M.R. contributed to clinical samples. All authors contributed to writing and editing of the paper.\n\nCorrespondence to\n                Sharad Purohit.",
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+            "section_text": "Tran, P.M.H., Dong, F., Kim, E. et al. Use of a glycomics array to establish the anti-carbohydrate antibody repertoire in type 1 diabetes.\n                    Nat Commun 13, 6527 (2022). https://doi.org/10.1038/s41467-022-34341-2\n\nDownload citation\n\nReceived: 25 March 2022\n\nAccepted: 24 October 2022\n\nPublished: 01 November 2022\n\nVersion of record: 01 November 2022\n\nDOI: https://doi.org/10.1038/s41467-022-34341-2\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": "Associated content",
+            "section_text": "Collection",
+            "section_image": []
+        }
+    ],
+    "supplementary_files": [
+        {
+            "title": "ACAT1DSuplMaterials4upload.pdf",
+            "link": "https://assets-eu.researchsquare.com/files/rs-1490184/v1/f3d75ceefc677c3da70a8980.pdf"
+        }
+    ]
+}

3bff87d1b34964d77e9b614b539205db568c98abb73c66f53d850637fc2e60a7/metadata.json

@@ -0,0 +1,118 @@
+{
+    "title": "Gate- and flux-tunable sin(2\u03c6) Josephson element with planar-Ge junctions",
+    "pre_title": "Gate- and flux-tunable sin(2\u03c6) Josephson element with proximitized Ge-based junctions",
+    "journal": "Nature Communications",
+    "published": "25 January 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56245-7/MediaObjects/41467_2025_56245_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-56245-7/MediaObjects/41467_2025_56245_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://zenodo.org/records/14169434"
+    ],
+    "code": [],
+    "subject": [
+        "Qubits",
+        "Superconducting devices",
+        "Superconducting properties and materials"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4575413/v1.pdf?c=1737810409000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4575413/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-56245-7.pdf",
+    "preprint_posted": "14 Jul, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as\r\nJosephson junctions with a gate-tunable critical current. Additionally, they can feature a non-\r\nsinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase\r\ndifference, a so-far underutilized property. In this work, we exploit this multi-harmonicity to create a\r\nJosephson circuit element with an almost perfectly \u03c0-periodic CPR, indicative of a largely dominant\r\ncharge-4e supercurrent transport. Such a Josephson element was recently proposed as the basic\r\nbuilding block of a protected superconducting qubit. Here, it is realized using a superconducting\r\nquantum interference device (SQUID) with low-inductance aluminum arms and two nominally\r\nidentical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure\r\nembedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages\r\nand finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve\r\na regime where the sin(2\u03c6) component accounts for more than 95 % of the total supercurrent.\r\nThis result demonstrates a new promising route for the realization of superconducting qubits with\r\nenhanced coherence properties.Physical sciences/Physics/Condensed-matter physics/Superconducting properties and materialsPhysical sciences/Nanoscience and technology/Nanoscale devices/Superconducting devices",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as Josephson junctions with gate-tunable critical current. Additionally, they can feature a non-sinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase difference, a so-far underutilized property. Here we exploit this multi-harmonicity to create a Josephson circuit element with an almost perfectly \u03c0-periodic CPR, indicative of a largely dominant charge-4e supercurrent transport. We realize such a Josephson element, recently proposed as building block of a protected superconducting qubit, using a superconducting quantum interference device (SQUID) with low-inductance aluminum arms and two nominally identical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure embedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages and finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve a regime where the sin\u2061(2\u03c6) component accounts for more than 95% of the total supercurrent. This result demonstrates a new promising route towards parity-protected superconducting qubits.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Quantum information processing requires qubits with long coherence time enabling high-fidelity quantum gates. Over the past two decades, superconducting circuits have led to the realization of quantum processors of ever-growing size made of qubits with steadily improving fidelities1. This way, superconducting qubits have become one of the most advanced physical platforms for quantum computing. Progress has been driven by material engineering and optimization, as well as by the development of new device concepts capable of providing a growing level of protection against noise sources in the environment2,3,4. Qubit protection against relaxation and dephasing processes can be granted from the symmetry properties of the qubit Hamiltonian. In this direction, a variety of possible solutions have been proposed and only partly explored5,6,7,8,9,10,11. One of the leading ideas is to create superconducting qubits whose two lowest energy states are associated with odd and even numbers of Cooper pairs in a superconducting island, respectively. Due to the different parity, these states are orthogonal to each other in both charge and phase space12,13,14,15,16,17,18,19. This type of parity-protected qubit requires a parity-preserving Josephson element that only allows the coherent transfer of correlated pairs of Cooper pairs, which translates into devising a Josephson circuit with a \u03c0-periodic, sin\u2061(2\u03c6) current phase relation (CPR).\n\nSome proposals to engineer such a sin\u2061(2\u03c6) qubits rely on conventional sin\u2061(\u03c6) Josephson junctions, either arranged into large arrays14 or embedded in a superconducting quantum interference device (SQUID) together with extremely large inductances15. The practical realization of these ideas is technologically challenging and some significant experimental progress was reported only recently19. Another approach is to leverage the multi-harmonic CPR and the gate tunability of superconductor(S)\u2013semiconductor(Sm) Josephson field-effect transistors (JoFETs)20,21,22,23,24,25,26,27,28,29. Various signatures of sin\u2061(2\u03c6) Josephson elements were recently reported30,31,32,33,34,35 and harnessed to demonstrate some first experimental evidence of parity protection16. However, a direct measurement of a sin\u2061(2\u03c6) CPR, a precise quantitative evaluation of its harmonic purity including the flux and gate tunability and the influence of the SQUID arm inductance, have been missing so far. These important aspects are addressed in the present work.\n\nOur experimental study takes advantage of a recently developed S\u2013Sm platform based on SiGe/Ge/SiGe quantum-well heterostructures36. Notably, these heterostructures embed a high-mobility two-dimensional hole gas enabling the reproducible top-down fabrication of multi-harmonic, gate-tunable Josephson junctions. We investigate the CPR of a SQUID incorporating two of such junctions, in short a G-SQUID. We demonstrate ample gate and magnetic-flux control of the Josephson harmonic content. By a quantitative analysis based on a fully comprehensive model of our circuit, we show that half a flux quantum through the SQUID results in an unprecedented suppression of the first junction harmonic, which is reduced by two orders of magnitude. Under these conditions, the desired sin\u2061(2\u03c6) (i.e., charge-4e) contribution to the supercurrent flow reaches up to 95.2% of the total supercurrent. This achievement is a significant step forward in the development and optimization of a semiconductor-based parity-protected qubit.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The G-SQUID (shown in Fig.\u00a01a) consists of an aluminum superconducting loop with nearly symmetric arms embedding two nominally identical JoFETs fabricated out of a SiGe/Ge/SiGe quantum-well heterostructure. The compressively strained Ge quantum well lies 22\u2009nm beneath the semiconductor surface and hosts a two-dimensional hole gas exhibiting mobility of 105\u2009cm2/Vs measured at a carrier density of 6\u2009\u00d7\u20091011\u2009cm\u22122. The two JoFETs, JN1 and JN2, have a 1\u2009\u03bcm-wide and a 300\u2009nm-long Ge channel, short enough to be considered as quasi-ballistic junctions (for more details on the JoFETs see Supplementary Note\u00a01). The G-SQUID is embedded in a second larger loop together with a wider reference JoFET, JW, (10\u2009\u03bcm-wide and 300\u2009nm-long Ge channel), enabling a direct CPR measurement20,22,37,38,39,40,41,42. To this purpose, JW is designed to have a critical current much larger than those of JN1 and JN2. The small and large superconducting loops are locally flux-biased by means of two 10\u2009\u03bcm-wide and 50\u2009nm-thick Al lines whose cross-talks have been calibrated in situ and then implicitly compensated throughout the rest of the paper (see Supplementary Note\u00a06).\n\na Schematic and scanning electron micrograph of the device. A Ge-based SQUID (G-SQUID), embedding JoFETs JN1 and JN2, is connected in parallel to a wider JoFET (JW) used as a reference Josephson junction for current-phase-relation (CPR) measurements. The aluminum arms are modeled by three inductances: L1, L2 and LW. b\u2013d Current-biased measurements of the JoFET characteristics for JW, JN1, and JN2, respectively. In each panel, the measured source-drain voltage is plotted as a function of gate voltage, VGi (i\u2009=\u2009W, N1, N2), and source-drain current bias IDC. e (resp. f), Left: critical current, IC, as a function of magnetic flux \u03a61 through the large loop in (a). The reference JoFET JW is biased to strong accumulation (VGW=\u22121.5V), JN2 (resp. JN1) is pinched off and VGN1=\u22120.6V (resp. VGN2=\u22121.5V). The IC oscillations are a direct measurement of JN2 (resp. JN1) CPR. Right: Fast Fourier transform (FFT) of the CPR on the left, calculated over 15 \u03a60. Black dashed line: calculated CPR and FFT based on the circuit model in a with parameters obtained from a fit of the data in Fig.\u00a02a.\n\nFurthermore, we stress that the Al arms have small but non-negligible inductances, mostly of kinetic origin, that we label as L1, L2, and LW. As our later analysis will reveal, properly extracting the intrinsic harmonic content of the JoFET CPRs from the measurements requires taking these inductances into account. In the rest of the paper, all of the calculated curves are obtained using the circuit model shown in Fig.\u00a01a (see Supplementary Note\u00a02 for more details).\n\nAll measurements were performed in a dilution refrigerator at a base temperature of 38\u2009mK, see Supplementary Note\u00a08. A detailed description of the fabrication process and the measurement methods was provided in our previous publications32,43.\n\nTo access the individual DC transport characteristic of a given JoFET in such a parallel configuration, we purposely apply large positive gate voltages (\u22481.5\u2009V) to the other JoFETs, thereby suppressing current flow through their respective arms. The resulting individual characteristics of JW, JN1, and JN2 as a function of their respective gate voltages are shown on the color scale in Fig.\u00a01b\u2013d, with the corresponding circuit measurement schematics displayed in the insets.\n\nFor all the JoFETs, the current at which the device switches from superconducting to normal state, close to the critical current IC, is clearly visible as an abrupt change of the measured source-drain voltage drop from 0 to a finite value. The three JoFETs exhibit a similar behavior denoting consistent properties of the Ge channel and the superconducting contacts. In particular, we note that the two narrow JoFETs, designed to be identical, have very similar ICNi(VGNi) characteristics.\n\nBy varying the magnetic flux, \u03a61, through the larger loop we can sequentially measure the CPR of each JoFET in the G-SQUID. To this aim, the reference JoFET, JW, is biased at full accumulation (VGW=\u22121.5V) such that the necessary condition ICW\u226bICN1,ICN2 is fulfilled37,44. To measure the JN1 (JN2) CPR, we apply VGN1=\u22120.6V (VGN2=\u22121.5V) while JN2 (JN1) is pinched off by setting VGN2=1.5V (VGN1=1.5V). The on-state voltages VGN1=\u22120.6V and VGN2=\u22121.5V are chosen to obtain equal amplitudes of the first CPR harmonic. As we shall see below, operating the G-SQUID at these gate voltages enables the suppression of the first harmonic by flux-induced destructive interference, hence leaving a dominant sin(2\u03c6) component.\n\nThe measured CPRs are shown in Fig.\u00a01e, f together with the respective Fourier transforms. A total of 15 flux periods were measured in order to ensure sufficient resolution of the harmonics in Fourier space. Each reported IC data point represents the median value obtained from 10 measurements, with the light green area indicating \u00a0\u00b11 standard deviation. Both CPRs are clearly skewed and we distinguish up to five harmonics. This multi-harmonicity indicates a high transparency of the superconducting contacts, which is consistent with earlier observations with similar devices30,32. Yet, as we shall discuss below, the higher harmonics, especially the fourth and fifth ones, have largely enhanced amplitudes due to the finite inductance of the aluminum arms.\n\nWith the two JoFETs JN1 and JN2 independently characterized, we now turn to the study of the G-SQUID CPR, once again using JW as a reference (VGW=\u22121.5V). With the ultimate goal to engineer a sin(2\u03c6) Josephson element, we symmetrize the G-SQUID by applying VGN1=\u22120.6V and VGN2=\u22121.5V. These two values have been chosen such that the critical current amplitudes of the two junctions are equal. As it will be shown later, it also implies very similar harmonic contents, corroborating the reproducible electronic properties of our junctions.\n\nFigure\u00a02a shows a measurement of the G-SQUID critical current as a function of \u03a61 and \u03a62, the latter being the magnetic flux through the G-SQUID loop. This is the most important data set.\n\nThe G-SQUID is symmetrized by setting VGN1=\u22121.5V and VGN2=\u22120.6V, which equalizes the amplitudes of the first harmonics in JN1 and JN2. JW is kept in strong accumulation (VGW=\u22121.5V). a Critical current as a function of the two compensated magnetic fluxes, \u03a61 and \u03a62, threading the large superconducting loop and the G-SQUID, respectively. b\u2013d G-SQUID CPR (IC vs \u03a61) for \u03a62\u2009=\u20090, \u00a0\u2212\u03a60/4, and \u00a0\u2212\u03a60/2, i.e., at the line cuts denoted by green lines in (a). e\u2013g The FFTs obtained from the CPRs in (b\u2013d), respectively, are calculated over 15 \u03a60. Black dashed lines in b\u2013g are calculated CPRs (FFTs) based on the circuit model in Fig.\u00a01a with parameters obtained from a fit of the data in a. In d, following a suppression of the odd harmonics (clearly shown in d), we observe the doubling of the CPR frequency as expected for a sin\u2061(2\u03c6) Josephson element.\n\nWe fit the entire two-dimensional plot to the circuit model shown in Fig.\u00a01a, with fixed inductances of the Al arms (see Supplementary Note\u00a01) and 12 free parameters accounting for the amplitudes of the first four harmonics of the three JoFETs (see Supplementary Note\u00a02 for details). Interestingly, the fit yields negligible amplitudes for all the fourth-order harmonics, implying that only three harmonics per JoFET are sufficient to reproduce the data. This outcome apparently contrasts with the experimental data in Fig.\u00a01e, f, where up to five harmonics can be distinguished for both JN1 and JN2. The presence of higher harmonics arises from the finite inductances of the Al arms42,45. We estimate L1\u00a0\u2248\u00a0L2\u00a0\u2248 50\u2009pH (i.e., 20 times smaller than the inductances of JN1 and JN2) and LW\u00a0\u2248 210\u2009pH. Even such relatively small inductances can significantly enhance the harmonic amplitudes. The enhancement becomes proportionally larger as the harmonic order increases42,45. This aspect is fully captured by our circuit model. Indeed, the black dashed lines in Fig.\u00a01e, f are calculated using the parameters extracted from the fit of Fig.\u00a02a. The experimental data are accurately reproduced despite the fact that only three harmonics effectively contribute to the CPR of each JoFET.\n\nIn Fig.\u00a01e, f the arm inductances amplify the 1st, 2nd, and 3rd harmonics of JN1 (JN2) by 7(6)%, 22(30)%, and 250(244)%, respectively, and lead to the emergence of a 4th and a 5th harmonic46. Hence our analysis reveals the importance of including even small contributions of arm inductances in order to avoid a crude overestimation of the harmonic amplitudes. Finally, we remark that arm inductances can also induce a phase shift in the CPR45.\n\nMoreover, we notice that the harmonic content of the two junctions obtained from our analysis is very similar (Supplementary Tab.\u00a01) despite the different gate-voltage dependence of their critical current (Supplementary Fig.\u00a010). This high level of symmetry indicates a good reproducibility of the fabrication process. In addition, we argue that the very large number of channels in our junctions should make the CPR less sensitive to the distribution of transmission coefficients. This can be a clear advantage over junctions based on one-dimensional semiconductor nanowires.\n\nThe magnetic-flux dependence of the G-SQUID CPR for three values of \u03a62 is shown in Fig.\u00a02 together with the Fourier decomposition. At \u03a62\u2009=\u20090 (Fig.\u00a02b, e), we expect the G-SQUID CPR to be the sum of the JN1 and JN2 CPRs shown in Fig.\u00a01e, f. Instead, we observe a CPR containing about ten harmonics. Moreover, all harmonics beyond the first one exhibit amplitudes clearly larger than expected from a simple addition. Fully captured by our circuit model (see dashed lines in Fig.\u00a02b, e), this finding is mostly a consequence of the moderate ratio between the critical current of the reference junction JW and the one of the G-SQUID44, i.e., ICW/ICG\u2212SQUID\u22485 at \u03a62\u2009=\u20090.\n\nAt \u03a62\u2009=\u2009\u2212\u03a60/4 (Fig.\u00a02c, f), JN1 and JN2 are dephased by \u03c0/2, resulting in a destructive interference between even harmonics. The 2nd and 4th harmonics are consequently suppressed while the 1st and 3rd preserve the same amplitude. The resulting CPR is clearly less skewed than at \u03a62\u2009=\u20090. From our model, we conclude that the residual 2nd and 4th harmonics are again due to a moderate ratio ICW/ICSQUID. Increasing the JW critical current by a factor of ten would further suppress the 2nd harmonic by the same factor.\n\nAt \u03a62\u2009=\u2009\u2212\u03a60/2 (Fig.\u00a02d, g), a \u03c0 phase shift induces a destructive interference between the odd harmonics of JN1 and JN2 with a reduction of the G-SQUID critical current. Following the suppression of the 1st and 3rd harmonics, the 2nd harmonic becomes the dominant one resulting in the emergence of a \u03a60/2 flux periodicity in the CPR. In conclusion, at half flux quantum, the G-SQUID behaves as a sin\u2061(2\u03c6) Josephson element.\n\nFigure\u00a02a shows how, in a symmetrized configuration with balanced Josephson junctions, the magnetic flux \u03a62 can profoundly change the harmonic composition of the G-SQUID CPR with singularities at \u03a62\u2009=\u2009\u00b1\u03a60/4 and \u03a62\u2009=\u2009\u00b1\u03a60/2. In order to gain more insight into this magnetic-flux control and to quantify the level of harmonic \u201cdistillation\u201d at the singularity points, we show in Fig.\u00a03a the complete \u03a62 dependence of the first four harmonics. The plotted amplitudes of these harmonics (colored dots) are extracted from Fig.\u00a02a by performing a Fourier transform of the measured IC(\u03a61) at every \u03a62 value. The corresponding uncertainties are represented by \u00a0\u00b11\u03c3-wide colored bands. These uncertainties are significant and visible only when the harmonic amplitudes are below \u00a0~1\u2009nA, which is always the case for the fourth harmonic.\n\na Amplitudes of the first four harmonics in the G-SQUID CPR as a function of \u03a62. The first harmonic vanishes at \u03a60/2, while the second one vanishes at \u03a60/4. b Flux dependence of sin\u2061(2\u03c6) purity, which is defined as the ratio between the amplitude of the second harmonic, A2\u03c6, and the sum of all four harmonic amplitudes, \u03a3nAn\u03c6. The sin\u2061(2\u03c6) purity has a sharp maximum at \u03a60/2 where it reaches 95.2(2.4)%. Inset: close-up around the maximum. Colored bands in a and b represent the \u00a0\u00b1\u00a0\u03c3 standard deviation originating from the experimental uncertainty on the CPR data points. Black dashed lines in a and b represent the harmonic amplitudes calculated from our circuit model using the fit parameters from Fig.\u00a02a.\n\nThe overlaid black dashed lines represent the amplitudes of the first four harmonics calculated using the circuit model of Fig.\u00a01a with model parameters obtained from the fitting of the data in Fig.\u00a02a as previously discussed. The remarkable quantitative agreement over four orders of magnitude confirms the validity of our circuit model.\n\nAt \u03a62\u2009=\u2009\u00b1\u03a60/2, the first and third harmonics exhibit cusp-like dips where their amplitude is suppressed by two orders of magnitude, while the second and fourth harmonics simultaneously attain local maxima. In particular, the amplitude of the second harmonic at \u03a62\u2009=\u2009\u00b1\u03a60/2 is almost identical to the one at \u03a62\u2009=\u20090. We can define a \u201cpurity\u201d level of the sin\u2061(2\u03c6) CPR as the ratio between the second harmonic amplitude, A2\u03c6, and the sum of the four harmonic amplitudes, \u03a3nAn\u03c6. Its flux dependence is displayed in Fig.\u00a03b. At \u03a62\u2009=\u2009\u00b1\u00a0\u03a60/2, we reach a second-harmonic purity of 95.2(2.4)%, largely exceeding the state-of-the-art33,35. We note that such a high purity level was reached owing to the very close electronic properties of the two S\u2013Sm SiGe/Ge junctions in the G-SQUID. We also argue that, with these very same junctions, further circuit optimization should have resulted in an even higher value of the measured purity level. In fact, based on the circuit model of Fig.\u00a01a, our measurement underestimates the purity value due to the relatively small ICW/ICG\u2212SQUID ratio. With a wider reference junction yielding a ten times larger ICW/ICG\u2212SQUID ratio, the same measurement should have given a purity level of 96.3%, much closer to the intrinsic value expected for exactly the same G-SQUID. Additionally, the intrinsic purity level could be increased by acting on other circuit parameters.\n\nTo illustrate that, we begin by noting that our fit of Fig.\u00a02a reveals a slightly imperfect symmetry of the G-SQUID, quantified by a 0.7% discrepancy between the amplitudes of the first harmonics of JN1 and JN2 (see Supplementary Note\u00a02). Reducing this discrepancy to less than 0.14% is, in principle, possible through a fine adjustment of the gate voltages. This would increase the weight of the even harmonics to more than 99%, with the fourth harmonic accounting for a few percent of the total weight. We note that both the second and the fourth harmonics contribute to parity protection since they reflect the simultaneous transport of even numbers of Cooper pairs. As discussed before, the fourth harmonic is essentially absent in the CPR of the individual JoFETs, and it originates from the non-negligible inductance for G-SQUID arms. Based on our circuit model, we estimate that in a properly symmetrized G-SQUID, reducing the arm inductances L1 and L2 from 51 to 46 would largely suppress the fourth harmonic resulting in sin\u2061(2\u03c6) purity above 99%.\n\nFinally, at \u03a62\u2009=\u2009\u00b1\u03a60/4 the contribution of the second harmonic goes down to 2.6(0.1)%. This suppression of the second harmonic could be further pushed below 1% by changing the gate configuration (see Supplementary Note\u00a05).\n\nSo far, we have demonstrated the flux dependence of the harmonic content in the CPR of the symmetrized G-SQUID. We will now address its gate voltage tunability while keeping the flux \u03a61 fixed at \u03a60/2.\n\nIn this experiment, the gate voltage of JN2 is fixed at VGN2=\u22121.5V, while the gate voltage of JN1 is swept. The amplitude of the first harmonic exhibits a strong suppression around VGN1=\u22120.7V (see Fig.\u00a04a), which corresponds to the symmetric condition. (In comparison to Fig.\u00a03, here, this condition is achieved for a slightly different gate-voltage setting, due to a small electrostatic charge reconfiguration that occurred between the two measurement runs, which were taken several weeks apart.) Since the second-harmonic shows only a weak dependence on VGN1, the sin\u2061(2\u03c6) purity attains its maximum at VGN1=\u22120.7V, as shown in Fig.\u00a04b. The maximal purity level is robust against VGN1 deviations of up to 50\u2009mV from the symmetry point. This robustness is largely reduced when operating the JoFETs JN1 and JN2 in a regime of moderate accumulation where their critical current is more sensitive to gate voltage variations (see Supplementary Note\u00a04).\n\na Amplitudes of the first four harmonics in the G-SQUID CPR as a function of VGN1, while VGN2 is fixed at \u22121.5\u2009V and \u03a61 is set to \u03a60/2. The symmetric SQUID regime is reached when VGN2 approaches \u22120.7\u2009V, coinciding with the maximum suppression of the first harmonic. b Gate dependence of the sin\u2061(2\u03c6) purity, defined as the ratio of the second harmonic amplitude, A2\u03c6, to the sum of the amplitudes of all four harmonics, \u03a3nAn\u03c6. The sin\u2061(2\u03c6) purity reaches its maximum near VGN2=\u22120.7V, as shown in the inset. Colored bands in a and b represent the \u00a0\u00b1\u03c3 standard deviation originating from the experimental uncertainty on the CPR data points.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Our study provides important insight to devise practical realizations of parity-protected superconducting qubits based on the demonstrated sin\u2061(2\u03c6) Josephson element16,17. By leveraging a recently developed S\u2013Sm platform based on SiGe/Ge/SiGe heterostructures, we obtained highly symmetric, multi-harmonic Josephson junctions leading to an unprecedented second-harmonic purity as high as 95%. Such a high purity should allow for enhanced protection against charge relaxation protection. We expect an improvement of two orders of magnitudes with respect to the nanowire-based cos\u2061(2\u03c6) qubit reported by Larsen et al.16 or to typical Transmon7 and Fluxonium8 qubits (see Supplementary Note\u00a09).\n\nIn principle, parity protection enhances the qubit lifetime at the cost of rendering the qubit resilient to external control pulses. Therefore, qubit operation would require temporarily exiting the protected regime, e.g., by controlling the ratio between the second and first harmonics. We show here that this ratio can be tuned by a magnetic flux or a gate voltage. A flux shift \u03b4\u03a62\u2009=\u20090.025\u03a60 from \u03a62\u2009=\u2009\u03a60/2 lowers the second-harmonic content from 95% to 60%. In Fig.\u00a04, we show that starting from a symmetric biasing of the G-SQUID, a gate voltage shift \u03b4VG\u2009=\u2009100\u2009mV in one of the two JoFETs lowers the sin\u2061(2\u03c6) purity by about 20%. An even smaller swing, \u03b4VG\u2009=\u200920\u2009mV, would result in a similar purity reduction in a regime of moderate hole accumulation (see Supplementary Fig.\u00a06e).\u00a0Such flux and gate-voltage shifts are experimentally accessible with electrical control pulses on the typical time scale (~10\u2009ns) of single-qubit operations.\n\nBuilding on the S\u2013Sm platform based on the SiGe/Ge/SiGe heterostructure presented in this report, future experimental efforts should integrate the sin\u2061(2\u03c6) element into a circuit quantum electrodynamics (cQED) architecture to investigate its potential parity protection. To achieve this, the challenge posed by the relatively large dielectric losses in the SiGe substrate47,48 could be addressed by fabricating the superconducting microwave circuitry on a separate low-loss chip and subsequently employing flip-chip assembly to connect it with the semiconductor-based Josephson elements49.\n\nIn conclusion, we have reported an experimental realization of a sin\u2061(2\u03c6) Josephson element leveraging the intrinsic multi-harmonicity and gate tunability of SiGe-based JoFETs. The CPRs of these JoFETs can be accurately described by the sum of only three harmonics albeit higher harmonics are measured due to the relatively modest ratio between ICref and ICW. The almost complete suppression of the odd harmonics at half a flux quantum leaves a sin\u2061(2\u03c6) CPR with a remarkably high purity level exceeding 95%. We argued that even higher values beyond 99% could be reached through further circuit optimization. All data analysis was based on a relatively simple but accurate circuit model taking into account the non-sinusoidal CPRs of the JoFETs as well as the inductances of the superconducting arms.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All of the data used to produce the figures in this paper and to support our analysis and conclusions are available at https://zenodo.org/records/14169434. This repository includes the original data, jupyter notebooks for data analysis and figure plotting. Additional data are available upon request to the corresponding author.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work has been supported by the ANR project SUNISIDEuP (ANR-19-CE47-0010), the PEPR projects ROBUSTSUPERQ (ANR-22-PETQ-0003), and PRESQUILE (ANR-22-PETQ-0002), the ERC Grant e-See (Grant No. 758385), and the Grenoble LaBEX LANEF. We thank the PTA (CEA-Grenoble) for the nanofabrication. We thank J. Renard and S. Messelot for discussions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Univ. Grenoble Alpes, CEA, Grenoble INP, IRIG-PHELIQS, 38000, Grenoble, France\n\nAxel Leblanc,\u00a0Chotivut Tangchingchai,\u00a0Elyjah Kiyooka,\u00a0Fr\u00e9d\u00e9ric Gustavo,\u00a0Jean-Luc Thomassin,\u00a0Boris Brun,\u00a0Vivien Schmitt,\u00a0Simon Zihlmann,\u00a0Romain Maurand,\u00a0\u00c9tienne Dumur,\u00a0Silvano De Franceschi\u00a0&\u00a0Fran\u00e7ois Lefloch\n\nInstitut N\u00e9el, CNRS/UGA, Grenoble, 38042, France\n\nZahra Sadre Momtaz\n\nUniv. Grenoble Alpes, CEA, LETI, 38000, Grenoble, France\n\nJean-Michel Hartmann\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\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nA.L. performed the experimental measurements. C.T., Z.S.M., E.K., F.G., and J.-L.T. developed the fabrication recipe. F.G. and J.-L.T. fabricated the device. J.-M.H. designed and grew the semiconductor heterostructure. E.K. characterized the heterostructure. A.L. and E.D. performed the data analysis. A.L., B.B., V.S., S.Z., R.M., E.D., S.D.F., and F.L. wrote the paper with inputs from all co-authors. F.L. and S.D.F. supervised the project.\n\nCorrespondence to\n                Axel Leblanc, Silvano De Franceschi or Fran\u00e7ois Lefloch.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Federico Paolucci, and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional information",
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+            "section_image": []
+        },
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, 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 licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Leblanc, A., Tangchingchai, C., Sadre Momtaz, Z. et al. Gate- and flux-tunable sin(2\u03c6) Josephson element with planar-Ge junctions.\n                    Nat Commun 16, 1010 (2025). https://doi.org/10.1038/s41467-025-56245-7\n\nDownload citation\n\nReceived: 13 June 2024\n\nAccepted: 10 January 2025\n\nPublished: 25 January 2025\n\nVersion of record: 25 January 2025\n\nDOI: https://doi.org/10.1038/s41467-025-56245-7\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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@@ -0,0 +1,157 @@
+{
+    "title": "Ultrafast decoupling of polarization and strain in ferroelectric BaTiO3",
+    "pre_title": "Ultrafast decoupling of polarization and strain in ferroelectric BaTiO3",
+    "journal": "Nature Communications",
+    "published": "26 August 2025",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63045-6/MediaObjects/41467_2025_63045_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63045-6/MediaObjects/41467_2025_63045_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63045-6/MediaObjects/41467_2025_63045_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.22003/XFEL.EU-DATA-003481-00",
+        "https://doi.org/10.6084/m9.figshare.28381727.v2"
+    ],
+    "code": [
+        "https://doi.org/10.24433/CO.9206382.v1"
+    ],
+    "subject": [
+        "Electronic properties and materials",
+        "Ferroelectrics and multiferroics",
+        "Structure of solids and liquids"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-6163672/v1.pdf?c=1756293027000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-6163672/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-63045-6.pdf",
+    "preprint_posted": "24 Mar, 2025",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "A fundamental understanding of the interplay between lattice structure, polarization and electrons is pivotal to the optical control of ferroelectrics. The interaction between light and matter enables the remote and wireless control of the ferroelectric polarization on the picosecond timescale, while inducing strain, i.e., lattice deformation. At equilibrium, the ferroelectric polarization is proportional to the strain, and is typically assumed to be so also out of equilibrium. Decoupling the polarization from the strain would remove the constraint of sample design and provide an effective knob to manipulate the polarization by light. Here, upon an above-bandgap laser excitation of the prototypical ferroelectric BaTiO3, we induce and measure an ultrafast decoupling between polarization and strain that begins within 350 fs, by softening Ti-O bonds via charge transfer, and lasts for several tens of picoseconds. We show that the ferroelectric polarization out of equilibrium is mainly determined by photoexcited electrons, instead of the strain. This excited state could serve as a starting point to achieve stable and reversible polarization switching via THz light. Our results demonstrate a light-induced transient and reversible control of the ferroelectric polarization and offer a pathway to control by light both electric and magnetic degrees of freedom in multiferroics.Physical sciences/Physics/Condensed-matter physics/Ferroelectrics and multiferroicsPhysical sciences/Materials science/Condensed-matter physics/Ferroelectrics and multiferroicsPhysical sciences/Physics/Condensed-matter physics/Structure of solids and liquidsPhysical sciences/Physics/Condensed-matter physics/Electronic properties and materials",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SIBTOXFELNaturePhysics.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "A fundamental understanding of the interplay between lattice structure, polarization and electrons is pivotal to the optical control of ferroelectrics. The interaction between light and matter enables the remote and wireless control of the ferroelectric polarization on the picosecond timescale, while inducing strain, i.e., lattice deformation. At equilibrium, the ferroelectric polarization is proportional to the strain, and is typically assumed to be so also out of equilibrium. Decoupling the polarization from the strain would remove the constraint of sample design and provide an effective knob to manipulate the polarization by light. Here, upon above-bandgap laser excitation of the prototypical ferroelectric BaTiO3, we induce and measure an ultrafast decoupling between polarization and strain that begins within 350\u2009fs, by softening Ti-O bonds via charge transfer, and lasts for several tens of picoseconds. We show that the ferroelectric polarization out of equilibrium is mainly determined by photoexcited electrons, instead of the strain.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Ferroelectric materials are characterized by many properties, including piezoelectricity and pyroelectricity, besides ferroelectricity, which make them attractive for a wide range of applications, such as nonvolatile memories, transistors, sensors, and actuators1,2. The key property of a ferroelectric material is the ability to switch its spontaneous polarization in response to an external electric field. This is typically achieved by a static or pulsed electric field with the consequent limitations given by the need for complex circuitry and switching times of hundreds of picoseconds to nanoseconds3. These challenges can be overcome by optical control of the ferroelectric polarization. Light-matter interaction enables remote and wireless control of the ferroelectric polarization on the picosecond timescale3. Moreover, since all ferroelectrics are also piezoelectrics, the ferroelectric polarization is strongly coupled to the strain, i.e., the lattice deformation4. Optical control of polarization and strain has been achieved in several cases. For example, in multilayers of ferroelectric and electrode thin films, an optical laser was used to excite the metal (or semiconductor) layer and indirectly the ferroelectric material, leading to a transient modification of the strain5,6,7,8, or the polarization by charge redistribution at the interface9. In other studies, light was absorbed directly by the ferroelectric material, inducing changes in the spontaneous polarization10,11 or lattice strain in clamped12,13,14,15,16,17,18 or freestanding19 ferroelectric thin films. THz light was employed to rotate20 or even transiently reverse the orientation of the spontaneous polarization21. In all these studies so far, either the polarization or the strain was measured, and a direct proportionality between spontaneous polarization and strain was typically assumed22. This proportionality is based on the piezoelectric effect, which is well captured by the Landau-Ginzburg-Devonshire theory when the lattice distortion is along the polarization axis23. While this assumption is valid under equilibrium conditions, as demonstrated experimentally, e.g., in refs. 24,25, it may not hold under out-of-equilibrium conditions following light-matter interaction. Decoupling the polarization from the strain would remove the constraint of sample design24,26 or strain tuning27,28 to achieve specific properties, and, at the same time, would provide a more effective and ultrafast knob to manipulate the polarization by light.\n\nTo explore this scenario, we probe the out-of-plane strain and the spontaneous polarization of the prototypical ferroelectric BaTiO3 upon above-bandgap absorption of ultrashort UV light pulses with a peak power intensity of a few tens of GW\u2009cm\u22122 (Fig.\u00a01a). A fundamental understanding of the relationship between strain and ferroelectric polarization out of equilibrium requires their investigation on their natural timescale encompassing\u00a0\u2248\u00a0100\u2009fs to several tens of ps. We employ a combination of time-resolved X-ray diffraction (tr-XRD), time-resolved optical second harmonic generation (tr-SHG), and time-resolved optical reflectivity (tr-refl) to obtain the magnitudes and the separate dynamics of the out-of-plane lattice parameter, the spontaneous polarization, and the photoexcited carrier density, respectively29, with a time resolution of\u00a0\u2248\u00a090\u2009fs. In this paper, we show the mechanisms that govern the structure and polarization changes in a ferroelectric material and their complex relationship out of equilibrium in the presence of photoexcited electrons and lattice deformation. In particular, since the strain wave propagates at the speed of sound, whereas electronic interactions are much faster, we induce and measure an ultrafast decoupling between polarization and strain, which we assign to the photoexcited electrons. First, we present the lattice response to the absorption of UV laser pulses and the corresponding data modeling. Next, we present tr-SHG and tr-refl data. Finally, we bring together all the results and discuss the underlying physical mechanisms in the context of hitherto known phenomena taking place in ferroelectric materials.\n\na Sketch of the BaTiO3 unit cell, the out-of-plane lattice parameter in the ground state c0, the relative displacement \u0394Ti\u2212O of the Ti atom from the center of the O octahedron, the spontaneous ferroelectric polarization Ps, the pump laser at 266\u2009nm, the incident and diffracted XFEL beams. b Selected experimental IXRD(E\u03bd) curves at different time delays t, and the difference \\(\\Delta {I}_{{{\\rm{XRD}}}}={I}_{{{\\rm{XRD}}}}^{2.6{\\,{\\rm{ps}}}}-{I}_{{{\\rm{XRD}}}}^{-14{\\,{\\rm{ps}}}}\\) (gray line). The vertical dashed cyan line marks E\u03bd\u2009=\u20091525\u2009eV. The shaded red area indicates the standard deviation value \\({{\\rm{SD}}}\\approx 0.1\\times {I}_{{{\\rm{XRD}}}}^{19.1\\,{\\rm{ps}}}\\), with similar values also for the diffraction curves at different delays t. For clarity, only the error bar of \\({I}_{{{\\rm{XRD}}}}^{19.1\\,{\\rm{ps}}}\\) is shown. c Delay dependence of \u0394IXRD/IXRD,0\u2009=\u2009[IXRD(t)\u2009\u2212\u2009IXRD,0]/IXRD,0, i.e., the relative change of IXRD(t) at the photon energy E\u03bd\u2009=\u20091525\u2009eV with respect to the equilibrium value at negative delays IXRD,0. The solid cyan line is a guide to the eye. The error bars indicate the standard deviation of the experimental data in a bin size of 300\u2009fs. Inset: sketch of Ti and O octahedron at negative delays (\u0394Ti\u2212O\u2009=\u200914\u2009pm), and at 3.5 ps (\u0394Ti\u2212O\u2009=\u20096\u2009pm). d Average BTO out-of-plane strain \\(\\overline{\\eta }(t)\\) as a function of pump-probe delay t. The error bars follow from the determination of c from IXRD(E\u03bd)\u2009\u00b1\u2009SD. The solid gray line is a fit to the data (Supplementary Note\u00a02). Inset: Modeled contributions to the average strain \\(\\overline{\\eta }(t)\\) due to deformation potential (DP) and thermoelastic (TE) stress (Supplementary Fig.\u00a06).",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-63045-6/MediaObjects/41467_2025_63045_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Our sample consists of a coherently strained, monodomain BaTiO3 (BTO) thin film, grown on a GdScO3 (GSO) substrate, with a SrRuO3 (SRO) bottom electrode sandwiched in between (see \u201cMethods\u201d). Under a compressive strain of\u00a0\u22120.55% imposed by the substrate, the BTO film shows an out-of-plane ferroelectric polarization Ps\u2009=\u2009Psz pointing toward the sample surface (Fig.\u00a01a), where Ps is the magnitude of the polarization and z is the unit vector along the out-of-plane direction. The sample is excited above the BTO band gap Eg\u2009=\u20093.4\u2009eV30 using 266\u2009nm laser pulses, with photon energy E\u2009=\u20094.66\u2009eV, at an incident pump laser fluence of 2.7\u2009mJ\u2009cm\u22122. Time-resolved X-ray diffraction of the (001) Bragg reflection is employed to probe the lattice response of our ferroelectric thin film along the out-of-plane direction. The lattice deformations along the in-plane directions on the picosecond timescale are negligible, given the large ratio between photoexcited area (330\u2009\u00d7\u2009240\u2009\u03bcm2) and BTO film thickness dBTO\u2009=\u200934.5\u2009nm.\n\nWe observe an initial reduction of the tetragonal distortion, which goes hand in hand with lattice compression, then followed by lattice expansion. In particular, Fig.\u00a01b shows the (001) diffraction intensity IXRD of BTO as a function of the photon energy E\u03bd and at different pump-probe delays t from \u00a0\u221214\u2009ps to 32.5\u2009ps. At t\u2009=\u20092.6\u2009ps we observe the following changes to the Bragg peak as compared to the ground state (at t\u2009=\u2009\u221214\u2009ps): a decrease in the diffraction intensity IXRD near the peak center, and a shift to higher photon energy, which implies a decrease in the out-of-plane lattice parameter c, i.e., lattice compression (see gray curve in Fig.\u00a01b). To further explore this initial structural dynamics, we measure the delay dependence of \u0394IXRD/IXRD,0\u2009=\u2009[IXRD(t)\u2009\u2212\u2009IXRD,0]/IXRD,0, which quantifies the relative change of IXRD(t) at the photon energy E\u03bd\u2009=\u20091525\u2009eV of the BTO peak with respect to the equilibrium value IXRD,0 at negative delays. We observe a maximum diffraction intensity drop of\u00a0\u2248\u00a04% at t\u2009=\u20093.5\u2009ps, with up to 99% recovery to the equilibrium value at t\u2009\u2248\u20097\u2009ps (Fig.\u00a01c and Supplementary Fig.\u00a01). We assign the initial 4% drop and recovery in diffraction intensity to the displacements of atoms within the BTO unit cell (inset of Fig.\u00a01c). Specifically, simulations based on the dynamical theory of diffraction31 (Supplementary Fig.\u00a02) exclude the Debye-Waller effect and show that a decrease in the displacement \u0394Ti\u2212O between the Ti atom and the center of the O octahedron by 8 pm can model the measured maximum change in peak diffraction intensity.\n\nWe focus next on the BTO (001) Bragg peak measured at longer time delays (Fig.\u00a01b). We observe that IXRD(E\u03bd) at t\u2009>\u20093\u2009ps are shifted toward lower photon energies, i.e., larger out-of-plane lattice parameters c, with respect to IXRD(E\u03bd) at smaller delays t. This can be clearly seen from the plot of the BTO out-of-plane strain \\(\\overline{\\eta }(t)\\), averaged over dBTO (Fig.\u00a01d). Here, \\(\\overline{\\eta }(t)=[c(t)-{c}_{0}]/{c}_{0}\\), with c(t) and c0 representing the average \\(\\overline{c}\\) at a given t\u2009>\u20090\u2009ps and t\u2009\u2264\u20090\u2009ps, respectively (see \u201cMethods\u201d). In Fig.\u00a01d, we find that: (i) the maximum compression of\u00a0\u22120.024% occurs at t\u2009=\u20092.6\u2009ps, (ii) \\(\\overline{\\eta }(t)\\) increases linearly at a rate of 0.04\u00a0%/ps in the range 4\u2009ps\u2009<\u2009t\u2009<\u200910\u2009ps, and (iii) settles at 0.34% at\u00a0\u2248\u00a020\u2009ps.\n\nThe model fitting \\(\\overline{\\eta }(t)\\) data in Fig.\u00a01d is presented in the following. When a photon with energy E\u2009>\u2009Eg is absorbed in BTO, electrons are photoexcited from the O 2p-derived valence band to the Ti 3d-derived conduction band32,33,34. The thermalization of photoexcited electrons leads to an increase in the electron temperature (Te), and to changes in the electronic system that can be modeled by the variation of the bandgap as a function of the electronic pressure (\u2202Eg/\u2202p)4. In turn, a modified electron system affects the interatomic potential, resulting in atomic motions and contributing to the deformation potential stress \u03c3DP(Te,\u00a0\u2202Eg/\u2202p). Subsequently, photoexcited electrons transfer part of their excess energy (E\u2009\u2212\u2009Eg) to the phonon system via electron-phonon scattering, increasing the phonon temperature (Tp) on the picosecond timescale. This, in turn, induces a lattice expansion dependent on the BTO thermal expansion coefficient (\u03b2), and contributes to the thermoelastic stress \u03c3TE(Tp,\u00a0\u03b2). The total stress4,35\u03c3\u2009=\u2009\u03c1v2\u03b7\u2009+\u2009\u03c3DP\u2009+\u2009\u03c3TE generates a strain wave \u03b7(z,\u00a0t) that propagates through the material of mass density \u03c1 at the longitudinal speed of sound \u03bd. Given the incident peak power intensity of 39\u2009GW\u2009cm\u22122 and other known sample parameters (Supplementary Table\u00a01), we solve analytically the two-temperature model (2TM, Supplementary Note\u00a01) and the lattice strain wave equation (Supplementary Note\u00a02) to obtain the strain \u03b7(z,\u00a0t). The 2TM describes electron and phonon temperatures, Te(z,\u00a0t) and Tp(z,\u00a0t), upon absorption of a laser pulse in our sample, thereby accounting for thermal effects (Supplementary Fig.\u00a03). Finally, we calculate the strain \\(\\overline{\\eta }(t)\\), averaged over dBTO, and obtain an accurate fit of the experimental data in Fig.\u00a01d. A similarly good fit of \\(\\overline{\\eta }(t)\\) data is obtained for incident pump fluence of 1.4\u2009mJ\u2009cm\u22122 (Supplementary Fig.\u00a04). The main outcome of our fit model is a negative \u2202Eg/\u2202p of the order of\u00a0\u2248\u00a010\u22123\u2009eV\u2009GPa\u22121 (Supplementary Table\u00a02), in agreement with first-principles calculations36, with a resulting bandgap decrease of about 3.2\u2009meV (Supplementary Note\u00a03). The negative \u2202Eg/\u2202p causes lattice compression along the out-of-plane direction within the first\u00a0\u2248\u00a03\u2009ps, when the negative \u03c3DP dominates over \u03c3TE (inset of Fig.\u00a01d). Conversely, at larger time delays (t\u2009>\u20093\u2009ps), Tp increases (Supplementary Fig.\u00a05) and the thermoelastic term becomes the dominant one, leading to an increase of the average out-of-plane strain \\(\\overline{\\eta }(t)\\) (Fig.\u00a01d and Supplementary Fig.\u00a06). The calculations of lattice temperature, out-of-plane strain and diffraction curves as a function of delay t and distance z from the BTO surface are reported in Supplementary Note\u00a04. The validity of the model employed to fit the strain \\(\\overline{\\eta }(z,t)\\) data is further corroborated by the good agreement between the experimental BTO (001) diffraction peaks measured at different pump-probe delays t and the corresponding calculated diffraction curves, based on the strain profiles as a function of delay t and distance z from the BTO surface (Supplementary Fig.\u00a07 and Supplementary Fig.\u00a08).\n\nWe turn now to investigating the dynamics of the ferroelectric polarization magnitude Ps and of the photoexcited carriers37,38,39,40,41, upon excitation of the BTO film by the same 266 nm pump laser with fluence 2.7\u2009mJ\u2009cm\u22122. Therefore, we perform tr-SHG experiments29,42 and simultaneously tr-refl in reflection geometry (Fig.\u00a02a). From SHG polarimetry, i.e., the dependence of SHG intensity \\({I}_{{{\\rm{SHG}}}}(\\varphi )\\propto | {\\chi }_{ijk}^{(2)}E{(\\omega )}^{2}{| }^{2}\\) on the polarization angle of the probe beam \u03c6, we learn about the optical tensor elements \\({\\chi }_{ijk}^{(2)}\\) of a material, and thus its symmetry42. By selecting either horizontal (p) or vertical (s) polarization of the SHG beam, we measure \\({I}_{{{\\rm{SHG}}}}^{p}(\\varphi )\\) and \\({I}_{{{\\rm{SHG}}}}^{s}(\\varphi )\\), shown in Fig.\u00a02b, c (blue points) together with the respective fit curves (see \u201cMethods\u201d), which are based on the 4mm point group symmetry with the following nonzero tensor elements: \\({\\chi }_{zxx}^{(2)}\\), \\({\\chi }_{xxz}^{(2)}\\), and \\({\\chi }_{zzz}^{(2)}\\).\n\na Sketch of the tr-SHG and tr-refl setup (see \u201cMethods\u201d). b, c Polar plots of \\({I}_{{{\\rm{SHG}}}}^{p}(\\varphi )\\) and \\({I}_{{{\\rm{SHG}}}}^{s}(\\varphi )\\) measured without pump laser (blue points) and with pump laser at the delay t\u2009=\u20090.35\u2009ps (orange points). The orange and blue solid lines are fit curves to the data resulting from equations (1) and (2). The shaded orange and blue areas refer to the standard deviation of the data and amount to\u00a0\u2248\u00a013%. d Relative change \u0394\u03c7/\u03c70 of the tensor elements \\({\\chi }_{xxz}^{(2)}\\), \\({\\chi }_{zxx}^{(2)}\\), and \\({\\chi }_{zzz}^{(2)}\\) as a function of delay t, and respective fit curves (Supplementary Note\u00a05). \\(\\Delta \\chi /{\\chi }_{0}=({\\chi }_{ijk}^{(2)}-{\\chi }_{ijk,0}^{(2)})/{\\chi }_{ijk,0}^{(2)}\\), where \\({\\chi }_{ijk,0}^{(2)}\\) refers to the tensor element \\({\\chi }_{ijk}^{(2)}\\) at t\u2009\u2264\u20090\u2009ps. The error bars refer to the standard deviation resulting from the fit of the tensor elements. Inset: sketch of Ti atom and O octahedron with the indication of O\u2225 (yellow spheres) and O\u22a5 (red spheres), and the softening of Ti-O\u2225 bonds (dashed olive and cyan lines) with respect to the Ti-O\u22a5 bonds (solid purple lines). e, f Relative change of SHG \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) and reflectivity \u0394R/R0 as a function of the delay t. \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}= [{I}_{{{\\rm{SHG}}}}^{p}(t)-{I}_{{{\\rm{SHG,0}}}}^{p}]/{I}_{{{\\rm{SHG,0}}}}^{p}\\), where \\({I}_{{{\\rm{SHG,0}}}}^{p}\\) refers to the SHG intensity at t\u2009\u2264\u20090\u2009ps. \u0394R/R0\u2009=\u2009[R(t)\u2009\u2212\u2009R0]/R0, where R0 refers to the reflectivity at t\u2009\u2264\u20090\u2009ps. The solid lines are fit curves to the data with fit parameters \u03c40, \u03c41, and \u03c42 reported in the text. The error bar of \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) and \u0394R/R0 data points are\u00a0\u2248\u00a08% and 2%, respectively. Since SHG is a nonlinear process, it is more significantly affected by fluctuations of the 800\u2009nm probe laser intensity of\u00a0\u2248\u00a02%. However, the standard deviation of \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) and \u0394R/R0 at t\u2009<\u20090\u2009ps are 0.6% and 0.06%, respectively.\n\nUpon laser excitation, the 4mm symmetry is preserved (orange points in Fig.\u00a02b, c) and the three tensor elements show similar dynamics (Fig.\u00a02d), characterized by a fast fall time with the maximum drop after\u00a0\u2248\u00a0500\u2009fs and two exponential recovery time constants of\u00a0\u2248\u00a05.5\u2009ps and\u00a0\u2248\u00a045\u2009ps (Supplementary Fig.\u00a09 for \u00a0\u22121\u2009ps\u2009<\u2009t\u2009<\u200930\u2009ps). Interestingly, the tensor elements representative of the induced electric dipole along the out-of-plane direction z (\\({\\chi }_{zxx}^{(2)}\\) and \\({\\chi }_{zzz}^{(2)}\\)) show a nearly identical time dependence and a larger relative change than \\({\\chi }_{xxz}^{(2)}\\), which refers to the in-plane induced electric dipole along the direction x. The difference between \\({\\chi }_{zxx}^{(2)}\\) (or \\({\\chi }_{zzz}^{(2)}\\)) and \\({\\chi }_{xxz}^{(2)}\\) reaches 0.5% after\u00a0\u2248\u00a0500\u2009fs and decreases in a few tens of picoseconds (Supplementary Fig.\u00a09). A purely thermal effect43 would cause a uniform change of all tensor elements \\({\\chi }_{ijk}^{(2)}\\), whereas the measured different dynamics of \\({\\chi }_{ijk}^{(2)}\\) indicates a time-dependent lattice distortion and/or change in the electronic distribution of non-thermal origin. In fact, TD-DFT calculations32,33 show that upon charge transfer, the Ti-O\u2225 bonds between Ti and apical O\u2225 atoms (parallel to Ps) are weakened more than Ti-O\u22a5 bonds between Ti and basal O\u22a5 atoms (perpendicular to Ps), as sketched in the inset of Fig.\u00a02d. Consequently, it is intuitive to expect a larger amplitude of the induced electric dipole along the Ti-O\u2225 direction (z) with respect to the Ti-O\u22a5 direction (in the xy plane), as experimentally demonstrated by our data.\n\nThe proportionality \\({I}_{{{\\rm{SHG}}}}\\propto | {\\chi }_{ijk}^{(2)}{| }^{2}\\propto | {P}_{s}{| }^{2}\\) gives direct access to the magnitude of the spontaneous polarization44. To this end, we measure the relative change \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) as a function of pump-probe delay t (Fig.\u00a02e), with the polarization of the 800 nm probe beam fixed to the maximum of \\({I}_{{{\\rm{SHG}}}}^{p}(\\varphi )\\) at \u03c6\u2009=\u20090\u00b0 (Fig.\u00a02b). Simultaneously, we measure the relative change in reflectivity \u0394R/R0 as a function of pump-probe delay t (Fig.\u00a02f). The data in Fig.\u00a02e [f] are well reproduced by a fit function consisting of the sum of three exponential decay terms, with fall [rise] time \u03c40, and recovery times \u03c41 and \u03c42, convoluted with a Gaussian function representing the experimental temporal resolution (Supplementary Note\u00a05). The initial drop in SHG intensity by 10% within 350\u2009fs is followed by \\({\\tau }_{1}^{{{\\rm{SHG}}}}=7.2\\pm 0.5\\,{\\rm{ps}}\\,\\) and \\({\\tau }_{2}^{{{\\rm{SHG}}}}=200\\pm 140\\,{\\rm{ps}}\\,\\) recovery times, resulting in a 2.3% drop at 40\u2009ps (Fig.\u00a02e). At the same time, we observe a fast increase in reflectivity by 7% within 350\u2009fs, followed by two recovery times, \\({\\tau }_{1}^{R}=5.2\\pm 0.1\\,{\\rm{ps}}\\,\\) and \\({\\tau }_{2}^{R}=29.8\\pm 0.5\\,{\\rm{ps}}\\,\\) (Fig.\u00a02f).\n\nIn both tr-SHG and tr-refl data, the time needed to reach the maximum relative change (\u2248 350\u2009fs) might be due to the thermalization of photoexcited electrons via electron-electron scattering. Subsequently, thermalized electrons, which are higher in the conduction band, move to the bottom of the conduction band, transferring energy to the phonon system, and recombining with holes in the valence band via electron-phonon scattering4,40,45 or radiatively46. These processes are characterized by the recovery times \u03c41 and \u03c42. Both \u03c41 and \u03c42 recovery constants of \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) are larger than those of \u0394R/R0 because the dynamics of the spontaneous polarization (seen by tr-SHG) results from the convolution of the faster dynamics of photoexcited carriers (seen by tr-refl) and the slower dynamics of atoms.\n\nTo interpret the SHG intensity drop and the reflectivity increase, it is useful to express the magnitude of the spontaneous polarization as22,47: Ps(t)\u00a0=\u00a0(1/V)\u2211iqi(t)\u0394zi(t), where V is the volume of the unit cell, qi(t) is the local charge and \u0394zi(t) is the out-of-plane displacement of atom i from the high symmetry position. The above-bandgap photoexcitation transfers electrons from the O 2p-derived valence band to the Ti 3d-derived conduction band of BTO. This charge transfer from O to Ti atoms reduces both the local negative charge at the O site (qO) and the local positive charge at the Ti site (qTi). We attribute the increase in R to the increase in photoexcited carrier density ne38,39,40, which decreases qi, while Ps results from changes in both qi and \u0394zi. This offers the opportunity to manipulate Ps by modifying qi, independently from the atomic displacements \u0394zi. In fact, in our experiments, after 350\u2009fs, before any significant atomic movement can occur, the increase in carrier density ne is responsible for the measured decrease in Ps and increase in R, shown in Fig.\u00a02e, f. This interpretation is corroborated by the increase of the maximum relative change of both \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) (negative, indicating decrease in polarization) and \u0394R/R0 (positive, indicating increase in photoexcited carrier density) with pump fluence (Supplementary Fig.\u00a010 and Supplementary Fig.\u00a011). After a few tens of picoseconds, the longer recovery time of the polarization, as compared to the photoexcited carriers, is due to the contribution of the much slower structural dynamics, affecting \u0394zi, characterized by a recovery time beyond the 40 ps timescale, as seen in Fig.\u00a01d.\n\nAn interpretation of SHG intensity and reflectivity in terms of nonlinear SHG coefficient and electric susceptibility, equivalent to the one discussed above, is reported in Methods. Furthermore, we note that measuring current-voltage (I-V) curves is an alternative tool to measure photocurrents under illumination48,49. These measurements are typically performed under steady-state conditions and require a top electrode. Given the absence of top electrode in our sample, adding it would certainly change the interfacial properties of our sample and influence the measured photogenerated electrons. As an example, it has been shown that the photocurrent may vary by more than 2 orders of magnitude, depending on the top electrode employed50. Furthermore, modifying the top interface would also modify the BTO ferroelectric polarization, at least locally near the surface, and possibly also deeper in the BTO layer, as investigated experimentally11,31,51 and theoretically47. Finally, adding a top electrode would also affect the strain propagation because of the different acoustic reflection coefficient at the BTO surface (Supplementary Table\u00a01). Therefore, we probe the photoexcited carrier dynamics in our sample by tr-refl, as previously done in other works38,39,40, and as typically done in ultrafast measurements29.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-63045-6/MediaObjects/41467_2025_63045_Fig2_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "We present here a unified picture in five stages of the electron, polarization, and lattice dynamics data presented above. Our observations are summarized in Fig.\u00a03a\u2013e, and the physical mechanisms involved are sketched in Fig.\u00a03f\u2013h. Before the arrival of the pump laser, the BTO is characterized by an out-of-plane polarization with given local charges at each atomic site (stage 1, Fig.\u00a03a). Upon absorption of the pump laser at t\u2009=\u20090\u2009ps, electrons move from the occupied O-derived valence band to the unoccupied Ti-derived conduction band (Fig.\u00a03f). Within\u00a0\u2248\u00a0350\u2009fs we observe the maximum increase in the photoexcited carrier density ne, as indicated by the increase in \u0394R/R0. This charge transfer reduces the local charges qi at Ti and O atoms, thereby decreasing the magnitude of the spontaneous polarization Ps, as indicated by the decrease in \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) (stage 2, Fig.\u00a03b). A smaller Ps is also consistent with a larger screening of long-range Coulomb interactions, which favor off-center atomic displacements and thus are responsible for the polar order. This effect is modeled by DFT calculations52,53, showing that an increase in photoexcited carriers in the conduction band of BTO indeed tends to induce a phase transition from the ferroelectric to the paraelectric phase. These theoretical studies52,53 investigated electron doping concentration per formula unit ne/f.u.\u00a0\u2a85 0.2, which corresponds precisely to the ne/f.u. range reached in our experiments (Supplementary Fig.\u00a012). Moreover, TD-DFT calculations32,33 predict that such photoinduced change of BTO electronic structure weakens more significantly Ti-O\u2225 bonds, parallel to Ps, as compared to Ti-O\u22a5 bonds, perpendicular to Ps. We demonstrate this effect experimentally by measuring a larger change of the out-of-plane tensor elements (\u03c7zxx, \u03c7zzz) as compared to the in-plane tensor element (\u03c7xxz). In stage 2, in contrast to the maximum change in carrier density ne and polarization magnitude Ps, the lattice remains unperturbed: this marks the onset of the decoupling between polarization and strain. At these early time delays, the bulk photovoltaic effect (BPVE)12 and the Schottky interface effect11 could potentially play a role, but we explain in the following why they are not dominant in our experiments.\n\nBTO unit cell, projected along the [100] direction, at the following time delays t: t\u2009<\u20090\u2009ps, i.e., ground state (a), 0\u2009ps\u2009<\u2009t\u2009<\u20090.35\u2009ps (b), 0.35\u2009ps\u2009<\u2009t\u2009<\u20093.5\u2009ps (c), 3.5\u2009ps\u2009<\u2009t\u2009<\u200920\u2009ps (d), \u2273 20\u2009ps (e). The distance between the horizontal dashed gray lines indicates the out-of-plane lattice parameter at equilibrium c0 in (a\u2013e). The size of the green and red shaded areas around Ti and O atoms, is proportional to the corresponding positive and negative local charges, respectively. For clarity, the local charge of Ba atoms is omitted. The length of the light blue arrow and the height of the blue shaded area are proportional to the magnitude of the spontaneous polarization Ps. Sketch of BTO valence and conduction band in stage 2 (f), in stages 3 and 4 (g), and in stage 5 (h). The purple vertical arrow indicates the photoexcitation of electrons from the valence to the conduction band upon absorption of a 266 nm laser photon. Eg\u2009=\u20093.4\u2009eV is the bandgap of the ground state, \\({E}_{g}^{{\\prime} }\\) is the bandgap of the excited state, modified by the deformation potential, with \\({E}_{g}^{{\\prime} }-{E}_{g}\\approx - 3.2\\,{\\mbox{meV}}\\,\\) (Supplementary Note\u00a03). The relaxation of the hot electrons to the bottom of the conduction band (green arrows) and the recombination with holes of the valence band (red dashed vertical arrow) induce an increase of Tp. h indicates the minor contribution of the deformation potential, resulting in a bandgap close to Eg, and the residual presence of electrons in the conduction band.\n\nFirst, in photoexcited ferroelectric materials it is common to observe the BPVE, i.e., the generation of photovoltage under light illumination54,55,56. The BPVE occurs under two conditions: the presence of a noncentrosymmetrical crystal and the excitation of nonthermalized electrons54. In our system both conditions are satisfied shortly after t\u2009=\u20090\u2009ps, i.e., before hot electron thermalization takes place (Fig.\u00a03f). In BTO, if the light polarization is perpendicular to the spontaneous polarization Ps, the induced photovoltage is parallel to Ps57,58. This enhances the magnitude of the spontaneous polarization Ps and induces, via the inverse piezoelectric effect, lattice expansion, similarly to what was observed in BiFeO359. However, in our study, although the polarization of the pump laser is perpendicular to Ps (Fig.\u00a02a), within\u00a0\u2248\u00a0350\u2009fs, when electrons are nonthermalized, we see a decrease in Ps (Fig.\u00a02e). Hence, we conclude that, at this early timescale, BPVE is not a dominant effect in our experiments. In fact, this observation can be explained by the wavelength dependence of the BPVE, which shows a maximum when the photon energy is close to Eg, as observed, e.g., in refs. 12,60. In contrast, in BTO at \u03bb\u2009=\u2009266\u2009nm the contribution of BPVE is negligible, as observed in experiments57,58 and calculations55.\n\nSecond, ferroelectric thin films grown on a metal substrate form a Schottky interface, where the electron-hole pairs generated by light absorption are separated by the built-in voltage of the Schottky barrier. The photoexcited carriers are most efficiently separated in the depletion region of width w, where the built-in field exists. At the BTO/SRO interface61 the width of the Schottky interface is w\u00a0\u2248\u00a05\u2009nm, similar to the one of other ferroelectrics, e.g., Pb(Zr0.2Ti0.8)O3/SRO interface11,62. Outside the depletion region, carrier recombination dominates because of the small diffusion length Ld\u2009\u2248\u20092\u2009nm (Supplementary Note\u00a06). Given the transmittance profile of the pump laser beam in our 34.5\u2009nm thick BTO film (Supplementary Note\u00a07 and Supplementary Fig.\u00a013), only\u00a0\u2248\u00a05% of the pulse energy deposited in BTO is absorbed in the depletion region of the Schottky barrier and may contribute to the variation of the polarization11. Therefore, in our case the Schottky interface effect is expected to play a minor role.\n\nIn the 350\u2009fs\u00a0\u2013\u00a03.5\u2009ps delay range (stage 3, Fig.\u00a03c), we observe polarization and strain following opposite trends. In fact, while the displacement between Ti and the center of the O octahedron as well as the strain starts to decrease, Ps starts to increase from its initial light-induced minimum. This is attributed to the start of recombination of photoexcited carriers, suggested by the incipient recovery in \u0394R/R. At this stage, we also observe lattice compression caused by the negative parameter \u2202Eg/\u2202p via the deformation potential. Our observation is in line with theory33,53,63,64 predicting a reduced bandgap Eg due to the presence of photoinduced carrier density, leading to a reduced magnitude of the polarization Ps (Fig.\u00a03g). Moreover, the polarization trend is also consistent with the theoretical prediction65 that photoexcited carriers screen dipole-dipole interaction, thereby reducing the overall polarization Ps and, conversely, the progressive recombination of carriers in the conduction band result in a recovery of the polarization.\n\nIn the 3.5\u00a0\u2212\u00a07 ps delay range (stage 4, Fig.\u00a03d), the relative displacement between Ti and O atoms tends to grow again as it starts to follow the increasing polarization, resulting in an increase of the out-of-plane strain. At the same time, the relaxation of photocarriers to the bottom of the conduction band and their recombination result in a further increase of the local charges, and an energy transfer to the phonon temperature (Fig.\u00a03g), which, in turn, leads to lattice expansion. The latter effects persist up to t\u2009\u2248\u200920\u2009ps.\n\nAt t\u2009\u2248\u200920\u2009ps (stage 5, Fig.\u00a03e), together with a further relaxation of the electronic system toward equilibrium, we observe a saturation of the BTO average strain. This results in a metastable state with a slightly reduced Ps and a significantly increased out-of-plane strain with respect to the ground state. The reduced Ps is attributed to the presence of residual photoexcited carriers in the conduction band (Fig.\u00a03h), while the increased out-of-plane strain is due to the thermoelastic contribution. We exclude the depolarization field screening as the main driving effect for the transient tensile strain seen in our experiments, because it would lead to the typical saturation of the strain with increasing pump fluence66. For example, in PbTiO312 the metastable lattice strain reaches saturation with 266 nm laser fluences of 0.01\u2009mJ\u2009cm\u22122. Conversely, in our study, we employ two orders of magnitude larger pump fluence, with similar laser pulse duration, and still the metastable strain scales approximately linearly with the pump fluence (Fig.\u00a01d and Supplementary Fig.\u00a04). In addition, on the\u00a0\u2248\u00a020\u2009ps timescale, the deformation potential plays a minor role (Supplementary Fig.\u00a06), thus its influence on the bandgap is expected to be marginal. Interestingly, although the out-of-plane lattice parameter is larger than in the ground state (c0), the polarization Ps is still smaller compared to equilibrium. This underscores the persistence of the decoupling between polarization and strain. Quantitatively, we estimate that in stage 5 the contribution of photoexcited electrons to Ps has\u00a0\u2248\u00a010% larger magnitude than the structural contribution from the strain \u03b7 (Supplementary Note\u00a08).\n\nIn summary, we demonstrate that, with an above-bandgap laser excitation, an ultrafast decoupling of spontaneous polarization and strain can be achieved and measured. The key difference to previous studies is that we measure both the polarization and the strain, and thus we are able to observe the ultrafast decoupling of polarization and strain taking place already within 350\u2009fs and lasting at least for several tens of picoseconds. Another important difference to previous reports is that we employ a larger peak power intensity of the pump laser (39\u2009GW\u2009cm\u22122, see Supplementary Note\u00a04) with excitation energy above the bandgap. This is important to excite a sufficient number of electrons from the O 2p-derived valence band to the Ti 3d-derived conduction band, reaching\u00a0\u2248\u00a00.2\u2009e/f.u. (Supplementary Fig.\u00a012), and to induce the change in polarization, as predicted by theory52,53. We assign the ultrafast decoupling of polarization and strain to the dominant contribution of photoexcited electrons in determining the magnitude of the spontaneous polarization when the system is out of equilibrium, and show that for an accurate description and fundamental understanding of a ferroelectric material in a photoexcited state, it is essential to combine multiple techniques that address the dynamical evolution of the various degrees of freedom, i.e., electrons, ferroelectric polarization, and lattice. The decoupling of the polarization from the strain offers the opportunity to change paradigm from strain engineering27,28,67 to light-induced polarization engineering, thereby lifting the constraint of selecting among a limited number of substrates24 or designing freestanding membranes26 to tune the spontaneous polarization. Moreover, by softening the Ti-O\u2225 bonds, we bring BTO to an excited state, where it could be further modified by THz light to achieve stable and reversible polarization switching at lower fluences than otherwise needed when starting from the ground state21. Finally, the transient and reversible control of the spontaneous polarization, shown in this study, offers a pathway to control by light both electric and magnetic degrees of freedom in multiferroic materials.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The epitaxial bilayer BTO/SRO was grown using pulsed laser deposition on a GSO substrate, with (110) orientation according to the orthorhombic notation. The ceramic targets of SRO and BTO were 8 cm away from the substrate and ablated using a KrF excimer laser (\u03bb\u2009=\u2009248\u2009nm, fluence 5.4\u2009J\u2009cm\u22122, 2\u2009Hz repetition rate). The deposition of SRO and BTO layers was conducted in O2 atmosphere with pressure pO2 = 100 mTorr and deposition temperatures of 908 K and 973 K, respectively. Sample cooling with the rate of \\(3\\,{\\rm{K}}\\,{\\min}^{-1}\\) was conducted in the environment of saturated O2 (pO2\u2009=\u2009104\u2009mTorr) to prevent the formation of oxygen vacancies. The thicknesses of BTO and SRO layers, dBTO\u2009=\u200934.5\u2009nm and dSRO\u2009=\u200947\u2009nm are extracted from a \u03b8\u20132\u03b8 scan of the as-grown sample around the (002) reflections (Supplementary Fig.\u00a014), while the GSO substrate is 0.5 mm thick. We performed \u03b8-2\u03b8 scans as a function of sample temperature (Supplementary Fig.\u00a015) to determine the thermal expansion coefficients of BTO above Tc\u2009=\u2009400\u2009\u00b0C, of SRO and GSO in the temperature range 35\u2009\u00b0C\u2009<\u2009T\u2009<\u2009700\u2009\u00b0C. We determine the out-of-plane lattice parameters cBTO\u2009=\u20094.074\u2009\u00c5, cSRO\u2009=\u20093.934\u2009\u00c5, and cGSO\u2009=\u20093.964\u2009\u00c5 by means of the reciprocal space map (RSM) shown in Supplementary Fig.\u00a016. The in-plane lattice parameter a\u2009=\u20093.970\u2009\u00c5, common to BTO, SRO and GSO, indicates that both BTO and SRO thin films are coherently strained to the substrate. The in-plane compressive strain of\u00a0\u22120.55% imposed to BTO by the substrate is calculated by comparing in-plane lattice parameter a with the respective bulk value ab,BTO\u2009=\u20093.992\u2009\u00c568, according to (a\u2009\u2212\u2009ab,BTO)/ab,BTO. The absence of satellite peaks in RSM data (Supplementary Fig.\u00a016) suggests the existence of a BTO monodomain. The single-crystalline nature of the BTO film, with no visible stress or dislocations, is demonstrated by scanning transmission electron microscopy (STEM) data (Supplementary Fig.\u00a017a and Supplementary Note\u00a09). Both SRO/GSO and BTO/SRO interfaces are of high-quality. The former is atomically sharp (Supplementary Fig.\u00a017b), and the latter has steps not exceeding one unit cell with interdiffusion below the detection limit (Supplementary Fig.\u00a017c\u2013g). The single-domain nature of the BTO film is further demonstrated by means of piezoresponse force microscopy (PFM, Supplementary Fig.\u00a018), which provides the spontaneous polarization of the as-grown sample Ps pointing upward (toward the surface). Furthermore, the independence of both SHG polar plots of \\({I}_{{{\\rm{SHG}}}}^{p}(\\varphi )\\) and \\({I}_{{{\\rm{SHG}}}}^{s}(\\varphi )\\) from the azimuthal angle \u03b3 (Fig.\u00a02a) confirms the out-of-plane nature of the spontaneous polarization of our BTO sample, and the absence of a net in-plane component of the polarization (Supplementary Fig.\u00a019).\n\nTime-resolved X-ray diffraction experiments were performed in the X-ray resonant diffraction chamber at the Spectroscopy and Coherent Scattering instrument (SCS) of the European X-Ray Free-Electron Laser Facility (EuXFEL), using an optical laser (OL) as pump and the XFEL as probe. The XFEL pulse pattern consisted of pulse trains at a repetition rate of 10 Hz, with 35 pulses per train at the intratrain repetition rate of 113 kHz. The full width at half maximum (FWHM) of the XFEL spectrum was 11.7\u2009eV. To reduce the energy bandwidth, the XFEL beam was monochromatized using a variable line spacing grating with 50 lines/mm in the first diffraction order and exit slits with a gap of 100\u2009\u03bcm, providing an energy resolution of\u00a0\u2248\u00a0650\u2009meV. The nominal pulse duration of the XFEL pulses was\u00a0\u2248\u00a025\u2009fs, with pulse stretching at the monochromator grating of\u00a0\u2248 10\u2009fs (FWHM). The XFEL pulses, with initial energy of 1.5 mJ per pulse, were then attenuated by transmission through a gas attenuator (GATT), consisting of a volume containing N2 gas at a variable pressure. In order to prevent detector saturation, the transmission of the GATT was set to have\u00a0\u2248\u00a015\u2009nJ per pulse at the sample. The XFEL pulse energy was measured by an X-ray gas monitor detector (XGM), located\u00a0\u2248\u00a07\u2009m upstream of the sample, just before the Kirkpatrick-Baez (KB) mirrors. The latter were used to focus the XFEL beam at the sample to a spot size of \\({w}_{x}^{{{\\rm{XFEL}}}}\\times {w}_{y}^{{{\\rm{XFEL}}}}=140\\,\\times 100\\,\\upmu{\\rm{m}}^{2}\\,\\) (determined by knife edge scans), where w is defined as the distance from the beam axis where the intensity drops to 1/e2 of the value on the beam axis. The angle of incidence (defined from the sample surface) of XFEL and OL beams at the sample was 86\u00b0 and 85\u00b0, respectively. The intensity of each XFEL pulse diffracted by the sample was measured by a Si avalanche photodiode (APD, model SAR3000G1X, Laser Components), converted to a voltage pulse and digitized. To prevent the pump laser intensity from reaching the APD, the latter was equipped with a filter made of 400 nm Ti, deposited on 200 nm polyimide.\n\nThe pump laser had a central wavelength of 266\u2009nm, the same pulse pattern as the XFEL with pulse duration of 70\u2009fs, and beam size \\({w}_{x}^{{{\\rm{OL}}}}\\times {w}_{y}^{{{\\rm{OL}}}}=330\\,\\times 240\\,\\upmu{\\rm{m}}^{2}\\,\\) determined by knife edge scans. The 266 nm pump laser incident on our sample is partially reflected at the BTO surface (18%), it is mostly absorbed in the BTO thin film (70%), and to a smaller extent it is absorbed in the SRO layer (12%), as shown in Supplementary Fig.\u00a013 and explained in Supplementary Note\u00a07. As a result, GSO has no contribution to the optical response of the ferroelectric thin film. The incident pump laser fluence at the sample was 2.7\u2009mJ\u2009cm\u22122, and we verified that diffraction curves IXRD(E\u03bd) measured at negative delays t coincide with those measured without the pump laser (Supplementary Fig.\u00a020). This confirms the reversibility of the pump effect induced by UV laser light. The temporal overlap between XFEL and OL was determined as detailed in Supplementary Fig.\u00a021. The diffracted intensity of the XFEL pulses in a train was averaged and the corresponding time delay of the OL was corrected by the respective bunch arrival monitor (BAM) value (Supplementary Fig.\u00a022), obtaining a time resolution \u0394t\u2009\u2248\u200990\u2009fs (Supplementary Note\u00a010). Data measured with incident pump laser fluence of 1.4\u2009mJ\u2009cm\u22122 are reported in Supplementary Note\u00a02 and Supplementary Note\u00a04.\n\nIn general, two kinds of tr-XRD experiments were performed: photon energy scans at a fixed pump-probe delay t (Fig.\u00a01b and Supplementary Fig.\u00a01), and time delay scans at a fixed photon energy E\u03bd\u2009=\u20091525\u2009eV (Fig.\u00a01c and Supplementary Fig.\u00a021). The energy scans were carried out by a simultaneous movement of the monochromator grating and the undulators gap, such to have always the peak of the XFEL spectrum at the desired photon energy. From the energy scans at different delay t, the out-of-plane lattice parameters c(t) and c0 are calculated as the center-of-mass of the BTO diffraction intensity IXRD(t) and refer to the average c over dBTO (\\(\\overline{c}\\)). Specifically, the BTO average out-of-plane parameters \\(\\overline{c}\\) is calculated from the corresponding (001) Bragg peaks using the Bragg condition \\(\\overline{c}\\)\u2009=\u2009(12400\u2009eV \u00c5)/(\\(2{\\overline{E}}_{\\nu }\\sin \\theta\\)), where \\({\\overline{E}}_{\\nu }\\) is the average of energy values, around the (001) BTO peak, weighted by IXRD(E\u03bd). Energy scans at different pump-probe delays t over the photon energy range covering also GSO (001) and SRO (001) Bragg peaks are reported in Supplementary Fig.\u00a023. The comparison of simulated and experimental diffraction curves before the arrival of the pump laser is reported in Supplementary Fig.\u00a024.\n\nTime-resolved Second Harmonic Generation and time-resolved reflectivity experiments were performed at the SCS instrument of the EuXFEL using the same optical laser employed for tr-XRD experiments and the same pulse pattern. A sketch of the setup is shown in Fig.\u00a02a. The 800 nm probe beam at frequency \u03c9 (red arrow), with electric field E(\u03c9), impinges on the sample at angle \u03b8\u2009=\u200950\u00b0 (defined from the normal to the surface) with polarization defined by the angle \u03c6 and varied by rotating a half waveplate. The angle \u03c6\u2009=\u20090\u00b0 [\u03c6\u2009=\u200990\u00b0] refers to p [s] polarized light. The 266 nm pump beam at frequency 3\u03c9 (purple arrow) impinges on the sample at normal incidence with p polarization. The 800\u2009nm probe beam is then reflected by the sample and a dichroic mirror before reaching a Si photodiode. The latter is used to measure tr-refl of our sample. The 400 nm beam at frequency 2\u03c9 (blue arrow) is the SHG signal generated in the BTO sample (Supplementary Fig.\u00a025). This SHG beam is transmitted through the dichroic mirror and Glan polarizer, which is set to select either the p or s component of the electric field (Ep(2\u03c9) or Es(2\u03c9)), corresponding to the p-out or s-out configuration, respectively. Finally, the SHG beam is filtered by a 400\u2009nm bandpass filter before reaching a photomultiplier (model H10721-210-Y004, Hamamatsu). The azimuthal rotation of the sample around the z axis is defined by the angle \u03b3. Both Si photodiode and photomultiplier measure respectively the reflectivity and SHG signal of each OL pulse in the train. The pulse duration of the 800\u2009nm probe and 266\u2009nm pump beams were \u2248 50\u2009fs and 70\u2009fs, providing a time resolution of\u00a0\u2248\u00a090\u2009fs. The beam sizes of 800\u2009nm and 266\u2009nm beams, determined by knife edge scans, were \\({w}_{x}^{800\\,{\\rm{nm}}\\,}\\times {w}_{y}^{800\\,{\\rm{nm}}\\,}=55\\,\\times 46\\,\\upmu{\\rm{m}}^{2}\\,\\) and \\({w}_{x}^{266\\,{\\rm{nm}}\\,}\\times {w}_{y}^{266\\,{\\rm{nm}}\\,}=165\\,\\times 311\\,\\upmu{\\rm{m}}^{2}\\,\\), respectively. The penetration depths of 800\u2009nm, 400\u2009nm and 266\u2009nm laser beams in BTO are reported in Supplementary Note\u00a07B. While the fluence of the 800 nm probe beam was kept at 1.3\u2009mJ\u2009cm\u22122, the fluence of the 266\u2009nm pump beam was set to 2.7\u2009mJ\u2009cm\u22122 for the data displayed in Fig.\u00a02. tr-SHG and tr-refl data with fluences between 1.4\u2009mJ\u2009cm\u22122 and 12.3\u2009mJ\u2009cm\u22122 are reported in Supplementary Fig.\u00a010 and Supplementary Fig.\u00a011.\n\nIn general, given the incoming electric field with components Ej(\u03c9) and Ek(\u03c9) at frequency \u03c9 along j and k directions, the electric dipole polarization induced in the material at frequency 2\u03c9 along the direction i is \\({P}_{i}(2\\omega )={\\chi }_{ijk}^{(2)}{E}_{j}(\\omega ){E}_{k}(\\omega )\\), where \\({\\chi }_{ijk}^{(2)}\\) is the second-order susceptibility, i.e., a third rank tensor reflecting the symmetry of the material. Each direction i, j, k can be x, or y, or z directions (Fig.\u00a02a). By selecting p or s polarization of the SHG beam, we measure \\({I}_{{{\\rm{SHG}}}}^{p}(\\varphi )\\) or \\({I}_{{{\\rm{SHG}}}}^{s}(\\varphi )\\), which, for a BTO single crystal with 4mm point group symmetry, can be expressed as11,42:\n\nThe resulting ratios of the tensor elements in Fig.\u00a02b, c, \\({\\chi }_{zzz}^{(2)}/{\\chi }_{zxx}^{(2)}=3.7\\) and \\({\\chi }_{zzz}^{(2)}/{\\chi }_{xxz}^{(2)}=6.5\\), reflect a thin film under tensile out-of-plane stress69. The good quality of the fit curves in Fig.\u00a02b, c confirms that our BTO thin film has 4mm point group symmetry. The minor discrepancies between data and fit model might be due to the fact that our BTO thin film is coherently strained to the substrate, and this leads to the appearance of additional minor nonzero tensor elements70.\n\nIn the section \u201cResults\u201d we discuss SHG intensity and reflectivity as proportional to the magnitude of the spontaneous polarization Ps and the photoexcited carrier density ne, respectively. In the following, we show an equivalent interpretation of SHG intensity and reflectivity in terms of nonlinear SHG coefficient and electric susceptibility.\n\nIn general, the material permittivity \u03b5 relates the applied electric field E to the electric displacement field D according to D\u2009=\u2009\u03b5E\u2009=\u2009\u03b50E\u2009+\u2009P, where \u03b50 is the vacuum permittivity and P is the induced electrical polarization. Following the notation in ref. 42, P can be expressed as:\n\nwhere P0 is a time-independent constant polarization. The second term in eq. (3) depends linearly on E(t) and induces electric dipole oscillations at \u03c9, i.e., the same oscillation frequency as the incident electric field of light, thus it is responsible for the optical reflectivity. In eq. (3), \\({\\chi }_{e}={n}_{\\omega }^{2}-1\\) is the electric susceptibility of the material and n\u03c9 is the refractive index at \u03c9. The third term in eq. (3) has a quadratic dependence on E(t) and induces electric dipole oscillation at 2\u03c9, twice the frequency of the incident light, thus it is responsible for the second harmonic generation process. In particular, if we ignore the tensor form, the nonlinear SHG coefficient can be expressed as42:\n\nwhere \\({\\chi }_{e}(2\\omega )={n}_{2\\omega }^{2}-1\\), with n2\u03c9 being the refractive index at 2\u03c9, and A is a structural parameter related to the atomic displacements \u0394zi from the high symmetry positions. In materials with a center of inversion symmetry, A\u2009=\u20090, \u03c7(2)\u2009=\u20090, and the second order term of the induced polarization vanishes. Therefore, tr-SHG measurements are sensitive to both electronic (via \u03c7e(\u03c9) and \u03c7e(2\u03c9)) and structural (via A) changes in the material. At the same time, tr-refl measures changes in the electric susceptibility \u03c7e(\u03c9), which, in our work, result from the photoexcitation of electrons from the O 2p-derived valence band to the Ti 3d-derived conduction band, while structural changes are monitored by tr-XRD. The SHG intensity is proportional to \u2223\u03c7(2)\u22232, and thus to a combination of both electronic and structural contributions. The time-evolution of \\(\\Delta {I}_{{{\\rm{SHG}}}}^{p}/{I}_{{{\\rm{SHG,0}}}}^{p}\\) and \u0394R/R0 (Fig.\u00a02e, f) indicates that \u03c7(2) is mostly determined by the changes in electric susceptibility \u03c7e(\u03c9), and to a smaller extent to the structural changes in A. This is equivalent to say that changes in the magnitude of the spontaneous polarization Ps are mainly determined by the photoexcited electrons and in minor part to the structural dynamics of the lattice, as discussed in the section \u201cPhotoinduced ferroelectric polarization and electron dynamics (Results)\u201d.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "Time-resolved X-ray diffraction raw data recorded at the European XFEL are available at https://doi.org/10.22003/XFEL.EU-DATA-003481-00. The data supporting the findings of the study are available in Figshare at https://doi.org/10.6084/m9.figshare.28381727.v2.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "Codes generated during the current study to fit the time-dependent strain profiles, and simulate the time-dependent strain profiles and X-ray diffraction curves are available at https://doi.org/10.24433/CO.9206382.v1.",
+            "section_image": []
+        },
+        {
+            "section_name": "Change history",
+            "section_text": "In the version of the article initially published, the Data availability section did not include a link to the supporting data as is now available at Figshare, https://doi.org/10.6084/m9.figshare.28381727.v2.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_name": "Acknowledgements",
+            "section_text": "We acknowledge the European XFEL in Schenefeld, Germany, for provision of the XFEL beamtime at the SCS scientific instrument and would like to thank the staff for their assistance. D.P. acknowledges funding from \u2019la Caixa\u2019 Foundation fellowship (ID 100010434) and the Spanish Ministry of Industry, Economy and Competitiveness (MINECO), grant no PID2019-109931GB-I00. The ICN2 is funded by the CERCA programme/Generalitat de Catalunya and by the Severo Ochoa Centres of Excellence Programme, funded by the Spanish Research Agency (AEI, CEX2021-001214-S). E.M.U., D.K., and M.D. acknowledge support from the Zukunftsfonds Steiermark for infrastructure funding (project \u201cASTEM Upgrade\u201d) and from the Wirtschaftskammer Steiermark (WKO Stmk.) for providing additional funds for maintenance. T.C.A. acknowledges funding from the Heisenberg Resonant Inelastic X-ray Scattering (hRIXS) Consortium. The work by G.Merz. was jointly supported by Politecnico di Milano and European X-ray Free Electron Laser Facility GmbH. G.C. acknowledges financial support from the Catalan government (grant number 2021 SGR 0129), and from the Spanish Research Agency (Agencia Estatal de Investigaci\u00f3n), project number PID2023-148673NB-I00. We thank D. Hickin for support with the automation of tr-SHG measurements. We thank A. Reich and J.T. Delitz for the design of mechanical components used in tr-XRD experiments. We are grateful to M. Altarelli for careful reading of the manuscript.",
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+            "section_name": "Funding",
+            "section_text": "Open Access funding enabled and organized by Projekt DEAL.",
+            "section_image": []
+        },
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+            "section_name": "Author information",
+            "section_text": "Zhong Yin\n\nPresent address: International Center for Synchrotron Radiation Innovation Smart (SRIS), Tohoku University, Sendai, Japan\n\nEuropean XFEL, Schenefeld, Germany\n\nLe Phuong Hoang,\u00a0Robert Carley,\u00a0Laurent Mercadier,\u00a0Martin Teichmann,\u00a0Teguh Citra Asmara,\u00a0Giacomo Merzoni,\u00a0Sergii Parchenko,\u00a0Justine Schlappa,\u00a0Zhong Yin,\u00a0Cammille Carinan,\u00a0Andreas Scherz\u00a0&\u00a0Giuseppe Mercurio\n\nMax Planck Institute for the Structure and Dynamics of Matter, Hamburg, Germany\n\nLe Phuong Hoang\n\nInstitute of Experimental and Applied Physics, Kiel University, Kiel, Germany\n\nLe Phuong Hoang\u00a0&\u00a0Kai Rossnagel\n\nCatalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST, Campus UAB, Bellaterra, Spain\n\nDavid Pesquera,\u00a0Saptam Ganguly,\u00a0Jos\u00e9 Manuel Caicedo Roque,\u00a0Jos\u00e9 Santiso\u00a0&\u00a0Gustau Catalan\n\nPhoton Science, Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany\n\nGerard N. Hinsley\u00a0&\u00a0Ivan A. Vartanyants\n\nInstitute of Electron Microscopy and Nanoanalysis (FELMI), Graz University of Technology, Graz, Austria\n\nElena Martina Unterleutner\u00a0&\u00a0Daniel Knez\n\nGraz Centre for Electron Microscopy (ZFE), Graz, Austria\n\nMartina Dienstleder\n\nDipartimento di Fisica, Politecnico di Milano, Milano, Italy\n\nGiacomo Merzoni\n\nDepartment de F\u00edsica, Universitat Aut\u00f2noma de Barcelona, Bellaterra, Spain\n\nIrena Spasojevic\n\nDiamond Light Source Ltd., Didcot, Oxfordshire, UK\n\nTien-Lin Lee\u00a0&\u00a0J\u00f6rg Zegenhagen\n\nRuprecht Haensel Laboratory, Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany\n\nKai Rossnagel\n\nInstitut Catal\u00e0 de Recerca i Estudis Avan\u00e7ats (ICREA), Barcelona, Spain\n\nGustau Catalan\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\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\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\nG.Merc., with input from L.P.H., G.C., I.A.V., J.Z. and T.L.L., conceived the experiments. G.C. and I.S., with input from G.Merc., designed the sample. J.M.C.R. manufactured the sample and D.P. characterized it with \u03b8\u20132\u03b8 scan, RSM and PFM. L.P.H., D.P., G.N.H., R.C., L.M., M.T., S.G., T.C.A., G.Merz., S.P., J.Sc., Z.Y., I.A.V. and G.Merc. performed tr-XRD experiments. C.C. developed an online analysis tool to visualize tr-XRD data in real time. G.Merc. and L.P.H. performed tr-SHG and tr-refl experiments. J.Sa. performed \u03b8\u20132\u03b8 measurements at different sample temperatures. E.M.U. performed STEM measurements with the supervision of D.K., and M.D. prepared the lamella for STEM measurements. L.P.H. and G.Merc. analyzed all the data. L.P.H. modeled tr-XRD and tr-SHG data. G.Merc., A.S., K.R. and I.A.V. supervised the project. G.Merc. wrote the manuscript, drafted by L.P.H., and with input from all authors. All authors provided critical feedback and helped shape the research, analysis and manuscript.\n\nCorrespondence to\n                Giuseppe Mercurio.",
+            "section_image": []
+        },
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+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Yulong Bai, Mengjiao Han, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Hoang, L.P., Pesquera, D., Hinsley, G.N. et al. Ultrafast decoupling of polarization and strain in ferroelectric BaTiO3.\n                    Nat Commun 16, 7966 (2025). https://doi.org/10.1038/s41467-025-63045-6\n\nDownload citation\n\nReceived: 14 March 2025\n\nAccepted: 07 August 2025\n\nPublished: 26 August 2025\n\nVersion of record: 26 August 2025\n\nDOI: https://doi.org/10.1038/s41467-025-63045-6\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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+            ]
+        }
+    ],
+    "supplementary_files": [
+        {
+            "title": "SIBTOXFELNaturePhysics.pdf",
+            "link": "https://assets-eu.researchsquare.com/files/rs-6163672/v1/cce030638162ab6518926314.pdf"
+        }
+    ]
+}

3d66c399a2dbcfa2ece0132fa58c977bdb5645afd48433f18cd6dc1d49d0d239/metadata.json

@@ -0,0 +1,176 @@
+{
+    "title": "Germline functional variants contribute to somatic mutation and outcomes in neuroblastoma",
+    "pre_title": "Germline Functional Variants Contribute to Somatic Mutation and Outcomes in Neuroblastoma",
+    "journal": "Nature Communications",
+    "published": "27 September 2024",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52128-5/MediaObjects/41467_2024_52128_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52128-5/MediaObjects/41467_2024_52128_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description Of Additional Supplementary File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52128-5/MediaObjects/41467_2024_52128_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Data 1\u20134",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52128-5/MediaObjects/41467_2024_52128_MOESM4_ESM.xlsx"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52128-5/MediaObjects/41467_2024_52128_MOESM5_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-024-52128-5/MediaObjects/41467_2024_52128_MOESM6_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://www.ncbi.nlm.nih.gov/sra/PRJNA592880",
+        "https://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000467.v23.p8",
+        "https://gdc.cancer.gov/about-data/publications/PanCanAtlas-Germline-AWG",
+        "https://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?study_id=phs000178.v11.p8",
+        "https://gdc.cancer.gov/about-data/publications/mc3-2017",
+        "http://koreangenome.org/",
+        "http://1000genomes.kr/",
+        "/articles/s41467-024-52128-5#Sec22"
+    ],
+    "code": [
+        "https://github.com/SGIlabes/NBL_Germline/",
+        "https://doi.org/10.5281/zenodo.13324781",
+        "/articles/s41467-024-52128-5#ref-CR63"
+    ],
+    "subject": [
+        "Cancer genetics",
+        "Cancer genomics",
+        "CNS cancer",
+        "Paediatric cancer"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-3037031/v1.pdf?c=1727521518000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-3037031/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-024-52128-5.pdf",
+    "preprint_posted": "27 Jun, 2023",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Germline genetic context may play a significant role in the development and evolution of cancer, particularly in childhood cancers such as neuroblastoma. We studied the role of putatively functional germline variants (pFGVs) in neuroblastoma, even if they do not directly increase disease risk. Our whole-exome sequencing analysis of 125 patients with neuroblastoma revealed a positive correlation between pFGV burden and somatic mutations. Moreover, patients with higher pFGV burdens exhibited worse outcomes. Similar findings were observed in the separate neuroblastoma cohort. However, contrasting results emerged in adult-onset cancer, emphasizing the importance of germline genetics in neuroblastoma. The enrichment of pFGVs in cancer predisposition genes was evident in neuroblastoma compared to that in healthy and adult-onset cancer populations, and their presence had prognostic significance in neuroblastoma. The combination of germline and clinical risk factors improves survival predictions. Our study highlights the importance of germline variants and their potential implications in pediatric cancer.Biological sciences/Cancer/Paediatric cancerBiological sciences/Genetics/Cancer genomics",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "6.supplementarytable14.xlsxSupplementary_Table_1234",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Germline genetic context may play a significant role in the development and evolution of cancer, particularly in childhood cancers such as neuroblastoma. This study investigates the role of putatively functional germline variants in neuroblastoma, even if they do not directly increase disease risk. Our whole-exome sequencing analysis of 125 patients with neuroblastoma reveals a positive correlation between germline variant burden and somatic mutations. Moreover, patients with higher germline variant burden exhibit worse outcomes. Similar findings are observed in the independent neuroblastoma cohort where a higher germline variant burden correlates with a higher somatic mutational burden and a worse overall survival outcome. However, contrasting results emerge in adult-onset cancer, emphasizing the importance of germline genetics in neuroblastoma. The enrichment of putatively functional germline variants in cancer predisposition genes is borderline significant when compared to healthy populations (P\u2009=\u20090.077; Odds Ratio, 1.45; 95% confidence intervals, 0.94\u22122.21) and significantly more pronounced against adult-onset cancers (P\u2009=\u20090.016; Odds Ratio, 2.13; 95% confidence intervals, 1.10\u22123.91). Additionally, the presence of these variants proves to have prognostic significance in neuroblastoma (log-rank P\u2009<\u20090.001), and combining germline with clinical risk factors notably improves survival predictions.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "As individuals age, the risk of accumulating mutations in their DNA increases significantly1,2. This accumulation of mutations is the primary reason that the risk of developing cancer increases over time3,4. However, the causes of childhood cancers such as neuroblastoma (the most common extracranial solid cancer in childhood5) may differ from those of adult-onset cancers6. Instead, inherited germline genetic variants may play a greater role in the development and presentation of tumors, as children have fewer opportunities to accumulate mutations.\n\nConsiderable research into germline genetics in neuroblastomas has revealed fundamental insights into predisposing germline variations. Genome-wide association studies (GWAS) have identified dozens of single-nucleotide polymorphisms associated with neuroblastoma risk7,8,9, while next-generation sequencing studies have reported several rare germline pathogenic variants in cancer predisposition genes (CPGs)10,11,12,13. However, variants identified from GWAS typically have modest effects14, and only a small proportion of patients with neuroblastoma exhibit known pathogenic germline variants in CPGs8,11,15,16. This indicates that most neuroblastomas occurred in the absence of highly penetrant germline variants. Additionally, previous studies have only focused on the predisposition to neuroblastoma associated with germline variants, but have overlooked the possibility that germline variants that do not possess a direct association with elevating the disease risk, could have a significant impact on neuroblastoma biology. Such variants could potentially contribute to the disease either collectively or by interacting with somatic mutations, as evidenced by recent research17,18,19,20.\n\nWe, therefore, hypothesized that putatively functional germline variants (pFGVs) that affect protein function or structure may influence tumor biology in neuroblastoma, even if they do not independently increase the risk of the disease. Furthermore, we anticipated that the degree of contribution to tumor biology would be greater in neuroblastoma than in adult-onset cancer. To explore these hypotheses, we conducted a germline whole-exome sequencing (WES) study of patients with neuroblastoma, focusing on two types of pFGVs: damaging missense and protein-truncating variants (PTVs). We investigated the role of pFGV burden as well as pFGVs in CPGs. To validate our findings in a separate neuroblastoma cohort, we replicated our analysis on WES data from the NCI-Therapeutically Applicable Research to Generate Effective Treatments (TARGET) neuroblastoma cohort6. We also analyzed pFGVs from The Cancer Genome Atlas (TCGA)21 and the Korean Genome Project (Korea1K)22 dataset to compare the roles of pFGVs in neuroblastoma patients to those in adult-onset cancer and healthy individuals.\n\nHerein, we describe the role of germline variants in neuroblastoma beyond their role in the initiation of the disease. In addition, we show the differences in the impact of germline variants on neuroblastoma and adult-onset cancers. Overall, our study highlights the importance of considering the impact of germline variants in neuroblastoma and their potential implications for patient care and management.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We performed WES of germline and somatic DNA from 125 Korean neuroblastoma patients at the Samsung Medical Center (SMC cohort), with 65 cases (52%) classified as high-risk and 60 cases (48%) classified as intermediate or low-risk (Supplementary Table\u00a01). Median age at diagnosis was 3.12 and 49% of the patients were male. Following multiple filtering steps, as depicted in Fig.\u00a01a, we identified a median burden of 41 (range, 27\u221258) pFGVs per patient, of which 24 were PTVs (Fig.\u00a01b). We observed that patients with a higher germline variant burden (above the mean) harbored a higher somatic mutational burden (the total number of nonsynonymous mutations per coding area) (P\u2009=\u20090.018; Fig.\u00a01c), indicating a positive association between the two factors. We also found a statistically significant but weak correlation (Pearson\u2019s r\u2009=\u20090.18; P\u2009=\u20090.041; Fig.\u00a01d) between the germline variant burden and log10-transformed somatic mutational burden across all protein-coding genes. This correlation maintained nominal statistical significance in patients without pFGVs in DNA damage repair (DDR) genes (Pearson\u2019s r\u2009=\u20090.23; P\u2009=\u20090.032; Supplementary Fig.\u00a01a). However, we found no significant correlation between the total number of rare synonymous germline variants and somatic mutational burden (Pearson\u2019s r\u2009=\u2009\u22120.01; P\u2009=\u20090.942; Fig.\u00a01e). These findings persisted when we implemented a down-sampling analysis, addressing potential biases due to the disproportionate volume of synonymous variants in relation to pFGVs (Supplementary Fig.\u00a01b, c).\n\na Flow chart of the pipeline to identify pFGVs. b Box plot of all pFGVs, protein-truncating variants (PTV), and missense pFGVs in all patients (n\u2009=\u2009125). c Box plot of somatic mutational burden compared with high (above mean, n\u2009=\u200966) vs. low germline variant burden (below mean, n\u2009=\u200959). d Correlation between germline variant burden and somatic mutational burden (log-transformed). e Correlation between number of rare synonymous germline variants and somatic mutational burden (log-transformed). Each box plot displays the median value as the center line, the upper and lower box boundaries at the first and third quartiles (25th and 75th percentiles) and the whiskers extend to points within 1.5 times the interquartile range. For all the scatter plots, the r represents Pearson\u2019s correlation coefficient and the black line represents the fitted values from linear regressions, with 95% confidence intervals in gray. All P values are derived from two-sided test. Source data are provided as a Source Data file.\n\nTo validate our findings in an independent cohort, we analyzed germline and somatic exome data from the TARGET dataset. Consistent with our observations in the SMC cohort, we found that patients with a higher germline variant burden (above the mean) also had a significantly higher somatic mutational burden (P\u2009=\u20090.007; Fig.\u00a02a). We also observed a significant correlation between germline variant burden and somatic mutational burden in all TARGET patients (Spearman\u2019s \u03c1\u2009=\u20090.26; P\u2009=\u20090.0001; Fig.\u00a02b). This correlation persisted in patients without pFGVs in DDR genes (Spearman\u2019s \u03c1\u2009=\u20090.33; P\u2009=\u20090.0002; Supplementary Fig.\u00a02a), as well as in analyses that excluded outliers identified using a Z-score threshold of 3 (Spearman\u2019s \u03c1\u2009=\u20090.24; P\u2009=\u20090.0005; Supplementary Fig.\u00a02b).\n\na Box plot of somatic mutational burden comparing high (above mean, n\u2009=\u200964) vs. low (n\u2009=\u2009156) germline variant burden in the TARGET. Boxes represent interquartile ranges with the center line corresponding to the median. The whiskers extend to points within 1.5 times the interquartile range. The statistical analysis was performed using the Wilcoxon rank-sum test. b Correlation between germline variant burden and somatic mutational burden (log-transformed) in the TARGET. c Correlation between germline variant burden and somatic mutational burden (log-transformed) in the TCGA. d Trends in Spearman\u2019s correlation coefficient and confidence intervals between germline variant burden and somatic mutational burden across age groups at diagnosis in the TARGET (white ethnicity, n\u2009=\u2009160) and TCGA (n\u2009=\u20097482). For all the scatter plots, the \u03c1 represents Spearman\u2019s correlation coefficient and the black line represents the fitted values from linear regressions, with 95% confidence intervals in gray. Statistical analysis for (a\u2013c) was performed using two-sided tests. The Jonckheere-Terpstra test for (d) was performed with a one-sided alternative hypothesis (less), indicating a decreasing trend. Source data are provided as a Source Data file.\n\nTo account for potential confounding factors, we employed a multivariable regression analysis. In analysis of the SMC cohort, after adjusting for median sequencing depth in both tumor and germline and the clinical risk, the somatic mutational burden continued to show a significant positive association with germline variant burden (\u03b2\u2009=\u20090.01, P\u2009=\u20090.045). This association was consistent among TARGET neuroblastoma patients, even when adjustments were made for race and median sequencing depth in both tumor and germline (\u03b2\u2009=\u20090.01, P\u2009=\u20090.016). We also investigated whether germline variants have a greater impact on neuroblastoma than adult-onset cancers. We analyzed the TCGA adult-onset solid cancer dataset and found a negligible negative correlation between germline variant burden and somatic mutational burden (Spearman\u2019s \u03c1\u2009=\u2009\u22120.03; P\u2009=\u20090.024; Fig.\u00a02c). However, we observed a different pattern of correlation when we analyzed the data across age groups. For patients with early-onset cancer (age at diagnosis <50 years), we found a very weak but positive association between germline variant burden and somatic mutational burden (Spearman\u2019s \u03c1\u2009=\u20090.08; P\u2009=\u20090.002; Supplementary Fig.\u00a02c), whereas for patients diagnosed at an older age (age at diagnosis \u226550 years), a very weak negative correlation was observed (Spearman\u2019s \u03c1\u2009=\u2009\u22120.06; P\u2009<\u20090.00001; Supplementary Fig.\u00a02d). Finally, we analyzed the association between germline variant burden and somatic mutational burden across all age groups at diagnosis. This analysis included patients with neuroblastoma from the white ethnicity subgroup within the TARGET cohort. Interestingly, we observed a decreasing trend in the correlation coefficient between germline variant burden and somatic mutational burden (Jonckheere-Terpstra test, P\u2009=\u20090.0006; Fig.\u00a02d).\n\nWhile no significant association was found between germline variant burden and any known clinical risk factors for neuroblastoma (Supplementary Fig.\u00a03), patients with a higher germline variant burden (above the mean) had a poorer progression-free survival (PFS) (Fig.\u00a03a; log-rank P\u2009=\u20090.018) but not reduced overall survival (OS) (Fig.\u00a03b; log-rank P\u2009=\u20090.455) in our SMC cohort. The clinical significance of germline variant burden persisted even after adjusting for age, stage, and MYCN status using a multivariable Cox model (adjusted HR, 2.78; 95% CI, 1.19\u22126.51; P\u2009=\u20090.018). In the TARGET cohort, patients with a higher germline variant burden (above the mean) had poorer OS than those with a lower germline variant burden (log-rank P\u2009=\u20090.005; Fig.\u00a03c). After adjusting for ethnicity and MYCN status, the impact of a higher germline variant burden remained statistically significant (adjusted hazard ratio [HR], 1.70; 95% CI, 1.19\u22122.42; P\u2009=\u20090.003). However, there was no prognostic significance according to germline variant burden in the TCGA cohort (log-rank P\u2009=\u20090.643; Fig.\u00a03d).\n\na Progression-free survival (PFS) for the patients in the SMC cohort. b Overall survival (OS) for the patients in the SMC cohort. c OS for patients in the TARGET cohort. d OS for patients in the TCGA cohort. Source data are provided as a Source Data file.\n\nTo prioritize genes with the greatest biological impact, we focused on 109 CPGs listed in the Cancer Gene Census (CGC) from the Catalogue Of Somatic Mutations In Cancer (COSMIC) database23 (Supplementary Data\u00a01). In this analysis, we considered the role of each gene in cancer development, specifically targeting only missense variants of oncogenes, while examining all pFGVs in tumor suppressor genes (TSGs). In our SMC cohort, we identified 45 pFGVs and 31 affected CPGs in 39 of 125 patients (31%) (Fig.\u00a04) (Supplementary Data\u00a02). In the TARGET cohort, 97 pFGVs were identified in 79 patients (36%) (Supplementary Data\u00a03). To determine whether pFGVs in CPGs were enriched in neuroblastoma compared with the general population and adult-onset cancers, we compared the prevalence of pFGVs in CPGs across cohorts while considering ethnicities. Our analysis revealed that pFGVs in CPGs were enriched in neuroblastoma in both the SMC and TARGET cohorts compared to healthy individuals (KOREA1K) and patients with adult-onset cancers (TCGA), respectively. In the SMC cohort, we observed a trend towards significance (P\u2009=\u20090.077; Odds Ratio, 1.45; 95% CI, 0.94\u22122.21) compared to KOREA1K, while in the TARGET cohort, we found a statistically significant difference (P\u2009=\u20090.027; Odds Ratio, 1.46; 95% CI, 1.04\u22122.05) compared to the TCGA cohort. Moreover, we observed a significant decreasing trend in the prevalence of pFGVs in CPGs across age in the TCGA cohort (Cochran\u2013Armitage test for trend P\u2009=\u20090.00007; Supplementary Fig.\u00a04). However, it was important to note that when refining our analysis based on the American College Medical Genetics (ACMG) guidelines for clinical interpretation24, which focuses sole on pathogenic or likely pathogenic (P/LP) variants in CPGs, there was a pronounced enrichment of these variants in neuroblastoma within the SMC cohort compared to the general population (P\u2009=\u20090.016; Odds Ratio, 2.13; 95% CI, 1.10\u22123.91).\n\nOncoprint of pFGVs in cancer predisposition genes (CPGs). The frequencies of pFGVs in CPGs are displayed as horizontal barplots (right). Source data are provided as a Source Data file.\n\nNext, we investigated whether pFGVs in CPGs were associated with clinical factors and outcomes. pFGVs in CPGs were not associated with known clinical risk factors (Supplementary Table\u00a02); however, we found that patients with pFGVs in CPGs had a higher incidence of family history of cancer in at least one second-degree relative (\u03c72(1)\u2009=\u20093.99; P\u2009=\u20090.046; Odds Ratio\u2009=\u20092.93; 95% CI, 1.00\u22128.61). Additionally,\u00a0we found that pFGVs in CPGs may be potential risk factors, as they were associated with worse PFS (log-rank P\u2009=\u20090.00058; Fig.\u00a05a) and OS (log-rank P\u2009=\u20090.025; Fig.\u00a05b). We also analyzed the prognostic impact of other cancer-relevant genes (not CPGs), which are classified as either TSG or oncogenes in CGC (n\u2009=\u2009565). However, no additional prognostic impact was observed for the other cancer-relevant genes (Supplementary Fig.\u00a05). When we considered only P/LP variants according to the ACMG guidelines, a more pronounced distinction was observed in the family history of cancer between patients harboring P/LP variants in CPGs and those without such variants (\u03c72(1)\u2009=\u20095.18; P\u2009=\u20090.023; Odds Ratio = 5.42; 95% CI, 1.11\u221226.52). However, the survival differences in survival outcomes were significantly only for only OS (log-rank P\u2009=\u20090.009; Supplementary Fig.\u00a06a), and not for PFS (log-rank P\u2009=\u20090.308; Supplementary Fig.\u00a06b). Univariable Cox proportional-hazards analysis revealed that MYCN status, germline variant burden, and pFGVs in CPGs were associated with the risk of progression or relapse (Supplementary Fig.\u00a07). Multivariable Cox proportional-hazards analysis showed that the presence of pFGVs in CPGs was independently associated with risk of progression or relapse, even after adjusting for age, stage, MYCN status, risk, and germline variant burden (adjusted HR, 2.91; 95% CI, 1.35\u22126.28; P\u2009=\u20090.006; Fig.\u00a05c). Interestingly, even after excluding patients with pFGVs in CPGs, there was still a significant prognostic impact of the germline variant burden (PFS; log-rank P\u2009=\u20090.013; Fig.\u00a05d). In the TARGET cohort, which consisted of patients aged >18 months, stage 4, and high-risk, a similar trend was observed, although the survival difference was not statistically significant when evaluating the presence of pFGVs in CPGs (OS, log-rank P\u2009=\u20090.191). However, in the subgroup analysis of the TARGET cohort, there was a significant difference in OS in patients without MYCN amplification based on the presence of pFGVs in CPGs (log-rank P\u2009=\u20090.016 and 0.414 for patients without and with MYCN amplification, respectively; Fig.\u00a06a, b). These results were also consistent in the SMC cohort with nominal statistical significance (Fig.\u00a06c, d). When assessing pathogenicity as per the ACMG guidelines, the TARGET cohort displayed significant differences in OS log-rank (P\u2009=\u20090.025). However, in the TCGA adult-onset cancer cohort, we observed the opposite trend, with no statistical significance in OS, as expected (log-rank P\u2009=\u20090.119).\n\na Kaplan\u2013Meier survival curves for progression-free survival (PFS). b Kaplan\u2013Meier survival curves for overall survival (OS). c Forest plot of Cox multivariable regression analysis for PFS. d Kaplan\u2013Meier survival curves for PFS in patients without pFGVs in cancer predisposition genes (CPGs) according to germline variant burden. All P values are two-sided without correction for multiple comparisons. Source data are provided as a Source Data file.\n\na Overall survival (OS) for patients without MYCN amplification (TARGET cohort). b OS for patients with MYCN amplification (TARGET cohort). c OS for patients without MYCN amplification (SMC cohort). d OS for patients with MYCN amplification (SMC cohort). Source data are provided as a Source Data file.\n\nAs both the burden and presence of affected CPGs were independent risk factors for PFS, we investigated whether germline risk factors (high germline variant burden and presence of pFGVs in CPGs) provide additional benefits for stratifying patients with neuroblastoma. Therefore, we obtained the C-index distribution of clinical risk stratification in the development and internal validation groups using the bootstrap method. In the development group, the combination of germline risk factors and clinical risk factors (age, stage, MYCN status) demonstrated better discrimination power than clinical risk factors alone (mean C-index; 0.85 vs. 0.77, P\u2009<\u20090.00001 after Bonferroni correction; Fig.\u00a07a). This finding was confirmed in the internal validation group (0.86 vs. 0.77; P\u2009<\u20090.00001 after Bonferroni correction; Fig.\u00a07b).\n\na Training group. b Internal validation group. The box plots represent the C-index values calculated from 500 bootstrap samples, with a 6:4 training to validation split for each iteration. For all the box plots, the central line represents the median value, the top and bottom of the box represent the 25th and 75th percentiles, and the whiskers extend to points within 1.5 times the interquartile range. All P values are two-sided t-test results with Bonferroni correction for multiple comparisons. Source data are provided as a Source Data file.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Cancer genomics research in pediatric patients has focused on the discovery of somatic drivers of tumorigenesis6,13,25,26, and has revealed that pediatric cancers, including neuroblastoma, have few somatic mutations. However, it is becoming increasingly clear that germline variants, inherent to each patient\u2019s genetic makeup, can significantly shape tumor characteristics. Mounting evidence underscores the significance of germline variants, extending beyond cancer susceptibility to influence tumor progression and phenotype8,15,17,18,19,20,27,28,29,30,31,32. Our work builds on this foundation, focusing on the comprehensive analysis of rare germline variants and their broader implication in tumor biology and patient outcomes. In the present study, we comprehensively analyzed the role of rare, potentially harmful germline variants in patients to gain a holistic understanding of their influence.\n\nIt is widely recognized that the tumor mutational burden correlates with age at diagnosis33,34. This is because, as individuals age, environmental mutagens and mutations in DNA repair genes accumulate, which can lead to cancer development33,34. However, childhood cancers arise from different processes21. Our findings suggest that the burden of pFGVs affects somatic mutagenesis in neuroblastoma as well as in young adult-onset cancer patients. These results were consistent even in patients without pFGVs in DDR genes. In addition, we observed that the degree to which germline variants contributed to somatic mutation decreased over the course of their lifetimes. These findings are particularly noteworthy because previous studies on germline variant burden have only been conducted in adult-onset cancer and have not identified a reverse association between early-onset and late-onset cancer. Furthermore, while many studies have identified a personal germline variant burden in specific or manually curated gene lists17,19,30, we avoided potential biases by refraining from selecting specific genes for analysis. Finally, we also demonstrated that germline variant burden contributes not only to somatic mutations but also to neuroblastoma survival outcomes, which represents a significant finding.\n\nQing et al.19 have clearly described the association between germline variants and somatic mutations in adult-onset solid cancer, whereas our variant filtering process differed from theirs. In our analysis, we opted for the REVEL35 method, which has demonstrated superior performance in comparison to MetaSVM36, employed by Qing et al. Additionally, we further refined our selection by excluding variants that were present in more than 10% of each cohort, aiming to minimize false positives. Consequently, our findings present a narrower range of variants, with no more than 203 variants per patient in the TCGA cohort, in contrast to the 79\u2212239 variant range reported in Qing\u2019s study. Another difference is our study\u2019s focus on pediatric patients and the inclusion of a wide array of genomic data, not limited to cancer-specific genes. This likely accounts for the observed weaker correlation between germline variants and somatic mutations compared to the associations reported by Qing et al.\n\nWe also investigated the prevalence and clinical relevance of germline variants in CPGs. The study by Kim et al., which includes analyses from the TARGET dataset that our research also examines, highlights the prevalence and potential prognostic implications of P/LP variants in CPGs29. However, it is important to recognize that our understanding of the role of these variants across a broader patient population remains limited. Additionally, most patients were predominantly of European ancestry, limiting their representativeness. Our study was designed to provide a comprehensive landscape of pFGVs in CPGs and explore the role of these variants in neuroblastoma, regardless of confirmed pathogenicity. We identified deleterious germline variants in CPGs of a substantial proportion of patients with neuroblastoma. We also demonstrated that using all pFGVs in CPGs was effective in predicting disease progression in a cohort of unselected patients (the SMC cohort). Importantly, we also observed that germline variant burden had a prognostic impact in patients without pFGVs in CPGs. This suggests that even pFGVs in nondefinitive CPGs may have a biological impact on neuroblastomas. Furthermore, we showed that pFGVs in CPGs serve as critical determinants of OS in patients without the strongest somatic driver alterations (MYCN amplification) in the both SMC and TARGET cohorts. Overall, our study may expand the definition of pathogenicity and highlights the significance of the identified pFGVs.\n\nNeuroblastoma treatment strategies have considerably evolved over time, reflecting advances in medical research and clinical practice. It is essential to contextualize our findings within the treatment era of the patient cohorts studied. The TARGET cohort, comprising exclusively high-risk patients, experienced a wide variety of high-risk treatment protocols. These included different induction regimens37, the use of high-dose chemotherapy38, variations in both the chemotherapy regimens39 and the number of high-dose chemotherapy cycles40, adjustments in radiation therapy doses41, and the introduction of anti-GD2 maintenance therapy42,43. In contrast, the SMC cohort, which included patients from all clinical risk groups, could not utilize anti-GD2 therapy. Instead, for high-risk patients, it adopted the implementation of intensified tandem high-dose chemotherapy and high-dose MIBG treatment44,45. Despite these differences and changes in treatment paradigms, the prognostic value of germline variants remains evident.\n\nHowever, our study has several limitations. First, we could not determine how the burden of germline variants affected somatic mutations. The association signals between germline variant burden and somatic mutation burden were weak, and it is important to note that it is unlikely that all the disruptions in protein-coding genes are equally important on somatic mutations. Furthermore, our control cohorts were not subjected to the same experimental conditions or variant calling processes as the case cohorts, as they relied on pre-processed variant data. This introduces a layer of complexity that might affect the comparability of our findings. The total count of germline variants and the identification of pFGVs in CPGs identified could have been affected by the specific experimental design and variant filtering processes, which varied across cohorts. Consequently, interpretations of the germline variant burden and the presence of pFGVs in CPGs should be approached with caution at an individual level, and this variance in methodology complicates direct comparisons between cohorts. Third, the lack of functional data on pFGVs hindered our ability to annotate and predict the effects of these variants on proteins, Additionally, the absence of analysis of parents\u2019 data precluded us from determining the origin of the identified pFGVs. Finally, our pFGVs cannot supplant or diminish the importance of P/LP variants as defined by the ACMG. This is because a family history of cancer, enrichment, and some observed survival differences are more pronounced when adhering strictly to P/LP classifications compared to pFGVs.\n\nDespite these limitations, this study has several important clinical implications. We showed that differences in somatic aberrations and outcomes between tumors could be partially explained by collectively considering a patient\u2019s germline variants. This suggests that a larger number of germline variants may affect somatic mutations and outcomes in neuroblastoma, which differs from observations in adult-onset cancers. Additionally, we have broadened our understanding of pathogenic variants in CPGs, encompassing aspects beyond disease predisposition. Our study highlights the feasibility of incorporating germline risk factors into the clinical risk assessment of patients with neuroblastoma, as these germline risk factors were independent of known clinical risk factors and had an impact on patient outcomes. Our approach of using WES to investigate a broader range of pFGVs in patients with neuroblastoma may be generalizable to patients with other pediatric cancers and could have a broad impact.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "This study adheres to all applicable ethical regulations. The Samsung Medical Center Institutional Review Board approved the study (IRB No. 2015-11-053-014). Written informed consent for germline and tumor sequencing, as well as for the review of medical records for demographic, clinical, and pathological information, was obtained from the parents or legal guardians of all patients. Participants were not compensated, as their participation did not incur any additional costs. The study design did not take sex and gender into account.\n\nWe analyzed blood and tissue DNA from 125 neuroblastoma patients diagnosed between 2012 and 2021, initially identifying 145 patients with peripheral neuroblastoma tumors. After excluding ganglioneuroma cases (n\u2009=\u20096), tumors obtained post-relapse (n\u2009=\u20099), patients with unmatched DNA pairs confirmed by NGSCheckMate546 (n\u2009=\u20091), and non-primary site tumors (n\u2009=\u20094), our analysis focused on the remaining 125 cases. Most patients (82%) underwent prospective clinical sequencing. However, 23 patients (18%) were also included in this study using samples deposited at the SMC BioBank. This study included high-risk patients (n\u2009=\u200954) enrolled in the NB-2014 clinical trial (NCT02771743) designed to evaluate the potential benefits of response-adapted strategies in consolidation therapy. The trial design and clinical trial protocol have been previously documented47. The clinical outcomes were reported according to the trial\u2019s objectives, including OS, PFS, and adverse events. In this analysis, we incorporated extended follow-up and survival data, which differs from the original trial that initiated follow-up after the induction period, as the original trial focused on the effects of consolidation treatment. Here, we calculated survival time starting from the time of diagnosis. Consequently, the outcome analysis used here includes non-prespecified exploratory outcomes for the NB-2014. These analyses, though not originally included in the NB-2014 trial specifications, were crucial for identifying the significance of germline variants. Genomic sequencing was performed on tumor and normal DNA extracted from fresh frozen (74%) or formalin-fixed paraffin-embedded tissues (26%) and mononuclear cells from peripheral blood, respectively, using a QIAamp DNA Mini Kit (Qiagen, Valencia, CA, USA). Tumor and matched DNA were enriched for exon regions using the SureSelectXT Human All Exon V5 kit (Agilent Technologies Inc., Santa Clara, CA, USA). All tumor specimens were reviewed by a pathologist to determine the percentage of viable tumors and their adequacy for sequencing. Patient samples were sequenced with pair-end 100-bp reads using the Illumina HiSeq 2500 platform (Illumina, Technologies Inc., San Diego, CA, USA). This study included only tumors obtained from the primary site.\n\nIllumina WES data were mapped to hg19 using Burrows-Wheeler Aligner (BWA)48 v0.7.17. Picard v2.17.5 (http://broadinstitute.github.io/picard/) and the genome analysis toolkit (GATK)49 v 4.0.2 was used for indel realignment, duplicate removal, and base- and quality-score recalibration. HaplotypeCaller in GATK was used for variant calling of SNVs and short indels. We removed variants with low quality (genotype quality-score <50) or inadequate read coverage (<10\u00d7), variants with a variant allele frequency (VAF) less than 30%, and variants commonly observed in healthy populations (>1% in ExAC50 or >1% KRGDB110051). The functional impact of missense germline variants was predicted using the REVEL score and annotated using the ClinVar52 (03-20-2022) database when available. We considered a missense variant to have a high functional impact if the REVEL score35 was \u22650.7 or listed as P/LP in ClinVar. PTVs, including frameshift indels, stop gain, stop loss, and splice-site variants, were also considered as pFGVs. Variants annotated as benign or likely benign in ClinVar were excluded. The deleterious variant burden in a sample was calculated as the total number of pFGVs in the coding regions. To remove platform-related artifacts, variants commonly observed (>10%) in the entire SMC cohort were also removed. Rare synonymous variants were defined as synonymous variants with an allele frequency <1% in the ExAC and KRGDB100 databases and as well as occurring in <10% of the cohort. The same QC filters were applied to both pFGVs and rare synonymous variants.\n\nWe obtained FASTQ files for germline and tumor samples from 222 patients using data from the Database of Genotypes and Phenotypes (dbGaP), accession phs000218.v24.p8 via the SRA Toolkit. We only retained individuals whose tumor sequencing was carried out on primary rather than metastatic tumors (220 patients). We then applied our variant calling pipeline to convert TARGET-NBL FASTQ files into a variant calling format (VCF) using the same methodology employed for our SMC cohort. The variants were then pre-filtered using previously reported QC steps29 for the TARGET data. We only retained variants with a read-depth coverage of at least 15 and a VAF of at least 0.2. Subsequently, we applied the same annotation steps and removed common variants within the TARGET cohort (>1% in ethnic-matched ExAC and >10% of the samples) to retrieve pFGVs, except KRGDB1100 (a variant resource specific to Koreans). Ethnicity was determined by using the R package EthSEQ53 (version 3.0.2) with a single-nucleotide polymorphism call rate threshold of 98% (Supplementary Fig.\u00a08).\n\nWe downloaded the filtered variant calls (VCF) from 10,389 patients released by TCGA pan-cancer germline study21 (https://gdc.cancer.gov/about-data/publications/PanCancerAtlas-Germline-AWG). We acquired pFGVs from TCGA data using the same QC and annotation steps applied to our SMC cohort. We also removed common variants in ExAC (<1%) and variants found in >10% of the TCGA cohort. Children (age at diagnosis <18 years) and patients with hematological malignancies were excluded from the study. We also limited the analysis to individuals of self-reported white ethnicity in the TCGA pan-cancer cohort and compared it to the self-reported white ethnicity group in the TARGET cohort. As a result, we included 7482 patients with 31 types of solid cancers.\n\nThe Korea1K22 dataset comprises the whole-genome data of 1094 healthy individuals. We downloaded the VCF files released by Korea1K and included 916 unrelated individuals. The variants were initially called on the hg38 genome assembly and lifted to the hg19 genome assembly using LiftoverVcf in the Picard package. We then extracted the pFGVs using our variant filtering pipeline.\n\nFor the SMC and TARGET data, we called SNPs and small indels using Mutect254 and Manta55/Strelka256. We excluded common variants (VAF\u2009>\u20090.001 in gnomAD v.2.0), low variant allele fractions (VAF\u2009<\u20090.05), variants that did not have a minimum read-depth coverage of 30 reads, and those with fewer than three reads supporting the altered allele. Filtered variants were annotated using Variant Effector Predictor57 from the Ensembl database. In the TARGET data, we further filtered potential oxoG artifacts by removing G\u2009>\u2009T or C\u2009>\u2009A mutations with VAF\u2009<\u20090.15, as suggested for the TARGET data in previous reports6,58. The somatic mutational burden was calculated as the number of nonsynonymous variants. Somatic mutations in the TCGA were obtained from TCGA PanCancer Atlas MC3 set59, which is the result of applying an ensemble of seven mutation-calling algorithms, complete with scoring and artifact filtering60. Then we applied the same somatic mutation call pipeline used in the SMC cohort.\n\nAmong the 733 genes listed in the COSMIC database23 (CGC) (Supplementary Data\u00a01), we compiled a list of 109 known CPGs according to their annotations. To account for their roles, we classified genes with only TSG annotations as TSG in our analysis. Eighty core DDR genes were obtained from Knijnenburg et al.61 (Supplementary Data\u00a04).\n\nMYCN amplification status was determined primarily by fluorescence in situ hybridization (FISH). In cases where FISH data were unavailable, CNVKit (v.0.9.6)62 was used to determine MYCN amplification status. According to CNVKit analysis, MYCN was considered to be copy-gained when there were gains with log2 fold changes greater than 2.0 relative to the normal.\n\nNormality of the data distribution was determined using the Shapiro\u2013Wilk test. Differences in continuous traits between the two groups were determined using independent t-tests or non-parametric equivalent Wilcoxon rank-sum tests. Pearson or Spearman correlation coefficients were used to assess the relationship between germline variant burden and somatic mutational burden. We used the log10-transformed somatic mutational burden to increase normality. In the down-sampling analysis of synonymous variants, we incrementally reduced their count in 1% increments, starting from 10% and progressing to 100%. At each step of this process, the correlation between the number of rare synonymous germline variants and the total somatic mutation burden was recalculated. To assess trends across age groups in the TCGA, we used the Jonckheere-Terpstra trend test for continuous variables and the Cochran\u2013Armitage trend test for categorical variables. Two-sided Fisher\u2019s exact test was used to compare the enrichment of pFGVs in neuroblastomas to controls, and odds ratios with 95% intervals were reported. Kaplan\u2013Meier analysis of PFS and OS were performed to compare the outcomes of patients with or without germline risk factors. The log-rank test was used to compare PFS and OS between groups. Univariable and multivariable Cox proportional-hazards regression models were used to assess whether a higher germline variant burden or the presence of pFGVs in CPGs were independently predictive of survival. A subgroup analysis between the presence of pFGVs in CPGs and MYCN status was also performed to evaluate any heterogeneous associations. Differences were considered statistically significant at P\u2009\u2264\u20090.05, and the tests were 2-tailed\u00a0unless otherwise specified. For internal validation of our predictive model, we performed permutation testing over 500 iterations, randomly dividing the dataset into development (60%) and internal validation (40%) sets for each cycle. The model\u2019s discriminatory power was quantitatively assessed using Harrell\u2019s C-index, conducted with 500 bootstrap replicates to ensure robustness. All analyses were performed in R version 4.2.\n\nFurther information on research design is available in the\u00a0Nature Portfolio Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The raw sequencing data generated in this study are available in the NCBI Sequence Read Archive Repository under accession number PRJNA592880 and are publicly available. The TARGET neuroblastoma WES data files were downloaded from dbGaP under accession number phs000467. These data are available under dbGaP-controlled access for general research purposes. Approved users will receive access to the data for a period of 12 months, after which they will need to either renew their access or close out the project. The TCGA germline variants can be accessed at [https://gdc.cancer.gov/about-data/publications/PanCanAtlas-Germline-AWG], and these data also require dbGaP authorization (accession number phs000178.v11.p8). The publicly available TCGA somatic mutations are accessible at [https://gdc.cancer.gov/about-data/publications/mc3-2017]. KOREA1K data available through [http://koreangenome.org/], and access is subject to approval from the committee, with the process detailed at [http://1000genomes.kr/]. The remaining source data are available within the Article, Supplementary Information, or Source Data file.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "All analyses were performed using standard publicly available software. Our custom code for analysis and figures is available at https://github.com/SGIlabes/NBL_Germline/ and a persistent copy of this repository is available via Zenodo (https://doi.org/10.5281/zenodo.13324781)63.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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Zenodo https://doi.org/10.5281/zenodo.13324781 (2024).\n\nDownload references",
+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We thank all the subjects who participated in this research. K.W.S. was supported by grants from the National R&D Program for Cancer Control, Ministry of Health and Welfare, Republic of Korea (Grant No. 1520210). J.W.L. received support from the National Research Foundation of Korea (NRF), funded by the Korean government (Grant No. NRF-2020R1A2C1012723). Additionally, W.P. was supported by a grant from the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), funded by the Ministry of Health and Welfare, Republic of Korea (Grant No. HR20C0025).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Eun Seop Seo, Ji Won Lee.\n\nDepartment of Pediatrics, Samsung Medical Center, Sungkyunkwan University School of Medicine, Seoul, South Korea\n\nEun Seop Seo,\u00a0Ji Won Lee,\u00a0Hee Won Cho,\u00a0Hee Young Ju,\u00a0Keon Hee Yoo\u00a0&\u00a0Ki Woong Sung\n\nDepartment of Digital Health, Samsung Advanced Institute for Health Science and Technology, Sungkyunkwan University, Seoul, South Korea\n\nEun Seop Seo\u00a0&\u00a0Woong-Yang Park\n\nSamsung Genome Institute, Samsung Medical Center, Seoul, South Korea\n\nEun Seop Seo,\u00a0Jinyeong Lim\u00a0&\u00a0Woong-Yang Park\n\nDepartment of Laboratory Medicine, Inje University Ilsan Paik Hospital, Goyang, South Korea\n\nSunghwan Shin\n\nDepartment of Molecular Cell Biology, Sungkyunkwan University School of Medicine, Suwon, South Korea\n\nWoong-Yang Park\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\nW.P. and K.W.S. designed and supervised the study. E.S.S. and J.L. conducted the bioinformatics analysis. K.W.S., J.W.L., H.W.C., H.Y.J., and K.H.Y. contributed clinical samples. S.S. assisted with variant interpretation and data validation. J.W.L., H.W.C., H.Y.J., and K.H.Y. contributed clinical annotations and follow-up data. E.S.S. and J.W.L. wrote the manuscript and all authors contributed to the writing and provided comments.\n\nCorrespondence to\n                Ki Woong Sung or Woong-Yang Park.",
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+            "section_name": "Ethics declarations",
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+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Jinghui Zhang, Anders Valind, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.",
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+            "section_name": "About this article",
+            "section_text": "Seo, E.S., Lee, J.W., Lim, J. et al. Germline functional variants contribute to somatic mutation and outcomes in neuroblastoma.\n                    Nat Commun 15, 8360 (2024). https://doi.org/10.1038/s41467-024-52128-5\n\nDownload citation\n\nReceived: 19 June 2023\n\nAccepted: 27 August 2024\n\nPublished: 27 September 2024\n\nVersion of record: 27 September 2024\n\nDOI: https://doi.org/10.1038/s41467-024-52128-5\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                        ",
+            "section_image": [
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+            ]
+        }
+    ],
+    "supplementary_files": [
+        {
+            "title": "6.supplementarytable14.xlsx",
+            "link": "https://assets-eu.researchsquare.com/files/rs-3037031/v1/5c44b81ce41433ee3baf4b59.xlsx"
+        }
+    ]
+}

3db73133208fbdb7959c6aefdf42a73c95e4108483437cc4dd7e9e5241c96b10/metadata.json

@@ -0,0 +1,151 @@
+{
+    "title": "Assessing the climate change exposure of foreign direct investment",
+    "pre_title": "Physical Climate Risk and Foreign Direct Investment: Is China Different?",
+    "journal": "Nature Communications",
+    "published": "18 March 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-28975-5/MediaObjects/41467_2022_28975_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-28975-5/MediaObjects/41467_2022_28975_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [],
+    "code": [],
+    "subject": [
+        "Business",
+        "Climate-change impacts"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-471186/v1.pdf?c=1648512332000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-471186/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-28975-5.pdf",
+    "preprint_posted": "20 May, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "This study deploys newly available data to examine the exposure of multinational companies\u2019 overseas investments to physical climate risk. Globally, we find that foreign investment in the agriculture and mining sectors is most associated with physical risk.   We also examine China, as it is fast becoming one of the largest centers of both inward and outward foreign investment across the globe. We find that foreign facilities located in China are associated with higher hurricanes and typhoon risk than their domestic counterparts in China. For Chinese firms operating abroad, we find that China\u2019s overseas facilities are associated with higher water stress, floods, and hurricanes & typhoon risks across host countries, compared with non-Chinese companies. Within host countries, however, climate risks of Chinese facilities are comparable to that of non-Chinese facilities.Environmental EconomicsInternational EconomicsClimate Analysis and ModelingOverseas InvestmentsAgriculture and Mining SectorsHurricane and Typhoon RiskWater Stress",
+            "section_image": []
+        },
+        {
+            "section_name": "Declaration",
+            "section_text": "Note: The designations employed and the presentation of the material on the included maps do not imply the expression of any opinion whatsoever on the part of Research Square concerning the legal status of any country, territory, city or area or of its authorities, or concerning the delimitation of its frontiers or boundaries. These maps have been provided by the authors.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "SupplementaryInformationFinal.pdf",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "This study deploys newly available data to examine the exposure of multinational companies\u2019 overseas investments to physical climate risks. Globally, foreign investments are significantly exposed to lower physical climate risks, compared with local firms across countries. Within countries however, the differences of physical climate risks between foreign and local facilities are small. We also examine China, as it is fast becoming one of the largest sources of outward foreign investment across the globe. We find that foreign direct investment from China is significantly more exposed to water stress, floods, hurricanes and typhoon risks across countries, compared with other foreign facilities. Within host countries however, once again the physical climate risks of Chinese overseas facilities are comparable to those of non-Chinese foreign investments.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Physical climate risks, defined as risks arising from the physical effects of climate change, increasingly affect facilities worldwide across industries1,2,3,4,5,6, including foreign assets, or foreign direct investment (FDI)7. For instance, increased rainfall and flooding interrupted business at Toyota\u2019s manufacturing facilities in Southeast Asia8. Water shortage shut down a Coca-Cola plant in India9. Risks from rising sea levels affects some of Chinese infrastructure investments in Pakistan10.\n\nDespite the increasing impact of physical climate risks on firms and facilities globally, little is known about how multinational companies incorporate such risks into their overseas investment decisions. Previous literature related to FDI and the environment focused on the theory of externalities, such as the extent to which firms might locate to countries that have less stringent regulation that requires firms to internalize environmental externalities11,12; how foreign companies may spread cleaner environmental technologies or practices in host countries;13 or whether foreign firms have better environmental performances than indigenous firms14. With respect to climate change, studies have primarily focused on the relationship between FDI and carbon emissions15,16. While the emerging literature on physical climate risk pays attention to the financial impact of climate change on firm performance, cost of capital, and asset value or price in general17,18,19,20, little attention has been paid to physical climate risks and FDI.\n\nThis paper represents an initial foray into this neglected research area and examines the physical climate risks of FDI. In this study, we find that FDI is exposed to lower physical climate risks, compared with local firms across countries. Within host countries however, the differences of physical climate risks between overseas and local facilities are small. We also find that Chinese FDI is exposed to higher climate risk than non-Chinese FDI. Chinese FDI is exposed to higher water stress, floods, and hurricanes and typhoon risks across host countries, compared with non-Chinese overseas facilities. Within host countries, however, the physical climate risks of Chinese overseas facilities are comparable to those of non-Chinese FDI.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Foreign firms tend to shy away from countries with the higher levels of physical climate risks than do local firms (firms that are not multinational or multinationals operating in their headquarter country), which by their nature have less choice regarding where they can locate their facilities. When firms to locate in particular countries, they take on similar levels of risk as do local firms. Chinese FDI on the other hand, is significantly more exposed to most physical climate risks than non-Chinese FDI across countries, but also is not significantly more exposed to such risks within the countries they choose to locate.\n\nWe begin by examining the physical climate risks of multinational companies\u2019 overseas facilities across the globe. Firms considering locations in areas that are susceptible to physical climate risks will have to bear the costs of climate-related events if they occur. Firms\u2019 decisions to locate facilities abroad involves considerations of the characteristics of the host country (e.g., market attractiveness and inputs factors)21,22 and the firms\u2019 own capabilities23,24,25. Compared with local firms, foreign firms investing abroad are at disadvantage in a local market because they lack information about local conditions, face discrimination by host country stakeholders, and have difficulty in responding to some local conditions26. To overcome the burden of foreignness and enhance their long-term competitiveness, foreign firms may be more cautious about risks in host countries, including climate risks. It is therefore possible that facilities owned by foreign firms have, on average, lower physical climate risks than those owned by local firms.\n\nWe compare whether facilities owned or operated by foreign companies are different from local firms by estimating a set of fixed-effects cross-sectional models based on our firm-host country-industry level climate risk dataset. We find that across host countries, facilities owned by foreign companies have significantly lower climate risks, particularly for floods, seas level rise, and hurricanes/typhoons risks. Within host countries, however, the differences are small and vary among different climate risk drivers. Also, we find that the climate risks of firm\u2019s overseas facilities vary by industry, with agriculture and mining industries having the highest aggregate climate risks. In addition, overseas facilities in the Caribbean, the Middle East, and Southeast Asia have the highest climate risks.\n\nWe then focus on the physical climate risks of Chinese overseas facilities and examine whether they are different from those of the non-Chinese overseas facilities. China is now among the largest outward foreign investors globally27,28. Also, some Chinese overseas investments have political and strategic considerations (e.g., those under the Belt and Road Initiative umbrella) and are not solely profit-seeking29,30. They may be more likely to locate in countries with higher risks (including climate risks) if these investments fit with the government\u2019s strategy. Further, because Chinese firms have expanded their overseas footprints only recently, they may have had to invest in locations with higher physical climate risks because the less-risky ones have already been taken31,32,33.\n\nDescriptive statistics suggest that overseas facilities owned or operated by mainland China and Hong Kong firms have higher aggregate climate risks across countries and industries, compared to overseas facilities owned or operated by companies headquartered in other countries with high FDI outflow stock. Further, we estimate a set of fixed-effects cross-sectional models based on our firm-host country-industry level climate risk data set. We find that overseas facilities owned or operated by Chinese companies have higher water stress, flood, and hurricane/typhoon risks across countries, compared to non-Chinese overseas facilities. Within host countries, however, the climate risks of Chinese overseas facilities are comparable to those of other FDI facilities. We also explore several potential mechanisms explaining why Chinese overseas facilities have higher climate risks across host countries.\n\nNote that physical climate risks are different from carbon risks or transition climate risks - that is, risks arising from transition to a low carbon economy that affect a firms\u2019 business34,35. A facility\u2019s physical climate risks are mainly determined by the facility\u2019s location and the nature of its activities. A facility\u2019s carbon risks are mainly determined by its energy use, technology choice, and a country\u2019s carbon policy. In this paper we focus on physical climate risks and the term \u201cclimate risks\u201d refers to physical climate risks unless otherwise specified. Also, we use the term \u201ccountry\u201d and \u201cjurisdiction\u201d interchangeably. Figure\u00a01 presents the structure of the paper and explains key terminologies.\n\nPresents the structure of the study and explains key terminologies used in the paper.\n\nWe compare climate risks of facilities owned or operated by foreign multinational companies with all facilities in the sample. The Methods section details the model specifications (Eqs. (1a) and (1b)) and explains the selection of control variables. We estimate Eq. (1a) (Model 1) to examine whether climate risks of foreign facilities are different from those of all facilities within industry and across host countries, and estimate Eq. (1b) (Model 2) to examine whether climate risks of overseas facilities are different from those of all facilities within industry and within host country. Outcome variables are physical climate risk scores for different climate risk drivers including heat stress, water stress, floods, sea level rise, and hurricanes/typhoons. The explanatory variable Foreign is a dummy which equals to 1 if facilities are owned or operated by foreign companies.\n\nAs suggested in Table\u00a01, foreign-owned/operated have lower climate risks across host countries. Specifically, they have significantly and substantially lower floods, seas level rise, and hurricanes/typhoons risks across host countries, compared with local facilities. This is probably because firms are more concerned with host country risks, including climate risks, when investing abroad. They may face discrimination by host country stakeholders, receive more attention because they look different, and have difficulty in responding to some local conditions14,27. Within host countries, however, we don\u2019t find substantial differences between climate risks of foreign-owned/operated facilities and those of local facilities. Although the differences for some climate risk drivers, such as heat stress, water stress, and floods risk, are statistically significant, they are economically small (e.g., foreign ownership is associated with less than a 2 percent standard deviation difference in heat stress). Also, there is variation amongst climate risk drivers: foreign facilities have higher water stress risk and lower heat stress and floods risk, compared with those of local facilities within host countries. This makes sense, as the climate risks of facilities, whether owned by local or foreign companies, are determined by their locations and the nature of their economic activities and are greatly influenced by the host country\u2019s climate. Foreign companies may be less likely to invest in countries with higher climate risks, but if they do, the climate risks they face are likely to be similar to the risks of local companies.\n\nFigure\u00a02 shows the climate risk scores of firms\u2019 overseas facilities by industry according to the SIC groups. On average, agriculture and mining industries have the highest aggregate climate risk, while the public administration sector has the lowest climate risk. Specifically, the agriculture, forestry, and fishing industry has the highest heat stress risk; the manufacturing industry has the highest water stress; the mining industry has the highest floods risk; and the whole trade industry has the highest sea level rise and hurricane/typhoon risks. These findings make sense as location-specific assets that are resource-intensive sectors such as agriculture, mining, and manufacturing with dependent upon natural resources for inputs are more directly affected by chronic risks36 such as heat and water stresses, while trade and transportation sectors are more directly affected by sea level rise and hurricane/typhoon risks, as their assets are usually near seaports.\n\nAnalysis is based on climate risk scores and facility statistics of 2233 public companies from Four Twenty Seven. Transportation and Communication sector includes transportation, communications, electric, gas and sanitary service.\n\nFigure\u00a03 compares average climate risk scores of overseas facilities in different countries. The descriptive statistics suggest that overseas facilities in the Caribbean (e.g., Trinidad and Tobago), the Middle East (e.g., Bahrain), and Southeast Asia (e.g., the Philippines) have the highest climate risks. Facilities in Africa (e.g., Rwanda), West Asia (e.g., Saudi Arabia), and South America (e.g., Venezuela) have high heat stress. Facilities in the Middle East (e.g., Bahrain) and central Asia (e.g., Tajikistan and Pakistan) have high water stress. Facilities in Southeast Asia (e.g., Indonesia and Laos) and Central Asia (e.g., Kyrgyzstan) have high floods risk. Facilities on certain islands (e.g., the Faroe Islands and the Solomon Islands) have high sea level rise risk. Facilities in East Asia (e.g., Taiwan, Hong Kong SAR, and Japan) have high hurricane and typhoon risk. Supplementary Fig.\u00a01 in the\u00a0Supplementary Document summarizes climate risk scores of overseas facilities in the 15 jurisdictions with the highest FDI inflow stock between 1970 and 2019; among these jurisdictions, overseas facilities in Hong Kong SAR have the highest aggregated climate risk.\n\nAnalysis based on climate risk scores and facility statistics of 2233 public companies from Four Twenty Seven. The map images are created by the authors using\u00a0ArcGIS. (a) Aggregate climate risk score, (b) heat stress score, (c) water stress score, (d) floods score, (e) sea level rise score, (f) hurricanes/typhoons score.\n\nFigure\u00a04 summarizes climate risk scores of overseas facilities owned by firms in the 15 jurisdictions with the highest FDI outflow stock between 1970 and 2019. Among those jurisdictions, facilities owned or operated by firms headquartered in China have the highest climate risks across industries and host countries among all foreign operating multinationals. Overseas facilities owned by Hong Kong SAR firms have the highest water stress and floods risks, while facilities owned by mainland Chinese firms have the highest hurricanes/typhoons and sea level rise risks.\n\nAnalysis based on climate risk scores and facility statistics of 2233 public companies from Four Twenty Seven. FDI outflow stocks based on World Bank data.\n\nThe descriptive statistics above suggest that overseas facilities owned or operated by Chinese companies (including Hong Kong SAR) have the highest aggregate climate risks across host countries and industries. However, it is not clear whether the difference is statistically significant, considering industry factors and firm characteristics. We therefore estimate a baseline specification to analyze whether the climate risks of Chinese-owned/operated overseas facilities differ from the average of all FDI facilities. We estimate Eq. (2a) (Model 1) to examine whether climate risks of Chinese-owned/operated overseas facilities differ from those of the global FDI within industry and across host countries, and estimate Eq. (2b) (Model 2) to examine whether climate risks of Chinese-owned/operated overseas facilities differ from the global FDI within industry and host country. Outcome variables are physical climate risk scores for different climate risk drivers: heat stress, water stress, floods, sea level rise, and hurricanes/typhoons. The explanatory variable ChineseFDI is a dummy which equals to 1 if overseas facilities are owned or operated by Chinese companies. Each analysis controls for headquarter countries\u2019 economic development and carbon emissions and for a set of firm-level control variables. The Methods section details the model specifications (Eqs. (2a) and (2b)) and explains the selection of control variables.\n\nTable\u00a02 presents the results. The statistically significant positive coefficients on ChineseFDI in Model 1 suggest that Chinese overseas facilities are exposed to higher water stress, flood, and hurricanes/typhoons risks across host countries (p-values <0.05), compared to all other overseas facilities. The heat stress and sea level rise risks of Chinese overseas facilities do not differ statistically from those of non-Chinese FDI across countries. Results in Model 2 suggest that within a host country, the climate risks of Chinese-owned/operated facilities do not differ significantly from those of non-Chinese overseas facilities except for water stress. Chinese overseas assets are associated with a 9 percent standard deviation decrease in water risk scores within host country (p-values <0.05). The results imply that the higher climate risks of Chinese overseas assets across host countries are driven by the countries Chinese companies invest. In other words, relative to other global public companies, Chinese companies locate facilities in host countries with higher climate risks. Within each host country and industry, Chinese facilities do not tend to be in areas with higher climate risks than are non-Chinese foreign facilities.\n\nThe\u00a0Supplementary Information includes robustness checks. Results are robust when we (a) remove resource-intensive industries such as mining, transportation, communications, electric, and gas (Supplementary Table\u00a03); (b) focus on firms from the top 15 FDI exporters (Supplementary Table\u00a04); (c) change control variables (Supplementary Table\u00a05); and (d) aggregate climate risk drivers at the firm level (Supplementary Table\u00a06).\n\nWe further explore why Chinese overseas facilities have higher climate risks across host countries. It may be that some Chinese companies are willing to invest in countries for political or strategic reasons, regardless of climate risks. For instance, the Belt and Road Initiative (BRI) was launched in China in 2013 to improve regional and transcontinental cooperation and connectivity through investments and trade37. As shown in Fig.\u00a03, facilities in a lot of BRI countries (e.g., countries in Africa, Southeast Asia, and Latin America) face higher climate risks. Second, Chinese companies started to invest overseas aggressively in the early 2000s and may therefore have had to invest in locations with higher climate risks because the less-risky locations had already been taken32,33. Third, as suggested in Table\u00a03, the climate risks of a firm\u2019s headquarter country are positively associated with those of its overseas facilities. As facilities in China have relatively high climate risks (see Fig.\u00a03), Chinese firms are likely to take above-average climate risks when investing overseas. This is consistent with previous research suggesting that firms with local experience of high risks (e.g., natural disasters or political risks) are more likely to expand into other countries posing such risks24,25.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "This paper fills a research gap by assessing climate risks of FDI. We find that foreign investments have substantially and significantly lower climate risks\u2014particularly flood, sea-level, and hurricane/typhoon\u2014compared with all facilities across host countries. The differences of climate risks of foreign facilities are small within host countries. We also document the heterogeneities of the climate risks of overseas facilities across industries and countries. Further, we focus on China and explore whether Chinese-owned/operated overseas facilities differ from those of the global FDI. Our findings suggest that Chinese FDI have higher water, floods, and hurricanes/typhoons risks across countries, compared to all overseas facilities. Within host countries, however, the climate risks of Chinese overseas facilities are comparable with those of non-Chinese counterparts.\n\nThis study has several contributions. First, it is related to the nascent but growing literature on physical climate risks. Most recent research has focused on the financial impact of climate risks on firm performance2,18,38, asset value39,40, and cost of capital19. We expand this literature by systematically evaluating the physical climate risks of firms\u2019 FDI.\n\nSecond, the insights of this paper shed light upon the multidisciplinary dialogue on FDI and the environment13,14,15,40,41 by exploring the physical climate constraints on firms, rather than firms\u2019 environmental externalities. As firms are already being affected by climate risks, they need to add those risks into their cost function.\n\nThird, this paper contributes to the emerging literature on Chinese overseas investment. While previous research focuses on environmental and social impacts of Chinese firms investing abroad such as carbon emissions, toxic pollutants, and ecological effects42,43,44,45, this paper focuses on the climate risks of Chinese FDI and compares it with the global average.\n\nFinally, our research has policy implications. Governments, investors, and communities are becoming more active in addressing their climate risks46,47,48,49,50,51. For instance, the Task Force on Climate-related Financial Disclosures was established in 2015 to improve and increase reporting of climate-related financial information52. The Network for Greening the Financial System was established in 2017 to share climate-risk\u2013management best practices among central banks and supervisors53. The 2020 version of the Equator Principles incorporated climate risk assessment into its guidelines and called for climate-resilient infrastructure54. Understanding the climate risk baseline of firms\u2019 global assets can help policymakers and international organizations craft climate-related policies or guidelines55,56,57,58. For instance, the Chinese government may want to take climate risks into consideration when promoting BRI investments.\n\nThis study has limitations. First, the analysis is cross-sectional, as time-specific information on when companies built or acquired each facility was not available. Future research can collect panel data on firms\u2019 overseas projects in certain industries and examine the extent to which climate risk is a factor in choosing locations. Second, there are inherent uncertainties in climate risk data predicted by geospatial, historical, and projection models59,60, but for now they are the best data available. Lastly, the unit of analysis is the firm-host country-industry, but for some large countries, such as the United States and China, climate risks vary within the country (e.g., coastal versus inland areas; west versus east). It would be interesting for future research to disentangle such within-country differences.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The assessment of firms\u2019 physical climate risks requires climate models with which to conduct forward-looking analysis, as climate risks cannot simply be calculated based on historical data. In this study, we use the physical climate risk scores at the firm\u2013industry\u2013host-country level collected from Four Twenty Seven (currently Moody\u2019s ESG Solutions). The sample covers 2233 public companies headquartered in 47 jurisdictions with more than 1 million facilities across 200 jurisdictions and 10 SIC groups. Around 28.8 percent of the facilities are outside the firm\u2019s headquarter country (i.e., overseas facilities). Facility is defined as any operational legal entity owned or operated by a company. This includes a wide range of operating activities\u2014such as factories, offices, ports, warehouses, and stores\u2014but does not include sites that are being developed and not yet operational. Other entities, such as European Central Bank, also use Four Twenty Seven data for climate risk analysis61.\n\nA facility\u2019s climate risks of its direct operations are mainly determined by the facility\u2019s location and the nature of its activities. Four Twenty Seven evaluates climate risks using several geospatial, historical, and projection models based on the specific locations of companies\u2019 facilities. The criteria for analysis include detailed climate projections that measure the change in extreme events such as heavy rainfall, high temperatures, hurricanes, coastal flooding, drought, and water stress. Four Twenty Seven\u2019s analysis focuses on extreme weather impacts (e.g., tropical cyclones) today and on other climate impacts at a mid-term projection period, 2030\u20132040. Supplementary Table\u00a01 explains in greater detail the methodology, including the spatial scale, baseline period, projection period, and specific measurement for analyzing different climate risk drivers. Further, to factor the differential impacts of climate risk drivers on different economic activities, Four Twenty Seven assigns a series of sensitivity factors to the facilities that they model based on the nature of their activities. These factors vary by climate risk driver, reflecting the sensitivity and vulnerability of the company\u2019s activities to the corresponding risk factors. For example, a data center is more energy intensive than an office and, thus, will be more sensitive to the impacts of increasing temperature on energy usage. As a result, an office would receive a lower heat stress score than a data center in the same area. The\u00a0Supplementary Discussion provides more details on how adjustments of climate risk scores are made based on facilities\u2019 economic activities.\n\nRaw indicators for each climate risk driver\u2014heat stress, water stress, floods, sea level rise, and hurricanes/typhoons\u2014are translated into a standardized score ranging from 0 to 100; higher scores reflect higher exposure. Four Twenty Seven started to provide physical climate risk data in 2018. We use the 2019 data because it covers more public firms and facilities than the 2018 data. Also, because the evaluation of climate risk is based on the mid-term climate projection (e.g., 2030\u20132040) and its difference with the historical baseline, facilities\u2019 climate risk scores do not change much across years.\n\nLike most climate projections, Four Twenty Seven\u2019s climate risk scores have limitations. First, its evaluation of future extreme weather does not necessarily capture the most severe weather events. Second, it uses multi-model means, which may under-sample tail-end extreme events by missing processes below the model\u2019s resolution62. Third, there is uncertainty in modeling average shift in climate, although Four Twenty Seven applies statistical validation methods to account for model uncertainties and to ensure practicable directional accuracy.\n\nFirm financial data are constructed from Compustat. Size is the natural logarithm of the book value of total assets. Return on assets (ROA) is the ratio of operating income before depreciation to the book value of total assets. Leverage is the ratio of debt (long-term debt plus short-term debt) to the book value of total assets. Cash holding is the ratio of cash and short-term investments to the book value of total assets. FirmLocalExp is a firm\u2019s average climate risk in its headquarter country, calculated from facility statistics from Four Twenty Seven. FDI outflow and inflow and country-level GDP per capita are from the World Bank. Country-level CO2 emissions per capita are from Our World in Data\u2019s CO2 and Greenhouse Gas Emissions database. Supplementary Table\u00a02 reports descriptive statistics for different variables.\n\nTo assess the difference between the climate risks of overseas facilities and that of the global average across host countries, we estimate Eq. (1a) for different climate risk drivers, using the sample of all overseas and local facilities owned or operated by the 2233 public firms globally.\n\nTo assess the difference between the climate risks of overseas facilities and the global average within the same host country, we estimate Eq. (1b) for different climate risk drivers.\n\nTo assess the difference of the climate risks of Chinese overseas facilities across host countries, we estimate Eq. (2a) for different climate risk drivers, using the sample of all overseas facilities owned operated by the 2233 public firms globally\n\nTo assess the difference of the climate risks of overseas facilities owned or operated by Chinese companies within countries, we estimate Eq. (2b) for different climate risk drivers:\n\nwhere i indexes firm, j indexes industry, c indexes host country, and h indexes headquarter country. \u03b1j are industry fixed effects. \u03b1c are host country-fixed effects. \\({\\varepsilon }_{{ijc}}\\) is the residual. The unit of analysis is firm-host country-industry. The regression is estimated by analytical weighted least squares, where the weight is the total facility count of a firm\u2019s operation in one industry and in one host country. Standard errors are clustered at the industry level.\n\nIn Eqs. (1a) and (1b), the coefficients of interest are \u03b21 and \u03b22, which measure the association of foreign ownership and climate risks of facilities. In Eqs. (2a) and (2b), the coefficients of interest are \u03b23 and \u03b24, which measure the association between Chinese ownership and climate risks of overseas facilities. Equations (1a) and (2a) include the industry-fixed effects which account for the unobserved heterogeneity of the industry. Equations (1b) and (2b) have both the industry fixed effects and host country fixed effects, which accounts for the unobserved heterogeneity of the industry and the host country.\n\nOutcome variables are physical climate risk scores for different climate risk drivers: heat stress, water stress, floods, sea level rise, and hurricanes/typhoons. The climate risk scores are standardized to a mean of 0 and a standard deviation of 1 for easy interpretation. The inclusion of control variables mitigates the possibility that our findings are driven by some firm- or country- level omitted variables. For example, it could be that larger companies have higher climate risks; controlling for firm size and cash holdings addresses this potential confounding influence. Similarly, the other controls account for differences in performance (ROA and market-to-book), and in financing policies (leverage and cash holdings) that may correlate with a firm\u2019s investment decisions. We also control for the firm\u2019s climate risk in its headquarter country (FirmLocalExp) because firms with experience of high-impact disasters maybe more likely to expand into countries experiencing such disasters26. We control for GDP per capita of the headquarter country because that country\u2019s economic development level may affect firms\u2019 overseas location choices. We also control for CO2 emissions per capita of the headquarter country because it may be associated with FDI and sovereign risks15,63.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data that support the findings of this study are available from Four Twenty Seven (currently Moody\u2019s ESG Solutions) but restrictions apply to the availability of these data. Data from Four Twenty Seven are proprietary and covered by Non-Disclosure Agreement, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of Four Twenty Seven.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The STATA code used to run the regression analysis is available from the authors upon request. Restrictions apply to the availability of the data underlying the analysis.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors acknowledge the funding support of the ClimateWorks Foundation (19-1494, K.P.G.).",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Questrom School of Business, Global Development Policy Center, Boston University, Boston, MA, 02215, USA\n\nXia Li\n\nPardee School of Global Studies, Global Development Policy Center, Boston University, Boston, MA, 02215, USA\n\nKevin P. Gallagher\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nX.L. conceived the study and performed the analysis K.P.G. supervised the project and oversaw the research design. X.L. and K.P.G. discussed results and edited the manuscript at all stages.\n\nCorrespondence to\n                Xia Li or Kevin P. Gallagher.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Ulf Moslener and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.",
+            "section_image": []
+        },
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+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Li, X., Gallagher, K.P. Assessing the climate change exposure of foreign direct investment.\n                    Nat Commun 13, 1451 (2022). https://doi.org/10.1038/s41467-022-28975-5\n\nDownload citation\n\nReceived: 04 May 2021\n\nAccepted: 16 February 2022\n\nPublished: 18 March 2022\n\nVersion of record: 18 March 2022\n\nDOI: https://doi.org/10.1038/s41467-022-28975-5\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_name": "This article is cited by",
+            "section_text": "Communications Earth & Environment (2025)\n\nEnvironment, Development and Sustainability (2025)\n\nNature Sustainability (2024)\n\nEnvironmental Science and Pollution Research (2024)\n\nEnvironment, Development and Sustainability (2023)",
+            "section_image": []
+        },
+        {
+            "section_name": "Associated content",
+            "section_text": "Focus",
+            "section_image": []
+        }
+    ],
+    "supplementary_files": [
+        {
+            "title": "SupplementaryInformationFinal.pdf",
+            "link": "https://assets-eu.researchsquare.com/files/rs-471186/v1/535178206f141084c12be175.pdf"
+        }
+    ]
+}

3e9c3359b0dbb9cebdc84cd7c3e91539ac216ffb4da3ccd80d3cfaacff69aa6e/metadata.json

@@ -0,0 +1,183 @@
+{
+    "title": "Single planar photonic chip with tailored angular transmission for multiple-order analog spatial differentiator",
+    "pre_title": "Single planar photonic chip with tailored angular transmission for multiple-order analog spatial differentiator",
+    "journal": "Nature Communications",
+    "published": "26 December 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35588-5/MediaObjects/41467_2022_35588_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35588-5/MediaObjects/41467_2022_35588_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Description of Additional Supplementary Files",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35588-5/MediaObjects/41467_2022_35588_MOESM3_ESM.pdf"
+        },
+        {
+            "label": "Supplementary Video 1",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35588-5/MediaObjects/41467_2022_35588_MOESM4_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Video 2",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35588-5/MediaObjects/41467_2022_35588_MOESM5_ESM.mp4"
+        },
+        {
+            "label": "Supplementary Video 3",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35588-5/MediaObjects/41467_2022_35588_MOESM6_ESM.avi"
+        },
+        {
+            "label": "Supplementary Video 4",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35588-5/MediaObjects/41467_2022_35588_MOESM7_ESM.avi"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "/articles/s41467-022-35588-5#Fig1",
+        "/articles/s41467-022-35588-5#Fig6",
+        "https://doi.org/10.6084/m9.figshare.21506229.v3"
+    ],
+    "code": [],
+    "subject": [
+        "Imaging and sensing",
+        "Transmission light microscopy"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1903675/v1.pdf?c=1662758635000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1903675/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-35588-5.pdf",
+    "preprint_posted": "09 Sep, 2022",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Analog spatial differentiation is used to realize edge-based enhancement, which plays an important role in data compression, microscopy, and computer vision applications. Here, a planar chip made from dielectric multilayers is proposed to operate as both first- and second-order spatial differentiator without any need to change the structural parameters. Third- and fourth-order differentiations that have never been realized before, are also experimentally demonstrated with this chip. A theoretical analysis is proposed to explain the experimental results, which furtherly reveals that more differentiations can be achieved. Taking advantages of its differentiation capability, when this chip is incorporated into conventional imaging systems as a substrate, it enhances the edges of features in optical amplitude and phase images, thus expanding the functions of standard microscopes. This planar chip offers the advantages of a thin form factor and a multifunctional wave-based analogue computing ability, which will bring opportunities in optical imaging and computing.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "Supportinformation18.pdfSupplementary InformationVideo1Secondorderspatialdifferentiation2.mp4The demonstration of the second-order spatial differentiationVideo2Firstorderspatialdifferentiation2.mp4The demonstration of the first-order spatial differentiationVideo3Fourthorderspatialdifferentiation.aviThe demonstration of the fourth-order spatial differentiationVideo4Thirdorderspatialdifferentiation.aviThe demonstration of the third-order spatial differentiation",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Analog spatial differentiation is used to realize edge-based enhancement, which plays an important role in data compression, microscopy, and computer vision applications. Here, a planar chip made from dielectric multilayers is proposed to operate as both first- and second-order spatial differentiator without any need to change the structural parameters. Third- and fourth-order differentiations that have never been realized before, are also experimentally demonstrated with this chip. A theoretical analysis is proposed to explain the experimental results, which furtherly reveals that more differentiations can be achieved. Taking advantages of its differentiation capability, when this chip is incorporated into conventional imaging systems as a substrate, it enhances the edges of features in optical amplitude and phase images, thus expanding the functions of standard microscopes. This planar chip offers the advantages of a thin form factor and a multifunctional wave-based analogue computing ability, which will bring opportunities in optical imaging and computing.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Currently, there is significant interest in optical analog signal processing because of the rapid increase in demand for large-scale, real-time data processing in the big data era, and the major advances being made in nanophotonics are leading to opportunities in this field. Although digital signal processing can offer great versatility, it suffers from problems with low processing speeds, high power consumption, and high complexity caused by the use of costly analogue-to-digital converters1, and these problems become obvious during the investigation of nonrepetitive and rare phenomena (e.g., nonlinear dynamics)2. These restrictions can be removed by using optical analog signal processing2,3,4,5, because it has an intrinsically parallel nature that offers high-speed operation and low power consumption. The conventional bulky lenses that are used in traditional optical signal processing and Fourier optics6 have now been replaced with nanophotonic materials, such as the compactible and power-efficient ultrathin devices that have been fabricated based on metasurfaces (or metamaterials)7,8,9,10, photonic crystals11,12, plasmonic structures13,14, spin Hall effect15,16 and topological photonics17.\n\nThe optical analog spatial differentiator is one of these devices. This differentiator can enable massively parallel processing of the edges detected from an entire image18, which has been shown to have important applications in machine and computer vision19, medical or biological imaging operation20,21 and autonomous vehicles22,23. However, most optical analog spatial differentiators based on nanophotonic materials can perform only one mathematical operation, producing either the first-order or the second-order derivative8,9,11,12,13,17,24,25,26,27. Complex materials and fabrication processes are also required for these devices, which contain artificially engineered structures.\n\nIn this work, a planar photonic chip composed of an all-dielectric multilayer structure is proposed and its nonlocality (or named as angular-dependent transmission) is tailored to enable signal manipulation in the momentum domain28,29. It can be used to perform various types of mathematical operations on optical signals, such as the first-, second-, third-, fourth- and even higher-order spatial derivative operations without altering the chip\u2019s structural parameters. This chip can be fabricated on a large scale using standard deposition techniques. Edge detection is realized for both amplitude and phase objects when this chip is integrated into the optical path of a commercial optical microscope.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The relationship between the input electric field \\({{{{{{\\bf{E}}}}}}}_{{{{{{\\bf{in}}}}}}}\\left(x,y\\right)\\) and the output electric field \\({{{{{{\\bf{E}}}}}}}_{{{{{{\\bf{out}}}}}}}\\left(x,y\\right)\\) for an optical device in Cartesian coordinate system can be described as follows:\n\nwhere \\(A({k}_{x},{k}_{y})\\) is the amplitude of the field, \\({k}_{x}\\),\\(\\,{k}_{y}\\) are the \\(x\\)- and \\(y\\)-components of the in-plane wavenumber, respectively, and \\(t({k}_{x},{k}_{y})\\) represents the optical transfer function (OTF)30. \\({{{{{{\\bf{e}}}}}}}_{{{{{{\\bf{in}}}}}}}\\) and \\({{{{{{\\bf{e}}}}}}}_{{{{{{\\bf{out}}}}}}}\\) represent the polarization states of input and output fields in real space, which are controlled by the polarizers elements used in the experiments.\n\nTo realize first-order spatial differentiation along \\(x\\)-direction, the condition \\({{{{{{\\bf{E}}}}}}}_{{{{{{\\bf{out}}}}}}}\\propto \\partial {{{{{{\\bf{E}}}}}}}_{{{{{{\\bf{in}}}}}}}/\\partial x\\) should be satisfied, and then \\(t({k}_{x},{k}_{y})\\propto {k}_{x}\\). In the same way, to achieve higher order one-dimensional differential operations, \\(t({k}_{x},{k}_{y})\\) should have the forms of \\(t({k}_{x},{k}_{y})\\propto {k}_{x}^{2},{k}_{x}^{3},{k}_{x}^{4},\\cdots \\cdots\\). In the polar coordinate system, to achieve multi-order radial differential operations (\\({{{{{{\\bf{E}}}}}}}_{{{{{{\\bf{out}}}}}}}\\propto {\\partial }^{n}{{{{{{\\bf{E}}}}}}}_{{{{{{\\bf{in}}}}}}}/\\partial {r}^{n}\\)) which enable two-dimensional processing, the optical transfer function should satisfy the forms of \\(t\\left({k}_{r},\\varphi \\right)\\propto {{k}_{r}^{1},k}_{r}^{2},{k}_{r}^{3},{k}_{r}^{4},\\cdots \\cdots\\), where \\({k}_{r}=\\sqrt{{k}_{x}^{2}+{k}_{y}^{2}}\\) is the in-plane wavevector along the radial direction.\n\nIn this work, a planar photonic chip made from a dielectric multilayer structure is designed to realize these first-, second-, and even higher order spatial differentiation operations on the same chip, as illustrated in Fig.\u00a01a. The chip is composed of alternating layers of Si3N4 and SiO2. There are 40 of these layers in total. The thicknesses of the Si3N4 and SiO2 layers are 56\u2009nm and 80\u2009nm, respectively. Further details of the structural parameters of this chip are provided in the supplementary information. The transmission band diagram of the multilayer structure is calculated using the transfer matrix method (TMM)31, as shown in Fig.\u00a01b, where the \\(p\\)- and \\(s\\)-polarization are plotted on the right and the left, respectively. The dark blue region corresponds to the forbidden band, and the red dashed line indicates the frequency of 467\u2009THz (\\(\\lambda \\,\\)= 643\u2009nm), at which the transmissivity satisfied the function \\(t={t}_{0}+{t}_{2}{k}_{r}^{2}\\) as illustrated in Fig. S1b in the supplementary information, where \\({t}_{0}\\) and \\({t}_{2}\\) are fitting coefficients. Note that \\({t}_{0}\\) can be regarded as the direct transmission component, which can be reduced to zero when an analyzer is used. The direct transmission component is not related to the wavenumber of the incident light, and will form the background of the output optical field.\n\na Schematic of a photonic chip acting as a spatial differentiator that transforms an image into its first-, second- and even higher order derivative. The chip is made from a well-designed dielectric multilayer structure. b Simulated color-coded transmission coefficient amplitude as a function of frequency and in-plane wavenumber for the \\(s\\)- and \\(p\\)-polarizations. c Simulated transmission BFP image through the dielectric multilayer at an incident wavelength of 643\u2009nm. The double arrow-headed black line at the top left corner indicates the polarization orientation of the incident light. The colored one-way arrows indicate the polarization direction of transmitted light in the momentum space, the polarization deflection increases as the color change from white to red. d Simulated transmission BFP image when an analyzer is placed after the dielectric multilayer. The polarization orientation of the analyzer lies perpendicular to the incident polarization orientation, as indicated by the double arrow-headed line. The green trapezoidal regions are designed to perform first-order differentiation, and the yellow circular region for second-order differentiation. The green dotted lines and the yellow dotted lines indicate the directions of first-order differentiation and second-order differentiation, respectively. e Simulated optical transfer function \\(\\left|t\\left({k}_{r}\\right)\\right|\\) for the second-order differentiation at \\(\\lambda\\) = 643\u2009nm in the case where \\(\\varphi={45}^{\\circ }\\) and for the quadratic fitting using the form \\(\\left|t\\left({k}_{r}\\right)\\right |=a{k}_{r}^{2}\\). The abbreviation \u201cSim.\u201d has a full name of \u201cSimulation\u201d. f Simulated optical transfer function \\(\\left|t\\left({k}_{x}\\right)\\right|\\) (along the direction \\({k}_{y}=-0.18{k}_{0}\\), which is marked using the green line in (d)) for first-order differentiation and for linear fitting using the form \\(\\left|t\\left({k}_{x}\\right)\\right |=b\\left|{k}_{x}\\right|\\).\n\nThe angular-dependent transmission image of this multilayer structure at \\(\\lambda \\,\\)= 643\u2009nm was calculated as shown in Fig.\u00a01c. The gradient color arrows represent the polarization orientation of the output electric field due to the difference between transmission coefficients \\({t}_{s}\\) and \\({t}_{p}\\). The figure shows that the polarization orientation of the output electric field in the central region (where \\({k}_{r}\\approx 0\\)) is nearly the same as that of the incident light. Then, if an analyzer with orientation perpendicular to the polarization direction of the polarizer is inserted between the photonic chip and the detector, the electric field intensity at the center (where \\({k}_{r}=0\\)) can be reduced to nearly zero and the directional transmission is removed (i.e., \\({t}_{0}=0\\)), as verified by the yellow circular region shown in Fig.\u00a01d. The OTF in this region can then be fitted using the function \\(t=a{k}_{r}^{2}\\). It is anticipated that this type of nonlocality in the momentum domain (here, the nonlocality means that the optical transmission through the multilayer is dependent on the incident angle) enables the second-order spatial differentiation of the input field along the in-plane radial direction, as shown in Fig.\u00a01e and in Fig. S1c,d in the supplementary information. The difference between \\({t}_{s}\\) and \\({t}_{p}\\) becomes larger in the region where \\({k}_{r}\\) is increasing, the polarization orientation of the transmitted electric field is obviously deflected compared to the incident polarization orientation. In this case, the analyzer not only removes the direct component, but also extends the range of quadratic line type to larger numerical apertures by modifying the transmission curve that enables the second-order differentiation.\n\nIt is worth noting that the polarization direction is not deflected along the horizontal (along \\({{{{{{\\bf{k}}}}}}}_{{{{{{\\bf{x}}}}}}}\\)) and vertical (along \\({{{{{{\\bf{k}}}}}}}_{{{{{{\\bf{y}}}}}}}\\)) directions, but is largely deflected along other azimuth angles. Therefore, the analyzer tangentially modulates the transmittance spectrum to get a transmission curve that satisfies the linear-line type, within the green trapezoidal regions (Fig.\u00a01c). It means that here the OTF is of the form \\(t=b\\left|{k}_{x}\\right|\\) or \\(t=b\\left|{k}_{y}\\right|\\) when the optical field passing through this analyzer, as illustrated in Fig.\u00a01f and Fig. S1e in the supplementary information. This indicates that the first-order spatial differentiation can be performed using the nonlocality of these regions. The fitting coefficients for both \\(a\\) and \\(b\\) are listed in Tables\u00a0S1 and S2 in the supplementary information. By comparing the magnitudes of the coefficients \\(a\\) and \\(b\\), the position and size of the yellow circular and the green trapezoidal regions are determined (Fig.\u00a01c).\n\nThe theoretical analysis on the origin of the multiple-order differentiations are described in details in the supplementary information (Sections 1 to 4). Here, this analysis is briefly described as follows. In the condition that the polarization directions of the input and output field are perpendicular to each other (\\({{{{{{\\bf{e}}}}}}}_{{{{{{\\bf{in}}}}}}}=[{{0}\\atop{1}}]\\) and \\({{{{{{\\bf{e}}}}}}}_{{{{{{\\bf{out}}}}}}}=[{{1}\\atop{0}}]\\)), the OTF has a form of (more details are shown in the Section 4 of the supplementary information):\n\nwhere the difference in transmission coefficients \\({t}_{s}\\) and \\({t}_{p}\\) (transmissivity for \\(s\\)- and \\(p\\)-polarized light through the chip) will induce the deflection of the output polarization direction from that of the incident polarization orientation (as shown in Fig.\u00a01c). The term \\({{\\sin }}\\left(2\\varphi \\right)\\) related to azimuth angle \\(\\varphi={{\\arctan }}({k}_{x}/{k}_{y})\\) represents the angular modulation of transmissivity by the analyzer. Due to the horizontal symmetry of the planar structure, the Taylor expansion of the term (\\({t}_{p}-{t}_{s}\\)) can be written as \\({t}_{p}-{t}_{s}=\\mathop{\\sum }\\nolimits_{n=1}^{N}({C}_{p2n}-{C}_{s2n}){\\theta }^{2n}\\) where \\({C}_{s2n\\left(p2n\\right)}\\) are the coefficients of even terms of the Taylor expansion of \\({t}_{s\\left(p\\right)}\\) and \\(\\theta={{\\arcsin }}\\left({k}_{r}/{k}_{0}\\right)\\,\\approx \\,{k}_{r}/{k}_{0}\\). Considering the continuous variation of transmissivity with the frequency of the input light, the term (\\({t}_{p}-{t}_{s}\\)) is in the quadratic form and the other expansion terms are smaller at the wavelength of 643\u2009nm, which satisfies \\({t}_{p}-{t}_{s}=({C}_{p2}-{C}_{s2}){\\theta }^{2}\\) (as shown in Figs. S2a, d). Thus, the OTF can be re-written as:\n\nInterestingly, when the azimuth angle \\(\\varphi\\) is fixed as a constant (along the direction of the diagonal dashed-line on Fig.\u00a01d), the OTF has a form:\n\nOn the other hand, when the vertical wave vector \\({k}_{y}\\) is fixed as a constant (along the direction of the horizontal dashed-line on Fig.\u00a01d), the OTF will have another form derived from Eq. (4):\n\nEquation\u00a05 indicates that the second-order differentiation can be performed along the in-plane radial direction (along \\({{{{{{\\bf{k}}}}}}}_{{{{{{\\bf{r}}}}}}}\\)), and Eq. 6 means that the first-order differentiation along the direction of \\({{{{{{\\bf{k}}}}}}}_{{{{{{\\bf{x}}}}}}}\\) can be realized.\n\nThe above theoretical analysis and numerical calculations show that the same chip has two types of nonlocality, which means that both first-order and second-order spatial differentiation can be performed on the same photonic chip. To verify this point, the planar photonic chip shown in Fig.\u00a02a was fabricated by plasma-enhanced chemical vapor deposition (PECVD). The fabrication process is described in greater detail in the section Methods, and a scanning electron microscope (SEM) image of the fabricated chip is shown in Fig.\u00a02b. An in-house-fabricated back focal plane (BFP) imaging setup, which is shown in Fig.\u00a02c, was used to characterize the angular-dependent transmission or nonlocality of this photonic chip32.\n\na Photograph of the fabricated planar photonic chip. b Cross-sectional SEM view of the photonic chip. c Schematic of the experimental setup used to perform BFP imaging. d Experimentally measured BFP image at \\(\\lambda\\) = 643\u2009nm. e, f Intensity profiles along the second-order and the first-order differentiation directions in (d), respectively, together with the corresponding simulated curves. g, h Optical transfer functions extracted from (c) and (d), respectively, using quadratic and linear fitting.\n\nThe transmitted BFP image shown in Fig.\u00a02d has a similar intensity distribution to that of the simulated image shown in Fig.\u00a01d. For example, the extracted intensity distributions along the two dashed lines in Fig.\u00a02d coincide with the two simulated curves shown in Fig.\u00a02e, f. This consistency between the experimental and simulated BFP images (\\(\\lambda\\) =643\u2009nm) within a large \\(k\\)-space is illustrated in the images shown in Fig. S3a, b, e, f in the supplementary information. The experimental OTF that was extracted from these BFP images can be fitted using a parabolic curve (Fig.\u00a02g, along the radial direction \\(\\varphi={45}^{\\circ }\\)), or fitted using a mirror-symmetrical line (Fig.\u00a02h, along the direction \\({k}_{y}=-0.18{k}_{0}\\)). The consistency between the experimental curves and the fitted curves clearly verifies that the chip has a nonlocality and thus will have the ability to perform both the first-order and second-order spatial differentiations.\n\nOne of the primary benefits of the planar photonic chip is its ability to be vertically integrated with conventional optical systems. Here, the chip is incorporated into a standard transmission optical microscopy system. In this system, the chip is placed below the amplitude step objects of a standard 1951 USAF resolution test chart (inset graph on Fig.\u00a03a). By using this chart with a step edge, there will be \\(n\\) peaks at the edge of the image when \\(n\\)-order spatial differentiation is performed. Figure\u00a03a shows a schematic of the imaging system, in which the sample is illuminated by an out-of-focus beam, and the different illuminated regions correspond to different angles of incidence. Imaging results acquired without the polarization analyzer for three elements on the test chart are shown in Fig.\u00a03b, c, which can be regarded as bright field optical images of these elements. Figure 3d shows the calculated second-order derivative of these bright field images. Figure\u00a03f shows images of the test chart acquired when the photonic chip was operating as a second-order differentiator and when the orthogonally polarized analyzer was inserted into the optical system, as demonstrated in Supplementary Video\u00a01. The edges of the micrometer-scale elements are presented clearly along both the horizontal and vertical directions for both the experimental and simulated images, thus indicating the two-dimensional (2D) spatial differentiation process. Figure\u00a03h shows the intensity profile along the dashed line through the differentiated image (shown in Fig.\u00a03d, f), in which two closely spaced peaks are formed around each edge. This phenomenon represents the typical nature of the second-order derivative process11,12.\n\na Schematic of the imaging set-up. The planar chip differentiator was placed directly below a standard 1951 USAF test chart (the sample, inset graph on the left corner). The target was illuminated using an out-of-focus linearly-polarized beam at a wavelength of 643\u2009nm. b, c Imaging results for the target without the polarizer 2 (analyzer) being placed before the detector. d, e Calculated second-order and first-order derivatives of the images shown in (b) and (c), respectively. f, g Imaging results for the target when the polarizer 2 was placed before the sCMOS. The orientations of the two polarizers are perpendicular. The insets in (d), (e), (f), and (g) show magnified images of the regions marked using a line-box in each case. h, i Vertical and horizontal cuts through the images shown in parts (d)\u2013(g) (white dashed lines), illustrating the consistency between the experimental and the calculated results. The grey dashed lines on (h) and (i) represent the background intensity. The full names of the abbreviations \u201carb. Units\u201d, \u201cExp.\u201d and \u201cBac.\u201d are \u201carbitrary units\u201d, \u201cExperiment\u201d and \u201cBackground\u201d, respectively.\n\nIn contrast, when the range of illumination angles for the incident beam (or for the incident wavevectors) is tuned to match the horizontal dashed line (where \\({k}_{y}=-0.18{k}_{0}\\) in \\(k\\)-space, in the momentum domain) as shown in Fig.\u00a02d, the first-order differentiation of the image (both experimental and simulated) will occur as shown in Fig.\u00a03e, g, i. One peak is formed around the edges, which represents the verification of the first-order derivative13,25. The edges of the elements are resolved clearly along the horizontal direction because the first-order derivative process is conducted along the \\(x\\)-axis. This is the one-dimensional (1D) first-order spatial differentiation process of the image. The image generation process is demonstrated intuitively in Supplementary Video\u00a02. If the test chart is rotated around the optical axis of the imaging objective by 45\u00b0, then the 2D first-order spatial differentiation can be performed on the image as shown in Fig. S4 in the supplementary information. In this case, the edges of the elements are resolved clearly along both the horizontal and vertical directions, with only one peak formed around the edges.\n\nTo quantify the resolution of the planar photonic chip for edge-enhancement imaging experimentally, a series of micrometer-scale elements on the resolution test chart were imaged as shown in Fig. S5a-g. The edges of elements with dimensions as small as 2 \u03bcm were resolved (Fig. S5g, h), thus indicating the possibility of 2D spatial differentiation with resolution of less than 2 \u03bcm. Detailed analysis on the resolution of the planar chip-based differential system is given in \u201cSection 5\u201d and Fig. S6 of the supplementary information.\n\nOne interesting phenomenon is observed when the working wavelength is tuned to 638\u2009nm, the coefficients\u2019 difference in transmission for \\(s\\)- and \\(p\\)-polarized light satisfies \\({t}_{p}-{t}_{s}=({C}_{p4}-{C}_{s4}){\\theta }^{4}\\) (as shown in Fig. S2b, e), so that a form of the OTF can be obtained as follows:\n\nWhen the azimuth \\(\\varphi\\) is fixed as a constant, the OTF has a form of:\n\nThen, the two-dimensional fourth-order spatial differentiation can be achieved, as illustrated in Fig.\u00a04a and shown in Supplementary Video\u00a03. Figure\u00a04c shows the intensity profile along the dashed line through the differentiated image (shown in Fig.\u00a04a), in which four closely spaced peaks are formed around the edge. This phenomenon represents the typical nature of the fourth-order derivative process. Similarly, when the \\({k}_{y}\\) is a constant (it can be experimentally realized by tuning the illumination directions), another form of the OTF is revealed:\n\na, b Imaging results for the target in the case of the fourth-order (a) and (b) the third-order spatial differentiation. The insets in (a) and (b) show magnified images of the regions marked using a line-box in each case. c, d Intensity profiles measured along the white dashed lines marked in (a) and (b). The grey dashed lines represent the background intensity. e Simulated BFP image at \\(\\lambda\\) = 638\u2009nm, the double arrow-headed line indicates the orientation of the analyzer. The trapezoidal regions are designed to perform the third-order differentiation, and the circular region for the fourth-order differentiation. The vertical and horizontal pink dotted lines indicate the directions of the third-order differentiation, the tilt orange dotted line indicates the fourth-order differentiation. f Experimentally measured BFP image at \\(\\lambda\\) = 638\u2009nm. g, h Intensity profiles along the differentiation directions of the fourth-order (along \\(\\varphi={45}^{\\circ }\\)) and the third-order(along \\({k}_{y}=-0.16{k}_{0}\\)) in (f), together with the corresponding simulated curves, and quartic and cubic fitting curves, respectively.\n\nThen, the third-order spatial differential image can be obtained as shown in Fig.\u00a04b and Supplementary Video\u00a04. The intensity profile (Fig.\u00a04d) along the dashed line through the differentiated image (Fig.\u00a04b), shows that three closely spaced peaks are formed around the edge, which is the typical nature of the third-order derivative process.\n\nThe simulated and experimental BFP images at the wavelength of 638\u2009nm are presented in Fig.\u00a04e f, which are consistent with each other. This consistency between the experimental and simulated BFP images (\\(\\lambda\\) =638\u2009nm) within a large \\(k\\)-space is illustrated in the images shown in Fig. S3c, d, g, h in the supplementary information. On the simulated BFP image (Fig.\u00a04e), the pink trapezoidal regions and orange circular region are designed for the third-order and fourth-order spatial differentiation, respectively, which are of the same principle as that for the first- and second-order differentiation, as demonstrated in Fig. S1f, g, h. As shown in Fig.\u00a04g, h, the simulated OTF for the fourth-order differentiation (at \\(\\varphi={45}^{\\circ }\\)) and the third-order differentiation (at \\({k}_{y}=-0.16{k}_{0}\\)) can be matched with the fitting curves in the form of \\(t=c{k}_{r}^{4}\\) and \\(t=d{\\left|{k}_{x}\\right|}^{3}\\), respectively. They are also consistent with the corresponding experimental curves derived from the experimental BFP image.\n\nBy using the same principle to tailor the angular transmission of this planar chip at other wavelengths, the fifth- and sixth-order differential operations can be implemented as shown in Fig. S3c, f in the supplementary information. To the best of our knowledge, third- and fourth-order spatial differentiation have never been experimentally realized before. Here, they are successfully demonstrated with one optical element. Based on the proposed theoretical analysis, the higher order spatial differentiation can also be realized with this chip. Spatial differentiation is one of the basic mathematical operation, and realization of different orders derivative with single optical element will be of great importance for optical analog signal processing. More importantly, combining multi-order differentiation operations, the Taylor expansion can be implemented on the electromagnetic field. In other words, optical analogue computing can be used to realize the Taylor expansion operation on the wave function of the input optical field.\n\nIn addition, the working wavelength for each-order spatial differential operation can be tuned by varying the thickness of each layer in the planar chip (More details are given in Section 6 of the supplementary information). For examples, 7 planar chips were fabricated via PECVD, whose operating wavelengths for second-order differential operation can be tuned precisely from 619\u2009nm to 627\u2009nm, as shown in Fig. S7 in the supplementary information. At these operating wavelengths, the edges of the microscale elements can be resolved clearly. Similar as those shown in Fig.\u00a04, based on the theoretical analysis described in the supplementary information, higher-order spatial differentiation can also be realized with these 7 planar chips, which will work in the desired wavelengths.\n\nIn this section, biological samples (B16F10 melanoma cells and onion epidermis) were used as imaging specimens. These samples only have a significant effect on the phase and not on its amplitude, and this class of specimens is thus referred to as a phase object class9,16,33. The experimental setup used is the same as that shown in Fig.\u00a03a, with the exception that the samples on the planar photonic chip were replaced with the biological specimens. Figure\u00a05a, e show the bright field images of the melanoma cells, and Fig.\u00a05c, g show the bright field images of the onion epidermis. These bright field images were obtained using a broad-band white light illumination source. The shapes and boundaries of the two specimens are not very clearly discernible in the bright field images because of their transparent nature. When the illumination wavelength is tuned to 643\u2009nm, the second-order (Fig.\u00a05b, d) and first-order (Fig.\u00a05f, h) differentiated images can then be obtained, and these images show both significant edge enhancement and high-contrast cell boundaries.\n\nBright field optical images of (a), (e) B16F10 melanoma cells and (c), (g) onion epidermis. b, d The second-order spatially differentiated images of the B16F10 melanoma cells and the onion epidermis, respectively. f, h The first-order spatially differentiated images of B16F10 melanoma cells and onion epidermis, respectively. The insets in (b), (d), (f), and (h) show magnified images of the regions marked using a line-box in each case.\n\nDark-field microscopy can also enhance the edges of these specimens, but it requires the use of complex components such as a condenser annulus, and also places high requirements on alignment of the optical path. Here, use of the planar photonic chip can reduce the system complexity significantly. The chip acts as a coverslip that provides edge enhancement automatically without use of additional optics. However, for conventional dark-field microscopy, the NA of the objective can be up to 0.70 in routine. For all the edge-enhancement imaging techniques based on the spatial differentiation, the allowed NA of the imaging objective (allowed angle-range for spatial differentiation) is smaller, such as NA less than 0.40 or even smaller8,9,12,25. It means that the conventional dark-field microscopy can achieve better spatial resolution. On the other hand, it also means that a high NA (larger than 0.70) condenser for dark-field illumination is required for the conventional dark-field microscope, which will reduce the illumination region and also the field of view of the microscope. This will not happen for the planar chip based dark-field imaging, because that the use of lower NA imaging objective will bring larger field of view and also there is no need for a larger NA condenser to realize the dark-field illumination.\n\nHere, when the first-order spatial differentiation is performed on the phase object (e.g., the transparent biological cell), the phase information of the specimen is obtained as follows25. The wave field that passes through the phase object can be written as \\({E}_{{in}}=1\\times {e}^{i\\phi \\left(x,y\\right)}\\) (the input intensity \\({I}_{{in}}={E}_{{in}}\\times {E}_{{in}}^{*}=1\\), showing no contrast). After the first-order differentiation operation (i.e., transmission through the planar chip), the output electric field can be written as \\({E}_{{out}}=\\partial {E}_{{in}}/\\partial x=i{e}^{i\\phi \\left(x,y\\right)}\\left[\\partial \\phi \\left(x,y\\right)/\\partial x\\right]\\), and the corresponding intensity \\(I={\\left|\\partial \\phi \\left(x,y\\right)/\\partial x\\right|}^{2}\\), which shows phase contrast that is proportional to phase gradients in the specimen. Therefore, the first-order differentiated image contains the phase information for this specimen.\n\nFor example, Fig.\u00a06a shows a commercial phase-type diffractive optical element called a vortex phase plate (topological charge =1, VPP-1b, RPC Photonics, Inc., USA) with an optical thickness that is proportional to the azimuth angle rotation. This element is always used to generate optical vortex beams34,35. There is a line that indicates the discontinuous spiral phase (i.e., the boundary between the spiral phase of 0 and the spiral phase of 2\u03c0; inset of Fig.\u00a06a) on this plate. This line is very blurred on the bright field image (Fig.\u00a06b), while in contrast, the line becomes obvious in the first-order differentiated image (Fig.\u00a06c) because of the existence of the phase gradient across this line.\n\na Photograph of a standard spiral phase plate, where the inset shows the spiral phase distribution. b Bright field image of the phase-discontinuous line on one element of this plate. c The first-order spatially differentiated image of this phase-discontinuous line.\n\nIt is known that most of the important features of specimens can be preserved even if only the phase is retained36, and thus retrieval of the optical phase information is highly important in many fields, particularly in biological science. For commonly used phase-contrast techniques such as differential interference contrast (DIC) and phase contrast microscope, of which the configuration is much more complex and precise alignment of the optical path is necessary. On the contrary, the proposed planar chip is both compact and easy to use. It does not mean that the proposed method should replace the conventional dark-field or phase contrast imaging techniques in all areas. The obvious advantages of the chip-based imaging technique are low cost, easy to use and large field of view. The same chip can be used as a cover slip and easily incorporating to the widely used optical microscopy to realize the functions of both the dark-field imaging and the phase information imaging.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In summary, a planar photonic chip composed of a well-designed dielectric multilayer structure is proposed to experimentally realize multiple mathematical operations, i.e., the first-, second-, third-, and fourth-order spatial differentiations, without the need to change the chip\u2019s structural parameters. The principle lies in the angular-dependent responses or nonlocality encoded within this dielectric multilayer structure. Through appropriate engineering of the nonlocality of this multilayer structure, the angle-dependent transmission along one direction in the momentum domain can match the requirements for one mathematical operation, and the other directions can be used to perform other operations. A theoretical analysis on the origin of these multiple spatial differentiations with single chip is proposed, which are consistent with the experimental results. It also reveals that higher order spatial differentiations can be achieved with the same chip. We have proved that multi-order differential operations can be imparted on the optical waves with one optical element so that this single multilayer chip can operate as a multifunctional compact device for optical analog signal processing. More importantly, the proposed approach also can realize the Taylor expansion of a mathematic function, which has never been proposed or realized before. Benefit from the ability for multiple-orders spatial differential operations, it is possible to use the planar photonic chip for solving the differential equations with constant coefficients37,38,39 and conducting beam shaping15,40,41. In addition, higher-order differentiations can lead to sharper peaks at the edges of the image, meaning that higher-order differentiation can play an important role in image sharpening24.\n\nBecause of its ability to perform spatial differentiation and the thin film factor, this planar chip can be incorporated easily into conventional imaging systems, thus enabling high-contrast edge imaging of both amplitude and phase objects. For pure phase objects (e.g., biological cells), the phase information in the spatial domain can also be derived. This dielectric multilayer structure does not require precise nanofabrication procedures and can be manufactured on a large scale at low cost. The chip working as spatial differentiator offers the advantage of a multifunctional wave-based analogue computing ability, thus it will provide a route for designing fast, power-efficient, compact and low-cost devices used in edge detection and optical image processing, and offers opportunities for the rapid developing research field where the engineered substrates are proposed to enhance the imaging performance of the conventional optical microscope12,42,43,44,45,46,47,48.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The photonic chip was fabricated via PECVD (Oxford System 100, UK) of SiO2 and Si3N4 layers on a standard microscope cover slip (thickness: 0.17\u2009mm) at a vacuum of <0.1 mTorr and a temperature of 300\u2009\u00b0C. Before the coating process, the coverslip was cleaned using acetone, absolute ethanol, piranha solution, and nanopure deionized water in turn, and was then dried using a N2 stream. The SiO2 layer is the low refractive index dielectric layer and the Si3N4 layer is the high refractive index dielectric layer. The process of Si3N4 generation is dependent on the chemical reaction of SiH4 with N2O and NH3 at high temperatures, and the process of SiO2 generation is dependent on the chemical reaction of SiH4 and N2O. By controlling the ventilation volumes and ventilation rates of the various gases, the thickness and refractive index of each layer can be determined precisely. To confirm that the designed optical functions of the fabricated photonic chip were realized, an in-house-built reflection BFP imaging setup was used to characterize the photonic band gaps of this dielectric multilayer structure (see Fig. S8).\n\nThe live biological cell is B16-F10, a mouse melanoma highly transfected cell which is a subline of B16-F0 cell and the cells for experiments were cultured in DMEM with 10% FBS and 1% PS. The onion cells were peeled from the upper epidermis and immersed in physiological saline solution.\n\nAll optical measurements were performed using a modified optical microscope (Ti2-U, Nikon, Japan). In the transmission BFP imaging setup (Fig.\u00a02c), the illumination beam with a central wavelength of 643\u2009nm and a bandwidth of 2\u2009nm was emitted from a supercontinuum fiber laser with an acousto-optic tunable filter (SuperK EXU-6, NKT Photonics, Denmark). The beam was collimated and passed through polarizer 1. Then, the beam was focused onto the photonic chip using objective 1 (S Plan Fluor, 40\u00d7, numerical aperture NA\u2009=\u20090.60; Nikon, Japan). The transmitted signals were collected using objective 2 (S Plan Fluor, 60\u00d7, NA\u2009=\u20090.70; Nikon, Japan). The analyzer (polarizer 2), which has an orientation that is perpendicular to that of polarizer 1, was placed between objective 2 and the tube lens. It was then used to eliminate the direct component of the transmitted signal and modify the transmission curves. The BFP images were then recorded using a Neo scientific complementary metal-oxide-semiconductor (sCMOS) detector (Andor Oxford Instruments, UK).\n\nIn the front focal plane imaging set-up (Fig.\u00a03a), the illumination beam remained unchanged. It was defocused using an objective (UPlanSApo, 10\u00d7, NA\u2009=\u20090.25; Olympus, Japan) onto the specimens that were placed on the photonic chip. This defocused beam can provide a variety of illumination angles in different areas, and can thus induce different mathematical operations as a result. The scattered and transmitted light from the specimens and the photonic chip was collected using objective 2 (S Plan Fluor, 20\u00d7, NA\u2009=\u20090.45; Nikon, Japan), and was then imaged onto the other camera (Andor Oxford Instruments, United Kingdom) with the aid of a tube lens. An analyzer (polarizer 2) was inserted between the tube lens and objective 2.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "The data that support the plots within this paper and other finding of this study are available from the corresponding author upon request. Source data for Figs.\u00a01\u20136 are available at https://doi.org/10.6084/m9.figshare.21506229.v3.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The codes that support the findings of this study are available from the corresponding authors upon reasonable request.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This work was supported by the National Key Research and Development Program of China (2021YFA1400700), the National Nature Science Foundation of China (grant nos. 12134013 and 62127818), the Hefei Municipal Natural Science Foundation (grant no. 2021007), the Key Research & Development Program of Anhui Province (202104a05020010), and the Fundamental Research Funds for the Central Universities (WK2340000109), Inovation Program for Quantum Science and Technology (No. 2021ZD0303301). D.G. Zhang is supported by a USTC Tang Scholarship. The work was partially performed at the University of Science and Technology of China\u2019s Center for Micro and Nanoscale Research and Fabrication.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Advanced Laser Technology Laboratory of Anhui Province, Department of Optics and Optical Engineering, University of Science and Technology of China, Hefei, Anhui, 230026, China\n\nYang Liu,\u00a0Mingchuan Huang,\u00a0Qiankun Chen\u00a0&\u00a0Douguo Zhang\n\nHefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China\n\nDouguo Zhang\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\nD.G.Z. and Y.L. initiated the work. Y.L., M.C.H., and Q.K.C. acquired the theoretical and simulated results. Y.L. fabricated the samples. Y.L. and D.G.Z. performed the optical experiments. D.G.Z. and Y.L. wrote the manuscript. D.G.Z. supervised the work. All authors discussed the results and commented on the manuscript.\n\nCorrespondence to\n                Douguo Zhang.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": ": Nature Communications thanks Amin Khavasi, Hailu Luo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.\u00a0Peer reviewer reports are available.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional information",
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+            "section_image": []
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+        },
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+            "section_name": "About this article",
+            "section_text": "Liu, Y., Huang, M., Chen, Q. et al. Single planar photonic chip with tailored angular transmission for multiple-order analog spatial differentiator.\n                    Nat Commun 13, 7944 (2022). https://doi.org/10.1038/s41467-022-35588-5\n\nDownload citation\n\nReceived: 28 July 2022\n\nAccepted: 09 December 2022\n\nPublished: 26 December 2022\n\nVersion of record: 26 December 2022\n\nDOI: https://doi.org/10.1038/s41467-022-35588-5\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": "Nature Communications (2025)\n\nNature Communications (2025)\n\nNature Communications (2025)\n\nNature Communications (2025)\n\nNature Reviews Electrical Engineering (2024)",
+            "section_image": []
+        }
+    ],
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+            "title": "Supportinformation18.pdf",
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+{
+    "title": "Prethermalization in one-dimensional quantum many-body systems with confinement",
+    "pre_title": "Prethermalization in confined spin chains",
+    "journal": "Nature Communications",
+    "published": "10 December 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35301-6/MediaObjects/41467_2022_35301_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-022-35301-6/MediaObjects/41467_2022_35301_MOESM2_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://doi.org/10.5281/zenodo.7034368"
+    ],
+    "code": [
+        "https://doi.org/10.5281/zenodo.7034368"
+    ],
+    "subject": [
+        "Phase transitions and critical phenomena",
+        "Statistical physics",
+        "Thermodynamics"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-1642071/v1.pdf?c=1653507585000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-1642071/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-022-35301-6.pdf",
+    "preprint_posted": "25 May, 2022",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Unconventional nonequilibrium phases with restricted correlation spreading and slow entanglement growth have been proposed to emerge in systems with confined excitations, calling their thermalization dynamics into question. Here, we investigate the many-body dynamics of a confined Ising spin chain, in which domain walls in the ordered phase form bound states reminiscent of mesons. We show that the thermalization dynamics after a quantum quench exhibits multiple stages with well separated time scales. The system first relaxes towards a prethermal state, described by a  Gibbs ensemble with conserved meson number. The prethermal state arises from rare events in which mesons are created in close vicinity, leading to an avalanche of scattering events. Only at much later times a true thermal equilibrium is achieved in which the meson number conservation is violated by a mechanism akin to the Schwinger effect.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        },
+        {
+            "section_name": "Supplementary Files",
+            "section_text": "ConfinementDynamicsSupplementary.pdfPrethermalization in confined spin chains",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Unconventional nonequilibrium phases with restricted correlation spreading and slow entanglement growth have been proposed to emerge in systems with confined excitations, calling their thermalization dynamics into question. Here, we show that in confined systems the thermalization dynamics after a quantum quench instead exhibits multiple stages with well separated time scales. As an example, we consider the confined Ising spin chain, in which domain walls in the ordered phase form bound states reminiscent of mesons. The system first relaxes towards a prethermal state, described by a Gibbs ensemble with conserved meson number. The prethermal state arises from rare events in which mesons are created in close vicinity, leading to an avalanche of scattering events. Only at much later times a true thermal equilibrium is achieved in which the meson number conservation is violated by a mechanism akin to the Schwinger effect. The discussed prethermalization dynamics is directly relevant to generic one-dimensional, many-body systems with confined excitations.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "Nonequilibrium states of quantum many-body systems play an important role in various fields of physics, including cosmology and condensed matter. Of particular interest is the time evolution of interacting quantum many-body systems that are well isolated from their environment1,2. This research has been fueled by the progress in engineering coherent and interacting quantum many-body systems which made it possible to experimentally study unconventional relaxation dynamics. A recent interest is to explore phenomena from high-energy physics with synthetic quantum systems in a controlled way; for example lattice gauge theories have been realized3,4,5,6,7,8,9 and phenomena akin to quark confinement have been explored3,6,10,11,12, with great emphasis on the atypical nonequilibrium features of confined systems. Confinement strongly affects the relaxation dynamics of the system, leading to unconventional spreading of correlations and slow entanglement growth13,14,15, with striking signatures in the energy spectrum reminicent of quantum scars16,17. In spite of many efforts, a proper characterization of the full many-body dynamics and thermalization in confined systems remaines elusive so far.\n\nAn archetypical model to study confinement phenomena in condensed-matter settings is the Ising model with both transverse and longitudinal magnetic fields18,19,20,21,22,23. In this model, domain walls\u2014interpreted as quarks\u2014are pairwise confined into mesons by a weak longitudinal field; see Fig.\u00a01a. A key feature of the model is the long lifetime of mesons, ascribed to a strong suppression of the Schwinger mechanism24,25,26,27,28,29, which creates new quarks from the energy stored in the confining force and viceversa. Hence, except for some fine-tuned regimes30,31,32, mesons are stable excitations. Due to the approximate conservation of the meson number, various exotic dynamical phenomena have been proposed, including Wannier-Stark localization33,34,35 and time crystals36. Even though the realization of these phenomena does not require particular fine tuning, they arise in a regime in which interactions between mesons are extremely unlikely. The few-meson scattering has been recently considered30,31,37,38, but so far, apart from special limits39, the full many-body dynamics of confined systems has not been addressed. Irrespective of these exciting effects, the Ising model with longitudinal and transverse fields is non-integrable19 and features a Wigner-Dyson level statistics of the eigenenergies40. Hence, one would expect on general grounds41,42,43 that the system thermalizes at late times and interactions between mesons can become relevant. Given this wealth of unconventional nonequilibrium phenomena and the discrepancy with the expected thermalization in non-integrable models, it is important to understand the mechanisms of relaxation and their timescales.\n\na Pairs of domain walls, interpreted as mesons, are confined by the longitudinal field. b For weak quantum quenches of the transverse and longitudinal fields the Ising chain exhibits a multi-stage relaxation dynamics. Insets: typical domain wall trajectories in the different dynamical phases. At short times, t\u2009<\u2009tPreTh\u2009\u221d\u2009\u03c1\u22122h\u2225 (with \u03c1 the density of mesons) a metastable state arises in which mesons are at rest and well separated. For intermediate times tPreTh\u2009<\u2009t\u2009<\u2009tTh, rare events initiate avalanches of scattering processes, leading to prethermal Gibbs ensemble with conserved density of mesons \u03c1. At late times \\(t\\, > \\,{t}_{{{\\mbox{Th}}}}\\propto \\exp [(...){h}_{\\parallel }^{-1}]\\), the Schwinger mechanism breaks the meson-number conservation leading to full thermalization. c The meson density \u03c1, computed with tensor network simulations, relaxes to the analytical prediction (dashed gray lines) of ref. 15 (see also\u00a0supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.)).\n\nIn this work, we investigate the relaxation dynamics of one-dimensional systems in the presence of confinement, with focus on the Ising chain as a primary example. Two scenarios could be envisioned for the thermalization process. The first one is that the Schwinger effect, leading to a violation of the meson-number conservation, could be the only responsible mechanism for equilibration, causing an extremely slow thermalization dynamics. A more exciting, second scenario involves an intermediate thermalization of the mesons themselves. Here, we show that indeed the second scenario is realized. Generic states first relax to a Gibbs ensemble in which the meson number is conserved up to extremely long times; Fig.\u00a01b, c. We show that relaxation to this state is activated through rare events in which two mesons are produced in their vicinity, initiating an avalanche of scattering events. This prethermal state can then be understood as a dilute thermal gas of mesons with conserved meson density. Only at exponentially long times, the Schwinger mechanism causes a full thermalization of the system coupling sectors with a different number of mesons. While we choose to focus on the Ising chain as the simplest example where both analytical and numerical progress can be made efficiently, our findings can be extended to generic confined many-body systems as we emphasize in the discussion section.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-022-35301-6/MediaObjects/41467_2022_35301_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "The Ising chain with both transverse and longitudinal fields is described by the Hamiltonian\n\nIn the pure transverse-field regime (h\u2225\u2009=\u20090) the model is equivalent to noninteracting fermions and exhibits spontaneous \\({{\\mathbb{Z}}}_{2}-\\)symmetry breaking for \u2223h\u22a5\u2223\u2009\u2264\u20091 in the thermodynamic limit. For h\u22a5\u2009\u2192\u20090, the two degenerate ground states \\(\\left|{{{\\mbox{GS}}}}_{\\pm }\\right\\rangle\\) are simple product states of maximally positive/negative magnetization, which are renormalized for finite transverse field, such that \\(\\left\\langle {{{\\mbox{GS}}}}_{\\pm }\\right|{\\hat{\\sigma }}_{j}^{z}\\left|{{{\\mbox{GS}}}}_{\\pm }\\right\\rangle=\\pm \\bar{\\sigma }\\), with \\(\\bar{\\sigma }={(1-{h}_{\\perp }^{2})}^{1/8}\\)44. In this phase, the fermionic modes are interpreted as (dressed) domain walls (or kinks) relating the two vacua and are thus of topological nature. A small longitudinal field h\u2225\u2009>\u20090 lifts the ground state degeneracy, leading to a low-energy \u201ctrue vacuum\" and a high-energy \u201cfalse vacuum,\" and induces a pairwise linear potential \\(\\propto 2{h}_{\\parallel }\\bar{\\sigma }\\) between kinks; Fig.\u00a01a.\n\nWe consider the following quantum quench13: The system is initialized for h\u2225\u2009=\u20090 in one of the two degenerate ground states (specifically, we select \\(\\langle {\\hat{\\sigma }}^{z}\\rangle \\, > \\,0\\)) and then brought out of equilibrium by suddenly changing both the transverse and the longitudinal field components. Building on the knowledge of quenches in the transverse field only45, one can argue that fermions are locally produced in pairs with opposite momenta13, each of them having a dispersion \\(\\epsilon (k)=2\\sqrt{{(\\cos k-{h}_{\\perp })}^{2}+{\\sin }^{2}k}\\). However, pairs of fermions are then confined due to the finite longitudinal field h\u2225\u2009\u2260\u20090. For weak quenches, very few excitations are produced and, due to translational invariance, mesons are mostly initialized at rest and are well isolated. Their stability is guaranteed by the strong suppression of fermion number-changing processes. In the case of small transverse field (\u2223h\u22a5\u2223\u2009<\u20091/3) two fermions cannot energetically couple to the four-fermion sector without using the energy stored in the false-vacuum string. Hence, this process resembles the false-vacuum decay, whose lifetime has been shown to scale exponentially with \\({h}_{\\parallel }^{-1}\\)24. Even in the less restricted regime where the scattering of two fermions into four is energetically allowed (1/3\u2009<\u2009\u2223h\u22a5\u2223\u2009<\u20091), the cross section is induced by the weak longitudinal term, leading to a meson lifetime that scales algebraically in the longitudinal field \\({h}_{\\parallel }^{-3}\\)46. To confirm this expectation, we perform tensor network simulations47,48,49 based on the TenPy library49 of the quantum quench and compute the meson density \u03c1; Fig.\u00a01c. We checked convergence of our data with bond dimension on the shown timescales (data are shown for \u03c7\u2009=\u2009256). In the limit of small h\u2225 the meson number is conserved on the numerically accessible timescales (see Methods).\n\nAssuming that the meson number is conserved, we now study the thermodynamics of a gas of mesons, which is expected to describe the prethermal state. In the dilute regime, the mean-free path is much larger than the typical meson length. In a first approximation, we therefore neglect the effects that the size of the meson has on the thermodynamics. A convenient starting point is the semiclassical limit of a single meson, in which one treats the two fermions as point-like particles with coordinates (x1,2,\u2009k1,2) governed by the classical Hamiltonian\n\nThe semiclassical approximation holds when interactions cannot resolve the discreteness of the underlying lattice, i.e., for h\u2225\u2009\u226a\u20091. Hence, the position of the particle x1,2 is a continuous variable. In the reduced two-body problem, the total momentum k\u2009=\u2009k1\u2009+\u2009k2 of a meson is conserved, thus the dynamics of the relative coordinates (q\u2009=\u2009(k1\u2009\u2212\u2009k2)/2,\u2009x\u2009=\u2009x1\u2009\u2212\u2009x2) is governed by \\({{{{{{{{\\mathcal{H}}}}}}}}}_{{{{{{{{\\rm{rel}}}}}}}}}(q,\\,x)=\\epsilon (k/2+q)+\\epsilon (k/2-q)+2\\bar{\\sigma }{h}_{\\parallel }|x|\\). Then, the thermal probability of having a meson with a given energy and momentum is \\(P(E,\\, k)={e}^{-\\beta (E-\\mu )}\\int\\frac{{{{{{{{\\rm{d}}}}}}}}q{{{{{{{\\rm{d}}}}}}}}x}{{(2\\pi )}^{2}}\\,\\delta ({{{{{{{{\\mathcal{H}}}}}}}}}_{{{{{{{{\\rm{rel}}}}}}}}}(q,\\,x)-E)\\), where the inverse temperature \u03b2 and chemical potential \u03bc must be fixed by matching the initial average energy and meson density, respectively. The integral over the relative coordinates is most conveniently tackled by transforming to action-angle variables (J,\u2009\u03d5)50, where \\(J\\equiv {\\oint }_{{{{{{{{{\\mathcal{H}}}}}}}}}_{{{{{{{{\\rm{rel}}}}}}}}}(q,x)={{{{{{{\\mathcal{E}}}}}}}}(J,k)}q{{{{{{{\\rm{d}}}}}}}}x\\) labels the phase-space orbits of the classical motion and \u03d5 is a periodic variable \u03d5\u2009\u2208\u2009[0,\u20091], leading to \\(P(E,\\, k)={e}^{-\\beta (E-\\mu )}\\int\\frac{{{{{{{{\\rm{d}}}}}}}}J}{{(2\\pi )}^{2}}\\delta ({{{{{{{\\mathcal{E}}}}}}}}(J,\\,k)-E)\\). Leaving the classical limit, the energy levels become quantized according to the Bohr-Sommerfeld rule J\u2009=\u20092\u03c0(n\u2009\u2212\u20091/2), where n is a natural number20.\n\nAway from the dilute regime mesons should be treated as extended objects and their thermodynamics needs to be suitably modified. To this end, we consider mesons as hard-rods of fixed length \u2113(J,\u2009k), the latter being the meson length averaged over one oscillation period. Within this assumption, P(E,\u2009k) gets modified as\n\nwith \u03c1 the meson density and M the average meson length, which are self-consistently determined by P(E,\u2009k); see also\u00a0supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.). The meson coverage \u03c1M is connected to the magnetization of the Ising chain as \\(\\rho M=1/2-{\\bar{\\sigma }}^{-1}\\langle {S}^{z}\\rangle\\).\n\nWhile we chose to present the thermodynamics from the semiclassical perspective for the sake of clarity, quantum effects can be important when the fermion bandwidth becomes comparable with the longitudinal field and the Born-Sommerfeld quantization is a poor approximation. In this regime, the classical Hamiltonian (2) can be directly promoted to a quantum object and explicitly diagonalized15, thus replacing the J\u2009\u2212\u2009integration in Eq. (3) with a discrete sum (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.).\n\nIn order to show that meson-meson scattering leads to a prethermal Gibbs Ensemble, we numerically calculate the time evolution in the subspace with a fixed number of mesons using exact diagonalization (see Methods). We consider a chain of length L with periodic boundary conditions, and focus on the limit 0\u2009<\u2009h\u22a5\u2009\u226a\u20091 where fermions can be identified with domain walls. In this regime, \\(\\bar{\\sigma }\\to 1\\) and the confinement strength is determined by h\u2225/h\u22a5. We initialize the state in the form of moving wave packets and probe relaxation by tracking the meson momentum distribution; Fig.\u00a02. Whereas for two mesons, energy and momentum conservation inhibits thermalization, see\u00a0supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.), for three mesons we observe the relaxation to the prethermal Gibbs ensemble; Eq. (3). Two-body scattering processes between different energy bands are responsible for the thermalization; Fig.\u00a02b. For wave packets which are initialized with energies below the second band thermalization is largely suppressed, as two-body collisions become elastic due to momentum-energy conservation and three-body scattering events are unlikely; Fig.\u00a02a. We provide additional details on the thermalization in the\u00a0supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.).\n\nWe create three mesons with Gaussian wave packets tuned to target the lowest energy band at momenta {\u2009\u2212\u2009k0,\u20090,\u2009k0} in a chain of length L\u2009=\u2009100 with confinement field h\u2225/h\u22a5\u2009=\u20090.1 (see Methods). Energy bands are computed through a numerical solution of the two-fermions quantum Hamiltonian (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.). The evolution of the momentum distribution P(k) of the meson initialized at rest (empty circle in upper panels) is shown. a For k0\u2009=\u2009\u03c0/4 the energy of the initial wave packets is below the second band of the single meson dispersion (upper panel), which causes meson scattering events to be elastic and prohibits relaxation to a prethermal ensemble (red curve). b For k0\u2009=\u20093\u03c0/4, the initial wave packets are resonant with other bands, which can then be populated, and lead to inelastic scattering. This quantum state relaxes to a prethermal configuration at late times. Prethermal curves are computed according to the hard-rods thermodynamics (3) using the exact quantum eigenfunctions rather than the semiclassical prediction (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.).\n\nEquipped with the meson conservation, the thermodynamics of the prethermal state, and the quantum thermalization of a few mesons, we now study the full quench protocol. In order to access large system sizes and timescales, we use the Truncated Wigner Approximation51 on the quantum dynamics projected in the fermion number conserving sector (see Methods). In order to study the relaxation dynamics, a precise knowledge of the excitation content of the initial state is crucial. The quantum quench of both the longitudinal and the transverse field excites dilute pairs of fermions with opposite momenta (k,\u2009\u2212\u2009k) at density n(k), which can be computed from the quench parameters13,15. These pairs of fermions are then confined into mesons by the longitudinal field according to Eq. (2).\n\nFor small quenches within the ferromagnetic phase, the density of mesons is low. Typically, mesons are excited far apart and are thus isolated and at rest. In this scenario, inter-meson scattering and thermalization seems impossible. However, considering only the typical behavior is misleading, as the probability of creating two nearby mesons is never strictly zero. To obtain a rough estimate, we consider the maximum size dmax that a meson can have when fermions are initially created at the same position, which is given by \\({d}_{{{{{{{\\rm{max}}}}}}}}=4{h}_{\\perp }/({h}_{\\parallel }\\bar{\\sigma })\\), and compare it with the meson density \u03c1. On a finite volume L, the probability P(L) that N\u2009=\u2009L\u03c1 randomly distributed particles are placed at distance larger than dmax is \\(P(L)=\\frac{1}{{L}^{N}}\\mathop{\\prod }\\nolimits_{\\,j=0}^{N-1}(L-j{d}_{{{{{{{{\\rm{max}}}}}}}}})\\simeq {e}^{-L{\\rho }^{2}{d}_{{{{{{{{\\rm{max}}}}}}}}}/2}\\). No matter how small the excitation density \u03c1 is, eventually in the thermodynamic limit the probability that all the excited mesons are far apart vanishes. Crucially, the rare nearby mesons scatter and acquire a finite velocity. These moving mesons consequently trigger an avalanche, that hits the surrounding mesons, and initiates prethermalization; see Fig.\u00a03a for a typical meson configuration. In Fig.\u00a03b, left, we first ensure that the semiclassical approximation is reliable for the chosen quench parameters, by comparing with tensor network simulations on the reachable timescale (convergence with bond dimension is checked; data shown for \u03c7\u2009=\u2009256). Then, we use the semiclassical approach to probe extremely long times, observing prethermalization of both the meson coverage \u03c1M (inset) and the momentum distribution of mesons P(k) (right panels). For the latter the initial\u2009\u221d\u2009\u03b4(k) peak decays due to the aforementioned avalanche effect and relaxes to a smooth prethermal Gibbs distribution.\n\na Typical semiclassical trajectories obtained with the Truncated Wigner Approximation. Most fermions belong to mesons at rest (blue lines), but rare events in which mesons are in close vicinity lead to an avalanche effect putting mesons in motion (red lines) and activating dynamics in the entire meson ensemble. b For comparably small values of h\u2225 semiclassical results for the average meson coverage \u03c1M agree well with exact quantum evolution obtained from tensor network techniques. (Inset) The semiclassical analysis reveals relaxation towards a prethermal plateau (red), which is distinct from the thermal state in the absence of meson conservation (green dashed). Side panels: Relaxation of the semiclassical ensemble is also reflected in the decay of the the momentum distribution P(k) at k\u2009\u2248\u20090. Thermal (\u03bc\u2009=\u20090) and prethermal (\u03bc fixed by number of mesons) predictions are computed with Eq. (3), directly in the classical limit.\n\nThe density dependence of the prethermalization timescale tPreTh can be understood as follows. Initially, the configuration consists of large regions of average size \\(\\sim {({\\rho }^{2}{d}_{{{{{{{{\\rm{max}}}}}}}}})}^{-1}\\) with mesons at rest separated by growing thermalizing domains. Hence, we estimate prethermalizing regions to cover the whole system on a typical time \\({t}^{*} \\sim {({\\rho }^{2}{d}_{{{{{{{{\\rm{max}}}}}}}}}{{{{{{{\\rm{v}}}}}}}})}^{-1}\\), where v is a typical velocity. Once all mesons are set in motion, two-body inelastic scatterings drive the relaxation of the system on a timescale t**\u2009~\u2009(\u03c1v)\u22121. At low excitation density, t*\u2009\u226b\u2009t**, hence \\({t}_{{{{{{{{\\rm{PreTh}}}}}}}}} \\sim {({\\rho }^{2}{d}_{{{{{{{{\\rm{max}}}}}}}}}{{{{{{{\\rm{v}}}}}}}})}^{-1}\\).\n\nBuilding on this approximation, we can understand the relaxation of local observables by assuming that prethermalizing regions contribute with \\({{{{{{{{\\mathcal{O}}}}}}}}}_{{{{{{{\\rm{PreTh}}}}}}}}\\), while regions with static mesons retain the initial value \\({{{{{{{{\\mathcal{O}}}}}}}}}_{0}\\) (after a short dephasing time). Hence, \\(\\langle {{{{{{{\\mathcal{O}}}}}}}}(t)\\rangle\\) follows the average growth of thermalizing regions\n\nwhere we approximate each prethermalizing region to growth in a lightcone fashion with velocity v and \\({{\\Delta }}{{{{{{{\\mathcal{O}}}}}}}}={{{{{{{{\\mathcal{O}}}}}}}}}_{0}-{{{{{{{{\\mathcal{O}}}}}}}}}_{{{{{{{\\rm{PreTh}}}}}}}}\\) Above, \u03b8(x) is the Heaviside theta function \u03b8(x\u2009>\u20090)\u2009=\u20091 and zero otherwise, D is the distance between two rare events which is distributed with probability distribution \\({{{{{{{\\mathcal{P}}}}}}}}(D)\\). By its very definition, \\({{{{{{{{\\mathcal{O}}}}}}}}}_{0}\\) can be computed as the late-time limit of the single meson approximation, since outside of the scrambling region the mesons are not interacting. Finally, the term \\(\\frac{D-2{{{{{{{\\rm{v}}}}}}}}t}{D}\\) is nothing else than the portion of frozen region that remained after the thermalizing region propagated with velocity v inside of it. The last step is now to estimate \\({{{{{{{\\mathcal{P}}}}}}}}\\). We have already computed the probability that, within a system of size L, there are no rare events. In the computation, we used the maximum extension of a meson dmax as an upper bound, but a better estimate is obtained using the average size of the excited mesons, which we call d. Hence, the probability that within an interval L there are no rare events is \\(P(L)={e}^{-L{\\rho }^{2}d/2}\\). The distributions P(L) and \\({{{{{{{\\mathcal{P}}}}}}}}(D)\\) are related by \\(P(L)=\\int\\nolimits_{L}^{\\infty }{{{{{{{\\rm{d}}}}}}}}D\\,{{{{{{{\\mathcal{P}}}}}}}}(D)\\), leading to \\({{{{{{{\\mathcal{P}}}}}}}}(D)=\\frac{{\\rho }^{2}d}{2}{e}^{-D{\\rho }^{2}d/2}\\). With this approximation, Eq. (4) can be recast in a scaling form \\(\\langle {{{{{{{\\mathcal{O}}}}}}}}(t)\\rangle={{{{{{{{\\mathcal{O}}}}}}}}}_{{{{{{{\\rm{PreTh}}}}}}}}+{{\\Delta }}{{{{{{{\\mathcal{O}}}}}}}}\\,F(t{{{{{{{\\rm{v}}}}}}}}{\\rho }^{2}d)\\) with \\(F(\\tau )=\\int\\nolimits_{\\tau }^{\\infty }{{{{{{{\\rm{d}}}}}}}}s\\,{e}^{-s}(1-\\tau /s)\\).\n\nThe full numerical results agree with this picture; Fig.\u00a04a. Since \\({d}_{{{{{{{{\\rm{max}}}}}}}}}\\propto {h}_{\\parallel }^{-1}\\), smaller longitudinal fields leads to a shorter prethermalization timescale for the same meson density \u03c1. Even in the less favorable case where h\u22a5 is kept constant and only h\u2225 is quenched (i.e., only the small longitudinal field is ultimately responsible of creating fermionic excitations), we find \\({\\rho }^{2}\\propto {h}_{\\parallel }^{-2}\\) (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.). Hence, there is in any case a separation of scales between the prethermalization time \\({t}_{{{{{{{{\\rm{PreTh}}}}}}}}}\\propto {h}_{\\parallel }^{-1}\\) and the violation of meson-number conservation \\({t}_{{{{Th}}}} \\sim \\exp [(...){h}_{\\parallel }^{-1}]\\), consistently ensuring the existence of the prethermal regime for a large class of quenches.\n\naThe late-time relaxation of the average meson length M to the prethermal plateau is well-described by the prediction \\(\\langle {{{{{{{\\mathcal{O}}}}}}}}(t)\\rangle={{{{{{{{\\mathcal{O}}}}}}}}}_{{{{{{{\\rm{PreTh}}}}}}}}+{{\\Delta }}{{{{{{{\\mathcal{O}}}}}}}}F(t{{{{{{{\\rm{v}}}}}}}}d{\\rho }^{2})\\). The quantity vd is obtained from a fit to the data. b The normalized one-meson phase-space occupation relaxes to a prethermal ensemble (prethermal: red continuous line; thermal: green dashed line; numerics: blue shaded area). Finite-density corrections are captured by the hard-rods approximation and cause an additional peak in the energy distribution P(E) (bottom). The relative difference in the meson densities between the thermal and prethermal ensemble \u0394\u03c1\u2009=\u2009(\u03c1PreTh\u2009\u2212\u2009\u03c1Th)/\u03c1Th are \u0394\u03c1\u2009=\u20090.16 and \\({{\\Delta }}\\rho={{{{{{{\\mathcal{O}}}}}}}}(1{0}^{-3})\\) for \\({h}_{\\parallel }^{f}=0.015\\) (top) and \\({h}_{\\parallel }^{f}=0.001\\) (bottom), respectively. Thermal and prethermal observables are computed with Eq. (3), real-time evolution is obtained within the Truncated Wigner Approximation.\n\nIn Fig.\u00a04b we study the semiclassical prethermal regime for different confining strengths, but the same average density and energy. For \\({h}_{\\parallel }^{f}=0.015\\) (top) the average meson length is shorter than for \\({h}_{\\parallel }^{f}=0.001\\) (bottom). We observe that the larger size of the mesons influences the phase-space distribution as follows: (i) it introduces a momentum-dependent cutoff in the energy, which is ultimately caused by the fact that the average meson length is bounded by the mean-free path, and (ii) the probability distribution is squeezed to the boundaries of the allowed phase space. A consequence of this is the emergence of a peak in the energy distribution corresponding to the Brillouin zone boundaries (compare bottom and top distibution functions). This effect is captured by our hard-rods approximation. For this choice of parameters, we observe the thermal number of mesons is lower than the prethermal one, hence thermalization is achieved by fusing small mesons into larger ones, i.e., by the reverse process of the Schwinger effect; Fig.\u00a01b. In order to conserve the total mean energy, the thermal distribution has more high-energy mesons excited than the prethermal case. The difference between the prethermal and thermal state is reduced at higher meson densities, where the hard-rods correction penalizes large mesons.\n\nBy virtue of the simple underlying kinetic mechanism, the validity of our study is expected beyond the classical realm to hold in the quantum case as well, with an additional refinement. As previously mentioned, thermalization is activated by two-body scattering between different energy bands. Hence, the estimate of tPreTh should be corrected considering that only a fraction of \u03c1 is contributing to the inelastic scattering.",
+            "section_image": [
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "Confined spin chains exhibit an intriguing multi-stage thermalization dynamics. We show that not the Schwinger mechanism is responsible for activating transport, but rather rare events in which two mesons are generated in their vicinity lead to a prethermal regime, that can be understood as a thermal gas of mesons. The different mechanism ensures the separation of timescales and the existence of a prethermal regime. The prethermalization time can be greatly reduced by considering quench protocols that create mesons with non-zero velocity. This, for example, can be realized with spatially modulated pulses of the transverse field52 (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.).\n\nWe used the Ising chain (1) as a prototypical model to demonstrate the rich relaxation dynamics. However, similar dynamics is expected in other confined many-body systems as well; for example lattice gauge theories53,54,55. Incidentally, we notice that the Ising chain (1) can be interpreted as a \\({{\\mathbb{Z}}}_{2}-\\)gauge theory in the zero charge sector, where matter degrees of freedom have been integrated out by virtue of the Gauss law33. A prominent example of a different lattice gauge theory is the U(1) quantum link model\n\nwhere staggered Kogut-Susskind fermionic matter \u03d5j56 interacts via the gauge degrees of freedom encoded in the spin variables \\({S}_{j,j+1}^{\\alpha }\\). In this model, (anti-)quarks correspond to defects in the staggered matter degrees of freedom and quark-antiquark pairs experience a linear confinement potential\u2009\u221d\u2009h\u2225. In a recent work57, it has been understood that the Hamiltonian (5) maps to the Fendley-Sengupta-Sachdev Hamiltonian58 describing one-dimensional Rydberg atom arrays59 which may experimentally probe our findings. Within this implementation, the vacuum of the gauge theory is mapped into a chain where atoms are excited in their Rydberg state on even sites, then quark-antiquark pairs are excited by placing defects in this configuration. Realizing a quantum quench akin to the one studied here, will thus lead to the same multi-stage thermalization dynamics. Further details can be found in\u00a0supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.).\n\nOther experimentally relevant models with confinement can be realized in spin ladders60,61,62 or long-range systems11,25. Particularly intriguing features can be expected for long-range models: in contrast to the short-range Ising chain (1) and the quantum link model (5) discussed above, long-range couplings induce slowly decaying (power-law) interactions between mesons which cannot be neglected. The long-range interactions can be envisaged to affect the approximation of dilute mesons, rendering prethermalization faster on the one hand, but making the approximation of the prethermal regime as a thermal gas of noninteracting mesons unreliable on the other hand. It would be interesting to extend our prethermal description to capture meson-meson interactions.\n\nAnother intriguing direction would be to address scenarios where the violation of the meson-number conservation is not negligible and must be properly considered. Can one observe and describe the drift to the thermal regime in such cases? A kinetic theory would require a quantitative understanding of meson creation-annihilation processes beyond the estimates discussed in this work.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "We used tensor network simulations to demonstrate the conservation of the meson number during the quantum evolution. Whereas time evolution can be carried out using the standard method of infinite Time-Evolving Block Decimation (iTEBD)48,49, measurements of the meson number are more subtle. We outline how the mesonic number operator can be embedded efficiently in tensor network formalism.\n\nThe construction relies on the exact solution of the transverse Ising model, which we summarize in\u00a0supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.). Let \\(\\{{\\gamma }_{k},\\,{\\gamma }_{k}^{{{{\\dagger}}} }\\}\\) be the fermionic creation and annihilation operators that diagonalize the transverse-field Ising model in the absence of a longitudinal field h\u2225\u2009=\u20090, the mesonic number operator is obtained as half of the mode number operator\n\nwhere the \\({\\hat{\\alpha }}_{k}=\\cos {\\theta }_{k}{\\hat{\\gamma }}_{k}+i\\sin {\\theta }_{k}{\\hat{\\gamma }}_{-k}^{{{{\\dagger}}} }\\) are the Jordan-Wigner fermions in the Fourier basis \\({\\hat{c}}_{j}=\\int\\nolimits_{-\\pi }^{\\pi }\\frac{{{{{{{{\\rm{d}}}}}}}}k}{\\sqrt{2\\pi }}{e}^{ikj}{\\hat{\\alpha }}_{k}\\), which are eventually related to the original spin variables as \\(({\\hat{\\sigma }}_{j}^{x}+i{\\hat{\\sigma }}_{j}^{y})/2=\\exp \\left(i\\pi {\\sum }_{i \\, < \\,j}{\\hat{c}}_{i}^{{{{\\dagger}}} }{\\hat{c}}_{i}\\right){\\hat{c}}_{j}^{{{{\\dagger}}} }\\). The Bogoliubov angle is tuned in such a way \\({\\theta }_{k}=-\\frac{1}{2i}\\log \\left(\\frac{{h}_{\\perp }-{e}^{ik}}{{(\\cos k-{h}_{\\perp })}^{2}+{\\sin }^{2}k}\\right)\\).\n\nThe divergent factor \u03b4(0) arises from equal-momentum commutation relation and it must be regularized \u03b4(0)\u2009=\u2009L, with the system size L. Moving to the coordinate space, the meson number can be thus written as\n\nIn Eq. (7) we introduced the functions f1(\u2113),\u2009f2(\u2113) encoding the non-locality of the Jordan-Wigner mapping\n\nFinally, we can also invert the Jordan-Wigner mapping to obtain the expression in the spin basis \\({c}_{j+\\ell }^{{{{\\dagger}}} }{c}_{j}^{}={\\sigma }_{j+\\ell }^{-}\\left(\\mathop{\\prod }\\limits_{i=j}^{j+\\ell -1}{\\sigma }_{i}^{z}\\right){\\sigma }_{j}^{+}\\) and \\({c}_{j+\\ell }^{}{c}_{j}^{}={\\sigma }_{j+\\ell }^{+}\\left(\\mathop{\\prod }\\limits_{i=j}^{j+\\ell -1}{\\sigma }_{i}^{z}\\right){\\sigma }_{j}^{+}\\).\n\nSince Nmes contains in general long-ranged terms an efficient representation in terms of an MPO strongly depends on the functional form of f1(\u2113),\u2009f2(\u2113). For small values of the transverse field h\u22a5 we find that both f1(\u2113) and f2(\u2113) can be approximated by an exponential decay for l\u2009>\u20090. This enables us to make use of the efficient representation of MPOs with coefficients exponentially decaying with distance discussed e.g., in ref. 48.\n\nWith this method, we can analyze quantum quenches in the Ising chain and follow the evolution of the number of mesons, checking whether it is approximately well-conserved or corrections are important. In Fig.\u00a01c of the main text, we focus on parameter regimes where the meson number is oscillating around a constant value, in very good agreement with the analytic prediction of ref. 15. Oscillations have a technical origin and are due to the fact that, strictly speaking, it is not the number of fermions that is conserved, but rather the fermion number after a perturbatively small basis rotation33. Hence, in the original basis the fermion number couples to non-conserved quantities as well, which cause the small superimposed oscillations. To complement the analysis of Fig.\u00a01c, in Fig.\u00a05 we analyze quantum quenches where meson conservation is not a good approximation any longer. This can be achieved, for example, by tuning the post quench transverse field closer to the critical point, thus reducing the fermionic mass and enhancing the Schwinger mechanism. It is worth emphasizing that an efficient representation of Nmes in terms of a MPO is no longer possible as f1(\u2113),\u2009f2(\u2113) show deviations from an exponential decay for values of h\u22a5\u2009\u2192\u20091. The meson number can, nonetheless, be computed by evaluating the terms contained in Eq. (7) individually and truncating the sum at large enough \\({\\ell }_{{\\max }}\\). With this, we indeed observe that the difference between the numerical data and the analytic prediction grows with time as the post quench transverse field is tuned sufficiently close to 1, in agreement with the observations of ref. 26. We, moreover, want to emphasize that results are converged with bond dimension \u03c7, as illustrated in Fig.\u00a05. Smaller bond dimensions can lead to deviations of the time traces. Ensuring convergence of tensor network results for different choices of \u03c7 is hence crucial to estimate the actual relevance of meson-number-changing processes.\n\nWe show results for a quantum quench of the ground state with initial field configuration (h\u22a5,\u2009h\u2225)\u2009=\u2009(0.4,\u20090.0) to values of the transverse field h\u22a5\u2009\u2208\u2009{0.65,\u20090.75,\u20090.85,\u20090.95} and additional confining longitudinal field h\u2225\u2009=\u20090.05. For all quenches we show results obtained using iTEBD time evolution for a unit cell of L\u2009=\u200940 sites with bond dimensions of \u03c7\u2009\u2208\u2009{256,\u2009384,\u2009512} (light to dark solid lines). We find that quenches close to the critical value of the transverse field only for a short time show the expected value of the meson number (gray dashed lines) before showing a decay in the number of mesons. The timescale, on which such a decay takes place increases and finally exceeds the numerically accessible times for quenches deep into the ferromagnetic phase (h\u22a5\u2009\u226a\u20091).\n\nWe notice the meson number decreases. Hence, rather than the usual Schwinger effect where a large meson decays in two (or more) smaller entities, what dominates the dynamics is the opposite process, namely inelastic scattering of two mesons that fuse and become a larger (i.e., more energetic) particle.\n\nWhile tensor networks are numerically-exact methods, their applicability is constrained to short times by the entanglement growth, hence they cannot explore the prethermal regime. To overcome this restriction, we neglect the Schwinger mechanism and promote the number of mesons to an exact conservation law, thus projecting the dynamics within a sector with a fixed number of fermions. Furthermore, we wish to focus on the regime of a small transverse field where fermions are well approximated by domain walls. Hence, we consider the restricted Hilbert space \\(|{j}_{1},\\,{j}_{2},...{j}_{2n-1},\\,{j}_{2n}\\rangle=|{\\uparrow }_{1}...{\\uparrow }_{{j}_{1}-1}{\\downarrow }_{{j}_{1}}....\\rangle\\) generated by all the states with n mesons, with ordered coordinates ji+1\u2009\u2212\u2009ji\u2009>\u20091 and having values on the interval [1,\u2009L]. While the full Hilbert space in the spin basis grows as 2L, the restricted Hilbert space grows polynomially \\(\\simeq \\frac{1}{(2n)!}{L}^{2n}\\) and much larger system sizes can be reached. This allows us to approach the regime where mesons are well separated, i.e., where our thermodynamic assumptions are valid. The same regime is naturally obtained after a quantum quench. By further taking into account translational invariance, the exponent of the polynomial growth in L can be lowered by one unit, allowing us to simulate the dynamics of three mesons on L\u2009=\u2009100 for very long times and eventually observing prethermalization (see Fig.\u00a02). Further technical details on this method and benchmarks are discussed in\u00a0supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.).\n\nFor large scale simulations in the semiclassical regime, we relied on a Truncated Wigner Approximation51 which consists of the following steps (see also refs. 15, 38 for similar approximations)\n\nApproximate the true Hamiltonian with the projected dynamics within the subspace with a fixed number of fermions (and its multiparticle generalization). This assumption is reliable as long as the Schwinger effect can be neglected.\n\nApproximate the quantum evolution with a classical one: \n\nReplace quantum expectation values with proper averages over classical ensembles of particles.\n\nReplace the quantum evolution with properly chosen classical equations of motion, derived from the semiclassical Hamiltonian (2) (and its multiparticle generalization).\n\nClassical configurations are sampled from the classical statistical ensemble, then deterministically evolved with the equations of motion. The expectation values of observables is recovered by averaging over the initial conditions.\n\nThe Truncated Wigner Approximation is expected to work in the semiclassical regime, i.e., in the case of weak confinement; see below. However, as it is well known in the literature, one should be aware that this is an uncontrolled approximation in the sense that quantum corrections cannot be easily included in the approximation in a systematic way.\n\nTo further quantify the method and keep the notation under control, we now focus on the dynamics in the two-particle sector: the generalization to the multiparticle case can be directly obtained. Let us assume in full generality that the initial state is described by a density matrix \\({\\hat{\\rho }}_{2{{{pt}}}}\\), we focus on the matrix elements in a coordinate representation for the position of the two fermions \\(\\left|{j}_{1},{j}_{2}\\right\\rangle\\). The Wigner distribution W is defined through a partial Fourier transform of the matrix elements in the coordinate basis\n\nAbove, one should impose integer values of the coordinates, but this restriction will not be important since classical physics emerges in the regime where the matrix elements are smooth functions of the coordinates, hence the discreteness of the lattice becomes irrelevant. We now move on to consider the dynamics by computing the Heisenberg equation of motion \\(i{\\partial }_{t}{\\hat{\\rho }}_{{{{2pt}}}}=[{\\hat{H}}_{{{{2pt}}}},\\,{\\hat{\\rho }}_{{{{2pt}}}}]\\), where \\({\\hat{H}}_{{{{2pt}}}}\\) is the quantum Hamiltonian projected in the two-fermions sector, namely the quantized version of Eq. (2). When expressing the Heisenberg equation of motion in terms of the Wigner distribution, one obtains after some straightforward calculations (we omit the W\u2009\u2212\u2009arguments for the sake of notation)\n\nwhere v(k)\u2009=\u2009\u2202k\u03f5(k) and \\({V}^{{\\prime} }(x)={\\partial }_{x}V(x)\\) with \\(V(x)=2{h}_{\\parallel }\\bar{\\sigma }|x|\\). The above equation is nothing else than the classical Liouville equation for the phase-space distribution W(x1,\u2009k1,\u2009x2,\u2009k2) evolving with the classical Hamiltonian \\({{{{{{{\\mathcal{H}}}}}}}}=\\epsilon ({k}_{1})+\\epsilon ({k}_{2})+2{h}_{\\parallel }\\bar{\\sigma }|{x}_{1}-{x}_{2}|\\). In the derivation, one assumes that both the matrix element and the potential V(x) are sufficiently smooth in the coordinates. Contributions neglected in the above equation are further orders in the derivative expansion. While V(x) is not strictly speaking smooth, in the limit of weak longitudinal field the cusp in V(x) gives negligible contributions. Notice that, if h\u2225 is weak, smooth Wigner distributions will remain smooth during the evolution, ensuring the consistency of the approximation.\n\nWe finally turn to the problem of determining the initial Wigner distribution resulting from the quench protocol. To this end, we can resort to the quasiparticle picture of quantum quenches in the Ising chain63, where the initial state is regarded as an incoherent gas of pairs of particles with opposite momentum (k,\u2009\u2212\u2009k), the probabilty distribution n(k) of the pair can be computed from the exact solution of the quench in the transverse field45 (see ref. 15 and supplementary information (Supplementary information for details on the confining dynamics; characterization of the prethermal state; initialization of moving mesons by staggered field pulses; further information on details of numerical simulations.) for details and corrections due to the finite longitudinal field). The distribution n(k) fixes the probability distribution of a single pair of fermions: since pairs are independently created in a homogeneous fashion, we impose that pairs are distributed according to a Poisson distribution.",
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+            "section_name": "Data availability",
+            "section_text": "Data analysis is available on Zenodo upon reasonable request (all data are available upon reasonable request at https://doi.org/10.5281/zenodo.7034368).",
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+            "section_name": "Code availability",
+            "section_text": "Simulation codes are available on Zenodo upon reasonable request (simulation codes are available upon reasonable request at https://doi.org/10.5281/zenodo.7034368).",
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+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "We thank S. Scopa and P. Calabrese for collaboration on closely related topics and A. Lerose for useful discussions. We acknowledge support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany\u2019s Excellence Strategy\u2013EXC\u20132111\u2013390814868, TRR80 and DFG grants No. KN1254/1-2 and No. KN1254/2-1, the European Research Council (ERC) under the European Union\u2019s Horizon 2020 research and innovation programme (grant agreement No. 851161), as well as the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus.",
+            "section_image": []
+        },
+        {
+            "section_name": "Funding",
+            "section_text": "Open Access funding enabled and organized by Projekt DEAL.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Department of Physics, Technical University of Munich, 85748, Garching, Germany\n\nStefan Birnkammer,\u00a0Alvise Bastianello\u00a0&\u00a0Michael Knap\n\nMunich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799, M\u00fcnchen, Germany\n\nStefan Birnkammer,\u00a0Alvise Bastianello\u00a0&\u00a0Michael Knap\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nSearch author on:PubMed\u00a0Google Scholar\n\nA.B. and S.B. carried out the numerical simulations contained in this work. M.K. supervised the work. All authors contributed critically to the writing of the manuscript and the interpretation of numerical and analytical results.\n\nCorrespondence to\n                Stefan Birnkammer.",
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+            "section_text": "Birnkammer, S., Bastianello, A. & Knap, M. Prethermalization in one-dimensional quantum many-body systems with confinement.\n                    Nat Commun 13, 7663 (2022). https://doi.org/10.1038/s41467-022-35301-6\n\nDownload citation\n\nReceived: 10 May 2022\n\nAccepted: 24 November 2022\n\nPublished: 10 December 2022\n\nVersion of record: 10 December 2022\n\nDOI: https://doi.org/10.1038/s41467-022-35301-6\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_name": "This article is cited by",
+            "section_text": "Communications Physics (2025)\n\nNature Physics (2025)\n\nnpj Quantum Information (2025)\n\nNature Communications (2024)\n\nNonlinear Dynamics (2024)",
+            "section_image": []
+        },
+        {
+            "section_name": "Associated content",
+            "section_text": "Collection",
+            "section_image": []
+        }
+    ],
+    "supplementary_files": [
+        {
+            "title": "ConfinementDynamicsSupplementary.pdf",
+            "link": "https://assets-eu.researchsquare.com/files/rs-1642071/v1/4bfea546b475c20c21ac0f82.pdf"
+        }
+    ]
+}

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+{
+    "title": "Multimodal super-resolution: discovering hidden physics and its application to fusion plasmas",
+    "pre_title": "Discovering hidden physics using ML-based multimodal super-resolution measurement and its application to fusion plasmas",
+    "journal": "Nature Communications",
+    "published": "26 September 2025",
+    "supplementary_0": [
+        {
+            "label": "Transparent Peer Review file",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-025-63492-1/MediaObjects/41467_2025_63492_MOESM1_ESM.pdf"
+        }
+    ],
+    "supplementary_1": NaN,
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://d3dfusion.org/become-a-user/",
+        "https://doi.org/10.34770/nex7-3y26"
+    ],
+    "code": [
+        "/articles/s41467-025-63492-1#ref-CR68"
+    ],
+    "subject": [
+        "Computer science",
+        "Nuclear fusion and fission"
+    ],
+    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-4646544/v1.pdf?c=1758971470000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-4646544/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-025-63492-1.pdf",
+    "preprint_posted": "05 Nov, 2024",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "A non-linear complex system governed by multi-spatial and multi-temporal physics scales cannot be fully understood with a single diagnostic, as each provides only a partial view and much information is lost during data extraction. Combining multiple diagnostics also results in imperfect projections of the system's physics. By identifying hidden inter-correlations between diagnostics, we can leverage mutual support to fill in these gaps, but uncovering these inter-correlations analytically is too complex.\r\nWe introduce a groundbreaking machine learning methodology to address this issue. Our multimodal approach generates super-resolution data encompassing multiple physics phenomena, capturing detailed structural evolution and responses to perturbations previously unobservable. This methodology addresses a critical problem in fusion plasmas: the Edge Localized Mode (ELM), a plasma instability that can severely damage reactor walls. One method to stabilize ELM is using resonant magnetic perturbation to trigger magnetic islands. However, low spatial and temporal resolution of measurements limits the analysis of these magnetic islands due to their small size, rapid dynamics, and complex interactions within the plasma.\r\nWith super-resolution diagnostics, we can experimentally verify theoretical models of magnetic islands for the first time, providing unprecedented insights into their role in ELM stabilization. This advancement aids in developing effective ELM suppression strategies for future fusion reactors like ITER and has broader applications, potentially revolutionizing diagnostics in fields such as astronomy, astrophysics, and medical imaging.Physical sciences/Energy science and technology/Nuclear energy/Nuclear fusion and fissionPhysical sciences/Mathematics and computing/Computational scienceFusion reactorMachine learningSynthetic diagnosticsPhysics-preserving super-resolution",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "Understanding complex physical systems often requires integrating data from multiple diagnostics, each with limited resolution or coverage. We present a machine learning framework that reconstructs synthetic high-temporal-resolution data for a target diagnostic using information from other diagnostics, without direct target measurements during the inference. This multimodal super-resolution technique improves diagnostic robustness and enables monitoring even in case of measurement failures or degradation. Applied to fusion plasmas, our method targets edge-localized modes (ELMs), which can damage plasma-facing materials. By reconstructing super-resolution Thomson Scattering data from complementary diagnostics, we uncover fine-scale plasma dynamics and validate the role of resonant magnetic perturbations (RMPs) in ELM suppression through magnetic island formation. The approach provides new observation supporting the plasma profile flattening due to these islands. Our results demonstrate the framework\u2019s ability to generate high-fidelity synthetic diagnostics, offering a powerful tool for ELM control development in future reactors like ITER. The approach is broadly transferable to other domains facing sparse, incomplete, or degraded diagnostic data, opening new avenues for discovery.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "In complex physical systems, diagnostic measurements are often intricately interconnected through fundamental physical principles. These connections arise from the laws of nature that govern the behavior of matter and energy. Electromagnetic phenomena can couple measured signals, while equations of state link variables such as pressure, volume, and temperature, enabling one quantity to be inferred from another. Similarly, coupled differential equations in fluid dynamics or plasma physics describe how multiple parameters evolve interdependently over time. Such relationships are particularly evident in fusion energy, the focus of this work, which is defined by the interplay of diverse physical processes.\n\nFusion energy and diagnostics: Achieving controlled fusion requires precise, real-time knowledge of plasma conditions to guide and optimize reactor performance. Modern fusion experiments meet this need by deploying a wide array of diagnostics and actuators, each measuring or influencing a different aspect of the plasma state. Recent advances have shown that Artificial Intelligence (AI) can effectively leverage these data streams to enhance plasma control1,2,3,4. Facilities such as DIII-D5 integrate diverse diagnostics to support such AI-driven control strategies6. However, limitations in the spatial and temporal resolution of many diagnostics continue to obscure fast-evolving plasma dynamics that are critical for achieving robust and optimized control7,8,9.\n\nFor example, a multi-diagnostic approach is essential to construct a complete picture of electron transport, confinement, and stability in DIII-D discharges. Thomson Scattering (TS)10,11, which employs a high-powered laser beam that scatters off plasma electrons, measures the local electron temperature and density from the scattered light spectrum. Electron Cyclotron Emission (ECE)12 provides spatially localized measurements of the electron temperature, whereas a CO2 Interferometer13 offers line-integrated measurements of the global electron density. Additionally, some diagnostics, though primarily designed for other purposes, can yield indirect yet valuable information on electrons. For instance, the Motional Stark Effect (MSE)14, used to determine the internal magnetic field pitch angle and current distribution, enhances equilibrium reconstructions, which in turn facilitate deeper insights into electron transport and confinement. Each different measurement captures different physical properties, and together form a complementary set for extracting as much information from the plasma as possible. Although it is likely that there is some kind of correlation or coupling between the measurements of different diagnostics (examples in section \u201cDiscussion\u201d subsection \u201cPhysical basis for multimodal diagnostic coupling\u201d), our current scientific understanding is still not capable of specifying some of these relationships analytically. Utilizing machine learning (ML) to identify such hidden relationships among different diagnostics would be a great asset to enhance their measurements, and it may also help to find a minimal set of diagnostics for a future reactor in which the availability of diagnostics is limited due to cost and hardware constraints.\n\nDiagnostic challenges in capturing plasma instabilities: One of the most critical issues for fusion reactors is the edge-localized mode (ELM), an instability that occurs at the plasma edge under high-confinement conditions. This edge instability delivers transient and intense heat flux outward, which can cause unacceptable levels of erosion of plasma-facing materials in a reactor-scale device. Therefore, understanding and controlling this phenomenon is a major challenge that must be resolved2. However, the detailed physical mechanism of ELMs and the structure of the response to the external field occurring within milliseconds are still subjects of ongoing debate. High-frequency diagnostics like ECE and Interferometer possess sufficient time resolution to track these fast dynamics, but their limited spatial resolution and measurement conditions pose challenges in clearly observing the structural characteristics of ELMs. On the other hand, TS offers high spatial resolution near the plasma edge capable of observing detailed structures, but its temporal resolution is too low to elucidate the exact mechanism of ELMs.\n\nThe current remedy to this issue is a specific operational method for TS, known as \u201cburst mode,\u201d to increase the sampling rate of up to 10\u2009kHz15,16. Despite its high pulse repetition, firing TS in \u201cburst mode\u201d is limited by the heat capacity of the laser medium and limited measurement repetition (see the section \u201cMethods\u201d subsection \u201cDiagnostic constraints in ELM measurements\u201d for more details). Therefore, such an approach is typically reserved for very short periods of time or specific experiments where high-resolution temporal data is crucial16.\n\nNeed for new approaches: Overcoming these diagnostic limitations calls for methods capable of generating high-resolution measurements from the limited and imperfect diagnostics already available. Various fields have developed ML-based spatial or temporal resolution enhancement techniques, but these mostly involve resolution enhancement by learning linear or nonlinear interpolation within single or limited types of data17,18,19,20,21. These are (1) applicable only to regularly sampled data, (2) largely dependent on the availability of the target sensor measurement for interpolation, and (3) challenging to generate finer-scale phenomena undetectable at the time resolution of the target sensor (more details in the section \u201cDiscussion\u201d subsection \u201cRelation to previous super-resolution methods\u201d).\n\nContribution: We hypothesize that a data-driven ML model, so-called Diag2Diag, with multimodal inputs comprising the high-frequency diagnostics can effectively make use of internal correlations in order to estimate TS accurately. This can enhance the temporal resolution of the existing TS diagnostics without upgrading hardware, so-called Multimodal Super-Resolution TS (SRTS) diagnostics, which enable deeper physical analysis of plasma behavior.\n\nFigure\u00a01 summarizes the main methodology for this work. DIII-D is a well-diagnosed tokamak equipped with more than eighty distinct diagnostic systems. Many of these systems include multiple measurement channels or chords, collectively producing several hundred data streams that monitor different aspects of the plasma. These diagnostics measure various characteristics of plasma at different spatial and temporal resolutions. A potential ML model can learn the intrinsic correlations among diagnostic data and thus generate one from the others. This works for both time series and spectrograms, although different variants of artificial neural network (ANN) are used. The design choices, the optimization, and training strategies are described in the following sections.\n\nDiagA is essential to capture fast transient events near the edge of plasma. But due to its low temporal resolution and accuracy, it fails to track the evolution of such events. Diag2Diag solves this problem by generating a synthetic super-resolution of DiagA by learning the correlation between DiagA data and other diagnostic measurements with higher resolutions and better accuracy.\n\nIn this work, we demonstrate that a multimodal super-resolution framework can reconstruct missing or low-resolution diagnostic signals with high fidelity by learning underlying correlations among multiple diagnostics. We show that this method enables synthetic SRTS signals, an inferred representation of TS, revealing experimental evidence of plasma profile flattening due to magnetic islands. These findings provide crucial insights into the mechanisms of ELM suppression via resonant magnetic perturbation (RMP), support robust ELM control strategies for future reactors like ITER, and establish a generalizable framework for diagnosing complex systems with limited sensor resolution. Our approach extends beyond interpolation by reconstructing and enhancing the resolution of a target diagnostic using complementary data from multiple other diagnostics. Specifically, the model learns the underlying physical correlations among different measurements in the fusion device, enabling it to generate a synthetic, high-resolution representation of the target diagnostic without requiring that diagnostic\u2019s own data as input. As a result, this method remains effective even if the target diagnostic is unavailable or not reliable during inference (e.g., due to hardware degradation or failure). Moreover, because the input diagnostics measure different aspects of plasma at higher resolutions, the model can recover events that the target diagnostic might miss due to its intrinsic resolution limits. To our knowledge, this constitutes the first multimodal super-resolution framework of its kind in the context of fusion diagnostics.",
+            "section_image": [
+                "https:////media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41467-025-63492-1/MediaObjects/41467_2025_63492_Fig1_HTML.png"
+            ]
+        },
+        {
+            "section_name": "Results",
+            "section_text": "Before investigating a multimodal ML-based model to generate synthetic SRTS using other diagnostics, it is crucial to first verify the existence, strength, and robustness of their underlying correlations. We therefore begin by demonstrating a fundamental capability of ML: leveraging one diagnostic\u2019s measurements to reconstruct another\u2019s. Specifically, we use ECE spectrograms, spatially resolved measurements with about 40 channels from edge to core, to reconstruct the line-integrated density fluctuation signals of the Interferometer. Because certain plasma instabilities and modes, such as Alfv\u00e9n Eigenmode (AE), manifest in both temperature and density measurements, it is reasonable to expect that correlations exist between ECE and Interferometer measurements during such events. Here, we show that a convolutional neural network (CNN) can learn these correlations and reconstruct Interferometer spectrograms from ECE spectrograms, as illustrated in Fig.\u00a02.\n\na The configuration of four Interferometer chords (R0, V1-3) and 40 ECE probes at DIII-D. b A tensor of (40\u2009\u00d7\u2009time\u2009\u00d7\u2009frequency) is supplied to CNN. c The configuration of CNN. d Visual comparison of measured and reconstructed spectrograms for DIII-D discharge 170669. e Comparison of the Alfven Eigenmode detector output23 supplied with the measured and reconstructed spectrograms.\n\nFigure\u00a02a shows the measurement positions and paths of ECE and Interferometer, as well as example spectrograms obtained from their raw signals (Fig.\u00a02b, d). We designed and trained a CNN that takes 40 ECE spectrograms as input and reconstructs 4 target Interferometer spectrograms. The reconstructed synthetic Interferometer spectrograms visually confirm the plausible reconstruction of features such as frequency chirping and harmonics, especially during the AE events22, as seen in Fig.\u00a02d.\n\nTo evaluate how well the underlying physical content is preserved in the reconstructed spectrograms, we employ both quantitative and physics-based assessments. First, achieving an \\({{\\mathscr{L}}}1\\) loss of 1.2\u2009\u00d7\u200910\u22123 on the validation set determines how closely the CNN reconstructions match the Interferometer\u2019s amplitude and time-frequency distribution (see the section \u201cMethods\u201d subsection \u201cSpectrogram model development\u201d for more details). Second, to verify that the essential physics is captured, we apply a previously published AE detection algorithm23, originally designed for interferometer data, to both the original and reconstructed spectrograms. The resulting average F1 score of 0.82 on the validation set after applying a threshold of 0.15, as suggested in ref. 23, indicates that the model largely reproduces the AE modes, reflecting a high degree of physics fidelity in the reconstructed signals. These findings confirm that neural networks can extract and retain the intrinsic correlations among diagnostic data, even when only one diagnostic serves as input.\n\nHaving established the efficacy of this unimodal-to-unimodal reconstruction using spectrogram data, we next extend our approach to raw time-series inputs and expand to multimodal cases. In the subsequent sections, we focus on generating TS signals from a diverse set of diagnostics, illustrating the broader potential of our method for super-resolution diagnostic reconstruction.\n\nIn this section, we switch from spectrograms to time-series signals and show that the amplitude of a diagnostic can be reconstructed from other diagnostics, while preserving intrinsic physics. More importantly, we will show that if the input diagnostics are of much higher temporal resolution compared to the target one, such a model can be used to increase the time resolution of the target signals in a much more intelligent way compared to the conventional unimodal interpolations. As a use case, we target TS, one of the most important diagnostics that measures the electron density and electron temperature profile of plasma. However, as mentioned earlier, its low temporal resolution is a bottleneck in studying the plasma evolution in the rapidly changing events such as ELM.\n\nFigure\u00a03 demonstrates a diagram of the data processing pipeline during training and inference of Diag2Diag. We consider a suite of input diagnostics available at DIII-D, including Interferometer, ECE, Magnetic probes (Magnetics), Charge Exchange Recombination (CER), and MSE with typical sampling rates of 1.66\u2009MHz, 500\u2009kHz, 2\u2009MHz, 200\u2009Hz, and 4\u2009kHz, respectively. Since our aim is not only to enhance TS but also to reconstruct it from other diagnostics, we do not use the available measurement of TS as input to Diag2Diag. To obtain a dataset that can be used to train and validate the model with the available TS measurements, all the included diagnostics are aligned with the TS sampling time steps by matching their most recent measured sample.\n\na During the training, the inputs are aligned and resampled with respect to TS timing, to have a ground truth for training and validation of the model. b During the inference, the inputs are resampled to 1\u2009MHz, which will be the resolution of synthetic SRTS. Since there is no ground truth for data-driven validation, we validate the SRTS by studying its behavior during fast physics phenomena, which are challenging to analyze with measured TS due to its low temporal resolution.\n\nSince the sampling steps of TS, which is also used to align the inputs for training the model, are not always uniform in time, we opted for a feed-forward neural network instead of recurrent neural networks, which are commonly used in time-series analysis. However, we included the first and second derivatives of the high-resolution input diagnostics, ECE and Interferometer, to include the temporal evolution information. During the inference, the input diagnostics are aligned to a fixed sampling rate of 1\u2009MHz to generate synthetic SRTS. The neural network consists of three dense layers with 512, 256, and 128 nodes per hidden layer. More details about the dataset preparation, model optimization, and uncertainty quantification are provided in sections \u201cMethods\u201d subsection \u201cTime-series model development\u201d and \u201cDiscussion\u201d \u201cAssessing model and measurement uncertainty\u201d.\n\nFigure\u00a04 shows, in blue, synthetic SRTS signals generated through the inference of Diag2Diag for the DIII-D discharge 153761, and the original TS measurements are also shown with black dots. For this discharge, TS was fired in the highest possible temporal resolution, so-called \u201cburst mode\u201d (see section \u201cMethods\u201d subsection \u201cDiagnostic constraints in ELM measurements\u201d for more details). We can observe that the synthetic signals closely follow the original measurements, achieving an R2 score of 0.92 in reconstructing the available TS measurement on the validation set. Diag2Diag\u2019s ability to reconstruct TS from other diagnostics ensures that crucial information is not lost, even in the absence of direct measurements. Furthermore, while the original TS measurement sometimes fails to capture ELM events, the synthetic SRTS accurately captures the events missed by TS.\n\na Comparison of the electron density by the measured TS and SRTS, for discharge 15376115 near the edge (Z\u2009=\u20090.71\u2009m). The spectral emission, D\u03b1, is plotted as an indicator of ELMs. b, c An example of an ELM event captured by both diagnostics, and examples only captured by SRTS are highlighted in green and red, respectively.\n\nHere, we note that our objective is not to replicate the entire physics of Magnetohydrodynamics (MHD) turbulence in plasma24 from first principles, but rather to learn empirically grounded correlations among multiple diagnostics. Our aim is to show that even a modestly sized neural network can reliably capture significant nonlinear relationships, for instance, shared fluctuations or mode signatures, by training on experimental data where these diagnostic measurements overlap in time and space. Crucially, the model does not need a complete, fundamental understanding of turbulence; instead, it identifies and exploits observed patterns that consistently appear across diagnostics, as confirmed by its alignment with known plasma behaviors and successful performance on held-out data. Thus, while the network\u2019s architecture may be relatively straightforward, it remains effective in generating physically meaningful reconstructions in a manner that is both computationally efficient and broadly adaptable, complementing (rather than replacing) fundamental physics-based models of MHD turbulence.\n\nWhen ELM instability occurs, a large amount of plasma quickly escapes from the boundary within milliseconds, and then the plasma gradually recovers. TS diagnostics can observe the density and temperature structure at this edge region, but are limited in capturing dynamics occurring over milliseconds. Recent research overcame these resolution limits by statistical analysis and aggregating the measurements from multiple repeated cycles of the fast activity under almost identical conditions to observe a complete evolution25. In that work, over 20 highly reproduced cycles of ELM crash and recovery were aggregated from DIII-D discharge 174823 to assume a ground truth of a complete evolution of an ELM cycle.\n\nThe aggregated density and temperature evolution measured by TS in three locations of plasma near the edge are shown in Fig.\u00a05a, b with transparent crosses, while measurements from a single cycle are shown with circles and different colors for different measurement locations. In a more typical tokamak discharge, the plasma state continually changes, and ELMs occur more irregularly, as shown in Fig.\u00a04. In such cases, it is not possible to reconstruct a single ELM cycle by aggregating multiple cycles, and our SRTS method will be highly beneficial.\n\na, b Aggregating the measured TS density and temperature in three locations of plasma near the edge for several ELM cycles of the DIII-D discharge 174823. The circle highlights the measures TS for one selected ELM cycle, and the solid lines present the SRTS, which agreeably match the measured TS. t\u2009=\u20090 represents the time when ELM is identified by D\u03b1. c, d The evolution of SRTS between two consecutive measured TS near one ELM cycle across the plasma location.\n\nWe used the Diag2Diag model to generate synthetic SRTS, shown with solid lines in Fig.\u00a05a, b. The SRTS signal from a single cycle around time 3795\u2009ms not only follows the trend of the aggregated multiple TS measurements but also well overlays the TS measurements within that cycle. Fig.\u00a05c, d shows the detailed evolution of plasma density and temperature across the plasma location captured by SRTS in the same ELM cycle at 3795\u2009ms, which is missed by TS between its two consecutive measurements at 3791\u2009ms and 3800\u2009ms.\n\nIn what follows, we investigate whether the synthetic super-resolution diagnostics can help to verify the hypotheses on the mechanism of plasma response to external field perturbations in fusion plasma physics that have been proposed theoretically or by simulations but have never been visualized with experimental data due to the lack of diagnostic resolution.\n\nOne promising strategy to control ELMs is employing RMPs26,27,28,29,30,31 generated by external 3D field coils depicted in Fig.\u00a06a. These fields effectively reduce the temperature and density at the confinement pedestal, stabilizing the energy bursts in the edge region. Consequently, ITER will rely on RMPs to maintain a burst-free burning plasma in a tokamak, making it essential for the fusion community to understand and predict its physics mechanism32. However, this issue has remained a challenge for decades.\n\nStructure of 3D coils and islands by perturbed field (a), along with the evidence in the simulation (b\u2013d) and SRTS diagnostic (e\u2013g) for RMP-induced island mechanism on the plasma boundary in DIII-D discharge 157545.\n\nThe leading theory33,34,35,36 for explaining the reduced pedestal by RMPs is the formation of magnetic islands by an external 3D field. The magnetic island is a ubiquitous feature in an electromagnetic system with plasmas37 formed by field reconnection38,39. This structure allows rapid heat (or temperature) and particle (or density) transport between adjacent magnetic field lines, strongly reducing the gradient of local heat and particle distribution, or, in other words, profile flattening40. The existing theories explain that RMP forms static magnetic islands at the pedestal top and foot region, therefore reducing the pedestal by local profile flattening. As illustrated in Fig.\u00a06a, the theory predicts that RMPs can create magnetic islands near the plasma boundary where the pedestal sits. This model has been successful in quantitatively explaining and predicting the RMP-induced pedestal degradation in real experiments35,41, reinforcing magnetic islands as a promising mechanism for RMP-induced pedestal degradation. Nevertheless, measuring evidence of island or local profile flattening still remains a challenge. Extensive experimental efforts have been conducted for this reason and were able to capture the local flattening electron temperature profile42 near the pedestal top, strongly supporting this theory. However, simultaneously measuring electron temperature and density both at the pedestal top and foot was not possible. In a previous study, rough evidence was observed in TS36, but it was insufficient to derive a concrete conclusion, mainly due to a large uncertainty of measurement originating from the narrow structure (expected from theory, see Fig.\u00a06a) and oscillatory nature of the plasma boundary. To address the diagnostic uncertainties caused by such system oscillation, one method is to increase the time sampling rate and use time averaging. However, in conventional TS, increasing the time resolution results in a trade-off with measured accuracy, eventually leading to observational limitations.\n\nInterestingly, the SRTS has once again illuminated the profile evolution by RMP application, providing the novel evidence of \u201csimultaneous\u201d flattening of temperature and density profile at both the top and the foot of the pedestal, strongly supporting the theoretical prediction of the magnetic islands effect. This is possible by capturing the statically reliable time trace of the profile with the Chebyshev time filter, leveraging the enhanced temporal resolution by SRTS.\n\nFigure\u00a06b\u2013g illustrates the recovery of temperature and density pedestals within 10\u2009ms after deactivating RMP, as captured through numerical modeling (Fig.\u00a06b\u2013d) and SRTS (Fig.\u00a06e\u2013g). The simulations reveal that the recovery of temperature and density pedestals begins at the top and foot, coinciding with the disappearance of islands. As depicted in Fig.\u00a06d, g, the profile gradient recovers at these island locations, enhancing the overall profile. For instance, the measured temperature pedestal shows recovery at both the top and the foot through an increasing gradient, displaying qualitative alignment with the simulation results. However, some discrepancies are noted, particularly in the density evolution at the pedestal foot in the SRTS, even though its gradient remains consistent with the modeling. These quantitative differences may stem from the TS\u2019s limited spatial resolution at the boundary and the modeling assumptions, such as fixed boundary conditions43. Nevertheless, the gradient evolution directly indicates a change in transport due to the RMP-induced islands during this perturbative profile evolution, highlighting that the SRTS successfully reveals the experimental island effect. This provides the new diagnostic evidence of profile flattening at magnetic islands, a key mechanism of RMP-induced pedestal degradation.\n\nThe strength of the SRTS in unveiling profile flattening during ELM suppression can be further highlighted with additional cases. Fig.\u00a07 shows the time traces of plasma for DIII-D discharge 136219 when the edge safety factor (q95), the magnetic pitch angle at the plasma edge, gradually decreases. Here, all other plasma operation parameters, including the RMP field, remain the same. From D\u03b1 emission looking perturbation of plasma edge (see Fig.\u00a07a), the bursty spikes disappear during q95\u2009=\u20093.5\u20133.6, corresponding to the ELM-suppressed phase followed by the transient ELM-free phase. This shows the strong dependence of ELM suppression on q95. The modeling work based on the island physics42 was able to explain this behavior through the sensitivity of island width at the pedestal top, where its width abruptly increases at certain q95 values due to nonlinear RMP response44. When the island becomes bigger, it leads to local flattening of electron pressure (Pe, product of temperature and density), resulting in ELM suppression. This explanation has successfully predicted this q95 dependency in multiple devices44. However, its experimental validation remains challenging as plasma becomes perturbative while q95 changes, making the pedestal diagnostic oscillatory. Such diagnostic oscillation can be overcome by time filtering, but the temporal resolution of TS was limited for resolving pedestal evolution with q95 with filtering processing.\n\na Time evolution of edge safety factor (q95) and D\u03b1 emission at plasma edge for DIII-D discharge 136219. b Contour of electron pressure versus normalized plasma radius and time. The numerically derived width of the magnetic island at the pedestal top is illustrated as green contours. c Comparison of TS (blue), SRTS (red), and filtered SRTS (orange solid line).\n\nThe SRTS has once again derived the profile evolution by q95 change, providing novel evidence of profile flattening of the pressure profile at the top of the pedestal, leveraging the enhanced temporal resolution by SRTS. Fig.\u00a07b illustrates the strong flattening of the pressure profile during the ELM-suppressed phase, coinciding with the location and width of the magnetic island from numerical modeling. Fig.\u00a07c shows the electron pedestal height measured in both TS and SRTS of the nearest channel to the pedestal top, where the filtered SRTS (orange solid line) follows TS while overcoming diagnostic oscillations. This successfully extracts a prominent impact (profile flattening) on the pedestal caused by island widening from evolving plasma, leveraging the enhanced temporal resolution. This successful application of SRTS underscores its potential to reveal new physics beyond the limitations of conventional diagnostic techniques.",
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+            ]
+        },
+        {
+            "section_name": "Discussion",
+            "section_text": "In recent years, different kinds of ANN have been used for upsampling visual data45,46,47,48 and for radar data49,50,51. Conceptually, our methodology shares some resemblance with such inbetweening techniques, which nonlinearly interpolate missing frames in a video48. However, traditional inbetweening is typically a unimodal technique that relies on partial information from the same data stream (e.g., adjacent video frames). In contrast, our approach is intrinsically multimodal, synthesizing data from multiple diagnostics (spatially resolved and path-integrated) to reconstruct a higher-fidelity representation of the plasma. Crucially, we do not use the target diagnostic\u2019s own measurements as inputs, allowing us to generate a synthetic super-resolution version of that diagnostic even if it fails during operation. This capability distinguishes our method from standard inbetweening algorithms and underscores its robustness and broader utility in real-world complex systems.\n\nMore examples for ML-based upsampling were proposed for medical data52 and for audio data53,54. Similar to the video upsampling approaches, these approaches can be considered a subcategory of nonlinear interpolation as well. Yoon et al.55 suggested an alternative to interpolation for estimating the gaps in temporal data streams. It is to some extent a multimodal approach, because it fuses different kinds of information. However, the algorithm is limited towards estimating missing data or dealing with irregularly sampled data. Approaches like these work well for enhancing existing sequences, which are quasi-stationary in a way such that consecutive frames or samples do not change very fast.\n\nHowever, in fusion energy, many spurious events like ELM can happen between two TS samples. By interpolating between consecutive TS samples, regardless of linear or nonlinear, it is likely that we would miss such spurious events. In our work, we thus develop a novel method to generate additional TS samples based on other diagnostics. This is roughly inspired by other multimodal ML approaches, such as ref. 56, where it was proposed to fuse Radar and camera data for an enhanced distance estimation. This is a multimodal approach and thus related to our approach, or ref. 57, where ML was used to reveal the control mechanics of an insect wing hinge. This was also a multimodal approach in a way that the ML algorithm received different features recorded from flying insects. However, similar to the other approaches, no attempts to upsample or estimate missing/in-between data are made. Also58 presents an ANN method to enhance historical electron temperature data from the decommissioned C-2U fusion device. The model significantly increases the effective sampling rate of TS temperature measurements, utilizing data from multiple diagnostics, including the measured TS. The method\u2019s effectiveness is demonstrated through comparisons with ensemble-averaged data for the micro-burst instability study. The model\u2019s main drawbacks include limited generalization to only the temperature profile study for one specific plasma regime. Notably, the work does not explore the model\u2019s potential for discovering new physics in fusion plasmas.\n\nDiagnostics of electromagnetic systems involve measuring photons or waves to determine the physical quantities of these systems through post-processing. Due to the nature of the systems, these diagnostics are connected. Firstly, the measured signals are interconnected through electromagnetic interactions during system events. Additionally, the physical quantities obtained from signal processing are closely linked through momentum balances. Electromagnetic plasma quantities are governed by a series of momentum equations that encompass variables such as density, flow, temperature, and higher-order terms. Figure\u00a08 illustrates the momentum equations for plasma density (n) and temperature (T\u2009), where D represents particle diffusivity, v is plasma flow, Sn is the particle source, q denotes heat flux, B stands for magnetic field, j is plasma current, ST is the heat source, and (\u03b1, \u03b2) are constant coefficients determined by plasma properties59. These equations demonstrate how the measured plasma quantities are interrelated both spatially and temporally. For instance, the line-averaged density obtained from Interferometer diagnostics is geometrically linked to the local density measured by TS by its definition. Simultaneously, temperatures measured by TS and ECE diagnostics, which are positioned differently, are spatially coupled through the gradient term in the momentum equations. Although the TS density and temperature do not directly interact in the equations, they are tightly linked via diffusive fluxes influenced by turbulence, flow, and sources in a self-consistent manner. This intricate physical coupling of various diagnostic measurements allows ML to identify and predict their interconnections effectively.\n\nThe diagnostics are connected through electromagnetic interactions between signals. Simultaneously, derived quantities from these signals are coupled via geometric definitions, momentum balances, and high-order physics, including turbulence, flow, and source in the system.\n\nTo quantify the uncertainty in SRTS, we integrate a Bayesian Neural Network (BNN) with a similar architecture described in section \u201cMethods\u201d subsection \u201cTime-series model development.\u201d The model is designed with Bayesian Dense Variational layers, where each layer approximates a posterior distribution over weights using Variational Inference60. Aleatoric uncertainty, which accounts for inherent error in TS measurement, is modeled through a heteroscedastic output that predicts both the mean and log-variance of the target variable at each time step. During inference, we perform Monte Carlo sampling by drawing multiple predictions from the Bayesian posterior, and we compute epistemic uncertainty as the variance of the outputs61. In order to have a fair comparison of the epistemic and aleatoric uncertainties, we calculated the uncertainty of the BNN outputs per channel on the validation set only on the time steps where the ground truth (measured TS) is available.\n\nFigure\u00a09a, b illustrates the average uncertainty of the neural network outputs for electron density (ne) and temperature (Te) per TS channel over the validation set of discharges, depicted as red error bars (Epistemic uncertainty). The TS channels are represented by their distance from the mid-plane of the tokamak (Z). For comparison, we also show the empirically measured diagnostic errors in gray (Aleatoric uncertainty). Given that the epistemic uncertainty is, on average, relatively smaller than the aleatoric uncertainty inherent in the measurements, it indicates that the model has effectively learned the data-generating patterns and is relatively confident in its predictions.\n\na Comparison of the Epistemic and Aleatoric Uncertainties spatially, averaged over the validation dataset for both electron density ne and temperature Te. b Zoomed-in on the plasma edge part, where TS has higher spatial resolution. c The evolution of Epistemic Uncertainty as a factor of training dataset size; as the training set grows, the average and deviation of models\u2019 uncertainty over all TS channels decrease.\n\nTo ensure that our estimated epistemic uncertainty is meaningful, we conducted an analysis where we trained the model with progressively larger subsets of the dataset and examined how epistemic uncertainty evolved on the validation set. Figure\u00a09c shows the average and deviation of uncertainty across all TS channels as a factor of the percentage of training data used to train the model. The results demonstrate the expected trend where uncertainty decreases as the size of the training dataset increases. At the smallest dataset size, the epistemic uncertainty is highest, indicating that the model lacks sufficient information to make confident predictions. As the training data size increases, epistemic uncertainty steadily declines, reflecting improved model confidence and reduced variability in predictions. This behavior is characteristic of BNNs, where more data helps to refine the posterior distribution over weights, leading to reduced model uncertainty. Notably, the uncertainty reduction follows a diminishing returns pattern; while initial dataset increments lead to significant reductions, the improvements become less pronounced at larger dataset sizes. This suggests that beyond a certain dataset size, additional data contributes less to resolving uncertainty, and the model approaches its inherent learning capacity. The asymptotic nature of this trend highlights the fundamental limit of epistemic uncertainty reduction through data alone, emphasizing the importance of training dataset coverage, model architecture, feature representation, and priors in further improving prediction confidence.\n\nWith regard to the source of aleatoric uncertainty and according to the DIII-D diagnostics documentation, the uncertainty in TS measurements arises from fundamental photon counting statistics (discharge noise), imperfect background subtraction, and detector dark noise, all of which are random and inherent to the measurement process62.\n\nDuring the hyperparameter optimization of our models, we considered both accuracy and uncertainty of the model\u2019s performance. Nevertheless, as shown in Fig.\u00a09, there is epistemic uncertainty, though statistically smaller than the aleatoric uncertainty. A hypothesis could come from the ambiguous or conflicting training data. For example, there have been reports on discrepancies between ECE and TS measurements of electron temperature at JET tokamak63 and such investigations are ongoing at DIII-D as well.\n\nThis study introduces a transformative approach in the field of signal processing and diagnostics through the development of a multimodal neural network, Diag2Diag, which significantly enhances temporal resolution. By leveraging the intrinsic correlations among various diagnostic measurements, we have demonstrated the potential to increase the temporal resolution of the TS diagnostics in fusion plasma from a standard 0.2\u2009kHz to an unprecedented 1\u2009MHz. This improvement has unlocked new potentials in analyzing fast transient phenomena in plasma, such as the ELMs and the effects of RMPs on pedestal degradation, which were previously blurred or missed in lower resolution data. The ability to inspect these dynamics in greater detail provides new insights into plasma behavior, particularly in conditions where key physics is hidden in the milliseconds. This enhancement is not merely a technical improvement but a crucial enabler for deeper insights into plasma behaviors that are pivotal for advancing fusion reactors. Furthermore, the model\u2019s ability to reconstruct and predict diagnostics from other available diagnostics opens new avenues for measurement failure mitigation, cost-effective and less hardware-dependent diagnostic systems. This is particularly beneficial for experimental setups where space and resources are limited, such as in smaller fusion test facilities or in environments where installing multiple high-resolution diagnostics is impractical.\n\nLooking ahead, several promising extensions and refinements stand out. First, incorporating additional physics knowledge, such as through physics-informed neural networks (PINNs), may further improve accuracy by constraining the solution space and guiding the network with relevant plasma dynamics. Second, although our current work focuses on temporal resolution enhancement of TS, the same framework can be applied to other diagnostics, potentially improving their temporal or spatial resolution. By generalizing to a broader set of diagnostics and refining the method to capture spatial structure, we can further strengthen this data-driven paradigm for a wide range of fusion applications. Ultimately, these future directions will help realize more comprehensive and high-fidelity diagnostic capabilities, offering deeper insights into complex plasma phenomena.\n\nThe implications of this work extend well beyond the immediate application to magnetic fusion. The multimodal super-resolution capabilities developed here can significantly impact areas such as laser fusion data analysis, accelerator data analysis, and molecular dynamics research. In these fields, similar challenges exist where the time and space resolution of diagnostics is inadequate to capture fast phenomena effectively. By applying our method, researchers can potentially uncover new physical phenomena or confirm theoretical predictions that were previously unverifiable through experiments due to resolution constraints.\n\nIn conclusion, the Diag2Diag model not only addresses a critical need within the fusion community but also sets a precedent for the broader application of AI and ML in physical sciences. By pushing the boundaries of what can be observed and measured, this work contributes to the foundational technologies necessary for the realization of fusion energy and advances our understanding of complex physical systems across various scientific domains.",
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+            ]
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+        {
+            "section_name": "Methods",
+            "section_text": "For this experiment, we used discharges from the DIII-D tokamak that include all data from the key diagnostics of interest (CER, Interferometer, ECE, MSE, and TS). We randomly selected 4000 discharges recorded between the years 2017 and 2022 to ensure a diverse and representative dataset. The diagnostic data were collected using the DIII-D MDSplus64 system. These diagnostics are generally provided as time-series data streams with varying sampling frequencies, ranging from 200 Hz for TS up to 2\u2009MHz for Magnetics. The specific preprocessing steps applied to the data for the different experiments conducted in this study are detailed in the following sections.\n\nFor the spectrogram experiments, we consider the Interferometer and ECE diagnostics. We compute a logarithmic magnitude spectrogram from a time series of the raw diagnostics. For each channel (40 ECE channels and 4 Interferometer channels), we therefore used Hamming windows of 1\u2009ms with 0.5\u2009ms overlap. In this way, it was ensured that the different magnitude spectrograms are aligned in time. The spectrograms were afterwards converted to a logarithmic scale, clipped, and rescaled to the range of [0, 1]. Given the noisy nature of the ECE signals and after rescaling the spectrograms to the range of [0,1], the spectrograms are enhanced using a pipeline of image processing filters that includes\n\nQuantile Filtering with a threshold of 0.9,\n\nGaussian Blur Filtering on patches of size 31\u2009\u00d7\u20093,\n\nSubtracting the average per frequency bin.\n\nWe used the ECE spectrograms as inputs to our model. Since we treated every ECE channel independently during feature extraction, we obtained one spectrogram per channel, resulting in 40 input spectrograms. Since our model is designed to estimate the Interferometer spectrograms, it predicts four output spectrogram channels corresponding to the four Interferometer interferometer channels.\n\nFor the time-series models, the different diagnostic measurements have varying sampling rates, and some are even non-uniformly sampled in time. Since the aim of time-series data analysis was to increase the resolution of TS, we used its timestamps as a reference and aligned all diagnostic modalities to TS by matching their most recent measured samples in time. We considered the first 5s of each discharge, which resulted in approximately 3.4M data-points, split into 80%, 20% respectively, for training and validation of the models. As described in the main text, to test the model, we evaluated SRTS during the ELM and RMP mechanisms.\n\nFor Interferometer and ECE inputs of the time-series models, we also included the first and second temporal derivatives. Therefore, we smoothed the signals with a moving average window of 1\u2009ms (1660 Interferometer samples and 500 ECE samples), and then computed the first and second temporal derivatives of the smoothed signal also with a window of 1\u2009ms.\n\nThe diagnostics CER and MSE have relatively lower temporal resolution (200\u2009Hz and 4\u2009kHz, respectively). In this paper, we assume that they evolve only slowly in time. For the upsampling experiments, we thus pad these diagnostics after a measured sample with constant values until the next measured sample arrives.\n\nThe input diagnostics (CER, Interferometer, ECE, Magnetics, and MSE) consist of 58, 4, 40, 8, and 38 channels, respectively, which, together with the first and second derivatives of ECE and Interferometer, form an input feature vector of 236 elements per time step. The outputs are 80 channels of TS measurements for electron density and temperature (40 each).\n\nThe multi-channel ECE spectrograms were used as the input to a CNN, and the multi-channel Interferometer spectrograms were used as the target outputs. We optimized all important hyperparameters based on the \\({{\\mathscr{L}}}1\\) loss to minimize the difference between the ground truth and the estimated outputs on the validation set.\n\nThe optimization process of the model involved several key steps:\n\nThe model underwent training for up to 500 epochs.\n\nWe implemented early stopping with a patience threshold of 20 epochs, during which we monitored the validation loss for any improvements.\n\nThe AdamW optimizer65, known for decoupling weight decay from the learning rate, was utilized to minimize the \\({{\\mathscr{L}}}1\\) loss function.\n\nWe conducted a comprehensive hyperparameter optimization through a randomized search across 1000 iterations for all hyperparameters such as batch size, kernel size, and the learning rate.\n\nTo reduce the amount of training time, we randomly selected 518 discharges from the entire dataset to conduct the hyperparameter optimization. The model with the best-performing hyperparameter setting (achieving an \\({{\\mathscr{L}}}1\\) loss of 1.2\u2009\u00d7\u200910\u22123 on the validation set) was then re-trained on all available discharges.\n\nThe best-performing model is a CNN that transforms the ECE spectrograms with 40 channels subsequently to 32, 16, and 8 feature maps, and finally to the Interferometer spectrograms with 4 channels. For each feature map, 2D filter kernels with a size of 7\u2009\u00d7\u20097 are used. Batch normalization was used separately for each channel, and parametric ReLU activation functions were used after each batch normalization layer. The model had in total of 95,823 trainable parameters (i.e., filter kernels for each feature map, batch normalization parameters, and negative slope of the parametric ReLU activation function).\n\nFor the time-series prediction task, we employed a Multilayer Perceptron (MLP) model. The input data to the MLP comprised the CER, Interferometer, ECE, MSE, and magnetic diagnostics, along with the first and second temporal derivatives of the Interferometer and ECE signals, resulting in a total input size of 236 dimensions. The target output was the TS diagnostic data, which had 80 dimensions representing electron temperature and density across various spatial locations. To take the uncertainty of TS measurements into account, the target data were augmented by factor 2 by using the upper and lower intervals of each sample as additional targets.\n\nThe MLP model was trained for a maximum of 500 epochs, with an early stopping mechanism implemented to halt the training process if the validation loss did not improve for 20 consecutive epochs. The AdamW optimizer65 was employed to minimize the \\({{\\mathscr{L}}}1\\) loss function during training.\n\nSimilar to the approach for optimizing the spectrogram model, a comprehensive hyperparameter optimization was undertaken using a randomized search approach spanning 2000 iterations. The hyperparameters jointly optimized included the batch size, hidden layer size, dropout rate, and learning rate. The final MLP comprises three hidden layers with 512, 256, and 128 nodes, which leads to a total of 295,888 trainable parameters.\n\nIn principle, incorporating additional physical constraints in the form of a loss function or adopting a PINN framework66 could further refine such a model by reducing the solution space and enhancing accuracy. However, our primary objective is to demonstrate a broadly applicable methodology rather than a domain-specific approach. Therefore, we employed a conventional network architecture with a straightforward \\({{\\mathscr{L}}}1\\) loss function, underscoring that the central concept, exploiting inter-diagnostic correlations for super-resolution, does not hinge on specialized physics priors. This design choice also preserves the generality of our method, making it adaptable to other domains (e.g., astrophysical observations, medical imaging) where detailed physical models may be less readily available. By showing that even a standard ML approach can yield physically meaningful results when carefully formulated, we set the stage for future improvements that may incorporate more explicit physics constraints as needed.\n\nValidating synthetic, high-resolution diagnostic reconstructions in fusion plasmas presents unique challenges. Specifically for this work, no MHz-level TS measurements exist in any tokamak, and full-discharge gyrokinetic or extended MHD simulations at MHz temporal fidelity are computationally prohibitive and not yet sufficiently reliable for validation of long-pulse behavior. Such a limitation is, in fact, a motivating factor behind our approach: to develop new data-driven inference capabilities that can extend diagnostic insights beyond what is currently achievable via direct measurement or physics-based modeling. Given these constraints, we employed a multifaceted validation strategy using the best available experimental and simulation data. This includes quantitative comparison with existing TS data using R2 score, benchmarking against the highest-resolution burst-mode TS signals, and consistency checks against known plasma phenomena such as ELMs, RMP-induced magnetic islands, and q95 profile evolution. These steps collectively support the physical relevance and robustness of the super-resolved reconstructions produced by our model.\n\nWhile we do not claim that the SRTS signals are identical to the actual measurements, as reflected by an R2 score that is very high but not equal to 1, our validation results demonstrate that the synthetic outputs are sufficiently accurate to provide high-value insights. These reconstructions offer practical utility for addressing diagnostic limitations such as low resolution, degradation, and failure, supporting plasma analysis, and enabling potential new physics discovery.\n\nIn order to let fusion energy be a viable energy source, it must achieve significant fusion gain through continuous fusion reactions. A prominent method to reach this objective is operating a tokamak in high-confinement mode (H-mode), which has a narrow edge transport barrier, also known as the pedestal. This feature significantly boosts plasma confinement within the reactor, enhancing fusion power and efficiency. However, operating in H-mode introduces a steep pressure gradient at the pedestal, leading to substantial operational risks. This gradient drives hazardous edge energy bursts due to a plasma instability known as ELMs. These bursts lead to sudden drops in the energy at the pedestal, causing severe, transient heat fluxes on the reactor walls. This results in damaging material, potential surface erosion and melting, with heat energy reaching approximately 20\u2009MJ\u2009m\u22122, which is an unacceptable level for fusion reactors. From ITER, future machines will not allow even the first ELM. Therefore, to advance tokamak designs toward practical application in fusion energy, it is crucial to develop dependable methods to consistently suppress these edge burst events.\n\nA limitation of some diagnostics, such as TS, is the low temporal resolution of only 200\u2009Hz, which does not allow for detecting and tracking fast events like ELM (\u22641\u2009ms). Nevertheless, it is still important to detect such events reliably, as they can have a strong impact on plasma behavior.\n\nTo accurately resolve the fast transient dynamics, the TS lasers can be fired in a burst mode, which enables temporal resolution of up to 10\u2009kHz. This increase in temporal resolution is achieved by using multiple lasers in the same path with pulses interleaved closely in time. Normally, the lasers are phased to produce pulses at fairly regular intervals (exact regularity is not possible with the specific combination of 20\u2009Hz and 50\u2009Hz lasers being used at DIII-D). Continuous burst mode operation is also not possible because the laser system would overheat, the optics would be stressed, and the components would wear out very quickly. Therefore, the phase shifts are adjusted so that all lasers fire in rapid succession, followed by a cool-down. This burst mode encompasses between 3 and 7 laser pulses, depending on the time in the discharge.\n\nOn the other hand, diagnostics like Interferometer and ECE have much higher temporal resolution with continuous sampling frequencies around MHz, which allows for a much more detailed analysis of the plasma. However, these diagnostics have different characteristics compared to TS. While TS offers detailed insights into both electron density and temperature with high accuracy, it requires complex setups and is usually more resource-intensive. Interferometer provides a more straightforward approach to measuring electron density, excelling in situations that require rapid response and continuous monitoring. Furthermore, ECE and TS are both pivotal diagnostic tools used in tokamaks for measuring electron temperature, yet they operate on distinctly different principles and offer unique advantages. ECE utilizes the natural microwave emissions from electrons gyrating around magnetic field lines to provide excellent temporal resolution, allowing for the monitoring of rapid plasma changes and instabilities, though its effectiveness can be limited by variations in magnetic field strength. On the other hand, TS involves firing a laser into the plasma and analyzing the scattered light, which provides robust, absolute measurements of both electron temperature and density with less susceptibility to magnetic influences. While ECE excels in continuous data collection and fine temporal analysis, TS offers superior spatial resolution and is less dependent on external conditions, making it invaluable for comprehensive, though typically less frequent, plasma evaluations. If it would be possible to find a correlation between the measurements of those high-resolution diagnostics and TS, this would be useful for developing new physical analyses.\n\nThe radial profiles for electron temperature, density, and pressure in this study are obtained using TS and SRTS with a reconstruction for plasma equilibrium. This equilibrium is calculated from the magnetic reconstruction using the EFIT code67. Normalized poloidal magnetic flux is used as a representation of normalized radial coordinates.\n\nTo avoid any bias during model development and evaluation, each of the following steps in this research was conducted independently by separate researchers in a feed-forward manner as follows:\n\nThe data scientists developed a diagnostic dataset for training the neural network, aiming for generating synthetic SRTS. In this phase, the evaluation metric was simply the similarity between the model\u2019s output and the measured TS, whenever the measurement was available.\n\nFor physics validation, we generated the super-resolution diagnostic for a known ELMy discharge and asked an ELM-expert physicist to validate the behavior of the super-resolution diagnostic.\n\nThe data scientist then delivered the generated super-resolution diagnostic for the target plasma discharge to an experimental physicist to extract the plasma profile from that.\n\nWe then asked another physicist with expertise in simulation to obtain the simulation results for the target plasma discharge.\n\nIn the final step, we compared the plasma profiles from our generated diagnostics with the simulation results and found a strong match.\n\nThis indicates that our results are not biased based on prior physics knowledge, and we also did not rework our ML model to match our results with the simulation.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "All relevant DIII-D data supporting the findings of this study are available from the DIII-D National Fusion Facility, which is operated by General Atomics for the U.S. Department of Energy. Access to DIII-D data requires following the user protocols described on the DIII-D website. Specific questions regarding data availability can be directed to the corresponding author of this paper. Also, the source data and a Python script to reproduce the figures can be found on Figure Data.",
+            "section_image": []
+        },
+        {
+            "section_name": "Code availability",
+            "section_text": "The source code for the models developed in this work is publicly available68.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+            "section_image": []
+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "The authors gratefully acknowledge the collaboration of the DIII-D Team supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, using the National Fusion Facility, a DOE Office of Science user facility, under Award No. DE-FC02-04ER54698. Additional support was provided by the U.S. Department of Energy under Award Nos. DE-SC0022270 and DE-SC0022272 (A.O.N.), DE-SC0024527 (P.S., M.C., E.K.), DE-SC0020413 (M.C.), DE-AC02-09CH11466 (S.K., Q.H.), DE-SC0015480 and DE-SC0024626 (A.J., E.K.), as well as by the Princeton Laboratory for Artificial Intelligence under Award No. 2025-97 (A.J., E.K.). This research was also supported by the National Research Foundation of Korea (NRF) under Award No. RS-2024-00346024 (J.S.), funded by the Korean Government (MSIT). The authors also gratefully acknowledge support from the Research Institute of Energy and Resources, the Institute of Engineering Research, and the SNU Energy Initiative at Seoul National University (Y.S.N.). This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.",
+            "section_image": []
+        },
+        {
+            "section_name": "Author information",
+            "section_text": "Princeton University, Princeton, NJ, USA\n\nAzarakhsh Jalalvand,\u00a0Max Curie,\u00a0Peter Steiner\u00a0&\u00a0Egemen Kolemen\n\nPrinceton Plasma Physics Laboratory, Princeton, NJ, USA\n\nSangKyeun Kim,\u00a0Qiming Hu\u00a0&\u00a0Egemen Kolemen\n\nChung-Ang University, Seoul, South Korea\n\nJaemin Seo\n\nColumbia University, New York, NY, USA\n\nAndrew Oakleigh Nelson\n\nSeoul National University, Seoul, South Korea\n\nYong-Su Na\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\nA.J. is the lead author of the manuscript and contributed to developing the multimodal model and data science analyses. S.K. contributed to the physics analysis of Diag2Diag for the RMP mechanism on the plasma boundary. J.S. contributed to the general physics analysis and wrote the manuscript. Q.H. contributed to the physics simulation of the RMP mechanism on the plasma boundary. M.C. and P.S. contributed to the DIII-D data collection and data preprocessing for the multimodal model development and writing the manuscript. A.O.N. contributed the physics analysis of Diag2Diag for ELM cycles. Y.S.N. and E.K. contributed to the conception of this work, analyses, and writing the manuscript.\n\nCorrespondence to\n                Azarakhsh Jalalvand or Egemen Kolemen.",
+            "section_image": []
+        },
+        {
+            "section_name": "Ethics declarations",
+            "section_text": "The authors declare no competing interests.",
+            "section_image": []
+        },
+        {
+            "section_name": "Peer review",
+            "section_text": "Nature Communications thanks Kai Fukami and the other, anonymous, reviewers for their contribution to the peer review of this work. A peer review file is available.",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional information",
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+            "section_image": []
+        },
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+            "section_text": "Open Access  This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, 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 licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article\u2019s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article\u2019s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.\n\nReprints and permissions",
+            "section_image": []
+        },
+        {
+            "section_name": "About this article",
+            "section_text": "Jalalvand, A., Kim, S., Seo, J. et al. Multimodal super-resolution: discovering hidden physics and its application to fusion plasmas.\n                    Nat Commun 16, 8506 (2025). https://doi.org/10.1038/s41467-025-63492-1\n\nDownload citation\n\nReceived: 03 November 2024\n\nAccepted: 20 August 2025\n\nPublished: 26 September 2025\n\nVersion of record: 26 September 2025\n\nDOI: https://doi.org/10.1038/s41467-025-63492-1\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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3fc72f1e9a17e2bb00988df2a93fef6b38f66719228bf0615d75dea379eea95e/metadata.json

@@ -0,0 +1,145 @@
+{
+    "title": "Single particle cryo-EM structure of the outer hair cell motor protein prestin",
+    "pre_title": "Single-particle cryo-EM structure of the outer hair cell motor protein prestin.",
+    "journal": "Nature Communications",
+    "published": "12 January 2022",
+    "supplementary_0": [
+        {
+            "label": "Supplementary Information",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-021-27915-z/MediaObjects/41467_2021_27915_MOESM1_ESM.pdf"
+        },
+        {
+            "label": "Peer Review File",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-021-27915-z/MediaObjects/41467_2021_27915_MOESM2_ESM.pdf"
+        },
+        {
+            "label": "Reporting Summary",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-021-27915-z/MediaObjects/41467_2021_27915_MOESM3_ESM.pdf"
+        }
+    ],
+    "supplementary_1": [
+        {
+            "label": "Source Data",
+            "link": "https://static-content.springer.com/esm/art%3A10.1038%2Fs41467-021-27915-z/MediaObjects/41467_2021_27915_MOESM4_ESM.xlsx"
+        }
+    ],
+    "supplementary_2": NaN,
+    "source_data": [
+        "https://www.ebi.ac.uk/pdbe/entry/emdb/EMD-25442",
+        "https://doi.org/10.2210/pdb7SUN/pdb",
+        "/articles/s41467-021-27915-z#Sec18"
+    ],
+    "code": [],
+    "subject": [
+        "Cryoelectron microscopy",
+        "Hair cell",
+        "Membrane proteins"
+    ],
+    "license": "http://creativecommons.org/licenses/by/4.0/",
+    "preprint_pdf": "https://www.researchsquare.com/article/rs-821978/v1.pdf?c=1646869195000",
+    "research_square_link": "https://www.researchsquare.com//article/rs-821978/v1",
+    "nature_pdf": "https://www.nature.com/articles/s41467-021-27915-z.pdf",
+    "preprint_posted": "03 Sep, 2021",
+    "research_square_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The mammalian outer hair cell (OHC) protein prestin (Slc26a5), a member of the solute carrier 26 (Slc26) family of membrane proteins, differs from other members of the family owing to its unique piezoelectric-like property that drives OHC electromotility. OHCs require prestin for cochlear amplification, a process that enhances mammalian hearing. Despite substantial biophysical characterization, the mechanistic basis for the prestin\u2019s electro-mechanical behavior is not fully understood.  To gain insight into such behavior, we have used cryo-electron microscopy at subnanometer resolution (overall resolution of 3.96\u00c5) to investigate the three-dimensional structure of prestin from gerbil (Meriones unguiculatus). Our studies show that prestin dimerizes with a 3D architecture strikingly similar to the dimeric conformation observed in the Slc26a9 anion transporter in an inside open/intermediate state, which we infer, based on patch-clamp recordings, to reflect the contracted state of prestin. The structure shows two well-separated transmembrane (TM) subunits and two cytoplasmic sulfate transporter and anti-sigma factor antagonist (STAS) domains forming a swapped dimer. The dimerization interface is defined by interactions between the domain-swapped STAS dimer and the transmembrane domains of the opposing half unit, further strengthened by an antiparallel beta-strand at its N terminus. The structure also shows that each one of its two transmembrane subunits consists of 14 transmembrane segments organized in two inverted 7-segment repeats with a topology that was first observed in the structure of bacterial symporter UraA  (Lu F, et al., Nature 472, 2011). Finally, the solved anion binding site structural features of prestin are quite similar to that of SLC26a9 and other family members. Despite this similarity, we find that SLC26a9 lacks the characteristic displacement currents (or nonlinear capacitance (NLC)) found with prestin, and we show that mutation of prestin\u2019s Cl- binding site removes salicylate competition with anions in the face of normal NLC, thus refuting the yet accepted extrinsic voltage sensor hypothesis and any associated transport-like requirements for voltage-driven electromotility.Cellular & Molecular NeuroscienceStructural BiologyPrestin (Slc26a5)Cryo-EMcochlear amplificationNonLinear Capacitance",
+            "section_image": []
+        },
+        {
+            "section_name": "Additional Declarations",
+            "section_text": "There is NO Competing Interest.",
+            "section_image": []
+        }
+    ],
+    "nature_content": [
+        {
+            "section_name": "Abstract",
+            "section_text": "The mammalian outer hair cell (OHC) protein prestin (Slc26a5) differs from other Slc26 family members due to its unique piezoelectric-like property that drives OHC electromotility, the putative mechanism for cochlear amplification. Here, we use cryo-electron microscopy to determine prestin\u2019s structure at 3.6 \u00c5 resolution. Prestin is structurally similar to the anion transporter Slc26a9. It is captured in an inward-open state which may reflect prestin\u2019s contracted state. Two well-separated transmembrane (TM) domains and two cytoplasmic sulfate transporter and anti-sigma factor antagonist (STAS) domains form a swapped dimer. The transmembrane domains consist of 14 transmembrane segments organized in two 7+7 inverted repeats, an architecture first observed in the bacterial symporter UraA. Mutation of prestin\u2019s chloride binding site removes salicylate competition with anions while retaining the prestin characteristic displacement currents (Nonlinear Capacitance), undermining the extrinsic voltage sensor hypothesis for prestin function.",
+            "section_image": []
+        },
+        {
+            "section_name": "Introduction",
+            "section_text": "The outer hair-cell (OHC) molecular motor prestin (Slc26a5) belongs to a diverse family of transporters that includes 10 members1. Unlike other members of this family, and unique to membrane proteins, prestin functions as a voltage-driven motor with rapid kinetics, likely providing cycle-by-cycle amplification of sound within the mammalian organ of Corti2,3. However, cycle-by-cycle amplification at frequencies higher than 50\u2009kHz, where mammals such as bats and whales can hear, may be limited by the low-pass nature of prestin\u2019s voltage-sensor charge movement, which is a power function of frequency that is 40 dB down (1%) in magnitude at 77\u2009kHz4,5,6. The underlying basis of prestin\u2019s electromechanical capabilities resides in its unique piezoelectric-like property that drives OHC electromotility7,8,9,10,11. For members of this diverse family, known structures are dimers with each protomer showing a common 7\u2009+\u20097 inverted-repeat topology containing a core and gate domain; these proteins function variably as coupled transporters and uncoupled transporters/ion channels with a range of substrates1,12,13. Within the Slc26 family, prestin and pendrin (Slc26a4) are unique in showing voltage sensitivity with signature nonlinear capacitance (NLC) or equivalently, displacement currents/gating charge movements14,15,16; while pendrin lacks intrinsic electromechanical behavior17, prestin is a minimal transporter18,19,20. Prestin\u2019s NLC can be modeled, in its most simplest form, to fit a two-state Boltzmann function21. Two competing ideas have been proposed to be responsible for prestin\u2019s electromotility: (1) Cl\u2212 serving as the (extrinsic) voltage sensor22 and (2) intrinsic charged residues in prestin serving as the voltage sensor with Cl\u2212 acting in an allosteric manner19,23,24. The former posits a transporter-like movement with an arrested hemimovement of Cl\u2212 in the transporter cycle acting as its voltage sensor25,26. With more structural information, there have been competing visions of transporter mechanisms (elevator vs. rocker) in the related proteins that share similar structural folds27,28, although how these fit with prestin\u2019s electromechanical behavior remains speculative at best. To be sure, the lack of structural information for full-length prestin has precluded an understanding of its unique molecular motor function.\n\nIn this work, we have used single-particle cryo-electron microscopy to determine the structure of prestin from gerbil (Meriones unguiculatus) at subnanometer resolution that confirms Oliver\u2019s initial modeling efforts25 and, remarkably, bears high concordance with the recently determined cryo-EM structures of Slc26a929,30. Prestin forms a dimer and the cryo-EM-density map has allowed us to build a nearly complete model of the protein. In combination with electrophysiological data, our structural results suggest that the inward cytosol-facing conformation is that of prestin in the contracted state. Furthermore, mutations within prestin\u2019s now structurally confirmed anion-binding site show that the extrinsic voltage-sensor hypothesis22 is likely incorrect26, with the wider implication that a transporter-like mechanism driving electromotility is unlikely.",
+            "section_image": []
+        },
+        {
+            "section_name": "Results",
+            "section_text": "We used single-particle cryo-electron microscopy to obtain the structure of detergent-solubilized prestin from gerbil (Meriones unguiculatus) (Fig.\u00a01, [https://www.rcsb.org/structure/7SUN]). The protein, extracted\u00a0in digitonin, and purified in the presence of GDN (glyco-diosgenin), appears to be a homogeneous oligomer when assessed with size-exclusion chromatography and by negative-stain electron microscopy (Supplementary Fig.\u00a01A\u2013E).\n\nA\u2013C Three views: side view (A), cytosolic view (B), and extracellular view (C) of the cryo-EM structure of the prestin dimer. The prestin structure is colored by the subunit in cyan and yellow, respectively. D\u2013F Atomic model based on the cryo-EM density, shown in the same orientations as the density maps in the panels (A\u2013C). The N terminus and C terminus of the prestin structure face the cytosol. The different domain structures of prestin are colored using the same color scheme as shown in the schematic representation of the prestin sequence (G). (H, I) Two close-up views, rotated ~45\u00b0 with respect to each other, showing a density segment of the IVS loop overlaid with the model (shown in green ribbon) within the STAS-domain structure (shown in surface representation, in orange). Panels (H, I) show enlarged views of the interface boxed in panel (D). The positions of residues (R571, K580, and E637) from the IVS loop (shown in green ribbon) are indicated. Residue A726 is labeled to highlight the C terminus of the structure.\n\nThe cryo-EM images obtained from plunge-frozen specimens of solubilized prestin (Supplementary Fig.\u00a03A) revealed clear density for the transmembrane helices (TM), the cytoplasmic domains, and the micelle belt around the protein (Supplementary Fig.\u00a03B). A density map (Fig.\u00a01A\u2013C) was refined to an overall resolution of 3.6\u2009\u00c5 according to the gold-standard Fourier shell correlation (FSC) from 111,863 particles using C2 symmetry (Supplementary Figs.\u00a02, 3E, Supplementary Table\u00a01). The density map displayed clear secondary structural elements and densities visible for many of the bulky side chains (Supplementary Fig.\u00a04A-0). An analysis of the local resolution of the cryo-EM map shows that the core of the structure is better resolved than the periphery (Supplementary Fig.\u00a03C,D), with the lowest resolution observed at the tips of the extracellular loops, the cytosolic IVS loop (variable or intervening sequence), and the cytosolic C-terminal domain, which is highly flexible. This map has allowed us to unambiguously build and refine a nearly complete model of full-length prestin (Fig.\u00a01D\u2013F). The cryo-EM-derived structure shows that prestin oligomerizes as a dimer, with overall dimensions of ~10\u2009nm in diameter and ~8\u2009nm in height. Each prestin protomer comprises 14 transmembrane helices (named TM1\u2013TM14), a C-terminal cytosolic STAS domain, and a short cytosolic N-terminal region. The 14-transmembrane segments exhibit the same inverted 7-segment repeat organization as first observed in the crystal structure of the bacterial symporter UraA31. Seven of the transmembrane segments (TMs 1\u20134, TMs 8\u201311), are referred to as the \u201ccore\u201d domain and the remaining seven helices (TMs 5\u20137, TMs 12\u201314) form the \u201cgate\u201d domain of the structure. Prestin dimerizes in a similar fashion to Slc26a9; it forms a stable dimer through a combined molecular interface that buries about 7712\u2009\u00c52. The N terminus of one protomer (residues 13\u201375) crosses over the STAS domain (residues 505\u2013726) of the opposing protomer so that the interface between the STAS domain and the N terminus of the opposing subunit is the largest in the dimeric assembly and buries a surface area of approximately 1438\u2009\u00c52 (19% of contacts). In addition, the surface area of the STAS domain of one protomer in contact with the transmembrane domain of the other protomer is approximately 1293\u2009\u00c52 (representing 17% of contacts). The majority of this interface is formed by residues at the tips of TM5, TM8 and TMs 12\u201314 helices exposed at the intracellular surface of one protomer and the residues located on the first 3 helices of the other protomer\u2019s STAS domain. Tight STAS\u2013STAS domain interactions facilitate prestin dimerization with a buried interface of about 1192\u2009\u00c52 (15% of contacts). Close contacts between residues located on the antiparallel beta-strands at the N-terminal domain of each prestin subunit also mediate the dimeric assembly and cover a surface area of about 1046\u2009\u00c52. This is in line with our previous biochemical evidence showing the importance of prestin\u2019s N terminus to dimerization32. The interface area between the TM\u2013TM domains has a modest contribution to the dimerization (Supplementary Table\u00a02).\n\nLast, the protein that was used for the cryo-EM experiments contained YFP at the C terminus of prestin. We do not see densities corresponding to YFP in our reconstructions. We believe this is owing to the highly mobile nature of the attachment to the C terminus of prestin.\n\nThe cryo-EM structure of prestin closely resembles the previously reported cryo-EM structures of Slc26a9, which is a representative Slc26 family member29,30. In particular, the dimer of Slc26a9 from mouse in \u201cintermediate\u201d conformation (PDB ID, 6RTF, pair-wise C\u03b1 RMSDs (root-mean-square deviation): 2.985\u2009\u00c5 overall) can be fitted into the cryo-EM-density map of prestin from gerbil reasonably well. The previously observed Slc26a9 \u201cintermediate\u201d conformation29 may represent a more closed conformation when compared with the \u201cinward-open\u201d (open toward the cytosolic side of the membrane) conformation of Slc26a929. Our prestin structure superimposes onto the \u201cinward-open\u201d conformation of Slc26a9 from mouse (PDB ID, 6RTC), with pairwise C\u03b1 RMSDs of 4.25\u2009\u00c5 overall. Notably, the two previously resolved \u201cinward-open\u201d conformations of human SLC26A9 (PDB ID, 7CH1, determined at a resolution of 2.6\u2009\u00c5) and mouse Slc26a9 (PDB ID, 6RTC, determined at a resolution of 3.96\u2009\u00c5) are essentially identical. Unless noted otherwise, all further comparisons with the \u201cinward-open\u201d conformation of SLc26a9 will concern the higher-resolution structure (PDB ID, 7CH1).\n\nWhen aligning one prestin protomer with one Slc26a9 protomer (in \u201cintermediate\u201d and \u201cinward-open\u201d conformations) by their corresponding STAS domains (Supplementary Fig.\u00a05A\u2013C), the first large displacements with the Slc26a9 structures are observed at the linker connection between the transmembrane and cytosolic domains, indicated by an arrow (Supplementary Fig.\u00a05A\u2013C). The displacements extend into the entire transmembrane domains (Supplementary Fig.\u00a05A\u2013C). An intriguing result becomes apparent when superimposing the transmembrane domain of prestin onto the transmembrane domains of the Slc26a9 structures (Fig.\u00a02A\u2013F, Supplementary Fig.\u00a05D\u2013F) through the C\u03b1 atoms of residues within TM13 and TM14 helices. We observe differences in the orientation of TM8 (from the core domain) with respect to the TMs 13 and 14 (from the gate domain) (Fig.\u00a02G\u2013I; Supplementary Fig.\u00a06A\u2013C) at the cytosolic side of the structures. Thus, the angle between the transmembrane helices 8 and 14 is smaller by about 10\u00b0 between prestin (at 57\u00b0) and the \u201cinward-open\u201d conformation of SLc26a9 (at 67\u00b0) and by about 4\u00b0 between prestin and the \u201cintermediate\u201d conformation of SLc26a9 (at 61\u00b0). Consequently, the gap between the cytosolic ends of TMs 13 and 14 (from the gate domain), and the cytosolic end of TM8 (from the core domain), is smaller in prestin compared with Slc26a9, particularly in the \u201cinward-open\u201d conformation (Fig.\u00a02G\u2013I; Fig.\u00a02, Supplement\u00a02A,B,C). We speculate that our cryo-EM prestin conformation, showing a narrower opening to the cytosol, would explain why this protein shows reduced ability to transport anions in comparison with Slc26a9. Moreover, the kinetic barrier afforded by this narrowing could explain the clearly measurable currents in the presence of the easily dehydrated SCN\u2212 ion that has a smaller diameter than the hydrated Cl\u2212 ion that shows reduced currents33,34. The position of the pair (TM3, TM10) in prestin, which contains residues important for the coordination of anion substrates, also differs from the positions of (TM3 and TM10) helices in Slc26a9. The (TM3, TM10) pair in prestin undergoes rotations relative to their counterparts in Slc26a9. Prestin\u2019s TM10 is retracted by about 12\u00b0 relative to TM10 of the \u201cinward-open\u201d Slc26a9 structure and by about 10\u00b0 relative to TM10 of the \u201cintermediate\u201d Slc26a9 structure (Fig.\u00a02C, F).\n\nA Superposition of the transmembrane-domain structures of prestin (colored in cyan) and Slc26a9 in the \u201cinward-open\u201d conformation (colored in orange, PDB 7CH1). The structures have been superimposed through the TM13 and TM14 helices from the \u201cgate\u201d domain. B Close-up view showing a portion (TM3, TM5, TM8, TM10, TM13 and TM14 helices) of the overlaid transmembrane domains (as shown in panel A). C Close-up view of the overlaid pair of helices (TM3 and TM10) from the two structures in the orientations shown in panel A. D Superposition of the transmembrane domain structures of prestin (colored in cyan) and Slc26a9 in the intermediate conformation (colored in gray, PDB 6RTF) (superimposed through the gate\u2019s TM13 and TM14 helices). E Close-up view of the overlaid (TM3, TM5, TM8, TM10, TM13, and TM14) helices from the two structures in the orientations shown in panel (D). F Close-up view showing the offset between the pair of helices (TM3 and TM10) from the two structures in the orientations shown in panel (D). G\u2013I Side-by-side comparisons of the opening between the TM8 helix (from the core domain) and the TM14 helix (from the gate domain) on the intracellular side of the membrane for the three structures. Consistent with the expectation, this opening (defined by the angle between the TM8 helix and TM14 helix) is the larger in the Slc26a9 structure (inward-open conformation) and the smaller in the prestin structure. The angle between TM8 and TM14 helices of prestin and of Slc26a9 is 57\u00b0 (for prestin), 61\u00b0 (for Slc26a9, the intermediate conformation), and 67\u00b0 (for Slc26a9, the \u201cinward-facing\u201d, open conformation). See also Supplementary Fig.\u00a06.\n\nWhen aligning the transmembrane domains of prestin and SLC26a9 structures, the C\u03b1 RMSD values of the superimposed structures are 4.3\u2009\u00c5 for prestin\u2013Slc26a9 (PDB ID, 7CH1) and 2.86\u2009\u00c5 for prestin\u2013Slc26a9 (PDB ID, 6RTF), respectively.\n\nThe C-terminal STAS domain of prestin is similar to the previously determined X-ray crystal structure (PDB ID, 3LLO), lacking the unstructured loop35. Thus, we see an identical core of five beta-sheets surrounded by 5 alpha-helices. The RMSD value when superimposing prestin\u2019s C-terminal domain solved by cryo-EM with prestin\u2019s C-terminal domain solved by X-ray crystallography (PDB ID, 3LLO) is 0.853\u2009\u00c5 over 105 C\u03b1 atoms. The prestin\u2019s STAS domain and the STAS domains of the two Slc26a9 conformations align with an RMSD value of 0.955\u2009\u00c5 over 123 C\u03b1 atoms (for prestin\u2014PDB ID, 7CH1) and of 1.038\u2009\u00c5, respectively, over 66 C\u03b1 atoms (for prestin\u2014PDB ID, 6RTF), revealing essentially identical structures (Supplementary Fig.\u00a05G\u2013I). In contrast to the previously reported SLC26a9 cryo-EM structures29,30, the cryo-EM density for the IVS loop resolved in the prestin structure shows a more ordered, interpretable density (Fig.\u00a01H,I). Therefore, we were able to build into this more interpretable density an extended helix between residues (R571\u2013K580) and the IVS sequence spanning residues (V614\u2013E637). As shown in Fig.\u00a01I, the IVS sequence (between residues 614 and 630) abuts on the tip of helix 2 (at residue G668) and the loop connecting helix3 with helix 4 (at residue N695) from the STAS domain.\n\nWe infer that the structure of prestin that we obtained is in the contracted state. Membrane depolarization from a negative resting voltage shifts prestin from an expanded to contracted state, evoking OHC shortening14,15. Furthermore, increases in intracellular Cl\u2212 ion concentration cause a hyperpolarizing shift in Vh, the voltage where, based on 2-state models, prestin is equally distributed between compact and expanded states22,23,36. The cell line from which we purified prestin37 displays Vh values near \u2212110\u2009mV in the presence of 140\u2009mM Cl\u2212 (Fig.\u00a03A). Since the voltage across detergent micelles is effectively 0\u2009mV, prestin is likely in a contracted state.\n\nA Prestin predominantly resides in the contracted state at 0\u2009mV. Average NLC (n\u2009=\u200910), 48\u2009h after induction of our inducible prestin HEK stable cell line (#C16). Recordings were done in the presence of 140\u2009mM intracellular Cl. NLC-fitted (Eq.\u00a01) parameters were Qmax\u2009=\u20090.40; z\u2009=\u20090.70; Vh\u2009=\u2009\u2212112\u2009mV; DCsa\u2009=\u20090.26 pF; NLC peaks at Vh; n\u2009=\u200910. B The S398E mutation in prestin preserves NLC after application of 20\u2009mM salicylate. Controls shows full block of NLC. The average unitary gating charge (z) in these mutants (0.69e \u00b1 0.03 SEM, n\u2009=\u20097) was similar to that of CHO cells expressing prestin\u2013YFP (0.73e \u00b1 0.14 SEM, n\u2009=\u200910, P\u2009>\u20090.05). Vh was significantly different, however (96.25\u2009mV\u00b1 4.6 WT; +73.8mV \u00b16.4, p\u2009<\u20090.05). C Close-up view showing the residues Q97, S398, R399, P136, and F137 in prestin (displayed as sticks, colored by atom type) that correspond to residues found to be important for Cl\u2212 binding in Slc26a9 (with prestin in cyan ribbon). The mean z and Vh values of fitted NLC of several mutations of residues that coordinate chloride binding were WT, 0.71e \u00b1 0.03 SEM, \u221298.12\u2009mV \u00b1 2.33SEM n\u2009=\u20099; Q97A 0.65 \u00b1 0.04, \u221294.1\u2009mV \u00b1 5.29, n\u2009=\u20095; P136T 0.64 \u00b1 0.05 SEM, \u221288.15 \u00b1 10.1 SEM, n\u2009=\u20099. The differences were not significant (p\u2009=\u20090.54, one-way ANOVA for z; p\u2009=\u20090.605, one-way ANOVA for Vh). D Close-up view of the corresponding region in the Slc26a9 structure (the \u201cinward-facing\u201d, open conformation, in orange ribbon). Residues Q88, S392, T127, and F128 (in stick representation) are involved in Cl-coordination in Slc26a9. E The location of the Cl binding site at the interface between TM1, TM3, and TM10 is conserved in prestin and Slc26a9. Overlay of portions of the transmembrane helices 1, 3, and 10, from prestin and Slc26a9, as shown in panels (C, D). F Overlay of the Cl-binding sites of prestin and Slc26a9 (\u201cinward-facing\u201d, open conformation). Equivalent residues are shown as pairs. Cyan sticks are prestin residues and orange sticks are Slc26a9 residues. Source data are provided as a Source Data file.\n\nThe analysis of mutations in the Cl\u2212 binding site can provide important information. Despite purification in high chloride, we were unable to resolve a density corresponding to a chloride ion within prestin. A similar observation was made with all three structures of Slc26a929,30, and in prestin\u2019s case, it may be due to its relatively poor Cl\u2212 binding affinity22,38. Nevertheless, prestin presents the canonical anion-binding site features identified in other structurally solved family members where substrates are resolved. The binding site is between TM3 and TM10 and the beta-sheets preceding these. Many of the residues important for coordinating substrate binding in those proteins are located in similar positions in prestin, including F137, S398, and R399 (Fig.\u00a03C\u2013F). Furthermore, with the exception of T127 in Slc26a9 (which is a proline P136 in prestin) other residues important for coordinating water molecules for substrate interactions are also conserved in prestin (Q97, F101). Although it has been speculated that Cl\u2212 acts as an extrinsic voltage sensor22, this speculation has never been confirmed; instead, anions have been shown to foster allosteric-like modulation of prestin activity and kinetics, with anion-substitute valence showing no correlation with the magnitude of prestin\u2019s unitary charge23,24,36,38,39,40. It is well known that salicylate blocks NLC and electromotility41,42, possibly by competitively displacing Cl\u2212\u200922. Here we show that mutation of S398 in the structurally identified anion-binding pocket of prestin to a negatively charged glutamate residue results in a protein that is insensitive to salicylate yet retains normal NLC (Fig.\u00a03B). This observation is further evidence against Cl\u2212 acting as an extrinsic voltage sensor. We see similar effects with R399E. Indeed, recently, Oliver et al.43 reported on S396E that shows insensitivity to salicylate as proof refuting his original extrinsic voltage-sensor hypothesis. They also previously observed salicylate insensitivity with R399S25. Another mutation within the anion-binding pocket of prestin, F137 to alanine resulted in a loss of NLC or a far-right shift in its voltage sensitivity that made its detection impossible44; membrane insertion was confirmed by detectable SCN- currents. We additionally mutated two residues in prestin that are implicated in Cl\u2212 binding in Slc26a9, substituting an alanine residue for Q97, and substituting a threonine residue for P136 that corresponds to T127 in Slc26a9. Both these mutants have normal unitary gating charge (z) (Q97 0.65 \u00b1 0.04 n\u2009=\u20095, P136\u00a00.64 \u00b1 0.05 n\u2009=\u20099). These z values were not significantly different (p\u2009>\u20090.05, one-way ANOVA) from WT (Fig.\u00a03). Residue mutations within a binding pocket are well known to alter binding (e.g., affinity) in many proteins. If normal binding of anions were required for sensor charge movement, then NLC would be altered, which it is not. That these mutations do not affect NLC is evidence refuting the extrinsic voltage-sensor hypothesis, and also make implausible any associated transport-like requirements for voltage-driven electromotility.\n\nThe marked structural similarity between prestin and Slc26a9 may provide insight into prestin\u2019s electromechanical behavior. In prestin, several charged residues have been shown to affect the size of the unitary gating charge and thus contribute to voltage sensing19. Of those twelve residues, nine are conserved in Slc26a9. We transiently expressed Slc26a9 in CHO cells but were unable to find NLC or gating currents in contrast to transiently transfected CHO cells expressing prestin (Fig.\u00a04A, B top panels). Slc26a9 surface expression in transfected cells was successful as demonstrated by enhanced currents in the presence of extracellular SCN\u2212 (Supplementary Fig.\u00a07A, B) and visualization of fluorescence on the surface of these cells expressing Slc26a9 with YFP tagged to its C-terminus (Fig.\u00a04A, inset). Thus, despite marked structural similarities to prestin, Slc26a9 does not mimic prestin\u2019s electromechanical behavior.\n\nA Top panel: Capacitance of CHO cells transiently infected with Slc26a9, scaled to linear capacitance near \u2212100\u2009mV. Measured with dual-sine voltage superimposed on a voltage ramp from \u2212175 to +150\u2009mV. A very slight increase in Cm occurs at +150\u2009mV, possibly indicating an extremely right-shifted NLC. Capacitance data are presented as mean values (\u00b1 SEM) of 10 independent cells. Inset: Confocal image of CHO cells transfected with Slc26a9-YFP that is expressed on the membrane. The scale bar is 10 microns. Bottom panel: Ramp induced currents simultaneously measured with membrane capacitance, also scaled to linear capacitance. Current data are presented as mean values (\u00b1 SEM) from the same 10 independent cells shown in the upper panel. Average (\u00b1 SEM) series and membrane resistance are shown. In red are mean (\u00b1SEM) currents observed in untransfected cells (n\u2009=\u20095). Inset: top traces show very small nonlinear currents extracted with P/\u22125 protocol, subtraction holding potential set to \u221250\u2009mV. Voltage protocol shown below traces. B Top panel: Capacitance of CHO cells transiently infected with prestin, scaled to linear capacitance near +100\u2009mV. Measured with dual-sine voltage superimposed on a voltage ramp from \u2212175 to +150\u2009mV. A prominent increase in Cm occurs at \u2212110\u2009mV, typical of prestin NLC. Capacitance data are presented as mean values (\u00b1 SEM) of nine independent cells. Bottom panel: Ramp-induced currents simultaneously measured with membrane capacitance, also scaled to linear capacitance. Current data are presented as mean values (\u00b1 SEM) from the same nine independent cells shown in the upper panel. Average (\u00b1 SEM) series and membrane resistance are shown. In red are mean (\u00b1 SEM) currents observed in untransfected cells (n\u2009=\u20095). Inset: top traces show large nonlinear displacement currents extracted with P/-5 protocol, subtraction holding potential set to +50\u2009mV. Voltage protocol (holding potential 0\u2009mV) shown below traces. Source data are provided as a Source Data file.\n\nWhile detergent micelles have distinct properties from the lipid bilayer, we note an intimate relationship between the protein and micelle. Moreover, with the caveat that micelles may not be analogous to a bilayer, we note that the distance between the inner and outer \u201cleaflets\u201d of the micelle tends to vary across the protein\u2019s landscape (Fig.\u00a05A, B). As indicated in Fig.\u00a05, the micelle density shows conspicuous depressions around a region spanning TMs 6, 7, 12 (helices from gate domain). Measurements of the micelle\u2019s thickness indicates a locally thinned micelle in the vicinity of TMs 6-7. Thus, the distance between the micelle\u2019s \u201cleaflets\u201d is locally reduced to about 3.4\u2009nm around the TM6 helix in comparison with a 4.4-nm thickness at the central part of the micelle. Supplementary Fig.\u00a08 shows a corresponding variation in prestin\u2019s surface hydrophobicity across its transmembrane domain.\n\nA Cryo-EM map for the gerbil prestin structure (colored by subunit in cyan and yellow, respectively) showing the surrounding micelle as a gray transparent surface. The dashed line (in navy) follows the micelle\u2019s boundaries. The micelle belt around the transmembrane domain of prestin is locally distorted (thinned) at the cytosolic side close to TM6 and TM12 helices. The approximate thickness of the micelle in these regions is indicated by black arrows. The transmembrane helices 6, 7, and 12 are labeled. B As in (A) but tilted by ~10\u00b0 to better illustrate the micelle\u2019s distortions at the cytosolic side. See also Supplementary Fig.\u00a09.\n\nCompared with other members of the extended transporter family, the two protomers of the prestin dimer show minimal interactions between the transmembrane domains as is the case with Slc26a9. Thus, the space between the membrane domains of the two protomers is filled by the detergent micelle (Fig.\u00a05A, B).\u00a0In addition, we identified a number of amorphous densities (Supplementary Fig.\u00a09A, B). These amorphous densities were analogous to similar densities found in Slc26a9 at 2.6\u2009\u00c5 (see Supplementary Fig.\u00a0S3, b in30). We interpreted these densities as lipids.\n\nThese data raise a number of issues pertaining to lipid effects on the protein\u2019s function. For example, perhaps the variations in \u201cleaflet\u201d thickness are a reason for the shallow voltage dependence of prestin\u2019s NLC. We consider the influence of the surrounding lipid bilayer below.",
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+        {
+            "section_name": "Discussion",
+            "section_text": "We found that the overall molecular architecture of prestin resembles the previously reported cryo-EM structures of full-length human SLC26A9 (29) and of a shorter version of mouse Slc26a9 protein29,30, whose functions are to facilitate the transport of anions. Slc26a9 allows entry of the substrates (anions) from the cytosol through the so-called \u201cinward-open\u201d conformation, which shows an opening between the \u201ccore\u201d and the \u201cgate\u201d domains as described in the solved cryo-EM structures29,30. Intriguingly, we found that the membrane-spanning portion of prestin does not conform to the \u201cinward-open\u201d conformation of Slc26a9 (PDB ID, 7CH1). Rather, prestin has a more compact conformation, closer to the \u201cintermediate\u201d conformation of Slc26a9 (PDB ID, 6RTF), which shows the cytosol-exposed space between the \u201ccore\u201d and the \u201cgate\u201d domains to be tighter. We reason that our prestin conformation solved by cryo-EM represents the contracted state of the protein at 0\u2009mV.\n\nSince submission of our paper, we note publication of a paper that presents the structure of human prestin in the presence of Cl\u2212 and SO42\u2212 anions45. Our structure in the presence of Cl\u2212 is highly concordant with that of Ge et al. (2021)45 (both in detergent and nanodisc), which is reassuring. Thus, the RMSD values between our structure and the structure of human prestin in Cl\u2212 with detergent (PDB ID, 7LGU) and with nanodiscs (PDB ID, 7LGW) are nearly identical with C\u03b1 RMSDs of ~0.800 \u00c5 and ~0.838 over 1348 residues, respectively (Supplementary Fig.\u00a011). The transmembrane helices and most of the loops connecting the TM helices remain at similar positions in gerbil prestin. The most prominent structural differences are at a region spanning residues (624\u2013637) in the STAS domain, at the loop connecting TM7 and TM8 (residues 317\u2013337), and especially at the cytosolic N-terminus (spanning residues 37\u201348), which shifts inside relative to the corresponding region in the human prestin structure (Supplementary Fig.\u00a011B\u2013E). These areas are the least well resolved in the density map of gerbil prestin, which suggests increased flexibility at these regions. Overall, prestin from gerbil in the presence of Cl\u2212 and detergent adopts a structural conformation very similar to the contracted conformation captured for human prestin.\n\nGe et al. also show prestin structures in the presence of SO42\u2212 (PDB ID 7LH2 RMSDs (C\u03b1 over 1348 residues) of 1.4 \u00c5 compared with our structure in Cl\u2212) that they ascribe as in the expanded state owing to the depolarizing shift in voltage dependence in the presence of this anion45. We would caution against such interpretation as the total charge movement (Qmax) in the presence of SO42\u2212 is reduced by ~2/324. Since unitary charge is also reduced by an ~30% in SO42\u2212, these data would argue that 50% of motors are in an inactive or unresponsive state24. Moreover, the ~30% reduction in unitary charge movement would mean that there is incomplete movement of the protein molecules that do show voltage-dependent movement. In a similar vein, we find that the increase in linear capacitance in the presence of salicylate to be twice that of voltage-induced expansion46,47, again making structures in its presence difficult to interpret in light of voltage-induced changes. These data together speak to the urgency in obtaining prestin\u2019s structure in changing voltage alone with physiological anions.\n\nWe have compared our prestin cryo-EM structure to the predicted structure by the AlphaFold algorithm and find that despite overall similar topology, the pairwise Calpha RMSD calculated over the number of residues resolved in the cryo-EM structure is 7.3\u2009\u00c5.\n\nThe essential work of the voltage-dependent protein prestin dwells at frequencies where mammals can hear, driven by OHC AC-receptor potentials. That is, the protein works in the kilohertz range of conformational change, with high-frequency measures of NLC reporting indirectly on those motions4. Cryo-EM structures of prestin, which necessarily define one or more steady-state conformations of the protein, may tell us little about its high-frequency physiology. Indeed, we cannot be sure that any identified state is actually occupied during high-frequency voltage stimulation, where molecular interactions, e.g., at the lipid\u2013protein interface (see Fig.\u00a05), may be influenced by rate (frequency) itself. The stretched-exponential nature of prestin\u2019s NLC likely reflects such interactions48. Nevertheless, static structures can inform on some key questions concerning prestin\u2019s molecular behavior.\n\nGiven the anion-binding pocket structural features (not assumed from other family members), we can assign relevance to prior and present mutational perturbations. Thus, we present data here that Cl\u2212 likely does not function as prestin\u2019s extrinsic voltage sensor, evidenced by the loss of anion sensitivity with structurally driven mutations in the anion-binding site. Instead, prestin possesses charged residues important for voltage sensing, akin to other voltage-sensing membrane proteins19,49. The distribution of twelve charged residues that sense voltage in prestin has important implications. Seven of the 12 residues are located in the gate/dimerization domain in TMs 5, 6, and 12 that are modeled to move minimally in the elevator model19,27,28. Notably, all but two of the 12 residues lie in the intracellular halves of the TM domains or in the intracellular loops connecting these TM domains (Supplementary Fig.\u00a010). In contrast, all but one of the five charged residues that have no effect on voltage sensing lie close to the extracellular halves of the TM domain or in the loops connecting these TM domains. This ineffectual group includes a charged residue in TM3 (R150) that is modeled to move significantly in the transporter cycle19,27,28. Together, these data suggest that contrary to functional expectations based solely on structural similarity between prestin and Slc26a9, electromechanical behavior in prestin is fundamentally different to transporter movements and is concentrated in proximity to the intracellular opening. It should be noted that majority of the charged residues responsible for NLC in prestin are also conserved in many of the other SLC26 transporter family members, including Slc26a6, that do not show NLC. In agreement with our conclusions, the recent paper by Ge et al.45 noted that the anion binding residues moved 1\u20132\u2009\u00c5 toward the cytoplasmic surface in the presence of SO42\u2212. Of course, these data would refute the extrinsic voltage-sensor hypothesis, as well, where movement of anions in the expanded state was predicted to be 25\u2009\u00c5 in the opposite direction45.\n\nThe wide dispersion of residue charges in several transmembrane domains that contribute to NLC and the inferred uneven lipid packing may underlie prestin\u2019s shallow voltage dependence. Indeed, the influence of lipids on prestin performance is well documented50,51,52,53. In agreement with the area motor model of prestin activity54,55, we previously identified an augmentation of linear capacitance (\u0394Csa) during hyperpolarization in prestin-transfected cells, our inducible prestin cell line (Fig.\u00a03A) and OHCs that likely reflects an increase in membrane-surface area and bilayer thinning accompanying movement of prestin into the expanded state46,47. Thus, we conclude that the compact state that we observe structurally corresponds to minimal membrane-surface area and maximal membrane thickness. The converse would be expected for the expanded state. In this regard, although salicylate blocks NLC and eM, the effect it has on changes in linear capacitance (\u0394Csa) indicates that it does not produce a natural state of prestin that is normally driven by voltage. That is, in the presence of salicylate, the area occupied by prestin, as indicated by \u0394Csa, is doubled that produced in its absence when driven by voltage46,47. Thus, we might expect that direct voltage-driven conformational changes in prestin could differ from unphysiological (e.g., salicylate or SO42\u2212) anion-induced steady state cryo-EM structures. Interestingly, we have recently shown that the \u0394Csa component of membrane capacitance exists only in the real (capacitive) part of complex NLC, not in the imaginary (conductive) part, ostensibly linking it directly to membrane bilayer influence rather than prestin charge movement56.\n\nInterestingly, we note several amorphous densities in our 3.6-\u00c5 map, which correspond to identified lipids in human prestin (PDB ID, 7LGU). Some of these lipids in our structure are found between transmembrane helices (see Supplementary Fig.\u00a09E\u2013I). Since lipid pockets like these have been shown to influence protein\u2013lipid interactions in the mechanosensitive Mscl channel57, we reason that they may serve a similar function with prestin that shows similar sensitivity to membrane tension11,58.\n\nWe have determined that prestin is dimeric as our previous studies have suggested32,59, although earlier reports asserted that prestin functions as a tetramer60,61. In Slc26a9, three features were identified as important for dimerization and likely are pertinent for prestin considering the proteins\u2019 remarkable similarity. These include (1) interactions between individual protomers exemplified by the valine zipper in TM14, (2) interactions between the C-terminal STAS domain of one protomer and the TM domain of the other and (3) an antiparallel beta-strand between the N terminus of both protomers. Prestin shows each of these same interactions with the valine zipper being replaced by leucine and isoleucine residues. The antiparallel beta-sheet between the N-terminal residues 15\u201320 of each protomer in prestin is likely critical for dimerization. Indeed, sequential deletion of residues 11\u201321 resulted in progressive loss of NLC, and loss of FRET signal confirming the loss of dimerization32. These data also argue that dimerization is critical for NLC, just as dimerization is important for transporter function in UraA12,31.\n\nThe C terminus of prestin has high homology to the previously determined X-ray crystal structure of the C-terminal STAS domain (PDB ID, 3LLO) lacking the unstructured loop35. Thus, the many interpretations made by the Battistutta group are likely to therefore apply, including confirmation in our structure of the orientation of the STAS domain to the transmembrane domain, and the importance of the alpha-5 helix in stabilizing the core beta-sheets suggested by truncation experiments32,62. A significant difference was in the first alpha-helix that is parallel to the second alpha-helix as in bacterial ASA (anti-sigma factor antagonistic) proteins63, and deviated by a 30\u00b0 angle in the crystal structure35. This is likely due to the unstructured loop at the end of the first alpha-helix that was lacking in the crystal structure.\n\nFinally, structural details of the C-terminal STAS domain can shed light on modulation of prestin by binding partners, for example, calcium/calmodulin64. Recently, calmodulin has been shown to bind to the STAS domain65. Such interactions may have physiological significance, since it was reported that Ca2+/calmodulin shifts the operating voltage of prestin, namely Vh66. However, it was subsequently shown that shifts in Vh were not due to direct action on prestin, but rather resulting from indirect tension effects on prestin due to OHC swelling67. The influence of the STAS domain on prestin\u2019s voltage-dependent activity remains an open question.\n\nOHC electromotility was discovered in 198568,69, and 15 years later, prestin was identified as the protein responsible for the OHC\u2019s unique role in cochlear amplification10,11,70. During the intervening years, enormous detail into the protein\u2019s function has been obtained, see26. Recent homology modeling of prestin25, based on presumed similarity to other family members, and confirmed in our structural data, has moved us closer to understanding prestin\u2019s electromechanical behavior. Indeed, the cryo-EM solution we provide here will permit us to rigorously interpret past studies and design experiments to more fully understand prestin\u2019s role in mammalian hearing. Given the remarkable similarity of prestin structure revealed in this present study to that of the inside-open/intermediate state of Slc26a9, key questions remain as to why the two proteins differ in their function. Indeed, established functional observations on prestin may have already identified key differences, for example, the observed negative cooperativity among the densely packed proteins interacting through membrane lipids (10,000/\u03bcm2 in OHCs)53,71, and subplasmalemmal cytoskeletal interactions with prestin72. Though key, prestin likely is a partner in the machinery that boosts our hearing abilities. Imperative in the overall effort to understand prestin is the need for alternative structures of prestin and other family members that are evoked by appropriate physiological stimuli, e.g., voltage in the case of prestin.",
+            "section_image": []
+        },
+        {
+            "section_name": "Methods",
+            "section_text": "The full-length prestin from gerbil (Meriones unguiculatus, Genbank accession number AF230376) was purified from a tetracycline-inducible stable HEK 293 cell line37. In establishing this cell line (16C), full-length gerbil prestin cDNA (a gift from J. Zheng and P. Dallos) tagged at its C terminus with enhanced yellow fluorescent protein (EYFP) was inserted into the multiple cloning site of pcDNA4/TO/myc-HisC that allowed purification using Ni affinity.\n\nCells were grown in DMEM media supplemented with 1\u2009mM l-glutamine, 100\u2009U\u2009ml\u20131 penicillin/streptomycin, 10% FBS, and 1\u2009mM sodium pyruvate. About 4\u2009\u03bcg/ml of blasticidin and 130\u2009\u03bcg/ml of zeocin were supplemented in the growth media to maintain prestin expression. Cells were harvested 48\u2009h after tetracycline (1\u2009\u03bcg/ml) was added to the cell-growth medium to induce prestin expression.\n\nCell pellets from 20 T175 flasks were harvested by centrifugation at 1000\u2009g for 10\u2009min, washed with PBS, and then resuspended in 5\u2009ml of resuspension buffer (25\u2009mM HEPES, pH 7.4, 200\u2009mM NaCl, 5% glycerol, 2\u2009mM CaCl2, 10\u2009\u00b5g/ml\u22121 DNase I, and 1 protease inhibitor) (complete EDTA-free, Roche) for each gram of pellet. About 2% (wt/vol final concentration) digitonin (Anatrace) powder was directly dissolved in the cell resuspension, and the mixture was incubated for 1.5\u2009h under gentle agitation (rocking) at 4 \u00b0C. Insoluble material was removed by centrifugation at 160,000\u2009g for 50 min (Beckman L90-XP ultracentrifuge with a 50.2 Ti rotor). The supernatant was passed through a 0.45\u2009\u00b5m filter. In all, 10\u2009mM imidazole (final concentration) and 1\u2009ml Ni-NTA resin (Qiagen) prewashed in 25\u2009mM Hepes, pH 7.4, 200\u2009mM NaCl, 5% glycerol, 2mM CaCl2, and 0.02% GDN (synthetic digitonin substitute glyco-diosgenin, Antrace) were added to the filtered supernatant and incubated with end-over-end rocking agitation at 4\u2009\u00b0C for 2\u2009h. The resin was collected using a bench Eppendorf microcentrifuge and washed sequentially with high-salt buffer Buffer A (25\u2009mM HEPES, pH 7.4, 500\u2009mM NaCl, 5% glycerol, and 0.02% GDN) and 25ml Buffer B (25\u2009mM HEPES, pH 7.4, 200\u2009mM NaCl, 10\u2009mM imidazole, 5% glycerol, and 0.02% GDN). The protein was eluted in 1.5\u2009ml Buffer C (25\u2009mM HEPES, pH 7.4, 200\u2009mM NaCl, 250\u2009mM imidazole, 5% glycerol, and 0.02% GDN). The 1.5\u2009ml eluted protein was concentrated to 500\u2009\u00b5l, passed through a 0.22\u2009\u00b5m filter, and loaded onto a FSEC column (Superdex 200 Increase 10/300 GL column, on a Shimadzu FPLC system) equilibrated with gel-filtration buffer (10\u2009mM HEPES, 200\u2009mM NaCl, and 0.02% GDN, pH 7.4). Two 0.5\u2009ml fractions corresponding to the fluorescent (excitation 488\u2009nm, emission 535\u2009nm) peak and A280 peak were collected and concentrated using an Amicon Ultra centrifugal filter with a molecular weight cutoff 100\u2009KDa and used for freezing grids.\n\nVarious combinations of detergents, including CHAPS, DM, DDM, and LMNG, were used to solubilize prestin. These detergents invariably resulted in broad peaks of the protein evidenced on the FSEC profile. We settled on the combination of digitonin/GDN that consistently gave us monodisperse profiles that were confirmed with uniform particles in negative-stain electron-microscopy images.\n\nAn aliquot of four microliters of purified prestin (at a concentration of approximately 2\u2009mg/ml) was applied to glow-discharged Quantifoil holey carbon grids (Gold R2/1, 200 mesh) overlaid with an additional 2-nm carbon layer (Electron Microscopy Sciences). The grids were blotted for 3\u20135\u2009s and plunge-frozen in liquid ethane using a Vitrobot Mark IV (FEI) instrument with the chamber maintained at 10\u00b0\u2009C and 100% humidity.\n\nCryo-EM micrograph movies were recorded using the SerialEM software (v3.8) on a Titan Krios G2 transmission electron microscope (Thermo Fisher/FEI) operated at a voltage of 300\u2009kV and equipped with a K3 Summit direct electron detector (Gatan, Pleasanton, CA). A quantum-energy filter with a 20-eV slit width (Gatan) was used to remove the inelastically scattered electrons. In total 4680 dose-fractionated super-resolution movies with 36 images per stack were recorded. The cryo-EM movies were recorded with a defocus varied from \u20131.15 to \u20132.15\u2009\u00b5m at a nominal magnification of 81,000x (corresponding to 0.534\u2009\u00c5 per physical pixel). The counting rate was 17.5 e\u2212/physical pix/s. The total exposure time was 3.6\u2009s per exposure with a total dose of ~54 e\u2212/\u00c52.\n\nData processing was carried out with Relion 3.173, except as noted. Movie frames were gain-normalized and motion-corrected using MotionCor2 (v1.3.2)74 with a binning factor of 2 and dividing micrographs into 4\u2009\u00d7\u20094 patches. The dose-weighted, motion-corrected micrographs (the sum of 36 movie frames) were used for all image-processing steps, except for defocus determination. The contrast transfer function (CTF) calculation was performed with CTFFIND4.1 (as implemented in Relion3.1)75 on movie sums that were motion-corrected but not dose-weighted. About 3000 particles were manually picked and subjected to 2D reference-free classification in Relion 3.173.\n\nClasses showing good signal (representing ~1100 particles) were chosen as references for automated particle picking in Relion 3.1, yielding a dataset of ~1,377,109 particles. Several rounds of 2D and 3D classification (carried out without application of symmetry) were used to remove unsuitable particles, leaving 111,863 particles that were used for structural determination with imposed C2 symmetry in Relion 3.1. Bayesian polishing73, followed by per-particle CTF refinement, 3D autorefinement, micelle-density subtraction and postprocessing generated a map that had an estimated resolution of ~3.6\u2009\u00c5 according to the Fourier shell correlation (FSC)\u2009=\u20090.143 criterion.\n\nThe Slc26a9 cryo-EM intermediate structure (PDB ID, 6RTF) (which is a polyalanine trace) was rigid-body docked into the prestin cryo-EM map and fitted using Chimera76. Next, the backbone was real-space-refined in Phenix (v 1.19.2)77 and adjusted in COOT (v 0.8.9.1)78 by manually going through the entire protomer chains. Sequence assignment was guided mainly by bulky residues such as Phe, Tyr, Trp, and Arg, and secondary structure predictions. Side chains in areas of the map with insufficient density were left as alanine. The model was refined through several rounds of model building in COOT and real-space refinement in PHENIX77 with secondary structure and geometry restraints. The model was validated using MolProbity79. Details on the statistics of cryo-EM data collection and structure determination are presented in Supplementary Table\u00a01. Figures were prepared using Chimera (v 1.12)76 and ChimeraX (v 0.9)80.\n\nRecordings were made of transiently transfected CHO (or HEK cells 48\u2009h after tetracycline induction) using a whole-cell configuration at room temperature using an Axon 200B amplifier (Molecular Devices, Sunnyvale, CA), as described previously. Cells were recorded 48\u201372\u2009h after tetracycline induction or transfection (Fugene (Promega) according to the manufacturer\u2019s instructions) to allow for stable measurement of current and NLC. Mutations were introduced in gerbil prestin YFP using the QuickChange Mutagenesis Kit (Agilent) according to the manufacturer\u2019s instructions. We recorded data from control cells on each day of experimentation, and group those within the same timeframes. Both controls were prestin\u2013YFP. Experiments with S398E were done first. Experiments with the second set of mutants were done afterward, about 3 weeks after S398E. Since the experiments were done separately, they are presented as such. In specific instances, blinding was not possible since the experimenter was responsible for both transfection of the cells and recording from them. Where the experimenters were different, electrophysiological experimenters were blinded to the identity of the constructs transfected into cells being recorded. Blinding is effective to avoid artificial group difference that is caused by performance bias. We reported mutants that show similar z. Unblinding has no bias on null results.\n\nRandomization was not done since electrophysiological recordings were performed in batches of cells transfected with the same construct. The benefit of randomization is to eliminate the bias from known and unknown confounding variables that distribute unbalanced between comparison groups. We compared NLC parameters on cultured cells rather than human or animal subjects. Randomization is not applicable to our study. The number of cells is standard in the field. For those results with p\u2009>\u20090.05 in our paper, the absolute differences are very small and in the normal range of NLC parameters. Thus, it is statistically insignificant. Increasing sample size may improve the SE but will not change the absolute difference and alter our conclusion. All recordings with Rm\u2009>\u2009300 mOhms and Rs < 10 mOhms were included in the analysis. The standard bath-solution components were (in mM) 100 NaCl (TEA)\u2013Cl 20, CsCl 20, CoCl2\u00a02, MgCl2\u00a02, and Hepes 5, pH 7.2. In addition, 20\u2009mM NaSCN was substituted for current recordings with cells transiently transfected with Slc26a9. The pipette solution contained (in mM): NaCl 100, CsCl 20, EGTA 5, MgCl2\u00a02, and Hepes 10, pH 7.2. Osmolarity was adjusted to 300\u2009\u00b1\u20092 mOsm with dextrose. After whole-cell configuration was achieved in extracellular NaCl a ramp protocol recorded to confirm baseline NLC and currents. Pipettes had resistances of 3\u20135\u2009M\u03a9. Gigaohm seals were made and stray capacitance was balanced out with amplifier circuitry prior to establishing whole-cell conditions. A Nikon Eclipse E600-FN microscope with 40\u00d7 water-immersion lens was used to observe cells during voltage clamp. Data were low-pass filtered at 10\u2009kHz and digitized at 100\u2009kHz with a Digidata 1320A.\n\nCommand delivery and data collections were carried out with a Windows-based whole-cell voltage-clamp program, jClamp (v 31.7.0, Scisoft, East Haven, CT), using a Digidata 1322A (Axon Instruments). A continuous high-resolution 2-sine voltage command was used, cell capacitance and current being extracted synchronously. In order to extract Boltzmann parameters, capacitance-voltage data were fit to the first derivative of a two-state Boltzmann function.\n\nQmax is the maximum nonlinear charge moved, Vh is voltage at peak capacitance or equivalently, at half-maximum charge transfer, Vm is membrane potential, z is valence, Clin is linear membrane capacitance, e is electron charge, kB is Boltzmann\u2019s constant, and T is absolute temperature. Csa is a component of capacitance that characterizes sigmoidal changes in specific membrane capacitance, with \u0394Csa referring to the maximal change at very negative voltages46,47. For fits of NLC in transiently transfected cells, Csa was not included. Qsp\u00a0the specific charge density, is the total charge moved (Qmax) normalized to linear capacitance. Voltages were corrected for series-resistance voltage drop. Separately, in specific experiments gating currents were also determined using voltage steps (50-ms duration) from \u2212100\u2009mV to 150\u2009mV, with 20\u2009mV step increments. Where anions were substituted, local perfusion of the cells was estimated to give rise to small junctional potentials (JPCalc function in pClamp). Since these numbers were small, no corrections were made to the IV plots. For solution-perfusion experiments, we used a QMM perfusion system (ALA Scientific, Instruments, Westbury, NY). The manifold\u2019s output tip was 200\u2009\u03bcm placed 1\u2009mm from the cell, and the flow rate increased by an applied pressure of approximately 20\u2009kPa. Statistical analysis was done with SAS software (SAS Institute Inc, NC).\n\nFurther information on research design is available in the\u00a0Nature Research Reporting Summary linked to this article.",
+            "section_image": []
+        },
+        {
+            "section_name": "Data availability",
+            "section_text": "Source data are provided with this paper. Cryo-EM map and atomic coordinates have been deposited to the EMDB and PDB with accession codes: EMD-25442 and PDB ID 7SUN.\u00a0Source data are provided with this paper.",
+            "section_image": []
+        },
+        {
+            "section_name": "References",
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+        },
+        {
+            "section_name": "Acknowledgements",
+            "section_text": "This research was supported by NIH-NIDCD R01 DC016318 (JSS) and R01 DC008130 (JSS, DN). The authors wish to thank Dr. Fred Sigworth for advice and helpful comments. This work used the electron microscopy facilities from Yale School of Medicine. We would like to thank Dr. Shenping Wu, Dr. Marc Llaguno, Dr. Xinran Liu, Kaifeng Zhou, and Dr. Jianfeng Lin for access to the TEM infrastructure and for managing Yale\u2019s electron microscopes.",
+            "section_image": []
+        },
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+            "section_name": "Author information",
+            "section_text": "These authors contributed equally: Carmen Butan, Qiang Song.\n\nDepartment of Surgery (Otolaryngology), Yale University School of Medicine, New Haven, CT, USA\n\nCarmen Butan,\u00a0Qiang Song,\u00a0Winston J. T. Tan,\u00a0Dhasakumar Navaratnam\u00a0&\u00a0Joseph Santos-Sacchi\n\nDepartment of Neurology, Yale University School of Medicine, New Haven, CT, USA\n\nJun-Ping Bai\u00a0&\u00a0Dhasakumar Navaratnam\n\nNeuroscience, Yale University School of Medicine, New Haven, CT, USA\n\nDhasakumar Navaratnam\u00a0&\u00a0Joseph Santos-Sacchi\n\nCellular and Molecular Physiology, Yale University School of Medicine, New Haven, CT, USA\n\nJoseph Santos-Sacchi\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\nC.B. designed experiments, optimized the protein-purification protocol, and carried out the cryo-EM experiments: grid freezing, single particle-data collection, data processing, and structure determination, and wrote the paper. Q.S. designed experiments, expressed and purified proteins, and performed mutagenesis. J.P. and W.T. designed experiments and performed electrophysiological experiments and analysis. D.S.N. and J.S.S. designed experiments, analyzed data, and wrote the paper.\n\nCorrespondence to\n                Dhasakumar Navaratnam or Joseph Santos-Sacchi.",
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+        {
+            "section_name": "About this article",
+            "section_text": "Butan, C., Song, Q., Bai, JP. et al. Single particle cryo-EM structure of the outer hair cell motor protein prestin.\n                    Nat Commun 13, 290 (2022). https://doi.org/10.1038/s41467-021-27915-z\n\nDownload citation\n\nReceived: 25 August 2021\n\nAccepted: 16 December 2021\n\nPublished: 12 January 2022\n\nVersion of record: 12 January 2022\n\nDOI: https://doi.org/10.1038/s41467-021-27915-z\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": "Journal of Translational Medicine (2025)\n\nNature Communications (2025)\n\nBMC Genomics (2024)\n\nNature Communications (2024)\n\nNature Communications (2024)",
+            "section_image": []
+        }
+    ]
+}